diff options
| author | dos-reis <gdr@axiomatics.org> | 2010-06-29 19:08:33 +0000 |
|---|---|---|
| committer | dos-reis <gdr@axiomatics.org> | 2010-06-29 19:08:33 +0000 |
| commit | 2394bfc186f7b57a7b8b737b4b17e1140d756416 (patch) | |
| tree | 7492c9de0429f3dfb0dd28bcaff91521f0be7d55 /src/share | |
| parent | 77d293322d11ad09575a85f421796da7db471797 (diff) | |
| download | open-axiom-2394bfc186f7b57a7b8b737b4b17e1140d756416.tar.gz | |
* algebra/catdef.spad.pamphlet (OrderedType): New.
Diffstat (limited to 'src/share')
| -rw-r--r-- | src/share/algebra/browse.daase | 2220 | ||||
| -rw-r--r-- | src/share/algebra/category.daase | 4015 | ||||
| -rw-r--r-- | src/share/algebra/compress.daase | 1328 | ||||
| -rw-r--r-- | src/share/algebra/interp.daase | 10218 | ||||
| -rw-r--r-- | src/share/algebra/operation.daase | 33130 |
5 files changed, 25457 insertions, 25454 deletions
diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase index 87bcc93c..97047609 100644 --- a/src/share/algebra/browse.daase +++ b/src/share/algebra/browse.daase @@ -1,12 +1,12 @@ -(2293583 . 3486815902) +(2293757 . 3486820627) (-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 therefore 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 therefore 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."))) -((-4464 . T) (-4463 . T)) +((-4465 . T) (-4464 . T)) NIL (-20 S) ((|constructor| (NIL "The class of abelian groups,{} \\spadignore{i.e.} additive monoids where each element has an additive inverse. \\blankline")) (- (($ $ $) "\\spad{x-y} is the difference of \\spad{x} and \\spad{y} \\spadignore{i.e.} \\spad{x + (-y)}.") (($ $) "\\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, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\spad{zerosOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) (|Polynomial| $)) "\\spad{zerosOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible. Otherwise they are implicit algebraic quantities. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|zeroOf| (($ (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{zeroOf(p, y)} returns \\spad{y} such that \\spad{p(y) = 0}; if possible,{} \\spad{y} is expressed in terms of radicals. Otherwise it is an implicit algebraic quantity which displays as \\spad{'y}.") (($ (|SparseUnivariatePolynomial| $)) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}; if possible,{} \\spad{y} is expressed in terms of radicals. Otherwise it is an implicit algebraic quantity.") (($ (|Polynomial| $)) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. If possible,{} \\spad{y} is expressed in terms of radicals. Otherwise it is an implicit algebraic quantity. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootsOf| (((|List| $) (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; The returned roots display as \\spad{'y1},{}...,{}\\spad{'yn}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\spad{rootsOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) (|Polynomial| $)) "\\spad{rootsOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{rootOf(p, y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ (|SparseUnivariatePolynomial| $)) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}.") (($ (|Polynomial| $)) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) -((-4455 . T) (-4461 . T) (-4456 . T) ((-4465 "*") . T) (-4457 . T) (-4458 . T) (-4460 . T)) +((-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-28 S R) ((|constructor| (NIL "Model for algebraically closed function spaces.")) (|zerosOf| (((|List| $) $ (|Symbol|)) "\\spad{zerosOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{zerosOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable.")) (|zeroOf| (($ $ (|Symbol|)) "\\spad{zeroOf(p, y)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity which displays as \\spad{'y}.") (($ $) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity. Error: if \\spad{p} has more than one variable.")) (|rootsOf| (((|List| $) $ (|Symbol|)) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; The returned roots display as \\spad{'y1},{}...,{}\\spad{'yn}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ $ (|Symbol|)) "\\spad{rootOf(p,y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) @@ -46,7 +46,7 @@ NIL NIL (-29 R) ((|constructor| (NIL "Model for algebraically closed function spaces.")) (|zerosOf| (((|List| $) $ (|Symbol|)) "\\spad{zerosOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{zerosOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable.")) (|zeroOf| (($ $ (|Symbol|)) "\\spad{zeroOf(p, y)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity which displays as \\spad{'y}.") (($ $) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity. Error: if \\spad{p} has more than one variable.")) (|rootsOf| (((|List| $) $ (|Symbol|)) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; The returned roots display as \\spad{'y1},{}...,{}\\spad{'yn}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ $ (|Symbol|)) "\\spad{rootOf(p,y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) -((-4460 . T) (-4458 . T) (-4457 . T) ((-4465 "*") . T) (-4456 . T) (-4461 . T) (-4455 . T)) +((-4461 . T) (-4459 . T) (-4458 . T) ((-4466 "*") . T) (-4457 . T) (-4462 . T) (-4456 . T)) NIL (-30) ((|constructor| (NIL "\\indented{1}{Plot a NON-SINGULAR plane algebraic curve \\spad{p}(\\spad{x},{}\\spad{y}) = 0.} Author: Clifton \\spad{J}. Williamson Date Created: Fall 1988 Date Last Updated: 27 April 1990 Keywords: algebraic curve,{} non-singular,{} plot Examples: References:")) (|refine| (($ $ (|DoubleFloat|)) "\\spad{refine(p,x)} \\undocumented{}")) (|makeSketch| (($ (|Polynomial| (|Integer|)) (|Symbol|) (|Symbol|) (|Segment| (|Fraction| (|Integer|))) (|Segment| (|Fraction| (|Integer|)))) "\\spad{makeSketch(p,x,y,a..b,c..d)} creates an ACPLOT of the curve \\spad{p = 0} in the region {\\em a <= x <= b, c <= y <= d}. More specifically,{} 'makeSketch' plots a non-singular algebraic curve \\spad{p = 0} in an rectangular region {\\em xMin <= x <= xMax},{} {\\em yMin <= y <= yMax}. The user inputs \\spad{makeSketch(p,x,y,xMin..xMax,yMin..yMax)}. Here \\spad{p} is a polynomial in the variables \\spad{x} and \\spad{y} with integer coefficients (\\spad{p} belongs to the domain \\spad{Polynomial Integer}). The case where \\spad{p} is a polynomial in only one of the variables is allowed. The variables \\spad{x} and \\spad{y} are input to specify the the coordinate axes. The horizontal axis is the \\spad{x}-axis and the vertical axis is the \\spad{y}-axis. The rational numbers xMin,{}...,{}yMax specify the boundaries of the region in which the curve is to be plotted."))) @@ -56,14 +56,14 @@ NIL ((|constructor| (NIL "This domain represents the syntax for an add-expression.")) (|body| (((|SpadAst|) $) "base(\\spad{d}) returns the actual body of the add-domain expression \\spad{`d'}.")) (|base| (((|SpadAst|) $) "\\spad{base(d)} returns the base domain(\\spad{s}) of the add-domain expression."))) NIL NIL -(-32 R -2117) +(-32 R -1959) ((|constructor| (NIL "This package provides algebraic functions over an integral domain.")) (|iroot| ((|#2| |#1| (|Integer|)) "\\spad{iroot(p, n)} should be a non-exported function.")) (|definingPolynomial| ((|#2| |#2|) "\\spad{definingPolynomial(f)} returns the defining polynomial of \\spad{f} as an element of \\spad{F}. Error: if \\spad{f} is not a kernel.")) (|minPoly| (((|SparseUnivariatePolynomial| |#2|) (|Kernel| |#2|)) "\\spad{minPoly(k)} returns the defining polynomial of \\spad{k}.")) (** ((|#2| |#2| (|Fraction| (|Integer|))) "\\spad{x ** q} is \\spad{x} raised to the rational power \\spad{q}.")) (|droot| (((|OutputForm|) (|List| |#2|)) "\\spad{droot(l)} should be a non-exported function.")) (|inrootof| ((|#2| (|SparseUnivariatePolynomial| |#2|) |#2|) "\\spad{inrootof(p, x)} should be a non-exported function.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} is \\spad{true} if \\spad{op} is an algebraic operator,{} that is,{} an \\spad{n}th root or implicit algebraic operator.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\spad{F}. Error: if \\spad{op} is not an algebraic operator,{} that is,{} an \\spad{n}th root or implicit algebraic operator.")) (|rootOf| ((|#2| (|SparseUnivariatePolynomial| |#2|) (|Symbol|)) "\\spad{rootOf(p, y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}."))) NIL -((|HasCategory| |#1| (LIST (QUOTE -1058) (QUOTE (-576))))) +((|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576))))) (-33 S) ((|constructor| (NIL "The notion of aggregate serves to model any data structure aggregate,{} designating any collection of objects,{} with heterogenous or homogeneous members,{} with a finite or infinite number of members,{} explicitly or implicitly represented. An aggregate can in principle represent everything from a string of characters to abstract sets such as \"the set of \\spad{x} satisfying relation {\\em r(x)}\" An attribute \\spadatt{finiteAggregate} is used to assert that a domain has a finite number of elements.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\# u} returns the number of items in \\spad{u}.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{size?(u,n)} tests if \\spad{u} has exactly \\spad{n} elements.")) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{more?(u,n)} tests if \\spad{u} has greater than \\spad{n} elements.")) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{less?(u,n)} tests if \\spad{u} has less than \\spad{n} elements.")) (|empty?| (((|Boolean|) $) "\\spad{empty?(u)} tests if \\spad{u} has 0 elements.")) (|empty| (($) "\\spad{empty()}\\$\\spad{D} creates an aggregate of type \\spad{D} with 0 elements. Note: The {\\em \\$D} can be dropped if understood by context,{} \\spadignore{e.g.} \\axiom{u: \\spad{D} \\spad{:=} empty()}.")) (|copy| (($ $) "\\spad{copy(u)} returns a top-level (non-recursive) copy of \\spad{u}. Note: for collections,{} \\axiom{copy(\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u}]}.")) (|eq?| (((|Boolean|) $ $) "\\spad{eq?(u,v)} tests if \\spad{u} and \\spad{v} are same objects."))) NIL -((|HasAttribute| |#1| (QUOTE -4463))) +((|HasAttribute| |#1| (QUOTE -4464))) (-34) ((|constructor| (NIL "The notion of aggregate serves to model any data structure aggregate,{} designating any collection of objects,{} with heterogenous or homogeneous members,{} with a finite or infinite number of members,{} explicitly or implicitly represented. An aggregate can in principle represent everything from a string of characters to abstract sets such as \"the set of \\spad{x} satisfying relation {\\em r(x)}\" An attribute \\spadatt{finiteAggregate} is used to assert that a domain has a finite number of elements.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\# u} returns the number of items in \\spad{u}.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{size?(u,n)} tests if \\spad{u} has exactly \\spad{n} elements.")) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{more?(u,n)} tests if \\spad{u} has greater than \\spad{n} elements.")) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{less?(u,n)} tests if \\spad{u} has less than \\spad{n} elements.")) (|empty?| (((|Boolean|) $) "\\spad{empty?(u)} tests if \\spad{u} has 0 elements.")) (|empty| (($) "\\spad{empty()}\\$\\spad{D} creates an aggregate of type \\spad{D} with 0 elements. Note: The {\\em \\$D} can be dropped if understood by context,{} \\spadignore{e.g.} \\axiom{u: \\spad{D} \\spad{:=} empty()}.")) (|copy| (($ $) "\\spad{copy(u)} returns a top-level (non-recursive) copy of \\spad{u}. Note: for collections,{} \\axiom{copy(\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u}]}.")) (|eq?| (((|Boolean|) $ $) "\\spad{eq?(u,v)} tests if \\spad{u} and \\spad{v} are same objects."))) NIL @@ -74,7 +74,7 @@ NIL NIL (-36 |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}."))) -((-4463 . T) (-4464 . T)) +((-4464 . T) (-4465 . T)) NIL (-37 S R) ((|constructor| (NIL "The category of associative algebras (modules which are themselves rings). \\blankline"))) @@ -82,20 +82,20 @@ NIL NIL (-38 R) ((|constructor| (NIL "The category of associative algebras (modules which are themselves rings). \\blankline"))) -((-4457 . T) (-4458 . T) (-4460 . T)) +((-4458 . T) (-4459 . T) (-4461 . T)) NIL (-39 UP) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in \\spadtype{AlgebraicNumber}.")) (|doublyTransitive?| (((|Boolean|) |#1|) "\\spad{doublyTransitive?(p)} is \\spad{true} if \\spad{p} is irreducible over over the field \\spad{K} generated by its coefficients,{} and if \\spad{p(X) / (X - a)} is irreducible over \\spad{K(a)} where \\spad{p(a) = 0}.")) (|split| (((|Factored| |#1|) |#1|) "\\spad{split(p)} returns a prime factorisation of \\spad{p} over its splitting field.")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p} over the field generated by its coefficients.") (((|Factored| |#1|) |#1| (|List| (|AlgebraicNumber|))) "\\spad{factor(p, [a1,...,an])} returns a prime factorisation of \\spad{p} over the field generated by its coefficients and a1,{}...,{}an."))) NIL NIL -(-40 -2117 UP UPUP -2182) +(-40 -1959 UP UPUP -3459) ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) -((-4456 |has| (-419 |#2|) (-374)) (-4461 |has| (-419 |#2|) (-374)) (-4455 |has| (-419 |#2|) (-374)) ((-4465 "*") . T) (-4457 . T) (-4458 . T) (-4460 . T)) -((|HasCategory| (-419 |#2|) (QUOTE (-146))) (|HasCategory| (-419 |#2|) (QUOTE (-148))) (|HasCategory| (-419 |#2|) (QUOTE (-360))) (-3794 (|HasCategory| (-419 |#2|) (QUOTE (-374))) (|HasCategory| (-419 |#2|) (QUOTE (-360)))) (|HasCategory| (-419 |#2|) (QUOTE (-374))) (|HasCategory| (-419 |#2|) (QUOTE (-379))) (-3794 (-12 (|HasCategory| (-419 |#2|) (QUOTE (-238))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (|HasCategory| (-419 |#2|) (QUOTE (-360)))) (-3794 (-12 (|HasCategory| (-419 |#2|) (QUOTE (-238))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-237))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (|HasCategory| (-419 |#2|) (QUOTE (-360)))) (-3794 (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -916) (QUOTE (-1196)))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -916) (QUOTE (-1196)))) (|HasCategory| (-419 |#2|) (QUOTE (-360))))) (-3794 (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -916) (QUOTE (-1196)))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -918) (QUOTE (-1196)))) (|HasCategory| (-419 |#2|) (QUOTE (-374))))) (|HasCategory| (-419 |#2|) (LIST (QUOTE -651) (QUOTE (-576)))) (-3794 (|HasCategory| (-419 |#2|) (LIST (QUOTE -1058) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (|HasCategory| (-419 |#2|) (LIST (QUOTE -1058) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-419 |#2|) (LIST (QUOTE -1058) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-379))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-237))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -918) (QUOTE (-1196)))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-238))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -916) (QUOTE (-1196)))) (|HasCategory| (-419 |#2|) (QUOTE (-374))))) -(-41 R -2117) +((-4457 |has| (-419 |#2|) (-374)) (-4462 |has| (-419 |#2|) (-374)) (-4456 |has| (-419 |#2|) (-374)) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) +((|HasCategory| (-419 |#2|) (QUOTE (-146))) (|HasCategory| (-419 |#2|) (QUOTE (-148))) (|HasCategory| (-419 |#2|) (QUOTE (-360))) (-2758 (|HasCategory| (-419 |#2|) (QUOTE (-374))) (|HasCategory| (-419 |#2|) (QUOTE (-360)))) (|HasCategory| (-419 |#2|) (QUOTE (-374))) (|HasCategory| (-419 |#2|) (QUOTE (-379))) (-2758 (-12 (|HasCategory| (-419 |#2|) (QUOTE (-238))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (|HasCategory| (-419 |#2|) (QUOTE (-360)))) (-2758 (-12 (|HasCategory| (-419 |#2|) (QUOTE (-238))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-237))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (|HasCategory| (-419 |#2|) (QUOTE (-360)))) (-2758 (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| (-419 |#2|) (QUOTE (-360))))) (-2758 (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -919) (QUOTE (-1197)))) (|HasCategory| (-419 |#2|) (QUOTE (-374))))) (|HasCategory| (-419 |#2|) (LIST (QUOTE -651) (QUOTE (-576)))) (-2758 (|HasCategory| (-419 |#2|) (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (|HasCategory| (-419 |#2|) (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-419 |#2|) (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-379))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-237))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -919) (QUOTE (-1197)))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (QUOTE (-238))) (|HasCategory| (-419 |#2|) (QUOTE (-374)))) (-12 (|HasCategory| (-419 |#2|) (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| (-419 |#2|) (QUOTE (-374))))) +(-41 R -1959) ((|constructor| (NIL "AlgebraicManipulations provides functions to simplify and expand expressions involving algebraic operators.")) (|rootKerSimp| ((|#2| (|BasicOperator|) |#2| (|NonNegativeInteger|)) "\\spad{rootKerSimp(op,f,n)} should be local but conditional.")) (|rootSimp| ((|#2| |#2|) "\\spad{rootSimp(f)} transforms every radical of the form \\spad{(a * b**(q*n+r))**(1/n)} appearing in \\spad{f} into \\spad{b**q * (a * b**r)**(1/n)}. This transformation is not in general valid for all complex numbers \\spad{b}.")) (|rootProduct| ((|#2| |#2|) "\\spad{rootProduct(f)} combines every product of the form \\spad{(a**(1/n))**m * (a**(1/s))**t} into a single power of a root of \\spad{a},{} and transforms every radical power of the form \\spad{(a**(1/n))**m} into a simpler form.")) (|rootPower| ((|#2| |#2|) "\\spad{rootPower(f)} transforms every radical power of the form \\spad{(a**(1/n))**m} into a simpler form if \\spad{m} and \\spad{n} have a common factor.")) (|ratPoly| (((|SparseUnivariatePolynomial| |#2|) |#2|) "\\spad{ratPoly(f)} returns a polynomial \\spad{p} such that \\spad{p} has no algebraic coefficients,{} and \\spad{p(f) = 0}.")) (|ratDenom| ((|#2| |#2| (|List| (|Kernel| |#2|))) "\\spad{ratDenom(f, [a1,...,an])} removes the \\spad{ai}\\spad{'s} which are algebraic from the denominators in \\spad{f}.") ((|#2| |#2| (|List| |#2|)) "\\spad{ratDenom(f, [a1,...,an])} removes the \\spad{ai}\\spad{'s} which are algebraic kernels from the denominators in \\spad{f}.") ((|#2| |#2| |#2|) "\\spad{ratDenom(f, a)} removes \\spad{a} from the denominators in \\spad{f} if \\spad{a} is an algebraic kernel.") ((|#2| |#2|) "\\spad{ratDenom(f)} rationalizes the denominators appearing in \\spad{f} by moving all the algebraic quantities into the numerators.")) (|rootSplit| ((|#2| |#2|) "\\spad{rootSplit(f)} transforms every radical of the form \\spad{(a/b)**(1/n)} appearing in \\spad{f} into \\spad{a**(1/n) / b**(1/n)}. This transformation is not in general valid for all complex numbers \\spad{a} and \\spad{b}.")) (|coerce| (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{coerce(x)} \\undocumented")) (|denom| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{denom(x)} \\undocumented")) (|numer| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{numer(x)} \\undocumented"))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (LIST (QUOTE -1058) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -442) (|devaluate| |#1|))))) +((-12 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -442) (|devaluate| |#1|))))) (-42 OV E P) ((|constructor| (NIL "This package factors multivariate polynomials over the domain of \\spadtype{AlgebraicNumber} by allowing the user to specify a list of algebraic numbers generating the particular extension to factor over.")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| |#3|)) (|SparseUnivariatePolynomial| |#3|) (|List| (|AlgebraicNumber|))) "\\spad{factor(p,lan)} factors the polynomial \\spad{p} over the extension generated by the algebraic numbers given by the list \\spad{lan}. \\spad{p} is presented as a univariate polynomial with multivariate coefficients.") (((|Factored| |#3|) |#3| (|List| (|AlgebraicNumber|))) "\\spad{factor(p,lan)} factors the polynomial \\spad{p} over the extension generated by the algebraic numbers given by the list \\spad{lan}."))) NIL @@ -106,31 +106,31 @@ NIL ((|HasCategory| |#1| (QUOTE (-317)))) (-44 R |n| |ls| |gamma|) ((|constructor| (NIL "AlgebraGivenByStructuralConstants implements finite rank algebras over a commutative ring,{} given by the structural constants \\spad{gamma} with respect to a fixed basis \\spad{[a1,..,an]},{} where \\spad{gamma} is an \\spad{n}-vector of \\spad{n} by \\spad{n} matrices \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{ai * aj = gammaij1 * a1 + ... + gammaijn * an}. The symbols for the fixed basis have to be given as a list of symbols.")) (|coerce| (($ (|Vector| |#1|)) "\\spad{coerce(v)} converts a vector to a member of the algebra by forming a linear combination with the basis element. Note: the vector is assumed to have length equal to the dimension of the algebra."))) -((-4460 |has| |#1| (-568)) (-4458 . T) (-4457 . T)) +((-4461 |has| |#1| (-568)) (-4459 . T) (-4458 . T)) ((|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-45 |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."))) -((-4463 . T) (-4464 . T)) -((-3794 (-12 (|HasCategory| (-2 (|:| -2239 |#1|) (|:| -2904 |#2|)) (QUOTE (-861))) (|HasCategory| (-2 (|:| -2239 |#1|) (|:| -2904 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2239) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2904) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -2239 |#1|) (|:| -2904 |#2|)) (QUOTE (-1120))) (|HasCategory| (-2 (|:| -2239 |#1|) (|:| -2904 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2239) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2904) (|devaluate| |#2|))))))) (-3794 (|HasCategory| (-2 (|:| -2239 |#1|) (|:| -2904 |#2|)) (QUOTE (-861))) (|HasCategory| (-2 (|:| -2239 |#1|) (|:| -2904 |#2|)) (QUOTE (-1120))) (|HasCategory| (-2 (|:| -2239 |#1|) (|:| -2904 |#2|)) (LIST (QUOTE -625) (QUOTE (-875)))) (|HasCategory| |#2| (QUOTE (-1120))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-875))))) (|HasCategory| (-2 (|:| -2239 |#1|) (|:| -2904 |#2|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#2| (QUOTE (-1120))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-3794 (|HasCategory| (-2 (|:| -2239 |#1|) (|:| -2904 |#2|)) (QUOTE (-861))) (|HasCategory| (-2 (|:| -2239 |#1|) (|:| -2904 |#2|)) (QUOTE (-1120))) (|HasCategory| |#2| (QUOTE (-1120)))) (|HasCategory| (-2 (|:| -2239 |#1|) (|:| -2904 |#2|)) (QUOTE (-861))) (-3794 (|HasCategory| (-2 (|:| -2239 |#1|) (|:| -2904 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2239 |#1|) (|:| -2904 |#2|)) (QUOTE (-861))) (|HasCategory| (-2 (|:| -2239 |#1|) (|:| -2904 |#2|)) (QUOTE (-1120))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1120)))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#2| (QUOTE (-1120))) (|HasCategory| (-576) (QUOTE (-861))) (|HasCategory| (-2 (|:| -2239 |#1|) (|:| -2904 |#2|)) (QUOTE (-1120))) (-3794 (|HasCategory| (-2 (|:| -2239 |#1|) (|:| -2904 |#2|)) (QUOTE (-1120))) (|HasCategory| |#2| (QUOTE (-1120)))) (-3794 (|HasCategory| (-2 (|:| -2239 |#1|) (|:| -2904 |#2|)) (LIST (QUOTE -625) (QUOTE (-875)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-875))))) (-3794 (|HasCategory| (-2 (|:| -2239 |#1|) (|:| -2904 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-875)))) (|HasCategory| (-2 (|:| -2239 |#1|) (|:| -2904 |#2|)) (LIST (QUOTE -625) (QUOTE (-875)))) (|HasCategory| (-2 (|:| -2239 |#1|) (|:| -2904 |#2|)) (QUOTE (-102))) (-12 (|HasCategory| (-2 (|:| -2239 |#1|) (|:| -2904 |#2|)) (QUOTE (-1120))) (|HasCategory| (-2 (|:| -2239 |#1|) (|:| -2904 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2239) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2904) (|devaluate| |#2|))))))) +((-4464 . T) (-4465 . T)) +((-2758 (-12 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4438 |#2|)) (QUOTE (-861))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4438 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4300) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4438) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4438 |#2|)) (QUOTE (-1121))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4438 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4300) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4438) (|devaluate| |#2|))))))) (-2758 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4438 |#2|)) (QUOTE (-861))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4438 |#2|)) (QUOTE (-1121))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4438 |#2|)) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4438 |#2|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-2758 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4438 |#2|)) (QUOTE (-861))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4438 |#2|)) (QUOTE (-1121))) (|HasCategory| |#2| (QUOTE (-1121)))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4438 |#2|)) (QUOTE (-861))) (-2758 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4438 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4438 |#2|)) (QUOTE (-861))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4438 |#2|)) (QUOTE (-1121))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1121)))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| (-576) (QUOTE (-861))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4438 |#2|)) (QUOTE (-1121))) (-2758 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4438 |#2|)) (QUOTE (-1121))) (|HasCategory| |#2| (QUOTE (-1121)))) (-2758 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4438 |#2|)) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-876))))) (-2758 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4438 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4438 |#2|)) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4438 |#2|)) (QUOTE (-102))) (-12 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4438 |#2|)) (QUOTE (-1121))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4438 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4300) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4438) (|devaluate| |#2|))))))) (-46 S R E) ((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#2|) "\\spad{p/c} divides \\spad{p} by the coefficient \\spad{c}.")) (|coefficient| ((|#2| $ |#3|) "\\spad{coefficient(p,e)} extracts the coefficient of the monomial with exponent \\spad{e} from polynomial \\spad{p},{} or returns zero if exponent is not present.")) (|reductum| (($ $) "\\spad{reductum(u)} returns \\spad{u} minus its leading monomial returns zero if handed the zero element.")) (|monomial| (($ |#2| |#3|) "\\spad{monomial(r,e)} makes a term from a coefficient \\spad{r} and an exponent \\spad{e}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(p)} tests if \\spad{p} is a single monomial.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(fn,u)} maps function \\spad{fn} onto the coefficients of the non-zero monomials of \\spad{u}.")) (|degree| ((|#3| $) "\\spad{degree(p)} returns the maximum of the exponents of the terms of \\spad{p}.")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(p)} returns the monomial of \\spad{p} with the highest degree.")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) NIL ((|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-374)))) (-47 R E) ((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#1|) "\\spad{p/c} divides \\spad{p} by the coefficient \\spad{c}.")) (|coefficient| ((|#1| $ |#2|) "\\spad{coefficient(p,e)} extracts the coefficient of the monomial with exponent \\spad{e} from polynomial \\spad{p},{} or returns zero if exponent is not present.")) (|reductum| (($ $) "\\spad{reductum(u)} returns \\spad{u} minus its leading monomial returns zero if handed the zero element.")) (|monomial| (($ |#1| |#2|) "\\spad{monomial(r,e)} makes a term from a coefficient \\spad{r} and an exponent \\spad{e}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(p)} tests if \\spad{p} is a single monomial.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,u)} maps function \\spad{fn} onto the coefficients of the non-zero monomials of \\spad{u}.")) (|degree| ((|#2| $) "\\spad{degree(p)} returns the maximum of the exponents of the terms of \\spad{p}.")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(p)} returns the monomial of \\spad{p} with the highest degree.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) -(((-4465 "*") |has| |#1| (-174)) (-4456 |has| |#1| (-568)) (-4457 . T) (-4458 . T) (-4460 . T)) +(((-4466 "*") |has| |#1| (-174)) (-4457 |has| |#1| (-568)) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-48) ((|constructor| (NIL "Algebraic closure of the rational numbers,{} with mathematical =")) (|norm| (($ $ (|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."))) -((-4455 . T) (-4461 . T) (-4456 . T) ((-4465 "*") . T) (-4457 . T) (-4458 . T) (-4460 . T)) -((|HasCategory| $ (QUOTE (-1069))) (|HasCategory| $ (LIST (QUOTE -1058) (QUOTE (-576))))) +((-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) +((|HasCategory| $ (QUOTE (-1070))) (|HasCategory| $ (LIST (QUOTE -1059) (QUOTE (-576))))) (-49) ((|constructor| (NIL "This domain implements anonymous functions")) (|body| (((|Syntax|) $) "\\spad{body(f)} returns the body of the unnamed function \\spad{`f'}.")) (|parameters| (((|List| (|Identifier|)) $) "\\spad{parameters(f)} returns the list of parameters bound by \\spad{`f'}."))) NIL NIL (-50 R |lVar|) ((|constructor| (NIL "The domain of antisymmetric polynomials.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,p)} changes each coefficient of \\spad{p} by the application of \\spad{f}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(p)} returns the homogeneous degree of \\spad{p}.")) (|retractable?| (((|Boolean|) $) "\\spad{retractable?(p)} tests if \\spad{p} is a 0-form,{} \\spadignore{i.e.} if degree(\\spad{p}) = 0.")) (|homogeneous?| (((|Boolean|) $) "\\spad{homogeneous?(p)} tests if all of the terms of \\spad{p} have the same degree.")) (|exp| (($ (|List| (|Integer|))) "\\spad{exp([i1,...in])} returns \\spad{u_1\\^{i_1} ... u_n\\^{i_n}}")) (|generator| (($ (|NonNegativeInteger|)) "\\spad{generator(n)} returns the \\spad{n}th multiplicative generator,{} a basis term.")) (|coefficient| ((|#1| $ $) "\\spad{coefficient(p,u)} returns the coefficient of the term in \\spad{p} containing the basis term \\spad{u} if such a term exists,{} and 0 otherwise. Error: if the second argument \\spad{u} is not a basis element.")) (|reductum| (($ $) "\\spad{reductum(p)},{} where \\spad{p} is an antisymmetric polynomial,{} returns \\spad{p} minus the leading term of \\spad{p} if \\spad{p} has at least two terms,{} and 0 otherwise.")) (|leadingBasisTerm| (($ $) "\\spad{leadingBasisTerm(p)} returns the leading basis term of antisymmetric polynomial \\spad{p}.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(p)} returns the leading coefficient of antisymmetric polynomial \\spad{p}."))) -((-4460 . T)) +((-4461 . T)) NIL (-51 S) ((|constructor| (NIL "\\spadtype{AnyFunctions1} implements several utility functions for working with \\spadtype{Any}. These functions are used to go back and forth between objects of \\spadtype{Any} and objects of other types.")) (|retract| ((|#1| (|Any|)) "\\spad{retract(a)} tries to convert \\spad{a} into an object of type \\spad{S}. If possible,{} it returns the object. Error: if no such retraction is possible.")) (|retractable?| (((|Boolean|) (|Any|)) "\\spad{retractable?(a)} tests if \\spad{a} can be converted into an object of type \\spad{S}.")) (|retractIfCan| (((|Union| |#1| "failed") (|Any|)) "\\spad{retractIfCan(a)} tries change \\spad{a} into an object of type \\spad{S}. If it can,{} then such an object is returned. Otherwise,{} \"failed\" is returned.")) (|coerce| (((|Any|) |#1|) "\\spad{coerce(s)} creates an object of \\spadtype{Any} from the object \\spad{s} of type \\spad{S}."))) @@ -144,7 +144,7 @@ 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, f, m)} returns \\spad{p(m)} where the action is given by \\spad{x m = f(m)}. \\spad{f} must be an \\spad{R}-pseudo linear map on \\spad{M}."))) NIL NIL -(-54 |Base| R -2117) +(-54 |Base| R -1959) ((|constructor| (NIL "This package apply rewrite rules to expressions,{} calling the pattern matcher.")) (|localUnquote| ((|#3| |#3| (|List| (|Symbol|))) "\\spad{localUnquote(f,ls)} is a local function.")) (|applyRules| ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3| (|PositiveInteger|)) "\\spad{applyRules([r1,...,rn], expr, n)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} a most \\spad{n} times.") ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3|) "\\spad{applyRules([r1,...,rn], expr)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} an unlimited number of times,{} \\spadignore{i.e.} until none of \\spad{r1},{}...,{}\\spad{rn} is applicable to the expression."))) NIL NIL @@ -158,7 +158,7 @@ NIL NIL (-57 R |Row| |Col|) ((|constructor| (NIL "\\indented{1}{TwoDimensionalArrayCategory is a general array category which} allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and columns returned as objects of type Col. The index of the 'first' row may be obtained by calling the function 'minRowIndex'. The index of the 'first' column may be obtained by calling the function 'minColIndex'. The index of the first element of a 'Row' is the same as the index of the first column in an array and vice versa.")) (|map!| (($ (|Mapping| |#1| |#1|) $) "\\spad{map!(f,a)} assign \\spad{a(i,j)} to \\spad{f(a(i,j))} for all \\spad{i, j}")) (|map| (($ (|Mapping| |#1| |#1| |#1|) $ $ |#1|) "\\spad{map(f,a,b,r)} returns \\spad{c},{} where \\spad{c(i,j) = f(a(i,j),b(i,j))} when both \\spad{a(i,j)} and \\spad{b(i,j)} exist; else \\spad{c(i,j) = f(r, b(i,j))} when \\spad{a(i,j)} does not exist; else \\spad{c(i,j) = f(a(i,j),r)} when \\spad{b(i,j)} does not exist; otherwise \\spad{c(i,j) = f(r,r)}.") (($ (|Mapping| |#1| |#1| |#1|) $ $) "\\spad{map(f,a,b)} returns \\spad{c},{} where \\spad{c(i,j) = f(a(i,j),b(i,j))} for all \\spad{i, j}") (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,a)} returns \\spad{b},{} where \\spad{b(i,j) = f(a(i,j))} for all \\spad{i, j}")) (|setColumn!| (($ $ (|Integer|) |#3|) "\\spad{setColumn!(m,j,v)} sets to \\spad{j}th column of \\spad{m} to \\spad{v}")) (|setRow!| (($ $ (|Integer|) |#2|) "\\spad{setRow!(m,i,v)} sets to \\spad{i}th row of \\spad{m} to \\spad{v}")) (|qsetelt!| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\spad{qsetelt!(m,i,j,r)} sets the element in the \\spad{i}th row and \\spad{j}th column of \\spad{m} to \\spad{r} NO error check to determine if indices are in proper ranges")) (|setelt| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\spad{setelt(m,i,j,r)} sets the element in the \\spad{i}th row and \\spad{j}th column of \\spad{m} to \\spad{r} error check to determine if indices are in proper ranges")) (|parts| (((|List| |#1|) $) "\\spad{parts(m)} returns a list of the elements of \\spad{m} in row major order")) (|column| ((|#3| $ (|Integer|)) "\\spad{column(m,j)} returns the \\spad{j}th column of \\spad{m} error check to determine if index is in proper ranges")) (|row| ((|#2| $ (|Integer|)) "\\spad{row(m,i)} returns the \\spad{i}th row of \\spad{m} error check to determine if index is in proper ranges")) (|qelt| ((|#1| $ (|Integer|) (|Integer|)) "\\spad{qelt(m,i,j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the array \\spad{m} NO error check to determine if indices are in proper ranges")) (|elt| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\spad{elt(m,i,j,r)} returns the element in the \\spad{i}th row and \\spad{j}th column of the array \\spad{m},{} if \\spad{m} has an \\spad{i}th row and a \\spad{j}th column,{} and returns \\spad{r} otherwise") ((|#1| $ (|Integer|) (|Integer|)) "\\spad{elt(m,i,j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the array \\spad{m} error check to determine if indices are in proper ranges")) (|ncols| (((|NonNegativeInteger|) $) "\\spad{ncols(m)} returns the number of columns in the array \\spad{m}")) (|nrows| (((|NonNegativeInteger|) $) "\\spad{nrows(m)} returns the number of rows in the array \\spad{m}")) (|maxColIndex| (((|Integer|) $) "\\spad{maxColIndex(m)} returns the index of the 'last' column of the array \\spad{m}")) (|minColIndex| (((|Integer|) $) "\\spad{minColIndex(m)} returns the index of the 'first' column of the array \\spad{m}")) (|maxRowIndex| (((|Integer|) $) "\\spad{maxRowIndex(m)} returns the index of the 'last' row of the array \\spad{m}")) (|minRowIndex| (((|Integer|) $) "\\spad{minRowIndex(m)} returns the index of the 'first' row of the array \\spad{m}")) (|fill!| (($ $ |#1|) "\\spad{fill!(m,r)} fills \\spad{m} with \\spad{r}\\spad{'s}")) (|new| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|) "\\spad{new(m,n,r)} is an \\spad{m}-by-\\spad{n} array all of whose entries are \\spad{r}")) (|finiteAggregate| ((|attribute|) "two-dimensional arrays are finite")) (|shallowlyMutable| ((|attribute|) "one may destructively alter arrays"))) -((-4463 . T) (-4464 . T)) +((-4464 . T) (-4465 . T)) NIL (-58 A B) ((|constructor| (NIL "\\indented{1}{This package provides tools for operating on one-dimensional arrays} with unary and binary functions involving different underlying types")) (|map| (((|OneDimensionalArray| |#2|) (|Mapping| |#2| |#1|) (|OneDimensionalArray| |#1|)) "\\spad{map(f,a)} applies function \\spad{f} to each member of one-dimensional array \\spad{a} resulting in a new one-dimensional array over a possibly different underlying domain.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|OneDimensionalArray| |#1|) |#2|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the one-dimensional array \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,[1,2,3],0)} does \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as the identity element for the function \\spad{f}.")) (|scan| (((|OneDimensionalArray| |#2|) (|Mapping| |#2| |#1| |#2|) (|OneDimensionalArray| |#1|) |#2|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-arrays \\spad{x} of one-dimensional array \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad{[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}."))) @@ -166,65 +166,65 @@ NIL NIL (-59 S) ((|constructor| (NIL "This is the domain of 1-based one dimensional arrays")) (|oneDimensionalArray| (($ (|NonNegativeInteger|) |#1|) "\\spad{oneDimensionalArray(n,s)} creates an array from \\spad{n} copies of element \\spad{s}") (($ (|List| |#1|)) "\\spad{oneDimensionalArray(l)} creates an array from a list of elements \\spad{l}"))) -((-4464 . T) (-4463 . T)) -((-3794 (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1120))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-3794 (-12 (|HasCategory| |#1| (QUOTE (-1120))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-875))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-3794 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1120)))) (|HasCategory| |#1| (QUOTE (-861))) (-3794 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1120)))) (|HasCategory| (-576) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1120))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-875)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1120))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) +((-4465 . T) (-4464 . T)) +((-2758 (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2758 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2758 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| |#1| (QUOTE (-861))) (-2758 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| (-576) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-60 R) ((|constructor| (NIL "\\indented{1}{A TwoDimensionalArray is a two dimensional array with} 1-based indexing for both rows and columns.")) (|shallowlyMutable| ((|attribute|) "One may destructively alter TwoDimensionalArray\\spad{'s}."))) -((-4463 . T) (-4464 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1120))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1120))) (-3794 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1120)))) (-3794 (-12 (|HasCategory| |#1| (QUOTE (-1120))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-875))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-875)))) (|HasCategory| |#1| (QUOTE (-102)))) -(-61 -4148) +((-4464 . T) (-4465 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1121))) (-2758 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1121)))) (-2758 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102)))) +(-61 -2627) ((|constructor| (NIL "\\spadtype{ASP10} produces Fortran for Type 10 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package}. This ASP computes the values of a set of functions,{} for example:\\begin{verbatim} SUBROUTINE COEFFN(P,Q,DQDL,X,ELAM,JINT) DOUBLE PRECISION ELAM,P,Q,X,DQDL INTEGER JINT P=1.0D0 Q=((-1.0D0*X**3)+ELAM*X*X-2.0D0)/(X*X) DQDL=1.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE JINT) (QUOTE X) (QUOTE ELAM)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-62 -4148) +(-62 -2627) ((|constructor| (NIL "\\spadtype{Asp12} produces Fortran for Type 12 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package} etc.,{} for example:\\begin{verbatim} SUBROUTINE MONIT (MAXIT,IFLAG,ELAM,FINFO) DOUBLE PRECISION ELAM,FINFO(15) INTEGER MAXIT,IFLAG IF(MAXIT.EQ.-1)THEN PRINT*,\"Output from Monit\" ENDIF PRINT*,MAXIT,IFLAG,ELAM,(FINFO(I),I=1,4) RETURN END\\end{verbatim}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP12}."))) NIL NIL -(-63 -4148) +(-63 -2627) ((|constructor| (NIL "\\spadtype{Asp19} produces Fortran for Type 19 ASPs,{} evaluating a set of functions and their jacobian at a given point,{} for example:\\begin{verbatim} SUBROUTINE LSFUN2(M,N,XC,FVECC,FJACC,LJC) DOUBLE PRECISION FVECC(M),FJACC(LJC,N),XC(N) INTEGER M,N,LJC INTEGER I,J DO 25003 I=1,LJC DO 25004 J=1,N FJACC(I,J)=0.0D025004 CONTINUE25003 CONTINUE FVECC(1)=((XC(1)-0.14D0)*XC(3)+(15.0D0*XC(1)-2.1D0)*XC(2)+1.0D0)/( &XC(3)+15.0D0*XC(2)) FVECC(2)=((XC(1)-0.18D0)*XC(3)+(7.0D0*XC(1)-1.26D0)*XC(2)+1.0D0)/( &XC(3)+7.0D0*XC(2)) FVECC(3)=((XC(1)-0.22D0)*XC(3)+(4.333333333333333D0*XC(1)-0.953333 &3333333333D0)*XC(2)+1.0D0)/(XC(3)+4.333333333333333D0*XC(2)) FVECC(4)=((XC(1)-0.25D0)*XC(3)+(3.0D0*XC(1)-0.75D0)*XC(2)+1.0D0)/( &XC(3)+3.0D0*XC(2)) FVECC(5)=((XC(1)-0.29D0)*XC(3)+(2.2D0*XC(1)-0.6379999999999999D0)* &XC(2)+1.0D0)/(XC(3)+2.2D0*XC(2)) FVECC(6)=((XC(1)-0.32D0)*XC(3)+(1.666666666666667D0*XC(1)-0.533333 &3333333333D0)*XC(2)+1.0D0)/(XC(3)+1.666666666666667D0*XC(2)) FVECC(7)=((XC(1)-0.35D0)*XC(3)+(1.285714285714286D0*XC(1)-0.45D0)* &XC(2)+1.0D0)/(XC(3)+1.285714285714286D0*XC(2)) FVECC(8)=((XC(1)-0.39D0)*XC(3)+(XC(1)-0.39D0)*XC(2)+1.0D0)/(XC(3)+ &XC(2)) FVECC(9)=((XC(1)-0.37D0)*XC(3)+(XC(1)-0.37D0)*XC(2)+1.285714285714 &286D0)/(XC(3)+XC(2)) FVECC(10)=((XC(1)-0.58D0)*XC(3)+(XC(1)-0.58D0)*XC(2)+1.66666666666 &6667D0)/(XC(3)+XC(2)) FVECC(11)=((XC(1)-0.73D0)*XC(3)+(XC(1)-0.73D0)*XC(2)+2.2D0)/(XC(3) &+XC(2)) FVECC(12)=((XC(1)-0.96D0)*XC(3)+(XC(1)-0.96D0)*XC(2)+3.0D0)/(XC(3) &+XC(2)) FVECC(13)=((XC(1)-1.34D0)*XC(3)+(XC(1)-1.34D0)*XC(2)+4.33333333333 &3333D0)/(XC(3)+XC(2)) FVECC(14)=((XC(1)-2.1D0)*XC(3)+(XC(1)-2.1D0)*XC(2)+7.0D0)/(XC(3)+X &C(2)) FVECC(15)=((XC(1)-4.39D0)*XC(3)+(XC(1)-4.39D0)*XC(2)+15.0D0)/(XC(3 &)+XC(2)) FJACC(1,1)=1.0D0 FJACC(1,2)=-15.0D0/(XC(3)**2+30.0D0*XC(2)*XC(3)+225.0D0*XC(2)**2) FJACC(1,3)=-1.0D0/(XC(3)**2+30.0D0*XC(2)*XC(3)+225.0D0*XC(2)**2) FJACC(2,1)=1.0D0 FJACC(2,2)=-7.0D0/(XC(3)**2+14.0D0*XC(2)*XC(3)+49.0D0*XC(2)**2) FJACC(2,3)=-1.0D0/(XC(3)**2+14.0D0*XC(2)*XC(3)+49.0D0*XC(2)**2) FJACC(3,1)=1.0D0 FJACC(3,2)=((-0.1110223024625157D-15*XC(3))-4.333333333333333D0)/( &XC(3)**2+8.666666666666666D0*XC(2)*XC(3)+18.77777777777778D0*XC(2) &**2) FJACC(3,3)=(0.1110223024625157D-15*XC(2)-1.0D0)/(XC(3)**2+8.666666 &666666666D0*XC(2)*XC(3)+18.77777777777778D0*XC(2)**2) FJACC(4,1)=1.0D0 FJACC(4,2)=-3.0D0/(XC(3)**2+6.0D0*XC(2)*XC(3)+9.0D0*XC(2)**2) FJACC(4,3)=-1.0D0/(XC(3)**2+6.0D0*XC(2)*XC(3)+9.0D0*XC(2)**2) FJACC(5,1)=1.0D0 FJACC(5,2)=((-0.1110223024625157D-15*XC(3))-2.2D0)/(XC(3)**2+4.399 &999999999999D0*XC(2)*XC(3)+4.839999999999998D0*XC(2)**2) FJACC(5,3)=(0.1110223024625157D-15*XC(2)-1.0D0)/(XC(3)**2+4.399999 &999999999D0*XC(2)*XC(3)+4.839999999999998D0*XC(2)**2) FJACC(6,1)=1.0D0 FJACC(6,2)=((-0.2220446049250313D-15*XC(3))-1.666666666666667D0)/( &XC(3)**2+3.333333333333333D0*XC(2)*XC(3)+2.777777777777777D0*XC(2) &**2) FJACC(6,3)=(0.2220446049250313D-15*XC(2)-1.0D0)/(XC(3)**2+3.333333 &333333333D0*XC(2)*XC(3)+2.777777777777777D0*XC(2)**2) FJACC(7,1)=1.0D0 FJACC(7,2)=((-0.5551115123125783D-16*XC(3))-1.285714285714286D0)/( &XC(3)**2+2.571428571428571D0*XC(2)*XC(3)+1.653061224489796D0*XC(2) &**2) FJACC(7,3)=(0.5551115123125783D-16*XC(2)-1.0D0)/(XC(3)**2+2.571428 &571428571D0*XC(2)*XC(3)+1.653061224489796D0*XC(2)**2) FJACC(8,1)=1.0D0 FJACC(8,2)=-1.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(8,3)=-1.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(9,1)=1.0D0 FJACC(9,2)=-1.285714285714286D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)* &*2) FJACC(9,3)=-1.285714285714286D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)* &*2) FJACC(10,1)=1.0D0 FJACC(10,2)=-1.666666666666667D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(10,3)=-1.666666666666667D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(11,1)=1.0D0 FJACC(11,2)=-2.2D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(11,3)=-2.2D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(12,1)=1.0D0 FJACC(12,2)=-3.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(12,3)=-3.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(13,1)=1.0D0 FJACC(13,2)=-4.333333333333333D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(13,3)=-4.333333333333333D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(14,1)=1.0D0 FJACC(14,2)=-7.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(14,3)=-7.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(15,1)=1.0D0 FJACC(15,2)=-15.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(15,3)=-15.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-64 -4148) +(-64 -2627) ((|constructor| (NIL "\\spadtype{Asp1} produces Fortran for Type 1 ASPs,{} needed for various NAG routines. Type 1 ASPs take a univariate expression (in the symbol \\spad{X}) and turn it into a Fortran Function like the following:\\begin{verbatim} DOUBLE PRECISION FUNCTION F(X) DOUBLE PRECISION X F=DSIN(X) RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-65 -4148) +(-65 -2627) ((|constructor| (NIL "\\spadtype{Asp20} produces Fortran for Type 20 ASPs,{} for example:\\begin{verbatim} SUBROUTINE QPHESS(N,NROWH,NCOLH,JTHCOL,HESS,X,HX) DOUBLE PRECISION HX(N),X(N),HESS(NROWH,NCOLH) INTEGER JTHCOL,N,NROWH,NCOLH HX(1)=2.0D0*X(1) HX(2)=2.0D0*X(2) HX(3)=2.0D0*X(4)+2.0D0*X(3) HX(4)=2.0D0*X(4)+2.0D0*X(3) HX(5)=2.0D0*X(5) HX(6)=(-2.0D0*X(7))+(-2.0D0*X(6)) HX(7)=(-2.0D0*X(7))+(-2.0D0*X(6)) RETURN END\\end{verbatim}"))) NIL NIL -(-66 -4148) +(-66 -2627) ((|constructor| (NIL "\\spadtype{Asp24} produces Fortran for Type 24 ASPs which evaluate a multivariate function at a point (needed for NAG routine \\axiomOpFrom{e04jaf}{e04Package}),{} for example:\\begin{verbatim} SUBROUTINE FUNCT1(N,XC,FC) DOUBLE PRECISION FC,XC(N) INTEGER N FC=10.0D0*XC(4)**4+(-40.0D0*XC(1)*XC(4)**3)+(60.0D0*XC(1)**2+5 &.0D0)*XC(4)**2+((-10.0D0*XC(3))+(-40.0D0*XC(1)**3))*XC(4)+16.0D0*X &C(3)**4+(-32.0D0*XC(2)*XC(3)**3)+(24.0D0*XC(2)**2+5.0D0)*XC(3)**2+ &(-8.0D0*XC(2)**3*XC(3))+XC(2)**4+100.0D0*XC(2)**2+20.0D0*XC(1)*XC( &2)+10.0D0*XC(1)**4+XC(1)**2 RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-67 -4148) +(-67 -2627) ((|constructor| (NIL "\\spadtype{Asp27} produces Fortran for Type 27 ASPs,{} needed for NAG routine \\axiomOpFrom{f02fjf}{f02Package} ,{}for example:\\begin{verbatim} FUNCTION DOT(IFLAG,N,Z,W,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION W(N),Z(N),RWORK(LRWORK) INTEGER N,LIWORK,IFLAG,LRWORK,IWORK(LIWORK) DOT=(W(16)+(-0.5D0*W(15)))*Z(16)+((-0.5D0*W(16))+W(15)+(-0.5D0*W(1 &4)))*Z(15)+((-0.5D0*W(15))+W(14)+(-0.5D0*W(13)))*Z(14)+((-0.5D0*W( &14))+W(13)+(-0.5D0*W(12)))*Z(13)+((-0.5D0*W(13))+W(12)+(-0.5D0*W(1 &1)))*Z(12)+((-0.5D0*W(12))+W(11)+(-0.5D0*W(10)))*Z(11)+((-0.5D0*W( &11))+W(10)+(-0.5D0*W(9)))*Z(10)+((-0.5D0*W(10))+W(9)+(-0.5D0*W(8)) &)*Z(9)+((-0.5D0*W(9))+W(8)+(-0.5D0*W(7)))*Z(8)+((-0.5D0*W(8))+W(7) &+(-0.5D0*W(6)))*Z(7)+((-0.5D0*W(7))+W(6)+(-0.5D0*W(5)))*Z(6)+((-0. &5D0*W(6))+W(5)+(-0.5D0*W(4)))*Z(5)+((-0.5D0*W(5))+W(4)+(-0.5D0*W(3 &)))*Z(4)+((-0.5D0*W(4))+W(3)+(-0.5D0*W(2)))*Z(3)+((-0.5D0*W(3))+W( &2)+(-0.5D0*W(1)))*Z(2)+((-0.5D0*W(2))+W(1))*Z(1) RETURN END\\end{verbatim}"))) NIL NIL -(-68 -4148) +(-68 -2627) ((|constructor| (NIL "\\spadtype{Asp28} produces Fortran for Type 28 ASPs,{} used in NAG routine \\axiomOpFrom{f02fjf}{f02Package},{} for example:\\begin{verbatim} SUBROUTINE IMAGE(IFLAG,N,Z,W,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION Z(N),W(N),IWORK(LRWORK),RWORK(LRWORK) INTEGER N,LIWORK,IFLAG,LRWORK W(1)=0.01707454969713436D0*Z(16)+0.001747395874954051D0*Z(15)+0.00 &2106973900813502D0*Z(14)+0.002957434991769087D0*Z(13)+(-0.00700554 &0882865317D0*Z(12))+(-0.01219194009813166D0*Z(11))+0.0037230647365 &3087D0*Z(10)+0.04932374658377151D0*Z(9)+(-0.03586220812223305D0*Z( &8))+(-0.04723268012114625D0*Z(7))+(-0.02434652144032987D0*Z(6))+0. &2264766947290192D0*Z(5)+(-0.1385343580686922D0*Z(4))+(-0.116530050 &8238904D0*Z(3))+(-0.2803531651057233D0*Z(2))+1.019463911841327D0*Z &(1) W(2)=0.0227345011107737D0*Z(16)+0.008812321197398072D0*Z(15)+0.010 &94012210519586D0*Z(14)+(-0.01764072463999744D0*Z(13))+(-0.01357136 &72105995D0*Z(12))+0.00157466157362272D0*Z(11)+0.05258889186338282D &0*Z(10)+(-0.01981532388243379D0*Z(9))+(-0.06095390688679697D0*Z(8) &)+(-0.04153119955569051D0*Z(7))+0.2176561076571465D0*Z(6)+(-0.0532 &5555586632358D0*Z(5))+(-0.1688977368984641D0*Z(4))+(-0.32440166056 &67343D0*Z(3))+0.9128222941872173D0*Z(2)+(-0.2419652703415429D0*Z(1 &)) W(3)=0.03371198197190302D0*Z(16)+0.02021603150122265D0*Z(15)+(-0.0 &06607305534689702D0*Z(14))+(-0.03032392238968179D0*Z(13))+0.002033 &305231024948D0*Z(12)+0.05375944956767728D0*Z(11)+(-0.0163213312502 &9967D0*Z(10))+(-0.05483186562035512D0*Z(9))+(-0.04901428822579872D &0*Z(8))+0.2091097927887612D0*Z(7)+(-0.05760560341383113D0*Z(6))+(- &0.1236679206156403D0*Z(5))+(-0.3523683853026259D0*Z(4))+0.88929961 &32269974D0*Z(3)+(-0.2995429545781457D0*Z(2))+(-0.02986582812574917 &D0*Z(1)) W(4)=0.05141563713660119D0*Z(16)+0.005239165960779299D0*Z(15)+(-0. &01623427735779699D0*Z(14))+(-0.01965809746040371D0*Z(13))+0.054688 &97337339577D0*Z(12)+(-0.014224695935687D0*Z(11))+(-0.0505181779315 &6355D0*Z(10))+(-0.04353074206076491D0*Z(9))+0.2012230497530726D0*Z &(8)+(-0.06630874514535952D0*Z(7))+(-0.1280829963720053D0*Z(6))+(-0 &.305169742604165D0*Z(5))+0.8600427128450191D0*Z(4)+(-0.32415033802 &68184D0*Z(3))+(-0.09033531980693314D0*Z(2))+0.09089205517109111D0* &Z(1) W(5)=0.04556369767776375D0*Z(16)+(-0.001822737697581869D0*Z(15))+( &-0.002512226501941856D0*Z(14))+0.02947046460707379D0*Z(13)+(-0.014 &45079632086177D0*Z(12))+(-0.05034242196614937D0*Z(11))+(-0.0376966 &3291725935D0*Z(10))+0.2171103102175198D0*Z(9)+(-0.0824949256021352 &4D0*Z(8))+(-0.1473995209288945D0*Z(7))+(-0.315042193418466D0*Z(6)) &+0.9591623347824002D0*Z(5)+(-0.3852396953763045D0*Z(4))+(-0.141718 &5427288274D0*Z(3))+(-0.03423495461011043D0*Z(2))+0.319820917706851 &6D0*Z(1) W(6)=0.04015147277405744D0*Z(16)+0.01328585741341559D0*Z(15)+0.048 &26082005465965D0*Z(14)+(-0.04319641116207706D0*Z(13))+(-0.04931323 &319055762D0*Z(12))+(-0.03526886317505474D0*Z(11))+0.22295383396730 &01D0*Z(10)+(-0.07375317649315155D0*Z(9))+(-0.1589391311991561D0*Z( &8))+(-0.328001910890377D0*Z(7))+0.952576555482747D0*Z(6)+(-0.31583 &09975786731D0*Z(5))+(-0.1846882042225383D0*Z(4))+(-0.0703762046700 &4427D0*Z(3))+0.2311852964327382D0*Z(2)+0.04254083491825025D0*Z(1) W(7)=0.06069778964023718D0*Z(16)+0.06681263884671322D0*Z(15)+(-0.0 &2113506688615768D0*Z(14))+(-0.083996867458326D0*Z(13))+(-0.0329843 &8523869648D0*Z(12))+0.2276878326327734D0*Z(11)+(-0.067356038933017 &95D0*Z(10))+(-0.1559813965382218D0*Z(9))+(-0.3363262957694705D0*Z( &8))+0.9442791158560948D0*Z(7)+(-0.3199955249404657D0*Z(6))+(-0.136 &2463839920727D0*Z(5))+(-0.1006185171570586D0*Z(4))+0.2057504515015 &423D0*Z(3)+(-0.02065879269286707D0*Z(2))+0.03160990266745513D0*Z(1 &) W(8)=0.126386868896738D0*Z(16)+0.002563370039476418D0*Z(15)+(-0.05 &581757739455641D0*Z(14))+(-0.07777893205900685D0*Z(13))+0.23117338 &45834199D0*Z(12)+(-0.06031581134427592D0*Z(11))+(-0.14805474755869 &52D0*Z(10))+(-0.3364014128402243D0*Z(9))+0.9364014128402244D0*Z(8) &+(-0.3269452524413048D0*Z(7))+(-0.1396841886557241D0*Z(6))+(-0.056 &1733845834199D0*Z(5))+0.1777789320590069D0*Z(4)+(-0.04418242260544 &359D0*Z(3))+(-0.02756337003947642D0*Z(2))+0.07361313110326199D0*Z( &1) W(9)=0.07361313110326199D0*Z(16)+(-0.02756337003947642D0*Z(15))+(- &0.04418242260544359D0*Z(14))+0.1777789320590069D0*Z(13)+(-0.056173 &3845834199D0*Z(12))+(-0.1396841886557241D0*Z(11))+(-0.326945252441 &3048D0*Z(10))+0.9364014128402244D0*Z(9)+(-0.3364014128402243D0*Z(8 &))+(-0.1480547475586952D0*Z(7))+(-0.06031581134427592D0*Z(6))+0.23 &11733845834199D0*Z(5)+(-0.07777893205900685D0*Z(4))+(-0.0558175773 &9455641D0*Z(3))+0.002563370039476418D0*Z(2)+0.126386868896738D0*Z( &1) W(10)=0.03160990266745513D0*Z(16)+(-0.02065879269286707D0*Z(15))+0 &.2057504515015423D0*Z(14)+(-0.1006185171570586D0*Z(13))+(-0.136246 &3839920727D0*Z(12))+(-0.3199955249404657D0*Z(11))+0.94427911585609 &48D0*Z(10)+(-0.3363262957694705D0*Z(9))+(-0.1559813965382218D0*Z(8 &))+(-0.06735603893301795D0*Z(7))+0.2276878326327734D0*Z(6)+(-0.032 &98438523869648D0*Z(5))+(-0.083996867458326D0*Z(4))+(-0.02113506688 &615768D0*Z(3))+0.06681263884671322D0*Z(2)+0.06069778964023718D0*Z( &1) W(11)=0.04254083491825025D0*Z(16)+0.2311852964327382D0*Z(15)+(-0.0 &7037620467004427D0*Z(14))+(-0.1846882042225383D0*Z(13))+(-0.315830 &9975786731D0*Z(12))+0.952576555482747D0*Z(11)+(-0.328001910890377D &0*Z(10))+(-0.1589391311991561D0*Z(9))+(-0.07375317649315155D0*Z(8) &)+0.2229538339673001D0*Z(7)+(-0.03526886317505474D0*Z(6))+(-0.0493 &1323319055762D0*Z(5))+(-0.04319641116207706D0*Z(4))+0.048260820054 &65965D0*Z(3)+0.01328585741341559D0*Z(2)+0.04015147277405744D0*Z(1) W(12)=0.3198209177068516D0*Z(16)+(-0.03423495461011043D0*Z(15))+(- &0.1417185427288274D0*Z(14))+(-0.3852396953763045D0*Z(13))+0.959162 &3347824002D0*Z(12)+(-0.315042193418466D0*Z(11))+(-0.14739952092889 &45D0*Z(10))+(-0.08249492560213524D0*Z(9))+0.2171103102175198D0*Z(8 &)+(-0.03769663291725935D0*Z(7))+(-0.05034242196614937D0*Z(6))+(-0. &01445079632086177D0*Z(5))+0.02947046460707379D0*Z(4)+(-0.002512226 &501941856D0*Z(3))+(-0.001822737697581869D0*Z(2))+0.045563697677763 &75D0*Z(1) W(13)=0.09089205517109111D0*Z(16)+(-0.09033531980693314D0*Z(15))+( &-0.3241503380268184D0*Z(14))+0.8600427128450191D0*Z(13)+(-0.305169 &742604165D0*Z(12))+(-0.1280829963720053D0*Z(11))+(-0.0663087451453 &5952D0*Z(10))+0.2012230497530726D0*Z(9)+(-0.04353074206076491D0*Z( &8))+(-0.05051817793156355D0*Z(7))+(-0.014224695935687D0*Z(6))+0.05 &468897337339577D0*Z(5)+(-0.01965809746040371D0*Z(4))+(-0.016234277 &35779699D0*Z(3))+0.005239165960779299D0*Z(2)+0.05141563713660119D0 &*Z(1) W(14)=(-0.02986582812574917D0*Z(16))+(-0.2995429545781457D0*Z(15)) &+0.8892996132269974D0*Z(14)+(-0.3523683853026259D0*Z(13))+(-0.1236 &679206156403D0*Z(12))+(-0.05760560341383113D0*Z(11))+0.20910979278 &87612D0*Z(10)+(-0.04901428822579872D0*Z(9))+(-0.05483186562035512D &0*Z(8))+(-0.01632133125029967D0*Z(7))+0.05375944956767728D0*Z(6)+0 &.002033305231024948D0*Z(5)+(-0.03032392238968179D0*Z(4))+(-0.00660 &7305534689702D0*Z(3))+0.02021603150122265D0*Z(2)+0.033711981971903 &02D0*Z(1) W(15)=(-0.2419652703415429D0*Z(16))+0.9128222941872173D0*Z(15)+(-0 &.3244016605667343D0*Z(14))+(-0.1688977368984641D0*Z(13))+(-0.05325 &555586632358D0*Z(12))+0.2176561076571465D0*Z(11)+(-0.0415311995556 &9051D0*Z(10))+(-0.06095390688679697D0*Z(9))+(-0.01981532388243379D &0*Z(8))+0.05258889186338282D0*Z(7)+0.00157466157362272D0*Z(6)+(-0. &0135713672105995D0*Z(5))+(-0.01764072463999744D0*Z(4))+0.010940122 &10519586D0*Z(3)+0.008812321197398072D0*Z(2)+0.0227345011107737D0*Z &(1) W(16)=1.019463911841327D0*Z(16)+(-0.2803531651057233D0*Z(15))+(-0. &1165300508238904D0*Z(14))+(-0.1385343580686922D0*Z(13))+0.22647669 &47290192D0*Z(12)+(-0.02434652144032987D0*Z(11))+(-0.04723268012114 &625D0*Z(10))+(-0.03586220812223305D0*Z(9))+0.04932374658377151D0*Z &(8)+0.00372306473653087D0*Z(7)+(-0.01219194009813166D0*Z(6))+(-0.0 &07005540882865317D0*Z(5))+0.002957434991769087D0*Z(4)+0.0021069739 &00813502D0*Z(3)+0.001747395874954051D0*Z(2)+0.01707454969713436D0* &Z(1) RETURN END\\end{verbatim}"))) NIL NIL -(-69 -4148) +(-69 -2627) ((|constructor| (NIL "\\spadtype{Asp29} produces Fortran for Type 29 ASPs,{} needed for NAG routine \\axiomOpFrom{f02fjf}{f02Package},{} for example:\\begin{verbatim} SUBROUTINE MONIT(ISTATE,NEXTIT,NEVALS,NEVECS,K,F,D) DOUBLE PRECISION D(K),F(K) INTEGER K,NEXTIT,NEVALS,NVECS,ISTATE CALL F02FJZ(ISTATE,NEXTIT,NEVALS,NEVECS,K,F,D) RETURN END\\end{verbatim}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP29}."))) NIL NIL -(-70 -4148) +(-70 -2627) ((|constructor| (NIL "\\spadtype{Asp30} produces Fortran for Type 30 ASPs,{} needed for NAG routine \\axiomOpFrom{f04qaf}{f04Package},{} for example:\\begin{verbatim} SUBROUTINE APROD(MODE,M,N,X,Y,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION X(N),Y(M),RWORK(LRWORK) INTEGER M,N,LIWORK,IFAIL,LRWORK,IWORK(LIWORK),MODE DOUBLE PRECISION A(5,5) EXTERNAL F06PAF A(1,1)=1.0D0 A(1,2)=0.0D0 A(1,3)=0.0D0 A(1,4)=-1.0D0 A(1,5)=0.0D0 A(2,1)=0.0D0 A(2,2)=1.0D0 A(2,3)=0.0D0 A(2,4)=0.0D0 A(2,5)=-1.0D0 A(3,1)=0.0D0 A(3,2)=0.0D0 A(3,3)=1.0D0 A(3,4)=-1.0D0 A(3,5)=0.0D0 A(4,1)=-1.0D0 A(4,2)=0.0D0 A(4,3)=-1.0D0 A(4,4)=4.0D0 A(4,5)=-1.0D0 A(5,1)=0.0D0 A(5,2)=-1.0D0 A(5,3)=0.0D0 A(5,4)=-1.0D0 A(5,5)=4.0D0 IF(MODE.EQ.1)THEN CALL F06PAF('N',M,N,1.0D0,A,M,X,1,1.0D0,Y,1) ELSEIF(MODE.EQ.2)THEN CALL F06PAF('T',M,N,1.0D0,A,M,Y,1,1.0D0,X,1) ENDIF RETURN END\\end{verbatim}"))) NIL NIL -(-71 -4148) +(-71 -2627) ((|constructor| (NIL "\\spadtype{Asp31} produces Fortran for Type 31 ASPs,{} needed for NAG routine \\axiomOpFrom{d02ejf}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE PEDERV(X,Y,PW) DOUBLE PRECISION X,Y(*) DOUBLE PRECISION PW(3,3) PW(1,1)=-0.03999999999999999D0 PW(1,2)=10000.0D0*Y(3) PW(1,3)=10000.0D0*Y(2) PW(2,1)=0.03999999999999999D0 PW(2,2)=(-10000.0D0*Y(3))+(-60000000.0D0*Y(2)) PW(2,3)=-10000.0D0*Y(2) PW(3,1)=0.0D0 PW(3,2)=60000000.0D0*Y(2) PW(3,3)=0.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-72 -4148) +(-72 -2627) ((|constructor| (NIL "\\spadtype{Asp33} produces Fortran for Type 33 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package}. The code is a dummy ASP:\\begin{verbatim} SUBROUTINE REPORT(X,V,JINT) DOUBLE PRECISION V(3),X INTEGER JINT RETURN END\\end{verbatim}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP33}."))) NIL NIL -(-73 -4148) +(-73 -2627) ((|constructor| (NIL "\\spadtype{Asp34} produces Fortran for Type 34 ASPs,{} needed for NAG routine \\axiomOpFrom{f04mbf}{f04Package},{} for example:\\begin{verbatim} SUBROUTINE MSOLVE(IFLAG,N,X,Y,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION RWORK(LRWORK),X(N),Y(N) INTEGER I,J,N,LIWORK,IFLAG,LRWORK,IWORK(LIWORK) DOUBLE PRECISION W1(3),W2(3),MS(3,3) IFLAG=-1 MS(1,1)=2.0D0 MS(1,2)=1.0D0 MS(1,3)=0.0D0 MS(2,1)=1.0D0 MS(2,2)=2.0D0 MS(2,3)=1.0D0 MS(3,1)=0.0D0 MS(3,2)=1.0D0 MS(3,3)=2.0D0 CALL F04ASF(MS,N,X,N,Y,W1,W2,IFLAG) IFLAG=-IFLAG RETURN END\\end{verbatim}"))) NIL NIL -(-74 -4148) +(-74 -2627) ((|constructor| (NIL "\\spadtype{Asp35} produces Fortran for Type 35 ASPs,{} needed for NAG routines \\axiomOpFrom{c05pbf}{c05Package},{} \\axiomOpFrom{c05pcf}{c05Package},{} for example:\\begin{verbatim} SUBROUTINE FCN(N,X,FVEC,FJAC,LDFJAC,IFLAG) DOUBLE PRECISION X(N),FVEC(N),FJAC(LDFJAC,N) INTEGER LDFJAC,N,IFLAG IF(IFLAG.EQ.1)THEN FVEC(1)=(-1.0D0*X(2))+X(1) FVEC(2)=(-1.0D0*X(3))+2.0D0*X(2) FVEC(3)=3.0D0*X(3) ELSEIF(IFLAG.EQ.2)THEN FJAC(1,1)=1.0D0 FJAC(1,2)=-1.0D0 FJAC(1,3)=0.0D0 FJAC(2,1)=0.0D0 FJAC(2,2)=2.0D0 FJAC(2,3)=-1.0D0 FJAC(3,1)=0.0D0 FJAC(3,2)=0.0D0 FJAC(3,3)=3.0D0 ENDIF END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL @@ -236,55 +236,55 @@ NIL ((|constructor| (NIL "\\spadtype{Asp42} produces Fortran for Type 42 ASPs,{} needed for NAG routines \\axiomOpFrom{d02raf}{d02Package} and \\axiomOpFrom{d02saf}{d02Package} in particular. These ASPs are in fact three Fortran routines which return a vector of functions,{} and their derivatives \\spad{wrt} \\spad{Y}(\\spad{i}) and also a continuation parameter EPS,{} for example:\\begin{verbatim} SUBROUTINE G(EPS,YA,YB,BC,N) DOUBLE PRECISION EPS,YA(N),YB(N),BC(N) INTEGER N BC(1)=YA(1) BC(2)=YA(2) BC(3)=YB(2)-1.0D0 RETURN END SUBROUTINE JACOBG(EPS,YA,YB,AJ,BJ,N) DOUBLE PRECISION EPS,YA(N),AJ(N,N),BJ(N,N),YB(N) INTEGER N AJ(1,1)=1.0D0 AJ(1,2)=0.0D0 AJ(1,3)=0.0D0 AJ(2,1)=0.0D0 AJ(2,2)=1.0D0 AJ(2,3)=0.0D0 AJ(3,1)=0.0D0 AJ(3,2)=0.0D0 AJ(3,3)=0.0D0 BJ(1,1)=0.0D0 BJ(1,2)=0.0D0 BJ(1,3)=0.0D0 BJ(2,1)=0.0D0 BJ(2,2)=0.0D0 BJ(2,3)=0.0D0 BJ(3,1)=0.0D0 BJ(3,2)=1.0D0 BJ(3,3)=0.0D0 RETURN END SUBROUTINE JACGEP(EPS,YA,YB,BCEP,N) DOUBLE PRECISION EPS,YA(N),YB(N),BCEP(N) INTEGER N BCEP(1)=0.0D0 BCEP(2)=0.0D0 BCEP(3)=0.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE EPS)) (|construct| (QUOTE YA) (QUOTE YB)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-77 -4148) +(-77 -2627) ((|constructor| (NIL "\\spadtype{Asp49} produces Fortran for Type 49 ASPs,{} needed for NAG routines \\axiomOpFrom{e04dgf}{e04Package},{} \\axiomOpFrom{e04ucf}{e04Package},{} for example:\\begin{verbatim} SUBROUTINE OBJFUN(MODE,N,X,OBJF,OBJGRD,NSTATE,IUSER,USER) DOUBLE PRECISION X(N),OBJF,OBJGRD(N),USER(*) INTEGER N,IUSER(*),MODE,NSTATE OBJF=X(4)*X(9)+((-1.0D0*X(5))+X(3))*X(8)+((-1.0D0*X(3))+X(1))*X(7) &+(-1.0D0*X(2)*X(6)) OBJGRD(1)=X(7) OBJGRD(2)=-1.0D0*X(6) OBJGRD(3)=X(8)+(-1.0D0*X(7)) OBJGRD(4)=X(9) OBJGRD(5)=-1.0D0*X(8) OBJGRD(6)=-1.0D0*X(2) OBJGRD(7)=(-1.0D0*X(3))+X(1) OBJGRD(8)=(-1.0D0*X(5))+X(3) OBJGRD(9)=X(4) RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-78 -4148) +(-78 -2627) ((|constructor| (NIL "\\spadtype{Asp4} produces Fortran for Type 4 ASPs,{} which take an expression in \\spad{X}(1) .. \\spad{X}(NDIM) and produce a real function of the form:\\begin{verbatim} DOUBLE PRECISION FUNCTION FUNCTN(NDIM,X) DOUBLE PRECISION X(NDIM) INTEGER NDIM FUNCTN=(4.0D0*X(1)*X(3)**2*DEXP(2.0D0*X(1)*X(3)))/(X(4)**2+(2.0D0* &X(2)+2.0D0)*X(4)+X(2)**2+2.0D0*X(2)+1.0D0) RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-79 -4148) +(-79 -2627) ((|constructor| (NIL "\\spadtype{Asp50} produces Fortran for Type 50 ASPs,{} needed for NAG routine \\axiomOpFrom{e04fdf}{e04Package},{} for example:\\begin{verbatim} SUBROUTINE LSFUN1(M,N,XC,FVECC) DOUBLE PRECISION FVECC(M),XC(N) INTEGER I,M,N FVECC(1)=((XC(1)-2.4D0)*XC(3)+(15.0D0*XC(1)-36.0D0)*XC(2)+1.0D0)/( &XC(3)+15.0D0*XC(2)) FVECC(2)=((XC(1)-2.8D0)*XC(3)+(7.0D0*XC(1)-19.6D0)*XC(2)+1.0D0)/(X &C(3)+7.0D0*XC(2)) FVECC(3)=((XC(1)-3.2D0)*XC(3)+(4.333333333333333D0*XC(1)-13.866666 &66666667D0)*XC(2)+1.0D0)/(XC(3)+4.333333333333333D0*XC(2)) FVECC(4)=((XC(1)-3.5D0)*XC(3)+(3.0D0*XC(1)-10.5D0)*XC(2)+1.0D0)/(X &C(3)+3.0D0*XC(2)) FVECC(5)=((XC(1)-3.9D0)*XC(3)+(2.2D0*XC(1)-8.579999999999998D0)*XC &(2)+1.0D0)/(XC(3)+2.2D0*XC(2)) FVECC(6)=((XC(1)-4.199999999999999D0)*XC(3)+(1.666666666666667D0*X &C(1)-7.0D0)*XC(2)+1.0D0)/(XC(3)+1.666666666666667D0*XC(2)) FVECC(7)=((XC(1)-4.5D0)*XC(3)+(1.285714285714286D0*XC(1)-5.7857142 &85714286D0)*XC(2)+1.0D0)/(XC(3)+1.285714285714286D0*XC(2)) FVECC(8)=((XC(1)-4.899999999999999D0)*XC(3)+(XC(1)-4.8999999999999 &99D0)*XC(2)+1.0D0)/(XC(3)+XC(2)) FVECC(9)=((XC(1)-4.699999999999999D0)*XC(3)+(XC(1)-4.6999999999999 &99D0)*XC(2)+1.285714285714286D0)/(XC(3)+XC(2)) FVECC(10)=((XC(1)-6.8D0)*XC(3)+(XC(1)-6.8D0)*XC(2)+1.6666666666666 &67D0)/(XC(3)+XC(2)) FVECC(11)=((XC(1)-8.299999999999999D0)*XC(3)+(XC(1)-8.299999999999 &999D0)*XC(2)+2.2D0)/(XC(3)+XC(2)) FVECC(12)=((XC(1)-10.6D0)*XC(3)+(XC(1)-10.6D0)*XC(2)+3.0D0)/(XC(3) &+XC(2)) FVECC(13)=((XC(1)-1.34D0)*XC(3)+(XC(1)-1.34D0)*XC(2)+4.33333333333 &3333D0)/(XC(3)+XC(2)) FVECC(14)=((XC(1)-2.1D0)*XC(3)+(XC(1)-2.1D0)*XC(2)+7.0D0)/(XC(3)+X &C(2)) FVECC(15)=((XC(1)-4.39D0)*XC(3)+(XC(1)-4.39D0)*XC(2)+15.0D0)/(XC(3 &)+XC(2)) END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-80 -4148) +(-80 -2627) ((|constructor| (NIL "\\spadtype{Asp55} produces Fortran for Type 55 ASPs,{} needed for NAG routines \\axiomOpFrom{e04dgf}{e04Package} and \\axiomOpFrom{e04ucf}{e04Package},{} for example:\\begin{verbatim} SUBROUTINE CONFUN(MODE,NCNLN,N,NROWJ,NEEDC,X,C,CJAC,NSTATE,IUSER &,USER) DOUBLE PRECISION C(NCNLN),X(N),CJAC(NROWJ,N),USER(*) INTEGER N,IUSER(*),NEEDC(NCNLN),NROWJ,MODE,NCNLN,NSTATE IF(NEEDC(1).GT.0)THEN C(1)=X(6)**2+X(1)**2 CJAC(1,1)=2.0D0*X(1) CJAC(1,2)=0.0D0 CJAC(1,3)=0.0D0 CJAC(1,4)=0.0D0 CJAC(1,5)=0.0D0 CJAC(1,6)=2.0D0*X(6) ENDIF IF(NEEDC(2).GT.0)THEN C(2)=X(2)**2+(-2.0D0*X(1)*X(2))+X(1)**2 CJAC(2,1)=(-2.0D0*X(2))+2.0D0*X(1) CJAC(2,2)=2.0D0*X(2)+(-2.0D0*X(1)) CJAC(2,3)=0.0D0 CJAC(2,4)=0.0D0 CJAC(2,5)=0.0D0 CJAC(2,6)=0.0D0 ENDIF IF(NEEDC(3).GT.0)THEN C(3)=X(3)**2+(-2.0D0*X(1)*X(3))+X(2)**2+X(1)**2 CJAC(3,1)=(-2.0D0*X(3))+2.0D0*X(1) CJAC(3,2)=2.0D0*X(2) CJAC(3,3)=2.0D0*X(3)+(-2.0D0*X(1)) CJAC(3,4)=0.0D0 CJAC(3,5)=0.0D0 CJAC(3,6)=0.0D0 ENDIF RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-81 -4148) +(-81 -2627) ((|constructor| (NIL "\\spadtype{Asp6} produces Fortran for Type 6 ASPs,{} needed for NAG routines \\axiomOpFrom{c05nbf}{c05Package},{} \\axiomOpFrom{c05ncf}{c05Package}. These represent vectors of functions of \\spad{X}(\\spad{i}) and look like:\\begin{verbatim} SUBROUTINE FCN(N,X,FVEC,IFLAG) DOUBLE PRECISION X(N),FVEC(N) INTEGER N,IFLAG FVEC(1)=(-2.0D0*X(2))+(-2.0D0*X(1)**2)+3.0D0*X(1)+1.0D0 FVEC(2)=(-2.0D0*X(3))+(-2.0D0*X(2)**2)+3.0D0*X(2)+(-1.0D0*X(1))+1. &0D0 FVEC(3)=(-2.0D0*X(4))+(-2.0D0*X(3)**2)+3.0D0*X(3)+(-1.0D0*X(2))+1. &0D0 FVEC(4)=(-2.0D0*X(5))+(-2.0D0*X(4)**2)+3.0D0*X(4)+(-1.0D0*X(3))+1. &0D0 FVEC(5)=(-2.0D0*X(6))+(-2.0D0*X(5)**2)+3.0D0*X(5)+(-1.0D0*X(4))+1. &0D0 FVEC(6)=(-2.0D0*X(7))+(-2.0D0*X(6)**2)+3.0D0*X(6)+(-1.0D0*X(5))+1. &0D0 FVEC(7)=(-2.0D0*X(8))+(-2.0D0*X(7)**2)+3.0D0*X(7)+(-1.0D0*X(6))+1. &0D0 FVEC(8)=(-2.0D0*X(9))+(-2.0D0*X(8)**2)+3.0D0*X(8)+(-1.0D0*X(7))+1. &0D0 FVEC(9)=(-2.0D0*X(9)**2)+3.0D0*X(9)+(-1.0D0*X(8))+1.0D0 RETURN END\\end{verbatim}"))) NIL NIL -(-82 -4148) +(-82 -2627) ((|constructor| (NIL "\\spadtype{Asp73} produces Fortran for Type 73 ASPs,{} needed for NAG routine \\axiomOpFrom{d03eef}{d03Package},{} for example:\\begin{verbatim} SUBROUTINE PDEF(X,Y,ALPHA,BETA,GAMMA,DELTA,EPSOLN,PHI,PSI) DOUBLE PRECISION ALPHA,EPSOLN,PHI,X,Y,BETA,DELTA,GAMMA,PSI ALPHA=DSIN(X) BETA=Y GAMMA=X*Y DELTA=DCOS(X)*DSIN(Y) EPSOLN=Y+X PHI=X PSI=Y RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X) (QUOTE Y)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-83 -4148) +(-83 -2627) ((|constructor| (NIL "\\spadtype{Asp74} produces Fortran for Type 74 ASPs,{} needed for NAG routine \\axiomOpFrom{d03eef}{d03Package},{} for example:\\begin{verbatim} SUBROUTINE BNDY(X,Y,A,B,C,IBND) DOUBLE PRECISION A,B,C,X,Y INTEGER IBND IF(IBND.EQ.0)THEN A=0.0D0 B=1.0D0 C=-1.0D0*DSIN(X) ELSEIF(IBND.EQ.1)THEN A=1.0D0 B=0.0D0 C=DSIN(X)*DSIN(Y) ELSEIF(IBND.EQ.2)THEN A=1.0D0 B=0.0D0 C=DSIN(X)*DSIN(Y) ELSEIF(IBND.EQ.3)THEN A=0.0D0 B=1.0D0 C=-1.0D0*DSIN(Y) ENDIF END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE X) (QUOTE Y)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-84 -4148) +(-84 -2627) ((|constructor| (NIL "\\spadtype{Asp77} produces Fortran for Type 77 ASPs,{} needed for NAG routine \\axiomOpFrom{d02gbf}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE FCNF(X,F) DOUBLE PRECISION X DOUBLE PRECISION F(2,2) F(1,1)=0.0D0 F(1,2)=1.0D0 F(2,1)=0.0D0 F(2,2)=-10.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-85 -4148) +(-85 -2627) ((|constructor| (NIL "\\spadtype{Asp78} produces Fortran for Type 78 ASPs,{} needed for NAG routine \\axiomOpFrom{d02gbf}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE FCNG(X,G) DOUBLE PRECISION G(*),X G(1)=0.0D0 G(2)=0.0D0 END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-86 -4148) +(-86 -2627) ((|constructor| (NIL "\\spadtype{Asp7} produces Fortran for Type 7 ASPs,{} needed for NAG routines \\axiomOpFrom{d02bbf}{d02Package},{} \\axiomOpFrom{d02gaf}{d02Package}. These represent a vector of functions of the scalar \\spad{X} and the array \\spad{Z},{} and look like:\\begin{verbatim} SUBROUTINE FCN(X,Z,F) DOUBLE PRECISION F(*),X,Z(*) F(1)=DTAN(Z(3)) F(2)=((-0.03199999999999999D0*DCOS(Z(3))*DTAN(Z(3)))+(-0.02D0*Z(2) &**2))/(Z(2)*DCOS(Z(3))) F(3)=-0.03199999999999999D0/(X*Z(2)**2) RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-87 -4148) +(-87 -2627) ((|constructor| (NIL "\\spadtype{Asp80} produces Fortran for Type 80 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE BDYVAL(XL,XR,ELAM,YL,YR) DOUBLE PRECISION ELAM,XL,YL(3),XR,YR(3) YL(1)=XL YL(2)=2.0D0 YR(1)=1.0D0 YR(2)=-1.0D0*DSQRT(XR+(-1.0D0*ELAM)) RETURN END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE XL) (QUOTE XR) (QUOTE ELAM)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-88 -4148) +(-88 -2627) ((|constructor| (NIL "\\spadtype{Asp8} produces Fortran for Type 8 ASPs,{} needed for NAG routine \\axiomOpFrom{d02bbf}{d02Package}. This ASP prints intermediate values of the computed solution of an ODE and might look like:\\begin{verbatim} SUBROUTINE OUTPUT(XSOL,Y,COUNT,M,N,RESULT,FORWRD) DOUBLE PRECISION Y(N),RESULT(M,N),XSOL INTEGER M,N,COUNT LOGICAL FORWRD DOUBLE PRECISION X02ALF,POINTS(8) EXTERNAL X02ALF INTEGER I POINTS(1)=1.0D0 POINTS(2)=2.0D0 POINTS(3)=3.0D0 POINTS(4)=4.0D0 POINTS(5)=5.0D0 POINTS(6)=6.0D0 POINTS(7)=7.0D0 POINTS(8)=8.0D0 COUNT=COUNT+1 DO 25001 I=1,N RESULT(COUNT,I)=Y(I)25001 CONTINUE IF(COUNT.EQ.M)THEN IF(FORWRD)THEN XSOL=X02ALF() ELSE XSOL=-X02ALF() ENDIF ELSE XSOL=POINTS(COUNT) ENDIF END\\end{verbatim}"))) NIL NIL -(-89 -4148) +(-89 -2627) ((|constructor| (NIL "\\spadtype{Asp9} produces Fortran for Type 9 ASPs,{} needed for NAG routines \\axiomOpFrom{d02bhf}{d02Package},{} \\axiomOpFrom{d02cjf}{d02Package},{} \\axiomOpFrom{d02ejf}{d02Package}. These ASPs represent a function of a scalar \\spad{X} and a vector \\spad{Y},{} for example:\\begin{verbatim} DOUBLE PRECISION FUNCTION G(X,Y) DOUBLE PRECISION X,Y(*) G=X+Y(1) RETURN END\\end{verbatim} If the user provides a constant value for \\spad{G},{} then extra information is added via COMMON blocks used by certain routines. This specifies that the value returned by \\spad{G} in this case is to be ignored.")) (|coerce| (($ (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL @@ -294,8 +294,8 @@ NIL ((|HasCategory| |#1| (QUOTE (-374)))) (-91 S) ((|constructor| (NIL "A stack represented as a flexible array.")) (|arrayStack| (($ (|List| |#1|)) "\\spad{arrayStack([x,y,...,z])} creates an array stack with first (top) element \\spad{x},{} second element \\spad{y},{}...,{}and last element \\spad{z}."))) -((-4463 . T) (-4464 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1120))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1120))) (-3794 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1120)))) (-3794 (-12 (|HasCategory| |#1| (QUOTE (-1120))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-875))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-875)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4464 . T) (-4465 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1121))) (-2758 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1121)))) (-2758 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102)))) (-92 S) ((|constructor| (NIL "This is the category of Spad abstract syntax trees."))) NIL @@ -318,15 +318,15 @@ NIL NIL (-97) ((|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. \\blankline")) (|setButtonValue| (((|Float|) (|String|) (|String|) (|Float|)) "\\axiom{setButtonValue(attributeName,{}routineName,{}\\spad{n})} sets the value of the button of attribute \\spad{attributeName} to routine \\spad{routineName} to \\spad{n}. \\spad{n} must be in the range [0..1]. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".") (((|Float|) (|String|) (|Float|)) "\\axiom{setButtonValue(attributeName,{}\\spad{n})} sets the value of all buttons of attribute \\spad{attributeName} to \\spad{n}. \\spad{n} must be in the range [0..1]. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".")) (|setAttributeButtonStep| (((|Float|) (|Float|)) "\\axiom{setAttributeButtonStep(\\spad{n})} sets the value of the steps for increasing and decreasing the button values. \\axiom{\\spad{n}} must be greater than 0 and less than 1. The preset value is 0.5.")) (|resetAttributeButtons| (((|Void|)) "\\axiom{resetAttributeButtons()} resets the Attribute buttons to a neutral level.")) (|getButtonValue| (((|Float|) (|String|) (|String|)) "\\axiom{getButtonValue(routineName,{}attributeName)} returns the current value for the effect of the attribute \\axiom{attributeName} with routine \\axiom{routineName}. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".")) (|decrease| (((|Float|) (|String|)) "\\axiom{decrease(attributeName)} decreases the value for the effect of the attribute \\axiom{attributeName} with all routines. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".") (((|Float|) (|String|) (|String|)) "\\axiom{decrease(routineName,{}attributeName)} decreases the value for the effect of the attribute \\axiom{attributeName} with routine \\axiom{routineName}. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".")) (|increase| (((|Float|) (|String|)) "\\axiom{increase(attributeName)} increases the value for the effect of the attribute \\axiom{attributeName} with all routines. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".") (((|Float|) (|String|) (|String|)) "\\axiom{increase(routineName,{}attributeName)} increases the value for the effect of the attribute \\axiom{attributeName} with routine \\axiom{routineName}. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\"."))) -((-4463 . T)) +((-4464 . T)) NIL (-98) ((|constructor| (NIL "This category exports the attributes in the AXIOM Library")) (|canonical| ((|attribute|) "\\spad{canonical} is \\spad{true} if and only if distinct elements have distinct data structures. For example,{} a domain of mathematical objects which has the \\spad{canonical} attribute means that two objects are mathematically equal if and only if their data structures are equal.")) (|multiplicativeValuation| ((|attribute|) "\\spad{multiplicativeValuation} implies \\spad{euclideanSize(a*b)=euclideanSize(a)*euclideanSize(b)}.")) (|additiveValuation| ((|attribute|) "\\spad{additiveValuation} implies \\spad{euclideanSize(a*b)=euclideanSize(a)+euclideanSize(b)}.")) (|noetherian| ((|attribute|) "\\spad{noetherian} is \\spad{true} if all of its ideals are finitely generated.")) (|central| ((|attribute|) "\\spad{central} is \\spad{true} if,{} given an algebra over a ring \\spad{R},{} the image of \\spad{R} is the center of the algebra,{} \\spadignore{i.e.} the set of members of the algebra which commute with all others is precisely the image of \\spad{R} in the algebra.")) (|partiallyOrderedSet| ((|attribute|) "\\spad{partiallyOrderedSet} is \\spad{true} if a set with \\spadop{<} which is transitive,{} but \\spad{not(a < b or a = b)} does not necessarily imply \\spad{b<a}.")) (|arbitraryPrecision| ((|attribute|) "\\spad{arbitraryPrecision} means the user can set the precision for subsequent calculations.")) (|canonicalsClosed| ((|attribute|) "\\spad{canonicalsClosed} is \\spad{true} if \\spad{unitCanonical(a)*unitCanonical(b) = unitCanonical(a*b)}.")) (|canonicalUnitNormal| ((|attribute|) "\\spad{canonicalUnitNormal} is \\spad{true} if we can choose a canonical representative for each class of associate elements,{} that is \\spad{associates?(a,b)} returns \\spad{true} if and only if \\spad{unitCanonical(a) = unitCanonical(b)}.")) (|noZeroDivisors| ((|attribute|) "\\spad{noZeroDivisors} is \\spad{true} if \\spad{x * y \\~~= 0} implies both \\spad{x} and \\spad{y} are non-zero.")) (|rightUnitary| ((|attribute|) "\\spad{rightUnitary} is \\spad{true} if \\spad{x * 1 = x} for all \\spad{x}.")) (|leftUnitary| ((|attribute|) "\\spad{leftUnitary} is \\spad{true} if \\spad{1 * x = x} for all \\spad{x}.")) (|unitsKnown| ((|attribute|) "\\spad{unitsKnown} is \\spad{true} if a monoid (a multiplicative semigroup with a 1) has \\spad{unitsKnown} means that the operation \\spadfun{recip} can only return \"failed\" if its argument is not a unit.")) (|shallowlyMutable| ((|attribute|) "\\spad{shallowlyMutable} is \\spad{true} if its values have immediate components that are updateable (mutable). Note: the properties of any component domain are irrevelant to the \\spad{shallowlyMutable} proper.")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} is \\spad{true} if it has an operation \\spad{\"*\": (D,D) -> D} which is commutative.")) (|finiteAggregate| ((|attribute|) "\\spad{finiteAggregate} is \\spad{true} if it is an aggregate with a finite number of elements."))) -((-4463 . T) ((-4465 "*") . T) (-4464 . T) (-4460 . T) (-4458 . T) (-4457 . T) (-4456 . T) (-4461 . T) (-4455 . T) (-4454 . T) (-4453 . T) (-4452 . T) (-4451 . T) (-4459 . T) (-4462 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-4450 . T)) +((-4464 . T) ((-4466 "*") . T) (-4465 . T) (-4461 . T) (-4459 . T) (-4458 . T) (-4457 . T) (-4462 . T) (-4456 . T) (-4455 . T) (-4454 . T) (-4453 . T) (-4452 . T) (-4460 . T) (-4463 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-4451 . T)) NIL (-99 R) ((|constructor| (NIL "Automorphism \\spad{R} is the multiplicative group of automorphisms of \\spad{R}.")) (|morphism| (($ (|Mapping| |#1| |#1| (|Integer|))) "\\spad{morphism(f)} returns the morphism given by \\spad{f^n(x) = f(x,n)}.") (($ (|Mapping| |#1| |#1|) (|Mapping| |#1| |#1|)) "\\spad{morphism(f, g)} returns the invertible morphism given by \\spad{f},{} where \\spad{g} is the inverse of \\spad{f}..") (($ (|Mapping| |#1| |#1|)) "\\spad{morphism(f)} returns the non-invertible morphism given by \\spad{f}."))) -((-4460 . T)) +((-4461 . T)) NIL (-100 R UP) ((|constructor| (NIL "This package provides balanced factorisations of polynomials.")) (|balancedFactorisation| (((|Factored| |#2|) |#2| (|List| |#2|)) "\\spad{balancedFactorisation(a, [b1,...,bn])} returns a factorisation \\spad{a = p1^e1 ... pm^em} such that each \\spad{pi} is balanced with respect to \\spad{[b1,...,bm]}.") (((|Factored| |#2|) |#2| |#2|) "\\spad{balancedFactorisation(a, b)} returns a factorisation \\spad{a = p1^e1 ... pm^em} such that each \\spad{pi} is balanced with respect to \\spad{b}."))) @@ -342,15 +342,15 @@ NIL NIL (-103 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|)) "\\spad{mapDown!(t,p,f)} returns \\spad{t} after traversing \\spad{t} in \"preorder\" (node then left then right) fashion replacing the successive interior nodes as follows. Let \\spad{l} and \\spad{r} denote the left and right subtrees of \\spad{t}. The root value \\spad{x} of \\spad{t} is replaced by \\spad{p}. Then \\spad{f}(value \\spad{l},{} value \\spad{r},{} \\spad{p}),{} where \\spad{l} and \\spad{r} denote the left and right subtrees of \\spad{t},{} is evaluated producing two values \\spad{pl} and \\spad{pr}. Then \\spad{mapDown!(l,pl,f)} and \\spad{mapDown!(l,pr,f)} are evaluated.") (($ $ |#1| (|Mapping| |#1| |#1| |#1|)) "\\spad{mapDown!(t,p,f)} returns \\spad{t} after traversing \\spad{t} in \"preorder\" (node then left then right) fashion replacing the successive interior nodes as follows. The root value \\spad{x} is replaced by \\spad{q} \\spad{:=} \\spad{f}(\\spad{p},{}\\spad{x}). The mapDown!(\\spad{l},{}\\spad{q},{}\\spad{f}) and mapDown!(\\spad{r},{}\\spad{q},{}\\spad{f}) are evaluated for the left and right subtrees \\spad{l} and \\spad{r} of \\spad{t}.")) (|mapUp!| (($ $ $ (|Mapping| |#1| |#1| |#1| |#1| |#1|)) "\\spad{mapUp!(t,t1,f)} traverses \\spad{t} in an \"endorder\" (left then right then node) fashion returning \\spad{t} with the value at each successive interior node of \\spad{t} replaced by \\spad{f}(\\spad{l},{}\\spad{r},{}\\spad{l1},{}\\spad{r1}) where \\spad{l} and \\spad{r} are the values at the immediate left and right nodes. Values \\spad{l1} and \\spad{r1} are values at the corresponding nodes of a balanced binary tree \\spad{t1},{} of identical shape at \\spad{t}.") ((|#1| $ (|Mapping| |#1| |#1| |#1|)) "\\spad{mapUp!(t,f)} traverses balanced binary tree \\spad{t} in an \"endorder\" (left then right then node) fashion returning \\spad{t} with the value at each successive interior node of \\spad{t} replaced by \\spad{f}(\\spad{l},{}\\spad{r}) where \\spad{l} and \\spad{r} are the values at the immediate left and right nodes.")) (|setleaves!| (($ $ (|List| |#1|)) "\\spad{setleaves!(t, ls)} sets the leaves of \\spad{t} in left-to-right order to the elements of \\spad{ls}.")) (|balancedBinaryTree| (($ (|NonNegativeInteger|) |#1|) "\\spad{balancedBinaryTree(n, s)} creates a balanced binary tree with \\spad{n} nodes each with value \\spad{s}."))) -((-4463 . T) (-4464 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1120))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1120))) (-3794 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1120)))) (-3794 (-12 (|HasCategory| |#1| (QUOTE (-1120))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-875))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-875)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4464 . T) (-4465 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1121))) (-2758 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1121)))) (-2758 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102)))) (-104 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 (-4465 "*")))) +((|HasAttribute| |#1| (QUOTE (-4466 "*")))) (-105) ((|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"))) -((-4463 . T)) +((-4464 . T)) NIL (-106 A S) ((|constructor| (NIL "A bag aggregate is an aggregate for which one can insert and extract objects,{} and where the order in which objects are inserted determines the order of extraction. Examples of bags are stacks,{} queues,{} and dequeues.")) (|inspect| ((|#2| $) "\\spad{inspect(u)} returns an (random) element from a bag.")) (|insert!| (($ |#2| $) "\\spad{insert!(x,u)} inserts item \\spad{x} into bag \\spad{u}.")) (|extract!| ((|#2| $) "\\spad{extract!(u)} destructively removes a (random) item from bag \\spad{u}.")) (|bag| (($ (|List| |#2|)) "\\spad{bag([x,y,...,z])} creates a bag with elements \\spad{x},{}\\spad{y},{}...,{}\\spad{z}.")) (|shallowlyMutable| ((|attribute|) "shallowlyMutable means that elements of bags may be destructively changed."))) @@ -358,23 +358,23 @@ NIL NIL (-107 S) ((|constructor| (NIL "A bag aggregate is an aggregate for which one can insert and extract objects,{} and where the order in which objects are inserted determines the order of extraction. Examples of bags are stacks,{} queues,{} and dequeues.")) (|inspect| ((|#1| $) "\\spad{inspect(u)} returns an (random) element from a bag.")) (|insert!| (($ |#1| $) "\\spad{insert!(x,u)} inserts item \\spad{x} into bag \\spad{u}.")) (|extract!| ((|#1| $) "\\spad{extract!(u)} destructively removes a (random) item from bag \\spad{u}.")) (|bag| (($ (|List| |#1|)) "\\spad{bag([x,y,...,z])} creates a bag with elements \\spad{x},{}\\spad{y},{}...,{}\\spad{z}.")) (|shallowlyMutable| ((|attribute|) "shallowlyMutable means that elements of bags may be destructively changed."))) -((-4464 . T)) +((-4465 . T)) NIL (-108) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating binary expansions.")) (|binary| (($ (|Fraction| (|Integer|))) "\\spad{binary(r)} converts a rational number to a binary expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(b)} returns the fractional part of a binary expansion."))) -((-4455 . T) (-4461 . T) (-4456 . T) ((-4465 "*") . T) (-4457 . T) (-4458 . T) (-4460 . T)) -((|HasCategory| (-576) (QUOTE (-927))) (|HasCategory| (-576) (LIST (QUOTE -1058) (QUOTE (-1196)))) (|HasCategory| (-576) (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-148))) (|HasCategory| (-576) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-576) (QUOTE (-1042))) (|HasCategory| (-576) (QUOTE (-832))) (|HasCategory| (-576) (QUOTE (-861))) (-3794 (|HasCategory| (-576) (QUOTE (-832))) (|HasCategory| (-576) (QUOTE (-861)))) (|HasCategory| (-576) (LIST (QUOTE -1058) (QUOTE (-576)))) (|HasCategory| (-576) (QUOTE (-1172))) (|HasCategory| (-576) (LIST (QUOTE -900) (QUOTE (-390)))) (|HasCategory| (-576) (LIST (QUOTE -900) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -626) (LIST (QUOTE -906) (QUOTE (-390))))) (|HasCategory| (-576) (LIST (QUOTE -626) (LIST (QUOTE -906) (QUOTE (-576))))) (|HasCategory| (-576) (QUOTE (-237))) (|HasCategory| (-576) (LIST (QUOTE -918) (QUOTE (-1196)))) (|HasCategory| (-576) (QUOTE (-238))) (|HasCategory| (-576) (LIST (QUOTE -916) (QUOTE (-1196)))) (|HasCategory| (-576) (LIST (QUOTE -526) (QUOTE (-1196)) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -319) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -296) (QUOTE (-576)) (QUOTE (-576)))) (|HasCategory| (-576) (QUOTE (-317))) (|HasCategory| (-576) (QUOTE (-557))) (|HasCategory| (-576) (LIST (QUOTE -651) (QUOTE (-576)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-927)))) (-3794 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-927)))) (|HasCategory| (-576) (QUOTE (-146))))) +((-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) +((|HasCategory| (-576) (QUOTE (-928))) (|HasCategory| (-576) (LIST (QUOTE -1059) (QUOTE (-1197)))) (|HasCategory| (-576) (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-148))) (|HasCategory| (-576) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-576) (QUOTE (-1043))) (|HasCategory| (-576) (QUOTE (-832))) (|HasCategory| (-576) (QUOTE (-861))) (-2758 (|HasCategory| (-576) (QUOTE (-832))) (|HasCategory| (-576) (QUOTE (-861)))) (|HasCategory| (-576) (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| (-576) (QUOTE (-1173))) (|HasCategory| (-576) (LIST (QUOTE -901) (QUOTE (-390)))) (|HasCategory| (-576) (LIST (QUOTE -901) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390))))) (|HasCategory| (-576) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576))))) (|HasCategory| (-576) (QUOTE (-237))) (|HasCategory| (-576) (LIST (QUOTE -919) (QUOTE (-1197)))) (|HasCategory| (-576) (QUOTE (-238))) (|HasCategory| (-576) (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| (-576) (LIST (QUOTE -526) (QUOTE (-1197)) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -319) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -296) (QUOTE (-576)) (QUOTE (-576)))) (|HasCategory| (-576) (QUOTE (-317))) (|HasCategory| (-576) (QUOTE (-557))) (|HasCategory| (-576) (LIST (QUOTE -651) (QUOTE (-576)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-928)))) (-2758 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-928)))) (|HasCategory| (-576) (QUOTE (-146))))) (-109) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. A `Binding' is a name asosciated with a collection of properties.")) (|binding| (($ (|Identifier|) (|List| (|Property|))) "\\spad{binding(n,props)} constructs a binding with name \\spad{`n'} and property list `props'.")) (|properties| (((|List| (|Property|)) $) "\\spad{properties(b)} returns the properties associated with binding \\spad{b}.")) (|name| (((|Identifier|) $) "\\spad{name(b)} returns the name of binding \\spad{b}"))) NIL NIL (-110) ((|constructor| (NIL "\\spadtype{Bits} provides logical functions for Indexed Bits.")) (|bits| (($ (|NonNegativeInteger|) (|Boolean|)) "\\spad{bits(n,b)} creates bits with \\spad{n} values of \\spad{b}"))) -((-4464 . T) (-4463 . T)) -((-12 (|HasCategory| (-112) (QUOTE (-1120))) (|HasCategory| (-112) (LIST (QUOTE -319) (QUOTE (-112))))) (|HasCategory| (-112) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-112) (QUOTE (-861))) (|HasCategory| (-576) (QUOTE (-861))) (|HasCategory| (-112) (QUOTE (-1120))) (|HasCategory| (-112) (LIST (QUOTE -625) (QUOTE (-875)))) (|HasCategory| (-112) (QUOTE (-102)))) +((-4465 . T) (-4464 . T)) +((-12 (|HasCategory| (-112) (QUOTE (-1121))) (|HasCategory| (-112) (LIST (QUOTE -319) (QUOTE (-112))))) (|HasCategory| (-112) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-112) (QUOTE (-861))) (|HasCategory| (-576) (QUOTE (-861))) (|HasCategory| (-112) (QUOTE (-1121))) (|HasCategory| (-112) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-112) (QUOTE (-102)))) (-111 R S) ((|constructor| (NIL "A \\spadtype{BiModule} is both a left and right module with respect to potentially different rings. \\blankline")) (|rightUnitary| ((|attribute|) "\\spad{x * 1 = x}")) (|leftUnitary| ((|attribute|) "\\spad{1 * x = x}"))) -((-4458 . T) (-4457 . T)) +((-4459 . T) (-4458 . T)) NIL (-112) ((|constructor| (NIL "\\indented{1}{\\spadtype{Boolean} is the elementary logic with 2 values:} \\spad{true} and \\spad{false}")) (|test| (($ $) "\\spad{test(b)} returns \\spad{b} and is provided for compatibility with the new compiler.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical negation of \\spad{a} or \\spad{b}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical negation of \\spad{a} and \\spad{b}.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical exclusive {\\em or} of Boolean \\spad{a} and \\spad{b}."))) @@ -392,22 +392,22 @@ NIL ((|constructor| (NIL "A basic operator is an object that can be applied to a list of arguments from a set,{} the result being a kernel over that set.")) (|setProperties| (($ $ (|AssociationList| (|String|) (|None|))) "\\spad{setProperties(op, l)} sets the property list of \\spad{op} to \\spad{l}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|setProperty| (($ $ (|Identifier|) (|None|)) "\\spad{setProperty(op, p, v)} attaches property \\spad{p} to \\spad{op},{} and sets its value to \\spad{v}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.") (($ $ (|String|) (|None|)) "\\spad{setProperty(op, s, v)} attaches property \\spad{s} to \\spad{op},{} and sets its value to \\spad{v}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|property| (((|Maybe| (|None|)) $ (|Identifier|)) "\\spad{property(op, p)} returns the value of property \\spad{p} if it is attached to \\spad{op},{} otherwise \\spad{nothing}.") (((|Union| (|None|) "failed") $ (|String|)) "\\spad{property(op, s)} returns the value of property \\spad{s} if it is attached to \\spad{op},{} and \"failed\" otherwise.")) (|deleteProperty!| (($ $ (|Identifier|)) "\\spad{deleteProperty!(op, p)} unattaches property \\spad{p} from \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.") (($ $ (|String|)) "\\spad{deleteProperty!(op, s)} unattaches property \\spad{s} from \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|assert| (($ $ (|Identifier|)) "\\spad{assert(op, p)} attaches property \\spad{p} to \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|has?| (((|Boolean|) $ (|Identifier|)) "\\spad{has?(op,p)} tests if property \\spad{s} is attached to \\spad{op}.")) (|input| (((|Union| (|Mapping| (|InputForm|) (|List| (|InputForm|))) "failed") $) "\\spad{input(op)} returns the \"\\%input\" property of \\spad{op} if it has one attached,{} \"failed\" otherwise.") (($ $ (|Mapping| (|InputForm|) (|List| (|InputForm|)))) "\\spad{input(op, foo)} attaches foo as the \"\\%input\" property of \\spad{op}. If \\spad{op} has a \"\\%input\" property \\spad{f},{} then \\spad{op(a1,...,an)} gets converted to InputForm as \\spad{f(a1,...,an)}.")) (|display| (($ $ (|Mapping| (|OutputForm|) (|OutputForm|))) "\\spad{display(op, foo)} attaches foo as the \"\\%display\" property of \\spad{op}. If \\spad{op} has a \"\\%display\" property \\spad{f},{} then \\spad{op(a)} gets converted to OutputForm as \\spad{f(a)}. Argument \\spad{op} must be unary.") (($ $ (|Mapping| (|OutputForm|) (|List| (|OutputForm|)))) "\\spad{display(op, foo)} attaches foo as the \"\\%display\" property of \\spad{op}. If \\spad{op} has a \"\\%display\" property \\spad{f},{} then \\spad{op(a1,...,an)} gets converted to OutputForm as \\spad{f(a1,...,an)}.") (((|Union| (|Mapping| (|OutputForm|) (|List| (|OutputForm|))) "failed") $) "\\spad{display(op)} returns the \"\\%display\" property of \\spad{op} if it has one attached,{} and \"failed\" otherwise.")) (|comparison| (($ $ (|Mapping| (|Boolean|) $ $)) "\\spad{comparison(op, foo?)} attaches foo? as the \"\\%less?\" property to \\spad{op}. If op1 and op2 have the same name,{} and one of them has a \"\\%less?\" property \\spad{f},{} then \\spad{f(op1, op2)} is called to decide whether \\spad{op1 < op2}.")) (|equality| (($ $ (|Mapping| (|Boolean|) $ $)) "\\spad{equality(op, foo?)} attaches foo? as the \"\\%equal?\" property to \\spad{op}. If op1 and op2 have the same name,{} and one of them has an \"\\%equal?\" property \\spad{f},{} then \\spad{f(op1, op2)} is called to decide whether op1 and op2 should be considered equal.")) (|weight| (($ $ (|NonNegativeInteger|)) "\\spad{weight(op, n)} attaches the weight \\spad{n} to \\spad{op}.") (((|NonNegativeInteger|) $) "\\spad{weight(op)} returns the weight attached to \\spad{op}.")) (|nary?| (((|Boolean|) $) "\\spad{nary?(op)} tests if \\spad{op} has arbitrary arity.")) (|unary?| (((|Boolean|) $) "\\spad{unary?(op)} tests if \\spad{op} is unary.")) (|nullary?| (((|Boolean|) $) "\\spad{nullary?(op)} tests if \\spad{op} is nullary.")) (|operator| (($ (|Symbol|) (|Arity|)) "\\spad{operator(f, a)} makes \\spad{f} into an operator of arity \\spad{a}.") (($ (|Symbol|) (|NonNegativeInteger|)) "\\spad{operator(f, n)} makes \\spad{f} into an \\spad{n}-ary operator.") (($ (|Symbol|)) "\\spad{operator(f)} makes \\spad{f} into an operator with arbitrary arity.")) (|copy| (($ $) "\\spad{copy(op)} returns a copy of \\spad{op}.")) (|properties| (((|AssociationList| (|String|) (|None|)) $) "\\spad{properties(op)} returns the list of all the properties currently attached to \\spad{op}."))) NIL NIL -(-116 -2117 UP) +(-116 -1959 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 (-117 |p|) ((|constructor| (NIL "Stream-based implementation of \\spad{Zp:} \\spad{p}-adic numbers are represented as sum(\\spad{i} = 0..,{} a[\\spad{i}] * p^i),{} where the a[\\spad{i}] lie in -(\\spad{p} - 1)\\spad{/2},{}...,{}(\\spad{p} - 1)\\spad{/2}."))) -((-4456 . T) ((-4465 "*") . T) (-4457 . T) (-4458 . T) (-4460 . T)) +((-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-118 |p|) ((|constructor| (NIL "Stream-based implementation of \\spad{Qp:} numbers are represented as sum(\\spad{i} = \\spad{k}..,{} a[\\spad{i}] * p^i),{} where the a[\\spad{i}] lie in -(\\spad{p} - 1)\\spad{/2},{}...,{}(\\spad{p} - 1)\\spad{/2}."))) -((-4455 . T) (-4461 . T) (-4456 . T) ((-4465 "*") . T) (-4457 . T) (-4458 . T) (-4460 . T)) -((|HasCategory| (-117 |#1|) (QUOTE (-927))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -1058) (QUOTE (-1196)))) (|HasCategory| (-117 |#1|) (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-148))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-117 |#1|) (QUOTE (-1042))) (|HasCategory| (-117 |#1|) (QUOTE (-832))) (|HasCategory| (-117 |#1|) (QUOTE (-861))) (-3794 (|HasCategory| (-117 |#1|) (QUOTE (-832))) (|HasCategory| (-117 |#1|) (QUOTE (-861)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -1058) (QUOTE (-576)))) (|HasCategory| (-117 |#1|) (QUOTE (-1172))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -900) (QUOTE (-390)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -900) (QUOTE (-576)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -906) (QUOTE (-390))))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -906) (QUOTE (-576))))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| (-117 |#1|) (QUOTE (-237))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -918) (QUOTE (-1196)))) (|HasCategory| (-117 |#1|) (QUOTE (-238))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -916) (QUOTE (-1196)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -526) (QUOTE (-1196)) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -319) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -296) (LIST (QUOTE -117) (|devaluate| |#1|)) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (QUOTE (-317))) (|HasCategory| (-117 |#1|) (QUOTE (-557))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-927)))) (-3794 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-927)))) (|HasCategory| (-117 |#1|) (QUOTE (-146))))) +((-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) +((|HasCategory| (-117 |#1|) (QUOTE (-928))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -1059) (QUOTE (-1197)))) (|HasCategory| (-117 |#1|) (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-148))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-117 |#1|) (QUOTE (-1043))) (|HasCategory| (-117 |#1|) (QUOTE (-832))) (|HasCategory| (-117 |#1|) (QUOTE (-861))) (-2758 (|HasCategory| (-117 |#1|) (QUOTE (-832))) (|HasCategory| (-117 |#1|) (QUOTE (-861)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| (-117 |#1|) (QUOTE (-1173))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -901) (QUOTE (-390)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -901) (QUOTE (-576)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390))))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576))))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| (-117 |#1|) (QUOTE (-237))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -919) (QUOTE (-1197)))) (|HasCategory| (-117 |#1|) (QUOTE (-238))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -526) (QUOTE (-1197)) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -319) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -296) (LIST (QUOTE -117) (|devaluate| |#1|)) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (QUOTE (-317))) (|HasCategory| (-117 |#1|) (QUOTE (-557))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-928)))) (-2758 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-928)))) (|HasCategory| (-117 |#1|) (QUOTE (-146))))) (-119 A S) ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "right" $) "\\spad{setelt(a,\"right\",b)} (also written \\axiom{\\spad{b} . right \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setright!(a,{}\\spad{b})}.") (($ $ "left" $) "\\spad{setelt(a,\"left\",b)} (also written \\axiom{a . left \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setleft!(a,{}\\spad{b})}.")) (|right| (($ $) "\\spad{right(a)} returns the right child.")) (|elt| (($ $ "right") "\\spad{elt(a,\"right\")} (also written: \\axiom{a . right}) is equivalent to \\axiom{right(a)}.") (($ $ "left") "\\spad{elt(u,\"left\")} (also written: \\axiom{a . left}) is equivalent to \\axiom{left(a)}.")) (|left| (($ $) "\\spad{left(u)} returns the left child."))) NIL -((|HasAttribute| |#1| (QUOTE -4464))) +((|HasAttribute| |#1| (QUOTE -4465))) (-120 S) ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "right" $) "\\spad{setelt(a,\"right\",b)} (also written \\axiom{\\spad{b} . right \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setright!(a,{}\\spad{b})}.") (($ $ "left" $) "\\spad{setelt(a,\"left\",b)} (also written \\axiom{a . left \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setleft!(a,{}\\spad{b})}.")) (|right| (($ $) "\\spad{right(a)} returns the right child.")) (|elt| (($ $ "right") "\\spad{elt(a,\"right\")} (also written: \\axiom{a . right}) is equivalent to \\axiom{right(a)}.") (($ $ "left") "\\spad{elt(u,\"left\")} (also written: \\axiom{a . left}) is equivalent to \\axiom{left(a)}.")) (|left| (($ $) "\\spad{left(u)} returns the left child."))) NIL @@ -418,15 +418,15 @@ NIL NIL (-122 S) ((|constructor| (NIL "BinarySearchTree(\\spad{S}) is the domain of a binary trees where elements are ordered across the tree. A binary search tree is either empty or has a value which is an \\spad{S},{} and a right and left which are both BinaryTree(\\spad{S}) Elements are ordered across the tree.")) (|split| (((|Record| (|:| |less| $) (|:| |greater| $)) |#1| $) "\\spad{split(x,b)} splits binary tree \\spad{b} into two trees,{} one with elements greater than \\spad{x},{} the other with elements less than \\spad{x}.")) (|insertRoot!| (($ |#1| $) "\\spad{insertRoot!(x,b)} inserts element \\spad{x} as a root of binary search tree \\spad{b}.")) (|insert!| (($ |#1| $) "\\spad{insert!(x,b)} inserts element \\spad{x} as leaves into binary search tree \\spad{b}.")) (|binarySearchTree| (($ (|List| |#1|)) "\\spad{binarySearchTree(l)} \\undocumented"))) -((-4463 . T) (-4464 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1120))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1120))) (-3794 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1120)))) (-3794 (-12 (|HasCategory| |#1| (QUOTE (-1120))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-875))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-875)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4464 . T) (-4465 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1121))) (-2758 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1121)))) (-2758 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102)))) (-123 S) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}."))) NIL NIL (-124) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}."))) -((-4464 . T) (-4463 . T)) +((-4465 . T) (-4464 . T)) NIL (-125 A S) ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#2| $) "\\spad{node(left,v,right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) @@ -434,20 +434,20 @@ NIL NIL (-126 S) ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#1| $) "\\spad{node(left,v,right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) -((-4463 . T) (-4464 . T)) +((-4464 . T) (-4465 . T)) NIL (-127 S) ((|constructor| (NIL "\\spadtype{BinaryTournament(S)} is the domain of binary trees where elements are ordered down the tree. A binary search tree is either empty or is a node containing a \\spadfun{value} of type \\spad{S},{} and a \\spadfun{right} and a \\spadfun{left} which are both \\spadtype{BinaryTree(S)}")) (|insert!| (($ |#1| $) "\\spad{insert!(x,b)} inserts element \\spad{x} as leaves into binary tournament \\spad{b}.")) (|binaryTournament| (($ (|List| |#1|)) "\\spad{binaryTournament(ls)} creates a binary tournament with the elements of \\spad{ls} as values at the nodes."))) -((-4463 . T) (-4464 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1120))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1120))) (-3794 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1120)))) (-3794 (-12 (|HasCategory| |#1| (QUOTE (-1120))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-875))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-875)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4464 . T) (-4465 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1121))) (-2758 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1121)))) (-2758 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102)))) (-128 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| $) "\\spad{binaryTree(l,v,r)} creates a binary tree with value \\spad{v} with left subtree \\spad{l} and right subtree \\spad{r}.") (($ |#1|) "\\spad{binaryTree(v)} is an non-empty binary tree with value \\spad{v},{} and left and right empty."))) -((-4463 . T) (-4464 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1120))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1120))) (-3794 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1120)))) (-3794 (-12 (|HasCategory| |#1| (QUOTE (-1120))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-875))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-875)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4464 . T) (-4465 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1121))) (-2758 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1121)))) (-2758 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102)))) (-129) ((|constructor| (NIL "ByteBuffer provides datatype for buffers of bytes. This domain differs from PrimitiveArray Byte in that it is not as rigid as PrimitiveArray Byte. That is,{} the typical use of ByteBuffer is to pre-allocate a vector of Byte of some capacity \\spad{`n'}. The array can then store up to \\spad{`n'} bytes. The actual interesting bytes count (the length of the buffer) is therefore different from the capacity. The length is no more than the capacity,{} but it can be set dynamically as needed. This functionality is used for example when reading bytes from input/output devices where we use buffers to transfer data in and out of the system. Note: a value of type ByteBuffer is 0-based indexed,{} as opposed \\indented{6}{Vector,{} but not unlike PrimitiveArray Byte.}")) (|finiteAggregate| ((|attribute|) "A ByteBuffer object is a finite aggregate")) (|setLength!| (((|NonNegativeInteger|) $ (|NonNegativeInteger|)) "\\spad{setLength!(buf,n)} sets the number of active bytes in the `buf'. Error if \\spad{`n'} is more than the capacity.")) (|capacity| (((|NonNegativeInteger|) $) "\\spad{capacity(buf)} returns the pre-allocated maximum size of `buf'.")) (|byteBuffer| (($ (|NonNegativeInteger|)) "\\spad{byteBuffer(n)} creates a buffer of capacity \\spad{n},{} and length 0."))) -((-4464 . T) (-4463 . T)) -((-3794 (-12 (|HasCategory| (-130) (QUOTE (-861))) (|HasCategory| (-130) (LIST (QUOTE -319) (QUOTE (-130))))) (-12 (|HasCategory| (-130) (QUOTE (-1120))) (|HasCategory| (-130) (LIST (QUOTE -319) (QUOTE (-130)))))) (-3794 (-12 (|HasCategory| (-130) (QUOTE (-1120))) (|HasCategory| (-130) (LIST (QUOTE -319) (QUOTE (-130))))) (|HasCategory| (-130) (LIST (QUOTE -625) (QUOTE (-875))))) (|HasCategory| (-130) (LIST (QUOTE -626) (QUOTE (-548)))) (-3794 (|HasCategory| (-130) (QUOTE (-861))) (|HasCategory| (-130) (QUOTE (-1120)))) (|HasCategory| (-130) (QUOTE (-861))) (-3794 (|HasCategory| (-130) (QUOTE (-102))) (|HasCategory| (-130) (QUOTE (-861))) (|HasCategory| (-130) (QUOTE (-1120)))) (|HasCategory| (-576) (QUOTE (-861))) (|HasCategory| (-130) (QUOTE (-1120))) (|HasCategory| (-130) (LIST (QUOTE -625) (QUOTE (-875)))) (|HasCategory| (-130) (QUOTE (-102))) (-12 (|HasCategory| (-130) (QUOTE (-1120))) (|HasCategory| (-130) (LIST (QUOTE -319) (QUOTE (-130)))))) +((-4465 . T) (-4464 . T)) +((-2758 (-12 (|HasCategory| (-130) (QUOTE (-861))) (|HasCategory| (-130) (LIST (QUOTE -319) (QUOTE (-130))))) (-12 (|HasCategory| (-130) (QUOTE (-1121))) (|HasCategory| (-130) (LIST (QUOTE -319) (QUOTE (-130)))))) (-2758 (-12 (|HasCategory| (-130) (QUOTE (-1121))) (|HasCategory| (-130) (LIST (QUOTE -319) (QUOTE (-130))))) (|HasCategory| (-130) (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| (-130) (LIST (QUOTE -626) (QUOTE (-548)))) (-2758 (|HasCategory| (-130) (QUOTE (-861))) (|HasCategory| (-130) (QUOTE (-1121)))) (|HasCategory| (-130) (QUOTE (-861))) (-2758 (|HasCategory| (-130) (QUOTE (-102))) (|HasCategory| (-130) (QUOTE (-861))) (|HasCategory| (-130) (QUOTE (-1121)))) (|HasCategory| (-576) (QUOTE (-861))) (|HasCategory| (-130) (QUOTE (-1121))) (|HasCategory| (-130) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-130) (QUOTE (-102))) (-12 (|HasCategory| (-130) (QUOTE (-1121))) (|HasCategory| (-130) (LIST (QUOTE -319) (QUOTE (-130)))))) (-130) ((|constructor| (NIL "Byte is the datatype of 8-bit sized unsigned integer values.")) (|sample| (($) "\\spad{sample} gives a sample datum of type Byte.")) (|bitior| (($ $ $) "bitor(\\spad{x},{}\\spad{y}) returns the bitwise `inclusive or' of \\spad{`x'} and \\spad{`y'}.")) (|bitand| (($ $ $) "\\spad{bitand(x,y)} returns the bitwise `and' of \\spad{`x'} and \\spad{`y'}.")) (|byte| (($ (|NonNegativeInteger|)) "\\spad{byte(x)} injects the unsigned integer value \\spad{`v'} into the Byte algebra. \\spad{`v'} must be non-negative and less than 256."))) NIL @@ -470,13 +470,13 @@ NIL NIL (-135) ((|constructor| (NIL "Members of the domain CardinalNumber are values indicating the cardinality of sets,{} both finite and infinite. Arithmetic operations are defined on cardinal numbers as follows. \\blankline If \\spad{x = \\#X} and \\spad{y = \\#Y} then \\indented{2}{\\spad{x+y\\space{2}= \\#(X+Y)}\\space{3}\\tab{30}disjoint union} \\indented{2}{\\spad{x-y\\space{2}= \\#(X-Y)}\\space{3}\\tab{30}relative complement} \\indented{2}{\\spad{x*y\\space{2}= \\#(X*Y)}\\space{3}\\tab{30}cartesian product} \\indented{2}{\\spad{x**y = \\#(X**Y)}\\space{2}\\tab{30}\\spad{X**Y = \\{g| g:Y->X\\}}} \\blankline The non-negative integers have a natural construction as cardinals \\indented{2}{\\spad{0 = \\#\\{\\}},{} \\spad{1 = \\{0\\}},{} \\spad{2 = \\{0, 1\\}},{} ...,{} \\spad{n = \\{i| 0 <= i < n\\}}.} \\blankline That \\spad{0} acts as a zero for the multiplication of cardinals is equivalent to the axiom of choice. \\blankline The generalized continuum hypothesis asserts \\center{\\spad{2**Aleph i = Aleph(i+1)}} and is independent of the axioms of set theory [Goedel 1940]. \\blankline Three commonly encountered cardinal numbers are \\indented{3}{\\spad{a = \\#Z}\\space{7}\\tab{30}countable infinity} \\indented{3}{\\spad{c = \\#R}\\space{7}\\tab{30}the continuum} \\indented{3}{\\spad{f = \\#\\{g| g:[0,1]->R\\}}} \\blankline In this domain,{} these values are obtained using \\indented{3}{\\spad{a := Aleph 0},{} \\spad{c := 2**a},{} \\spad{f := 2**c}.} \\blankline")) (|generalizedContinuumHypothesisAssumed| (((|Boolean|) (|Boolean|)) "\\spad{generalizedContinuumHypothesisAssumed(bool)} is used to dictate whether the hypothesis is to be assumed.")) (|generalizedContinuumHypothesisAssumed?| (((|Boolean|)) "\\spad{generalizedContinuumHypothesisAssumed?()} tests if the hypothesis is currently assumed.")) (|countable?| (((|Boolean|) $) "\\spad{countable?(\\spad{a})} determines whether \\spad{a} is a countable cardinal,{} \\spadignore{i.e.} an integer or \\spad{Aleph 0}.")) (|finite?| (((|Boolean|) $) "\\spad{finite?(\\spad{a})} determines whether \\spad{a} is a finite cardinal,{} \\spadignore{i.e.} an integer.")) (|Aleph| (($ (|NonNegativeInteger|)) "\\spad{Aleph(n)} provides the named (infinite) cardinal number.")) (** (($ $ $) "\\spad{x**y} returns \\spad{\\#(X**Y)} where \\spad{X**Y} is defined \\indented{1}{as \\spad{\\{g| g:Y->X\\}}.}")) (- (((|Union| $ "failed") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,D) -> D} which is commutative."))) -(((-4465 "*") . T)) +(((-4466 "*") . T)) NIL -(-136 |minix| -1911 S T$) +(-136 |minix| -2704 S T$) ((|constructor| (NIL "This package provides functions to enable conversion of tensors given conversion of the components.")) (|map| (((|CartesianTensor| |#1| |#2| |#4|) (|Mapping| |#4| |#3|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{map(f,ts)} does a componentwise conversion of the tensor \\spad{ts} to a tensor with components of type \\spad{T}.")) (|reshape| (((|CartesianTensor| |#1| |#2| |#4|) (|List| |#4|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{reshape(lt,ts)} organizes the list of components \\spad{lt} into a tensor with the same shape as \\spad{ts}."))) NIL NIL -(-137 |minix| -1911 R) +(-137 |minix| -2704 R) ((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\spad{sample()} returns an object of type \\%.")) (|unravel| (($ (|List| |#3|)) "\\spad{unravel(t)} produces a tensor from a list of components such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|ravel| (((|List| |#3|) $) "\\spad{ravel(t)} produces a list of components from a tensor such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|leviCivitaSymbol| (($) "\\spad{leviCivitaSymbol()} is the rank \\spad{dim} tensor defined by \\spad{leviCivitaSymbol()(i1,...idim) = +1/0/-1} if \\spad{i1,...,idim} is an even/is nota /is an odd permutation of \\spad{minix,...,minix+dim-1}.")) (|kroneckerDelta| (($) "\\spad{kroneckerDelta()} is the rank 2 tensor defined by \\indented{3}{\\spad{kroneckerDelta()(i,j)}} \\indented{6}{\\spad{= 1\\space{2}if i = j}} \\indented{6}{\\spad{= 0 if\\space{2}i \\~= j}}")) (|reindex| (($ $ (|List| (|Integer|))) "\\spad{reindex(t,[i1,...,idim])} permutes the indices of \\spad{t}. For example,{} if \\spad{r = reindex(t, [4,1,2,3])} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank for tensor given by \\indented{4}{\\spad{r(i,j,k,l) = t(l,i,j,k)}.}")) (|transpose| (($ $ (|Integer|) (|Integer|)) "\\spad{transpose(t,i,j)} exchanges the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices of \\spad{t}. For example,{} if \\spad{r = transpose(t,2,3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,j,k,l) = t(i,k,j,l)}.}") (($ $) "\\spad{transpose(t)} exchanges the first and last indices of \\spad{t}. For example,{} if \\spad{r = transpose(t)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,j,k,l) = t(l,j,k,i)}.}")) (|contract| (($ $ (|Integer|) (|Integer|)) "\\spad{contract(t,i,j)} is the contraction of tensor \\spad{t} which sums along the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices. For example,{} if \\spad{r = contract(t,1,3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 2 \\spad{(= 4 - 2)} tensor given by \\indented{4}{\\spad{r(i,j) = sum(h=1..dim,t(h,i,h,j))}.}") (($ $ (|Integer|) $ (|Integer|)) "\\spad{contract(t,i,s,j)} is the inner product of tenors \\spad{s} and \\spad{t} which sums along the \\spad{k1}\\spad{-}th index of \\spad{t} and the \\spad{k2}\\spad{-}th index of \\spad{s}. For example,{} if \\spad{r = contract(s,2,t,1)} for rank 3 tensors rank 3 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is the rank 4 \\spad{(= 3 + 3 - 2)} tensor given by \\indented{4}{\\spad{r(i,j,k,l) = sum(h=1..dim,s(i,h,j)*t(h,k,l))}.}")) (* (($ $ $) "\\spad{s*t} is the inner product of the tensors \\spad{s} and \\spad{t} which contracts the last index of \\spad{s} with the first index of \\spad{t},{} \\spadignore{i.e.} \\indented{4}{\\spad{t*s = contract(t,rank t, s, 1)}} \\indented{4}{\\spad{t*s = sum(k=1..N, t[i1,..,iN,k]*s[k,j1,..,jM])}} This is compatible with the use of \\spad{M*v} to denote the matrix-vector inner product.")) (|product| (($ $ $) "\\spad{product(s,t)} is the outer product of the tensors \\spad{s} and \\spad{t}. For example,{} if \\spad{r = product(s,t)} for rank 2 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is a rank 4 tensor given by \\indented{4}{\\spad{r(i,j,k,l) = s(i,j)*t(k,l)}.}")) (|elt| ((|#3| $ (|List| (|Integer|))) "\\spad{elt(t,[i1,...,iN])} gives a component of a rank \\spad{N} tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,i,j,k,l)} gives a component of a rank 4 tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,i,j,k)} gives a component of a rank 3 tensor.") ((|#3| $ (|Integer|) (|Integer|)) "\\spad{elt(t,i,j)} gives a component of a rank 2 tensor.") ((|#3| $) "\\spad{elt(t)} gives the component of a rank 0 tensor.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(t)} returns the tensorial rank of \\spad{t} (that is,{} the number of indices). This is the same as the graded module degree.")) (|coerce| (($ (|List| $)) "\\spad{coerce([t_1,...,t_dim])} allows tensors to be constructed using lists.") (($ (|List| |#3|)) "\\spad{coerce([r_1,...,r_dim])} allows tensors to be constructed using lists.") (($ (|SquareMatrix| |#2| |#3|)) "\\spad{coerce(m)} views a matrix as a rank 2 tensor.") (($ (|DirectProduct| |#2| |#3|)) "\\spad{coerce(v)} views a vector as a rank 1 tensor."))) NIL NIL @@ -498,8 +498,8 @@ NIL NIL (-142) ((|constructor| (NIL "This domain allows classes of characters to be defined and manipulated efficiently.")) (|alphanumeric| (($) "\\spad{alphanumeric()} returns the class of all characters for which \\spadfunFrom{alphanumeric?}{Character} is \\spad{true}.")) (|alphabetic| (($) "\\spad{alphabetic()} returns the class of all characters for which \\spadfunFrom{alphabetic?}{Character} is \\spad{true}.")) (|lowerCase| (($) "\\spad{lowerCase()} returns the class of all characters for which \\spadfunFrom{lowerCase?}{Character} is \\spad{true}.")) (|upperCase| (($) "\\spad{upperCase()} returns the class of all characters for which \\spadfunFrom{upperCase?}{Character} is \\spad{true}.")) (|hexDigit| (($) "\\spad{hexDigit()} returns the class of all characters for which \\spadfunFrom{hexDigit?}{Character} is \\spad{true}.")) (|digit| (($) "\\spad{digit()} returns the class of all characters for which \\spadfunFrom{digit?}{Character} is \\spad{true}.")) (|charClass| (($ (|List| (|Character|))) "\\spad{charClass(l)} creates a character class which contains exactly the characters given in the list \\spad{l}.") (($ (|String|)) "\\spad{charClass(s)} creates a character class which contains exactly the characters given in the string \\spad{s}."))) -((-4463 . T) (-4453 . T) (-4464 . T)) -((-3794 (-12 (|HasCategory| (-145) (QUOTE (-379))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1120))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-145) (QUOTE (-379))) (|HasCategory| (-145) (QUOTE (-861))) (|HasCategory| (-145) (QUOTE (-1120))) (|HasCategory| (-145) (LIST (QUOTE -625) (QUOTE (-875)))) (|HasCategory| (-145) (QUOTE (-102))) (-12 (|HasCategory| (-145) (QUOTE (-1120))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145)))))) +((-4464 . T) (-4454 . T) (-4465 . T)) +((-2758 (-12 (|HasCategory| (-145) (QUOTE (-379))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1121))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-145) (QUOTE (-379))) (|HasCategory| (-145) (QUOTE (-861))) (|HasCategory| (-145) (QUOTE (-1121))) (|HasCategory| (-145) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-145) (QUOTE (-102))) (-12 (|HasCategory| (-145) (QUOTE (-1121))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145)))))) (-143 R Q A) ((|constructor| (NIL "CommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#3|) "\\spad{splitDenominator([q1,...,qn])} returns \\spad{[[p1,...,pn], d]} such that \\spad{qi = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|clearDenominator| ((|#3| |#3|) "\\spad{clearDenominator([q1,...,qn])} returns \\spad{[p1,...,pn]} such that \\spad{qi = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|commonDenominator| ((|#1| |#3|) "\\spad{commonDenominator([q1,...,qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}\\spad{qn}."))) NIL @@ -514,7 +514,7 @@ NIL NIL (-146) ((|constructor| (NIL "Rings of Characteristic Non Zero")) (|charthRoot| (((|Union| $ "failed") $) "\\spad{charthRoot(x)} returns the \\spad{p}th root of \\spad{x} where \\spad{p} is the characteristic of the ring."))) -((-4460 . T)) +((-4461 . T)) NIL (-147 R) ((|constructor| (NIL "This package provides a characteristicPolynomial function for any matrix over a commutative ring.")) (|characteristicPolynomial| ((|#1| (|Matrix| |#1|) |#1|) "\\spad{characteristicPolynomial(m,r)} computes the characteristic polynomial of the matrix \\spad{m} evaluated at the point \\spad{r}. In particular,{} if \\spad{r} is the polynomial \\spad{'x},{} then it returns the characteristic polynomial expressed as a polynomial in \\spad{'x}."))) @@ -522,9 +522,9 @@ NIL NIL (-148) ((|constructor| (NIL "Rings of Characteristic Zero."))) -((-4460 . T)) +((-4461 . T)) NIL -(-149 -2117 UP UPUP) +(-149 -1959 UP UPUP) ((|constructor| (NIL "Tools to send a point to infinity on an algebraic curve.")) (|chvar| (((|Record| (|:| |func| |#3|) (|:| |poly| |#3|) (|:| |c1| (|Fraction| |#2|)) (|:| |c2| (|Fraction| |#2|)) (|:| |deg| (|NonNegativeInteger|))) |#3| |#3|) "\\spad{chvar(f(x,y), p(x,y))} returns \\spad{[g(z,t), q(z,t), c1(z), c2(z), n]} such that under the change of variable \\spad{x = c1(z)},{} \\spad{y = t * c2(z)},{} one gets \\spad{f(x,y) = g(z,t)}. The algebraic relation between \\spad{x} and \\spad{y} is \\spad{p(x, y) = 0}. The algebraic relation between \\spad{z} and \\spad{t} is \\spad{q(z, t) = 0}.")) (|eval| ((|#3| |#3| (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{eval(p(x,y), f(x), g(x))} returns \\spad{p(f(x), y * g(x))}.")) (|goodPoint| ((|#1| |#3| |#3|) "\\spad{goodPoint(p, q)} returns an integer a such that a is neither a pole of \\spad{p(x,y)} nor a branch point of \\spad{q(x,y) = 0}.")) (|rootPoly| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| (|Fraction| |#2|)) (|:| |radicand| |#2|)) (|Fraction| |#2|) (|NonNegativeInteger|)) "\\spad{rootPoly(g, n)} returns \\spad{[m, c, P]} such that \\spad{c * g ** (1/n) = P ** (1/m)} thus if \\spad{y**n = g},{} then \\spad{z**m = P} where \\spad{z = c * y}.")) (|radPoly| (((|Union| (|Record| (|:| |radicand| (|Fraction| |#2|)) (|:| |deg| (|NonNegativeInteger|))) "failed") |#3|) "\\spad{radPoly(p(x, y))} returns \\spad{[c(x), n]} if \\spad{p} is of the form \\spad{y**n - c(x)},{} \"failed\" otherwise.")) (|mkIntegral| (((|Record| (|:| |coef| (|Fraction| |#2|)) (|:| |poly| |#3|)) |#3|) "\\spad{mkIntegral(p(x,y))} returns \\spad{[c(x), q(x,z)]} such that \\spad{z = c * y} is integral. The algebraic relation between \\spad{x} and \\spad{y} is \\spad{p(x, y) = 0}. The algebraic relation between \\spad{x} and \\spad{z} is \\spad{q(x, z) = 0}."))) NIL NIL @@ -535,14 +535,14 @@ NIL (-151 A S) ((|constructor| (NIL "A collection is a homogeneous aggregate which can built from list of members. The operation used to build the aggregate is generically named \\spadfun{construct}. However,{} each collection provides its own special function with the same name as the data type,{} except with an initial lower case letter,{} \\spadignore{e.g.} \\spadfun{list} for \\spadtype{List},{} \\spadfun{flexibleArray} for \\spadtype{FlexibleArray},{} and so on.")) (|removeDuplicates| (($ $) "\\spad{removeDuplicates(u)} returns a copy of \\spad{u} with all duplicates removed.")) (|select| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{select(p,u)} returns a copy of \\spad{u} containing only those elements such \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{select(\\spad{p},{}\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})]}.")) (|remove| (($ |#2| $) "\\spad{remove(x,u)} returns a copy of \\spad{u} with all elements \\axiom{\\spad{y} = \\spad{x}} removed. Note: \\axiom{remove(\\spad{y},{}\\spad{c}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{c} | \\spad{x} \\spad{~=} \\spad{y}]}.") (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{remove(p,u)} returns a copy of \\spad{u} removing all elements \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{remove(\\spad{p},{}\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u} | not \\spad{p}(\\spad{x})]}.")) (|reduce| ((|#2| (|Mapping| |#2| |#2| |#2|) $ |#2| |#2|) "\\spad{reduce(f,u,x,z)} reduces the binary operation \\spad{f} across \\spad{u},{} stopping when an \"absorbing element\" \\spad{z} is encountered. As for \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})},{} \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})} when \\spad{u} contains no element \\spad{z}. Thus the third argument \\spad{x} is returned when \\spad{u} is empty.") ((|#2| (|Mapping| |#2| |#2| |#2|) $ |#2|) "\\spad{reduce(f,u,x)} reduces the binary operation \\spad{f} across \\spad{u},{} where \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u})} if \\spad{u} has 2 or more elements. Returns \\axiom{\\spad{f}(\\spad{x},{}\\spad{y})} if \\spad{u} has one element \\spad{y},{} \\spad{x} if \\spad{u} is empty. For example,{} \\axiom{reduce(+,{}\\spad{u},{}0)} returns the sum of the elements of \\spad{u}.") ((|#2| (|Mapping| |#2| |#2| |#2|) $) "\\spad{reduce(f,u)} reduces the binary operation \\spad{f} across \\spad{u}. For example,{} if \\spad{u} is \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]} then \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\axiom{\\spad{f}(..\\spad{f}(\\spad{f}(\\spad{x},{}\\spad{y}),{}...),{}\\spad{z})}. Note: if \\spad{u} has one element \\spad{x},{} \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\spad{x}. Error: if \\spad{u} is empty.")) (|find| (((|Union| |#2| "failed") (|Mapping| (|Boolean|) |#2|) $) "\\spad{find(p,u)} returns the first \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \"failed\" otherwise.")) (|construct| (($ (|List| |#2|)) "\\axiom{construct(\\spad{x},{}\\spad{y},{}...,{}\\spad{z})} returns the collection of elements \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}} ordered as given. Equivalently written as \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]\\$\\spad{D}},{} where \\spad{D} is the domain. \\spad{D} may be omitted for those of type List."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (QUOTE (-1120))) (|HasAttribute| |#1| (QUOTE -4463))) +((|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (QUOTE (-1121))) (|HasAttribute| |#1| (QUOTE -4464))) (-152 S) ((|constructor| (NIL "A collection is a homogeneous aggregate which can built from list of members. The operation used to build the aggregate is generically named \\spadfun{construct}. However,{} each collection provides its own special function with the same name as the data type,{} except with an initial lower case letter,{} \\spadignore{e.g.} \\spadfun{list} for \\spadtype{List},{} \\spadfun{flexibleArray} for \\spadtype{FlexibleArray},{} and so on.")) (|removeDuplicates| (($ $) "\\spad{removeDuplicates(u)} returns a copy of \\spad{u} with all duplicates removed.")) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select(p,u)} returns a copy of \\spad{u} containing only those elements such \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{select(\\spad{p},{}\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})]}.")) (|remove| (($ |#1| $) "\\spad{remove(x,u)} returns a copy of \\spad{u} with all elements \\axiom{\\spad{y} = \\spad{x}} removed. Note: \\axiom{remove(\\spad{y},{}\\spad{c}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{c} | \\spad{x} \\spad{~=} \\spad{y}]}.") (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove(p,u)} returns a copy of \\spad{u} removing all elements \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{remove(\\spad{p},{}\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u} | not \\spad{p}(\\spad{x})]}.")) (|reduce| ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) "\\spad{reduce(f,u,x,z)} reduces the binary operation \\spad{f} across \\spad{u},{} stopping when an \"absorbing element\" \\spad{z} is encountered. As for \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})},{} \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})} when \\spad{u} contains no element \\spad{z}. Thus the third argument \\spad{x} is returned when \\spad{u} is empty.") ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1|) "\\spad{reduce(f,u,x)} reduces the binary operation \\spad{f} across \\spad{u},{} where \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u})} if \\spad{u} has 2 or more elements. Returns \\axiom{\\spad{f}(\\spad{x},{}\\spad{y})} if \\spad{u} has one element \\spad{y},{} \\spad{x} if \\spad{u} is empty. For example,{} \\axiom{reduce(+,{}\\spad{u},{}0)} returns the sum of the elements of \\spad{u}.") ((|#1| (|Mapping| |#1| |#1| |#1|) $) "\\spad{reduce(f,u)} reduces the binary operation \\spad{f} across \\spad{u}. For example,{} if \\spad{u} is \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]} then \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\axiom{\\spad{f}(..\\spad{f}(\\spad{f}(\\spad{x},{}\\spad{y}),{}...),{}\\spad{z})}. Note: if \\spad{u} has one element \\spad{x},{} \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\spad{x}. Error: if \\spad{u} is empty.")) (|find| (((|Union| |#1| "failed") (|Mapping| (|Boolean|) |#1|) $) "\\spad{find(p,u)} returns the first \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \"failed\" otherwise.")) (|construct| (($ (|List| |#1|)) "\\axiom{construct(\\spad{x},{}\\spad{y},{}...,{}\\spad{z})} returns the collection of elements \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}} ordered as given. Equivalently written as \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]\\$\\spad{D}},{} where \\spad{D} is the domain. \\spad{D} may be omitted for those of type List."))) NIL NIL (-153 |n| K Q) ((|constructor| (NIL "CliffordAlgebra(\\spad{n},{} \\spad{K},{} \\spad{Q}) defines a vector space of dimension \\spad{2**n} over \\spad{K},{} given a quadratic form \\spad{Q} on \\spad{K**n}. \\blankline If \\spad{e[i]},{} \\spad{1<=i<=n} is a basis for \\spad{K**n} then \\indented{3}{1,{} \\spad{e[i]} (\\spad{1<=i<=n}),{} \\spad{e[i1]*e[i2]}} (\\spad{1<=i1<i2<=n}),{}...,{}\\spad{e[1]*e[2]*..*e[n]} is a basis for the Clifford Algebra. \\blankline The algebra is defined by the relations \\indented{3}{\\spad{e[i]*e[j] = -e[j]*e[i]}\\space{2}(\\spad{i \\~~= j}),{}} \\indented{3}{\\spad{e[i]*e[i] = Q(e[i])}} \\blankline Examples of Clifford Algebras are: gaussians,{} quaternions,{} exterior algebras and spin algebras.")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} computes the multiplicative inverse of \\spad{x} or \"failed\" if \\spad{x} is not invertible.")) (|coefficient| ((|#2| $ (|List| (|PositiveInteger|))) "\\spad{coefficient(x,[i1,i2,...,iN])} extracts the coefficient of \\spad{e(i1)*e(i2)*...*e(iN)} in \\spad{x}.")) (|monomial| (($ |#2| (|List| (|PositiveInteger|))) "\\spad{monomial(c,[i1,i2,...,iN])} produces the value given by \\spad{c*e(i1)*e(i2)*...*e(iN)}.")) (|e| (($ (|PositiveInteger|)) "\\spad{e(n)} produces the appropriate unit element."))) -((-4458 . T) (-4457 . T) (-4460 . T)) +((-4459 . T) (-4458 . T) (-4461 . T)) NIL (-154) ((|constructor| (NIL "\\indented{1}{The purpose of this package is to provide reasonable plots of} functions with singularities.")) (|clipWithRanges| (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|List| (|List| (|Point| (|DoubleFloat|)))) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{clipWithRanges(pointLists,xMin,xMax,yMin,yMax)} performs clipping on a list of lists of points,{} \\spad{pointLists}. Clipping is done within the specified ranges of \\spad{xMin},{} \\spad{xMax} and \\spad{yMin},{} \\spad{yMax}. This function is used internally by the \\fakeAxiomFun{iClipParametric} subroutine in this package.")) (|clipParametric| (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|Plot|) (|Fraction| (|Integer|)) (|Fraction| (|Integer|))) "\\spad{clipParametric(p,frac,sc)} performs two-dimensional clipping on a plot,{} \\spad{p},{} from the domain \\spadtype{Plot} for the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)}; the fraction parameter is specified by \\spad{frac} and the scale parameter is specified by \\spad{sc} for use in the \\fakeAxiomFun{iClipParametric} subroutine,{} which is called by this function.") (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|Plot|)) "\\spad{clipParametric(p)} performs two-dimensional clipping on a plot,{} \\spad{p},{} from the domain \\spadtype{Plot} for the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)}; the default parameters \\spad{1/2} for the fraction and \\spad{5/1} for the scale are used in the \\fakeAxiomFun{iClipParametric} subroutine,{} which is called by this function.")) (|clip| (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{clip(ll)} performs two-dimensional clipping on a list of lists of points,{} \\spad{ll}; the default parameters \\spad{1/2} for the fraction and \\spad{5/1} for the scale are used in the \\fakeAxiomFun{iClipParametric} subroutine,{} which is called by this function.") (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|List| (|Point| (|DoubleFloat|)))) "\\spad{clip(l)} performs two-dimensional clipping on a curve \\spad{l},{} which is a list of points; the default parameters \\spad{1/2} for the fraction and \\spad{5/1} for the scale are used in the \\fakeAxiomFun{iClipParametric} subroutine,{} which is called by this function.") (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|Plot|) (|Fraction| (|Integer|)) (|Fraction| (|Integer|))) "\\spad{clip(p,frac,sc)} performs two-dimensional clipping on a plot,{} \\spad{p},{} from the domain \\spadtype{Plot} for the graph of one variable \\spad{y = f(x)}; the fraction parameter is specified by \\spad{frac} and the scale parameter is specified by \\spad{sc} for use in the \\spadfun{clip} function.") (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|Plot|)) "\\spad{clip(p)} performs two-dimensional clipping on a plot,{} \\spad{p},{} from the domain \\spadtype{Plot} for the graph of one variable,{} \\spad{y = f(x)}; the default parameters \\spad{1/4} for the fraction and \\spad{5/1} for the scale are used in the \\spadfun{clip} function."))) @@ -564,7 +564,7 @@ NIL ((|constructor| (NIL "Color() specifies a domain of 27 colors provided in the \\Language{} system (the colors mix additively).")) (|color| (($ (|Integer|)) "\\spad{color(i)} returns a color of the indicated hue \\spad{i}.")) (|numberOfHues| (((|PositiveInteger|)) "\\spad{numberOfHues()} returns the number of total hues,{} set in totalHues.")) (|hue| (((|Integer|) $) "\\spad{hue(c)} returns the hue index of the indicated color \\spad{c}.")) (|blue| (($) "\\spad{blue()} returns the position of the blue hue from total hues.")) (|green| (($) "\\spad{green()} returns the position of the green hue from total hues.")) (|yellow| (($) "\\spad{yellow()} returns the position of the yellow hue from total hues.")) (|red| (($) "\\spad{red()} returns the position of the red hue from total hues.")) (+ (($ $ $) "\\spad{c1 + c2} additively mixes the two colors \\spad{c1} and \\spad{c2}.")) (* (($ (|DoubleFloat|) $) "\\spad{s * c},{} returns the color \\spad{c},{} whose weighted shade has been scaled by \\spad{s}.") (($ (|PositiveInteger|) $) "\\spad{s * c},{} returns the color \\spad{c},{} whose weighted shade has been scaled by \\spad{s}."))) NIL NIL -(-159 R -2117) +(-159 R -1959) ((|constructor| (NIL "Provides combinatorial functions over an integral domain.")) (|ipow| ((|#2| (|List| |#2|)) "\\spad{ipow(l)} should be local but conditional.")) (|iidprod| ((|#2| (|List| |#2|)) "\\spad{iidprod(l)} should be local but conditional.")) (|iidsum| ((|#2| (|List| |#2|)) "\\spad{iidsum(l)} should be local but conditional.")) (|iipow| ((|#2| (|List| |#2|)) "\\spad{iipow(l)} should be local but conditional.")) (|iiperm| ((|#2| (|List| |#2|)) "\\spad{iiperm(l)} should be local but conditional.")) (|iibinom| ((|#2| (|List| |#2|)) "\\spad{iibinom(l)} should be local but conditional.")) (|iifact| ((|#2| |#2|) "\\spad{iifact(x)} should be local but conditional.")) (|product| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{product(f(n), n = a..b)} returns \\spad{f}(a) * ... * \\spad{f}(\\spad{b}) as a formal product.") ((|#2| |#2| (|Symbol|)) "\\spad{product(f(n), n)} returns the formal product \\spad{P}(\\spad{n}) which verifies \\spad{P}(\\spad{n+1})\\spad{/P}(\\spad{n}) = \\spad{f}(\\spad{n}).")) (|summation| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{summation(f(n), n = a..b)} returns \\spad{f}(a) + ... + \\spad{f}(\\spad{b}) as a formal sum.") ((|#2| |#2| (|Symbol|)) "\\spad{summation(f(n), n)} returns the formal sum \\spad{S}(\\spad{n}) which verifies \\spad{S}(\\spad{n+1}) - \\spad{S}(\\spad{n}) = \\spad{f}(\\spad{n}).")) (|factorials| ((|#2| |#2| (|Symbol|)) "\\spad{factorials(f, x)} rewrites the permutations and binomials in \\spad{f} involving \\spad{x} in terms of factorials.") ((|#2| |#2|) "\\spad{factorials(f)} rewrites the permutations and binomials in \\spad{f} in terms of factorials.")) (|factorial| ((|#2| |#2|) "\\spad{factorial(n)} returns the factorial of \\spad{n},{} \\spadignore{i.e.} \\spad{n!}.")) (|permutation| ((|#2| |#2| |#2|) "\\spad{permutation(n, r)} returns the number of permutations of \\spad{n} objects taken \\spad{r} at a time,{} \\spadignore{i.e.} \\spad{n!/}(\\spad{n}-\\spad{r})!.")) (|binomial| ((|#2| |#2| |#2|) "\\spad{binomial(n, r)} returns the number of subsets of \\spad{r} objects taken among \\spad{n} objects,{} \\spadignore{i.e.} \\spad{n!/}(\\spad{r!} * (\\spad{n}-\\spad{r})!).")) (** ((|#2| |#2| |#2|) "\\spad{a ** b} is the formal exponential a**b.")) (|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 combinatorial operator.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} is \\spad{true} if \\spad{op} is a combinatorial operator."))) NIL NIL @@ -595,10 +595,10 @@ NIL (-166 S R) ((|constructor| (NIL "This category represents the extension of a ring by a square root of \\spad{-1}.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a rational number,{} or \"failed\" if \\spad{x} is not a rational number.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a rational number. Error: if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a rational number.")) (|polarCoordinates| (((|Record| (|:| |r| |#2|) (|:| |phi| |#2|)) $) "\\spad{polarCoordinates(x)} returns (\\spad{r},{} phi) such that \\spad{x} = \\spad{r} * exp(\\%\\spad{i} * phi).")) (|argument| ((|#2| $) "\\spad{argument(x)} returns the angle made by (0,{}1) and (0,{}\\spad{x}).")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x} = sqrt(norm(\\spad{x})).")) (|exquo| (((|Union| $ "failed") $ |#2|) "\\spad{exquo(x, r)} returns the exact quotient of \\spad{x} by \\spad{r},{} or \"failed\" if \\spad{r} does not divide \\spad{x} exactly.")) (|norm| ((|#2| $) "\\spad{norm(x)} returns \\spad{x} * conjugate(\\spad{x})")) (|real| ((|#2| $) "\\spad{real(x)} returns real part of \\spad{x}.")) (|imag| ((|#2| $) "\\spad{imag(x)} returns imaginary part of \\spad{x}.")) (|conjugate| (($ $) "\\spad{conjugate(x + \\%i y)} returns \\spad{x} - \\%\\spad{i} \\spad{y}.")) (|imaginary| (($) "\\spad{imaginary()} = sqrt(\\spad{-1}) = \\%\\spad{i}.")) (|complex| (($ |#2| |#2|) "\\spad{complex(x,y)} constructs \\spad{x} + \\%i*y.") ((|attribute|) "indicates that \\% has sqrt(\\spad{-1})"))) NIL -((|HasCategory| |#2| (QUOTE (-927))) (|HasCategory| |#2| (QUOTE (-557))) (|HasCategory| |#2| (QUOTE (-1022))) (|HasCategory| |#2| (QUOTE (-1222))) (|HasCategory| |#2| (QUOTE (-1080))) (|HasCategory| |#2| (QUOTE (-1042))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (QUOTE (-374))) (|HasAttribute| |#2| (QUOTE -4459)) (|HasAttribute| |#2| (QUOTE -4462)) (|HasCategory| |#2| (QUOTE (-317))) (|HasCategory| |#2| (QUOTE (-568)))) +((|HasCategory| |#2| (QUOTE (-928))) (|HasCategory| |#2| (QUOTE (-557))) (|HasCategory| |#2| (QUOTE (-1023))) (|HasCategory| |#2| (QUOTE (-1223))) (|HasCategory| |#2| (QUOTE (-1081))) (|HasCategory| |#2| (QUOTE (-1043))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (QUOTE (-374))) (|HasAttribute| |#2| (QUOTE -4460)) (|HasAttribute| |#2| (QUOTE -4463)) (|HasCategory| |#2| (QUOTE (-317))) (|HasCategory| |#2| (QUOTE (-568)))) (-167 R) ((|constructor| (NIL "This category represents the extension of a ring by a square root of \\spad{-1}.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a rational number,{} or \"failed\" if \\spad{x} is not a rational number.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a rational number. Error: if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a rational number.")) (|polarCoordinates| (((|Record| (|:| |r| |#1|) (|:| |phi| |#1|)) $) "\\spad{polarCoordinates(x)} returns (\\spad{r},{} phi) such that \\spad{x} = \\spad{r} * exp(\\%\\spad{i} * phi).")) (|argument| ((|#1| $) "\\spad{argument(x)} returns the angle made by (0,{}1) and (0,{}\\spad{x}).")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x} = sqrt(norm(\\spad{x})).")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(x, r)} returns the exact quotient of \\spad{x} by \\spad{r},{} or \"failed\" if \\spad{r} does not divide \\spad{x} exactly.")) (|norm| ((|#1| $) "\\spad{norm(x)} returns \\spad{x} * conjugate(\\spad{x})")) (|real| ((|#1| $) "\\spad{real(x)} returns real part of \\spad{x}.")) (|imag| ((|#1| $) "\\spad{imag(x)} returns imaginary part of \\spad{x}.")) (|conjugate| (($ $) "\\spad{conjugate(x + \\%i y)} returns \\spad{x} - \\%\\spad{i} \\spad{y}.")) (|imaginary| (($) "\\spad{imaginary()} = sqrt(\\spad{-1}) = \\%\\spad{i}.")) (|complex| (($ |#1| |#1|) "\\spad{complex(x,y)} constructs \\spad{x} + \\%i*y.") ((|attribute|) "indicates that \\% has sqrt(\\spad{-1})"))) -((-4456 -3794 (|has| |#1| (-568)) (-12 (|has| |#1| (-317)) (|has| |#1| (-927)))) (-4461 |has| |#1| (-374)) (-4455 |has| |#1| (-374)) (-4459 |has| |#1| (-6 -4459)) (-4462 |has| |#1| (-6 -4462)) (-2648 . T) ((-4465 "*") . T) (-4457 . T) (-4458 . T) (-4460 . T)) +((-4457 -2758 (|has| |#1| (-568)) (-12 (|has| |#1| (-317)) (|has| |#1| (-928)))) (-4462 |has| |#1| (-374)) (-4456 |has| |#1| (-374)) (-4460 |has| |#1| (-6 -4460)) (-4463 |has| |#1| (-6 -4463)) (-4177 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-168 RR PR) ((|constructor| (NIL "\\indented{1}{Author:} Date Created: Date Last Updated: Basic Functions: Related Constructors: Complex,{} UnivariatePolynomial Also See: AMS Classifications: Keywords: complex,{} polynomial factorization,{} factor References:")) (|factor| (((|Factored| |#2|) |#2|) "\\spad{factor(p)} factorizes the polynomial \\spad{p} with complex coefficients."))) @@ -614,8 +614,8 @@ NIL NIL (-171 R) ((|constructor| (NIL "\\spadtype {Complex(R)} creates the domain of elements of the form \\spad{a + b * i} where \\spad{a} and \\spad{b} come from the ring \\spad{R},{} and \\spad{i} is a new element such that \\spad{i**2 = -1}."))) -((-4456 -3794 (|has| |#1| (-568)) (-12 (|has| |#1| (-317)) (|has| |#1| (-927)))) (-4461 |has| |#1| (-374)) (-4455 |has| |#1| (-374)) (-4459 |has| |#1| (-6 -4459)) (-4462 |has| |#1| (-6 -4462)) (-2648 . T) ((-4465 "*") . T) (-4457 . T) (-4458 . T) (-4460 . 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T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) +((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-360))) (-2758 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-360)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-379))) (-2758 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-360)))) (-2758 (-12 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-360)))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1197)))) (-2758 (|HasCategory| |#1| (LIST (QUOTE -919) (QUOTE (-1197)))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1197)))))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))) (-2758 (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576)))) (-2758 (-12 (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-928)))) (|HasCategory| |#1| (QUOTE (-374))) (-12 (|HasCategory| |#1| (QUOTE (-360))) (|HasCategory| |#1| (QUOTE (-928))))) (-2758 (-12 (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-928)))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-928)))) (-12 (|HasCategory| |#1| (QUOTE (-360))) (|HasCategory| |#1| (QUOTE (-928))))) (-2758 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasCategory| |#1| (QUOTE (-1023))) (|HasCategory| |#1| (QUOTE (-1223)))) (|HasCategory| |#1| (QUOTE (-1223))) (|HasCategory| |#1| (QUOTE (-1043))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2758 (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-360))) (|HasCategory| |#1| (QUOTE (-568)))) (-2758 (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-360)))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-390)))) (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -526) (QUOTE (-1197)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -296) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-840))) (|HasCategory| |#1| (QUOTE (-1081))) (-12 (|HasCategory| |#1| (QUOTE (-1081))) (|HasCategory| |#1| (QUOTE (-1223)))) (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-928))) (-2758 (-12 (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-928)))) (|HasCategory| |#1| (QUOTE (-374)))) (-2758 (-12 (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-928)))) (|HasCategory| |#1| (QUOTE (-568)))) (-2758 (-12 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (QUOTE (-237)))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (LIST (QUOTE -919) (QUOTE (-1197)))) (|HasCategory| |#1| (QUOTE (-238))) (-12 (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-928)))) (|HasAttribute| |#1| (QUOTE -4460)) (|HasAttribute| |#1| (QUOTE -4463)) (-12 (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-374)))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -919) (QUOTE (-1197))))) (-12 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-374)))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1197))))) (-2758 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-928)))) (|HasCategory| |#1| (QUOTE (-146)))) (-2758 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-928)))) (|HasCategory| |#1| (QUOTE (-360))))) (-172 R S CS) ((|constructor| (NIL "This package supports converting complex expressions to patterns")) (|convert| (((|Pattern| |#1|) |#3|) "\\spad{convert(cs)} converts the complex expression \\spad{cs} to a pattern"))) NIL @@ -626,7 +626,7 @@ NIL NIL (-174) ((|constructor| (NIL "The category of commutative rings with unity,{} \\spadignore{i.e.} rings where \\spadop{*} is commutative,{} and which have a multiplicative identity. element.")) (|commutative| ((|attribute| "*") "multiplication is commutative."))) -(((-4465 "*") . T) (-4457 . T) (-4458 . T) (-4460 . T)) +(((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-175) ((|constructor| (NIL "This category is the root of the I/O conduits.")) (|close!| (($ $) "\\spad{close!(c)} closes the conduit \\spad{c},{} changing its state to one that is invalid for future read or write operations."))) @@ -634,7 +634,7 @@ NIL NIL (-176 R) ((|constructor| (NIL "\\spadtype{ContinuedFraction} implements general \\indented{1}{continued fractions.\\space{2}This version is not restricted to simple,{}} \\indented{1}{finite fractions and uses the \\spadtype{Stream} as a} \\indented{1}{representation.\\space{2}The arithmetic functions assume that the} \\indented{1}{approximants alternate below/above the convergence point.} \\indented{1}{This is enforced by ensuring the partial numerators and partial} \\indented{1}{denominators are greater than 0 in the Euclidean domain view of \\spad{R}} \\indented{1}{(\\spadignore{i.e.} \\spad{sizeLess?(0, x)}).}")) (|complete| (($ $) "\\spad{complete(x)} causes all entries in \\spadvar{\\spad{x}} to be computed. Normally entries are only computed as needed. If \\spadvar{\\spad{x}} is an infinite continued fraction,{} a user-initiated interrupt is necessary to stop the computation.")) (|extend| (($ $ (|Integer|)) "\\spad{extend(x,n)} causes the first \\spadvar{\\spad{n}} entries in the continued fraction \\spadvar{\\spad{x}} to be computed. Normally entries are only computed as needed.")) (|denominators| (((|Stream| |#1|) $) "\\spad{denominators(x)} returns the stream of denominators of the approximants of the continued fraction \\spadvar{\\spad{x}}. If the continued fraction is finite,{} then the stream will be finite.")) (|numerators| (((|Stream| |#1|) $) "\\spad{numerators(x)} returns the stream of numerators of the approximants of the continued fraction \\spadvar{\\spad{x}}. If the continued fraction is finite,{} then the stream will be finite.")) (|convergents| (((|Stream| (|Fraction| |#1|)) $) "\\spad{convergents(x)} returns the stream of the convergents of the continued fraction \\spadvar{\\spad{x}}. If the continued fraction is finite,{} then the stream will be finite.")) (|approximants| (((|Stream| (|Fraction| |#1|)) $) "\\spad{approximants(x)} returns the stream of approximants of the continued fraction \\spadvar{\\spad{x}}. If the continued fraction is finite,{} then the stream will be infinite and periodic with period 1.")) (|reducedForm| (($ $) "\\spad{reducedForm(x)} puts the continued fraction \\spadvar{\\spad{x}} in reduced form,{} \\spadignore{i.e.} the function returns an equivalent continued fraction of the form \\spad{continuedFraction(b0,[1,1,1,...],[b1,b2,b3,...])}.")) (|wholePart| ((|#1| $) "\\spad{wholePart(x)} extracts the whole part of \\spadvar{\\spad{x}}. That is,{} if \\spad{x = continuedFraction(b0, [a1,a2,a3,...], [b1,b2,b3,...])},{} then \\spad{wholePart(x) = b0}.")) (|partialQuotients| (((|Stream| |#1|) $) "\\spad{partialQuotients(x)} extracts the partial quotients in \\spadvar{\\spad{x}}. That is,{} if \\spad{x = continuedFraction(b0, [a1,a2,a3,...], [b1,b2,b3,...])},{} then \\spad{partialQuotients(x) = [b0,b1,b2,b3,...]}.")) (|partialDenominators| (((|Stream| |#1|) $) "\\spad{partialDenominators(x)} extracts the denominators in \\spadvar{\\spad{x}}. That is,{} if \\spad{x = continuedFraction(b0, [a1,a2,a3,...], [b1,b2,b3,...])},{} then \\spad{partialDenominators(x) = [b1,b2,b3,...]}.")) (|partialNumerators| (((|Stream| |#1|) $) "\\spad{partialNumerators(x)} extracts the numerators in \\spadvar{\\spad{x}}. That is,{} if \\spad{x = continuedFraction(b0, [a1,a2,a3,...], [b1,b2,b3,...])},{} then \\spad{partialNumerators(x) = [a1,a2,a3,...]}.")) (|reducedContinuedFraction| (($ |#1| (|Stream| |#1|)) "\\spad{reducedContinuedFraction(b0,b)} constructs a continued fraction in the following way: if \\spad{b = [b1,b2,...]} then the result is the continued fraction \\spad{b0 + 1/(b1 + 1/(b2 + ...))}. That is,{} the result is the same as \\spad{continuedFraction(b0,[1,1,1,...],[b1,b2,b3,...])}.")) (|continuedFraction| (($ |#1| (|Stream| |#1|) (|Stream| |#1|)) "\\spad{continuedFraction(b0,a,b)} constructs a continued fraction in the following way: if \\spad{a = [a1,a2,...]} and \\spad{b = [b1,b2,...]} then the result is the continued fraction \\spad{b0 + a1/(b1 + a2/(b2 + ...))}.") (($ (|Fraction| |#1|)) "\\spad{continuedFraction(r)} converts the fraction \\spadvar{\\spad{r}} with components of type \\spad{R} to a continued fraction over \\spad{R}."))) -(((-4465 "*") . T) (-4456 . T) (-4461 . T) (-4455 . T) (-4457 . T) (-4458 . T) (-4460 . T)) +(((-4466 "*") . T) (-4457 . T) (-4462 . T) (-4456 . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-177) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. A `Contour' a list of bindings making up a `virtual scope'.")) (|findBinding| (((|Maybe| (|Binding|)) (|Identifier|) $) "\\spad{findBinding(c,n)} returns the first binding associated with \\spad{`n'}. Otherwise `nothing.")) (|push| (($ (|Binding|) $) "\\spad{push(c,b)} augments the contour with binding \\spad{`b'}.")) (|bindings| (((|List| (|Binding|)) $) "\\spad{bindings(c)} returns the list of bindings in countour \\spad{c}."))) @@ -651,7 +651,7 @@ NIL (-180 R S CS) ((|constructor| (NIL "This package supports matching patterns involving complex expressions")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(cexpr, pat, res)} matches the pattern \\spad{pat} to the complex expression \\spad{cexpr}. res contains the variables of \\spad{pat} which are already matched and their matches."))) NIL -((|HasCategory| (-970 |#2|) (LIST (QUOTE -900) (|devaluate| |#1|)))) +((|HasCategory| (-971 |#2|) (LIST (QUOTE -901) (|devaluate| |#1|)))) (-181 R) ((|constructor| (NIL "This package \\undocumented{}")) (|multiEuclideanTree| (((|List| |#1|) (|List| |#1|) |#1|) "\\spad{multiEuclideanTree(l,r)} \\undocumented{}")) (|chineseRemainder| (((|List| |#1|) (|List| (|List| |#1|)) (|List| |#1|)) "\\spad{chineseRemainder(llv,lm)} returns a list of values,{} each of which corresponds to the Chinese remainder of the associated element of \\axiom{\\spad{llv}} and axiom{\\spad{lm}}. This is more efficient than applying chineseRemainder several times.") ((|#1| (|List| |#1|) (|List| |#1|)) "\\spad{chineseRemainder(lv,lm)} returns a value \\axiom{\\spad{v}} such that,{} if \\spad{x} is \\axiom{\\spad{lv}.\\spad{i}} modulo \\axiom{\\spad{lm}.\\spad{i}} for all \\axiom{\\spad{i}},{} then \\spad{x} is \\axiom{\\spad{v}} modulo \\axiom{\\spad{lm}(1)\\spad{*lm}(2)*...\\spad{*lm}(\\spad{n})}.")) (|modTree| (((|List| |#1|) |#1| (|List| |#1|)) "\\spad{modTree(r,l)} \\undocumented{}"))) NIL @@ -688,7 +688,7 @@ NIL ((|constructor| (NIL "This domain provides implementations for constructors.")) (|findConstructor| (((|Maybe| $) (|Identifier|)) "\\spad{findConstructor(s)} attempts to find a constructor named \\spad{s}. If successful,{} returns that constructor; otherwise,{} returns \\spad{nothing}."))) NIL NIL -(-190 R -2117) +(-190 R -1959) ((|constructor| (NIL "\\spadtype{ComplexTrigonometricManipulations} provides function that compute the real and imaginary parts of complex functions.")) (|complexForm| (((|Complex| (|Expression| |#1|)) |#2|) "\\spad{complexForm(f)} returns \\spad{[real f, imag f]}.")) (|trigs| ((|#2| |#2|) "\\spad{trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (|real?| (((|Boolean|) |#2|) "\\spad{real?(f)} returns \\spad{true} if \\spad{f = real f}.")) (|imag| (((|Expression| |#1|) |#2|) "\\spad{imag(f)} returns the imaginary part of \\spad{f} where \\spad{f} is a complex function.")) (|real| (((|Expression| |#1|) |#2|) "\\spad{real(f)} returns the real part of \\spad{f} where \\spad{f} is a complex function.")) (|complexElementary| ((|#2| |#2| (|Symbol|)) "\\spad{complexElementary(f, x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.") ((|#2| |#2|) "\\spad{complexElementary(f)} rewrites \\spad{f} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.")) (|complexNormalize| ((|#2| |#2| (|Symbol|)) "\\spad{complexNormalize(f, x)} rewrites \\spad{f} using the least possible number of complex independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{complexNormalize(f)} rewrites \\spad{f} using the least possible number of complex independent kernels."))) NIL NIL @@ -796,23 +796,23 @@ NIL ((|constructor| (NIL "\\indented{1}{This domain implements a simple view of a database whose fields are} indexed by symbols")) (- (($ $ $) "\\spad{db1-db2} returns the difference of databases \\spad{db1} and \\spad{db2} \\spadignore{i.e.} consisting of elements in \\spad{db1} but not in \\spad{db2}")) (+ (($ $ $) "\\spad{db1+db2} returns the merge of databases \\spad{db1} and \\spad{db2}")) (|fullDisplay| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{fullDisplay(db,start,end )} prints full details of entries in the range \\axiom{\\spad{start}..end} in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{fullDisplay(db)} prints full details of each entry in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{fullDisplay(x)} displays \\spad{x} in detail")) (|display| (((|Void|) $) "\\spad{display(db)} prints a summary line for each entry in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{display(x)} displays \\spad{x} in some form")) (|elt| (((|DataList| (|String|)) $ (|Symbol|)) "\\spad{elt(db,s)} returns the \\axiom{\\spad{s}} field of each element of \\axiom{\\spad{db}}.") (($ $ (|QueryEquation|)) "\\spad{elt(db,q)} returns all elements of \\axiom{\\spad{db}} which satisfy \\axiom{\\spad{q}}.") (((|String|) $ (|Symbol|)) "\\spad{elt(x,s)} returns an element of \\spad{x} indexed by \\spad{s}"))) NIL NIL -(-217 -2117 UP UPUP R) +(-217 -1959 UP UPUP R) ((|constructor| (NIL "This package provides functions for computing the residues of a function on an algebraic curve.")) (|doubleResultant| ((|#2| |#4| (|Mapping| |#2| |#2|)) "\\spad{doubleResultant(f, ')} returns \\spad{p}(\\spad{x}) whose roots are rational multiples of the residues of \\spad{f} at all its finite poles. Argument ' is the derivation to use."))) NIL NIL -(-218 -2117 FP) +(-218 -1959 FP) ((|constructor| (NIL "Package for the factorization of a univariate polynomial with coefficients in a finite field. The algorithm used is the \"distinct degree\" algorithm of Cantor-Zassenhaus,{} modified to use trace instead of the norm and a table for computing Frobenius as suggested by Naudin and Quitte .")) (|irreducible?| (((|Boolean|) |#2|) "\\spad{irreducible?(p)} tests whether the polynomial \\spad{p} is irreducible.")) (|tracePowMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{tracePowMod(u,k,v)} produces the sum of \\spad{u**(q**i)} for \\spad{i} running and \\spad{q=} size \\spad{F}")) (|trace2PowMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{trace2PowMod(u,k,v)} produces the sum of \\spad{u**(2**i)} for \\spad{i} running from 1 to \\spad{k} all computed modulo the polynomial \\spad{v}.")) (|exptMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{exptMod(u,k,v)} raises the polynomial \\spad{u} to the \\spad{k}th power modulo the polynomial \\spad{v}.")) (|separateFactors| (((|List| |#2|) (|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |prod| |#2|)))) "\\spad{separateFactors(lfact)} takes the list produced by \\spadfunFrom{separateDegrees}{DistinctDegreeFactorization} and produces the complete list of factors.")) (|separateDegrees| (((|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |prod| |#2|))) |#2|) "\\spad{separateDegrees(p)} splits the square free polynomial \\spad{p} into factors each of which is a product of irreducibles of the same degree.")) (|distdfact| (((|Record| (|:| |cont| |#1|) (|:| |factors| (|List| (|Record| (|:| |irr| |#2|) (|:| |pow| (|Integer|)))))) |#2| (|Boolean|)) "\\spad{distdfact(p,sqfrflag)} produces the complete factorization of the polynomial \\spad{p} returning an internal data structure. If argument \\spad{sqfrflag} is \\spad{true},{} the polynomial is assumed square free.")) (|factorSquareFree| (((|Factored| |#2|) |#2|) "\\spad{factorSquareFree(p)} produces the complete factorization of the square free polynomial \\spad{p}.")) (|factor| (((|Factored| |#2|) |#2|) "\\spad{factor(p)} produces the complete factorization of the polynomial \\spad{p}."))) NIL NIL (-219) ((|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."))) -((-4455 . T) (-4461 . T) (-4456 . T) ((-4465 "*") . T) (-4457 . T) (-4458 . T) (-4460 . T)) -((|HasCategory| (-576) (QUOTE (-927))) (|HasCategory| (-576) (LIST (QUOTE -1058) (QUOTE (-1196)))) (|HasCategory| (-576) (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-148))) (|HasCategory| (-576) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-576) (QUOTE (-1042))) (|HasCategory| (-576) (QUOTE (-832))) (|HasCategory| (-576) (QUOTE (-861))) (-3794 (|HasCategory| (-576) (QUOTE (-832))) (|HasCategory| (-576) (QUOTE (-861)))) (|HasCategory| (-576) (LIST (QUOTE -1058) (QUOTE (-576)))) (|HasCategory| (-576) (QUOTE (-1172))) (|HasCategory| (-576) (LIST (QUOTE -900) (QUOTE (-390)))) (|HasCategory| (-576) (LIST (QUOTE -900) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -626) (LIST (QUOTE -906) (QUOTE (-390))))) (|HasCategory| (-576) (LIST (QUOTE -626) (LIST (QUOTE -906) (QUOTE (-576))))) (|HasCategory| (-576) (QUOTE (-237))) (|HasCategory| (-576) (LIST (QUOTE -918) (QUOTE (-1196)))) (|HasCategory| (-576) (QUOTE (-238))) (|HasCategory| (-576) (LIST (QUOTE -916) (QUOTE (-1196)))) (|HasCategory| (-576) (LIST (QUOTE -526) (QUOTE (-1196)) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -319) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -296) (QUOTE (-576)) (QUOTE (-576)))) (|HasCategory| (-576) (QUOTE (-317))) (|HasCategory| (-576) (QUOTE (-557))) (|HasCategory| (-576) (LIST (QUOTE -651) (QUOTE (-576)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-927)))) (-3794 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-927)))) (|HasCategory| (-576) (QUOTE (-146))))) +((-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) +((|HasCategory| (-576) (QUOTE (-928))) (|HasCategory| (-576) (LIST (QUOTE -1059) (QUOTE (-1197)))) (|HasCategory| (-576) (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-148))) (|HasCategory| (-576) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-576) (QUOTE (-1043))) (|HasCategory| (-576) (QUOTE (-832))) (|HasCategory| (-576) (QUOTE (-861))) (-2758 (|HasCategory| (-576) (QUOTE (-832))) (|HasCategory| (-576) (QUOTE (-861)))) (|HasCategory| (-576) (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| (-576) (QUOTE (-1173))) (|HasCategory| (-576) (LIST (QUOTE -901) (QUOTE (-390)))) (|HasCategory| (-576) (LIST (QUOTE -901) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390))))) (|HasCategory| (-576) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576))))) (|HasCategory| (-576) (QUOTE (-237))) (|HasCategory| (-576) (LIST (QUOTE -919) (QUOTE (-1197)))) (|HasCategory| (-576) (QUOTE (-238))) (|HasCategory| (-576) (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| (-576) (LIST (QUOTE -526) (QUOTE (-1197)) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -319) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -296) (QUOTE (-576)) (QUOTE (-576)))) (|HasCategory| (-576) (QUOTE (-317))) (|HasCategory| (-576) (QUOTE (-557))) (|HasCategory| (-576) (LIST (QUOTE -651) (QUOTE (-576)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-928)))) (-2758 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-928)))) (|HasCategory| (-576) (QUOTE (-146))))) (-220) ((|constructor| (NIL "This domain represents the syntax of a definition.")) (|body| (((|SpadAst|) $) "\\spad{body(d)} returns the right hand side of the definition \\spad{`d'}.")) (|signature| (((|Signature|) $) "\\spad{signature(d)} returns the signature of the operation being defined. Note that this list may be partial in that it contains only the types actually specified in the definition.")) (|head| (((|HeadAst|) $) "\\spad{head(d)} returns the head of the definition \\spad{`d'}. This is a list of identifiers starting with the name of the operation followed by the name of the parameters,{} if any."))) NIL NIL -(-221 R -2117) +(-221 R -1959) ((|constructor| (NIL "\\spadtype{ElementaryFunctionDefiniteIntegration} provides functions to compute definite integrals of elementary functions.")) (|innerint| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{innerint(f, x, a, b, ignore?)} should be local but conditional")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|)) (|String|)) "\\spad{integrate(f, x = a..b, \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|))) "\\spad{integrate(f, x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}."))) NIL NIL @@ -826,19 +826,19 @@ NIL NIL (-224 S) ((|constructor| (NIL "Linked list implementation of a Dequeue")) (|dequeue| (($ (|List| |#1|)) "\\spad{dequeue([x,y,...,z])} creates a dequeue with first (top or front) element \\spad{x},{} second element \\spad{y},{}...,{}and last (bottom or back) element \\spad{z}."))) -((-4463 . T) (-4464 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1120))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1120))) (-3794 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1120)))) (-3794 (-12 (|HasCategory| |#1| (QUOTE (-1120))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-875))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-875)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4464 . T) (-4465 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1121))) (-2758 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1121)))) (-2758 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102)))) (-225 |CoefRing| |listIndVar|) ((|constructor| (NIL "The deRham complex of Euclidean space,{} that is,{} the class of differential forms of arbitary degree over a coefficient ring. See Flanders,{} Harley,{} Differential Forms,{} With Applications to the Physical Sciences,{} New York,{} Academic Press,{} 1963.")) (|exteriorDifferential| (($ $) "\\spad{exteriorDifferential(df)} returns the exterior derivative (gradient,{} curl,{} divergence,{} ...) of the differential form \\spad{df}.")) (|totalDifferential| (($ (|Expression| |#1|)) "\\spad{totalDifferential(x)} returns the total differential (gradient) form for element \\spad{x}.")) (|map| (($ (|Mapping| (|Expression| |#1|) (|Expression| |#1|)) $) "\\spad{map(f,df)} replaces each coefficient \\spad{x} of differential form \\spad{df} by \\spad{f(x)}.")) (|degree| (((|Integer|) $) "\\spad{degree(df)} returns the homogeneous degree of differential form \\spad{df}.")) (|retractable?| (((|Boolean|) $) "\\spad{retractable?(df)} tests if differential form \\spad{df} is a 0-form,{} \\spadignore{i.e.} if degree(\\spad{df}) = 0.")) (|homogeneous?| (((|Boolean|) $) "\\spad{homogeneous?(df)} tests if all of the terms of differential form \\spad{df} have the same degree.")) (|generator| (($ (|NonNegativeInteger|)) "\\spad{generator(n)} returns the \\spad{n}th basis term for a differential form.")) (|coefficient| (((|Expression| |#1|) $ $) "\\spad{coefficient(df,u)},{} where \\spad{df} is a differential form,{} returns the coefficient of \\spad{df} containing the basis term \\spad{u} if such a term exists,{} and 0 otherwise.")) (|reductum| (($ $) "\\spad{reductum(df)},{} where \\spad{df} is a differential form,{} returns \\spad{df} minus the leading term of \\spad{df} if \\spad{df} has two or more terms,{} and 0 otherwise.")) (|leadingBasisTerm| (($ $) "\\spad{leadingBasisTerm(df)} returns the leading basis term of differential form \\spad{df}.")) (|leadingCoefficient| (((|Expression| |#1|) $) "\\spad{leadingCoefficient(df)} returns the leading coefficient of differential form \\spad{df}."))) -((-4460 . T)) +((-4461 . T)) NIL -(-226 R -2117) +(-226 R -1959) ((|constructor| (NIL "\\spadtype{DefiniteIntegrationTools} provides common tools used by the definite integration of both rational and elementary functions.")) (|checkForZero| (((|Union| (|Boolean|) "failed") (|SparseUnivariatePolynomial| |#2|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{checkForZero(p, a, b, incl?)} is \\spad{true} if \\spad{p} has a zero between a and \\spad{b},{} \\spad{false} otherwise,{} \"failed\" if this cannot be determined. Check for a and \\spad{b} inclusive if incl? is \\spad{true},{} exclusive otherwise.") (((|Union| (|Boolean|) "failed") (|Polynomial| |#1|) (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{checkForZero(p, x, a, b, incl?)} is \\spad{true} if \\spad{p} has a zero for \\spad{x} between a and \\spad{b},{} \\spad{false} otherwise,{} \"failed\" if this cannot be determined. Check for a and \\spad{b} inclusive if incl? is \\spad{true},{} exclusive otherwise.")) (|computeInt| (((|Union| (|OrderedCompletion| |#2|) "failed") (|Kernel| |#2|) |#2| (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{computeInt(x, g, a, b, eval?)} returns the integral of \\spad{f} for \\spad{x} between a and \\spad{b},{} assuming that \\spad{g} is an indefinite integral of \\spad{f} and \\spad{f} has no pole between a and \\spad{b}. If \\spad{eval?} is \\spad{true},{} then \\spad{g} can be evaluated safely at \\spad{a} and \\spad{b},{} provided that they are finite values. Otherwise,{} limits must be computed.")) (|ignore?| (((|Boolean|) (|String|)) "\\spad{ignore?(s)} is \\spad{true} if \\spad{s} is the string that tells the integrator to assume that the function has no pole in the integration interval."))) NIL NIL (-227) ((|constructor| (NIL "\\indented{1}{\\spadtype{DoubleFloat} is intended to make accessible} hardware floating point arithmetic in \\Language{},{} either native double precision,{} or IEEE. On most machines,{} there will be hardware support for the arithmetic operations: \\spadfunFrom{+}{DoubleFloat},{} \\spadfunFrom{*}{DoubleFloat},{} \\spadfunFrom{/}{DoubleFloat} and possibly also the \\spadfunFrom{sqrt}{DoubleFloat} operation. The operations \\spadfunFrom{exp}{DoubleFloat},{} \\spadfunFrom{log}{DoubleFloat},{} \\spadfunFrom{sin}{DoubleFloat},{} \\spadfunFrom{cos}{DoubleFloat},{} \\spadfunFrom{atan}{DoubleFloat} are normally coded in software based on minimax polynomial/rational approximations. Note that under Lisp/VM,{} \\spadfunFrom{atan}{DoubleFloat} is not available at this time. Some general comments about the accuracy of the operations: the operations \\spadfunFrom{+}{DoubleFloat},{} \\spadfunFrom{*}{DoubleFloat},{} \\spadfunFrom{/}{DoubleFloat} and \\spadfunFrom{sqrt}{DoubleFloat} are expected to be fully accurate. The operations \\spadfunFrom{exp}{DoubleFloat},{} \\spadfunFrom{log}{DoubleFloat},{} \\spadfunFrom{sin}{DoubleFloat},{} \\spadfunFrom{cos}{DoubleFloat} and \\spadfunFrom{atan}{DoubleFloat} are not expected to be fully accurate. In particular,{} \\spadfunFrom{sin}{DoubleFloat} and \\spadfunFrom{cos}{DoubleFloat} will lose all precision for large arguments. \\blankline The \\spadtype{Float} domain provides an alternative to the \\spad{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 \\spadfunFrom{erf}{DoubleFloat},{} the error function in addition to the elementary functions. The disadvantage of \\spadtype{Float} is that it is much more expensive than small floats when the latter can be used.")) (|rationalApproximation| (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rationalApproximation(f, n, b)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< b**(-n)} (that is,{} \\spad{|(r-f)/f| < b**(-n)}).") (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|)) "\\spad{rationalApproximation(f, n)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< 10**(-n)}.")) (|Beta| (($ $ $) "\\spad{Beta(x,y)} is \\spad{Gamma(x) * Gamma(y)/Gamma(x+y)}.")) (|Gamma| (($ $) "\\spad{Gamma(x)} is the Euler Gamma function.")) (|atan| (($ $ $) "\\spad{atan(x,y)} computes the arc tangent from \\spad{x} with phase \\spad{y}.")) (|log10| (($ $) "\\spad{log10(x)} computes the logarithm with base 10 for \\spad{x}.")) (|log2| (($ $) "\\spad{log2(x)} computes the logarithm with base 2 for \\spad{x}.")) (|exp1| (($) "\\spad{exp1()} returns the natural log base \\spad{2.718281828...}.")) (** (($ $ $) "\\spad{x ** y} returns the \\spad{y}th power of \\spad{x} (equal to \\spad{exp(y log x)}).")) (/ (($ $ (|Integer|)) "\\spad{x / i} computes the division from \\spad{x} by an integer \\spad{i}."))) -((-2641 . T) (-4455 . T) (-4461 . T) (-4456 . T) ((-4465 "*") . T) (-4457 . T) (-4458 . T) (-4460 . T)) +((-4165 . T) (-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-228) ((|constructor| (NIL "This package provides special functions for double precision real and complex floating point.")) (|hypergeometric0F1| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{hypergeometric0F1(c,z)} is the hypergeometric function \\spad{0F1(; c; z)}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{hypergeometric0F1(c,z)} is the hypergeometric function \\spad{0F1(; c; z)}.")) (|airyBi| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyBi(x)} is the Airy function \\spad{Bi(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Bi''(x) - 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) - 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) - 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) - x * Ai(x) = 0}.}")) (|besselK| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselK(v,x)} is the modified Bessel function of the first kind,{} \\spad{K(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{K(v,x) = \\%pi/2*(I(-v,x) - I(v,x))/sin(v*\\%pi)}} so is not valid for integer values of \\spad{v}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselK(v,x)} is the modified Bessel function of the first kind,{} \\spad{K(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{K(v,x) = \\%pi/2*(I(-v,x) - I(v,x))/sin(v*\\%pi)}.} so is not valid for integer values of \\spad{v}.")) (|besselI| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselI(v,x)} is the modified Bessel function of the first kind,{} \\spad{I(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselI(v,x)} is the modified Bessel function of the first kind,{} \\spad{I(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.}")) (|besselY| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselY(v,x)} is the Bessel function of the second kind,{} \\spad{Y(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{Y(v,x) = (J(v,x) cos(v*\\%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) + x w'(x) + (x^2-v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{Y(v,x) = (J(v,x) cos(v*\\%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) + x w'(x) + (x^2-v^2)w(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselJ(v,x)} is the Bessel function of the first kind,{} \\spad{J(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.}")) (|polygamma| (((|Complex| (|DoubleFloat|)) (|NonNegativeInteger|) (|Complex| (|DoubleFloat|))) "\\spad{polygamma(n, x)} is the \\spad{n}-th derivative of \\spad{digamma(x)}.") (((|DoubleFloat|) (|NonNegativeInteger|) (|DoubleFloat|)) "\\spad{polygamma(n, x)} is the \\spad{n}-th derivative of \\spad{digamma(x)}.")) (|digamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{digamma(x)} is the function,{} \\spad{psi(x)},{} defined by \\indented{2}{\\spad{psi(x) = Gamma'(x)/Gamma(x)}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{digamma(x)} is the function,{} \\spad{psi(x)},{} defined by \\indented{2}{\\spad{psi(x) = Gamma'(x)/Gamma(x)}.}")) (|logGamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{logGamma(x)} is the natural log of \\spad{Gamma(x)}. This can often be computed even if \\spad{Gamma(x)} cannot.") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{logGamma(x)} is the natural log of \\spad{Gamma(x)}. This can often be computed even if \\spad{Gamma(x)} cannot.")) (|Beta| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{Beta(x, y)} is the Euler beta function,{} \\spad{B(x,y)},{} defined by \\indented{2}{\\spad{Beta(x,y) = integrate(t^(x-1)*(1-t)^(y-1), t=0..1)}.} This is related to \\spad{Gamma(x)} by \\indented{2}{\\spad{Beta(x,y) = Gamma(x)*Gamma(y) / Gamma(x + y)}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{Beta(x, y)} is the Euler beta function,{} \\spad{B(x,y)},{} defined by \\indented{2}{\\spad{Beta(x,y) = integrate(t^(x-1)*(1-t)^(y-1), t=0..1)}.} This is related to \\spad{Gamma(x)} by \\indented{2}{\\spad{Beta(x,y) = Gamma(x)*Gamma(y) / Gamma(x + y)}.}")) (|Gamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{Gamma(x)} is the Euler gamma function,{} \\spad{Gamma(x)},{} defined by \\indented{2}{\\spad{Gamma(x) = integrate(t^(x-1)*exp(-t), t=0..\\%infinity)}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{Gamma(x)} is the Euler gamma function,{} \\spad{Gamma(x)},{} defined by \\indented{2}{\\spad{Gamma(x) = integrate(t^(x-1)*exp(-t), t=0..\\%infinity)}.}"))) @@ -846,19 +846,19 @@ NIL NIL (-229 R) ((|constructor| (NIL "\\indented{1}{A Denavit-Hartenberg Matrix is a 4x4 Matrix of the form:} \\indented{1}{\\spad{nx ox ax px}} \\indented{1}{\\spad{ny oy ay py}} \\indented{1}{\\spad{nz oz az pz}} \\indented{2}{\\spad{0\\space{2}0\\space{2}0\\space{2}1}} (\\spad{n},{} \\spad{o},{} and a are the direction cosines)")) (|translate| (($ |#1| |#1| |#1|) "\\spad{translate(X,Y,Z)} returns a dhmatrix for translation by \\spad{X},{} \\spad{Y},{} and \\spad{Z}")) (|scale| (($ |#1| |#1| |#1|) "\\spad{scale(sx,sy,sz)} returns a dhmatrix for scaling in the \\spad{X},{} \\spad{Y} and \\spad{Z} directions")) (|rotatez| (($ |#1|) "\\spad{rotatez(r)} returns a dhmatrix for rotation about axis \\spad{Z} for \\spad{r} degrees")) (|rotatey| (($ |#1|) "\\spad{rotatey(r)} returns a dhmatrix for rotation about axis \\spad{Y} for \\spad{r} degrees")) (|rotatex| (($ |#1|) "\\spad{rotatex(r)} returns a dhmatrix for rotation about axis \\spad{X} for \\spad{r} degrees")) (|identity| (($) "\\spad{identity()} create the identity dhmatrix")) (* (((|Point| |#1|) $ (|Point| |#1|)) "\\spad{t*p} applies the dhmatrix \\spad{t} to point \\spad{p}"))) -((-4463 . T) (-4464 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1120))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1120))) (-3794 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1120)))) (-3794 (-12 (|HasCategory| |#1| (QUOTE (-1120))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-875))))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-568))) (|HasAttribute| |#1| (QUOTE (-4465 "*"))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-875)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4464 . T) (-4465 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1121))) (-2758 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1121)))) (-2758 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-568))) (|HasAttribute| |#1| (QUOTE (-4466 "*"))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102)))) (-230 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 (-231 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."))) -((-4464 . T)) +((-4465 . T)) NIL (-232 R) ((|constructor| (NIL "Differential extensions of a ring \\spad{R}. Given a differentiation on \\spad{R},{} extend it to a differentiation on \\%."))) -((-4460 . T)) +((-4461 . T)) NIL (-233 S T$) ((|constructor| (NIL "This category captures the interface of domains with a distinguished operation named \\spad{differentiate}. Usually,{} additional properties are wanted. For example,{} that it obeys the usual Leibniz identity of differentiation of product,{} in case of differential rings. One could also want \\spad{differentiate} to obey the chain rule when considering differential manifolds. The lack of specific requirement in this category is an implicit admission that currently \\Language{} is not expressive enough to express the most general notion of differentiation in an adequate manner,{} suitable for computational purposes.")) (D ((|#2| $) "\\spad{D x} is a shorthand for \\spad{differentiate x}")) (|differentiate| ((|#2| $) "\\spad{differentiate x} compute the derivative of \\spad{x}."))) @@ -870,7 +870,7 @@ NIL NIL (-235 R) ((|constructor| (NIL "An \\spad{R}-module equipped with a distinguised differential operator. If \\spad{R} is a differential ring,{} then differentiation on the module should extend differentiation on the differential ring \\spad{R}. The latter can be the null operator. In that case,{} the differentiation operator on the module is just an \\spad{R}-linear operator. For that reason,{} we do not require that the ring \\spad{R} be a DifferentialRing; \\blankline"))) -((-4458 . T) (-4457 . T)) +((-4459 . T) (-4458 . T)) NIL (-236 S) ((|constructor| (NIL "This category is like \\spadtype{DifferentialDomain} where the target of the differentiation operator is the same as its source.")) (D (($ $ (|NonNegativeInteger|)) "\\spad{D(x, n)} returns the \\spad{n}\\spad{-}th derivative of \\spad{x}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(x,n)} returns the \\spad{n}\\spad{-}th derivative of \\spad{x}."))) @@ -882,36 +882,36 @@ NIL NIL (-238) ((|constructor| (NIL "An ordinary differential ring,{} that is,{} a ring with an operation \\spadfun{differentiate}. \\blankline"))) -((-4460 . T)) +((-4461 . T)) NIL (-239 A S) ((|constructor| (NIL "This category is a collection of operations common to both categories \\spadtype{Dictionary} and \\spadtype{MultiDictionary}")) (|select!| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{select!(p,d)} destructively changes dictionary \\spad{d} by removing all entries \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is not \\spad{true}.")) (|remove!| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{remove!(p,d)} destructively changes dictionary \\spad{d} by removeing all entries \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}.") (($ |#2| $) "\\spad{remove!(x,d)} destructively changes dictionary \\spad{d} by removing all entries \\spad{y} such that \\axiom{\\spad{y} = \\spad{x}}.")) (|dictionary| (($ (|List| |#2|)) "\\spad{dictionary([x,y,...,z])} creates a dictionary consisting of entries \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}}.") (($) "\\spad{dictionary()}\\$\\spad{D} creates an empty dictionary of type \\spad{D}."))) NIL -((|HasAttribute| |#1| (QUOTE -4463))) +((|HasAttribute| |#1| (QUOTE -4464))) (-240 S) ((|constructor| (NIL "This category is a collection of operations common to both categories \\spadtype{Dictionary} and \\spadtype{MultiDictionary}")) (|select!| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select!(p,d)} destructively changes dictionary \\spad{d} by removing all entries \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is not \\spad{true}.")) (|remove!| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove!(p,d)} destructively changes dictionary \\spad{d} by removeing all entries \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}.") (($ |#1| $) "\\spad{remove!(x,d)} destructively changes dictionary \\spad{d} by removing all entries \\spad{y} such that \\axiom{\\spad{y} = \\spad{x}}.")) (|dictionary| (($ (|List| |#1|)) "\\spad{dictionary([x,y,...,z])} creates a dictionary consisting of entries \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}}.") (($) "\\spad{dictionary()}\\$\\spad{D} creates an empty dictionary of type \\spad{D}."))) -((-4464 . T)) +((-4465 . T)) NIL (-241) ((|constructor| (NIL "any solution of a homogeneous linear Diophantine equation can be represented as a sum of minimal solutions,{} which form a \"basis\" (a minimal solution cannot be represented as a nontrivial sum of solutions) in the case of an inhomogeneous linear Diophantine equation,{} each solution is the sum of a inhomogeneous solution and any number of homogeneous solutions therefore,{} it suffices to compute two sets: \\indented{3}{1. all minimal inhomogeneous solutions} \\indented{3}{2. all minimal homogeneous solutions} the algorithm implemented is a completion procedure,{} which enumerates all solutions in a recursive depth-first-search it can be seen as finding monotone paths in a graph for more details see Reference")) (|dioSolve| (((|Record| (|:| |varOrder| (|List| (|Symbol|))) (|:| |inhom| (|Union| (|List| (|Vector| (|NonNegativeInteger|))) "failed")) (|:| |hom| (|List| (|Vector| (|NonNegativeInteger|))))) (|Equation| (|Polynomial| (|Integer|)))) "\\spad{dioSolve(u)} computes a basis of all minimal solutions for linear homogeneous Diophantine equation \\spad{u},{} then all minimal solutions of inhomogeneous equation"))) NIL NIL -(-242 S -1911 R) +(-242 S -2704 R) ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (|dot| ((|#3| $ $) "\\spad{dot(x,y)} computes the inner product of the vectors \\spad{x} and \\spad{y}.")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#3|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim.")) (|finiteAggregate| ((|attribute|) "attribute to indicate an aggregate of finite size"))) NIL -((|HasCategory| |#3| (QUOTE (-374))) (|HasCategory| |#3| (QUOTE (-805))) (|HasCategory| |#3| (QUOTE (-861))) (|HasAttribute| |#3| (QUOTE -4460)) (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-379))) (|HasCategory| |#3| (QUOTE (-738))) (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-132))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1069))) (|HasCategory| |#3| (QUOTE (-1120)))) -(-243 -1911 R) +((|HasCategory| |#3| (QUOTE (-374))) (|HasCategory| |#3| (QUOTE (-805))) (|HasCategory| |#3| (QUOTE (-861))) (|HasAttribute| |#3| (QUOTE -4461)) (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-379))) (|HasCategory| |#3| (QUOTE (-738))) (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-132))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1070))) (|HasCategory| |#3| (QUOTE (-1121)))) +(-243 -2704 R) ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (|dot| ((|#2| $ $) "\\spad{dot(x,y)} computes the inner product of the vectors \\spad{x} and \\spad{y}.")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#2|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim.")) (|finiteAggregate| ((|attribute|) "attribute to indicate an aggregate of finite size"))) -((-4457 |has| |#2| (-1069)) (-4458 |has| |#2| (-1069)) (-4460 |has| |#2| (-6 -4460)) (-4463 . T)) +((-4458 |has| |#2| (-1070)) (-4459 |has| |#2| (-1070)) (-4461 |has| |#2| (-6 -4461)) (-4464 . T)) NIL -(-244 -1911 A B) +(-244 -2704 A B) ((|constructor| (NIL "\\indented{2}{This package provides operations which all take as arguments} direct products of elements of some type \\spad{A} and functions from \\spad{A} to another type \\spad{B}. The operations all iterate over their vector argument and either return a value of type \\spad{B} or a direct product over \\spad{B}.")) (|map| (((|DirectProduct| |#1| |#3|) (|Mapping| |#3| |#2|) (|DirectProduct| |#1| |#2|)) "\\spad{map(f, v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values.")) (|reduce| ((|#3| (|Mapping| |#3| |#2| |#3|) (|DirectProduct| |#1| |#2|) |#3|) "\\spad{reduce(func,vec,ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if the vector is empty.")) (|scan| (((|DirectProduct| |#1| |#3|) (|Mapping| |#3| |#2| |#3|) (|DirectProduct| |#1| |#2|) |#3|) "\\spad{scan(func,vec,ident)} creates a new vector whose elements are the result of applying reduce to the binary function \\spad{func},{} increasing initial subsequences of the vector \\spad{vec},{} and the element \\spad{ident}."))) NIL NIL -(-245 -1911 R) +(-245 -2704 R) ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying component type. This contrasts with simple vectors in that the members can be viewed as having constant length. Thus many categorical properties can by lifted from the underlying component type. Component extraction operations are provided but no updating operations. Thus new direct product elements can either be created by converting vector elements using the \\spadfun{directProduct} function or by taking appropriate linear combinations of basis vectors provided by the \\spad{unitVector} operation."))) -((-4457 |has| |#2| (-1069)) (-4458 |has| |#2| (-1069)) (-4460 |has| |#2| (-6 -4460)) (-4463 . T)) -((-3794 (-12 (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-379))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-738))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-805))) (|HasCategory| |#2| (LIST 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(-12 (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (LIST (QUOTE -1059) (QUOTE (-576))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (QUOTE (-1121)))) (|HasAttribute| |#2| (QUOTE -4461)) (-12 (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (QUOTE (-1070)))) (-12 (|HasCategory| |#2| (QUOTE (-1070))) (|HasCategory| |#2| (LIST (QUOTE -917) (QUOTE (-1197))))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|))))) (-246) ((|constructor| (NIL "DisplayPackage allows one to print strings in a nice manner,{} including highlighting substrings.")) (|sayLength| (((|Integer|) (|List| (|String|))) "\\spad{sayLength(l)} returns the length of a list of strings \\spad{l} as an integer.") (((|Integer|) (|String|)) "\\spad{sayLength(s)} returns the length of a string \\spad{s} as an integer.")) (|say| (((|Void|) (|List| (|String|))) "\\spad{say(l)} sends a list of strings \\spad{l} to output.") (((|Void|) (|String|)) "\\spad{say(s)} sends a string \\spad{s} to output.")) (|center| (((|List| (|String|)) (|List| (|String|)) (|Integer|) (|String|)) "\\spad{center(l,i,s)} takes a list of strings \\spad{l},{} and centers them within a list of strings which is \\spad{i} characters long,{} in which the remaining spaces are filled with strings composed of as many repetitions as possible of the last string parameter \\spad{s}.") (((|String|) (|String|) (|Integer|) (|String|)) "\\spad{center(s,i,s)} takes the first string \\spad{s},{} and centers it within a string of length \\spad{i},{} in which the other elements of the string are composed of as many replications as possible of the second indicated string,{} \\spad{s} which must have a length greater than that of an empty string.")) (|copies| (((|String|) (|Integer|) (|String|)) "\\spad{copies(i,s)} will take a string \\spad{s} and create a new string composed of \\spad{i} copies of \\spad{s}.")) (|newLine| (((|String|)) "\\spad{newLine()} sends a new line command to output.")) (|bright| (((|List| (|String|)) (|List| (|String|))) "\\spad{bright(l)} sets the font property of a list of strings,{} \\spad{l},{} to bold-face type.") (((|List| (|String|)) (|String|)) "\\spad{bright(s)} sets the font property of the string \\spad{s} to bold-face type."))) NIL @@ -922,7 +922,7 @@ NIL NIL (-248) ((|constructor| (NIL "A division ring (sometimes called a skew field),{} \\spadignore{i.e.} a not necessarily commutative ring where all non-zero elements have multiplicative inverses.")) (|inv| (($ $) "\\spad{inv x} returns the multiplicative inverse of \\spad{x}. Error: if \\spad{x} is 0.")) (** (($ $ (|Integer|)) "\\spad{x**n} returns \\spad{x} raised to the integer power \\spad{n}."))) -((-4456 . T) (-4457 . T) (-4458 . T) (-4460 . T)) +((-4457 . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-249 S) ((|constructor| (NIL "A doubly-linked aggregate serves as a model for a doubly-linked list,{} that is,{} a list which can has links to both next and previous nodes and thus can be efficiently traversed in both directions.")) (|setnext!| (($ $ $) "\\spad{setnext!(u,v)} destructively sets the next node of doubly-linked aggregate \\spad{u} to \\spad{v},{} returning \\spad{v}.")) (|setprevious!| (($ $ $) "\\spad{setprevious!(u,v)} destructively sets the previous node of doubly-linked aggregate \\spad{u} to \\spad{v},{} returning \\spad{v}.")) (|concat!| (($ $ $) "\\spad{concat!(u,v)} destructively concatenates doubly-linked aggregate \\spad{v} to the end of doubly-linked aggregate \\spad{u}.")) (|next| (($ $) "\\spad{next(l)} returns the doubly-linked aggregate beginning with its next element. Error: if \\spad{l} has no next element. Note: \\axiom{next(\\spad{l}) = rest(\\spad{l})} and \\axiom{previous(next(\\spad{l})) = \\spad{l}}.")) (|previous| (($ $) "\\spad{previous(l)} returns the doubly-link list beginning with its previous element. Error: if \\spad{l} has no previous element. Note: \\axiom{next(previous(\\spad{l})) = \\spad{l}}.")) (|tail| (($ $) "\\spad{tail(l)} returns the doubly-linked aggregate \\spad{l} starting at its second element. Error: if \\spad{l} is empty.")) (|head| (($ $) "\\spad{head(l)} returns the first element of a doubly-linked aggregate \\spad{l}. Error: if \\spad{l} is empty.")) (|last| ((|#1| $) "\\spad{last(l)} returns the last element of a doubly-linked aggregate \\spad{l}. Error: if \\spad{l} is empty."))) @@ -930,20 +930,20 @@ NIL NIL (-250 S) ((|constructor| (NIL "This domain provides some nice functions on lists")) (|elt| (((|NonNegativeInteger|) $ "count") "\\axiom{\\spad{l}.\"count\"} returns the number of elements in \\axiom{\\spad{l}}.") (($ $ "sort") "\\axiom{\\spad{l}.sort} returns \\axiom{\\spad{l}} with elements sorted. Note: \\axiom{\\spad{l}.sort = sort(\\spad{l})}") (($ $ "unique") "\\axiom{\\spad{l}.unique} returns \\axiom{\\spad{l}} with duplicates removed. Note: \\axiom{\\spad{l}.unique = removeDuplicates(\\spad{l})}.")) (|datalist| (($ (|List| |#1|)) "\\spad{datalist(l)} creates a datalist from \\spad{l}"))) -((-4464 . T) (-4463 . T)) -((-3794 (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1120))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-3794 (-12 (|HasCategory| |#1| (QUOTE (-1120))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-875))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-3794 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1120)))) (|HasCategory| |#1| (QUOTE (-861))) (-3794 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1120)))) (|HasCategory| (-576) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1120))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-875)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1120))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) +((-4465 . T) (-4464 . T)) +((-2758 (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2758 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2758 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| |#1| (QUOTE (-861))) (-2758 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| (-576) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-251 M) ((|constructor| (NIL "DiscreteLogarithmPackage implements help functions for discrete logarithms in monoids using small cyclic groups.")) (|shanksDiscLogAlgorithm| (((|Union| (|NonNegativeInteger|) "failed") |#1| |#1| (|NonNegativeInteger|)) "\\spad{shanksDiscLogAlgorithm(b,a,p)} computes \\spad{s} with \\spad{b**s = a} for assuming that \\spad{a} and \\spad{b} are elements in a 'small' cyclic group of order \\spad{p} by Shank\\spad{'s} algorithm. Note: this is a subroutine of the function \\spadfun{discreteLog}.")) (** ((|#1| |#1| (|Integer|)) "\\spad{x ** n} returns \\spad{x} raised to the integer power \\spad{n}"))) NIL NIL (-252 R) ((|constructor| (NIL "Category of modules that extend differential rings. \\blankline"))) -((-4458 . T) (-4457 . T)) +((-4459 . T) (-4458 . T)) NIL (-253 |vl| R) ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is lexicographic specified by the variable list parameter with the most significant variable first in the list.")) (|reorder| (($ $ (|List| (|Integer|))) "\\spad{reorder(p, perm)} applies the permutation perm to the variables in a polynomial and returns the new correctly ordered polynomial"))) -(((-4465 "*") |has| |#2| (-174)) (-4456 |has| |#2| (-568)) (-4461 |has| |#2| (-6 -4461)) (-4458 . T) (-4457 . T) (-4460 . 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T) (-4458 . T) (-4461 . 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(|reflect| (($ (|ConstructorCall| (|DomainConstructor|))) "\\spad{reflect cc} returns the domain object designated by the ConstructorCall syntax `cc'. The constructor implied by `cc' must be known to the system since it is instantiated.")) (|reify| (((|ConstructorCall| (|DomainConstructor|)) $) "\\spad{reify(d)} returns the abstract syntax for the domain \\spad{`x'}.")) (|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Create: October 18,{} 2007. Date Last Updated: December 20,{} 2008. Basic Operations: coerce,{} reify Related Constructors: Type,{} Syntax,{} OutputForm Also See: Type,{} ConstructorCall") (((|DomainConstructor|) $) "\\spad{constructor(d)} returns the domain constructor that is instantiated to the domain object \\spad{`d'}."))) 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category constructor specifying basic functions in an ordinary differential polynomial ring with a given ordered set of differential indeterminates. In addition,{} it implements defaults for the basic functions. The functions \\spadfun{order} and \\spadfun{weight} are extended from the set of derivatives of differential indeterminates to the set of differential polynomials. Other operations provided on differential polynomials are \\spadfun{leader},{} \\spadfun{initial},{} \\spadfun{separant},{} \\spadfun{differentialVariables},{} and \\spadfun{isobaric?}. Furthermore,{} if the ground ring is a differential ring,{} then evaluation (substitution of differential indeterminates by elements of the ground ring or by differential polynomials) is provided by \\spadfun{eval}. A convenient way of referencing derivatives is provided by the functions \\spadfun{makeVariable}. \\blankline To construct a domain using this constructor,{} one needs to provide a ground ring \\spad{R},{} an ordered set \\spad{S} of differential indeterminates,{} a ranking \\spad{V} on the set of derivatives of the differential indeterminates,{} and a set \\spad{E} of exponents in bijection with the set of differential monomials in the given differential indeterminates. \\blankline")) (|separant| (($ $) "\\spad{separant(p)} returns the partial derivative of the differential polynomial \\spad{p} with respect to its leader.")) (|initial| (($ $) "\\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: an error occurs if \\spad{p} is in the ground ring.")) (|isobaric?| (((|Boolean|) $) "\\spad{isobaric?(p)} returns \\spad{true} if every differential monomial appearing in the differential polynomial \\spad{p} has same weight,{} and returns \\spad{false} otherwise.")) (|weight| (((|NonNegativeInteger|) $ |#3|) "\\spad{weight(p, s)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|NonNegativeInteger|) $) "\\spad{weight(p)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p}.")) (|weights| (((|List| (|NonNegativeInteger|)) $ |#3|) "\\spad{weights(p, s)} returns a list of weights of differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|List| (|NonNegativeInteger|)) $) "\\spad{weights(p)} returns a list of weights of differential monomials appearing in differential polynomial \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $ |#3|) "\\spad{degree(p, s)} returns the maximum degree of the differential polynomial \\spad{p} viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of the differential polynomial \\spad{p},{} which is the maximum number of differentiations of a differential indeterminate,{} among all those appearing in \\spad{p}.") (((|NonNegativeInteger|) $ |#3|) "\\spad{order(p,s)} returns the order of the differential polynomial \\spad{p} in differential indeterminate \\spad{s}.")) (|differentialVariables| (((|List| |#3|) $) "\\spad{differentialVariables(p)} returns a list of differential indeterminates occurring in a differential polynomial \\spad{p}.")) (|makeVariable| (((|Mapping| $ (|NonNegativeInteger|)) $) "\\spad{makeVariable(p)} views \\spad{p} as an element of a differential ring,{} in such a way that the \\spad{n}-th derivative of \\spad{p} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} \\spad{:=} makeVariable(\\spad{p}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored.") (((|Mapping| $ (|NonNegativeInteger|)) |#3|) "\\spad{makeVariable(s)} views \\spad{s} as a differential indeterminate,{} in such a way that the \\spad{n}-th derivative of \\spad{s} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} :=makeVariable(\\spad{s}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored."))) NIL ((|HasCategory| |#2| (QUOTE (-238)))) (-260 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. \\blankline")) (|separant| (($ $) "\\spad{separant(p)} returns the partial derivative of the differential polynomial \\spad{p} with respect to its leader.")) (|initial| (($ $) "\\spad{initial(p)} returns the leading coefficient when the differential polynomial \\spad{p} is written as a univariate polynomial in its leader.")) (|leader| ((|#3| $) "\\spad{leader(p)} returns the derivative of the highest rank appearing in the differential polynomial \\spad{p} Note: an error occurs if \\spad{p} is in the ground ring.")) (|isobaric?| (((|Boolean|) $) "\\spad{isobaric?(p)} returns \\spad{true} if every differential monomial appearing in the differential polynomial \\spad{p} has same weight,{} and returns \\spad{false} otherwise.")) (|weight| (((|NonNegativeInteger|) $ |#2|) "\\spad{weight(p, s)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|NonNegativeInteger|) $) "\\spad{weight(p)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p}.")) (|weights| (((|List| (|NonNegativeInteger|)) $ |#2|) "\\spad{weights(p, s)} returns a list of weights of differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|List| (|NonNegativeInteger|)) $) "\\spad{weights(p)} returns a list of weights of differential monomials appearing in differential polynomial \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $ |#2|) "\\spad{degree(p, s)} returns the maximum degree of the differential polynomial \\spad{p} viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of the differential polynomial \\spad{p},{} which is the maximum number of differentiations of a differential indeterminate,{} among all those appearing in \\spad{p}.") (((|NonNegativeInteger|) $ |#2|) "\\spad{order(p,s)} returns the order of the differential polynomial \\spad{p} in differential indeterminate \\spad{s}.")) (|differentialVariables| (((|List| |#2|) $) "\\spad{differentialVariables(p)} returns a list of differential indeterminates occurring in a differential polynomial \\spad{p}.")) (|makeVariable| (((|Mapping| $ (|NonNegativeInteger|)) $) "\\spad{makeVariable(p)} views \\spad{p} as an element of a differential ring,{} in such a way that the \\spad{n}-th derivative of \\spad{p} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} \\spad{:=} makeVariable(\\spad{p}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored.") (((|Mapping| $ (|NonNegativeInteger|)) |#2|) "\\spad{makeVariable(s)} views \\spad{s} as a differential indeterminate,{} in such a way that the \\spad{n}-th derivative of \\spad{s} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} :=makeVariable(\\spad{s}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored."))) -(((-4465 "*") |has| |#1| (-174)) (-4456 |has| |#1| (-568)) (-4461 |has| |#1| (-6 -4461)) (-4458 . T) (-4457 . T) (-4460 . T)) +(((-4466 "*") |has| |#1| (-174)) (-4457 |has| |#1| (-568)) (-4462 |has| |#1| (-6 -4462)) (-4459 . T) (-4458 . T) (-4461 . T)) NIL (-261 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|) $) "\\spad{height(d)} returns the number of elements in dequeue \\spad{d}. Note: \\axiom{height(\\spad{d}) = \\# \\spad{d}}.")) (|dequeue| (($ (|List| |#1|)) "\\spad{dequeue([x,y,...,z])} creates a dequeue with first (top or front) element \\spad{x},{} second element \\spad{y},{}...,{}and last (bottom or back) element \\spad{z}.") (($) "\\spad{dequeue()}\\$\\spad{D} creates an empty dequeue of type \\spad{D}."))) -((-4463 . T) (-4464 . T)) +((-4464 . T) (-4465 . T)) NIL (-262) ((|constructor| (NIL "TopLevelDrawFunctionsForCompiledFunctions provides top level functions for drawing graphics of expressions.")) (|recolor| (((|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) "\\spad{recolor()},{} uninteresting to top level user; exported in order to compile package.")) (|makeObject| (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSurface| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{makeObject(surface(f,g,h),a..b,c..d,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{x = f(u,v)},{} \\spad{y = g(u,v)},{} \\spad{z = h(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSurface| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(surface(f,g,h),a..b,c..d,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{x = f(u,v)},{} \\spad{y = g(u,v)},{} \\spad{z = h(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{makeObject(f,a..b,c..d,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{f(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(f,a..b,c..d,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{f(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{makeObject(f,a..b,c..d)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of \\spad{z = f(x,y)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{y} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(f,a..b,c..d,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of \\spad{z = f(x,y)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{y} ranges from \\spad{min(c,d)} to \\spad{max(c,d)},{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|Float|))) "\\spad{makeObject(sp,curve(f,g,h),a..b)} returns the space \\spad{sp} of the domain \\spadtype{ThreeSpace} with the addition of the graph of the parametric curve \\spad{x = f(t), y = g(t), z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(curve(f,g,h),a..b,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric curve \\spad{x = f(t), y = g(t), z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|))) "\\spad{makeObject(sp,curve(f,g,h),a..b)} returns the space \\spad{sp} of the domain \\spadtype{ThreeSpace} with the addition of the graph of the parametric curve \\spad{x = f(t), y = g(t), z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(curve(f,g,h),a..b,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric curve \\spad{x = f(t), y = g(t), z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.")) (|draw| (((|ThreeDimensionalViewport|) (|ParametricSurface| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{draw(surface(f,g,h),a..b,c..d)} draws the graph of the parametric surface \\spad{x = f(u,v)},{} \\spad{y = g(u,v)},{} \\spad{z = h(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}.") (((|ThreeDimensionalViewport|) (|ParametricSurface| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(surface(f,g,h),a..b,c..d)} draws the graph of the parametric surface \\spad{x = f(u,v)},{} \\spad{y = g(u,v)},{} \\spad{z = h(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{draw(f,a..b,c..d)} draws the graph of the parametric surface \\spad{f(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)} The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f,a..b,c..d)} draws the graph of the parametric surface \\spad{f(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{draw(f,a..b,c..d)} draws the graph of \\spad{z = f(x,y)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{y} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}.") (((|ThreeDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f,a..b,c..d,l)} draws the graph of \\spad{z = f(x,y)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{y} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}. and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|Float|))) "\\spad{draw(f,a..b,l)} draws the graph of the parametric curve \\spad{f} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}.") (((|ThreeDimensionalViewport|) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f,a..b,l)} draws the graph of the parametric curve \\spad{f} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|))) "\\spad{draw(curve(f,g,h),a..b,l)} draws the graph of the parametric curve \\spad{x = f(t), y = g(t), z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}.") (((|ThreeDimensionalViewport|) (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(curve(f,g,h),a..b,l)} draws the graph of the parametric curve \\spad{x = f(t), y = g(t), z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) (|ParametricPlaneCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|))) "\\spad{draw(curve(f,g),a..b)} draws the graph of the parametric curve \\spad{x = f(t), y = g(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}.") (((|TwoDimensionalViewport|) (|ParametricPlaneCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(curve(f,g),a..b,l)} draws the graph of the parametric curve \\spad{x = f(t), y = g(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|))) "\\spad{draw(f,a..b)} draws the graph of \\spad{y = f(x)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}.") (((|TwoDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f,a..b,l)} draws the graph of \\spad{y = f(x)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied."))) @@ -1015,15 +1015,15 @@ NIL (-271 S R) ((|constructor| (NIL "Extension of a base differential space with a derivation. \\blankline")) (D (($ $ (|Mapping| |#2| |#2|) (|NonNegativeInteger|)) "\\spad{D(x,d,n)} is a shorthand for \\spad{differentiate(x,d,n)}.") (($ $ (|Mapping| |#2| |#2|)) "\\spad{D(x,d)} is a shorthand for \\spad{differentiate(x,d)}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|) (|NonNegativeInteger|)) "\\spad{differentiate(x,d,n)} computes the \\spad{n}\\spad{-}th derivative of \\spad{x} using a derivation extending \\spad{d} on \\spad{R}.") (($ $ (|Mapping| |#2| |#2|)) "\\spad{differentiate(x,d)} computes the derivative of \\spad{x},{} extending differentiation \\spad{d} on \\spad{R}."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -918) (QUOTE (-1196)))) (|HasCategory| |#2| (QUOTE (-237)))) +((|HasCategory| |#2| (LIST (QUOTE -919) (QUOTE (-1197)))) (|HasCategory| |#2| (QUOTE (-237)))) (-272 R) ((|constructor| (NIL "Extension of a base differential space with a derivation. \\blankline")) (D (($ $ (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) "\\spad{D(x,d,n)} is a shorthand for \\spad{differentiate(x,d,n)}.") (($ $ (|Mapping| |#1| |#1|)) "\\spad{D(x,d)} is a shorthand for \\spad{differentiate(x,d)}.")) (|differentiate| (($ $ (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) "\\spad{differentiate(x,d,n)} computes the \\spad{n}\\spad{-}th derivative of \\spad{x} using a derivation extending \\spad{d} on \\spad{R}.") (($ $ (|Mapping| |#1| |#1|)) "\\spad{differentiate(x,d)} computes the derivative of \\spad{x},{} extending differentiation \\spad{d} on \\spad{R}."))) NIL NIL (-273 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}. \\blankline"))) -(((-4465 "*") |has| |#1| (-174)) (-4456 |has| |#1| (-568)) (-4461 |has| |#1| (-6 -4461)) (-4458 . T) (-4457 . T) (-4460 . T)) -((|HasCategory| |#1| (QUOTE (-927))) (-3794 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-927)))) (-3794 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-927)))) (-3794 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-927)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-3794 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-390)))) (|HasCategory| |#3| (LIST (QUOTE -900) (QUOTE (-390))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-576)))) (|HasCategory| |#3| (LIST (QUOTE -900) (QUOTE (-576))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -906) (QUOTE (-390))))) (|HasCategory| |#3| (LIST (QUOTE -626) (LIST (QUOTE -906) (QUOTE (-390)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -906) (QUOTE (-576))))) (|HasCategory| |#3| (LIST (QUOTE -626) (LIST (QUOTE -906) (QUOTE (-576)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#3| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1058) (QUOTE (-576)))) (-3794 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1058) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#1| (LIST (QUOTE -1058) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (LIST (QUOTE -918) (QUOTE (-1196)))) (|HasCategory| |#1| (LIST (QUOTE -916) (QUOTE (-1196)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasAttribute| |#1| (QUOTE -4461)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-927)))) (-3794 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-927)))) (|HasCategory| |#1| (QUOTE (-146))))) +(((-4466 "*") |has| |#1| (-174)) (-4457 |has| |#1| (-568)) (-4462 |has| |#1| (-6 -4462)) (-4459 . T) (-4458 . T) (-4461 . 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If \\spad{x},{}...,{}\\spad{y} is an ordered set of differential indeterminates,{} and the prime notation is used for differentiation,{} then the set of derivatives (including zero-th order) of the differential indeterminates is \\spad{x},{}\\spad{x'},{}\\spad{x''},{}...,{} \\spad{y},{}\\spad{y'},{}\\spad{y''},{}... (Note: 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}.")) (|weight| (((|NonNegativeInteger|) $) "\\spad{weight(v)} returns the weight of the derivative \\spad{v}.")) (|variable| ((|#2| $) "\\spad{variable(v)} returns \\spad{s} if \\spad{v} is any derivative of the differential indeterminate \\spad{s}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(v)} returns \\spad{n} if \\spad{v} is the \\spad{n}-th derivative of any differential indeterminate.")) (|makeVariable| (($ |#2| (|NonNegativeInteger|)) "\\spad{makeVariable(s, n)} returns the \\spad{n}-th derivative of a differential indeterminate \\spad{s} as an algebraic indeterminate."))) NIL @@ -1068,11 +1068,11 @@ NIL ((|constructor| (NIL "A domain used in the construction of the exterior algebra on a set \\spad{X} over a ring \\spad{R}. This domain represents the set of all ordered subsets of the set \\spad{X},{} assumed to be in correspondance with {1,{}2,{}3,{} ...}. The ordered subsets are themselves ordered lexicographically and are in bijective correspondance with an ordered basis of the exterior algebra. In this domain we are dealing strictly with the exponents of basis elements which can only be 0 or 1. \\blankline The multiplicative identity element of the exterior algebra corresponds to the empty subset of \\spad{X}. A coerce from List Integer to an ordered basis element is provided to allow the convenient input of expressions. Another exported function forgets the ordered structure and simply returns the list corresponding to an ordered subset.")) (|Nul| (($ (|NonNegativeInteger|)) "\\spad{Nul()} gives the basis element 1 for the algebra generated by \\spad{n} generators.")) (|exponents| (((|List| (|Integer|)) $) "\\spad{exponents(x)} converts a domain element into a list of zeros and ones corresponding to the exponents in the basis element that \\spad{x} represents.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(x)} gives the numbers of 1\\spad{'s} in \\spad{x},{} \\spadignore{i.e.} the number of non-zero exponents in the basis element that \\spad{x} represents.")) (|coerce| (($ (|List| (|Integer|))) "\\spad{coerce(l)} converts a list of 0\\spad{'s} and 1\\spad{'s} into a basis element,{} where 1 (respectively 0) designates that the variable of the corresponding index of \\spad{l} is (respectively,{} is not) present. Error: if an element of \\spad{l} is not 0 or 1."))) NIL NIL -(-285 R -2117) +(-285 R -1959) ((|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 -(-286 R -2117) +(-286 R -1959) ((|constructor| (NIL "ElementaryFunctionStructurePackage provides functions to test the algebraic independence of various elementary functions,{} using the Risch structure theorem (real and complex versions). It also provides transformations on elementary functions which are not considered simplifications.")) (|tanQ| ((|#2| (|Fraction| (|Integer|)) |#2|) "\\spad{tanQ(q,a)} is a local function with a conditional implementation.")) (|rootNormalize| ((|#2| |#2| (|Kernel| |#2|)) "\\spad{rootNormalize(f, k)} returns \\spad{f} rewriting either \\spad{k} which must be an \\spad{n}th-root in terms of radicals already in \\spad{f},{} or some radicals in \\spad{f} in terms of \\spad{k}.")) (|validExponential| (((|Union| |#2| "failed") (|List| (|Kernel| |#2|)) |#2| (|Symbol|)) "\\spad{validExponential([k1,...,kn],f,x)} returns \\spad{g} if \\spad{exp(f)=g} and \\spad{g} involves only \\spad{k1...kn},{} and \"failed\" otherwise.")) (|realElementary| ((|#2| |#2| (|Symbol|)) "\\spad{realElementary(f,x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 4 fundamental real transcendental elementary functions: \\spad{log, exp, tan, atan}.") ((|#2| |#2|) "\\spad{realElementary(f)} rewrites \\spad{f} in terms of the 4 fundamental real transcendental elementary functions: \\spad{log, exp, tan, atan}.")) (|rischNormalize| (((|Record| (|:| |func| |#2|) (|:| |kers| (|List| (|Kernel| |#2|))) (|:| |vals| (|List| |#2|))) |#2| (|Symbol|)) "\\spad{rischNormalize(f, x)} returns \\spad{[g, [k1,...,kn], [h1,...,hn]]} such that \\spad{g = normalize(f, x)} and each \\spad{ki} was rewritten as \\spad{hi} during the normalization.")) (|normalize| ((|#2| |#2| (|Symbol|)) "\\spad{normalize(f, x)} rewrites \\spad{f} using the least possible number of real algebraically independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{normalize(f)} rewrites \\spad{f} using the least possible number of real algebraically independent kernels."))) NIL NIL @@ -1095,10 +1095,10 @@ NIL (-291 A S) ((|constructor| (NIL "An extensible aggregate is one which allows insertion and deletion of entries. These aggregates are models of lists and streams which are represented by linked structures so as to make insertion,{} deletion,{} and concatenation efficient. However,{} access to elements of these extensible aggregates is generally slow since access is made from the end. See \\spadtype{FlexibleArray} for an exception.")) (|removeDuplicates!| (($ $) "\\spad{removeDuplicates!(u)} destructively removes duplicates from \\spad{u}.")) (|select!| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{select!(p,u)} destructively changes \\spad{u} by keeping only values \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})}.")) (|merge!| (($ $ $) "\\spad{merge!(u,v)} destructively merges \\spad{u} and \\spad{v} in ascending order.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $ $) "\\spad{merge!(p,u,v)} destructively merges \\spad{u} and \\spad{v} using predicate \\spad{p}.")) (|insert!| (($ $ $ (|Integer|)) "\\spad{insert!(v,u,i)} destructively inserts aggregate \\spad{v} into \\spad{u} at position \\spad{i}.") (($ |#2| $ (|Integer|)) "\\spad{insert!(x,u,i)} destructively inserts \\spad{x} into \\spad{u} at position \\spad{i}.")) (|remove!| (($ |#2| $) "\\spad{remove!(x,u)} destructively removes all values \\spad{x} from \\spad{u}.") (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{remove!(p,u)} destructively removes all elements \\spad{x} of \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}.")) (|delete!| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete!(u,i..j)} destructively deletes elements \\spad{u}.\\spad{i} through \\spad{u}.\\spad{j}.") (($ $ (|Integer|)) "\\spad{delete!(u,i)} destructively deletes the \\axiom{\\spad{i}}th element of \\spad{u}.")) (|concat!| (($ $ $) "\\spad{concat!(u,v)} destructively appends \\spad{v} to the end of \\spad{u}. \\spad{v} is unchanged") (($ $ |#2|) "\\spad{concat!(u,x)} destructively adds element \\spad{x} to the end of \\spad{u}."))) NIL -((|HasCategory| |#2| (QUOTE (-861))) (|HasCategory| |#2| (QUOTE (-1120)))) +((|HasCategory| |#2| (QUOTE (-861))) (|HasCategory| |#2| (QUOTE (-1121)))) (-292 S) ((|constructor| (NIL "An extensible aggregate is one which allows insertion and deletion of entries. These aggregates are models of lists and streams which are represented by linked structures so as to make insertion,{} deletion,{} and concatenation efficient. However,{} access to elements of these extensible aggregates is generally slow since access is made from the end. See \\spadtype{FlexibleArray} for an exception.")) (|removeDuplicates!| (($ $) "\\spad{removeDuplicates!(u)} destructively removes duplicates from \\spad{u}.")) (|select!| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select!(p,u)} destructively changes \\spad{u} by keeping only values \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})}.")) (|merge!| (($ $ $) "\\spad{merge!(u,v)} destructively merges \\spad{u} and \\spad{v} in ascending order.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $ $) "\\spad{merge!(p,u,v)} destructively merges \\spad{u} and \\spad{v} using predicate \\spad{p}.")) (|insert!| (($ $ $ (|Integer|)) "\\spad{insert!(v,u,i)} destructively inserts aggregate \\spad{v} into \\spad{u} at position \\spad{i}.") (($ |#1| $ (|Integer|)) "\\spad{insert!(x,u,i)} destructively inserts \\spad{x} into \\spad{u} at position \\spad{i}.")) (|remove!| (($ |#1| $) "\\spad{remove!(x,u)} destructively removes all values \\spad{x} from \\spad{u}.") (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove!(p,u)} destructively removes all elements \\spad{x} of \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}.")) (|delete!| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete!(u,i..j)} destructively deletes elements \\spad{u}.\\spad{i} through \\spad{u}.\\spad{j}.") (($ $ (|Integer|)) "\\spad{delete!(u,i)} destructively deletes the \\axiom{\\spad{i}}th element of \\spad{u}.")) (|concat!| (($ $ $) "\\spad{concat!(u,v)} destructively appends \\spad{v} to the end of \\spad{u}. \\spad{v} is unchanged") (($ $ |#1|) "\\spad{concat!(u,x)} destructively adds element \\spad{x} to the end of \\spad{u}."))) -((-4464 . T)) +((-4465 . T)) NIL (-293 S) ((|constructor| (NIL "Category for the elementary functions.")) (** (($ $ $) "\\spad{x**y} returns \\spad{x} to the power \\spad{y}.")) (|exp| (($ $) "\\spad{exp(x)} returns \\%\\spad{e} to the power \\spad{x}.")) (|log| (($ $) "\\spad{log(x)} returns the natural logarithm of \\spad{x}."))) @@ -1119,18 +1119,18 @@ NIL (-297 S |Dom| |Im|) ((|constructor| (NIL "An eltable aggregate is one which can be viewed as a function. For example,{} the list \\axiom{[1,{}7,{}4]} can applied to 0,{}1,{} and 2 respectively will return the integers 1,{}7,{} and 4; thus this list may be viewed as mapping 0 to 1,{} 1 to 7 and 2 to 4. In general,{} an aggregate can map members of a domain {\\em Dom} to an image domain {\\em Im}.")) (|qsetelt!| ((|#3| $ |#2| |#3|) "\\spad{qsetelt!(u,x,y)} sets the image of \\axiom{\\spad{x}} to be \\axiom{\\spad{y}} under \\axiom{\\spad{u}},{} without checking that \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If such a check is required use the function \\axiom{setelt}.")) (|setelt| ((|#3| $ |#2| |#3|) "\\spad{setelt(u,x,y)} sets the image of \\spad{x} to be \\spad{y} under \\spad{u},{} assuming \\spad{x} is in the domain of \\spad{u}. Error: if \\spad{x} is not in the domain of \\spad{u}.")) (|qelt| ((|#3| $ |#2|) "\\spad{qelt(u, x)} applies \\axiom{\\spad{u}} to \\axiom{\\spad{x}} without checking whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If \\axiom{\\spad{x}} is not in the domain of \\axiom{\\spad{u}} a memory-access violation may occur. If a check on whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}} is required,{} use the function \\axiom{elt}.")) (|elt| ((|#3| $ |#2| |#3|) "\\spad{elt(u, x, y)} applies \\spad{u} to \\spad{x} if \\spad{x} is in the domain of \\spad{u},{} and returns \\spad{y} otherwise. For example,{} if \\spad{u} is a polynomial in \\axiom{\\spad{x}} over the rationals,{} \\axiom{elt(\\spad{u},{}\\spad{n},{}0)} may define the coefficient of \\axiom{\\spad{x}} to the power \\spad{n},{} returning 0 when \\spad{n} is out of range."))) NIL -((|HasAttribute| |#1| (QUOTE -4464))) +((|HasAttribute| |#1| (QUOTE -4465))) (-298 |Dom| |Im|) ((|constructor| (NIL "An eltable aggregate is one which can be viewed as a function. For example,{} the list \\axiom{[1,{}7,{}4]} can applied to 0,{}1,{} and 2 respectively will return the integers 1,{}7,{} and 4; thus this list may be viewed as mapping 0 to 1,{} 1 to 7 and 2 to 4. In general,{} an aggregate can map members of a domain {\\em Dom} to an image domain {\\em Im}.")) (|qsetelt!| ((|#2| $ |#1| |#2|) "\\spad{qsetelt!(u,x,y)} sets the image of \\axiom{\\spad{x}} to be \\axiom{\\spad{y}} under \\axiom{\\spad{u}},{} without checking that \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If such a check is required use the function \\axiom{setelt}.")) (|setelt| ((|#2| $ |#1| |#2|) "\\spad{setelt(u,x,y)} sets the image of \\spad{x} to be \\spad{y} under \\spad{u},{} assuming \\spad{x} is in the domain of \\spad{u}. Error: if \\spad{x} is not in the domain of \\spad{u}.")) (|qelt| ((|#2| $ |#1|) "\\spad{qelt(u, x)} applies \\axiom{\\spad{u}} to \\axiom{\\spad{x}} without checking whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If \\axiom{\\spad{x}} is not in the domain of \\axiom{\\spad{u}} a memory-access violation may occur. If a check on whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}} is required,{} use the function \\axiom{elt}.")) (|elt| ((|#2| $ |#1| |#2|) "\\spad{elt(u, x, y)} applies \\spad{u} to \\spad{x} if \\spad{x} is in the domain of \\spad{u},{} and returns \\spad{y} otherwise. For example,{} if \\spad{u} is a polynomial in \\axiom{\\spad{x}} over the rationals,{} \\axiom{elt(\\spad{u},{}\\spad{n},{}0)} may define the coefficient of \\axiom{\\spad{x}} to the power \\spad{n},{} returning 0 when \\spad{n} is out of range."))) NIL NIL -(-299 S R |Mod| -3735 -2144 |exactQuo|) +(-299 S R |Mod| -2391 -4335 |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}")) (|inv| (($ $) "\\spad{inv(x)} \\undocumented")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} \\undocumented")) (|exQuo| (((|Union| $ "failed") $ $) "\\spad{exQuo(x,y)} \\undocumented")) (|reduce| (($ |#2| |#3|) "\\spad{reduce(r,m)} \\undocumented")) (|coerce| ((|#2| $) "\\spad{coerce(x)} \\undocumented")) (|modulus| ((|#3| $) "\\spad{modulus(x)} \\undocumented"))) -((-4456 . T) ((-4465 "*") . T) (-4457 . T) (-4458 . T) (-4460 . T)) +((-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-300) ((|constructor| (NIL "Entire Rings (non-commutative Integral Domains),{} \\spadignore{i.e.} a ring not necessarily commutative which has no zero divisors. \\blankline")) (|noZeroDivisors| ((|attribute|) "if a product is zero then one of the factors must be zero."))) -((-4456 . T) (-4457 . T) (-4458 . T) (-4460 . T)) +((-4457 . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-301) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: March 18,{} 2010. An `Environment' is a stack of scope.")) (|categoryFrame| (($) "the current category environment in the interpreter.")) (|interactiveEnv| (($) "the current interactive environment in effect.")) (|currentEnv| (($) "the current normal environment in effect.")) (|putProperties| (($ (|Identifier|) (|List| (|Property|)) $) "\\spad{putProperties(n,props,e)} set the list of properties of \\spad{n} to \\spad{props} in \\spad{e}.")) (|getProperties| (((|List| (|Property|)) (|Identifier|) $) "\\spad{getBinding(n,e)} returns the list of properties of \\spad{n} in \\spad{e}.")) (|putProperty| (($ (|Identifier|) (|Identifier|) (|SExpression|) $) "\\spad{putProperty(n,p,v,e)} binds the property \\spad{(p,v)} to \\spad{n} in the topmost scope of \\spad{e}.")) (|getProperty| (((|Maybe| (|SExpression|)) (|Identifier|) (|Identifier|) $) "\\spad{getProperty(n,p,e)} returns the value of property with name \\spad{p} for the symbol \\spad{n} in environment \\spad{e}. Otherwise,{} \\spad{nothing}.")) (|scopes| (((|List| (|Scope|)) $) "\\spad{scopes(e)} returns the stack of scopes in environment \\spad{e}.")) (|empty| (($) "\\spad{empty()} constructs an empty environment"))) @@ -1146,21 +1146,21 @@ NIL NIL (-304 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 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| $)) "\\spad{eval(eqn, [x1=v1, ... xn=vn])} replaces \\spad{xi} by \\spad{vi} in equation \\spad{eqn}.") (($ $ $) "\\spad{eval(eqn, x=f)} replaces \\spad{x} by \\spad{f} in equation \\spad{eqn}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,eqn)} constructs a new equation by applying \\spad{f} to both sides of \\spad{eqn}.")) (|rhs| ((|#1| $) "\\spad{rhs(eqn)} returns the right hand side of equation \\spad{eqn}.")) (|lhs| ((|#1| $) "\\spad{lhs(eqn)} returns the left hand side of equation \\spad{eqn}.")) (|swap| (($ $) "\\spad{swap(eq)} interchanges left and right hand side of equation \\spad{eq}.")) (|equation| (($ |#1| |#1|) "\\spad{equation(a,b)} creates an equation.")) 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Thus keys are considered equal only if they are the same instance of a structure."))) -((-4463 . T) (-4464 . T)) -((-12 (|HasCategory| (-2 (|:| -2239 |#1|) (|:| -2904 |#2|)) (QUOTE (-1120))) (|HasCategory| (-2 (|:| -2239 |#1|) (|:| -2904 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2239) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2904) (|devaluate| |#2|)))))) (-3794 (|HasCategory| (-2 (|:| -2239 |#1|) (|:| -2904 |#2|)) (QUOTE (-1120))) (|HasCategory| |#2| (QUOTE (-1120)))) (-3794 (|HasCategory| (-2 (|:| -2239 |#1|) (|:| -2904 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2239 |#1|) (|:| -2904 |#2|)) (QUOTE (-1120))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1120)))) (-3794 (|HasCategory| (-2 (|:| -2239 |#1|) (|:| -2904 |#2|)) (QUOTE (-1120))) (|HasCategory| (-2 (|:| -2239 |#1|) (|:| -2904 |#2|)) (LIST (QUOTE -625) (QUOTE (-875)))) (|HasCategory| |#2| (QUOTE (-1120))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-875))))) (|HasCategory| (-2 (|:| -2239 |#1|) (|:| -2904 |#2|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#2| (QUOTE (-1120))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2239 |#1|) (|:| -2904 |#2|)) (QUOTE (-1120))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#2| (QUOTE (-1120))) (-3794 (|HasCategory| (-2 (|:| -2239 |#1|) (|:| -2904 |#2|)) (LIST (QUOTE -625) (QUOTE (-875)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-875))))) (-3794 (|HasCategory| (-2 (|:| -2239 |#1|) (|:| -2904 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-875)))) (|HasCategory| (-2 (|:| -2239 |#1|) (|:| -2904 |#2|)) (LIST (QUOTE -625) (QUOTE (-875)))) (|HasCategory| (-2 (|:| -2239 |#1|) (|:| -2904 |#2|)) (QUOTE (-102)))) +((-4464 . 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T)) +((-12 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4438 |#2|)) (QUOTE (-1121))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4438 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4300) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4438) (|devaluate| |#2|)))))) (-2758 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4438 |#2|)) (QUOTE (-1121))) (|HasCategory| |#2| (QUOTE (-1121)))) (-2758 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4438 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4438 |#2|)) (QUOTE (-1121))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1121)))) (-2758 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4438 |#2|)) (QUOTE (-1121))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4438 |#2|)) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4438 |#2|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4438 |#2|)) (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#2| (QUOTE (-1121))) (-2758 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4438 |#2|)) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-876))))) (-2758 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4438 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4438 |#2|)) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4438 |#2|)) (QUOTE (-102)))) (-306) ((|constructor| (NIL "ErrorFunctions implements error functions callable from the system interpreter. Typically,{} these functions would be called in user functions. The simple forms of the functions take one argument which is either a string (an error message) or a list of strings which all together make up a message. The list can contain formatting codes (see below). The more sophisticated versions takes two arguments where the first argument is the name of the function from which the error was invoked and the second argument is either a string or a list of strings,{} as above. When you use the one argument version in an interpreter function,{} the system will automatically insert the name of the function as the new first argument. Thus in the user interpreter function \\indented{2}{\\spad{f x == if x < 0 then error \"negative argument\" else x}} the call to error will actually be of the form \\indented{2}{\\spad{error(\"f\",\"negative argument\")}} because the interpreter will have created a new first argument. \\blankline Formatting codes: error messages may contain the following formatting codes (they should either start or end a string or else have blanks around them): \\indented{3}{\\spad{\\%l}\\space{6}start a new line} \\indented{3}{\\spad{\\%b}\\space{6}start printing in a bold font (where available)} \\indented{3}{\\spad{\\%d}\\space{6}stop\\space{2}printing in a bold font (where available)} \\indented{3}{\\spad{ \\%ceon}\\space{2}start centering message lines} \\indented{3}{\\spad{\\%ceoff}\\space{2}stop\\space{2}centering message lines} \\indented{3}{\\spad{\\%rjon}\\space{3}start displaying lines \"ragged left\"} \\indented{3}{\\spad{\\%rjoff}\\space{2}stop\\space{2}displaying lines \"ragged left\"} \\indented{3}{\\spad{\\%i}\\space{6}indent\\space{3}following lines 3 additional spaces} \\indented{3}{\\spad{\\%u}\\space{6}unindent following lines 3 additional spaces} \\indented{3}{\\spad{\\%xN}\\space{5}insert \\spad{N} blanks (eg,{} \\spad{\\%x10} inserts 10 blanks)} \\blankline")) (|error| (((|Exit|) (|String|) (|List| (|String|))) "\\spad{error(nam,lmsg)} displays error messages \\spad{lmsg} preceded by a message containing the name \\spad{nam} of the function in which the error is contained.") (((|Exit|) (|String|) (|String|)) "\\spad{error(nam,msg)} displays error message \\spad{msg} preceded by a message containing the name \\spad{nam} of the function in which the error is contained.") (((|Exit|) (|List| (|String|))) "\\spad{error(lmsg)} displays error message \\spad{lmsg} and terminates.") (((|Exit|) (|String|)) "\\spad{error(msg)} displays error message \\spad{msg} and terminates."))) NIL NIL -(-307 -2117 S) +(-307 -1959 S) ((|constructor| (NIL "This package allows a map from any expression space into any object to be lifted to a kernel over the expression set,{} using a given property of the operator of the kernel.")) (|map| ((|#2| (|Mapping| |#2| |#1|) (|String|) (|Kernel| |#1|)) "\\spad{map(f, p, k)} uses the property \\spad{p} of the operator of \\spad{k},{} in order to lift \\spad{f} and apply it to \\spad{k}."))) NIL NIL -(-308 E -2117) +(-308 E -1959) ((|constructor| (NIL "This package allows a mapping \\spad{E} \\spad{->} \\spad{F} to be lifted to a kernel over \\spad{E}; This lifting can fail if the operator of the kernel cannot be applied in \\spad{F}; Do not use this package with \\spad{E} = \\spad{F},{} since this may drop some properties of the operators.")) (|map| ((|#2| (|Mapping| |#2| |#1|) (|Kernel| |#1|)) "\\spad{map(f, k)} returns \\spad{g = op(f(a1),...,f(an))} where \\spad{k = op(a1,...,an)}."))) NIL NIL @@ -1175,7 +1175,7 @@ NIL (-311 S) ((|constructor| (NIL "An expression space is a set which is closed under certain operators.")) (|odd?| (((|Boolean|) $) "\\spad{odd? x} is \\spad{true} if \\spad{x} is an odd integer.")) (|even?| (((|Boolean|) $) "\\spad{even? x} is \\spad{true} if \\spad{x} is an even integer.")) (|definingPolynomial| (($ $) "\\spad{definingPolynomial(x)} returns an expression \\spad{p} such that \\spad{p(x) = 0}.")) (|minPoly| (((|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{minPoly(k)} returns \\spad{p} such that \\spad{p(k) = 0}.")) (|eval| (($ $ (|BasicOperator|) (|Mapping| $ $)) "\\spad{eval(x, s, f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|BasicOperator|) (|Mapping| $ (|List| $))) "\\spad{eval(x, s, f)} replaces every \\spad{s(a1,..,am)} in \\spad{x} by \\spad{f(a1,..,am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|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| $ $)) "\\spad{eval(x, s, f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ (|List| $))) "\\spad{eval(x, s, f)} replaces every \\spad{s(a1,..,am)} in \\spad{x} by \\spad{f(a1,..,am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|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, s)} tests if \\spad{x} does not contain any operator whose name is \\spad{s}.") (((|Boolean|) $ $) "\\spad{freeOf?(x, y)} tests if \\spad{x} does not contain any occurrence of \\spad{y},{} where \\spad{y} is a single kernel.")) (|map| (($ (|Mapping| $ $) (|Kernel| $)) "\\spad{map(f, k)} returns \\spad{op(f(x1),...,f(xn))} where \\spad{k = op(x1,...,xn)}.")) (|kernel| (($ (|BasicOperator|) (|List| $)) "\\spad{kernel(op, [f1,...,fn])} constructs \\spad{op(f1,...,fn)} without evaluating it.") (($ (|BasicOperator|) $) "\\spad{kernel(op, x)} constructs \\spad{op}(\\spad{x}) without evaluating it.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(x, s)} tests if \\spad{x} is a kernel and is the name of its operator is \\spad{s}.") (((|Boolean|) $ (|BasicOperator|)) "\\spad{is?(x, op)} tests if \\spad{x} is a kernel and is its operator is op.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} tests if \\% accepts \\spad{op} as applicable to its elements.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\%.")) (|operators| (((|List| (|BasicOperator|)) $) "\\spad{operators(f)} returns all the basic operators appearing in \\spad{f},{} no matter what their levels are.")) (|tower| (((|List| (|Kernel| $)) $) "\\spad{tower(f)} returns all the kernels appearing in \\spad{f},{} no matter what their levels are.")) (|kernels| (((|List| (|Kernel| $)) $) "\\spad{kernels(f)} returns the list of all the top-level kernels appearing in \\spad{f},{} but not the ones appearing in the arguments of the top-level kernels.")) (|mainKernel| (((|Union| (|Kernel| $) "failed") $) "\\spad{mainKernel(f)} returns a kernel of \\spad{f} with maximum nesting level,{} or if \\spad{f} has no kernels (\\spadignore{i.e.} \\spad{f} is a constant).")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(f)} returns the highest nesting level appearing in \\spad{f}. Constants have height 0. Symbols have height 1. For any operator op and expressions \\spad{f1},{}...,{}\\spad{fn},{} \\spad{op(f1,...,fn)} has height equal to \\spad{1 + max(height(f1),...,height(fn))}.")) (|distribute| (($ $ $) "\\spad{distribute(f, g)} expands all the kernels in \\spad{f} that contain \\spad{g} in their arguments and that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or a \\spadfunFrom{paren}{ExpressionSpace} expression.") (($ $) "\\spad{distribute(f)} expands all the kernels in \\spad{f} that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or \\spadfunFrom{paren}{ExpressionSpace} expression.")) (|paren| (($ (|List| $)) "\\spad{paren([f1,...,fn])} returns \\spad{(f1,...,fn)}. This prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(paren [x, 2])} returns the formal kernel \\spad{atan((x, 2))}.") (($ $) "\\spad{paren(f)} returns (\\spad{f}). This prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(paren 1)} returns the formal kernel log((1)).")) (|box| (($ (|List| $)) "\\spad{box([f1,...,fn])} returns \\spad{(f1,...,fn)} with a 'box' around them that prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(box [x, 2])} returns the formal kernel \\spad{atan(x, 2)}.") (($ $) "\\spad{box(f)} returns \\spad{f} with a 'box' around it that prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(box 1)} returns the formal kernel log(1).")) (|subst| (($ $ (|List| (|Kernel| $)) (|List| $)) "\\spad{subst(f, [k1...,kn], [g1,...,gn])} replaces the kernels \\spad{k1},{}...,{}\\spad{kn} by \\spad{g1},{}...,{}\\spad{gn} formally in \\spad{f}.") (($ $ (|List| (|Equation| $))) "\\spad{subst(f, [k1 = g1,...,kn = gn])} replaces the kernels \\spad{k1},{}...,{}\\spad{kn} by \\spad{g1},{}...,{}\\spad{gn} formally in \\spad{f}.") (($ $ (|Equation| $)) "\\spad{subst(f, k = g)} replaces the kernel \\spad{k} by \\spad{g} formally in \\spad{f}.")) (|elt| (($ (|BasicOperator|) (|List| $)) "\\spad{elt(op,[x1,...,xn])} or \\spad{op}([\\spad{x1},{}...,{}\\spad{xn}]) applies the \\spad{n}-ary operator \\spad{op} to \\spad{x1},{}...,{}\\spad{xn}.") (($ (|BasicOperator|) $ $ $ $) "\\spad{elt(op,x,y,z,t)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z},{} \\spad{t}) applies the 4-ary operator \\spad{op} to \\spad{x},{} \\spad{y},{} \\spad{z} and \\spad{t}.") (($ (|BasicOperator|) $ $ $) "\\spad{elt(op,x,y,z)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z}) applies the ternary operator \\spad{op} to \\spad{x},{} \\spad{y} and \\spad{z}.") (($ (|BasicOperator|) $ $) "\\spad{elt(op,x,y)} or \\spad{op}(\\spad{x},{} \\spad{y}) applies the binary operator \\spad{op} to \\spad{x} and \\spad{y}.") (($ (|BasicOperator|) $) "\\spad{elt(op,x)} or \\spad{op}(\\spad{x}) applies the unary operator \\spad{op} to \\spad{x}."))) NIL -((|HasCategory| |#1| (LIST (QUOTE -1058) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-1069)))) +((|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-1070)))) (-312) ((|constructor| (NIL "An expression space is a set which is closed under certain operators.")) (|odd?| (((|Boolean|) $) "\\spad{odd? x} is \\spad{true} if \\spad{x} is an odd integer.")) (|even?| (((|Boolean|) $) "\\spad{even? x} is \\spad{true} if \\spad{x} is an even integer.")) (|definingPolynomial| (($ $) "\\spad{definingPolynomial(x)} returns an expression \\spad{p} such that \\spad{p(x) = 0}.")) (|minPoly| (((|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{minPoly(k)} returns \\spad{p} such that \\spad{p(k) = 0}.")) (|eval| (($ $ (|BasicOperator|) (|Mapping| $ $)) "\\spad{eval(x, s, f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|BasicOperator|) (|Mapping| $ (|List| $))) "\\spad{eval(x, s, f)} replaces every \\spad{s(a1,..,am)} in \\spad{x} by \\spad{f(a1,..,am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|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| $ $)) "\\spad{eval(x, s, f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ (|List| $))) "\\spad{eval(x, s, f)} replaces every \\spad{s(a1,..,am)} in \\spad{x} by \\spad{f(a1,..,am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|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, s)} tests if \\spad{x} does not contain any operator whose name is \\spad{s}.") (((|Boolean|) $ $) "\\spad{freeOf?(x, y)} tests if \\spad{x} does not contain any occurrence of \\spad{y},{} where \\spad{y} is a single kernel.")) (|map| (($ (|Mapping| $ $) (|Kernel| $)) "\\spad{map(f, k)} returns \\spad{op(f(x1),...,f(xn))} where \\spad{k = op(x1,...,xn)}.")) (|kernel| (($ (|BasicOperator|) (|List| $)) "\\spad{kernel(op, [f1,...,fn])} constructs \\spad{op(f1,...,fn)} without evaluating it.") (($ (|BasicOperator|) $) "\\spad{kernel(op, x)} constructs \\spad{op}(\\spad{x}) without evaluating it.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(x, s)} tests if \\spad{x} is a kernel and is the name of its operator is \\spad{s}.") (((|Boolean|) $ (|BasicOperator|)) "\\spad{is?(x, op)} tests if \\spad{x} is a kernel and is its operator is op.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} tests if \\% accepts \\spad{op} as applicable to its elements.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\%.")) (|operators| (((|List| (|BasicOperator|)) $) "\\spad{operators(f)} returns all the basic operators appearing in \\spad{f},{} no matter what their levels are.")) (|tower| (((|List| (|Kernel| $)) $) "\\spad{tower(f)} returns all the kernels appearing in \\spad{f},{} no matter what their levels are.")) (|kernels| (((|List| (|Kernel| $)) $) "\\spad{kernels(f)} returns the list of all the top-level kernels appearing in \\spad{f},{} but not the ones appearing in the arguments of the top-level kernels.")) (|mainKernel| (((|Union| (|Kernel| $) "failed") $) "\\spad{mainKernel(f)} returns a kernel of \\spad{f} with maximum nesting level,{} or if \\spad{f} has no kernels (\\spadignore{i.e.} \\spad{f} is a constant).")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(f)} returns the highest nesting level appearing in \\spad{f}. Constants have height 0. Symbols have height 1. For any operator op and expressions \\spad{f1},{}...,{}\\spad{fn},{} \\spad{op(f1,...,fn)} has height equal to \\spad{1 + max(height(f1),...,height(fn))}.")) (|distribute| (($ $ $) "\\spad{distribute(f, g)} expands all the kernels in \\spad{f} that contain \\spad{g} in their arguments and that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or a \\spadfunFrom{paren}{ExpressionSpace} expression.") (($ $) "\\spad{distribute(f)} expands all the kernels in \\spad{f} that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or \\spadfunFrom{paren}{ExpressionSpace} expression.")) (|paren| (($ (|List| $)) "\\spad{paren([f1,...,fn])} returns \\spad{(f1,...,fn)}. This prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(paren [x, 2])} returns the formal kernel \\spad{atan((x, 2))}.") (($ $) "\\spad{paren(f)} returns (\\spad{f}). This prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(paren 1)} returns the formal kernel log((1)).")) (|box| (($ (|List| $)) "\\spad{box([f1,...,fn])} returns \\spad{(f1,...,fn)} with a 'box' around them that prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(box [x, 2])} returns the formal kernel \\spad{atan(x, 2)}.") (($ $) "\\spad{box(f)} returns \\spad{f} with a 'box' around it that prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(box 1)} returns the formal kernel log(1).")) (|subst| (($ $ (|List| (|Kernel| $)) (|List| $)) "\\spad{subst(f, [k1...,kn], [g1,...,gn])} replaces the kernels \\spad{k1},{}...,{}\\spad{kn} by \\spad{g1},{}...,{}\\spad{gn} formally in \\spad{f}.") (($ $ (|List| (|Equation| $))) "\\spad{subst(f, [k1 = g1,...,kn = gn])} replaces the kernels \\spad{k1},{}...,{}\\spad{kn} by \\spad{g1},{}...,{}\\spad{gn} formally in \\spad{f}.") (($ $ (|Equation| $)) "\\spad{subst(f, k = g)} replaces the kernel \\spad{k} by \\spad{g} formally in \\spad{f}.")) (|elt| (($ (|BasicOperator|) (|List| $)) "\\spad{elt(op,[x1,...,xn])} or \\spad{op}([\\spad{x1},{}...,{}\\spad{xn}]) applies the \\spad{n}-ary operator \\spad{op} to \\spad{x1},{}...,{}\\spad{xn}.") (($ (|BasicOperator|) $ $ $ $) "\\spad{elt(op,x,y,z,t)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z},{} \\spad{t}) applies the 4-ary operator \\spad{op} to \\spad{x},{} \\spad{y},{} \\spad{z} and \\spad{t}.") (($ (|BasicOperator|) $ $ $) "\\spad{elt(op,x,y,z)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z}) applies the ternary operator \\spad{op} to \\spad{x},{} \\spad{y} and \\spad{z}.") (($ (|BasicOperator|) $ $) "\\spad{elt(op,x,y)} or \\spad{op}(\\spad{x},{} \\spad{y}) applies the binary operator \\spad{op} to \\spad{x} and \\spad{y}.") (($ (|BasicOperator|) $) "\\spad{elt(op,x)} or \\spad{op}(\\spad{x}) applies the unary operator \\spad{op} to \\spad{x}."))) NIL @@ -1198,7 +1198,7 @@ NIL NIL (-317) ((|constructor| (NIL "A constructive euclidean domain,{} \\spadignore{i.e.} one can divide producing a quotient and a remainder where the remainder is either zero or is smaller (\\spadfun{euclideanSize}) than the divisor. \\blankline Conditional attributes: \\indented{2}{multiplicativeValuation\\tab{25}\\spad{Size(a*b)=Size(a)*Size(b)}} \\indented{2}{additiveValuation\\tab{25}\\spad{Size(a*b)=Size(a)+Size(b)}}")) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) "\\spad{multiEuclidean([f1,...,fn],z)} returns a list of coefficients \\spad{[a1, ..., an]} such that \\spad{ z / prod fi = sum aj/fj}. If no such list of coefficients exists,{} \"failed\" is returned.")) (|extendedEuclidean| (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) "\\spad{extendedEuclidean(x,y,z)} either returns a record rec where \\spad{rec.coef1*x+rec.coef2*y=z} or returns \"failed\" if \\spad{z} cannot be expressed as a linear combination of \\spad{x} and \\spad{y}.") (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{extendedEuclidean(x,y)} returns a record rec where \\spad{rec.coef1*x+rec.coef2*y = rec.generator} and rec.generator is a \\spad{gcd} of \\spad{x} and \\spad{y}. The \\spad{gcd} is unique only up to associates if \\spadatt{canonicalUnitNormal} is not asserted. \\spadfun{principalIdeal} provides a version of this operation which accepts an arbitrary length list of arguments.")) (|rem| (($ $ $) "\\spad{x rem y} is the same as \\spad{divide(x,y).remainder}. See \\spadfunFrom{divide}{EuclideanDomain}.")) (|quo| (($ $ $) "\\spad{x quo y} is the same as \\spad{divide(x,y).quotient}. See \\spadfunFrom{divide}{EuclideanDomain}.")) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{divide(x,y)} divides \\spad{x} by \\spad{y} producing a record containing a \\spad{quotient} and \\spad{remainder},{} where the remainder is smaller (see \\spadfunFrom{sizeLess?}{EuclideanDomain}) than the divisor \\spad{y}.")) (|euclideanSize| (((|NonNegativeInteger|) $) "\\spad{euclideanSize(x)} returns the euclidean size of the element \\spad{x}. Error: if \\spad{x} is zero.")) (|sizeLess?| (((|Boolean|) $ $) "\\spad{sizeLess?(x,y)} tests whether \\spad{x} is strictly smaller than \\spad{y} with respect to the \\spadfunFrom{euclideanSize}{EuclideanDomain}."))) -((-4456 . T) ((-4465 "*") . T) (-4457 . T) (-4458 . T) (-4460 . T)) +((-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-318 S R) ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation\\spad{''} substitutions.")) (|eval| (($ $ (|List| (|Equation| |#2|))) "\\spad{eval(f, [x1 = v1,...,xn = vn])} replaces \\spad{xi} by \\spad{vi} in \\spad{f}.") (($ $ (|Equation| |#2|)) "\\spad{eval(f,x = v)} replaces \\spad{x} by \\spad{v} in \\spad{f}."))) @@ -1208,7 +1208,7 @@ NIL ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation\\spad{''} substitutions.")) (|eval| (($ $ (|List| (|Equation| |#1|))) "\\spad{eval(f, [x1 = v1,...,xn = vn])} replaces \\spad{xi} by \\spad{vi} in \\spad{f}.") (($ $ (|Equation| |#1|)) "\\spad{eval(f,x = v)} replaces \\spad{x} by \\spad{v} in \\spad{f}."))) NIL NIL -(-320 -2117) +(-320 -1959) ((|constructor| (NIL "This package is to be used in conjuction with \\indented{12}{the CycleIndicators package. It provides an evaluation} \\indented{12}{function for SymmetricPolynomials.}")) (|eval| ((|#1| (|Mapping| |#1| (|Integer|)) (|SymmetricPolynomial| (|Fraction| (|Integer|)))) "\\spad{eval(f,s)} evaluates the cycle index \\spad{s} by applying \\indented{1}{the function \\spad{f} to each integer in a monomial partition,{}} \\indented{1}{forms their product and sums the results over all monomials.}"))) NIL NIL @@ -1222,8 +1222,8 @@ NIL NIL (-323 R FE |var| |cen|) ((|constructor| (NIL "UnivariatePuiseuxSeriesWithExponentialSingularity is a domain used to represent essential singularities of functions. Objects in this domain are quotients of sums,{} where each term in the sum is a univariate Puiseux series times the exponential of a univariate Puiseux series.")) (|coerce| (($ (|UnivariatePuiseuxSeries| |#2| |#3| |#4|)) "\\spad{coerce(f)} converts a \\spadtype{UnivariatePuiseuxSeries} to an \\spadtype{ExponentialExpansion}.")) (|limitPlus| (((|Union| (|OrderedCompletion| |#2|) "failed") $) "\\spad{limitPlus(f(var))} returns \\spad{limit(var -> a+,f(var))}."))) -((-4455 . T) (-4461 . T) (-4456 . T) ((-4465 "*") . T) (-4457 . T) (-4458 . T) (-4460 . T)) -((|HasCategory| (-1273 |#1| |#2| |#3| |#4|) (QUOTE (-927))) (|HasCategory| (-1273 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1058) (QUOTE (-1196)))) (|HasCategory| (-1273 |#1| |#2| |#3| |#4|) (QUOTE (-146))) (|HasCategory| (-1273 |#1| |#2| |#3| |#4|) (QUOTE (-148))) (|HasCategory| (-1273 |#1| |#2| |#3| |#4|) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-1273 |#1| |#2| |#3| |#4|) (QUOTE (-1042))) (|HasCategory| (-1273 |#1| |#2| |#3| |#4|) (QUOTE (-832))) (|HasCategory| (-1273 |#1| |#2| |#3| |#4|) (QUOTE (-861))) (-3794 (|HasCategory| (-1273 |#1| |#2| |#3| |#4|) (QUOTE (-832))) (|HasCategory| (-1273 |#1| |#2| |#3| |#4|) (QUOTE (-861)))) (|HasCategory| (-1273 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1058) (QUOTE (-576)))) (|HasCategory| (-1273 |#1| |#2| |#3| |#4|) (QUOTE (-1172))) (|HasCategory| (-1273 |#1| |#2| |#3| |#4|) (LIST (QUOTE -900) (QUOTE (-390)))) (|HasCategory| (-1273 |#1| |#2| |#3| |#4|) (LIST (QUOTE -900) (QUOTE (-576)))) (|HasCategory| (-1273 |#1| |#2| |#3| |#4|) (LIST (QUOTE -626) (LIST (QUOTE -906) (QUOTE (-390))))) (|HasCategory| (-1273 |#1| |#2| |#3| |#4|) (LIST (QUOTE -626) (LIST (QUOTE -906) (QUOTE (-576))))) (|HasCategory| (-1273 |#1| |#2| |#3| |#4|) (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| (-1273 |#1| |#2| |#3| |#4|) (QUOTE (-237))) (|HasCategory| (-1273 |#1| |#2| |#3| |#4|) (LIST (QUOTE -918) (QUOTE (-1196)))) (|HasCategory| (-1273 |#1| |#2| |#3| |#4|) (QUOTE (-238))) (|HasCategory| (-1273 |#1| |#2| |#3| |#4|) (LIST (QUOTE -916) (QUOTE (-1196)))) (|HasCategory| (-1273 |#1| |#2| |#3| |#4|) (LIST (QUOTE -526) (QUOTE (-1196)) (LIST (QUOTE -1273) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1273 |#1| |#2| |#3| |#4|) (LIST (QUOTE -319) (LIST (QUOTE -1273) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1273 |#1| |#2| |#3| |#4|) (LIST (QUOTE -296) (LIST (QUOTE -1273) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1273) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1273 |#1| |#2| |#3| |#4|) (QUOTE (-317))) (|HasCategory| (-1273 |#1| |#2| |#3| |#4|) (QUOTE (-557))) (-12 (|HasCategory| (-1273 |#1| |#2| |#3| |#4|) (QUOTE (-927))) (|HasCategory| $ (QUOTE (-146)))) (-3794 (|HasCategory| (-1273 |#1| |#2| |#3| |#4|) (QUOTE (-146))) (-12 (|HasCategory| (-1273 |#1| |#2| |#3| |#4|) (QUOTE (-927))) (|HasCategory| $ (QUOTE (-146)))))) +((-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) +((|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (QUOTE (-928))) (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1059) (QUOTE (-1197)))) (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (QUOTE (-146))) (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (QUOTE (-148))) (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (QUOTE (-1043))) (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (QUOTE (-832))) (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (QUOTE (-861))) (-2758 (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (QUOTE (-832))) (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (QUOTE (-861)))) (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (QUOTE (-1173))) (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (LIST (QUOTE -901) (QUOTE (-390)))) (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (LIST (QUOTE -901) (QUOTE (-576)))) (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390))))) (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576))))) (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (QUOTE (-237))) (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (LIST (QUOTE -919) (QUOTE (-1197)))) (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (QUOTE (-238))) (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (LIST (QUOTE -526) (QUOTE (-1197)) (LIST (QUOTE -1274) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (LIST (QUOTE -319) (LIST (QUOTE -1274) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (LIST (QUOTE -296) (LIST (QUOTE -1274) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1274) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (QUOTE (-317))) (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (QUOTE (-557))) (-12 (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (QUOTE (-928))) (|HasCategory| $ (QUOTE (-146)))) (-2758 (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (QUOTE (-146))) (-12 (|HasCategory| (-1274 |#1| |#2| |#3| |#4|) (QUOTE (-928))) (|HasCategory| $ (QUOTE (-146)))))) (-324 R S) ((|constructor| (NIL "Lifting of maps to Expressions. Date Created: 16 Jan 1989 Date Last Updated: 22 Jan 1990")) (|map| (((|Expression| |#2|) (|Mapping| |#2| |#1|) (|Expression| |#1|)) "\\spad{map(f, e)} applies \\spad{f} to all the constants appearing in \\spad{e}."))) NIL @@ -1234,9 +1234,9 @@ NIL NIL (-326 R) ((|constructor| (NIL "Expressions involving symbolic functions.")) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{squareFreePolynomial(p)} \\undocumented{}")) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorPolynomial(p)} \\undocumented{}")) (|simplifyPower| (($ $ (|Integer|)) "simplifyPower?(\\spad{f},{}\\spad{n}) \\undocumented{}")) (|number?| (((|Boolean|) $) "\\spad{number?(f)} tests if \\spad{f} is rational")) (|reduce| (($ $) "\\spad{reduce(f)} simplifies all the unreduced algebraic quantities present in \\spad{f} by applying their defining relations."))) -((-4460 -3794 (-12 (|has| |#1| (-568)) (-3794 (|has| |#1| (-1069)) (|has| |#1| (-485)))) (|has| |#1| (-1069)) (|has| |#1| (-485))) (-4458 |has| |#1| (-174)) (-4457 |has| |#1| (-174)) ((-4465 "*") |has| |#1| (-568)) (-4456 |has| |#1| (-568)) (-4461 |has| |#1| (-568)) (-4455 |has| |#1| (-568))) -((-3794 (|HasCategory| |#1| (LIST (QUOTE -1058) (LIST (QUOTE -419) (QUOTE (-576))))) (-12 (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (LIST (QUOTE -1058) (QUOTE (-576)))))) (|HasCategory| |#1| (QUOTE (-568))) (-3794 (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-1069)))) (|HasCategory| |#1| (QUOTE (-21))) (-3794 (|HasCategory| |#1| (LIST (QUOTE -1058) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-3794 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-1069)))) (|HasCategory| |#1| (QUOTE (-1069))) (-3794 (-12 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576))))) (-12 (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576))))) (-12 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576))))) (-12 (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (LIST (QUOTE -651) 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(|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-1070)))) (-2758 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-1070)))) (-2758 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-1070)))) (-12 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568)))) (-2758 (|HasCategory| |#1| (QUOTE (-485))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasCategory| |#1| (QUOTE (-1070))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576))))) (-2758 (|HasCategory| |#1| (QUOTE (-21))) (-12 (|HasCategory| |#1| (QUOTE (-1070))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))))) (-2758 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1070))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-1133)))) (-2758 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1070))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))))) (-2758 (|HasCategory| |#1| (QUOTE (-485))) (|HasCategory| |#1| (QUOTE (-1070)))) (-2758 (-12 (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576)))))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1133))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| $ (QUOTE (-1070))) (|HasCategory| $ (LIST (QUOTE -1059) (QUOTE (-576))))) +(-327 R -1959) ((|constructor| (NIL "Taylor series solutions of explicit ODE\\spad{'s}.")) (|seriesSolve| (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq, y, x = a, [b0,...,bn])} is equivalent to \\spad{seriesSolve(eq = 0, y, x = a, [b0,...,b(n-1)])}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq, y, x = a, y a = b)} is equivalent to \\spad{seriesSolve(eq=0, y, x=a, y a = b)}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq, y, x = a, b)} is equivalent to \\spad{seriesSolve(eq = 0, y, x = a, y a = b)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq,y, x=a, b)} is equivalent to \\spad{seriesSolve(eq, y, x=a, y a = b)}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x = a,[y1 a = b1,..., yn a = bn])} is equivalent to \\spad{seriesSolve([eq1=0,...,eqn=0], [y1,...,yn], x = a, [y1 a = b1,..., yn a = bn])}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x=a, [b1,...,bn])} is equivalent to \\spad{seriesSolve([eq1=0,...,eqn=0], [y1,...,yn], x=a, [b1,...,bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x=a, [b1,...,bn])} is equivalent to \\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x = a, [y1 a = b1,..., yn a = bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,...,eqn],[y1,...,yn],x = a,[y1 a = b1,...,yn a = bn])} returns a taylor series solution of \\spad{[eq1,...,eqn]} around \\spad{x = a} with initial conditions \\spad{yi(a) = bi}. Note: eqi must be of the form \\spad{fi(x, y1 x, y2 x,..., yn x) y1'(x) + gi(x, y1 x, y2 x,..., yn x) = h(x, y1 x, y2 x,..., yn x)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq,y,x=a,[b0,...,b(n-1)])} returns a Taylor series solution of \\spad{eq} around \\spad{x = a} with initial conditions \\spad{y(a) = b0},{} \\spad{y'(a) = b1},{} \\spad{y''(a) = b2},{} ...,{}\\spad{y(n-1)(a) = b(n-1)} \\spad{eq} must be of the form \\spad{f(x, y x, y'(x),..., y(n-1)(x)) y(n)(x) + g(x,y x,y'(x),...,y(n-1)(x)) = h(x,y x, y'(x),..., y(n-1)(x))}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq,y,x=a, y a = b)} returns a Taylor series solution of \\spad{eq} around \\spad{x} = a with initial condition \\spad{y(a) = b}. Note: \\spad{eq} must be of the form \\spad{f(x, y x) y'(x) + g(x, y x) = h(x, y x)}."))) NIL NIL @@ -1246,8 +1246,8 @@ NIL NIL (-329 FE |var| |cen|) ((|constructor| (NIL "ExponentialOfUnivariatePuiseuxSeries is a domain used to represent essential singularities of functions. An object in this domain is a function of the form \\spad{exp(f(x))},{} where \\spad{f(x)} is a Puiseux series with no terms of non-negative degree. Objects are ordered according to order of singularity,{} with functions which tend more rapidly to zero or infinity considered to be larger. Thus,{} if \\spad{order(f(x)) < order(g(x))},{} \\spadignore{i.e.} the first non-zero term of \\spad{f(x)} has lower degree than the first non-zero term of \\spad{g(x)},{} then \\spad{exp(f(x)) > exp(g(x))}. If \\spad{order(f(x)) = order(g(x))},{} then the ordering is essentially random. This domain is used in computing limits involving functions with essential singularities.")) (|exponentialOrder| (((|Fraction| (|Integer|)) $) "\\spad{exponentialOrder(exp(c * x **(-n) + ...))} returns \\spad{-n}. exponentialOrder(0) returns \\spad{0}.")) (|exponent| (((|UnivariatePuiseuxSeries| |#1| |#2| |#3|) $) "\\spad{exponent(exp(f(x)))} returns \\spad{f(x)}")) (|exponential| (($ (|UnivariatePuiseuxSeries| |#1| |#2| |#3|)) "\\spad{exponential(f(x))} returns \\spad{exp(f(x))}. Note: the function does NOT check that \\spad{f(x)} has no non-negative terms."))) -(((-4465 "*") |has| |#1| (-174)) (-4456 |has| |#1| (-568)) (-4461 |has| |#1| (-374)) (-4455 |has| |#1| (-374)) (-4457 . T) (-4458 . T) (-4460 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-3794 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -916) (QUOTE (-1196)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|)))) (|HasCategory| (-419 (-576)) (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-374))) (-3794 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-3794 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasSignature| |#1| (LIST (QUOTE -4112) (LIST (|devaluate| |#1|) (QUOTE (-1196)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (-3794 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-977))) (|HasCategory| |#1| (QUOTE (-1222))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasSignature| |#1| (LIST (QUOTE -2944) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1196))))) (|HasSignature| |#1| (LIST (QUOTE -1582) (LIST (LIST (QUOTE -656) (QUOTE (-1196))) (|devaluate| |#1|))))))) +(((-4466 "*") |has| |#1| (-174)) (-4457 |has| |#1| (-568)) (-4462 |has| |#1| (-374)) (-4456 |has| |#1| (-374)) (-4458 . T) (-4459 . T) (-4461 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-2758 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|)))) (|HasCategory| (-419 (-576)) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-374))) (-2758 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-2758 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasSignature| |#1| (LIST (QUOTE -3569) (LIST (|devaluate| |#1|) (QUOTE (-1197)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (-2758 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-978))) (|HasCategory| |#1| (QUOTE (-1223))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasSignature| |#1| (LIST (QUOTE -3441) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1197))))) (|HasSignature| |#1| (LIST (QUOTE -1966) (LIST (LIST (QUOTE -656) (QUOTE (-1197))) (|devaluate| |#1|))))))) (-330 M) ((|constructor| (NIL "computes various functions on factored arguments.")) (|log| (((|List| (|Record| (|:| |coef| (|NonNegativeInteger|)) (|:| |logand| |#1|))) (|Factored| |#1|)) "\\spad{log(f)} returns \\spad{[(a1,b1),...,(am,bm)]} such that the logarithm of \\spad{f} is equal to \\spad{a1*log(b1) + ... + am*log(bm)}.")) (|nthRoot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#1|) (|:| |radicand| (|List| |#1|))) (|Factored| |#1|) (|NonNegativeInteger|)) "\\spad{nthRoot(f, n)} returns \\spad{(p, r, [r1,...,rm])} such that the \\spad{n}th-root of \\spad{f} is equal to \\spad{r * \\spad{p}th-root(r1 * ... * rm)},{} where \\spad{r1},{}...,{}\\spad{rm} are distinct factors of \\spad{f},{} each of which has an exponent smaller than \\spad{p} in \\spad{f}."))) NIL @@ -1258,7 +1258,7 @@ NIL NIL (-332 S) ((|constructor| (NIL "The free abelian group on a set \\spad{S} is the monoid of finite sums of the form \\spad{reduce(+,[ni * si])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are integers. The operation is commutative."))) -((-4458 . T) (-4457 . T)) +((-4459 . T) (-4458 . T)) ((|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| (-576) (QUOTE (-804)))) (-333 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 \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are in a given abelian monoid. The operation is commutative.")) (|highCommonTerms| (($ $ $) "\\spad{highCommonTerms(e1 a1 + ... + en an, f1 b1 + ... + fm bm)} returns \\indented{2}{\\spad{reduce(+,[max(ei, fi) ci])}} where \\spad{ci} ranges in the intersection of \\spad{{a1,...,an}} and \\spad{{b1,...,bm}}.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f, e1 a1 +...+ en an)} returns \\spad{e1 f(a1) +...+ en f(an)}.")) (|mapCoef| (($ (|Mapping| |#2| |#2|) $) "\\spad{mapCoef(f, e1 a1 +...+ en an)} returns \\spad{f(e1) a1 +...+ f(en) an}.")) (|coefficient| ((|#2| |#1| $) "\\spad{coefficient(s, e1 a1 + ... + en an)} returns \\spad{ei} such that \\spad{ai} = \\spad{s},{} or 0 if \\spad{s} is not one of the \\spad{ai}\\spad{'s}.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(x, n)} returns the factor of the n^th term of \\spad{x}.")) (|nthCoef| ((|#2| $ (|Integer|)) "\\spad{nthCoef(x, n)} returns the coefficient of the n^th term of \\spad{x}.")) (|terms| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| |#2|))) $) "\\spad{terms(e1 a1 + ... + en an)} returns \\spad{[[a1, e1],...,[an, en]]}.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(x)} returns the number of terms in \\spad{x}. mapGen(\\spad{f},{} a1\\spad{\\^}e1 ... an\\spad{\\^}en) returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (* (($ |#2| |#1|) "\\spad{e * s} returns \\spad{e} times \\spad{s}.")) (+ (($ |#1| $) "\\spad{s + x} returns the sum of \\spad{s} and \\spad{x}."))) @@ -1274,19 +1274,19 @@ NIL ((|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-174)))) (-336 R E) ((|constructor| (NIL "This category is similar to AbelianMonoidRing,{} except that the sum is assumed to be finite. It is a useful model for polynomials,{} but is somewhat more general.")) (|primitivePart| (($ $) "\\spad{primitivePart(p)} returns the unit normalized form of polynomial \\spad{p} divided by the content of \\spad{p}.")) (|content| ((|#1| $) "\\spad{content(p)} gives the \\spad{gcd} of the coefficients of polynomial \\spad{p}.")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(p,r)} returns the exact quotient of polynomial \\spad{p} by \\spad{r},{} or \"failed\" if none exists.")) (|binomThmExpt| (($ $ $ (|NonNegativeInteger|)) "\\spad{binomThmExpt(p,q,n)} returns \\spad{(x+y)^n} by means of the binomial theorem trick.")) (|pomopo!| (($ $ |#1| |#2| $) "\\spad{pomopo!(p1,r,e,p2)} returns \\spad{p1 + monomial(e,r) * p2} and may use \\spad{p1} as workspace. The constaant \\spad{r} is assumed to be nonzero.")) (|mapExponents| (($ (|Mapping| |#2| |#2|) $) "\\spad{mapExponents(fn,u)} maps function \\spad{fn} onto the exponents of the non-zero monomials of polynomial \\spad{u}.")) (|minimumDegree| ((|#2| $) "\\spad{minimumDegree(p)} gives the least exponent of a non-zero term of polynomial \\spad{p}. Error: if applied to 0.")) (|numberOfMonomials| (((|NonNegativeInteger|) $) "\\spad{numberOfMonomials(p)} gives the number of non-zero monomials in polynomial \\spad{p}.")) (|coefficients| (((|List| |#1|) $) "\\spad{coefficients(p)} gives the list of non-zero coefficients of polynomial \\spad{p}.")) (|ground| ((|#1| $) "\\spad{ground(p)} retracts polynomial \\spad{p} to the coefficient ring.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(p)} tests if polynomial \\spad{p} is a member of the coefficient ring."))) -(((-4465 "*") |has| |#1| (-174)) (-4456 |has| |#1| (-568)) (-4457 . T) (-4458 . T) (-4460 . T)) +(((-4466 "*") |has| |#1| (-174)) (-4457 |has| |#1| (-568)) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-337 S) ((|constructor| (NIL "\\indented{1}{A FlexibleArray is the notion of an array intended to allow for growth} at the end only. Hence the following efficient operations \\indented{2}{\\spad{append(x,a)} meaning append item \\spad{x} at the end of the array \\spad{a}} \\indented{2}{\\spad{delete(a,n)} meaning delete the last item from the array \\spad{a}} Flexible arrays support the other operations inherited from \\spadtype{ExtensibleLinearAggregate}. However,{} these are not efficient. Flexible arrays combine the \\spad{O(1)} access time property of arrays with growing and shrinking at the end in \\spad{O(1)} (average) time. This is done by using an ordinary array which may have zero or more empty slots at the end. When the array becomes full it is copied into a new larger (50\\% larger) array. Conversely,{} when the array becomes less than 1/2 full,{} it is copied into a smaller array. Flexible arrays provide for an efficient implementation of many data structures in particular heaps,{} stacks and sets."))) -((-4464 . T) (-4463 . T)) -((-3794 (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1120))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-3794 (-12 (|HasCategory| |#1| (QUOTE (-1120))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-875))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-3794 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1120)))) (|HasCategory| |#1| (QUOTE (-861))) (-3794 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1120)))) (|HasCategory| (-576) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1120))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-875)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1120))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) -(-338 S -2117) +((-4465 . T) (-4464 . T)) +((-2758 (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2758 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2758 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| |#1| (QUOTE (-861))) (-2758 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| (-576) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) +(-338 S -1959) ((|constructor| (NIL "FiniteAlgebraicExtensionField {\\em F} is the category of fields which are finite algebraic extensions of the field {\\em F}. If {\\em F} is finite then any finite algebraic extension of {\\em F} is finite,{} too. Let {\\em K} be a finite algebraic extension of the finite field {\\em F}. The exponentiation of elements of {\\em K} defines a \\spad{Z}-module structure on the multiplicative group of {\\em K}. The additive group of {\\em K} becomes a module over the ring of polynomials over {\\em F} via the operation \\spadfun{linearAssociatedExp}(a:K,{}f:SparseUnivariatePolynomial \\spad{F}) which is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em K},{} {\\em c,d} from {\\em F} and {\\em f,g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\spad{\\$}SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)} where {\\em q=size()\\$F}. 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 {\\em g},{} such that the \\spadfun{linearAssociatedExp}(\\spad{b},{}\\spad{g}) equals {\\em a}. If there is no such polynomial {\\em g},{} then \\spadfun{linearAssociatedLog} fails.") (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{linearAssociatedLog(a)} returns a polynomial {\\em g},{} such that \\spadfun{linearAssociatedExp}(normalElement(),{}\\spad{g}) equals {\\em a}.")) (|linearAssociatedOrder| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{linearAssociatedOrder(a)} retruns the monic polynomial {\\em g} of least degree,{} such that \\spadfun{linearAssociatedExp}(a,{}\\spad{g}) is 0.")) (|linearAssociatedExp| (($ $ (|SparseUnivariatePolynomial| |#2|)) "\\spad{linearAssociatedExp(a,f)} is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em \\$},{} {\\em c,d} form {\\em F} and {\\em f,g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\spad{\\$}SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)},{} where {\\em q=size()\\$F}.")) (|generator| (($) "\\spad{generator()} returns a root of the defining polynomial. This element generates the field as an algebra over the ground field.")) (|normal?| (((|Boolean|) $) "\\spad{normal?(a)} tests whether the element \\spad{a} is normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i), 0 <= i <= extensionDegree()-1} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Implementation according to Lidl/Niederreiter: Theorem 2.39.")) (|normalElement| (($) "\\spad{normalElement()} returns a element,{} normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i), 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. At the first call,{} the element is computed by \\spadfunFrom{createNormalElement}{FiniteAlgebraicExtensionField} then cached in a global variable. On subsequent calls,{} the element is retrieved by referencing the global variable.")) (|createNormalElement| (($) "\\spad{createNormalElement()} computes a normal element over the ground field \\spad{F},{} that is,{} \\spad{a**(q**i), 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Reference: Such an element exists Lidl/Niederreiter: Theorem 2.35.")) (|trace| (($ $ (|PositiveInteger|)) "\\spad{trace(a,d)} computes the trace of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size \\spad{q}. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: \\spad{trace(a,d) = reduce(+,[a**(q**(d*i)) for i in 0..n/d])}.") ((|#2| $) "\\spad{trace(a)} computes the trace of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|norm| (($ $ (|PositiveInteger|)) "\\spad{norm(a,d)} computes the norm of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: norm(a,{}\\spad{d}) = reduce(*,{}[a**(\\spad{q**}(d*i)) for \\spad{i} in 0..\\spad{n/d}])") ((|#2| $) "\\spad{norm(a)} computes the norm of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|degree| (((|PositiveInteger|) $) "\\spad{degree(a)} returns the degree of the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|extensionDegree| (((|PositiveInteger|)) "\\spad{extensionDegree()} returns the degree of field extension.")) (|definingPolynomial| (((|SparseUnivariatePolynomial| |#2|)) "\\spad{definingPolynomial()} returns the polynomial used to define the field extension.")) (|minimalPolynomial| (((|SparseUnivariatePolynomial| $) $ (|PositiveInteger|)) "\\spad{minimalPolynomial(x,n)} computes the minimal polynomial of \\spad{x} over the field of extension degree \\spad{n} over the ground field \\spad{F}.") (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|represents| (($ (|Vector| |#2|)) "\\spad{represents([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $)) "\\spad{coordinates([v1,...,vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#2|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{F}-vectorspace basis.")) (|basis| (((|Vector| $) (|PositiveInteger|)) "\\spad{basis(n)} returns a fixed basis of a subfield of \\spad{\\$} as \\spad{F}-vectorspace.") (((|Vector| $)) "\\spad{basis()} returns a fixed basis of \\spad{\\$} as \\spad{F}-vectorspace."))) NIL ((|HasCategory| |#2| (QUOTE (-379)))) -(-339 -2117) +(-339 -1959) ((|constructor| (NIL "FiniteAlgebraicExtensionField {\\em F} is the category of fields which are finite algebraic extensions of the field {\\em F}. If {\\em F} is finite then any finite algebraic extension of {\\em F} is finite,{} too. Let {\\em K} be a finite algebraic extension of the finite field {\\em F}. The exponentiation of elements of {\\em K} defines a \\spad{Z}-module structure on the multiplicative group of {\\em K}. The additive group of {\\em K} becomes a module over the ring of polynomials over {\\em F} via the operation \\spadfun{linearAssociatedExp}(a:K,{}f:SparseUnivariatePolynomial \\spad{F}) which is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em K},{} {\\em c,d} from {\\em F} and {\\em f,g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\spad{\\$}SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)} where {\\em q=size()\\$F}. 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 {\\em g},{} such that the \\spadfun{linearAssociatedExp}(\\spad{b},{}\\spad{g}) equals {\\em a}. If there is no such polynomial {\\em g},{} then \\spadfun{linearAssociatedLog} fails.") (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{linearAssociatedLog(a)} returns a polynomial {\\em g},{} such that \\spadfun{linearAssociatedExp}(normalElement(),{}\\spad{g}) equals {\\em a}.")) (|linearAssociatedOrder| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{linearAssociatedOrder(a)} retruns the monic polynomial {\\em g} of least degree,{} such that \\spadfun{linearAssociatedExp}(a,{}\\spad{g}) is 0.")) (|linearAssociatedExp| (($ $ (|SparseUnivariatePolynomial| |#1|)) "\\spad{linearAssociatedExp(a,f)} is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em \\$},{} {\\em c,d} form {\\em F} and {\\em f,g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\spad{\\$}SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)},{} where {\\em q=size()\\$F}.")) (|generator| (($) "\\spad{generator()} returns a root of the defining polynomial. This element generates the field as an algebra over the ground field.")) (|normal?| (((|Boolean|) $) "\\spad{normal?(a)} tests whether the element \\spad{a} is normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i), 0 <= i <= extensionDegree()-1} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Implementation according to Lidl/Niederreiter: Theorem 2.39.")) (|normalElement| (($) "\\spad{normalElement()} returns a element,{} normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i), 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. At the first call,{} the element is computed by \\spadfunFrom{createNormalElement}{FiniteAlgebraicExtensionField} then cached in a global variable. On subsequent calls,{} the element is retrieved by referencing the global variable.")) (|createNormalElement| (($) "\\spad{createNormalElement()} computes a normal element over the ground field \\spad{F},{} that is,{} \\spad{a**(q**i), 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Reference: Such an element exists Lidl/Niederreiter: Theorem 2.35.")) (|trace| (($ $ (|PositiveInteger|)) "\\spad{trace(a,d)} computes the trace of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size \\spad{q}. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: \\spad{trace(a,d) = reduce(+,[a**(q**(d*i)) for i in 0..n/d])}.") ((|#1| $) "\\spad{trace(a)} computes the trace of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|norm| (($ $ (|PositiveInteger|)) "\\spad{norm(a,d)} computes the norm of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: norm(a,{}\\spad{d}) = reduce(*,{}[a**(\\spad{q**}(d*i)) for \\spad{i} in 0..\\spad{n/d}])") ((|#1| $) "\\spad{norm(a)} computes the norm of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|degree| (((|PositiveInteger|) $) "\\spad{degree(a)} returns the degree of the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|extensionDegree| (((|PositiveInteger|)) "\\spad{extensionDegree()} returns the degree of field extension.")) (|definingPolynomial| (((|SparseUnivariatePolynomial| |#1|)) "\\spad{definingPolynomial()} returns the polynomial used to define the field extension.")) (|minimalPolynomial| (((|SparseUnivariatePolynomial| $) $ (|PositiveInteger|)) "\\spad{minimalPolynomial(x,n)} computes the minimal polynomial of \\spad{x} over the field of extension degree \\spad{n} over the ground field \\spad{F}.") (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([v1,...,vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#1|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{F}-vectorspace basis.")) (|basis| (((|Vector| $) (|PositiveInteger|)) "\\spad{basis(n)} returns a fixed basis of a subfield of \\spad{\\$} as \\spad{F}-vectorspace.") (((|Vector| $)) "\\spad{basis()} returns a fixed basis of \\spad{\\$} as \\spad{F}-vectorspace."))) -((-4455 . T) (-4461 . T) (-4456 . T) ((-4465 "*") . T) (-4457 . T) (-4458 . T) (-4460 . T)) +((-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-340) ((|constructor| (NIL "This domain builds representations of program code segments for use with the FortranProgram domain.")) (|setLabelValue| (((|SingleInteger|) (|SingleInteger|)) "\\spad{setLabelValue(i)} resets the counter which produces labels to \\spad{i}")) (|getCode| (((|SExpression|) $) "\\spad{getCode(f)} returns a Lisp list of strings representing \\spad{f} in Fortran notation. This is used by the FortranProgram domain.")) (|printCode| (((|Void|) $) "\\spad{printCode(f)} prints out \\spad{f} in FORTRAN notation.")) (|code| (((|Union| (|:| |nullBranch| "null") (|:| |assignmentBranch| (|Record| (|:| |var| (|Symbol|)) (|:| |arrayIndex| (|List| (|Polynomial| (|Integer|)))) (|:| |rand| (|Record| (|:| |ints2Floats?| (|Boolean|)) (|:| |expr| (|OutputForm|)))))) (|:| |arrayAssignmentBranch| (|Record| (|:| |var| (|Symbol|)) (|:| |rand| (|OutputForm|)) (|:| |ints2Floats?| (|Boolean|)))) (|:| |conditionalBranch| (|Record| (|:| |switch| (|Switch|)) (|:| |thenClause| $) (|:| |elseClause| $))) (|:| |returnBranch| (|Record| (|:| |empty?| (|Boolean|)) (|:| |value| (|Record| (|:| |ints2Floats?| (|Boolean|)) (|:| |expr| (|OutputForm|)))))) (|:| |blockBranch| (|List| $)) (|:| |commentBranch| (|List| (|String|))) (|:| |callBranch| (|String|)) (|:| |forBranch| (|Record| (|:| |range| (|SegmentBinding| (|Polynomial| (|Integer|)))) (|:| |span| (|Polynomial| (|Integer|))) (|:| |body| $))) (|:| |labelBranch| (|SingleInteger|)) (|:| |loopBranch| (|Record| (|:| |switch| (|Switch|)) (|:| |body| $))) (|:| |commonBranch| (|Record| (|:| |name| (|Symbol|)) (|:| |contents| (|List| (|Symbol|))))) (|:| |printBranch| (|List| (|OutputForm|)))) $) "\\spad{code(f)} returns the internal representation of the object represented by \\spad{f}.")) (|operation| (((|Union| (|:| |Null| "null") (|:| |Assignment| "assignment") (|:| |Conditional| "conditional") (|:| |Return| "return") (|:| |Block| "block") (|:| |Comment| "comment") (|:| |Call| "call") (|:| |For| "for") (|:| |While| "while") (|:| |Repeat| "repeat") (|:| |Goto| "goto") (|:| |Continue| "continue") (|:| |ArrayAssignment| "arrayAssignment") (|:| |Save| "save") (|:| |Stop| "stop") (|:| |Common| "common") (|:| |Print| "print")) $) "\\spad{operation(f)} returns the name of the operation represented by \\spad{f}.")) (|common| (($ (|Symbol|) (|List| (|Symbol|))) "\\spad{common(name,contents)} creates a representation a named common block.")) (|printStatement| (($ (|List| (|OutputForm|))) "\\spad{printStatement(l)} creates a representation of a PRINT statement.")) (|save| (($) "\\spad{save()} creates a representation of a SAVE statement.")) (|stop| (($) "\\spad{stop()} creates a representation of a STOP statement.")) (|block| (($ (|List| $)) "\\spad{block(l)} creates a representation of the statements in \\spad{l} as a block.")) (|assign| (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|Complex| (|Float|)))) "\\spad{assign(x,l,y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|Float|))) "\\spad{assign(x,l,y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|Integer|))) "\\spad{assign(x,l,y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|Vector| (|Expression| (|Complex| (|Float|))))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|Expression| (|Float|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|Expression| (|Integer|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|Complex| (|Float|))))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|Float|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|Integer|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|Complex| (|Float|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|Float|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|Integer|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|MachineComplex|))) "\\spad{assign(x,l,y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|MachineFloat|))) "\\spad{assign(x,l,y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|MachineInteger|))) "\\spad{assign(x,l,y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|Vector| (|Expression| (|MachineComplex|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|Expression| (|MachineFloat|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|Expression| (|MachineInteger|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|MachineComplex|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|MachineFloat|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|MachineInteger|)))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|MachineComplex|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|MachineFloat|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|MachineInteger|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|MachineComplex|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|MachineFloat|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|MachineInteger|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|MachineComplex|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|MachineFloat|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|MachineInteger|))) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|String|)) "\\spad{assign(x,y)} creates a representation of the FORTRAN expression x=y.")) (|cond| (($ (|Switch|) $ $) "\\spad{cond(s,e,f)} creates a representation of the FORTRAN expression IF (\\spad{s}) THEN \\spad{e} ELSE \\spad{f}.") (($ (|Switch|) $) "\\spad{cond(s,e)} creates a representation of the FORTRAN expression IF (\\spad{s}) THEN \\spad{e}.")) (|returns| (($ (|Expression| (|Complex| (|Float|)))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|Integer|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|Float|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|MachineComplex|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|MachineInteger|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|MachineFloat|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($) "\\spad{returns()} creates a representation of a FORTRAN RETURN statement.")) (|call| (($ (|String|)) "\\spad{call(s)} creates a representation of a FORTRAN CALL statement")) (|comment| (($ (|List| (|String|))) "\\spad{comment(s)} creates a representation of the Strings \\spad{s} as a multi-line FORTRAN comment.") (($ (|String|)) "\\spad{comment(s)} creates a representation of the String \\spad{s} as a single FORTRAN comment.")) (|continue| (($ (|SingleInteger|)) "\\spad{continue(l)} creates a representation of a FORTRAN CONTINUE labelled with \\spad{l}")) (|goto| (($ (|SingleInteger|)) "\\spad{goto(l)} creates a representation of a FORTRAN GOTO statement")) (|repeatUntilLoop| (($ (|Switch|) $) "\\spad{repeatUntilLoop(s,c)} creates a repeat ... until loop in FORTRAN.")) (|whileLoop| (($ (|Switch|) $) "\\spad{whileLoop(s,c)} creates a while loop in FORTRAN.")) (|forLoop| (($ (|SegmentBinding| (|Polynomial| (|Integer|))) (|Polynomial| (|Integer|)) $) "\\spad{forLoop(i=1..10,n,c)} creates a representation of a FORTRAN DO loop with \\spad{i} ranging over the values 1 to 10 by \\spad{n}.") (($ (|SegmentBinding| (|Polynomial| (|Integer|))) $) "\\spad{forLoop(i=1..10,c)} creates a representation of a FORTRAN DO loop with \\spad{i} ranging over the values 1 to 10."))) @@ -1308,54 +1308,54 @@ NIL ((|constructor| (NIL "\\indented{1}{Lift a map to finite divisors.} Author: Manuel Bronstein Date Created: 1988 Date Last Updated: 19 May 1993")) (|map| (((|FiniteDivisor| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FiniteDivisor| |#1| |#2| |#3| |#4|)) "\\spad{map(f,d)} \\undocumented{}"))) NIL NIL -(-345 S -2117 UP UPUP R) +(-345 S -1959 UP UPUP R) ((|constructor| (NIL "This category describes finite rational divisors on a curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}\\spad{'s} are integers and the \\spad{P}\\spad{'s} are finite rational points on the curve.")) (|generator| (((|Union| |#5| "failed") $) "\\spad{generator(d)} returns \\spad{f} if \\spad{(f) = d},{} \"failed\" if \\spad{d} is not principal.")) (|principal?| (((|Boolean|) $) "\\spad{principal?(D)} tests if the argument is the divisor of a function.")) (|reduce| (($ $) "\\spad{reduce(D)} converts \\spad{D} to some reduced form (the reduced forms can be differents in different implementations).")) (|decompose| (((|Record| (|:| |id| (|FractionalIdeal| |#3| (|Fraction| |#3|) |#4| |#5|)) (|:| |principalPart| |#5|)) $) "\\spad{decompose(d)} returns \\spad{[id, f]} where \\spad{d = (id) + div(f)}.")) (|divisor| (($ |#5| |#3| |#3| |#3| |#2|) "\\spad{divisor(h, d, d', g, r)} returns the sum of all the finite points where \\spad{h/d} has residue \\spad{r}. \\spad{h} must be integral. \\spad{d} must be squarefree. \\spad{d'} is some derivative of \\spad{d} (not necessarily dd/dx). \\spad{g = gcd(d,discriminant)} contains the ramified zeros of \\spad{d}") (($ |#2| |#2| (|Integer|)) "\\spad{divisor(a, b, n)} makes the divisor \\spad{nP} where \\spad{P:} \\spad{(x = a, y = b)}. \\spad{P} is allowed to be singular if \\spad{n} is a multiple of the rank.") (($ |#2| |#2|) "\\spad{divisor(a, b)} makes the divisor \\spad{P:} \\spad{(x = a, y = b)}. Error: if \\spad{P} is singular.") (($ |#5|) "\\spad{divisor(g)} returns the divisor of the function \\spad{g}.") (($ (|FractionalIdeal| |#3| (|Fraction| |#3|) |#4| |#5|)) "\\spad{divisor(I)} makes a divisor \\spad{D} from an ideal \\spad{I}.")) (|ideal| (((|FractionalIdeal| |#3| (|Fraction| |#3|) |#4| |#5|) $) "\\spad{ideal(D)} returns the ideal corresponding to a divisor \\spad{D}."))) NIL NIL -(-346 -2117 UP UPUP R) +(-346 -1959 UP UPUP R) ((|constructor| (NIL "This category describes finite rational divisors on a curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}\\spad{'s} are integers and the \\spad{P}\\spad{'s} are finite rational points on the curve.")) (|generator| (((|Union| |#4| "failed") $) "\\spad{generator(d)} returns \\spad{f} if \\spad{(f) = d},{} \"failed\" if \\spad{d} is not principal.")) (|principal?| (((|Boolean|) $) "\\spad{principal?(D)} tests if the argument is the divisor of a function.")) (|reduce| (($ $) "\\spad{reduce(D)} converts \\spad{D} to some reduced form (the reduced forms can be differents in different implementations).")) (|decompose| (((|Record| (|:| |id| (|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|)) (|:| |principalPart| |#4|)) $) "\\spad{decompose(d)} returns \\spad{[id, f]} where \\spad{d = (id) + div(f)}.")) (|divisor| (($ |#4| |#2| |#2| |#2| |#1|) "\\spad{divisor(h, d, d', g, r)} returns the sum of all the finite points where \\spad{h/d} has residue \\spad{r}. \\spad{h} must be integral. \\spad{d} must be squarefree. \\spad{d'} is some derivative of \\spad{d} (not necessarily dd/dx). \\spad{g = gcd(d,discriminant)} contains the ramified zeros of \\spad{d}") (($ |#1| |#1| (|Integer|)) "\\spad{divisor(a, b, n)} makes the divisor \\spad{nP} where \\spad{P:} \\spad{(x = a, y = b)}. \\spad{P} is allowed to be singular if \\spad{n} is a multiple of the rank.") (($ |#1| |#1|) "\\spad{divisor(a, b)} makes the divisor \\spad{P:} \\spad{(x = a, y = b)}. Error: if \\spad{P} is singular.") (($ |#4|) "\\spad{divisor(g)} returns the divisor of the function \\spad{g}.") (($ (|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|)) "\\spad{divisor(I)} makes a divisor \\spad{D} from an ideal \\spad{I}.")) (|ideal| (((|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|) $) "\\spad{ideal(D)} returns the ideal corresponding to a divisor \\spad{D}."))) NIL NIL -(-347 -2117 UP UPUP R) +(-347 -1959 UP UPUP R) ((|constructor| (NIL "This domains implements finite rational divisors on a curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}\\spad{'s} are integers and the \\spad{P}\\spad{'s} are finite rational points on the curve.")) (|lSpaceBasis| (((|Vector| |#4|) $) "\\spad{lSpaceBasis(d)} returns a basis for \\spad{L(d) = {f | (f) >= -d}} as a module over \\spad{K[x]}.")) (|finiteBasis| (((|Vector| |#4|) $) "\\spad{finiteBasis(d)} returns a basis for \\spad{d} as a module over {\\em K[x]}."))) NIL NIL (-348 S R) ((|constructor| (NIL "This category provides a selection of evaluation operations depending on what the argument type \\spad{R} provides.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(f, ex)} evaluates ex,{} applying \\spad{f} to values of type \\spad{R} in ex."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -526) (QUOTE (-1196)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -296) (|devaluate| |#2|) (|devaluate| |#2|)))) +((|HasCategory| |#2| (LIST (QUOTE -526) (QUOTE (-1197)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -296) (|devaluate| |#2|) (|devaluate| |#2|)))) (-349 R) ((|constructor| (NIL "This category provides a selection of evaluation operations depending on what the argument type \\spad{R} provides.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f, ex)} evaluates ex,{} applying \\spad{f} to values of type \\spad{R} in ex."))) NIL NIL (-350 |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 \\spad{pi}}")) (|tanh| (($ $) "\\spad{tanh(x)} represents the Fortran intrinsic function TANH")) (|cosh| (($ $) "\\spad{cosh(x)} represents the Fortran intrinsic function COSH")) (|sinh| (($ $) "\\spad{sinh(x)} represents the Fortran intrinsic function SINH")) (|atan| (($ $) "\\spad{atan(x)} represents the Fortran intrinsic function ATAN")) (|acos| (($ $) "\\spad{acos(x)} represents the Fortran intrinsic function ACOS")) (|asin| (($ $) "\\spad{asin(x)} represents the Fortran intrinsic function ASIN")) (|tan| (($ $) "\\spad{tan(x)} represents the Fortran intrinsic function TAN")) (|cos| (($ $) "\\spad{cos(x)} represents the Fortran intrinsic function COS")) (|sin| (($ $) "\\spad{sin(x)} represents the Fortran intrinsic function SIN")) (|log10| (($ $) "\\spad{log10(x)} represents the Fortran intrinsic function LOG10")) (|log| (($ $) "\\spad{log(x)} represents the Fortran intrinsic function LOG")) (|exp| (($ $) "\\spad{exp(x)} represents the Fortran intrinsic function EXP")) (|sqrt| (($ $) "\\spad{sqrt(x)} represents the Fortran intrinsic function SQRT")) (|abs| (($ $) "\\spad{abs(x)} represents the Fortran intrinsic function ABS")) (|coerce| (((|Expression| |#3|) $) "\\spad{coerce(x)} \\undocumented{}")) (|retractIfCan| (((|Union| $ "failed") (|Polynomial| (|Float|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Expression| (|Float|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Expression| (|Integer|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Symbol|)) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a FortranExpression \\indented{1}{checking that it is one of the given basic symbols} \\indented{1}{or subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Expression| |#3|)) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}")) (|retract| (($ (|Polynomial| (|Float|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Expression| (|Float|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Polynomial| (|Integer|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Expression| (|Integer|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Symbol|)) "\\spad{retract(e)} takes \\spad{e} and transforms it into a FortranExpression \\indented{1}{checking that it is one of the given basic symbols} \\indented{1}{or subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Expression| |#3|)) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}"))) -((-4457 . T) (-4458 . T) (-4460 . T)) -((|HasCategory| |#3| (LIST (QUOTE -1058) (QUOTE (-576)))) (|HasCategory| |#3| (LIST (QUOTE -1058) (QUOTE (-390)))) (|HasCategory| $ (QUOTE (-1069))) (|HasCategory| $ (LIST (QUOTE -1058) (QUOTE (-576))))) +((-4458 . T) (-4459 . T) (-4461 . T)) +((|HasCategory| |#3| (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| |#3| (LIST (QUOTE -1059) (QUOTE (-390)))) (|HasCategory| $ (QUOTE (-1070))) (|HasCategory| $ (LIST (QUOTE -1059) (QUOTE (-576))))) (-351 R1 UP1 UPUP1 F1 R2 UP2 UPUP2 F2) ((|constructor| (NIL "Lifts a map from rings to function fields over them.")) (|map| ((|#8| (|Mapping| |#5| |#1|) |#4|) "\\spad{map(f, p)} lifts \\spad{f} to \\spad{F1} and applies it to \\spad{p}."))) NIL NIL -(-352 S -2117 UP UPUP) +(-352 S -1959 UP UPUP) ((|constructor| (NIL "This category is a model for the function field of a plane algebraic curve.")) (|rationalPoints| (((|List| (|List| |#2|))) "\\spad{rationalPoints()} returns the list of all the affine rational points.")) (|nonSingularModel| (((|List| (|Polynomial| |#2|)) (|Symbol|)) "\\spad{nonSingularModel(u)} returns the equations in u1,{}...,{}un of an affine non-singular model for the curve.")) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#3|) (|:| |derivden| |#3|) (|:| |gd| |#3|)) $ (|Mapping| |#3| |#3|)) "\\spad{algSplitSimple(f, D)} returns \\spad{[h,d,d',g]} such that \\spad{f=h/d},{} \\spad{h} is integral at all the normal places \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{d' = Dd},{} \\spad{g = gcd(d, discriminant())} and \\spad{D} is the derivation to use. \\spad{f} must have at most simple finite poles.")) (|hyperelliptic| (((|Union| |#3| "failed")) "\\spad{hyperelliptic()} returns \\spad{p(x)} if the curve is the hyperelliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elliptic| (((|Union| |#3| "failed")) "\\spad{elliptic()} returns \\spad{p(x)} if the curve is the elliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elt| ((|#2| $ |#2| |#2|) "\\spad{elt(f,a,b)} or \\spad{f}(a,{} \\spad{b}) returns the value of \\spad{f} at the point \\spad{(x = a, y = b)} if it is not singular.")) (|primitivePart| (($ $) "\\spad{primitivePart(f)} removes the content of the denominator and the common content of the numerator of \\spad{f}.")) (|differentiate| (($ $ (|Mapping| |#3| |#3|)) "\\spad{differentiate(x, d)} extends the derivation \\spad{d} from UP to \\$ and applies it to \\spad{x}.")) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#3|)) (|:| |den| |#3|)) (|Mapping| |#3| |#3|)) "\\spad{integralDerivationMatrix(d)} extends the derivation \\spad{d} from UP to \\$ and returns (\\spad{M},{} \\spad{Q}) such that the i^th row of \\spad{M} divided by \\spad{Q} form the coordinates of \\spad{d(wi)} with respect to \\spad{(w1,...,wn)} where \\spad{(w1,...,wn)} is the integral basis returned by integralBasis().")) (|integralRepresents| (($ (|Vector| |#3|) |#3|) "\\spad{integralRepresents([A1,...,An], D)} returns \\spad{(A1 w1+...+An wn)/D} where \\spad{(w1,...,wn)} is the integral basis of \\spad{integralBasis()}.")) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#3|)) (|:| |den| |#3|)) $) "\\spad{integralCoordinates(f)} returns \\spad{[[A1,...,An], D]} such that \\spad{f = (A1 w1 +...+ An wn) / D} where \\spad{(w1,...,wn)} is the integral basis returned by \\spad{integralBasis()}.")) (|represents| (($ (|Vector| |#3|) |#3|) "\\spad{represents([A0,...,A(n-1)],D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.")) (|yCoordinates| (((|Record| (|:| |num| (|Vector| |#3|)) (|:| |den| |#3|)) $) "\\spad{yCoordinates(f)} returns \\spad{[[A1,...,An], D]} such that \\spad{f = (A1 + A2 y +...+ An y**(n-1)) / D}.")) (|inverseIntegralMatrixAtInfinity| (((|Matrix| (|Fraction| |#3|))) "\\spad{inverseIntegralMatrixAtInfinity()} returns \\spad{M} such that \\spad{M (v1,...,vn) = (1, y, ..., y**(n-1))} where \\spad{(v1,...,vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|integralMatrixAtInfinity| (((|Matrix| (|Fraction| |#3|))) "\\spad{integralMatrixAtInfinity()} returns \\spad{M} such that \\spad{(v1,...,vn) = M (1, y, ..., y**(n-1))} where \\spad{(v1,...,vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|inverseIntegralMatrix| (((|Matrix| (|Fraction| |#3|))) "\\spad{inverseIntegralMatrix()} returns \\spad{M} such that \\spad{M (w1,...,wn) = (1, y, ..., y**(n-1))} where \\spad{(w1,...,wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|integralMatrix| (((|Matrix| (|Fraction| |#3|))) "\\spad{integralMatrix()} returns \\spad{M} such that \\spad{(w1,...,wn) = M (1, y, ..., y**(n-1))},{} where \\spad{(w1,...,wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|reduceBasisAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{reduceBasisAtInfinity(b1,...,bn)} returns \\spad{(x**i * bj)} for all \\spad{i},{}\\spad{j} such that \\spad{x**i*bj} is locally integral at infinity.")) (|normalizeAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{normalizeAtInfinity(v)} makes \\spad{v} normal at infinity.")) (|complementaryBasis| (((|Vector| $) (|Vector| $)) "\\spad{complementaryBasis(b1,...,bn)} returns the complementary basis \\spad{(b1',...,bn')} of \\spad{(b1,...,bn)}.")) (|integral?| (((|Boolean|) $ |#3|) "\\spad{integral?(f, p)} tests whether \\spad{f} is locally integral at \\spad{p(x) = 0}.") (((|Boolean|) $ |#2|) "\\spad{integral?(f, a)} tests whether \\spad{f} is locally integral at \\spad{x = a}.") (((|Boolean|) $) "\\spad{integral?()} tests if \\spad{f} is integral over \\spad{k[x]}.")) (|integralAtInfinity?| (((|Boolean|) $) "\\spad{integralAtInfinity?()} tests if \\spad{f} is locally integral at infinity.")) (|integralBasisAtInfinity| (((|Vector| $)) "\\spad{integralBasisAtInfinity()} returns the local integral basis at infinity.")) (|integralBasis| (((|Vector| $)) "\\spad{integralBasis()} returns the integral basis for the curve.")) (|ramified?| (((|Boolean|) |#3|) "\\spad{ramified?(p)} tests whether \\spad{p(x) = 0} is ramified.") (((|Boolean|) |#2|) "\\spad{ramified?(a)} tests whether \\spad{x = a} is ramified.")) (|ramifiedAtInfinity?| (((|Boolean|)) "\\spad{ramifiedAtInfinity?()} tests if infinity is ramified.")) (|singular?| (((|Boolean|) |#3|) "\\spad{singular?(p)} tests whether \\spad{p(x) = 0} is singular.") (((|Boolean|) |#2|) "\\spad{singular?(a)} tests whether \\spad{x = a} is singular.")) (|singularAtInfinity?| (((|Boolean|)) "\\spad{singularAtInfinity?()} tests if there is a singularity at infinity.")) (|branchPoint?| (((|Boolean|) |#3|) "\\spad{branchPoint?(p)} tests whether \\spad{p(x) = 0} is a branch point.") (((|Boolean|) |#2|) "\\spad{branchPoint?(a)} tests whether \\spad{x = a} is a branch point.")) (|branchPointAtInfinity?| (((|Boolean|)) "\\spad{branchPointAtInfinity?()} tests if there is a branch point at infinity.")) (|rationalPoint?| (((|Boolean|) |#2| |#2|) "\\spad{rationalPoint?(a, b)} tests if \\spad{(x=a,y=b)} is on the curve.")) (|absolutelyIrreducible?| (((|Boolean|)) "\\spad{absolutelyIrreducible?()} tests if the curve absolutely irreducible?")) (|genus| (((|NonNegativeInteger|)) "\\spad{genus()} returns the genus of one absolutely irreducible component")) (|numberOfComponents| (((|NonNegativeInteger|)) "\\spad{numberOfComponents()} returns the number of absolutely irreducible components."))) NIL ((|HasCategory| |#2| (QUOTE (-379))) (|HasCategory| |#2| (QUOTE (-374)))) -(-353 -2117 UP UPUP) +(-353 -1959 UP UPUP) ((|constructor| (NIL "This category is a model for the function field of a plane algebraic curve.")) (|rationalPoints| (((|List| (|List| |#1|))) "\\spad{rationalPoints()} returns the list of all the affine rational points.")) (|nonSingularModel| (((|List| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{nonSingularModel(u)} returns the equations in u1,{}...,{}un of an affine non-singular model for the curve.")) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#2|) (|:| |derivden| |#2|) (|:| |gd| |#2|)) $ (|Mapping| |#2| |#2|)) "\\spad{algSplitSimple(f, D)} returns \\spad{[h,d,d',g]} such that \\spad{f=h/d},{} \\spad{h} is integral at all the normal places \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{d' = Dd},{} \\spad{g = gcd(d, discriminant())} and \\spad{D} is the derivation to use. \\spad{f} must have at most simple finite poles.")) (|hyperelliptic| (((|Union| |#2| "failed")) "\\spad{hyperelliptic()} returns \\spad{p(x)} if the curve is the hyperelliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elliptic| (((|Union| |#2| "failed")) "\\spad{elliptic()} returns \\spad{p(x)} if the curve is the elliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elt| ((|#1| $ |#1| |#1|) "\\spad{elt(f,a,b)} or \\spad{f}(a,{} \\spad{b}) returns the value of \\spad{f} at the point \\spad{(x = a, y = b)} if it is not singular.")) (|primitivePart| (($ $) "\\spad{primitivePart(f)} removes the content of the denominator and the common content of the numerator of \\spad{f}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|)) "\\spad{differentiate(x, d)} extends the derivation \\spad{d} from UP to \\$ and applies it to \\spad{x}.")) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#2|)) (|:| |den| |#2|)) (|Mapping| |#2| |#2|)) "\\spad{integralDerivationMatrix(d)} extends the derivation \\spad{d} from UP to \\$ and returns (\\spad{M},{} \\spad{Q}) such that the i^th row of \\spad{M} divided by \\spad{Q} form the coordinates of \\spad{d(wi)} with respect to \\spad{(w1,...,wn)} where \\spad{(w1,...,wn)} is the integral basis returned by integralBasis().")) (|integralRepresents| (($ (|Vector| |#2|) |#2|) "\\spad{integralRepresents([A1,...,An], D)} returns \\spad{(A1 w1+...+An wn)/D} where \\spad{(w1,...,wn)} is the integral basis of \\spad{integralBasis()}.")) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) "\\spad{integralCoordinates(f)} returns \\spad{[[A1,...,An], D]} such that \\spad{f = (A1 w1 +...+ An wn) / D} where \\spad{(w1,...,wn)} is the integral basis returned by \\spad{integralBasis()}.")) (|represents| (($ (|Vector| |#2|) |#2|) "\\spad{represents([A0,...,A(n-1)],D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.")) (|yCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) "\\spad{yCoordinates(f)} returns \\spad{[[A1,...,An], D]} such that \\spad{f = (A1 + A2 y +...+ An y**(n-1)) / D}.")) (|inverseIntegralMatrixAtInfinity| (((|Matrix| (|Fraction| |#2|))) "\\spad{inverseIntegralMatrixAtInfinity()} returns \\spad{M} such that \\spad{M (v1,...,vn) = (1, y, ..., y**(n-1))} where \\spad{(v1,...,vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|integralMatrixAtInfinity| (((|Matrix| (|Fraction| |#2|))) "\\spad{integralMatrixAtInfinity()} returns \\spad{M} such that \\spad{(v1,...,vn) = M (1, y, ..., y**(n-1))} where \\spad{(v1,...,vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|inverseIntegralMatrix| (((|Matrix| (|Fraction| |#2|))) "\\spad{inverseIntegralMatrix()} returns \\spad{M} such that \\spad{M (w1,...,wn) = (1, y, ..., y**(n-1))} where \\spad{(w1,...,wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|integralMatrix| (((|Matrix| (|Fraction| |#2|))) "\\spad{integralMatrix()} returns \\spad{M} such that \\spad{(w1,...,wn) = M (1, y, ..., y**(n-1))},{} where \\spad{(w1,...,wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|reduceBasisAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{reduceBasisAtInfinity(b1,...,bn)} returns \\spad{(x**i * bj)} for all \\spad{i},{}\\spad{j} such that \\spad{x**i*bj} is locally integral at infinity.")) (|normalizeAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{normalizeAtInfinity(v)} makes \\spad{v} normal at infinity.")) (|complementaryBasis| (((|Vector| $) (|Vector| $)) "\\spad{complementaryBasis(b1,...,bn)} returns the complementary basis \\spad{(b1',...,bn')} of \\spad{(b1,...,bn)}.")) (|integral?| (((|Boolean|) $ |#2|) "\\spad{integral?(f, p)} tests whether \\spad{f} is locally integral at \\spad{p(x) = 0}.") (((|Boolean|) $ |#1|) "\\spad{integral?(f, a)} tests whether \\spad{f} is locally integral at \\spad{x = a}.") (((|Boolean|) $) "\\spad{integral?()} tests if \\spad{f} is integral over \\spad{k[x]}.")) (|integralAtInfinity?| (((|Boolean|) $) "\\spad{integralAtInfinity?()} tests if \\spad{f} is locally integral at infinity.")) (|integralBasisAtInfinity| (((|Vector| $)) "\\spad{integralBasisAtInfinity()} returns the local integral basis at infinity.")) (|integralBasis| (((|Vector| $)) "\\spad{integralBasis()} returns the integral basis for the curve.")) (|ramified?| (((|Boolean|) |#2|) "\\spad{ramified?(p)} tests whether \\spad{p(x) = 0} is ramified.") (((|Boolean|) |#1|) "\\spad{ramified?(a)} tests whether \\spad{x = a} is ramified.")) (|ramifiedAtInfinity?| (((|Boolean|)) "\\spad{ramifiedAtInfinity?()} tests if infinity is ramified.")) (|singular?| (((|Boolean|) |#2|) "\\spad{singular?(p)} tests whether \\spad{p(x) = 0} is singular.") (((|Boolean|) |#1|) "\\spad{singular?(a)} tests whether \\spad{x = a} is singular.")) (|singularAtInfinity?| (((|Boolean|)) "\\spad{singularAtInfinity?()} tests if there is a singularity at infinity.")) (|branchPoint?| (((|Boolean|) |#2|) "\\spad{branchPoint?(p)} tests whether \\spad{p(x) = 0} is a branch point.") (((|Boolean|) |#1|) "\\spad{branchPoint?(a)} tests whether \\spad{x = a} is a branch point.")) (|branchPointAtInfinity?| (((|Boolean|)) "\\spad{branchPointAtInfinity?()} tests if there is a branch point at infinity.")) (|rationalPoint?| (((|Boolean|) |#1| |#1|) "\\spad{rationalPoint?(a, b)} tests if \\spad{(x=a,y=b)} is on the curve.")) (|absolutelyIrreducible?| (((|Boolean|)) "\\spad{absolutelyIrreducible?()} tests if the curve absolutely irreducible?")) (|genus| (((|NonNegativeInteger|)) "\\spad{genus()} returns the genus of one absolutely irreducible component")) (|numberOfComponents| (((|NonNegativeInteger|)) "\\spad{numberOfComponents()} returns the number of absolutely irreducible components."))) -((-4456 |has| (-419 |#2|) (-374)) (-4461 |has| (-419 |#2|) (-374)) (-4455 |has| (-419 |#2|) (-374)) ((-4465 "*") . T) (-4457 . T) (-4458 . T) (-4460 . T)) +((-4457 |has| (-419 |#2|) (-374)) (-4462 |has| (-419 |#2|) (-374)) (-4456 |has| (-419 |#2|) (-374)) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-354 |p| |extdeg|) ((|constructor| (NIL "FiniteFieldCyclicGroup(\\spad{p},{}\\spad{n}) implements a finite field extension of degee \\spad{n} over the prime field with \\spad{p} elements. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial,{} which is created by {\\em createPrimitivePoly} from \\spadtype{FiniteFieldPolynomialPackage}. The Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field. This table is used to perform additions in the field quickly."))) -((-4455 . T) (-4461 . T) (-4456 . T) ((-4465 "*") . T) (-4457 . T) (-4458 . T) (-4460 . T)) -((-3794 (|HasCategory| (-928 |#1|) (QUOTE (-146))) (|HasCategory| (-928 |#1|) (QUOTE (-379)))) (|HasCategory| (-928 |#1|) (QUOTE (-148))) (|HasCategory| (-928 |#1|) (QUOTE (-379))) (|HasCategory| (-928 |#1|) (QUOTE (-146)))) +((-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) +((-2758 (|HasCategory| (-929 |#1|) (QUOTE (-146))) (|HasCategory| (-929 |#1|) (QUOTE (-379)))) (|HasCategory| (-929 |#1|) (QUOTE (-148))) (|HasCategory| (-929 |#1|) (QUOTE (-379))) (|HasCategory| (-929 |#1|) (QUOTE (-146)))) (-355 GF |defpol|) ((|constructor| (NIL "FiniteFieldCyclicGroupExtensionByPolynomial(\\spad{GF},{}defpol) implements a finite extension field of the ground field {\\em GF}. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial {\\em defpol},{} which MUST be primitive (user responsibility). Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field it is used to perform additions in the field quickly."))) -((-4455 . T) (-4461 . T) (-4456 . T) ((-4465 "*") . T) (-4457 . T) (-4458 . T) (-4460 . T)) -((-3794 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-379)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-146)))) +((-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) +((-2758 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-379)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-146)))) (-356 GF |extdeg|) ((|constructor| (NIL "FiniteFieldCyclicGroupExtension(\\spad{GF},{}\\spad{n}) implements a extension of degree \\spad{n} over the ground field {\\em GF}. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial,{} which is created by {\\em createPrimitivePoly} from \\spadtype{FiniteFieldPolynomialPackage}. Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field. This table is used to perform additions in the field quickly."))) -((-4455 . T) (-4461 . T) (-4456 . T) ((-4465 "*") . T) (-4457 . T) (-4458 . T) (-4460 . T)) -((-3794 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-379)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-146)))) +((-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) +((-2758 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-379)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-146)))) (-357 GF) ((|constructor| (NIL "FiniteFieldFunctions(\\spad{GF}) is a package with functions concerning finite extension fields of the finite ground field {\\em GF},{} \\spadignore{e.g.} Zech logarithms.")) (|createLowComplexityNormalBasis| (((|Union| (|SparseUnivariatePolynomial| |#1|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) (|PositiveInteger|)) "\\spad{createLowComplexityNormalBasis(n)} tries to find a a low complexity normal basis of degree {\\em n} over {\\em GF} and returns its multiplication matrix If no low complexity basis is found it calls \\axiomFunFrom{createNormalPoly}{FiniteFieldPolynomialPackage}(\\spad{n}) to produce a normal polynomial of degree {\\em n} over {\\em GF}")) (|createLowComplexityTable| (((|Union| (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) "failed") (|PositiveInteger|)) "\\spad{createLowComplexityTable(n)} tries to find a low complexity normal basis of degree {\\em n} over {\\em GF} and returns its multiplication matrix Fails,{} if it does not find a low complexity basis")) (|sizeMultiplication| (((|NonNegativeInteger|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{sizeMultiplication(m)} returns the number of entries of the multiplication table {\\em m}.")) (|createMultiplicationMatrix| (((|Matrix| |#1|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{createMultiplicationMatrix(m)} forms the multiplication table {\\em m} into a matrix over the ground field.")) (|createMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) (|SparseUnivariatePolynomial| |#1|)) "\\spad{createMultiplicationTable(f)} generates a multiplication table for the normal basis of the field extension determined by {\\em f}. This is needed to perform multiplications between elements represented as coordinate vectors to this basis. See \\spadtype{FFNBP},{} \\spadtype{FFNBX}.")) (|createZechTable| (((|PrimitiveArray| (|SingleInteger|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{createZechTable(f)} generates a Zech logarithm table for the cyclic group representation of a extension of the ground field by the primitive polynomial {\\em f(x)},{} \\spadignore{i.e.} \\spad{Z(i)},{} defined by {\\em x**Z(i) = 1+x**i} is stored at index \\spad{i}. This is needed in particular to perform addition of field elements in finite fields represented in this way. See \\spadtype{FFCGP},{} \\spadtype{FFCGX}."))) NIL @@ -1370,33 +1370,33 @@ NIL NIL (-360) ((|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|) $) "\\spad{primitive?(b)} tests whether the element \\spad{b} is a generator of the (cyclic) multiplicative group of the field,{} \\spadignore{i.e.} is a primitive element. Implementation Note: see \\spad{ch}.IX.1.3,{} th.2 in \\spad{D}. Lipson.")) (|primitiveElement| (($) "\\spad{primitiveElement()} returns a primitive element stored in a global variable in the domain. At first call,{} the primitive element is computed by calling \\spadfun{createPrimitiveElement}.")) (|createPrimitiveElement| (($) "\\spad{createPrimitiveElement()} computes a generator of the (cyclic) multiplicative group of the field.")) (|tableForDiscreteLogarithm| (((|Table| (|PositiveInteger|) (|NonNegativeInteger|)) (|Integer|)) "\\spad{tableForDiscreteLogarithm(a,n)} returns a table of the discrete logarithms of \\spad{a**0} up to \\spad{a**(n-1)} which,{} called with key \\spad{lookup(a**i)} returns \\spad{i} for \\spad{i} in \\spad{0..n-1}. Error: if not called for prime divisors of order of \\indented{7}{multiplicative group.}")) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| (|Integer|)) (|:| |exponent| (|Integer|))))) "\\spad{factorsOfCyclicGroupSize()} returns the factorization of size()\\spad{-1}")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(mat)},{} given a matrix representing a homogeneous system of equations,{} returns a vector whose characteristic'th powers is a non-trivial solution,{} or \"failed\" if no such vector exists.")) (|charthRoot| (($ $) "\\spad{charthRoot(a)} takes the characteristic'th root of {\\em a}. Note: such a root is alway defined in finite fields."))) -((-4455 . T) (-4461 . T) (-4456 . T) ((-4465 "*") . T) (-4457 . T) (-4458 . T) (-4460 . T)) +((-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL -(-361 R UP -2117) +(-361 R UP -1959) ((|constructor| (NIL "In this package \\spad{R} is a Euclidean domain and \\spad{F} is a framed algebra over \\spad{R}. The package provides functions to compute the integral closure of \\spad{R} in the quotient field of \\spad{F}. It is assumed that \\spad{char(R/P) = char(R)} for any prime \\spad{P} of \\spad{R}. A typical instance of this is when \\spad{R = K[x]} and \\spad{F} is a function field over \\spad{R}.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) |#1|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the integral closure of \\spad{R} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL (-362 |p| |extdeg|) ((|constructor| (NIL "FiniteFieldNormalBasis(\\spad{p},{}\\spad{n}) implements a finite extension field of degree \\spad{n} over the prime field with \\spad{p} elements. The elements are represented by coordinate vectors with respect to a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element. This is chosen as a root of the extension polynomial created by \\spadfunFrom{createNormalPoly}{FiniteFieldPolynomialPackage}.")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: The time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| (|PrimeField| |#1|))) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| (|PrimeField| |#1|)) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) -((-4455 . T) (-4461 . T) (-4456 . T) ((-4465 "*") . T) (-4457 . T) (-4458 . T) (-4460 . T)) -((-3794 (|HasCategory| (-928 |#1|) (QUOTE (-146))) (|HasCategory| (-928 |#1|) (QUOTE (-379)))) (|HasCategory| (-928 |#1|) (QUOTE (-148))) (|HasCategory| (-928 |#1|) (QUOTE (-379))) (|HasCategory| (-928 |#1|) (QUOTE (-146)))) +((-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) +((-2758 (|HasCategory| (-929 |#1|) (QUOTE (-146))) (|HasCategory| (-929 |#1|) (QUOTE (-379)))) (|HasCategory| (-929 |#1|) (QUOTE (-148))) (|HasCategory| (-929 |#1|) (QUOTE (-379))) (|HasCategory| (-929 |#1|) (QUOTE (-146)))) (-363 GF |uni|) ((|constructor| (NIL "FiniteFieldNormalBasisExtensionByPolynomial(\\spad{GF},{}uni) implements a finite extension of the ground field {\\em GF}. The elements are represented by coordinate vectors with respect to. a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element,{} where \\spad{q} is the size of {\\em GF}. The normal element is chosen as a root of the extension polynomial,{} which MUST be normal over {\\em GF} (user responsibility)")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: the time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| |#1|)) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) -((-4455 . T) (-4461 . T) (-4456 . T) ((-4465 "*") . T) (-4457 . T) (-4458 . T) (-4460 . T)) -((-3794 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-379)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-146)))) +((-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) +((-2758 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-379)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-146)))) (-364 GF |extdeg|) ((|constructor| (NIL "FiniteFieldNormalBasisExtensionByPolynomial(\\spad{GF},{}\\spad{n}) implements a finite extension field of degree \\spad{n} over the ground field {\\em GF}. The elements are represented by coordinate vectors with respect to a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element. This is chosen as a root of the extension polynomial,{} created by {\\em createNormalPoly} from \\spadtype{FiniteFieldPolynomialPackage}")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: the time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| |#1|)) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) -((-4455 . T) (-4461 . T) (-4456 . T) ((-4465 "*") . T) (-4457 . T) (-4458 . T) (-4460 . T)) -((-3794 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-379)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-146)))) +((-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) +((-2758 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-379)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-146)))) (-365 |p| |n|) ((|constructor| (NIL "FiniteField(\\spad{p},{}\\spad{n}) implements finite fields with p**n elements. This packages checks that \\spad{p} is prime. For a non-checking version,{} see \\spadtype{InnerFiniteField}."))) -((-4455 . T) (-4461 . T) (-4456 . T) ((-4465 "*") . T) (-4457 . T) (-4458 . T) (-4460 . T)) -((-3794 (|HasCategory| (-928 |#1|) (QUOTE (-146))) (|HasCategory| (-928 |#1|) (QUOTE (-379)))) (|HasCategory| (-928 |#1|) (QUOTE (-148))) (|HasCategory| (-928 |#1|) (QUOTE (-379))) (|HasCategory| (-928 |#1|) (QUOTE (-146)))) +((-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) +((-2758 (|HasCategory| (-929 |#1|) (QUOTE (-146))) (|HasCategory| (-929 |#1|) (QUOTE (-379)))) (|HasCategory| (-929 |#1|) (QUOTE (-148))) (|HasCategory| (-929 |#1|) (QUOTE (-379))) (|HasCategory| (-929 |#1|) (QUOTE (-146)))) (-366 GF |defpol|) ((|constructor| (NIL "FiniteFieldExtensionByPolynomial(\\spad{GF},{} defpol) implements the extension of the finite field {\\em GF} generated by the extension polynomial {\\em defpol} which MUST be irreducible. Note: the user has the responsibility to ensure that {\\em defpol} is irreducible."))) -((-4455 . T) (-4461 . T) (-4456 . T) ((-4465 "*") . T) (-4457 . T) (-4458 . T) (-4460 . T)) -((-3794 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-379)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-146)))) -(-367 -2117 GF) +((-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) +((-2758 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-379)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-146)))) +(-367 -1959 GF) ((|constructor| (NIL "FiniteFieldPolynomialPackage2(\\spad{F},{}\\spad{GF}) exports some functions concerning finite fields,{} which depend on a finite field {\\em GF} and an algebraic extension \\spad{F} of {\\em GF},{} \\spadignore{e.g.} a zero of a polynomial over {\\em GF} in \\spad{F}.")) (|rootOfIrreduciblePoly| ((|#1| (|SparseUnivariatePolynomial| |#2|)) "\\spad{rootOfIrreduciblePoly(f)} computes one root of the monic,{} irreducible polynomial \\spad{f},{} which degree must divide the extension degree of {\\em F} over {\\em GF},{} \\spadignore{i.e.} \\spad{f} splits into linear factors over {\\em F}.")) (|Frobenius| ((|#1| |#1|) "\\spad{Frobenius(x)} \\undocumented{}")) (|basis| (((|Vector| |#1|) (|PositiveInteger|)) "\\spad{basis(n)} \\undocumented{}")) (|lookup| (((|PositiveInteger|) |#1|) "\\spad{lookup(x)} \\undocumented{}")) (|coerce| ((|#1| |#2|) "\\spad{coerce(x)} \\undocumented{}"))) NIL NIL @@ -1404,21 +1404,21 @@ NIL ((|constructor| (NIL "This package provides a number of functions for generating,{} counting and testing irreducible,{} normal,{} primitive,{} random polynomials over finite fields.")) (|reducedQPowers| (((|PrimitiveArray| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{reducedQPowers(f)} generates \\spad{[x,x**q,x**(q**2),...,x**(q**(n-1))]} reduced modulo \\spad{f} where \\spad{q = size()\\$GF} and \\spad{n = degree f}.")) (|leastAffineMultiple| (((|SparseUnivariatePolynomial| |#1|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{leastAffineMultiple(f)} computes the least affine polynomial which is divisible by the polynomial \\spad{f} over the finite field {\\em GF},{} \\spadignore{i.e.} a polynomial whose exponents are 0 or a power of \\spad{q},{} the size of {\\em GF}.")) (|random| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{random(m,n)}\\$FFPOLY(\\spad{GF}) generates a random monic polynomial of degree \\spad{d} over the finite field {\\em GF},{} \\spad{d} between \\spad{m} and \\spad{n}.") (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{random(n)}\\$FFPOLY(\\spad{GF}) generates a random monic polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|nextPrimitiveNormalPoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextPrimitiveNormalPoly(f)} yields the next primitive normal polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g} or,{} in case these numbers are equal,{} if the {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than this number for \\spad{g}. If these numbers are equals,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than that for \\spad{g},{} or if the lists of exponents for \\spad{f} are lexicographically less than those for \\spad{g}. If these lists are also equal,{} the lists of coefficients are coefficients according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}. This operation is equivalent to nextNormalPrimitivePoly(\\spad{f}).")) (|nextNormalPrimitivePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextNormalPrimitivePoly(f)} yields the next normal primitive polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g} or if {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than this number for \\spad{g}. Otherwise,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than that for \\spad{g} or if the lists of exponents for \\spad{f} are lexicographically less than those for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}. This operation is equivalent to nextPrimitiveNormalPoly(\\spad{f}).")) (|nextNormalPoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextNormalPoly(f)} yields the next normal polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than that for \\spad{g}. In case these numbers are equal,{} \\spad{f < g} if if the number of monomials of \\spad{f} is less that for \\spad{g} or if the list of exponents of \\spad{f} are lexicographically less than the corresponding list for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|nextPrimitivePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextPrimitivePoly(f)} yields the next primitive polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g}. If these values are equal,{} then \\spad{f < g} if if the number of monomials of \\spad{f} is less than that for \\spad{g} or if the lists of exponents of \\spad{f} are lexicographically less than the corresponding list for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|nextIrreduciblePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextIrreduciblePoly(f)} yields the next monic irreducible polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than this number for \\spad{g}. If \\spad{f} and \\spad{g} have the same number of monomials,{} the lists of exponents are compared lexicographically. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|createPrimitiveNormalPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createPrimitiveNormalPoly(n)}\\$FFPOLY(\\spad{GF}) generates a normal and primitive polynomial of degree \\spad{n} over the field {\\em GF}. polynomial of degree \\spad{n} over the field {\\em GF}.")) (|createNormalPrimitivePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createNormalPrimitivePoly(n)}\\$FFPOLY(\\spad{GF}) generates a normal and primitive polynomial of degree \\spad{n} over the field {\\em GF}. Note: this function is equivalent to createPrimitiveNormalPoly(\\spad{n})")) (|createNormalPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createNormalPoly(n)}\\$FFPOLY(\\spad{GF}) generates a normal polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|createPrimitivePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createPrimitivePoly(n)}\\$FFPOLY(\\spad{GF}) generates a primitive polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|createIrreduciblePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createIrreduciblePoly(n)}\\$FFPOLY(\\spad{GF}) generates a monic irreducible univariate polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfNormalPoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfNormalPoly(n)}\\$FFPOLY(\\spad{GF}) yields the number of normal polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfPrimitivePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfPrimitivePoly(n)}\\$FFPOLY(\\spad{GF}) yields the number of primitive polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfIrreduciblePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfIrreduciblePoly(n)}\\$FFPOLY(\\spad{GF}) yields the number of monic irreducible univariate polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|normal?| (((|Boolean|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{normal?(f)} tests whether the polynomial \\spad{f} over a finite field is normal,{} \\spadignore{i.e.} its roots are linearly independent over the field.")) (|primitive?| (((|Boolean|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{primitive?(f)} tests whether the polynomial \\spad{f} over a finite field is primitive,{} \\spadignore{i.e.} all its roots are primitive."))) NIL NIL -(-369 -2117 FP FPP) +(-369 -1959 FP FPP) ((|constructor| (NIL "This package solves linear diophantine equations for Bivariate polynomials over finite fields")) (|solveLinearPolynomialEquation| (((|Union| (|List| |#3|) "failed") (|List| |#3|) |#3|) "\\spad{solveLinearPolynomialEquation([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists."))) NIL NIL (-370 GF |n|) ((|constructor| (NIL "FiniteFieldExtensionByPolynomial(\\spad{GF},{} \\spad{n}) implements an extension of the finite field {\\em GF} of degree \\spad{n} generated by the extension polynomial constructed by \\spadfunFrom{createIrreduciblePoly}{FiniteFieldPolynomialPackage} from \\spadtype{FiniteFieldPolynomialPackage}."))) -((-4455 . T) (-4461 . T) (-4456 . T) ((-4465 "*") . T) (-4457 . T) (-4458 . T) (-4460 . T)) -((-3794 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-379)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-146)))) +((-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) +((-2758 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-379)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-146)))) (-371 R |ls|) ((|constructor| (NIL "This is just an interface between several packages and domains. The goal is to compute lexicographical Groebner bases of sets of polynomial with type \\spadtype{Polynomial R} by the {\\em FGLM} algorithm if this is possible (\\spadignore{i.e.} if the input system generates a zero-dimensional ideal).")) (|groebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|))) "\\axiom{groebner(\\spad{lq1})} returns the lexicographical Groebner basis of \\axiom{\\spad{lq1}}. If \\axiom{\\spad{lq1}} generates a zero-dimensional ideal then the {\\em FGLM} strategy is used,{} otherwise the {\\em Sugar} strategy is used.")) (|fglmIfCan| (((|Union| (|List| (|Polynomial| |#1|)) "failed") (|List| (|Polynomial| |#1|))) "\\axiom{fglmIfCan(\\spad{lq1})} returns the lexicographical Groebner basis of \\axiom{\\spad{lq1}} by using the {\\em FGLM} strategy,{} if \\axiom{zeroDimensional?(\\spad{lq1})} holds.")) (|zeroDimensional?| (((|Boolean|) (|List| (|Polynomial| |#1|))) "\\axiom{zeroDimensional?(\\spad{lq1})} returns \\spad{true} iff \\axiom{\\spad{lq1}} generates a zero-dimensional ideal \\spad{w}.\\spad{r}.\\spad{t}. the variables of \\axiom{\\spad{ls}}."))) NIL NIL (-372 S) ((|constructor| (NIL "The free group on a set \\spad{S} is the group of finite products of the form \\spad{reduce(*,[si ** ni])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are integers. The multiplication is not commutative.")) (|factors| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| (|Integer|)))) $) "\\spad{factors(a1\\^e1,...,an\\^en)} returns \\spad{[[a1, e1],...,[an, en]]}.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f, a1\\^e1 ... an\\^en)} returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (|mapExpon| (($ (|Mapping| (|Integer|) (|Integer|)) $) "\\spad{mapExpon(f, a1\\^e1 ... an\\^en)} returns \\spad{a1\\^f(e1) ... an\\^f(en)}.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(x, n)} returns the factor of the n^th monomial of \\spad{x}.")) (|nthExpon| (((|Integer|) $ (|Integer|)) "\\spad{nthExpon(x, n)} returns the exponent of the n^th monomial of \\spad{x}.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(x)} returns the number of monomials in \\spad{x}.")) (** (($ |#1| (|Integer|)) "\\spad{s ** n} returns the product of \\spad{s} by itself \\spad{n} times.")) (* (($ $ |#1|) "\\spad{x * s} returns the product of \\spad{x} by \\spad{s} on the right.") (($ |#1| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) -((-4460 . T)) +((-4461 . T)) NIL (-373 S) ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) @@ -1426,7 +1426,7 @@ NIL NIL (-374) ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) -((-4455 . T) (-4461 . T) (-4456 . T) ((-4465 "*") . T) (-4457 . T) (-4458 . T) (-4460 . T)) +((-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-375 |Name| S) ((|constructor| (NIL "This category provides an interface to operate on files in the computer\\spad{'s} file system. The precise method of naming files is determined by the Name parameter. The type of the contents of the file is determined by \\spad{S}.")) (|write!| ((|#2| $ |#2|) "\\spad{write!(f,s)} puts the value \\spad{s} into the file \\spad{f}. The state of \\spad{f} is modified so subsequents call to \\spad{write!} will append one after another.")) (|read!| ((|#2| $) "\\spad{read!(f)} extracts a value from file \\spad{f}. The state of \\spad{f} is modified so a subsequent call to \\spadfun{read!} will return the next element.")) (|iomode| (((|String|) $) "\\spad{iomode(f)} returns the status of the file \\spad{f}. The input/output status of \\spad{f} may be \"input\",{} \"output\" or \"closed\" mode.")) (|name| ((|#1| $) "\\spad{name(f)} returns the external name of the file \\spad{f}.")) (|close!| (($ $) "\\spad{close!(f)} returns the file \\spad{f} closed to input and output.")) (|reopen!| (($ $ (|String|)) "\\spad{reopen!(f,mode)} returns a file \\spad{f} reopened for operation in the indicated mode: \"input\" or \"output\". \\spad{reopen!(f,\"input\")} will reopen the file \\spad{f} for input.")) (|open| (($ |#1| (|String|)) "\\spad{open(s,mode)} returns a file \\spad{s} open for operation in the indicated mode: \"input\" or \"output\".") (($ |#1|) "\\spad{open(s)} returns the file \\spad{s} open for input."))) @@ -1442,7 +1442,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-568)))) (-378 R) ((|constructor| (NIL "A FiniteRankNonAssociativeAlgebra is a non associative algebra over a commutative ring \\spad{R} which is a free \\spad{R}-module of finite rank.")) (|unitsKnown| ((|attribute|) "unitsKnown means that \\spadfun{recip} truly yields reciprocal or \\spad{\"failed\"} if not a unit,{} similarly for \\spadfun{leftRecip} and \\spadfun{rightRecip}. The reason is that we use left,{} respectively right,{} minimal polynomials to decide this question.")) (|unit| (((|Union| $ "failed")) "\\spad{unit()} returns a unit of the algebra (necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnit| (((|Union| $ "failed")) "\\spad{rightUnit()} returns a right unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|leftUnit| (((|Union| $ "failed")) "\\spad{leftUnit()} returns a left unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{rightUnits()} returns the affine space of all right units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|leftUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{leftUnits()} returns the affine space of all left units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|rightMinimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{rightMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of right powers of \\spad{a}. Note: the polynomial never has a constant term as in general the algebra has no unit.")) (|leftMinimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{leftMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of left powers of \\spad{a}. Note: the polynomial never has a constant term as in general the algebra has no unit.")) (|associatorDependence| (((|List| (|Vector| |#1|))) "\\spad{associatorDependence()} looks for the associator identities,{} \\spadignore{i.e.} finds a basis of the solutions of the linear combinations of the six permutations of \\spad{associator(a,b,c)} which yield 0,{} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra. The order of the permutations is \\spad{123 231 312 132 321 213}.")) (|rightRecip| (((|Union| $ "failed") $) "\\spad{rightRecip(a)} returns an element,{} which is a right inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|leftRecip| (((|Union| $ "failed") $) "\\spad{leftRecip(a)} returns an element,{} which is a left inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(a)} returns an element,{} which is both a left and a right inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|lieAlgebra?| (((|Boolean|)) "\\spad{lieAlgebra?()} tests if the algebra is anticommutative and \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra (Jacobi identity). Example: for every associative algebra \\spad{(A,+,@)} we can construct a Lie algebra \\spad{(A,+,*)},{} where \\spad{a*b := a@b-b@a}.")) (|jordanAlgebra?| (((|Boolean|)) "\\spad{jordanAlgebra?()} tests if the algebra is commutative,{} characteristic is not 2,{} and \\spad{(a*b)*a**2 - a*(b*a**2) = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra (Jordan identity). Example: for every associative algebra \\spad{(A,+,@)} we can construct a Jordan algebra \\spad{(A,+,*)},{} where \\spad{a*b := (a@b+b@a)/2}.")) (|noncommutativeJordanAlgebra?| (((|Boolean|)) "\\spad{noncommutativeJordanAlgebra?()} tests if the algebra is flexible and Jordan admissible.")) (|jordanAdmissible?| (((|Boolean|)) "\\spad{jordanAdmissible?()} tests if 2 is invertible in the coefficient domain and the multiplication defined by \\spad{(1/2)(a*b+b*a)} determines a Jordan algebra,{} \\spadignore{i.e.} satisfies the Jordan identity. The property of \\spadatt{commutative(\\spad{\"*\"})} follows from by definition.")) (|lieAdmissible?| (((|Boolean|)) "\\spad{lieAdmissible?()} tests if the algebra defined by the commutators is a Lie algebra,{} \\spadignore{i.e.} satisfies the Jacobi identity. The property of anticommutativity follows from definition.")) (|jacobiIdentity?| (((|Boolean|)) "\\spad{jacobiIdentity?()} tests if \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra. For example,{} this holds for crossed products of 3-dimensional vectors.")) (|powerAssociative?| (((|Boolean|)) "\\spad{powerAssociative?()} tests if all subalgebras generated by a single element are associative.")) (|alternative?| (((|Boolean|)) "\\spad{alternative?()} tests if \\spad{2*associator(a,a,b) = 0 = 2*associator(a,b,b)} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|flexible?| (((|Boolean|)) "\\spad{flexible?()} tests if \\spad{2*associator(a,b,a) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|rightAlternative?| (((|Boolean|)) "\\spad{rightAlternative?()} tests if \\spad{2*associator(a,b,b) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|leftAlternative?| (((|Boolean|)) "\\spad{leftAlternative?()} tests if \\spad{2*associator(a,a,b) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|antiAssociative?| (((|Boolean|)) "\\spad{antiAssociative?()} tests if multiplication in algebra is anti-associative,{} \\spadignore{i.e.} \\spad{(a*b)*c + a*(b*c) = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra.")) (|associative?| (((|Boolean|)) "\\spad{associative?()} tests if multiplication in algebra is associative.")) (|antiCommutative?| (((|Boolean|)) "\\spad{antiCommutative?()} tests if \\spad{a*a = 0} for all \\spad{a} in the algebra. Note: this implies \\spad{a*b + b*a = 0} for all \\spad{a} and \\spad{b}.")) (|commutative?| (((|Boolean|)) "\\spad{commutative?()} tests if multiplication in the algebra is commutative.")) (|rightCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{rightCharacteristicPolynomial(a)} returns the characteristic polynomial of the right regular representation of \\spad{a} with respect to any basis.")) (|leftCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{leftCharacteristicPolynomial(a)} returns the characteristic polynomial of the left regular representation of \\spad{a} with respect to any basis.")) (|rightTraceMatrix| (((|Matrix| |#1|) (|Vector| $)) "\\spad{rightTraceMatrix([v1,...,vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj}.")) (|leftTraceMatrix| (((|Matrix| |#1|) (|Vector| $)) "\\spad{leftTraceMatrix([v1,...,vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj}.")) (|rightDiscriminant| ((|#1| (|Vector| $)) "\\spad{rightDiscriminant([v1,...,vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj}. Note: the same as \\spad{determinant(rightTraceMatrix([v1,...,vn]))}.")) (|leftDiscriminant| ((|#1| (|Vector| $)) "\\spad{leftDiscriminant([v1,...,vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj}. Note: the same as \\spad{determinant(leftTraceMatrix([v1,...,vn]))}.")) (|represents| (($ (|Vector| |#1|) (|Vector| $)) "\\spad{represents([a1,...,am],[v1,...,vm])} returns the linear combination \\spad{a1*vm + ... + an*vm}.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $) (|Vector| $)) "\\spad{coordinates([a1,...,am],[v1,...,vn])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{ai} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.") (((|Vector| |#1|) $ (|Vector| $)) "\\spad{coordinates(a,[v1,...,vn])} returns the coordinates of \\spad{a} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rightNorm| ((|#1| $) "\\spad{rightNorm(a)} returns the determinant of the right regular representation of \\spad{a}.")) (|leftNorm| ((|#1| $) "\\spad{leftNorm(a)} returns the determinant of the left regular representation of \\spad{a}.")) (|rightTrace| ((|#1| $) "\\spad{rightTrace(a)} returns the trace of the right regular representation of \\spad{a}.")) (|leftTrace| ((|#1| $) "\\spad{leftTrace(a)} returns the trace of the left regular representation of \\spad{a}.")) (|rightRegularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) "\\spad{rightRegularRepresentation(a,[v1,...,vn])} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,...,vn]}.")) (|leftRegularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) "\\spad{leftRegularRepresentation(a,[v1,...,vn])} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,...,vn]}.")) (|structuralConstants| (((|Vector| (|Matrix| |#1|)) (|Vector| $)) "\\spad{structuralConstants([v1,v2,...,vm])} calculates the structural constants \\spad{[(gammaijk) for k in 1..m]} defined by \\spad{vi * vj = gammaij1 * v1 + ... + gammaijm * vm},{} where \\spad{[v1,...,vm]} is an \\spad{R}-module basis of a subalgebra.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|)) (|Vector| $)) "\\spad{conditionsForIdempotents([v1,...,vn])} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra as \\spad{R}-module.")) (|someBasis| (((|Vector| $)) "\\spad{someBasis()} returns some \\spad{R}-module basis."))) -((-4460 |has| |#1| (-568)) (-4458 . T) (-4457 . T)) +((-4461 |has| |#1| (-568)) (-4459 . T) (-4458 . T)) NIL (-379) ((|constructor| (NIL "The category of domains composed of a finite set of elements. We include the functions \\spadfun{lookup} and \\spadfun{index} to give a bijection between the finite set and an initial segment of positive integers. \\blankline")) (|random| (($) "\\spad{random()} returns a random element from the set.")) (|lookup| (((|PositiveInteger|) $) "\\spad{lookup(x)} returns a positive integer such that \\spad{x = index lookup x}.")) (|index| (($ (|PositiveInteger|)) "\\spad{index(i)} takes a positive integer \\spad{i} less than or equal to \\spad{size()} and returns the \\spad{i}\\spad{-}th element of the set. This operation establishs a bijection between the elements of the finite set and \\spad{1..size()}.")) (|size| (((|NonNegativeInteger|)) "\\spad{size()} returns the number of elements in the set."))) @@ -1454,7 +1454,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-374)))) (-381 R UP) ((|constructor| (NIL "A FiniteRankAlgebra is an algebra over a commutative ring \\spad{R} which is a free \\spad{R}-module of finite rank.")) (|minimalPolynomial| ((|#2| $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of \\spad{a}.")) (|characteristicPolynomial| ((|#2| $) "\\spad{characteristicPolynomial(a)} returns the characteristic polynomial of the regular representation of \\spad{a} with respect to any basis.")) (|traceMatrix| (((|Matrix| |#1|) (|Vector| $)) "\\spad{traceMatrix([v1,..,vn])} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr}(\\spad{vi} * \\spad{vj}) )")) (|discriminant| ((|#1| (|Vector| $)) "\\spad{discriminant([v1,..,vn])} returns \\spad{determinant(traceMatrix([v1,..,vn]))}.")) (|represents| (($ (|Vector| |#1|) (|Vector| $)) "\\spad{represents([a1,..,an],[v1,..,vn])} returns \\spad{a1*v1 + ... + an*vn}.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $) (|Vector| $)) "\\spad{coordinates([v1,...,vm], basis)} returns the coordinates of the \\spad{vi}\\spad{'s} with to the basis \\spad{basis}. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#1|) $ (|Vector| $)) "\\spad{coordinates(a,basis)} returns the coordinates of \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|norm| ((|#1| $) "\\spad{norm(a)} returns the determinant of the regular representation of \\spad{a} with respect to any basis.")) (|trace| ((|#1| $) "\\spad{trace(a)} returns the trace of the regular representation of \\spad{a} with respect to any basis.")) (|regularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) "\\spad{regularRepresentation(a,basis)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra."))) -((-4457 . T) (-4458 . T) (-4460 . T)) +((-4458 . T) (-4459 . T) (-4461 . T)) NIL (-382 S A R B) ((|constructor| (NIL "FiniteLinearAggregateFunctions2 provides functions involving two FiniteLinearAggregates where the underlying domains might be different. An example of this might be creating a list of rational numbers by mapping a function across a list of integers where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-aggregates \\spad{x} of aggregrate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad{[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,[1,2,3],0)} does \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as the identity element for the function \\spad{f}.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f,a)} applies function \\spad{f} to each member of aggregate \\spad{a} resulting in a new aggregate over a possibly different underlying domain."))) @@ -1463,14 +1463,14 @@ NIL (-383 A S) ((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $) "\\spad{sort!(p,u)} returns \\spad{u} with its elements ordered by \\spad{p}.")) (|reverse!| (($ $) "\\spad{reverse!(u)} returns \\spad{u} with its elements in reverse order.")) (|copyInto!| (($ $ $ (|Integer|)) "\\spad{copyInto!(u,v,i)} returns aggregate \\spad{u} containing a copy of \\spad{v} inserted at element \\spad{i}.")) (|position| (((|Integer|) |#2| $ (|Integer|)) "\\spad{position(x,a,n)} returns the index \\spad{i} of the first occurrence of \\spad{x} in \\axiom{a} where \\axiom{\\spad{i} \\spad{>=} \\spad{n}},{} and \\axiom{minIndex(a) - 1} if no such \\spad{x} is found.") (((|Integer|) |#2| $) "\\spad{position(x,a)} returns the index \\spad{i} of the first occurrence of \\spad{x} in a,{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.") (((|Integer|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{position(p,a)} returns the index \\spad{i} of the first \\spad{x} in \\axiom{a} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.")) (|sorted?| (((|Boolean|) $) "\\spad{sorted?(u)} tests if the elements of \\spad{u} are in ascending order.") (((|Boolean|) (|Mapping| (|Boolean|) |#2| |#2|) $) "\\spad{sorted?(p,a)} tests if \\axiom{a} is sorted according to predicate \\spad{p}.")) (|sort| (($ $) "\\spad{sort(u)} returns an \\spad{u} with elements in ascending order. Note: \\axiom{sort(\\spad{u}) = sort(\\spad{<=},{}\\spad{u})}.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $) "\\spad{sort(p,a)} returns a copy of \\axiom{a} sorted using total ordering predicate \\spad{p}.")) (|reverse| (($ $) "\\spad{reverse(a)} returns a copy of \\axiom{a} with elements in reverse order.")) (|merge| (($ $ $) "\\spad{merge(u,v)} merges \\spad{u} and \\spad{v} in ascending order. Note: \\axiom{merge(\\spad{u},{}\\spad{v}) = merge(\\spad{<=},{}\\spad{u},{}\\spad{v})}.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $ $) "\\spad{merge(p,a,b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) NIL -((|HasAttribute| |#1| (QUOTE -4464)) (|HasCategory| |#2| (QUOTE (-861))) (|HasCategory| |#2| (QUOTE (-1120)))) +((|HasAttribute| |#1| (QUOTE -4465)) (|HasCategory| |#2| (QUOTE (-861))) (|HasCategory| |#2| (QUOTE (-1121)))) (-384 S) ((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $) "\\spad{sort!(p,u)} returns \\spad{u} with its elements ordered by \\spad{p}.")) (|reverse!| (($ $) "\\spad{reverse!(u)} returns \\spad{u} with its elements in reverse order.")) (|copyInto!| (($ $ $ (|Integer|)) "\\spad{copyInto!(u,v,i)} returns aggregate \\spad{u} containing a copy of \\spad{v} inserted at element \\spad{i}.")) (|position| (((|Integer|) |#1| $ (|Integer|)) "\\spad{position(x,a,n)} returns the index \\spad{i} of the first occurrence of \\spad{x} in \\axiom{a} where \\axiom{\\spad{i} \\spad{>=} \\spad{n}},{} and \\axiom{minIndex(a) - 1} if no such \\spad{x} is found.") (((|Integer|) |#1| $) "\\spad{position(x,a)} returns the index \\spad{i} of the first occurrence of \\spad{x} in a,{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.") (((|Integer|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{position(p,a)} returns the index \\spad{i} of the first \\spad{x} in \\axiom{a} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.")) (|sorted?| (((|Boolean|) $) "\\spad{sorted?(u)} tests if the elements of \\spad{u} are in ascending order.") (((|Boolean|) (|Mapping| (|Boolean|) |#1| |#1|) $) "\\spad{sorted?(p,a)} tests if \\axiom{a} is sorted according to predicate \\spad{p}.")) (|sort| (($ $) "\\spad{sort(u)} returns an \\spad{u} with elements in ascending order. Note: \\axiom{sort(\\spad{u}) = sort(\\spad{<=},{}\\spad{u})}.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $) "\\spad{sort(p,a)} returns a copy of \\axiom{a} sorted using total ordering predicate \\spad{p}.")) (|reverse| (($ $) "\\spad{reverse(a)} returns a copy of \\axiom{a} with elements in reverse order.")) (|merge| (($ $ $) "\\spad{merge(u,v)} merges \\spad{u} and \\spad{v} in ascending order. Note: \\axiom{merge(\\spad{u},{}\\spad{v}) = merge(\\spad{<=},{}\\spad{u},{}\\spad{v})}.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $ $) "\\spad{merge(p,a,b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) -((-4463 . T)) +((-4464 . T)) NIL (-385 |VarSet| R) ((|constructor| (NIL "The category of free Lie algebras. It is used by domains of non-commutative algebra: \\spadtype{LiePolynomial} and \\spadtype{XPBWPolynomial}. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr})")) (|eval| (($ $ (|List| |#1|) (|List| $)) "\\axiom{eval(\\spad{p},{} [\\spad{x1},{}...,{}\\spad{xn}],{} [\\spad{v1},{}...,{}\\spad{vn}])} replaces \\axiom{\\spad{xi}} by \\axiom{\\spad{vi}} in \\axiom{\\spad{p}}.") (($ $ |#1| $) "\\axiom{eval(\\spad{p},{} \\spad{x},{} \\spad{v})} replaces \\axiom{\\spad{x}} by \\axiom{\\spad{v}} in \\axiom{\\spad{p}}.")) (|varList| (((|List| |#1|) $) "\\axiom{varList(\\spad{x})} returns the list of distinct entries of \\axiom{\\spad{x}}.")) (|trunc| (($ $ (|NonNegativeInteger|)) "\\axiom{trunc(\\spad{p},{}\\spad{n})} returns the polynomial \\axiom{\\spad{p}} truncated at order \\axiom{\\spad{n}}.")) (|mirror| (($ $) "\\axiom{mirror(\\spad{x})} returns \\axiom{Sum(r_i mirror(w_i))} if \\axiom{\\spad{x}} is \\axiom{Sum(r_i w_i)}.")) (|LiePoly| (($ (|LyndonWord| |#1|)) "\\axiom{LiePoly(\\spad{l})} returns the bracketed form of \\axiom{\\spad{l}} as a Lie polynomial.")) (|rquo| (((|XRecursivePolynomial| |#1| |#2|) (|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{rquo(\\spad{x},{}\\spad{y})} returns the right simplification of \\axiom{\\spad{x}} by \\axiom{\\spad{y}}.")) (|lquo| (((|XRecursivePolynomial| |#1| |#2|) (|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{lquo(\\spad{x},{}\\spad{y})} returns the left simplification of \\axiom{\\spad{x}} by \\axiom{\\spad{y}}.")) (|degree| (((|NonNegativeInteger|) $) "\\axiom{degree(\\spad{x})} returns the greatest length of a word in the support of \\axiom{\\spad{x}}.")) (|coerce| (((|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{x})} returns \\axiom{\\spad{x}} as a recursive polynomial.") (((|XDistributedPolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{x})} returns \\axiom{\\spad{x}} as distributed polynomial.") (($ |#1|) "\\axiom{coerce(\\spad{x})} returns \\axiom{\\spad{x}} as a Lie polynomial.")) (|coef| ((|#2| (|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{coef(\\spad{x},{}\\spad{y})} returns the scalar product of \\axiom{\\spad{x}} by \\axiom{\\spad{y}},{} the set of words being regarded as an orthogonal basis."))) -((|JacobiIdentity| . T) (|NullSquare| . T) (-4458 . T) (-4457 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-4459 . T) (-4458 . T)) NIL (-386 S V) ((|constructor| (NIL "This package exports 3 sorting algorithms which work over FiniteLinearAggregates.")) (|shellSort| ((|#2| (|Mapping| (|Boolean|) |#1| |#1|) |#2|) "\\spad{shellSort(f, agg)} sorts the aggregate agg with the ordering function \\spad{f} using the shellSort algorithm.")) (|heapSort| ((|#2| (|Mapping| (|Boolean|) |#1| |#1|) |#2|) "\\spad{heapSort(f, agg)} sorts the aggregate agg with the ordering function \\spad{f} using the heapsort algorithm.")) (|quickSort| ((|#2| (|Mapping| (|Boolean|) |#1| |#1|) |#2|) "\\spad{quickSort(f, agg)} sorts the aggregate agg with the ordering function \\spad{f} using the quicksort algorithm."))) @@ -1490,7 +1490,7 @@ NIL NIL (-390) ((|constructor| (NIL "\\spadtype{Float} implements arbitrary precision floating point arithmetic. The number of significant digits of each operation can be set to an arbitrary value (the default is 20 decimal digits). The operation \\spad{float(mantissa,exponent,\\spadfunFrom{base}{FloatingPointSystem})} for integer \\spad{mantissa},{} \\spad{exponent} specifies the number \\spad{mantissa * \\spadfunFrom{base}{FloatingPointSystem} ** exponent} The underlying representation for floats is binary not decimal. The implications of this are described below. \\blankline The model adopted is that arithmetic operations are rounded to to nearest unit in the last place,{} that is,{} accurate to within \\spad{2**(-\\spadfunFrom{bits}{FloatingPointSystem})}. Also,{} the elementary functions and constants are accurate to one unit in the last place. A float is represented as a record of two integers,{} the mantissa and the exponent. The \\spadfunFrom{base}{FloatingPointSystem} of the representation is binary,{} hence a \\spad{Record(m:mantissa,e:exponent)} represents the number \\spad{m * 2 ** e}. Though it is not assumed that the underlying integers are represented with a binary \\spadfunFrom{base}{FloatingPointSystem},{} the code will be most efficient when this is the the case (this is \\spad{true} in most implementations of Lisp). The decision to choose the \\spadfunFrom{base}{FloatingPointSystem} to be binary has some unfortunate consequences. First,{} decimal numbers like 0.3 cannot be represented exactly. Second,{} there is a further loss of accuracy during conversion to decimal for output. To compensate for this,{} if \\spad{d} digits of precision are specified,{} \\spad{1 + ceiling(log2 d)} bits are used. Two numbers that are displayed identically may therefore be not equal. On the other hand,{} a significant efficiency loss would be incurred if we chose to use a decimal \\spadfunFrom{base}{FloatingPointSystem} when the underlying integer base is binary. \\blankline Algorithms used: For the elementary functions,{} the general approach is to apply identities so that the taylor series can be used,{} and,{} so that it will converge within \\spad{O( sqrt n )} steps. For example,{} using the identity \\spad{exp(x) = exp(x/2)**2},{} we can compute \\spad{exp(1/3)} to \\spad{n} digits of precision as follows. We have \\spad{exp(1/3) = exp(2 ** (-sqrt s) / 3) ** (2 ** sqrt s)}. The taylor series will converge in less than sqrt \\spad{n} steps and the exponentiation requires sqrt \\spad{n} multiplications for a total of \\spad{2 sqrt n} multiplications. Assuming integer multiplication costs \\spad{O( n**2 )} the overall running time is \\spad{O( sqrt(n) n**2 )}. This approach is the best known approach for precisions up to about 10,{}000 digits at which point the methods of Brent which are \\spad{O( log(n) n**2 )} become competitive. Note also that summing the terms of the taylor series for the elementary functions is done using integer operations. This avoids the overhead of floating point operations and results in efficient code at low precisions. This implementation makes no attempt to reuse storage,{} relying on the underlying system to do \\spadgloss{garbage collection}. \\spad{I} estimate that the efficiency of this package at low precisions could be improved by a factor of 2 if in-place operations were available. \\blankline Running times: in the following,{} \\spad{n} is the number of bits of precision \\indented{5}{\\spad{*},{} \\spad{/},{} \\spad{sqrt},{} \\spad{pi},{} \\spad{exp1},{} \\spad{log2},{} \\spad{log10}: \\spad{ O( n**2 )}} \\indented{5}{\\spad{exp},{} \\spad{log},{} \\spad{sin},{} \\spad{atan}:\\space{2}\\spad{ O( sqrt(n) n**2 )}} The other elementary functions are coded in terms of the ones above.")) (|outputSpacing| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputSpacing(n)} inserts a space after \\spad{n} (default 10) digits on output; outputSpacing(0) means no spaces are inserted.")) (|outputGeneral| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputGeneral(n)} sets the output mode to general notation with \\spad{n} significant digits displayed.") (((|Void|)) "\\spad{outputGeneral()} sets the output mode (default mode) to general notation; numbers will be displayed in either fixed or floating (scientific) notation depending on the magnitude.")) (|outputFixed| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFixed(n)} sets the output mode to fixed point notation,{} with \\spad{n} digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFixed()} sets the output mode to fixed point notation; the output will contain a decimal point.")) (|outputFloating| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFloating(n)} sets the output mode to floating (scientific) notation with \\spad{n} significant digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFloating()} sets the output mode to floating (scientific) notation,{} \\spadignore{i.e.} \\spad{mantissa * 10 exponent} is displayed as \\spad{0.mantissa E exponent}.")) (|atan| (($ $ $) "\\spad{atan(x,y)} computes the arc tangent from \\spad{x} with phase \\spad{y}.")) (|exp1| (($) "\\spad{exp1()} returns exp 1: \\spad{2.7182818284...}.")) (|log10| (($ $) "\\spad{log10(x)} computes the logarithm for \\spad{x} to base 10.") (($) "\\spad{log10()} returns \\spad{ln 10}: \\spad{2.3025809299...}.")) (|log2| (($ $) "\\spad{log2(x)} computes the logarithm for \\spad{x} to base 2.") (($) "\\spad{log2()} returns \\spad{ln 2},{} \\spadignore{i.e.} \\spad{0.6931471805...}.")) (|rationalApproximation| (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rationalApproximation(f, n, b)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< b**(-n)},{} that is \\spad{|(r-f)/f| < b**(-n)}.") (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|)) "\\spad{rationalApproximation(f, n)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< 10**(-n)}.")) (|shift| (($ $ (|Integer|)) "\\spad{shift(x,n)} adds \\spad{n} to the exponent of float \\spad{x}.")) (|relerror| (((|Integer|) $ $) "\\spad{relerror(x,y)} computes the absolute value of \\spad{x - y} divided by \\spad{y},{} when \\spad{y \\~= 0}.")) (|normalize| (($ $) "\\spad{normalize(x)} normalizes \\spad{x} at current precision.")) (** (($ $ $) "\\spad{x ** y} computes \\spad{exp(y log x)} where \\spad{x >= 0}.")) (/ (($ $ (|Integer|)) "\\spad{x / i} computes the division from \\spad{x} by an integer \\spad{i}."))) -((-4446 . T) (-4454 . T) (-2641 . T) (-4455 . T) (-4461 . T) (-4456 . T) ((-4465 "*") . T) (-4457 . T) (-4458 . T) (-4460 . T)) +((-4447 . T) (-4455 . T) (-4165 . T) (-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-391 |Par|) ((|constructor| (NIL "\\indented{3}{This is a package for the approximation of real solutions for} systems of polynomial equations over the rational numbers. The results are expressed as either rational numbers or floats depending on the type of the precision parameter which can be either a rational number or a floating point number.")) (|realRoots| (((|List| |#1|) (|Fraction| (|Polynomial| (|Integer|))) |#1|) "\\spad{realRoots(rf, eps)} finds the real zeros of a univariate rational function with precision given by eps.") (((|List| (|List| |#1|)) (|List| (|Fraction| (|Polynomial| (|Integer|)))) (|List| (|Symbol|)) |#1|) "\\spad{realRoots(lp,lv,eps)} computes the list of the real solutions of the list \\spad{lp} of rational functions with rational coefficients with respect to the variables in \\spad{lv},{} with precision \\spad{eps}. Each solution is expressed as a list of numbers in order corresponding to the variables in \\spad{lv}.")) (|solve| (((|List| (|Equation| (|Polynomial| |#1|))) (|Equation| (|Fraction| (|Polynomial| (|Integer|)))) |#1|) "\\spad{solve(eq,eps)} finds all of the real solutions of the univariate equation \\spad{eq} of rational functions with respect to the unique variables appearing in \\spad{eq},{} with precision \\spad{eps}.") (((|List| (|Equation| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| (|Integer|))) |#1|) "\\spad{solve(p,eps)} finds all of the real solutions of the univariate rational function \\spad{p} with rational coefficients with respect to the unique variable appearing in \\spad{p},{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| |#1|)))) (|List| (|Equation| (|Fraction| (|Polynomial| (|Integer|))))) |#1|) "\\spad{solve(leq,eps)} finds all of the real solutions of the system \\spad{leq} of equationas of rational functions with respect to all the variables appearing in \\spad{lp},{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| |#1|)))) (|List| (|Fraction| (|Polynomial| (|Integer|)))) |#1|) "\\spad{solve(lp,eps)} finds all of the real solutions of the system \\spad{lp} of rational functions over the rational numbers with respect to all the variables appearing in \\spad{lp},{} with precision \\spad{eps}."))) @@ -1498,11 +1498,11 @@ NIL NIL (-392 R S) ((|constructor| (NIL "This domain implements linear combinations of elements from the domain \\spad{S} with coefficients in the domain \\spad{R} where \\spad{S} is an ordered set and \\spad{R} is a ring (which may be non-commutative). This domain is used by domains of non-commutative algebra such as: \\indented{4}{\\spadtype{XDistributedPolynomial},{}} \\indented{4}{\\spadtype{XRecursivePolynomial}.} Author: Michel Petitot (petitot@lifl.\\spad{fr})")) (* (($ |#2| |#1|) "\\spad{s*r} returns the product \\spad{r*s} used by \\spadtype{XRecursivePolynomial}"))) -((-4458 . T) (-4457 . T)) +((-4459 . T) (-4458 . T)) ((|HasCategory| |#1| (QUOTE (-174)))) (-393 R |Basis|) ((|constructor| (NIL "A domain of this category implements formal linear combinations of elements from a domain \\spad{Basis} with coefficients in a domain \\spad{R}. The domain \\spad{Basis} needs only to belong to the category \\spadtype{SetCategory} and \\spad{R} to the category \\spadtype{Ring}. Thus the coefficient ring may be non-commutative. See the \\spadtype{XDistributedPolynomial} constructor for examples of domains built with the \\spadtype{FreeModuleCat} category constructor. Author: Michel Petitot (petitot@lifl.\\spad{fr})")) (|reductum| (($ $) "\\spad{reductum(x)} returns \\spad{x} minus its leading term.")) (|leadingTerm| (((|Record| (|:| |k| |#2|) (|:| |c| |#1|)) $) "\\spad{leadingTerm(x)} returns the first term which appears in \\spad{ListOfTerms(x)}.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(x)} returns the first coefficient which appears in \\spad{ListOfTerms(x)}.")) (|leadingMonomial| ((|#2| $) "\\spad{leadingMonomial(x)} returns the first element from \\spad{Basis} which appears in \\spad{ListOfTerms(x)}.")) (|numberOfMonomials| (((|NonNegativeInteger|) $) "\\spad{numberOfMonomials(x)} returns the number of monomials of \\spad{x}.")) (|monomials| (((|List| $) $) "\\spad{monomials(x)} returns the list of \\spad{r_i*b_i} whose sum is \\spad{x}.")) (|coefficients| (((|List| |#1|) $) "\\spad{coefficients(x)} returns the list of coefficients of \\spad{x}.")) (|ListOfTerms| (((|List| (|Record| (|:| |k| |#2|) (|:| |c| |#1|))) $) "\\spad{ListOfTerms(x)} returns a list \\spad{lt} of terms with type \\spad{Record(k: Basis, c: R)} such that \\spad{x} equals \\spad{reduce(+, map(x +-> monom(x.k, x.c), lt))}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(x)} returns \\spad{true} if \\spad{x} contains a single monomial.")) (|monom| (($ |#2| |#1|) "\\spad{monom(b,r)} returns the element with the single monomial \\indented{1}{\\spad{b} and coefficient \\spad{r}.}")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,u)} maps function \\spad{fn} onto the coefficients \\indented{1}{of the non-zero monomials of \\spad{u}.}")) (|coefficient| ((|#1| $ |#2|) "\\spad{coefficient(x,b)} returns the coefficient of \\spad{b} in \\spad{x}.")) (* (($ |#1| |#2|) "\\spad{r*b} returns the product of \\spad{r} by \\spad{b}."))) -((-4458 . T) (-4457 . T)) +((-4459 . T) (-4458 . T)) NIL (-394) ((|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}."))) @@ -1514,7 +1514,7 @@ NIL NIL (-396 R S) ((|constructor| (NIL "A \\spad{bi}-module is a free module over a ring with generators indexed by an ordered set. Each element can be expressed as a finite linear combination of generators. Only non-zero terms are stored."))) -((-4458 . T) (-4457 . T)) +((-4459 . T) (-4458 . T)) ((|HasCategory| |#1| (QUOTE (-174)))) (-397 S) ((|constructor| (NIL "A free monoid on a set \\spad{S} is the monoid of finite products of the form \\spad{reduce(*,[si ** ni])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are nonnegative integers. The multiplication is not commutative.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f, a1\\^e1 ... an\\^en)} returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (|mapExpon| (($ (|Mapping| (|NonNegativeInteger|) (|NonNegativeInteger|)) $) "\\spad{mapExpon(f, a1\\^e1 ... an\\^en)} returns \\spad{a1\\^f(e1) ... an\\^f(en)}.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(x, n)} returns the factor of the n^th monomial of \\spad{x}.")) (|nthExpon| (((|NonNegativeInteger|) $ (|Integer|)) "\\spad{nthExpon(x, n)} returns the exponent of the n^th monomial of \\spad{x}.")) (|factors| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| (|NonNegativeInteger|)))) $) "\\spad{factors(a1\\^e1,...,an\\^en)} returns \\spad{[[a1, e1],...,[an, en]]}.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(x)} returns the number of monomials in \\spad{x}.")) (|overlap| (((|Record| (|:| |lm| $) (|:| |mm| $) (|:| |rm| $)) $ $) "\\spad{overlap(x, y)} returns \\spad{[l, m, r]} such that \\spad{x = l * m},{} \\spad{y = m * r} and \\spad{l} and \\spad{r} have no overlap,{} \\spadignore{i.e.} \\spad{overlap(l, r) = [l, 1, r]}.")) (|divide| (((|Union| (|Record| (|:| |lm| $) (|:| |rm| $)) "failed") $ $) "\\spad{divide(x, y)} returns the left and right exact quotients of \\spad{x} by \\spad{y},{} \\spadignore{i.e.} \\spad{[l, r]} such that \\spad{x = l * y * r},{} \"failed\" if \\spad{x} is not of the form \\spad{l * y * r}.")) (|rquo| (((|Union| $ "failed") $ $) "\\spad{rquo(x, y)} returns the exact right quotient of \\spad{x} by \\spad{y} \\spadignore{i.e.} \\spad{q} such that \\spad{x = q * y},{} \"failed\" if \\spad{x} is not of the form \\spad{q * y}.")) (|lquo| (((|Union| $ "failed") $ $) "\\spad{lquo(x, y)} returns the exact left quotient of \\spad{x} by \\spad{y} \\spadignore{i.e.} \\spad{q} such that \\spad{x = y * q},{} \"failed\" if \\spad{x} is not of the form \\spad{y * q}.")) (|hcrf| (($ $ $) "\\spad{hcrf(x, y)} returns the highest common right factor of \\spad{x} and \\spad{y},{} \\spadignore{i.e.} the largest \\spad{d} such that \\spad{x = a d} and \\spad{y = b d}.")) (|hclf| (($ $ $) "\\spad{hclf(x, y)} returns the highest common left factor of \\spad{x} and \\spad{y},{} \\spadignore{i.e.} the largest \\spad{d} such that \\spad{x = d a} and \\spad{y = d b}.")) (** (($ |#1| (|NonNegativeInteger|)) "\\spad{s ** n} returns the product of \\spad{s} by itself \\spad{n} times.")) (* (($ $ |#1|) "\\spad{x * s} returns the product of \\spad{x} by \\spad{s} on the right.") (($ |#1| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) @@ -1526,7 +1526,7 @@ NIL ((|HasCategory| |#1| (QUOTE (-861)))) (-399) ((|constructor| (NIL "A category of domains which model machine arithmetic used by machines in the AXIOM-NAG link."))) -((-4456 . T) ((-4465 "*") . T) (-4457 . T) (-4458 . T) (-4460 . T)) +((-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-400) ((|constructor| (NIL "This domain provides an interface to names in the file system."))) @@ -1538,13 +1538,13 @@ NIL NIL (-402 |n| |class| R) ((|constructor| (NIL "Generate the Free Lie Algebra over a ring \\spad{R} with identity; A \\spad{P}. Hall basis is generated by a package call to HallBasis.")) (|generator| (($ (|NonNegativeInteger|)) "\\spad{generator(i)} is the \\spad{i}th Hall Basis element")) (|shallowExpand| (((|OutputForm|) $) "\\spad{shallowExpand(x)} \\undocumented{}")) (|deepExpand| (((|OutputForm|) $) "\\spad{deepExpand(x)} \\undocumented{}")) (|dimension| (((|NonNegativeInteger|)) "\\spad{dimension()} is the rank of this Lie algebra"))) -((-4458 . T) (-4457 . T)) +((-4459 . T) (-4458 . T)) NIL (-403) ((|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 -(-404 -2117 UP UPUP R) +(-404 -1959 UP UPUP R) ((|constructor| (NIL "\\indented{1}{Finds the order of a divisor over a finite field} Author: Manuel Bronstein Date Created: 1988 Date Last Updated: 11 Jul 1990")) (|order| (((|NonNegativeInteger|) (|FiniteDivisor| |#1| |#2| |#3| |#4|)) "\\spad{order(x)} \\undocumented"))) NIL NIL @@ -1568,11 +1568,11 @@ NIL ((|constructor| (NIL "provides an interface to the boot code for calling Fortran")) (|setLegalFortranSourceExtensions| (((|List| (|String|)) (|List| (|String|))) "\\spad{setLegalFortranSourceExtensions(l)} \\undocumented{}")) (|outputAsFortran| (((|Void|) (|FileName|)) "\\spad{outputAsFortran(fn)} \\undocumented{}")) (|linkToFortran| (((|SExpression|) (|Symbol|) (|List| (|Symbol|)) (|TheSymbolTable|) (|List| (|Symbol|))) "\\spad{linkToFortran(s,l,t,lv)} \\undocumented{}") (((|SExpression|) (|Symbol|) (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|)))) (|List| (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|))))) (|List| (|Symbol|)) (|Symbol|)) "\\spad{linkToFortran(s,l,ll,lv,t)} \\undocumented{}") (((|SExpression|) (|Symbol|) (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|)))) (|List| (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|))))) (|List| (|Symbol|))) "\\spad{linkToFortran(s,l,ll,lv)} \\undocumented{}"))) NIL NIL -(-410 -4148 |returnType| -4284 |symbols|) +(-410 -2627 |returnType| -1928 |symbols|) ((|constructor| (NIL "\\axiomType{FortranProgram} allows the user to build and manipulate simple models of FORTRAN subprograms. These can then be transformed into actual FORTRAN notation.")) (|coerce| (($ (|Equation| (|Expression| (|Complex| (|Float|))))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Equation| (|Expression| (|Float|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Equation| (|Expression| (|Integer|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Expression| (|Complex| (|Float|)))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Expression| (|Float|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Expression| (|Integer|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Equation| (|Expression| (|MachineComplex|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Equation| (|Expression| (|MachineFloat|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Equation| (|Expression| (|MachineInteger|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Expression| (|MachineComplex|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Expression| (|MachineFloat|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Expression| (|MachineInteger|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(r)} \\undocumented{}") (($ (|List| (|FortranCode|))) "\\spad{coerce(lfc)} \\undocumented{}") (($ (|FortranCode|)) "\\spad{coerce(fc)} \\undocumented{}"))) NIL NIL -(-411 -2117 UP) +(-411 -1959 UP) ((|constructor| (NIL "\\indented{1}{Full partial fraction expansion of rational functions} Author: Manuel Bronstein Date Created: 9 December 1992 Date Last Updated: June 18,{} 2010 References: \\spad{M}.Bronstein & \\spad{B}.Salvy,{} \\indented{12}{Full Partial Fraction Decomposition of Rational Functions,{}} \\indented{12}{in Proceedings of ISSAC'93,{} Kiev,{} ACM Press.}")) (|construct| (($ (|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| |#2|) (|:| |num| |#2|)))) "\\spad{construct(l)} is the inverse of fracPart.")) (|fracPart| (((|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| |#2|) (|:| |num| |#2|))) $) "\\spad{fracPart(f)} returns the list of summands of the fractional part of \\spad{f}.")) (|polyPart| ((|#2| $) "\\spad{polyPart(f)} returns the polynomial part of \\spad{f}.")) (|fullPartialFraction| (($ (|Fraction| |#2|)) "\\spad{fullPartialFraction(f)} returns \\spad{[p, [[j, Dj, Hj]...]]} such that \\spad{f = p(x) + \\sum_{[j,Dj,Hj] in l} \\sum_{Dj(a)=0} Hj(a)/(x - a)\\^j}.")) (+ (($ |#2| $) "\\spad{p + x} returns the sum of \\spad{p} and \\spad{x}"))) NIL NIL @@ -1586,15 +1586,15 @@ NIL NIL (-414) ((|constructor| (NIL "FieldOfPrimeCharacteristic is the category of fields of prime characteristic,{} \\spadignore{e.g.} finite fields,{} algebraic closures of fields of prime characteristic,{} transcendental extensions of of fields of prime characteristic.")) (|primeFrobenius| (($ $ (|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|)) $) "\\spad{order(a)} computes the order of an element in the multiplicative group of the field. Error: if \\spad{a} is 0."))) -((-4455 . T) (-4461 . T) (-4456 . T) ((-4465 "*") . T) (-4457 . T) (-4458 . T) (-4460 . T)) +((-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-415 S) ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\\spad{\"+\"}) does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\spad{max()} returns the maximum floating point number.")) (|min| (($) "\\spad{min()} returns the minimum floating point number.")) (|decreasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{decreasePrecision(n)} decreases the current \\spadfunFrom{precision}{FloatingPointSystem} precision by \\spad{n} decimal digits.")) (|increasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{increasePrecision(n)} increases the current \\spadfunFrom{precision}{FloatingPointSystem} by \\spad{n} decimal digits.")) (|precision| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{precision(n)} set the precision in the base to \\spad{n} decimal digits.") (((|PositiveInteger|)) "\\spad{precision()} returns the precision in digits base.")) (|digits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{digits(d)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{d} digits.") (((|PositiveInteger|)) "\\spad{digits()} returns ceiling\\spad{'s} precision in decimal digits.")) (|bits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{bits(n)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{n} bits.") (((|PositiveInteger|)) "\\spad{bits()} returns ceiling\\spad{'s} precision in bits.")) (|mantissa| (((|Integer|) $) "\\spad{mantissa(x)} returns the mantissa part of \\spad{x}.")) (|exponent| (((|Integer|) $) "\\spad{exponent(x)} returns the \\spadfunFrom{exponent}{FloatingPointSystem} part of \\spad{x}.")) (|base| (((|PositiveInteger|)) "\\spad{base()} returns the base of the \\spadfunFrom{exponent}{FloatingPointSystem}.")) (|order| (((|Integer|) $) "\\spad{order x} is the order of magnitude of \\spad{x}. Note: \\spad{base ** order x <= |x| < base ** (1 + order x)}.")) (|float| (($ (|Integer|) (|Integer|) (|PositiveInteger|)) "\\spad{float(a,e,b)} returns \\spad{a * b ** e}.") (($ (|Integer|) (|Integer|)) "\\spad{float(a,e)} returns \\spad{a * base() ** e}.")) (|approximate| ((|attribute|) "\\spad{approximate} means \"is an approximation to the real numbers\"."))) NIL -((|HasAttribute| |#1| (QUOTE -4446)) (|HasAttribute| |#1| (QUOTE -4454))) +((|HasAttribute| |#1| (QUOTE -4447)) (|HasAttribute| |#1| (QUOTE -4455))) (-416) ((|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 \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\\spad{\"+\"}) does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\spad{max()} returns the maximum floating point number.")) (|min| (($) "\\spad{min()} returns the minimum floating point number.")) (|decreasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{decreasePrecision(n)} decreases the current \\spadfunFrom{precision}{FloatingPointSystem} precision by \\spad{n} decimal digits.")) (|increasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{increasePrecision(n)} increases the current \\spadfunFrom{precision}{FloatingPointSystem} by \\spad{n} decimal digits.")) (|precision| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{precision(n)} set the precision in the base to \\spad{n} decimal digits.") (((|PositiveInteger|)) "\\spad{precision()} returns the precision in digits base.")) (|digits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{digits(d)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{d} digits.") (((|PositiveInteger|)) "\\spad{digits()} returns ceiling\\spad{'s} precision in decimal digits.")) (|bits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{bits(n)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{n} bits.") (((|PositiveInteger|)) "\\spad{bits()} returns ceiling\\spad{'s} precision in bits.")) (|mantissa| (((|Integer|) $) "\\spad{mantissa(x)} returns the mantissa part of \\spad{x}.")) (|exponent| (((|Integer|) $) "\\spad{exponent(x)} returns the \\spadfunFrom{exponent}{FloatingPointSystem} part of \\spad{x}.")) (|base| (((|PositiveInteger|)) "\\spad{base()} returns the base of the \\spadfunFrom{exponent}{FloatingPointSystem}.")) (|order| (((|Integer|) $) "\\spad{order x} is the order of magnitude of \\spad{x}. Note: \\spad{base ** order x <= |x| < base ** (1 + order x)}.")) (|float| (($ (|Integer|) (|Integer|) (|PositiveInteger|)) "\\spad{float(a,e,b)} returns \\spad{a * b ** e}.") (($ (|Integer|) (|Integer|)) "\\spad{float(a,e)} returns \\spad{a * base() ** e}.")) (|approximate| ((|attribute|) "\\spad{approximate} means \"is an approximation to the real numbers\"."))) -((-2641 . T) (-4455 . T) (-4461 . T) (-4456 . T) ((-4465 "*") . T) (-4457 . T) (-4458 . T) (-4460 . T)) +((-4165 . T) (-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-417 R S) ((|constructor| (NIL "\\spadtype{FactoredFunctions2} contains functions that involve factored objects whose underlying domains may not be the same. For example,{} \\spadfun{map} might be used to coerce an object of type \\spadtype{Factored(Integer)} to \\spadtype{Factored(Complex(Integer))}.")) (|map| (((|Factored| |#2|) (|Mapping| |#2| |#1|) (|Factored| |#1|)) "\\spad{map(fn,u)} is used to apply the function \\userfun{\\spad{fn}} to every factor of \\spadvar{\\spad{u}}. The new factored object will have all its information flags set to \"nil\". This function is used,{} for example,{} to coerce every factor base to another type."))) @@ -1606,20 +1606,20 @@ NIL NIL (-419 S) ((|constructor| (NIL "Fraction takes an IntegralDomain \\spad{S} and produces the domain of Fractions with numerators and denominators from \\spad{S}. If \\spad{S} is also a GcdDomain,{} then \\spad{gcd}\\spad{'s} between numerator and denominator will be cancelled during all operations.")) (|canonical| ((|attribute|) "\\spad{canonical} means that equal elements are in fact identical."))) -((-4450 -12 (|has| |#1| (-6 -4461)) (|has| |#1| (-464)) (|has| |#1| (-6 -4450))) (-4455 . T) (-4461 . T) (-4456 . T) ((-4465 "*") . T) (-4457 . T) (-4458 . T) (-4460 . T)) -((|HasCategory| |#1| (QUOTE (-927))) (|HasCategory| |#1| (LIST (QUOTE -1058) (QUOTE (-1196)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-3794 (-12 (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#1| (QUOTE (-1042))) (|HasCategory| |#1| (QUOTE (-832))) (|HasCategory| |#1| (QUOTE (-861))) (-3794 (|HasCategory| |#1| (QUOTE (-832))) (|HasCategory| |#1| (QUOTE (-861)))) (-3794 (-12 (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (LIST (QUOTE -1058) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-1172))) (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-390)))) (-3794 (-12 (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -906) (QUOTE (-390))))) (-3794 (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -906) (QUOTE (-576))))) (-12 (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-840))))) (-3794 (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))) (-12 (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-840))))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (LIST (QUOTE -918) (QUOTE (-1196)))) (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (LIST (QUOTE -916) (QUOTE (-1196)))) (|HasCategory| |#1| (LIST (QUOTE -526) (QUOTE (-1196)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -296) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-557))) (-12 (|HasAttribute| |#1| (QUOTE -4461)) (|HasAttribute| |#1| (QUOTE -4450)) (|HasCategory| |#1| (QUOTE (-464)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (LIST (QUOTE -1058) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -906) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-927)))) (-3794 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-927)))) (|HasCategory| |#1| (QUOTE (-146))))) +((-4451 -12 (|has| |#1| (-6 -4462)) (|has| |#1| (-464)) (|has| |#1| (-6 -4451))) (-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) +((|HasCategory| |#1| (QUOTE (-928))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-1197)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-2758 (-12 (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#1| (QUOTE (-1043))) (|HasCategory| |#1| (QUOTE (-832))) (|HasCategory| |#1| (QUOTE (-861))) (-2758 (|HasCategory| |#1| (QUOTE (-832))) (|HasCategory| |#1| (QUOTE (-861)))) (-2758 (-12 (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-1173))) (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-390)))) (-2758 (-12 (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390))))) (-2758 (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576))))) (-12 (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-840))))) (-2758 (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))) (-12 (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-840))))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (LIST (QUOTE -919) (QUOTE (-1197)))) (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| |#1| (LIST (QUOTE -526) (QUOTE (-1197)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -296) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-557))) (-12 (|HasAttribute| |#1| (QUOTE -4462)) (|HasAttribute| |#1| (QUOTE -4451)) (|HasCategory| |#1| (QUOTE (-464)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-928)))) (-2758 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-928)))) (|HasCategory| |#1| (QUOTE (-146))))) (-420 S R UP) ((|constructor| (NIL "A \\spadtype{FramedAlgebra} is a \\spadtype{FiniteRankAlgebra} together with a fixed \\spad{R}-module basis.")) (|regularRepresentation| (((|Matrix| |#2|) $) "\\spad{regularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed basis.")) (|discriminant| ((|#2|) "\\spad{discriminant()} = determinant(traceMatrix()).")) (|traceMatrix| (((|Matrix| |#2|)) "\\spad{traceMatrix()} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr(vi * vj)} ),{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|convert| (($ (|Vector| |#2|)) "\\spad{convert([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.") (((|Vector| |#2|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#2|)) "\\spad{represents([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $)) "\\spad{coordinates([v1,...,vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#2|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) NIL NIL (-421 R UP) ((|constructor| (NIL "A \\spadtype{FramedAlgebra} is a \\spadtype{FiniteRankAlgebra} together with a fixed \\spad{R}-module basis.")) (|regularRepresentation| (((|Matrix| |#1|) $) "\\spad{regularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed basis.")) (|discriminant| ((|#1|) "\\spad{discriminant()} = determinant(traceMatrix()).")) (|traceMatrix| (((|Matrix| |#1|)) "\\spad{traceMatrix()} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr(vi * vj)} ),{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|convert| (($ (|Vector| |#1|)) "\\spad{convert([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.") (((|Vector| |#1|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([v1,...,vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#1|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) -((-4457 . T) (-4458 . T) (-4460 . T)) +((-4458 . T) (-4459 . T) (-4461 . T)) NIL (-422 A S) ((|constructor| (NIL "\\indented{2}{A is fully retractable to \\spad{B} means that A is retractable to \\spad{B},{} and,{}} \\indented{2}{in addition,{} if \\spad{B} is retractable to the integers or rational} \\indented{2}{numbers then so is A.} \\indented{2}{In particular,{} what we are asserting is that there are no integers} \\indented{2}{(rationals) in A which don\\spad{'t} retract into \\spad{B}.} Date Created: March 1990 Date Last Updated: 9 April 1991"))) NIL -((|HasCategory| |#2| (LIST (QUOTE -1058) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1058) (QUOTE (-576))))) +((|HasCategory| |#2| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1059) (QUOTE (-576))))) (-423 S) ((|constructor| (NIL "\\indented{2}{A is fully retractable to \\spad{B} means that A is retractable to \\spad{B},{} and,{}} \\indented{2}{in addition,{} if \\spad{B} is retractable to the integers or rational} \\indented{2}{numbers then so is A.} \\indented{2}{In particular,{} what we are asserting is that there are no integers} \\indented{2}{(rationals) in A which don\\spad{'t} retract into \\spad{B}.} Date Created: March 1990 Date Last Updated: 9 April 1991"))) NIL @@ -1628,14 +1628,14 @@ NIL ((|constructor| (NIL "\\indented{1}{Lifting of morphisms to fractional ideals.} Author: Manuel Bronstein Date Created: 1 Feb 1989 Date Last Updated: 27 Feb 1990 Keywords: ideal,{} algebra,{} module.")) (|map| (((|FractionalIdeal| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FractionalIdeal| |#1| |#2| |#3| |#4|)) "\\spad{map(f,i)} \\undocumented{}"))) NIL NIL -(-425 R -2117 UP A) +(-425 R -1959 UP A) ((|constructor| (NIL "Fractional ideals in a framed algebra.")) (|randomLC| ((|#4| (|NonNegativeInteger|) (|Vector| |#4|)) "\\spad{randomLC(n,x)} should be local but conditional.")) (|minimize| (($ $) "\\spad{minimize(I)} returns a reduced set of generators for \\spad{I}.")) (|denom| ((|#1| $) "\\spad{denom(1/d * (f1,...,fn))} returns \\spad{d}.")) (|numer| (((|Vector| |#4|) $) "\\spad{numer(1/d * (f1,...,fn))} = the vector \\spad{[f1,...,fn]}.")) (|norm| ((|#2| $) "\\spad{norm(I)} returns the norm of the ideal \\spad{I}.")) (|basis| (((|Vector| |#4|) $) "\\spad{basis((f1,...,fn))} returns the vector \\spad{[f1,...,fn]}.")) (|ideal| (($ (|Vector| |#4|)) "\\spad{ideal([f1,...,fn])} returns the ideal \\spad{(f1,...,fn)}."))) -((-4460 . T)) +((-4461 . T)) NIL -(-426 R -2117 UP A |ibasis|) +(-426 R -1959 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|) $) "\\spad{basis((f1,...,fn))} = the vector \\spad{[f1,...,fn]}."))) NIL -((|HasCategory| |#4| (LIST (QUOTE -1058) (|devaluate| |#2|)))) +((|HasCategory| |#4| (LIST (QUOTE -1059) (|devaluate| |#2|)))) (-427 AR R AS S) ((|constructor| (NIL "FramedNonAssociativeAlgebraFunctions2 implements functions between two framed non associative algebra domains defined over different rings. The function map is used to coerce between algebras over different domains having the same structural constants.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,u)} maps \\spad{f} onto the coordinates of \\spad{u} to get an element in \\spad{AS} via identification of the basis of \\spad{AR} as beginning part of the basis of \\spad{AS}."))) NIL @@ -1646,12 +1646,12 @@ NIL ((|HasCategory| |#2| (QUOTE (-374)))) (-429 R) ((|constructor| (NIL "FramedNonAssociativeAlgebra(\\spad{R}) is a \\spadtype{FiniteRankNonAssociativeAlgebra} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank) over a commutative ring \\spad{R} together with a fixed \\spad{R}-module basis.")) (|apply| (($ (|Matrix| |#1|) $) "\\spad{apply(m,a)} defines a left operation of \\spad{n} by \\spad{n} matrices where \\spad{n} is the rank of the algebra in terms of matrix-vector multiplication,{} this is a substitute for a left module structure. Error: if shape of matrix doesn\\spad{'t} fit.")) (|rightRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#1|))) "\\spad{rightRankPolynomial()} calculates the right minimal polynomial of the generic element in the algebra,{} defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|leftRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#1|))) "\\spad{leftRankPolynomial()} calculates the left minimal polynomial of the generic element in the algebra,{} defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|rightRegularRepresentation| (((|Matrix| |#1|) $) "\\spad{rightRegularRepresentation(a)} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|leftRegularRepresentation| (((|Matrix| |#1|) $) "\\spad{leftRegularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|rightTraceMatrix| (((|Matrix| |#1|)) "\\spad{rightTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|leftTraceMatrix| (((|Matrix| |#1|)) "\\spad{leftTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|rightDiscriminant| ((|#1|) "\\spad{rightDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note: the same as \\spad{determinant(rightTraceMatrix())}.")) (|leftDiscriminant| ((|#1|) "\\spad{leftDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note: the same as \\spad{determinant(leftTraceMatrix())}.")) (|convert| (($ (|Vector| |#1|)) "\\spad{convert([a1,...,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed \\spad{R}-module basis.") (((|Vector| |#1|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,...,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|))) "\\spad{conditionsForIdempotents()} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the fixed \\spad{R}-module basis.")) (|structuralConstants| (((|Vector| (|Matrix| |#1|))) "\\spad{structuralConstants()} calculates the structural constants \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{vi * vj = gammaij1 * v1 + ... + gammaijn * vn},{} where \\spad{v1},{}...,{}\\spad{vn} is 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."))) -((-4460 |has| |#1| (-568)) (-4458 . T) (-4457 . T)) +((-4461 |has| |#1| (-568)) (-4459 . T) (-4458 . T)) NIL (-430 R) ((|constructor| (NIL "\\spadtype{Factored} creates a domain whose objects are kept in factored form as long as possible. Thus certain operations like multiplication and \\spad{gcd} are relatively easy to do. Others,{} like addition require somewhat more work,{} and unless the argument domain provides a factor function,{} the result may not be completely factored. Each object consists of a unit and a list of factors,{} where a factor has a member of \\spad{R} (the \"base\"),{} and exponent and a flag indicating what is known about the base. A flag may be one of \"nil\",{} \"sqfr\",{} \"irred\" or \"prime\",{} which respectively mean that nothing is known about the base,{} it is square-free,{} it is irreducible,{} or it is prime. The current restriction to integral domains allows simplification to be performed without worrying about multiplication order.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(u)} returns a rational number if \\spad{u} really is one,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(u)} assumes spadvar{\\spad{u}} is actually a rational number and does the conversion to rational number (see \\spadtype{Fraction Integer}).")) (|rational?| (((|Boolean|) $) "\\spad{rational?(u)} tests if \\spadvar{\\spad{u}} is actually a rational number (see \\spadtype{Fraction Integer}).")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,u)} maps the function \\userfun{\\spad{fn}} across the factors of \\spadvar{\\spad{u}} and creates a new factored object. Note: this clears the information flags (sets them to \"nil\") because the effect of \\userfun{\\spad{fn}} is clearly not known in general.")) (|unitNormalize| (($ $) "\\spad{unitNormalize(u)} normalizes the unit part of the factorization. For example,{} when working with factored integers,{} this operation will ensure that the bases are all positive integers.")) (|unit| ((|#1| $) "\\spad{unit(u)} extracts the unit part of the factorization.")) (|flagFactor| (($ |#1| (|Integer|) (|Union| "nil" "sqfr" "irred" "prime")) "\\spad{flagFactor(base,exponent,flag)} creates a factored object with a single factor whose \\spad{base} is asserted to be properly described by the information \\spad{flag}.")) (|sqfrFactor| (($ |#1| (|Integer|)) "\\spad{sqfrFactor(base,exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be square-free (flag = \"sqfr\").")) (|primeFactor| (($ |#1| (|Integer|)) "\\spad{primeFactor(base,exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be prime (flag = \"prime\").")) (|numberOfFactors| (((|NonNegativeInteger|) $) "\\spad{numberOfFactors(u)} returns the number of factors in \\spadvar{\\spad{u}}.")) (|nthFlag| (((|Union| "nil" "sqfr" "irred" "prime") $ (|Integer|)) "\\spad{nthFlag(u,n)} returns the information flag of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} \"nil\" is returned.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(u,n)} returns the base of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} 1 is returned. If \\spadvar{\\spad{u}} consists only of a unit,{} the unit is returned.")) (|nthExponent| (((|Integer|) $ (|Integer|)) "\\spad{nthExponent(u,n)} returns the exponent of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} 0 is returned.")) (|irreducibleFactor| (($ |#1| (|Integer|)) "\\spad{irreducibleFactor(base,exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be irreducible (flag = \"irred\").")) (|factors| (((|List| (|Record| (|:| |factor| |#1|) (|:| |exponent| (|Integer|)))) $) "\\spad{factors(u)} returns a list of the factors in a form suitable for iteration. That is,{} it returns a list where each element is a record containing a base and exponent. The original object is the product of all the factors and the unit (which can be extracted by \\axiom{unit(\\spad{u})}).")) (|nilFactor| (($ |#1| (|Integer|)) "\\spad{nilFactor(base,exponent)} creates a factored object with a single factor with no information about the kind of \\spad{base} (flag = \"nil\").")) (|factorList| (((|List| (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#1|) (|:| |xpnt| (|Integer|)))) $) "\\spad{factorList(u)} returns the list of factors with flags (for use by factoring code).")) (|makeFR| (($ |#1| (|List| (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#1|) (|:| |xpnt| (|Integer|))))) "\\spad{makeFR(unit,listOfFactors)} creates a factored object (for use by factoring code).")) (|exponent| (((|Integer|) $) "\\spad{exponent(u)} returns the exponent of the first factor of \\spadvar{\\spad{u}},{} or 0 if the factored form consists solely of a unit.")) (|expand| ((|#1| $) "\\spad{expand(f)} multiplies the unit and factors together,{} yielding an \"unfactored\" object. Note: this is purposely not called \\spadfun{coerce} which would cause the interpreter to do this automatically."))) -((-4456 . T) ((-4465 "*") . T) (-4457 . T) (-4458 . T) (-4460 . T)) -((|HasCategory| |#1| (LIST (QUOTE -526) (QUOTE (-1196)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -319) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -296) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (QUOTE (-1241))) (-3794 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-1241)))) (|HasCategory| |#1| (QUOTE (-1042))) (|HasCategory| |#1| (LIST (QUOTE -1058) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1058) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -526) (QUOTE (-1196)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -296) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (LIST (QUOTE -918) (QUOTE (-1196)))) (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (LIST (QUOTE -916) (QUOTE (-1196)))) (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-464)))) +((-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) +((|HasCategory| |#1| (LIST (QUOTE -526) (QUOTE (-1197)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -319) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -296) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (QUOTE (-1242))) (-2758 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-1242)))) (|HasCategory| |#1| (QUOTE (-1043))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -526) (QUOTE (-1197)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -296) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (LIST (QUOTE -919) (QUOTE (-1197)))) (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-464)))) (-431 R) ((|constructor| (NIL "\\spadtype{FactoredFunctionUtilities} implements some utility functions for manipulating factored objects.")) (|mergeFactors| (((|Factored| |#1|) (|Factored| |#1|) (|Factored| |#1|)) "\\spad{mergeFactors(u,v)} is used when the factorizations of \\spadvar{\\spad{u}} and \\spadvar{\\spad{v}} are known to be disjoint,{} \\spadignore{e.g.} resulting from a content/primitive part split. Essentially,{} it creates a new factored object by multiplying the units together and appending the lists of factors.")) (|refine| (((|Factored| |#1|) (|Factored| |#1|) (|Mapping| (|Factored| |#1|) |#1|)) "\\spad{refine(u,fn)} is used to apply the function \\userfun{\\spad{fn}} to each factor of \\spadvar{\\spad{u}} and then build a new factored object from the results. For example,{} if \\spadvar{\\spad{u}} were created by calling \\spad{nilFactor(10,2)} then \\spad{refine(u,factor)} would create a factored object equal to that created by \\spad{factor(100)} or \\spad{primeFactor(2,2) * primeFactor(5,2)}."))) NIL @@ -1678,37 +1678,37 @@ NIL ((|HasCategory| |#2| (QUOTE (-861))) (|HasCategory| |#2| (QUOTE (-379)))) (-437 S) ((|constructor| (NIL "A finite-set aggregate models the notion of a finite set,{} that is,{} a collection of elements characterized by membership,{} but not by order or multiplicity. See \\spadtype{Set} for an example.")) (|min| ((|#1| $) "\\spad{min(u)} returns the smallest element of aggregate \\spad{u}.")) (|max| ((|#1| $) "\\spad{max(u)} returns the largest element of aggregate \\spad{u}.")) (|universe| (($) "\\spad{universe()}\\$\\spad{D} returns the universal set for finite set aggregate \\spad{D}.")) (|complement| (($ $) "\\spad{complement(u)} returns the complement of the set \\spad{u},{} \\spadignore{i.e.} the set of all values not in \\spad{u}.")) (|cardinality| (((|NonNegativeInteger|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) -((-4463 . T) (-4453 . T) (-4464 . T)) +((-4464 . T) (-4454 . T) (-4465 . T)) NIL -(-438 R -2117) +(-438 R -1959) ((|constructor| (NIL "\\spadtype{FunctionSpaceComplexIntegration} provides functions for the indefinite integration of complex-valued functions.")) (|complexIntegrate| ((|#2| |#2| (|Symbol|)) "\\spad{complexIntegrate(f, x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable.")) (|internalIntegrate0| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate0 should} be a local function,{} but is conditional.")) (|internalIntegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate(f, x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable."))) NIL NIL (-439 R E) ((|constructor| (NIL "\\indented{1}{Author: James Davenport} Date Created: 17 April 1992 Date Last Updated: Basic Functions: Related Constructors: Also See: AMS Classifications: Keywords: References: Description:")) (|makeCos| (($ |#2| |#1|) "\\spad{makeCos(e,r)} makes a sin expression with given argument and coefficient")) (|makeSin| (($ |#2| |#1|) "\\spad{makeSin(e,r)} makes a sin expression with given argument and coefficient")) (|coerce| (($ (|FourierComponent| |#2|)) "\\spad{coerce(c)} converts sin/cos terms into Fourier Series") (($ |#1|) "\\spad{coerce(r)} converts coefficients into Fourier Series"))) -((-4450 -12 (|has| |#1| (-6 -4450)) (|has| |#2| (-6 -4450))) (-4457 . T) (-4458 . T) (-4460 . T)) -((-12 (|HasAttribute| |#1| (QUOTE -4450)) (|HasAttribute| |#2| (QUOTE -4450)))) -(-440 R -2117) +((-4451 -12 (|has| |#1| (-6 -4451)) (|has| |#2| (-6 -4451))) (-4458 . T) (-4459 . T) (-4461 . T)) +((-12 (|HasAttribute| |#1| (QUOTE -4451)) (|HasAttribute| |#2| (QUOTE -4451)))) +(-440 R -1959) ((|constructor| (NIL "\\spadtype{FunctionSpaceIntegration} provides functions for the indefinite integration of real-valued functions.")) (|integrate| (((|Union| |#2| (|List| |#2|)) |#2| (|Symbol|)) "\\spad{integrate(f, x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a real variable."))) NIL NIL (-441 S R) ((|constructor| (NIL "A space of formal functions with arguments in an arbitrary ordered set.")) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| $)) $ (|Kernel| $)) "\\spad{univariate(f, k)} returns \\spad{f} viewed as a univariate fraction in \\spad{k}.")) (/ (($ (|SparseMultivariatePolynomial| |#2| (|Kernel| $)) (|SparseMultivariatePolynomial| |#2| (|Kernel| $))) "\\spad{p1/p2} returns the quotient of \\spad{p1} and \\spad{p2} as an element of \\%.")) (|denominator| (($ $) "\\spad{denominator(f)} returns the denominator of \\spad{f} converted to \\%.")) (|denom| (((|SparseMultivariatePolynomial| |#2| (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|convert| (($ (|Factored| $)) "\\spad{convert(f1\\^e1 ... fm\\^em)} returns \\spad{(f1)\\^e1 ... (fm)\\^em} as an element of \\%,{} using formal kernels created using a \\spadfunFrom{paren}{ExpressionSpace}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isPower(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|numerator| (($ $) "\\spad{numerator(f)} returns the numerator of \\spad{f} converted to \\%.")) (|numer| (((|SparseMultivariatePolynomial| |#2| (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R} if \\spad{R} is an integral domain. If not,{} then numer(\\spad{f}) = \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|coerce| (($ (|Fraction| (|Polynomial| (|Fraction| |#2|)))) "\\spad{coerce(f)} returns \\spad{f} as an element of \\%.") (($ (|Polynomial| (|Fraction| |#2|))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.") (($ (|Fraction| |#2|)) "\\spad{coerce(q)} returns \\spad{q} as an element of \\%.") (($ (|SparseMultivariatePolynomial| |#2| (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.")) (|isMult| (((|Union| (|Record| (|:| |coef| (|Integer|)) (|:| |var| (|Kernel| $))) "failed") $) "\\spad{isMult(p)} returns \\spad{[n, x]} if \\spad{p = n * x} and \\spad{n <> 0}.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,...,mn]} if \\spad{p = m1 +...+ mn} and \\spad{n > 1}.")) (|isExpt| (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|Symbol|)) "\\spad{isExpt(p,f)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = f(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|BasicOperator|)) "\\spad{isExpt(p,op)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = op(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if \\spad{p = a1*...*an} and \\spad{n > 1}.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns \\spad{x} * \\spad{x} * \\spad{x} * ... * \\spad{x} (\\spad{n} times).")) (|eval| (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ $)) "\\spad{eval(x, s, n, f)} replaces every \\spad{s(a)**n} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ (|List| $))) "\\spad{eval(x, s, n, f)} replaces every \\spad{s(a1,...,am)**n} in \\spad{x} by \\spad{f(a1,...,am)} for any a1,{}...,{}am.") (($ $ (|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| $) (|Symbol|)) "\\spad{eval(x, [s1,...,sm], [f1,...,fm], y)} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $ (|BasicOperator|) $ (|Symbol|)) "\\spad{eval(x, s, f, y)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $) "\\spad{eval(f)} unquotes all the quoted operators in \\spad{f}.") (($ $ (|List| (|Symbol|))) "\\spad{eval(f, [foo1,...,foon])} unquotes all the \\spad{fooi}\\spad{'s} in \\spad{f}.") (($ $ (|Symbol|)) "\\spad{eval(f, foo)} unquotes all the foo\\spad{'s} in \\spad{f}.")) (|applyQuote| (($ (|Symbol|) (|List| $)) "\\spad{applyQuote(foo, [x1,...,xn])} returns \\spad{'foo(x1,...,xn)}.") (($ (|Symbol|) $ $ $ $) "\\spad{applyQuote(foo, x, y, z, t)} returns \\spad{'foo(x,y,z,t)}.") (($ (|Symbol|) $ $ $) "\\spad{applyQuote(foo, x, y, z)} returns \\spad{'foo(x,y,z)}.") (($ (|Symbol|) $ $) "\\spad{applyQuote(foo, x, y)} returns \\spad{'foo(x,y)}.") (($ (|Symbol|) $) "\\spad{applyQuote(foo, x)} returns \\spad{'foo(x)}.")) (|variables| (((|List| (|Symbol|)) $) "\\spad{variables(f)} returns the list of all the variables of \\spad{f}.")) (|ground| ((|#2| $) "\\spad{ground(f)} returns \\spad{f} as an element of \\spad{R}. An error occurs if \\spad{f} is not an element of \\spad{R}.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(f)} tests if \\spad{f} is an element of \\spad{R}."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -1058) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-1069))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-485))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548))))) +((|HasCategory| |#2| (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-1070))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-485))) (|HasCategory| |#2| (QUOTE (-1133))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548))))) (-442 R) ((|constructor| (NIL "A space of formal functions with arguments in an arbitrary ordered set.")) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| $)) $ (|Kernel| $)) "\\spad{univariate(f, k)} returns \\spad{f} viewed as a univariate fraction in \\spad{k}.")) (/ (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $)) (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{p1/p2} returns the quotient of \\spad{p1} and \\spad{p2} as an element of \\%.")) (|denominator| (($ $) "\\spad{denominator(f)} returns the denominator of \\spad{f} converted to \\%.")) (|denom| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|convert| (($ (|Factored| $)) "\\spad{convert(f1\\^e1 ... fm\\^em)} returns \\spad{(f1)\\^e1 ... (fm)\\^em} as an element of \\%,{} using formal kernels created using a \\spadfunFrom{paren}{ExpressionSpace}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isPower(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|numerator| (($ $) "\\spad{numerator(f)} returns the numerator of \\spad{f} converted to \\%.")) (|numer| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R} if \\spad{R} is an integral domain. If not,{} then numer(\\spad{f}) = \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|coerce| (($ (|Fraction| (|Polynomial| (|Fraction| |#1|)))) "\\spad{coerce(f)} returns \\spad{f} as an element of \\%.") (($ (|Polynomial| (|Fraction| |#1|))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.") (($ (|Fraction| |#1|)) "\\spad{coerce(q)} returns \\spad{q} as an element of \\%.") (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.")) (|isMult| (((|Union| (|Record| (|:| |coef| (|Integer|)) (|:| |var| (|Kernel| $))) "failed") $) "\\spad{isMult(p)} returns \\spad{[n, x]} if \\spad{p = n * x} and \\spad{n <> 0}.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,...,mn]} if \\spad{p = m1 +...+ mn} and \\spad{n > 1}.")) (|isExpt| (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|Symbol|)) "\\spad{isExpt(p,f)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = f(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|BasicOperator|)) "\\spad{isExpt(p,op)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = op(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if \\spad{p = a1*...*an} and \\spad{n > 1}.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns \\spad{x} * \\spad{x} * \\spad{x} * ... * \\spad{x} (\\spad{n} times).")) (|eval| (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ $)) "\\spad{eval(x, s, n, f)} replaces every \\spad{s(a)**n} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ (|List| $))) "\\spad{eval(x, s, n, f)} replaces every \\spad{s(a1,...,am)**n} in \\spad{x} by \\spad{f(a1,...,am)} for any a1,{}...,{}am.") (($ $ (|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| $) (|Symbol|)) "\\spad{eval(x, [s1,...,sm], [f1,...,fm], y)} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $ (|BasicOperator|) $ (|Symbol|)) "\\spad{eval(x, s, f, y)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $) "\\spad{eval(f)} unquotes all the quoted operators in \\spad{f}.") (($ $ (|List| (|Symbol|))) "\\spad{eval(f, [foo1,...,foon])} unquotes all the \\spad{fooi}\\spad{'s} in \\spad{f}.") (($ $ (|Symbol|)) "\\spad{eval(f, foo)} unquotes all the foo\\spad{'s} in \\spad{f}.")) (|applyQuote| (($ (|Symbol|) (|List| $)) "\\spad{applyQuote(foo, [x1,...,xn])} returns \\spad{'foo(x1,...,xn)}.") (($ (|Symbol|) $ $ $ $) "\\spad{applyQuote(foo, x, y, z, t)} returns \\spad{'foo(x,y,z,t)}.") (($ (|Symbol|) $ $ $) "\\spad{applyQuote(foo, x, y, z)} returns \\spad{'foo(x,y,z)}.") (($ (|Symbol|) $ $) "\\spad{applyQuote(foo, x, y)} returns \\spad{'foo(x,y)}.") (($ (|Symbol|) $) "\\spad{applyQuote(foo, x)} returns \\spad{'foo(x)}.")) (|variables| (((|List| (|Symbol|)) $) "\\spad{variables(f)} returns the list of all the variables of \\spad{f}.")) (|ground| ((|#1| $) "\\spad{ground(f)} returns \\spad{f} as an element of \\spad{R}. An error occurs if \\spad{f} is not an element of \\spad{R}.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(f)} tests if \\spad{f} is an element of \\spad{R}."))) -((-4460 -3794 (|has| |#1| (-1069)) (|has| |#1| (-485))) (-4458 |has| |#1| (-174)) (-4457 |has| |#1| (-174)) ((-4465 "*") |has| |#1| (-568)) (-4456 |has| |#1| (-568)) (-4461 |has| |#1| (-568)) (-4455 |has| |#1| (-568))) +((-4461 -2758 (|has| |#1| (-1070)) (|has| |#1| (-485))) (-4459 |has| |#1| (-174)) (-4458 |has| |#1| (-174)) ((-4466 "*") |has| |#1| (-568)) (-4457 |has| |#1| (-568)) (-4462 |has| |#1| (-568)) (-4456 |has| |#1| (-568))) NIL -(-443 R -2117) +(-443 R -1959) ((|constructor| (NIL "Provides some special functions over an integral domain.")) (|iiabs| ((|#2| |#2|) "\\spad{iiabs(x)} should be local but conditional.")) (|iiGamma| ((|#2| |#2|) "\\spad{iiGamma(x)} should be local but conditional.")) (|airyBi| ((|#2| |#2|) "\\spad{airyBi(x)} returns the airybi function applied to \\spad{x}")) (|airyAi| ((|#2| |#2|) "\\spad{airyAi(x)} returns the airyai function applied to \\spad{x}")) (|besselK| ((|#2| |#2| |#2|) "\\spad{besselK(x,y)} returns the besselk function applied to \\spad{x} and \\spad{y}")) (|besselI| ((|#2| |#2| |#2|) "\\spad{besselI(x,y)} returns the besseli function applied to \\spad{x} and \\spad{y}")) (|besselY| ((|#2| |#2| |#2|) "\\spad{besselY(x,y)} returns the bessely function applied to \\spad{x} and \\spad{y}")) (|besselJ| ((|#2| |#2| |#2|) "\\spad{besselJ(x,y)} returns the besselj function applied to \\spad{x} and \\spad{y}")) (|polygamma| ((|#2| |#2| |#2|) "\\spad{polygamma(x,y)} returns the polygamma function applied to \\spad{x} and \\spad{y}")) (|digamma| ((|#2| |#2|) "\\spad{digamma(x)} returns the digamma function applied to \\spad{x}")) (|Beta| ((|#2| |#2| |#2|) "\\spad{Beta(x,y)} returns the beta function applied to \\spad{x} and \\spad{y}")) (|Gamma| ((|#2| |#2| |#2|) "\\spad{Gamma(a,x)} returns the incomplete Gamma function applied to a and \\spad{x}") ((|#2| |#2|) "\\spad{Gamma(f)} returns the formal Gamma function applied to \\spad{f}")) (|abs| ((|#2| |#2|) "\\spad{abs(f)} returns the absolute value operator applied to \\spad{f}")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\spad{F}; error if \\spad{op} is not a special function operator")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} is \\spad{true} if \\spad{op} is a special function operator."))) NIL NIL -(-444 R -2117) +(-444 R -1959) ((|constructor| (NIL "FunctionsSpacePrimitiveElement provides functions to compute primitive elements in functions spaces.")) (|primitiveElement| (((|Record| (|:| |primelt| |#2|) (|:| |pol1| (|SparseUnivariatePolynomial| |#2|)) (|:| |pol2| (|SparseUnivariatePolynomial| |#2|)) (|:| |prim| (|SparseUnivariatePolynomial| |#2|))) |#2| |#2|) "\\spad{primitiveElement(a1, a2)} returns \\spad{[a, q1, q2, q]} such that \\spad{k(a1, a2) = k(a)},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. The minimal polynomial for a2 may involve \\spad{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], 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)))) -(-445 R -2117) +(-445 R -1959) ((|constructor| (NIL "This package provides function which replaces transcendental kernels in a function space by random integers. The correspondence between the kernels and the integers is fixed between calls to new().")) (|newReduc| (((|Void|)) "\\spad{newReduc()} \\undocumented")) (|bringDown| (((|SparseUnivariatePolynomial| (|Fraction| (|Integer|))) |#2| (|Kernel| |#2|)) "\\spad{bringDown(f,k)} \\undocumented") (((|Fraction| (|Integer|)) |#2|) "\\spad{bringDown(f)} \\undocumented"))) NIL NIL @@ -1716,10 +1716,10 @@ NIL ((|constructor| (NIL "Creates and manipulates objects which correspond to the basic FORTRAN data types: REAL,{} INTEGER,{} COMPLEX,{} LOGICAL and CHARACTER")) (= (((|Boolean|) $ $) "\\spad{x=y} tests for equality")) (|logical?| (((|Boolean|) $) "\\spad{logical?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type LOGICAL.")) (|character?| (((|Boolean|) $) "\\spad{character?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type CHARACTER.")) (|doubleComplex?| (((|Boolean|) $) "\\spad{doubleComplex?(t)} tests whether \\spad{t} is equivalent to the (non-standard) FORTRAN type DOUBLE COMPLEX.")) (|complex?| (((|Boolean|) $) "\\spad{complex?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type COMPLEX.")) (|integer?| (((|Boolean|) $) "\\spad{integer?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type INTEGER.")) (|double?| (((|Boolean|) $) "\\spad{double?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type DOUBLE PRECISION")) (|real?| (((|Boolean|) $) "\\spad{real?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type REAL.")) (|coerce| (((|SExpression|) $) "\\spad{coerce(x)} returns the \\spad{s}-expression associated with \\spad{x}") (((|Symbol|) $) "\\spad{coerce(x)} returns the symbol associated with \\spad{x}") (($ (|Symbol|)) "\\spad{coerce(s)} transforms the symbol \\spad{s} into an element of FortranScalarType provided \\spad{s} is one of real,{} complex,{}double precision,{} logical,{} integer,{} character,{} REAL,{} COMPLEX,{} LOGICAL,{} INTEGER,{} CHARACTER,{} DOUBLE PRECISION") (($ (|String|)) "\\spad{coerce(s)} transforms the string \\spad{s} into an element of FortranScalarType provided \\spad{s} is one of \"real\",{} \"double precision\",{} \"complex\",{} \"logical\",{} \"integer\",{} \"character\",{} \"REAL\",{} \"COMPLEX\",{} \"LOGICAL\",{} \"INTEGER\",{} \"CHARACTER\",{} \"DOUBLE PRECISION\""))) NIL NIL -(-447 R -2117 UP) +(-447 R -1959 UP) ((|constructor| (NIL "\\indented{1}{Used internally by IR2F} Author: Manuel Bronstein Date Created: 12 May 1988 Date Last Updated: 22 September 1993 Keywords: function,{} space,{} polynomial,{} factoring")) (|anfactor| (((|Union| (|Factored| (|SparseUnivariatePolynomial| (|AlgebraicNumber|))) "failed") |#3|) "\\spad{anfactor(p)} tries to factor \\spad{p} over algebraic numbers,{} returning \"failed\" if it cannot")) (|UP2ifCan| (((|Union| (|:| |overq| (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) (|:| |overan| (|SparseUnivariatePolynomial| (|AlgebraicNumber|))) (|:| |failed| (|Boolean|))) |#3|) "\\spad{UP2ifCan(x)} should be local but conditional.")) (|qfactor| (((|Union| (|Factored| (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) "failed") |#3|) "\\spad{qfactor(p)} tries to factor \\spad{p} over fractions of integers,{} returning \"failed\" if it cannot")) (|ffactor| (((|Factored| |#3|) |#3|) "\\spad{ffactor(p)} tries to factor a univariate polynomial \\spad{p} over \\spad{F}"))) NIL -((|HasCategory| |#2| (LIST (QUOTE -1058) (QUOTE (-48))))) +((|HasCategory| |#2| (LIST (QUOTE -1059) (QUOTE (-48))))) (-448) ((|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 @@ -1748,7 +1748,7 @@ NIL ((|constructor| (NIL "\\spadtype{GaloisGroupFactorizer} provides functions to factor resolvents.")) (|btwFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|) (|Set| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{btwFact(p,sqf,pd,r)} returns the factorization of \\spad{p},{} the result is a Record such that \\spad{contp=}content \\spad{p},{} \\spad{factors=}List of irreducible factors of \\spad{p} with exponent. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors). \\spad{pd} is the \\spadtype{Set} of possible degrees. \\spad{r} is a lower bound for the number of factors of \\spad{p}. Please do not use this function in your code because its design may change.")) (|henselFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|)) "\\spad{henselFact(p,sqf)} returns the factorization of \\spad{p},{} the result is a Record such that \\spad{contp=}content \\spad{p},{} \\spad{factors=}List of irreducible factors of \\spad{p} with exponent. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors).")) (|factorOfDegree| (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|) (|Boolean|)) "\\spad{factorOfDegree(d,p,listOfDegrees,r,sqf)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees},{} and that \\spad{p} has at least \\spad{r} factors. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors).") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factorOfDegree(d,p,listOfDegrees,r)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees},{} and that \\spad{p} has at least \\spad{r} factors.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factorOfDegree(d,p,listOfDegrees)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|NonNegativeInteger|)) "\\spad{factorOfDegree(d,p,r)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has at least \\spad{r} factors.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1|) "\\spad{factorOfDegree(d,p)} returns a factor of \\spad{p} of degree \\spad{d}.")) (|factorSquareFree| (((|Factored| |#1|) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,d,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{d} divides the degree of all factors of \\spad{p} and that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,listOfDegrees,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees} and that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factorSquareFree(p,listOfDegrees)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(p)} returns the factorization of \\spad{p} which is supposed not having any repeated factor (this is not checked).")) (|factor| (((|Factored| |#1|) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factor(p,d,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{d} divides the degree of all factors of \\spad{p} and that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factor(p,listOfDegrees,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees} and that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factor(p,listOfDegrees)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}.") (((|Factored| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{factor(p,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns the factorization of \\spad{p} over the integers.")) (|tryFunctionalDecomposition| (((|Boolean|) (|Boolean|)) "\\spad{tryFunctionalDecomposition(b)} chooses whether factorizers have to look for functional decomposition of polynomials (\\spad{true}) or not (\\spad{false}). Returns the previous value.")) (|tryFunctionalDecomposition?| (((|Boolean|)) "\\spad{tryFunctionalDecomposition?()} returns \\spad{true} if factorizers try functional decomposition of polynomials before factoring them.")) (|eisensteinIrreducible?| (((|Boolean|) |#1|) "\\spad{eisensteinIrreducible?(p)} returns \\spad{true} if \\spad{p} can be shown to be irreducible by Eisenstein\\spad{'s} criterion,{} \\spad{false} is inconclusive.")) (|useEisensteinCriterion| (((|Boolean|) (|Boolean|)) "\\spad{useEisensteinCriterion(b)} chooses whether factorizers check Eisenstein\\spad{'s} criterion before factoring: \\spad{true} for using it,{} \\spad{false} else. Returns the previous value.")) (|useEisensteinCriterion?| (((|Boolean|)) "\\spad{useEisensteinCriterion?()} returns \\spad{true} if factorizers check Eisenstein\\spad{'s} criterion before factoring.")) (|useSingleFactorBound| (((|Boolean|) (|Boolean|)) "\\spad{useSingleFactorBound(b)} chooses the algorithm to be used by the factorizers: \\spad{true} for algorithm with single factor bound,{} \\spad{false} for algorithm with overall bound. Returns the previous value.")) (|useSingleFactorBound?| (((|Boolean|)) "\\spad{useSingleFactorBound?()} returns \\spad{true} if algorithm with single factor bound is used for factorization,{} \\spad{false} for algorithm with overall bound.")) (|modularFactor| (((|Record| (|:| |prime| (|Integer|)) (|:| |factors| (|List| |#1|))) |#1|) "\\spad{modularFactor(f)} chooses a \"good\" prime and returns the factorization of \\spad{f} modulo this prime in a form that may be used by \\spadfunFrom{completeHensel}{GeneralHenselPackage}. If prime is zero it means that \\spad{f} has been proved to be irreducible over the integers or that \\spad{f} is a unit (\\spadignore{i.e.} 1 or \\spad{-1}). \\spad{f} shall be primitive (\\spadignore{i.e.} content(\\spad{p})\\spad{=1}) and square free (\\spadignore{i.e.} without repeated factors).")) (|numberOfFactors| (((|NonNegativeInteger|) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|))))) "\\spad{numberOfFactors(ddfactorization)} returns the number of factors of the polynomial \\spad{f} modulo \\spad{p} where \\spad{ddfactorization} is the distinct degree factorization of \\spad{f} computed by \\spadfunFrom{ddFact}{ModularDistinctDegreeFactorizer} for some prime \\spad{p}.")) (|stopMusserTrials| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{stopMusserTrials(n)} sets to \\spad{n} the bound on the number of factors for which \\spadfun{modularFactor} stops to look for an other prime. You will have to remember that the step of recombining the extraneous factors may take up to \\spad{2**n} trials. Returns the previous value.") (((|PositiveInteger|)) "\\spad{stopMusserTrials()} returns the bound on the number of factors for which \\spadfun{modularFactor} stops to look for an other prime. You will have to remember that the step of recombining the extraneous factors may take up to \\spad{2**stopMusserTrials()} trials.")) (|musserTrials| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{musserTrials(n)} sets to \\spad{n} the number of primes to be tried in \\spadfun{modularFactor} and returns the previous value.") (((|PositiveInteger|)) "\\spad{musserTrials()} returns the number of primes that are tried in \\spadfun{modularFactor}.")) (|degreePartition| (((|Multiset| (|NonNegativeInteger|)) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|))))) "\\spad{degreePartition(ddfactorization)} returns the degree partition of the polynomial \\spad{f} modulo \\spad{p} where \\spad{ddfactorization} is the distinct degree factorization of \\spad{f} computed by \\spadfunFrom{ddFact}{ModularDistinctDegreeFactorizer} for some prime \\spad{p}.")) (|makeFR| (((|Factored| |#1|) (|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|))))))) "\\spad{makeFR(flist)} turns the final factorization of henselFact into a \\spadtype{Factored} object."))) NIL NIL -(-455 R UP -2117) +(-455 R UP -1959) ((|constructor| (NIL "\\spadtype{GaloisGroupFactorizationUtilities} provides functions that will be used by the factorizer.")) (|length| ((|#3| |#2|) "\\spad{length(p)} returns the sum of the absolute values of the coefficients of the polynomial \\spad{p}.")) (|height| ((|#3| |#2|) "\\spad{height(p)} returns the maximal absolute value of the coefficients of the polynomial \\spad{p}.")) (|infinityNorm| ((|#3| |#2|) "\\spad{infinityNorm(f)} returns the maximal absolute value of the coefficients of the polynomial \\spad{f}.")) (|quadraticNorm| ((|#3| |#2|) "\\spad{quadraticNorm(f)} returns the \\spad{l2} norm of the polynomial \\spad{f}.")) (|norm| ((|#3| |#2| (|PositiveInteger|)) "\\spad{norm(f,p)} returns the \\spad{lp} norm of the polynomial \\spad{f}.")) (|singleFactorBound| (((|Integer|) |#2|) "\\spad{singleFactorBound(p,r)} returns a bound on the infinite norm of the factor of \\spad{p} with smallest Bombieri\\spad{'s} norm. \\spad{p} shall be of degree higher or equal to 2.") (((|Integer|) |#2| (|NonNegativeInteger|)) "\\spad{singleFactorBound(p,r)} returns a bound on the infinite norm of the factor of \\spad{p} with smallest Bombieri\\spad{'s} norm. \\spad{r} is a lower bound for the number of factors of \\spad{p}. \\spad{p} shall be of degree higher or equal to 2.")) (|rootBound| (((|Integer|) |#2|) "\\spad{rootBound(p)} returns a bound on the largest norm of the complex roots of \\spad{p}.")) (|bombieriNorm| ((|#3| |#2| (|PositiveInteger|)) "\\spad{bombieriNorm(p,n)} returns the \\spad{n}th Bombieri\\spad{'s} norm of \\spad{p}.") ((|#3| |#2|) "\\spad{bombieriNorm(p)} returns quadratic Bombieri\\spad{'s} norm of \\spad{p}.")) (|beauzamyBound| (((|Integer|) |#2|) "\\spad{beauzamyBound(p)} returns a bound on the larger coefficient of any factor of \\spad{p}."))) NIL NIL @@ -1786,16 +1786,16 @@ NIL NIL (-464) ((|constructor| (NIL "This category describes domains where \\spadfun{\\spad{gcd}} can be computed but where there is no guarantee of the existence of \\spadfun{factor} operation for factorisation into irreducibles. However,{} if such a \\spadfun{factor} operation exist,{} factorization will be unique up to order and units.")) (|lcm| (($ (|List| $)) "\\spad{lcm(l)} returns the least common multiple of the elements of the list \\spad{l}.") (($ $ $) "\\spad{lcm(x,y)} returns the least common multiple of \\spad{x} and \\spad{y}.")) (|gcd| (($ (|List| $)) "\\spad{gcd(l)} returns the common \\spad{gcd} of the elements in the list \\spad{l}.") (($ $ $) "\\spad{gcd(x,y)} returns the greatest common divisor of \\spad{x} and \\spad{y}."))) -((-4456 . T) ((-4465 "*") . T) (-4457 . T) (-4458 . T) (-4460 . T)) +((-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-465 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"))) -((-4460 |has| (-419 (-970 |#1|)) (-568)) (-4458 . T) (-4457 . T)) -((|HasCategory| (-419 (-970 |#1|)) (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| (-419 (-970 |#1|)) (QUOTE (-568)))) +((-4461 |has| (-419 (-971 |#1|)) (-568)) (-4459 . T) (-4458 . T)) +((|HasCategory| (-419 (-971 |#1|)) (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| (-419 (-971 |#1|)) (QUOTE (-568)))) (-466 |vl| R E) ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is specified by its third parameter. Suggested types which define term orderings include: \\spadtype{DirectProduct},{} \\spadtype{HomogeneousDirectProduct},{} \\spadtype{SplitHomogeneousDirectProduct} and finally \\spadtype{OrderedDirectProduct} which accepts an arbitrary user function to define a term ordering.")) (|reorder| (($ $ (|List| (|Integer|))) "\\spad{reorder(p, perm)} applies the permutation perm to the variables in a polynomial and returns the new correctly ordered polynomial"))) -(((-4465 "*") |has| |#2| (-174)) (-4456 |has| |#2| (-568)) (-4461 |has| |#2| (-6 -4461)) (-4458 . T) (-4457 . T) (-4460 . T)) -((|HasCategory| |#2| (QUOTE (-927))) (-3794 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-927)))) (-3794 (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-927)))) (-3794 (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-927)))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-174))) (-3794 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-568)))) (-12 (|HasCategory| (-877 |#1|) (LIST (QUOTE -900) (QUOTE (-390)))) (|HasCategory| |#2| (LIST (QUOTE -900) (QUOTE (-390))))) (-12 (|HasCategory| (-877 |#1|) (LIST (QUOTE -900) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -900) (QUOTE (-576))))) (-12 (|HasCategory| (-877 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -906) (QUOTE (-390))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -906) (QUOTE (-390)))))) (-12 (|HasCategory| (-877 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -906) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -906) (QUOTE (-576)))))) (-12 (|HasCategory| (-877 |#1|) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#2| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1058) (QUOTE (-576)))) (-3794 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1058) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#2| (LIST (QUOTE -1058) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (QUOTE (-374))) (|HasAttribute| |#2| (QUOTE -4461)) (|HasCategory| |#2| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-927)))) (-3794 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-927)))) (|HasCategory| |#2| (QUOTE (-146))))) +(((-4466 "*") |has| |#2| (-174)) (-4457 |has| |#2| (-568)) (-4462 |has| |#2| (-6 -4462)) (-4459 . T) (-4458 . T) (-4461 . 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A table containing the solutions of \\spad{Af+Bg=x**k} is used. The operations are performed modulus a prime which are in principle big enough,{} but the solutions are tested and,{} in case of failure,{} a hensel lifting process is used to get to the right solutions. It will be used in the factorization of multivariate polynomials over finite field,{} with \\spad{R=F[x]}.")) (|testModulus| (((|Boolean|) |#1| (|List| |#2|)) "\\spad{testModulus(p,lp)} returns \\spad{true} if the the prime \\spad{p} is valid for the list of polynomials \\spad{lp},{} \\spadignore{i.e.} preserves the degree and they remain relatively prime.")) (|solveid| (((|Union| (|List| |#2|) "failed") |#2| |#1| (|Vector| (|List| |#2|))) "\\spad{solveid(h,table)} computes the coefficients of the extended euclidean algorithm for a list of polynomials whose tablePow is \\spad{table} and with right side \\spad{h}.")) (|tablePow| (((|Union| (|Vector| (|List| |#2|)) "failed") (|NonNegativeInteger|) |#1| (|List| |#2|)) "\\spad{tablePow(maxdeg,prime,lpol)} constructs the table with the coefficients of the Extended Euclidean Algorithm for \\spad{lpol}. Here the right side is \\spad{x**k},{} for \\spad{k} less or equal to \\spad{maxdeg}. The operation returns \"failed\" when the elements are not coprime modulo \\spad{prime}.")) (|compBound| (((|NonNegativeInteger|) |#2| (|List| |#2|)) "\\spad{compBound(p,lp)} computes a bound for the coefficients of the solution polynomials. Given a polynomial right hand side \\spad{p},{} and a list \\spad{lp} of left hand side polynomials. Exported because it depends on the valuation.")) (|reduction| ((|#2| |#2| |#1|) "\\spad{reduction(p,prime)} reduces the polynomial \\spad{p} modulo \\spad{prime} of \\spad{R}. Note: this function is exported only because it\\spad{'s} conditional."))) NIL @@ -1822,7 +1822,7 @@ NIL NIL (-473 |vl| R IS E |ff| P) ((|constructor| (NIL "This package \\undocumented")) (* (($ |#6| $) "\\spad{p*x} \\undocumented")) (|multMonom| (($ |#2| |#4| $) "\\spad{multMonom(r,e,x)} \\undocumented")) (|build| (($ |#2| |#3| |#4|) "\\spad{build(r,i,e)} \\undocumented")) (|unitVector| (($ |#3|) "\\spad{unitVector(x)} \\undocumented")) (|monomial| (($ |#2| (|ModuleMonomial| |#3| |#4| |#5|)) "\\spad{monomial(r,x)} \\undocumented")) (|reductum| (($ $) "\\spad{reductum(x)} \\undocumented")) (|leadingIndex| ((|#3| $) "\\spad{leadingIndex(x)} \\undocumented")) (|leadingExponent| ((|#4| $) "\\spad{leadingExponent(x)} \\undocumented")) (|leadingMonomial| (((|ModuleMonomial| |#3| |#4| |#5|) $) "\\spad{leadingMonomial(x)} \\undocumented")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(x)} \\undocumented"))) -((-4458 . T) (-4457 . T)) +((-4459 . T) (-4458 . T)) NIL (-474 E V R P Q) ((|constructor| (NIL "Gosper\\spad{'s} summation algorithm.")) (|GospersMethod| (((|Union| |#5| "failed") |#5| |#2| (|Mapping| |#2|)) "\\spad{GospersMethod(b, n, new)} returns a rational function \\spad{rf(n)} such that \\spad{a(n) * rf(n)} is the indefinite sum of \\spad{a(n)} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{a(n+1) * rf(n+1) - a(n) * rf(n) = a(n)},{} where \\spad{b(n) = a(n)/a(n-1)} is a rational function. Returns \"failed\" if no such rational function \\spad{rf(n)} exists. Note: \\spad{new} is a nullary function returning a new \\spad{V} every time. The condition on \\spad{a(n)} is that \\spad{a(n)/a(n-1)} is a rational function of \\spad{n}."))) @@ -1830,8 +1830,8 @@ NIL NIL (-475 R E |VarSet| P) ((|constructor| (NIL "A domain for polynomial sets.")) (|convert| (($ (|List| |#4|)) "\\axiom{convert(\\spad{lp})} returns the polynomial set whose members are the polynomials of \\axiom{\\spad{lp}}."))) -((-4464 . T) (-4463 . T)) -((-12 (|HasCategory| |#4| (QUOTE (-1120))) (|HasCategory| |#4| (LIST (QUOTE -319) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#4| (QUOTE (-1120))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#4| (LIST (QUOTE -625) (QUOTE (-875)))) (|HasCategory| |#4| (QUOTE (-102)))) +((-4465 . T) (-4464 . T)) +((-12 (|HasCategory| |#4| (QUOTE (-1121))) (|HasCategory| |#4| (LIST (QUOTE -319) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#4| (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#4| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#4| (QUOTE (-102)))) (-476 S R E) ((|constructor| (NIL "GradedAlgebra(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-algebra\\spad{''}. A graded algebra is a graded module together with a degree preserving \\spad{R}-linear map,{} called the {\\em product}. \\blankline The name ``product\\spad{''} is written out in full so inner and outer products with the same mapping type can be distinguished by name.")) (|product| (($ $ $) "\\spad{product(a,b)} is the degree-preserving \\spad{R}-linear product: \\blankline \\indented{2}{\\spad{degree product(a,b) = degree a + degree b}} \\indented{2}{\\spad{product(a1+a2,b) = product(a1,b) + product(a2,b)}} \\indented{2}{\\spad{product(a,b1+b2) = product(a,b1) + product(a,b2)}} \\indented{2}{\\spad{product(r*a,b) = product(a,r*b) = r*product(a,b)}} \\indented{2}{\\spad{product(a,product(b,c)) = product(product(a,b),c)}}")) ((|One|) (($) "1 is the identity for \\spad{product}."))) NIL @@ -1860,7 +1860,7 @@ NIL ((|constructor| (NIL "GradedModule(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-module\\spad{''},{} \\spadignore{i.e.} collection of \\spad{R}-modules indexed by an abelian monoid \\spad{E}. An element \\spad{g} of \\spad{G[s]} for some specific \\spad{s} in \\spad{E} is said to be an element of \\spad{G} with {\\em degree} \\spad{s}. Sums are defined in each module \\spad{G[s]} so two elements of \\spad{G} have a sum if they have the same degree. \\blankline Morphisms can be defined and composed by degree to give the mathematical category of graded modules.")) (+ (($ $ $) "\\spad{g+h} is the sum of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.")) (- (($ $ $) "\\spad{g-h} is the difference of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.") (($ $) "\\spad{-g} is the additive inverse of \\spad{g} in the module of elements of the same grade as \\spad{g}.")) (* (($ $ |#1|) "\\spad{g*r} is right module multiplication.") (($ |#1| $) "\\spad{r*g} is left module multiplication.")) ((|Zero|) (($) "0 denotes the zero of degree 0.")) (|degree| ((|#2| $) "\\spad{degree(g)} names the degree of \\spad{g}. The set of all elements of a given degree form an \\spad{R}-module."))) NIL NIL -(-483 |lv| -2117 R) +(-483 |lv| -1959 R) ((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni,{} Summer \\spad{'88},{} revised November \\spad{'89}} Solve systems of polynomial equations using Groebner bases Total order Groebner bases are computed and then converted to lex ones This package is mostly intended for internal use.")) (|genericPosition| (((|Record| (|:| |dpolys| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |coords| (|List| (|Integer|)))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{genericPosition(lp,lv)} puts a radical zero dimensional ideal in general position,{} for system \\spad{lp} in variables \\spad{lv}.")) (|testDim| (((|Union| (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "failed") (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{testDim(lp,lv)} tests if the polynomial system \\spad{lp} in variables \\spad{lv} is zero dimensional.")) (|groebSolve| (((|List| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{groebSolve(lp,lv)} reduces the polynomial system \\spad{lp} in variables \\spad{lv} to triangular form. Algorithm based on groebner bases algorithm with linear algebra for change of ordering. Preprocessing for the general solver. The polynomials in input are of type \\spadtype{DMP}."))) NIL NIL @@ -1870,23 +1870,23 @@ NIL NIL (-485) ((|constructor| (NIL "The class of multiplicative groups,{} \\spadignore{i.e.} monoids with multiplicative inverses. \\blankline")) (|commutator| (($ $ $) "\\spad{commutator(p,q)} computes \\spad{inv(p) * inv(q) * p * q}.")) (|conjugate| (($ $ $) "\\spad{conjugate(p,q)} computes \\spad{inv(q) * p * q}; this is 'right action by conjugation'.")) (|unitsKnown| ((|attribute|) "unitsKnown asserts that recip only returns \"failed\" for non-units.")) (** (($ $ (|Integer|)) "\\spad{x**n} returns \\spad{x} raised to the integer power \\spad{n}.")) (/ (($ $ $) "\\spad{x/y} is the same as \\spad{x} times the inverse of \\spad{y}.")) (|inv| (($ $) "\\spad{inv(x)} returns the inverse of \\spad{x}."))) -((-4460 . T)) +((-4461 . 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T)) +((-12 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4438 |#2|)) (QUOTE (-1121))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4438 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4300) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4438) (|devaluate| |#2|)))))) (-2758 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4438 |#2|)) (QUOTE (-1121))) (|HasCategory| |#2| (QUOTE (-1121)))) (-2758 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4438 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4438 |#2|)) (QUOTE (-1121))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1121)))) (-2758 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4438 |#2|)) (QUOTE (-1121))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4438 |#2|)) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4438 |#2|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-861))) (-2758 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4438 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (-2758 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4438 |#2|)) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4438 |#2|)) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4438 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4438 |#2|)) (QUOTE (-1121)))) (-488 R E V P) ((|constructor| (NIL "A domain constructor of the category \\axiomType{TriangularSetCategory}. The only requirement for a list of polynomials to be a member of such a domain is the following: no polynomial is constant and two distinct polynomials have distinct main variables. Such a triangular set may not be auto-reduced or consistent. Triangular sets are stored as sorted lists \\spad{w}.\\spad{r}.\\spad{t}. the main variables of their members but they are displayed in reverse order.\\newline References : \\indented{1}{[1] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)}"))) -((-4464 . T) (-4463 . T)) -((-12 (|HasCategory| |#4| (QUOTE (-1120))) (|HasCategory| |#4| (LIST (QUOTE -319) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#4| (QUOTE (-1120))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#3| (QUOTE (-379))) (|HasCategory| |#4| (LIST (QUOTE -625) (QUOTE (-875)))) (|HasCategory| |#4| (QUOTE (-102)))) +((-4465 . T) (-4464 . T)) +((-12 (|HasCategory| |#4| (QUOTE (-1121))) (|HasCategory| |#4| (LIST (QUOTE -319) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#4| (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#3| (QUOTE (-379))) (|HasCategory| |#4| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#4| (QUOTE (-102)))) (-489) ((|constructor| (NIL "\\indented{1}{Symbolic fractions in \\%\\spad{pi} with integer coefficients;} \\indented{1}{The point for using \\spad{Pi} as the default domain for those fractions} \\indented{1}{is that \\spad{Pi} is coercible to the float types,{} and not Expression.} Date Created: 21 Feb 1990 Date Last Updated: 12 Mai 1992")) (|pi| (($) "\\spad{pi()} returns the symbolic \\%\\spad{pi}."))) -((-4455 . T) (-4461 . T) (-4456 . T) ((-4465 "*") . T) (-4457 . T) (-4458 . T) (-4460 . T)) +((-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-490) ((|constructor| (NIL "This domain represents a `has' expression.")) (|rhs| (((|SpadAst|) $) "\\spad{rhs(e)} returns the right hand side of the case expression `e'.")) (|lhs| (((|SpadAst|) $) "\\spad{lhs(e)} returns the left hand side of the has expression `e'."))) @@ -1894,29 +1894,29 @@ NIL NIL (-491 |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."))) -((-4463 . T) (-4464 . T)) -((-12 (|HasCategory| (-2 (|:| -2239 |#1|) (|:| -2904 |#2|)) (QUOTE (-1120))) (|HasCategory| (-2 (|:| -2239 |#1|) (|:| -2904 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2239) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2904) (|devaluate| |#2|)))))) (-3794 (|HasCategory| (-2 (|:| -2239 |#1|) (|:| -2904 |#2|)) (QUOTE (-1120))) (|HasCategory| |#2| (QUOTE (-1120)))) (-3794 (|HasCategory| (-2 (|:| -2239 |#1|) (|:| -2904 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2239 |#1|) (|:| -2904 |#2|)) (QUOTE (-1120))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1120)))) (-3794 (|HasCategory| (-2 (|:| -2239 |#1|) (|:| -2904 |#2|)) (QUOTE (-1120))) (|HasCategory| (-2 (|:| -2239 |#1|) (|:| -2904 |#2|)) (LIST (QUOTE -625) (QUOTE (-875)))) (|HasCategory| |#2| (QUOTE (-1120))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-875))))) (|HasCategory| (-2 (|:| -2239 |#1|) (|:| -2904 |#2|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#2| (QUOTE (-1120))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2239 |#1|) (|:| -2904 |#2|)) (QUOTE (-1120))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#2| (QUOTE (-1120))) (-3794 (|HasCategory| (-2 (|:| -2239 |#1|) (|:| -2904 |#2|)) (LIST (QUOTE -625) (QUOTE (-875)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-875))))) (-3794 (|HasCategory| (-2 (|:| -2239 |#1|) (|:| -2904 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-875)))) (|HasCategory| (-2 (|:| -2239 |#1|) (|:| -2904 |#2|)) (LIST (QUOTE -625) (QUOTE (-875)))) (|HasCategory| (-2 (|:| -2239 |#1|) (|:| -2904 |#2|)) (QUOTE (-102)))) +((-4464 . T) (-4465 . T)) +((-12 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4438 |#2|)) (QUOTE (-1121))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4438 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4300) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4438) (|devaluate| |#2|)))))) (-2758 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4438 |#2|)) (QUOTE (-1121))) (|HasCategory| |#2| (QUOTE (-1121)))) (-2758 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4438 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4438 |#2|)) (QUOTE (-1121))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1121)))) (-2758 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4438 |#2|)) (QUOTE (-1121))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4438 |#2|)) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4438 |#2|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4438 |#2|)) (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#2| (QUOTE (-1121))) (-2758 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4438 |#2|)) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-876))))) (-2758 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4438 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4438 |#2|)) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4438 |#2|)) (QUOTE (-102)))) (-492) ((|constructor| (NIL "\\indented{1}{Author : Larry Lambe} Date Created : August 1988 Date Last Updated : March 9 1990 Related Constructors: OrderedSetInts,{} Commutator,{} FreeNilpotentLie AMS Classification: Primary 17B05,{} 17B30; Secondary 17A50 Keywords: free Lie algebra,{} Hall basis,{} basic commutators Description : Generate a basis for the free Lie algebra on \\spad{n} generators over a ring \\spad{R} with identity up to basic commutators of length \\spad{c} using the algorithm of \\spad{P}. Hall as given in Serre\\spad{'s} book Lie Groups \\spad{--} Lie Algebras")) (|generate| (((|Vector| (|List| (|Integer|))) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{generate(numberOfGens, maximalWeight)} generates a vector of elements of the form [left,{}weight,{}right] which represents a \\spad{P}. Hall basis element for the free lie algebra on \\spad{numberOfGens} generators. We only generate those basis elements of weight less than or equal to maximalWeight")) (|inHallBasis?| (((|Boolean|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{inHallBasis?(numberOfGens, leftCandidate, rightCandidate, left)} tests to see if a new element should be added to the \\spad{P}. Hall basis being constructed. The list \\spad{[leftCandidate,wt,rightCandidate]} is included in the basis if in the unique factorization of \\spad{rightCandidate},{} we have left factor leftOfRight,{} and leftOfRight \\spad{<=} \\spad{leftCandidate}")) (|lfunc| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{lfunc(d,n)} computes the rank of the \\spad{n}th factor in the lower central series of the free \\spad{d}-generated free Lie algebra; This rank is \\spad{d} if \\spad{n} = 1 and binom(\\spad{d},{}2) if \\spad{n} = 2"))) NIL NIL (-493 |vl| R) ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is total degree ordering refined by reverse lexicographic ordering with respect to the position that the variables appear in the list of variables parameter.")) 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T) (-4458 . T) (-4461 . 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(|parameters| (((|List| (|ParameterAst|)) $) "\\spad{parameters(h)} gives the parameters specified in the definition header \\spad{`h'}.")) (|name| (((|Identifier|) $) "\\spad{name(h)} returns the name of the operation defined defined.")) (|headAst| (($ (|Identifier|) (|List| (|ParameterAst|))) "\\spad{headAst(f,[x1,..,xn])} constructs a function definition header."))) NIL NIL (-496 S) ((|constructor| (NIL "Heap implemented in a flexible array to allow for insertions")) (|heap| (($ (|List| |#1|)) "\\spad{heap(ls)} creates a heap of elements consisting of the elements of \\spad{ls}."))) -((-4463 . T) (-4464 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1120))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1120))) (-3794 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1120)))) (-3794 (-12 (|HasCategory| |#1| (QUOTE (-1120))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-875))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-875)))) (|HasCategory| |#1| (QUOTE (-102)))) -(-497 -2117 UP UPUP R) +((-4464 . T) (-4465 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1121))) (-2758 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1121)))) (-2758 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102)))) +(-497 -1959 UP UPUP R) ((|constructor| (NIL "This domains implements finite rational divisors on an hyperelliptic curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}\\spad{'s} are integers and the \\spad{P}\\spad{'s} are finite rational points on the curve. The equation of the curve must be \\spad{y^2} = \\spad{f}(\\spad{x}) and \\spad{f} must have odd degree."))) NIL NIL @@ -1926,12 +1926,12 @@ NIL NIL (-499) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating hexadecimal expansions.")) (|hex| (($ (|Fraction| (|Integer|))) "\\spad{hex(r)} converts a rational number to a hexadecimal expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(h)} returns the fractional part of a hexadecimal expansion."))) -((-4455 . T) (-4461 . T) (-4456 . T) ((-4465 "*") . T) (-4457 . T) (-4458 . T) (-4460 . T)) -((|HasCategory| (-576) (QUOTE (-927))) (|HasCategory| (-576) (LIST (QUOTE -1058) (QUOTE (-1196)))) (|HasCategory| (-576) (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-148))) (|HasCategory| (-576) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-576) (QUOTE (-1042))) (|HasCategory| (-576) (QUOTE (-832))) (|HasCategory| (-576) (QUOTE (-861))) (-3794 (|HasCategory| (-576) (QUOTE (-832))) (|HasCategory| (-576) (QUOTE (-861)))) (|HasCategory| (-576) (LIST (QUOTE -1058) (QUOTE (-576)))) (|HasCategory| (-576) (QUOTE (-1172))) (|HasCategory| (-576) (LIST (QUOTE -900) (QUOTE (-390)))) (|HasCategory| (-576) (LIST (QUOTE -900) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -626) (LIST (QUOTE -906) (QUOTE (-390))))) (|HasCategory| (-576) (LIST (QUOTE -626) (LIST (QUOTE -906) (QUOTE (-576))))) (|HasCategory| (-576) (QUOTE (-237))) (|HasCategory| (-576) (LIST (QUOTE -918) (QUOTE (-1196)))) (|HasCategory| (-576) (QUOTE (-238))) (|HasCategory| (-576) (LIST (QUOTE -916) (QUOTE (-1196)))) (|HasCategory| (-576) (LIST (QUOTE -526) (QUOTE (-1196)) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -319) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -296) (QUOTE (-576)) (QUOTE (-576)))) (|HasCategory| (-576) (QUOTE (-317))) (|HasCategory| (-576) (QUOTE (-557))) (|HasCategory| (-576) (LIST (QUOTE -651) (QUOTE (-576)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-927)))) (-3794 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-927)))) (|HasCategory| (-576) (QUOTE (-146))))) +((-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) +((|HasCategory| (-576) (QUOTE (-928))) (|HasCategory| (-576) (LIST (QUOTE -1059) (QUOTE (-1197)))) (|HasCategory| (-576) (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-148))) (|HasCategory| (-576) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-576) (QUOTE (-1043))) (|HasCategory| (-576) (QUOTE (-832))) (|HasCategory| (-576) (QUOTE (-861))) (-2758 (|HasCategory| (-576) (QUOTE (-832))) (|HasCategory| (-576) (QUOTE (-861)))) (|HasCategory| (-576) (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| (-576) (QUOTE (-1173))) (|HasCategory| (-576) (LIST (QUOTE -901) (QUOTE (-390)))) (|HasCategory| (-576) (LIST (QUOTE -901) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390))))) (|HasCategory| (-576) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576))))) (|HasCategory| (-576) (QUOTE (-237))) (|HasCategory| (-576) (LIST (QUOTE -919) (QUOTE (-1197)))) (|HasCategory| (-576) (QUOTE (-238))) (|HasCategory| (-576) (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| (-576) (LIST (QUOTE -526) (QUOTE (-1197)) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -319) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -296) (QUOTE (-576)) (QUOTE (-576)))) (|HasCategory| (-576) (QUOTE (-317))) (|HasCategory| (-576) (QUOTE (-557))) (|HasCategory| (-576) (LIST (QUOTE -651) (QUOTE (-576)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-928)))) (-2758 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-928)))) (|HasCategory| (-576) (QUOTE (-146))))) (-500 A S) ((|constructor| (NIL "A homogeneous aggregate is an aggregate of elements all of the same type. In the current system,{} all aggregates are homogeneous. Two attributes characterize classes of aggregates. Aggregates from domains with attribute \\spadatt{finiteAggregate} have a finite number of members. Those with attribute \\spadatt{shallowlyMutable} allow an element to be modified or updated without changing its overall value.")) (|member?| (((|Boolean|) |#2| $) "\\spad{member?(x,u)} tests if \\spad{x} is a member of \\spad{u}. For collections,{} \\axiom{member?(\\spad{x},{}\\spad{u}) = reduce(or,{}[x=y for \\spad{y} in \\spad{u}],{}\\spad{false})}.")) (|members| (((|List| |#2|) $) "\\spad{members(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|parts| (((|List| |#2|) $) "\\spad{parts(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|count| (((|NonNegativeInteger|) |#2| $) "\\spad{count(x,u)} returns the number of occurrences of \\spad{x} in \\spad{u}. For collections,{} \\axiom{count(\\spad{x},{}\\spad{u}) = reduce(+,{}[x=y for \\spad{y} in \\spad{u}],{}0)}.") (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{count(p,u)} returns the number of elements \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. For collections,{} \\axiom{count(\\spad{p},{}\\spad{u}) = reduce(+,{}[1 for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})],{}0)}.")) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{every?(f,u)} tests if \\spad{p}(\\spad{x}) is \\spad{true} for all elements \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{every?(\\spad{p},{}\\spad{u}) = reduce(and,{}map(\\spad{f},{}\\spad{u}),{}\\spad{true},{}\\spad{false})}.")) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{any?(p,u)} tests if \\axiom{\\spad{p}(\\spad{x})} is \\spad{true} for any element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{any?(\\spad{p},{}\\spad{u}) = reduce(or,{}map(\\spad{f},{}\\spad{u}),{}\\spad{false},{}\\spad{true})}.")) (|map!| (($ (|Mapping| |#2| |#2|) $) "\\spad{map!(f,u)} destructively replaces each element \\spad{x} of \\spad{u} by \\axiom{\\spad{f}(\\spad{x})}.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(f,u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) NIL -((|HasAttribute| |#1| (QUOTE -4463)) (|HasAttribute| |#1| (QUOTE -4464)) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1120))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-875))))) +((|HasAttribute| |#1| (QUOTE -4464)) (|HasAttribute| |#1| (QUOTE -4465)) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-876))))) (-501 S) ((|constructor| (NIL "A homogeneous aggregate is an aggregate of elements all of the same type. In the current system,{} all aggregates are homogeneous. Two attributes characterize classes of aggregates. Aggregates from domains with attribute \\spadatt{finiteAggregate} have a finite number of members. Those with attribute \\spadatt{shallowlyMutable} allow an element to be modified or updated without changing its overall value.")) (|member?| (((|Boolean|) |#1| $) "\\spad{member?(x,u)} tests if \\spad{x} is a member of \\spad{u}. For collections,{} \\axiom{member?(\\spad{x},{}\\spad{u}) = reduce(or,{}[x=y for \\spad{y} in \\spad{u}],{}\\spad{false})}.")) (|members| (((|List| |#1|) $) "\\spad{members(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|parts| (((|List| |#1|) $) "\\spad{parts(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|count| (((|NonNegativeInteger|) |#1| $) "\\spad{count(x,u)} returns the number of occurrences of \\spad{x} in \\spad{u}. For collections,{} \\axiom{count(\\spad{x},{}\\spad{u}) = reduce(+,{}[x=y for \\spad{y} in \\spad{u}],{}0)}.") (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{count(p,u)} returns the number of elements \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. For collections,{} \\axiom{count(\\spad{p},{}\\spad{u}) = reduce(+,{}[1 for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})],{}0)}.")) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{every?(f,u)} tests if \\spad{p}(\\spad{x}) is \\spad{true} for all elements \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{every?(\\spad{p},{}\\spad{u}) = reduce(and,{}map(\\spad{f},{}\\spad{u}),{}\\spad{true},{}\\spad{false})}.")) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{any?(p,u)} tests if \\axiom{\\spad{p}(\\spad{x})} is \\spad{true} for any element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{any?(\\spad{p},{}\\spad{u}) = reduce(or,{}map(\\spad{f},{}\\spad{u}),{}\\spad{false},{}\\spad{true})}.")) (|map!| (($ (|Mapping| |#1| |#1|) $) "\\spad{map!(f,u)} destructively replaces each element \\spad{x} of \\spad{u} by \\axiom{\\spad{f}(\\spad{x})}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) NIL @@ -1952,34 +1952,34 @@ NIL ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) NIL NIL -(-506 -2117 UP |AlExt| |AlPol|) +(-506 -1959 UP |AlExt| |AlPol|) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of a field over which we can factor UP\\spad{'s}.")) (|factor| (((|Factored| |#4|) |#4| (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{factor(p, f)} returns a prime factorisation of \\spad{p}; \\spad{f} is a factorisation map for elements of UP."))) NIL NIL (-507) ((|constructor| (NIL "Algebraic closure of the rational numbers.")) (|norm| (($ $ (|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."))) -((-4455 . T) (-4461 . T) (-4456 . T) ((-4465 "*") . T) (-4457 . T) (-4458 . T) (-4460 . T)) -((|HasCategory| $ (QUOTE (-1069))) (|HasCategory| $ (LIST (QUOTE -1058) (QUOTE (-576))))) +((-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) +((|HasCategory| $ (QUOTE (-1070))) (|HasCategory| $ (LIST (QUOTE -1059) (QUOTE (-576))))) (-508 S |mn|) ((|constructor| (NIL "\\indented{1}{Author Micheal Monagan Aug/87} This is the basic one dimensional array data type."))) -((-4464 . T) (-4463 . T)) -((-3794 (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1120))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-3794 (-12 (|HasCategory| |#1| (QUOTE (-1120))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-875))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-3794 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1120)))) (|HasCategory| |#1| (QUOTE (-861))) (-3794 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1120)))) (|HasCategory| (-576) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1120))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-875)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1120))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) +((-4465 . T) (-4464 . T)) +((-2758 (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2758 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2758 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| |#1| (QUOTE (-861))) (-2758 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| (-576) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-509 R |mnRow| |mnCol|) ((|constructor| (NIL "\\indented{1}{An IndexedTwoDimensionalArray is a 2-dimensional array where} the minimal row and column indices are parameters of the type. Rows and columns are returned as IndexedOneDimensionalArray\\spad{'s} with minimal indices matching those of the IndexedTwoDimensionalArray. The index of the 'first' row may be obtained by calling the function 'minRowIndex'. The index of the 'first' column may be obtained by calling the function 'minColIndex'. The index of the first element of a 'Row' is the same as the index of the first column in an array and vice versa."))) -((-4463 . T) (-4464 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1120))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1120))) (-3794 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1120)))) (-3794 (-12 (|HasCategory| |#1| (QUOTE (-1120))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-875))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-875)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4464 . T) (-4465 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1121))) (-2758 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1121)))) (-2758 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102)))) (-510 K R UP) ((|constructor| (NIL "\\indented{1}{Author: Clifton Williamson} Date Created: 9 August 1993 Date Last Updated: 3 December 1993 Basic Operations: chineseRemainder,{} factorList Related Domains: PAdicWildFunctionFieldIntegralBasis(\\spad{K},{}\\spad{R},{}UP,{}\\spad{F}) Also See: WildFunctionFieldIntegralBasis,{} FunctionFieldIntegralBasis AMS Classifications: Keywords: function field,{} finite field,{} integral basis Examples: References: Description:")) (|chineseRemainder| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) (|List| |#3|) (|List| (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) (|NonNegativeInteger|)) "\\spad{chineseRemainder(lu,lr,n)} \\undocumented")) (|listConjugateBases| (((|List| (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{listConjugateBases(bas,q,n)} returns the list \\spad{[bas,bas^Frob,bas^(Frob^2),...bas^(Frob^(n-1))]},{} where \\spad{Frob} raises the coefficients of all polynomials appearing in the basis \\spad{bas} to the \\spad{q}th power.")) (|factorList| (((|List| (|SparseUnivariatePolynomial| |#1|)) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factorList(k,n,m,j)} \\undocumented"))) NIL NIL -(-511 R UP -2117) +(-511 R UP -1959) ((|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 \\spad{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, i = 1..n, j = 1..n)},{} then a basis \\spad{v1,...,vn} for \\spad{mi} is given by \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|idealiserMatrix| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{idealiserMatrix(m1, m2)} returns the matrix representing the linear conditions on the Ring associatied with an ideal defined by \\spad{m1} and \\spad{m2}.")) (|idealiser| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{idealiser(m1,m2,d)} computes the order of an ideal defined by \\spad{m1} and \\spad{m2} where \\spad{d} is the known part of the denominator") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{idealiser(m1,m2)} computes the order of an ideal defined by \\spad{m1} and \\spad{m2}")) (|leastPower| (((|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{leastPower(p,n)} returns \\spad{e},{} where \\spad{e} is the smallest integer such that \\spad{p **e >= n}")) (|divideIfCan!| ((|#1| (|Matrix| |#1|) (|Matrix| |#1|) |#1| (|Integer|)) "\\spad{divideIfCan!(matrix,matrixOut,prime,n)} attempts to divide the entries of \\spad{matrix} by \\spad{prime} and store the result in \\spad{matrixOut}. If it is successful,{} 1 is returned and if not,{} \\spad{prime} is returned. Here both \\spad{matrix} and \\spad{matrixOut} are \\spad{n}-by-\\spad{n} upper triangular matrices.")) (|matrixGcd| ((|#1| (|Matrix| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{matrixGcd(mat,sing,n)} is \\spad{gcd(sing,g)} where \\spad{g} is the \\spad{gcd} of the entries of the \\spad{n}-by-\\spad{n} upper-triangular matrix \\spad{mat}.")) (|diagonalProduct| ((|#1| (|Matrix| |#1|)) "\\spad{diagonalProduct(m)} returns the product of the elements on the diagonal of the matrix \\spad{m}")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL (-512 |mn|) ((|constructor| (NIL "\\spadtype{IndexedBits} is a domain to compactly represent large quantities of Boolean data.")) (|And| (($ $ $) "\\spad{And(n,m)} returns the bit-by-bit logical {\\em And} of \\spad{n} and \\spad{m}.")) (|Or| (($ $ $) "\\spad{Or(n,m)} returns the bit-by-bit logical {\\em Or} of \\spad{n} and \\spad{m}.")) (|Not| (($ $) "\\spad{Not(n)} returns the bit-by-bit logical {\\em Not} of \\spad{n}."))) -((-4464 . T) (-4463 . T)) -((-12 (|HasCategory| (-112) (QUOTE (-1120))) (|HasCategory| (-112) (LIST (QUOTE -319) (QUOTE (-112))))) (|HasCategory| (-112) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-112) (QUOTE (-861))) (|HasCategory| (-576) (QUOTE (-861))) (|HasCategory| (-112) (QUOTE (-1120))) (|HasCategory| (-112) (LIST (QUOTE -625) (QUOTE (-875)))) (|HasCategory| (-112) (QUOTE (-102)))) +((-4465 . T) (-4464 . T)) +((-12 (|HasCategory| (-112) (QUOTE (-1121))) (|HasCategory| (-112) (LIST (QUOTE -319) (QUOTE (-112))))) (|HasCategory| (-112) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-112) (QUOTE (-861))) (|HasCategory| (-576) (QUOTE (-861))) (|HasCategory| (-112) (QUOTE (-1121))) (|HasCategory| (-112) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-112) (QUOTE (-102)))) (-513 K R UP L) ((|constructor| (NIL "IntegralBasisPolynomialTools provides functions for \\indented{1}{mapping functions on the coefficients of univariate and bivariate} \\indented{1}{polynomials.}")) (|mapBivariate| (((|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#4|)) (|Mapping| |#4| |#1|) |#3|) "\\spad{mapBivariate(f,p(x,y))} applies the function \\spad{f} to the coefficients of \\spad{p(x,y)}.")) (|mapMatrixIfCan| (((|Union| (|Matrix| |#2|) "failed") (|Mapping| (|Union| |#1| "failed") |#4|) (|Matrix| (|SparseUnivariatePolynomial| |#4|))) "\\spad{mapMatrixIfCan(f,mat)} applies the function \\spad{f} to the coefficients of the entries of \\spad{mat} if possible,{} and returns \\spad{\"failed\"} otherwise.")) (|mapUnivariateIfCan| (((|Union| |#2| "failed") (|Mapping| (|Union| |#1| "failed") |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{mapUnivariateIfCan(f,p(x))} applies the function \\spad{f} to the coefficients of \\spad{p(x)},{} if possible,{} and returns \\spad{\"failed\"} otherwise.")) (|mapUnivariate| (((|SparseUnivariatePolynomial| |#4|) (|Mapping| |#4| |#1|) |#2|) "\\spad{mapUnivariate(f,p(x))} applies the function \\spad{f} to the coefficients of \\spad{p(x)}.") ((|#2| (|Mapping| |#1| |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{mapUnivariate(f,p(x))} applies the function \\spad{f} to the coefficients of \\spad{p(x)}."))) NIL @@ -1992,10 +1992,10 @@ NIL ((|constructor| (NIL "InnerCommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#4|) "\\spad{splitDenominator([q1,...,qn])} returns \\spad{[[p1,...,pn], d]} such that \\spad{qi = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|clearDenominator| ((|#3| |#4|) "\\spad{clearDenominator([q1,...,qn])} returns \\spad{[p1,...,pn]} such that \\spad{qi = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|commonDenominator| ((|#1| |#4|) "\\spad{commonDenominator([q1,...,qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}\\spad{qn}."))) NIL NIL -(-516 -2117 |Expon| |VarSet| |DPoly|) +(-516 -1959 |Expon| |VarSet| |DPoly|) ((|constructor| (NIL "This domain represents polynomial ideals with coefficients in any field and supports the basic ideal operations,{} including intersection sum and quotient. An ideal is represented by a list of polynomials (the generators of the ideal) and a boolean that is \\spad{true} if the generators are a Groebner basis. The algorithms used are based on Groebner basis computations. The ordering is determined by the datatype of the input polynomials. Users may use refinements of total degree orderings.")) (|relationsIdeal| (((|SuchThat| (|List| (|Polynomial| |#1|)) (|List| (|Equation| (|Polynomial| |#1|)))) (|List| |#4|)) "\\spad{relationsIdeal(polyList)} returns the ideal of relations among the polynomials in \\spad{polyList}.")) (|saturate| (($ $ |#4| (|List| |#3|)) "\\spad{saturate(I,f,lvar)} is the saturation with respect to the prime principal ideal which is generated by \\spad{f} in the polynomial ring \\spad{F[lvar]}.") (($ $ |#4|) "\\spad{saturate(I,f)} is the saturation of the ideal \\spad{I} with respect to the multiplicative set generated by the polynomial \\spad{f}.")) (|coerce| (($ (|List| |#4|)) "\\spad{coerce(polyList)} converts the list of polynomials \\spad{polyList} to an ideal.")) (|generators| (((|List| |#4|) $) "\\spad{generators(I)} returns a list of generators for the ideal \\spad{I}.")) (|groebner?| (((|Boolean|) $) "\\spad{groebner?(I)} tests if the generators of the ideal \\spad{I} are a Groebner basis.")) (|groebnerIdeal| (($ (|List| |#4|)) "\\spad{groebnerIdeal(polyList)} constructs the ideal generated by the list of polynomials \\spad{polyList} which are assumed to be a Groebner basis. Note: this operation avoids a Groebner basis computation.")) (|ideal| (($ (|List| |#4|)) "\\spad{ideal(polyList)} constructs the ideal generated by the list of polynomials \\spad{polyList}.")) (|leadingIdeal| (($ $) "\\spad{leadingIdeal(I)} is the ideal generated by the leading terms of the elements of the ideal \\spad{I}.")) (|dimension| (((|Integer|) $) "\\spad{dimension(I)} gives the dimension of the ideal \\spad{I}. in the ring \\spad{F[lvar]},{} where lvar are the variables appearing in \\spad{I}") (((|Integer|) $ (|List| |#3|)) "\\spad{dimension(I,lvar)} gives the dimension of the ideal \\spad{I},{} in the ring \\spad{F[lvar]}")) (|backOldPos| (($ (|Record| (|:| |mval| (|Matrix| |#1|)) (|:| |invmval| (|Matrix| |#1|)) (|:| |genIdeal| $))) "\\spad{backOldPos(genPos)} takes the result produced by \\spadfunFrom{generalPosition}{PolynomialIdeals} and performs the inverse transformation,{} returning the original ideal \\spad{backOldPos(generalPosition(I,listvar))} = \\spad{I}.")) (|generalPosition| (((|Record| (|:| |mval| (|Matrix| |#1|)) (|:| |invmval| (|Matrix| |#1|)) (|:| |genIdeal| $)) $ (|List| |#3|)) "\\spad{generalPosition(I,listvar)} perform a random linear transformation on the variables in \\spad{listvar} and returns the transformed ideal along with the change of basis matrix.")) (|groebner| (($ $) "\\spad{groebner(I)} returns a set of generators of \\spad{I} that are a Groebner basis for \\spad{I}.")) (|quotient| (($ $ |#4|) "\\spad{quotient(I,f)} computes the quotient of the ideal \\spad{I} by the principal ideal generated by the polynomial \\spad{f},{} \\spad{(I:(f))}.") (($ $ $) "\\spad{quotient(I,J)} computes the quotient of the ideals \\spad{I} and \\spad{J},{} \\spad{(I:J)}.")) (|intersect| (($ (|List| $)) "\\spad{intersect(LI)} computes the intersection of the list of ideals \\spad{LI}.") (($ $ $) "\\spad{intersect(I,J)} computes the intersection of the ideals \\spad{I} and \\spad{J}.")) (|zeroDim?| (((|Boolean|) $) "\\spad{zeroDim?(I)} tests if the ideal \\spad{I} is zero dimensional,{} \\spadignore{i.e.} all its associated primes are maximal,{} in the ring \\spad{F[lvar]},{} where lvar are the variables appearing in \\spad{I}") (((|Boolean|) $ (|List| |#3|)) "\\spad{zeroDim?(I,lvar)} tests if the ideal \\spad{I} is zero dimensional,{} \\spadignore{i.e.} all its associated primes are maximal,{} in the ring \\spad{F[lvar]}")) (|inRadical?| (((|Boolean|) |#4| $) "\\spad{inRadical?(f,I)} tests if some power of the polynomial \\spad{f} belongs to the ideal \\spad{I}.")) (|in?| (((|Boolean|) $ $) "\\spad{in?(I,J)} tests if the ideal \\spad{I} is contained in the ideal \\spad{J}.")) (|element?| (((|Boolean|) |#4| $) "\\spad{element?(f,I)} tests whether the polynomial \\spad{f} belongs to the ideal \\spad{I}.")) (|zero?| (((|Boolean|) $) "\\spad{zero?(I)} tests whether the ideal \\spad{I} is the zero ideal")) (|one?| (((|Boolean|) $) "\\spad{one?(I)} tests whether the ideal \\spad{I} is the unit ideal,{} \\spadignore{i.e.} contains 1.")) (+ (($ $ $) "\\spad{I+J} computes the ideal generated by the union of \\spad{I} and \\spad{J}.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{I**n} computes the \\spad{n}th power of the ideal \\spad{I}.")) (* (($ $ $) "\\spad{I*J} computes the product of the ideal \\spad{I} and \\spad{J}."))) NIL -((|HasCategory| |#3| (LIST (QUOTE -626) (QUOTE (-1196))))) +((|HasCategory| |#3| (LIST (QUOTE -626) (QUOTE (-1197))))) (-517 |vl| |nv|) ((|constructor| (NIL "\\indented{2}{This package provides functions for the primary decomposition of} polynomial ideals over the rational numbers. The ideals are members of the \\spadtype{PolynomialIdeals} domain,{} and the polynomial generators are required to be from the \\spadtype{DistributedMultivariatePolynomial} domain.")) (|contract| (((|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|)))) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|)))) (|List| (|OrderedVariableList| |#1|))) "\\spad{contract(I,lvar)} contracts the ideal \\spad{I} to the polynomial ring \\spad{F[lvar]}.")) (|primaryDecomp| (((|List| (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{primaryDecomp(I)} returns a list of primary ideals such that their intersection is the ideal \\spad{I}.")) (|radical| (((|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|)))) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{radical(I)} returns the radical of the ideal \\spad{I}.")) (|prime?| (((|Boolean|) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{prime?(I)} tests if the ideal \\spad{I} is prime.")) (|zeroDimPrimary?| (((|Boolean|) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{zeroDimPrimary?(I)} tests if the ideal \\spad{I} is 0-dimensional primary.")) (|zeroDimPrime?| (((|Boolean|) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{zeroDimPrime?(I)} tests if the ideal \\spad{I} is a 0-dimensional prime."))) NIL @@ -2042,36 +2042,36 @@ NIL ((|HasCategory| |#2| (QUOTE (-804)))) (-528 S |mn|) ((|constructor| (NIL "\\indented{1}{Author: Michael Monagan July/87,{} modified \\spad{SMW} June/91} A FlexibleArray is the notion of an array intended to allow for growth at the end only. Hence the following efficient operations \\indented{2}{\\spad{append(x,a)} meaning append item \\spad{x} at the end of the array \\spad{a}} \\indented{2}{\\spad{delete(a,n)} meaning delete the last item from the array \\spad{a}} Flexible arrays support the other operations inherited from \\spadtype{ExtensibleLinearAggregate}. However,{} these are not efficient. Flexible arrays combine the \\spad{O(1)} access time property of arrays with growing and shrinking at the end in \\spad{O(1)} (average) time. This is done by using an ordinary array which may have zero or more empty slots at the end. When the array becomes full it is copied into a new larger (50\\% larger) array. Conversely,{} when the array becomes less than 1/2 full,{} it is copied into a smaller array. Flexible arrays provide for an efficient implementation of many data structures in particular heaps,{} stacks and sets.")) (|shrinkable| (((|Boolean|) (|Boolean|)) "\\spad{shrinkable(b)} sets the shrinkable attribute of flexible arrays to \\spad{b} and returns the previous value")) (|physicalLength!| (($ $ (|Integer|)) "\\spad{physicalLength!(x,n)} changes the physical length of \\spad{x} to be \\spad{n} and returns the new array.")) (|physicalLength| (((|NonNegativeInteger|) $) "\\spad{physicalLength(x)} returns the number of elements \\spad{x} can accomodate before growing")) (|flexibleArray| (($ (|List| |#1|)) "\\spad{flexibleArray(l)} creates a flexible array from the list of elements \\spad{l}"))) -((-4464 . T) (-4463 . T)) -((-3794 (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1120))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-3794 (-12 (|HasCategory| |#1| (QUOTE (-1120))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-875))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-3794 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1120)))) (|HasCategory| |#1| (QUOTE (-861))) (-3794 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1120)))) (|HasCategory| (-576) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1120))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-875)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1120))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) +((-4465 . T) (-4464 . T)) +((-2758 (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2758 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2758 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| |#1| (QUOTE (-861))) (-2758 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| (-576) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-529) ((|constructor| (NIL "This domain represents AST for conditional expressions.")) (|elseBranch| (((|SpadAst|) $) "thenBranch(\\spad{e}) returns the `else-branch' of `e'.")) (|thenBranch| (((|SpadAst|) $) "\\spad{thenBranch(e)} returns the `then-branch' of `e'.")) (|condition| (((|SpadAst|) $) "\\spad{condition(e)} returns the condition of the if-expression `e'."))) NIL NIL (-530 |p| |n|) ((|constructor| (NIL "InnerFiniteField(\\spad{p},{}\\spad{n}) implements finite fields with \\spad{p**n} elements where \\spad{p} is assumed prime but does not check. For a version which checks that \\spad{p} is prime,{} see \\spadtype{FiniteField}."))) -((-4455 . T) (-4461 . T) (-4456 . T) ((-4465 "*") . T) (-4457 . T) (-4458 . T) (-4460 . T)) -((-3794 (|HasCategory| (-593 |#1|) (QUOTE (-146))) (|HasCategory| (-593 |#1|) (QUOTE (-379)))) (|HasCategory| (-593 |#1|) (QUOTE (-148))) (|HasCategory| (-593 |#1|) (QUOTE (-379))) (|HasCategory| (-593 |#1|) (QUOTE (-146)))) +((-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) +((-2758 (|HasCategory| (-593 |#1|) (QUOTE (-146))) (|HasCategory| (-593 |#1|) (QUOTE (-379)))) (|HasCategory| (-593 |#1|) (QUOTE (-148))) (|HasCategory| (-593 |#1|) (QUOTE (-379))) (|HasCategory| (-593 |#1|) (QUOTE (-146)))) (-531 R |mnRow| |mnCol| |Row| |Col|) ((|constructor| (NIL "\\indented{1}{This is an internal type which provides an implementation of} 2-dimensional arrays as PrimitiveArray\\spad{'s} of PrimitiveArray\\spad{'s}."))) -((-4463 . T) (-4464 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1120))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1120))) (-3794 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1120)))) (-3794 (-12 (|HasCategory| |#1| (QUOTE (-1120))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-875))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-875)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4464 . T) (-4465 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1121))) (-2758 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1121)))) (-2758 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102)))) (-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."))) -((-4464 . T) (-4463 . T)) -((-3794 (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1120))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-3794 (-12 (|HasCategory| |#1| (QUOTE (-1120))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-875))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-3794 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1120)))) (|HasCategory| |#1| (QUOTE (-861))) (-3794 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1120)))) (|HasCategory| (-576) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1120))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-875)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1120))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) +((-4465 . T) (-4464 . T)) +((-2758 (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2758 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2758 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| |#1| (QUOTE (-861))) (-2758 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| (-576) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-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 -4464))) +((|HasAttribute| |#3| (QUOTE -4465))) (-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: 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 -4464))) +((|HasAttribute| |#7| (QUOTE -4465))) (-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."))) -((-4463 . T) (-4464 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1120))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1120))) (-3794 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1120)))) (-3794 (-12 (|HasCategory| |#1| (QUOTE (-1120))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-875))))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-568))) (|HasAttribute| |#1| (QUOTE (-4465 "*"))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-875)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4464 . T) (-4465 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1121))) (-2758 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1121)))) (-2758 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-568))) (|HasAttribute| |#1| (QUOTE (-4466 "*"))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102)))) (-536) ((|constructor| (NIL "This domain represents an `import' of types.")) (|imports| (((|List| (|TypeAst|)) $) "\\spad{imports(x)} returns the list of imported types.")) (|coerce| (($ (|List| (|TypeAst|))) "ts::ImportAst constructs an ImportAst for the list if types `ts'."))) NIL @@ -2104,7 +2104,7 @@ NIL ((|constructor| (NIL "\\indented{2}{IndexedExponents of an ordered set of variables gives a representation} for the degree of polynomials in commuting variables. It gives an ordered pairing of non negative integer exponents with variables"))) NIL NIL -(-544 K -2117 |Par|) +(-544 K -1959 |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 @@ -2128,7 +2128,7 @@ NIL ((|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 -(-550 K -2117 |Par|) +(-550 K -1959 |Par|) ((|constructor| (NIL "This is an internal package for computing approximate solutions to systems of polynomial equations. The parameter \\spad{K} specifies the coefficient field of the input polynomials and must be either \\spad{Fraction(Integer)} or \\spad{Complex(Fraction Integer)}. The parameter \\spad{F} specifies where the solutions must lie and can be one of the following: \\spad{Float},{} \\spad{Fraction(Integer)},{} \\spad{Complex(Float)},{} \\spad{Complex(Fraction Integer)}. The last parameter specifies the type of the precision operand and must be either \\spad{Fraction(Integer)} or \\spad{Float}.")) (|makeEq| (((|List| (|Equation| (|Polynomial| |#2|))) (|List| |#2|) (|List| (|Symbol|))) "\\spad{makeEq(lsol,lvar)} returns a list of equations formed by corresponding members of \\spad{lvar} and \\spad{lsol}.")) (|innerSolve| (((|List| (|List| |#2|)) (|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|)) |#3|) "\\spad{innerSolve(lnum,lden,lvar,eps)} returns a list of solutions of the system of polynomials \\spad{lnum},{} with the side condition that none of the members of \\spad{lden} vanish identically on any solution. Each solution is expressed as a list corresponding to the list of variables in \\spad{lvar} and with precision specified by \\spad{eps}.")) (|innerSolve1| (((|List| |#2|) (|Polynomial| |#1|) |#3|) "\\spad{innerSolve1(p,eps)} returns the list of the zeros of the polynomial \\spad{p} with precision \\spad{eps}.") (((|List| |#2|) (|SparseUnivariatePolynomial| |#1|) |#3|) "\\spad{innerSolve1(up,eps)} returns the list of the zeros of the univariate polynomial \\spad{up} with precision \\spad{eps}."))) NIL NIL @@ -2158,7 +2158,7 @@ NIL NIL (-557) ((|constructor| (NIL "An \\spad{IntegerNumberSystem} is a model for the integers.")) (|invmod| (($ $ $) "\\spad{invmod(a,b)},{} \\spad{0<=a<b>1},{} \\spad{(a,b)=1} means \\spad{1/a mod b}.")) (|powmod| (($ $ $ $) "\\spad{powmod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a**b mod p}.")) (|mulmod| (($ $ $ $) "\\spad{mulmod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a*b mod p}.")) (|submod| (($ $ $ $) "\\spad{submod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a-b mod p}.")) (|addmod| (($ $ $ $) "\\spad{addmod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a+b mod p}.")) (|mask| (($ $) "\\spad{mask(n)} returns \\spad{2**n-1} (an \\spad{n} bit mask).")) (|dec| (($ $) "\\spad{dec(x)} returns \\spad{x - 1}.")) (|inc| (($ $) "\\spad{inc(x)} returns \\spad{x + 1}.")) (|copy| (($ $) "\\spad{copy(n)} gives a copy of \\spad{n}.")) (|random| (($ $) "\\spad{random(a)} creates a random element from 0 to \\spad{a-1}.") (($) "\\spad{random()} creates a random element.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(n)} creates a rational number,{} or returns \"failed\" if this is not possible.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(n)} creates a rational number (see \\spadtype{Fraction Integer})..")) (|rational?| (((|Boolean|) $) "\\spad{rational?(n)} tests if \\spad{n} is a rational number (see \\spadtype{Fraction Integer}).")) (|symmetricRemainder| (($ $ $) "\\spad{symmetricRemainder(a,b)} (where \\spad{b > 1}) yields \\spad{r} where \\spad{ -b/2 <= r < b/2 }.")) (|positiveRemainder| (($ $ $) "\\spad{positiveRemainder(a,b)} (where \\spad{b > 1}) yields \\spad{r} where \\spad{0 <= r < b} and \\spad{r == a rem b}.")) (|bit?| (((|Boolean|) $ $) "\\spad{bit?(n,i)} returns \\spad{true} if and only if \\spad{i}-th bit of \\spad{n} is a 1.")) (|shift| (($ $ $) "\\spad{shift(a,i)} shift \\spad{a} by \\spad{i} digits.")) (|length| (($ $) "\\spad{length(a)} length of \\spad{a} in digits.")) (|base| (($) "\\spad{base()} returns the base for the operations of \\spad{IntegerNumberSystem}.")) (|multiplicativeValuation| ((|attribute|) "euclideanSize(a*b) returns \\spad{euclideanSize(a)*euclideanSize(b)}.")) (|even?| (((|Boolean|) $) "\\spad{even?(n)} returns \\spad{true} if and only if \\spad{n} is even.")) (|odd?| (((|Boolean|) $) "\\spad{odd?(n)} returns \\spad{true} if and only if \\spad{n} is odd."))) -((-4461 . T) (-4462 . T) (-4456 . T) ((-4465 "*") . T) (-4457 . T) (-4458 . T) (-4460 . T)) +((-4462 . T) (-4463 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-558) ((|constructor| (NIL "This domain is a datatype for (signed) integer values of precision 16 bits."))) @@ -2178,13 +2178,13 @@ NIL NIL (-562 |Key| |Entry| |addDom|) ((|constructor| (NIL "This domain is used to provide a conditional \"add\" domain for the implementation of \\spadtype{Table}."))) -((-4463 . T) (-4464 . T)) -((-12 (|HasCategory| (-2 (|:| -2239 |#1|) (|:| -2904 |#2|)) (QUOTE (-1120))) (|HasCategory| (-2 (|:| -2239 |#1|) (|:| -2904 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2239) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2904) (|devaluate| |#2|)))))) (-3794 (|HasCategory| (-2 (|:| -2239 |#1|) (|:| -2904 |#2|)) (QUOTE (-1120))) (|HasCategory| |#2| (QUOTE (-1120)))) (-3794 (|HasCategory| (-2 (|:| -2239 |#1|) (|:| -2904 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2239 |#1|) (|:| -2904 |#2|)) (QUOTE (-1120))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1120)))) (-3794 (|HasCategory| (-2 (|:| -2239 |#1|) (|:| -2904 |#2|)) (QUOTE (-1120))) (|HasCategory| (-2 (|:| -2239 |#1|) (|:| -2904 |#2|)) (LIST (QUOTE -625) (QUOTE (-875)))) (|HasCategory| |#2| (QUOTE (-1120))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-875))))) (|HasCategory| (-2 (|:| -2239 |#1|) (|:| -2904 |#2|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#2| (QUOTE (-1120))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2239 |#1|) (|:| -2904 |#2|)) (QUOTE (-1120))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#2| (QUOTE (-1120))) (-3794 (|HasCategory| (-2 (|:| -2239 |#1|) (|:| -2904 |#2|)) (LIST (QUOTE -625) (QUOTE (-875)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-875))))) (-3794 (|HasCategory| (-2 (|:| -2239 |#1|) (|:| -2904 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-875)))) (|HasCategory| (-2 (|:| -2239 |#1|) (|:| -2904 |#2|)) (LIST (QUOTE -625) (QUOTE (-875)))) (|HasCategory| (-2 (|:| -2239 |#1|) (|:| -2904 |#2|)) (QUOTE (-102)))) -(-563 R -2117) +((-4464 . T) (-4465 . T)) +((-12 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4438 |#2|)) (QUOTE (-1121))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4438 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4300) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4438) (|devaluate| |#2|)))))) (-2758 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4438 |#2|)) (QUOTE (-1121))) (|HasCategory| |#2| (QUOTE (-1121)))) (-2758 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4438 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4438 |#2|)) (QUOTE (-1121))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1121)))) (-2758 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4438 |#2|)) (QUOTE (-1121))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4438 |#2|)) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4438 |#2|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4438 |#2|)) (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#2| (QUOTE (-1121))) (-2758 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4438 |#2|)) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-876))))) (-2758 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4438 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4438 |#2|)) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4438 |#2|)) (QUOTE (-102)))) +(-563 R -1959) ((|constructor| (NIL "This package provides functions for the integration of algebraic integrands over transcendental functions.")) (|algint| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|SparseUnivariatePolynomial| |#2|) (|SparseUnivariatePolynomial| |#2|))) "\\spad{algint(f, x, y, d)} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x}; \\spad{d} is the derivation to use on \\spad{k[x]}."))) NIL NIL -(-564 R0 -2117 UP UPUP R) +(-564 R0 -1959 UP UPUP R) ((|constructor| (NIL "This package provides functions for integrating a function on an algebraic curve.")) (|palginfieldint| (((|Union| |#5| "failed") |#5| (|Mapping| |#3| |#3|)) "\\spad{palginfieldint(f, d)} returns an algebraic function \\spad{g} such that \\spad{dg = f} if such a \\spad{g} exists,{} \"failed\" otherwise. Argument \\spad{f} must be a pure algebraic function.")) (|palgintegrate| (((|IntegrationResult| |#5|) |#5| (|Mapping| |#3| |#3|)) "\\spad{palgintegrate(f, d)} integrates \\spad{f} with respect to the derivation \\spad{d}. Argument \\spad{f} must be a pure algebraic function.")) (|algintegrate| (((|IntegrationResult| |#5|) |#5| (|Mapping| |#3| |#3|)) "\\spad{algintegrate(f, d)} integrates \\spad{f} with respect to the derivation \\spad{d}."))) NIL NIL @@ -2194,7 +2194,7 @@ NIL NIL (-566 R) ((|constructor| (NIL "\\indented{1}{+ Author: Mike Dewar} + Date Created: November 1996 + Date Last Updated: + Basic Functions: + Related Constructors: + Also See: + AMS Classifications: + Keywords: + References: + Description: + This category implements of interval arithmetic and transcendental + functions over intervals.")) (|contains?| (((|Boolean|) $ |#1|) "\\spad{contains?(i,f)} returns \\spad{true} if \\axiom{\\spad{f}} is contained within the interval \\axiom{\\spad{i}},{} \\spad{false} otherwise.")) (|negative?| (((|Boolean|) $) "\\spad{negative?(u)} returns \\axiom{\\spad{true}} if every element of \\spad{u} is negative,{} \\axiom{\\spad{false}} otherwise.")) (|positive?| (((|Boolean|) $) "\\spad{positive?(u)} returns \\axiom{\\spad{true}} if every element of \\spad{u} is positive,{} \\axiom{\\spad{false}} otherwise.")) (|width| ((|#1| $) "\\spad{width(u)} returns \\axiom{sup(\\spad{u}) - inf(\\spad{u})}.")) (|sup| ((|#1| $) "\\spad{sup(u)} returns the supremum of \\axiom{\\spad{u}}.")) (|inf| ((|#1| $) "\\spad{inf(u)} returns the infinum of \\axiom{\\spad{u}}.")) (|qinterval| (($ |#1| |#1|) "\\spad{qinterval(inf,sup)} creates a new interval \\axiom{[\\spad{inf},{}\\spad{sup}]},{} without checking the ordering on the elements.")) (|interval| (($ (|Fraction| (|Integer|))) "\\spad{interval(f)} creates a new interval around \\spad{f}.") (($ |#1|) "\\spad{interval(f)} creates a new interval around \\spad{f}.") (($ |#1| |#1|) "\\spad{interval(inf,sup)} creates a new interval,{} either \\axiom{[\\spad{inf},{}\\spad{sup}]} if \\axiom{\\spad{inf} \\spad{<=} \\spad{sup}} or \\axiom{[\\spad{sup},{}in]} otherwise."))) -((-2641 . T) (-4456 . T) ((-4465 "*") . T) (-4457 . T) (-4458 . T) (-4460 . T)) +((-4165 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-567 S) ((|constructor| (NIL "The category of commutative integral domains,{} \\spadignore{i.e.} commutative rings with no zero divisors. \\blankline Conditional attributes: \\indented{2}{canonicalUnitNormal\\tab{20}the canonical field is the same for all associates} \\indented{2}{canonicalsClosed\\tab{20}the product of two canonicals is itself canonical}")) (|unit?| (((|Boolean|) $) "\\spad{unit?(x)} tests whether \\spad{x} is a unit,{} \\spadignore{i.e.} is invertible.")) (|associates?| (((|Boolean|) $ $) "\\spad{associates?(x,y)} tests whether \\spad{x} and \\spad{y} are associates,{} \\spadignore{i.e.} differ by a unit factor.")) (|unitCanonical| (($ $) "\\spad{unitCanonical(x)} returns \\spad{unitNormal(x).canonical}.")) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) "\\spad{unitNormal(x)} tries to choose a canonical element from the associate class of \\spad{x}. The attribute canonicalUnitNormal,{} if asserted,{} means that the \"canonical\" element is the same across all associates of \\spad{x} if \\spad{unitNormal(x) = [u,c,a]} then \\spad{u*c = x},{} \\spad{a*u = 1}.")) (|exquo| (((|Union| $ "failed") $ $) "\\spad{exquo(a,b)} either returns an element \\spad{c} such that \\spad{c*b=a} or \"failed\" if no such element can be found."))) @@ -2202,9 +2202,9 @@ NIL NIL (-568) ((|constructor| (NIL "The category of commutative integral domains,{} \\spadignore{i.e.} commutative rings with no zero divisors. \\blankline Conditional attributes: \\indented{2}{canonicalUnitNormal\\tab{20}the canonical field is the same for all associates} \\indented{2}{canonicalsClosed\\tab{20}the product of two canonicals is itself canonical}")) (|unit?| (((|Boolean|) $) "\\spad{unit?(x)} tests whether \\spad{x} is a unit,{} \\spadignore{i.e.} is invertible.")) (|associates?| (((|Boolean|) $ $) "\\spad{associates?(x,y)} tests whether \\spad{x} and \\spad{y} are associates,{} \\spadignore{i.e.} differ by a unit factor.")) (|unitCanonical| (($ $) "\\spad{unitCanonical(x)} returns \\spad{unitNormal(x).canonical}.")) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) "\\spad{unitNormal(x)} tries to choose a canonical element from the associate class of \\spad{x}. The attribute canonicalUnitNormal,{} if asserted,{} means that the \"canonical\" element is the same across all associates of \\spad{x} if \\spad{unitNormal(x) = [u,c,a]} then \\spad{u*c = x},{} \\spad{a*u = 1}.")) (|exquo| (((|Union| $ "failed") $ $) "\\spad{exquo(a,b)} either returns an element \\spad{c} such that \\spad{c*b=a} or \"failed\" if no such element can be found."))) -((-4456 . T) ((-4465 "*") . T) (-4457 . T) (-4458 . T) (-4460 . T)) +((-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL -(-569 R -2117) +(-569 R -1959) ((|constructor| (NIL "This package provides functions for integration,{} limited integration,{} extended integration and the risch differential equation for elemntary functions.")) (|lfextlimint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Symbol|) (|Kernel| |#2|) (|List| (|Kernel| |#2|))) "\\spad{lfextlimint(f,x,k,[k1,...,kn])} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f - c dk/dx}. Value \\spad{h} is looked for in a field containing \\spad{f} and \\spad{k1},{}...,{}\\spad{kn} (the \\spad{ki}\\spad{'s} must be logs).")) (|lfintegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{lfintegrate(f, x)} = \\spad{g} such that \\spad{dg/dx = f}.")) (|lfinfieldint| (((|Union| |#2| "failed") |#2| (|Symbol|)) "\\spad{lfinfieldint(f, x)} returns a function \\spad{g} such that \\spad{dg/dx = f} if \\spad{g} exists,{} \"failed\" otherwise.")) (|lflimitedint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Symbol|) (|List| |#2|)) "\\spad{lflimitedint(f,x,[g1,...,gn])} returns functions \\spad{[h,[[ci, gi]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,...,gn]},{} and \\spad{d(h+sum(ci log(gi)))/dx = f},{} if possible,{} \"failed\" otherwise.")) (|lfextendedint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Symbol|) |#2|) "\\spad{lfextendedint(f, x, g)} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f - cg},{} if (\\spad{h},{} \\spad{c}) exist,{} \"failed\" otherwise."))) NIL NIL @@ -2216,7 +2216,7 @@ NIL ((|constructor| (NIL "\\blankline")) (|entry| (((|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{entry(n)} \\undocumented{}")) (|entries| (((|List| (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))))) $) "\\spad{entries(x)} \\undocumented{}")) (|showAttributes| (((|Union| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))) "failed") (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{showAttributes(x)} \\undocumented{}")) (|insert!| (($ (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))))) "\\spad{insert!(r)} inserts an entry \\spad{r} into theIFTable")) (|fTable| (($ (|List| (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))))))) "\\spad{fTable(l)} creates a functions table from the elements of \\spad{l}.")) (|keys| (((|List| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) $) "\\spad{keys(f)} returns the list of keys of \\spad{f}")) (|clearTheFTable| (((|Void|)) "\\spad{clearTheFTable()} clears the current table of functions.")) (|showTheFTable| (($) "\\spad{showTheFTable()} returns the current table of functions."))) NIL NIL -(-572 R -2117 L) +(-572 R -1959 L) ((|constructor| (NIL "This internal package rationalises integrands on curves of the form: \\indented{2}{\\spad{y\\^2 = a x\\^2 + b x + c}} \\indented{2}{\\spad{y\\^2 = (a x + b) / (c x + d)}} \\indented{2}{\\spad{f(x, y) = 0} where \\spad{f} has degree 1 in \\spad{x}} The rationalization is done for integration,{} limited integration,{} extended integration and the risch differential equation.")) (|palgLODE0| (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgLODE0(op,g,x,y,z,t,c)} returns the solution of \\spad{op f = g} Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}.") (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgLODE0(op, g, x, y, d, p)} returns the solution of \\spad{op f = g}. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}.")) (|lift| (((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|SparseUnivariatePolynomial| |#2|) (|Kernel| |#2|)) "\\spad{lift(u,k)} \\undocumented")) (|multivariate| ((|#2| (|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|Kernel| |#2|) |#2|) "\\spad{multivariate(u,k,f)} \\undocumented")) (|univariate| (((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|SparseUnivariatePolynomial| |#2|)) "\\spad{univariate(f,k,k,p)} \\undocumented")) (|palgRDE0| (((|Union| |#2| "failed") |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|)) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgRDE0(f, g, x, y, foo, t, c)} returns a function \\spad{z(x,y)} such that \\spad{dz/dx + n * df/dx z(x,y) = g(x,y)} if such a \\spad{z} exists,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{foo},{} called by \\spad{foo(a, b, x)},{} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}.") (((|Union| |#2| "failed") |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|)) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgRDE0(f, g, x, y, foo, d, p)} returns a function \\spad{z(x,y)} such that \\spad{dz/dx + n * df/dx z(x,y) = g(x,y)} if such a \\spad{z} exists,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}. Argument \\spad{foo},{} called by \\spad{foo(a, b, x)},{} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}.")) (|palglimint0| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palglimint0(f, x, y, [u1,...,un], z, t, c)} returns functions \\spad{[h,[[ci, ui]]]} such that the \\spad{ui}\\spad{'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 = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}.") (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palglimint0(f, x, y, [u1,...,un], d, p)} returns functions \\spad{[h,[[ci, ui]]]} such that the \\spad{ui}\\spad{'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, x, y, g, z, t, c)} returns functions \\spad{[h, d]} such that \\spad{dh/dx = f(x,y) - d g},{} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy},{} and \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{z} is a dummy variable not appearing in \\spad{f(x,y)}. The operation returns \"failed\" if no such functions exist.") (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgextint0(f, x, y, g, d, p)} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f(x,y) - c g},{} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2 y(x)\\^2 = P(x)},{} or \"failed\" if no such functions exist.")) (|palgint0| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgint0(f, x, y, z, t, c)} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{z} is a dummy variable not appearing in \\spad{f(x,y)}.") (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgint0(f, x, y, d, p)} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2 y(x)\\^2 = P(x)}."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -668) (|devaluate| |#2|)))) @@ -2224,31 +2224,31 @@ NIL ((|constructor| (NIL "This package provides various number theoretic functions on the integers.")) (|sumOfKthPowerDivisors| (((|Integer|) (|Integer|) (|NonNegativeInteger|)) "\\spad{sumOfKthPowerDivisors(n,k)} returns the sum of the \\spad{k}th powers of the integers between 1 and \\spad{n} (inclusive) which divide \\spad{n}. the sum of the \\spad{k}th powers of the divisors of \\spad{n} is often denoted by \\spad{sigma_k(n)}.")) (|sumOfDivisors| (((|Integer|) (|Integer|)) "\\spad{sumOfDivisors(n)} returns the sum of the integers between 1 and \\spad{n} (inclusive) which divide \\spad{n}. The sum of the divisors of \\spad{n} is often denoted by \\spad{sigma(n)}.")) (|numberOfDivisors| (((|Integer|) (|Integer|)) "\\spad{numberOfDivisors(n)} returns the number of integers between 1 and \\spad{n} (inclusive) which divide \\spad{n}. The number of divisors of \\spad{n} is often denoted by \\spad{tau(n)}.")) (|moebiusMu| (((|Integer|) (|Integer|)) "\\spad{moebiusMu(n)} returns the Moebius function \\spad{mu(n)}. \\spad{mu(n)} is either \\spad{-1},{}0 or 1 as follows: \\spad{mu(n) = 0} if \\spad{n} is divisible by a square > 1,{} \\spad{mu(n) = (-1)^k} if \\spad{n} is square-free and has \\spad{k} distinct prime divisors.")) (|legendre| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{legendre(a,p)} returns the Legendre symbol \\spad{L(a/p)}. \\spad{L(a/p) = (-1)**((p-1)/2) mod p} (\\spad{p} prime),{} which is 0 if \\spad{a} is 0,{} 1 if \\spad{a} is a quadratic residue \\spad{mod p} and \\spad{-1} otherwise. Note: because the primality test is expensive,{} if it is known that \\spad{p} is prime then use \\spad{jacobi(a,p)}.")) (|jacobi| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{jacobi(a,b)} returns the Jacobi symbol \\spad{J(a/b)}. When \\spad{b} is odd,{} \\spad{J(a/b) = product(L(a/p) for p in factor b )}. Note: by convention,{} 0 is returned if \\spad{gcd(a,b) ~= 1}. Iterative \\spad{O(log(b)^2)} version coded by Michael Monagan June 1987.")) (|harmonic| (((|Fraction| (|Integer|)) (|Integer|)) "\\spad{harmonic(n)} returns the \\spad{n}th harmonic number. This is \\spad{H[n] = sum(1/k,k=1..n)}.")) (|fibonacci| (((|Integer|) (|Integer|)) "\\spad{fibonacci(n)} returns the \\spad{n}th Fibonacci number. the Fibonacci numbers \\spad{F[n]} are defined by \\spad{F[0] = F[1] = 1} and \\spad{F[n] = F[n-1] + F[n-2]}. The algorithm has running time \\spad{O(log(n)^3)}. Reference: Knuth,{} The Art of Computer Programming Vol 2,{} Semi-Numerical Algorithms.")) (|eulerPhi| (((|Integer|) (|Integer|)) "\\spad{eulerPhi(n)} returns the number of integers between 1 and \\spad{n} (including 1) which are relatively prime to \\spad{n}. This is the Euler phi function \\spad{\\phi(n)} is also called the totient function.")) (|euler| (((|Integer|) (|Integer|)) "\\spad{euler(n)} returns the \\spad{n}th Euler number. This is \\spad{2^n E(n,1/2)},{} where \\spad{E(n,x)} is the \\spad{n}th Euler polynomial.")) (|divisors| (((|List| (|Integer|)) (|Integer|)) "\\spad{divisors(n)} returns a list of the divisors of \\spad{n}.")) (|chineseRemainder| (((|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{chineseRemainder(x1,m1,x2,m2)} returns \\spad{w},{} where \\spad{w} is such that \\spad{w = x1 mod m1} and \\spad{w = x2 mod m2}. Note: \\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 -(-574 -2117 UP UPUP R) +(-574 -1959 UP UPUP R) ((|constructor| (NIL "algebraic Hermite redution.")) (|HermiteIntegrate| (((|Record| (|:| |answer| |#4|) (|:| |logpart| |#4|)) |#4| (|Mapping| |#2| |#2|)) "\\spad{HermiteIntegrate(f, ')} returns \\spad{[g,h]} such that \\spad{f = g' + h} and \\spad{h} has a only simple finite normal poles."))) NIL NIL -(-575 -2117 UP) +(-575 -1959 UP) ((|constructor| (NIL "Hermite integration,{} transcendental case.")) (|HermiteIntegrate| (((|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |logpart| (|Fraction| |#2|)) (|:| |specpart| (|Fraction| |#2|)) (|:| |polypart| |#2|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{HermiteIntegrate(f, D)} returns \\spad{[g, h, s, p]} such that \\spad{f = Dg + h + s + p},{} \\spad{h} has a squarefree denominator normal \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} and all the squarefree factors of the denominator of \\spad{s} are special \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D}. Furthermore,{} \\spad{h} and \\spad{s} have no polynomial parts. \\spad{D} is the derivation to use on \\spadtype{UP}."))) NIL NIL (-576) ((|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."))) -((-4445 . T) (-4451 . T) (-4455 . T) (-4450 . T) (-4461 . T) (-4462 . T) (-4456 . T) ((-4465 "*") . T) (-4457 . T) (-4458 . T) (-4460 . T)) +((-4446 . T) (-4452 . T) (-4456 . T) (-4451 . T) (-4462 . T) (-4463 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-577) ((|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|))) (|:| |extra| (|Result|))) (|NumericalIntegrationProblem|) (|RoutinesTable|)) "\\spad{measure(prob,R)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical integration problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} listed in \\axiom{\\spad{R}} of \\axiom{category} \\axiomType{NumericalIntegrationCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information.") (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|))) (|:| |extra| (|Result|))) (|NumericalIntegrationProblem|)) "\\spad{measure(prob)} is a top level ANNA function for identifying the most appropriate numerical routine for solving the numerical integration problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} of \\axiom{category} \\axiomType{NumericalIntegrationCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information.")) (|integrate| (((|Union| (|Result|) "failed") (|Expression| (|Float|)) (|SegmentBinding| (|OrderedCompletion| (|Float|))) (|Symbol|)) "\\spad{integrate(exp, x = a..b, numerical)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range,{} {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.\\newline \\blankline Default values for the absolute and relative error are used. \\blankline It is an error if the last argument is not {\\spad{\\tt} numerical}.") (((|Union| (|Result|) "failed") (|Expression| (|Float|)) (|SegmentBinding| (|OrderedCompletion| (|Float|))) (|String|)) "\\spad{integrate(exp, x = a..b, \"numerical\")} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range,{} {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.\\newline \\blankline Default values for the absolute and relative error are used. \\blankline It is an error of the last argument is not {\\spad{\\tt} \"numerical\"}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|)))) (|Float|) (|Float|) (|RoutinesTable|)) "\\spad{integrate(exp, [a..b,c..d,...], epsabs, epsrel, routines)} is a top level ANNA function to integrate a multivariate expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given set of ranges to the required absolute and relative accuracy,{} using the routines available in the RoutinesTable provided. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|)))) (|Float|) (|Float|)) "\\spad{integrate(exp, [a..b,c..d,...], epsabs, epsrel)} is a top level ANNA function to integrate a multivariate expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given set of ranges to the required absolute and relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|)))) (|Float|)) "\\spad{integrate(exp, [a..b,c..d,...], epsrel)} is a top level ANNA function to integrate a multivariate expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given set of ranges to the required relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline If epsrel = 0,{} a default absolute accuracy is used.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|))))) "\\spad{integrate(exp, [a..b,c..d,...])} is a top level ANNA function to integrate a multivariate expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given set of ranges. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline Default values for the absolute and relative error are used.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|)))) "\\spad{integrate(exp, a..b)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline Default values for the absolute and relative error are used.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|))) (|Float|)) "\\spad{integrate(exp, a..b, epsrel)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}} to the required relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline If epsrel = 0,{} a default absolute accuracy is used.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|))) (|Float|) (|Float|)) "\\spad{integrate(exp, a..b, epsabs, epsrel)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}} to the required absolute and relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|NumericalIntegrationProblem|)) "\\spad{integrate(IntegrationProblem)} is a top level ANNA function to integrate an expression over a given range or ranges to the required absolute and relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|))) (|Float|) (|Float|) (|RoutinesTable|)) "\\spad{integrate(exp, a..b, epsrel, routines)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}} to the required absolute and relative accuracy using the routines available in the RoutinesTable provided. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}."))) NIL NIL -(-578 R -2117 L) +(-578 R -1959 L) ((|constructor| (NIL "This package provides functions for integration,{} limited integration,{} extended integration and the risch differential equation for pure algebraic integrands.")) (|palgLODE| (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Symbol|)) "\\spad{palgLODE(op, g, kx, y, x)} returns the solution of \\spad{op f = g}. \\spad{y} is an algebraic function of \\spad{x}.")) (|palgRDE| (((|Union| |#2| "failed") |#2| |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|))) "\\spad{palgRDE(nfp, f, g, x, y, foo)} returns a function \\spad{z(x,y)} such that \\spad{dz/dx + n * df/dx z(x,y) = g(x,y)} if such a \\spad{z} exists,{} \"failed\" otherwise; \\spad{y} is an algebraic function of \\spad{x}; \\spad{foo(a, b, x)} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}. \\spad{nfp} is \\spad{n * df/dx}.")) (|palglimint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|)) "\\spad{palglimint(f, x, y, [u1,...,un])} returns functions \\spad{[h,[[ci, ui]]]} such that the \\spad{ui}\\spad{'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, x, y, g)} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f(x,y) - c g},{} where \\spad{y} is an algebraic function of \\spad{x}; returns \"failed\" if no such functions exist.")) (|palgint| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|)) "\\spad{palgint(f, x, y)} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x}."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -668) (|devaluate| |#2|)))) -(-579 R -2117) +(-579 R -1959) ((|constructor| (NIL "\\spadtype{PatternMatchIntegration} provides functions that use the pattern matcher to find some indefinite and definite integrals involving special functions and found in the litterature.")) (|pmintegrate| (((|Union| |#2| "failed") |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|)) "\\spad{pmintegrate(f, x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b} if it can be found by the built-in pattern matching rules.") (((|Union| (|Record| (|:| |special| |#2|) (|:| |integrand| |#2|)) "failed") |#2| (|Symbol|)) "\\spad{pmintegrate(f, x)} returns either \"failed\" or \\spad{[g,h]} such that \\spad{integrate(f,x) = g + integrate(h,x)}.")) (|pmComplexintegrate| (((|Union| (|Record| (|:| |special| |#2|) (|:| |integrand| |#2|)) "failed") |#2| (|Symbol|)) "\\spad{pmComplexintegrate(f, x)} returns either \"failed\" or \\spad{[g,h]} such that \\spad{integrate(f,x) = g + integrate(h,x)}. It only looks for special complex integrals that pmintegrate does not return.")) (|splitConstant| (((|Record| (|:| |const| |#2|) (|:| |nconst| |#2|)) |#2| (|Symbol|)) "\\spad{splitConstant(f, x)} returns \\spad{[c, g]} such that \\spad{f = c * g} and \\spad{c} does not involve \\spad{t}."))) NIL -((-12 (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -906) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-1159)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -906) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-641))))) -(-580 -2117 UP) +((-12 (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-1160)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-641))))) +(-580 -1959 UP) ((|constructor| (NIL "This package provides functions for the base case of the Risch algorithm.")) (|limitedint| (((|Union| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|)))))) "failed") (|Fraction| |#2|) (|List| (|Fraction| |#2|))) "\\spad{limitedint(f, [g1,...,gn])} returns fractions \\spad{[h,[[ci, gi]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,...,gn]},{} \\spad{ci' = 0},{} and \\spad{(h+sum(ci log(gi)))' = f},{} if possible,{} \"failed\" otherwise.")) (|extendedint| (((|Union| (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{extendedint(f, g)} returns fractions \\spad{[h, c]} such that \\spad{c' = 0} and \\spad{h' = f - cg},{} if \\spad{(h, c)} exist,{} \"failed\" otherwise.")) (|infieldint| (((|Union| (|Fraction| |#2|) "failed") (|Fraction| |#2|)) "\\spad{infieldint(f)} returns \\spad{g} such that \\spad{g' = f} or \"failed\" if the integral of \\spad{f} is not a rational function.")) (|integrate| (((|IntegrationResult| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{integrate(f)} returns \\spad{g} such that \\spad{g' = f}."))) NIL NIL @@ -2256,27 +2256,27 @@ NIL ((|constructor| (NIL "Provides integer testing and retraction functions. Date Created: March 1990 Date Last Updated: 9 April 1991")) (|integerIfCan| (((|Union| (|Integer|) "failed") |#1|) "\\spad{integerIfCan(x)} returns \\spad{x} as an integer,{} \"failed\" if \\spad{x} is not an integer.")) (|integer?| (((|Boolean|) |#1|) "\\spad{integer?(x)} is \\spad{true} if \\spad{x} is an integer,{} \\spad{false} otherwise.")) (|integer| (((|Integer|) |#1|) "\\spad{integer(x)} returns \\spad{x} as an integer; error if \\spad{x} is not an integer."))) NIL NIL -(-582 -2117) +(-582 -1959) ((|constructor| (NIL "This package provides functions for the integration of rational functions.")) (|extendedIntegrate| (((|Union| (|Record| (|:| |ratpart| (|Fraction| (|Polynomial| |#1|))) (|:| |coeff| (|Fraction| (|Polynomial| |#1|)))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|))) "\\spad{extendedIntegrate(f, x, g)} returns fractions \\spad{[h, c]} such that \\spad{dc/dx = 0} and \\spad{dh/dx = f - cg},{} if \\spad{(h, c)} exist,{} \"failed\" otherwise.")) (|limitedIntegrate| (((|Union| (|Record| (|:| |mainpart| (|Fraction| (|Polynomial| |#1|))) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| (|Polynomial| |#1|))) (|:| |logand| (|Fraction| (|Polynomial| |#1|))))))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|List| (|Fraction| (|Polynomial| |#1|)))) "\\spad{limitedIntegrate(f, x, [g1,...,gn])} returns fractions \\spad{[h, [[ci,gi]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,...,gn]},{} \\spad{dci/dx = 0},{} and \\spad{d(h + sum(ci log(gi)))/dx = f} if possible,{} \"failed\" otherwise.")) (|infieldIntegrate| (((|Union| (|Fraction| (|Polynomial| |#1|)) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{infieldIntegrate(f, x)} returns a fraction \\spad{g} such that \\spad{dg/dx = f} if \\spad{g} exists,{} \"failed\" otherwise.")) (|internalIntegrate| (((|IntegrationResult| (|Fraction| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{internalIntegrate(f, x)} returns \\spad{g} such that \\spad{dg/dx = f}."))) NIL NIL (-583 R) ((|constructor| (NIL "\\indented{1}{+ Author: Mike Dewar} + Date Created: November 1996 + Date Last Updated: + Basic Functions: + Related Constructors: + Also See: + AMS Classifications: + Keywords: + References: + Description: + This domain is an implementation of interval arithmetic and transcendental + functions over intervals."))) -((-2641 . T) (-4456 . T) ((-4465 "*") . T) (-4457 . T) (-4458 . T) (-4460 . T)) +((-4165 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-584) ((|constructor| (NIL "This package provides the implementation for the \\spadfun{solveLinearPolynomialEquation} operation over the integers. It uses a lifting technique from the package GenExEuclid")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| (|Integer|))) "failed") (|List| (|SparseUnivariatePolynomial| (|Integer|))) (|SparseUnivariatePolynomial| (|Integer|))) "\\spad{solveLinearPolynomialEquation([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists."))) NIL NIL -(-585 R -2117) +(-585 R -1959) ((|constructor| (NIL "\\indented{1}{Tools for the integrator} Author: Manuel Bronstein Date Created: 25 April 1990 Date Last Updated: 9 June 1993 Keywords: elementary,{} function,{} integration.")) (|intPatternMatch| (((|IntegrationResult| |#2|) |#2| (|Symbol|) (|Mapping| (|IntegrationResult| |#2|) |#2| (|Symbol|)) (|Mapping| (|Union| (|Record| (|:| |special| |#2|) (|:| |integrand| |#2|)) "failed") |#2| (|Symbol|))) "\\spad{intPatternMatch(f, x, int, pmint)} tries to integrate \\spad{f} first by using the integration function \\spad{int},{} and then by using the pattern match intetgration function \\spad{pmint} on any remaining unintegrable part.")) (|mkPrim| ((|#2| |#2| (|Symbol|)) "\\spad{mkPrim(f, x)} makes the logs in \\spad{f} which are linear in \\spad{x} primitive with respect to \\spad{x}.")) (|removeConstantTerm| ((|#2| |#2| (|Symbol|)) "\\spad{removeConstantTerm(f, x)} returns \\spad{f} minus any additive constant with respect to \\spad{x}.")) (|vark| (((|List| (|Kernel| |#2|)) (|List| |#2|) (|Symbol|)) "\\spad{vark([f1,...,fn],x)} returns the set-theoretic union of \\spad{(varselect(f1,x),...,varselect(fn,x))}.")) (|union| (((|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|))) "\\spad{union(l1, l2)} returns set-theoretic union of \\spad{l1} and \\spad{l2}.")) (|ksec| (((|Kernel| |#2|) (|Kernel| |#2|) (|List| (|Kernel| |#2|)) (|Symbol|)) "\\spad{ksec(k, [k1,...,kn], x)} returns the second top-level \\spad{ki} after \\spad{k} involving \\spad{x}.")) (|kmax| (((|Kernel| |#2|) (|List| (|Kernel| |#2|))) "\\spad{kmax([k1,...,kn])} returns the top-level \\spad{ki} for integration.")) (|varselect| (((|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|)) (|Symbol|)) "\\spad{varselect([k1,...,kn], x)} returns the \\spad{ki} which involve \\spad{x}."))) NIL -((-12 (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -906) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-294))) (|HasCategory| |#2| (QUOTE (-641))) (|HasCategory| |#2| (LIST (QUOTE -1058) (QUOTE (-1196))))) (-12 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-294)))) (|HasCategory| |#1| (QUOTE (-568)))) -(-586 -2117 UP) +((-12 (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-294))) (|HasCategory| |#2| (QUOTE (-641))) (|HasCategory| |#2| (LIST (QUOTE -1059) (QUOTE (-1197))))) (-12 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-294)))) (|HasCategory| |#1| (QUOTE (-568)))) +(-586 -1959 UP) ((|constructor| (NIL "This package provides functions for the transcendental case of the Risch algorithm.")) (|monomialIntPoly| (((|Record| (|:| |answer| |#2|) (|:| |polypart| |#2|)) |#2| (|Mapping| |#2| |#2|)) "\\spad{monomialIntPoly(p, ')} returns [\\spad{q},{} \\spad{r}] such that \\spad{p = q' + r} and \\spad{degree(r) < degree(t')}. Error if \\spad{degree(t') < 2}.")) (|monomialIntegrate| (((|Record| (|:| |ir| (|IntegrationResult| (|Fraction| |#2|))) (|:| |specpart| (|Fraction| |#2|)) (|:| |polypart| |#2|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{monomialIntegrate(f, ')} returns \\spad{[ir, s, p]} such that \\spad{f = ir' + s + p} and all the squarefree factors of the denominator of \\spad{s} are special \\spad{w}.\\spad{r}.\\spad{t} the derivation '.")) (|expintfldpoly| (((|Union| (|LaurentPolynomial| |#1| |#2|) "failed") (|LaurentPolynomial| |#1| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|)) "\\spad{expintfldpoly(p, foo)} returns \\spad{q} such that \\spad{p' = q} or \"failed\" if no such \\spad{q} exists. Argument foo is a Risch differential equation function on \\spad{F}.")) (|primintfldpoly| (((|Union| |#2| "failed") |#2| (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) |#1|) "\\spad{primintfldpoly(p, ', t')} returns \\spad{q} such that \\spad{p' = q} or \"failed\" if no such \\spad{q} exists. Argument \\spad{t'} is the derivative of the primitive generating the extension.")) (|primlimintfrac| (((|Union| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|)))))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|List| (|Fraction| |#2|))) "\\spad{primlimintfrac(f, ', [u1,...,un])} returns \\spad{[v, [c1,...,cn]]} such that \\spad{ci' = 0} and \\spad{f = v' + +/[ci * ui'/ui]}. Error: if \\spad{degree numer f >= degree denom f}.")) (|primextintfrac| (((|Union| (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Fraction| |#2|)) "\\spad{primextintfrac(f, ', g)} returns \\spad{[v, c]} such that \\spad{f = v' + c g} and \\spad{c' = 0}. Error: if \\spad{degree numer f >= degree denom f} or if \\spad{degree numer g >= degree denom g} or if \\spad{denom g} is not squarefree.")) (|explimitedint| (((|Union| (|Record| (|:| |answer| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|))))))) (|:| |a0| |#1|)) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|) (|List| (|Fraction| |#2|))) "\\spad{explimitedint(f, ', foo, [u1,...,un])} returns \\spad{[v, [c1,...,cn], a]} such that \\spad{ci' = 0},{} \\spad{f = v' + a + reduce(+,[ci * ui'/ui])},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}. Returns \"failed\" if no such \\spad{v},{} \\spad{ci},{} a exist. Argument \\spad{foo} is a Risch differential equation function on \\spad{F}.")) (|primlimitedint| (((|Union| (|Record| (|:| |answer| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|))))))) (|:| |a0| |#1|)) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) (|List| (|Fraction| |#2|))) "\\spad{primlimitedint(f, ', foo, [u1,...,un])} returns \\spad{[v, [c1,...,cn], a]} such that \\spad{ci' = 0},{} \\spad{f = v' + a + reduce(+,[ci * ui'/ui])},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Returns \"failed\" if no such \\spad{v},{} \\spad{ci},{} a exist. Argument \\spad{foo} is an extended integration function on \\spad{F}.")) (|expextendedint| (((|Union| (|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |a0| |#1|)) (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|) (|Fraction| |#2|)) "\\spad{expextendedint(f, ', foo, g)} returns either \\spad{[v, c]} such that \\spad{f = v' + c g} and \\spad{c' = 0},{} or \\spad{[v, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}. Returns \"failed\" if neither case can hold. Argument \\spad{foo} is a Risch differential equation function on \\spad{F}.")) (|primextendedint| (((|Union| (|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |a0| |#1|)) (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) (|Fraction| |#2|)) "\\spad{primextendedint(f, ', foo, g)} returns either \\spad{[v, c]} such that \\spad{f = v' + c g} and \\spad{c' = 0},{} or \\spad{[v, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Returns \"failed\" if neither case can hold. Argument \\spad{foo} is an extended integration function on \\spad{F}.")) (|tanintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|List| |#1|) "failed") (|Integer|) |#1| |#1|)) "\\spad{tanintegrate(f, ', foo)} returns \\spad{[g, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}; Argument foo is a Risch differential system solver on \\spad{F}.")) (|expintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|)) "\\spad{expintegrate(f, ', foo)} returns \\spad{[g, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}; Argument foo is a Risch differential equation solver on \\spad{F}.")) (|primintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|)) "\\spad{primintegrate(f, ', foo)} returns \\spad{[g, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Argument foo is an extended integration function on \\spad{F}."))) NIL NIL -(-587 R -2117) +(-587 R -1959) ((|constructor| (NIL "This package computes the inverse Laplace Transform.")) (|inverseLaplace| (((|Union| |#2| "failed") |#2| (|Symbol|) (|Symbol|)) "\\spad{inverseLaplace(f, s, t)} returns the Inverse Laplace transform of \\spad{f(s)} using \\spad{t} as the new variable or \"failed\" if unable to find a closed form."))) NIL NIL @@ -2298,21 +2298,21 @@ NIL NIL (-592 |p| |unBalanced?|) ((|constructor| (NIL "This domain implements \\spad{Zp},{} the \\spad{p}-adic completion of the integers. This is an internal domain."))) -((-4456 . T) ((-4465 "*") . T) (-4457 . T) (-4458 . T) (-4460 . T)) +((-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-593 |p|) ((|constructor| (NIL "InnerPrimeField(\\spad{p}) implements the field with \\spad{p} elements. Note: argument \\spad{p} MUST be a prime (this domain does not check). See \\spadtype{PrimeField} for a domain that does check."))) -((-4455 . T) (-4461 . T) (-4456 . T) ((-4465 "*") . T) (-4457 . T) (-4458 . T) (-4460 . T)) +((-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) ((|HasCategory| $ (QUOTE (-148))) (|HasCategory| $ (QUOTE (-146))) (|HasCategory| $ (QUOTE (-379)))) (-594) ((|constructor| (NIL "A package to print strings without line-feed nor carriage-return.")) (|iprint| (((|Void|) (|String|)) "\\axiom{iprint(\\spad{s})} prints \\axiom{\\spad{s}} at the current position of the cursor."))) NIL NIL -(-595 R -2117) +(-595 R -1959) ((|constructor| (NIL "This package allows a sum of logs over the roots of a polynomial to be expressed as explicit logarithms and arc tangents,{} provided that the indexing polynomial can be factored into quadratics.")) (|complexExpand| ((|#2| (|IntegrationResult| |#2|)) "\\spad{complexExpand(i)} returns the expanded complex function corresponding to \\spad{i}.")) (|expand| (((|List| |#2|) (|IntegrationResult| |#2|)) "\\spad{expand(i)} returns the list of possible real functions corresponding to \\spad{i}.")) (|split| (((|IntegrationResult| |#2|) (|IntegrationResult| |#2|)) "\\spad{split(u(x) + sum_{P(a)=0} Q(a,x))} returns \\spad{u(x) + sum_{P1(a)=0} Q(a,x) + ... + sum_{Pn(a)=0} Q(a,x)} where \\spad{P1},{}...,{}\\spad{Pn} are the factors of \\spad{P}."))) NIL NIL -(-596 E -2117) +(-596 E -1959) ((|constructor| (NIL "\\indented{1}{Internally used by the integration packages} Author: Manuel Bronstein Date Created: 1987 Date Last Updated: 12 August 1992 Keywords: integration.")) (|map| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") (|Mapping| |#2| |#1|) (|Union| (|Record| (|:| |mainpart| |#1|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#1|) (|:| |logand| |#1|))))) "failed")) "\\spad{map(f,ufe)} \\undocumented") (((|Union| |#2| "failed") (|Mapping| |#2| |#1|) (|Union| |#1| "failed")) "\\spad{map(f,ue)} \\undocumented") (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") (|Mapping| |#2| |#1|) (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed")) "\\spad{map(f,ure)} \\undocumented") (((|IntegrationResult| |#2|) (|Mapping| |#2| |#1|) (|IntegrationResult| |#1|)) "\\spad{map(f,ire)} \\undocumented"))) NIL NIL @@ -2320,10 +2320,10 @@ NIL ((|constructor| (NIL "This domain provides representations for the intermediate form data structure used by the Spad elaborator.")) (|irDef| (($ (|Identifier|) (|InternalTypeForm|) $) "\\spad{irDef(f,ts,e)} returns an IR representation for a definition of a function named \\spad{f},{} with signature \\spad{ts} and body \\spad{e}.")) (|irCtor| (($ (|Identifier|) (|InternalTypeForm|)) "\\spad{irCtor(n,t)} returns an IR for a constructor reference of type designated by the type form \\spad{t}")) (|irVar| (($ (|Identifier|) (|InternalTypeForm|)) "\\spad{irVar(x,t)} returns an IR for a variable reference of type designated by the type form \\spad{t}"))) NIL NIL -(-598 -2117) +(-598 -1959) ((|constructor| (NIL "If a function \\spad{f} has an elementary integral \\spad{g},{} then \\spad{g} can be written in the form \\spad{g = h + c1 log(u1) + c2 log(u2) + ... + cn log(un)} where \\spad{h},{} which is in the same field than \\spad{f},{} is called the rational part of the integral,{} and \\spad{c1 log(u1) + ... cn log(un)} is called the logarithmic part of the integral. This domain manipulates integrals represented in that form,{} by keeping both parts separately. The logs are not explicitly computed.")) (|differentiate| ((|#1| $ (|Symbol|)) "\\spad{differentiate(ir,x)} differentiates \\spad{ir} with respect to \\spad{x}") ((|#1| $ (|Mapping| |#1| |#1|)) "\\spad{differentiate(ir,D)} differentiates \\spad{ir} with respect to the derivation \\spad{D}.")) (|integral| (($ |#1| (|Symbol|)) "\\spad{integral(f,x)} returns the formal integral of \\spad{f} with respect to \\spad{x}") (($ |#1| |#1|) "\\spad{integral(f,x)} returns the formal integral of \\spad{f} with respect to \\spad{x}")) (|elem?| (((|Boolean|) $) "\\spad{elem?(ir)} tests if an integration result is elementary over \\spad{F?}")) (|notelem| (((|List| (|Record| (|:| |integrand| |#1|) (|:| |intvar| |#1|))) $) "\\spad{notelem(ir)} returns the non-elementary part of an integration result")) (|logpart| (((|List| (|Record| (|:| |scalar| (|Fraction| (|Integer|))) (|:| |coeff| (|SparseUnivariatePolynomial| |#1|)) (|:| |logand| (|SparseUnivariatePolynomial| |#1|)))) $) "\\spad{logpart(ir)} returns the logarithmic part of an integration result")) (|ratpart| ((|#1| $) "\\spad{ratpart(ir)} returns the rational part of an integration result")) (|mkAnswer| (($ |#1| (|List| (|Record| (|:| |scalar| (|Fraction| (|Integer|))) (|:| |coeff| (|SparseUnivariatePolynomial| |#1|)) (|:| |logand| (|SparseUnivariatePolynomial| |#1|)))) (|List| (|Record| (|:| |integrand| |#1|) (|:| |intvar| |#1|)))) "\\spad{mkAnswer(r,l,ne)} creates an integration result from a rational part \\spad{r},{} a logarithmic part \\spad{l},{} and a non-elementary part \\spad{ne}."))) -((-4458 . T) (-4457 . T)) -((|HasCategory| |#1| (LIST (QUOTE -916) (QUOTE (-1196)))) (|HasCategory| |#1| (LIST (QUOTE -1058) (QUOTE (-1196))))) +((-4459 . T) (-4458 . T)) +((|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-1197))))) (-599 I) ((|constructor| (NIL "The \\spadtype{IntegerRoots} package computes square roots and \\indented{2}{\\spad{n}th roots of integers efficiently.}")) (|approxSqrt| ((|#1| |#1|) "\\spad{approxSqrt(n)} returns an approximation \\spad{x} to \\spad{sqrt(n)} such that \\spad{-1 < x - sqrt(n) < 1}. Compute an approximation \\spad{s} to \\spad{sqrt(n)} such that \\indented{10}{\\spad{-1 < s - sqrt(n) < 1}} A variable precision Newton iteration is used. The running time is \\spad{O( log(n)**2 )}.")) (|perfectSqrt| (((|Union| |#1| "failed") |#1|) "\\spad{perfectSqrt(n)} returns the square root of \\spad{n} if \\spad{n} is a perfect square and returns \"failed\" otherwise")) (|perfectSquare?| (((|Boolean|) |#1|) "\\spad{perfectSquare?(n)} returns \\spad{true} if \\spad{n} is a perfect square and \\spad{false} otherwise")) (|approxNthRoot| ((|#1| |#1| (|NonNegativeInteger|)) "\\spad{approxRoot(n,r)} returns an approximation \\spad{x} to \\spad{n**(1/r)} such that \\spad{-1 < x - n**(1/r) < 1}")) (|perfectNthRoot| (((|Record| (|:| |base| |#1|) (|:| |exponent| (|NonNegativeInteger|))) |#1|) "\\spad{perfectNthRoot(n)} returns \\spad{[x,r]},{} where \\spad{n = x\\^r} and \\spad{r} is the largest integer such that \\spad{n} is a perfect \\spad{r}th power") (((|Union| |#1| "failed") |#1| (|NonNegativeInteger|)) "\\spad{perfectNthRoot(n,r)} returns the \\spad{r}th root of \\spad{n} if \\spad{n} is an \\spad{r}th power and returns \"failed\" otherwise")) (|perfectNthPower?| (((|Boolean|) |#1| (|NonNegativeInteger|)) "\\spad{perfectNthPower?(n,r)} returns \\spad{true} if \\spad{n} is an \\spad{r}th power and \\spad{false} otherwise"))) NIL @@ -2350,19 +2350,19 @@ NIL NIL (-605 |mn|) ((|constructor| (NIL "This domain implements low-level strings"))) -((-4464 . T) (-4463 . T)) -((-3794 (-12 (|HasCategory| (-145) (QUOTE (-861))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1120))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145)))))) (-3794 (|HasCategory| (-145) (LIST (QUOTE -625) (QUOTE (-875)))) (-12 (|HasCategory| (-145) (QUOTE (-1120))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -626) (QUOTE (-548)))) (-3794 (|HasCategory| (-145) (QUOTE (-861))) (|HasCategory| (-145) (QUOTE (-1120)))) (|HasCategory| (-145) (QUOTE (-861))) (-3794 (|HasCategory| (-145) (QUOTE (-102))) (|HasCategory| (-145) (QUOTE (-861))) (|HasCategory| (-145) (QUOTE (-1120)))) (|HasCategory| (-576) (QUOTE (-861))) (|HasCategory| (-145) (QUOTE (-1120))) (|HasCategory| (-145) (LIST (QUOTE -625) (QUOTE (-875)))) (|HasCategory| (-145) (QUOTE (-102))) (-12 (|HasCategory| (-145) (QUOTE (-1120))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145)))))) +((-4465 . T) (-4464 . T)) +((-2758 (-12 (|HasCategory| (-145) (QUOTE (-861))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1121))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145)))))) (-2758 (|HasCategory| (-145) (LIST (QUOTE -625) (QUOTE (-876)))) (-12 (|HasCategory| (-145) (QUOTE (-1121))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -626) (QUOTE (-548)))) (-2758 (|HasCategory| (-145) (QUOTE (-861))) (|HasCategory| (-145) (QUOTE (-1121)))) (|HasCategory| (-145) (QUOTE (-861))) (-2758 (|HasCategory| (-145) (QUOTE (-102))) (|HasCategory| (-145) (QUOTE (-861))) (|HasCategory| (-145) (QUOTE (-1121)))) (|HasCategory| (-576) (QUOTE (-861))) (|HasCategory| (-145) (QUOTE (-1121))) (|HasCategory| (-145) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-145) (QUOTE (-102))) (-12 (|HasCategory| (-145) (QUOTE (-1121))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145)))))) (-606 E V R P) ((|constructor| (NIL "tools for the summation packages.")) (|sum| (((|Record| (|:| |num| |#4|) (|:| |den| (|Integer|))) |#4| |#2|) "\\spad{sum(p(n), n)} returns \\spad{P(n)},{} the indefinite sum of \\spad{p(n)} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{P(n+1) - P(n) = a(n)}.") (((|Record| (|:| |num| |#4|) (|:| |den| (|Integer|))) |#4| |#2| (|Segment| |#4|)) "\\spad{sum(p(n), n = a..b)} returns \\spad{p(a) + p(a+1) + ... + p(b)}."))) NIL NIL (-607 |Coef|) ((|constructor| (NIL "InnerSparseUnivariatePowerSeries is an internal domain \\indented{2}{used for creating sparse Taylor and Laurent series.}")) (|cAcsch| (($ $) "\\spad{cAcsch(f)} computes the inverse hyperbolic cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsech| (($ $) "\\spad{cAsech(f)} computes the inverse hyperbolic secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcoth| (($ $) "\\spad{cAcoth(f)} computes the inverse hyperbolic cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAtanh| (($ $) "\\spad{cAtanh(f)} computes the inverse hyperbolic tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcosh| (($ $) "\\spad{cAcosh(f)} computes the inverse hyperbolic cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsinh| (($ $) "\\spad{cAsinh(f)} computes the inverse hyperbolic sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCsch| (($ $) "\\spad{cCsch(f)} computes the hyperbolic cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSech| (($ $) "\\spad{cSech(f)} computes the hyperbolic secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCoth| (($ $) "\\spad{cCoth(f)} computes the hyperbolic cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cTanh| (($ $) "\\spad{cTanh(f)} computes the hyperbolic tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCosh| (($ $) "\\spad{cCosh(f)} computes the hyperbolic cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSinh| (($ $) "\\spad{cSinh(f)} computes the hyperbolic sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcsc| (($ $) "\\spad{cAcsc(f)} computes the arccosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsec| (($ $) "\\spad{cAsec(f)} computes the arcsecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcot| (($ $) "\\spad{cAcot(f)} computes the arccotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAtan| (($ $) "\\spad{cAtan(f)} computes the arctangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcos| (($ $) "\\spad{cAcos(f)} computes the arccosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsin| (($ $) "\\spad{cAsin(f)} computes the arcsine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCsc| (($ $) "\\spad{cCsc(f)} computes the cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSec| (($ $) "\\spad{cSec(f)} computes the secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCot| (($ $) "\\spad{cCot(f)} computes the cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cTan| (($ $) "\\spad{cTan(f)} computes the tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCos| (($ $) "\\spad{cCos(f)} computes the cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSin| (($ $) "\\spad{cSin(f)} computes the sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cLog| (($ $) "\\spad{cLog(f)} computes the logarithm of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cExp| (($ $) "\\spad{cExp(f)} computes the exponential of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cRationalPower| (($ $ (|Fraction| (|Integer|))) "\\spad{cRationalPower(f,r)} computes \\spad{f^r}. For use when the coefficient ring is commutative.")) (|cPower| (($ $ |#1|) "\\spad{cPower(f,r)} computes \\spad{f^r},{} where \\spad{f} has constant coefficient 1. For use when the coefficient ring is commutative.")) (|integrate| (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. Warning: function does not check for a term of degree \\spad{-1}.")) (|seriesToOutputForm| (((|OutputForm|) (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|))) (|Reference| (|OrderedCompletion| (|Integer|))) (|Symbol|) |#1| (|Fraction| (|Integer|))) "\\spad{seriesToOutputForm(st,refer,var,cen,r)} prints the series \\spad{f((var - cen)^r)}.")) (|iCompose| (($ $ $) "\\spad{iCompose(f,g)} returns \\spad{f(g(x))}. This is an internal function which should only be called for Taylor series \\spad{f(x)} and \\spad{g(x)} such that the constant coefficient of \\spad{g(x)} is zero.")) (|taylorQuoByVar| (($ $) "\\spad{taylorQuoByVar(a0 + a1 x + a2 x**2 + ...)} returns \\spad{a1 + a2 x + a3 x**2 + ...}")) (|iExquo| (((|Union| $ "failed") $ $ (|Boolean|)) "\\spad{iExquo(f,g,taylor?)} is the quotient of the power series \\spad{f} and \\spad{g}. If \\spad{taylor?} is \\spad{true},{} then we must have \\spad{order(f) >= order(g)}.")) (|multiplyCoefficients| (($ (|Mapping| |#1| (|Integer|)) $) "\\spad{multiplyCoefficients(fn,f)} returns the series \\spad{sum(fn(n) * an * x^n,n = n0..)},{} where \\spad{f} is the series \\spad{sum(an * x^n,n = n0..)}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(f)} tests if \\spad{f} is a single monomial.")) (|series| (($ (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)))) "\\spad{series(st)} creates a series from a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents.")) (|getStream| (((|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|))) $) "\\spad{getStream(f)} returns the stream of terms representing the series \\spad{f}.")) (|getRef| (((|Reference| (|OrderedCompletion| (|Integer|))) $) "\\spad{getRef(f)} returns a reference containing the order to which the terms of \\spad{f} have been computed.")) (|makeSeries| (($ (|Reference| (|OrderedCompletion| (|Integer|))) (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)))) "\\spad{makeSeries(refer,str)} creates a power series from the reference \\spad{refer} and the stream \\spad{str}."))) -(((-4465 "*") |has| |#1| (-174)) (-4456 |has| |#1| (-568)) (-4457 . T) (-4458 . T) (-4460 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (-3794 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -916) (QUOTE (-1196)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-576)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-576)) (|devaluate| |#1|)))) (|HasCategory| (-576) (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-374))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-576))))) (|HasSignature| |#1| (LIST (QUOTE -4112) (LIST (|devaluate| |#1|) (QUOTE (-1196)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-576)))))) +(((-4466 "*") |has| |#1| (-174)) (-4457 |has| |#1| (-568)) (-4458 . T) (-4459 . T) (-4461 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (-2758 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-576)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-576)) (|devaluate| |#1|)))) (|HasCategory| (-576) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-374))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-576))))) (|HasSignature| |#1| (LIST (QUOTE -3569) (LIST (|devaluate| |#1|) (QUOTE (-1197)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-576)))))) (-608 |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}.")) (|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|) $) "\\spad{coefficients(x)} returns a stream of ring elements. \\indented{1}{When \\spad{x} is a univariate series,{} this is a stream of Taylor} \\indented{1}{coefficients. When \\spad{x} is a multivariate series,{} the} \\indented{1}{\\spad{n}th element of the stream is a form of} \\indented{1}{degree \\spad{n} in the power series variables.}"))) -(((-4465 "*") |has| |#1| (-568)) (-4456 |has| |#1| (-568)) (-4457 . T) (-4458 . T) (-4460 . T)) +(((-4466 "*") |has| |#1| (-568)) (-4457 |has| |#1| (-568)) (-4458 . T) (-4459 . T) (-4461 . T)) ((|HasCategory| |#1| (QUOTE (-568)))) (-609) ((|constructor| (NIL "This domain provides representations for internal type form.")) (|mappingMode| (($ $ (|List| $)) "\\spad{mappingMode(r,ts)} returns a mapping mode with return mode \\spad{r},{} and parameter modes \\spad{ts}.")) (|categoryMode| (($) "\\spad{categoryMode} is a constant mode denoting Category.")) (|voidMode| (($) "\\spad{voidMode} is a constant mode denoting Void.")) (|noValueMode| (($) "\\spad{noValueMode} is a constant mode that indicates that the value of an expression is to be ignored.")) (|jokerMode| (($) "\\spad{jokerMode} is a constant that stands for any mode in a type inference context"))) @@ -2376,7 +2376,7 @@ NIL ((|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 -(-612 R -2117 FG) +(-612 R -1959 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) b)} returns \\spad{a + i b}.")) (FG2F ((|#2| |#3|) "\\spad{FG2F(a + i b)} returns \\spad{a + sqrt(-1) b}.")) (GF2FG ((|#3| (|Complex| |#2|)) "\\spad{GF2FG(a + i b)} returns \\spad{a + i b} viewed as a function with the \\spad{i} pushed down into the coefficient domain."))) NIL NIL @@ -2386,12 +2386,12 @@ NIL NIL (-614 R |mn|) ((|constructor| (NIL "\\indented{2}{This type represents vector like objects with varying lengths} and a user-specified initial index."))) -((-4464 . T) (-4463 . T)) -((-3794 (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1120))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-3794 (-12 (|HasCategory| |#1| (QUOTE (-1120))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-875))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-3794 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1120)))) (|HasCategory| |#1| (QUOTE (-861))) (-3794 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1120)))) (|HasCategory| (-576) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1120))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-738))) (|HasCategory| |#1| (QUOTE (-1069))) (-12 (|HasCategory| |#1| (QUOTE (-1022))) (|HasCategory| |#1| (QUOTE (-1069)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-875)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1120))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) +((-4465 . T) (-4464 . T)) +((-2758 (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2758 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2758 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| |#1| (QUOTE (-861))) (-2758 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| (-576) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-738))) (|HasCategory| |#1| (QUOTE (-1070))) (-12 (|HasCategory| |#1| (QUOTE (-1023))) (|HasCategory| |#1| (QUOTE (-1070)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-615 S |Index| |Entry|) ((|constructor| (NIL "An indexed aggregate is a many-to-one mapping of indices to entries. For example,{} a one-dimensional-array is an indexed aggregate where the index is an integer. Also,{} a table is an indexed aggregate where the indices and entries may have any type.")) (|swap!| (((|Void|) $ |#2| |#2|) "\\spad{swap!(u,i,j)} interchanges elements \\spad{i} and \\spad{j} of aggregate \\spad{u}. No meaningful value is returned.")) (|fill!| (($ $ |#3|) "\\spad{fill!(u,x)} replaces each entry in aggregate \\spad{u} by \\spad{x}. The modified \\spad{u} is returned as value.")) (|first| ((|#3| $) "\\spad{first(u)} returns the first element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{first([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = \\spad{x}}. Error: if \\spad{u} is empty.")) (|minIndex| ((|#2| $) "\\spad{minIndex(u)} returns the minimum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{minIndex(a) = reduce(min,{}[\\spad{i} for \\spad{i} in indices a])}; for lists,{} \\axiom{minIndex(a) = 1}.")) (|maxIndex| ((|#2| $) "\\spad{maxIndex(u)} returns the maximum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{maxIndex(\\spad{u}) = reduce(max,{}[\\spad{i} for \\spad{i} in indices \\spad{u}])}; if \\spad{u} is a list,{} \\axiom{maxIndex(\\spad{u}) = \\#u}.")) (|entry?| (((|Boolean|) |#3| $) "\\spad{entry?(x,u)} tests if \\spad{x} equals \\axiom{\\spad{u} . \\spad{i}} for some index \\spad{i}.")) (|indices| (((|List| |#2|) $) "\\spad{indices(u)} returns a list of indices of aggregate \\spad{u} in no particular order.")) (|index?| (((|Boolean|) |#2| $) "\\spad{index?(i,u)} tests if \\spad{i} is an index of aggregate \\spad{u}.")) (|entries| (((|List| |#3|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) NIL -((|HasAttribute| |#1| (QUOTE -4464)) (|HasCategory| |#2| (QUOTE (-861))) (|HasAttribute| |#1| (QUOTE -4463)) (|HasCategory| |#3| (QUOTE (-1120)))) +((|HasAttribute| |#1| (QUOTE -4465)) (|HasCategory| |#2| (QUOTE (-861))) (|HasAttribute| |#1| (QUOTE -4464)) (|HasCategory| |#3| (QUOTE (-1121)))) (-616 |Index| |Entry|) ((|constructor| (NIL "An indexed aggregate is a many-to-one mapping of indices to entries. For example,{} a one-dimensional-array is an indexed aggregate where the index is an integer. Also,{} a table is an indexed aggregate where the indices and entries may have any type.")) (|swap!| (((|Void|) $ |#1| |#1|) "\\spad{swap!(u,i,j)} interchanges elements \\spad{i} and \\spad{j} of aggregate \\spad{u}. No meaningful value is returned.")) (|fill!| (($ $ |#2|) "\\spad{fill!(u,x)} replaces each entry in aggregate \\spad{u} by \\spad{x}. The modified \\spad{u} is returned as value.")) (|first| ((|#2| $) "\\spad{first(u)} returns the first element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{first([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = \\spad{x}}. Error: if \\spad{u} is empty.")) (|minIndex| ((|#1| $) "\\spad{minIndex(u)} returns the minimum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{minIndex(a) = reduce(min,{}[\\spad{i} for \\spad{i} in indices a])}; for lists,{} \\axiom{minIndex(a) = 1}.")) (|maxIndex| ((|#1| $) "\\spad{maxIndex(u)} returns the maximum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{maxIndex(\\spad{u}) = reduce(max,{}[\\spad{i} for \\spad{i} in indices \\spad{u}])}; if \\spad{u} is a list,{} \\axiom{maxIndex(\\spad{u}) = \\#u}.")) (|entry?| (((|Boolean|) |#2| $) "\\spad{entry?(x,u)} tests if \\spad{x} equals \\axiom{\\spad{u} . \\spad{i}} for some index \\spad{i}.")) (|indices| (((|List| |#1|) $) "\\spad{indices(u)} returns a list of indices of aggregate \\spad{u} in no particular order.")) (|index?| (((|Boolean|) |#1| $) "\\spad{index?(i,u)} tests if \\spad{i} is an index of aggregate \\spad{u}.")) (|entries| (((|List| |#2|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) NIL @@ -2406,19 +2406,19 @@ NIL NIL (-619 R A) ((|constructor| (NIL "\\indented{1}{AssociatedJordanAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$A}} \\indented{1}{to define the new multiplications \\spad{a*b := (a *\\$A b + b *\\$A a)/2}} \\indented{1}{(anticommutator).} \\indented{1}{The usual notation \\spad{{a,b}_+} cannot be used due to} \\indented{1}{restrictions in the current language.} \\indented{1}{This domain only gives a Jordan algebra if the} \\indented{1}{Jordan-identity \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} holds} \\indented{1}{for all \\spad{a},{}\\spad{b},{}\\spad{c} in \\spad{A}.} \\indented{1}{This relation can be checked by} \\indented{1}{\\spadfun{jordanAdmissible?()\\$A}.} \\blankline If the underlying algebra is of type \\spadtype{FramedNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank,{} together with a fixed \\spad{R}-module basis),{} then the same is \\spad{true} for the associated Jordan algebra. Moreover,{} if the underlying algebra is of type \\spadtype{FiniteRankNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank),{} then the same \\spad{true} for the associated Jordan algebra.")) (|coerce| (($ |#2|) "\\spad{coerce(a)} coerces the element \\spad{a} of the algebra \\spad{A} to an element of the Jordan algebra \\spadtype{AssociatedJordanAlgebra}(\\spad{R},{}A)."))) -((-4460 -3794 (-2310 (|has| |#2| (-378 |#1|)) (|has| |#1| (-568))) (-12 (|has| |#2| (-429 |#1|)) (|has| |#1| (-568)))) (-4458 . T) (-4457 . T)) -((-3794 (|HasCategory| |#2| (LIST (QUOTE -378) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|)))) (-3794 (-12 (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#2| (LIST (QUOTE -378) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -378) (|devaluate| |#1|)))) +((-4461 -2758 (-2673 (|has| |#2| (-378 |#1|)) (|has| |#1| (-568))) (-12 (|has| |#2| (-429 |#1|)) (|has| |#1| (-568)))) (-4459 . T) (-4458 . T)) +((-2758 (|HasCategory| |#2| (LIST (QUOTE -378) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|)))) (-2758 (-12 (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#2| (LIST (QUOTE -378) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -378) (|devaluate| |#1|)))) (-620 |Entry|) ((|constructor| (NIL "This domain allows a random access file to be viewed both as a table and as a file object.")) (|pack!| (($ $) "\\spad{pack!(f)} reorganizes the file \\spad{f} on disk to recover unused space."))) -((-4463 . T) (-4464 . T)) -((-12 (|HasCategory| (-2 (|:| -2239 (-1178)) (|:| -2904 |#1|)) (QUOTE (-1120))) (|HasCategory| (-2 (|:| -2239 (-1178)) (|:| -2904 |#1|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2239) (QUOTE (-1178))) (LIST (QUOTE |:|) (QUOTE -2904) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -2239 (-1178)) (|:| -2904 |#1|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#1| (QUOTE (-1120))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1120))) (|HasCategory| (-1178) (QUOTE (-861))) (|HasCategory| (-2 (|:| -2239 (-1178)) (|:| -2904 |#1|)) (QUOTE (-1120))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-875)))) (|HasCategory| (-2 (|:| -2239 (-1178)) (|:| -2904 |#1|)) (LIST (QUOTE -625) (QUOTE (-875)))) (|HasCategory| (-2 (|:| -2239 (-1178)) (|:| -2904 |#1|)) (QUOTE (-102)))) +((-4464 . T) (-4465 . T)) +((-12 (|HasCategory| (-2 (|:| -4300 (-1179)) (|:| -4438 |#1|)) (QUOTE (-1121))) (|HasCategory| (-2 (|:| -4300 (-1179)) (|:| -4438 |#1|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4300) (QUOTE (-1179))) (LIST (QUOTE |:|) (QUOTE -4438) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -4300 (-1179)) (|:| -4438 |#1|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| (-1179) (QUOTE (-861))) (|HasCategory| (-2 (|:| -4300 (-1179)) (|:| -4438 |#1|)) (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -4300 (-1179)) (|:| -4438 |#1|)) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -4300 (-1179)) (|:| -4438 |#1|)) (QUOTE (-102)))) (-621 S |Key| |Entry|) ((|constructor| (NIL "A keyed dictionary is a dictionary of key-entry pairs for which there is a unique entry for each key.")) (|search| (((|Union| |#3| "failed") |#2| $) "\\spad{search(k,t)} searches the table \\spad{t} for the key \\spad{k},{} returning the entry stored in \\spad{t} for key \\spad{k}. If \\spad{t} has no such key,{} \\axiom{search(\\spad{k},{}\\spad{t})} returns \"failed\".")) (|remove!| (((|Union| |#3| "failed") |#2| $) "\\spad{remove!(k,t)} searches the table \\spad{t} for the key \\spad{k} removing (and return) the entry if there. If \\spad{t} has no such key,{} \\axiom{remove!(\\spad{k},{}\\spad{t})} returns \"failed\".")) (|keys| (((|List| |#2|) $) "\\spad{keys(t)} returns the list the keys in table \\spad{t}.")) (|key?| (((|Boolean|) |#2| $) "\\spad{key?(k,t)} tests if \\spad{k} is a key in table \\spad{t}."))) NIL NIL (-622 |Key| |Entry|) ((|constructor| (NIL "A keyed dictionary is a dictionary of key-entry pairs for which there is a unique entry for each key.")) (|search| (((|Union| |#2| "failed") |#1| $) "\\spad{search(k,t)} searches the table \\spad{t} for the key \\spad{k},{} returning the entry stored in \\spad{t} for key \\spad{k}. If \\spad{t} has no such key,{} \\axiom{search(\\spad{k},{}\\spad{t})} returns \"failed\".")) (|remove!| (((|Union| |#2| "failed") |#1| $) "\\spad{remove!(k,t)} searches the table \\spad{t} for the key \\spad{k} removing (and return) the entry if there. If \\spad{t} has no such key,{} \\axiom{remove!(\\spad{k},{}\\spad{t})} returns \"failed\".")) (|keys| (((|List| |#1|) $) "\\spad{keys(t)} returns the list the keys in table \\spad{t}.")) (|key?| (((|Boolean|) |#1| $) "\\spad{key?(k,t)} tests if \\spad{k} is a key in table \\spad{t}."))) -((-4464 . T)) +((-4465 . T)) NIL (-623 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"))) @@ -2427,7 +2427,7 @@ NIL (-624 S) ((|constructor| (NIL "A kernel over a set \\spad{S} is an operator applied to a given list of arguments from \\spad{S}.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(op(a1,...,an), s)} tests if the name of op is \\spad{s}.") (((|Boolean|) $ (|BasicOperator|)) "\\spad{is?(op(a1,...,an), f)} tests if op = \\spad{f}.")) (|symbolIfCan| (((|Union| (|Symbol|) "failed") $) "\\spad{symbolIfCan(k)} returns \\spad{k} viewed as a symbol if \\spad{k} is a symbol,{} and \"failed\" otherwise.")) (|kernel| (($ (|Symbol|)) "\\spad{kernel(x)} returns \\spad{x} viewed as a kernel.") (($ (|BasicOperator|) (|List| |#1|) (|NonNegativeInteger|)) "\\spad{kernel(op, [a1,...,an], m)} returns the kernel \\spad{op(a1,...,an)} of nesting level \\spad{m}. Error: if \\spad{op} is \\spad{k}-ary for some \\spad{k} not equal to \\spad{m}.")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(k)} returns the nesting level of \\spad{k}.")) (|argument| (((|List| |#1|) $) "\\spad{argument(op(a1,...,an))} returns \\spad{[a1,...,an]}.")) (|operator| (((|BasicOperator|) $) "\\spad{operator(op(a1,...,an))} returns the operator op."))) NIL -((|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -906) (QUOTE (-390))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -906) (QUOTE (-576)))))) +((|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576)))))) (-625 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 @@ -2436,7 +2436,7 @@ NIL ((|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| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}."))) NIL NIL -(-627 -2117 UP) +(-627 -1959 UP) ((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic\\spad{'s} algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,a_1,a_2,ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$e^{\\int(-a_1/2a_2)} e^{\\int u}\\$} is a solution of \\indented{5}{\\spad{\\$a_2 y'' + a_1 y' + a0 y = 0\\$}} whenever \\spad{u} is a solution of \\spad{P u = 0}. The equation must be already irreducible over the rational functions. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{kovacic(a_0,a_1,a_2)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$e^{\\int(-a_1/2a_2)} e^{\\int u}\\$} is a solution of \\indented{5}{\\spad{a_2 y'' + a_1 y' + a0 y = 0}} whenever \\spad{u} is a solution of \\spad{P u = 0}. The equation must be already irreducible over the rational functions."))) NIL NIL @@ -2458,20 +2458,20 @@ NIL NIL (-632 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."))) -((-4460 . T)) +((-4461 . T)) NIL (-633 A R S) ((|constructor| (NIL "LocalAlgebra produces the localization of an algebra,{} \\spadignore{i.e.} fractions whose numerators come from some \\spad{R} algebra.")) (|denom| ((|#3| $) "\\spad{denom x} returns the denominator of \\spad{x}.")) (|numer| ((|#1| $) "\\spad{numer x} returns the numerator of \\spad{x}.")) (/ (($ |#1| |#3|) "\\spad{a / d} divides the element \\spad{a} by \\spad{d}.") (($ $ |#3|) "\\spad{x / d} divides the element \\spad{x} by \\spad{d}."))) -((-4457 . T) (-4458 . T) (-4460 . T)) +((-4458 . T) (-4459 . T) (-4461 . T)) ((|HasCategory| |#1| (QUOTE (-860)))) -(-634 R -2117) +(-634 R -1959) ((|constructor| (NIL "This package computes the forward Laplace Transform.")) (|laplace| ((|#2| |#2| (|Symbol|) (|Symbol|)) "\\spad{laplace(f, t, s)} returns the Laplace transform of \\spad{f(t)} using \\spad{s} as the new variable. This is \\spad{integral(exp(-s*t)*f(t), t = 0..\\%plusInfinity)}. Returns the formal object \\spad{laplace(f, t, s)} if it cannot compute the transform."))) NIL NIL (-635 R UP) ((|constructor| (NIL "\\indented{1}{Univariate polynomials with negative and positive exponents.} Author: Manuel Bronstein Date Created: May 1988 Date Last Updated: 26 Apr 1990")) (|separate| (((|Record| (|:| |polyPart| $) (|:| |fracPart| (|Fraction| |#2|))) (|Fraction| |#2|)) "\\spad{separate(x)} \\undocumented")) (|monomial| (($ |#1| (|Integer|)) "\\spad{monomial(x,n)} \\undocumented")) (|coefficient| ((|#1| $ (|Integer|)) "\\spad{coefficient(x,n)} \\undocumented")) (|trailingCoefficient| ((|#1| $) "\\spad{trailingCoefficient }\\undocumented")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient }\\undocumented")) (|reductum| (($ $) "\\spad{reductum(x)} \\undocumented")) (|order| (((|Integer|) $) "\\spad{order(x)} \\undocumented")) (|degree| (((|Integer|) $) "\\spad{degree(x)} \\undocumented")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(x)} \\undocumented"))) -((-4458 . T) (-4457 . T) ((-4465 "*") . T) (-4456 . T) (-4460 . T)) -((|HasCategory| |#2| (LIST (QUOTE -916) (QUOTE (-1196)))) (|HasCategory| |#2| (LIST (QUOTE -918) (QUOTE (-1196)))) (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -1058) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1058) (QUOTE (-576))))) +((-4459 . T) (-4458 . T) ((-4466 "*") . T) (-4457 . T) (-4461 . T)) +((|HasCategory| |#2| (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| |#2| (LIST (QUOTE -919) (QUOTE (-1197)))) (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576))))) (-636 R E V P TS ST) ((|constructor| (NIL "A package for solving polynomial systems by means of Lazard triangular sets [1]. This package provides two operations. One for solving in the sense of the regular zeros,{} and the other for solving in the sense of the Zariski closure. Both produce square-free regular sets. Moreover,{} the decompositions do not contain any redundant component. However,{} only zero-dimensional regular sets are normalized,{} since normalization may be time consumming in positive dimension. The decomposition process is that of [2].\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|zeroSetSplit| (((|List| |#6|) (|List| |#4|) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{}clos?)} has the same specifications as \\axiomOpFrom{zeroSetSplit(\\spad{lp},{}clos?)}{RegularTriangularSetCategory}.")) (|normalizeIfCan| ((|#6| |#6|) "\\axiom{normalizeIfCan(\\spad{ts})} returns \\axiom{\\spad{ts}} in an normalized shape if \\axiom{\\spad{ts}} is zero-dimensional."))) NIL @@ -2486,7 +2486,7 @@ NIL NIL (-639 |VarSet| R |Order|) ((|constructor| (NIL "Management of the Lie Group associated with a free nilpotent Lie algebra. Every Lie bracket with length greater than \\axiom{Order} are assumed to be null. The implementation inherits from the \\spadtype{XPBWPolynomial} domain constructor: Lyndon coordinates are exponential coordinates of the second kind. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|identification| (((|List| (|Equation| |#2|)) $ $) "\\axiom{identification(\\spad{g},{}\\spad{h})} returns the list of equations \\axiom{g_i = h_i},{} where \\axiom{g_i} (resp. \\axiom{h_i}) are exponential coordinates of \\axiom{\\spad{g}} (resp. \\axiom{\\spad{h}}).")) (|LyndonCoordinates| (((|List| (|Record| (|:| |k| (|LyndonWord| |#1|)) (|:| |c| |#2|))) $) "\\axiom{LyndonCoordinates(\\spad{g})} returns the exponential coordinates of \\axiom{\\spad{g}}.")) (|LyndonBasis| (((|List| (|LiePolynomial| |#1| |#2|)) (|List| |#1|)) "\\axiom{LyndonBasis(\\spad{lv})} returns the Lyndon basis of the nilpotent free Lie algebra.")) (|varList| (((|List| |#1|) $) "\\axiom{varList(\\spad{g})} returns the list of variables of \\axiom{\\spad{g}}.")) (|mirror| (($ $) "\\axiom{mirror(\\spad{g})} is the mirror of the internal representation of \\axiom{\\spad{g}}.")) (|coerce| (((|XPBWPolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{g})} returns the internal representation of \\axiom{\\spad{g}}.") (((|XDistributedPolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{g})} returns the internal representation of \\axiom{\\spad{g}}.")) (|ListOfTerms| (((|List| (|Record| (|:| |k| (|PoincareBirkhoffWittLyndonBasis| |#1|)) (|:| |c| |#2|))) $) "\\axiom{ListOfTerms(\\spad{p})} returns the internal representation of \\axiom{\\spad{p}}.")) (|log| (((|LiePolynomial| |#1| |#2|) $) "\\axiom{log(\\spad{p})} returns the logarithm of \\axiom{\\spad{p}}.")) (|exp| (($ (|LiePolynomial| |#1| |#2|)) "\\axiom{exp(\\spad{p})} returns the exponential of \\axiom{\\spad{p}}."))) -((-4460 . T)) +((-4461 . T)) NIL (-640 R |ls|) ((|constructor| (NIL "A package for solving polynomial systems with finitely many solutions. The decompositions are given by means of regular triangular sets. The computations use lexicographical Groebner bases. The main operations are \\axiomOpFrom{lexTriangular}{LexTriangularPackage} and \\axiomOpFrom{squareFreeLexTriangular}{LexTriangularPackage}. The second one provide decompositions by means of square-free regular triangular sets. Both are based on the {\\em lexTriangular} method described in [1]. They differ from the algorithm described in [2] by the fact that multiciplities of the roots are not kept. With the \\axiomOpFrom{squareFreeLexTriangular}{LexTriangularPackage} operation all multiciplities are removed. With the other operation some multiciplities may remain. Both operations admit an optional argument to produce normalized triangular sets. \\newline")) (|zeroSetSplit| (((|List| (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#2|)) (|OrderedVariableList| |#2|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{} norm?)} decomposes the variety associated with \\axiom{\\spad{lp}} into square-free regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{\\spad{lp}} needs to generate a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.") (((|List| (|RegularChain| |#1| |#2|)) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{} norm?)} decomposes the variety associated with \\axiom{\\spad{lp}} into regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{\\spad{lp}} needs to generate a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.")) (|squareFreeLexTriangular| (((|List| (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#2|)) (|OrderedVariableList| |#2|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{squareFreeLexTriangular(base,{} norm?)} decomposes the variety associated with \\axiom{base} into square-free regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{base} needs to be a lexicographical Groebner basis of a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.")) (|lexTriangular| (((|List| (|RegularChain| |#1| |#2|)) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{lexTriangular(base,{} norm?)} decomposes the variety associated with \\axiom{base} into regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{base} needs to be a lexicographical Groebner basis of a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.")) (|groebner| (((|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) "\\axiom{groebner(\\spad{lp})} returns the lexicographical Groebner basis of \\axiom{\\spad{lp}}. If \\axiom{\\spad{lp}} generates a zero-dimensional ideal then the {\\em FGLM} strategy is used,{} otherwise the {\\em Sugar} strategy is used.")) (|fglmIfCan| (((|Union| (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) "failed") (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) "\\axiom{fglmIfCan(\\spad{lp})} returns the lexicographical Groebner basis of \\axiom{\\spad{lp}} by using the {\\em FGLM} strategy,{} if \\axiom{zeroDimensional?(\\spad{lp})} holds .")) (|zeroDimensional?| (((|Boolean|) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) "\\axiom{zeroDimensional?(\\spad{lp})} returns \\spad{true} iff \\axiom{\\spad{lp}} generates a zero-dimensional ideal \\spad{w}.\\spad{r}.\\spad{t}. the variables involved in \\axiom{\\spad{lp}}."))) @@ -2496,30 +2496,30 @@ NIL ((|constructor| (NIL "Category for the transcendental Liouvillian functions.")) (|erf| (($ $) "\\spad{erf(x)} returns the error function of \\spad{x},{} \\spadignore{i.e.} \\spad{2 / sqrt(\\%pi)} times the integral of \\spad{exp(-x**2) dx}.")) (|dilog| (($ $) "\\spad{dilog(x)} returns the dilogarithm of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{log(x) / (1 - x) dx}.")) (|li| (($ $) "\\spad{li(x)} returns the logarithmic integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{dx / log(x)}.")) (|Ci| (($ $) "\\spad{Ci(x)} returns the cosine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{cos(x) / x dx}.")) (|Si| (($ $) "\\spad{Si(x)} returns the sine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{sin(x) / x dx}.")) (|Ei| (($ $) "\\spad{Ei(x)} returns the exponential integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{exp(x)/x dx}."))) NIL NIL -(-642 R -2117) +(-642 R -1959) ((|constructor| (NIL "This package provides liouvillian functions over an integral domain.")) (|integral| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{integral(f,x = a..b)} denotes the definite integral of \\spad{f} with respect to \\spad{x} from \\spad{a} to \\spad{b}.") ((|#2| |#2| (|Symbol|)) "\\spad{integral(f,x)} indefinite integral of \\spad{f} with respect to \\spad{x}.")) (|dilog| ((|#2| |#2|) "\\spad{dilog(f)} denotes the dilogarithm")) (|erf| ((|#2| |#2|) "\\spad{erf(f)} denotes the error function")) (|li| ((|#2| |#2|) "\\spad{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 -(-643 |lv| -2117) +(-643 |lv| -1959) ((|constructor| (NIL "\\indented{1}{Given a Groebner basis \\spad{B} with respect to the total degree ordering for} a zero-dimensional ideal \\spad{I},{} compute a Groebner basis with respect to the lexicographical ordering by using linear algebra.")) (|transform| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{transform }\\undocumented")) (|choosemon| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{choosemon }\\undocumented")) (|intcompBasis| (((|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|OrderedVariableList| |#1|) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{intcompBasis }\\undocumented")) (|anticoord| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|List| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{anticoord }\\undocumented")) (|coord| (((|Vector| |#2|) (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{coord }\\undocumented")) (|computeBasis| (((|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{computeBasis }\\undocumented")) (|minPol| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|OrderedVariableList| |#1|)) "\\spad{minPol }\\undocumented") (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|OrderedVariableList| |#1|)) "\\spad{minPol }\\undocumented")) (|totolex| (((|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{totolex }\\undocumented")) (|groebgen| (((|Record| (|:| |glbase| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |glval| (|List| (|Integer|)))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{groebgen }\\undocumented")) (|linGenPos| (((|Record| (|:| |gblist| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |gvlist| (|List| (|Integer|)))) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{linGenPos }\\undocumented"))) NIL NIL (-644) ((|constructor| (NIL "This domain provides a simple way to save values in files.")) (|setelt| (((|Any|) $ (|Symbol|) (|Any|)) "\\spad{lib.k := v} saves the value \\spad{v} in the library \\spad{lib}. It can later be extracted using the key \\spad{k}.")) (|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."))) -((-4464 . T)) -((-12 (|HasCategory| (-2 (|:| -2239 (-1178)) (|:| -2904 (-52))) (QUOTE (-1120))) (|HasCategory| (-2 (|:| -2239 (-1178)) (|:| -2904 (-52))) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2239) (QUOTE (-1178))) (LIST (QUOTE |:|) (QUOTE -2904) (QUOTE (-52))))))) (-3794 (|HasCategory| (-2 (|:| -2239 (-1178)) (|:| -2904 (-52))) (QUOTE (-1120))) (|HasCategory| (-52) (QUOTE (-1120)))) (-3794 (|HasCategory| (-2 (|:| -2239 (-1178)) (|:| -2904 (-52))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2239 (-1178)) (|:| -2904 (-52))) (QUOTE (-1120))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-1120)))) (-3794 (|HasCategory| (-2 (|:| -2239 (-1178)) (|:| -2904 (-52))) (QUOTE (-1120))) (|HasCategory| (-2 (|:| -2239 (-1178)) (|:| -2904 (-52))) (LIST (QUOTE -625) (QUOTE (-875)))) (|HasCategory| (-52) (QUOTE (-1120))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-875))))) (|HasCategory| (-2 (|:| -2239 (-1178)) (|:| -2904 (-52))) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| (-52) (QUOTE (-1120))) (|HasCategory| (-52) (LIST (QUOTE -319) (QUOTE (-52))))) (|HasCategory| (-1178) (QUOTE (-861))) (-3794 (|HasCategory| (-2 (|:| -2239 (-1178)) (|:| -2904 (-52))) (LIST (QUOTE -625) (QUOTE (-875)))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-875))))) (-3794 (|HasCategory| (-2 (|:| -2239 (-1178)) (|:| -2904 (-52))) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-102)))) (|HasCategory| (-52) (QUOTE (-1120))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-875)))) (|HasCategory| (-2 (|:| -2239 (-1178)) (|:| -2904 (-52))) (LIST (QUOTE -625) (QUOTE (-875)))) (|HasCategory| (-2 (|:| -2239 (-1178)) (|:| -2904 (-52))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2239 (-1178)) (|:| -2904 (-52))) (QUOTE (-1120)))) +((-4465 . T)) +((-12 (|HasCategory| (-2 (|:| -4300 (-1179)) (|:| -4438 (-52))) (QUOTE (-1121))) (|HasCategory| (-2 (|:| -4300 (-1179)) (|:| -4438 (-52))) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4300) (QUOTE (-1179))) (LIST (QUOTE |:|) (QUOTE -4438) (QUOTE (-52))))))) (-2758 (|HasCategory| (-2 (|:| -4300 (-1179)) (|:| -4438 (-52))) (QUOTE (-1121))) (|HasCategory| (-52) (QUOTE (-1121)))) (-2758 (|HasCategory| (-2 (|:| -4300 (-1179)) (|:| -4438 (-52))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4300 (-1179)) (|:| -4438 (-52))) (QUOTE (-1121))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-1121)))) (-2758 (|HasCategory| (-2 (|:| -4300 (-1179)) (|:| -4438 (-52))) (QUOTE (-1121))) (|HasCategory| (-2 (|:| -4300 (-1179)) (|:| -4438 (-52))) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-52) (QUOTE (-1121))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| (-2 (|:| -4300 (-1179)) (|:| -4438 (-52))) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| (-52) (QUOTE (-1121))) (|HasCategory| (-52) (LIST (QUOTE -319) (QUOTE (-52))))) (|HasCategory| (-1179) (QUOTE (-861))) (-2758 (|HasCategory| (-2 (|:| -4300 (-1179)) (|:| -4438 (-52))) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-876))))) (-2758 (|HasCategory| (-2 (|:| -4300 (-1179)) (|:| -4438 (-52))) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-102)))) (|HasCategory| (-52) (QUOTE (-1121))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -4300 (-1179)) (|:| -4438 (-52))) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -4300 (-1179)) (|:| -4438 (-52))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4300 (-1179)) (|:| -4438 (-52))) (QUOTE (-1121)))) (-645 S R) ((|constructor| (NIL "\\axiom{JacobiIdentity} means that \\axiom{[\\spad{x},{}[\\spad{y},{}\\spad{z}]]+[\\spad{y},{}[\\spad{z},{}\\spad{x}]]+[\\spad{z},{}[\\spad{x},{}\\spad{y}]] = 0} holds.")) (/ (($ $ |#2|) "\\axiom{\\spad{x/r}} returns the division of \\axiom{\\spad{x}} by \\axiom{\\spad{r}}.")) (|construct| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) NIL ((|HasCategory| |#2| (QUOTE (-374)))) (-646 R) ((|constructor| (NIL "\\axiom{JacobiIdentity} means that \\axiom{[\\spad{x},{}[\\spad{y},{}\\spad{z}]]+[\\spad{y},{}[\\spad{z},{}\\spad{x}]]+[\\spad{z},{}[\\spad{x},{}\\spad{y}]] = 0} holds.")) (/ (($ $ |#1|) "\\axiom{\\spad{x/r}} returns the division of \\axiom{\\spad{x}} by \\axiom{\\spad{r}}.")) (|construct| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) -((|JacobiIdentity| . T) (|NullSquare| . T) (-4458 . T) (-4457 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-4459 . T) (-4458 . T)) NIL (-647 R A) ((|constructor| (NIL "AssociatedLieAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$A} to define the Lie bracket \\spad{a*b := (a *\\$A b - b *\\$A a)} (commutator). Note that the notation \\spad{[a,b]} cannot be used due to restrictions of the current compiler. This domain only gives a Lie algebra if the Jacobi-identity \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} holds for all \\spad{a},{}\\spad{b},{}\\spad{c} in \\spad{A}. This relation can be checked by \\spad{lieAdmissible?()\\$A}. \\blankline If the underlying algebra is of type \\spadtype{FramedNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank,{} together with a fixed \\spad{R}-module basis),{} then the same is \\spad{true} for the associated Lie algebra. Also,{} if the underlying algebra is of type \\spadtype{FiniteRankNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank),{} then the same is \\spad{true} for the associated Lie algebra.")) (|coerce| (($ |#2|) "\\spad{coerce(a)} coerces the element \\spad{a} of the algebra \\spad{A} to an element of the Lie algebra \\spadtype{AssociatedLieAlgebra}(\\spad{R},{}A)."))) -((-4460 -3794 (-2310 (|has| |#2| (-378 |#1|)) (|has| |#1| (-568))) (-12 (|has| |#2| (-429 |#1|)) (|has| |#1| (-568)))) (-4458 . T) (-4457 . T)) -((-3794 (|HasCategory| |#2| (LIST (QUOTE -378) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|)))) (-3794 (-12 (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#2| (LIST (QUOTE -378) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -378) (|devaluate| |#1|)))) +((-4461 -2758 (-2673 (|has| |#2| (-378 |#1|)) (|has| |#1| (-568))) (-12 (|has| |#2| (-429 |#1|)) (|has| |#1| (-568)))) (-4459 . T) (-4458 . T)) +((-2758 (|HasCategory| |#2| (LIST (QUOTE -378) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|)))) (-2758 (-12 (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#2| (LIST (QUOTE -378) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -378) (|devaluate| |#1|)))) (-648 R FE) ((|constructor| (NIL "PowerSeriesLimitPackage implements limits of expressions in one or more variables as one of the variables approaches a limiting value. Included are two-sided limits,{} left- and right- hand limits,{} and limits at plus or minus infinity.")) (|complexLimit| (((|Union| (|OnePointCompletion| |#2|) "failed") |#2| (|Equation| (|OnePointCompletion| |#2|))) "\\spad{complexLimit(f(x),x = a)} computes the complex limit \\spad{lim(x -> a,f(x))}.")) (|limit| (((|Union| (|OrderedCompletion| |#2|) "failed") |#2| (|Equation| |#2|) (|String|)) "\\spad{limit(f(x),x=a,\"left\")} computes the left hand real limit \\spad{lim(x -> a-,f(x))}; \\spad{limit(f(x),x=a,\"right\")} computes the right hand real limit \\spad{lim(x -> a+,f(x))}.") (((|Union| (|OrderedCompletion| |#2|) (|Record| (|:| |leftHandLimit| (|Union| (|OrderedCompletion| |#2|) "failed")) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| |#2|) "failed"))) "failed") |#2| (|Equation| (|OrderedCompletion| |#2|))) "\\spad{limit(f(x),x = a)} computes the real limit \\spad{lim(x -> a,f(x))}."))) NIL @@ -2531,7 +2531,7 @@ NIL (-650 S R) ((|constructor| (NIL "Test for linear dependence.")) (|solveLinear| (((|Union| (|Vector| (|Fraction| |#1|)) "failed") (|Vector| |#2|) |#2|) "\\spad{solveLinear([v1,...,vn], u)} returns \\spad{[c1,...,cn]} such that \\spad{c1*v1 + ... + cn*vn = u},{} \"failed\" if no such \\spad{ci}\\spad{'s} exist in the quotient field of \\spad{S}.") (((|Union| (|Vector| |#1|) "failed") (|Vector| |#2|) |#2|) "\\spad{solveLinear([v1,...,vn], u)} returns \\spad{[c1,...,cn]} such that \\spad{c1*v1 + ... + cn*vn = u},{} \"failed\" if no such \\spad{ci}\\spad{'s} exist in \\spad{S}.")) (|linearDependence| (((|Union| (|Vector| |#1|) "failed") (|Vector| |#2|)) "\\spad{linearDependence([v1,...,vn])} returns \\spad{[c1,...,cn]} if \\spad{c1*v1 + ... + cn*vn = 0} and not all the \\spad{ci}\\spad{'s} are 0,{} \"failed\" if the \\spad{vi}\\spad{'s} are linearly independent over \\spad{S}.")) (|linearlyDependent?| (((|Boolean|) (|Vector| |#2|)) "\\spad{linearlyDependent?([v1,...,vn])} returns \\spad{true} if the \\spad{vi}\\spad{'s} are linearly dependent over \\spad{S},{} \\spad{false} otherwise."))) NIL -((-2298 (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (QUOTE (-374)))) +((-2662 (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (QUOTE (-374)))) (-651 R) ((|constructor| (NIL "An extension of left-module with an explicit linear dependence test.")) (|reducedSystem| (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| $) (|Vector| $)) "\\spad{reducedSystem(A, v)} returns a matrix \\spad{B} and a vector \\spad{w} such that \\spad{A x = v} and \\spad{B x = w} have the same solutions in \\spad{R}.") (((|Matrix| |#1|) (|Matrix| $)) "\\spad{reducedSystem(A)} returns a matrix \\spad{B} such that \\spad{A x = 0} and \\spad{B x = 0} have the same solutions in \\spad{R}.")) (|leftReducedSystem| (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) (|Vector| $) $) "\\spad{reducedSystem([v1,...,vn],u)} returns a matrix \\spad{M} with coefficients in \\spad{R} and a vector \\spad{w} such that the system of equations \\spad{c1*v1 + ... + cn*vn = u} has the same solution as \\spad{c * M = w} where \\spad{c} is the row vector \\spad{[c1,...cn]}.") (((|Matrix| |#1|) (|Vector| $)) "\\spad{leftReducedSystem [v1,...,vn]} returns a matrix \\spad{M} with coefficients in \\spad{R} such that the system of equations \\spad{c1*v1 + ... + cn*vn = 0\\$\\%} has the same solution as \\spad{c * M = 0} where \\spad{c} is the row vector \\spad{[c1,...cn]}."))) NIL @@ -2554,8 +2554,8 @@ NIL NIL (-656 S) ((|constructor| (NIL "\\spadtype{List} implements singly-linked lists that are addressable by indices; the index of the first element is 1. In addition to the operations provided by \\spadtype{IndexedList},{} this constructor provides some LISP-like functions such as \\spadfun{null} and \\spadfun{cons}.")) (|setDifference| (($ $ $) "\\spad{setDifference(u1,u2)} returns a list of the elements of \\spad{u1} that are not also in \\spad{u2}. The order of elements in the resulting list is unspecified.")) (|setIntersection| (($ $ $) "\\spad{setIntersection(u1,u2)} returns a list of the elements that lists \\spad{u1} and \\spad{u2} have in common. The order of elements in the resulting list is unspecified.")) (|setUnion| (($ $ $) "\\spad{setUnion(u1,u2)} appends the two lists \\spad{u1} and \\spad{u2},{} then removes all duplicates. The order of elements in the resulting list is unspecified.")) (|append| (($ $ $) "\\spad{append(u1,u2)} appends the elements of list \\spad{u1} onto the front of list \\spad{u2}. This new list and \\spad{u2} will share some structure.")) (|cons| (($ |#1| $) "\\spad{cons(element,u)} appends \\spad{element} onto the front of list \\spad{u} and returns the new list. This new list and the old one will share some structure.")) (|null| (((|Boolean|) $) "\\spad{null(u)} tests if list \\spad{u} is the empty list.")) (|nil| (($) "\\spad{nil} is the empty list."))) -((-4464 . T) (-4463 . T)) -((-3794 (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1120))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-3794 (-12 (|HasCategory| |#1| (QUOTE (-1120))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-875))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-3794 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1120)))) (|HasCategory| |#1| (QUOTE (-861))) (-3794 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1120)))) (|HasCategory| |#1| (QUOTE (-840))) (|HasCategory| (-576) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1120))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-875)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1120))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) +((-4465 . T) (-4464 . T)) +((-2758 (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2758 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2758 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| |#1| (QUOTE (-861))) (-2758 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| |#1| (QUOTE (-840))) (|HasCategory| (-576) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-657 T$) ((|constructor| (NIL "This domain represents AST for Spad literals."))) NIL @@ -2566,8 +2566,8 @@ NIL NIL (-659 S) ((|substitute| (($ |#1| |#1| $) "\\spad{substitute(x,y,d)} replace \\spad{x}\\spad{'s} with \\spad{y}\\spad{'s} in dictionary \\spad{d}.")) (|duplicates?| (((|Boolean|) $) "\\spad{duplicates?(d)} tests if dictionary \\spad{d} has duplicate entries."))) -((-4463 . T) (-4464 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1120))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1120))) (-3794 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1120)))) (-3794 (-12 (|HasCategory| |#1| (QUOTE (-1120))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-875))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-875)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4464 . T) (-4465 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1121))) (-2758 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1121)))) (-2758 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102)))) (-660 R) ((|constructor| (NIL "The category of left modules over an \\spad{rng} (ring not necessarily with unit). This is an abelian group which supports left multiplation by elements of the \\spad{rng}. \\blankline"))) NIL @@ -2579,39 +2579,39 @@ NIL (-662 A S) ((|constructor| (NIL "A linear aggregate is an aggregate whose elements are indexed by integers. Examples of linear aggregates are strings,{} lists,{} and arrays. Most of the exported operations for linear aggregates are non-destructive but are not always efficient for a particular aggregate. For example,{} \\spadfun{concat} of two lists needs only to copy its first argument,{} whereas \\spadfun{concat} of two arrays needs to copy both arguments. Most of the operations exported here apply to infinite objects (\\spadignore{e.g.} streams) as well to finite ones. For finite linear aggregates,{} see \\spadtype{FiniteLinearAggregate}.")) (|setelt| ((|#2| $ (|UniversalSegment| (|Integer|)) |#2|) "\\spad{setelt(u,i..j,x)} (also written: \\axiom{\\spad{u}(\\spad{i}..\\spad{j}) \\spad{:=} \\spad{x}}) destructively replaces each element in the segment \\axiom{\\spad{u}(\\spad{i}..\\spad{j})} by \\spad{x}. The value \\spad{x} is returned. Note: \\spad{u} is destructively change so that \\axiom{\\spad{u}.\\spad{k} \\spad{:=} \\spad{x} for \\spad{k} in \\spad{i}..\\spad{j}}; its length remains unchanged.")) (|insert| (($ $ $ (|Integer|)) "\\spad{insert(v,u,k)} returns a copy of \\spad{u} having \\spad{v} inserted beginning at the \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{v},{}\\spad{u},{}\\spad{k}) = concat( \\spad{u}(0..\\spad{k}-1),{} \\spad{v},{} \\spad{u}(\\spad{k}..) )}.") (($ |#2| $ (|Integer|)) "\\spad{insert(x,u,i)} returns a copy of \\spad{u} having \\spad{x} as its \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{x},{}a,{}\\spad{k}) = concat(concat(a(0..\\spad{k}-1),{}\\spad{x}),{}a(\\spad{k}..))}.")) (|delete| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete(u,i..j)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th through \\axiom{\\spad{j}}th element deleted. Note: \\axiom{delete(a,{}\\spad{i}..\\spad{j}) = concat(a(0..\\spad{i}-1),{}a(\\spad{j+1}..))}.") (($ $ (|Integer|)) "\\spad{delete(u,i)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th element deleted. Note: for lists,{} \\axiom{delete(a,{}\\spad{i}) \\spad{==} concat(a(0..\\spad{i} - 1),{}a(\\spad{i} + 1,{}..))}.")) (|map| (($ (|Mapping| |#2| |#2| |#2|) $ $) "\\spad{map(f,u,v)} returns a new collection \\spad{w} with elements \\axiom{\\spad{z} = \\spad{f}(\\spad{x},{}\\spad{y})} for corresponding elements \\spad{x} and \\spad{y} from \\spad{u} and \\spad{v}. Note: for linear aggregates,{} \\axiom{\\spad{w}.\\spad{i} = \\spad{f}(\\spad{u}.\\spad{i},{}\\spad{v}.\\spad{i})}.")) (|concat| (($ (|List| $)) "\\spad{concat(u)},{} where \\spad{u} is a lists of aggregates \\axiom{[a,{}\\spad{b},{}...,{}\\spad{c}]},{} returns a single aggregate consisting of the elements of \\axiom{a} followed by those of \\spad{b} followed ... by the elements of \\spad{c}. Note: \\axiom{concat(a,{}\\spad{b},{}...,{}\\spad{c}) = concat(a,{}concat(\\spad{b},{}...,{}\\spad{c}))}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} then \\axiom{\\spad{w}.\\spad{i} = \\spad{u}.\\spad{i} for \\spad{i} in indices \\spad{u}} and \\axiom{\\spad{w}.(\\spad{j} + maxIndex \\spad{u}) = \\spad{v}.\\spad{j} for \\spad{j} in indices \\spad{v}}.") (($ |#2| $) "\\spad{concat(x,u)} returns aggregate \\spad{u} with additional element at the front. Note: for lists: \\axiom{concat(\\spad{x},{}\\spad{u}) \\spad{==} concat([\\spad{x}],{}\\spad{u})}.") (($ $ |#2|) "\\spad{concat(u,x)} returns aggregate \\spad{u} with additional element \\spad{x} at the end. Note: for lists,{} \\axiom{concat(\\spad{u},{}\\spad{x}) \\spad{==} concat(\\spad{u},{}[\\spad{x}])}")) (|new| (($ (|NonNegativeInteger|) |#2|) "\\spad{new(n,x)} returns \\axiom{fill!(new \\spad{n},{}\\spad{x})}."))) NIL -((|HasAttribute| |#1| (QUOTE -4464))) +((|HasAttribute| |#1| (QUOTE -4465))) (-663 S) ((|constructor| (NIL "A linear aggregate is an aggregate whose elements are indexed by integers. Examples of linear aggregates are strings,{} lists,{} and arrays. Most of the exported operations for linear aggregates are non-destructive but are not always efficient for a particular aggregate. For example,{} \\spadfun{concat} of two lists needs only to copy its first argument,{} whereas \\spadfun{concat} of two arrays needs to copy both arguments. Most of the operations exported here apply to infinite objects (\\spadignore{e.g.} streams) as well to finite ones. For finite linear aggregates,{} see \\spadtype{FiniteLinearAggregate}.")) (|setelt| ((|#1| $ (|UniversalSegment| (|Integer|)) |#1|) "\\spad{setelt(u,i..j,x)} (also written: \\axiom{\\spad{u}(\\spad{i}..\\spad{j}) \\spad{:=} \\spad{x}}) destructively replaces each element in the segment \\axiom{\\spad{u}(\\spad{i}..\\spad{j})} by \\spad{x}. The value \\spad{x} is returned. Note: \\spad{u} is destructively change so that \\axiom{\\spad{u}.\\spad{k} \\spad{:=} \\spad{x} for \\spad{k} in \\spad{i}..\\spad{j}}; its length remains unchanged.")) (|insert| (($ $ $ (|Integer|)) "\\spad{insert(v,u,k)} returns a copy of \\spad{u} having \\spad{v} inserted beginning at the \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{v},{}\\spad{u},{}\\spad{k}) = concat( \\spad{u}(0..\\spad{k}-1),{} \\spad{v},{} \\spad{u}(\\spad{k}..) )}.") (($ |#1| $ (|Integer|)) "\\spad{insert(x,u,i)} returns a copy of \\spad{u} having \\spad{x} as its \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{x},{}a,{}\\spad{k}) = concat(concat(a(0..\\spad{k}-1),{}\\spad{x}),{}a(\\spad{k}..))}.")) (|delete| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete(u,i..j)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th through \\axiom{\\spad{j}}th element deleted. Note: \\axiom{delete(a,{}\\spad{i}..\\spad{j}) = concat(a(0..\\spad{i}-1),{}a(\\spad{j+1}..))}.") (($ $ (|Integer|)) "\\spad{delete(u,i)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th element deleted. Note: for lists,{} \\axiom{delete(a,{}\\spad{i}) \\spad{==} concat(a(0..\\spad{i} - 1),{}a(\\spad{i} + 1,{}..))}.")) (|map| (($ (|Mapping| |#1| |#1| |#1|) $ $) "\\spad{map(f,u,v)} returns a new collection \\spad{w} with elements \\axiom{\\spad{z} = \\spad{f}(\\spad{x},{}\\spad{y})} for corresponding elements \\spad{x} and \\spad{y} from \\spad{u} and \\spad{v}. Note: for linear aggregates,{} \\axiom{\\spad{w}.\\spad{i} = \\spad{f}(\\spad{u}.\\spad{i},{}\\spad{v}.\\spad{i})}.")) (|concat| (($ (|List| $)) "\\spad{concat(u)},{} where \\spad{u} is a lists of aggregates \\axiom{[a,{}\\spad{b},{}...,{}\\spad{c}]},{} returns a single aggregate consisting of the elements of \\axiom{a} followed by those of \\spad{b} followed ... by the elements of \\spad{c}. Note: \\axiom{concat(a,{}\\spad{b},{}...,{}\\spad{c}) = concat(a,{}concat(\\spad{b},{}...,{}\\spad{c}))}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} then \\axiom{\\spad{w}.\\spad{i} = \\spad{u}.\\spad{i} for \\spad{i} in indices \\spad{u}} and \\axiom{\\spad{w}.(\\spad{j} + maxIndex \\spad{u}) = \\spad{v}.\\spad{j} for \\spad{j} in indices \\spad{v}}.") (($ |#1| $) "\\spad{concat(x,u)} returns aggregate \\spad{u} with additional element at the front. Note: for lists: \\axiom{concat(\\spad{x},{}\\spad{u}) \\spad{==} concat([\\spad{x}],{}\\spad{u})}.") (($ $ |#1|) "\\spad{concat(u,x)} returns aggregate \\spad{u} with additional element \\spad{x} at the end. Note: for lists,{} \\axiom{concat(\\spad{u},{}\\spad{x}) \\spad{==} concat(\\spad{u},{}[\\spad{x}])}")) (|new| (($ (|NonNegativeInteger|) |#1|) "\\spad{new(n,x)} returns \\axiom{fill!(new \\spad{n},{}\\spad{x})}."))) NIL NIL -(-664 R -2117 L) +(-664 R -1959 L) ((|constructor| (NIL "\\spad{ElementaryFunctionLODESolver} provides the top-level functions for finding closed form solutions of linear ordinary differential equations and initial value problems.")) (|solve| (((|Union| |#2| "failed") |#3| |#2| (|Symbol|) |#2| (|List| |#2|)) "\\spad{solve(op, g, x, a, [y0,...,ym])} returns either the solution of the initial value problem \\spad{op y = g, y(a) = y0, y'(a) = y1,...} or \"failed\" if the solution cannot be found; \\spad{x} is the dependent variable.") (((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) "failed") |#3| |#2| (|Symbol|)) "\\spad{solve(op, g, x)} returns either a solution of the ordinary differential equation \\spad{op y = g} or \"failed\" if no non-trivial solution can be found; When found,{} the solution is returned in the form \\spad{[h, [b1,...,bm]]} where \\spad{h} is a particular solution and and \\spad{[b1,...bm]} are linearly independent solutions of the associated homogenuous equation \\spad{op y = 0}. A full basis for the solutions of the homogenuous equation is not always returned,{} only the solutions which were found; \\spad{x} is the dependent variable."))) NIL NIL (-665 A) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperator1} defines a ring of differential operators with coefficients in a differential ring A. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}"))) -((-4457 . T) (-4458 . T) (-4460 . T)) -((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -1058) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1058) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-374)))) +((-4458 . T) (-4459 . T) (-4461 . T)) +((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-374)))) (-666 A M) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperator2} defines a ring of differential operators with coefficients in a differential ring A and acting on an A-module \\spad{M}. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|differentiate| (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}"))) -((-4457 . T) (-4458 . T) (-4460 . T)) -((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -1058) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1058) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-374)))) +((-4458 . T) (-4459 . T) (-4461 . T)) +((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-374)))) (-667 S A) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorCategory} is the category of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|directSum| (($ $ $) "\\spad{directSum(a,b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}.")) (|symmetricSquare| (($ $) "\\spad{symmetricSquare(a)} computes \\spad{symmetricProduct(a,a)} using a more efficient method.")) (|symmetricPower| (($ $ (|NonNegativeInteger|)) "\\spad{symmetricPower(a,n)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of \\spad{n} solutions of \\spad{a}.")) (|symmetricProduct| (($ $ $) "\\spad{symmetricProduct(a,b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of a solution of \\spad{a} by a solution of \\spad{b}.")) (|adjoint| (($ $) "\\spad{adjoint(a)} returns the adjoint operator of a.")) (D (($) "\\spad{D()} provides the operator corresponding to a derivation in the ring \\spad{A}."))) NIL ((|HasCategory| |#2| (QUOTE (-374)))) (-668 A) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorCategory} is the category of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|directSum| (($ $ $) "\\spad{directSum(a,b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}.")) (|symmetricSquare| (($ $) "\\spad{symmetricSquare(a)} computes \\spad{symmetricProduct(a,a)} using a more efficient method.")) (|symmetricPower| (($ $ (|NonNegativeInteger|)) "\\spad{symmetricPower(a,n)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of \\spad{n} solutions of \\spad{a}.")) (|symmetricProduct| (($ $ $) "\\spad{symmetricProduct(a,b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of a solution of \\spad{a} by a solution of \\spad{b}.")) (|adjoint| (($ $) "\\spad{adjoint(a)} returns the adjoint operator of a.")) (D (($) "\\spad{D()} provides the operator corresponding to a derivation in the ring \\spad{A}."))) -((-4457 . T) (-4458 . T) (-4460 . T)) +((-4458 . T) (-4459 . T) (-4461 . T)) NIL -(-669 -2117 UP) +(-669 -1959 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)))) -(-670 A -2005) +(-670 A -2221) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperator} defines a ring of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}"))) -((-4457 . T) (-4458 . T) (-4460 . T)) -((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -1058) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1058) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-374)))) +((-4458 . T) (-4459 . T) (-4461 . T)) +((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-374)))) (-671 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 @@ -2626,7 +2626,7 @@ NIL NIL (-674 M R S) ((|constructor| (NIL "Localize(\\spad{M},{}\\spad{R},{}\\spad{S}) produces fractions with numerators from an \\spad{R} module \\spad{M} and denominators from some multiplicative subset \\spad{D} of \\spad{R}.")) (|denom| ((|#3| $) "\\spad{denom x} returns the denominator of \\spad{x}.")) (|numer| ((|#1| $) "\\spad{numer x} returns the numerator of \\spad{x}.")) (/ (($ |#1| |#3|) "\\spad{m / d} divides the element \\spad{m} by \\spad{d}.") (($ $ |#3|) "\\spad{x / d} divides the element \\spad{x} by \\spad{d}."))) -((-4458 . T) (-4457 . T)) +((-4459 . T) (-4458 . T)) ((|HasCategory| |#1| (QUOTE (-803)))) (-675 R) ((|constructor| (NIL "Given a PolynomialFactorizationExplicit ring,{} this package provides a defaulting rule for the \\spad{solveLinearPolynomialEquation} operation,{} by moving into the field of fractions,{} and solving it there via the \\spad{multiEuclidean} operation.")) (|solveLinearPolynomialEquationByFractions| (((|Union| (|List| (|SparseUnivariatePolynomial| |#1|)) "failed") (|List| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{solveLinearPolynomialEquationByFractions([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such exists."))) @@ -2634,7 +2634,7 @@ NIL NIL (-676 |VarSet| R) ((|constructor| (NIL "This type supports Lie polynomials in Lyndon basis see Free Lie Algebras by \\spad{C}. Reutenauer (Oxford science publications). \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|construct| (($ $ (|LyndonWord| |#1|)) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket \\axiom{[\\spad{x},{}\\spad{y}]}.") (($ (|LyndonWord| |#1|) $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket \\axiom{[\\spad{x},{}\\spad{y}]}.") (($ (|LyndonWord| |#1|) (|LyndonWord| |#1|)) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket \\axiom{[\\spad{x},{}\\spad{y}]}.")) (|LiePolyIfCan| (((|Union| $ "failed") (|XDistributedPolynomial| |#1| |#2|)) "\\axiom{LiePolyIfCan(\\spad{p})} returns \\axiom{\\spad{p}} in Lyndon basis if \\axiom{\\spad{p}} is a Lie polynomial,{} otherwise \\axiom{\"failed\"} is returned."))) -((|JacobiIdentity| . T) (|NullSquare| . T) (-4458 . T) (-4457 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-4459 . T) (-4458 . T)) ((|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-174)))) (-677 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}."))) @@ -2642,13 +2642,13 @@ NIL NIL (-678 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}."))) -((-4464 . T) (-4463 . T)) +((-4465 . T) (-4464 . T)) NIL -(-679 -2117) +(-679 -1959) ((|constructor| (NIL "This package solves linear system in the matrix form \\spad{AX = B}. It is essentially a particular instantiation of the package \\spadtype{LinearSystemMatrixPackage} for Matrix and Vector. This package\\spad{'s} existence makes it easier to use \\spadfun{solve} in the AXIOM interpreter.")) (|rank| (((|NonNegativeInteger|) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{rank(A,B)} computes the rank of the complete matrix \\spad{(A|B)} of the linear system \\spad{AX = B}.")) (|hasSolution?| (((|Boolean|) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{hasSolution?(A,B)} tests if the linear system \\spad{AX = B} has a solution.")) (|particularSolution| (((|Union| (|Vector| |#1|) "failed") (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{particularSolution(A,B)} finds a particular solution of the linear system \\spad{AX = B}.")) (|solve| (((|List| (|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|))))) (|List| (|List| |#1|)) (|List| (|Vector| |#1|))) "\\spad{solve(A,LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|List| (|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|))))) (|Matrix| |#1|) (|List| (|Vector| |#1|))) "\\spad{solve(A,LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|)))) (|List| (|List| |#1|)) (|Vector| |#1|)) "\\spad{solve(A,B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}.") (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|)))) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{solve(A,B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}."))) NIL NIL -(-680 -2117 |Row| |Col| M) +(-680 -1959 |Row| |Col| M) ((|constructor| (NIL "This package solves linear system in the matrix form \\spad{AX = B}.")) (|rank| (((|NonNegativeInteger|) |#4| |#3|) "\\spad{rank(A,B)} computes the rank of the complete matrix \\spad{(A|B)} of the linear system \\spad{AX = B}.")) (|hasSolution?| (((|Boolean|) |#4| |#3|) "\\spad{hasSolution?(A,B)} tests if the linear system \\spad{AX = B} has a solution.")) (|particularSolution| (((|Union| |#3| "failed") |#4| |#3|) "\\spad{particularSolution(A,B)} finds a particular solution of the linear system \\spad{AX = B}.")) (|solve| (((|List| (|Record| (|:| |particular| (|Union| |#3| "failed")) (|:| |basis| (|List| |#3|)))) |#4| (|List| |#3|)) "\\spad{solve(A,LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|Record| (|:| |particular| (|Union| |#3| "failed")) (|:| |basis| (|List| |#3|))) |#4| |#3|) "\\spad{solve(A,B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}."))) NIL NIL @@ -2658,8 +2658,8 @@ NIL NIL (-682 |n| R) ((|constructor| (NIL "LieSquareMatrix(\\spad{n},{}\\spad{R}) implements the Lie algebra of the \\spad{n} by \\spad{n} matrices over the commutative ring \\spad{R}. The Lie bracket (commutator) of the algebra is given by \\spad{a*b := (a *\\$SQMATRIX(n,R) b - b *\\$SQMATRIX(n,R) a)},{} where \\spadfun{*\\$SQMATRIX(\\spad{n},{}\\spad{R})} is the usual matrix multiplication."))) -((-4460 . T) (-4463 . T) (-4457 . T) (-4458 . T)) -((|HasCategory| |#2| (LIST (QUOTE -916) (QUOTE (-1196)))) (|HasCategory| |#2| (LIST (QUOTE -918) (QUOTE (-1196)))) (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (QUOTE (-237))) (|HasAttribute| |#2| (QUOTE (-4465 "*"))) (|HasCategory| |#2| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -1058) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1058) (QUOTE (-576)))) (-3794 (-12 (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1120))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -651) (QUOTE (-576))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -916) (QUOTE (-1196)))))) (|HasCategory| |#2| (QUOTE (-317))) (|HasCategory| |#2| (QUOTE (-1120))) (|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-568))) (-3794 (|HasAttribute| |#2| (QUOTE (-4465 "*"))) (|HasCategory| |#2| (LIST (QUOTE -916) (QUOTE (-1196)))) (|HasCategory| |#2| (QUOTE (-238)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-875)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1120))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-174)))) +((-4461 . T) (-4464 . T) (-4458 . T) (-4459 . T)) +((|HasCategory| |#2| (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| |#2| (LIST (QUOTE -919) (QUOTE (-1197)))) (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (QUOTE (-237))) (|HasAttribute| |#2| (QUOTE (-4466 "*"))) (|HasCategory| |#2| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1059) (QUOTE (-576)))) (-2758 (-12 (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -651) (QUOTE (-576))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -917) (QUOTE (-1197)))))) (|HasCategory| |#2| (QUOTE (-317))) (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-568))) (-2758 (|HasAttribute| |#2| (QUOTE (-4466 "*"))) (|HasCategory| |#2| (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| |#2| (QUOTE (-238)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-174)))) (-683) ((|constructor| (NIL "This domain represents `literal sequence' syntax.")) (|elements| (((|List| (|SpadAst|)) $) "\\spad{elements(e)} returns the list of expressions in the `literal' list `e'."))) NIL @@ -2679,7 +2679,7 @@ NIL (-687 R) ((|constructor| (NIL "This domain represents three dimensional matrices over a general object type")) (|matrixDimensions| (((|Vector| (|NonNegativeInteger|)) $) "\\spad{matrixDimensions(x)} returns the dimensions of a matrix")) (|matrixConcat3D| (($ (|Symbol|) $ $) "\\spad{matrixConcat3D(s,x,y)} concatenates two 3-\\spad{D} matrices along a specified axis")) (|coerce| (((|PrimitiveArray| (|PrimitiveArray| (|PrimitiveArray| |#1|))) $) "\\spad{coerce(x)} moves from the domain to the representation type") (($ (|PrimitiveArray| (|PrimitiveArray| (|PrimitiveArray| |#1|)))) "\\spad{coerce(p)} moves from the representation type (PrimitiveArray PrimitiveArray PrimitiveArray \\spad{R}) to the domain")) (|setelt!| ((|#1| $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|) "\\spad{setelt!(x,i,j,k,s)} (or \\spad{x}.\\spad{i}.\\spad{j}.k:=s) sets a specific element of the array to some value of type \\spad{R}")) (|elt| ((|#1| $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{elt(x,i,j,k)} extract an element from the matrix \\spad{x}")) (|construct| (($ (|List| (|List| (|List| |#1|)))) "\\spad{construct(lll)} creates a 3-\\spad{D} matrix from a List List List \\spad{R} \\spad{lll}")) (|plus| (($ $ $) "\\spad{plus(x,y)} adds two matrices,{} term by term we note that they must be the same size")) (|identityMatrix| (($ (|NonNegativeInteger|)) "\\spad{identityMatrix(n)} create an identity matrix we note that this must be square")) (|zeroMatrix| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{zeroMatrix(i,j,k)} create a matrix with all zero terms"))) NIL -((-3794 (-12 (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1120))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1120))) (-3794 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1120)))) (-3794 (-12 (|HasCategory| |#1| (QUOTE (-1120))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-875))))) (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-875)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1120))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) +((-2758 (-12 (|HasCategory| |#1| (QUOTE (-1070))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1121))) (-2758 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1121)))) (-2758 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (QUOTE (-1070))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-688) ((|constructor| (NIL "This domain represents the syntax of a macro definition.")) (|body| (((|SpadAst|) $) "\\spad{body(m)} returns the right hand side of the definition \\spad{`m'}.")) (|head| (((|HeadAst|) $) "\\spad{head(m)} returns the head of the macro definition \\spad{`m'}. This is a list of identifiers starting with the name of the macro followed by the name of the parameters,{} if any."))) NIL @@ -2723,10 +2723,10 @@ NIL (-698 S R |Row| |Col|) ((|constructor| (NIL "\\spadtype{MatrixCategory} is a general matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col. A domain belonging to this category will be shallowly mutable. The index of the 'first' row may be obtained by calling the function \\spadfun{minRowIndex}. The index of the 'first' column may be obtained by calling the function \\spadfun{minColIndex}. The index of the first element of a Row is the same as the index of the first column in a matrix and vice versa.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|minordet| ((|#2| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors. Error: if the matrix is not square.")) (|determinant| ((|#2| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. Error: if the matrix is not square.")) (|nullSpace| (((|List| |#4|) $) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#2|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#2|) "\\spad{exquo(m,r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if matrix is not square or if the matrix is square but not invertible.") (($ $ (|NonNegativeInteger|)) "\\spad{x ** n} computes a non-negative integral power of the matrix \\spad{x}. Error: if the matrix is not square.")) (* ((|#3| |#3| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#4| $ |#4|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.") (($ (|Integer|) $) "\\spad{n * x} is an integer multiple.") (($ $ |#2|) "\\spad{x * r} is the right scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ |#2| $) "\\spad{r*x} is the left scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ $ $) "\\spad{x * y} is the product of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (- (($ $) "\\spad{-x} returns the negative of the matrix \\spad{x}.") (($ $ $) "\\spad{x - y} is the difference of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (+ (($ $ $) "\\spad{x + y} is the sum of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (|setsubMatrix!| (($ $ (|Integer|) (|Integer|) $) "\\spad{setsubMatrix(x,i1,j1,y)} destructively alters the matrix \\spad{x}. Here \\spad{x(i,j)} is set to \\spad{y(i-i1+1,j-j1+1)} for \\spad{i = i1,...,i1-1+nrows y} and \\spad{j = j1,...,j1-1+ncols y}.")) (|subMatrix| (($ $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{subMatrix(x,i1,i2,j1,j2)} extracts the submatrix \\spad{[x(i,j)]} where the index \\spad{i} ranges from \\spad{i1} to \\spad{i2} and the index \\spad{j} ranges from \\spad{j1} to \\spad{j2}.")) (|swapColumns!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapColumns!(m,i,j)} interchanges the \\spad{i}th and \\spad{j}th columns of \\spad{m}. This destructively alters the matrix.")) (|swapRows!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapRows!(m,i,j)} interchanges the \\spad{i}th and \\spad{j}th rows of \\spad{m}. This destructively alters the matrix.")) (|setelt| (($ $ (|List| (|Integer|)) (|List| (|Integer|)) $) "\\spad{setelt(x,rowList,colList,y)} destructively alters the matrix \\spad{x}. If \\spad{y} is \\spad{m}-by-\\spad{n},{} \\spad{rowList = [i<1>,i<2>,...,i<m>]} and \\spad{colList = [j<1>,j<2>,...,j<n>]},{} then \\spad{x(i<k>,j<l>)} is set to \\spad{y(k,l)} for \\spad{k = 1,...,m} and \\spad{l = 1,...,n}.")) (|elt| (($ $ (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{elt(x,rowList,colList)} returns an \\spad{m}-by-\\spad{n} matrix consisting of elements of \\spad{x},{} where \\spad{m = \\# rowList} and \\spad{n = \\# colList}. If \\spad{rowList = [i<1>,i<2>,...,i<m>]} and \\spad{colList = [j<1>,j<2>,...,j<n>]},{} then the \\spad{(k,l)}th entry of \\spad{elt(x,rowList,colList)} is \\spad{x(i<k>,j<l>)}.")) (|listOfLists| (((|List| (|List| |#2|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|vertConcat| (($ $ $) "\\spad{vertConcat(x,y)} vertically concatenates two matrices with an equal number of columns. The entries of \\spad{y} appear below of the entries of \\spad{x}. Error: if the matrices do not have the same number of columns.")) (|horizConcat| (($ $ $) "\\spad{horizConcat(x,y)} horizontally concatenates two matrices with an equal number of rows. The entries of \\spad{y} appear to the right of the entries of \\spad{x}. Error: if the matrices do not have the same number of rows.")) (|squareTop| (($ $) "\\spad{squareTop(m)} returns an \\spad{n}-by-\\spad{n} matrix consisting of the first \\spad{n} rows of the \\spad{m}-by-\\spad{n} matrix \\spad{m}. Error: if \\spad{m < n}.")) (|transpose| (($ $) "\\spad{transpose(m)} returns the transpose of the matrix \\spad{m}.") (($ |#3|) "\\spad{transpose(r)} converts the row \\spad{r} to a row matrix.")) (|coerce| (($ |#4|) "\\spad{coerce(col)} converts the column \\spad{col} to a column matrix.")) (|diagonalMatrix| (($ (|List| $)) "\\spad{diagonalMatrix([m1,...,mk])} creates a block diagonal matrix \\spad{M} with block matrices {\\em m1},{}...,{}{\\em mk} down the diagonal,{} with 0 block matrices elsewhere. More precisly: if \\spad{ri := nrows mi},{} \\spad{ci := ncols mi},{} then \\spad{m} is an (\\spad{r1+}..\\spad{+rk}) by (\\spad{c1+}..\\spad{+ck}) - matrix with entries \\spad{m.i.j = ml.(i-r1-..-r(l-1)).(j-n1-..-n(l-1))},{} if \\spad{(r1+..+r(l-1)) < i <= r1+..+rl} and \\spad{(c1+..+c(l-1)) < i <= c1+..+cl},{} \\spad{m.i.j} = 0 otherwise.") (($ (|List| |#2|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ (|NonNegativeInteger|) |#2|) "\\spad{scalarMatrix(n,r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}\\spad{'s} on the diagonal and zeroes elsewhere.")) (|matrix| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) (|Mapping| |#2| (|Integer|) (|Integer|))) "\\spad{matrix(n,m,f)} construcys and \\spad{n * m} matrix with the \\spad{(i,j)} entry equal to \\spad{f(i,j)}.") (($ (|List| (|List| |#2|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix.")) (|zero| (($ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{zero(m,n)} returns an \\spad{m}-by-\\spad{n} zero matrix.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,j] = -m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,j] = m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.")) (|finiteAggregate| ((|attribute|) "matrices are finite")) (|shallowlyMutable| ((|attribute|) "One may destructively alter matrices"))) NIL -((|HasAttribute| |#2| (QUOTE (-4465 "*"))) (|HasCategory| |#2| (QUOTE (-317))) (|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-568)))) +((|HasAttribute| |#2| (QUOTE (-4466 "*"))) (|HasCategory| |#2| (QUOTE (-317))) (|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-568)))) (-699 R |Row| |Col|) ((|constructor| (NIL "\\spadtype{MatrixCategory} is a general matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col. A domain belonging to this category will be shallowly mutable. The index of the 'first' row may be obtained by calling the function \\spadfun{minRowIndex}. The index of the 'first' column may be obtained by calling the function \\spadfun{minColIndex}. The index of the first element of a Row is the same as the index of the first column in a matrix and vice versa.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|minordet| ((|#1| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors. Error: if the matrix is not square.")) (|determinant| ((|#1| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. Error: if the matrix is not square.")) (|nullSpace| (((|List| |#3|) $) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#1|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(m,r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if matrix is not square or if the matrix is square but not invertible.") (($ $ (|NonNegativeInteger|)) "\\spad{x ** n} computes a non-negative integral power of the matrix \\spad{x}. Error: if the matrix is not square.")) (* ((|#2| |#2| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#3| $ |#3|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.") (($ (|Integer|) $) "\\spad{n * x} is an integer multiple.") (($ $ |#1|) "\\spad{x * r} is the right scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ |#1| $) "\\spad{r*x} is the left scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ $ $) "\\spad{x * y} is the product of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (- (($ $) "\\spad{-x} returns the negative of the matrix \\spad{x}.") (($ $ $) "\\spad{x - y} is the difference of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (+ (($ $ $) "\\spad{x + y} is the sum of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (|setsubMatrix!| (($ $ (|Integer|) (|Integer|) $) "\\spad{setsubMatrix(x,i1,j1,y)} destructively alters the matrix \\spad{x}. Here \\spad{x(i,j)} is set to \\spad{y(i-i1+1,j-j1+1)} for \\spad{i = i1,...,i1-1+nrows y} and \\spad{j = j1,...,j1-1+ncols y}.")) (|subMatrix| (($ $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{subMatrix(x,i1,i2,j1,j2)} extracts the submatrix \\spad{[x(i,j)]} where the index \\spad{i} ranges from \\spad{i1} to \\spad{i2} and the index \\spad{j} ranges from \\spad{j1} to \\spad{j2}.")) (|swapColumns!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapColumns!(m,i,j)} interchanges the \\spad{i}th and \\spad{j}th columns of \\spad{m}. This destructively alters the matrix.")) (|swapRows!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapRows!(m,i,j)} interchanges the \\spad{i}th and \\spad{j}th rows of \\spad{m}. This destructively alters the matrix.")) (|setelt| (($ $ (|List| (|Integer|)) (|List| (|Integer|)) $) "\\spad{setelt(x,rowList,colList,y)} destructively alters the matrix \\spad{x}. If \\spad{y} is \\spad{m}-by-\\spad{n},{} \\spad{rowList = [i<1>,i<2>,...,i<m>]} and \\spad{colList = [j<1>,j<2>,...,j<n>]},{} then \\spad{x(i<k>,j<l>)} is set to \\spad{y(k,l)} for \\spad{k = 1,...,m} and \\spad{l = 1,...,n}.")) (|elt| (($ $ (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{elt(x,rowList,colList)} returns an \\spad{m}-by-\\spad{n} matrix consisting of elements of \\spad{x},{} where \\spad{m = \\# rowList} and \\spad{n = \\# colList}. If \\spad{rowList = [i<1>,i<2>,...,i<m>]} and \\spad{colList = [j<1>,j<2>,...,j<n>]},{} then the \\spad{(k,l)}th entry of \\spad{elt(x,rowList,colList)} is \\spad{x(i<k>,j<l>)}.")) (|listOfLists| (((|List| (|List| |#1|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|vertConcat| (($ $ $) "\\spad{vertConcat(x,y)} vertically concatenates two matrices with an equal number of columns. The entries of \\spad{y} appear below of the entries of \\spad{x}. Error: if the matrices do not have the same number of columns.")) (|horizConcat| (($ $ $) "\\spad{horizConcat(x,y)} horizontally concatenates two matrices with an equal number of rows. The entries of \\spad{y} appear to the right of the entries of \\spad{x}. Error: if the matrices do not have the same number of rows.")) (|squareTop| (($ $) "\\spad{squareTop(m)} returns an \\spad{n}-by-\\spad{n} matrix consisting of the first \\spad{n} rows of the \\spad{m}-by-\\spad{n} matrix \\spad{m}. Error: if \\spad{m < n}.")) (|transpose| (($ $) "\\spad{transpose(m)} returns the transpose of the matrix \\spad{m}.") (($ |#2|) "\\spad{transpose(r)} converts the row \\spad{r} to a row matrix.")) (|coerce| (($ |#3|) "\\spad{coerce(col)} converts the column \\spad{col} to a column matrix.")) (|diagonalMatrix| (($ (|List| $)) "\\spad{diagonalMatrix([m1,...,mk])} creates a block diagonal matrix \\spad{M} with block matrices {\\em m1},{}...,{}{\\em mk} down the diagonal,{} with 0 block matrices elsewhere. More precisly: if \\spad{ri := nrows mi},{} \\spad{ci := ncols mi},{} then \\spad{m} is an (\\spad{r1+}..\\spad{+rk}) by (\\spad{c1+}..\\spad{+ck}) - matrix with entries \\spad{m.i.j = ml.(i-r1-..-r(l-1)).(j-n1-..-n(l-1))},{} if \\spad{(r1+..+r(l-1)) < i <= r1+..+rl} and \\spad{(c1+..+c(l-1)) < i <= c1+..+cl},{} \\spad{m.i.j} = 0 otherwise.") (($ (|List| |#1|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ (|NonNegativeInteger|) |#1|) "\\spad{scalarMatrix(n,r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}\\spad{'s} on the diagonal and zeroes elsewhere.")) (|matrix| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) (|Mapping| |#1| (|Integer|) (|Integer|))) "\\spad{matrix(n,m,f)} construcys and \\spad{n * m} matrix with the \\spad{(i,j)} entry equal to \\spad{f(i,j)}.") (($ (|List| (|List| |#1|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix.")) (|zero| (($ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{zero(m,n)} returns an \\spad{m}-by-\\spad{n} zero matrix.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,j] = -m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,j] = m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.")) (|finiteAggregate| ((|attribute|) "matrices are finite")) (|shallowlyMutable| ((|attribute|) "One may destructively alter matrices"))) -((-4463 . T) (-4464 . T)) +((-4464 . T) (-4465 . T)) NIL (-700 R |Row| |Col| M) ((|constructor| (NIL "\\spadtype{MatrixLinearAlgebraFunctions} provides functions to compute inverses and canonical forms.")) (|inverse| (((|Union| |#4| "failed") |#4|) "\\spad{inverse(m)} returns the inverse of the matrix. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|normalizedDivide| (((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|) "\\spad{normalizedDivide(n,d)} returns a normalized quotient and remainder such that consistently unique representatives for the residue class are chosen,{} \\spadignore{e.g.} positive remainders")) (|rowEchelon| ((|#4| |#4|) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (|adjoint| (((|Record| (|:| |adjMat| |#4|) (|:| |detMat| |#1|)) |#4|) "\\spad{adjoint(m)} returns the ajoint matrix of \\spad{m} (\\spadignore{i.e.} the matrix \\spad{n} such that \\spad{m*n} = determinant(\\spad{m})*id) and the detrminant of \\spad{m}.")) (|invertIfCan| (((|Union| |#4| "failed") |#4|) "\\spad{invertIfCan(m)} returns the inverse of \\spad{m} over \\spad{R}")) (|fractionFreeGauss!| ((|#4| |#4|) "\\spad{fractionFreeGauss(m)} performs the fraction free gaussian elimination on the matrix \\spad{m}.")) (|nullSpace| (((|List| |#3|) |#4|) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) |#4|) "\\spad{nullity(m)} returns the mullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) |#4|) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|elColumn2!| ((|#4| |#4| |#1| (|Integer|) (|Integer|)) "\\spad{elColumn2!(m,a,i,j)} adds to column \\spad{i} a*column(\\spad{m},{}\\spad{j}) : elementary operation of second kind. (\\spad{i} \\spad{~=j})")) (|elRow2!| ((|#4| |#4| |#1| (|Integer|) (|Integer|)) "\\spad{elRow2!(m,a,i,j)} adds to row \\spad{i} a*row(\\spad{m},{}\\spad{j}) : elementary operation of second kind. (\\spad{i} \\spad{~=j})")) (|elRow1!| ((|#4| |#4| (|Integer|) (|Integer|)) "\\spad{elRow1!(m,i,j)} swaps rows \\spad{i} and \\spad{j} of matrix \\spad{m} : elementary operation of first kind")) (|minordet| ((|#1| |#4|) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors. Error: if the matrix is not square.")) (|determinant| ((|#1| |#4|) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. an error message is returned if the matrix is not square."))) @@ -2734,8 +2734,8 @@ NIL ((|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-568)))) (-701 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."))) -((-4463 . T) (-4464 . T)) -((-3794 (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1120))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1120))) (-3794 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1120)))) (-3794 (-12 (|HasCategory| |#1| (QUOTE (-1120))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-875))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-568))) (|HasAttribute| |#1| (QUOTE (-4465 "*"))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-875)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1120))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) +((-4464 . T) (-4465 . T)) +((-2758 (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1121))) (-2758 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1121)))) (-2758 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-568))) (|HasAttribute| |#1| (QUOTE (-4466 "*"))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-702 R) ((|constructor| (NIL "This package provides standard arithmetic operations on matrices. The functions in this package store the results of computations in existing matrices,{} rather than creating new matrices. This package works only for matrices of type Matrix and uses the internal representation of this type.")) (** (((|Matrix| |#1|) (|Matrix| |#1|) (|NonNegativeInteger|)) "\\spad{x ** n} computes the \\spad{n}-th power of a square matrix. The power \\spad{n} is assumed greater than 1.")) (|power!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|NonNegativeInteger|)) "\\spad{power!(a,b,c,m,n)} computes \\spad{m} \\spad{**} \\spad{n} and stores the result in \\spad{a}. The matrices \\spad{b} and \\spad{c} are used to store intermediate results. Error: if \\spad{a},{} \\spad{b},{} \\spad{c},{} and \\spad{m} are not square and of the same dimensions.")) (|times!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{times!(c,a,b)} computes the matrix product \\spad{a * b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have compatible dimensions.")) (|rightScalarTimes!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{rightScalarTimes!(c,a,r)} computes the scalar product \\spad{a * r} and stores the result in the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions.")) (|leftScalarTimes!| (((|Matrix| |#1|) (|Matrix| |#1|) |#1| (|Matrix| |#1|)) "\\spad{leftScalarTimes!(c,r,a)} computes the scalar product \\spad{r * a} and stores the result in the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions.")) (|minus!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{!minus!(c,a,b)} computes the matrix difference \\spad{a - b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have the same dimensions.") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{minus!(c,a)} computes \\spad{-a} and stores the result in the matrix \\spad{c}. Error: if a and \\spad{c} do not have the same dimensions.")) (|plus!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{plus!(c,a,b)} computes the matrix sum \\spad{a + b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have the same dimensions.")) (|copy!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{copy!(c,a)} copies the matrix \\spad{a} into the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions."))) NIL @@ -2744,7 +2744,7 @@ NIL ((|constructor| (NIL "This domain implements the notion of optional value,{} where a computation may fail to produce expected value.")) (|nothing| (($) "\\spad{nothing} represents failure or absence of value.")) (|autoCoerce| ((|#1| $) "\\spad{autoCoerce} is a courtesy coercion function used by the compiler in case it knows that \\spad{`x'} really is a \\spadtype{T}.")) (|case| (((|Boolean|) $ (|[\|\|]| |nothing|)) "\\spad{x case nothing} holds if the value for \\spad{x} is missing.") (((|Boolean|) $ (|[\|\|]| |#1|)) "\\spad{x case T} returns \\spad{true} if \\spad{x} is actually a data of type \\spad{T}.")) (|just| (($ |#1|) "\\spad{just x} injects the value \\spad{`x'} into \\%."))) NIL NIL -(-704 S -2117 FLAF FLAS) +(-704 S -1959 FLAF FLAS) ((|constructor| (NIL "\\indented{1}{\\spadtype{MultiVariableCalculusFunctions} Package provides several} \\indented{1}{functions for multivariable calculus.} These include gradient,{} hessian and jacobian,{} divergence and laplacian. Various forms for banded and sparse storage of matrices are included.")) (|bandedJacobian| (((|Matrix| |#2|) |#3| |#4| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{bandedJacobian(vf,xlist,kl,ku)} computes the jacobian,{} the matrix of first partial derivatives,{} of the vector field \\spad{vf},{} \\spad{vf} a vector function of the variables listed in \\spad{xlist},{} \\spad{kl} is the number of nonzero subdiagonals,{} \\spad{ku} is the number of nonzero superdiagonals,{} kl+ku+1 being actual bandwidth. Stores the nonzero band in a matrix,{} dimensions 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 LAPACK/NAG-\\spad{F07} conventions.)")) (|jacobian| (((|Matrix| |#2|) |#3| |#4|) "\\spad{jacobian(vf,xlist)} computes the jacobian,{} the matrix of first partial derivatives,{} of the vector field \\spad{vf},{} \\spad{vf} a vector function of the variables listed in \\spad{xlist}.")) (|bandedHessian| (((|Matrix| |#2|) |#2| |#4| (|NonNegativeInteger|)) "\\spad{bandedHessian(v,xlist,k)} computes the hessian,{} the matrix of second partial derivatives,{} of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist},{} \\spad{k} is the semi-bandwidth,{} the number of nonzero subdiagonals,{} 2*k+1 being actual bandwidth. Stores the nonzero band in lower triangle in a matrix,{} dimensions \\spad{k+1} by \\#xlist,{} whose rows are the vectors formed by diagonal,{} subdiagonal,{} etc. of the real,{} full-matrix,{} hessian. (The notation conforms to LAPACK/NAG-\\spad{F07} conventions.)")) (|hessian| (((|Matrix| |#2|) |#2| |#4|) "\\spad{hessian(v,xlist)} computes the hessian,{} the matrix of second partial derivatives,{} of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist}.")) (|laplacian| ((|#2| |#2| |#4|) "\\spad{laplacian(v,xlist)} computes the laplacian of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist}.")) (|divergence| ((|#2| |#3| |#4|) "\\spad{divergence(vf,xlist)} computes the divergence of the vector field \\spad{vf},{} \\spad{vf} a vector function of the variables listed in \\spad{xlist}.")) (|gradient| (((|Vector| |#2|) |#2| |#4|) "\\spad{gradient(v,xlist)} computes the gradient,{} the vector of first partial derivatives,{} of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist}."))) NIL NIL @@ -2754,11 +2754,11 @@ NIL NIL (-706) ((|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"))) -((-4456 . T) (-4461 |has| (-711) (-374)) (-4455 |has| (-711) (-374)) (-2648 . T) (-4462 |has| (-711) (-6 -4462)) (-4459 |has| (-711) (-6 -4459)) ((-4465 "*") . T) (-4457 . T) (-4458 . T) (-4460 . T)) -((|HasCategory| (-711) (QUOTE (-148))) (|HasCategory| (-711) (QUOTE (-146))) (|HasCategory| (-711) (LIST (QUOTE -1058) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-711) (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| (-711) (QUOTE (-379))) (|HasCategory| (-711) (QUOTE (-374))) (-3794 (|HasCategory| (-711) (LIST (QUOTE -1058) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-711) (QUOTE (-374)))) (|HasCategory| (-711) (LIST (QUOTE -916) (QUOTE (-1196)))) (|HasCategory| (-711) (QUOTE (-238))) (|HasCategory| (-711) (QUOTE (-237))) (-3794 (-12 (|HasCategory| (-711) (LIST (QUOTE -916) (QUOTE (-1196)))) (|HasCategory| (-711) (QUOTE (-374)))) (|HasCategory| (-711) (LIST (QUOTE -918) (QUOTE (-1196))))) (-3794 (|HasCategory| (-711) (QUOTE (-374))) (|HasCategory| (-711) (QUOTE (-360)))) (|HasCategory| (-711) (QUOTE (-360))) (|HasCategory| (-711) (LIST (QUOTE -296) (QUOTE (-711)) (QUOTE (-711)))) (|HasCategory| (-711) (LIST (QUOTE -319) (QUOTE (-711)))) (|HasCategory| (-711) (LIST (QUOTE -526) (QUOTE (-1196)) (QUOTE (-711)))) (|HasCategory| (-711) (LIST (QUOTE -900) (QUOTE (-576)))) (|HasCategory| (-711) (LIST (QUOTE -900) (QUOTE (-390)))) (|HasCategory| (-711) (LIST (QUOTE -626) (LIST (QUOTE -906) (QUOTE (-576))))) (|HasCategory| (-711) (LIST (QUOTE -626) (LIST (QUOTE -906) (QUOTE (-390))))) (-3794 (|HasCategory| (-711) (QUOTE (-317))) (|HasCategory| (-711) (QUOTE (-374))) (|HasCategory| (-711) (QUOTE (-360)))) (|HasCategory| (-711) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-711) (QUOTE (-1042))) (|HasCategory| (-711) (QUOTE (-1222))) (-12 (|HasCategory| (-711) (QUOTE (-1022))) (|HasCategory| (-711) (QUOTE (-1222)))) (-3794 (-12 (|HasCategory| (-711) (QUOTE (-317))) (|HasCategory| (-711) (QUOTE (-927)))) (|HasCategory| (-711) (QUOTE (-374))) (-12 (|HasCategory| (-711) (QUOTE (-360))) (|HasCategory| (-711) (QUOTE (-927))))) (-3794 (-12 (|HasCategory| (-711) (QUOTE (-317))) (|HasCategory| (-711) (QUOTE (-927)))) (-12 (|HasCategory| (-711) (QUOTE (-374))) (|HasCategory| (-711) (QUOTE (-927)))) (-12 (|HasCategory| (-711) (QUOTE (-360))) (|HasCategory| (-711) (QUOTE (-927))))) (|HasCategory| (-711) (QUOTE (-557))) (-12 (|HasCategory| (-711) (QUOTE (-1080))) (|HasCategory| (-711) (QUOTE (-1222)))) (|HasCategory| (-711) (QUOTE (-1080))) (|HasCategory| (-711) (QUOTE (-317))) (|HasCategory| (-711) (QUOTE (-927))) (-3794 (-12 (|HasCategory| (-711) (QUOTE (-317))) (|HasCategory| (-711) (QUOTE (-927)))) (|HasCategory| (-711) (QUOTE (-374)))) (-3794 (-12 (|HasCategory| (-711) (QUOTE (-238))) (|HasCategory| (-711) (QUOTE (-374)))) (|HasCategory| (-711) (QUOTE (-237)))) (-3794 (-12 (|HasCategory| (-711) (QUOTE (-317))) (|HasCategory| (-711) (QUOTE (-927)))) (|HasCategory| (-711) (QUOTE (-568)))) (-12 (|HasCategory| (-711) (QUOTE (-237))) (|HasCategory| (-711) (QUOTE (-374)))) (-12 (|HasCategory| (-711) (LIST (QUOTE -918) (QUOTE (-1196)))) (|HasCategory| (-711) (QUOTE (-374)))) (-12 (|HasCategory| (-711) (QUOTE (-238))) (|HasCategory| (-711) (QUOTE (-374)))) (-12 (|HasCategory| (-711) (LIST (QUOTE -916) (QUOTE (-1196)))) (|HasCategory| (-711) (QUOTE (-374)))) (|HasCategory| (-711) (LIST (QUOTE -1058) (QUOTE (-576)))) (|HasCategory| (-711) (QUOTE (-568))) (|HasAttribute| (-711) (QUOTE -4462)) (|HasAttribute| (-711) (QUOTE -4459)) (-12 (|HasCategory| (-711) (QUOTE (-317))) (|HasCategory| (-711) (QUOTE (-927)))) (|HasCategory| (-711) (LIST (QUOTE -918) (QUOTE (-1196)))) (-3794 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-711) (QUOTE (-317))) (|HasCategory| (-711) (QUOTE (-927)))) (|HasCategory| (-711) (QUOTE (-146)))) (-3794 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-711) (QUOTE (-317))) (|HasCategory| (-711) (QUOTE (-927)))) (|HasCategory| (-711) (QUOTE (-360))))) +((-4457 . T) (-4462 |has| (-711) (-374)) (-4456 |has| (-711) (-374)) (-4177 . T) (-4463 |has| (-711) (-6 -4463)) (-4460 |has| (-711) (-6 -4460)) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) +((|HasCategory| (-711) (QUOTE (-148))) (|HasCategory| (-711) (QUOTE (-146))) (|HasCategory| (-711) (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-711) (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| (-711) (QUOTE (-379))) (|HasCategory| (-711) (QUOTE (-374))) (-2758 (|HasCategory| (-711) (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-711) (QUOTE (-374)))) (|HasCategory| (-711) (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| (-711) (QUOTE (-238))) (|HasCategory| (-711) (QUOTE (-237))) (-2758 (-12 (|HasCategory| (-711) (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| (-711) (QUOTE (-374)))) (|HasCategory| (-711) (LIST (QUOTE -919) (QUOTE (-1197))))) (-2758 (|HasCategory| (-711) (QUOTE (-374))) (|HasCategory| (-711) (QUOTE (-360)))) (|HasCategory| (-711) (QUOTE (-360))) (|HasCategory| (-711) (LIST (QUOTE -296) (QUOTE (-711)) (QUOTE (-711)))) (|HasCategory| (-711) (LIST (QUOTE -319) (QUOTE (-711)))) (|HasCategory| (-711) (LIST (QUOTE -526) (QUOTE (-1197)) (QUOTE (-711)))) (|HasCategory| (-711) (LIST (QUOTE -901) (QUOTE (-576)))) (|HasCategory| (-711) (LIST (QUOTE -901) (QUOTE (-390)))) (|HasCategory| (-711) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576))))) (|HasCategory| (-711) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390))))) (-2758 (|HasCategory| (-711) (QUOTE (-317))) (|HasCategory| (-711) (QUOTE (-374))) (|HasCategory| (-711) (QUOTE (-360)))) (|HasCategory| (-711) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-711) (QUOTE (-1043))) (|HasCategory| (-711) (QUOTE (-1223))) (-12 (|HasCategory| (-711) (QUOTE (-1023))) (|HasCategory| (-711) (QUOTE (-1223)))) (-2758 (-12 (|HasCategory| (-711) (QUOTE (-317))) (|HasCategory| (-711) (QUOTE (-928)))) (|HasCategory| (-711) (QUOTE (-374))) (-12 (|HasCategory| (-711) (QUOTE (-360))) (|HasCategory| (-711) (QUOTE (-928))))) (-2758 (-12 (|HasCategory| (-711) (QUOTE (-317))) (|HasCategory| (-711) (QUOTE (-928)))) (-12 (|HasCategory| (-711) (QUOTE (-374))) (|HasCategory| (-711) (QUOTE (-928)))) (-12 (|HasCategory| (-711) (QUOTE (-360))) (|HasCategory| (-711) (QUOTE (-928))))) (|HasCategory| (-711) (QUOTE (-557))) (-12 (|HasCategory| (-711) (QUOTE (-1081))) (|HasCategory| (-711) (QUOTE (-1223)))) (|HasCategory| (-711) (QUOTE (-1081))) (|HasCategory| (-711) (QUOTE (-317))) (|HasCategory| (-711) (QUOTE (-928))) (-2758 (-12 (|HasCategory| (-711) (QUOTE (-317))) (|HasCategory| (-711) (QUOTE (-928)))) (|HasCategory| (-711) (QUOTE (-374)))) (-2758 (-12 (|HasCategory| (-711) (QUOTE (-238))) (|HasCategory| (-711) (QUOTE (-374)))) (|HasCategory| (-711) (QUOTE (-237)))) (-2758 (-12 (|HasCategory| (-711) (QUOTE (-317))) (|HasCategory| (-711) (QUOTE (-928)))) (|HasCategory| (-711) (QUOTE (-568)))) (-12 (|HasCategory| (-711) (QUOTE (-237))) (|HasCategory| (-711) (QUOTE (-374)))) (-12 (|HasCategory| (-711) (LIST (QUOTE -919) (QUOTE (-1197)))) (|HasCategory| (-711) (QUOTE (-374)))) (-12 (|HasCategory| (-711) (QUOTE (-238))) (|HasCategory| (-711) (QUOTE (-374)))) (-12 (|HasCategory| (-711) (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| (-711) (QUOTE (-374)))) (|HasCategory| (-711) (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| (-711) (QUOTE (-568))) (|HasAttribute| (-711) (QUOTE -4463)) (|HasAttribute| (-711) (QUOTE -4460)) (-12 (|HasCategory| (-711) (QUOTE (-317))) (|HasCategory| (-711) (QUOTE (-928)))) (|HasCategory| (-711) (LIST (QUOTE -919) (QUOTE (-1197)))) (-2758 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-711) (QUOTE (-317))) (|HasCategory| (-711) (QUOTE (-928)))) (|HasCategory| (-711) (QUOTE (-146)))) (-2758 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-711) (QUOTE (-317))) (|HasCategory| (-711) (QUOTE (-928)))) (|HasCategory| (-711) (QUOTE (-360))))) (-707 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}."))) -((-4464 . T)) +((-4465 . T)) NIL (-708 U) ((|constructor| (NIL "This package supports factorization and gcds of univariate polynomials over the integers modulo different primes. The inputs are given as polynomials over the integers with the prime passed explicitly as an extra argument.")) (|exptMod| ((|#1| |#1| (|Integer|) |#1| (|Integer|)) "\\spad{exptMod(f,n,g,p)} raises the univariate polynomial \\spad{f} to the \\spad{n}th power modulo the polynomial \\spad{g} and the prime \\spad{p}.")) (|separateFactors| (((|List| |#1|) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|)))) (|Integer|)) "\\spad{separateFactors(ddl, p)} refines the distinct degree factorization produced by \\spadfunFrom{ddFact}{ModularDistinctDegreeFactorizer} to give a complete list of factors.")) (|ddFact| (((|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|)))) |#1| (|Integer|)) "\\spad{ddFact(f,p)} computes a distinct degree factorization of the polynomial \\spad{f} modulo the prime \\spad{p},{} \\spadignore{i.e.} such that each factor is a product of irreducibles of the same degrees. The input polynomial \\spad{f} is assumed to be square-free modulo \\spad{p}.")) (|factor| (((|List| |#1|) |#1| (|Integer|)) "\\spad{factor(f1,p)} returns the list of factors of the univariate polynomial \\spad{f1} modulo the integer prime \\spad{p}. Error: if \\spad{f1} is not square-free modulo \\spad{p}.")) (|linears| ((|#1| |#1| (|Integer|)) "\\spad{linears(f,p)} returns the product of all the linear factors of \\spad{f} modulo \\spad{p}. Potentially incorrect result if \\spad{f} is not square-free modulo \\spad{p}.")) (|gcd| ((|#1| |#1| |#1| (|Integer|)) "\\spad{gcd(f1,f2,p)} computes the \\spad{gcd} of the univariate polynomials \\spad{f1} and \\spad{f2} modulo the integer prime \\spad{p}."))) @@ -2768,13 +2768,13 @@ NIL ((|constructor| (NIL "\\indented{1}{<description of package>} Author: Jim Wen Date Created: \\spad{??} Date Last Updated: October 1991 by Jon Steinbach Keywords: Examples: References:")) (|ptFunc| (((|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) "\\spad{ptFunc(a,b,c,d)} is an internal function exported in order to compile packages.")) (|meshPar1Var| (((|ThreeSpace| (|DoubleFloat|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar1Var(s,t,u,f,s1,l)} \\undocumented")) (|meshFun2Var| (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Union| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "undefined") (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshFun2Var(f,g,s1,s2,l)} \\undocumented")) (|meshPar2Var| (((|ThreeSpace| (|DoubleFloat|)) (|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(sp,f,s1,s2,l)} \\undocumented") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(f,s1,s2,l)} \\undocumented") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Union| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "undefined") (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(f,g,h,j,s1,s2,l)} \\undocumented"))) NIL NIL -(-710 OV E -2117 PG) +(-710 OV E -1959 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 (-711) ((|constructor| (NIL "A domain which models the floating point representation used by machines in the AXIOM-NAG link.")) (|changeBase| (($ (|Integer|) (|Integer|) (|PositiveInteger|)) "\\spad{changeBase(exp,man,base)} \\undocumented{}")) (|exponent| (((|Integer|) $) "\\spad{exponent(u)} returns the exponent of \\spad{u}")) (|mantissa| (((|Integer|) $) "\\spad{mantissa(u)} returns the mantissa of \\spad{u}")) (|coerce| (($ (|MachineInteger|)) "\\spad{coerce(u)} transforms a MachineInteger into a MachineFloat") (((|Float|) $) "\\spad{coerce(u)} transforms a MachineFloat to a standard Float")) (|minimumExponent| (((|Integer|)) "\\spad{minimumExponent()} returns the minimum exponent in the model") (((|Integer|) (|Integer|)) "\\spad{minimumExponent(e)} sets the minimum exponent in the model to \\spad{e}")) (|maximumExponent| (((|Integer|)) "\\spad{maximumExponent()} returns the maximum exponent in the model") (((|Integer|) (|Integer|)) "\\spad{maximumExponent(e)} sets the maximum exponent in the model to \\spad{e}")) (|base| (((|PositiveInteger|) (|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}"))) -((-2641 . T) (-4455 . T) (-4461 . T) (-4456 . T) ((-4465 "*") . T) (-4457 . T) (-4458 . T) (-4460 . T)) +((-4165 . T) (-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-712 R) ((|constructor| (NIL "\\indented{1}{Modular hermitian row reduction.} Author: Manuel Bronstein Date Created: 22 February 1989 Date Last Updated: 24 November 1993 Keywords: matrix,{} reduction.")) (|normalizedDivide| (((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|) "\\spad{normalizedDivide(n,d)} returns a normalized quotient and remainder such that consistently unique representatives for the residue class are chosen,{} \\spadignore{e.g.} positive remainders")) (|rowEchelonLocal| (((|Matrix| |#1|) (|Matrix| |#1|) |#1| |#1|) "\\spad{rowEchelonLocal(m, d, p)} computes the row-echelon form of \\spad{m} concatenated with \\spad{d} times the identity matrix over a local ring where \\spad{p} is the only prime.")) (|rowEchLocal| (((|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{rowEchLocal(m,p)} computes a modular row-echelon form of \\spad{m},{} finding an appropriate modulus over a local ring where \\spad{p} is the only prime.")) (|rowEchelon| (((|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{rowEchelon(m, d)} computes a modular row-echelon form mod \\spad{d} of \\indented{3}{[\\spad{d}\\space{5}]} \\indented{3}{[\\space{2}\\spad{d}\\space{3}]} \\indented{3}{[\\space{4}. ]} \\indented{3}{[\\space{5}\\spad{d}]} \\indented{3}{[\\space{3}\\spad{M}\\space{2}]} where \\spad{M = m mod d}.")) (|rowEch| (((|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{rowEch(m)} computes a modular row-echelon form of \\spad{m},{} finding an appropriate modulus."))) @@ -2782,7 +2782,7 @@ NIL NIL (-713) ((|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}"))) -((-4462 . T) (-4461 . T) (-4456 . T) ((-4465 "*") . T) (-4457 . T) (-4458 . T) (-4460 . T)) +((-4463 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-714 S D1 D2 I) ((|constructor| (NIL "transforms top-level objects into compiled functions.")) (|compiledFunction| (((|Mapping| |#4| |#2| |#3|) |#1| (|Symbol|) (|Symbol|)) "\\spad{compiledFunction(expr,x,y)} returns a function \\spad{f: (D1, D2) -> I} defined by \\spad{f(x, y) == expr}. Function \\spad{f} is compiled and directly applicable to objects of type \\spad{(D1, D2)}")) (|binaryFunction| (((|Mapping| |#4| |#2| |#3|) (|Symbol|)) "\\spad{binaryFunction(s)} is a local function"))) @@ -2800,7 +2800,7 @@ NIL ((|constructor| (NIL "MakeRecord is used internally by the interpreter to create record types which are used for doing parallel iterations on streams.")) (|makeRecord| (((|Record| (|:| |part1| |#1|) (|:| |part2| |#2|)) |#1| |#2|) "\\spad{makeRecord(a,b)} creates a record object with type Record(part1:S,{} part2:R),{} where part1 is \\spad{a} and part2 is \\spad{b}."))) NIL NIL -(-718 S -3155 I) +(-718 S -2018 I) ((|constructor| (NIL "transforms top-level objects into compiled functions.")) (|compiledFunction| (((|Mapping| |#3| |#2|) |#1| (|Symbol|)) "\\spad{compiledFunction(expr, x)} returns a function \\spad{f: D -> I} defined by \\spad{f(x) == expr}. Function \\spad{f} is compiled and directly applicable to objects of type \\spad{D}.")) (|unaryFunction| (((|Mapping| |#3| |#2|) (|Symbol|)) "\\spad{unaryFunction(a)} is a local function"))) NIL NIL @@ -2810,7 +2810,7 @@ NIL NIL (-720 R) ((|constructor| (NIL "This is the category of linear operator rings with one generator. The generator is not named by the category but can always be constructed as \\spad{monomial(1,1)}. \\blankline For convenience,{} call the generator \\spad{G}. Then each value is equal to \\indented{4}{\\spad{sum(a(i)*G**i, i = 0..n)}} for some unique \\spad{n} and \\spad{a(i)} in \\spad{R}. \\blankline Note that multiplication is not necessarily commutative. In fact,{} if \\spad{a} is in \\spad{R},{} it is quite normal to have \\spad{a*G \\~= G*a}.")) (|monomial| (($ |#1| (|NonNegativeInteger|)) "\\spad{monomial(c,k)} produces \\spad{c} times the \\spad{k}-th power of the generating operator,{} \\spad{monomial(1,1)}.")) (|coefficient| ((|#1| $ (|NonNegativeInteger|)) "\\spad{coefficient(l,k)} is \\spad{a(k)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|reductum| (($ $) "\\spad{reductum(l)} is \\spad{l - monomial(a(n),n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(l)} is \\spad{a(n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|minimumDegree| (((|NonNegativeInteger|) $) "\\spad{minimumDegree(l)} is the smallest \\spad{k} such that \\spad{a(k) \\~= 0} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(l)} is \\spad{n} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}"))) -((-4457 . T) (-4458 . T) (-4460 . T)) +((-4458 . T) (-4459 . T) (-4461 . T)) NIL (-721 R1 UP1 UPUP1 R2 UP2 UPUP2) ((|constructor| (NIL "Lifting of a map through 2 levels of polynomials.")) (|map| ((|#6| (|Mapping| |#4| |#1|) |#3|) "\\spad{map(f, p)} lifts \\spad{f} to the domain of \\spad{p} then applies it to \\spad{p}."))) @@ -2820,25 +2820,25 @@ NIL ((|constructor| (NIL "\\spadtype{MathMLFormat} provides a coercion from \\spadtype{OutputForm} to MathML format.")) (|display| (((|Void|) (|String|)) "prints the string returned by coerce,{} adding <math ...> tags.")) (|exprex| (((|String|) (|OutputForm|)) "coverts \\spadtype{OutputForm} to \\spadtype{String} with the structure preserved with braces. Actually this is not quite accurate. The function \\spadfun{precondition} is first applied to the \\spadtype{OutputForm} expression before \\spadfun{exprex}. The raw \\spadtype{OutputForm} and the nature of the \\spadfun{precondition} function is still obscure to me at the time of this writing (2007-02-14).")) (|coerceL| (((|String|) (|OutputForm|)) "coerceS(\\spad{o}) changes \\spad{o} in the standard output format to MathML format and displays result as one long string.")) (|coerceS| (((|String|) (|OutputForm|)) "\\spad{coerceS(o)} changes \\spad{o} in the standard output format to MathML format and displays formatted result.")) (|coerce| (((|String|) (|OutputForm|)) "coerceS(\\spad{o}) changes \\spad{o} in the standard output format to MathML format."))) NIL NIL -(-723 R |Mod| -3735 -2144 |exactQuo|) +(-723 R |Mod| -2391 -4335 |exactQuo|) ((|constructor| (NIL "\\indented{1}{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") $ $) "\\spad{exQuo(x,y)} \\undocumented")) (|reduce| (($ |#1| |#2|) "\\spad{reduce(r,m)} \\undocumented")) (|coerce| ((|#1| $) "\\spad{coerce(x)} \\undocumented")) (|modulus| ((|#2| $) "\\spad{modulus(x)} \\undocumented"))) -((-4455 . T) (-4461 . T) (-4456 . T) ((-4465 "*") . T) (-4457 . T) (-4458 . T) (-4460 . T)) +((-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-724 R |Rep|) ((|constructor| (NIL "This package \\undocumented")) (|frobenius| (($ $) "\\spad{frobenius(x)} \\undocumented")) (|computePowers| (((|PrimitiveArray| $)) "\\spad{computePowers()} \\undocumented")) (|pow| (((|PrimitiveArray| $)) "\\spad{pow()} \\undocumented")) (|An| (((|Vector| |#1|) $) "\\spad{An(x)} \\undocumented")) (|UnVectorise| (($ (|Vector| |#1|)) "\\spad{UnVectorise(v)} \\undocumented")) (|Vectorise| (((|Vector| |#1|) $) "\\spad{Vectorise(x)} \\undocumented")) (|lift| ((|#2| $) "\\spad{lift(x)} \\undocumented")) (|reduce| (($ |#2|) "\\spad{reduce(x)} \\undocumented")) (|modulus| ((|#2|) "\\spad{modulus()} \\undocumented")) (|setPoly| ((|#2| |#2|) "\\spad{setPoly(x)} \\undocumented"))) -(((-4465 "*") |has| |#1| (-174)) (-4456 |has| |#1| (-568)) (-4459 |has| |#1| (-374)) (-4461 |has| |#1| (-6 -4461)) (-4458 . T) (-4457 . T) (-4460 . T)) -((|HasCategory| |#1| (QUOTE (-927))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-3794 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasCategory| (-1102) (LIST (QUOTE -900) (QUOTE (-390)))) (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-390))))) (-12 (|HasCategory| (-1102) (LIST (QUOTE -900) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-576))))) (-12 (|HasCategory| (-1102) (LIST (QUOTE -626) (LIST (QUOTE -906) (QUOTE (-390))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -906) (QUOTE (-390)))))) (-12 (|HasCategory| (-1102) (LIST (QUOTE -626) (LIST (QUOTE -906) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -906) (QUOTE (-576)))))) (-12 (|HasCategory| (-1102) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1058) (QUOTE (-576)))) (-3794 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1058) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#1| (LIST (QUOTE -1058) (LIST (QUOTE -419) (QUOTE (-576))))) (-3794 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-927)))) (-3794 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-927)))) (-3794 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-927)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-1172))) (|HasCategory| |#1| (LIST (QUOTE -918) (QUOTE (-1196)))) (|HasCategory| |#1| (LIST (QUOTE -916) (QUOTE (-1196)))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-360))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-238))) (|HasAttribute| |#1| (QUOTE -4461)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-927)))) (-3794 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-927)))) (|HasCategory| |#1| (QUOTE (-146))))) +(((-4466 "*") |has| |#1| (-174)) (-4457 |has| |#1| (-568)) (-4460 |has| |#1| (-374)) (-4462 |has| |#1| (-6 -4462)) (-4459 . T) (-4458 . T) (-4461 . T)) +((|HasCategory| |#1| (QUOTE (-928))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-2758 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasCategory| (-1103) (LIST (QUOTE -901) (QUOTE (-390)))) (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-390))))) (-12 (|HasCategory| (-1103) (LIST (QUOTE -901) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-576))))) (-12 (|HasCategory| (-1103) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390)))))) (-12 (|HasCategory| (-1103) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576)))))) (-12 (|HasCategory| (-1103) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576)))) (-2758 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (-2758 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-928)))) (-2758 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-928)))) (-2758 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-928)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-1173))) (|HasCategory| |#1| (LIST (QUOTE -919) (QUOTE (-1197)))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-360))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-238))) (|HasAttribute| |#1| (QUOTE -4462)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-928)))) (-2758 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-928)))) (|HasCategory| |#1| (QUOTE (-146))))) (-725 IS E |ff|) ((|constructor| (NIL "This package \\undocumented")) (|construct| (($ |#1| |#2|) "\\spad{construct(i,e)} \\undocumented")) (|index| ((|#1| $) "\\spad{index(x)} \\undocumented")) (|exponent| ((|#2| $) "\\spad{exponent(x)} \\undocumented"))) NIL NIL (-726 R M) ((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#1| (|FreeGroup| (|BasicOperator|))) "\\spad{makeop should} be local but conditional")) (|opeval| ((|#2| (|BasicOperator|) |#2|) "\\spad{opeval should} be local but conditional")) (** (($ $ (|Integer|)) "\\spad{op**n} \\undocumented") (($ (|BasicOperator|) (|Integer|)) "\\spad{op**n} \\undocumented")) (|evaluateInverse| (($ $ (|Mapping| |#2| |#2|)) "\\spad{evaluateInverse(x,f)} \\undocumented")) (|evaluate| (($ $ (|Mapping| |#2| |#2|)) "\\spad{evaluate(f, u +-> g u)} attaches the map \\spad{g} to \\spad{f}. \\spad{f} must be a basic operator \\spad{g} MUST be additive,{} \\spadignore{i.e.} \\spad{g(a + b) = g(a) + g(b)} for any \\spad{a},{} \\spad{b} in \\spad{M}. This implies that \\spad{g(n a) = n g(a)} for any \\spad{a} in \\spad{M} and integer \\spad{n > 0}.")) (|conjug| ((|#1| |#1|) "\\spad{conjug(x)}should be local but conditional")) (|adjoint| (($ $ $) "\\spad{adjoint(op1, op2)} sets the adjoint of \\spad{op1} to be op2. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) -((-4458 |has| |#1| (-174)) (-4457 |has| |#1| (-174)) (-4460 . T)) +((-4459 |has| |#1| (-174)) (-4458 |has| |#1| (-174)) (-4461 . T)) ((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148)))) -(-727 R |Mod| -3735 -2144 |exactQuo|) +(-727 R |Mod| -2391 -4335 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\spad{inv(x)} \\undocumented")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} \\undocumented")) (|exQuo| (((|Union| $ "failed") $ $) "\\spad{exQuo(x,y)} \\undocumented")) (|reduce| (($ |#1| |#2|) "\\spad{reduce(r,m)} \\undocumented")) (|coerce| ((|#1| $) "\\spad{coerce(x)} \\undocumented")) (|modulus| ((|#2| $) "\\spad{modulus(x)} \\undocumented"))) -((-4460 . T)) +((-4461 . T)) NIL (-728 S R) ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) @@ -2846,11 +2846,11 @@ NIL NIL (-729 R) ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) -((-4458 . T) (-4457 . T)) +((-4459 . T) (-4458 . T)) NIL -(-730 -2117) +(-730 -1959) ((|constructor| (NIL "\\indented{1}{MoebiusTransform(\\spad{F}) is the domain of fractional linear (Moebius)} transformations over \\spad{F}.")) (|eval| (((|OnePointCompletion| |#1|) $ (|OnePointCompletion| |#1|)) "\\spad{eval(m,x)} returns \\spad{(a*x + b)/(c*x + d)} where \\spad{m = moebius(a,b,c,d)} (see \\spadfunFrom{moebius}{MoebiusTransform}).") ((|#1| $ |#1|) "\\spad{eval(m,x)} returns \\spad{(a*x + b)/(c*x + d)} where \\spad{m = moebius(a,b,c,d)} (see \\spadfunFrom{moebius}{MoebiusTransform}).")) (|recip| (($ $) "\\spad{recip(m)} = recip() * \\spad{m}") (($) "\\spad{recip()} returns \\spad{matrix [[0,1],[1,0]]} representing the map \\spad{x -> 1 / x}.")) (|scale| (($ $ |#1|) "\\spad{scale(m,h)} returns \\spad{scale(h) * m} (see \\spadfunFrom{shift}{MoebiusTransform}).") (($ |#1|) "\\spad{scale(k)} returns \\spad{matrix [[k,0],[0,1]]} representing the map \\spad{x -> k * x}.")) (|shift| (($ $ |#1|) "\\spad{shift(m,h)} returns \\spad{shift(h) * m} (see \\spadfunFrom{shift}{MoebiusTransform}).") (($ |#1|) "\\spad{shift(k)} returns \\spad{matrix [[1,k],[0,1]]} representing the map \\spad{x -> x + k}.")) (|moebius| (($ |#1| |#1| |#1| |#1|) "\\spad{moebius(a,b,c,d)} returns \\spad{matrix [[a,b],[c,d]]}."))) -((-4460 . T)) +((-4461 . T)) NIL (-731 S) ((|constructor| (NIL "Monad is the class of all multiplicative monads,{} \\spadignore{i.e.} sets with a binary operation.")) (** (($ $ (|PositiveInteger|)) "\\spad{a**n} returns the \\spad{n}\\spad{-}th power of \\spad{a},{} defined by repeated squaring.")) (|leftPower| (($ $ (|PositiveInteger|)) "\\spad{leftPower(a,n)} returns the \\spad{n}\\spad{-}th left power of \\spad{a},{} \\spadignore{i.e.} \\spad{leftPower(a,n) := a * leftPower(a,n-1)} and \\spad{leftPower(a,1) := a}.")) (|rightPower| (($ $ (|PositiveInteger|)) "\\spad{rightPower(a,n)} returns the \\spad{n}\\spad{-}th right power of \\spad{a},{} \\spadignore{i.e.} \\spad{rightPower(a,n) := rightPower(a,n-1) * a} and \\spad{rightPower(a,1) := a}.")) (* (($ $ $) "\\spad{a*b} is the product of \\spad{a} and \\spad{b} in a set with a binary operation."))) @@ -2874,7 +2874,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-360))) (|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-379)))) (-736 R UP) ((|constructor| (NIL "A \\spadtype{MonogenicAlgebra} is an algebra of finite rank which can be generated by a single element.")) (|derivationCoordinates| (((|Matrix| |#1|) (|Vector| $) (|Mapping| |#1| |#1|)) "\\spad{derivationCoordinates(b, ')} returns \\spad{M} such that \\spad{b' = M b}.")) (|lift| ((|#2| $) "\\spad{lift(z)} returns a minimal degree univariate polynomial up such that \\spad{z=reduce up}.")) (|convert| (($ |#2|) "\\spad{convert(up)} converts the univariate polynomial \\spad{up} to an algebra element,{} reducing by the \\spad{definingPolynomial()} if necessary.")) (|reduce| (((|Union| $ "failed") (|Fraction| |#2|)) "\\spad{reduce(frac)} converts the fraction \\spad{frac} to an algebra element.") (($ |#2|) "\\spad{reduce(up)} converts the univariate polynomial \\spad{up} to an algebra element,{} reducing by the \\spad{definingPolynomial()} if necessary.")) (|definingPolynomial| ((|#2|) "\\spad{definingPolynomial()} returns the minimal polynomial which \\spad{generator()} satisfies.")) (|generator| (($) "\\spad{generator()} returns the generator for this domain."))) -((-4456 |has| |#1| (-374)) (-4461 |has| |#1| (-374)) (-4455 |has| |#1| (-374)) ((-4465 "*") . T) (-4457 . T) (-4458 . T) (-4460 . T)) +((-4457 |has| |#1| (-374)) (-4462 |has| |#1| (-374)) (-4456 |has| |#1| (-374)) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-737 S) ((|constructor| (NIL "The class of multiplicative monoids,{} \\spadignore{i.e.} semigroups with a multiplicative identity element. \\blankline")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} tries to compute the multiplicative inverse for \\spad{x} or \"failed\" if it cannot find the inverse (see unitsKnown).")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (|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."))) @@ -2884,7 +2884,7 @@ NIL ((|constructor| (NIL "The class of multiplicative monoids,{} \\spadignore{i.e.} semigroups with a multiplicative identity element. \\blankline")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} tries to compute the multiplicative inverse for \\spad{x} or \"failed\" if it cannot find the inverse (see unitsKnown).")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (|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 -(-739 -2117 UP) +(-739 -1959 UP) ((|constructor| (NIL "Tools for handling monomial extensions.")) (|decompose| (((|Record| (|:| |poly| |#2|) (|:| |normal| (|Fraction| |#2|)) (|:| |special| (|Fraction| |#2|))) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{decompose(f, D)} returns \\spad{[p,n,s]} such that \\spad{f = p+n+s},{} all the squarefree factors of \\spad{denom(n)} are normal \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{denom(s)} is special \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} and \\spad{n} and \\spad{s} are proper fractions (no pole at infinity). \\spad{D} is the derivation to use.")) (|normalDenom| ((|#2| (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{normalDenom(f, D)} returns the product of all the normal factors of \\spad{denom(f)}. \\spad{D} is the derivation to use.")) (|splitSquarefree| (((|Record| (|:| |normal| (|Factored| |#2|)) (|:| |special| (|Factored| |#2|))) |#2| (|Mapping| |#2| |#2|)) "\\spad{splitSquarefree(p, D)} returns \\spad{[n_1 n_2\\^2 ... n_m\\^m, s_1 s_2\\^2 ... s_q\\^q]} such that \\spad{p = n_1 n_2\\^2 ... n_m\\^m s_1 s_2\\^2 ... s_q\\^q},{} each \\spad{n_i} is normal \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D} and each \\spad{s_i} is special \\spad{w}.\\spad{r}.\\spad{t} \\spad{D}. \\spad{D} is the derivation to use.")) (|split| (((|Record| (|:| |normal| |#2|) (|:| |special| |#2|)) |#2| (|Mapping| |#2| |#2|)) "\\spad{split(p, D)} returns \\spad{[n,s]} such that \\spad{p = n s},{} all the squarefree factors of \\spad{n} are normal \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} and \\spad{s} is special \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D}. \\spad{D} is the derivation to use."))) NIL NIL @@ -2902,8 +2902,8 @@ NIL NIL (-743 |vl| R) ((|constructor| (NIL "\\indented{2}{This type is the basic representation of sparse recursive multivariate} polynomials whose variables are from a user specified list of symbols. The ordering is specified by the position of the variable in the list. The coefficient ring may be non commutative,{} but the variables are assumed to commute."))) -(((-4465 "*") |has| |#2| (-174)) (-4456 |has| |#2| (-568)) (-4461 |has| |#2| (-6 -4461)) (-4458 . T) (-4457 . T) (-4460 . T)) -((|HasCategory| |#2| (QUOTE (-927))) (-3794 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-927)))) (-3794 (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-927)))) (-3794 (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-927)))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-174))) (-3794 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-568)))) (-12 (|HasCategory| (-877 |#1|) (LIST (QUOTE -900) (QUOTE (-390)))) (|HasCategory| |#2| (LIST (QUOTE -900) (QUOTE (-390))))) (-12 (|HasCategory| (-877 |#1|) (LIST (QUOTE -900) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -900) (QUOTE (-576))))) (-12 (|HasCategory| (-877 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -906) (QUOTE (-390))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -906) (QUOTE (-390)))))) (-12 (|HasCategory| (-877 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -906) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -906) (QUOTE (-576)))))) (-12 (|HasCategory| (-877 |#1|) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#2| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1058) (QUOTE (-576)))) (-3794 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1058) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#2| (LIST (QUOTE -1058) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (QUOTE (-374))) (|HasAttribute| |#2| (QUOTE -4461)) (|HasCategory| |#2| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-927)))) (-3794 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-927)))) (|HasCategory| |#2| (QUOTE (-146))))) +(((-4466 "*") |has| |#2| (-174)) (-4457 |has| |#2| (-568)) (-4462 |has| |#2| (-6 -4462)) (-4459 . T) (-4458 . T) (-4461 . T)) +((|HasCategory| |#2| (QUOTE (-928))) (-2758 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-928)))) (-2758 (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-928)))) (-2758 (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-928)))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-174))) (-2758 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-568)))) (-12 (|HasCategory| (-878 |#1|) (LIST (QUOTE -901) (QUOTE (-390)))) (|HasCategory| |#2| (LIST (QUOTE -901) (QUOTE (-390))))) (-12 (|HasCategory| (-878 |#1|) (LIST (QUOTE -901) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -901) (QUOTE (-576))))) (-12 (|HasCategory| (-878 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390)))))) (-12 (|HasCategory| (-878 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576)))))) (-12 (|HasCategory| (-878 |#1|) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#2| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1059) (QUOTE (-576)))) (-2758 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#2| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (QUOTE (-374))) (|HasAttribute| |#2| (QUOTE -4462)) (|HasCategory| |#2| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-928)))) (-2758 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-928)))) (|HasCategory| |#2| (QUOTE (-146))))) (-744 E OV R PRF) ((|constructor| (NIL "\\indented{3}{This package exports a factor operation for multivariate polynomials} with coefficients which are rational functions over some ring \\spad{R} over which we can factor. It is used internally by packages such as primary decomposition which need to work with polynomials with rational function coefficients,{} \\spadignore{i.e.} themselves fractions of polynomials.")) (|factor| (((|Factored| |#4|) |#4|) "\\spad{factor(prf)} factors a polynomial with rational function coefficients.")) (|pushuconst| ((|#4| (|Fraction| (|Polynomial| |#3|)) |#2|) "\\spad{pushuconst(r,var)} takes a rational function and raises all occurances of the variable \\spad{var} to the polynomial level.")) (|pushucoef| ((|#4| (|SparseUnivariatePolynomial| (|Polynomial| |#3|)) |#2|) "\\spad{pushucoef(upoly,var)} converts the anonymous univariate polynomial \\spad{upoly} to a polynomial in \\spad{var} over rational functions.")) (|pushup| ((|#4| |#4| |#2|) "\\spad{pushup(prf,var)} raises all occurences of the variable \\spad{var} in the coefficients of the polynomial \\spad{prf} back to the polynomial level.")) (|pushdterm| ((|#4| (|SparseUnivariatePolynomial| |#4|) |#2|) "\\spad{pushdterm(monom,var)} pushes all top level occurences of the variable \\spad{var} into the coefficient domain for the monomial \\spad{monom}.")) (|pushdown| ((|#4| |#4| |#2|) "\\spad{pushdown(prf,var)} pushes all top level occurences of the variable \\spad{var} into the coefficient domain for the polynomial \\spad{prf}.")) (|totalfract| (((|Record| (|:| |sup| (|Polynomial| |#3|)) (|:| |inf| (|Polynomial| |#3|))) |#4|) "\\spad{totalfract(prf)} takes a polynomial whose coefficients are themselves fractions of polynomials and returns a record containing the numerator and denominator resulting from putting \\spad{prf} over a common denominator.")) (|convert| (((|Symbol|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) NIL @@ -2918,16 +2918,16 @@ NIL NIL (-747 R M) ((|constructor| (NIL "\\spadtype{MonoidRing}(\\spad{R},{}\\spad{M}),{} implements the algebra of all maps from the monoid \\spad{M} to the commutative ring \\spad{R} with finite support. Multiplication of two maps \\spad{f} and \\spad{g} is defined to map an element \\spad{c} of \\spad{M} to the (convolution) sum over {\\em f(a)g(b)} such that {\\em ab = c}. Thus \\spad{M} can be identified with a canonical basis and the maps can also be considered as formal linear combinations of the elements in \\spad{M}. Scalar multiples of a basis element are called monomials. A prominent example is the class of polynomials where the monoid is a direct product of the natural numbers with pointwise addition. When \\spad{M} is \\spadtype{FreeMonoid Symbol},{} one gets polynomials in infinitely many non-commuting variables. Another application area is representation theory of finite groups \\spad{G},{} where modules over \\spadtype{MonoidRing}(\\spad{R},{}\\spad{G}) are studied.")) (|reductum| (($ $) "\\spad{reductum(f)} is \\spad{f} minus its leading monomial.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(f)} gives the coefficient of \\spad{f},{} whose corresponding monoid element is the greatest among all those with non-zero coefficients.")) (|leadingMonomial| ((|#2| $) "\\spad{leadingMonomial(f)} gives the monomial of \\spad{f} whose corresponding monoid element is the greatest among all those with non-zero coefficients.")) (|numberOfMonomials| (((|NonNegativeInteger|) $) "\\spad{numberOfMonomials(f)} is the number of non-zero coefficients with respect to the canonical basis.")) (|monomials| (((|List| $) $) "\\spad{monomials(f)} gives the list of all monomials whose sum is \\spad{f}.")) (|coefficients| (((|List| |#1|) $) "\\spad{coefficients(f)} lists all non-zero coefficients.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(f)} tests if \\spad{f} is a single monomial.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,u)} maps function \\spad{fn} onto the coefficients of the non-zero monomials of \\spad{u}.")) (|terms| (((|List| (|Record| (|:| |coef| |#1|) (|:| |monom| |#2|))) $) "\\spad{terms(f)} gives the list of non-zero coefficients combined with their corresponding basis element as records. This is the internal representation.")) (|coerce| (($ (|List| (|Record| (|:| |coef| |#1|) (|:| |monom| |#2|)))) "\\spad{coerce(lt)} converts a list of terms and coefficients to a member of the domain.")) (|coefficient| ((|#1| $ |#2|) "\\spad{coefficient(f,m)} extracts the coefficient of \\spad{m} in \\spad{f} with respect to the canonical basis \\spad{M}.")) (|monomial| (($ |#1| |#2|) "\\spad{monomial(r,m)} creates a scalar multiple of the basis element \\spad{m}."))) -((-4458 |has| |#1| (-174)) (-4457 |has| |#1| (-174)) (-4460 . T)) +((-4459 |has| |#1| (-174)) (-4458 |has| |#1| (-174)) (-4461 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#2| (QUOTE (-379)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-861)))) (-748 S) ((|constructor| (NIL "A multi-set aggregate is a set which keeps track of the multiplicity of its elements."))) -((-4453 . T) (-4464 . T)) +((-4454 . T) (-4465 . T)) NIL (-749 S) ((|constructor| (NIL "A multiset is a set with multiplicities.")) (|remove!| (($ (|Mapping| (|Boolean|) |#1|) $ (|Integer|)) "\\spad{remove!(p,ms,number)} removes destructively at most \\spad{number} copies of elements \\spad{x} such that \\spad{p(x)} is \\spadfun{\\spad{true}} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.") (($ |#1| $ (|Integer|)) "\\spad{remove!(x,ms,number)} removes destructively at most \\spad{number} copies of element \\spad{x} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.")) (|remove| (($ (|Mapping| (|Boolean|) |#1|) $ (|Integer|)) "\\spad{remove(p,ms,number)} removes at most \\spad{number} copies of elements \\spad{x} such that \\spad{p(x)} is \\spadfun{\\spad{true}} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.") (($ |#1| $ (|Integer|)) "\\spad{remove(x,ms,number)} removes at most \\spad{number} copies of element \\spad{x} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.")) (|members| (((|List| |#1|) $) "\\spad{members(ms)} returns a list of the elements of \\spad{ms} {\\em without} their multiplicity. See also \\spadfun{parts}.")) (|multiset| (($ (|List| |#1|)) "\\spad{multiset(ls)} creates a multiset with elements from \\spad{ls}.") (($ |#1|) "\\spad{multiset(s)} creates a multiset with singleton \\spad{s}.") (($) "\\spad{multiset()}\\$\\spad{D} creates an empty multiset of domain \\spad{D}."))) -((-4463 . T) (-4453 . T) (-4464 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1120))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (QUOTE (-1120))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-875)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4464 . T) (-4454 . T) (-4465 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102)))) (-750) ((|constructor| (NIL "\\spadtype{MoreSystemCommands} implements an interface with the system command facility. These are the commands that are issued from source files or the system interpreter and they start with a close parenthesis,{} \\spadignore{e.g.} \\spadsyscom{what} commands.")) (|systemCommand| (((|Void|) (|String|)) "\\spad{systemCommand(cmd)} takes the string \\spadvar{\\spad{cmd}} and passes it to the runtime environment for execution as a system command. Although various things may be printed,{} no usable value is returned."))) NIL @@ -2938,7 +2938,7 @@ NIL NIL (-752 |Coef| |Var|) ((|constructor| (NIL "\\spadtype{MultivariateTaylorSeriesCategory} is the most general multivariate Taylor series category.")) (|integrate| (($ $ |#2|) "\\spad{integrate(f,x)} returns the anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{x} with constant coefficient 1. We may integrate a series when we can divide coefficients by integers.")) (|polynomial| (((|Polynomial| |#1|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{polynomial(f,k1,k2)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (((|Polynomial| |#1|) $ (|NonNegativeInteger|)) "\\spad{polynomial(f,k)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| (((|NonNegativeInteger|) $ |#2| (|NonNegativeInteger|)) "\\spad{order(f,x,n)} returns \\spad{min(n,order(f,x))}.") (((|NonNegativeInteger|) $ |#2|) "\\spad{order(f,x)} returns the order of \\spad{f} viewed as a series in \\spad{x} may result in an infinite loop if \\spad{f} has no non-zero terms.")) (|monomial| (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) "\\spad{monomial(a,[x1,x2,...,xk],[n1,n2,...,nk])} returns \\spad{a * x1^n1 * ... * xk^nk}.") (($ $ |#2| (|NonNegativeInteger|)) "\\spad{monomial(a,x,n)} returns \\spad{a*x^n}.")) (|extend| (($ $ (|NonNegativeInteger|)) "\\spad{extend(f,n)} causes all terms of \\spad{f} of degree \\spad{<= n} to be computed.")) (|coefficient| (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) "\\spad{coefficient(f,[x1,x2,...,xk],[n1,n2,...,nk])} returns the coefficient of \\spad{x1^n1 * ... * xk^nk} in \\spad{f}.") (($ $ |#2| (|NonNegativeInteger|)) "\\spad{coefficient(f,x,n)} returns the coefficient of \\spad{x^n} in \\spad{f}."))) -(((-4465 "*") |has| |#1| (-174)) (-4456 |has| |#1| (-568)) (-4458 . T) (-4457 . T) (-4460 . T)) +(((-4466 "*") |has| |#1| (-174)) (-4457 |has| |#1| (-568)) (-4459 . T) (-4458 . T) (-4461 . T)) NIL (-753 OV E R P) ((|constructor| (NIL "\\indented{2}{This is the top level package for doing multivariate factorization} over basic domains like \\spadtype{Integer} or \\spadtype{Fraction Integer}.")) (|factor| (((|Factored| (|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"))) @@ -2954,7 +2954,7 @@ NIL NIL (-756 R) ((|constructor| (NIL "NonAssociativeAlgebra is the category of non associative algebras (modules which are themselves non associative rngs). Axioms \\indented{3}{\\spad{r*}(a*b) = (r*a)\\spad{*b} = a*(\\spad{r*b})}")) (|plenaryPower| (($ $ (|PositiveInteger|)) "\\spad{plenaryPower(a,n)} is recursively defined to be \\spad{plenaryPower(a,n-1)*plenaryPower(a,n-1)} for \\spad{n>1} and \\spad{a} for \\spad{n=1}."))) -((-4458 . T) (-4457 . T)) +((-4459 . T) (-4458 . T)) NIL (-757) ((|constructor| (NIL "This package uses the NAG Library to compute the zeros of a polynomial with real or complex coefficients. See \\downlink{Manual Page}{manpageXXc02}.")) (|c02agf| (((|Result|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Boolean|) (|Integer|)) "\\spad{c02agf(a,n,scale,ifail)} finds all the roots of a real polynomial equation,{} using a variant of Laguerre\\spad{'s} Method. See \\downlink{Manual Page}{manpageXXc02agf}.")) (|c02aff| (((|Result|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Boolean|) (|Integer|)) "\\spad{c02aff(a,n,scale,ifail)} finds all the roots of a complex polynomial equation,{} using a variant of Laguerre\\spad{'s} Method. See \\downlink{Manual Page}{manpageXXc02aff}."))) @@ -3036,11 +3036,11 @@ NIL ((|constructor| (NIL "This package computes explicitly eigenvalues and eigenvectors of matrices with entries over the complex rational numbers. The results are expressed either as complex floating numbers or as complex rational numbers depending on the type of the precision parameter.")) (|complexEigenvectors| (((|List| (|Record| (|:| |outval| (|Complex| |#1|)) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| (|Complex| |#1|)))))) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) |#1|) "\\spad{complexEigenvectors(m,eps)} returns a list of records each one containing a complex eigenvalue,{} its algebraic multiplicity,{} and a list of associated eigenvectors. All these results are computed to precision \\spad{eps} and are expressed as complex floats or complex rational numbers depending on the type of \\spad{eps} (float or rational).")) (|complexEigenvalues| (((|List| (|Complex| |#1|)) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) |#1|) "\\spad{complexEigenvalues(m,eps)} computes the eigenvalues of the matrix \\spad{m} to precision \\spad{eps}. The eigenvalues are expressed as complex floats or complex rational numbers depending on the type of \\spad{eps} (float or rational).")) (|characteristicPolynomial| (((|Polynomial| (|Complex| (|Fraction| (|Integer|)))) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) (|Symbol|)) "\\spad{characteristicPolynomial(m,x)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over Complex Rationals with variable \\spad{x}.") (((|Polynomial| (|Complex| (|Fraction| (|Integer|)))) (|Matrix| (|Complex| (|Fraction| (|Integer|))))) "\\spad{characteristicPolynomial(m)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over complex rationals with a new symbol as variable."))) NIL NIL -(-777 -2117) +(-777 -1959) ((|constructor| (NIL "\\spadtype{NumericContinuedFraction} provides functions \\indented{2}{for converting floating point numbers to continued fractions.}")) (|continuedFraction| (((|ContinuedFraction| (|Integer|)) |#1|) "\\spad{continuedFraction(f)} converts the floating point number \\spad{f} to a reduced continued fraction."))) NIL NIL -(-778 P -2117) +(-778 P -1959) ((|constructor| (NIL "This package provides a division and related operations for \\spadtype{MonogenicLinearOperator}\\spad{s} over a \\spadtype{Field}. Since the multiplication is in general non-commutative,{} these operations all have left- and right-hand versions. This package provides the operations based on left-division.")) (|leftLcm| ((|#1| |#1| |#1|) "\\spad{leftLcm(a,b)} computes the value \\spad{m} of lowest degree such that \\spad{m = a*aa = b*bb} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using left-division.")) (|leftGcd| ((|#1| |#1| |#1|) "\\spad{leftGcd(a,b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = aa*g}} \\indented{3}{\\spad{b = bb*g}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using left-division.")) (|leftExactQuotient| (((|Union| |#1| "failed") |#1| |#1|) "\\spad{leftExactQuotient(a,b)} computes the value \\spad{q},{} if it exists,{} \\indented{1}{such that \\spad{a = b*q}.}")) (|leftRemainder| ((|#1| |#1| |#1|) "\\spad{leftRemainder(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|leftQuotient| ((|#1| |#1| |#1|) "\\spad{leftQuotient(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|leftDivide| (((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|) "\\spad{leftDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division\\spad{''}."))) NIL NIL @@ -3048,7 +3048,7 @@ NIL NIL NIL NIL -(-780 UP -2117) +(-780 UP -1959) ((|constructor| (NIL "In this package \\spad{F} is a framed algebra over the integers (typically \\spad{F = Z[a]} for some algebraic integer a). The package provides functions to compute the integral closure of \\spad{Z} in the quotient quotient field of \\spad{F}.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| (|Integer|))) (|:| |basisDen| (|Integer|)) (|:| |basisInv| (|Matrix| (|Integer|)))) (|Integer|)) "\\spad{integralBasis(p)} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the local integral closure of \\spad{Z} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{Z}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| (|Integer|))) (|:| |basisDen| (|Integer|)) (|:| |basisInv| (|Matrix| (|Integer|))))) "\\spad{integralBasis()} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the integral closure of \\spad{Z} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{Z}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|discriminant| (((|Integer|)) "\\spad{discriminant()} returns the discriminant of the integral closure of \\spad{Z} in the quotient field of the framed algebra \\spad{F}."))) NIL NIL @@ -3062,9 +3062,9 @@ NIL NIL (-783) ((|constructor| (NIL "\\spadtype{NonNegativeInteger} provides functions for non \\indented{2}{negative integers.}")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} means multiplication is commutative : \\spad{x*y = y*x}.")) (|random| (($ $) "\\spad{random(n)} returns a random integer from 0 to \\spad{n-1}.")) (|shift| (($ $ (|Integer|)) "\\spad{shift(a,i)} shift \\spad{a} by \\spad{i} bits.")) (|exquo| (((|Union| $ "failed") $ $) "\\spad{exquo(a,b)} returns the quotient of \\spad{a} and \\spad{b},{} or \"failed\" if \\spad{b} is zero or \\spad{a} rem \\spad{b} is zero.")) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{divide(a,b)} returns a record containing both remainder and quotient.")) (|gcd| (($ $ $) "\\spad{gcd(a,b)} computes the greatest common divisor of two non negative integers \\spad{a} and \\spad{b}.")) (|rem| (($ $ $) "\\spad{a rem b} returns the remainder of \\spad{a} and \\spad{b}.")) (|quo| (($ $ $) "\\spad{a quo b} returns the quotient of \\spad{a} and \\spad{b},{} forgetting the remainder."))) -(((-4465 "*") . T)) +(((-4466 "*") . T)) NIL -(-784 R -2117) +(-784 R -1959) ((|constructor| (NIL "NonLinearFirstOrderODESolver provides a function for finding closed form first integrals of nonlinear ordinary differential equations of order 1.")) (|solve| (((|Union| |#2| "failed") |#2| |#2| (|BasicOperator|) (|Symbol|)) "\\spad{solve(M(x,y), N(x,y), y, x)} returns \\spad{F(x,y)} such that \\spad{F(x,y) = c} for a constant \\spad{c} is a first integral of the equation \\spad{M(x,y) dx + N(x,y) dy = 0},{} or \"failed\" if no first-integral can be found."))) NIL NIL @@ -3084,7 +3084,7 @@ NIL ((|constructor| (NIL "A package for computing normalized assocites of univariate polynomials with coefficients in a tower of simple extensions of a field.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. MORENO MAZA and \\spad{R}. RIOBOO \"Computations of \\spad{gcd} over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of AAECC11} \\indented{5}{Paris,{} 1995.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.}")) (|normInvertible?| (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{normInvertible?(\\spad{p},{}\\spad{ts})} is an internal subroutine,{} exported only for developement.")) (|outputArgs| (((|Void|) (|String|) (|String|) |#4| |#5|) "\\axiom{outputArgs(\\spad{s1},{}\\spad{s2},{}\\spad{p},{}\\spad{ts})} is an internal subroutine,{} exported only for developement.")) (|normalize| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{normalize(\\spad{p},{}\\spad{ts})} normalizes \\axiom{\\spad{p}} \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}.")) (|normalizedAssociate| ((|#4| |#4| |#5|) "\\axiom{normalizedAssociate(\\spad{p},{}\\spad{ts})} returns a normalized polynomial \\axiom{\\spad{n}} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts} such that \\axiom{\\spad{n}} and \\axiom{\\spad{p}} are associates \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts} and assuming that \\axiom{\\spad{p}} is invertible \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}.")) (|recip| (((|Record| (|:| |num| |#4|) (|:| |den| |#4|)) |#4| |#5|) "\\axiom{recip(\\spad{p},{}\\spad{ts})} returns the inverse of \\axiom{\\spad{p}} \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts} assuming that \\axiom{\\spad{p}} is invertible \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}."))) NIL NIL -(-789 -2117 |ExtF| |SUEx| |ExtP| |n|) +(-789 -1959 |ExtF| |SUEx| |ExtP| |n|) ((|constructor| (NIL "This package \\undocumented")) (|Frobenius| ((|#4| |#4|) "\\spad{Frobenius(x)} \\undocumented")) (|retractIfCan| (((|Union| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|)) "failed") |#4|) "\\spad{retractIfCan(x)} \\undocumented")) (|normFactors| (((|List| |#4|) |#4|) "\\spad{normFactors(x)} \\undocumented"))) NIL NIL @@ -3098,28 +3098,28 @@ NIL NIL (-792 R |VarSet|) ((|constructor| (NIL "A post-facto extension for \\axiomType{\\spad{SMP}} in order to speed up operations related to pseudo-division and \\spad{gcd}. This domain is based on the \\axiomType{NSUP} constructor which is itself a post-facto extension of the \\axiomType{SUP} constructor."))) -(((-4465 "*") |has| |#1| (-174)) (-4456 |has| |#1| (-568)) (-4461 |has| |#1| (-6 -4461)) (-4458 . T) (-4457 . T) (-4460 . 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Note that the mapping is assumed to send zero to zero,{} since it will only be applied to the non-zero coefficients of the polynomial.")) (|map| (((|NewSparseUnivariatePolynomial| |#2|) (|Mapping| |#2| |#1|) (|NewSparseUnivariatePolynomial| |#1|)) "\\axiom{map(func,{} poly)} creates a new polynomial by applying func to every non-zero coefficient of the polynomial poly."))) NIL NIL (-794 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,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} \\spad{cb}]}")) (|halfExtendedResultant1| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedResultant1(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} \\spad{cb}]}")) (|extendedResultant| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{}\\spad{cb}]} such that \\axiom{\\spad{r}} is the resultant of \\axiom{a} and \\axiom{\\spad{b}} and \\axiom{\\spad{r} = ca * a + \\spad{cb} * \\spad{b}}")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedSubResultantGcd2(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}\\spad{cb}]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]}")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedSubResultantGcd1(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]}")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]} such that \\axiom{\\spad{g}} is a \\spad{gcd} of \\axiom{a} and \\axiom{\\spad{b}} in \\axiom{\\spad{R^}(\\spad{-1}) \\spad{P}} and \\axiom{\\spad{g} = ca * a + \\spad{cb} * \\spad{b}}")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns \\axiom{resultant(a,{}\\spad{b})} if \\axiom{a} and \\axiom{\\spad{b}} has no non-trivial \\spad{gcd} in \\axiom{\\spad{R^}(\\spad{-1}) \\spad{P}} otherwise the non-zero sub-resultant with smallest index.")) (|subResultantsChain| (((|List| $) $ $) "\\axiom{subResultantsChain(a,{}\\spad{b})} returns the list of the non-zero sub-resultants of \\axiom{a} and \\axiom{\\spad{b}} sorted by increasing degree.")) (|lazyPseudoQuotient| (($ $ $) "\\axiom{lazyPseudoQuotient(a,{}\\spad{b})} returns \\axiom{\\spad{q}} if \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}")) (|lazyPseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{c^n} * a = \\spad{q*b} \\spad{+r}} and \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} where \\axiom{\\spad{n} + \\spad{g} = max(0,{} degree(\\spad{b}) - degree(a) + 1)}.")) (|lazyPseudoRemainder| (($ $ $) "\\axiom{lazyPseudoRemainder(a,{}\\spad{b})} returns \\axiom{\\spad{r}} if \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]}. This lazy pseudo-remainder is computed by means of the \\axiomOpFrom{fmecg}{NewSparseUnivariatePolynomial} operation.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| |#1|) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{\\spad{c^n} * a - \\spad{r}} where \\axiom{\\spad{c}} is \\axiom{leadingCoefficient(\\spad{b})} and \\axiom{\\spad{n}} is as small as possible with the previous properties.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} returns \\axiom{\\spad{r}} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{a \\spad{-r}} where \\axiom{\\spad{b}} is monic.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#1| $) "\\axiom{fmecg(\\spad{p1},{}\\spad{e},{}\\spad{r},{}\\spad{p2})} returns \\axiom{\\spad{p1} - \\spad{r} * X**e * \\spad{p2}} where \\axiom{\\spad{X}} is \\axiom{monomial(1,{}1)}"))) -(((-4465 "*") |has| |#1| (-174)) (-4456 |has| |#1| (-568)) (-4459 |has| |#1| (-374)) (-4461 |has| |#1| (-6 -4461)) (-4458 . T) (-4457 . T) (-4460 . T)) -((|HasCategory| |#1| (QUOTE (-927))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-3794 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasCategory| (-1102) (LIST (QUOTE -900) (QUOTE (-390)))) (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-390))))) (-12 (|HasCategory| (-1102) (LIST (QUOTE -900) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-576))))) (-12 (|HasCategory| (-1102) (LIST (QUOTE -626) (LIST (QUOTE -906) (QUOTE (-390))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -906) (QUOTE (-390)))))) (-12 (|HasCategory| (-1102) (LIST (QUOTE -626) (LIST (QUOTE -906) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -906) (QUOTE (-576)))))) (-12 (|HasCategory| (-1102) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1058) (QUOTE (-576)))) (-3794 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1058) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#1| (LIST (QUOTE -1058) (LIST (QUOTE -419) (QUOTE (-576))))) (-3794 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-927)))) (-3794 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-927)))) (-3794 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-927)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-1172))) (|HasCategory| |#1| (LIST (QUOTE -918) (QUOTE (-1196)))) (|HasCategory| |#1| (LIST (QUOTE -916) (QUOTE (-1196)))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-238))) (|HasAttribute| |#1| (QUOTE -4461)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-927)))) (-3794 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-927)))) (|HasCategory| |#1| (QUOTE (-146))))) +(((-4466 "*") |has| |#1| (-174)) (-4457 |has| |#1| (-568)) (-4460 |has| |#1| (-374)) (-4462 |has| |#1| (-6 -4462)) (-4459 . T) (-4458 . T) (-4461 . T)) +((|HasCategory| |#1| (QUOTE (-928))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-2758 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasCategory| (-1103) (LIST (QUOTE -901) (QUOTE (-390)))) (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-390))))) (-12 (|HasCategory| (-1103) (LIST (QUOTE -901) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-576))))) (-12 (|HasCategory| (-1103) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390)))))) (-12 (|HasCategory| (-1103) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576)))))) (-12 (|HasCategory| (-1103) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576)))) (-2758 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (-2758 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-928)))) (-2758 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-928)))) (-2758 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-928)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-1173))) (|HasCategory| |#1| (LIST (QUOTE -919) (QUOTE (-1197)))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-238))) (|HasAttribute| |#1| (QUOTE -4462)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-928)))) (-2758 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-928)))) (|HasCategory| |#1| (QUOTE (-146))))) (-795 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 -38) (LIST (QUOTE -419) (QUOTE (-576)))))) (-796 R E V P) ((|constructor| (NIL "The category of normalized triangular sets. A triangular set \\spad{ts} is said normalized if for every algebraic variable \\spad{v} of \\spad{ts} the polynomial \\spad{select(ts,v)} is normalized \\spad{w}.\\spad{r}.\\spad{t}. every polynomial in \\spad{collectUnder(ts,v)}. A polynomial \\spad{p} is said normalized \\spad{w}.\\spad{r}.\\spad{t}. a non-constant polynomial \\spad{q} if \\spad{p} is constant or \\spad{degree(p,mdeg(q)) = 0} and \\spad{init(p)} is normalized \\spad{w}.\\spad{r}.\\spad{t}. \\spad{q}. One of the important features of normalized triangular sets is that they are regular sets.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)} \\indented{1}{[3] \\spad{M}. MORENO MAZA and \\spad{R}. RIOBOO \"Computations of \\spad{gcd} over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of AAECC11} \\indented{5}{Paris,{} 1995.} \\indented{1}{[4] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.}"))) -((-4464 . T) (-4463 . T)) +((-4465 . T) (-4464 . T)) NIL (-797 S) ((|constructor| (NIL "Numeric provides real and complex numerical evaluation functions for various symbolic types.")) (|numericIfCan| (((|Union| (|Float|) "failed") (|Expression| |#1|) (|PositiveInteger|)) "\\spad{numericIfCan(x, n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Expression| |#1|)) "\\spad{numericIfCan(x)} returns a real approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{numericIfCan(x,n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Fraction| (|Polynomial| |#1|))) "\\spad{numericIfCan(x)} returns a real approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{numericIfCan(x,n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Polynomial| |#1|)) "\\spad{numericIfCan(x)} returns a real approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.")) (|complexNumericIfCan| (((|Union| (|Complex| (|Float|)) "failed") (|Expression| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Expression| (|Complex| |#1|))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Expression| |#1|) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Expression| |#1|)) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| (|Complex| |#1|))) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| (|Complex| |#1|)))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x, n)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| |#1|))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| |#1|)) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| (|Complex| |#1|))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not constant.")) (|complexNumeric| (((|Complex| (|Float|)) (|Expression| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Expression| (|Complex| |#1|))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Expression| |#1|) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Expression| |#1|)) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| (|Complex| |#1|))) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| (|Complex| |#1|)))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x}") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| |#1|))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Polynomial| |#1|)) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Polynomial| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Polynomial| (|Complex| |#1|))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Complex| |#1|) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Complex| |#1|)) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) |#1| (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) |#1|) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.")) (|numeric| (((|Float|) (|Expression| |#1|) (|PositiveInteger|)) "\\spad{numeric(x, n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) (|Expression| |#1|)) "\\spad{numeric(x)} returns a real approximation of \\spad{x}.") (((|Float|) (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{numeric(x,n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) (|Fraction| (|Polynomial| |#1|))) "\\spad{numeric(x)} returns a real approximation of \\spad{x}.") (((|Float|) (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{numeric(x,n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) (|Polynomial| |#1|)) "\\spad{numeric(x)} returns a real approximation of \\spad{x}.") (((|Float|) |#1| (|PositiveInteger|)) "\\spad{numeric(x, n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) |#1|) "\\spad{numeric(x)} returns a real approximation of \\spad{x}."))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-861)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-1069))) (|HasCategory| |#1| (QUOTE (-174)))) +((-12 (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-861)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-1070))) (|HasCategory| |#1| (QUOTE (-174)))) (-798) ((|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 @@ -3163,28 +3163,28 @@ NIL (-808 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 \\spad{o}.")) (|imagJ| ((|#2| $) "\\spad{imagJ(o)} extracts the imaginary \\spad{J} part of octonion \\spad{o}.")) (|imagI| ((|#2| $) "\\spad{imagI(o)} extracts the imaginary \\spad{I} part of octonion \\spad{o}.")) (|imagE| ((|#2| $) "\\spad{imagE(o)} extracts the imaginary \\spad{E} part of octonion \\spad{o}.")) (|imagk| ((|#2| $) "\\spad{imagk(o)} extracts the \\spad{k} part of octonion \\spad{o}.")) (|imagj| ((|#2| $) "\\spad{imagj(o)} extracts the \\spad{j} part of octonion \\spad{o}.")) (|imagi| ((|#2| $) "\\spad{imagi(o)} extracts the \\spad{i} part of octonion \\spad{o}.")) (|real| ((|#2| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) NIL -((|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-557))) (|HasCategory| |#2| (QUOTE (-1080))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (QUOTE (-861))) (|HasCategory| |#2| (QUOTE (-379)))) +((|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-557))) (|HasCategory| |#2| (QUOTE (-1081))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (QUOTE (-861))) (|HasCategory| |#2| (QUOTE (-379)))) (-809 R) ((|constructor| (NIL "OctonionCategory gives the categorial frame for the octonions,{} and eight-dimensional non-associative algebra,{} doubling the the quaternions in the same way as doubling the Complex numbers to get the quaternions.")) (|inv| (($ $) "\\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 \\spad{o}.")) (|imagJ| ((|#1| $) "\\spad{imagJ(o)} extracts the imaginary \\spad{J} part of octonion \\spad{o}.")) (|imagI| ((|#1| $) "\\spad{imagI(o)} extracts the imaginary \\spad{I} part of octonion \\spad{o}.")) (|imagE| ((|#1| $) "\\spad{imagE(o)} extracts the imaginary \\spad{E} part of octonion \\spad{o}.")) (|imagk| ((|#1| $) "\\spad{imagk(o)} extracts the \\spad{k} part of octonion \\spad{o}.")) (|imagj| ((|#1| $) "\\spad{imagj(o)} extracts the \\spad{j} part of octonion \\spad{o}.")) (|imagi| ((|#1| $) "\\spad{imagi(o)} extracts the \\spad{i} part of octonion \\spad{o}.")) (|real| ((|#1| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) -((-4457 . T) (-4458 . T) (-4460 . T)) +((-4458 . T) (-4459 . T) (-4461 . T)) NIL -(-810 -3794 R OS S) +(-810 -2758 R OS S) ((|constructor| (NIL "OctonionCategoryFunctions2 implements functions between two octonion domains defined over different rings. The function map is used to coerce between octonion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,u)} maps \\spad{f} onto the component parts of the octonion \\spad{u}."))) NIL NIL (-811 R) ((|constructor| (NIL "Octonion implements octonions (Cayley-Dixon algebra) over a commutative ring,{} an eight-dimensional non-associative algebra,{} doubling the quaternions in the same way as doubling the complex numbers to get the quaternions the main constructor function is {\\em octon} which takes 8 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j} imaginary part,{} the \\spad{k} imaginary part,{} (as with quaternions) and in addition the imaginary parts \\spad{E},{} \\spad{I},{} \\spad{J},{} \\spad{K}.")) (|octon| (($ (|Quaternion| |#1|) (|Quaternion| |#1|)) "\\spad{octon(qe,qE)} constructs an octonion from two quaternions using the relation {\\em O = Q + QE}."))) -((-4457 . T) (-4458 . T) (-4460 . T)) -((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (LIST (QUOTE -526) (QUOTE (-1196)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -296) (|devaluate| |#1|) (|devaluate| |#1|))) (-3794 (|HasCategory| (-1019 |#1|) (LIST (QUOTE -1058) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1058) (LIST (QUOTE -419) (QUOTE (-576)))))) (-3794 (|HasCategory| (-1019 |#1|) (LIST (QUOTE -1058) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -1058) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-1080))) (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| (-1019 |#1|) (LIST (QUOTE -1058) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-1019 |#1|) (LIST (QUOTE -1058) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -1058) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1058) (QUOTE (-576))))) +((-4458 . T) (-4459 . T) (-4461 . T)) +((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (LIST (QUOTE -526) (QUOTE (-1197)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -296) (|devaluate| |#1|) (|devaluate| |#1|))) (-2758 (|HasCategory| (-1020 |#1|) (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576)))))) (-2758 (|HasCategory| (-1020 |#1|) (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-1081))) (|HasCategory| |#1| (QUOTE (-557))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| (-1020 |#1|) (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-1020 |#1|) (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576))))) (-812) ((|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 -(-813 R -2117 L) +(-813 R -1959 L) ((|constructor| (NIL "Solution of linear ordinary differential equations,{} constant coefficient case.")) (|constDsolve| (((|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Symbol|)) "\\spad{constDsolve(op, g, x)} returns \\spad{[f, [y1,...,ym]]} where \\spad{f} is a particular solution of the equation \\spad{op y = g},{} and the \\spad{yi}\\spad{'s} form a basis for the solutions of \\spad{op y = 0}."))) NIL NIL -(-814 R -2117) +(-814 R -1959) ((|constructor| (NIL "\\spad{ElementaryFunctionODESolver} provides the top-level functions for finding closed form solutions of ordinary differential equations and initial value problems.")) (|solve| (((|Union| |#2| "failed") |#2| (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{solve(eq, y, x = a, [y0,...,ym])} returns either the solution of the initial value problem \\spad{eq, y(a) = y0, y'(a) = y1,...} or \"failed\" if the solution cannot be found; error if the equation is not one linear ordinary or of the form \\spad{dy/dx = f(x,y)}.") (((|Union| |#2| "failed") (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{solve(eq, y, x = a, [y0,...,ym])} returns either the solution of the initial value problem \\spad{eq, y(a) = y0, y'(a) = y1,...} or \"failed\" if the solution cannot be found; error if the equation is not one linear ordinary or of the form \\spad{dy/dx = f(x,y)}.") (((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#2| "failed") |#2| (|BasicOperator|) (|Symbol|)) "\\spad{solve(eq, y, x)} returns either a solution of the ordinary differential equation \\spad{eq} or \"failed\" if no non-trivial solution can be found; If the equation is linear ordinary,{} a solution is of the form \\spad{[h, [b1,...,bm]]} where \\spad{h} is a particular solution and and \\spad{[b1,...bm]} are linearly independent solutions of the associated homogenuous equation \\spad{f(x,y) = 0}; A full basis for the solutions of the homogenuous equation is not always returned,{} only the solutions which were found; If the equation is of the form {dy/dx = \\spad{f}(\\spad{x},{}\\spad{y})},{} a solution is of the form \\spad{h(x,y)} where \\spad{h(x,y) = c} is a first integral of the equation for any constant \\spad{c}.") (((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#2| "failed") (|Equation| |#2|) (|BasicOperator|) (|Symbol|)) "\\spad{solve(eq, y, x)} returns either a solution of the ordinary differential equation \\spad{eq} or \"failed\" if no non-trivial solution can be found; If the equation is linear ordinary,{} a solution is of the form \\spad{[h, [b1,...,bm]]} where \\spad{h} is a particular solution and \\spad{[b1,...bm]} are linearly independent solutions of the associated homogenuous equation \\spad{f(x,y) = 0}; A full basis for the solutions of the homogenuous equation is not always returned,{} only the solutions which were found; If the equation is of the form {dy/dx = \\spad{f}(\\spad{x},{}\\spad{y})},{} a solution is of the form \\spad{h(x,y)} where \\spad{h(x,y) = c} is a first integral of the equation for any constant \\spad{c}; error if the equation is not one of those 2 forms.") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|List| |#2|) (|List| (|BasicOperator|)) (|Symbol|)) "\\spad{solve([eq_1,...,eq_n], [y_1,...,y_n], x)} returns either \"failed\" or,{} if the equations form a fist order linear system,{} a solution of the form \\spad{[y_p, [b_1,...,b_n]]} where \\spad{h_p} is a particular solution and \\spad{[b_1,...b_m]} are linearly independent solutions of the associated homogenuous system. error if the equations do not form a first order linear system") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Symbol|)) "\\spad{solve([eq_1,...,eq_n], [y_1,...,y_n], x)} returns either \"failed\" or,{} if the equations form a fist order linear system,{} a solution of the form \\spad{[y_p, [b_1,...,b_n]]} where \\spad{h_p} is a particular solution and \\spad{[b_1,...b_m]} are linearly independent solutions of the associated homogenuous system. error if the equations do not form a first order linear system") (((|Union| (|List| (|Vector| |#2|)) "failed") (|Matrix| |#2|) (|Symbol|)) "\\spad{solve(m, x)} returns a basis for the solutions of \\spad{D y = m y}. \\spad{x} is the dependent variable.") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|Matrix| |#2|) (|Vector| |#2|) (|Symbol|)) "\\spad{solve(m, v, x)} returns \\spad{[v_p, [v_1,...,v_m]]} such that the solutions of the system \\spad{D y = m y + v} are \\spad{v_p + c_1 v_1 + ... + c_m v_m} where the \\spad{c_i's} are constants,{} and the \\spad{v_i's} form a basis for the solutions of \\spad{D y = m y}. \\spad{x} is the dependent variable."))) NIL NIL @@ -3192,7 +3192,7 @@ NIL ((|constructor| (NIL "\\axiom{ODEIntensityFunctionsTable()} provides a dynamic table and a set of functions to store details found out about sets of ODE\\spad{'s}.")) (|showIntensityFunctions| (((|Union| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|))) "failed") (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{showIntensityFunctions(k)} returns the entries in the table of intensity functions \\spad{k}.")) (|insert!| (($ (|Record| (|:| |key| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|)))))) "\\spad{insert!(r)} inserts an entry \\spad{r} into theIFTable")) (|iFTable| (($ (|List| (|Record| (|:| |key| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|))))))) "\\spad{iFTable(l)} creates an intensity-functions table from the elements of \\spad{l}.")) (|keys| (((|List| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) $) "\\spad{keys(tab)} returns the list of keys of \\spad{f}")) (|clearTheIFTable| (((|Void|)) "\\spad{clearTheIFTable()} clears the current table of intensity functions.")) (|showTheIFTable| (($) "\\spad{showTheIFTable()} returns the current table of intensity functions."))) NIL NIL -(-816 R -2117) +(-816 R -1959) ((|constructor| (NIL "\\spadtype{ODEIntegration} provides an interface to the integrator. This package is intended for use by the differential equations solver but not at top-level.")) (|diff| (((|Mapping| |#2| |#2|) (|Symbol|)) "\\spad{diff(x)} returns the derivation with respect to \\spad{x}.")) (|expint| ((|#2| |#2| (|Symbol|)) "\\spad{expint(f, x)} returns e^{the integral of \\spad{f} with respect to \\spad{x}}.")) (|int| ((|#2| |#2| (|Symbol|)) "\\spad{int(f, x)} returns the integral of \\spad{f} with respect to \\spad{x}."))) NIL NIL @@ -3200,11 +3200,11 @@ NIL ((|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalODEProblem|) (|RoutinesTable|)) "\\spad{measure(prob,R)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical ODE problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} listed in \\axiom{\\spad{R}} of \\axiom{category} \\axiomType{OrdinaryDifferentialEquationsSolverCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information. It predicts the likely most effective NAG numerical Library routine to solve the input set of ODEs by checking various attributes of the system of ODEs and calculating a measure of compatibility of each routine to these attributes.") (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalODEProblem|)) "\\spad{measure(prob)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical ODE problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} of \\axiom{category} \\axiomType{OrdinaryDifferentialEquationsSolverCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information. It predicts the likely most effective NAG numerical Library routine to solve the input set of ODEs by checking various attributes of the system of ODEs and calculating a measure of compatibility of each routine to these attributes.")) (|solve| (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|List| (|Float|)) (|Float|) (|Float|)) "\\spad{solve(f,xStart,xEnd,yInitial,G,intVals,epsabs,epsrel)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to an absolute error requirement \\axiom{\\spad{epsabs}} and relative error \\axiom{\\spad{epsrel}}. The values of \\spad{Y}[1]..\\spad{Y}[\\spad{n}] will be output for the values of \\spad{X} in \\axiom{\\spad{intVals}}. The calculation will stop if the function \\spad{G}(\\spad{X},{}\\spad{Y}[1],{}..,{}\\spad{Y}[\\spad{n}]) evaluates to zero before \\spad{X} = \\spad{xEnd}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|List| (|Float|)) (|Float|)) "\\spad{solve(f,xStart,xEnd,yInitial,G,intVals,tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. The values of \\spad{Y}[1]..\\spad{Y}[\\spad{n}] will be output for the values of \\spad{X} in \\axiom{\\spad{intVals}}. The calculation will stop if the function \\spad{G}(\\spad{X},{}\\spad{Y}[1],{}..,{}\\spad{Y}[\\spad{n}]) evaluates to zero before \\spad{X} = \\spad{xEnd}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|List| (|Float|)) (|Float|)) "\\spad{solve(f,xStart,xEnd,yInitial,intVals,tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. The values of \\spad{Y}[1]..\\spad{Y}[\\spad{n}] will be output for the values of \\spad{X} in \\axiom{\\spad{intVals}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|Float|)) "\\spad{solve(f,xStart,xEnd,yInitial,G,tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. The calculation will stop if the function \\spad{G}(\\spad{X},{}\\spad{Y}[1],{}..,{}\\spad{Y}[\\spad{n}]) evaluates to zero before \\spad{X} = \\spad{xEnd}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Float|)) "\\spad{solve(f,xStart,xEnd,yInitial,tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|))) "\\spad{solve(f,xStart,xEnd,yInitial)} is a top level ANNA function to solve numerically a system of ordinary differential equations \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}],{} together with a starting value for \\spad{X} and \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (called the initial conditions) and a final value of \\spad{X}. A default value is used for the accuracy requirement. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|NumericalODEProblem|) (|RoutinesTable|)) "\\spad{solve(odeProblem,R)} is a top level ANNA function to solve numerically a system of ordinary differential equations \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}],{} together with starting values for \\spad{X} and \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (called the initial conditions),{} a final value of \\spad{X},{} an accuracy requirement and any intermediate points at which the result is required. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|NumericalODEProblem|)) "\\spad{solve(odeProblem)} is a top level ANNA function to solve numerically a system of ordinary differential equations \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}],{} together with starting values for \\spad{X} and \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (called the initial conditions),{} a final value of \\spad{X},{} an accuracy requirement and any intermediate points at which the result is required. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine."))) NIL NIL -(-818 -2117 UP UPUP R) +(-818 -1959 UP UPUP R) ((|constructor| (NIL "In-field solution of an linear ordinary differential equation,{} pure algebraic case.")) (|algDsolve| (((|Record| (|:| |particular| (|Union| |#4| "failed")) (|:| |basis| (|List| |#4|))) (|LinearOrdinaryDifferentialOperator1| |#4|) |#4|) "\\spad{algDsolve(op, g)} returns \\spad{[\"failed\", []]} if the equation \\spad{op y = g} has no solution in \\spad{R}. Otherwise,{} it returns \\spad{[f, [y1,...,ym]]} where \\spad{f} is a particular rational solution and the \\spad{y_i's} form a basis for the solutions in \\spad{R} of the homogeneous equation."))) NIL NIL -(-819 -2117 UP L LQ) +(-819 -1959 UP L LQ) ((|constructor| (NIL "\\spad{PrimitiveRatDE} provides functions for in-field solutions of linear \\indented{1}{ordinary differential equations,{} in the transcendental case.} \\indented{1}{The derivation to use is given by the parameter \\spad{L}.}")) (|splitDenominator| (((|Record| (|:| |eq| |#3|) (|:| |rh| (|List| (|Fraction| |#2|)))) |#4| (|List| (|Fraction| |#2|))) "\\spad{splitDenominator(op, [g1,...,gm])} returns \\spad{op0, [h1,...,hm]} such that the equations \\spad{op y = c1 g1 + ... + cm gm} and \\spad{op0 y = c1 h1 + ... + cm hm} have the same solutions.")) (|indicialEquation| ((|#2| |#4| |#1|) "\\spad{indicialEquation(op, a)} returns the indicial equation of \\spad{op} at \\spad{a}.") ((|#2| |#3| |#1|) "\\spad{indicialEquation(op, a)} returns the indicial equation of \\spad{op} at \\spad{a}.")) (|indicialEquations| (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#4| |#2|) "\\spad{indicialEquations(op, p)} returns \\spad{[[d1,e1],...,[dq,eq]]} where the \\spad{d_i}\\spad{'s} are the affine singularities of \\spad{op} above the roots of \\spad{p},{} and the \\spad{e_i}\\spad{'s} are the indicial equations at each \\spad{d_i}.") (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#4|) "\\spad{indicialEquations op} returns \\spad{[[d1,e1],...,[dq,eq]]} where the \\spad{d_i}\\spad{'s} are the affine singularities of \\spad{op},{} and the \\spad{e_i}\\spad{'s} are the indicial equations at each \\spad{d_i}.") (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#3| |#2|) "\\spad{indicialEquations(op, p)} returns \\spad{[[d1,e1],...,[dq,eq]]} where the \\spad{d_i}\\spad{'s} are the affine singularities of \\spad{op} above the roots of \\spad{p},{} and the \\spad{e_i}\\spad{'s} are the indicial equations at each \\spad{d_i}.") (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#3|) "\\spad{indicialEquations op} returns \\spad{[[d1,e1],...,[dq,eq]]} where the \\spad{d_i}\\spad{'s} are the affine singularities of \\spad{op},{} and the \\spad{e_i}\\spad{'s} are the indicial equations at each \\spad{d_i}.")) (|denomLODE| ((|#2| |#3| (|List| (|Fraction| |#2|))) "\\spad{denomLODE(op, [g1,...,gm])} returns a polynomial \\spad{d} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{p/d} for some polynomial \\spad{p}.") (((|Union| |#2| "failed") |#3| (|Fraction| |#2|)) "\\spad{denomLODE(op, g)} returns a polynomial \\spad{d} such that any rational solution of \\spad{op y = g} is of the form \\spad{p/d} for some polynomial \\spad{p},{} and \"failed\",{} if the equation has no rational solution."))) NIL NIL @@ -3212,41 +3212,41 @@ NIL ((|retract| (((|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))) $) "\\spad{retract(x)} \\undocumented{}")) (|coerce| (($ (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{coerce(x)} \\undocumented{}"))) NIL NIL -(-821 -2117 UP L LQ) +(-821 -1959 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], ... , [fk, Lk]]} such that the singular part of any rational solution of the associated Riccati equation of \\spad{op y=0} must be one of the \\spad{fi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z=y e^{-int p}} is \\spad{Li z=0}. \\spad{zeros(C(x),H(x,y))} returns all the \\spad{P_i(x)}\\spad{'s} such that \\spad{H(x,P_i(x)) = 0 modulo C(x)}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.")) (|polyRicDE| (((|List| (|Record| (|:| |poly| |#2|) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#1|) |#2|)) "\\spad{polyRicDE(op, zeros)} returns \\spad{[[p1, L1], [p2, L2], ... , [pk, Lk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y=0} must be one of the \\spad{pi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z=y e^{-int p}} is \\spad{Li z =0}. \\spad{zeros} is a zero finder in \\spad{UP}.")) (|constantCoefficientRicDE| (((|List| (|Record| (|:| |constant| |#1|) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#1|) |#2|)) "\\spad{constantCoefficientRicDE(op, ric)} returns \\spad{[[a1, L1], [a2, L2], ... , [ak, Lk]]} such that any rational solution with no polynomial part of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{ai}\\spad{'s} in which case the equation for \\spad{z = y e^{-int ai}} is \\spad{Li z = 0}. \\spad{ric} is a Riccati equation solver over \\spad{F},{} whose input is the associated linear equation.")) (|leadingCoefficientRicDE| (((|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |eq| |#2|))) |#3|) "\\spad{leadingCoefficientRicDE(op)} returns \\spad{[[m1, p1], [m2, p2], ... , [mk, pk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must have degree \\spad{mj} for some \\spad{j},{} and its leading coefficient is then a zero of \\spad{pj}. In addition,{}\\spad{m1>m2> ... >mk}.")) (|denomRicDE| ((|#2| |#3|) "\\spad{denomRicDE(op)} returns a polynomial \\spad{d} such that any rational solution of the associated Riccati equation of \\spad{op y = 0} is of the form \\spad{p/d + q'/q + r} for some polynomials \\spad{p} and \\spad{q} and a reduced \\spad{r}. Also,{} \\spad{deg(p) < deg(d)} and {\\spad{gcd}(\\spad{d},{}\\spad{q}) = 1}."))) NIL NIL -(-822 -2117 UP) +(-822 -1959 UP) ((|constructor| (NIL "\\spad{RationalLODE} provides functions for in-field solutions of linear \\indented{1}{ordinary differential equations,{} in the rational case.}")) (|indicialEquationAtInfinity| ((|#2| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))) "\\spad{indicialEquationAtInfinity op} returns the indicial equation of \\spad{op} at infinity.") ((|#2| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{indicialEquationAtInfinity op} returns the indicial equation of \\spad{op} at infinity.")) (|ratDsolve| (((|Record| (|:| |basis| (|List| (|Fraction| |#2|))) (|:| |mat| (|Matrix| |#1|))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|List| (|Fraction| |#2|))) "\\spad{ratDsolve(op, [g1,...,gm])} returns \\spad{[[h1,...,hq], M]} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{d1 h1 + ... + dq hq} where \\spad{M [d1,...,dq,c1,...,cm] = 0}.") (((|Record| (|:| |particular| (|Union| (|Fraction| |#2|) "failed")) (|:| |basis| (|List| (|Fraction| |#2|)))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{ratDsolve(op, g)} returns \\spad{[\"failed\", []]} if the equation \\spad{op y = g} has no rational solution. Otherwise,{} it returns \\spad{[f, [y1,...,ym]]} where \\spad{f} is a particular rational solution and the \\spad{yi}\\spad{'s} form a basis for the rational solutions of the homogeneous equation.") (((|Record| (|:| |basis| (|List| (|Fraction| |#2|))) (|:| |mat| (|Matrix| |#1|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|List| (|Fraction| |#2|))) "\\spad{ratDsolve(op, [g1,...,gm])} returns \\spad{[[h1,...,hq], M]} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{d1 h1 + ... + dq hq} where \\spad{M [d1,...,dq,c1,...,cm] = 0}.") (((|Record| (|:| |particular| (|Union| (|Fraction| |#2|) "failed")) (|:| |basis| (|List| (|Fraction| |#2|)))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{ratDsolve(op, g)} returns \\spad{[\"failed\", []]} if the equation \\spad{op y = g} has no rational solution. Otherwise,{} it returns \\spad{[f, [y1,...,ym]]} where \\spad{f} is a particular rational solution and the \\spad{yi}\\spad{'s} form a basis for the rational solutions of the homogeneous equation."))) NIL NIL -(-823 -2117 L UP A LO) +(-823 -1959 L UP A LO) ((|constructor| (NIL "Elimination of an algebraic from the coefficentss of a linear ordinary differential equation.")) (|reduceLODE| (((|Record| (|:| |mat| (|Matrix| |#2|)) (|:| |vec| (|Vector| |#1|))) |#5| |#4|) "\\spad{reduceLODE(op, g)} returns \\spad{[m, v]} such that any solution in \\spad{A} of \\spad{op z = g} is of the form \\spad{z = (z_1,...,z_m) . (b_1,...,b_m)} where the \\spad{b_i's} are the basis of \\spad{A} over \\spad{F} returned by \\spadfun{basis}() from \\spad{A},{} and the \\spad{z_i's} satisfy the differential system \\spad{M.z = v}."))) NIL NIL -(-824 -2117 UP) +(-824 -1959 UP) ((|constructor| (NIL "In-field solution of Riccati equations,{} rational case.")) (|polyRicDE| (((|List| (|Record| (|:| |poly| |#2|) (|:| |eq| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{polyRicDE(op, zeros)} returns \\spad{[[p1, L1], [p2, L2], ... , [pk,Lk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{pi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z = y e^{-int p}} is \\spad{Li z = 0}. \\spad{zeros} is a zero finder in \\spad{UP}.")) (|singRicDE| (((|List| (|Record| (|:| |frac| (|Fraction| |#2|)) (|:| |eq| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{singRicDE(op, ezfactor)} returns \\spad{[[f1,L1], [f2,L2],..., [fk,Lk]]} such that the singular \\spad{++} part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{fi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z = y e^{-int ai}} is \\spad{Li z = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.")) (|ricDsolve| (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))) "\\spad{ricDsolve(op)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{ricDsolve(op)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, zeros, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{ricDsolve(op, zeros)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, zeros, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{ricDsolve(op, zeros)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}."))) NIL ((|HasCategory| |#1| (QUOTE (-27)))) -(-825 -2117 LO) +(-825 -1959 LO) ((|constructor| (NIL "SystemODESolver provides tools for triangulating and solving some systems of linear ordinary differential equations.")) (|solveInField| (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|)))) (|Matrix| |#2|) (|Vector| |#1|) (|Mapping| (|Record| (|:| |particular| (|Union| |#1| "failed")) (|:| |basis| (|List| |#1|))) |#2| |#1|)) "\\spad{solveInField(m, v, solve)} returns \\spad{[[v_1,...,v_m], v_p]} such that the solutions in \\spad{F} of the system \\spad{m x = v} are \\spad{v_p + c_1 v_1 + ... + c_m v_m} where the \\spad{c_i's} are constants,{} and the \\spad{v_i's} form a basis for the solutions of \\spad{m x = 0}. Argument \\spad{solve} is a function for solving a single linear ordinary differential equation in \\spad{F}.")) 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(((|Record| (|:| A (|Matrix| |#1|)) (|:| |eqs| (|List| (|Record| (|:| C (|Matrix| |#1|)) (|:| |g| (|Vector| |#1|)) (|:| |eq| |#2|) (|:| |rh| |#1|))))) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{triangulate(M,v)} returns \\spad{A,[[C_1,g_1,L_1,h_1],...,[C_k,g_k,L_k,h_k]]} such that under the change of variable \\spad{y = A z},{} the first order linear system \\spad{D y = M y + v} is uncoupled as \\spad{D z_i = C_i z_i + g_i} and each \\spad{C_i} is a companion matrix corresponding to the scalar equation \\spad{L_i z_j = h_i}."))) NIL NIL -(-826 -2117 LODO) +(-826 -1959 LODO) ((|constructor| (NIL "\\spad{ODETools} provides tools for the linear ODE solver.")) (|particularSolution| (((|Union| |#1| "failed") |#2| |#1| (|List| |#1|) (|Mapping| |#1| |#1|)) "\\spad{particularSolution(op, g, [f1,...,fm], I)} returns a particular solution \\spad{h} of the equation \\spad{op y = g} where \\spad{[f1,...,fm]} are linearly independent and \\spad{op(fi)=0}. The value \"failed\" is returned if no particular solution is found. Note: the method of variations of parameters is used.")) (|variationOfParameters| (((|Union| (|Vector| |#1|) "failed") |#2| |#1| (|List| |#1|)) "\\spad{variationOfParameters(op, g, [f1,...,fm])} returns \\spad{[u1,...,um]} such that a particular solution of the equation \\spad{op y = g} is \\spad{f1 int(u1) + ... + fm int(um)} where \\spad{[f1,...,fm]} are linearly independent and \\spad{op(fi)=0}. The value \"failed\" is returned if \\spad{m < n} and no particular solution is found.")) (|wronskianMatrix| (((|Matrix| |#1|) (|List| |#1|) (|NonNegativeInteger|)) "\\spad{wronskianMatrix([f1,...,fn], q, D)} returns the \\spad{q x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),...,fn^(i-1)]}.") (((|Matrix| |#1|) (|List| |#1|)) "\\spad{wronskianMatrix([f1,...,fn])} returns the \\spad{n x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),...,fn^(i-1)]}."))) 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T) (-4458 . T) (-4457 . T)) +(((-4466 "*") |has| |#2| (-374)) (-4457 |has| |#2| (-374)) (-4462 |has| |#2| (-374)) (-4456 |has| |#2| (-374)) (-4461 . T) (-4459 . T) (-4458 . T)) ((|HasCategory| |#2| (QUOTE (-374)))) (-830 S) ((|constructor| (NIL "\\spadtype{OrderlyDifferentialVariable} adds a commonly used orderly ranking to the set of derivatives of an ordered list of differential indeterminates. An orderly ranking is a ranking \\spadfun{<} of the derivatives with the property that for two derivatives \\spad{u} and \\spad{v},{} \\spad{u} \\spadfun{<} \\spad{v} if the \\spadfun{order} of \\spad{u} is less than that of \\spad{v}. This domain belongs to \\spadtype{DifferentialVariableCategory}. It defines \\spadfun{weight} to be just \\spadfun{order},{} and it defines an orderly ranking \\spadfun{<} on derivatives \\spad{u} via the lexicographic order on the pair (\\spadfun{order}(\\spad{u}),{} \\spadfun{variable}(\\spad{u}))."))) @@ -3258,7 +3258,7 @@ NIL ((|HasCategory| |#1| (QUOTE (-861)))) (-832) ((|constructor| (NIL "The category of ordered commutative integral domains,{} where ordering and the arithmetic operations are compatible \\blankline"))) -((-4456 . T) ((-4465 "*") . T) (-4457 . T) (-4458 . T) (-4460 . T)) +((-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL (-833) ((|constructor| (NIL "\\spadtype{OpenMathConnection} provides low-level functions for handling connections to and from \\spadtype{OpenMathDevice}\\spad{s}.")) (|OMbindTCP| (((|Boolean|) $ (|SingleInteger|)) "\\spad{OMbindTCP}")) (|OMconnectTCP| (((|Boolean|) $ (|String|) (|SingleInteger|)) "\\spad{OMconnectTCP}")) (|OMconnOutDevice| (((|OpenMathDevice|) $) "\\spad{OMconnOutDevice:}")) (|OMconnInDevice| (((|OpenMathDevice|) $) "\\spad{OMconnInDevice:}")) (|OMcloseConn| (((|Void|) $) "\\spad{OMcloseConn}")) (|OMmakeConn| (($ (|SingleInteger|)) "\\spad{OMmakeConn}"))) @@ -3286,7 +3286,7 @@ NIL NIL (-839 P R) ((|constructor| (NIL "This constructor creates the \\spadtype{MonogenicLinearOperator} domain which is ``opposite\\spad{''} in the ring sense to \\spad{P}. That is,{} as sets \\spad{P = \\$} but \\spad{a * b} in \\spad{\\$} is equal to \\spad{b * a} in \\spad{P}.")) (|po| ((|#1| $) "\\spad{po(q)} creates a value in \\spad{P} equal to \\spad{q} in \\$.")) (|op| (($ |#1|) "\\spad{op(p)} creates a value in \\$ equal to \\spad{p} in \\spad{P}."))) -((-4457 . T) (-4458 . T) (-4460 . T)) +((-4458 . T) (-4459 . T) (-4461 . T)) ((|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-238)))) (-840) ((|constructor| (NIL "\\spadtype{OpenMath} provides operations for exporting an object in OpenMath format.")) (|OMwrite| (((|Void|) (|OpenMathDevice|) $ (|Boolean|)) "\\spad{OMwrite(dev, u, true)} writes the OpenMath form of \\axiom{\\spad{u}} to the OpenMath device \\axiom{\\spad{dev}} as a complete OpenMath object; OMwrite(\\spad{dev},{} \\spad{u},{} \\spad{false}) writes the object as an OpenMath fragment.") (((|Void|) (|OpenMathDevice|) $) "\\spad{OMwrite(dev, u)} writes the OpenMath form of \\axiom{\\spad{u}} to the OpenMath device \\axiom{\\spad{dev}} as a complete OpenMath object.") (((|String|) $ (|Boolean|)) "\\spad{OMwrite(u, true)} returns the OpenMath \\spad{XML} encoding of \\axiom{\\spad{u}} as a complete OpenMath object; OMwrite(\\spad{u},{} \\spad{false}) returns the OpenMath \\spad{XML} encoding of \\axiom{\\spad{u}} as an OpenMath fragment.") (((|String|) $) "\\spad{OMwrite(u)} returns the OpenMath \\spad{XML} encoding of \\axiom{\\spad{u}} as a complete OpenMath object."))) @@ -3298,7 +3298,7 @@ NIL NIL (-842 S) ((|constructor| (NIL "to become an in order iterator")) (|min| ((|#1| $) "\\spad{min(u)} returns the smallest entry in the multiset aggregate \\spad{u}."))) -((-4463 . T) (-4453 . T) (-4464 . T)) +((-4464 . T) (-4454 . T) (-4465 . T)) NIL (-843) ((|constructor| (NIL "\\spadtype{OpenMathServerPackage} provides the necessary operations to run AXIOM as an OpenMath server,{} reading/writing objects to/from a port. Please note the facilities available here are very basic. The idea is that a user calls \\spadignore{e.g.} \\axiom{Omserve(4000,{}60)} and then another process sends OpenMath objects to port 4000 and reads the result.")) (|OMserve| (((|Void|) (|SingleInteger|) (|SingleInteger|)) "\\spad{OMserve(portnum,timeout)} puts AXIOM into server mode on port number \\axiom{\\spad{portnum}}. The parameter \\axiom{\\spad{timeout}} specifies the \\spad{timeout} period for the connection.")) (|OMsend| (((|Void|) (|OpenMathConnection|) (|Any|)) "\\spad{OMsend(c,u)} attempts to output \\axiom{\\spad{u}} on \\aciom{\\spad{c}} in OpenMath.")) (|OMreceive| (((|Any|) (|OpenMathConnection|)) "\\spad{OMreceive(c)} reads an OpenMath object from connection \\axiom{\\spad{c}} and returns the appropriate AXIOM object."))) @@ -3310,8 +3310,8 @@ NIL NIL (-845 R) ((|constructor| (NIL "Adjunction of a complex infinity to a set. Date Created: 4 Oct 1989 Date Last Updated: 1 Nov 1989")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a finite rational number if it is one,{} \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a finite rational number. Error: if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a finite rational number.")) (|infinite?| (((|Boolean|) $) "\\spad{infinite?(x)} tests if \\spad{x} is infinite.")) (|finite?| (((|Boolean|) $) "\\spad{finite?(x)} tests if \\spad{x} is finite.")) (|infinity| (($) "\\spad{infinity()} returns infinity."))) -((-4460 |has| |#1| (-860))) -((|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-21))) (-3794 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-860)))) (|HasCategory| |#1| (LIST (QUOTE -1058) (LIST (QUOTE -419) (QUOTE (-576))))) (-3794 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (LIST (QUOTE -1058) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1058) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-557)))) +((-4461 |has| |#1| (-860))) +((|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-21))) (-2758 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-860)))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (-2758 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-557)))) (-846 A S) ((|constructor| (NIL "This category specifies the interface for operators used to build terms,{} in the sense of Universal Algebra. The domain parameter \\spad{S} provides representation for the `external name' of an operator.")) (|is?| (((|Boolean|) $ |#2|) "\\spad{is?(op,n)} holds if the name of the operator \\spad{op} is \\spad{n}.")) (|arity| (((|Arity|) $) "\\spad{arity(op)} returns the arity of the operator \\spad{op}.")) (|name| ((|#2| $) "\\spad{name(op)} returns the externam name of \\spad{op}."))) NIL @@ -3322,7 +3322,7 @@ NIL NIL (-848 R) ((|constructor| (NIL "Algebra of ADDITIVE operators over a ring."))) -((-4458 |has| |#1| (-174)) (-4457 |has| |#1| (-174)) (-4460 . T)) +((-4459 |has| |#1| (-174)) (-4458 |has| |#1| (-174)) (-4461 . T)) ((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148)))) (-849) ((|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)."))) @@ -3350,13 +3350,13 @@ NIL NIL (-855 R) ((|constructor| (NIL "Adjunction of two real infinites quantities to a set. Date Created: 4 Oct 1989 Date Last Updated: 1 Nov 1989")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a finite rational number if it is one and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a finite rational number. Error: if \\spad{x} cannot be so converted.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a finite rational number.")) (|whatInfinity| (((|SingleInteger|) $) "\\spad{whatInfinity(x)} returns 0 if \\spad{x} is finite,{} 1 if \\spad{x} is +infinity,{} and \\spad{-1} if \\spad{x} is -infinity.")) (|infinite?| (((|Boolean|) $) "\\spad{infinite?(x)} tests if \\spad{x} is +infinity or -infinity,{}")) (|finite?| (((|Boolean|) $) "\\spad{finite?(x)} tests if \\spad{x} is finite.")) (|minusInfinity| (($) "\\spad{minusInfinity()} returns -infinity.")) (|plusInfinity| (($) "\\spad{plusInfinity()} returns +infinity."))) -((-4460 |has| |#1| (-860))) -((|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-21))) (-3794 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-860)))) (|HasCategory| |#1| (LIST (QUOTE -1058) (LIST (QUOTE -419) (QUOTE (-576))))) (-3794 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (LIST (QUOTE -1058) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1058) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-557)))) +((-4461 |has| |#1| (-860))) +((|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-21))) (-2758 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-860)))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (-2758 (|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-557)))) (-856) ((|constructor| (NIL "Ordered finite sets.")) (|max| (($) "\\spad{max} is the maximum value of \\%.")) (|min| (($) "\\spad{min} is the minimum value of \\%."))) NIL NIL -(-857 -1911 S) +(-857 -2704 S) ((|constructor| (NIL "\\indented{3}{This package provides ordering functions on vectors which} are suitable parameters for OrderedDirectProduct.")) (|reverseLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{reverseLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by the reverse lexicographic ordering.")) (|totalLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{totalLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by lexicographic ordering.")) (|pureLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{pureLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the lexicographic ordering."))) NIL NIL @@ -3370,1831 +3370,1835 @@ NIL NIL (-860) ((|constructor| (NIL "Ordered sets which are also rings,{} that is,{} domains where the ring operations are compatible with the ordering. \\blankline")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x}.")) (|sign| (((|Integer|) $) "\\spad{sign(x)} is 1 if \\spad{x} is positive,{} \\spad{-1} if \\spad{x} is negative,{} 0 if \\spad{x} equals 0.")) (|negative?| (((|Boolean|) $) "\\spad{negative?(x)} tests whether \\spad{x} is strictly less than 0.")) (|positive?| (((|Boolean|) $) "\\spad{positive?(x)} tests whether \\spad{x} is strictly greater than 0."))) -((-4460 . T)) +((-4461 . T)) NIL (-861) ((|constructor| (NIL "The class of totally ordered sets,{} that is,{} sets such that for each pair of elements \\spad{(a,b)} exactly one of the following relations holds \\spad{a<b or a=b or b<a} and the relation is transitive,{} \\spadignore{i.e.} \\spad{a<b and b<c => a<c}."))) NIL NIL -(-862 S) +(-862 T$ |f|) +((|constructor| (NIL "This domain turns any total ordering \\spad{f} on a type \\spad{T} into a model of the category \\spadtype{OrderedType}."))) +NIL +NIL +(-863 S) ((|constructor| (NIL "Category of types equipped with a total ordering.")) (|min| (($ $ $) "\\spad{min(x,y)} returns the minimum of \\spad{x} and \\spad{y} relative to the ordering.")) (|max| (($ $ $) "\\spad{max(x,y)} returns the maximum of \\spad{x} and \\spad{y} relative to the ordering.")) (>= (((|Boolean|) $ $) "\\spad{x <= y} holds if \\spad{x} is greater or equal than \\spad{y} in the current domain.")) (<= (((|Boolean|) $ $) "\\spad{x <= y} holds if \\spad{x} is less or equal than \\spad{y} in the current domain.")) (> (((|Boolean|) $ $) "\\spad{x > y} holds if \\spad{x} is greater than \\spad{y} in the current domain.")) (< (((|Boolean|) $ $) "\\spad{x < y} holds if \\spad{x} is less than \\spad{y} in the current domain."))) NIL NIL -(-863) +(-864) ((|constructor| (NIL "Category of types equipped with a total ordering.")) (|min| (($ $ $) "\\spad{min(x,y)} returns the minimum of \\spad{x} and \\spad{y} relative to the ordering.")) (|max| (($ $ $) "\\spad{max(x,y)} returns the maximum of \\spad{x} and \\spad{y} relative to the ordering.")) (>= (((|Boolean|) $ $) "\\spad{x <= y} holds if \\spad{x} is greater or equal than \\spad{y} in the current domain.")) (<= (((|Boolean|) $ $) "\\spad{x <= y} holds if \\spad{x} is less or equal than \\spad{y} in the current domain.")) (> (((|Boolean|) $ $) "\\spad{x > y} holds if \\spad{x} is greater than \\spad{y} in the current domain.")) (< (((|Boolean|) $ $) "\\spad{x < y} holds if \\spad{x} is less than \\spad{y} in the current domain."))) NIL NIL -(-864 S R) +(-865 S R) ((|constructor| (NIL "This is the category of univariate skew polynomials over an Ore coefficient ring. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}. This category is an evolution of the types \\indented{2}{MonogenicLinearOperator,{} OppositeMonogenicLinearOperator,{} and} \\indented{2}{NonCommutativeOperatorDivision} developped by Jean Della Dora and Stephen \\spad{M}. Watt.")) (|leftLcm| (($ $ $) "\\spad{leftLcm(a,b)} computes the value \\spad{m} of lowest degree such that \\spad{m = aa*a = bb*b} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using right-division.")) (|rightExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{rightExtendedGcd(a,b)} returns \\spad{[c,d]} such that \\spad{g = c * a + d * b = rightGcd(a, b)}.")) (|rightGcd| (($ $ $) "\\spad{rightGcd(a,b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = aa*g}} \\indented{3}{\\spad{b = bb*g}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using right-division.")) (|rightExactQuotient| (((|Union| $ "failed") $ $) "\\spad{rightExactQuotient(a,b)} computes the value \\spad{q},{} if it exists such that \\spad{a = q*b}.")) (|rightRemainder| (($ $ $) "\\spad{rightRemainder(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|rightQuotient| (($ $ $) "\\spad{rightQuotient(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|rightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{rightDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``right division\\spad{''}.")) (|rightLcm| (($ $ $) "\\spad{rightLcm(a,b)} computes the value \\spad{m} of lowest degree such that \\spad{m = a*aa = b*bb} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using left-division.")) (|leftExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{leftExtendedGcd(a,b)} returns \\spad{[c,d]} such that \\spad{g = a * c + b * d = leftGcd(a, b)}.")) (|leftGcd| (($ $ $) "\\spad{leftGcd(a,b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = g*aa}} \\indented{3}{\\spad{b = g*bb}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using left-division.")) (|leftExactQuotient| (((|Union| $ "failed") $ $) "\\spad{leftExactQuotient(a,b)} computes the value \\spad{q},{} if it exists,{} \\indented{1}{such that \\spad{a = b*q}.}")) (|leftRemainder| (($ $ $) "\\spad{leftRemainder(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|leftQuotient| (($ $ $) "\\spad{leftQuotient(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|leftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{leftDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division\\spad{''}.")) (|primitivePart| (($ $) "\\spad{primitivePart(l)} returns \\spad{l0} such that \\spad{l = a * l0} for some a in \\spad{R},{} and \\spad{content(l0) = 1}.")) (|content| ((|#2| $) "\\spad{content(l)} returns the \\spad{gcd} of all the coefficients of \\spad{l}.")) (|monicRightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicRightDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``right division\\spad{''}.")) (|monicLeftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicLeftDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``left division\\spad{''}.")) (|exquo| (((|Union| $ "failed") $ |#2|) "\\spad{exquo(l, a)} returns the exact quotient of \\spad{l} by a,{} returning \\axiom{\"failed\"} if this is not possible.")) (|apply| ((|#2| $ |#2| |#2|) "\\spad{apply(p, c, m)} returns \\spad{p(m)} where the action is given by \\spad{x m = c sigma(m) + delta(m)}.")) (|coefficients| (((|List| |#2|) $) "\\spad{coefficients(l)} returns the list of all the nonzero coefficients of \\spad{l}.")) (|monomial| (($ |#2| (|NonNegativeInteger|)) "\\spad{monomial(c,k)} produces \\spad{c} times the \\spad{k}-th power of the generating operator,{} \\spad{monomial(1,1)}.")) (|coefficient| ((|#2| $ (|NonNegativeInteger|)) "\\spad{coefficient(l,k)} is \\spad{a(k)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|reductum| (($ $) "\\spad{reductum(l)} is \\spad{l - monomial(a(n),n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(l)} is \\spad{a(n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|minimumDegree| (((|NonNegativeInteger|) $) "\\spad{minimumDegree(l)} is the smallest \\spad{k} such that \\spad{a(k) ~= 0} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(l)} is \\spad{n} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}"))) NIL ((|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-174)))) -(-865 R) +(-866 R) ((|constructor| (NIL "This is the category of univariate skew polynomials over an Ore coefficient ring. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}. This category is an evolution of the types \\indented{2}{MonogenicLinearOperator,{} OppositeMonogenicLinearOperator,{} and} \\indented{2}{NonCommutativeOperatorDivision} developped by Jean Della Dora and Stephen \\spad{M}. Watt.")) (|leftLcm| (($ $ $) "\\spad{leftLcm(a,b)} computes the value \\spad{m} of lowest degree such that \\spad{m = aa*a = bb*b} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using right-division.")) (|rightExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{rightExtendedGcd(a,b)} returns \\spad{[c,d]} such that \\spad{g = c * a + d * b = rightGcd(a, b)}.")) (|rightGcd| (($ $ $) "\\spad{rightGcd(a,b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = aa*g}} \\indented{3}{\\spad{b = bb*g}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using right-division.")) (|rightExactQuotient| (((|Union| $ "failed") $ $) "\\spad{rightExactQuotient(a,b)} computes the value \\spad{q},{} if it exists such that \\spad{a = q*b}.")) (|rightRemainder| (($ $ $) "\\spad{rightRemainder(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|rightQuotient| (($ $ $) "\\spad{rightQuotient(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|rightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{rightDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``right division\\spad{''}.")) (|rightLcm| (($ $ $) "\\spad{rightLcm(a,b)} computes the value \\spad{m} of lowest degree such that \\spad{m = a*aa = b*bb} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using left-division.")) (|leftExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{leftExtendedGcd(a,b)} returns \\spad{[c,d]} such that \\spad{g = a * c + b * d = leftGcd(a, b)}.")) (|leftGcd| (($ $ $) "\\spad{leftGcd(a,b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = g*aa}} \\indented{3}{\\spad{b = g*bb}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using left-division.")) (|leftExactQuotient| (((|Union| $ "failed") $ $) "\\spad{leftExactQuotient(a,b)} computes the value \\spad{q},{} if it exists,{} \\indented{1}{such that \\spad{a = b*q}.}")) (|leftRemainder| (($ $ $) "\\spad{leftRemainder(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|leftQuotient| (($ $ $) "\\spad{leftQuotient(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|leftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{leftDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division\\spad{''}.")) (|primitivePart| (($ $) "\\spad{primitivePart(l)} returns \\spad{l0} such that \\spad{l = a * l0} for some a in \\spad{R},{} and \\spad{content(l0) = 1}.")) (|content| ((|#1| $) "\\spad{content(l)} returns the \\spad{gcd} of all the coefficients of \\spad{l}.")) (|monicRightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicRightDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``right division\\spad{''}.")) (|monicLeftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicLeftDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``left division\\spad{''}.")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(l, a)} returns the exact quotient of \\spad{l} by a,{} returning \\axiom{\"failed\"} if this is not possible.")) (|apply| ((|#1| $ |#1| |#1|) "\\spad{apply(p, c, m)} returns \\spad{p(m)} where the action is given by \\spad{x m = c sigma(m) + delta(m)}.")) (|coefficients| (((|List| |#1|) $) "\\spad{coefficients(l)} returns the list of all the nonzero coefficients of \\spad{l}.")) (|monomial| (($ |#1| (|NonNegativeInteger|)) "\\spad{monomial(c,k)} produces \\spad{c} times the \\spad{k}-th power of the generating operator,{} \\spad{monomial(1,1)}.")) (|coefficient| ((|#1| $ (|NonNegativeInteger|)) "\\spad{coefficient(l,k)} is \\spad{a(k)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|reductum| (($ $) "\\spad{reductum(l)} is \\spad{l - monomial(a(n),n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(l)} is \\spad{a(n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|minimumDegree| (((|NonNegativeInteger|) $) "\\spad{minimumDegree(l)} is the smallest \\spad{k} such that \\spad{a(k) ~= 0} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(l)} is \\spad{n} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}"))) -((-4457 . T) (-4458 . T) (-4460 . T)) +((-4458 . T) (-4459 . T) (-4461 . T)) NIL -(-866 R C) +(-867 R C) ((|constructor| (NIL "\\spad{UnivariateSkewPolynomialCategoryOps} provides products and \\indented{1}{divisions of univariate skew polynomials.}")) (|rightDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{rightDivide(a, b, sigma)} returns the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``right division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|leftDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{leftDivide(a, b, sigma)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|monicRightDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{monicRightDivide(a, b, sigma)} returns the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``right division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|monicLeftDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{monicLeftDivide(a, b, sigma)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``left division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|apply| ((|#1| |#2| |#1| |#1| (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{apply(p, c, m, sigma, delta)} returns \\spad{p(m)} where the action is given by \\spad{x m = c sigma(m) + delta(m)}.")) (|times| ((|#2| |#2| |#2| (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{times(p, q, sigma, delta)} returns \\spad{p * q}. \\spad{\\sigma} and \\spad{\\delta} are the maps to use."))) NIL ((|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) -(-867 R |sigma| -1991) +(-868 R |sigma| -3642) ((|constructor| (NIL "This is the domain of sparse univariate skew polynomials over an Ore coefficient field. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}.")) (|outputForm| (((|OutputForm|) $ (|OutputForm|)) "\\spad{outputForm(p, x)} returns the output form of \\spad{p} using \\spad{x} for the otherwise anonymous variable."))) -((-4457 . T) (-4458 . T) (-4460 . T)) -((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -1058) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1058) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-374)))) -(-868 |x| R |sigma| -1991) +((-4458 . T) (-4459 . T) (-4461 . T)) +((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-374)))) +(-869 |x| R |sigma| -3642) ((|constructor| (NIL "This is the domain of univariate skew polynomials over an Ore coefficient field in a named variable. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}."))) -((-4457 . T) (-4458 . T) (-4460 . T)) -((|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (LIST (QUOTE -1058) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1058) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-374)))) -(-869 R) +((-4458 . T) (-4459 . T) (-4461 . T)) +((|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-374)))) +(-870 R) ((|constructor| (NIL "This package provides orthogonal polynomials as functions on a ring.")) (|legendreP| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{legendreP(n,x)} is the \\spad{n}-th Legendre polynomial,{} \\spad{P[n](x)}. These are defined by \\spad{1/sqrt(1-2*x*t+t**2) = sum(P[n](x)*t**n, n = 0..)}.")) (|laguerreL| ((|#1| (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|) "\\spad{laguerreL(m,n,x)} is the associated Laguerre polynomial,{} \\spad{L<m>[n](x)}. This is the \\spad{m}-th derivative of \\spad{L[n](x)}.") ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{laguerreL(n,x)} is the \\spad{n}-th Laguerre polynomial,{} \\spad{L[n](x)}. These are defined by \\spad{exp(-t*x/(1-t))/(1-t) = sum(L[n](x)*t**n/n!, n = 0..)}.")) (|hermiteH| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{hermiteH(n,x)} is the \\spad{n}-th Hermite polynomial,{} \\spad{H[n](x)}. These are defined by \\spad{exp(2*t*x-t**2) = sum(H[n](x)*t**n/n!, n = 0..)}.")) (|chebyshevU| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{chebyshevU(n,x)} is the \\spad{n}-th Chebyshev polynomial of the second kind,{} \\spad{U[n](x)}. These are defined by \\spad{1/(1-2*t*x+t**2) = sum(T[n](x) *t**n, n = 0..)}.")) (|chebyshevT| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{chebyshevT(n,x)} is the \\spad{n}-th Chebyshev polynomial of the first kind,{} \\spad{T[n](x)}. These are defined by \\spad{(1-t*x)/(1-2*t*x+t**2) = sum(T[n](x) *t**n, n = 0..)}."))) NIL ((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) -(-870) +(-871) ((|constructor| (NIL "Semigroups with compatible ordering."))) NIL NIL -(-871) +(-872) ((|constructor| (NIL "\\indented{1}{Author : Larry Lambe} Date created : 14 August 1988 Date Last Updated : 11 March 1991 Description : A domain used in order to take the free \\spad{R}-module on the Integers \\spad{I}. This is actually the forgetful functor from OrderedRings to OrderedSets applied to \\spad{I}")) (|value| (((|Integer|) $) "\\spad{value(x)} returns the integer associated with \\spad{x}")) (|coerce| (($ (|Integer|)) "\\spad{coerce(i)} returns the element corresponding to \\spad{i}"))) NIL NIL -(-872 S) +(-873 S) ((|constructor| (NIL "This category describes output byte stream conduits.")) (|writeBytes!| (((|NonNegativeInteger|) $ (|ByteBuffer|)) "\\spad{writeBytes!(c,b)} write bytes from buffer \\spad{`b'} onto the conduit \\spad{`c'}. The actual number of written bytes is returned.")) (|writeUInt8!| (((|Maybe| (|UInt8|)) $ (|UInt8|)) "\\spad{writeUInt8!(c,b)} attempts to write the unsigned 8-bit value \\spad{`v'} on the conduit \\spad{`c'}. Returns the written value if successful,{} otherwise,{} returns \\spad{nothing}.")) (|writeInt8!| (((|Maybe| (|Int8|)) $ (|Int8|)) "\\spad{writeInt8!(c,b)} attempts to write the 8-bit value \\spad{`v'} on the conduit \\spad{`c'}. Returns the written value if successful,{} otherwise,{} returns \\spad{nothing}.")) (|writeByte!| (((|Maybe| (|Byte|)) $ (|Byte|)) "\\spad{writeByte!(c,b)} attempts to write the byte \\spad{`b'} on the conduit \\spad{`c'}. Returns the written byte if successful,{} otherwise,{} returns \\spad{nothing}."))) NIL NIL -(-873) +(-874) ((|constructor| (NIL "This category describes output byte stream conduits.")) (|writeBytes!| (((|NonNegativeInteger|) $ (|ByteBuffer|)) "\\spad{writeBytes!(c,b)} write bytes from buffer \\spad{`b'} onto the conduit \\spad{`c'}. The actual number of written bytes is returned.")) (|writeUInt8!| (((|Maybe| (|UInt8|)) $ (|UInt8|)) "\\spad{writeUInt8!(c,b)} attempts to write the unsigned 8-bit value \\spad{`v'} on the conduit \\spad{`c'}. Returns the written value if successful,{} otherwise,{} returns \\spad{nothing}.")) (|writeInt8!| (((|Maybe| (|Int8|)) $ (|Int8|)) "\\spad{writeInt8!(c,b)} attempts to write the 8-bit value \\spad{`v'} on the conduit \\spad{`c'}. Returns the written value if successful,{} otherwise,{} returns \\spad{nothing}.")) (|writeByte!| (((|Maybe| (|Byte|)) $ (|Byte|)) "\\spad{writeByte!(c,b)} attempts to write the byte \\spad{`b'} on the conduit \\spad{`c'}. Returns the written byte if successful,{} otherwise,{} returns \\spad{nothing}."))) NIL NIL -(-874) +(-875) ((|constructor| (NIL "This domain provides representation for binary files open for output operations. `Binary' here means that the conduits do not interpret their contents.")) (|isOpen?| (((|Boolean|) $) "open?(ifile) holds if `ifile' is in open state.")) (|outputBinaryFile| (($ (|String|)) "\\spad{outputBinaryFile(f)} returns an output conduit obtained by opening the file named by \\spad{`f'} as a binary file.") (($ (|FileName|)) "\\spad{outputBinaryFile(f)} returns an output conduit obtained by opening the file named by \\spad{`f'} as a binary file."))) NIL NIL -(-875) +(-876) ((|constructor| (NIL "This domain is used to create and manipulate mathematical expressions for output. It is intended to provide an insulating layer between the expression rendering software (\\spadignore{e.g.} TeX,{} or Script) and the output coercions in the various domains.")) (SEGMENT (($ $) "\\spad{SEGMENT(x)} creates the prefix form: \\spad{x..}.") (($ $ $) "\\spad{SEGMENT(x,y)} creates the infix form: \\spad{x..y}.")) (|not| (($ $) "\\spad{not f} creates the equivalent prefix form.")) (|or| (($ $ $) "\\spad{f or g} creates the equivalent infix form.")) (|and| (($ $ $) "\\spad{f and g} creates the equivalent infix form.")) (|exquo| (($ $ $) "\\spad{exquo(f,g)} creates the equivalent infix form.")) (|quo| (($ $ $) "\\spad{f quo g} creates the equivalent infix form.")) (|rem| (($ $ $) "\\spad{f rem g} creates the equivalent infix form.")) (|div| (($ $ $) "\\spad{f div g} creates the equivalent infix form.")) (** (($ $ $) "\\spad{f ** g} creates the equivalent infix form.")) (/ (($ $ $) "\\spad{f / g} creates the equivalent infix form.")) (* (($ $ $) "\\spad{f * g} creates the equivalent infix form.")) (- (($ $) "\\spad{- f} creates the equivalent prefix form.") (($ $ $) "\\spad{f - g} creates the equivalent infix form.")) (+ (($ $ $) "\\spad{f + g} creates the equivalent infix form.")) (>= (($ $ $) "\\spad{f >= g} creates the equivalent infix form.")) (<= (($ $ $) "\\spad{f <= g} creates the equivalent infix form.")) (> (($ $ $) "\\spad{f > g} creates the equivalent infix form.")) (< (($ $ $) "\\spad{f < g} creates the equivalent infix form.")) (~= (($ $ $) "\\spad{f ~= g} creates the equivalent infix form.")) (= (($ $ $) "\\spad{f = g} creates the equivalent infix form.")) (|blankSeparate| (($ (|List| $)) "\\spad{blankSeparate(l)} creates the form separating the elements of \\spad{l} by blanks.")) (|semicolonSeparate| (($ (|List| $)) "\\spad{semicolonSeparate(l)} creates the form separating the elements of \\spad{l} by semicolons.")) (|commaSeparate| (($ (|List| $)) "\\spad{commaSeparate(l)} creates the form separating the elements of \\spad{l} by commas.")) (|pile| (($ (|List| $)) "\\spad{pile(l)} creates the form consisting of the elements of \\spad{l} which displays as a pile,{} \\spadignore{i.e.} the elements begin on a new line and are indented right to the same margin.")) (|paren| (($ (|List| $)) "\\spad{paren(lf)} creates the form separating the elements of \\spad{lf} by commas and encloses the result in parentheses.") (($ $) "\\spad{paren(f)} creates the form enclosing \\spad{f} in parentheses.")) (|bracket| (($ (|List| $)) "\\spad{bracket(lf)} creates the form separating the elements of \\spad{lf} by commas and encloses the result in square brackets.") (($ $) "\\spad{bracket(f)} creates the form enclosing \\spad{f} in square brackets.")) (|brace| (($ (|List| $)) "\\spad{brace(lf)} creates the form separating the elements of \\spad{lf} by commas and encloses the result in curly brackets.") (($ $) "\\spad{brace(f)} creates the form enclosing \\spad{f} in braces (curly brackets).")) (|int| (($ $ $ $) "\\spad{int(expr,lowerlimit,upperlimit)} creates the form prefixing \\spad{expr} by an integral sign with both a \\spad{lowerlimit} and \\spad{upperlimit}.") (($ $ $) "\\spad{int(expr,lowerlimit)} creates the form prefixing \\spad{expr} by an integral sign with a \\spad{lowerlimit}.") (($ $) "\\spad{int(expr)} creates the form prefixing \\spad{expr} with an integral sign.")) (|prod| (($ $ $ $) "\\spad{prod(expr,lowerlimit,upperlimit)} creates the form prefixing \\spad{expr} by a capital \\spad{pi} with both a \\spad{lowerlimit} and \\spad{upperlimit}.") (($ $ $) "\\spad{prod(expr,lowerlimit)} creates the form prefixing \\spad{expr} by a capital \\spad{pi} with a \\spad{lowerlimit}.") (($ $) "\\spad{prod(expr)} creates the form prefixing \\spad{expr} by a capital \\spad{pi}.")) (|sum| (($ $ $ $) "\\spad{sum(expr,lowerlimit,upperlimit)} creates the form prefixing \\spad{expr} by a capital sigma with both a \\spad{lowerlimit} and \\spad{upperlimit}.") (($ $ $) "\\spad{sum(expr,lowerlimit)} creates the form prefixing \\spad{expr} by a capital sigma with a \\spad{lowerlimit}.") (($ $) "\\spad{sum(expr)} creates the form prefixing \\spad{expr} by a capital sigma.")) (|overlabel| (($ $ $) "\\spad{overlabel(x,f)} creates the form \\spad{f} with \\spad{\"x} overbar\" over the top.")) (|overbar| (($ $) "\\spad{overbar(f)} creates the form \\spad{f} with an overbar.")) (|prime| (($ $ (|NonNegativeInteger|)) "\\spad{prime(f,n)} creates the form \\spad{f} followed by \\spad{n} primes.") (($ $) "\\spad{prime(f)} creates the form \\spad{f} followed by a suffix prime (single quote).")) (|dot| (($ $ (|NonNegativeInteger|)) "\\spad{dot(f,n)} creates the form \\spad{f} with \\spad{n} dots overhead.") (($ $) "\\spad{dot(f)} creates the form with a one dot overhead.")) (|quote| (($ $) "\\spad{quote(f)} creates the form \\spad{f} with a prefix quote.")) (|supersub| (($ $ (|List| $)) "\\spad{supersub(a,[sub1,super1,sub2,super2,...])} creates a form with each subscript aligned under each superscript.")) (|scripts| (($ $ (|List| $)) "\\spad{scripts(f, [sub, super, presuper, presub])} \\indented{1}{creates a form for \\spad{f} with scripts on all 4 corners.}")) (|presuper| (($ $ $) "\\spad{presuper(f,n)} creates a form for \\spad{f} presuperscripted by \\spad{n}.")) (|presub| (($ $ $) "\\spad{presub(f,n)} creates a form for \\spad{f} presubscripted by \\spad{n}.")) (|super| (($ $ $) "\\spad{super(f,n)} creates a form for \\spad{f} superscripted by \\spad{n}.")) (|sub| (($ $ $) "\\spad{sub(f,n)} creates a form for \\spad{f} subscripted by \\spad{n}.")) (|binomial| (($ $ $) "\\spad{binomial(n,m)} creates a form for the binomial coefficient of \\spad{n} and \\spad{m}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(f,n)} creates a form for the \\spad{n}th derivative of \\spad{f},{} \\spadignore{e.g.} \\spad{f'},{} \\spad{f''},{} \\spad{f'''},{} \\spad{\"f} super \\spad{iv}\".")) (|rarrow| (($ $ $) "\\spad{rarrow(f,g)} creates a form for the mapping \\spad{f -> g}.")) (|assign| (($ $ $) "\\spad{assign(f,g)} creates a form for the assignment \\spad{f := g}.")) (|slash| (($ $ $) "\\spad{slash(f,g)} creates a form for the horizontal fraction of \\spad{f} over \\spad{g}.")) (|over| (($ $ $) "\\spad{over(f,g)} creates a form for the vertical fraction of \\spad{f} over \\spad{g}.")) (|root| (($ $ $) "\\spad{root(f,n)} creates a form for the \\spad{n}th root of form \\spad{f}.") (($ $) "\\spad{root(f)} creates a form for the square root of form \\spad{f}.")) (|zag| (($ $ $) "\\spad{zag(f,g)} creates a form for the continued fraction form for \\spad{f} over \\spad{g}.")) (|matrix| (($ (|List| (|List| $))) "\\spad{matrix(llf)} makes \\spad{llf} (a list of lists of forms) into a form which displays as a matrix.")) (|box| (($ $) "\\spad{box(f)} encloses \\spad{f} in a box.")) (|label| (($ $ $) "\\spad{label(n,f)} gives form \\spad{f} an equation label \\spad{n}.")) (|string| (($ $) "\\spad{string(f)} creates \\spad{f} with string quotes.")) (|elt| (($ $ (|List| $)) "\\spad{elt(op,l)} creates a form for application of \\spad{op} to list of arguments \\spad{l}.")) (|infix?| (((|Boolean|) $) "\\spad{infix?(op)} returns \\spad{true} if \\spad{op} is an infix operator,{} and \\spad{false} otherwise.")) (|postfix| (($ $ $) "\\spad{postfix(op, a)} creates a form which prints as: a \\spad{op}.")) (|infix| (($ $ $ $) "\\spad{infix(op, a, b)} creates a form which prints as: a \\spad{op} \\spad{b}.") (($ $ (|List| $)) "\\spad{infix(f,l)} creates a form depicting the \\spad{n}-ary application of infix operation \\spad{f} to a tuple of arguments \\spad{l}.")) (|prefix| (($ $ (|List| $)) "\\spad{prefix(f,l)} creates a form depicting the \\spad{n}-ary prefix application of \\spad{f} to a tuple of arguments given by list \\spad{l}.")) (|vconcat| (($ (|List| $)) "\\spad{vconcat(u)} vertically concatenates all forms in list \\spad{u}.") (($ $ $) "\\spad{vconcat(f,g)} vertically concatenates forms \\spad{f} and \\spad{g}.")) (|hconcat| (($ (|List| $)) "\\spad{hconcat(u)} horizontally concatenates all forms in list \\spad{u}.") (($ $ $) "\\spad{hconcat(f,g)} horizontally concatenate forms \\spad{f} and \\spad{g}.")) (|center| (($ $) "\\spad{center(f)} centers form \\spad{f} in total space.") (($ $ (|Integer|)) "\\spad{center(f,n)} centers form \\spad{f} within space of width \\spad{n}.")) (|right| (($ $) "\\spad{right(f)} right-justifies form \\spad{f} in total space.") (($ $ (|Integer|)) "\\spad{right(f,n)} right-justifies form \\spad{f} within space of width \\spad{n}.")) (|left| (($ $) "\\spad{left(f)} left-justifies form \\spad{f} in total space.") (($ $ (|Integer|)) "\\spad{left(f,n)} left-justifies form \\spad{f} within space of width \\spad{n}.")) (|rspace| (($ (|Integer|) (|Integer|)) "\\spad{rspace(n,m)} creates rectangular white space,{} \\spad{n} wide by \\spad{m} high.")) (|vspace| (($ (|Integer|)) "\\spad{vspace(n)} creates white space of height \\spad{n}.")) (|hspace| (($ (|Integer|)) "\\spad{hspace(n)} creates white space of width \\spad{n}.")) (|superHeight| (((|Integer|) $) "\\spad{superHeight(f)} returns the height of form \\spad{f} above the base line.")) (|subHeight| (((|Integer|) $) "\\spad{subHeight(f)} returns the height of form \\spad{f} below the base line.")) (|height| (((|Integer|)) "\\spad{height()} returns the height of the display area (an integer).") (((|Integer|) $) "\\spad{height(f)} returns the height of form \\spad{f} (an integer).")) (|width| (((|Integer|)) "\\spad{width()} returns the width of the display area (an integer).") (((|Integer|) $) "\\spad{width(f)} returns the width of form \\spad{f} (an integer).")) (|doubleFloatFormat| (((|String|) (|String|)) "change the output format for doublefloats using lisp format strings")) (|empty| (($) "\\spad{empty()} creates an empty form.")) (|outputForm| (($ (|DoubleFloat|)) "\\spad{outputForm(sf)} creates an form for small float \\spad{sf}.") (($ (|String|)) "\\spad{outputForm(s)} creates an form for string \\spad{s}.") (($ (|Symbol|)) "\\spad{outputForm(s)} creates an form for symbol \\spad{s}.") (($ (|Integer|)) "\\spad{outputForm(n)} creates an form for integer \\spad{n}.")) (|messagePrint| (((|Void|) (|String|)) "\\spad{messagePrint(s)} prints \\spad{s} without string quotes. Note: \\spad{messagePrint(s)} is equivalent to \\spad{print message(s)}.")) (|message| (($ (|String|)) "\\spad{message(s)} creates an form with no string quotes from string \\spad{s}.")) (|print| (((|Void|) $) "\\spad{print(u)} prints the form \\spad{u}."))) NIL NIL -(-876) +(-877) ((|constructor| (NIL "OutPackage allows pretty-printing from programs.")) (|outputList| (((|Void|) (|List| (|Any|))) "\\spad{outputList(l)} displays the concatenated components of the list \\spad{l} on the ``algebra output\\spad{''} stream,{} as defined by \\spadsyscom{set output algebra}; quotes are stripped from strings.")) (|output| (((|Void|) (|String|) (|OutputForm|)) "\\spad{output(s,x)} displays the string \\spad{s} followed by the form \\spad{x} on the ``algebra output\\spad{''} stream,{} as defined by \\spadsyscom{set output algebra}.") (((|Void|) (|OutputForm|)) "\\spad{output(x)} displays the output form \\spad{x} on the ``algebra output\\spad{''} stream,{} as defined by \\spadsyscom{set output algebra}.") (((|Void|) (|String|)) "\\spad{output(s)} displays the string \\spad{s} on the ``algebra output\\spad{''} stream,{} as defined by \\spadsyscom{set output algebra}."))) NIL NIL -(-877 |VariableList|) +(-878 |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 -(-878) +(-879) ((|constructor| (NIL "This domain represents set of overloaded operators (in fact operator descriptors).")) (|members| (((|List| (|FunctionDescriptor|)) $) "\\spad{members(x)} returns the list of operator descriptors,{} \\spadignore{e.g.} signature and implementation slots,{} of the overload set \\spad{x}.")) (|name| (((|Identifier|) $) "\\spad{name(x)} returns the name of the overload set \\spad{x}."))) NIL NIL -(-879 R |vl| |wl| |wtlevel|) +(-880 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)"))) -((-4458 |has| |#1| (-174)) (-4457 |has| |#1| (-174)) (-4460 . T)) +((-4459 |has| |#1| (-174)) (-4458 |has| |#1| (-174)) (-4461 . T)) ((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374)))) -(-880 R PS UP) +(-881 R PS UP) ((|constructor| (NIL "\\indented{1}{This package computes reliable Pad&ea. approximants using} a generalized Viskovatov continued fraction algorithm. Authors: Burge,{} Hassner & Watt. Date Created: April 1987 Date Last Updated: 12 April 1990 Keywords: Pade,{} series Examples: References: \\indented{2}{\"Pade Approximants,{} Part I: Basic Theory\",{} Baker & Graves-Morris.}")) (|padecf| (((|Union| (|ContinuedFraction| |#3|) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) |#2| |#2|) "\\spad{padecf(nd,dd,ns,ds)} computes the approximant as a continued fraction of polynomials (if it exists) for arguments \\spad{nd} (numerator degree of approximant),{} \\spad{dd} (denominator degree of approximant),{} \\spad{ns} (numerator series of function),{} and \\spad{ds} (denominator series of function).")) (|pade| (((|Union| (|Fraction| |#3|) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) |#2| |#2|) "\\spad{pade(nd,dd,ns,ds)} computes the approximant as a quotient of polynomials (if it exists) for arguments \\spad{nd} (numerator degree of approximant),{} \\spad{dd} (denominator degree of approximant),{} \\spad{ns} (numerator series of function),{} and \\spad{ds} (denominator series of function)."))) NIL NIL -(-881 R |x| |pt|) +(-882 R |x| |pt|) ((|constructor| (NIL "\\indented{1}{This package computes reliable Pad&ea. approximants using} a generalized Viskovatov continued fraction algorithm. Authors: Trager,{}Burge,{} Hassner & Watt. Date Created: April 1987 Date Last Updated: 12 April 1990 Keywords: Pade,{} series Examples: References: \\indented{2}{\"Pade Approximants,{} Part I: Basic Theory\",{} Baker & Graves-Morris.}")) (|pade| (((|Union| (|Fraction| (|UnivariatePolynomial| |#2| |#1|)) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) (|UnivariateTaylorSeries| |#1| |#2| |#3|)) "\\spad{pade(nd,dd,s)} computes the quotient of polynomials (if it exists) with numerator degree at most \\spad{nd} and denominator degree at most \\spad{dd} which matches the series \\spad{s} to order \\spad{nd + dd}.") (((|Union| (|Fraction| (|UnivariatePolynomial| |#2| |#1|)) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) (|UnivariateTaylorSeries| |#1| |#2| |#3|) (|UnivariateTaylorSeries| |#1| |#2| |#3|)) "\\spad{pade(nd,dd,ns,ds)} computes the approximant as a quotient of polynomials (if it exists) for arguments \\spad{nd} (numerator degree of approximant),{} \\spad{dd} (denominator degree of approximant),{} \\spad{ns} (numerator series of function),{} and \\spad{ds} (denominator series of function)."))) NIL NIL -(-882 |p|) +(-883 |p|) ((|constructor| (NIL "This is the catefory of stream-based representations of \\indented{2}{the \\spad{p}-adic integers.}")) (|root| (($ (|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{root(f,a)} returns a root of the polynomial \\spad{f}. Argument \\spad{a} must be a root of \\spad{f} \\spad{(mod p)}.")) (|sqrt| (($ $ (|Integer|)) "\\spad{sqrt(b,a)} returns a square root of \\spad{b}. Argument \\spad{a} is a square root of \\spad{b} \\spad{(mod p)}.")) (|approximate| (((|Integer|) $ (|Integer|)) "\\spad{approximate(x,n)} returns an integer \\spad{y} such that \\spad{y = x (mod p^n)} when \\spad{n} is positive,{} and 0 otherwise.")) (|quotientByP| (($ $) "\\spad{quotientByP(x)} returns \\spad{b},{} where \\spad{x = a + b p}.")) (|moduloP| (((|Integer|) $) "\\spad{modulo(x)} returns a,{} where \\spad{x = a + b p}.")) (|modulus| (((|Integer|)) "\\spad{modulus()} returns the value of \\spad{p}.")) (|complete| (($ $) "\\spad{complete(x)} forces the computation of all digits.")) (|extend| (($ $ (|Integer|)) "\\spad{extend(x,n)} forces the computation of digits up to order \\spad{n}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(x)} returns the exponent of the highest power of \\spad{p} dividing \\spad{x}.")) (|digits| (((|Stream| (|Integer|)) $) "\\spad{digits(x)} returns a stream of \\spad{p}-adic digits of \\spad{x}."))) -((-4456 . T) ((-4465 "*") . T) (-4457 . T) (-4458 . T) (-4460 . T)) +((-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL -(-883 |p|) +(-884 |p|) ((|constructor| (NIL "Stream-based implementation of \\spad{Zp:} \\spad{p}-adic numbers are represented as sum(\\spad{i} = 0..,{} a[\\spad{i}] * p^i),{} where the a[\\spad{i}] lie in 0,{}1,{}...,{}(\\spad{p} - 1)."))) -((-4456 . T) ((-4465 "*") . T) (-4457 . T) (-4458 . T) (-4460 . T)) +((-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL -(-884 |p|) +(-885 |p|) ((|constructor| (NIL "Stream-based implementation of \\spad{Qp:} numbers are represented as sum(\\spad{i} = \\spad{k}..,{} a[\\spad{i}] * p^i) where the a[\\spad{i}] lie in 0,{}1,{}...,{}(\\spad{p} - 1)."))) -((-4455 . T) (-4461 . T) (-4456 . T) ((-4465 "*") . T) (-4457 . T) (-4458 . T) (-4460 . T)) -((|HasCategory| (-883 |#1|) (QUOTE (-927))) (|HasCategory| (-883 |#1|) (LIST (QUOTE -1058) (QUOTE (-1196)))) (|HasCategory| (-883 |#1|) (QUOTE (-146))) (|HasCategory| (-883 |#1|) (QUOTE (-148))) (|HasCategory| (-883 |#1|) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-883 |#1|) (QUOTE (-1042))) (|HasCategory| (-883 |#1|) (QUOTE (-832))) (|HasCategory| (-883 |#1|) (QUOTE (-861))) (-3794 (|HasCategory| (-883 |#1|) (QUOTE (-832))) (|HasCategory| (-883 |#1|) (QUOTE (-861)))) (|HasCategory| (-883 |#1|) (LIST (QUOTE -1058) (QUOTE (-576)))) (|HasCategory| (-883 |#1|) (QUOTE (-1172))) (|HasCategory| (-883 |#1|) (LIST (QUOTE -900) (QUOTE (-390)))) (|HasCategory| (-883 |#1|) (LIST (QUOTE -900) (QUOTE (-576)))) (|HasCategory| (-883 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -906) (QUOTE (-390))))) (|HasCategory| (-883 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -906) (QUOTE (-576))))) (|HasCategory| (-883 |#1|) (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| (-883 |#1|) (QUOTE (-237))) (|HasCategory| (-883 |#1|) (LIST (QUOTE -918) (QUOTE (-1196)))) (|HasCategory| (-883 |#1|) (QUOTE (-238))) (|HasCategory| (-883 |#1|) (LIST (QUOTE -916) (QUOTE (-1196)))) (|HasCategory| (-883 |#1|) (LIST (QUOTE -526) (QUOTE (-1196)) (LIST (QUOTE -883) (|devaluate| |#1|)))) (|HasCategory| (-883 |#1|) (LIST (QUOTE -319) (LIST (QUOTE -883) (|devaluate| |#1|)))) (|HasCategory| (-883 |#1|) (LIST (QUOTE -296) (LIST (QUOTE -883) (|devaluate| |#1|)) (LIST (QUOTE -883) (|devaluate| |#1|)))) (|HasCategory| (-883 |#1|) (QUOTE (-317))) (|HasCategory| (-883 |#1|) (QUOTE (-557))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-883 |#1|) (QUOTE (-927)))) (-3794 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-883 |#1|) (QUOTE (-927)))) (|HasCategory| (-883 |#1|) (QUOTE (-146))))) -(-885 |p| PADIC) +((-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) +((|HasCategory| (-884 |#1|) (QUOTE (-928))) (|HasCategory| (-884 |#1|) (LIST (QUOTE -1059) (QUOTE (-1197)))) (|HasCategory| (-884 |#1|) (QUOTE (-146))) (|HasCategory| (-884 |#1|) (QUOTE (-148))) (|HasCategory| (-884 |#1|) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-884 |#1|) (QUOTE (-1043))) (|HasCategory| (-884 |#1|) (QUOTE (-832))) (|HasCategory| (-884 |#1|) (QUOTE (-861))) (-2758 (|HasCategory| (-884 |#1|) (QUOTE (-832))) (|HasCategory| (-884 |#1|) (QUOTE (-861)))) (|HasCategory| (-884 |#1|) (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| (-884 |#1|) (QUOTE (-1173))) (|HasCategory| (-884 |#1|) (LIST (QUOTE -901) (QUOTE (-390)))) (|HasCategory| (-884 |#1|) (LIST (QUOTE -901) (QUOTE (-576)))) (|HasCategory| (-884 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390))))) (|HasCategory| (-884 |#1|) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576))))) (|HasCategory| (-884 |#1|) (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| (-884 |#1|) (QUOTE (-237))) (|HasCategory| (-884 |#1|) (LIST (QUOTE -919) (QUOTE (-1197)))) (|HasCategory| (-884 |#1|) (QUOTE (-238))) (|HasCategory| (-884 |#1|) (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| (-884 |#1|) (LIST (QUOTE -526) (QUOTE (-1197)) (LIST (QUOTE -884) (|devaluate| |#1|)))) (|HasCategory| (-884 |#1|) (LIST (QUOTE -319) (LIST (QUOTE -884) (|devaluate| |#1|)))) (|HasCategory| (-884 |#1|) (LIST (QUOTE -296) (LIST (QUOTE -884) (|devaluate| |#1|)) (LIST (QUOTE -884) (|devaluate| |#1|)))) (|HasCategory| (-884 |#1|) (QUOTE (-317))) (|HasCategory| (-884 |#1|) (QUOTE (-557))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-884 |#1|) (QUOTE (-928)))) (-2758 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-884 |#1|) (QUOTE (-928)))) (|HasCategory| (-884 |#1|) (QUOTE (-146))))) +(-886 |p| PADIC) ((|constructor| (NIL "This is the category of stream-based representations of \\spad{Qp}.")) (|removeZeroes| (($ (|Integer|) $) "\\spad{removeZeroes(n,x)} removes up to \\spad{n} leading zeroes from the \\spad{p}-adic rational \\spad{x}.") (($ $) "\\spad{removeZeroes(x)} removes leading zeroes from the representation of the \\spad{p}-adic rational \\spad{x}. A \\spad{p}-adic rational is represented by (1) an exponent and (2) a \\spad{p}-adic integer which may have leading zero digits. When the \\spad{p}-adic integer has a leading zero digit,{} a 'leading zero' is removed from the \\spad{p}-adic rational as follows: the number is rewritten by increasing the exponent by 1 and dividing the \\spad{p}-adic integer by \\spad{p}. Note: \\spad{removeZeroes(f)} removes all leading zeroes from \\spad{f}.")) (|continuedFraction| (((|ContinuedFraction| (|Fraction| (|Integer|))) $) "\\spad{continuedFraction(x)} converts the \\spad{p}-adic rational number \\spad{x} to a continued fraction.")) (|approximate| (((|Fraction| (|Integer|)) $ (|Integer|)) "\\spad{approximate(x,n)} returns a rational number \\spad{y} such that \\spad{y = x (mod p^n)}."))) -((-4455 . T) (-4461 . T) (-4456 . T) ((-4465 "*") . T) (-4457 . T) (-4458 . T) (-4460 . T)) -((|HasCategory| |#2| (QUOTE (-927))) (|HasCategory| |#2| (LIST (QUOTE -1058) (QUOTE (-1196)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (QUOTE (-1042))) (|HasCategory| |#2| (QUOTE (-832))) (|HasCategory| |#2| (QUOTE (-861))) (-3794 (|HasCategory| |#2| (QUOTE (-832))) (|HasCategory| |#2| (QUOTE (-861)))) (|HasCategory| |#2| (LIST (QUOTE -1058) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-1172))) (|HasCategory| |#2| (LIST (QUOTE -900) (QUOTE (-390)))) (|HasCategory| |#2| (LIST (QUOTE -900) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -906) (QUOTE (-390))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -906) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-237))) (|HasCategory| |#2| (LIST (QUOTE -918) (QUOTE (-1196)))) (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (LIST (QUOTE -916) (QUOTE (-1196)))) (|HasCategory| |#2| (LIST (QUOTE -526) (QUOTE (-1196)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -296) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-317))) (|HasCategory| |#2| (QUOTE (-557))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-927)))) (-3794 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-927)))) (|HasCategory| |#2| (QUOTE (-146))))) -(-886 S T$) +((-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) +((|HasCategory| |#2| (QUOTE (-928))) (|HasCategory| |#2| (LIST (QUOTE -1059) (QUOTE (-1197)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (QUOTE (-1043))) (|HasCategory| |#2| (QUOTE (-832))) (|HasCategory| |#2| (QUOTE (-861))) (-2758 (|HasCategory| |#2| (QUOTE (-832))) (|HasCategory| |#2| (QUOTE (-861)))) (|HasCategory| |#2| (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-1173))) (|HasCategory| |#2| (LIST (QUOTE -901) (QUOTE (-390)))) (|HasCategory| |#2| (LIST (QUOTE -901) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-237))) (|HasCategory| |#2| (LIST (QUOTE -919) (QUOTE (-1197)))) (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| |#2| (LIST (QUOTE -526) (QUOTE (-1197)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -296) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-317))) (|HasCategory| |#2| (QUOTE (-557))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-928)))) (-2758 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-928)))) (|HasCategory| |#2| (QUOTE (-146))))) +(-887 S T$) ((|constructor| (NIL "\\indented{1}{This domain provides a very simple representation} of the notion of `pair of objects'. It does not try to achieve all possible imaginable things.")) (|second| ((|#2| $) "\\spad{second(p)} extracts the second components of \\spad{`p'}.")) (|first| ((|#1| $) "\\spad{first(p)} extracts the first component of \\spad{`p'}.")) (|construct| (($ |#1| |#2|) "\\spad{construct(s,t)} is same as pair(\\spad{s},{}\\spad{t}),{} with syntactic sugar.")) (|pair| (($ |#1| |#2|) "\\spad{pair(s,t)} returns a pair object composed of \\spad{`s'} and \\spad{`t'}."))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1120))) (|HasCategory| |#2| (QUOTE (-1120)))) (-3794 (-12 (|HasCategory| |#1| (QUOTE (-1120))) (|HasCategory| |#2| (QUOTE (-1120)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-875)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-875)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-875)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-875)))))) -(-887) +((-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#2| (QUOTE (-1121)))) (-2758 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#2| (QUOTE (-1121)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-876)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-876)))))) +(-888) ((|constructor| (NIL "This domain describes four groups of color shades (palettes).")) (|coerce| (($ (|Color|)) "\\spad{coerce(c)} sets the average shade for the palette to that of the indicated color \\spad{c}.")) (|shade| (((|Integer|) $) "\\spad{shade(p)} returns the shade index of the indicated palette \\spad{p}.")) (|hue| (((|Color|) $) "\\spad{hue(p)} returns the hue field of the indicated palette \\spad{p}.")) (|light| (($ (|Color|)) "\\spad{light(c)} sets the shade of a hue,{} \\spad{c},{} to it\\spad{'s} highest value.")) (|pastel| (($ (|Color|)) "\\spad{pastel(c)} sets the shade of a hue,{} \\spad{c},{} above bright,{} but below light.")) (|bright| (($ (|Color|)) "\\spad{bright(c)} sets the shade of a hue,{} \\spad{c},{} above dim,{} but below pastel.")) (|dim| (($ (|Color|)) "\\spad{dim(c)} sets the shade of a hue,{} \\spad{c},{} above dark,{} but below bright.")) (|dark| (($ (|Color|)) "\\spad{dark(c)} sets the shade of the indicated hue of \\spad{c} to it\\spad{'s} lowest value."))) NIL NIL -(-888) +(-889) ((|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 -(-889) +(-890) ((|constructor| (NIL "Representation of parameters to functions or constructors. For the most part,{} they are Identifiers. However,{} in very cases,{} they are \"flags\",{} \\spadignore{e.g.} string literals.")) (|autoCoerce| (((|String|) $) "\\spad{autoCoerce(x)@String} implicitly coerce the object \\spad{x} to \\spadtype{String}. This function is left at the discretion of the compiler.") (((|Identifier|) $) "\\spad{autoCoerce(x)@Identifier} implicitly coerce the object \\spad{x} to \\spadtype{Identifier}. This function is left at the discretion of the compiler.")) (|case| (((|Boolean|) $ (|[\|\|]| (|String|))) "\\spad{x case String} if the parameter AST object \\spad{x} designates a flag.") (((|Boolean|) $ (|[\|\|]| (|Identifier|))) "\\spad{x case Identifier} if the parameter AST object \\spad{x} designates an \\spadtype{Identifier}."))) NIL NIL -(-890 CF1 CF2) +(-891 CF1 CF2) ((|constructor| (NIL "This package \\undocumented")) (|map| (((|ParametricPlaneCurve| |#2|) (|Mapping| |#2| |#1|) (|ParametricPlaneCurve| |#1|)) "\\spad{map(f,x)} \\undocumented"))) NIL NIL -(-891 |ComponentFunction|) +(-892 |ComponentFunction|) ((|constructor| (NIL "ParametricPlaneCurve is used for plotting parametric plane curves in the affine plane.")) (|coordinate| ((|#1| $ (|NonNegativeInteger|)) "\\spad{coordinate(c,i)} returns a coordinate function for \\spad{c} using 1-based indexing according to \\spad{i}. This indicates what the function for the coordinate component \\spad{i} of the plane curve is.")) (|curve| (($ |#1| |#1|) "\\spad{curve(c1,c2)} creates a plane curve from 2 component functions \\spad{c1} and \\spad{c2}."))) NIL NIL -(-892 CF1 CF2) +(-893 CF1 CF2) ((|constructor| (NIL "This package \\undocumented")) (|map| (((|ParametricSpaceCurve| |#2|) (|Mapping| |#2| |#1|) (|ParametricSpaceCurve| |#1|)) "\\spad{map(f,x)} \\undocumented"))) NIL NIL -(-893 |ComponentFunction|) +(-894 |ComponentFunction|) ((|constructor| (NIL "ParametricSpaceCurve is used for plotting parametric space curves in affine 3-space.")) (|coordinate| ((|#1| $ (|NonNegativeInteger|)) "\\spad{coordinate(c,i)} returns a coordinate function of \\spad{c} using 1-based indexing according to \\spad{i}. This indicates what the function for the coordinate component,{} \\spad{i},{} of the space curve is.")) (|curve| (($ |#1| |#1| |#1|) "\\spad{curve(c1,c2,c3)} creates a space curve from 3 component functions \\spad{c1},{} \\spad{c2},{} and \\spad{c3}."))) NIL NIL -(-894) +(-895) ((|constructor| (NIL "\\indented{1}{This package provides a simple Spad script parser.} Related Constructors: Syntax. See Also: Syntax.")) (|getSyntaxFormsFromFile| (((|List| (|Syntax|)) (|String|)) "\\spad{getSyntaxFormsFromFile(f)} parses the source file \\spad{f} (supposedly containing Spad scripts) and returns a List Syntax. The filename \\spad{f} is supposed to have the proper extension. Note that source location information is not part of result."))) NIL NIL -(-895 CF1 CF2) +(-896 CF1 CF2) ((|constructor| (NIL "This package \\undocumented")) (|map| (((|ParametricSurface| |#2|) (|Mapping| |#2| |#1|) (|ParametricSurface| |#1|)) "\\spad{map(f,x)} \\undocumented"))) NIL NIL -(-896 |ComponentFunction|) +(-897 |ComponentFunction|) ((|constructor| (NIL "ParametricSurface is used for plotting parametric surfaces in affine 3-space.")) (|coordinate| ((|#1| $ (|NonNegativeInteger|)) "\\spad{coordinate(s,i)} returns a coordinate function of \\spad{s} using 1-based indexing according to \\spad{i}. This indicates what the function for the coordinate component,{} \\spad{i},{} of the surface is.")) (|surface| (($ |#1| |#1| |#1|) "\\spad{surface(c1,c2,c3)} creates a surface from 3 parametric component functions \\spad{c1},{} \\spad{c2},{} and \\spad{c3}."))) NIL NIL -(-897) +(-898) ((|constructor| (NIL "PartitionsAndPermutations contains functions for generating streams of integer partitions,{} and streams of sequences of integers composed from a multi-set.")) (|permutations| (((|Stream| (|List| (|Integer|))) (|Integer|)) "\\spad{permutations(n)} is the stream of permutations \\indented{1}{formed from \\spad{1,2,3,...,n}.}")) (|sequences| (((|Stream| (|List| (|Integer|))) (|List| (|Integer|))) "\\spad{sequences([l0,l1,l2,..,ln])} is the set of \\indented{1}{all sequences formed from} \\spad{l0} 0\\spad{'s},{}\\spad{l1} 1\\spad{'s},{}\\spad{l2} 2\\spad{'s},{}...,{}\\spad{ln} \\spad{n}\\spad{'s}.") (((|Stream| (|List| (|Integer|))) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{sequences(l1,l2)} is the stream of all sequences that \\indented{1}{can be composed from the multiset defined from} \\indented{1}{two lists of integers \\spad{l1} and \\spad{l2}.} \\indented{1}{For example,{}the pair \\spad{([1,2,4],[2,3,5])} represents} \\indented{1}{multi-set with 1 \\spad{2},{} 2 \\spad{3}\\spad{'s},{} and 4 \\spad{5}\\spad{'s}.}")) (|shufflein| (((|Stream| (|List| (|Integer|))) (|List| (|Integer|)) (|Stream| (|List| (|Integer|)))) "\\spad{shufflein(l,st)} maps shuffle(\\spad{l},{}\\spad{u}) on to all \\indented{1}{members \\spad{u} of \\spad{st},{} concatenating the results.}")) (|shuffle| (((|Stream| (|List| (|Integer|))) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{shuffle(l1,l2)} forms the stream of all shuffles of \\spad{l1} \\indented{1}{and \\spad{l2},{} \\spadignore{i.e.} all sequences that can be formed from} \\indented{1}{merging \\spad{l1} and \\spad{l2}.}")) (|conjugates| (((|Stream| (|List| (|PositiveInteger|))) (|Stream| (|List| (|PositiveInteger|)))) "\\spad{conjugates(lp)} is the stream of conjugates of a stream \\indented{1}{of partitions \\spad{lp}.}")) (|conjugate| (((|List| (|PositiveInteger|)) (|List| (|PositiveInteger|))) "\\spad{conjugate(pt)} is the conjugate of the partition \\spad{pt}."))) NIL NIL -(-898 R) +(-899 R) ((|constructor| (NIL "An object \\spad{S} is Patternable over an object \\spad{R} if \\spad{S} can lift the conversions from \\spad{R} into \\spadtype{Pattern(Integer)} and \\spadtype{Pattern(Float)} to itself."))) NIL NIL -(-899 R S L) +(-900 R S L) ((|constructor| (NIL "A PatternMatchListResult is an object internally returned by the pattern matcher when matching on lists. It is either a failed match,{} or a pair of PatternMatchResult,{} one for atoms (elements of the list),{} and one for lists.")) (|lists| (((|PatternMatchResult| |#1| |#3|) $) "\\spad{lists(r)} returns the list of matches that match lists.")) (|atoms| (((|PatternMatchResult| |#1| |#2|) $) "\\spad{atoms(r)} returns the list of matches that match atoms (elements of the lists).")) (|makeResult| (($ (|PatternMatchResult| |#1| |#2|) (|PatternMatchResult| |#1| |#3|)) "\\spad{makeResult(r1,r2)} makes the combined result [\\spad{r1},{}\\spad{r2}].")) (|new| (($) "\\spad{new()} returns a new empty match result.")) (|failed| (($) "\\spad{failed()} returns a failed match.")) (|failed?| (((|Boolean|) $) "\\spad{failed?(r)} tests if \\spad{r} is a failed match."))) NIL NIL -(-900 S) +(-901 S) ((|constructor| (NIL "A set \\spad{R} is PatternMatchable over \\spad{S} if elements of \\spad{R} can be matched to patterns over \\spad{S}.")) (|patternMatch| (((|PatternMatchResult| |#1| $) $ (|Pattern| |#1|) (|PatternMatchResult| |#1| $)) "\\spad{patternMatch(expr, pat, res)} matches the pattern \\spad{pat} to the expression \\spad{expr}. res contains the variables of \\spad{pat} which are already matched and their matches (necessary for recursion). Initially,{} res is just the result of \\spadfun{new} which is an empty list of matches."))) NIL NIL -(-901 |Base| |Subject| |Pat|) +(-902 |Base| |Subject| |Pat|) ((|constructor| (NIL "This package provides the top-level pattern macthing functions.")) (|Is| (((|PatternMatchResult| |#1| |#2|) |#2| |#3|) "\\spad{Is(expr, pat)} matches the pattern pat on the expression \\spad{expr} and returns a match of the form \\spad{[v1 = e1,...,vn = en]}; returns an empty match if \\spad{expr} is exactly equal to pat. returns a \\spadfun{failed} match if pat does not match \\spad{expr}.") (((|List| (|Equation| (|Polynomial| |#2|))) |#2| |#3|) "\\spad{Is(expr, pat)} matches the pattern pat on the expression \\spad{expr} and returns a list of matches \\spad{[v1 = e1,...,vn = en]}; returns an empty list if either \\spad{expr} is exactly equal to pat or if pat does not match \\spad{expr}.") (((|List| (|Equation| |#2|)) |#2| |#3|) "\\spad{Is(expr, pat)} matches the pattern pat on the expression \\spad{expr} and returns a list of matches \\spad{[v1 = e1,...,vn = en]}; returns an empty list if either \\spad{expr} is exactly equal to pat or if pat does not match \\spad{expr}.") (((|PatternMatchListResult| |#1| |#2| (|List| |#2|)) (|List| |#2|) |#3|) "\\spad{Is([e1,...,en], pat)} matches the pattern pat on the list of expressions \\spad{[e1,...,en]} and returns the result.")) (|is?| (((|Boolean|) (|List| |#2|) |#3|) "\\spad{is?([e1,...,en], pat)} tests if the list of expressions \\spad{[e1,...,en]} matches the pattern pat.") (((|Boolean|) |#2| |#3|) "\\spad{is?(expr, pat)} tests if the expression \\spad{expr} matches the pattern pat."))) NIL -((-12 (-2298 (|HasCategory| |#2| (QUOTE (-1069)))) (-2298 (|HasCategory| |#2| (LIST (QUOTE -1058) (QUOTE (-1196)))))) (-12 (|HasCategory| |#2| (QUOTE (-1069))) (-2298 (|HasCategory| |#2| (LIST (QUOTE -1058) (QUOTE (-1196)))))) (|HasCategory| |#2| (LIST (QUOTE -1058) (QUOTE (-1196))))) -(-902 R A B) +((-12 (-2662 (|HasCategory| |#2| (QUOTE (-1070)))) (-2662 (|HasCategory| |#2| (LIST (QUOTE -1059) (QUOTE (-1197)))))) (-12 (|HasCategory| |#2| (QUOTE (-1070))) (-2662 (|HasCategory| |#2| (LIST (QUOTE -1059) (QUOTE (-1197)))))) (|HasCategory| |#2| (LIST (QUOTE -1059) (QUOTE (-1197))))) +(-903 R A B) ((|constructor| (NIL "Lifts maps to pattern matching results.")) (|map| (((|PatternMatchResult| |#1| |#3|) (|Mapping| |#3| |#2|) (|PatternMatchResult| |#1| |#2|)) "\\spad{map(f, [(v1,a1),...,(vn,an)])} returns the matching result [(\\spad{v1},{}\\spad{f}(a1)),{}...,{}(\\spad{vn},{}\\spad{f}(an))]."))) NIL NIL -(-903 R S) +(-904 R S) ((|constructor| (NIL "A PatternMatchResult is an object internally returned by the pattern matcher; It is either a failed match,{} or a list of matches of the form (var,{} expr) meaning that the variable var matches the expression expr.")) (|satisfy?| (((|Union| (|Boolean|) "failed") $ (|Pattern| |#1|)) "\\spad{satisfy?(r, p)} returns \\spad{true} if the matches satisfy the top-level predicate of \\spad{p},{} \\spad{false} if they don\\spad{'t},{} and \"failed\" if not enough variables of \\spad{p} are matched in \\spad{r} to decide.")) (|construct| (($ (|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| |#2|)))) "\\spad{construct([v1,e1],...,[vn,en])} returns the match result containing the matches (\\spad{v1},{}e1),{}...,{}(\\spad{vn},{}en).")) (|destruct| (((|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| |#2|))) $) "\\spad{destruct(r)} returns the list of matches (var,{} expr) in \\spad{r}. Error: if \\spad{r} is a failed match.")) (|addMatchRestricted| (($ (|Pattern| |#1|) |#2| $ |#2|) "\\spad{addMatchRestricted(var, expr, r, val)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} provided that \\spad{expr} satisfies the predicates attached to \\spad{var},{} that \\spad{var} is not matched to another expression already,{} and that either \\spad{var} is an optional pattern variable or that \\spad{expr} is not equal to val (usually an identity).")) (|insertMatch| (($ (|Pattern| |#1|) |#2| $) "\\spad{insertMatch(var, expr, r)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} without checking predicates or previous matches for \\spad{var}.")) (|addMatch| (($ (|Pattern| |#1|) |#2| $) "\\spad{addMatch(var, expr, r)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} provided that \\spad{expr} satisfies the predicates attached to \\spad{var},{} and that \\spad{var} is not matched to another expression already.")) (|getMatch| (((|Union| |#2| "failed") (|Pattern| |#1|) $) "\\spad{getMatch(var, r)} returns the expression that \\spad{var} matches in the result \\spad{r},{} and \"failed\" if \\spad{var} is not matched in \\spad{r}.")) (|union| (($ $ $) "\\spad{union(a, b)} makes the set-union of two match results.")) (|new| (($) "\\spad{new()} returns a new empty match result.")) (|failed| (($) "\\spad{failed()} returns a failed match.")) (|failed?| (((|Boolean|) $) "\\spad{failed?(r)} tests if \\spad{r} is a failed match."))) NIL NIL -(-904 R -3155) +(-905 R -2018) ((|constructor| (NIL "Tools for patterns.")) (|badValues| (((|List| |#2|) (|Pattern| |#1|)) "\\spad{badValues(p)} returns the list of \"bad values\" for \\spad{p}; \\spad{p} is not allowed to match any of its \"bad values\".")) (|addBadValue| (((|Pattern| |#1|) (|Pattern| |#1|) |#2|) "\\spad{addBadValue(p, v)} adds \\spad{v} to the list of \"bad values\" for \\spad{p}; \\spad{p} is not allowed to match any of its \"bad values\".")) (|satisfy?| (((|Boolean|) (|List| |#2|) (|Pattern| |#1|)) "\\spad{satisfy?([v1,...,vn], p)} returns \\spad{f(v1,...,vn)} where \\spad{f} is the top-level predicate attached to \\spad{p}.") (((|Boolean|) |#2| (|Pattern| |#1|)) "\\spad{satisfy?(v, p)} returns \\spad{f}(\\spad{v}) where \\spad{f} is the predicate attached to \\spad{p}.")) (|predicate| (((|Mapping| (|Boolean|) |#2|) (|Pattern| |#1|)) "\\spad{predicate(p)} returns the predicate attached to \\spad{p},{} the constant function \\spad{true} if \\spad{p} has no predicates attached to it.")) (|suchThat| (((|Pattern| |#1|) (|Pattern| |#1|) (|List| (|Symbol|)) (|Mapping| (|Boolean|) (|List| |#2|))) "\\spad{suchThat(p, [a1,...,an], f)} returns a copy of \\spad{p} with the top-level predicate set to \\spad{f(a1,...,an)}.") (((|Pattern| |#1|) (|Pattern| |#1|) (|List| (|Mapping| (|Boolean|) |#2|))) "\\spad{suchThat(p, [f1,...,fn])} makes a copy of \\spad{p} and adds the predicate \\spad{f1} and ... and \\spad{fn} to the copy,{} which is returned.") (((|Pattern| |#1|) (|Pattern| |#1|) (|Mapping| (|Boolean|) |#2|)) "\\spad{suchThat(p, f)} makes a copy of \\spad{p} and adds the predicate \\spad{f} to the copy,{} which is returned."))) NIL NIL -(-905 R S) +(-906 R S) ((|constructor| (NIL "Lifts maps to patterns.")) (|map| (((|Pattern| |#2|) (|Mapping| |#2| |#1|) (|Pattern| |#1|)) "\\spad{map(f, p)} applies \\spad{f} to all the leaves of \\spad{p} and returns the result as a pattern over \\spad{S}."))) NIL NIL -(-906 R) +(-907 R) ((|constructor| (NIL "Patterns for use by the pattern matcher.")) (|optpair| (((|Union| (|List| $) "failed") (|List| $)) "\\spad{optpair(l)} returns \\spad{l} has the form \\spad{[a, b]} and a is optional,{} and \"failed\" otherwise.")) (|variables| (((|List| $) $) "\\spad{variables(p)} returns the list of matching variables appearing in \\spad{p}.")) (|getBadValues| (((|List| (|Any|)) $) "\\spad{getBadValues(p)} returns the list of \"bad values\" for \\spad{p}. Note: \\spad{p} is not allowed to match any of its \"bad values\".")) (|addBadValue| (($ $ (|Any|)) "\\spad{addBadValue(p, v)} adds \\spad{v} to the list of \"bad values\" for \\spad{p}. Note: \\spad{p} is not allowed to match any of its \"bad values\".")) (|resetBadValues| (($ $) "\\spad{resetBadValues(p)} initializes the list of \"bad values\" for \\spad{p} to \\spad{[]}. Note: \\spad{p} is not allowed to match any of its \"bad values\".")) (|hasTopPredicate?| (((|Boolean|) $) "\\spad{hasTopPredicate?(p)} tests if \\spad{p} has a top-level predicate.")) (|topPredicate| (((|Record| (|:| |var| (|List| (|Symbol|))) (|:| |pred| (|Any|))) $) "\\spad{topPredicate(x)} returns \\spad{[[a1,...,an], f]} where the top-level predicate of \\spad{x} is \\spad{f(a1,...,an)}. Note: \\spad{n} is 0 if \\spad{x} has no top-level predicate.")) (|setTopPredicate| (($ $ (|List| (|Symbol|)) (|Any|)) "\\spad{setTopPredicate(x, [a1,...,an], f)} returns \\spad{x} with the top-level predicate set to \\spad{f(a1,...,an)}.")) (|patternVariable| (($ (|Symbol|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\spad{patternVariable(x, c?, o?, m?)} creates a pattern variable \\spad{x},{} which is constant if \\spad{c? = true},{} optional if \\spad{o? = true},{} and multiple if \\spad{m? = true}.")) (|withPredicates| (($ $ (|List| (|Any|))) "\\spad{withPredicates(p, [p1,...,pn])} makes a copy of \\spad{p} and attaches the predicate \\spad{p1} and ... and \\spad{pn} to the copy,{} which is returned.")) (|setPredicates| (($ $ (|List| (|Any|))) "\\spad{setPredicates(p, [p1,...,pn])} attaches the predicate \\spad{p1} and ... and \\spad{pn} to \\spad{p}.")) (|predicates| (((|List| (|Any|)) $) "\\spad{predicates(p)} returns \\spad{[p1,...,pn]} such that the predicate attached to \\spad{p} is \\spad{p1} and ... and \\spad{pn}.")) (|hasPredicate?| (((|Boolean|) $) "\\spad{hasPredicate?(p)} tests if \\spad{p} has predicates attached to it.")) (|optional?| (((|Boolean|) $) "\\spad{optional?(p)} tests if \\spad{p} is a single matching variable which can match an identity.")) (|multiple?| (((|Boolean|) $) "\\spad{multiple?(p)} tests if \\spad{p} is a single matching variable allowing list matching or multiple term matching in a sum or product.")) (|generic?| (((|Boolean|) $) "\\spad{generic?(p)} tests if \\spad{p} is a single matching variable.")) (|constant?| (((|Boolean|) $) "\\spad{constant?(p)} tests if \\spad{p} contains no matching variables.")) (|symbol?| (((|Boolean|) $) "\\spad{symbol?(p)} tests if \\spad{p} is a symbol.")) (|quoted?| (((|Boolean|) $) "\\spad{quoted?(p)} tests if \\spad{p} is of the form \\spad{'s} for a symbol \\spad{s}.")) (|inR?| (((|Boolean|) $) "\\spad{inR?(p)} tests if \\spad{p} is an atom (\\spadignore{i.e.} an element of \\spad{R}).")) (|copy| (($ $) "\\spad{copy(p)} returns a recursive copy of \\spad{p}.")) (|convert| (($ (|List| $)) "\\spad{convert([a1,...,an])} returns the pattern \\spad{[a1,...,an]}.")) (|depth| (((|NonNegativeInteger|) $) "\\spad{depth(p)} returns the nesting level of \\spad{p}.")) (/ (($ $ $) "\\spad{a / b} returns the pattern \\spad{a / b}.")) (** (($ $ $) "\\spad{a ** b} returns the pattern \\spad{a ** b}.") (($ $ (|NonNegativeInteger|)) "\\spad{a ** n} returns the pattern \\spad{a ** n}.")) (* (($ $ $) "\\spad{a * b} returns the pattern \\spad{a * b}.")) (+ (($ $ $) "\\spad{a + b} returns the pattern \\spad{a + b}.")) (|elt| (($ (|BasicOperator|) (|List| $)) "\\spad{elt(op, [a1,...,an])} returns \\spad{op(a1,...,an)}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| $)) "failed") $) "\\spad{isPower(p)} returns \\spad{[a, b]} if \\spad{p = a ** b},{} and \"failed\" otherwise.")) (|isList| (((|Union| (|List| $) "failed") $) "\\spad{isList(p)} returns \\spad{[a1,...,an]} if \\spad{p = [a1,...,an]},{} \"failed\" otherwise.")) (|isQuotient| (((|Union| (|Record| (|:| |num| $) (|:| |den| $)) "failed") $) "\\spad{isQuotient(p)} returns \\spad{[a, b]} if \\spad{p = a / b},{} and \"failed\" otherwise.")) (|isExpt| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|NonNegativeInteger|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[q, n]} if \\spad{n > 0} and \\spad{p = q ** n},{} and \"failed\" otherwise.")) (|isOp| (((|Union| (|Record| (|:| |op| (|BasicOperator|)) (|:| |arg| (|List| $))) "failed") $) "\\spad{isOp(p)} returns \\spad{[op, [a1,...,an]]} if \\spad{p = op(a1,...,an)},{} and \"failed\" otherwise.") (((|Union| (|List| $) "failed") $ (|BasicOperator|)) "\\spad{isOp(p, op)} returns \\spad{[a1,...,an]} if \\spad{p = op(a1,...,an)},{} and \"failed\" otherwise.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if \\spad{n > 1} and \\spad{p = a1 * ... * an},{} and \"failed\" otherwise.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[a1,...,an]} if \\spad{n > 1} \\indented{1}{and \\spad{p = a1 + ... + an},{}} and \"failed\" otherwise.")) ((|One|) (($) "1")) ((|Zero|) (($) "0"))) NIL NIL -(-907 |VarSet|) +(-908 |VarSet|) ((|constructor| (NIL "This domain provides the internal representation of polynomials in non-commutative variables written over the Poincare-Birkhoff-Witt basis. See the \\spadtype{XPBWPolynomial} domain constructor. See Free Lie Algebras by \\spad{C}. Reutenauer (Oxford science publications). \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|varList| (((|List| |#1|) $) "\\spad{varList([l1]*[l2]*...[ln])} returns the list of variables in the word \\spad{l1*l2*...*ln}.")) (|retractable?| (((|Boolean|) $) "\\spad{retractable?([l1]*[l2]*...[ln])} returns \\spad{true} iff \\spad{n} equals \\spad{1}.")) (|rest| (($ $) "\\spad{rest([l1]*[l2]*...[ln])} returns the list \\spad{l2, .... ln}.")) (|ListOfTerms| (((|List| (|LyndonWord| |#1|)) $) "\\spad{ListOfTerms([l1]*[l2]*...[ln])} returns the list of words \\spad{l1, l2, .... ln}.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length([l1]*[l2]*...[ln])} returns the length of the word \\spad{l1*l2*...*ln}.")) (|first| (((|LyndonWord| |#1|) $) "\\spad{first([l1]*[l2]*...[ln])} returns the Lyndon word \\spad{l1}.")) (|coerce| (($ |#1|) "\\spad{coerce(v)} return \\spad{v}") (((|OrderedFreeMonoid| |#1|) $) "\\spad{coerce([l1]*[l2]*...[ln])} returns the word \\spad{l1*l2*...*ln},{} where \\spad{[l_i]} is the backeted form of the Lyndon word \\spad{l_i}.")) ((|One|) (($) "\\spad{1} returns the empty list."))) NIL NIL -(-908 UP R) +(-909 UP R) ((|constructor| (NIL "This package \\undocumented")) (|compose| ((|#1| |#1| |#1|) "\\spad{compose(p,q)} \\undocumented"))) NIL NIL -(-909 A T$ S) +(-910 A T$ S) ((|constructor| (NIL "\\indented{2}{This category captures the interface of domains with a distinguished} \\indented{2}{operation named \\spad{differentiate} for partial differentiation with} \\indented{2}{respect to some domain of variables.} See Also: \\indented{2}{DifferentialDomain,{} PartialDifferentialSpace}")) (D ((|#2| $ |#3|) "\\spad{D(x,v)} is a shorthand for \\spad{differentiate(x,v)}")) (|differentiate| ((|#2| $ |#3|) "\\spad{differentiate(x,v)} computes the partial derivative of \\spad{x} with respect to \\spad{v}."))) NIL NIL -(-910 T$ S) +(-911 T$ S) ((|constructor| (NIL "\\indented{2}{This category captures the interface of domains with a distinguished} \\indented{2}{operation named \\spad{differentiate} for partial differentiation with} \\indented{2}{respect to some domain of variables.} See Also: \\indented{2}{DifferentialDomain,{} PartialDifferentialSpace}")) (D ((|#1| $ |#2|) "\\spad{D(x,v)} is a shorthand for \\spad{differentiate(x,v)}")) (|differentiate| ((|#1| $ |#2|) "\\spad{differentiate(x,v)} computes the partial derivative of \\spad{x} with respect to \\spad{v}."))) NIL NIL -(-911) +(-912) ((|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 -(-912 UP -2117) +(-913 UP -1959) ((|constructor| (NIL "This package \\undocumented")) (|rightFactorCandidate| ((|#1| |#1| (|NonNegativeInteger|)) "\\spad{rightFactorCandidate(p,n)} \\undocumented")) (|leftFactor| (((|Union| |#1| "failed") |#1| |#1|) "\\spad{leftFactor(p,q)} \\undocumented")) (|decompose| (((|Union| (|Record| (|:| |left| |#1|) (|:| |right| |#1|)) "failed") |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{decompose(up,m,n)} \\undocumented") (((|List| |#1|) |#1|) "\\spad{decompose(up)} \\undocumented"))) NIL NIL -(-913) +(-914) ((|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalPDEProblem|) (|RoutinesTable|)) "\\spad{measure(prob,R)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical PDE problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} listed in \\axiom{\\spad{R}} of \\axiom{category} \\axiomType{PartialDifferentialEquationsSolverCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information. It predicts the likely most effective NAG numerical Library routine to solve the input set of PDEs by checking various attributes of the system of PDEs and calculating a measure of compatibility of each routine to these attributes.") (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalPDEProblem|)) "\\spad{measure(prob)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical PDE problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} of \\axiom{category} \\axiomType{PartialDifferentialEquationsSolverCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information. It predicts the likely most effective NAG numerical Library routine to solve the input set of PDEs by checking various attributes of the system of PDEs and calculating a measure of compatibility of each routine to these attributes.")) (|solve| (((|Result|) (|Float|) (|Float|) (|Float|) (|Float|) (|NonNegativeInteger|) (|NonNegativeInteger|) (|List| (|Expression| (|Float|))) (|List| (|List| (|Expression| (|Float|)))) (|String|)) "\\spad{solve(xmin,ymin,xmax,ymax,ngx,ngy,pde,bounds,st)} is a top level ANNA function to solve numerically a system of partial differential equations. This is defined as a list of coefficients (\\axiom{\\spad{pde}}),{} a grid (\\axiom{\\spad{xmin}},{} \\axiom{\\spad{ymin}},{} \\axiom{\\spad{xmax}},{} \\axiom{\\spad{ymax}},{} \\axiom{\\spad{ngx}},{} \\axiom{\\spad{ngy}}) and the boundary values (\\axiom{\\spad{bounds}}). A default value for tolerance is used. There is also a parameter (\\axiom{\\spad{st}}) which should contain the value \"elliptic\" if the PDE is known to be elliptic,{} or \"unknown\" if it is uncertain. This causes the routine to check whether the PDE is elliptic. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of PDE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine. \\blankline \\spad{**} At the moment,{} only Second Order Elliptic Partial Differential Equations are solved \\spad{**}") (((|Result|) (|Float|) (|Float|) (|Float|) (|Float|) (|NonNegativeInteger|) (|NonNegativeInteger|) (|List| (|Expression| (|Float|))) (|List| (|List| (|Expression| (|Float|)))) (|String|) (|DoubleFloat|)) "\\spad{solve(xmin,ymin,xmax,ymax,ngx,ngy,pde,bounds,st,tol)} is a top level ANNA function to solve numerically a system of partial differential equations. This is defined as a list of coefficients (\\axiom{\\spad{pde}}),{} a grid (\\axiom{\\spad{xmin}},{} \\axiom{\\spad{ymin}},{} \\axiom{\\spad{xmax}},{} \\axiom{\\spad{ymax}},{} \\axiom{\\spad{ngx}},{} \\axiom{\\spad{ngy}}),{} the boundary values (\\axiom{\\spad{bounds}}) and a tolerance requirement (\\axiom{\\spad{tol}}). There is also a parameter (\\axiom{\\spad{st}}) which should contain the value \"elliptic\" if the PDE is known to be elliptic,{} or \"unknown\" if it is uncertain. This causes the routine to check whether the PDE is elliptic. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of PDE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine. \\blankline \\spad{**} At the moment,{} only Second Order Elliptic Partial Differential Equations are solved \\spad{**}") (((|Result|) (|NumericalPDEProblem|) (|RoutinesTable|)) "\\spad{solve(PDEProblem,routines)} is a top level ANNA function to solve numerically a system of partial differential equations. \\blankline The method used to perform the numerical process will be one of the \\spad{routines} contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of PDE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine. \\blankline \\spad{**} At the moment,{} only Second Order Elliptic Partial Differential Equations are solved \\spad{**}") (((|Result|) (|NumericalPDEProblem|)) "\\spad{solve(PDEProblem)} is a top level ANNA function to solve numerically a system of partial differential equations. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of PDE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine. \\blankline \\spad{**} At the moment,{} only Second Order Elliptic Partial Differential Equations are solved \\spad{**}"))) NIL NIL -(-914) +(-915) ((|retract| (((|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|))) $) "\\spad{retract(x)} \\undocumented{}")) (|coerce| (($ (|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|)))) "\\spad{coerce(x)} \\undocumented{}"))) NIL NIL -(-915 R S) +(-916 R S) ((|constructor| (NIL "A partial differential \\spad{R}-module with differentiations indexed by a parameter type \\spad{S}. \\blankline"))) -((-4458 . T) (-4457 . T)) +((-4459 . T) (-4458 . T)) NIL -(-916 S) +(-917 S) ((|constructor| (NIL "A partial differential ring with differentiations indexed by a parameter type \\spad{S}. \\blankline"))) -((-4460 . T)) +((-4461 . T)) NIL -(-917 A S) +(-918 A S) ((|constructor| (NIL "\\indented{2}{This category captures the interface of domains stable by partial} \\indented{2}{differentiation with respect to variables from some domain.} See Also: \\indented{2}{PartialDifferentialDomain}")) (D (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) "\\spad{D(x,[s1,...,sn],[n1,...,nn])} is a shorthand for \\spad{differentiate(x,[s1,...,sn],[n1,...,nn])}.") (($ $ |#2| (|NonNegativeInteger|)) "\\spad{D(x,s,n)} is a shorthand for \\spad{differentiate(x,s,n)}.") (($ $ (|List| |#2|)) "\\spad{D(x,[s1,...sn])} is a shorthand for \\spad{differentiate(x,[s1,...sn])}.")) (|differentiate| (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) "\\spad{differentiate(x,[s1,...,sn],[n1,...,nn])} computes multiple partial derivatives,{} \\spadignore{i.e.}") (($ $ |#2| (|NonNegativeInteger|)) "\\spad{differentiate(x,s,n)} computes multiple partial derivatives,{} \\spadignore{i.e.} \\spad{n}\\spad{-}th derivative of \\spad{x} with respect to \\spad{s}.") (($ $ (|List| |#2|)) "\\spad{differentiate(x,[s1,...sn])} computes successive partial derivatives,{} \\spadignore{i.e.} \\spad{differentiate(...differentiate(x, s1)..., sn)}."))) NIL NIL -(-918 S) +(-919 S) ((|constructor| (NIL "\\indented{2}{This category captures the interface of domains stable by partial} \\indented{2}{differentiation with respect to variables from some domain.} See Also: \\indented{2}{PartialDifferentialDomain}")) (D (($ $ (|List| |#1|) (|List| (|NonNegativeInteger|))) "\\spad{D(x,[s1,...,sn],[n1,...,nn])} is a shorthand for \\spad{differentiate(x,[s1,...,sn],[n1,...,nn])}.") (($ $ |#1| (|NonNegativeInteger|)) "\\spad{D(x,s,n)} is a shorthand for \\spad{differentiate(x,s,n)}.") (($ $ (|List| |#1|)) "\\spad{D(x,[s1,...sn])} is a shorthand for \\spad{differentiate(x,[s1,...sn])}.")) (|differentiate| (($ $ (|List| |#1|) (|List| (|NonNegativeInteger|))) "\\spad{differentiate(x,[s1,...,sn],[n1,...,nn])} computes multiple partial derivatives,{} \\spadignore{i.e.}") (($ $ |#1| (|NonNegativeInteger|)) "\\spad{differentiate(x,s,n)} computes multiple partial derivatives,{} \\spadignore{i.e.} \\spad{n}\\spad{-}th derivative of \\spad{x} with respect to \\spad{s}.") (($ $ (|List| |#1|)) "\\spad{differentiate(x,[s1,...sn])} computes successive partial derivatives,{} \\spadignore{i.e.} \\spad{differentiate(...differentiate(x, s1)..., sn)}."))) NIL NIL -(-919 S) +(-920 S) ((|constructor| (NIL "\\indented{1}{A PendantTree(\\spad{S})is either a leaf? and is an \\spad{S} or has} a left and a right both PendantTree(\\spad{S})\\spad{'s}")) (|ptree| (($ $ $) "\\spad{ptree(x,y)} \\undocumented") (($ |#1|) "\\spad{ptree(s)} is a leaf? pendant tree"))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1120))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1120))) (-3794 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1120)))) (-3794 (-12 (|HasCategory| |#1| (QUOTE (-1120))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-875))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-875)))) (|HasCategory| |#1| (QUOTE (-102)))) -(-920 |n| R) +((-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1121))) (-2758 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1121)))) (-2758 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102)))) +(-921 |n| R) ((|constructor| (NIL "Permanent implements the functions {\\em permanent},{} the permanent for square matrices.")) (|permanent| ((|#2| (|SquareMatrix| |#1| |#2|)) "\\spad{permanent(x)} computes the permanent of a square matrix \\spad{x}. The {\\em permanent} is equivalent to the \\spadfun{determinant} except that coefficients have no change of sign. This function is much more difficult to compute than the {\\em determinant}. The formula used is by \\spad{H}.\\spad{J}. Ryser,{} improved by [Nijenhuis and Wilf,{} \\spad{Ch}. 19]. Note: permanent(\\spad{x}) choose one of three algorithms,{} depending on the underlying ring \\spad{R} and on \\spad{n},{} the number of rows (and columns) of \\spad{x:}\\begin{items} \\item 1. if 2 has an inverse in \\spad{R} we can use the algorithm of \\indented{3}{[Nijenhuis and Wilf,{} \\spad{ch}.19,{}\\spad{p}.158]; if 2 has no inverse,{}} \\indented{3}{some modifications are necessary:} \\item 2. if {\\em n > 6} and \\spad{R} is an integral domain with characteristic \\indented{3}{different from 2 (the algorithm works if and only 2 is not a} \\indented{3}{zero-divisor of \\spad{R} and {\\em characteristic()\\$R ~= 2},{}} \\indented{3}{but how to check that for any given \\spad{R} ?),{}} \\indented{3}{the local function {\\em permanent2} is called;} \\item 3. else,{} the local function {\\em permanent3} is called \\indented{3}{(works for all commutative rings \\spad{R}).} \\end{items}"))) NIL NIL -(-921 S) +(-922 S) ((|constructor| (NIL "PermutationCategory provides a categorial environment \\indented{1}{for subgroups of bijections of a set (\\spadignore{i.e.} permutations)}")) (< (((|Boolean|) $ $) "\\spad{p < q} is an order relation on permutations. Note: this order is only total if and only if \\spad{S} is totally ordered or \\spad{S} is finite.")) (|orbit| (((|Set| |#1|) $ |#1|) "\\spad{orbit(p, el)} returns the orbit of {\\em el} under the permutation \\spad{p},{} \\spadignore{i.e.} the set which is given by applications of the powers of \\spad{p} to {\\em el}.")) (|support| (((|Set| |#1|) $) "\\spad{support p} returns the set of points not fixed by the permutation \\spad{p}.")) (|cycles| (($ (|List| (|List| |#1|))) "\\spad{cycles(lls)} coerces a list list of cycles {\\em lls} to a permutation,{} each cycle being a list with not repetitions,{} is coerced to the permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list,{} then these permutations are mutiplied. Error: if repetitions occur in one cycle.")) (|cycle| (($ (|List| |#1|)) "\\spad{cycle(ls)} coerces a cycle {\\em ls},{} \\spadignore{i.e.} a list with not repetitions to a permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list. Error: if repetitions occur."))) -((-4460 . T)) +((-4461 . T)) NIL -(-922 S) +(-923 S) ((|constructor| (NIL "PermutationGroup implements permutation groups acting on a set \\spad{S},{} \\spadignore{i.e.} all subgroups of the symmetric group of \\spad{S},{} represented as a list of permutations (generators). Note that therefore the objects are not members of the \\Language category \\spadtype{Group}. Using the idea of base and strong generators by Sims,{} basic routines and algorithms are implemented so that the word problem for permutation groups can be solved.")) (|initializeGroupForWordProblem| (((|Void|) $ (|Integer|) (|Integer|)) "\\spad{initializeGroupForWordProblem(gp,m,n)} initializes the group {\\em gp} for the word problem. Notes: (1) with a small integer you get shorter words,{} but the routine takes longer than the standard routine for longer words. (2) be careful: invoking this routine will destroy the possibly stored information about your group (but will recompute it again). (3) users need not call this function normally for the soultion of the word problem.") (((|Void|) $) "\\spad{initializeGroupForWordProblem(gp)} initializes the group {\\em gp} for the word problem. Notes: it calls the other function of this name with parameters 0 and 1: {\\em initializeGroupForWordProblem(gp,0,1)}. Notes: (1) be careful: invoking this routine will destroy the possibly information about your group (but will recompute it again) (2) users need not call this function normally for the soultion of the word problem.")) (<= (((|Boolean|) $ $) "\\spad{gp1 <= gp2} returns \\spad{true} if and only if {\\em gp1} is a subgroup of {\\em gp2}. Note: because of a bug in the parser you have to call this function explicitly by {\\em gp1 <=\\$(PERMGRP S) gp2}.")) (< (((|Boolean|) $ $) "\\spad{gp1 < gp2} returns \\spad{true} if and only if {\\em gp1} is a proper subgroup of {\\em gp2}.")) (|support| (((|Set| |#1|) $) "\\spad{support(gp)} returns the points moved by the group {\\em gp}.")) (|wordInGenerators| (((|List| (|NonNegativeInteger|)) (|Permutation| |#1|) $) "\\spad{wordInGenerators(p,gp)} returns the word for the permutation \\spad{p} in the original generators of the group {\\em gp},{} represented by the indices of the list,{} given by {\\em generators}.")) (|wordInStrongGenerators| (((|List| (|NonNegativeInteger|)) (|Permutation| |#1|) $) "\\spad{wordInStrongGenerators(p,gp)} returns the word for the permutation \\spad{p} in the strong generators of the group {\\em gp},{} represented by the indices of the list,{} given by {\\em strongGenerators}.")) (|member?| (((|Boolean|) (|Permutation| |#1|) $) "\\spad{member?(pp,gp)} answers the question,{} whether the permutation {\\em pp} is in the group {\\em gp} or not.")) (|orbits| (((|Set| (|Set| |#1|)) $) "\\spad{orbits(gp)} returns the orbits of the group {\\em gp},{} \\spadignore{i.e.} it partitions the (finite) of all moved points.")) (|orbit| (((|Set| (|List| |#1|)) $ (|List| |#1|)) "\\spad{orbit(gp,ls)} returns the orbit of the ordered list {\\em ls} under the group {\\em gp}. Note: return type is \\spad{L} \\spad{L} \\spad{S} temporarily because FSET \\spad{L} \\spad{S} has an error.") (((|Set| (|Set| |#1|)) $ (|Set| |#1|)) "\\spad{orbit(gp,els)} returns the orbit of the unordered set {\\em els} under the group {\\em gp}.") (((|Set| |#1|) $ |#1|) "\\spad{orbit(gp,el)} returns the orbit of the element {\\em el} under the group {\\em gp},{} \\spadignore{i.e.} the set of all points gained by applying each group element to {\\em el}.")) (|permutationGroup| (($ (|List| (|Permutation| |#1|))) "\\spad{permutationGroup(ls)} coerces a list of permutations {\\em ls} to the group generated by this list.")) (|wordsForStrongGenerators| (((|List| (|List| (|NonNegativeInteger|))) $) "\\spad{wordsForStrongGenerators(gp)} returns the words for the strong generators of the group {\\em gp} in the original generators of {\\em gp},{} represented by their indices in the list,{} given by {\\em generators}.")) (|strongGenerators| (((|List| (|Permutation| |#1|)) $) "\\spad{strongGenerators(gp)} returns strong generators for the group {\\em gp}.")) (|base| (((|List| |#1|) $) "\\spad{base(gp)} returns a base for the group {\\em gp}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(gp)} returns the number of points moved by all permutations of the group {\\em gp}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(gp)} returns the order of the group {\\em gp}.")) (|random| (((|Permutation| |#1|) $) "\\spad{random(gp)} returns a random product of maximal 20 generators of the group {\\em gp}. Note: {\\em random(gp)=random(gp,20)}.") (((|Permutation| |#1|) $ (|Integer|)) "\\spad{random(gp,i)} returns a random product of maximal \\spad{i} generators of the group {\\em gp}.")) (|elt| (((|Permutation| |#1|) $ (|NonNegativeInteger|)) "\\spad{elt(gp,i)} returns the \\spad{i}-th generator of the group {\\em gp}.")) (|generators| (((|List| (|Permutation| |#1|)) $) "\\spad{generators(gp)} returns the generators of the group {\\em gp}.")) (|coerce| (($ (|List| (|Permutation| |#1|))) "\\spad{coerce(ls)} coerces a list of permutations {\\em ls} to the group generated by this list.") (((|List| (|Permutation| |#1|)) $) "\\spad{coerce(gp)} returns the generators of the group {\\em gp}."))) NIL NIL -(-923 S) +(-924 S) ((|constructor| (NIL "Permutation(\\spad{S}) implements the group of all bijections \\indented{2}{on a set \\spad{S},{} which move only a finite number of points.} \\indented{2}{A permutation is considered as a map from \\spad{S} into \\spad{S}. In particular} \\indented{2}{multiplication is defined as composition of maps:} \\indented{2}{{\\em pi1 * pi2 = pi1 o pi2}.} \\indented{2}{The internal representation of permuatations are two lists} \\indented{2}{of equal length representing preimages and images.}")) (|coerceImages| (($ (|List| |#1|)) "\\spad{coerceImages(ls)} coerces the list {\\em ls} to a permutation whose image is given by {\\em ls} and the preimage is fixed to be {\\em [1,...,n]}. Note: {coerceImages(\\spad{ls})=coercePreimagesImages([1,{}...,{}\\spad{n}],{}\\spad{ls})}. We assume that both preimage and image do not contain repetitions.")) (|fixedPoints| (((|Set| |#1|) $) "\\spad{fixedPoints(p)} returns the points fixed by the permutation \\spad{p}.")) (|sort| (((|List| $) (|List| $)) "\\spad{sort(lp)} sorts a list of permutations {\\em lp} according to cycle structure first according to length of cycles,{} second,{} if \\spad{S} has \\spadtype{Finite} or \\spad{S} has \\spadtype{OrderedSet} according to lexicographical order of entries in cycles of equal length.")) (|odd?| (((|Boolean|) $) "\\spad{odd?(p)} returns \\spad{true} if and only if \\spad{p} is an odd permutation \\spadignore{i.e.} {\\em sign(p)} is {\\em -1}.")) (|even?| (((|Boolean|) $) "\\spad{even?(p)} returns \\spad{true} if and only if \\spad{p} is an even permutation,{} \\spadignore{i.e.} {\\em sign(p)} is 1.")) (|sign| (((|Integer|) $) "\\spad{sign(p)} returns the signum of the permutation \\spad{p},{} \\spad{+1} or \\spad{-1}.")) (|numberOfCycles| (((|NonNegativeInteger|) $) "\\spad{numberOfCycles(p)} returns the number of non-trivial cycles of the permutation \\spad{p}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of a permutation \\spad{p} as a group element.")) (|cyclePartition| (((|Partition|) $) "\\spad{cyclePartition(p)} returns the cycle structure of a permutation \\spad{p} including cycles of length 1 only if \\spad{S} is finite.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(p)} retuns the number of points moved by the permutation \\spad{p}.")) (|coerceListOfPairs| (($ (|List| (|List| |#1|))) "\\spad{coerceListOfPairs(lls)} coerces a list of pairs {\\em lls} to a permutation. Error: if not consistent,{} \\spadignore{i.e.} the set of the first elements coincides with the set of second elements. coerce(\\spad{p}) generates output of the permutation \\spad{p} with domain OutputForm.")) (|coerce| (($ (|List| |#1|)) "\\spad{coerce(ls)} coerces a cycle {\\em ls},{} \\spadignore{i.e.} a list with not repetitions to a permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list. Error: if repetitions occur.") (($ (|List| (|List| |#1|))) "\\spad{coerce(lls)} coerces a list of cycles {\\em lls} to a permutation,{} each cycle being a list with no repetitions,{} is coerced to the permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list,{} then these permutations are mutiplied. Error: if repetitions occur in one cycle.")) (|coercePreimagesImages| (($ (|List| (|List| |#1|))) "\\spad{coercePreimagesImages(lls)} coerces the representation {\\em lls} of a permutation as a list of preimages and images to a permutation. We assume that both preimage and image do not contain repetitions.")) (|listRepresentation| (((|Record| (|:| |preimage| (|List| |#1|)) (|:| |image| (|List| |#1|))) $) "\\spad{listRepresentation(p)} produces a representation {\\em rep} of the permutation \\spad{p} as a list of preimages and images,{} \\spad{i}.\\spad{e} \\spad{p} maps {\\em (rep.preimage).k} to {\\em (rep.image).k} for all indices \\spad{k}. Elements of \\spad{S} not in {\\em (rep.preimage).k} are fixed points,{} and these are the only fixed points of the permutation."))) -((-4460 . T)) -((-3794 (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-861)))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-861)))) -(-924 R E |VarSet| S) +((-4461 . T)) +((-2758 (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-861)))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-861)))) +(-925 R E |VarSet| S) ((|constructor| (NIL "PolynomialFactorizationByRecursion(\\spad{R},{}\\spad{E},{}\\spad{VarSet},{}\\spad{S}) is used for factorization of sparse univariate polynomials over a domain \\spad{S} of multivariate polynomials over \\spad{R}.")) (|factorSFBRlcUnit| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|List| |#3|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorSFBRlcUnit(p)} returns the square free factorization of polynomial \\spad{p} (see \\spadfun{factorSquareFreeByRecursion}{PolynomialFactorizationByRecursionUnivariate}) in the case where the leading coefficient of \\spad{p} is a unit.")) (|bivariateSLPEBR| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|List| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|) |#3|) "\\spad{bivariateSLPEBR(lp,p,v)} implements the bivariate case of \\spadfunFrom{solveLinearPolynomialEquationByRecursion}{PolynomialFactorizationByRecursionUnivariate}; its implementation depends on \\spad{R}")) (|randomR| ((|#1|) "\\spad{randomR produces} a random element of \\spad{R}")) (|factorSquareFreeByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorSquareFreeByRecursion(p)} returns the square free factorization of \\spad{p}. This functions performs the recursion step for factorSquareFreePolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorSquareFreePolynomial}).")) (|factorByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorByRecursion(p)} factors polynomial \\spad{p}. This function performs the recursion step for factorPolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorPolynomial})")) (|solveLinearPolynomialEquationByRecursion| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|List| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{solveLinearPolynomialEquationByRecursion([p1,...,pn],p)} returns the list of polynomials \\spad{[q1,...,qn]} such that \\spad{sum qi/pi = p / prod 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 -(-925 R S) +(-926 R S) ((|constructor| (NIL "\\indented{1}{PolynomialFactorizationByRecursionUnivariate} \\spad{R} is a \\spadfun{PolynomialFactorizationExplicit} domain,{} \\spad{S} is univariate polynomials over \\spad{R} We are interested in handling SparseUnivariatePolynomials over \\spad{S},{} is a variable we shall call \\spad{z}")) (|factorSFBRlcUnit| (((|Factored| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|)) "\\spad{factorSFBRlcUnit(p)} returns the square free factorization of polynomial \\spad{p} (see \\spadfun{factorSquareFreeByRecursion}{PolynomialFactorizationByRecursionUnivariate}) in the case where the leading coefficient of \\spad{p} is a unit.")) (|randomR| ((|#1|) "\\spad{randomR()} produces a random element of \\spad{R}")) (|factorSquareFreeByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|)) "\\spad{factorSquareFreeByRecursion(p)} returns the square free factorization of \\spad{p}. This functions performs the recursion step for factorSquareFreePolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorSquareFreePolynomial}).")) (|factorByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|)) "\\spad{factorByRecursion(p)} factors polynomial \\spad{p}. This function performs the recursion step for factorPolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorPolynomial})")) (|solveLinearPolynomialEquationByRecursion| (((|Union| (|List| (|SparseUnivariatePolynomial| |#2|)) "failed") (|List| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|)) "\\spad{solveLinearPolynomialEquationByRecursion([p1,...,pn],p)} returns the list of polynomials \\spad{[q1,...,qn]} such that \\spad{sum qi/pi = p / prod 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 -(-926 S) +(-927 S) ((|constructor| (NIL "This is the category of domains that know \"enough\" about themselves in order to factor univariate polynomials over themselves. This will be used in future releases for supporting factorization over finitely generated coefficient fields,{} it is not yet available in the current release of axiom.")) (|charthRoot| (((|Union| $ "failed") $) "\\spad{charthRoot(r)} returns the \\spad{p}\\spad{-}th root of \\spad{r},{} or \"failed\" if none exists in the domain.")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(m)} returns a vector of elements,{} not all zero,{} whose \\spad{p}\\spad{-}th powers (\\spad{p} is the characteristic of the domain) are a solution of the homogenous linear system represented by \\spad{m},{} or \"failed\" is there is no such vector.")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| $)) "failed") (|List| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{solveLinearPolynomialEquation([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists.")) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) "\\spad{gcdPolynomial(p,q)} returns the \\spad{gcd} of the univariate polynomials \\spad{p} \\spad{qnd} \\spad{q}.")) (|factorSquareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorSquareFreePolynomial(p)} factors the univariate polynomial \\spad{p} into irreducibles where \\spad{p} is known to be square free and primitive with respect to its main variable.")) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorPolynomial(p)} returns the factorization into irreducibles of the univariate polynomial \\spad{p}.")) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{squareFreePolynomial(p)} returns the square-free factorization of the univariate polynomial \\spad{p}."))) NIL ((|HasCategory| |#1| (QUOTE (-146)))) -(-927) +(-928) ((|constructor| (NIL "This is the category of domains that know \"enough\" about themselves in order to factor univariate polynomials over themselves. This will be used in future releases for supporting factorization over finitely generated coefficient fields,{} it is not yet available in the current release of axiom.")) (|charthRoot| (((|Union| $ "failed") $) "\\spad{charthRoot(r)} returns the \\spad{p}\\spad{-}th root of \\spad{r},{} or \"failed\" if none exists in the domain.")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(m)} returns a vector of elements,{} not all zero,{} whose \\spad{p}\\spad{-}th powers (\\spad{p} is the characteristic of the domain) are a solution of the homogenous linear system represented by \\spad{m},{} or \"failed\" is there is no such vector.")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| $)) "failed") (|List| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{solveLinearPolynomialEquation([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists.")) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) "\\spad{gcdPolynomial(p,q)} returns the \\spad{gcd} of the univariate polynomials \\spad{p} \\spad{qnd} \\spad{q}.")) (|factorSquareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorSquareFreePolynomial(p)} factors the univariate polynomial \\spad{p} into irreducibles where \\spad{p} is known to be square free and primitive with respect to its main variable.")) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorPolynomial(p)} returns the factorization into irreducibles of the univariate polynomial \\spad{p}.")) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{squareFreePolynomial(p)} returns the square-free factorization of the univariate polynomial \\spad{p}."))) -((-4456 . T) ((-4465 "*") . T) (-4457 . T) (-4458 . T) (-4460 . T)) +((-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL -(-928 |p|) +(-929 |p|) ((|constructor| (NIL "PrimeField(\\spad{p}) implements the field with \\spad{p} elements if \\spad{p} is a prime number. Error: if \\spad{p} is not prime. Note: this domain does not check that argument is a prime."))) -((-4455 . T) (-4461 . T) (-4456 . T) ((-4465 "*") . T) (-4457 . T) (-4458 . T) (-4460 . T)) +((-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) ((|HasCategory| $ (QUOTE (-148))) (|HasCategory| $ (QUOTE (-146))) (|HasCategory| $ (QUOTE (-379)))) -(-929 R0 -2117 UP UPUP R) +(-930 R0 -1959 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 -(-930 UP UPUP R) +(-931 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 -(-931 UP UPUP) +(-932 UP UPUP) ((|constructor| (NIL "\\indented{1}{Utilities for PFOQ and PFO} Author: Manuel Bronstein Date Created: 25 Aug 1988 Date Last Updated: 11 Jul 1990")) (|polyred| ((|#2| |#2|) "\\spad{polyred(u)} \\undocumented")) (|doubleDisc| (((|Integer|) |#2|) "\\spad{doubleDisc(u)} \\undocumented")) (|mix| (((|Integer|) (|List| (|Record| (|:| |den| (|Integer|)) (|:| |gcdnum| (|Integer|))))) "\\spad{mix(l)} \\undocumented")) (|badNum| (((|Integer|) |#2|) "\\spad{badNum(u)} \\undocumented") (((|Record| (|:| |den| (|Integer|)) (|:| |gcdnum| (|Integer|))) |#1|) "\\spad{badNum(p)} \\undocumented")) (|getGoodPrime| (((|PositiveInteger|) (|Integer|)) "\\spad{getGoodPrime n} returns the smallest prime not dividing \\spad{n}"))) NIL NIL -(-932 R) +(-933 R) ((|constructor| (NIL "The domain \\spadtype{PartialFraction} implements partial fractions over a euclidean domain \\spad{R}. This requirement on the argument domain allows us to normalize the fractions. Of particular interest are the 2 forms for these fractions. The ``compact\\spad{''} form has only one fractional term per prime in the denominator,{} while the \\spad{``p}-adic\\spad{''} form expands each numerator \\spad{p}-adically via the prime \\spad{p} in the denominator. For computational efficiency,{} the compact form is used,{} though the \\spad{p}-adic form may be gotten by calling the function \\spadfunFrom{padicFraction}{PartialFraction}. For a general euclidean domain,{} it is not known how to factor the denominator. Thus the function \\spadfunFrom{partialFraction}{PartialFraction} takes as its second argument an element of \\spadtype{Factored(R)}.")) (|wholePart| ((|#1| $) "\\spad{wholePart(p)} extracts the whole part of the partial fraction \\spad{p}.")) (|partialFraction| (($ |#1| (|Factored| |#1|)) "\\spad{partialFraction(numer,denom)} is the main function for constructing partial fractions. The second argument is the denominator and should be factored.")) (|padicFraction| (($ $) "\\spad{padicFraction(q)} expands the fraction \\spad{p}-adically in the primes \\spad{p} in the denominator of \\spad{q}. For example,{} \\spad{padicFraction(3/(2**2)) = 1/2 + 1/(2**2)}. Use \\spadfunFrom{compactFraction}{PartialFraction} to return to compact form.")) (|padicallyExpand| (((|SparseUnivariatePolynomial| |#1|) |#1| |#1|) "\\spad{padicallyExpand(p,x)} is a utility function that expands the second argument \\spad{x} \\spad{``p}-adically\\spad{''} in the first.")) (|numberOfFractionalTerms| (((|Integer|) $) "\\spad{numberOfFractionalTerms(p)} computes the number of fractional terms in \\spad{p}. This returns 0 if there is no fractional part.")) (|nthFractionalTerm| (($ $ (|Integer|)) "\\spad{nthFractionalTerm(p,n)} extracts the \\spad{n}th fractional term from the partial fraction \\spad{p}. This returns 0 if the index \\spad{n} is out of range.")) (|firstNumer| ((|#1| $) "\\spad{firstNumer(p)} extracts the numerator of the first fractional term. This returns 0 if there is no fractional part (use \\spadfunFrom{wholePart}{PartialFraction} to get the whole part).")) (|firstDenom| (((|Factored| |#1|) $) "\\spad{firstDenom(p)} extracts the denominator of the first fractional term. This returns 1 if there is no fractional part (use \\spadfunFrom{wholePart}{PartialFraction} to get the whole part).")) (|compactFraction| (($ $) "\\spad{compactFraction(p)} normalizes the partial fraction \\spad{p} to the compact representation. In this form,{} the partial fraction has only one fractional term per prime in the denominator.")) (|coerce| (($ (|Fraction| (|Factored| |#1|))) "\\spad{coerce(f)} takes a fraction with numerator and denominator in factored form and creates a partial fraction. It is necessary for the parts to be factored because it is not known in general how to factor elements of \\spad{R} and this is needed to decompose into partial fractions.") (((|Fraction| |#1|) $) "\\spad{coerce(p)} sums up the components of the partial fraction and returns a single fraction."))) -((-4455 . T) (-4461 . T) (-4456 . T) ((-4465 "*") . T) (-4457 . T) (-4458 . T) (-4460 . T)) +((-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL -(-933 R) +(-934 R) ((|constructor| (NIL "The package \\spadtype{PartialFractionPackage} gives an easier to use interfact the domain \\spadtype{PartialFraction}. The user gives a fraction of polynomials,{} and a variable and the package converts it to the proper datatype for the \\spadtype{PartialFraction} domain.")) (|partialFraction| (((|Any|) (|Polynomial| |#1|) (|Factored| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{partialFraction(num, facdenom, var)} returns the partial fraction decomposition of the rational function whose numerator is \\spad{num} and whose factored denominator is \\spad{facdenom} with respect to the variable var.") (((|Any|) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{partialFraction(rf, var)} returns the partial fraction decomposition of the rational function \\spad{rf} with respect to the variable var."))) NIL NIL -(-934 E OV R P) +(-935 E OV R P) ((|gcdPrimitive| ((|#4| (|List| |#4|)) "\\spad{gcdPrimitive lp} computes the \\spad{gcd} of the list of primitive polynomials \\spad{lp}.") (((|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{gcdPrimitive(p,q)} computes the \\spad{gcd} of the primitive polynomials \\spad{p} and \\spad{q}.") ((|#4| |#4| |#4|) "\\spad{gcdPrimitive(p,q)} computes the \\spad{gcd} of the primitive polynomials \\spad{p} and \\spad{q}.")) (|gcd| (((|SparseUnivariatePolynomial| |#4|) (|List| (|SparseUnivariatePolynomial| |#4|))) "\\spad{gcd(lp)} computes the \\spad{gcd} of the list of polynomials \\spad{lp}.") (((|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{gcd(p,q)} computes the \\spad{gcd} of the two polynomials \\spad{p} and \\spad{q}.") ((|#4| (|List| |#4|)) "\\spad{gcd(lp)} computes the \\spad{gcd} of the list of polynomials \\spad{lp}.") ((|#4| |#4| |#4|) "\\spad{gcd(p,q)} computes the \\spad{gcd} of the two polynomials \\spad{p} and \\spad{q}."))) NIL NIL -(-935) +(-936) ((|constructor| (NIL "PermutationGroupExamples provides permutation groups for some classes of groups: symmetric,{} alternating,{} dihedral,{} cyclic,{} direct products of cyclic,{} which are in fact the finite abelian groups of symmetric groups called Young subgroups. Furthermore,{} Rubik\\spad{'s} group as permutation group of 48 integers and a list of sporadic simple groups derived from the atlas of finite groups.")) (|youngGroup| (((|PermutationGroup| (|Integer|)) (|Partition|)) "\\spad{youngGroup(lambda)} constructs the direct product of the symmetric groups given by the parts of the partition {\\em lambda}.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{youngGroup([n1,...,nk])} constructs the direct product of the symmetric groups {\\em Sn1},{}...,{}{\\em Snk}.")) (|rubiksGroup| (((|PermutationGroup| (|Integer|))) "\\spad{rubiksGroup constructs} the permutation group representing Rubic\\spad{'s} Cube acting on integers {\\em 10*i+j} for {\\em 1 <= i <= 6},{} {\\em 1 <= j <= 8}. The faces of Rubik\\spad{'s} Cube are labelled in the obvious way Front,{} Right,{} Up,{} Down,{} Left,{} Back and numbered from 1 to 6 in this given ordering,{} the pieces on each face (except the unmoveable center piece) are clockwise numbered from 1 to 8 starting with the piece in the upper left corner. The moves of the cube are represented as permutations on these pieces,{} represented as a two digit integer {\\em ij} where \\spad{i} is the numer of theface (1 to 6) and \\spad{j} is the number of the piece on this face. The remaining ambiguities are resolved by looking at the 6 generators,{} which represent a 90 degree turns of the faces,{} or from the following pictorial description. Permutation group representing Rubic\\spad{'s} Cube acting on integers 10*i+j for 1 \\spad{<=} \\spad{i} \\spad{<=} 6,{} 1 \\spad{<=} \\spad{j} \\spad{<=8}. \\blankline\\begin{verbatim}Rubik's Cube: +-----+ +-- B where: marks Side # : / U /|/ / / | F(ront) <-> 1 L --> +-----+ R| R(ight) <-> 2 | | + U(p) <-> 3 | F | / D(own) <-> 4 | |/ L(eft) <-> 5 +-----+ B(ack) <-> 6 ^ | DThe Cube's surface: The pieces on each side +---+ (except the unmoveable center |567| piece) are clockwise numbered |4U8| from 1 to 8 starting with the |321| piece in the upper left +---+---+---+ corner (see figure on the |781|123|345| left). The moves of the cube |6L2|8F4|2R6| are represented as |543|765|187| permutations on these pieces. +---+---+---+ Each of the pieces is |123| represented as a two digit |8D4| integer ij where i is the |765| # of the side ( 1 to 6 for +---+ F to B (see table above )) |567| and j is the # of the piece. |4B8| |321| +---+\\end{verbatim}")) (|janko2| (((|PermutationGroup| (|Integer|))) "\\spad{janko2 constructs} the janko group acting on the integers 1,{}...,{}100.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{janko2(li)} constructs the janko group acting on the 100 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em 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 {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em 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 {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em 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 {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em 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 {\\em li}. Note: duplicates in the list will be removed Error: if {\\em 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 {\\em li}. Note: duplicates in the list will be removed. error,{} if {\\em li} has less or more than 11 different entries.")) (|dihedralGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{dihedralGroup([i1,...,ik])} constructs the dihedral group of order 2k acting on the integers out of {\\em i1},{}...,{}{\\em ik}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{dihedralGroup(n)} constructs the dihedral group of order 2n acting on integers 1,{}...,{}\\spad{N}.")) (|cyclicGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{cyclicGroup([i1,...,ik])} constructs the cyclic group of order \\spad{k} acting on the integers {\\em i1},{}...,{}{\\em ik}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{cyclicGroup(n)} constructs the cyclic group of order \\spad{n} acting on the integers 1,{}...,{}\\spad{n}.")) (|abelianGroup| (((|PermutationGroup| (|Integer|)) (|List| (|PositiveInteger|))) "\\spad{abelianGroup([n1,...,nk])} constructs the abelian group that is the direct product of cyclic groups with order {\\em ni}.")) (|alternatingGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{alternatingGroup(li)} constructs the alternating group acting on the integers in the list {\\em li},{} generators are in general the {\\em n-2}-cycle {\\em (li.3,...,li.n)} and the 3-cycle {\\em (li.1,li.2,li.3)},{} if \\spad{n} is odd and product of the 2-cycle {\\em (li.1,li.2)} with {\\em n-2}-cycle {\\em (li.3,...,li.n)} and the 3-cycle {\\em (li.1,li.2,li.3)},{} if \\spad{n} is even. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{alternatingGroup(n)} constructs the alternating group {\\em An} acting on the integers 1,{}...,{}\\spad{n},{} generators are in general the {\\em n-2}-cycle {\\em (3,...,n)} and the 3-cycle {\\em (1,2,3)} if \\spad{n} is odd and the product of the 2-cycle {\\em (1,2)} with {\\em n-2}-cycle {\\em (3,...,n)} and the 3-cycle {\\em (1,2,3)} if \\spad{n} is even.")) (|symmetricGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{symmetricGroup(li)} constructs the symmetric group acting on the integers in the list {\\em li},{} generators are the cycle given by {\\em li} and the 2-cycle {\\em (li.1,li.2)}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{symmetricGroup(n)} constructs the symmetric group {\\em Sn} acting on the integers 1,{}...,{}\\spad{n},{} generators are the {\\em n}-cycle {\\em (1,...,n)} and the 2-cycle {\\em (1,2)}."))) NIL NIL -(-936 -2117) +(-937 -1959) ((|constructor| (NIL "Groebner functions for \\spad{P} \\spad{F} \\indented{2}{This package is an interface package to the groebner basis} package which allows you to compute groebner bases for polynomials in either lexicographic ordering or total degree ordering refined by reverse lex. The input is the ordinary polynomial type which is internally converted to a type with the required ordering. The resulting grobner basis is converted back to ordinary polynomials. The ordering among the variables is controlled by an explicit list of variables which is passed as a second argument. The coefficient domain is allowed to be any \\spad{gcd} domain,{} but the groebner basis is computed as if the polynomials were over a field.")) (|totalGroebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{totalGroebner(lp,lv)} computes Groebner basis for the list of polynomials \\spad{lp} with the terms ordered first by total degree and then refined by reverse lexicographic ordering. The variables are ordered by their position in the list \\spad{lv}.")) (|lexGroebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{lexGroebner(lp,lv)} computes Groebner basis for the list of polynomials \\spad{lp} in lexicographic order. The variables are ordered by their position in the list \\spad{lv}."))) NIL NIL -(-937 R) +(-938 R) ((|constructor| (NIL "\\indented{1}{Provides a coercion from the symbolic fractions in \\%\\spad{pi} with} integer coefficients to any Expression type. Date Created: 21 Feb 1990 Date Last Updated: 21 Feb 1990")) (|coerce| (((|Expression| |#1|) (|Pi|)) "\\spad{coerce(f)} returns \\spad{f} as an Expression(\\spad{R})."))) NIL NIL -(-938) +(-939) ((|constructor| (NIL "The category of constructive principal ideal domains,{} \\spadignore{i.e.} where a single generator can be constructively found for any ideal given by a finite set of generators. Note that this constructive definition only implies that finitely generated ideals are principal. It is not clear what we would mean by an infinitely generated ideal.")) (|expressIdealMember| (((|Union| (|List| $) "failed") (|List| $) $) "\\spad{expressIdealMember([f1,...,fn],h)} returns a representation of \\spad{h} as a linear combination of the \\spad{fi} or \"failed\" if \\spad{h} is not in the ideal generated by the \\spad{fi}.")) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) "\\spad{principalIdeal([f1,...,fn])} returns a record whose generator component is a generator of the ideal generated by \\spad{[f1,...,fn]} whose coef component satisfies \\spad{generator = sum (input.i * coef.i)}"))) -((-4456 . T) ((-4465 "*") . T) (-4457 . T) (-4458 . T) (-4460 . T)) +((-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL -(-939) +(-940) ((|constructor| (NIL "\\spadtype{PositiveInteger} provides functions for \\indented{2}{positive integers.}")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} means multiplication is commutative : x*y = \\spad{y*x}")) (|gcd| (($ $ $) "\\spad{gcd(a,b)} computes the greatest common divisor of two positive integers \\spad{a} and \\spad{b}."))) -(((-4465 "*") . T)) +(((-4466 "*") . T)) NIL -(-940 -2117 P) +(-941 -1959 P) ((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,l2)} \\undocumented"))) NIL NIL -(-941 |xx| -2117) +(-942 |xx| -1959) ((|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 -(-942 R |Var| |Expon| GR) +(-943 R |Var| |Expon| GR) ((|constructor| (NIL "Author: William Sit,{} spring 89")) (|inconsistent?| (((|Boolean|) (|List| (|Polynomial| |#1|))) "inconsistant?(\\spad{pl}) returns \\spad{true} if the system of equations \\spad{p} = 0 for \\spad{p} in \\spad{pl} is inconsistent. It is assumed that \\spad{pl} is a groebner basis.") (((|Boolean|) (|List| |#4|)) "inconsistant?(\\spad{pl}) returns \\spad{true} if the system of equations \\spad{p} = 0 for \\spad{p} in \\spad{pl} is inconsistent. It is assumed that \\spad{pl} is a groebner basis.")) (|sqfree| ((|#4| |#4|) "\\spad{sqfree(p)} returns the product of square free factors of \\spad{p}")) (|regime| (((|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))))) (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))) (|Matrix| |#4|) (|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|List| |#4|)) (|NonNegativeInteger|) (|NonNegativeInteger|) (|Integer|)) "\\spad{regime(y,c, w, p, r, rm, m)} returns a regime,{} a list of polynomials specifying the consistency conditions,{} a particular solution and basis representing the general solution of the parametric linear system \\spad{c} \\spad{z} = \\spad{w} on that regime. The regime returned depends on the subdeterminant \\spad{y}.det and the row and column indices. The solutions are simplified using the assumption that the system has rank \\spad{r} and maximum rank \\spad{rm}. The list \\spad{p} represents a list of list of factors of polynomials in a groebner basis of the ideal generated by higher order subdeterminants,{} and ius used for the simplification. The mode \\spad{m} distinguishes the cases when the system is homogeneous,{} or the right hand side is arbitrary,{} or when there is no new right hand side variables.")) (|redmat| (((|Matrix| |#4|) (|Matrix| |#4|) (|List| |#4|)) "\\spad{redmat(m,g)} returns a matrix whose entries are those of \\spad{m} modulo the ideal generated by the groebner basis \\spad{g}")) (|ParCond| (((|List| (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|))))) (|Matrix| |#4|) (|NonNegativeInteger|)) "\\spad{ParCond(m,k)} returns the list of all \\spad{k} by \\spad{k} subdeterminants in the matrix \\spad{m}")) (|overset?| (((|Boolean|) (|List| |#4|) (|List| (|List| |#4|))) "\\spad{overset?(s,sl)} returns \\spad{true} if \\spad{s} properly a sublist of a member of \\spad{sl}; otherwise it returns \\spad{false}")) (|nextSublist| (((|List| (|List| (|Integer|))) (|Integer|) (|Integer|)) "\\spad{nextSublist(n,k)} returns a list of \\spad{k}-subsets of {1,{} ...,{} \\spad{n}}.")) (|minset| (((|List| (|List| |#4|)) (|List| (|List| |#4|))) "\\spad{minset(sl)} returns the sublist of \\spad{sl} consisting of the minimal lists (with respect to inclusion) in the list \\spad{sl} of lists")) (|minrank| (((|NonNegativeInteger|) (|List| (|Record| (|:| |rank| (|NonNegativeInteger|)) (|:| |eqns| (|List| (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))))) (|:| |fgb| (|List| |#4|))))) "\\spad{minrank(r)} returns the minimum rank in the list \\spad{r} of regimes")) (|maxrank| (((|NonNegativeInteger|) (|List| (|Record| (|:| |rank| (|NonNegativeInteger|)) (|:| |eqns| (|List| (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))))) (|:| |fgb| (|List| |#4|))))) "\\spad{maxrank(r)} returns the maximum rank in the list \\spad{r} of regimes")) (|factorset| (((|List| |#4|) |#4|) "\\spad{factorset(p)} returns the set of irreducible factors of \\spad{p}.")) (|B1solve| (((|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))) (|Record| (|:| |mat| (|Matrix| (|Fraction| (|Polynomial| |#1|)))) (|:| |vec| (|List| (|Fraction| (|Polynomial| |#1|)))) (|:| |rank| (|NonNegativeInteger|)) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|))))) "\\spad{B1solve(s)} solves the system (\\spad{s}.mat) \\spad{z} = \\spad{s}.vec for the variables given by the column indices of \\spad{s}.cols in terms of the other variables and the right hand side \\spad{s}.vec by assuming that the rank is \\spad{s}.rank,{} that the system is consistent,{} with the linearly independent equations indexed by the given row indices \\spad{s}.rows; the coefficients in \\spad{s}.mat involving parameters are treated as polynomials. B1solve(\\spad{s}) returns a particular solution to the system and a basis of the homogeneous system (\\spad{s}.mat) \\spad{z} = 0.")) (|redpps| (((|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))) (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))) (|List| |#4|)) "\\spad{redpps(s,g)} returns the simplified form of \\spad{s} after reducing modulo a groebner basis \\spad{g}")) (|ParCondList| (((|List| (|Record| (|:| |rank| (|NonNegativeInteger|)) (|:| |eqns| (|List| (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))))) (|:| |fgb| (|List| |#4|)))) (|Matrix| |#4|) (|NonNegativeInteger|)) "\\spad{ParCondList(c,r)} computes a list of subdeterminants of each rank \\spad{>=} \\spad{r} of the matrix \\spad{c} and returns a groebner basis for the ideal they generate")) (|hasoln| (((|Record| (|:| |sysok| (|Boolean|)) (|:| |z0| (|List| |#4|)) (|:| |n0| (|List| |#4|))) (|List| |#4|) (|List| |#4|)) "\\spad{hasoln(g, l)} tests whether the quasi-algebraic set defined by \\spad{p} = 0 for \\spad{p} in \\spad{g} and \\spad{q} \\spad{~=} 0 for \\spad{q} in \\spad{l} is empty or not and returns a simplified definition of the quasi-algebraic set")) (|pr2dmp| ((|#4| (|Polynomial| |#1|)) "\\spad{pr2dmp(p)} converts \\spad{p} to target domain")) (|se2rfi| (((|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|Symbol|))) "\\spad{se2rfi(l)} converts \\spad{l} to target domain")) (|dmp2rfi| (((|List| (|Fraction| (|Polynomial| |#1|))) (|List| |#4|)) "\\spad{dmp2rfi(l)} converts \\spad{l} to target domain") (((|Matrix| (|Fraction| (|Polynomial| |#1|))) (|Matrix| |#4|)) "\\spad{dmp2rfi(m)} converts \\spad{m} to target domain") (((|Fraction| (|Polynomial| |#1|)) |#4|) "\\spad{dmp2rfi(p)} converts \\spad{p} to target domain")) (|bsolve| (((|Record| (|:| |rgl| (|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))))))) (|:| |rgsz| (|Integer|))) (|Matrix| |#4|) (|List| (|Fraction| (|Polynomial| |#1|))) (|NonNegativeInteger|) (|String|) (|Integer|)) "\\spad{bsolve(c, w, r, s, m)} returns a list of regimes and solutions of the system \\spad{c} \\spad{z} = \\spad{w} for ranks at least \\spad{r}; depending on the mode \\spad{m} chosen,{} it writes the output to a file given by the string \\spad{s}.")) (|rdregime| (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|String|)) "\\spad{rdregime(s)} reads in a list from a file with name \\spad{s}")) (|wrregime| (((|Integer|) (|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|String|)) "\\spad{wrregime(l,s)} writes a list of regimes to a file named \\spad{s} and returns the number of regimes written")) (|psolve| (((|Integer|) (|Matrix| |#4|) (|PositiveInteger|) (|String|)) "\\spad{psolve(c,k,s)} solves \\spad{c} \\spad{z} = 0 for all possible ranks \\spad{>=} \\spad{k} of the matrix \\spad{c},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|List| (|Symbol|)) (|PositiveInteger|) (|String|)) "\\spad{psolve(c,w,k,s)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks \\spad{>=} \\spad{k} of the matrix \\spad{c} and indeterminate right hand side \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|List| |#4|) (|PositiveInteger|) (|String|)) "\\spad{psolve(c,w,k,s)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks \\spad{>=} \\spad{k} of the matrix \\spad{c} and given right hand side \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|String|)) "\\spad{psolve(c,s)} solves \\spad{c} \\spad{z} = 0 for all possible ranks of the matrix \\spad{c} and given right hand side vector \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|List| (|Symbol|)) (|String|)) "\\spad{psolve(c,w,s)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks of the matrix \\spad{c} and indeterminate right hand side \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|List| |#4|) (|String|)) "\\spad{psolve(c,w,s)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks of the matrix \\spad{c} and given right hand side vector \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|PositiveInteger|)) "\\spad{psolve(c)} solves the homogeneous linear system \\spad{c} \\spad{z} = 0 for all possible ranks \\spad{>=} \\spad{k} of the matrix \\spad{c}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|List| (|Symbol|)) (|PositiveInteger|)) "\\spad{psolve(c,w,k)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks \\spad{>=} \\spad{k} of the matrix \\spad{c} and indeterminate right hand side \\spad{w}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|List| |#4|) (|PositiveInteger|)) "\\spad{psolve(c,w,k)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks \\spad{>=} \\spad{k} of the matrix \\spad{c} and given right hand side vector \\spad{w}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|)) "\\spad{psolve(c)} solves the homogeneous linear system \\spad{c} \\spad{z} = 0 for all possible ranks of the matrix \\spad{c}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|List| (|Symbol|))) "\\spad{psolve(c,w)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks of the matrix \\spad{c} and indeterminate right hand side \\spad{w}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|List| |#4|)) "\\spad{psolve(c,w)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks of the matrix \\spad{c} and given right hand side vector \\spad{w}"))) NIL NIL -(-943 S) +(-944 S) ((|constructor| (NIL "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 -(-944) +(-945) ((|constructor| (NIL "Plot3D supports parametric plots defined over a real number system. A real number system is a model for the real numbers and as such may be an approximation. For example,{} floating point numbers and infinite continued fractions are real number systems. The facilities at this point are limited to 3-dimensional parametric plots.")) (|debug3D| (((|Boolean|) (|Boolean|)) "\\spad{debug3D(true)} turns debug mode on; debug3D(\\spad{false}) turns debug mode off.")) (|numFunEvals3D| (((|Integer|)) "\\spad{numFunEvals3D()} returns the number of points computed.")) (|setAdaptive3D| (((|Boolean|) (|Boolean|)) "\\spad{setAdaptive3D(true)} turns adaptive plotting on; setAdaptive3D(\\spad{false}) turns adaptive plotting off.")) (|adaptive3D?| (((|Boolean|)) "\\spad{adaptive3D?()} determines whether plotting be done adaptively.")) (|setScreenResolution3D| (((|Integer|) (|Integer|)) "\\spad{setScreenResolution3D(i)} sets the screen resolution for a 3d graph to \\spad{i}.")) (|screenResolution3D| (((|Integer|)) "\\spad{screenResolution3D()} returns the screen resolution for a 3d graph.")) (|setMaxPoints3D| (((|Integer|) (|Integer|)) "\\spad{setMaxPoints3D(i)} sets the maximum number of points in a plot to \\spad{i}.")) (|maxPoints3D| (((|Integer|)) "\\spad{maxPoints3D()} returns the maximum number of points in a plot.")) (|setMinPoints3D| (((|Integer|) (|Integer|)) "\\spad{setMinPoints3D(i)} sets the minimum number of points in a plot to \\spad{i}.")) (|minPoints3D| (((|Integer|)) "\\spad{minPoints3D()} returns the minimum number of points in a plot.")) (|tValues| (((|List| (|List| (|DoubleFloat|))) $) "\\spad{tValues(p)} returns a list of lists of the values of the parameter for which a point is computed,{} one list for each curve in the plot \\spad{p}.")) (|tRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{tRange(p)} returns the range of the parameter in a parametric plot \\spad{p}.")) (|refine| (($ $) "\\spad{refine(x)} \\undocumented") (($ $ (|Segment| (|DoubleFloat|))) "\\spad{refine(x,r)} \\undocumented")) (|zoom| (($ $ (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{zoom(x,r,s,t)} \\undocumented")) (|plot| (($ $ (|Segment| (|DoubleFloat|))) "\\spad{plot(x,r)} \\undocumented") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f1,f2,f3,f4,x,y,z,w)} \\undocumented") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,g,h,a..b)} plots {/emx = \\spad{f}(\\spad{t}),{} \\spad{y} = \\spad{g}(\\spad{t}),{} \\spad{z} = \\spad{h}(\\spad{t})} as \\spad{t} ranges over {/em[a,{}\\spad{b}]}.")) (|pointPlot| (($ (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{pointPlot(f,x,y,z,w)} \\undocumented") (($ (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{pointPlot(f,g,h,a..b)} plots {/emx = \\spad{f}(\\spad{t}),{} \\spad{y} = \\spad{g}(\\spad{t}),{} \\spad{z} = \\spad{h}(\\spad{t})} as \\spad{t} ranges over {/em[a,{}\\spad{b}]}."))) NIL NIL -(-945) +(-946) ((|constructor| (NIL "The Plot domain supports plotting of functions defined over a real number system. A real number system is a model for the real numbers and as such may be an approximation. For example floating point numbers and infinite continued fractions. The facilities at this point are limited to 2-dimensional plots or either a single function or a parametric function.")) (|debug| (((|Boolean|) (|Boolean|)) "\\spad{debug(true)} turns debug mode on \\spad{debug(false)} turns debug mode off")) (|numFunEvals| (((|Integer|)) "\\spad{numFunEvals()} returns the number of points computed")) (|setAdaptive| (((|Boolean|) (|Boolean|)) "\\spad{setAdaptive(true)} turns adaptive plotting on \\spad{setAdaptive(false)} turns adaptive plotting off")) (|adaptive?| (((|Boolean|)) "\\spad{adaptive?()} determines whether plotting be done adaptively")) (|setScreenResolution| (((|Integer|) (|Integer|)) "\\spad{setScreenResolution(i)} sets the screen resolution to \\spad{i}")) (|screenResolution| (((|Integer|)) "\\spad{screenResolution()} returns the screen resolution")) (|setMaxPoints| (((|Integer|) (|Integer|)) "\\spad{setMaxPoints(i)} sets the maximum number of points in a plot to \\spad{i}")) (|maxPoints| (((|Integer|)) "\\spad{maxPoints()} returns the maximum number of points in a plot")) (|setMinPoints| (((|Integer|) (|Integer|)) "\\spad{setMinPoints(i)} sets the minimum number of points in a plot to \\spad{i}")) (|minPoints| (((|Integer|)) "\\spad{minPoints()} returns the minimum number of points in a plot")) (|tRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{tRange(p)} returns the range of the parameter in a parametric plot \\spad{p}")) (|refine| (($ $) "\\spad{refine(p)} performs a refinement on the plot \\spad{p}") (($ $ (|Segment| (|DoubleFloat|))) "\\spad{refine(x,r)} \\undocumented")) (|zoom| (($ $ (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{zoom(x,r,s)} \\undocumented") (($ $ (|Segment| (|DoubleFloat|))) "\\spad{zoom(x,r)} \\undocumented")) (|parametric?| (((|Boolean|) $) "\\spad{parametric? determines} whether it is a parametric plot?")) (|plotPolar| (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) "\\spad{plotPolar(f)} plots the polar curve \\spad{r = f(theta)} as theta ranges over the interval \\spad{[0,2*\\%pi]}; this is the same as the parametric curve \\spad{x = f(t) * cos(t)},{} \\spad{y = f(t) * sin(t)}.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plotPolar(f,a..b)} plots the polar curve \\spad{r = f(theta)} as theta ranges over the interval \\spad{[a,b]}; this is the same as the parametric curve \\spad{x = f(t) * cos(t)},{} \\spad{y = f(t) * sin(t)}.")) (|pointPlot| (($ (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{pointPlot(t +-> (f(t),g(t)),a..b,c..d,e..f)} plots the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over the interval \\spad{[a,b]}; \\spad{x}-range of \\spad{[c,d]} and \\spad{y}-range of \\spad{[e,f]} are noted in Plot object.") (($ (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{pointPlot(t +-> (f(t),g(t)),a..b)} plots the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over the interval \\spad{[a,b]}.")) (|plot| (($ $ (|Segment| (|DoubleFloat|))) "\\spad{plot(x,r)} \\undocumented") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,g,a..b,c..d,e..f)} plots the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over the interval \\spad{[a,b]}; \\spad{x}-range of \\spad{[c,d]} and \\spad{y}-range of \\spad{[e,f]} are noted in Plot object.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,g,a..b)} plots the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over the interval \\spad{[a,b]}.") (($ (|List| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot([f1,...,fm],a..b,c..d)} plots the functions \\spad{y = f1(x)},{}...,{} \\spad{y = fm(x)} on the interval \\spad{a..b}; \\spad{y}-range of \\spad{[c,d]} is noted in Plot object.") (($ (|List| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|DoubleFloat|))) "\\spad{plot([f1,...,fm],a..b)} plots the functions \\spad{y = f1(x)},{}...,{} \\spad{y = fm(x)} on the interval \\spad{a..b}.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,a..b,c..d)} plots the function \\spad{f(x)} on the interval \\spad{[a,b]}; \\spad{y}-range of \\spad{[c,d]} is noted in Plot object.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,a..b)} plots the function \\spad{f(x)} on the interval \\spad{[a,b]}."))) NIL NIL -(-946) +(-947) ((|constructor| (NIL "This package exports plotting tools")) (|calcRanges| (((|List| (|Segment| (|DoubleFloat|))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{calcRanges(l)} \\undocumented"))) NIL NIL -(-947 R -2117) +(-948 R -1959) ((|constructor| (NIL "Attaching assertions to symbols for pattern matching; Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|multiple| ((|#2| |#2|) "\\spad{multiple(x)} tells the pattern matcher that \\spad{x} should preferably match a multi-term quantity in a sum or product. For matching on lists,{} multiple(\\spad{x}) tells the pattern matcher that \\spad{x} should match a list instead of an element of a list. Error: if \\spad{x} is not a symbol.")) (|optional| ((|#2| |#2|) "\\spad{optional(x)} tells the pattern matcher that \\spad{x} can match an identity (0 in a sum,{} 1 in a product or exponentiation). Error: if \\spad{x} is not a symbol.")) (|constant| ((|#2| |#2|) "\\spad{constant(x)} tells the pattern matcher that \\spad{x} should match only the symbol \\spad{'x} and no other quantity. Error: if \\spad{x} is not a symbol.")) (|assert| ((|#2| |#2| (|Identifier|)) "\\spad{assert(x, s)} makes the assertion \\spad{s} about \\spad{x}. Error: if \\spad{x} is not a symbol."))) NIL NIL -(-948) +(-949) ((|constructor| (NIL "Attaching assertions to symbols for pattern matching. Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|multiple| (((|Expression| (|Integer|)) (|Symbol|)) "\\spad{multiple(x)} tells the pattern matcher that \\spad{x} should preferably match a multi-term quantity in a sum or product. For matching on lists,{} multiple(\\spad{x}) tells the pattern matcher that \\spad{x} should match a list instead of an element of a list.")) (|optional| (((|Expression| (|Integer|)) (|Symbol|)) "\\spad{optional(x)} tells the pattern matcher that \\spad{x} can match an identity (0 in a sum,{} 1 in a product or exponentiation)..")) (|constant| (((|Expression| (|Integer|)) (|Symbol|)) "\\spad{constant(x)} tells the pattern matcher that \\spad{x} should match only the symbol \\spad{'x} and no other quantity.")) (|assert| (((|Expression| (|Integer|)) (|Symbol|) (|Identifier|)) "\\spad{assert(x, s)} makes the assertion \\spad{s} about \\spad{x}."))) NIL NIL -(-949 S A B) +(-950 S A B) ((|constructor| (NIL "This packages provides tools for matching recursively in type towers.")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#2| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(expr, pat, res)} matches the pattern \\spad{pat} to the expression \\spad{expr}; res contains the variables of \\spad{pat} which are already matched and their matches. Note: this function handles type towers by changing the predicates and calling the matching function provided by \\spad{A}.")) (|fixPredicate| (((|Mapping| (|Boolean|) |#2|) (|Mapping| (|Boolean|) |#3|)) "\\spad{fixPredicate(f)} returns \\spad{g} defined by \\spad{g}(a) = \\spad{f}(a::B)."))) NIL NIL -(-950 S R -2117) +(-951 S R -1959) ((|constructor| (NIL "This package provides pattern matching functions on function spaces.")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(expr, pat, res)} matches the pattern \\spad{pat} to the expression \\spad{expr}; res contains the variables of \\spad{pat} which are already matched and their matches."))) NIL NIL -(-951 I) +(-952 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 -(-952 S E) +(-953 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 -(-953 S R L) +(-954 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 -(-954 S E V R P) +(-955 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 -900) (|devaluate| |#1|)))) -(-955 R -2117 -3155) +((|HasCategory| |#3| (LIST (QUOTE -901) (|devaluate| |#1|)))) +(-956 R -1959 -2018) ((|constructor| (NIL "Attaching predicates to symbols for pattern matching. Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|suchThat| ((|#2| |#2| (|List| (|Mapping| (|Boolean|) |#3|))) "\\spad{suchThat(x, [f1, f2, ..., fn])} attaches the predicate \\spad{f1} and \\spad{f2} and ... and \\spad{fn} to \\spad{x}. Error: if \\spad{x} is not a symbol.") ((|#2| |#2| (|Mapping| (|Boolean|) |#3|)) "\\spad{suchThat(x, foo)} attaches the predicate foo to \\spad{x}; error if \\spad{x} is not a symbol."))) NIL NIL -(-956 -3155) +(-957 -2018) ((|constructor| (NIL "Attaching predicates to symbols for pattern matching. Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|suchThat| (((|Expression| (|Integer|)) (|Symbol|) (|List| (|Mapping| (|Boolean|) |#1|))) "\\spad{suchThat(x, [f1, f2, ..., fn])} attaches the predicate \\spad{f1} and \\spad{f2} and ... and \\spad{fn} to \\spad{x}.") (((|Expression| (|Integer|)) (|Symbol|) (|Mapping| (|Boolean|) |#1|)) "\\spad{suchThat(x, foo)} attaches the predicate foo to \\spad{x}."))) NIL NIL -(-957 S R Q) +(-958 S R Q) ((|constructor| (NIL "This package provides pattern matching functions on quotients.")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(a/b, pat, res)} matches the pattern \\spad{pat} to the quotient \\spad{a/b}; res contains the variables of \\spad{pat} which are already matched and their matches."))) NIL NIL -(-958 S) +(-959 S) ((|constructor| (NIL "This package provides pattern matching functions on symbols.")) (|patternMatch| (((|PatternMatchResult| |#1| (|Symbol|)) (|Symbol|) (|Pattern| |#1|) (|PatternMatchResult| |#1| (|Symbol|))) "\\spad{patternMatch(expr, pat, res)} matches the pattern \\spad{pat} to the expression \\spad{expr}; res contains the variables of \\spad{pat} which are already matched and their matches (necessary for recursion)."))) NIL NIL -(-959 S R P) +(-960 S R P) ((|constructor| (NIL "This package provides tools for the pattern matcher.")) (|patternMatchTimes| (((|PatternMatchResult| |#1| |#3|) (|List| |#3|) (|List| (|Pattern| |#1|)) (|PatternMatchResult| |#1| |#3|) (|Mapping| (|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|))) "\\spad{patternMatchTimes(lsubj, lpat, res, match)} matches the product of patterns \\spad{reduce(*,lpat)} to the product of subjects \\spad{reduce(*,lsubj)}; \\spad{r} contains the previous matches and match is a pattern-matching function on \\spad{P}.")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) (|List| |#3|) (|List| (|Pattern| |#1|)) (|Mapping| |#3| (|List| |#3|)) (|PatternMatchResult| |#1| |#3|) (|Mapping| (|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|))) "\\spad{patternMatch(lsubj, lpat, op, res, match)} matches the list of patterns \\spad{lpat} to the list of subjects \\spad{lsubj},{} allowing for commutativity; \\spad{op} is the operator such that \\spad{op}(\\spad{lpat}) should match \\spad{op}(\\spad{lsubj}) at the end,{} \\spad{r} contains the previous matches,{} and match is a pattern-matching function on \\spad{P}."))) NIL NIL -(-960) +(-961) ((|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: Legendre polynomials,{} denoted \\spad{P[n](x)},{} are computed from the two term recurrence. The generating function is: \\spad{1/sqrt(1-2*t*x+t**2) = sum(P[n](x)*t**n, n=0..infinity)}.")) (|laguerre| (((|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{laguerre(n)} returns the \\spad{n}th Laguerre polynomial \\spad{L[n](x)}. Note: Laguerre polynomials,{} denoted \\spad{L[n](x)},{} are computed from the two term recurrence. The generating function is: \\spad{exp(x*t/(t-1))/(1-t) = sum(L[n](x)*t**n/n!, n=0..infinity)}.")) (|hermite| (((|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{hermite(n)} returns the \\spad{n}th Hermite polynomial \\spad{H[n](x)}. Note: Hermite polynomials,{} denoted \\spad{H[n](x)},{} are computed from the two term recurrence. The generating function is: \\spad{exp(2*t*x-t**2) = sum(H[n](x)*t**n/n!, n=0..infinity)}.")) (|fixedDivisor| (((|Integer|) (|SparseUnivariatePolynomial| (|Integer|))) "\\spad{fixedDivisor(a)} for \\spad{a(x)} in \\spad{Z[x]} is the largest integer \\spad{f} such that \\spad{f} divides \\spad{a(x=k)} for all integers \\spad{k}. Note: fixed divisor of \\spad{a} is \\spad{reduce(gcd,[a(x=k) for k in 0..degree(a)])}.")) (|euler| (((|SparseUnivariatePolynomial| (|Fraction| (|Integer|))) (|Integer|)) "\\spad{euler(n)} returns the \\spad{n}th Euler polynomial \\spad{E[n](x)}. Note: Euler polynomials denoted \\spad{E(n,x)} computed by solving the differential equation \\spad{differentiate(E(n,x),x) = n E(n-1,x)} where \\spad{E(0,x) = 1} and initial condition comes from \\spad{E(n) = 2**n E(n,1/2)}.")) (|cyclotomic| (((|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{cyclotomic(n)} returns the \\spad{n}th cyclotomic polynomial \\spad{phi[n](x)}. Note: \\spad{phi[n](x)} is the factor of \\spad{x**n - 1} whose roots are the primitive \\spad{n}th roots of unity.")) (|chebyshevU| (((|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{chebyshevU(n)} returns the \\spad{n}th Chebyshev polynomial \\spad{U[n](x)}. Note: Chebyshev polynomials of the second kind,{} denoted \\spad{U[n](x)},{} computed from the two term recurrence. The generating function \\spad{1/(1-2*t*x+t**2) = sum(T[n](x)*t**n, n=0..infinity)}.")) (|chebyshevT| (((|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{chebyshevT(n)} returns the \\spad{n}th Chebyshev polynomial \\spad{T[n](x)}. Note: Chebyshev polynomials of the first kind,{} denoted \\spad{T[n](x)},{} computed from the two term recurrence. The generating function \\spad{(1-t*x)/(1-2*t*x+t**2) = sum(T[n](x)*t**n, n=0..infinity)}.")) (|bernoulli| (((|SparseUnivariatePolynomial| (|Fraction| (|Integer|))) (|Integer|)) "\\spad{bernoulli(n)} returns the \\spad{n}th Bernoulli polynomial \\spad{B[n](x)}. Note: Bernoulli polynomials denoted \\spad{B(n,x)} computed by solving the differential equation \\spad{differentiate(B(n,x),x) = n B(n-1,x)} where \\spad{B(0,x) = 1} and initial condition comes from \\spad{B(n) = B(n,0)}."))) NIL NIL -(-961 R) +(-962 R) ((|constructor| (NIL "This domain implements points in coordinate space"))) -((-4464 . T) (-4463 . T)) -((-3794 (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1120))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-3794 (-12 (|HasCategory| |#1| (QUOTE (-1120))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-875))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-3794 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1120)))) (|HasCategory| |#1| (QUOTE (-861))) (-3794 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1120)))) (|HasCategory| (-576) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1120))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-738))) (|HasCategory| |#1| (QUOTE (-1069))) (-12 (|HasCategory| |#1| (QUOTE (-1022))) (|HasCategory| |#1| (QUOTE (-1069)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-875)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1120))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) -(-962 |lv| R) +((-4465 . T) (-4464 . T)) +((-2758 (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2758 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2758 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| |#1| (QUOTE (-861))) (-2758 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| (-576) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-738))) (|HasCategory| |#1| (QUOTE (-1070))) (-12 (|HasCategory| |#1| (QUOTE (-1023))) (|HasCategory| |#1| (QUOTE (-1070)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) +(-963 |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 -(-963 |TheField| |ThePols|) +(-964 |TheField| |ThePols|) ((|constructor| (NIL "\\axiomType{RealPolynomialUtilitiesPackage} provides common functions used by interval coding.")) (|lazyVariations| (((|NonNegativeInteger|) (|List| |#1|) (|Integer|) (|Integer|)) "\\axiom{lazyVariations(\\spad{l},{}\\spad{s1},{}\\spad{sn})} is the number of sign variations in the list of non null numbers [s1::l]\\spad{@sn},{}")) (|sturmVariationsOf| (((|NonNegativeInteger|) (|List| |#1|)) "\\axiom{sturmVariationsOf(\\spad{l})} is the number of sign variations in the list of numbers \\spad{l},{} note that the first term counts as a sign")) (|boundOfCauchy| ((|#1| |#2|) "\\axiom{boundOfCauchy(\\spad{p})} bounds the roots of \\spad{p}")) (|sturmSequence| (((|List| |#2|) |#2|) "\\axiom{sturmSequence(\\spad{p}) = sylvesterSequence(\\spad{p},{}\\spad{p'})}")) (|sylvesterSequence| (((|List| |#2|) |#2| |#2|) "\\axiom{sylvesterSequence(\\spad{p},{}\\spad{q})} is the negated remainder sequence of \\spad{p} and \\spad{q} divided by the last computed term"))) NIL ((|HasCategory| |#1| (QUOTE (-860)))) -(-964 R S) +(-965 R S) ((|constructor| (NIL "\\indented{2}{This package takes a mapping between coefficient rings,{} and lifts} it to a mapping between polynomials over those rings.")) (|map| (((|Polynomial| |#2|) (|Mapping| |#2| |#1|) (|Polynomial| |#1|)) "\\spad{map(f, p)} produces a new polynomial as a result of applying the function \\spad{f} to every coefficient of the polynomial \\spad{p}."))) NIL NIL -(-965 |x| R) +(-966 |x| R) ((|constructor| (NIL "This package is primarily to help the interpreter do coercions. It allows you to view a polynomial as a univariate polynomial in one of its variables with coefficients which are again a polynomial in all the other variables.")) (|univariate| (((|UnivariatePolynomial| |#1| (|Polynomial| |#2|)) (|Polynomial| |#2|) (|Variable| |#1|)) "\\spad{univariate(p, x)} converts the polynomial \\spad{p} to a one of type \\spad{UnivariatePolynomial(x,Polynomial(R))},{} ie. as a member of \\spad{R[...][x]}."))) NIL NIL -(-966 S R E |VarSet|) +(-967 S R E |VarSet|) ((|constructor| (NIL "The category for general multi-variate polynomials over a ring \\spad{R},{} in variables from VarSet,{} with exponents from the \\spadtype{OrderedAbelianMonoidSup}.")) (|canonicalUnitNormal| ((|attribute|) "we can choose a unique representative for each associate class. This normalization is chosen to be normalization of leading coefficient (by default).")) (|squareFreePart| (($ $) "\\spad{squareFreePart(p)} returns product of all the irreducible factors of polynomial \\spad{p} each taken with multiplicity one.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(p)} returns the square free factorization of the polynomial \\spad{p}.")) (|primitivePart| (($ $ |#4|) "\\spad{primitivePart(p,v)} returns the unitCanonical associate of the polynomial \\spad{p} with its content with respect to the variable \\spad{v} divided out.") (($ $) "\\spad{primitivePart(p)} returns the unitCanonical associate of the polynomial \\spad{p} with its content divided out.")) (|content| (($ $ |#4|) "\\spad{content(p,v)} is the \\spad{gcd} of the coefficients of the polynomial \\spad{p} when \\spad{p} is viewed as a univariate polynomial with respect to the variable \\spad{v}. Thus,{} for polynomial 7*x**2*y + 14*x*y**2,{} the \\spad{gcd} of the coefficients with respect to \\spad{x} is 7*y.")) (|discriminant| (($ $ |#4|) "\\spad{discriminant(p,v)} returns the disriminant of the polynomial \\spad{p} with respect to the variable \\spad{v}.")) (|resultant| (($ $ $ |#4|) "\\spad{resultant(p,q,v)} returns the resultant of the polynomials \\spad{p} and \\spad{q} with respect to the variable \\spad{v}.")) (|primitiveMonomials| (((|List| $) $) "\\spad{primitiveMonomials(p)} gives the list of monomials of the polynomial \\spad{p} with their coefficients removed. Note: \\spad{primitiveMonomials(sum(a_(i) X^(i))) = [X^(1),...,X^(n)]}.")) (|variables| (((|List| |#4|) $) "\\spad{variables(p)} returns the list of those variables actually appearing in the polynomial \\spad{p}.")) (|totalDegree| (((|NonNegativeInteger|) $ (|List| |#4|)) "\\spad{totalDegree(p, lv)} returns the maximum sum (over all monomials of polynomial \\spad{p}) of the variables in the list \\spad{lv}.") (((|NonNegativeInteger|) $) "\\spad{totalDegree(p)} returns the largest sum over all monomials of all exponents of a monomial.")) (|isExpt| (((|Union| (|Record| (|:| |var| |#4|) (|:| |exponent| (|NonNegativeInteger|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x, n]} if polynomial \\spad{p} has the form \\spad{x**n} and \\spad{n > 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if polynomial \\spad{p = a1 ... an} and \\spad{n >= 2},{} and,{} for each \\spad{i},{} \\spad{ai} is either a nontrivial constant in \\spad{R} or else of the form \\spad{x**e},{} where \\spad{e > 0} is an integer and \\spad{x} in a member of VarSet.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,...,mn]} if polynomial \\spad{p = m1 + ... + mn} and \\spad{n >= 2} and each \\spad{mi} is a nonzero monomial.")) (|multivariate| (($ (|SparseUnivariatePolynomial| $) |#4|) "\\spad{multivariate(sup,v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.") (($ (|SparseUnivariatePolynomial| |#2|) |#4|) "\\spad{multivariate(sup,v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.")) (|monomial| (($ $ (|List| |#4|) (|List| (|NonNegativeInteger|))) "\\spad{monomial(a,[v1..vn],[e1..en])} returns \\spad{a*prod(vi**ei)}.") (($ $ |#4| (|NonNegativeInteger|)) "\\spad{monomial(a,x,n)} creates the monomial \\spad{a*x**n} where \\spad{a} is a polynomial,{} \\spad{x} is a variable and \\spad{n} is a nonnegative integer.")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $ |#4|) "\\spad{monicDivide(a,b,v)} divides the polynomial a by the polynomial \\spad{b},{} with each viewed as a univariate polynomial in \\spad{v} returning both the quotient and remainder. Error: if \\spad{b} is not monic with respect to \\spad{v}.")) (|minimumDegree| (((|List| (|NonNegativeInteger|)) $ (|List| |#4|)) "\\spad{minimumDegree(p, lv)} gives the list of minimum degrees of the polynomial \\spad{p} with respect to each of the variables in the list \\spad{lv}") (((|NonNegativeInteger|) $ |#4|) "\\spad{minimumDegree(p,v)} gives the minimum degree of polynomial \\spad{p} with respect to \\spad{v},{} \\spadignore{i.e.} viewed a univariate polynomial in \\spad{v}")) (|mainVariable| (((|Union| |#4| "failed") $) "\\spad{mainVariable(p)} returns the biggest variable which actually occurs in the polynomial \\spad{p},{} or \"failed\" if no variables are present. fails precisely if polynomial satisfies ground?")) (|univariate| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{univariate(p)} converts the multivariate polynomial \\spad{p},{} which should actually involve only one variable,{} into a univariate polynomial in that variable,{} whose coefficients are in the ground ring. Error: if polynomial is genuinely multivariate") (((|SparseUnivariatePolynomial| $) $ |#4|) "\\spad{univariate(p,v)} converts the multivariate polynomial \\spad{p} into a univariate polynomial in \\spad{v},{} whose coefficients are still multivariate polynomials (in all the other variables).")) (|monomials| (((|List| $) $) "\\spad{monomials(p)} returns the list of non-zero monomials of polynomial \\spad{p},{} \\spadignore{i.e.} \\spad{monomials(sum(a_(i) X^(i))) = [a_(1) X^(1),...,a_(n) X^(n)]}.")) (|coefficient| (($ $ (|List| |#4|) (|List| (|NonNegativeInteger|))) "\\spad{coefficient(p, lv, ln)} views the polynomial \\spad{p} as a polynomial in the variables of \\spad{lv} and returns the coefficient of the term \\spad{lv**ln},{} \\spadignore{i.e.} \\spad{prod(lv_i ** ln_i)}.") (($ $ |#4| (|NonNegativeInteger|)) "\\spad{coefficient(p,v,n)} views the polynomial \\spad{p} as a univariate polynomial in \\spad{v} and returns the coefficient of the \\spad{v**n} term.")) (|degree| (((|List| (|NonNegativeInteger|)) $ (|List| |#4|)) "\\spad{degree(p,lv)} gives the list of degrees of polynomial \\spad{p} with respect to each of the variables in the list \\spad{lv}.") (((|NonNegativeInteger|) $ |#4|) "\\spad{degree(p,v)} gives the degree of polynomial \\spad{p} with respect to the variable \\spad{v}."))) NIL -((|HasCategory| |#2| (QUOTE (-927))) (|HasAttribute| |#2| (QUOTE -4461)) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#4| (LIST (QUOTE -900) (QUOTE (-390)))) (|HasCategory| |#2| (LIST (QUOTE -900) (QUOTE (-390)))) (|HasCategory| |#4| (LIST (QUOTE -900) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -900) (QUOTE (-576)))) (|HasCategory| |#4| (LIST (QUOTE -626) (LIST (QUOTE -906) (QUOTE (-390))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -906) (QUOTE (-390))))) (|HasCategory| |#4| (LIST (QUOTE -626) (LIST (QUOTE -906) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -906) (QUOTE (-576))))) (|HasCategory| |#4| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548))))) -(-967 R E |VarSet|) +((|HasCategory| |#2| (QUOTE (-928))) (|HasAttribute| |#2| (QUOTE -4462)) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#4| (LIST (QUOTE -901) (QUOTE (-390)))) (|HasCategory| |#2| (LIST (QUOTE -901) (QUOTE (-390)))) (|HasCategory| |#4| (LIST (QUOTE -901) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -901) (QUOTE (-576)))) (|HasCategory| |#4| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390))))) (|HasCategory| |#4| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576))))) (|HasCategory| |#4| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548))))) +(-968 R E |VarSet|) ((|constructor| (NIL "The category for general multi-variate polynomials over a ring \\spad{R},{} in variables from VarSet,{} with exponents from the \\spadtype{OrderedAbelianMonoidSup}.")) (|canonicalUnitNormal| ((|attribute|) "we can choose a unique representative for each associate class. This normalization is chosen to be normalization of leading coefficient (by default).")) (|squareFreePart| (($ $) "\\spad{squareFreePart(p)} returns product of all the irreducible factors of polynomial \\spad{p} each taken with multiplicity one.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(p)} returns the square free factorization of the polynomial \\spad{p}.")) (|primitivePart| (($ $ |#3|) "\\spad{primitivePart(p,v)} returns the unitCanonical associate of the polynomial \\spad{p} with its content with respect to the variable \\spad{v} divided out.") (($ $) "\\spad{primitivePart(p)} returns the unitCanonical associate of the polynomial \\spad{p} with its content divided out.")) (|content| (($ $ |#3|) "\\spad{content(p,v)} is the \\spad{gcd} of the coefficients of the polynomial \\spad{p} when \\spad{p} is viewed as a univariate polynomial with respect to the variable \\spad{v}. Thus,{} for polynomial 7*x**2*y + 14*x*y**2,{} the \\spad{gcd} of the coefficients with respect to \\spad{x} is 7*y.")) (|discriminant| (($ $ |#3|) "\\spad{discriminant(p,v)} returns the disriminant of the polynomial \\spad{p} with respect to the variable \\spad{v}.")) (|resultant| (($ $ $ |#3|) "\\spad{resultant(p,q,v)} returns the resultant of the polynomials \\spad{p} and \\spad{q} with respect to the variable \\spad{v}.")) (|primitiveMonomials| (((|List| $) $) "\\spad{primitiveMonomials(p)} gives the list of monomials of the polynomial \\spad{p} with their coefficients removed. Note: \\spad{primitiveMonomials(sum(a_(i) X^(i))) = [X^(1),...,X^(n)]}.")) (|variables| (((|List| |#3|) $) "\\spad{variables(p)} returns the list of those variables actually appearing in the polynomial \\spad{p}.")) (|totalDegree| (((|NonNegativeInteger|) $ (|List| |#3|)) "\\spad{totalDegree(p, lv)} returns the maximum sum (over all monomials of polynomial \\spad{p}) of the variables in the list \\spad{lv}.") (((|NonNegativeInteger|) $) "\\spad{totalDegree(p)} returns the largest sum over all monomials of all exponents of a monomial.")) (|isExpt| (((|Union| (|Record| (|:| |var| |#3|) (|:| |exponent| (|NonNegativeInteger|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x, n]} if polynomial \\spad{p} has the form \\spad{x**n} and \\spad{n > 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if polynomial \\spad{p = a1 ... an} and \\spad{n >= 2},{} and,{} for each \\spad{i},{} \\spad{ai} is either a nontrivial constant in \\spad{R} or else of the form \\spad{x**e},{} where \\spad{e > 0} is an integer and \\spad{x} in a member of VarSet.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,...,mn]} if polynomial \\spad{p = m1 + ... + mn} and \\spad{n >= 2} and each \\spad{mi} is a nonzero monomial.")) (|multivariate| (($ (|SparseUnivariatePolynomial| $) |#3|) "\\spad{multivariate(sup,v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.") (($ (|SparseUnivariatePolynomial| |#1|) |#3|) "\\spad{multivariate(sup,v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.")) (|monomial| (($ $ (|List| |#3|) (|List| (|NonNegativeInteger|))) "\\spad{monomial(a,[v1..vn],[e1..en])} returns \\spad{a*prod(vi**ei)}.") (($ $ |#3| (|NonNegativeInteger|)) "\\spad{monomial(a,x,n)} creates the monomial \\spad{a*x**n} where \\spad{a} is a polynomial,{} \\spad{x} is a variable and \\spad{n} is a nonnegative integer.")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $ |#3|) "\\spad{monicDivide(a,b,v)} divides the polynomial a by the polynomial \\spad{b},{} with each viewed as a univariate polynomial in \\spad{v} returning both the quotient and remainder. Error: if \\spad{b} is not monic with respect to \\spad{v}.")) (|minimumDegree| (((|List| (|NonNegativeInteger|)) $ (|List| |#3|)) "\\spad{minimumDegree(p, lv)} gives the list of minimum degrees of the polynomial \\spad{p} with respect to each of the variables in the list \\spad{lv}") (((|NonNegativeInteger|) $ |#3|) "\\spad{minimumDegree(p,v)} gives the minimum degree of polynomial \\spad{p} with respect to \\spad{v},{} \\spadignore{i.e.} viewed a univariate polynomial in \\spad{v}")) (|mainVariable| (((|Union| |#3| "failed") $) "\\spad{mainVariable(p)} returns the biggest variable which actually occurs in the polynomial \\spad{p},{} or \"failed\" if no variables are present. fails precisely if polynomial satisfies ground?")) (|univariate| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{univariate(p)} converts the multivariate polynomial \\spad{p},{} which should actually involve only one variable,{} into a univariate polynomial in that variable,{} whose coefficients are in the ground ring. Error: if polynomial is genuinely multivariate") (((|SparseUnivariatePolynomial| $) $ |#3|) "\\spad{univariate(p,v)} converts the multivariate polynomial \\spad{p} into a univariate polynomial in \\spad{v},{} whose coefficients are still multivariate polynomials (in all the other variables).")) (|monomials| (((|List| $) $) "\\spad{monomials(p)} returns the list of non-zero monomials of polynomial \\spad{p},{} \\spadignore{i.e.} \\spad{monomials(sum(a_(i) X^(i))) = [a_(1) X^(1),...,a_(n) X^(n)]}.")) (|coefficient| (($ $ (|List| |#3|) (|List| (|NonNegativeInteger|))) "\\spad{coefficient(p, lv, ln)} views the polynomial \\spad{p} as a polynomial in the variables of \\spad{lv} and returns the coefficient of the term \\spad{lv**ln},{} \\spadignore{i.e.} \\spad{prod(lv_i ** ln_i)}.") (($ $ |#3| (|NonNegativeInteger|)) "\\spad{coefficient(p,v,n)} views the polynomial \\spad{p} as a univariate polynomial in \\spad{v} and returns the coefficient of the \\spad{v**n} term.")) (|degree| (((|List| (|NonNegativeInteger|)) $ (|List| |#3|)) "\\spad{degree(p,lv)} gives the list of degrees of polynomial \\spad{p} with respect to each of the variables in the list \\spad{lv}.") (((|NonNegativeInteger|) $ |#3|) "\\spad{degree(p,v)} gives the degree of polynomial \\spad{p} with respect to the variable \\spad{v}."))) -(((-4465 "*") |has| |#1| (-174)) (-4456 |has| |#1| (-568)) (-4461 |has| |#1| (-6 -4461)) (-4458 . T) (-4457 . T) (-4460 . T)) +(((-4466 "*") |has| |#1| (-174)) (-4457 |has| |#1| (-568)) (-4462 |has| |#1| (-6 -4462)) (-4459 . T) (-4458 . T) (-4461 . T)) NIL -(-968 E V R P -2117) +(-969 E V R P -1959) ((|constructor| (NIL "This package transforms multivariate polynomials or fractions into univariate polynomials or fractions,{} and back.")) (|isPower| (((|Union| (|Record| (|:| |val| |#5|) (|:| |exponent| (|Integer|))) "failed") |#5|) "\\spad{isPower(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0},{} \"failed\" otherwise.")) (|isExpt| (((|Union| (|Record| (|:| |var| |#2|) (|:| |exponent| (|Integer|))) "failed") |#5|) "\\spad{isExpt(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0},{} \"failed\" otherwise.")) (|isTimes| (((|Union| (|List| |#5|) "failed") |#5|) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if \\spad{p = a1 ... an} and \\spad{n > 1},{} \"failed\" otherwise.")) (|isPlus| (((|Union| (|List| |#5|) "failed") |#5|) "\\spad{isPlus(p)} returns [\\spad{m1},{}...,{}\\spad{mn}] if \\spad{p = m1 + ... + mn} and \\spad{n > 1},{} \"failed\" otherwise.")) (|multivariate| ((|#5| (|Fraction| (|SparseUnivariatePolynomial| |#5|)) |#2|) "\\spad{multivariate(f, v)} applies both the numerator and denominator of \\spad{f} to \\spad{v}.")) (|univariate| (((|SparseUnivariatePolynomial| |#5|) |#5| |#2| (|SparseUnivariatePolynomial| |#5|)) "\\spad{univariate(f, x, p)} returns \\spad{f} viewed as a univariate polynomial in \\spad{x},{} using the side-condition \\spad{p(x) = 0}.") (((|Fraction| (|SparseUnivariatePolynomial| |#5|)) |#5| |#2|) "\\spad{univariate(f, v)} returns \\spad{f} viewed as a univariate rational function in \\spad{v}.")) (|mainVariable| (((|Union| |#2| "failed") |#5|) "\\spad{mainVariable(f)} returns the highest variable appearing in the numerator or the denominator of \\spad{f},{} \"failed\" if \\spad{f} has no variables.")) (|variables| (((|List| |#2|) |#5|) "\\spad{variables(f)} returns the list of variables appearing in the numerator or the denominator of \\spad{f}."))) NIL NIL -(-969 E |Vars| R P S) +(-970 E |Vars| R P S) ((|constructor| (NIL "This package provides a very general map function,{} which given a set \\spad{S} and polynomials over \\spad{R} with maps from the variables into \\spad{S} and the coefficients into \\spad{S},{} maps polynomials into \\spad{S}. \\spad{S} is assumed to support \\spad{+},{} \\spad{*} and \\spad{**}.")) (|map| ((|#5| (|Mapping| |#5| |#2|) (|Mapping| |#5| |#3|) |#4|) "\\spad{map(varmap, coefmap, p)} takes a \\spad{varmap},{} a mapping from the variables of polynomial \\spad{p} into \\spad{S},{} \\spad{coefmap},{} a mapping from coefficients of \\spad{p} into \\spad{S},{} and \\spad{p},{} and produces a member of \\spad{S} using the corresponding arithmetic. in \\spad{S}"))) NIL NIL -(-970 R) +(-971 R) ((|constructor| (NIL "\\indented{2}{This type is the basic representation of sparse recursive multivariate} polynomials whose variables are arbitrary symbols. The ordering is alphabetic determined by the Symbol type. The coefficient ring may be non commutative,{} but the variables are assumed to commute.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(p,x)} computes the integral of \\spad{p*dx},{} \\spadignore{i.e.} integrates the polynomial \\spad{p} with respect to the variable \\spad{x}."))) -(((-4465 "*") |has| |#1| (-174)) (-4456 |has| |#1| (-568)) (-4461 |has| |#1| (-6 -4461)) (-4458 . T) (-4457 . T) (-4460 . T)) -((|HasCategory| |#1| (QUOTE (-927))) (-3794 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-927)))) (-3794 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-927)))) (-3794 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-927)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-3794 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasCategory| (-1196) (LIST (QUOTE -900) (QUOTE (-390)))) (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-390))))) (-12 (|HasCategory| (-1196) (LIST (QUOTE -900) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-576))))) (-12 (|HasCategory| (-1196) (LIST (QUOTE -626) (LIST (QUOTE -906) (QUOTE (-390))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -906) (QUOTE (-390)))))) (-12 (|HasCategory| (-1196) (LIST (QUOTE -626) (LIST (QUOTE -906) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -906) (QUOTE (-576)))))) (-12 (|HasCategory| (-1196) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1058) (QUOTE (-576)))) (-3794 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1058) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#1| (LIST (QUOTE -1058) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-374))) (|HasAttribute| |#1| (QUOTE -4461)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-927)))) (-3794 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-927)))) (|HasCategory| |#1| (QUOTE (-146))))) -(-971 E V R P -2117) +(((-4466 "*") |has| |#1| (-174)) (-4457 |has| |#1| (-568)) (-4462 |has| |#1| (-6 -4462)) (-4459 . T) (-4458 . T) (-4461 . T)) +((|HasCategory| |#1| (QUOTE (-928))) (-2758 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-928)))) (-2758 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-928)))) (-2758 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-928)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-2758 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasCategory| (-1197) (LIST (QUOTE -901) (QUOTE (-390)))) (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-390))))) (-12 (|HasCategory| (-1197) (LIST (QUOTE -901) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-576))))) (-12 (|HasCategory| (-1197) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390)))))) (-12 (|HasCategory| (-1197) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576)))))) (-12 (|HasCategory| (-1197) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576)))) (-2758 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-374))) (|HasAttribute| |#1| (QUOTE -4462)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-928)))) (-2758 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-928)))) (|HasCategory| |#1| (QUOTE (-146))))) +(-972 E V R P -1959) ((|constructor| (NIL "computes \\spad{n}-th roots of quotients of multivariate polynomials")) (|nthr| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#4|) (|:| |radicand| (|List| |#4|))) |#4| (|NonNegativeInteger|)) "\\spad{nthr(p,n)} should be local but conditional")) (|froot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) |#5| (|NonNegativeInteger|)) "\\spad{froot(f, n)} returns \\spad{[m,c,r]} such that \\spad{f**(1/n) = c * r**(1/m)}.")) (|qroot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) (|Fraction| (|Integer|)) (|NonNegativeInteger|)) "\\spad{qroot(f, n)} returns \\spad{[m,c,r]} such that \\spad{f**(1/n) = c * r**(1/m)}.")) (|rroot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) |#3| (|NonNegativeInteger|)) "\\spad{rroot(f, n)} returns \\spad{[m,c,r]} such that \\spad{f**(1/n) = c * r**(1/m)}.")) (|denom| ((|#4| $) "\\spad{denom(x)} \\undocumented")) (|numer| ((|#4| $) "\\spad{numer(x)} \\undocumented"))) NIL ((|HasCategory| |#3| (QUOTE (-464)))) -(-972) +(-973) ((|constructor| (NIL "This domain represents network port numbers (notable \\spad{TCP} and UDP).")) (|port| (($ (|SingleInteger|)) "\\spad{port(n)} constructs a PortNumber from the integer \\spad{`n'}."))) NIL NIL -(-973) +(-974) ((|constructor| (NIL "PlottablePlaneCurveCategory is the category of curves in the plane which may be plotted via the graphics facilities. Functions are provided for obtaining lists of lists of points,{} representing the branches of the curve,{} and for determining the ranges of the \\spad{x}-coordinates and \\spad{y}-coordinates of the points on the curve.")) (|yRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{yRange(c)} returns the range of the \\spad{y}-coordinates of the points on the curve \\spad{c}.")) (|xRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{xRange(c)} returns the range of the \\spad{x}-coordinates of the points on the curve \\spad{c}.")) (|listBranches| (((|List| (|List| (|Point| (|DoubleFloat|)))) $) "\\spad{listBranches(c)} returns a list of lists of points,{} representing the branches of the curve \\spad{c}."))) NIL NIL -(-974 R L) +(-975 R L) ((|constructor| (NIL "\\spadtype{PrecomputedAssociatedEquations} stores some generic precomputations which speed up the computations of the associated equations needed for factoring operators.")) (|firstUncouplingMatrix| (((|Union| (|Matrix| |#1|) "failed") |#2| (|PositiveInteger|)) "\\spad{firstUncouplingMatrix(op, m)} returns the matrix A such that \\spad{A w = (W',W'',...,W^N)} in the corresponding associated equations for right-factors of order \\spad{m} of \\spad{op}. Returns \"failed\" if the matrix A has not been precomputed for the particular combination \\spad{degree(L), m}."))) NIL NIL -(-975 A B) +(-976 A B) ((|constructor| (NIL "\\indented{1}{This package provides tools for operating on primitive arrays} with unary and binary functions involving different underlying types")) (|map| (((|PrimitiveArray| |#2|) (|Mapping| |#2| |#1|) (|PrimitiveArray| |#1|)) "\\spad{map(f,a)} applies function \\spad{f} to each member of primitive array \\spad{a} resulting in a new primitive array over a possibly different underlying domain.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|PrimitiveArray| |#1|) |#2|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the primitive array \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,[1,2,3],0)} does \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as the identity element for the function \\spad{f}.")) (|scan| (((|PrimitiveArray| |#2|) (|Mapping| |#2| |#1| |#2|) (|PrimitiveArray| |#1|) |#2|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-arrays \\spad{x} of primitive array \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad{[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}."))) NIL NIL -(-976 S) +(-977 S) ((|constructor| (NIL "\\indented{1}{This provides a fast array type with no bound checking on elt\\spad{'s}.} Minimum index is 0 in this type,{} cannot be changed"))) -((-4464 . T) (-4463 . T)) -((-3794 (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1120))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-3794 (-12 (|HasCategory| |#1| (QUOTE (-1120))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-875))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-3794 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1120)))) (|HasCategory| |#1| (QUOTE (-861))) (-3794 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1120)))) (|HasCategory| (-576) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1120))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-875)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1120))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) -(-977) +((-4465 . T) (-4464 . T)) +((-2758 (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2758 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2758 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| |#1| (QUOTE (-861))) (-2758 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| (-576) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) +(-978) ((|constructor| (NIL "Category for the functions defined by integrals.")) (|integral| (($ $ (|SegmentBinding| $)) "\\spad{integral(f, x = a..b)} returns the formal definite integral of \\spad{f} \\spad{dx} for \\spad{x} between \\spad{a} and \\spad{b}.") (($ $ (|Symbol|)) "\\spad{integral(f, x)} returns the formal integral of \\spad{f} \\spad{dx}."))) NIL NIL -(-978 -2117) +(-979 -1959) ((|constructor| (NIL "PrimitiveElement provides functions to compute primitive elements in algebraic extensions.")) (|primitiveElement| (((|Record| (|:| |coef| (|List| (|Integer|))) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#1|))) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|)) (|Symbol|)) "\\spad{primitiveElement([p1,...,pn], [a1,...,an], a)} returns \\spad{[[c1,...,cn], [q1,...,qn], q]} such that then \\spad{k(a1,...,an) = k(a)},{} where \\spad{a = a1 c1 + ... + an cn},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. The \\spad{pi}\\spad{'s} are the defining polynomials for the \\spad{ai}\\spad{'s}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}.") (((|Record| (|:| |coef| (|List| (|Integer|))) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#1|))) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{primitiveElement([p1,...,pn], [a1,...,an])} returns \\spad{[[c1,...,cn], [q1,...,qn], q]} such that then \\spad{k(a1,...,an) = k(a)},{} where \\spad{a = a1 c1 + ... + an cn},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. The \\spad{pi}\\spad{'s} are the defining polynomials for the \\spad{ai}\\spad{'s}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}.") (((|Record| (|:| |coef1| (|Integer|)) (|:| |coef2| (|Integer|)) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|Polynomial| |#1|) (|Symbol|) (|Polynomial| |#1|) (|Symbol|)) "\\spad{primitiveElement(p1, a1, p2, a2)} returns \\spad{[c1, c2, q]} such that \\spad{k(a1, a2) = k(a)} where \\spad{a = c1 a1 + c2 a2, and q(a) = 0}. The \\spad{pi}\\spad{'s} are the defining polynomials for the \\spad{ai}\\spad{'s}. The \\spad{p2} may involve \\spad{a1},{} but \\spad{p1} must not involve a2. This operation uses \\spadfun{resultant}."))) NIL NIL -(-979 I) +(-980 I) ((|constructor| (NIL "The \\spadtype{IntegerPrimesPackage} implements a modification of Rabin\\spad{'s} probabilistic primality test and the utility functions \\spadfun{nextPrime},{} \\spadfun{prevPrime} and \\spadfun{primes}.")) (|primes| (((|List| |#1|) |#1| |#1|) "\\spad{primes(a,b)} returns a list of all primes \\spad{p} with \\spad{a <= p <= b}")) (|prevPrime| ((|#1| |#1|) "\\spad{prevPrime(n)} returns the largest prime strictly smaller than \\spad{n}")) (|nextPrime| ((|#1| |#1|) "\\spad{nextPrime(n)} returns the smallest prime strictly larger than \\spad{n}")) (|prime?| (((|Boolean|) |#1|) "\\spad{prime?(n)} returns \\spad{true} if \\spad{n} is prime and \\spad{false} if not. The algorithm used is Rabin\\spad{'s} probabilistic primality test (reference: Knuth Volume 2 Semi Numerical Algorithms). If \\spad{prime? n} returns \\spad{false},{} \\spad{n} is proven composite. If \\spad{prime? n} returns \\spad{true},{} prime? may be in error however,{} the probability of error is very low. and is zero below 25*10**9 (due to a result of Pomerance et al),{} below 10**12 and 10**13 due to results of Pinch,{} and below 341550071728321 due to a result of Jaeschke. Specifically,{} this implementation does at least 10 pseudo prime tests and so the probability of error is \\spad{< 4**(-10)}. The running time of this method is cubic in the length of the input \\spad{n},{} that is \\spad{O( (log n)**3 )},{} for n<10**20. beyond that,{} the algorithm is quartic,{} \\spad{O( (log n)**4 )}. Two improvements due to Davenport have been incorporated which catches some trivial strong pseudo-primes,{} such as [Jaeschke,{} 1991] 1377161253229053 * 413148375987157,{} which the original algorithm regards as prime"))) NIL NIL -(-980) +(-981) ((|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 -(-981 R E) +(-982 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}"))) -(((-4465 "*") |has| |#1| (-174)) (-4456 |has| |#1| (-568)) (-4461 |has| |#1| (-6 -4461)) (-4457 . T) (-4458 . T) (-4460 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (-3794 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-3794 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1058) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#1| (LIST (QUOTE -1058) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1058) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-132)))) (|HasAttribute| |#1| (QUOTE -4461))) -(-982 A B) +(((-4466 "*") |has| |#1| (-174)) (-4457 |has| |#1| (-568)) (-4462 |has| |#1| (-6 -4462)) (-4458 . T) (-4459 . T) (-4461 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (-2758 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-2758 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-132)))) (|HasAttribute| |#1| (QUOTE -4462))) +(-983 A B) ((|constructor| (NIL "This domain implements cartesian product")) (|selectsecond| ((|#2| $) "\\spad{selectsecond(x)} \\undocumented")) (|selectfirst| ((|#1| $) "\\spad{selectfirst(x)} \\undocumented")) 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(QUOTE (-805))) (|HasCategory| |#2| (QUOTE (-805))))) (-12 (|HasCategory| |#1| (QUOTE (-485))) (|HasCategory| |#2| (QUOTE (-485)))) (-2758 (-12 (|HasCategory| |#1| (QUOTE (-485))) (|HasCategory| |#2| (QUOTE (-485)))) (-12 (|HasCategory| |#1| (QUOTE (-738))) (|HasCategory| |#2| (QUOTE (-738))))) (-12 (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#2| (QUOTE (-379)))) (-2758 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#1| (QUOTE (-485))) (|HasCategory| |#2| (QUOTE (-485)))) (-12 (|HasCategory| |#1| (QUOTE (-738))) (|HasCategory| |#2| (QUOTE (-738)))) (-12 (|HasCategory| |#1| (QUOTE (-805))) (|HasCategory| |#2| (QUOTE (-805))))) (-12 (|HasCategory| |#1| (QUOTE (-738))) (|HasCategory| |#2| (QUOTE (-738)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#2| (QUOTE (-861))))) +(-984) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. An `Property' is a pair of name and value.")) (|property| (($ (|Identifier|) (|SExpression|)) "\\spad{property(n,val)} constructs a property with name \\spad{`n'} and value `val'.")) (|value| (((|SExpression|) $) "\\spad{value(p)} returns value of property \\spad{p}")) (|name| (((|Identifier|) $) "\\spad{name(p)} returns the name of property \\spad{p}"))) NIL NIL -(-984 T$) +(-985 T$) ((|constructor| (NIL "This domain implements propositional formula build over a term domain,{} that itself belongs to PropositionalLogic")) (|disjunction| (($ $ $) "\\spad{disjunction(p,q)} returns a formula denoting the disjunction of \\spad{p} and \\spad{q}.")) (|conjunction| (($ $ $) "\\spad{conjunction(p,q)} returns a formula denoting the conjunction of \\spad{p} and \\spad{q}.")) (|isEquiv| (((|Maybe| (|Pair| $ $)) $) "\\spad{isEquiv f} returns a value \\spad{v} such that \\spad{v case Pair(\\%,\\%)} holds if the formula \\spad{f} is an equivalence formula.")) (|isImplies| (((|Maybe| (|Pair| $ $)) $) "\\spad{isImplies f} returns a value \\spad{v} such that \\spad{v case Pair(\\%,\\%)} holds if the formula \\spad{f} is an implication formula.")) (|isOr| (((|Maybe| (|Pair| $ $)) $) "\\spad{isOr f} returns a value \\spad{v} such that \\spad{v case Pair(\\%,\\%)} holds if the formula \\spad{f} is a disjunction formula.")) (|isAnd| (((|Maybe| (|Pair| $ $)) $) "\\spad{isAnd f} returns a value \\spad{v} such that \\spad{v case Pair(\\%,\\%)} holds if the formula \\spad{f} is a conjunction formula.")) (|isNot| (((|Maybe| $) $) "\\spad{isNot f} returns a value \\spad{v} such that \\spad{v case \\%} holds if the formula \\spad{f} is a negation.")) (|isAtom| (((|Maybe| |#1|) $) "\\spad{isAtom f} returns a value \\spad{v} such that \\spad{v case T} holds if the formula \\spad{f} is a term."))) NIL NIL -(-985 T$) +(-986 T$) ((|constructor| (NIL "This package collects unary functions operating on propositional formulae.")) (|simplify| (((|PropositionalFormula| |#1|) (|PropositionalFormula| |#1|)) "\\spad{simplify f} returns a formula logically equivalent to \\spad{f} where obvious tautologies have been removed.")) (|atoms| (((|Set| |#1|) (|PropositionalFormula| |#1|)) "\\spad{atoms f} \\spad{++} returns the set of atoms appearing in the formula \\spad{f}.")) (|dual| (((|PropositionalFormula| |#1|) (|PropositionalFormula| |#1|)) "\\spad{dual f} returns the dual of the proposition \\spad{f}."))) NIL NIL -(-986 S T$) +(-987 S T$) ((|constructor| (NIL "This package collects binary functions operating on propositional formulae.")) (|map| (((|PropositionalFormula| |#2|) (|Mapping| |#2| |#1|) (|PropositionalFormula| |#1|)) "\\spad{map(f,x)} returns a propositional formula where all atoms in \\spad{x} have been replaced by the result of applying the function \\spad{f} to them."))) NIL NIL -(-987) +(-988) ((|constructor| (NIL "This category declares the connectives of Propositional Logic.")) (|equiv| (($ $ $) "\\spad{equiv(p,q)} returns the logical equivalence of \\spad{`p'},{} \\spad{`q'}.")) (|implies| (($ $ $) "\\spad{implies(p,q)} returns the logical implication of \\spad{`q'} by \\spad{`p'}.")) (|false| (($) "\\spad{false} is a logical constant.")) (|true| (($) "\\spad{true} is a logical constant."))) NIL NIL -(-988 S) +(-989 S) ((|constructor| (NIL "A priority queue is a bag of items from an ordered set where the item extracted is always the maximum element.")) (|merge!| (($ $ $) "\\spad{merge!(q,q1)} destructively changes priority queue \\spad{q} to include the values from priority queue \\spad{q1}.")) (|merge| (($ $ $) "\\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}."))) -((-4463 . T) (-4464 . T)) +((-4464 . T) (-4465 . T)) NIL -(-989 R |polR|) +(-990 R |polR|) ((|constructor| (NIL "This package contains some functions: \\axiomOpFrom{discriminant}{PseudoRemainderSequence},{} \\axiomOpFrom{resultant}{PseudoRemainderSequence},{} \\axiomOpFrom{subResultantGcd}{PseudoRemainderSequence},{} \\axiomOpFrom{chainSubResultants}{PseudoRemainderSequence},{} \\axiomOpFrom{degreeSubResultant}{PseudoRemainderSequence},{} \\axiomOpFrom{lastSubResultant}{PseudoRemainderSequence},{} \\axiomOpFrom{resultantEuclidean}{PseudoRemainderSequence},{} \\axiomOpFrom{subResultantGcdEuclidean}{PseudoRemainderSequence},{} \\axiomOpFrom{semiSubResultantGcdEuclidean1}{PseudoRemainderSequence},{} \\axiomOpFrom{semiSubResultantGcdEuclidean2}{PseudoRemainderSequence},{} etc. This procedures are coming from improvements of the subresultants algorithm. \\indented{2}{Version : 7} \\indented{2}{References : Lionel Ducos \"Optimizations of the subresultant algorithm\"} \\indented{2}{to appear in the Journal of Pure and Applied Algebra.} \\indented{2}{Author : Ducos Lionel \\axiom{Lionel.Ducos@mathlabo.univ-poitiers.\\spad{fr}}}")) (|semiResultantEuclideannaif| (((|Record| (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{resultantEuclidean_naif(\\spad{P},{}\\spad{Q})} returns the semi-extended resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}} computed by means of the naive algorithm.")) (|resultantEuclideannaif| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{resultantEuclidean_naif(\\spad{P},{}\\spad{Q})} returns the extended resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}} computed by means of the naive algorithm.")) (|resultantnaif| ((|#1| |#2| |#2|) "\\axiom{resultantEuclidean_naif(\\spad{P},{}\\spad{Q})} returns the resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}} computed by means of the naive algorithm.")) (|nextsousResultant2| ((|#2| |#2| |#2| |#2| |#1|) "\\axiom{nextsousResultant2(\\spad{P},{} \\spad{Q},{} \\spad{Z},{} \\spad{s})} returns the subresultant \\axiom{\\spad{S_}{\\spad{e}-1}} where \\axiom{\\spad{P} ~ \\spad{S_d},{} \\spad{Q} = \\spad{S_}{\\spad{d}-1},{} \\spad{Z} = S_e,{} \\spad{s} = \\spad{lc}(\\spad{S_d})}")) (|Lazard2| ((|#2| |#2| |#1| |#1| (|NonNegativeInteger|)) "\\axiom{Lazard2(\\spad{F},{} \\spad{x},{} \\spad{y},{} \\spad{n})} computes \\axiom{(x/y)\\spad{**}(\\spad{n}-1) * \\spad{F}}")) (|Lazard| ((|#1| |#1| |#1| (|NonNegativeInteger|)) "\\axiom{Lazard(\\spad{x},{} \\spad{y},{} \\spad{n})} computes \\axiom{x**n/y**(\\spad{n}-1)}")) (|divide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2|) "\\axiom{divide(\\spad{F},{}\\spad{G})} computes quotient and rest of the exact euclidean division of \\axiom{\\spad{F}} by \\axiom{\\spad{G}}.")) (|pseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2|) "\\axiom{pseudoDivide(\\spad{P},{}\\spad{Q})} computes the pseudoDivide of \\axiom{\\spad{P}} by \\axiom{\\spad{Q}}.")) (|exquo| (((|Vector| |#2|) (|Vector| |#2|) |#1|) "\\axiom{\\spad{v} exquo \\spad{r}} computes the exact quotient of \\axiom{\\spad{v}} by \\axiom{\\spad{r}}")) (* (((|Vector| |#2|) |#1| (|Vector| |#2|)) "\\axiom{\\spad{r} * \\spad{v}} computes the product of \\axiom{\\spad{r}} and \\axiom{\\spad{v}}")) (|gcd| ((|#2| |#2| |#2|) "\\axiom{\\spad{gcd}(\\spad{P},{} \\spad{Q})} returns the \\spad{gcd} of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiResultantReduitEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |resultantReduit| |#1|)) |#2| |#2|) "\\axiom{semiResultantReduitEuclidean(\\spad{P},{}\\spad{Q})} returns the \"reduce resultant\" and carries out the equality \\axiom{...\\spad{P} + coef2*Q = resultantReduit(\\spad{P},{}\\spad{Q})}.")) (|resultantReduitEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |resultantReduit| |#1|)) |#2| |#2|) "\\axiom{resultantReduitEuclidean(\\spad{P},{}\\spad{Q})} returns the \"reduce resultant\" and carries out the equality \\axiom{coef1*P + coef2*Q = resultantReduit(\\spad{P},{}\\spad{Q})}.")) (|resultantReduit| ((|#1| |#2| |#2|) "\\axiom{resultantReduit(\\spad{P},{}\\spad{Q})} returns the \"reduce resultant\" of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|schema| (((|List| (|NonNegativeInteger|)) |#2| |#2|) "\\axiom{schema(\\spad{P},{}\\spad{Q})} returns the list of degrees of non zero subresultants of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|chainSubResultants| (((|List| |#2|) |#2| |#2|) "\\axiom{chainSubResultants(\\spad{P},{} \\spad{Q})} computes the list of non zero subresultants of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiDiscriminantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |discriminant| |#1|)) |#2|) "\\axiom{discriminantEuclidean(\\spad{P})} carries out the equality \\axiom{...\\spad{P} + coef2 * \\spad{D}(\\spad{P}) = discriminant(\\spad{P})}. Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|discriminantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |discriminant| |#1|)) |#2|) "\\axiom{discriminantEuclidean(\\spad{P})} carries out the equality \\axiom{coef1 * \\spad{P} + coef2 * \\spad{D}(\\spad{P}) = discriminant(\\spad{P})}.")) (|discriminant| ((|#1| |#2|) "\\axiom{discriminant(\\spad{P},{} \\spad{Q})} returns the discriminant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiSubResultantGcdEuclidean1| (((|Record| (|:| |coef1| |#2|) (|:| |gcd| |#2|)) |#2| |#2|) "\\axiom{semiSubResultantGcdEuclidean1(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1*P + ? \\spad{Q} = \\spad{+/-} S_i(\\spad{P},{}\\spad{Q})} where the degree (not the indice) of the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} is the smaller as possible.")) (|semiSubResultantGcdEuclidean2| (((|Record| (|:| |coef2| |#2|) (|:| |gcd| |#2|)) |#2| |#2|) "\\axiom{semiSubResultantGcdEuclidean2(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{...\\spad{P} + coef2*Q = \\spad{+/-} S_i(\\spad{P},{}\\spad{Q})} where the degree (not the indice) of the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} is the smaller as possible. Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|subResultantGcdEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |gcd| |#2|)) |#2| |#2|) "\\axiom{subResultantGcdEuclidean(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1*P + coef2*Q = \\spad{+/-} S_i(\\spad{P},{}\\spad{Q})} where the degree (not the indice) of the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} is the smaller as possible.")) (|subResultantGcd| ((|#2| |#2| |#2|) "\\axiom{subResultantGcd(\\spad{P},{} \\spad{Q})} returns the \\spad{gcd} of two primitive polynomials \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiLastSubResultantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2|) "\\axiom{semiLastSubResultantEuclidean(\\spad{P},{} \\spad{Q})} computes the last non zero subresultant \\axiom{\\spad{S}} and carries out the equality \\axiom{...\\spad{P} + coef2*Q = \\spad{S}}. Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|lastSubResultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2|) "\\axiom{lastSubResultantEuclidean(\\spad{P},{} \\spad{Q})} computes the last non zero subresultant \\axiom{\\spad{S}} and carries out the equality \\axiom{coef1*P + coef2*Q = \\spad{S}}.")) (|lastSubResultant| ((|#2| |#2| |#2|) "\\axiom{lastSubResultant(\\spad{P},{} \\spad{Q})} computes the last non zero subresultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}")) (|semiDegreeSubResultantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns a subresultant \\axiom{\\spad{S}} of degree \\axiom{\\spad{d}} and carries out the equality \\axiom{...\\spad{P} + coef2*Q = S_i}. Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|degreeSubResultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns a subresultant \\axiom{\\spad{S}} of degree \\axiom{\\spad{d}} and carries out the equality \\axiom{coef1*P + coef2*Q = S_i}.")) (|degreeSubResultant| ((|#2| |#2| |#2| (|NonNegativeInteger|)) "\\axiom{degreeSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{d})} computes a subresultant of degree \\axiom{\\spad{d}}.")) (|semiIndiceSubResultantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{semiIndiceSubResultantEuclidean(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} and carries out the equality \\axiom{...\\spad{P} + coef2*Q = S_i(\\spad{P},{}\\spad{Q})} Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|indiceSubResultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} and carries out the equality \\axiom{coef1*P + coef2*Q = S_i(\\spad{P},{}\\spad{Q})}")) (|indiceSubResultant| ((|#2| |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns the subresultant of indice \\axiom{\\spad{i}}")) (|semiResultantEuclidean1| (((|Record| (|:| |coef1| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{semiResultantEuclidean1(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1.\\spad{P} + ? \\spad{Q} = resultant(\\spad{P},{}\\spad{Q})}.")) (|semiResultantEuclidean2| (((|Record| (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{semiResultantEuclidean2(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{...\\spad{P} + coef2*Q = resultant(\\spad{P},{}\\spad{Q})}. Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|resultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{resultantEuclidean(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1*P + coef2*Q = resultant(\\spad{P},{}\\spad{Q})}")) (|resultant| ((|#1| |#2| |#2|) "\\axiom{resultant(\\spad{P},{} \\spad{Q})} returns the resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}"))) NIL ((|HasCategory| |#1| (QUOTE (-464)))) -(-990) +(-991) ((|constructor| (NIL "This domain represents `pretend' expressions.")) (|target| (((|TypeAst|) $) "\\spad{target(e)} returns the target type of the conversion..")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression being converted."))) NIL NIL -(-991) +(-992) ((|constructor| (NIL "Partition is an OrderedCancellationAbelianMonoid which is used as the basis for symmetric polynomial representation of the sums of powers in SymmetricPolynomial. Thus,{} \\spad{(5 2 2 1)} will represent \\spad{s5 * s2**2 * s1}.")) (|conjugate| (($ $) "\\spad{conjugate(p)} returns the conjugate partition of a partition \\spad{p}")) (|pdct| (((|PositiveInteger|) $) "\\spad{pdct(a1**n1 a2**n2 ...)} returns \\spad{n1! * a1**n1 * n2! * a2**n2 * ...}. This function is used in the package \\spadtype{CycleIndicators}.")) (|powers| (((|List| (|Pair| (|PositiveInteger|) (|PositiveInteger|))) $) "\\spad{powers(x)} returns a list of pairs. The second component of each pair is the multiplicity with which the first component occurs in \\spad{li}.")) (|partitions| (((|Stream| $) (|NonNegativeInteger|)) "\\spad{partitions n} returns the stream of all partitions of size \\spad{n}.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\#x} returns the sum of all parts of the partition \\spad{x}.")) (|parts| (((|List| (|PositiveInteger|)) $) "\\spad{parts x} returns the list of decreasing integer sequence making up the partition \\spad{x}.")) (|partition| (($ (|List| (|PositiveInteger|))) "\\spad{partition(li)} converts a list of integers \\spad{li} to a partition"))) NIL NIL -(-992 S |Coef| |Expon| |Var|) +(-993 S |Coef| |Expon| |Var|) ((|constructor| (NIL "\\spadtype{PowerSeriesCategory} is the most general power series category with exponents in an ordered abelian monoid.")) (|complete| (($ $) "\\spad{complete(f)} causes all terms of \\spad{f} to be computed. Note: this results in an infinite loop if \\spad{f} has infinitely many terms.")) (|pole?| (((|Boolean|) $) "\\spad{pole?(f)} determines if the power series \\spad{f} has a pole.")) (|variables| (((|List| |#4|) $) "\\spad{variables(f)} returns a list of the variables occuring in the power series \\spad{f}.")) (|degree| ((|#3| $) "\\spad{degree(f)} returns the exponent of the lowest order term of \\spad{f}.")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(f)} returns the coefficient of the lowest order term of \\spad{f}")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(f)} returns the monomial of \\spad{f} of lowest order.")) (|monomial| (($ $ (|List| |#4|) (|List| |#3|)) "\\spad{monomial(a,[x1,..,xk],[n1,..,nk])} computes \\spad{a * x1**n1 * .. * xk**nk}.") (($ $ |#4| |#3|) "\\spad{monomial(a,x,n)} computes \\spad{a*x**n}."))) NIL NIL -(-993 |Coef| |Expon| |Var|) +(-994 |Coef| |Expon| |Var|) ((|constructor| (NIL "\\spadtype{PowerSeriesCategory} is the most general power series category with exponents in an ordered abelian monoid.")) (|complete| (($ $) "\\spad{complete(f)} causes all terms of \\spad{f} to be computed. Note: this results in an infinite loop if \\spad{f} has infinitely many terms.")) (|pole?| (((|Boolean|) $) "\\spad{pole?(f)} determines if the power series \\spad{f} has a pole.")) (|variables| (((|List| |#3|) $) "\\spad{variables(f)} returns a list of the variables occuring in the power series \\spad{f}.")) (|degree| ((|#2| $) "\\spad{degree(f)} returns the exponent of the lowest order term of \\spad{f}.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(f)} returns the coefficient of the lowest order term of \\spad{f}")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(f)} returns the monomial of \\spad{f} of lowest order.")) (|monomial| (($ $ (|List| |#3|) (|List| |#2|)) "\\spad{monomial(a,[x1,..,xk],[n1,..,nk])} computes \\spad{a * x1**n1 * .. * xk**nk}.") (($ $ |#3| |#2|) "\\spad{monomial(a,x,n)} computes \\spad{a*x**n}."))) -(((-4465 "*") |has| |#1| (-174)) (-4456 |has| |#1| (-568)) (-4457 . T) (-4458 . T) (-4460 . T)) +(((-4466 "*") |has| |#1| (-174)) (-4457 |has| |#1| (-568)) (-4458 . T) (-4459 . T) (-4461 . T)) NIL -(-994) +(-995) ((|constructor| (NIL "PlottableSpaceCurveCategory is the category of curves in 3-space which may be plotted via the graphics facilities. Functions are provided for obtaining lists of lists of points,{} representing the branches of the curve,{} and for determining the ranges of the \\spad{x-},{} \\spad{y-},{} and \\spad{z}-coordinates of the points on the curve.")) (|zRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{zRange(c)} returns the range of the \\spad{z}-coordinates of the points on the curve \\spad{c}.")) (|yRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{yRange(c)} returns the range of the \\spad{y}-coordinates of the points on the curve \\spad{c}.")) (|xRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{xRange(c)} returns the range of the \\spad{x}-coordinates of the points on the curve \\spad{c}.")) (|listBranches| (((|List| (|List| (|Point| (|DoubleFloat|)))) $) "\\spad{listBranches(c)} returns a list of lists of points,{} representing the branches of the curve \\spad{c}."))) NIL NIL -(-995 S R E |VarSet| P) +(-996 S R E |VarSet| P) ((|constructor| (NIL "A category for finite subsets of a polynomial ring. Such a set is only regarded as a set of polynomials and not identified to the ideal it generates. So two distinct sets may generate the same the ideal. Furthermore,{} for \\spad{R} being an integral domain,{} a set of polynomials may be viewed as a representation of the ideal it generates in the polynomial ring \\spad{(R)^(-1) P},{} or the set of its zeros (described for instance by the radical of the previous ideal,{} or a split of the associated affine variety) and so on. So this category provides operations about those different notions.")) (|triangular?| (((|Boolean|) $) "\\axiom{triangular?(\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{ps}} is a triangular set,{} \\spadignore{i.e.} two distinct polynomials have distinct main variables and no constant lies in \\axiom{\\spad{ps}}.")) (|rewriteIdealWithRemainder| (((|List| |#5|) (|List| |#5|) $) "\\axiom{rewriteIdealWithRemainder(\\spad{lp},{}\\spad{cs})} returns \\axiom{\\spad{lr}} such that every polynomial in \\axiom{\\spad{lr}} is fully reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{cs}} and \\axiom{(\\spad{lp},{}\\spad{cs})} and \\axiom{(\\spad{lr},{}\\spad{cs})} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}.")) (|rewriteIdealWithHeadRemainder| (((|List| |#5|) (|List| |#5|) $) "\\axiom{rewriteIdealWithHeadRemainder(\\spad{lp},{}\\spad{cs})} returns \\axiom{\\spad{lr}} such that the leading monomial of every polynomial in \\axiom{\\spad{lr}} is reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{cs}} and \\axiom{(\\spad{lp},{}\\spad{cs})} and \\axiom{(\\spad{lr},{}\\spad{cs})} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}.")) (|remainder| (((|Record| (|:| |rnum| |#2|) (|:| |polnum| |#5|) (|:| |den| |#2|)) |#5| $) "\\axiom{remainder(a,{}\\spad{ps})} returns \\axiom{[\\spad{c},{}\\spad{b},{}\\spad{r}]} such that \\axiom{\\spad{b}} is fully reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ps}},{} \\axiom{r*a - \\spad{c*b}} lies in the ideal generated by \\axiom{\\spad{ps}}. Furthermore,{} if \\axiom{\\spad{R}} is a \\spad{gcd}-domain,{} \\axiom{\\spad{b}} is primitive.")) (|headRemainder| (((|Record| (|:| |num| |#5|) (|:| |den| |#2|)) |#5| $) "\\axiom{headRemainder(a,{}\\spad{ps})} returns \\axiom{[\\spad{b},{}\\spad{r}]} such that the leading monomial of \\axiom{\\spad{b}} is reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ps}} and \\axiom{r*a - \\spad{b}} lies in the ideal generated by \\axiom{\\spad{ps}}.")) (|roughUnitIdeal?| (((|Boolean|) $) "\\axiom{roughUnitIdeal?(\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{ps}} contains some non null element lying in the base ring \\axiom{\\spad{R}}.")) (|roughEqualIdeals?| (((|Boolean|) $ $) "\\axiom{roughEqualIdeals?(\\spad{ps1},{}\\spad{ps2})} returns \\spad{true} iff it can proved that \\axiom{\\spad{ps1}} and \\axiom{\\spad{ps2}} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}} without computing Groebner bases.")) (|roughSubIdeal?| (((|Boolean|) $ $) "\\axiom{roughSubIdeal?(\\spad{ps1},{}\\spad{ps2})} returns \\spad{true} iff it can proved that all polynomials in \\axiom{\\spad{ps1}} lie in the ideal generated by \\axiom{\\spad{ps2}} in \\axiom{\\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}} without computing Groebner bases.")) (|roughBase?| (((|Boolean|) $) "\\axiom{roughBase?(\\spad{ps})} returns \\spad{true} iff for every pair \\axiom{{\\spad{p},{}\\spad{q}}} of polynomials in \\axiom{\\spad{ps}} their leading monomials are relatively prime.")) (|trivialIdeal?| (((|Boolean|) $) "\\axiom{trivialIdeal?(\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{ps}} does not contain non-zero elements.")) (|sort| (((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |#4|) "\\axiom{sort(\\spad{v},{}\\spad{ps})} returns \\axiom{us,{}\\spad{vs},{}\\spad{ws}} such that \\axiom{us} is \\axiom{collectUnder(\\spad{ps},{}\\spad{v})},{} \\axiom{\\spad{vs}} is \\axiom{collect(\\spad{ps},{}\\spad{v})} and \\axiom{\\spad{ws}} is \\axiom{collectUpper(\\spad{ps},{}\\spad{v})}.")) (|collectUpper| (($ $ |#4|) "\\axiom{collectUpper(\\spad{ps},{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{\\spad{ps}} with main variable greater than \\axiom{\\spad{v}}.")) (|collect| (($ $ |#4|) "\\axiom{collect(\\spad{ps},{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{\\spad{ps}} with \\axiom{\\spad{v}} as main variable.")) (|collectUnder| (($ $ |#4|) "\\axiom{collectUnder(\\spad{ps},{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{\\spad{ps}} with main variable less than \\axiom{\\spad{v}}.")) (|mainVariable?| (((|Boolean|) |#4| $) "\\axiom{mainVariable?(\\spad{v},{}\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{\\spad{ps}}.")) (|mainVariables| (((|List| |#4|) $) "\\axiom{mainVariables(\\spad{ps})} returns the decreasingly sorted list of the variables which are main variables of some polynomial in \\axiom{\\spad{ps}}.")) (|variables| (((|List| |#4|) $) "\\axiom{variables(\\spad{ps})} returns the decreasingly sorted list of the variables which are variables of some polynomial in \\axiom{\\spad{ps}}.")) (|mvar| ((|#4| $) "\\axiom{mvar(\\spad{ps})} returns the main variable of the non constant polynomial with the greatest main variable,{} if any,{} else an error is returned.")) (|retract| (($ (|List| |#5|)) "\\axiom{retract(\\spad{lp})} returns an element of the domain whose elements are the members of \\axiom{\\spad{lp}} if such an element exists,{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|List| |#5|)) "\\axiom{retractIfCan(\\spad{lp})} returns an element of the domain whose elements are the members of \\axiom{\\spad{lp}} if such an element exists,{} otherwise \\axiom{\"failed\"} is returned."))) NIL ((|HasCategory| |#2| (QUOTE (-568)))) -(-996 R E |VarSet| P) +(-997 R E |VarSet| P) ((|constructor| (NIL "A category for finite subsets of a polynomial ring. Such a set is only regarded as a set of polynomials and not identified to the ideal it generates. So two distinct sets may generate the same the ideal. Furthermore,{} for \\spad{R} being an integral domain,{} a set of polynomials may be viewed as a representation of the ideal it generates in the polynomial ring \\spad{(R)^(-1) P},{} or the set of its zeros (described for instance by the radical of the previous ideal,{} or a split of the associated affine variety) and so on. So this category provides operations about those different notions.")) (|triangular?| (((|Boolean|) $) "\\axiom{triangular?(\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{ps}} is a triangular set,{} \\spadignore{i.e.} two distinct polynomials have distinct main variables and no constant lies in \\axiom{\\spad{ps}}.")) (|rewriteIdealWithRemainder| (((|List| |#4|) (|List| |#4|) $) "\\axiom{rewriteIdealWithRemainder(\\spad{lp},{}\\spad{cs})} returns \\axiom{\\spad{lr}} such that every polynomial in \\axiom{\\spad{lr}} is fully reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{cs}} and \\axiom{(\\spad{lp},{}\\spad{cs})} and \\axiom{(\\spad{lr},{}\\spad{cs})} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}.")) (|rewriteIdealWithHeadRemainder| (((|List| |#4|) (|List| |#4|) $) "\\axiom{rewriteIdealWithHeadRemainder(\\spad{lp},{}\\spad{cs})} returns \\axiom{\\spad{lr}} such that the leading monomial of every polynomial in \\axiom{\\spad{lr}} is reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{cs}} and \\axiom{(\\spad{lp},{}\\spad{cs})} and \\axiom{(\\spad{lr},{}\\spad{cs})} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}.")) (|remainder| (((|Record| (|:| |rnum| |#1|) (|:| |polnum| |#4|) (|:| |den| |#1|)) |#4| $) "\\axiom{remainder(a,{}\\spad{ps})} returns \\axiom{[\\spad{c},{}\\spad{b},{}\\spad{r}]} such that \\axiom{\\spad{b}} is fully reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ps}},{} \\axiom{r*a - \\spad{c*b}} lies in the ideal generated by \\axiom{\\spad{ps}}. Furthermore,{} if \\axiom{\\spad{R}} is a \\spad{gcd}-domain,{} \\axiom{\\spad{b}} is primitive.")) (|headRemainder| (((|Record| (|:| |num| |#4|) (|:| |den| |#1|)) |#4| $) "\\axiom{headRemainder(a,{}\\spad{ps})} returns \\axiom{[\\spad{b},{}\\spad{r}]} such that the leading monomial of \\axiom{\\spad{b}} is reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ps}} and \\axiom{r*a - \\spad{b}} lies in the ideal generated by \\axiom{\\spad{ps}}.")) (|roughUnitIdeal?| (((|Boolean|) $) "\\axiom{roughUnitIdeal?(\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{ps}} contains some non null element lying in the base ring \\axiom{\\spad{R}}.")) (|roughEqualIdeals?| (((|Boolean|) $ $) "\\axiom{roughEqualIdeals?(\\spad{ps1},{}\\spad{ps2})} returns \\spad{true} iff it can proved that \\axiom{\\spad{ps1}} and \\axiom{\\spad{ps2}} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}} without computing Groebner bases.")) (|roughSubIdeal?| (((|Boolean|) $ $) "\\axiom{roughSubIdeal?(\\spad{ps1},{}\\spad{ps2})} returns \\spad{true} iff it can proved that all polynomials in \\axiom{\\spad{ps1}} lie in the ideal generated by \\axiom{\\spad{ps2}} in \\axiom{\\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}} without computing Groebner bases.")) (|roughBase?| (((|Boolean|) $) "\\axiom{roughBase?(\\spad{ps})} returns \\spad{true} iff for every pair \\axiom{{\\spad{p},{}\\spad{q}}} of polynomials in \\axiom{\\spad{ps}} their leading monomials are relatively prime.")) (|trivialIdeal?| (((|Boolean|) $) "\\axiom{trivialIdeal?(\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{ps}} does not contain non-zero elements.")) (|sort| (((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |#3|) "\\axiom{sort(\\spad{v},{}\\spad{ps})} returns \\axiom{us,{}\\spad{vs},{}\\spad{ws}} such that \\axiom{us} is \\axiom{collectUnder(\\spad{ps},{}\\spad{v})},{} \\axiom{\\spad{vs}} is \\axiom{collect(\\spad{ps},{}\\spad{v})} and \\axiom{\\spad{ws}} is \\axiom{collectUpper(\\spad{ps},{}\\spad{v})}.")) (|collectUpper| (($ $ |#3|) "\\axiom{collectUpper(\\spad{ps},{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{\\spad{ps}} with main variable greater than \\axiom{\\spad{v}}.")) (|collect| (($ $ |#3|) "\\axiom{collect(\\spad{ps},{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{\\spad{ps}} with \\axiom{\\spad{v}} as main variable.")) (|collectUnder| (($ $ |#3|) "\\axiom{collectUnder(\\spad{ps},{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{\\spad{ps}} with main variable less than \\axiom{\\spad{v}}.")) (|mainVariable?| (((|Boolean|) |#3| $) "\\axiom{mainVariable?(\\spad{v},{}\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{\\spad{ps}}.")) (|mainVariables| (((|List| |#3|) $) "\\axiom{mainVariables(\\spad{ps})} returns the decreasingly sorted list of the variables which are main variables of some polynomial in \\axiom{\\spad{ps}}.")) (|variables| (((|List| |#3|) $) "\\axiom{variables(\\spad{ps})} returns the decreasingly sorted list of the variables which are variables of some polynomial in \\axiom{\\spad{ps}}.")) (|mvar| ((|#3| $) "\\axiom{mvar(\\spad{ps})} returns the main variable of the non constant polynomial with the greatest main variable,{} if any,{} else an error is returned.")) (|retract| (($ (|List| |#4|)) "\\axiom{retract(\\spad{lp})} returns an element of the domain whose elements are the members of \\axiom{\\spad{lp}} if such an element exists,{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|List| |#4|)) "\\axiom{retractIfCan(\\spad{lp})} returns an element of the domain whose elements are the members of \\axiom{\\spad{lp}} if such an element exists,{} otherwise \\axiom{\"failed\"} is returned."))) -((-4463 . T)) +((-4464 . T)) NIL -(-997 R E V P) +(-998 R E V P) ((|constructor| (NIL "This package provides modest routines for polynomial system solving. The aim of many of the operations of this package is to remove certain factors in some polynomials in order to avoid unnecessary computations in algorithms involving splitting techniques by partial factorization.")) (|removeIrreducibleRedundantFactors| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeIrreducibleRedundantFactors(\\spad{lp},{}\\spad{lq})} returns the same as \\axiom{irreducibleFactors(concat(\\spad{lp},{}\\spad{lq}))} assuming that \\axiom{irreducibleFactors(\\spad{lp})} returns \\axiom{\\spad{lp}} up to replacing some polynomial \\axiom{\\spad{pj}} in \\axiom{\\spad{lp}} by some polynomial \\axiom{\\spad{qj}} associated to \\axiom{\\spad{pj}}.")) (|lazyIrreducibleFactors| (((|List| |#4|) (|List| |#4|)) "\\axiom{lazyIrreducibleFactors(\\spad{lp})} returns \\axiom{\\spad{lf}} such that if \\axiom{\\spad{lp} = [\\spad{p1},{}...,{}\\spad{pn}]} and \\axiom{\\spad{lf} = [\\spad{f1},{}...,{}\\spad{fm}]} then \\axiom{p1*p2*...*pn=0} means \\axiom{f1*f2*...*fm=0},{} and the \\axiom{\\spad{fi}} are irreducible over \\axiom{\\spad{R}} and are pairwise distinct. The algorithm tries to avoid factorization into irreducible factors as far as possible and makes previously use of \\spad{gcd} techniques over \\axiom{\\spad{R}}.")) (|irreducibleFactors| (((|List| |#4|) (|List| |#4|)) "\\axiom{irreducibleFactors(\\spad{lp})} returns \\axiom{\\spad{lf}} such that if \\axiom{\\spad{lp} = [\\spad{p1},{}...,{}\\spad{pn}]} and \\axiom{\\spad{lf} = [\\spad{f1},{}...,{}\\spad{fm}]} then \\axiom{p1*p2*...*pn=0} means \\axiom{f1*f2*...*fm=0},{} and the \\axiom{\\spad{fi}} are irreducible over \\axiom{\\spad{R}} and are pairwise distinct.")) (|removeRedundantFactorsInPols| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactorsInPols(\\spad{lp},{}\\spad{lf})} returns \\axiom{newlp} where \\axiom{newlp} is obtained from \\axiom{\\spad{lp}} by removing in every polynomial \\axiom{\\spad{p}} of \\axiom{\\spad{lp}} any non trivial factor of any polynomial \\axiom{\\spad{f}} in \\axiom{\\spad{lf}}. Moreover,{} squares over \\axiom{\\spad{R}} are first removed in every polynomial \\axiom{\\spad{lp}}.")) (|removeRedundantFactorsInContents| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactorsInContents(\\spad{lp},{}\\spad{lf})} returns \\axiom{newlp} where \\axiom{newlp} is obtained from \\axiom{\\spad{lp}} by removing in the content of every polynomial of \\axiom{\\spad{lp}} any non trivial factor of any polynomial \\axiom{\\spad{f}} in \\axiom{\\spad{lf}}. Moreover,{} squares over \\axiom{\\spad{R}} are first removed in the content of every polynomial of \\axiom{\\spad{lp}}.")) (|removeRoughlyRedundantFactorsInContents| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRoughlyRedundantFactorsInContents(\\spad{lp},{}\\spad{lf})} returns \\axiom{newlp}where \\axiom{newlp} is obtained from \\axiom{\\spad{lp}} by removing in the content of every polynomial of \\axiom{\\spad{lp}} any occurence of a polynomial \\axiom{\\spad{f}} in \\axiom{\\spad{lf}}. Moreover,{} squares over \\axiom{\\spad{R}} are first removed in the content of every polynomial of \\axiom{\\spad{lp}}.")) (|univariatePolynomialsGcds| (((|List| |#4|) (|List| |#4|) (|Boolean|)) "\\axiom{univariatePolynomialsGcds(\\spad{lp},{}opt)} returns the same as \\axiom{univariatePolynomialsGcds(\\spad{lp})} if \\axiom{opt} is \\axiom{\\spad{false}} and if the previous operation does not return any non null and constant polynomial,{} else return \\axiom{[1]}.") (((|List| |#4|) (|List| |#4|)) "\\axiom{univariatePolynomialsGcds(\\spad{lp})} returns \\axiom{\\spad{lg}} where \\axiom{\\spad{lg}} is a list of the gcds of every pair in \\axiom{\\spad{lp}} of univariate polynomials in the same main variable.")) (|squareFreeFactors| (((|List| |#4|) |#4|) "\\axiom{squareFreeFactors(\\spad{p})} returns the square-free factors of \\axiom{\\spad{p}} over \\axiom{\\spad{R}}")) (|rewriteIdealWithQuasiMonicGenerators| (((|List| |#4|) (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{rewriteIdealWithQuasiMonicGenerators(\\spad{lp},{}redOp?,{}redOp)} returns \\axiom{\\spad{lq}} where \\axiom{\\spad{lq}} and \\axiom{\\spad{lp}} generate the same ideal in \\axiom{\\spad{R^}(\\spad{-1}) \\spad{P}} and \\axiom{\\spad{lq}} has rank not higher than the one of \\axiom{\\spad{lp}}. Moreover,{} \\axiom{\\spad{lq}} is computed by reducing \\axiom{\\spad{lp}} \\spad{w}.\\spad{r}.\\spad{t}. some basic set of the ideal generated by the quasi-monic polynomials in \\axiom{\\spad{lp}}.")) (|rewriteSetByReducingWithParticularGenerators| (((|List| |#4|) (|List| |#4|) (|Mapping| (|Boolean|) |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{rewriteSetByReducingWithParticularGenerators(\\spad{lp},{}pred?,{}redOp?,{}redOp)} returns \\axiom{\\spad{lq}} where \\axiom{\\spad{lq}} is computed by the following algorithm. Chose a basic set \\spad{w}.\\spad{r}.\\spad{t}. the reduction-test \\axiom{redOp?} among the polynomials satisfying property \\axiom{pred?},{} if it is empty then leave,{} else reduce the other polynomials by this basic set \\spad{w}.\\spad{r}.\\spad{t}. the reduction-operation \\axiom{redOp}. Repeat while another basic set with smaller rank can be computed. See code. If \\axiom{pred?} is \\axiom{quasiMonic?} the ideal is unchanged.")) (|crushedSet| (((|List| |#4|) (|List| |#4|)) "\\axiom{crushedSet(\\spad{lp})} returns \\axiom{\\spad{lq}} such that \\axiom{\\spad{lp}} and and \\axiom{\\spad{lq}} generate the same ideal and no rough basic sets reduce (in the sense of Groebner bases) the other polynomials in \\axiom{\\spad{lq}}.")) (|roughBasicSet| (((|Union| (|Record| (|:| |bas| (|GeneralTriangularSet| |#1| |#2| |#3| |#4|)) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|)) "\\axiom{roughBasicSet(\\spad{lp})} returns the smallest (with Ritt-Wu ordering) triangular set contained in \\axiom{\\spad{lp}}.")) (|interReduce| (((|List| |#4|) (|List| |#4|)) "\\axiom{interReduce(\\spad{lp})} returns \\axiom{\\spad{lq}} such that \\axiom{\\spad{lp}} and \\axiom{\\spad{lq}} generate the same ideal and no polynomial in \\axiom{\\spad{lq}} is reducuble by the others in the sense of Groebner bases. Since no assumptions are required the result may depend on the ordering the reductions are performed.")) (|removeRoughlyRedundantFactorsInPol| ((|#4| |#4| (|List| |#4|)) "\\axiom{removeRoughlyRedundantFactorsInPol(\\spad{p},{}\\spad{lf})} returns the same as removeRoughlyRedundantFactorsInPols([\\spad{p}],{}\\spad{lf},{}\\spad{true})")) (|removeRoughlyRedundantFactorsInPols| (((|List| |#4|) (|List| |#4|) (|List| |#4|) (|Boolean|)) "\\axiom{removeRoughlyRedundantFactorsInPols(\\spad{lp},{}\\spad{lf},{}opt)} returns the same as \\axiom{removeRoughlyRedundantFactorsInPols(\\spad{lp},{}\\spad{lf})} if \\axiom{opt} is \\axiom{\\spad{false}} and if the previous operation does not return any non null and constant polynomial,{} else return \\axiom{[1]}.") (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRoughlyRedundantFactorsInPols(\\spad{lp},{}\\spad{lf})} returns \\axiom{newlp}where \\axiom{newlp} is obtained from \\axiom{\\spad{lp}} by removing in every polynomial \\axiom{\\spad{p}} of \\axiom{\\spad{lp}} any occurence of a polynomial \\axiom{\\spad{f}} in \\axiom{\\spad{lf}}. This may involve a lot of exact-quotients computations.")) (|bivariatePolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{bivariatePolynomials(\\spad{lp})} returns \\axiom{\\spad{bps},{}nbps} where \\axiom{\\spad{bps}} is a list of the bivariate polynomials,{} and \\axiom{nbps} are the other ones.")) (|bivariate?| (((|Boolean|) |#4|) "\\axiom{bivariate?(\\spad{p})} returns \\spad{true} iff \\axiom{\\spad{p}} involves two and only two variables.")) (|linearPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{linearPolynomials(\\spad{lp})} returns \\axiom{\\spad{lps},{}nlps} where \\axiom{\\spad{lps}} is a list of the linear polynomials in \\spad{lp},{} and \\axiom{nlps} are the other ones.")) (|linear?| (((|Boolean|) |#4|) "\\axiom{linear?(\\spad{p})} returns \\spad{true} iff \\axiom{\\spad{p}} does not lie in the base ring \\axiom{\\spad{R}} and has main degree \\axiom{1}.")) (|univariatePolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{univariatePolynomials(\\spad{lp})} returns \\axiom{ups,{}nups} where \\axiom{ups} is a list of the univariate polynomials,{} and \\axiom{nups} are the other ones.")) (|univariate?| (((|Boolean|) |#4|) "\\axiom{univariate?(\\spad{p})} returns \\spad{true} iff \\axiom{\\spad{p}} involves one and only one variable.")) (|quasiMonicPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{quasiMonicPolynomials(\\spad{lp})} returns \\axiom{qmps,{}nqmps} where \\axiom{qmps} is a list of the quasi-monic polynomials in \\axiom{\\spad{lp}} and \\axiom{nqmps} are the other ones.")) (|selectAndPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| (|Mapping| (|Boolean|) |#4|)) (|List| |#4|)) "\\axiom{selectAndPolynomials(lpred?,{}\\spad{ps})} returns \\axiom{\\spad{gps},{}\\spad{bps}} where \\axiom{\\spad{gps}} is a list of the polynomial \\axiom{\\spad{p}} in \\axiom{\\spad{ps}} such that \\axiom{pred?(\\spad{p})} holds for every \\axiom{pred?} in \\axiom{lpred?} and \\axiom{\\spad{bps}} are the other ones.")) (|selectOrPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| (|Mapping| (|Boolean|) |#4|)) (|List| |#4|)) "\\axiom{selectOrPolynomials(lpred?,{}\\spad{ps})} returns \\axiom{\\spad{gps},{}\\spad{bps}} where \\axiom{\\spad{gps}} is a list of the polynomial \\axiom{\\spad{p}} in \\axiom{\\spad{ps}} such that \\axiom{pred?(\\spad{p})} holds for some \\axiom{pred?} in \\axiom{lpred?} and \\axiom{\\spad{bps}} are the other ones.")) (|selectPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|Mapping| (|Boolean|) |#4|) (|List| |#4|)) "\\axiom{selectPolynomials(pred?,{}\\spad{ps})} returns \\axiom{\\spad{gps},{}\\spad{bps}} where \\axiom{\\spad{gps}} is a list of the polynomial \\axiom{\\spad{p}} in \\axiom{\\spad{ps}} such that \\axiom{pred?(\\spad{p})} holds and \\axiom{\\spad{bps}} are the other ones.")) (|probablyZeroDim?| (((|Boolean|) (|List| |#4|)) "\\axiom{probablyZeroDim?(\\spad{lp})} returns \\spad{true} iff the number of polynomials in \\axiom{\\spad{lp}} is not smaller than the number of variables occurring in these polynomials.")) (|possiblyNewVariety?| (((|Boolean|) (|List| |#4|) (|List| (|List| |#4|))) "\\axiom{possiblyNewVariety?(newlp,{}\\spad{llp})} returns \\spad{true} iff for every \\axiom{\\spad{lp}} in \\axiom{\\spad{llp}} certainlySubVariety?(newlp,{}\\spad{lp}) does not hold.")) (|certainlySubVariety?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{certainlySubVariety?(newlp,{}\\spad{lp})} returns \\spad{true} iff for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}} the remainder of \\axiom{\\spad{p}} by \\axiom{newlp} using the division algorithm of Groebner techniques is zero.")) (|unprotectedRemoveRedundantFactors| (((|List| |#4|) |#4| |#4|) "\\axiom{unprotectedRemoveRedundantFactors(\\spad{p},{}\\spad{q})} returns the same as \\axiom{removeRedundantFactors(\\spad{p},{}\\spad{q})} but does assume that neither \\axiom{\\spad{p}} nor \\axiom{\\spad{q}} lie in the base ring \\axiom{\\spad{R}} and assumes that \\axiom{infRittWu?(\\spad{p},{}\\spad{q})} holds. Moreover,{} if \\axiom{\\spad{R}} is \\spad{gcd}-domain,{} then \\axiom{\\spad{p}} and \\axiom{\\spad{q}} are assumed to be square free.")) (|removeSquaresIfCan| (((|List| |#4|) (|List| |#4|)) "\\axiom{removeSquaresIfCan(\\spad{lp})} returns \\axiom{removeDuplicates [squareFreePart(\\spad{p})\\$\\spad{P} for \\spad{p} in \\spad{lp}]} if \\axiom{\\spad{R}} is \\spad{gcd}-domain else returns \\axiom{\\spad{lp}}.")) (|removeRedundantFactors| (((|List| |#4|) (|List| |#4|) (|List| |#4|) (|Mapping| (|List| |#4|) (|List| |#4|))) "\\axiom{removeRedundantFactors(\\spad{lp},{}\\spad{lq},{}remOp)} returns the same as \\axiom{concat(remOp(removeRoughlyRedundantFactorsInPols(\\spad{lp},{}\\spad{lq})),{}\\spad{lq})} assuming that \\axiom{remOp(\\spad{lq})} returns \\axiom{\\spad{lq}} up to similarity.") (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactors(\\spad{lp},{}\\spad{lq})} returns the same as \\axiom{removeRedundantFactors(concat(\\spad{lp},{}\\spad{lq}))} assuming that \\axiom{removeRedundantFactors(\\spad{lp})} returns \\axiom{\\spad{lp}} up to replacing some polynomial \\axiom{\\spad{pj}} in \\axiom{\\spad{lp}} by some polynomial \\axiom{\\spad{qj}} associated to \\axiom{\\spad{pj}}.") (((|List| |#4|) (|List| |#4|) |#4|) "\\axiom{removeRedundantFactors(\\spad{lp},{}\\spad{q})} returns the same as \\axiom{removeRedundantFactors(cons(\\spad{q},{}\\spad{lp}))} assuming that \\axiom{removeRedundantFactors(\\spad{lp})} returns \\axiom{\\spad{lp}} up to replacing some polynomial \\axiom{\\spad{pj}} in \\axiom{\\spad{lp}} by some some polynomial \\axiom{\\spad{qj}} associated to \\axiom{\\spad{pj}}.") (((|List| |#4|) |#4| |#4|) "\\axiom{removeRedundantFactors(\\spad{p},{}\\spad{q})} returns the same as \\axiom{removeRedundantFactors([\\spad{p},{}\\spad{q}])}") (((|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactors(\\spad{lp})} returns \\axiom{\\spad{lq}} such that if \\axiom{\\spad{lp} = [\\spad{p1},{}...,{}\\spad{pn}]} and \\axiom{\\spad{lq} = [\\spad{q1},{}...,{}\\spad{qm}]} then the product \\axiom{p1*p2*...\\spad{*pn}} vanishes iff the product \\axiom{q1*q2*...\\spad{*qm}} vanishes,{} and the product of degrees of the \\axiom{\\spad{qi}} is not greater than the one of the \\axiom{\\spad{pj}},{} and no polynomial in \\axiom{\\spad{lq}} divides another polynomial in \\axiom{\\spad{lq}}. In particular,{} polynomials lying in the base ring \\axiom{\\spad{R}} are removed. Moreover,{} \\axiom{\\spad{lq}} is sorted \\spad{w}.\\spad{r}.\\spad{t} \\axiom{infRittWu?}. Furthermore,{} if \\spad{R} is \\spad{gcd}-domain,{} the polynomials in \\axiom{\\spad{lq}} are pairwise without common non trivial factor."))) NIL ((-12 (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-317)))) (|HasCategory| |#1| (QUOTE (-464)))) -(-998 K) +(-999 K) ((|constructor| (NIL "PseudoLinearNormalForm provides a function for computing a block-companion form for pseudo-linear operators.")) (|companionBlocks| (((|List| (|Record| (|:| C (|Matrix| |#1|)) (|:| |g| (|Vector| |#1|)))) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{companionBlocks(m, v)} returns \\spad{[[C_1, g_1],...,[C_k, g_k]]} such that each \\spad{C_i} is a companion block and \\spad{m = diagonal(C_1,...,C_k)}.")) (|changeBase| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{changeBase(M, A, sig, der)}: computes the new matrix of a pseudo-linear transform given by the matrix \\spad{M} under the change of base A")) (|normalForm| (((|Record| (|:| R (|Matrix| |#1|)) (|:| A (|Matrix| |#1|)) (|:| |Ainv| (|Matrix| |#1|))) (|Matrix| |#1|) (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{normalForm(M, sig, der)} returns \\spad{[R, A, A^{-1}]} such that the pseudo-linear operator whose matrix in the basis \\spad{y} is \\spad{M} had matrix \\spad{R} in the basis \\spad{z = A y}. \\spad{der} is a \\spad{sig}-derivation."))) NIL NIL -(-999 |VarSet| E RC P) +(-1000 |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 -(-1000 R) +(-1001 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")) (|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}."))) -((-4464 . T) (-4463 . T)) +((-4465 . T) (-4464 . T)) NIL -(-1001 R1 R2) +(-1002 R1 R2) ((|constructor| (NIL "This package \\undocumented")) (|map| (((|Point| |#2|) (|Mapping| |#2| |#1|) (|Point| |#1|)) "\\spad{map(f,p)} \\undocumented"))) NIL NIL -(-1002 R) +(-1003 R) ((|constructor| (NIL "This package \\undocumented")) (|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 -(-1003 K) +(-1004 K) ((|constructor| (NIL "This is the description of any package which provides partial functions on a domain belonging to TranscendentalFunctionCategory.")) (|acschIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acschIfCan(z)} returns acsch(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|asechIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{asechIfCan(z)} returns asech(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|acothIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acothIfCan(z)} returns acoth(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|atanhIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{atanhIfCan(z)} returns atanh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|acoshIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acoshIfCan(z)} returns acosh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|asinhIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{asinhIfCan(z)} returns asinh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|cschIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cschIfCan(z)} returns csch(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|sechIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{sechIfCan(z)} returns sech(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|cothIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cothIfCan(z)} returns coth(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|tanhIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{tanhIfCan(z)} returns tanh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|coshIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{coshIfCan(z)} returns cosh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|sinhIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{sinhIfCan(z)} returns sinh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|acscIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acscIfCan(z)} returns acsc(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|asecIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{asecIfCan(z)} returns asec(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|acotIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acotIfCan(z)} returns acot(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|atanIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{atanIfCan(z)} returns atan(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|acosIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acosIfCan(z)} returns acos(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|asinIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{asinIfCan(z)} returns asin(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|cscIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cscIfCan(z)} returns \\spad{csc}(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|secIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{secIfCan(z)} returns sec(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|cotIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cotIfCan(z)} returns cot(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|tanIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{tanIfCan(z)} returns tan(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|cosIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cosIfCan(z)} returns cos(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|sinIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{sinIfCan(z)} returns sin(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|logIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{logIfCan(z)} returns log(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|expIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{expIfCan(z)} returns exp(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|nthRootIfCan| (((|Union| |#1| "failed") |#1| (|NonNegativeInteger|)) "\\spad{nthRootIfCan(z,n)} returns the \\spad{n}th root of \\spad{z} if possible,{} and \"failed\" otherwise."))) NIL NIL -(-1004 R E OV PPR) +(-1005 R E OV PPR) ((|constructor| (NIL "This package \\undocumented{}")) (|map| ((|#4| (|Mapping| |#4| (|Polynomial| |#1|)) |#4|) "\\spad{map(f,p)} \\undocumented{}")) (|pushup| ((|#4| |#4| (|List| |#3|)) "\\spad{pushup(p,lv)} \\undocumented{}") ((|#4| |#4| |#3|) "\\spad{pushup(p,v)} \\undocumented{}")) (|pushdown| ((|#4| |#4| (|List| |#3|)) "\\spad{pushdown(p,lv)} \\undocumented{}") ((|#4| |#4| |#3|) "\\spad{pushdown(p,v)} \\undocumented{}")) (|variable| (((|Union| $ "failed") (|Symbol|)) "\\spad{variable(s)} makes an element from symbol \\spad{s} or fails")) (|convert| (((|Symbol|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) NIL NIL -(-1005 K R UP -2117) +(-1006 K R UP -1959) ((|constructor| (NIL "In this package \\spad{K} is a finite field,{} \\spad{R} is a ring of univariate polynomials over \\spad{K},{} and \\spad{F} is a monogenic algebra over \\spad{R}. We require that \\spad{F} is monogenic,{} \\spadignore{i.e.} that \\spad{F = K[x,y]/(f(x,y))},{} because the integral basis algorithm used will factor the polynomial \\spad{f(x,y)}. The package provides a function to compute the integral closure of \\spad{R} in the quotient field of \\spad{F} as well as a function to compute a \"local integral basis\" at a specific prime.")) (|reducedDiscriminant| ((|#2| |#3|) "\\spad{reducedDiscriminant(up)} \\undocumented")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) |#2|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,basisDen,basisInv] } containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of the framed algebra \\spad{F}. \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If 'basis' is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix 'basisInv' contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if 'basisInv' is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,basisDen,basisInv] } containing information regarding the integral closure of \\spad{R} in the quotient field of the framed algebra \\spad{F}. \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If 'basis' is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix 'basisInv' contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if 'basisInv' is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}."))) NIL NIL -(-1006 |vl| |nv|) +(-1007 |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 -(-1007 R |Var| |Expon| |Dpoly|) +(-1008 R |Var| |Expon| |Dpoly|) ((|constructor| (NIL "\\spadtype{QuasiAlgebraicSet} constructs a domain representing quasi-algebraic sets,{} which is the intersection of a Zariski closed set,{} defined as the common zeros of a given list of polynomials (the defining polynomials for equations),{} and a principal Zariski open set,{} defined as the complement of the common zeros of a polynomial \\spad{f} (the defining polynomial for the inequation). This domain provides simplification of a user-given representation using groebner basis computations. There are two simplification routines: the first function \\spadfun{idealSimplify} uses groebner basis of ideals alone,{} while the second,{} \\spadfun{simplify} uses both groebner basis and factorization. The resulting defining equations \\spad{L} always form a groebner basis,{} and the resulting defining inequation \\spad{f} is always reduced. The function \\spadfun{simplify} may be applied several times if desired. A third simplification routine \\spadfun{radicalSimplify} is provided in \\spadtype{QuasiAlgebraicSet2} for comparison study only,{} as it is inefficient compared to the other two,{} as well as is restricted to only certain coefficient domains. For detail analysis and a comparison of the three methods,{} please consult the reference cited. \\blankline A polynomial function \\spad{q} defined on the quasi-algebraic set is equivalent to its reduced form with respect to \\spad{L}. While this may be obtained using the usual normal form algorithm,{} there is no canonical form for \\spad{q}. \\blankline The ordering in groebner basis computation is determined by the data type of the input polynomials. If it is possible we suggest to use refinements of total degree orderings.")) (|simplify| (($ $) "\\spad{simplify(s)} returns a different and presumably simpler representation of \\spad{s} with the defining polynomials for the equations forming a groebner basis,{} and the defining polynomial for the inequation reduced with respect to the basis,{} using a heuristic algorithm based on factoring.")) (|idealSimplify| (($ $) "\\spad{idealSimplify(s)} returns a different and presumably simpler representation of \\spad{s} with the defining polynomials for the equations forming a groebner basis,{} and the defining polynomial for the inequation reduced with respect to the basis,{} using Buchberger\\spad{'s} algorithm.")) (|definingInequation| ((|#4| $) "\\spad{definingInequation(s)} returns a single defining polynomial for the inequation,{} that is,{} the Zariski open part of \\spad{s}.")) (|definingEquations| (((|List| |#4|) $) "\\spad{definingEquations(s)} returns a list of defining polynomials for equations,{} that is,{} for the Zariski closed part of \\spad{s}.")) (|empty?| (((|Boolean|) $) "\\spad{empty?(s)} returns \\spad{true} if the quasialgebraic set \\spad{s} has no points,{} and \\spad{false} otherwise.")) (|setStatus| (($ $ (|Union| (|Boolean|) "failed")) "\\spad{setStatus(s,t)} returns the same representation for \\spad{s},{} but asserts the following: if \\spad{t} is \\spad{true},{} then \\spad{s} is empty,{} if \\spad{t} is \\spad{false},{} then \\spad{s} is non-empty,{} and if \\spad{t} = \"failed\",{} then no assertion is made (that is,{} \"don\\spad{'t} know\"). Note: for internal use only,{} with care.")) (|status| (((|Union| (|Boolean|) "failed") $) "\\spad{status(s)} returns \\spad{true} if the quasi-algebraic set is empty,{} \\spad{false} if it is not,{} and \"failed\" if not yet known")) (|quasiAlgebraicSet| (($ (|List| |#4|) |#4|) "\\spad{quasiAlgebraicSet(pl,q)} returns the quasi-algebraic set with defining equations \\spad{p} = 0 for \\spad{p} belonging to the list \\spad{pl},{} and defining inequation \\spad{q} \\spad{~=} 0.")) (|empty| (($) "\\spad{empty()} returns the empty quasi-algebraic set"))) NIL ((-12 (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-317))))) -(-1008 R E V P TS) +(-1009 R E V P TS) ((|constructor| (NIL "A package for removing redundant quasi-components and redundant branches when decomposing a variety by means of quasi-components of regular triangular sets. \\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|branchIfCan| (((|Union| (|Record| (|:| |eq| (|List| |#4|)) (|:| |tower| |#5|) (|:| |ineq| (|List| |#4|))) "failed") (|List| |#4|) |#5| (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{branchIfCan(leq,{}\\spad{ts},{}lineq,{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement.")) (|prepareDecompose| (((|List| (|Record| (|:| |eq| (|List| |#4|)) (|:| |tower| |#5|) (|:| |ineq| (|List| |#4|)))) (|List| |#4|) (|List| |#5|) (|Boolean|) (|Boolean|)) "\\axiom{prepareDecompose(\\spad{lp},{}\\spad{lts},{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|removeSuperfluousCases| (((|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|)))) "\\axiom{removeSuperfluousCases(llpwt)} is an internal subroutine,{} exported only for developement.")) (|subCase?| (((|Boolean|) (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|)) (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) "\\axiom{subCase?(lpwt1,{}lpwt2)} is an internal subroutine,{} exported only for developement.")) (|removeSuperfluousQuasiComponents| (((|List| |#5|) (|List| |#5|)) "\\axiom{removeSuperfluousQuasiComponents(\\spad{lts})} removes from \\axiom{\\spad{lts}} any \\spad{ts} such that \\axiom{subQuasiComponent?(\\spad{ts},{}us)} holds for another \\spad{us} in \\axiom{\\spad{lts}}.")) (|subQuasiComponent?| (((|Boolean|) |#5| (|List| |#5|)) "\\axiom{subQuasiComponent?(\\spad{ts},{}lus)} returns \\spad{true} iff \\axiom{subQuasiComponent?(\\spad{ts},{}us)} holds for one \\spad{us} in \\spad{lus}.") (((|Boolean|) |#5| |#5|) "\\axiom{subQuasiComponent?(\\spad{ts},{}us)} returns \\spad{true} iff \\axiomOpFrom{internalSubQuasiComponent?}{QuasiComponentPackage} returs \\spad{true}.")) (|internalSubQuasiComponent?| (((|Union| (|Boolean|) "failed") |#5| |#5|) "\\axiom{internalSubQuasiComponent?(\\spad{ts},{}us)} returns a boolean \\spad{b} value if the fact that the regular zero set of \\axiom{us} contains that of \\axiom{\\spad{ts}} can be decided (and in that case \\axiom{\\spad{b}} gives this inclusion) otherwise returns \\axiom{\"failed\"}.")) (|infRittWu?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{infRittWu?(\\spad{lp1},{}\\spad{lp2})} is an internal subroutine,{} exported only for developement.")) (|internalInfRittWu?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{internalInfRittWu?(\\spad{lp1},{}\\spad{lp2})} is an internal subroutine,{} exported only for developement.")) (|internalSubPolSet?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{internalSubPolSet?(\\spad{lp1},{}\\spad{lp2})} returns \\spad{true} iff \\axiom{\\spad{lp1}} is a sub-set of \\axiom{\\spad{lp2}} assuming that these lists are sorted increasingly \\spad{w}.\\spad{r}.\\spad{t}. \\axiomOpFrom{infRittWu?}{RecursivePolynomialCategory}.")) (|subPolSet?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{subPolSet?(\\spad{lp1},{}\\spad{lp2})} returns \\spad{true} iff \\axiom{\\spad{lp1}} is a sub-set of \\axiom{\\spad{lp2}}.")) (|subTriSet?| (((|Boolean|) |#5| |#5|) "\\axiom{subTriSet?(\\spad{ts},{}us)} returns \\spad{true} iff \\axiom{\\spad{ts}} is a sub-set of \\axiom{us}.")) (|moreAlgebraic?| (((|Boolean|) |#5| |#5|) "\\axiom{moreAlgebraic?(\\spad{ts},{}us)} returns \\spad{false} iff \\axiom{\\spad{ts}} and \\axiom{us} are both empty,{} or \\axiom{\\spad{ts}} has less elements than \\axiom{us},{} or some variable is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{us} and is not \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ts}}.")) (|algebraicSort| (((|List| |#5|) (|List| |#5|)) "\\axiom{algebraicSort(\\spad{lts})} sorts \\axiom{\\spad{lts}} \\spad{w}.\\spad{r}.\\spad{t} \\axiomOpFrom{supDimElseRittWu?}{QuasiComponentPackage}.")) (|supDimElseRittWu?| (((|Boolean|) |#5| |#5|) "\\axiom{supDimElseRittWu(\\spad{ts},{}us)} returns \\spad{true} iff \\axiom{\\spad{ts}} has less elements than \\axiom{us} otherwise if \\axiom{\\spad{ts}} has higher rank than \\axiom{us} \\spad{w}.\\spad{r}.\\spad{t}. Riit and Wu ordering.")) (|stopTable!| (((|Void|)) "\\axiom{stopTableGcd!()} is an internal subroutine,{} exported only for developement.")) (|startTable!| (((|Void|) (|String|) (|String|) (|String|)) "\\axiom{startTableGcd!(\\spad{s1},{}\\spad{s2},{}\\spad{s3})} is an internal subroutine,{} exported only for developement."))) NIL NIL -(-1009) +(-1010) ((|constructor| (NIL "This domain implements simple database queries")) (|value| (((|String|) $) "\\spad{value(q)} returns the value (\\spadignore{i.e.} right hand side) of \\axiom{\\spad{q}}.")) (|variable| (((|Symbol|) $) "\\spad{variable(q)} returns the variable (\\spadignore{i.e.} left hand side) of \\axiom{\\spad{q}}.")) (|equation| (($ (|Symbol|) (|String|)) "\\spad{equation(s,\"a\")} creates a new equation."))) NIL NIL -(-1010 A B R S) +(-1011 A B R S) ((|constructor| (NIL "This package extends a function between integral domains to a mapping between their quotient fields.")) (|map| ((|#4| (|Mapping| |#2| |#1|) |#3|) "\\spad{map(func,frac)} applies the function \\spad{func} to the numerator and denominator of \\spad{frac}."))) NIL NIL -(-1011 A S) +(-1012 A S) ((|constructor| (NIL "QuotientField(\\spad{S}) is the category of fractions of an Integral Domain \\spad{S}.")) (|floor| ((|#2| $) "\\spad{floor(x)} returns the largest integral element below \\spad{x}.")) (|ceiling| ((|#2| $) "\\spad{ceiling(x)} returns the smallest integral element above \\spad{x}.")) (|random| (($) "\\spad{random()} returns a random fraction.")) (|fractionPart| (($ $) "\\spad{fractionPart(x)} returns the fractional part of \\spad{x}. \\spad{x} = wholePart(\\spad{x}) + fractionPart(\\spad{x})")) (|wholePart| ((|#2| $) "\\spad{wholePart(x)} returns the whole part of the fraction \\spad{x} \\spadignore{i.e.} the truncated quotient of the numerator by the denominator.")) (|denominator| (($ $) "\\spad{denominator(x)} is the denominator of the fraction \\spad{x} converted to \\%.")) (|numerator| (($ $) "\\spad{numerator(x)} is the numerator of the fraction \\spad{x} converted to \\%.")) (|denom| ((|#2| $) "\\spad{denom(x)} returns the denominator of the fraction \\spad{x}.")) (|numer| ((|#2| $) "\\spad{numer(x)} returns the numerator of the fraction \\spad{x}.")) (/ (($ |#2| |#2|) "\\spad{d1 / d2} returns the fraction \\spad{d1} divided by \\spad{d2}."))) NIL -((|HasCategory| |#2| (QUOTE (-927))) (|HasCategory| |#2| (QUOTE (-557))) (|HasCategory| |#2| (QUOTE (-317))) (|HasCategory| |#2| (LIST (QUOTE -1058) (QUOTE (-1196)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (QUOTE (-1042))) (|HasCategory| |#2| (QUOTE (-832))) (|HasCategory| |#2| (QUOTE (-861))) (|HasCategory| |#2| (LIST (QUOTE -1058) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-1172)))) -(-1012 S) +((|HasCategory| |#2| (QUOTE (-928))) (|HasCategory| |#2| (QUOTE (-557))) (|HasCategory| |#2| (QUOTE (-317))) (|HasCategory| |#2| (LIST (QUOTE -1059) (QUOTE (-1197)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (QUOTE (-1043))) (|HasCategory| |#2| (QUOTE (-832))) (|HasCategory| |#2| (QUOTE (-861))) (|HasCategory| |#2| (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-1173)))) +(-1013 S) ((|constructor| (NIL "QuotientField(\\spad{S}) is the category of fractions of an Integral Domain \\spad{S}.")) (|floor| ((|#1| $) "\\spad{floor(x)} returns the largest integral element below \\spad{x}.")) (|ceiling| ((|#1| $) "\\spad{ceiling(x)} returns the smallest integral element above \\spad{x}.")) (|random| (($) "\\spad{random()} returns a random fraction.")) (|fractionPart| (($ $) "\\spad{fractionPart(x)} returns the fractional part of \\spad{x}. \\spad{x} = wholePart(\\spad{x}) + fractionPart(\\spad{x})")) (|wholePart| ((|#1| $) "\\spad{wholePart(x)} returns the whole part of the fraction \\spad{x} \\spadignore{i.e.} the truncated quotient of the numerator by the denominator.")) (|denominator| (($ $) "\\spad{denominator(x)} is the denominator of the fraction \\spad{x} converted to \\%.")) (|numerator| (($ $) "\\spad{numerator(x)} is the numerator of the fraction \\spad{x} converted to \\%.")) (|denom| ((|#1| $) "\\spad{denom(x)} returns the denominator of the fraction \\spad{x}.")) (|numer| ((|#1| $) "\\spad{numer(x)} returns the numerator of the fraction \\spad{x}.")) (/ (($ |#1| |#1|) "\\spad{d1 / d2} returns the fraction \\spad{d1} divided by \\spad{d2}."))) -((-4455 . T) (-4461 . T) (-4456 . T) ((-4465 "*") . T) (-4457 . T) (-4458 . T) (-4460 . T)) +((-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL -(-1013 |n| K) +(-1014 |n| K) ((|constructor| (NIL "This domain provides modest support for quadratic forms.")) (|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 -(-1014) +(-1015) ((|constructor| (NIL "This domain represents the syntax of a quasiquote \\indented{2}{expression.}")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the syntax for the expression being quoted."))) NIL NIL -(-1015 S) +(-1016 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|) $) "\\spad{length(q)} returns the number of elements in the queue. Note: \\axiom{length(\\spad{q}) = \\spad{#q}}.")) (|rotate!| (($ $) "\\spad{rotate! q} rotates queue \\spad{q} so that the element at the front of the queue goes to the back of the queue. Note: rotate! \\spad{q} is equivalent to enqueue!(dequeue!(\\spad{q})).")) (|dequeue!| ((|#1| $) "\\spad{dequeue! s} destructively extracts the first (top) element from queue \\spad{q}. The element previously second in the queue becomes the first element. Error: if \\spad{q} is empty.")) (|enqueue!| ((|#1| |#1| $) "\\spad{enqueue!(x,q)} inserts \\spad{x} into the queue \\spad{q} at the back end."))) -((-4463 . T) (-4464 . T)) +((-4464 . T) (-4465 . T)) NIL -(-1016 S R) +(-1017 S R) ((|constructor| (NIL "\\spadtype{QuaternionCategory} describes the category of quaternions and implements functions that are not representation specific.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(q)} returns \\spad{q} as a rational number,{} or \"failed\" if this is not possible. Note: if \\spad{rational?(q)} is \\spad{true},{} the conversion can be done and the rational number will be returned.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(q)} tries to convert \\spad{q} into a rational number. Error: if this is not possible. If \\spad{rational?(q)} is \\spad{true},{} the conversion will be done and the rational number returned.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(q)} returns {\\it \\spad{true}} if all the imaginary parts of \\spad{q} are zero and the real part can be converted into a rational number,{} and {\\it \\spad{false}} otherwise.")) (|abs| ((|#2| $) "\\spad{abs(q)} computes the absolute value of quaternion \\spad{q} (sqrt of norm).")) (|real| ((|#2| $) "\\spad{real(q)} extracts the real part of quaternion \\spad{q}.")) (|quatern| (($ |#2| |#2| |#2| |#2|) "\\spad{quatern(r,i,j,k)} constructs a quaternion from scalars.")) (|norm| ((|#2| $) "\\spad{norm(q)} computes the norm of \\spad{q} (the sum of the squares of the components).")) (|imagK| ((|#2| $) "\\spad{imagK(q)} extracts the imaginary \\spad{k} part of quaternion \\spad{q}.")) (|imagJ| ((|#2| $) "\\spad{imagJ(q)} extracts the imaginary \\spad{j} part of quaternion \\spad{q}.")) (|imagI| ((|#2| $) "\\spad{imagI(q)} extracts the imaginary \\spad{i} part of quaternion \\spad{q}.")) (|conjugate| (($ $) "\\spad{conjugate(q)} negates the imaginary parts of quaternion \\spad{q}."))) NIL -((|HasCategory| |#2| (QUOTE (-557))) (|HasCategory| |#2| (QUOTE (-1080))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-861))) (|HasCategory| |#2| (QUOTE (-300)))) -(-1017 R) +((|HasCategory| |#2| (QUOTE (-557))) (|HasCategory| |#2| (QUOTE (-1081))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-861))) (|HasCategory| |#2| (QUOTE (-300)))) +(-1018 R) ((|constructor| (NIL "\\spadtype{QuaternionCategory} describes the category of quaternions and implements functions that are not representation specific.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(q)} returns \\spad{q} as a rational number,{} or \"failed\" if this is not possible. Note: if \\spad{rational?(q)} is \\spad{true},{} the conversion can be done and the rational number will be returned.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(q)} tries to convert \\spad{q} into a rational number. Error: if this is not possible. If \\spad{rational?(q)} is \\spad{true},{} the conversion will be done and the rational number returned.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(q)} returns {\\it \\spad{true}} if all the imaginary parts of \\spad{q} are zero and the real part can be converted into a rational number,{} and {\\it \\spad{false}} otherwise.")) (|abs| ((|#1| $) "\\spad{abs(q)} computes the absolute value of quaternion \\spad{q} (sqrt of norm).")) (|real| ((|#1| $) "\\spad{real(q)} extracts the real part of quaternion \\spad{q}.")) (|quatern| (($ |#1| |#1| |#1| |#1|) "\\spad{quatern(r,i,j,k)} constructs a quaternion from scalars.")) (|norm| ((|#1| $) "\\spad{norm(q)} computes the norm of \\spad{q} (the sum of the squares of the components).")) (|imagK| ((|#1| $) "\\spad{imagK(q)} extracts the imaginary \\spad{k} part of quaternion \\spad{q}.")) (|imagJ| ((|#1| $) "\\spad{imagJ(q)} extracts the imaginary \\spad{j} part of quaternion \\spad{q}.")) (|imagI| ((|#1| $) "\\spad{imagI(q)} extracts the imaginary \\spad{i} part of quaternion \\spad{q}.")) (|conjugate| (($ $) "\\spad{conjugate(q)} negates the imaginary parts of quaternion \\spad{q}."))) -((-4456 |has| |#1| (-300)) (-4457 . T) (-4458 . T) (-4460 . T)) +((-4457 |has| |#1| (-300)) (-4458 . T) (-4459 . T) (-4461 . T)) NIL -(-1018 QR R QS S) +(-1019 QR R QS S) ((|constructor| (NIL "\\spadtype{QuaternionCategoryFunctions2} implements functions between two quaternion domains. The function \\spadfun{map} is used by the system interpreter to coerce between quaternion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,u)} maps \\spad{f} onto the component parts of the quaternion \\spad{u}."))) NIL NIL -(-1019 R) +(-1020 R) ((|constructor| (NIL "\\spadtype{Quaternion} implements quaternions over a \\indented{2}{commutative ring. The main constructor function is \\spadfun{quatern}} \\indented{2}{which takes 4 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j}} \\indented{2}{imaginary part and the \\spad{k} imaginary part.}"))) -((-4456 |has| |#1| (-300)) (-4457 . T) (-4458 . T) (-4460 . T)) -((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (QUOTE (-374))) (-3794 (|HasCategory| |#1| (QUOTE (-300))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (QUOTE (-300))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -526) (QUOTE (-1196)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -296) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (LIST (QUOTE -918) (QUOTE (-1196)))) (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (LIST (QUOTE -916) (QUOTE (-1196)))) (-3794 (|HasCategory| |#1| (LIST (QUOTE -1058) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (LIST (QUOTE -1058) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1058) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-1080))) (|HasCategory| |#1| (QUOTE (-557)))) -(-1020 S) -((|constructor| (NIL "Linked List implementation of a Queue")) (|queue| (($ (|List| |#1|)) "\\spad{queue([x,y,...,z])} creates a queue with first (top) element \\spad{x},{} second element \\spad{y},{}...,{}and last (bottom) element \\spad{z}."))) -((-4463 . T) (-4464 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1120))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1120))) (-3794 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1120)))) (-3794 (-12 (|HasCategory| |#1| (QUOTE (-1120))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-875))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-875)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4457 |has| |#1| (-300)) (-4458 . T) (-4459 . T) (-4461 . 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T) (-4465 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1121))) (-2758 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1121)))) (-2758 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102)))) +(-1022 S) ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|Fraction| (|Integer|))) "\\spad{x ** y} is the rational exponentiation of \\spad{x} by the power \\spad{y}.")) (|nthRoot| (($ $ (|Integer|)) "\\spad{nthRoot(x,n)} returns the \\spad{n}th root of \\spad{x}.")) (|sqrt| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) 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T) (-4458 . T) (-4459 . T) (-4461 . 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(|fractRadix| (($ (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{fractRadix(pre,cyc)} creates a fractional radix expansion from a list of prefix ragits and a list of cyclic ragits. For example,{} \\spad{fractRadix([1],[6])} will return \\spad{0.16666666...}.")) (|wholeRadix| (($ (|List| (|Integer|))) "\\spad{wholeRadix(l)} creates an integral radix expansion from a list of ragits. For example,{} \\spad{wholeRadix([1,3,4])} will return \\spad{134}.")) (|cycleRagits| (((|List| (|Integer|)) $) "\\spad{cycleRagits(rx)} returns the cyclic part of the ragits of the fractional part of a radix expansion. For example,{} if \\spad{x = 3/28 = 0.10 714285 714285 ...},{} then \\spad{cycleRagits(x) = [7,1,4,2,8,5]}.")) (|prefixRagits| (((|List| (|Integer|)) $) "\\spad{prefixRagits(rx)} returns the non-cyclic part of the ragits of the fractional part of a radix expansion. For example,{} if \\spad{x = 3/28 = 0.10 714285 714285 ...},{} then \\spad{prefixRagits(x)=[1,0]}.")) (|fractRagits| (((|Stream| (|Integer|)) $) "\\spad{fractRagits(rx)} returns the ragits of the fractional part of a radix expansion.")) (|wholeRagits| (((|List| (|Integer|)) $) "\\spad{wholeRagits(rx)} returns the ragits of the integer part of a radix expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(rx)} returns the fractional part of a radix expansion."))) -((-4455 . T) (-4461 . T) (-4456 . T) ((-4465 "*") . T) (-4457 . T) (-4458 . T) (-4460 . T)) -((|HasCategory| (-576) (QUOTE (-927))) (|HasCategory| (-576) (LIST (QUOTE -1058) (QUOTE (-1196)))) (|HasCategory| (-576) (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-148))) (|HasCategory| (-576) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-576) (QUOTE (-1042))) (|HasCategory| (-576) (QUOTE (-832))) (|HasCategory| (-576) (QUOTE (-861))) (-3794 (|HasCategory| (-576) (QUOTE (-832))) (|HasCategory| (-576) (QUOTE (-861)))) (|HasCategory| (-576) (LIST (QUOTE -1058) (QUOTE (-576)))) (|HasCategory| (-576) (QUOTE (-1172))) (|HasCategory| (-576) (LIST (QUOTE -900) (QUOTE (-390)))) (|HasCategory| (-576) (LIST (QUOTE -900) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -626) (LIST (QUOTE -906) (QUOTE (-390))))) (|HasCategory| (-576) (LIST (QUOTE -626) (LIST (QUOTE -906) (QUOTE (-576))))) (|HasCategory| (-576) (QUOTE (-237))) (|HasCategory| (-576) (LIST (QUOTE -918) (QUOTE (-1196)))) (|HasCategory| (-576) (QUOTE (-238))) (|HasCategory| (-576) (LIST (QUOTE -916) (QUOTE (-1196)))) (|HasCategory| (-576) (LIST (QUOTE -526) (QUOTE (-1196)) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -319) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -296) (QUOTE (-576)) (QUOTE (-576)))) (|HasCategory| (-576) (QUOTE (-317))) (|HasCategory| (-576) (QUOTE (-557))) (|HasCategory| (-576) (LIST (QUOTE -651) (QUOTE (-576)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-927)))) (-3794 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-927)))) (|HasCategory| (-576) (QUOTE (-146))))) -(-1025) +((-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) +((|HasCategory| (-576) (QUOTE (-928))) (|HasCategory| (-576) (LIST (QUOTE -1059) (QUOTE (-1197)))) (|HasCategory| (-576) (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-148))) (|HasCategory| (-576) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-576) (QUOTE (-1043))) (|HasCategory| (-576) (QUOTE (-832))) (|HasCategory| (-576) (QUOTE (-861))) (-2758 (|HasCategory| (-576) (QUOTE (-832))) (|HasCategory| (-576) (QUOTE (-861)))) (|HasCategory| (-576) (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| (-576) (QUOTE (-1173))) (|HasCategory| (-576) (LIST (QUOTE -901) (QUOTE (-390)))) (|HasCategory| (-576) (LIST (QUOTE -901) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390))))) (|HasCategory| (-576) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576))))) (|HasCategory| (-576) (QUOTE (-237))) (|HasCategory| (-576) (LIST (QUOTE -919) (QUOTE (-1197)))) (|HasCategory| (-576) (QUOTE (-238))) (|HasCategory| (-576) (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| (-576) (LIST (QUOTE -526) (QUOTE (-1197)) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -319) (QUOTE (-576)))) (|HasCategory| (-576) (LIST (QUOTE -296) (QUOTE (-576)) (QUOTE (-576)))) (|HasCategory| (-576) (QUOTE (-317))) (|HasCategory| (-576) (QUOTE (-557))) (|HasCategory| (-576) (LIST (QUOTE -651) (QUOTE (-576)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-928)))) (-2758 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-576) (QUOTE (-928)))) (|HasCategory| (-576) (QUOTE (-146))))) +(-1026) ((|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 -(-1026) +(-1027) ((|constructor| (NIL "Random number generators \\indented{2}{All random numbers used in the system should originate from} \\indented{2}{the same generator.\\space{2}This package is intended to be the source.}")) (|seed| (((|Integer|)) "\\spad{seed()} returns the current seed value.")) (|reseed| (((|Void|) (|Integer|)) "\\spad{reseed(n)} restarts the random number generator at \\spad{n}.")) (|size| (((|Integer|)) "\\spad{size()} is the base of the random number generator")) (|randnum| (((|Integer|) (|Integer|)) "\\spad{randnum(n)} is a random number between 0 and \\spad{n}.") (((|Integer|)) "\\spad{randnum()} is a random number between 0 and size()."))) NIL NIL -(-1027 RP) +(-1028 RP) ((|factorSquareFree| (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(p)} factors an extended squareFree polynomial \\spad{p} over the rational numbers.")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(p)} factors an extended polynomial \\spad{p} over the rational numbers."))) NIL NIL -(-1028 S) +(-1029 S) ((|constructor| (NIL "rational number testing and retraction functions. Date Created: March 1990 Date Last Updated: 9 April 1991")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") |#1|) "\\spad{rationalIfCan(x)} returns \\spad{x} as a rational number,{} \"failed\" if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) |#1|) "\\spad{rational?(x)} returns \\spad{true} if \\spad{x} is a rational number,{} \\spad{false} otherwise.")) (|rational| (((|Fraction| (|Integer|)) |#1|) "\\spad{rational(x)} returns \\spad{x} as a rational number; error if \\spad{x} is not a rational number."))) NIL NIL -(-1029 A S) +(-1030 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 {\\em node} consisting of a \\spadfun{value} from \\spad{S} and 0 or more \\spadfun{children} which are recursive aggregates. A node with no children is called a \\spadfun{leaf} node. A recursive aggregate may be cyclic for which some operations as noted may go into an infinite loop.")) (|setvalue!| ((|#2| $ |#2|) "\\spad{setvalue!(u,x)} sets the value of node \\spad{u} to \\spad{x}.")) (|setelt| ((|#2| $ "value" |#2|) "\\spad{setelt(a,\"value\",x)} (also written \\axiom{a . value \\spad{:=} \\spad{x}}) is equivalent to \\axiom{setvalue!(a,{}\\spad{x})}")) (|setchildren!| (($ $ (|List| $)) "\\spad{setchildren!(u,v)} replaces the current children of node \\spad{u} with the members of \\spad{v} in left-to-right order.")) (|node?| (((|Boolean|) $ $) "\\spad{node?(u,v)} tests if node \\spad{u} is contained in node \\spad{v} (either as a child,{} a child of a child,{} etc.).")) (|child?| (((|Boolean|) $ $) "\\spad{child?(u,v)} tests if node \\spad{u} is a child of node \\spad{v}.")) (|distance| (((|Integer|) $ $) "\\spad{distance(u,v)} returns the path length (an integer) from node \\spad{u} to \\spad{v}.")) (|leaves| (((|List| |#2|) $) "\\spad{leaves(t)} returns the list of values in obtained by visiting the nodes of tree \\axiom{\\spad{t}} in left-to-right order.")) (|cyclic?| (((|Boolean|) $) "\\spad{cyclic?(u)} tests if \\spad{u} has a cycle.")) (|elt| ((|#2| $ "value") "\\spad{elt(u,\"value\")} (also written: \\axiom{a. value}) is equivalent to \\axiom{value(a)}.")) (|value| ((|#2| $) "\\spad{value(u)} returns the value of the node \\spad{u}.")) (|leaf?| (((|Boolean|) $) "\\spad{leaf?(u)} tests if \\spad{u} is a terminal node.")) (|nodes| (((|List| $) $) "\\spad{nodes(u)} returns a list of all of the nodes of aggregate \\spad{u}.")) (|children| (((|List| $) $) "\\spad{children(u)} returns a list of the children of aggregate \\spad{u}."))) NIL -((|HasAttribute| |#1| (QUOTE -4464)) (|HasCategory| |#2| (QUOTE (-1120)))) -(-1030 S) +((|HasAttribute| |#1| (QUOTE -4465)) (|HasCategory| |#2| (QUOTE (-1121)))) +(-1031 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 {\\em node} consisting of a \\spadfun{value} from \\spad{S} and 0 or more \\spadfun{children} which are recursive aggregates. A node with no children is called a \\spadfun{leaf} node. A recursive aggregate may be cyclic for which some operations as noted may go into an infinite loop.")) (|setvalue!| ((|#1| $ |#1|) "\\spad{setvalue!(u,x)} sets the value of node \\spad{u} to \\spad{x}.")) (|setelt| ((|#1| $ "value" |#1|) "\\spad{setelt(a,\"value\",x)} (also written \\axiom{a . value \\spad{:=} \\spad{x}}) is equivalent to \\axiom{setvalue!(a,{}\\spad{x})}")) (|setchildren!| (($ $ (|List| $)) "\\spad{setchildren!(u,v)} replaces the current children of node \\spad{u} with the members of \\spad{v} in left-to-right order.")) (|node?| (((|Boolean|) $ $) "\\spad{node?(u,v)} tests if node \\spad{u} is contained in node \\spad{v} (either as a child,{} a child of a child,{} etc.).")) (|child?| (((|Boolean|) $ $) "\\spad{child?(u,v)} tests if node \\spad{u} is a child of node \\spad{v}.")) (|distance| (((|Integer|) $ $) "\\spad{distance(u,v)} returns the path length (an integer) from node \\spad{u} to \\spad{v}.")) (|leaves| (((|List| |#1|) $) "\\spad{leaves(t)} returns the list of values in obtained by visiting the nodes of tree \\axiom{\\spad{t}} in left-to-right order.")) (|cyclic?| (((|Boolean|) $) "\\spad{cyclic?(u)} tests if \\spad{u} has a cycle.")) (|elt| ((|#1| $ "value") "\\spad{elt(u,\"value\")} (also written: \\axiom{a. value}) is equivalent to \\axiom{value(a)}.")) (|value| ((|#1| $) "\\spad{value(u)} returns the value of the node \\spad{u}.")) (|leaf?| (((|Boolean|) $) "\\spad{leaf?(u)} tests if \\spad{u} is a terminal node.")) (|nodes| (((|List| $) $) "\\spad{nodes(u)} returns a list of all of the nodes of aggregate \\spad{u}.")) (|children| (((|List| $) $) "\\spad{children(u)} returns a list of the children of aggregate \\spad{u}."))) NIL NIL -(-1031 S) +(-1032 S) ((|constructor| (NIL "\\axiomType{RealClosedField} provides common acces functions for all real closed fields.")) (|approximate| (((|Fraction| (|Integer|)) $ $) "\\axiom{approximate(\\spad{n},{}\\spad{p})} gives an approximation of \\axiom{\\spad{n}} that has precision \\axiom{\\spad{p}}")) (|rename| (($ $ (|OutputForm|)) "\\axiom{rename(\\spad{x},{}name)} gives a new number that prints as name")) (|rename!| (($ $ (|OutputForm|)) "\\axiom{rename!(\\spad{x},{}name)} changes the way \\axiom{\\spad{x}} is printed")) (|sqrt| (($ (|Integer|)) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ (|Fraction| (|Integer|))) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $ (|PositiveInteger|)) "\\axiom{sqrt(\\spad{x},{}\\spad{n})} is \\axiom{\\spad{x} \\spad{**} (1/n)}")) (|allRootsOf| (((|List| $) (|Polynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely")) (|rootOf| (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|)) "\\axiom{rootOf(pol,{}\\spad{n})} creates the \\spad{n}th root for the order of \\axiom{pol} and gives it unique name") (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|) (|OutputForm|)) "\\axiom{rootOf(pol,{}\\spad{n},{}name)} creates the \\spad{n}th root for the order of \\axiom{pol} and names it \\axiom{name}")) (|mainValue| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainValue(\\spad{x})} is the expression of \\axiom{\\spad{x}} in terms of \\axiom{SparseUnivariatePolynomial(\\$)}")) (|mainDefiningPolynomial| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainDefiningPolynomial(\\spad{x})} is the defining polynomial for the main algebraic quantity of \\axiom{\\spad{x}}")) (|mainForm| (((|Union| (|OutputForm|) "failed") $) "\\axiom{mainForm(\\spad{x})} is the main algebraic quantity name of \\axiom{\\spad{x}}"))) NIL NIL -(-1032) +(-1033) ((|constructor| (NIL "\\axiomType{RealClosedField} provides common acces functions for all real closed fields.")) (|approximate| (((|Fraction| (|Integer|)) $ $) "\\axiom{approximate(\\spad{n},{}\\spad{p})} gives an approximation of \\axiom{\\spad{n}} that has precision \\axiom{\\spad{p}}")) (|rename| (($ $ (|OutputForm|)) "\\axiom{rename(\\spad{x},{}name)} gives a new number that prints as name")) (|rename!| (($ $ (|OutputForm|)) "\\axiom{rename!(\\spad{x},{}name)} changes the way \\axiom{\\spad{x}} is printed")) (|sqrt| (($ (|Integer|)) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ (|Fraction| (|Integer|))) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $ (|PositiveInteger|)) "\\axiom{sqrt(\\spad{x},{}\\spad{n})} is \\axiom{\\spad{x} \\spad{**} (1/n)}")) (|allRootsOf| (((|List| $) (|Polynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely")) (|rootOf| (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|)) "\\axiom{rootOf(pol,{}\\spad{n})} creates the \\spad{n}th root for the order of \\axiom{pol} and gives it unique name") (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|) (|OutputForm|)) "\\axiom{rootOf(pol,{}\\spad{n},{}name)} creates the \\spad{n}th root for the order of \\axiom{pol} and names it \\axiom{name}")) (|mainValue| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainValue(\\spad{x})} is the expression of \\axiom{\\spad{x}} in terms of \\axiom{SparseUnivariatePolynomial(\\$)}")) (|mainDefiningPolynomial| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainDefiningPolynomial(\\spad{x})} is the defining polynomial for the main algebraic quantity of \\axiom{\\spad{x}}")) (|mainForm| (((|Union| (|OutputForm|) "failed") $) "\\axiom{mainForm(\\spad{x})} is the main algebraic quantity name of \\axiom{\\spad{x}}"))) -((-4456 . T) (-4461 . T) (-4455 . T) (-4458 . T) (-4457 . T) ((-4465 "*") . T) (-4460 . T)) +((-4457 . T) (-4462 . T) (-4456 . T) (-4459 . T) (-4458 . T) ((-4466 "*") . T) (-4461 . T)) NIL -(-1033 R -2117) +(-1034 R -1959) ((|constructor| (NIL "\\indented{1}{Risch differential equation,{} elementary case.} Author: Manuel Bronstein Date Created: 1 February 1988 Date Last Updated: 2 November 1995 Keywords: elementary,{} function,{} integration.")) (|rischDE| (((|Record| (|:| |ans| |#2|) (|:| |right| |#2|) (|:| |sol?| (|Boolean|))) (|Integer|) |#2| |#2| (|Symbol|) (|Mapping| (|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|List| |#2|)) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| |#2|)) "\\spad{rischDE(n, f, g, x, lim, ext)} returns \\spad{[y, h, b]} such that \\spad{dy/dx + n df/dx y = h} and \\spad{b := h = g}. The equation \\spad{dy/dx + n df/dx y = g} has no solution if \\spad{h \\~~= g} (\\spad{y} is a partial solution in that case). Notes: \\spad{lim} is a limited integration function,{} and ext is an extended integration function."))) NIL NIL -(-1034 R -2117) +(-1035 R -1959) ((|constructor| (NIL "\\indented{1}{Risch differential equation,{} elementary case.} Author: Manuel Bronstein Date Created: 12 August 1992 Date Last Updated: 17 August 1992 Keywords: elementary,{} function,{} integration.")) (|rischDEsys| (((|Union| (|List| |#2|) "failed") (|Integer|) |#2| |#2| |#2| (|Symbol|) (|Mapping| (|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|List| |#2|)) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| |#2|)) "\\spad{rischDEsys(n, f, g_1, g_2, x,lim,ext)} returns \\spad{y_1.y_2} such that \\spad{(dy1/dx,dy2/dx) + ((0, - n df/dx),(n df/dx,0)) (y1,y2) = (g1,g2)} if \\spad{y_1,y_2} exist,{} \"failed\" otherwise. \\spad{lim} is a limited integration function,{} \\spad{ext} is an extended integration function."))) NIL NIL -(-1035 -2117 UP) +(-1036 -1959 UP) ((|constructor| (NIL "\\indented{1}{Risch differential equation,{} transcendental case.} Author: Manuel Bronstein Date Created: Jan 1988 Date Last Updated: 2 November 1995")) (|polyRDE| (((|Union| (|:| |ans| (|Record| (|:| |ans| |#2|) (|:| |nosol| (|Boolean|)))) (|:| |eq| (|Record| (|:| |b| |#2|) (|:| |c| |#2|) (|:| |m| (|Integer|)) (|:| |alpha| |#2|) (|:| |beta| |#2|)))) |#2| |#2| |#2| (|Integer|) (|Mapping| |#2| |#2|)) "\\spad{polyRDE(a, B, C, n, D)} returns either: 1. \\spad{[Q, b]} such that \\spad{degree(Q) <= n} and \\indented{3}{\\spad{a Q'+ B Q = C} if \\spad{b = true},{} \\spad{Q} is a partial solution} \\indented{3}{otherwise.} 2. \\spad{[B1, C1, m, \\alpha, \\beta]} such that any polynomial solution \\indented{3}{of degree at most \\spad{n} of \\spad{A Q' + BQ = C} must be of the form} \\indented{3}{\\spad{Q = \\alpha H + \\beta} where \\spad{degree(H) <= m} and} \\indented{3}{\\spad{H} satisfies \\spad{H' + B1 H = C1}.} \\spad{D} is the derivation to use.")) (|baseRDE| (((|Record| (|:| |ans| (|Fraction| |#2|)) (|:| |nosol| (|Boolean|))) (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{baseRDE(f, g)} returns a \\spad{[y, b]} such that \\spad{y' + fy = g} if \\spad{b = true},{} \\spad{y} is a partial solution otherwise (no solution in that case). \\spad{D} is the derivation to use.")) (|monomRDE| (((|Union| (|Record| (|:| |a| |#2|) (|:| |b| (|Fraction| |#2|)) (|:| |c| (|Fraction| |#2|)) (|:| |t| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{monomRDE(f,g,D)} returns \\spad{[A, B, C, T]} such that \\spad{y' + f y = g} has a solution if and only if \\spad{y = Q / T},{} where \\spad{Q} satisfies \\spad{A Q' + B Q = C} and has no normal pole. A and \\spad{T} are polynomials and \\spad{B} and \\spad{C} have no normal poles. \\spad{D} is the derivation to use."))) NIL NIL -(-1036 -2117 UP) +(-1037 -1959 UP) ((|constructor| (NIL "\\indented{1}{Risch differential equation system,{} transcendental case.} Author: Manuel Bronstein Date Created: 17 August 1992 Date Last Updated: 3 February 1994")) (|baseRDEsys| (((|Union| (|List| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{baseRDEsys(f, g1, g2)} returns fractions \\spad{y_1.y_2} such that \\spad{(y1', y2') + ((0, -f), (f, 0)) (y1,y2) = (g1,g2)} if \\spad{y_1,y_2} exist,{} \"failed\" otherwise.")) (|monomRDEsys| (((|Union| (|Record| (|:| |a| |#2|) (|:| |b| (|Fraction| |#2|)) (|:| |h| |#2|) (|:| |c1| (|Fraction| |#2|)) (|:| |c2| (|Fraction| |#2|)) (|:| |t| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{monomRDEsys(f,g1,g2,D)} returns \\spad{[A, B, H, C1, C2, T]} such that \\spad{(y1', y2') + ((0, -f), (f, 0)) (y1,y2) = (g1,g2)} has a solution if and only if \\spad{y1 = Q1 / T, y2 = Q2 / T},{} where \\spad{B,C1,C2,Q1,Q2} have no normal poles and satisfy A \\spad{(Q1', Q2') + ((H, -B), (B, H)) (Q1,Q2) = (C1,C2)} \\spad{D} is the derivation to use."))) NIL NIL -(-1037 S) +(-1038 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 -(-1038 F1 UP UPUP R F2) +(-1039 F1 UP UPUP R F2) ((|constructor| (NIL "\\indented{1}{Finds the order of a divisor over a finite field} Author: Manuel Bronstein Date Created: 1988 Date Last Updated: 8 November 1994")) (|order| (((|NonNegativeInteger|) (|FiniteDivisor| |#1| |#2| |#3| |#4|) |#3| (|Mapping| |#5| |#1|)) "\\spad{order(f,u,g)} \\undocumented"))) NIL NIL -(-1039) +(-1040) ((|constructor| (NIL "This domain represents list reduction syntax.")) (|body| (((|SpadAst|) $) "\\spad{body(e)} return the list of expressions being redcued.")) (|operator| (((|SpadAst|) $) "\\spad{operator(e)} returns the magma operation being applied."))) NIL NIL -(-1040 |Pol|) +(-1041 |Pol|) ((|constructor| (NIL "\\indented{2}{This package provides functions for finding the real zeros} of univariate polynomials over the integers to arbitrary user-specified precision. The results are returned as a list of isolating intervals which are expressed as records with \"left\" and \"right\" rational number components.")) (|midpoints| (((|List| (|Fraction| (|Integer|))) (|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))))) "\\spad{midpoints(isolist)} returns the list of midpoints for the list of intervals \\spad{isolist}.")) (|midpoint| (((|Fraction| (|Integer|)) (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{midpoint(int)} returns the midpoint of the interval \\spad{int}.")) (|refine| (((|Union| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) "failed") |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{refine(pol, int, range)} takes a univariate polynomial \\spad{pol} and and isolating interval \\spad{int} containing exactly one real root of \\spad{pol}; the operation returns an isolating interval which is contained within range,{} or \"failed\" if no such isolating interval exists.") (((|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|))) "\\spad{refine(pol, int, eps)} refines the interval \\spad{int} containing exactly one root of the univariate polynomial \\spad{pol} to size less than the rational number eps.")) (|realZeros| (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|))) "\\spad{realZeros(pol, int, eps)} returns a list of intervals of length less than the rational number eps for all the real roots of the polynomial \\spad{pol} which lie in the interval expressed by the record \\spad{int}.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Fraction| (|Integer|))) "\\spad{realZeros(pol, eps)} returns a list of intervals of length less than the rational number eps for all the real roots of the polynomial \\spad{pol}.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{realZeros(pol, range)} returns a list of isolating intervals for all the real zeros of the univariate polynomial \\spad{pol} which lie in the interval expressed by the record range.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1|) "\\spad{realZeros(pol)} returns a list of isolating intervals for all the real zeros of the univariate polynomial \\spad{pol}."))) NIL NIL -(-1041 |Pol|) +(-1042 |Pol|) ((|constructor| (NIL "\\indented{2}{This package provides functions for finding the real zeros} of univariate polynomials over the rational numbers to arbitrary user-specified precision. The results are returned as a list of isolating intervals,{} expressed as records with \"left\" and \"right\" rational number components.")) (|refine| (((|Union| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) "failed") |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{refine(pol, int, range)} takes a univariate polynomial \\spad{pol} and and isolating interval \\spad{int} which must contain exactly one real root of \\spad{pol},{} and returns an isolating interval which is contained within range,{} or \"failed\" if no such isolating interval exists.") (((|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|))) "\\spad{refine(pol, int, eps)} refines the interval \\spad{int} containing exactly one root of the univariate polynomial \\spad{pol} to size less than the rational number eps.")) (|realZeros| (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|))) "\\spad{realZeros(pol, int, eps)} returns a list of intervals of length less than the rational number eps for all the real roots of the polynomial \\spad{pol} which lie in the interval expressed by the record \\spad{int}.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Fraction| (|Integer|))) "\\spad{realZeros(pol, eps)} returns a list of intervals of length less than the rational number eps for all the real roots of the polynomial \\spad{pol}.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{realZeros(pol, range)} returns a list of isolating intervals for all the real zeros of the univariate polynomial \\spad{pol} which lie in the interval expressed by the record range.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1|) "\\spad{realZeros(pol)} returns a list of isolating intervals for all the real zeros of the univariate polynomial \\spad{pol}."))) NIL NIL -(-1042) +(-1043) ((|constructor| (NIL "The category of real numeric domains,{} \\spadignore{i.e.} convertible to floats."))) NIL NIL -(-1043) +(-1044) ((|constructor| (NIL "\\indented{1}{This package provides numerical solutions of systems of polynomial} equations for use in ACPLOT.")) (|realSolve| (((|List| (|List| (|Float|))) (|List| (|Polynomial| (|Integer|))) (|List| (|Symbol|)) (|Float|)) "\\spad{realSolve(lp,lv,eps)} = compute the list of the real solutions of the list \\spad{lp} of polynomials with integer coefficients with respect to the variables in \\spad{lv},{} with precision \\spad{eps}.")) (|solve| (((|List| (|Float|)) (|Polynomial| (|Integer|)) (|Float|)) "\\spad{solve(p,eps)} finds the real zeroes of a univariate integer polynomial \\spad{p} with precision \\spad{eps}.") (((|List| (|Float|)) (|Polynomial| (|Fraction| (|Integer|))) (|Float|)) "\\spad{solve(p,eps)} finds the real zeroes of a univariate rational polynomial \\spad{p} with precision \\spad{eps}."))) NIL NIL -(-1044 |TheField|) +(-1045 |TheField|) ((|constructor| (NIL "This domain implements the real closure of an ordered field.")) (|relativeApprox| (((|Fraction| (|Integer|)) $ $) "\\axiom{relativeApprox(\\spad{n},{}\\spad{p})} gives a relative approximation of \\axiom{\\spad{n}} that has precision \\axiom{\\spad{p}}")) (|mainCharacterization| (((|Union| (|RightOpenIntervalRootCharacterization| $ (|SparseUnivariatePolynomial| $)) "failed") $) "\\axiom{mainCharacterization(\\spad{x})} is the main algebraic quantity of \\axiom{\\spad{x}} (\\axiom{SEG})")) (|algebraicOf| (($ (|RightOpenIntervalRootCharacterization| $ (|SparseUnivariatePolynomial| $)) (|OutputForm|)) "\\axiom{algebraicOf(char)} is the external number"))) -((-4456 . T) (-4461 . T) (-4455 . T) (-4458 . T) (-4457 . T) ((-4465 "*") . T) (-4460 . T)) -((-3794 (|HasCategory| (-419 (-576)) (LIST (QUOTE -1058) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -1058) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1058) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1058) (QUOTE (-576)))) (|HasCategory| (-419 (-576)) (LIST (QUOTE -1058) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-419 (-576)) (LIST (QUOTE -1058) (QUOTE (-576))))) -(-1045 -2117 L) +((-4457 . T) (-4462 . T) (-4456 . T) (-4459 . T) (-4458 . T) ((-4466 "*") . T) (-4461 . T)) +((-2758 (|HasCategory| (-419 (-576)) (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| (-419 (-576)) (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-419 (-576)) (LIST (QUOTE -1059) (QUOTE (-576))))) +(-1046 -1959 L) ((|constructor| (NIL "\\spadtype{ReductionOfOrder} provides functions for reducing the order of linear ordinary differential equations once some solutions are known.")) (|ReduceOrder| (((|Record| (|:| |eq| |#2|) (|:| |op| (|List| |#1|))) |#2| (|List| |#1|)) "\\spad{ReduceOrder(op, [f1,...,fk])} returns \\spad{[op1,[g1,...,gk]]} such that for any solution \\spad{z} of \\spad{op1 z = 0},{} \\spad{y = gk \\int(g_{k-1} \\int(... \\int(g1 \\int z)...)} is a solution of \\spad{op y = 0}. Each \\spad{fi} must satisfy \\spad{op fi = 0}.") ((|#2| |#2| |#1|) "\\spad{ReduceOrder(op, s)} returns \\spad{op1} such that for any solution \\spad{z} of \\spad{op1 z = 0},{} \\spad{y = s \\int z} is a solution of \\spad{op y = 0}. \\spad{s} must satisfy \\spad{op s = 0}."))) NIL NIL -(-1046 S) +(-1047 S) ((|constructor| (NIL "\\indented{1}{\\spadtype{Reference} is for making a changeable instance} of something.")) (= (((|Boolean|) $ $) "\\spad{a=b} tests if \\spad{a} and \\spad{b} are equal.")) (|setref| ((|#1| $ |#1|) "\\spad{setref(n,m)} same as \\spad{setelt(n,m)}.")) (|deref| ((|#1| $) "\\spad{deref(n)} is equivalent to \\spad{elt(n)}.")) (|setelt| ((|#1| $ |#1|) "\\spad{setelt(n,m)} changes the value of the object \\spad{n} to \\spad{m}.")) (|elt| ((|#1| $) "\\spad{elt(n)} returns the object \\spad{n}.")) (|ref| (($ |#1|) "\\spad{ref(n)} creates a pointer (reference) to the object \\spad{n}."))) NIL -((|HasCategory| |#1| (QUOTE (-1120)))) -(-1047 R E V P) +((|HasCategory| |#1| (QUOTE (-1121)))) +(-1048 R E V P) ((|constructor| (NIL "This domain provides an implementation of regular chains. Moreover,{} the operation \\axiomOpFrom{zeroSetSplit}{RegularTriangularSetCategory} is an implementation of a new algorithm for solving polynomial systems by means of regular chains.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|preprocess| (((|Record| (|:| |val| (|List| |#4|)) (|:| |towers| (|List| $))) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{pre_process(\\spad{lp},{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|internalZeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalZeroSetSplit(\\spad{lp},{}\\spad{b1},{}\\spad{b2},{}\\spad{b3})} is an internal subroutine,{} exported only for developement.")) (|zeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{}\\spad{b1},{}\\spad{b2}.\\spad{b3},{}\\spad{b4})} is an internal subroutine,{} exported only for developement.") (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{}clos?,{}info?)} has the same specifications as \\axiomOpFrom{zeroSetSplit}{RegularTriangularSetCategory}. Moreover,{} if \\axiom{clos?} then solves in the sense of the Zariski closure else solves in the sense of the regular zeros. If \\axiom{info?} then do print messages during the computations.")) (|internalAugment| (((|List| $) |#4| $ (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalAugment(\\spad{p},{}\\spad{ts},{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement."))) -((-4464 . T) (-4463 . T)) -((-12 (|HasCategory| |#4| (QUOTE (-1120))) (|HasCategory| |#4| (LIST (QUOTE -319) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#4| (QUOTE (-1120))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#3| (QUOTE (-379))) (|HasCategory| |#4| (LIST (QUOTE -625) (QUOTE (-875)))) (|HasCategory| |#4| (QUOTE (-102)))) -(-1048 R) +((-4465 . T) (-4464 . T)) +((-12 (|HasCategory| |#4| (QUOTE (-1121))) (|HasCategory| |#4| (LIST (QUOTE -319) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#4| (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#3| (QUOTE (-379))) (|HasCategory| |#4| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#4| (QUOTE (-102)))) +(-1049 R) ((|constructor| (NIL "RepresentationPackage1 provides functions for representation theory for finite groups and algebras. The package creates permutation representations and uses tensor products and its symmetric and antisymmetric components to create new representations of larger degree from given ones. Note: instead of having parameters from \\spadtype{Permutation} this package allows list notation of permutations as well: \\spadignore{e.g.} \\spad{[1,4,3,2]} denotes permutes 2 and 4 and fixes 1 and 3.")) (|permutationRepresentation| (((|List| (|Matrix| (|Integer|))) (|List| (|List| (|Integer|)))) "\\spad{permutationRepresentation([pi1,...,pik],n)} returns the list of matrices {\\em [(deltai,pi1(i)),...,(deltai,pik(i))]} if the permutations {\\em pi1},{}...,{}{\\em pik} are in list notation and are permuting {\\em {1,2,...,n}}.") (((|List| (|Matrix| (|Integer|))) (|List| (|Permutation| (|Integer|))) (|Integer|)) "\\spad{permutationRepresentation([pi1,...,pik],n)} returns the list of matrices {\\em [(deltai,pi1(i)),...,(deltai,pik(i))]} (Kronecker delta) for the permutations {\\em pi1,...,pik} of {\\em {1,2,...,n}}.") (((|Matrix| (|Integer|)) (|List| (|Integer|))) "\\spad{permutationRepresentation(pi,n)} returns the matrix {\\em (deltai,pi(i))} (Kronecker delta) if the permutation {\\em pi} is in list notation and permutes {\\em {1,2,...,n}}.") (((|Matrix| (|Integer|)) (|Permutation| (|Integer|)) (|Integer|)) "\\spad{permutationRepresentation(pi,n)} returns the matrix {\\em (deltai,pi(i))} (Kronecker delta) for a permutation {\\em pi} of {\\em {1,2,...,n}}.")) (|tensorProduct| (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{tensorProduct([a1,...ak])} calculates the list of Kronecker products of each matrix {\\em ai} with itself for {1 \\spad{<=} \\spad{i} \\spad{<=} \\spad{k}}. Note: If the list of matrices corresponds to a group representation (repr. of generators) of one group,{} then these matrices correspond to the tensor product of the representation with itself.") (((|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{tensorProduct(a)} calculates the Kronecker product of the matrix {\\em a} with itself.") (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{tensorProduct([a1,...,ak],[b1,...,bk])} calculates the list of Kronecker products of the matrices {\\em ai} and {\\em bi} for {1 \\spad{<=} \\spad{i} \\spad{<=} \\spad{k}}. Note: If each list of matrices corresponds to a group representation (repr. of generators) of one group,{} then these matrices correspond to the tensor product of the two representations.") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{tensorProduct(a,b)} calculates the Kronecker product of the matrices {\\em a} and \\spad{b}. Note: if each matrix corresponds to a group representation (repr. of generators) of one group,{} then these matrices correspond to the tensor product of the two representations.")) (|symmetricTensors| (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|PositiveInteger|)) "\\spad{symmetricTensors(la,n)} applies to each \\spad{m}-by-\\spad{m} square matrix in the list {\\em la} the irreducible,{} polynomial representation of the general linear group {\\em GLm} which corresponds to the partition {\\em (n,0,...,0)} of \\spad{n}. Error: if the matrices in {\\em la} are not square matrices. Note: this corresponds to the symmetrization of the representation with the trivial representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the symmetric tensors of the \\spad{n}-fold tensor product.") (((|Matrix| |#1|) (|Matrix| |#1|) (|PositiveInteger|)) "\\spad{symmetricTensors(a,n)} applies to the \\spad{m}-by-\\spad{m} square matrix {\\em a} the irreducible,{} polynomial representation of the general linear group {\\em GLm} which corresponds to the partition {\\em (n,0,...,0)} of \\spad{n}. Error: if {\\em a} is not a square matrix. Note: this corresponds to the symmetrization of the representation with the trivial representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the symmetric tensors of the \\spad{n}-fold tensor product.")) (|createGenericMatrix| (((|Matrix| (|Polynomial| |#1|)) (|NonNegativeInteger|)) "\\spad{createGenericMatrix(m)} creates a square matrix of dimension \\spad{k} whose entry at the \\spad{i}-th row and \\spad{j}-th column is the indeterminate {\\em x[i,j]} (double subscripted).")) (|antisymmetricTensors| (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|PositiveInteger|)) "\\spad{antisymmetricTensors(la,n)} applies to each \\spad{m}-by-\\spad{m} square matrix in the list {\\em la} the irreducible,{} polynomial representation of the general linear group {\\em GLm} which corresponds to the partition {\\em (1,1,...,1,0,0,...,0)} of \\spad{n}. Error: if \\spad{n} is greater than \\spad{m}. Note: this corresponds to the symmetrization of the representation with the sign representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the antisymmetric tensors of the \\spad{n}-fold tensor product.") (((|Matrix| |#1|) (|Matrix| |#1|) (|PositiveInteger|)) "\\spad{antisymmetricTensors(a,n)} applies to the square matrix {\\em a} the irreducible,{} polynomial representation of the general linear group {\\em GLm},{} where \\spad{m} is the number of rows of {\\em a},{} which corresponds to the partition {\\em (1,1,...,1,0,0,...,0)} of \\spad{n}. Error: if \\spad{n} is greater than \\spad{m}. Note: this corresponds to the symmetrization of the representation with the sign representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the antisymmetric tensors of the \\spad{n}-fold tensor product."))) NIL -((|HasAttribute| |#1| (QUOTE (-4465 "*")))) -(-1049 R) +((|HasAttribute| |#1| (QUOTE (-4466 "*")))) +(-1050 R) ((|constructor| (NIL "RepresentationPackage2 provides functions for working with modular representations of finite groups and algebra. The routines in this package are created,{} using ideas of \\spad{R}. Parker,{} (the meat-Axe) to get smaller representations from bigger ones,{} \\spadignore{i.e.} finding sub- and factormodules,{} or to show,{} that such the representations are irreducible. Note: most functions are randomized functions of Las Vegas type \\spadignore{i.e.} every answer is correct,{} but with small probability the algorithm fails to get an answer.")) (|scanOneDimSubspaces| (((|Vector| |#1|) (|List| (|Vector| |#1|)) (|Integer|)) "\\spad{scanOneDimSubspaces(basis,n)} gives a canonical representative of the {\\em n}\\spad{-}th one-dimensional subspace of the vector space generated by the elements of {\\em basis},{} all from {\\em R**n}. The coefficients of the representative are of shape {\\em (0,...,0,1,*,...,*)},{} {\\em *} in \\spad{R}. If the size of \\spad{R} is \\spad{q},{} then there are {\\em (q**n-1)/(q-1)} of them. We first reduce \\spad{n} modulo this number,{} then find the largest \\spad{i} such that {\\em +/[q**i for i in 0..i-1] <= n}. Subtracting this sum of powers from \\spad{n} results in an \\spad{i}-digit number to \\spad{basis} \\spad{q}. This fills the positions of the stars.")) (|meatAxe| (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|PositiveInteger|)) "\\spad{meatAxe(aG, numberOfTries)} calls {\\em meatAxe(aG,true,numberOfTries,7)}. Notes: 7 covers the case of three-dimensional kernels over the field with 2 elements.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Boolean|)) "\\spad{meatAxe(aG, randomElements)} calls {\\em meatAxe(aG,false,6,7)},{} only using Parker\\spad{'s} fingerprints,{} if {\\em randomElemnts} is \\spad{false}. If it is \\spad{true},{} it calls {\\em meatAxe(aG,true,25,7)},{} only using random elements. Note: the choice of 25 was rather arbitrary. Also,{} 7 covers the case of three-dimensional kernels over the field with 2 elements.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|))) "\\spad{meatAxe(aG)} calls {\\em meatAxe(aG,false,25,7)} returns a 2-list of representations as follows. All matrices of argument \\spad{aG} are assumed to be square and of equal size. Then \\spad{aG} generates a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an A-module in the usual way. meatAxe(\\spad{aG}) creates at most 25 random elements of the algebra,{} tests them for singularity. If singular,{} it tries at most 7 elements of its kernel to generate a proper submodule. If successful a list which contains first the list of the representations of the submodule,{} then a list of the representations of the factor module is returned. Otherwise,{} if we know that all the kernel is already scanned,{} Norton\\spad{'s} irreducibility test can be used either to prove irreducibility or to find the splitting. Notes: the first 6 tries use Parker\\spad{'s} fingerprints. Also,{} 7 covers the case of three-dimensional kernels over the field with 2 elements.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Boolean|) (|Integer|) (|Integer|)) "\\spad{meatAxe(aG,randomElements,numberOfTries, maxTests)} returns a 2-list of representations as follows. All matrices of argument \\spad{aG} are assumed to be square and of equal size. Then \\spad{aG} generates a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an A-module in the usual way. meatAxe(\\spad{aG},{}\\spad{numberOfTries},{} maxTests) creates at most {\\em numberOfTries} random elements of the algebra,{} tests them for singularity. If singular,{} it tries at most {\\em maxTests} elements of its kernel to generate a proper submodule. If successful,{} a 2-list is returned: first,{} a list containing first the list of the representations of the submodule,{} then a list of the representations of the factor module. Otherwise,{} if we know that all the kernel is already scanned,{} Norton\\spad{'s} irreducibility test can be used either to prove irreducibility or to find the splitting. If {\\em randomElements} is {\\em false},{} the first 6 tries use Parker\\spad{'s} fingerprints.")) (|split| (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Vector| (|Vector| |#1|))) "\\spad{split(aG,submodule)} uses a proper \\spad{submodule} of {\\em R**n} to create the representations of the \\spad{submodule} and of the factor module.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Vector| |#1|)) "\\spad{split(aG, vector)} returns a subalgebra \\spad{A} of all square matrix of dimension \\spad{n} as a list of list of matrices,{} generated by the list of matrices \\spad{aG},{} where \\spad{n} denotes both the size of vector as well as the dimension of each of the square matrices. {\\em V R} is an A-module in the natural way. split(\\spad{aG},{} vector) then checks whether the cyclic submodule generated by {\\em vector} is a proper submodule of {\\em V R}. If successful,{} it returns a two-element list,{} which contains first the list of the representations of the submodule,{} then the list of the representations of the factor module. If the vector generates the whole module,{} a one-element list of the old representation is given. Note: a later version this should call the other split.")) (|isAbsolutelyIrreducible?| (((|Boolean|) (|List| (|Matrix| |#1|))) "\\spad{isAbsolutelyIrreducible?(aG)} calls {\\em isAbsolutelyIrreducible?(aG,25)}. Note: the choice of 25 was rather arbitrary.") (((|Boolean|) (|List| (|Matrix| |#1|)) (|Integer|)) "\\spad{isAbsolutelyIrreducible?(aG, numberOfTries)} uses Norton\\spad{'s} irreducibility test to check for absolute irreduciblity,{} assuming if a one-dimensional kernel is found. As no field extension changes create \"new\" elements in a one-dimensional space,{} the criterium stays \\spad{true} for every extension. The method looks for one-dimensionals only by creating random elements (no fingerprints) since a run of {\\em meatAxe} would have proved absolute irreducibility anyway.")) (|areEquivalent?| (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|Integer|)) "\\spad{areEquivalent?(aG0,aG1,numberOfTries)} calls {\\em areEquivalent?(aG0,aG1,true,25)}. Note: the choice of 25 was rather arbitrary.") (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{areEquivalent?(aG0,aG1)} calls {\\em areEquivalent?(aG0,aG1,true,25)}. Note: the choice of 25 was rather arbitrary.") (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|Boolean|) (|Integer|)) "\\spad{areEquivalent?(aG0,aG1,randomelements,numberOfTries)} tests whether the two lists of matrices,{} all assumed of same square shape,{} can be simultaneously conjugated by a non-singular matrix. If these matrices represent the same group generators,{} the representations are equivalent. The algorithm tries {\\em numberOfTries} times to create elements in the generated algebras in the same fashion. If their ranks differ,{} they are not equivalent. If an isomorphism is assumed,{} then the kernel of an element of the first algebra is mapped to the kernel of the corresponding element in the second algebra. Now consider the one-dimensional ones. If they generate the whole space (\\spadignore{e.g.} irreducibility !) we use {\\em standardBasisOfCyclicSubmodule} to create the only possible transition matrix. The method checks whether the matrix conjugates all corresponding matrices from {\\em aGi}. The way to choose the singular matrices is as in {\\em meatAxe}. If the two representations are equivalent,{} this routine returns the transformation matrix {\\em TM} with {\\em aG0.i * TM = TM * aG1.i} for all \\spad{i}. If the representations are not equivalent,{} a small 0-matrix is returned. Note: the case with different sets of group generators cannot be handled.")) (|standardBasisOfCyclicSubmodule| (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|Vector| |#1|)) "\\spad{standardBasisOfCyclicSubmodule(lm,v)} returns a matrix as follows. It is assumed that the size \\spad{n} of the vector equals the number of rows and columns of the matrices. Then the matrices generate a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an \\spad{A}-module in the natural way. standardBasisOfCyclicSubmodule(\\spad{lm},{}\\spad{v}) calculates a matrix whose non-zero column vectors are the \\spad{R}-Basis of {\\em Av} achieved in the way as described in section 6 of \\spad{R}. A. Parker\\spad{'s} \"The Meat-Axe\". Note: in contrast to {\\em cyclicSubmodule},{} the result is not in echelon form.")) (|cyclicSubmodule| (((|Vector| (|Vector| |#1|)) (|List| (|Matrix| |#1|)) (|Vector| |#1|)) "\\spad{cyclicSubmodule(lm,v)} generates a basis as follows. It is assumed that the size \\spad{n} of the vector equals the number of rows and columns of the matrices. Then the matrices generate a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an \\spad{A}-module in the natural way. cyclicSubmodule(\\spad{lm},{}\\spad{v}) generates the \\spad{R}-Basis of {\\em Av} as described in section 6 of \\spad{R}. A. Parker\\spad{'s} \"The Meat-Axe\". Note: in contrast to the description in \"The Meat-Axe\" and to {\\em standardBasisOfCyclicSubmodule} the result is in echelon form.")) (|createRandomElement| (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|Matrix| |#1|)) "\\spad{createRandomElement(aG,x)} creates a random element of the group algebra generated by {\\em aG}.")) (|completeEchelonBasis| (((|Matrix| |#1|) (|Vector| (|Vector| |#1|))) "\\spad{completeEchelonBasis(lv)} completes the basis {\\em lv} assumed to be in echelon form of a subspace of {\\em R**n} (\\spad{n} the length of all the vectors in {\\em lv}) with unit vectors to a basis of {\\em R**n}. It is assumed that the argument is not an empty vector and that it is not the basis of the 0-subspace. Note: the rows of the result correspond to the vectors of the basis."))) NIL ((-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-379)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-317)))) -(-1050 S) +(-1051 S) ((|constructor| (NIL "Implements multiplication by repeated addition")) (|double| ((|#1| (|PositiveInteger|) |#1|) "\\spad{double(i, r)} multiplies \\spad{r} by \\spad{i} using repeated doubling.")) (+ (($ $ $) "\\spad{x+y} returns the sum of \\spad{x} and \\spad{y}"))) NIL NIL -(-1051) +(-1052) ((|constructor| (NIL "Package for the computation of eigenvalues and eigenvectors. This package works for matrices with coefficients which are rational functions over the integers. (see \\spadtype{Fraction Polynomial Integer}). The eigenvalues and eigenvectors are expressed in terms of radicals.")) (|orthonormalBasis| (((|List| (|Matrix| (|Expression| (|Integer|)))) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{orthonormalBasis(m)} returns the orthogonal matrix \\spad{b} such that \\spad{b*m*(inverse b)} is diagonal. Error: if \\spad{m} is not a symmetric matrix.")) (|gramschmidt| (((|List| (|Matrix| (|Expression| (|Integer|)))) (|List| (|Matrix| (|Expression| (|Integer|))))) "\\spad{gramschmidt(lv)} converts the list of column vectors \\spad{lv} into a set of orthogonal column vectors of euclidean length 1 using the Gram-Schmidt algorithm.")) (|normalise| (((|Matrix| (|Expression| (|Integer|))) (|Matrix| (|Expression| (|Integer|)))) "\\spad{normalise(v)} returns the column vector \\spad{v} divided by its euclidean norm; when possible,{} the vector \\spad{v} is expressed in terms of radicals.")) (|eigenMatrix| (((|Union| (|Matrix| (|Expression| (|Integer|))) "failed") (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{eigenMatrix(m)} returns the matrix \\spad{b} such that \\spad{b*m*(inverse b)} is diagonal,{} or \"failed\" if no such \\spad{b} exists.")) (|radicalEigenvalues| (((|List| (|Expression| (|Integer|))) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{radicalEigenvalues(m)} computes the eigenvalues of the matrix \\spad{m}; when possible,{} the eigenvalues are expressed in terms of radicals.")) (|radicalEigenvector| (((|List| (|Matrix| (|Expression| (|Integer|)))) (|Expression| (|Integer|)) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{radicalEigenvector(c,m)} computes the eigenvector(\\spad{s}) of the matrix \\spad{m} corresponding to the eigenvalue \\spad{c}; when possible,{} values are expressed in terms of radicals.")) (|radicalEigenvectors| (((|List| (|Record| (|:| |radval| (|Expression| (|Integer|))) (|:| |radmult| (|Integer|)) (|:| |radvect| (|List| (|Matrix| (|Expression| (|Integer|))))))) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{radicalEigenvectors(m)} computes the eigenvalues and the corresponding eigenvectors of the matrix \\spad{m}; when possible,{} values are expressed in terms of radicals."))) NIL NIL -(-1052 S) +(-1053 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 -(-1053 S) +(-1054 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 -(-1054 -2117 |Expon| |VarSet| |FPol| |LFPol|) +(-1055 -1959 |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"))) -(((-4465 "*") . T) (-4457 . T) (-4458 . T) (-4460 . T)) +(((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL -(-1055) -((|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.}"))) -((-4463 . T) (-4464 . T)) -((-12 (|HasCategory| (-2 (|:| -2239 (-1196)) (|:| -2904 (-52))) (QUOTE (-1120))) (|HasCategory| (-2 (|:| -2239 (-1196)) (|:| -2904 (-52))) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2239) (QUOTE (-1196))) (LIST (QUOTE |:|) (QUOTE -2904) (QUOTE (-52))))))) (-3794 (|HasCategory| (-2 (|:| -2239 (-1196)) (|:| -2904 (-52))) (QUOTE (-1120))) (|HasCategory| (-52) (QUOTE (-1120)))) (-3794 (|HasCategory| (-2 (|:| -2239 (-1196)) (|:| -2904 (-52))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2239 (-1196)) (|:| -2904 (-52))) (QUOTE (-1120))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-1120)))) (-3794 (|HasCategory| (-2 (|:| -2239 (-1196)) (|:| -2904 (-52))) (QUOTE (-1120))) (|HasCategory| (-2 (|:| -2239 (-1196)) (|:| -2904 (-52))) (LIST (QUOTE -625) (QUOTE (-875)))) (|HasCategory| (-52) (QUOTE (-1120))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-875))))) (|HasCategory| (-2 (|:| -2239 (-1196)) (|:| -2904 (-52))) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| (-52) (QUOTE (-1120))) (|HasCategory| (-52) (LIST (QUOTE -319) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2239 (-1196)) (|:| -2904 (-52))) (QUOTE (-1120))) (|HasCategory| (-1196) (QUOTE (-861))) (|HasCategory| (-52) (QUOTE (-1120))) (-3794 (|HasCategory| (-2 (|:| -2239 (-1196)) (|:| -2904 (-52))) (LIST (QUOTE -625) (QUOTE (-875)))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-875))))) (-3794 (|HasCategory| (-2 (|:| -2239 (-1196)) (|:| -2904 (-52))) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-102)))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-875)))) (|HasCategory| (-2 (|:| -2239 (-1196)) (|:| -2904 (-52))) (LIST (QUOTE -625) (QUOTE (-875)))) (|HasCategory| (-2 (|:| -2239 (-1196)) (|:| -2904 (-52))) (QUOTE (-102)))) (-1056) +((|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.}"))) +((-4464 . T) (-4465 . T)) +((-12 (|HasCategory| (-2 (|:| -4300 (-1197)) (|:| -4438 (-52))) (QUOTE (-1121))) (|HasCategory| (-2 (|:| -4300 (-1197)) (|:| -4438 (-52))) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4300) (QUOTE (-1197))) (LIST (QUOTE |:|) (QUOTE -4438) (QUOTE (-52))))))) (-2758 (|HasCategory| (-2 (|:| -4300 (-1197)) (|:| -4438 (-52))) (QUOTE (-1121))) (|HasCategory| (-52) (QUOTE (-1121)))) (-2758 (|HasCategory| (-2 (|:| -4300 (-1197)) (|:| -4438 (-52))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4300 (-1197)) (|:| -4438 (-52))) (QUOTE (-1121))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-1121)))) (-2758 (|HasCategory| (-2 (|:| -4300 (-1197)) (|:| -4438 (-52))) (QUOTE (-1121))) (|HasCategory| (-2 (|:| -4300 (-1197)) (|:| -4438 (-52))) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-52) (QUOTE (-1121))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| (-2 (|:| -4300 (-1197)) (|:| -4438 (-52))) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| (-52) (QUOTE (-1121))) (|HasCategory| (-52) (LIST (QUOTE -319) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -4300 (-1197)) (|:| -4438 (-52))) (QUOTE (-1121))) (|HasCategory| (-1197) (QUOTE (-861))) (|HasCategory| (-52) (QUOTE (-1121))) (-2758 (|HasCategory| (-2 (|:| -4300 (-1197)) (|:| -4438 (-52))) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-876))))) (-2758 (|HasCategory| (-2 (|:| -4300 (-1197)) (|:| -4438 (-52))) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-102)))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -4300 (-1197)) (|:| -4438 (-52))) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -4300 (-1197)) (|:| -4438 (-52))) (QUOTE (-102)))) +(-1057) ((|constructor| (NIL "This domain represents `return' expressions.")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression returned by `e'."))) NIL NIL -(-1057 A S) +(-1058 A S) ((|constructor| (NIL "A is retractable to \\spad{B} means that some elementsif A can be converted into elements of \\spad{B} and any element of \\spad{B} can be converted into an element of A.")) (|retract| ((|#2| $) "\\spad{retract(a)} transforms a into an element of \\spad{S} if possible. Error: if a cannot be made into an element of \\spad{S}.")) (|retractIfCan| (((|Union| |#2| "failed") $) "\\spad{retractIfCan(a)} transforms a into an element of \\spad{S} if possible. Returns \"failed\" if a cannot be made into an element of \\spad{S}."))) NIL NIL -(-1058 S) +(-1059 S) ((|constructor| (NIL "A is retractable to \\spad{B} means that some elementsif A can be converted into elements of \\spad{B} and any element of \\spad{B} can be converted into an element of A.")) (|retract| ((|#1| $) "\\spad{retract(a)} transforms a into an element of \\spad{S} if possible. Error: if a cannot be made into an element of \\spad{S}.")) (|retractIfCan| (((|Union| |#1| "failed") $) "\\spad{retractIfCan(a)} transforms a into an element of \\spad{S} if possible. Returns \"failed\" if a cannot be made into an element of \\spad{S}."))) NIL NIL -(-1059 Q R) +(-1060 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 -(-1060) +(-1061) ((|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 -(-1061 UP) +(-1062 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 -(-1062 R) +(-1063 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 -(-1063 R) +(-1064 R) ((|constructor| (NIL "Utilities that provide the same top-level manipulations on fractions than on polynomials.")) (|coerce| (((|Fraction| (|Polynomial| |#1|)) |#1|) "\\spad{coerce(r)} returns \\spad{r} viewed as a rational function over \\spad{R}.")) (|eval| (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) "\\spad{eval(f, [v1 = g1,...,vn = gn])} returns \\spad{f} with each \\spad{vi} replaced by \\spad{gi} in parallel,{} \\spadignore{i.e.} \\spad{vi}\\spad{'s} appearing inside the \\spad{gi}\\spad{'s} are not replaced. Error: if any \\spad{vi} is not a symbol.") (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|)))) "\\spad{eval(f, v = g)} returns \\spad{f} with \\spad{v} replaced by \\spad{g}. Error: if \\spad{v} is not a symbol.") (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|List| (|Symbol|)) (|List| (|Fraction| (|Polynomial| |#1|)))) "\\spad{eval(f, [v1,...,vn], [g1,...,gn])} returns \\spad{f} with each \\spad{vi} replaced by \\spad{gi} in parallel,{} \\spadignore{i.e.} \\spad{vi}\\spad{'s} appearing inside the \\spad{gi}\\spad{'s} are not replaced.") (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|))) "\\spad{eval(f, v, g)} returns \\spad{f} with \\spad{v} replaced by \\spad{g}.")) (|multivariate| (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|)))) (|Symbol|)) "\\spad{multivariate(f, v)} applies both the numerator and denominator of \\spad{f} to \\spad{v}.")) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|)))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{univariate(f, v)} returns \\spad{f} viewed as a univariate rational function in \\spad{v}.")) (|mainVariable| (((|Union| (|Symbol|) "failed") (|Fraction| (|Polynomial| |#1|))) "\\spad{mainVariable(f)} returns the highest variable appearing in the numerator or the denominator of \\spad{f},{} \"failed\" if \\spad{f} has no variables.")) (|variables| (((|List| (|Symbol|)) (|Fraction| (|Polynomial| |#1|))) "\\spad{variables(f)} returns the list of variables appearing in the numerator or the denominator of \\spad{f}."))) NIL NIL -(-1064 T$) +(-1065 T$) ((|constructor| (NIL "This category defines the common interface for \\spad{RGB} color models.")) (|componentUpperBound| ((|#1|) "componentUpperBound is an upper bound for all component values.")) (|blue| ((|#1| $) "\\spad{blue(c)} returns the `blue' component of \\spad{`c'}.")) (|green| ((|#1| $) "\\spad{green(c)} returns the `green' component of \\spad{`c'}.")) (|red| ((|#1| $) "\\spad{red(c)} returns the `red' component of \\spad{`c'}."))) NIL NIL -(-1065 T$) +(-1066 T$) ((|constructor| (NIL "This category defines the common interface for \\spad{RGB} color spaces.")) (|whitePoint| (($) "whitePoint is the contant indicating the white point of this color space."))) NIL NIL -(-1066 R |ls|) +(-1067 R |ls|) ((|constructor| (NIL "A domain for regular chains (\\spadignore{i.e.} regular triangular sets) over a \\spad{Gcd}-Domain and with a fix list of variables. This is just a front-end for the \\spadtype{RegularTriangularSet} domain constructor.")) (|zeroSetSplit| (((|List| $) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|) (|Boolean|)) "\\spad{zeroSetSplit(lp,clos?,info?)} returns a list \\spad{lts} of regular chains such that the union of the closures of their regular zero sets equals the affine variety associated with \\spad{lp}. Moreover,{} if \\spad{clos?} is \\spad{false} then the union of the regular zero set of the \\spad{ts} (for \\spad{ts} in \\spad{lts}) equals this variety. If \\spad{info?} is \\spad{true} then some information is displayed during the computations. See \\axiomOpFrom{zeroSetSplit}{RegularTriangularSet}."))) -((-4464 . T) (-4463 . T)) -((-12 (|HasCategory| (-792 |#1| (-877 |#2|)) (QUOTE (-1120))) (|HasCategory| (-792 |#1| (-877 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -792) (|devaluate| |#1|) (LIST (QUOTE -877) (|devaluate| |#2|)))))) (|HasCategory| (-792 |#1| (-877 |#2|)) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-792 |#1| (-877 |#2|)) (QUOTE (-1120))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| (-877 |#2|) (QUOTE (-379))) (|HasCategory| (-792 |#1| (-877 |#2|)) (LIST (QUOTE -625) (QUOTE (-875)))) (|HasCategory| (-792 |#1| (-877 |#2|)) (QUOTE (-102)))) -(-1067) +((-4465 . T) (-4464 . T)) +((-12 (|HasCategory| (-792 |#1| (-878 |#2|)) (QUOTE (-1121))) (|HasCategory| (-792 |#1| (-878 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -792) (|devaluate| |#1|) (LIST (QUOTE -878) (|devaluate| |#2|)))))) (|HasCategory| (-792 |#1| (-878 |#2|)) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-792 |#1| (-878 |#2|)) (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| (-878 |#2|) (QUOTE (-379))) (|HasCategory| (-792 |#1| (-878 |#2|)) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-792 |#1| (-878 |#2|)) (QUOTE (-102)))) +(-1068) ((|constructor| (NIL "This package exports integer distributions")) (|ridHack1| (((|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{ridHack1(i,j,k,l)} \\undocumented")) (|geometric| (((|Mapping| (|Integer|)) |RationalNumber|) "\\spad{geometric(f)} \\undocumented")) (|poisson| (((|Mapping| (|Integer|)) |RationalNumber|) "\\spad{poisson(f)} \\undocumented")) (|binomial| (((|Mapping| (|Integer|)) (|Integer|) |RationalNumber|) "\\spad{binomial(n,f)} \\undocumented")) (|uniform| (((|Mapping| (|Integer|)) (|Segment| (|Integer|))) "\\spad{uniform(s)} \\undocumented"))) NIL NIL -(-1068 S) +(-1069 S) ((|constructor| (NIL "The category of rings with unity,{} always associative,{} but not necessarily commutative.")) (|unitsKnown| ((|attribute|) "recip truly yields reciprocal or \"failed\" if not a unit. Note: \\spad{recip(0) = \"failed\"}.")) (|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 -(-1069) +(-1070) ((|constructor| (NIL "The category of rings with unity,{} always associative,{} but not necessarily commutative.")) (|unitsKnown| ((|attribute|) "recip truly yields reciprocal or \"failed\" if not a unit. Note: \\spad{recip(0) = \"failed\"}.")) (|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."))) -((-4460 . T)) +((-4461 . T)) NIL -(-1070 |xx| -2117) +(-1071 |xx| -1959) ((|constructor| (NIL "This package exports rational interpolation algorithms"))) NIL NIL -(-1071 S) +(-1072 S) ((|constructor| (NIL "\\indented{2}{A set is an \\spad{S}-right linear set if it is stable by right-dilation} \\indented{2}{by elements in the semigroup \\spad{S}.} See Also: LeftLinearSet.")) (* (($ $ |#1|) "\\spad{x*s} is the right-dilation of \\spad{x} by \\spad{s}."))) NIL NIL -(-1072 S |m| |n| R |Row| |Col|) +(-1073 S |m| |n| R |Row| |Col|) ((|constructor| (NIL "\\spadtype{RectangularMatrixCategory} is a category of matrices of fixed dimensions. The dimensions of the matrix will be parameters of the domain. Domains in this category will be \\spad{R}-modules and will be non-mutable.")) (|nullSpace| (((|List| |#6|) $) "\\spad{nullSpace(m)}+ returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#4|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#4|) "\\spad{exquo(m,r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (|map| (($ (|Mapping| |#4| |#4| |#4|) $ $) "\\spad{map(f,a,b)} returns \\spad{c},{} where \\spad{c} is such that \\spad{c(i,j) = f(a(i,j),b(i,j))} for all \\spad{i},{} \\spad{j}.") (($ (|Mapping| |#4| |#4|) $) "\\spad{map(f,a)} returns \\spad{b},{} where \\spad{b(i,j) = a(i,j)} for all \\spad{i},{} \\spad{j}.")) (|column| ((|#6| $ (|Integer|)) "\\spad{column(m,j)} returns the \\spad{j}th column of the matrix \\spad{m}. Error: if the index outside the proper range.")) (|row| ((|#5| $ (|Integer|)) "\\spad{row(m,i)} returns the \\spad{i}th row of the matrix \\spad{m}. Error: if the index is outside the proper range.")) (|qelt| ((|#4| $ (|Integer|) (|Integer|)) "\\spad{qelt(m,i,j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m}. Note: there is NO error check to determine if indices are in the proper ranges.")) (|elt| ((|#4| $ (|Integer|) (|Integer|) |#4|) "\\spad{elt(m,i,j,r)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m},{} if \\spad{m} has an \\spad{i}th row and a \\spad{j}th column,{} and returns \\spad{r} otherwise.") ((|#4| $ (|Integer|) (|Integer|)) "\\spad{elt(m,i,j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m}. Error: if indices are outside the proper ranges.")) (|listOfLists| (((|List| (|List| |#4|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|ncols| (((|NonNegativeInteger|) $) "\\spad{ncols(m)} returns the number of columns in the matrix \\spad{m}.")) (|nrows| (((|NonNegativeInteger|) $) "\\spad{nrows(m)} returns the number of rows in the matrix \\spad{m}.")) (|maxColIndex| (((|Integer|) $) "\\spad{maxColIndex(m)} returns the index of the 'last' column of the matrix \\spad{m}.")) (|minColIndex| (((|Integer|) $) "\\spad{minColIndex(m)} returns the index of the 'first' column of the matrix \\spad{m}.")) (|maxRowIndex| (((|Integer|) $) "\\spad{maxRowIndex(m)} returns the index of the 'last' row of the matrix \\spad{m}.")) (|minRowIndex| (((|Integer|) $) "\\spad{minRowIndex(m)} returns the index of the 'first' row of the matrix \\spad{m}.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,j] = -m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,j] = m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.")) (|matrix| (($ (|List| (|List| |#4|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix.")) (|finiteAggregate| ((|attribute|) "matrices are finite"))) NIL ((|HasCategory| |#4| (QUOTE (-317))) (|HasCategory| |#4| (QUOTE (-374))) (|HasCategory| |#4| (QUOTE (-568))) (|HasCategory| |#4| (QUOTE (-174)))) -(-1073 |m| |n| R |Row| |Col|) +(-1074 |m| |n| R |Row| |Col|) ((|constructor| (NIL "\\spadtype{RectangularMatrixCategory} is a category of matrices of fixed dimensions. The dimensions of the matrix will be parameters of the domain. Domains in this category will be \\spad{R}-modules and will be non-mutable.")) (|nullSpace| (((|List| |#5|) $) "\\spad{nullSpace(m)}+ returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#3|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#3|) "\\spad{exquo(m,r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (|map| (($ (|Mapping| |#3| |#3| |#3|) $ $) "\\spad{map(f,a,b)} returns \\spad{c},{} where \\spad{c} is such that \\spad{c(i,j) = f(a(i,j),b(i,j))} for all \\spad{i},{} \\spad{j}.") (($ (|Mapping| |#3| |#3|) $) "\\spad{map(f,a)} returns \\spad{b},{} where \\spad{b(i,j) = a(i,j)} for all \\spad{i},{} \\spad{j}.")) (|column| ((|#5| $ (|Integer|)) "\\spad{column(m,j)} returns the \\spad{j}th column of the matrix \\spad{m}. Error: if the index outside the proper range.")) (|row| ((|#4| $ (|Integer|)) "\\spad{row(m,i)} returns the \\spad{i}th row of the matrix \\spad{m}. Error: if the index is outside the proper range.")) (|qelt| ((|#3| $ (|Integer|) (|Integer|)) "\\spad{qelt(m,i,j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m}. Note: there is NO error check to determine if indices are in the proper ranges.")) (|elt| ((|#3| $ (|Integer|) (|Integer|) |#3|) "\\spad{elt(m,i,j,r)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m},{} if \\spad{m} has an \\spad{i}th row and a \\spad{j}th column,{} and returns \\spad{r} otherwise.") ((|#3| $ (|Integer|) (|Integer|)) "\\spad{elt(m,i,j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m}. Error: if indices are outside the proper ranges.")) (|listOfLists| (((|List| (|List| |#3|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|ncols| (((|NonNegativeInteger|) $) "\\spad{ncols(m)} returns the number of columns in the matrix \\spad{m}.")) (|nrows| (((|NonNegativeInteger|) $) "\\spad{nrows(m)} returns the number of rows in the matrix \\spad{m}.")) (|maxColIndex| (((|Integer|) $) "\\spad{maxColIndex(m)} returns the index of the 'last' column of the matrix \\spad{m}.")) (|minColIndex| (((|Integer|) $) "\\spad{minColIndex(m)} returns the index of the 'first' column of the matrix \\spad{m}.")) (|maxRowIndex| (((|Integer|) $) "\\spad{maxRowIndex(m)} returns the index of the 'last' row of the matrix \\spad{m}.")) (|minRowIndex| (((|Integer|) $) "\\spad{minRowIndex(m)} returns the index of the 'first' row of the matrix \\spad{m}.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,j] = -m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,j] = m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.")) (|matrix| (($ (|List| (|List| |#3|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix.")) (|finiteAggregate| ((|attribute|) "matrices are finite"))) -((-4463 . T) (-4458 . T) (-4457 . T)) +((-4464 . T) (-4459 . T) (-4458 . T)) NIL -(-1074 |m| |n| R) +(-1075 |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.")) (|rectangularMatrix| (($ (|Matrix| |#3|)) "\\spad{rectangularMatrix(m)} converts a matrix of type \\spadtype{Matrix} to a matrix of type \\spad{RectangularMatrix}."))) -((-4463 . T) (-4458 . T) (-4457 . T)) -((|HasCategory| |#3| (QUOTE (-174))) (-3794 (-12 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (LIST (QUOTE -319) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-374))) (|HasCategory| |#3| (LIST (QUOTE -319) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1120))) (|HasCategory| |#3| (LIST (QUOTE -319) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -626) (QUOTE (-548)))) (-3794 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-374)))) (|HasCategory| |#3| (QUOTE (-374))) (|HasCategory| |#3| (QUOTE (-1120))) (|HasCategory| |#3| (QUOTE (-317))) (|HasCategory| |#3| (QUOTE (-568))) (-12 (|HasCategory| |#3| (QUOTE (-1120))) (|HasCategory| |#3| (LIST (QUOTE -319) (|devaluate| |#3|)))) (|HasCategory| |#3| (QUOTE (-102))) (|HasCategory| |#3| (LIST (QUOTE -625) (QUOTE (-875))))) -(-1075 |m| |n| R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2) +((-4464 . T) (-4459 . T) (-4458 . T)) +((|HasCategory| |#3| (QUOTE (-174))) (-2758 (-12 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (LIST (QUOTE -319) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-374))) (|HasCategory| |#3| (LIST (QUOTE -319) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1121))) (|HasCategory| |#3| (LIST (QUOTE -319) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -626) (QUOTE (-548)))) (-2758 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-374)))) (|HasCategory| |#3| (QUOTE (-374))) (|HasCategory| |#3| (QUOTE (-1121))) (|HasCategory| |#3| (QUOTE (-317))) (|HasCategory| |#3| (QUOTE (-568))) (-12 (|HasCategory| |#3| (QUOTE (-1121))) (|HasCategory| |#3| (LIST (QUOTE -319) (|devaluate| |#3|)))) (|HasCategory| |#3| (QUOTE (-102))) (|HasCategory| |#3| (LIST (QUOTE -625) (QUOTE (-876))))) +(-1076 |m| |n| R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2) ((|constructor| (NIL "\\spadtype{RectangularMatrixCategoryFunctions2} provides functions between two matrix domains. The functions provided are \\spadfun{map} and \\spadfun{reduce}.")) (|reduce| ((|#7| (|Mapping| |#7| |#3| |#7|) |#6| |#7|) "\\spad{reduce(f,m,r)} returns a matrix \\spad{n} where \\spad{n[i,j] = f(m[i,j],r)} for all indices spad{\\spad{i}} and \\spad{j}.")) (|map| ((|#10| (|Mapping| |#7| |#3|) |#6|) "\\spad{map(f,m)} applies the function \\spad{f} to the elements of the matrix \\spad{m}."))) NIL NIL -(-1076 R) +(-1077 R) ((|constructor| (NIL "The category of right modules over an \\spad{rng} (ring not necessarily with unit). This is an abelian group which supports right multiplation by elements of the \\spad{rng}. \\blankline"))) NIL NIL -(-1077 S T$) +(-1078 S T$) ((|constructor| (NIL "This domain represents the notion of binding a variable to range over a specific segment (either bounded,{} or half bounded).")) (|segment| ((|#1| $) "\\spad{segment(x)} returns the segment from the right hand side of the \\spadtype{RangeBinding}. For example,{} if \\spad{x} is \\spad{v=s},{} then \\spad{segment(x)} returns \\spad{s}.")) (|variable| (((|Symbol|) $) "\\spad{variable(x)} returns the variable from the left hand side of the \\spadtype{RangeBinding}. For example,{} if \\spad{x} is \\spad{v=s},{} then \\spad{variable(x)} returns \\spad{v}.")) (|equation| (($ (|Symbol|) |#1|) "\\spad{equation(v,s)} creates a segment binding value with variable \\spad{v} and segment \\spad{s}. Note that the interpreter parses \\spad{v=s} to this form."))) NIL -((|HasCategory| |#1| (QUOTE (-1120)))) -(-1078) +((|HasCategory| |#1| (QUOTE (-1121)))) +(-1079) ((|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"))) NIL NIL -(-1079 S) +(-1080 S) ((|constructor| (NIL "The real number system category is intended as a model for the real numbers. The real numbers form an ordered normed field. Note that we have purposely not included \\spadtype{DifferentialRing} or the elementary functions (see \\spadtype{TranscendentalFunctionCategory}) in the definition.")) (|abs| (($ $) "\\spad{abs x} returns the absolute value of \\spad{x}.")) (|round| (($ $) "\\spad{round x} computes the integer closest to \\spad{x}.")) (|truncate| (($ $) "\\spad{truncate x} returns the integer between \\spad{x} and 0 closest to \\spad{x}.")) (|fractionPart| (($ $) "\\spad{fractionPart x} returns the fractional part of \\spad{x}.")) (|wholePart| (((|Integer|) $) "\\spad{wholePart x} returns the integer part of \\spad{x}.")) (|floor| (($ $) "\\spad{floor x} returns the largest integer \\spad{<= x}.")) (|ceiling| (($ $) "\\spad{ceiling x} returns the small integer \\spad{>= x}.")) (|norm| (($ $) "\\spad{norm x} returns the same as absolute value."))) NIL NIL -(-1080) +(-1081) ((|constructor| (NIL "The real number system category is intended as a model for the real numbers. The real numbers form an ordered normed field. Note that we have purposely not included \\spadtype{DifferentialRing} or the elementary functions (see \\spadtype{TranscendentalFunctionCategory}) in the definition.")) (|abs| (($ $) "\\spad{abs x} returns the absolute value of \\spad{x}.")) (|round| (($ $) "\\spad{round x} computes the integer closest to \\spad{x}.")) (|truncate| (($ $) "\\spad{truncate x} returns the integer between \\spad{x} and 0 closest to \\spad{x}.")) (|fractionPart| (($ $) "\\spad{fractionPart x} returns the fractional part of \\spad{x}.")) (|wholePart| (((|Integer|) $) "\\spad{wholePart x} returns the integer part of \\spad{x}.")) (|floor| (($ $) "\\spad{floor x} returns the largest integer \\spad{<= x}.")) (|ceiling| (($ $) "\\spad{ceiling x} returns the small integer \\spad{>= x}.")) (|norm| (($ $) "\\spad{norm x} returns the same as absolute value."))) -((-4455 . T) (-4461 . T) (-4456 . T) ((-4465 "*") . T) (-4457 . T) (-4458 . T) (-4460 . T)) +((-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL -(-1081 |TheField| |ThePolDom|) +(-1082 |TheField| |ThePolDom|) ((|constructor| (NIL "\\axiomType{RightOpenIntervalRootCharacterization} provides work with interval root coding.")) (|relativeApprox| ((|#1| |#2| $ |#1|) "\\axiom{relativeApprox(exp,{}\\spad{c},{}\\spad{p}) = a} is relatively close to exp as a polynomial in \\spad{c} ip to precision \\spad{p}")) (|mightHaveRoots| (((|Boolean|) |#2| $) "\\axiom{mightHaveRoots(\\spad{p},{}\\spad{r})} is \\spad{false} if \\axiom{\\spad{p}.\\spad{r}} is not 0")) (|refine| (($ $) "\\axiom{refine(rootChar)} shrinks isolating interval around \\axiom{rootChar}")) (|middle| ((|#1| $) "\\axiom{middle(rootChar)} is the middle of the isolating interval")) (|size| ((|#1| $) "The size of the isolating interval")) (|right| ((|#1| $) "\\axiom{right(rootChar)} is the right bound of the isolating interval")) (|left| ((|#1| $) "\\axiom{left(rootChar)} is the left bound of the isolating interval"))) NIL NIL -(-1082) +(-1083) ((|constructor| (NIL "\\spadtype{RomanNumeral} provides functions for converting \\indented{1}{integers to roman numerals.}")) (|roman| (($ (|Integer|)) "\\spad{roman(n)} creates a roman numeral for \\spad{n}.") (($ (|Symbol|)) "\\spad{roman(n)} creates a roman numeral for symbol \\spad{n}.")) (|noetherian| ((|attribute|) "ascending chain condition on ideals.")) (|canonicalsClosed| ((|attribute|) "two positives multiply to give positive.")) (|canonical| ((|attribute|) "mathematical equality is data structure equality."))) -((-4451 . T) (-4455 . T) (-4450 . T) (-4461 . T) (-4462 . T) (-4456 . T) ((-4465 "*") . T) (-4457 . T) (-4458 . T) (-4460 . T)) +((-4452 . T) (-4456 . T) (-4451 . T) (-4462 . T) (-4463 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL -(-1083) +(-1084) ((|constructor| (NIL "\\axiomType{RoutinesTable} implements a database and associated tuning mechanisms for a set of known NAG routines")) (|recoverAfterFail| (((|Union| (|String|) "failed") $ (|String|) (|Integer|)) "\\spad{recoverAfterFail(routs,routineName,ifailValue)} acts on the instructions given by the ifail list")) (|showTheRoutinesTable| (($) "\\spad{showTheRoutinesTable()} returns the current table of NAG routines.")) (|deleteRoutine!| (($ $ (|Symbol|)) "\\spad{deleteRoutine!(R,s)} destructively deletes the given routine from the current database of NAG routines")) (|getExplanations| (((|List| (|String|)) $ (|String|)) "\\spad{getExplanations(R,s)} gets the explanations of the output parameters for the given NAG routine.")) (|getMeasure| (((|Float|) $ (|Symbol|)) "\\spad{getMeasure(R,s)} gets the current value of the maximum measure for the given NAG routine.")) (|changeMeasure| (($ $ (|Symbol|) (|Float|)) "\\spad{changeMeasure(R,s,newValue)} changes the maximum value for a measure of the given NAG routine.")) (|changeThreshhold| (($ $ (|Symbol|) (|Float|)) "\\spad{changeThreshhold(R,s,newValue)} changes the value below which,{} given a NAG routine generating a higher measure,{} the routines will make no attempt to generate a measure.")) (|selectMultiDimensionalRoutines| (($ $) "\\spad{selectMultiDimensionalRoutines(R)} chooses only those routines from the database which are designed for use with multi-dimensional expressions")) (|selectNonFiniteRoutines| (($ $) "\\spad{selectNonFiniteRoutines(R)} chooses only those routines from the database which are designed for use with non-finite expressions.")) (|selectSumOfSquaresRoutines| (($ $) "\\spad{selectSumOfSquaresRoutines(R)} chooses only those routines from the database which are designed for use with sums of squares")) (|selectFiniteRoutines| (($ $) "\\spad{selectFiniteRoutines(R)} chooses only those routines from the database which are designed for use with finite expressions")) (|selectODEIVPRoutines| (($ $) "\\spad{selectODEIVPRoutines(R)} chooses only those routines from the database which are for the solution of ODE\\spad{'s}")) (|selectPDERoutines| (($ $) "\\spad{selectPDERoutines(R)} chooses only those routines from the database which are for the solution of PDE\\spad{'s}")) (|selectOptimizationRoutines| (($ $) "\\spad{selectOptimizationRoutines(R)} chooses only those routines from the database which are for integration")) (|selectIntegrationRoutines| (($ $) "\\spad{selectIntegrationRoutines(R)} chooses only those routines from the database which are for integration")) (|routines| (($) "\\spad{routines()} initialises a database of known NAG routines")) (|concat| (($ $ $) "\\spad{concat(x,y)} merges two tables \\spad{x} and \\spad{y}"))) -((-4463 . T) (-4464 . T)) -((-12 (|HasCategory| (-2 (|:| -2239 (-1196)) (|:| -2904 (-52))) (QUOTE (-1120))) (|HasCategory| (-2 (|:| -2239 (-1196)) (|:| -2904 (-52))) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2239) (QUOTE (-1196))) (LIST (QUOTE |:|) (QUOTE -2904) (QUOTE (-52))))))) (-3794 (|HasCategory| (-2 (|:| -2239 (-1196)) (|:| -2904 (-52))) (QUOTE (-1120))) (|HasCategory| (-52) (QUOTE (-1120)))) (-3794 (|HasCategory| (-2 (|:| -2239 (-1196)) (|:| -2904 (-52))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2239 (-1196)) (|:| -2904 (-52))) (QUOTE (-1120))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-1120)))) (-3794 (|HasCategory| (-2 (|:| -2239 (-1196)) (|:| -2904 (-52))) (QUOTE (-1120))) (|HasCategory| (-2 (|:| -2239 (-1196)) (|:| -2904 (-52))) (LIST (QUOTE -625) (QUOTE (-875)))) (|HasCategory| (-52) (QUOTE (-1120))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-875))))) (|HasCategory| (-2 (|:| -2239 (-1196)) (|:| -2904 (-52))) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| (-52) (QUOTE (-1120))) (|HasCategory| (-52) (LIST (QUOTE -319) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2239 (-1196)) (|:| -2904 (-52))) (QUOTE (-1120))) (|HasCategory| (-1196) (QUOTE (-861))) (|HasCategory| (-52) (QUOTE (-1120))) (-3794 (|HasCategory| (-2 (|:| -2239 (-1196)) (|:| -2904 (-52))) (LIST (QUOTE -625) (QUOTE (-875)))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-875))))) (-3794 (|HasCategory| (-2 (|:| -2239 (-1196)) (|:| -2904 (-52))) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-102)))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-875)))) (|HasCategory| (-2 (|:| -2239 (-1196)) (|:| -2904 (-52))) (LIST (QUOTE -625) (QUOTE (-875)))) (|HasCategory| (-2 (|:| -2239 (-1196)) (|:| -2904 (-52))) (QUOTE (-102)))) -(-1084 S R E V) +((-4464 . T) (-4465 . T)) +((-12 (|HasCategory| (-2 (|:| -4300 (-1197)) (|:| -4438 (-52))) (QUOTE (-1121))) (|HasCategory| (-2 (|:| -4300 (-1197)) (|:| -4438 (-52))) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4300) (QUOTE (-1197))) (LIST (QUOTE |:|) (QUOTE -4438) (QUOTE (-52))))))) (-2758 (|HasCategory| (-2 (|:| -4300 (-1197)) (|:| -4438 (-52))) (QUOTE (-1121))) (|HasCategory| (-52) (QUOTE (-1121)))) (-2758 (|HasCategory| (-2 (|:| -4300 (-1197)) (|:| -4438 (-52))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4300 (-1197)) (|:| -4438 (-52))) (QUOTE (-1121))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-1121)))) (-2758 (|HasCategory| (-2 (|:| -4300 (-1197)) (|:| -4438 (-52))) (QUOTE (-1121))) (|HasCategory| (-2 (|:| -4300 (-1197)) (|:| -4438 (-52))) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-52) (QUOTE (-1121))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| (-2 (|:| -4300 (-1197)) (|:| -4438 (-52))) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| (-52) (QUOTE (-1121))) (|HasCategory| (-52) (LIST (QUOTE -319) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -4300 (-1197)) (|:| -4438 (-52))) (QUOTE (-1121))) (|HasCategory| (-1197) (QUOTE (-861))) (|HasCategory| (-52) (QUOTE (-1121))) (-2758 (|HasCategory| (-2 (|:| -4300 (-1197)) (|:| -4438 (-52))) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-876))))) (-2758 (|HasCategory| (-2 (|:| -4300 (-1197)) (|:| -4438 (-52))) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-102)))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -4300 (-1197)) (|:| -4438 (-52))) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -4300 (-1197)) (|:| -4438 (-52))) (QUOTE (-102)))) +(-1085 S R E V) ((|constructor| (NIL "A category for general multi-variate polynomials with coefficients in a ring,{} variables in an ordered set,{} and exponents from an ordered abelian monoid,{} with a \\axiomOp{sup} operation. When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\axiom{primitivePart!(\\spad{p})} replaces \\axiom{\\spad{p}} by its primitive part.")) (|gcd| ((|#2| |#2| $) "\\axiom{\\spad{gcd}(\\spad{r},{}\\spad{p})} returns the \\spad{gcd} of \\axiom{\\spad{r}} and the content of \\axiom{\\spad{p}}.")) (|nextsubResultant2| (($ $ $ $ $) "\\axiom{nextsubResultant2(\\spad{p},{}\\spad{q},{}\\spad{z},{}\\spad{s})} is the multivariate version of the operation \\axiomOpFrom{next_sousResultant2}{PseudoRemainderSequence} from the \\axiomType{PseudoRemainderSequence} constructor.")) (|LazardQuotient2| (($ $ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient2(\\spad{p},{}a,{}\\spad{b},{}\\spad{n})} returns \\axiom{(a**(\\spad{n}-1) * \\spad{p}) exquo \\spad{b**}(\\spad{n}-1)} assuming that this quotient does not fail.")) (|LazardQuotient| (($ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient(a,{}\\spad{b},{}\\spad{n})} returns \\axiom{a**n exquo \\spad{b**}(\\spad{n}-1)} assuming that this quotient does not fail.")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns the last non-zero subresultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|subResultantChain| (((|List| $) $ $) "\\axiom{subResultantChain(a,{}\\spad{b})},{} where \\axiom{a} and \\axiom{\\spad{b}} are not contant polynomials with the same main variable,{} returns the subresultant chain of \\axiom{a} and \\axiom{\\spad{b}}.")) (|resultant| (($ $ $) "\\axiom{resultant(a,{}\\spad{b})} computes the resultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedSubResultantGcd2(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}\\spad{cb}]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}\\spad{cb}]} otherwise produces an error.")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedSubResultantGcd1(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}\\spad{cb}]} otherwise produces an error.")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[ca,{}\\spad{cb},{}\\spad{r}]} such that \\axiom{\\spad{r}} is \\axiom{subResultantGcd(a,{}\\spad{b})} and we have \\axiom{ca * a + \\spad{cb} * \\spad{cb} = \\spad{r}} .")) (|subResultantGcd| (($ $ $) "\\axiom{subResultantGcd(a,{}\\spad{b})} computes a \\spad{gcd} of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}} with coefficients in the fraction field of the polynomial ring generated by their other variables over \\axiom{\\spad{R}}.")) (|exactQuotient!| (($ $ $) "\\axiom{exactQuotient!(a,{}\\spad{b})} replaces \\axiom{a} by \\axiom{exactQuotient(a,{}\\spad{b})}") (($ $ |#2|) "\\axiom{exactQuotient!(\\spad{p},{}\\spad{r})} replaces \\axiom{\\spad{p}} by \\axiom{exactQuotient(\\spad{p},{}\\spad{r})}.")) (|exactQuotient| (($ $ $) "\\axiom{exactQuotient(a,{}\\spad{b})} computes the exact quotient of \\axiom{a} by \\axiom{\\spad{b}},{} which is assumed to be a divisor of \\axiom{a}. No error is returned if this exact quotient fails!") (($ $ |#2|) "\\axiom{exactQuotient(\\spad{p},{}\\spad{r})} computes the exact quotient of \\axiom{\\spad{p}} by \\axiom{\\spad{r}},{} which is assumed to be a divisor of \\axiom{\\spad{p}}. No error is returned if this exact quotient fails!")) (|primPartElseUnitCanonical!| (($ $) "\\axiom{primPartElseUnitCanonical!(\\spad{p})} replaces \\axiom{\\spad{p}} by \\axiom{primPartElseUnitCanonical(\\spad{p})}.")) (|primPartElseUnitCanonical| (($ $) "\\axiom{primPartElseUnitCanonical(\\spad{p})} returns \\axiom{primitivePart(\\spad{p})} if \\axiom{\\spad{R}} is a \\spad{gcd}-domain,{} otherwise \\axiom{unitCanonical(\\spad{p})}.")) (|convert| (($ (|Polynomial| |#2|)) "\\axiom{convert(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}},{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.")) (|retract| (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.")) (|initiallyReduce| (($ $ $) "\\axiom{initiallyReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|headReduce| (($ $ $) "\\axiom{headReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| $) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{p},{}\\spad{q},{}\\spad{n}]} where \\axiom{\\spad{p} / q**n} represents the residue class of \\axiom{a} modulo \\axiom{\\spad{b}} and \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{q}} is \\axiom{init(\\spad{b})}.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} computes \\axiom{a mod \\spad{b}},{} if \\axiom{\\spad{b}} is monic as univariate polynomial in its main variable.")) (|pseudoDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{pseudoDivide(a,{}\\spad{b})} computes \\axiom{[pquo(a,{}\\spad{b}),{}prem(a,{}\\spad{b})]},{} both polynomials viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}},{} if \\axiom{\\spad{b}} is not a constant polynomial.")) (|lazyPseudoDivide| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $ |#4|) "\\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})},{} \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}] = lazyPremWithDefault(a,{}\\spad{b})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.")) (|lazyPremWithDefault| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $ |#4|) "\\axiom{lazyPremWithDefault(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b},{}\\spad{v})}.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $) "\\axiom{lazyPremWithDefault(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b})} and \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b})}.")) (|lazyPquo| (($ $ $ |#4|) "\\axiom{lazyPquo(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.") (($ $ $) "\\axiom{lazyPquo(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.")) (|lazyPrem| (($ $ $ |#4|) "\\axiom{lazyPrem(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} viewed as univariate polynomials in the variable \\axiom{\\spad{v}} such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.") (($ $ $) "\\axiom{lazyPrem(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.")) (|pquo| (($ $ $ |#4|) "\\axiom{pquo(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{pquo(a,{}\\spad{b})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|prem| (($ $ $ |#4|) "\\axiom{prem(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{prem(a,{}\\spad{b})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|normalized?| (((|Boolean|) $ (|List| $)) "\\axiom{normalized?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{normalized?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{normalized?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{a} and its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variable of \\axiom{\\spad{b}}")) (|initiallyReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{initiallyReduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{initiallyReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{initiallyReduced?(a,{}\\spad{b})} returns \\spad{false} iff there exists an iterated initial of \\axiom{a} which is not reduced \\spad{w}.\\spad{r}.\\spad{t} \\axiom{\\spad{b}}.")) (|headReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{headReduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{headReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{headReduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(head(a),{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|reduced?| (((|Boolean|) $ (|List| $)) "\\axiom{reduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{reduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{reduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(a,{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|supRittWu?| (((|Boolean|) $ $) "\\axiom{supRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is greater than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is less than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|RittWuCompare| (((|Union| (|Boolean|) "failed") $ $) "\\axiom{RittWuCompare(a,{}\\spad{b})} returns \\axiom{\"failed\"} if \\axiom{a} and \\axiom{\\spad{b}} have same rank \\spad{w}.\\spad{r}.\\spad{t}. Ritt and Wu Wen Tsun ordering using the refinement of Lazard,{} otherwise returns \\axiom{infRittWu?(a,{}\\spad{b})}.")) (|mainMonomials| (((|List| $) $) "\\axiom{mainMonomials(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [1],{} otherwise returns the list of the monomials of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainCoefficients| (((|List| $) $) "\\axiom{mainCoefficients(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [\\spad{p}],{} otherwise returns the list of the coefficients of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|leastMonomial| (($ $) "\\axiom{leastMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} the monomial of \\axiom{\\spad{p}} with lowest degree,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainMonomial| (($ $) "\\axiom{mainMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} \\axiom{mvar(\\spad{p})} raised to the power \\axiom{mdeg(\\spad{p})}.")) (|quasiMonic?| (((|Boolean|) $) "\\axiom{quasiMonic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff the initial of \\axiom{\\spad{p}} lies in the base ring \\axiom{\\spad{R}}.")) (|monic?| (((|Boolean|) $) "\\axiom{monic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff \\axiom{\\spad{p}} is monic as a univariate polynomial in its main variable.")) (|reductum| (($ $ |#4|) "\\axiom{reductum(\\spad{p},{}\\spad{v})} returns the reductum of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in \\axiom{\\spad{v}}.")) (|leadingCoefficient| (($ $ |#4|) "\\axiom{leadingCoefficient(\\spad{p},{}\\spad{v})} returns the leading coefficient of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as A univariate polynomial in \\axiom{\\spad{v}}.")) (|deepestInitial| (($ $) "\\axiom{deepestInitial(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the last term of \\axiom{iteratedInitials(\\spad{p})}.")) (|iteratedInitials| (((|List| $) $) "\\axiom{iteratedInitials(\\spad{p})} returns \\axiom{[]} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the list of the iterated initials of \\axiom{\\spad{p}}.")) (|deepestTail| (($ $) "\\axiom{deepestTail(\\spad{p})} returns \\axiom{0} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns tail(\\spad{p}),{} if \\axiom{tail(\\spad{p})} belongs to \\axiom{\\spad{R}} or \\axiom{mvar(tail(\\spad{p})) < mvar(\\spad{p})},{} otherwise returns \\axiom{deepestTail(tail(\\spad{p}))}.")) (|tail| (($ $) "\\axiom{tail(\\spad{p})} returns its reductum,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|head| (($ $) "\\axiom{head(\\spad{p})} returns \\axiom{\\spad{p}} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading term (monomial in the AXIOM sense),{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|init| (($ $) "\\axiom{init(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading coefficient,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mdeg| (((|NonNegativeInteger|) $) "\\axiom{mdeg(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{0},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{0},{} otherwise,{} returns the degree of \\axiom{\\spad{p}} in its main variable.")) (|mvar| ((|#4| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}."))) NIL -((|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (LIST (QUOTE -1058) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-557))) (|HasCategory| |#2| (LIST (QUOTE -38) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -1012) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#4| (LIST (QUOTE -626) (QUOTE (-1196))))) -(-1085 R E V) +((|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-557))) (|HasCategory| |#2| (LIST (QUOTE -38) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -1013) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#4| (LIST (QUOTE -626) (QUOTE (-1197))))) +(-1086 R E V) ((|constructor| (NIL "A category for general multi-variate polynomials with coefficients in a ring,{} variables in an ordered set,{} and exponents from an ordered abelian monoid,{} with a \\axiomOp{sup} operation. When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\axiom{primitivePart!(\\spad{p})} replaces \\axiom{\\spad{p}} by its primitive part.")) (|gcd| ((|#1| |#1| $) "\\axiom{\\spad{gcd}(\\spad{r},{}\\spad{p})} returns the \\spad{gcd} of \\axiom{\\spad{r}} and the content of \\axiom{\\spad{p}}.")) (|nextsubResultant2| (($ $ $ $ $) "\\axiom{nextsubResultant2(\\spad{p},{}\\spad{q},{}\\spad{z},{}\\spad{s})} is the multivariate version of the operation \\axiomOpFrom{next_sousResultant2}{PseudoRemainderSequence} from the \\axiomType{PseudoRemainderSequence} constructor.")) (|LazardQuotient2| (($ $ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient2(\\spad{p},{}a,{}\\spad{b},{}\\spad{n})} returns \\axiom{(a**(\\spad{n}-1) * \\spad{p}) exquo \\spad{b**}(\\spad{n}-1)} assuming that this quotient does not fail.")) (|LazardQuotient| (($ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient(a,{}\\spad{b},{}\\spad{n})} returns \\axiom{a**n exquo \\spad{b**}(\\spad{n}-1)} assuming that this quotient does not fail.")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns the last non-zero subresultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|subResultantChain| (((|List| $) $ $) "\\axiom{subResultantChain(a,{}\\spad{b})},{} where \\axiom{a} and \\axiom{\\spad{b}} are not contant polynomials with the same main variable,{} returns the subresultant chain of \\axiom{a} and \\axiom{\\spad{b}}.")) (|resultant| (($ $ $) "\\axiom{resultant(a,{}\\spad{b})} computes the resultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedSubResultantGcd2(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}\\spad{cb}]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}\\spad{cb}]} otherwise produces an error.")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedSubResultantGcd1(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}\\spad{cb}]} otherwise produces an error.")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[ca,{}\\spad{cb},{}\\spad{r}]} such that \\axiom{\\spad{r}} is \\axiom{subResultantGcd(a,{}\\spad{b})} and we have \\axiom{ca * a + \\spad{cb} * \\spad{cb} = \\spad{r}} .")) (|subResultantGcd| (($ $ $) "\\axiom{subResultantGcd(a,{}\\spad{b})} computes a \\spad{gcd} of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}} with coefficients in the fraction field of the polynomial ring generated by their other variables over \\axiom{\\spad{R}}.")) (|exactQuotient!| (($ $ $) "\\axiom{exactQuotient!(a,{}\\spad{b})} replaces \\axiom{a} by \\axiom{exactQuotient(a,{}\\spad{b})}") (($ $ |#1|) "\\axiom{exactQuotient!(\\spad{p},{}\\spad{r})} replaces \\axiom{\\spad{p}} by \\axiom{exactQuotient(\\spad{p},{}\\spad{r})}.")) (|exactQuotient| (($ $ $) "\\axiom{exactQuotient(a,{}\\spad{b})} computes the exact quotient of \\axiom{a} by \\axiom{\\spad{b}},{} which is assumed to be a divisor of \\axiom{a}. No error is returned if this exact quotient fails!") (($ $ |#1|) "\\axiom{exactQuotient(\\spad{p},{}\\spad{r})} computes the exact quotient of \\axiom{\\spad{p}} by \\axiom{\\spad{r}},{} which is assumed to be a divisor of \\axiom{\\spad{p}}. No error is returned if this exact quotient fails!")) (|primPartElseUnitCanonical!| (($ $) "\\axiom{primPartElseUnitCanonical!(\\spad{p})} replaces \\axiom{\\spad{p}} by \\axiom{primPartElseUnitCanonical(\\spad{p})}.")) (|primPartElseUnitCanonical| (($ $) "\\axiom{primPartElseUnitCanonical(\\spad{p})} returns \\axiom{primitivePart(\\spad{p})} if \\axiom{\\spad{R}} is a \\spad{gcd}-domain,{} otherwise \\axiom{unitCanonical(\\spad{p})}.")) (|convert| (($ (|Polynomial| |#1|)) "\\axiom{convert(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}},{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.")) (|retract| (($ (|Polynomial| |#1|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#1|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#1|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|Polynomial| |#1|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#1|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#1|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.")) (|initiallyReduce| (($ $ $) "\\axiom{initiallyReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|headReduce| (($ $ $) "\\axiom{headReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| $) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{p},{}\\spad{q},{}\\spad{n}]} where \\axiom{\\spad{p} / q**n} represents the residue class of \\axiom{a} modulo \\axiom{\\spad{b}} and \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{q}} is \\axiom{init(\\spad{b})}.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} computes \\axiom{a mod \\spad{b}},{} if \\axiom{\\spad{b}} is monic as univariate polynomial in its main variable.")) (|pseudoDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{pseudoDivide(a,{}\\spad{b})} computes \\axiom{[pquo(a,{}\\spad{b}),{}prem(a,{}\\spad{b})]},{} both polynomials viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}},{} if \\axiom{\\spad{b}} is not a constant polynomial.")) (|lazyPseudoDivide| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $ |#3|) "\\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})},{} \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}] = lazyPremWithDefault(a,{}\\spad{b})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.")) (|lazyPremWithDefault| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $ |#3|) "\\axiom{lazyPremWithDefault(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b},{}\\spad{v})}.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $) "\\axiom{lazyPremWithDefault(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b})} and \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b})}.")) (|lazyPquo| (($ $ $ |#3|) "\\axiom{lazyPquo(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.") (($ $ $) "\\axiom{lazyPquo(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.")) (|lazyPrem| (($ $ $ |#3|) "\\axiom{lazyPrem(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} viewed as univariate polynomials in the variable \\axiom{\\spad{v}} such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.") (($ $ $) "\\axiom{lazyPrem(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.")) (|pquo| (($ $ $ |#3|) "\\axiom{pquo(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{pquo(a,{}\\spad{b})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|prem| (($ $ $ |#3|) "\\axiom{prem(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{prem(a,{}\\spad{b})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|normalized?| (((|Boolean|) $ (|List| $)) "\\axiom{normalized?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{normalized?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{normalized?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{a} and its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variable of \\axiom{\\spad{b}}")) (|initiallyReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{initiallyReduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{initiallyReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{initiallyReduced?(a,{}\\spad{b})} returns \\spad{false} iff there exists an iterated initial of \\axiom{a} which is not reduced \\spad{w}.\\spad{r}.\\spad{t} \\axiom{\\spad{b}}.")) (|headReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{headReduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{headReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{headReduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(head(a),{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|reduced?| (((|Boolean|) $ (|List| $)) "\\axiom{reduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{reduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{reduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(a,{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|supRittWu?| (((|Boolean|) $ $) "\\axiom{supRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is greater than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is less than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|RittWuCompare| (((|Union| (|Boolean|) "failed") $ $) "\\axiom{RittWuCompare(a,{}\\spad{b})} returns \\axiom{\"failed\"} if \\axiom{a} and \\axiom{\\spad{b}} have same rank \\spad{w}.\\spad{r}.\\spad{t}. Ritt and Wu Wen Tsun ordering using the refinement of Lazard,{} otherwise returns \\axiom{infRittWu?(a,{}\\spad{b})}.")) (|mainMonomials| (((|List| $) $) "\\axiom{mainMonomials(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [1],{} otherwise returns the list of the monomials of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainCoefficients| (((|List| $) $) "\\axiom{mainCoefficients(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [\\spad{p}],{} otherwise returns the list of the coefficients of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|leastMonomial| (($ $) "\\axiom{leastMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} the monomial of \\axiom{\\spad{p}} with lowest degree,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainMonomial| (($ $) "\\axiom{mainMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} \\axiom{mvar(\\spad{p})} raised to the power \\axiom{mdeg(\\spad{p})}.")) (|quasiMonic?| (((|Boolean|) $) "\\axiom{quasiMonic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff the initial of \\axiom{\\spad{p}} lies in the base ring \\axiom{\\spad{R}}.")) (|monic?| (((|Boolean|) $) "\\axiom{monic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff \\axiom{\\spad{p}} is monic as a univariate polynomial in its main variable.")) (|reductum| (($ $ |#3|) "\\axiom{reductum(\\spad{p},{}\\spad{v})} returns the reductum of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in \\axiom{\\spad{v}}.")) (|leadingCoefficient| (($ $ |#3|) "\\axiom{leadingCoefficient(\\spad{p},{}\\spad{v})} returns the leading coefficient of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as A univariate polynomial in \\axiom{\\spad{v}}.")) (|deepestInitial| (($ $) "\\axiom{deepestInitial(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the last term of \\axiom{iteratedInitials(\\spad{p})}.")) (|iteratedInitials| (((|List| $) $) "\\axiom{iteratedInitials(\\spad{p})} returns \\axiom{[]} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the list of the iterated initials of \\axiom{\\spad{p}}.")) (|deepestTail| (($ $) "\\axiom{deepestTail(\\spad{p})} returns \\axiom{0} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns tail(\\spad{p}),{} if \\axiom{tail(\\spad{p})} belongs to \\axiom{\\spad{R}} or \\axiom{mvar(tail(\\spad{p})) < mvar(\\spad{p})},{} otherwise returns \\axiom{deepestTail(tail(\\spad{p}))}.")) (|tail| (($ $) "\\axiom{tail(\\spad{p})} returns its reductum,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|head| (($ $) "\\axiom{head(\\spad{p})} returns \\axiom{\\spad{p}} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading term (monomial in the AXIOM sense),{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|init| (($ $) "\\axiom{init(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading coefficient,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mdeg| (((|NonNegativeInteger|) $) "\\axiom{mdeg(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{0},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{0},{} otherwise,{} returns the degree of \\axiom{\\spad{p}} in its main variable.")) (|mvar| ((|#3| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}."))) -(((-4465 "*") |has| |#1| (-174)) (-4456 |has| |#1| (-568)) (-4461 |has| |#1| (-6 -4461)) (-4458 . T) (-4457 . T) (-4460 . T)) +(((-4466 "*") |has| |#1| (-174)) (-4457 |has| |#1| (-568)) (-4462 |has| |#1| (-6 -4462)) (-4459 . T) (-4458 . T) (-4461 . T)) NIL -(-1086) +(-1087) ((|constructor| (NIL "This domain represents the `repeat' iterator syntax.")) (|body| (((|SpadAst|) $) "\\spad{body(e)} returns the body of the loop `e'.")) (|iterators| (((|List| (|SpadAst|)) $) "\\spad{iterators(e)} returns the list of iterators controlling the loop `e'."))) NIL NIL -(-1087 S |TheField| |ThePols|) +(-1088 S |TheField| |ThePols|) ((|constructor| (NIL "\\axiomType{RealRootCharacterizationCategory} provides common acces functions for all real root codings.")) (|relativeApprox| ((|#2| |#3| $ |#2|) "\\axiom{approximate(term,{}root,{}prec)} gives an approximation of \\axiom{term} over \\axiom{root} with precision \\axiom{prec}")) (|approximate| ((|#2| |#3| $ |#2|) "\\axiom{approximate(term,{}root,{}prec)} gives an approximation of \\axiom{term} over \\axiom{root} with precision \\axiom{prec}")) (|rootOf| (((|Union| $ "failed") |#3| (|PositiveInteger|)) "\\axiom{rootOf(pol,{}\\spad{n})} gives the \\spad{n}th root for the order of the Real Closure")) (|allRootsOf| (((|List| $) |#3|) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} in the Real Closure,{} assumed in order.")) (|definingPolynomial| ((|#3| $) "\\axiom{definingPolynomial(aRoot)} gives a polynomial such that \\axiom{definingPolynomial(aRoot).aRoot = 0}")) (|recip| (((|Union| |#3| "failed") |#3| $) "\\axiom{recip(pol,{}aRoot)} tries to inverse \\axiom{pol} interpreted as \\axiom{aRoot}")) (|positive?| (((|Boolean|) |#3| $) "\\axiom{positive?(pol,{}aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is positive")) (|negative?| (((|Boolean|) |#3| $) "\\axiom{negative?(pol,{}aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is negative")) (|zero?| (((|Boolean|) |#3| $) "\\axiom{zero?(pol,{}aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is \\axiom{0}")) (|sign| (((|Integer|) |#3| $) "\\axiom{sign(pol,{}aRoot)} gives the sign of \\axiom{pol} interpreted as \\axiom{aRoot}"))) NIL NIL -(-1088 |TheField| |ThePols|) +(-1089 |TheField| |ThePols|) ((|constructor| (NIL "\\axiomType{RealRootCharacterizationCategory} provides common acces functions for all real root codings.")) (|relativeApprox| ((|#1| |#2| $ |#1|) "\\axiom{approximate(term,{}root,{}prec)} gives an approximation of \\axiom{term} over \\axiom{root} with precision \\axiom{prec}")) (|approximate| ((|#1| |#2| $ |#1|) "\\axiom{approximate(term,{}root,{}prec)} gives an approximation of \\axiom{term} over \\axiom{root} with precision \\axiom{prec}")) (|rootOf| (((|Union| $ "failed") |#2| (|PositiveInteger|)) "\\axiom{rootOf(pol,{}\\spad{n})} gives the \\spad{n}th root for the order of the Real Closure")) (|allRootsOf| (((|List| $) |#2|) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} in the Real Closure,{} assumed in order.")) (|definingPolynomial| ((|#2| $) "\\axiom{definingPolynomial(aRoot)} gives a polynomial such that \\axiom{definingPolynomial(aRoot).aRoot = 0}")) (|recip| (((|Union| |#2| "failed") |#2| $) "\\axiom{recip(pol,{}aRoot)} tries to inverse \\axiom{pol} interpreted as \\axiom{aRoot}")) (|positive?| (((|Boolean|) |#2| $) "\\axiom{positive?(pol,{}aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is positive")) (|negative?| (((|Boolean|) |#2| $) "\\axiom{negative?(pol,{}aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is negative")) (|zero?| (((|Boolean|) |#2| $) "\\axiom{zero?(pol,{}aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is \\axiom{0}")) (|sign| (((|Integer|) |#2| $) "\\axiom{sign(pol,{}aRoot)} gives the sign of \\axiom{pol} interpreted as \\axiom{aRoot}"))) NIL NIL -(-1089 R E V P TS) +(-1090 R E V P TS) ((|constructor| (NIL "A package providing a new algorithm for solving polynomial systems by means of regular chains. Two ways of solving are proposed: in the sense of Zariski closure (like in Kalkbrener\\spad{'s} algorithm) or in the sense of the regular zeros (like in Wu,{} Wang or Lazard methods). This algorithm is valid for nay type of regular set. It does not care about the way a polynomial is added in an regular set,{} or how two quasi-components are compared (by an inclusion-test),{} or how the invertibility test is made in the tower of simple extensions associated with a regular set. These operations are realized respectively by the domain \\spad{TS} and the packages \\axiomType{QCMPACK}(\\spad{R},{}\\spad{E},{}\\spad{V},{}\\spad{P},{}\\spad{TS}) and \\axiomType{RSETGCD}(\\spad{R},{}\\spad{E},{}\\spad{V},{}\\spad{P},{}\\spad{TS}). The same way it does not care about the way univariate polynomial \\spad{gcd} (with coefficients in the tower of simple extensions associated with a regular set) are computed. The only requirement is that these \\spad{gcd} need to have invertible initials (normalized or not). WARNING. There is no need for a user to call diectly any operation of this package since they can be accessed by the domain \\axiom{\\spad{TS}}. Thus,{} the operations of this package are not documented.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}"))) NIL NIL -(-1090 S R E V P) +(-1091 S R E V P) ((|constructor| (NIL "The category of regular triangular sets,{} introduced under the name regular chains in [1] (and other papers). In [3] it is proved that regular triangular sets and towers of simple extensions of a field are equivalent notions. In the following definitions,{} all polynomials and ideals are taken from the polynomial ring \\spad{k[x1,...,xn]} where \\spad{k} is the fraction field of \\spad{R}. The triangular set \\spad{[t1,...,tm]} is regular iff for every \\spad{i} the initial of \\spad{ti+1} is invertible in the tower of simple extensions associated with \\spad{[t1,...,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} (\\spad{w}.\\spad{r}.\\spad{t}. Zariski topology). A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Lazard of a given triangular set \\spad{T} if it is a split of Lazard of \\spad{W(T)}. Note that if \\spad{[T1,...,Ts]} is a split of Lazard of \\spad{T} then it is also a split of Kalkbrener of \\spad{T}. The converse is \\spad{false}. This category provides operations related to both kinds of splits,{} the former being related to ideals decomposition whereas the latter deals with varieties decomposition. See the example illustrating the \\spadtype{RegularTriangularSet} constructor for more explanations about decompositions by means of regular triangular sets. \\newline References : \\indented{1}{[1] \\spad{M}. KALKBRENER \"Three contributions to elimination theory\"} \\indented{5}{\\spad{Phd} Thesis,{} University of Linz,{} Austria,{} 1991.} \\indented{1}{[2] \\spad{M}. KALKBRENER \"Algorithmic properties of polynomial rings\"} \\indented{5}{Journal of Symbol. Comp. 1998} \\indented{1}{[3] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)} \\indented{1}{[4] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|zeroSetSplit| (((|List| $) (|List| |#5|) (|Boolean|)) "\\spad{zeroSetSplit(lp,clos?)} returns \\spad{lts} a split of Kalkbrener of the radical ideal associated with \\spad{lp}. If \\spad{clos?} is \\spad{false},{} it is also a decomposition of the variety associated with \\spad{lp} into the regular zero set of the \\spad{ts} in \\spad{lts} (or,{} in other words,{} a split of Lazard of this variety). See the example illustrating the \\spadtype{RegularTriangularSet} constructor for more explanations about decompositions by means of regular triangular sets.")) (|extend| (((|List| $) (|List| |#5|) (|List| $)) "\\spad{extend(lp,lts)} returns the same as \\spad{concat([extend(lp,ts) for ts in lts])|}") (((|List| $) (|List| |#5|) $) "\\spad{extend(lp,ts)} returns \\spad{ts} if \\spad{empty? lp} \\spad{extend(p,ts)} if \\spad{lp = [p]} else \\spad{extend(first lp, extend(rest lp, ts))}") (((|List| $) |#5| (|List| $)) "\\spad{extend(p,lts)} returns the same as \\spad{concat([extend(p,ts) for ts in lts])|}") (((|List| $) |#5| $) "\\spad{extend(p,ts)} assumes that \\spad{p} is a non-constant polynomial whose main variable is greater than any variable of \\spad{ts}. Then it returns a split of Kalkbrener of \\spad{ts+p}. This may not be \\spad{ts+p} itself,{} if for instance \\spad{ts+p} is not a regular triangular set.")) (|internalAugment| (($ (|List| |#5|) $) "\\spad{internalAugment(lp,ts)} returns \\spad{ts} if \\spad{lp} is empty otherwise returns \\spad{internalAugment(rest lp, internalAugment(first lp, ts))}") (($ |#5| $) "\\spad{internalAugment(p,ts)} assumes that \\spad{augment(p,ts)} returns a singleton and returns it.")) (|augment| (((|List| $) (|List| |#5|) (|List| $)) "\\spad{augment(lp,lts)} returns the same as \\spad{concat([augment(lp,ts) for ts in lts])}") (((|List| $) (|List| |#5|) $) "\\spad{augment(lp,ts)} returns \\spad{ts} if \\spad{empty? lp},{} \\spad{augment(p,ts)} if \\spad{lp = [p]},{} otherwise \\spad{augment(first lp, augment(rest lp, ts))}") (((|List| $) |#5| (|List| $)) "\\spad{augment(p,lts)} returns the same as \\spad{concat([augment(p,ts) for ts in lts])}") (((|List| $) |#5| $) "\\spad{augment(p,ts)} assumes that \\spad{p} is a non-constant polynomial whose main variable is greater than any variable of \\spad{ts}. This operation assumes also that if \\spad{p} is added to \\spad{ts} the resulting set,{} say \\spad{ts+p},{} is a regular triangular set. Then it returns a split of Kalkbrener of \\spad{ts+p}. This may not be \\spad{ts+p} itself,{} if for instance \\spad{ts+p} is required to be square-free.")) (|intersect| (((|List| $) |#5| (|List| $)) "\\spad{intersect(p,lts)} returns the same as \\spad{intersect([p],lts)}") (((|List| $) (|List| |#5|) (|List| $)) "\\spad{intersect(lp,lts)} returns the same as \\spad{concat([intersect(lp,ts) for ts in lts])|}") (((|List| $) (|List| |#5|) $) "\\spad{intersect(lp,ts)} returns \\spad{lts} a split of Lazard of the intersection of the affine variety associated with \\spad{lp} and the regular zero set of \\spad{ts}.") (((|List| $) |#5| $) "\\spad{intersect(p,ts)} returns the same as \\spad{intersect([p],ts)}")) (|squareFreePart| (((|List| (|Record| (|:| |val| |#5|) (|:| |tower| $))) |#5| $) "\\spad{squareFreePart(p,ts)} returns \\spad{lpwt} such that \\spad{lpwt.i.val} is a square-free polynomial \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower},{} this polynomial being associated with \\spad{p} modulo \\spad{lpwt.i.tower},{} for every \\spad{i}. Moreover,{} the list of the \\spad{lpwt.i.tower} is a split of Kalkbrener of \\spad{ts}. WARNING: This assumes that \\spad{p} is a non-constant polynomial such that if \\spad{p} is added to \\spad{ts},{} then the resulting set is a regular triangular set.")) (|lastSubResultant| (((|List| (|Record| (|:| |val| |#5|) (|:| |tower| $))) |#5| |#5| $) "\\spad{lastSubResultant(p1,p2,ts)} returns \\spad{lpwt} such that \\spad{lpwt.i.val} is a quasi-monic \\spad{gcd} of \\spad{p1} and \\spad{p2} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower},{} for every \\spad{i},{} and such that the list of the \\spad{lpwt.i.tower} is a split of Kalkbrener of \\spad{ts}. Moreover,{} if \\spad{p1} and \\spad{p2} do not have a non-trivial \\spad{gcd} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower} then \\spad{lpwt.i.val} is the resultant of these polynomials \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower}. This assumes that \\spad{p1} and \\spad{p2} have the same maim variable and that this variable is greater that any variable occurring in \\spad{ts}.")) (|lastSubResultantElseSplit| (((|Union| |#5| (|List| $)) |#5| |#5| $) "\\spad{lastSubResultantElseSplit(p1,p2,ts)} returns either \\spad{g} a quasi-monic \\spad{gcd} of \\spad{p1} and \\spad{p2} \\spad{w}.\\spad{r}.\\spad{t}. the \\spad{ts} or a split of Kalkbrener of \\spad{ts}. This assumes that \\spad{p1} and \\spad{p2} have the same maim variable and that this variable is greater that any variable occurring in \\spad{ts}.")) (|invertibleSet| (((|List| $) |#5| $) "\\spad{invertibleSet(p,ts)} returns a split of Kalkbrener of the quotient ideal of the ideal \\axiom{\\spad{I}} by \\spad{p} where \\spad{I} is the radical of saturated of \\spad{ts}.")) (|invertible?| (((|Boolean|) |#5| $) "\\spad{invertible?(p,ts)} returns \\spad{true} iff \\spad{p} is invertible in the tower associated with \\spad{ts}.") (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| $))) |#5| $) "\\spad{invertible?(p,ts)} returns \\spad{lbwt} where \\spad{lbwt.i} is the result of \\spad{invertibleElseSplit?(p,lbwt.i.tower)} and the list of the \\spad{(lqrwt.i).tower} is a split of Kalkbrener of \\spad{ts}.")) (|invertibleElseSplit?| (((|Union| (|Boolean|) (|List| $)) |#5| $) "\\spad{invertibleElseSplit?(p,ts)} returns \\spad{true} (resp. \\spad{false}) if \\spad{p} is invertible in the tower associated with \\spad{ts} or returns a split of Kalkbrener of \\spad{ts}.")) (|purelyAlgebraicLeadingMonomial?| (((|Boolean|) |#5| $) "\\spad{purelyAlgebraicLeadingMonomial?(p,ts)} returns \\spad{true} iff the main variable of any non-constant iterarted initial of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}.")) (|algebraicCoefficients?| (((|Boolean|) |#5| $) "\\spad{algebraicCoefficients?(p,ts)} returns \\spad{true} iff every variable of \\spad{p} which is not the main one of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}.")) (|purelyTranscendental?| (((|Boolean|) |#5| $) "\\spad{purelyTranscendental?(p,ts)} returns \\spad{true} iff every variable of \\spad{p} is not algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}")) (|purelyAlgebraic?| (((|Boolean|) $) "\\spad{purelyAlgebraic?(ts)} returns \\spad{true} iff for every algebraic variable \\spad{v} of \\spad{ts} we have \\spad{algebraicCoefficients?(t_v,ts_v_-)} where \\spad{ts_v} is \\axiomOpFrom{select}{TriangularSetCategory}(\\spad{ts},{}\\spad{v}) and \\spad{ts_v_-} is \\axiomOpFrom{collectUnder}{TriangularSetCategory}(\\spad{ts},{}\\spad{v}).") (((|Boolean|) |#5| $) "\\spad{purelyAlgebraic?(p,ts)} returns \\spad{true} iff every variable of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}."))) NIL NIL -(-1091 R E V P) +(-1092 R E V P) ((|constructor| (NIL "The category of regular triangular sets,{} introduced under the name regular chains in [1] (and other papers). In [3] it is proved that regular triangular sets and towers of simple extensions of a field are equivalent notions. In the following definitions,{} all polynomials and ideals are taken from the polynomial ring \\spad{k[x1,...,xn]} where \\spad{k} is the fraction field of \\spad{R}. The triangular set \\spad{[t1,...,tm]} is regular iff for every \\spad{i} the initial of \\spad{ti+1} is invertible in the tower of simple extensions associated with \\spad{[t1,...,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} (\\spad{w}.\\spad{r}.\\spad{t}. Zariski topology). A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Lazard of a given triangular set \\spad{T} if it is a split of Lazard of \\spad{W(T)}. Note that if \\spad{[T1,...,Ts]} is a split of Lazard of \\spad{T} then it is also a split of Kalkbrener of \\spad{T}. The converse is \\spad{false}. This category provides operations related to both kinds of splits,{} the former being related to ideals decomposition whereas the latter deals with varieties decomposition. See the example illustrating the \\spadtype{RegularTriangularSet} constructor for more explanations about decompositions by means of regular triangular sets. \\newline References : \\indented{1}{[1] \\spad{M}. KALKBRENER \"Three contributions to elimination theory\"} \\indented{5}{\\spad{Phd} Thesis,{} University of Linz,{} Austria,{} 1991.} \\indented{1}{[2] \\spad{M}. KALKBRENER \"Algorithmic properties of polynomial rings\"} \\indented{5}{Journal of Symbol. Comp. 1998} \\indented{1}{[3] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)} \\indented{1}{[4] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|zeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|)) "\\spad{zeroSetSplit(lp,clos?)} returns \\spad{lts} a split of Kalkbrener of the radical ideal associated with \\spad{lp}. If \\spad{clos?} is \\spad{false},{} it is also a decomposition of the variety associated with \\spad{lp} into the regular zero set of the \\spad{ts} in \\spad{lts} (or,{} in other words,{} a split of Lazard of this variety). See the example illustrating the \\spadtype{RegularTriangularSet} constructor for more explanations about decompositions by means of regular triangular sets.")) (|extend| (((|List| $) (|List| |#4|) (|List| $)) "\\spad{extend(lp,lts)} returns the same as \\spad{concat([extend(lp,ts) for ts in lts])|}") (((|List| $) (|List| |#4|) $) "\\spad{extend(lp,ts)} returns \\spad{ts} if \\spad{empty? lp} \\spad{extend(p,ts)} if \\spad{lp = [p]} else \\spad{extend(first lp, extend(rest lp, ts))}") (((|List| $) |#4| (|List| $)) "\\spad{extend(p,lts)} returns the same as \\spad{concat([extend(p,ts) for ts in lts])|}") (((|List| $) |#4| $) "\\spad{extend(p,ts)} assumes that \\spad{p} is a non-constant polynomial whose main variable is greater than any variable of \\spad{ts}. Then it returns a split of Kalkbrener of \\spad{ts+p}. This may not be \\spad{ts+p} itself,{} if for instance \\spad{ts+p} is not a regular triangular set.")) (|internalAugment| (($ (|List| |#4|) $) "\\spad{internalAugment(lp,ts)} returns \\spad{ts} if \\spad{lp} is empty otherwise returns \\spad{internalAugment(rest lp, internalAugment(first lp, ts))}") (($ |#4| $) "\\spad{internalAugment(p,ts)} assumes that \\spad{augment(p,ts)} returns a singleton and returns it.")) (|augment| (((|List| $) (|List| |#4|) (|List| $)) "\\spad{augment(lp,lts)} returns the same as \\spad{concat([augment(lp,ts) for ts in lts])}") (((|List| $) (|List| |#4|) $) "\\spad{augment(lp,ts)} returns \\spad{ts} if \\spad{empty? lp},{} \\spad{augment(p,ts)} if \\spad{lp = [p]},{} otherwise \\spad{augment(first lp, augment(rest lp, ts))}") (((|List| $) |#4| (|List| $)) "\\spad{augment(p,lts)} returns the same as \\spad{concat([augment(p,ts) for ts in lts])}") (((|List| $) |#4| $) "\\spad{augment(p,ts)} assumes that \\spad{p} is a non-constant polynomial whose main variable is greater than any variable of \\spad{ts}. This operation assumes also that if \\spad{p} is added to \\spad{ts} the resulting set,{} say \\spad{ts+p},{} is a regular triangular set. Then it returns a split of Kalkbrener of \\spad{ts+p}. This may not be \\spad{ts+p} itself,{} if for instance \\spad{ts+p} is required to be square-free.")) (|intersect| (((|List| $) |#4| (|List| $)) "\\spad{intersect(p,lts)} returns the same as \\spad{intersect([p],lts)}") (((|List| $) (|List| |#4|) (|List| $)) "\\spad{intersect(lp,lts)} returns the same as \\spad{concat([intersect(lp,ts) for ts in lts])|}") (((|List| $) (|List| |#4|) $) "\\spad{intersect(lp,ts)} returns \\spad{lts} a split of Lazard of the intersection of the affine variety associated with \\spad{lp} and the regular zero set of \\spad{ts}.") (((|List| $) |#4| $) "\\spad{intersect(p,ts)} returns the same as \\spad{intersect([p],ts)}")) (|squareFreePart| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| $))) |#4| $) "\\spad{squareFreePart(p,ts)} returns \\spad{lpwt} such that \\spad{lpwt.i.val} is a square-free polynomial \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower},{} this polynomial being associated with \\spad{p} modulo \\spad{lpwt.i.tower},{} for every \\spad{i}. Moreover,{} the list of the \\spad{lpwt.i.tower} is a split of Kalkbrener of \\spad{ts}. WARNING: This assumes that \\spad{p} is a non-constant polynomial such that if \\spad{p} is added to \\spad{ts},{} then the resulting set is a regular triangular set.")) (|lastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| $))) |#4| |#4| $) "\\spad{lastSubResultant(p1,p2,ts)} returns \\spad{lpwt} such that \\spad{lpwt.i.val} is a quasi-monic \\spad{gcd} of \\spad{p1} and \\spad{p2} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower},{} for every \\spad{i},{} and such that the list of the \\spad{lpwt.i.tower} is a split of Kalkbrener of \\spad{ts}. Moreover,{} if \\spad{p1} and \\spad{p2} do not have a non-trivial \\spad{gcd} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower} then \\spad{lpwt.i.val} is the resultant of these polynomials \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower}. This assumes that \\spad{p1} and \\spad{p2} have the same maim variable and that this variable is greater that any variable occurring in \\spad{ts}.")) (|lastSubResultantElseSplit| (((|Union| |#4| (|List| $)) |#4| |#4| $) "\\spad{lastSubResultantElseSplit(p1,p2,ts)} returns either \\spad{g} a quasi-monic \\spad{gcd} of \\spad{p1} and \\spad{p2} \\spad{w}.\\spad{r}.\\spad{t}. the \\spad{ts} or a split of Kalkbrener of \\spad{ts}. This assumes that \\spad{p1} and \\spad{p2} have the same maim variable and that this variable is greater that any variable occurring in \\spad{ts}.")) (|invertibleSet| (((|List| $) |#4| $) "\\spad{invertibleSet(p,ts)} returns a split of Kalkbrener of the quotient ideal of the ideal \\axiom{\\spad{I}} by \\spad{p} where \\spad{I} is the radical of saturated of \\spad{ts}.")) (|invertible?| (((|Boolean|) |#4| $) "\\spad{invertible?(p,ts)} returns \\spad{true} iff \\spad{p} is invertible in the tower associated with \\spad{ts}.") (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| $))) |#4| $) "\\spad{invertible?(p,ts)} returns \\spad{lbwt} where \\spad{lbwt.i} is the result of \\spad{invertibleElseSplit?(p,lbwt.i.tower)} and the list of the \\spad{(lqrwt.i).tower} is a split of Kalkbrener of \\spad{ts}.")) (|invertibleElseSplit?| (((|Union| (|Boolean|) (|List| $)) |#4| $) "\\spad{invertibleElseSplit?(p,ts)} returns \\spad{true} (resp. \\spad{false}) if \\spad{p} is invertible in the tower associated with \\spad{ts} or returns a split of Kalkbrener of \\spad{ts}.")) (|purelyAlgebraicLeadingMonomial?| (((|Boolean|) |#4| $) "\\spad{purelyAlgebraicLeadingMonomial?(p,ts)} returns \\spad{true} iff the main variable of any non-constant iterarted initial of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}.")) (|algebraicCoefficients?| (((|Boolean|) |#4| $) "\\spad{algebraicCoefficients?(p,ts)} returns \\spad{true} iff every variable of \\spad{p} which is not the main one of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}.")) (|purelyTranscendental?| (((|Boolean|) |#4| $) "\\spad{purelyTranscendental?(p,ts)} returns \\spad{true} iff every variable of \\spad{p} is not algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}")) (|purelyAlgebraic?| (((|Boolean|) $) "\\spad{purelyAlgebraic?(ts)} returns \\spad{true} iff for every algebraic variable \\spad{v} of \\spad{ts} we have \\spad{algebraicCoefficients?(t_v,ts_v_-)} where \\spad{ts_v} is \\axiomOpFrom{select}{TriangularSetCategory}(\\spad{ts},{}\\spad{v}) and \\spad{ts_v_-} is \\axiomOpFrom{collectUnder}{TriangularSetCategory}(\\spad{ts},{}\\spad{v}).") (((|Boolean|) |#4| $) "\\spad{purelyAlgebraic?(p,ts)} returns \\spad{true} iff every variable of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}."))) -((-4464 . T) (-4463 . T)) +((-4465 . T) (-4464 . T)) NIL -(-1092 R E V P TS) +(-1093 R E V P TS) ((|constructor| (NIL "An internal package for computing gcds and resultants of univariate polynomials with coefficients in a tower of simple extensions of a field.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA and \\spad{R}. RIOBOO \"Computations of \\spad{gcd} over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of AAECC11} \\indented{5}{Paris,{} 1995.} \\indented{1}{[2] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|toseSquareFreePart| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{toseSquareFreePart(\\spad{p},{}\\spad{ts})} has the same specifications as \\axiomOpFrom{squareFreePart}{RegularTriangularSetCategory}.")) (|toseInvertibleSet| (((|List| |#5|) |#4| |#5|) "\\axiom{toseInvertibleSet(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} has the same specifications as \\axiomOpFrom{invertibleSet}{RegularTriangularSetCategory}.")) (|toseInvertible?| (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{toseInvertible?(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} has the same specifications as \\axiomOpFrom{invertible?}{RegularTriangularSetCategory}.") (((|Boolean|) |#4| |#5|) "\\axiom{toseInvertible?(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} has the same specifications as \\axiomOpFrom{invertible?}{RegularTriangularSetCategory}.")) (|toseLastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#4| |#5|) "\\axiom{toseLastSubResultant(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} has the same specifications as \\axiomOpFrom{lastSubResultant}{RegularTriangularSetCategory}.")) (|integralLastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#4| |#5|) "\\axiom{integralLastSubResultant(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} is an internal subroutine,{} exported only for developement.")) (|internalLastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) |#3| (|Boolean|)) "\\axiom{internalLastSubResultant(lpwt,{}\\spad{v},{}flag)} is an internal subroutine,{} exported only for developement.") (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#4| |#5| (|Boolean|) (|Boolean|)) "\\axiom{internalLastSubResultant(\\spad{p1},{}\\spad{p2},{}\\spad{ts},{}inv?,{}break?)} is an internal subroutine,{} exported only for developement.")) (|prepareSubResAlgo| (((|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) |#4| |#4| |#5|) "\\axiom{prepareSubResAlgo(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} is an internal subroutine,{} exported only for developement.")) (|stopTableInvSet!| (((|Void|)) "\\axiom{stopTableInvSet!()} is an internal subroutine,{} exported only for developement.")) (|startTableInvSet!| (((|Void|) (|String|) (|String|) (|String|)) "\\axiom{startTableInvSet!(\\spad{s1},{}\\spad{s2},{}\\spad{s3})} is an internal subroutine,{} exported only for developement.")) (|stopTableGcd!| (((|Void|)) "\\axiom{stopTableGcd!()} is an internal subroutine,{} exported only for developement.")) (|startTableGcd!| (((|Void|) (|String|) (|String|) (|String|)) "\\axiom{startTableGcd!(\\spad{s1},{}\\spad{s2},{}\\spad{s3})} is an internal subroutine,{} exported only for developement."))) NIL NIL -(-1093) +(-1094) ((|constructor| (NIL "This domain represents `restrict' expressions.")) (|target| (((|TypeAst|) $) "\\spad{target(e)} returns the target type of the conversion..")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression being converted."))) NIL NIL -(-1094) +(-1095) ((|constructor| (NIL "This is the datatype of OpenAxiom runtime values. It exists solely for internal purposes.")) (|eq| (((|Boolean|) $ $) "\\spad{eq(x,y)} holds if both values \\spad{x} and \\spad{y} resides at the same address in memory."))) NIL NIL -(-1095 |f|) +(-1096 |f|) ((|constructor| (NIL "This domain implements named rules")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) NIL NIL -(-1096 |Base| R -2117) +(-1097 |Base| R -1959) ((|constructor| (NIL "\\indented{1}{Rules for the pattern matcher} Author: Manuel Bronstein Date Created: 24 Oct 1988 Date Last Updated: 26 October 1993 Keywords: pattern,{} matching,{} rule.")) (|quotedOperators| (((|List| (|Symbol|)) $) "\\spad{quotedOperators(r)} returns the list of operators on the right hand side of \\spad{r} that are considered quoted,{} that is they are not evaluated during any rewrite,{} but just applied formally to their arguments.")) (|elt| ((|#3| $ |#3| (|PositiveInteger|)) "\\spad{elt(r,f,n)} or \\spad{r}(\\spad{f},{} \\spad{n}) applies the rule \\spad{r} to \\spad{f} at most \\spad{n} times.")) (|rhs| ((|#3| $) "\\spad{rhs(r)} returns the right hand side of the rule \\spad{r}.")) (|lhs| ((|#3| $) "\\spad{lhs(r)} returns the left hand side of the rule \\spad{r}.")) (|pattern| (((|Pattern| |#1|) $) "\\spad{pattern(r)} returns the pattern corresponding to the left hand side of the rule \\spad{r}.")) (|suchThat| (($ $ (|List| (|Symbol|)) (|Mapping| (|Boolean|) (|List| |#3|))) "\\spad{suchThat(r, [a1,...,an], f)} returns the rewrite rule \\spad{r} with the predicate \\spad{f(a1,...,an)} attached to it.")) (|rule| (($ |#3| |#3| (|List| (|Symbol|))) "\\spad{rule(f, g, [f1,...,fn])} creates the rewrite rule \\spad{f == eval(eval(g, g is f), [f1,...,fn])},{} that is a rule with left-hand side \\spad{f} and right-hand side \\spad{g}; The symbols \\spad{f1},{}...,{}\\spad{fn} are the operators that are considered quoted,{} that is they are not evaluated during any rewrite,{} but just applied formally to their arguments.") (($ |#3| |#3|) "\\spad{rule(f, g)} creates the rewrite rule: \\spad{f == eval(g, g is f)},{} with left-hand side \\spad{f} and right-hand side \\spad{g}."))) NIL NIL -(-1097 |Base| R -2117) +(-1098 |Base| R -1959) ((|constructor| (NIL "A ruleset is a set of pattern matching rules grouped together.")) (|elt| ((|#3| $ |#3| (|PositiveInteger|)) "\\spad{elt(r,f,n)} or \\spad{r}(\\spad{f},{} \\spad{n}) applies all the rules of \\spad{r} to \\spad{f} at most \\spad{n} times.")) (|rules| (((|List| (|RewriteRule| |#1| |#2| |#3|)) $) "\\spad{rules(r)} returns the rules contained in \\spad{r}.")) (|ruleset| (($ (|List| (|RewriteRule| |#1| |#2| |#3|))) "\\spad{ruleset([r1,...,rn])} creates the rule set \\spad{{r1,...,rn}}."))) NIL NIL -(-1098 R |ls|) +(-1099 R |ls|) ((|constructor| (NIL "\\indented{1}{A package for computing the rational univariate representation} \\indented{1}{of a zero-dimensional algebraic variety given by a regular} \\indented{1}{triangular set. This package is essentially an interface for the} \\spadtype{InternalRationalUnivariateRepresentationPackage} constructor. It is used in the \\spadtype{ZeroDimensionalSolvePackage} for solving polynomial systems with finitely many solutions.")) (|rur| (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{rur(lp,univ?,check?)} returns the same as \\spad{rur(lp,true)}. Moreover,{} if \\spad{check?} is \\spad{true} then the result is checked.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|))) "\\spad{rur(lp)} returns the same as \\spad{rur(lp,true)}") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{rur(lp,univ?)} returns a rational univariate representation of \\spad{lp}. This assumes that \\spad{lp} defines a regular triangular \\spad{ts} whose associated variety is zero-dimensional over \\spad{R}. \\spad{rur(lp,univ?)} returns a list of items \\spad{[u,lc]} where \\spad{u} is an irreducible univariate polynomial and each \\spad{c} in \\spad{lc} involves two variables: one from \\spad{ls},{} called the coordinate of \\spad{c},{} and an extra variable which represents any root of \\spad{u}. Every root of \\spad{u} leads to a tuple of values for the coordinates of \\spad{lc}. Moreover,{} a point \\spad{x} belongs to the variety associated with \\spad{lp} iff there exists an item \\spad{[u,lc]} in \\spad{rur(lp,univ?)} and a root \\spad{r} of \\spad{u} such that \\spad{x} is given by the tuple of values for the coordinates of \\spad{lc} evaluated at \\spad{r}. If \\spad{univ?} is \\spad{true} then each polynomial \\spad{c} will have a constant leading coefficient \\spad{w}.\\spad{r}.\\spad{t}. its coordinate. See the example which illustrates the \\spadtype{ZeroDimensionalSolvePackage} package constructor."))) NIL NIL -(-1099 UP SAE UPA) +(-1100 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 -(-1100 R UP M) +(-1101 R UP M) ((|constructor| (NIL "Domain which represents simple algebraic extensions of arbitrary rings. The first argument to the domain,{} \\spad{R},{} is the underlying ring,{} the second argument is a domain of univariate polynomials over \\spad{K},{} while the last argument specifies the defining minimal polynomial. The elements of the domain are canonically represented as polynomials of degree less than that of the minimal polynomial with coefficients in \\spad{R}. The second argument is both the type of the third argument and the underlying representation used by \\spadtype{SAE} itself."))) -((-4456 |has| |#1| (-374)) (-4461 |has| |#1| (-374)) (-4455 |has| |#1| (-374)) ((-4465 "*") . T) (-4457 . T) (-4458 . T) (-4460 . 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T) (-4458 . T) (-4459 . T) (-4461 . T)) +((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-360))) (-2758 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-360)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-379))) (-2758 (-12 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (QUOTE (-360)))) (-2758 (-12 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-374)))) (-12 (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (QUOTE (-360)))) (-2758 (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1197))))) (-12 (|HasCategory| |#1| (QUOTE (-360))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1197)))))) (-2758 (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1197))))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -919) (QUOTE (-1197)))))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))) (-2758 (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576)))) (-2758 (-12 (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-374)))) (|HasCategory| |#1| (QUOTE (-360)))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -919) (QUOTE (-1197))))) (-12 (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (QUOTE (-374)))) (-12 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-374)))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1197)))))) +(-1102 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 -(-1102) +(-1103) ((|constructor| (NIL "This trivial domain lets us build Univariate Polynomials in an anonymous variable"))) NIL NIL -(-1103) +(-1104) ((|constructor| (NIL "This is the category of Spad syntax objects."))) NIL NIL -(-1104 S) +(-1105 S) ((|constructor| (NIL "\\indented{1}{Cache of elements in a set} Author: Manuel Bronstein Date Created: 31 Oct 1988 Date Last Updated: 14 May 1991 \\indented{2}{A sorted cache of a cachable set \\spad{S} is a dynamic structure that} \\indented{2}{keeps the elements of \\spad{S} sorted and assigns an integer to each} \\indented{2}{element of \\spad{S} once it is in the cache. This way,{} equality and ordering} \\indented{2}{on \\spad{S} are tested directly on the integers associated with the elements} \\indented{2}{of \\spad{S},{} once they have been entered in the cache.}")) (|enterInCache| ((|#1| |#1| (|Mapping| (|Integer|) |#1| |#1|)) "\\spad{enterInCache(x, f)} enters \\spad{x} in the cache,{} calling \\spad{f(x, y)} to determine whether \\spad{x < y (f(x,y) < 0), x = y (f(x,y) = 0)},{} or \\spad{x > y (f(x,y) > 0)}. It returns \\spad{x} with an integer associated with it.") ((|#1| |#1| (|Mapping| (|Boolean|) |#1|)) "\\spad{enterInCache(x, f)} enters \\spad{x} in the cache,{} calling \\spad{f(y)} to determine whether \\spad{x} is equal to \\spad{y}. It returns \\spad{x} with an integer associated with it.")) (|cache| (((|List| |#1|)) "\\spad{cache()} returns the current cache as a list.")) (|clearCache| (((|Void|)) "\\spad{clearCache()} empties the cache."))) NIL NIL -(-1105) +(-1106) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. A `Scope' is a sequence of contours.")) (|currentCategoryFrame| (($) "\\spad{currentCategoryFrame()} returns the category frame currently in effect.")) (|currentScope| (($) "\\spad{currentScope()} returns the scope currently in effect")) (|pushNewContour| (($ (|Binding|) $) "\\spad{pushNewContour(b,s)} pushs a new contour with sole binding \\spad{`b'}.")) (|findBinding| (((|Maybe| (|Binding|)) (|Identifier|) $) "\\spad{findBinding(n,s)} returns the first binding of \\spad{`n'} in \\spad{`s'}; otherwise `nothing'.")) (|contours| (((|List| (|Contour|)) $) "\\spad{contours(s)} returns the list of contours in scope \\spad{s}.")) (|empty| (($) "\\spad{empty()} returns an empty scope."))) NIL NIL -(-1106 R) +(-1107 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 -(-1107 R) +(-1108 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. \\blankline"))) -(((-4465 "*") |has| |#1| (-174)) (-4456 |has| |#1| (-568)) (-4461 |has| |#1| (-6 -4461)) (-4458 . T) (-4457 . T) (-4460 . T)) -((|HasCategory| |#1| (QUOTE (-927))) (-3794 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-927)))) (-3794 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-927)))) (-3794 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-927)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-3794 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasCategory| (-1108 (-1196)) (LIST (QUOTE -900) (QUOTE (-390)))) (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-390))))) (-12 (|HasCategory| (-1108 (-1196)) (LIST (QUOTE -900) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-576))))) (-12 (|HasCategory| (-1108 (-1196)) (LIST (QUOTE -626) (LIST (QUOTE -906) (QUOTE (-390))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -906) (QUOTE (-390)))))) (-12 (|HasCategory| (-1108 (-1196)) (LIST (QUOTE -626) (LIST (QUOTE -906) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -906) (QUOTE (-576)))))) (-12 (|HasCategory| (-1108 (-1196)) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1058) (QUOTE (-576)))) (-3794 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1058) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#1| (LIST (QUOTE -1058) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (LIST (QUOTE -918) (QUOTE (-1196)))) (|HasCategory| |#1| (LIST (QUOTE -916) (QUOTE (-1196)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasAttribute| |#1| (QUOTE -4461)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-927)))) (-3794 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-927)))) (|HasCategory| |#1| (QUOTE (-146))))) -(-1108 S) +(((-4466 "*") |has| |#1| (-174)) (-4457 |has| |#1| (-568)) (-4462 |has| |#1| (-6 -4462)) (-4459 . T) (-4458 . T) (-4461 . T)) +((|HasCategory| |#1| (QUOTE (-928))) (-2758 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-928)))) (-2758 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-928)))) (-2758 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-928)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-2758 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasCategory| (-1109 (-1197)) (LIST (QUOTE -901) (QUOTE (-390)))) (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-390))))) (-12 (|HasCategory| (-1109 (-1197)) (LIST (QUOTE -901) (QUOTE (-576)))) (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-576))))) (-12 (|HasCategory| (-1109 (-1197)) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390)))))) (-12 (|HasCategory| (-1109 (-1197)) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576)))))) (-12 (|HasCategory| (-1109 (-1197)) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576)))) (-2758 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-237))) (|HasCategory| |#1| (LIST (QUOTE -919) (QUOTE (-1197)))) (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasAttribute| |#1| (QUOTE -4462)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-928)))) (-2758 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-928)))) (|HasCategory| |#1| (QUOTE (-146))))) +(-1109 S) ((|constructor| (NIL "\\spadtype{OrderlyDifferentialVariable} adds a commonly used sequential ranking to the set of derivatives of an ordered list of differential indeterminates. A sequential ranking is a ranking \\spadfun{<} of the derivatives with the property that for any derivative \\spad{v},{} there are only a finite number of derivatives \\spad{u} with \\spad{u} \\spadfun{<} \\spad{v}. This domain belongs to \\spadtype{DifferentialVariableCategory}. It defines \\spadfun{weight} to be just \\spadfun{order},{} and it defines a sequential ranking \\spadfun{<} on derivatives \\spad{u} by the lexicographic order on the pair (\\spadfun{variable}(\\spad{u}),{} \\spadfun{order}(\\spad{u}))."))) NIL NIL -(-1109 R S) +(-1110 R S) ((|constructor| (NIL "This package provides operations for mapping functions onto segments.")) (|map| (((|List| |#2|) (|Mapping| |#2| |#1|) (|Segment| |#1|)) "\\spad{map(f,s)} expands the segment \\spad{s},{} applying \\spad{f} to each value. For example,{} if \\spad{s = l..h by k},{} then the list \\spad{[f(l), f(l+k),..., f(lN)]} is computed,{} where \\spad{lN <= h < lN+k}.") (((|Segment| |#2|) (|Mapping| |#2| |#1|) (|Segment| |#1|)) "\\spad{map(f,l..h)} returns a new segment \\spad{f(l)..f(h)}."))) NIL ((|HasCategory| |#1| (QUOTE (-860)))) -(-1110) +(-1111) ((|constructor| (NIL "This domain represents segement expressions.")) (|bounds| (((|List| (|SpadAst|)) $) "\\spad{bounds(s)} returns the bounds of the segment \\spad{`s'}. If \\spad{`s'} designates an infinite interval,{} then the returns list a singleton list."))) NIL NIL -(-1111 R S) +(-1112 R S) ((|constructor| (NIL "This package provides operations for mapping functions onto \\spadtype{SegmentBinding}\\spad{s}.")) (|map| (((|SegmentBinding| |#2|) (|Mapping| |#2| |#1|) (|SegmentBinding| |#1|)) "\\spad{map(f,v=a..b)} returns the value given by \\spad{v=f(a)..f(b)}."))) NIL NIL -(-1112 S) +(-1113 S) ((|constructor| (NIL "This domain is used to provide the function argument syntax \\spad{v=a..b}. This is used,{} for example,{} by the top-level \\spadfun{draw} functions."))) NIL -((|HasCategory| (-1114 |#1|) (QUOTE (-1120)))) -(-1113 S) +((|HasCategory| (-1115 |#1|) (QUOTE (-1121)))) +(-1114 S) ((|constructor| (NIL "This category provides operations on ranges,{} or {\\em segments} as they are called.")) (|segment| (($ |#1| |#1|) "\\spad{segment(i,j)} is an alternate way to create the segment \\spad{i..j}.")) (|incr| (((|Integer|) $) "\\spad{incr(s)} returns \\spad{n},{} where \\spad{s} is a segment in which every \\spad{n}\\spad{-}th element is used. Note: \\spad{incr(l..h by n) = n}.")) (|high| ((|#1| $) "\\spad{high(s)} returns the second endpoint of \\spad{s}. Note: \\spad{high(l..h) = h}.")) (|low| ((|#1| $) "\\spad{low(s)} returns the first endpoint of \\spad{s}. Note: \\spad{low(l..h) = l}.")) (|hi| ((|#1| $) "\\spad{hi(s)} returns the second endpoint of \\spad{s}. Note: \\spad{hi(l..h) = h}.")) (|lo| ((|#1| $) "\\spad{lo(s)} returns the first endpoint of \\spad{s}. Note: \\spad{lo(l..h) = l}.")) (BY (($ $ (|Integer|)) "\\spad{s by n} creates a new segment in which only every \\spad{n}\\spad{-}th element is used.")) (SEGMENT (($ |#1| |#1|) "\\spad{l..h} creates a segment with \\spad{l} and \\spad{h} as the endpoints."))) NIL NIL -(-1114 S) +(-1115 S) ((|constructor| (NIL "This type is used to specify a range of values from type \\spad{S}."))) NIL -((|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1120)))) -(-1115 S L) +((|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1121)))) +(-1116 S L) ((|constructor| (NIL "This category provides an interface for expanding segments to a stream of elements.")) (|map| ((|#2| (|Mapping| |#1| |#1|) $) "\\spad{map(f,l..h by k)} produces a value of type \\spad{L} by applying \\spad{f} to each of the succesive elements of the segment,{} that is,{} \\spad{[f(l), f(l+k), ..., f(lN)]},{} where \\spad{lN <= h < lN+k}.")) (|expand| ((|#2| $) "\\spad{expand(l..h by k)} creates value of type \\spad{L} with elements \\spad{l, l+k, ... lN} where \\spad{lN <= h < lN+k}. For example,{} \\spad{expand(1..5 by 2) = [1,3,5]}.") ((|#2| (|List| $)) "\\spad{expand(l)} creates a new value of type \\spad{L} in which each segment \\spad{l..h by k} is replaced with \\spad{l, l+k, ... lN},{} where \\spad{lN <= h < lN+k}. For example,{} \\spad{expand [1..4, 7..9] = [1,2,3,4,7,8,9]}."))) NIL NIL -(-1116) +(-1117) ((|constructor| (NIL "This domain represents a block of expressions.")) (|last| (((|SpadAst|) $) "\\spad{last(e)} returns the last instruction in `e'.")) (|body| (((|List| (|SpadAst|)) $) "\\spad{body(e)} returns the list of expressions in the sequence of instruction `e'."))) NIL NIL -(-1117 A S) +(-1118 A S) ((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#2| $) "\\spad{union(x,u)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{x},{}\\spad{u})} returns a copy of \\spad{u}.") (($ $ |#2|) "\\spad{union(u,x)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{u},{}\\spad{x})} returns a copy of \\spad{u}.") (($ $ $) "\\spad{union(u,v)} returns the set aggregate of elements which are members of either set aggregate \\spad{u} or \\spad{v}.")) (|subset?| (((|Boolean|) $ $) "\\spad{subset?(u,v)} tests if \\spad{u} is a subset of \\spad{v}. Note: equivalent to \\axiom{reduce(and,{}{member?(\\spad{x},{}\\spad{v}) for \\spad{x} in \\spad{u}},{}\\spad{true},{}\\spad{false})}.")) (|symmetricDifference| (($ $ $) "\\spad{symmetricDifference(u,v)} returns the set aggregate of elements \\spad{x} which are members of set aggregate \\spad{u} or set aggregate \\spad{v} but not both. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{symmetricDifference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: \\axiom{symmetricDifference(\\spad{u},{}\\spad{v}) = union(difference(\\spad{u},{}\\spad{v}),{}difference(\\spad{v},{}\\spad{u}))}")) (|difference| (($ $ |#2|) "\\spad{difference(u,x)} returns the set aggregate \\spad{u} with element \\spad{x} removed. If \\spad{u} does not contain \\spad{x},{} a copy of \\spad{u} is returned. Note: \\axiom{difference(\\spad{s},{} \\spad{x}) = difference(\\spad{s},{} {\\spad{x}})}.") (($ $ $) "\\spad{difference(u,v)} returns the set aggregate \\spad{w} consisting of elements in set aggregate \\spad{u} but not in set aggregate \\spad{v}. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{difference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: equivalent to the notation (not currently supported) \\axiom{{\\spad{x} for \\spad{x} in \\spad{u} | not member?(\\spad{x},{}\\spad{v})}}.")) (|intersect| (($ $ $) "\\spad{intersect(u,v)} returns the set aggregate \\spad{w} consisting of elements common to both set aggregates \\spad{u} and \\spad{v}. Note: equivalent to the notation (not currently supported) {\\spad{x} for \\spad{x} in \\spad{u} | member?(\\spad{x},{}\\spad{v})}.")) (|set| (($ (|List| |#2|)) "\\spad{set([x,y,...,z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}.") (($) "\\spad{set()}\\$\\spad{D} creates an empty set aggregate of type \\spad{D}.")) (|brace| (($ (|List| |#2|)) "\\spad{brace([x,y,...,z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}. This form is considered obsolete. Use \\axiomFun{set} instead.") (($) "\\spad{brace()}\\$\\spad{D} (otherwise written {}\\$\\spad{D}) creates an empty set aggregate of type \\spad{D}. This form is considered obsolete. Use \\axiomFun{set} instead.")) (|part?| (((|Boolean|) $ $) "\\spad{s} < \\spad{t} returns \\spad{true} if all elements of set aggregate \\spad{s} are also elements of set aggregate \\spad{t}."))) NIL NIL -(-1118 S) +(-1119 S) ((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#1| $) "\\spad{union(x,u)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{x},{}\\spad{u})} returns a copy of \\spad{u}.") (($ $ |#1|) "\\spad{union(u,x)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{u},{}\\spad{x})} returns a copy of \\spad{u}.") (($ $ $) "\\spad{union(u,v)} returns the set aggregate of elements which are members of either set aggregate \\spad{u} or \\spad{v}.")) (|subset?| (((|Boolean|) $ $) "\\spad{subset?(u,v)} tests if \\spad{u} is a subset of \\spad{v}. Note: equivalent to \\axiom{reduce(and,{}{member?(\\spad{x},{}\\spad{v}) for \\spad{x} in \\spad{u}},{}\\spad{true},{}\\spad{false})}.")) (|symmetricDifference| (($ $ $) "\\spad{symmetricDifference(u,v)} returns the set aggregate of elements \\spad{x} which are members of set aggregate \\spad{u} or set aggregate \\spad{v} but not both. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{symmetricDifference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: \\axiom{symmetricDifference(\\spad{u},{}\\spad{v}) = union(difference(\\spad{u},{}\\spad{v}),{}difference(\\spad{v},{}\\spad{u}))}")) (|difference| (($ $ |#1|) "\\spad{difference(u,x)} returns the set aggregate \\spad{u} with element \\spad{x} removed. If \\spad{u} does not contain \\spad{x},{} a copy of \\spad{u} is returned. Note: \\axiom{difference(\\spad{s},{} \\spad{x}) = difference(\\spad{s},{} {\\spad{x}})}.") (($ $ $) "\\spad{difference(u,v)} returns the set aggregate \\spad{w} consisting of elements in set aggregate \\spad{u} but not in set aggregate \\spad{v}. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{difference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: equivalent to the notation (not currently supported) \\axiom{{\\spad{x} for \\spad{x} in \\spad{u} | not member?(\\spad{x},{}\\spad{v})}}.")) (|intersect| (($ $ $) "\\spad{intersect(u,v)} returns the set aggregate \\spad{w} consisting of elements common to both set aggregates \\spad{u} and \\spad{v}. Note: equivalent to the notation (not currently supported) {\\spad{x} for \\spad{x} in \\spad{u} | member?(\\spad{x},{}\\spad{v})}.")) (|set| (($ (|List| |#1|)) "\\spad{set([x,y,...,z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}.") (($) "\\spad{set()}\\$\\spad{D} creates an empty set aggregate of type \\spad{D}.")) (|brace| (($ (|List| |#1|)) "\\spad{brace([x,y,...,z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}. This form is considered obsolete. Use \\axiomFun{set} instead.") (($) "\\spad{brace()}\\$\\spad{D} (otherwise written {}\\$\\spad{D}) creates an empty set aggregate of type \\spad{D}. This form is considered obsolete. Use \\axiomFun{set} instead.")) (|part?| (((|Boolean|) $ $) "\\spad{s} < \\spad{t} returns \\spad{true} if all elements of set aggregate \\spad{s} are also elements of set aggregate \\spad{t}."))) -((-4453 . T)) +((-4454 . T)) NIL -(-1119 S) +(-1120 S) ((|constructor| (NIL "\\spadtype{SetCategory} is the basic category for describing a collection of elements with \\spadop{=} (equality) and \\spadfun{coerce} to output form. \\blankline Conditional Attributes: \\indented{3}{canonical\\tab{15}data structure equality is the same as \\spadop{=}}")) (|latex| (((|String|) $) "\\spad{latex(s)} returns a LaTeX-printable output representation of \\spad{s}.")) (|hash| (((|SingleInteger|) $) "\\spad{hash(s)} calculates a hash code for \\spad{s}."))) NIL NIL -(-1120) +(-1121) ((|constructor| (NIL "\\spadtype{SetCategory} is the basic category for describing a collection of elements with \\spadop{=} (equality) and \\spadfun{coerce} to output form. \\blankline Conditional Attributes: \\indented{3}{canonical\\tab{15}data structure equality is the same as \\spadop{=}}")) (|latex| (((|String|) $) "\\spad{latex(s)} returns a LaTeX-printable output representation of \\spad{s}.")) (|hash| (((|SingleInteger|) $) "\\spad{hash(s)} calculates a hash code for \\spad{s}."))) NIL NIL -(-1121 |m| |n|) +(-1122 |m| |n|) ((|constructor| (NIL "\\spadtype{SetOfMIntegersInOneToN} implements the subsets of \\spad{M} integers in the interval \\spad{[1..n]}")) (|delta| (((|NonNegativeInteger|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{delta(S,k,p)} returns the number of elements of \\spad{S} which are strictly between \\spad{p} and the \\spad{k^}{th} element of \\spad{S}.")) (|member?| (((|Boolean|) (|PositiveInteger|) $) "\\spad{member?(p, s)} returns \\spad{true} is \\spad{p} is in \\spad{s},{} \\spad{false} otherwise.")) (|enumerate| (((|Vector| $)) "\\spad{enumerate()} returns a vector of all the sets of \\spad{M} integers in \\spad{1..n}.")) (|setOfMinN| (($ (|List| (|PositiveInteger|))) "\\spad{setOfMinN([a_1,...,a_m])} returns the set {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 \\spad{k^}{th} element of \\spad{S} by \\spad{p},{} and returns \"failed\" if the result is not a set of \\spad{M} integers in \\spad{1..n} any more.")) (|incrementKthElement| (((|Union| $ "failed") $ (|PositiveInteger|)) "\\spad{incrementKthElement(S,k)} increments the \\spad{k^}{th} element of \\spad{S},{} and returns \"failed\" if the result is not a set of \\spad{M} integers in \\spad{1..n} any more."))) NIL NIL -(-1122 S) +(-1123 S) ((|constructor| (NIL "A set over a domain \\spad{D} models the usual mathematical notion of a finite set of elements from \\spad{D}. Sets are unordered collections of distinct elements (that is,{} order and duplication does not matter). The notation \\spad{set [a,b,c]} can be used to create a set and the usual operations such as union and intersection are available to form new sets. In our implementation,{} \\Language{} maintains the entries in sorted order. Specifically,{} the parts function returns the entries as a list in ascending order and the extract operation returns the maximum entry. Given two sets \\spad{s} and \\spad{t} where \\spad{\\#s = m} and \\spad{\\#t = n},{} the complexity of \\indented{2}{\\spad{s = t} is \\spad{O(min(n,m))}} \\indented{2}{\\spad{s < t} is \\spad{O(max(n,m))}} \\indented{2}{\\spad{union(s,t)},{} \\spad{intersect(s,t)},{} \\spad{minus(s,t)},{} \\spad{symmetricDifference(s,t)} is \\spad{O(max(n,m))}} \\indented{2}{\\spad{member(x,t)} is \\spad{O(n log n)}} \\indented{2}{\\spad{insert(x,t)} and \\spad{remove(x,t)} is \\spad{O(n)}}"))) -((-4463 . T) (-4453 . T) (-4464 . T)) -((-3794 (-12 (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1120))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-1120))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-875)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1120))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) -(-1123 |Str| |Sym| |Int| |Flt| |Expr|) +((-4464 . T) (-4454 . T) (-4465 . T)) +((-2758 (-12 (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#1| (QUOTE (-379))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) +(-1124 |Str| |Sym| |Int| |Flt| |Expr|) ((|constructor| (NIL "This category allows the manipulation of Lisp values while keeping the grunge fairly localized.")) (|#| (((|Integer|) $) "\\spad{\\#((a1,...,an))} returns \\spad{n}.")) (|cdr| (($ $) "\\spad{cdr((a1,...,an))} returns \\spad{(a2,...,an)}.")) (|car| (($ $) "\\spad{car((a1,...,an))} returns a1.")) (|expr| ((|#5| $) "\\spad{expr(s)} returns \\spad{s} as an element of Expr; Error: if \\spad{s} is not an atom that also belongs to Expr.")) (|float| ((|#4| $) "\\spad{float(s)} returns \\spad{s} as an element of \\spad{Flt}; Error: if \\spad{s} is not an atom that also belongs to \\spad{Flt}.")) (|integer| ((|#3| $) "\\spad{integer(s)} returns \\spad{s} as an element of Int. Error: if \\spad{s} is not an atom that also belongs to Int.")) (|symbol| ((|#2| $) "\\spad{symbol(s)} returns \\spad{s} as an element of \\spad{Sym}. Error: if \\spad{s} is not an atom that also belongs to \\spad{Sym}.")) (|string| ((|#1| $) "\\spad{string(s)} returns \\spad{s} as an element of \\spad{Str}. Error: if \\spad{s} is not an atom that also belongs to \\spad{Str}.")) (|destruct| (((|List| $) $) "\\spad{destruct((a1,...,an))} returns the list [a1,{}...,{}an].")) (|float?| (((|Boolean|) $) "\\spad{float?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Flt}.")) (|integer?| (((|Boolean|) $) "\\spad{integer?(s)} is \\spad{true} if \\spad{s} is an atom and belong to Int.")) (|symbol?| (((|Boolean|) $) "\\spad{symbol?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Sym}.")) (|string?| (((|Boolean|) $) "\\spad{string?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Str}.")) (|list?| (((|Boolean|) $) "\\spad{list?(s)} is \\spad{true} if \\spad{s} is a Lisp list,{} possibly ().")) (|pair?| (((|Boolean|) $) "\\spad{pair?(s)} is \\spad{true} if \\spad{s} has is a non-null Lisp list.")) (|atom?| (((|Boolean|) $) "\\spad{atom?(s)} is \\spad{true} if \\spad{s} is a Lisp atom.")) (|null?| (((|Boolean|) $) "\\spad{null?(s)} is \\spad{true} if \\spad{s} is the \\spad{S}-expression ().")) (|eq| (((|Boolean|) $ $) "\\spad{eq(s, t)} is \\spad{true} if \\%peq(\\spad{s},{}\\spad{t}) is \\spad{true} for pointers."))) NIL NIL -(-1124) +(-1125) ((|constructor| (NIL "This domain allows the manipulation of the usual Lisp values."))) NIL NIL -(-1125 |Str| |Sym| |Int| |Flt| |Expr|) +(-1126 |Str| |Sym| |Int| |Flt| |Expr|) ((|constructor| (NIL "This domain allows the manipulation of Lisp values over arbitrary atomic types."))) NIL NIL -(-1126 R FS) +(-1127 R FS) ((|constructor| (NIL "\\axiomType{SimpleFortranProgram(\\spad{f},{}type)} provides a simple model of some FORTRAN subprograms,{} making it possible to coerce objects of various domains into a FORTRAN subprogram called \\axiom{\\spad{f}}. These can then be translated into legal FORTRAN code.")) (|fortran| (($ (|Symbol|) (|FortranScalarType|) |#2|) "\\spad{fortran(fname,ftype,body)} builds an object of type \\axiomType{FortranProgramCategory}. The three arguments specify the name,{} the type and the \\spad{body} of the program."))) NIL NIL -(-1127 R E V P TS) +(-1128 R E V P TS) ((|constructor| (NIL "\\indented{2}{A internal package for removing redundant quasi-components and redundant} \\indented{2}{branches when decomposing a variety by means of quasi-components} \\indented{2}{of regular triangular sets. \\newline} References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{5}{Tech. Report (PoSSo project)} \\indented{1}{[2] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|branchIfCan| (((|Union| (|Record| (|:| |eq| (|List| |#4|)) (|:| |tower| |#5|) (|:| |ineq| (|List| |#4|))) "failed") (|List| |#4|) |#5| (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{branchIfCan(leq,{}\\spad{ts},{}lineq,{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement.")) (|prepareDecompose| (((|List| (|Record| (|:| |eq| (|List| |#4|)) (|:| |tower| |#5|) (|:| |ineq| (|List| |#4|)))) (|List| |#4|) (|List| |#5|) (|Boolean|) (|Boolean|)) "\\axiom{prepareDecompose(\\spad{lp},{}\\spad{lts},{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|removeSuperfluousCases| (((|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|)))) "\\axiom{removeSuperfluousCases(llpwt)} is an internal subroutine,{} exported only for developement.")) (|subCase?| (((|Boolean|) (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|)) (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) "\\axiom{subCase?(lpwt1,{}lpwt2)} is an internal subroutine,{} exported only for developement.")) (|removeSuperfluousQuasiComponents| (((|List| |#5|) (|List| |#5|)) "\\axiom{removeSuperfluousQuasiComponents(\\spad{lts})} removes from \\axiom{\\spad{lts}} any \\spad{ts} such that \\axiom{subQuasiComponent?(\\spad{ts},{}us)} holds for another \\spad{us} in \\axiom{\\spad{lts}}.")) (|subQuasiComponent?| (((|Boolean|) |#5| (|List| |#5|)) "\\axiom{subQuasiComponent?(\\spad{ts},{}lus)} returns \\spad{true} iff \\axiom{subQuasiComponent?(\\spad{ts},{}us)} holds for one \\spad{us} in \\spad{lus}.") (((|Boolean|) |#5| |#5|) "\\axiom{subQuasiComponent?(\\spad{ts},{}us)} returns \\spad{true} iff \\axiomOpFrom{internalSubQuasiComponent?(\\spad{ts},{}us)}{QuasiComponentPackage} returs \\spad{true}.")) (|internalSubQuasiComponent?| (((|Union| (|Boolean|) "failed") |#5| |#5|) "\\axiom{internalSubQuasiComponent?(\\spad{ts},{}us)} returns a boolean \\spad{b} value if the fact the regular zero set of \\axiom{us} contains that of \\axiom{\\spad{ts}} can be decided (and in that case \\axiom{\\spad{b}} gives this inclusion) otherwise returns \\axiom{\"failed\"}.")) (|infRittWu?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{infRittWu?(\\spad{lp1},{}\\spad{lp2})} is an internal subroutine,{} exported only for developement.")) (|internalInfRittWu?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{internalInfRittWu?(\\spad{lp1},{}\\spad{lp2})} is an internal subroutine,{} exported only for developement.")) (|internalSubPolSet?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{internalSubPolSet?(\\spad{lp1},{}\\spad{lp2})} returns \\spad{true} iff \\axiom{\\spad{lp1}} is a sub-set of \\axiom{\\spad{lp2}} assuming that these lists are sorted increasingly \\spad{w}.\\spad{r}.\\spad{t}. \\axiomOpFrom{infRittWu?}{RecursivePolynomialCategory}.")) (|subPolSet?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{subPolSet?(\\spad{lp1},{}\\spad{lp2})} returns \\spad{true} iff \\axiom{\\spad{lp1}} is a sub-set of \\axiom{\\spad{lp2}}.")) (|subTriSet?| (((|Boolean|) |#5| |#5|) "\\axiom{subTriSet?(\\spad{ts},{}us)} returns \\spad{true} iff \\axiom{\\spad{ts}} is a sub-set of \\axiom{us}.")) (|moreAlgebraic?| (((|Boolean|) |#5| |#5|) "\\axiom{moreAlgebraic?(\\spad{ts},{}us)} returns \\spad{false} iff \\axiom{\\spad{ts}} and \\axiom{us} are both empty,{} or \\axiom{\\spad{ts}} has less elements than \\axiom{us},{} or some variable is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{us} and is not \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ts}}.")) (|algebraicSort| (((|List| |#5|) (|List| |#5|)) "\\axiom{algebraicSort(\\spad{lts})} sorts \\axiom{\\spad{lts}} \\spad{w}.\\spad{r}.\\spad{t} \\axiomOpFrom{supDimElseRittWu}{QuasiComponentPackage}.")) (|supDimElseRittWu?| (((|Boolean|) |#5| |#5|) "\\axiom{supDimElseRittWu(\\spad{ts},{}us)} returns \\spad{true} iff \\axiom{\\spad{ts}} has less elements than \\axiom{us} otherwise if \\axiom{\\spad{ts}} has higher rank than \\axiom{us} \\spad{w}.\\spad{r}.\\spad{t}. Riit and Wu ordering.")) (|stopTable!| (((|Void|)) "\\axiom{stopTableGcd!()} is an internal subroutine,{} exported only for developement.")) (|startTable!| (((|Void|) (|String|) (|String|) (|String|)) "\\axiom{startTableGcd!(\\spad{s1},{}\\spad{s2},{}\\spad{s3})} is an internal subroutine,{} exported only for developement."))) NIL NIL -(-1128 R E V P TS) +(-1129 R E V P TS) ((|constructor| (NIL "A internal package for computing gcds and resultants of univariate polynomials with coefficients in a tower of simple extensions of a field. There is no need to use directly this package since its main operations are available from \\spad{TS}. \\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA and \\spad{R}. RIOBOO \"Computations of \\spad{gcd} over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of AAECC11} \\indented{5}{Paris,{} 1995.} \\indented{1}{[2] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}"))) NIL NIL -(-1129 R E V P) +(-1130 R E V P) ((|constructor| (NIL "The category of square-free regular triangular sets. A regular triangular set \\spad{ts} is square-free if the \\spad{gcd} of any polynomial \\spad{p} in \\spad{ts} and \\spad{differentiate(p,mvar(p))} \\spad{w}.\\spad{r}.\\spad{t}. \\axiomOpFrom{collectUnder}{TriangularSetCategory}(\\spad{ts},{}\\axiomOpFrom{mvar}{RecursivePolynomialCategory}(\\spad{p})) has degree zero \\spad{w}.\\spad{r}.\\spad{t}. \\spad{mvar(p)}. Thus any square-free regular set defines a tower of square-free simple extensions.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. KALKBRENER \"Algorithmic properties of polynomial rings\"} \\indented{5}{Habilitation Thesis,{} ETZH,{} Zurich,{} 1995.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}"))) -((-4464 . T) (-4463 . T)) +((-4465 . T) (-4464 . T)) NIL -(-1130) +(-1131) ((|constructor| (NIL "SymmetricGroupCombinatoricFunctions contains combinatoric functions concerning symmetric groups and representation theory: list young tableaus,{} improper partitions,{} subsets bijection of Coleman.")) (|unrankImproperPartitions1| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{unrankImproperPartitions1(n,m,k)} computes the {\\em k}\\spad{-}th improper partition of nonnegative \\spad{n} in at most \\spad{m} nonnegative parts ordered as follows: first,{} in reverse lexicographically according to their non-zero parts,{} then according to their positions (\\spadignore{i.e.} lexicographical order using {\\em subSet}: {\\em [3,0,0] < [0,3,0] < [0,0,3] < [2,1,0] < [2,0,1] < [0,2,1] < [1,2,0] < [1,0,2] < [0,1,2] < [1,1,1]}). Note: counting of subtrees is done by {\\em numberOfImproperPartitionsInternal}.")) (|unrankImproperPartitions0| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{unrankImproperPartitions0(n,m,k)} computes the {\\em k}\\spad{-}th improper partition of nonnegative \\spad{n} in \\spad{m} nonnegative parts in reverse lexicographical order. Example: {\\em [0,0,3] < [0,1,2] < [0,2,1] < [0,3,0] < [1,0,2] < [1,1,1] < [1,2,0] < [2,0,1] < [2,1,0] < [3,0,0]}. Error: if \\spad{k} is negative or too big. Note: counting of subtrees is done by \\spadfunFrom{numberOfImproperPartitions}{SymmetricGroupCombinatoricFunctions}.")) (|subSet| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{subSet(n,m,k)} calculates the {\\em k}\\spad{-}th {\\em m}-subset of the set {\\em 0,1,...,(n-1)} in the lexicographic order considered as a decreasing map from {\\em 0,...,(m-1)} into {\\em 0,...,(n-1)}. See \\spad{S}.\\spad{G}. Williamson: Theorem 1.60. Error: if not {\\em (0 <= m <= n and 0 < = k < (n choose m))}.")) (|numberOfImproperPartitions| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{numberOfImproperPartitions(n,m)} computes the number of partitions of the nonnegative integer \\spad{n} in \\spad{m} nonnegative parts with regarding the order (improper partitions). Example: {\\em numberOfImproperPartitions (3,3)} is 10,{} since {\\em [0,0,3], [0,1,2], [0,2,1], [0,3,0], [1,0,2], [1,1,1], [1,2,0], [2,0,1], [2,1,0], [3,0,0]} are the possibilities. Note: this operation has a recursive implementation.")) (|nextPartition| (((|Vector| (|Integer|)) (|List| (|Integer|)) (|Vector| (|Integer|)) (|Integer|)) "\\spad{nextPartition(gamma,part,number)} generates the partition of {\\em number} which follows {\\em part} according to the right-to-left lexicographical order. The partition has the property that its components do not exceed the corresponding components of {\\em gamma}. the first partition is achieved by {\\em part=[]}. Also,{} {\\em []} indicates that {\\em part} is the last partition.") (((|Vector| (|Integer|)) (|Vector| (|Integer|)) (|Vector| (|Integer|)) (|Integer|)) "\\spad{nextPartition(gamma,part,number)} generates the partition of {\\em number} which follows {\\em part} according to the right-to-left lexicographical order. The partition has the property that its components do not exceed the corresponding components of {\\em gamma}. The first partition is achieved by {\\em part=[]}. Also,{} {\\em []} indicates that {\\em part} is the last partition.")) (|nextLatticePermutation| (((|List| (|Integer|)) (|List| (|PositiveInteger|)) (|List| (|Integer|)) (|Boolean|)) "\\spad{nextLatticePermutation(lambda,lattP,constructNotFirst)} generates the lattice permutation according to the proper partition {\\em lambda} succeeding the lattice permutation {\\em lattP} in lexicographical order as long as {\\em constructNotFirst} is \\spad{true}. If {\\em constructNotFirst} is \\spad{false},{} the first lattice permutation is returned. The result {\\em nil} indicates that {\\em lattP} has no successor.")) (|nextColeman| (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|Matrix| (|Integer|))) "\\spad{nextColeman(alpha,beta,C)} generates the next Coleman matrix of column sums {\\em alpha} and row sums {\\em beta} according to the lexicographical order from bottom-to-top. The first Coleman matrix is achieved by {\\em C=new(1,1,0)}. Also,{} {\\em new(1,1,0)} indicates that \\spad{C} is the last Coleman matrix.")) (|makeYoungTableau| (((|Matrix| (|Integer|)) (|List| (|PositiveInteger|)) (|List| (|Integer|))) "\\spad{makeYoungTableau(lambda,gitter)} computes for a given lattice permutation {\\em gitter} and for an improper partition {\\em lambda} the corresponding standard tableau of shape {\\em lambda}. Notes: see {\\em listYoungTableaus}. The entries are from {\\em 0,...,n-1}.")) (|listYoungTableaus| (((|List| (|Matrix| (|Integer|))) (|List| (|PositiveInteger|))) "\\spad{listYoungTableaus(lambda)} where {\\em lambda} is a proper partition generates the list of all standard tableaus of shape {\\em lambda} by means of lattice permutations. The numbers of the lattice permutation are interpreted as column labels. Hence the contents of these lattice permutations are the conjugate of {\\em lambda}. Notes: the functions {\\em nextLatticePermutation} and {\\em makeYoungTableau} are used. The entries are from {\\em 0,...,n-1}.")) (|inverseColeman| (((|List| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|Matrix| (|Integer|))) "\\spad{inverseColeman(alpha,beta,C)}: there is a bijection from the set of matrices having nonnegative entries and row sums {\\em alpha},{} column sums {\\em beta} to the set of {\\em Salpha - Sbeta} double cosets of the symmetric group {\\em Sn}. ({\\em Salpha} is the Young subgroup corresponding to the improper partition {\\em alpha}). For such a matrix \\spad{C},{} inverseColeman(\\spad{alpha},{}\\spad{beta},{}\\spad{C}) calculates the lexicographical smallest {\\em pi} in the corresponding double coset. Note: the resulting permutation {\\em pi} of {\\em {1,2,...,n}} is given in list form. Notes: the inverse of this map is {\\em coleman}. For details,{} see James/Kerber.")) (|coleman| (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{coleman(alpha,beta,pi)}: there is a bijection from the set of matrices having nonnegative entries and row sums {\\em alpha},{} column sums {\\em beta} to the set of {\\em Salpha - Sbeta} double cosets of the symmetric group {\\em Sn}. ({\\em Salpha} is the Young subgroup corresponding to the improper partition {\\em alpha}). For a representing element {\\em pi} of such a double coset,{} coleman(\\spad{alpha},{}\\spad{beta},{}\\spad{pi}) generates the Coleman-matrix corresponding to {\\em alpha, beta, pi}. Note: The permutation {\\em pi} of {\\em {1,2,...,n}} has to be given in list form. Note: the inverse of this map is {\\em inverseColeman} (if {\\em pi} is the lexicographical smallest permutation in the coset). For details see James/Kerber."))) NIL NIL -(-1131 S) +(-1132 S) ((|constructor| (NIL "the class of all multiplicative semigroups,{} \\spadignore{i.e.} a set with an associative operation \\spadop{*}. \\blankline")) (** (($ $ (|PositiveInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (* (($ $ $) "\\spad{x*y} returns the product of \\spad{x} and \\spad{y}."))) NIL NIL -(-1132) +(-1133) ((|constructor| (NIL "the class of all multiplicative semigroups,{} \\spadignore{i.e.} a set with an associative operation \\spadop{*}. \\blankline")) (** (($ $ (|PositiveInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) 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(((|Integer|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{countRealRootsMultiple(p)} says how many real roots \\spad{p} has,{} counted with multiplicity")) (|SturmHabichtMultiple| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtMultiple(p1,p2)} computes \\spad{c_}{+}\\spad{-c_}{-} where \\spad{c_}{+} is the number of real roots of \\spad{p1} with p2>0 and \\spad{c_}{-} is the number of real roots of \\spad{p1} with p2<0. If p2=1 what you get is the number of real roots of \\spad{p1}.")) (|countRealRoots| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{countRealRoots(p)} says how many real roots \\spad{p} has")) (|SturmHabicht| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabicht(p1,p2)} computes \\spad{c_}{+}\\spad{-c_}{-} where \\spad{c_}{+} is the number of real roots of \\spad{p1} with p2>0 and \\spad{c_}{-} is the number of real roots of \\spad{p1} with p2<0. If 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 (-464)))) -(-1135) +(-1136) ((|constructor| (NIL "This domain represents a signature AST. A signature AST \\indented{2}{is a description of an exported operation,{} \\spadignore{e.g.} its name,{} result} \\indented{2}{type,{} and the list of its argument types.}")) (|signature| (((|Signature|) $) "\\spad{signature(s)} returns AST of the declared signature for \\spad{`s'}.")) (|name| (((|Identifier|) $) "\\spad{name(s)} returns the name of the signature \\spad{`s'}.")) (|signatureAst| (($ (|Identifier|) (|Signature|)) "\\spad{signatureAst(n,s,t)} builds the signature AST \\spad{n:} \\spad{s} \\spad{->} \\spad{t}"))) NIL NIL -(-1136 R -2117) +(-1137 R -1959) ((|constructor| (NIL "This package provides functions to determine the sign of an elementary function around a point or infinity.")) (|sign| (((|Union| (|Integer|) "failed") |#2| (|Symbol|) |#2| (|String|)) "\\spad{sign(f, x, a, s)} returns the sign of \\spad{f} as \\spad{x} nears \\spad{a} from below if \\spad{s} is \"left\",{} or above if \\spad{s} is \"right\".") (((|Union| (|Integer|) "failed") |#2| (|Symbol|) (|OrderedCompletion| |#2|)) "\\spad{sign(f, x, a)} returns the sign of \\spad{f} as \\spad{x} nears \\spad{a},{} from both sides if \\spad{a} is finite.") (((|Union| (|Integer|) "failed") |#2|) "\\spad{sign(f)} returns the sign of \\spad{f} if it is constant everywhere."))) NIL NIL -(-1137 R) +(-1138 R) ((|constructor| (NIL "Find the sign of a rational function around a point or infinity.")) (|sign| (((|Union| (|Integer|) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|)) (|String|)) "\\spad{sign(f, x, a, s)} returns the sign of \\spad{f} as \\spad{x} nears \\spad{a} from the left (below) if \\spad{s} is the string \\spad{\"left\"},{} or from the right (above) if \\spad{s} is the string \\spad{\"right\"}.") (((|Union| (|Integer|) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|)))) "\\spad{sign(f, x, a)} returns the sign of \\spad{f} as \\spad{x} approaches \\spad{a},{} from both sides if \\spad{a} is finite.") (((|Union| (|Integer|) "failed") (|Fraction| (|Polynomial| |#1|))) "\\spad{sign f} returns the sign of \\spad{f} if it is constant everywhere."))) NIL NIL -(-1138) +(-1139) ((|constructor| (NIL "This is the datatype for operation signatures as \\indented{2}{used by the compiler and the interpreter.\\space{2}Note that this domain} \\indented{2}{differs from SignatureAst.} See also: ConstructorCall,{} Domain.")) (|source| (((|List| (|Syntax|)) $) "\\spad{source(s)} returns the list of parameter types of \\spad{`s'}.")) (|target| (((|Syntax|) $) "\\spad{target(s)} returns the target type of the signature \\spad{`s'}.")) (|signature| (($ (|List| (|Syntax|)) (|Syntax|)) "\\spad{signature(s,t)} constructs a Signature object with parameter types indicaded by \\spad{`s'},{} and return type indicated by \\spad{`t'}."))) NIL NIL -(-1139) +(-1140) ((|constructor| (NIL "\\indented{1}{Package to allow simplify to be called on AlgebraicNumbers} by converting to EXPR(INT)")) (|simplify| (((|Expression| (|Integer|)) (|AlgebraicNumber|)) "\\spad{simplify(an)} applies simplifications to \\spad{an}"))) NIL NIL -(-1140) +(-1141) ((|constructor| (NIL "SingleInteger is intended to support machine integer arithmetic.")) (|Or| (($ $ $) "\\spad{Or(n,m)} returns the bit-by-bit logical {\\em or} of the single integers \\spad{n} and \\spad{m}.")) (|And| (($ $ $) "\\spad{And(n,m)} returns the bit-by-bit logical {\\em and} of the single integers \\spad{n} and \\spad{m}.")) (|Not| (($ $) "\\spad{Not(n)} returns the bit-by-bit logical {\\em not} of the single integer \\spad{n}.")) (|xor| (($ $ $) "\\spad{xor(n,m)} returns the bit-by-bit logical {\\em xor} of the single integers \\spad{n} and \\spad{m}.")) (|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."))) -((-4451 . T) (-4455 . T) (-4450 . T) (-4461 . T) (-4462 . T) (-4456 . T) ((-4465 "*") . T) (-4457 . T) (-4458 . T) (-4460 . T)) +((-4452 . T) (-4456 . T) (-4451 . T) (-4462 . T) (-4463 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL -(-1141 S) +(-1142 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}. Note: \\axiom{depth(\\spad{s}) = \\spad{#s}}.")) (|top| ((|#1| $) "\\spad{top(s)} returns the top element \\spad{x} from \\spad{s}; \\spad{s} remains unchanged. Note: Use \\axiom{pop!(\\spad{s})} to obtain \\spad{x} and remove it from \\spad{s}.")) (|pop!| ((|#1| $) "\\spad{pop!(s)} returns the top element \\spad{x},{} destructively removing \\spad{x} from \\spad{s}. Note: Use \\axiom{top(\\spad{s})} to obtain \\spad{x} without removing it from \\spad{s}. Error: if \\spad{s} is empty.")) (|push!| ((|#1| |#1| $) "\\spad{push!(x,s)} pushes \\spad{x} onto stack \\spad{s},{} \\spadignore{i.e.} destructively changing \\spad{s} so as to have a new first (top) element \\spad{x}. Afterwards,{} pop!(\\spad{s}) produces \\spad{x} and pop!(\\spad{s}) produces the original \\spad{s}."))) -((-4463 . T) (-4464 . T)) +((-4464 . T) (-4465 . T)) NIL -(-1142 S |ndim| R |Row| |Col|) +(-1143 S |ndim| R |Row| |Col|) ((|constructor| (NIL "\\spadtype{SquareMatrixCategory} is a general square matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if the matrix is not invertible.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m},{} if that matrix is invertible and returns \"failed\" otherwise.")) (|minordet| ((|#3| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors.")) (|determinant| ((|#3| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}.")) (* ((|#4| |#4| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#5| $ |#5|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.")) (|diagonalProduct| ((|#3| $) "\\spad{diagonalProduct(m)} returns the product of the elements on the diagonal of the matrix \\spad{m}.")) (|trace| ((|#3| $) "\\spad{trace(m)} returns the trace of the matrix \\spad{m}. this is the sum of the elements on the diagonal of the matrix \\spad{m}.")) (|diagonal| ((|#4| $) "\\spad{diagonal(m)} returns a row consisting of the elements on the diagonal of the matrix \\spad{m}.")) (|diagonalMatrix| (($ (|List| |#3|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ |#3|) "\\spad{scalarMatrix(r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}\\spad{'s} on the diagonal and zeroes elsewhere."))) NIL -((|HasCategory| |#3| (QUOTE (-374))) (|HasAttribute| |#3| (QUOTE (-4465 "*"))) (|HasCategory| |#3| (QUOTE (-174)))) -(-1143 |ndim| R |Row| |Col|) +((|HasCategory| |#3| (QUOTE (-374))) (|HasAttribute| |#3| (QUOTE (-4466 "*"))) (|HasCategory| |#3| (QUOTE (-174)))) +(-1144 |ndim| R |Row| |Col|) ((|constructor| (NIL "\\spadtype{SquareMatrixCategory} is a general square matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if the matrix is not invertible.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m},{} if that matrix is invertible and returns \"failed\" otherwise.")) (|minordet| ((|#2| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors.")) (|determinant| ((|#2| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}.")) (* ((|#3| |#3| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#4| $ |#4|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.")) (|diagonalProduct| ((|#2| $) "\\spad{diagonalProduct(m)} returns the product of the elements on the diagonal of the matrix \\spad{m}.")) (|trace| ((|#2| $) "\\spad{trace(m)} returns the trace of the matrix \\spad{m}. this is the sum of the elements on the diagonal of the matrix \\spad{m}.")) (|diagonal| ((|#3| $) "\\spad{diagonal(m)} returns a row consisting of the elements on the diagonal of the matrix \\spad{m}.")) (|diagonalMatrix| (($ (|List| |#2|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ |#2|) "\\spad{scalarMatrix(r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}\\spad{'s} on the diagonal and zeroes elsewhere."))) -((-4463 . T) (-4457 . T) (-4458 . T) (-4460 . T)) +((-4464 . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL -(-1144 R |Row| |Col| M) +(-1145 R |Row| |Col| M) ((|constructor| (NIL "\\spadtype{SmithNormalForm} is a package which provides some standard canonical forms for matrices.")) (|diophantineSystem| (((|Record| (|:| |particular| (|Union| |#3| "failed")) (|:| |basis| (|List| |#3|))) |#4| |#3|) "\\spad{diophantineSystem(A,B)} returns a particular integer solution and an integer basis of the equation \\spad{AX = B}.")) (|completeSmith| (((|Record| (|:| |Smith| |#4|) (|:| |leftEqMat| |#4|) (|:| |rightEqMat| |#4|)) |#4|) "\\spad{completeSmith} returns a record that contains the Smith normal form \\spad{H} of the matrix and the left and right equivalence matrices \\spad{U} and \\spad{V} such that U*m*v = \\spad{H}")) (|smith| ((|#4| |#4|) "\\spad{smith(m)} returns the Smith Normal form of the matrix \\spad{m}.")) (|completeHermite| (((|Record| (|:| |Hermite| |#4|) (|:| |eqMat| |#4|)) |#4|) "\\spad{completeHermite} returns a record that contains the Hermite normal form \\spad{H} of the matrix and the equivalence matrix \\spad{U} such that U*m = \\spad{H}")) (|hermite| ((|#4| |#4|) "\\spad{hermite(m)} returns the Hermite normal form of the matrix \\spad{m}."))) NIL NIL -(-1145 R |VarSet|) +(-1146 R |VarSet|) ((|constructor| (NIL "\\indented{2}{This type is the basic representation of sparse recursive multivariate} polynomials. It is parameterized by the coefficient ring and the variable set which may be infinite. The variable ordering is determined by the variable set parameter. The coefficient ring may be non-commutative,{} but the variables are assumed to commute."))) -(((-4465 "*") |has| |#1| (-174)) (-4456 |has| |#1| (-568)) (-4461 |has| |#1| (-6 -4461)) (-4458 . T) (-4457 . T) (-4460 . T)) -((|HasCategory| |#1| (QUOTE (-927))) (-3794 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-927)))) (-3794 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-927)))) (-3794 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-927)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-3794 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-390)))) (|HasCategory| |#2| (LIST (QUOTE -900) (QUOTE (-390))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -900) (QUOTE (-576))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -906) (QUOTE (-390))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -906) (QUOTE (-390)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -906) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -906) (QUOTE (-576)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1058) (QUOTE (-576)))) (-3794 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1058) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#1| (LIST (QUOTE -1058) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-374))) (|HasAttribute| |#1| (QUOTE -4461)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-927)))) (-3794 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-927)))) (|HasCategory| |#1| (QUOTE (-146))))) -(-1146 |Coef| |Var| SMP) +(((-4466 "*") |has| |#1| (-174)) (-4457 |has| |#1| (-568)) (-4462 |has| |#1| (-6 -4462)) (-4459 . T) (-4458 . T) (-4461 . T)) +((|HasCategory| |#1| (QUOTE (-928))) (-2758 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-928)))) (-2758 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-928)))) (-2758 (|HasCategory| |#1| (QUOTE (-464))) (|HasCategory| |#1| (QUOTE (-928)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-2758 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-390)))) (|HasCategory| |#2| (LIST (QUOTE -901) (QUOTE (-390))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -901) (QUOTE (-576))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#1| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576)))) (-2758 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-374))) (|HasAttribute| |#1| (QUOTE -4462)) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-928)))) (-2758 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-928)))) (|HasCategory| |#1| (QUOTE (-146))))) +(-1147 |Coef| |Var| SMP) ((|constructor| (NIL "This domain provides multivariate Taylor series with variables from an arbitrary ordered set. A Taylor series is represented by a stream of polynomials from the polynomial domain \\spad{SMP}. The \\spad{n}th element of the stream is a form of degree \\spad{n}. SMTS is an internal domain.")) (|fintegrate| (($ (|Mapping| $) |#2| |#1|) "\\spad{fintegrate(f,v,c)} is the integral of \\spad{f()} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.} \\indented{1}{The evaluation of \\spad{f()} is delayed.}")) (|integrate| (($ $ |#2| |#1|) "\\spad{integrate(s,v,c)} is the integral of \\spad{s} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.}")) (|csubst| (((|Mapping| (|Stream| |#3|) |#3|) (|List| |#2|) (|List| (|Stream| |#3|))) "\\spad{csubst(a,b)} is for internal use only")) (* (($ |#3| $) "\\spad{smp*ts} multiplies a TaylorSeries by a monomial \\spad{SMP}.")) (|coerce| (($ |#3|) "\\spad{coerce(poly)} regroups the terms by total degree and forms a series.") (($ |#2|) "\\spad{coerce(var)} converts a variable to a Taylor series")) (|coefficient| ((|#3| $ (|NonNegativeInteger|)) "\\spad{coefficient(s, n)} gives the terms of total degree \\spad{n}."))) -(((-4465 "*") |has| |#1| (-174)) (-4456 |has| |#1| (-568)) (-4458 . T) (-4457 . T) (-4460 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (-3794 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-374)))) -(-1147 R E V P) +(((-4466 "*") |has| |#1| (-174)) (-4457 |has| |#1| (-568)) (-4459 . T) (-4458 . T) (-4461 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (-2758 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-374)))) +(-1148 R E V P) ((|constructor| (NIL "The category of square-free and normalized triangular sets. Thus,{} up to the primitivity axiom of [1],{} these sets are Lazard triangular sets.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991}"))) -((-4464 . T) (-4463 . T)) +((-4465 . T) (-4464 . T)) NIL -(-1148 UP -2117) +(-1149 UP -1959) ((|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 -(-1149 R) +(-1150 R) ((|constructor| (NIL "This package tries to find solutions expressed in terms of radicals for systems of equations of rational functions with coefficients in an integral domain \\spad{R}.")) (|contractSolve| (((|SuchThat| (|List| (|Expression| |#1|)) (|List| (|Equation| (|Expression| |#1|)))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{contractSolve(rf,x)} finds the solutions expressed in terms of radicals of the equation \\spad{rf} = 0 with respect to the symbol \\spad{x},{} where \\spad{rf} is a rational function. The result contains new symbols for common subexpressions in order to reduce the size of the output.") (((|SuchThat| (|List| (|Expression| |#1|)) (|List| (|Equation| (|Expression| |#1|)))) (|Equation| (|Fraction| (|Polynomial| |#1|))) (|Symbol|)) "\\spad{contractSolve(eq,x)} finds the solutions expressed in terms of radicals of the equation of rational functions \\spad{eq} with respect to the symbol \\spad{x}. The result contains new symbols for common subexpressions in order to reduce the size of the output.")) (|radicalRoots| (((|List| (|List| (|Expression| |#1|))) (|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|Symbol|))) "\\spad{radicalRoots(lrf,lvar)} finds the roots expressed in terms of radicals of the list of rational functions \\spad{lrf} with respect to the list of symbols \\spad{lvar}.") (((|List| (|Expression| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{radicalRoots(rf,x)} finds the roots expressed in terms of radicals of the rational function \\spad{rf} with respect to the symbol \\spad{x}.")) (|radicalSolve| (((|List| (|List| (|Equation| (|Expression| |#1|)))) (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) "\\spad{radicalSolve(leq)} finds the solutions expressed in terms of radicals of the system of equations of rational functions \\spad{leq} with respect to the unique symbol \\spad{x} appearing in \\spad{leq}.") (((|List| (|List| (|Equation| (|Expression| |#1|)))) (|List| (|Equation| (|Fraction| (|Polynomial| |#1|)))) (|List| (|Symbol|))) "\\spad{radicalSolve(leq,lvar)} finds the solutions expressed in terms of radicals of the system of equations of rational functions \\spad{leq} with respect to the list of symbols \\spad{lvar}.") (((|List| (|List| (|Equation| (|Expression| |#1|)))) (|List| (|Fraction| (|Polynomial| |#1|)))) "\\spad{radicalSolve(lrf)} finds the solutions expressed in terms of radicals of the system of equations \\spad{lrf} = 0,{} where \\spad{lrf} is a system of univariate rational functions.") (((|List| (|List| (|Equation| (|Expression| |#1|)))) (|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|Symbol|))) "\\spad{radicalSolve(lrf,lvar)} finds the solutions expressed in terms of radicals of the system of equations \\spad{lrf} = 0 with respect to the list of symbols \\spad{lvar},{} where \\spad{lrf} is a list of rational functions.") (((|List| (|Equation| (|Expression| |#1|))) (|Equation| (|Fraction| (|Polynomial| |#1|)))) "\\spad{radicalSolve(eq)} finds the solutions expressed in terms of radicals of the equation of rational functions \\spad{eq} with respect to the unique symbol \\spad{x} appearing in \\spad{eq}.") (((|List| (|Equation| (|Expression| |#1|))) (|Equation| (|Fraction| (|Polynomial| |#1|))) (|Symbol|)) "\\spad{radicalSolve(eq,x)} finds the solutions expressed in terms of radicals of the equation of rational functions \\spad{eq} with respect to the symbol \\spad{x}.") (((|List| (|Equation| (|Expression| |#1|))) (|Fraction| (|Polynomial| |#1|))) "\\spad{radicalSolve(rf)} finds the solutions expressed in terms of radicals of the equation \\spad{rf} = 0,{} where \\spad{rf} is a univariate rational function.") (((|List| (|Equation| (|Expression| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{radicalSolve(rf,x)} finds the solutions expressed in terms of radicals of the equation \\spad{rf} = 0 with respect to the symbol \\spad{x},{} where \\spad{rf} is a rational function."))) NIL NIL -(-1150 R) +(-1151 R) ((|constructor| (NIL "This package finds the function func3 where func1 and func2 \\indented{1}{are given and\\space{2}func1 = func3(func2) .\\space{2}If there is no solution then} \\indented{1}{function func1 will be returned.} \\indented{1}{An example would be\\space{2}\\spad{func1:= 8*X**3+32*X**2-14*X ::EXPR INT} and} \\indented{1}{\\spad{func2:=2*X ::EXPR INT} convert them via univariate} \\indented{1}{to FRAC SUP EXPR INT and then the solution is \\spad{func3:=X**3+X**2-X}} \\indented{1}{of type FRAC SUP EXPR INT}")) (|unvectorise| (((|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Vector| (|Expression| |#1|)) (|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Integer|)) "\\spad{unvectorise(vect, var, n)} returns \\spad{vect(1) + vect(2)*var + ... + vect(n+1)*var**(n)} where \\spad{vect} is the vector of the coefficients of the polynomail ,{} \\spad{var} the new variable and \\spad{n} the degree.")) (|decomposeFunc| (((|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|)))) "\\spad{decomposeFunc(func1, func2, newvar)} returns a function func3 where \\spad{func1} = func3(\\spad{func2}) and expresses it in the new variable newvar. If there is no solution then \\spad{func1} will be returned."))) NIL NIL -(-1151 R) +(-1152 R) ((|constructor| (NIL "This package tries to find solutions of equations of type Expression(\\spad{R}). This means expressions involving transcendental,{} exponential,{} logarithmic and nthRoot functions. After trying to transform different kernels to one kernel by applying several rules,{} it calls zerosOf for the SparseUnivariatePolynomial in the remaining kernel. For example the expression \\spad{sin(x)*cos(x)-2} will be transformed to \\indented{3}{\\spad{-2 tan(x/2)**4 -2 tan(x/2)**3 -4 tan(x/2)**2 +2 tan(x/2) -2}} by using the function normalize and then to \\indented{3}{\\spad{-2 tan(x)**2 + tan(x) -2}} with help of subsTan. This function tries to express the given function in terms of \\spad{tan(x/2)} to express in terms of \\spad{tan(x)} . Other examples are the expressions \\spad{sqrt(x+1)+sqrt(x+7)+1} or \\indented{1}{\\spad{sqrt(sin(x))+1} .}")) (|solve| (((|List| (|List| (|Equation| (|Expression| |#1|)))) (|List| (|Equation| (|Expression| |#1|))) (|List| (|Symbol|))) "\\spad{solve(leqs, lvar)} returns a list of solutions to the list of equations \\spad{leqs} with respect to the list of symbols lvar.") (((|List| (|Equation| (|Expression| |#1|))) (|Expression| |#1|) (|Symbol|)) "\\spad{solve(expr,x)} finds the solutions of the equation \\spad{expr} = 0 with respect to the symbol \\spad{x} where \\spad{expr} is a function of type Expression(\\spad{R}).") (((|List| (|Equation| (|Expression| |#1|))) (|Equation| (|Expression| |#1|)) (|Symbol|)) "\\spad{solve(eq,x)} finds the solutions of the equation \\spad{eq} where \\spad{eq} is an equation of functions of type Expression(\\spad{R}) with respect to the symbol \\spad{x}.") (((|List| (|Equation| (|Expression| |#1|))) (|Equation| (|Expression| |#1|))) "\\spad{solve(eq)} finds the solutions of the equation \\spad{eq} where \\spad{eq} is an equation of functions of type Expression(\\spad{R}) with respect to the unique symbol \\spad{x} appearing in \\spad{eq}.") (((|List| (|Equation| (|Expression| |#1|))) (|Expression| |#1|)) "\\spad{solve(expr)} finds the solutions of the equation \\spad{expr} = 0 where \\spad{expr} is a function of type Expression(\\spad{R}) with respect to the unique symbol \\spad{x} appearing in eq."))) NIL NIL -(-1152 S A) +(-1153 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 (-861)))) -(-1153 R) +(-1154 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 -(-1154 R) +(-1155 R) ((|constructor| (NIL "The category ThreeSpaceCategory is used for creating three dimensional objects using functions for defining points,{} curves,{} polygons,{} constructs and the subspaces containing them.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(s)} returns the \\spadtype{ThreeSpace} \\spad{s} to Output format.")) (|subspace| (((|SubSpace| 3 |#1|) $) "\\spad{subspace(s)} returns the \\spadtype{SubSpace} which holds all the point information in the \\spadtype{ThreeSpace},{} \\spad{s}.")) (|check| (($ $) "\\spad{check(s)} returns lllpt,{} list of lists of lists of point information about the \\spadtype{ThreeSpace} \\spad{s}.")) (|objects| (((|Record| (|:| |points| (|NonNegativeInteger|)) (|:| |curves| (|NonNegativeInteger|)) (|:| |polygons| (|NonNegativeInteger|)) (|:| |constructs| (|NonNegativeInteger|))) $) "\\spad{objects(s)} returns the \\spadtype{ThreeSpace},{} \\spad{s},{} in the form of a 3D object record containing information on the number of points,{} curves,{} polygons and constructs comprising the \\spadtype{ThreeSpace}..")) (|lprop| (((|List| (|SubSpaceComponentProperty|)) $) "\\spad{lprop(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a list of subspace component properties,{} and if so,{} returns the list; An error is signaled otherwise.")) (|llprop| (((|List| (|List| (|SubSpaceComponentProperty|))) $) "\\spad{llprop(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a list of curves which are lists of the subspace component properties of the curves,{} and if so,{} returns the list of lists; An error is signaled otherwise.")) (|lllp| (((|List| (|List| (|List| (|Point| |#1|)))) $) "\\spad{lllp(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a list of components,{} which are lists of curves,{} which are lists of points,{} and if so,{} returns the list of lists of lists; An error is signaled otherwise.")) (|lllip| (((|List| (|List| (|List| (|NonNegativeInteger|)))) $) "\\spad{lllip(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a list of components,{} which are lists of curves,{} which are lists of indices to points,{} and if so,{} returns the list of lists of lists; An error is signaled otherwise.")) (|lp| (((|List| (|Point| |#1|)) $) "\\spad{lp(s)} returns the list of points component which the \\spadtype{ThreeSpace},{} \\spad{s},{} contains; these points are used by reference,{} \\spadignore{i.e.} the component holds indices referring to the points rather than the points themselves. This allows for sharing of the points.")) (|mesh?| (((|Boolean|) $) "\\spad{mesh?(s)} returns \\spad{true} if the \\spadtype{ThreeSpace} \\spad{s} is composed of one component,{} a mesh comprising a list of curves which are lists of points,{} or returns \\spad{false} if otherwise")) (|mesh| (((|List| (|List| (|Point| |#1|))) $) "\\spad{mesh(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single surface component defined by a list curves which contain lists of points,{} and if so,{} returns the list of lists of points; An error is signaled otherwise.") (($ (|List| (|List| (|Point| |#1|))) (|Boolean|) (|Boolean|)) "\\spad{mesh([[p0],[p1],...,[pn]], close1, close2)} creates a surface defined over a list of curves,{} \\spad{p0} through \\spad{pn},{} which are lists of points; the booleans \\spad{close1} and 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); close2 set to \\spad{true} means that the boundary at one end of the surface is to be connected to the boundary at the other end (the boundaries are defined as the first list of points (curve) and the last list of points (curve)); the \\spadtype{ThreeSpace} containing this surface is returned.") (($ (|List| (|List| (|Point| |#1|)))) "\\spad{mesh([[p0],[p1],...,[pn]])} creates a surface defined by a list of curves which are lists,{} \\spad{p0} through \\spad{pn},{} of points,{} and returns a \\spadtype{ThreeSpace} whose component is the surface.") (($ $ (|List| (|List| (|List| |#1|))) (|Boolean|) (|Boolean|)) "\\spad{mesh(s,[ [[r10]...,[r1m]], [[r20]...,[r2m]],..., [[rn0]...,[rnm]] ], close1, close2)} adds a surface component to the \\spadtype{ThreeSpace} \\spad{s},{} which is defined over a rectangular domain of size \\spad{WxH} where \\spad{W} is the number of lists of points from the domain \\spad{PointDomain(R)} and \\spad{H} is the number of elements in each of those lists; the booleans \\spad{close1} and close2 indicate how the surface is to be closed: if \\spad{close1} is \\spad{true} this means that each individual list (a curve) is to be closed (\\spadignore{i.e.} the last point of the list is to be connected to the first point); if close2 is \\spad{true},{} this means that the boundary at one end of the surface is to be connected to the boundary at the other end (the boundaries are defined as the first list of points (curve) and the last list of points (curve)).") (($ $ (|List| (|List| (|Point| |#1|))) (|Boolean|) (|Boolean|)) "\\spad{mesh(s,[[p0],[p1],...,[pn]], close1, close2)} adds a surface component to the \\spadtype{ThreeSpace},{} which is defined over a list of curves,{} in which each of these curves is a list of points. The boolean arguments \\spad{close1} and close2 indicate how the surface is to be closed. Argument \\spad{close1} equal \\spad{true} means that each individual list (a curve) is to be closed,{} \\spadignore{i.e.} the last point of the list is to be connected to the first point. Argument close2 equal \\spad{true} means that the boundary at one end of the surface is to be connected to the boundary at the other end,{} \\spadignore{i.e.} the boundaries are defined as the first list of points (curve) and the last list of points (curve).") (($ $ (|List| (|List| (|List| |#1|))) (|List| (|SubSpaceComponentProperty|)) (|SubSpaceComponentProperty|)) "\\spad{mesh(s,[ [[r10]...,[r1m]], [[r20]...,[r2m]],..., [[rn0]...,[rnm]] ], [props], prop)} adds a surface component to the \\spadtype{ThreeSpace} \\spad{s},{} which is defined over a rectangular domain of size \\spad{WxH} where \\spad{W} is the number of lists of points from the domain \\spad{PointDomain(R)} and \\spad{H} is the number of elements in each of those lists; lprops is the list of the subspace component properties for each curve list,{} and prop is the subspace component property by which the points are defined.") (($ $ (|List| (|List| (|Point| |#1|))) (|List| (|SubSpaceComponentProperty|)) (|SubSpaceComponentProperty|)) "\\spad{mesh(s,[[p0],[p1],...,[pn]],[props],prop)} adds a surface component,{} defined over a list curves which contains lists of points,{} to the \\spadtype{ThreeSpace} \\spad{s}; props is a list which contains the subspace component properties for each surface parameter,{} and \\spad{prop} is the subspace component property by which the points are defined.")) (|polygon?| (((|Boolean|) $) "\\spad{polygon?(s)} returns \\spad{true} if the \\spadtype{ThreeSpace} \\spad{s} contains a single polygon component,{} or \\spad{false} otherwise.")) (|polygon| (((|List| (|Point| |#1|)) $) "\\spad{polygon(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single polygon component defined by a list of points,{} and if so,{} returns the list of points; An error is signaled otherwise.") (($ (|List| (|Point| |#1|))) "\\spad{polygon([p0,p1,...,pn])} creates a polygon defined by a list of points,{} \\spad{p0} through \\spad{pn},{} and returns a \\spadtype{ThreeSpace} whose component is the polygon.") (($ $ (|List| (|List| |#1|))) "\\spad{polygon(s,[[r0],[r1],...,[rn]])} adds a polygon component defined by a list of points \\spad{r0} through \\spad{rn},{} which are lists of elements from the domain \\spad{PointDomain(m,R)} to the \\spadtype{ThreeSpace} \\spad{s},{} where \\spad{m} is the dimension of the points and \\spad{R} is the \\spadtype{Ring} over which the points are defined.") (($ $ (|List| (|Point| |#1|))) "\\spad{polygon(s,[p0,p1,...,pn])} adds a polygon component defined by a list of points,{} \\spad{p0} throught \\spad{pn},{} to the \\spadtype{ThreeSpace} \\spad{s}.")) (|closedCurve?| (((|Boolean|) $) "\\spad{closedCurve?(s)} returns \\spad{true} if the \\spadtype{ThreeSpace} \\spad{s} contains a single closed curve component,{} \\spadignore{i.e.} the first element of the curve is also the last element,{} or \\spad{false} otherwise.")) (|closedCurve| (((|List| (|Point| |#1|)) $) "\\spad{closedCurve(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single closed curve component defined by a list of points in which the first point is also the last point,{} all of which are from the domain \\spad{PointDomain(m,R)} and if so,{} returns the list of points. An error is signaled otherwise.") (($ (|List| (|Point| |#1|))) "\\spad{closedCurve(lp)} sets a list of points defined by the first element of \\spad{lp} through the last element of \\spad{lp} and back to the first elelment again and returns a \\spadtype{ThreeSpace} whose component is the closed curve defined by \\spad{lp}.") (($ $ (|List| (|List| |#1|))) "\\spad{closedCurve(s,[[lr0],[lr1],...,[lrn],[lr0]])} adds a closed curve component defined by a list of points \\spad{lr0} through \\spad{lrn},{} which are lists of elements from the domain \\spad{PointDomain(m,R)},{} where \\spad{R} is the \\spadtype{Ring} over which the point elements are defined and \\spad{m} is the dimension of the points,{} in which the last element of the list of points contains a copy of the first element list,{} \\spad{lr0}. The closed curve is added to the \\spadtype{ThreeSpace},{} \\spad{s}.") (($ $ (|List| (|Point| |#1|))) "\\spad{closedCurve(s,[p0,p1,...,pn,p0])} adds a closed curve component which is a list of points defined by the first element \\spad{p0} through the last element \\spad{pn} and back to the first element \\spad{p0} again,{} to the \\spadtype{ThreeSpace} \\spad{s}.")) (|curve?| (((|Boolean|) $) "\\spad{curve?(s)} queries whether the \\spadtype{ThreeSpace},{} \\spad{s},{} is a curve,{} \\spadignore{i.e.} has one component,{} a list of list of points,{} and returns \\spad{true} if it is,{} or \\spad{false} otherwise.")) (|curve| (((|List| (|Point| |#1|)) $) "\\spad{curve(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single curve defined by a list of points and if so,{} returns the curve,{} \\spadignore{i.e.} list of points. An error is signaled otherwise.") (($ (|List| (|Point| |#1|))) "\\spad{curve([p0,p1,p2,...,pn])} creates a space curve defined by the list of points \\spad{p0} through \\spad{pn},{} and returns the \\spadtype{ThreeSpace} whose component is the curve.") (($ $ (|List| (|List| |#1|))) "\\spad{curve(s,[[p0],[p1],...,[pn]])} adds a space curve which is a list of points \\spad{p0} through \\spad{pn} defined by lists of elements from the domain \\spad{PointDomain(m,R)},{} where \\spad{R} is the \\spadtype{Ring} over which the point elements are defined and \\spad{m} is the dimension of the points,{} to the \\spadtype{ThreeSpace} \\spad{s}.") (($ $ (|List| (|Point| |#1|))) "\\spad{curve(s,[p0,p1,...,pn])} adds a space curve component defined by a list of points \\spad{p0} through \\spad{pn},{} to the \\spadtype{ThreeSpace} \\spad{s}.")) (|point?| (((|Boolean|) $) "\\spad{point?(s)} queries whether the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single component which is a point and returns the boolean result.")) (|point| (((|Point| |#1|) $) "\\spad{point(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of only a single point and if so,{} returns the point. An error is signaled otherwise.") (($ (|Point| |#1|)) "\\spad{point(p)} returns a \\spadtype{ThreeSpace} object which is composed of one component,{} the point \\spad{p}.") (($ $ (|NonNegativeInteger|)) "\\spad{point(s,i)} adds a point component which is placed into a component list of the \\spadtype{ThreeSpace},{} \\spad{s},{} at the index given by \\spad{i}.") (($ $ (|List| |#1|)) "\\spad{point(s,[x,y,z])} adds a point component defined by a list of elements which are from the \\spad{PointDomain(R)} to the \\spadtype{ThreeSpace},{} \\spad{s},{} where \\spad{R} is the \\spadtype{Ring} over which the point elements are defined.") (($ $ (|Point| |#1|)) "\\spad{point(s,p)} adds a point component defined by the point,{} \\spad{p},{} specified as a list from \\spad{List(R)},{} to the \\spadtype{ThreeSpace},{} \\spad{s},{} where \\spad{R} is the \\spadtype{Ring} over which the point is defined.")) (|modifyPointData| (($ $ (|NonNegativeInteger|) (|Point| |#1|)) "\\spad{modifyPointData(s,i,p)} changes the point at the indexed location \\spad{i} in the \\spadtype{ThreeSpace},{} \\spad{s},{} to that of point \\spad{p}. This is useful for making changes to a point which has been transformed.")) (|enterPointData| (((|NonNegativeInteger|) $ (|List| (|Point| |#1|))) "\\spad{enterPointData(s,[p0,p1,...,pn])} adds a list of points from \\spad{p0} through \\spad{pn} to the \\spadtype{ThreeSpace},{} \\spad{s},{} and returns the index,{} to the starting point of the list.")) (|copy| (($ $) "\\spad{copy(s)} returns a new \\spadtype{ThreeSpace} that is an exact copy of \\spad{s}.")) (|composites| (((|List| $) $) "\\spad{composites(s)} takes the \\spadtype{ThreeSpace} \\spad{s},{} and creates a list containing a unique \\spadtype{ThreeSpace} for each single composite of \\spad{s}. If \\spad{s} has no composites defined (composites need to be explicitly created),{} the list returned is empty. Note that not all the components need to be part of a composite.")) (|components| (((|List| $) $) "\\spad{components(s)} takes the \\spadtype{ThreeSpace} \\spad{s},{} and creates a list containing a unique \\spadtype{ThreeSpace} for each single component of \\spad{s}. If \\spad{s} has no components defined,{} the list returned is empty.")) (|composite| (($ (|List| $)) "\\spad{composite([s1,s2,...,sn])} will create a new \\spadtype{ThreeSpace} that is a union of all the components from each \\spadtype{ThreeSpace} in the parameter list,{} grouped as a composite.")) (|merge| (($ $ $) "\\spad{merge(s1,s2)} will create a new \\spadtype{ThreeSpace} that has the components of \\spad{s1} and \\spad{s2}; Groupings of components into composites are maintained.") (($ (|List| $)) "\\spad{merge([s1,s2,...,sn])} will create a new \\spadtype{ThreeSpace} that has the components of all the ones in the list; Groupings of components into composites are maintained.")) (|numberOfComposites| (((|NonNegativeInteger|) $) "\\spad{numberOfComposites(s)} returns the number of supercomponents,{} or composites,{} in the \\spadtype{ThreeSpace},{} \\spad{s}; Composites are arbitrary groupings of otherwise distinct and unrelated components; A \\spadtype{ThreeSpace} need not have any composites defined at all and,{} outside of the requirement that no component can belong to more than one composite at a time,{} the definition and interpretation of composites are unrestricted.")) (|numberOfComponents| (((|NonNegativeInteger|) $) "\\spad{numberOfComponents(s)} returns the number of distinct object components in the indicated \\spadtype{ThreeSpace},{} \\spad{s},{} such as points,{} curves,{} polygons,{} and constructs.")) (|create3Space| (($ (|SubSpace| 3 |#1|)) "\\spad{create3Space(s)} creates a \\spadtype{ThreeSpace} object containing objects pre-defined within some \\spadtype{SubSpace} \\spad{s}.") (($) "\\spad{create3Space()} creates a \\spadtype{ThreeSpace} object capable of holding point,{} curve,{} mesh components and any combination."))) NIL NIL -(-1155) +(-1156) ((|constructor| (NIL "This domain represents a kind of base domain \\indented{2}{for Spad syntax domain.\\space{2}It merely exists as a kind of} \\indented{2}{of abstract base in object-oriented programming language.} \\indented{2}{However,{} this is not an abstract class.}"))) NIL NIL -(-1156) +(-1157) ((|constructor| (NIL "\\indented{1}{This package provides a simple Spad algebra parser.} Related Constructors: Syntax. See Also: Syntax.")) (|parse| (((|List| (|Syntax|)) (|String|)) "\\spad{parse(f)} parses the source file \\spad{f} (supposedly containing Spad algebras) and returns a List Syntax. The filename \\spad{f} is supposed to have the proper extension. Note that this function has the side effect of executing any system command contained in the file \\spad{f},{} even if it might not be meaningful."))) NIL NIL -(-1157) +(-1158) ((|constructor| (NIL "This category describes the exported \\indented{2}{signatures of the SpadAst domain.}")) (|autoCoerce| (((|Integer|) $) "\\spad{autoCoerce(s)} returns the Integer view of \\spad{`s'}. Left at the discretion of the compiler.") (((|String|) $) "\\spad{autoCoerce(s)} returns the String view of \\spad{`s'}. Left at the discretion of the compiler.") (((|Identifier|) $) "\\spad{autoCoerce(s)} returns the Identifier view of \\spad{`s'}. Left at the discretion of the compiler.") (((|IsAst|) $) "\\spad{autoCoerce(s)} returns the IsAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|HasAst|) $) "\\spad{autoCoerce(s)} returns the HasAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|CaseAst|) $) "\\spad{autoCoerce(s)} returns the CaseAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|ColonAst|) $) "\\spad{autoCoerce(s)} returns the ColoonAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|SuchThatAst|) $) "\\spad{autoCoerce(s)} returns the SuchThatAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|LetAst|) $) "\\spad{autoCoerce(s)} returns the LetAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|SequenceAst|) $) "\\spad{autoCoerce(s)} returns the SequenceAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|SegmentAst|) $) "\\spad{autoCoerce(s)} returns the SegmentAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|RestrictAst|) $) "\\spad{autoCoerce(s)} returns the RestrictAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|PretendAst|) $) "\\spad{autoCoerce(s)} returns the PretendAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|CoerceAst|) $) "\\spad{autoCoerce(s)} returns the CoerceAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|ReturnAst|) $) "\\spad{autoCoerce(s)} returns the ReturnAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|ExitAst|) $) "\\spad{autoCoerce(s)} returns the ExitAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|ConstructAst|) $) "\\spad{autoCoerce(s)} returns the ConstructAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|CollectAst|) $) "\\spad{autoCoerce(s)} returns the CollectAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|StepAst|) $) "\\spad{autoCoerce(s)} returns the InAst view of \\spad{s}. Left at the discretion of the compiler.") (((|InAst|) $) "\\spad{autoCoerce(s)} returns the InAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|WhileAst|) $) "\\spad{autoCoerce(s)} returns the WhileAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|RepeatAst|) $) "\\spad{autoCoerce(s)} returns the RepeatAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|IfAst|) $) "\\spad{autoCoerce(s)} returns the IfAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|MappingAst|) $) "\\spad{autoCoerce(s)} returns the MappingAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|AttributeAst|) $) "\\spad{autoCoerce(s)} returns the AttributeAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|SignatureAst|) $) "\\spad{autoCoerce(s)} returns the SignatureAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|CapsuleAst|) $) "\\spad{autoCoerce(s)} returns the CapsuleAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|JoinAst|) $) "\\spad{autoCoerce(s)} returns the \\spadype{JoinAst} view of of the AST object \\spad{s}. Left at the discretion of the compiler.") (((|CategoryAst|) $) "\\spad{autoCoerce(s)} returns the CategoryAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|WhereAst|) $) "\\spad{autoCoerce(s)} returns the WhereAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|MacroAst|) $) "\\spad{autoCoerce(s)} returns the MacroAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|DefinitionAst|) $) "\\spad{autoCoerce(s)} returns the DefinitionAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|ImportAst|) $) "\\spad{autoCoerce(s)} returns the ImportAst view of \\spad{`s'}. Left at the discretion of the compiler.")) (|case| (((|Boolean|) $ (|[\|\|]| (|Integer|))) "\\spad{s case Integer} holds if \\spad{`s'} represents an integer literal.") (((|Boolean|) $ (|[\|\|]| (|String|))) "\\spad{s case String} holds if \\spad{`s'} represents a string literal.") (((|Boolean|) $ (|[\|\|]| (|Identifier|))) "\\spad{s case Identifier} holds if \\spad{`s'} represents an identifier.") (((|Boolean|) $ (|[\|\|]| (|IsAst|))) "\\spad{s case IsAst} holds if \\spad{`s'} represents an is-expression.") (((|Boolean|) $ (|[\|\|]| (|HasAst|))) "\\spad{s case HasAst} holds if \\spad{`s'} represents a has-expression.") (((|Boolean|) $ (|[\|\|]| (|CaseAst|))) "\\spad{s case CaseAst} holds if \\spad{`s'} represents a case-expression.") (((|Boolean|) $ (|[\|\|]| (|ColonAst|))) "\\spad{s case ColonAst} holds if \\spad{`s'} represents a colon-expression.") (((|Boolean|) $ (|[\|\|]| (|SuchThatAst|))) "\\spad{s case SuchThatAst} holds if \\spad{`s'} represents a qualified-expression.") (((|Boolean|) $ (|[\|\|]| (|LetAst|))) "\\spad{s case LetAst} holds if \\spad{`s'} represents an assignment-expression.") (((|Boolean|) $ (|[\|\|]| (|SequenceAst|))) "\\spad{s case SequenceAst} holds if \\spad{`s'} represents a sequence-of-statements.") (((|Boolean|) $ (|[\|\|]| (|SegmentAst|))) "\\spad{s case SegmentAst} holds if \\spad{`s'} represents a segment-expression.") (((|Boolean|) $ (|[\|\|]| (|RestrictAst|))) "\\spad{s case RestrictAst} holds if \\spad{`s'} represents a restrict-expression.") (((|Boolean|) $ (|[\|\|]| (|PretendAst|))) "\\spad{s case PretendAst} holds if \\spad{`s'} represents a pretend-expression.") (((|Boolean|) $ (|[\|\|]| (|CoerceAst|))) "\\spad{s case ReturnAst} holds if \\spad{`s'} represents a coerce-expression.") (((|Boolean|) $ (|[\|\|]| (|ReturnAst|))) "\\spad{s case ReturnAst} holds if \\spad{`s'} represents a return-statement.") (((|Boolean|) $ (|[\|\|]| (|ExitAst|))) "\\spad{s case ExitAst} holds if \\spad{`s'} represents an exit-expression.") (((|Boolean|) $ (|[\|\|]| (|ConstructAst|))) "\\spad{s case ConstructAst} holds if \\spad{`s'} represents a list-expression.") (((|Boolean|) $ (|[\|\|]| (|CollectAst|))) "\\spad{s case CollectAst} holds if \\spad{`s'} represents a list-comprehension.") (((|Boolean|) $ (|[\|\|]| (|StepAst|))) "\\spad{s case StepAst} holds if \\spad{s} represents an arithmetic progression iterator.") (((|Boolean|) $ (|[\|\|]| (|InAst|))) "\\spad{s case InAst} holds if \\spad{`s'} represents a in-iterator") (((|Boolean|) $ (|[\|\|]| (|WhileAst|))) "\\spad{s case WhileAst} holds if \\spad{`s'} represents a while-iterator") (((|Boolean|) $ (|[\|\|]| (|RepeatAst|))) "\\spad{s case RepeatAst} holds if \\spad{`s'} represents an repeat-loop.") (((|Boolean|) $ (|[\|\|]| (|IfAst|))) "\\spad{s case IfAst} holds if \\spad{`s'} represents an if-statement.") (((|Boolean|) $ (|[\|\|]| (|MappingAst|))) "\\spad{s case MappingAst} holds if \\spad{`s'} represents a mapping type.") (((|Boolean|) $ (|[\|\|]| (|AttributeAst|))) "\\spad{s case AttributeAst} holds if \\spad{`s'} represents an attribute.") (((|Boolean|) $ (|[\|\|]| (|SignatureAst|))) "\\spad{s case SignatureAst} holds if \\spad{`s'} represents a signature export.") (((|Boolean|) $ (|[\|\|]| (|CapsuleAst|))) "\\spad{s case CapsuleAst} holds if \\spad{`s'} represents a domain capsule.") (((|Boolean|) $ (|[\|\|]| (|JoinAst|))) "\\spad{s case JoinAst} holds is the syntax object \\spad{s} denotes the join of several categories.") (((|Boolean|) $ (|[\|\|]| (|CategoryAst|))) "\\spad{s case CategoryAst} holds if \\spad{`s'} represents an unnamed category.") (((|Boolean|) $ (|[\|\|]| (|WhereAst|))) "\\spad{s case WhereAst} holds if \\spad{`s'} represents an expression with local definitions.") (((|Boolean|) $ (|[\|\|]| (|MacroAst|))) "\\spad{s case MacroAst} holds if \\spad{`s'} represents a macro definition.") (((|Boolean|) $ (|[\|\|]| (|DefinitionAst|))) "\\spad{s case DefinitionAst} holds if \\spad{`s'} represents a definition.") (((|Boolean|) $ (|[\|\|]| (|ImportAst|))) "\\spad{s case ImportAst} holds if \\spad{`s'} represents an `import' statement."))) NIL NIL -(-1158) +(-1159) ((|constructor| (NIL "SpecialOutputPackage allows FORTRAN,{} Tex and \\indented{2}{Script Formula Formatter output from programs.}")) (|outputAsTex| (((|Void|) (|List| (|OutputForm|))) "\\spad{outputAsTex(l)} sends (for each expression in the list \\spad{l}) output in Tex format to the destination as defined by \\spadsyscom{set output tex}.") (((|Void|) (|OutputForm|)) "\\spad{outputAsTex(o)} sends output \\spad{o} in Tex format to the destination defined by \\spadsyscom{set output tex}.")) (|outputAsScript| (((|Void|) (|List| (|OutputForm|))) "\\spad{outputAsScript(l)} sends (for each expression in the list \\spad{l}) output in Script Formula Formatter format to the destination defined. by \\spadsyscom{set output forumula}.") (((|Void|) (|OutputForm|)) "\\spad{outputAsScript(o)} sends output \\spad{o} in Script Formula Formatter format to the destination defined by \\spadsyscom{set output formula}.")) (|outputAsFortran| (((|Void|) (|List| (|OutputForm|))) "\\spad{outputAsFortran(l)} sends (for each expression in the list \\spad{l}) output in FORTRAN format to the destination defined by \\spadsyscom{set output fortran}.") (((|Void|) (|OutputForm|)) "\\spad{outputAsFortran(o)} sends output \\spad{o} in FORTRAN format.") (((|Void|) (|String|) (|OutputForm|)) "\\spad{outputAsFortran(v,o)} sends output \\spad{v} = \\spad{o} in FORTRAN format to the destination defined by \\spadsyscom{set output fortran}."))) NIL NIL -(-1159) +(-1160) ((|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 -(-1160 V C) +(-1161 V C) ((|constructor| (NIL "This domain exports a modest implementation for the vertices of splitting trees. These vertices are called here splitting nodes. Every of these nodes store 3 informations. The first one is its value,{} that is the current expression to evaluate. The second one is its condition,{} that is the hypothesis under which the value has to be evaluated. The last one is its status,{} that is a boolean flag which is \\spad{true} iff the value is the result of its evaluation under its condition. Two splitting vertices are equal iff they have the sane values and the same conditions (so their status do not matter).")) (|subNode?| (((|Boolean|) $ $ (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{subNode?(\\spad{n1},{}\\spad{n2},{}o2)} returns \\spad{true} iff \\axiom{value(\\spad{n1}) = value(\\spad{n2})} and \\axiom{o2(condition(\\spad{n1}),{}condition(\\spad{n2}))}")) (|infLex?| (((|Boolean|) $ $ (|Mapping| (|Boolean|) |#1| |#1|) (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{infLex?(\\spad{n1},{}\\spad{n2},{}o1,{}o2)} returns \\spad{true} iff \\axiom{o1(value(\\spad{n1}),{}value(\\spad{n2}))} or \\axiom{value(\\spad{n1}) = value(\\spad{n2})} and \\axiom{o2(condition(\\spad{n1}),{}condition(\\spad{n2}))}.")) (|setEmpty!| (($ $) "\\axiom{setEmpty!(\\spad{n})} replaces \\spad{n} by \\axiom{empty()\\$\\%}.")) (|setStatus!| (($ $ (|Boolean|)) "\\axiom{setStatus!(\\spad{n},{}\\spad{b})} returns \\spad{n} whose status has been replaced by \\spad{b} if it is not empty,{} else an error is produced.")) (|setCondition!| (($ $ |#2|) "\\axiom{setCondition!(\\spad{n},{}\\spad{t})} returns \\spad{n} whose condition has been replaced by \\spad{t} if it is not empty,{} else an error is produced.")) (|setValue!| (($ $ |#1|) "\\axiom{setValue!(\\spad{n},{}\\spad{v})} returns \\spad{n} whose value has been replaced by \\spad{v} if it is not empty,{} else an error is produced.")) (|copy| (($ $) "\\axiom{copy(\\spad{n})} returns a copy of \\spad{n}.")) (|construct| (((|List| $) |#1| (|List| |#2|)) "\\axiom{construct(\\spad{v},{}\\spad{lt})} returns the same as \\axiom{[construct(\\spad{v},{}\\spad{t}) for \\spad{t} in \\spad{lt}]}") (((|List| $) (|List| (|Record| (|:| |val| |#1|) (|:| |tower| |#2|)))) "\\axiom{construct(\\spad{lvt})} returns the same as \\axiom{[construct(\\spad{vt}.val,{}\\spad{vt}.tower) for \\spad{vt} in \\spad{lvt}]}") (($ (|Record| (|:| |val| |#1|) (|:| |tower| |#2|))) "\\axiom{construct(\\spad{vt})} returns the same as \\axiom{construct(\\spad{vt}.val,{}\\spad{vt}.tower)}") (($ |#1| |#2|) "\\axiom{construct(\\spad{v},{}\\spad{t})} returns the same as \\axiom{construct(\\spad{v},{}\\spad{t},{}\\spad{false})}") (($ |#1| |#2| (|Boolean|)) "\\axiom{construct(\\spad{v},{}\\spad{t},{}\\spad{b})} returns the non-empty node with value \\spad{v},{} condition \\spad{t} and flag \\spad{b}")) (|status| (((|Boolean|) $) "\\axiom{status(\\spad{n})} returns the status of the node \\spad{n}.")) (|condition| ((|#2| $) "\\axiom{condition(\\spad{n})} returns the condition of the node \\spad{n}.")) (|value| ((|#1| $) "\\axiom{value(\\spad{n})} returns the value of the node \\spad{n}.")) (|empty?| (((|Boolean|) $) "\\axiom{empty?(\\spad{n})} returns \\spad{true} iff the node \\spad{n} is \\axiom{empty()\\$\\%}.")) (|empty| (($) "\\axiom{empty()} returns the same as \\axiom{[empty()\\$\\spad{V},{}empty()\\$\\spad{C},{}\\spad{false}]\\$\\%}"))) NIL NIL -(-1161 V C) +(-1162 V C) ((|constructor| (NIL "This domain exports a modest implementation of splitting trees. Spliiting trees are needed when the evaluation of some quantity under some hypothesis requires to split the hypothesis into sub-cases. For instance by adding some new hypothesis on one hand and its negation on another hand. The computations are terminated is a splitting tree \\axiom{a} when \\axiom{status(value(a))} is \\axiom{\\spad{true}}. Thus,{} if for the splitting tree \\axiom{a} the flag \\axiom{status(value(a))} is \\axiom{\\spad{true}},{} then \\axiom{status(value(\\spad{d}))} is \\axiom{\\spad{true}} for any subtree \\axiom{\\spad{d}} of \\axiom{a}. This property of splitting trees is called the termination condition. If no vertex in a splitting tree \\axiom{a} is equal to another,{} \\axiom{a} is said to satisfy the no-duplicates condition. The splitting tree \\axiom{a} will satisfy this condition if nodes are added to \\axiom{a} by mean of \\axiom{splitNodeOf!} and if \\axiom{construct} is only used to create the root of \\axiom{a} with no children.")) (|splitNodeOf!| (($ $ $ (|List| (|SplittingNode| |#1| |#2|)) (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{splitNodeOf!(\\spad{l},{}a,{}\\spad{ls},{}sub?)} returns \\axiom{a} where the children list of \\axiom{\\spad{l}} has been set to \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in \\spad{ls} | not subNodeOf?(\\spad{s},{}a,{}sub?)]}. Thus,{} if \\axiom{\\spad{l}} is not a node of \\axiom{a},{} this latter splitting tree is unchanged.") (($ $ $ (|List| (|SplittingNode| |#1| |#2|))) "\\axiom{splitNodeOf!(\\spad{l},{}a,{}\\spad{ls})} returns \\axiom{a} where the children list of \\axiom{\\spad{l}} has been set to \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in \\spad{ls} | not nodeOf?(\\spad{s},{}a)]}. Thus,{} if \\axiom{\\spad{l}} is not a node of \\axiom{a},{} this latter splitting tree is unchanged.")) (|remove!| (($ (|SplittingNode| |#1| |#2|) $) "\\axiom{remove!(\\spad{s},{}a)} replaces a by remove(\\spad{s},{}a)")) (|remove| (($ (|SplittingNode| |#1| |#2|) $) "\\axiom{remove(\\spad{s},{}a)} returns the splitting tree obtained from a by removing every sub-tree \\axiom{\\spad{b}} such that \\axiom{value(\\spad{b})} and \\axiom{\\spad{s}} have the same value,{} condition and status.")) (|subNodeOf?| (((|Boolean|) (|SplittingNode| |#1| |#2|) $ (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{subNodeOf?(\\spad{s},{}a,{}sub?)} returns \\spad{true} iff for some node \\axiom{\\spad{n}} in \\axiom{a} we have \\axiom{\\spad{s} = \\spad{n}} or \\axiom{status(\\spad{n})} and \\axiom{subNode?(\\spad{s},{}\\spad{n},{}sub?)}.")) (|nodeOf?| (((|Boolean|) (|SplittingNode| |#1| |#2|) $) "\\axiom{nodeOf?(\\spad{s},{}a)} returns \\spad{true} iff some node of \\axiom{a} is equal to \\axiom{\\spad{s}}")) (|result| (((|List| (|Record| (|:| |val| |#1|) (|:| |tower| |#2|))) $) "\\axiom{result(a)} where \\axiom{\\spad{ls}} is the leaves list of \\axiom{a} returns \\axiom{[[value(\\spad{s}),{}condition(\\spad{s})]\\$\\spad{VT} for \\spad{s} in \\spad{ls}]} if the computations are terminated in \\axiom{a} else an error is produced.")) (|conditions| (((|List| |#2|) $) "\\axiom{conditions(a)} returns the list of the conditions of the leaves of a")) (|construct| (($ |#1| |#2| |#1| (|List| |#2|)) "\\axiom{construct(\\spad{v1},{}\\spad{t},{}\\spad{v2},{}\\spad{lt})} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with children list given by \\axiom{[[[\\spad{v},{}\\spad{t}]\\$\\spad{S}]\\$\\% for \\spad{s} in \\spad{ls}]}.") (($ |#1| |#2| (|List| (|SplittingNode| |#1| |#2|))) "\\axiom{construct(\\spad{v},{}\\spad{t},{}\\spad{ls})} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with children list given by \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in \\spad{ls}]}.") (($ |#1| |#2| (|List| $)) "\\axiom{construct(\\spad{v},{}\\spad{t},{}la)} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with \\axiom{la} as children list.") (($ (|SplittingNode| |#1| |#2|)) "\\axiom{construct(\\spad{s})} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{\\spad{s}} and no children. Thus,{} if the status of \\axiom{\\spad{s}} is \\spad{false},{} \\axiom{[\\spad{s}]} represents the starting point of the evaluation \\axiom{value(\\spad{s})} under the hypothesis \\axiom{condition(\\spad{s})}.")) (|updateStatus!| (($ $) "\\axiom{updateStatus!(a)} returns a where the status of the vertices are updated to satisfy the \"termination condition\".")) (|extractSplittingLeaf| (((|Union| $ "failed") $) "\\axiom{extractSplittingLeaf(a)} returns the left most leaf (as a tree) whose status is \\spad{false} if any,{} else \"failed\" is returned."))) -((-4463 . T) (-4464 . T)) -((-12 (|HasCategory| (-1160 |#1| |#2|) (LIST (QUOTE -319) (LIST (QUOTE -1160) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1160 |#1| |#2|) (QUOTE (-1120)))) (|HasCategory| (-1160 |#1| |#2|) (QUOTE (-1120))) (-3794 (|HasCategory| (-1160 |#1| |#2|) (QUOTE (-102))) (|HasCategory| (-1160 |#1| |#2|) (QUOTE (-1120)))) (-3794 (|HasCategory| (-1160 |#1| |#2|) (LIST (QUOTE -625) (QUOTE (-875)))) (-12 (|HasCategory| (-1160 |#1| |#2|) (LIST (QUOTE -319) (LIST (QUOTE -1160) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1160 |#1| |#2|) (QUOTE (-1120))))) (|HasCategory| (-1160 |#1| |#2|) (LIST (QUOTE -625) (QUOTE (-875)))) (|HasCategory| (-1160 |#1| |#2|) (QUOTE (-102)))) -(-1162 |ndim| R) +((-4464 . T) (-4465 . T)) +((-12 (|HasCategory| (-1161 |#1| |#2|) (LIST (QUOTE -319) (LIST (QUOTE -1161) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1161 |#1| |#2|) (QUOTE (-1121)))) (|HasCategory| (-1161 |#1| |#2|) (QUOTE (-1121))) (-2758 (|HasCategory| (-1161 |#1| |#2|) (QUOTE (-102))) (|HasCategory| (-1161 |#1| |#2|) (QUOTE (-1121)))) (-2758 (|HasCategory| (-1161 |#1| |#2|) (LIST (QUOTE -625) (QUOTE (-876)))) (-12 (|HasCategory| (-1161 |#1| |#2|) (LIST (QUOTE -319) (LIST (QUOTE -1161) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1161 |#1| |#2|) (QUOTE (-1121))))) (|HasCategory| (-1161 |#1| |#2|) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-1161 |#1| |#2|) (QUOTE (-102)))) +(-1163 |ndim| R) ((|constructor| (NIL "\\spadtype{SquareMatrix} is a matrix domain of square matrices,{} where the number of rows (= number of columns) is a parameter of the type.")) (|unitsKnown| ((|attribute|) "the invertible matrices are simply the matrices whose determinants are units in the Ring \\spad{R}.")) (|central| ((|attribute|) "the elements of the Ring \\spad{R},{} viewed as diagonal matrices,{} commute with all matrices and,{} indeed,{} are the only matrices which commute with all matrices.")) (|squareMatrix| (($ (|Matrix| |#2|)) "\\spad{squareMatrix(m)} converts a matrix of type \\spadtype{Matrix} to a matrix of type \\spadtype{SquareMatrix}.")) (|transpose| (($ $) "\\spad{transpose(m)} returns the transpose of the matrix \\spad{m}.")) (|new| (($ |#2|) "\\spad{new(c)} constructs a new \\spadtype{SquareMatrix} object of dimension \\spad{ndim} with initial entries equal to \\spad{c}."))) -((-4460 . T) (-4452 |has| |#2| (-6 (-4465 "*"))) (-4463 . T) (-4457 . T) (-4458 . 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T) (-4453 |has| |#2| (-6 (-4466 "*"))) (-4464 . T) (-4458 . T) (-4459 . T)) +((|HasCategory| |#2| (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| |#2| (LIST (QUOTE -919) (QUOTE (-1197)))) (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (QUOTE (-237))) (|HasAttribute| |#2| (QUOTE (-4466 "*"))) (|HasCategory| |#2| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1059) (QUOTE (-576)))) (-2758 (-12 (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -651) (QUOTE (-576))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -917) (QUOTE (-1197)))))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (QUOTE (-317))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (QUOTE (-374))) (-2758 (|HasAttribute| |#2| (QUOTE (-4466 "*"))) (|HasCategory| |#2| (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| |#2| (QUOTE (-238)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-174)))) +(-1164 S) ((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|CharacterClass|)) "\\spad{rightTrim(s,cc)} returns \\spad{s} with all trailing occurences of characters in \\spad{cc} deleted. For example,{} \\axiom{rightTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"(abc\"}.") (($ $ (|Character|)) "\\spad{rightTrim(s,c)} returns \\spad{s} with all trailing occurrences of \\spad{c} deleted. For example,{} \\axiom{rightTrim(\" abc \",{} char \" \")} returns \\axiom{\" abc\"}.")) (|leftTrim| (($ $ (|CharacterClass|)) "\\spad{leftTrim(s,cc)} returns \\spad{s} with all leading characters in \\spad{cc} deleted. For example,{} \\axiom{leftTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc)\"}.") (($ $ (|Character|)) "\\spad{leftTrim(s,c)} returns \\spad{s} with all leading characters \\spad{c} deleted. For example,{} \\axiom{leftTrim(\" abc \",{} char \" \")} returns \\axiom{\"abc \"}.")) (|trim| (($ $ (|CharacterClass|)) "\\spad{trim(s,cc)} returns \\spad{s} with all characters in \\spad{cc} deleted from right and left ends. For example,{} \\axiom{trim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc\"}.") (($ $ (|Character|)) "\\spad{trim(s,c)} returns \\spad{s} with all characters \\spad{c} deleted from right and left ends. For example,{} \\axiom{trim(\" abc \",{} char \" \")} returns \\axiom{\"abc\"}.")) (|split| (((|List| $) $ (|CharacterClass|)) "\\spad{split(s,cc)} returns a list of substrings delimited by characters in \\spad{cc}.") (((|List| $) $ (|Character|)) "\\spad{split(s,c)} returns a list of substrings delimited by character \\spad{c}.")) (|coerce| (($ (|Character|)) "\\spad{coerce(c)} returns \\spad{c} as a string \\spad{s} with the character \\spad{c}.")) (|position| (((|Integer|) (|CharacterClass|) $ (|Integer|)) "\\spad{position(cc,t,i)} returns the position \\axiom{\\spad{j} \\spad{>=} \\spad{i}} in \\spad{t} of the first character belonging to \\spad{cc}.") (((|Integer|) $ $ (|Integer|)) "\\spad{position(s,t,i)} returns the position \\spad{j} of the substring \\spad{s} in string \\spad{t},{} where \\axiom{\\spad{j} \\spad{>=} \\spad{i}} is required.")) (|replace| (($ $ (|UniversalSegment| (|Integer|)) $) "\\spad{replace(s,i..j,t)} replaces the substring \\axiom{\\spad{s}(\\spad{i}..\\spad{j})} of \\spad{s} by string \\spad{t}.")) (|match?| (((|Boolean|) $ $ (|Character|)) "\\spad{match?(s,t,c)} tests if \\spad{s} matches \\spad{t} except perhaps for multiple and consecutive occurrences of character \\spad{c}. Typically \\spad{c} is the blank character.")) (|match| (((|NonNegativeInteger|) $ $ (|Character|)) "\\spad{match(p,s,wc)} tests if pattern \\axiom{\\spad{p}} matches subject \\axiom{\\spad{s}} where \\axiom{\\spad{wc}} is a wild card character. If no match occurs,{} the index \\axiom{0} is returned; otheriwse,{} the value returned is the first index of the first character in the subject matching the subject (excluding that matched by an initial wild-card). For example,{} \\axiom{match(\"*to*\",{}\"yorktown\",{}\\spad{\"*\"})} returns \\axiom{5} indicating a successful match starting at index \\axiom{5} of \\axiom{\"yorktown\"}.")) (|substring?| (((|Boolean|) $ $ (|Integer|)) "\\spad{substring?(s,t,i)} tests if \\spad{s} is a substring of \\spad{t} beginning at index \\spad{i}. Note: \\axiom{substring?(\\spad{s},{}\\spad{t},{}0) = prefix?(\\spad{s},{}\\spad{t})}.")) (|suffix?| (((|Boolean|) $ $) "\\spad{suffix?(s,t)} tests if the string \\spad{s} is the final substring of \\spad{t}. Note: \\axiom{suffix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.(\\spad{n} - \\spad{m} + \\spad{i}) for \\spad{i} in 0..maxIndex \\spad{s}])} where \\spad{m} and \\spad{n} denote the maxIndex of \\spad{s} and \\spad{t} respectively.")) (|prefix?| (((|Boolean|) $ $) "\\spad{prefix?(s,t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) NIL NIL -(-1164) +(-1165) ((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|CharacterClass|)) "\\spad{rightTrim(s,cc)} returns \\spad{s} with all trailing occurences of characters in \\spad{cc} deleted. For example,{} \\axiom{rightTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"(abc\"}.") (($ $ (|Character|)) "\\spad{rightTrim(s,c)} returns \\spad{s} with all trailing occurrences of \\spad{c} deleted. For example,{} \\axiom{rightTrim(\" abc \",{} char \" \")} returns \\axiom{\" abc\"}.")) (|leftTrim| (($ $ (|CharacterClass|)) "\\spad{leftTrim(s,cc)} returns \\spad{s} with all leading characters in \\spad{cc} deleted. For example,{} \\axiom{leftTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc)\"}.") (($ $ (|Character|)) "\\spad{leftTrim(s,c)} returns \\spad{s} with all leading characters \\spad{c} deleted. For example,{} \\axiom{leftTrim(\" abc \",{} char \" \")} returns \\axiom{\"abc \"}.")) (|trim| (($ $ (|CharacterClass|)) "\\spad{trim(s,cc)} returns \\spad{s} with all characters in \\spad{cc} deleted from right and left ends. For example,{} \\axiom{trim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc\"}.") (($ $ (|Character|)) "\\spad{trim(s,c)} returns \\spad{s} with all characters \\spad{c} deleted from right and left ends. For example,{} \\axiom{trim(\" abc \",{} char \" \")} returns \\axiom{\"abc\"}.")) (|split| (((|List| $) $ (|CharacterClass|)) "\\spad{split(s,cc)} returns a list of substrings delimited by characters in \\spad{cc}.") (((|List| $) $ (|Character|)) "\\spad{split(s,c)} returns a list of substrings delimited by character \\spad{c}.")) (|coerce| (($ (|Character|)) "\\spad{coerce(c)} returns \\spad{c} as a string \\spad{s} with the character \\spad{c}.")) (|position| (((|Integer|) (|CharacterClass|) $ (|Integer|)) "\\spad{position(cc,t,i)} returns the position \\axiom{\\spad{j} \\spad{>=} \\spad{i}} in \\spad{t} of the first character belonging to \\spad{cc}.") (((|Integer|) $ $ (|Integer|)) "\\spad{position(s,t,i)} returns the position \\spad{j} of the substring \\spad{s} in string \\spad{t},{} where \\axiom{\\spad{j} \\spad{>=} \\spad{i}} is required.")) (|replace| (($ $ (|UniversalSegment| (|Integer|)) $) "\\spad{replace(s,i..j,t)} replaces the substring \\axiom{\\spad{s}(\\spad{i}..\\spad{j})} of \\spad{s} by string \\spad{t}.")) (|match?| (((|Boolean|) $ $ (|Character|)) "\\spad{match?(s,t,c)} tests if \\spad{s} matches \\spad{t} except perhaps for multiple and consecutive occurrences of character \\spad{c}. Typically \\spad{c} is the blank character.")) (|match| (((|NonNegativeInteger|) $ $ (|Character|)) "\\spad{match(p,s,wc)} tests if pattern \\axiom{\\spad{p}} matches subject \\axiom{\\spad{s}} where \\axiom{\\spad{wc}} is a wild card character. If no match occurs,{} the index \\axiom{0} is returned; otheriwse,{} the value returned is the first index of the first character in the subject matching the subject (excluding that matched by an initial wild-card). For example,{} \\axiom{match(\"*to*\",{}\"yorktown\",{}\\spad{\"*\"})} returns \\axiom{5} indicating a successful match starting at index \\axiom{5} of \\axiom{\"yorktown\"}.")) (|substring?| (((|Boolean|) $ $ (|Integer|)) "\\spad{substring?(s,t,i)} tests if \\spad{s} is a substring of \\spad{t} beginning at index \\spad{i}. Note: \\axiom{substring?(\\spad{s},{}\\spad{t},{}0) = prefix?(\\spad{s},{}\\spad{t})}.")) (|suffix?| (((|Boolean|) $ $) "\\spad{suffix?(s,t)} tests if the string \\spad{s} is the final substring of \\spad{t}. Note: \\axiom{suffix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.(\\spad{n} - \\spad{m} + \\spad{i}) for \\spad{i} in 0..maxIndex \\spad{s}])} where \\spad{m} and \\spad{n} denote the maxIndex of \\spad{s} and \\spad{t} respectively.")) (|prefix?| (((|Boolean|) $ $) "\\spad{prefix?(s,t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) -((-4464 . T) (-4463 . T)) +((-4465 . T) (-4464 . T)) NIL -(-1165 R E V P TS) +(-1166 R E V P TS) ((|constructor| (NIL "A package providing a new algorithm for solving polynomial systems by means of regular chains. Two ways of solving are provided: in the sense of Zariski closure (like in Kalkbrener\\spad{'s} algorithm) or in the sense of the regular zeros (like in Wu,{} Wang or Lazard- Moreno methods). This algorithm is valid for nay type of regular set. It does not care about the way a polynomial is added in an regular set,{} or how two quasi-components are compared (by an inclusion-test),{} or how the invertibility test is made in the tower of simple extensions associated with a regular set. These operations are realized respectively by the domain \\spad{TS} and the packages \\spad{QCMPPK(R,E,V,P,TS)} and \\spad{RSETGCD(R,E,V,P,TS)}. The same way it does not care about the way univariate polynomial gcds (with coefficients in the tower of simple extensions associated with a regular set) are computed. The only requirement is that these gcds need to have invertible initials (normalized or not). WARNING. There is no need for a user to call diectly any operation of this package since they can be accessed by the domain \\axiomType{\\spad{TS}}. Thus,{} the operations of this package are not documented.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}"))) NIL NIL -(-1166 R E V P) +(-1167 R E V P) ((|constructor| (NIL "This domain provides an implementation of square-free regular chains. Moreover,{} the operation \\axiomOpFrom{zeroSetSplit}{SquareFreeRegularTriangularSetCategory} is an implementation of a new algorithm for solving polynomial systems by means of regular chains.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.} \\indented{2}{Version: 2}")) (|preprocess| (((|Record| (|:| |val| (|List| |#4|)) (|:| |towers| (|List| $))) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{pre_process(\\spad{lp},{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|internalZeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalZeroSetSplit(\\spad{lp},{}\\spad{b1},{}\\spad{b2},{}\\spad{b3})} is an internal subroutine,{} exported only for developement.")) (|zeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{}\\spad{b1},{}\\spad{b2}.\\spad{b3},{}\\spad{b4})} is an internal subroutine,{} exported only for developement.") (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{}clos?,{}info?)} has the same specifications as \\axiomOpFrom{zeroSetSplit}{RegularTriangularSetCategory} from \\spadtype{RegularTriangularSetCategory} Moreover,{} if \\axiom{clos?} then solves in the sense of the Zariski closure else solves in the sense of the regular zeros. If \\axiom{info?} then do print messages during the computations.")) (|internalAugment| (((|List| $) |#4| $ (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalAugment(\\spad{p},{}\\spad{ts},{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement."))) -((-4464 . T) (-4463 . T)) -((-12 (|HasCategory| |#4| (QUOTE (-1120))) (|HasCategory| |#4| (LIST (QUOTE -319) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#4| (QUOTE (-1120))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#3| (QUOTE (-379))) (|HasCategory| |#4| (LIST (QUOTE -625) (QUOTE (-875)))) (|HasCategory| |#4| (QUOTE (-102)))) -(-1167 S) +((-4465 . T) (-4464 . T)) +((-12 (|HasCategory| |#4| (QUOTE (-1121))) (|HasCategory| |#4| (LIST (QUOTE -319) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#4| (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#3| (QUOTE (-379))) (|HasCategory| |#4| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#4| (QUOTE (-102)))) +(-1168 S) ((|constructor| (NIL "Linked List implementation of a Stack")) (|stack| (($ (|List| |#1|)) "\\spad{stack([x,y,...,z])} creates a stack with first (top) element \\spad{x},{} second element \\spad{y},{}...,{}and last element \\spad{z}."))) -((-4463 . T) (-4464 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1120))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1120))) (-3794 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1120)))) (-3794 (-12 (|HasCategory| |#1| (QUOTE (-1120))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-875))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-875)))) (|HasCategory| |#1| (QUOTE (-102)))) -(-1168 A S) +((-4464 . T) (-4465 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1121))) (-2758 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1121)))) (-2758 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102)))) +(-1169 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: for many datatypes,{} \\axiom{possiblyInfinite?(\\spad{s}) = not explictlyFinite?(\\spad{s})}.")) (|explicitlyFinite?| (((|Boolean|) $) "\\spad{explicitlyFinite?(s)} tests if the stream has a finite number of elements,{} and \\spad{false} otherwise. Note: for many datatypes,{} \\axiom{explicitlyFinite?(\\spad{s}) = not possiblyInfinite?(\\spad{s})}."))) NIL NIL -(-1169 S) +(-1170 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: for many datatypes,{} \\axiom{possiblyInfinite?(\\spad{s}) = not explictlyFinite?(\\spad{s})}.")) (|explicitlyFinite?| (((|Boolean|) $) "\\spad{explicitlyFinite?(s)} tests if the stream has a finite number of elements,{} and \\spad{false} otherwise. Note: for many datatypes,{} \\axiom{explicitlyFinite?(\\spad{s}) = not possiblyInfinite?(\\spad{s})}."))) NIL NIL -(-1170 |Key| |Ent| |dent|) +(-1171 |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."))) -((-4464 . T)) -((-12 (|HasCategory| (-2 (|:| -2239 |#1|) (|:| -2904 |#2|)) (QUOTE (-1120))) (|HasCategory| (-2 (|:| -2239 |#1|) (|:| -2904 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2239) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2904) (|devaluate| |#2|)))))) (-3794 (|HasCategory| (-2 (|:| -2239 |#1|) (|:| -2904 |#2|)) (QUOTE (-1120))) (|HasCategory| |#2| (QUOTE (-1120)))) (-3794 (|HasCategory| (-2 (|:| -2239 |#1|) (|:| -2904 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2239 |#1|) (|:| -2904 |#2|)) (QUOTE (-1120))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1120)))) (-3794 (|HasCategory| (-2 (|:| -2239 |#1|) (|:| -2904 |#2|)) (QUOTE (-1120))) (|HasCategory| (-2 (|:| -2239 |#1|) (|:| -2904 |#2|)) (LIST (QUOTE -625) (QUOTE (-875)))) (|HasCategory| |#2| (QUOTE (-1120))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-875))))) (|HasCategory| (-2 (|:| -2239 |#1|) (|:| -2904 |#2|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#2| (QUOTE (-1120))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-861))) (-3794 (|HasCategory| (-2 (|:| -2239 |#1|) (|:| -2904 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (-3794 (|HasCategory| (-2 (|:| -2239 |#1|) (|:| -2904 |#2|)) (LIST (QUOTE -625) (QUOTE (-875)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-875))))) (|HasCategory| |#2| (QUOTE (-1120))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-875)))) (|HasCategory| (-2 (|:| -2239 |#1|) (|:| -2904 |#2|)) (LIST (QUOTE -625) (QUOTE (-875)))) (|HasCategory| (-2 (|:| -2239 |#1|) (|:| -2904 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2239 |#1|) (|:| -2904 |#2|)) (QUOTE (-1120)))) -(-1171) +((-4465 . T)) +((-12 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4438 |#2|)) (QUOTE (-1121))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4438 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4300) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4438) (|devaluate| |#2|)))))) (-2758 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4438 |#2|)) (QUOTE (-1121))) (|HasCategory| |#2| (QUOTE (-1121)))) (-2758 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4438 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4438 |#2|)) (QUOTE (-1121))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1121)))) (-2758 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4438 |#2|)) (QUOTE (-1121))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4438 |#2|)) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4438 |#2|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-861))) (-2758 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4438 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (-2758 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4438 |#2|)) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4438 |#2|)) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4438 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4438 |#2|)) (QUOTE (-1121)))) +(-1172) ((|constructor| (NIL "This domain represents an arithmetic progression iterator syntax.")) (|step| (((|SpadAst|) $) "\\spad{step(i)} returns the Spad AST denoting the step of the arithmetic progression represented by the iterator \\spad{i}.")) (|upperBound| (((|Maybe| (|SpadAst|)) $) "If the set of values assumed by the iteration variable is bounded from above,{} \\spad{upperBound(i)} returns the upper bound. Otherwise,{} its returns \\spad{nothing}.")) (|lowerBound| (((|SpadAst|) $) "\\spad{lowerBound(i)} returns the lower bound on the values assumed by the iteration variable.")) (|iterationVar| (((|Identifier|) $) "\\spad{iterationVar(i)} returns the name of the iterating variable of the arithmetic progression iterator \\spad{i}."))) NIL NIL -(-1172) +(-1173) ((|constructor| (NIL "A class of objects which can be 'stepped through'. Repeated applications of \\spadfun{nextItem} is guaranteed never to return duplicate items and only return \"failed\" after exhausting all elements of the domain. This assumes that the sequence starts with \\spad{init()}. For infinite domains,{} repeated application of \\spadfun{nextItem} is not required to reach all possible domain elements starting from any initial element. \\blankline Conditional attributes: \\indented{2}{infinite\\tab{15}repeated \\spad{nextItem}\\spad{'s} are never \"failed\".}")) (|nextItem| (((|Union| $ "failed") $) "\\spad{nextItem(x)} returns the next item,{} or \"failed\" if domain is exhausted.")) (|init| (($) "\\spad{init()} chooses an initial object for stepping."))) NIL NIL -(-1173 |Coef|) +(-1174 |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 -(-1174 S) +(-1175 S) ((|constructor| (NIL "Functions defined on streams with entries in one set.")) (|concat| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{concat(u)} returns the left-to-right concatentation of the streams in \\spad{u}. Note: \\spad{concat(u) = reduce(concat,u)}."))) NIL NIL -(-1175 A B) +(-1176 A B) ((|constructor| (NIL "Functions defined on streams with entries in two sets.")) (|reduce| ((|#2| |#2| (|Mapping| |#2| |#1| |#2|) (|Stream| |#1|)) "\\spad{reduce(b,f,u)},{} where \\spad{u} is a finite stream \\spad{[x0,x1,...,xn]},{} returns the value \\spad{r(n)} computed as follows: \\spad{r0 = f(x0,b), r1 = f(x1,r0),..., r(n) = f(xn,r(n-1))}.")) (|scan| (((|Stream| |#2|) |#2| (|Mapping| |#2| |#1| |#2|) (|Stream| |#1|)) "\\spad{scan(b,h,[x0,x1,x2,...])} returns \\spad{[y0,y1,y2,...]},{} where \\spad{y0 = h(x0,b)},{} \\spad{y1 = h(x1,y0)},{}\\spad{...} \\spad{yn = h(xn,y(n-1))}.")) (|map| (((|Stream| |#2|) (|Mapping| |#2| |#1|) (|Stream| |#1|)) "\\spad{map(f,s)} returns a stream whose elements are the function \\spad{f} applied to the corresponding elements of \\spad{s}. Note: \\spad{map(f,[x0,x1,x2,...]) = [f(x0),f(x1),f(x2),..]}."))) NIL NIL -(-1176 A B C) +(-1177 A B C) ((|constructor| (NIL "Functions defined on streams with entries in three sets.")) (|map| (((|Stream| |#3|) (|Mapping| |#3| |#1| |#2|) (|Stream| |#1|) (|Stream| |#2|)) "\\spad{map(f,st1,st2)} returns the stream whose elements are the function \\spad{f} applied to the corresponding elements of \\spad{st1} and \\spad{st2}. Note: \\spad{map(f,[x0,x1,x2,..],[y0,y1,y2,..]) = [f(x0,y0),f(x1,y1),..]}."))) NIL NIL -(-1177 S) +(-1178 S) ((|constructor| (NIL "A stream is an implementation of an infinite sequence using a list of terms that have been computed and a function closure to compute additional terms when needed.")) (|filterUntil| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterUntil(p,s)} returns \\spad{[x0,x1,...,x(n)]} where \\spad{s = [x0,x1,x2,..]} and \\spad{n} is the smallest index such that \\spad{p(xn) = true}.")) (|filterWhile| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterWhile(p,s)} returns \\spad{[x0,x1,...,x(n-1)]} where \\spad{s = [x0,x1,x2,..]} and \\spad{n} is the smallest index such that \\spad{p(xn) = false}.")) (|generate| (($ (|Mapping| |#1| |#1|) |#1|) "\\spad{generate(f,x)} creates an infinite stream whose first element is \\spad{x} and whose \\spad{n}th element (\\spad{n > 1}) is \\spad{f} applied to the previous element. Note: \\spad{generate(f,x) = [x,f(x),f(f(x)),...]}.") (($ (|Mapping| |#1|)) "\\spad{generate(f)} creates an infinite stream all of whose elements are equal to \\spad{f()}. Note: \\spad{generate(f) = [f(),f(),f(),...]}.")) (|setrest!| (($ $ (|Integer|) $) "\\spad{setrest!(x,n,y)} sets rest(\\spad{x},{}\\spad{n}) to \\spad{y}. The function will expand cycles if necessary.")) (|showAll?| (((|Boolean|)) "\\spad{showAll?()} returns \\spad{true} if all computed entries of streams will be displayed.")) (|showAllElements| (((|OutputForm|) $) "\\spad{showAllElements(s)} creates an output form which displays all computed elements.")) (|output| (((|Void|) (|Integer|) $) "\\spad{output(n,st)} computes and displays the first \\spad{n} entries of \\spad{st}.")) (|cons| (($ |#1| $) "\\spad{cons(a,s)} returns a stream whose \\spad{first} is \\spad{a} and whose \\spad{rest} is \\spad{s}. Note: \\spad{cons(a,s) = concat(a,s)}.")) (|delay| (($ (|Mapping| $)) "\\spad{delay(f)} creates a stream with a lazy evaluation defined by function \\spad{f}. Caution: This function can only be called in compiled code.")) (|findCycle| (((|Record| (|:| |cycle?| (|Boolean|)) (|:| |prefix| (|NonNegativeInteger|)) (|:| |period| (|NonNegativeInteger|))) (|NonNegativeInteger|) $) "\\spad{findCycle(n,st)} determines if \\spad{st} is periodic within \\spad{n}.")) (|repeating?| (((|Boolean|) (|List| |#1|) $) "\\spad{repeating?(l,s)} returns \\spad{true} if a stream \\spad{s} is periodic with period \\spad{l},{} and \\spad{false} otherwise.")) (|repeating| (($ (|List| |#1|)) "\\spad{repeating(l)} is a repeating stream whose period is the list \\spad{l}.")) (|shallowlyMutable| ((|attribute|) "one may destructively alter a stream by assigning new values to its entries."))) -((-4464 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1120))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1120))) (-3794 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1120)))) (-3794 (-12 (|HasCategory| |#1| (QUOTE (-1120))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-875))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-576) (QUOTE (-861))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-875)))) (|HasCategory| |#1| (QUOTE (-102)))) -(-1178) +((-4465 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1121))) (-2758 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1121)))) (-2758 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| (-576) (QUOTE (-861))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102)))) +(-1179) ((|string| (($ (|DoubleFloat|)) "\\spad{string f} returns the decimal representation of \\spad{f} in a string") (($ (|Integer|)) "\\spad{string i} returns the decimal representation of \\spad{i} in a string"))) -((-4464 . T) (-4463 . T)) -((-3794 (-12 (|HasCategory| (-145) (QUOTE (-861))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1120))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145)))))) (-3794 (|HasCategory| (-145) (LIST (QUOTE -625) (QUOTE (-875)))) (-12 (|HasCategory| (-145) (QUOTE (-1120))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -626) (QUOTE (-548)))) (-3794 (|HasCategory| (-145) (QUOTE (-861))) (|HasCategory| (-145) (QUOTE (-1120)))) (|HasCategory| (-145) (QUOTE (-861))) (-3794 (|HasCategory| (-145) (QUOTE (-102))) (|HasCategory| (-145) (QUOTE (-861))) (|HasCategory| (-145) (QUOTE (-1120)))) (|HasCategory| (-576) (QUOTE (-861))) (|HasCategory| (-145) (QUOTE (-1120))) (|HasCategory| (-145) (LIST (QUOTE -625) (QUOTE (-875)))) (|HasCategory| (-145) (QUOTE (-102))) (-12 (|HasCategory| (-145) (QUOTE (-1120))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145)))))) -(-1179 |Entry|) +((-4465 . T) (-4464 . T)) +((-2758 (-12 (|HasCategory| (-145) (QUOTE (-861))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1121))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145)))))) (-2758 (|HasCategory| (-145) (LIST (QUOTE -625) (QUOTE (-876)))) (-12 (|HasCategory| (-145) (QUOTE (-1121))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -626) (QUOTE (-548)))) (-2758 (|HasCategory| (-145) (QUOTE (-861))) (|HasCategory| (-145) (QUOTE (-1121)))) (|HasCategory| (-145) (QUOTE (-861))) (-2758 (|HasCategory| (-145) (QUOTE (-102))) (|HasCategory| (-145) (QUOTE (-861))) (|HasCategory| (-145) (QUOTE (-1121)))) (|HasCategory| (-576) (QUOTE (-861))) (|HasCategory| (-145) (QUOTE (-1121))) (|HasCategory| (-145) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-145) (QUOTE (-102))) (-12 (|HasCategory| (-145) (QUOTE (-1121))) (|HasCategory| (-145) (LIST (QUOTE -319) (QUOTE (-145)))))) +(-1180 |Entry|) ((|constructor| (NIL "This domain provides tables where the keys are strings. A specialized hash function for strings is used."))) -((-4463 . T) (-4464 . T)) -((-12 (|HasCategory| (-2 (|:| -2239 (-1178)) (|:| -2904 |#1|)) (QUOTE (-1120))) (|HasCategory| (-2 (|:| -2239 (-1178)) (|:| -2904 |#1|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2239) (QUOTE (-1178))) (LIST (QUOTE |:|) (QUOTE -2904) (|devaluate| |#1|)))))) (-3794 (|HasCategory| (-2 (|:| -2239 (-1178)) (|:| -2904 |#1|)) (QUOTE (-1120))) (|HasCategory| |#1| (QUOTE (-1120)))) (-3794 (|HasCategory| (-2 (|:| -2239 (-1178)) (|:| -2904 |#1|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2239 (-1178)) (|:| -2904 |#1|)) (QUOTE (-1120))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1120)))) (-3794 (|HasCategory| (-2 (|:| -2239 (-1178)) (|:| -2904 |#1|)) (QUOTE (-1120))) (|HasCategory| (-2 (|:| -2239 (-1178)) (|:| -2904 |#1|)) (LIST (QUOTE -625) (QUOTE (-875)))) (|HasCategory| |#1| (QUOTE (-1120))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-875))))) (|HasCategory| (-2 (|:| -2239 (-1178)) (|:| -2904 |#1|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#1| (QUOTE (-1120))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -2239 (-1178)) (|:| -2904 |#1|)) (QUOTE (-1120))) (|HasCategory| (-1178) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1120))) (-3794 (|HasCategory| (-2 (|:| -2239 (-1178)) (|:| -2904 |#1|)) (LIST (QUOTE -625) (QUOTE (-875)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-875))))) (-3794 (|HasCategory| (-2 (|:| -2239 (-1178)) (|:| -2904 |#1|)) (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-102)))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-875)))) (|HasCategory| (-2 (|:| -2239 (-1178)) (|:| -2904 |#1|)) (LIST (QUOTE -625) (QUOTE (-875)))) (|HasCategory| (-2 (|:| -2239 (-1178)) (|:| -2904 |#1|)) (QUOTE (-102)))) -(-1180 A) +((-4464 . T) (-4465 . T)) +((-12 (|HasCategory| (-2 (|:| -4300 (-1179)) (|:| -4438 |#1|)) (QUOTE (-1121))) (|HasCategory| (-2 (|:| -4300 (-1179)) (|:| -4438 |#1|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4300) (QUOTE (-1179))) (LIST (QUOTE |:|) (QUOTE -4438) (|devaluate| |#1|)))))) (-2758 (|HasCategory| (-2 (|:| -4300 (-1179)) (|:| -4438 |#1|)) (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-1121)))) (-2758 (|HasCategory| (-2 (|:| -4300 (-1179)) (|:| -4438 |#1|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4300 (-1179)) (|:| -4438 |#1|)) (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1121)))) (-2758 (|HasCategory| (-2 (|:| -4300 (-1179)) (|:| -4438 |#1|)) (QUOTE (-1121))) (|HasCategory| (-2 (|:| -4300 (-1179)) (|:| -4438 |#1|)) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| (-2 (|:| -4300 (-1179)) (|:| -4438 |#1|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -4300 (-1179)) (|:| -4438 |#1|)) (QUOTE (-1121))) (|HasCategory| (-1179) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1121))) (-2758 (|HasCategory| (-2 (|:| -4300 (-1179)) (|:| -4438 |#1|)) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (-2758 (|HasCategory| (-2 (|:| -4300 (-1179)) (|:| -4438 |#1|)) (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-102)))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -4300 (-1179)) (|:| -4438 |#1|)) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -4300 (-1179)) (|:| -4438 |#1|)) (QUOTE (-102)))) +(-1181 A) ((|constructor| (NIL "StreamTaylorSeriesOperations implements Taylor series arithmetic,{} where a Taylor series is represented by a stream of its coefficients.")) (|power| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{power(a,f)} returns the power series \\spad{f} raised to the power \\spad{a}.")) (|lazyGintegrate| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyGintegrate(f,r,g)} is used for fixed point computations.")) (|mapdiv| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapdiv([a0,a1,..],[b0,b1,..])} returns \\spad{[a0/b0,a1/b1,..]}.")) (|powern| (((|Stream| |#1|) (|Fraction| (|Integer|)) (|Stream| |#1|)) "\\spad{powern(r,f)} raises power series \\spad{f} to the power \\spad{r}.")) (|nlde| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{nlde(u)} solves a first order non-linear differential equation described by \\spad{u} of the form \\spad{[[b<0,0>,b<0,1>,...],[b<1,0>,b<1,1>,.],...]}. the differential equation has the form \\spad{y' = sum(i=0 to infinity,j=0 to infinity,b<i,j>*(x**i)*(y**j))}.")) (|lazyIntegrate| (((|Stream| |#1|) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyIntegrate(r,f)} is a local function used for fixed point computations.")) (|integrate| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{integrate(r,a)} returns the integral of the power series \\spad{a} with respect to the power series variableintegration where \\spad{r} denotes the constant of integration. Thus \\spad{integrate(a,[a0,a1,a2,...]) = [a,a0,a1/2,a2/3,...]}.")) (|invmultisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{invmultisect(a,b,st)} substitutes \\spad{x**((a+b)*n)} for \\spad{x**n} and multiplies by \\spad{x**b}.")) (|multisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{multisect(a,b,st)} selects the coefficients of \\spad{x**((a+b)*n+a)},{} and changes them to \\spad{x**n}.")) (|generalLambert| (((|Stream| |#1|) (|Stream| |#1|) (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),a,d)} returns \\spad{f(x**a) + f(x**(a + d)) + f(x**(a + 2 d)) + ...}. \\spad{f(x)} should have zero constant coefficient and \\spad{a} and \\spad{d} should be positive.")) (|evenlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{evenlambert(st)} computes \\spad{f(x**2) + f(x**4) + f(x**6) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1,{} then \\spad{prod(f(x**(2*n)),n=1..infinity) = exp(evenlambert(log(f(x))))}.")) (|oddlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{oddlambert(st)} computes \\spad{f(x) + f(x**3) + f(x**5) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f}(\\spad{x}) is a power series with constant coefficient 1 then \\spad{prod(f(x**(2*n-1)),n=1..infinity) = exp(oddlambert(log(f(x))))}.")) (|lambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lambert(st)} computes \\spad{f(x) + f(x**2) + f(x**3) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1 then \\spad{prod(f(x**n),n = 1..infinity) = exp(lambert(log(f(x))))}.")) (|addiag| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{addiag(x)} performs diagonal addition of a stream of streams. if \\spad{x} = \\spad{[[a<0,0>,a<0,1>,..],[a<1,0>,a<1,1>,..],[a<2,0>,a<2,1>,..],..]} and \\spad{addiag(x) = [b<0,b<1>,...], then b<k> = sum(i+j=k,a<i,j>)}.")) (|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 should be invertible.")) (|lagrange| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lagrange(g)} produces the power series for \\spad{f} where \\spad{f} is implicitly defined as \\spad{f(z) = z*g(f(z))}.")) (|compose| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{compose(a,b)} composes the power series \\spad{a} with the power series \\spad{b}.")) (|eval| (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{eval(a,r)} returns a stream of partial sums of the power series \\spad{a} evaluated at the power series variable equal to \\spad{r}.")) (|coerce| (((|Stream| |#1|) |#1|) "\\spad{coerce(r)} converts a ring element \\spad{r} to a stream with one element.")) (|gderiv| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) (|Stream| |#1|)) "\\spad{gderiv(f,[a0,a1,a2,..])} returns \\spad{[f(0)*a0,f(1)*a1,f(2)*a2,..]}.")) (|deriv| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{deriv(a)} returns the derivative of the power series with respect to the power series variable. Thus \\spad{deriv([a0,a1,a2,...])} returns \\spad{[a1,2 a2,3 a3,...]}.")) (|mapmult| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapmult([a0,a1,..],[b0,b1,..])} returns \\spad{[a0*b0,a1*b1,..]}.")) (|int| (((|Stream| |#1|) |#1|) "\\spad{int(r)} returns [\\spad{r},{}\\spad{r+1},{}\\spad{r+2},{}...],{} where \\spad{r} is a ring element.")) (|oddintegers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{oddintegers(n)} returns \\spad{[n,n+2,n+4,...]}.")) (|integers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{integers(n)} returns \\spad{[n,n+1,n+2,...]}.")) (|monom| (((|Stream| |#1|) |#1| (|Integer|)) "\\spad{monom(deg,coef)} is a monomial of degree \\spad{deg} with coefficient \\spad{coef}.")) (|recip| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|)) "\\spad{recip(a)} returns the power series reciprocal of \\spad{a},{} or \"failed\" if not possible.")) (/ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a / b} returns the power series quotient of \\spad{a} by \\spad{b}. An error message is returned if \\spad{b} is not invertible. This function is used in fixed point computations.")) (|exquo| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|) (|Stream| |#1|)) "\\spad{exquo(a,b)} returns the power series quotient of \\spad{a} by \\spad{b},{} if the quotient exists,{} and \"failed\" otherwise")) (* (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{a * r} returns the power series scalar multiplication of \\spad{a} by \\spad{r:} \\spad{[a0,a1,...] * r = [a0 * r,a1 * r,...]}") (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{r * a} returns the power series scalar multiplication of \\spad{r} by \\spad{a}: \\spad{r * [a0,a1,...] = [r * a0,r * a1,...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a * b} returns the power series (Cauchy) product of \\spad{a} and \\spad{b:} \\spad{[a0,a1,...] * [b0,b1,...] = [c0,c1,...]} where \\spad{ck = sum(i + j = k,ai * bk)}.")) (- (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{- a} returns the power series negative of \\spad{a}: \\spad{- [a0,a1,...] = [- a0,- a1,...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a - b} returns the power series difference of \\spad{a} and \\spad{b}: \\spad{[a0,a1,..] - [b0,b1,..] = [a0 - b0,a1 - b1,..]}")) (+ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a + b} returns the power series sum of \\spad{a} and \\spad{b}: \\spad{[a0,a1,..] + [b0,b1,..] = [a0 + b0,a1 + b1,..]}"))) NIL ((|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) -(-1181 |Coef|) +(-1182 |Coef|) ((|constructor| (NIL "StreamTranscendentalFunctionsNonCommutative implements transcendental functions on Taylor series over a non-commutative ring,{} where a Taylor series is represented by a stream of its coefficients.")) (|acsch| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acsch(st)} computes the inverse hyperbolic cosecant of a power series \\spad{st}.")) (|asech| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asech(st)} computes the inverse hyperbolic secant of a power series \\spad{st}.")) (|acoth| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acoth(st)} computes the inverse hyperbolic cotangent of a power series \\spad{st}.")) (|atanh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{atanh(st)} computes the inverse hyperbolic tangent of a power series \\spad{st}.")) (|acosh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acosh(st)} computes the inverse hyperbolic cosine of a power series \\spad{st}.")) (|asinh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asinh(st)} computes the inverse hyperbolic sine of a power series \\spad{st}.")) (|csch| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{csch(st)} computes the hyperbolic cosecant of a power series \\spad{st}.")) (|sech| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sech(st)} computes the hyperbolic secant of a power series \\spad{st}.")) (|coth| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{coth(st)} computes the hyperbolic cotangent of a power series \\spad{st}.")) (|tanh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{tanh(st)} computes the hyperbolic tangent of a power series \\spad{st}.")) (|cosh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cosh(st)} computes the hyperbolic cosine of a power series \\spad{st}.")) (|sinh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sinh(st)} computes the hyperbolic sine of a power series \\spad{st}.")) (|acsc| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acsc(st)} computes arccosecant of a power series \\spad{st}.")) (|asec| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asec(st)} computes arcsecant of a power series \\spad{st}.")) (|acot| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acot(st)} computes arccotangent of a power series \\spad{st}.")) (|atan| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{atan(st)} computes arctangent of a power series \\spad{st}.")) (|acos| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acos(st)} computes arccosine of a power series \\spad{st}.")) (|asin| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asin(st)} computes arcsine of a power series \\spad{st}.")) (|csc| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{csc(st)} computes cosecant of a power series \\spad{st}.")) (|sec| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sec(st)} computes secant of a power series \\spad{st}.")) (|cot| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cot(st)} computes cotangent of a power series \\spad{st}.")) (|tan| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{tan(st)} computes tangent of a power series \\spad{st}.")) (|cos| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cos(st)} computes cosine of a power series \\spad{st}.")) (|sin| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sin(st)} computes sine of a power series \\spad{st}.")) (** (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{st1 ** st2} computes the power of a power series \\spad{st1} by another power series \\spad{st2}.")) (|log| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{log(st)} computes the log of a power series.")) (|exp| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{exp(st)} computes the exponential of a power series \\spad{st}."))) NIL NIL -(-1182 |Coef|) +(-1183 |Coef|) ((|constructor| (NIL "StreamTranscendentalFunctions implements transcendental functions on Taylor series,{} where a Taylor series is represented by a stream of its coefficients.")) (|acsch| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acsch(st)} computes the inverse hyperbolic cosecant of a power series \\spad{st}.")) (|asech| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asech(st)} computes the inverse hyperbolic secant of a power series \\spad{st}.")) (|acoth| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acoth(st)} computes the inverse hyperbolic cotangent of a power series \\spad{st}.")) (|atanh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{atanh(st)} computes the inverse hyperbolic tangent of a power series \\spad{st}.")) (|acosh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acosh(st)} computes the inverse hyperbolic cosine of a power series \\spad{st}.")) (|asinh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asinh(st)} computes the inverse hyperbolic sine of a power series \\spad{st}.")) (|csch| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{csch(st)} computes the hyperbolic cosecant of a power series \\spad{st}.")) (|sech| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sech(st)} computes the hyperbolic secant of a power series \\spad{st}.")) (|coth| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{coth(st)} computes the hyperbolic cotangent of a power series \\spad{st}.")) (|tanh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{tanh(st)} computes the hyperbolic tangent of a power series \\spad{st}.")) (|cosh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cosh(st)} computes the hyperbolic cosine of a power series \\spad{st}.")) (|sinh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sinh(st)} computes the hyperbolic sine of a power series \\spad{st}.")) (|sinhcosh| (((|Record| (|:| |sinh| (|Stream| |#1|)) (|:| |cosh| (|Stream| |#1|))) (|Stream| |#1|)) "\\spad{sinhcosh(st)} returns a record containing the hyperbolic sine and cosine of a power series \\spad{st}.")) (|acsc| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acsc(st)} computes arccosecant of a power series \\spad{st}.")) (|asec| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asec(st)} computes arcsecant of a power series \\spad{st}.")) (|acot| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acot(st)} computes arccotangent of a power series \\spad{st}.")) (|atan| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{atan(st)} computes arctangent of a power series \\spad{st}.")) (|acos| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acos(st)} computes arccosine of a power series \\spad{st}.")) (|asin| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asin(st)} computes arcsine of a power series \\spad{st}.")) (|csc| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{csc(st)} computes cosecant of a power series \\spad{st}.")) (|sec| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sec(st)} computes secant of a power series \\spad{st}.")) (|cot| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cot(st)} computes cotangent of a power series \\spad{st}.")) (|tan| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{tan(st)} computes tangent of a power series \\spad{st}.")) (|cos| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cos(st)} computes cosine of a power series \\spad{st}.")) (|sin| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sin(st)} computes sine of a power series \\spad{st}.")) (|sincos| (((|Record| (|:| |sin| (|Stream| |#1|)) (|:| |cos| (|Stream| |#1|))) (|Stream| |#1|)) "\\spad{sincos(st)} returns a record containing the sine and cosine of a power series \\spad{st}.")) (** (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{st1 ** st2} computes the power of a power series \\spad{st1} by another power series \\spad{st2}.")) (|log| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{log(st)} computes the log of a power series.")) (|exp| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{exp(st)} computes the exponential of a power series \\spad{st}."))) NIL NIL -(-1183 R UP) +(-1184 R UP) ((|constructor| (NIL "This package computes the subresultants of two polynomials which is needed for the `Lazard Rioboo' enhancement to Tragers integrations formula For efficiency reasons this has been rewritten to call Lionel Ducos package which is currently the best one. \\blankline")) (|primitivePart| ((|#2| |#2| |#1|) "\\spad{primitivePart(p, q)} reduces the coefficient of \\spad{p} modulo \\spad{q},{} takes the primitive part of the result,{} and ensures that the leading coefficient of that result is monic.")) (|subresultantVector| (((|PrimitiveArray| |#2|) |#2| |#2|) "\\spad{subresultantVector(p, q)} returns \\spad{[p0,...,pn]} where \\spad{pi} is the \\spad{i}-th subresultant of \\spad{p} and \\spad{q}. In particular,{} \\spad{p0 = resultant(p, q)}."))) NIL ((|HasCategory| |#1| (QUOTE (-317)))) -(-1184 |n| R) +(-1185 |n| R) ((|constructor| (NIL "This domain \\undocumented")) (|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,{} \\spad{li},{} which points to the component which has been traversed to. The subspace,{} \\spad{s},{} is returned,{} where \\spad{s} is now the subspace pointed to by \\spad{li}.")) (|defineProperty| (($ $ (|List| (|NonNegativeInteger|)) (|SubSpaceComponentProperty|)) "\\spad{defineProperty(s,li,p)} defines the component property in the 3 dimensional subspace,{} \\spad{s},{} to be that of \\spad{p},{} where \\spad{p} is of the domain \\spadtype{SubSpaceComponentProperty}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component whose property is being defined. The subspace,{} \\spad{s},{} is returned with the component property definition.")) (|closeComponent| (($ $ (|List| (|NonNegativeInteger|)) (|Boolean|)) "\\spad{closeComponent(s,li,b)} sets the property of the component in the 3 dimensional subspace,{} \\spad{s},{} to be closed if \\spad{b} is \\spad{true},{} or open if \\spad{b} is \\spad{false}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component whose closed property is to be set. The subspace,{} \\spad{s},{} is returned with the component property modification.")) (|modifyPoint| (($ $ (|NonNegativeInteger|) (|Point| |#2|)) "\\spad{modifyPoint(s,ind,p)} modifies the point referenced by the index location,{} \\spad{ind},{} by replacing it with the point,{} \\spad{p} in the 3 dimensional subspace,{} \\spad{s}. An error message occurs if \\spad{s} is empty,{} otherwise the subspace \\spad{s} is returned with the point modification.") (($ $ (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{modifyPoint(s,li,i)} replaces an existing point in the 3 dimensional subspace,{} \\spad{s},{} with the 4 dimensional point indicated by the index location,{} \\spad{i}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component in which the existing point is to be modified. An error message occurs if \\spad{s} is empty,{} otherwise the subspace \\spad{s} is returned with the point modification.") (($ $ (|List| (|NonNegativeInteger|)) (|Point| |#2|)) "\\spad{modifyPoint(s,li,p)} replaces an existing point in the 3 dimensional subspace,{} \\spad{s},{} with the 4 dimensional point,{} \\spad{p}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component in which the existing point is to be modified. An error message occurs if \\spad{s} is empty,{} otherwise the subspace \\spad{s} is returned with the point modification.")) (|addPointLast| (($ $ $ (|Point| |#2|) (|NonNegativeInteger|)) "\\spad{addPointLast(s,s2,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,{} \\spad{i},{} to the 3 dimensional subspace,{} \\spad{s}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component in which the point is to be added. It\\spad{'s} length should range from 0 to \\spad{n - 1} where \\spad{n} is the dimension of the subspace. If the length is \\spad{n - 1},{} then a specific lowest level component is being referenced. If it is less than \\spad{n - 1},{} then some higher level component (0 indicates top level component) is being referenced and a component of that level with the desired point is created. The subspace \\spad{s} is returned with the additional point.") (($ $ (|List| (|NonNegativeInteger|)) (|Point| |#2|)) "\\spad{addPoint(s,li,p)} adds the 4 dimensional point,{} \\spad{p},{} to the 3 dimensional subspace,{} \\spad{s}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component in which the point is to be added. It\\spad{'s} length should range from 0 to \\spad{n - 1} where \\spad{n} is the dimension of the subspace. If the length is \\spad{n - 1},{} then a specific lowest level component is being referenced. If it is less than \\spad{n - 1},{} then some higher level component (0 indicates top level component) is being referenced and a component of that level with the desired point is created. The subspace \\spad{s} is returned with the additional point.")) (|separate| (((|List| $) $) "\\spad{separate(s)} makes each of the components of the \\spadtype{SubSpace},{} \\spad{s},{} into a list of separate and distinct subspaces and returns the list.")) (|merge| (($ (|List| $)) "\\spad{merge(ls)} a list of subspaces,{} \\spad{ls},{} into one subspace.") (($ $ $) "\\spad{merge(s1,s2)} the subspaces \\spad{s1} and \\spad{s2} into a single subspace.")) 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We may integrate a series when we can divide coefficients by integers.")) (|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}."))) -(((-4465 "*") |has| |#1| (-174)) (-4456 |has| |#1| (-568)) (-4457 . T) (-4458 . T) (-4460 . 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(NOT (($ $) "\\spad{NOT(x)} returns the \\axiomType{Switch} expression representing \\spad{\\~~x}.") (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{NOT(x)} returns the \\axiomType{Switch} expression representing \\spad{\\~~x}.")) (AND (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{AND(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x and y}.")) (EQ (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{EQ(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x = y}.")) (OR (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{OR(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x or y}.")) 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(GT (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{GT(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x>y}.")) (LT (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{LT(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x<y}.")) (|coerce| (($ (|Symbol|)) "\\spad{coerce(s)} \\undocumented{}"))) NIL NIL -(-1196) +(-1197) ((|constructor| (NIL "Basic and scripted symbols.")) 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T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (-3794 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-3794 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1058) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#1| (LIST (QUOTE -1058) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1058) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| (-991) (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasAttribute| |#1| (QUOTE -4461))) -(-1199) +(((-4466 "*") |has| |#1| (-174)) (-4457 |has| |#1| (-568)) (-4462 |has| |#1| (-6 -4462)) (-4458 . T) (-4459 . T) (-4461 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (-2758 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-2758 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-464))) (-12 (|HasCategory| (-992) (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasAttribute| |#1| (QUOTE -4462))) +(-1200) ((|constructor| (NIL "Creates and manipulates one global symbol table for FORTRAN code generation,{} containing details of types,{} dimensions,{} and argument lists.")) (|symbolTableOf| (((|SymbolTable|) (|Symbol|) $) "\\spad{symbolTableOf(f,tab)} returns the symbol table of \\spad{f}")) (|argumentListOf| (((|List| (|Symbol|)) (|Symbol|) $) "\\spad{argumentListOf(f,tab)} returns the argument list of \\spad{f}")) (|returnTypeOf| (((|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) (|Symbol|) $) "\\spad{returnTypeOf(f,tab)} returns the type of the object returned by \\spad{f}")) (|empty| (($) "\\spad{empty()} creates a new,{} empty symbol table.")) (|printTypes| (((|Void|) (|Symbol|)) "\\spad{printTypes(tab)} produces FORTRAN type declarations from \\spad{tab},{} on the current FORTRAN output stream")) (|printHeader| (((|Void|)) "\\spad{printHeader()} produces the FORTRAN header for the current subprogram in the global symbol table on the current FORTRAN output stream.") (((|Void|) (|Symbol|)) "\\spad{printHeader(f)} produces the FORTRAN header for subprogram \\spad{f} in the global symbol table on the current FORTRAN output stream.") (((|Void|) (|Symbol|) $) "\\spad{printHeader(f,tab)} produces the FORTRAN header for subprogram \\spad{f} in symbol table \\spad{tab} on the current FORTRAN output stream.")) (|returnType!| (((|Void|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void"))) "\\spad{returnType!(t)} declares that the return type of he current subprogram in the global symbol table is \\spad{t}.") (((|Void|) (|Symbol|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void"))) "\\spad{returnType!(f,t)} declares that the return type of subprogram \\spad{f} in the global symbol table is \\spad{t}.") (((|Void|) (|Symbol|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) $) "\\spad{returnType!(f,t,tab)} declares that the return type of subprogram \\spad{f} in symbol table \\spad{tab} is \\spad{t}.")) (|argumentList!| (((|Void|) (|List| (|Symbol|))) "\\spad{argumentList!(l)} declares that the argument list for the current subprogram in the global symbol table is \\spad{l}.") (((|Void|) (|Symbol|) (|List| (|Symbol|))) "\\spad{argumentList!(f,l)} declares that the argument list for subprogram \\spad{f} in the global symbol table is \\spad{l}.") (((|Void|) (|Symbol|) (|List| (|Symbol|)) $) "\\spad{argumentList!(f,l,tab)} declares that the argument list for subprogram \\spad{f} in symbol table \\spad{tab} is \\spad{l}.")) (|endSubProgram| (((|Symbol|)) "\\spad{endSubProgram()} asserts that we are no longer processing the current subprogram.")) (|currentSubProgram| (((|Symbol|)) "\\spad{currentSubProgram()} returns the name of the current subprogram being processed")) (|newSubProgram| (((|Void|) (|Symbol|)) "\\spad{newSubProgram(f)} asserts that from now on type declarations are part of subprogram \\spad{f}.")) (|declare!| (((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|)) "\\spad{declare!(u,t,asp)} declares the parameter \\spad{u} to have type \\spad{t} in \\spad{asp}.") (((|FortranType|) (|Symbol|) (|FortranType|)) "\\spad{declare!(u,t)} declares the parameter \\spad{u} to have type \\spad{t} in the current level of the symbol table.") (((|FortranType|) (|List| (|Symbol|)) (|FortranType|) (|Symbol|) $) "\\spad{declare!(u,t,asp,tab)} declares the parameters \\spad{u} of subprogram \\spad{asp} to have type \\spad{t} in symbol table \\spad{tab}.") (((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|) $) "\\spad{declare!(u,t,asp,tab)} declares the parameter \\spad{u} of subprogram \\spad{asp} to have type \\spad{t} in symbol table \\spad{tab}.")) (|clearTheSymbolTable| (((|Void|) (|Symbol|)) "\\spad{clearTheSymbolTable(x)} removes the symbol \\spad{x} from the table") (((|Void|)) "\\spad{clearTheSymbolTable()} clears the current symbol table.")) (|showTheSymbolTable| (($) "\\spad{showTheSymbolTable()} returns the current symbol table."))) NIL NIL -(-1200) +(-1201) ((|constructor| (NIL "Create and manipulate a symbol table for generated FORTRAN code")) (|symbolTable| (($ (|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| (|FortranType|))))) "\\spad{symbolTable(l)} creates a symbol table from the elements of \\spad{l}.")) (|printTypes| (((|Void|) $) "\\spad{printTypes(tab)} produces FORTRAN type declarations from \\spad{tab},{} on the current FORTRAN output stream")) (|newTypeLists| (((|SExpression|) $) "\\spad{newTypeLists(x)} \\undocumented")) (|typeLists| (((|List| (|List| (|Union| (|:| |name| (|Symbol|)) (|:| |bounds| (|List| (|Union| (|:| S (|Symbol|)) (|:| P (|Polynomial| (|Integer|))))))))) $) "\\spad{typeLists(tab)} returns a list of lists of types of objects in \\spad{tab}")) (|externalList| (((|List| (|Symbol|)) $) "\\spad{externalList(tab)} returns a list of all the external symbols in \\spad{tab}")) (|typeList| (((|List| (|Union| (|:| |name| (|Symbol|)) (|:| |bounds| (|List| (|Union| (|:| S (|Symbol|)) (|:| P (|Polynomial| (|Integer|)))))))) (|FortranScalarType|) $) "\\spad{typeList(t,tab)} returns a list of all the objects of type \\spad{t} in \\spad{tab}")) (|parametersOf| (((|List| (|Symbol|)) $) "\\spad{parametersOf(tab)} returns a list of all the symbols declared in \\spad{tab}")) (|fortranTypeOf| (((|FortranType|) (|Symbol|) $) "\\spad{fortranTypeOf(u,tab)} returns the type of \\spad{u} in \\spad{tab}")) (|declare!| (((|FortranType|) (|Symbol|) (|FortranType|) $) "\\spad{declare!(u,t,tab)} creates a new entry in \\spad{tab},{} declaring \\spad{u} to be of type \\spad{t}") (((|FortranType|) (|List| (|Symbol|)) (|FortranType|) $) "\\spad{declare!(l,t,tab)} creates new entrys in \\spad{tab},{} declaring each of \\spad{l} to be of type \\spad{t}")) (|empty| (($) "\\spad{empty()} returns a new,{} empty symbol table")) (|coerce| (((|Table| (|Symbol|) (|FortranType|)) $) "\\spad{coerce(x)} returns a table view of \\spad{x}"))) NIL NIL -(-1201) +(-1202) ((|constructor| (NIL "\\indented{1}{This domain provides a simple domain,{} general enough for} \\indented{2}{building complete representation of Spad programs as objects} \\indented{2}{of a term algebra built from ground terms of type integers,{} foats,{}} \\indented{2}{identifiers,{} and strings.} \\indented{2}{This domain differs from InputForm in that it represents} \\indented{2}{any entity in a Spad program,{} not just expressions.\\space{2}Furthermore,{}} \\indented{2}{while InputForm may contain atoms like vectors and other Lisp} \\indented{2}{objects,{} the Syntax domain is supposed to contain only that} \\indented{2}{initial algebra build from the primitives listed above.} Related Constructors: \\indented{2}{Integer,{} DoubleFloat,{} Identifier,{} String,{} SExpression.} See Also: SExpression,{} InputForm. The equality supported by this domain is structural.")) (|case| (((|Boolean|) $ (|[\|\|]| (|String|))) "\\spad{x case String} is \\spad{true} if \\spad{`x'} really is a String") (((|Boolean|) $ (|[\|\|]| (|Identifier|))) "\\spad{x case Identifier} is \\spad{true} if \\spad{`x'} really is an Identifier") (((|Boolean|) $ (|[\|\|]| (|DoubleFloat|))) "\\spad{x case DoubleFloat} is \\spad{true} if \\spad{`x'} really is a DoubleFloat") (((|Boolean|) $ (|[\|\|]| (|Integer|))) "\\spad{x case Integer} is \\spad{true} if \\spad{`x'} really is an Integer")) (|compound?| (((|Boolean|) $) "\\spad{compound? x} is \\spad{true} when \\spad{`x'} is not an atomic syntax.")) (|getOperands| (((|List| $) $) "\\spad{getOperands(x)} returns the list of operands to the operator in \\spad{`x'}.")) (|getOperator| (((|Union| (|Integer|) (|DoubleFloat|) (|Identifier|) (|String|) $) $) "\\spad{getOperator(x)} returns the operator,{} or tag,{} of the syntax \\spad{`x'}. The value returned is itself a syntax if \\spad{`x'} really is an application of a function symbol as opposed to being an atomic ground term.")) (|nil?| (((|Boolean|) $) "\\spad{nil?(s)} is \\spad{true} when \\spad{`s'} is a syntax for the constant nil.")) (|buildSyntax| (($ $ (|List| $)) "\\spad{buildSyntax(op, [a1, ..., an])} builds a syntax object for \\spad{op}(a1,{}...,{}an).") (($ (|Identifier|) (|List| $)) "\\spad{buildSyntax(op, [a1, ..., an])} builds a syntax object for \\spad{op}(a1,{}...,{}an).")) (|autoCoerce| (((|String|) $) "\\spad{autoCoerce(s)} forcibly extracts a string value from the syntax \\spad{`s'}; no check performed. To be called only at the discretion of the compiler.") (((|Identifier|) $) "\\spad{autoCoerce(s)} forcibly extracts an identifier from the Syntax domain \\spad{`s'}; no check performed. To be called only at at the discretion of the compiler.") (((|DoubleFloat|) $) "\\spad{autoCoerce(s)} forcibly extracts a float value from the syntax \\spad{`s'}; no check performed. To be called only at the discretion of the compiler") (((|Integer|) $) "\\spad{autoCoerce(s)} forcibly extracts an integer value from the syntax \\spad{`s'}; no check performed. To be called only at the discretion of the compiler.")) (|coerce| (((|String|) $) "\\spad{coerce(s)} extracts a string value from the syntax \\spad{`s'}.") (((|Identifier|) $) "\\spad{coerce(s)} extracts an identifier from the syntax \\spad{`s'}.") (((|DoubleFloat|) $) "\\spad{coerce(s)} extracts a float value from the syntax \\spad{`s'}.") (((|Integer|) $) "\\spad{coerce(s)} extracts and integer value from the syntax \\spad{`s'}")) (|convert| (($ (|SExpression|)) "\\spad{convert(s)} converts an \\spad{s}-expression to Syntax. Note,{} when \\spad{`s'} is not an atom,{} it is expected that it designates a proper list,{} \\spadignore{e.g.} a sequence of cons cells ending with nil.") (((|SExpression|) $) "\\spad{convert(s)} returns the \\spad{s}-expression representation of a syntax."))) NIL NIL -(-1202 N) +(-1203 N) ((|constructor| (NIL "This domain implements sized (signed) integer datatypes parameterized by the precision (or width) of the underlying representation. The intent is that they map directly to the hosting hardware natural integer datatypes. Consequently,{} natural values for \\spad{N} are: 8,{} 16,{} 32,{} 64,{} etc. These datatypes are mostly useful for system programming tasks,{} \\spadignore{i.e.} interfacting with the hosting operating system,{} reading/writing external binary format files.")) (|sample| (($) "\\spad{sample} gives a sample datum of this type."))) NIL NIL -(-1203 N) +(-1204 N) ((|constructor| (NIL "This domain implements sized (unsigned) integer datatypes parameterized by the precision (or width) of the underlying representation. The intent is that they map directly to the hosting hardware natural integer datatypes. Consequently,{} natural values for \\spad{N} are: 8,{} 16,{} 32,{} 64,{} etc. These datatypes are mostly useful for system programming tasks,{} \\spadignore{i.e.} interfacting with the hosting operating system,{} reading/writing external binary format files.")) (|sample| (($) "\\spad{sample} gives a sample datum of type Byte.")) (|bitior| (($ $ $) "bitor(\\spad{x},{}\\spad{y}) returns the bitwise `inclusive or' of \\spad{`x'} and \\spad{`y'}.")) (|bitand| (($ $ $) "\\spad{bitand(x,y)} returns the bitwise `and' of \\spad{`x'} and \\spad{`y'}."))) NIL NIL -(-1204) +(-1205) ((|constructor| (NIL "This domain is a datatype system-level pointer values."))) NIL NIL -(-1205 R) +(-1206 R) ((|triangularSystems| (((|List| (|List| (|Polynomial| |#1|))) (|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|Symbol|))) "\\spad{triangularSystems(lf,lv)} solves the system of equations defined by \\spad{lf} with respect to the list of symbols \\spad{lv}; the system of equations is obtaining by equating to zero the list of rational functions \\spad{lf}. The output is a list of solutions where each solution is expressed as a \"reduced\" triangular system of polynomials.")) (|solve| (((|List| (|Equation| (|Fraction| (|Polynomial| |#1|)))) (|Equation| (|Fraction| (|Polynomial| |#1|)))) "\\spad{solve(eq)} finds the solutions of the equation \\spad{eq} with respect to the unique variable appearing in \\spad{eq}.") (((|List| (|Equation| (|Fraction| (|Polynomial| |#1|)))) (|Fraction| (|Polynomial| |#1|))) "\\spad{solve(p)} finds the solution of a rational function \\spad{p} = 0 with respect to the unique variable appearing in \\spad{p}.") (((|List| (|Equation| (|Fraction| (|Polynomial| |#1|)))) (|Equation| (|Fraction| (|Polynomial| |#1|))) (|Symbol|)) "\\spad{solve(eq,v)} finds the solutions of the equation \\spad{eq} with respect to the variable \\spad{v}.") (((|List| (|Equation| (|Fraction| (|Polynomial| |#1|)))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{solve(p,v)} solves the equation \\spad{p=0},{} where \\spad{p} is a rational function with respect to the variable \\spad{v}.") (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) "\\spad{solve(le)} finds the solutions of the list \\spad{le} of equations of rational functions with respect to all symbols appearing in \\spad{le}.") (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Fraction| (|Polynomial| |#1|)))) "\\spad{solve(lp)} finds the solutions of the list \\spad{lp} of rational functions with respect to all symbols appearing in \\spad{lp}.") (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Equation| (|Fraction| (|Polynomial| |#1|)))) (|List| (|Symbol|))) "\\spad{solve(le,lv)} finds the solutions of the list \\spad{le} of equations of rational functions with respect to the list of symbols \\spad{lv}.") (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|Symbol|))) "\\spad{solve(lp,lv)} finds the solutions of the list \\spad{lp} of rational functions with respect to the list of symbols \\spad{lv}."))) NIL NIL -(-1206) +(-1207) ((|constructor| (NIL "The package \\spadtype{System} provides information about the runtime system and its characteristics.")) (|loadNativeModule| (((|Void|) (|String|)) "\\spad{loadNativeModule(path)} loads the native modile designated by \\spadvar{\\spad{path}}.")) (|nativeModuleExtension| (((|String|)) "\\spad{nativeModuleExtension} is a string representation of a filename extension for native modules.")) (|hostByteOrder| (((|ByteOrder|)) "\\sapd{hostByteOrder}")) (|hostPlatform| (((|String|)) "\\spad{hostPlatform} is a string `triplet' description of the platform hosting the running OpenAxiom system.")) (|rootDirectory| (((|String|)) "\\spad{rootDirectory()} returns the pathname of the root directory for the running OpenAxiom system."))) NIL NIL -(-1207 S) +(-1208 S) ((|constructor| (NIL "TableauBumpers implements the Schenstead-Knuth correspondence between sequences and pairs of Young tableaux. The 2 Young tableaux are represented as a single tableau with pairs as components.")) (|mr| (((|Record| (|:| |f1| (|List| |#1|)) (|:| |f2| (|List| (|List| (|List| |#1|)))) (|:| |f3| (|List| (|List| |#1|))) (|:| |f4| (|List| (|List| (|List| |#1|))))) (|List| (|List| (|List| |#1|)))) "\\spad{mr(t)} is an auxiliary function which finds the position of the maximum element of a tableau \\spad{t} which is in the lowest row,{} producing a record of results")) (|maxrow| (((|Record| (|:| |f1| (|List| |#1|)) (|:| |f2| (|List| (|List| (|List| |#1|)))) (|:| |f3| (|List| (|List| |#1|))) (|:| |f4| (|List| (|List| (|List| |#1|))))) (|List| |#1|) (|List| (|List| (|List| |#1|))) (|List| (|List| |#1|)) (|List| (|List| (|List| |#1|))) (|List| (|List| (|List| |#1|))) (|List| (|List| (|List| |#1|)))) "\\spad{maxrow(a,b,c,d,e)} is an auxiliary function for \\spad{mr}")) (|inverse| (((|List| |#1|) (|List| |#1|)) "\\spad{inverse(ls)} forms the inverse of a sequence \\spad{ls}")) (|slex| (((|List| (|List| |#1|)) (|List| |#1|)) "\\spad{slex(ls)} sorts the argument sequence \\spad{ls},{} then zips (see \\spadfunFrom{map}{ListFunctions3}) the original argument sequence with the sorted result to a list of pairs")) (|lex| (((|List| (|List| |#1|)) (|List| (|List| |#1|))) "\\spad{lex(ls)} sorts a list of pairs to lexicographic order")) (|tab| (((|Tableau| (|List| |#1|)) (|List| |#1|)) "\\spad{tab(ls)} creates a tableau from \\spad{ls} by first creating a list of pairs using \\spadfunFrom{slex}{TableauBumpers},{} then creating a tableau using \\spadfunFrom{tab1}{TableauBumpers}.")) (|tab1| (((|List| (|List| (|List| |#1|))) (|List| (|List| |#1|))) "\\spad{tab1(lp)} creates a tableau from a list of pairs \\spad{lp}")) (|bat| (((|List| (|List| |#1|)) (|Tableau| (|List| |#1|))) "\\spad{bat(ls)} unbumps a tableau \\spad{ls}")) (|bat1| (((|List| (|List| |#1|)) (|List| (|List| (|List| |#1|)))) "\\spad{bat1(llp)} unbumps a tableau \\spad{llp}. Operation bat1 is the inverse of tab1.")) (|untab| (((|List| (|List| |#1|)) (|List| (|List| |#1|)) (|List| (|List| (|List| |#1|)))) "\\spad{untab(lp,llp)} is an auxiliary function which unbumps a tableau \\spad{llp},{} using \\spad{lp} to accumulate pairs")) (|bumptab1| (((|List| (|List| (|List| |#1|))) (|List| |#1|) (|List| (|List| (|List| |#1|)))) "\\spad{bumptab1(pr,t)} bumps a tableau \\spad{t} with a pair \\spad{pr} using comparison function \\spadfun{<},{} returning a new tableau")) (|bumptab| (((|List| (|List| (|List| |#1|))) (|Mapping| (|Boolean|) |#1| |#1|) (|List| |#1|) (|List| (|List| (|List| |#1|)))) "\\spad{bumptab(cf,pr,t)} bumps a tableau \\spad{t} with a pair \\spad{pr} using comparison function \\spad{cf},{} returning a new tableau")) (|bumprow| (((|Record| (|:| |fs| (|Boolean|)) (|:| |sd| (|List| |#1|)) (|:| |td| (|List| (|List| |#1|)))) (|Mapping| (|Boolean|) |#1| |#1|) (|List| |#1|) (|List| (|List| |#1|))) "\\spad{bumprow(cf,pr,r)} is an auxiliary function which bumps a row \\spad{r} with a pair \\spad{pr} using comparison function \\spad{cf},{} and returns a record"))) NIL NIL -(-1208 S) +(-1209 S) ((|constructor| (NIL "\\indented{1}{The tableau domain is for printing Young tableaux,{} and} coercions to and from List List \\spad{S} where \\spad{S} is a set.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(t)} converts a tableau \\spad{t} to an output form.")) (|listOfLists| (((|List| (|List| |#1|)) $) "\\spad{listOfLists t} converts a tableau \\spad{t} to a list of lists.")) (|tableau| (($ (|List| (|List| |#1|))) "\\spad{tableau(ll)} converts a list of lists \\spad{ll} to a tableau."))) NIL NIL -(-1209 |Key| |Entry|) +(-1210 |Key| |Entry|) ((|constructor| (NIL "This is the general purpose table type. The keys are hashed to look up the entries. This creates a \\spadtype{HashTable} if equal for the Key domain is consistent with Lisp EQUAL otherwise an \\spadtype{AssociationList}"))) -((-4463 . T) (-4464 . T)) -((-12 (|HasCategory| (-2 (|:| -2239 |#1|) (|:| -2904 |#2|)) (QUOTE (-1120))) (|HasCategory| (-2 (|:| -2239 |#1|) (|:| -2904 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2239) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2904) (|devaluate| |#2|)))))) (-3794 (|HasCategory| (-2 (|:| -2239 |#1|) (|:| -2904 |#2|)) (QUOTE (-1120))) (|HasCategory| |#2| (QUOTE (-1120)))) (-3794 (|HasCategory| (-2 (|:| -2239 |#1|) (|:| -2904 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -2239 |#1|) (|:| -2904 |#2|)) (QUOTE (-1120))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1120)))) (-3794 (|HasCategory| (-2 (|:| -2239 |#1|) (|:| -2904 |#2|)) (QUOTE (-1120))) (|HasCategory| (-2 (|:| -2239 |#1|) (|:| -2904 |#2|)) (LIST (QUOTE -625) (QUOTE (-875)))) (|HasCategory| |#2| (QUOTE (-1120))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-875))))) (|HasCategory| (-2 (|:| -2239 |#1|) (|:| -2904 |#2|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#2| (QUOTE (-1120))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2239 |#1|) (|:| -2904 |#2|)) (QUOTE (-1120))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#2| (QUOTE (-1120))) (-3794 (|HasCategory| (-2 (|:| -2239 |#1|) (|:| -2904 |#2|)) (LIST (QUOTE -625) (QUOTE (-875)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-875))))) (-3794 (|HasCategory| (-2 (|:| -2239 |#1|) (|:| -2904 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-875)))) (|HasCategory| (-2 (|:| -2239 |#1|) (|:| -2904 |#2|)) (LIST (QUOTE -625) (QUOTE (-875)))) (|HasCategory| (-2 (|:| -2239 |#1|) (|:| -2904 |#2|)) (QUOTE (-102)))) -(-1210 S) +((-4464 . T) (-4465 . T)) +((-12 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4438 |#2|)) (QUOTE (-1121))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4438 |#2|)) (LIST (QUOTE -319) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4300) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4438) (|devaluate| |#2|)))))) (-2758 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4438 |#2|)) (QUOTE (-1121))) (|HasCategory| |#2| (QUOTE (-1121)))) (-2758 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4438 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4438 |#2|)) (QUOTE (-1121))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1121)))) (-2758 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4438 |#2|)) (QUOTE (-1121))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4438 |#2|)) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4438 |#2|)) (LIST (QUOTE -626) (QUOTE (-548)))) (-12 (|HasCategory| |#2| (QUOTE (-1121))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4438 |#2|)) (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#2| (QUOTE (-1121))) (-2758 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4438 |#2|)) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-876))))) (-2758 (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4438 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4438 |#2|)) (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| (-2 (|:| -4300 |#1|) (|:| -4438 |#2|)) (QUOTE (-102)))) +(-1211 S) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: April 17,{} 2010 Date Last Modified: April 17,{} 2010")) (|operator| (($ |#1| (|Arity|)) "\\spad{operator(n,a)} returns an operator named \\spad{n} and with arity \\spad{a}."))) NIL NIL -(-1211 R) +(-1212 R) ((|constructor| (NIL "Expands tangents of sums and scalar products.")) (|tanNa| ((|#1| |#1| (|Integer|)) "\\spad{tanNa(a, n)} returns \\spad{f(a)} such that if \\spad{a = tan(u)} then \\spad{f(a) = tan(n * u)}.")) (|tanAn| (((|SparseUnivariatePolynomial| |#1|) |#1| (|PositiveInteger|)) "\\spad{tanAn(a, n)} returns \\spad{P(x)} such that if \\spad{a = tan(u)} then \\spad{P(tan(u/n)) = 0}.")) (|tanSum| ((|#1| (|List| |#1|)) "\\spad{tanSum([a1,...,an])} returns \\spad{f(a1,...,an)} such that if \\spad{ai = tan(ui)} then \\spad{f(a1,...,an) = tan(u1 + ... + un)}."))) NIL NIL -(-1212 S |Key| |Entry|) +(-1213 S |Key| |Entry|) ((|constructor| (NIL "A table aggregate is a model of a table,{} \\spadignore{i.e.} a discrete many-to-one mapping from keys to entries.")) (|map| (($ (|Mapping| |#3| |#3| |#3|) $ $) "\\spad{map(fn,t1,t2)} creates a new table \\spad{t} from given tables \\spad{t1} and \\spad{t2} with elements \\spad{fn}(\\spad{x},{}\\spad{y}) where \\spad{x} and \\spad{y} are corresponding elements from \\spad{t1} and \\spad{t2} respectively.")) (|table| (($ (|List| (|Record| (|:| |key| |#2|) (|:| |entry| |#3|)))) "\\spad{table([x,y,...,z])} creates a table consisting of entries \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}}.") (($) "\\spad{table()}\\$\\spad{T} creates an empty table of type \\spad{T}.")) (|setelt| ((|#3| $ |#2| |#3|) "\\spad{setelt(t,k,e)} (also written \\axiom{\\spad{t}.\\spad{k} \\spad{:=} \\spad{e}}) is equivalent to \\axiom{(insert([\\spad{k},{}\\spad{e}],{}\\spad{t}); \\spad{e})}."))) NIL NIL -(-1213 |Key| |Entry|) +(-1214 |Key| |Entry|) ((|constructor| (NIL "A table aggregate is a model of a table,{} \\spadignore{i.e.} a discrete many-to-one mapping from keys to entries.")) (|map| (($ (|Mapping| |#2| |#2| |#2|) $ $) "\\spad{map(fn,t1,t2)} creates a new table \\spad{t} from given tables \\spad{t1} and \\spad{t2} with elements \\spad{fn}(\\spad{x},{}\\spad{y}) where \\spad{x} and \\spad{y} are corresponding elements from \\spad{t1} and \\spad{t2} respectively.")) (|table| (($ (|List| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) "\\spad{table([x,y,...,z])} creates a table consisting of entries \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}}.") (($) "\\spad{table()}\\$\\spad{T} creates an empty table of type \\spad{T}.")) (|setelt| ((|#2| $ |#1| |#2|) "\\spad{setelt(t,k,e)} (also written \\axiom{\\spad{t}.\\spad{k} \\spad{:=} \\spad{e}}) is equivalent to \\axiom{(insert([\\spad{k},{}\\spad{e}],{}\\spad{t}); \\spad{e})}."))) -((-4464 . T)) +((-4465 . T)) NIL -(-1214 |Key| |Entry|) +(-1215 |Key| |Entry|) ((|constructor| (NIL "\\axiom{TabulatedComputationPackage(Key ,{}Entry)} provides some modest support for dealing with operations with type \\axiom{Key \\spad{->} Entry}. The result of such operations can be stored and retrieved with this package by using a hash-table. The user does not need to worry about the management of this hash-table. However,{} onnly one hash-table is built by calling \\axiom{TabulatedComputationPackage(Key ,{}Entry)}.")) (|insert!| (((|Void|) |#1| |#2|) "\\axiom{insert!(\\spad{x},{}\\spad{y})} stores the item whose key is \\axiom{\\spad{x}} and whose entry is \\axiom{\\spad{y}}.")) (|extractIfCan| (((|Union| |#2| "failed") |#1|) "\\axiom{extractIfCan(\\spad{x})} searches the item whose key is \\axiom{\\spad{x}}.")) (|makingStats?| (((|Boolean|)) "\\axiom{makingStats?()} returns \\spad{true} iff the statisitics process is running.")) (|printingInfo?| (((|Boolean|)) "\\axiom{printingInfo?()} returns \\spad{true} iff messages are printed when manipulating items from the hash-table.")) (|usingTable?| (((|Boolean|)) "\\axiom{usingTable?()} returns \\spad{true} iff the hash-table is used")) (|clearTable!| (((|Void|)) "\\axiom{clearTable!()} clears the hash-table and assumes that it will no longer be used.")) (|printStats!| (((|Void|)) "\\axiom{printStats!()} prints the statistics.")) (|startStats!| (((|Void|) (|String|)) "\\axiom{startStats!(\\spad{x})} initializes the statisitics process and sets the comments to display when statistics are printed")) (|printInfo!| (((|Void|) (|String|) (|String|)) "\\axiom{printInfo!(\\spad{x},{}\\spad{y})} initializes the mesages to be printed when manipulating items from the hash-table. If a key is retrieved then \\axiom{\\spad{x}} is displayed. If an item is stored then \\axiom{\\spad{y}} is displayed.")) (|initTable!| (((|Void|)) "\\axiom{initTable!()} initializes the hash-table."))) NIL NIL -(-1215) +(-1216) ((|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 -(-1216 S) +(-1217 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 -(-1217) +(-1218) ((|constructor| (NIL "\\spadtype{TexFormat} provides a coercion from \\spadtype{OutputForm} to \\TeX{} format. The particular dialect of \\TeX{} used is \\LaTeX{}. The basic object consists of three parts: a prologue,{} a tex part and an epilogue. The functions \\spadfun{prologue},{} \\spadfun{tex} and \\spadfun{epilogue} extract these parts,{} respectively. The main guts of the expression go into the tex part. The other parts can be set (\\spadfun{setPrologue!},{} \\spadfun{setEpilogue!}) so that contain the appropriate tags for printing. For example,{} the prologue and epilogue might simply contain \\spad{``}\\verb+\\spad{\\[}+\\spad{''} and \\spad{``}\\verb+\\spad{\\]}+\\spad{''},{} respectively,{} so that the TeX section will be printed in LaTeX display math mode.")) (|setPrologue!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setPrologue!(t,strings)} sets the prologue section of a TeX form \\spad{t} to \\spad{strings}.")) (|setTex!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setTex!(t,strings)} sets the TeX section of a TeX form \\spad{t} to \\spad{strings}.")) (|setEpilogue!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setEpilogue!(t,strings)} sets the epilogue section of a TeX form \\spad{t} to \\spad{strings}.")) (|prologue| (((|List| (|String|)) $) "\\spad{prologue(t)} extracts the prologue section of a TeX form \\spad{t}.")) (|new| (($) "\\spad{new()} create a new,{} empty object. Use \\spadfun{setPrologue!},{} \\spadfun{setTex!} and \\spadfun{setEpilogue!} to set the various components of this object.")) (|tex| (((|List| (|String|)) $) "\\spad{tex(t)} extracts the TeX section of a TeX form \\spad{t}.")) (|epilogue| (((|List| (|String|)) $) "\\spad{epilogue(t)} extracts the epilogue section of a TeX form \\spad{t}.")) (|display| (((|Void|) $) "\\spad{display(t)} outputs the TeX formatted code \\spad{t} so that each line has length less than or equal to the value set by the system command \\spadsyscom{set output length}.") (((|Void|) $ (|Integer|)) "\\spad{display(t,width)} outputs the TeX formatted code \\spad{t} so that each line has length less than or equal to \\spadvar{\\spad{width}}.")) (|convert| (($ (|OutputForm|) (|Integer|) (|OutputForm|)) "\\spad{convert(o,step,type)} changes \\spad{o} in standard output format to TeX format and also adds the given \\spad{step} number and \\spad{type}. This is useful if you want to create equations with given numbers or have the equation numbers correspond to the interpreter \\spad{step} numbers.") (($ (|OutputForm|) (|Integer|)) "\\spad{convert(o,step)} changes \\spad{o} in standard output format to TeX format and also adds the given \\spad{step} number. This is useful if you want to create equations with given numbers or have the equation numbers correspond to the interpreter \\spad{step} numbers."))) NIL NIL -(-1218) +(-1219) ((|constructor| (NIL "This domain provides an implementation of text files. Text is stored in these files using the native character set of the computer.")) (|endOfFile?| (((|Boolean|) $) "\\spad{endOfFile?(f)} tests whether the file \\spad{f} is positioned after the end of all text. If the file is open for output,{} then this test is always \\spad{true}.")) (|readIfCan!| (((|Union| (|String|) "failed") $) "\\spad{readIfCan!(f)} returns a string of the contents of a line from file \\spad{f},{} if possible. If \\spad{f} is not readable or if it is positioned at the end of file,{} then \\spad{\"failed\"} is returned.")) (|readLineIfCan!| (((|Union| (|String|) "failed") $) "\\spad{readLineIfCan!(f)} returns a string of the contents of a line from file \\spad{f},{} if possible. If \\spad{f} is not readable or if it is positioned at the end of file,{} then \\spad{\"failed\"} is returned.")) (|readLine!| (((|String|) $) "\\spad{readLine!(f)} returns a string of the contents of a line from the file \\spad{f}.")) (|writeLine!| (((|String|) $) "\\spad{writeLine!(f)} finishes the current line in the file \\spad{f}. An empty string is returned. The call \\spad{writeLine!(f)} is equivalent to \\spad{writeLine!(f,\"\")}.") (((|String|) $ (|String|)) "\\spad{writeLine!(f,s)} writes the contents of the string \\spad{s} and finishes the current line in the file \\spad{f}. The value of \\spad{s} is returned."))) NIL NIL -(-1219 R) +(-1220 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 -(-1220) +(-1221) ((|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 -(-1221 S) +(-1222 S) ((|constructor| (NIL "Category for the transcendental elementary functions.")) (|pi| (($) "\\spad{pi()} returns the constant \\spad{pi}."))) NIL NIL -(-1222) +(-1223) ((|constructor| (NIL "Category for the transcendental elementary functions.")) (|pi| (($) "\\spad{pi()} returns the constant \\spad{pi}."))) NIL NIL -(-1223 S) -((|constructor| (NIL "\\spadtype{Tree(S)} is a basic domains of tree structures. Each tree is either empty or else is a {\\it node} consisting of a value and a list of (sub)trees.")) (|cyclicParents| (((|List| $) $) "\\spad{cyclicParents(t)} returns a list of cycles that are parents of \\spad{t}.")) (|cyclicEqual?| (((|Boolean|) $ $) "\\spad{cyclicEqual?(t1, t2)} tests of two cyclic trees have the same structure.")) (|cyclicEntries| (((|List| $) $) "\\spad{cyclicEntries(t)} returns a list of top-level cycles in tree \\spad{t}.")) (|cyclicCopy| (($ $) "\\spad{cyclicCopy(l)} makes a copy of a (possibly) cyclic tree \\spad{l}.")) (|cyclic?| (((|Boolean|) $) "\\spad{cyclic?(t)} tests if \\spad{t} is a cyclic tree.")) (|tree| (($ |#1|) "\\spad{tree(nd)} creates a tree with value \\spad{nd},{} and no children") (($ (|List| |#1|)) "\\spad{tree(ls)} creates a tree from a list of elements of \\spad{s}.") (($ |#1| (|List| $)) "\\spad{tree(nd,ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}."))) -((-4464 . T) (-4463 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1120))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1120))) (-3794 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1120)))) (-3794 (-12 (|HasCategory| |#1| (QUOTE (-1120))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-875))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-875)))) (|HasCategory| |#1| (QUOTE (-102)))) (-1224 S) +((|constructor| (NIL "\\spadtype{Tree(S)} is a basic domains of tree structures. Each tree is either empty or else is a {\\it node} consisting of a value and a list of (sub)trees.")) (|cyclicParents| (((|List| $) $) "\\spad{cyclicParents(t)} returns a list of cycles that are parents of \\spad{t}.")) (|cyclicEqual?| (((|Boolean|) $ $) "\\spad{cyclicEqual?(t1, t2)} tests of two cyclic trees have the same structure.")) (|cyclicEntries| (((|List| $) $) "\\spad{cyclicEntries(t)} returns a list of top-level cycles in tree \\spad{t}.")) (|cyclicCopy| (($ $) "\\spad{cyclicCopy(l)} makes a copy of a (possibly) cyclic tree \\spad{l}.")) (|cyclic?| (((|Boolean|) $) "\\spad{cyclic?(t)} tests if \\spad{t} is a cyclic tree.")) (|tree| (($ |#1|) "\\spad{tree(nd)} creates a tree with value \\spad{nd},{} and no children") (($ (|List| |#1|)) "\\spad{tree(ls)} creates a tree from a list of elements of \\spad{s}.") (($ |#1| (|List| $)) "\\spad{tree(nd,ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}."))) +((-4465 . T) (-4464 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1121))) (-2758 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1121)))) (-2758 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102)))) +(-1225 S) ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL NIL -(-1225) +(-1226) ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL NIL -(-1226 R -2117) +(-1227 R -1959) ((|constructor| (NIL "\\spadtype{TrigonometricManipulations} provides transformations from trigonometric functions to complex exponentials and logarithms,{} and back.")) (|complexForm| (((|Complex| |#2|) |#2|) "\\spad{complexForm(f)} returns \\spad{[real f, imag f]}.")) (|real?| (((|Boolean|) |#2|) "\\spad{real?(f)} returns \\spad{true} if \\spad{f = real f}.")) (|imag| ((|#2| |#2|) "\\spad{imag(f)} returns the imaginary part of \\spad{f} where \\spad{f} is a complex function.")) (|real| ((|#2| |#2|) "\\spad{real(f)} returns the real part of \\spad{f} where \\spad{f} is a complex function.")) (|trigs| ((|#2| |#2|) "\\spad{trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (|complexElementary| ((|#2| |#2| (|Symbol|)) "\\spad{complexElementary(f, x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.") ((|#2| |#2|) "\\spad{complexElementary(f)} rewrites \\spad{f} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.")) (|complexNormalize| ((|#2| |#2| (|Symbol|)) "\\spad{complexNormalize(f, x)} rewrites \\spad{f} using the least possible number of complex independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{complexNormalize(f)} rewrites \\spad{f} using the least possible number of complex independent kernels."))) NIL NIL -(-1227 R |Row| |Col| M) +(-1228 R |Row| |Col| M) ((|constructor| (NIL "This package provides functions that compute \"fraction-free\" inverses of upper and lower triangular matrices over a integral domain. By \"fraction-free inverses\" we mean the following: given a matrix \\spad{B} with entries in \\spad{R} and an element \\spad{d} of \\spad{R} such that \\spad{d} * inv(\\spad{B}) also has entries in \\spad{R},{} we return \\spad{d} * inv(\\spad{B}). Thus,{} it is not necessary to pass to the quotient field in any of our computations.")) (|LowTriBddDenomInv| ((|#4| |#4| |#1|) "\\spad{LowTriBddDenomInv(B,d)} returns \\spad{M},{} where \\spad{B} is a non-singular lower triangular matrix and \\spad{d} is an element of \\spad{R} such that \\spad{M = d * inv(B)} has entries in \\spad{R}.")) (|UpTriBddDenomInv| ((|#4| |#4| |#1|) "\\spad{UpTriBddDenomInv(B,d)} returns \\spad{M},{} where \\spad{B} is a non-singular upper triangular matrix and \\spad{d} is an element of \\spad{R} such that \\spad{M = d * inv(B)} has entries in \\spad{R}."))) NIL NIL -(-1228 R -2117) +(-1229 R -1959) ((|constructor| (NIL "TranscendentalManipulations provides functions to simplify and expand expressions involving transcendental operators.")) (|expandTrigProducts| ((|#2| |#2|) "\\spad{expandTrigProducts(e)} replaces \\axiom{sin(\\spad{x})*sin(\\spad{y})} by \\spad{(cos(x-y)-cos(x+y))/2},{} \\axiom{cos(\\spad{x})*cos(\\spad{y})} by \\spad{(cos(x-y)+cos(x+y))/2},{} and \\axiom{sin(\\spad{x})*cos(\\spad{y})} by \\spad{(sin(x-y)+sin(x+y))/2}. Note that this operation uses the pattern matcher and so is relatively expensive. To avoid getting into an infinite loop the transformations are applied at most ten times.")) (|removeSinhSq| ((|#2| |#2|) "\\spad{removeSinhSq(f)} converts every \\spad{sinh(u)**2} appearing in \\spad{f} into \\spad{1 - cosh(x)**2},{} and also reduces higher powers of \\spad{sinh(u)} with that formula.")) (|removeCoshSq| ((|#2| |#2|) "\\spad{removeCoshSq(f)} converts every \\spad{cosh(u)**2} appearing in \\spad{f} into \\spad{1 - sinh(x)**2},{} and also reduces higher powers of \\spad{cosh(u)} with that formula.")) (|removeSinSq| ((|#2| |#2|) "\\spad{removeSinSq(f)} converts every \\spad{sin(u)**2} appearing in \\spad{f} into \\spad{1 - cos(x)**2},{} and also reduces higher powers of \\spad{sin(u)} with that formula.")) (|removeCosSq| ((|#2| |#2|) "\\spad{removeCosSq(f)} converts every \\spad{cos(u)**2} appearing in \\spad{f} into \\spad{1 - sin(x)**2},{} and also reduces higher powers of \\spad{cos(u)} with that formula.")) (|coth2tanh| ((|#2| |#2|) "\\spad{coth2tanh(f)} converts every \\spad{coth(u)} appearing in \\spad{f} into \\spad{1/tanh(u)}.")) (|cot2tan| ((|#2| |#2|) "\\spad{cot2tan(f)} converts every \\spad{cot(u)} appearing in \\spad{f} into \\spad{1/tan(u)}.")) (|tanh2coth| ((|#2| |#2|) "\\spad{tanh2coth(f)} converts every \\spad{tanh(u)} appearing in \\spad{f} into \\spad{1/coth(u)}.")) (|tan2cot| ((|#2| |#2|) "\\spad{tan2cot(f)} converts every \\spad{tan(u)} appearing in \\spad{f} into \\spad{1/cot(u)}.")) (|tanh2trigh| ((|#2| |#2|) "\\spad{tanh2trigh(f)} converts every \\spad{tanh(u)} appearing in \\spad{f} into \\spad{sinh(u)/cosh(u)}.")) (|tan2trig| ((|#2| |#2|) "\\spad{tan2trig(f)} converts every \\spad{tan(u)} appearing in \\spad{f} into \\spad{sin(u)/cos(u)}.")) (|sinh2csch| ((|#2| |#2|) "\\spad{sinh2csch(f)} converts every \\spad{sinh(u)} appearing in \\spad{f} into \\spad{1/csch(u)}.")) (|sin2csc| ((|#2| |#2|) "\\spad{sin2csc(f)} converts every \\spad{sin(u)} appearing in \\spad{f} into \\spad{1/csc(u)}.")) (|sech2cosh| ((|#2| |#2|) "\\spad{sech2cosh(f)} converts every \\spad{sech(u)} appearing in \\spad{f} into \\spad{1/cosh(u)}.")) (|sec2cos| ((|#2| |#2|) "\\spad{sec2cos(f)} converts every \\spad{sec(u)} appearing in \\spad{f} into \\spad{1/cos(u)}.")) (|csch2sinh| ((|#2| |#2|) "\\spad{csch2sinh(f)} converts every \\spad{csch(u)} appearing in \\spad{f} into \\spad{1/sinh(u)}.")) (|csc2sin| ((|#2| |#2|) "\\spad{csc2sin(f)} converts every \\spad{csc(u)} appearing in \\spad{f} into \\spad{1/sin(u)}.")) (|coth2trigh| ((|#2| |#2|) "\\spad{coth2trigh(f)} converts every \\spad{coth(u)} appearing in \\spad{f} into \\spad{cosh(u)/sinh(u)}.")) (|cot2trig| ((|#2| |#2|) "\\spad{cot2trig(f)} converts every \\spad{cot(u)} appearing in \\spad{f} into \\spad{cos(u)/sin(u)}.")) (|cosh2sech| ((|#2| |#2|) "\\spad{cosh2sech(f)} converts every \\spad{cosh(u)} appearing in \\spad{f} into \\spad{1/sech(u)}.")) (|cos2sec| ((|#2| |#2|) "\\spad{cos2sec(f)} converts every \\spad{cos(u)} appearing in \\spad{f} into \\spad{1/sec(u)}.")) (|expandLog| ((|#2| |#2|) "\\spad{expandLog(f)} converts every \\spad{log(a/b)} appearing in \\spad{f} into \\spad{log(a) - log(b)},{} and every \\spad{log(a*b)} into \\spad{log(a) + log(b)}..")) (|expandPower| ((|#2| |#2|) "\\spad{expandPower(f)} converts every power \\spad{(a/b)**c} appearing in \\spad{f} into \\spad{a**c * b**(-c)}.")) (|simplifyLog| ((|#2| |#2|) "\\spad{simplifyLog(f)} converts every \\spad{log(a) - log(b)} appearing in \\spad{f} into \\spad{log(a/b)},{} every \\spad{log(a) + log(b)} into \\spad{log(a*b)} and every \\spad{n*log(a)} into \\spad{log(a^n)}.")) (|simplifyExp| ((|#2| |#2|) "\\spad{simplifyExp(f)} converts every product \\spad{exp(a)*exp(b)} appearing in \\spad{f} into \\spad{exp(a+b)}.")) (|htrigs| ((|#2| |#2|) "\\spad{htrigs(f)} converts all the exponentials in \\spad{f} into hyperbolic sines and cosines.")) (|simplify| ((|#2| |#2|) "\\spad{simplify(f)} performs the following simplifications on \\spad{f:}\\begin{items} \\item 1. rewrites trigs and hyperbolic trigs in terms of \\spad{sin} ,{}\\spad{cos},{} \\spad{sinh},{} \\spad{cosh}. \\item 2. rewrites \\spad{sin**2} and \\spad{sinh**2} in terms of \\spad{cos} and \\spad{cosh},{} \\item 3. rewrites \\spad{exp(a)*exp(b)} as \\spad{exp(a+b)}. \\item 4. rewrites \\spad{(a**(1/n))**m * (a**(1/s))**t} as a single power of a single radical of \\spad{a}. \\end{items}")) (|expand| ((|#2| |#2|) "\\spad{expand(f)} performs the following expansions on \\spad{f:}\\begin{items} \\item 1. logs of products are expanded into sums of logs,{} \\item 2. trigonometric and hyperbolic trigonometric functions of sums are expanded into sums of products of trigonometric and hyperbolic trigonometric functions. \\item 3. formal powers of the form \\spad{(a/b)**c} are expanded into \\spad{a**c * b**(-c)}. \\end{items}"))) NIL -((-12 (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -906) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -900) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -906) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -900) (|devaluate| |#1|))))) -(-1229 S R E V P) +((-12 (|HasCategory| |#1| (LIST (QUOTE -626) (LIST (QUOTE -907) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -901) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -907) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -901) (|devaluate| |#1|))))) +(-1230 S R E V P) ((|constructor| (NIL "The category of triangular sets of multivariate polynomials with coefficients in an integral domain. Let \\axiom{\\spad{R}} be an integral domain and \\axiom{\\spad{V}} a finite ordered set of variables,{} say \\axiom{\\spad{X1} < \\spad{X2} < ... < \\spad{Xn}}. A set \\axiom{\\spad{S}} of polynomials in \\axiom{\\spad{R}[\\spad{X1},{}\\spad{X2},{}...,{}\\spad{Xn}]} is triangular if no elements of \\axiom{\\spad{S}} lies in \\axiom{\\spad{R}},{} and if two distinct elements of \\axiom{\\spad{S}} have distinct main variables. Note that the empty set is a triangular set. A triangular set is not necessarily a (lexicographical) Groebner basis and the notion of reduction related to triangular sets is based on the recursive view of polynomials. We recall this notion here and refer to [1] for more details. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a non-constant polynomial \\axiom{\\spad{Q}} if the degree of \\axiom{\\spad{P}} in the main variable of \\axiom{\\spad{Q}} is less than the main degree of \\axiom{\\spad{Q}}. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a triangular set \\axiom{\\spad{T}} if it is reduced \\spad{w}.\\spad{r}.\\spad{t}. every polynomial of \\axiom{\\spad{T}}. \\newline References : \\indented{1}{[1] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)}")) (|coHeight| (((|NonNegativeInteger|) $) "\\axiom{coHeight(\\spad{ts})} returns \\axiom{size()\\spad{\\$}\\spad{V}} minus \\axiom{\\spad{\\#}\\spad{ts}}.")) (|extend| (($ $ |#5|) "\\axiom{extend(\\spad{ts},{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{\\spad{ts}},{} according to the properties of triangular sets of the current category If the required properties do not hold an error is returned.")) (|extendIfCan| (((|Union| $ "failed") $ |#5|) "\\axiom{extendIfCan(\\spad{ts},{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{\\spad{ts}},{} according to the properties of triangular sets of the current domain. If the required properties do not hold then \"failed\" is returned. This operation encodes in some sense the properties of the triangular sets of the current category. Is is used to implement the \\axiom{construct} operation to guarantee that every triangular set build from a list of polynomials has the required properties.")) (|select| (((|Union| |#5| "failed") $ |#4|) "\\axiom{select(\\spad{ts},{}\\spad{v})} returns the polynomial of \\axiom{\\spad{ts}} with \\axiom{\\spad{v}} as main variable,{} if any.")) (|algebraic?| (((|Boolean|) |#4| $) "\\axiom{algebraic?(\\spad{v},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{\\spad{ts}}.")) (|algebraicVariables| (((|List| |#4|) $) "\\axiom{algebraicVariables(\\spad{ts})} returns the decreasingly sorted list of the main variables of the polynomials of \\axiom{\\spad{ts}}.")) (|rest| (((|Union| $ "failed") $) "\\axiom{rest(\\spad{ts})} returns the polynomials of \\axiom{\\spad{ts}} with smaller main variable than \\axiom{mvar(\\spad{ts})} if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \"failed\"")) (|last| (((|Union| |#5| "failed") $) "\\axiom{last(\\spad{ts})} returns the polynomial of \\axiom{\\spad{ts}} with smallest main variable if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|first| (((|Union| |#5| "failed") $) "\\axiom{first(\\spad{ts})} returns the polynomial of \\axiom{\\spad{ts}} with greatest main variable if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) (|:| |open| (|List| |#5|)))) (|List| |#5|)) "\\axiom{zeroSetSplitIntoTriangularSystems(\\spad{lp})} returns a list of triangular systems \\axiom{[[\\spad{ts1},{}\\spad{qs1}],{}...,{}[\\spad{tsn},{}\\spad{qsn}]]} such that the zero set of \\axiom{\\spad{lp}} is the union of the closures of the \\axiom{W_i} where \\axiom{W_i} consists of the zeros of \\axiom{\\spad{ts}} which do not cancel any polynomial in \\axiom{qsi}.")) (|zeroSetSplit| (((|List| $) (|List| |#5|)) "\\axiom{zeroSetSplit(\\spad{lp})} returns a list \\axiom{\\spad{lts}} of triangular sets such that the zero set of \\axiom{\\spad{lp}} is the union of the closures of the regular zero sets of the members of \\axiom{\\spad{lts}}.")) (|reduceByQuasiMonic| ((|#5| |#5| $) "\\axiom{reduceByQuasiMonic(\\spad{p},{}\\spad{ts})} returns the same as \\axiom{remainder(\\spad{p},{}collectQuasiMonic(\\spad{ts})).polnum}.")) (|collectQuasiMonic| (($ $) "\\axiom{collectQuasiMonic(\\spad{ts})} returns the subset of \\axiom{\\spad{ts}} consisting of the polynomials with initial in \\axiom{\\spad{R}}.")) (|removeZero| ((|#5| |#5| $) "\\axiom{removeZero(\\spad{p},{}\\spad{ts})} returns \\axiom{0} if \\axiom{\\spad{p}} reduces to \\axiom{0} by pseudo-division \\spad{w}.\\spad{r}.\\spad{t} \\axiom{\\spad{ts}} otherwise returns a polynomial \\axiom{\\spad{q}} computed from \\axiom{\\spad{p}} by removing any coefficient in \\axiom{\\spad{p}} reducing to \\axiom{0}.")) (|initiallyReduce| ((|#5| |#5| $) "\\axiom{initiallyReduce(\\spad{p},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|headReduce| ((|#5| |#5| $) "\\axiom{headReduce(\\spad{p},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduce?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|stronglyReduce| ((|#5| |#5| $) "\\axiom{stronglyReduce(\\spad{p},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{stronglyReduced?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|rewriteSetWithReduction| (((|List| |#5|) (|List| |#5|) $ (|Mapping| |#5| |#5| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{rewriteSetWithReduction(\\spad{lp},{}\\spad{ts},{}redOp,{}redOp?)} returns a list \\axiom{\\spad{lq}} of polynomials such that \\axiom{[reduce(\\spad{p},{}\\spad{ts},{}redOp,{}redOp?) for \\spad{p} in \\spad{lp}]} and \\axiom{\\spad{lp}} have the same zeros inside the regular zero set of \\axiom{\\spad{ts}}. Moreover,{} for every polynomial \\axiom{\\spad{q}} in \\axiom{\\spad{lq}} and every polynomial \\axiom{\\spad{t}} in \\axiom{\\spad{ts}} \\axiom{redOp?(\\spad{q},{}\\spad{t})} holds and there exists a polynomial \\axiom{\\spad{p}} in the ideal generated by \\axiom{\\spad{lp}} and a product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = \\spad{f*q} + redOp(\\spad{p},{}\\spad{q})}.")) (|reduce| ((|#5| |#5| $ (|Mapping| |#5| |#5| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{reduce(\\spad{p},{}\\spad{ts},{}redOp,{}redOp?)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{redOp?(\\spad{r},{}\\spad{p})} holds for every \\axiom{\\spad{p}} of \\axiom{\\spad{ts}} and there exists some product \\axiom{\\spad{h}} of the initials of the members of \\axiom{\\spad{ts}} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = \\spad{f*q} + redOp(\\spad{p},{}\\spad{q})}.")) (|autoReduced?| (((|Boolean|) $ (|Mapping| (|Boolean|) |#5| (|List| |#5|))) "\\axiom{autoReduced?(\\spad{ts},{}redOp?)} returns \\spad{true} iff every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to every other in the sense of \\axiom{redOp?}")) (|initiallyReduced?| (((|Boolean|) $) "\\spad{initiallyReduced?(ts)} returns \\spad{true} iff for every element \\axiom{\\spad{p}} of \\axiom{\\spad{ts}} \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the other elements of \\axiom{\\spad{ts}} with the same main variable.") (((|Boolean|) |#5| $) "\\axiom{initiallyReduced?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the elements of \\axiom{\\spad{ts}} with the same main variable.")) (|headReduced?| (((|Boolean|) $) "\\spad{headReduced?(ts)} returns \\spad{true} iff the head of every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{\\spad{ts}}.") (((|Boolean|) |#5| $) "\\axiom{headReduced?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff the head of \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ts}}.")) (|stronglyReduced?| (((|Boolean|) $) "\\axiom{stronglyReduced?(\\spad{ts})} returns \\spad{true} iff every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{\\spad{ts}}.") (((|Boolean|) |#5| $) "\\axiom{stronglyReduced?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ts}}.")) (|reduced?| (((|Boolean|) |#5| $ (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{reduced?(\\spad{p},{}\\spad{ts},{}redOp?)} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. in the sense of the operation \\axiom{redOp?},{} that is if for every \\axiom{\\spad{t}} in \\axiom{\\spad{ts}} \\axiom{redOp?(\\spad{p},{}\\spad{t})} holds.")) (|normalized?| (((|Boolean|) $) "\\axiom{normalized?(\\spad{ts})} returns \\spad{true} iff for every axiom{\\spad{p}} in axiom{\\spad{ts}} we have \\axiom{normalized?(\\spad{p},{}us)} where \\axiom{us} is \\axiom{collectUnder(\\spad{ts},{}mvar(\\spad{p}))}.") (((|Boolean|) |#5| $) "\\axiom{normalized?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variables of the polynomials of \\axiom{\\spad{ts}}")) (|quasiComponent| (((|Record| (|:| |close| (|List| |#5|)) (|:| |open| (|List| |#5|))) $) "\\axiom{quasiComponent(\\spad{ts})} returns \\axiom{[\\spad{lp},{}\\spad{lq}]} where \\axiom{\\spad{lp}} is the list of the members of \\axiom{\\spad{ts}} and \\axiom{\\spad{lq}}is \\axiom{initials(\\spad{ts})}.")) (|degree| (((|NonNegativeInteger|) $) "\\axiom{degree(\\spad{ts})} returns the product of main degrees of the members of \\axiom{\\spad{ts}}.")) (|initials| (((|List| |#5|) $) "\\axiom{initials(\\spad{ts})} returns the list of the non-constant initials of the members of \\axiom{\\spad{ts}}.")) (|basicSet| (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#5|))) "failed") (|List| |#5|) (|Mapping| (|Boolean|) |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{basicSet(\\spad{ps},{}pred?,{}redOp?)} returns the same as \\axiom{basicSet(\\spad{qs},{}redOp?)} where \\axiom{\\spad{qs}} consists of the polynomials of \\axiom{\\spad{ps}} satisfying property \\axiom{pred?}.") (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#5|))) "failed") (|List| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{basicSet(\\spad{ps},{}redOp?)} returns \\axiom{[\\spad{bs},{}\\spad{ts}]} where \\axiom{concat(\\spad{bs},{}\\spad{ts})} is \\axiom{\\spad{ps}} and \\axiom{\\spad{bs}} is a basic set in Wu Wen Tsun sense of \\axiom{\\spad{ps}} \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?},{} if no non-zero constant polynomial lie in \\axiom{\\spad{ps}},{} otherwise \\axiom{\"failed\"} is returned.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(\\spad{ts1},{}\\spad{ts2})} returns \\spad{true} iff \\axiom{\\spad{ts2}} has higher rank than \\axiom{\\spad{ts1}} in Wu Wen Tsun sense."))) NIL ((|HasCategory| |#4| (QUOTE (-379)))) -(-1230 R E V P) +(-1231 R E V P) ((|constructor| (NIL "The category of triangular sets of multivariate polynomials with coefficients in an integral domain. Let \\axiom{\\spad{R}} be an integral domain and \\axiom{\\spad{V}} a finite ordered set of variables,{} say \\axiom{\\spad{X1} < \\spad{X2} < ... < \\spad{Xn}}. A set \\axiom{\\spad{S}} of polynomials in \\axiom{\\spad{R}[\\spad{X1},{}\\spad{X2},{}...,{}\\spad{Xn}]} is triangular if no elements of \\axiom{\\spad{S}} lies in \\axiom{\\spad{R}},{} and if two distinct elements of \\axiom{\\spad{S}} have distinct main variables. Note that the empty set is a triangular set. A triangular set is not necessarily a (lexicographical) Groebner basis and the notion of reduction related to triangular sets is based on the recursive view of polynomials. We recall this notion here and refer to [1] for more details. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a non-constant polynomial \\axiom{\\spad{Q}} if the degree of \\axiom{\\spad{P}} in the main variable of \\axiom{\\spad{Q}} is less than the main degree of \\axiom{\\spad{Q}}. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a triangular set \\axiom{\\spad{T}} if it is reduced \\spad{w}.\\spad{r}.\\spad{t}. every polynomial of \\axiom{\\spad{T}}. \\newline References : \\indented{1}{[1] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)}")) (|coHeight| (((|NonNegativeInteger|) $) "\\axiom{coHeight(\\spad{ts})} returns \\axiom{size()\\spad{\\$}\\spad{V}} minus \\axiom{\\spad{\\#}\\spad{ts}}.")) (|extend| (($ $ |#4|) "\\axiom{extend(\\spad{ts},{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{\\spad{ts}},{} according to the properties of triangular sets of the current category If the required properties do not hold an error is returned.")) (|extendIfCan| (((|Union| $ "failed") $ |#4|) "\\axiom{extendIfCan(\\spad{ts},{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{\\spad{ts}},{} according to the properties of triangular sets of the current domain. If the required properties do not hold then \"failed\" is returned. This operation encodes in some sense the properties of the triangular sets of the current category. Is is used to implement the \\axiom{construct} operation to guarantee that every triangular set build from a list of polynomials has the required properties.")) (|select| (((|Union| |#4| "failed") $ |#3|) "\\axiom{select(\\spad{ts},{}\\spad{v})} returns the polynomial of \\axiom{\\spad{ts}} with \\axiom{\\spad{v}} as main variable,{} if any.")) (|algebraic?| (((|Boolean|) |#3| $) "\\axiom{algebraic?(\\spad{v},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{\\spad{ts}}.")) (|algebraicVariables| (((|List| |#3|) $) "\\axiom{algebraicVariables(\\spad{ts})} returns the decreasingly sorted list of the main variables of the polynomials of \\axiom{\\spad{ts}}.")) (|rest| (((|Union| $ "failed") $) "\\axiom{rest(\\spad{ts})} returns the polynomials of \\axiom{\\spad{ts}} with smaller main variable than \\axiom{mvar(\\spad{ts})} if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \"failed\"")) (|last| (((|Union| |#4| "failed") $) "\\axiom{last(\\spad{ts})} returns the polynomial of \\axiom{\\spad{ts}} with smallest main variable if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|first| (((|Union| |#4| "failed") $) "\\axiom{first(\\spad{ts})} returns the polynomial of \\axiom{\\spad{ts}} with greatest main variable if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) (|:| |open| (|List| |#4|)))) (|List| |#4|)) "\\axiom{zeroSetSplitIntoTriangularSystems(\\spad{lp})} returns a list of triangular systems \\axiom{[[\\spad{ts1},{}\\spad{qs1}],{}...,{}[\\spad{tsn},{}\\spad{qsn}]]} such that the zero set of \\axiom{\\spad{lp}} is the union of the closures of the \\axiom{W_i} where \\axiom{W_i} consists of the zeros of \\axiom{\\spad{ts}} which do not cancel any polynomial in \\axiom{qsi}.")) (|zeroSetSplit| (((|List| $) (|List| |#4|)) "\\axiom{zeroSetSplit(\\spad{lp})} returns a list \\axiom{\\spad{lts}} of triangular sets such that the zero set of \\axiom{\\spad{lp}} is the union of the closures of the regular zero sets of the members of \\axiom{\\spad{lts}}.")) (|reduceByQuasiMonic| ((|#4| |#4| $) "\\axiom{reduceByQuasiMonic(\\spad{p},{}\\spad{ts})} returns the same as \\axiom{remainder(\\spad{p},{}collectQuasiMonic(\\spad{ts})).polnum}.")) (|collectQuasiMonic| (($ $) "\\axiom{collectQuasiMonic(\\spad{ts})} returns the subset of \\axiom{\\spad{ts}} consisting of the polynomials with initial in \\axiom{\\spad{R}}.")) (|removeZero| ((|#4| |#4| $) "\\axiom{removeZero(\\spad{p},{}\\spad{ts})} returns \\axiom{0} if \\axiom{\\spad{p}} reduces to \\axiom{0} by pseudo-division \\spad{w}.\\spad{r}.\\spad{t} \\axiom{\\spad{ts}} otherwise returns a polynomial \\axiom{\\spad{q}} computed from \\axiom{\\spad{p}} by removing any coefficient in \\axiom{\\spad{p}} reducing to \\axiom{0}.")) (|initiallyReduce| ((|#4| |#4| $) "\\axiom{initiallyReduce(\\spad{p},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|headReduce| ((|#4| |#4| $) "\\axiom{headReduce(\\spad{p},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduce?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|stronglyReduce| ((|#4| |#4| $) "\\axiom{stronglyReduce(\\spad{p},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{stronglyReduced?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|rewriteSetWithReduction| (((|List| |#4|) (|List| |#4|) $ (|Mapping| |#4| |#4| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{rewriteSetWithReduction(\\spad{lp},{}\\spad{ts},{}redOp,{}redOp?)} returns a list \\axiom{\\spad{lq}} of polynomials such that \\axiom{[reduce(\\spad{p},{}\\spad{ts},{}redOp,{}redOp?) for \\spad{p} in \\spad{lp}]} and \\axiom{\\spad{lp}} have the same zeros inside the regular zero set of \\axiom{\\spad{ts}}. Moreover,{} for every polynomial \\axiom{\\spad{q}} in \\axiom{\\spad{lq}} and every polynomial \\axiom{\\spad{t}} in \\axiom{\\spad{ts}} \\axiom{redOp?(\\spad{q},{}\\spad{t})} holds and there exists a polynomial \\axiom{\\spad{p}} in the ideal generated by \\axiom{\\spad{lp}} and a product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = \\spad{f*q} + redOp(\\spad{p},{}\\spad{q})}.")) (|reduce| ((|#4| |#4| $ (|Mapping| |#4| |#4| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{reduce(\\spad{p},{}\\spad{ts},{}redOp,{}redOp?)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{redOp?(\\spad{r},{}\\spad{p})} holds for every \\axiom{\\spad{p}} of \\axiom{\\spad{ts}} and there exists some product \\axiom{\\spad{h}} of the initials of the members of \\axiom{\\spad{ts}} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = \\spad{f*q} + redOp(\\spad{p},{}\\spad{q})}.")) (|autoReduced?| (((|Boolean|) $ (|Mapping| (|Boolean|) |#4| (|List| |#4|))) "\\axiom{autoReduced?(\\spad{ts},{}redOp?)} returns \\spad{true} iff every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to every other in the sense of \\axiom{redOp?}")) (|initiallyReduced?| (((|Boolean|) $) "\\spad{initiallyReduced?(ts)} returns \\spad{true} iff for every element \\axiom{\\spad{p}} of \\axiom{\\spad{ts}} \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the other elements of \\axiom{\\spad{ts}} with the same main variable.") (((|Boolean|) |#4| $) "\\axiom{initiallyReduced?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the elements of \\axiom{\\spad{ts}} with the same main variable.")) (|headReduced?| (((|Boolean|) $) "\\spad{headReduced?(ts)} returns \\spad{true} iff the head of every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{\\spad{ts}}.") (((|Boolean|) |#4| $) "\\axiom{headReduced?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff the head of \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ts}}.")) (|stronglyReduced?| (((|Boolean|) $) "\\axiom{stronglyReduced?(\\spad{ts})} returns \\spad{true} iff every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{\\spad{ts}}.") (((|Boolean|) |#4| $) "\\axiom{stronglyReduced?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ts}}.")) (|reduced?| (((|Boolean|) |#4| $ (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{reduced?(\\spad{p},{}\\spad{ts},{}redOp?)} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. in the sense of the operation \\axiom{redOp?},{} that is if for every \\axiom{\\spad{t}} in \\axiom{\\spad{ts}} \\axiom{redOp?(\\spad{p},{}\\spad{t})} holds.")) (|normalized?| (((|Boolean|) $) "\\axiom{normalized?(\\spad{ts})} returns \\spad{true} iff for every axiom{\\spad{p}} in axiom{\\spad{ts}} we have \\axiom{normalized?(\\spad{p},{}us)} where \\axiom{us} is \\axiom{collectUnder(\\spad{ts},{}mvar(\\spad{p}))}.") (((|Boolean|) |#4| $) "\\axiom{normalized?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variables of the polynomials of \\axiom{\\spad{ts}}")) (|quasiComponent| (((|Record| (|:| |close| (|List| |#4|)) (|:| |open| (|List| |#4|))) $) "\\axiom{quasiComponent(\\spad{ts})} returns \\axiom{[\\spad{lp},{}\\spad{lq}]} where \\axiom{\\spad{lp}} is the list of the members of \\axiom{\\spad{ts}} and \\axiom{\\spad{lq}}is \\axiom{initials(\\spad{ts})}.")) (|degree| (((|NonNegativeInteger|) $) "\\axiom{degree(\\spad{ts})} returns the product of main degrees of the members of \\axiom{\\spad{ts}}.")) (|initials| (((|List| |#4|) $) "\\axiom{initials(\\spad{ts})} returns the list of the non-constant initials of the members of \\axiom{\\spad{ts}}.")) (|basicSet| (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{basicSet(\\spad{ps},{}pred?,{}redOp?)} returns the same as \\axiom{basicSet(\\spad{qs},{}redOp?)} where \\axiom{\\spad{qs}} consists of the polynomials of \\axiom{\\spad{ps}} satisfying property \\axiom{pred?}.") (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{basicSet(\\spad{ps},{}redOp?)} returns \\axiom{[\\spad{bs},{}\\spad{ts}]} where \\axiom{concat(\\spad{bs},{}\\spad{ts})} is \\axiom{\\spad{ps}} and \\axiom{\\spad{bs}} is a basic set in Wu Wen Tsun sense of \\axiom{\\spad{ps}} \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?},{} if no non-zero constant polynomial lie in \\axiom{\\spad{ps}},{} otherwise \\axiom{\"failed\"} is returned.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(\\spad{ts1},{}\\spad{ts2})} returns \\spad{true} iff \\axiom{\\spad{ts2}} has higher rank than \\axiom{\\spad{ts1}} in Wu Wen Tsun sense."))) -((-4464 . T) (-4463 . T)) +((-4465 . T) (-4464 . T)) NIL -(-1231 |Coef|) +(-1232 |Coef|) ((|constructor| (NIL "\\spadtype{TaylorSeries} is a general multivariate Taylor series domain over the ring Coef and with variables of type Symbol.")) (|fintegrate| (($ (|Mapping| $) (|Symbol|) |#1|) "\\spad{fintegrate(f,v,c)} is the integral of \\spad{f()} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.} \\indented{1}{The evaluation of \\spad{f()} is delayed.}")) (|integrate| (($ $ (|Symbol|) |#1|) "\\spad{integrate(s,v,c)} is the integral of \\spad{s} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.}")) (|coerce| (($ (|Polynomial| |#1|)) "\\spad{coerce(s)} regroups terms of \\spad{s} by total degree \\indented{1}{and forms a series.}") (($ (|Symbol|)) "\\spad{coerce(s)} converts a variable to a Taylor series")) (|coefficient| (((|Polynomial| |#1|) $ (|NonNegativeInteger|)) "\\spad{coefficient(s, n)} gives the terms of total degree \\spad{n}."))) -(((-4465 "*") |has| |#1| (-174)) (-4456 |has| |#1| (-568)) (-4458 . T) (-4457 . T) (-4460 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (-3794 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-374)))) -(-1232 |Curve|) +(((-4466 "*") |has| |#1| (-174)) (-4457 |has| |#1| (-568)) (-4459 . T) (-4458 . T) (-4461 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (-2758 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-374)))) +(-1233 |Curve|) ((|constructor| (NIL "\\indented{2}{Package for constructing tubes around 3-dimensional parametric curves.} Domain of tubes around 3-dimensional parametric curves.")) (|tube| (($ |#1| (|List| (|List| (|Point| (|DoubleFloat|)))) (|Boolean|)) "\\spad{tube(c,ll,b)} creates a tube of the domain \\spadtype{TubePlot} from a space curve \\spad{c} of the category \\spadtype{PlottableSpaceCurveCategory},{} a list of lists of points (loops) \\spad{ll} and a boolean \\spad{b} which if \\spad{true} indicates a closed tube,{} or if \\spad{false} an open tube.")) (|setClosed| (((|Boolean|) $ (|Boolean|)) "\\spad{setClosed(t,b)} declares the given tube plot \\spad{t} to be closed if \\spad{b} is \\spad{true},{} or if \\spad{b} is \\spad{false},{} \\spad{t} is set to be open.")) (|open?| (((|Boolean|) $) "\\spad{open?(t)} tests whether the given tube plot \\spad{t} is open.")) (|closed?| (((|Boolean|) $) "\\spad{closed?(t)} tests whether the given tube plot \\spad{t} is closed.")) (|listLoops| (((|List| (|List| (|Point| (|DoubleFloat|)))) $) "\\spad{listLoops(t)} returns the list of lists of points,{} or the 'loops',{} of the given tube plot \\spad{t}.")) (|getCurve| ((|#1| $) "\\spad{getCurve(t)} returns the \\spadtype{PlottableSpaceCurveCategory} representing the parametric curve of the given tube plot \\spad{t}."))) NIL NIL -(-1233) +(-1234) ((|constructor| (NIL "Tools for constructing tubes around 3-dimensional parametric curves.")) (|loopPoints| (((|List| (|Point| (|DoubleFloat|))) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|List| (|List| (|DoubleFloat|)))) "\\spad{loopPoints(p,n,b,r,lls)} creates and returns a list of points which form the loop with radius \\spad{r},{} around the center point indicated by the point \\spad{p},{} with the principal normal vector of the space curve at point \\spad{p} given by the point(vector) \\spad{n},{} and the binormal vector given by the point(vector) \\spad{b},{} and a list of lists,{} \\spad{lls},{} which is the \\spadfun{cosSinInfo} of the number of points defining the loop.")) (|cosSinInfo| (((|List| (|List| (|DoubleFloat|))) (|Integer|)) "\\spad{cosSinInfo(n)} returns the list of lists of values for \\spad{n},{} in the form: \\spad{[[cos(n - 1) a,sin(n - 1) a],...,[cos 2 a,sin 2 a],[cos a,sin a]]} where \\spad{a = 2 pi/n}. Note: \\spad{n} should be greater than 2.")) (|unitVector| (((|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))) "\\spad{unitVector(p)} creates the unit vector of the point \\spad{p} and returns the result as a point. Note: \\spad{unitVector(p) = p/|p|}.")) (|cross| (((|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))) "\\spad{cross(p,q)} computes the cross product of the two points \\spad{p} and \\spad{q} using only the first three coordinates,{} and keeping the color of the first point \\spad{p}. The result is returned as a point.")) (|dot| (((|DoubleFloat|) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))) "\\spad{dot(p,q)} computes the dot product of the two points \\spad{p} and \\spad{q} using only the first three coordinates,{} and returns the resulting \\spadtype{DoubleFloat}.")) (- (((|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))) "\\spad{p - q} computes and returns a point whose coordinates are the differences of the coordinates of two points \\spad{p} and \\spad{q},{} using the color,{} or fourth coordinate,{} of the first point \\spad{p} as the color also of the point \\spad{q}.")) (+ (((|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))) "\\spad{p + q} computes and returns a point whose coordinates are the sums of the coordinates of the two points \\spad{p} and \\spad{q},{} using the color,{} or fourth coordinate,{} of the first point \\spad{p} as the color also of the point \\spad{q}.")) (* (((|Point| (|DoubleFloat|)) (|DoubleFloat|) (|Point| (|DoubleFloat|))) "\\spad{s * p} returns a point whose coordinates are the scalar multiple of the point \\spad{p} by the scalar \\spad{s},{} preserving the color,{} or fourth coordinate,{} of \\spad{p}.")) (|point| (((|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{point(x1,x2,x3,c)} creates and returns a point from the three specified coordinates \\spad{x1},{} \\spad{x2},{} \\spad{x3},{} and also a fourth coordinate,{} \\spad{c},{} which is generally used to specify the color of the point."))) NIL NIL -(-1234 S) +(-1235 S) ((|constructor| (NIL "\\indented{1}{This domain is used to interface with the interpreter\\spad{'s} notion} of comma-delimited sequences of values.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length(x)} returns the number of elements in tuple \\spad{x}")) (|select| ((|#1| $ (|NonNegativeInteger|)) "\\spad{select(x,n)} returns the \\spad{n}-th element of tuple \\spad{x}. tuples are 0-based"))) NIL -((|HasCategory| |#1| (QUOTE (-1120))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-875))))) -(-1235 -2117) +((|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) +(-1236 -1959) ((|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 -(-1236) +(-1237) ((|constructor| (NIL "This domain represents a type AST."))) NIL NIL -(-1237) +(-1238) ((|constructor| (NIL "The fundamental Type."))) NIL NIL -(-1238 S) +(-1239 S) ((|constructor| (NIL "Provides functions to force a partial ordering on any set.")) (|more?| (((|Boolean|) |#1| |#1|) "\\spad{more?(a, b)} compares \\spad{a} and \\spad{b} in the partial ordering induced by setOrder,{} and uses the ordering on \\spad{S} if \\spad{a} and \\spad{b} are not comparable in the partial ordering.")) (|userOrdered?| (((|Boolean|)) "\\spad{userOrdered?()} tests if the partial ordering induced by \\spadfunFrom{setOrder}{UserDefinedPartialOrdering} is not empty.")) (|largest| ((|#1| (|List| |#1|)) "\\spad{largest l} returns the largest element of \\spad{l} where the partial ordering induced by setOrder is completed into a total one by the ordering on \\spad{S}.") ((|#1| (|List| |#1|) (|Mapping| (|Boolean|) |#1| |#1|)) "\\spad{largest(l, fn)} returns the largest element of \\spad{l} where the partial ordering induced by setOrder is completed into a total one by \\spad{fn}.")) (|less?| (((|Boolean|) |#1| |#1| (|Mapping| (|Boolean|) |#1| |#1|)) "\\spad{less?(a, b, fn)} compares \\spad{a} and \\spad{b} in the partial ordering induced by setOrder,{} and returns \\spad{fn(a, b)} if \\spad{a} and \\spad{b} are not comparable in that ordering.") (((|Union| (|Boolean|) "failed") |#1| |#1|) "\\spad{less?(a, b)} compares \\spad{a} and \\spad{b} in the partial ordering induced by setOrder.")) (|getOrder| (((|Record| (|:| |low| (|List| |#1|)) (|:| |high| (|List| |#1|)))) "\\spad{getOrder()} returns \\spad{[[b1,...,bm], [a1,...,an]]} such that the partial ordering on \\spad{S} was given by \\spad{setOrder([b1,...,bm],[a1,...,an])}.")) (|setOrder| (((|Void|) (|List| |#1|) (|List| |#1|)) "\\spad{setOrder([b1,...,bm], [a1,...,an])} defines a partial ordering on \\spad{S} given \\spad{by:} \\indented{3}{(1)\\space{2}\\spad{b1 < b2 < ... < bm < a1 < a2 < ... < an}.} \\indented{3}{(2)\\space{2}\\spad{bj < c < ai}\\space{2}for \\spad{c} not among the \\spad{ai}\\spad{'s} and \\spad{bj}\\spad{'s}.} \\indented{3}{(3)\\space{2}undefined on \\spad{(c,d)} if neither is among the \\spad{ai}\\spad{'s},{}\\spad{bj}\\spad{'s}.}") (((|Void|) (|List| |#1|)) "\\spad{setOrder([a1,...,an])} defines a partial ordering on \\spad{S} given \\spad{by:} \\indented{3}{(1)\\space{2}\\spad{a1 < a2 < ... < an}.} \\indented{3}{(2)\\space{2}\\spad{b < ai\\space{3}for i = 1..n} and \\spad{b} not among the \\spad{ai}\\spad{'s}.} \\indented{3}{(3)\\space{2}undefined on \\spad{(b, c)} if neither is among the \\spad{ai}\\spad{'s}.}"))) NIL ((|HasCategory| |#1| (QUOTE (-861)))) -(-1239) +(-1240) ((|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 > b2 > ... > bm >} other variables \\spad{> a1 > a2 > ... > an}.") (((|Void|) (|List| (|Symbol|))) "\\spad{setVariableOrder([a1,...,an])} defines an ordering on the variables given by \\spad{a1 > a2 > ... > an > other variables}."))) NIL NIL -(-1240 S) +(-1241 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 -(-1241) +(-1242) ((|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|) $) "\\spad{prime?(x)} tests if \\spad{x} can never be written as the product of two non-units of the ring,{} \\spadignore{i.e.} \\spad{x} is an irreducible element."))) -((-4456 . T) ((-4465 "*") . T) (-4457 . T) (-4458 . T) (-4460 . T)) +((-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL -(-1242) +(-1243) ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 16 bits."))) NIL NIL -(-1243) +(-1244) ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 32 bits."))) NIL NIL -(-1244) +(-1245) ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 64 bits."))) NIL NIL -(-1245) +(-1246) ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 8 bits."))) NIL NIL -(-1246 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) +(-1247 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) ((|constructor| (NIL "Mapping package for univariate Laurent series \\indented{2}{This package allows one to apply a function to the coefficients of} \\indented{2}{a univariate Laurent series.}")) (|map| (((|UnivariateLaurentSeries| |#2| |#4| |#6|) (|Mapping| |#2| |#1|) (|UnivariateLaurentSeries| |#1| |#3| |#5|)) "\\spad{map(f,g(x))} applies the map \\spad{f} to the coefficients of the Laurent series \\spad{g(x)}."))) NIL NIL -(-1247 |Coef|) +(-1248 |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateLaurentSeriesCategory} is the category of Laurent series in one variable.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(f(x),y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $ (|Symbol|)) "\\spad{integrate(f(x),y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 1. We may integrate a series when we can divide coefficients by integers.")) (|rationalFunction| (((|Fraction| (|Polynomial| |#1|)) $ (|Integer|) (|Integer|)) "\\spad{rationalFunction(f,k1,k2)} returns a rational function consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (((|Fraction| (|Polynomial| |#1|)) $ (|Integer|)) "\\spad{rationalFunction(f,k)} returns a rational function consisting of the sum of all terms of \\spad{f} of degree \\spad{<=} \\spad{k}.")) (|multiplyCoefficients| (($ (|Mapping| |#1| (|Integer|)) $) "\\spad{multiplyCoefficients(f,sum(n = n0..infinity,a[n] * x**n)) = sum(n = 0..infinity,f(n) * a[n] * x**n)}. This function is used when Puiseux series are represented by a Laurent series and an exponent.")) (|series| (($ (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)))) "\\spad{series(st)} creates a series from a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents."))) -(((-4465 "*") |has| |#1| (-174)) (-4456 |has| |#1| (-568)) (-4461 |has| |#1| (-374)) (-4455 |has| |#1| (-374)) (-4457 . T) (-4458 . T) (-4460 . T)) +(((-4466 "*") |has| |#1| (-174)) (-4457 |has| |#1| (-568)) (-4462 |has| |#1| (-374)) (-4456 |has| |#1| (-374)) (-4458 . T) (-4459 . T) (-4461 . T)) NIL -(-1248 S |Coef| UTS) +(-1249 S |Coef| UTS) ((|constructor| (NIL "This is a category of univariate Laurent series constructed from univariate Taylor series. A Laurent series is represented by a pair \\spad{[n,f(x)]},{} where \\spad{n} is an arbitrary integer and \\spad{f(x)} is a Taylor series. This pair represents the Laurent series \\spad{x**n * f(x)}.")) (|taylorIfCan| (((|Union| |#3| "failed") $) "\\spad{taylorIfCan(f(x))} converts the Laurent series \\spad{f(x)} to a Taylor series,{} if possible. If this is not possible,{} \"failed\" is returned.")) (|taylor| ((|#3| $) "\\spad{taylor(f(x))} converts the Laurent series \\spad{f}(\\spad{x}) to a Taylor series,{} if possible. Error: if this is not possible.")) (|removeZeroes| (($ (|Integer|) $) "\\spad{removeZeroes(n,f(x))} removes up to \\spad{n} leading zeroes from the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable.") (($ $) "\\spad{removeZeroes(f(x))} removes leading zeroes from the representation of the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable. Note: \\spad{removeZeroes(f)} removes all leading zeroes from \\spad{f}")) (|taylorRep| ((|#3| $) "\\spad{taylorRep(f(x))} returns \\spad{g(x)},{} where \\spad{f = x**n * g(x)} is represented by \\spad{[n,g(x)]}.")) (|degree| (((|Integer|) $) "\\spad{degree(f(x))} returns the degree of the lowest order term of \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurent| (($ (|Integer|) |#3|) "\\spad{laurent(n,f(x))} returns \\spad{x**n * f(x)}."))) NIL ((|HasCategory| |#2| (QUOTE (-374)))) -(-1249 |Coef| UTS) +(-1250 |Coef| UTS) ((|constructor| (NIL "This is a category of univariate Laurent series constructed from univariate Taylor series. A Laurent series is represented by a pair \\spad{[n,f(x)]},{} where \\spad{n} is an arbitrary integer and \\spad{f(x)} is a Taylor series. This pair represents the Laurent series \\spad{x**n * f(x)}.")) (|taylorIfCan| (((|Union| |#2| "failed") $) "\\spad{taylorIfCan(f(x))} converts the Laurent series \\spad{f(x)} to a Taylor series,{} if possible. If this is not possible,{} \"failed\" is returned.")) (|taylor| ((|#2| $) "\\spad{taylor(f(x))} converts the Laurent series \\spad{f}(\\spad{x}) to a Taylor series,{} if possible. Error: if this is not possible.")) (|removeZeroes| (($ (|Integer|) $) "\\spad{removeZeroes(n,f(x))} removes up to \\spad{n} leading zeroes from the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable.") (($ $) "\\spad{removeZeroes(f(x))} removes leading zeroes from the representation of the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable. Note: \\spad{removeZeroes(f)} removes all leading zeroes from \\spad{f}")) (|taylorRep| ((|#2| $) "\\spad{taylorRep(f(x))} returns \\spad{g(x)},{} where \\spad{f = x**n * g(x)} is represented by \\spad{[n,g(x)]}.")) (|degree| (((|Integer|) $) "\\spad{degree(f(x))} returns the degree of the lowest order term of \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurent| (($ (|Integer|) |#2|) "\\spad{laurent(n,f(x))} returns \\spad{x**n * f(x)}."))) -(((-4465 "*") |has| |#1| (-174)) (-4456 |has| |#1| (-568)) (-4461 |has| |#1| (-374)) (-4455 |has| |#1| (-374)) (-4457 . T) (-4458 . T) (-4460 . T)) +(((-4466 "*") |has| |#1| (-174)) (-4457 |has| |#1| (-568)) (-4462 |has| |#1| (-374)) (-4456 |has| |#1| (-374)) (-4458 . T) (-4459 . T) (-4461 . T)) NIL -(-1250 |Coef| UTS) +(-1251 |Coef| UTS) ((|constructor| (NIL "This package enables one to construct a univariate Laurent series domain from a univariate Taylor series domain. Univariate Laurent series are represented by a pair \\spad{[n,f(x)]},{} where \\spad{n} is an arbitrary integer and \\spad{f(x)} is a Taylor series. This pair represents the Laurent series \\spad{x**n * f(x)}."))) -(((-4465 "*") |has| |#1| (-174)) (-4456 |has| |#1| (-568)) (-4461 |has| |#1| (-374)) (-4455 |has| |#1| (-374)) (-4457 . T) (-4458 . T) (-4460 . T)) -((-3794 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#2| (LIST (QUOTE -296) (|devaluate| |#2|) (|devaluate| |#2|)))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#2| (LIST (QUOTE -526) (QUOTE (-1196)) (|devaluate| |#2|)))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-832)))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-861)))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-927)))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-1042)))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-1172)))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548))))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#2| (LIST (QUOTE -319) (|devaluate| |#2|)))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#2| (LIST (QUOTE -1058) (QUOTE (-576))))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#2| (LIST (QUOTE -1058) (QUOTE (-1196)))))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-3794 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (-3794 (|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-146))))) (-3794 (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-148))))) (-3794 (-12 (|HasCategory| |#1| (LIST (QUOTE -916) (QUOTE (-1196)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-576)) (|devaluate| |#1|))))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#2| (LIST (QUOTE -916) (QUOTE (-1196)))))) (-3794 (-12 (|HasCategory| |#1| (LIST (QUOTE -916) (QUOTE (-1196)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-576)) (|devaluate| |#1|))))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#2| (LIST (QUOTE -916) (QUOTE (-1196))))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#2| (LIST (QUOTE -918) (QUOTE (-1196)))))) (-3794 (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-238)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-576)) (|devaluate| |#1|))))) (-3794 (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-238)))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-237)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-576)) (|devaluate| |#1|))))) (|HasCategory| (-576) (QUOTE (-1132))) (-3794 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-374))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-927)))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#2| (LIST (QUOTE -1058) (QUOTE (-1196))))) (-12 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#2| 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The factorization is done by \"lifting\" (HENSEL) the factorization over a finite field.")) (|henselFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|)) "\\spad{henselFact(m,flag)} returns the factorization of \\spad{m},{} FinalFact is a Record \\spad{s}.\\spad{t}. FinalFact.contp=content \\spad{m},{} FinalFact.factors=List of irreducible factors of \\spad{m} with exponent ,{} if \\spad{flag} =true the polynomial is assumed square free.")) (|factorSquareFree| (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(m)} returns the factorization of \\spad{m} square free polynomial")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(m)} returns the factorization of \\spad{m}"))) NIL NIL -(-1253 R S) +(-1254 R S) ((|constructor| (NIL "This package provides operations for mapping functions onto segments.")) (|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 \\spad{seg}."))) NIL ((|HasCategory| |#1| (QUOTE (-860)))) -(-1254 S) +(-1255 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 \\%.")) (|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 (-860))) (|HasCategory| |#1| (QUOTE (-1120)))) -(-1255 |x| R |y| S) +((|HasCategory| |#1| (QUOTE (-860))) (|HasCategory| |#1| (QUOTE (-1121)))) +(-1256 |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}(\\spad{x},{}\\spad{R}) to \\spadtype{UnivariatePolynomial}(\\spad{y},{}\\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| (((|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 -(-1256 R Q UP) +(-1257 R Q UP) ((|constructor| (NIL "UnivariatePolynomialCommonDenominator provides functions to compute the common denominator of the coefficients of univariate polynomials over the quotient field of a \\spad{gcd} domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#3|) "\\spad{splitDenominator(q)} returns \\spad{[p, d]} such that \\spad{q = p/d} and \\spad{d} is a common denominator for the coefficients of \\spad{q}.")) (|clearDenominator| ((|#3| |#3|) "\\spad{clearDenominator(q)} returns \\spad{p} such that \\spad{q = p/d} where \\spad{d} is a common denominator for the coefficients of \\spad{q}.")) (|commonDenominator| ((|#1| |#3|) "\\spad{commonDenominator(q)} returns a common denominator \\spad{d} for the coefficients of \\spad{q}."))) NIL NIL -(-1257 R UP) +(-1258 R UP) ((|constructor| (NIL "UnivariatePolynomialDecompositionPackage implements functional decomposition of univariate polynomial with coefficients in an \\spad{IntegralDomain} of \\spad{CharacteristicZero}.")) (|monicCompleteDecompose| (((|List| |#2|) |#2|) "\\spad{monicCompleteDecompose(f)} returns a list of factors of \\spad{f} for the functional decomposition ([ \\spad{f1},{} ...,{} \\spad{fn} ] means \\spad{f} = \\spad{f1} \\spad{o} ... \\spad{o} \\spad{fn}).")) (|monicDecomposeIfCan| (((|Union| (|Record| (|:| |left| |#2|) (|:| |right| |#2|)) "failed") |#2|) "\\spad{monicDecomposeIfCan(f)} returns a functional decomposition of the monic polynomial \\spad{f} of \"failed\" if it has not found any.")) (|leftFactorIfCan| (((|Union| |#2| "failed") |#2| |#2|) "\\spad{leftFactorIfCan(f,h)} returns the left factor (\\spad{g} in \\spad{f} = \\spad{g} \\spad{o} \\spad{h}) of the functional decomposition of the polynomial \\spad{f} with given \\spad{h} or \\spad{\"failed\"} if \\spad{g} does not exist.")) (|rightFactorIfCan| (((|Union| |#2| "failed") |#2| (|NonNegativeInteger|) |#1|) "\\spad{rightFactorIfCan(f,d,c)} returns a candidate to be the right factor (\\spad{h} in \\spad{f} = \\spad{g} \\spad{o} \\spad{h}) of degree \\spad{d} with leading coefficient \\spad{c} of a functional decomposition of the polynomial \\spad{f} or \\spad{\"failed\"} if no such candidate.")) (|monicRightFactorIfCan| (((|Union| |#2| "failed") |#2| (|NonNegativeInteger|)) "\\spad{monicRightFactorIfCan(f,d)} returns a candidate to be the monic right factor (\\spad{h} in \\spad{f} = \\spad{g} \\spad{o} \\spad{h}) of degree \\spad{d} of a functional decomposition of the polynomial \\spad{f} or \\spad{\"failed\"} if no such candidate."))) NIL NIL -(-1258 R UP) +(-1259 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 -(-1259 R U) +(-1260 R U) ((|constructor| (NIL "This package implements Karatsuba\\spad{'s} trick for multiplying (large) univariate polynomials. It could be improved with a version doing the work on place and also with a special case for squares. We've done this in Basicmath,{} but we believe that this out of the scope of AXIOM.")) (|karatsuba| ((|#2| |#2| |#2| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{karatsuba(a,b,l,k)} returns \\spad{a*b} by applying Karatsuba\\spad{'s} trick provided that both \\spad{a} and \\spad{b} have at least \\spad{l} terms and \\spad{k > 0} holds and by calling \\spad{noKaratsuba} otherwise. The other multiplications are performed by recursive calls with the same third argument and \\spad{k-1} as fourth argument.")) (|karatsubaOnce| ((|#2| |#2| |#2|) "\\spad{karatsuba(a,b)} returns \\spad{a*b} by applying Karatsuba\\spad{'s} trick once. The other multiplications are performed by calling \\spad{*} from \\spad{U}.")) (|noKaratsuba| ((|#2| |#2| |#2|) "\\spad{noKaratsuba(a,b)} returns \\spad{a*b} without using Karatsuba\\spad{'s} trick at all."))) NIL NIL -(-1260 |x| R) +(-1261 |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.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#2| $) "\\spad{fmecg(p1,e,r,p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}"))) -(((-4465 "*") |has| |#2| (-174)) (-4456 |has| |#2| (-568)) (-4459 |has| |#2| (-374)) (-4461 |has| |#2| (-6 -4461)) (-4458 . T) (-4457 . T) (-4460 . T)) -((|HasCategory| |#2| (QUOTE (-927))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-174))) (-3794 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-568)))) (-12 (|HasCategory| (-1102) (LIST (QUOTE -900) (QUOTE (-390)))) (|HasCategory| |#2| (LIST (QUOTE -900) (QUOTE (-390))))) (-12 (|HasCategory| (-1102) (LIST (QUOTE -900) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -900) (QUOTE (-576))))) (-12 (|HasCategory| (-1102) (LIST (QUOTE -626) (LIST (QUOTE -906) (QUOTE (-390))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -906) (QUOTE (-390)))))) (-12 (|HasCategory| (-1102) (LIST (QUOTE -626) (LIST (QUOTE -906) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -906) (QUOTE (-576)))))) (-12 (|HasCategory| (-1102) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#2| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1058) (QUOTE (-576)))) (-3794 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1058) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#2| (LIST (QUOTE -1058) (LIST (QUOTE -419) (QUOTE (-576))))) (-3794 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-927)))) (-3794 (|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-927)))) (-3794 (|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-927)))) (|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-1172))) (|HasCategory| |#2| (LIST (QUOTE -918) (QUOTE (-1196)))) (|HasCategory| |#2| (LIST (QUOTE -916) (QUOTE (-1196)))) (|HasCategory| |#2| (QUOTE (-237))) (|HasCategory| |#2| (QUOTE (-238))) (|HasAttribute| |#2| (QUOTE -4461)) (|HasCategory| |#2| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-927)))) (-3794 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-927)))) (|HasCategory| |#2| (QUOTE (-146))))) -(-1261 R PR S PS) +(((-4466 "*") |has| |#2| (-174)) (-4457 |has| |#2| (-568)) (-4460 |has| |#2| (-374)) (-4462 |has| |#2| (-6 -4462)) (-4459 . T) (-4458 . T) (-4461 . T)) +((|HasCategory| |#2| (QUOTE (-928))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-174))) (-2758 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-568)))) (-12 (|HasCategory| (-1103) (LIST (QUOTE -901) (QUOTE (-390)))) (|HasCategory| |#2| (LIST (QUOTE -901) (QUOTE (-390))))) (-12 (|HasCategory| (-1103) (LIST (QUOTE -901) (QUOTE (-576)))) (|HasCategory| |#2| (LIST (QUOTE -901) (QUOTE (-576))))) (-12 (|HasCategory| (-1103) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-390)))))) (-12 (|HasCategory| (-1103) (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -626) (LIST (QUOTE -907) (QUOTE (-576)))))) (-12 (|HasCategory| (-1103) (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-548))))) (|HasCategory| |#2| (LIST (QUOTE -651) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1059) (QUOTE (-576)))) (-2758 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| |#2| (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (-2758 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-928)))) (-2758 (|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-928)))) (-2758 (|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-928)))) (|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-1173))) (|HasCategory| |#2| (LIST (QUOTE -919) (QUOTE (-1197)))) (|HasCategory| |#2| (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasCategory| |#2| (QUOTE (-237))) (|HasCategory| |#2| (QUOTE (-238))) (|HasAttribute| |#2| (QUOTE -4462)) (|HasCategory| |#2| (QUOTE (-464))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-928)))) (-2758 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-928)))) (|HasCategory| |#2| (QUOTE (-146))))) +(-1262 R PR S PS) ((|constructor| (NIL "Mapping from polynomials over \\spad{R} to polynomials over \\spad{S} given a map from \\spad{R} to \\spad{S} assumed to send zero to zero.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f, p)} takes a function \\spad{f} from \\spad{R} to \\spad{S},{} and applies it to each (non-zero) coefficient of a polynomial \\spad{p} over \\spad{R},{} getting a new polynomial over \\spad{S}. Note: since the map is not applied to zero elements,{} it may map zero to zero."))) NIL NIL -(-1262 S R) +(-1263 S R) ((|constructor| (NIL "The category of univariate polynomials over a ring \\spad{R}. No particular model is assumed - implementations can be either sparse or dense.")) (|integrate| (($ $) "\\spad{integrate(p)} integrates the univariate polynomial \\spad{p} with respect to its distinguished variable.")) (|additiveValuation| ((|attribute|) "euclideanSize(a*b) = euclideanSize(a) + euclideanSize(\\spad{b})")) (|separate| (((|Record| (|:| |primePart| $) (|:| |commonPart| $)) $ $) "\\spad{separate(p, q)} returns \\spad{[a, b]} such that polynomial \\spad{p = a b} and \\spad{a} is relatively prime to \\spad{q}.")) (|pseudoDivide| (((|Record| (|:| |coef| |#2|) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{pseudoDivide(p,q)} returns \\spad{[c, q, r]},{} when \\spad{p' := p*lc(q)**(deg p - deg q + 1) = c * p} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|pseudoQuotient| (($ $ $) "\\spad{pseudoQuotient(p,q)} returns \\spad{r},{} the quotient when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|composite| (((|Union| (|Fraction| $) "failed") (|Fraction| $) $) "\\spad{composite(f, q)} returns \\spad{h} if \\spad{f} = \\spad{h}(\\spad{q}),{} and \"failed\" is no such \\spad{h} exists.") (((|Union| $ "failed") $ $) "\\spad{composite(p, q)} returns \\spad{h} if \\spad{p = h(q)},{} and \"failed\" no such \\spad{h} exists.")) (|subResultantGcd| (($ $ $) "\\spad{subResultantGcd(p,q)} computes the \\spad{gcd} of the polynomials \\spad{p} and \\spad{q} using the SubResultant \\spad{GCD} algorithm.")) (|order| (((|NonNegativeInteger|) $ $) "\\spad{order(p, q)} returns the largest \\spad{n} such that \\spad{q**n} divides polynomial \\spad{p} \\spadignore{i.e.} the order of \\spad{p(x)} at \\spad{q(x)=0}.")) (|elt| ((|#2| (|Fraction| $) |#2|) "\\spad{elt(a,r)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by the constant \\spad{r}.") (((|Fraction| $) (|Fraction| $) (|Fraction| $)) "\\spad{elt(a,b)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by \\spad{b}.")) (|resultant| ((|#2| $ $) "\\spad{resultant(p,q)} returns the resultant of the polynomials \\spad{p} and \\spad{q}.")) (|discriminant| ((|#2| $) "\\spad{discriminant(p)} returns the discriminant of the polynomial \\spad{p}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|) $) "\\spad{differentiate(p, d, x')} extends the \\spad{R}-derivation \\spad{d} to an extension \\spad{D} in \\spad{R[x]} where \\spad{Dx} is given by \\spad{x'},{} and returns \\spad{Dp}.")) (|pseudoRemainder| (($ $ $) "\\spad{pseudoRemainder(p,q)} = \\spad{r},{} for polynomials \\spad{p} and \\spad{q},{} returns the remainder when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|shiftLeft| (($ $ (|NonNegativeInteger|)) "\\spad{shiftLeft(p,n)} returns \\spad{p * monomial(1,n)}")) (|shiftRight| (($ $ (|NonNegativeInteger|)) "\\spad{shiftRight(p,n)} returns \\spad{monicDivide(p,monomial(1,n)).quotient}")) (|karatsubaDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ (|NonNegativeInteger|)) "\\spad{karatsubaDivide(p,n)} returns the same as \\spad{monicDivide(p,monomial(1,n))}")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicDivide(p,q)} divide the polynomial \\spad{p} by the monic polynomial \\spad{q},{} returning the pair \\spad{[quotient, remainder]}. Error: if \\spad{q} isn\\spad{'t} monic.")) (|divideExponents| (((|Union| $ "failed") $ (|NonNegativeInteger|)) "\\spad{divideExponents(p,n)} returns a new polynomial resulting from dividing all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n},{} or \"failed\" if some exponent is not exactly divisible by \\spad{n}.")) (|multiplyExponents| (($ $ (|NonNegativeInteger|)) "\\spad{multiplyExponents(p,n)} returns a new polynomial resulting from multiplying all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n}.")) (|unmakeSUP| (($ (|SparseUnivariatePolynomial| |#2|)) "\\spad{unmakeSUP(sup)} converts \\spad{sup} of type \\spadtype{SparseUnivariatePolynomial(R)} to be a member of the given type. Note: converse of makeSUP.")) (|makeSUP| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{makeSUP(p)} converts the polynomial \\spad{p} to be of type SparseUnivariatePolynomial over the same coefficients.")) (|vectorise| (((|Vector| |#2|) $ (|NonNegativeInteger|)) "\\spad{vectorise(p, n)} returns \\spad{[a0,...,a(n-1)]} where \\spad{p = a0 + a1*x + ... + a(n-1)*x**(n-1)} + higher order terms. The degree of polynomial \\spad{p} can be different from \\spad{n-1}."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-1172)))) -(-1263 R) +((|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (QUOTE (-374))) (|HasCategory| |#2| (QUOTE (-464))) (|HasCategory| |#2| (QUOTE (-568))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-1173)))) +(-1264 R) ((|constructor| (NIL "The category of univariate polynomials over a ring \\spad{R}. No particular model is assumed - implementations can be either sparse or dense.")) (|integrate| (($ $) "\\spad{integrate(p)} integrates the univariate polynomial \\spad{p} with respect to its distinguished variable.")) (|additiveValuation| ((|attribute|) "euclideanSize(a*b) = euclideanSize(a) + euclideanSize(\\spad{b})")) (|separate| (((|Record| (|:| |primePart| $) (|:| |commonPart| $)) $ $) "\\spad{separate(p, q)} returns \\spad{[a, b]} such that polynomial \\spad{p = a b} and \\spad{a} is relatively prime to \\spad{q}.")) (|pseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{pseudoDivide(p,q)} returns \\spad{[c, q, r]},{} when \\spad{p' := p*lc(q)**(deg p - deg q + 1) = c * p} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|pseudoQuotient| (($ $ $) "\\spad{pseudoQuotient(p,q)} returns \\spad{r},{} the quotient when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|composite| (((|Union| (|Fraction| $) "failed") (|Fraction| $) $) "\\spad{composite(f, q)} returns \\spad{h} if \\spad{f} = \\spad{h}(\\spad{q}),{} and \"failed\" is no such \\spad{h} exists.") (((|Union| $ "failed") $ $) "\\spad{composite(p, q)} returns \\spad{h} if \\spad{p = h(q)},{} and \"failed\" no such \\spad{h} exists.")) (|subResultantGcd| (($ $ $) "\\spad{subResultantGcd(p,q)} computes the \\spad{gcd} of the polynomials \\spad{p} and \\spad{q} using the SubResultant \\spad{GCD} algorithm.")) (|order| (((|NonNegativeInteger|) $ $) "\\spad{order(p, q)} returns the largest \\spad{n} such that \\spad{q**n} divides polynomial \\spad{p} \\spadignore{i.e.} the order of \\spad{p(x)} at \\spad{q(x)=0}.")) (|elt| ((|#1| (|Fraction| $) |#1|) "\\spad{elt(a,r)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by the constant \\spad{r}.") (((|Fraction| $) (|Fraction| $) (|Fraction| $)) "\\spad{elt(a,b)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by \\spad{b}.")) (|resultant| ((|#1| $ $) "\\spad{resultant(p,q)} returns the resultant of the polynomials \\spad{p} and \\spad{q}.")) (|discriminant| ((|#1| $) "\\spad{discriminant(p)} returns the discriminant of the polynomial \\spad{p}.")) (|differentiate| (($ $ (|Mapping| |#1| |#1|) $) "\\spad{differentiate(p, d, x')} extends the \\spad{R}-derivation \\spad{d} to an extension \\spad{D} in \\spad{R[x]} where \\spad{Dx} is given by \\spad{x'},{} and returns \\spad{Dp}.")) (|pseudoRemainder| (($ $ $) "\\spad{pseudoRemainder(p,q)} = \\spad{r},{} for polynomials \\spad{p} and \\spad{q},{} returns the remainder when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|shiftLeft| (($ $ (|NonNegativeInteger|)) "\\spad{shiftLeft(p,n)} returns \\spad{p * monomial(1,n)}")) (|shiftRight| (($ $ (|NonNegativeInteger|)) "\\spad{shiftRight(p,n)} returns \\spad{monicDivide(p,monomial(1,n)).quotient}")) (|karatsubaDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ (|NonNegativeInteger|)) "\\spad{karatsubaDivide(p,n)} returns the same as \\spad{monicDivide(p,monomial(1,n))}")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicDivide(p,q)} divide the polynomial \\spad{p} by the monic polynomial \\spad{q},{} returning the pair \\spad{[quotient, remainder]}. Error: if \\spad{q} isn\\spad{'t} monic.")) (|divideExponents| (((|Union| $ "failed") $ (|NonNegativeInteger|)) "\\spad{divideExponents(p,n)} returns a new polynomial resulting from dividing all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n},{} or \"failed\" if some exponent is not exactly divisible by \\spad{n}.")) (|multiplyExponents| (($ $ (|NonNegativeInteger|)) "\\spad{multiplyExponents(p,n)} returns a new polynomial resulting from multiplying all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n}.")) (|unmakeSUP| (($ (|SparseUnivariatePolynomial| |#1|)) "\\spad{unmakeSUP(sup)} converts \\spad{sup} of type \\spadtype{SparseUnivariatePolynomial(R)} to be a member of the given type. Note: converse of makeSUP.")) (|makeSUP| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{makeSUP(p)} converts the polynomial \\spad{p} to be of type SparseUnivariatePolynomial over the same coefficients.")) (|vectorise| (((|Vector| |#1|) $ (|NonNegativeInteger|)) "\\spad{vectorise(p, n)} returns \\spad{[a0,...,a(n-1)]} where \\spad{p = a0 + a1*x + ... + a(n-1)*x**(n-1)} + higher order terms. The degree of polynomial \\spad{p} can be different from \\spad{n-1}."))) -(((-4465 "*") |has| |#1| (-174)) (-4456 |has| |#1| (-568)) (-4459 |has| |#1| (-374)) (-4461 |has| |#1| (-6 -4461)) (-4458 . T) (-4457 . T) (-4460 . T)) +(((-4466 "*") |has| |#1| (-174)) (-4457 |has| |#1| (-568)) (-4460 |has| |#1| (-374)) (-4462 |has| |#1| (-6 -4462)) (-4459 . T) (-4458 . T) (-4461 . T)) NIL -(-1264 S |Coef| |Expon|) +(-1265 S |Coef| |Expon|) ((|constructor| (NIL "\\spadtype{UnivariatePowerSeriesCategory} is the most general univariate power series category with exponents in an ordered abelian monoid. Note: this category exports a substitution function if it is possible to multiply exponents. Note: this category exports a derivative operation if it is possible to multiply coefficients by exponents.")) (|eval| (((|Stream| |#2|) $ |#2|) "\\spad{eval(f,a)} evaluates a power series at a value in the ground ring by returning a stream of partial sums.")) (|extend| (($ $ |#3|) "\\spad{extend(f,n)} causes all terms of \\spad{f} of degree \\spad{<=} \\spad{n} to be computed.")) (|approximate| ((|#2| $ |#3|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#3| |#3|) "\\spad{truncate(f,k1,k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#3|) "\\spad{truncate(f,k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#3| $ |#3|) "\\spad{order(f,n) = min(m,n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#3| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#2| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|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 -916) (QUOTE (-1196)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1132))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -4112) (LIST (|devaluate| |#2|) (QUOTE (-1196)))))) -(-1265 |Coef| |Expon|) +((|HasCategory| |#2| (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1133))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -3569) (LIST (|devaluate| |#2|) (QUOTE (-1197)))))) +(-1266 |Coef| |Expon|) ((|constructor| (NIL "\\spadtype{UnivariatePowerSeriesCategory} is the most general univariate power series category with exponents in an ordered abelian monoid. Note: this category exports a substitution function if it is possible to multiply exponents. Note: this category exports a derivative operation if it is possible to multiply coefficients by exponents.")) (|eval| (((|Stream| |#1|) $ |#1|) "\\spad{eval(f,a)} evaluates a power series at a value in the ground ring by returning a stream of partial sums.")) (|extend| (($ $ |#2|) "\\spad{extend(f,n)} causes all terms of \\spad{f} of degree \\spad{<=} \\spad{n} to be computed.")) (|approximate| ((|#1| $ |#2|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#2| |#2|) "\\spad{truncate(f,k1,k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#2|) "\\spad{truncate(f,k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#2| $ |#2|) "\\spad{order(f,n) = min(m,n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#2| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#1| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#2|) (|:| |c| |#1|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) -(((-4465 "*") |has| |#1| (-174)) (-4456 |has| |#1| (-568)) (-4457 . T) (-4458 . T) (-4460 . T)) +(((-4466 "*") |has| |#1| (-174)) (-4457 |has| |#1| (-568)) (-4458 . T) (-4459 . T) (-4461 . T)) NIL -(-1266 RC P) +(-1267 RC P) ((|constructor| (NIL "This package provides for square-free decomposition of univariate polynomials over arbitrary rings,{} \\spadignore{i.e.} a partial factorization such that each factor is a product of irreducibles with multiplicity one and the factors are pairwise relatively prime. If the ring has characteristic zero,{} the result is guaranteed to satisfy this condition. If the ring is an infinite ring of finite characteristic,{} then it may not be possible to decide when polynomials contain factors which are \\spad{p}th powers. In this case,{} the flag associated with that polynomial is set to \"nil\" (meaning that that polynomials are not guaranteed to be square-free).")) (|BumInSepFFE| (((|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|))) (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|)))) "\\spad{BumInSepFFE(f)} is a local function,{} exported only because it has multiple conditional definitions.")) (|squareFreePart| ((|#2| |#2|) "\\spad{squareFreePart(p)} returns a polynomial which has the same irreducible factors as the univariate polynomial \\spad{p},{} but each factor has multiplicity one.")) (|squareFree| (((|Factored| |#2|) |#2|) "\\spad{squareFree(p)} computes the square-free factorization of the univariate polynomial \\spad{p}. Each factor has no repeated roots,{} and the factors are pairwise relatively prime.")) (|gcd| (($ $ $) "\\spad{gcd(p,q)} computes the greatest-common-divisor of \\spad{p} and \\spad{q}."))) NIL NIL -(-1267 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) +(-1268 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) ((|constructor| (NIL "Mapping package for univariate Puiseux series. This package allows one to apply a function to the coefficients of a univariate Puiseux series.")) (|map| (((|UnivariatePuiseuxSeries| |#2| |#4| |#6|) (|Mapping| |#2| |#1|) (|UnivariatePuiseuxSeries| |#1| |#3| |#5|)) "\\spad{map(f,g(x))} applies the map \\spad{f} to the coefficients of the Puiseux series \\spad{g(x)}."))) NIL NIL -(-1268 |Coef|) +(-1269 |Coef|) ((|constructor| (NIL "\\spadtype{UnivariatePuiseuxSeriesCategory} is the category of Puiseux series in one variable.")) (|integrate| (($ $ (|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."))) -(((-4465 "*") |has| |#1| (-174)) (-4456 |has| |#1| (-568)) (-4461 |has| |#1| (-374)) (-4455 |has| |#1| (-374)) (-4457 . T) (-4458 . T) (-4460 . T)) +(((-4466 "*") |has| |#1| (-174)) (-4457 |has| |#1| (-568)) (-4462 |has| |#1| (-374)) (-4456 |has| |#1| (-374)) (-4458 . T) (-4459 . T) (-4461 . T)) NIL -(-1269 S |Coef| ULS) +(-1270 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.")) (|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 -(-1270 |Coef| ULS) +(-1271 |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.")) (|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)}."))) -(((-4465 "*") |has| |#1| (-174)) (-4456 |has| |#1| (-568)) (-4461 |has| |#1| (-374)) (-4455 |has| |#1| (-374)) (-4457 . T) (-4458 . T) (-4460 . T)) +(((-4466 "*") |has| |#1| (-174)) (-4457 |has| |#1| (-568)) (-4462 |has| |#1| (-374)) (-4456 |has| |#1| (-374)) (-4458 . T) (-4459 . T) (-4461 . T)) NIL -(-1271 |Coef| ULS) +(-1272 |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)}."))) -(((-4465 "*") |has| |#1| (-174)) (-4456 |has| |#1| (-568)) (-4461 |has| |#1| (-374)) (-4455 |has| |#1| (-374)) (-4457 . T) (-4458 . T) (-4460 . T)) -((|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-3794 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -916) (QUOTE (-1196)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|)))) (|HasCategory| (-419 (-576)) (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-374))) (-3794 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-3794 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasSignature| |#1| (LIST (QUOTE -4112) (LIST (|devaluate| |#1|) (QUOTE (-1196)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (-3794 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-977))) (|HasCategory| |#1| (QUOTE (-1222))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasSignature| |#1| (LIST (QUOTE -2944) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1196))))) (|HasSignature| |#1| (LIST (QUOTE -1582) (LIST (LIST (QUOTE -656) (QUOTE (-1196))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) -(-1272 |Coef| |var| |cen|) +(((-4466 "*") |has| |#1| (-174)) (-4457 |has| |#1| (-568)) (-4462 |has| |#1| (-374)) (-4456 |has| |#1| (-374)) (-4458 . T) (-4459 . T) (-4461 . T)) +((|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-2758 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|)))) (|HasCategory| (-419 (-576)) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-374))) (-2758 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-2758 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasSignature| |#1| (LIST (QUOTE -3569) (LIST (|devaluate| |#1|) (QUOTE (-1197)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (-2758 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-978))) (|HasCategory| |#1| (QUOTE (-1223))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasSignature| |#1| (LIST (QUOTE -3441) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1197))))) (|HasSignature| |#1| (LIST (QUOTE -1966) (LIST (LIST (QUOTE -656) (QUOTE (-1197))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) +(-1273 |Coef| |var| |cen|) ((|constructor| (NIL "Dense Puiseux series in one variable \\indented{2}{\\spadtype{UnivariatePuiseuxSeries} is a domain representing Puiseux} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{UnivariatePuiseuxSeries(Integer,x,3)} represents Puiseux series in} \\indented{2}{\\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers."))) -(((-4465 "*") |has| |#1| (-174)) (-4456 |has| |#1| (-568)) (-4461 |has| |#1| (-374)) (-4455 |has| |#1| (-374)) (-4457 . T) (-4458 . T) (-4460 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-3794 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -916) (QUOTE (-1196)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|)))) (|HasCategory| (-419 (-576)) (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-374))) (-3794 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-3794 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasSignature| |#1| (LIST (QUOTE -4112) (LIST (|devaluate| |#1|) (QUOTE (-1196)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (-3794 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-977))) (|HasCategory| |#1| (QUOTE (-1222))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasSignature| |#1| (LIST (QUOTE -2944) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1196))))) (|HasSignature| |#1| (LIST (QUOTE -1582) (LIST (LIST (QUOTE -656) (QUOTE (-1196))) (|devaluate| |#1|))))))) -(-1273 R FE |var| |cen|) +(((-4466 "*") |has| |#1| (-174)) (-4457 |has| |#1| (-568)) (-4462 |has| |#1| (-374)) (-4456 |has| |#1| (-374)) (-4458 . T) (-4459 . T) (-4461 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#1| (QUOTE (-174))) (-2758 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576))) (|devaluate| |#1|)))) (|HasCategory| (-419 (-576)) (QUOTE (-1133))) (|HasCategory| |#1| (QUOTE (-374))) (-2758 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-2758 (|HasCategory| |#1| (QUOTE (-374))) (|HasCategory| |#1| (QUOTE (-568)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasSignature| |#1| (LIST (QUOTE -3569) (LIST (|devaluate| |#1|) (QUOTE (-1197)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -419) (QUOTE (-576)))))) (-2758 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-978))) (|HasCategory| |#1| (QUOTE (-1223))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasSignature| |#1| (LIST (QUOTE -3441) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1197))))) (|HasSignature| |#1| (LIST (QUOTE -1966) (LIST (LIST (QUOTE -656) (QUOTE (-1197))) (|devaluate| |#1|))))))) +(-1274 R FE |var| |cen|) ((|constructor| (NIL "UnivariatePuiseuxSeriesWithExponentialSingularity is a domain used to represent functions with essential singularities. Objects in this domain are sums,{} where each term in the sum is a univariate Puiseux series times the exponential of a univariate Puiseux series. Thus,{} the elements of this domain are sums of expressions of the form \\spad{g(x) * exp(f(x))},{} where \\spad{g}(\\spad{x}) is a univariate Puiseux series and \\spad{f}(\\spad{x}) is a univariate Puiseux series with no terms of non-negative degree.")) (|dominantTerm| (((|Union| (|Record| (|:| |%term| (|Record| (|:| |%coef| (|UnivariatePuiseuxSeries| |#2| |#3| |#4|)) (|:| |%expon| (|ExponentialOfUnivariatePuiseuxSeries| |#2| |#3| |#4|)) (|:| |%expTerms| (|List| (|Record| (|:| |k| (|Fraction| (|Integer|))) (|:| |c| |#2|)))))) (|:| |%type| (|String|))) "failed") $) "\\spad{dominantTerm(f(var))} returns the term that dominates the limiting behavior of \\spad{f(var)} as \\spad{var -> cen+} together with a \\spadtype{String} which briefly describes that behavior. The value of the \\spadtype{String} will be \\spad{\"zero\"} (resp. \\spad{\"infinity\"}) if the term tends to zero (resp. infinity) exponentially and will \\spad{\"series\"} if the term is a Puiseux series.")) (|limitPlus| (((|Union| (|OrderedCompletion| |#2|) "failed") $) "\\spad{limitPlus(f(var))} returns \\spad{limit(var -> cen+,f(var))}."))) -(((-4465 "*") |has| (-1272 |#2| |#3| |#4|) (-174)) (-4456 |has| (-1272 |#2| |#3| |#4|) (-568)) (-4457 . T) (-4458 . T) (-4460 . T)) -((|HasCategory| (-1272 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-1272 |#2| |#3| |#4|) (QUOTE (-146))) (|HasCategory| (-1272 |#2| |#3| |#4|) (QUOTE (-148))) (|HasCategory| (-1272 |#2| |#3| |#4|) (QUOTE (-174))) (-3794 (|HasCategory| (-1272 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-1272 |#2| |#3| |#4|) (LIST (QUOTE -1058) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| (-1272 |#2| |#3| |#4|) (LIST (QUOTE -1058) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-1272 |#2| |#3| |#4|) (LIST (QUOTE -1058) (QUOTE (-576)))) (|HasCategory| (-1272 |#2| |#3| |#4|) (QUOTE (-374))) (|HasCategory| (-1272 |#2| |#3| |#4|) (QUOTE (-464))) (|HasCategory| (-1272 |#2| |#3| |#4|) (QUOTE (-568)))) -(-1274 A S) +(((-4466 "*") |has| (-1273 |#2| |#3| |#4|) (-174)) (-4457 |has| (-1273 |#2| |#3| |#4|) (-568)) (-4458 . T) (-4459 . T) (-4461 . T)) +((|HasCategory| (-1273 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-1273 |#2| |#3| |#4|) (QUOTE (-146))) (|HasCategory| (-1273 |#2| |#3| |#4|) (QUOTE (-148))) (|HasCategory| (-1273 |#2| |#3| |#4|) (QUOTE (-174))) (-2758 (|HasCategory| (-1273 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-1273 |#2| |#3| |#4|) (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576)))))) (|HasCategory| (-1273 |#2| |#3| |#4|) (LIST (QUOTE -1059) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| (-1273 |#2| |#3| |#4|) (LIST (QUOTE -1059) (QUOTE (-576)))) (|HasCategory| (-1273 |#2| |#3| |#4|) (QUOTE (-374))) (|HasCategory| (-1273 |#2| |#3| |#4|) (QUOTE (-464))) (|HasCategory| (-1273 |#2| |#3| |#4|) (QUOTE (-568)))) +(-1275 A S) ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|Integer|)) "\\spad{split!(u,n)} splits \\spad{u} into two aggregates: \\axiom{\\spad{v} = rest(\\spad{u},{}\\spad{n})} and \\axiom{\\spad{w} = first(\\spad{u},{}\\spad{n})},{} returning \\axiom{\\spad{v}}. Note: afterwards \\axiom{rest(\\spad{u},{}\\spad{n})} returns \\axiom{empty()}.")) (|setlast!| ((|#2| $ |#2|) "\\spad{setlast!(u,x)} destructively changes the last element of \\spad{u} to \\spad{x}.")) (|setrest!| (($ $ $) "\\spad{setrest!(u,v)} destructively changes the rest of \\spad{u} to \\spad{v}.")) (|setelt| ((|#2| $ "last" |#2|) "\\spad{setelt(u,\"last\",x)} (also written: \\axiom{\\spad{u}.last \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setlast!(\\spad{u},{}\\spad{v})}.") (($ $ "rest" $) "\\spad{setelt(u,\"rest\",v)} (also written: \\axiom{\\spad{u}.rest \\spad{:=} \\spad{v}}) is equivalent to \\axiom{setrest!(\\spad{u},{}\\spad{v})}.") ((|#2| $ "first" |#2|) "\\spad{setelt(u,\"first\",x)} (also written: \\axiom{\\spad{u}.first \\spad{:=} \\spad{x}}) is equivalent to \\axiom{setfirst!(\\spad{u},{}\\spad{x})}.")) (|setfirst!| ((|#2| $ |#2|) "\\spad{setfirst!(u,x)} destructively changes the first element of a to \\spad{x}.")) (|cycleSplit!| (($ $) "\\spad{cycleSplit!(u)} splits the aggregate by dropping off the cycle. The value returned is the cycle entry,{} or nil if none exists. For example,{} if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} is the cyclic list where \\spad{v} is the head of the cycle,{} \\axiom{cycleSplit!(\\spad{w})} will drop \\spad{v} off \\spad{w} thus destructively changing \\spad{w} to \\spad{u},{} and returning \\spad{v}.")) (|concat!| (($ $ |#2|) "\\spad{concat!(u,x)} destructively adds element \\spad{x} to the end of \\spad{u}. Note: \\axiom{concat!(a,{}\\spad{x}) = setlast!(a,{}[\\spad{x}])}.") (($ $ $) "\\spad{concat!(u,v)} destructively concatenates \\spad{v} to the end of \\spad{u}. Note: \\axiom{concat!(\\spad{u},{}\\spad{v}) = setlast!(\\spad{u},{}\\spad{v})}.")) (|cycleTail| (($ $) "\\spad{cycleTail(u)} returns the last node in the cycle,{} or empty if none exists.")) (|cycleLength| (((|NonNegativeInteger|) $) "\\spad{cycleLength(u)} returns the length of a top-level cycle contained in aggregate \\spad{u},{} or 0 is \\spad{u} has no such cycle.")) (|cycleEntry| (($ $) "\\spad{cycleEntry(u)} returns the head of a top-level cycle contained in aggregate \\spad{u},{} or \\axiom{empty()} if none exists.")) (|third| ((|#2| $) "\\spad{third(u)} returns the third element of \\spad{u}. Note: \\axiom{third(\\spad{u}) = first(rest(rest(\\spad{u})))}.")) (|second| ((|#2| $) "\\spad{second(u)} returns the second element of \\spad{u}. Note: \\axiom{second(\\spad{u}) = first(rest(\\spad{u}))}.")) (|tail| (($ $) "\\spad{tail(u)} returns the last node of \\spad{u}. Note: if \\spad{u} is \\axiom{shallowlyMutable},{} \\axiom{setrest(tail(\\spad{u}),{}\\spad{v}) = concat(\\spad{u},{}\\spad{v})}.")) (|last| (($ $ (|NonNegativeInteger|)) "\\spad{last(u,n)} returns a copy of the last \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) nodes of \\spad{u}. Note: \\axiom{last(\\spad{u},{}\\spad{n})} is a list of \\spad{n} elements.") ((|#2| $) "\\spad{last(u)} resturn the last element of \\spad{u}. Note: for lists,{} \\axiom{last(\\spad{u}) = \\spad{u} . (maxIndex \\spad{u}) = \\spad{u} . (\\# \\spad{u} - 1)}.")) (|rest| (($ $ (|NonNegativeInteger|)) "\\spad{rest(u,n)} returns the \\axiom{\\spad{n}}th (\\spad{n} \\spad{>=} 0) node of \\spad{u}. Note: \\axiom{rest(\\spad{u},{}0) = \\spad{u}}.") (($ $) "\\spad{rest(u)} returns an aggregate consisting of all but the first element of \\spad{u} (equivalently,{} the next node of \\spad{u}).")) (|elt| ((|#2| $ "last") "\\spad{elt(u,\"last\")} (also written: \\axiom{\\spad{u} . last}) is equivalent to last \\spad{u}.") (($ $ "rest") "\\spad{elt(\\%,\"rest\")} (also written: \\axiom{\\spad{u}.rest}) is equivalent to \\axiom{rest \\spad{u}}.") ((|#2| $ "first") "\\spad{elt(u,\"first\")} (also written: \\axiom{\\spad{u} . first}) is equivalent to first \\spad{u}.")) (|first| (($ $ (|NonNegativeInteger|)) "\\spad{first(u,n)} returns a copy of the first \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) elements of \\spad{u}.") ((|#2| $) "\\spad{first(u)} returns the first element of \\spad{u} (equivalently,{} the value at the current node).")) (|concat| (($ |#2| $) "\\spad{concat(x,u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL -((|HasAttribute| |#1| (QUOTE -4464))) -(-1275 S) +((|HasAttribute| |#1| (QUOTE -4465))) +(-1276 S) ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|Integer|)) "\\spad{split!(u,n)} splits \\spad{u} into two aggregates: \\axiom{\\spad{v} = rest(\\spad{u},{}\\spad{n})} and \\axiom{\\spad{w} = first(\\spad{u},{}\\spad{n})},{} returning \\axiom{\\spad{v}}. Note: afterwards \\axiom{rest(\\spad{u},{}\\spad{n})} returns \\axiom{empty()}.")) (|setlast!| ((|#1| $ |#1|) "\\spad{setlast!(u,x)} destructively changes the last element of \\spad{u} to \\spad{x}.")) (|setrest!| (($ $ $) "\\spad{setrest!(u,v)} destructively changes the rest of \\spad{u} to \\spad{v}.")) (|setelt| ((|#1| $ "last" |#1|) "\\spad{setelt(u,\"last\",x)} (also written: \\axiom{\\spad{u}.last \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setlast!(\\spad{u},{}\\spad{v})}.") (($ $ "rest" $) "\\spad{setelt(u,\"rest\",v)} (also written: \\axiom{\\spad{u}.rest \\spad{:=} \\spad{v}}) is equivalent to \\axiom{setrest!(\\spad{u},{}\\spad{v})}.") ((|#1| $ "first" |#1|) "\\spad{setelt(u,\"first\",x)} (also written: \\axiom{\\spad{u}.first \\spad{:=} \\spad{x}}) is equivalent to \\axiom{setfirst!(\\spad{u},{}\\spad{x})}.")) (|setfirst!| ((|#1| $ |#1|) "\\spad{setfirst!(u,x)} destructively changes the first element of a to \\spad{x}.")) (|cycleSplit!| (($ $) "\\spad{cycleSplit!(u)} splits the aggregate by dropping off the cycle. The value returned is the cycle entry,{} or nil if none exists. For example,{} if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} is the cyclic list where \\spad{v} is the head of the cycle,{} \\axiom{cycleSplit!(\\spad{w})} will drop \\spad{v} off \\spad{w} thus destructively changing \\spad{w} to \\spad{u},{} and returning \\spad{v}.")) (|concat!| (($ $ |#1|) "\\spad{concat!(u,x)} destructively adds element \\spad{x} to the end of \\spad{u}. Note: \\axiom{concat!(a,{}\\spad{x}) = setlast!(a,{}[\\spad{x}])}.") (($ $ $) "\\spad{concat!(u,v)} destructively concatenates \\spad{v} to the end of \\spad{u}. Note: \\axiom{concat!(\\spad{u},{}\\spad{v}) = setlast!(\\spad{u},{}\\spad{v})}.")) (|cycleTail| (($ $) "\\spad{cycleTail(u)} returns the last node in the cycle,{} or empty if none exists.")) (|cycleLength| (((|NonNegativeInteger|) $) "\\spad{cycleLength(u)} returns the length of a top-level cycle contained in aggregate \\spad{u},{} or 0 is \\spad{u} has no such cycle.")) (|cycleEntry| (($ $) "\\spad{cycleEntry(u)} returns the head of a top-level cycle contained in aggregate \\spad{u},{} or \\axiom{empty()} if none exists.")) (|third| ((|#1| $) "\\spad{third(u)} returns the third element of \\spad{u}. Note: \\axiom{third(\\spad{u}) = first(rest(rest(\\spad{u})))}.")) (|second| ((|#1| $) "\\spad{second(u)} returns the second element of \\spad{u}. Note: \\axiom{second(\\spad{u}) = first(rest(\\spad{u}))}.")) (|tail| (($ $) "\\spad{tail(u)} returns the last node of \\spad{u}. Note: if \\spad{u} is \\axiom{shallowlyMutable},{} \\axiom{setrest(tail(\\spad{u}),{}\\spad{v}) = concat(\\spad{u},{}\\spad{v})}.")) (|last| (($ $ (|NonNegativeInteger|)) "\\spad{last(u,n)} returns a copy of the last \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) nodes of \\spad{u}. Note: \\axiom{last(\\spad{u},{}\\spad{n})} is a list of \\spad{n} elements.") ((|#1| $) "\\spad{last(u)} resturn the last element of \\spad{u}. Note: for lists,{} \\axiom{last(\\spad{u}) = \\spad{u} . (maxIndex \\spad{u}) = \\spad{u} . (\\# \\spad{u} - 1)}.")) (|rest| (($ $ (|NonNegativeInteger|)) "\\spad{rest(u,n)} returns the \\axiom{\\spad{n}}th (\\spad{n} \\spad{>=} 0) node of \\spad{u}. Note: \\axiom{rest(\\spad{u},{}0) = \\spad{u}}.") (($ $) "\\spad{rest(u)} returns an aggregate consisting of all but the first element of \\spad{u} (equivalently,{} the next node of \\spad{u}).")) (|elt| ((|#1| $ "last") "\\spad{elt(u,\"last\")} (also written: \\axiom{\\spad{u} . last}) is equivalent to last \\spad{u}.") (($ $ "rest") "\\spad{elt(\\%,\"rest\")} (also written: \\axiom{\\spad{u}.rest}) is equivalent to \\axiom{rest \\spad{u}}.") ((|#1| $ "first") "\\spad{elt(u,\"first\")} (also written: \\axiom{\\spad{u} . first}) is equivalent to first \\spad{u}.")) (|first| (($ $ (|NonNegativeInteger|)) "\\spad{first(u,n)} returns a copy of the first \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) elements of \\spad{u}.") ((|#1| $) "\\spad{first(u)} returns the first element of \\spad{u} (equivalently,{} the value at the current node).")) (|concat| (($ |#1| $) "\\spad{concat(x,u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL NIL -(-1276 |Coef1| |Coef2| UTS1 UTS2) +(-1277 |Coef1| |Coef2| UTS1 UTS2) ((|constructor| (NIL "Mapping package for univariate Taylor series. \\indented{2}{This package allows one to apply a function to the coefficients of} \\indented{2}{a univariate Taylor series.}")) (|map| ((|#4| (|Mapping| |#2| |#1|) |#3|) "\\spad{map(f,g(x))} applies the map \\spad{f} to the coefficients of \\indented{1}{the Taylor series \\spad{g(x)}.}"))) NIL NIL -(-1277 S |Coef|) +(-1278 S |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(f(x),y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $ (|Symbol|)) "\\spad{integrate(f(x),y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (** (($ $ |#2|) "\\spad{f(x) ** a} computes a power of a power series. When the coefficient ring is a field,{} we may raise a series to an exponent from the coefficient ring provided that the constant coefficient of the series is 1.")) (|polynomial| (((|Polynomial| |#2|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{polynomial(f,k1,k2)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (((|Polynomial| |#2|) $ (|NonNegativeInteger|)) "\\spad{polynomial(f,k)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|multiplyCoefficients| (($ (|Mapping| |#2| (|Integer|)) $) "\\spad{multiplyCoefficients(f,sum(n = 0..infinity,a[n] * x**n))} returns \\spad{sum(n = 0..infinity,f(n) * a[n] * x**n)}. This function is used when Laurent series are represented by a Taylor series and an order.")) (|quoByVar| (($ $) "\\spad{quoByVar(a0 + a1 x + a2 x**2 + ...)} returns \\spad{a1 + a2 x + a3 x**2 + ...} Thus,{} this function substracts the constant term and divides by the series variable. This function is used when Laurent series are represented by a Taylor series and an order.")) (|coefficients| (((|Stream| |#2|) $) "\\spad{coefficients(a0 + a1 x + a2 x**2 + ...)} returns a stream of coefficients: \\spad{[a0,a1,a2,...]}. The entries of the stream may be zero.")) (|series| (($ (|Stream| |#2|)) "\\spad{series([a0,a1,a2,...])} is the Taylor series \\spad{a0 + a1 x + a2 x**2 + ...}.") (($ (|Stream| (|Record| (|:| |k| (|NonNegativeInteger|)) (|:| |c| |#2|)))) "\\spad{series(st)} creates a series from a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-977))) (|HasCategory| |#2| (QUOTE (-1222))) (|HasSignature| |#2| (LIST (QUOTE -1582) (LIST (LIST (QUOTE -656) (QUOTE (-1196))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -2944) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1196))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (QUOTE (-374)))) -(-1278 |Coef|) +((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-576)))) (|HasCategory| |#2| (QUOTE (-978))) (|HasCategory| |#2| (QUOTE (-1223))) (|HasSignature| |#2| (LIST (QUOTE -1966) (LIST (LIST (QUOTE -656) (QUOTE (-1197))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -3441) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1197))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#2| (QUOTE (-374)))) +(-1279 |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(f(x),y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $ (|Symbol|)) "\\spad{integrate(f(x),y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (** (($ $ |#1|) "\\spad{f(x) ** a} computes a power of a power series. When the coefficient ring is a field,{} we may raise a series to an exponent from the coefficient ring provided that the constant coefficient of the series is 1.")) (|polynomial| (((|Polynomial| |#1|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{polynomial(f,k1,k2)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (((|Polynomial| |#1|) $ (|NonNegativeInteger|)) "\\spad{polynomial(f,k)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|multiplyCoefficients| (($ (|Mapping| |#1| (|Integer|)) $) "\\spad{multiplyCoefficients(f,sum(n = 0..infinity,a[n] * x**n))} returns \\spad{sum(n = 0..infinity,f(n) * a[n] * x**n)}. This function is used when Laurent series are represented by a Taylor series and an order.")) (|quoByVar| (($ $) "\\spad{quoByVar(a0 + a1 x + a2 x**2 + ...)} returns \\spad{a1 + a2 x + a3 x**2 + ...} Thus,{} this function substracts the constant term and divides by the series variable. This function is used when Laurent series are represented by a Taylor series and an order.")) (|coefficients| (((|Stream| |#1|) $) "\\spad{coefficients(a0 + a1 x + a2 x**2 + ...)} returns a stream of coefficients: \\spad{[a0,a1,a2,...]}. The entries of the stream may be zero.")) (|series| (($ (|Stream| |#1|)) "\\spad{series([a0,a1,a2,...])} is the Taylor series \\spad{a0 + a1 x + a2 x**2 + ...}.") (($ (|Stream| (|Record| (|:| |k| (|NonNegativeInteger|)) (|:| |c| |#1|)))) "\\spad{series(st)} creates a series from a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents."))) -(((-4465 "*") |has| |#1| (-174)) (-4456 |has| |#1| (-568)) (-4457 . T) (-4458 . T) (-4460 . T)) +(((-4466 "*") |has| |#1| (-174)) (-4457 |has| |#1| (-568)) (-4458 . T) (-4459 . T) (-4461 . T)) NIL -(-1279 |Coef| |var| |cen|) +(-1280 |Coef| |var| |cen|) ((|constructor| (NIL "Dense Taylor series in one variable \\spadtype{UnivariateTaylorSeries} is a domain representing Taylor series in one variable with coefficients in an arbitrary ring. The parameters of the type specify the coefficient ring,{} the power series variable,{} and the center of the power series expansion. For example,{} \\spadtype{UnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x),x)} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|invmultisect| (($ (|Integer|) (|Integer|) $) "\\spad{invmultisect(a,b,f(x))} substitutes \\spad{x^((a+b)*n)} \\indented{1}{for \\spad{x^n} and multiples by \\spad{x^b}.}")) (|multisect| (($ (|Integer|) (|Integer|) $) "\\spad{multisect(a,b,f(x))} selects the coefficients of \\indented{1}{\\spad{x^((a+b)*n+a)},{} and changes this monomial to \\spad{x^n}.}")) (|revert| (($ $) "\\spad{revert(f(x))} returns a Taylor series \\spad{g(x)} such that \\spad{f(g(x)) = g(f(x)) = x}. Series \\spad{f(x)} should have constant coefficient 0 and invertible 1st order coefficient.")) (|generalLambert| (($ $ (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),a,d)} returns \\spad{f(x^a) + f(x^(a + d)) + \\indented{1}{f(x^(a + 2 d)) + ... }. \\spad{f(x)} should have zero constant} \\indented{1}{coefficient and \\spad{a} and \\spad{d} should be positive.}")) (|evenlambert| (($ $) "\\spad{evenlambert(f(x))} returns \\spad{f(x^2) + f(x^4) + f(x^6) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,f(x^(2*n))) = exp(log(evenlambert(f(x))))}.}")) (|oddlambert| (($ $) "\\spad{oddlambert(f(x))} returns \\spad{f(x) + f(x^3) + f(x^5) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,f(x^(2*n-1)))=exp(log(oddlambert(f(x))))}.}")) (|lambert| (($ $) "\\spad{lambert(f(x))} returns \\spad{f(x) + f(x^2) + f(x^3) + ...}. \\indented{1}{This function is used for computing infinite products.} \\indented{1}{\\spad{f(x)} should have zero constant coefficient.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n = 1..infinity,f(x^n)) = exp(log(lambert(f(x))))}.}")) (|lagrange| (($ $) "\\spad{lagrange(g(x))} produces the Taylor series for \\spad{f(x)} \\indented{1}{where \\spad{f(x)} is implicitly defined as \\spad{f(x) = x*g(f(x))}.}")) (|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}."))) -(((-4465 "*") |has| |#1| (-174)) (-4456 |has| |#1| (-568)) (-4457 . T) (-4458 . T) (-4460 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (-3794 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -916) (QUOTE (-1196)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-783)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-783)) (|devaluate| |#1|)))) (|HasCategory| (-783) (QUOTE (-1132))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-783))))) (|HasSignature| |#1| (LIST (QUOTE -4112) (LIST (|devaluate| |#1|) (QUOTE (-1196)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-783))))) (|HasCategory| |#1| (QUOTE (-374))) (-3794 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-977))) (|HasCategory| |#1| (QUOTE (-1222))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasSignature| |#1| (LIST (QUOTE -2944) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1196))))) (|HasSignature| |#1| (LIST (QUOTE -1582) (LIST (LIST (QUOTE -656) (QUOTE (-1196))) (|devaluate| |#1|))))))) -(-1280 |Coef| UTS) +(((-4466 "*") |has| |#1| (-174)) (-4457 |has| |#1| (-568)) (-4458 . T) (-4459 . T) (-4461 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasCategory| |#1| (QUOTE (-568))) (-2758 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-568)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -917) (QUOTE (-1197)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-783)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-783)) (|devaluate| |#1|)))) (|HasCategory| (-783) (QUOTE (-1133))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-783))))) (|HasSignature| |#1| (LIST (QUOTE -3569) (LIST (|devaluate| |#1|) (QUOTE (-1197)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-783))))) (|HasCategory| |#1| (QUOTE (-374))) (-2758 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-576)))) (|HasCategory| |#1| (QUOTE (-978))) (|HasCategory| |#1| (QUOTE (-1223))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasSignature| |#1| (LIST (QUOTE -3441) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1197))))) (|HasSignature| |#1| (LIST (QUOTE -1966) (LIST (LIST (QUOTE -656) (QUOTE (-1197))) (|devaluate| |#1|))))))) +(-1281 |Coef| UTS) ((|constructor| (NIL "\\indented{1}{This package provides Taylor series solutions to regular} linear or non-linear ordinary differential equations of arbitrary order.")) (|mpsode| (((|List| |#2|) (|List| |#1|) (|List| (|Mapping| |#2| (|List| |#2|)))) "\\spad{mpsode(r,f)} solves the system of differential equations \\spad{dy[i]/dx =f[i] [x,y[1],y[2],...,y[n]]},{} \\spad{y[i](a) = r[i]} for \\spad{i} in 1..\\spad{n}.")) (|ode| ((|#2| (|Mapping| |#2| (|List| |#2|)) (|List| |#1|)) "\\spad{ode(f,cl)} is the solution to \\spad{y<n>=f(y,y',..,y<n-1>)} such that \\spad{y<i>(a) = cl.i} for \\spad{i} in 1..\\spad{n}.")) (|ode2| ((|#2| (|Mapping| |#2| |#2| |#2|) |#1| |#1|) "\\spad{ode2(f,c0,c1)} is the solution to \\spad{y'' = f(y,y')} such that \\spad{y(a) = c0} and \\spad{y'(a) = c1}.")) (|ode1| ((|#2| (|Mapping| |#2| |#2|) |#1|) "\\spad{ode1(f,c)} is the solution to \\spad{y' = f(y)} such that \\spad{y(a) = c}.")) (|fixedPointExquo| ((|#2| |#2| |#2|) "\\spad{fixedPointExquo(f,g)} computes the exact quotient of \\spad{f} and \\spad{g} using a fixed point computation.")) (|stFuncN| (((|Mapping| (|Stream| |#1|) (|List| (|Stream| |#1|))) (|Mapping| |#2| (|List| |#2|))) "\\spad{stFuncN(f)} is a local function xported due to compiler problem. This function is of no interest to the top-level user.")) (|stFunc2| (((|Mapping| (|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) (|Mapping| |#2| |#2| |#2|)) "\\spad{stFunc2(f)} is a local function exported due to compiler problem. This function is of no interest to the top-level user.")) (|stFunc1| (((|Mapping| (|Stream| |#1|) (|Stream| |#1|)) (|Mapping| |#2| |#2|)) "\\spad{stFunc1(f)} is a local function exported due to compiler problem. This function is of no interest to the top-level user."))) NIL NIL -(-1281 -2117 UP L UTS) +(-1282 -1959 UP L UTS) ((|constructor| (NIL "\\spad{RUTSodetools} provides tools to interface with the series \\indented{1}{ODE solver when presented with linear ODEs.}")) (RF2UTS ((|#4| (|Fraction| |#2|)) "\\spad{RF2UTS(f)} converts \\spad{f} to a Taylor series.")) (LODO2FUN (((|Mapping| |#4| (|List| |#4|)) |#3|) "\\spad{LODO2FUN(op)} returns the function to pass to the series ODE solver in order to solve \\spad{op y = 0}.")) (UTS2UP ((|#2| |#4| (|NonNegativeInteger|)) "\\spad{UTS2UP(s, n)} converts the first \\spad{n} terms of \\spad{s} to a univariate polynomial.")) (UP2UTS ((|#4| |#2|) "\\spad{UP2UTS(p)} converts \\spad{p} to a Taylor series."))) NIL ((|HasCategory| |#1| (QUOTE (-568)))) -(-1282) +(-1283) ((|constructor| (NIL "The category of domains that act like unions. UnionType,{} like Type or Category,{} acts mostly as a take that communicates `union-like' intended semantics to the compiler. A domain \\spad{D} that satifies UnionType should provide definitions for `case' operators,{} with corresponding `autoCoerce' operators."))) NIL NIL -(-1283 |sym|) +(-1284 |sym|) ((|constructor| (NIL "This domain implements variables")) (|variable| (((|Symbol|)) "\\spad{variable()} returns the symbol")) (|coerce| (((|Symbol|) $) "\\spad{coerce(x)} returns the symbol"))) NIL NIL -(-1284 S R) +(-1285 S R) ((|constructor| (NIL "\\spadtype{VectorCategory} represents the type of vector like objects,{} \\spadignore{i.e.} finite sequences indexed by some finite segment of the integers. The operations available on vectors depend on the structure of the underlying components. Many operations from the component domain are defined for vectors componentwise. It can by assumed that extraction or updating components can be done in constant time.")) (|magnitude| ((|#2| $) "\\spad{magnitude(v)} computes the sqrt(dot(\\spad{v},{}\\spad{v})),{} \\spadignore{i.e.} the length")) (|length| ((|#2| $) "\\spad{length(v)} computes the sqrt(dot(\\spad{v},{}\\spad{v})),{} \\spadignore{i.e.} the magnitude")) (|cross| (($ $ $) "vectorProduct(\\spad{u},{}\\spad{v}) constructs the cross product of \\spad{u} and \\spad{v}. Error: if \\spad{u} and \\spad{v} are not of length 3.")) (|outerProduct| (((|Matrix| |#2|) $ $) "\\spad{outerProduct(u,v)} constructs the matrix whose (\\spad{i},{}\\spad{j})\\spad{'}th element is \\spad{u}(\\spad{i})\\spad{*v}(\\spad{j}).")) (|dot| ((|#2| $ $) "\\spad{dot(x,y)} computes the inner product of the two vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.")) (* (($ $ |#2|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#2| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.") (($ (|Integer|) $) "\\spad{n * y} multiplies each component of the vector \\spad{y} by the integer \\spad{n}.")) (- (($ $ $) "\\spad{x - y} returns the component-wise difference of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.") (($ $) "\\spad{-x} negates all components of the vector \\spad{x}.")) (|zero| (($ (|NonNegativeInteger|)) "\\spad{zero(n)} creates a zero vector of length \\spad{n}.")) (+ (($ $ $) "\\spad{x + y} returns the component-wise sum of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length."))) NIL -((|HasCategory| |#2| (QUOTE (-1022))) (|HasCategory| |#2| (QUOTE (-1069))) (|HasCategory| |#2| (QUOTE (-738))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25)))) -(-1285 R) +((|HasCategory| |#2| (QUOTE (-1023))) (|HasCategory| |#2| (QUOTE (-1070))) (|HasCategory| |#2| (QUOTE (-738))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25)))) +(-1286 R) ((|constructor| (NIL "\\spadtype{VectorCategory} represents the type of vector like objects,{} \\spadignore{i.e.} finite sequences indexed by some finite segment of the integers. The operations available on vectors depend on the structure of the underlying components. Many operations from the component domain are defined for vectors componentwise. It can by assumed that extraction or updating components can be done in constant time.")) (|magnitude| ((|#1| $) "\\spad{magnitude(v)} computes the sqrt(dot(\\spad{v},{}\\spad{v})),{} \\spadignore{i.e.} the length")) (|length| ((|#1| $) "\\spad{length(v)} computes the sqrt(dot(\\spad{v},{}\\spad{v})),{} \\spadignore{i.e.} the magnitude")) (|cross| (($ $ $) "vectorProduct(\\spad{u},{}\\spad{v}) constructs the cross product of \\spad{u} and \\spad{v}. Error: if \\spad{u} and \\spad{v} are not of length 3.")) (|outerProduct| (((|Matrix| |#1|) $ $) "\\spad{outerProduct(u,v)} constructs the matrix whose (\\spad{i},{}\\spad{j})\\spad{'}th element is \\spad{u}(\\spad{i})\\spad{*v}(\\spad{j}).")) (|dot| ((|#1| $ $) "\\spad{dot(x,y)} computes the inner product of the two vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.")) (* (($ $ |#1|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#1| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.") (($ (|Integer|) $) "\\spad{n * y} multiplies each component of the vector \\spad{y} by the integer \\spad{n}.")) (- (($ $ $) "\\spad{x - y} returns the component-wise difference of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.") (($ $) "\\spad{-x} negates all components of the vector \\spad{x}.")) (|zero| (($ (|NonNegativeInteger|)) "\\spad{zero(n)} creates a zero vector of length \\spad{n}.")) (+ (($ $ $) "\\spad{x + y} returns the component-wise sum of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length."))) -((-4464 . T) (-4463 . T)) +((-4465 . T) (-4464 . T)) NIL -(-1286 A B) +(-1287 A B) ((|constructor| (NIL "\\indented{2}{This package provides operations which all take as arguments} vectors of elements of some type \\spad{A} and functions from \\spad{A} to another of type \\spad{B}. The operations all iterate over their vector argument and either return a value of type \\spad{B} or a vector over \\spad{B}.")) (|map| (((|Union| (|Vector| |#2|) "failed") (|Mapping| (|Union| |#2| "failed") |#1|) (|Vector| |#1|)) "\\spad{map(f, v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values or \\spad{\"failed\"}.") (((|Vector| |#2|) (|Mapping| |#2| |#1|) (|Vector| |#1|)) "\\spad{map(f, v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{reduce(func,vec,ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if \\spad{vec} is empty.")) (|scan| (((|Vector| |#2|) (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{scan(func,vec,ident)} creates a new vector whose elements are the result of applying reduce to the binary function \\spad{func},{} increasing initial subsequences of the vector \\spad{vec},{} and the element \\spad{ident}."))) NIL NIL -(-1287 R) +(-1288 R) ((|constructor| (NIL "This type represents vector like objects with varying lengths and indexed by a finite segment of integers starting at 1.")) (|vector| (($ (|List| |#1|)) "\\spad{vector(l)} converts the list \\spad{l} to a vector."))) -((-4464 . T) (-4463 . T)) -((-3794 (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1120))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-3794 (-12 (|HasCategory| |#1| (QUOTE (-1120))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-875))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-3794 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1120)))) (|HasCategory| |#1| (QUOTE (-861))) (-3794 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1120)))) (|HasCategory| (-576) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1120))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-738))) (|HasCategory| |#1| (QUOTE (-1069))) (-12 (|HasCategory| |#1| (QUOTE (-1022))) (|HasCategory| |#1| (QUOTE (-1069)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-875)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1120))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) -(-1288) +((-4465 . T) (-4464 . T)) +((-2758 (-12 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) (-2758 (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-548)))) (-2758 (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| |#1| (QUOTE (-861))) (-2758 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1121)))) (|HasCategory| (-576) (QUOTE (-861))) (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-738))) (|HasCategory| |#1| (QUOTE (-1070))) (-12 (|HasCategory| |#1| (QUOTE (-1023))) (|HasCategory| |#1| (QUOTE (-1070)))) (|HasCategory| |#1| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1121))) (|HasCategory| |#1| (LIST (QUOTE -319) (|devaluate| |#1|))))) +(-1289) ((|constructor| (NIL "TwoDimensionalViewport creates viewports to display graphs.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(v)} returns the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport} as output of the domain \\spadtype{OutputForm}.")) (|key| (((|Integer|) $) "\\spad{key(v)} returns the process ID number of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport}.")) (|reset| (((|Void|) $) "\\spad{reset(v)} sets the current state of the graph characteristics of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} back to their initial settings.")) (|write| (((|String|) $ (|String|) (|List| (|String|))) "\\spad{write(v,s,lf)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v} and the optional file types indicated by the list \\spad{lf}.") (((|String|) $ (|String|) (|String|)) "\\spad{write(v,s,f)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v} and an optional file type \\spad{f}.") (((|String|) $ (|String|)) "\\spad{write(v,s)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v}.")) (|resize| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{resize(v,w,h)} displays the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with a width of \\spad{w} and a height of \\spad{h},{} keeping the upper left-hand corner position unchanged.")) (|update| (((|Void|) $ (|GraphImage|) (|PositiveInteger|)) "\\spad{update(v,gr,n)} drops the graph \\spad{gr} in slot \\spad{n} of viewport \\spad{v}. The graph \\spad{gr} must have been transmitted already and acquired an integer key.")) (|move| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{move(v,x,y)} displays the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the upper left-hand corner of the viewport window at the screen coordinate position \\spad{x},{} \\spad{y}.")) (|show| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{show(v,n,s)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the graph if \\spad{s} is \"off\".")) (|translate| (((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|)) "\\spad{translate(v,n,dx,dy)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} translated by \\spad{dx} in the \\spad{x}-coordinate direction from the center of the viewport,{} and by \\spad{dy} in the \\spad{y}-coordinate direction from the center. Setting \\spad{dx} and \\spad{dy} to \\spad{0} places the center of the graph at the center of the viewport.")) (|scale| (((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|)) "\\spad{scale(v,n,sx,sy)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} scaled by the factor \\spad{sx} in the \\spad{x}-coordinate direction and by the factor \\spad{sy} in the \\spad{y}-coordinate direction.")) (|dimensions| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{dimensions(v,x,y,width,height)} sets the position of the upper left-hand corner of the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} to the window coordinate \\spad{x},{} \\spad{y},{} and sets the dimensions of the window to that of \\spad{width},{} \\spad{height}. The new dimensions are not displayed until the function \\spadfun{makeViewport2D} is executed again for \\spad{v}.")) (|close| (((|Void|) $) "\\spad{close(v)} closes the viewport window of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and terminates the corresponding process ID.")) (|controlPanel| (((|Void|) $ (|String|)) "\\spad{controlPanel(v,s)} displays the control panel of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or hides the control panel if \\spad{s} is \"off\".")) (|connect| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{connect(v,n,s)} displays the lines connecting the graph points in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the lines if \\spad{s} is \"off\".")) (|region| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{region(v,n,s)} displays the bounding box of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the bounding box if \\spad{s} is \"off\".")) (|points| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{points(v,n,s)} displays the points of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the points if \\spad{s} is \"off\".")) (|units| (((|Void|) $ (|PositiveInteger|) (|Palette|)) "\\spad{units(v,n,c)} displays the units of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the units color set to the given palette color \\spad{c}.") (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{units(v,n,s)} displays the units of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the units if \\spad{s} is \"off\".")) (|axes| (((|Void|) $ (|PositiveInteger|) (|Palette|)) "\\spad{axes(v,n,c)} displays the axes of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the axes color set to the given palette color \\spad{c}.") (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{axes(v,n,s)} displays the axes of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the axes if \\spad{s} is \"off\".")) (|getGraph| (((|GraphImage|) $ (|PositiveInteger|)) "\\spad{getGraph(v,n)} returns the graph which is of the domain \\spadtype{GraphImage} which is located in graph field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of the domain \\spadtype{TwoDimensionalViewport}.")) (|putGraph| (((|Void|) $ (|GraphImage|) (|PositiveInteger|)) "\\spad{putGraph(v,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 \\spad{box},{} \\spad{axes},{} or units will be shown in the viewport if their given parameters \\spad{pts},{} \\spad{lns},{} \\spad{box},{} \\spad{axes} or \\spad{un} are set to be \\spad{1},{} but will not be shown if they are set to \\spad{0}. The color of the \\spad{axes} and the color of the units are indicated by the palette colors \\spad{axesC} and \\spad{unC} respectively. To display the control panel when the viewport window is displayed,{} set \\spad{cP} to \\spad{1},{} otherwise set it to \\spad{0}.")) (|options| (($ $ (|List| (|DrawOption|))) "\\spad{options(v,lopt)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and returns \\spad{v} with it\\spad{'s} draw options modified to be those which are indicated in the given list,{} \\spad{lopt} of domain \\spadtype{DrawOption}.") (((|List| (|DrawOption|)) $) "\\spad{options(v)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and returns a list containing the draw options from the domain \\spadtype{DrawOption} for \\spad{v}.")) (|makeViewport2D| (($ (|GraphImage|) (|List| (|DrawOption|))) "\\spad{makeViewport2D(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 -(-1289) +(-1290) ((|key| (((|Integer|) $) "\\spad{key(v)} returns the process ID number of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|close| (((|Void|) $) "\\spad{close(v)} closes the viewport window of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} and terminates the corresponding process ID.")) (|write| (((|String|) $ (|String|) (|List| (|String|))) "\\spad{write(v,s,lf)} takes the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data file for \\spad{v} and the optional file types indicated by the list \\spad{lf}.") (((|String|) $ (|String|) (|String|)) "\\spad{write(v,s,f)} takes the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data file for \\spad{v} and an optional file type \\spad{f}.") (((|String|) $ (|String|)) "\\spad{write(v,s)} takes the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data file for \\spad{v}.")) (|colorDef| (((|Void|) $ (|Color|) (|Color|)) "\\spad{colorDef(v,c1,c2)} sets the range of colors along the colormap so that the lower end of the colormap is defined by \\spad{c1} and the top end of the colormap is defined by \\spad{c2},{} for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|reset| (((|Void|) $) "\\spad{reset(v)} sets the current state of the graph characteristics of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} back to their initial settings.")) (|intensity| (((|Void|) $ (|Float|)) "\\spad{intensity(v,i)} sets the intensity of the light source to \\spad{i},{} for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|lighting| (((|Void|) $ (|Float|) (|Float|) (|Float|)) "\\spad{lighting(v,x,y,z)} sets the position of the light source to the coordinates \\spad{x},{} \\spad{y},{} and \\spad{z} and displays the graph for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|clipSurface| (((|Void|) $ (|String|)) "\\spad{clipSurface(v,s)} displays the graph with the specified clipping region removed if \\spad{s} is \"on\",{} or displays the graph without clipping implemented if \\spad{s} is \"off\",{} for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|showClipRegion| (((|Void|) $ (|String|)) "\\spad{showClipRegion(v,s)} displays the clipping region of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the region if \\spad{s} is \"off\".")) (|showRegion| (((|Void|) $ (|String|)) "\\spad{showRegion(v,s)} displays the bounding box of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the box if \\spad{s} is \"off\".")) (|hitherPlane| (((|Void|) $ (|Float|)) "\\spad{hitherPlane(v,h)} sets the hither clipping plane of the graph to \\spad{h},{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|eyeDistance| (((|Void|) $ (|Float|)) "\\spad{eyeDistance(v,d)} sets the distance of the observer from the center of the graph to \\spad{d},{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|perspective| (((|Void|) $ (|String|)) "\\spad{perspective(v,s)} displays the graph in perspective if \\spad{s} is \"on\",{} or does not display perspective if \\spad{s} is \"off\" for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|translate| (((|Void|) $ (|Float|) (|Float|)) "\\spad{translate(v,dx,dy)} sets the horizontal viewport offset to \\spad{dx} and the vertical viewport offset to \\spad{dy},{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|zoom| (((|Void|) $ (|Float|) (|Float|) (|Float|)) "\\spad{zoom(v,sx,sy,sz)} sets the graph scaling factors for the \\spad{x}-coordinate axis to \\spad{sx},{} the \\spad{y}-coordinate axis to \\spad{sy} and the \\spad{z}-coordinate axis to \\spad{sz} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.") (((|Void|) $ (|Float|)) "\\spad{zoom(v,s)} sets the graph scaling factor to \\spad{s},{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|rotate| (((|Void|) $ (|Integer|) (|Integer|)) "\\spad{rotate(v,th,phi)} rotates the graph to the longitudinal view angle \\spad{th} degrees and the latitudinal view angle \\spad{phi} degrees for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}. The new rotation position is not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.") (((|Void|) $ (|Float|) (|Float|)) "\\spad{rotate(v,th,phi)} rotates the graph to the longitudinal view angle \\spad{th} radians and the latitudinal view angle \\spad{phi} radians for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|drawStyle| (((|Void|) $ (|String|)) "\\spad{drawStyle(v,s)} displays the surface for the given three-dimensional viewport \\spad{v} which is of domain \\spadtype{ThreeDimensionalViewport} in the style of drawing indicated by \\spad{s}. If \\spad{s} is not a valid drawing style the style is wireframe by default. Possible styles are \\spad{\"shade\"},{} \\spad{\"solid\"} or \\spad{\"opaque\"},{} \\spad{\"smooth\"},{} and \\spad{\"wireMesh\"}.")) (|outlineRender| (((|Void|) $ (|String|)) "\\spad{outlineRender(v,s)} displays the polygon outline showing either triangularized surface or a quadrilateral surface outline depending on the whether the \\spadfun{diagonals} function has been set,{} for the given three-dimensional viewport \\spad{v} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the polygon outline if \\spad{s} is \"off\".")) (|diagonals| (((|Void|) $ (|String|)) "\\spad{diagonals(v,s)} displays the diagonals of the polygon outline showing a triangularized surface instead of a quadrilateral surface outline,{} for the given three-dimensional viewport \\spad{v} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the diagonals if \\spad{s} is \"off\".")) (|axes| (((|Void|) $ (|String|)) "\\spad{axes(v,s)} displays the axes of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the axes if \\spad{s} is \"off\".")) (|controlPanel| (((|Void|) $ (|String|)) "\\spad{controlPanel(v,s)} displays the control panel of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or hides the control panel if \\spad{s} is \"off\".")) (|viewpoint| (((|Void|) $ (|Float|) (|Float|) (|Float|)) "\\spad{viewpoint(v,rotx,roty,rotz)} sets the rotation about the \\spad{x}-axis to be \\spad{rotx} radians,{} sets the rotation about the \\spad{y}-axis to be \\spad{roty} radians,{} and sets the rotation about the \\spad{z}-axis to be \\spad{rotz} radians,{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport} and displays \\spad{v} with the new view position.") (((|Void|) $ (|Float|) (|Float|)) "\\spad{viewpoint(v,th,phi)} sets the longitudinal view angle to \\spad{th} radians and the latitudinal view angle to \\spad{phi} radians for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}. The new viewpoint position is not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.") (((|Void|) $ (|Integer|) (|Integer|) (|Float|) (|Float|) (|Float|)) "\\spad{viewpoint(v,th,phi,s,dx,dy)} sets the longitudinal view angle to \\spad{th} degrees,{} the latitudinal view angle to \\spad{phi} degrees,{} the scale factor to \\spad{s},{} the horizontal viewport offset to \\spad{dx},{} and the vertical viewport offset to \\spad{dy} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}. The new viewpoint position is not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.") (((|Void|) $ (|Record| (|:| |theta| (|DoubleFloat|)) (|:| |phi| (|DoubleFloat|)) (|:| |scale| (|DoubleFloat|)) (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |scaleZ| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)))) "\\spad{viewpoint(v,viewpt)} sets the viewpoint for the viewport. The viewport record consists of the latitudal and longitudal angles,{} the zoom factor,{} the \\spad{X},{} \\spad{Y},{} and \\spad{Z} scales,{} and the \\spad{X} and \\spad{Y} displacements.") (((|Record| (|:| |theta| (|DoubleFloat|)) (|:| |phi| (|DoubleFloat|)) (|:| |scale| (|DoubleFloat|)) (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |scaleZ| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|))) $) "\\spad{viewpoint(v)} returns the current viewpoint setting of the given viewport,{} \\spad{v}. This function is useful in the situation where the user has created a viewport,{} proceeded to interact with it via the control panel and desires to save the values of the viewpoint as the default settings for another viewport to be created using the system.") (((|Void|) $ (|Float|) (|Float|) (|Float|) (|Float|) (|Float|)) "\\spad{viewpoint(v,th,phi,s,dx,dy)} sets the longitudinal view angle to \\spad{th} radians,{} the latitudinal view angle to \\spad{phi} radians,{} the scale factor to \\spad{s},{} the horizontal viewport offset to \\spad{dx},{} and the vertical viewport offset to \\spad{dy} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}. The new viewpoint position is not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.")) (|dimensions| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{dimensions(v,x,y,width,height)} sets the position of the upper left-hand corner of the three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} to the window coordinate \\spad{x},{} \\spad{y},{} and sets the dimensions of the window to that of \\spad{width},{} \\spad{height}. The new dimensions are not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.")) (|title| (((|Void|) $ (|String|)) "\\spad{title(v,s)} changes the title which is shown in the three-dimensional viewport window,{} \\spad{v} of domain \\spadtype{ThreeDimensionalViewport}.")) (|resize| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{resize(v,w,h)} displays the three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} with a width of \\spad{w} and a height of \\spad{h},{} keeping the upper left-hand corner position unchanged.")) (|move| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{move(v,x,y)} displays the three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} with the upper left-hand corner of the viewport window at the screen coordinate position \\spad{x},{} \\spad{y}.")) (|options| (($ $ (|List| (|DrawOption|))) "\\spad{options(v,lopt)} takes the viewport,{} \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport} and sets the draw options being used by \\spad{v} to those indicated in the list,{} \\spad{lopt},{} which is a list of options from the domain \\spad{DrawOption}.") (((|List| (|DrawOption|)) $) "\\spad{options(v)} takes the viewport,{} \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport} and returns a list of all the draw options from the domain \\spad{DrawOption} which are being used by \\spad{v}.")) (|modifyPointData| (((|Void|) $ (|NonNegativeInteger|) (|Point| (|DoubleFloat|))) "\\spad{modifyPointData(v,ind,pt)} takes the viewport,{} \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport},{} and places the data point,{} \\spad{pt} into the list of points database of \\spad{v} at the index location given by \\spad{ind}.")) (|subspace| (($ $ (|ThreeSpace| (|DoubleFloat|))) "\\spad{subspace(v,sp)} places the contents of the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport},{} in the subspace \\spad{sp},{} which is of the domain \\spad{ThreeSpace}.") (((|ThreeSpace| (|DoubleFloat|)) $) "\\spad{subspace(v)} returns the contents of the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport},{} as a subspace of the domain \\spad{ThreeSpace}.")) (|makeViewport3D| (($ (|ThreeSpace| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{makeViewport3D(sp,lopt)} takes the given space,{} \\spad{sp} which is of the domain \\spadtype{ThreeSpace} and displays a viewport window on the screen which contains the contents of \\spad{sp},{} and whose draw options are indicated by the list \\spad{lopt},{} which is a list of options from the domain \\spad{DrawOption}.") (($ (|ThreeSpace| (|DoubleFloat|)) (|String|)) "\\spad{makeViewport3D(sp,s)} takes the given space,{} \\spad{sp} which is of the domain \\spadtype{ThreeSpace} and displays a viewport window on the screen which contains the contents of \\spad{sp},{} and whose title is given by \\spad{s}.") (($ $) "\\spad{makeViewport3D(v)} takes the given three-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{ThreeDimensionalViewport} and displays a viewport window on the screen which contains the contents of \\spad{v}.")) (|viewport3D| (($) "\\spad{viewport3D()} returns an undefined three-dimensional viewport of the domain \\spadtype{ThreeDimensionalViewport} whose contents are empty.")) (|viewDeltaYDefault| (((|Float|) (|Float|)) "\\spad{viewDeltaYDefault(dy)} sets the current default vertical offset from the center of the viewport window to be \\spad{dy} and returns \\spad{dy}.") (((|Float|)) "\\spad{viewDeltaYDefault()} returns the current default vertical offset from the center of the viewport window.")) (|viewDeltaXDefault| (((|Float|) (|Float|)) "\\spad{viewDeltaXDefault(dx)} sets the current default horizontal offset from the center of the viewport window to be \\spad{dx} and returns \\spad{dx}.") (((|Float|)) "\\spad{viewDeltaXDefault()} returns the current default horizontal offset from the center of the viewport window.")) (|viewZoomDefault| (((|Float|) (|Float|)) "\\spad{viewZoomDefault(s)} sets the current default graph scaling value to \\spad{s} and returns \\spad{s}.") (((|Float|)) "\\spad{viewZoomDefault()} returns the current default graph scaling value.")) (|viewPhiDefault| (((|Float|) (|Float|)) "\\spad{viewPhiDefault(p)} sets the current default latitudinal view angle in radians to the value \\spad{p} and returns \\spad{p}.") (((|Float|)) "\\spad{viewPhiDefault()} returns the current default latitudinal view angle in radians.")) (|viewThetaDefault| (((|Float|) (|Float|)) "\\spad{viewThetaDefault(t)} sets the current default longitudinal view angle in radians to the value \\spad{t} and returns \\spad{t}.") (((|Float|)) "\\spad{viewThetaDefault()} returns the current default longitudinal view angle in radians."))) NIL NIL -(-1290) +(-1291) ((|constructor| (NIL "ViewportDefaultsPackage describes default and user definable values for graphics")) (|tubeRadiusDefault| (((|DoubleFloat|)) "\\spad{tubeRadiusDefault()} returns the radius used for a 3D tube plot.") (((|DoubleFloat|) (|Float|)) "\\spad{tubeRadiusDefault(r)} sets the default radius for a 3D tube plot to \\spad{r}.")) (|tubePointsDefault| (((|PositiveInteger|)) "\\spad{tubePointsDefault()} returns the number of points to be used when creating the circle to be used in creating a 3D tube plot.") (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{tubePointsDefault(i)} sets the number of points to use when creating the circle to be used in creating a 3D tube plot to \\spad{i}.")) (|var2StepsDefault| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{var2StepsDefault(i)} sets the number of steps to take when creating a 3D mesh in the direction of the first defined free variable to \\spad{i} (a free variable is considered defined when its range is specified (\\spadignore{e.g.} \\spad{x=0}..10)).") (((|PositiveInteger|)) "\\spad{var2StepsDefault()} is the current setting for the number of steps to take when creating a 3D mesh in the direction of the first defined free variable (a free variable is considered defined when its range is specified (\\spadignore{e.g.} \\spad{x=0}..10)).")) (|var1StepsDefault| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{var1StepsDefault(i)} sets the number of steps to take when creating a 3D mesh in the direction of the first defined free variable to \\spad{i} (a free variable is considered defined when its range is specified (\\spadignore{e.g.} \\spad{x=0}..10)).") (((|PositiveInteger|)) "\\spad{var1StepsDefault()} is the current setting for the number of steps to take when creating a 3D mesh in the direction of the first defined free variable (a free variable is considered defined when its range is specified (\\spadignore{e.g.} \\spad{x=0}..10)).")) (|viewWriteAvailable| (((|List| (|String|))) "\\spad{viewWriteAvailable()} returns a list of available methods for writing,{} such as BITMAP,{} POSTSCRIPT,{} etc.")) (|viewWriteDefault| (((|List| (|String|)) (|List| (|String|))) "\\spad{viewWriteDefault(l)} sets the default list of things to write in a viewport data file to the strings in \\spad{l}; a viewAlone file is always genereated.") (((|List| (|String|))) "\\spad{viewWriteDefault()} returns the list of things to write in a viewport data file; a viewAlone file is always generated.")) (|viewDefaults| (((|Void|)) "\\spad{viewDefaults()} resets all the default graphics settings.")) (|viewSizeDefault| (((|List| (|PositiveInteger|)) (|List| (|PositiveInteger|))) "\\spad{viewSizeDefault([w,h])} sets the default viewport width to \\spad{w} and height to \\spad{h}.") (((|List| (|PositiveInteger|))) "\\spad{viewSizeDefault()} returns the default viewport width and height.")) (|viewPosDefault| (((|List| (|NonNegativeInteger|)) (|List| (|NonNegativeInteger|))) "\\spad{viewPosDefault([x,y])} sets the default \\spad{X} and \\spad{Y} position of a viewport window unless overriden explicityly,{} newly created viewports will have th \\spad{X} and \\spad{Y} coordinates \\spad{x},{} \\spad{y}.") (((|List| (|NonNegativeInteger|))) "\\spad{viewPosDefault()} returns the default \\spad{X} and \\spad{Y} position of a viewport window unless overriden explicityly,{} newly created viewports will have this \\spad{X} and \\spad{Y} coordinate.")) (|pointSizeDefault| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{pointSizeDefault(i)} sets the default size of the points in a 2D viewport to \\spad{i}.") (((|PositiveInteger|)) "\\spad{pointSizeDefault()} returns the default size of the points in a 2D viewport.")) (|unitsColorDefault| (((|Palette|) (|Palette|)) "\\spad{unitsColorDefault(p)} sets the default color of the unit ticks in a 2D viewport to the palette \\spad{p}.") (((|Palette|)) "\\spad{unitsColorDefault()} returns the default color of the unit ticks in a 2D viewport.")) (|axesColorDefault| (((|Palette|) (|Palette|)) "\\spad{axesColorDefault(p)} sets the default color of the axes in a 2D viewport to the palette \\spad{p}.") (((|Palette|)) "\\spad{axesColorDefault()} returns the default color of the axes in a 2D viewport.")) (|lineColorDefault| (((|Palette|) (|Palette|)) "\\spad{lineColorDefault(p)} sets the default color of lines connecting points in a 2D viewport to the palette \\spad{p}.") (((|Palette|)) "\\spad{lineColorDefault()} returns the default color of lines connecting points in a 2D viewport.")) (|pointColorDefault| (((|Palette|) (|Palette|)) "\\spad{pointColorDefault(p)} sets the default color of points in a 2D viewport to the palette \\spad{p}.") (((|Palette|)) "\\spad{pointColorDefault()} returns the default color of points in a 2D viewport."))) NIL NIL -(-1291) +(-1292) ((|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},{} \\spad{gi},{} into the \\spadtype{TwoDimensionalViewport} form.")) (|drawCurves| (((|TwoDimensionalViewport|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|DrawOption|))) "\\spad{drawCurves([[p0],[p1],...,[pn]],[options])} creates a \\spadtype{TwoDimensionalViewport} from the list of lists of points,{} \\spad{p0} throught \\spad{pn},{} using the options specified in the list \\spad{options}.") (((|TwoDimensionalViewport|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|Palette|) (|Palette|) (|PositiveInteger|) (|List| (|DrawOption|))) "\\spad{drawCurves([[p0],[p1],...,[pn]],ptColor,lineColor,ptSize,[options])} creates a \\spadtype{TwoDimensionalViewport} from the list of lists of points,{} \\spad{p0} throught \\spad{pn},{} using the options specified in the list \\spad{options}. The point color is specified by \\spad{ptColor},{} the line color is specified by \\spad{lineColor},{} and the point size is specified by \\spad{ptSize}.")) (|graphCurves| (((|GraphImage|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|DrawOption|))) "\\spad{graphCurves([[p0],[p1],...,[pn]],[options])} creates a \\spadtype{GraphImage} from the list of lists of points,{} \\spad{p0} throught \\spad{pn},{} using the options specified in the list \\spad{options}.") (((|GraphImage|) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{graphCurves([[p0],[p1],...,[pn]])} creates a \\spadtype{GraphImage} from the list of lists of points indicated by \\spad{p0} through \\spad{pn}.") (((|GraphImage|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|Palette|) (|Palette|) (|PositiveInteger|) (|List| (|DrawOption|))) "\\spad{graphCurves([[p0],[p1],...,[pn]],ptColor,lineColor,ptSize,[options])} creates a \\spadtype{GraphImage} from the list of lists of points,{} \\spad{p0} throught \\spad{pn},{} using the options specified in the list \\spad{options}. The graph point color is specified by \\spad{ptColor},{} the graph line color is specified by \\spad{lineColor},{} and the size of the points is specified by \\spad{ptSize}."))) NIL NIL -(-1292) +(-1293) ((|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.")) (|void| (($) "\\spad{void()} produces a void object."))) NIL NIL -(-1293 A S) +(-1294 A S) ((|constructor| (NIL "Vector Spaces (not necessarily finite dimensional) over a field.")) (|dimension| (((|CardinalNumber|)) "\\spad{dimension()} returns the dimensionality of the vector space.")) (/ (($ $ |#2|) "\\spad{x/y} divides the vector \\spad{x} by the scalar \\spad{y}."))) NIL NIL -(-1294 S) +(-1295 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}."))) -((-4458 . T) (-4457 . T)) +((-4459 . T) (-4458 . T)) NIL -(-1295 R) +(-1296 R) ((|constructor| (NIL "This package implements the Weierstrass preparation theorem \\spad{f} or multivariate power series. weierstrass(\\spad{v},{}\\spad{p}) where \\spad{v} is a variable,{} and \\spad{p} is a TaylorSeries(\\spad{R}) in which the terms of lowest degree \\spad{s} must include c*v**s where \\spad{c} is a constant,{}\\spad{s>0},{} is a list of TaylorSeries coefficients A[\\spad{i}] of the equivalent polynomial A = A[0] + A[1]\\spad{*v} + A[2]*v**2 + ... + A[\\spad{s}-1]*v**(\\spad{s}-1) + v**s such that p=A*B ,{} \\spad{B} being a TaylorSeries of minimum degree 0")) (|qqq| (((|Mapping| (|Stream| (|TaylorSeries| |#1|)) (|Stream| (|TaylorSeries| |#1|))) (|NonNegativeInteger|) (|TaylorSeries| |#1|) (|Stream| (|TaylorSeries| |#1|))) "\\spad{qqq(n,s,st)} is used internally.")) (|weierstrass| (((|List| (|TaylorSeries| |#1|)) (|Symbol|) (|TaylorSeries| |#1|)) "\\spad{weierstrass(v,ts)} where \\spad{v} is a variable and \\spad{ts} is \\indented{1}{a TaylorSeries,{} impements the Weierstrass Preparation} \\indented{1}{Theorem. The result is a list of TaylorSeries that} \\indented{1}{are the coefficients of the equivalent series.}")) (|clikeUniv| (((|Mapping| (|SparseUnivariatePolynomial| (|Polynomial| |#1|)) (|Polynomial| |#1|)) (|Symbol|)) "\\spad{clikeUniv(v)} is used internally.")) (|sts2stst| (((|Stream| (|Stream| (|Polynomial| |#1|))) (|Symbol|) (|Stream| (|Polynomial| |#1|))) "\\spad{sts2stst(v,s)} is used internally.")) (|cfirst| (((|Mapping| (|Stream| (|Polynomial| |#1|)) (|Stream| (|Polynomial| |#1|))) (|NonNegativeInteger|)) "\\spad{cfirst n} is used internally.")) (|crest| (((|Mapping| (|Stream| (|Polynomial| |#1|)) (|Stream| (|Polynomial| |#1|))) (|NonNegativeInteger|)) "\\spad{crest n} is used internally."))) NIL NIL -(-1296 K R UP -2117) +(-1297 K R UP -1959) ((|constructor| (NIL "In this package \\spad{K} is a finite field,{} \\spad{R} is a ring of univariate polynomials over \\spad{K},{} and \\spad{F} is a framed algebra over \\spad{R}. The package provides a function to compute the integral closure of \\spad{R} in the quotient field of \\spad{F} as well as a function to compute a \"local integral basis\" at a specific prime.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) |#2|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the integral closure of \\spad{R} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}."))) NIL NIL -(-1297) +(-1298) ((|constructor| (NIL "This domain represents the syntax of a `where' expression.")) (|qualifier| (((|SpadAst|) $) "\\spad{qualifier(e)} returns the qualifier of the expression `e'.")) (|mainExpression| (((|SpadAst|) $) "\\spad{mainExpression(e)} returns the main expression of the `where' expression `e'."))) NIL NIL -(-1298) +(-1299) ((|constructor| (NIL "This domain represents the `while' iterator syntax.")) (|condition| (((|SpadAst|) $) "\\spad{condition(i)} returns the condition of the while iterator `i'."))) NIL NIL -(-1299 R |VarSet| E P |vl| |wl| |wtlevel|) +(-1300 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)"))) -((-4458 |has| |#1| (-174)) (-4457 |has| |#1| (-174)) (-4460 . T)) +((-4459 |has| |#1| (-174)) (-4458 |has| |#1| (-174)) (-4461 . T)) ((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374)))) -(-1300 R E V P) +(-1301 R E V P) ((|constructor| (NIL "A domain constructor of the category \\axiomType{GeneralTriangularSet}. The only requirement for a list of polynomials to be a member of such a domain is the following: no polynomial is constant and two distinct polynomials have distinct main variables. Such a triangular set may not be auto-reduced or consistent. The \\axiomOpFrom{construct}{WuWenTsunTriangularSet} operation does not check the previous requirement. Triangular sets are stored as sorted lists \\spad{w}.\\spad{r}.\\spad{t}. the main variables of their members. Furthermore,{} this domain exports operations dealing with the characteristic set method of Wu Wen Tsun and some optimizations mainly proposed by Dong Ming Wang.\\newline References : \\indented{1}{[1] \\spad{W}. \\spad{T}. WU \"A Zero Structure Theorem for polynomial equations solving\"} \\indented{6}{\\spad{MM} Research Preprints,{} 1987.} \\indented{1}{[2] \\spad{D}. \\spad{M}. WANG \"An implementation of the characteristic set method in Maple\"} \\indented{6}{Proc. DISCO'92. Bath,{} England.}")) (|characteristicSerie| (((|List| $) (|List| |#4|)) "\\axiom{characteristicSerie(\\spad{ps})} returns the same as \\axiom{characteristicSerie(\\spad{ps},{}initiallyReduced?,{}initiallyReduce)}.") (((|List| $) (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{characteristicSerie(\\spad{ps},{}redOp?,{}redOp)} returns a list \\axiom{\\spad{lts}} of triangular sets such that the zero set of \\axiom{\\spad{ps}} is the union of the regular zero sets of the members of \\axiom{\\spad{lts}}. This is made by the Ritt and Wu Wen Tsun process applying the operation \\axiom{characteristicSet(\\spad{ps},{}redOp?,{}redOp)} to compute characteristic sets in Wu Wen Tsun sense.")) (|characteristicSet| (((|Union| $ "failed") (|List| |#4|)) "\\axiom{characteristicSet(\\spad{ps})} returns the same as \\axiom{characteristicSet(\\spad{ps},{}initiallyReduced?,{}initiallyReduce)}.") (((|Union| $ "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{characteristicSet(\\spad{ps},{}redOp?,{}redOp)} returns a non-contradictory characteristic set of \\axiom{\\spad{ps}} in Wu Wen Tsun sense \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?} (using \\axiom{redOp} to reduce polynomials \\spad{w}.\\spad{r}.\\spad{t} a \\axiom{redOp?} basic set),{} if no non-zero constant polynomial appear during those reductions,{} else \\axiom{\"failed\"} is returned. The operations \\axiom{redOp} and \\axiom{redOp?} must satisfy the following conditions: \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} holds for every polynomials \\axiom{\\spad{p},{}\\spad{q}} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that we have \\axiom{init(\\spad{q})^e*p = \\spad{f*q} + redOp(\\spad{p},{}\\spad{q})}.")) (|medialSet| (((|Union| $ "failed") (|List| |#4|)) "\\axiom{medial(\\spad{ps})} returns the same as \\axiom{medialSet(\\spad{ps},{}initiallyReduced?,{}initiallyReduce)}.") (((|Union| $ "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{medialSet(\\spad{ps},{}redOp?,{}redOp)} returns \\axiom{\\spad{bs}} a basic set (in Wu Wen Tsun sense \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?}) of some set generating the same ideal as \\axiom{\\spad{ps}} (with rank not higher than any basic set of \\axiom{\\spad{ps}}),{} if no non-zero constant polynomials appear during the computatioms,{} else \\axiom{\"failed\"} is returned. In the former case,{} \\axiom{\\spad{bs}} has to be understood as a candidate for being a characteristic set of \\axiom{\\spad{ps}}. In the original algorithm,{} \\axiom{\\spad{bs}} is simply a basic set of \\axiom{\\spad{ps}}."))) -((-4464 . T) (-4463 . T)) -((-12 (|HasCategory| |#4| (QUOTE (-1120))) (|HasCategory| |#4| (LIST (QUOTE -319) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#4| (QUOTE (-1120))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#3| (QUOTE (-379))) (|HasCategory| |#4| (LIST (QUOTE -625) (QUOTE (-875)))) (|HasCategory| |#4| (QUOTE (-102)))) -(-1301 R) +((-4465 . T) (-4464 . T)) +((-12 (|HasCategory| |#4| (QUOTE (-1121))) (|HasCategory| |#4| (LIST (QUOTE -319) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -626) (QUOTE (-548)))) (|HasCategory| |#4| (QUOTE (-1121))) (|HasCategory| |#1| (QUOTE (-568))) (|HasCategory| |#3| (QUOTE (-379))) (|HasCategory| |#4| (LIST (QUOTE -625) (QUOTE (-876)))) (|HasCategory| |#4| (QUOTE (-102)))) +(-1302 R) ((|constructor| (NIL "This is the category of algebras over non-commutative rings. It is used by constructors of non-commutative algebras such as: \\indented{4}{\\spadtype{XPolynomialRing}.} \\indented{4}{\\spadtype{XFreeAlgebra}} Author: Michel Petitot (petitot@lifl.\\spad{fr})"))) -((-4457 . T) (-4458 . T) (-4460 . T)) +((-4458 . T) (-4459 . T) (-4461 . T)) NIL -(-1302 |vl| R) +(-1303 |vl| R) ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables do not commute. The coefficient ring may be non-commutative too. However,{} coefficients and variables commute."))) -((-4460 . T) (-4456 |has| |#2| (-6 -4456)) (-4458 . T) (-4457 . T)) -((|HasCategory| |#2| (QUOTE (-174))) (|HasAttribute| |#2| (QUOTE -4456))) -(-1303 R |VarSet| XPOLY) +((-4461 . T) (-4457 |has| |#2| (-6 -4457)) (-4459 . T) (-4458 . T)) +((|HasCategory| |#2| (QUOTE (-174))) (|HasAttribute| |#2| (QUOTE -4457))) +(-1304 R |VarSet| XPOLY) ((|constructor| (NIL "This package provides computations of logarithms and exponentials for polynomials in non-commutative variables. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|Hausdorff| ((|#3| |#3| |#3| (|NonNegativeInteger|)) "\\axiom{Hausdorff(a,{}\\spad{b},{}\\spad{n})} returns log(exp(a)*exp(\\spad{b})) truncated at order \\axiom{\\spad{n}}.")) (|log| ((|#3| |#3| (|NonNegativeInteger|)) "\\axiom{log(\\spad{p},{} \\spad{n})} returns the logarithm of \\axiom{\\spad{p}} truncated at order \\axiom{\\spad{n}}.")) (|exp| ((|#3| |#3| (|NonNegativeInteger|)) "\\axiom{exp(\\spad{p},{} \\spad{n})} returns the exponential of \\axiom{\\spad{p}} truncated at order \\axiom{\\spad{n}}."))) NIL NIL -(-1304 |vl| R) +(-1305 |vl| R) ((|constructor| (NIL "This category specifies opeations for polynomials and formal series with non-commutative variables.")) (|varList| (((|List| |#1|) $) "\\spad{varList(x)} returns the list of variables which appear in \\spad{x}.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(fn,x)} returns \\spad{Sum(fn(r_i) w_i)} if \\spad{x} writes \\spad{Sum(r_i w_i)}.")) (|sh| (($ $ (|NonNegativeInteger|)) "\\spad{sh(x,n)} returns the shuffle power of \\spad{x} to the \\spad{n}.") (($ $ $) "\\spad{sh(x,y)} returns the shuffle-product of \\spad{x} by \\spad{y}. This multiplication is associative and commutative.")) (|quasiRegular| (($ $) "\\spad{quasiRegular(x)} return \\spad{x} minus its constant term.")) (|quasiRegular?| (((|Boolean|) $) "\\spad{quasiRegular?(x)} return \\spad{true} if \\spad{constant(x)} is zero.")) (|constant| ((|#2| $) "\\spad{constant(x)} returns the constant term of \\spad{x}.")) (|constant?| (((|Boolean|) $) "\\spad{constant?(x)} returns \\spad{true} if \\spad{x} is constant.")) (|coerce| (($ |#1|) "\\spad{coerce(v)} returns \\spad{v}.")) (|mirror| (($ $) "\\spad{mirror(x)} returns \\spad{Sum(r_i mirror(w_i))} if \\spad{x} writes \\spad{Sum(r_i w_i)}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(x)} returns \\spad{true} if \\spad{x} is a monomial")) (|monom| (($ (|OrderedFreeMonoid| |#1|) |#2|) "\\spad{monom(w,r)} returns the product of the word \\spad{w} by the coefficient \\spad{r}.")) (|rquo| (($ $ $) "\\spad{rquo(x,y)} returns the right simplification of \\spad{x} by \\spad{y}.") (($ $ (|OrderedFreeMonoid| |#1|)) "\\spad{rquo(x,w)} returns the right simplification of \\spad{x} by \\spad{w}.") (($ $ |#1|) "\\spad{rquo(x,v)} returns the right simplification of \\spad{x} by the variable \\spad{v}.")) (|lquo| (($ $ $) "\\spad{lquo(x,y)} returns the left simplification of \\spad{x} by \\spad{y}.") (($ $ (|OrderedFreeMonoid| |#1|)) "\\spad{lquo(x,w)} returns the left simplification of \\spad{x} by the word \\spad{w}.") (($ $ |#1|) "\\spad{lquo(x,v)} returns the left simplification of \\spad{x} by the variable \\spad{v}.")) (|coef| ((|#2| $ $) "\\spad{coef(x,y)} returns scalar product of \\spad{x} by \\spad{y},{} the set of words being regarded as an orthogonal basis.") ((|#2| $ (|OrderedFreeMonoid| |#1|)) "\\spad{coef(x,w)} returns the coefficient of the word \\spad{w} in \\spad{x}.")) (|mindegTerm| (((|Record| (|:| |k| (|OrderedFreeMonoid| |#1|)) (|:| |c| |#2|)) $) "\\spad{mindegTerm(x)} returns the term whose word is \\spad{mindeg(x)}.")) (|mindeg| (((|OrderedFreeMonoid| |#1|) $) "\\spad{mindeg(x)} returns the little word which appears in \\spad{x}. Error if \\spad{x=0}.")) (* (($ $ |#2|) "\\spad{x * r} returns the product of \\spad{x} by \\spad{r}. Usefull if \\spad{R} is a non-commutative Ring.") (($ |#1| $) "\\spad{v * x} returns the product of a variable \\spad{x} by \\spad{x}."))) -((-4456 |has| |#2| (-6 -4456)) (-4458 . T) (-4457 . T) (-4460 . T)) +((-4457 |has| |#2| (-6 -4457)) (-4459 . T) (-4458 . T) (-4461 . T)) NIL -(-1305 S -2117) +(-1306 S -1959) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|NonNegativeInteger|)) "\\spad{Frobenius(a,s)} returns \\spad{a**(q**s)} where \\spad{q} is the size()\\$\\spad{F}.") (($ $) "\\spad{Frobenius(a)} returns \\spad{a ** q} where \\spad{q} is the \\spad{size()\\$F}.")) (|transcendenceDegree| (((|NonNegativeInteger|)) "\\spad{transcendenceDegree()} returns the transcendence degree of the field extension,{} 0 if the extension is algebraic.")) (|extensionDegree| (((|OnePointCompletion| (|PositiveInteger|))) "\\spad{extensionDegree()} returns the degree of the field extension if the extension is algebraic,{} and \\spad{infinity} if it is not.")) (|degree| (((|OnePointCompletion| (|PositiveInteger|)) $) "\\spad{degree(a)} returns the degree of minimal polynomial of an element \\spad{a} if \\spad{a} is algebraic with respect to the ground field \\spad{F},{} and \\spad{infinity} otherwise.")) (|inGroundField?| (((|Boolean|) $) "\\spad{inGroundField?(a)} tests whether an element \\spad{a} is already in the ground field \\spad{F}.")) (|transcendent?| (((|Boolean|) $) "\\spad{transcendent?(a)} tests whether an element \\spad{a} is transcendent with respect to the ground field \\spad{F}.")) (|algebraic?| (((|Boolean|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) NIL ((|HasCategory| |#2| (QUOTE (-379))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148)))) -(-1306 -2117) +(-1307 -1959) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|NonNegativeInteger|)) "\\spad{Frobenius(a,s)} returns \\spad{a**(q**s)} where \\spad{q} is the size()\\$\\spad{F}.") (($ $) "\\spad{Frobenius(a)} returns \\spad{a ** q} where \\spad{q} is the \\spad{size()\\$F}.")) (|transcendenceDegree| (((|NonNegativeInteger|)) "\\spad{transcendenceDegree()} returns the transcendence degree of the field extension,{} 0 if the extension is algebraic.")) (|extensionDegree| (((|OnePointCompletion| (|PositiveInteger|))) "\\spad{extensionDegree()} returns the degree of the field extension if the extension is algebraic,{} and \\spad{infinity} if it is not.")) (|degree| (((|OnePointCompletion| (|PositiveInteger|)) $) "\\spad{degree(a)} returns the degree of minimal polynomial of an element \\spad{a} if \\spad{a} is algebraic with respect to the ground field \\spad{F},{} and \\spad{infinity} otherwise.")) (|inGroundField?| (((|Boolean|) $) "\\spad{inGroundField?(a)} tests whether an element \\spad{a} is already in the ground field \\spad{F}.")) (|transcendent?| (((|Boolean|) $) "\\spad{transcendent?(a)} tests whether an element \\spad{a} is transcendent with respect to the ground field \\spad{F}.")) (|algebraic?| (((|Boolean|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) -((-4455 . T) (-4461 . T) (-4456 . T) ((-4465 "*") . T) (-4457 . T) (-4458 . T) (-4460 . T)) +((-4456 . T) (-4462 . T) (-4457 . T) ((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL -(-1307 |VarSet| R) +(-1308 |VarSet| R) ((|constructor| (NIL "This domain constructor implements polynomials in non-commutative variables written in the Poincare-Birkhoff-Witt basis from the Lyndon basis. These polynomials can be used to compute Baker-Campbell-Hausdorff relations. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|log| (($ $ (|NonNegativeInteger|)) "\\axiom{log(\\spad{p},{}\\spad{n})} returns the logarithm of \\axiom{\\spad{p}} (truncated up to order \\axiom{\\spad{n}}).")) (|exp| (($ $ (|NonNegativeInteger|)) "\\axiom{exp(\\spad{p},{}\\spad{n})} returns the exponential of \\axiom{\\spad{p}} (truncated up to order \\axiom{\\spad{n}}).")) (|product| (($ $ $ (|NonNegativeInteger|)) "\\axiom{product(a,{}\\spad{b},{}\\spad{n})} returns \\axiom{a*b} (truncated up to order \\axiom{\\spad{n}}).")) (|LiePolyIfCan| (((|Union| (|LiePolynomial| |#1| |#2|) "failed") $) "\\axiom{LiePolyIfCan(\\spad{p})} return \\axiom{\\spad{p}} if \\axiom{\\spad{p}} is a Lie polynomial.")) (|coerce| (((|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{p})} returns \\axiom{\\spad{p}} as a recursive polynomial.") (((|XDistributedPolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{p})} returns \\axiom{\\spad{p}} as a distributed polynomial.") (($ (|LiePolynomial| |#1| |#2|)) "\\axiom{coerce(\\spad{p})} returns \\axiom{\\spad{p}}."))) -((-4456 |has| |#2| (-6 -4456)) (-4458 . T) (-4457 . T) (-4460 . T)) -((|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (LIST (QUOTE -729) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasAttribute| |#2| (QUOTE -4456))) -(-1308 |vl| R) +((-4457 |has| |#2| (-6 -4457)) (-4459 . T) (-4458 . T) (-4461 . T)) +((|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (LIST (QUOTE -729) (LIST (QUOTE -419) (QUOTE (-576))))) (|HasAttribute| |#2| (QUOTE -4457))) +(-1309 |vl| R) ((|constructor| (NIL "The Category of polynomial rings with non-commutative variables. The coefficient ring may be non-commutative too. However coefficients commute with vaiables.")) (|trunc| (($ $ (|NonNegativeInteger|)) "\\spad{trunc(p,n)} returns the polynomial \\spad{p} truncated at order \\spad{n}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(p)} returns the degree of \\spad{p}. \\indented{1}{Note that the degree of a word is its length.}")) (|maxdeg| (((|OrderedFreeMonoid| |#1|) $) "\\spad{maxdeg(p)} returns the greatest leading word in the support of \\spad{p}."))) -((-4456 |has| |#2| (-6 -4456)) (-4458 . T) (-4457 . T) (-4460 . T)) +((-4457 |has| |#2| (-6 -4457)) (-4459 . T) (-4458 . T) (-4461 . T)) NIL -(-1309 R) +(-1310 R) ((|constructor| (NIL "\\indented{2}{This type supports multivariate polynomials} whose set of variables is \\spadtype{Symbol}. The representation is recursive. The coefficient ring may be non-commutative and the variables do not commute. However,{} coefficients and variables commute."))) -((-4456 |has| |#1| (-6 -4456)) (-4458 . T) (-4457 . T) (-4460 . T)) -((|HasCategory| |#1| (QUOTE (-174))) (|HasAttribute| |#1| (QUOTE -4456))) -(-1310 R E) +((-4457 |has| |#1| (-6 -4457)) (-4459 . T) (-4458 . T) (-4461 . T)) +((|HasCategory| |#1| (QUOTE (-174))) (|HasAttribute| |#1| (QUOTE -4457))) +(-1311 R E) ((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and words belonging to an arbitrary \\spadtype{OrderedMonoid}. This type is used,{} for instance,{} by the \\spadtype{XDistributedPolynomial} domain constructor where the Monoid is free.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (/ (($ $ |#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.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\# p} returns the number of terms in \\spad{p}.")) (* (($ $ |#1|) "\\spad{p*r} returns the product of \\spad{p} by \\spad{r}."))) -((-4460 . T) (-4461 |has| |#1| (-6 -4461)) (-4456 |has| |#1| (-6 -4456)) (-4458 . T) (-4457 . T)) -((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasAttribute| |#1| (QUOTE -4460)) (|HasAttribute| |#1| (QUOTE -4461)) (|HasAttribute| |#1| (QUOTE -4456))) -(-1311 |VarSet| R) +((-4461 . T) (-4462 |has| |#1| (-6 -4462)) (-4457 |has| |#1| (-6 -4457)) (-4459 . T) (-4458 . T)) +((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-374))) (|HasAttribute| |#1| (QUOTE -4461)) (|HasAttribute| |#1| (QUOTE -4462)) (|HasAttribute| |#1| (QUOTE -4457))) +(-1312 |VarSet| R) ((|constructor| (NIL "\\indented{2}{This type supports multivariate polynomials} whose variables do not commute. The representation is recursive. The coefficient ring may be non-commutative. Coefficients and variables commute.")) (|RemainderList| (((|List| (|Record| (|:| |k| |#1|) (|:| |c| $))) $) "\\spad{RemainderList(p)} returns the regular part of \\spad{p} as a list of terms.")) (|unexpand| (($ (|XDistributedPolynomial| |#1| |#2|)) "\\spad{unexpand(p)} returns \\spad{p} in recursive form.")) (|expand| (((|XDistributedPolynomial| |#1| |#2|) $) "\\spad{expand(p)} returns \\spad{p} in distributed form."))) -((-4456 |has| |#2| (-6 -4456)) (-4458 . T) (-4457 . T) (-4460 . T)) -((|HasCategory| |#2| (QUOTE (-174))) (|HasAttribute| |#2| (QUOTE -4456))) -(-1312) +((-4457 |has| |#2| (-6 -4457)) (-4459 . T) (-4458 . T) (-4461 . T)) +((|HasCategory| |#2| (QUOTE (-174))) (|HasAttribute| |#2| (QUOTE -4457))) +(-1313) ((|constructor| (NIL "This domain provides representations of Young diagrams.")) (|shape| (((|Partition|) $) "\\spad{shape x} returns the partition shaping \\spad{x}.")) (|youngDiagram| (($ (|List| (|PositiveInteger|))) "\\spad{youngDiagram l} returns an object representing a Young diagram with shape given by the list of integers \\spad{l}"))) NIL NIL -(-1313 A) +(-1314 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 -(-1314 R |ls| |ls2|) +(-1315 R |ls| |ls2|) ((|constructor| (NIL "A package for computing symbolically the complex and real roots of zero-dimensional algebraic systems over the integer or rational numbers. Complex roots are given by means of univariate representations of irreducible regular chains. Real roots are given by means of tuples of coordinates lying in the \\spadtype{RealClosure} of the coefficient ring. This constructor takes three arguments. The first one \\spad{R} is the coefficient ring. The second one \\spad{ls} is the list of variables involved in the systems to solve. The third one must be \\spad{concat(ls,s)} where \\spad{s} is an additional symbol used for the univariate representations. WARNING: The third argument is not checked. All operations are based on triangular decompositions. The default is to compute these decompositions directly from the input system by using the \\spadtype{RegularChain} domain constructor. The lexTriangular algorithm can also be used for computing these decompositions (see the \\spadtype{LexTriangularPackage} package constructor). For that purpose,{} the operations \\axiomOpFrom{univariateSolve}{ZeroDimensionalSolvePackage},{} \\axiomOpFrom{realSolve}{ZeroDimensionalSolvePackage} and \\axiomOpFrom{positiveSolve}{ZeroDimensionalSolvePackage} admit an optional argument. \\newline Author: Marc Moreno Maza.")) (|convert| (((|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|))) (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#3|)) (|OrderedVariableList| |#3|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|)))) "\\spad{convert(st)} returns the members of \\spad{st}.") (((|SparseUnivariatePolynomial| (|RealClosure| (|Fraction| |#1|))) (|SparseUnivariatePolynomial| |#1|)) "\\spad{convert(u)} converts \\spad{u}.") (((|Polynomial| (|RealClosure| (|Fraction| |#1|))) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|))) "\\spad{convert(q)} converts \\spad{q}.") (((|Polynomial| (|RealClosure| (|Fraction| |#1|))) (|Polynomial| |#1|)) "\\spad{convert(p)} converts \\spad{p}.") (((|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|)) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) "\\spad{convert(q)} converts \\spad{q}.")) (|squareFree| (((|List| (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#3|)) (|OrderedVariableList| |#3|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|)))) (|RegularChain| |#1| |#2|)) "\\spad{squareFree(ts)} returns the square-free factorization of \\spad{ts}. Moreover,{} each factor is a Lazard triangular set and the decomposition is a Kalkbrener split of \\spad{ts},{} which is enough here for the matter of solving zero-dimensional algebraic systems. WARNING: \\spad{ts} is not checked to be zero-dimensional.")) (|positiveSolve| (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|))) "\\spad{positiveSolve(lp)} returns the same as \\spad{positiveSolve(lp,false,false)}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{positiveSolve(lp)} returns the same as \\spad{positiveSolve(lp,info?,false)}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{positiveSolve(lp,info?,lextri?)} returns the set of the points in the variety associated with \\spad{lp} whose coordinates are (real) strictly positive. Moreover,{} if \\spad{info?} is \\spad{true} then some information is displayed during decomposition into regular chains. If \\spad{lextri?} is \\spad{true} then the lexTriangular algorithm is called from the \\spadtype{LexTriangularPackage} constructor (see \\axiomOpFrom{zeroSetSplit}{LexTriangularPackage}(\\spad{lp},{}\\spad{false})). Otherwise,{} the triangular decomposition is computed directly from the input system by using the \\axiomOpFrom{zeroSetSplit}{RegularChain} from \\spadtype{RegularChain}. WARNING: For each set of coordinates given by \\spad{positiveSolve(lp,info?,lextri?)} the ordering of the indeterminates is reversed \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ls}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|RegularChain| |#1| |#2|)) "\\spad{positiveSolve(ts)} returns the points of the regular set of \\spad{ts} with (real) strictly positive coordinates.")) (|realSolve| (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|))) "\\spad{realSolve(lp)} returns the same as \\spad{realSolve(ts,false,false,false)}") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{realSolve(ts,info?)} returns the same as \\spad{realSolve(ts,info?,false,false)}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{realSolve(ts,info?,check?)} returns the same as \\spad{realSolve(ts,info?,check?,false)}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|) (|Boolean|)) "\\spad{realSolve(ts,info?,check?,lextri?)} returns the set of the points in the variety associated with \\spad{lp} whose coordinates are all real. Moreover,{} if \\spad{info?} is \\spad{true} then some information is displayed during decomposition into regular chains. If \\spad{check?} is \\spad{true} then the result is checked. If \\spad{lextri?} is \\spad{true} then the lexTriangular algorithm is called from the \\spadtype{LexTriangularPackage} constructor (see \\axiomOpFrom{zeroSetSplit}{LexTriangularPackage}(\\spad{lp},{}\\spad{false})). Otherwise,{} the triangular decomposition is computed directly from the input system by using the \\axiomOpFrom{zeroSetSplit}{RegularChain} from \\spadtype{RegularChain}. WARNING: For each set of coordinates given by \\spad{realSolve(ts,info?,check?,lextri?)} the ordering of the indeterminates is reversed \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ls}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|RegularChain| |#1| |#2|)) "\\spad{realSolve(ts)} returns the set of the points in the regular zero set of \\spad{ts} whose coordinates are all real. WARNING: For each set of coordinates given by \\spad{realSolve(ts)} the ordering of the indeterminates is reversed \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ls}.")) (|univariateSolve| (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|))) "\\spad{univariateSolve(lp)} returns the same as \\spad{univariateSolve(lp,false,false,false)}.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{univariateSolve(lp,info?)} returns the same as \\spad{univariateSolve(lp,info?,false,false)}.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{univariateSolve(lp,info?,check?)} returns the same as \\spad{univariateSolve(lp,info?,check?,false)}.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|) (|Boolean|)) "\\spad{univariateSolve(lp,info?,check?,lextri?)} returns a univariate representation of the variety associated with \\spad{lp}. Moreover,{} if \\spad{info?} is \\spad{true} then some information is displayed during the decomposition into regular chains. If \\spad{check?} is \\spad{true} then the result is checked. See \\axiomOpFrom{rur}{RationalUnivariateRepresentationPackage}(\\spad{lp},{}\\spad{true}). If \\spad{lextri?} is \\spad{true} then the lexTriangular algorithm is called from the \\spadtype{LexTriangularPackage} constructor (see \\axiomOpFrom{zeroSetSplit}{LexTriangularPackage}(\\spad{lp},{}\\spad{false})). Otherwise,{} the triangular decomposition is computed directly from the input system by using the \\axiomOpFrom{zeroSetSplit}{RegularChain} from \\spadtype{RegularChain}.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|RegularChain| |#1| |#2|)) "\\spad{univariateSolve(ts)} returns a univariate representation of \\spad{ts}. See \\axiomOpFrom{rur}{RationalUnivariateRepresentationPackage}(\\spad{lp},{}\\spad{true}).")) (|triangSolve| (((|List| (|RegularChain| |#1| |#2|)) (|List| (|Polynomial| |#1|))) "\\spad{triangSolve(lp)} returns the same as \\spad{triangSolve(lp,false,false)}") (((|List| (|RegularChain| |#1| |#2|)) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{triangSolve(lp,info?)} returns the same as \\spad{triangSolve(lp,false)}") (((|List| (|RegularChain| |#1| |#2|)) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{triangSolve(lp,info?,lextri?)} decomposes the variety associated with \\axiom{\\spad{lp}} into regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{\\spad{lp}} needs to generate a zero-dimensional ideal. If \\axiom{\\spad{lp}} is not zero-dimensional then the result is only a decomposition of its zero-set in the sense of the closure (\\spad{w}.\\spad{r}.\\spad{t}. Zarisky topology). Moreover,{} if \\spad{info?} is \\spad{true} then some information is displayed during the computations. See \\axiomOpFrom{zeroSetSplit}{RegularTriangularSetCategory}(\\spad{lp},{}\\spad{true},{}\\spad{info?}). If \\spad{lextri?} is \\spad{true} then the lexTriangular algorithm is called from the \\spadtype{LexTriangularPackage} constructor (see \\axiomOpFrom{zeroSetSplit}{LexTriangularPackage}(\\spad{lp},{}\\spad{false})). Otherwise,{} the triangular decomposition is computed directly from the input system by using the \\axiomOpFrom{zeroSetSplit}{RegularChain} from \\spadtype{RegularChain}."))) NIL NIL -(-1315 R) +(-1316 R) ((|constructor| (NIL "Test for linear dependence over the integers.")) (|solveLinearlyOverQ| (((|Union| (|Vector| (|Fraction| (|Integer|))) "failed") (|Vector| |#1|) |#1|) "\\spad{solveLinearlyOverQ([v1,...,vn], u)} returns \\spad{[c1,...,cn]} such that \\spad{c1*v1 + ... + cn*vn = u},{} \"failed\" if no such rational numbers \\spad{ci}\\spad{'s} exist.")) (|linearDependenceOverZ| (((|Union| (|Vector| (|Integer|)) "failed") (|Vector| |#1|)) "\\spad{linearlyDependenceOverZ([v1,...,vn])} returns \\spad{[c1,...,cn]} if \\spad{c1*v1 + ... + cn*vn = 0} and not all the \\spad{ci}\\spad{'s} are 0,{} \"failed\" if the \\spad{vi}\\spad{'s} are linearly independent over the integers.")) (|linearlyDependentOverZ?| (((|Boolean|) (|Vector| |#1|)) "\\spad{linearlyDependentOverZ?([v1,...,vn])} returns \\spad{true} if the \\spad{vi}\\spad{'s} are linearly dependent over the integers,{} \\spad{false} otherwise."))) NIL NIL -(-1316 |p|) +(-1317 |p|) ((|constructor| (NIL "IntegerMod(\\spad{n}) creates the ring of integers reduced modulo the integer \\spad{n}."))) -(((-4465 "*") . T) (-4457 . T) (-4458 . T) (-4460 . T)) +(((-4466 "*") . T) (-4458 . T) (-4459 . T) (-4461 . T)) NIL NIL NIL @@ -5212,4 +5216,4 @@ NIL NIL NIL NIL -((-3 NIL 2293563 2293568 2293573 2293578) (-2 NIL 2293543 2293548 2293553 2293558) (-1 NIL 2293523 2293528 2293533 2293538) (0 NIL 2293503 2293508 2293513 2293518) (-1316 "ZMOD.spad" 2293312 2293325 2293441 2293498) (-1315 "ZLINDEP.spad" 2292378 2292389 2293302 2293307) (-1314 "ZDSOLVE.spad" 2282323 2282345 2292368 2292373) (-1313 "YSTREAM.spad" 2281818 2281829 2282313 2282318) (-1312 "YDIAGRAM.spad" 2281452 2281461 2281808 2281813) (-1311 "XRPOLY.spad" 2280672 2280692 2281308 2281377) (-1310 "XPR.spad" 2278467 2278480 2280390 2280489) (-1309 "XPOLY.spad" 2278022 2278033 2278323 2278392) (-1308 "XPOLYC.spad" 2277341 2277357 2277948 2278017) (-1307 "XPBWPOLY.spad" 2275778 2275798 2277121 2277190) (-1306 "XF.spad" 2274241 2274256 2275680 2275773) (-1305 "XF.spad" 2272684 2272701 2274125 2274130) (-1304 "XFALG.spad" 2269732 2269748 2272610 2272679) (-1303 "XEXPPKG.spad" 2268983 2269009 2269722 2269727) (-1302 "XDPOLY.spad" 2268597 2268613 2268839 2268908) (-1301 "XALG.spad" 2268257 2268268 2268553 2268592) (-1300 "WUTSET.spad" 2264060 2264077 2267867 2267894) (-1299 "WP.spad" 2263259 2263303 2263918 2263985) (-1298 "WHILEAST.spad" 2263057 2263066 2263249 2263254) (-1297 "WHEREAST.spad" 2262728 2262737 2263047 2263052) (-1296 "WFFINTBS.spad" 2260391 2260413 2262718 2262723) (-1295 "WEIER.spad" 2258613 2258624 2260381 2260386) (-1294 "VSPACE.spad" 2258286 2258297 2258581 2258608) (-1293 "VSPACE.spad" 2257979 2257992 2258276 2258281) (-1292 "VOID.spad" 2257656 2257665 2257969 2257974) (-1291 "VIEW.spad" 2255336 2255345 2257646 2257651) (-1290 "VIEWDEF.spad" 2250537 2250546 2255326 2255331) (-1289 "VIEW3D.spad" 2234498 2234507 2250527 2250532) (-1288 "VIEW2D.spad" 2222389 2222398 2234488 2234493) (-1287 "VECTOR.spad" 2220910 2220921 2221161 2221188) (-1286 "VECTOR2.spad" 2219549 2219562 2220900 2220905) (-1285 "VECTCAT.spad" 2217453 2217464 2219517 2219544) (-1284 "VECTCAT.spad" 2215164 2215177 2217230 2217235) (-1283 "VARIABLE.spad" 2214944 2214959 2215154 2215159) (-1282 "UTYPE.spad" 2214588 2214597 2214934 2214939) (-1281 "UTSODETL.spad" 2213883 2213907 2214544 2214549) (-1280 "UTSODE.spad" 2212099 2212119 2213873 2213878) (-1279 "UTS.spad" 2207046 2207074 2210566 2210663) (-1278 "UTSCAT.spad" 2204525 2204541 2206944 2207041) (-1277 "UTSCAT.spad" 2201648 2201666 2204069 2204074) (-1276 "UTS2.spad" 2201243 2201278 2201638 2201643) (-1275 "URAGG.spad" 2195916 2195927 2201233 2201238) (-1274 "URAGG.spad" 2190553 2190566 2195872 2195877) (-1273 "UPXSSING.spad" 2188198 2188224 2189634 2189767) (-1272 "UPXS.spad" 2185494 2185522 2186330 2186479) (-1271 "UPXSCONS.spad" 2183253 2183273 2183626 2183775) (-1270 "UPXSCCA.spad" 2181824 2181844 2183099 2183248) (-1269 "UPXSCCA.spad" 2180537 2180559 2181814 2181819) (-1268 "UPXSCAT.spad" 2179126 2179142 2180383 2180532) (-1267 "UPXS2.spad" 2178669 2178722 2179116 2179121) (-1266 "UPSQFREE.spad" 2177083 2177097 2178659 2178664) (-1265 "UPSCAT.spad" 2174870 2174894 2176981 2177078) (-1264 "UPSCAT.spad" 2172363 2172389 2174476 2174481) (-1263 "UPOLYC.spad" 2167403 2167414 2172205 2172358) (-1262 "UPOLYC.spad" 2162335 2162348 2167139 2167144) (-1261 "UPOLYC2.spad" 2161806 2161825 2162325 2162330) (-1260 "UP.spad" 2158912 2158927 2159299 2159452) (-1259 "UPMP.spad" 2157812 2157825 2158902 2158907) (-1258 "UPDIVP.spad" 2157377 2157391 2157802 2157807) (-1257 "UPDECOMP.spad" 2155622 2155636 2157367 2157372) (-1256 "UPCDEN.spad" 2154831 2154847 2155612 2155617) (-1255 "UP2.spad" 2154195 2154216 2154821 2154826) (-1254 "UNISEG.spad" 2153548 2153559 2154114 2154119) (-1253 "UNISEG2.spad" 2153045 2153058 2153504 2153509) (-1252 "UNIFACT.spad" 2152148 2152160 2153035 2153040) (-1251 "ULS.spad" 2141932 2141960 2142877 2143306) (-1250 "ULSCONS.spad" 2133066 2133086 2133436 2133585) (-1249 "ULSCCAT.spad" 2130803 2130823 2132912 2133061) (-1248 "ULSCCAT.spad" 2128648 2128670 2130759 2130764) (-1247 "ULSCAT.spad" 2126880 2126896 2128494 2128643) (-1246 "ULS2.spad" 2126394 2126447 2126870 2126875) (-1245 "UINT8.spad" 2126271 2126280 2126384 2126389) (-1244 "UINT64.spad" 2126147 2126156 2126261 2126266) (-1243 "UINT32.spad" 2126023 2126032 2126137 2126142) (-1242 "UINT16.spad" 2125899 2125908 2126013 2126018) (-1241 "UFD.spad" 2124964 2124973 2125825 2125894) (-1240 "UFD.spad" 2124091 2124102 2124954 2124959) (-1239 "UDVO.spad" 2122972 2122981 2124081 2124086) (-1238 "UDPO.spad" 2120465 2120476 2122928 2122933) (-1237 "TYPE.spad" 2120397 2120406 2120455 2120460) (-1236 "TYPEAST.spad" 2120316 2120325 2120387 2120392) (-1235 "TWOFACT.spad" 2118968 2118983 2120306 2120311) (-1234 "TUPLE.spad" 2118454 2118465 2118867 2118872) (-1233 "TUBETOOL.spad" 2115321 2115330 2118444 2118449) (-1232 "TUBE.spad" 2113968 2113985 2115311 2115316) (-1231 "TS.spad" 2112567 2112583 2113533 2113630) (-1230 "TSETCAT.spad" 2099694 2099711 2112535 2112562) (-1229 "TSETCAT.spad" 2086807 2086826 2099650 2099655) (-1228 "TRMANIP.spad" 2081173 2081190 2086513 2086518) (-1227 "TRIMAT.spad" 2080136 2080161 2081163 2081168) (-1226 "TRIGMNIP.spad" 2078663 2078680 2080126 2080131) (-1225 "TRIGCAT.spad" 2078175 2078184 2078653 2078658) (-1224 "TRIGCAT.spad" 2077685 2077696 2078165 2078170) (-1223 "TREE.spad" 2076143 2076154 2077175 2077202) (-1222 "TRANFUN.spad" 2075982 2075991 2076133 2076138) (-1221 "TRANFUN.spad" 2075819 2075830 2075972 2075977) (-1220 "TOPSP.spad" 2075493 2075502 2075809 2075814) (-1219 "TOOLSIGN.spad" 2075156 2075167 2075483 2075488) (-1218 "TEXTFILE.spad" 2073717 2073726 2075146 2075151) (-1217 "TEX.spad" 2070863 2070872 2073707 2073712) (-1216 "TEX1.spad" 2070419 2070430 2070853 2070858) (-1215 "TEMUTL.spad" 2069974 2069983 2070409 2070414) (-1214 "TBCMPPK.spad" 2068067 2068090 2069964 2069969) (-1213 "TBAGG.spad" 2067117 2067140 2068047 2068062) (-1212 "TBAGG.spad" 2066175 2066200 2067107 2067112) (-1211 "TANEXP.spad" 2065583 2065594 2066165 2066170) (-1210 "TALGOP.spad" 2065307 2065318 2065573 2065578) (-1209 "TABLE.spad" 2063276 2063299 2063546 2063573) (-1208 "TABLEAU.spad" 2062757 2062768 2063266 2063271) (-1207 "TABLBUMP.spad" 2059560 2059571 2062747 2062752) (-1206 "SYSTEM.spad" 2058788 2058797 2059550 2059555) (-1205 "SYSSOLP.spad" 2056271 2056282 2058778 2058783) (-1204 "SYSPTR.spad" 2056170 2056179 2056261 2056266) (-1203 "SYSNNI.spad" 2055352 2055363 2056160 2056165) (-1202 "SYSINT.spad" 2054756 2054767 2055342 2055347) (-1201 "SYNTAX.spad" 2050962 2050971 2054746 2054751) (-1200 "SYMTAB.spad" 2049030 2049039 2050952 2050957) (-1199 "SYMS.spad" 2045053 2045062 2049020 2049025) (-1198 "SYMPOLY.spad" 2044060 2044071 2044142 2044269) (-1197 "SYMFUNC.spad" 2043561 2043572 2044050 2044055) (-1196 "SYMBOL.spad" 2041064 2041073 2043551 2043556) (-1195 "SWITCH.spad" 2037835 2037844 2041054 2041059) (-1194 "SUTS.spad" 2034883 2034911 2036302 2036399) (-1193 "SUPXS.spad" 2032166 2032194 2033015 2033164) (-1192 "SUP.spad" 2028886 2028897 2029659 2029812) (-1191 "SUPFRACF.spad" 2027991 2028009 2028876 2028881) (-1190 "SUP2.spad" 2027383 2027396 2027981 2027986) (-1189 "SUMRF.spad" 2026357 2026368 2027373 2027378) (-1188 "SUMFS.spad" 2025994 2026011 2026347 2026352) (-1187 "SULS.spad" 2015765 2015793 2016723 2017152) (-1186 "SUCHTAST.spad" 2015534 2015543 2015755 2015760) (-1185 "SUCH.spad" 2015216 2015231 2015524 2015529) (-1184 "SUBSPACE.spad" 2007331 2007346 2015206 2015211) (-1183 "SUBRESP.spad" 2006501 2006515 2007287 2007292) (-1182 "STTF.spad" 2002600 2002616 2006491 2006496) (-1181 "STTFNC.spad" 1999068 1999084 2002590 2002595) (-1180 "STTAYLOR.spad" 1991703 1991714 1998949 1998954) (-1179 "STRTBL.spad" 1989754 1989771 1989903 1989930) (-1178 "STRING.spad" 1988541 1988550 1988762 1988789) (-1177 "STREAM.spad" 1985342 1985353 1987949 1987964) (-1176 "STREAM3.spad" 1984915 1984930 1985332 1985337) (-1175 "STREAM2.spad" 1984043 1984056 1984905 1984910) (-1174 "STREAM1.spad" 1983749 1983760 1984033 1984038) (-1173 "STINPROD.spad" 1982685 1982701 1983739 1983744) (-1172 "STEP.spad" 1981886 1981895 1982675 1982680) (-1171 "STEPAST.spad" 1981120 1981129 1981876 1981881) (-1170 "STBL.spad" 1979204 1979232 1979371 1979386) (-1169 "STAGG.spad" 1978279 1978290 1979194 1979199) (-1168 "STAGG.spad" 1977352 1977365 1978269 1978274) (-1167 "STACK.spad" 1976592 1976603 1976842 1976869) (-1166 "SREGSET.spad" 1974260 1974277 1976202 1976229) (-1165 "SRDCMPK.spad" 1972821 1972841 1974250 1974255) (-1164 "SRAGG.spad" 1967964 1967973 1972789 1972816) (-1163 "SRAGG.spad" 1963127 1963138 1967954 1967959) (-1162 "SQMATRIX.spad" 1960670 1960688 1961586 1961673) (-1161 "SPLTREE.spad" 1955066 1955079 1959950 1959977) (-1160 "SPLNODE.spad" 1951654 1951667 1955056 1955061) (-1159 "SPFCAT.spad" 1950463 1950472 1951644 1951649) (-1158 "SPECOUT.spad" 1949015 1949024 1950453 1950458) (-1157 "SPADXPT.spad" 1940610 1940619 1949005 1949010) (-1156 "spad-parser.spad" 1940075 1940084 1940600 1940605) (-1155 "SPADAST.spad" 1939776 1939785 1940065 1940070) (-1154 "SPACEC.spad" 1923975 1923986 1939766 1939771) (-1153 "SPACE3.spad" 1923751 1923762 1923965 1923970) (-1152 "SORTPAK.spad" 1923300 1923313 1923707 1923712) (-1151 "SOLVETRA.spad" 1921063 1921074 1923290 1923295) (-1150 "SOLVESER.spad" 1919591 1919602 1921053 1921058) (-1149 "SOLVERAD.spad" 1915617 1915628 1919581 1919586) (-1148 "SOLVEFOR.spad" 1914079 1914097 1915607 1915612) (-1147 "SNTSCAT.spad" 1913679 1913696 1914047 1914074) (-1146 "SMTS.spad" 1911951 1911977 1913244 1913341) (-1145 "SMP.spad" 1909426 1909446 1909816 1909943) (-1144 "SMITH.spad" 1908271 1908296 1909416 1909421) (-1143 "SMATCAT.spad" 1906381 1906411 1908215 1908266) (-1142 "SMATCAT.spad" 1904423 1904455 1906259 1906264) (-1141 "SKAGG.spad" 1903386 1903397 1904391 1904418) (-1140 "SINT.spad" 1902326 1902335 1903252 1903381) (-1139 "SIMPAN.spad" 1902054 1902063 1902316 1902321) (-1138 "SIG.spad" 1901384 1901393 1902044 1902049) (-1137 "SIGNRF.spad" 1900502 1900513 1901374 1901379) (-1136 "SIGNEF.spad" 1899781 1899798 1900492 1900497) (-1135 "SIGAST.spad" 1899166 1899175 1899771 1899776) (-1134 "SHP.spad" 1897094 1897109 1899122 1899127) (-1133 "SHDP.spad" 1884772 1884799 1885281 1885380) (-1132 "SGROUP.spad" 1884380 1884389 1884762 1884767) (-1131 "SGROUP.spad" 1883986 1883997 1884370 1884375) (-1130 "SGCF.spad" 1877125 1877134 1883976 1883981) (-1129 "SFRTCAT.spad" 1876055 1876072 1877093 1877120) (-1128 "SFRGCD.spad" 1875118 1875138 1876045 1876050) (-1127 "SFQCMPK.spad" 1869755 1869775 1875108 1875113) (-1126 "SFORT.spad" 1869194 1869208 1869745 1869750) (-1125 "SEXOF.spad" 1869037 1869077 1869184 1869189) (-1124 "SEX.spad" 1868929 1868938 1869027 1869032) (-1123 "SEXCAT.spad" 1866701 1866741 1868919 1868924) (-1122 "SET.spad" 1864989 1865000 1866086 1866125) (-1121 "SETMN.spad" 1863439 1863456 1864979 1864984) (-1120 "SETCAT.spad" 1862924 1862933 1863429 1863434) (-1119 "SETCAT.spad" 1862407 1862418 1862914 1862919) (-1118 "SETAGG.spad" 1858956 1858967 1862387 1862402) (-1117 "SETAGG.spad" 1855513 1855526 1858946 1858951) (-1116 "SEQAST.spad" 1855216 1855225 1855503 1855508) (-1115 "SEGXCAT.spad" 1854372 1854385 1855206 1855211) (-1114 "SEG.spad" 1854185 1854196 1854291 1854296) (-1113 "SEGCAT.spad" 1853110 1853121 1854175 1854180) (-1112 "SEGBIND.spad" 1852868 1852879 1853057 1853062) (-1111 "SEGBIND2.spad" 1852566 1852579 1852858 1852863) (-1110 "SEGAST.spad" 1852280 1852289 1852556 1852561) (-1109 "SEG2.spad" 1851715 1851728 1852236 1852241) (-1108 "SDVAR.spad" 1850991 1851002 1851705 1851710) (-1107 "SDPOL.spad" 1848324 1848335 1848615 1848742) (-1106 "SCPKG.spad" 1846413 1846424 1848314 1848319) (-1105 "SCOPE.spad" 1845566 1845575 1846403 1846408) (-1104 "SCACHE.spad" 1844262 1844273 1845556 1845561) (-1103 "SASTCAT.spad" 1844171 1844180 1844252 1844257) (-1102 "SAOS.spad" 1844043 1844052 1844161 1844166) (-1101 "SAERFFC.spad" 1843756 1843776 1844033 1844038) (-1100 "SAE.spad" 1841226 1841242 1841837 1841972) (-1099 "SAEFACT.spad" 1840927 1840947 1841216 1841221) (-1098 "RURPK.spad" 1838586 1838602 1840917 1840922) (-1097 "RULESET.spad" 1838039 1838063 1838576 1838581) (-1096 "RULE.spad" 1836279 1836303 1838029 1838034) (-1095 "RULECOLD.spad" 1836131 1836144 1836269 1836274) (-1094 "RTVALUE.spad" 1835866 1835875 1836121 1836126) (-1093 "RSTRCAST.spad" 1835583 1835592 1835856 1835861) (-1092 "RSETGCD.spad" 1831961 1831981 1835573 1835578) (-1091 "RSETCAT.spad" 1821897 1821914 1831929 1831956) (-1090 "RSETCAT.spad" 1811853 1811872 1821887 1821892) (-1089 "RSDCMPK.spad" 1810305 1810325 1811843 1811848) (-1088 "RRCC.spad" 1808689 1808719 1810295 1810300) (-1087 "RRCC.spad" 1807071 1807103 1808679 1808684) (-1086 "RPTAST.spad" 1806773 1806782 1807061 1807066) (-1085 "RPOLCAT.spad" 1786133 1786148 1806641 1806768) (-1084 "RPOLCAT.spad" 1765206 1765223 1785716 1785721) (-1083 "ROUTINE.spad" 1760627 1760636 1763391 1763418) (-1082 "ROMAN.spad" 1759955 1759964 1760493 1760622) (-1081 "ROIRC.spad" 1759035 1759067 1759945 1759950) (-1080 "RNS.spad" 1757938 1757947 1758937 1759030) (-1079 "RNS.spad" 1756927 1756938 1757928 1757933) (-1078 "RNG.spad" 1756662 1756671 1756917 1756922) (-1077 "RNGBIND.spad" 1755822 1755836 1756617 1756622) (-1076 "RMODULE.spad" 1755587 1755598 1755812 1755817) (-1075 "RMCAT2.spad" 1755007 1755064 1755577 1755582) (-1074 "RMATRIX.spad" 1753795 1753814 1754138 1754177) (-1073 "RMATCAT.spad" 1749374 1749405 1753751 1753790) (-1072 "RMATCAT.spad" 1744843 1744876 1749222 1749227) (-1071 "RLINSET.spad" 1744547 1744558 1744833 1744838) (-1070 "RINTERP.spad" 1744435 1744455 1744537 1744542) (-1069 "RING.spad" 1743905 1743914 1744415 1744430) (-1068 "RING.spad" 1743383 1743394 1743895 1743900) (-1067 "RIDIST.spad" 1742775 1742784 1743373 1743378) (-1066 "RGCHAIN.spad" 1741303 1741319 1742205 1742232) (-1065 "RGBCSPC.spad" 1741084 1741096 1741293 1741298) (-1064 "RGBCMDL.spad" 1740614 1740626 1741074 1741079) (-1063 "RF.spad" 1738256 1738267 1740604 1740609) (-1062 "RFFACTOR.spad" 1737718 1737729 1738246 1738251) (-1061 "RFFACT.spad" 1737453 1737465 1737708 1737713) (-1060 "RFDIST.spad" 1736449 1736458 1737443 1737448) (-1059 "RETSOL.spad" 1735868 1735881 1736439 1736444) (-1058 "RETRACT.spad" 1735296 1735307 1735858 1735863) (-1057 "RETRACT.spad" 1734722 1734735 1735286 1735291) (-1056 "RETAST.spad" 1734534 1734543 1734712 1734717) (-1055 "RESULT.spad" 1732132 1732141 1732719 1732746) (-1054 "RESRING.spad" 1731479 1731526 1732070 1732127) (-1053 "RESLATC.spad" 1730803 1730814 1731469 1731474) (-1052 "REPSQ.spad" 1730534 1730545 1730793 1730798) (-1051 "REP.spad" 1728088 1728097 1730524 1730529) (-1050 "REPDB.spad" 1727795 1727806 1728078 1728083) (-1049 "REP2.spad" 1717453 1717464 1727637 1727642) (-1048 "REP1.spad" 1711649 1711660 1717403 1717408) (-1047 "REGSET.spad" 1709410 1709427 1711259 1711286) (-1046 "REF.spad" 1708745 1708756 1709365 1709370) (-1045 "REDORDER.spad" 1707951 1707968 1708735 1708740) (-1044 "RECLOS.spad" 1706734 1706754 1707438 1707531) (-1043 "REALSOLV.spad" 1705874 1705883 1706724 1706729) (-1042 "REAL.spad" 1705746 1705755 1705864 1705869) (-1041 "REAL0Q.spad" 1703044 1703059 1705736 1705741) (-1040 "REAL0.spad" 1699888 1699903 1703034 1703039) (-1039 "RDUCEAST.spad" 1699609 1699618 1699878 1699883) (-1038 "RDIV.spad" 1699264 1699289 1699599 1699604) (-1037 "RDIST.spad" 1698831 1698842 1699254 1699259) (-1036 "RDETRS.spad" 1697695 1697713 1698821 1698826) (-1035 "RDETR.spad" 1695834 1695852 1697685 1697690) (-1034 "RDEEFS.spad" 1694933 1694950 1695824 1695829) (-1033 "RDEEF.spad" 1693943 1693960 1694923 1694928) (-1032 "RCFIELD.spad" 1691129 1691138 1693845 1693938) (-1031 "RCFIELD.spad" 1688401 1688412 1691119 1691124) (-1030 "RCAGG.spad" 1686329 1686340 1688391 1688396) (-1029 "RCAGG.spad" 1684184 1684197 1686248 1686253) (-1028 "RATRET.spad" 1683544 1683555 1684174 1684179) (-1027 "RATFACT.spad" 1683236 1683248 1683534 1683539) (-1026 "RANDSRC.spad" 1682555 1682564 1683226 1683231) (-1025 "RADUTIL.spad" 1682311 1682320 1682545 1682550) (-1024 "RADIX.spad" 1679135 1679149 1680681 1680774) (-1023 "RADFF.spad" 1676874 1676911 1676993 1677149) (-1022 "RADCAT.spad" 1676469 1676478 1676864 1676869) (-1021 "RADCAT.spad" 1676062 1676073 1676459 1676464) (-1020 "QUEUE.spad" 1675293 1675304 1675552 1675579) (-1019 "QUAT.spad" 1673781 1673792 1674124 1674189) (-1018 "QUATCT2.spad" 1673401 1673420 1673771 1673776) (-1017 "QUATCAT.spad" 1671571 1671582 1673331 1673396) (-1016 "QUATCAT.spad" 1669492 1669505 1671254 1671259) (-1015 "QUAGG.spad" 1668319 1668330 1669460 1669487) (-1014 "QQUTAST.spad" 1668087 1668096 1668309 1668314) (-1013 "QFORM.spad" 1667705 1667720 1668077 1668082) (-1012 "QFCAT.spad" 1666407 1666418 1667607 1667700) (-1011 "QFCAT.spad" 1664700 1664713 1665902 1665907) (-1010 "QFCAT2.spad" 1664392 1664409 1664690 1664695) (-1009 "QEQUAT.spad" 1663950 1663959 1664382 1664387) (-1008 "QCMPACK.spad" 1658696 1658716 1663940 1663945) (-1007 "QALGSET.spad" 1654774 1654807 1658610 1658615) (-1006 "QALGSET2.spad" 1652769 1652788 1654764 1654769) (-1005 "PWFFINTB.spad" 1650184 1650206 1652759 1652764) (-1004 "PUSHVAR.spad" 1649522 1649542 1650174 1650179) (-1003 "PTRANFN.spad" 1645649 1645660 1649512 1649517) (-1002 "PTPACK.spad" 1642736 1642747 1645639 1645644) (-1001 "PTFUNC2.spad" 1642558 1642573 1642726 1642731) (-1000 "PTCAT.spad" 1641812 1641823 1642526 1642553) (-999 "PSQFR.spad" 1641119 1641143 1641802 1641807) (-998 "PSEUDLIN.spad" 1640005 1640015 1641109 1641114) (-997 "PSETPK.spad" 1625438 1625454 1639883 1639888) (-996 "PSETCAT.spad" 1619358 1619381 1625418 1625433) (-995 "PSETCAT.spad" 1613252 1613277 1619314 1619319) (-994 "PSCURVE.spad" 1612235 1612243 1613242 1613247) (-993 "PSCAT.spad" 1611018 1611047 1612133 1612230) (-992 "PSCAT.spad" 1609891 1609922 1611008 1611013) (-991 "PRTITION.spad" 1608589 1608597 1609881 1609886) (-990 "PRTDAST.spad" 1608308 1608316 1608579 1608584) (-989 "PRS.spad" 1597870 1597887 1608264 1608269) (-988 "PRQAGG.spad" 1597305 1597315 1597838 1597865) (-987 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"FLAGG.spad" 615982 615992 618920 618935) (-383 "FLAGG.spad" 612925 612937 615865 615870) (-382 "FLAGG2.spad" 611650 611666 612915 612920) (-381 "FINRALG.spad" 609711 609724 611606 611645) (-380 "FINRALG.spad" 607698 607713 609595 609600) (-379 "FINITE.spad" 606850 606858 607688 607693) (-378 "FINAALG.spad" 595971 595981 606792 606845) (-377 "FINAALG.spad" 585104 585116 595927 595932) (-376 "FILE.spad" 584687 584697 585094 585099) (-375 "FILECAT.spad" 583213 583230 584677 584682) (-374 "FIELD.spad" 582619 582627 583115 583208) (-373 "FIELD.spad" 582111 582121 582609 582614) (-372 "FGROUP.spad" 580758 580768 582091 582106) (-371 "FGLMICPK.spad" 579545 579560 580748 580753) (-370 "FFX.spad" 578920 578935 579261 579354) (-369 "FFSLPE.spad" 578423 578444 578910 578915) (-368 "FFPOLY.spad" 569685 569696 578413 578418) (-367 "FFPOLY2.spad" 568745 568762 569675 569680) (-366 "FFP.spad" 568142 568162 568461 568554) (-365 "FF.spad" 567590 567606 567823 567916) (-364 "FFNBX.spad" 566102 566122 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"FCTRDATA.spad" 519867 519875 520849 520854) (-342 "FCPAK1.spad" 518434 518442 519857 519862) (-341 "FCOMP.spad" 517813 517823 518424 518429) (-340 "FC.spad" 507820 507828 517803 517808) (-339 "FAXF.spad" 500791 500805 507722 507815) (-338 "FAXF.spad" 493814 493830 500747 500752) (-337 "FARRAY.spad" 491811 491821 492844 492871) (-336 "FAMR.spad" 489947 489959 491709 491806) (-335 "FAMR.spad" 488067 488081 489831 489836) (-334 "FAMONOID.spad" 487735 487745 488021 488026) (-333 "FAMONC.spad" 486031 486043 487725 487730) (-332 "FAGROUP.spad" 485655 485665 485927 485954) (-331 "FACUTIL.spad" 483859 483876 485645 485650) (-330 "FACTFUNC.spad" 483053 483063 483849 483854) (-329 "EXPUPXS.spad" 479886 479909 481185 481334) (-328 "EXPRTUBE.spad" 477174 477182 479876 479881) (-327 "EXPRODE.spad" 474334 474350 477164 477169) (-326 "EXPR.spad" 469509 469519 470223 470518) (-325 "EXPR2UPS.spad" 465631 465644 469499 469504) (-324 "EXPR2.spad" 465336 465348 465621 465626) (-323 "EXPEXPAN.spad" 462137 462162 462769 462862) (-322 "EXIT.spad" 461808 461816 462127 462132) (-321 "EXITAST.spad" 461544 461552 461798 461803) (-320 "EVALCYC.spad" 461004 461018 461534 461539) (-319 "EVALAB.spad" 460576 460586 460994 460999) (-318 "EVALAB.spad" 460146 460158 460566 460571) (-317 "EUCDOM.spad" 457720 457728 460072 460141) (-316 "EUCDOM.spad" 455356 455366 457710 457715) (-315 "ESTOOLS.spad" 447202 447210 455346 455351) (-314 "ESTOOLS2.spad" 446805 446819 447192 447197) (-313 "ESTOOLS1.spad" 446490 446501 446795 446800) (-312 "ES.spad" 439305 439313 446480 446485) (-311 "ES.spad" 432026 432036 439203 439208) (-310 "ESCONT.spad" 428819 428827 432016 432021) (-309 "ESCONT1.spad" 428568 428580 428809 428814) (-308 "ES2.spad" 428073 428089 428558 428563) (-307 "ES1.spad" 427643 427659 428063 428068) (-306 "ERROR.spad" 424970 424978 427633 427638) (-305 "EQTBL.spad" 423000 423022 423209 423236) (-304 "EQ.spad" 417805 417815 420592 420704) (-303 "EQ2.spad" 417523 417535 417795 417800) (-302 "EP.spad" 413849 413859 417513 417518) (-301 "ENV.spad" 412527 412535 413839 413844) (-300 "ENTIRER.spad" 412195 412203 412471 412522) (-299 "EMR.spad" 411483 411524 412121 412190) (-298 "ELTAGG.spad" 409737 409756 411473 411478) (-297 "ELTAGG.spad" 407955 407976 409693 409698) (-296 "ELTAB.spad" 407430 407443 407945 407950) (-295 "ELFUTS.spad" 406817 406836 407420 407425) (-294 "ELEMFUN.spad" 406506 406514 406807 406812) (-293 "ELEMFUN.spad" 406193 406203 406496 406501) (-292 "ELAGG.spad" 404164 404174 406173 406188) (-291 "ELAGG.spad" 402072 402084 404083 404088) (-290 "ELABOR.spad" 401418 401426 402062 402067) (-289 "ELABEXPR.spad" 400350 400358 401408 401413) (-288 "EFUPXS.spad" 397126 397156 400306 400311) (-287 "EFULS.spad" 393962 393985 397082 397087) (-286 "EFSTRUC.spad" 391977 391993 393952 393957) (-285 "EF.spad" 386753 386769 391967 391972) (-284 "EAB.spad" 385029 385037 386743 386748) (-283 "E04UCFA.spad" 384565 384573 385019 385024) (-282 "E04NAFA.spad" 384142 384150 384555 384560) (-281 "E04MBFA.spad" 383722 383730 384132 384137) (-280 "E04JAFA.spad" 383258 383266 383712 383717) (-279 "E04GCFA.spad" 382794 382802 383248 383253) (-278 "E04FDFA.spad" 382330 382338 382784 382789) (-277 "E04DGFA.spad" 381866 381874 382320 382325) (-276 "E04AGNT.spad" 377716 377724 381856 381861) (-275 "DVARCAT.spad" 374606 374616 377706 377711) (-274 "DVARCAT.spad" 371494 371506 374596 374601) (-273 "DSMP.spad" 368868 368882 369173 369300) (-272 "DSEXT.spad" 368170 368180 368858 368863) (-271 "DSEXT.spad" 367379 367391 368069 368074) (-270 "DROPT.spad" 361338 361346 367369 367374) (-269 "DROPT1.spad" 361003 361013 361328 361333) (-268 "DROPT0.spad" 355860 355868 360993 360998) (-267 "DRAWPT.spad" 354033 354041 355850 355855) (-266 "DRAW.spad" 346909 346922 354023 354028) (-265 "DRAWHACK.spad" 346217 346227 346899 346904) (-264 "DRAWCX.spad" 343687 343695 346207 346212) (-263 "DRAWCURV.spad" 343234 343249 343677 343682) (-262 "DRAWCFUN.spad" 332766 332774 343224 343229) (-261 "DQAGG.spad" 330944 330954 332734 332761) (-260 "DPOLCAT.spad" 326293 326309 330812 330939) (-259 "DPOLCAT.spad" 321728 321746 326249 326254) (-258 "DPMO.spad" 313488 313504 313626 313839) (-257 "DPMM.spad" 305261 305279 305386 305599) (-256 "DOMTMPLT.spad" 305032 305040 305251 305256) (-255 "DOMCTOR.spad" 304787 304795 305022 305027) (-254 "DOMAIN.spad" 303874 303882 304777 304782) (-253 "DMP.spad" 301134 301149 301704 301831) (-252 "DMEXT.spad" 301001 301011 301102 301129) (-251 "DLP.spad" 300353 300363 300991 300996) (-250 "DLIST.spad" 298779 298789 299383 299410) (-249 "DLAGG.spad" 297196 297206 298769 298774) (-248 "DIVRING.spad" 296738 296746 297140 297191) (-247 "DIVRING.spad" 296324 296334 296728 296733) (-246 "DISPLAY.spad" 294514 294522 296314 296319) (-245 "DIRPROD.spad" 282061 282077 282701 282800) (-244 "DIRPROD2.spad" 280879 280897 282051 282056) (-243 "DIRPCAT.spad" 280072 280088 280775 280874) (-242 "DIRPCAT.spad" 278892 278910 279597 279602) (-241 "DIOSP.spad" 277717 277725 278882 278887) (-240 "DIOPS.spad" 276713 276723 277697 277712) (-239 "DIOPS.spad" 275683 275695 276669 276674) (-238 "DIFRING.spad" 275521 275529 275663 275678) (-237 "DIFFSPC.spad" 275100 275108 275511 275516) (-236 "DIFFSPC.spad" 274677 274687 275090 275095) (-235 "DIFFMOD.spad" 274166 274176 274645 274672) (-234 "DIFFDOM.spad" 273331 273342 274156 274161) (-233 "DIFFDOM.spad" 272494 272507 273321 273326) (-232 "DIFEXT.spad" 272313 272323 272474 272489) (-231 "DIAGG.spad" 271943 271953 272293 272308) (-230 "DIAGG.spad" 271581 271593 271933 271938) (-229 "DHMATRIX.spad" 269776 269786 270921 270948) (-228 "DFSFUN.spad" 263416 263424 269766 269771) (-227 "DFLOAT.spad" 260147 260155 263306 263411) (-226 "DFINTTLS.spad" 258378 258394 260137 260142) (-225 "DERHAM.spad" 256292 256324 258358 258373) (-224 "DEQUEUE.spad" 255499 255509 255782 255809) (-223 "DEGRED.spad" 255116 255130 255489 255494) (-222 "DEFINTRF.spad" 252653 252663 255106 255111) (-221 "DEFINTEF.spad" 251163 251179 252643 252648) (-220 "DEFAST.spad" 250531 250539 251153 251158) (-219 "DECIMAL.spad" 248540 248548 248901 248994) (-218 "DDFACT.spad" 246353 246370 248530 248535) (-217 "DBLRESP.spad" 245953 245977 246343 246348) (-216 "DBASE.spad" 244617 244627 245943 245948) (-215 "DATAARY.spad" 244079 244092 244607 244612) (-214 "D03FAFA.spad" 243907 243915 244069 244074) (-213 "D03EEFA.spad" 243727 243735 243897 243902) (-212 "D03AGNT.spad" 242813 242821 243717 243722) (-211 "D02EJFA.spad" 242275 242283 242803 242808) (-210 "D02CJFA.spad" 241753 241761 242265 242270) (-209 "D02BHFA.spad" 241243 241251 241743 241748) (-208 "D02BBFA.spad" 240733 240741 241233 241238) (-207 "D02AGNT.spad" 235547 235555 240723 240728) (-206 "D01WGTS.spad" 233866 233874 235537 235542) (-205 "D01TRNS.spad" 233843 233851 233856 233861) (-204 "D01GBFA.spad" 233365 233373 233833 233838) (-203 "D01FCFA.spad" 232887 232895 233355 233360) (-202 "D01ASFA.spad" 232355 232363 232877 232882) (-201 "D01AQFA.spad" 231801 231809 232345 232350) (-200 "D01APFA.spad" 231225 231233 231791 231796) (-199 "D01ANFA.spad" 230719 230727 231215 231220) (-198 "D01AMFA.spad" 230229 230237 230709 230714) (-197 "D01ALFA.spad" 229769 229777 230219 230224) (-196 "D01AKFA.spad" 229295 229303 229759 229764) (-195 "D01AJFA.spad" 228818 228826 229285 229290) (-194 "D01AGNT.spad" 224885 224893 228808 228813) (-193 "CYCLOTOM.spad" 224391 224399 224875 224880) (-192 "CYCLES.spad" 221183 221191 224381 224386) (-191 "CVMP.spad" 220600 220610 221173 221178) (-190 "CTRIGMNP.spad" 219100 219116 220590 220595) (-189 "CTOR.spad" 218791 218799 219090 219095) (-188 "CTORKIND.spad" 218394 218402 218781 218786) (-187 "CTORCAT.spad" 217643 217651 218384 218389) (-186 "CTORCAT.spad" 216890 216900 217633 217638) (-185 "CTORCALL.spad" 216479 216489 216880 216885) (-184 "CSTTOOLS.spad" 215724 215737 216469 216474) (-183 "CRFP.spad" 209448 209461 215714 215719) (-182 "CRCEAST.spad" 209168 209176 209438 209443) (-181 "CRAPACK.spad" 208219 208229 209158 209163) (-180 "CPMATCH.spad" 207723 207738 208144 208149) (-179 "CPIMA.spad" 207428 207447 207713 207718) (-178 "COORDSYS.spad" 202437 202447 207418 207423) (-177 "CONTOUR.spad" 201848 201856 202427 202432) (-176 "CONTFRAC.spad" 197598 197608 201750 201843) (-175 "CONDUIT.spad" 197356 197364 197588 197593) (-174 "COMRING.spad" 197030 197038 197294 197351) (-173 "COMPPROP.spad" 196548 196556 197020 197025) (-172 "COMPLPAT.spad" 196315 196330 196538 196543) (-171 "COMPLEX.spad" 191692 191702 191936 192197) (-170 "COMPLEX2.spad" 191407 191419 191682 191687) (-169 "COMPILER.spad" 190956 190964 191397 191402) (-168 "COMPFACT.spad" 190558 190572 190946 190951) (-167 "COMPCAT.spad" 188630 188640 190292 190553) (-166 "COMPCAT.spad" 186430 186442 188094 188099) (-165 "COMMUPC.spad" 186178 186196 186420 186425) (-164 "COMMONOP.spad" 185711 185719 186168 186173) (-163 "COMM.spad" 185522 185530 185701 185706) (-162 "COMMAAST.spad" 185285 185293 185512 185517) (-161 "COMBOPC.spad" 184200 184208 185275 185280) (-160 "COMBINAT.spad" 182967 182977 184190 184195) (-159 "COMBF.spad" 180349 180365 182957 182962) (-158 "COLOR.spad" 179186 179194 180339 180344) (-157 "COLONAST.spad" 178852 178860 179176 179181) (-156 "CMPLXRT.spad" 178563 178580 178842 178847) (-155 "CLLCTAST.spad" 178225 178233 178553 178558) (-154 "CLIP.spad" 174333 174341 178215 178220) (-153 "CLIF.spad" 172988 173004 174289 174328) (-152 "CLAGG.spad" 169493 169503 172978 172983) (-151 "CLAGG.spad" 165869 165881 169356 169361) (-150 "CINTSLPE.spad" 165200 165213 165859 165864) (-149 "CHVAR.spad" 163338 163360 165190 165195) (-148 "CHARZ.spad" 163253 163261 163318 163333) (-147 "CHARPOL.spad" 162763 162773 163243 163248) (-146 "CHARNZ.spad" 162516 162524 162743 162758) (-145 "CHAR.spad" 160390 160398 162506 162511) (-144 "CFCAT.spad" 159718 159726 160380 160385) (-143 "CDEN.spad" 158914 158928 159708 159713) (-142 "CCLASS.spad" 157025 157033 158287 158326) (-141 "CATEGORY.spad" 156067 156075 157015 157020) (-140 "CATCTOR.spad" 155958 155966 156057 156062) (-139 "CATAST.spad" 155576 155584 155948 155953) (-138 "CASEAST.spad" 155290 155298 155566 155571) (-137 "CARTEN.spad" 150657 150681 155280 155285) (-136 "CARTEN2.spad" 150047 150074 150647 150652) (-135 "CARD.spad" 147342 147350 150021 150042) (-134 "CAPSLAST.spad" 147116 147124 147332 147337) (-133 "CACHSET.spad" 146740 146748 147106 147111) (-132 "CABMON.spad" 146295 146303 146730 146735) (-131 "BYTEORD.spad" 145970 145978 146285 146290) (-130 "BYTE.spad" 145397 145405 145960 145965) (-129 "BYTEBUF.spad" 143095 143103 144405 144432) (-128 "BTREE.spad" 142051 142061 142585 142612) (-127 "BTOURN.spad" 140939 140949 141541 141568) (-126 "BTCAT.spad" 140331 140341 140907 140934) (-125 "BTCAT.spad" 139743 139755 140321 140326) (-124 "BTAGG.spad" 139209 139217 139711 139738) (-123 "BTAGG.spad" 138695 138705 139199 139204) (-122 "BSTREE.spad" 137319 137329 138185 138212) (-121 "BRILL.spad" 135516 135527 137309 137314) (-120 "BRAGG.spad" 134456 134466 135506 135511) (-119 "BRAGG.spad" 133360 133372 134412 134417) (-118 "BPADICRT.spad" 131234 131246 131489 131582) (-117 "BPADIC.spad" 130898 130910 131160 131229) (-116 "BOUNDZRO.spad" 130554 130571 130888 130893) (-115 "BOP.spad" 125736 125744 130544 130549) (-114 "BOP1.spad" 123202 123212 125726 125731) (-113 "BOOLE.spad" 122852 122860 123192 123197) (-112 "BOOLEAN.spad" 122290 122298 122842 122847) (-111 "BMODULE.spad" 122002 122014 122258 122285) (-110 "BITS.spad" 121385 121393 121600 121627) (-109 "BINDING.spad" 120798 120806 121375 121380) (-108 "BINARY.spad" 118812 118820 119168 119261) (-107 "BGAGG.spad" 118017 118027 118792 118807) (-106 "BGAGG.spad" 117230 117242 118007 118012) (-105 "BFUNCT.spad" 116794 116802 117210 117225) (-104 "BEZOUT.spad" 115934 115961 116744 116749) (-103 "BBTREE.spad" 112662 112672 115424 115451) (-102 "BASTYPE.spad" 112158 112166 112652 112657) (-101 "BASTYPE.spad" 111652 111662 112148 112153) (-100 "BALFACT.spad" 111111 111124 111642 111647) (-99 "AUTOMOR.spad" 110562 110571 111091 111106) (-98 "ATTREG.spad" 107285 107292 110314 110557) (-97 "ATTRBUT.spad" 103308 103315 107265 107280) (-96 "ATTRAST.spad" 103025 103032 103298 103303) (-95 "ATRIG.spad" 102495 102502 103015 103020) (-94 "ATRIG.spad" 101963 101972 102485 102490) (-93 "ASTCAT.spad" 101867 101874 101953 101958) (-92 "ASTCAT.spad" 101769 101778 101857 101862) (-91 "ASTACK.spad" 100991 101000 101259 101286) (-90 "ASSOCEQ.spad" 99817 99828 100947 100952) (-89 "ASP9.spad" 98898 98911 99807 99812) (-88 "ASP8.spad" 97941 97954 98888 98893) (-87 "ASP80.spad" 97263 97276 97931 97936) (-86 "ASP7.spad" 96423 96436 97253 97258) (-85 "ASP78.spad" 95874 95887 96413 96418) (-84 "ASP77.spad" 95243 95256 95864 95869) (-83 "ASP74.spad" 94335 94348 95233 95238) (-82 "ASP73.spad" 93606 93619 94325 94330) (-81 "ASP6.spad" 92473 92486 93596 93601) (-80 "ASP55.spad" 90982 90995 92463 92468) (-79 "ASP50.spad" 88799 88812 90972 90977) (-78 "ASP4.spad" 88094 88107 88789 88794) (-77 "ASP49.spad" 87093 87106 88084 88089) (-76 "ASP42.spad" 85500 85539 87083 87088) (-75 "ASP41.spad" 84079 84118 85490 85495) (-74 "ASP35.spad" 83067 83080 84069 84074) (-73 "ASP34.spad" 82368 82381 83057 83062) (-72 "ASP33.spad" 81928 81941 82358 82363) (-71 "ASP31.spad" 81068 81081 81918 81923) (-70 "ASP30.spad" 79960 79973 81058 81063) (-69 "ASP29.spad" 79426 79439 79950 79955) (-68 "ASP28.spad" 70699 70712 79416 79421) (-67 "ASP27.spad" 69596 69609 70689 70694) (-66 "ASP24.spad" 68683 68696 69586 69591) (-65 "ASP20.spad" 68147 68160 68673 68678) (-64 "ASP1.spad" 67528 67541 68137 68142) (-63 "ASP19.spad" 62214 62227 67518 67523) (-62 "ASP12.spad" 61628 61641 62204 62209) (-61 "ASP10.spad" 60899 60912 61618 61623) (-60 "ARRAY2.spad" 60142 60151 60389 60416) (-59 "ARRAY1.spad" 58826 58835 59172 59199) (-58 "ARRAY12.spad" 57539 57550 58816 58821) (-57 "ARR2CAT.spad" 53313 53334 57507 57534) (-56 "ARR2CAT.spad" 49107 49130 53303 53308) (-55 "ARITY.spad" 48479 48486 49097 49102) (-54 "APPRULE.spad" 47739 47761 48469 48474) (-53 "APPLYORE.spad" 47358 47371 47729 47734) (-52 "ANY.spad" 46217 46224 47348 47353) (-51 "ANY1.spad" 45288 45297 46207 46212) (-50 "ANTISYM.spad" 43733 43749 45268 45283) (-49 "ANON.spad" 43426 43433 43723 43728) (-48 "AN.spad" 41735 41742 43242 43335) (-47 "AMR.spad" 39920 39931 41633 41730) (-46 "AMR.spad" 37942 37955 39657 39662) (-45 "ALIST.spad" 34842 34863 35192 35219) (-44 "ALGSC.spad" 33977 34003 34714 34767) (-43 "ALGPKG.spad" 29760 29771 33933 33938) (-42 "ALGMFACT.spad" 28953 28967 29750 29755) (-41 "ALGMANIP.spad" 26427 26442 28786 28791) (-40 "ALGFF.spad" 24068 24095 24285 24441) (-39 "ALGFACT.spad" 23195 23205 24058 24063) (-38 "ALGEBRA.spad" 23028 23037 23151 23190) (-37 "ALGEBRA.spad" 22893 22904 23018 23023) (-36 "ALAGG.spad" 22405 22426 22861 22888) (-35 "AHYP.spad" 21786 21793 22395 22400) (-34 "AGG.spad" 20103 20110 21776 21781) (-33 "AGG.spad" 18384 18393 20059 20064) (-32 "AF.spad" 16815 16830 18319 18324) (-31 "ADDAST.spad" 16493 16500 16805 16810) (-30 "ACPLOT.spad" 15084 15091 16483 16488) (-29 "ACFS.spad" 12893 12902 14986 15079) (-28 "ACFS.spad" 10788 10799 12883 12888) (-27 "ACF.spad" 7470 7477 10690 10783) (-26 "ACF.spad" 4238 4247 7460 7465) (-25 "ABELSG.spad" 3779 3786 4228 4233) (-24 "ABELSG.spad" 3318 3327 3769 3774) (-23 "ABELMON.spad" 2861 2868 3308 3313) (-22 "ABELMON.spad" 2402 2411 2851 2856) (-21 "ABELGRP.spad" 2067 2074 2392 2397) (-20 "ABELGRP.spad" 1730 1739 2057 2062) (-19 "A1AGG.spad" 870 879 1698 1725) (-18 "A1AGG.spad" 30 41 860 865))
\ No newline at end of file +((-3 NIL 2293737 2293742 2293747 2293752) (-2 NIL 2293717 2293722 2293727 2293732) (-1 NIL 2293697 2293702 2293707 2293712) (0 NIL 2293677 2293682 2293687 2293692) (-1317 "ZMOD.spad" 2293486 2293499 2293615 2293672) (-1316 "ZLINDEP.spad" 2292552 2292563 2293476 2293481) (-1315 "ZDSOLVE.spad" 2282497 2282519 2292542 2292547) (-1314 "YSTREAM.spad" 2281992 2282003 2282487 2282492) (-1313 "YDIAGRAM.spad" 2281626 2281635 2281982 2281987) (-1312 "XRPOLY.spad" 2280846 2280866 2281482 2281551) (-1311 "XPR.spad" 2278641 2278654 2280564 2280663) (-1310 "XPOLY.spad" 2278196 2278207 2278497 2278566) (-1309 "XPOLYC.spad" 2277515 2277531 2278122 2278191) (-1308 "XPBWPOLY.spad" 2275952 2275972 2277295 2277364) (-1307 "XF.spad" 2274415 2274430 2275854 2275947) (-1306 "XF.spad" 2272858 2272875 2274299 2274304) (-1305 "XFALG.spad" 2269906 2269922 2272784 2272853) (-1304 "XEXPPKG.spad" 2269157 2269183 2269896 2269901) (-1303 "XDPOLY.spad" 2268771 2268787 2269013 2269082) (-1302 "XALG.spad" 2268431 2268442 2268727 2268766) (-1301 "WUTSET.spad" 2264234 2264251 2268041 2268068) (-1300 "WP.spad" 2263433 2263477 2264092 2264159) (-1299 "WHILEAST.spad" 2263231 2263240 2263423 2263428) (-1298 "WHEREAST.spad" 2262902 2262911 2263221 2263226) (-1297 "WFFINTBS.spad" 2260565 2260587 2262892 2262897) (-1296 "WEIER.spad" 2258787 2258798 2260555 2260560) (-1295 "VSPACE.spad" 2258460 2258471 2258755 2258782) (-1294 "VSPACE.spad" 2258153 2258166 2258450 2258455) (-1293 "VOID.spad" 2257830 2257839 2258143 2258148) (-1292 "VIEW.spad" 2255510 2255519 2257820 2257825) (-1291 "VIEWDEF.spad" 2250711 2250720 2255500 2255505) (-1290 "VIEW3D.spad" 2234672 2234681 2250701 2250706) (-1289 "VIEW2D.spad" 2222563 2222572 2234662 2234667) (-1288 "VECTOR.spad" 2221084 2221095 2221335 2221362) (-1287 "VECTOR2.spad" 2219723 2219736 2221074 2221079) (-1286 "VECTCAT.spad" 2217627 2217638 2219691 2219718) (-1285 "VECTCAT.spad" 2215338 2215351 2217404 2217409) (-1284 "VARIABLE.spad" 2215118 2215133 2215328 2215333) (-1283 "UTYPE.spad" 2214762 2214771 2215108 2215113) (-1282 "UTSODETL.spad" 2214057 2214081 2214718 2214723) (-1281 "UTSODE.spad" 2212273 2212293 2214047 2214052) (-1280 "UTS.spad" 2207220 2207248 2210740 2210837) (-1279 "UTSCAT.spad" 2204699 2204715 2207118 2207215) (-1278 "UTSCAT.spad" 2201822 2201840 2204243 2204248) (-1277 "UTS2.spad" 2201417 2201452 2201812 2201817) (-1276 "URAGG.spad" 2196090 2196101 2201407 2201412) (-1275 "URAGG.spad" 2190727 2190740 2196046 2196051) (-1274 "UPXSSING.spad" 2188372 2188398 2189808 2189941) (-1273 "UPXS.spad" 2185668 2185696 2186504 2186653) (-1272 "UPXSCONS.spad" 2183427 2183447 2183800 2183949) (-1271 "UPXSCCA.spad" 2181998 2182018 2183273 2183422) (-1270 "UPXSCCA.spad" 2180711 2180733 2181988 2181993) (-1269 "UPXSCAT.spad" 2179300 2179316 2180557 2180706) (-1268 "UPXS2.spad" 2178843 2178896 2179290 2179295) (-1267 "UPSQFREE.spad" 2177257 2177271 2178833 2178838) (-1266 "UPSCAT.spad" 2175044 2175068 2177155 2177252) (-1265 "UPSCAT.spad" 2172537 2172563 2174650 2174655) (-1264 "UPOLYC.spad" 2167577 2167588 2172379 2172532) (-1263 "UPOLYC.spad" 2162509 2162522 2167313 2167318) (-1262 "UPOLYC2.spad" 2161980 2161999 2162499 2162504) (-1261 "UP.spad" 2159086 2159101 2159473 2159626) (-1260 "UPMP.spad" 2157986 2157999 2159076 2159081) (-1259 "UPDIVP.spad" 2157551 2157565 2157976 2157981) (-1258 "UPDECOMP.spad" 2155796 2155810 2157541 2157546) (-1257 "UPCDEN.spad" 2155005 2155021 2155786 2155791) (-1256 "UP2.spad" 2154369 2154390 2154995 2155000) (-1255 "UNISEG.spad" 2153722 2153733 2154288 2154293) (-1254 "UNISEG2.spad" 2153219 2153232 2153678 2153683) (-1253 "UNIFACT.spad" 2152322 2152334 2153209 2153214) (-1252 "ULS.spad" 2142106 2142134 2143051 2143480) (-1251 "ULSCONS.spad" 2133240 2133260 2133610 2133759) (-1250 "ULSCCAT.spad" 2130977 2130997 2133086 2133235) (-1249 "ULSCCAT.spad" 2128822 2128844 2130933 2130938) (-1248 "ULSCAT.spad" 2127054 2127070 2128668 2128817) (-1247 "ULS2.spad" 2126568 2126621 2127044 2127049) (-1246 "UINT8.spad" 2126445 2126454 2126558 2126563) (-1245 "UINT64.spad" 2126321 2126330 2126435 2126440) (-1244 "UINT32.spad" 2126197 2126206 2126311 2126316) (-1243 "UINT16.spad" 2126073 2126082 2126187 2126192) (-1242 "UFD.spad" 2125138 2125147 2125999 2126068) (-1241 "UFD.spad" 2124265 2124276 2125128 2125133) (-1240 "UDVO.spad" 2123146 2123155 2124255 2124260) (-1239 "UDPO.spad" 2120639 2120650 2123102 2123107) (-1238 "TYPE.spad" 2120571 2120580 2120629 2120634) (-1237 "TYPEAST.spad" 2120490 2120499 2120561 2120566) (-1236 "TWOFACT.spad" 2119142 2119157 2120480 2120485) (-1235 "TUPLE.spad" 2118628 2118639 2119041 2119046) (-1234 "TUBETOOL.spad" 2115495 2115504 2118618 2118623) (-1233 "TUBE.spad" 2114142 2114159 2115485 2115490) (-1232 "TS.spad" 2112741 2112757 2113707 2113804) (-1231 "TSETCAT.spad" 2099868 2099885 2112709 2112736) (-1230 "TSETCAT.spad" 2086981 2087000 2099824 2099829) (-1229 "TRMANIP.spad" 2081347 2081364 2086687 2086692) (-1228 "TRIMAT.spad" 2080310 2080335 2081337 2081342) (-1227 "TRIGMNIP.spad" 2078837 2078854 2080300 2080305) (-1226 "TRIGCAT.spad" 2078349 2078358 2078827 2078832) (-1225 "TRIGCAT.spad" 2077859 2077870 2078339 2078344) (-1224 "TREE.spad" 2076317 2076328 2077349 2077376) (-1223 "TRANFUN.spad" 2076156 2076165 2076307 2076312) (-1222 "TRANFUN.spad" 2075993 2076004 2076146 2076151) (-1221 "TOPSP.spad" 2075667 2075676 2075983 2075988) (-1220 "TOOLSIGN.spad" 2075330 2075341 2075657 2075662) (-1219 "TEXTFILE.spad" 2073891 2073900 2075320 2075325) (-1218 "TEX.spad" 2071037 2071046 2073881 2073886) (-1217 "TEX1.spad" 2070593 2070604 2071027 2071032) (-1216 "TEMUTL.spad" 2070148 2070157 2070583 2070588) (-1215 "TBCMPPK.spad" 2068241 2068264 2070138 2070143) (-1214 "TBAGG.spad" 2067291 2067314 2068221 2068236) (-1213 "TBAGG.spad" 2066349 2066374 2067281 2067286) (-1212 "TANEXP.spad" 2065757 2065768 2066339 2066344) (-1211 "TALGOP.spad" 2065481 2065492 2065747 2065752) (-1210 "TABLE.spad" 2063450 2063473 2063720 2063747) (-1209 "TABLEAU.spad" 2062931 2062942 2063440 2063445) (-1208 "TABLBUMP.spad" 2059734 2059745 2062921 2062926) (-1207 "SYSTEM.spad" 2058962 2058971 2059724 2059729) (-1206 "SYSSOLP.spad" 2056445 2056456 2058952 2058957) (-1205 "SYSPTR.spad" 2056344 2056353 2056435 2056440) (-1204 "SYSNNI.spad" 2055526 2055537 2056334 2056339) (-1203 "SYSINT.spad" 2054930 2054941 2055516 2055521) (-1202 "SYNTAX.spad" 2051136 2051145 2054920 2054925) (-1201 "SYMTAB.spad" 2049204 2049213 2051126 2051131) (-1200 "SYMS.spad" 2045227 2045236 2049194 2049199) (-1199 "SYMPOLY.spad" 2044234 2044245 2044316 2044443) (-1198 "SYMFUNC.spad" 2043735 2043746 2044224 2044229) (-1197 "SYMBOL.spad" 2041238 2041247 2043725 2043730) (-1196 "SWITCH.spad" 2038009 2038018 2041228 2041233) (-1195 "SUTS.spad" 2035057 2035085 2036476 2036573) (-1194 "SUPXS.spad" 2032340 2032368 2033189 2033338) (-1193 "SUP.spad" 2029060 2029071 2029833 2029986) (-1192 "SUPFRACF.spad" 2028165 2028183 2029050 2029055) (-1191 "SUP2.spad" 2027557 2027570 2028155 2028160) (-1190 "SUMRF.spad" 2026531 2026542 2027547 2027552) (-1189 "SUMFS.spad" 2026168 2026185 2026521 2026526) (-1188 "SULS.spad" 2015939 2015967 2016897 2017326) (-1187 "SUCHTAST.spad" 2015708 2015717 2015929 2015934) (-1186 "SUCH.spad" 2015390 2015405 2015698 2015703) (-1185 "SUBSPACE.spad" 2007505 2007520 2015380 2015385) (-1184 "SUBRESP.spad" 2006675 2006689 2007461 2007466) (-1183 "STTF.spad" 2002774 2002790 2006665 2006670) (-1182 "STTFNC.spad" 1999242 1999258 2002764 2002769) (-1181 "STTAYLOR.spad" 1991877 1991888 1999123 1999128) (-1180 "STRTBL.spad" 1989928 1989945 1990077 1990104) (-1179 "STRING.spad" 1988715 1988724 1988936 1988963) (-1178 "STREAM.spad" 1985516 1985527 1988123 1988138) (-1177 "STREAM3.spad" 1985089 1985104 1985506 1985511) (-1176 "STREAM2.spad" 1984217 1984230 1985079 1985084) (-1175 "STREAM1.spad" 1983923 1983934 1984207 1984212) (-1174 "STINPROD.spad" 1982859 1982875 1983913 1983918) (-1173 "STEP.spad" 1982060 1982069 1982849 1982854) (-1172 "STEPAST.spad" 1981294 1981303 1982050 1982055) (-1171 "STBL.spad" 1979378 1979406 1979545 1979560) (-1170 "STAGG.spad" 1978453 1978464 1979368 1979373) (-1169 "STAGG.spad" 1977526 1977539 1978443 1978448) (-1168 "STACK.spad" 1976766 1976777 1977016 1977043) (-1167 "SREGSET.spad" 1974434 1974451 1976376 1976403) (-1166 "SRDCMPK.spad" 1972995 1973015 1974424 1974429) (-1165 "SRAGG.spad" 1968138 1968147 1972963 1972990) (-1164 "SRAGG.spad" 1963301 1963312 1968128 1968133) (-1163 "SQMATRIX.spad" 1960844 1960862 1961760 1961847) (-1162 "SPLTREE.spad" 1955240 1955253 1960124 1960151) (-1161 "SPLNODE.spad" 1951828 1951841 1955230 1955235) (-1160 "SPFCAT.spad" 1950637 1950646 1951818 1951823) (-1159 "SPECOUT.spad" 1949189 1949198 1950627 1950632) (-1158 "SPADXPT.spad" 1940784 1940793 1949179 1949184) (-1157 "spad-parser.spad" 1940249 1940258 1940774 1940779) (-1156 "SPADAST.spad" 1939950 1939959 1940239 1940244) (-1155 "SPACEC.spad" 1924149 1924160 1939940 1939945) (-1154 "SPACE3.spad" 1923925 1923936 1924139 1924144) (-1153 "SORTPAK.spad" 1923474 1923487 1923881 1923886) (-1152 "SOLVETRA.spad" 1921237 1921248 1923464 1923469) (-1151 "SOLVESER.spad" 1919765 1919776 1921227 1921232) (-1150 "SOLVERAD.spad" 1915791 1915802 1919755 1919760) (-1149 "SOLVEFOR.spad" 1914253 1914271 1915781 1915786) (-1148 "SNTSCAT.spad" 1913853 1913870 1914221 1914248) (-1147 "SMTS.spad" 1912125 1912151 1913418 1913515) (-1146 "SMP.spad" 1909600 1909620 1909990 1910117) (-1145 "SMITH.spad" 1908445 1908470 1909590 1909595) (-1144 "SMATCAT.spad" 1906555 1906585 1908389 1908440) (-1143 "SMATCAT.spad" 1904597 1904629 1906433 1906438) (-1142 "SKAGG.spad" 1903560 1903571 1904565 1904592) (-1141 "SINT.spad" 1902500 1902509 1903426 1903555) (-1140 "SIMPAN.spad" 1902228 1902237 1902490 1902495) (-1139 "SIG.spad" 1901558 1901567 1902218 1902223) (-1138 "SIGNRF.spad" 1900676 1900687 1901548 1901553) (-1137 "SIGNEF.spad" 1899955 1899972 1900666 1900671) (-1136 "SIGAST.spad" 1899340 1899349 1899945 1899950) (-1135 "SHP.spad" 1897268 1897283 1899296 1899301) (-1134 "SHDP.spad" 1884946 1884973 1885455 1885554) (-1133 "SGROUP.spad" 1884554 1884563 1884936 1884941) (-1132 "SGROUP.spad" 1884160 1884171 1884544 1884549) (-1131 "SGCF.spad" 1877299 1877308 1884150 1884155) (-1130 "SFRTCAT.spad" 1876229 1876246 1877267 1877294) (-1129 "SFRGCD.spad" 1875292 1875312 1876219 1876224) (-1128 "SFQCMPK.spad" 1869929 1869949 1875282 1875287) (-1127 "SFORT.spad" 1869368 1869382 1869919 1869924) (-1126 "SEXOF.spad" 1869211 1869251 1869358 1869363) (-1125 "SEX.spad" 1869103 1869112 1869201 1869206) (-1124 "SEXCAT.spad" 1866875 1866915 1869093 1869098) (-1123 "SET.spad" 1865163 1865174 1866260 1866299) (-1122 "SETMN.spad" 1863613 1863630 1865153 1865158) (-1121 "SETCAT.spad" 1863098 1863107 1863603 1863608) (-1120 "SETCAT.spad" 1862581 1862592 1863088 1863093) (-1119 "SETAGG.spad" 1859130 1859141 1862561 1862576) (-1118 "SETAGG.spad" 1855687 1855700 1859120 1859125) (-1117 "SEQAST.spad" 1855390 1855399 1855677 1855682) (-1116 "SEGXCAT.spad" 1854546 1854559 1855380 1855385) (-1115 "SEG.spad" 1854359 1854370 1854465 1854470) (-1114 "SEGCAT.spad" 1853284 1853295 1854349 1854354) (-1113 "SEGBIND.spad" 1853042 1853053 1853231 1853236) (-1112 "SEGBIND2.spad" 1852740 1852753 1853032 1853037) (-1111 "SEGAST.spad" 1852454 1852463 1852730 1852735) (-1110 "SEG2.spad" 1851889 1851902 1852410 1852415) (-1109 "SDVAR.spad" 1851165 1851176 1851879 1851884) (-1108 "SDPOL.spad" 1848498 1848509 1848789 1848916) (-1107 "SCPKG.spad" 1846587 1846598 1848488 1848493) (-1106 "SCOPE.spad" 1845740 1845749 1846577 1846582) (-1105 "SCACHE.spad" 1844436 1844447 1845730 1845735) (-1104 "SASTCAT.spad" 1844345 1844354 1844426 1844431) (-1103 "SAOS.spad" 1844217 1844226 1844335 1844340) (-1102 "SAERFFC.spad" 1843930 1843950 1844207 1844212) (-1101 "SAE.spad" 1841400 1841416 1842011 1842146) (-1100 "SAEFACT.spad" 1841101 1841121 1841390 1841395) (-1099 "RURPK.spad" 1838760 1838776 1841091 1841096) (-1098 "RULESET.spad" 1838213 1838237 1838750 1838755) (-1097 "RULE.spad" 1836453 1836477 1838203 1838208) (-1096 "RULECOLD.spad" 1836305 1836318 1836443 1836448) (-1095 "RTVALUE.spad" 1836040 1836049 1836295 1836300) (-1094 "RSTRCAST.spad" 1835757 1835766 1836030 1836035) (-1093 "RSETGCD.spad" 1832135 1832155 1835747 1835752) (-1092 "RSETCAT.spad" 1822071 1822088 1832103 1832130) (-1091 "RSETCAT.spad" 1812027 1812046 1822061 1822066) (-1090 "RSDCMPK.spad" 1810479 1810499 1812017 1812022) (-1089 "RRCC.spad" 1808863 1808893 1810469 1810474) (-1088 "RRCC.spad" 1807245 1807277 1808853 1808858) (-1087 "RPTAST.spad" 1806947 1806956 1807235 1807240) (-1086 "RPOLCAT.spad" 1786307 1786322 1806815 1806942) (-1085 "RPOLCAT.spad" 1765380 1765397 1785890 1785895) (-1084 "ROUTINE.spad" 1760801 1760810 1763565 1763592) (-1083 "ROMAN.spad" 1760129 1760138 1760667 1760796) (-1082 "ROIRC.spad" 1759209 1759241 1760119 1760124) (-1081 "RNS.spad" 1758112 1758121 1759111 1759204) (-1080 "RNS.spad" 1757101 1757112 1758102 1758107) (-1079 "RNG.spad" 1756836 1756845 1757091 1757096) (-1078 "RNGBIND.spad" 1755996 1756010 1756791 1756796) (-1077 "RMODULE.spad" 1755761 1755772 1755986 1755991) (-1076 "RMCAT2.spad" 1755181 1755238 1755751 1755756) (-1075 "RMATRIX.spad" 1753969 1753988 1754312 1754351) (-1074 "RMATCAT.spad" 1749548 1749579 1753925 1753964) (-1073 "RMATCAT.spad" 1745017 1745050 1749396 1749401) (-1072 "RLINSET.spad" 1744721 1744732 1745007 1745012) (-1071 "RINTERP.spad" 1744609 1744629 1744711 1744716) (-1070 "RING.spad" 1744079 1744088 1744589 1744604) (-1069 "RING.spad" 1743557 1743568 1744069 1744074) (-1068 "RIDIST.spad" 1742949 1742958 1743547 1743552) (-1067 "RGCHAIN.spad" 1741477 1741493 1742379 1742406) (-1066 "RGBCSPC.spad" 1741258 1741270 1741467 1741472) (-1065 "RGBCMDL.spad" 1740788 1740800 1741248 1741253) (-1064 "RF.spad" 1738430 1738441 1740778 1740783) (-1063 "RFFACTOR.spad" 1737892 1737903 1738420 1738425) (-1062 "RFFACT.spad" 1737627 1737639 1737882 1737887) (-1061 "RFDIST.spad" 1736623 1736632 1737617 1737622) (-1060 "RETSOL.spad" 1736042 1736055 1736613 1736618) (-1059 "RETRACT.spad" 1735470 1735481 1736032 1736037) (-1058 "RETRACT.spad" 1734896 1734909 1735460 1735465) (-1057 "RETAST.spad" 1734708 1734717 1734886 1734891) (-1056 "RESULT.spad" 1732306 1732315 1732893 1732920) (-1055 "RESRING.spad" 1731653 1731700 1732244 1732301) (-1054 "RESLATC.spad" 1730977 1730988 1731643 1731648) (-1053 "REPSQ.spad" 1730708 1730719 1730967 1730972) (-1052 "REP.spad" 1728262 1728271 1730698 1730703) (-1051 "REPDB.spad" 1727969 1727980 1728252 1728257) (-1050 "REP2.spad" 1717627 1717638 1727811 1727816) (-1049 "REP1.spad" 1711823 1711834 1717577 1717582) (-1048 "REGSET.spad" 1709584 1709601 1711433 1711460) (-1047 "REF.spad" 1708919 1708930 1709539 1709544) (-1046 "REDORDER.spad" 1708125 1708142 1708909 1708914) (-1045 "RECLOS.spad" 1706908 1706928 1707612 1707705) (-1044 "REALSOLV.spad" 1706048 1706057 1706898 1706903) (-1043 "REAL.spad" 1705920 1705929 1706038 1706043) (-1042 "REAL0Q.spad" 1703218 1703233 1705910 1705915) (-1041 "REAL0.spad" 1700062 1700077 1703208 1703213) (-1040 "RDUCEAST.spad" 1699783 1699792 1700052 1700057) (-1039 "RDIV.spad" 1699438 1699463 1699773 1699778) (-1038 "RDIST.spad" 1699005 1699016 1699428 1699433) (-1037 "RDETRS.spad" 1697869 1697887 1698995 1699000) (-1036 "RDETR.spad" 1696008 1696026 1697859 1697864) (-1035 "RDEEFS.spad" 1695107 1695124 1695998 1696003) (-1034 "RDEEF.spad" 1694117 1694134 1695097 1695102) (-1033 "RCFIELD.spad" 1691303 1691312 1694019 1694112) (-1032 "RCFIELD.spad" 1688575 1688586 1691293 1691298) (-1031 "RCAGG.spad" 1686503 1686514 1688565 1688570) (-1030 "RCAGG.spad" 1684358 1684371 1686422 1686427) (-1029 "RATRET.spad" 1683718 1683729 1684348 1684353) (-1028 "RATFACT.spad" 1683410 1683422 1683708 1683713) (-1027 "RANDSRC.spad" 1682729 1682738 1683400 1683405) (-1026 "RADUTIL.spad" 1682485 1682494 1682719 1682724) (-1025 "RADIX.spad" 1679309 1679323 1680855 1680948) (-1024 "RADFF.spad" 1677048 1677085 1677167 1677323) (-1023 "RADCAT.spad" 1676643 1676652 1677038 1677043) (-1022 "RADCAT.spad" 1676236 1676247 1676633 1676638) (-1021 "QUEUE.spad" 1675467 1675478 1675726 1675753) (-1020 "QUAT.spad" 1673955 1673966 1674298 1674363) (-1019 "QUATCT2.spad" 1673575 1673594 1673945 1673950) (-1018 "QUATCAT.spad" 1671745 1671756 1673505 1673570) (-1017 "QUATCAT.spad" 1669666 1669679 1671428 1671433) (-1016 "QUAGG.spad" 1668493 1668504 1669634 1669661) (-1015 "QQUTAST.spad" 1668261 1668270 1668483 1668488) (-1014 "QFORM.spad" 1667879 1667894 1668251 1668256) (-1013 "QFCAT.spad" 1666581 1666592 1667781 1667874) (-1012 "QFCAT.spad" 1664874 1664887 1666076 1666081) (-1011 "QFCAT2.spad" 1664566 1664583 1664864 1664869) (-1010 "QEQUAT.spad" 1664124 1664133 1664556 1664561) (-1009 "QCMPACK.spad" 1658870 1658890 1664114 1664119) (-1008 "QALGSET.spad" 1654948 1654981 1658784 1658789) (-1007 "QALGSET2.spad" 1652943 1652962 1654938 1654943) (-1006 "PWFFINTB.spad" 1650358 1650380 1652933 1652938) (-1005 "PUSHVAR.spad" 1649696 1649716 1650348 1650353) (-1004 "PTRANFN.spad" 1645823 1645834 1649686 1649691) (-1003 "PTPACK.spad" 1642910 1642921 1645813 1645818) (-1002 "PTFUNC2.spad" 1642732 1642747 1642900 1642905) (-1001 "PTCAT.spad" 1641986 1641997 1642700 1642727) (-1000 "PSQFR.spad" 1641292 1641317 1641976 1641981) (-999 "PSEUDLIN.spad" 1640178 1640188 1641282 1641287) (-998 "PSETPK.spad" 1625611 1625627 1640056 1640061) (-997 "PSETCAT.spad" 1619531 1619554 1625591 1625606) (-996 "PSETCAT.spad" 1613425 1613450 1619487 1619492) (-995 "PSCURVE.spad" 1612408 1612416 1613415 1613420) (-994 "PSCAT.spad" 1611191 1611220 1612306 1612403) (-993 "PSCAT.spad" 1610064 1610095 1611181 1611186) (-992 "PRTITION.spad" 1608762 1608770 1610054 1610059) (-991 "PRTDAST.spad" 1608481 1608489 1608752 1608757) (-990 "PRS.spad" 1598043 1598060 1608437 1608442) (-989 "PRQAGG.spad" 1597478 1597488 1598011 1598038) (-988 "PROPLOG.spad" 1597050 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1433001) (-875 "OUTBFILE.spad" 1421816 1421824 1422388 1422393) (-874 "OUTBCON.spad" 1420822 1420830 1421806 1421811) (-873 "OUTBCON.spad" 1419826 1419836 1420812 1420817) (-872 "OSI.spad" 1419301 1419309 1419816 1419821) (-871 "OSGROUP.spad" 1419219 1419227 1419291 1419296) (-870 "ORTHPOL.spad" 1417704 1417714 1419136 1419141) (-869 "OREUP.spad" 1417157 1417185 1417384 1417423) (-868 "ORESUP.spad" 1416458 1416482 1416837 1416876) (-867 "OREPCTO.spad" 1414315 1414327 1416378 1416383) (-866 "OREPCAT.spad" 1408462 1408472 1414271 1414310) (-865 "OREPCAT.spad" 1402499 1402511 1408310 1408315) (-864 "ORDTYPE.spad" 1401736 1401744 1402489 1402494) (-863 "ORDTYPE.spad" 1400971 1400981 1401726 1401731) (-862 "ORDSTRCT.spad" 1400798 1400813 1400961 1400966) (-861 "ORDSET.spad" 1400498 1400506 1400788 1400793) (-860 "ORDRING.spad" 1399888 1399896 1400478 1400493) (-859 "ORDRING.spad" 1399286 1399296 1399878 1399883) (-858 "ORDMON.spad" 1399141 1399149 1399276 1399281) (-857 "ORDFUNS.spad" 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"OMEXPR.spad" 1376263 1376273 1376419 1376424) (-837 "OMERR.spad" 1375808 1375816 1376253 1376258) (-836 "OMERRK.spad" 1374842 1374850 1375798 1375803) (-835 "OMENC.spad" 1374186 1374194 1374832 1374837) (-834 "OMDEV.spad" 1368495 1368503 1374176 1374181) (-833 "OMCONN.spad" 1367904 1367912 1368485 1368490) (-832 "OINTDOM.spad" 1367667 1367675 1367830 1367899) (-831 "OFMONOID.spad" 1365790 1365800 1367623 1367628) (-830 "ODVAR.spad" 1365051 1365061 1365780 1365785) (-829 "ODR.spad" 1364695 1364721 1364863 1365012) (-828 "ODPOL.spad" 1361984 1361994 1362324 1362451) (-827 "ODP.spad" 1349798 1349818 1350171 1350270) (-826 "ODETOOLS.spad" 1348447 1348466 1349788 1349793) (-825 "ODESYS.spad" 1346141 1346158 1348437 1348442) (-824 "ODERTRIC.spad" 1342150 1342167 1346098 1346103) (-823 "ODERED.spad" 1341549 1341573 1342140 1342145) (-822 "ODERAT.spad" 1339164 1339181 1341539 1341544) (-821 "ODEPRRIC.spad" 1336201 1336223 1339154 1339159) (-820 "ODEPROB.spad" 1335458 1335466 1336191 1336196) (-819 "ODEPRIM.spad" 1332792 1332814 1335448 1335453) (-818 "ODEPAL.spad" 1332178 1332202 1332782 1332787) (-817 "ODEPACK.spad" 1318844 1318852 1332168 1332173) (-816 "ODEINT.spad" 1318279 1318295 1318834 1318839) (-815 "ODEIFTBL.spad" 1315674 1315682 1318269 1318274) (-814 "ODEEF.spad" 1311165 1311181 1315664 1315669) (-813 "ODECONST.spad" 1310702 1310720 1311155 1311160) (-812 "ODECAT.spad" 1309300 1309308 1310692 1310697) (-811 "OCT.spad" 1307436 1307446 1308150 1308189) (-810 "OCTCT2.spad" 1307082 1307103 1307426 1307431) (-809 "OC.spad" 1304878 1304888 1307038 1307077) (-808 "OC.spad" 1302399 1302411 1304561 1304566) (-807 "OCAMON.spad" 1302247 1302255 1302389 1302394) (-806 "OASGP.spad" 1302062 1302070 1302237 1302242) (-805 "OAMONS.spad" 1301584 1301592 1302052 1302057) (-804 "OAMON.spad" 1301445 1301453 1301574 1301579) (-803 "OAGROUP.spad" 1301307 1301315 1301435 1301440) (-802 "NUMTUBE.spad" 1300898 1300914 1301297 1301302) (-801 "NUMQUAD.spad" 1288874 1288882 1300888 1300893) (-800 "NUMODE.spad" 1280228 1280236 1288864 1288869) (-799 "NUMINT.spad" 1277794 1277802 1280218 1280223) (-798 "NUMFMT.spad" 1276634 1276642 1277784 1277789) (-797 "NUMERIC.spad" 1268748 1268758 1276439 1276444) (-796 "NTSCAT.spad" 1267256 1267272 1268716 1268743) (-795 "NTPOLFN.spad" 1266807 1266817 1267173 1267178) (-794 "NSUP.spad" 1259760 1259770 1264300 1264453) (-793 "NSUP2.spad" 1259152 1259164 1259750 1259755) (-792 "NSMP.spad" 1255382 1255401 1255690 1255817) (-791 "NREP.spad" 1253760 1253774 1255372 1255377) (-790 "NPCOEF.spad" 1253006 1253026 1253750 1253755) (-789 "NORMRETR.spad" 1252604 1252643 1252996 1253001) (-788 "NORMPK.spad" 1250506 1250525 1252594 1252599) (-787 "NORMMA.spad" 1250194 1250220 1250496 1250501) (-786 "NONE.spad" 1249935 1249943 1250184 1250189) (-785 "NONE1.spad" 1249611 1249621 1249925 1249930) (-784 "NODE1.spad" 1249098 1249114 1249601 1249606) (-783 "NNI.spad" 1247993 1248001 1249072 1249093) (-782 "NLINSOL.spad" 1246619 1246629 1247983 1247988) (-781 "NIPROB.spad" 1245160 1245168 1246609 1246614) (-780 "NFINTBAS.spad" 1242720 1242737 1245150 1245155) (-779 "NETCLT.spad" 1242694 1242705 1242710 1242715) (-778 "NCODIV.spad" 1240910 1240926 1242684 1242689) (-777 "NCNTFRAC.spad" 1240552 1240566 1240900 1240905) (-776 "NCEP.spad" 1238718 1238732 1240542 1240547) (-775 "NASRING.spad" 1238314 1238322 1238708 1238713) (-774 "NASRING.spad" 1237908 1237918 1238304 1238309) (-773 "NARNG.spad" 1237260 1237268 1237898 1237903) (-772 "NARNG.spad" 1236610 1236620 1237250 1237255) (-771 "NAGSP.spad" 1235687 1235695 1236600 1236605) (-770 "NAGS.spad" 1225348 1225356 1235677 1235682) (-769 "NAGF07.spad" 1223779 1223787 1225338 1225343) (-768 "NAGF04.spad" 1218181 1218189 1223769 1223774) (-767 "NAGF02.spad" 1212250 1212258 1218171 1218176) (-766 "NAGF01.spad" 1208011 1208019 1212240 1212245) (-765 "NAGE04.spad" 1201711 1201719 1208001 1208006) (-764 "NAGE02.spad" 1192371 1192379 1201701 1201706) (-763 "NAGE01.spad" 1188373 1188381 1192361 1192366) (-762 "NAGD03.spad" 1186377 1186385 1188363 1188368) (-761 "NAGD02.spad" 1179124 1179132 1186367 1186372) (-760 "NAGD01.spad" 1173417 1173425 1179114 1179119) (-759 "NAGC06.spad" 1169292 1169300 1173407 1173412) (-758 "NAGC05.spad" 1167793 1167801 1169282 1169287) (-757 "NAGC02.spad" 1167060 1167068 1167783 1167788) (-756 "NAALG.spad" 1166601 1166611 1167028 1167055) (-755 "NAALG.spad" 1166162 1166174 1166591 1166596) (-754 "MULTSQFR.spad" 1163120 1163137 1166152 1166157) (-753 "MULTFACT.spad" 1162503 1162520 1163110 1163115) (-752 "MTSCAT.spad" 1160597 1160618 1162401 1162498) (-751 "MTHING.spad" 1160256 1160266 1160587 1160592) (-750 "MSYSCMD.spad" 1159690 1159698 1160246 1160251) (-749 "MSET.spad" 1157612 1157622 1159360 1159399) (-748 "MSETAGG.spad" 1157457 1157467 1157580 1157607) (-747 "MRING.spad" 1154434 1154446 1157165 1157232) (-746 "MRF2.spad" 1154004 1154018 1154424 1154429) (-745 "MRATFAC.spad" 1153550 1153567 1153994 1153999) (-744 "MPRFF.spad" 1151590 1151609 1153540 1153545) (-743 "MPOLY.spad" 1149061 1149076 1149420 1149547) (-742 "MPCPF.spad" 1148325 1148344 1149051 1149056) (-741 "MPC3.spad" 1148142 1148182 1148315 1148320) (-740 "MPC2.spad" 1147788 1147821 1148132 1148137) (-739 "MONOTOOL.spad" 1146139 1146156 1147778 1147783) (-738 "MONOID.spad" 1145458 1145466 1146129 1146134) (-737 "MONOID.spad" 1144775 1144785 1145448 1145453) (-736 "MONOGEN.spad" 1143523 1143536 1144635 1144770) (-735 "MONOGEN.spad" 1142293 1142308 1143407 1143412) (-734 "MONADWU.spad" 1140323 1140331 1142283 1142288) (-733 "MONADWU.spad" 1138351 1138361 1140313 1140318) (-732 "MONAD.spad" 1137511 1137519 1138341 1138346) (-731 "MONAD.spad" 1136669 1136679 1137501 1137506) (-730 "MOEBIUS.spad" 1135405 1135419 1136649 1136664) (-729 "MODULE.spad" 1135275 1135285 1135373 1135400) (-728 "MODULE.spad" 1135165 1135177 1135265 1135270) (-727 "MODRING.spad" 1134500 1134539 1135145 1135160) (-726 "MODOP.spad" 1133165 1133177 1134322 1134389) (-725 "MODMONOM.spad" 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"MCMPLX.spad" 1108227 1108235 1108841 1109042) (-705 "MCDEN.spad" 1107437 1107449 1108217 1108222) (-704 "MCALCFN.spad" 1104559 1104585 1107427 1107432) (-703 "MAYBE.spad" 1103843 1103854 1104549 1104554) (-702 "MATSTOR.spad" 1101151 1101161 1103833 1103838) (-701 "MATRIX.spad" 1099738 1099748 1100222 1100249) (-700 "MATLIN.spad" 1097082 1097106 1099622 1099627) (-699 "MATCAT.spad" 1088604 1088626 1097050 1097077) (-698 "MATCAT.spad" 1079998 1080022 1088446 1088451) (-697 "MATCAT2.spad" 1079280 1079328 1079988 1079993) (-696 "MAPPKG3.spad" 1078195 1078209 1079270 1079275) (-695 "MAPPKG2.spad" 1077533 1077545 1078185 1078190) (-694 "MAPPKG1.spad" 1076361 1076371 1077523 1077528) (-693 "MAPPAST.spad" 1075676 1075684 1076351 1076356) (-692 "MAPHACK3.spad" 1075488 1075502 1075666 1075671) (-691 "MAPHACK2.spad" 1075257 1075269 1075478 1075483) (-690 "MAPHACK1.spad" 1074901 1074911 1075247 1075252) (-689 "MAGMA.spad" 1072691 1072708 1074891 1074896) (-688 "MACROAST.spad" 1072270 1072278 1072681 1072686) (-687 "M3D.spad" 1069873 1069883 1071531 1071536) (-686 "LZSTAGG.spad" 1067111 1067121 1069863 1069868) (-685 "LZSTAGG.spad" 1064347 1064359 1067101 1067106) (-684 "LWORD.spad" 1061052 1061069 1064337 1064342) (-683 "LSTAST.spad" 1060836 1060844 1061042 1061047) (-682 "LSQM.spad" 1058993 1059007 1059387 1059438) (-681 "LSPP.spad" 1058528 1058545 1058983 1058988) (-680 "LSMP.spad" 1057378 1057406 1058518 1058523) (-679 "LSMP1.spad" 1055196 1055210 1057368 1057373) (-678 "LSAGG.spad" 1054865 1054875 1055164 1055191) (-677 "LSAGG.spad" 1054554 1054566 1054855 1054860) (-676 "LPOLY.spad" 1053508 1053527 1054410 1054479) (-675 "LPEFRAC.spad" 1052779 1052789 1053498 1053503) (-674 "LO.spad" 1052180 1052194 1052713 1052740) (-673 "LOGIC.spad" 1051782 1051790 1052170 1052175) (-672 "LOGIC.spad" 1051382 1051392 1051772 1051777) (-671 "LODOOPS.spad" 1050312 1050324 1051372 1051377) (-670 "LODO.spad" 1049696 1049712 1049992 1050031) (-669 "LODOF.spad" 1048742 1048759 1049653 1049658) (-668 "LODOCAT.spad" 1047408 1047418 1048698 1048737) (-667 "LODOCAT.spad" 1046072 1046084 1047364 1047369) (-666 "LODO2.spad" 1045345 1045357 1045752 1045791) (-665 "LODO1.spad" 1044745 1044755 1045025 1045064) (-664 "LODEEF.spad" 1043547 1043565 1044735 1044740) (-663 "LNAGG.spad" 1039694 1039704 1043537 1043542) (-662 "LNAGG.spad" 1035805 1035817 1039650 1039655) (-661 "LMOPS.spad" 1032573 1032590 1035795 1035800) (-660 "LMODULE.spad" 1032341 1032351 1032563 1032568) (-659 "LMDICT.spad" 1031511 1031521 1031775 1031802) (-658 "LLINSET.spad" 1031218 1031228 1031501 1031506) (-657 "LITERAL.spad" 1031124 1031135 1031208 1031213) (-656 "LIST.spad" 1028706 1028716 1030118 1030145) (-655 "LIST3.spad" 1028017 1028031 1028696 1028701) (-654 "LIST2.spad" 1026719 1026731 1028007 1028012) (-653 "LIST2MAP.spad" 1023622 1023634 1026709 1026714) (-652 "LINSET.spad" 1023401 1023411 1023612 1023617) (-651 "LINEXP.spad" 1022144 1022154 1023391 1023396) (-650 "LINDEP.spad" 1020953 1020965 1022056 1022061) (-649 "LIMITRF.spad" 1018881 1018891 1020943 1020948) (-648 "LIMITPS.spad" 1017784 1017797 1018871 1018876) (-647 "LIE.spad" 1015800 1015812 1017074 1017219) (-646 "LIECAT.spad" 1015276 1015286 1015726 1015795) (-645 "LIECAT.spad" 1014780 1014792 1015232 1015237) (-644 "LIB.spad" 1012531 1012539 1012977 1012992) (-643 "LGROBP.spad" 1009884 1009903 1012521 1012526) (-642 "LF.spad" 1008839 1008855 1009874 1009879) (-641 "LFCAT.spad" 1007898 1007906 1008829 1008834) (-640 "LEXTRIPK.spad" 1003401 1003416 1007888 1007893) (-639 "LEXP.spad" 1001404 1001431 1003381 1003396) (-638 "LETAST.spad" 1001103 1001111 1001394 1001399) (-637 "LEADCDET.spad" 999501 999518 1001093 1001098) (-636 "LAZM3PK.spad" 998205 998227 999491 999496) (-635 "LAUPOL.spad" 996805 996818 997705 997774) (-634 "LAPLACE.spad" 996388 996404 996795 996800) (-633 "LA.spad" 995828 995842 996310 996349) (-632 "LALG.spad" 995604 995614 995808 995823) (-631 "LALG.spad" 995388 995400 995594 995599) (-630 "KVTFROM.spad" 995123 995133 995378 995383) (-629 "KTVLOGIC.spad" 994635 994643 995113 995118) (-628 "KRCFROM.spad" 994373 994383 994625 994630) (-627 "KOVACIC.spad" 993096 993113 994363 994368) (-626 "KONVERT.spad" 992818 992828 993086 993091) (-625 "KOERCE.spad" 992555 992565 992808 992813) (-624 "KERNEL.spad" 991210 991220 992339 992344) (-623 "KERNEL2.spad" 990913 990925 991200 991205) (-622 "KDAGG.spad" 990022 990044 990893 990908) (-621 "KDAGG.spad" 989139 989163 990012 990017) (-620 "KAFILE.spad" 987993 988009 988228 988255) (-619 "JORDAN.spad" 985822 985834 987283 987428) (-618 "JOINAST.spad" 985516 985524 985812 985817) (-617 "JAVACODE.spad" 985382 985390 985506 985511) (-616 "IXAGG.spad" 983515 983539 985372 985377) (-615 "IXAGG.spad" 981503 981529 983362 983367) (-614 "IVECTOR.spad" 980120 980135 980275 980302) (-613 "ITUPLE.spad" 979281 979291 980110 980115) (-612 "ITRIGMNP.spad" 978120 978139 979271 979276) (-611 "ITFUN3.spad" 977626 977640 978110 978115) (-610 "ITFUN2.spad" 977370 977382 977616 977621) (-609 "ITFORM.spad" 976725 976733 977360 977365) (-608 "ITAYLOR.spad" 974719 974734 976589 976686) (-607 "ISUPS.spad" 967156 967171 973693 973790) (-606 "ISUMP.spad" 966657 966673 967146 967151) (-605 "ISTRING.spad" 965584 965597 965665 965692) (-604 "ISAST.spad" 965303 965311 965574 965579) (-603 "IRURPK.spad" 964020 964039 965293 965298) (-602 "IRSN.spad" 961992 962000 964010 964015) (-601 "IRRF2F.spad" 960477 960487 961948 961953) (-600 "IRREDFFX.spad" 960078 960089 960467 960472) (-599 "IROOT.spad" 958417 958427 960068 960073) (-598 "IR.spad" 956218 956232 958272 958299) (-597 "IRFORM.spad" 955542 955550 956208 956213) (-596 "IR2.spad" 954570 954586 955532 955537) (-595 "IR2F.spad" 953776 953792 954560 954565) (-594 "IPRNTPK.spad" 953536 953544 953766 953771) (-593 "IPF.spad" 953101 953113 953341 953434) (-592 "IPADIC.spad" 952862 952888 953027 953096) (-591 "IP4ADDR.spad" 952419 952427 952852 952857) (-590 "IOMODE.spad" 951941 951949 952409 952414) (-589 "IOBFILE.spad" 951302 951310 951931 951936) (-588 "IOBCON.spad" 951167 951175 951292 951297) (-587 "INVLAPLA.spad" 950816 950832 951157 951162) (-586 "INTTR.spad" 944198 944215 950806 950811) (-585 "INTTOOLS.spad" 941953 941969 943772 943777) (-584 "INTSLPE.spad" 941273 941281 941943 941948) (-583 "INTRVL.spad" 940839 940849 941187 941268) (-582 "INTRF.spad" 939263 939277 940829 940834) (-581 "INTRET.spad" 938695 938705 939253 939258) (-580 "INTRAT.spad" 937422 937439 938685 938690) (-579 "INTPM.spad" 935807 935823 937065 937070) (-578 "INTPAF.spad" 933671 933689 935739 935744) (-577 "INTPACK.spad" 924045 924053 933661 933666) (-576 "INT.spad" 923493 923501 923899 924040) (-575 "INTHERTR.spad" 922767 922784 923483 923488) (-574 "INTHERAL.spad" 922437 922461 922757 922762) (-573 "INTHEORY.spad" 918876 918884 922427 922432) (-572 "INTG0.spad" 912609 912627 918808 918813) (-571 "INTFTBL.spad" 906638 906646 912599 912604) (-570 "INTFACT.spad" 905697 905707 906628 906633) (-569 "INTEF.spad" 904082 904098 905687 905692) (-568 "INTDOM.spad" 902705 902713 904008 904077) (-567 "INTDOM.spad" 901390 901400 902695 902700) (-566 "INTCAT.spad" 899649 899659 901304 901385) (-565 "INTBIT.spad" 899156 899164 899639 899644) (-564 "INTALG.spad" 898344 898371 899146 899151) (-563 "INTAF.spad" 897844 897860 898334 898339) (-562 "INTABL.spad" 895920 895951 896083 896110) (-561 "INT8.spad" 895800 895808 895910 895915) (-560 "INT64.spad" 895679 895687 895790 895795) (-559 "INT32.spad" 895558 895566 895669 895674) (-558 "INT16.spad" 895437 895445 895548 895553) (-557 "INS.spad" 892940 892948 895339 895432) (-556 "INS.spad" 890529 890539 892930 892935) (-555 "INPSIGN.spad" 889977 889990 890519 890524) (-554 "INPRODPF.spad" 889073 889092 889967 889972) (-553 "INPRODFF.spad" 888161 888185 889063 889068) (-552 "INNMFACT.spad" 887136 887153 888151 888156) (-551 "INMODGCD.spad" 886624 886654 887126 887131) (-550 "INFSP.spad" 884921 884943 886614 886619) (-549 "INFPROD0.spad" 884001 884020 884911 884916) (-548 "INFORM.spad" 881200 881208 883991 883996) (-547 "INFORM1.spad" 880825 880835 881190 881195) (-546 "INFINITY.spad" 880377 880385 880815 880820) (-545 "INETCLTS.spad" 880354 880362 880367 880372) (-544 "INEP.spad" 878892 878914 880344 880349) (-543 "INDE.spad" 878621 878638 878882 878887) (-542 "INCRMAPS.spad" 878042 878052 878611 878616) (-541 "INBFILE.spad" 877114 877122 878032 878037) (-540 "INBFF.spad" 872908 872919 877104 877109) (-539 "INBCON.spad" 871198 871206 872898 872903) (-538 "INBCON.spad" 869486 869496 871188 871193) (-537 "INAST.spad" 869147 869155 869476 869481) (-536 "IMPTAST.spad" 868855 868863 869137 869142) (-535 "IMATRIX.spad" 867683 867709 868195 868222) (-534 "IMATQF.spad" 866777 866821 867639 867644) (-533 "IMATLIN.spad" 865382 865406 866733 866738) (-532 "ILIST.spad" 863887 863902 864412 864439) (-531 "IIARRAY2.spad" 863158 863196 863377 863404) (-530 "IFF.spad" 862568 862584 862839 862932) (-529 "IFAST.spad" 862182 862190 862558 862563) (-528 "IFARRAY.spad" 859522 859537 861212 861239) (-527 "IFAMON.spad" 859384 859401 859478 859483) (-526 "IEVALAB.spad" 858789 858801 859374 859379) (-525 "IEVALAB.spad" 858192 858206 858779 858784) (-524 "IDPO.spad" 858005 858017 858182 858187) (-523 "IDPOAMS.spad" 857761 857773 857995 858000) (-522 "IDPOAM.spad" 857481 857493 857751 857756) (-521 "IDPC.spad" 856210 856222 857471 857476) (-520 "IDPAM.spad" 855955 855967 856200 856205) (-519 "IDPAG.spad" 855702 855714 855945 855950) (-518 "IDENT.spad" 855352 855360 855692 855697) (-517 "IDECOMP.spad" 852591 852609 855342 855347) (-516 "IDEAL.spad" 847540 847579 852526 852531) (-515 "ICDEN.spad" 846729 846745 847530 847535) (-514 "ICARD.spad" 845920 845928 846719 846724) (-513 "IBPTOOLS.spad" 844527 844544 845910 845915) (-512 "IBITS.spad" 843692 843705 844125 844152) (-511 "IBATOOL.spad" 840669 840688 843682 843687) (-510 "IBACHIN.spad" 839176 839191 840659 840664) (-509 "IARRAY2.spad" 838047 838073 838666 838693) (-508 "IARRAY1.spad" 836939 836954 837077 837104) (-507 "IAN.spad" 835162 835170 836755 836848) (-506 "IALGFACT.spad" 834765 834798 835152 835157) (-505 "HYPCAT.spad" 834189 834197 834755 834760) (-504 "HYPCAT.spad" 833611 833621 834179 834184) (-503 "HOSTNAME.spad" 833419 833427 833601 833606) (-502 "HOMOTOP.spad" 833162 833172 833409 833414) (-501 "HOAGG.spad" 830444 830454 833152 833157) (-500 "HOAGG.spad" 827465 827477 830175 830180) (-499 "HEXADEC.spad" 825470 825478 825835 825928) (-498 "HEUGCD.spad" 824505 824516 825460 825465) (-497 "HELLFDIV.spad" 824095 824119 824495 824500) (-496 "HEAP.spad" 823370 823380 823585 823612) (-495 "HEADAST.spad" 822903 822911 823360 823365) (-494 "HDP.spad" 810713 810729 811090 811189) (-493 "HDMP.spad" 807927 807942 808543 808670) (-492 "HB.spad" 806178 806186 807917 807922) (-491 "HASHTBL.spad" 804206 804237 804417 804444) (-490 "HASAST.spad" 803922 803930 804196 804201) (-489 "HACKPI.spad" 803413 803421 803824 803917) (-488 "GTSET.spad" 802316 802332 803023 803050) (-487 "GSTBL.spad" 800393 800428 800567 800582) (-486 "GSERIES.spad" 797706 797733 798525 798674) (-485 "GROUP.spad" 796979 796987 797686 797701) (-484 "GROUP.spad" 796260 796270 796969 796974) (-483 "GROEBSOL.spad" 794754 794775 796250 796255) (-482 "GRMOD.spad" 793325 793337 794744 794749) (-481 "GRMOD.spad" 791894 791908 793315 793320) (-480 "GRIMAGE.spad" 784783 784791 791884 791889) (-479 "GRDEF.spad" 783162 783170 784773 784778) (-478 "GRAY.spad" 781625 781633 783152 783157) (-477 "GRALG.spad" 780702 780714 781615 781620) (-476 "GRALG.spad" 779777 779791 780692 780697) (-475 "GPOLSET.spad" 779195 779218 779423 779450) (-474 "GOSPER.spad" 778464 778482 779185 779190) (-473 "GMODPOL.spad" 777612 777639 778432 778459) (-472 "GHENSEL.spad" 776695 776709 777602 777607) (-471 "GENUPS.spad" 772988 773001 776685 776690) (-470 "GENUFACT.spad" 772565 772575 772978 772983) (-469 "GENPGCD.spad" 772151 772168 772555 772560) (-468 "GENMFACT.spad" 771603 771622 772141 772146) (-467 "GENEEZ.spad" 769554 769567 771593 771598) (-466 "GDMP.spad" 766610 766627 767384 767511) (-465 "GCNAALG.spad" 760533 760560 766404 766471) (-464 "GCDDOM.spad" 759709 759717 760459 760528) (-463 "GCDDOM.spad" 758947 758957 759699 759704) (-462 "GB.spad" 756473 756511 758903 758908) (-461 "GBINTERN.spad" 752493 752531 756463 756468) (-460 "GBF.spad" 748260 748298 752483 752488) (-459 "GBEUCLID.spad" 746142 746180 748250 748255) (-458 "GAUSSFAC.spad" 745455 745463 746132 746137) (-457 "GALUTIL.spad" 743781 743791 745411 745416) (-456 "GALPOLYU.spad" 742235 742248 743771 743776) (-455 "GALFACTU.spad" 740408 740427 742225 742230) (-454 "GALFACT.spad" 730597 730608 740398 740403) (-453 "FVFUN.spad" 727620 727628 730587 730592) (-452 "FVC.spad" 726672 726680 727610 727615) (-451 "FUNDESC.spad" 726350 726358 726662 726667) (-450 "FUNCTION.spad" 726199 726211 726340 726345) (-449 "FT.spad" 724496 724504 726189 726194) (-448 "FTEM.spad" 723661 723669 724486 724491) (-447 "FSUPFACT.spad" 722561 722580 723597 723602) (-446 "FST.spad" 720647 720655 722551 722556) (-445 "FSRED.spad" 720127 720143 720637 720642) (-444 "FSPRMELT.spad" 719009 719025 720084 720089) (-443 "FSPECF.spad" 717100 717116 718999 719004) (-442 "FS.spad" 711368 711378 716875 717095) (-441 "FS.spad" 705414 705426 710923 710928) (-440 "FSINT.spad" 705074 705090 705404 705409) (-439 "FSERIES.spad" 704265 704277 704894 704993) (-438 "FSCINT.spad" 703582 703598 704255 704260) (-437 "FSAGG.spad" 702699 702709 703538 703577) (-436 "FSAGG.spad" 701778 701790 702619 702624) (-435 "FSAGG2.spad" 700521 700537 701768 701773) (-434 "FS2UPS.spad" 695012 695046 700511 700516) (-433 "FS2.spad" 694659 694675 695002 695007) (-432 "FS2EXPXP.spad" 693784 693807 694649 694654) (-431 "FRUTIL.spad" 692738 692748 693774 693779) (-430 "FR.spad" 686361 686371 691669 691738) (-429 "FRNAALG.spad" 681630 681640 686303 686356) (-428 "FRNAALG.spad" 676911 676923 681586 681591) (-427 "FRNAAF2.spad" 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(-406 "FORMULA.spad" 648400 648408 650916 650921) (-405 "FORMULA1.spad" 647879 647889 648390 648395) (-404 "FORDER.spad" 647570 647594 647869 647874) (-403 "FOP.spad" 646771 646779 647560 647565) (-402 "FNLA.spad" 646195 646217 646739 646766) (-401 "FNCAT.spad" 644790 644798 646185 646190) (-400 "FNAME.spad" 644682 644690 644780 644785) (-399 "FMTC.spad" 644480 644488 644608 644677) (-398 "FMONOID.spad" 644145 644155 644436 644441) (-397 "FMONCAT.spad" 641298 641308 644135 644140) (-396 "FM.spad" 640993 641005 641232 641259) (-395 "FMFUN.spad" 638023 638031 640983 640988) (-394 "FMC.spad" 637075 637083 638013 638018) (-393 "FMCAT.spad" 634743 634761 637043 637070) (-392 "FM1.spad" 634100 634112 634677 634704) (-391 "FLOATRP.spad" 631835 631849 634090 634095) (-390 "FLOAT.spad" 625149 625157 631701 631830) (-389 "FLOATCP.spad" 622580 622594 625139 625144) (-388 "FLINEXP.spad" 622302 622312 622570 622575) (-387 "FLINEXP.spad" 621968 621980 622238 622243) (-386 "FLASORT.spad" 621294 621306 621958 621963) (-385 "FLALG.spad" 618940 618959 621220 621289) (-384 "FLAGG.spad" 615982 615992 618920 618935) (-383 "FLAGG.spad" 612925 612937 615865 615870) (-382 "FLAGG2.spad" 611650 611666 612915 612920) (-381 "FINRALG.spad" 609711 609724 611606 611645) (-380 "FINRALG.spad" 607698 607713 609595 609600) (-379 "FINITE.spad" 606850 606858 607688 607693) (-378 "FINAALG.spad" 595971 595981 606792 606845) (-377 "FINAALG.spad" 585104 585116 595927 595932) (-376 "FILE.spad" 584687 584697 585094 585099) (-375 "FILECAT.spad" 583213 583230 584677 584682) (-374 "FIELD.spad" 582619 582627 583115 583208) (-373 "FIELD.spad" 582111 582121 582609 582614) (-372 "FGROUP.spad" 580758 580768 582091 582106) (-371 "FGLMICPK.spad" 579545 579560 580748 580753) (-370 "FFX.spad" 578920 578935 579261 579354) (-369 "FFSLPE.spad" 578423 578444 578910 578915) (-368 "FFPOLY.spad" 569685 569696 578413 578418) (-367 "FFPOLY2.spad" 568745 568762 569675 569680) (-366 "FFP.spad" 568142 568162 568461 568554) (-365 "FF.spad" 567590 567606 567823 567916) (-364 "FFNBX.spad" 566102 566122 567306 567399) (-363 "FFNBP.spad" 564615 564632 565818 565911) (-362 "FFNB.spad" 563080 563101 564296 564389) (-361 "FFINTBAS.spad" 560594 560613 563070 563075) (-360 "FFIELDC.spad" 558171 558179 560496 560589) (-359 "FFIELDC.spad" 555834 555844 558161 558166) (-358 "FFHOM.spad" 554582 554599 555824 555829) (-357 "FFF.spad" 552017 552028 554572 554577) (-356 "FFCGX.spad" 550864 550884 551733 551826) (-355 "FFCGP.spad" 549753 549773 550580 550673) (-354 "FFCG.spad" 548545 548566 549434 549527) (-353 "FFCAT.spad" 541718 541740 548384 548540) (-352 "FFCAT.spad" 534970 534994 541638 541643) (-351 "FFCAT2.spad" 534717 534757 534960 534965) (-350 "FEXPR.spad" 526434 526480 534473 534512) (-349 "FEVALAB.spad" 526142 526152 526424 526429) (-348 "FEVALAB.spad" 525635 525647 525919 525924) (-347 "FDIV.spad" 525077 525101 525625 525630) (-346 "FDIVCAT.spad" 523141 523165 525067 525072) (-345 "FDIVCAT.spad" 521203 521229 523131 523136) (-344 "FDIV2.spad" 520859 520899 521193 521198) (-343 "FCTRDATA.spad" 519867 519875 520849 520854) (-342 "FCPAK1.spad" 518434 518442 519857 519862) (-341 "FCOMP.spad" 517813 517823 518424 518429) (-340 "FC.spad" 507820 507828 517803 517808) (-339 "FAXF.spad" 500791 500805 507722 507815) (-338 "FAXF.spad" 493814 493830 500747 500752) (-337 "FARRAY.spad" 491811 491821 492844 492871) (-336 "FAMR.spad" 489947 489959 491709 491806) (-335 "FAMR.spad" 488067 488081 489831 489836) (-334 "FAMONOID.spad" 487735 487745 488021 488026) (-333 "FAMONC.spad" 486031 486043 487725 487730) (-332 "FAGROUP.spad" 485655 485665 485927 485954) (-331 "FACUTIL.spad" 483859 483876 485645 485650) (-330 "FACTFUNC.spad" 483053 483063 483849 483854) (-329 "EXPUPXS.spad" 479886 479909 481185 481334) (-328 "EXPRTUBE.spad" 477174 477182 479876 479881) (-327 "EXPRODE.spad" 474334 474350 477164 477169) (-326 "EXPR.spad" 469509 469519 470223 470518) (-325 "EXPR2UPS.spad" 465631 465644 469499 469504) (-324 "EXPR2.spad" 465336 465348 465621 465626) (-323 "EXPEXPAN.spad" 462137 462162 462769 462862) (-322 "EXIT.spad" 461808 461816 462127 462132) (-321 "EXITAST.spad" 461544 461552 461798 461803) (-320 "EVALCYC.spad" 461004 461018 461534 461539) (-319 "EVALAB.spad" 460576 460586 460994 460999) (-318 "EVALAB.spad" 460146 460158 460566 460571) (-317 "EUCDOM.spad" 457720 457728 460072 460141) (-316 "EUCDOM.spad" 455356 455366 457710 457715) (-315 "ESTOOLS.spad" 447202 447210 455346 455351) (-314 "ESTOOLS2.spad" 446805 446819 447192 447197) (-313 "ESTOOLS1.spad" 446490 446501 446795 446800) (-312 "ES.spad" 439305 439313 446480 446485) (-311 "ES.spad" 432026 432036 439203 439208) (-310 "ESCONT.spad" 428819 428827 432016 432021) (-309 "ESCONT1.spad" 428568 428580 428809 428814) (-308 "ES2.spad" 428073 428089 428558 428563) (-307 "ES1.spad" 427643 427659 428063 428068) (-306 "ERROR.spad" 424970 424978 427633 427638) (-305 "EQTBL.spad" 423000 423022 423209 423236) (-304 "EQ.spad" 417805 417815 420592 420704) (-303 "EQ2.spad" 417523 417535 417795 417800) (-302 "EP.spad" 413849 413859 417513 417518) (-301 "ENV.spad" 412527 412535 413839 413844) (-300 "ENTIRER.spad" 412195 412203 412471 412522) (-299 "EMR.spad" 411483 411524 412121 412190) (-298 "ELTAGG.spad" 409737 409756 411473 411478) (-297 "ELTAGG.spad" 407955 407976 409693 409698) (-296 "ELTAB.spad" 407430 407443 407945 407950) (-295 "ELFUTS.spad" 406817 406836 407420 407425) (-294 "ELEMFUN.spad" 406506 406514 406807 406812) (-293 "ELEMFUN.spad" 406193 406203 406496 406501) (-292 "ELAGG.spad" 404164 404174 406173 406188) (-291 "ELAGG.spad" 402072 402084 404083 404088) (-290 "ELABOR.spad" 401418 401426 402062 402067) (-289 "ELABEXPR.spad" 400350 400358 401408 401413) (-288 "EFUPXS.spad" 397126 397156 400306 400311) (-287 "EFULS.spad" 393962 393985 397082 397087) (-286 "EFSTRUC.spad" 391977 391993 393952 393957) (-285 "EF.spad" 386753 386769 391967 391972) (-284 "EAB.spad" 385029 385037 386743 386748) (-283 "E04UCFA.spad" 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343677 343682) (-262 "DRAWCFUN.spad" 332766 332774 343224 343229) (-261 "DQAGG.spad" 330944 330954 332734 332761) (-260 "DPOLCAT.spad" 326293 326309 330812 330939) (-259 "DPOLCAT.spad" 321728 321746 326249 326254) (-258 "DPMO.spad" 313488 313504 313626 313839) (-257 "DPMM.spad" 305261 305279 305386 305599) (-256 "DOMTMPLT.spad" 305032 305040 305251 305256) (-255 "DOMCTOR.spad" 304787 304795 305022 305027) (-254 "DOMAIN.spad" 303874 303882 304777 304782) (-253 "DMP.spad" 301134 301149 301704 301831) (-252 "DMEXT.spad" 301001 301011 301102 301129) (-251 "DLP.spad" 300353 300363 300991 300996) (-250 "DLIST.spad" 298779 298789 299383 299410) (-249 "DLAGG.spad" 297196 297206 298769 298774) (-248 "DIVRING.spad" 296738 296746 297140 297191) (-247 "DIVRING.spad" 296324 296334 296728 296733) (-246 "DISPLAY.spad" 294514 294522 296314 296319) (-245 "DIRPROD.spad" 282061 282077 282701 282800) (-244 "DIRPROD2.spad" 280879 280897 282051 282056) (-243 "DIRPCAT.spad" 280072 280088 280775 280874) (-242 "DIRPCAT.spad" 278892 278910 279597 279602) (-241 "DIOSP.spad" 277717 277725 278882 278887) (-240 "DIOPS.spad" 276713 276723 277697 277712) (-239 "DIOPS.spad" 275683 275695 276669 276674) (-238 "DIFRING.spad" 275521 275529 275663 275678) (-237 "DIFFSPC.spad" 275100 275108 275511 275516) (-236 "DIFFSPC.spad" 274677 274687 275090 275095) (-235 "DIFFMOD.spad" 274166 274176 274645 274672) (-234 "DIFFDOM.spad" 273331 273342 274156 274161) (-233 "DIFFDOM.spad" 272494 272507 273321 273326) (-232 "DIFEXT.spad" 272313 272323 272474 272489) (-231 "DIAGG.spad" 271943 271953 272293 272308) (-230 "DIAGG.spad" 271581 271593 271933 271938) (-229 "DHMATRIX.spad" 269776 269786 270921 270948) (-228 "DFSFUN.spad" 263416 263424 269766 269771) (-227 "DFLOAT.spad" 260147 260155 263306 263411) (-226 "DFINTTLS.spad" 258378 258394 260137 260142) (-225 "DERHAM.spad" 256292 256324 258358 258373) (-224 "DEQUEUE.spad" 255499 255509 255782 255809) (-223 "DEGRED.spad" 255116 255130 255489 255494) (-222 "DEFINTRF.spad" 252653 252663 255106 255111) (-221 "DEFINTEF.spad" 251163 251179 252643 252648) (-220 "DEFAST.spad" 250531 250539 251153 251158) (-219 "DECIMAL.spad" 248540 248548 248901 248994) (-218 "DDFACT.spad" 246353 246370 248530 248535) (-217 "DBLRESP.spad" 245953 245977 246343 246348) (-216 "DBASE.spad" 244617 244627 245943 245948) (-215 "DATAARY.spad" 244079 244092 244607 244612) (-214 "D03FAFA.spad" 243907 243915 244069 244074) (-213 "D03EEFA.spad" 243727 243735 243897 243902) (-212 "D03AGNT.spad" 242813 242821 243717 243722) (-211 "D02EJFA.spad" 242275 242283 242803 242808) (-210 "D02CJFA.spad" 241753 241761 242265 242270) (-209 "D02BHFA.spad" 241243 241251 241743 241748) (-208 "D02BBFA.spad" 240733 240741 241233 241238) (-207 "D02AGNT.spad" 235547 235555 240723 240728) (-206 "D01WGTS.spad" 233866 233874 235537 235542) (-205 "D01TRNS.spad" 233843 233851 233856 233861) (-204 "D01GBFA.spad" 233365 233373 233833 233838) (-203 "D01FCFA.spad" 232887 232895 233355 233360) (-202 "D01ASFA.spad" 232355 232363 232877 232882) (-201 "D01AQFA.spad" 231801 231809 232345 232350) (-200 "D01APFA.spad" 231225 231233 231791 231796) (-199 "D01ANFA.spad" 230719 230727 231215 231220) (-198 "D01AMFA.spad" 230229 230237 230709 230714) (-197 "D01ALFA.spad" 229769 229777 230219 230224) (-196 "D01AKFA.spad" 229295 229303 229759 229764) (-195 "D01AJFA.spad" 228818 228826 229285 229290) (-194 "D01AGNT.spad" 224885 224893 228808 228813) (-193 "CYCLOTOM.spad" 224391 224399 224875 224880) (-192 "CYCLES.spad" 221183 221191 224381 224386) (-191 "CVMP.spad" 220600 220610 221173 221178) (-190 "CTRIGMNP.spad" 219100 219116 220590 220595) (-189 "CTOR.spad" 218791 218799 219090 219095) (-188 "CTORKIND.spad" 218394 218402 218781 218786) (-187 "CTORCAT.spad" 217643 217651 218384 218389) (-186 "CTORCAT.spad" 216890 216900 217633 217638) (-185 "CTORCALL.spad" 216479 216489 216880 216885) (-184 "CSTTOOLS.spad" 215724 215737 216469 216474) (-183 "CRFP.spad" 209448 209461 215714 215719) (-182 "CRCEAST.spad" 209168 209176 209438 209443) (-181 "CRAPACK.spad" 208219 208229 209158 209163) (-180 "CPMATCH.spad" 207723 207738 208144 208149) (-179 "CPIMA.spad" 207428 207447 207713 207718) (-178 "COORDSYS.spad" 202437 202447 207418 207423) (-177 "CONTOUR.spad" 201848 201856 202427 202432) (-176 "CONTFRAC.spad" 197598 197608 201750 201843) (-175 "CONDUIT.spad" 197356 197364 197588 197593) (-174 "COMRING.spad" 197030 197038 197294 197351) (-173 "COMPPROP.spad" 196548 196556 197020 197025) (-172 "COMPLPAT.spad" 196315 196330 196538 196543) (-171 "COMPLEX.spad" 191692 191702 191936 192197) (-170 "COMPLEX2.spad" 191407 191419 191682 191687) (-169 "COMPILER.spad" 190956 190964 191397 191402) (-168 "COMPFACT.spad" 190558 190572 190946 190951) (-167 "COMPCAT.spad" 188630 188640 190292 190553) (-166 "COMPCAT.spad" 186430 186442 188094 188099) (-165 "COMMUPC.spad" 186178 186196 186420 186425) (-164 "COMMONOP.spad" 185711 185719 186168 186173) (-163 "COMM.spad" 185522 185530 185701 185706) (-162 "COMMAAST.spad" 185285 185293 185512 185517) (-161 "COMBOPC.spad" 184200 184208 185275 185280) (-160 "COMBINAT.spad" 182967 182977 184190 184195) (-159 "COMBF.spad" 180349 180365 182957 182962) (-158 "COLOR.spad" 179186 179194 180339 180344) (-157 "COLONAST.spad" 178852 178860 179176 179181) (-156 "CMPLXRT.spad" 178563 178580 178842 178847) (-155 "CLLCTAST.spad" 178225 178233 178553 178558) (-154 "CLIP.spad" 174333 174341 178215 178220) (-153 "CLIF.spad" 172988 173004 174289 174328) (-152 "CLAGG.spad" 169493 169503 172978 172983) (-151 "CLAGG.spad" 165869 165881 169356 169361) (-150 "CINTSLPE.spad" 165200 165213 165859 165864) (-149 "CHVAR.spad" 163338 163360 165190 165195) (-148 "CHARZ.spad" 163253 163261 163318 163333) (-147 "CHARPOL.spad" 162763 162773 163243 163248) (-146 "CHARNZ.spad" 162516 162524 162743 162758) (-145 "CHAR.spad" 160390 160398 162506 162511) (-144 "CFCAT.spad" 159718 159726 160380 160385) (-143 "CDEN.spad" 158914 158928 159708 159713) (-142 "CCLASS.spad" 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138185 138212) (-121 "BRILL.spad" 135516 135527 137309 137314) (-120 "BRAGG.spad" 134456 134466 135506 135511) (-119 "BRAGG.spad" 133360 133372 134412 134417) (-118 "BPADICRT.spad" 131234 131246 131489 131582) (-117 "BPADIC.spad" 130898 130910 131160 131229) (-116 "BOUNDZRO.spad" 130554 130571 130888 130893) (-115 "BOP.spad" 125736 125744 130544 130549) (-114 "BOP1.spad" 123202 123212 125726 125731) (-113 "BOOLE.spad" 122852 122860 123192 123197) (-112 "BOOLEAN.spad" 122290 122298 122842 122847) (-111 "BMODULE.spad" 122002 122014 122258 122285) (-110 "BITS.spad" 121385 121393 121600 121627) (-109 "BINDING.spad" 120798 120806 121375 121380) (-108 "BINARY.spad" 118812 118820 119168 119261) (-107 "BGAGG.spad" 118017 118027 118792 118807) (-106 "BGAGG.spad" 117230 117242 118007 118012) (-105 "BFUNCT.spad" 116794 116802 117210 117225) (-104 "BEZOUT.spad" 115934 115961 116744 116749) (-103 "BBTREE.spad" 112662 112672 115424 115451) (-102 "BASTYPE.spad" 112158 112166 112652 112657) (-101 "BASTYPE.spad" 111652 111662 112148 112153) (-100 "BALFACT.spad" 111111 111124 111642 111647) (-99 "AUTOMOR.spad" 110562 110571 111091 111106) (-98 "ATTREG.spad" 107285 107292 110314 110557) (-97 "ATTRBUT.spad" 103308 103315 107265 107280) (-96 "ATTRAST.spad" 103025 103032 103298 103303) (-95 "ATRIG.spad" 102495 102502 103015 103020) (-94 "ATRIG.spad" 101963 101972 102485 102490) (-93 "ASTCAT.spad" 101867 101874 101953 101958) (-92 "ASTCAT.spad" 101769 101778 101857 101862) (-91 "ASTACK.spad" 100991 101000 101259 101286) (-90 "ASSOCEQ.spad" 99817 99828 100947 100952) (-89 "ASP9.spad" 98898 98911 99807 99812) (-88 "ASP8.spad" 97941 97954 98888 98893) (-87 "ASP80.spad" 97263 97276 97931 97936) (-86 "ASP7.spad" 96423 96436 97253 97258) (-85 "ASP78.spad" 95874 95887 96413 96418) (-84 "ASP77.spad" 95243 95256 95864 95869) (-83 "ASP74.spad" 94335 94348 95233 95238) (-82 "ASP73.spad" 93606 93619 94325 94330) (-81 "ASP6.spad" 92473 92486 93596 93601) (-80 "ASP55.spad" 90982 90995 92463 92468) (-79 "ASP50.spad" 88799 88812 90972 90977) (-78 "ASP4.spad" 88094 88107 88789 88794) (-77 "ASP49.spad" 87093 87106 88084 88089) (-76 "ASP42.spad" 85500 85539 87083 87088) (-75 "ASP41.spad" 84079 84118 85490 85495) (-74 "ASP35.spad" 83067 83080 84069 84074) (-73 "ASP34.spad" 82368 82381 83057 83062) (-72 "ASP33.spad" 81928 81941 82358 82363) (-71 "ASP31.spad" 81068 81081 81918 81923) (-70 "ASP30.spad" 79960 79973 81058 81063) (-69 "ASP29.spad" 79426 79439 79950 79955) (-68 "ASP28.spad" 70699 70712 79416 79421) (-67 "ASP27.spad" 69596 69609 70689 70694) (-66 "ASP24.spad" 68683 68696 69586 69591) (-65 "ASP20.spad" 68147 68160 68673 68678) (-64 "ASP1.spad" 67528 67541 68137 68142) (-63 "ASP19.spad" 62214 62227 67518 67523) (-62 "ASP12.spad" 61628 61641 62204 62209) (-61 "ASP10.spad" 60899 60912 61618 61623) (-60 "ARRAY2.spad" 60142 60151 60389 60416) (-59 "ARRAY1.spad" 58826 58835 59172 59199) (-58 "ARRAY12.spad" 57539 57550 58816 58821) (-57 "ARR2CAT.spad" 53313 53334 57507 57534) (-56 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. -349) 198666) ((-1161 . -501) 198637) ((-1187 . -388) 198589) ((-1107 . -1078) T) ((-449 . -102) T) ((-185 . -1120) T) ((-258 . -34) T) ((-257 . -34) T) ((-1178 . -863) T) ((-794 . -1078) T) ((-792 . -1078) T) ((-743 . -916) 198566) ((-466 . -1078) T) ((-59 . -501) 198550) ((-1054 . -1076) 198524) ((-531 . -501) 198508) ((-528 . -501) 198492) ((-509 . -501) 198476) ((-508 . -501) 198460) ((-250 . -526) 198393) ((-1054 . -111) 198360) ((-1194 . -916) 198273) ((-1193 . -916) 198179) ((-682 . -1132) T) ((-1187 . -916) 198012) ((-657 . -93) T) ((-1146 . -916) 197996) ((-365 . -1172) T) ((-332 . -1076) 197978) ((-31 . -502) 197959) ((-258 . -806) 197938) ((-258 . -805) 197917) ((-257 . -806) 197896) ((-257 . -805) 197875) ((-31 . -625) 197841) ((-50 . -1078) T) ((-258 . -738) 197819) ((-257 . -738) 197797) ((-1231 . -1120) T) ((-682 . -23) T) ((-593 . -1078) T) ((-530 . -1078) T) ((-390 . -1076) 197762) ((-332 . -111) 197737) ((-73 . -394) T) ((-73 . -407) T) ((-1044 . -38) 197674) ((-706 . -412) 197656) ((-99 . -102) T) ((-1316 . -1071) 197643) ((-723 . -1120) T) ((-1133 . -863) 197594) ((-1023 . -146) 197566) ((-1023 . -148) 197538) ((-883 . -658) 197510) ((-390 . -111) 197466) ((-329 . -1241) 197445) ((-486 . -1022) 197411) ((-365 . -38) 197376) ((-40 . -381) 197348) ((-886 . -625) 197220) ((-128 . -126) 197204) ((-122 . -126) 197188) ((-848 . -1076) 197158) ((-845 . -21) 197110) ((-839 . -1076) 197094) ((-845 . -25) 197046) ((-329 . -568) 196997) ((-529 . -628) 196978) ((-576 . -840) T) ((-245 . -1237) T) ((-1054 . -628) 196947) ((-848 . -111) 196912) ((-839 . -111) 196891) ((-1271 . -625) 196873) ((-1250 . -625) 196855) ((-1250 . -626) 196526) ((-1192 . -927) 196505) ((-1145 . -927) 196484) ((-48 . -38) 196449) ((-1309 . -1132) T) ((-548 . -296) 196405) ((-614 . -625) 196317) ((-614 . -626) 196278) ((-1307 . -1132) T) ((-372 . -628) 196262) ((-332 . -628) 196246) ((-1162 . -237) 196197) ((-245 . -1058) 196024) ((-1192 . -660) 195913) ((-1145 . -660) 195802) ((-867 . -660) 195776) ((-730 . -625) 195758) ((-558 . -379) T) ((-1309 . -23) T) ((-706 . -918) NIL) ((-1307 . -23) T) ((-503 . -1120) T) ((-390 . -628) 195708) ((-390 . -630) 195690) ((-1054 . -1069) T) ((-878 . -102) T) ((-1209 . -296) 195669) ((-171 . -379) 195620) ((-1024 . -1237) T) ((-991 . -1237) T) ((-932 . -1237) T) ((-848 . -628) 195574) ((-839 . -628) 195529) ((-44 . -23) T) ((-1316 . -102) T) ((-491 . -296) 195508) ((-598 . -1120) T) ((-1166 . -1129) 195477) ((-439 . -1237) T) ((-1124 . -1123) 195429) ((-402 . -21) T) ((-402 . -25) T) ((-153 . -1132) T) ((-1231 . -729) 195326) ((-1217 . -1120) T) ((-1024 . -898) 195308) ((-1024 . -900) 195290) ((-635 . -232) 195274) ((-635 . -272) 195258) ((-633 . -21) T) ((-299 . -568) T) ((-633 . -25) T) ((-1024 . -1058) 195218) ((-723 . -729) 195183) ((-245 . -388) 195152) ((-390 . -1069) T) ((-225 . -1078) T) ((-118 . -272) 195129) ((-118 . -232) 195106) ((-59 . -296) 195058) ((-153 . -23) T) ((-528 . -296) 195010) ((-337 . -526) 194943) 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193593) ((-1023 . -237) 193530) ((-919 . -102) 193480) ((-867 . -738) T) ((-794 . -1120) T) ((-528 . -616) 193457) ((-508 . -616) 193434) ((-792 . -1120) T) ((-792 . -1085) 193401) ((-473 . -1120) T) ((-466 . -1120) T) ((-598 . -729) 193376) ((-661 . -1120) T) ((-1279 . -47) 193353) ((-1273 . -102) T) ((-1272 . -47) 193323) ((-1251 . -47) 193300) ((-1231 . -174) 193251) ((-1193 . -317) 193230) ((-1187 . -317) 193209) ((-1116 . -628) 193190) ((-1110 . -628) 193171) ((-1100 . -568) 193122) ((-1100 . -1241) 193073) ((-1024 . -916) NIL) ((-1093 . -628) 193054) ((-682 . -132) T) ((-639 . -1132) T) ((-1086 . -628) 193035) ((-1056 . -628) 193016) ((-1039 . -628) 192997) ((-726 . -1076) 192967) ((-711 . -658) 192917) ((-284 . -1120) T) ((-85 . -453) T) ((-85 . -407) T) ((-724 . -910) 192820) ((-723 . -174) T) ((-50 . -1120) T) ((-607 . -47) 192797) ((-227 . -660) 192762) ((-593 . -1120) T) ((-530 . -1120) T) ((-499 . -832) T) ((-499 . -938) T) ((-370 . -1241) T) ((-364 . -1241) T) ((-356 . 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191864) ((-1162 . -1143) 191809) ((-493 . -927) 191788) ((-1107 . -729) 191637) ((-1082 . -660) 191609) ((-970 . -660) 191498) ((-830 . -863) T) ((-794 . -729) 191327) ((-609 . -502) 191308) ((-597 . -502) 191289) ((-609 . -625) 191255) ((-597 . -625) 191221) ((-548 . -625) 191203) ((-591 . -1237) T) ((-548 . -626) 191184) ((-792 . -729) 191033) ((-1097 . -102) T) ((-635 . -658) 191005) ((-392 . -25) T) ((-392 . -21) T) ((-493 . -660) 190894) ((-473 . -729) 190865) ((-466 . -729) 190714) ((-1007 . -102) T) ((-1066 . -1230) 190643) ((-919 . -319) 190581) ((-889 . -93) T) ((-749 . -102) T) ((-118 . -658) 190511) ((-617 . -628) 190493) ((-726 . -628) 190447) ((-693 . -93) T) ((-543 . -25) T) ((-688 . -93) T) ((-676 . -625) 190429) ((-657 . -502) 190410) ((-657 . -625) 190363) ((-142 . -102) T) ((-44 . -132) T) ((-608 . -1237) T) ((-607 . -1237) T) ((-354 . -1078) T) ((-299 . -1132) T) ((-490 . -93) T) ((-419 . -237) 190314) ((-366 . -625) 190296) ((-363 . -625) 190278) ((-355 . -625) 190260) ((-273 . -626) 190008) ((-273 . -625) 189990) ((-253 . -625) 189972) ((-253 . -626) 189833) ((-139 . -93) T) ((-138 . -93) T) ((-134 . -93) T) ((-1161 . -625) 189815) ((-1140 . -652) 189802) ((-1140 . -1071) 189789) ((-831 . -738) T) ((-831 . -870) T) ((-614 . -298) 189766) ((-593 . -729) 189731) ((-491 . -626) NIL) ((-491 . -625) 189713) ((-530 . -729) 189658) ((-326 . -102) T) ((-323 . -102) T) ((-299 . -23) T) ((-153 . -132) T) ((-928 . -625) 189640) ((-928 . -626) 189622) ((-398 . -738) T) ((-885 . -1076) 189574) ((-885 . -111) 189512) ((-726 . -1069) T) ((-724 . -1263) 189496) ((-706 . -360) NIL) ((-115 . -102) T) ((-140 . -102) T) ((-137 . -102) T) ((-531 . -625) 189428) ((-390 . -807) T) ((-169 . -1237) T) ((-225 . -1120) T) ((-390 . -804) T) ((-59 . -626) 189389) ((-227 . -806) T) ((-227 . -803) T) ((-59 . -625) 189301) ((-227 . -738) T) ((-528 . -626) 189262) ((-528 . -625) 189174) ((-509 . -625) 189106) ((-508 . -626) 189067) ((-508 . -625) 188979) ((-1100 . -374) 188930) ((-40 . -423) 188907) ((-77 . -1237) T) ((-884 . -927) NIL) ((-370 . -339) 188891) ((-370 . -374) T) ((-364 . -339) 188875) ((-364 . -374) T) ((-356 . -339) 188859) ((-356 . -374) T) ((-326 . -294) 188838) ((-108 . -374) T) ((-70 . -1237) T) ((-1251 . -349) 188790) ((-884 . -660) 188735) ((-1251 . -388) 188687) ((-982 . -132) 188542) ((-827 . -132) 188413) ((-45 . -863) NIL) ((-976 . -663) 188397) ((-1107 . -174) 188308) ((-976 . -384) 188292) ((-1082 . -806) T) ((-1082 . -803) T) ((-885 . -628) 188190) ((-794 . -174) 188081) ((-792 . -174) 187992) ((-828 . -47) 187954) ((-1082 . -738) T) ((-337 . -501) 187938) ((-970 . -738) T) ((-1300 . -319) 187876) ((-1279 . -916) 187789) ((-466 . -174) 187700) ((-250 . -296) 187652) ((-1272 . -916) 187558) ((-1271 . -1076) 187393) ((-1251 . -916) 187226) ((-493 . -738) T) ((-1250 . -1076) 187034) ((-1231 . -300) 187013) ((-1206 . -1237) T) ((-1203 . -379) T) ((-1202 . -379) T) ((-1166 . -152) 186997) ((-1140 . -102) T) ((-1138 . -1120) T) ((-1100 . -23) T) ((-1100 . -1132) T) ((-1095 . -102) T) ((-1077 . -625) 186964) ((-1023 . -421) 186936) ((-945 . -973) T) ((-749 . -319) 186874) ((-75 . -1237) T) ((-676 . -393) 186846) ((-171 . -927) 186799) ((-30 . -973) T) ((-112 . -856) T) ((-1 . -625) 186781) ((-1019 . -910) 186702) ((-129 . -663) 186684) ((-50 . -632) 186668) ((-706 . -658) 186603) ((-607 . -916) 186516) ((-450 . -102) T) ((-129 . -384) 186498) ((-142 . -319) NIL) ((-885 . -1069) T) ((-845 . -861) 186477) ((-81 . -1237) T) ((-723 . -300) T) ((-40 . -1078) T) ((-593 . -174) T) ((-530 . -174) T) ((-523 . -625) 186459) ((-171 . -660) 186333) ((-519 . -625) 186315) ((-362 . -148) 186297) ((-362 . -146) T) ((-370 . -1132) T) ((-364 . -1132) T) ((-356 . -1132) T) ((-1024 . -317) T) ((-932 . -317) T) ((-885 . -248) T) ((-108 . -1132) T) ((-885 . -238) 186276) ((-1271 . -111) 186097) ((-1250 . -111) 185886) ((-250 . -1275) 185870) ((-576 . -860) T) ((-370 . -23) T) ((-365 . -360) T) ((-326 . -319) 185857) ((-323 . -319) 185798) ((-364 . -23) T) ((-329 . -132) T) ((-356 . -23) T) ((-1024 . -1042) T) ((-31 . -628) 185779) ((-108 . -23) T) ((-666 . -1071) 185763) ((-250 . -616) 185740) ((-343 . -1120) T) ((-666 . -652) 185710) ((-1273 . -38) 185602) ((-1260 . -927) 185581) ((-112 . -1120) T) ((-828 . -1237) T) ((-425 . -1237) T) ((-1055 . -102) T) ((-1260 . -660) 185470) ((-884 . -806) NIL) ((-868 . -660) 185444) ((-884 . -803) NIL) ((-828 . -900) NIL) ((-884 . -738) T) ((-1107 . -526) 185317) ((-794 . -526) 185264) ((-792 . -526) 185216) ((-583 . -660) 185203) ((-828 . -1058) 185031) ((-466 . -526) 184974) ((-400 . -401) T) ((-1271 . -628) 184787) ((-1250 . -628) 184535) ((-60 . -1237) T) ((-633 . -861) 184514) ((-512 . -673) T) ((-1166 . -996) 184483) ((-1044 . -658) 184420) ((-1023 . -464) T) ((-711 . -860) T) ((-522 . -804) T) ((-486 . -1076) 184255) ((-512 . -113) T) ((-354 . -1120) T) ((-323 . -1172) NIL) ((-299 . -132) T) ((-406 . -1120) T) ((-883 . -1078) T) ((-706 . -381) 184222) ((-365 . -658) 184152) ((-225 . -632) 184129) ((-337 . -296) 184081) ((-486 . -111) 183902) ((-1271 . -1069) T) ((-1250 . -1069) T) ((-828 . -388) 183886) ((-836 . -1237) T) ((-171 . -738) T) ((-1302 . -1237) T) ((-666 . -102) T) ((-1271 . -248) 183865) ((-1271 . -238) 183817) ((-1250 . -238) 183722) ((-1250 . -248) 183701) ((-1023 . -414) NIL) ((-682 . -651) 183649) ((-326 . -38) 183559) ((-323 . -38) 183488) ((-69 . -625) 183470) ((-329 . -505) 183436) ((-48 . -658) 183386) ((-1209 . -298) 183365) ((-1245 . -861) T) ((-1133 . -1132) 183343) ((-83 . -1237) T) ((-61 . -625) 183325) ((-877 . -863) T) ((-491 . -298) 183304) ((-1302 . -1058) 183281) ((-1184 . -1120) T) ((-1133 . -23) 183133) ((-828 . -916) 183069) ((-1260 . -738) T) ((-1122 . -1237) T) ((-486 . -628) 182895) ((-362 . -237) T) ((-1107 . -300) 182826) ((-984 . -1120) T) ((-907 . -102) T) ((-794 . -300) 182737) ((-337 . -19) 182721) ((-59 . -298) 182698) ((-792 . -300) 182629) ((-868 . -738) T) ((-118 . -860) NIL) ((-528 . -298) 182606) ((-337 . -616) 182583) ((-508 . -298) 182560) ((-466 . -300) 182491) ((-1055 . -319) 182342) ((-889 . -502) 182323) ((-889 . -625) 182289) ((-693 . -502) 182270) ((-583 . -738) T) ((-688 . -502) 182251) ((-693 . -625) 182201) ((-688 . -625) 182167) ((-674 . -625) 182149) ((-490 . -502) 182130) ((-490 . -625) 182096) ((-250 . -626) 182057) ((-250 . -502) 182034) ((-139 . -502) 182015) ((-138 . -502) 181996) ((-134 . -502) 181977) ((-250 . -625) 181869) ((-215 . -102) T) ((-139 . -625) 181835) ((-138 . -625) 181801) ((-134 . -625) 181767) ((-1167 . -34) T) ((-961 . -1237) T) ((-354 . -729) 181712) ((-682 . -25) T) ((-682 . -21) T) ((-1196 . -628) 181693) ((-341 . -1237) T) ((-486 . -1069) T) ((-647 . -429) 181658) ((-619 . -429) 181623) ((-1140 . -1172) T) ((-1272 . -317) 181602) ((-724 . -1071) 181425) ((-593 . -300) T) ((-530 . -300) T) ((-1251 . -317) 181404) ((-486 . -238) 181356) ((-486 . -248) 181335) ((-451 . -1237) T) ((-724 . -652) 181164) ((-1251 . -1042) NIL) ((-1100 . -132) T) ((-885 . -807) 181143) ((-145 . -102) T) ((-40 . -1120) T) ((-885 . -804) 181122) ((-656 . -1030) 181106) ((-592 . -1078) T) ((-576 . -1078) T) ((-507 . -1078) T) ((-419 . -464) T) ((-370 . -132) T) ((-326 . -412) 181090) ((-323 . -412) 181051) ((-364 . -132) T) ((-356 . -132) T) ((-1201 . -1120) T) ((-1140 . -38) 181038) ((-1114 . -625) 181005) ((-108 . -132) T) ((-972 . -1120) T) ((-939 . -1120) T) ((-783 . -1120) T) ((-684 . -1120) T) ((-713 . -148) T) ((-117 . -148) T) ((-1309 . -21) T) ((-1309 . -25) T) ((-1307 . -21) T) ((-1307 . -25) T) ((-676 . -1076) 180989) ((-543 . -861) T) ((-512 . -861) T) ((-376 . -1237) T) ((-366 . -1076) 180941) ((-363 . -1076) 180893) ((-355 . -1076) 180845) ((-258 . -1237) T) ((-257 . -1237) T) ((-273 . -1076) 180688) ((-253 . -1076) 180531) ((-676 . -111) 180510) ((-829 . -1241) 180489) ((-559 . -856) T) ((-326 . -918) 180455) ((-366 . -111) 180393) ((-363 . -111) 180331) ((-355 . -111) 180269) ((-273 . -111) 180098) ((-253 . -111) 179927) ((-323 . -918) NIL) ((-635 . -423) 179911) ((-44 . -21) T) ((-44 . -25) T) ((-923 . -863) 179862) ((-827 . -651) 179768) ((-829 . -568) 179747) ((-499 . -863) T) ((-258 . -1058) 179574) ((-257 . -1058) 179401) ((-127 . -120) 179385) ((-219 . -863) T) ((-928 . -1076) 179350) ((-724 . -102) T) ((-711 . -1078) T) ((-609 . -628) 179331) ((-597 . -628) 179312) ((-548 . -630) 179215) ((-354 . -174) T) ((-153 . -21) T) ((-153 . -25) T) ((-88 . -625) 179197) ((-928 . -111) 179153) ((-40 . -729) 179098) ((-883 . -1120) T) ((-676 . -628) 179075) ((-657 . -628) 179056) ((-366 . -628) 178993) ((-363 . -628) 178930) ((-355 . -628) 178867) ((-559 . -1120) T) ((-337 . -626) 178828) ((-337 . -625) 178740) ((-273 . -628) 178493) ((-253 . -628) 178278) ((-188 . -1237) T) ((-1250 . -804) 178231) ((-1250 . -807) 178184) ((-258 . -388) 178153) ((-257 . -388) 178122) ((-561 . -863) T) ((-666 . -38) 178092) ((-620 . -34) T) ((-494 . -1132) 178070) ((-487 . -34) T) ((-1133 . -132) 177941) ((-982 . -25) 177752) ((-928 . -628) 177702) ((-887 . -625) 177684) ((-982 . -21) 177639) ((-827 . -25) 177472) ((-827 . -21) 177383) ((-1243 . -379) T) ((-635 . -1078) T) ((-1198 . -568) 177362) ((-1192 . -47) 177339) ((-366 . -1069) T) ((-363 . -1069) T) ((-494 . -23) 177191) ((-355 . -1069) T) ((-273 . -1069) T) ((-253 . -1069) T) ((-1145 . -47) 177163) ((-118 . -1078) T) ((-1054 . -660) 177137) ((-976 . -34) T) ((-366 . -238) 177116) ((-366 . -248) T) ((-363 . -238) 177095) ((-363 . -248) T) ((-355 . -238) 177074) ((-355 . -248) T) ((-273 . -336) 177046) ((-253 . -336) 177003) ((-273 . -238) 176982) ((-1177 . -152) 176966) ((-258 . -916) 176898) ((-257 . -916) 176830) ((-1162 . -910) 176751) ((-1102 . -861) T) ((-1254 . -1237) 176729) ((-426 . -1132) T) ((-1074 . -23) T) ((-1044 . -860) T) ((-928 . -1069) T) ((-332 . -660) 176711) ((-713 . -237) T) ((-682 . -234) 176656) ((-1231 . -1022) 176622) ((-1193 . -938) 176601) ((-1187 . -938) 176580) ((-1187 . -832) NIL) ((-1019 . -1071) 176476) ((-985 . -1237) T) ((-928 . -248) T) ((-829 . -374) 176455) ((-396 . -23) T) ((-128 . -1120) 176433) ((-122 . -1120) 176411) ((-928 . -238) T) ((-129 . -34) T) ((-390 . -660) 176376) ((-1019 . -652) 176324) ((-883 . -729) 176311) ((-1316 . -658) 176283) ((-1066 . -152) 176248) ((-1013 . -1237) T) ((-875 . -1237) T) ((-40 . -174) T) ((-706 . -423) 176230) ((-724 . -319) 176217) ((-848 . -660) 176177) ((-839 . -660) 176151) ((-329 . -25) T) ((-329 . -21) T) ((-670 . -296) 176130) ((-592 . -1120) T) ((-576 . -1120) T) ((-507 . -1120) T) ((-1192 . -1237) T) ((-250 . -298) 176107) ((-1145 . -1237) T) ((-867 . -1237) T) ((-323 . -272) 176068) ((-323 . -232) 176029) ((-1242 . -863) T) ((-1192 . -900) NIL) ((-55 . -1120) T) ((-1145 . -900) 175888) ((-130 . -861) T) ((-1192 . -1058) 175768) ((-1145 . -1058) 175651) ((-185 . -625) 175633) ((-867 . -1058) 175529) ((-794 . -296) 175456) ((-829 . -1132) T) ((-1054 . -738) T) ((-1066 . -996) 175385) ((-614 . -663) 175369) ((-1023 . -910) 175276) ((-1019 . -102) T) ((-829 . -23) T) ((-724 . -1172) 175254) ((-706 . -1078) T) ((-614 . -384) 175238) ((-362 . -464) T) ((-354 . -300) T) ((-1288 . -1120) T) ((-254 . -1120) T) ((-411 . -102) T) ((-299 . -21) T) ((-299 . -25) T) ((-372 . -738) T) ((-722 . -1120) T) ((-711 . -1120) T) ((-372 . -485) T) ((-1231 . -625) 175220) ((-1192 . -388) 175204) ((-1145 . -388) 175188) ((-1044 . -423) 175150) ((-142 . -231) 175132) ((-390 . -806) T) ((-390 . -803) T) ((-883 . -174) T) ((-390 . -738) T) ((-723 . -625) 175114) ((-724 . -38) 174943) ((-1287 . -1285) 174927) ((-362 . -414) T) ((-1287 . -1120) 174877) ((-1210 . -1120) T) ((-592 . -729) 174864) ((-576 . -729) 174851) ((-507 . -729) 174816) ((-1273 . -658) 174706) ((-326 . -641) 174685) ((-848 . -738) T) ((-839 . -738) T) ((-1135 . -1237) T) ((-656 . -1237) T) ((-1100 . -651) 174633) ((-1192 . -916) 174576) ((-1145 . -916) 174560) ((-827 . -234) 174451) ((-674 . -1076) 174435) ((-108 . -651) 174417) ((-494 . -132) 174288) ((-1198 . -1132) T) ((-831 . -1237) T) ((-970 . -47) 174257) ((-635 . -1120) T) ((-674 . -111) 174236) ((-503 . -625) 174202) ((-337 . -298) 174179) ((-398 . -1237) T) ((-334 . -1237) T) ((-493 . -47) 174136) ((-1198 . -23) T) ((-118 . -1120) T) ((-103 . -102) 174086) ((-1299 . -1132) T) ((-560 . -861) T) ((-227 . -1237) T) ((-1074 . -132) T) ((-1044 . -1078) T) ((-1299 . -23) T) ((-831 . -1058) 174070) ((-1217 . -625) 174052) ((-1023 . -736) 174024) ((-1140 . -840) T) ((-711 . -729) 173989) ((-598 . -625) 173971) ((-398 . -1058) 173955) ((-365 . -1078) T) ((-396 . -132) T) ((-334 . -1058) 173939) ((-1125 . -1120) T) ((-1100 . -21) T) ((-1100 . -25) T) ((-227 . -900) 173921) ((-1024 . -938) T) ((-91 . -34) T) ((-1024 . -832) T) ((-932 . -938) T) ((-1019 . -319) 173886) ((-889 . -628) 173867) ((-499 . -1241) T) ((-726 . -660) 173827) ((-693 . -628) 173808) ((-688 . -628) 173789) ((-219 . -1241) T) ((-419 . -910) 173710) ((-227 . -1058) 173670) ((-40 . -300) T) ((-499 . -568) T) ((-490 . -628) 173651) ((-370 . -25) T) ((-326 . -658) 173306) ((-323 . -658) 173220) ((-370 . -21) T) ((-364 . -25) T) ((-364 . -21) T) ((-219 . -568) T) ((-356 . -25) T) ((-356 . -21) T) ((-329 . -234) 173166) ((-250 . -628) 173143) ((-139 . -628) 173124) ((-138 . -628) 173105) ((-134 . -628) 173086) ((-108 . -25) T) ((-108 . -21) T) ((-48 . -1078) T) ((-592 . -174) T) ((-576 . -174) T) ((-507 . -174) T) ((-1082 . -1237) T) ((-970 . -1237) T) ((-725 . -1237) T) ((-670 . -625) 173068) ((-493 . -1237) T) ((-749 . -748) 173052) ((-347 . -625) 173034) ((-68 . -394) T) ((-68 . -407) T) ((-1122 . -107) 173018) ((-1082 . -900) 173000) ((-970 . -900) 172925) ((-665 . -1132) T) ((-635 . -729) 172912) ((-493 . -900) NIL) ((-1166 . -102) T) ((-1114 . -630) 172896) ((-1082 . -1058) 172878) ((-97 . -625) 172860) ((-489 . -148) T) ((-970 . -1058) 172740) ((-118 . -729) 172685) ((-724 . -918) 172592) ((-665 . -23) T) ((-493 . -1058) 172468) ((-1107 . -626) NIL) ((-1107 . -625) 172450) ((-794 . -626) NIL) ((-794 . -625) 172411) ((-792 . -626) 172045) ((-792 . -625) 171959) ((-1133 . -651) 171865) ((-811 . -863) 171844) ((-473 . -625) 171826) ((-466 . -625) 171808) ((-466 . -626) 171669) ((-1055 . -231) 171615) ((-885 . -927) 171594) ((-127 . -34) T) ((-829 . -132) T) ((-661 . -625) 171576) ((-590 . -102) T) ((-366 . -1306) 171560) ((-363 . -1306) 171544) ((-355 . -1306) 171528) ((-122 . -526) 171461) ((-128 . -526) 171394) ((-523 . -804) T) ((-523 . -807) T) ((-522 . -806) T) ((-103 . -319) 171332) ((-224 . -102) 171282) ((-711 . -174) T) ((-706 . -1120) T) ((-885 . -660) 171198) ((-65 . -395) T) ((-284 . -625) 171180) ((-65 . -407) T) ((-970 . -388) 171164) ((-883 . -300) T) ((-50 . -625) 171146) ((-1019 . -38) 171094) ((-1140 . -658) 171066) ((-593 . -625) 171048) ((-493 . -388) 171032) ((-593 . -626) 171014) ((-530 . -625) 170996) ((-928 . -1306) 170983) ((-884 . -1237) T) ((-713 . -464) T) ((-507 . -526) 170949) ((-1298 . -1237) T) ((-1297 . -1237) T) ((-499 . -374) T) ((-366 . -379) 170928) ((-363 . -379) 170907) ((-355 . -379) 170886) ((-726 . -738) T) ((-219 . -374) T) ((-117 . -464) T) ((-1310 . -1301) 170870) ((-884 . -898) 170847) ((-884 . -900) NIL) ((-982 . -861) 170746) ((-827 . -861) 170697) ((-1244 . -102) T) ((-666 . -668) 170681) ((-1223 . -34) T) ((-173 . -625) 170663) ((-1133 . -25) 170496) ((-1133 . -21) 170407) ((-884 . -1058) 170384) ((-970 . -916) 170365) ((-1260 . -47) 170342) ((-928 . -379) T) ((-605 . -863) T) ((-59 . -663) 170326) ((-528 . -663) 170310) ((-493 . -916) 170287) ((-71 . -453) T) ((-71 . -407) T) ((-508 . -663) 170271) ((-59 . -384) 170255) ((-635 . -174) T) ((-528 . -384) 170239) ((-508 . -384) 170223) ((-558 . -1237) T) ((-839 . -720) 170207) ((-1192 . -317) 170186) ((-1198 . -132) T) ((-1162 . -1071) 170170) ((-118 . -174) T) ((-1162 . -652) 170102) ((-1166 . -319) 170040) ((-171 . -1237) T) ((-1299 . -132) T) ((-1272 . -938) 170019) ((-1251 . -938) 169998) ((-1251 . -832) NIL) ((-879 . -1071) 169968) ((-647 . -756) 169952) ((-619 . -756) 169936) ((-1250 . -927) 169889) ((-1044 . -1120) T) ((-923 . -1132) T) ((-879 . -652) 169859) ((-706 . -729) 169809) ((-914 . -1237) T) ((-884 . -388) 169786) ((-884 . -349) 169763) ((-853 . -1237) T) ((-820 . -1237) T) ((-171 . -898) 169747) ((-171 . -900) 169672) ((-781 . -1237) T) ((-689 . -1237) T) ((-1287 . -526) 169605) ((-1271 . -660) 169502) ((-1100 . -234) 169375) ((-499 . -1132) T) ((-365 . -1120) T) ((-219 . -1132) T) ((-76 . -453) T) ((-76 . -407) T) ((-171 . -1058) 169271) ((-304 . -910) 169228) ((-329 . -861) T) ((-1250 . -660) 169036) ((-885 . -806) 169015) ((-885 . -803) 168994) ((-885 . -738) T) ((-499 . -23) T) ((-370 . -234) 168967) ((-364 . -234) 168940) ((-356 . -234) 168913) ((-176 . -464) T) ((-86 . -453) T) ((-224 . -319) 168851) ((-86 . -407) T) ((-225 . -625) 168833) ((-108 . -234) 168820) ((-219 . -23) T) ((-1311 . -1304) 168799) ((-689 . -1058) 168783) ((-592 . -300) T) ((-576 . -300) T) ((-507 . -300) T) ((-1260 . -1237) T) ((-137 . -482) 168738) ((-868 . -1237) T) ((-666 . -658) 168697) ((-48 . -1120) T) ((-724 . -272) 168681) ((-724 . -232) 168665) ((-884 . -916) NIL) ((-583 . -1237) T) ((-1260 . -900) NIL) ((-903 . -102) T) ((-899 . -102) T) ((-400 . -1120) T) ((-171 . -388) 168649) ((-171 . -349) 168633) ((-1260 . -1058) 168513) ((-868 . -1058) 168409) ((-1162 . -102) T) ((-1019 . -918) 168332) ((-674 . -804) 168311) ((-665 . -132) T) ((-674 . -807) 168290) ((-118 . -526) 168198) ((-583 . -1058) 168180) ((-304 . -1294) 168150) ((-1187 . -863) NIL) ((-879 . -102) T) ((-981 . -568) 168129) ((-1231 . -1076) 168012) ((-1023 . -1071) 167957) ((-494 . -651) 167863) ((-922 . -1120) T) ((-1044 . -729) 167800) ((-723 . -1076) 167765) ((-1023 . -652) 167710) ((-629 . -102) T) ((-614 . -34) T) ((-1167 . -1237) T) ((-1231 . -111) 167579) ((-486 . -660) 167476) ((-365 . -729) 167421) ((-171 . -916) 167380) ((-711 . -300) T) ((-706 . -174) T) ((-723 . -111) 167336) ((-1316 . -1078) T) ((-1260 . -388) 167320) ((-430 . -1241) 167298) ((-1138 . -625) 167280) ((-323 . -860) NIL) ((-430 . -568) T) ((-227 . -317) T) ((-1250 . -803) 167233) ((-1250 . -806) 167186) ((-1271 . -738) T) ((-1250 . -738) T) ((-48 . -729) 167151) ((-227 . -1042) T) ((-1273 . -423) 167117) ((-1260 . -916) 167060) ((-362 . -1294) 167037) ((-1231 . -628) 166919) ((-730 . -738) T) ((-343 . -625) 166901) ((-532 . -863) 166880) ((-1133 . -234) 166771) ((-112 . -625) 166753) ((-112 . -626) 166735) ((-730 . -485) T) ((-723 . -628) 166685) ((-1310 . -1071) 166669) ((-494 . -25) 166502) ((-128 . -501) 166486) ((-122 . -501) 166470) ((-494 . -21) 166381) ((-1310 . -652) 166351) ((-635 . -300) T) ((-598 . -1076) 166326) ((-449 . -1120) T) ((-1082 . -317) T) ((-118 . -300) T) ((-1124 . -102) T) ((-1023 . -102) T) ((-598 . -111) 166294) ((-1231 . -1069) T) ((-1162 . -319) 166232) ((-1082 . -1042) T) ((-1074 . -25) T) ((-66 . -1237) T) ((-906 . -1237) T) ((-1074 . -21) T) ((-723 . -1069) T) ((-396 . -21) T) ((-396 . -25) T) ((-706 . -526) NIL) ((-1044 . -174) T) ((-723 . -248) T) ((-1082 . -557) T) ((-724 . -658) 166142) ((-518 . -102) T) ((-514 . -102) T) ((-365 . -174) T) ((-354 . -625) 166124) ((-419 . -1071) 166076) ((-406 . -625) 166058) ((-1140 . -860) T) ((-486 . -738) T) ((-906 . -1058) 166026) ((-419 . -652) 165978) ((-108 . -861) T) ((-670 . -1076) 165962) ((-499 . -132) T) ((-1273 . -1078) T) ((-219 . -132) T) ((-1177 . -102) 165912) ((-99 . -1120) T) ((-245 . -863) 165863) ((-250 . -678) 165847) ((-250 . -663) 165831) ((-670 . -111) 165810) ((-598 . -628) 165794) ((-326 . -423) 165778) ((-250 . -384) 165762) ((-1179 . -240) 165709) ((-1019 . -272) 165693) ((-1019 . -232) 165677) ((-74 . -1237) T) ((-48 . -174) T) ((-713 . -399) T) ((-713 . -144) T) ((-1310 . -102) T) ((-1218 . -1237) T) ((-1217 . -628) 165659) ((-1108 . -1237) T) ((-1107 . -1076) 165502) ((-1096 . -1237) T) ((-273 . -927) 165481) ((-253 . -927) 165460) ((-794 . -1076) 165283) ((-792 . -1076) 165126) ((-620 . -1237) T) ((-1184 . -625) 165108) ((-1107 . -111) 164937) ((-1066 . -102) T) ((-487 . -1237) T) ((-473 . -1076) 164908) ((-466 . -1076) 164751) ((-676 . -660) 164735) ((-884 . -317) T) ((-794 . -111) 164544) ((-792 . -111) 164373) ((-366 . -660) 164325) ((-363 . -660) 164277) ((-355 . -660) 164229) ((-273 . -660) 164118) ((-253 . -660) 164007) ((-1178 . -861) T) ((-1108 . -1058) 163991) ((-1096 . -1058) 163968) ((-1024 . -863) T) ((-473 . -111) 163929) ((-466 . -111) 163758) ((-1020 . -34) T) ((-991 . -863) T) ((-984 . -625) 163740) ((-976 . -1237) T) ((-127 . -1030) 163724) ((-981 . -1132) T) ((-884 . -1042) NIL) ((-747 . -1132) T) ((-727 . -1132) T) ((-670 . -628) 163642) ((-1287 . -501) 163626) ((-1204 . -1237) T) ((-1203 . -1237) T) ((-1162 . -38) 163586) ((-981 . -23) T) ((-928 . -660) 163551) ((-878 . -1120) T) ((-855 . -102) T) ((-829 . -21) T) ((-647 . -1071) 163535) ((-619 . -1071) 163519) ((-829 . -25) T) ((-747 . -23) T) ((-727 . -23) T) ((-647 . -652) 163503) ((-110 . -673) T) ((-619 . -652) 163487) ((-593 . -1076) 163452) ((-530 . -1076) 163397) ((-229 . -57) 163355) ((-465 . -23) T) ((-419 . -102) T) ((-1202 . -1237) T) ((-270 . -102) T) ((-110 . -113) T) ((-706 . -300) T) ((-879 . -38) 163325) ((-1107 . -628) 163061) ((-593 . -111) 163017) ((-530 . -111) 162946) ((-430 . -1132) T) ((-326 . -1078) 162836) ((-323 . -1078) T) ((-129 . -1237) T) ((-131 . -1237) T) ((-794 . -628) 162584) ((-792 . -628) 162350) ((-670 . -1069) T) ((-1316 . -1120) T) ((-466 . -628) 162135) ((-171 . -317) 162066) ((-430 . -23) T) ((-40 . -625) 162048) ((-40 . -626) 162032) ((-108 . -1012) 162014) ((-117 . -882) 161998) ((-661 . -628) 161982) ((-48 . -526) 161948) ((-1223 . -1030) 161932) ((-1201 . -625) 161899) ((-1209 . -34) T) ((-972 . -625) 161865) ((-939 . -625) 161847) ((-1133 . -861) 161798) ((-783 . -625) 161780) ((-684 . -625) 161762) ((-529 . -1237) T) ((-1260 . -317) 161741) ((-1177 . -319) 161679) ((-1161 . -34) T) ((-491 . -34) T) ((-1112 . -1237) T) ((-489 . -464) T) ((-1054 . -1237) T) ((-1107 . -1069) T) ((-50 . -628) 161648) ((-794 . -1069) T) ((-792 . -1069) T) ((-659 . -240) 161632) ((-644 . -240) 161578) ((-1198 . -21) T) ((-593 . -628) 161528) ((-530 . -628) 161458) ((-494 . -234) 161349) ((-1198 . -25) T) ((-1107 . -336) 161310) ((-466 . -1069) T) ((-1107 . -238) 161289) ((-794 . -336) 161266) ((-794 . -238) T) ((-792 . -336) 161238) ((-743 . -1241) 161217) ((-531 . -34) T) ((-337 . -663) 161201) ((-528 . -34) T) ((-59 . -34) T) ((-509 . -34) T) ((-508 . -34) T) ((-466 . -336) 161180) ((-337 . -384) 161164) ((-372 . -1237) T) ((-332 . -1237) T) ((-1023 . -1172) NIL) ((-743 . -568) 161095) ((-647 . -102) T) ((-619 . -102) T) ((-366 . -738) T) ((-363 . -738) T) ((-355 . -738) T) ((-273 . -738) T) ((-253 . -738) T) ((-390 . -1237) T) ((-1299 . -21) T) ((-1066 . -319) 161003) ((-1299 . -25) T) ((-919 . -1120) 160981) ((-830 . -234) 160968) ((-50 . -1069) T) ((-1194 . -568) 160947) ((-1193 . -1241) 160926) ((-1193 . -568) 160877) ((-1187 . -1241) 160856) ((-1187 . -568) 160807) ((-1044 . -300) T) ((-593 . -1069) T) ((-530 . -1069) T) ((-1023 . -38) 160752) ((-372 . -1058) 160736) ((-332 . -1058) 160720) ((-1019 . -658) 160643) ((-390 . -900) 160625) ((-848 . -1237) T) ((-839 . -1237) T) ((-837 . -1237) T) ((-811 . -1132) T) ((-928 . -738) T) ((-593 . -248) T) ((-593 . -238) T) ((-530 . -238) T) ((-530 . -248) T) ((-1146 . -568) 160604) ((-365 . -300) T) ((-659 . -707) 160588) ((-390 . -1058) 160548) ((-304 . -1071) 160469) ((-350 . -910) 160448) ((-1140 . -1078) T) ((-103 . -126) 160432) ((-304 . -652) 160374) ((-811 . -23) T) ((-1309 . -1304) 160350) ((-1307 . -1304) 160329) ((-1287 . -296) 160281) ((-419 . -319) 160246) ((-1273 . -1120) T) ((-1162 . -918) 160169) ((-883 . -625) 160151) ((-848 . -1058) 160120) ((-205 . -799) T) ((-204 . -799) T) ((-203 . -799) T) ((-202 . -799) T) ((-201 . -799) T) ((-200 . -799) T) ((-199 . -799) T) ((-198 . -799) T) ((-197 . -799) T) ((-196 . -799) T) ((-559 . -625) 160102) ((-507 . -1022) T) ((-283 . -851) T) ((-282 . -851) T) ((-281 . -851) T) ((-280 . -851) T) 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. -1132) T) ((-1146 . -1132) T) ((-354 . -111) 158463) ((-1024 . -1241) T) ((-127 . -1237) T) ((-932 . -1241) T) ((-1187 . -23) T) ((-1162 . -272) 158447) ((-706 . -296) NIL) ((-726 . -1237) T) ((-1162 . -232) 158431) ((-1146 . -23) T) ((-1095 . -1120) T) ((-1024 . -568) T) ((-932 . -568) T) ((-255 . -1237) T) ((-189 . -1237) T) ((-163 . -1237) T) ((-158 . -1237) T) ((-254 . -625) 158413) ((-827 . -237) 158310) ((-811 . -132) T) ((-722 . -625) 158292) ((-326 . -729) 158202) ((-323 . -729) 158131) ((-711 . -625) 158113) ((-711 . -626) 158058) ((-419 . -412) 158042) ((-450 . -1120) T) ((-499 . -25) T) ((-499 . -21) T) ((-1140 . -1120) T) ((-219 . -25) T) ((-219 . -21) T) ((-724 . -423) 158026) ((-726 . -1058) 157995) ((-1287 . -625) 157907) ((-1287 . -626) 157868) ((-1273 . -174) T) ((-1210 . -625) 157850) ((-250 . -34) T) ((-354 . -628) 157780) ((-406 . -628) 157762) ((-944 . -994) T) ((-1223 . -1237) T) ((-674 . -803) 157741) ((-674 . -806) 157720) ((-410 . -407) T) ((-535 . -102) 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-152) 142694) ((-1019 . -300) 142645) ((-887 . -1237) T) ((-629 . -1120) T) ((-227 . -568) T) ((-329 . -1268) 142629) ((-329 . -1265) 142599) ((-713 . -658) 142571) ((-1209 . -1213) 142550) ((-1095 . -625) 142532) ((-1209 . -107) 142482) ((-659 . -152) 142466) ((-644 . -152) 142412) ((-117 . -658) 142384) ((-491 . -1213) 142363) ((-499 . -148) T) ((-499 . -146) NIL) ((-1140 . -626) 142278) ((-450 . -625) 142260) ((-219 . -148) T) ((-219 . -146) NIL) ((-1140 . -625) 142242) ((-130 . -102) T) ((-52 . -102) T) ((-1251 . -651) 142194) ((-491 . -107) 142144) ((-1013 . -23) T) ((-1311 . -38) 142114) ((-1192 . -1132) T) ((-1145 . -1132) T) ((-1082 . -1241) T) ((-245 . -234) 142005) ((-321 . -102) T) ((-867 . -1132) T) ((-970 . -1241) 141984) ((-493 . -1241) 141963) ((-1082 . -568) T) ((-970 . -568) 141894) ((-1192 . -23) T) ((-1171 . -1103) T) ((-1145 . -23) T) ((-867 . -23) T) ((-493 . -568) 141825) ((-1162 . -729) 141757) ((-682 . -1071) 141741) ((-1166 . -526) 141674) ((-682 . -652) 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T) ((-334 . -23) T) ((-1187 . -1012) 140171) ((-1273 . -1076) 140076) ((-855 . -1120) T) ((-129 . -863) T) ((-1146 . -752) 140055) ((-1271 . -938) 140034) ((-1250 . -938) 140013) ((-883 . -738) T) ((-171 . -568) 139924) ((-592 . -660) 139911) ((-576 . -660) 139883) ((-419 . -1120) T) ((-270 . -1120) T) ((-215 . -625) 139865) ((-507 . -660) 139815) ((-227 . -23) T) ((-1250 . -832) 139768) ((-1309 . -102) T) ((-503 . -1237) T) ((-365 . -1306) 139745) ((-1307 . -102) T) ((-1273 . -111) 139637) ((-1133 . -910) 139504) ((-827 . -1071) 139405) ((-827 . -652) 139327) ((-145 . -625) 139309) ((-1013 . -132) T) ((-44 . -102) T) ((-245 . -861) 139260) ((-598 . -1237) T) ((-1260 . -1241) 139239) ((-103 . -501) 139223) ((-1310 . -729) 139193) ((-1107 . -47) 139154) ((-1082 . -1132) T) ((-970 . -1132) T) ((-128 . -34) T) ((-122 . -34) T) ((-1260 . -568) 139065) ((-794 . -47) 139042) ((-792 . -47) 139014) ((-1217 . -1237) T) ((-1192 . -132) T) ((-365 . -379) T) ((-493 . -1132) T) ((-1145 . -132) T) 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. -111) 137332) ((-97 . -1237) T) ((-982 . -102) T) ((-827 . -102) 137064) ((-724 . -626) NIL) ((-724 . -625) 137046) ((-1273 . -336) 136990) ((-670 . -1058) 136886) ((-1107 . -1237) T) ((-1055 . -298) 136861) ((-592 . -738) T) ((-576 . -806) T) ((-171 . -374) 136812) ((-576 . -803) T) ((-576 . -738) T) ((-507 . -738) T) ((-794 . -1237) T) ((-792 . -1237) T) ((-1166 . -501) 136796) ((-473 . -1237) T) ((-466 . -1237) T) ((-1309 . -1308) 136772) ((-1107 . -900) NIL) ((-884 . -1132) T) ((-118 . -927) NIL) ((-1307 . -1308) 136751) ((-661 . -1237) T) ((-794 . -900) NIL) ((-792 . -900) 136610) ((-1302 . -25) T) ((-1302 . -21) T) ((-1234 . -102) 136588) ((-1126 . -407) T) ((-635 . -660) 136575) ((-466 . -900) NIL) ((-687 . -102) 136525) ((-1107 . -1058) 136352) ((-884 . -23) T) ((-794 . -1058) 136211) ((-792 . -1058) 136068) ((-118 . -660) 136013) ((-466 . -1058) 135889) ((-284 . -1237) T) ((-326 . -628) 135453) ((-323 . -628) 135336) ((-50 . -1237) T) ((-402 . -658) 135305) ((-661 . -1058) 135289) ((-639 . -102) T) ((-593 . -1237) T) ((-530 . -1237) T) ((-224 . -501) 135273) ((-1287 . -34) T) ((-633 . -658) 135232) ((-299 . -1071) 135219) ((-137 . -628) 135203) ((-299 . -652) 135190) ((-647 . -729) 135174) ((-619 . -729) 135158) ((-682 . -38) 135118) ((-329 . -102) T) ((-1140 . -1076) 135105) ((-85 . -625) 135087) ((-50 . -1058) 135071) ((-1107 . -388) 135055) ((-794 . -388) 135039) ((-711 . -738) T) ((-711 . -806) T) ((-711 . -803) T) ((-60 . -57) 135001) ((-593 . -1058) 134988) ((-530 . -1058) 134965) ((-173 . -1237) T) ((-334 . -132) T) ((-326 . -1069) 134855) ((-323 . -1069) T) ((-171 . -1132) T) ((-792 . -388) 134839) ((-45 . -152) 134789) ((-1024 . -1012) 134771) ((-466 . -388) 134755) ((-419 . -174) T) ((-326 . -248) 134734) ((-323 . -248) T) ((-323 . -238) NIL) ((-304 . -1120) 134516) ((-227 . -132) T) ((-1140 . -111) 134501) ((-171 . -23) T) ((-811 . -148) 134480) ((-811 . -146) 134459) ((-258 . -651) 134365) ((-257 . -651) 134271) ((-329 . -294) 134237) ((-1177 . -526) 134170) ((-489 . -658) 134120) ((-494 . -910) 133987) ((-1153 . -1120) T) ((-227 . -1080) T) ((-827 . -319) 133925) ((-1107 . -916) 133860) ((-794 . -916) 133803) ((-792 . -916) 133787) ((-1309 . -38) 133757) ((-1307 . -38) 133727) ((-1260 . -1132) T) ((-868 . -1132) T) ((-466 . -916) 133704) ((-871 . -1120) T) ((-1260 . -23) T) ((-1140 . -628) 133676) ((-1082 . -132) T) ((-868 . -23) T) ((-583 . -1132) T) ((-635 . -738) T) ((-522 . -863) T) ((-366 . -938) T) ((-363 . -938) T) ((-299 . -102) T) ((-355 . -938) T) ((-990 . -1103) T) ((-970 . -132) T) ((-828 . -234) 133621) ((-118 . -806) NIL) ((-118 . -803) NIL) ((-118 . -738) T) ((-1066 . -526) 133522) ((-706 . -927) NIL) ((-583 . -23) T) ((-493 . -132) T) ((-430 . -237) 133473) ((-687 . -319) 133411) ((-225 . -1237) T) ((-647 . -773) T) ((-619 . -773) T) ((-1251 . -861) NIL) ((-1100 . -1071) 133321) ((-1023 . -300) T) ((-706 . -660) 133271) ((-258 . -25) T) ((-362 . -1120) T) ((-258 . -21) T) ((-257 . -25) T) ((-257 . -21) T) 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-102) T) ((-362 . -729) 132033) ((-885 . -863) 131984) ((-743 . -148) 131963) ((-743 . -146) 131942) ((-666 . -628) 131860) ((-1044 . -660) 131797) ((-535 . -1120) 131775) ((-370 . -102) T) ((-364 . -102) T) ((-356 . -102) T) ((-108 . -102) T) ((-516 . -1120) T) ((-365 . -660) 131720) ((-1192 . -651) 131668) ((-1145 . -651) 131616) ((-396 . -521) 131595) ((-845 . -860) 131574) ((-706 . -738) T) ((-390 . -1241) T) ((-343 . -1237) T) ((-1251 . -1012) 131526) ((-350 . -1078) T) ((-112 . -1237) T) ((-176 . -1078) T) ((-103 . -625) 131458) ((-1194 . -146) 131437) ((-1194 . -148) 131416) ((-390 . -568) T) ((-1193 . -148) 131395) ((-1193 . -146) 131374) ((-1187 . -146) 131281) ((-419 . -300) T) ((-1187 . -148) 131188) ((-1146 . -148) 131167) ((-1146 . -146) 131146) ((-329 . -38) 130987) ((-171 . -132) T) ((-323 . -807) NIL) ((-323 . -804) NIL) ((-666 . -1069) T) ((-48 . -660) 130937) ((-1133 . -1071) 130838) ((-907 . -628) 130815) ((-1133 . -652) 130737) ((-1186 . -102) T) ((-1014 . -102) T) 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((-211 . -102) T) ((-210 . -102) T) ((-209 . -102) T) ((-208 . -102) T) ((-205 . -102) T) ((-204 . -102) T) ((-203 . -102) T) ((-202 . -102) T) ((-201 . -102) T) ((-200 . -102) T) ((-199 . -102) T) ((-198 . -102) T) ((-197 . -102) T) ((-196 . -102) T) ((-195 . -102) T) ((-724 . -111) 129282) ((-365 . -738) T) ((-682 . -272) 129266) ((-682 . -232) 129250) ((-593 . -317) T) ((-530 . -317) T) ((-304 . -526) 129199) ((-1184 . -1237) T) ((-108 . -319) NIL) ((-72 . -407) T) ((-1133 . -102) 128931) ((-845 . -423) 128915) ((-1140 . -807) T) ((-1140 . -804) T) ((-713 . -1120) T) ((-590 . -625) 128897) ((-390 . -374) T) ((-171 . -505) 128875) ((-224 . -625) 128807) ((-135 . -1120) T) ((-117 . -1120) T) ((-984 . -1237) T) ((-48 . -738) T) ((-1066 . -501) 128772) ((-142 . -437) 128754) ((-142 . -379) T) ((-1047 . -102) T) ((-524 . -521) 128733) ((-724 . -628) 128489) ((-1244 . -625) 128471) ((-1201 . -1237) T) ((-1201 . -1058) 128407) ((-1194 . -237) 128366) ((-488 . -102) T) ((-475 . -102) T) 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. -381) 115378) ((-362 . -625) 115360) ((-332 . -21) T) ((-365 . -1058) 115337) ((-332 . -25) T) ((-1187 . -993) 115306) ((-48 . -1237) T) ((-76 . -625) 115288) ((-1146 . -993) 115255) ((-711 . -317) T) ((-130 . -856) T) ((-928 . -374) T) ((-390 . -25) T) ((-390 . -21) T) ((-928 . -339) 115242) ((-86 . -625) 115224) ((-711 . -1042) T) ((-689 . -861) T) ((-400 . -1237) T) ((-1271 . -132) T) ((-1250 . -132) T) ((-919 . -1030) 115208) ((-848 . -21) T) ((-48 . -1058) 115151) ((-848 . -25) T) ((-839 . -25) T) ((-839 . -21) T) ((-1133 . -658) 114930) ((-1309 . -1078) T) ((-561 . -102) T) ((-1307 . -1078) T) ((-666 . -738) T) ((-1124 . -630) 114833) ((-1023 . -628) 114763) ((-1310 . -1076) 114747) ((-922 . -1237) T) ((-827 . -423) 114716) ((-103 . -120) 114700) ((-130 . -1120) T) ((-52 . -1120) T) ((-944 . -625) 114682) ((-884 . -1012) 114659) ((-835 . -102) T) ((-1310 . -111) 114638) ((-743 . -910) 114613) ((-665 . -38) 114583) ((-583 . -861) T) ((-366 . -1132) T) ((-363 . -1132) T) ((-355 . 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T) ((-362 . -238) T) ((-362 . -248) T) ((-323 . -1237) T) ((-299 . -1120) T) ((-1193 . -1071) 106905) ((-1187 . -1071) 106695) ((-1146 . -1071) 106578) ((-1194 . -652) 106475) ((-1193 . -652) 106316) ((-723 . -1241) T) ((-1187 . -652) 106112) ((-1177 . -663) 106096) ((-1146 . -652) 105993) ((-831 . -397) 105977) ((-723 . -568) T) ((-607 . -910) 105888) ((-326 . -898) 105872) ((-326 . -900) 105797) ((-323 . -898) 105758) ((-140 . -1237) T) ((-137 . -1237) T) ((-115 . -1237) T) ((-323 . -900) NIL) ((-811 . -319) 105723) ((-329 . -729) 105564) ((-398 . -397) 105548) ((-334 . -333) 105525) ((-497 . -102) T) ((-486 . -25) T) ((-486 . -21) T) ((-430 . -38) 105499) ((-326 . -1058) 105162) ((-227 . -1222) T) ((-227 . -1225) T) ((-3 . -625) 105144) ((-323 . -1058) 105074) ((-885 . -234) 105019) ((-2 . -1120) T) ((-2 . |RecordCategory|) T) ((-1133 . -1078) 104997) ((-845 . -625) 104979) ((-1082 . -237) T) ((-592 . -938) T) ((-576 . -832) T) ((-576 . -938) T) ((-507 . -938) T) ((-137 . -1058) 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-248) T) ((-1250 . -861) 98219) ((-108 . -174) T) ((-885 . -1012) 98203) ((-670 . -1132) T) ((-593 . -374) T) ((-593 . -339) 98190) ((-530 . -339) 98167) ((-530 . -374) T) ((-326 . -317) 98146) ((-323 . -317) T) ((-614 . -861) 98125) ((-1133 . -729) 98067) ((-532 . -292) 98051) ((-670 . -23) T) ((-430 . -232) 98035) ((-430 . -272) 98019) ((-323 . -1042) NIL) ((-347 . -23) T) ((-103 . -1030) 98003) ((-45 . -36) 97982) ((-624 . -1120) T) ((-362 . -379) T) ((-536 . -102) T) ((-507 . -27) T) ((-245 . -319) 97920) ((-1107 . -1132) T) ((-1310 . -660) 97894) ((-794 . -1132) T) ((-792 . -1132) T) ((-1198 . -423) 97878) ((-466 . -1132) T) ((-1082 . -464) T) ((-1171 . -1120) T) ((-970 . -464) 97829) ((-1135 . -1103) T) ((-110 . -1120) T) ((-1107 . -23) T) ((-1179 . -526) 97612) ((-829 . -1078) T) ((-794 . -23) T) ((-792 . -23) T) ((-493 . -464) 97563) ((-473 . -23) T) ((-392 . -393) 97542) ((-366 . -234) 97515) ((-363 . -234) 97488) ((-355 . -234) 97461) ((-466 . -23) T) ((-273 . -234) 97406) 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92795) ((-225 . -23) T) ((-108 . -300) T) ((-419 . -806) 92774) ((-419 . -803) 92753) ((-419 . -738) T) ((-512 . -298) 92728) ((-489 . -1076) 92693) ((-670 . -132) T) ((-633 . -628) 92662) ((-1133 . -526) 92595) ((-347 . -132) T) ((-171 . -414) 92574) ((-494 . -729) 92516) ((-827 . -296) 92493) ((-489 . -111) 92449) ((-665 . -1078) T) ((-1192 . -910) 92352) ((-1145 . -910) 92334) ((-828 . -1071) 92177) ((-1298 . -1103) T) ((-1260 . -464) 92108) ((-828 . -652) 91957) ((-1297 . -1103) T) ((-1107 . -132) T) ((-1074 . -729) 91899) ((-1047 . -526) 91832) ((-794 . -132) T) ((-792 . -132) T) ((-711 . -863) T) ((-583 . -464) T) ((-633 . -1069) T) ((-604 . -1120) T) ((-545 . -175) T) ((-473 . -132) T) ((-466 . -132) T) ((-390 . -237) T) ((-1019 . -1237) T) ((-45 . -1120) T) ((-396 . -729) 91802) ((-829 . -1120) T) ((-488 . -526) 91735) ((-475 . -526) 91668) ((-1312 . -628) 91650) ((-465 . -378) 91620) ((-45 . -622) 91599) ((-411 . -1237) T) ((-326 . -312) T) ((-1287 . -863) 91578) ((-839 . 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T) ((-1311 . -111) 90199) ((-1019 . -388) 90183) ((-425 . -102) T) ((-392 . -111) 90162) ((-1019 . -349) 90146) ((-288 . -1003) 90130) ((-287 . -1003) 90114) ((-1024 . -918) NIL) ((-1309 . -625) 90096) ((-1307 . -625) 90078) ((-110 . -526) NIL) ((-1192 . -1263) 90062) ((-867 . -865) 90046) ((-1198 . -1120) T) ((-103 . -1237) T) ((-970 . -967) 90007) ((-829 . -729) 89949) ((-1251 . -1172) NIL) ((-493 . -967) 89894) ((-1082 . -144) T) ((-60 . -102) 89844) ((-44 . -625) 89826) ((-78 . -625) 89808) ((-362 . -660) 89753) ((-1299 . -1120) T) ((-523 . -861) T) ((-299 . -296) 89732) ((-354 . -1132) T) ((-305 . -1120) T) ((-1019 . -916) 89691) ((-305 . -622) 89670) ((-1311 . -628) 89619) ((-1279 . -38) 89516) ((-1272 . -38) 89357) ((-1251 . -38) 89153) ((-499 . -1078) T) ((-392 . -628) 89137) ((-219 . -1078) T) ((-354 . -23) T) ((-153 . -625) 89119) ((-845 . -807) 89098) ((-845 . -804) 89077) ((-1236 . -628) 89058) ((-608 . -38) 89031) ((-607 . -38) 88928) ((-883 . -568) T) ((-225 . -132) T) 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. -25) T) ((-561 . -1120) T) ((-1107 . -21) T) ((-981 . -1078) T) ((-543 . -804) T) ((-543 . -807) T) ((-118 . -1241) T) ((-879 . -1237) T) ((-635 . -568) T) ((-794 . -25) T) ((-794 . -21) T) ((-792 . -21) T) ((-792 . -25) T) ((-747 . -1078) T) ((-727 . -1078) T) ((-682 . -1076) 82675) ((-529 . -1103) T) ((-473 . -25) T) ((-118 . -568) T) ((-473 . -21) T) ((-466 . -25) T) ((-466 . -21) T) ((-1251 . -272) 82627) ((-1171 . -93) T) ((-1162 . -1058) 82523) ((-829 . -300) 82502) ((-1250 . -1222) 82468) ((-835 . -1120) T) ((-984 . -987) T) ((-682 . -111) 82447) ((-629 . -1237) T) ((-305 . -526) 82239) ((-1250 . -1225) 82205) ((-1250 . -237) 82064) ((-1245 . -379) T) ((-258 . -319) 82002) ((-257 . -319) 81940) ((-1242 . -856) T) ((-1179 . -626) NIL) ((-1179 . -625) 81922) ((-1162 . -388) 81906) ((-1140 . -832) T) ((-1140 . -938) T) ((-96 . -93) T) ((-1133 . -616) 81883) ((-1100 . -626) 81867) ((-1100 . -625) 81849) ((-1024 . -658) 81799) ((-932 . -658) 81736) ((-827 . -298) 81713) ((-496 . 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. -234) 77273) ((-831 . -102) T) ((-638 . -1103) T) ((-635 . -23) T) ((-1170 . -526) 77065) ((-495 . -1103) T) ((-981 . -1120) T) ((-398 . -102) T) ((-334 . -102) T) ((-220 . -1103) T) ((-855 . -1237) T) ((-153 . -1069) T) ((-743 . -423) 77049) ((-118 . -23) T) ((-1023 . -916) 77001) ((-747 . -1120) T) ((-727 . -1120) T) ((-1279 . -658) 76911) ((-1272 . -658) 76793) ((-465 . -1120) T) ((-419 . -1237) T) ((-326 . -442) 76777) ((-604 . -93) T) ((-1047 . -626) 76738) ((-270 . -1237) T) ((-1044 . -1241) T) ((-227 . -102) T) ((-1047 . -625) 76700) ((-828 . -272) 76684) ((-828 . -232) 76668) ((-827 . -628) 76466) ((-1251 . -658) 76303) ((-1044 . -568) T) ((-845 . -660) 76276) ((-365 . -1241) T) ((-488 . -625) 76238) ((-488 . -626) 76199) ((-475 . -626) 76160) ((-475 . -625) 76122) ((-608 . -658) 76081) ((-419 . -898) 76065) ((-329 . -1076) 75900) ((-419 . -900) 75825) ((-607 . -658) 75735) ((-855 . -1058) 75631) ((-499 . -526) NIL) ((-494 . -616) 75608) ((-593 . -234) 75595) ((-365 . -568) T) ((-530 . -234) 75582) ((-219 . -526) NIL) ((-885 . -464) T) ((-430 . -1120) T) ((-419 . -1058) 75446) ((-329 . -111) 75267) ((-706 . -374) T) ((-227 . -294) T) ((-1234 . -628) 75244) ((-48 . -1241) T) ((-1192 . -1172) 75222) ((-1179 . -298) 75198) ((-1082 . -102) T) ((-970 . -102) T) ((-827 . -1069) 75176) ((-592 . -132) T) ((-576 . -132) T) ((-507 . -132) T) ((-366 . -237) 75155) ((-363 . -237) 75134) ((-355 . -237) 75113) ((-48 . -568) T) ((-884 . -1071) 75058) ((-273 . -237) 75009) ((-827 . -238) 74961) ((-326 . -27) 74940) ((-258 . -918) 74809) ((-257 . -918) 74678) ((-255 . -847) 74660) ((-189 . -847) 74642) ((-725 . -102) T) ((-305 . -501) 74579) ((-884 . -652) 74524) ((-493 . -102) T) ((-743 . -1078) T) ((-624 . -625) 74506) ((-624 . -626) 74367) ((-419 . -388) 74351) ((-419 . -349) 74335) ((-1192 . -38) 74164) ((-1145 . -38) 74013) ((-329 . -628) 73839) ((-928 . -237) T) ((-647 . -1237) T) ((-619 . -1237) T) ((-867 . -38) 73809) ((-402 . -660) 73793) ((-656 . -319) 73731) 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T) ((-227 . -38) 69911) ((-108 . -111) 69845) ((-40 . -25) T) ((-40 . -21) T) ((-682 . -732) T) ((-171 . -294) 69823) ((-48 . -1132) T) ((-871 . -1237) T) ((-939 . -25) T) ((-783 . -25) T) ((-1311 . -660) 69797) ((-1170 . -501) 69734) ((-497 . -1120) T) ((-1302 . -658) 69693) ((-1260 . -102) T) ((-1082 . -1172) T) ((-868 . -102) T) ((-245 . -1078) 69671) ((-982 . -804) 69624) ((-982 . -807) 69577) ((-392 . -660) 69561) ((-48 . -23) T) ((-827 . -807) 69540) ((-827 . -804) 69519) ((-560 . -379) T) ((-305 . -616) 69498) ((-489 . -738) T) ((-583 . -102) T) ((-1100 . -628) 69316) ((-255 . -187) T) ((-189 . -187) T) ((-884 . -319) 69273) ((-665 . -296) 69252) ((-112 . -673) T) ((-362 . -1237) T) ((-370 . -628) 69189) ((-364 . -628) 69126) ((-356 . -628) 69063) ((-76 . -1237) T) ((-108 . -628) 69013) ((-112 . -113) T) ((-1082 . -38) 69000) ((-676 . -385) 68979) ((-970 . -38) 68828) ((-743 . -1120) T) ((-493 . -38) 68677) ((-86 . -1237) T) ((-604 . -502) 68658) ((-1251 . -860) NIL) ((-1194 . 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T) ((-337 . -1121) 201163) ((-326 . -911) 201127) ((-323 . -911) NIL) ((-724 . -464) 201058) ((-48 . -102) T) ((-1272 . -296) 201016) ((-1251 . -296) 200916) ((-656 . -678) 200900) ((-656 . -663) 200884) ((-350 . -21) T) ((-350 . -25) T) ((-40 . -360) NIL) ((-176 . -21) T) ((-176 . -25) T) ((-656 . -384) 200868) ((-617 . -502) 200850) ((-614 . -296) 200802) ((-617 . -625) 200769) ((-400 . -102) T) ((-1141 . -144) T) ((-127 . -625) 200701) ((-888 . -1121) T) ((-670 . -423) 200685) ((-743 . -1238) T) ((-726 . -625) 200667) ((-255 . -625) 200634) ((-189 . -625) 200616) ((-163 . -625) 200598) ((-158 . -625) 200580) ((-1303 . -738) T) ((-1123 . -34) T) ((-885 . -807) NIL) ((-885 . -804) NIL) ((-872 . -861) T) ((-743 . -901) NIL) ((-1312 . -132) T) ((-392 . -132) T) ((-907 . -628) 200548) ((-923 . -102) T) ((-743 . -1059) 200424) ((-1195 . -1238) T) ((-1194 . -1238) T) ((-543 . -132) T) ((-1188 . -1238) T) ((-1108 . -423) 200408) ((-1021 . -501) 200392) ((-118 . -412) 200369) ((-1147 . -1238) T) ((-794 . -423) 200353) ((-792 . -423) 200337) ((-962 . -34) T) ((-706 . -1173) NIL) ((-258 . -660) 200157) ((-257 . -660) 199964) ((-829 . -939) 199943) ((-466 . -423) 199927) ((-614 . -19) 199911) ((-1167 . -1231) 199880) ((-1188 . -901) NIL) ((-1188 . -899) 199832) ((-614 . -616) 199809) ((-108 . -864) T) ((-1224 . -625) 199741) ((-1196 . -625) 199723) ((-62 . -407) T) ((-1194 . -1059) 199658) ((-1188 . -1059) 199624) ((-706 . -38) 199574) ((-40 . -658) 199504) ((-486 . -296) 199462) ((-1244 . -625) 199444) ((-743 . -388) 199428) ((-850 . -625) 199410) ((-670 . -1079) T) ((-635 . -919) 199333) ((-1272 . -1023) 199299) ((-448 . -1238) T) ((-1251 . -1023) 199265) ((-256 . -1238) T) ((-1109 . -628) 199249) ((-1084 . -1214) 199224) ((-1097 . -628) 199201) ((-886 . -626) 199008) ((-886 . -625) 198990) ((-118 . -919) NIL) ((-713 . -234) 198977) ((-1210 . -501) 198914) ((-430 . -1043) 198892) ((-48 . -319) 198879) ((-1084 . -107) 198825) ((-491 . -501) 198762) ((-537 . -1238) T) 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-23) T) ((-528 . -296) 195042) ((-337 . -526) 194975) ((-508 . -296) 194927) ((-390 . -248) T) ((-390 . -238) T) ((-848 . -1070) T) ((-839 . -1070) T) ((-724 . -968) 194896) ((-713 . -861) T) ((-624 . -864) T) ((-486 . -625) 194878) ((-1274 . -1072) 194783) ((-592 . -658) 194755) ((-576 . -658) 194727) ((-507 . -658) 194677) ((-839 . -238) 194656) ((-135 . -861) T) ((-1274 . -652) 194548) ((-670 . -1121) T) ((-1210 . -616) 194527) ((-562 . -1214) 194506) ((-347 . -1121) T) ((-329 . -374) 194485) ((-419 . -148) 194464) ((-419 . -146) 194443) ((-983 . -1133) 194342) ((-827 . -1133) 194320) ((-245 . -917) 194252) ((-666 . -866) 194236) ((-491 . -616) 194215) ((-110 . -864) T) ((-536 . -1238) T) ((-562 . -107) 194165) ((-1025 . -388) 194147) ((-1025 . -349) 194129) ((-1197 . -625) 194111) ((-97 . -1121) T) ((-983 . -23) 193922) ((-489 . -21) T) ((-489 . -25) T) ((-827 . -23) 193774) ((-1197 . -626) 193696) ((-59 . -19) 193680) ((-1193 . -738) T) ((-1146 . -738) T) ((-1108 . -1121) T) 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. -628) 191914) ((-1210 . -626) NIL) ((-1210 . -625) 191896) ((-1163 . -1144) 191841) ((-493 . -928) 191820) ((-1108 . -729) 191669) ((-1083 . -660) 191641) ((-971 . -660) 191530) ((-830 . -864) T) ((-794 . -729) 191359) ((-609 . -502) 191340) ((-597 . -502) 191321) ((-609 . -625) 191287) ((-597 . -625) 191253) ((-548 . -625) 191235) ((-591 . -1238) T) ((-548 . -626) 191216) ((-792 . -729) 191065) ((-1098 . -102) T) ((-635 . -658) 191037) ((-392 . -25) T) ((-392 . -21) T) ((-493 . -660) 190926) ((-473 . -729) 190897) ((-466 . -729) 190746) ((-1008 . -102) T) ((-1067 . -1231) 190675) ((-920 . -319) 190613) ((-890 . -93) T) ((-749 . -102) T) ((-118 . -658) 190543) ((-617 . -628) 190525) ((-726 . -628) 190479) ((-693 . -93) T) ((-543 . -25) T) ((-688 . -93) T) ((-676 . -625) 190461) ((-657 . -502) 190442) ((-657 . -625) 190395) ((-142 . -102) T) ((-44 . -132) T) ((-608 . -1238) T) ((-607 . -1238) T) ((-354 . -1079) T) ((-299 . -1133) T) ((-490 . -93) T) ((-419 . -237) 190346) ((-366 . -625) 190328) ((-363 . -625) 190310) ((-355 . -625) 190292) ((-273 . -626) 190040) ((-273 . -625) 190022) ((-253 . -625) 190004) ((-253 . -626) 189865) ((-139 . -93) T) ((-138 . -93) T) ((-134 . -93) T) ((-1162 . -625) 189847) ((-1141 . -652) 189834) ((-1141 . -1072) 189821) ((-831 . -738) T) ((-831 . -871) T) ((-614 . -298) 189798) ((-593 . -729) 189763) ((-491 . -626) NIL) ((-491 . -625) 189745) ((-530 . -729) 189690) ((-326 . -102) T) ((-323 . -102) T) ((-299 . -23) T) ((-153 . -132) T) ((-929 . -625) 189672) ((-929 . -626) 189654) ((-398 . -738) T) ((-886 . -1077) 189606) ((-886 . -111) 189544) ((-726 . -1070) T) ((-724 . -1264) 189528) ((-706 . -360) NIL) ((-115 . -102) T) ((-140 . -102) T) ((-137 . -102) T) ((-531 . -625) 189460) ((-390 . -807) T) ((-169 . -1238) T) ((-225 . -1121) T) ((-390 . -804) T) ((-59 . -626) 189421) ((-227 . -806) T) ((-227 . -803) T) ((-59 . -625) 189333) ((-227 . -738) T) ((-528 . -626) 189294) ((-528 . -625) 189206) ((-509 . -625) 189138) ((-508 . -626) 189099) ((-508 . -625) 189011) ((-1101 . -374) 188962) ((-40 . -423) 188939) ((-77 . -1238) T) ((-885 . -928) NIL) ((-370 . -339) 188923) ((-370 . -374) T) ((-364 . -339) 188907) ((-364 . -374) T) ((-356 . -339) 188891) ((-356 . -374) T) ((-326 . -294) 188870) ((-108 . -374) T) ((-70 . -1238) T) ((-1252 . -349) 188822) ((-885 . -660) 188767) ((-1252 . -388) 188719) ((-983 . -132) 188574) ((-827 . -132) 188445) ((-45 . -864) NIL) ((-977 . -663) 188429) ((-1108 . -174) 188340) ((-977 . -384) 188324) ((-1083 . -806) T) ((-1083 . -803) T) ((-886 . -628) 188222) ((-794 . -174) 188113) ((-792 . -174) 188024) ((-828 . -47) 187986) ((-1083 . -738) T) ((-337 . -501) 187970) ((-971 . -738) T) ((-1301 . -319) 187908) ((-1280 . -917) 187821) ((-466 . -174) 187732) ((-250 . -296) 187684) ((-1273 . -917) 187590) ((-1272 . -1077) 187425) ((-1252 . -917) 187258) ((-493 . -738) T) ((-1251 . -1077) 187066) ((-1232 . -300) 187045) ((-1207 . -1238) T) ((-1204 . -379) T) ((-1203 . -379) T) ((-1167 . -152) 187029) ((-1141 . -102) T) ((-1139 . -1121) T) ((-1101 . -23) T) ((-1101 . -1133) T) ((-1096 . -102) T) ((-1078 . -625) 186996) ((-1024 . -421) 186968) ((-946 . -974) T) ((-749 . -319) 186906) ((-75 . -1238) T) ((-676 . -393) 186878) ((-171 . -928) 186831) ((-30 . -974) T) ((-112 . -856) T) ((-1 . -625) 186813) ((-1020 . -911) 186734) ((-129 . -663) 186716) ((-50 . -632) 186700) ((-706 . -658) 186635) ((-607 . -917) 186548) ((-450 . -102) T) ((-129 . -384) 186530) ((-142 . -319) NIL) ((-886 . -1070) T) ((-845 . -861) 186509) ((-81 . -1238) T) ((-723 . -300) T) ((-40 . -1079) T) ((-593 . -174) T) ((-530 . -174) T) ((-523 . -625) 186491) ((-171 . -660) 186365) ((-519 . -625) 186347) ((-362 . -148) 186329) ((-362 . -146) T) ((-370 . -1133) T) ((-364 . -1133) T) ((-356 . -1133) T) ((-1025 . -317) T) ((-933 . -317) T) ((-886 . -248) T) ((-108 . -1133) T) ((-886 . -238) 186308) ((-1272 . -111) 186129) ((-1251 . -111) 185918) ((-250 . -1276) 185902) ((-576 . -860) T) ((-370 . -23) T) 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. -738) T) ((-118 . -860) NIL) ((-528 . -298) 182638) ((-337 . -616) 182615) ((-508 . -298) 182592) ((-466 . -300) 182523) ((-1056 . -319) 182374) ((-890 . -502) 182355) ((-890 . -625) 182321) ((-693 . -502) 182302) ((-583 . -738) T) ((-688 . -502) 182283) ((-693 . -625) 182233) ((-688 . -625) 182199) ((-674 . -625) 182181) ((-490 . -502) 182162) ((-490 . -625) 182128) ((-250 . -626) 182089) ((-250 . -502) 182066) ((-139 . -502) 182047) ((-138 . -502) 182028) ((-134 . -502) 182009) ((-250 . -625) 181901) ((-215 . -102) T) ((-139 . -625) 181867) ((-138 . -625) 181833) ((-134 . -625) 181799) ((-1168 . -34) T) ((-962 . -1238) T) ((-354 . -729) 181744) ((-682 . -25) T) ((-682 . -21) T) ((-1197 . -628) 181725) ((-341 . -1238) T) ((-486 . -1070) T) ((-647 . -429) 181690) ((-619 . -429) 181655) ((-1141 . -1173) T) ((-1273 . -317) 181634) ((-724 . -1072) 181457) ((-593 . -300) T) ((-530 . -300) T) ((-1252 . -317) 181436) ((-486 . -238) 181388) ((-486 . -248) 181367) ((-451 . -1238) T) ((-724 . -652) 181196) ((-1252 . -1043) NIL) ((-1101 . -132) T) ((-886 . -807) 181175) ((-145 . -102) T) ((-40 . -1121) T) ((-886 . -804) 181154) ((-656 . -1031) 181138) ((-592 . -1079) T) ((-576 . -1079) T) ((-507 . -1079) T) ((-419 . -464) T) ((-370 . -132) T) ((-326 . -412) 181122) ((-323 . -412) 181083) ((-364 . -132) T) ((-356 . -132) T) ((-1202 . -1121) T) ((-1141 . -38) 181070) ((-1115 . -625) 181037) ((-108 . -132) T) ((-973 . -1121) T) ((-940 . -1121) T) ((-783 . -1121) T) ((-684 . -1121) T) ((-713 . -148) T) ((-117 . -148) T) ((-1310 . -21) T) ((-1310 . -25) T) ((-1308 . -21) T) ((-1308 . -25) T) ((-676 . -1077) 181021) ((-543 . -861) T) ((-512 . -861) T) ((-376 . -1238) T) ((-366 . -1077) 180973) ((-363 . -1077) 180925) ((-355 . -1077) 180877) ((-258 . -1238) T) ((-257 . -1238) T) ((-273 . -1077) 180720) ((-253 . -1077) 180563) ((-676 . -111) 180542) ((-829 . -1242) 180521) ((-559 . -856) T) ((-326 . -919) 180487) ((-366 . -111) 180425) ((-363 . -111) 180363) ((-355 . -111) 180301) 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-1238) T) ((-137 . -482) 168770) ((-869 . -1238) T) ((-666 . -658) 168729) ((-48 . -1121) T) ((-724 . -272) 168713) ((-724 . -232) 168697) ((-885 . -917) NIL) ((-583 . -1238) T) ((-1261 . -901) NIL) ((-904 . -102) T) ((-900 . -102) T) ((-400 . -1121) T) ((-171 . -388) 168681) ((-171 . -349) 168665) ((-1261 . -1059) 168545) ((-869 . -1059) 168441) ((-1163 . -102) T) ((-1020 . -919) 168364) ((-674 . -804) 168343) ((-665 . -132) T) ((-674 . -807) 168322) ((-118 . -526) 168230) ((-583 . -1059) 168212) ((-304 . -1295) 168182) ((-1188 . -864) NIL) ((-880 . -102) T) ((-982 . -568) 168161) ((-1232 . -1077) 168044) ((-1024 . -1072) 167989) ((-494 . -651) 167895) ((-923 . -1121) T) ((-1045 . -729) 167832) ((-723 . -1077) 167797) ((-1024 . -652) 167742) ((-629 . -102) T) ((-614 . -34) T) ((-1168 . -1238) T) ((-1232 . -111) 167611) ((-486 . -660) 167508) ((-365 . -729) 167453) ((-171 . -917) 167412) ((-711 . -300) T) ((-706 . -174) T) ((-723 . -111) 167368) ((-1317 . -1079) T) ((-1261 . -388) 167352) ((-430 . -1242) 167330) ((-1139 . -625) 167312) ((-323 . -860) NIL) ((-430 . -568) T) ((-227 . -317) T) ((-1251 . -803) 167265) ((-1251 . -806) 167218) ((-1272 . -738) T) ((-1251 . -738) T) ((-48 . -729) 167183) ((-227 . -1043) T) ((-1274 . -423) 167149) ((-1261 . -917) 167092) ((-362 . -1295) 167069) ((-1232 . -628) 166951) ((-730 . -738) T) ((-343 . -625) 166933) ((-532 . -864) 166912) ((-1134 . -234) 166803) ((-112 . -625) 166785) ((-112 . -626) 166767) ((-730 . -485) T) ((-723 . -628) 166717) ((-1311 . -1072) 166701) ((-494 . -25) 166534) ((-128 . -501) 166518) ((-122 . -501) 166502) ((-494 . -21) 166413) ((-1311 . -652) 166383) ((-635 . -300) T) ((-598 . -1077) 166358) ((-449 . -1121) T) ((-1083 . -317) T) ((-118 . -300) T) ((-1125 . -102) T) ((-1024 . -102) T) ((-598 . -111) 166326) ((-1232 . -1070) T) ((-1163 . -319) 166264) ((-1083 . -1043) T) ((-1075 . -25) T) ((-66 . -1238) T) ((-907 . -1238) T) ((-1075 . -21) T) ((-723 . -1070) T) ((-396 . -21) T) ((-396 . -25) T) 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. -625) 165140) ((-1108 . -111) 164969) ((-1067 . -102) T) ((-487 . -1238) T) ((-473 . -1077) 164940) ((-466 . -1077) 164783) ((-676 . -660) 164767) ((-885 . -317) T) ((-794 . -111) 164576) ((-792 . -111) 164405) ((-366 . -660) 164357) ((-363 . -660) 164309) ((-355 . -660) 164261) ((-273 . -660) 164150) ((-253 . -660) 164039) ((-1179 . -861) T) ((-1109 . -1059) 164023) ((-1097 . -1059) 164000) ((-1025 . -864) T) ((-1021 . -34) T) ((-473 . -111) 163961) ((-466 . -111) 163790) ((-992 . -864) T) ((-985 . -625) 163772) ((-982 . -1133) T) ((-977 . -1238) T) ((-127 . -1031) 163756) ((-862 . -1238) T) ((-885 . -1043) NIL) ((-747 . -1133) T) ((-727 . -1133) T) ((-670 . -628) 163674) ((-1288 . -501) 163658) ((-1205 . -1238) T) ((-1204 . -1238) T) ((-1163 . -38) 163618) ((-982 . -23) T) ((-929 . -660) 163583) ((-879 . -1121) T) ((-855 . -102) T) ((-829 . -21) T) ((-647 . -1072) 163567) ((-619 . -1072) 163551) ((-829 . -25) T) ((-747 . -23) T) ((-727 . -23) T) ((-647 . -652) 163535) ((-110 . 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. -651) 149056) ((-1020 . -1121) T) ((-724 . -174) 148947) ((-635 . -628) 148842) ((-499 . -1013) 148824) ((-430 . -234) 148769) ((-273 . -388) 148753) ((-253 . -388) 148737) ((-411 . -1121) T) ((-1047 . -102) 148715) ((-350 . -38) 148699) ((-219 . -1013) 148681) ((-118 . -628) 148611) ((-176 . -38) 148543) ((-1272 . -317) 148522) ((-1251 . -317) 148501) ((-670 . -738) T) ((-99 . -625) 148483) ((-489 . -1072) 148448) ((-1188 . -651) 148400) ((-489 . -652) 148365) ((-656 . -864) 148344) ((-497 . -25) T) ((-497 . -21) T) ((-1251 . -1043) 148296) ((-1078 . -1238) T) ((-1 . -1238) T) ((-635 . -1070) T) ((-390 . -416) T) ((-402 . -102) T) ((-1126 . -630) 148211) ((-273 . -917) 148157) ((-253 . -917) 148134) ((-118 . -1070) T) ((-1108 . -738) T) ((-828 . -1133) T) ((-831 . -864) T) ((-635 . -238) 148113) ((-633 . -102) T) ((-523 . -1238) T) ((-519 . -1238) T) ((-794 . -738) T) ((-792 . -738) T) ((-1243 . -861) T) ((-425 . -1133) T) ((-118 . -248) T) ((-40 . -379) NIL) ((-118 . -238) NIL) 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-464) T) ((-79 . -453) T) ((-79 . -407) T) ((-489 . -102) T) ((-703 . -628) 146993) ((-1317 . -625) 146975) ((-1317 . -626) 146957) ((-1101 . -414) 146936) ((-1056 . -501) 146867) ((-137 . -296) 146844) ((-576 . -807) T) ((-576 . -804) T) ((-1084 . -240) 146790) ((-1083 . -864) T) ((-725 . -864) T) ((-370 . -414) 146741) ((-364 . -414) 146692) ((-356 . -414) 146643) ((-1303 . -1133) T) ((-1312 . -1072) 146627) ((-392 . -1072) 146611) ((-1312 . -652) 146581) ((-830 . -237) T) ((-392 . -652) 146551) ((-706 . -628) 146486) ((-1303 . -23) T) ((-1290 . -102) T) ((-350 . -919) 146467) ((-177 . -625) 146449) ((-1163 . -1079) T) ((-559 . -379) T) ((-682 . -756) 146433) ((-1199 . -146) 146412) ((-1199 . -148) 146391) ((-1167 . -1121) T) ((-1167 . -1092) 146360) ((-69 . -1238) T) ((-1045 . -1077) 146297) ((-362 . -658) 146227) ((-880 . -1079) T) ((-245 . -651) 146133) ((-706 . -1070) T) ((-365 . -1077) 146078) ((-61 . -1238) T) ((-1045 . -111) 145994) ((-920 . -625) 145905) ((-706 . -248) T) 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-1121) T) ((-514 . -1121) T) ((-783 . -738) T) ((-227 . -374) T) ((-1310 . -1072) 141059) ((-1308 . -1072) 141043) ((-1310 . -652) 141013) ((-1178 . -1121) 140991) ((-885 . -1242) T) ((-1308 . -652) 140961) ((-1109 . -864) T) ((-666 . -625) 140943) ((-885 . -568) T) ((-706 . -379) NIL) ((-44 . -1072) 140927) ((-1317 . -628) 140909) ((-1311 . -1121) T) ((-682 . -102) T) ((-370 . -1295) 140893) ((-364 . -1295) 140877) ((-44 . -652) 140861) ((-356 . -1295) 140845) ((-560 . -102) T) ((-1232 . -1238) T) ((-532 . -861) 140824) ((-723 . -1238) T) ((-977 . -864) 140803) ((-862 . -864) T) ((-499 . -237) T) ((-219 . -237) T) ((-1067 . -1121) T) ((-829 . -464) 140782) ((-153 . -1072) 140766) ((-1067 . -1092) 140695) ((-1048 . -997) 140664) ((-831 . -1133) T) ((-1024 . -729) 140609) ((-153 . -652) 140593) ((-398 . -1133) T) ((-488 . -997) 140562) ((-475 . -997) 140531) ((-1204 . -864) T) ((-110 . -152) 140513) ((-73 . -625) 140495) ((-908 . -625) 140477) ((-1203 . -864) T) ((-1101 . -736) 140456) 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-47) 139046) ((-1218 . -1238) T) ((-1193 . -132) T) ((-365 . -379) T) ((-493 . -1133) T) ((-1146 . -132) T) ((-885 . -374) T) ((-466 . -47) 139025) ((-868 . -132) T) ((-332 . -864) 139004) ((-153 . -102) T) ((-1083 . -23) T) ((-971 . -23) T) ((-583 . -568) T) ((-828 . -25) T) ((-828 . -21) T) ((-1163 . -526) 138937) ((-604 . -1104) T) ((-598 . -1059) 138921) ((-1274 . -628) 138795) ((-493 . -23) T) ((-362 . -1079) T) ((-390 . -864) T) ((-1232 . -917) 138776) ((-682 . -319) 138714) ((-1280 . -234) 138667) ((-1134 . -1295) 138637) ((-711 . -660) 138602) ((-1025 . -861) T) ((-1024 . -174) T) ((-982 . -146) 138581) ((-647 . -1121) T) ((-619 . -1121) T) ((-982 . -148) 138560) ((-747 . -148) 138539) ((-747 . -146) 138518) ((-670 . -1238) T) ((-992 . -861) T) ((-1273 . -234) 138464) ((-1252 . -234) 138281) ((-845 . -658) 138198) ((-486 . -939) 138177) ((-347 . -1238) T) ((-329 . -1072) 138012) ((-326 . -1077) 137922) ((-323 . -1077) 137851) ((-1020 . -296) 137809) ((-419 . -729) 137761) 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-148) 134512) ((-811 . -146) 134491) ((-258 . -651) 134397) ((-257 . -651) 134303) ((-329 . -294) 134269) ((-1178 . -526) 134202) ((-489 . -658) 134152) ((-494 . -911) 134019) ((-1154 . -1121) T) ((-227 . -1081) T) ((-827 . -319) 133957) ((-1108 . -917) 133892) ((-794 . -917) 133835) ((-792 . -917) 133819) ((-1310 . -38) 133789) ((-1308 . -38) 133759) ((-1261 . -1133) T) ((-869 . -1133) T) ((-466 . -917) 133736) ((-872 . -1121) T) ((-1261 . -23) T) ((-1141 . -628) 133708) ((-1083 . -132) T) ((-869 . -23) T) ((-583 . -1133) T) ((-635 . -738) T) ((-522 . -864) T) ((-366 . -939) T) ((-363 . -939) T) ((-299 . -102) T) ((-355 . -939) T) ((-991 . -1104) T) ((-971 . -132) T) ((-828 . -234) 133653) ((-118 . -806) NIL) ((-118 . -803) NIL) ((-118 . -738) T) ((-1067 . -526) 133554) ((-706 . -928) NIL) ((-583 . -23) T) ((-493 . -132) T) ((-430 . -237) 133505) ((-687 . -319) 133443) ((-225 . -1238) T) ((-647 . -773) T) ((-619 . -773) T) ((-1252 . -861) NIL) ((-1101 . -1072) 133353) ((-1024 . -300) T) ((-706 . -660) 133303) ((-258 . -25) T) ((-362 . -1121) T) ((-258 . -21) T) ((-257 . -25) T) ((-257 . -21) T) ((-153 . -38) 133287) ((-2 . -102) T) ((-929 . -939) T) ((-1101 . -652) 133155) ((-494 . -1295) 133125) ((-1141 . -1070) T) ((-723 . -317) T) ((-370 . -1072) 133077) ((-364 . -1072) 133029) ((-356 . -1072) 132981) ((-370 . -652) 132933) ((-225 . -1059) 132910) ((-364 . -652) 132862) ((-108 . -1072) 132812) ((-356 . -652) 132764) ((-304 . -729) 132706) ((-713 . -1079) T) ((-499 . -464) T) ((-419 . -526) 132618) ((-108 . -652) 132568) ((-219 . -464) T) ((-1141 . -238) T) ((-305 . -152) 132518) ((-1020 . -626) 132479) ((-1020 . -625) 132461) ((-1010 . -625) 132443) ((-117 . -1079) T) ((-666 . -1077) 132427) ((-227 . -505) T) ((-411 . -625) 132409) ((-411 . -626) 132386) ((-1075 . -1295) 132356) ((-666 . -111) 132335) ((-682 . -919) 132258) ((-1163 . -501) 132242) ((-1312 . -658) 132201) ((-392 . -658) 132170) ((-63 . -453) T) ((-63 . -407) T) ((-1180 . -102) T) ((-885 . -132) 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130969) ((-1134 . -1072) 130870) ((-908 . -628) 130847) ((-1134 . -652) 130769) ((-1187 . -102) T) ((-1015 . -102) T) ((-1014 . -21) T) ((-128 . -1031) 130753) ((-122 . -1031) 130737) ((-1014 . -25) T) ((-920 . -120) 130721) ((-1179 . -102) T) ((-1261 . -132) T) ((-1251 . -864) 130620) ((-1193 . -25) T) ((-1193 . -21) T) ((-1180 . -319) 130415) ((-354 . -1238) T) ((-1146 . -25) T) ((-869 . -132) T) ((-406 . -1238) T) ((-1146 . -21) T) ((-868 . -25) T) ((-868 . -21) T) ((-794 . -317) 130394) ((-1178 . -501) 130378) ((-1171 . -152) 130328) ((-1167 . -625) 130290) ((-659 . -102) 130240) ((-644 . -102) T) ((-1167 . -626) 130201) ((-583 . -132) T) ((-633 . -860) 130180) ((-1045 . -803) T) ((-1045 . -806) T) ((-1045 . -738) T) ((-827 . -919) 130049) ((-724 . -1077) 129872) ((-614 . -864) 129851) ((-496 . -319) 129789) ((-465 . -429) 129759) ((-362 . -174) T) ((-299 . -38) 129746) ((-258 . -234) 129637) ((-257 . -234) 129528) ((-283 . -102) T) ((-282 . -102) T) ((-281 . -102) T) ((-280 . 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-625) 128503) ((-1202 . -1238) T) ((-1202 . -1059) 128439) ((-1195 . -237) 128398) ((-488 . -102) T) ((-475 . -102) T) ((-1194 . -237) 128350) ((-1188 . -237) 128173) ((-1055 . -1133) T) ((-329 . -919) 128079) ((-1197 . -864) T) ((-1195 . -35) 128045) ((-1195 . -95) 128011) ((-1195 . -1226) 127977) ((-1195 . -1223) 127943) ((-1194 . -1223) 127909) ((-1194 . -1226) 127875) ((-1194 . -95) 127841) ((-1194 . -35) 127807) ((-1188 . -1223) 127773) ((-1188 . -1226) 127739) ((-1179 . -319) NIL) ((-89 . -408) T) ((-89 . -407) T) ((-1101 . -1173) 127718) ((-40 . -1238) T) ((-1188 . -95) 127684) ((-1055 . -23) T) ((-1188 . -35) 127650) ((-583 . -505) T) ((-1147 . -35) 127616) ((-1147 . -95) 127582) ((-1147 . -1226) 127548) ((-1147 . -1223) 127514) ((-372 . -1133) T) ((-370 . -1173) 127493) ((-364 . -1173) 127472) ((-356 . -1173) 127451) ((-1125 . -296) 127407) ((-973 . -1238) T) ((-940 . -1238) T) ((-108 . -1173) T) ((-845 . -1079) 127386) ((-783 . -1238) T) ((-659 . -319) 127324) ((-644 . -319) 127175) ((-684 . -1238) T) ((-724 . -1070) T) ((-1083 . -651) 127157) ((-1101 . -38) 127025) ((-971 . -651) 126973) ((-1025 . -148) T) ((-1025 . -146) NIL) ((-390 . -1133) T) ((-334 . -25) T) ((-332 . -23) T) ((-962 . -861) 126952) ((-724 . -336) 126929) ((-493 . -651) 126877) ((-40 . -1059) 126765) ((-724 . -238) T) ((-713 . -729) 126752) ((-350 . -1121) T) ((-176 . -1121) T) ((-341 . -861) T) ((-430 . -464) 126702) ((-390 . -23) T) ((-370 . -38) 126667) ((-364 . -38) 126632) ((-356 . -38) 126597) ((-80 . -453) T) ((-80 . -407) T) ((-227 . -25) T) ((-227 . -21) T) ((-848 . -1133) T) ((-108 . -38) 126547) ((-839 . -1133) T) ((-786 . -1121) T) ((-117 . -729) 126534) ((-684 . -1059) 126518) ((-624 . -102) T) ((-848 . -23) T) ((-839 . -23) T) ((-1178 . -296) 126470) ((-1134 . -319) 126408) ((-494 . -1072) 126309) ((-1123 . -240) 126293) ((-64 . -408) T) ((-64 . -407) T) ((-1172 . -102) T) ((-110 . -102) T) ((-494 . -652) 126215) ((-40 . -388) 126192) ((-96 . -102) T) ((-665 . -866) 126176) ((-1193 . -234) 126163) ((-1156 . -1104) T) ((-1083 . -21) T) ((-1083 . -25) T) ((-1075 . -1072) 126147) ((-827 . -272) 126116) ((-827 . -232) 126085) ((-971 . -25) T) ((-971 . -21) T) ((-1141 . -379) T) ((-1075 . -652) 126027) ((-633 . -1079) T) ((-1048 . -319) 125965) ((-904 . -625) 125947) ((-682 . -658) 125906) ((-493 . -25) T) ((-493 . -21) T) ((-396 . -1072) 125890) ((-900 . -625) 125872) ((-884 . -1238) T) ((-535 . -526) 125805) ((-258 . -861) 125756) ((-257 . -861) 125707) ((-396 . -652) 125677) ((-885 . -651) 125654) ((-488 . -319) 125592) ((-559 . -1238) T) ((-475 . -319) 125530) ((-362 . -300) T) ((-1178 . -1276) 125514) ((-1163 . -625) 125476) ((-1163 . -626) 125437) ((-1161 . -102) T) ((-1020 . -1077) 125333) ((-40 . -917) 125285) ((-1178 . -616) 125262) ((-1317 . -660) 125249) ((-1084 . -152) 125195) ((-499 . -911) NIL) ((-880 . -502) 125172) ((-1020 . -111) 125054) ((-886 . -1242) T) ((-219 . -911) NIL) ((-350 . -729) 125038) ((-880 . -625) 125000) ((-176 . -729) 124932) ((-886 . -568) T) ((-419 . -296) 124890) ((-245 . -237) 124787) ((-108 . -412) 124769) ((-84 . -395) T) ((-84 . -407) T) ((-713 . -174) T) ((-629 . -625) 124751) ((-99 . -738) T) ((-494 . -102) 124483) ((-99 . -485) T) ((-117 . -174) T) ((-1310 . -658) 124442) ((-1308 . -658) 124401) ((-171 . -651) 124349) ((-1101 . -919) 124220) ((-1075 . -102) T) ((-1020 . -628) 124110) ((-885 . -25) T) ((-827 . -243) 124089) ((-885 . -21) T) ((-830 . -102) T) ((-44 . -658) 124032) ((-1025 . -237) T) ((-426 . -102) T) ((-396 . -102) T) ((-110 . -319) NIL) ((-229 . -102) 123982) ((-128 . -1238) T) ((-122 . -1238) T) ((-108 . -919) NIL) ((-829 . -1072) 123933) ((-59 . -864) 123912) ((-829 . -652) 123854) ((-528 . -864) 123833) ((-508 . -864) 123812) ((-1055 . -132) T) ((-682 . -378) 123796) ((-153 . -658) 123755) ((-1317 . -738) T) ((-647 . -296) 123713) ((-619 . -296) 123671) ((-1280 . -146) 123650) ((-1261 . -651) 123598) ((-1020 . -1070) T) ((-1125 . -625) 123580) ((-1024 . -625) 123562) 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. -1079) T) ((-390 . -1081) T) ((-1047 . -1121) 122521) ((-55 . -1059) 122503) ((-920 . -34) T) ((-494 . -319) 122441) ((-604 . -102) T) ((-1178 . -626) 122402) ((-1178 . -625) 122334) ((-1199 . -1072) 122217) ((-45 . -102) T) ((-829 . -102) T) ((-1199 . -652) 122114) ((-1289 . -1238) T) ((-1261 . -25) T) ((-1261 . -21) T) ((-1083 . -234) 122101) ((-869 . -25) T) ((-523 . -864) T) ((-254 . -1238) T) ((-44 . -378) 122085) ((-869 . -21) T) ((-743 . -464) 122036) ((-1311 . -625) 122018) ((-722 . -1238) T) ((-711 . -1238) T) ((-1300 . -1072) 121988) ((-1075 . -319) 121926) ((-683 . -1104) T) ((-618 . -1104) T) ((-402 . -1121) T) ((-583 . -25) T) ((-583 . -21) T) ((-182 . -1104) T) ((-162 . -1104) T) ((-157 . -1104) T) ((-155 . -1104) T) ((-1300 . -652) 121896) ((-633 . -1121) T) ((-711 . -901) 121878) ((-1288 . -1238) T) ((-229 . -319) 121816) ((-145 . -379) T) ((-1211 . -1238) T) ((-1067 . -626) 121758) ((-1067 . -625) 121701) ((-323 . -928) NIL) ((-1246 . -856) T) ((-1134 . -919) 121570) 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. -237) 120231) ((-656 . -861) 120210) ((-1273 . -237) 120162) ((-1252 . -237) 119985) ((-305 . -102) T) ((-724 . -379) 119964) ((-118 . -1059) 119941) ((-402 . -729) 119925) ((-607 . -237) 119884) ((-633 . -729) 119868) ((-1126 . -1238) T) ((-45 . -319) 119672) ((-828 . -146) 119651) ((-828 . -148) 119630) ((-299 . -658) 119602) ((-1311 . -393) 119581) ((-831 . -861) T) ((-1290 . -1121) T) ((-1180 . -231) 119528) ((-398 . -861) 119507) ((-1280 . -35) 119473) ((-1280 . -1226) 119439) ((-1280 . -1223) 119405) ((-1273 . -1223) 119371) ((-527 . -132) T) ((-1273 . -1226) 119337) ((-1252 . -1223) 119303) ((-1252 . -1226) 119269) ((-1280 . -95) 119235) ((-1273 . -95) 119201) ((-430 . -911) 119122) ((-647 . -625) 119091) ((-619 . -625) 119060) ((-227 . -861) T) ((-1273 . -35) 119026) ((-1272 . -1133) T) ((-1252 . -95) 118992) ((-1141 . -660) 118964) ((-1252 . -35) 118930) ((-1251 . -1133) T) ((-605 . -152) 118912) ((-1101 . -360) 118891) ((-176 . -300) T) ((-118 . -388) 118868) ((-118 . -349) 118845) ((-171 . -234) 118770) ((-884 . -317) T) ((-323 . -806) NIL) ((-323 . -803) NIL) ((-326 . -738) 118619) ((-323 . -738) T) ((-486 . -374) 118598) ((-370 . -360) 118577) ((-364 . -360) 118556) ((-356 . -360) 118535) ((-326 . -485) 118514) ((-1272 . -23) T) ((-1251 . -23) T) ((-730 . -1133) T) ((-726 . -132) T) ((-665 . -102) T) ((-489 . -729) 118479) ((-674 . -864) 118458) ((-45 . -292) 118408) ((-105 . -1121) T) ((-68 . -625) 118390) ((-250 . -864) 118369) ((-991 . -102) T) ((-878 . -102) T) ((-635 . -917) 118328) ((-1312 . -1121) T) ((-392 . -1121) T) ((-1261 . -234) 118315) ((-1237 . -1121) T) ((-82 . -1238) T) ((-1134 . -272) 118284) ((-1083 . -861) T) ((-118 . -917) NIL) ((-794 . -939) 118263) ((-725 . -861) T) ((-543 . -1121) T) ((-512 . -1121) T) ((-366 . -1242) T) ((-363 . -1242) T) ((-355 . -1242) T) ((-273 . -1242) 118242) ((-253 . -1242) 118221) ((-545 . -874) T) ((-1134 . -232) 118190) ((-1179 . -840) T) ((-1163 . -1077) 118174) ((-402 . -773) T) ((-706 . -1238) T) 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. -628) 116367) ((-1056 . -34) T) ((-828 . -237) 116318) ((-592 . -317) T) ((-576 . -317) T) ((-507 . -317) T) ((-1312 . -729) 116288) ((-706 . -388) 116270) ((-706 . -349) 116252) ((-489 . -174) T) ((-392 . -729) 116222) ((-880 . -628) 116157) ((-885 . -861) NIL) ((-576 . -1043) T) ((-507 . -1043) T) ((-1154 . -625) 116139) ((-1134 . -243) 116118) ((-216 . -102) T) ((-1171 . -102) T) ((-71 . -625) 116100) ((-1045 . -1238) T) ((-1163 . -1070) T) ((-1199 . -38) 115997) ((-872 . -625) 115979) ((-576 . -557) T) ((-682 . -1079) T) ((-743 . -968) 115932) ((-1163 . -238) 115911) ((-365 . -1238) T) ((-1103 . -1121) T) ((-1055 . -25) T) ((-1055 . -21) T) ((-1024 . -1077) 115856) ((-337 . -864) 115835) ((-924 . -102) T) ((-880 . -1070) T) ((-706 . -917) NIL) ((-366 . -339) 115819) ((-366 . -374) T) ((-363 . -339) 115803) ((-363 . -374) T) ((-355 . -339) 115787) ((-355 . -374) T) ((-499 . -102) T) ((-1300 . -38) 115757) ((-558 . -861) T) ((-535 . -699) 115707) ((-219 . -102) T) ((-1045 . -1059) 115587) ((-1024 . -111) 115516) ((-1195 . -994) 115485) ((-1194 . -994) 115447) ((-532 . -152) 115431) ((-1101 . -381) 115410) ((-362 . -625) 115392) ((-332 . -21) T) ((-365 . -1059) 115369) ((-332 . -25) T) ((-1188 . -994) 115338) ((-48 . -1238) T) ((-76 . -625) 115320) ((-1147 . -994) 115287) ((-711 . -317) T) ((-130 . -856) T) ((-929 . -374) T) ((-390 . -25) T) ((-390 . -21) T) ((-929 . -339) 115274) ((-86 . -625) 115256) ((-711 . -1043) T) ((-689 . -861) T) ((-400 . -1238) T) ((-1272 . -132) T) ((-1251 . -132) T) ((-920 . -1031) 115240) ((-848 . -21) T) ((-48 . -1059) 115183) ((-848 . -25) T) ((-839 . -25) T) ((-839 . -21) T) ((-1134 . -658) 114962) ((-1310 . -1079) T) ((-561 . -102) T) ((-1308 . -1079) T) ((-666 . -738) T) ((-1125 . -630) 114865) ((-1024 . -628) 114795) ((-1311 . -1077) 114779) ((-923 . -1238) T) ((-827 . -423) 114748) ((-103 . -120) 114732) ((-130 . -1121) T) ((-52 . -1121) T) ((-945 . -625) 114714) ((-885 . -1013) 114691) ((-835 . -102) T) ((-1311 . -111) 114670) ((-743 . -911) 114645) ((-665 . -38) 114615) ((-583 . -861) T) ((-366 . -1133) T) ((-363 . -1133) T) ((-355 . -1133) T) ((-273 . -1133) T) ((-253 . -1133) T) ((-1171 . -319) 114419) ((-1109 . -234) 114406) ((-635 . -317) 114385) ((-676 . -23) T) ((-536 . -1104) T) ((-321 . -1121) T) ((-494 . -272) 114354) ((-494 . -232) 114323) ((-153 . -1079) T) ((-366 . -23) T) ((-363 . -23) T) ((-355 . -23) T) ((-118 . -317) T) ((-273 . -23) T) ((-253 . -23) T) ((-1024 . -1070) T) ((-724 . -928) 114302) ((-1195 . -911) 114190) ((-1194 . -911) 114071) ((-1188 . -911) 113807) ((-1178 . -628) 113784) ((-1024 . -238) 113756) ((-1024 . -248) T) ((-1147 . -911) 113738) ((-118 . -1043) NIL) ((-929 . -1133) T) ((-1273 . -464) 113717) ((-1252 . -464) 113696) ((-535 . -625) 113628) ((-724 . -660) 113517) ((-419 . -1077) 113469) ((-516 . -625) 113451) ((-929 . -23) T) ((-499 . -319) NIL) ((-1311 . -628) 113407) ((-486 . -132) T) ((-219 . -319) NIL) ((-419 . -111) 113345) ((-827 . -1079) 113323) ((-749 . -1119) 113307) ((-1272 . -505) 113273) ((-1251 . -505) 113239) ((-449 . -1238) T) ((-560 . -856) T) ((-142 . -1119) 113221) ((-489 . -300) T) ((-1311 . -1070) T) ((-258 . -237) 113118) ((-257 . -237) 113015) ((-1243 . -102) T) ((-1084 . -102) T) ((-855 . -628) 112883) ((-512 . -526) NIL) ((-494 . -243) 112862) ((-419 . -628) 112760) ((-982 . -1072) 112643) ((-747 . -1072) 112613) ((-982 . -652) 112510) ((-1193 . -146) 112489) ((-747 . -652) 112459) ((-465 . -1072) 112429) ((-1193 . -148) 112408) ((-1146 . -148) 112387) ((-1146 . -146) 112366) ((-647 . -1077) 112350) ((-619 . -1077) 112334) ((-465 . -652) 112304) ((-1195 . -1279) 112288) ((-1195 . -1266) 112265) ((-1194 . -1271) 112226) ((-682 . -1121) T) ((-682 . -1074) 112166) ((-1194 . -1266) 112136) ((-560 . -1121) T) ((-499 . -1173) T) ((-1194 . -1269) 112120) ((-1188 . -1250) 112081) ((-830 . -275) 112065) ((-219 . -1173) T) ((-354 . -939) T) ((-99 . -1238) T) ((-647 . -111) 112044) ((-619 . -111) 112023) ((-1188 . -1266) 112000) ((-855 . -1070) 111979) ((-1188 . -1248) 111963) ((-527 . -25) T) ((-507 . -312) T) ((-523 . -23) T) ((-522 . -25) T) ((-520 . -25) T) ((-519 . -23) T) ((-430 . -1072) 111937) ((-419 . -1070) T) ((-329 . -1079) T) ((-706 . -317) T) ((-430 . -652) 111911) ((-108 . -860) T) ((-724 . -738) T) ((-419 . -248) T) ((-419 . -238) 111890) ((-390 . -234) 111877) ((-499 . -38) 111827) ((-219 . -38) 111777) ((-486 . -505) 111743) ((-1245 . -379) T) ((-1179 . -1165) T) ((-1122 . -102) T) ((-839 . -234) 111716) ((-713 . -625) 111698) ((-713 . -626) 111613) ((-726 . -21) T) ((-726 . -25) T) ((-1156 . -102) T) ((-494 . -658) 111392) ((-245 . -911) 111259) ((-135 . -625) 111241) ((-117 . -625) 111223) ((-158 . -25) T) ((-1310 . -1121) T) ((-886 . -651) 111171) ((-1308 . -1121) T) ((-879 . -1238) T) ((-982 . -102) T) ((-747 . -102) T) ((-727 . -102) T) ((-465 . -102) T) ((-828 . -464) 111122) ((-44 . -1121) T) ((-1109 . -861) T) ((-1084 . -319) 110973) ((-676 . -132) T) ((-1075 . -658) 110942) 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. -1043) T) ((-1251 . -651) 109765) ((-701 . -102) 109715) ((-44 . -729) 109699) ((-562 . -102) T) ((-304 . -628) 109630) ((-67 . -394) T) ((-499 . -919) NIL) ((-67 . -407) T) ((-284 . -864) T) ((-219 . -919) NIL) ((-674 . -23) T) ((-829 . -658) 109566) ((-682 . -773) T) ((-1235 . -1121) 109544) ((-362 . -1077) 109489) ((-687 . -1121) 109467) ((-1083 . -148) T) ((-971 . -148) 109446) ((-971 . -146) 109425) ((-811 . -102) T) ((-153 . -729) 109409) ((-493 . -148) 109388) ((-493 . -146) 109367) ((-362 . -111) 109296) ((-1101 . -1079) T) ((-332 . -861) 109275) ((-1280 . -994) 109244) ((-1274 . -1238) T) ((-639 . -1121) T) ((-1273 . -994) 109206) ((-523 . -132) T) ((-519 . -132) T) ((-305 . -231) 109156) ((-370 . -1079) T) ((-364 . -1079) T) ((-356 . -1079) T) ((-304 . -1070) 109098) ((-1252 . -994) 109067) ((-390 . -861) T) ((-108 . -1079) T) ((-1020 . -738) T) ((-884 . -939) T) ((-855 . -807) 109046) ((-855 . -804) 109025) ((-430 . -319) 108964) ((-480 . -102) T) ((-607 . -994) 108933) 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. -738) 92912) ((-370 . -300) T) ((-364 . -300) T) ((-356 . -300) T) ((-171 . -464) 92843) ((-439 . -38) 92827) ((-225 . -23) T) ((-108 . -300) T) ((-419 . -806) 92806) ((-419 . -803) 92785) ((-419 . -738) T) ((-512 . -298) 92760) ((-489 . -1077) 92725) ((-670 . -132) T) ((-633 . -628) 92694) ((-1134 . -526) 92627) ((-347 . -132) T) ((-171 . -414) 92606) ((-494 . -729) 92548) ((-827 . -296) 92525) ((-489 . -111) 92481) ((-665 . -1079) T) ((-1193 . -911) 92384) ((-1146 . -911) 92366) ((-828 . -1072) 92209) ((-1299 . -1104) T) ((-1261 . -464) 92140) ((-828 . -652) 91989) ((-1298 . -1104) T) ((-1108 . -132) T) ((-1075 . -729) 91931) ((-1048 . -526) 91864) ((-794 . -132) T) ((-792 . -132) T) ((-711 . -864) T) ((-583 . -464) T) ((-633 . -1070) T) ((-604 . -1121) T) ((-545 . -175) T) ((-473 . -132) T) ((-466 . -132) T) ((-390 . -237) T) ((-1020 . -1238) T) ((-45 . -1121) T) ((-396 . -729) 91834) ((-829 . -1121) T) ((-488 . -526) 91767) ((-475 . -526) 91700) ((-1313 . -628) 91682) ((-465 . 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. -651) 84448) ((-171 . -911) 84369) ((-924 . -922) 84353) ((-390 . -464) T) ((-499 . -1121) T) ((-962 . -319) 84291) ((-713 . -660) 84263) ((-561 . -856) T) ((-219 . -1121) T) ((-326 . -939) 84242) ((-323 . -939) T) ((-323 . -832) NIL) ((-402 . -732) T) ((-884 . -23) T) ((-117 . -660) 84229) ((-486 . -146) 84208) ((-430 . -423) 84192) ((-486 . -148) 84171) ((-110 . -501) 84153) ((-321 . -628) 84134) ((-2 . -625) 84116) ((-188 . -102) T) ((-1179 . -19) 84098) ((-1179 . -616) 84073) ((-670 . -21) T) ((-670 . -25) T) ((-605 . -1165) T) ((-1134 . -296) 84050) ((-347 . -25) T) ((-347 . -21) T) ((-904 . -1238) T) ((-900 . -1238) T) ((-1310 . -1077) 84034) ((-245 . -658) 83813) ((-507 . -374) T) ((-1308 . -1077) 83797) ((-1303 . -38) 83767) ((-1272 . -1223) 83733) ((-1272 . -1226) 83699) ((-1261 . -911) 83602) ((-1193 . -1072) 83425) ((-1163 . -1238) T) ((-1146 . -1072) 83268) ((-868 . -1072) 83252) ((-644 . -616) 83227) ((-1272 . -95) 83193) ((-1272 . -237) 83145) ((-1255 . -102) 83123) 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. -146) 79948) ((-355 . -148) 79927) ((-355 . -146) 79878) ((-273 . -146) 79857) ((-273 . -148) 79836) ((-253 . -148) 79815) ((-118 . -374) T) ((-253 . -146) 79794) ((-1179 . -626) NIL) ((-153 . -111) 79773) ((-1024 . -1059) 79661) ((-1178 . -1238) T) ((-706 . -1242) T) ((-811 . -1079) T) ((-711 . -1133) T) ((-1024 . -388) 79638) ((-518 . -1238) T) ((-514 . -1238) T) ((-929 . -146) T) ((-929 . -148) 79620) ((-884 . -132) T) ((-827 . -1077) 79541) ((-711 . -23) T) ((-706 . -568) T) ((-227 . -1072) 79506) ((-659 . -625) 79438) ((-659 . -626) 79399) ((-644 . -626) NIL) ((-644 . -625) 79381) ((-499 . -174) T) ((-227 . -652) 79346) ((-219 . -174) T) ((-225 . -21) T) ((-225 . -25) T) ((-486 . -1226) 79312) ((-486 . -1223) 79278) ((-283 . -625) 79260) ((-282 . -625) 79242) ((-281 . -625) 79224) ((-280 . -625) 79206) ((-279 . -625) 79188) ((-512 . -663) 79170) ((-278 . -625) 79152) ((-350 . -738) T) ((-277 . -625) 79134) ((-110 . -19) 79116) ((-176 . -738) T) ((-512 . -384) 79098) ((-214 . 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. -1121) T) ((-493 . -38) 68709) ((-86 . -1238) T) ((-604 . -502) 68690) ((-1252 . -860) NIL) ((-1195 . -1121) T) ((-583 . -294) T) ((-1194 . -1121) T) ((-604 . -625) 68656) ((-1188 . -1121) T) ((-1141 . -864) T) ((-1101 . -1070) T) ((-362 . -1059) 68633) ((-829 . -502) 68617) ((-1025 . -1079) T) ((-45 . -625) 68599) ((-45 . -626) NIL) ((-933 . -1079) T) ((-829 . -625) 68568) ((-1168 . -102) 68518) ((-1101 . -248) 68469) ((-439 . -1079) T) ((-370 . -1070) T) ((-364 . -1070) T) ((-376 . -375) 68446) ((-356 . -1070) T) ((-354 . -234) 68433) ((-258 . -243) 68412) ((-257 . -243) 68391) ((-1101 . -238) 68316) ((-1147 . -1121) T) ((-304 . -917) 68275) ((-108 . -1070) T) ((-706 . -132) T) ((-430 . -526) 68117) ((-370 . -238) 68096) ((-370 . -248) T) ((-44 . -732) T) ((-364 . -238) 68075) ((-364 . -248) T) ((-356 . -238) 68054) ((-356 . -248) T) ((-1187 . -628) 68035) ((-171 . -319) 68000) ((-108 . -248) T) ((-108 . -238) T) ((-1015 . -628) 67981) ((-329 . -804) T) ((-884 . -21) T) ((-884 . 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. -414) NIL) ((-118 . -237) NIL) ((-1195 . -628) 34107) ((-1141 . -673) T) ((-885 . -729) 34052) ((-258 . -501) 34036) ((-257 . -501) 34020) ((-1194 . -628) 33763) ((-1188 . -628) 33558) ((-724 . -651) 33506) ((-665 . -660) 33480) ((-1147 . -628) 33362) ((-305 . -34) T) ((-1141 . -113) T) ((-743 . -1070) T) ((-593 . -1295) 33349) ((-530 . -1295) 33326) ((-1261 . -1121) T) ((-1193 . -300) 33237) ((-1146 . -300) 33168) ((-1083 . -174) T) ((-299 . -1238) T) ((-869 . -1121) T) ((-971 . -174) 33079) ((-794 . -1264) 33063) ((-656 . -526) 32996) ((-77 . -625) 32978) ((-743 . -336) 32943) ((-1199 . -738) T) ((-583 . -1121) T) ((-493 . -174) 32854) ((-250 . -319) 32792) ((-1163 . -1133) T) ((-70 . -625) 32774) ((-1300 . -738) T) ((-1195 . -1070) T) ((-1194 . -1070) T) ((-1188 . -1070) T) ((-337 . -102) 32704) ((-1163 . -23) T) ((-2 . -1238) T) ((-1147 . -1070) T) ((-91 . -1142) 32688) ((-880 . -1133) T) ((-1195 . -238) 32647) ((-1194 . -248) 32626) ((-1194 . -238) 32578) ((-1188 . -238) 32465) 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T) ((-839 . -1079) T) ((-706 . -35) NIL) ((-706 . -95) NIL) ((-323 . -1013) 29619) ((-185 . -102) T) ((-1311 . -1133) T) ((-1311 . -23) T) ((-592 . -464) T) ((-576 . -464) T) ((-507 . -464) T) ((-1303 . -625) 29601) ((-1261 . -174) 29492) ((-1232 . -102) T) ((-419 . -374) T) ((-1219 . -1121) T) ((-1210 . -231) 29442) ((-1204 . -856) T) ((-1203 . -856) T) ((-1187 . -1238) T) ((-245 . -1070) 29420) ((-1015 . -1238) T) ((-1171 . -34) T) ((-1188 . -804) NIL) ((-1188 . -807) NIL) ((-1179 . -1238) T) ((-489 . -939) T) ((-1020 . -651) 29368) ((-258 . -616) 29345) ((-257 . -616) 29322) ((-1163 . -132) T) ((-1123 . -626) 29283) ((-1101 . -388) 29267) ((-885 . -526) 29175) ((-245 . -238) 29127) ((-1123 . -625) 29109) ((-1109 . -1121) T) ((-1025 . -628) 29059) ((-1101 . -917) 28992) ((-933 . -628) 28929) ((-836 . -625) 28911) ((-1097 . -1121) T) ((-1083 . -300) T) ((-1025 . -248) T) ((-1025 . -238) T) ((-1025 . -1070) T) ((-977 . -1121) 28861) ((-971 . -300) 28792) ((-439 . -628) 28761) ((-108 . 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. -238) 13209) ((-1141 . -237) T) ((-40 . -102) T) ((-929 . -1079) T) ((-706 . -911) NIL) ((-1202 . -102) T) ((-129 . -501) 13191) ((-1195 . -738) T) ((-1194 . -738) T) ((-1188 . -738) T) ((-1188 . -803) NIL) ((-1188 . -806) NIL) ((-973 . -102) T) ((-940 . -102) T) ((-884 . -1072) 13178) ((-1147 . -738) T) ((-783 . -102) T) ((-684 . -102) T) ((-884 . -652) 13165) ((-558 . -625) 13147) ((-486 . -1121) T) ((-350 . -1133) T) ((-176 . -1133) T) ((-329 . -939) 13126) ((-1272 . -729) 12967) ((-886 . -174) T) ((-1251 . -729) 12781) ((-855 . -21) 12733) ((-855 . -25) 12685) ((-250 . -1170) 12669) ((-127 . -526) 12602) ((-419 . -25) T) ((-419 . -21) T) ((-350 . -23) T) ((-171 . -626) 12368) ((-171 . -625) 12350) ((-176 . -23) T) ((-656 . -298) 12327) ((-532 . -34) T) ((-915 . -625) 12309) ((-89 . -1238) T) ((-853 . -625) 12291) ((-820 . -625) 12273) ((-781 . -625) 12255) ((-689 . -625) 12237) ((-245 . -660) 12070) ((-629 . -113) T) ((-1197 . -1121) T) ((-1193 . -1077) 11893) ((-216 . -1238) T) 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. -658) 6570) ((-1084 . -1238) T) ((-1083 . -1077) 6557) ((-1083 . -111) 6542) ((-971 . -111) 6371) ((-971 . -1077) 6214) ((-794 . -658) 6124) ((-792 . -658) 6034) ((-676 . -729) 6018) ((-635 . -1072) 6005) ((-635 . -652) 5992) ((-560 . -864) T) ((-493 . -1077) 5835) ((-489 . -374) T) ((-473 . -658) 5791) ((-466 . -658) 5701) ((-227 . -628) 5651) ((-366 . -729) 5603) ((-363 . -729) 5555) ((-118 . -1072) 5500) ((-355 . -729) 5452) ((-273 . -729) 5301) ((-253 . -729) 5150) ((-1111 . -93) T) ((-1094 . -93) T) ((-118 . -652) 5095) ((-1087 . -93) T) ((-962 . -663) 5079) ((-1078 . -1121) 5057) ((-493 . -111) 4886) ((-1057 . -93) T) ((-1040 . -93) T) ((-962 . -384) 4870) ((-254 . -102) T) ((-982 . -47) 4849) ((-74 . -625) 4831) ((-724 . -237) T) ((-722 . -102) T) ((-711 . -102) T) ((-1 . -1121) T) ((-633 . -1133) T) ((-1109 . -625) 4813) ((-638 . -93) T) ((-1097 . -625) 4795) ((-929 . -729) 4760) ((-127 . -501) 4744) ((-495 . -93) T) ((-633 . -23) T) ((-402 . -23) T) ((-87 . -1238) T) ((-220 . -93) T) ((-620 . -625) 4726) ((-620 . -626) NIL) ((-487 . -626) NIL) ((-487 . -625) 4708) ((-362 . -25) T) ((-362 . -21) T) ((-50 . -658) 4667) ((-523 . -1121) T) ((-519 . -1121) T) ((-122 . -319) 4605) ((-128 . -319) 4543) ((-608 . -660) 4517) ((-607 . -660) 4442) ((-593 . -658) 4392) ((-227 . -1070) T) ((-530 . -658) 4322) ((-1083 . -628) 4294) ((-390 . -1023) T) ((-227 . -248) T) ((-227 . -238) T) ((-862 . -502) 4278) ((-1083 . -630) 4259) ((-977 . -626) 4220) ((-977 . -625) 4132) ((-971 . -628) 3921) ((-862 . -625) 3905) ((-884 . -38) 3892) ((-725 . -628) 3842) ((-1272 . -300) 3793) ((-1251 . -300) 3744) ((-493 . -628) 3529) ((-1141 . -464) T) ((-514 . -861) T) ((-326 . -1160) 3508) ((-1122 . -1238) T) ((-1020 . -148) 3487) ((-1020 . -146) 3466) ((-507 . -319) 3453) ((-1205 . -625) 3435) ((-305 . -1214) 3414) ((-1204 . -625) 3396) ((-1156 . -1238) T) ((-1203 . -625) 3378) ((-885 . -1077) 3323) ((-489 . -1133) T) ((-140 . -847) 3305) ((-115 . -847) 3286) ((-1224 . -501) 3270) 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-658) 2039) ((-1021 . -526) 1972) ((-855 . -861) 1951) ((-576 . -1173) T) ((-486 . -300) 1902) ((-608 . -738) T) ((-372 . -625) 1884) ((-332 . -625) 1866) ((-430 . -1059) 1762) ((-607 . -738) T) ((-419 . -861) 1713) ((-171 . -111) 1609) ((-845 . -132) 1561) ((-1288 . -319) 1499) ((-749 . -152) 1483) ((-983 . -864) 1382) ((-827 . -864) 1333) ((-499 . -317) T) ((-390 . -625) 1300) ((-532 . -1031) 1284) ((-390 . -626) 1198) ((-219 . -317) T) ((-142 . -152) 1180) ((-726 . -296) 1159) ((-499 . -1043) T) ((-592 . -38) 1146) ((-576 . -38) 1133) ((-507 . -38) 1098) ((-219 . -1043) T) ((-885 . -1070) T) ((-848 . -625) 1080) ((-839 . -625) 1062) ((-837 . -625) 1044) ((-828 . -928) 1023) ((-1312 . -1133) T) ((-322 . -1238) T) ((-1261 . -1077) 846) ((-869 . -1077) 830) ((-885 . -248) T) ((-885 . -238) NIL) ((-701 . -1238) T) ((-1312 . -23) T) ((-828 . -660) 719) ((-562 . -1238) T) ((-430 . -349) 703) ((-583 . -1077) 690) ((-1261 . -111) 499) ((-713 . -651) 481) ((-869 . -111) 460) ((-392 . -23) T) ((-171 . -628) 238) ((-1210 . -526) 30) ((-890 . -1121) T) ((-693 . -1121) T) ((-688 . -1121) T) ((-674 . -1121) T))
\ No newline at end of file diff --git a/src/share/algebra/compress.daase b/src/share/algebra/compress.daase index ed1af87e..8aff76dc 100644 --- a/src/share/algebra/compress.daase +++ b/src/share/algebra/compress.daase @@ -1,6 +1,6 @@ -(30 . 3486815900) -(4466 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| +(30 . 3486820625) +(4467 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| ATTRIBUTE |package| |domain| |category| CATEGORY |nobranch| AND |Join| |ofType| SIGNATURE "failed" "algebra" |OneDimensionalArrayAggregate&| |OneDimensionalArrayAggregate| |AbelianGroup&| |AbelianGroup| @@ -313,7 +313,7 @@ |AnnaNumericalOptimizationPackage| |NumericalOptimizationProblem| |OrderedCompletionFunctions2| |OrderedCompletion| |OrderedFinite| |OrderingFunctions| |OrderedMonoid| |OrderedRing&| |OrderedRing| - |OrderedSet| |OrderedType&| |OrderedType| + |OrderedSet| |OrderedStructure| |OrderedType&| |OrderedType| |UnivariateSkewPolynomialCategory&| |UnivariateSkewPolynomialCategory| |UnivariateSkewPolynomialCategoryOps| |SparseUnivariateSkewPolynomial| |UnivariateSkewPolynomial| |OrthogonalPolynomialFunctions| @@ -488,668 +488,660 @@ |XPolynomial| |XPolynomialRing| |XRecursivePolynomial| |YoungDiagram| |ParadoxicalCombinatorsForStreams| |ZeroDimensionalSolvePackage| |IntegerLinearDependence| |IntegerMod| |Enumeration| |Mapping| - |Record| |Union| |stop| |exponential| |sin?| |leftTrim| |newLine| - |optional?| |linearDependence| |Is| |divergence| |infiniteProduct| - |fortranReal| |divisors| |moebius| |reciprocalPolynomial| - |getExplanations| |sincos| |fortranLiteral| - |purelyAlgebraicLeadingMonomial?| |isOp| |reverseLex| - |integralRepresents| |nodeOf?| |normalizedAssociate| |iisin| |prime| - |d03eef| |magnitude| |newTypeLists| |hessian| |genericRightNorm| - |isAnd| |neglist| |c05pbf| |OMputAtp| |f04maf| |createThreeSpace| - |float?| |mapCoef| |inf| |mantissa| |splitDenominator| |stirling2| - |stopTableInvSet!| |tableau| |hermiteH| |isImplies| |list?| |iomode| - |readBytes!| |cSec| |complexNumeric| |getProperties| |paraboloidal| - |numericIfCan| |outputSpacing| |complement| |sequence| |lintgcd| - |perfectSquare?| |badValues| |fullPartialFraction| |power!| - |replaceKthElement| |internalSubPolSet?| |countRealRoots| |getCurve| - |inrootof| |airyAi| |kernels| |paren| |acothIfCan| |normalDeriv| - |euclideanGroebner| |gcdcofactprim| |incrementKthElement| |split!| - |pdf2ef| |primitivePart!| |KrullNumber| |operator| |heapSort| - |mapExpon| |conjug| |rightRank| |printTypes| |countRealRootsMultiple| - |f04mbf| |groebner?| |OMgetString| |coefficients| |addmod| |e04naf| - |c06gcf| |f01brf| |mainContent| |e02ajf| |varList| |unexpand| - |tValues| |univariate| |arg1| |iFTable| |computePowers| |dmpToP| - |redmat| |mpsode| |LiePolyIfCan| |reduceBasisAtInfinity| |critMTonD1| - |hasoln| |arg2| |interpretString| |nary?| |generalTwoFactor| - |alphabetic| |numericalIntegration| |dictionary| Y |findBinding| - |kmax| |elem?| |shiftRight| |internalIntegrate0| |closeComponent| - |patternMatch| |graphState| |callForm?| |measure2Result| |lexGroebner| - |factor| |discriminant| |normalise| |conditions| |applyRules| - |exprHasAlgebraicWeight| |goto| |rootDirectory| |critT| - |genericLeftTrace| |bit?| |dequeue!| |sqrt| |blue| |match| - |basisOfNucleus| |mapUnivariate| |unrankImproperPartitions0| - |makeViewport2D| |s17agf| |balancedFactorisation| |symmetricSquare| - |mathieu12| |real| |index?| |generic?| |halfExtendedSubResultantGcd2| - |tubePointsDefault| |tree| |getGraph| |rootOf| |interactiveEnv| - |rewriteIdealWithQuasiMonicGenerators| |imag| |outlineRender| - |invertIfCan| |graphs| |viewDeltaYDefault| |s18adf| |usingTable?| - |signatureAst| |directProduct| |removeRoughlyRedundantFactorsInPols| - |monomialIntPoly| |rationalPower| |exponent| |currentCategoryFrame| - |linearDependenceOverZ| |symbolIfCan| |OMgetFloat| |pointColorPalette| - |doubleResultant| |options| |SFunction| |stoseInvertible?reg| - |polyred| |explogs2trigs| |PDESolve| |clearFortranOutputStack| - |fortranComplex| |fortranLogical| |BasicMethod| |getGoodPrime| - |factorset| |brace| |c02agf| |insertMatch| |cot2trig| |tablePow| - |leftGcd| |eigenvalues| |showTheRoutinesTable| |airyBi| |destruct| - |stoseInvertibleSet| |upperCase| |extract!| |integralBasis| - |antiCommutative?| |d01gaf| |jordanAdmissible?| |roughBasicSet| - |string| |copy!| |OMputEndObject| |firstDenom| |hdmpToDmp| |repeating| - |solveid| |s20adf| |symmetric?| |bandedJacobian| - |degreeSubResultantEuclidean| |explicitEntries?| |backOldPos| - |OMputObject| |freeOf?| |cTan| |macroExpand| |insertBottom!| |plus| - |eq?| |OMputEndApp| |part?| |convert| |frobenius| |less?| - |polarCoordinates| |OMencodingBinary| |postfix| |terms| - |partialFraction| |monomial| |realEigenvectors| |exprToUPS| - |removeRoughlyRedundantFactorsInContents| |palginfieldint| |rk4qc| - |identityMatrix| |ptree| |collect| |multivariate| |extractIfCan| - |simplifyExp| |flatten| |identification| |mightHaveRoots| |linGenPos| - |showIntensityFunctions| |linearAssociatedExp| |eulerE| |times| - |variables| |var2StepsDefault| |iiacos| |opeval| |startTable!| - |noLinearFactor?| |setOrder| |odd?| |primextendedint| |froot| - |transpose| |exprHasWeightCosWXorSinWX| |trapezoidalo| |close| - |localReal?| |selectPolynomials| |linSolve| |iidsum| - |drawComplexVectorField| |dAndcExp| |innerint| |safeCeiling| - |leftPower| |yCoord| |gradient| |hasTopPredicate?| |simplify| - |setPredicates| |rightZero| |shuffle| |display| |squareTop| |orbits| - |expr| |ldf2lst| |monom| |palgextint| |initiallyReduce| |untab| - |constantIfCan| |totalLex| |univariatePolynomial| |eyeDistance| - |integralBasisAtInfinity| |plotPolar| |taylor| |viewDefaults| - |numberOfIrreduciblePoly| |singularitiesOf| - |factorSquareFreeByRecursion| |expintegrate| |FormatArabic| |iiacsch| - |problemPoints| |randomR| |laurent| |symmetricGroup| |quotedOperators| - |subNodeOf?| |e01daf| |numberOfImproperPartitions| |common| |module| - |leftExtendedGcd| |puiseux| |leftTraceMatrix| |deepestInitial| - |tubeRadiusDefault| |basisOfRightNucleus| |stopTable!| |variable| - |selectODEIVPRoutines| |max| |clearTheSymbolTable| |dimension| - |showSummary| |jordanAlgebra?| |input| |numberOfFractionalTerms| - |compose| |outerProduct| |Hausdorff| |iterators| |getMeasure| |iiperm| - |inv| |extractProperty| |branchPoint?| |powerAssociative?| |library| - |remove!| |in?| |selectFiniteRoutines| |enterInCache| |fracPart| - |ground?| |setAdaptive| |determinant| |littleEndian| |is?| |any?| |id| - |clipWithRanges| |ground| |irDef| |initializeGroupForWordProblem| - |value| |OMputBind| |optimize| |resetVariableOrder| |doubleRank| - |exportedOperators| |element?| |lo| |sumSquares| |algDsolve| - |leadingMonomial| |internalAugment| |lflimitedint| |sub| |UP2ifCan| - |showAttributes| |hspace| |wholePart| |setProperties| - |stiffnessAndStabilityOfODEIF| |laguerreL| |leadingCoefficient| - |exponents| |f02bbf| |asimpson| |zeroDimPrime?| |lifting1| |sort!| - |assert| |submod| |rangePascalTriangle| |s14aaf| |cyclicParents| - |algintegrate| |cycle| |extractTop!| |positiveRemainder| |pr2dmp| - |rdregime| |validExponential| |meatAxe| |errorInfo| |mathieu24| - |laurentRep| |logical?| |ODESolve| |makeSeries| |exprToXXP| - |lowerCase| |reduceLODE| |UpTriBddDenomInv| |slex| GF2FG - |restorePrecision| |sqfree| |close!| |constant?| |presuper| |escape| - |atanIfCan| |rightCharacteristicPolynomial| |factors| |makeFR| - |iprint| |selectMultiDimensionalRoutines| |first| |enqueue!| |nullary| - |squareFreeFactors| |numberOfMonomials| |linearPart| |makingStats?| - |vectorise| |infRittWu?| |rest| |ode1| |createZechTable| |rk4a| - |inverseLaplace| |hex| |minPoints| |nthFlag| |shiftRoots| |f07fdf| - |OMsetEncoding| |radicalSimplify| |lhs| |moebiusMu| |cross| |exptMod| - |f07fef| |copies| |antisymmetric?| |lepol| |rhs| |outputAsScript| - |constructor| |seriesToOutputForm| |mathieu22| |tubePlot| - |cycleSplit!| |bezoutResultant| |errorKind| |subst| - |absolutelyIrreducible?| |leftRecip| |supRittWu?| - |constantToUnaryFunction| |square?| |computeBasis| |s13aaf| - |currentEnv| |pointData| |f04atf| |polyRDE| |putGraph| |overlabel| - |hasSolution?| |fixPredicate| |LyndonBasis| |supersub| |youngGroup| - |dimensionsOf| |halfExtendedSubResultantGcd1| |padecf| |vconcat| - |createLowComplexityTable| |redPo| |generateIrredPoly| - |resultantEuclideannaif| |monic?| |varselect| |indicialEquations| - |pastel| |associatedSystem| |logGamma| |rationalApproximation| |li| - |OMgetApp| |hclf| |e02dcf| |midpoints| |ref| |increase| - |makeYoungTableau| |hyperelliptic| |rdHack1| |generic| - |toseSquareFreePart| |cyclic| |e04jaf| |leftScalarTimes!| |OMopenFile| - |f01ref| |fortranTypeOf| |ldf2vmf| |setDifference| |leftNorm| - |consnewpol| |aromberg| |rootRadius| |lifting| |bivariateSLPEBR| - |countable?| |approximants| |redPol| |pointColorDefault| |objects| - |evenInfiniteProduct| |unparse| |prem| |nextItem| |cSin| |over| - |OMputString| |primeFactor| |collectQuasiMonic| |base| |debug3D| - |scalarMatrix| |aQuadratic| |s21bdf| |rotate| |randnum| |solveRetract| - |factorGroebnerBasis| |secIfCan| |euclideanNormalForm| |root?| - |degree| |bat1| |tryFunctionalDecomposition?| |trapezoidal| - |leftTrace| |setEpilogue!| |removeSquaresIfCan| |real?| - |skewSFunction| |clipPointsDefault| |unitNormal| |prefixRagits| |type| - |c06gbf| |factorSFBRlcUnit| |contractSolve| |rem| |monomials| |plus!| - |map!| |parabolicCylindrical| |conical| |c06fqf| |setVariableOrder| - |readLine!| |multiset| |quo| |mesh?| |addPoint| - |stripCommentsAndBlanks| |difference| |qsetelt!| |computeCycleEntry| - |makeMulti| |dim| |addiag| |leadingSupport| |fractionPart| - |setMinPoints3D| |extractSplittingLeaf| |Ci| |intChoose| - |branchPointAtInfinity?| |inc| |test| |width| |withPredicates| - |readInt32!| |scan| |checkForZero| |ideal| |binaryFunction| - |normDeriv2| |nthr| |div| |lllp| |conjugates| |csch2sinh| |bringDown| - |palglimint| |empty?| |roughSubIdeal?| |tryFunctionalDecomposition| - |testDim| |hermite| |imagj| |exquo| RF2UTS |cyclePartition| - |squareFreePolynomial| |biRank| |legendre| |finite?| |infinite?| - |createIrreduciblePoly| ~= |eigenMatrix| |lllip| |SturmHabicht| - |setCondition!| |deleteRoutine!| |pattern| |makeGraphImage| |iibinom| - |optpair| |associative?| |firstUncouplingMatrix| |alphanumeric?| - |nextNormalPoly| |OMgetEndError| |f01rcf| |#| |findConstructor| - |acsch| |morphism| |charthRoot| |leadingBasisTerm| |divisor| - |atrapezoidal| |table| |character?| |leftLcm| |algebraicCoefficients?| - ~ |nextPrime| |rational| |localUnquote| |createPrimitiveElement| - |reopen!| |singRicDE| |rules| |factorPolynomial| |new| |sparsityIF| - |delta| |prefix| |clearTable!| |before?| |returnType!| |obj| - |sylvesterMatrix| |previous| |quasiComponent| |isTimes| - |completeEchelonBasis| |s15aef| |cyclic?| |lyndonIfCan| |diff| - |mapMatrixIfCan| |limitedint| |swapRows!| |cache| |message| - |OMgetAttr| |optional| |cycles| |numberOfComponents| |dihedral| - |tRange| |complexLimit| |selectAndPolynomials| |atanhIfCan| |/\\| - |ddFact| |find| |interReduce| |rischNormalize| |irVar| |euclideanSize| - |antiCommutator| |space| |leftDivide| |lazyVariations| |\\/| - |characteristicSet| |selectSumOfSquaresRoutines| |pop!| |readByte!| - |SturmHabichtMultiple| |bipolar| |invmod| |rightScalarTimes!| - |BumInSepFFE| |generalizedContinuumHypothesisAssumed?| |writeBytes!| - |latex| |corrPoly| |clipParametric| |s20acf| |iiacot| |cschIfCan| - |search| |bag| |blankSeparate| |clip| |tableForDiscreteLogarithm| - |infLex?| |cosSinInfo| |s18dcf| |augment| |f01qdf| |f01qef| |e01bgf| - |wordInGenerators| |pointSizeDefault| |constDsolve| |rightFactorIfCan| - |ratDenom| |minIndex| |binaryTournament| |bat| |exprToGenUPS| |deref| - |lambda| |isNot| |lazyGintegrate| |safeFloor| |complexEigenvectors| - |curveColorPalette| |f07adf| |unitNormalize| |invmultisect| - |zeroDimPrimary?| |binaryTree| |fractRadix| |triangular?| - |showScalarValues| |lyndon| |functionIsFracPolynomial?| |transform| - |upDateBranches| |zeroOf| |e04dgf| |mkAnswer| |OMgetSymbol| FG2F - |drawStyle| |complexEigenvalues| |numberOfHues| |arbitrary| - |matrixConcat3D| |capacity| |left| |iiasinh| |pack!| |c02aff| - |changeBase| |level| |create| |doubleDisc| |structuralConstants| - |evenlambert| |right| |recoverAfterFail| |c05nbf| |getOperator| - |f02adf| |printHeader| |algint| F |elaborateFile| |finiteBound| - |lookupFunction| |rotatez| |bright| |position!| |extractIndex| - |basisOfRightNucloid| |addPointLast| |acoshIfCan| |trueEqual| - |setClipValue| |lazyPquo| |increment| |upperCase!| |push!| - |internalDecompose| |more?| |sh| |separate| |nextLatticePermutation| - |createPrimitivePoly| |readable?| |createGenericMatrix| |setValue!| - |eval| |merge| |resetNew| |select!| |ranges| |sayLength| - |nextIrreduciblePoly| |outputFloating| |eulerPhi| |cAsec| - |lazyPseudoRemainder| |zero| |exp| |reducedContinuedFraction| - |sumOfSquares| |outputArgs| |OMlistCDs| - |semiIndiceSubResultantEuclidean| |uniform01| |style| |e04mbf| - |maxPoints3D| |roman| |quadraticNorm| |extendedResultant| |prod| - |ParCondList| |leftZero| |normalized?| |number?| |complexExpand| |And| - |nullSpace| |error| |solveLinearPolynomialEquationByRecursion| - |sturmVariationsOf| |setMaxPoints3D| |middle| |axes| |modulus| - |inRadical?| |laurentIfCan| |mapUp!| |Or| |moduleSum| - |radicalEigenvectors| |cCot| |prepareSubResAlgo| |imagi| |isPower| - |binary| |e02zaf| |nextPrimitiveNormalPoly| |Not| |curveColor| - |leftReducedSystem| |size| |push| |exponentialOrder| |argumentListOf| - |relativeApprox| |outputForm| |setLegalFortranSourceExtensions| - |rightTraceMatrix| |c06fpf| |nullary?| |createNormalElement| |notelem| - |cAcos| |nthFractionalTerm| |anticoord| |randomLC| |critB| |row| - |dflist| |symbol| |critBonD| |f04mcf| |cycleElt| |Nul| |positiveSolve| - |maxint| |rightExtendedGcd| |pdf2df| |alternatingGroup| |f02fjf| - |expression| |attributeData| |flexible?| |mvar| |OMputEndAttr| - |substring?| |elseBranch| |cartesian| |leftFactorIfCan| - |systemCommand| |key| |OMReadError?| |lighting| |innerSolve1| - |integer| |double| |clearTheFTable| |htrigs| |getCode| - |processTemplate| |elRow1!| |dn| |basisOfRightAnnihilator| - |palglimint0| |certainlySubVariety?| |compBound| |euler| - |subResultantGcd| |suffix?| |expandLog| |hconcat| |OMgetEndApp| - |upperBound| |filename| |resetBadValues| |nlde| |userOrdered?| - |duplicates?| |readLineIfCan!| |OMgetBVar| |Frobenius| |charpol| - |completeHensel| |isOpen?| |setFormula!| |powern| |RittWuCompare| - |functionIsContinuousAtEndPoints| |trace2PowMod| |innerEigenvectors| - |isPlus| |prefix?| |defineProperty| |localIntegralBasis| - |leadingIdeal| |s17aef| |null| |parse| |one?| |OMencodingUnknown| - |alternative?| |radicalEigenvector| |e04gcf| |loopPoints| |unary?| - |functionIsOscillatory| |initial| |intPatternMatch| - |exteriorDifferential| |not| |lex| |sPol| |iteratedInitials| - |initTable!| |node| |lieAdmissible?| |s15adf| |bitLength| |ratPoly| - |fillPascalTriangle| |logpart| |and| |surface| |OMgetEndAttr| - |leftOne| |removeCoshSq| |writeInt8!| |rischDE| |retract| |iiatanh| - |comparison| |null?| |distdfact| |or| |generalInfiniteProduct| - |continuedFraction| |declare!| |nextSubsetGray| |addMatch| |qfactor| - |chiSquare| |getIdentifier| |normalDenom| |commaSeparate| - |exponential1| |delete| |cRationalPower| |startStats!| |size?| - |c06ekf| |iicsch| |reseed| |associatorDependence| |reorder| - |purelyAlgebraic?| |box| |integer?| |generalizedEigenvectors| - |poisson| |putColorInfo| |infix?| |basicSet| |keys| |setStatus| - |recolor| |minimalPolynomial| |rename| |integers| - |partialDenominators| ** |e04ucf| |shallowCopy| |mask| |commutator| - |ratDsolve| |viewWriteDefault| |sizeMultiplication| |cAcsch| - |LazardQuotient| |crest| |writable?| |predicate| |sdf2lst| - |irreducibleFactors| |optAttributes| |cExp| |squareFreePrim| - |identitySquareMatrix| |d01aqf| |unit?| |sort| |ipow| - |linearlyDependent?| |d02cjf| |leftFactor| |writeLine!| - |internalIntegrate| |ScanRoman| |tubeRadius| |abs| |d01ajf| |sup| - |transcendent?| |eof?| |groebner| |reducedForm| |ode| |lieAlgebra?| - |trivialIdeal?| |gensym| |simplifyLog| |iisqrt3| |segment| |iisqrt2| - |initials| |minimize| |deepCopy| |weakBiRank| |schwerpunkt| |headAst| - |index| |OMencodingXML| |OMencodingSGML| |tanh2trigh| |mainKernel| - |s21baf| |reindex| |nthRootIfCan| |hypergeometric0F1| - |generalizedInverse| |updateStatus!| |measure| |mainVariable?| |map| - |convergents| |primintfldpoly| |createMultiplicationMatrix| - |rightUnit| |outputMeasure| |oddintegers| |polCase| |stoseInvertible?| - |belong?| |pow| |startTableGcd!| |void| |environment| |gcdprim| - |printCode| |permanent| |closedCurve?| |equation| |setClosed| - |zeroVector| |prime?| |parseString| |jacobi| |SturmHabichtSequence| - |pair| |aspFilename| |degreeSubResultant| |dihedralGroup| - |showClipRegion| |printStatement| F2FG |support| |dominantTerm| - |LyndonCoordinates| |rightDivide| |OMunhandledSymbol| |maxrank| - |limit| |numerator| |mdeg| |connectTo| |bsolve| - |eisensteinIrreducible?| |genericPosition| |groebnerIdeal| |iifact| - |asecIfCan| |reducedDiscriminant| |expandPower| |complexSolve| - |parameters| |OMgetType| |pair?| |simpleBounds?| |multiEuclidean| - |repSq| |linearlyDependentOverZ?| |prinshINFO| |tab1| - |intermediateResultsIF| |divideIfCan| |log10| - |removeRedundantFactorsInContents| |sec2cos| |OMbindTCP| - |numberOfVariables| |createPrimitiveNormalPoly| |alphabetic?| |say| - |mainCoefficients| |stoseInvertible?sqfreg| - |dimensionOfIrreducibleRepresentation| |d02bhf| SEGMENT |decompose| - |initiallyReduced?| |e01sbf| |stoseInternalLastSubResultant| - |whatInfinity| |jacobiIdentity?| |e02baf| |parametric?| |expIfCan| - |monicRightFactorIfCan| |datalist| |recur| |viewpoint| - |genericLeftMinimalPolynomial| |OMserve| |c06ecf| |reset| - |characteristicSerie| |reify| |d03edf| |associatedEquations| |zerosOf| - |cotIfCan| |node?| |denominator| |setOfMinN| |csubst| - |monicCompleteDecompose| |genericLeftNorm| |partitions| |df2mf| - |makeSUP| |generalizedEigenvector| |stopMusserTrials| - |conditionsForIdempotents| |failed| |setright!| |schema| - |doubleFloatFormat| |setColumn!| |write| |choosemon| |extractClosed| - |lfintegrate| |linearPolynomials| |mathieu11| |primintegrate| - |addBadValue| |argumentList!| |expandTrigProducts| |generator| - |isEquiv| |rotatey| |save| |insertTop!| |subSet| |ReduceOrder| - |extractPoint| |pascalTriangle| |fill!| |leftMinimalPolynomial| - |normalElement| |subtractIfCan| |shufflein| |component| - |physicalLength!| |brillhartIrreducible?| |contours| |basisOfCentroid| - |setUnion| |setStatus!| |genericLeftTraceForm| |zeroDimensional?| - |subResultantGcdEuclidean| |rotatex| |diagonalProduct| |exprex| - |linear?| |patternVariable| |coHeight| |lyndon?| |OMputSymbol| - |boundOfCauchy| |harmonic| |bivariate?| |noncommutativeJordanAlgebra?| - |nilFactor| |e02akf| |integralLastSubResultant| |linearAssociatedLog| - |acscIfCan| |normal?| |pade| |rightNorm| |FormatRoman| |leastPower| - |ord| |d03faf| |currentScope| |superscript| |distFact| |triangulate| - |generalizedContinuumHypothesisAssumed| |cap| |nil| |bumprow| - |changeWeightLevel| |addPoint2| |intensity| |controlPanel| |log| - |perfectNthRoot| |subResultantsChain| |readInt8!| |clipSurface| - |getMultiplicationMatrix| |diagonal?| |primitive?| - |leadingCoefficientRicDE| |ParCond| |companionBlocks| |d01bbf| - |resultantnaif| |polar| |topFortranOutputStack| |definingInequation| - |birth| |getMultiplicationTable| |c06frf| |setIntersection| - |showAllElements| |selectsecond| |viewThetaDefault| |critMonD1| - |commutative?| |float| |conjugate| |parametersOf| |f02agf| - |particularSolution| |makeSin| |fortranDoubleComplex| - |minimumExponent| |changeVar| |approximate| |f04qaf| |normal01| - |green| |weierstrass| |iidprod| |norm| |complex| |apply| - |subQuasiComponent?| |tanNa| |imagI| |mainVariable| |startPolynomial| - |incr| |bezoutMatrix| |palgextint0| |inverse| |fortranInteger| - |conjunction| |constantOperator| |setLength!| |pushup| |scale| - |constant| |overlap| |hi| |nonLinearPart| |mainPrimitivePart| |arity| - |ceiling| |times!| |s19aaf| |fprindINFO| |resultantEuclidean| - |cyclicEntries| |makeViewport3D| |distribute| |rootProduct| - |kroneckerDelta| |partialNumerators| |ksec| |prinpolINFO| - |internalInfRittWu?| |bothWays| |numer| |gramschmidt| - |encodingDirectory| |cSech| |positive?| |logIfCan| |entries| - |rightFactorCandidate| |iicot| |normalizeAtInfinity| |c06gsf| |denom| - |traverse| |digit?| |leftRemainder| |compound?| |clearTheIFTable| - |s01eaf| |evaluateInverse| |contract| |sinhIfCan| |formula| |lift| - |updatD| |intersect| |rightPower| |sech2cosh| |integralMatrix| - |iiacsc| |s14baf| |po| |B1solve| |showTheIFTable| |subresultantVector| - |exQuo| |reduce| |pi| |simpsono| |disjunction| |trunc| |slash| - |lastSubResultantElseSplit| |setTopPredicate| GE |mergeFactors| - |nthExpon| |shade| |standardBasisOfCyclicSubmodule| |infinity| - |rightLcm| |truncate| |multiEuclideanTree| |totalDifferential| - |oddlambert| |mapUnivariateIfCan| GT |subMatrix| |d01alf| - |integralMatrixAtInfinity| |OMsupportsCD?| |buildSyntax| - |multiplyExponents| |realRoots| |setPrologue!| |f02aaf| |mapdiv| LE - |iiacoth| |rowEchLocal| |insertRoot!| |rationalPoints| |precision| - |nrows| |invertible?| |viewPhiDefault| |pushdterm| |diagonalMatrix| - |isList| |alternating| LT |concat| |rightQuotient| |generators| |pol| - |nthRoot| |leftRank| |ncols| |bottom!| |kernel| |wreath| |e01baf| - |child?| |highCommonTerms| |duplicates| |tanSum| |updatF| |insert!| - |integerBound| |fglmIfCan| |list| |d01amf| |diophantineSystem| - |clikeUniv| |realEigenvalues| |entry?| |taylorIfCan| |presub| - |unitVector| |draw| |outputFixed| |imagE| |groebSolve| - |expextendedint| |useSingleFactorBound?| |perfectSqrt| - |shanksDiscLogAlgorithm| |f04jgf| |extractBottom!| |floor| |pureLex| - |monomRDE| |OMgetBind| |permutationRepresentation| - |indicialEquationAtInfinity| |setprevious!| |vark| |normInvertible?| - |fortran| |cyclicCopy| |elements| |factorSquareFree| |polynomial| - |imports| |point| |cycleEntry| |solid| |zeroSetSplit| |rarrow| - |remove| |hasHi| |var1Steps| |realElementary| |toScale| |equiv| - |listexp| |polygon| |accuracyIF| |getMatch| |complementaryBasis| - |OMputInteger| |lazyPrem| |lSpaceBasis| |stoseInvertibleSetsqfreg| - |SturmHabichtCoefficients| |points| |lfextlimint| |karatsubaDivide| - |makeObject| |iiabs| |cAsin| |singular?| |s19acf| |iiasin| |last| - |ricDsolve| |lp| |singleFactorBound| |viewPosDefault| |prinb| - |inverseColeman| |byte| |HenselLift| |fortranLinkerArgs| |cycleRagits| - |series| |coef| |nthExponent| |fTable| |assoc| |fixedPoint| |sin2csc| - |modifyPoint| |epilogue| |weight| |nextPrimitivePoly| - |resetAttributeButtons| |mapDown!| |discriminantEuclidean| - |packageCall| |curry| |reduced?| |univariate?| |quote| - |removeRedundantFactors| |selectfirst| |multisect| - |leftRegularRepresentation| |ListOfTerms| |pile| |laguerre| - |createLowComplexityNormalBasis| |leaf?| |crushedSet| |tensorProduct| - |elaborate| |irreducibleFactor| |prolateSpheroidal| |light| - |polyRicDE| |cos2sec| |rightAlternative?| |c06fuf| |sturmSequence| - |isQuotient| |numberOfChildren| |changeName| |maxColIndex| |cup| - |entry| |min| |lastSubResultantEuclidean| |parabolic| |OMmakeConn| - |besselK| |makeUnit| |firstSubsetGray| |bernoulliB| |digits| |psolve| - |any| |OMputAttr| |extendIfCan| |primextintfrac| |perspective| - |rightMult| |rootPoly| |strongGenerators| |OMcloseConn| - |quasiAlgebraicSet| |range| |showAll?| |f02abf| - |resultantReduitEuclidean| |possiblyNewVariety?| |OMputEndBVar| - |exprHasLogarithmicWeights| |leftMult| |df2fi| |prologue| - |pmComplexintegrate| |rationalIfCan| |semiLastSubResultantEuclidean| - |rowEchelon| |virtualDegree| |rationalFunction| |critpOrder| - |rightRecip| |representationType| |integrate| |fixedPoints| - |cyclicGroup| |oneDimensionalArray| |roughBase?| |rootSplit| - |lowerCase?| |function| |height| |script| |printingInfo?| |vspace| - |sechIfCan| |computeCycleLength| |s21bbf| |infinityNorm| |remainder| - |option?| |directory| |setnext!| |cAcosh| |lowerBound| - |rightExactQuotient| |atoms| |inputOutputBinaryFile| |findCycle| - |numerators| |removeZeroes| |e04ycf| |subresultantSequence| |child| - |returnTypeOf| |inspect| |cot2tan| |factorial| |solveLinear| - |retractIfCan| |OMUnknownSymbol?| |ignore?| |LazardQuotient2| - |universe| |removeRedundantFactorsInPols| |extension| |iipow| - |fortranCompilerName| |tex| |meshPar1Var| |makeop| |baseRDE| - |OMgetEndObject| |semiResultantReduitEuclidean| |call| |makeEq| - |viewDeltaXDefault| |infix| |gderiv| |cyclotomicDecomposition| - |numeric| |qualifier| |linearAssociatedOrder| |subNode?| |thetaCoord| - |startTableInvSet!| |seed| |e04fdf| |readUInt8!| |definingEquations| - |radical| |dmpToHdmp| |routines| |chvar| |top| |adjoint| |expint| - |univariatePolynomialsGcds| |OMUnknownCD?| |iisec| |label| |edf2df| - |elliptic| |d02gaf| |halfExtendedResultant1| |continue| - |repeatUntilLoop| |cAsech| |monicDecomposeIfCan| UP2UTS - |stoseIntegralLastSubResultant| |radicalRoots| |dimensions| |f2df| - |preprocess| |shiftLeft| |lambert| |OMgetObject| |lprop| |localAbs| - |extendedIntegrate| EQ |d02raf| |unknownEndian| |f02ajf| |credPol| - |symmetricTensors| |unknown| |mainValue| |realZeros| |direction| - |lquo| |sn| |trailingCoefficient| |mainVariables| |computeInt| - |matrixDimensions| |bitTruth| |ip4Address| |invertibleSet| |status| - |edf2fi| |sorted?| |UnVectorise| |listOfLists| |minPoly| |printInfo!| - |GospersMethod| |characteristicPolynomial| |functorData| |external?| - |increasePrecision| |lazyEvaluate| |c06eaf| |lcm| |LyndonWordsList| - |extendedint| |setvalue!| |rspace| |conditionP| |elliptic?| |s13adf| - |goodPoint| |medialSet| |printInfo| |principalIdeal| |deriv| - |normalForm| |setref| |palgLODE| |maximumExponent| |denominators| - |groebnerFactorize| |tail| |octon| |dualSignature| |att2Result| - |append| |viewSizeDefault| |cyclotomicFactorization| |twist| - |lazyIntegrate| |s21bcf| |weighted| |unmakeSUP| - |selectIntegrationRoutines| |length| |digit| |option| - |quasiMonicPolynomials| |associates?| |cyclicSubmodule| |symFunc| - |gcd| |hash| |subscript| |declare| |delay| |category| |separant| - |besselY| |listYoungTableaus| |triangSolve| |scripts| |count| - |makeTerm| |d02gbf| |getVariableOrder| |false| |fibonacci| |mapSolve| - |domain| |root| |setrest!| |weights| |rischDEsys| |chineseRemainder| - |rightMinimalPolynomial| |pointLists| |f02wef| |debug| - |roughEqualIdeals?| |currentSubProgram| |package| |iitanh| |monomial?| - |OMgetEndAtp| |stFunc1| |largest| |iilog| |normalizedDivide| - |OMreceive| |qqq| |changeMeasure| D |complexNormalize| |coerceImages| - |patternMatchTimes| |rootNormalize| |karatsubaOnce| |iisech| |modTree| - |squareFree| |denomRicDE| |aCubic| |bfKeys| |zero?| |brillhartTrials| - |pdct| |musserTrials| |listConjugateBases| |toseInvertibleSet| - |domainTemplate| |connect| |definingPolynomial| |endSubProgram| - |solve| |mindegTerm| |socf2socdf| |critM| |nextsubResultant2| - |removeZero| |distance| |makeCos| |semiDiscriminantEuclidean| - |prevPrime| |center| |d01asf| |subCase?| |decimal| - |solveLinearPolynomialEquationByFractions| |uncouplingMatrices| - |s18acf| |solve1| |s18aff| |leastMonomial| |negative?| |mkIntegral| - |radix| |genericRightTrace| |f02bjf| |closed| |simpson| - |LyndonWordsList1| |phiCoord| |decreasePrecision| |permutation| - |flexibleArray| |operators| |graphImage| |curryLeft| |bracket| |cCos| - |Vectorise| |splitSquarefree| |f04faf| |quadraticForm| - |viewWriteAvailable| |palgint| |hue| |bindings| |reducedSystem| - |rewriteIdealWithRemainder| |factorsOfCyclicGroupSize| |setsubMatrix!| - |multinomial| |iitan| |identity| |categoryFrame| |interval| - |internalSubQuasiComponent?| |binding| |normalize| |pushNewContour| - |multiplyCoefficients| |limitedIntegrate| |c06gqf| |makeCrit| - |genericRightTraceForm| |associator| |order| |var2Steps| |cAcsc| - |numericalOptimization| |removeSinhSq| |semiSubResultantGcdEuclidean1| - |df2ef| |integralCoordinates| |print| |ode2| |axesColorDefault| - |youngDiagram| |tubePoints| |generalLambert| |factorByRecursion| - |maxdeg| |imagK| |forLoop| |flagFactor| |expPot| |cCsc| |resolve| - |minRowIndex| |basisOfMiddleNucleus| |setfirst!| |dfRange| |directSum| - |headReduced?| |chebyshevU| |condition| |categoryMode| |s17ajf| - |removeSinSq| |inGroundField?| |bfEntry| |minPol| |s17dgf| |power| - |predicates| |chebyshevT| |separateFactors| |gcdcofact| - |lexTriangular| |algebraicDecompose| |setRealSteps| |removeCosSq| - |HermiteIntegrate| |fi2df| |cAcoth| |readUInt16!| |algebraicSort| - |squareFreeLexTriangular| |f02akf| |move| |linkToFortran| - |primitiveMonomials| |summation| |replace| |externalList| |diagonals| - |radicalOfLeftTraceForm| |homogeneous?| |evaluate| |badNum| - |complexElementary| |red| |comment| |removeDuplicates!| |reductum| - |pseudoQuotient| |fixedPointExquo| |setLabelValue| |traceMatrix| - |equality| |partialQuotients| |complex?| |raisePolynomial| |linear| - |ptFunc| |LiePoly| |factorFraction| |trigs2explogs| |abelianGroup| - |step| |reduceByQuasiMonic| |meshFun2Var| |dmp2rfi| |btwFact| |s17dcf| - |compactFraction| |algebraic?| |sumOfDivisors| |polygamma| - |discreteLog| |mergeDifference| |charClass| |toseLastSubResultant| - |whileLoop| |adaptive3D?| |palgintegrate| |fortranCarriageReturn| - |contains?| |createRandomElement| |setAttributeButtonStep| - |splitNodeOf!| |OMreadStr| |makeResult| |systemSizeIF| |appendPoint| - |sum| |pseudoRemainder| |padicallyExpand| |rubiksGroup| |revert| - |lexico| |OMParseError?| |zeroDim?| |redpps| - |genericRightDiscriminant| |setFieldInfo| |selectOptimizationRoutines| - |erf| |tanIfCan| |compdegd| |pole?| |iisinh| |host| |sncndn| |region| - |removeConstantTerm| |acotIfCan| |getConstant| |oblateSpheroidal| - |ramifiedAtInfinity?| |exists?| |cAtanh| |s19abf| |eq| |cosh2sech| - |tan2cot| |numberOfCycles| |subPolSet?| |e02ddf| |shift| |drawComplex| - |insert| |addMatchRestricted| |setAdaptive3D| |basisOfLeftAnnihilator| - |decrease| |iter| |reflect| |figureUnits| |createNormalPoly| |nodes| - |bipolarCylindrical| |ravel| |dilog| |infieldint| |c05adf| |output| - |stronglyReduced?| |leftAlternative?| |parent| |edf2ef| |key?| - |point?| |algebraicOf| |matrix| |setPoly| |sin| - |createNormalPrimitivePoly| |reshape| |variable?| |e02dff| |edf2efi| - |generalPosition| |algSplitSimple| |getZechTable| |knownInfBasis| - |expt| |s17adf| |cos| |concat!| |newReduc| |zCoord| |rightUnits| - |primaryDecomp| |rightGcd| |content| |changeNameToObjf| |reverse!| - |permutations| |tan| |coordinates| |e01bff| |sts2stst| |jokerMode| - |closedCurve| |nextNormalPrimitivePoly| |coordinate| |second| - |prindINFO| |denomLODE| |numberOfFactors| |cn| |cot| |compile| - |listOfMonoms| |quadratic?| |typeLists| |getProperty| |adaptive?| - |complete| |minColIndex| |third| |infieldIntegrate| |squareMatrix| - |pointPlot| |sec| |midpoint| |e02bbf| |ScanFloatIgnoreSpaces| - |primlimitedint| |gcdPolynomial| |approxNthRoot| |symbolTableOf| - |rootsOf| |bandedHessian| |pushdown| - |removeSuperfluousQuasiComponents| |finiteBasis| |csc| |pToHdmp| - |update| |leadingExponent| |saturate| |getOperands| |units| |jacobian| - |rk4f| |d01akf| |var1StepsDefault| |antiAssociative?| |noKaratsuba| - |asin| |f07aef| |factorsOfDegree| |decomposeFunc| |scopes| - |leftCharacteristicPolynomial| |halfExtendedResultant2| |csc2sin| - |divideIfCan!| |cAtan| |mappingAst| |acos| |explicitlyFinite?| - |basisOfCenter| |rightTrace| |maxIndex| |showArrayValues| |iiatan| - |limitPlus| |numberOfComputedEntries| |mix| |smith| |color| |atan| - |leftUnit| |screenResolution3D| |signature| |complexForm| |solid?| - |beauzamyBound| |spherical| |f02awf| |irreducible?| |nullity| - |byteBuffer| |primPartElseUnitCanonical!| |acot| |block| |shrinkable| - |f01rdf| |overbar| |mapBivariate| |generate| |super| - |coerceListOfPairs| |lowerCase!| |tanQ| |putProperties| - |completeSmith| |code| |asec| |trim| |position| |leastAffineMultiple| - |hMonic| |readUInt32!| |quotientByP| |f2st| |leadingTerm| - |complexNumericIfCan| |closed?| |operation| |solveLinearlyOverQ| - |acsc| |incrementBy| |laplacian| |PollardSmallFactor| |chiSquare1| - |torsion?| |wrregime| |makeprod| |primitivePart| |isobaric?| - |permutationGroup| |torsionIfCan| |sinh| |nor| |OMputEndBind| |expand| - |indicialEquation| |bumptab1| |LowTriBddDenomInv| |d01apf| |e02adf| - |sortConstraints| |delete!| |clipBoolean| |cosh| - |stiffnessAndStabilityFactor| |squareFreePart| |cSinh| - |mainExpression| |basis| |filterWhile| |wholeRadix| |hostByteOrder| - |dioSolve| |lazyPseudoQuotient| |superHeight| |tanh| |factorOfDegree| - |every?| |possiblyInfinite?| |const| |filterUntil| |specialTrigs| - |transcendentalDecompose| |nonSingularModel| |e01sef| |e02bdf| - |failed?| |supDimElseRittWu?| |coth| |constantOpIfCan| |elementary| - |testModulus| |ScanFloatIgnoreSpacesIfCan| |select| - |numberOfPrimitivePoly| |indiceSubResultantEuclidean| - |genericLeftDiscriminant| |create3Space| |mat| |headReduce| - |indiceSubResultant| |sech| |iiGamma| |unvectorise| |multiple?| - |unprotectedRemoveRedundantFactors| |constantLeft| |lineColorDefault| - |rootPower| |OMgetEndBVar| |viewport3D| |complexZeros| |csch| - |modularGcdPrimitive| |primes| |useEisensteinCriterion| |trigs| - |read!| |atom?| |d01anf| |differentialVariables| |asinh| - |bombieriNorm| |retractable?| |ef2edf| |LagrangeInterpolation| - |e02bcf| |overset?| |tan2trig| |divideExponents| |elRow2!| |acosh| - |whitePoint| |oddInfiniteProduct| |minGbasis| |s17dlf| |getStream| - |ffactor| |fortranCharacter| |mkPrim| |init| |wronskianMatrix| |atanh| - |setErrorBound| |cond| |collectUpper| |isMult| |rroot| |iiacosh| - |completeEval| |hitherPlane| |minimumDegree| |degreePartition| |acoth| - |makeRecord| |f02aef| |semiSubResultantGcdEuclidean2| |scalarTypeOf| - |modularFactor| |toseInvertible?| |newSubProgram| |signAround| |asech| - |basisOfLeftNucleus| |radicalEigenvalues| |basisOfCommutingElements| - |cylindrical| |separateDegrees| |OMwrite| |extend| |digamma| - |integral| |factorAndSplit| |writeByte!| |isAtom| |exactQuotient| - |quoByVar| |mapGen| |coerceS| |leftRankPolynomial| |getPickedPoints| - |multiple| |relerror| |iterationVar| |d02bbf| |d02kef| |OMgetInteger| - |dom| |reducedQPowers| |curve| |applyQuote| |lfextendedint| |subset?| - |set| |simplifyPower| |factorSquareFreePolynomial| LODO2FUN - |pmintegrate| |mainForm| |f01mcf| |divisorCascade| |iiasec| |llprop| - |hdmpToP| |Lazard2| BY |wordInStrongGenerators| |selectPDERoutines| - |internalZeroSetSplit| |qelt| |generalSqFr| |parts| - |makeFloatFunction| |lfinfieldint| |besselI| |nothing| |geometric| - |internal?| |palgRDE| |s17dhf| |ridHack1| |qsetelt| |kovacic| - |solveInField| |ruleset| |reduction| |padicFraction| |imagJ| - |makeVariable| |check| |d01fcf| |xRange| |mainMonomial| |baseRDEsys| - UTS2UP |splitLinear| |implies| |polyPart| |quasiRegular?| - |rectangularMatrix| |title| |alphanumeric| |laplace| |yRange| - |coerceP| |dec| |typeForm| |copyInto!| |coord| |xCoord| |branchIfCan| - |iflist2Result| |removeRoughlyRedundantFactorsInPol| - |compiledFunction| |zRange| |inR?| |suchThat| |sizePascalTriangle| - |monicDivide| |mainMonomials| |sinhcosh| |iicos| |iroot| |sign| - |cAsinh| |fractionFreeGauss!| |c06ebf| |getDatabase| |low| |e| - |topPredicate| |subResultantChain| |radicalSolve| |f04axf| NOT - |numFunEvals| |nsqfree| |quatern| |fortranDouble| - |useEisensteinCriterion?| |subHeight| |someBasis| |rotate!| |exp1| OR - |yellow| |iiexp| |shape| |linears| |cyclotomic| - |univariatePolynomials| |OMputEndError| |purelyTranscendental?| - |voidMode| |basisOfLeftNucloid| AND |properties| |irCtor| |vedf2vef| - |show| |balancedBinaryTree| |ellipticCylindrical| |Si| |pointColor| - |OMsupportsSymbol?| |monicModulo| |bumptab| |translate| |rightOne| - |Ei| |mapExponents| |pushucoef| |open| |typeList| |rst| |dark| - |inverseIntegralMatrixAtInfinity| |firstNumer| |yCoordinates| - |complexIntegrate| |cAcot| |allRootsOf| |trace| - |getSyntaxFormsFromFile| |lazyPremWithDefault| |derivationCoordinates| - |semiResultantEuclidean2| |collectUnder| |s18aef| |polygon?| - |argument| |intcompBasis| |s19adf| |rCoord| |graphStates| - |univariateSolve| |round| |tab| |mirror| |createMultiplicationTable| - |noValueMode| |OMlistSymbols| |monicRightDivide| |numberOfNormalPoly| - |front| |getButtonValue| |safetyMargin| |minus!| |viewport2D| |bitand| - |char| |lazyResidueClass| |leftExactQuotient| |symmetricDifference| - |deepestTail| |sinh2csch| |operations| |hcrf| |imaginary| - |constantCoefficientRicDE| |dual| |expressIdealMember| |bitior| - |integralDerivationMatrix| |qPot| |setScreenResolution| |upperCase?| - |autoReduced?| |primeFrobenius| |rowEchelonLocal| - |integralAtInfinity?| |merge!| |head| |string?| |result| |s17def| - |ran| |OMsend| |mainCharacterization| |aLinear| |s13acf| - |nativeModuleExtension| |genus| |build| |insertionSort!| - |setButtonValue| |maxPoints| |pomopo!| |rational?| |wholeRagits| - |recip| |linearMatrix| |toroidal| |matrixGcd| - |wordsForStrongGenerators| * |gethi| |rationalPoint?| |nthFactor| - |asechIfCan| |tanh2coth| |monicLeftDivide| |stoseInvertibleSetreg| - |leftUnits| |numberOfDivisors| |pToDmp| |unitsColorDefault| - |unaryFunction| |cdr| |setProperty| |complexRoots| |OMconnectTCP| - |setleaves!| |removeSuperfluousCases| |coerceL| |symbolTable| |orbit| - |setScreenResolution3D| |cscIfCan| |iiasech| |double?| |iicoth| - |palgLODE0| |primitiveElement| |swapColumns!| |empty| - |genericRightMinimalPolynomial| |cosIfCan| = |interpret| |mindeg| - |e02aef| |f02axf| |rightRemainder| |listBranches| - |lazyIrreducibleFactors| |readInt16!| |inconsistent?| - |pushFortranOutputStack| |kind| |setMaxPoints| |OMgetEndBind| |queue| - |aQuartic| |resultant| |stopTableGcd!| |multMonom| |iExquo| |members| - |shellSort| |popFortranOutputStack| |op| < |indices| |subTriSet?| - |leviCivitaSymbol| |removeDuplicates| |loadNativeModule| |graeffe| - |property| |sinIfCan| |OMgetAtp| |outputAsFortran| |romberg| > - |numberOfOperations| |totalGroebner| |OMputFloat| |mainSquareFreePart| - |useNagFunctions| |curryRight| |writeUInt8!| |argscript| <= |quartic| - |expintfldpoly| |goodnessOfFit| |sqfrFactor| |sylvesterSequence| - |iicsc| |invertibleElseSplit?| |mesh| |column| >= |chainSubResultants| - |high| |minordet| |f01maf| |scanOneDimSubspaces| |semicolonSeparate| - |monomialIntegrate| |quasiRegular| |removeIrreducibleRedundantFactors| - |setImagSteps| |clearCache| |represents| |rombergo| |df2st| - |perfectNthPower?| |isConnected?| |gcdPrimitive| |components| - |primPartElseUnitCanonical| |roughUnitIdeal?| |refine| |diagonal| - |splitConstant| |plot| |mr| |ScanArabic| |f02aff| |minrank| - |repeating?| |derivative| |categories| |union| + |lazy?| |nextColeman| - |powerSum| |semiResultantEuclidean1| |e02def| - |rightRegularRepresentation| |just| |frst| |checkRur| - - |leftDiscriminant| |coth2trigh| |OMputError| |leftQuotient| - |acschIfCan| |e02daf| |f04adf| |isExpt| |enumerate| / |bytes| |s17acf| - |shallowExpand| |semiDegreeSubResultantEuclidean| |parents| - |rangeIsFinite| |stirling1| |Lazard| |idealSimplify| |setTex!| - |sizeLess?| |cons| |drawToScale| |asinIfCan| |principal?| - |monomRDEsys| |isAbsolutelyIrreducible?| |f04asf| |normFactors| - |d01gbf| |viewZoomDefault| |univcase| |idealiserMatrix| - |unitCanonical| |getlo| |zag| |myDegree| |mainDefiningPolynomial| - |stFunc2| |coercePreimagesImages| |qinterval| |rightDiscriminant| - |variationOfParameters| |putProperty| |binomThmExpt| |rk4| - |zeroMatrix| |uniform| |inHallBasis?| |tanAn| |substitute| |rur| - |adaptive| |cLog| |enterPointData| |e01sff| |cycleLength| |diag| - |vector| |symmetricPower| |bits| |physicalLength| - |sumOfKthPowerDivisors| |swap!| |arrayStack| |areEquivalent?| - |unravel| |comp| |fixedDivisor| |differentiate| |coefChoose| - |pleskenSplit| |lastSubResultant| |setRow!| |curve?| |coerce| - |cyclicEqual?| |nand| |characteristic| |outputAsTex| |hexDigit| - |source| |hexDigit?| |mulmod| |relationsIdeal| |OMputApp| |vertConcat| - |construct| |scaleRoots| |realSolve| |endOfFile?| |swap| |nonQsign| - |factor1| |stack| |xn| |elColumn2!| |rank| |maxrow| |deepExpand| - |rightRankPolynomial| |fortranLiteralLine| |dot| - |inverseIntegralMatrix| |karatsuba| |modularGcd| |imagk| |e02agf| - |constantKernel| |s17akf| |symmetricProduct| |name| |split| |top!| - |meshPar2Var| |idealiser| |ratpart| |droot| |powers| - |changeThreshhold| |setMinPoints| |body| |log2| |cPower| |car| - |selectNonFiniteRoutines| |printStats!| |rootBound| |heap| |Gamma| - |e02bef| |outputList| |target| |interpolate| |setelt!| |showRegion| - |expenseOfEvaluationIF| |horizConcat| |next| |nextsousResultant2| - |f01qcf| |stoseSquareFreePart| |e02gaf| |tube| |headRemainder| - |fintegrate| |bitCoef| |triangularSystems| |leaves| - |transcendenceDegree| |integral?| |OMreadFile| |gbasis| |e01bhf| - |product| |combineFeatureCompatibility| |f01bsf| |leader| |isOr| - |quickSort| |rename!| |inputBinaryFile| |write!| |thenBranch| |janko2| - |extendedSubResultantGcd| |reverse| |lists| |listLoops| |factorials| - |rewriteSetByReducingWithParticularGenerators| |npcoef| - |numberOfComposites| |Beta| |subscriptedVariables| |commonDenominator| - |seriesSolve| |iicosh| |tracePowMod| |OMclose| |member?| - |checkPrecision| |cardinality| |regime| |colorFunction| |plenaryPower| - |elaboration| |OMread| |minset| |rquo| |port| |regularRepresentation| - |fullDisplay| |totalDegree| |acosIfCan| |besselJ| |has?| - |modifyPointData| |integerIfCan| |s17aff| |prepareDecompose| - |OMputEndAtp| |stosePrepareSubResAlgo| |RemainderList| - |extendedEuclidean| |e01bef| |OMconnInDevice| |t| |setPosition| - |numFunEvals3D| |OMgetError| |back| |showTheFTable| |normal| - |solveLinearPolynomialEquation| |getOrder| |An| |getRef| |f02xef| - |quoted?| |primlimintfrac| |symmetricRemainder| |coshIfCan| - |nextSublist| |assign| |coleman| |Aleph| |getBadValues| |pseudoDivide| - |open?| |setelt| |fractRagits| |coefficient| |powmod| |d02ejf| - |f04arf| |ramified?| |setEmpty!| |e02ahf| |cTanh| |totolex| |rule| - |stronglyReduce| |groebgen| |partition| |lowerPolynomial| - |probablyZeroDim?| |arguments| |maxRowIndex| |copy| |colorDef| |unit| - |outputBinaryFile| |showFortranOutputStack| |internalLastSubResultant| - |xor| |divide| |rewriteSetWithReduction| |graphCurves| |even?| - |deleteProperty!| |showTheSymbolTable| |quotient| |tanintegrate| - |dequeue| |qroot| |asinhIfCan| |case| |depth| |cubic| - |rootOfIrreduciblePoly| |setlast!| |binarySearchTree| - |irreducibleRepresentation| |radPoly| |OMopenString| - |zeroSquareMatrix| |Zero| |omError| |useSingleFactorBound| |mapmult| - |OMputVariable| |OMputBVar| |One| |nextPartition| - |rewriteIdealWithHeadRemainder| |leadingIndex| |twoFactor| |true| - |match?| |s18def| |hasPredicate?| |cCosh| |normalizeIfCan| |sample| - |autoCoerce| |pquo| |mkcomm| |children| |moreAlgebraic?| |resize| - |nil?| |commutativeEquality| |constantRight| |listRepresentation| - |doubleComplex?| |moduloP| |semiResultantEuclideannaif| |eigenvector| - |OMgetVariable| |hostPlatform| |zoom| |returns| |minPoints3D| - |explicitlyEmpty?| |sequences| |innerSolve| |bounds| |plusInfinity| - |se2rfi| |palgRDE0| |calcRanges| |componentUpperBound| - |taylorQuoByVar| |selectOrPolynomials| |iCompose| |messagePrint| - |minusInfinity| |algebraicVariables| |composites| - |zeroSetSplitIntoTriangularSystems| |elt| |random| |setchildren!| - |doublyTransitive?| |cCsch| |totalfract| |coth2tanh| |lookup| - |bigEndian| |scripted?| |stoseLastSubResultant| |central?| |subspace| - |irForm| |expenseOfEvaluation| |bubbleSort!| |symbol?| |cycleTail| - |nthCoef| |mappingMode| |antisymmetricTensors| |e01saf| |cfirst| - |screenResolution| |explimitedint| |approxSqrt| |pushuconst| |rowEch| - |s14abf| |henselFact| |bezoutDiscriminant| |quadratic| - |exactQuotient!| |singularAtInfinity?| |setleft!| |ocf2ocdf| - |orthonormalBasis| |int| |mathieu23| |unrankImproperPartitions1| - |s17ahf| |completeHermite| |binomial| |outputGeneral| - |OMconnOutDevice| |resultantReduit| |tanhIfCan| |clearDenominator| - |extensionDegree| |rootKerSimp| |composite| |lagrange| |readIfCan!| - |legendreP| |stFuncN| |anfactor| |rootSimp| |cCoth| |lfunc| |satisfy?| - |eigenvectors| |quasiMonic?| |palgint0| |cothIfCan| |polynomialZeros| - |lazyPseudoDivide| |rightTrim| |factorList| |taylorRep| - |principalAncestors| |fmecg| |bernoulli| |bivariatePolynomials| - |makeSketch| |tower| |drawCurves| |nil| |infinite| |arbitraryExponent| - |approximate| |complex| |shallowMutable| |canonical| |noetherian| - |central| |partiallyOrderedSet| |arbitraryPrecision| - |canonicalsClosed| |noZeroDivisors| |rightUnitary| |leftUnitary| - |additiveValuation| |unitsKnown| |canonicalUnitNormal| - |multiplicativeValuation| |finiteAggregate| |shallowlyMutable| - 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\ No newline at end of file + |Record| |Union| |integerBound| |sumOfSquares| |autoReduced?| + |magnitude| |arg2| |complexSolve| |f01ref| |string| |chiSquare1| + |combineFeatureCompatibility| |primeFrobenius| |normalize| + |outputArgs| |fglmIfCan| |newTypeLists| |fortranTypeOf| |OMgetType| + |torsion?| |say| |f01bsf| |hessian| |OMlistCDs| |pushNewContour| + |rowEchelonLocal| |d01amf| |conditions| |ldf2vmf| |wrregime| |pair?| + |isOr| |integralAtInfinity?| |semiIndiceSubResultantEuclidean| + |multiplyCoefficients| |genericRightNorm| |diophantineSystem| |title| + |match| |simpleBounds?| |setDifference| |makeprod| |reset| |quickSort| + |limitedIntegrate| |isAnd| |uniform01| |merge!| |clikeUniv| |sum| + |multiEuclidean| |primitivePart| |rename!| |inc| |style| |neglist| + |c06gqf| |realEigenvalues| |head| |pr2dmp| |isobaric?| |repSq| |write| + |inputBinaryFile| |makeCrit| |entry?| |e04mbf| |c05pbf| |string?| |e| + |rdregime| |save| |permutationGroup| |linearlyDependentOverZ?| + |write!| |lp| |genericRightTraceForm| |s17def| |maxPoints3D| + |OMputAtp| |taylorIfCan| |validExponential| |prinshINFO| |nothing| + |torsionIfCan| |thenBranch| |ran| |f04maf| |presub| |meatAxe| |nor| + |tab1| |janko2| |latex| |delay| |OMsend| |createThreeSpace| + |unitVector| |errorInfo| |top| |intermediateResultsIF| |OMputEndBind| + |extendedSubResultantGcd| |separant| |corrPoly| |outputFixed| + |mainCharacterization| |float?| |mathieu24| |continue| + |indicialEquation| |divideIfCan| |listLoops| |clipParametric| + |besselY| |mapCoef| |imagE| |aLinear| |laurentRep| |factorials| + |s20acf| |listYoungTableaus| |groebSolve| |inf| |s13acf| |logical?| + |ratDsolve| |rightGcd| |rewriteSetByReducingWithParticularGenerators| + ** |hash| |iiacot| |triangSolve| |expextendedint| + |nativeModuleExtension| |splitDenominator| |ODESolve| |content| + |viewWriteDefault| |npcoef| |count| |makeTerm| |cschIfCan| |stirling2| + |genus| |useSingleFactorBound?| |makeSeries| |changeNameToObjf| + |sizeMultiplication| |numberOfComposites| |bag| |d02gbf| |exprToXXP| + |cAcsch| |reverse!| |Beta| |blankSeparate| |getVariableOrder| + |sizePascalTriangle| |arity| |constant| |lowerCase| |permutations| + |LazardQuotient| |subscriptedVariables| |clip| |fibonacci| |ceiling| + |monicDivide| |reduceLODE| |coordinates| |crest| |mantissa| + |commonDenominator| |tableForDiscreteLogarithm| |mapSolve| |times!| + |mainMonomials| |UpTriBddDenomInv| |writable?| |e01bff| |power!| + |root| |infLex?| |s19aaf| |sinhcosh| |slex| |sdf2lst| |sts2stst| + |uniform| |replaceKthElement| |cosSinInfo| |setrest!| |iicos| + |fprindINFO| GF2FG |jokerMode| |irreducibleFactors| |inHallBasis?| + |weights| |s18dcf| |iroot| |resultantEuclidean| |restorePrecision| + |optAttributes| |closedCurve| |tanAn| |rischDEsys| |augment| |sign| + |cyclicEntries| |sqfree| |nextNormalPrimitivePoly| |cExp| |substitute| + |chineseRemainder| |f01qdf| |cAsinh| |makeViewport3D| + |singularAtInfinity?| |close!| |squareFreePrim| |coordinate| |rur| + |rightMinimalPolynomial| |f01qef| |distribute| |fractionFreeGauss!| + |setleft!| |constant?| |identitySquareMatrix| |prindINFO| |adaptive| + |internalSubPolSet?| |pointLists| |e01bgf| |rootProduct| |c06ebf| + |ocf2ocdf| |presuper| |d01aqf| |denomLODE| |cLog| |countRealRoots| + |categories| |f02wef| |wordInGenerators| |kroneckerDelta| + |getDatabase| |orthonormalBasis| |numer| |escape| |retractIfCan| + |numberOfFactors| |unit?| |enterPointData| |roughEqualIdeals?| + |pointSizeDefault| |partialNumerators| |low| |mathieu23| |denom| + |atanIfCan| |ipow| |listOfMonoms| |e01sff| |constDsolve| + |currentSubProgram| |ksec| |topPredicate| |unrankImproperPartitions1| + |rightCharacteristicPolynomial| |quadratic?| |linearlyDependent?| + |cycleLength| |iitanh| |rightFactorIfCan| |prinpolINFO| + |subResultantChain| |s17ahf| |pi| |factors| |d02cjf| |typeLists| + |diag| |ratDenom| |monomial?| |internalInfRittWu?| |radicalSolve| + |completeHermite| |infinity| |makeFR| |getProperty| |leftFactor| + |symmetricPower| |concat| |step| |minIndex| |OMgetEndAtp| |bothWays| + |f04axf| |binomial| |iprint| |adaptive?| |writeLine!| |bits| + |binaryTournament| |stFunc1| |numFunEvals| |gramschmidt| + |outputGeneral| |selectMultiDimensionalRoutines| |internalIntegrate| + |complete| |physicalLength| |bat| |largest| |encodingDirectory| + |nsqfree| |kernel| |OMconnOutDevice| |enqueue!| |ScanRoman| + |minColIndex| |sumOfKthPowerDivisors| |formula| |iilog| |exprToGenUPS| + |cSech| |list| |quatern| |ptree| |resultantReduit| |nullary| + |tubeRadius| |infieldIntegrate| |swap!| |lhs| |normalizedDivide| + |deref| |fortranDouble| |positive?| |draw| |tanhIfCan| + |squareFreeFactors| |abs| |squareMatrix| |clearCache| |arrayStack| + |rhs| |OMreceive| |isNot| |useEisensteinCriterion?| |logIfCan| + |clearDenominator| |numberOfMonomials| |d01ajf| |pointPlot| + |areEquivalent?| |lazyGintegrate| |qqq| |entries| |subHeight| + |extensionDegree| |linearPart| |sup| |midpoint| |unravel| |currentEnv| + |nrows| |safeFloor| |changeMeasure| |someBasis| |rightFactorCandidate| + |rootKerSimp| |makingStats?| |e02bbf| |transcendent?| |fixedDivisor| + |ncols| |complexEigenvectors| |complexNormalize| |iicot| |rotate!| + |makeObject| |composite| |vectorise| |eof?| |ScanFloatIgnoreSpaces| + |coefChoose| |curveColorPalette| |coerceImages| |normalizeAtInfinity| + |exp1| |coef| |lagrange| |infRittWu?| |primlimitedint| |groebner| + |pleskenSplit| |f07adf| |patternMatchTimes| |yellow| |c06gsf| + |readIfCan!| |ode1| |reducedForm| |gcdPolynomial| |lastSubResultant| + |rootNormalize| |unitNormalize| |iiexp| |traverse| |legendreP| + |createZechTable| |approxNthRoot| |ode| |setRow!| |karatsubaOnce| + |invmultisect| |digit?| |shape| |stFuncN| |rk4a| |lieAlgebra?| + |symbolTableOf| |curve?| |kind| |iisech| |zeroDimPrimary?| |linears| + |leftRemainder| |anfactor| |inverseLaplace| |rootsOf| |trivialIdeal?| + |cyclicEqual?| |op| |binaryTree| |modTree| |cyclotomic| |compound?| + |rootSimp| |kernels| |hex| |gensym| |bandedHessian| |nand| |getCurve| + |fractRadix| |squareFree| |clearTheIFTable| |univariatePolynomials| + |cCoth| |minPoints| |operator| |pushdown| |simplifyLog| + |characteristic| |inrootof| |denomRicDE| |triangular?| |s01eaf| + |OMputEndError| |lfunc| SEGMENT |nthFlag| |iisqrt3| + |removeSuperfluousQuasiComponents| |outputAsTex| |showScalarValues| + |aCubic| |evaluateInverse| |purelyTranscendental?| |satisfy?| |sort| + |iisqrt2| |shiftRoots| |finiteBasis| |univariate| |hexDigit| |bfKeys| + |lyndon| |contract| |voidMode| |eigenvectors| |dec| |f07fdf| |pToHdmp| + |initials| |hexDigit?| |functionIsFracPolynomial?| |zero?| + |basisOfLeftNucloid| |sinhIfCan| |quasiMonic?| |OMsetEncoding| + |minimize| |leadingExponent| |mulmod| |union| |brillhartTrials| + |transform| |updatD| |irCtor| |palgint0| |saturate| |radicalSimplify| + |factor| |deepCopy| |relationsIdeal| |pdct| |upDateBranches| + |vedf2vef| |intersect| |cothIfCan| |random| |weakBiRank| |moebiusMu| + |sqrt| |getOperands| |OMputApp| |zeroOf| |musserTrials| + |balancedBinaryTree| |rightPower| |polynomialZeros| |comp| + |schwerpunkt| |cross| |jacobian| |real| |vertConcat| + |listConjugateBases| |e04dgf| |ellipticCylindrical| |sech2cosh| + |lazyPseudoDivide| |headAst| |exptMod| |rk4f| |imag| |scaleRoots| + |super| |properties| |mkAnswer| |toseInvertibleSet| |integralMatrix| + |Si| |factorList| |copy| |directProduct| |f07fef| |d01akf| + |OMencodingXML| |realSolve| |domainTemplate| |OMgetSymbol| |translate| + |pointColor| |iiacsc| |taylorRep| |copies| |OMencodingSGML| + |var1StepsDefault| |endOfFile?| FG2F |depth| |connect| |s14baf| + |OMsupportsSymbol?| |principalAncestors| |antiAssociative?| + |antisymmetric?| |brace| |tanh2trigh| |swap| |definingPolynomial| + |drawStyle| |po| |monicModulo| |fmecg| |mainKernel| |lepol| |destruct| + |noKaratsuba| |nonQsign| |complexEigenvalues| |endSubProgram| + |B1solve| |bumptab| |bernoulli| |outputAsScript| |f07aef| |s21baf| + |factor1| |match?| |numberOfHues| |solve| |rightOne| |showTheIFTable| + |bivariatePolynomials| |autoCoerce| |seriesToOutputForm| |reindex| + |factorsOfDegree| |xn| |arbitrary| |arguments| |mindegTerm| |Ei| + |subresultantVector| |makeSketch| |nthRootIfCan| |decomposeFunc| + |elColumn2!| |socf2socdf| |matrixConcat3D| |mapExponents| |exQuo| + |drawCurves| |selectODEIVPRoutines| |expand| |hypergeometric0F1| + |scopes| |monomial| |maxrow| |capacity| |critM| |pushucoef| |simpsono| + |max| |filterWhile| |leftCharacteristicPolynomial| + |generalizedInverse| |multivariate| |deepExpand| |close| |iiasinh| F + |nextsubResultant2| |disjunction| |typeList| |filterUntil| + |clearTheSymbolTable| |halfExtendedResultant2| |variables| + |updateStatus!| |rightRankPolynomial| |rst| |trunc| |select| + |dimension| |measure| |csc2sin| |fortranLiteralLine| |display| + |divisor| |lquo| |slash| |dark| |jordanAlgebra?| |divideIfCan!| + |mainVariable?| |dot| |trailingCoefficient| |atrapezoidal| + |inverseIntegralMatrixAtInfinity| |lastSubResultantElseSplit| + |numberOfFractionalTerms| |convergents| |cAtan| + |inverseIntegralMatrix| |character?| |mainVariables| |setTopPredicate| + |firstNumer| |compose| |karatsuba| |predicate| |computeInt| |leftLcm| + |yCoordinates| |mergeFactors| |Hausdorff| |functionIsOscillatory| + |selectOptimizationRoutines| |debug| |taylor| |modularGcd| + |matrixDimensions| |algebraicCoefficients?| |complexIntegrate| + |nthExpon| |cn| |getMeasure| |intPatternMatch| |tanIfCan| D |laurent| + |input| |imagk| |bitTruth| |nextPrime| |cAcot| |shade| |iiperm| + |exteriorDifferential| |compdegd| |puiseux| |library| |e02agf| + |f04mbf| |ip4Address| |rational| EQ |extractProperty| |pole?| |lex| + |constantKernel| |groebner?| |localUnquote| |invertibleSet| |d02kef| + |controlPanel| |branchPoint?| |iisinh| |sPol| |inv| |s17akf| + |OMgetString| |createPrimitiveElement| |status| |perfectNthRoot| + |OMgetInteger| |powerAssociative?| |host| |iteratedInitials| |ground?| + |symmetricProduct| |coefficients| |edf2fi| |reopen!| |reducedQPowers| + |subResultantsChain| |remove!| |sncndn| |initTable!| |ground| |set| + |addmod| |sorted?| |singRicDE| |readInt8!| |curve| |in?| + |lieAdmissible?| |region| |minrank| |leadingMonomial| |e04naf| + |UnVectorise| |factorPolynomial| |lfextendedint| |clipSurface| + |selectFiniteRoutines| |removeConstantTerm| |s15adf| |repeating?| + |leadingCoefficient| |parameters| |c06gcf| |sparsityIF| |listOfLists| + |getMultiplicationMatrix| |subset?| |size| |enterInCache| |bitLength| + |acotIfCan| |derivative| |primitiveMonomials| |f01brf| |minPoly| + |clearTable!| |simplifyPower| |diagonal?| |ratPoly| |fracPart| + |getConstant| |lazy?| |print| |reductum| |before?| |mainContent| + |substring?| |printInfo!| |primitive?| |factorSquareFreePolynomial| + |listRepresentation| |setAdaptive| |oblateSpheroidal| + |fillPascalTriangle| |resolve| |nextColeman| |e02ajf| |GospersMethod| + |returnType!| |leadingCoefficientRicDE| LODO2FUN |doubleComplex?| + |determinant| |ramifiedAtInfinity?| |logpart| |powerSum| |readBytes!| + |sylvesterMatrix| |characteristicPolynomial| |unexpand| |suffix?| + |true| |pmintegrate| |ParCond| |category| |moduloP| |littleEndian| + |exists?| |surface| |cSec| |semiResultantEuclidean1| |domain| + |tValues| |functorData| |quasiComponent| |companionBlocks| |mainForm| + |optional| |semiResultantEuclideannaif| |is?| |cAtanh| |OMgetEndAttr| + |e02def| |external?| |iFTable| |isTimes| |prefix?| |d01bbf| |f01mcf| + |package| |eigenvector| |any?| |leftOne| |s19abf| + |rightRegularRepresentation| |insert| |computePowers| + |increasePrecision| |completeEchelonBasis| |divisorCascade| + |resultantnaif| |OMgetVariable| |clipWithRanges| |cosh2sech| + |removeCoshSq| |just| |show| |dmpToP| |lazyEvaluate| |s15aef| |polar| + |iiasec| |hostPlatform| |irDef| |writeInt8!| |tan2cot| |search| |frst| + |redmat| |c06eaf| |cyclic?| |topFortranOutputStack| |llprop| |zoom| + |node| |initializeGroupForWordProblem| |numberOfCycles| |rischDE| + |checkRur| |trace| |mpsode| |LyndonWordsList| |lyndonIfCan| |hdmpToP| + |definingInequation| |returns| |OMputBind| |iiatanh| |subPolSet?| + |leftDiscriminant| |LiePolyIfCan| |extendedint| |diff| |Lazard2| + |birth| |minPoints3D| |resetVariableOrder| |comparison| |e02ddf| + |coth2trigh| |reduceBasisAtInfinity| |mapMatrixIfCan| |infix?| + |setvalue!| |getMultiplicationTable| |wordInStrongGenerators| + |explicitlyEmpty?| |doubleRank| |drawComplex| |null?| |OMputError| + |critMTonD1| |mask| |limitedint| |rspace| |c06frf| |selectPDERoutines| + |sequences| |exportedOperators| |distdfact| |addMatchRestricted| + |leftQuotient| |flatten| |hasoln| |swapRows!| |conditionP| + |setIntersection| |internalZeroSetSplit| |innerSolve| |element?| + |setAdaptive3D| |generalInfiniteProduct| |acschIfCan| + |interpretString| |elliptic?| |OMgetAttr| |showAllElements| + |generalSqFr| |bounds| |sumSquares| |basisOfLeftAnnihilator| + |continuedFraction| |e02daf| |isQuotient| |nary?| |s13adf| |cycles| + |makeFloatFunction| |selectsecond| |se2rfi| |algDsolve| |decrease| + |nextSubsetGray| |f04adf| |generalTwoFactor| |goodPoint| + |numberOfComponents| |lfinfieldint| |viewThetaDefault| |palgRDE0| + |internalAugment| |reflect| |addMatch| |isExpt| |alphabetic| + |dihedral| |medialSet| |critMonD1| |besselI| |calcRanges| + |lflimitedint| |qfactor| |figureUnits| |enumerate| + |numericalIntegration| |principalIdeal| |tRange| |commutative?| + |geometric| |directory| |componentUpperBound| |sub| |createNormalPoly| + |chiSquare| |bytes| |dictionary| |complexLimit| |deriv| |badValues| + |conjugate| |internal?| |taylorQuoByVar| |getIdentifier| |UP2ifCan| + |s17acf| |nodes| |height| |units| |log10| |fullPartialFraction| + |findBinding| |selectAndPolynomials| |normalForm| |palgRDE| + |parametersOf| |selectOrPolynomials| |equation| |hspace| + |bipolarCylindrical| |normalDenom| |shallowExpand| |kmax| |bitand| + |atanhIfCan| |setref| |f02agf| |s17dhf| |iCompose| |wholePart| + |infieldint| |commaSeparate| |semiDegreeSubResultantEuclidean| + |leaves| |palgLODE| |outerProduct| |elem?| |bitior| |ddFact| + |ridHack1| |particularSolution| |linear| |messagePrint| + |setProperties| |c05adf| |exponential1| |rangeIsFinite| |shiftRight| + |find| |maximumExponent| |makeSin| |kovacic| |algebraicVariables| + |stiffnessAndStabilityOfODEIF| |cRationalPower| |stronglyReduced?| + |stirling1| |macroExpand| |denominators| |internalIntegrate0| + |fortranDoubleComplex| |interReduce| |solveInField| |polynomial| + |composites| |laguerreL| |leftAlternative?| |startStats!| |Lazard| + |comment| |closeComponent| |rischNormalize| |groebnerFactorize| + |reduction| |minimumExponent| |zeroSetSplitIntoTriangularSystems| + |center| |exponents| |size?| |parent| |idealSimplify| |patternMatch| + |irVar| |octon| |changeVar| |padicFraction| |setchildren!| |f02bbf| + |edf2ef| |c06ekf| |setTex!| |dualSignature| |graphState| + |euclideanSize| |f04qaf| |imagJ| |rule| |doublyTransitive?| |declare| + |asimpson| |iicsch| |key?| |sizeLess?| |makeVariable| |callForm?| + |att2Result| |antiCommutator| |common| |normal01| |cCsch| + |zeroDimPrime?| |reseed| |point?| |drawToScale| |space| + |measure2Result| |length| |viewSizeDefault| |green| |check| + |totalfract| |lifting1| |associatorDependence| |algebraicOf| + |asinIfCan| |cyclotomicFactorization| |lexGroebner| |scripts| + |leftDivide| |d01fcf| |weierstrass| |coth2tanh| |sort!| + |stopTableInvSet!| |reorder| |setPoly| |principal?| |discriminant| + |twist| |lazyVariations| |iidprod| |mainMonomial| |lookup| + |createNormalPrimitivePoly| |submod| |tableau| |purelyAlgebraic?| + |matrix| |monomRDEsys| |normalise| |lazyIntegrate| |characteristicSet| + |baseRDEsys| |norm| |bigEndian| |rangePascalTriangle| |variable?| + |integer?| |isAbsolutelyIrreducible?| |applyRules| |s21bcf| + |selectSumOfSquaresRoutines| |subQuasiComponent?| UTS2UP |scripted?| + |s14aaf| |generalizedEigenvectors| |e02dff| |f04asf| + |exprHasAlgebraicWeight| |weighted| |pop!| |splitLinear| |tanNa| + |stoseLastSubResultant| Y |cyclicParents| |edf2efi| |poisson| + |normFactors| |goto| |readByte!| |unmakeSUP| |label| |implies| |imagI| + |central?| |algintegrate| |putColorInfo| |generalPosition| |d01gbf| + |selectIntegrationRoutines| |SturmHabichtMultiple| |polyPart| + |mainVariable| |subspace| |cycle| |algSplitSimple| |basicSet| + |viewZoomDefault| |digit| |bipolar| |startPolynomial| |quasiRegular?| + |irForm| |extractTop!| |getZechTable| |setStatus| |univcase| |invmod| + |quasiMonicPolynomials| |result| |bezoutMatrix| |rectangularMatrix| + |expenseOfEvaluation| |positiveRemainder| |knownInfBasis| |recolor| + |idealiserMatrix| |associates?| |rightScalarTimes!| |alphanumeric| + |palgextint0| |bubbleSort!| |minimalPolynomial| |expt| |unitCanonical| + |laplace| |cyclicSubmodule| |BumInSepFFE| |numeric| |inverse| + |symbol?| |setOrder| |s17adf| |rename| |getlo| + |generalizedContinuumHypothesisAssumed?| |coerceP| |symFunc| + |fortranInteger| |radical| |cycleTail| |odd?| |integers| |concat!| + |constructor| |zag| |writeBytes!| |subscript| |copyInto!| + |conjunction| |nthCoef| |primextendedint| |partialDenominators| + |newReduc| |myDegree| |constantOperator| |bindings| |option| |coord| + |mappingMode| |froot| |symbolTable| |showSummary| |e04ucf| |zCoord| + |mainDefiningPolynomial| |fortranCompilerName| |difference| + |setLength!| |xCoord| |antisymmetricTensors| |transpose| |rightUnits| + |shallowCopy| |stFunc2| |computeCycleEntry| |meshPar1Var| |pushup| + |branchIfCan| |e01saf| |exprHasWeightCosWXorSinWX| + |pushFortranOutputStack| |primaryDecomp| |showAttributes| |commutator| + |coercePreimagesImages| |makeMulti| |makeop| |iflist2Result| + |makeRecord| |scale| |cfirst| |popFortranOutputStack| |trapezoidalo| + |qinterval| |baseRDE| |addiag| |overlap| + |removeRoughlyRedundantFactorsInPol| |screenResolution| |localReal?| + |outputAsFortran| |alternatingGroup| |diagonals| |rightDiscriminant| + |leadingSupport| |OMgetEndObject| |name| |parents| |nonLinearPart| + |compiledFunction| |explimitedint| |selectPolynomials| + |radicalOfLeftTraceForm| |f02fjf| |variationOfParameters| |rightTrim| + |semiResultantReduitEuclidean| |fractionPart| |body| |inR?| + |mainPrimitivePart| |approxSqrt| |linSolve| |homogeneous?| + |attributeData| |putProperty| |leftTrim| |call| |setMinPoints3D| + |null| |pushuconst| |iidsum| |flexible?| |evaluate| |binomThmExpt| + |stack| |makeEq| |extractSplittingLeaf| |differentialVariables| + |isEquiv| |rowEch| |not| |drawComplexVectorField| |badNum| |mvar| + |rk4| BY |Ci| |viewDeltaXDefault| |rotatey| |bombieriNorm| |s14abf| + |and| |dAndcExp| |OMputEndAttr| |complexElementary| |zeroMatrix| + |outputList| |intChoose| |infix| |insertTop!| |retractable?| |or| + |henselFact| |innerint| |elseBranch| |red| |branchPointAtInfinity?| + |gderiv| |ef2edf| |subSet| |bezoutDiscriminant| |xor| |safeCeiling| + |cartesian| |removeDuplicates!| |stopTableGcd!| |modifyPoint| + |cyclotomicDecomposition| |LagrangeInterpolation| |withPredicates| + |ReduceOrder| |signature| |dim| |case| |quadratic| |leftPower| + |leftFactorIfCan| |pseudoQuotient| |assert| |multMonom| |epilogue| + |readInt32!| |port| |qualifier| |e02bcf| |extractPoint| |pattern| + |Zero| |exactQuotient!| |yCoord| |OMReadError?| |fixedPointExquo| + |weight| |iExquo| |linearAssociatedOrder| |scan| |pascalTriangle| + |overset?| |One| |gradient| |setLabelValue| |lighting| + |nextPrimitivePoly| |members| |checkForZero| |complement| |t| + |subNode?| |fill!| |tan2trig| |shift| |setEmpty!| NOT + |resetAttributeButtons| |hasTopPredicate?| |traceMatrix| |innerSolve1| + |shellSort| |output| |sequence| |ideal| |thetaCoord| + |leftMinimalPolynomial| |divideExponents| |e02ahf| |mapDown!| OR + |simplify| |vector| |equality| |clearTheFTable| |leader| |indices| + |binaryFunction| |startTableInvSet!| |normalElement| |elRow2!| |cTanh| + |message| AND |setPredicates| |differentiate| |partialQuotients| + |htrigs| |discriminantEuclidean| |subTriSet?| |normDeriv2| |seed| + |subtractIfCan| |whitePoint| |totolex| |leviCivitaSymbol| |rightZero| + |getCode| |complex?| |packageCall| |fortran| |atanh| |e04fdf| |nthr| + |shufflein| |oddInfiniteProduct| |exponential| |stronglyReduce| |elt| + |shuffle| |raisePolynomial| |processTemplate| |removeDuplicates| + |curry| |acoth| |readUInt8!| |lllp| |minGbasis| |component| |sin?| + |groebgen| |squareTop| |elRow1!| |ptFunc| |graeffe| |reduced?| |asech| + |level| |conjugates| |definingEquations| |physicalLength!| |s17dlf| + |newLine| |partition| |orbits| |dn| |LiePoly| |property| |univariate?| + |dmpToHdmp| |csch2sinh| |brillhartIrreducible?| |getStream| + |lowerPolynomial| |optional?| |ldf2lst| |basisOfRightAnnihilator| + |factorFraction| |quote| |sinIfCan| |multiple| |cons| |bringDown| + |routines| |ffactor| |contours| |linearDependence| |probablyZeroDim?| + |palgextint| |palglimint0| |trigs2explogs| |OMgetAtp| + |removeRedundantFactors| |applyQuote| |basisOfCentroid| |chvar| + |palglimint| |cond| |fortranCharacter| |Is| |maxRowIndex| |retract| + |initiallyReduce| |abelianGroup| |certainlySubVariety?| |romberg| + |selectfirst| |adjoint| |empty?| |mkPrim| |setUnion| |divergence| + |colorDef| |untab| |compBound| |reduceByQuasiMonic| + |numberOfOperations| |multisect| |unit| |wronskianMatrix| |expint| + |roughSubIdeal?| |setStatus!| |acothIfCan| |second| |infiniteProduct| + * |constantIfCan| |meshFun2Var| |euler| |leftRegularRepresentation| + |totalGroebner| |ruleset| |setErrorBound| |normalDeriv| + |tryFunctionalDecomposition| |univariatePolynomialsGcds| |fortranReal| + |genericLeftTraceForm| |third| |outputBinaryFile| |totalLex| |dmp2rfi| + |subResultantGcd| |OMputFloat| |ListOfTerms| |testDim| |OMUnknownCD?| + |zeroDimensional?| |collectUpper| |showFortranOutputStack| |divisors| + |univariatePolynomial| |btwFact| |expandLog| |pile| + |mainSquareFreePart| |source| |void| |iisec| |hermite| |isMult| + |subResultantGcdEuclidean| |moebius| |internalLastSubResultant| = + |eyeDistance| |s17dcf| |hconcat| |useNagFunctions| |laguerre| + |suchThat| |edf2df| |imagj| |rotatex| |rroot| |reciprocalPolynomial| + |divide| |integralBasisAtInfinity| |createLowComplexityNormalBasis| + |OMgetEndApp| |compactFraction| |curryRight| |script| |elliptic| + RF2UTS |iiacosh| |diagonalProduct| |getExplanations| + |rewriteSetWithReduction| < |plotPolar| |upperBound| |algebraic?| + |writeUInt8!| |leaf?| |plusInfinity| |d02gaf| |cyclePartition| + |completeEval| |exprex| |sincos| |graphCurves| |char| > |viewDefaults| + |sumOfDivisors| |resetBadValues| |crushedSet| |argscript| + |systemCommand| |minusInfinity| |halfExtendedResultant1| + |squareFreePolynomial| |linear?| |hitherPlane| |fortranLiteral| + |even?| |numberOfIrreduciblePoly| |polygamma| <= |nlde| + |tensorProduct| |quartic| |tex| |target| |biRank| |repeatUntilLoop| + |patternVariable| |minimumDegree| |deleteProperty!| + |purelyAlgebraicLeadingMonomial?| |singularitiesOf| >= |discreteLog| + |userOrdered?| |elaborate| |expintfldpoly| |degreePartition| |cAsech| + |legendre| |euclideanGroebner| |coHeight| |isOp| |showTheSymbolTable| + |expr| |factorSquareFreeByRecursion| |duplicates?| |mergeDifference| + |irreducibleFactor| |goodnessOfFit| |gcdcofactprim| |lyndon?| + |finite?| |monicDecomposeIfCan| |f02aef| |normal| |quotient| + |reverseLex| |expintegrate| |charClass| |readLineIfCan!| + |prolateSpheroidal| |sqfrFactor| |infinite?| UP2UTS |OMputSymbol| + |semiSubResultantGcdEuclidean2| |integralRepresents| |tanintegrate| + |FormatArabic| + |OMgetBVar| |toseLastSubResultant| |light| + |sylvesterSequence| |type| |createIrreduciblePoly| + |stoseIntegralLastSubResultant| |scalarTypeOf| |boundOfCauchy| + |dequeue| |nodeOf?| |iiacsch| |point| - |float| |whileLoop| + |Frobenius| |iicsc| |polyRicDE| |eigenMatrix| |radicalRoots| + |modularFactor| |harmonic| |qroot| |variable| |problemPoints| / + |charpol| |adaptive3D?| |invertibleElseSplit?| |cos2sec| |lllip| + |dimensions| |bivariate?| |toseInvertible?| |asinhIfCan| |iterators| + |randomR| |completeHensel| |palgintegrate| |rightAlternative?| |mesh| + |f2df| |noncommutativeJordanAlgebra?| |SturmHabicht| |mapExpon| + |newSubProgram| |cubic| |symmetricGroup| |series| + |fortranCarriageReturn| |isOpen?| |c06fuf| |column| |setCondition!| + |preprocess| |nilFactor| |signAround| |rootOfIrreduciblePoly| + |quotedOperators| |setFormula!| |contains?| |sturmSequence| + |chainSubResultants| |deleteRoutine!| |shiftLeft| |basisOfLeftNucleus| + |e02akf| |id| |setlast!| |subNodeOf?| |high| |createRandomElement| + |powern| |value| |numberOfChildren| |makeGraphImage| |symbol| + |lambert| |radicalEigenvalues| |integralLastSubResultant| + |binarySearchTree| |lo| |e01daf| |setAttributeButtonStep| + |RittWuCompare| |changeName| |minordet| |basisOfCommutingElements| + |iibinom| |OMgetObject| |linearAssociatedLog| |expression| + |irreducibleRepresentation| |min| |numberOfImproperPartitions| + |functionIsContinuousAtEndPoints| |splitNodeOf!| |f01maf| + |maxColIndex| |cylindrical| |optpair| |lprop| |integer| |acscIfCan| + |radPoly| |normalizedAssociate| |module| GE |trace2PowMod| |OMreadStr| + |cup| |scanOneDimSubspaces| |associative?| |localAbs| + |separateDegrees| |normal?| |iisin| |OMopenString| |leftExtendedGcd| + GT |innerEigenvectors| |makeResult| |semicolonSeparate| + |lastSubResultantEuclidean| |extendedIntegrate| + |firstUncouplingMatrix| |OMwrite| |pade| |zeroSquareMatrix| + |leftTraceMatrix| LE |systemSizeIF| |isPlus| |parabolic| + |monomialIntegrate| |alphanumeric?| |d02raf| |rightNorm| |extend| + |omError| |deepestInitial| LT |appendPoint| |defineProperty| + |OMmakeConn| |quasiRegular| |unknownEndian| |nextNormalPoly| + |FormatRoman| |digamma| |useSingleFactorBound| |tubeRadiusDefault| + |removeIrreducibleRedundantFactors| |pseudoRemainder| + |localIntegralBasis| |besselK| |list?| |f02ajf| |OMgetEndError| + |leastPower| |integral| |mapmult| |basisOfRightNucleus| |setImagSteps| + |leadingIdeal| |padicallyExpand| |iomode| |makeUnit| |ord| |credPol| + |f01rcf| |factorAndSplit| |keys| |OMputVariable| |stopTable!| |s17aef| + |rubiksGroup| |represents| |firstSubsetGray| |findConstructor| + |symmetricTensors| |d03faf| |writeByte!| |OMputBVar| |one?| |revert| + |bernoulliB| |rombergo| |morphism| |mainValue| |isAtom| |currentScope| + |index| |nextPartition| |showTheRoutinesTable| |lexico| + |OMencodingUnknown| |df2st| |digits| |charthRoot| |realZeros| + |exactQuotient| |superscript| |rewriteIdealWithHeadRemainder| |airyBi| + |alternative?| |OMParseError?| |perfectNthPower?| |psolve| + |leadingBasisTerm| |direction| |distFact| |quoByVar| |leadingIndex| + |stoseInvertibleSet| |zeroDim?| |radicalEigenvector| |isConnected?| + |OMputAttr| |mapGen| |triangulate| |pair| |twoFactor| |upperCase| + |tree| |open| |e04gcf| |redpps| |gcdPrimitive| |extendIfCan| + |leftNorm| |f02abf| |bright| |generalizedContinuumHypothesisAssumed| + |coerceS| |s18def| |extract!| |genericRightDiscriminant| |loopPoints| + |primextintfrac| |components| |consnewpol| |resultantReduitEuclidean| + |cap| |leftRankPolynomial| |hasPredicate?| |integralBasis| |unary?| + |setFieldInfo| |primPartElseUnitCanonical| |perspective| |aromberg| + |eval| |possiblyNewVariety?| |bumprow| |getPickedPoints| |cCosh| + |antiCommutative?| |rightMult| |roughUnitIdeal?| |rootRadius| + |OMputEndBVar| |relerror| |changeWeightLevel| |normalizeIfCan| + |operations| |d01gaf| |associator| |roman| |rootPoly| |refine| + |exprHasLogarithmicWeights| |lifting| |iterationVar| |addPoint2| + |sample| |jordanAdmissible?| |quadraticNorm| |order| |interpret| + |strongGenerators| |diagonal| |error| |leftMult| |bivariateSLPEBR| + |d02bbf| |intensity| |pquo| |roughBasicSet| |var2Steps| + |extendedResultant| |splitConstant| |OMcloseConn| |countable?| |df2fi| + |mkcomm| |copy!| |cAcsc| |prod| |plot| |quasiAlgebraicSet| |optimize| + |approximants| |prologue| |removeRedundantFactorsInContents| + |bumptab1| |precision| |children| |function| |OMputEndObject| + |numericalOptimization| |ParCondList| |range| |ScanArabic| |redPol| + |pmComplexintegrate| |LowTriBddDenomInv| |sec2cos| |moreAlgebraic?| + |firstDenom| |leftZero| |removeSinhSq| |f02aff| |showAll?| + |rationalIfCan| |pointColorDefault| |d01apf| |OMbindTCP| |width| + |resize| |hdmpToDmp| |semiSubResultantGcdEuclidean1| |normalized?| + |e02adf| |semiLastSubResultantEuclidean| |evenInfiniteProduct| |rules| + |numberOfVariables| |double| |nil?| |repeating| |df2ef| |number?| + |build| |perfectSqrt| |unparse| |rowEchelon| |sortConstraints| + |createPrimitiveNormalPoly| |commutativeEquality| |solveid| + |integralCoordinates| |complexExpand| |shanksDiscLogAlgorithm| + |insertionSort!| |virtualDegree| |prem| |alphabetic?| |delete!| + |constantRight| |s20adf| |nullSpace| |ode2| |setButtonValue| |f04jgf| + |nextItem| |rationalFunction| |clipBoolean| |mainCoefficients| + |symmetric?| |solveLinearPolynomialEquationByRecursion| + |axesColorDefault| |extractBottom!| |maxPoints| |checkPrecision| |mr| + |critpOrder| |cSin| |stiffnessAndStabilityFactor| + |stoseInvertible?sqfreg| |seriesSolve| |bandedJacobian| + |sturmVariationsOf| |youngDiagram| |pomopo!| |floor| |rightRecip| + |over| |dimensionOfIrreducibleRepresentation| |squareFreePart| + |iicosh| |degreeSubResultantEuclidean| |tubePoints| |setMaxPoints3D| + |pureLex| |rational?| |subst| |rem| |representationType| |OMputString| + |cSinh| |d02bhf| |tracePowMod| |explicitEntries?| |middle| + |generalLambert| |wholeRagits| |monomRDE| |primeFactor| |quo| + |integrate| |OMclose| |decompose| |mainExpression| |declare!| + |varList| |backOldPos| |factorByRecursion| |axes| |OMgetBind| |recip| + |fixedPoints| |collectQuasiMonic| |basis| |initiallyReduced?| + |member?| |lcm| |OMputObject| |modulus| |maxdeg| |linearMatrix| + |permutationRepresentation| |delete| |div| |cyclicGroup| |debug3D| + |e01sbf| |wholeRadix| |cardinality| |freeOf?| |inRadical?| |imagK| + |toroidal| |indicialEquationAtInfinity| |exquo| |oneDimensionalArray| + |scalarMatrix| |stoseInternalLastSubResultant| |hostByteOrder| + |regime| |any| |forLoop| |cTan| |append| |laurentIfCan| |setprevious!| + |matrixGcd| ~= |roughBase?| |aQuadratic| |dioSolve| |whatInfinity| + |colorFunction| |primitivePart!| |mapUp!| |insertBottom!| |flagFactor| + |gcd| |vark| |wordsForStrongGenerators| |objects| |#| |rootSplit| + |s21bdf| |jacobiIdentity?| |lazyPseudoQuotient| |plenaryPower| + |KrullNumber| |eq?| |moduleSum| |expPot| |false| |gethi| + |normInvertible?| |base| ~ |lowerCase?| |rotate| |e02baf| + |superHeight| |elaboration| |OMputEndApp| |cCsc| |radicalEigenvectors| + |rationalPoint?| |cyclicCopy| |ravel| |randnum| |printingInfo?| + |factorOfDegree| |parametric?| |OMread| |segment| |part?| |cCot| + |minRowIndex| |nthFactor| |elements| |init| |vspace| |solveRetract| + |every?| |expIfCan| |reshape| |minset| |frobenius| + |basisOfMiddleNucleus| |prepareSubResAlgo| |asechIfCan| + |factorSquareFree| |/\\| |factorGroebnerBasis| |sechIfCan| + |possiblyInfinite?| |monicRightFactorIfCan| |rquo| |less?| |imagi| + |setfirst!| |imports| |tanh2coth| |\\/| |computeCycleLength| + |secIfCan| |recur| |const| |regularRepresentation| |apply| |coerce| + |polarCoordinates| |dfRange| |isPower| |monicLeftDivide| |cycleEntry| + |euclideanNormalForm| |s21bbf| |specialTrigs| |viewpoint| + |fullDisplay| |first| |construct| |OMencodingBinary| |binary| + |directSum| |solid| |stoseInvertibleSetreg| |infinityNorm| |root?| + |genericLeftMinimalPolynomial| |transcendentalDecompose| |totalDegree| + |rest| |postfix| |e02zaf| |headReduced?| |leftUnits| |zeroSetSplit| + |nonSingularModel| |remainder| |degree| |plus| |OMserve| |acosIfCan| + |update| |terms| |nextPrimitiveNormalPoly| |chebyshevU| + |numberOfDivisors| |rarrow| |option?| |bat1| |c06ecf| |e01sef| + |besselJ| |partialFraction| |curveColor| |categoryMode| |pToDmp| + |hasHi| |setnext!| |tryFunctionalDecomposition?| |e02bdf| + |characteristicSerie| |has?| |realEigenvectors| |leftReducedSystem| + |s17ajf| |var1Steps| |unitsColorDefault| |cAcosh| |trapezoidal| + |reify| |failed?| |modifyPointData| |times| |exprToUPS| |push| + |removeSinSq| |realElementary| |unaryFunction| |previous| |delta| + |leftTrace| |lowerBound| |d03edf| |supDimElseRittWu?| |integerIfCan| + |typeForm| |removeRoughlyRedundantFactorsInContents| + |exponentialOrder| |inGroundField?| |toScale| |cdr| + |rightExactQuotient| |setEpilogue!| |associatedEquations| + |constantOpIfCan| |s17aff| |position| |palginfieldint| |bfEntry| + |argumentListOf| |setProperty| |equiv| |atoms| |removeSquaresIfCan| + |elementary| |zerosOf| |prepareDecompose| |datalist| |lift| |rk4qc| + |conjug| |minPol| |relativeApprox| |complexRoots| |listexp| + |inputOutputBinaryFile| |real?| |box| |testModulus| |cotIfCan| + |OMputEndAtp| |monom| |reduce| |rightRank| |identityMatrix| |s17dgf| + |outputForm| |OMconnectTCP| |polygon| |skewSFunction| |findCycle| + |ScanFloatIgnoreSpacesIfCan| |node?| |stosePrepareSubResAlgo| + |loadNativeModule| |collect| |printTypes| + |setLegalFortranSourceExtensions| |power| |setleaves!| |accuracyIF| + |airyAi| |numerators| |clipPointsDefault| |numberOfPrimitivePoly| + |denominator| |RemainderList| |countRealRootsMultiple| |extractIfCan| + |rightTraceMatrix| |predicates| |getMatch| |removeSuperfluousCases| + |paren| |unitNormal| |removeZeroes| |indiceSubResultantEuclidean| + |setOfMinN| |extendedEuclidean| |simplifyExp| |c06fpf| |chebyshevT| + |complementaryBasis| |coerceL| |lambda| |e04ycf| |prefixRagits| + |genericLeftDiscriminant| |csubst| |e01bef| |rank| |identification| + |nullary?| |separateFactors| |OMputInteger| |orbit| |c06gbf| + |subresultantSequence| |create3Space| |monicCompleteDecompose| + |OMconnInDevice| |log| |mightHaveRoots| |createNormalElement| + |gcdcofact| |setScreenResolution3D| |lazyPrem| |factorSFBRlcUnit| + |child| |mat| |genericLeftNorm| |setPosition| |setelt| |linGenPos| + |notelem| |lexTriangular| |lSpaceBasis| |cscIfCan| |contractSolve| + |returnTypeOf| |partitions| |headReduce| |numFunEvals3D| |isImplies| + |showIntensityFunctions| |cAcos| |algebraicDecompose| |iiasech| + |stoseInvertibleSetsqfreg| |inspect| |monomials| |df2mf| + |indiceSubResultant| |OMgetError| |linearAssociatedExp| |setRealSteps| + |nthFractionalTerm| |double?| |SturmHabichtCoefficients| |plus!| + |cot2tan| |iiGamma| |makeSUP| |back| |eulerE| |anticoord| + |removeCosSq| |iicoth| |points| |factorial| |parabolicCylindrical| + |generalizedEigenvector| |unvectorise| |showTheFTable| |getProperties| + |var2StepsDefault| |randomLC| |HermiteIntegrate| |lfextlimint| + |palgLODE0| |conical| |solveLinear| |stopMusserTrials| |multiple?| + |solveLinearPolynomialEquation| |byte| |lists| |paraboloidal| |iiacos| + |fi2df| |critB| |primitiveElement| |karatsubaDivide| |c06fqf| + |OMUnknownSymbol?| |conditionsForIdempotents| + |unprotectedRemoveRedundantFactors| |getOrder| |opeval| |cAcoth| |row| + |iiabs| |swapColumns!| |erf| |setright!| |ignore?| |setVariableOrder| + |constantLeft| |zero| |lintgcd| |An| |reverse| |startTable!| |dflist| + |readUInt16!| |cAsin| |empty| |LazardQuotient2| |readLine!| |schema| + |lineColorDefault| |perfectSquare?| |getRef| |noLinearFactor?| + |singular?| |critBonD| |algebraicSort| |genericRightMinimalPolynomial| + |li| |rootPower| |universe| |multiset| |doubleFloatFormat| |And| + |f02xef| |unknown| |squareFreeLexTriangular| |f04mcf| |s19acf| + |cosIfCan| |dilog| |setColumn!| |removeRedundantFactorsInPols| |mesh?| + |OMgetEndBVar| |Or| |quoted?| |hermiteH| |rootDirectory| |cycleElt| + |f02akf| |iiasin| |mindeg| |sin| |extension| |choosemon| |addPoint| + |viewport3D| |Not| |primlimintfrac| |critT| |Nul| |move| |e02aef| + |ricDsolve| |cos| |iipow| |stripCommentsAndBlanks| |complexZeros| + |extractClosed| |symmetricRemainder| |genericLeftTrace| |int| + |linkToFortran| |positiveSolve| |singleFactorBound| |f02axf| |tan| + |modularGcdPrimitive| |lfintegrate| |coshIfCan| |bit?| |summation| + |maxint| |rightRemainder| |viewPosDefault| |cot| |mathieu22| |primes| + |linearPolynomials| |nextSublist| |dequeue!| |rightExtendedGcd| + |replace| |prinb| |listBranches| |sec| |tubePlot| + |useEisensteinCriterion| |mathieu11| |assign| |blue| |pdf2df| + |externalList| |lazyIrreducibleFactors| |inverseColeman| |csc| + |cycleSplit!| |primintegrate| |trigs| |coleman| |basisOfNucleus| + |HenselLift| |readInt16!| |asin| |bezoutResultant| |test| |read!| + |addBadValue| |Aleph| |operation| |mapUnivariate| |remove| |pack!| + |removeZero| |fortranLinkerArgs| |inconsistent?| |acos| |errorKind| + |atom?| |argumentList!| |getBadValues| |unrankImproperPartitions0| + |c02aff| |distance| |setMaxPoints| |cycleRagits| |atan| + |absolutelyIrreducible?| |sn| |d01anf| |expandTrigProducts| |parts| + |pseudoDivide| |last| |makeViewport2D| |makeCos| |changeBase| + |nthExponent| |OMgetEndBind| |acot| |leftRecip| |open?| |assoc| + |s17agf| |semiDiscriminantEuclidean| |create| |fTable| |queue| |asec| + |primintfldpoly| |supRittWu?| |mappingAst| |condition| |tower| + |fractRagits| |balancedFactorisation| |doubleDisc| |prevPrime| + |fixedPoint| |aQuartic| |acsc| |constantToUnaryFunction| + |createMultiplicationMatrix| |explicitlyFinite?| |coefficient| + |symmetricSquare| |d01asf| |structuralConstants| |prefix| |sin2csc| + |resultant| |sinh| |square?| |basisOfCenter| |rightUnit| |powmod| + |mathieu12| |subCase?| |evenlambert| |cosh| |computeBasis| + |outputMeasure| |rightTrace| |d02ejf| |index?| |decimal| + |recoverAfterFail| |standardBasisOfCyclicSubmodule| |allRootsOf| |obj| + |tanh| |s13aaf| |eq| |maxIndex| |oddintegers| |f04arf| |generic?| + |solveLinearPolynomialEquationByFractions| |c05nbf| |rightLcm| + |getSyntaxFormsFromFile| |cache| |coth| |iter| |pointData| |polCase| + |showArrayValues| |ramified?| |complexNumeric| |uncouplingMatrices| + |halfExtendedSubResultantGcd2| |getOperator| |prime| + |lazyPremWithDefault| |truncate| |sech| |f04atf| |iiatan| + |stoseInvertible?| |incrementKthElement| |multiEuclideanTree| + |tubePointsDefault| |f02adf| |s18acf| |derivationCoordinates| |d03eef| + |csch| |polyRDE| |belong?| |limitPlus| |split| |getGraph| |solve1| + |printHeader| |totalDifferential| |semiResultantEuclidean2| |asinh| + |putGraph| |numberOfComputedEntries| |pow| |top!| |split!| |heapSort| + |rootOf| |algint| |s18aff| |collectUnder| |oddlambert| |acosh| + |overlabel| |mix| |startTableGcd!| |pdf2ef| |meshPar2Var| + |interactiveEnv| |elaborateFile| |leastMonomial| |mapUnivariateIfCan| + |s18aef| |hasSolution?| |environment| |smith| |idealiser| + |rewriteIdealWithQuasiMonicGenerators| |finiteBound| |negative?| + |subMatrix| |polygon?| |fixPredicate| |exp| |gcdprim| |color| + |ratpart| |outlineRender| |mkIntegral| |lookupFunction| |argument| + |d01alf| |LyndonBasis| |printCode| |leftUnit| |droot| |map| + |invertIfCan| |rotatez| |radix| |integralMatrixAtInfinity| + |intcompBasis| |numericIfCan| |supersub| |permanent| + |screenResolution3D| |powers| |table| |generator| |graphs| + |genericRightTrace| |position!| |s19adf| |OMsupportsCD?| |nil| + |outputSpacing| |youngGroup| |closedCurve?| |complexForm| + |changeThreshhold| |new| |viewDeltaYDefault| |f02bjf| |extractIndex| + |rCoord| |buildSyntax| |solid?| |dimensionsOf| |compile| |setClosed| + |setMinPoints| |s18adf| |basisOfRightNucloid| |closed| + |multiplyExponents| |graphStates| |halfExtendedSubResultantGcd1| + |zeroVector| |beauzamyBound| |log2| |usingTable?| |simpson| + |addPointLast| |realRoots| |univariateSolve| |approximate| |spherical| + |padecf| |stop| |prime?| |cPower| |convert| |signatureAst| + |LyndonWordsList1| |acoshIfCan| |round| |setPrologue!| |complex| + |vconcat| |parseString| |f02awf| |car| + |removeRoughlyRedundantFactorsInPols| |trueEqual| |phiCoord| |f02aaf| + |tab| |createLowComplexityTable| |irreducible?| |jacobi| + |selectNonFiniteRoutines| |monomialIntPoly| |setClipValue| + |decreasePrecision| |mapdiv| |mirror| |failed| |redPo| |nullity| + |SturmHabichtSequence| |printStats!| |rationalPower| |permutation| + |lazyPquo| |iiacoth| |createMultiplicationTable| |generateIrredPoly| + |byteBuffer| |aspFilename| |rootBound| |exponent| |flexibleArray| + |increment| |noValueMode| |rowEchLocal| |resultantEuclideannaif| + |degreeSubResultant| |primPartElseUnitCanonical!| |heap| |incr| + |currentCategoryFrame| |operators| |upperCase!| |insertRoot!| + |OMlistSymbols| |monic?| |block| |dihedralGroup| |Gamma| |hi| + |linearDependenceOverZ| |graphImage| |push!| |rationalPoints| + |monicRightDivide| |varselect| |shrinkable| |showClipRegion| |e02bef| + |left| |symbolIfCan| |curryLeft| |internalDecompose| + |numberOfNormalPoly| |invertible?| |indicialEquations| + |printStatement| |f01rdf| |interpolate| |right| |OMgetFloat| |bracket| + |more?| |front| |viewPhiDefault| |pastel| F2FG |overbar| |setelt!| + |pointColorPalette| |cCos| |sh| |getButtonValue| |pushdterm| + |associatedSystem| |mapBivariate| |support| |showRegion| + |doubleResultant| |safetyMargin| |Vectorise| |separate| |qelt| + |diagonalMatrix| |logGamma| |coerceListOfPairs| |dominantTerm| + |expenseOfEvaluationIF| |SFunction| |qsetelt| |splitSquarefree| + |nextLatticePermutation| |minus!| |isList| |initial| + |rationalApproximation| |LyndonCoordinates| |lowerCase!| |horizConcat| + |alternating| |stoseInvertible?reg| |createPrimitivePoly| |f04faf| + |xRange| |viewport2D| |next| |OMgetApp| |tanQ| |rightDivide| + |nextsousResultant2| |key| |readable?| |polyred| |quadraticForm| + |rightQuotient| |yRange| |lazyResidueClass| |hclf| |putProperties| + |OMunhandledSymbol| |f01qcf| |explogs2trigs| |createGenericMatrix| + |viewWriteAvailable| |leftExactQuotient| |generators| |zRange| + |e02dcf| |maxrank| |completeSmith| |stoseSquareFreePart| |filename| + |map!| |PDESolve| |palgint| |setValue!| |pol| |symmetricDifference| + |midpoints| |limit| |trim| |e02gaf| |qsetelt!| + |clearFortranOutputStack| |hue| |merge| |nthRoot| |deepestTail| |ref| + |leastAffineMultiple| |numerator| |tube| |parse| |fortranComplex| + |reducedSystem| |resetNew| |leftRank| |sinh2csch| |increase| |code| + |hMonic| |mdeg| |headRemainder| |generate| |fortranLogical| |select!| + |rewriteIdealWithRemainder| |bottom!| |hcrf| |makeYoungTableau| + |readUInt32!| |connectTo| |fintegrate| |BasicMethod| + |factorsOfCyclicGroupSize| |ranges| |imaginary| |wreath| + |hyperelliptic| |quotientByP| |bsolve| |bitCoef| |incrementBy| + |getGoodPrime| |sayLength| |setsubMatrix!| |e01baf| + |constantCoefficientRicDE| |rdHack1| |f2st| |eisensteinIrreducible?| + |triangularSystems| |multinomial| |factorset| |nextIrreduciblePoly| + |dual| |child?| |acsch| |generic| |leadingTerm| |genericPosition| + |transcendenceDegree| |iitan| |c02agf| |outputFloating| |printInfo| + |highCommonTerms| |expressIdealMember| |toseSquareFreePart| + |groebnerIdeal| |complexNumericIfCan| |integral?| |insertMatch| + |identity| |eulerPhi| |integralDerivationMatrix| |duplicates| |cyclic| + |iifact| |closed?| |OMreadFile| |cot2trig| |categoryFrame| |cAsec| + |qPot| |tanSum| |e04jaf| |asecIfCan| |solveLinearlyOverQ| |options| + |gbasis| |updatF| |tablePow| |interval| |lazyPseudoRemainder| |tail| + |setScreenResolution| |dom| |leftScalarTimes!| |laplacian| + |reducedDiscriminant| |e01bhf| |leftGcd| |reducedContinuedFraction| + |internalSubQuasiComponent?| |upperCase?| |insert!| |arg1| |entry| + |OMopenFile| |PollardSmallFactor| |expandPower| |product| |binding| + |eigenvalues| |nil| |infinite| |arbitraryExponent| |approximate| + |complex| |shallowMutable| |canonical| |noetherian| |central| + |partiallyOrderedSet| |arbitraryPrecision| |canonicalsClosed| + |noZeroDivisors| |rightUnitary| |leftUnitary| |additiveValuation| + |unitsKnown| |canonicalUnitNormal| |multiplicativeValuation| + |finiteAggregate| |shallowlyMutable| |commutative|)
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T) ((-23) . T) ((-25) . T) ((-38 #0=(-419 (-576))) -3794 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-38 |#1|) . T) ((-38 $) -3794 (|has| |#1| (-568)) (|has| |#1| (-360)) (|has| |#1| (-374)) (|has| |#1| (-317))) ((-35) |has| |#1| (-1222)) ((-95) |has| |#1| (-1222)) ((-102) . T) ((-111 #0# #0#) -3794 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-111 |#1| |#1|) . T) ((-111 $ $) . T) ((-132) . T) ((-146) -3794 (|has| |#1| (-360)) (|has| |#1| (-146))) ((-148) |has| |#1| (-148)) ((-628 #0#) -3794 (|has| |#1| (-1058 (-419 (-576)))) (|has| |#1| (-360)) (|has| |#1| (-374))) ((-628 (-576)) . T) ((-628 |#1|) . T) ((-628 $) -3794 (|has| |#1| (-568)) (|has| |#1| (-360)) (|has| |#1| (-374)) (|has| |#1| (-317))) ((-625 (-875)) . T) ((-174) . T) ((-626 (-171 (-227))) |has| |#1| (-1042)) ((-626 (-171 (-390))) |has| |#1| (-1042)) ((-626 (-548)) |has| |#1| (-626 (-548))) ((-626 (-906 (-390))) |has| |#1| (-626 (-906 (-390)))) ((-626 (-906 (-576))) |has| |#1| (-626 (-906 (-576)))) ((-626 #1=(-1192 |#1|)) . 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T) ((-23) . T) ((-25) . T) ((-38 #0=(-419 (-576))) -2758 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-38 |#1|) . T) ((-38 $) -2758 (|has| |#1| (-568)) (|has| |#1| (-360)) (|has| |#1| (-374)) (|has| |#1| (-317))) ((-35) |has| |#1| (-1223)) ((-95) |has| |#1| (-1223)) ((-102) . T) ((-111 #0# #0#) -2758 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-111 |#1| |#1|) . T) ((-111 $ $) . T) ((-132) . T) ((-146) -2758 (|has| |#1| (-360)) (|has| |#1| (-146))) ((-148) |has| |#1| (-148)) ((-628 #0#) -2758 (|has| |#1| (-1059 (-419 (-576)))) (|has| |#1| (-360)) (|has| |#1| (-374))) ((-628 (-576)) . T) ((-628 |#1|) . T) ((-628 $) -2758 (|has| |#1| (-568)) (|has| |#1| (-360)) (|has| |#1| (-374)) (|has| |#1| (-317))) ((-625 (-876)) . T) ((-174) . T) ((-626 (-171 (-227))) |has| |#1| (-1043)) ((-626 (-171 (-390))) |has| |#1| (-1043)) ((-626 (-548)) |has| |#1| (-626 (-548))) ((-626 (-907 (-390))) |has| |#1| (-626 (-907 (-390)))) ((-626 (-907 (-576))) |has| |#1| (-626 (-907 (-576)))) ((-626 #1=(-1193 |#1|)) . 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T) ((-464) -2758 (|has| |#1| (-360)) (|has| |#1| (-374)) (|has| |#1| (-317))) ((-505) |has| |#1| (-1223)) ((-526 (-1197) |#1|) |has| |#1| (-526 (-1197) |#1|)) ((-526 |#1| |#1|) |has| |#1| (-319 |#1|)) ((-568) -2758 (|has| |#1| (-568)) (|has| |#1| (-360)) (|has| |#1| (-374)) (|has| |#1| (-317))) ((-658 #0#) -2758 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-658 (-576)) . T) ((-658 |#1|) . T) ((-658 $) . T) ((-660 #0#) -2758 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-660 #2=(-576)) |has| |#1| (-651 (-576))) ((-660 |#1|) . T) ((-660 $) . T) ((-652 #0#) -2758 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-652 |#1|) . T) ((-652 $) -2758 (|has| |#1| (-568)) (|has| |#1| (-360)) (|has| |#1| (-374)) (|has| |#1| (-317))) ((-651 #2#) |has| |#1| (-651 (-576))) ((-651 |#1|) . T) ((-729 #0#) -2758 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-729 |#1|) . T) ((-729 $) -2758 (|has| |#1| (-568)) (|has| |#1| (-360)) (|has| |#1| (-374)) (|has| |#1| (-317))) ((-736 |#1| #1#) . T) ((-738) . T) ((-911 $ #3=(-1197)) -2758 (|has| |#1| (-919 (-1197))) (|has| |#1| (-917 (-1197)))) ((-917 (-1197)) |has| |#1| (-917 (-1197))) ((-919 #3#) -2758 (|has| |#1| (-919 (-1197))) (|has| |#1| (-917 (-1197)))) ((-901 (-390)) |has| |#1| (-901 (-390))) ((-901 (-576)) |has| |#1| (-901 (-576))) ((-899 |#1|) . T) ((-928) -12 (|has| |#1| (-317)) (|has| |#1| (-928))) ((-939) -2758 (|has| |#1| (-360)) (|has| |#1| (-374)) (|has| |#1| (-317))) ((-1023) -12 (|has| |#1| (-1023)) (|has| |#1| (-1223))) ((-1059 (-419 (-576))) |has| |#1| (-1059 (-419 (-576)))) ((-1059 (-576)) |has| |#1| (-1059 (-576))) ((-1059 |#1|) . T) ((-1072 #0#) -2758 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-1072 |#1|) . T) ((-1072 $) . T) ((-1077 #0#) -2758 (|has| |#1| (-360)) (|has| |#1| (-374))) ((-1077 |#1|) . T) ((-1077 $) . T) ((-1070) . T) ((-1079) . T) ((-1133) . T) ((-1121) . T) ((-1173) |has| |#1| (-360)) ((-1223) |has| |#1| (-1223)) ((-1226) |has| |#1| (-1223)) ((-1238) . 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(|has| |#2| (-21))) (($ $) 80 (|has| |#2| (-21)))) (-4026 (($ $ $) 73 (|has| |#2| (-25)))) (** (($ $ (-783)) 87 (|has| |#2| (-1069))) (($ $ (-939)) 84 (|has| |#2| (-1069)))) (* (($ $ $) 85 (|has| |#2| (-1069))) (($ $ |#2|) 83 (|has| |#2| (-738))) (($ |#2| $) 82 (|has| |#2| (-738))) (($ (-576) $) 79 (|has| |#2| (-21))) (($ (-783) $) 77 (|has| |#2| (-23))) (($ (-939) $) 74 (|has| |#2| (-25)))) (-1968 (((-783) $) 6 (|has| $ (-6 -4463))))) -(((-243 |#1| |#2|) (-141) (-783) (-1237)) (T -243)) -((-1491 (*1 *1 *2) (-12 (-5 *2 (-1287 *4)) (-4 *4 (-1237)) (-4 *1 (-243 *3 *4)))) (-2793 (*1 *1 *2) (-12 (-5 *2 (-939)) (-4 *1 (-243 *3 *4)) (-4 *4 (-1069)) (-4 *4 (-1237)))) (-4139 (*1 *2 *1 *1) (-12 (-4 *1 (-243 *3 *2)) (-4 *2 (-1237)) (-4 *2 (-1069))))) -(-13 (-616 (-576) |t#2|) (-625 (-1287 |t#2|)) (-10 -8 (-6 -4463) (-15 -1491 ($ (-1287 |t#2|))) (IF (|has| |t#2| (-1120)) (-6 (-423 |t#2|)) |%noBranch|) (IF (|has| |t#2| (-1069)) (PROGN (-6 (-111 |t#2| |t#2|)) (-6 (-232 |t#2|)) (-6 (-388 |t#2|)) 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|#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-34) . T) ((-102) -3794 (|has| |#2| (-1120)) (|has| |#2| (-1069)) (|has| |#2| (-861)) (|has| |#2| (-805)) (|has| |#2| (-738)) (|has| |#2| (-379)) (|has| |#2| (-374)) (|has| |#2| (-174)) (|has| |#2| (-132)) (|has| |#2| (-102)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-111 |#2| |#2|) -3794 (|has| |#2| (-1069)) (|has| |#2| (-374)) (|has| |#2| (-174))) ((-132) -3794 (|has| |#2| (-1069)) (|has| |#2| (-805)) (|has| |#2| (-374)) (|has| |#2| (-174)) (|has| |#2| (-132)) (|has| |#2| (-21))) ((-628 #0=(-419 (-576))) -12 (|has| |#2| (-1058 (-419 (-576)))) (|has| |#2| (-1120))) ((-628 (-576)) -3794 (|has| |#2| (-1069)) (-12 (|has| |#2| (-1058 (-576))) (|has| |#2| (-1120)))) ((-628 |#2|) |has| |#2| (-1120)) ((-625 (-875)) -3794 (|has| |#2| (-1120)) (|has| |#2| (-1069)) (|has| |#2| (-861)) (|has| |#2| (-805)) (|has| |#2| (-738)) (|has| |#2| (-379)) (|has| |#2| (-374)) (|has| |#2| (-174)) (|has| |#2| (-625 (-875))) (|has| |#2| (-132)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-625 (-1287 |#2|)) . T) ((-234 $) -3794 (-12 (|has| |#2| (-237)) (|has| |#2| (-1069))) (-12 (|has| |#2| (-238)) (|has| |#2| (-1069)))) ((-232 |#2|) |has| |#2| (-1069)) ((-238) -12 (|has| |#2| (-238)) (|has| |#2| (-1069))) ((-237) -3794 (-12 (|has| |#2| (-237)) (|has| |#2| (-1069))) (-12 (|has| |#2| (-238)) (|has| |#2| (-1069)))) ((-272 |#2|) |has| |#2| (-1069)) ((-296 #1=(-576) |#2|) . T) ((-298 #1# |#2|) . T) ((-319 |#2|) -12 (|has| |#2| (-319 |#2|)) (|has| |#2| (-1120))) ((-379) |has| |#2| (-379)) ((-388 |#2|) |has| |#2| (-1069)) ((-423 |#2|) |has| |#2| (-1120)) ((-501 |#2|) . T) ((-616 #1# |#2|) . T) ((-526 |#2| |#2|) -12 (|has| |#2| (-319 |#2|)) (|has| |#2| (-1120))) ((-658 (-576)) -3794 (|has| |#2| (-1069)) (|has| |#2| (-374)) (|has| |#2| (-174)) (|has| |#2| (-21))) ((-658 |#2|) -3794 (|has| |#2| (-1069)) (|has| |#2| (-738)) (|has| |#2| (-374)) (|has| |#2| (-174))) ((-658 $) |has| |#2| (-1069)) ((-660 #2=(-576)) -12 (|has| |#2| (-651 (-576))) (|has| |#2| (-1069))) ((-660 |#2|) -3794 (|has| |#2| (-1069)) (|has| |#2| (-374)) (|has| |#2| (-174))) ((-660 $) |has| |#2| (-1069)) ((-652 |#2|) -3794 (|has| |#2| (-738)) (|has| |#2| (-374)) (|has| |#2| (-174))) ((-651 #2#) -12 (|has| |#2| (-651 (-576))) (|has| |#2| (-1069))) ((-651 |#2|) |has| |#2| (-1069)) ((-729 |#2|) -3794 (|has| |#2| (-374)) (|has| |#2| (-174))) ((-738) |has| |#2| (-1069)) ((-804) |has| |#2| (-805)) ((-805) |has| |#2| (-805)) ((-806) |has| |#2| (-805)) ((-807) |has| |#2| (-805)) ((-861) -3794 (|has| |#2| (-861)) (|has| |#2| (-805))) ((-863) -3794 (|has| |#2| (-861)) (|has| |#2| (-805))) ((-910 $ #3=(-1196)) -3794 (-12 (|has| |#2| (-918 (-1196))) (|has| |#2| (-1069))) (-12 (|has| |#2| (-916 (-1196))) (|has| |#2| (-1069)))) ((-916 (-1196)) -12 (|has| |#2| (-916 (-1196))) (|has| |#2| (-1069))) ((-918 #3#) -3794 (-12 (|has| |#2| (-918 (-1196))) (|has| |#2| (-1069))) (-12 (|has| |#2| (-916 (-1196))) (|has| |#2| (-1069)))) ((-1058 #0#) -12 (|has| |#2| (-1058 (-419 (-576)))) (|has| |#2| (-1120))) ((-1058 (-576)) -12 (|has| |#2| (-1058 (-576))) (|has| |#2| (-1120))) ((-1058 |#2|) |has| |#2| (-1120)) ((-1071 |#2|) -3794 (|has| |#2| (-1069)) (|has| |#2| (-738)) (|has| |#2| (-374)) (|has| |#2| (-174))) ((-1076 |#2|) -3794 (|has| |#2| (-1069)) (|has| |#2| (-374)) (|has| |#2| (-174))) ((-1069) |has| |#2| (-1069)) ((-1078) |has| |#2| (-1069)) ((-1132) |has| |#2| (-1069)) ((-1120) -3794 (|has| |#2| (-1120)) (|has| |#2| (-1069)) (|has| |#2| (-861)) (|has| |#2| (-805)) (|has| |#2| (-738)) (|has| |#2| (-379)) (|has| |#2| (-374)) (|has| |#2| (-174)) (|has| |#2| (-132)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-1237) . T) ((-1294 |#2|) |has| |#2| (-374))) -((-1925 (((-245 |#1| |#3|) (-1 |#3| |#2| |#3|) (-245 |#1| |#2|) |#3|) 21)) (-2721 ((|#3| (-1 |#3| |#2| |#3|) (-245 |#1| |#2|) |#3|) 23)) (-2422 (((-245 |#1| |#3|) (-1 |#3| |#2|) (-245 |#1| |#2|)) 18))) -(((-244 |#1| |#2| |#3|) (-10 -7 (-15 -1925 ((-245 |#1| |#3|) (-1 |#3| |#2| |#3|) (-245 |#1| |#2|) |#3|)) (-15 -2721 (|#3| (-1 |#3| |#2| |#3|) (-245 |#1| |#2|) |#3|)) (-15 -2422 ((-245 |#1| |#3|) (-1 |#3| |#2|) (-245 |#1| |#2|)))) (-783) (-1237) (-1237)) (T -244)) -((-2422 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-245 *5 *6)) (-14 *5 (-783)) (-4 *6 (-1237)) (-4 *7 (-1237)) (-5 *2 (-245 *5 *7)) (-5 *1 (-244 *5 *6 *7)))) (-2721 (*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *6 *2)) (-5 *4 (-245 *5 *6)) (-14 *5 (-783)) (-4 *6 (-1237)) (-4 *2 (-1237)) (-5 *1 (-244 *5 *6 *2)))) (-1925 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *5 *7 *5)) (-5 *4 (-245 *6 *7)) (-14 *6 (-783)) (-4 *7 (-1237)) (-4 *5 (-1237)) (-5 *2 (-245 *6 *5)) (-5 *1 (-244 *6 *7 *5))))) -(-10 -7 (-15 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(|has| |#2| (-1058 (-419 (-576)))) (|has| |#2| (-1120)))) ((|#2| $) 28 (|has| |#2| (-1120)))) (-3222 (((-701 (-576)) (-701 $)) NIL (-12 (|has| |#2| (-651 (-576))) (|has| |#2| (-1069)))) (((-2 (|:| -3608 (-701 (-576))) (|:| |vec| (-1287 (-576)))) (-701 $) (-1287 $)) NIL (-12 (|has| |#2| (-651 (-576))) (|has| |#2| (-1069)))) (((-2 (|:| -3608 (-701 |#2|)) (|:| |vec| (-1287 |#2|))) (-701 $) (-1287 $)) NIL (|has| |#2| (-1069))) (((-701 |#2|) (-701 $)) NIL (|has| |#2| (-1069)))) (-3900 (((-3 $ "failed") $) 58 (|has| |#2| (-1069)))) (-4369 (($) NIL (|has| |#2| (-379)))) (-1908 ((|#2| $ (-576) |#2|) NIL (|has| $ (-6 -4464)))) (-3719 ((|#2| $ (-576)) 56)) (-3721 (((-656 |#2|) $) 14 (|has| $ (-6 -4463)))) (-2287 (((-112) $) NIL (|has| |#2| (-1069)))) (-2135 (((-112) $ (-783)) NIL)) (-2066 (((-576) $) 19 (|has| (-576) (-861)))) (-2905 (($ $ $) NIL (|has| |#2| (-861)))) (-3958 (((-656 |#2|) $) NIL (|has| $ (-6 -4463)))) (-4217 (((-112) |#2| $) NIL (-12 (|has| $ (-6 -4463)) (|has| |#2| (-1120))))) 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(-15 -1417 ($ (-940))) (-15 -1984 (|t#2| $ $))) |%noBranch|) (IF (|has| |t#2| (-25)) (-6 (-25)) |%noBranch|) (IF (|has| |t#2| (-132)) (-6 (-132)) |%noBranch|) (IF (|has| |t#2| (-23)) (-6 (-23)) |%noBranch|) (IF (|has| |t#2| (-21)) (-6 (-21)) |%noBranch|) (IF (|has| |t#2| (-738)) (-6 (-652 |t#2|)) |%noBranch|) (IF (|has| |t#2| (-379)) (-6 (-379)) |%noBranch|) (IF (|has| |t#2| (-174)) (-6 (-729 |t#2|)) |%noBranch|) (IF (|has| |t#2| (-6 -4461)) (-6 -4461) |%noBranch|) (IF (|has| |t#2| (-861)) (-6 (-861)) |%noBranch|) (IF (|has| |t#2| (-805)) (-6 (-805)) |%noBranch|) (IF (|has| |t#2| (-374)) (-6 (-1295 |t#2|)) |%noBranch|))) +(((-21) -2758 (|has| |#2| (-1070)) (|has| |#2| (-374)) (|has| |#2| (-174)) (|has| |#2| (-21))) ((-23) -2758 (|has| |#2| (-1070)) (|has| |#2| (-805)) (|has| |#2| (-374)) (|has| |#2| (-174)) (|has| |#2| (-132)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-25) -2758 (|has| |#2| (-1070)) (|has| |#2| (-805)) (|has| |#2| (-374)) (|has| |#2| (-174)) (|has| |#2| (-132)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-34) . T) ((-102) -2758 (|has| |#2| (-1121)) (|has| |#2| (-1070)) (|has| |#2| (-861)) (|has| |#2| (-805)) (|has| |#2| (-738)) (|has| |#2| (-379)) (|has| |#2| (-374)) (|has| |#2| (-174)) (|has| |#2| (-132)) (|has| |#2| (-102)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-111 |#2| |#2|) -2758 (|has| |#2| (-1070)) (|has| |#2| (-374)) (|has| |#2| (-174))) ((-132) -2758 (|has| |#2| (-1070)) (|has| |#2| (-805)) (|has| |#2| (-374)) (|has| |#2| (-174)) (|has| |#2| (-132)) (|has| |#2| (-21))) ((-628 #0=(-419 (-576))) -12 (|has| |#2| (-1059 (-419 (-576)))) (|has| |#2| (-1121))) ((-628 (-576)) -2758 (|has| |#2| (-1070)) (-12 (|has| |#2| (-1059 (-576))) (|has| |#2| (-1121)))) ((-628 |#2|) |has| |#2| (-1121)) ((-625 (-876)) -2758 (|has| |#2| (-1121)) (|has| |#2| (-1070)) (|has| |#2| (-861)) (|has| |#2| (-805)) (|has| |#2| (-738)) (|has| |#2| (-379)) (|has| |#2| (-374)) (|has| |#2| (-174)) (|has| |#2| (-625 (-876))) (|has| |#2| (-132)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-625 (-1288 |#2|)) . T) ((-234 $) -2758 (-12 (|has| |#2| (-237)) (|has| |#2| (-1070))) (-12 (|has| |#2| (-238)) (|has| |#2| (-1070)))) ((-232 |#2|) |has| |#2| (-1070)) ((-238) -12 (|has| |#2| (-238)) (|has| |#2| (-1070))) ((-237) -2758 (-12 (|has| |#2| (-237)) (|has| |#2| (-1070))) (-12 (|has| |#2| (-238)) (|has| |#2| (-1070)))) ((-272 |#2|) |has| |#2| (-1070)) ((-296 #1=(-576) |#2|) . T) ((-298 #1# |#2|) . T) ((-319 |#2|) -12 (|has| |#2| (-319 |#2|)) (|has| |#2| (-1121))) ((-379) |has| |#2| (-379)) ((-388 |#2|) |has| |#2| (-1070)) ((-423 |#2|) |has| |#2| (-1121)) ((-501 |#2|) . T) ((-616 #1# |#2|) . T) ((-526 |#2| |#2|) -12 (|has| |#2| (-319 |#2|)) (|has| |#2| (-1121))) ((-658 (-576)) -2758 (|has| |#2| (-1070)) (|has| |#2| (-374)) (|has| |#2| (-174)) (|has| |#2| (-21))) ((-658 |#2|) -2758 (|has| |#2| (-1070)) (|has| |#2| (-738)) (|has| |#2| (-374)) (|has| |#2| (-174))) ((-658 $) |has| |#2| (-1070)) ((-660 #2=(-576)) -12 (|has| |#2| (-651 (-576))) (|has| |#2| (-1070))) ((-660 |#2|) -2758 (|has| |#2| (-1070)) (|has| |#2| (-374)) (|has| |#2| (-174))) ((-660 $) |has| |#2| (-1070)) ((-652 |#2|) -2758 (|has| |#2| (-738)) (|has| |#2| (-374)) (|has| |#2| (-174))) ((-651 #2#) -12 (|has| |#2| (-651 (-576))) (|has| |#2| (-1070))) ((-651 |#2|) |has| |#2| (-1070)) ((-729 |#2|) -2758 (|has| |#2| (-374)) (|has| |#2| (-174))) ((-738) |has| |#2| (-1070)) ((-804) |has| |#2| (-805)) ((-805) |has| |#2| (-805)) ((-806) |has| |#2| (-805)) ((-807) |has| |#2| (-805)) ((-861) -2758 (|has| |#2| (-861)) (|has| |#2| (-805))) ((-864) -2758 (|has| |#2| (-861)) (|has| |#2| (-805))) ((-911 $ #3=(-1197)) -2758 (-12 (|has| |#2| (-919 (-1197))) (|has| |#2| (-1070))) (-12 (|has| |#2| (-917 (-1197))) (|has| |#2| (-1070)))) ((-917 (-1197)) -12 (|has| |#2| (-917 (-1197))) (|has| |#2| (-1070))) ((-919 #3#) -2758 (-12 (|has| |#2| (-919 (-1197))) (|has| |#2| (-1070))) (-12 (|has| |#2| (-917 (-1197))) (|has| |#2| (-1070)))) ((-1059 #0#) -12 (|has| |#2| (-1059 (-419 (-576)))) (|has| |#2| (-1121))) ((-1059 (-576)) -12 (|has| |#2| (-1059 (-576))) (|has| |#2| (-1121))) ((-1059 |#2|) |has| |#2| (-1121)) ((-1072 |#2|) -2758 (|has| |#2| (-1070)) (|has| |#2| (-738)) (|has| |#2| (-374)) (|has| |#2| (-174))) ((-1077 |#2|) -2758 (|has| |#2| (-1070)) (|has| |#2| (-374)) (|has| |#2| (-174))) ((-1070) |has| |#2| (-1070)) ((-1079) |has| |#2| (-1070)) ((-1133) |has| |#2| (-1070)) ((-1121) -2758 (|has| |#2| (-1121)) (|has| |#2| (-1070)) (|has| |#2| (-861)) (|has| |#2| (-805)) (|has| |#2| (-738)) (|has| |#2| (-379)) (|has| |#2| (-374)) (|has| |#2| (-174)) (|has| |#2| (-132)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-1238) . T) ((-1295 |#2|) |has| |#2| (-374))) +((-2727 (((-245 |#1| |#3|) (-1 |#3| |#2| |#3|) (-245 |#1| |#2|) |#3|) 21)) (-3685 ((|#3| (-1 |#3| |#2| |#3|) (-245 |#1| |#2|) |#3|) 23)) (-4116 (((-245 |#1| |#3|) (-1 |#3| |#2|) (-245 |#1| |#2|)) 18))) +(((-244 |#1| |#2| |#3|) (-10 -7 (-15 -2727 ((-245 |#1| |#3|) (-1 |#3| |#2| |#3|) (-245 |#1| |#2|) |#3|)) (-15 -3685 (|#3| (-1 |#3| |#2| |#3|) (-245 |#1| |#2|) |#3|)) (-15 -4116 ((-245 |#1| |#3|) (-1 |#3| |#2|) (-245 |#1| |#2|)))) (-783) (-1238) (-1238)) (T -244)) +((-4116 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-245 *5 *6)) (-14 *5 (-783)) (-4 *6 (-1238)) (-4 *7 (-1238)) (-5 *2 (-245 *5 *7)) (-5 *1 (-244 *5 *6 *7)))) (-3685 (*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *6 *2)) (-5 *4 (-245 *5 *6)) (-14 *5 (-783)) (-4 *6 (-1238)) (-4 *2 (-1238)) (-5 *1 (-244 *5 *6 *2)))) (-2727 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *5 *7 *5)) (-5 *4 (-245 *6 *7)) (-14 *6 (-783)) (-4 *7 (-1238)) (-4 *5 (-1238)) (-5 *2 (-245 *6 *5)) (-5 *1 (-244 *6 *7 *5))))) +(-10 -7 (-15 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|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| (-1177 (-227))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -2925 (-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 (-571)))) (-2351 (*1 *2 *1) (-12 (-5 *2 (-656 (-2 (|:| |var| (-1196)) (|:| |fn| (-326 (-227))) (|:| -2925 (-1114 (-855 (-227)))) (|:| |abserr| (-227)) (|:| |relerr| (-227))))) (-5 *1 (-571)))) (-2245 (*1 *2) (-12 (-5 *2 (-1292)) (-5 *1 (-571)))) 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T) ((-23) . T) ((-47 |#1| #0=(-576)) . T) ((-25) . T) ((-38 #1=(-419 (-576))) -3794 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-38 |#1|) |has| |#1| (-174)) ((-38 |#2|) |has| |#1| (-374)) ((-38 $) -3794 (|has| |#1| (-568)) (|has| |#1| (-374))) ((-35) |has| |#1| (-38 (-419 (-576)))) ((-95) |has| |#1| (-38 (-419 (-576)))) ((-102) . T) ((-111 #1# #1#) -3794 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-111 |#1| |#1|) . T) ((-111 |#2| |#2|) |has| |#1| (-374)) ((-111 $ $) -3794 (|has| |#1| (-568)) (|has| |#1| (-374)) (|has| |#1| (-174))) ((-132) . T) ((-146) -3794 (-12 (|has| |#1| (-374)) (|has| |#2| (-146))) (|has| |#1| (-146))) ((-148) -3794 (-12 (|has| |#1| (-374)) (|has| |#2| (-148))) (|has| |#1| (-148))) ((-628 #1#) -3794 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-628 (-576)) . T) ((-628 #2=(-1196)) -12 (|has| |#1| (-374)) (|has| |#2| (-1058 (-1196)))) ((-628 |#1|) |has| |#1| (-174)) ((-628 |#2|) . T) ((-628 $) -3794 (|has| |#1| (-568)) (|has| |#1| (-374))) ((-625 (-875)) . T) ((-174) -3794 (|has| |#1| (-568)) (|has| |#1| (-374)) (|has| |#1| (-174))) ((-626 (-227)) -12 (|has| |#1| (-374)) (|has| |#2| (-1042))) ((-626 (-390)) -12 (|has| |#1| (-374)) (|has| |#2| (-1042))) ((-626 (-548)) -12 (|has| |#1| (-374)) (|has| |#2| (-626 (-548)))) ((-626 (-906 (-390))) -12 (|has| |#1| (-374)) (|has| |#2| (-626 (-906 (-390))))) ((-626 (-906 (-576))) -12 (|has| |#1| (-374)) (|has| |#2| (-626 (-906 (-576))))) ((-234 $) -3794 (-12 (|has| |#1| (-374)) (|has| |#2| (-237))) (-12 (|has| |#1| (-374)) (|has| |#2| (-238))) (|has| |#1| (-15 * (|#1| (-576) |#1|)))) ((-232 |#2|) |has| |#1| (-374)) ((-238) -3794 (-12 (|has| |#1| (-374)) (|has| |#2| (-238))) (|has| |#1| (-15 * (|#1| (-576) |#1|)))) ((-237) -3794 (-12 (|has| |#1| (-374)) (|has| |#2| (-237))) (-12 (|has| |#1| (-374)) (|has| |#2| (-238))) (|has| |#1| (-15 * (|#1| (-576) |#1|)))) ((-272 |#2|) |has| |#1| (-374)) ((-248) |has| |#1| (-374)) ((-294) |has| |#1| (-38 (-419 (-576)))) ((-296 #0# |#1|) . T) ((-296 |#2| $) -12 (|has| |#1| (-374)) (|has| |#2| (-296 |#2| |#2|))) ((-296 $ $) |has| (-576) (-1132)) ((-300) -3794 (|has| |#1| (-568)) (|has| |#1| (-374))) ((-317) |has| |#1| (-374)) ((-319 |#2|) -12 (|has| |#1| (-374)) (|has| |#2| (-319 |#2|))) ((-374) |has| |#1| (-374)) ((-349 |#2|) |has| |#1| (-374)) ((-388 |#2|) |has| |#1| (-374)) ((-412 |#2|) |has| |#1| (-374)) ((-464) |has| |#1| (-374)) ((-505) |has| |#1| (-38 (-419 (-576)))) ((-526 (-1196) |#2|) -12 (|has| |#1| (-374)) (|has| |#2| (-526 (-1196) |#2|))) ((-526 |#2| |#2|) -12 (|has| |#1| (-374)) (|has| |#2| (-319 |#2|))) ((-568) -3794 (|has| |#1| (-568)) (|has| |#1| (-374))) ((-658 #1#) -3794 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-658 (-576)) . T) ((-658 |#1|) . T) ((-658 |#2|) |has| |#1| (-374)) ((-658 $) . T) ((-660 #1#) -3794 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-660 #3=(-576)) -12 (|has| |#1| (-374)) (|has| |#2| (-651 (-576)))) ((-660 |#1|) . T) ((-660 |#2|) |has| |#1| (-374)) ((-660 $) . T) ((-652 #1#) -3794 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-652 |#1|) |has| |#1| (-174)) ((-652 |#2|) |has| |#1| (-374)) ((-652 $) -3794 (|has| |#1| (-568)) (|has| |#1| (-374))) ((-651 #3#) -12 (|has| |#1| (-374)) (|has| |#2| (-651 (-576)))) ((-651 |#2|) |has| |#1| (-374)) ((-729 #1#) -3794 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-729 |#1|) |has| |#1| (-174)) ((-729 |#2|) |has| |#1| (-374)) ((-729 $) -3794 (|has| |#1| (-568)) (|has| |#1| (-374))) ((-738) . T) ((-803) -12 (|has| |#1| (-374)) (|has| |#2| (-832))) ((-804) -12 (|has| |#1| (-374)) (|has| |#2| (-832))) ((-806) -12 (|has| |#1| (-374)) (|has| |#2| (-832))) ((-807) -12 (|has| |#1| (-374)) (|has| |#2| (-832))) ((-832) -12 (|has| |#1| (-374)) (|has| |#2| (-832))) ((-860) -12 (|has| |#1| (-374)) (|has| |#2| (-832))) ((-861) -3794 (-12 (|has| |#1| (-374)) (|has| |#2| (-861))) (-12 (|has| |#1| (-374)) (|has| |#2| (-832)))) ((-863) -3794 (-12 (|has| |#1| (-374)) (|has| |#2| (-861))) (-12 (|has| |#1| (-374)) (|has| |#2| (-832)))) ((-910 $ #4=(-1196)) -3794 (-12 (|has| |#1| (-374)) (|has| |#2| (-918 (-1196)))) (-12 (|has| |#1| (-374)) (|has| |#2| (-916 (-1196)))) (-12 (|has| |#1| (-15 * (|#1| (-576) |#1|))) (|has| |#1| (-916 (-1196))))) ((-916 (-1196)) -3794 (-12 (|has| |#1| (-374)) (|has| |#2| (-916 (-1196)))) (-12 (|has| |#1| (-15 * (|#1| (-576) |#1|))) (|has| |#1| (-916 (-1196))))) ((-918 #4#) -3794 (-12 (|has| |#1| (-374)) (|has| |#2| (-918 (-1196)))) (-12 (|has| |#1| (-374)) (|has| |#2| (-916 (-1196)))) (-12 (|has| |#1| (-15 * (|#1| (-576) |#1|))) (|has| |#1| (-916 (-1196))))) ((-900 (-390)) -12 (|has| |#1| (-374)) (|has| |#2| (-900 (-390)))) ((-900 (-576)) -12 (|has| |#1| (-374)) (|has| |#2| (-900 (-576)))) ((-898 |#2|) |has| |#1| (-374)) ((-927) -12 (|has| |#1| (-374)) (|has| |#2| (-927))) ((-993 |#1| #0# (-1102)) . 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T) ((-1076 $) -3794 (|has| |#1| (-568)) (|has| |#1| (-374)) (|has| |#1| (-174))) ((-1069) . T) ((-1078) . T) ((-1132) . T) ((-1120) . T) ((-1222) |has| |#1| (-38 (-419 (-576)))) ((-1225) |has| |#1| (-38 (-419 (-576)))) ((-1237) . T) ((-1241) |has| |#1| (-374)) ((-1265 |#1| #0#) . T) ((-1268 |#1|) . 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T) ((-23) . T) ((-47 |#1| #0=(-783)) . T) ((-25) . T) ((-38 #1=(-419 (-576))) |has| |#1| (-38 (-419 (-576)))) ((-38 |#1|) |has| |#1| (-174)) ((-38 $) |has| |#1| (-568)) ((-35) |has| |#1| (-38 (-419 (-576)))) ((-95) |has| |#1| (-38 (-419 (-576)))) ((-102) . T) ((-111 #1# #1#) |has| |#1| (-38 (-419 (-576)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -3794 (|has| |#1| (-568)) (|has| |#1| (-174))) ((-132) . T) ((-146) |has| |#1| (-146)) ((-148) |has| |#1| (-148)) ((-628 #1#) |has| |#1| (-38 (-419 (-576)))) ((-628 (-576)) . T) ((-628 |#1|) |has| |#1| (-174)) ((-628 $) |has| |#1| (-568)) ((-625 (-875)) . T) ((-174) -3794 (|has| |#1| (-568)) (|has| |#1| (-174))) ((-234 $) |has| |#1| (-15 * (|#1| (-783) |#1|))) ((-238) |has| |#1| (-15 * (|#1| (-783) |#1|))) ((-237) |has| |#1| (-15 * (|#1| (-783) |#1|))) ((-294) |has| |#1| (-38 (-419 (-576)))) ((-296 #0# |#1|) . 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T) ((-1071 $) -3794 (|has| |#1| (-568)) (|has| |#1| (-174))) ((-1076 #1#) |has| |#1| (-38 (-419 (-576)))) ((-1076 |#1|) . T) ((-1076 $) -3794 (|has| |#1| (-568)) (|has| |#1| (-174))) ((-1069) . T) ((-1078) . T) ((-1132) . T) ((-1120) . T) ((-1222) |has| |#1| (-38 (-419 (-576)))) ((-1225) |has| |#1| (-38 (-419 (-576)))) ((-1237) . T) ((-1265 |#1| #0#) . 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NIL) (-1248 2996092 2996337 2996725 "ULSCCAT-" 2996730 NIL ULSCCAT- (NIL T T T) -8 NIL NIL NIL) (-1247 2985156 2991639 2991682 "ULSCAT" 2992545 NIL ULSCAT (NIL T) -9 NIL 2993276 NIL) (-1246 2984586 2984665 2984844 "ULS2" 2985071 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1245 2983705 2984215 2984322 "UINT8" 2984433 T UINT8 (NIL) -8 NIL NIL 2984518) (-1244 2982823 2983333 2983440 "UINT64" 2983551 T UINT64 (NIL) -8 NIL NIL 2983636) (-1243 2981941 2982451 2982558 "UINT32" 2982669 T UINT32 (NIL) -8 NIL NIL 2982754) (-1242 2981059 2981569 2981676 "UINT16" 2981787 T UINT16 (NIL) -8 NIL NIL 2981872) (-1241 2979348 2980305 2980335 "UFD" 2980547 T UFD (NIL) -9 NIL 2980661 NIL) (-1240 2979142 2979188 2979283 "UFD-" 2979288 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1239 2978224 2978407 2978623 "UDVO" 2978948 T UDVO (NIL) -7 NIL NIL NIL) (-1238 2976040 2976449 2976920 "UDPO" 2977788 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1237 2975973 2975978 2976008 "TYPE" 2976013 T TYPE (NIL) -9 NIL NIL NIL) (-1236 2975733 2975928 2975959 "TYPEAST" 2975964 T TYPEAST (NIL) -8 NIL NIL NIL) (-1235 2974704 2974906 2975146 "TWOFACT" 2975527 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1234 2973727 2974113 2974348 "TUPLE" 2974504 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1233 2971418 2971937 2972476 "TUBETOOL" 2973210 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1232 2970267 2970472 2970713 "TUBE" 2971211 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1231 2964996 2969239 2969522 "TS" 2970019 NIL TS (NIL T) -8 NIL NIL NIL) (-1230 2953636 2957755 2957852 "TSETCAT" 2963121 NIL TSETCAT (NIL T T T T) -9 NIL 2964652 NIL) (-1229 2948368 2949968 2951859 "TSETCAT-" 2951864 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1228 2943007 2943854 2944783 "TRMANIP" 2947504 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1227 2942448 2942511 2942674 "TRIMAT" 2942939 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1226 2940314 2940551 2940908 "TRIGMNIP" 2942197 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1225 2939834 2939947 2939977 "TRIGCAT" 2940190 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1224 2939503 2939582 2939723 "TRIGCAT-" 2939728 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1223 2936351 2938361 2938642 "TREE" 2939257 NIL TREE (NIL T) -8 NIL NIL NIL) (-1222 2935625 2936153 2936183 "TRANFUN" 2936218 T TRANFUN (NIL) -9 NIL 2936284 NIL) (-1221 2934904 2935095 2935375 "TRANFUN-" 2935380 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1220 2934708 2934740 2934801 "TOPSP" 2934865 T TOPSP (NIL) -7 NIL NIL NIL) (-1219 2934056 2934171 2934325 "TOOLSIGN" 2934589 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1218 2932690 2933233 2933472 "TEXTFILE" 2933839 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1217 2930602 2931143 2931572 "TEX" 2932283 T TEX (NIL) -8 NIL NIL NIL) (-1216 2930383 2930414 2930486 "TEX1" 2930565 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1215 2930031 2930094 2930184 "TEMUTL" 2930315 T TEMUTL (NIL) -7 NIL NIL NIL) (-1214 2928185 2928465 2928790 "TBCMPPK" 2929754 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1213 2919894 2926271 2926327 "TBAGG" 2926727 NIL TBAGG (NIL T T) -9 NIL 2926938 NIL) (-1212 2914964 2916452 2918206 "TBAGG-" 2918211 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1211 2914348 2914455 2914600 "TANEXP" 2914853 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1210 2913859 2914123 2914213 "TALGOP" 2914293 NIL TALGOP (NIL T) -8 NIL NIL NIL) (-1209 2907255 2913716 2913809 "TABLE" 2913814 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1208 2906667 2906766 2906904 "TABLEAU" 2907152 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1207 2901275 2902495 2903743 "TABLBUMP" 2905453 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1206 2900497 2900644 2900825 "SYSTEM" 2901116 T SYSTEM (NIL) -8 NIL NIL NIL) (-1205 2896956 2897655 2898438 "SYSSOLP" 2899748 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1204 2896754 2896911 2896942 "SYSPTR" 2896947 T SYSPTR (NIL) -8 NIL NIL NIL) (-1203 2895790 2896295 2896414 "SYSNNI" 2896600 NIL SYSNNI (NIL NIL) -8 NIL NIL 2896685) (-1202 2895089 2895548 2895627 "SYSINT" 2895687 NIL SYSINT (NIL NIL) -8 NIL NIL 2895732) (-1201 2891421 2892367 2893077 "SYNTAX" 2894401 T SYNTAX (NIL) -8 NIL NIL NIL) (-1200 2888579 2889181 2889813 "SYMTAB" 2890811 T SYMTAB (NIL) -8 NIL NIL NIL) (-1199 2883828 2884730 2885713 "SYMS" 2887618 T SYMS (NIL) -8 NIL NIL NIL) (-1198 2881063 2883286 2883516 "SYMPOLY" 2883633 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1197 2880580 2880655 2880778 "SYMFUNC" 2880975 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1196 2876600 2877892 2878705 "SYMBOL" 2879789 T SYMBOL (NIL) -8 NIL NIL NIL) (-1195 2870139 2871828 2873548 "SWITCH" 2874902 T SWITCH (NIL) -8 NIL NIL NIL) (-1194 2863483 2869095 2869389 "SUTS" 2869903 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1193 2855659 2862865 2863129 "SUPXS" 2863277 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1192 2847142 2855277 2855403 "SUP" 2855568 NIL SUP (NIL T) -8 NIL NIL NIL) (-1191 2846301 2846428 2846645 "SUPFRACF" 2847010 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1190 2845922 2845981 2846094 "SUP2" 2846236 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1189 2844370 2844644 2845000 "SUMRF" 2845621 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1188 2843705 2843771 2843963 "SUMFS" 2844291 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1187 2826492 2843017 2843259 "SULS" 2843521 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1186 2826094 2826314 2826384 "SUCHTAST" 2826444 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1185 2825389 2825619 2825759 "SUCH" 2826002 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1184 2819256 2820295 2821254 "SUBSPACE" 2824477 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1183 2818686 2818776 2818940 "SUBRESP" 2819144 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1182 2812054 2813351 2814662 "STTF" 2817422 NIL STTF (NIL T) -7 NIL NIL NIL) (-1181 2806227 2807347 2808494 "STTFNC" 2810954 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1180 2797540 2799409 2801203 "STTAYLOR" 2804468 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1179 2790676 2797404 2797487 "STRTBL" 2797492 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1178 2785637 2790385 2790484 "STRING" 2790599 T STRING (NIL) -8 NIL NIL NIL) (-1177 2778393 2783256 2783867 "STREAM" 2785061 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1176 2777903 2777980 2778124 "STREAM3" 2778310 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1175 2776885 2777068 2777303 "STREAM2" 2777716 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1174 2776573 2776625 2776718 "STREAM1" 2776827 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1173 2775589 2775770 2776001 "STINPROD" 2776389 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1172 2775127 2775337 2775367 "STEP" 2775447 T STEP (NIL) -9 NIL 2775525 NIL) (-1171 2774314 2774616 2774764 "STEPAST" 2775001 T STEPAST (NIL) -8 NIL NIL NIL) (-1170 2767752 2774213 2774290 "STBL" 2774295 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1169 2762822 2766915 2766958 "STAGG" 2767111 NIL STAGG (NIL T) -9 NIL 2767200 NIL) (-1168 2760524 2761126 2761998 "STAGG-" 2762003 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1167 2758674 2760294 2760386 "STACK" 2760467 NIL STACK (NIL T) -8 NIL NIL NIL) (-1166 2751369 2756815 2757271 "SREGSET" 2758304 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1165 2743794 2745163 2746676 "SRDCMPK" 2749975 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1164 2736631 2741153 2741183 "SRAGG" 2742486 T SRAGG (NIL) -9 NIL 2743094 NIL) (-1163 2735648 2735903 2736282 "SRAGG-" 2736287 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1162 2729832 2734595 2735016 "SQMATRIX" 2735274 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1161 2723520 2726550 2727277 "SPLTREE" 2729177 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1160 2719483 2720176 2720822 "SPLNODE" 2722946 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1159 2718530 2718763 2718793 "SPFCAT" 2719237 T SPFCAT (NIL) -9 NIL NIL NIL) (-1158 2717267 2717477 2717741 "SPECOUT" 2718288 T SPECOUT (NIL) -7 NIL NIL NIL) (-1157 2708363 2710235 2710265 "SPADXPT" 2714941 T SPADXPT (NIL) -9 NIL 2717105 NIL) (-1156 2708124 2708164 2708233 "SPADPRSR" 2708316 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1155 2706173 2708079 2708110 "SPADAST" 2708115 T SPADAST (NIL) -8 NIL NIL NIL) (-1154 2698104 2699877 2699920 "SPACEC" 2704293 NIL SPACEC (NIL T) -9 NIL 2706109 NIL) (-1153 2696234 2698036 2698085 "SPACE3" 2698090 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1152 2694986 2695157 2695448 "SORTPAK" 2696039 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1151 2693078 2693381 2693793 "SOLVETRA" 2694650 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1150 2692128 2692350 2692611 "SOLVESER" 2692851 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1149 2687432 2688320 2689315 "SOLVERAD" 2691180 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1148 2683247 2683856 2684585 "SOLVEFOR" 2686799 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1147 2677517 2682596 2682693 "SNTSCAT" 2682698 NIL SNTSCAT (NIL T T T T) -9 NIL 2682768 NIL) (-1146 2671623 2675840 2676231 "SMTS" 2677207 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1145 2666032 2671511 2671588 "SMP" 2671593 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1144 2664191 2664492 2664890 "SMITH" 2665729 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1143 2656295 2660770 2660873 "SMATCAT" 2662224 NIL SMATCAT (NIL NIL T T T) -9 NIL 2662774 NIL) (-1142 2653235 2654058 2655236 "SMATCAT-" 2655241 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1141 2650876 2652443 2652486 "SKAGG" 2652747 NIL SKAGG (NIL T) -9 NIL 2652882 NIL) (-1140 2647066 2650349 2650533 "SINT" 2650685 T SINT (NIL) -8 NIL NIL 2650847) (-1139 2646838 2646876 2646942 "SIMPAN" 2647022 T SIMPAN (NIL) -7 NIL NIL NIL) (-1138 2646117 2646373 2646513 "SIG" 2646720 T SIG (NIL) -8 NIL NIL NIL) (-1137 2644955 2645176 2645451 "SIGNRF" 2645876 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1136 2643788 2643939 2644223 "SIGNEF" 2644784 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1135 2643094 2643371 2643495 "SIGAST" 2643686 T SIGAST (NIL) -8 NIL NIL NIL) (-1134 2640784 2641238 2641744 "SHP" 2642635 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1133 2634613 2640685 2640761 "SHDP" 2640766 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1132 2634172 2634364 2634394 "SGROUP" 2634487 T SGROUP (NIL) -9 NIL 2634549 NIL) (-1131 2634030 2634056 2634129 "SGROUP-" 2634134 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1130 2630821 2631519 2632242 "SGCF" 2633329 T SGCF (NIL) -7 NIL NIL NIL) (-1129 2625189 2630268 2630365 "SFRTCAT" 2630370 NIL SFRTCAT (NIL T T T T) -9 NIL 2630409 NIL) (-1128 2618610 2619628 2620764 "SFRGCD" 2624172 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1127 2611736 2612809 2613995 "SFQCMPK" 2617543 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1126 2611356 2611445 2611556 "SFORT" 2611677 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1125 2610474 2611196 2611317 "SEXOF" 2611322 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1124 2609581 2610355 2610423 "SEX" 2610428 T SEX (NIL) -8 NIL NIL NIL) (-1123 2605362 2606077 2606172 "SEXCAT" 2608794 NIL SEXCAT (NIL T T T T T) -9 NIL 2609354 NIL) (-1122 2602515 2605296 2605344 "SET" 2605349 NIL SET (NIL T) -8 NIL NIL NIL) (-1121 2600739 2601228 2601533 "SETMN" 2602256 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1120 2600305 2600457 2600487 "SETCAT" 2600604 T SETCAT (NIL) -9 NIL 2600689 NIL) (-1119 2600085 2600137 2600236 "SETCAT-" 2600241 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1118 2596446 2598546 2598589 "SETAGG" 2599459 NIL SETAGG (NIL T) -9 NIL 2599799 NIL) (-1117 2595904 2596020 2596257 "SETAGG-" 2596262 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1116 2595347 2595600 2595701 "SEQAST" 2595825 T SEQAST (NIL) -8 NIL NIL NIL) (-1115 2594546 2594840 2594901 "SEGXCAT" 2595187 NIL SEGXCAT (NIL T T) -9 NIL 2595307 NIL) (-1114 2593552 2594212 2594394 "SEG" 2594399 NIL SEG (NIL T) -8 NIL NIL NIL) (-1113 2592531 2592745 2592788 "SEGCAT" 2593310 NIL SEGCAT (NIL T) -9 NIL 2593531 NIL) (-1112 2591463 2591894 2592102 "SEGBIND" 2592358 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1111 2591084 2591143 2591256 "SEGBIND2" 2591398 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1110 2590657 2590885 2590962 "SEGAST" 2591029 T SEGAST (NIL) -8 NIL NIL NIL) (-1109 2589876 2590002 2590206 "SEG2" 2590501 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1108 2589247 2589811 2589858 "SDVAR" 2589863 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1107 2581498 2589017 2589147 "SDPOL" 2589152 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1106 2580091 2580357 2580676 "SCPKG" 2581213 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1105 2579255 2579427 2579619 "SCOPE" 2579921 T SCOPE (NIL) -8 NIL NIL NIL) (-1104 2578475 2578609 2578788 "SCACHE" 2579110 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1103 2578107 2578293 2578323 "SASTCAT" 2578328 T SASTCAT (NIL) -9 NIL 2578341 NIL) (-1102 2577594 2577942 2578018 "SAOS" 2578053 T SAOS (NIL) -8 NIL NIL NIL) (-1101 2577159 2577194 2577367 "SAERFFC" 2577553 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1100 2570822 2577056 2577136 "SAE" 2577141 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1099 2570415 2570450 2570609 "SAEFACT" 2570781 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1098 2568736 2569050 2569451 "RURPK" 2570081 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1097 2567373 2567679 2567984 "RULESET" 2568570 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1096 2564596 2565126 2565584 "RULE" 2567054 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1095 2564208 2564390 2564473 "RULECOLD" 2564548 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1094 2563998 2564026 2564097 "RTVALUE" 2564159 T RTVALUE (NIL) -8 NIL NIL NIL) (-1093 2563469 2563715 2563809 "RSTRCAST" 2563926 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1092 2558317 2559112 2560032 "RSETGCD" 2562668 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1091 2547547 2552626 2552723 "RSETCAT" 2556842 NIL RSETCAT (NIL T T T T) -9 NIL 2557939 NIL) (-1090 2545474 2546013 2546837 "RSETCAT-" 2546842 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1089 2537860 2539236 2540756 "RSDCMPK" 2544073 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1088 2535825 2536292 2536366 "RRCC" 2537452 NIL RRCC (NIL T T) -9 NIL 2537796 NIL) (-1087 2535176 2535350 2535629 "RRCC-" 2535634 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1086 2534619 2534872 2534973 "RPTAST" 2535097 T RPTAST (NIL) -8 NIL NIL NIL) (-1085 2508095 2517731 2517798 "RPOLCAT" 2528464 NIL RPOLCAT (NIL T T T) -9 NIL 2531624 NIL) (-1084 2499593 2501933 2505055 "RPOLCAT-" 2505060 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1083 2490530 2497804 2498286 "ROUTINE" 2499133 T ROUTINE (NIL) -8 NIL NIL NIL) (-1082 2487191 2490156 2490296 "ROMAN" 2490412 T ROMAN (NIL) -8 NIL NIL NIL) (-1081 2485435 2486051 2486311 "ROIRC" 2486996 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1080 2481639 2483924 2483954 "RNS" 2484258 T RNS (NIL) -9 NIL 2484532 NIL) (-1079 2480148 2480531 2481065 "RNS-" 2481140 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1078 2479537 2479945 2479975 "RNG" 2479980 T RNG (NIL) -9 NIL 2480001 NIL) (-1077 2478540 2478902 2479104 "RNGBIND" 2479388 NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-1076 2477925 2478313 2478356 "RMODULE" 2478361 NIL RMODULE (NIL T) -9 NIL 2478388 NIL) (-1075 2476761 2476855 2477191 "RMCAT2" 2477826 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1074 2473611 2476107 2476404 "RMATRIX" 2476523 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1073 2466438 2468698 2468813 "RMATCAT" 2472172 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2473154 NIL) (-1072 2465813 2465960 2466267 "RMATCAT-" 2466272 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1071 2465428 2465600 2465643 "RLINSET" 2465705 NIL RLINSET (NIL T) -9 NIL 2465749 NIL) (-1070 2464995 2465070 2465198 "RINTERP" 2465347 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1069 2464039 2464593 2464623 "RING" 2464679 T RING (NIL) -9 NIL 2464771 NIL) (-1068 2463831 2463875 2463972 "RING-" 2463977 NIL RING- (NIL T) -8 NIL NIL NIL) (-1067 2462672 2462909 2463167 "RIDIST" 2463595 T RIDIST (NIL) -7 NIL NIL NIL) (-1066 2453961 2462140 2462346 "RGCHAIN" 2462520 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1065 2453297 2453703 2453744 "RGBCSPC" 2453802 NIL RGBCSPC (NIL T) -9 NIL 2453854 NIL) (-1064 2452441 2452822 2452863 "RGBCMDL" 2453095 NIL RGBCMDL (NIL T) -9 NIL 2453209 NIL) (-1063 2449435 2450049 2450719 "RF" 2451805 NIL RF (NIL T) -7 NIL NIL NIL) (-1062 2449081 2449144 2449247 "RFFACTOR" 2449366 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1061 2448806 2448841 2448938 "RFFACT" 2449040 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1060 2446923 2447287 2447669 "RFDIST" 2448446 T RFDIST (NIL) -7 NIL NIL NIL) (-1059 2446376 2446468 2446631 "RETSOL" 2446825 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1058 2446012 2446092 2446135 "RETRACT" 2446268 NIL RETRACT (NIL T) -9 NIL 2446355 NIL) (-1057 2445861 2445886 2445973 "RETRACT-" 2445978 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1056 2445463 2445683 2445753 "RETAST" 2445813 T RETAST (NIL) -8 NIL NIL NIL) (-1055 2438207 2445116 2445243 "RESULT" 2445358 T RESULT (NIL) -8 NIL NIL NIL) (-1054 2436798 2437476 2437675 "RESRING" 2438110 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1053 2436434 2436483 2436581 "RESLATC" 2436735 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1052 2436139 2436174 2436281 "REPSQ" 2436393 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1051 2433561 2434141 2434743 "REP" 2435559 T REP (NIL) -7 NIL NIL NIL) (-1050 2433258 2433293 2433404 "REPDB" 2433520 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1049 2427158 2428547 2429770 "REP2" 2432070 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1048 2423535 2424216 2425024 "REP1" 2426385 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1047 2416231 2421676 2422132 "REGSET" 2423165 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1046 2414996 2415379 2415629 "REF" 2416016 NIL REF (NIL T) -8 NIL NIL NIL) (-1045 2414373 2414476 2414643 "REDORDER" 2414880 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1044 2410341 2413586 2413813 "RECLOS" 2414201 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1043 2409393 2409574 2409789 "REALSOLV" 2410148 T REALSOLV (NIL) -7 NIL NIL NIL) (-1042 2409239 2409280 2409310 "REAL" 2409315 T REAL (NIL) -9 NIL 2409350 NIL) (-1041 2405722 2406524 2407408 "REAL0Q" 2408404 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1040 2401323 2402311 2403372 "REAL0" 2404703 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1039 2400794 2401040 2401134 "RDUCEAST" 2401251 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1038 2400199 2400271 2400478 "RDIV" 2400716 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1037 2399267 2399441 2399654 "RDIST" 2400021 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1036 2397864 2398151 2398523 "RDETRS" 2398975 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1035 2395676 2396130 2396668 "RDETR" 2397406 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1034 2394301 2394579 2394976 "RDEEFS" 2395392 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1033 2392810 2393116 2393541 "RDEEF" 2393989 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1032 2386843 2389764 2389794 "RCFIELD" 2391089 T RCFIELD (NIL) -9 NIL 2391820 NIL) (-1031 2384907 2385411 2386107 "RCFIELD-" 2386182 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1030 2381151 2382980 2383023 "RCAGG" 2384107 NIL RCAGG (NIL T) -9 NIL 2384572 NIL) (-1029 2380779 2380873 2381036 "RCAGG-" 2381041 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1028 2380114 2380226 2380391 "RATRET" 2380663 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1027 2379667 2379734 2379855 "RATFACT" 2380042 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1026 2378975 2379095 2379247 "RANDSRC" 2379537 T RANDSRC (NIL) -7 NIL NIL NIL) (-1025 2378709 2378753 2378826 "RADUTIL" 2378924 T RADUTIL (NIL) -7 NIL NIL NIL) (-1024 2371537 2377540 2377851 "RADIX" 2378432 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-1023 2361997 2371379 2371509 "RADFF" 2371514 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-1022 2361644 2361719 2361749 "RADCAT" 2361909 T RADCAT (NIL) -9 NIL NIL NIL) (-1021 2361426 2361474 2361574 "RADCAT-" 2361579 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-1020 2359527 2361196 2361288 "QUEUE" 2361369 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-1019 2355788 2359460 2359508 "QUAT" 2359513 NIL QUAT (NIL T) -8 NIL NIL NIL) (-1018 2355419 2355462 2355593 "QUATCT2" 2355739 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-1017 2348217 2351842 2351884 "QUATCAT" 2352675 NIL QUATCAT (NIL T) -9 NIL 2353441 NIL) (-1016 2344356 2345393 2346783 "QUATCAT-" 2346879 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-1015 2341796 2343404 2343447 "QUAGG" 2343828 NIL QUAGG (NIL T) -9 NIL 2344003 NIL) (-1014 2341398 2341618 2341688 "QQUTAST" 2341748 T QQUTAST (NIL) -8 NIL NIL NIL) (-1013 2340411 2340911 2341076 "QFORM" 2341279 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-1012 2330743 2336258 2336300 "QFCAT" 2336968 NIL QFCAT (NIL T) -9 NIL 2337969 NIL) (-1011 2326310 2327511 2329105 "QFCAT-" 2329201 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-1010 2325941 2325984 2326115 "QFCAT2" 2326261 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-1009 2325396 2325506 2325638 "QEQUAT" 2325831 T QEQUAT (NIL) -8 NIL NIL NIL) (-1008 2318522 2319595 2320781 "QCMPACK" 2324329 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-1007 2316060 2316508 2316938 "QALGSET" 2318177 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-1006 2315295 2315471 2315707 "QALGSET2" 2315878 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-1005 2313980 2314204 2314523 "PWFFINTB" 2315068 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-1004 2312155 2312323 2312679 "PUSHVAR" 2313794 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-1003 2308044 2309098 2309141 "PTRANFN" 2311052 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-1002 2306435 2306726 2307050 "PTPACK" 2307755 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-1001 2306064 2306121 2306232 "PTFUNC2" 2306372 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-1000 2300459 2304853 2304896 "PTCAT" 2305196 NIL PTCAT (NIL T) -9 NIL 2305349 NIL) (-999 2300117 2300152 2300276 "PSQFR" 2300418 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-998 2298712 2299010 2299344 "PSEUDLIN" 2299815 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-997 2285475 2287846 2290170 "PSETPK" 2296472 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-996 2278493 2281233 2281329 "PSETCAT" 2284350 NIL PSETCAT (NIL T T T T) -9 NIL 2285164 NIL) (-995 2276329 2276963 2277784 "PSETCAT-" 2277789 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-994 2275678 2275843 2275871 "PSCURVE" 2276139 T PSCURVE (NIL) -9 NIL 2276306 NIL) (-993 2271662 2273178 2273243 "PSCAT" 2274087 NIL PSCAT (NIL T T T) -9 NIL 2274327 NIL) (-992 2270725 2270941 2271341 "PSCAT-" 2271346 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-991 2269084 2269794 2270057 "PRTITION" 2270482 T PRTITION (NIL) -8 NIL NIL NIL) (-990 2268559 2268805 2268897 "PRTDAST" 2269012 T PRTDAST (NIL) -8 NIL NIL NIL) (-989 2257649 2259863 2262051 "PRS" 2266421 NIL PRS (NIL T T) -7 NIL NIL NIL) (-988 2255435 2256971 2257011 "PRQAGG" 2257194 NIL PRQAGG (NIL T) -9 NIL 2257296 NIL) (-987 2254771 2255076 2255104 "PROPLOG" 2255243 T PROPLOG (NIL) -9 NIL 2255358 NIL) (-986 2254375 2254432 2254555 "PROPFUN2" 2254694 NIL PROPFUN2 (NIL T T) -8 NIL NIL NIL) (-985 2253690 2253811 2253983 "PROPFUN1" 2254236 NIL PROPFUN1 (NIL T) -8 NIL NIL NIL) (-984 2251871 2252437 2252734 "PROPFRML" 2253426 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-983 2251340 2251447 2251575 "PROPERTY" 2251763 T PROPERTY (NIL) -8 NIL NIL NIL) (-982 2245398 2249506 2250326 "PRODUCT" 2250566 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-981 2242676 2244856 2245090 "PR" 2245209 NIL PR (NIL T T) -8 NIL NIL NIL) (-980 2242472 2242504 2242563 "PRINT" 2242637 T PRINT (NIL) -7 NIL NIL NIL) (-979 2241812 2241929 2242081 "PRIMES" 2242352 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-978 2239877 2240278 2240744 "PRIMELT" 2241391 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-977 2239606 2239655 2239683 "PRIMCAT" 2239807 T PRIMCAT (NIL) -9 NIL NIL NIL) (-976 2235724 2239544 2239589 "PRIMARR" 2239594 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-975 2234731 2234909 2235137 "PRIMARR2" 2235542 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-974 2234374 2234430 2234541 "PREASSOC" 2234669 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-973 2233849 2233982 2234010 "PPCURVE" 2234215 T PPCURVE (NIL) -9 NIL 2234351 NIL) (-972 2233444 2233644 2233727 "PORTNUM" 2233786 T PORTNUM (NIL) -8 NIL NIL NIL) (-971 2230803 2231202 2231794 "POLYROOT" 2233025 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-970 2224709 2230407 2230567 "POLY" 2230676 NIL POLY (NIL T) -8 NIL NIL NIL) (-969 2224092 2224150 2224384 "POLYLIFT" 2224645 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-968 2220367 2220816 2221445 "POLYCATQ" 2223637 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-967 2206709 2212114 2212179 "POLYCAT" 2215693 NIL POLYCAT (NIL T T T) -9 NIL 2217571 NIL) (-966 2200158 2202020 2204404 "POLYCAT-" 2204409 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-965 2199745 2199813 2199933 "POLY2UP" 2200084 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-964 2199377 2199434 2199543 "POLY2" 2199682 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-963 2198062 2198301 2198577 "POLUTIL" 2199151 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-962 2196417 2196694 2197025 "POLTOPOL" 2197784 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-961 2191883 2196351 2196398 "POINT" 2196403 NIL POINT (NIL T) -8 NIL NIL NIL) (-960 2190070 2190427 2190802 "PNTHEORY" 2191528 T PNTHEORY (NIL) -7 NIL NIL NIL) (-959 2188528 2188825 2189224 "PMTOOLS" 2189768 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-958 2188121 2188199 2188316 "PMSYM" 2188444 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-957 2187629 2187698 2187873 "PMQFCAT" 2188046 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-956 2186984 2187094 2187250 "PMPRED" 2187506 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-955 2186377 2186463 2186625 "PMPREDFS" 2186885 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-954 2185041 2185249 2185627 "PMPLCAT" 2186139 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-953 2184573 2184652 2184804 "PMLSAGG" 2184956 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-952 2184046 2184122 2184304 "PMKERNEL" 2184491 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-951 2183663 2183738 2183851 "PMINS" 2183965 NIL PMINS (NIL T) -7 NIL NIL NIL) (-950 2183105 2183174 2183383 "PMFS" 2183588 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-949 2182333 2182451 2182656 "PMDOWN" 2182982 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-948 2181500 2181658 2181839 "PMASS" 2182172 T PMASS (NIL) -7 NIL NIL NIL) (-947 2180773 2180883 2181046 "PMASSFS" 2181387 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-946 2180428 2180496 2180590 "PLOTTOOL" 2180699 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-945 2175035 2176239 2177387 "PLOT" 2179300 T PLOT (NIL) -8 NIL NIL NIL) (-944 2170839 2171883 2172804 "PLOT3D" 2174134 T PLOT3D (NIL) -8 NIL NIL NIL) (-943 2169751 2169928 2170163 "PLOT1" 2170643 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-942 2145142 2149817 2154668 "PLEQN" 2165017 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-941 2144460 2144582 2144762 "PINTERP" 2145007 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-940 2144153 2144200 2144303 "PINTERPA" 2144407 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-939 2143369 2143917 2144004 "PI" 2144044 T PI (NIL) -8 NIL NIL 2144111) (-938 2141652 2142627 2142655 "PID" 2142837 T PID (NIL) -9 NIL 2142971 NIL) (-937 2141403 2141440 2141515 "PICOERCE" 2141609 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-936 2140723 2140862 2141038 "PGROEB" 2141259 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-935 2136310 2137124 2138029 "PGE" 2139838 T PGE (NIL) -7 NIL NIL NIL) (-934 2134433 2134680 2135046 "PGCD" 2136027 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-933 2133771 2133874 2134035 "PFRPAC" 2134317 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-932 2130411 2132319 2132672 "PFR" 2133450 NIL PFR (NIL T) -8 NIL NIL NIL) (-931 2128800 2129044 2129369 "PFOTOOLS" 2130158 NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-930 2127333 2127572 2127923 "PFOQ" 2128557 NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-929 2125834 2126046 2126402 "PFO" 2127117 NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-928 2122387 2125723 2125792 "PF" 2125797 NIL PF (NIL NIL) -8 NIL NIL NIL) (-927 2119707 2120978 2121006 "PFECAT" 2121591 T PFECAT (NIL) -9 NIL 2121975 NIL) (-926 2119152 2119306 2119520 "PFECAT-" 2119525 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-925 2117755 2118007 2118308 "PFBRU" 2118901 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-924 2115621 2115973 2116405 "PFBR" 2117406 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-923 2111667 2113133 2113780 "PERM" 2115007 NIL PERM (NIL T) -8 NIL NIL NIL) (-922 2106901 2107874 2108744 "PERMGRP" 2110830 NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-921 2104965 2105925 2105966 "PERMCAT" 2106366 NIL PERMCAT (NIL T) -9 NIL 2106664 NIL) (-920 2104618 2104659 2104783 "PERMAN" 2104918 NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-919 2102109 2104283 2104405 "PENDTREE" 2104529 NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-918 2101038 2101253 2101294 "PDSPC" 2101827 NIL PDSPC (NIL T) -9 NIL 2102072 NIL) (-917 2100141 2100359 2100721 "PDSPC-" 2100726 NIL PDSPC- (NIL T T) -8 NIL NIL NIL) (-916 2099023 2099791 2099832 "PDRING" 2099837 NIL PDRING (NIL T) -9 NIL 2099865 NIL) (-915 2097910 2098528 2098582 "PDMOD" 2098587 NIL PDMOD (NIL T T) -9 NIL 2098691 NIL) (-914 2095125 2095903 2096571 "PDEPROB" 2097262 T PDEPROB (NIL) -8 NIL NIL NIL) (-913 2092670 2093174 2093729 "PDEPACK" 2094590 T PDEPACK (NIL) -7 NIL NIL NIL) (-912 2091582 2091772 2092023 "PDECOMP" 2092469 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-911 2089147 2089990 2090018 "PDECAT" 2090805 T PDECAT (NIL) -9 NIL 2091518 NIL) (-910 2088776 2088831 2088885 "PDDOM" 2089050 NIL PDDOM (NIL T T) -9 NIL 2089130 NIL) (-909 2088595 2088625 2088732 "PDDOM-" 2088737 NIL PDDOM- (NIL T T T) -8 NIL NIL NIL) (-908 2088346 2088379 2088469 "PCOMP" 2088556 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-907 2086524 2087147 2087444 "PBWLB" 2088075 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-906 2078997 2080597 2081935 "PATTERN" 2085207 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-905 2078629 2078686 2078795 "PATTERN2" 2078934 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-904 2076386 2076774 2077231 "PATTERN1" 2078218 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-903 2073754 2074335 2074816 "PATRES" 2075951 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-902 2073318 2073385 2073517 "PATRES2" 2073681 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-901 2071201 2071606 2072013 "PATMATCH" 2072985 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-900 2070697 2070906 2070947 "PATMAB" 2071054 NIL PATMAB (NIL T) -9 NIL 2071137 NIL) (-899 2069215 2069551 2069809 "PATLRES" 2070502 NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-898 2068761 2068884 2068925 "PATAB" 2068930 NIL PATAB (NIL T) -9 NIL 2069102 NIL) (-897 2066943 2067338 2067761 "PARTPERM" 2068358 T PARTPERM (NIL) -7 NIL NIL NIL) (-896 2066564 2066627 2066729 "PARSURF" 2066874 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-895 2066196 2066253 2066362 "PARSU2" 2066501 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-894 2065960 2066000 2066067 "PARSER" 2066149 T PARSER (NIL) -7 NIL NIL NIL) (-893 2065581 2065644 2065746 "PARSCURV" 2065891 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-892 2065213 2065270 2065379 "PARSC2" 2065518 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-891 2064852 2064910 2065007 "PARPCURV" 2065149 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-890 2064484 2064541 2064650 "PARPC2" 2064789 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-889 2063545 2063857 2064039 "PARAMAST" 2064322 T PARAMAST (NIL) -8 NIL NIL NIL) (-888 2063065 2063151 2063270 "PAN2EXPR" 2063446 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-887 2061842 2062186 2062414 "PALETTE" 2062857 T PALETTE (NIL) -8 NIL NIL NIL) (-886 2060235 2060847 2061207 "PAIR" 2061528 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-885 2053827 2059492 2059687 "PADICRC" 2060089 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-884 2046743 2053171 2053356 "PADICRAT" 2053674 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-883 2045058 2046680 2046725 "PADIC" 2046730 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-882 2042154 2043718 2043758 "PADICCT" 2044339 NIL PADICCT (NIL NIL) -9 NIL 2044621 NIL) (-881 2041111 2041311 2041579 "PADEPAC" 2041941 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-880 2040323 2040456 2040662 "PADE" 2040973 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-879 2038710 2039531 2039811 "OWP" 2040127 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-878 2038203 2038416 2038513 "OVERSET" 2038633 T OVERSET (NIL) -8 NIL NIL NIL) (-877 2037249 2037808 2037980 "OVAR" 2038071 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-876 2036513 2036634 2036795 "OUT" 2037108 T OUT (NIL) -7 NIL NIL NIL) (-875 2025385 2027622 2029822 "OUTFORM" 2034333 T OUTFORM (NIL) -8 NIL NIL NIL) (-874 2024721 2024982 2025109 "OUTBFILE" 2025278 T OUTBFILE (NIL) -8 NIL NIL NIL) (-873 2024028 2024193 2024221 "OUTBCON" 2024539 T OUTBCON (NIL) -9 NIL 2024705 NIL) (-872 2023629 2023741 2023898 "OUTBCON-" 2023903 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-871 2023009 2023358 2023447 "OSI" 2023560 T OSI (NIL) -8 NIL NIL NIL) (-870 2022512 2022850 2022878 "OSGROUP" 2022883 T OSGROUP (NIL) -9 NIL 2022905 NIL) (-869 2021257 2021484 2021769 "ORTHPOL" 2022259 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-868 2018808 2021092 2021213 "OREUP" 2021218 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-867 2016211 2018499 2018626 "ORESUP" 2018750 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-866 2013739 2014239 2014800 "OREPCTO" 2015700 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-865 2007411 2009612 2009653 "OREPCAT" 2012001 NIL OREPCAT (NIL T) -9 NIL 2013105 NIL) (-864 2004558 2005340 2006398 "OREPCAT-" 2006403 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-863 2003805 2004028 2004056 "ORDTYPE" 2004365 T ORDTYPE (NIL) -9 NIL 2004528 NIL) (-862 2003148 2003322 2003577 "ORDTYPE-" 2003582 NIL ORDTYPE- (NIL T) -8 NIL NIL NIL) (-861 2002718 2003016 2003044 "ORDSET" 2003049 T ORDSET (NIL) -9 NIL 2003071 NIL) (-860 2001256 2002047 2002075 "ORDRING" 2002277 T ORDRING (NIL) -9 NIL 2002402 NIL) (-859 2000901 2000995 2001139 "ORDRING-" 2001144 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-858 2000254 2000717 2000745 "ORDMON" 2000750 T ORDMON (NIL) -9 NIL 2000771 NIL) (-857 1999416 1999563 1999758 "ORDFUNS" 2000103 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-856 1998727 1999146 1999174 "ORDFIN" 1999239 T ORDFIN (NIL) -9 NIL 1999313 NIL) (-855 1995286 1997313 1997722 "ORDCOMP" 1998351 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-854 1994552 1994679 1994865 "ORDCOMP2" 1995146 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-853 1991133 1992043 1992857 "OPTPROB" 1993758 T OPTPROB (NIL) -8 NIL NIL NIL) (-852 1987935 1988574 1989278 "OPTPACK" 1990449 T OPTPACK (NIL) -7 NIL NIL NIL) (-851 1985608 1986374 1986402 "OPTCAT" 1987221 T OPTCAT (NIL) -9 NIL 1987871 NIL) (-850 1984992 1985285 1985390 "OPSIG" 1985523 T OPSIG (NIL) -8 NIL NIL NIL) (-849 1984760 1984799 1984865 "OPQUERY" 1984946 T OPQUERY (NIL) -7 NIL NIL NIL) (-848 1981891 1983071 1983575 "OP" 1984289 NIL OP (NIL T) -8 NIL NIL NIL) (-847 1981251 1981477 1981518 "OPERCAT" 1981730 NIL OPERCAT (NIL T) -9 NIL 1981827 NIL) (-846 1981006 1981062 1981179 "OPERCAT-" 1981184 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-845 1977819 1979803 1980172 "ONECOMP" 1980670 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-844 1977124 1977239 1977413 "ONECOMP2" 1977691 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-843 1976543 1976649 1976779 "OMSERVER" 1977014 T OMSERVER (NIL) -7 NIL NIL NIL) (-842 1973405 1975983 1976023 "OMSAGG" 1976084 NIL OMSAGG (NIL T) -9 NIL 1976148 NIL) (-841 1972028 1972291 1972573 "OMPKG" 1973143 T OMPKG (NIL) -7 NIL NIL NIL) (-840 1971458 1971561 1971589 "OM" 1971888 T OM (NIL) -9 NIL NIL NIL) (-839 1970005 1971007 1971176 "OMLO" 1971339 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-838 1968965 1969112 1969332 "OMEXPR" 1969831 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-837 1968256 1968511 1968647 "OMERR" 1968849 T OMERR (NIL) -8 NIL NIL NIL) (-836 1967407 1967677 1967837 "OMERRK" 1968116 T OMERRK (NIL) -8 NIL NIL NIL) (-835 1966858 1967084 1967192 "OMENC" 1967319 T OMENC (NIL) -8 NIL NIL NIL) (-834 1960753 1961938 1963109 "OMDEV" 1965707 T OMDEV (NIL) -8 NIL NIL NIL) (-833 1959822 1959993 1960187 "OMCONN" 1960579 T OMCONN (NIL) -8 NIL NIL NIL) (-832 1958316 1959292 1959320 "OINTDOM" 1959325 T OINTDOM (NIL) -9 NIL 1959346 NIL) (-831 1955654 1957004 1957341 "OFMONOID" 1958011 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-830 1955026 1955591 1955636 "ODVAR" 1955641 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-829 1952449 1954771 1954926 "ODR" 1954931 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-828 1944754 1952225 1952351 "ODPOL" 1952356 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-827 1938553 1944626 1944731 "ODP" 1944736 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-826 1937319 1937534 1937809 "ODETOOLS" 1938327 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-825 1934286 1934944 1935660 "ODESYS" 1936652 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-824 1929168 1930076 1931101 "ODERTRIC" 1933361 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-823 1928594 1928676 1928870 "ODERED" 1929080 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-822 1925482 1926030 1926707 "ODERAT" 1928017 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-821 1922441 1922906 1923503 "ODEPRRIC" 1925011 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-820 1920384 1920980 1921466 "ODEPROB" 1921975 T ODEPROB (NIL) -8 NIL NIL NIL) (-819 1916904 1917389 1918036 "ODEPRIM" 1919863 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-818 1916153 1916255 1916515 "ODEPAL" 1916796 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-817 1912315 1913106 1913970 "ODEPACK" 1915309 T ODEPACK (NIL) -7 NIL NIL NIL) (-816 1911376 1911483 1911705 "ODEINT" 1912204 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-815 1905477 1906902 1908349 "ODEIFTBL" 1909949 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-814 1900875 1901661 1902613 "ODEEF" 1904636 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-813 1900224 1900313 1900536 "ODECONST" 1900780 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-812 1898335 1898996 1899024 "ODECAT" 1899629 T ODECAT (NIL) -9 NIL 1900160 NIL) (-811 1895190 1898040 1898162 "OCT" 1898245 NIL OCT (NIL T) -8 NIL NIL NIL) (-810 1894828 1894871 1894998 "OCTCT2" 1895141 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-809 1889435 1891871 1891911 "OC" 1893008 NIL OC (NIL T) -9 NIL 1893866 NIL) (-808 1886662 1887410 1888400 "OC-" 1888494 NIL OC- (NIL T T) -8 NIL NIL NIL) (-807 1885987 1886455 1886483 "OCAMON" 1886488 T OCAMON (NIL) -9 NIL 1886509 NIL) (-806 1885491 1885832 1885860 "OASGP" 1885865 T OASGP (NIL) -9 NIL 1885885 NIL) (-805 1884725 1885214 1885242 "OAMONS" 1885282 T OAMONS (NIL) -9 NIL 1885325 NIL) (-804 1884112 1884545 1884573 "OAMON" 1884578 T OAMON (NIL) -9 NIL 1884598 NIL) (-803 1883343 1883861 1883889 "OAGROUP" 1883894 T OAGROUP (NIL) -9 NIL 1883914 NIL) (-802 1883033 1883083 1883171 "NUMTUBE" 1883287 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-801 1876606 1878124 1879660 "NUMQUAD" 1881517 T NUMQUAD (NIL) -7 NIL NIL NIL) (-800 1872362 1873350 1874375 "NUMODE" 1875601 T NUMODE (NIL) -7 NIL NIL NIL) (-799 1869703 1870583 1870611 "NUMINT" 1871534 T NUMINT (NIL) -9 NIL 1872298 NIL) (-798 1868651 1868848 1869066 "NUMFMT" 1869505 T NUMFMT (NIL) -7 NIL NIL NIL) (-797 1855010 1857955 1860487 "NUMERIC" 1866158 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-796 1849380 1854459 1854554 "NTSCAT" 1854559 NIL NTSCAT (NIL T T T T) -9 NIL 1854598 NIL) (-795 1848574 1848739 1848932 "NTPOLFN" 1849219 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-794 1836375 1845399 1846211 "NSUP" 1847795 NIL NSUP (NIL T) -8 NIL NIL NIL) (-793 1836007 1836064 1836173 "NSUP2" 1836312 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-792 1825957 1835781 1835914 "NSMP" 1835919 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-791 1824389 1824690 1825047 "NREP" 1825645 NIL NREP (NIL T) -7 NIL NIL NIL) (-790 1822980 1823232 1823590 "NPCOEF" 1824132 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-789 1822046 1822161 1822377 "NORMRETR" 1822861 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-788 1820087 1820377 1820786 "NORMPK" 1821754 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-787 1819772 1819800 1819924 "NORMMA" 1820053 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-786 1819572 1819729 1819758 "NONE" 1819763 T NONE (NIL) -8 NIL NIL NIL) (-785 1819361 1819390 1819459 "NONE1" 1819536 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-784 1818858 1818920 1819099 "NODE1" 1819293 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-783 1817139 1817990 1818245 "NNI" 1818592 T NNI (NIL) -8 NIL NIL 1818827) (-782 1815559 1815872 1816236 "NLINSOL" 1816807 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-781 1811800 1812795 1813694 "NIPROB" 1814680 T NIPROB (NIL) -8 NIL NIL NIL) (-780 1810557 1810791 1811093 "NFINTBAS" 1811562 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-779 1809731 1810207 1810248 "NETCLT" 1810420 NIL NETCLT (NIL T) -9 NIL 1810502 NIL) (-778 1808439 1808670 1808951 "NCODIV" 1809499 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-777 1808201 1808238 1808313 "NCNTFRAC" 1808396 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-776 1806381 1806745 1807165 "NCEP" 1807826 NIL NCEP (NIL T) -7 NIL NIL NIL) (-775 1805218 1805991 1806019 "NASRING" 1806129 T NASRING (NIL) -9 NIL 1806209 NIL) (-774 1805013 1805057 1805151 "NASRING-" 1805156 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-773 1804106 1804631 1804659 "NARNG" 1804776 T NARNG (NIL) -9 NIL 1804867 NIL) (-772 1803798 1803865 1803999 "NARNG-" 1804004 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-771 1802677 1802884 1803119 "NAGSP" 1803583 T NAGSP (NIL) -7 NIL NIL NIL) (-770 1793949 1795633 1797306 "NAGS" 1801024 T NAGS (NIL) -7 NIL NIL NIL) (-769 1792497 1792805 1793136 "NAGF07" 1793638 T NAGF07 (NIL) -7 NIL NIL NIL) (-768 1787035 1788326 1789633 "NAGF04" 1791210 T NAGF04 (NIL) -7 NIL NIL NIL) (-767 1780003 1781617 1783250 "NAGF02" 1785422 T NAGF02 (NIL) -7 NIL NIL NIL) (-766 1775227 1776327 1777444 "NAGF01" 1778906 T NAGF01 (NIL) -7 NIL NIL NIL) (-765 1768855 1770421 1772006 "NAGE04" 1773662 T NAGE04 (NIL) -7 NIL NIL NIL) (-764 1760024 1762145 1764275 "NAGE02" 1766745 T NAGE02 (NIL) -7 NIL NIL NIL) (-763 1755977 1756924 1757888 "NAGE01" 1759080 T NAGE01 (NIL) -7 NIL NIL NIL) (-762 1753772 1754306 1754864 "NAGD03" 1755439 T NAGD03 (NIL) -7 NIL NIL NIL) (-761 1745522 1747450 1749404 "NAGD02" 1751838 T NAGD02 (NIL) -7 NIL NIL NIL) (-760 1739333 1740758 1742198 "NAGD01" 1744102 T NAGD01 (NIL) -7 NIL NIL NIL) (-759 1735542 1736364 1737201 "NAGC06" 1738516 T NAGC06 (NIL) -7 NIL NIL NIL) (-758 1734007 1734339 1734695 "NAGC05" 1735206 T NAGC05 (NIL) -7 NIL NIL NIL) (-757 1733383 1733502 1733646 "NAGC02" 1733883 T NAGC02 (NIL) -7 NIL NIL NIL) (-756 1732328 1732911 1732951 "NAALG" 1733030 NIL NAALG (NIL T) -9 NIL 1733091 NIL) (-755 1732163 1732192 1732282 "NAALG-" 1732287 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-754 1726113 1727221 1728408 "MULTSQFR" 1731059 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-753 1725432 1725507 1725691 "MULTFACT" 1726025 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-752 1718103 1722017 1722070 "MTSCAT" 1723140 NIL MTSCAT (NIL T T) -9 NIL 1723655 NIL) (-751 1717815 1717869 1717961 "MTHING" 1718043 NIL MTHING (NIL T) -7 NIL NIL NIL) (-750 1717607 1717640 1717700 "MSYSCMD" 1717775 T MSYSCMD (NIL) -7 NIL NIL NIL) (-749 1713689 1716362 1716682 "MSET" 1717320 NIL MSET (NIL T) -8 NIL NIL NIL) (-748 1710758 1713250 1713291 "MSETAGG" 1713296 NIL MSETAGG (NIL T) -9 NIL 1713330 NIL) (-747 1706600 1708137 1708882 "MRING" 1710058 NIL MRING (NIL T T) -8 NIL NIL NIL) (-746 1706166 1706233 1706364 "MRF2" 1706527 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-745 1705784 1705819 1705963 "MRATFAC" 1706125 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-744 1703396 1703691 1704122 "MPRFF" 1705489 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-743 1697417 1703250 1703347 "MPOLY" 1703352 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-742 1696907 1696942 1697150 "MPCPF" 1697376 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-741 1696421 1696464 1696648 "MPC3" 1696858 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-740 1695616 1695697 1695918 "MPC2" 1696336 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-739 1693917 1694254 1694644 "MONOTOOL" 1695276 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-738 1693128 1693445 1693473 "MONOID" 1693692 T MONOID (NIL) -9 NIL 1693839 NIL) (-737 1692674 1692793 1692974 "MONOID-" 1692979 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-736 1682264 1688494 1688553 "MONOGEN" 1689227 NIL MONOGEN (NIL T T) -9 NIL 1689683 NIL) (-735 1679482 1680217 1681217 "MONOGEN-" 1681336 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-734 1678301 1678747 1678775 "MONADWU" 1679167 T MONADWU (NIL) -9 NIL 1679405 NIL) (-733 1677673 1677832 1678080 "MONADWU-" 1678085 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-732 1677018 1677262 1677290 "MONAD" 1677497 T MONAD (NIL) -9 NIL 1677609 NIL) (-731 1676703 1676781 1676913 "MONAD-" 1676918 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-730 1674992 1675616 1675895 "MOEBIUS" 1676456 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-729 1674256 1674660 1674700 "MODULE" 1674705 NIL MODULE (NIL T) -9 NIL 1674744 NIL) (-728 1673824 1673920 1674110 "MODULE-" 1674115 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-727 1671504 1672188 1672515 "MODRING" 1673648 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-726 1668448 1669609 1670130 "MODOP" 1671033 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-725 1667036 1667515 1667792 "MODMONOM" 1668311 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-724 1656804 1665327 1665741 "MODMON" 1666673 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-723 1653960 1655648 1655924 "MODFIELD" 1656679 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-722 1652937 1653241 1653431 "MMLFORM" 1653790 T MMLFORM (NIL) -8 NIL NIL NIL) (-721 1652463 1652506 1652685 "MMAP" 1652888 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-720 1650528 1651295 1651336 "MLO" 1651759 NIL MLO (NIL T) -9 NIL 1652001 NIL) (-719 1647894 1648410 1649012 "MLIFT" 1650009 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-718 1647285 1647369 1647523 "MKUCFUNC" 1647805 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-717 1646884 1646954 1647077 "MKRECORD" 1647208 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-716 1645931 1646093 1646321 "MKFUNC" 1646695 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-715 1645319 1645423 1645579 "MKFLCFN" 1645814 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-714 1644596 1644698 1644883 "MKBCFUNC" 1645212 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-713 1641185 1644150 1644286 "MINT" 1644480 T MINT (NIL) -8 NIL NIL NIL) (-712 1639997 1640240 1640517 "MHROWRED" 1640940 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-711 1635377 1638532 1638937 "MFLOAT" 1639612 T MFLOAT (NIL) -8 NIL NIL NIL) (-710 1634734 1634810 1634981 "MFINFACT" 1635289 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-709 1631049 1631897 1632781 "MESH" 1633870 T MESH (NIL) -7 NIL NIL NIL) (-708 1629439 1629751 1630104 "MDDFACT" 1630736 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-707 1626209 1628570 1628611 "MDAGG" 1628866 NIL MDAGG (NIL T) -9 NIL 1629009 NIL) (-706 1614903 1625502 1625709 "MCMPLX" 1626022 T MCMPLX (NIL) -8 NIL NIL NIL) (-705 1614040 1614186 1614387 "MCDEN" 1614752 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-704 1611930 1612200 1612580 "MCALCFN" 1613770 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-703 1610855 1611095 1611328 "MAYBE" 1611736 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-702 1608467 1608990 1609552 "MATSTOR" 1610326 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-701 1604379 1607839 1608087 "MATRIX" 1608252 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-700 1600145 1600852 1601588 "MATLIN" 1603736 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-699 1589971 1593202 1593279 "MATCAT" 1598311 NIL MATCAT (NIL T T T) -9 NIL 1599783 NIL) (-698 1586164 1587234 1588647 "MATCAT-" 1588652 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-697 1584758 1584911 1585244 "MATCAT2" 1585999 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-696 1582870 1583194 1583578 "MAPPKG3" 1584433 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-695 1581851 1582024 1582246 "MAPPKG2" 1582694 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-694 1580350 1580634 1580961 "MAPPKG1" 1581557 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-693 1579429 1579756 1579933 "MAPPAST" 1580193 T MAPPAST (NIL) -8 NIL NIL NIL) (-692 1579040 1579098 1579221 "MAPHACK3" 1579365 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-691 1578632 1578693 1578807 "MAPHACK2" 1578972 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-690 1578070 1578173 1578315 "MAPHACK1" 1578523 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-689 1576149 1576770 1577074 "MAGMA" 1577798 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-688 1575628 1575873 1575964 "MACROAST" 1576078 T MACROAST (NIL) -8 NIL NIL NIL) (-687 1572049 1573867 1574328 "M3D" 1575200 NIL M3D (NIL T) -8 NIL NIL NIL) (-686 1566099 1570360 1570401 "LZSTAGG" 1571183 NIL LZSTAGG (NIL T) -9 NIL 1571478 NIL) (-685 1562057 1563230 1564687 "LZSTAGG-" 1564692 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-684 1559144 1559948 1560435 "LWORD" 1561602 NIL LWORD (NIL T) -8 NIL NIL NIL) (-683 1558720 1558948 1559023 "LSTAST" 1559089 T LSTAST (NIL) -8 NIL NIL NIL) (-682 1551610 1558491 1558625 "LSQM" 1558630 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-681 1550834 1550973 1551201 "LSPP" 1551465 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-680 1548646 1548947 1549403 "LSMP" 1550523 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-679 1545425 1546099 1546829 "LSMP1" 1547948 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-678 1539227 1544515 1544556 "LSAGG" 1544618 NIL LSAGG (NIL T) -9 NIL 1544696 NIL) (-677 1535922 1536846 1538059 "LSAGG-" 1538064 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-676 1533521 1535066 1535315 "LPOLY" 1535717 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-675 1533103 1533188 1533311 "LPEFRAC" 1533430 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-674 1531424 1532197 1532450 "LO" 1532935 NIL LO (NIL T T T) -8 NIL NIL NIL) (-673 1531036 1531174 1531202 "LOGIC" 1531313 T LOGIC (NIL) -9 NIL 1531394 NIL) (-672 1530898 1530921 1530992 "LOGIC-" 1530997 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-671 1530091 1530231 1530424 "LODOOPS" 1530754 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-670 1527514 1530007 1530073 "LODO" 1530078 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-669 1526052 1526287 1526640 "LODOF" 1527261 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-668 1522256 1524687 1524728 "LODOCAT" 1525166 NIL LODOCAT (NIL T) -9 NIL 1525377 NIL) (-667 1521989 1522047 1522174 "LODOCAT-" 1522179 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-666 1519309 1521830 1521948 "LODO2" 1521953 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-665 1516744 1519246 1519291 "LODO1" 1519296 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-664 1515625 1515790 1516095 "LODEEF" 1516567 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-663 1510903 1513791 1513832 "LNAGG" 1514694 NIL LNAGG (NIL T) -9 NIL 1515129 NIL) (-662 1510050 1510264 1510606 "LNAGG-" 1510611 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-661 1506186 1506975 1507614 "LMOPS" 1509465 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-660 1505575 1505963 1506004 "LMODULE" 1506009 NIL LMODULE (NIL T) -9 NIL 1506035 NIL) (-659 1502776 1505220 1505343 "LMDICT" 1505485 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-658 1502394 1502566 1502607 "LLINSET" 1502668 NIL LLINSET (NIL T) -9 NIL 1502712 NIL) (-657 1502093 1502302 1502362 "LITERAL" 1502367 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-656 1495259 1501027 1501331 "LIST" 1501822 NIL LIST (NIL T) -8 NIL NIL NIL) (-655 1494784 1494858 1494997 "LIST3" 1495179 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-654 1493791 1493969 1494197 "LIST2" 1494602 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-653 1491925 1492237 1492636 "LIST2MAP" 1493438 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-652 1491556 1491744 1491785 "LINSET" 1491790 NIL LINSET (NIL T) -9 NIL 1491824 NIL) (-651 1489969 1490583 1490624 "LINEXP" 1491114 NIL LINEXP (NIL T) -9 NIL 1491387 NIL) (-650 1488546 1488806 1489117 "LINDEP" 1489721 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-649 1485313 1486032 1486809 "LIMITRF" 1487801 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-648 1483616 1483912 1484321 "LIMITPS" 1485008 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-647 1478044 1483127 1483355 "LIE" 1483437 NIL LIE (NIL T T) -8 NIL NIL NIL) (-646 1476978 1477447 1477487 "LIECAT" 1477627 NIL LIECAT (NIL T) -9 NIL 1477778 NIL) (-645 1476819 1476846 1476934 "LIECAT-" 1476939 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-644 1469412 1476359 1476515 "LIB" 1476683 T LIB (NIL) -8 NIL NIL NIL) (-643 1465047 1465930 1466865 "LGROBP" 1468529 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-642 1463045 1463319 1463669 "LF" 1464768 NIL LF (NIL T T) -7 NIL NIL NIL) (-641 1461885 1462577 1462605 "LFCAT" 1462812 T LFCAT (NIL) -9 NIL 1462951 NIL) (-640 1458787 1459417 1460105 "LEXTRIPK" 1461249 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-639 1455531 1456357 1456860 "LEXP" 1458367 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-638 1455007 1455252 1455344 "LETAST" 1455459 T LETAST (NIL) -8 NIL NIL NIL) (-637 1453405 1453718 1454119 "LEADCDET" 1454689 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-636 1452595 1452669 1452898 "LAZM3PK" 1453326 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-635 1447512 1450672 1451210 "LAUPOL" 1452107 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-634 1447091 1447135 1447296 "LAPLACE" 1447462 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-633 1445030 1446192 1446443 "LA" 1446924 NIL LA (NIL T T T) -8 NIL NIL NIL) (-632 1444010 1444594 1444635 "LALG" 1444697 NIL LALG (NIL T) -9 NIL 1444756 NIL) (-631 1443724 1443783 1443919 "LALG-" 1443924 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-630 1443559 1443583 1443624 "KVTFROM" 1443686 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-629 1442482 1442926 1443111 "KTVLOGIC" 1443394 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-628 1442317 1442341 1442382 "KRCFROM" 1442444 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-627 1441221 1441408 1441707 "KOVACIC" 1442117 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-626 1441056 1441080 1441121 "KONVERT" 1441183 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-625 1440891 1440915 1440956 "KOERCE" 1441018 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-624 1438722 1439484 1439861 "KERNEL" 1440547 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-623 1438218 1438299 1438431 "KERNEL2" 1438636 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-622 1431929 1436695 1436749 "KDAGG" 1437126 NIL KDAGG (NIL T T) -9 NIL 1437332 NIL) (-621 1431458 1431582 1431787 "KDAGG-" 1431792 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-620 1424606 1431119 1431274 "KAFILE" 1431336 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-619 1419034 1424117 1424345 "JORDAN" 1424427 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-618 1418413 1418683 1418804 "JOINAST" 1418933 T JOINAST (NIL) -8 NIL NIL NIL) (-617 1418259 1418318 1418373 "JAVACODE" 1418378 T JAVACODE (NIL) -8 NIL NIL NIL) (-616 1414486 1416436 1416490 "IXAGG" 1417419 NIL IXAGG (NIL T T) -9 NIL 1417878 NIL) (-615 1413405 1413711 1414130 "IXAGG-" 1414135 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-614 1408938 1413327 1413386 "IVECTOR" 1413391 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-613 1407704 1407941 1408207 "ITUPLE" 1408705 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-612 1406206 1406383 1406678 "ITRIGMNP" 1407526 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-611 1404951 1405155 1405438 "ITFUN3" 1405982 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-610 1404583 1404640 1404749 "ITFUN2" 1404888 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-609 1403742 1404063 1404237 "ITFORM" 1404429 T ITFORM (NIL) -8 NIL NIL NIL) (-608 1401703 1402762 1403040 "ITAYLOR" 1403497 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-607 1390648 1395840 1397003 "ISUPS" 1400573 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-606 1389752 1389892 1390128 "ISUMP" 1390495 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-605 1385130 1389697 1389738 "ISTRING" 1389743 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-604 1384606 1384851 1384943 "ISAST" 1385058 T ISAST (NIL) -8 NIL NIL NIL) (-603 1383815 1383897 1384113 "IRURPK" 1384520 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-602 1382751 1382952 1383192 "IRSN" 1383595 T IRSN (NIL) -7 NIL NIL NIL) (-601 1380822 1381177 1381606 "IRRF2F" 1382389 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-600 1380569 1380607 1380683 "IRREDFFX" 1380778 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-599 1379184 1379443 1379742 "IROOT" 1380302 NIL IROOT (NIL T) -7 NIL NIL NIL) (-598 1375788 1376868 1377560 "IR" 1378524 NIL IR (NIL T) -8 NIL NIL NIL) (-597 1374993 1375281 1375432 "IRFORM" 1375657 T IRFORM (NIL) -8 NIL NIL NIL) (-596 1372606 1373101 1373667 "IR2" 1374471 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-595 1371706 1371819 1372033 "IR2F" 1372489 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-594 1371497 1371531 1371591 "IPRNTPK" 1371666 T IPRNTPK (NIL) -7 NIL NIL NIL) (-593 1368078 1371386 1371455 "IPF" 1371460 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-592 1366405 1368003 1368060 "IPADIC" 1368065 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-591 1365717 1365965 1366095 "IP4ADDR" 1366295 T IP4ADDR (NIL) -8 NIL NIL NIL) (-590 1365091 1365346 1365478 "IOMODE" 1365605 T IOMODE (NIL) -8 NIL NIL NIL) (-589 1364164 1364688 1364815 "IOBFILE" 1364984 T IOBFILE (NIL) -8 NIL NIL NIL) (-588 1363652 1364068 1364096 "IOBCON" 1364101 T IOBCON (NIL) -9 NIL 1364122 NIL) (-587 1363163 1363221 1363404 "INVLAPLA" 1363588 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-586 1352811 1355165 1357551 "INTTR" 1360827 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-585 1349146 1349888 1350753 "INTTOOLS" 1351996 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-584 1348732 1348823 1348940 "INTSLPE" 1349049 T INTSLPE (NIL) -7 NIL NIL NIL) (-583 1346685 1348655 1348714 "INTRVL" 1348719 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-582 1344287 1344799 1345374 "INTRF" 1346170 NIL INTRF (NIL T) -7 NIL NIL NIL) (-581 1343698 1343795 1343937 "INTRET" 1344185 NIL INTRET (NIL T) -7 NIL NIL NIL) (-580 1341695 1342084 1342554 "INTRAT" 1343306 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-579 1338958 1339541 1340160 "INTPM" 1341180 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-578 1335703 1336302 1337040 "INTPAF" 1338344 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-577 1330882 1331844 1332895 "INTPACK" 1334672 T INTPACK (NIL) -7 NIL NIL NIL) (-576 1327694 1330679 1330788 "INT" 1330793 T INT (NIL) -8 NIL NIL NIL) (-575 1326946 1327098 1327306 "INTHERTR" 1327536 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-574 1326385 1326465 1326653 "INTHERAL" 1326860 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-573 1324231 1324674 1325131 "INTHEORY" 1325948 T INTHEORY (NIL) -7 NIL NIL NIL) (-572 1315637 1317258 1319030 "INTG0" 1322583 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-571 1296210 1301000 1305810 "INTFTBL" 1310847 T INTFTBL (NIL) -8 NIL NIL NIL) (-570 1295459 1295597 1295770 "INTFACT" 1296069 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-569 1292886 1293332 1293889 "INTEF" 1295013 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-568 1291239 1291978 1292006 "INTDOM" 1292307 T INTDOM (NIL) -9 NIL 1292514 NIL) (-567 1290608 1290782 1291024 "INTDOM-" 1291029 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-566 1286968 1288897 1288951 "INTCAT" 1289750 NIL INTCAT (NIL T) -9 NIL 1290071 NIL) (-565 1286440 1286543 1286671 "INTBIT" 1286860 T INTBIT (NIL) -7 NIL NIL NIL) (-564 1285139 1285293 1285600 "INTALG" 1286285 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-563 1284622 1284712 1284869 "INTAF" 1285043 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-562 1277971 1284432 1284572 "INTABL" 1284577 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-561 1277304 1277770 1277835 "INT8" 1277869 T INT8 (NIL) -8 NIL NIL 1277914) (-560 1276636 1277102 1277167 "INT64" 1277201 T INT64 (NIL) -8 NIL NIL 1277246) (-559 1275968 1276434 1276499 "INT32" 1276533 T INT32 (NIL) -8 NIL NIL 1276578) (-558 1275300 1275766 1275831 "INT16" 1275865 T INT16 (NIL) -8 NIL NIL 1275910) (-557 1269995 1272848 1272876 "INS" 1273810 T INS (NIL) -9 NIL 1274475 NIL) (-556 1267235 1268006 1268980 "INS-" 1269053 NIL INS- (NIL T) -8 NIL NIL NIL) (-555 1266010 1266237 1266535 "INPSIGN" 1266988 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-554 1265128 1265245 1265442 "INPRODPF" 1265890 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-553 1264022 1264139 1264376 "INPRODFF" 1265008 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-552 1263022 1263174 1263434 "INNMFACT" 1263858 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-551 1262219 1262316 1262504 "INMODGCD" 1262921 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-550 1260727 1260972 1261296 "INFSP" 1261964 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-549 1259911 1260028 1260211 "INFPROD0" 1260607 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-548 1256766 1257976 1258491 "INFORM" 1259404 T INFORM (NIL) -8 NIL NIL NIL) (-547 1256376 1256436 1256534 "INFORM1" 1256701 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-546 1255899 1255988 1256102 "INFINITY" 1256282 T INFINITY (NIL) -7 NIL NIL NIL) (-545 1255075 1255619 1255720 "INETCLTS" 1255818 T INETCLTS (NIL) -8 NIL NIL NIL) (-544 1253691 1253941 1254262 "INEP" 1254823 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-543 1252896 1253588 1253653 "INDE" 1253658 NIL INDE (NIL T) -8 NIL NIL NIL) (-542 1252460 1252528 1252645 "INCRMAPS" 1252823 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-541 1251278 1251729 1251935 "INBFILE" 1252274 T INBFILE (NIL) -8 NIL NIL NIL) (-540 1246577 1247514 1248458 "INBFF" 1250366 NIL INBFF (NIL T) -7 NIL NIL NIL) (-539 1245485 1245754 1245782 "INBCON" 1246295 T INBCON (NIL) -9 NIL 1246561 NIL) (-538 1244737 1244960 1245236 "INBCON-" 1245241 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-537 1244216 1244461 1244552 "INAST" 1244666 T INAST (NIL) -8 NIL NIL NIL) (-536 1243643 1243895 1244001 "IMPTAST" 1244130 T IMPTAST (NIL) -8 NIL NIL NIL) (-535 1240044 1243487 1243591 "IMATRIX" 1243596 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-534 1238752 1238875 1239191 "IMATQF" 1239900 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-533 1236972 1237199 1237536 "IMATLIN" 1238508 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-532 1231553 1236896 1236954 "ILIST" 1236959 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-531 1229461 1231413 1231526 "IIARRAY2" 1231531 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-530 1224859 1229372 1229436 "IFF" 1229441 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-529 1224206 1224476 1224592 "IFAST" 1224763 T IFAST (NIL) -8 NIL NIL NIL) (-528 1219204 1223498 1223686 "IFARRAY" 1224063 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-527 1218384 1219108 1219181 "IFAMON" 1219186 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-526 1217968 1218033 1218087 "IEVALAB" 1218294 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-525 1217643 1217711 1217871 "IEVALAB-" 1217876 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-524 1217233 1217557 1217620 "IDPO" 1217625 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-523 1216441 1217122 1217197 "IDPOAMS" 1217202 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-522 1215706 1216330 1216405 "IDPOAM" 1216410 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-521 1214563 1214880 1214933 "IDPC" 1215451 NIL IDPC (NIL T T) -9 NIL 1215642 NIL) (-520 1213990 1214455 1214528 "IDPAM" 1214533 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-519 1213324 1213882 1213955 "IDPAG" 1213960 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-518 1212969 1213160 1213235 "IDENT" 1213269 T IDENT (NIL) -8 NIL NIL NIL) (-517 1209224 1210072 1210967 "IDECOMP" 1212126 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-516 1202061 1203147 1204194 "IDEAL" 1208260 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-515 1201221 1201333 1201533 "ICDEN" 1201945 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-514 1200292 1200701 1200848 "ICARD" 1201094 T ICARD (NIL) -8 NIL NIL NIL) (-513 1198352 1198665 1199070 "IBPTOOLS" 1199969 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-512 1193959 1197972 1198085 "IBITS" 1198271 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-511 1190682 1191258 1191953 "IBATOOL" 1193376 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-510 1188461 1188923 1189456 "IBACHIN" 1190217 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-509 1186293 1188307 1188410 "IARRAY2" 1188415 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-508 1182402 1186219 1186276 "IARRAY1" 1186281 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-507 1176262 1180814 1181295 "IAN" 1181941 T IAN (NIL) -8 NIL NIL NIL) (-506 1175773 1175830 1176003 "IALGFACT" 1176199 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-505 1175301 1175414 1175442 "HYPCAT" 1175649 T HYPCAT (NIL) -9 NIL NIL NIL) (-504 1174839 1174956 1175142 "HYPCAT-" 1175147 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-503 1174434 1174634 1174717 "HOSTNAME" 1174776 T HOSTNAME (NIL) -8 NIL NIL NIL) (-502 1174279 1174316 1174357 "HOMOTOP" 1174362 NIL HOMOTOP (NIL T) -9 NIL 1174395 NIL) (-501 1170836 1172211 1172252 "HOAGG" 1173233 NIL HOAGG (NIL T) -9 NIL 1173962 NIL) (-500 1169430 1169829 1170355 "HOAGG-" 1170360 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-499 1163146 1169023 1169173 "HEXADEC" 1169300 T HEXADEC (NIL) -8 NIL NIL NIL) (-498 1161894 1162116 1162379 "HEUGCD" 1162923 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-497 1160970 1161731 1161861 "HELLFDIV" 1161866 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-496 1159152 1160747 1160835 "HEAP" 1160914 NIL HEAP (NIL T) -8 NIL NIL NIL) (-495 1158415 1158704 1158838 "HEADAST" 1159038 T HEADAST (NIL) -8 NIL NIL NIL) (-494 1152258 1158330 1158392 "HDP" 1158397 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-493 1145970 1151893 1152045 "HDMP" 1152159 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-492 1145294 1145434 1145598 "HB" 1145826 T HB (NIL) -7 NIL NIL NIL) (-491 1138686 1145140 1145244 "HASHTBL" 1145249 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-490 1138162 1138407 1138499 "HASAST" 1138614 T HASAST (NIL) -8 NIL NIL NIL) (-489 1135940 1137784 1137966 "HACKPI" 1138000 T HACKPI (NIL) -8 NIL NIL NIL) (-488 1131608 1135793 1135906 "GTSET" 1135911 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-487 1125029 1131486 1131584 "GSTBL" 1131589 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-486 1117416 1124194 1124450 "GSERIES" 1124829 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-485 1116543 1116960 1116988 "GROUP" 1117191 T GROUP (NIL) -9 NIL 1117325 NIL) (-484 1115909 1116068 1116319 "GROUP-" 1116324 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-483 1114276 1114597 1114984 "GROEBSOL" 1115586 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-482 1113176 1113464 1113515 "GRMOD" 1114044 NIL GRMOD (NIL T T) -9 NIL 1114212 NIL) (-481 1112944 1112980 1113108 "GRMOD-" 1113113 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-480 1108234 1109298 1110298 "GRIMAGE" 1111964 T GRIMAGE (NIL) -8 NIL NIL NIL) (-479 1106700 1106961 1107285 "GRDEF" 1107930 T GRDEF (NIL) -7 NIL NIL NIL) (-478 1106144 1106260 1106401 "GRAY" 1106579 T GRAY (NIL) -7 NIL NIL NIL) (-477 1105317 1105723 1105774 "GRALG" 1105927 NIL GRALG (NIL T T) -9 NIL 1106020 NIL) (-476 1104978 1105051 1105214 "GRALG-" 1105219 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-475 1101755 1104563 1104741 "GPOLSET" 1104885 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-474 1101109 1101166 1101424 "GOSPER" 1101692 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-473 1096841 1097547 1098073 "GMODPOL" 1100808 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-472 1095846 1096030 1096268 "GHENSEL" 1096653 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-471 1090002 1090845 1091865 "GENUPS" 1094930 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-470 1089699 1089750 1089839 "GENUFACT" 1089945 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-469 1089111 1089188 1089353 "GENPGCD" 1089617 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-468 1088585 1088620 1088833 "GENMFACT" 1089070 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-467 1087151 1087408 1087715 "GENEEZ" 1088328 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-466 1081023 1086762 1086924 "GDMP" 1087074 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-465 1070366 1074794 1075900 "GCNAALG" 1080006 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-464 1068679 1069541 1069569 "GCDDOM" 1069824 T GCDDOM (NIL) -9 NIL 1069981 NIL) (-463 1068149 1068276 1068491 "GCDDOM-" 1068496 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-462 1066821 1067006 1067310 "GB" 1067928 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-461 1055437 1057767 1060159 "GBINTERN" 1064512 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-460 1053274 1053566 1053987 "GBF" 1055112 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-459 1052055 1052220 1052487 "GBEUCLID" 1053090 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-458 1051404 1051529 1051678 "GAUSSFAC" 1051926 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-457 1049771 1050073 1050387 "GALUTIL" 1051123 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-456 1048079 1048353 1048677 "GALPOLYU" 1049498 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-455 1045444 1045734 1046141 "GALFACTU" 1047776 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-454 1037250 1038749 1040357 "GALFACT" 1043876 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-453 1034638 1035296 1035324 "FVFUN" 1036480 T FVFUN (NIL) -9 NIL 1037200 NIL) (-452 1033904 1034086 1034114 "FVC" 1034405 T FVC (NIL) -9 NIL 1034588 NIL) (-451 1033547 1033729 1033797 "FUNDESC" 1033856 T FUNDESC (NIL) -8 NIL NIL NIL) (-450 1033162 1033344 1033425 "FUNCTION" 1033499 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-449 1030906 1031484 1031950 "FT" 1032716 T FT (NIL) -8 NIL NIL NIL) (-448 1029697 1030207 1030410 "FTEM" 1030723 T FTEM (NIL) -8 NIL NIL NIL) (-447 1027988 1028277 1028674 "FSUPFACT" 1029388 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-446 1026385 1026674 1027006 "FST" 1027676 T FST (NIL) -8 NIL NIL NIL) (-445 1025584 1025690 1025878 "FSRED" 1026267 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-444 1024283 1024539 1024886 "FSPRMELT" 1025299 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-443 1021589 1022027 1022513 "FSPECF" 1023846 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-442 1002654 1011363 1011404 "FS" 1015288 NIL FS (NIL T) -9 NIL 1017577 NIL) (-441 991297 994290 998347 "FS-" 998647 NIL FS- (NIL T T) -8 NIL NIL NIL) (-440 990825 990879 991049 "FSINT" 991238 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-439 989117 989818 990121 "FSERIES" 990604 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-438 988159 988275 988499 "FSCINT" 988997 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-437 984367 987103 987144 "FSAGG" 987514 NIL FSAGG (NIL T) -9 NIL 987773 NIL) (-436 982129 982730 983526 "FSAGG-" 983621 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-435 981171 981314 981541 "FSAGG2" 981982 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-434 978849 979129 979677 "FS2UPS" 980889 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-433 978483 978526 978655 "FS2" 978800 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-432 977361 977532 977834 "FS2EXPXP" 978308 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-431 976787 976902 977054 "FRUTIL" 977241 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-430 968200 972282 973640 "FR" 975461 NIL FR (NIL T) -8 NIL NIL NIL) (-429 963214 965889 965929 "FRNAALG" 967249 NIL FRNAALG (NIL T) -9 NIL 967847 NIL) (-428 958887 959963 961238 "FRNAALG-" 961988 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-427 958525 958568 958695 "FRNAAF2" 958838 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-426 956900 957374 957670 "FRMOD" 958337 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-425 954643 955275 955593 "FRIDEAL" 956691 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-424 953834 953921 954212 "FRIDEAL2" 954550 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-423 952967 953381 953422 "FRETRCT" 953427 NIL FRETRCT (NIL T) -9 NIL 953603 NIL) (-422 952079 952310 952661 "FRETRCT-" 952666 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-421 949153 950363 950422 "FRAMALG" 951304 NIL FRAMALG (NIL T T) -9 NIL 951596 NIL) (-420 947287 947742 948372 "FRAMALG-" 948595 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-419 940930 946760 947037 "FRAC" 947042 NIL FRAC (NIL T) -8 NIL NIL NIL) (-418 940566 940623 940730 "FRAC2" 940867 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-417 940202 940259 940366 "FR2" 940503 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-416 934687 937581 937609 "FPS" 938728 T FPS (NIL) -9 NIL 939285 NIL) (-415 934136 934245 934409 "FPS-" 934555 NIL FPS- (NIL T) -8 NIL NIL NIL) (-414 931424 933093 933121 "FPC" 933346 T FPC (NIL) -9 NIL 933488 NIL) (-413 931217 931257 931354 "FPC-" 931359 NIL FPC- (NIL T) -8 NIL NIL NIL) (-412 930007 930705 930746 "FPATMAB" 930751 NIL FPATMAB (NIL T) -9 NIL 930903 NIL) (-411 928246 928749 929096 "FPARFRAC" 929723 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-410 923640 924138 924820 "FORTRAN" 927678 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-409 921356 921856 922395 "FORT" 923121 T FORT (NIL) -7 NIL NIL NIL) (-408 919032 919594 919622 "FORTFN" 920682 T FORTFN (NIL) -9 NIL 921306 NIL) (-407 918796 918846 918874 "FORTCAT" 918933 T FORTCAT (NIL) -9 NIL 918995 NIL) (-406 916902 917412 917802 "FORMULA" 918426 T FORMULA (NIL) -8 NIL NIL NIL) (-405 916690 916720 916789 "FORMULA1" 916866 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-404 916213 916265 916438 "FORDER" 916632 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-403 915309 915473 915666 "FOP" 916040 T FOP (NIL) -7 NIL NIL NIL) (-402 913890 914589 914763 "FNLA" 915191 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-401 912605 913020 913048 "FNCAT" 913508 T FNCAT (NIL) -9 NIL 913768 NIL) (-400 912144 912564 912592 "FNAME" 912597 T FNAME (NIL) -8 NIL NIL NIL) (-399 910680 911643 911671 "FMTC" 911676 T FMTC (NIL) -9 NIL 911712 NIL) (-398 909426 910616 910662 "FMONOID" 910667 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-397 906213 907381 907422 "FMONCAT" 908639 NIL FMONCAT (NIL T) -9 NIL 909244 NIL) (-396 905363 905955 906104 "FM" 906109 NIL FM (NIL T T) -8 NIL NIL NIL) (-395 902787 903433 903461 "FMFUN" 904605 T FMFUN (NIL) -9 NIL 905313 NIL) (-394 902056 902237 902265 "FMC" 902555 T FMC (NIL) -9 NIL 902737 NIL) (-393 899121 899981 900035 "FMCAT" 901230 NIL FMCAT (NIL T T) -9 NIL 901725 NIL) (-392 897987 898887 898987 "FM1" 899066 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-391 895761 896177 896671 "FLOATRP" 897538 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-390 889339 893490 894111 "FLOAT" 895160 T FLOAT (NIL) -8 NIL NIL NIL) (-389 886777 887277 887855 "FLOATCP" 888806 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-388 885425 886369 886410 "FLINEXP" 886415 NIL FLINEXP (NIL T) -9 NIL 886508 NIL) (-387 884579 884814 885142 "FLINEXP-" 885147 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-386 883655 883799 884023 "FLASORT" 884431 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-385 880757 881625 881677 "FLALG" 882904 NIL FLALG (NIL T T) -9 NIL 883371 NIL) (-384 874417 878166 878207 "FLAGG" 879469 NIL FLAGG (NIL T) -9 NIL 880121 NIL) (-383 873143 873482 873972 "FLAGG-" 873977 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-382 872185 872328 872555 "FLAGG2" 872996 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-381 869022 870030 870089 "FINRALG" 871217 NIL FINRALG (NIL T T) -9 NIL 871725 NIL) (-380 868182 868411 868750 "FINRALG-" 868755 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-379 867548 867787 867815 "FINITE" 868011 T FINITE (NIL) -9 NIL 868118 NIL) (-378 859891 862078 862118 "FINAALG" 865785 NIL FINAALG (NIL T) -9 NIL 867238 NIL) (-377 855223 856273 857417 "FINAALG-" 858796 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-376 854591 854978 855081 "FILE" 855153 NIL FILE (NIL T) -8 NIL NIL NIL) (-375 853235 853573 853627 "FILECAT" 854311 NIL FILECAT (NIL T T) -9 NIL 854527 NIL) (-374 850937 852465 852493 "FIELD" 852533 T FIELD (NIL) -9 NIL 852613 NIL) (-373 849557 849942 850453 "FIELD-" 850458 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-372 847407 848192 848539 "FGROUP" 849243 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-371 846497 846661 846881 "FGLMICPK" 847239 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-370 842329 846422 846479 "FFX" 846484 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-369 841930 841991 842126 "FFSLPE" 842262 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-368 837920 838702 839498 "FFPOLY" 841166 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-367 837424 837460 837669 "FFPOLY2" 837878 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-366 833270 837343 837406 "FFP" 837411 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-365 828668 833181 833245 "FF" 833250 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-364 823794 828011 828201 "FFNBX" 828522 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-363 818722 822929 823187 "FFNBP" 823648 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-362 813355 818006 818217 "FFNB" 818555 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-361 812187 812385 812700 "FFINTBAS" 813152 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-360 808213 810434 810462 "FFIELDC" 811082 T FFIELDC (NIL) -9 NIL 811458 NIL) (-359 806875 807246 807743 "FFIELDC-" 807748 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-358 806444 806490 806614 "FFHOM" 806817 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-357 804139 804626 805143 "FFF" 805959 NIL FFF (NIL T) -7 NIL NIL NIL) (-356 799757 803881 803982 "FFCGX" 804082 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-355 795379 799489 799596 "FFCGP" 799700 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-354 790562 795106 795214 "FFCG" 795315 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-353 770091 780294 780380 "FFCAT" 785545 NIL FFCAT (NIL T T T) -9 NIL 786996 NIL) (-352 765288 766336 767650 "FFCAT-" 768880 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-351 764699 764742 764977 "FFCAT2" 765239 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-350 754022 757671 758891 "FEXPR" 763551 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-349 752984 753419 753460 "FEVALAB" 753544 NIL FEVALAB (NIL T) -9 NIL 753805 NIL) (-348 752143 752353 752691 "FEVALAB-" 752696 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-347 750709 751526 751729 "FDIV" 752042 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-346 747715 748456 748571 "FDIVCAT" 750139 NIL FDIVCAT (NIL T T T T) -9 NIL 750576 NIL) (-345 747477 747504 747674 "FDIVCAT-" 747679 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-344 746697 746784 747061 "FDIV2" 747384 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-343 745671 745992 746194 "FCTRDATA" 746515 T FCTRDATA (NIL) -8 NIL NIL NIL) (-342 744357 744616 744905 "FCPAK1" 745402 T FCPAK1 (NIL) -7 NIL NIL NIL) (-341 743456 743857 743998 "FCOMP" 744248 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-340 727161 730606 734144 "FC" 739938 T FC (NIL) -8 NIL NIL NIL) (-339 719454 723482 723522 "FAXF" 725324 NIL FAXF (NIL T) -9 NIL 726016 NIL) (-338 716731 717388 718213 "FAXF-" 718678 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-337 711786 716107 716283 "FARRAY" 716588 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-336 706666 708733 708786 "FAMR" 709809 NIL FAMR (NIL T T) -9 NIL 710269 NIL) (-335 705556 705858 706293 "FAMR-" 706298 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-334 704725 705478 705531 "FAMONOID" 705536 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-333 702497 703207 703260 "FAMONC" 704201 NIL FAMONC (NIL T T) -9 NIL 704587 NIL) (-332 701161 702251 702388 "FAGROUP" 702393 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-331 698956 699275 699678 "FACUTIL" 700842 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-330 698055 698240 698462 "FACTFUNC" 698766 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-329 690477 697358 697557 "EXPUPXS" 697911 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-328 687960 688500 689086 "EXPRTUBE" 689911 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-327 684231 684823 685553 "EXPRODE" 687299 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-326 669715 682880 683309 "EXPR" 683835 NIL EXPR (NIL T) -8 NIL NIL NIL) (-325 664269 664856 665662 "EXPR2UPS" 669013 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-324 663901 663958 664067 "EXPR2" 664206 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-323 654898 663052 663343 "EXPEXPAN" 663737 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-322 654698 654855 654884 "EXIT" 654889 T EXIT (NIL) -8 NIL NIL NIL) (-321 654178 654422 654513 "EXITAST" 654627 T EXITAST (NIL) -8 NIL NIL NIL) (-320 653805 653867 653980 "EVALCYC" 654110 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-319 653346 653464 653505 "EVALAB" 653675 NIL EVALAB (NIL T) -9 NIL 653779 NIL) (-318 652827 652949 653170 "EVALAB-" 653175 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-317 650181 651483 651511 "EUCDOM" 652066 T EUCDOM (NIL) -9 NIL 652416 NIL) (-316 648586 649028 649618 "EUCDOM-" 649623 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-315 636125 638884 641634 "ESTOOLS" 645856 T ESTOOLS (NIL) -7 NIL NIL NIL) (-314 635757 635814 635923 "ESTOOLS2" 636062 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-313 635508 635550 635630 "ESTOOLS1" 635709 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-312 629531 631139 631167 "ES" 633935 T ES (NIL) -9 NIL 635345 NIL) (-311 624478 625765 627582 "ES-" 627746 NIL ES- (NIL T) -8 NIL NIL NIL) (-310 620852 621613 622393 "ESCONT" 623718 T ESCONT (NIL) -7 NIL NIL NIL) (-309 620597 620629 620711 "ESCONT1" 620814 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-308 620272 620322 620422 "ES2" 620541 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-307 619902 619960 620069 "ES1" 620208 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-306 619118 619247 619423 "ERROR" 619746 T ERROR (NIL) -7 NIL NIL NIL) (-305 612516 618977 619068 "EQTBL" 619073 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-304 605019 607830 609279 "EQ" 611100 NIL -3042 (NIL T) -8 NIL NIL NIL) (-303 604651 604708 604817 "EQ2" 604956 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-302 599942 600989 602082 "EP" 603590 NIL EP (NIL T) -7 NIL NIL NIL) (-301 598542 598833 599139 "ENV" 599656 T ENV (NIL) -8 NIL NIL NIL) (-300 597622 598176 598204 "ENTIRER" 598209 T ENTIRER (NIL) -9 NIL 598255 NIL) (-299 594316 595804 596165 "EMR" 597430 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-298 593446 593631 593685 "ELTAGG" 594065 NIL ELTAGG (NIL T T) -9 NIL 594276 NIL) (-297 593165 593227 593368 "ELTAGG-" 593373 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-296 592929 592958 593012 "ELTAB" 593096 NIL ELTAB (NIL T T) -9 NIL 593148 NIL) (-295 592055 592201 592400 "ELFUTS" 592780 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-294 591797 591853 591881 "ELEMFUN" 591986 T ELEMFUN (NIL) -9 NIL NIL NIL) (-293 591667 591688 591756 "ELEMFUN-" 591761 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-292 586456 589709 589750 "ELAGG" 590690 NIL ELAGG (NIL T) -9 NIL 591153 NIL) (-291 584741 585175 585838 "ELAGG-" 585843 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-290 584053 584190 584346 "ELABOR" 584605 T ELABOR (NIL) -8 NIL NIL NIL) (-289 582714 582993 583287 "ELABEXPR" 583779 T ELABEXPR (NIL) -8 NIL NIL NIL) (-288 575548 577351 578180 "EFUPXS" 581989 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-287 568996 570797 571608 "EFULS" 574823 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-286 566481 566839 567311 "EFSTRUC" 568628 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-285 556272 557838 559386 "EF" 564996 NIL EF (NIL T T) -7 NIL NIL NIL) (-284 555346 555757 555906 "EAB" 556143 T EAB (NIL) -8 NIL NIL NIL) (-283 554528 555305 555333 "E04UCFA" 555338 T E04UCFA (NIL) -8 NIL NIL NIL) (-282 553710 554487 554515 "E04NAFA" 554520 T E04NAFA (NIL) -8 NIL NIL NIL) (-281 552892 553669 553697 "E04MBFA" 553702 T E04MBFA (NIL) -8 NIL NIL NIL) (-280 552074 552851 552879 "E04JAFA" 552884 T E04JAFA (NIL) -8 NIL NIL NIL) (-279 551258 552033 552061 "E04GCFA" 552066 T E04GCFA (NIL) -8 NIL NIL NIL) (-278 550442 551217 551245 "E04FDFA" 551250 T E04FDFA (NIL) -8 NIL NIL NIL) (-277 549624 550401 550429 "E04DGFA" 550434 T E04DGFA (NIL) -8 NIL NIL NIL) (-276 543797 545149 546513 "E04AGNT" 548280 T E04AGNT (NIL) -7 NIL NIL NIL) (-275 542555 543098 543138 "DVARCAT" 543479 NIL DVARCAT (NIL T) -9 NIL 543642 NIL) (-274 541759 541971 542285 "DVARCAT-" 542290 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-273 534620 541558 541687 "DSMP" 541692 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-272 533043 533762 533803 "DSEXT" 534166 NIL DSEXT (NIL T) -9 NIL 534460 NIL) (-271 531328 531756 532422 "DSEXT-" 532427 NIL DSEXT- (NIL T T) -8 NIL NIL NIL) (-270 526109 527273 528341 "DROPT" 530280 T DROPT (NIL) -8 NIL NIL NIL) (-269 525774 525833 525931 "DROPT1" 526044 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-268 520889 522015 523152 "DROPT0" 524657 T DROPT0 (NIL) -7 NIL NIL NIL) (-267 519234 519559 519945 "DRAWPT" 520523 T DRAWPT (NIL) -7 NIL NIL NIL) (-266 513821 514744 515823 "DRAW" 518208 NIL DRAW (NIL T) -7 NIL NIL NIL) (-265 513454 513507 513625 "DRAWHACK" 513762 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-264 512185 512454 512745 "DRAWCX" 513183 T DRAWCX (NIL) -7 NIL NIL NIL) (-263 511700 511769 511920 "DRAWCURV" 512111 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-262 502168 504130 506245 "DRAWCFUN" 509605 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-261 498907 500833 500874 "DQAGG" 501503 NIL DQAGG (NIL T) -9 NIL 501777 NIL) (-260 486372 493118 493201 "DPOLCAT" 495053 NIL DPOLCAT (NIL T T T T) -9 NIL 495598 NIL) (-259 481209 482557 484515 "DPOLCAT-" 484520 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-258 474556 481070 481168 "DPMO" 481173 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-257 467806 474336 474503 "DPMM" 474508 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-256 467376 467590 467679 "DOMTMPLT" 467737 T DOMTMPLT (NIL) -8 NIL NIL NIL) (-255 466809 467178 467258 "DOMCTOR" 467316 T DOMCTOR (NIL) -8 NIL NIL NIL) (-254 466021 466289 466440 "DOMAIN" 466678 T DOMAIN (NIL) -8 NIL NIL NIL) (-253 459733 465656 465808 "DMP" 465922 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-252 457678 458800 458841 "DMEXT" 458846 NIL DMEXT (NIL T) -9 NIL 459022 NIL) (-251 457278 457334 457478 "DLP" 457616 NIL DLP (NIL T) -7 NIL NIL NIL) (-250 451103 456605 456795 "DLIST" 457120 NIL DLIST (NIL T) -8 NIL NIL NIL) (-249 447875 449928 449969 "DLAGG" 450519 NIL DLAGG (NIL T) -9 NIL 450749 NIL) (-248 446537 447201 447229 "DIVRING" 447321 T DIVRING (NIL) -9 NIL 447404 NIL) (-247 445774 445964 446264 "DIVRING-" 446269 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-246 443876 444233 444639 "DISPLAY" 445388 T DISPLAY (NIL) -7 NIL NIL NIL) (-245 437739 443790 443853 "DIRPROD" 443858 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-244 436587 436790 437055 "DIRPROD2" 437532 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-243 425262 431298 431351 "DIRPCAT" 431609 NIL DIRPCAT (NIL NIL T) -9 NIL 432484 NIL) (-242 422588 423230 424111 "DIRPCAT-" 424448 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-241 421875 422035 422221 "DIOSP" 422422 T DIOSP (NIL) -7 NIL NIL NIL) (-240 418505 420759 420800 "DIOPS" 421234 NIL DIOPS (NIL T) -9 NIL 421463 NIL) (-239 418054 418168 418359 "DIOPS-" 418364 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-238 417105 417733 417761 "DIFRING" 417766 T DIFRING (NIL) -9 NIL 417788 NIL) (-237 416777 416851 416879 "DIFFSPC" 416998 T DIFFSPC (NIL) -9 NIL 417073 NIL) (-236 416422 416500 416652 "DIFFSPC-" 416657 NIL DIFFSPC- (NIL T) -8 NIL NIL NIL) (-235 415478 415956 415997 "DIFFMOD" 416002 NIL DIFFMOD (NIL T) -9 NIL 416100 NIL) (-234 415186 415231 415272 "DIFFDOM" 415393 NIL DIFFDOM (NIL T) -9 NIL 415461 NIL) (-233 415039 415063 415147 "DIFFDOM-" 415152 NIL DIFFDOM- (NIL T T) -8 NIL NIL NIL) (-232 412971 414243 414284 "DIFEXT" 414289 NIL DIFEXT (NIL T) -9 NIL 414442 NIL) (-231 410221 412475 412516 "DIAGG" 412521 NIL DIAGG (NIL T) -9 NIL 412541 NIL) (-230 409605 409762 410014 "DIAGG-" 410019 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-229 404977 408564 408841 "DHMATRIX" 409374 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-228 400589 401498 402508 "DFSFUN" 403987 T DFSFUN (NIL) -7 NIL NIL NIL) (-227 395667 399520 399832 "DFLOAT" 400297 T DFLOAT (NIL) -8 NIL NIL NIL) (-226 393930 394211 394600 "DFINTTLS" 395375 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-225 390959 391951 392351 "DERHAM" 393596 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-224 388763 390734 390823 "DEQUEUE" 390903 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-223 388017 388150 388333 "DEGRED" 388625 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-222 384447 385192 386038 "DEFINTRF" 387245 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-221 382002 382471 383063 "DEFINTEF" 383966 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-220 381352 381622 381737 "DEFAST" 381907 T DEFAST (NIL) -8 NIL NIL NIL) (-219 375068 380945 381095 "DECIMAL" 381222 T DECIMAL (NIL) -8 NIL NIL NIL) (-218 372580 373038 373544 "DDFACT" 374612 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-217 372176 372219 372370 "DBLRESP" 372531 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-216 370044 370406 370767 "DBASE" 371942 NIL DBASE (NIL T) -8 NIL NIL NIL) (-215 369286 369524 369670 "DATAARY" 369943 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-214 368392 369245 369273 "D03FAFA" 369278 T D03FAFA (NIL) -8 NIL NIL NIL) (-213 367499 368351 368379 "D03EEFA" 368384 T D03EEFA (NIL) -8 NIL NIL NIL) (-212 365449 365915 366404 "D03AGNT" 367030 T D03AGNT (NIL) -7 NIL NIL NIL) (-211 364738 365408 365436 "D02EJFA" 365441 T D02EJFA (NIL) -8 NIL NIL NIL) (-210 364027 364697 364725 "D02CJFA" 364730 T D02CJFA (NIL) -8 NIL NIL NIL) (-209 363316 363986 364014 "D02BHFA" 364019 T D02BHFA (NIL) -8 NIL NIL NIL) (-208 362605 363275 363303 "D02BBFA" 363308 T D02BBFA (NIL) -8 NIL NIL NIL) (-207 355802 357391 358997 "D02AGNT" 361019 T D02AGNT (NIL) -7 NIL NIL NIL) (-206 353570 354093 354639 "D01WGTS" 355276 T D01WGTS (NIL) -7 NIL NIL NIL) (-205 352637 353529 353557 "D01TRNS" 353562 T D01TRNS (NIL) -8 NIL NIL NIL) (-204 351705 352596 352624 "D01GBFA" 352629 T D01GBFA (NIL) -8 NIL NIL NIL) (-203 350773 351664 351692 "D01FCFA" 351697 T D01FCFA (NIL) -8 NIL NIL NIL) (-202 349841 350732 350760 "D01ASFA" 350765 T D01ASFA (NIL) -8 NIL NIL NIL) (-201 348909 349800 349828 "D01AQFA" 349833 T D01AQFA (NIL) -8 NIL NIL NIL) (-200 347977 348868 348896 "D01APFA" 348901 T D01APFA (NIL) -8 NIL NIL NIL) (-199 347045 347936 347964 "D01ANFA" 347969 T D01ANFA (NIL) -8 NIL NIL NIL) (-198 346113 347004 347032 "D01AMFA" 347037 T D01AMFA (NIL) -8 NIL NIL NIL) (-197 345181 346072 346100 "D01ALFA" 346105 T D01ALFA (NIL) -8 NIL NIL NIL) (-196 344249 345140 345168 "D01AKFA" 345173 T D01AKFA (NIL) -8 NIL NIL NIL) (-195 343317 344208 344236 "D01AJFA" 344241 T D01AJFA (NIL) -8 NIL NIL NIL) (-194 336612 338165 339726 "D01AGNT" 341776 T D01AGNT (NIL) -7 NIL NIL NIL) (-193 335949 336077 336229 "CYCLOTOM" 336480 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-192 332682 333397 334124 "CYCLES" 335242 T CYCLES (NIL) -7 NIL NIL NIL) (-191 331994 332128 332299 "CVMP" 332543 NIL CVMP (NIL T) -7 NIL NIL NIL) (-190 329835 330093 330462 "CTRIGMNP" 331722 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-189 329271 329629 329702 "CTOR" 329782 T CTOR (NIL) -8 NIL NIL NIL) (-188 328780 329002 329103 "CTORKIND" 329190 T CTORKIND (NIL) -8 NIL NIL NIL) (-187 328057 328373 328401 "CTORCAT" 328583 T CTORCAT (NIL) -9 NIL 328696 NIL) (-186 327655 327766 327925 "CTORCAT-" 327930 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-185 327117 327329 327437 "CTORCALL" 327579 NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-184 326491 326590 326743 "CSTTOOLS" 327014 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-183 322290 322947 323705 "CRFP" 325803 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-182 321765 322011 322103 "CRCEAST" 322218 T CRCEAST (NIL) -8 NIL NIL NIL) (-181 320812 320997 321225 "CRAPACK" 321569 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-180 320196 320297 320501 "CPMATCH" 320688 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-179 319921 319949 320055 "CPIMA" 320162 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-178 316269 316941 317660 "COORDSYS" 319256 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-177 315681 315802 315944 "CONTOUR" 316147 T CONTOUR (NIL) -8 NIL NIL NIL) (-176 311572 313684 314176 "CONTFRAC" 315221 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-175 311452 311473 311501 "CONDUIT" 311538 T CONDUIT (NIL) -9 NIL NIL NIL) (-174 310526 311080 311108 "COMRING" 311113 T COMRING (NIL) -9 NIL 311165 NIL) (-173 309580 309884 310068 "COMPPROP" 310362 T COMPPROP (NIL) -8 NIL NIL NIL) (-172 309241 309276 309404 "COMPLPAT" 309539 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-171 298544 309050 309159 "COMPLEX" 309164 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-170 298180 298237 298344 "COMPLEX2" 298481 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-169 297519 297640 297800 "COMPILER" 298040 T COMPILER (NIL) -8 NIL NIL NIL) (-168 297237 297272 297370 "COMPFACT" 297478 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-167 279516 290941 290981 "COMPCAT" 291985 NIL COMPCAT (NIL T) -9 NIL 293333 NIL) (-166 269028 271955 275582 "COMPCAT-" 275938 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-165 268757 268785 268888 "COMMUPC" 268994 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-164 268551 268585 268644 "COMMONOP" 268718 T COMMONOP (NIL) -7 NIL NIL NIL) (-163 268107 268302 268389 "COMM" 268484 T COMM (NIL) -8 NIL NIL NIL) 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T) ((-23) . T) ((-47 |#1| #0=(-576)) . T) ((-25) . T) ((-38 #1=(-419 (-576))) -2758 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-38 |#1|) |has| |#1| (-174)) ((-38 |#2|) |has| |#1| (-374)) ((-38 $) -2758 (|has| |#1| (-568)) (|has| |#1| (-374))) ((-35) |has| |#1| (-38 (-419 (-576)))) ((-95) |has| |#1| (-38 (-419 (-576)))) ((-102) . T) ((-111 #1# #1#) -2758 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-111 |#1| |#1|) . T) ((-111 |#2| |#2|) |has| |#1| (-374)) ((-111 $ $) -2758 (|has| |#1| (-568)) (|has| |#1| (-374)) (|has| |#1| (-174))) ((-132) . T) ((-146) -2758 (-12 (|has| |#1| (-374)) (|has| |#2| (-146))) (|has| |#1| (-146))) ((-148) -2758 (-12 (|has| |#1| (-374)) (|has| |#2| (-148))) (|has| |#1| (-148))) ((-628 #1#) -2758 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-628 (-576)) . T) ((-628 #2=(-1197)) -12 (|has| |#1| (-374)) (|has| |#2| (-1059 (-1197)))) ((-628 |#1|) |has| |#1| (-174)) ((-628 |#2|) . T) ((-628 $) -2758 (|has| |#1| (-568)) (|has| |#1| (-374))) ((-625 (-876)) . T) ((-174) -2758 (|has| |#1| (-568)) (|has| |#1| (-374)) (|has| |#1| (-174))) ((-626 (-227)) -12 (|has| |#1| (-374)) (|has| |#2| (-1043))) ((-626 (-390)) -12 (|has| |#1| (-374)) (|has| |#2| (-1043))) ((-626 (-548)) -12 (|has| |#1| (-374)) (|has| |#2| (-626 (-548)))) ((-626 (-907 (-390))) -12 (|has| |#1| (-374)) (|has| |#2| (-626 (-907 (-390))))) ((-626 (-907 (-576))) -12 (|has| |#1| (-374)) (|has| |#2| (-626 (-907 (-576))))) ((-234 $) -2758 (-12 (|has| |#1| (-374)) (|has| |#2| (-237))) (-12 (|has| |#1| (-374)) (|has| |#2| (-238))) (|has| |#1| (-15 * (|#1| (-576) |#1|)))) ((-232 |#2|) |has| |#1| (-374)) ((-238) -2758 (-12 (|has| |#1| (-374)) (|has| |#2| (-238))) (|has| |#1| (-15 * (|#1| (-576) |#1|)))) ((-237) -2758 (-12 (|has| |#1| (-374)) (|has| |#2| (-237))) (-12 (|has| |#1| (-374)) (|has| |#2| (-238))) (|has| |#1| (-15 * (|#1| (-576) |#1|)))) ((-272 |#2|) |has| |#1| (-374)) ((-248) |has| |#1| (-374)) ((-294) |has| |#1| (-38 (-419 (-576)))) ((-296 #0# |#1|) . T) ((-296 |#2| $) -12 (|has| |#1| (-374)) (|has| |#2| (-296 |#2| |#2|))) ((-296 $ $) |has| (-576) (-1133)) ((-300) -2758 (|has| |#1| (-568)) (|has| |#1| (-374))) ((-317) |has| |#1| (-374)) ((-319 |#2|) -12 (|has| |#1| (-374)) (|has| |#2| (-319 |#2|))) ((-374) |has| |#1| (-374)) ((-349 |#2|) |has| |#1| (-374)) ((-388 |#2|) |has| |#1| (-374)) ((-412 |#2|) |has| |#1| (-374)) ((-464) |has| |#1| (-374)) ((-505) |has| |#1| (-38 (-419 (-576)))) ((-526 (-1197) |#2|) -12 (|has| |#1| (-374)) (|has| |#2| (-526 (-1197) |#2|))) ((-526 |#2| |#2|) -12 (|has| |#1| (-374)) (|has| |#2| (-319 |#2|))) ((-568) -2758 (|has| |#1| (-568)) (|has| |#1| (-374))) ((-658 #1#) -2758 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-658 (-576)) . T) ((-658 |#1|) . T) ((-658 |#2|) |has| |#1| (-374)) ((-658 $) . T) ((-660 #1#) -2758 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-660 #3=(-576)) -12 (|has| |#1| (-374)) (|has| |#2| (-651 (-576)))) ((-660 |#1|) . T) ((-660 |#2|) |has| |#1| (-374)) ((-660 $) . T) ((-652 #1#) -2758 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-652 |#1|) |has| |#1| (-174)) ((-652 |#2|) |has| |#1| (-374)) ((-652 $) -2758 (|has| |#1| (-568)) (|has| |#1| (-374))) ((-651 #3#) -12 (|has| |#1| (-374)) (|has| |#2| (-651 (-576)))) ((-651 |#2|) |has| |#1| (-374)) ((-729 #1#) -2758 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-729 |#1|) |has| |#1| (-174)) ((-729 |#2|) |has| |#1| (-374)) ((-729 $) -2758 (|has| |#1| (-568)) (|has| |#1| (-374))) ((-738) . 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T) ((-939) |has| |#1| (-374)) ((-1013 |#2|) |has| |#1| (-374)) ((-1023) |has| |#1| (-38 (-419 (-576)))) ((-1043) -12 (|has| |#1| (-374)) (|has| |#2| (-1043))) ((-1059 (-419 (-576))) -12 (|has| |#1| (-374)) (|has| |#2| (-1059 (-576)))) ((-1059 (-576)) -12 (|has| |#1| (-374)) (|has| |#2| (-1059 (-576)))) ((-1059 #2#) -12 (|has| |#1| (-374)) (|has| |#2| (-1059 (-1197)))) ((-1059 |#2|) . T) ((-1072 #1#) -2758 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-1072 |#1|) . T) ((-1072 |#2|) |has| |#1| (-374)) ((-1072 $) -2758 (|has| |#1| (-568)) (|has| |#1| (-374)) (|has| |#1| (-174))) ((-1077 #1#) -2758 (|has| |#1| (-374)) (|has| |#1| (-38 (-419 (-576))))) ((-1077 |#1|) . T) ((-1077 |#2|) |has| |#1| (-374)) ((-1077 $) -2758 (|has| |#1| (-568)) (|has| |#1| (-374)) (|has| |#1| (-174))) ((-1070) . T) ((-1079) . T) ((-1133) . T) ((-1121) . T) ((-1173) -12 (|has| |#1| (-374)) (|has| |#2| (-1173))) ((-1223) |has| |#1| (-38 (-419 (-576)))) ((-1226) |has| |#1| (-38 (-419 (-576)))) ((-1238) . T) ((-1242) |has| |#1| (-374)) ((-1248 |#1|) . T) ((-1266 |#1| #0#) . 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T) ((-1077 $) -2758 (|has| |#1| (-568)) (|has| |#1| (-374)) (|has| |#1| (-174))) ((-1070) . T) ((-1079) . T) ((-1133) . T) ((-1121) . T) ((-1223) |has| |#1| (-38 (-419 (-576)))) ((-1226) |has| |#1| (-38 (-419 (-576)))) ((-1238) . T) ((-1242) |has| |#1| (-374)) ((-1266 |#1| #0#) . T) ((-1269 |#1|) . 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T) ((-23) . T) ((-47 |#1| #0=(-783)) . T) ((-25) . T) ((-38 #1=(-419 (-576))) |has| |#1| (-38 (-419 (-576)))) ((-38 |#1|) |has| |#1| (-174)) ((-38 $) |has| |#1| (-568)) ((-35) |has| |#1| (-38 (-419 (-576)))) ((-95) |has| |#1| (-38 (-419 (-576)))) ((-102) . T) ((-111 #1# #1#) |has| |#1| (-38 (-419 (-576)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2758 (|has| |#1| (-568)) (|has| |#1| (-174))) ((-132) . T) ((-146) |has| |#1| (-146)) ((-148) |has| |#1| (-148)) ((-628 #1#) |has| |#1| (-38 (-419 (-576)))) ((-628 (-576)) . T) ((-628 |#1|) |has| |#1| (-174)) ((-628 $) |has| |#1| (-568)) ((-625 (-876)) . T) ((-174) -2758 (|has| |#1| (-568)) (|has| |#1| (-174))) ((-234 $) |has| |#1| (-15 * (|#1| (-783) |#1|))) ((-238) |has| |#1| (-15 * (|#1| (-783) |#1|))) ((-237) |has| |#1| (-15 * (|#1| (-783) |#1|))) ((-294) |has| |#1| (-38 (-419 (-576)))) ((-296 #0# |#1|) . 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T) ((-1072 $) -2758 (|has| |#1| (-568)) (|has| |#1| (-174))) ((-1077 #1#) |has| |#1| (-38 (-419 (-576)))) ((-1077 |#1|) . T) ((-1077 $) -2758 (|has| |#1| (-568)) (|has| |#1| (-174))) ((-1070) . T) ((-1079) . T) ((-1133) . T) ((-1121) . T) ((-1223) |has| |#1| (-38 (-419 (-576)))) ((-1226) |has| |#1| (-38 (-419 (-576)))) ((-1238) . T) ((-1266 |#1| #0#) . 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NIL) (-1249 2996481 2996726 2997114 "ULSCCAT-" 2997119 NIL ULSCCAT- (NIL T T T) -8 NIL NIL NIL) (-1248 2985545 2992028 2992071 "ULSCAT" 2992934 NIL ULSCAT (NIL T) -9 NIL 2993665 NIL) (-1247 2984975 2985054 2985233 "ULS2" 2985460 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1246 2984094 2984604 2984711 "UINT8" 2984822 T UINT8 (NIL) -8 NIL NIL 2984907) (-1245 2983212 2983722 2983829 "UINT64" 2983940 T UINT64 (NIL) -8 NIL NIL 2984025) (-1244 2982330 2982840 2982947 "UINT32" 2983058 T UINT32 (NIL) -8 NIL NIL 2983143) (-1243 2981448 2981958 2982065 "UINT16" 2982176 T UINT16 (NIL) -8 NIL NIL 2982261) (-1242 2979737 2980694 2980724 "UFD" 2980936 T UFD (NIL) -9 NIL 2981050 NIL) (-1241 2979531 2979577 2979672 "UFD-" 2979677 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1240 2978613 2978796 2979012 "UDVO" 2979337 T UDVO (NIL) -7 NIL NIL NIL) (-1239 2976429 2976838 2977309 "UDPO" 2978177 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1238 2976362 2976367 2976397 "TYPE" 2976402 T TYPE (NIL) -9 NIL NIL NIL) (-1237 2976122 2976317 2976348 "TYPEAST" 2976353 T TYPEAST (NIL) -8 NIL NIL NIL) (-1236 2975093 2975295 2975535 "TWOFACT" 2975916 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1235 2974116 2974502 2974737 "TUPLE" 2974893 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1234 2971807 2972326 2972865 "TUBETOOL" 2973599 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1233 2970656 2970861 2971102 "TUBE" 2971600 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1232 2965385 2969628 2969911 "TS" 2970408 NIL TS (NIL T) -8 NIL NIL NIL) (-1231 2954025 2958144 2958241 "TSETCAT" 2963510 NIL TSETCAT (NIL T T T T) -9 NIL 2965041 NIL) (-1230 2948757 2950357 2952248 "TSETCAT-" 2952253 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1229 2943396 2944243 2945172 "TRMANIP" 2947893 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1228 2942837 2942900 2943063 "TRIMAT" 2943328 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1227 2940703 2940940 2941297 "TRIGMNIP" 2942586 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1226 2940223 2940336 2940366 "TRIGCAT" 2940579 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1225 2939892 2939971 2940112 "TRIGCAT-" 2940117 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1224 2936740 2938750 2939031 "TREE" 2939646 NIL TREE (NIL T) -8 NIL NIL NIL) (-1223 2936014 2936542 2936572 "TRANFUN" 2936607 T TRANFUN (NIL) -9 NIL 2936673 NIL) (-1222 2935293 2935484 2935764 "TRANFUN-" 2935769 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1221 2935097 2935129 2935190 "TOPSP" 2935254 T TOPSP (NIL) -7 NIL NIL NIL) (-1220 2934445 2934560 2934714 "TOOLSIGN" 2934978 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1219 2933079 2933622 2933861 "TEXTFILE" 2934228 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1218 2930991 2931532 2931961 "TEX" 2932672 T TEX (NIL) -8 NIL NIL NIL) (-1217 2930772 2930803 2930875 "TEX1" 2930954 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1216 2930420 2930483 2930573 "TEMUTL" 2930704 T TEMUTL (NIL) -7 NIL NIL NIL) (-1215 2928574 2928854 2929179 "TBCMPPK" 2930143 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1214 2920283 2926660 2926716 "TBAGG" 2927116 NIL TBAGG (NIL T T) -9 NIL 2927327 NIL) (-1213 2915353 2916841 2918595 "TBAGG-" 2918600 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1212 2914737 2914844 2914989 "TANEXP" 2915242 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1211 2914248 2914512 2914602 "TALGOP" 2914682 NIL TALGOP (NIL T) -8 NIL NIL NIL) (-1210 2907644 2914105 2914198 "TABLE" 2914203 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1209 2907056 2907155 2907293 "TABLEAU" 2907541 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1208 2901664 2902884 2904132 "TABLBUMP" 2905842 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1207 2900886 2901033 2901214 "SYSTEM" 2901505 T SYSTEM (NIL) -8 NIL NIL NIL) (-1206 2897345 2898044 2898827 "SYSSOLP" 2900137 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1205 2897143 2897300 2897331 "SYSPTR" 2897336 T SYSPTR (NIL) -8 NIL NIL NIL) (-1204 2896179 2896684 2896803 "SYSNNI" 2896989 NIL SYSNNI (NIL NIL) -8 NIL NIL 2897074) (-1203 2895478 2895937 2896016 "SYSINT" 2896076 NIL SYSINT (NIL NIL) -8 NIL NIL 2896121) (-1202 2891810 2892756 2893466 "SYNTAX" 2894790 T SYNTAX (NIL) -8 NIL NIL NIL) (-1201 2888968 2889570 2890202 "SYMTAB" 2891200 T SYMTAB (NIL) -8 NIL NIL NIL) (-1200 2884217 2885119 2886102 "SYMS" 2888007 T SYMS (NIL) -8 NIL NIL NIL) (-1199 2881452 2883675 2883905 "SYMPOLY" 2884022 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1198 2880969 2881044 2881167 "SYMFUNC" 2881364 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1197 2876989 2878281 2879094 "SYMBOL" 2880178 T SYMBOL (NIL) -8 NIL NIL NIL) (-1196 2870528 2872217 2873937 "SWITCH" 2875291 T SWITCH (NIL) -8 NIL NIL NIL) (-1195 2863872 2869484 2869778 "SUTS" 2870292 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1194 2856048 2863254 2863518 "SUPXS" 2863666 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1193 2847531 2855666 2855792 "SUP" 2855957 NIL SUP (NIL T) -8 NIL NIL NIL) (-1192 2846690 2846817 2847034 "SUPFRACF" 2847399 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1191 2846311 2846370 2846483 "SUP2" 2846625 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1190 2844759 2845033 2845389 "SUMRF" 2846010 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1189 2844094 2844160 2844352 "SUMFS" 2844680 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1188 2826881 2843406 2843648 "SULS" 2843910 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1187 2826483 2826703 2826773 "SUCHTAST" 2826833 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1186 2825778 2826008 2826148 "SUCH" 2826391 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1185 2819645 2820684 2821643 "SUBSPACE" 2824866 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1184 2819075 2819165 2819329 "SUBRESP" 2819533 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1183 2812443 2813740 2815051 "STTF" 2817811 NIL STTF (NIL T) -7 NIL NIL NIL) (-1182 2806616 2807736 2808883 "STTFNC" 2811343 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1181 2797929 2799798 2801592 "STTAYLOR" 2804857 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1180 2791065 2797793 2797876 "STRTBL" 2797881 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1179 2786026 2790774 2790873 "STRING" 2790988 T STRING (NIL) -8 NIL NIL NIL) (-1178 2778782 2783645 2784256 "STREAM" 2785450 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1177 2778292 2778369 2778513 "STREAM3" 2778699 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1176 2777274 2777457 2777692 "STREAM2" 2778105 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1175 2776962 2777014 2777107 "STREAM1" 2777216 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1174 2775978 2776159 2776390 "STINPROD" 2776778 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1173 2775516 2775726 2775756 "STEP" 2775836 T STEP (NIL) -9 NIL 2775914 NIL) (-1172 2774703 2775005 2775153 "STEPAST" 2775390 T STEPAST (NIL) -8 NIL NIL NIL) (-1171 2768141 2774602 2774679 "STBL" 2774684 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1170 2763211 2767304 2767347 "STAGG" 2767500 NIL STAGG (NIL T) -9 NIL 2767589 NIL) (-1169 2760913 2761515 2762387 "STAGG-" 2762392 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1168 2759063 2760683 2760775 "STACK" 2760856 NIL STACK (NIL T) -8 NIL NIL NIL) (-1167 2751758 2757204 2757660 "SREGSET" 2758693 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1166 2744183 2745552 2747065 "SRDCMPK" 2750364 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1165 2737020 2741542 2741572 "SRAGG" 2742875 T SRAGG (NIL) -9 NIL 2743483 NIL) (-1164 2736037 2736292 2736671 "SRAGG-" 2736676 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1163 2730221 2734984 2735405 "SQMATRIX" 2735663 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1162 2723909 2726939 2727666 "SPLTREE" 2729566 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1161 2719872 2720565 2721211 "SPLNODE" 2723335 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1160 2718919 2719152 2719182 "SPFCAT" 2719626 T SPFCAT (NIL) -9 NIL NIL NIL) (-1159 2717656 2717866 2718130 "SPECOUT" 2718677 T SPECOUT (NIL) -7 NIL NIL NIL) (-1158 2708752 2710624 2710654 "SPADXPT" 2715330 T SPADXPT (NIL) -9 NIL 2717494 NIL) (-1157 2708513 2708553 2708622 "SPADPRSR" 2708705 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1156 2706562 2708468 2708499 "SPADAST" 2708504 T SPADAST (NIL) -8 NIL NIL NIL) (-1155 2698493 2700266 2700309 "SPACEC" 2704682 NIL SPACEC (NIL T) -9 NIL 2706498 NIL) (-1154 2696623 2698425 2698474 "SPACE3" 2698479 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1153 2695375 2695546 2695837 "SORTPAK" 2696428 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1152 2693467 2693770 2694182 "SOLVETRA" 2695039 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1151 2692517 2692739 2693000 "SOLVESER" 2693240 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1150 2687821 2688709 2689704 "SOLVERAD" 2691569 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1149 2683636 2684245 2684974 "SOLVEFOR" 2687188 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1148 2677906 2682985 2683082 "SNTSCAT" 2683087 NIL SNTSCAT (NIL T T T T) -9 NIL 2683157 NIL) (-1147 2672012 2676229 2676620 "SMTS" 2677596 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1146 2666421 2671900 2671977 "SMP" 2671982 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1145 2664580 2664881 2665279 "SMITH" 2666118 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1144 2656684 2661159 2661262 "SMATCAT" 2662613 NIL SMATCAT (NIL NIL T T T) -9 NIL 2663163 NIL) (-1143 2653624 2654447 2655625 "SMATCAT-" 2655630 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1142 2651265 2652832 2652875 "SKAGG" 2653136 NIL SKAGG (NIL T) -9 NIL 2653271 NIL) (-1141 2647455 2650738 2650922 "SINT" 2651074 T SINT (NIL) -8 NIL NIL 2651236) (-1140 2647227 2647265 2647331 "SIMPAN" 2647411 T SIMPAN (NIL) -7 NIL NIL NIL) (-1139 2646506 2646762 2646902 "SIG" 2647109 T SIG (NIL) -8 NIL NIL NIL) (-1138 2645344 2645565 2645840 "SIGNRF" 2646265 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1137 2644177 2644328 2644612 "SIGNEF" 2645173 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1136 2643483 2643760 2643884 "SIGAST" 2644075 T SIGAST (NIL) -8 NIL NIL NIL) (-1135 2641173 2641627 2642133 "SHP" 2643024 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1134 2635002 2641074 2641150 "SHDP" 2641155 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1133 2634561 2634753 2634783 "SGROUP" 2634876 T SGROUP (NIL) -9 NIL 2634938 NIL) (-1132 2634419 2634445 2634518 "SGROUP-" 2634523 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1131 2631210 2631908 2632631 "SGCF" 2633718 T SGCF (NIL) -7 NIL NIL NIL) (-1130 2625578 2630657 2630754 "SFRTCAT" 2630759 NIL SFRTCAT (NIL T T T T) -9 NIL 2630798 NIL) (-1129 2618999 2620017 2621153 "SFRGCD" 2624561 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1128 2612125 2613198 2614384 "SFQCMPK" 2617932 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1127 2611745 2611834 2611945 "SFORT" 2612066 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1126 2610863 2611585 2611706 "SEXOF" 2611711 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1125 2609970 2610744 2610812 "SEX" 2610817 T SEX (NIL) -8 NIL NIL NIL) (-1124 2605751 2606466 2606561 "SEXCAT" 2609183 NIL SEXCAT (NIL T T T T T) -9 NIL 2609743 NIL) (-1123 2602904 2605685 2605733 "SET" 2605738 NIL SET (NIL T) -8 NIL NIL NIL) (-1122 2601128 2601617 2601922 "SETMN" 2602645 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1121 2600694 2600846 2600876 "SETCAT" 2600993 T SETCAT (NIL) -9 NIL 2601078 NIL) (-1120 2600474 2600526 2600625 "SETCAT-" 2600630 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1119 2596835 2598935 2598978 "SETAGG" 2599848 NIL SETAGG (NIL T) -9 NIL 2600188 NIL) (-1118 2596293 2596409 2596646 "SETAGG-" 2596651 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1117 2595736 2595989 2596090 "SEQAST" 2596214 T SEQAST (NIL) -8 NIL NIL NIL) (-1116 2594935 2595229 2595290 "SEGXCAT" 2595576 NIL SEGXCAT (NIL T T) -9 NIL 2595696 NIL) (-1115 2593941 2594601 2594783 "SEG" 2594788 NIL SEG (NIL T) -8 NIL NIL NIL) (-1114 2592920 2593134 2593177 "SEGCAT" 2593699 NIL SEGCAT (NIL T) -9 NIL 2593920 NIL) (-1113 2591852 2592283 2592491 "SEGBIND" 2592747 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1112 2591473 2591532 2591645 "SEGBIND2" 2591787 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1111 2591046 2591274 2591351 "SEGAST" 2591418 T SEGAST (NIL) -8 NIL NIL NIL) (-1110 2590265 2590391 2590595 "SEG2" 2590890 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1109 2589636 2590200 2590247 "SDVAR" 2590252 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1108 2581887 2589406 2589536 "SDPOL" 2589541 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1107 2580480 2580746 2581065 "SCPKG" 2581602 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1106 2579644 2579816 2580008 "SCOPE" 2580310 T SCOPE (NIL) -8 NIL NIL NIL) (-1105 2578864 2578998 2579177 "SCACHE" 2579499 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1104 2578496 2578682 2578712 "SASTCAT" 2578717 T SASTCAT (NIL) -9 NIL 2578730 NIL) (-1103 2577983 2578331 2578407 "SAOS" 2578442 T SAOS (NIL) -8 NIL NIL NIL) (-1102 2577548 2577583 2577756 "SAERFFC" 2577942 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1101 2571211 2577445 2577525 "SAE" 2577530 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1100 2570804 2570839 2570998 "SAEFACT" 2571170 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1099 2569125 2569439 2569840 "RURPK" 2570470 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1098 2567762 2568068 2568373 "RULESET" 2568959 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1097 2564985 2565515 2565973 "RULE" 2567443 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1096 2564597 2564779 2564862 "RULECOLD" 2564937 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1095 2564387 2564415 2564486 "RTVALUE" 2564548 T RTVALUE (NIL) -8 NIL NIL NIL) (-1094 2563858 2564104 2564198 "RSTRCAST" 2564315 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1093 2558706 2559501 2560421 "RSETGCD" 2563057 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1092 2547936 2553015 2553112 "RSETCAT" 2557231 NIL RSETCAT (NIL T T T T) -9 NIL 2558328 NIL) (-1091 2545863 2546402 2547226 "RSETCAT-" 2547231 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1090 2538249 2539625 2541145 "RSDCMPK" 2544462 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1089 2536214 2536681 2536755 "RRCC" 2537841 NIL RRCC (NIL T T) -9 NIL 2538185 NIL) (-1088 2535565 2535739 2536018 "RRCC-" 2536023 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1087 2535008 2535261 2535362 "RPTAST" 2535486 T RPTAST (NIL) -8 NIL NIL NIL) (-1086 2508484 2518120 2518187 "RPOLCAT" 2528853 NIL RPOLCAT (NIL T T T) -9 NIL 2532013 NIL) (-1085 2499982 2502322 2505444 "RPOLCAT-" 2505449 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1084 2490919 2498193 2498675 "ROUTINE" 2499522 T ROUTINE (NIL) -8 NIL NIL NIL) (-1083 2487580 2490545 2490685 "ROMAN" 2490801 T ROMAN (NIL) -8 NIL NIL NIL) (-1082 2485824 2486440 2486700 "ROIRC" 2487385 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1081 2482028 2484313 2484343 "RNS" 2484647 T RNS (NIL) -9 NIL 2484921 NIL) (-1080 2480537 2480920 2481454 "RNS-" 2481529 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1079 2479926 2480334 2480364 "RNG" 2480369 T RNG (NIL) -9 NIL 2480390 NIL) (-1078 2478929 2479291 2479493 "RNGBIND" 2479777 NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-1077 2478314 2478702 2478745 "RMODULE" 2478750 NIL RMODULE (NIL T) -9 NIL 2478777 NIL) (-1076 2477150 2477244 2477580 "RMCAT2" 2478215 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1075 2474000 2476496 2476793 "RMATRIX" 2476912 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1074 2466827 2469087 2469202 "RMATCAT" 2472561 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2473543 NIL) (-1073 2466202 2466349 2466656 "RMATCAT-" 2466661 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1072 2465817 2465989 2466032 "RLINSET" 2466094 NIL RLINSET (NIL T) -9 NIL 2466138 NIL) (-1071 2465384 2465459 2465587 "RINTERP" 2465736 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1070 2464428 2464982 2465012 "RING" 2465068 T RING (NIL) -9 NIL 2465160 NIL) (-1069 2464220 2464264 2464361 "RING-" 2464366 NIL RING- (NIL T) -8 NIL NIL NIL) (-1068 2463061 2463298 2463556 "RIDIST" 2463984 T RIDIST (NIL) -7 NIL NIL NIL) (-1067 2454350 2462529 2462735 "RGCHAIN" 2462909 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1066 2453686 2454092 2454133 "RGBCSPC" 2454191 NIL RGBCSPC (NIL T) -9 NIL 2454243 NIL) (-1065 2452830 2453211 2453252 "RGBCMDL" 2453484 NIL RGBCMDL (NIL T) -9 NIL 2453598 NIL) (-1064 2449824 2450438 2451108 "RF" 2452194 NIL RF (NIL T) -7 NIL NIL NIL) (-1063 2449470 2449533 2449636 "RFFACTOR" 2449755 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1062 2449195 2449230 2449327 "RFFACT" 2449429 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1061 2447312 2447676 2448058 "RFDIST" 2448835 T RFDIST (NIL) -7 NIL NIL NIL) (-1060 2446765 2446857 2447020 "RETSOL" 2447214 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1059 2446401 2446481 2446524 "RETRACT" 2446657 NIL RETRACT (NIL T) -9 NIL 2446744 NIL) (-1058 2446250 2446275 2446362 "RETRACT-" 2446367 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1057 2445852 2446072 2446142 "RETAST" 2446202 T RETAST (NIL) -8 NIL NIL NIL) (-1056 2438596 2445505 2445632 "RESULT" 2445747 T RESULT (NIL) -8 NIL NIL NIL) (-1055 2437187 2437865 2438064 "RESRING" 2438499 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1054 2436823 2436872 2436970 "RESLATC" 2437124 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1053 2436528 2436563 2436670 "REPSQ" 2436782 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1052 2433950 2434530 2435132 "REP" 2435948 T REP (NIL) -7 NIL NIL NIL) (-1051 2433647 2433682 2433793 "REPDB" 2433909 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1050 2427547 2428936 2430159 "REP2" 2432459 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1049 2423924 2424605 2425413 "REP1" 2426774 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1048 2416620 2422065 2422521 "REGSET" 2423554 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1047 2415385 2415768 2416018 "REF" 2416405 NIL REF (NIL T) -8 NIL NIL NIL) (-1046 2414762 2414865 2415032 "REDORDER" 2415269 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1045 2410730 2413975 2414202 "RECLOS" 2414590 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1044 2409782 2409963 2410178 "REALSOLV" 2410537 T REALSOLV (NIL) -7 NIL NIL NIL) (-1043 2409628 2409669 2409699 "REAL" 2409704 T REAL (NIL) -9 NIL 2409739 NIL) (-1042 2406111 2406913 2407797 "REAL0Q" 2408793 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1041 2401712 2402700 2403761 "REAL0" 2405092 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1040 2401183 2401429 2401523 "RDUCEAST" 2401640 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1039 2400588 2400660 2400867 "RDIV" 2401105 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1038 2399656 2399830 2400043 "RDIST" 2400410 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1037 2398253 2398540 2398912 "RDETRS" 2399364 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1036 2396065 2396519 2397057 "RDETR" 2397795 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1035 2394690 2394968 2395365 "RDEEFS" 2395781 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1034 2393199 2393505 2393930 "RDEEF" 2394378 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1033 2387232 2390153 2390183 "RCFIELD" 2391478 T RCFIELD (NIL) -9 NIL 2392209 NIL) (-1032 2385296 2385800 2386496 "RCFIELD-" 2386571 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1031 2381540 2383369 2383412 "RCAGG" 2384496 NIL RCAGG (NIL T) -9 NIL 2384961 NIL) (-1030 2381168 2381262 2381425 "RCAGG-" 2381430 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1029 2380503 2380615 2380780 "RATRET" 2381052 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1028 2380056 2380123 2380244 "RATFACT" 2380431 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1027 2379364 2379484 2379636 "RANDSRC" 2379926 T RANDSRC (NIL) -7 NIL NIL NIL) (-1026 2379098 2379142 2379215 "RADUTIL" 2379313 T RADUTIL (NIL) -7 NIL NIL NIL) (-1025 2371926 2377929 2378240 "RADIX" 2378821 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-1024 2362386 2371768 2371898 "RADFF" 2371903 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-1023 2362033 2362108 2362138 "RADCAT" 2362298 T RADCAT (NIL) -9 NIL NIL NIL) (-1022 2361815 2361863 2361963 "RADCAT-" 2361968 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-1021 2359916 2361585 2361677 "QUEUE" 2361758 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-1020 2356177 2359849 2359897 "QUAT" 2359902 NIL QUAT (NIL T) -8 NIL NIL NIL) (-1019 2355808 2355851 2355982 "QUATCT2" 2356128 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-1018 2348606 2352231 2352273 "QUATCAT" 2353064 NIL QUATCAT (NIL T) -9 NIL 2353830 NIL) (-1017 2344745 2345782 2347172 "QUATCAT-" 2347268 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-1016 2342185 2343793 2343836 "QUAGG" 2344217 NIL QUAGG (NIL T) -9 NIL 2344392 NIL) (-1015 2341787 2342007 2342077 "QQUTAST" 2342137 T QQUTAST (NIL) -8 NIL NIL NIL) (-1014 2340800 2341300 2341465 "QFORM" 2341668 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-1013 2331132 2336647 2336689 "QFCAT" 2337357 NIL QFCAT (NIL T) -9 NIL 2338358 NIL) (-1012 2326699 2327900 2329494 "QFCAT-" 2329590 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-1011 2326330 2326373 2326504 "QFCAT2" 2326650 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-1010 2325785 2325895 2326027 "QEQUAT" 2326220 T QEQUAT (NIL) -8 NIL NIL NIL) (-1009 2318911 2319984 2321170 "QCMPACK" 2324718 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-1008 2316449 2316897 2317327 "QALGSET" 2318566 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-1007 2315684 2315860 2316096 "QALGSET2" 2316267 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-1006 2314369 2314593 2314912 "PWFFINTB" 2315457 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-1005 2312544 2312712 2313068 "PUSHVAR" 2314183 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-1004 2308433 2309487 2309530 "PTRANFN" 2311441 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-1003 2306824 2307115 2307439 "PTPACK" 2308144 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-1002 2306453 2306510 2306621 "PTFUNC2" 2306761 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-1001 2300848 2305242 2305285 "PTCAT" 2305585 NIL PTCAT (NIL T) -9 NIL 2305738 NIL) (-1000 2300503 2300538 2300664 "PSQFR" 2300807 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-999 2299098 2299396 2299730 "PSEUDLIN" 2300201 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-998 2285861 2288232 2290556 "PSETPK" 2296858 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-997 2278879 2281619 2281715 "PSETCAT" 2284736 NIL PSETCAT (NIL T T T T) -9 NIL 2285550 NIL) (-996 2276715 2277349 2278170 "PSETCAT-" 2278175 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-995 2276064 2276229 2276257 "PSCURVE" 2276525 T PSCURVE (NIL) -9 NIL 2276692 NIL) (-994 2272048 2273564 2273629 "PSCAT" 2274473 NIL PSCAT (NIL T T T) -9 NIL 2274713 NIL) (-993 2271111 2271327 2271727 "PSCAT-" 2271732 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-992 2269470 2270180 2270443 "PRTITION" 2270868 T PRTITION (NIL) -8 NIL NIL NIL) (-991 2268945 2269191 2269283 "PRTDAST" 2269398 T PRTDAST (NIL) -8 NIL NIL NIL) (-990 2258035 2260249 2262437 "PRS" 2266807 NIL PRS (NIL T T) -7 NIL NIL NIL) (-989 2255821 2257357 2257397 "PRQAGG" 2257580 NIL PRQAGG (NIL T) -9 NIL 2257682 NIL) (-988 2255157 2255462 2255490 "PROPLOG" 2255629 T PROPLOG (NIL) -9 NIL 2255744 NIL) (-987 2254761 2254818 2254941 "PROPFUN2" 2255080 NIL PROPFUN2 (NIL T T) -8 NIL NIL NIL) (-986 2254076 2254197 2254369 "PROPFUN1" 2254622 NIL PROPFUN1 (NIL T) -8 NIL NIL NIL) (-985 2252257 2252823 2253120 "PROPFRML" 2253812 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-984 2251726 2251833 2251961 "PROPERTY" 2252149 T PROPERTY (NIL) -8 NIL NIL NIL) (-983 2245784 2249892 2250712 "PRODUCT" 2250952 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-982 2243062 2245242 2245476 "PR" 2245595 NIL PR (NIL T T) -8 NIL NIL NIL) (-981 2242858 2242890 2242949 "PRINT" 2243023 T PRINT (NIL) -7 NIL NIL NIL) (-980 2242198 2242315 2242467 "PRIMES" 2242738 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-979 2240263 2240664 2241130 "PRIMELT" 2241777 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-978 2239992 2240041 2240069 "PRIMCAT" 2240193 T PRIMCAT (NIL) -9 NIL NIL NIL) (-977 2236110 2239930 2239975 "PRIMARR" 2239980 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-976 2235117 2235295 2235523 "PRIMARR2" 2235928 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-975 2234760 2234816 2234927 "PREASSOC" 2235055 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-974 2234235 2234368 2234396 "PPCURVE" 2234601 T PPCURVE (NIL) -9 NIL 2234737 NIL) (-973 2233830 2234030 2234113 "PORTNUM" 2234172 T PORTNUM (NIL) -8 NIL NIL NIL) (-972 2231189 2231588 2232180 "POLYROOT" 2233411 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-971 2225095 2230793 2230953 "POLY" 2231062 NIL POLY (NIL T) -8 NIL NIL NIL) (-970 2224478 2224536 2224770 "POLYLIFT" 2225031 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-969 2220753 2221202 2221831 "POLYCATQ" 2224023 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-968 2207095 2212500 2212565 "POLYCAT" 2216079 NIL POLYCAT (NIL T T T) -9 NIL 2217957 NIL) (-967 2200544 2202406 2204790 "POLYCAT-" 2204795 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-966 2200131 2200199 2200319 "POLY2UP" 2200470 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-965 2199763 2199820 2199929 "POLY2" 2200068 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-964 2198448 2198687 2198963 "POLUTIL" 2199537 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-963 2196803 2197080 2197411 "POLTOPOL" 2198170 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-962 2192269 2196737 2196784 "POINT" 2196789 NIL POINT (NIL T) -8 NIL NIL NIL) (-961 2190456 2190813 2191188 "PNTHEORY" 2191914 T PNTHEORY (NIL) -7 NIL NIL NIL) (-960 2188914 2189211 2189610 "PMTOOLS" 2190154 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-959 2188507 2188585 2188702 "PMSYM" 2188830 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-958 2188015 2188084 2188259 "PMQFCAT" 2188432 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-957 2187370 2187480 2187636 "PMPRED" 2187892 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-956 2186763 2186849 2187011 "PMPREDFS" 2187271 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-955 2185427 2185635 2186013 "PMPLCAT" 2186525 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-954 2184959 2185038 2185190 "PMLSAGG" 2185342 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-953 2184432 2184508 2184690 "PMKERNEL" 2184877 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-952 2184049 2184124 2184237 "PMINS" 2184351 NIL PMINS (NIL T) -7 NIL NIL NIL) (-951 2183491 2183560 2183769 "PMFS" 2183974 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-950 2182719 2182837 2183042 "PMDOWN" 2183368 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-949 2181886 2182044 2182225 "PMASS" 2182558 T PMASS (NIL) -7 NIL NIL NIL) (-948 2181159 2181269 2181432 "PMASSFS" 2181773 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-947 2180814 2180882 2180976 "PLOTTOOL" 2181085 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-946 2175421 2176625 2177773 "PLOT" 2179686 T PLOT (NIL) -8 NIL NIL NIL) (-945 2171225 2172269 2173190 "PLOT3D" 2174520 T PLOT3D (NIL) -8 NIL NIL NIL) (-944 2170137 2170314 2170549 "PLOT1" 2171029 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-943 2145528 2150203 2155054 "PLEQN" 2165403 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-942 2144846 2144968 2145148 "PINTERP" 2145393 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-941 2144539 2144586 2144689 "PINTERPA" 2144793 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-940 2143755 2144303 2144390 "PI" 2144430 T PI (NIL) -8 NIL NIL 2144497) (-939 2142038 2143013 2143041 "PID" 2143223 T PID (NIL) -9 NIL 2143357 NIL) (-938 2141789 2141826 2141901 "PICOERCE" 2141995 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-937 2141109 2141248 2141424 "PGROEB" 2141645 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-936 2136696 2137510 2138415 "PGE" 2140224 T PGE (NIL) -7 NIL NIL NIL) (-935 2134819 2135066 2135432 "PGCD" 2136413 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-934 2134157 2134260 2134421 "PFRPAC" 2134703 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-933 2130797 2132705 2133058 "PFR" 2133836 NIL PFR (NIL T) -8 NIL NIL NIL) (-932 2129186 2129430 2129755 "PFOTOOLS" 2130544 NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-931 2127719 2127958 2128309 "PFOQ" 2128943 NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-930 2126220 2126432 2126788 "PFO" 2127503 NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-929 2122773 2126109 2126178 "PF" 2126183 NIL PF (NIL NIL) -8 NIL NIL NIL) (-928 2120093 2121364 2121392 "PFECAT" 2121977 T PFECAT (NIL) -9 NIL 2122361 NIL) (-927 2119538 2119692 2119906 "PFECAT-" 2119911 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-926 2118141 2118393 2118694 "PFBRU" 2119287 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-925 2116007 2116359 2116791 "PFBR" 2117792 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-924 2112053 2113519 2114166 "PERM" 2115393 NIL PERM (NIL T) -8 NIL NIL NIL) (-923 2107287 2108260 2109130 "PERMGRP" 2111216 NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-922 2105351 2106311 2106352 "PERMCAT" 2106752 NIL PERMCAT (NIL T) -9 NIL 2107050 NIL) (-921 2105004 2105045 2105169 "PERMAN" 2105304 NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-920 2102495 2104669 2104791 "PENDTREE" 2104915 NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-919 2101424 2101639 2101680 "PDSPC" 2102213 NIL PDSPC (NIL T) -9 NIL 2102458 NIL) (-918 2100527 2100745 2101107 "PDSPC-" 2101112 NIL PDSPC- (NIL T T) -8 NIL NIL NIL) (-917 2099409 2100177 2100218 "PDRING" 2100223 NIL PDRING (NIL T) -9 NIL 2100251 NIL) (-916 2098296 2098914 2098968 "PDMOD" 2098973 NIL PDMOD (NIL T T) -9 NIL 2099077 NIL) (-915 2095511 2096289 2096957 "PDEPROB" 2097648 T PDEPROB (NIL) -8 NIL NIL NIL) (-914 2093056 2093560 2094115 "PDEPACK" 2094976 T PDEPACK (NIL) -7 NIL NIL NIL) (-913 2091968 2092158 2092409 "PDECOMP" 2092855 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-912 2089533 2090376 2090404 "PDECAT" 2091191 T PDECAT (NIL) -9 NIL 2091904 NIL) (-911 2089162 2089217 2089271 "PDDOM" 2089436 NIL PDDOM (NIL T T) -9 NIL 2089516 NIL) (-910 2088981 2089011 2089118 "PDDOM-" 2089123 NIL PDDOM- (NIL T T T) -8 NIL NIL NIL) (-909 2088732 2088765 2088855 "PCOMP" 2088942 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-908 2086910 2087533 2087830 "PBWLB" 2088461 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-907 2079383 2080983 2082321 "PATTERN" 2085593 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-906 2079015 2079072 2079181 "PATTERN2" 2079320 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-905 2076772 2077160 2077617 "PATTERN1" 2078604 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-904 2074140 2074721 2075202 "PATRES" 2076337 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-903 2073704 2073771 2073903 "PATRES2" 2074067 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-902 2071587 2071992 2072399 "PATMATCH" 2073371 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-901 2071083 2071292 2071333 "PATMAB" 2071440 NIL PATMAB (NIL T) -9 NIL 2071523 NIL) (-900 2069601 2069937 2070195 "PATLRES" 2070888 NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-899 2069147 2069270 2069311 "PATAB" 2069316 NIL PATAB (NIL T) -9 NIL 2069488 NIL) (-898 2067329 2067724 2068147 "PARTPERM" 2068744 T PARTPERM (NIL) -7 NIL NIL NIL) (-897 2066950 2067013 2067115 "PARSURF" 2067260 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-896 2066582 2066639 2066748 "PARSU2" 2066887 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-895 2066346 2066386 2066453 "PARSER" 2066535 T PARSER (NIL) -7 NIL NIL NIL) (-894 2065967 2066030 2066132 "PARSCURV" 2066277 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-893 2065599 2065656 2065765 "PARSC2" 2065904 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-892 2065238 2065296 2065393 "PARPCURV" 2065535 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-891 2064870 2064927 2065036 "PARPC2" 2065175 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-890 2063931 2064243 2064425 "PARAMAST" 2064708 T PARAMAST (NIL) -8 NIL NIL NIL) (-889 2063451 2063537 2063656 "PAN2EXPR" 2063832 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-888 2062228 2062572 2062800 "PALETTE" 2063243 T PALETTE (NIL) -8 NIL NIL NIL) (-887 2060621 2061233 2061593 "PAIR" 2061914 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-886 2054213 2059878 2060073 "PADICRC" 2060475 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-885 2047129 2053557 2053742 "PADICRAT" 2054060 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-884 2045444 2047066 2047111 "PADIC" 2047116 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-883 2042540 2044104 2044144 "PADICCT" 2044725 NIL PADICCT (NIL NIL) -9 NIL 2045007 NIL) (-882 2041497 2041697 2041965 "PADEPAC" 2042327 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-881 2040709 2040842 2041048 "PADE" 2041359 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-880 2039096 2039917 2040197 "OWP" 2040513 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-879 2038589 2038802 2038899 "OVERSET" 2039019 T OVERSET (NIL) -8 NIL NIL NIL) (-878 2037635 2038194 2038366 "OVAR" 2038457 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-877 2036899 2037020 2037181 "OUT" 2037494 T OUT (NIL) -7 NIL NIL NIL) (-876 2025771 2028008 2030208 "OUTFORM" 2034719 T OUTFORM (NIL) -8 NIL NIL NIL) (-875 2025107 2025368 2025495 "OUTBFILE" 2025664 T OUTBFILE (NIL) -8 NIL NIL NIL) (-874 2024414 2024579 2024607 "OUTBCON" 2024925 T OUTBCON (NIL) -9 NIL 2025091 NIL) (-873 2024015 2024127 2024284 "OUTBCON-" 2024289 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-872 2023395 2023744 2023833 "OSI" 2023946 T OSI (NIL) -8 NIL NIL NIL) (-871 2022898 2023236 2023264 "OSGROUP" 2023269 T OSGROUP (NIL) -9 NIL 2023291 NIL) (-870 2021643 2021870 2022155 "ORTHPOL" 2022645 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-869 2019194 2021478 2021599 "OREUP" 2021604 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-868 2016597 2018885 2019012 "ORESUP" 2019136 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-867 2014125 2014625 2015186 "OREPCTO" 2016086 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-866 2007797 2009998 2010039 "OREPCAT" 2012387 NIL OREPCAT (NIL T) -9 NIL 2013491 NIL) (-865 2004944 2005726 2006784 "OREPCAT-" 2006789 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-864 2004191 2004414 2004442 "ORDTYPE" 2004751 T ORDTYPE (NIL) -9 NIL 2004914 NIL) (-863 2003534 2003708 2003963 "ORDTYPE-" 2003968 NIL ORDTYPE- (NIL T) -8 NIL NIL NIL) (-862 2003148 2003417 2003503 "ORDSTRCT" 2003508 NIL ORDSTRCT (NIL T NIL) -8 NIL NIL NIL) (-861 2002718 2003016 2003044 "ORDSET" 2003049 T ORDSET (NIL) -9 NIL 2003071 NIL) (-860 2001256 2002047 2002075 "ORDRING" 2002277 T ORDRING (NIL) -9 NIL 2002402 NIL) (-859 2000901 2000995 2001139 "ORDRING-" 2001144 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-858 2000254 2000717 2000745 "ORDMON" 2000750 T ORDMON (NIL) -9 NIL 2000771 NIL) (-857 1999416 1999563 1999758 "ORDFUNS" 2000103 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-856 1998727 1999146 1999174 "ORDFIN" 1999239 T ORDFIN (NIL) -9 NIL 1999313 NIL) (-855 1995286 1997313 1997722 "ORDCOMP" 1998351 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-854 1994552 1994679 1994865 "ORDCOMP2" 1995146 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-853 1991133 1992043 1992857 "OPTPROB" 1993758 T OPTPROB (NIL) -8 NIL NIL NIL) (-852 1987935 1988574 1989278 "OPTPACK" 1990449 T OPTPACK (NIL) -7 NIL NIL NIL) (-851 1985608 1986374 1986402 "OPTCAT" 1987221 T OPTCAT (NIL) -9 NIL 1987871 NIL) (-850 1984992 1985285 1985390 "OPSIG" 1985523 T OPSIG (NIL) -8 NIL NIL NIL) (-849 1984760 1984799 1984865 "OPQUERY" 1984946 T OPQUERY (NIL) -7 NIL NIL NIL) (-848 1981891 1983071 1983575 "OP" 1984289 NIL OP (NIL T) -8 NIL NIL NIL) (-847 1981251 1981477 1981518 "OPERCAT" 1981730 NIL OPERCAT (NIL T) -9 NIL 1981827 NIL) (-846 1981006 1981062 1981179 "OPERCAT-" 1981184 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-845 1977819 1979803 1980172 "ONECOMP" 1980670 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-844 1977124 1977239 1977413 "ONECOMP2" 1977691 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-843 1976543 1976649 1976779 "OMSERVER" 1977014 T OMSERVER (NIL) -7 NIL NIL NIL) (-842 1973405 1975983 1976023 "OMSAGG" 1976084 NIL OMSAGG (NIL T) -9 NIL 1976148 NIL) (-841 1972028 1972291 1972573 "OMPKG" 1973143 T OMPKG (NIL) -7 NIL NIL NIL) (-840 1971458 1971561 1971589 "OM" 1971888 T OM (NIL) -9 NIL NIL NIL) (-839 1970005 1971007 1971176 "OMLO" 1971339 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-838 1968965 1969112 1969332 "OMEXPR" 1969831 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-837 1968256 1968511 1968647 "OMERR" 1968849 T OMERR (NIL) -8 NIL NIL NIL) (-836 1967407 1967677 1967837 "OMERRK" 1968116 T OMERRK (NIL) -8 NIL NIL NIL) (-835 1966858 1967084 1967192 "OMENC" 1967319 T OMENC (NIL) -8 NIL NIL NIL) (-834 1960753 1961938 1963109 "OMDEV" 1965707 T OMDEV (NIL) -8 NIL NIL NIL) (-833 1959822 1959993 1960187 "OMCONN" 1960579 T OMCONN (NIL) -8 NIL NIL NIL) (-832 1958316 1959292 1959320 "OINTDOM" 1959325 T OINTDOM (NIL) -9 NIL 1959346 NIL) (-831 1955654 1957004 1957341 "OFMONOID" 1958011 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-830 1955026 1955591 1955636 "ODVAR" 1955641 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-829 1952449 1954771 1954926 "ODR" 1954931 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-828 1944754 1952225 1952351 "ODPOL" 1952356 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-827 1938553 1944626 1944731 "ODP" 1944736 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-826 1937319 1937534 1937809 "ODETOOLS" 1938327 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-825 1934286 1934944 1935660 "ODESYS" 1936652 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-824 1929168 1930076 1931101 "ODERTRIC" 1933361 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-823 1928594 1928676 1928870 "ODERED" 1929080 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-822 1925482 1926030 1926707 "ODERAT" 1928017 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-821 1922441 1922906 1923503 "ODEPRRIC" 1925011 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-820 1920384 1920980 1921466 "ODEPROB" 1921975 T ODEPROB (NIL) -8 NIL NIL NIL) (-819 1916904 1917389 1918036 "ODEPRIM" 1919863 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-818 1916153 1916255 1916515 "ODEPAL" 1916796 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-817 1912315 1913106 1913970 "ODEPACK" 1915309 T ODEPACK (NIL) -7 NIL NIL NIL) (-816 1911376 1911483 1911705 "ODEINT" 1912204 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-815 1905477 1906902 1908349 "ODEIFTBL" 1909949 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-814 1900875 1901661 1902613 "ODEEF" 1904636 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-813 1900224 1900313 1900536 "ODECONST" 1900780 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-812 1898335 1898996 1899024 "ODECAT" 1899629 T ODECAT (NIL) -9 NIL 1900160 NIL) (-811 1895190 1898040 1898162 "OCT" 1898245 NIL OCT (NIL T) -8 NIL NIL NIL) (-810 1894828 1894871 1894998 "OCTCT2" 1895141 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-809 1889435 1891871 1891911 "OC" 1893008 NIL OC (NIL T) -9 NIL 1893866 NIL) (-808 1886662 1887410 1888400 "OC-" 1888494 NIL OC- (NIL T T) -8 NIL NIL NIL) (-807 1885987 1886455 1886483 "OCAMON" 1886488 T OCAMON (NIL) -9 NIL 1886509 NIL) (-806 1885491 1885832 1885860 "OASGP" 1885865 T OASGP (NIL) -9 NIL 1885885 NIL) (-805 1884725 1885214 1885242 "OAMONS" 1885282 T OAMONS (NIL) -9 NIL 1885325 NIL) (-804 1884112 1884545 1884573 "OAMON" 1884578 T OAMON (NIL) -9 NIL 1884598 NIL) (-803 1883343 1883861 1883889 "OAGROUP" 1883894 T OAGROUP (NIL) -9 NIL 1883914 NIL) (-802 1883033 1883083 1883171 "NUMTUBE" 1883287 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-801 1876606 1878124 1879660 "NUMQUAD" 1881517 T NUMQUAD (NIL) -7 NIL NIL NIL) (-800 1872362 1873350 1874375 "NUMODE" 1875601 T NUMODE (NIL) -7 NIL NIL NIL) (-799 1869703 1870583 1870611 "NUMINT" 1871534 T NUMINT (NIL) -9 NIL 1872298 NIL) (-798 1868651 1868848 1869066 "NUMFMT" 1869505 T NUMFMT (NIL) -7 NIL NIL NIL) (-797 1855010 1857955 1860487 "NUMERIC" 1866158 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-796 1849380 1854459 1854554 "NTSCAT" 1854559 NIL NTSCAT (NIL T T T T) -9 NIL 1854598 NIL) (-795 1848574 1848739 1848932 "NTPOLFN" 1849219 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-794 1836375 1845399 1846211 "NSUP" 1847795 NIL NSUP (NIL T) -8 NIL NIL NIL) (-793 1836007 1836064 1836173 "NSUP2" 1836312 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-792 1825957 1835781 1835914 "NSMP" 1835919 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-791 1824389 1824690 1825047 "NREP" 1825645 NIL NREP (NIL T) -7 NIL NIL NIL) (-790 1822980 1823232 1823590 "NPCOEF" 1824132 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-789 1822046 1822161 1822377 "NORMRETR" 1822861 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-788 1820087 1820377 1820786 "NORMPK" 1821754 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-787 1819772 1819800 1819924 "NORMMA" 1820053 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-786 1819572 1819729 1819758 "NONE" 1819763 T NONE (NIL) -8 NIL NIL NIL) (-785 1819361 1819390 1819459 "NONE1" 1819536 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-784 1818858 1818920 1819099 "NODE1" 1819293 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-783 1817139 1817990 1818245 "NNI" 1818592 T NNI (NIL) -8 NIL NIL 1818827) (-782 1815559 1815872 1816236 "NLINSOL" 1816807 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-781 1811800 1812795 1813694 "NIPROB" 1814680 T NIPROB (NIL) -8 NIL NIL NIL) (-780 1810557 1810791 1811093 "NFINTBAS" 1811562 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-779 1809731 1810207 1810248 "NETCLT" 1810420 NIL NETCLT (NIL T) -9 NIL 1810502 NIL) (-778 1808439 1808670 1808951 "NCODIV" 1809499 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-777 1808201 1808238 1808313 "NCNTFRAC" 1808396 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-776 1806381 1806745 1807165 "NCEP" 1807826 NIL NCEP (NIL T) -7 NIL NIL NIL) (-775 1805218 1805991 1806019 "NASRING" 1806129 T NASRING (NIL) -9 NIL 1806209 NIL) (-774 1805013 1805057 1805151 "NASRING-" 1805156 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-773 1804106 1804631 1804659 "NARNG" 1804776 T NARNG (NIL) -9 NIL 1804867 NIL) (-772 1803798 1803865 1803999 "NARNG-" 1804004 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-771 1802677 1802884 1803119 "NAGSP" 1803583 T NAGSP (NIL) -7 NIL NIL NIL) (-770 1793949 1795633 1797306 "NAGS" 1801024 T NAGS (NIL) -7 NIL NIL NIL) (-769 1792497 1792805 1793136 "NAGF07" 1793638 T NAGF07 (NIL) -7 NIL NIL NIL) (-768 1787035 1788326 1789633 "NAGF04" 1791210 T NAGF04 (NIL) -7 NIL NIL NIL) (-767 1780003 1781617 1783250 "NAGF02" 1785422 T NAGF02 (NIL) -7 NIL NIL NIL) (-766 1775227 1776327 1777444 "NAGF01" 1778906 T NAGF01 (NIL) -7 NIL NIL NIL) (-765 1768855 1770421 1772006 "NAGE04" 1773662 T NAGE04 (NIL) -7 NIL NIL NIL) (-764 1760024 1762145 1764275 "NAGE02" 1766745 T NAGE02 (NIL) -7 NIL NIL NIL) (-763 1755977 1756924 1757888 "NAGE01" 1759080 T NAGE01 (NIL) -7 NIL NIL NIL) (-762 1753772 1754306 1754864 "NAGD03" 1755439 T NAGD03 (NIL) -7 NIL NIL NIL) (-761 1745522 1747450 1749404 "NAGD02" 1751838 T NAGD02 (NIL) -7 NIL NIL NIL) (-760 1739333 1740758 1742198 "NAGD01" 1744102 T NAGD01 (NIL) -7 NIL NIL NIL) (-759 1735542 1736364 1737201 "NAGC06" 1738516 T NAGC06 (NIL) -7 NIL NIL NIL) (-758 1734007 1734339 1734695 "NAGC05" 1735206 T NAGC05 (NIL) -7 NIL NIL NIL) (-757 1733383 1733502 1733646 "NAGC02" 1733883 T NAGC02 (NIL) -7 NIL NIL NIL) (-756 1732328 1732911 1732951 "NAALG" 1733030 NIL NAALG (NIL T) -9 NIL 1733091 NIL) (-755 1732163 1732192 1732282 "NAALG-" 1732287 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-754 1726113 1727221 1728408 "MULTSQFR" 1731059 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-753 1725432 1725507 1725691 "MULTFACT" 1726025 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-752 1718103 1722017 1722070 "MTSCAT" 1723140 NIL MTSCAT (NIL T T) -9 NIL 1723655 NIL) (-751 1717815 1717869 1717961 "MTHING" 1718043 NIL MTHING (NIL T) -7 NIL NIL NIL) (-750 1717607 1717640 1717700 "MSYSCMD" 1717775 T MSYSCMD (NIL) -7 NIL NIL NIL) (-749 1713689 1716362 1716682 "MSET" 1717320 NIL MSET (NIL T) -8 NIL NIL NIL) (-748 1710758 1713250 1713291 "MSETAGG" 1713296 NIL MSETAGG (NIL T) -9 NIL 1713330 NIL) (-747 1706600 1708137 1708882 "MRING" 1710058 NIL MRING (NIL T T) -8 NIL NIL NIL) (-746 1706166 1706233 1706364 "MRF2" 1706527 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-745 1705784 1705819 1705963 "MRATFAC" 1706125 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-744 1703396 1703691 1704122 "MPRFF" 1705489 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-743 1697417 1703250 1703347 "MPOLY" 1703352 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-742 1696907 1696942 1697150 "MPCPF" 1697376 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-741 1696421 1696464 1696648 "MPC3" 1696858 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-740 1695616 1695697 1695918 "MPC2" 1696336 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-739 1693917 1694254 1694644 "MONOTOOL" 1695276 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-738 1693128 1693445 1693473 "MONOID" 1693692 T MONOID (NIL) -9 NIL 1693839 NIL) (-737 1692674 1692793 1692974 "MONOID-" 1692979 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-736 1682264 1688494 1688553 "MONOGEN" 1689227 NIL MONOGEN (NIL T T) -9 NIL 1689683 NIL) (-735 1679482 1680217 1681217 "MONOGEN-" 1681336 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-734 1678301 1678747 1678775 "MONADWU" 1679167 T MONADWU (NIL) -9 NIL 1679405 NIL) (-733 1677673 1677832 1678080 "MONADWU-" 1678085 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-732 1677018 1677262 1677290 "MONAD" 1677497 T MONAD (NIL) -9 NIL 1677609 NIL) (-731 1676703 1676781 1676913 "MONAD-" 1676918 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-730 1674992 1675616 1675895 "MOEBIUS" 1676456 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-729 1674256 1674660 1674700 "MODULE" 1674705 NIL MODULE (NIL T) -9 NIL 1674744 NIL) (-728 1673824 1673920 1674110 "MODULE-" 1674115 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-727 1671504 1672188 1672515 "MODRING" 1673648 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-726 1668448 1669609 1670130 "MODOP" 1671033 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-725 1667036 1667515 1667792 "MODMONOM" 1668311 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-724 1656804 1665327 1665741 "MODMON" 1666673 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-723 1653960 1655648 1655924 "MODFIELD" 1656679 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-722 1652937 1653241 1653431 "MMLFORM" 1653790 T MMLFORM (NIL) -8 NIL NIL NIL) (-721 1652463 1652506 1652685 "MMAP" 1652888 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-720 1650528 1651295 1651336 "MLO" 1651759 NIL MLO (NIL T) -9 NIL 1652001 NIL) (-719 1647894 1648410 1649012 "MLIFT" 1650009 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-718 1647285 1647369 1647523 "MKUCFUNC" 1647805 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-717 1646884 1646954 1647077 "MKRECORD" 1647208 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-716 1645931 1646093 1646321 "MKFUNC" 1646695 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-715 1645319 1645423 1645579 "MKFLCFN" 1645814 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-714 1644596 1644698 1644883 "MKBCFUNC" 1645212 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-713 1641185 1644150 1644286 "MINT" 1644480 T MINT (NIL) -8 NIL NIL NIL) (-712 1639997 1640240 1640517 "MHROWRED" 1640940 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-711 1635377 1638532 1638937 "MFLOAT" 1639612 T MFLOAT (NIL) -8 NIL NIL NIL) (-710 1634734 1634810 1634981 "MFINFACT" 1635289 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-709 1631049 1631897 1632781 "MESH" 1633870 T MESH (NIL) -7 NIL NIL NIL) (-708 1629439 1629751 1630104 "MDDFACT" 1630736 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-707 1626209 1628570 1628611 "MDAGG" 1628866 NIL MDAGG (NIL T) -9 NIL 1629009 NIL) (-706 1614903 1625502 1625709 "MCMPLX" 1626022 T MCMPLX (NIL) -8 NIL NIL NIL) (-705 1614040 1614186 1614387 "MCDEN" 1614752 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-704 1611930 1612200 1612580 "MCALCFN" 1613770 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-703 1610855 1611095 1611328 "MAYBE" 1611736 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-702 1608467 1608990 1609552 "MATSTOR" 1610326 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-701 1604379 1607839 1608087 "MATRIX" 1608252 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-700 1600145 1600852 1601588 "MATLIN" 1603736 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-699 1589971 1593202 1593279 "MATCAT" 1598311 NIL MATCAT (NIL T T T) -9 NIL 1599783 NIL) (-698 1586164 1587234 1588647 "MATCAT-" 1588652 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-697 1584758 1584911 1585244 "MATCAT2" 1585999 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-696 1582870 1583194 1583578 "MAPPKG3" 1584433 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-695 1581851 1582024 1582246 "MAPPKG2" 1582694 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-694 1580350 1580634 1580961 "MAPPKG1" 1581557 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-693 1579429 1579756 1579933 "MAPPAST" 1580193 T MAPPAST (NIL) -8 NIL NIL NIL) (-692 1579040 1579098 1579221 "MAPHACK3" 1579365 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-691 1578632 1578693 1578807 "MAPHACK2" 1578972 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-690 1578070 1578173 1578315 "MAPHACK1" 1578523 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-689 1576149 1576770 1577074 "MAGMA" 1577798 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-688 1575628 1575873 1575964 "MACROAST" 1576078 T MACROAST (NIL) -8 NIL NIL NIL) (-687 1572049 1573867 1574328 "M3D" 1575200 NIL M3D (NIL T) -8 NIL NIL NIL) (-686 1566099 1570360 1570401 "LZSTAGG" 1571183 NIL LZSTAGG (NIL T) -9 NIL 1571478 NIL) (-685 1562057 1563230 1564687 "LZSTAGG-" 1564692 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-684 1559144 1559948 1560435 "LWORD" 1561602 NIL LWORD (NIL T) -8 NIL NIL NIL) (-683 1558720 1558948 1559023 "LSTAST" 1559089 T LSTAST (NIL) -8 NIL NIL NIL) (-682 1551610 1558491 1558625 "LSQM" 1558630 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-681 1550834 1550973 1551201 "LSPP" 1551465 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-680 1548646 1548947 1549403 "LSMP" 1550523 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-679 1545425 1546099 1546829 "LSMP1" 1547948 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-678 1539227 1544515 1544556 "LSAGG" 1544618 NIL LSAGG (NIL T) -9 NIL 1544696 NIL) (-677 1535922 1536846 1538059 "LSAGG-" 1538064 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-676 1533521 1535066 1535315 "LPOLY" 1535717 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-675 1533103 1533188 1533311 "LPEFRAC" 1533430 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-674 1531424 1532197 1532450 "LO" 1532935 NIL LO (NIL T T T) -8 NIL NIL NIL) (-673 1531036 1531174 1531202 "LOGIC" 1531313 T LOGIC (NIL) -9 NIL 1531394 NIL) (-672 1530898 1530921 1530992 "LOGIC-" 1530997 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-671 1530091 1530231 1530424 "LODOOPS" 1530754 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-670 1527514 1530007 1530073 "LODO" 1530078 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-669 1526052 1526287 1526640 "LODOF" 1527261 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-668 1522256 1524687 1524728 "LODOCAT" 1525166 NIL LODOCAT (NIL T) -9 NIL 1525377 NIL) (-667 1521989 1522047 1522174 "LODOCAT-" 1522179 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-666 1519309 1521830 1521948 "LODO2" 1521953 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-665 1516744 1519246 1519291 "LODO1" 1519296 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-664 1515625 1515790 1516095 "LODEEF" 1516567 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-663 1510903 1513791 1513832 "LNAGG" 1514694 NIL LNAGG (NIL T) -9 NIL 1515129 NIL) (-662 1510050 1510264 1510606 "LNAGG-" 1510611 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-661 1506186 1506975 1507614 "LMOPS" 1509465 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-660 1505575 1505963 1506004 "LMODULE" 1506009 NIL LMODULE (NIL T) -9 NIL 1506035 NIL) (-659 1502776 1505220 1505343 "LMDICT" 1505485 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-658 1502394 1502566 1502607 "LLINSET" 1502668 NIL LLINSET (NIL T) -9 NIL 1502712 NIL) (-657 1502093 1502302 1502362 "LITERAL" 1502367 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-656 1495259 1501027 1501331 "LIST" 1501822 NIL LIST (NIL T) -8 NIL NIL NIL) (-655 1494784 1494858 1494997 "LIST3" 1495179 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-654 1493791 1493969 1494197 "LIST2" 1494602 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-653 1491925 1492237 1492636 "LIST2MAP" 1493438 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-652 1491556 1491744 1491785 "LINSET" 1491790 NIL LINSET (NIL T) -9 NIL 1491824 NIL) (-651 1489969 1490583 1490624 "LINEXP" 1491114 NIL LINEXP (NIL T) -9 NIL 1491387 NIL) (-650 1488546 1488806 1489117 "LINDEP" 1489721 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-649 1485313 1486032 1486809 "LIMITRF" 1487801 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-648 1483616 1483912 1484321 "LIMITPS" 1485008 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-647 1478044 1483127 1483355 "LIE" 1483437 NIL LIE (NIL T T) -8 NIL NIL NIL) (-646 1476978 1477447 1477487 "LIECAT" 1477627 NIL LIECAT (NIL T) -9 NIL 1477778 NIL) (-645 1476819 1476846 1476934 "LIECAT-" 1476939 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-644 1469412 1476359 1476515 "LIB" 1476683 T LIB (NIL) -8 NIL NIL NIL) (-643 1465047 1465930 1466865 "LGROBP" 1468529 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-642 1463045 1463319 1463669 "LF" 1464768 NIL LF (NIL T T) -7 NIL NIL NIL) (-641 1461885 1462577 1462605 "LFCAT" 1462812 T LFCAT (NIL) -9 NIL 1462951 NIL) (-640 1458787 1459417 1460105 "LEXTRIPK" 1461249 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-639 1455531 1456357 1456860 "LEXP" 1458367 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-638 1455007 1455252 1455344 "LETAST" 1455459 T LETAST (NIL) -8 NIL NIL NIL) (-637 1453405 1453718 1454119 "LEADCDET" 1454689 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-636 1452595 1452669 1452898 "LAZM3PK" 1453326 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-635 1447512 1450672 1451210 "LAUPOL" 1452107 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-634 1447091 1447135 1447296 "LAPLACE" 1447462 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-633 1445030 1446192 1446443 "LA" 1446924 NIL LA (NIL T T T) -8 NIL NIL NIL) (-632 1444010 1444594 1444635 "LALG" 1444697 NIL LALG (NIL T) -9 NIL 1444756 NIL) (-631 1443724 1443783 1443919 "LALG-" 1443924 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-630 1443559 1443583 1443624 "KVTFROM" 1443686 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-629 1442482 1442926 1443111 "KTVLOGIC" 1443394 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-628 1442317 1442341 1442382 "KRCFROM" 1442444 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-627 1441221 1441408 1441707 "KOVACIC" 1442117 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-626 1441056 1441080 1441121 "KONVERT" 1441183 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-625 1440891 1440915 1440956 "KOERCE" 1441018 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-624 1438722 1439484 1439861 "KERNEL" 1440547 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-623 1438218 1438299 1438431 "KERNEL2" 1438636 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-622 1431929 1436695 1436749 "KDAGG" 1437126 NIL KDAGG (NIL T T) -9 NIL 1437332 NIL) (-621 1431458 1431582 1431787 "KDAGG-" 1431792 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-620 1424606 1431119 1431274 "KAFILE" 1431336 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-619 1419034 1424117 1424345 "JORDAN" 1424427 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-618 1418413 1418683 1418804 "JOINAST" 1418933 T JOINAST (NIL) -8 NIL NIL NIL) (-617 1418259 1418318 1418373 "JAVACODE" 1418378 T JAVACODE (NIL) -8 NIL NIL NIL) (-616 1414486 1416436 1416490 "IXAGG" 1417419 NIL IXAGG (NIL T T) -9 NIL 1417878 NIL) (-615 1413405 1413711 1414130 "IXAGG-" 1414135 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-614 1408938 1413327 1413386 "IVECTOR" 1413391 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-613 1407704 1407941 1408207 "ITUPLE" 1408705 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-612 1406206 1406383 1406678 "ITRIGMNP" 1407526 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-611 1404951 1405155 1405438 "ITFUN3" 1405982 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-610 1404583 1404640 1404749 "ITFUN2" 1404888 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-609 1403742 1404063 1404237 "ITFORM" 1404429 T ITFORM (NIL) -8 NIL NIL NIL) (-608 1401703 1402762 1403040 "ITAYLOR" 1403497 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-607 1390648 1395840 1397003 "ISUPS" 1400573 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-606 1389752 1389892 1390128 "ISUMP" 1390495 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-605 1385130 1389697 1389738 "ISTRING" 1389743 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-604 1384606 1384851 1384943 "ISAST" 1385058 T ISAST (NIL) -8 NIL NIL NIL) (-603 1383815 1383897 1384113 "IRURPK" 1384520 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-602 1382751 1382952 1383192 "IRSN" 1383595 T IRSN (NIL) -7 NIL NIL NIL) (-601 1380822 1381177 1381606 "IRRF2F" 1382389 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-600 1380569 1380607 1380683 "IRREDFFX" 1380778 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-599 1379184 1379443 1379742 "IROOT" 1380302 NIL IROOT (NIL T) -7 NIL NIL NIL) (-598 1375788 1376868 1377560 "IR" 1378524 NIL IR (NIL T) -8 NIL NIL NIL) (-597 1374993 1375281 1375432 "IRFORM" 1375657 T IRFORM (NIL) -8 NIL NIL NIL) (-596 1372606 1373101 1373667 "IR2" 1374471 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-595 1371706 1371819 1372033 "IR2F" 1372489 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-594 1371497 1371531 1371591 "IPRNTPK" 1371666 T IPRNTPK (NIL) -7 NIL NIL NIL) (-593 1368078 1371386 1371455 "IPF" 1371460 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-592 1366405 1368003 1368060 "IPADIC" 1368065 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-591 1365717 1365965 1366095 "IP4ADDR" 1366295 T IP4ADDR (NIL) -8 NIL NIL NIL) (-590 1365091 1365346 1365478 "IOMODE" 1365605 T IOMODE (NIL) -8 NIL NIL NIL) (-589 1364164 1364688 1364815 "IOBFILE" 1364984 T IOBFILE (NIL) -8 NIL NIL NIL) (-588 1363652 1364068 1364096 "IOBCON" 1364101 T IOBCON (NIL) -9 NIL 1364122 NIL) (-587 1363163 1363221 1363404 "INVLAPLA" 1363588 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-586 1352811 1355165 1357551 "INTTR" 1360827 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-585 1349146 1349888 1350753 "INTTOOLS" 1351996 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-584 1348732 1348823 1348940 "INTSLPE" 1349049 T INTSLPE (NIL) -7 NIL NIL NIL) (-583 1346685 1348655 1348714 "INTRVL" 1348719 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-582 1344287 1344799 1345374 "INTRF" 1346170 NIL INTRF (NIL T) -7 NIL NIL NIL) (-581 1343698 1343795 1343937 "INTRET" 1344185 NIL INTRET (NIL T) -7 NIL NIL NIL) (-580 1341695 1342084 1342554 "INTRAT" 1343306 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-579 1338958 1339541 1340160 "INTPM" 1341180 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-578 1335703 1336302 1337040 "INTPAF" 1338344 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-577 1330882 1331844 1332895 "INTPACK" 1334672 T INTPACK (NIL) -7 NIL NIL NIL) (-576 1327694 1330679 1330788 "INT" 1330793 T INT (NIL) -8 NIL NIL NIL) (-575 1326946 1327098 1327306 "INTHERTR" 1327536 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-574 1326385 1326465 1326653 "INTHERAL" 1326860 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-573 1324231 1324674 1325131 "INTHEORY" 1325948 T INTHEORY (NIL) -7 NIL NIL NIL) (-572 1315637 1317258 1319030 "INTG0" 1322583 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-571 1296210 1301000 1305810 "INTFTBL" 1310847 T INTFTBL (NIL) -8 NIL NIL NIL) (-570 1295459 1295597 1295770 "INTFACT" 1296069 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-569 1292886 1293332 1293889 "INTEF" 1295013 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-568 1291239 1291978 1292006 "INTDOM" 1292307 T INTDOM (NIL) -9 NIL 1292514 NIL) (-567 1290608 1290782 1291024 "INTDOM-" 1291029 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-566 1286968 1288897 1288951 "INTCAT" 1289750 NIL INTCAT (NIL T) -9 NIL 1290071 NIL) (-565 1286440 1286543 1286671 "INTBIT" 1286860 T INTBIT (NIL) -7 NIL NIL NIL) (-564 1285139 1285293 1285600 "INTALG" 1286285 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-563 1284622 1284712 1284869 "INTAF" 1285043 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-562 1277971 1284432 1284572 "INTABL" 1284577 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-561 1277304 1277770 1277835 "INT8" 1277869 T INT8 (NIL) -8 NIL NIL 1277914) (-560 1276636 1277102 1277167 "INT64" 1277201 T INT64 (NIL) -8 NIL NIL 1277246) (-559 1275968 1276434 1276499 "INT32" 1276533 T INT32 (NIL) -8 NIL NIL 1276578) (-558 1275300 1275766 1275831 "INT16" 1275865 T INT16 (NIL) -8 NIL NIL 1275910) (-557 1269995 1272848 1272876 "INS" 1273810 T INS (NIL) -9 NIL 1274475 NIL) (-556 1267235 1268006 1268980 "INS-" 1269053 NIL INS- (NIL T) -8 NIL NIL NIL) (-555 1266010 1266237 1266535 "INPSIGN" 1266988 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-554 1265128 1265245 1265442 "INPRODPF" 1265890 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-553 1264022 1264139 1264376 "INPRODFF" 1265008 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-552 1263022 1263174 1263434 "INNMFACT" 1263858 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-551 1262219 1262316 1262504 "INMODGCD" 1262921 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-550 1260727 1260972 1261296 "INFSP" 1261964 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-549 1259911 1260028 1260211 "INFPROD0" 1260607 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-548 1256766 1257976 1258491 "INFORM" 1259404 T INFORM (NIL) -8 NIL NIL NIL) (-547 1256376 1256436 1256534 "INFORM1" 1256701 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-546 1255899 1255988 1256102 "INFINITY" 1256282 T INFINITY (NIL) -7 NIL NIL NIL) (-545 1255075 1255619 1255720 "INETCLTS" 1255818 T INETCLTS (NIL) -8 NIL NIL NIL) (-544 1253691 1253941 1254262 "INEP" 1254823 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-543 1252896 1253588 1253653 "INDE" 1253658 NIL INDE (NIL T) -8 NIL NIL NIL) (-542 1252460 1252528 1252645 "INCRMAPS" 1252823 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-541 1251278 1251729 1251935 "INBFILE" 1252274 T INBFILE (NIL) -8 NIL NIL NIL) (-540 1246577 1247514 1248458 "INBFF" 1250366 NIL INBFF (NIL T) -7 NIL NIL NIL) (-539 1245485 1245754 1245782 "INBCON" 1246295 T INBCON (NIL) -9 NIL 1246561 NIL) (-538 1244737 1244960 1245236 "INBCON-" 1245241 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-537 1244216 1244461 1244552 "INAST" 1244666 T INAST (NIL) -8 NIL NIL NIL) (-536 1243643 1243895 1244001 "IMPTAST" 1244130 T IMPTAST (NIL) -8 NIL NIL NIL) (-535 1240044 1243487 1243591 "IMATRIX" 1243596 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-534 1238752 1238875 1239191 "IMATQF" 1239900 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-533 1236972 1237199 1237536 "IMATLIN" 1238508 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-532 1231553 1236896 1236954 "ILIST" 1236959 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-531 1229461 1231413 1231526 "IIARRAY2" 1231531 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-530 1224859 1229372 1229436 "IFF" 1229441 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-529 1224206 1224476 1224592 "IFAST" 1224763 T IFAST (NIL) -8 NIL NIL NIL) (-528 1219204 1223498 1223686 "IFARRAY" 1224063 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-527 1218384 1219108 1219181 "IFAMON" 1219186 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-526 1217968 1218033 1218087 "IEVALAB" 1218294 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-525 1217643 1217711 1217871 "IEVALAB-" 1217876 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-524 1217233 1217557 1217620 "IDPO" 1217625 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-523 1216441 1217122 1217197 "IDPOAMS" 1217202 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-522 1215706 1216330 1216405 "IDPOAM" 1216410 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-521 1214563 1214880 1214933 "IDPC" 1215451 NIL IDPC (NIL T T) -9 NIL 1215642 NIL) (-520 1213990 1214455 1214528 "IDPAM" 1214533 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-519 1213324 1213882 1213955 "IDPAG" 1213960 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-518 1212969 1213160 1213235 "IDENT" 1213269 T IDENT (NIL) -8 NIL NIL NIL) (-517 1209224 1210072 1210967 "IDECOMP" 1212126 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-516 1202061 1203147 1204194 "IDEAL" 1208260 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-515 1201221 1201333 1201533 "ICDEN" 1201945 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-514 1200292 1200701 1200848 "ICARD" 1201094 T ICARD (NIL) -8 NIL NIL NIL) (-513 1198352 1198665 1199070 "IBPTOOLS" 1199969 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-512 1193959 1197972 1198085 "IBITS" 1198271 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-511 1190682 1191258 1191953 "IBATOOL" 1193376 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-510 1188461 1188923 1189456 "IBACHIN" 1190217 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-509 1186293 1188307 1188410 "IARRAY2" 1188415 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-508 1182402 1186219 1186276 "IARRAY1" 1186281 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-507 1176262 1180814 1181295 "IAN" 1181941 T IAN (NIL) -8 NIL NIL NIL) (-506 1175773 1175830 1176003 "IALGFACT" 1176199 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-505 1175301 1175414 1175442 "HYPCAT" 1175649 T HYPCAT (NIL) -9 NIL NIL NIL) (-504 1174839 1174956 1175142 "HYPCAT-" 1175147 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-503 1174434 1174634 1174717 "HOSTNAME" 1174776 T HOSTNAME (NIL) -8 NIL NIL NIL) (-502 1174279 1174316 1174357 "HOMOTOP" 1174362 NIL HOMOTOP (NIL T) -9 NIL 1174395 NIL) (-501 1170836 1172211 1172252 "HOAGG" 1173233 NIL HOAGG (NIL T) -9 NIL 1173962 NIL) (-500 1169430 1169829 1170355 "HOAGG-" 1170360 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-499 1163146 1169023 1169173 "HEXADEC" 1169300 T HEXADEC (NIL) -8 NIL NIL NIL) (-498 1161894 1162116 1162379 "HEUGCD" 1162923 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-497 1160970 1161731 1161861 "HELLFDIV" 1161866 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-496 1159152 1160747 1160835 "HEAP" 1160914 NIL HEAP (NIL T) -8 NIL NIL NIL) (-495 1158415 1158704 1158838 "HEADAST" 1159038 T HEADAST (NIL) -8 NIL NIL NIL) (-494 1152258 1158330 1158392 "HDP" 1158397 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-493 1145970 1151893 1152045 "HDMP" 1152159 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-492 1145294 1145434 1145598 "HB" 1145826 T HB (NIL) -7 NIL NIL NIL) (-491 1138686 1145140 1145244 "HASHTBL" 1145249 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-490 1138162 1138407 1138499 "HASAST" 1138614 T HASAST (NIL) -8 NIL NIL NIL) (-489 1135940 1137784 1137966 "HACKPI" 1138000 T HACKPI (NIL) -8 NIL NIL NIL) (-488 1131608 1135793 1135906 "GTSET" 1135911 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-487 1125029 1131486 1131584 "GSTBL" 1131589 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-486 1117416 1124194 1124450 "GSERIES" 1124829 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-485 1116543 1116960 1116988 "GROUP" 1117191 T GROUP (NIL) -9 NIL 1117325 NIL) (-484 1115909 1116068 1116319 "GROUP-" 1116324 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-483 1114276 1114597 1114984 "GROEBSOL" 1115586 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-482 1113176 1113464 1113515 "GRMOD" 1114044 NIL GRMOD (NIL T T) -9 NIL 1114212 NIL) (-481 1112944 1112980 1113108 "GRMOD-" 1113113 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-480 1108234 1109298 1110298 "GRIMAGE" 1111964 T GRIMAGE (NIL) -8 NIL NIL NIL) (-479 1106700 1106961 1107285 "GRDEF" 1107930 T GRDEF (NIL) -7 NIL NIL NIL) (-478 1106144 1106260 1106401 "GRAY" 1106579 T GRAY (NIL) -7 NIL NIL NIL) (-477 1105317 1105723 1105774 "GRALG" 1105927 NIL GRALG (NIL T T) -9 NIL 1106020 NIL) (-476 1104978 1105051 1105214 "GRALG-" 1105219 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-475 1101755 1104563 1104741 "GPOLSET" 1104885 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-474 1101109 1101166 1101424 "GOSPER" 1101692 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-473 1096841 1097547 1098073 "GMODPOL" 1100808 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-472 1095846 1096030 1096268 "GHENSEL" 1096653 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-471 1090002 1090845 1091865 "GENUPS" 1094930 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-470 1089699 1089750 1089839 "GENUFACT" 1089945 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-469 1089111 1089188 1089353 "GENPGCD" 1089617 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-468 1088585 1088620 1088833 "GENMFACT" 1089070 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-467 1087151 1087408 1087715 "GENEEZ" 1088328 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-466 1081023 1086762 1086924 "GDMP" 1087074 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-465 1070366 1074794 1075900 "GCNAALG" 1080006 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-464 1068679 1069541 1069569 "GCDDOM" 1069824 T GCDDOM (NIL) -9 NIL 1069981 NIL) (-463 1068149 1068276 1068491 "GCDDOM-" 1068496 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-462 1066821 1067006 1067310 "GB" 1067928 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-461 1055437 1057767 1060159 "GBINTERN" 1064512 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-460 1053274 1053566 1053987 "GBF" 1055112 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-459 1052055 1052220 1052487 "GBEUCLID" 1053090 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-458 1051404 1051529 1051678 "GAUSSFAC" 1051926 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-457 1049771 1050073 1050387 "GALUTIL" 1051123 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-456 1048079 1048353 1048677 "GALPOLYU" 1049498 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-455 1045444 1045734 1046141 "GALFACTU" 1047776 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-454 1037250 1038749 1040357 "GALFACT" 1043876 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-453 1034638 1035296 1035324 "FVFUN" 1036480 T FVFUN (NIL) -9 NIL 1037200 NIL) (-452 1033904 1034086 1034114 "FVC" 1034405 T FVC (NIL) -9 NIL 1034588 NIL) (-451 1033547 1033729 1033797 "FUNDESC" 1033856 T FUNDESC (NIL) -8 NIL NIL NIL) (-450 1033162 1033344 1033425 "FUNCTION" 1033499 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-449 1030906 1031484 1031950 "FT" 1032716 T FT (NIL) -8 NIL NIL NIL) (-448 1029697 1030207 1030410 "FTEM" 1030723 T FTEM (NIL) -8 NIL NIL NIL) (-447 1027988 1028277 1028674 "FSUPFACT" 1029388 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-446 1026385 1026674 1027006 "FST" 1027676 T FST (NIL) -8 NIL NIL NIL) (-445 1025584 1025690 1025878 "FSRED" 1026267 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-444 1024283 1024539 1024886 "FSPRMELT" 1025299 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-443 1021589 1022027 1022513 "FSPECF" 1023846 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-442 1002654 1011363 1011404 "FS" 1015288 NIL FS (NIL T) -9 NIL 1017577 NIL) (-441 991297 994290 998347 "FS-" 998647 NIL FS- (NIL T T) -8 NIL NIL NIL) (-440 990825 990879 991049 "FSINT" 991238 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-439 989117 989818 990121 "FSERIES" 990604 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-438 988159 988275 988499 "FSCINT" 988997 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-437 984367 987103 987144 "FSAGG" 987514 NIL FSAGG (NIL T) -9 NIL 987773 NIL) (-436 982129 982730 983526 "FSAGG-" 983621 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-435 981171 981314 981541 "FSAGG2" 981982 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-434 978849 979129 979677 "FS2UPS" 980889 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-433 978483 978526 978655 "FS2" 978800 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-432 977361 977532 977834 "FS2EXPXP" 978308 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-431 976787 976902 977054 "FRUTIL" 977241 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-430 968200 972282 973640 "FR" 975461 NIL FR (NIL T) -8 NIL NIL NIL) (-429 963214 965889 965929 "FRNAALG" 967249 NIL FRNAALG (NIL T) -9 NIL 967847 NIL) (-428 958887 959963 961238 "FRNAALG-" 961988 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-427 958525 958568 958695 "FRNAAF2" 958838 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-426 956900 957374 957670 "FRMOD" 958337 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-425 954643 955275 955593 "FRIDEAL" 956691 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-424 953834 953921 954212 "FRIDEAL2" 954550 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-423 952967 953381 953422 "FRETRCT" 953427 NIL FRETRCT (NIL T) -9 NIL 953603 NIL) (-422 952079 952310 952661 "FRETRCT-" 952666 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-421 949153 950363 950422 "FRAMALG" 951304 NIL FRAMALG (NIL T T) -9 NIL 951596 NIL) (-420 947287 947742 948372 "FRAMALG-" 948595 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-419 940930 946760 947037 "FRAC" 947042 NIL FRAC (NIL T) -8 NIL NIL NIL) (-418 940566 940623 940730 "FRAC2" 940867 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-417 940202 940259 940366 "FR2" 940503 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-416 934687 937581 937609 "FPS" 938728 T FPS (NIL) -9 NIL 939285 NIL) (-415 934136 934245 934409 "FPS-" 934555 NIL FPS- (NIL T) -8 NIL NIL NIL) (-414 931424 933093 933121 "FPC" 933346 T FPC (NIL) -9 NIL 933488 NIL) (-413 931217 931257 931354 "FPC-" 931359 NIL FPC- (NIL T) -8 NIL NIL NIL) (-412 930007 930705 930746 "FPATMAB" 930751 NIL FPATMAB (NIL T) -9 NIL 930903 NIL) (-411 928246 928749 929096 "FPARFRAC" 929723 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-410 923640 924138 924820 "FORTRAN" 927678 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-409 921356 921856 922395 "FORT" 923121 T FORT (NIL) -7 NIL NIL NIL) (-408 919032 919594 919622 "FORTFN" 920682 T FORTFN (NIL) -9 NIL 921306 NIL) (-407 918796 918846 918874 "FORTCAT" 918933 T FORTCAT (NIL) -9 NIL 918995 NIL) (-406 916902 917412 917802 "FORMULA" 918426 T FORMULA (NIL) -8 NIL NIL NIL) (-405 916690 916720 916789 "FORMULA1" 916866 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-404 916213 916265 916438 "FORDER" 916632 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-403 915309 915473 915666 "FOP" 916040 T FOP (NIL) -7 NIL NIL NIL) (-402 913890 914589 914763 "FNLA" 915191 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-401 912605 913020 913048 "FNCAT" 913508 T FNCAT (NIL) -9 NIL 913768 NIL) (-400 912144 912564 912592 "FNAME" 912597 T FNAME (NIL) -8 NIL NIL NIL) (-399 910680 911643 911671 "FMTC" 911676 T FMTC (NIL) -9 NIL 911712 NIL) (-398 909426 910616 910662 "FMONOID" 910667 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-397 906213 907381 907422 "FMONCAT" 908639 NIL FMONCAT (NIL T) -9 NIL 909244 NIL) (-396 905363 905955 906104 "FM" 906109 NIL FM (NIL T T) -8 NIL NIL NIL) (-395 902787 903433 903461 "FMFUN" 904605 T FMFUN (NIL) -9 NIL 905313 NIL) (-394 902056 902237 902265 "FMC" 902555 T FMC (NIL) -9 NIL 902737 NIL) (-393 899121 899981 900035 "FMCAT" 901230 NIL FMCAT (NIL T T) -9 NIL 901725 NIL) (-392 897987 898887 898987 "FM1" 899066 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-391 895761 896177 896671 "FLOATRP" 897538 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-390 889339 893490 894111 "FLOAT" 895160 T FLOAT (NIL) -8 NIL NIL NIL) (-389 886777 887277 887855 "FLOATCP" 888806 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-388 885425 886369 886410 "FLINEXP" 886415 NIL FLINEXP (NIL T) -9 NIL 886508 NIL) (-387 884579 884814 885142 "FLINEXP-" 885147 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-386 883655 883799 884023 "FLASORT" 884431 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-385 880757 881625 881677 "FLALG" 882904 NIL FLALG (NIL T T) -9 NIL 883371 NIL) (-384 874417 878166 878207 "FLAGG" 879469 NIL FLAGG (NIL T) -9 NIL 880121 NIL) (-383 873143 873482 873972 "FLAGG-" 873977 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-382 872185 872328 872555 "FLAGG2" 872996 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-381 869022 870030 870089 "FINRALG" 871217 NIL FINRALG (NIL T T) -9 NIL 871725 NIL) (-380 868182 868411 868750 "FINRALG-" 868755 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-379 867548 867787 867815 "FINITE" 868011 T FINITE (NIL) -9 NIL 868118 NIL) (-378 859891 862078 862118 "FINAALG" 865785 NIL FINAALG (NIL T) -9 NIL 867238 NIL) (-377 855223 856273 857417 "FINAALG-" 858796 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-376 854591 854978 855081 "FILE" 855153 NIL FILE (NIL T) -8 NIL NIL NIL) (-375 853235 853573 853627 "FILECAT" 854311 NIL FILECAT (NIL T T) -9 NIL 854527 NIL) (-374 850937 852465 852493 "FIELD" 852533 T FIELD (NIL) -9 NIL 852613 NIL) (-373 849557 849942 850453 "FIELD-" 850458 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-372 847407 848192 848539 "FGROUP" 849243 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-371 846497 846661 846881 "FGLMICPK" 847239 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-370 842329 846422 846479 "FFX" 846484 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-369 841930 841991 842126 "FFSLPE" 842262 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-368 837920 838702 839498 "FFPOLY" 841166 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-367 837424 837460 837669 "FFPOLY2" 837878 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-366 833270 837343 837406 "FFP" 837411 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-365 828668 833181 833245 "FF" 833250 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-364 823794 828011 828201 "FFNBX" 828522 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-363 818722 822929 823187 "FFNBP" 823648 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-362 813355 818006 818217 "FFNB" 818555 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-361 812187 812385 812700 "FFINTBAS" 813152 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-360 808213 810434 810462 "FFIELDC" 811082 T FFIELDC (NIL) -9 NIL 811458 NIL) (-359 806875 807246 807743 "FFIELDC-" 807748 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-358 806444 806490 806614 "FFHOM" 806817 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-357 804139 804626 805143 "FFF" 805959 NIL FFF (NIL T) -7 NIL NIL NIL) (-356 799757 803881 803982 "FFCGX" 804082 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-355 795379 799489 799596 "FFCGP" 799700 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-354 790562 795106 795214 "FFCG" 795315 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-353 770091 780294 780380 "FFCAT" 785545 NIL FFCAT (NIL T T T) -9 NIL 786996 NIL) (-352 765288 766336 767650 "FFCAT-" 768880 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-351 764699 764742 764977 "FFCAT2" 765239 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-350 754022 757671 758891 "FEXPR" 763551 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-349 752984 753419 753460 "FEVALAB" 753544 NIL FEVALAB (NIL T) -9 NIL 753805 NIL) (-348 752143 752353 752691 "FEVALAB-" 752696 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-347 750709 751526 751729 "FDIV" 752042 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-346 747715 748456 748571 "FDIVCAT" 750139 NIL FDIVCAT (NIL T T T T) -9 NIL 750576 NIL) (-345 747477 747504 747674 "FDIVCAT-" 747679 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-344 746697 746784 747061 "FDIV2" 747384 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-343 745671 745992 746194 "FCTRDATA" 746515 T FCTRDATA (NIL) -8 NIL NIL NIL) (-342 744357 744616 744905 "FCPAK1" 745402 T FCPAK1 (NIL) -7 NIL NIL NIL) (-341 743456 743857 743998 "FCOMP" 744248 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-340 727161 730606 734144 "FC" 739938 T FC (NIL) -8 NIL NIL NIL) (-339 719454 723482 723522 "FAXF" 725324 NIL FAXF (NIL T) -9 NIL 726016 NIL) (-338 716731 717388 718213 "FAXF-" 718678 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-337 711786 716107 716283 "FARRAY" 716588 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-336 706666 708733 708786 "FAMR" 709809 NIL FAMR (NIL T T) -9 NIL 710269 NIL) (-335 705556 705858 706293 "FAMR-" 706298 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-334 704725 705478 705531 "FAMONOID" 705536 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-333 702497 703207 703260 "FAMONC" 704201 NIL FAMONC (NIL T T) -9 NIL 704587 NIL) (-332 701161 702251 702388 "FAGROUP" 702393 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-331 698956 699275 699678 "FACUTIL" 700842 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-330 698055 698240 698462 "FACTFUNC" 698766 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-329 690477 697358 697557 "EXPUPXS" 697911 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-328 687960 688500 689086 "EXPRTUBE" 689911 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-327 684231 684823 685553 "EXPRODE" 687299 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-326 669715 682880 683309 "EXPR" 683835 NIL EXPR (NIL T) -8 NIL NIL NIL) (-325 664269 664856 665662 "EXPR2UPS" 669013 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-324 663901 663958 664067 "EXPR2" 664206 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-323 654898 663052 663343 "EXPEXPAN" 663737 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-322 654698 654855 654884 "EXIT" 654889 T EXIT (NIL) -8 NIL NIL NIL) (-321 654178 654422 654513 "EXITAST" 654627 T EXITAST (NIL) -8 NIL NIL NIL) (-320 653805 653867 653980 "EVALCYC" 654110 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-319 653346 653464 653505 "EVALAB" 653675 NIL EVALAB (NIL T) -9 NIL 653779 NIL) (-318 652827 652949 653170 "EVALAB-" 653175 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-317 650181 651483 651511 "EUCDOM" 652066 T EUCDOM (NIL) -9 NIL 652416 NIL) (-316 648586 649028 649618 "EUCDOM-" 649623 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-315 636125 638884 641634 "ESTOOLS" 645856 T ESTOOLS (NIL) -7 NIL NIL NIL) (-314 635757 635814 635923 "ESTOOLS2" 636062 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-313 635508 635550 635630 "ESTOOLS1" 635709 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-312 629531 631139 631167 "ES" 633935 T ES (NIL) -9 NIL 635345 NIL) (-311 624478 625765 627582 "ES-" 627746 NIL ES- (NIL T) -8 NIL NIL NIL) (-310 620852 621613 622393 "ESCONT" 623718 T ESCONT (NIL) -7 NIL NIL NIL) (-309 620597 620629 620711 "ESCONT1" 620814 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-308 620272 620322 620422 "ES2" 620541 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-307 619902 619960 620069 "ES1" 620208 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-306 619118 619247 619423 "ERROR" 619746 T ERROR (NIL) -7 NIL NIL NIL) (-305 612516 618977 619068 "EQTBL" 619073 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-304 605019 607830 609279 "EQ" 611100 NIL -2035 (NIL T) -8 NIL NIL NIL) (-303 604651 604708 604817 "EQ2" 604956 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-302 599942 600989 602082 "EP" 603590 NIL EP (NIL T) -7 NIL NIL NIL) (-301 598542 598833 599139 "ENV" 599656 T ENV (NIL) -8 NIL NIL NIL) (-300 597622 598176 598204 "ENTIRER" 598209 T ENTIRER (NIL) -9 NIL 598255 NIL) (-299 594316 595804 596165 "EMR" 597430 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-298 593446 593631 593685 "ELTAGG" 594065 NIL ELTAGG (NIL T T) -9 NIL 594276 NIL) (-297 593165 593227 593368 "ELTAGG-" 593373 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-296 592929 592958 593012 "ELTAB" 593096 NIL ELTAB (NIL T T) -9 NIL 593148 NIL) (-295 592055 592201 592400 "ELFUTS" 592780 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-294 591797 591853 591881 "ELEMFUN" 591986 T ELEMFUN (NIL) -9 NIL NIL NIL) (-293 591667 591688 591756 "ELEMFUN-" 591761 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-292 586456 589709 589750 "ELAGG" 590690 NIL ELAGG (NIL T) -9 NIL 591153 NIL) (-291 584741 585175 585838 "ELAGG-" 585843 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-290 584053 584190 584346 "ELABOR" 584605 T ELABOR (NIL) -8 NIL NIL NIL) (-289 582714 582993 583287 "ELABEXPR" 583779 T ELABEXPR (NIL) -8 NIL NIL NIL) (-288 575548 577351 578180 "EFUPXS" 581989 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-287 568996 570797 571608 "EFULS" 574823 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-286 566481 566839 567311 "EFSTRUC" 568628 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-285 556272 557838 559386 "EF" 564996 NIL EF (NIL T T) -7 NIL NIL NIL) (-284 555346 555757 555906 "EAB" 556143 T EAB (NIL) -8 NIL NIL NIL) (-283 554528 555305 555333 "E04UCFA" 555338 T E04UCFA (NIL) -8 NIL NIL NIL) (-282 553710 554487 554515 "E04NAFA" 554520 T E04NAFA (NIL) -8 NIL NIL NIL) (-281 552892 553669 553697 "E04MBFA" 553702 T E04MBFA (NIL) -8 NIL NIL NIL) (-280 552074 552851 552879 "E04JAFA" 552884 T E04JAFA (NIL) -8 NIL NIL NIL) (-279 551258 552033 552061 "E04GCFA" 552066 T E04GCFA (NIL) -8 NIL NIL NIL) (-278 550442 551217 551245 "E04FDFA" 551250 T E04FDFA (NIL) -8 NIL NIL NIL) (-277 549624 550401 550429 "E04DGFA" 550434 T E04DGFA (NIL) -8 NIL NIL NIL) (-276 543797 545149 546513 "E04AGNT" 548280 T E04AGNT (NIL) -7 NIL NIL NIL) (-275 542555 543098 543138 "DVARCAT" 543479 NIL DVARCAT (NIL T) -9 NIL 543642 NIL) (-274 541759 541971 542285 "DVARCAT-" 542290 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-273 534620 541558 541687 "DSMP" 541692 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-272 533043 533762 533803 "DSEXT" 534166 NIL DSEXT (NIL T) -9 NIL 534460 NIL) (-271 531328 531756 532422 "DSEXT-" 532427 NIL DSEXT- (NIL T T) -8 NIL NIL NIL) (-270 526109 527273 528341 "DROPT" 530280 T DROPT (NIL) -8 NIL NIL NIL) (-269 525774 525833 525931 "DROPT1" 526044 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-268 520889 522015 523152 "DROPT0" 524657 T DROPT0 (NIL) -7 NIL NIL NIL) (-267 519234 519559 519945 "DRAWPT" 520523 T DRAWPT (NIL) -7 NIL NIL NIL) (-266 513821 514744 515823 "DRAW" 518208 NIL DRAW (NIL T) -7 NIL NIL NIL) (-265 513454 513507 513625 "DRAWHACK" 513762 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-264 512185 512454 512745 "DRAWCX" 513183 T DRAWCX (NIL) -7 NIL NIL NIL) (-263 511700 511769 511920 "DRAWCURV" 512111 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-262 502168 504130 506245 "DRAWCFUN" 509605 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-261 498907 500833 500874 "DQAGG" 501503 NIL DQAGG (NIL T) -9 NIL 501777 NIL) (-260 486372 493118 493201 "DPOLCAT" 495053 NIL DPOLCAT (NIL T T T T) -9 NIL 495598 NIL) (-259 481209 482557 484515 "DPOLCAT-" 484520 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-258 474556 481070 481168 "DPMO" 481173 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-257 467806 474336 474503 "DPMM" 474508 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-256 467376 467590 467679 "DOMTMPLT" 467737 T DOMTMPLT (NIL) -8 NIL NIL NIL) (-255 466809 467178 467258 "DOMCTOR" 467316 T DOMCTOR (NIL) -8 NIL NIL NIL) (-254 466021 466289 466440 "DOMAIN" 466678 T DOMAIN (NIL) -8 NIL NIL NIL) (-253 459733 465656 465808 "DMP" 465922 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-252 457678 458800 458841 "DMEXT" 458846 NIL DMEXT (NIL T) -9 NIL 459022 NIL) (-251 457278 457334 457478 "DLP" 457616 NIL DLP (NIL T) -7 NIL NIL NIL) (-250 451103 456605 456795 "DLIST" 457120 NIL DLIST (NIL T) -8 NIL NIL NIL) (-249 447875 449928 449969 "DLAGG" 450519 NIL DLAGG (NIL T) -9 NIL 450749 NIL) (-248 446537 447201 447229 "DIVRING" 447321 T DIVRING (NIL) -9 NIL 447404 NIL) (-247 445774 445964 446264 "DIVRING-" 446269 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-246 443876 444233 444639 "DISPLAY" 445388 T DISPLAY (NIL) -7 NIL NIL NIL) (-245 437739 443790 443853 "DIRPROD" 443858 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-244 436587 436790 437055 "DIRPROD2" 437532 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-243 425262 431298 431351 "DIRPCAT" 431609 NIL DIRPCAT (NIL NIL T) -9 NIL 432484 NIL) (-242 422588 423230 424111 "DIRPCAT-" 424448 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-241 421875 422035 422221 "DIOSP" 422422 T DIOSP (NIL) -7 NIL NIL NIL) (-240 418505 420759 420800 "DIOPS" 421234 NIL DIOPS (NIL T) -9 NIL 421463 NIL) (-239 418054 418168 418359 "DIOPS-" 418364 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-238 417105 417733 417761 "DIFRING" 417766 T DIFRING (NIL) -9 NIL 417788 NIL) (-237 416777 416851 416879 "DIFFSPC" 416998 T DIFFSPC (NIL) -9 NIL 417073 NIL) (-236 416422 416500 416652 "DIFFSPC-" 416657 NIL DIFFSPC- (NIL T) -8 NIL NIL NIL) (-235 415478 415956 415997 "DIFFMOD" 416002 NIL DIFFMOD (NIL T) -9 NIL 416100 NIL) (-234 415186 415231 415272 "DIFFDOM" 415393 NIL DIFFDOM (NIL T) -9 NIL 415461 NIL) (-233 415039 415063 415147 "DIFFDOM-" 415152 NIL DIFFDOM- (NIL T T) -8 NIL NIL NIL) (-232 412971 414243 414284 "DIFEXT" 414289 NIL DIFEXT (NIL T) -9 NIL 414442 NIL) (-231 410221 412475 412516 "DIAGG" 412521 NIL DIAGG (NIL T) -9 NIL 412541 NIL) (-230 409605 409762 410014 "DIAGG-" 410019 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-229 404977 408564 408841 "DHMATRIX" 409374 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-228 400589 401498 402508 "DFSFUN" 403987 T DFSFUN (NIL) -7 NIL NIL NIL) (-227 395667 399520 399832 "DFLOAT" 400297 T DFLOAT (NIL) -8 NIL NIL NIL) (-226 393930 394211 394600 "DFINTTLS" 395375 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-225 390959 391951 392351 "DERHAM" 393596 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-224 388763 390734 390823 "DEQUEUE" 390903 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-223 388017 388150 388333 "DEGRED" 388625 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-222 384447 385192 386038 "DEFINTRF" 387245 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-221 382002 382471 383063 "DEFINTEF" 383966 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-220 381352 381622 381737 "DEFAST" 381907 T DEFAST (NIL) -8 NIL NIL NIL) (-219 375068 380945 381095 "DECIMAL" 381222 T DECIMAL (NIL) -8 NIL NIL NIL) (-218 372580 373038 373544 "DDFACT" 374612 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-217 372176 372219 372370 "DBLRESP" 372531 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-216 370044 370406 370767 "DBASE" 371942 NIL DBASE (NIL T) -8 NIL NIL NIL) (-215 369286 369524 369670 "DATAARY" 369943 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-214 368392 369245 369273 "D03FAFA" 369278 T D03FAFA (NIL) -8 NIL NIL NIL) (-213 367499 368351 368379 "D03EEFA" 368384 T D03EEFA (NIL) -8 NIL NIL NIL) (-212 365449 365915 366404 "D03AGNT" 367030 T D03AGNT (NIL) -7 NIL NIL NIL) (-211 364738 365408 365436 "D02EJFA" 365441 T D02EJFA (NIL) -8 NIL NIL NIL) (-210 364027 364697 364725 "D02CJFA" 364730 T D02CJFA (NIL) -8 NIL NIL NIL) (-209 363316 363986 364014 "D02BHFA" 364019 T D02BHFA (NIL) -8 NIL NIL NIL) (-208 362605 363275 363303 "D02BBFA" 363308 T D02BBFA (NIL) -8 NIL NIL NIL) (-207 355802 357391 358997 "D02AGNT" 361019 T D02AGNT (NIL) -7 NIL NIL NIL) (-206 353570 354093 354639 "D01WGTS" 355276 T D01WGTS (NIL) -7 NIL NIL NIL) (-205 352637 353529 353557 "D01TRNS" 353562 T D01TRNS (NIL) -8 NIL NIL NIL) (-204 351705 352596 352624 "D01GBFA" 352629 T D01GBFA (NIL) -8 NIL NIL NIL) (-203 350773 351664 351692 "D01FCFA" 351697 T D01FCFA (NIL) -8 NIL NIL NIL) (-202 349841 350732 350760 "D01ASFA" 350765 T D01ASFA (NIL) -8 NIL NIL NIL) (-201 348909 349800 349828 "D01AQFA" 349833 T D01AQFA (NIL) -8 NIL NIL NIL) (-200 347977 348868 348896 "D01APFA" 348901 T D01APFA (NIL) -8 NIL NIL NIL) (-199 347045 347936 347964 "D01ANFA" 347969 T D01ANFA (NIL) -8 NIL NIL NIL) (-198 346113 347004 347032 "D01AMFA" 347037 T D01AMFA (NIL) -8 NIL NIL NIL) (-197 345181 346072 346100 "D01ALFA" 346105 T D01ALFA (NIL) -8 NIL NIL NIL) (-196 344249 345140 345168 "D01AKFA" 345173 T D01AKFA (NIL) -8 NIL NIL NIL) (-195 343317 344208 344236 "D01AJFA" 344241 T D01AJFA (NIL) -8 NIL NIL NIL) (-194 336612 338165 339726 "D01AGNT" 341776 T D01AGNT (NIL) -7 NIL NIL NIL) (-193 335949 336077 336229 "CYCLOTOM" 336480 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-192 332682 333397 334124 "CYCLES" 335242 T CYCLES (NIL) -7 NIL NIL NIL) (-191 331994 332128 332299 "CVMP" 332543 NIL CVMP (NIL T) -7 NIL NIL NIL) (-190 329835 330093 330462 "CTRIGMNP" 331722 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-189 329271 329629 329702 "CTOR" 329782 T CTOR (NIL) -8 NIL NIL NIL) (-188 328780 329002 329103 "CTORKIND" 329190 T CTORKIND (NIL) -8 NIL NIL NIL) (-187 328057 328373 328401 "CTORCAT" 328583 T CTORCAT (NIL) -9 NIL 328696 NIL) (-186 327655 327766 327925 "CTORCAT-" 327930 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-185 327117 327329 327437 "CTORCALL" 327579 NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-184 326491 326590 326743 "CSTTOOLS" 327014 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-183 322290 322947 323705 "CRFP" 325803 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-182 321765 322011 322103 "CRCEAST" 322218 T CRCEAST (NIL) -8 NIL NIL NIL) (-181 320812 320997 321225 "CRAPACK" 321569 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-180 320196 320297 320501 "CPMATCH" 320688 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-179 319921 319949 320055 "CPIMA" 320162 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-178 316269 316941 317660 "COORDSYS" 319256 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-177 315681 315802 315944 "CONTOUR" 316147 T CONTOUR (NIL) -8 NIL NIL NIL) (-176 311572 313684 314176 "CONTFRAC" 315221 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-175 311452 311473 311501 "CONDUIT" 311538 T CONDUIT (NIL) -9 NIL NIL NIL) (-174 310526 311080 311108 "COMRING" 311113 T COMRING (NIL) -9 NIL 311165 NIL) (-173 309580 309884 310068 "COMPPROP" 310362 T COMPPROP (NIL) -8 NIL NIL NIL) (-172 309241 309276 309404 "COMPLPAT" 309539 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-171 298544 309050 309159 "COMPLEX" 309164 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-170 298180 298237 298344 "COMPLEX2" 298481 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-169 297519 297640 297800 "COMPILER" 298040 T COMPILER (NIL) -8 NIL NIL NIL) (-168 297237 297272 297370 "COMPFACT" 297478 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-167 279516 290941 290981 "COMPCAT" 291985 NIL COMPCAT (NIL T) -9 NIL 293333 NIL) (-166 269028 271955 275582 "COMPCAT-" 275938 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-165 268757 268785 268888 "COMMUPC" 268994 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-164 268551 268585 268644 "COMMONOP" 268718 T COMMONOP (NIL) -7 NIL NIL NIL) (-163 268107 268302 268389 "COMM" 268484 T COMM (NIL) -8 NIL NIL NIL) (-162 267683 267911 267986 "COMMAAST" 268052 T COMMAAST (NIL) -8 NIL NIL NIL) (-161 266932 267126 267154 "COMBOPC" 267492 T COMBOPC (NIL) -9 NIL 267667 NIL) (-160 265828 266038 266280 "COMBINAT" 266722 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-159 262285 262859 263486 "COMBF" 265250 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-158 261043 261401 261636 "COLOR" 262070 T COLOR (NIL) -8 NIL NIL NIL) (-157 260519 260764 260856 "COLONAST" 260971 T COLONAST (NIL) -8 NIL NIL NIL) (-156 260159 260206 260331 "CMPLXRT" 260466 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-155 259607 259859 259958 "CLLCTAST" 260080 T CLLCTAST (NIL) -8 NIL NIL NIL) (-154 255109 256137 257217 "CLIP" 258547 T CLIP (NIL) -7 NIL NIL NIL) (-153 253450 254210 254450 "CLIF" 254936 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-152 249600 251568 251609 "CLAGG" 252538 NIL CLAGG (NIL T) -9 NIL 253074 NIL) (-151 248022 248479 249062 "CLAGG-" 249067 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-150 247566 247651 247791 "CINTSLPE" 247931 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-149 245067 245538 246086 "CHVAR" 247094 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-148 244227 244781 244809 "CHARZ" 244814 T CHARZ (NIL) -9 NIL 244829 NIL) (-147 243981 244021 244099 "CHARPOL" 244181 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-146 243025 243612 243640 "CHARNZ" 243687 T CHARNZ (NIL) -9 NIL 243743 NIL) (-145 240931 241679 242032 "CHAR" 242692 T CHAR (NIL) -8 NIL NIL NIL) (-144 240657 240718 240746 "CFCAT" 240857 T CFCAT (NIL) -9 NIL NIL NIL) (-143 239898 240009 240192 "CDEN" 240541 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-142 235863 239051 239331 "CCLASS" 239638 T CCLASS (NIL) -8 NIL NIL NIL) (-141 235114 235271 235448 "CATEGORY" 235706 T -10 (NIL) -8 NIL NIL NIL) (-140 234687 235033 235081 "CATCTOR" 235086 T CATCTOR (NIL) -8 NIL NIL NIL) (-139 234138 234390 234488 "CATAST" 234609 T CATAST (NIL) -8 NIL NIL NIL) (-138 233614 233859 233951 "CASEAST" 234066 T CASEAST (NIL) -8 NIL NIL NIL) (-137 228752 229771 230515 "CARTEN" 232926 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-136 227860 228008 228229 "CARTEN2" 228599 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-135 226176 227010 227267 "CARD" 227623 T CARD (NIL) -8 NIL NIL NIL) (-134 225752 225980 226055 "CAPSLAST" 226121 T CAPSLAST (NIL) -8 NIL NIL NIL) (-133 225242 225450 225478 "CACHSET" 225610 T CACHSET (NIL) -9 NIL 225688 NIL) (-132 224698 225020 225048 "CABMON" 225098 T CABMON (NIL) -9 NIL 225154 NIL) (-131 224171 224402 224512 "BYTEORD" 224608 T BYTEORD (NIL) -8 NIL NIL NIL) (-130 223148 223700 223842 "BYTE" 224005 T BYTE (NIL) -8 NIL NIL 224127) (-129 218501 222653 222825 "BYTEBUF" 222996 T BYTEBUF (NIL) -8 NIL NIL NIL) (-128 216013 218193 218300 "BTREE" 218427 NIL BTREE (NIL T) -8 NIL NIL NIL) (-127 213465 215661 215783 "BTOURN" 215923 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-126 210810 212907 212948 "BTCAT" 213016 NIL BTCAT (NIL T) -9 NIL 213093 NIL) (-125 210477 210557 210706 "BTCAT-" 210711 NIL BTCAT- (NIL T T) -8 NIL NIL NIL) (-124 205842 209723 209751 "BTAGG" 209865 T BTAGG (NIL) -9 NIL 209975 NIL) (-123 205332 205457 205663 "BTAGG-" 205668 NIL BTAGG- (NIL T) -8 NIL NIL NIL) (-122 202330 204610 204825 "BSTREE" 205149 NIL BSTREE (NIL T) -8 NIL NIL NIL) (-121 201468 201594 201778 "BRILL" 202186 NIL BRILL (NIL T) -7 NIL NIL NIL) (-120 198095 200166 200207 "BRAGG" 200856 NIL BRAGG (NIL T) -9 NIL 201114 NIL) (-119 196624 197030 197585 "BRAGG-" 197590 NIL BRAGG- (NIL T T) -8 NIL NIL NIL) (-118 189540 195968 196153 "BPADICRT" 196471 NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-117 187855 189477 189522 "BPADIC" 189527 NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-116 187553 187583 187697 "BOUNDZRO" 187819 NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-115 182781 183979 184891 "BOP" 186661 T BOP (NIL) -8 NIL NIL NIL) (-114 180562 180966 181441 "BOP1" 182339 NIL BOP1 (NIL T) -7 NIL NIL NIL) (-113 180263 180324 180352 "BOOLE" 180463 T BOOLE (NIL) -9 NIL 180545 NIL) (-112 179088 179837 179986 "BOOLEAN" 180134 T BOOLEAN (NIL) -8 NIL NIL NIL) (-111 178353 178757 178811 "BMODULE" 178816 NIL BMODULE (NIL T T) -9 NIL 178881 NIL) (-110 174154 178151 178224 "BITS" 178300 T BITS (NIL) -8 NIL NIL NIL) (-109 173575 173694 173834 "BINDING" 174034 T BINDING (NIL) -8 NIL NIL NIL) (-108 167294 173170 173319 "BINARY" 173446 T BINARY (NIL) -8 NIL NIL NIL) (-107 165049 166521 166562 "BGAGG" 166822 NIL BGAGG (NIL T) -9 NIL 166959 NIL) (-106 164880 164912 165003 "BGAGG-" 165008 NIL BGAGG- (NIL T T) -8 NIL NIL NIL) (-105 163951 164264 164469 "BFUNCT" 164695 T BFUNCT (NIL) -8 NIL NIL NIL) (-104 162641 162819 163107 "BEZOUT" 163775 NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 159113 161493 161823 "BBTREE" 162344 NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 158714 158792 158820 "BASTYPE" 158997 T BASTYPE (NIL) -9 NIL 159096 NIL) (-101 158390 158471 158606 "BASTYPE-" 158611 NIL BASTYPE- (NIL T) -8 NIL NIL NIL) (-100 157824 157900 158052 "BALFACT" 158301 NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 156680 157239 157425 "AUTOMOR" 157669 NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-98 156406 156411 156437 "ATTREG" 156442 T ATTREG (NIL) -9 NIL NIL NIL) (-97 154658 155103 155455 "ATTRBUT" 156072 T ATTRBUT (NIL) -8 NIL NIL NIL) (-96 154266 154486 154552 "ATTRAST" 154610 T ATTRAST (NIL) -8 NIL NIL NIL) (-95 153802 153915 153941 "ATRIG" 154142 T ATRIG (NIL) -9 NIL NIL NIL) (-94 153611 153652 153739 "ATRIG-" 153744 NIL ATRIG- (NIL T) -8 NIL NIL NIL) (-93 153242 153428 153454 "ASTCAT" 153459 T ASTCAT (NIL) -9 NIL 153489 NIL) (-92 152969 153028 153147 "ASTCAT-" 153152 NIL ASTCAT- (NIL T) -8 NIL NIL NIL) (-91 151121 152745 152833 "ASTACK" 152912 NIL ASTACK (NIL T) -8 NIL NIL NIL) (-90 149626 149923 150288 "ASSOCEQ" 150803 NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-89 148658 149285 149409 "ASP9" 149533 NIL ASP9 (NIL NIL) -8 NIL NIL NIL) (-88 148421 148606 148645 "ASP8" 148650 NIL ASP8 (NIL NIL) -8 NIL NIL NIL) (-87 147289 148026 148168 "ASP80" 148310 NIL ASP80 (NIL NIL) -8 NIL NIL NIL) (-86 146187 146924 147056 "ASP7" 147188 NIL ASP7 (NIL NIL) -8 NIL NIL NIL) (-85 145141 145864 145982 "ASP78" 146100 NIL ASP78 (NIL NIL) -8 NIL NIL NIL) (-84 144110 144821 144938 "ASP77" 145055 NIL ASP77 (NIL NIL) -8 NIL NIL NIL) (-83 143022 143748 143879 "ASP74" 144010 NIL ASP74 (NIL NIL) -8 NIL NIL NIL) (-82 141922 142657 142789 "ASP73" 142921 NIL ASP73 (NIL NIL) -8 NIL NIL NIL) (-81 141026 141748 141848 "ASP6" 141853 NIL ASP6 (NIL NIL) -8 NIL NIL NIL) (-80 139973 140703 140821 "ASP55" 140939 NIL ASP55 (NIL NIL) -8 NIL NIL NIL) (-79 138922 139647 139766 "ASP50" 139885 NIL ASP50 (NIL NIL) -8 NIL NIL NIL) (-78 138010 138623 138733 "ASP4" 138843 NIL ASP4 (NIL NIL) -8 NIL NIL NIL) (-77 137098 137711 137821 "ASP49" 137931 NIL ASP49 (NIL NIL) -8 NIL NIL NIL) (-76 135882 136637 136805 "ASP42" 136987 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-75 134659 135415 135585 "ASP41" 135769 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-74 133609 134336 134454 "ASP35" 134572 NIL ASP35 (NIL NIL) -8 NIL NIL NIL) (-73 133374 133557 133596 "ASP34" 133601 NIL ASP34 (NIL NIL) -8 NIL NIL NIL) (-72 133111 133178 133254 "ASP33" 133329 NIL ASP33 (NIL NIL) -8 NIL NIL NIL) (-71 132005 132746 132878 "ASP31" 133010 NIL ASP31 (NIL NIL) -8 NIL NIL NIL) (-70 131770 131953 131992 "ASP30" 131997 NIL ASP30 (NIL NIL) -8 NIL NIL NIL) (-69 131505 131574 131650 "ASP29" 131725 NIL ASP29 (NIL NIL) -8 NIL NIL NIL) (-68 131270 131453 131492 "ASP28" 131497 NIL ASP28 (NIL NIL) -8 NIL NIL NIL) (-67 131035 131218 131257 "ASP27" 131262 NIL ASP27 (NIL NIL) -8 NIL NIL NIL) (-66 130119 130733 130844 "ASP24" 130955 NIL ASP24 (NIL NIL) -8 NIL NIL NIL) (-65 129196 129921 130033 "ASP20" 130038 NIL ASP20 (NIL NIL) -8 NIL NIL NIL) (-64 128284 128897 129007 "ASP1" 129117 NIL ASP1 (NIL NIL) -8 NIL NIL NIL) (-63 127227 127958 128077 "ASP19" 128196 NIL ASP19 (NIL NIL) -8 NIL NIL NIL) (-62 126964 127031 127107 "ASP12" 127182 NIL ASP12 (NIL NIL) -8 NIL NIL NIL) (-61 125816 126563 126707 "ASP10" 126851 NIL ASP10 (NIL NIL) -8 NIL NIL NIL) (-60 123670 125660 125751 "ARRAY2" 125756 NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 119438 123318 123432 "ARRAY1" 123587 NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-58 118470 118643 118864 "ARRAY12" 119261 NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-57 112757 114672 114747 "ARR2CAT" 117377 NIL ARR2CAT (NIL T T T) -9 NIL 118135 NIL) (-56 110191 110935 111889 "ARR2CAT-" 111894 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL NIL) (-55 109508 109818 109943 "ARITY" 110084 T ARITY (NIL) -8 NIL NIL NIL) (-54 108284 108436 108735 "APPRULE" 109344 NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 107935 107983 108102 "APPLYORE" 108230 NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 107289 107528 107648 "ANY" 107833 T ANY (NIL) -8 NIL NIL NIL) (-51 106567 106690 106847 "ANY1" 107163 NIL ANY1 (NIL T) -7 NIL NIL NIL) (-50 104097 105004 105331 "ANTISYM" 106291 NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 103589 103804 103900 "ANON" 104019 T ANON (NIL) -8 NIL NIL NIL) (-48 97589 102128 102582 "AN" 103153 T AN (NIL) -8 NIL NIL NIL) (-47 93473 94861 94912 "AMR" 95660 NIL AMR (NIL T T) -9 NIL 96260 NIL) (-46 92585 92806 93169 "AMR-" 93174 NIL AMR- (NIL T T T) -8 NIL NIL NIL) (-45 77030 92502 92563 "ALIST" 92568 NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 73835 76624 76793 "ALGSC" 76948 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 70391 70945 71552 "ALGPKG" 73275 NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 69668 69769 69953 "ALGMFACT" 70277 NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 65703 66282 66876 "ALGMANIP" 69252 NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 55914 65329 65479 "ALGFF" 65636 NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 55110 55241 55420 "ALGFACT" 55772 NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 54037 54637 54675 "ALGEBRA" 54680 NIL ALGEBRA (NIL T) -9 NIL 54721 NIL) (-37 53755 53814 53946 "ALGEBRA-" 53951 NIL ALGEBRA- (NIL T T) -8 NIL NIL NIL) (-36 35692 51592 51644 "ALAGG" 51780 NIL ALAGG (NIL T T) -9 NIL 51941 NIL) (-35 35228 35341 35367 "AHYP" 35568 T AHYP (NIL) -9 NIL NIL NIL) (-34 34159 34407 34433 "AGG" 34932 T AGG (NIL) -9 NIL 35211 NIL) (-33 33593 33755 33969 "AGG-" 33974 NIL AGG- (NIL T) -8 NIL NIL NIL) (-32 31399 31822 32227 "AF" 33235 NIL AF (NIL T T) -7 NIL NIL NIL) (-31 30879 31124 31214 "ADDAST" 31327 T ADDAST (NIL) -8 NIL NIL NIL) (-30 30147 30406 30562 "ACPLOT" 30741 T ACPLOT (NIL) -8 NIL NIL NIL) (-29 18770 27079 27117 "ACFS" 27724 NIL ACFS (NIL T) -9 NIL 27963 NIL) (-28 16797 17287 18049 "ACFS-" 18054 NIL ACFS- (NIL T T) -8 NIL NIL NIL) (-27 12901 14830 14856 "ACF" 15735 T ACF (NIL) -9 NIL 16148 NIL) (-26 11605 11939 12432 "ACF-" 12437 NIL ACF- (NIL T) -8 NIL NIL NIL) (-25 11163 11358 11384 "ABELSG" 11476 T ABELSG (NIL) -9 NIL 11541 NIL) (-24 11030 11055 11121 "ABELSG-" 11126 NIL ABELSG- (NIL T) -8 NIL NIL NIL) (-23 10359 10646 10672 "ABELMON" 10842 T ABELMON (NIL) -9 NIL 10954 NIL) (-22 10023 10107 10245 "ABELMON-" 10250 NIL ABELMON- (NIL T) -8 NIL NIL NIL) (-21 9357 9729 9755 "ABELGRP" 9827 T ABELGRP (NIL) -9 NIL 9902 NIL) (-20 8820 8949 9165 "ABELGRP-" 9170 NIL ABELGRP- (NIL T) -8 NIL NIL NIL) (-19 4333 8082 8121 "A1AGG" 8126 NIL A1AGG (NIL T) -9 NIL 8166 NIL) (-18 30 1251 2813 "A1AGG-" 2818 NIL A1AGG- (NIL T T) -8 NIL NIL NIL))
\ No newline at end of file diff --git a/src/share/algebra/operation.daase b/src/share/algebra/operation.daase index be7adb0f..d19c8f79 100644 --- a/src/share/algebra/operation.daase +++ b/src/share/algebra/operation.daase @@ -1,1773 +1,4796 @@ -(731540 . 3486815903) -(((*1 *2 *3 *4 *4 *5 *6) - (-12 (-5 *3 (-656 (-656 (-961 (-227))))) (-5 *4 (-887)) - (-5 *5 (-939)) (-5 *6 (-656 (-270))) (-5 *2 (-1288)) - (-5 *1 (-1291)))) - ((*1 *2 *3 *4) - (-12 (-5 *3 (-656 (-656 (-961 (-227))))) (-5 *4 (-656 (-270))) - (-5 *2 (-1288)) (-5 *1 (-1291))))) -(((*1 *2 *1) (-12 (-5 *2 (-656 (-624 *1))) (-4 *1 (-312))))) -(((*1 *1 *2 *3 *3 *4 *4) - (-12 (-5 *2 (-970 (-576))) (-5 *3 (-1196)) - (-5 *4 (-1114 (-419 (-576)))) (-5 *1 (-30))))) +(731541 . 3486820629) +(((*1 *2 *3) + (-12 (-5 *3 (-701 (-419 (-971 *4)))) (-4 *4 (-464)) + (-5 *2 (-656 (-3 (-419 (-971 *4)) (-1186 (-1197) (-971 *4))))) + (-5 *1 (-302 *4))))) +(((*1 *1 *2 *3) + (-12 (-5 *2 (-518)) (-5 *3 (-656 (-984))) (-5 *1 (-109))))) +(((*1 *1 *1 *1) + (-12 (-5 *1 (-137 *2 *3 *4)) (-14 *2 (-576)) (-14 *3 (-783)) + (-4 *4 (-174)))) + ((*1 *2 *2 *3) + (-12 (-5 *3 (-1197)) (-4 *4 (-568)) (-5 *1 (-159 *4 *2)) + (-4 *2 (-442 *4)))) + ((*1 *2 *2 *3) + (-12 (-5 *3 (-1113 *2)) (-4 *2 (-442 *4)) (-4 *4 (-568)) + (-5 *1 (-159 *4 *2)))) + ((*1 *1 *1 *2) (-12 (-5 *2 (-1113 *1)) (-4 *1 (-161)))) + ((*1 *1 *1 *2) (-12 (-4 *1 (-161)) (-5 *2 (-1197)))) + ((*1 *1 *1 *1) + (-12 (-4 *1 (-477 *2 *3)) (-4 *2 (-174)) (-4 *3 (-23)))) + ((*1 *1 *1 *1 *2) + (-12 (-5 *2 (-783)) (-5 *1 (-1308 *3 *4)) (-4 *3 (-861)) + (-4 *4 (-174))))) +(((*1 *2 *2) + (-12 (-4 *3 (-464)) (-5 *1 (-1229 *3 *2)) + (-4 *2 (-13 (-442 *3) (-1223)))))) +(((*1 *2 *2) (|partial| -12 (-5 *1 (-570 *2)) (-4 *2 (-557))))) +(((*1 *1 *2 *2 *3) (-12 (-5 *2 (-1179)) (-5 *3 (-835)) (-5 *1 (-834))))) (((*1 *2 *3) - (-12 (-4 *4 (-568)) (-4 *5 (-805)) (-4 *6 (-861)) - (-4 *7 (-1085 *4 *5 *6)) - (-5 *2 (-2 (|:| |goodPols| (-656 *7)) (|:| |badPols| (-656 *7)))) - (-5 *1 (-997 *4 *5 *6 *7)) (-5 *3 (-656 *7))))) -(((*1 *2 *3) (-12 (-5 *2 (-419 (-576))) (-5 *1 (-573)) (-5 *3 (-576)))) - ((*1 *2 *3) - (-12 (-5 *2 (-1192 (-419 (-576)))) (-5 *1 (-960)) (-5 *3 (-576))))) -(((*1 *1 *1 *2 *3 *1) - (-12 (-5 *2 (-783)) (-5 *1 (-794 *3)) (-4 *3 (-1069)))) - ((*1 *1 *1 *2 *3 *1) - (-12 (-5 *1 (-981 *3 *2)) (-4 *2 (-132)) (-4 *3 (-568)) - (-4 *3 (-1069)) (-4 *2 (-804)))) - ((*1 *1 *1 *2 *3 *1) - (-12 (-5 *2 (-783)) (-5 *1 (-1192 *3)) (-4 *3 (-1069)))) - ((*1 *1 *1 *2 *3 *1) - (-12 (-5 *2 (-991)) (-4 *2 (-132)) (-5 *1 (-1198 *3)) (-4 *3 (-568)) - (-4 *3 (-1069)))) - ((*1 *1 *1 *2 *3 *1) - (-12 (-5 *2 (-783)) (-5 *1 (-1260 *4 *3)) (-14 *4 (-1196)) - (-4 *3 (-1069))))) -(((*1 *2 *1) (-12 (-5 *2 (-656 (-185 (-140)))) (-5 *1 (-141))))) -(((*1 *2 *1) - (-12 (-4 *1 (-1249 *3 *2)) (-4 *3 (-1069)) (-4 *2 (-1278 *3))))) -(((*1 *2 *1) (-12 + (-5 *3 + (-2 (|:| |var| (-1197)) (|:| |fn| (-326 (-227))) + (|:| -3343 (-1115 (-855 (-227)))) (|:| |abserr| (-227)) + (|:| |relerr| (-227)))) (-5 *2 - (-656 - (-2 (|:| |flg| (-3 "nil" "sqfr" "irred" "prime")) (|:| |fctr| *3) - (|:| |xpnt| (-576))))) - (-5 *1 (-430 *3)) (-4 *3 (-568)))) - ((*1 *2 *3 *4 *4 *4) - (-12 (-5 *4 (-783)) (-4 *3 (-360)) (-4 *5 (-1263 *3)) - (-5 *2 (-656 (-1192 *3))) (-5 *1 (-510 *3 *5 *6)) - (-4 *6 (-1263 *5))))) -(((*1 *1 *1 *2) (-12 (-4 *1 (-1164)) (-5 *2 (-142)))) - ((*1 *1 *1 *2) (-12 (-4 *1 (-1164)) (-5 *2 (-145))))) -(((*1 *2 *1 *1) + (-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| (-1178 (-227))) + (|:| |notEvaluated| + "Internal singularities not yet evaluated"))) + (|:| -3343 + (-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 (-571))))) +(((*1 *2 *2 *3) + (-12 (-5 *1 (-691 *2 *3)) (-4 *2 (-1121)) (-4 *3 (-1121))))) +(((*1 *1 *2 *1) (-12 (-4 *1 (-107 *2)) (-4 *2 (-1238)))) + ((*1 *1 *2 *1) (-12 (-5 *1 (-122 *2)) (-4 *2 (-861)))) + ((*1 *1 *2 *1) (-12 (-5 *1 (-127 *2)) (-4 *2 (-861)))) + ((*1 *1 *1 *1 *2) + (-12 (-5 *2 (-576)) (-4 *1 (-292 *3)) (-4 *3 (-1238)))) + ((*1 *1 *2 *1 *3) + (-12 (-5 *3 (-576)) (-4 *1 (-292 *2)) (-4 *2 (-1238)))) + ((*1 *1 *2) (-12 (-5 *2 - (-2 (|:| -2861 *3) (|:| |gap| (-783)) (|:| -4299 (-794 *3)) - (|:| -2960 (-794 *3)))) - (-5 *1 (-794 *3)) (-4 *3 (-1069)))) - ((*1 *2 *1 *1 *3) - (-12 (-4 *4 (-1069)) (-4 *5 (-805)) (-4 *3 (-861)) - (-5 *2 - (-2 (|:| -2861 *1) (|:| |gap| (-783)) (|:| -4299 *1) - (|:| -2960 *1))) - (-4 *1 (-1085 *4 *5 *3)))) - ((*1 *2 *1 *1) - (-12 (-4 *3 (-1069)) (-4 *4 (-805)) (-4 *5 (-861)) + (-2 + (|:| -4300 + (-2 (|:| |var| (-1197)) (|:| |fn| (-326 (-227))) + (|:| -3343 (-1115 (-855 (-227)))) (|:| |abserr| (-227)) + (|:| |relerr| (-227)))) + (|:| -4438 + (-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| (-1178 (-227))) + (|:| |notEvaluated| + "Internal singularities not yet evaluated"))) + (|:| -3343 + (-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 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\ No newline at end of file |