From 372cd9bfe6aa41bacd17b25579a10a69b3933e2a Mon Sep 17 00:00:00 2001 From: dos-reis Date: Mon, 15 Jun 2009 00:57:36 +0000 Subject: * algebra/any.spad.pamphlet (Any): Remove domainOf, objectOf, and showTypeInOutput. Tidy. * algebra/fortran.spad.pamphlet: Coerce Any objects to Output; don't use objectOf. --- src/share/algebra/browse.daase | 1134 +- src/share/algebra/category.daase | 222 +- src/share/algebra/compress.daase | 1317 +- src/share/algebra/interp.daase | 8870 +++++----- src/share/algebra/operation.daase | 33355 ++++++++++++++++++------------------ 5 files changed, 22446 insertions(+), 22452 deletions(-) (limited to 'src/share/algebra') diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase index 5c151794..4296fdaf 100644 --- a/src/share/algebra/browse.daase +++ b/src/share/algebra/browse.daase @@ -1,12 +1,12 @@ -(2285497 . 3453749792) +(2284982 . 3453990495) (-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."))) -((-4418 . T) (-4417 . T)) +((-4415 . T) (-4414 . 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(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\spad{zerosOf(p)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) (|Polynomial| $)) "\\spad{zerosOf(p)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible. Otherwise they are implicit algebraic quantities. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|zeroOf| (($ (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{zeroOf(p,{} y)} returns \\spad{y} such that \\spad{p(y) = 0}; if possible,{} \\spad{y} is expressed in terms of radicals. Otherwise it is an implicit algebraic quantity which displays as \\spad{'y}.") (($ (|SparseUnivariatePolynomial| $)) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}; if possible,{} \\spad{y} is expressed in terms of radicals. Otherwise it is an implicit algebraic quantity.") (($ (|Polynomial| $)) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. If possible,{} \\spad{y} is expressed in terms of radicals. Otherwise it is an implicit algebraic quantity. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootsOf| (((|List| $) (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{rootsOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}; The returned roots display as \\spad{'y1},{}...,{}\\spad{'yn}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\spad{rootsOf(p)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) (|Polynomial| $)) "\\spad{rootsOf(p)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{rootOf(p,{} y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ (|SparseUnivariatePolynomial| $)) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}.") (($ (|Polynomial| $)) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) -((-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) +((-4406 . T) (-4412 . T) (-4407 . T) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) NIL (-28 S R) ((|constructor| (NIL "Model for algebraically closed function spaces.")) (|zerosOf| (((|List| $) $ (|Symbol|)) "\\spad{zerosOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{zerosOf(p)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable.")) (|zeroOf| (($ $ (|Symbol|)) "\\spad{zeroOf(p,{} y)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity which displays as \\spad{'y}.") (($ $) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity. Error: if \\spad{p} has more than one variable.")) (|rootsOf| (((|List| $) $ (|Symbol|)) "\\spad{rootsOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}; The returned roots display as \\spad{'y1},{}...,{}\\spad{'yn}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{rootsOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}; Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ $ (|Symbol|)) "\\spad{rootOf(p,{}y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) @@ -46,7 +46,7 @@ NIL NIL (-29 R) ((|constructor| (NIL "Model for algebraically closed function spaces.")) (|zerosOf| (((|List| $) $ (|Symbol|)) "\\spad{zerosOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{zerosOf(p)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable.")) (|zeroOf| (($ $ (|Symbol|)) "\\spad{zeroOf(p,{} y)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity which displays as \\spad{'y}.") (($ $) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity. Error: if \\spad{p} has more than one variable.")) (|rootsOf| (((|List| $) $ (|Symbol|)) "\\spad{rootsOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}; The returned roots display as \\spad{'y1},{}...,{}\\spad{'yn}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{rootsOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}; Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ $ (|Symbol|)) "\\spad{rootOf(p,{}y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) -((-4414 . T) (-4412 . T) (-4411 . T) ((-4419 "*") . T) (-4410 . T) (-4415 . T) (-4409 . T)) +((-4411 . T) (-4409 . T) (-4408 . T) ((-4416 "*") . T) (-4407 . T) (-4412 . T) (-4406 . T)) NIL (-30) ((|constructor| (NIL "\\indented{1}{Plot a NON-SINGULAR plane algebraic curve \\spad{p}(\\spad{x},{}\\spad{y}) = 0.} Author: Clifton \\spad{J}. Williamson Date Created: Fall 1988 Date Last Updated: 27 April 1990 Keywords: algebraic curve,{} non-singular,{} plot Examples: References:")) (|refine| (($ $ (|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 -2382) +(-32 R -2386) ((|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 -1038) (QUOTE (-566))))) (-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 -4417))) +((|HasAttribute| |#1| (QUOTE -4414))) (-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}."))) -((-4417 . T) (-4418 . T)) +((-4414 . T) (-4415 . T)) NIL (-37 S R) ((|constructor| (NIL "The category of associative algebras (modules which are themselves rings). \\blankline"))) @@ -82,17 +82,17 @@ NIL NIL (-38 R) ((|constructor| (NIL "The category of associative algebras (modules which are themselves rings). \\blankline"))) -((-4411 . T) (-4412 . T) (-4414 . T)) +((-4408 . T) (-4409 . T) (-4411 . 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 -2382 UP UPUP -4030) +(-40 -2386 UP UPUP -2468) ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) -((-4410 |has| (-409 |#2|) (-365)) (-4415 |has| (-409 |#2|) (-365)) (-4409 |has| (-409 |#2|) (-365)) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) +((-4407 |has| (-409 |#2|) (-365)) (-4412 |has| (-409 |#2|) (-365)) (-4406 |has| (-409 |#2|) (-365)) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) ((|HasCategory| (-409 |#2|) (QUOTE (-145))) (|HasCategory| (-409 |#2|) (QUOTE (-147))) (|HasCategory| (-409 |#2|) (QUOTE (-351))) (-2805 (|HasCategory| (-409 |#2|) (QUOTE (-365))) (|HasCategory| (-409 |#2|) (QUOTE (-351)))) (|HasCategory| (-409 |#2|) (QUOTE (-365))) (|HasCategory| (-409 |#2|) (QUOTE (-370))) (-2805 (-12 (|HasCategory| (-409 |#2|) (QUOTE (-233))) (|HasCategory| (-409 |#2|) (QUOTE (-365)))) (|HasCategory| (-409 |#2|) (QUOTE (-351)))) (-2805 (-12 (|HasCategory| (-409 |#2|) (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| (-409 |#2|) (QUOTE (-365)))) (-12 (|HasCategory| (-409 |#2|) (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| (-409 |#2|) (QUOTE (-351))))) (|HasCategory| (-409 |#2|) (LIST (QUOTE -639) (QUOTE (-566)))) (-2805 (|HasCategory| (-409 |#2|) (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| (-409 |#2|) (QUOTE (-365)))) (|HasCategory| (-409 |#2|) (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| (-409 |#2|) (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-370))) (-12 (|HasCategory| (-409 |#2|) (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| (-409 |#2|) (QUOTE (-365)))) (-12 (|HasCategory| (-409 |#2|) (QUOTE (-233))) (|HasCategory| (-409 |#2|) (QUOTE (-365))))) -(-41 R -2382) +(-41 R -2386) ((|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| $)) $) "\\spad{numer(x)} \\undocumented"))) NIL ((-12 (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| |#2| (LIST (QUOTE -432) (|devaluate| |#1|))))) @@ -106,23 +106,23 @@ NIL ((|HasCategory| |#1| (QUOTE (-308)))) (-44 R |n| |ls| |gamma|) ((|constructor| (NIL "AlgebraGivenByStructuralConstants implements finite rank algebras over a commutative ring,{} given by the structural constants \\spad{gamma} with respect to a fixed basis \\spad{[a1,{}..,{}an]},{} where \\spad{gamma} is an \\spad{n}-vector of \\spad{n} by \\spad{n} matrices \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{\\spad{ai} * aj = gammaij1 * a1 + ... + gammaijn * an}. The symbols for the fixed basis have to be given as a list of symbols.")) (|coerce| (($ (|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."))) -((-4414 |has| |#1| (-558)) (-4412 . T) (-4411 . T)) +((-4411 |has| |#1| (-558)) (-4409 . T) (-4408 . T)) ((|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-558)))) (-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."))) -((-4417 . T) (-4418 . T)) -((-2805 (-12 (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (QUOTE (-850))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2010) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2818) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2010) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2818) (|devaluate| |#2|))))))) (-2805 (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (QUOTE (-850))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (LIST (QUOTE -614) (QUOTE (-538)))) (-12 (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (-2805 (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (QUOTE (-850))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (QUOTE (-1099))) (|HasCategory| |#2| (QUOTE (-1099)))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| (-566) (QUOTE (-850))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (QUOTE (-1099))) (-2805 (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (-2805 (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (QUOTE (-1099))) (|HasCategory| |#2| (QUOTE (-1099)))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2010) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2818) (|devaluate| |#2|))))))) +((-4414 . T) (-4415 . T)) +((-2805 (-12 (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (QUOTE (-850))) (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2050) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2849) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2050) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2849) (|devaluate| |#2|))))))) (-2805 (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (QUOTE (-850))) (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (LIST (QUOTE -614) (QUOTE (-538)))) (-12 (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (-2805 (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (QUOTE (-850))) (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (QUOTE (-1099))) (|HasCategory| |#2| (QUOTE (-1099)))) (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| (-566) (QUOTE (-850))) (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (QUOTE (-1099))) (-2805 (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (-2805 (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (QUOTE (-1099))) (|HasCategory| |#2| (QUOTE (-1099)))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2050) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2849) (|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| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) NIL ((|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-365)))) (-47 R E) ((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#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| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) -(((-4419 "*") |has| |#1| (-172)) (-4410 |has| |#1| (-558)) (-4411 . T) (-4412 . T) (-4414 . T)) +(((-4416 "*") |has| |#1| (-172)) (-4407 |has| |#1| (-558)) (-4408 . T) (-4409 . T) (-4411 . T)) NIL (-48) ((|constructor| (NIL "Algebraic closure of the rational numbers,{} with mathematical =")) (|norm| (($ $ (|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."))) -((-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) +((-4406 . T) (-4412 . T) (-4407 . T) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) ((|HasCategory| $ (QUOTE (-1049))) (|HasCategory| $ (LIST (QUOTE -1038) (QUOTE (-566))))) (-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|)) $) "\\spad{parameters(f)} returns the list of parameters bound by \\spad{`f'}."))) @@ -130,21 +130,21 @@ NIL NIL (-50 R |lVar|) ((|constructor| (NIL "The domain of antisymmetric polynomials.")) (|map| (($ (|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}."))) -((-4414 . T)) +((-4411 . 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}."))) NIL NIL (-52) -((|constructor| (NIL "\\spadtype{Any} implements a type that packages up objects and their types in objects of \\spadtype{Any}. Roughly speaking that means that if \\spad{s : S} then when converted to \\spadtype{Any},{} the new object will include both the original object and its type. This is a way of converting arbitrary objects into a single type without losing any of the original information. Any object can be converted to one of \\spadtype{Any}.")) (|showTypeInOutput| (((|String|) (|Boolean|)) "\\spad{showTypeInOutput(bool)} affects the way objects of \\spadtype{Any} are displayed. If \\spad{bool} is \\spad{true} then the type of the original object that was converted to \\spadtype{Any} will be printed. If \\spad{bool} is \\spad{false},{} it will not be printed.")) (|obj| (((|None|) $) "\\spad{obj(a)} essentially returns the original object that was converted to \\spadtype{Any} except that the type is forced to be \\spadtype{None}.")) (|dom| (((|SExpression|) $) "\\spad{dom(a)} returns a \\spadgloss{LISP} form of the type of the original object that was converted to \\spadtype{Any}.")) (|objectOf| (((|OutputForm|) $) "\\spad{objectOf(a)} returns a printable form of the original object that was converted to \\spadtype{Any}.")) (|domainOf| (((|OutputForm|) $) "\\spad{domainOf(a)} returns a printable form of the type of the original object that was converted to \\spadtype{Any}.")) (|any| (($ (|SExpression|) (|None|)) "\\spad{any(type,{}object)} is a technical function for creating an \\spad{object} of \\spadtype{Any}. Arugment \\spad{type} is a \\spadgloss{LISP} form for the \\spad{type} of \\spad{object}."))) +((|constructor| (NIL "\\spadtype{Any} implements a type that packages up objects and their types in objects of \\spadtype{Any}. Roughly speaking that means that if \\spad{s : S} then when converted to \\spadtype{Any},{} the new object will include both the original object and its type. This is a way of converting arbitrary objects into a single type without losing any of the original information. Any object can be converted to one of \\spadtype{Any}. The original object can be recovered by `is-case' pattern matching as exemplified here and AnyFunctions1.")) (|obj| (((|None|) $) "\\spad{obj(a)} essentially returns the original object that was converted to \\spadtype{Any} except that the type is forced to be \\spadtype{None}.")) (|dom| (((|SExpression|) $) "\\spad{dom(a)} returns a \\spadgloss{LISP} form of the type of the original object that was converted to \\spadtype{Any}.")) (|any| (($ (|SExpression|) (|None|)) "\\spad{any(type,{}object)} is a technical function for creating an \\spad{object} of \\spadtype{Any}. Arugment \\spad{type} is a \\spadgloss{LISP} form for the \\spad{type} of \\spad{object}."))) NIL NIL (-53 R M P) ((|constructor| (NIL "\\spad{ApplyUnivariateSkewPolynomial} (internal) allows univariate skew polynomials to be applied to appropriate modules.")) (|apply| ((|#2| |#3| (|Mapping| |#2| |#2|) |#2|) "\\spad{apply(p,{} f,{} m)} returns \\spad{p(m)} where the action is given by \\spad{x m = f(m)}. \\spad{f} must be an \\spad{R}-pseudo linear map on \\spad{M}."))) NIL NIL -(-54 |Base| R -2382) +(-54 |Base| R -2386) ((|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"))) -((-4417 . T) (-4418 . T)) +((-4414 . T) (-4415 . 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}"))) -((-4418 . T) (-4417 . T)) +((-4415 . T) (-4414 . T)) ((-2805 (-12 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538)))) (-2805 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099)))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| (-566) (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|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}."))) -((-4417 . T) (-4418 . T)) +((-4414 . T) (-4415 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) -(-61 -2628) +(-61 -2639) ((|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 -2628) +(-62 -2639) ((|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 -2628) +(-63 -2639) ((|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 -2628) +(-64 -2639) ((|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 -2628) +(-65 -2639) ((|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 -2628) +(-66 -2639) ((|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 -2628) +(-67 -2639) ((|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 -2628) +(-68 -2639) ((|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 -2628) +(-69 -2639) ((|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 -2628) +(-70 -2639) ((|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 -2628) +(-71 -2639) ((|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 -2628) +(-72 -2639) ((|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 -2628) +(-73 -2639) ((|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 -2628) +(-74 -2639) ((|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 -2628) +(-77 -2639) ((|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 -2628) +(-78 -2639) ((|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 -2628) +(-79 -2639) ((|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 -2628) +(-80 -2639) ((|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 -2628) +(-81 -2639) ((|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 -2628) +(-82 -2639) ((|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 -2628) +(-83 -2639) ((|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 -2628) +(-84 -2639) ((|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 -2628) +(-85 -2639) ((|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 -2628) +(-86 -2639) ((|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 -2628) +(-87 -2639) ((|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 -2628) +(-88 -2639) ((|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 -2628) +(-89 -2639) ((|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 @@ -294,7 +294,7 @@ NIL ((|HasCategory| |#1| (QUOTE (-365)))) (-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}."))) -((-4417 . T) (-4418 . T)) +((-4414 . T) (-4415 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (-92 S) ((|constructor| (NIL "This is the category of Spad abstract syntax trees."))) @@ -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\"."))) -((-4417 . T)) +((-4414 . 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 D} which is commutative.")) (|finiteAggregate| ((|attribute|) "\\spad{finiteAggregate} is \\spad{true} if it is an aggregate with a finite number of elements."))) -((-4417 . T) ((-4419 "*") . T) (-4418 . T) (-4414 . T) (-4412 . T) (-4411 . T) (-4410 . T) (-4415 . T) (-4409 . T) (-4408 . T) (-4407 . T) (-4406 . T) (-4405 . T) (-4413 . T) (-4416 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-4404 . T)) +((-4414 . T) ((-4416 "*") . T) (-4415 . T) (-4411 . T) (-4409 . T) (-4408 . T) (-4407 . T) (-4412 . T) (-4406 . T) (-4405 . T) (-4404 . T) (-4403 . T) (-4402 . T) (-4410 . T) (-4413 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-4401 . 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}."))) -((-4414 . T)) +((-4411 . 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{\\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}."))) -((-4417 . T) (-4418 . T)) +((-4414 . T) (-4415 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (-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 (-4419 "*")))) +((|HasAttribute| |#1| (QUOTE (-4416 "*")))) (-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"))) -((-4417 . T)) +((-4414 . 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."))) @@ -358,11 +358,11 @@ 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."))) -((-4418 . T)) +((-4415 . 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."))) -((-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) +((-4406 . T) (-4412 . T) (-4407 . T) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) ((|HasCategory| (-566) (QUOTE (-909))) (|HasCategory| (-566) (LIST (QUOTE -1038) (QUOTE (-1175)))) (|HasCategory| (-566) (QUOTE (-145))) (|HasCategory| (-566) (QUOTE (-147))) (|HasCategory| (-566) (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| (-566) (QUOTE (-1022))) (|HasCategory| (-566) (QUOTE (-820))) (-2805 (|HasCategory| (-566) (QUOTE (-820))) (|HasCategory| (-566) (QUOTE (-850)))) (|HasCategory| (-566) (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| (-566) (QUOTE (-1150))) (|HasCategory| (-566) (LIST (QUOTE -886) (QUOTE (-381)))) (|HasCategory| (-566) (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| (-566) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (|HasCategory| (-566) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| (-566) (QUOTE (-233))) (|HasCategory| (-566) (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| (-566) (LIST (QUOTE -516) (QUOTE (-1175)) (QUOTE (-566)))) (|HasCategory| (-566) (LIST (QUOTE -310) (QUOTE (-566)))) (|HasCategory| (-566) (LIST (QUOTE -287) (QUOTE (-566)) (QUOTE (-566)))) (|HasCategory| (-566) (QUOTE (-308))) (|HasCategory| (-566) (QUOTE (-547))) (|HasCategory| (-566) (QUOTE (-850))) (|HasCategory| (-566) (LIST (QUOTE -639) (QUOTE (-566)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-566) (QUOTE (-909)))) (-2805 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-566) (QUOTE (-909)))) (|HasCategory| (-566) (QUOTE (-145))))) (-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|) $) "\\spad{name(b)} returns the name of binding \\spad{b}"))) @@ -370,11 +370,11 @@ NIL NIL (-110) ((|constructor| (NIL "\\spadtype{Bits} provides logical functions for Indexed Bits.")) (|bits| (($ (|NonNegativeInteger|) (|Boolean|)) "\\spad{bits(n,{}b)} creates bits with \\spad{n} values of \\spad{b}"))) -((-4418 . T) (-4417 . T)) +((-4415 . T) (-4414 . T)) ((-12 (|HasCategory| (-112) (QUOTE (-1099))) (|HasCategory| (-112) (LIST (QUOTE -310) (QUOTE (-112))))) (|HasCategory| (-112) (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| (-112) (QUOTE (-850))) (|HasCategory| (-566) (QUOTE (-850))) (|HasCategory| (-112) (QUOTE (-1099))) (|HasCategory| (-112) (LIST (QUOTE -613) (QUOTE (-862))))) (-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}"))) -((-4412 . T) (-4411 . T)) +((-4409 . T) (-4408 . T)) NIL (-112) ((|constructor| (NIL "\\indented{1}{\\spadtype{Boolean} is the elementary logic with 2 values:} \\spad{true} and \\spad{false}")) (|test| (($ $) "\\spad{test(b)} returns \\spad{b} and is provided for compatibility with the new compiler.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical negation of \\spad{a} or \\spad{b}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical negation of \\spad{a} and \\spad{b}.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical exclusive {\\em or} of Boolean \\spad{a} and \\spad{b}."))) @@ -388,22 +388,22 @@ NIL ((|constructor| (NIL "A basic operator is an object that can be applied to a list of arguments from a set,{} the result being a kernel over that set.")) (|setProperties| (($ $ (|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 -(-115 -2382 UP) +(-115 -2386 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 (-116 |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}."))) -((-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) +((-4407 . T) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) NIL (-117 |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}."))) -((-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) +((-4406 . T) (-4412 . T) (-4407 . T) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) ((|HasCategory| (-116 |#1|) (QUOTE (-909))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1038) (QUOTE (-1175)))) (|HasCategory| (-116 |#1|) (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-147))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| (-116 |#1|) (QUOTE (-1022))) (|HasCategory| (-116 |#1|) (QUOTE (-820))) (-2805 (|HasCategory| (-116 |#1|) (QUOTE (-820))) (|HasCategory| (-116 |#1|) (QUOTE (-850)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| (-116 |#1|) (QUOTE (-1150))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -886) (QUOTE (-381)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| (-116 |#1|) (QUOTE (-233))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -516) (QUOTE (-1175)) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -310) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -287) (LIST (QUOTE -116) (|devaluate| |#1|)) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (QUOTE (-308))) (|HasCategory| (-116 |#1|) (QUOTE (-547))) (|HasCategory| (-116 |#1|) (QUOTE (-850))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-909)))) (-2805 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-909)))) (|HasCategory| (-116 |#1|) (QUOTE (-145))))) (-118 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| (($ $) "\\spad{left(u)} returns the left child."))) NIL -((|HasAttribute| |#1| (QUOTE -4418))) +((|HasAttribute| |#1| (QUOTE -4415))) (-119 S) ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,{}x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,{}b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "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 @@ -414,7 +414,7 @@ NIL NIL (-121 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"))) -((-4417 . T) (-4418 . T)) +((-4414 . T) (-4415 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (-122 S) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|or| (($ $ $) "\\spad{a or b} returns the logical {\\em or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|and| (($ $ $) "\\spad{a and b} returns the logical {\\em and} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|not| (($ $) "\\spad{not(b)} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}."))) @@ -422,7 +422,7 @@ NIL NIL (-123) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|or| (($ $ $) "\\spad{a or b} returns the logical {\\em or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|and| (($ $ $) "\\spad{a and b} returns the logical {\\em and} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|not| (($ $) "\\spad{not(b)} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}."))) -((-4418 . T) (-4417 . T)) +((-4415 . T) (-4414 . T)) NIL (-124 A S) ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#2| $) "\\spad{node(left,{}v,{}right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) @@ -430,19 +430,19 @@ NIL NIL (-125 S) ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#1| $) "\\spad{node(left,{}v,{}right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) -((-4417 . T) (-4418 . T)) +((-4414 . T) (-4415 . T)) NIL (-126 S) ((|constructor| (NIL "\\spadtype{BinaryTournament(S)} is the domain of binary trees where elements are ordered down the tree. A binary search tree is either empty or is a node containing a \\spadfun{value} of type \\spad{S},{} and a \\spadfun{right} and a \\spadfun{left} which are both \\spadtype{BinaryTree(S)}")) (|insert!| (($ |#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."))) -((-4417 . T) (-4418 . T)) +((-4414 . T) (-4415 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (-127 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."))) -((-4417 . T) (-4418 . T)) +((-4414 . T) (-4415 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (-128) ((|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."))) -((-4418 . T) (-4417 . T)) +((-4415 . T) (-4414 . T)) ((-2805 (-12 (|HasCategory| (-129) (QUOTE (-850))) (|HasCategory| (-129) (LIST (QUOTE -310) (QUOTE (-129))))) (-12 (|HasCategory| (-129) (QUOTE (-1099))) (|HasCategory| (-129) (LIST (QUOTE -310) (QUOTE (-129)))))) (-2805 (-12 (|HasCategory| (-129) (QUOTE (-1099))) (|HasCategory| (-129) (LIST (QUOTE -310) (QUOTE (-129))))) (|HasCategory| (-129) (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-129) (LIST (QUOTE -614) (QUOTE (-538)))) (-2805 (|HasCategory| (-129) (QUOTE (-850))) (|HasCategory| (-129) (QUOTE (-1099)))) (|HasCategory| (-129) (QUOTE (-850))) (|HasCategory| (-566) (QUOTE (-850))) (|HasCategory| (-129) (QUOTE (-1099))) (|HasCategory| (-129) (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| (-129) (QUOTE (-1099))) (|HasCategory| (-129) (LIST (QUOTE -310) (QUOTE (-129)))))) (-129) ((|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."))) @@ -466,13 +466,13 @@ NIL NIL (-134) ((|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") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,{}D) -> D} which is commutative."))) -(((-4419 "*") . T)) +(((-4416 "*") . T)) NIL -(-135 |minix| -2293 S T$) +(-135 |minix| -4225 S T$) ((|constructor| (NIL "This package provides functions to enable conversion of tensors given conversion of the components.")) (|map| (((|CartesianTensor| |#1| |#2| |#4|) (|Mapping| |#4| |#3|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{map(f,{}ts)} does a componentwise conversion of the tensor \\spad{ts} to a tensor with components of type \\spad{T}.")) (|reshape| (((|CartesianTensor| |#1| |#2| |#4|) (|List| |#4|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{reshape(lt,{}ts)} organizes the list of components \\spad{lt} into a tensor with the same shape as \\spad{ts}."))) NIL NIL -(-136 |minix| -2293 R) +(-136 |minix| -4225 R) ((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\spad{sample()} returns an object of type \\%.")) (|unravel| (($ (|List| |#3|)) "\\spad{unravel(t)} produces a tensor from a list of components such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|ravel| (((|List| |#3|) $) "\\spad{ravel(t)} produces a list of components from a tensor such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|leviCivitaSymbol| (($) "\\spad{leviCivitaSymbol()} is the rank \\spad{dim} tensor defined by \\spad{leviCivitaSymbol()(i1,{}...idim) = +1/0/-1} if \\spad{i1,{}...,{}idim} is an even/is nota /is an odd permutation of \\spad{minix,{}...,{}minix+dim-1}.")) (|kroneckerDelta| (($) "\\spad{kroneckerDelta()} is the rank 2 tensor defined by \\indented{3}{\\spad{kroneckerDelta()(i,{}j)}} \\indented{6}{\\spad{= 1\\space{2}if i = j}} \\indented{6}{\\spad{= 0 if\\space{2}i \\~= j}}")) (|reindex| (($ $ (|List| (|Integer|))) "\\spad{reindex(t,{}[i1,{}...,{}idim])} permutes the indices of \\spad{t}. For example,{} if \\spad{r = reindex(t,{} [4,{}1,{}2,{}3])} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank for tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = t(l,{}i,{}j,{}k)}.}")) (|transpose| (($ $ (|Integer|) (|Integer|)) "\\spad{transpose(t,{}i,{}j)} exchanges the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices of \\spad{t}. For example,{} if \\spad{r = transpose(t,{}2,{}3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = t(i,{}k,{}j,{}l)}.}") (($ $) "\\spad{transpose(t)} exchanges the first and last indices of \\spad{t}. For example,{} if \\spad{r = transpose(t)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = t(l,{}j,{}k,{}i)}.}")) (|contract| (($ $ (|Integer|) (|Integer|)) "\\spad{contract(t,{}i,{}j)} is the contraction of tensor \\spad{t} which sums along the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices. For example,{} if \\spad{r = contract(t,{}1,{}3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 2 \\spad{(= 4 - 2)} tensor given by \\indented{4}{\\spad{r(i,{}j) = sum(h=1..dim,{}t(h,{}i,{}h,{}j))}.}") (($ $ (|Integer|) $ (|Integer|)) "\\spad{contract(t,{}i,{}s,{}j)} is the inner product of tenors \\spad{s} and \\spad{t} which sums along the \\spad{k1}\\spad{-}th index of \\spad{t} and the \\spad{k2}\\spad{-}th index of \\spad{s}. For example,{} if \\spad{r = contract(s,{}2,{}t,{}1)} for rank 3 tensors rank 3 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is the rank 4 \\spad{(= 3 + 3 - 2)} tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = sum(h=1..dim,{}s(i,{}h,{}j)*t(h,{}k,{}l))}.}")) (* (($ $ $) "\\spad{s*t} is the inner product of the tensors \\spad{s} and \\spad{t} which contracts the last index of \\spad{s} with the first index of \\spad{t},{} \\spadignore{i.e.} \\indented{4}{\\spad{t*s = contract(t,{}rank t,{} s,{} 1)}} \\indented{4}{\\spad{t*s = sum(k=1..N,{} t[i1,{}..,{}iN,{}k]*s[k,{}j1,{}..,{}jM])}} This is compatible with the use of \\spad{M*v} to denote the matrix-vector inner product.")) (|product| (($ $ $) "\\spad{product(s,{}t)} is the outer product of the tensors \\spad{s} and \\spad{t}. For example,{} if \\spad{r = product(s,{}t)} for rank 2 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is a rank 4 tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = s(i,{}j)*t(k,{}l)}.}")) (|elt| ((|#3| $ (|List| (|Integer|))) "\\spad{elt(t,{}[i1,{}...,{}iN])} gives a component of a rank \\spad{N} tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,{}i,{}j,{}k,{}l)} gives a component of a rank 4 tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,{}i,{}j,{}k)} gives a component of a rank 3 tensor.") ((|#3| $ (|Integer|) (|Integer|)) "\\spad{elt(t,{}i,{}j)} gives a component of a rank 2 tensor.") ((|#3| $ (|Integer|)) "\\spad{elt(t,{}i)} gives a component of a rank 1 tensor.") ((|#3| $) "\\spad{elt(t)} gives the component of a rank 0 tensor.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(t)} returns the tensorial rank of \\spad{t} (that is,{} the number of indices). This is the same as the graded module degree.")) (|coerce| (($ (|List| $)) "\\spad{coerce([t_1,{}...,{}t_dim])} allows tensors to be constructed using lists.") (($ (|List| |#3|)) "\\spad{coerce([r_1,{}...,{}r_dim])} allows tensors to be constructed using lists.") (($ (|SquareMatrix| |#2| |#3|)) "\\spad{coerce(m)} views a matrix as a rank 2 tensor.") (($ (|DirectProduct| |#2| |#3|)) "\\spad{coerce(v)} views a vector as a rank 1 tensor."))) NIL NIL @@ -494,7 +494,7 @@ NIL NIL (-141) ((|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}."))) -((-4417 . T) (-4407 . T) (-4418 . T)) +((-4414 . T) (-4404 . T) (-4415 . T)) ((-2805 (-12 (|HasCategory| (-144) (QUOTE (-370))) (|HasCategory| (-144) (LIST (QUOTE -310) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1099))) (|HasCategory| (-144) (LIST (QUOTE -310) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| (-144) (QUOTE (-370))) (|HasCategory| (-144) (QUOTE (-850))) (|HasCategory| (-144) (QUOTE (-1099))) (|HasCategory| (-144) (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| (-144) (QUOTE (-1099))) (|HasCategory| (-144) (LIST (QUOTE -310) (QUOTE (-144)))))) (-142 R Q A) ((|constructor| (NIL "CommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#3|) "\\spad{splitDenominator([q1,{}...,{}qn])} returns \\spad{[[p1,{}...,{}pn],{} d]} such that \\spad{\\spad{qi} = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|clearDenominator| ((|#3| |#3|) "\\spad{clearDenominator([q1,{}...,{}qn])} returns \\spad{[p1,{}...,{}pn]} such that \\spad{\\spad{qi} = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|commonDenominator| ((|#1| |#3|) "\\spad{commonDenominator([q1,{}...,{}qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}\\spad{qn}."))) @@ -510,7 +510,7 @@ NIL NIL (-145) ((|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."))) -((-4414 . T)) +((-4411 . T)) NIL (-146 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}."))) @@ -518,9 +518,9 @@ NIL NIL (-147) ((|constructor| (NIL "Rings of Characteristic Zero."))) -((-4414 . T)) +((-4411 . T)) NIL -(-148 -2382 UP UPUP) +(-148 -2386 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 @@ -531,14 +531,14 @@ NIL (-150 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 -614) (QUOTE (-538)))) (|HasCategory| |#2| (QUOTE (-1099))) (|HasAttribute| |#1| (QUOTE -4417))) +((|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#2| (QUOTE (-1099))) (|HasAttribute| |#1| (QUOTE -4414))) (-151 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 (-152 |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} \\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 @@ -1162,7 +1162,7 @@ NIL NIL (-308) ((|constructor| (NIL "A constructive euclidean domain,{} \\spadignore{i.e.} one can divide producing a quotient and a remainder where the remainder is either zero or is smaller (\\spadfun{euclideanSize}) than the divisor. \\blankline Conditional attributes: \\indented{2}{multiplicativeValuation\\tab{25}\\spad{Size(a*b)=Size(a)*Size(b)}} \\indented{2}{additiveValuation\\tab{25}\\spad{Size(a*b)=Size(a)+Size(b)}}")) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) "\\spad{multiEuclidean([f1,{}...,{}fn],{}z)} returns a list of coefficients \\spad{[a1,{} ...,{} an]} such that \\spad{ z / prod \\spad{fi} = sum aj/fj}. If no such list of coefficients exists,{} \"failed\" is returned.")) (|extendedEuclidean| (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) "\\spad{extendedEuclidean(x,{}y,{}z)} either returns a record rec where \\spad{rec.coef1*x+rec.coef2*y=z} or returns \"failed\" if \\spad{z} cannot be expressed as a linear combination of \\spad{x} and \\spad{y}.") (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{extendedEuclidean(x,{}y)} returns a record rec where \\spad{rec.coef1*x+rec.coef2*y = rec.generator} and rec.generator is a \\spad{gcd} of \\spad{x} and \\spad{y}. The \\spad{gcd} is unique only up to associates if \\spadatt{canonicalUnitNormal} is not asserted. \\spadfun{principalIdeal} provides a version of this operation which accepts an arbitrary length list of arguments.")) (|rem| (($ $ $) "\\spad{x rem y} is the same as \\spad{divide(x,{}y).remainder}. See \\spadfunFrom{divide}{EuclideanDomain}.")) (|quo| (($ $ $) "\\spad{x quo y} is the same as \\spad{divide(x,{}y).quotient}. See \\spadfunFrom{divide}{EuclideanDomain}.")) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{divide(x,{}y)} divides \\spad{x} by \\spad{y} producing a record containing a \\spad{quotient} and \\spad{remainder},{} where the remainder is smaller (see \\spadfunFrom{sizeLess?}{EuclideanDomain}) than the divisor \\spad{y}.")) (|euclideanSize| (((|NonNegativeInteger|) $) "\\spad{euclideanSize(x)} returns the euclidean size of the element \\spad{x}. Error: if \\spad{x} is zero.")) (|sizeLess?| (((|Boolean|) $ $) "\\spad{sizeLess?(x,{}y)} tests whether \\spad{x} is strictly smaller than \\spad{y} with respect to the \\spadfunFrom{euclideanSize}{EuclideanDomain}."))) -((-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) +((-4407 . T) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) NIL (-309 S R) ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation\\spad{''} substitutions.")) (|eval| (($ $ (|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}."))) @@ -1172,7 +1172,7 @@ 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 -(-311 -2382) +(-311 -2386) ((|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 @@ -1186,7 +1186,7 @@ NIL NIL (-314 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))}."))) -((-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) +((-4406 . T) (-4412 . T) (-4407 . T) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) ((|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (QUOTE (-909))) (|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1038) (QUOTE (-1175)))) (|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (QUOTE (-145))) (|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (QUOTE (-1022))) (|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (QUOTE (-820))) (-2805 (|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (QUOTE (-820))) (|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (QUOTE (-850)))) (|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (QUOTE (-1150))) (|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (LIST (QUOTE -886) (QUOTE (-381)))) (|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (QUOTE (-233))) (|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (LIST (QUOTE -516) (QUOTE (-1175)) (LIST (QUOTE -1250) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (LIST (QUOTE -310) (LIST (QUOTE -1250) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (LIST (QUOTE -287) (LIST (QUOTE -1250) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1250) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (QUOTE (-308))) (|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (QUOTE (-547))) (|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (QUOTE (-850))) (-12 (|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (QUOTE (-909))) (|HasCategory| $ (QUOTE (-145)))) (-2805 (|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (QUOTE (-145))) (-12 (|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (QUOTE (-909))) (|HasCategory| $ (QUOTE (-145)))))) (-315 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}."))) @@ -1198,9 +1198,9 @@ NIL NIL (-317 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."))) -((-4414 -2805 (-2438 (|has| |#1| (-1049)) (|has| |#1| (-639 (-566)))) (-12 (|has| |#1| (-558)) (-2805 (-2438 (|has| |#1| (-1049)) (|has| |#1| (-639 (-566)))) (|has| |#1| (-1049)) (|has| |#1| (-475)))) (|has| |#1| (-1049)) (|has| |#1| (-475))) (-4412 |has| |#1| (-172)) (-4411 |has| |#1| (-172)) ((-4419 "*") |has| |#1| (-558)) (-4410 |has| |#1| (-558)) (-4415 |has| |#1| (-558)) (-4409 |has| |#1| (-558))) +((-4411 -2805 (-2447 (|has| |#1| (-1049)) (|has| |#1| (-639 (-566)))) (-12 (|has| |#1| (-558)) (-2805 (-2447 (|has| |#1| (-1049)) (|has| |#1| (-639 (-566)))) (|has| |#1| (-1049)) (|has| |#1| (-475)))) (|has| |#1| (-1049)) (|has| |#1| (-475))) (-4409 |has| |#1| (-172)) (-4408 |has| |#1| (-172)) ((-4416 "*") |has| |#1| (-558)) (-4407 |has| |#1| (-558)) (-4412 |has| |#1| (-558)) (-4406 |has| |#1| (-558))) ((-2805 (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (-12 (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))))) (|HasCategory| |#1| (QUOTE (-558))) (-2805 (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-1049)))) (|HasCategory| |#1| (QUOTE (-21))) (-2805 (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-1049))) (|HasCategory| |#1| (LIST (QUOTE -639) (QUOTE (-566)))) (-2805 (|HasCategory| |#1| (QUOTE (-475))) (|HasCategory| |#1| (QUOTE (-1111)))) (|HasCategory| |#1| (QUOTE (-475))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538)))) (-2805 (|HasCategory| |#1| (QUOTE (-1049))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-381)))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (-12 (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566))))) (-2805 (|HasCategory| |#1| (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| 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(QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-1111)))) (-2805 (|HasCategory| |#1| (QUOTE (-21))) (-12 (|HasCategory| |#1| (QUOTE (-1049))) (|HasCategory| |#1| (LIST (QUOTE -639) (QUOTE (-566)))))) (-2805 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1049))) (|HasCategory| |#1| (LIST (QUOTE -639) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-1111)))) (-2805 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1049))) (|HasCategory| |#1| (LIST (QUOTE -639) (QUOTE (-566)))))) (-2805 (|HasCategory| |#1| (QUOTE (-475))) (|HasCategory| |#1| (QUOTE (-1049)))) (-2805 (-12 (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-558)))) (-12 (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| $ (QUOTE (-1049))) (|HasCategory| $ (LIST (QUOTE -1038) (QUOTE (-566))))) -(-318 R -2382) +(-318 R -2386) ((|constructor| (NIL "Taylor series solutions of explicit ODE\\spad{'s}.")) (|seriesSolve| (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq,{} y,{} x = a,{} [b0,{}...,{}bn])} is equivalent to \\spad{seriesSolve(eq = 0,{} y,{} x = a,{} [b0,{}...,{}b(n-1)])}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq,{} y,{} x = a,{} y a = b)} is equivalent to \\spad{seriesSolve(eq=0,{} y,{} x=a,{} y a = b)}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq,{} y,{} x = a,{} b)} is equivalent to \\spad{seriesSolve(eq = 0,{} y,{} x = a,{} y a = b)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq,{}y,{} x=a,{} b)} is equivalent to \\spad{seriesSolve(eq,{} y,{} x=a,{} y a = b)}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,{}...,{}eqn],{} [y1,{}...,{}yn],{} x = a,{}[y1 a = b1,{}...,{} yn a = bn])} is equivalent to \\spad{seriesSolve([eq1=0,{}...,{}eqn=0],{} [y1,{}...,{}yn],{} x = a,{} [y1 a = b1,{}...,{} yn a = bn])}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,{}...,{}eqn],{} [y1,{}...,{}yn],{} x=a,{} [b1,{}...,{}bn])} is equivalent to \\spad{seriesSolve([eq1=0,{}...,{}eqn=0],{} [y1,{}...,{}yn],{} x=a,{} [b1,{}...,{}bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,{}...,{}eqn],{} [y1,{}...,{}yn],{} x=a,{} [b1,{}...,{}bn])} is equivalent to \\spad{seriesSolve([eq1,{}...,{}eqn],{} [y1,{}...,{}yn],{} x = a,{} [y1 a = b1,{}...,{} yn a = bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,{}...,{}eqn],{}[y1,{}...,{}yn],{}x = a,{}[y1 a = b1,{}...,{}yn a = bn])} returns a taylor series solution of \\spad{[eq1,{}...,{}eqn]} around \\spad{x = a} with initial conditions \\spad{\\spad{yi}(a) = \\spad{bi}}. Note: eqi must be of the form \\spad{\\spad{fi}(x,{} y1 x,{} y2 x,{}...,{} yn x) y1'(x) + \\spad{gi}(x,{} y1 x,{} y2 x,{}...,{} yn x) = h(x,{} y1 x,{} y2 x,{}...,{} yn x)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq,{}y,{}x=a,{}[b0,{}...,{}b(n-1)])} returns a Taylor series solution of \\spad{eq} around \\spad{x = a} with initial conditions \\spad{y(a) = b0},{} \\spad{y'(a) = b1},{} \\spad{y''(a) = b2},{} ...,{}\\spad{y(n-1)(a) = b(n-1)} \\spad{eq} must be of the form \\spad{f(x,{} y x,{} y'(x),{}...,{} y(n-1)(x)) y(n)(x) + g(x,{}y x,{}y'(x),{}...,{}y(n-1)(x)) = h(x,{}y x,{} y'(x),{}...,{} y(n-1)(x))}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq,{}y,{}x=a,{} y a = b)} returns a Taylor series solution of \\spad{eq} around \\spad{x} = a with initial condition \\spad{y(a) = b}. Note: \\spad{eq} must be of the form \\spad{f(x,{} y x) y'(x) + g(x,{} y x) = h(x,{} y x)}."))) NIL NIL @@ -1210,8 +1210,8 @@ NIL NIL (-320 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."))) -(((-4419 "*") |has| |#1| (-172)) (-4410 |has| |#1| (-558)) (-4415 |has| |#1| (-365)) (-4409 |has| |#1| (-365)) (-4411 . T) (-4412 . T) (-4414 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-172))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-566))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-566))) (|devaluate| |#1|)))) (|HasCategory| (-409 (-566)) (QUOTE (-1111))) (|HasCategory| |#1| (QUOTE (-365))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-558)))) (-2805 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-558)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-566)))))) (|HasSignature| |#1| (LIST (QUOTE -2512) (LIST (|devaluate| |#1|) (QUOTE (-1175)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-566)))))) (-2805 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-959))) (|HasCategory| |#1| (QUOTE (-1199))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasSignature| |#1| (LIST (QUOTE -4117) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1175))))) (|HasSignature| |#1| (LIST (QUOTE -2540) (LIST (LIST (QUOTE -644) (QUOTE (-1175))) (|devaluate| |#1|))))))) +(((-4416 "*") |has| |#1| (-172)) (-4407 |has| |#1| (-558)) (-4412 |has| |#1| (-365)) (-4406 |has| |#1| (-365)) (-4408 . T) (-4409 . T) (-4411 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-172))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-566))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-566))) (|devaluate| |#1|)))) (|HasCategory| (-409 (-566)) (QUOTE (-1111))) (|HasCategory| |#1| (QUOTE (-365))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-558)))) (-2805 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-558)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-566)))))) (|HasSignature| |#1| (LIST (QUOTE -3780) (LIST (|devaluate| |#1|) (QUOTE (-1175)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-566)))))) (-2805 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-959))) (|HasCategory| |#1| (QUOTE (-1199))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasSignature| |#1| (LIST (QUOTE -3921) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1175))))) (|HasSignature| |#1| (LIST (QUOTE -2608) (LIST (LIST (QUOTE -644) (QUOTE (-1175))) (|devaluate| |#1|))))))) (-321 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 @@ -1222,7 +1222,7 @@ NIL NIL (-323 S) ((|constructor| (NIL "The free abelian group on a set \\spad{S} is the monoid of finite sums of the form \\spad{reduce(+,{}[\\spad{ni} * \\spad{si}])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are integers. The operation is commutative."))) -((-4412 . T) (-4411 . T)) +((-4409 . T) (-4408 . T)) ((|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| (-566) (QUOTE (-792)))) (-324 S E) ((|constructor| (NIL "A free abelian monoid on a set \\spad{S} is the monoid of finite sums of the form \\spad{reduce(+,{}[\\spad{ni} * \\spad{si}])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are in a given abelian monoid. The operation is commutative.")) (|highCommonTerms| (($ $ $) "\\spad{highCommonTerms(e1 a1 + ... + en an,{} f1 b1 + ... + fm bm)} returns \\indented{2}{\\spad{reduce(+,{}[max(\\spad{ei},{} \\spad{fi}) \\spad{ci}])}} where \\spad{ci} ranges in the intersection of \\spad{{a1,{}...,{}an}} and \\spad{{b1,{}...,{}bm}}.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f,{} e1 a1 +...+ en an)} returns \\spad{e1 f(a1) +...+ en f(an)}.")) (|mapCoef| (($ (|Mapping| |#2| |#2|) $) "\\spad{mapCoef(f,{} e1 a1 +...+ en an)} returns \\spad{f(e1) a1 +...+ f(en) an}.")) (|coefficient| ((|#2| |#1| $) "\\spad{coefficient(s,{} e1 a1 + ... + en an)} returns \\spad{ei} such that \\spad{ai} = \\spad{s},{} or 0 if \\spad{s} is not one of the \\spad{ai}\\spad{'s}.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(x,{} n)} returns the factor of the n^th term of \\spad{x}.")) (|nthCoef| ((|#2| $ (|Integer|)) "\\spad{nthCoef(x,{} n)} returns the coefficient of the n^th term of \\spad{x}.")) (|terms| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| |#2|))) $) "\\spad{terms(e1 a1 + ... + en an)} returns \\spad{[[a1,{} e1],{}...,{}[an,{} en]]}.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(x)} returns the number of terms in \\spad{x}. mapGen(\\spad{f},{} a1\\spad{\\^}e1 ... an\\spad{\\^}en) returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (* (($ |#2| |#1|) "\\spad{e * s} returns \\spad{e} times \\spad{s}.")) (+ (($ |#1| $) "\\spad{s + x} returns the sum of \\spad{s} and \\spad{x}."))) @@ -1238,19 +1238,19 @@ NIL ((|HasCategory| |#2| (QUOTE (-454))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-172)))) (-327 R E) ((|constructor| (NIL "This category is similar to AbelianMonoidRing,{} except that the sum is assumed to be finite. It is a useful model for polynomials,{} but is somewhat more general.")) (|primitivePart| (($ $) "\\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."))) -(((-4419 "*") |has| |#1| (-172)) (-4410 |has| |#1| (-558)) (-4411 . T) (-4412 . T) (-4414 . T)) +(((-4416 "*") |has| |#1| (-172)) (-4407 |has| |#1| (-558)) (-4408 . T) (-4409 . T) (-4411 . T)) NIL (-328 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."))) -((-4418 . T) (-4417 . T)) +((-4415 . T) (-4414 . T)) ((-2805 (-12 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538)))) (-2805 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099)))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| (-566) (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) -(-329 S -2382) +(-329 S -2386) ((|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 (-370)))) -(-330 -2382) +(-330 -2386) ((|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."))) -((-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) +((-4406 . T) (-4412 . T) (-4407 . T) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) NIL (-331) ((|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."))) @@ -1272,15 +1272,15 @@ 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 -(-336 S -2382 UP UPUP R) +(-336 S -2386 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 -(-337 -2382 UP UPUP R) +(-337 -2386 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 -(-338 -2382 UP UPUP R) +(-338 -2386 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 @@ -1294,31 +1294,31 @@ NIL NIL (-341 |basicSymbols| |subscriptedSymbols| R) ((|constructor| (NIL "A domain of expressions involving functions which can be translated into standard Fortran-77,{} with some extra extensions from the NAG Fortran Library.")) (|useNagFunctions| (((|Boolean|) (|Boolean|)) "\\spad{useNagFunctions(v)} sets the flag which controls whether NAG functions \\indented{1}{are being used for mathematical and machine constants.\\space{2}The previous} \\indented{1}{value is returned.}") (((|Boolean|)) "\\spad{useNagFunctions()} indicates whether NAG functions are being used \\indented{1}{for mathematical and machine constants.}")) (|variables| (((|List| (|Symbol|)) $) "\\spad{variables(e)} return a list of all the variables in \\spad{e}.")) (|pi| (($) "\\spad{\\spad{pi}(x)} represents the NAG Library function X01AAF which returns \\indented{1}{an approximation to the value of \\spad{pi}}")) (|tanh| (($ $) "\\spad{tanh(x)} represents the Fortran intrinsic function TANH")) (|cosh| (($ $) "\\spad{cosh(x)} represents the Fortran intrinsic function COSH")) (|sinh| (($ $) "\\spad{sinh(x)} represents the Fortran intrinsic function SINH")) (|atan| (($ $) "\\spad{atan(x)} represents the Fortran intrinsic function ATAN")) (|acos| (($ $) "\\spad{acos(x)} represents the Fortran intrinsic function ACOS")) (|asin| (($ $) "\\spad{asin(x)} represents the Fortran intrinsic function ASIN")) (|tan| (($ $) "\\spad{tan(x)} represents the Fortran intrinsic function TAN")) (|cos| (($ $) "\\spad{cos(x)} represents the Fortran intrinsic function COS")) (|sin| (($ $) "\\spad{sin(x)} represents the Fortran intrinsic function SIN")) (|log10| (($ $) "\\spad{log10(x)} represents the Fortran intrinsic function LOG10")) (|log| (($ $) "\\spad{log(x)} represents the Fortran intrinsic function LOG")) (|exp| (($ $) "\\spad{exp(x)} represents the Fortran intrinsic function EXP")) (|sqrt| (($ $) "\\spad{sqrt(x)} represents the Fortran intrinsic function SQRT")) (|abs| (($ $) "\\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.}"))) -((-4411 . T) (-4412 . T) (-4414 . T)) +((-4408 . T) (-4409 . T) (-4411 . T)) ((|HasCategory| |#3| (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| |#3| (LIST (QUOTE -1038) (QUOTE (-381)))) (|HasCategory| $ (QUOTE (-1049))) (|HasCategory| $ (LIST (QUOTE -1038) (QUOTE (-566))))) (-342 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 -(-343 S -2382 UP UPUP) +(-343 S -2386 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(\\spad{wi})} with respect to \\spad{(w1,{}...,{}wn)} where \\spad{(w1,{}...,{}wn)} is the integral basis returned by integralBasis().")) (|integralRepresents| (($ (|Vector| |#3|) |#3|) "\\spad{integralRepresents([A1,{}...,{}An],{} D)} returns \\spad{(A1 w1+...+An wn)/D} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spad{integralBasis()}.")) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#3|)) (|:| |den| |#3|)) $) "\\spad{integralCoordinates(f)} returns \\spad{[[A1,{}...,{}An],{} D]} such that \\spad{f = (A1 w1 +...+ An wn) / D} where \\spad{(w1,{}...,{}wn)} is the integral basis returned by \\spad{integralBasis()}.")) (|represents| (($ (|Vector| |#3|) |#3|) "\\spad{represents([A0,{}...,{}A(n-1)],{}D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.")) (|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 (-370))) (|HasCategory| |#2| (QUOTE (-365)))) -(-344 -2382 UP UPUP) +(-344 -2386 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(\\spad{wi})} with respect to \\spad{(w1,{}...,{}wn)} where \\spad{(w1,{}...,{}wn)} is the integral basis returned by integralBasis().")) (|integralRepresents| (($ (|Vector| |#2|) |#2|) "\\spad{integralRepresents([A1,{}...,{}An],{} D)} returns \\spad{(A1 w1+...+An wn)/D} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spad{integralBasis()}.")) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) "\\spad{integralCoordinates(f)} returns \\spad{[[A1,{}...,{}An],{} D]} such that \\spad{f = (A1 w1 +...+ An wn) / D} where \\spad{(w1,{}...,{}wn)} is the integral basis returned by \\spad{integralBasis()}.")) (|represents| (($ (|Vector| |#2|) |#2|) "\\spad{represents([A0,{}...,{}A(n-1)],{}D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.")) (|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."))) -((-4410 |has| (-409 |#2|) (-365)) (-4415 |has| (-409 |#2|) (-365)) (-4409 |has| (-409 |#2|) (-365)) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) +((-4407 |has| (-409 |#2|) (-365)) (-4412 |has| (-409 |#2|) (-365)) (-4406 |has| (-409 |#2|) (-365)) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) NIL (-345 |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."))) -((-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) +((-4406 . T) (-4412 . T) (-4407 . T) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) ((-2805 (|HasCategory| (-910 |#1|) (QUOTE (-145))) (|HasCategory| (-910 |#1|) (QUOTE (-370)))) (|HasCategory| (-910 |#1|) (QUOTE (-147))) (|HasCategory| (-910 |#1|) (QUOTE (-370))) (|HasCategory| (-910 |#1|) (QUOTE (-145)))) (-346 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."))) -((-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) +((-4406 . T) (-4412 . T) (-4407 . T) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) ((-2805 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-145)))) (-347 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."))) -((-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) +((-4406 . T) (-4412 . T) (-4407 . T) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) ((-2805 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-145)))) (-348 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}."))) @@ -1334,33 +1334,33 @@ NIL NIL (-351) ((|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."))) -((-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) +((-4406 . T) (-4412 . T) (-4407 . T) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) NIL -(-352 R UP -2382) +(-352 R UP -2386) ((|constructor| (NIL "In this package \\spad{R} is a Euclidean domain and \\spad{F} is a framed algebra over \\spad{R}. The package provides functions to compute the integral closure of \\spad{R} in the quotient field of \\spad{F}. It is assumed that \\spad{char(R/P) = char(R)} for any prime \\spad{P} of \\spad{R}. A typical instance of this is when \\spad{R = K[x]} and \\spad{F} is a function field over \\spad{R}.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) |#1|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the integral closure of \\spad{R} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL (-353 |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."))) -((-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) +((-4406 . T) (-4412 . T) (-4407 . T) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) ((-2805 (|HasCategory| (-910 |#1|) (QUOTE (-145))) (|HasCategory| (-910 |#1|) (QUOTE (-370)))) (|HasCategory| (-910 |#1|) (QUOTE (-147))) (|HasCategory| (-910 |#1|) (QUOTE (-370))) (|HasCategory| (-910 |#1|) (QUOTE (-145)))) (-354 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."))) -((-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) +((-4406 . T) (-4412 . T) (-4407 . T) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) ((-2805 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-145)))) (-355 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."))) -((-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) +((-4406 . T) (-4412 . T) (-4407 . T) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) ((-2805 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-145)))) (-356 |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}."))) -((-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) +((-4406 . T) (-4412 . T) (-4407 . T) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) ((-2805 (|HasCategory| (-910 |#1|) (QUOTE (-145))) (|HasCategory| (-910 |#1|) (QUOTE (-370)))) (|HasCategory| (-910 |#1|) (QUOTE (-147))) (|HasCategory| (-910 |#1|) (QUOTE (-370))) (|HasCategory| (-910 |#1|) (QUOTE (-145)))) (-357 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."))) -((-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) +((-4406 . T) (-4412 . T) (-4407 . T) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) ((-2805 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-145)))) -(-358 -2382 GF) +(-358 -2386 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 @@ -1368,13 +1368,13 @@ 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 -(-360 -2382 FP FPP) +(-360 -2386 FP FPP) ((|constructor| (NIL "This package solves linear diophantine equations for Bivariate polynomials over finite fields")) (|solveLinearPolynomialEquation| (((|Union| (|List| |#3|) "failed") (|List| |#3|) |#3|) "\\spad{solveLinearPolynomialEquation([f1,{} ...,{} fn],{} g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod \\spad{fi} = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists."))) NIL NIL (-361 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}."))) -((-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) +((-4406 . T) (-4412 . T) (-4407 . T) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) ((-2805 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-145)))) (-362 R |ls|) ((|constructor| (NIL "This is just an interface between several packages and domains. The goal is to compute lexicographical Groebner bases of sets of polynomial with type \\spadtype{Polynomial R} by the {\\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}}."))) @@ -1382,7 +1382,7 @@ NIL NIL (-363 S) ((|constructor| (NIL "The free group on a set \\spad{S} is the group of finite products of the form \\spad{reduce(*,{}[\\spad{si} ** \\spad{ni}])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are integers. The multiplication is not commutative.")) (|factors| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| (|Integer|)))) $) "\\spad{factors(a1\\^e1,{}...,{}an\\^en)} returns \\spad{[[a1,{} e1],{}...,{}[an,{} en]]}.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f,{} a1\\^e1 ... an\\^en)} returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (|mapExpon| (($ (|Mapping| (|Integer|) (|Integer|)) $) "\\spad{mapExpon(f,{} a1\\^e1 ... an\\^en)} returns \\spad{a1\\^f(e1) ... an\\^f(en)}.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(x,{} n)} returns the factor of the n^th monomial of \\spad{x}.")) (|nthExpon| (((|Integer|) $ (|Integer|)) "\\spad{nthExpon(x,{} n)} returns the exponent of the n^th monomial of \\spad{x}.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(x)} returns the number of monomials in \\spad{x}.")) (** (($ |#1| (|Integer|)) "\\spad{s ** n} returns the product of \\spad{s} by itself \\spad{n} times.")) (* (($ $ |#1|) "\\spad{x * s} returns the product of \\spad{x} by \\spad{s} on the right.") (($ |#1| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) -((-4414 . T)) +((-4411 . T)) NIL (-364 S) ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) @@ -1390,7 +1390,7 @@ NIL NIL (-365) ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) -((-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) +((-4406 . T) (-4412 . T) (-4407 . T) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) NIL (-366 |Name| S) ((|constructor| (NIL "This category provides an interface to operate on files in the computer\\spad{'s} file system. The precise method of naming files is determined by the Name parameter. The type of the contents of the file is determined by \\spad{S}.")) (|write!| ((|#2| $ |#2|) "\\spad{write!(f,{}s)} puts the value \\spad{s} into the file \\spad{f}. The state of \\spad{f} is modified so subsequents call to \\spad{write!} will append one after another.")) (|read!| ((|#2| $) "\\spad{read!(f)} extracts a value from file \\spad{f}. The state of \\spad{f} is modified so a subsequent call to \\spadfun{read!} will return the next element.")) (|iomode| (((|String|) $) "\\spad{iomode(f)} returns the status of the file \\spad{f}. The input/output status of \\spad{f} may be \"input\",{} \"output\" or \"closed\" mode.")) (|name| ((|#1| $) "\\spad{name(f)} returns the external name of the file \\spad{f}.")) (|close!| (($ $) "\\spad{close!(f)} returns the file \\spad{f} closed to input and output.")) (|reopen!| (($ $ (|String|)) "\\spad{reopen!(f,{}mode)} returns a file \\spad{f} reopened for operation in the indicated mode: \"input\" or \"output\". \\spad{reopen!(f,{}\"input\")} will reopen the file \\spad{f} for input.")) (|open| (($ |#1| (|String|)) "\\spad{open(s,{}mode)} returns a file \\spad{s} open for operation in the indicated mode: \"input\" or \"output\".") (($ |#1|) "\\spad{open(s)} returns the file \\spad{s} open for input."))) @@ -1406,7 +1406,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-558)))) (-369 R) ((|constructor| (NIL "A FiniteRankNonAssociativeAlgebra is a non associative algebra over a commutative ring \\spad{R} which is a free \\spad{R}-module of finite rank.")) (|unitsKnown| ((|attribute|) "unitsKnown means that \\spadfun{recip} truly yields reciprocal or \\spad{\"failed\"} if not a unit,{} similarly for \\spadfun{leftRecip} and \\spadfun{rightRecip}. The reason is that we use left,{} respectively right,{} minimal polynomials to decide this question.")) (|unit| (((|Union| $ "failed")) "\\spad{unit()} returns a unit of the algebra (necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnit| (((|Union| $ "failed")) "\\spad{rightUnit()} returns a right unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|leftUnit| (((|Union| $ "failed")) "\\spad{leftUnit()} returns a left unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{rightUnits()} returns the affine space of all right units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|leftUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{leftUnits()} returns the affine space of all left units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|rightMinimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{rightMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of right powers of \\spad{a}. Note: the polynomial never has a constant term as in general the algebra has no unit.")) (|leftMinimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{leftMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of left powers of \\spad{a}. Note: the polynomial never has a constant term as in general the algebra has no unit.")) (|associatorDependence| (((|List| (|Vector| |#1|))) "\\spad{associatorDependence()} looks for the associator identities,{} \\spadignore{i.e.} finds a basis of the solutions of the linear combinations of the six permutations of \\spad{associator(a,{}b,{}c)} which yield 0,{} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra. The order of the permutations is \\spad{123 231 312 132 321 213}.")) (|rightRecip| (((|Union| $ "failed") $) "\\spad{rightRecip(a)} returns an element,{} which is a right inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|leftRecip| (((|Union| $ "failed") $) "\\spad{leftRecip(a)} returns an element,{} which is a left inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(a)} returns an element,{} which is both a left and a right inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|lieAlgebra?| (((|Boolean|)) "\\spad{lieAlgebra?()} tests if the algebra is anticommutative and \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra (Jacobi identity). Example: for every associative algebra \\spad{(A,{}+,{}@)} we can construct a Lie algebra \\spad{(A,{}+,{}*)},{} where \\spad{a*b := a@b-b@a}.")) (|jordanAlgebra?| (((|Boolean|)) "\\spad{jordanAlgebra?()} tests if the algebra is commutative,{} characteristic is not 2,{} and \\spad{(a*b)*a**2 - a*(b*a**2) = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra (Jordan identity). Example: for every associative algebra \\spad{(A,{}+,{}@)} we can construct a Jordan algebra \\spad{(A,{}+,{}*)},{} where \\spad{a*b := (a@b+b@a)/2}.")) (|noncommutativeJordanAlgebra?| (((|Boolean|)) "\\spad{noncommutativeJordanAlgebra?()} tests if the algebra is flexible and Jordan admissible.")) (|jordanAdmissible?| (((|Boolean|)) "\\spad{jordanAdmissible?()} tests if 2 is invertible in the coefficient domain and the multiplication defined by \\spad{(1/2)(a*b+b*a)} determines a Jordan algebra,{} \\spadignore{i.e.} satisfies the Jordan identity. The property of \\spadatt{commutative(\\spad{\"*\"})} follows from by definition.")) (|lieAdmissible?| (((|Boolean|)) "\\spad{lieAdmissible?()} tests if the algebra defined by the commutators is a Lie algebra,{} \\spadignore{i.e.} satisfies the Jacobi identity. The property of anticommutativity follows from definition.")) (|jacobiIdentity?| (((|Boolean|)) "\\spad{jacobiIdentity?()} tests if \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra. For example,{} this holds for crossed products of 3-dimensional vectors.")) (|powerAssociative?| (((|Boolean|)) "\\spad{powerAssociative?()} tests if all subalgebras generated by a single element are associative.")) (|alternative?| (((|Boolean|)) "\\spad{alternative?()} tests if \\spad{2*associator(a,{}a,{}b) = 0 = 2*associator(a,{}b,{}b)} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|flexible?| (((|Boolean|)) "\\spad{flexible?()} tests if \\spad{2*associator(a,{}b,{}a) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|rightAlternative?| (((|Boolean|)) "\\spad{rightAlternative?()} tests if \\spad{2*associator(a,{}b,{}b) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|leftAlternative?| (((|Boolean|)) "\\spad{leftAlternative?()} tests if \\spad{2*associator(a,{}a,{}b) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|antiAssociative?| (((|Boolean|)) "\\spad{antiAssociative?()} tests if multiplication in algebra is anti-associative,{} \\spadignore{i.e.} \\spad{(a*b)*c + a*(b*c) = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra.")) (|associative?| (((|Boolean|)) "\\spad{associative?()} tests if multiplication in algebra is associative.")) (|antiCommutative?| (((|Boolean|)) "\\spad{antiCommutative?()} tests if \\spad{a*a = 0} for all \\spad{a} in the algebra. Note: this implies \\spad{a*b + b*a = 0} for all \\spad{a} and \\spad{b}.")) (|commutative?| (((|Boolean|)) "\\spad{commutative?()} tests if multiplication in the algebra is commutative.")) (|rightCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{rightCharacteristicPolynomial(a)} returns the characteristic polynomial of the right regular representation of \\spad{a} with respect to any basis.")) (|leftCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{leftCharacteristicPolynomial(a)} returns the characteristic polynomial of the left regular representation of \\spad{a} with respect to any basis.")) (|rightTraceMatrix| (((|Matrix| |#1|) (|Vector| $)) "\\spad{rightTraceMatrix([v1,{}...,{}vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj}.")) (|leftTraceMatrix| (((|Matrix| |#1|) (|Vector| $)) "\\spad{leftTraceMatrix([v1,{}...,{}vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj}.")) (|rightDiscriminant| ((|#1| (|Vector| $)) "\\spad{rightDiscriminant([v1,{}...,{}vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj}. Note: the same as \\spad{determinant(rightTraceMatrix([v1,{}...,{}vn]))}.")) (|leftDiscriminant| ((|#1| (|Vector| $)) "\\spad{leftDiscriminant([v1,{}...,{}vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj}. Note: the same as \\spad{determinant(leftTraceMatrix([v1,{}...,{}vn]))}.")) (|represents| (($ (|Vector| |#1|) (|Vector| $)) "\\spad{represents([a1,{}...,{}am],{}[v1,{}...,{}vm])} returns the linear combination \\spad{a1*vm + ... + an*vm}.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $) (|Vector| $)) "\\spad{coordinates([a1,{}...,{}am],{}[v1,{}...,{}vn])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{\\spad{ai}} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.") (((|Vector| |#1|) $ (|Vector| $)) "\\spad{coordinates(a,{}[v1,{}...,{}vn])} returns the coordinates of \\spad{a} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rightNorm| ((|#1| $) "\\spad{rightNorm(a)} returns the determinant of the right regular representation of \\spad{a}.")) (|leftNorm| ((|#1| $) "\\spad{leftNorm(a)} returns the determinant of the left regular representation of \\spad{a}.")) (|rightTrace| ((|#1| $) "\\spad{rightTrace(a)} returns the trace of the right regular representation of \\spad{a}.")) (|leftTrace| ((|#1| $) "\\spad{leftTrace(a)} returns the trace of the left regular representation of \\spad{a}.")) (|rightRegularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) "\\spad{rightRegularRepresentation(a,{}[v1,{}...,{}vn])} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,{}...,{}vn]}.")) (|leftRegularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) "\\spad{leftRegularRepresentation(a,{}[v1,{}...,{}vn])} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,{}...,{}vn]}.")) (|structuralConstants| (((|Vector| (|Matrix| |#1|)) (|Vector| $)) "\\spad{structuralConstants([v1,{}v2,{}...,{}vm])} calculates the structural constants \\spad{[(gammaijk) for k in 1..m]} defined by \\spad{\\spad{vi} * vj = gammaij1 * v1 + ... + gammaijm * vm},{} where \\spad{[v1,{}...,{}vm]} is an \\spad{R}-module basis of a subalgebra.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|)) (|Vector| $)) "\\spad{conditionsForIdempotents([v1,{}...,{}vn])} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra as \\spad{R}-module.")) (|someBasis| (((|Vector| $)) "\\spad{someBasis()} returns some \\spad{R}-module basis."))) -((-4414 |has| |#1| (-558)) (-4412 . T) (-4411 . T)) +((-4411 |has| |#1| (-558)) (-4409 . T) (-4408 . T)) NIL (-370) ((|constructor| (NIL "The category of domains composed of a finite set of elements. We include the functions \\spadfun{lookup} and \\spadfun{index} to give a bijection between the finite set and an initial segment of positive integers. \\blankline")) (|random| (($) "\\spad{random()} returns a random element from the set.")) (|lookup| (((|PositiveInteger|) $) "\\spad{lookup(x)} returns a positive integer such that \\spad{x = index lookup x}.")) (|index| (($ (|PositiveInteger|)) "\\spad{index(i)} takes a positive integer \\spad{i} less than or equal to \\spad{size()} and returns the \\spad{i}\\spad{-}th element of the set. This operation establishs a bijection between the elements of the finite set and \\spad{1..size()}.")) (|size| (((|NonNegativeInteger|)) "\\spad{size()} returns the number of elements in the set."))) @@ -1418,7 +1418,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-365)))) (-372 R UP) ((|constructor| (NIL "A FiniteRankAlgebra is an algebra over a commutative ring \\spad{R} which is a free \\spad{R}-module of finite rank.")) (|minimalPolynomial| ((|#2| $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of \\spad{a}.")) (|characteristicPolynomial| ((|#2| $) "\\spad{characteristicPolynomial(a)} returns the characteristic polynomial of the regular representation of \\spad{a} with respect to any basis.")) (|traceMatrix| (((|Matrix| |#1|) (|Vector| $)) "\\spad{traceMatrix([v1,{}..,{}vn])} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr}(\\spad{vi} * \\spad{vj}) )")) (|discriminant| ((|#1| (|Vector| $)) "\\spad{discriminant([v1,{}..,{}vn])} returns \\spad{determinant(traceMatrix([v1,{}..,{}vn]))}.")) (|represents| (($ (|Vector| |#1|) (|Vector| $)) "\\spad{represents([a1,{}..,{}an],{}[v1,{}..,{}vn])} returns \\spad{a1*v1 + ... + an*vn}.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $) (|Vector| $)) "\\spad{coordinates([v1,{}...,{}vm],{} basis)} returns the coordinates of the \\spad{vi}\\spad{'s} with to the basis \\spad{basis}. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#1|) $ (|Vector| $)) "\\spad{coordinates(a,{}basis)} returns the coordinates of \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|norm| ((|#1| $) "\\spad{norm(a)} returns the determinant of the regular representation of \\spad{a} with respect to any basis.")) (|trace| ((|#1| $) "\\spad{trace(a)} returns the trace of the regular representation of \\spad{a} with respect to any basis.")) (|regularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) "\\spad{regularRepresentation(a,{}basis)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra."))) -((-4411 . T) (-4412 . T) (-4414 . T)) +((-4408 . T) (-4409 . T) (-4411 . T)) NIL (-373 S A R B) ((|constructor| (NIL "FiniteLinearAggregateFunctions2 provides functions involving two FiniteLinearAggregates where the underlying domains might be different. An example of this might be creating a list of rational numbers by mapping a function across a list of integers where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,{}a,{}r)} successively applies \\spad{reduce(f,{}x,{}r)} to more and more leading sub-aggregates \\spad{x} of aggregrate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,{}a2,{}...]},{} then \\spad{scan(f,{}a,{}r)} returns \\spad{[reduce(f,{}[a1],{}r),{}reduce(f,{}[a1,{}a2],{}r),{}...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,{}a,{}r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$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."))) @@ -1427,14 +1427,14 @@ NIL (-374 A S) ((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $) "\\spad{sort!(p,{}u)} returns \\spad{u} with its elements ordered by \\spad{p}.")) (|reverse!| (($ $) "\\spad{reverse!(u)} returns \\spad{u} with its elements in reverse order.")) (|copyInto!| (($ $ $ (|Integer|)) "\\spad{copyInto!(u,{}v,{}i)} returns aggregate \\spad{u} containing a copy of \\spad{v} inserted at element \\spad{i}.")) (|position| (((|Integer|) |#2| $ (|Integer|)) "\\spad{position(x,{}a,{}n)} returns the index \\spad{i} of the first occurrence of \\spad{x} in \\axiom{a} where \\axiom{\\spad{i} \\spad{>=} \\spad{n}},{} and \\axiom{minIndex(a) - 1} if no such \\spad{x} is found.") (((|Integer|) |#2| $) "\\spad{position(x,{}a)} returns the index \\spad{i} of the first occurrence of \\spad{x} in a,{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.") (((|Integer|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{position(p,{}a)} returns the index \\spad{i} of the first \\spad{x} in \\axiom{a} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.")) (|sorted?| (((|Boolean|) $) "\\spad{sorted?(u)} tests if the elements of \\spad{u} are in ascending order.") (((|Boolean|) (|Mapping| (|Boolean|) |#2| |#2|) $) "\\spad{sorted?(p,{}a)} tests if \\axiom{a} is sorted according to predicate \\spad{p}.")) (|sort| (($ $) "\\spad{sort(u)} returns an \\spad{u} with elements in ascending order. Note: \\axiom{sort(\\spad{u}) = sort(\\spad{<=},{}\\spad{u})}.") (($ (|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|) $ $) "\\spad{merge(p,{}a,{}b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) NIL -((|HasAttribute| |#1| (QUOTE -4418)) (|HasCategory| |#2| (QUOTE (-850))) (|HasCategory| |#2| (QUOTE (-1099)))) +((|HasAttribute| |#1| (QUOTE -4415)) (|HasCategory| |#2| (QUOTE (-850))) (|HasCategory| |#2| (QUOTE (-1099)))) (-375 S) ((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $) "\\spad{sort!(p,{}u)} returns \\spad{u} with its elements ordered by \\spad{p}.")) (|reverse!| (($ $) "\\spad{reverse!(u)} returns \\spad{u} with its elements in reverse order.")) (|copyInto!| (($ $ $ (|Integer|)) "\\spad{copyInto!(u,{}v,{}i)} returns aggregate \\spad{u} containing a copy of \\spad{v} inserted at element \\spad{i}.")) (|position| (((|Integer|) |#1| $ (|Integer|)) "\\spad{position(x,{}a,{}n)} returns the index \\spad{i} of the first occurrence of \\spad{x} in \\axiom{a} where \\axiom{\\spad{i} \\spad{>=} \\spad{n}},{} and \\axiom{minIndex(a) - 1} if no such \\spad{x} is found.") (((|Integer|) |#1| $) "\\spad{position(x,{}a)} returns the index \\spad{i} of the first occurrence of \\spad{x} in a,{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.") (((|Integer|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{position(p,{}a)} returns the index \\spad{i} of the first \\spad{x} in \\axiom{a} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.")) (|sorted?| (((|Boolean|) $) "\\spad{sorted?(u)} tests if the elements of \\spad{u} are in ascending order.") (((|Boolean|) (|Mapping| (|Boolean|) |#1| |#1|) $) "\\spad{sorted?(p,{}a)} tests if \\axiom{a} is sorted according to predicate \\spad{p}.")) (|sort| (($ $) "\\spad{sort(u)} returns an \\spad{u} with elements in ascending order. Note: \\axiom{sort(\\spad{u}) = sort(\\spad{<=},{}\\spad{u})}.") (($ (|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|) $ $) "\\spad{merge(p,{}a,{}b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) -((-4417 . T)) +((-4414 . T)) NIL (-376 |VarSet| R) ((|constructor| (NIL "The category of free Lie algebras. It is used by domains of non-commutative algebra: \\spadtype{LiePolynomial} and \\spadtype{XPBWPolynomial}. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr})")) (|eval| (($ $ (|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) (-4412 . T) (-4411 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-4409 . T) (-4408 . T)) NIL (-377 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."))) @@ -1446,7 +1446,7 @@ NIL ((|HasCategory| |#2| (LIST (QUOTE -639) (QUOTE (-566))))) (-379 R) ((|constructor| (NIL "\\spad{S} is \\spadtype{FullyLinearlyExplicitRingOver R} means that \\spad{S} is a \\spadtype{LinearlyExplicitRingOver R} and,{} in addition,{} if \\spad{R} is a \\spadtype{LinearlyExplicitRingOver Integer},{} then so is \\spad{S}"))) -((-4414 . T)) +((-4411 . T)) NIL (-380 |Par|) ((|constructor| (NIL "\\indented{3}{This is a package for the approximation of complex solutions for} systems of equations of rational functions with complex rational coefficients. The results are expressed as either complex rational numbers or complex floats depending on the type of the precision parameter which can be either a rational number or a floating point number.")) (|complexRoots| (((|List| (|List| (|Complex| |#1|))) (|List| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) (|List| (|Symbol|)) |#1|) "\\spad{complexRoots(lrf,{} lv,{} eps)} finds all the complex solutions of a list of rational functions with rational number coefficients with respect the the variables appearing in \\spad{lv}. Each solution is computed to precision eps and returned as list corresponding to the order of variables in \\spad{lv}.") (((|List| (|Complex| |#1|)) (|Fraction| (|Polynomial| (|Complex| (|Integer|)))) |#1|) "\\spad{complexRoots(rf,{} eps)} finds all the complex solutions of a univariate rational function with rational number coefficients. The solutions are computed to precision eps.")) (|complexSolve| (((|List| (|Equation| (|Polynomial| (|Complex| |#1|)))) (|Equation| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) |#1|) "\\spad{complexSolve(eq,{}eps)} finds all the complex solutions of the equation \\spad{eq} of rational functions with rational rational coefficients with respect to all the variables appearing in \\spad{eq},{} with precision \\spad{eps}.") (((|List| (|Equation| (|Polynomial| (|Complex| |#1|)))) (|Fraction| (|Polynomial| (|Complex| (|Integer|)))) |#1|) "\\spad{complexSolve(p,{}eps)} find all the complex solutions of the rational function \\spad{p} with complex rational coefficients with respect to all the variables appearing in \\spad{p},{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| (|Complex| |#1|))))) (|List| (|Equation| (|Fraction| (|Polynomial| (|Complex| (|Integer|)))))) |#1|) "\\spad{complexSolve(leq,{}eps)} finds all the complex solutions to precision \\spad{eps} of the system \\spad{leq} of equations of rational functions over complex rationals with respect to all the variables appearing in \\spad{lp}.") (((|List| (|List| (|Equation| (|Polynomial| (|Complex| |#1|))))) (|List| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) |#1|) "\\spad{complexSolve(lp,{}eps)} finds all the complex solutions to precision \\spad{eps} of the system \\spad{lp} of rational functions over the complex rationals with respect to all the variables appearing in \\spad{lp}."))) @@ -1454,7 +1454,7 @@ NIL NIL (-381) ((|constructor| (NIL "\\spadtype{Float} implements arbitrary precision floating point arithmetic. The number of significant digits of each operation can be set to an arbitrary value (the default is 20 decimal digits). The operation \\spad{float(mantissa,{}exponent,{}\\spadfunFrom{base}{FloatingPointSystem})} for integer \\spad{mantissa},{} \\spad{exponent} specifies the number \\spad{mantissa * \\spadfunFrom{base}{FloatingPointSystem} ** exponent} The underlying representation for floats is binary not decimal. The implications of this are described below. \\blankline The model adopted is that arithmetic operations are rounded to to nearest unit in the last place,{} that is,{} accurate to within \\spad{2**(-\\spadfunFrom{bits}{FloatingPointSystem})}. Also,{} the elementary functions and constants are accurate to one unit in the last place. A float is represented as a record of two integers,{} the mantissa and the exponent. The \\spadfunFrom{base}{FloatingPointSystem} of the representation is binary,{} hence a \\spad{Record(m:mantissa,{}e:exponent)} represents the number \\spad{m * 2 ** e}. Though it is not assumed that the underlying integers are represented with a binary \\spadfunFrom{base}{FloatingPointSystem},{} the code will be most efficient when this is the the case (this is \\spad{true} in most implementations of Lisp). The decision to choose the \\spadfunFrom{base}{FloatingPointSystem} to be binary has some unfortunate consequences. First,{} decimal numbers like 0.3 cannot be represented exactly. Second,{} there is a further loss of accuracy during conversion to decimal for output. To compensate for this,{} if \\spad{d} digits of precision are specified,{} \\spad{1 + ceiling(log2 d)} bits are used. Two numbers that are displayed identically may therefore be not equal. On the other hand,{} a significant efficiency loss would be incurred if we chose to use a decimal \\spadfunFrom{base}{FloatingPointSystem} when the underlying integer base is binary. \\blankline Algorithms used: For the elementary functions,{} the general approach is to apply identities so that the taylor series can be used,{} and,{} so that it will converge within \\spad{O( sqrt n )} steps. For example,{} using the identity \\spad{exp(x) = exp(x/2)**2},{} we can compute \\spad{exp(1/3)} to \\spad{n} digits of precision as follows. We have \\spad{exp(1/3) = exp(2 ** (-sqrt s) / 3) ** (2 ** sqrt s)}. The taylor series will converge in less than sqrt \\spad{n} steps and the exponentiation requires sqrt \\spad{n} multiplications for a total of \\spad{2 sqrt n} multiplications. Assuming integer multiplication costs \\spad{O( n**2 )} the overall running time is \\spad{O( sqrt(n) n**2 )}. This approach is the best known approach for precisions up to about 10,{}000 digits at which point the methods of Brent which are \\spad{O( log(n) n**2 )} become competitive. Note also that summing the terms of the taylor series for the elementary functions is done using integer operations. This avoids the overhead of floating point operations and results in efficient code at low precisions. This implementation makes no attempt to reuse storage,{} relying on the underlying system to do \\spadgloss{garbage collection}. \\spad{I} estimate that the efficiency of this package at low precisions could be improved by a factor of 2 if in-place operations were available. \\blankline Running times: in the following,{} \\spad{n} is the number of bits of precision \\indented{5}{\\spad{*},{} \\spad{/},{} \\spad{sqrt},{} \\spad{\\spad{pi}},{} \\spad{exp1},{} \\spad{log2},{} \\spad{log10}: \\spad{ O( n**2 )}} \\indented{5}{\\spad{exp},{} \\spad{log},{} \\spad{sin},{} \\spad{atan}:\\space{2}\\spad{ O( sqrt(n) n**2 )}} The other elementary functions are coded in terms of the ones above.")) (|outputSpacing| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputSpacing(n)} inserts a space after \\spad{n} (default 10) digits on output; outputSpacing(0) means no spaces are inserted.")) (|outputGeneral| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputGeneral(n)} sets the output mode to general notation with \\spad{n} significant digits displayed.") (((|Void|)) "\\spad{outputGeneral()} sets the output mode (default mode) to general notation; numbers will be displayed in either fixed or floating (scientific) notation depending on the magnitude.")) (|outputFixed| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFixed(n)} sets the output mode to fixed point notation,{} with \\spad{n} digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFixed()} sets the output mode to fixed point notation; the output will contain a decimal point.")) (|outputFloating| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFloating(n)} sets the output mode to floating (scientific) notation with \\spad{n} significant digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFloating()} sets the output mode to floating (scientific) notation,{} \\spadignore{i.e.} \\spad{mantissa * 10 exponent} is displayed as \\spad{0.mantissa E exponent}.")) (|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}."))) -((-4400 . T) (-4408 . T) (-3645 . T) (-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) +((-4397 . T) (-4405 . T) (-3651 . T) (-4406 . T) (-4412 . T) (-4407 . T) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) NIL (-382 |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}."))) @@ -1462,11 +1462,11 @@ NIL NIL (-383 R S) ((|constructor| (NIL "This domain implements linear combinations of elements from the domain \\spad{S} with coefficients in the domain \\spad{R} where \\spad{S} is an ordered set and \\spad{R} is a ring (which may be non-commutative). This domain is used by domains of non-commutative algebra such as: \\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}"))) -((-4412 . T) (-4411 . T)) +((-4409 . T) (-4408 . T)) ((|HasCategory| |#1| (QUOTE (-172)))) (-384 R |Basis|) ((|constructor| (NIL "A domain of this category implements formal linear combinations of elements from a domain \\spad{Basis} with coefficients in a domain \\spad{R}. The domain \\spad{Basis} needs only to belong to the category \\spadtype{SetCategory} and \\spad{R} to the category \\spadtype{Ring}. Thus the coefficient ring may be non-commutative. See the \\spadtype{XDistributedPolynomial} constructor for examples of domains built with the \\spadtype{FreeModuleCat} category constructor. 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}."))) -((-4412 . T) (-4411 . T)) +((-4409 . T) (-4408 . T)) NIL (-385) ((|constructor| (NIL "\\axiomType{FortranMatrixCategory} provides support for producing Functions and Subroutines when the input to these is an AXIOM object of type \\axiomType{Matrix} or in domains involving \\axiomType{FortranCode}.")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|Matrix| (|MachineFloat|))) "\\spad{coerce(v)} produces an ASP which returns the value of \\spad{v}."))) @@ -1478,7 +1478,7 @@ NIL NIL (-387 R S) ((|constructor| (NIL "A \\spad{bi}-module is a free module over a ring with generators indexed by an ordered set. Each element can be expressed as a finite linear combination of generators. Only non-zero terms are stored."))) -((-4412 . T) (-4411 . T)) +((-4409 . T) (-4408 . T)) ((|HasCategory| |#1| (QUOTE (-172)))) (-388 S) ((|constructor| (NIL "The free monoid on a set \\spad{S} is the monoid of finite products of the form \\spad{reduce(*,{}[\\spad{si} ** \\spad{ni}])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are nonnegative integers. The multiplication is not commutative.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f,{} a1\\^e1 ... an\\^en)} returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (|mapExpon| (($ (|Mapping| (|NonNegativeInteger|) (|NonNegativeInteger|)) $) "\\spad{mapExpon(f,{} a1\\^e1 ... an\\^en)} returns \\spad{a1\\^f(e1) ... an\\^f(en)}.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(x,{} n)} returns the factor of the n^th monomial of \\spad{x}.")) (|nthExpon| (((|NonNegativeInteger|) $ (|Integer|)) "\\spad{nthExpon(x,{} n)} returns the exponent of the n^th monomial of \\spad{x}.")) (|factors| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| (|NonNegativeInteger|)))) $) "\\spad{factors(a1\\^e1,{}...,{}an\\^en)} returns \\spad{[[a1,{} e1],{}...,{}[an,{} en]]}.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(x)} returns the number of monomials in \\spad{x}.")) (|overlap| (((|Record| (|:| |lm| $) (|:| |mm| $) (|:| |rm| $)) $ $) "\\spad{overlap(x,{} y)} returns \\spad{[l,{} m,{} r]} such that \\spad{x = l * m},{} \\spad{y = m * r} and \\spad{l} and \\spad{r} have no overlap,{} \\spadignore{i.e.} \\spad{overlap(l,{} r) = [l,{} 1,{} r]}.")) (|divide| (((|Union| (|Record| (|:| |lm| $) (|:| |rm| $)) "failed") $ $) "\\spad{divide(x,{} y)} returns the left and right exact quotients of \\spad{x} by \\spad{y},{} \\spadignore{i.e.} \\spad{[l,{} r]} such that \\spad{x = l * y * r},{} \"failed\" if \\spad{x} is not of the form \\spad{l * y * r}.")) (|rquo| (((|Union| $ "failed") $ $) "\\spad{rquo(x,{} y)} returns the exact right quotient of \\spad{x} by \\spad{y} \\spadignore{i.e.} \\spad{q} such that \\spad{x = q * y},{} \"failed\" if \\spad{x} is not of the form \\spad{q * y}.")) (|lquo| (((|Union| $ "failed") $ $) "\\spad{lquo(x,{} y)} returns the exact left quotient of \\spad{x} by \\spad{y} \\spadignore{i.e.} \\spad{q} such that \\spad{x = y * q},{} \"failed\" if \\spad{x} is not of the form \\spad{y * q}.")) (|hcrf| (($ $ $) "\\spad{hcrf(x,{} y)} returns the highest common right factor of \\spad{x} and \\spad{y},{} \\spadignore{i.e.} the largest \\spad{d} such that \\spad{x = a d} and \\spad{y = b d}.")) (|hclf| (($ $ $) "\\spad{hclf(x,{} y)} returns the highest common left factor of \\spad{x} and \\spad{y},{} \\spadignore{i.e.} the largest \\spad{d} such that \\spad{x = d a} and \\spad{y = d b}.")) (** (($ |#1| (|NonNegativeInteger|)) "\\spad{s ** n} returns the product of \\spad{s} by itself \\spad{n} times.")) (* (($ $ |#1|) "\\spad{x * s} returns the product of \\spad{x} by \\spad{s} on the right.") (($ |#1| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) @@ -1486,7 +1486,7 @@ NIL ((|HasCategory| |#1| (QUOTE (-850)))) (-389) ((|constructor| (NIL "A category of domains which model machine arithmetic used by machines in the AXIOM-NAG link."))) -((-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) +((-4407 . T) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) NIL (-390) ((|constructor| (NIL "This domain provides an interface to names in the file system."))) @@ -1498,13 +1498,13 @@ NIL NIL (-392 |n| |class| R) ((|constructor| (NIL "Generate the Free Lie Algebra over a ring \\spad{R} with identity; A \\spad{P}. Hall basis is generated by a package call to HallBasis.")) (|generator| (($ (|NonNegativeInteger|)) "\\spad{generator(i)} is the \\spad{i}th Hall Basis element")) (|shallowExpand| (((|OutputForm|) $) "\\spad{shallowExpand(x)} \\undocumented{}")) (|deepExpand| (((|OutputForm|) $) "\\spad{deepExpand(x)} \\undocumented{}")) (|dimension| (((|NonNegativeInteger|)) "\\spad{dimension()} is the rank of this Lie algebra"))) -((-4412 . T) (-4411 . T)) +((-4409 . T) (-4408 . T)) NIL (-393) ((|constructor| (NIL "Code to manipulate Fortran Output Stack")) (|topFortranOutputStack| (((|String|)) "\\spad{topFortranOutputStack()} returns the top element of the Fortran output stack")) (|pushFortranOutputStack| (((|Void|) (|String|)) "\\spad{pushFortranOutputStack(f)} pushes \\spad{f} onto the Fortran output stack") (((|Void|) (|FileName|)) "\\spad{pushFortranOutputStack(f)} pushes \\spad{f} onto the Fortran output stack")) (|popFortranOutputStack| (((|Void|)) "\\spad{popFortranOutputStack()} pops the Fortran output stack")) (|showFortranOutputStack| (((|Stack| (|String|))) "\\spad{showFortranOutputStack()} returns the Fortran output stack")) (|clearFortranOutputStack| (((|Stack| (|String|))) "\\spad{clearFortranOutputStack()} clears the Fortran output stack"))) NIL NIL -(-394 -2382 UP UPUP R) +(-394 -2386 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 @@ -1528,11 +1528,11 @@ 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 -(-400 -2628 |returnType| -2763 |symbols|) +(-400 -2639 |returnType| -3072 |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 -(-401 -2382 UP) +(-401 -2386 UP) ((|constructor| (NIL "\\indented{1}{Full partial fraction expansion of rational functions} Author: Manuel Bronstein Date Created: 9 December 1992 Date Last Updated: 6 October 1993 References: \\spad{M}.Bronstein & \\spad{B}.Salvy,{} \\indented{12}{Full Partial Fraction Decomposition of Rational Functions,{}} \\indented{12}{in Proceedings of ISSAC'93,{} Kiev,{} ACM Press.}")) (D (($ $ (|NonNegativeInteger|)) "\\spad{D(f,{} n)} returns the \\spad{n}-th derivative of \\spad{f}.") (($ $) "\\spad{D(f)} returns the derivative of \\spad{f}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(f,{} n)} returns the \\spad{n}-th derivative of \\spad{f}.") (($ $) "\\spad{differentiate(f)} returns the derivative of \\spad{f}.")) (|construct| (($ (|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| |#2|) (|:| |num| |#2|)))) "\\spad{construct(l)} is the inverse of fracPart.")) (|fracPart| (((|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| |#2|) (|:| |num| |#2|))) $) "\\spad{fracPart(f)} returns the list of summands of the fractional part of \\spad{f}.")) (|polyPart| ((|#2| $) "\\spad{polyPart(f)} returns the polynomial part of \\spad{f}.")) (|fullPartialFraction| (($ (|Fraction| |#2|)) "\\spad{fullPartialFraction(f)} returns \\spad{[p,{} [[j,{} Dj,{} Hj]...]]} such that \\spad{f = p(x) + \\sum_{[j,{}Dj,{}Hj] in l} \\sum_{Dj(a)=0} Hj(a)/(x - a)\\^j}.")) (+ (($ |#2| $) "\\spad{p + x} returns the sum of \\spad{p} and \\spad{x}"))) NIL NIL @@ -1546,15 +1546,15 @@ NIL NIL (-404) ((|constructor| (NIL "FieldOfPrimeCharacteristic is the category of fields of prime characteristic,{} \\spadignore{e.g.} finite fields,{} algebraic closures of fields of prime characteristic,{} transcendental extensions of of fields of prime characteristic.")) (|primeFrobenius| (($ $ (|NonNegativeInteger|)) "\\spad{primeFrobenius(a,{}s)} returns \\spad{a**(p**s)} where \\spad{p} is the characteristic.") (($ $) "\\spad{primeFrobenius(a)} returns \\spad{a ** p} where \\spad{p} is the characteristic.")) (|discreteLog| (((|Union| (|NonNegativeInteger|) "failed") $ $) "\\spad{discreteLog(b,{}a)} computes \\spad{s} with \\spad{b**s = a} if such an \\spad{s} exists.")) (|order| (((|OnePointCompletion| (|PositiveInteger|)) $) "\\spad{order(a)} computes the order of an element in the multiplicative group of the field. Error: if \\spad{a} is 0."))) -((-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) +((-4406 . T) (-4412 . T) (-4407 . T) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) NIL (-405 S) ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\\spad{\"+\"}) does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\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 -4400)) (|HasAttribute| |#1| (QUOTE -4408))) +((|HasAttribute| |#1| (QUOTE -4397)) (|HasAttribute| |#1| (QUOTE -4405))) (-406) ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\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\"."))) -((-3645 . T) (-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) +((-3651 . T) (-4406 . T) (-4412 . T) (-4407 . T) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) NIL (-407 R S) ((|constructor| (NIL "\\spadtype{FactoredFunctions2} contains functions that involve factored objects whose underlying domains may not be the same. For example,{} \\spadfun{map} might be used to coerce an object of type \\spadtype{Factored(Integer)} to \\spadtype{Factored(Complex(Integer))}.")) (|map| (((|Factored| |#2|) (|Mapping| |#2| |#1|) (|Factored| |#1|)) "\\spad{map(fn,{}u)} is used to apply the function \\userfun{\\spad{fn}} to every factor of \\spadvar{\\spad{u}}. The new factored object will have all its information flags set to \"nil\". This function is used,{} for example,{} to coerce every factor base to another type."))) @@ -1566,15 +1566,15 @@ NIL NIL (-409 S) ((|constructor| (NIL "Fraction takes an IntegralDomain \\spad{S} and produces the domain of Fractions with numerators and denominators from \\spad{S}. If \\spad{S} is also a GcdDomain,{} then \\spad{gcd}\\spad{'s} between numerator and denominator will be cancelled during all operations.")) (|canonical| ((|attribute|) "\\spad{canonical} means that equal elements are in fact identical."))) -((-4404 -12 (|has| |#1| (-6 -4415)) (|has| |#1| (-454)) (|has| |#1| (-6 -4404))) (-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) -((|HasCategory| |#1| (QUOTE (-909))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-1175)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-547))) (|HasCategory| |#1| (QUOTE (-828)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538))))) (|HasCategory| |#1| (QUOTE (-1022))) (|HasCategory| |#1| (QUOTE (-820))) (-2805 (|HasCategory| |#1| (QUOTE (-820))) (|HasCategory| |#1| (QUOTE (-850)))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-547))) (|HasCategory| |#1| (QUOTE (-828)))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-1150))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-381)))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-547))) (|HasCategory| |#1| (QUOTE (-828)))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (-2805 (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (-12 (|HasCategory| |#1| (QUOTE (-547))) (|HasCategory| |#1| (QUOTE (-828))))) (-2805 (|HasCategory| |#1| (LIST (QUOTE -639) (QUOTE (-566)))) (-12 (|HasCategory| |#1| (QUOTE (-547))) (|HasCategory| |#1| (QUOTE (-828))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| |#1| (LIST (QUOTE -516) (QUOTE (-1175)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -287) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-547))) (|HasCategory| |#1| (QUOTE (-828)))) (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-547))) (-12 (|HasAttribute| |#1| (QUOTE -4415)) (|HasAttribute| |#1| (QUOTE -4404)) (|HasCategory| |#1| (QUOTE (-454)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -639) (QUOTE (-566)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-909)))) (-2805 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-145))))) +((-4401 -12 (|has| |#1| (-6 -4412)) (|has| |#1| (-454)) (|has| |#1| (-6 -4401))) (-4406 . T) (-4412 . T) (-4407 . T) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) +((|HasCategory| |#1| (QUOTE (-909))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-1175)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-547))) (|HasCategory| |#1| (QUOTE (-828)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538))))) (|HasCategory| |#1| (QUOTE (-1022))) (|HasCategory| |#1| (QUOTE (-820))) (-2805 (|HasCategory| |#1| (QUOTE (-820))) (|HasCategory| |#1| (QUOTE (-850)))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-547))) (|HasCategory| |#1| (QUOTE (-828)))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-1150))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-381)))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-547))) (|HasCategory| |#1| (QUOTE (-828)))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (-2805 (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (-12 (|HasCategory| |#1| (QUOTE (-547))) (|HasCategory| |#1| (QUOTE (-828))))) (-2805 (|HasCategory| |#1| (LIST (QUOTE -639) (QUOTE (-566)))) (-12 (|HasCategory| |#1| (QUOTE (-547))) (|HasCategory| |#1| (QUOTE (-828))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| |#1| (LIST (QUOTE -516) (QUOTE (-1175)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -287) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-547))) (|HasCategory| |#1| (QUOTE (-828)))) (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-547))) (-12 (|HasAttribute| |#1| (QUOTE -4412)) (|HasAttribute| |#1| (QUOTE -4401)) (|HasCategory| |#1| (QUOTE (-454)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -639) (QUOTE (-566)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-909)))) (-2805 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-145))))) (-410 S R UP) ((|constructor| (NIL "A \\spadtype{FramedAlgebra} is a \\spadtype{FiniteRankAlgebra} together with a fixed \\spad{R}-module basis.")) (|regularRepresentation| (((|Matrix| |#2|) $) "\\spad{regularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed basis.")) (|discriminant| ((|#2|) "\\spad{discriminant()} = determinant(traceMatrix()).")) (|traceMatrix| (((|Matrix| |#2|)) "\\spad{traceMatrix()} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr(\\spad{vi} * vj)} ),{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|convert| (($ (|Vector| |#2|)) "\\spad{convert([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.") (((|Vector| |#2|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#2|)) "\\spad{represents([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $)) "\\spad{coordinates([v1,{}...,{}vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#2|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) NIL NIL (-411 R UP) ((|constructor| (NIL "A \\spadtype{FramedAlgebra} is a \\spadtype{FiniteRankAlgebra} together with a fixed \\spad{R}-module basis.")) (|regularRepresentation| (((|Matrix| |#1|) $) "\\spad{regularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed basis.")) (|discriminant| ((|#1|) "\\spad{discriminant()} = determinant(traceMatrix()).")) (|traceMatrix| (((|Matrix| |#1|)) "\\spad{traceMatrix()} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr(\\spad{vi} * vj)} ),{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|convert| (($ (|Vector| |#1|)) "\\spad{convert([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.") (((|Vector| |#1|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([v1,{}...,{}vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#1|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) -((-4411 . T) (-4412 . T) (-4414 . T)) +((-4408 . T) (-4409 . T) (-4411 . T)) NIL (-412 A S) ((|constructor| (NIL "\\indented{2}{A is fully retractable to \\spad{B} means that A is retractable to \\spad{B},{} and,{}} \\indented{2}{in addition,{} if \\spad{B} is retractable to the integers or rational} \\indented{2}{numbers then so is A.} \\indented{2}{In particular,{} what we are asserting is that there are no integers} \\indented{2}{(rationals) in A which don\\spad{'t} retract into \\spad{B}.} Date Created: March 1990 Date Last Updated: 9 April 1991"))) @@ -1588,11 +1588,11 @@ NIL ((|constructor| (NIL "\\indented{1}{Lifting of morphisms to fractional ideals.} Author: Manuel Bronstein Date Created: 1 Feb 1989 Date Last Updated: 27 Feb 1990 Keywords: ideal,{} algebra,{} module.")) (|map| (((|FractionalIdeal| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FractionalIdeal| |#1| |#2| |#3| |#4|)) "\\spad{map(f,{}i)} \\undocumented{}"))) NIL NIL -(-415 R -2382 UP A) +(-415 R -2386 UP A) ((|constructor| (NIL "Fractional ideals in a framed algebra.")) (|randomLC| ((|#4| (|NonNegativeInteger|) (|Vector| |#4|)) "\\spad{randomLC(n,{}x)} should be local but conditional.")) (|minimize| (($ $) "\\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)}."))) -((-4414 . T)) +((-4411 . T)) NIL -(-416 R -2382 UP A |ibasis|) +(-416 R -2386 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|) $) "\\spad{basis((f1,{}...,{}fn))} = the vector \\spad{[f1,{}...,{}fn]}."))) NIL ((|HasCategory| |#4| (LIST (QUOTE -1038) (|devaluate| |#2|)))) @@ -1606,11 +1606,11 @@ NIL ((|HasCategory| |#2| (QUOTE (-365)))) (-419 R) ((|constructor| (NIL "FramedNonAssociativeAlgebra(\\spad{R}) is a \\spadtype{FiniteRankNonAssociativeAlgebra} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank) over a commutative ring \\spad{R} together with a fixed \\spad{R}-module basis.")) (|apply| (($ (|Matrix| |#1|) $) "\\spad{apply(m,{}a)} defines a left operation of \\spad{n} by \\spad{n} matrices where \\spad{n} is the rank of the algebra in terms of matrix-vector multiplication,{} this is a substitute for a left module structure. Error: if shape of matrix doesn\\spad{'t} fit.")) (|rightRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#1|))) "\\spad{rightRankPolynomial()} calculates the right minimal polynomial of the generic element in the algebra,{} defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|leftRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#1|))) "\\spad{leftRankPolynomial()} calculates the left minimal polynomial of the generic element in the algebra,{} defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|rightRegularRepresentation| (((|Matrix| |#1|) $) "\\spad{rightRegularRepresentation(a)} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|leftRegularRepresentation| (((|Matrix| |#1|) $) "\\spad{leftRegularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|rightTraceMatrix| (((|Matrix| |#1|)) "\\spad{rightTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|leftTraceMatrix| (((|Matrix| |#1|)) "\\spad{leftTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|rightDiscriminant| ((|#1|) "\\spad{rightDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note: the same as \\spad{determinant(rightTraceMatrix())}.")) (|leftDiscriminant| ((|#1|) "\\spad{leftDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note: the same as \\spad{determinant(leftTraceMatrix())}.")) (|convert| (($ (|Vector| |#1|)) "\\spad{convert([a1,{}...,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed \\spad{R}-module basis.") (((|Vector| |#1|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,{}...,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|))) "\\spad{conditionsForIdempotents()} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the fixed \\spad{R}-module basis.")) (|structuralConstants| (((|Vector| (|Matrix| |#1|))) "\\spad{structuralConstants()} calculates the structural constants \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{\\spad{vi} * vj = gammaij1 * v1 + ... + gammaijn * vn},{} where \\spad{v1},{}...,{}\\spad{vn} is the fixed \\spad{R}-module basis.")) (|elt| ((|#1| $ (|Integer|)) "\\spad{elt(a,{}i)} returns the \\spad{i}-th coefficient of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([a1,{}...,{}am])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{\\spad{ai}} with respect to the fixed \\spad{R}-module basis.") (((|Vector| |#1|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) -((-4414 |has| |#1| (-558)) (-4412 . T) (-4411 . T)) +((-4411 |has| |#1| (-558)) (-4409 . T) (-4408 . T)) NIL (-420 R) ((|constructor| (NIL "\\spadtype{Factored} creates a domain whose objects are kept in factored form as long as possible. Thus certain operations like multiplication and \\spad{gcd} are relatively easy to do. Others,{} like addition require somewhat more work,{} and unless the argument domain provides a factor function,{} the result may not be completely factored. Each object consists of a unit and a list of factors,{} where a factor has a member of \\spad{R} (the \"base\"),{} and exponent and a flag indicating what is known about the base. A flag may be one of \"nil\",{} \"sqfr\",{} \"irred\" or \"prime\",{} which respectively mean that nothing is known about the base,{} it is square-free,{} it is irreducible,{} or it is prime. The current restriction to integral domains allows simplification to be performed without worrying about multiplication order.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(u)} returns a rational number if \\spad{u} really is one,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(u)} assumes spadvar{\\spad{u}} is actually a rational number and does the conversion to rational number (see \\spadtype{Fraction Integer}).")) (|rational?| (((|Boolean|) $) "\\spad{rational?(u)} tests if \\spadvar{\\spad{u}} is actually a rational number (see \\spadtype{Fraction Integer}).")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,{}u)} maps the function \\userfun{\\spad{fn}} across the factors of \\spadvar{\\spad{u}} and creates a new factored object. Note: this clears the information flags (sets them to \"nil\") because the effect of \\userfun{\\spad{fn}} is clearly not known in general.")) (|unitNormalize| (($ $) "\\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."))) -((-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) +((-4407 . T) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) ((|HasCategory| |#1| (LIST (QUOTE -516) (QUOTE (-1175)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -310) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -287) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#1| (QUOTE (-1218))) (-2805 (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-1218)))) (|HasCategory| |#1| (QUOTE (-1022))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| |#1| (LIST (QUOTE -516) (QUOTE (-1175)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -287) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| |#1| (QUOTE (-547))) (|HasCategory| |#1| (QUOTE (-454)))) (-421 R) ((|constructor| (NIL "\\spadtype{FactoredFunctionUtilities} implements some utility functions for manipulating factored objects.")) (|mergeFactors| (((|Factored| |#1|) (|Factored| |#1|) (|Factored| |#1|)) "\\spad{mergeFactors(u,{}v)} is used when the factorizations of \\spadvar{\\spad{u}} and \\spadvar{\\spad{v}} are known to be disjoint,{} \\spadignore{e.g.} resulting from a content/primitive part split. Essentially,{} it creates a new factored object by multiplying the units together and appending the lists of factors.")) (|refine| (((|Factored| |#1|) (|Factored| |#1|) (|Mapping| (|Factored| |#1|) |#1|)) "\\spad{refine(u,{}fn)} is used to apply the function \\userfun{\\spad{fn}} to each factor of \\spadvar{\\spad{u}} and then build a new factored object from the results. For example,{} if \\spadvar{\\spad{u}} were created by calling \\spad{nilFactor(10,{}2)} then \\spad{refine(u,{}factor)} would create a factored object equal to that created by \\spad{factor(100)} or \\spad{primeFactor(2,{}2) * primeFactor(5,{}2)}."))) @@ -1638,17 +1638,17 @@ NIL ((|HasCategory| |#2| (QUOTE (-850))) (|HasCategory| |#2| (QUOTE (-370)))) (-427 S) ((|constructor| (NIL "A finite-set aggregate models the notion of a finite set,{} that is,{} a collection of elements characterized by membership,{} but not by order or multiplicity. See \\spadtype{Set} for an example.")) (|min| ((|#1| $) "\\spad{min(u)} returns the smallest element of aggregate \\spad{u}.")) (|max| ((|#1| $) "\\spad{max(u)} returns the largest element of aggregate \\spad{u}.")) (|universe| (($) "\\spad{universe()}\\$\\spad{D} returns the universal set for finite set aggregate \\spad{D}.")) (|complement| (($ $) "\\spad{complement(u)} returns the complement of the set \\spad{u},{} \\spadignore{i.e.} the set of all values not in \\spad{u}.")) (|cardinality| (((|NonNegativeInteger|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) -((-4417 . T) (-4407 . T) (-4418 . T)) +((-4414 . T) (-4404 . T) (-4415 . T)) NIL -(-428 R -2382) +(-428 R -2386) ((|constructor| (NIL "\\spadtype{FunctionSpaceComplexIntegration} provides functions for the indefinite integration of complex-valued functions.")) (|complexIntegrate| ((|#2| |#2| (|Symbol|)) "\\spad{complexIntegrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable.")) (|internalIntegrate0| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate0 should} be a local function,{} but is conditional.")) (|internalIntegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable."))) NIL NIL (-429 R E) ((|constructor| (NIL "\\indented{1}{Author: James Davenport} Date Created: 17 April 1992 Date Last Updated: Basic Functions: Related Constructors: Also See: AMS Classifications: Keywords: References: Description:")) (|makeCos| (($ |#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"))) -((-4404 -12 (|has| |#1| (-6 -4404)) (|has| |#2| (-6 -4404))) (-4411 . T) (-4412 . T) (-4414 . T)) -((-12 (|HasAttribute| |#1| (QUOTE -4404)) (|HasAttribute| |#2| (QUOTE -4404)))) -(-430 R -2382) +((-4401 -12 (|has| |#1| (-6 -4401)) (|has| |#2| (-6 -4401))) (-4408 . T) (-4409 . T) (-4411 . T)) +((-12 (|HasAttribute| |#1| (QUOTE -4401)) (|HasAttribute| |#2| (QUOTE -4401)))) +(-430 R -2386) ((|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 @@ -1658,17 +1658,17 @@ NIL ((|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-1049))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-475))) (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-538))))) (-432 R) ((|constructor| (NIL "A space of formal functions with arguments in an arbitrary ordered set.")) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| $)) $ (|Kernel| $)) "\\spad{univariate(f,{} k)} returns \\spad{f} viewed as a univariate fraction in \\spad{k}.")) (/ (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $)) (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{p1/p2} returns the quotient of \\spad{p1} and \\spad{p2} as an element of \\%.")) (|denominator| (($ $) "\\spad{denominator(f)} returns the denominator of \\spad{f} converted to \\%.")) (|denom| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|convert| (($ (|Factored| $)) "\\spad{convert(f1\\^e1 ... fm\\^em)} returns \\spad{(f1)\\^e1 ... (fm)\\^em} as an element of \\%,{} using formal kernels created using a \\spadfunFrom{paren}{ExpressionSpace}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isPower(p)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|numerator| (($ $) "\\spad{numerator(f)} returns the numerator of \\spad{f} converted to \\%.")) (|numer| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R} if \\spad{R} is an integral domain. If not,{} then numer(\\spad{f}) = \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|coerce| (($ (|Fraction| (|Polynomial| (|Fraction| |#1|)))) "\\spad{coerce(f)} returns \\spad{f} as an element of \\%.") (($ (|Polynomial| (|Fraction| |#1|))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.") (($ (|Fraction| |#1|)) "\\spad{coerce(q)} returns \\spad{q} as an element of \\%.") (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.")) (|isMult| (((|Union| (|Record| (|:| |coef| (|Integer|)) (|:| |var| (|Kernel| $))) "failed") $) "\\spad{isMult(p)} returns \\spad{[n,{} x]} if \\spad{p = n * x} and \\spad{n <> 0}.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,{}...,{}mn]} if \\spad{p = m1 +...+ mn} and \\spad{n > 1}.")) (|isExpt| (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|Symbol|)) "\\spad{isExpt(p,{}f)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = f(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|BasicOperator|)) "\\spad{isExpt(p,{}op)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = op(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,{}...,{}an]} if \\spad{p = a1*...*an} and \\spad{n > 1}.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns \\spad{x} * \\spad{x} * \\spad{x} * ... * \\spad{x} (\\spad{n} times).")) (|eval| (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ $)) "\\spad{eval(x,{} s,{} n,{} f)} replaces every \\spad{s(a)**n} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ (|List| $))) "\\spad{eval(x,{} s,{} n,{} f)} replaces every \\spad{s(a1,{}...,{}am)**n} in \\spad{x} by \\spad{f(a1,{}...,{}am)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [n1,{}...,{}nm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a1,{}...,{}an)**ni} in \\spad{x} by \\spad{\\spad{fi}(a1,{}...,{}an)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ $))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [n1,{}...,{}nm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a)**ni} in \\spad{x} by \\spad{\\spad{fi}(a)} for any \\spad{a}.") (($ $ (|List| (|BasicOperator|)) (|List| $) (|Symbol|)) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm],{} y)} replaces every \\spad{\\spad{si}(a)} in \\spad{x} by \\spad{\\spad{fi}(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $ (|BasicOperator|) $ (|Symbol|)) "\\spad{eval(x,{} s,{} f,{} y)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $) "\\spad{eval(f)} unquotes all the quoted operators in \\spad{f}.") (($ $ (|List| (|Symbol|))) "\\spad{eval(f,{} [foo1,{}...,{}foon])} unquotes all the \\spad{fooi}\\spad{'s} in \\spad{f}.") (($ $ (|Symbol|)) "\\spad{eval(f,{} foo)} unquotes all the foo\\spad{'s} in \\spad{f}.")) (|applyQuote| (($ (|Symbol|) (|List| $)) "\\spad{applyQuote(foo,{} [x1,{}...,{}xn])} returns \\spad{'foo(x1,{}...,{}xn)}.") (($ (|Symbol|) $ $ $ $) "\\spad{applyQuote(foo,{} x,{} y,{} z,{} t)} returns \\spad{'foo(x,{}y,{}z,{}t)}.") (($ (|Symbol|) $ $ $) "\\spad{applyQuote(foo,{} x,{} y,{} z)} returns \\spad{'foo(x,{}y,{}z)}.") (($ (|Symbol|) $ $) "\\spad{applyQuote(foo,{} x,{} y)} returns \\spad{'foo(x,{}y)}.") (($ (|Symbol|) $) "\\spad{applyQuote(foo,{} x)} returns \\spad{'foo(x)}.")) (|variables| (((|List| (|Symbol|)) $) "\\spad{variables(f)} returns the list of all the variables of \\spad{f}.")) (|ground| ((|#1| $) "\\spad{ground(f)} returns \\spad{f} as an element of \\spad{R}. An error occurs if \\spad{f} is not an element of \\spad{R}.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(f)} tests if \\spad{f} is an element of \\spad{R}."))) -((-4414 -2805 (|has| |#1| (-1049)) (|has| |#1| (-475))) (-4412 |has| |#1| (-172)) (-4411 |has| |#1| (-172)) ((-4419 "*") |has| |#1| (-558)) (-4410 |has| |#1| (-558)) (-4415 |has| |#1| (-558)) (-4409 |has| |#1| (-558))) +((-4411 -2805 (|has| |#1| (-1049)) (|has| |#1| (-475))) (-4409 |has| |#1| (-172)) (-4408 |has| |#1| (-172)) ((-4416 "*") |has| |#1| (-558)) (-4407 |has| |#1| (-558)) (-4412 |has| |#1| (-558)) (-4406 |has| |#1| (-558))) NIL -(-433 R -2382) +(-433 R -2386) ((|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 -(-434 R -2382) +(-434 R -2386) ((|constructor| (NIL "FunctionsSpacePrimitiveElement provides functions to compute primitive elements in functions spaces.")) (|primitiveElement| (((|Record| (|:| |primelt| |#2|) (|:| |pol1| (|SparseUnivariatePolynomial| |#2|)) (|:| |pol2| (|SparseUnivariatePolynomial| |#2|)) (|:| |prim| (|SparseUnivariatePolynomial| |#2|))) |#2| |#2|) "\\spad{primitiveElement(a1,{} a2)} returns \\spad{[a,{} q1,{} q2,{} q]} such that \\spad{k(a1,{} a2) = k(a)},{} \\spad{\\spad{ai} = \\spad{qi}(a)},{} and \\spad{q(a) = 0}. The minimal polynomial for 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{\\spad{ai} = \\spad{qi}(a)},{} and \\spad{q(a) = 0}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}."))) NIL ((|HasCategory| |#2| (QUOTE (-27)))) -(-435 R -2382) +(-435 R -2386) ((|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 @@ -1676,7 +1676,7 @@ 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 -(-437 R -2382 UP) +(-437 R -2386 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 -1038) (QUOTE (-48))))) @@ -1708,7 +1708,7 @@ 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 -(-445 R UP -2382) +(-445 R UP -2386) ((|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 @@ -1746,16 +1746,16 @@ NIL NIL (-454) ((|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}."))) -((-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) +((-4407 . T) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) NIL (-455 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"))) -((-4414 |has| (-409 (-952 |#1|)) (-558)) (-4412 . T) (-4411 . T)) +((-4411 |has| (-409 (-952 |#1|)) (-558)) (-4409 . T) (-4408 . T)) ((|HasCategory| (-409 (-952 |#1|)) (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| (-409 (-952 |#1|)) (QUOTE (-558)))) (-456 |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"))) -(((-4419 "*") |has| |#2| (-172)) (-4410 |has| |#2| (-558)) (-4415 |has| |#2| (-6 -4415)) (-4412 . T) (-4411 . T) (-4414 . T)) -((|HasCategory| |#2| (QUOTE (-909))) (-2805 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-454))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-909)))) (-2805 (|HasCategory| |#2| (QUOTE (-454))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-909)))) (-2805 (|HasCategory| |#2| (QUOTE (-454))) (|HasCategory| |#2| (QUOTE (-909)))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-172))) (-2805 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-558)))) (-12 (|HasCategory| (-864 |#1|) (LIST (QUOTE -886) (QUOTE (-381)))) (|HasCategory| |#2| (LIST (QUOTE -886) (QUOTE (-381))))) (-12 (|HasCategory| (-864 |#1|) (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| |#2| (LIST (QUOTE -886) (QUOTE (-566))))) (-12 (|HasCategory| (-864 |#1|) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (|HasCategory| |#2| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381)))))) (-12 (|HasCategory| (-864 |#1|) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| |#2| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566)))))) (-12 (|HasCategory| (-864 |#1|) (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-538))))) (|HasCategory| |#2| (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-566)))) (-2805 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#2| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566)))))) (|HasCategory| |#2| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#2| (QUOTE (-365))) (|HasAttribute| |#2| (QUOTE -4415)) (|HasCategory| |#2| (QUOTE (-454))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-909)))) (-2805 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-909)))) (|HasCategory| |#2| (QUOTE (-145))))) +(((-4416 "*") |has| |#2| (-172)) (-4407 |has| |#2| (-558)) (-4412 |has| |#2| (-6 -4412)) (-4409 . T) (-4408 . T) (-4411 . T)) +((|HasCategory| |#2| (QUOTE (-909))) (-2805 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-454))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-909)))) (-2805 (|HasCategory| |#2| (QUOTE (-454))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-909)))) (-2805 (|HasCategory| |#2| (QUOTE (-454))) (|HasCategory| |#2| (QUOTE (-909)))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-172))) (-2805 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-558)))) (-12 (|HasCategory| (-864 |#1|) (LIST (QUOTE -886) (QUOTE (-381)))) (|HasCategory| |#2| (LIST (QUOTE -886) (QUOTE (-381))))) (-12 (|HasCategory| (-864 |#1|) (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| |#2| (LIST (QUOTE -886) (QUOTE (-566))))) (-12 (|HasCategory| (-864 |#1|) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (|HasCategory| |#2| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381)))))) (-12 (|HasCategory| (-864 |#1|) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| |#2| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566)))))) (-12 (|HasCategory| (-864 |#1|) (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-538))))) (|HasCategory| |#2| (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-566)))) (-2805 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#2| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566)))))) (|HasCategory| |#2| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#2| (QUOTE (-365))) (|HasAttribute| |#2| (QUOTE -4412)) (|HasCategory| |#2| (QUOTE (-454))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-909)))) (-2805 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-909)))) (|HasCategory| |#2| (QUOTE (-145))))) (-457 R BP) ((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni.} January 1990 The equation \\spad{Af+Bg=h} and its generalization to \\spad{n} polynomials is solved for solutions over the \\spad{R},{} euclidean domain. A table containing the solutions of \\spad{Af+Bg=x**k} is used. The operations are performed modulus a prime which are in principle big enough,{} but the solutions are tested and,{} in case of failure,{} a hensel lifting process is used to get to the right solutions. It will be used in the factorization of multivariate polynomials over finite field,{} with \\spad{R=F[x]}.")) (|testModulus| (((|Boolean|) |#1| (|List| |#2|)) "\\spad{testModulus(p,{}lp)} returns \\spad{true} if the the prime \\spad{p} is valid for the list of polynomials \\spad{lp},{} \\spadignore{i.e.} preserves the degree and they remain relatively prime.")) (|solveid| (((|Union| (|List| |#2|) "failed") |#2| |#1| (|Vector| (|List| |#2|))) "\\spad{solveid(h,{}table)} computes the coefficients of the extended euclidean algorithm for a list of polynomials whose tablePow is \\spad{table} and with right side \\spad{h}.")) (|tablePow| (((|Union| (|Vector| (|List| |#2|)) "failed") (|NonNegativeInteger|) |#1| (|List| |#2|)) "\\spad{tablePow(maxdeg,{}prime,{}lpol)} constructs the table with the coefficients of the Extended Euclidean Algorithm for \\spad{lpol}. Here the right side is \\spad{x**k},{} for \\spad{k} less or equal to \\spad{maxdeg}. The operation returns \"failed\" when the elements are not coprime modulo \\spad{prime}.")) (|compBound| (((|NonNegativeInteger|) |#2| (|List| |#2|)) "\\spad{compBound(p,{}lp)} computes a bound for the coefficients of the solution polynomials. Given a polynomial right hand side \\spad{p},{} and a list \\spad{lp} of left hand side polynomials. Exported because it depends on the valuation.")) (|reduction| ((|#2| |#2| |#1|) "\\spad{reduction(p,{}prime)} reduces the polynomial \\spad{p} modulo \\spad{prime} of \\spad{R}. Note: this function is exported only because it\\spad{'s} conditional."))) NIL @@ -1782,7 +1782,7 @@ NIL NIL (-463 |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| $) "\\spad{leadingCoefficient(x)} \\undocumented"))) -((-4412 . T) (-4411 . T)) +((-4409 . T) (-4408 . T)) NIL (-464 E V R P Q) ((|constructor| (NIL "Gosper\\spad{'s} summation algorithm.")) (|GospersMethod| (((|Union| |#5| "failed") |#5| |#2| (|Mapping| |#2|)) "\\spad{GospersMethod(b,{} n,{} new)} returns a rational function \\spad{rf(n)} such that \\spad{a(n) * rf(n)} is the indefinite sum of \\spad{a(n)} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{a(n+1) * rf(n+1) - a(n) * rf(n) = a(n)},{} where \\spad{b(n) = a(n)/a(n-1)} is a rational function. Returns \"failed\" if no such rational function \\spad{rf(n)} exists. Note: \\spad{new} is a nullary function returning a new \\spad{V} every time. The condition on \\spad{a(n)} is that \\spad{a(n)/a(n-1)} is a rational function of \\spad{n}."))) @@ -1790,7 +1790,7 @@ NIL NIL (-465 R E |VarSet| P) ((|constructor| (NIL "A domain for polynomial sets.")) (|convert| (($ (|List| |#4|)) "\\axiom{convert(\\spad{lp})} returns the polynomial set whose members are the polynomials of \\axiom{\\spad{lp}}."))) -((-4418 . T) (-4417 . T)) +((-4415 . T) (-4414 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1099))) (|HasCategory| |#4| (LIST (QUOTE -310) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#4| (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#4| (LIST (QUOTE -613) (QUOTE (-862))))) (-466 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}."))) @@ -1820,7 +1820,7 @@ 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| $) "\\spad{degree(g)} names the degree of \\spad{g}. The set of all elements of a given degree form an \\spad{R}-module."))) NIL NIL -(-473 |lv| -2382 R) +(-473 |lv| -2386 R) ((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni,{} Summer \\spad{'88},{} revised November \\spad{'89}} Solve systems of polynomial equations using Groebner bases Total order Groebner bases are computed and then converted to lex ones This package is mostly intended for internal use.")) (|genericPosition| (((|Record| (|:| |dpolys| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |coords| (|List| (|Integer|)))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{genericPosition(lp,{}lv)} puts a radical zero dimensional ideal in general position,{} for system \\spad{lp} in variables \\spad{lv}.")) (|testDim| (((|Union| (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "failed") (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{testDim(lp,{}lv)} tests if the polynomial system \\spad{lp} in variables \\spad{lv} is zero dimensional.")) (|groebSolve| (((|List| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{groebSolve(lp,{}lv)} reduces the polynomial system \\spad{lp} in variables \\spad{lv} to triangular form. Algorithm based on groebner bases algorithm with linear algebra for change of ordering. Preprocessing for the general solver. The polynomials in input are of type \\spadtype{DMP}."))) NIL NIL @@ -1830,23 +1830,23 @@ NIL NIL (-475) ((|constructor| (NIL "The class of multiplicative groups,{} \\spadignore{i.e.} monoids with multiplicative inverses. \\blankline")) (|commutator| (($ $ $) "\\spad{commutator(p,{}q)} computes \\spad{inv(p) * inv(q) * p * q}.")) (|conjugate| (($ $ $) "\\spad{conjugate(p,{}q)} computes \\spad{inv(q) * p * q}; this is 'right action by conjugation'.")) (|unitsKnown| ((|attribute|) "unitsKnown asserts that recip only returns \"failed\" for non-units.")) (** (($ $ (|Integer|)) "\\spad{x**n} returns \\spad{x} raised to the integer power \\spad{n}.")) (/ (($ $ $) "\\spad{x/y} is the same as \\spad{x} times the inverse of \\spad{y}.")) (|inv| (($ $) "\\spad{inv(x)} returns the inverse of \\spad{x}."))) -((-4414 . T)) +((-4411 . T)) NIL (-476 |Coef| |var| |cen|) ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,{}f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x\\^r)}.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|coerce| (($ (|UnivariatePuiseuxSeries| |#1| |#2| |#3|)) "\\spad{coerce(f)} converts a Puiseux series to a general power series.") (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Puiseux series."))) -(((-4419 "*") |has| |#1| (-172)) (-4410 |has| |#1| (-558)) (-4415 |has| |#1| (-365)) (-4409 |has| |#1| (-365)) (-4411 . T) (-4412 . T) (-4414 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-172))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-566))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-566))) (|devaluate| |#1|)))) (|HasCategory| (-409 (-566)) (QUOTE (-1111))) (|HasCategory| |#1| (QUOTE (-365))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-558)))) (-2805 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-558)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-566)))))) (|HasSignature| |#1| (LIST (QUOTE -2512) (LIST (|devaluate| |#1|) (QUOTE (-1175)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-566)))))) (-2805 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-959))) (|HasCategory| |#1| (QUOTE (-1199))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasSignature| |#1| (LIST (QUOTE -4117) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1175))))) (|HasSignature| |#1| (LIST (QUOTE -2540) (LIST (LIST (QUOTE -644) (QUOTE (-1175))) (|devaluate| |#1|))))))) +(((-4416 "*") |has| |#1| (-172)) (-4407 |has| |#1| (-558)) (-4412 |has| |#1| (-365)) (-4406 |has| |#1| (-365)) (-4408 . T) (-4409 . T) (-4411 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-172))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-566))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-566))) (|devaluate| |#1|)))) (|HasCategory| (-409 (-566)) (QUOTE (-1111))) (|HasCategory| |#1| (QUOTE (-365))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-558)))) (-2805 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-558)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-566)))))) (|HasSignature| |#1| (LIST (QUOTE -3780) (LIST (|devaluate| |#1|) (QUOTE (-1175)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-566)))))) (-2805 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-959))) (|HasCategory| |#1| (QUOTE (-1199))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasSignature| |#1| (LIST (QUOTE -3921) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1175))))) (|HasSignature| |#1| (LIST (QUOTE -2608) (LIST (LIST (QUOTE -644) (QUOTE (-1175))) (|devaluate| |#1|))))))) (-477 |Key| |Entry| |Tbl| |dent|) ((|constructor| (NIL "A sparse table has a default entry,{} which is returned if no other value has been explicitly stored for a key."))) -((-4418 . T)) -((-12 (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2010) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2818) (|devaluate| |#2|)))))) (-2805 (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (QUOTE (-1099))) (|HasCategory| |#2| (QUOTE (-1099)))) (-2805 (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (LIST (QUOTE -614) (QUOTE (-538)))) (-12 (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-850))) (-2805 (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (QUOTE (-1099)))) +((-4415 . T)) +((-12 (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2050) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2849) (|devaluate| |#2|)))))) (-2805 (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (QUOTE (-1099))) (|HasCategory| |#2| (QUOTE (-1099)))) (-2805 (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (LIST (QUOTE -614) (QUOTE (-538)))) (-12 (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-850))) (-2805 (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (QUOTE (-1099)))) (-478 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)}"))) -((-4418 . T) (-4417 . T)) +((-4415 . T) (-4414 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1099))) (|HasCategory| |#4| (LIST (QUOTE -310) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#4| (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#3| (QUOTE (-370))) (|HasCategory| |#4| (LIST (QUOTE -613) (QUOTE (-862))))) (-479) ((|constructor| (NIL "\\indented{1}{Symbolic fractions in \\%\\spad{pi} with integer coefficients;} \\indented{1}{The point for using \\spad{Pi} as the default domain for those fractions} \\indented{1}{is that \\spad{Pi} is coercible to the float types,{} and not Expression.} Date Created: 21 Feb 1990 Date Last Updated: 12 Mai 1992")) (|pi| (($) "\\spad{\\spad{pi}()} returns the symbolic \\%\\spad{pi}."))) -((-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) +((-4406 . T) (-4412 . T) (-4407 . T) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) NIL (-480) ((|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'."))) @@ -1854,29 +1854,29 @@ NIL NIL (-481 |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."))) -((-4417 . T) (-4418 . T)) -((-12 (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2010) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2818) (|devaluate| |#2|)))))) (-2805 (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (QUOTE (-1099))) (|HasCategory| |#2| (QUOTE (-1099)))) (-2805 (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (LIST (QUOTE -614) (QUOTE (-538)))) (-12 (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#2| (QUOTE (-1099))) (-2805 (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (LIST (QUOTE -613) (QUOTE (-862))))) +((-4414 . T) (-4415 . T)) +((-12 (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2050) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2849) (|devaluate| |#2|)))))) (-2805 (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (QUOTE (-1099))) (|HasCategory| |#2| (QUOTE (-1099)))) (-2805 (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (LIST (QUOTE -614) (QUOTE (-538)))) (-12 (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#2| (QUOTE (-1099))) (-2805 (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (LIST (QUOTE -613) (QUOTE (-862))))) (-482) ((|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 (-483 |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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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 -4417)) (|HasAttribute| |#1| (QUOTE -4418)) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) +((|HasAttribute| |#1| (QUOTE -4414)) (|HasAttribute| |#1| (QUOTE -4415)) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (-491 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|) $) "\\spad{map(f,{}u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) NIL @@ -1912,33 +1912,33 @@ NIL ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) NIL NIL -(-496 -2382 UP |AlExt| |AlPol|) +(-496 -2386 UP |AlExt| |AlPol|) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of a field over which we can factor UP\\spad{'s}.")) (|factor| (((|Factored| |#4|) |#4| (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{factor(p,{} f)} returns a prime factorisation of \\spad{p}; \\spad{f} is a factorisation map for elements of UP."))) NIL NIL (-497) ((|constructor| (NIL "Algebraic closure of the rational numbers.")) (|norm| (($ $ (|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."))) -((-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) +((-4406 . T) (-4412 . T) (-4407 . T) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) ((|HasCategory| $ (QUOTE (-1049))) (|HasCategory| $ (LIST (QUOTE -1038) (QUOTE (-566))))) (-498 S |mn|) ((|constructor| (NIL "\\indented{1}{Author Micheal Monagan Aug/87} This is the basic one dimensional array data type."))) -((-4418 . T) (-4417 . T)) +((-4415 . T) (-4414 . T)) ((-2805 (-12 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538)))) (-2805 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099)))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| (-566) (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-499 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."))) -((-4417 . T) (-4418 . T)) +((-4414 . T) (-4415 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (-500 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 -(-501 R UP -2382) +(-501 R UP -2386) ((|constructor| (NIL "This package contains functions used in the packages FunctionFieldIntegralBasis and NumberFieldIntegralBasis.")) (|moduleSum| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) (|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) (|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|)))) "\\spad{moduleSum(m1,{}m2)} returns the sum of two modules in the framed algebra \\spad{F}. Each module \\spad{\\spad{mi}} is represented as follows: \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn} and \\spad{\\spad{mi}} is a record \\spad{[basis,{}basisDen,{}basisInv]}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then a basis \\spad{v1,{}...,{}vn} for \\spad{\\spad{mi}} is given by \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|idealiserMatrix| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{idealiserMatrix(m1,{} m2)} returns the matrix representing the linear conditions on the Ring associatied with an ideal defined by \\spad{m1} and \\spad{m2}.")) (|idealiser| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{idealiser(m1,{}m2,{}d)} computes the order of an ideal defined by \\spad{m1} and \\spad{m2} where \\spad{d} is the known part of the denominator") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{idealiser(m1,{}m2)} computes the order of an ideal defined by \\spad{m1} and \\spad{m2}")) (|leastPower| (((|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{leastPower(p,{}n)} returns \\spad{e},{} where \\spad{e} is the smallest integer such that \\spad{p **e >= n}")) (|divideIfCan!| ((|#1| (|Matrix| |#1|) (|Matrix| |#1|) |#1| (|Integer|)) "\\spad{divideIfCan!(matrix,{}matrixOut,{}prime,{}n)} attempts to divide the entries of \\spad{matrix} by \\spad{prime} and store the result in \\spad{matrixOut}. If it is successful,{} 1 is returned and if not,{} \\spad{prime} is returned. Here both \\spad{matrix} and \\spad{matrixOut} are \\spad{n}-by-\\spad{n} upper triangular matrices.")) (|matrixGcd| ((|#1| (|Matrix| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{matrixGcd(mat,{}sing,{}n)} is \\spad{gcd(sing,{}g)} where \\spad{g} is the \\spad{gcd} of the entries of the \\spad{n}-by-\\spad{n} upper-triangular matrix \\spad{mat}.")) (|diagonalProduct| ((|#1| (|Matrix| |#1|)) "\\spad{diagonalProduct(m)} returns the product of the elements on the diagonal of the matrix \\spad{m}")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL (-502 |mn|) ((|constructor| (NIL "\\spadtype{IndexedBits} is a domain to compactly represent large quantities of Boolean data.")) (|And| (($ $ $) "\\spad{And(n,{}m)} returns the bit-by-bit logical {\\em And} of \\spad{n} and \\spad{m}.")) (|Or| (($ $ $) "\\spad{Or(n,{}m)} returns the bit-by-bit logical {\\em Or} of \\spad{n} and \\spad{m}.")) (|Not| (($ $) "\\spad{Not(n)} returns the bit-by-bit logical {\\em Not} of \\spad{n}."))) -((-4418 . T) (-4417 . T)) +((-4415 . T) (-4414 . T)) ((-12 (|HasCategory| (-112) (QUOTE (-1099))) (|HasCategory| (-112) (LIST (QUOTE -310) (QUOTE (-112))))) (|HasCategory| (-112) (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| (-112) (QUOTE (-850))) (|HasCategory| (-566) (QUOTE (-850))) (|HasCategory| (-112) (QUOTE (-1099))) (|HasCategory| (-112) (LIST (QUOTE -613) (QUOTE (-862))))) (-503 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)}."))) @@ -1952,7 +1952,7 @@ 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{\\spad{qi} = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|clearDenominator| ((|#3| |#4|) "\\spad{clearDenominator([q1,{}...,{}qn])} returns \\spad{[p1,{}...,{}pn]} such that \\spad{\\spad{qi} = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|commonDenominator| ((|#1| |#4|) "\\spad{commonDenominator([q1,{}...,{}qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}\\spad{qn}."))) NIL NIL -(-506 -2382 |Expon| |VarSet| |DPoly|) +(-506 -2386 |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}.")) (* (($ $ $) "\\spad{I*J} computes the product of the ideal \\spad{I} and \\spad{J}."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -614) (QUOTE (-1175))))) @@ -2002,7 +2002,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-792)))) (-518 S |mn|) ((|constructor| (NIL "\\indented{1}{Author: Michael Monagan July/87,{} modified \\spad{SMW} June/91} A FlexibleArray is the notion of an array intended to allow for growth at the end only. Hence the following efficient operations \\indented{2}{\\spad{append(x,{}a)} meaning append item \\spad{x} at the end of the array \\spad{a}} \\indented{2}{\\spad{delete(a,{}n)} meaning delete the last item from the array \\spad{a}} Flexible arrays support the other operations inherited from \\spadtype{ExtensibleLinearAggregate}. However,{} these are not efficient. Flexible arrays combine the \\spad{O(1)} access time property of arrays with growing and shrinking at the end in \\spad{O(1)} (average) time. This is done by using an ordinary array which may have zero or more empty slots at the end. When the array becomes full it is copied into a new larger (50\\% larger) array. Conversely,{} when the array becomes less than 1/2 full,{} it is copied into a smaller array. Flexible arrays provide for an efficient implementation of many data structures in particular heaps,{} stacks and sets.")) (|shrinkable| (((|Boolean|) (|Boolean|)) "\\spad{shrinkable(b)} sets the shrinkable attribute of flexible arrays to \\spad{b} and returns the previous value")) (|physicalLength!| (($ $ (|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}"))) -((-4418 . T) (-4417 . T)) +((-4415 . T) (-4414 . T)) ((-2805 (-12 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538)))) (-2805 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099)))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| (-566) (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-519) ((|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'."))) @@ -2010,28 +2010,28 @@ NIL NIL (-520 |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}."))) -((-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) +((-4406 . T) (-4412 . T) (-4407 . T) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) ((-2805 (|HasCategory| (-583 |#1|) (QUOTE (-145))) (|HasCategory| (-583 |#1|) (QUOTE (-370)))) (|HasCategory| (-583 |#1|) (QUOTE (-147))) (|HasCategory| (-583 |#1|) (QUOTE (-370))) (|HasCategory| (-583 |#1|) (QUOTE (-145)))) (-521 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}."))) -((-4417 . T) (-4418 . T)) +((-4414 . T) (-4415 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (-522 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."))) -((-4418 . T) (-4417 . T)) +((-4415 . T) (-4414 . T)) ((-2805 (-12 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538)))) (-2805 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099)))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| (-566) (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-523 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 -4418))) +((|HasAttribute| |#3| (QUOTE -4415))) (-524 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 -4418))) +((|HasAttribute| |#7| (QUOTE -4415))) (-525 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."))) -((-4417 . T) (-4418 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-558))) (|HasAttribute| |#1| (QUOTE (-4419 "*"))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) +((-4414 . T) (-4415 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-558))) (|HasAttribute| |#1| (QUOTE (-4416 "*"))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (-526) ((|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 @@ -2064,7 +2064,7 @@ 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 -(-534 K -2382 |Par|) +(-534 K -2386 |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 @@ -2088,7 +2088,7 @@ 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 -(-540 K -2382 |Par|) +(-540 K -2386 |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 @@ -2118,7 +2118,7 @@ NIL NIL (-547) ((|constructor| (NIL "An \\spad{IntegerNumberSystem} is a model for the integers.")) (|invmod| (($ $ $) "\\spad{invmod(a,{}b)},{} \\spad{0<=a1},{} \\spad{(a,{}b)=1} means \\spad{1/a mod b}.")) (|powmod| (($ $ $ $) "\\spad{powmod(a,{}b,{}p)},{} \\spad{0<=a,{}b

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

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

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

1},{} means \\spad{a+b mod p}.")) (|mask| (($ $) "\\spad{mask(n)} returns \\spad{2**n-1} (an \\spad{n} bit mask).")) (|dec| (($ $) "\\spad{dec(x)} returns \\spad{x - 1}.")) (|inc| (($ $) "\\spad{inc(x)} returns \\spad{x + 1}.")) (|copy| (($ $) "\\spad{copy(n)} gives a copy of \\spad{n}.")) (|random| (($ $) "\\spad{random(a)} creates a random element from 0 to \\spad{n-1}.") (($) "\\spad{random()} creates a random element.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(n)} creates a rational number,{} or returns \"failed\" if this is not possible.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(n)} creates a rational number (see \\spadtype{Fraction Integer})..")) (|rational?| (((|Boolean|) $) "\\spad{rational?(n)} tests if \\spad{n} is a rational number (see \\spadtype{Fraction Integer}).")) (|symmetricRemainder| (($ $ $) "\\spad{symmetricRemainder(a,{}b)} (where \\spad{b > 1}) yields \\spad{r} where \\spad{ -b/2 <= r < b/2 }.")) (|positiveRemainder| (($ $ $) "\\spad{positiveRemainder(a,{}b)} (where \\spad{b > 1}) yields \\spad{r} where \\spad{0 <= r < b} and \\spad{r == a rem b}.")) (|bit?| (((|Boolean|) $ $) "\\spad{bit?(n,{}i)} returns \\spad{true} if and only if \\spad{i}-th bit of \\spad{n} is a 1.")) (|shift| (($ $ $) "\\spad{shift(a,{}i)} shift \\spad{a} by \\spad{i} digits.")) (|length| (($ $) "\\spad{length(a)} length of \\spad{a} in digits.")) (|base| (($) "\\spad{base()} returns the base for the operations of \\spad{IntegerNumberSystem}.")) (|multiplicativeValuation| ((|attribute|) "euclideanSize(a*b) returns \\spad{euclideanSize(a)*euclideanSize(b)}.")) (|even?| (((|Boolean|) $) "\\spad{even?(n)} returns \\spad{true} if and only if \\spad{n} is even.")) (|odd?| (((|Boolean|) $) "\\spad{odd?(n)} returns \\spad{true} if and only if \\spad{n} is odd."))) -((-4415 . T) (-4416 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) +((-4412 . T) (-4413 . T) (-4407 . T) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) NIL (-548) ((|constructor| (NIL "This domain is a datatype for (signed) integer values of precision 16 bits."))) @@ -2138,13 +2138,13 @@ NIL NIL (-552 |Key| |Entry| |addDom|) ((|constructor| (NIL "This domain is used to provide a conditional \"add\" domain for the implementation of \\spadtype{Table}."))) -((-4417 . T) (-4418 . T)) -((-12 (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2010) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2818) (|devaluate| |#2|)))))) (-2805 (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (QUOTE (-1099))) (|HasCategory| |#2| (QUOTE (-1099)))) (-2805 (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (LIST (QUOTE -614) (QUOTE (-538)))) (-12 (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#2| (QUOTE (-1099))) (-2805 (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (LIST (QUOTE -613) (QUOTE (-862))))) -(-553 R -2382) +((-4414 . T) (-4415 . T)) +((-12 (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2050) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2849) (|devaluate| |#2|)))))) (-2805 (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (QUOTE (-1099))) (|HasCategory| |#2| (QUOTE (-1099)))) (-2805 (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (LIST (QUOTE -614) (QUOTE (-538)))) (-12 (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#2| (QUOTE (-1099))) (-2805 (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (LIST (QUOTE -613) (QUOTE (-862))))) +(-553 R -2386) ((|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 -(-554 R0 -2382 UP UPUP R) +(-554 R0 -2386 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 @@ -2154,7 +2154,7 @@ NIL NIL (-556 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."))) -((-3645 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) +((-3651 . T) (-4407 . T) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) NIL (-557 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."))) @@ -2162,9 +2162,9 @@ NIL NIL (-558) ((|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."))) -((-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) +((-4407 . T) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) NIL -(-559 R -2382) +(-559 R -2386) ((|constructor| (NIL "This package provides functions for integration,{} limited integration,{} extended integration and the risch differential equation for elemntary functions.")) (|lfextlimint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Symbol|) (|Kernel| |#2|) (|List| (|Kernel| |#2|))) "\\spad{lfextlimint(f,{}x,{}k,{}[k1,{}...,{}kn])} returns functions \\spad{[h,{} c]} such that \\spad{dh/dx = f - c dk/dx}. Value \\spad{h} is looked for in a field containing \\spad{f} and \\spad{k1},{}...,{}\\spad{kn} (the \\spad{ki}\\spad{'s} must be logs).")) (|lfintegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{lfintegrate(f,{} x)} = \\spad{g} such that \\spad{dg/dx = f}.")) (|lfinfieldint| (((|Union| |#2| "failed") |#2| (|Symbol|)) "\\spad{lfinfieldint(f,{} x)} returns a function \\spad{g} such that \\spad{dg/dx = f} if \\spad{g} exists,{} \"failed\" otherwise.")) (|lflimitedint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Symbol|) (|List| |#2|)) "\\spad{lflimitedint(f,{}x,{}[g1,{}...,{}gn])} returns functions \\spad{[h,{}[[\\spad{ci},{} \\spad{gi}]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,{}...,{}gn]},{} and \\spad{d(h+sum(\\spad{ci} log(\\spad{gi})))/dx = f},{} if possible,{} \"failed\" otherwise.")) (|lfextendedint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Symbol|) |#2|) "\\spad{lfextendedint(f,{} x,{} g)} returns functions \\spad{[h,{} c]} such that \\spad{dh/dx = f - cg},{} if (\\spad{h},{} \\spad{c}) exist,{} \"failed\" otherwise."))) NIL NIL @@ -2176,7 +2176,7 @@ 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 -(-562 R -2382 L) +(-562 R -2386 L) ((|constructor| (NIL "This internal package rationalises integrands on curves of the form: \\indented{2}{\\spad{y\\^2 = a x\\^2 + b x + c}} \\indented{2}{\\spad{y\\^2 = (a x + b) / (c x + d)}} \\indented{2}{\\spad{f(x,{} y) = 0} where \\spad{f} has degree 1 in \\spad{x}} The rationalization is done for integration,{} limited integration,{} extended integration and the risch differential equation.")) (|palgLODE0| (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgLODE0(op,{}g,{}x,{}y,{}z,{}t,{}c)} returns the solution of \\spad{op f = g} Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,{}y)dx = c f(t,{}y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}.") (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgLODE0(op,{} g,{} x,{} y,{} d,{} p)} returns the solution of \\spad{op f = g}. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}.")) (|lift| (((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|SparseUnivariatePolynomial| |#2|) (|Kernel| |#2|)) "\\spad{lift(u,{}k)} \\undocumented")) (|multivariate| ((|#2| (|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|Kernel| |#2|) |#2|) "\\spad{multivariate(u,{}k,{}f)} \\undocumented")) (|univariate| (((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|SparseUnivariatePolynomial| |#2|)) "\\spad{univariate(f,{}k,{}k,{}p)} \\undocumented")) (|palgRDE0| (((|Union| |#2| "failed") |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|)) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgRDE0(f,{} g,{} x,{} y,{} foo,{} t,{} c)} returns a function \\spad{z(x,{}y)} such that \\spad{dz/dx + n * df/dx z(x,{}y) = g(x,{}y)} if such a \\spad{z} exists,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,{}y)dx = c f(t,{}y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{foo},{} called by \\spad{foo(a,{} b,{} x)},{} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}.") (((|Union| |#2| "failed") |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|)) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgRDE0(f,{} g,{} x,{} y,{} foo,{} d,{} p)} returns a function \\spad{z(x,{}y)} such that \\spad{dz/dx + n * df/dx z(x,{}y) = g(x,{}y)} if such a \\spad{z} exists,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}. Argument \\spad{foo},{} called by \\spad{foo(a,{} b,{} x)},{} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}.")) (|palglimint0| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palglimint0(f,{} x,{} y,{} [u1,{}...,{}un],{} z,{} t,{} c)} returns functions \\spad{[h,{}[[\\spad{ci},{} \\spad{ui}]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,{}...,{}un]} and \\spad{d(h + sum(\\spad{ci} log(\\spad{ui})))/dx = f(x,{}y)} if such functions exist,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,{}y)dx = c f(t,{}y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}.") (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palglimint0(f,{} x,{} y,{} [u1,{}...,{}un],{} d,{} p)} returns functions \\spad{[h,{}[[\\spad{ci},{} \\spad{ui}]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,{}...,{}un]} and \\spad{d(h + sum(\\spad{ci} log(\\spad{ui})))/dx = f(x,{}y)} if such functions exist,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}.")) (|palgextint0| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgextint0(f,{} x,{} y,{} g,{} z,{} t,{} c)} returns functions \\spad{[h,{} d]} such that \\spad{dh/dx = f(x,{}y) - d g},{} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,{}y)dx = c f(t,{}y) dy},{} and \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{z} is a dummy variable not appearing in \\spad{f(x,{}y)}. The operation returns \"failed\" if no such functions exist.") (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgextint0(f,{} x,{} y,{} g,{} d,{} p)} returns functions \\spad{[h,{} c]} such that \\spad{dh/dx = f(x,{}y) - c g},{} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2 y(x)\\^2 = P(x)},{} or \"failed\" if no such functions exist.")) (|palgint0| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgint0(f,{} x,{} y,{} z,{} t,{} c)} returns the integral of \\spad{f(x,{}y)dx} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,{}y)dx = c f(t,{}y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{z} is a dummy variable not appearing in \\spad{f(x,{}y)}.") (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgint0(f,{} x,{} y,{} d,{} p)} returns the integral of \\spad{f(x,{}y)dx} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2 y(x)\\^2 = P(x)}."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -656) (|devaluate| |#2|)))) @@ -2184,31 +2184,31 @@ 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 -(-564 -2382 UP UPUP R) +(-564 -2386 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 -(-565 -2382 UP) +(-565 -2386 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 (-566) ((|constructor| (NIL "\\spadtype{Integer} provides the domain of arbitrary precision integers.")) (|infinite| ((|attribute|) "nextItem never returns \"failed\".")) (|noetherian| ((|attribute|) "ascending chain condition on ideals.")) (|canonicalsClosed| ((|attribute|) "two positives multiply to give positive.")) (|canonical| ((|attribute|) "mathematical equality is data structure equality.")) (|random| (($ $) "\\spad{random(n)} returns a random integer from 0 to \\spad{n-1}."))) -((-4399 . T) (-4405 . T) (-4409 . T) (-4404 . T) (-4415 . T) (-4416 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) +((-4396 . T) (-4402 . T) (-4406 . T) (-4401 . T) (-4412 . T) (-4413 . T) (-4407 . T) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) NIL (-567) ((|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 -(-568 R -2382 L) +(-568 R -2386 L) ((|constructor| (NIL "This package provides functions for integration,{} limited integration,{} extended integration and the risch differential equation for pure algebraic integrands.")) (|palgLODE| (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Symbol|)) "\\spad{palgLODE(op,{} g,{} kx,{} y,{} x)} returns the solution of \\spad{op f = g}. \\spad{y} is an algebraic function of \\spad{x}.")) (|palgRDE| (((|Union| |#2| "failed") |#2| |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|))) "\\spad{palgRDE(nfp,{} f,{} g,{} x,{} y,{} foo)} returns a function \\spad{z(x,{}y)} such that \\spad{dz/dx + n * df/dx z(x,{}y) = g(x,{}y)} if such a \\spad{z} exists,{} \"failed\" otherwise; \\spad{y} is an algebraic function of \\spad{x}; \\spad{foo(a,{} b,{} x)} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}. \\spad{nfp} is \\spad{n * df/dx}.")) (|palglimint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|)) "\\spad{palglimint(f,{} x,{} y,{} [u1,{}...,{}un])} returns functions \\spad{[h,{}[[\\spad{ci},{} \\spad{ui}]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,{}...,{}un]} and \\spad{d(h + sum(\\spad{ci} log(\\spad{ui})))/dx = f(x,{}y)} if such functions exist,{} \"failed\" otherwise; \\spad{y} is an algebraic function of \\spad{x}.")) (|palgextint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2|) "\\spad{palgextint(f,{} x,{} y,{} g)} returns functions \\spad{[h,{} c]} such that \\spad{dh/dx = f(x,{}y) - c g},{} where \\spad{y} is an algebraic function of \\spad{x}; returns \"failed\" if no such functions exist.")) (|palgint| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|)) "\\spad{palgint(f,{} x,{} y)} returns the integral of \\spad{f(x,{}y)dx} where \\spad{y} is an algebraic function of \\spad{x}."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -656) (|devaluate| |#2|)))) -(-569 R -2382) +(-569 R -2386) ((|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 -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| |#2| (QUOTE (-1138)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| |#2| (QUOTE (-629))))) -(-570 -2382 UP) +(-570 -2386 UP) ((|constructor| (NIL "This package provides functions for the base case of the Risch algorithm.")) (|limitedint| (((|Union| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|)))))) "failed") (|Fraction| |#2|) (|List| (|Fraction| |#2|))) "\\spad{limitedint(f,{} [g1,{}...,{}gn])} returns fractions \\spad{[h,{}[[\\spad{ci},{} \\spad{gi}]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,{}...,{}gn]},{} \\spad{ci' = 0},{} and \\spad{(h+sum(\\spad{ci} log(\\spad{gi})))' = f},{} if possible,{} \"failed\" otherwise.")) (|extendedint| (((|Union| (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{extendedint(f,{} g)} returns fractions \\spad{[h,{} c]} such that \\spad{c' = 0} and \\spad{h' = f - cg},{} if \\spad{(h,{} c)} exist,{} \"failed\" otherwise.")) (|infieldint| (((|Union| (|Fraction| |#2|) "failed") (|Fraction| |#2|)) "\\spad{infieldint(f)} returns \\spad{g} such that \\spad{g' = f} or \"failed\" if the integral of \\spad{f} is not a rational function.")) (|integrate| (((|IntegrationResult| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{integrate(f)} returns \\spad{g} such that \\spad{g' = f}."))) NIL NIL @@ -2216,27 +2216,27 @@ 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 -(-572 -2382) +(-572 -2386) ((|constructor| (NIL "This package provides functions for the integration of rational functions.")) (|extendedIntegrate| (((|Union| (|Record| (|:| |ratpart| (|Fraction| (|Polynomial| |#1|))) (|:| |coeff| (|Fraction| (|Polynomial| |#1|)))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|))) "\\spad{extendedIntegrate(f,{} x,{} g)} returns fractions \\spad{[h,{} c]} such that \\spad{dc/dx = 0} and \\spad{dh/dx = f - cg},{} if \\spad{(h,{} c)} exist,{} \"failed\" otherwise.")) (|limitedIntegrate| (((|Union| (|Record| (|:| |mainpart| (|Fraction| (|Polynomial| |#1|))) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| (|Polynomial| |#1|))) (|:| |logand| (|Fraction| (|Polynomial| |#1|))))))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|List| (|Fraction| (|Polynomial| |#1|)))) "\\spad{limitedIntegrate(f,{} x,{} [g1,{}...,{}gn])} returns fractions \\spad{[h,{} [[\\spad{ci},{}\\spad{gi}]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,{}...,{}gn]},{} \\spad{dci/dx = 0},{} and \\spad{d(h + sum(\\spad{ci} log(\\spad{gi})))/dx = f} if possible,{} \"failed\" otherwise.")) (|infieldIntegrate| (((|Union| (|Fraction| (|Polynomial| |#1|)) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{infieldIntegrate(f,{} x)} returns a fraction \\spad{g} such that \\spad{dg/dx = f} if \\spad{g} exists,{} \"failed\" otherwise.")) (|internalIntegrate| (((|IntegrationResult| (|Fraction| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{internalIntegrate(f,{} x)} returns \\spad{g} such that \\spad{dg/dx = f}."))) NIL NIL (-573 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."))) -((-3645 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) +((-3651 . T) (-4407 . T) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) NIL (-574) ((|constructor| (NIL "This package provides the implementation for the \\spadfun{solveLinearPolynomialEquation} operation over the integers. It uses a lifting technique from the package GenExEuclid")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| (|Integer|))) "failed") (|List| (|SparseUnivariatePolynomial| (|Integer|))) (|SparseUnivariatePolynomial| (|Integer|))) "\\spad{solveLinearPolynomialEquation([f1,{} ...,{} fn],{} g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod \\spad{fi} = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists."))) NIL NIL -(-575 R -2382) +(-575 R -2386) ((|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 -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| |#2| (QUOTE (-285))) (|HasCategory| |#2| (QUOTE (-629))) (|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-1175))))) (-12 (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#2| (QUOTE (-285)))) (|HasCategory| |#1| (QUOTE (-558)))) -(-576 -2382 UP) +(-576 -2386 UP) ((|constructor| (NIL "This package provides functions for the transcendental case of the Risch algorithm.")) (|monomialIntPoly| (((|Record| (|:| |answer| |#2|) (|:| |polypart| |#2|)) |#2| (|Mapping| |#2| |#2|)) "\\spad{monomialIntPoly(p,{} ')} returns [\\spad{q},{} \\spad{r}] such that \\spad{p = q' + r} and \\spad{degree(r) < degree(t')}. Error if \\spad{degree(t') < 2}.")) (|monomialIntegrate| (((|Record| (|:| |ir| (|IntegrationResult| (|Fraction| |#2|))) (|:| |specpart| (|Fraction| |#2|)) (|:| |polypart| |#2|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{monomialIntegrate(f,{} ')} returns \\spad{[ir,{} s,{} p]} such that \\spad{f = ir' + s + p} and all the squarefree factors of the denominator of \\spad{s} are special \\spad{w}.\\spad{r}.\\spad{t} the derivation '.")) (|expintfldpoly| (((|Union| (|LaurentPolynomial| |#1| |#2|) "failed") (|LaurentPolynomial| |#1| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|)) "\\spad{expintfldpoly(p,{} foo)} returns \\spad{q} such that \\spad{p' = q} or \"failed\" if no such \\spad{q} exists. Argument foo is a Risch differential equation function on \\spad{F}.")) (|primintfldpoly| (((|Union| |#2| "failed") |#2| (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) |#1|) "\\spad{primintfldpoly(p,{} ',{} t')} returns \\spad{q} such that \\spad{p' = q} or \"failed\" if no such \\spad{q} exists. Argument \\spad{t'} is the derivative of the primitive generating the extension.")) (|primlimintfrac| (((|Union| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|)))))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|List| (|Fraction| |#2|))) "\\spad{primlimintfrac(f,{} ',{} [u1,{}...,{}un])} returns \\spad{[v,{} [c1,{}...,{}cn]]} such that \\spad{ci' = 0} and \\spad{f = v' + +/[\\spad{ci} * ui'/ui]}. Error: if \\spad{degree numer f >= degree denom f}.")) (|primextintfrac| (((|Union| (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Fraction| |#2|)) "\\spad{primextintfrac(f,{} ',{} g)} returns \\spad{[v,{} c]} such that \\spad{f = v' + c g} and \\spad{c' = 0}. Error: if \\spad{degree numer f >= degree denom f} or if \\spad{degree numer g >= degree denom g} or if \\spad{denom g} is not squarefree.")) (|explimitedint| (((|Union| (|Record| (|:| |answer| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|))))))) (|:| |a0| |#1|)) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|) (|List| (|Fraction| |#2|))) "\\spad{explimitedint(f,{} ',{} foo,{} [u1,{}...,{}un])} returns \\spad{[v,{} [c1,{}...,{}cn],{} a]} such that \\spad{ci' = 0},{} \\spad{f = v' + a + reduce(+,{}[\\spad{ci} * ui'/ui])},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}. Returns \"failed\" if no such \\spad{v},{} \\spad{ci},{} a exist. Argument \\spad{foo} is a Risch differential equation function on \\spad{F}.")) (|primlimitedint| (((|Union| (|Record| (|:| |answer| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|))))))) (|:| |a0| |#1|)) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) (|List| (|Fraction| |#2|))) "\\spad{primlimitedint(f,{} ',{} foo,{} [u1,{}...,{}un])} returns \\spad{[v,{} [c1,{}...,{}cn],{} a]} such that \\spad{ci' = 0},{} \\spad{f = v' + a + reduce(+,{}[\\spad{ci} * ui'/ui])},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Returns \"failed\" if no such \\spad{v},{} \\spad{ci},{} a exist. Argument \\spad{foo} is an extended integration function on \\spad{F}.")) (|expextendedint| (((|Union| (|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |a0| |#1|)) (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|) (|Fraction| |#2|)) "\\spad{expextendedint(f,{} ',{} foo,{} g)} returns either \\spad{[v,{} c]} such that \\spad{f = v' + c g} and \\spad{c' = 0},{} or \\spad{[v,{} a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}. Returns \"failed\" if neither case can hold. Argument \\spad{foo} is a Risch differential equation function on \\spad{F}.")) (|primextendedint| (((|Union| (|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |a0| |#1|)) (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) (|Fraction| |#2|)) "\\spad{primextendedint(f,{} ',{} foo,{} g)} returns either \\spad{[v,{} c]} such that \\spad{f = v' + c g} and \\spad{c' = 0},{} or \\spad{[v,{} a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Returns \"failed\" if neither case can hold. Argument \\spad{foo} is an extended integration function on \\spad{F}.")) (|tanintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|List| |#1|) "failed") (|Integer|) |#1| |#1|)) "\\spad{tanintegrate(f,{} ',{} foo)} returns \\spad{[g,{} a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}; Argument foo is a Risch differential system solver on \\spad{F}.")) (|expintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|)) "\\spad{expintegrate(f,{} ',{} foo)} returns \\spad{[g,{} a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}; Argument foo is a Risch differential equation solver on \\spad{F}.")) (|primintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|)) "\\spad{primintegrate(f,{} ',{} foo)} returns \\spad{[g,{} a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Argument foo is an extended integration function on \\spad{F}."))) NIL NIL -(-577 R -2382) +(-577 R -2386) ((|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 @@ -2258,27 +2258,27 @@ NIL NIL (-582 |p| |unBalanced?|) ((|constructor| (NIL "This domain implements \\spad{Zp},{} the \\spad{p}-adic completion of the integers. This is an internal domain."))) -((-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) +((-4407 . T) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) NIL (-583 |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."))) -((-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) +((-4406 . T) (-4412 . T) (-4407 . T) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) ((|HasCategory| $ (QUOTE (-147))) (|HasCategory| $ (QUOTE (-145))) (|HasCategory| $ (QUOTE (-370)))) (-584) ((|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 -(-585 R -2382) +(-585 R -2386) ((|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 -(-586 E -2382) +(-586 E -2386) ((|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 -(-587 -2382) +(-587 -2386) ((|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}."))) -((-4412 . T) (-4411 . T)) +((-4409 . T) (-4408 . T)) ((|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-1175))))) (-588 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"))) @@ -2306,7 +2306,7 @@ NIL NIL (-594 |mn|) ((|constructor| (NIL "This domain implements low-level strings")) (|hash| (((|Integer|) $) "\\spad{hash(x)} provides a hashing function for strings"))) -((-4418 . T) (-4417 . T)) +((-4415 . T) (-4414 . T)) ((-2805 (-12 (|HasCategory| (-144) (QUOTE (-850))) (|HasCategory| (-144) (LIST (QUOTE -310) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1099))) (|HasCategory| (-144) (LIST (QUOTE -310) (QUOTE (-144)))))) (-2805 (|HasCategory| (-144) (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| (-144) (QUOTE (-1099))) (|HasCategory| (-144) (LIST (QUOTE -310) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -614) (QUOTE (-538)))) (-2805 (|HasCategory| (-144) (QUOTE (-850))) (|HasCategory| (-144) (QUOTE (-1099)))) (|HasCategory| (-144) (QUOTE (-850))) (|HasCategory| (-566) (QUOTE (-850))) (|HasCategory| (-144) (QUOTE (-1099))) (|HasCategory| (-144) (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| (-144) (QUOTE (-1099))) (|HasCategory| (-144) (LIST (QUOTE -310) (QUOTE (-144)))))) (-595 E V R P) ((|constructor| (NIL "tools for the summation packages.")) (|sum| (((|Record| (|:| |num| |#4|) (|:| |den| (|Integer|))) |#4| |#2|) "\\spad{sum(p(n),{} n)} returns \\spad{P(n)},{} the indefinite sum of \\spad{p(n)} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{P(n+1) - P(n) = a(n)}.") (((|Record| (|:| |num| |#4|) (|:| |den| (|Integer|))) |#4| |#2| (|Segment| |#4|)) "\\spad{sum(p(n),{} n = a..b)} returns \\spad{p(a) + p(a+1) + ... + p(b)}."))) @@ -2314,11 +2314,11 @@ NIL NIL (-596 |Coef|) ((|constructor| (NIL "InnerSparseUnivariatePowerSeries is an internal domain \\indented{2}{used for creating sparse Taylor and Laurent series.}")) (|cAcsch| (($ $) "\\spad{cAcsch(f)} computes the inverse hyperbolic cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsech| (($ $) "\\spad{cAsech(f)} computes the inverse hyperbolic secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcoth| (($ $) "\\spad{cAcoth(f)} computes the inverse hyperbolic cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAtanh| (($ $) "\\spad{cAtanh(f)} computes the inverse hyperbolic tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcosh| (($ $) "\\spad{cAcosh(f)} computes the inverse hyperbolic cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsinh| (($ $) "\\spad{cAsinh(f)} computes the inverse hyperbolic sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCsch| (($ $) "\\spad{cCsch(f)} computes the hyperbolic cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSech| (($ $) "\\spad{cSech(f)} computes the hyperbolic secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCoth| (($ $) "\\spad{cCoth(f)} computes the hyperbolic cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cTanh| (($ $) "\\spad{cTanh(f)} computes the hyperbolic tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCosh| (($ $) "\\spad{cCosh(f)} computes the hyperbolic cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSinh| (($ $) "\\spad{cSinh(f)} computes the hyperbolic sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcsc| (($ $) "\\spad{cAcsc(f)} computes the arccosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsec| (($ $) "\\spad{cAsec(f)} computes the arcsecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcot| (($ $) "\\spad{cAcot(f)} computes the arccotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAtan| (($ $) "\\spad{cAtan(f)} computes the arctangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcos| (($ $) "\\spad{cAcos(f)} computes the arccosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsin| (($ $) "\\spad{cAsin(f)} computes the arcsine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCsc| (($ $) "\\spad{cCsc(f)} computes the cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSec| (($ $) "\\spad{cSec(f)} computes the secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCot| (($ $) "\\spad{cCot(f)} computes the cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cTan| (($ $) "\\spad{cTan(f)} computes the tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCos| (($ $) "\\spad{cCos(f)} computes the cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSin| (($ $) "\\spad{cSin(f)} computes the sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cLog| (($ $) "\\spad{cLog(f)} computes the logarithm of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cExp| (($ $) "\\spad{cExp(f)} computes the exponential of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cRationalPower| (($ $ (|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}."))) -(((-4419 "*") |has| |#1| (-172)) (-4410 |has| |#1| (-558)) (-4411 . T) (-4412 . T) (-4414 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-558))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-566)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-566)) (|devaluate| |#1|)))) (|HasCategory| (-566) (QUOTE (-1111))) (|HasCategory| |#1| (QUOTE (-365))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-566))))) (|HasSignature| |#1| (LIST (QUOTE -2512) (LIST (|devaluate| |#1|) (QUOTE (-1175)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-566)))))) +(((-4416 "*") |has| |#1| (-172)) (-4407 |has| |#1| (-558)) (-4408 . T) (-4409 . T) (-4411 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-558))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-566)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-566)) (|devaluate| |#1|)))) (|HasCategory| (-566) (QUOTE (-1111))) (|HasCategory| |#1| (QUOTE (-365))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-566))))) (|HasSignature| |#1| (LIST (QUOTE -3780) (LIST (|devaluate| |#1|) (QUOTE (-1175)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-566)))))) (-597 |Coef|) ((|constructor| (NIL "Internal package for dense Taylor series. This is an internal Taylor series type in which Taylor series are represented by a \\spadtype{Stream} of \\spadtype{Ring} elements. For univariate series,{} the \\spad{Stream} elements are the Taylor coefficients. For multivariate series,{} the \\spad{n}th Stream element is a form of degree \\spad{n} in the power series variables.")) (* (($ $ (|Integer|)) "\\spad{x*i} returns the product of integer \\spad{i} and the series \\spad{x}.") (($ $ |#1|) "\\spad{x*c} returns the product of \\spad{c} and the series \\spad{x}.") (($ |#1| $) "\\spad{c*x} returns the product of \\spad{c} and the series \\spad{x}.")) (|order| (((|NonNegativeInteger|) $ (|NonNegativeInteger|)) "\\spad{order(x,{}n)} returns the minimum of \\spad{n} and the order of \\spad{x}.") (((|NonNegativeInteger|) $) "\\spad{order(x)} returns the order of a power series \\spad{x},{} \\indented{1}{\\spadignore{i.e.} the degree of the first non-zero term of the series.}")) (|pole?| (((|Boolean|) $) "\\spad{pole?(x)} tests if the series \\spad{x} has a pole. \\indented{1}{Note: this is \\spad{false} when \\spad{x} is a Taylor series.}")) (|series| (($ (|Stream| |#1|)) "\\spad{series(s)} creates a power series from a stream of \\indented{1}{ring elements.} \\indented{1}{For univariate series types,{} the stream \\spad{s} should be a stream} \\indented{1}{of Taylor coefficients. For multivariate series types,{} the} \\indented{1}{stream \\spad{s} should be a stream of forms the \\spad{n}th element} \\indented{1}{of which is a} \\indented{1}{form of degree \\spad{n} in the power series variables.}")) (|coefficients| (((|Stream| |#1|) $) "\\spad{coefficients(x)} returns a stream of ring elements. \\indented{1}{When \\spad{x} is a univariate series,{} this is a stream of Taylor} \\indented{1}{coefficients. When \\spad{x} is a multivariate series,{} the} \\indented{1}{\\spad{n}th element of the stream is a form of} \\indented{1}{degree \\spad{n} in the power series variables.}"))) -((-4412 |has| |#1| (-558)) (-4411 |has| |#1| (-558)) ((-4419 "*") |has| |#1| (-558)) (-4410 |has| |#1| (-558)) (-4414 . T)) +((-4409 |has| |#1| (-558)) (-4408 |has| |#1| (-558)) ((-4416 "*") |has| |#1| (-558)) (-4407 |has| |#1| (-558)) (-4411 . T)) ((|HasCategory| |#1| (QUOTE (-558)))) (-598 A B) ((|constructor| (NIL "Functions defined on streams with entries in two sets.")) (|map| (((|InfiniteTuple| |#2|) (|Mapping| |#2| |#1|) (|InfiniteTuple| |#1|)) "\\spad{map(f,{}[x0,{}x1,{}x2,{}...])} returns \\spad{[f(x0),{}f(x1),{}f(x2),{}..]}."))) @@ -2328,7 +2328,7 @@ 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 -(-600 R -2382 FG) +(-600 R -2386 FG) ((|constructor| (NIL "This package provides transformations from trigonometric functions to exponentials and logarithms,{} and back. \\spad{F} and \\spad{FG} should be the same type of function space.")) (|trigs2explogs| ((|#3| |#3| (|List| (|Kernel| |#3|)) (|List| (|Symbol|))) "\\spad{trigs2explogs(f,{} [k1,{}...,{}kn],{} [x1,{}...,{}xm])} rewrites all the trigonometric functions appearing in \\spad{f} and involving one of the \\spad{\\spad{xi}'s} in terms of complex logarithms and exponentials. A kernel of the form \\spad{tan(u)} is expressed using \\spad{exp(u)**2} if it is one of the \\spad{\\spad{ki}'s},{} in terms of \\spad{exp(2*u)} otherwise.")) (|explogs2trigs| (((|Complex| |#2|) |#3|) "\\spad{explogs2trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (F2FG ((|#3| |#2|) "\\spad{F2FG(a + sqrt(-1) b)} returns \\spad{a + i b}.")) (FG2F ((|#2| |#3|) "\\spad{FG2F(a + i b)} returns \\spad{a + sqrt(-1) b}.")) (GF2FG ((|#3| (|Complex| |#2|)) "\\spad{GF2FG(a + i b)} returns \\spad{a + i b} viewed as a function with the \\spad{i} pushed down into the coefficient domain."))) NIL NIL @@ -2338,12 +2338,12 @@ NIL NIL (-602 R |mn|) ((|constructor| (NIL "\\indented{2}{This type represents vector like objects with varying lengths} and a user-specified initial index."))) -((-4418 . T) (-4417 . T)) +((-4415 . T) (-4414 . T)) ((-2805 (-12 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538)))) (-2805 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099)))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| (-566) (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-726))) (|HasCategory| |#1| (QUOTE (-1049))) (-12 (|HasCategory| |#1| (QUOTE (-1002))) (|HasCategory| |#1| (QUOTE (-1049)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-603 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 -4418)) (|HasCategory| |#2| (QUOTE (-850))) (|HasAttribute| |#1| (QUOTE -4417)) (|HasCategory| |#3| (QUOTE (-1099)))) +((|HasAttribute| |#1| (QUOTE -4415)) (|HasCategory| |#2| (QUOTE (-850))) (|HasAttribute| |#1| (QUOTE -4414)) (|HasCategory| |#3| (QUOTE (-1099)))) (-604 |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|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) NIL @@ -2358,19 +2358,19 @@ NIL NIL (-607 R A) ((|constructor| (NIL "\\indented{1}{AssociatedJordanAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$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)."))) -((-4414 -2805 (-2438 (|has| |#2| (-369 |#1|)) (|has| |#1| (-558))) (-12 (|has| |#2| (-419 |#1|)) (|has| |#1| (-558)))) (-4412 . T) (-4411 . T)) +((-4411 -2805 (-2447 (|has| |#2| (-369 |#1|)) (|has| |#1| (-558))) (-12 (|has| |#2| (-419 |#1|)) (|has| |#1| (-558)))) (-4409 . T) (-4408 . T)) ((-2805 (|HasCategory| |#2| (LIST (QUOTE -369) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -419) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -419) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#2| (LIST (QUOTE -419) (|devaluate| |#1|)))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#2| (LIST (QUOTE -369) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#2| (LIST (QUOTE -419) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -369) (|devaluate| |#1|)))) (-608 |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."))) -((-4417 . T) (-4418 . T)) -((-12 (|HasCategory| (-2 (|:| -2010 (-1157)) (|:| -2818 |#1|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2010 (-1157)) (|:| -2818 |#1|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2010) (QUOTE (-1157))) (LIST (QUOTE |:|) (QUOTE -2818) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -2010 (-1157)) (|:| -2818 |#1|)) (LIST (QUOTE -614) (QUOTE (-538)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| (-1157) (QUOTE (-850))) (|HasCategory| (-2 (|:| -2010 (-1157)) (|:| -2818 |#1|)) (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -2010 (-1157)) (|:| -2818 |#1|)) (LIST (QUOTE -613) (QUOTE (-862))))) +((-4414 . T) (-4415 . T)) +((-12 (|HasCategory| (-2 (|:| -2050 (-1157)) (|:| -2849 |#1|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2050 (-1157)) (|:| -2849 |#1|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2050) (QUOTE (-1157))) (LIST (QUOTE |:|) (QUOTE -2849) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -2050 (-1157)) (|:| -2849 |#1|)) (LIST (QUOTE -614) (QUOTE (-538)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| (-1157) (QUOTE (-850))) (|HasCategory| (-2 (|:| -2050 (-1157)) (|:| -2849 |#1|)) (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -2050 (-1157)) (|:| -2849 |#1|)) (LIST (QUOTE -613) (QUOTE (-862))))) (-609 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 (-610 |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}."))) -((-4418 . T)) +((-4415 . T)) NIL (-611 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"))) @@ -2388,7 +2388,7 @@ 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| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}."))) NIL NIL -(-615 -2382 UP) +(-615 -2386 UP) ((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic\\spad{'s} algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,{}a_1,{}a_2,{}ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$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 @@ -2410,19 +2410,19 @@ NIL NIL (-620 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."))) -((-4414 . T)) +((-4411 . T)) NIL (-621 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}."))) -((-4411 . T) (-4412 . T) (-4414 . T)) +((-4408 . T) (-4409 . T) (-4411 . T)) ((|HasCategory| |#1| (QUOTE (-848)))) -(-622 R -2382) +(-622 R -2386) ((|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 (-623 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"))) -((-4412 . T) (-4411 . T) ((-4419 "*") . T) (-4410 . T) (-4414 . T)) +((-4409 . T) (-4408 . T) ((-4416 "*") . T) (-4407 . T) (-4411 . T)) ((|HasCategory| |#2| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566))))) (-624 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."))) @@ -2438,7 +2438,7 @@ NIL NIL (-627 |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}}."))) -((-4414 . T)) +((-4411 . T)) NIL (-628 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}}."))) @@ -2448,29 +2448,29 @@ NIL ((|constructor| (NIL "Category for the transcendental Liouvillian functions.")) (|erf| (($ $) "\\spad{erf(x)} returns the error function of \\spad{x},{} \\spadignore{i.e.} \\spad{2 / sqrt(\\%\\spad{pi})} times the integral of \\spad{exp(-x**2) dx}.")) (|dilog| (($ $) "\\spad{dilog(x)} returns the dilogarithm of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{log(x) / (1 - x) dx}.")) (|li| (($ $) "\\spad{\\spad{li}(x)} returns the logarithmic integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{dx / log(x)}.")) (|Ci| (($ $) "\\spad{\\spad{Ci}(x)} returns the cosine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{cos(x) / x dx}.")) (|Si| (($ $) "\\spad{\\spad{Si}(x)} returns the sine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{sin(x) / x dx}.")) (|Ei| (($ $) "\\spad{\\spad{Ei}(x)} returns the exponential integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{exp(x)/x dx}."))) NIL NIL -(-630 R -2382) +(-630 R -2386) ((|constructor| (NIL "This package provides liouvillian functions over an integral domain.")) (|integral| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{integral(f,{}x = a..b)} denotes the definite integral of \\spad{f} with respect to \\spad{x} from \\spad{a} to \\spad{b}.") ((|#2| |#2| (|Symbol|)) "\\spad{integral(f,{}x)} indefinite integral of \\spad{f} with respect to \\spad{x}.")) (|dilog| ((|#2| |#2|) "\\spad{dilog(f)} denotes the dilogarithm")) (|erf| ((|#2| |#2|) "\\spad{erf(f)} denotes the error function")) (|li| ((|#2| |#2|) "\\spad{\\spad{li}(f)} denotes the logarithmic integral")) (|Ci| ((|#2| |#2|) "\\spad{\\spad{Ci}(f)} denotes the cosine integral")) (|Si| ((|#2| |#2|) "\\spad{\\spad{Si}(f)} denotes the sine integral")) (|Ei| ((|#2| |#2|) "\\spad{\\spad{Ei}(f)} denotes the exponential integral")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns the Liouvillian operator based on \\spad{op}")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} checks if \\spad{op} is Liouvillian"))) NIL NIL -(-631 |lv| -2382) +(-631 |lv| -2386) ((|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 (-632) ((|constructor| (NIL "This domain provides a simple way to save values in files.")) (|setelt| (((|Any|) $ (|Symbol|) (|Any|)) "\\spad{lib.k := v} saves the value \\spad{v} in the library \\spad{lib}. It can later be extracted using the key \\spad{k}.")) (|elt| (((|Any|) $ (|Symbol|)) "\\spad{elt(lib,{}k)} or \\spad{lib}.\\spad{k} extracts the value corresponding to the key \\spad{k} from the library \\spad{lib}.")) (|pack!| (($ $) "\\spad{pack!(f)} reorganizes the file \\spad{f} on disk to recover unused space.")) (|library| (($ (|FileName|)) "\\spad{library(ln)} creates a new library file."))) -((-4418 . T)) -((-12 (|HasCategory| (-2 (|:| -2010 (-1157)) (|:| -2818 (-52))) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2010 (-1157)) (|:| -2818 (-52))) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2010) (QUOTE (-1157))) (LIST (QUOTE |:|) (QUOTE -2818) (QUOTE (-52))))))) (-2805 (|HasCategory| (-2 (|:| -2010 (-1157)) (|:| -2818 (-52))) (QUOTE (-1099))) (|HasCategory| (-52) (QUOTE (-1099)))) (-2805 (|HasCategory| (-2 (|:| -2010 (-1157)) (|:| -2818 (-52))) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2010 (-1157)) (|:| -2818 (-52))) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-52) (QUOTE (-1099))) (|HasCategory| (-52) (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-2 (|:| -2010 (-1157)) (|:| -2818 (-52))) (LIST (QUOTE -614) (QUOTE (-538)))) (-12 (|HasCategory| (-52) (QUOTE (-1099))) (|HasCategory| (-52) (LIST (QUOTE -310) (QUOTE (-52))))) (|HasCategory| (-1157) (QUOTE (-850))) (-2805 (|HasCategory| (-2 (|:| -2010 (-1157)) (|:| -2818 (-52))) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-52) (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-52) (QUOTE (-1099))) (|HasCategory| (-52) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -2010 (-1157)) (|:| -2818 (-52))) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -2010 (-1157)) (|:| -2818 (-52))) (QUOTE (-1099)))) +((-4415 . T)) +((-12 (|HasCategory| (-2 (|:| -2050 (-1157)) (|:| -2849 (-52))) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2050 (-1157)) (|:| -2849 (-52))) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2050) (QUOTE (-1157))) (LIST (QUOTE |:|) (QUOTE -2849) (QUOTE (-52))))))) (-2805 (|HasCategory| (-2 (|:| -2050 (-1157)) (|:| -2849 (-52))) (QUOTE (-1099))) (|HasCategory| (-52) (QUOTE (-1099)))) (-2805 (|HasCategory| (-2 (|:| -2050 (-1157)) (|:| -2849 (-52))) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2050 (-1157)) (|:| -2849 (-52))) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-52) (QUOTE (-1099))) (|HasCategory| (-52) (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-2 (|:| -2050 (-1157)) (|:| -2849 (-52))) (LIST (QUOTE -614) (QUOTE (-538)))) (-12 (|HasCategory| (-52) (QUOTE (-1099))) (|HasCategory| (-52) (LIST (QUOTE -310) (QUOTE (-52))))) (|HasCategory| (-1157) (QUOTE (-850))) (-2805 (|HasCategory| (-2 (|:| -2050 (-1157)) (|:| -2849 (-52))) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-52) (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-52) (QUOTE (-1099))) (|HasCategory| (-52) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -2050 (-1157)) (|:| -2849 (-52))) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -2050 (-1157)) (|:| -2849 (-52))) (QUOTE (-1099)))) (-633 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| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) NIL ((|HasCategory| |#2| (QUOTE (-365)))) (-634 R) ((|constructor| (NIL "\\axiom{JacobiIdentity} means that \\axiom{[\\spad{x},{}[\\spad{y},{}\\spad{z}]]+[\\spad{y},{}[\\spad{z},{}\\spad{x}]]+[\\spad{z},{}[\\spad{x},{}\\spad{y}]] = 0} holds.")) (/ (($ $ |#1|) "\\axiom{\\spad{x/r}} returns the division of \\axiom{\\spad{x}} by \\axiom{\\spad{r}}.")) (|construct| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) -((|JacobiIdentity| . T) (|NullSquare| . T) (-4412 . T) (-4411 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-4409 . T) (-4408 . T)) NIL (-635 R A) ((|constructor| (NIL "AssociatedLieAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$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)."))) -((-4414 -2805 (-2438 (|has| |#2| (-369 |#1|)) (|has| |#1| (-558))) (-12 (|has| |#2| (-419 |#1|)) (|has| |#1| (-558)))) (-4412 . T) (-4411 . T)) +((-4411 -2805 (-2447 (|has| |#2| (-369 |#1|)) (|has| |#1| (-558))) (-12 (|has| |#2| (-419 |#1|)) (|has| |#1| (-558)))) (-4409 . T) (-4408 . T)) ((-2805 (|HasCategory| |#2| (LIST (QUOTE -369) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -419) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -419) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#2| (LIST (QUOTE -419) (|devaluate| |#1|)))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#2| (LIST (QUOTE -369) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#2| (LIST (QUOTE -419) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -369) (|devaluate| |#1|)))) (-636 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))}."))) @@ -2483,10 +2483,10 @@ NIL (-638 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 -((-2426 (|HasCategory| |#1| (QUOTE (-365)))) (|HasCategory| |#1| (QUOTE (-365)))) +((-2436 (|HasCategory| |#1| (QUOTE (-365)))) (|HasCategory| |#1| (QUOTE (-365)))) (-639 R) ((|constructor| (NIL "An extension ring with an explicit linear dependence test.")) (|reducedSystem| (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| $) (|Vector| $)) "\\spad{reducedSystem(A,{} v)} returns a matrix \\spad{B} and a vector \\spad{w} such that \\spad{A x = v} and \\spad{B x = w} have the same solutions in \\spad{R}.") (((|Matrix| |#1|) (|Matrix| $)) "\\spad{reducedSystem(A)} returns a matrix \\spad{B} such that \\spad{A x = 0} and \\spad{B x = 0} have the same solutions in \\spad{R}."))) -((-4414 . T)) +((-4411 . T)) NIL (-640 R) ((|constructor| (NIL "\\indented{2}{A set is an \\spad{R}-linear set if it is stable by dilation} \\indented{2}{by elements in the ring \\spad{R}.\\space{2}This category differs from} \\indented{2}{\\spad{Module} in that no other assumption (such as addition)} \\indented{2}{is made about the underlying set.} See Also: LeftLinearSet,{} RightLinearSet."))) @@ -2506,7 +2506,7 @@ NIL NIL (-644 S) ((|constructor| (NIL "\\spadtype{List} implements singly-linked lists that are addressable by indices; the index of the first element is 1. In addition to the operations provided by \\spadtype{IndexedList},{} this constructor provides some LISP-like functions such as \\spadfun{null} and \\spadfun{cons}.")) (|setDifference| (($ $ $) "\\spad{setDifference(u1,{}u2)} returns a list of the elements of \\spad{u1} that are not also in \\spad{u2}. The order of elements in the resulting list is unspecified.")) (|setIntersection| (($ $ $) "\\spad{setIntersection(u1,{}u2)} returns a list of the elements that lists \\spad{u1} and \\spad{u2} have in common. The order of elements in the resulting list is unspecified.")) (|setUnion| (($ $ $) "\\spad{setUnion(u1,{}u2)} appends the two lists \\spad{u1} and \\spad{u2},{} then removes all duplicates. The order of elements in the resulting list is unspecified.")) (|append| (($ $ $) "\\spad{append(u1,{}u2)} appends the elements of list \\spad{u1} onto the front of list \\spad{u2}. This new list and \\spad{u2} will share some structure.")) (|cons| (($ |#1| $) "\\spad{cons(element,{}u)} appends \\spad{element} onto the front of list \\spad{u} and returns the new list. This new list and the old one will share some structure.")) (|null| (((|Boolean|) $) "\\spad{null(u)} tests if list \\spad{u} is the empty list.")) (|nil| (($) "\\spad{nil()} returns the empty list."))) -((-4418 . T) (-4417 . T)) +((-4415 . T) (-4414 . T)) ((-2805 (-12 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538)))) (-2805 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099)))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-828))) (|HasCategory| (-566) (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-645 T$) ((|constructor| (NIL "This domain represents AST for Spad literals."))) @@ -2518,7 +2518,7 @@ NIL NIL (-647 S) ((|substitute| (($ |#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."))) -((-4417 . T) (-4418 . T)) +((-4414 . T) (-4415 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (-648 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"))) @@ -2531,22 +2531,22 @@ NIL (-650 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,{}..))}.")) (|elt| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{elt(u,{}i..j)} (also written: \\axiom{a(\\spad{i}..\\spad{j})}) returns the aggregate of elements \\axiom{\\spad{u}} for \\spad{k} from \\spad{i} to \\spad{j} in that order. Note: in general,{} \\axiom{a.\\spad{s} = [a.\\spad{k} for \\spad{i} in \\spad{s}]}.")) (|map| (($ (|Mapping| |#2| |#2| |#2|) $ $) "\\spad{map(f,{}u,{}v)} returns a new collection \\spad{w} with elements \\axiom{\\spad{z} = \\spad{f}(\\spad{x},{}\\spad{y})} for corresponding elements \\spad{x} and \\spad{y} from \\spad{u} and \\spad{v}. Note: for linear aggregates,{} \\axiom{\\spad{w}.\\spad{i} = \\spad{f}(\\spad{u}.\\spad{i},{}\\spad{v}.\\spad{i})}.")) (|concat| (($ (|List| $)) "\\spad{concat(u)},{} where \\spad{u} is a lists of aggregates \\axiom{[a,{}\\spad{b},{}...,{}\\spad{c}]},{} returns a single aggregate consisting of the elements of \\axiom{a} followed by those of \\spad{b} followed ... by the elements of \\spad{c}. Note: \\axiom{concat(a,{}\\spad{b},{}...,{}\\spad{c}) = concat(a,{}concat(\\spad{b},{}...,{}\\spad{c}))}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} then \\axiom{\\spad{w}.\\spad{i} = \\spad{u}.\\spad{i} for \\spad{i} in indices \\spad{u}} and \\axiom{\\spad{w}.(\\spad{j} + maxIndex \\spad{u}) = \\spad{v}.\\spad{j} for \\spad{j} in indices \\spad{v}}.") (($ |#2| $) "\\spad{concat(x,{}u)} returns aggregate \\spad{u} with additional element at the front. Note: for lists: \\axiom{concat(\\spad{x},{}\\spad{u}) \\spad{==} concat([\\spad{x}],{}\\spad{u})}.") (($ $ |#2|) "\\spad{concat(u,{}x)} returns aggregate \\spad{u} with additional element \\spad{x} at the end. Note: for lists,{} \\axiom{concat(\\spad{u},{}\\spad{x}) \\spad{==} concat(\\spad{u},{}[\\spad{x}])}")) (|new| (($ (|NonNegativeInteger|) |#2|) "\\spad{new(n,{}x)} returns \\axiom{fill!(new \\spad{n},{}\\spad{x})}."))) NIL -((|HasAttribute| |#1| (QUOTE -4418))) +((|HasAttribute| |#1| (QUOTE -4415))) (-651 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,{}..))}.")) (|elt| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{elt(u,{}i..j)} (also written: \\axiom{a(\\spad{i}..\\spad{j})}) returns the aggregate of elements \\axiom{\\spad{u}} for \\spad{k} from \\spad{i} to \\spad{j} in that order. Note: in general,{} \\axiom{a.\\spad{s} = [a.\\spad{k} for \\spad{i} in \\spad{s}]}.")) (|map| (($ (|Mapping| |#1| |#1| |#1|) $ $) "\\spad{map(f,{}u,{}v)} returns a new collection \\spad{w} with elements \\axiom{\\spad{z} = \\spad{f}(\\spad{x},{}\\spad{y})} for corresponding elements \\spad{x} and \\spad{y} from \\spad{u} and \\spad{v}. Note: for linear aggregates,{} \\axiom{\\spad{w}.\\spad{i} = \\spad{f}(\\spad{u}.\\spad{i},{}\\spad{v}.\\spad{i})}.")) (|concat| (($ (|List| $)) "\\spad{concat(u)},{} where \\spad{u} is a lists of aggregates \\axiom{[a,{}\\spad{b},{}...,{}\\spad{c}]},{} returns a single aggregate consisting of the elements of \\axiom{a} followed by those of \\spad{b} followed ... by the elements of \\spad{c}. Note: \\axiom{concat(a,{}\\spad{b},{}...,{}\\spad{c}) = concat(a,{}concat(\\spad{b},{}...,{}\\spad{c}))}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} then \\axiom{\\spad{w}.\\spad{i} = \\spad{u}.\\spad{i} for \\spad{i} in indices \\spad{u}} and \\axiom{\\spad{w}.(\\spad{j} + maxIndex \\spad{u}) = \\spad{v}.\\spad{j} for \\spad{j} in indices \\spad{v}}.") (($ |#1| $) "\\spad{concat(x,{}u)} returns aggregate \\spad{u} with additional element at the front. Note: for lists: \\axiom{concat(\\spad{x},{}\\spad{u}) \\spad{==} concat([\\spad{x}],{}\\spad{u})}.") (($ $ |#1|) "\\spad{concat(u,{}x)} returns aggregate \\spad{u} with additional element \\spad{x} at the end. Note: for lists,{} \\axiom{concat(\\spad{u},{}\\spad{x}) \\spad{==} concat(\\spad{u},{}[\\spad{x}])}")) (|new| (($ (|NonNegativeInteger|) |#1|) "\\spad{new(n,{}x)} returns \\axiom{fill!(new \\spad{n},{}\\spad{x})}."))) NIL NIL -(-652 R -2382 L) +(-652 R -2386 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 (-653 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}}"))) -((-4411 . T) (-4412 . T) (-4414 . T)) +((-4408 . T) (-4409 . T) (-4411 . T)) ((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-365)))) (-654 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| (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}"))) -((-4411 . T) (-4412 . T) (-4414 . T)) +((-4408 . T) (-4409 . T) (-4411 . T)) ((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-365)))) (-655 S A) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorCategory} is the category of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|directSum| (($ $ $) "\\spad{directSum(a,{}b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}.")) (|symmetricSquare| (($ $) "\\spad{symmetricSquare(a)} computes \\spad{symmetricProduct(a,{}a)} using a more efficient method.")) (|symmetricPower| (($ $ (|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}."))) @@ -2554,15 +2554,15 @@ NIL ((|HasCategory| |#2| (QUOTE (-365)))) (-656 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}."))) -((-4411 . T) (-4412 . T) (-4414 . T)) +((-4408 . T) (-4409 . T) (-4411 . T)) NIL -(-657 -2382 UP) +(-657 -2386 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)))) -(-658 A -2614) +(-658 A -1554) ((|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}}"))) -((-4411 . T) (-4412 . T) (-4414 . T)) +((-4408 . T) (-4409 . T) (-4411 . T)) ((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-365)))) (-659 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."))) @@ -2578,7 +2578,7 @@ NIL NIL (-662 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}."))) -((-4412 . T) (-4411 . T)) +((-4409 . T) (-4408 . T)) ((|HasCategory| |#1| (QUOTE (-791)))) (-663 R) ((|constructor| (NIL "Given a PolynomialFactorizationExplicit ring,{} this package provides a defaulting rule for the \\spad{solveLinearPolynomialEquation} operation,{} by moving into the field of fractions,{} and solving it there via the \\spad{multiEuclidean} operation.")) (|solveLinearPolynomialEquationByFractions| (((|Union| (|List| (|SparseUnivariatePolynomial| |#1|)) "failed") (|List| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{solveLinearPolynomialEquationByFractions([f1,{} ...,{} fn],{} g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod \\spad{fi} = sum ai/fi} or returns \"failed\" if no such exists."))) @@ -2586,7 +2586,7 @@ NIL NIL (-664 |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) (-4412 . T) (-4411 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-4409 . T) (-4408 . T)) ((|HasCategory| |#2| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-172)))) (-665 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}."))) @@ -2594,13 +2594,13 @@ NIL NIL (-666 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}."))) -((-4418 . T) (-4417 . T)) +((-4415 . T) (-4414 . T)) NIL -(-667 -2382) +(-667 -2386) ((|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 -(-668 -2382 |Row| |Col| M) +(-668 -2386 |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 @@ -2610,8 +2610,8 @@ NIL NIL (-670 |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."))) -((-4414 . T) (-4417 . T) (-4411 . T) (-4412 . T)) -((|HasCategory| |#2| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasAttribute| |#2| (QUOTE (-4419 "*"))) (|HasCategory| |#2| (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| |#2| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-566)))) (-2805 (-12 (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -639) (QUOTE (-566))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -900) (QUOTE (-1175)))))) (|HasCategory| |#2| (QUOTE (-308))) (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-558))) (-2805 (|HasAttribute| |#2| (QUOTE (-4419 "*"))) (|HasCategory| |#2| (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| |#2| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| |#2| (QUOTE (-233)))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-172)))) +((-4411 . T) (-4414 . T) (-4408 . T) (-4409 . T)) +((|HasCategory| |#2| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasAttribute| |#2| (QUOTE (-4416 "*"))) (|HasCategory| |#2| (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| |#2| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-566)))) (-2805 (-12 (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -639) (QUOTE (-566))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -900) (QUOTE (-1175)))))) (|HasCategory| |#2| (QUOTE (-308))) (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-558))) (-2805 (|HasAttribute| |#2| (QUOTE (-4416 "*"))) (|HasCategory| |#2| (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| |#2| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| |#2| (QUOTE (-233)))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-172)))) (-671) ((|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 @@ -2675,10 +2675,10 @@ NIL (-686 S R |Row| |Col|) ((|constructor| (NIL "\\spadtype{MatrixCategory} is a general matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col. A domain belonging to this category will be shallowly mutable. The index of the 'first' row may be obtained by calling the function \\spadfun{minRowIndex}. The index of the 'first' column may be obtained by calling the function \\spadfun{minColIndex}. The index of the first element of a Row is the same as the index of the first column in a matrix and vice versa.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|minordet| ((|#2| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors. Error: if the matrix is not square.")) (|determinant| ((|#2| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. Error: if the matrix is not square.")) (|nullSpace| (((|List| |#4|) $) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#2|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#2|) "\\spad{exquo(m,{}r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if matrix is not square or if the matrix is square but not invertible.") (($ $ (|NonNegativeInteger|)) "\\spad{x ** n} computes a non-negative integral power of the matrix \\spad{x}. Error: if the matrix is not square.")) (* ((|#3| |#3| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#4| $ |#4|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.") (($ (|Integer|) $) "\\spad{n * x} is an integer multiple.") (($ $ |#2|) "\\spad{x * r} is the right scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ |#2| $) "\\spad{r*x} is the left scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ $ $) "\\spad{x * y} is the product of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (- (($ $) "\\spad{-x} returns the negative of the matrix \\spad{x}.") (($ $ $) "\\spad{x - y} is the difference of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (+ (($ $ $) "\\spad{x + y} is the sum of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (|setsubMatrix!| (($ $ (|Integer|) (|Integer|) $) "\\spad{setsubMatrix(x,{}i1,{}j1,{}y)} destructively alters the matrix \\spad{x}. Here \\spad{x(i,{}j)} is set to \\spad{y(i-i1+1,{}j-j1+1)} for \\spad{i = i1,{}...,{}i1-1+nrows y} and \\spad{j = j1,{}...,{}j1-1+ncols y}.")) (|subMatrix| (($ $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{subMatrix(x,{}i1,{}i2,{}j1,{}j2)} extracts the submatrix \\spad{[x(i,{}j)]} where the index \\spad{i} ranges from \\spad{i1} to \\spad{i2} and the index \\spad{j} ranges from \\spad{j1} to \\spad{j2}.")) (|swapColumns!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapColumns!(m,{}i,{}j)} interchanges the \\spad{i}th and \\spad{j}th columns of \\spad{m}. This destructively alters the matrix.")) (|swapRows!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapRows!(m,{}i,{}j)} interchanges the \\spad{i}th and \\spad{j}th rows of \\spad{m}. This destructively alters the matrix.")) (|setelt| (($ $ (|List| (|Integer|)) (|List| (|Integer|)) $) "\\spad{setelt(x,{}rowList,{}colList,{}y)} destructively alters the matrix \\spad{x}. If \\spad{y} is \\spad{m}-by-\\spad{n},{} \\spad{rowList = [i<1>,{}i<2>,{}...,{}i]} and \\spad{colList = [j<1>,{}j<2>,{}...,{}j]},{} then \\spad{x(i,{}j)} is set to \\spad{y(k,{}l)} for \\spad{k = 1,{}...,{}m} and \\spad{l = 1,{}...,{}n}.")) (|elt| (($ $ (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{elt(x,{}rowList,{}colList)} returns an \\spad{m}-by-\\spad{n} matrix consisting of elements of \\spad{x},{} where \\spad{m = \\# rowList} and \\spad{n = \\# colList}. If \\spad{rowList = [i<1>,{}i<2>,{}...,{}i]} and \\spad{colList = [j<1>,{}j<2>,{}...,{}j]},{} then the \\spad{(k,{}l)}th entry of \\spad{elt(x,{}rowList,{}colList)} is \\spad{x(i,{}j)}.")) (|listOfLists| (((|List| (|List| |#2|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|vertConcat| (($ $ $) "\\spad{vertConcat(x,{}y)} vertically concatenates two matrices with an equal number of columns. The entries of \\spad{y} appear below of the entries of \\spad{x}. Error: if the matrices do not have the same number of columns.")) (|horizConcat| (($ $ $) "\\spad{horizConcat(x,{}y)} horizontally concatenates two matrices with an equal number of rows. The entries of \\spad{y} appear to the right of the entries of \\spad{x}. Error: if the matrices do not have the same number of rows.")) (|squareTop| (($ $) "\\spad{squareTop(m)} returns an \\spad{n}-by-\\spad{n} matrix consisting of the first \\spad{n} rows of the \\spad{m}-by-\\spad{n} matrix \\spad{m}. Error: if \\spad{m < n}.")) (|transpose| (($ $) "\\spad{transpose(m)} returns the transpose of the matrix \\spad{m}.") (($ |#3|) "\\spad{transpose(r)} converts the row \\spad{r} to a row matrix.")) (|coerce| (($ |#4|) "\\spad{coerce(col)} converts the column \\spad{col} to a column matrix.")) (|diagonalMatrix| (($ (|List| $)) "\\spad{diagonalMatrix([m1,{}...,{}mk])} creates a block diagonal matrix \\spad{M} with block matrices {\\em m1},{}...,{}{\\em mk} down the diagonal,{} with 0 block matrices elsewhere. More precisly: if \\spad{\\spad{ri} := nrows \\spad{mi}},{} \\spad{\\spad{ci} := ncols \\spad{mi}},{} then \\spad{m} is an (\\spad{r1+}..\\spad{+rk}) by (\\spad{c1+}..\\spad{+ck}) - matrix with entries \\spad{m.i.j = ml.(i-r1-..-r(l-1)).(j-n1-..-n(l-1))},{} if \\spad{(r1+..+r(l-1)) < i <= r1+..+rl} and \\spad{(c1+..+c(l-1)) < i <= c1+..+cl},{} \\spad{m.i.j} = 0 otherwise.") (($ (|List| |#2|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ (|NonNegativeInteger|) |#2|) "\\spad{scalarMatrix(n,{}r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}\\spad{'s} on the diagonal and zeroes elsewhere.")) (|matrix| (($ (|List| (|List| |#2|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix.")) (|zero| (($ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{zero(m,{}n)} returns an \\spad{m}-by-\\spad{n} zero matrix.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,{}j] = -m[j,{}i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,{}j] = m[j,{}i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.")) (|finiteAggregate| ((|attribute|) "matrices are finite")) (|shallowlyMutable| ((|attribute|) "One may destructively alter matrices"))) NIL -((|HasAttribute| |#2| (QUOTE (-4419 "*"))) (|HasCategory| |#2| (QUOTE (-308))) (|HasCategory| |#2| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-558)))) +((|HasAttribute| |#2| (QUOTE (-4416 "*"))) (|HasCategory| |#2| (QUOTE (-308))) (|HasCategory| |#2| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-558)))) (-687 R |Row| |Col|) ((|constructor| (NIL "\\spadtype{MatrixCategory} is a general matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col. A domain belonging to this category will be shallowly mutable. The index of the 'first' row may be obtained by calling the function \\spadfun{minRowIndex}. The index of the 'first' column may be obtained by calling the function \\spadfun{minColIndex}. The index of the first element of a Row is the same as the index of the first column in a matrix and vice versa.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|minordet| ((|#1| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors. Error: if the matrix is not square.")) (|determinant| ((|#1| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. Error: if the matrix is not square.")) (|nullSpace| (((|List| |#3|) $) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#1|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(m,{}r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if matrix is not square or if the matrix is square but not invertible.") (($ $ (|NonNegativeInteger|)) "\\spad{x ** n} computes a non-negative integral power of the matrix \\spad{x}. Error: if the matrix is not square.")) (* ((|#2| |#2| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#3| $ |#3|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.") (($ (|Integer|) $) "\\spad{n * x} is an integer multiple.") (($ $ |#1|) "\\spad{x * r} is the right scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ |#1| $) "\\spad{r*x} is the left scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ $ $) "\\spad{x * y} is the product of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (- (($ $) "\\spad{-x} returns the negative of the matrix \\spad{x}.") (($ $ $) "\\spad{x - y} is the difference of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (+ (($ $ $) "\\spad{x + y} is the sum of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (|setsubMatrix!| (($ $ (|Integer|) (|Integer|) $) "\\spad{setsubMatrix(x,{}i1,{}j1,{}y)} destructively alters the matrix \\spad{x}. Here \\spad{x(i,{}j)} is set to \\spad{y(i-i1+1,{}j-j1+1)} for \\spad{i = i1,{}...,{}i1-1+nrows y} and \\spad{j = j1,{}...,{}j1-1+ncols y}.")) (|subMatrix| (($ $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{subMatrix(x,{}i1,{}i2,{}j1,{}j2)} extracts the submatrix \\spad{[x(i,{}j)]} where the index \\spad{i} ranges from \\spad{i1} to \\spad{i2} and the index \\spad{j} ranges from \\spad{j1} to \\spad{j2}.")) (|swapColumns!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapColumns!(m,{}i,{}j)} interchanges the \\spad{i}th and \\spad{j}th columns of \\spad{m}. This destructively alters the matrix.")) (|swapRows!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapRows!(m,{}i,{}j)} interchanges the \\spad{i}th and \\spad{j}th rows of \\spad{m}. This destructively alters the matrix.")) (|setelt| (($ $ (|List| (|Integer|)) (|List| (|Integer|)) $) "\\spad{setelt(x,{}rowList,{}colList,{}y)} destructively alters the matrix \\spad{x}. If \\spad{y} is \\spad{m}-by-\\spad{n},{} \\spad{rowList = [i<1>,{}i<2>,{}...,{}i]} and \\spad{colList = [j<1>,{}j<2>,{}...,{}j]},{} then \\spad{x(i,{}j)} is set to \\spad{y(k,{}l)} for \\spad{k = 1,{}...,{}m} and \\spad{l = 1,{}...,{}n}.")) (|elt| (($ $ (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{elt(x,{}rowList,{}colList)} returns an \\spad{m}-by-\\spad{n} matrix consisting of elements of \\spad{x},{} where \\spad{m = \\# rowList} and \\spad{n = \\# colList}. If \\spad{rowList = [i<1>,{}i<2>,{}...,{}i]} and \\spad{colList = [j<1>,{}j<2>,{}...,{}j]},{} then the \\spad{(k,{}l)}th entry of \\spad{elt(x,{}rowList,{}colList)} is \\spad{x(i,{}j)}.")) (|listOfLists| (((|List| (|List| |#1|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|vertConcat| (($ $ $) "\\spad{vertConcat(x,{}y)} vertically concatenates two matrices with an equal number of columns. The entries of \\spad{y} appear below of the entries of \\spad{x}. Error: if the matrices do not have the same number of columns.")) (|horizConcat| (($ $ $) "\\spad{horizConcat(x,{}y)} horizontally concatenates two matrices with an equal number of rows. The entries of \\spad{y} appear to the right of the entries of \\spad{x}. Error: if the matrices do not have the same number of rows.")) (|squareTop| (($ $) "\\spad{squareTop(m)} returns an \\spad{n}-by-\\spad{n} matrix consisting of the first \\spad{n} rows of the \\spad{m}-by-\\spad{n} matrix \\spad{m}. Error: if \\spad{m < n}.")) (|transpose| (($ $) "\\spad{transpose(m)} returns the transpose of the matrix \\spad{m}.") (($ |#2|) "\\spad{transpose(r)} converts the row \\spad{r} to a row matrix.")) (|coerce| (($ |#3|) "\\spad{coerce(col)} converts the column \\spad{col} to a column matrix.")) (|diagonalMatrix| (($ (|List| $)) "\\spad{diagonalMatrix([m1,{}...,{}mk])} creates a block diagonal matrix \\spad{M} with block matrices {\\em m1},{}...,{}{\\em mk} down the diagonal,{} with 0 block matrices elsewhere. More precisly: if \\spad{\\spad{ri} := nrows \\spad{mi}},{} \\spad{\\spad{ci} := ncols \\spad{mi}},{} then \\spad{m} is an (\\spad{r1+}..\\spad{+rk}) by (\\spad{c1+}..\\spad{+ck}) - matrix with entries \\spad{m.i.j = ml.(i-r1-..-r(l-1)).(j-n1-..-n(l-1))},{} if \\spad{(r1+..+r(l-1)) < i <= r1+..+rl} and \\spad{(c1+..+c(l-1)) < i <= c1+..+cl},{} \\spad{m.i.j} = 0 otherwise.") (($ (|List| |#1|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ (|NonNegativeInteger|) |#1|) "\\spad{scalarMatrix(n,{}r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}\\spad{'s} on the diagonal and zeroes elsewhere.")) (|matrix| (($ (|List| (|List| |#1|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix.")) (|zero| (($ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{zero(m,{}n)} returns an \\spad{m}-by-\\spad{n} zero matrix.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,{}j] = -m[j,{}i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,{}j] = m[j,{}i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.")) (|finiteAggregate| ((|attribute|) "matrices are finite")) (|shallowlyMutable| ((|attribute|) "One may destructively alter matrices"))) -((-4417 . T) (-4418 . T)) +((-4414 . T) (-4415 . T)) NIL (-688 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."))) @@ -2686,8 +2686,8 @@ NIL ((|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-558)))) (-689 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."))) -((-4417 . T) (-4418 . T)) -((-2805 (-12 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1099))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-558))) (|HasAttribute| |#1| (QUOTE (-4419 "*"))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) +((-4414 . T) (-4415 . T)) +((-2805 (-12 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1099))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-558))) (|HasAttribute| |#1| (QUOTE (-4416 "*"))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-690 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 @@ -2696,7 +2696,7 @@ 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 -(-692 S -2382 FLAF FLAS) +(-692 S -2386 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 @@ -2706,11 +2706,11 @@ NIL NIL (-694) ((|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"))) -((-4410 . T) (-4415 |has| (-699) (-365)) (-4409 |has| (-699) (-365)) (-3654 . T) (-4416 |has| (-699) (-6 -4416)) (-4413 |has| (-699) (-6 -4413)) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) -((|HasCategory| (-699) (QUOTE (-147))) (|HasCategory| (-699) (QUOTE (-145))) (|HasCategory| (-699) (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| (-699) (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| (-699) (QUOTE (-370))) (|HasCategory| (-699) (QUOTE (-365))) (-2805 (|HasCategory| (-699) (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| (-699) (QUOTE (-365)))) (|HasCategory| (-699) (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| (-699) (QUOTE (-233))) (-2805 (|HasCategory| (-699) (QUOTE (-365))) (|HasCategory| (-699) (QUOTE (-351)))) (|HasCategory| (-699) (QUOTE (-351))) (|HasCategory| (-699) (LIST (QUOTE -287) (QUOTE (-699)) (QUOTE (-699)))) (|HasCategory| (-699) (LIST (QUOTE -310) (QUOTE (-699)))) (|HasCategory| (-699) (LIST (QUOTE -516) (QUOTE (-1175)) (QUOTE (-699)))) (|HasCategory| (-699) (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| (-699) (LIST (QUOTE -886) (QUOTE (-381)))) (|HasCategory| (-699) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| (-699) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (-2805 (|HasCategory| (-699) (QUOTE (-308))) (|HasCategory| (-699) (QUOTE (-365))) (|HasCategory| (-699) (QUOTE (-351)))) (|HasCategory| (-699) (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| (-699) (QUOTE (-1022))) (|HasCategory| (-699) (QUOTE (-1199))) (-12 (|HasCategory| (-699) (QUOTE (-1002))) (|HasCategory| (-699) (QUOTE (-1199)))) (-2805 (-12 (|HasCategory| (-699) (QUOTE (-308))) (|HasCategory| (-699) (QUOTE (-909)))) (|HasCategory| (-699) (QUOTE (-365))) (-12 (|HasCategory| (-699) (QUOTE (-351))) (|HasCategory| (-699) (QUOTE (-909))))) (-2805 (-12 (|HasCategory| (-699) (QUOTE (-308))) (|HasCategory| (-699) (QUOTE (-909)))) (-12 (|HasCategory| (-699) (QUOTE (-365))) (|HasCategory| (-699) (QUOTE (-909)))) (-12 (|HasCategory| (-699) (QUOTE (-351))) (|HasCategory| (-699) (QUOTE (-909))))) (|HasCategory| (-699) (QUOTE (-547))) (-12 (|HasCategory| (-699) (QUOTE (-1059))) (|HasCategory| (-699) (QUOTE (-1199)))) (|HasCategory| (-699) (QUOTE (-1059))) (|HasCategory| (-699) (QUOTE (-308))) (|HasCategory| (-699) (QUOTE (-909))) (-2805 (-12 (|HasCategory| (-699) (QUOTE (-308))) (|HasCategory| (-699) (QUOTE (-909)))) (|HasCategory| (-699) (QUOTE (-365)))) (-2805 (-12 (|HasCategory| (-699) (QUOTE (-308))) (|HasCategory| (-699) (QUOTE (-909)))) (|HasCategory| (-699) (QUOTE (-558)))) (-12 (|HasCategory| (-699) (QUOTE (-233))) (|HasCategory| (-699) (QUOTE (-365)))) (-12 (|HasCategory| (-699) (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| (-699) (QUOTE (-365)))) (|HasCategory| (-699) (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| (-699) (QUOTE (-558))) (|HasAttribute| (-699) (QUOTE -4416)) (|HasAttribute| (-699) (QUOTE -4413)) (-12 (|HasCategory| (-699) (QUOTE (-308))) (|HasCategory| (-699) (QUOTE (-909)))) (-2805 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-699) (QUOTE (-308))) (|HasCategory| (-699) (QUOTE (-909)))) (|HasCategory| (-699) (QUOTE (-145)))) (-2805 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-699) (QUOTE (-308))) (|HasCategory| (-699) (QUOTE (-909)))) (|HasCategory| (-699) (QUOTE (-351))))) +((-4407 . T) (-4412 |has| (-699) (-365)) (-4406 |has| (-699) (-365)) (-3661 . T) (-4413 |has| (-699) (-6 -4413)) (-4410 |has| (-699) (-6 -4410)) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) +((|HasCategory| (-699) (QUOTE (-147))) (|HasCategory| (-699) (QUOTE (-145))) (|HasCategory| (-699) (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| (-699) (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| (-699) (QUOTE (-370))) (|HasCategory| (-699) (QUOTE (-365))) (-2805 (|HasCategory| (-699) (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| (-699) (QUOTE (-365)))) (|HasCategory| (-699) (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| (-699) (QUOTE (-233))) (-2805 (|HasCategory| (-699) (QUOTE (-365))) (|HasCategory| (-699) (QUOTE (-351)))) (|HasCategory| (-699) (QUOTE (-351))) (|HasCategory| (-699) (LIST (QUOTE -287) (QUOTE (-699)) (QUOTE (-699)))) (|HasCategory| (-699) (LIST (QUOTE -310) (QUOTE (-699)))) (|HasCategory| (-699) (LIST (QUOTE -516) (QUOTE (-1175)) (QUOTE (-699)))) (|HasCategory| (-699) (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| (-699) (LIST (QUOTE -886) (QUOTE (-381)))) (|HasCategory| (-699) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| (-699) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (-2805 (|HasCategory| (-699) (QUOTE (-308))) (|HasCategory| (-699) (QUOTE (-365))) (|HasCategory| (-699) (QUOTE (-351)))) (|HasCategory| (-699) (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| (-699) (QUOTE (-1022))) (|HasCategory| (-699) (QUOTE (-1199))) (-12 (|HasCategory| (-699) (QUOTE (-1002))) (|HasCategory| (-699) (QUOTE (-1199)))) (-2805 (-12 (|HasCategory| (-699) (QUOTE (-308))) (|HasCategory| (-699) (QUOTE (-909)))) (|HasCategory| (-699) (QUOTE (-365))) (-12 (|HasCategory| (-699) (QUOTE (-351))) (|HasCategory| (-699) (QUOTE (-909))))) (-2805 (-12 (|HasCategory| (-699) (QUOTE (-308))) (|HasCategory| (-699) (QUOTE (-909)))) (-12 (|HasCategory| (-699) (QUOTE (-365))) (|HasCategory| (-699) (QUOTE (-909)))) (-12 (|HasCategory| (-699) (QUOTE (-351))) (|HasCategory| (-699) (QUOTE (-909))))) (|HasCategory| (-699) (QUOTE (-547))) (-12 (|HasCategory| (-699) (QUOTE (-1059))) (|HasCategory| (-699) (QUOTE (-1199)))) (|HasCategory| (-699) (QUOTE (-1059))) (|HasCategory| (-699) (QUOTE (-308))) (|HasCategory| (-699) (QUOTE (-909))) (-2805 (-12 (|HasCategory| (-699) (QUOTE (-308))) (|HasCategory| (-699) (QUOTE (-909)))) (|HasCategory| (-699) (QUOTE (-365)))) (-2805 (-12 (|HasCategory| (-699) (QUOTE (-308))) (|HasCategory| (-699) (QUOTE (-909)))) (|HasCategory| (-699) (QUOTE (-558)))) (-12 (|HasCategory| (-699) (QUOTE (-233))) (|HasCategory| (-699) (QUOTE (-365)))) (-12 (|HasCategory| (-699) (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| (-699) (QUOTE (-365)))) (|HasCategory| (-699) (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| (-699) (QUOTE (-558))) (|HasAttribute| (-699) (QUOTE -4413)) (|HasAttribute| (-699) (QUOTE -4410)) (-12 (|HasCategory| (-699) (QUOTE (-308))) (|HasCategory| (-699) (QUOTE (-909)))) (-2805 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-699) (QUOTE (-308))) (|HasCategory| (-699) (QUOTE (-909)))) (|HasCategory| (-699) (QUOTE (-145)))) (-2805 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-699) (QUOTE (-308))) (|HasCategory| (-699) (QUOTE (-909)))) (|HasCategory| (-699) (QUOTE (-351))))) (-695 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}."))) -((-4418 . T)) +((-4415 . T)) NIL (-696 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}."))) @@ -2720,13 +2720,13 @@ NIL ((|constructor| (NIL "\\indented{1}{} Author: Jim Wen Date Created: \\spad{??} Date Last Updated: October 1991 by Jon Steinbach Keywords: Examples: References:")) (|ptFunc| (((|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) "\\spad{ptFunc(a,{}b,{}c,{}d)} is an internal function exported in order to compile packages.")) (|meshPar1Var| (((|ThreeSpace| (|DoubleFloat|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar1Var(s,{}t,{}u,{}f,{}s1,{}l)} \\undocumented")) (|meshFun2Var| (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Union| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "undefined") (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshFun2Var(f,{}g,{}s1,{}s2,{}l)} \\undocumented")) (|meshPar2Var| (((|ThreeSpace| (|DoubleFloat|)) (|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(sp,{}f,{}s1,{}s2,{}l)} \\undocumented") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(f,{}s1,{}s2,{}l)} \\undocumented") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Union| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "undefined") (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(f,{}g,{}h,{}j,{}s1,{}s2,{}l)} \\undocumented"))) NIL NIL -(-698 OV E -2382 PG) +(-698 OV E -2386 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 (-699) ((|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}"))) -((-3645 . T) (-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) +((-3651 . T) (-4406 . T) (-4412 . T) (-4407 . T) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) NIL (-700 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."))) @@ -2734,7 +2734,7 @@ NIL NIL (-701) ((|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}"))) -((-4416 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) +((-4413 . T) (-4412 . T) (-4407 . T) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) NIL (-702 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"))) @@ -2752,7 +2752,7 @@ 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 -(-706 S -2840 I) +(-706 S -2876 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 @@ -2762,7 +2762,7 @@ NIL NIL (-708 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)}.}"))) -((-4411 . T) (-4412 . T) (-4414 . T)) +((-4408 . T) (-4409 . T) (-4411 . T)) NIL (-709 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}."))) @@ -2772,25 +2772,25 @@ NIL ((|constructor| (NIL "\\spadtype{MathMLFormat} provides a coercion from \\spadtype{OutputForm} to MathML format.")) (|display| (((|Void|) (|String|)) "prints the string returned by coerce,{} adding 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 -(-711 R |Mod| -3550 -3132 |exactQuo|) +(-711 R |Mod| -3418 -3891 |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| $) "\\spad{modulus(x)} \\undocumented"))) -((-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) +((-4406 . T) (-4412 . T) (-4407 . T) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) NIL (-712 R |Rep|) ((|constructor| (NIL "This package \\undocumented")) (|frobenius| (($ $) "\\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"))) -(((-4419 "*") |has| |#1| (-172)) (-4410 |has| |#1| (-558)) (-4413 |has| |#1| (-365)) (-4415 |has| |#1| (-6 -4415)) (-4412 . T) (-4411 . T) (-4414 . T)) -((|HasCategory| |#1| (QUOTE (-909))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-172))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (-12 (|HasCategory| (-1081) (LIST (QUOTE -886) (QUOTE (-381)))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-381))))) (-12 (|HasCategory| (-1081) (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-566))))) (-12 (|HasCategory| (-1081) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381)))))) (-12 (|HasCategory| (-1081) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566)))))) (-12 (|HasCategory| (-1081) (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))) (-2805 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566)))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-909)))) (-2805 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-909)))) (-2805 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-1150))) (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-351))) (|HasCategory| |#1| (QUOTE (-233))) (|HasAttribute| |#1| (QUOTE -4415)) (|HasCategory| |#1| (QUOTE (-454))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-909)))) (-2805 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-145))))) +(((-4416 "*") |has| |#1| (-172)) (-4407 |has| |#1| (-558)) (-4410 |has| |#1| (-365)) (-4412 |has| |#1| (-6 -4412)) (-4409 . T) (-4408 . T) (-4411 . T)) +((|HasCategory| |#1| (QUOTE (-909))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-172))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (-12 (|HasCategory| (-1081) (LIST (QUOTE -886) (QUOTE (-381)))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-381))))) (-12 (|HasCategory| (-1081) (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-566))))) (-12 (|HasCategory| (-1081) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381)))))) (-12 (|HasCategory| (-1081) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566)))))) (-12 (|HasCategory| (-1081) (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))) (-2805 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566)))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-909)))) (-2805 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-909)))) (-2805 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-1150))) (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-351))) (|HasCategory| |#1| (QUOTE (-233))) (|HasAttribute| |#1| (QUOTE -4412)) (|HasCategory| |#1| (QUOTE (-454))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-909)))) (-2805 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-145))))) (-713 IS E |ff|) ((|constructor| (NIL "This package \\undocumented")) (|construct| (($ |#1| |#2|) "\\spad{construct(i,{}e)} \\undocumented")) (|index| ((|#1| $) "\\spad{index(x)} \\undocumented")) (|exponent| ((|#2| $) "\\spad{exponent(x)} \\undocumented"))) NIL NIL (-714 R M) ((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#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| (($ $ $) "\\spad{adjoint(op1,{} op2)} sets the adjoint of \\spad{op1} to be op2. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) -((-4412 |has| |#1| (-172)) (-4411 |has| |#1| (-172)) (-4414 . T)) +((-4409 |has| |#1| (-172)) (-4408 |has| |#1| (-172)) (-4411 . T)) ((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147)))) -(-715 R |Mod| -3550 -3132 |exactQuo|) +(-715 R |Mod| -3418 -3891 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\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"))) -((-4414 . T)) +((-4411 . T)) NIL (-716 S R) ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) @@ -2798,11 +2798,11 @@ NIL NIL (-717 R) ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) -((-4412 . T) (-4411 . T)) +((-4409 . T) (-4408 . T)) NIL -(-718 -2382) +(-718 -2386) ((|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]]}."))) -((-4414 . T)) +((-4411 . T)) NIL (-719 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."))) @@ -2826,7 +2826,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-351))) (|HasCategory| |#2| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-370)))) (-724 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."))) -((-4410 |has| |#1| (-365)) (-4415 |has| |#1| (-365)) (-4409 |has| |#1| (-365)) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) +((-4407 |has| |#1| (-365)) (-4412 |has| |#1| (-365)) (-4406 |has| |#1| (-365)) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) NIL (-725 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."))) @@ -2836,7 +2836,7 @@ 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 -(-727 -2382 UP) +(-727 -2386 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 @@ -2854,8 +2854,8 @@ NIL NIL (-731 |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."))) -(((-4419 "*") |has| |#2| (-172)) (-4410 |has| |#2| (-558)) (-4415 |has| |#2| (-6 -4415)) (-4412 . T) (-4411 . T) (-4414 . T)) -((|HasCategory| |#2| (QUOTE (-909))) (-2805 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-454))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-909)))) (-2805 (|HasCategory| |#2| (QUOTE (-454))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-909)))) (-2805 (|HasCategory| |#2| (QUOTE (-454))) (|HasCategory| |#2| (QUOTE (-909)))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-172))) (-2805 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-558)))) (-12 (|HasCategory| (-864 |#1|) (LIST (QUOTE -886) (QUOTE (-381)))) (|HasCategory| |#2| (LIST (QUOTE -886) (QUOTE (-381))))) (-12 (|HasCategory| (-864 |#1|) (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| |#2| (LIST (QUOTE -886) (QUOTE (-566))))) (-12 (|HasCategory| (-864 |#1|) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (|HasCategory| |#2| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381)))))) (-12 (|HasCategory| (-864 |#1|) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| |#2| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566)))))) (-12 (|HasCategory| (-864 |#1|) (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-538))))) (|HasCategory| |#2| (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-566)))) (-2805 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#2| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566)))))) (|HasCategory| |#2| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#2| (QUOTE (-365))) (|HasAttribute| |#2| (QUOTE -4415)) (|HasCategory| |#2| (QUOTE (-454))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-909)))) (-2805 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-909)))) (|HasCategory| |#2| (QUOTE (-145))))) +(((-4416 "*") |has| |#2| (-172)) (-4407 |has| |#2| (-558)) (-4412 |has| |#2| (-6 -4412)) (-4409 . T) (-4408 . T) (-4411 . T)) +((|HasCategory| |#2| (QUOTE (-909))) (-2805 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-454))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-909)))) (-2805 (|HasCategory| |#2| (QUOTE (-454))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-909)))) (-2805 (|HasCategory| |#2| (QUOTE (-454))) (|HasCategory| |#2| (QUOTE (-909)))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-172))) (-2805 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-558)))) (-12 (|HasCategory| (-864 |#1|) (LIST (QUOTE -886) (QUOTE (-381)))) (|HasCategory| |#2| (LIST (QUOTE -886) (QUOTE (-381))))) (-12 (|HasCategory| (-864 |#1|) (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| |#2| (LIST (QUOTE -886) (QUOTE (-566))))) (-12 (|HasCategory| (-864 |#1|) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (|HasCategory| |#2| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381)))))) (-12 (|HasCategory| (-864 |#1|) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| |#2| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566)))))) (-12 (|HasCategory| (-864 |#1|) (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-538))))) (|HasCategory| |#2| (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-566)))) (-2805 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#2| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566)))))) (|HasCategory| |#2| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#2| (QUOTE (-365))) (|HasAttribute| |#2| (QUOTE -4412)) (|HasCategory| |#2| (QUOTE (-454))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-909)))) (-2805 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-909)))) (|HasCategory| |#2| (QUOTE (-145))))) (-732 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|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) NIL @@ -2870,15 +2870,15 @@ NIL NIL (-735 R M) ((|constructor| (NIL "\\spadtype{MonoidRing}(\\spad{R},{}\\spad{M}),{} implements the algebra of all maps from the monoid \\spad{M} to the commutative ring \\spad{R} with finite support. Multiplication of two maps \\spad{f} and \\spad{g} is defined to map an element \\spad{c} of \\spad{M} to the (convolution) sum over {\\em f(a)g(b)} such that {\\em ab = c}. Thus \\spad{M} can be identified with a canonical basis and the maps can also be considered as formal linear combinations of the elements in \\spad{M}. Scalar multiples of a basis element are called monomials. A prominent example is the class of polynomials where the monoid is a direct product of the natural numbers with pointwise addition. When \\spad{M} is \\spadtype{FreeMonoid Symbol},{} one gets polynomials in infinitely many non-commuting variables. Another application area is representation theory of finite groups \\spad{G},{} where modules over \\spadtype{MonoidRing}(\\spad{R},{}\\spad{G}) are studied.")) (|reductum| (($ $) "\\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}."))) -((-4412 |has| |#1| (-172)) (-4411 |has| |#1| (-172)) (-4414 . T)) +((-4409 |has| |#1| (-172)) (-4408 |has| |#1| (-172)) (-4411 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (QUOTE (-370)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-850)))) (-736 S) ((|constructor| (NIL "A multi-set aggregate is a set which keeps track of the multiplicity of its elements."))) -((-4407 . T) (-4418 . T)) +((-4404 . T) (-4415 . T)) NIL (-737 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}."))) -((-4417 . T) (-4407 . T) (-4418 . T)) +((-4414 . T) (-4404 . T) (-4415 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (-738) ((|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."))) @@ -2890,7 +2890,7 @@ NIL NIL (-740 |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}."))) -(((-4419 "*") |has| |#1| (-172)) (-4410 |has| |#1| (-558)) (-4412 . T) (-4411 . T) (-4414 . T)) +(((-4416 "*") |has| |#1| (-172)) (-4407 |has| |#1| (-558)) (-4409 . T) (-4408 . T) (-4411 . T)) NIL (-741 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"))) @@ -2906,7 +2906,7 @@ NIL NIL (-744 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}."))) -((-4412 . T) (-4411 . T)) +((-4409 . T) (-4408 . T)) NIL (-745) ((|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}."))) @@ -2988,11 +2988,11 @@ 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 -(-765 -2382) +(-765 -2386) ((|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 -(-766 P -2382) +(-766 P -2386) ((|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 @@ -3000,7 +3000,7 @@ NIL NIL NIL NIL -(-768 UP -2382) +(-768 UP -2386) ((|constructor| (NIL "In this package \\spad{F} is a framed algebra over the integers (typically \\spad{F = Z[a]} for some algebraic integer a). The package provides functions to compute the integral closure of \\spad{Z} in the quotient quotient field of \\spad{F}.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| (|Integer|))) (|:| |basisDen| (|Integer|)) (|:| |basisInv| (|Matrix| (|Integer|)))) (|Integer|)) "\\spad{integralBasis(p)} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the local integral closure of \\spad{Z} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{Z}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| (|Integer|))) (|:| |basisDen| (|Integer|)) (|:| |basisInv| (|Matrix| (|Integer|))))) "\\spad{integralBasis()} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the integral closure of \\spad{Z} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{Z}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|discriminant| (((|Integer|)) "\\spad{discriminant()} returns the discriminant of the integral closure of \\spad{Z} in the quotient field of the framed algebra \\spad{F}."))) NIL NIL @@ -3014,9 +3014,9 @@ NIL NIL (-771) ((|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."))) -(((-4419 "*") . T)) +(((-4416 "*") . T)) NIL -(-772 R -2382) +(-772 R -2386) ((|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 @@ -3036,7 +3036,7 @@ 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 -(-777 -2382 |ExtF| |SUEx| |ExtP| |n|) +(-777 -2386 |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 @@ -3050,23 +3050,23 @@ NIL NIL (-780 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."))) -(((-4419 "*") |has| |#1| (-172)) (-4410 |has| |#1| (-558)) (-4415 |has| |#1| (-6 -4415)) (-4412 . T) (-4411 . T) (-4414 . 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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 (-782 R) ((|constructor| (NIL "A post-facto extension for \\axiomType{SUP} in order to speed up operations related to pseudo-division and \\spad{gcd} for both \\axiomType{SUP} and,{} consequently,{} \\axiomType{NSMP}.")) (|halfExtendedResultant2| (((|Record| (|:| |resultant| |#1|) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedResultant2(a,{}\\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)}"))) -(((-4419 "*") |has| |#1| (-172)) (-4410 |has| |#1| (-558)) (-4413 |has| |#1| (-365)) (-4415 |has| |#1| (-6 -4415)) (-4412 . T) (-4411 . T) (-4414 . T)) -((|HasCategory| |#1| (QUOTE (-909))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-172))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (-12 (|HasCategory| (-1081) (LIST (QUOTE -886) (QUOTE (-381)))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-381))))) (-12 (|HasCategory| (-1081) (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-566))))) (-12 (|HasCategory| (-1081) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381)))))) (-12 (|HasCategory| (-1081) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566)))))) (-12 (|HasCategory| (-1081) (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))) (-2805 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566)))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-909)))) (-2805 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-909)))) (-2805 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-1150))) (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| |#1| (QUOTE (-233))) (|HasAttribute| |#1| (QUOTE -4415)) (|HasCategory| |#1| (QUOTE (-454))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-909)))) (-2805 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-145))))) +(((-4416 "*") |has| |#1| (-172)) (-4407 |has| |#1| (-558)) (-4410 |has| |#1| (-365)) (-4412 |has| |#1| (-6 -4412)) (-4409 . T) (-4408 . T) (-4411 . T)) +((|HasCategory| |#1| (QUOTE (-909))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-172))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (-12 (|HasCategory| (-1081) (LIST (QUOTE -886) (QUOTE (-381)))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-381))))) (-12 (|HasCategory| (-1081) (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-566))))) (-12 (|HasCategory| (-1081) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381)))))) (-12 (|HasCategory| (-1081) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566)))))) (-12 (|HasCategory| (-1081) (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))) (-2805 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566)))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-909)))) (-2805 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-909)))) (-2805 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-1150))) (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| |#1| (QUOTE (-233))) (|HasAttribute| |#1| (QUOTE -4412)) (|HasCategory| |#1| (QUOTE (-454))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-909)))) (-2805 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-145))))) (-783 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 -409) (QUOTE (-566)))))) (-784 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.}"))) -((-4418 . T) (-4417 . T)) +((-4415 . T) (-4414 . T)) NIL (-785 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}."))) @@ -3118,7 +3118,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-547))) (|HasCategory| |#2| (QUOTE (-1059))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#2| (QUOTE (-850))) (|HasCategory| |#2| (QUOTE (-370)))) (-797 R) ((|constructor| (NIL "OctonionCategory gives the categorial frame for the octonions,{} and eight-dimensional non-associative algebra,{} doubling the the quaternions in the same way as doubling the Complex numbers to get the quaternions.")) (|inv| (($ $) "\\spad{inv(o)} returns the inverse of \\spad{o} if it exists.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(o)} returns the real part if all seven imaginary parts are 0,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(o)} returns the real part if all seven imaginary parts are 0. Error: if \\spad{o} is not rational.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(o)} tests if \\spad{o} is rational,{} \\spadignore{i.e.} that all seven imaginary parts are 0.")) (|abs| ((|#1| $) "\\spad{abs(o)} computes the absolute value of an octonion,{} equal to the square root of the \\spadfunFrom{norm}{Octonion}.")) (|octon| (($ |#1| |#1| |#1| |#1| |#1| |#1| |#1| |#1|) "\\spad{octon(re,{}\\spad{ri},{}rj,{}rk,{}rE,{}rI,{}rJ,{}rK)} constructs an octonion from scalars.")) (|norm| ((|#1| $) "\\spad{norm(o)} returns the norm of an octonion,{} equal to the sum of the squares of its coefficients.")) (|imagK| ((|#1| $) "\\spad{imagK(o)} extracts the imaginary \\spad{K} part of octonion \\spad{o}.")) (|imagJ| ((|#1| $) "\\spad{imagJ(o)} extracts the imaginary \\spad{J} part of octonion \\spad{o}.")) (|imagI| ((|#1| $) "\\spad{imagI(o)} extracts the imaginary \\spad{I} part of octonion \\spad{o}.")) (|imagE| ((|#1| $) "\\spad{imagE(o)} extracts the imaginary \\spad{E} part of octonion \\spad{o}.")) (|imagk| ((|#1| $) "\\spad{imagk(o)} extracts the \\spad{k} part of octonion \\spad{o}.")) (|imagj| ((|#1| $) "\\spad{imagj(o)} extracts the \\spad{j} part of octonion \\spad{o}.")) (|imagi| ((|#1| $) "\\spad{imagi(o)} extracts the \\spad{i} part of octonion \\spad{o}.")) (|real| ((|#1| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) -((-4411 . T) (-4412 . T) (-4414 . T)) +((-4408 . T) (-4409 . T) (-4411 . T)) NIL (-798 -2805 R OS S) ((|constructor| (NIL "OctonionCategoryFunctions2 implements functions between two octonion domains defined over different rings. The function map is used to coerce between octonion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,{}u)} maps \\spad{f} onto the component parts of the octonion \\spad{u}."))) @@ -3126,17 +3126,17 @@ NIL NIL (-799 R) ((|constructor| (NIL "Octonion implements octonions (Cayley-Dixon algebra) over a commutative ring,{} an eight-dimensional non-associative algebra,{} doubling the quaternions in the same way as doubling the complex numbers to get the quaternions the main constructor function is {\\em octon} which takes 8 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j} imaginary part,{} the \\spad{k} imaginary part,{} (as with quaternions) and in addition the imaginary parts \\spad{E},{} \\spad{I},{} \\spad{J},{} \\spad{K}.")) (|octon| (($ (|Quaternion| |#1|) (|Quaternion| |#1|)) "\\spad{octon(qe,{}qE)} constructs an octonion from two quaternions using the relation {\\em O = Q + QE}."))) -((-4411 . T) (-4412 . T) (-4414 . T)) +((-4408 . T) (-4409 . T) (-4411 . T)) ((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (LIST (QUOTE -516) (QUOTE (-1175)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -287) (|devaluate| |#1|) (|devaluate| |#1|))) (-2805 (|HasCategory| (-999 |#1|) (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566)))))) (-2805 (|HasCategory| (-999 |#1|) (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-1059))) (|HasCategory| |#1| (QUOTE (-547))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| (-999 |#1|) (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| (-999 |#1|) (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566))))) (-800) ((|ODESolve| (((|Result|) (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{ODESolve(args)} performs the integration of the function given the strategy or method returned by \\axiomFun{measure}.")) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{measure(R,{}args)} calculates an estimate of the ability of a particular method to solve a problem. \\blankline This method may be either a specific NAG routine or a strategy (such as transforming the function from one which is difficult to one which is easier to solve). \\blankline It will call whichever agents are needed to perform analysis on the problem in order to calculate the measure. There is a parameter,{} labelled \\axiom{sofar},{} which would contain the best compatibility found so far."))) NIL NIL -(-801 R -2382 L) +(-801 R -2386 L) ((|constructor| (NIL "Solution of linear ordinary differential equations,{} constant coefficient case.")) (|constDsolve| (((|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Symbol|)) "\\spad{constDsolve(op,{} g,{} x)} returns \\spad{[f,{} [y1,{}...,{}ym]]} where \\spad{f} is a particular solution of the equation \\spad{op y = g},{} and the \\spad{\\spad{yi}}\\spad{'s} form a basis for the solutions of \\spad{op y = 0}."))) NIL NIL -(-802 R -2382) +(-802 R -2386) ((|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 @@ -3144,7 +3144,7 @@ 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 -(-804 R -2382) +(-804 R -2386) ((|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 @@ -3152,11 +3152,11 @@ 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 -(-806 -2382 UP UPUP R) +(-806 -2386 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 -(-807 -2382 UP L LQ) +(-807 -2386 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 @@ -3164,41 +3164,41 @@ 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 -(-809 -2382 UP L LQ) +(-809 -2386 UP L LQ) ((|constructor| (NIL "In-field solution of Riccati equations,{} primitive case.")) (|changeVar| ((|#3| |#3| (|Fraction| |#2|)) "\\spad{changeVar(+/[\\spad{ai} D^i],{} a)} returns the operator \\spad{+/[\\spad{ai} (D+a)\\spad{^i}]}.") ((|#3| |#3| |#2|) "\\spad{changeVar(+/[\\spad{ai} D^i],{} a)} returns the operator \\spad{+/[\\spad{ai} (D+a)\\spad{^i}]}.")) (|singRicDE| (((|List| (|Record| (|:| |frac| (|Fraction| |#2|)) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{singRicDE(op,{} zeros,{} ezfactor)} returns \\spad{[[f1,{} L1],{} [f2,{} L2],{} ... ,{} [fk,{} Lk]]} such that the singular part of any rational solution of the associated Riccati equation of \\spad{op y=0} must be one of the \\spad{fi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z=y e^{-int p}} is \\spad{\\spad{Li} z=0}. \\spad{zeros(C(x),{}H(x,{}y))} returns all the \\spad{P_i(x)}\\spad{'s} such that \\spad{H(x,{}P_i(x)) = 0 modulo C(x)}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.")) (|polyRicDE| (((|List| (|Record| (|:| |poly| |#2|) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#1|) |#2|)) "\\spad{polyRicDE(op,{} zeros)} returns \\spad{[[p1,{} L1],{} [p2,{} L2],{} ... ,{} [pk,{} Lk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y=0} must be one of the \\spad{pi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z=y e^{-int p}} is \\spad{\\spad{Li} z =0}. \\spad{zeros} is a zero finder in \\spad{UP}.")) (|constantCoefficientRicDE| (((|List| (|Record| (|:| |constant| |#1|) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#1|) |#2|)) "\\spad{constantCoefficientRicDE(op,{} ric)} returns \\spad{[[a1,{} L1],{} [a2,{} L2],{} ... ,{} [ak,{} Lk]]} such that any rational solution with no polynomial part of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{ai}\\spad{'s} in which case the equation for \\spad{z = y e^{-int \\spad{ai}}} is \\spad{\\spad{Li} z = 0}. \\spad{ric} is a Riccati equation solver over \\spad{F},{} whose input is the associated linear equation.")) (|leadingCoefficientRicDE| (((|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |eq| |#2|))) |#3|) "\\spad{leadingCoefficientRicDE(op)} returns \\spad{[[m1,{} p1],{} [m2,{} p2],{} ... ,{} [mk,{} pk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must have degree \\spad{mj} for some \\spad{j},{} and its leading coefficient is then a zero of \\spad{pj}. In addition,{}\\spad{m1>m2> ... >mk}.")) (|denomRicDE| ((|#2| |#3|) "\\spad{denomRicDE(op)} returns a polynomial \\spad{d} such that any rational solution of the associated Riccati equation of \\spad{op y = 0} is of the form \\spad{p/d + q'/q + r} for some polynomials \\spad{p} and \\spad{q} and a reduced \\spad{r}. Also,{} \\spad{deg(p) < deg(d)} and {\\spad{gcd}(\\spad{d},{}\\spad{q}) = 1}."))) NIL NIL -(-810 -2382 UP) +(-810 -2386 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 -(-811 -2382 L UP A LO) +(-811 -2386 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 -(-812 -2382 UP) +(-812 -2386 UP) ((|constructor| (NIL "In-field solution of Riccati equations,{} rational case.")) (|polyRicDE| (((|List| (|Record| (|:| |poly| |#2|) (|:| |eq| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{polyRicDE(op,{} zeros)} returns \\spad{[[p1,{} L1],{} [p2,{} L2],{} ... ,{} [pk,{}Lk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{pi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z = y e^{-int p}} is \\spad{\\spad{Li} z = 0}. \\spad{zeros} is a zero finder in \\spad{UP}.")) (|singRicDE| (((|List| (|Record| (|:| |frac| (|Fraction| |#2|)) (|:| |eq| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{singRicDE(op,{} ezfactor)} returns \\spad{[[f1,{}L1],{} [f2,{}L2],{}...,{} [fk,{}Lk]]} such that the singular \\spad{++} part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{fi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z = y e^{-int \\spad{ai}}} is \\spad{\\spad{Li} z = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.")) (|ricDsolve| (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op,{} ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))) "\\spad{ricDsolve(op)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op,{} ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{ricDsolve(op)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op,{} zeros,{} ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{ricDsolve(op,{} zeros)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op,{} zeros,{} ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{ricDsolve(op,{} zeros)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}."))) NIL ((|HasCategory| |#1| (QUOTE (-27)))) -(-813 -2382 LO) +(-813 -2386 LO) ((|constructor| (NIL "SystemODESolver provides tools for triangulating and solving some systems of linear ordinary differential equations.")) (|solveInField| (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|)))) (|Matrix| |#2|) (|Vector| |#1|) (|Mapping| (|Record| (|:| |particular| (|Union| |#1| "failed")) (|:| |basis| (|List| |#1|))) |#2| |#1|)) "\\spad{solveInField(m,{} v,{} solve)} returns \\spad{[[v_1,{}...,{}v_m],{} v_p]} such that the solutions in \\spad{F} of the system \\spad{m x = v} are \\spad{v_p + c_1 v_1 + ... + c_m v_m} where the \\spad{c_i's} are constants,{} and the \\spad{v_i's} form a basis for the solutions of \\spad{m x = 0}. Argument \\spad{solve} is a function for solving a single linear ordinary differential equation in \\spad{F}.")) (|solve| (((|Union| (|Record| (|:| |particular| (|Vector| |#1|)) (|:| |basis| (|Matrix| |#1|))) "failed") (|Matrix| |#1|) (|Vector| |#1|) (|Mapping| (|Union| (|Record| (|:| |particular| |#1|) (|:| |basis| (|List| |#1|))) "failed") |#2| |#1|)) "\\spad{solve(m,{} v,{} solve)} returns \\spad{[[v_1,{}...,{}v_m],{} v_p]} such that the solutions in \\spad{F} of the system \\spad{D x = m x + v} are \\spad{v_p + c_1 v_1 + ... + c_m v_m} where the \\spad{c_i's} are constants,{} and the \\spad{v_i's} form a basis for the solutions of \\spad{D x = m x}. Argument \\spad{solve} is a function for solving a single linear ordinary differential equation in \\spad{F}.")) (|triangulate| (((|Record| (|:| |mat| (|Matrix| |#2|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| |#2|) (|Vector| |#1|)) "\\spad{triangulate(m,{} v)} returns \\spad{[m_0,{} v_0]} such that \\spad{m_0} is upper triangular and the system \\spad{m_0 x = v_0} is equivalent to \\spad{m x = v}.") (((|Record| (|:| A (|Matrix| |#1|)) (|:| |eqs| (|List| (|Record| (|:| C (|Matrix| |#1|)) (|:| |g| (|Vector| |#1|)) (|:| |eq| |#2|) (|:| |rh| |#1|))))) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{triangulate(M,{}v)} returns \\spad{A,{}[[C_1,{}g_1,{}L_1,{}h_1],{}...,{}[C_k,{}g_k,{}L_k,{}h_k]]} such that under the change of variable \\spad{y = A z},{} the first order linear system \\spad{D y = M y + v} is uncoupled as \\spad{D z_i = C_i z_i + g_i} and each \\spad{C_i} is a companion matrix corresponding to the scalar equation \\spad{L_i z_j = h_i}."))) NIL NIL -(-814 -2382 LODO) +(-814 -2386 LODO) ((|constructor| (NIL "\\spad{ODETools} provides tools for the linear ODE solver.")) (|particularSolution| (((|Union| |#1| "failed") |#2| |#1| (|List| |#1|) (|Mapping| |#1| |#1|)) "\\spad{particularSolution(op,{} g,{} [f1,{}...,{}fm],{} I)} returns a particular solution \\spad{h} of the equation \\spad{op y = g} where \\spad{[f1,{}...,{}fm]} are linearly independent and \\spad{op(\\spad{fi})=0}. The value \"failed\" is returned if no particular solution is found. Note: the method of variations of parameters is used.")) (|variationOfParameters| (((|Union| (|Vector| |#1|) "failed") |#2| |#1| (|List| |#1|)) "\\spad{variationOfParameters(op,{} g,{} [f1,{}...,{}fm])} returns \\spad{[u1,{}...,{}um]} such that a particular solution of the equation \\spad{op y = g} is \\spad{f1 int(u1) + ... + fm int(um)} where \\spad{[f1,{}...,{}fm]} are linearly independent and \\spad{op(\\spad{fi})=0}. The value \"failed\" is returned if \\spad{m < n} and no particular solution is found.")) (|wronskianMatrix| (((|Matrix| |#1|) (|List| |#1|) (|NonNegativeInteger|)) "\\spad{wronskianMatrix([f1,{}...,{}fn],{} q,{} D)} returns the \\spad{q x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),{}...,{}fn^(i-1)]}.") (((|Matrix| |#1|) (|List| |#1|)) "\\spad{wronskianMatrix([f1,{}...,{}fn])} returns the \\spad{n x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),{}...,{}fn^(i-1)]}."))) NIL NIL -(-815 -2293 S |f|) +(-815 -4225 S |f|) ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying ordered component type. The ordering on the type is determined by its third argument which represents the less than function on vectors. This type is a suitable third argument for \\spadtype{GeneralDistributedMultivariatePolynomial}."))) -((-4411 |has| |#2| (-1049)) (-4412 |has| |#2| (-1049)) (-4414 |has| |#2| (-6 -4414)) ((-4419 "*") |has| |#2| (-172)) (-4417 . T)) -((-2805 (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-131))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-365))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-370))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-726))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-793))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-848))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1049))) (|HasCategory| |#2| (LIST 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(LIST (QUOTE -1038) (QUOTE (-566))))) (-12 (|HasCategory| |#2| (QUOTE (-365))) (|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-566))))) (-12 (|HasCategory| |#2| (QUOTE (-370))) (|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-566))))) (-12 (|HasCategory| |#2| (QUOTE (-726))) (|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-566))))) (-12 (|HasCategory| |#2| (QUOTE (-793))) (|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-566))))) (-12 (|HasCategory| |#2| (QUOTE (-848))) (|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-566))))) (-12 (|HasCategory| |#2| (QUOTE (-1049))) (|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-566))))) (-12 (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-566)))))) (|HasCategory| (-566) (QUOTE (-850))) (-12 (|HasCategory| |#2| (QUOTE (-1049))) (|HasCategory| |#2| (LIST (QUOTE -639) (QUOTE (-566))))) (-12 (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (QUOTE (-1049)))) (-12 (|HasCategory| |#2| (QUOTE (-1049))) (|HasCategory| |#2| (LIST (QUOTE -900) (QUOTE (-1175))))) (-2805 (|HasCategory| |#2| (QUOTE (-1049))) (-12 (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-566)))))) (-12 (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-566))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#2| (QUOTE (-1099)))) (|HasAttribute| |#2| (QUOTE -4411)) (|HasCategory| |#2| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|))))) (-816 R) ((|constructor| (NIL "\\spadtype{OrderlyDifferentialPolynomial} implements an ordinary differential polynomial ring in arbitrary number of differential indeterminates,{} with coefficients in a ring. The ranking on the differential indeterminate is orderly. This is analogous to the domain \\spadtype{Polynomial}. \\blankline"))) -(((-4419 "*") |has| |#1| (-172)) (-4410 |has| |#1| (-558)) (-4415 |has| |#1| (-6 -4415)) (-4412 . T) (-4411 . T) (-4414 . T)) -((|HasCategory| |#1| (QUOTE (-909))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-909)))) (-2805 (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-909)))) (-2805 (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-172))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (-12 (|HasCategory| (-818 (-1175)) (LIST (QUOTE -886) (QUOTE (-381)))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-381))))) (-12 (|HasCategory| (-818 (-1175)) (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-566))))) (-12 (|HasCategory| (-818 (-1175)) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381)))))) (-12 (|HasCategory| (-818 (-1175)) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566)))))) (-12 (|HasCategory| (-818 (-1175)) (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))) (-2805 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566)))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| |#1| (QUOTE (-365))) (|HasAttribute| |#1| (QUOTE -4415)) (|HasCategory| |#1| (QUOTE (-454))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-909)))) (-2805 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-145))))) +(((-4416 "*") |has| |#1| (-172)) (-4407 |has| |#1| (-558)) (-4412 |has| |#1| (-6 -4412)) (-4409 . T) (-4408 . T) (-4411 . T)) +((|HasCategory| |#1| (QUOTE (-909))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-909)))) (-2805 (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-909)))) (-2805 (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-172))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (-12 (|HasCategory| (-818 (-1175)) (LIST (QUOTE -886) (QUOTE (-381)))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-381))))) (-12 (|HasCategory| (-818 (-1175)) (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-566))))) (-12 (|HasCategory| (-818 (-1175)) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381)))))) (-12 (|HasCategory| (-818 (-1175)) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566)))))) (-12 (|HasCategory| (-818 (-1175)) (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))) (-2805 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566)))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| |#1| (QUOTE (-365))) (|HasAttribute| |#1| (QUOTE -4412)) (|HasCategory| |#1| (QUOTE (-454))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-909)))) (-2805 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-145))))) (-817 |Kernels| R |var|) ((|constructor| (NIL "This constructor produces an ordinary differential ring from a partial differential ring by specifying a variable."))) -(((-4419 "*") |has| |#2| (-365)) (-4410 |has| |#2| (-365)) (-4415 |has| |#2| (-365)) (-4409 |has| |#2| (-365)) (-4414 . T) (-4412 . T) (-4411 . T)) +(((-4416 "*") |has| |#2| (-365)) (-4407 |has| |#2| (-365)) (-4412 |has| |#2| (-365)) (-4406 |has| |#2| (-365)) (-4411 . T) (-4409 . T) (-4408 . T)) ((|HasCategory| |#2| (QUOTE (-365)))) (-818 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}))."))) @@ -3210,7 +3210,7 @@ NIL NIL (-820) ((|constructor| (NIL "The category of ordered commutative integral domains,{} where ordering and the arithmetic operations are compatible \\blankline"))) -((-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) +((-4407 . T) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) NIL (-821) ((|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}"))) @@ -3238,7 +3238,7 @@ NIL NIL (-827 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}."))) -((-4411 . T) (-4412 . T) (-4414 . T)) +((-4408 . T) (-4409 . T) (-4411 . T)) ((|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-233)))) (-828) ((|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."))) @@ -3250,7 +3250,7 @@ NIL NIL (-830 S) ((|constructor| (NIL "to become an in order iterator")) (|min| ((|#1| $) "\\spad{min(u)} returns the smallest entry in the multiset aggregate \\spad{u}."))) -((-4417 . T) (-4407 . T) (-4418 . T)) +((-4414 . T) (-4404 . T) (-4415 . T)) NIL (-831) ((|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."))) @@ -3262,7 +3262,7 @@ NIL NIL (-833 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."))) -((-4414 |has| |#1| (-848))) +((-4411 |has| |#1| (-848))) ((|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-21))) (-2805 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-848)))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (-2805 (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-547)))) (-834 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}."))) @@ -3274,7 +3274,7 @@ NIL NIL (-836 R) ((|constructor| (NIL "Algebra of ADDITIVE operators over a ring."))) -((-4412 |has| |#1| (-172)) (-4411 |has| |#1| (-172)) (-4414 . T)) +((-4409 |has| |#1| (-172)) (-4408 |has| |#1| (-172)) (-4411 . T)) ((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147)))) (-837) ((|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)."))) @@ -3302,13 +3302,13 @@ NIL NIL (-843 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| (($) "\\spad{plusInfinity()} returns +infinity."))) -((-4414 |has| |#1| (-848))) +((-4411 |has| |#1| (-848))) ((|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-21))) (-2805 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-848)))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (-2805 (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-547)))) (-844) ((|constructor| (NIL "Ordered finite sets.")) (|max| (($) "\\spad{max} is the maximum value of \\%.")) (|min| (($) "\\spad{min} is the minimum value of \\%."))) NIL NIL -(-845 -2293 S) +(-845 -4225 S) ((|constructor| (NIL "\\indented{3}{This package provides ordering functions on vectors which} are suitable parameters for OrderedDirectProduct.")) (|reverseLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{reverseLex(v1,{}v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by the reverse lexicographic ordering.")) (|totalLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{totalLex(v1,{}v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by lexicographic ordering.")) (|pureLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{pureLex(v1,{}v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the lexicographic ordering."))) NIL NIL @@ -3322,7 +3322,7 @@ NIL NIL (-848) ((|constructor| (NIL "Ordered sets which are also rings,{} that is,{} domains where the ring operations are compatible with the ordering. \\blankline")) (|abs| (($ $) "\\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."))) -((-4414 . T)) +((-4411 . T)) NIL (-849 S) ((|constructor| (NIL "The class of totally ordered sets,{} that is,{} sets such that for each pair of elements \\spad{(a,{}b)} exactly one of the following relations holds \\spad{a a= (((|Boolean|) $ $) "\\spad{x >= y} is a greater than or equal test.")) (> (((|Boolean|) $ $) "\\spad{x > y} is a greater than test.")) (< (((|Boolean|) $ $) "\\spad{x < y} is a strict total ordering on the elements of the set."))) @@ -3338,19 +3338,19 @@ NIL ((|HasCategory| |#2| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-454))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-172)))) (-852 R) ((|constructor| (NIL "This is the category of univariate skew polynomials over an Ore coefficient ring. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}. This category is an evolution of the types \\indented{2}{MonogenicLinearOperator,{} OppositeMonogenicLinearOperator,{} and} \\indented{2}{NonCommutativeOperatorDivision} developped by Jean Della Dora and Stephen \\spad{M}. Watt.")) (|leftLcm| (($ $ $) "\\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)}.}"))) -((-4411 . T) (-4412 . T) (-4414 . T)) +((-4408 . T) (-4409 . T) (-4411 . T)) NIL (-853 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 (-365))) (|HasCategory| |#1| (QUOTE (-558)))) -(-854 R |sigma| -2916) +(-854 R |sigma| -1545) ((|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."))) -((-4411 . T) (-4412 . T) (-4414 . T)) +((-4408 . T) (-4409 . T) (-4411 . T)) ((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-365)))) -(-855 |x| R |sigma| -2916) +(-855 |x| R |sigma| -1545) ((|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}."))) -((-4411 . T) (-4412 . T) (-4414 . T)) +((-4408 . T) (-4409 . T) (-4411 . T)) ((|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-454))) (|HasCategory| |#2| (QUOTE (-365)))) (-856 R) ((|constructor| (NIL "This package provides orthogonal polynomials as functions on a ring.")) (|legendreP| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{legendreP(n,{}x)} is the \\spad{n}-th Legendre polynomial,{} \\spad{P[n](x)}. These are defined by \\spad{1/sqrt(1-2*x*t+t**2) = sum(P[n](x)*t**n,{} n = 0..)}.")) (|laguerreL| ((|#1| (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|) "\\spad{laguerreL(m,{}n,{}x)} is the associated Laguerre polynomial,{} \\spad{L[n](x)}. This is the \\spad{m}-th derivative of \\spad{L[n](x)}.") ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{laguerreL(n,{}x)} is the \\spad{n}-th Laguerre polynomial,{} \\spad{L[n](x)}. These are defined by \\spad{exp(-t*x/(1-t))/(1-t) = sum(L[n](x)*t**n/n!,{} n = 0..)}.")) (|hermiteH| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{hermiteH(n,{}x)} is the \\spad{n}-th Hermite polynomial,{} \\spad{H[n](x)}. These are defined by \\spad{exp(2*t*x-t**2) = sum(H[n](x)*t**n/n!,{} n = 0..)}.")) (|chebyshevU| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{chebyshevU(n,{}x)} is the \\spad{n}-th Chebyshev polynomial of the second kind,{} \\spad{U[n](x)}. These are defined by \\spad{1/(1-2*t*x+t**2) = sum(T[n](x) *t**n,{} n = 0..)}.")) (|chebyshevT| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{chebyshevT(n,{}x)} is the \\spad{n}-th Chebyshev polynomial of the first kind,{} \\spad{T[n](x)}. These are defined by \\spad{(1-t*x)/(1-2*t*x+t**2) = sum(T[n](x) *t**n,{} n = 0..)}."))) @@ -3394,7 +3394,7 @@ NIL NIL (-866 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") $ $) "\\spad{x/y} division (only works if minimum weight of divisor is zero,{} and if \\spad{R} is a Field)"))) -((-4412 |has| |#1| (-172)) (-4411 |has| |#1| (-172)) (-4414 . T)) +((-4409 |has| |#1| (-172)) (-4408 |has| |#1| (-172)) (-4411 . T)) ((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365)))) (-867 R PS UP) ((|constructor| (NIL "\\indented{1}{This package computes reliable Pad&ea. approximants using} a generalized Viskovatov continued fraction algorithm. Authors: Burge,{} Hassner & Watt. Date Created: April 1987 Date Last Updated: 12 April 1990 Keywords: Pade,{} series Examples: References: \\indented{2}{\"Pade Approximants,{} Part I: Basic Theory\",{} Baker & Graves-Morris.}")) (|padecf| (((|Union| (|ContinuedFraction| |#3|) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) |#2| |#2|) "\\spad{padecf(nd,{}dd,{}ns,{}ds)} computes the approximant as a continued fraction of polynomials (if it exists) for arguments \\spad{nd} (numerator degree of approximant),{} \\spad{dd} (denominator degree of approximant),{} \\spad{ns} (numerator series of function),{} and \\spad{ds} (denominator series of function).")) (|pade| (((|Union| (|Fraction| |#3|) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) |#2| |#2|) "\\spad{pade(nd,{}dd,{}ns,{}ds)} computes the approximant as a quotient of polynomials (if it exists) for arguments \\spad{nd} (numerator degree of approximant),{} \\spad{dd} (denominator degree of approximant),{} \\spad{ns} (numerator series of function),{} and \\spad{ds} (denominator series of function)."))) @@ -3406,19 +3406,19 @@ NIL NIL (-869 |p|) ((|constructor| (NIL "This is the catefory of stream-based representations of \\indented{2}{the \\spad{p}-adic integers.}")) (|root| (($ (|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}."))) -((-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) +((-4407 . T) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) NIL (-870 |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)."))) -((-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) +((-4407 . T) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) NIL (-871 |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)."))) -((-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) +((-4406 . T) (-4412 . T) (-4407 . T) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) ((|HasCategory| (-870 |#1|) (QUOTE (-909))) (|HasCategory| (-870 |#1|) (LIST (QUOTE -1038) (QUOTE (-1175)))) (|HasCategory| (-870 |#1|) (QUOTE (-145))) (|HasCategory| (-870 |#1|) (QUOTE (-147))) (|HasCategory| (-870 |#1|) (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| (-870 |#1|) (QUOTE (-1022))) (|HasCategory| (-870 |#1|) (QUOTE (-820))) (-2805 (|HasCategory| (-870 |#1|) (QUOTE (-820))) (|HasCategory| (-870 |#1|) (QUOTE (-850)))) (|HasCategory| (-870 |#1|) (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| (-870 |#1|) (QUOTE (-1150))) (|HasCategory| (-870 |#1|) (LIST (QUOTE -886) (QUOTE (-381)))) (|HasCategory| (-870 |#1|) (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| (-870 |#1|) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (|HasCategory| (-870 |#1|) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| (-870 |#1|) (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| (-870 |#1|) (QUOTE (-233))) (|HasCategory| (-870 |#1|) (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| (-870 |#1|) (LIST (QUOTE -516) (QUOTE (-1175)) (LIST (QUOTE -870) (|devaluate| |#1|)))) (|HasCategory| (-870 |#1|) (LIST (QUOTE -310) (LIST (QUOTE -870) (|devaluate| |#1|)))) (|HasCategory| (-870 |#1|) (LIST (QUOTE -287) (LIST (QUOTE -870) (|devaluate| |#1|)) (LIST (QUOTE -870) (|devaluate| |#1|)))) (|HasCategory| (-870 |#1|) (QUOTE (-308))) (|HasCategory| (-870 |#1|) (QUOTE (-547))) (|HasCategory| (-870 |#1|) (QUOTE (-850))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-870 |#1|) (QUOTE (-909)))) (-2805 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-870 |#1|) (QUOTE (-909)))) (|HasCategory| (-870 |#1|) (QUOTE (-145))))) (-872 |p| PADIC) ((|constructor| (NIL "This is the category of stream-based representations of \\spad{Qp}.")) (|removeZeroes| (($ (|Integer|) $) "\\spad{removeZeroes(n,{}x)} removes up to \\spad{n} leading zeroes from the \\spad{p}-adic rational \\spad{x}.") (($ $) "\\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)}."))) -((-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) +((-4406 . T) (-4412 . T) (-4407 . T) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) ((|HasCategory| |#2| (QUOTE (-909))) (|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-1175)))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#2| (QUOTE (-1022))) (|HasCategory| |#2| (QUOTE (-820))) (-2805 (|HasCategory| |#2| (QUOTE (-820))) (|HasCategory| |#2| (QUOTE (-850)))) (|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| |#2| (QUOTE (-1150))) (|HasCategory| |#2| (LIST (QUOTE -886) (QUOTE (-381)))) (|HasCategory| |#2| (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| |#2| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (|HasCategory| |#2| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| |#2| (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| |#2| (LIST (QUOTE -516) (QUOTE (-1175)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -287) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-308))) (|HasCategory| |#2| (QUOTE (-547))) (|HasCategory| |#2| (QUOTE (-850))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-909)))) (-2805 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-909)))) (|HasCategory| |#2| (QUOTE (-145))))) (-873 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'}."))) @@ -3479,7 +3479,7 @@ NIL (-887 |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 (-2426 (|HasCategory| |#2| (QUOTE (-1049)))) (-2426 (|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-1175)))))) (-12 (|HasCategory| |#2| (QUOTE (-1049))) (-2426 (|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-1175)))))) (|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-1175))))) +((-12 (-2436 (|HasCategory| |#2| (QUOTE (-1049)))) (-2436 (|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-1175)))))) (-12 (|HasCategory| |#2| (QUOTE (-1049))) (-2436 (|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-1175)))))) (|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-1175))))) (-888 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 @@ -3488,7 +3488,7 @@ NIL ((|constructor| (NIL "A PatternMatchResult is an object internally returned by the pattern matcher; It is either a failed match,{} or a list of matches of the form (var,{} expr) meaning that the variable var matches the expression expr.")) (|satisfy?| (((|Union| (|Boolean|) "failed") $ (|Pattern| |#1|)) "\\spad{satisfy?(r,{} p)} returns \\spad{true} if the matches satisfy the top-level predicate of \\spad{p},{} \\spad{false} if they don\\spad{'t},{} and \"failed\" if not enough variables of \\spad{p} are matched in \\spad{r} to decide.")) (|construct| (($ (|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| |#2|)))) "\\spad{construct([v1,{}e1],{}...,{}[vn,{}en])} returns the match result containing the matches (\\spad{v1},{}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 -(-890 R -2840) +(-890 R -2876) ((|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 @@ -3512,7 +3512,7 @@ NIL ((|PDESolve| (((|Result|) (|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|)))) "\\spad{PDESolve(args)} performs the integration of the function given the strategy or method returned by \\axiomFun{measure}.")) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|)))) "\\spad{measure(R,{}args)} calculates an estimate of the ability of a particular method to solve a problem. \\blankline This method may be either a specific NAG routine or a strategy (such as transforming the function from one which is difficult to one which is easier to solve). \\blankline It will call whichever agents are needed to perform analysis on the problem in order to calculate the measure. There is a parameter,{} labelled \\axiom{sofar},{} which would contain the best compatibility found so far."))) NIL NIL -(-896 UP -2382) +(-896 UP -2386) ((|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 @@ -3530,7 +3530,7 @@ NIL NIL (-900 S) ((|constructor| (NIL "A partial differential ring with differentiations indexed by a parameter type \\spad{S}. \\blankline")) (D (($ $ (|List| |#1|) (|List| (|NonNegativeInteger|))) "\\spad{D(x,{} [s1,{}...,{}sn],{} [n1,{}...,{}nn])} computes multiple partial derivatives,{} \\spadignore{i.e.} \\spad{D(...D(x,{} s1,{} n1)...,{} sn,{} nn)}.") (($ $ |#1| (|NonNegativeInteger|)) "\\spad{D(x,{} s,{} n)} computes multiple partial derivatives,{} \\spadignore{i.e.} \\spad{n}-th derivative of \\spad{x} with respect to \\spad{s}.") (($ $ (|List| |#1|)) "\\spad{D(x,{}[s1,{}...sn])} computes successive partial derivatives,{} \\spadignore{i.e.} \\spad{D(...D(x,{} s1)...,{} sn)}.") (($ $ |#1|) "\\spad{D(x,{}v)} computes the partial derivative of \\spad{x} with respect to \\spad{v}.")) (|differentiate| (($ $ (|List| |#1|) (|List| (|NonNegativeInteger|))) "\\spad{differentiate(x,{} [s1,{}...,{}sn],{} [n1,{}...,{}nn])} computes multiple partial derivatives,{} \\spadignore{i.e.}") (($ $ |#1| (|NonNegativeInteger|)) "\\spad{differentiate(x,{} s,{} n)} computes multiple partial derivatives,{} \\spadignore{i.e.} \\spad{n}-th derivative of \\spad{x} with respect to \\spad{s}.") (($ $ (|List| |#1|)) "\\spad{differentiate(x,{}[s1,{}...sn])} computes successive partial derivatives,{} \\spadignore{i.e.} \\spad{differentiate(...differentiate(x,{} s1)...,{} sn)}.") (($ $ |#1|) "\\spad{differentiate(x,{}v)} computes the partial derivative of \\spad{x} with respect to \\spad{v}."))) -((-4414 . T)) +((-4411 . T)) NIL (-901 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"))) @@ -3542,7 +3542,7 @@ NIL NIL (-903 S) ((|constructor| (NIL "PermutationCategory provides a categorial environment \\indented{1}{for subgroups of bijections of a set (\\spadignore{i.e.} permutations)}")) (< (((|Boolean|) $ $) "\\spad{p < q} is an order relation on permutations. Note: this order is only total if and only if \\spad{S} is totally ordered or \\spad{S} is finite.")) (|orbit| (((|Set| |#1|) $ |#1|) "\\spad{orbit(p,{} el)} returns the orbit of {\\em el} under the permutation \\spad{p},{} \\spadignore{i.e.} the set which is given by applications of the powers of \\spad{p} to {\\em el}.")) (|elt| ((|#1| $ |#1|) "\\spad{elt(p,{} el)} returns the image of {\\em el} under the permutation \\spad{p}.")) (|eval| ((|#1| $ |#1|) "\\spad{eval(p,{} el)} returns the image of {\\em el} under the permutation \\spad{p}.")) (|cycles| (($ (|List| (|List| |#1|))) "\\spad{cycles(lls)} coerces a list list of cycles {\\em lls} to a permutation,{} each cycle being a list with not repetitions,{} is coerced to the permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list,{} then these permutations are mutiplied. Error: if repetitions occur in one cycle.")) (|cycle| (($ (|List| |#1|)) "\\spad{cycle(ls)} coerces a cycle {\\em ls},{} \\spadignore{i.e.} a list with not repetitions to a permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list. Error: if repetitions occur."))) -((-4414 . T)) +((-4411 . T)) NIL (-904 S) ((|constructor| (NIL "PermutationGroup implements permutation groups acting on a set \\spad{S},{} \\spadignore{i.e.} all subgroups of the symmetric group of \\spad{S},{} represented as a list of permutations (generators). Note that therefore the objects are not members of the \\Language category \\spadtype{Group}. Using the idea of base and strong generators by Sims,{} basic routines and algorithms are implemented so that the word problem for permutation groups can be solved.")) (|initializeGroupForWordProblem| (((|Void|) $ (|Integer|) (|Integer|)) "\\spad{initializeGroupForWordProblem(gp,{}m,{}n)} initializes the group {\\em gp} for the word problem. Notes: (1) with a small integer you get shorter words,{} but the routine takes longer than the standard routine for longer words. (2) be careful: invoking this routine will destroy the possibly stored information about your group (but will recompute it again). (3) users need not call this function normally for the soultion of the word problem.") (((|Void|) $) "\\spad{initializeGroupForWordProblem(gp)} initializes the group {\\em gp} for the word problem. Notes: it calls the other function of this name with parameters 0 and 1: {\\em initializeGroupForWordProblem(gp,{}0,{}1)}. Notes: (1) be careful: invoking this routine will destroy the possibly information about your group (but will recompute it again) (2) users need not call this function normally for the soultion of the word problem.")) (<= (((|Boolean|) $ $) "\\spad{gp1 <= gp2} returns \\spad{true} if and only if {\\em gp1} is a subgroup of {\\em gp2}. Note: because of a bug in the parser you have to call this function explicitly by {\\em gp1 <=\\$(PERMGRP S) gp2}.")) (< (((|Boolean|) $ $) "\\spad{gp1 < gp2} returns \\spad{true} if and only if {\\em gp1} is a proper subgroup of {\\em gp2}.")) (|movedPoints| (((|Set| |#1|) $) "\\spad{movedPoints(gp)} returns the points moved by the group {\\em gp}.")) (|wordInGenerators| (((|List| (|NonNegativeInteger|)) (|Permutation| |#1|) $) "\\spad{wordInGenerators(p,{}gp)} returns the word for the permutation \\spad{p} in the original generators of the group {\\em gp},{} represented by the indices of the list,{} given by {\\em generators}.")) (|wordInStrongGenerators| (((|List| (|NonNegativeInteger|)) (|Permutation| |#1|) $) "\\spad{wordInStrongGenerators(p,{}gp)} returns the word for the permutation \\spad{p} in the strong generators of the group {\\em gp},{} represented by the indices of the list,{} given by {\\em strongGenerators}.")) (|member?| (((|Boolean|) (|Permutation| |#1|) $) "\\spad{member?(pp,{}gp)} answers the question,{} whether the permutation {\\em pp} is in the group {\\em gp} or not.")) (|orbits| (((|Set| (|Set| |#1|)) $) "\\spad{orbits(gp)} returns the orbits of the group {\\em gp},{} \\spadignore{i.e.} it partitions the (finite) of all moved points.")) (|orbit| (((|Set| (|List| |#1|)) $ (|List| |#1|)) "\\spad{orbit(gp,{}ls)} returns the orbit of the ordered list {\\em ls} under the group {\\em gp}. Note: return type is \\spad{L} \\spad{L} \\spad{S} temporarily because FSET \\spad{L} \\spad{S} has an error.") (((|Set| (|Set| |#1|)) $ (|Set| |#1|)) "\\spad{orbit(gp,{}els)} returns the orbit of the unordered set {\\em els} under the group {\\em gp}.") (((|Set| |#1|) $ |#1|) "\\spad{orbit(gp,{}el)} returns the orbit of the element {\\em el} under the group {\\em gp},{} \\spadignore{i.e.} the set of all points gained by applying each group element to {\\em el}.")) (|permutationGroup| (($ (|List| (|Permutation| |#1|))) "\\spad{permutationGroup(ls)} coerces a list of permutations {\\em ls} to the group generated by this list.")) (|wordsForStrongGenerators| (((|List| (|List| (|NonNegativeInteger|))) $) "\\spad{wordsForStrongGenerators(gp)} returns the words for the strong generators of the group {\\em gp} in the original generators of {\\em gp},{} represented by their indices in the list,{} given by {\\em generators}.")) (|strongGenerators| (((|List| (|Permutation| |#1|)) $) "\\spad{strongGenerators(gp)} returns strong generators for the group {\\em gp}.")) (|base| (((|List| |#1|) $) "\\spad{base(gp)} returns a base for the group {\\em gp}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(gp)} returns the number of points moved by all permutations of the group {\\em gp}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(gp)} returns the order of the group {\\em gp}.")) (|random| (((|Permutation| |#1|) $) "\\spad{random(gp)} returns a random product of maximal 20 generators of the group {\\em gp}. Note: {\\em random(gp)=random(gp,{}20)}.") (((|Permutation| |#1|) $ (|Integer|)) "\\spad{random(gp,{}i)} returns a random product of maximal \\spad{i} generators of the group {\\em gp}.")) (|elt| (((|Permutation| |#1|) $ (|NonNegativeInteger|)) "\\spad{elt(gp,{}i)} returns the \\spad{i}-th generator of the group {\\em gp}.")) (|generators| (((|List| (|Permutation| |#1|)) $) "\\spad{generators(gp)} returns the generators of the group {\\em gp}.")) (|coerce| (($ (|List| (|Permutation| |#1|))) "\\spad{coerce(ls)} coerces a list of permutations {\\em ls} to the group generated by this list.") (((|List| (|Permutation| |#1|)) $) "\\spad{coerce(gp)} returns the generators of the group {\\em gp}."))) @@ -3550,7 +3550,7 @@ NIL NIL (-905 S) ((|constructor| (NIL "Permutation(\\spad{S}) implements the group of all bijections \\indented{2}{on a set \\spad{S},{} which move only a finite number of points.} \\indented{2}{A permutation is considered as a map from \\spad{S} into \\spad{S}. In particular} \\indented{2}{multiplication is defined as composition of maps:} \\indented{2}{{\\em pi1 * pi2 = pi1 o pi2}.} \\indented{2}{The internal representation of permuatations are two lists} \\indented{2}{of equal length representing preimages and images.}")) (|coerceImages| (($ (|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.")) (|movedPoints| (((|Set| |#1|) $) "\\spad{movedPoints(p)} returns the set of points moved by the permutation \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(p)} retuns the number of points moved by the permutation \\spad{p}.")) (|coerceListOfPairs| (($ (|List| (|List| |#1|))) "\\spad{coerceListOfPairs(lls)} coerces a list of pairs {\\em lls} to a permutation. Error: if not consistent,{} \\spadignore{i.e.} the set of the first elements coincides with the set of second elements. coerce(\\spad{p}) generates output of the permutation \\spad{p} with domain OutputForm.")) (|coerce| (($ (|List| |#1|)) "\\spad{coerce(ls)} coerces a cycle {\\em ls},{} \\spadignore{i.e.} a list with not repetitions to a permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list. Error: if repetitions occur.") (($ (|List| (|List| |#1|))) "\\spad{coerce(lls)} coerces a list of cycles {\\em lls} to a permutation,{} each cycle being a list with 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."))) -((-4414 . T)) +((-4411 . T)) ((-2805 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-850)))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-850)))) (-906 R E |VarSet| S) ((|constructor| (NIL "PolynomialFactorizationByRecursion(\\spad{R},{}\\spad{E},{}\\spad{VarSet},{}\\spad{S}) is used for factorization of sparse univariate polynomials over a domain \\spad{S} of multivariate polynomials over \\spad{R}.")) (|factorSFBRlcUnit| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|List| |#3|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorSFBRlcUnit(p)} returns the square free factorization of polynomial \\spad{p} (see \\spadfun{factorSquareFreeByRecursion}{PolynomialFactorizationByRecursionUnivariate}) in the case where the leading coefficient of \\spad{p} is a unit.")) (|bivariateSLPEBR| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|List| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|) |#3|) "\\spad{bivariateSLPEBR(lp,{}p,{}v)} implements the bivariate case of \\spadfunFrom{solveLinearPolynomialEquationByRecursion}{PolynomialFactorizationByRecursionUnivariate}; its implementation depends on \\spad{R}")) (|randomR| ((|#1|) "\\spad{randomR produces} a random element of \\spad{R}")) (|factorSquareFreeByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorSquareFreeByRecursion(p)} returns the square free factorization of \\spad{p}. This functions performs the recursion step for factorSquareFreePolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorSquareFreePolynomial}).")) (|factorByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorByRecursion(p)} factors polynomial \\spad{p}. This function performs the recursion step for factorPolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorPolynomial})")) (|solveLinearPolynomialEquationByRecursion| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|List| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{solveLinearPolynomialEquationByRecursion([p1,{}...,{}pn],{}p)} returns the list of polynomials \\spad{[q1,{}...,{}qn]} such that \\spad{sum qi/pi = p / prod \\spad{pi}},{} a recursion step for solveLinearPolynomialEquation as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{solveLinearPolynomialEquation}). If no such list of \\spad{qi} exists,{} then \"failed\" is returned."))) @@ -3566,13 +3566,13 @@ NIL ((|HasCategory| |#1| (QUOTE (-145)))) (-909) ((|constructor| (NIL "This is the category of domains that know \"enough\" about themselves in order to factor univariate polynomials over themselves. This will be used in future releases for supporting factorization over finitely generated coefficient fields,{} it is not yet available in the current release of axiom.")) (|charthRoot| (((|Union| $ "failed") $) "\\spad{charthRoot(r)} returns the \\spad{p}\\spad{-}th root of \\spad{r},{} or \"failed\" if none exists in the domain.")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(m)} returns a vector of elements,{} not all zero,{} whose \\spad{p}\\spad{-}th powers (\\spad{p} is the characteristic of the domain) are a solution of the homogenous linear system represented by \\spad{m},{} or \"failed\" is there is no such vector.")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| $)) "failed") (|List| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{solveLinearPolynomialEquation([f1,{} ...,{} fn],{} g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod \\spad{fi} = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists.")) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) "\\spad{gcdPolynomial(p,{}q)} returns the \\spad{gcd} of the univariate polynomials \\spad{p} \\spad{qnd} \\spad{q}.")) (|factorSquareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorSquareFreePolynomial(p)} factors the univariate polynomial \\spad{p} into irreducibles where \\spad{p} is known to be square free and primitive with respect to its main variable.")) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorPolynomial(p)} returns the factorization into irreducibles of the univariate polynomial \\spad{p}.")) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{squareFreePolynomial(p)} returns the square-free factorization of the univariate polynomial \\spad{p}."))) -((-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) +((-4407 . T) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) NIL (-910 |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."))) -((-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) +((-4406 . T) (-4412 . T) (-4407 . T) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) ((|HasCategory| $ (QUOTE (-147))) (|HasCategory| $ (QUOTE (-145))) (|HasCategory| $ (QUOTE (-370)))) -(-911 R0 -2382 UP UPUP R) +(-911 R0 -2386 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 @@ -3586,7 +3586,7 @@ NIL NIL (-914 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."))) -((-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) +((-4406 . T) (-4412 . T) (-4407 . T) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) NIL (-915 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."))) @@ -3600,7 +3600,7 @@ NIL ((|constructor| (NIL "PermutationGroupExamples provides permutation groups for some classes of groups: symmetric,{} alternating,{} dihedral,{} cyclic,{} direct products of cyclic,{} which are in fact the finite abelian groups of symmetric groups called Young subgroups. Furthermore,{} Rubik\\spad{'s} group as permutation group of 48 integers and a list of sporadic simple groups derived from the atlas of finite groups.")) (|youngGroup| (((|PermutationGroup| (|Integer|)) (|Partition|)) "\\spad{youngGroup(lambda)} constructs the direct product of the symmetric groups given by the parts of the partition {\\em lambda}.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{youngGroup([n1,{}...,{}nk])} constructs the direct product of the symmetric groups {\\em Sn1},{}...,{}{\\em Snk}.")) (|rubiksGroup| (((|PermutationGroup| (|Integer|))) "\\spad{rubiksGroup constructs} the permutation group representing Rubic\\spad{'s} Cube acting on integers {\\em 10*i+j} for {\\em 1 <= i <= 6},{} {\\em 1 <= j <= 8}. The faces of Rubik\\spad{'s} Cube are labelled in the obvious way Front,{} Right,{} Up,{} Down,{} Left,{} Back and numbered from 1 to 6 in this given ordering,{} the pieces on each face (except the unmoveable center piece) are clockwise numbered from 1 to 8 starting with the piece in the upper left corner. The moves of the cube are represented as permutations on these pieces,{} represented as a two digit integer {\\em ij} where \\spad{i} is the numer of theface (1 to 6) and \\spad{j} is the number of the piece on this face. The remaining ambiguities are resolved by looking at the 6 generators,{} which represent a 90 degree turns of the faces,{} or from the following pictorial description. Permutation group representing Rubic\\spad{'s} Cube acting on integers 10*i+j for 1 \\spad{<=} \\spad{i} \\spad{<=} 6,{} 1 \\spad{<=} \\spad{j} \\spad{<=8}. \\blankline\\begin{verbatim}Rubik's Cube: +-----+ +-- B where: marks Side # : / U /|/ / / | F(ront) <-> 1 L --> +-----+ R| R(ight) <-> 2 | | + U(p) <-> 3 | F | / D(own) <-> 4 | |/ L(eft) <-> 5 +-----+ B(ack) <-> 6 ^ | DThe Cube's surface: The pieces on each side +---+ (except the unmoveable center |567| piece) are clockwise numbered |4U8| from 1 to 8 starting with the |321| piece in the upper left +---+---+---+ corner (see figure on the |781|123|345| left). The moves of the cube |6L2|8F4|2R6| are represented as |543|765|187| permutations on these pieces. +---+---+---+ Each of the pieces is |123| represented as a two digit |8D4| integer ij where i is the |765| # of the side ( 1 to 6 for +---+ F to B (see table above )) |567| and j is the # of the piece. |4B8| |321| +---+\\end{verbatim}")) (|janko2| (((|PermutationGroup| (|Integer|))) "\\spad{janko2 constructs} the janko group acting on the integers 1,{}...,{}100.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{janko2(\\spad{li})} constructs the janko group acting on the 100 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. Error: if {\\em \\spad{li}} has less or more than 100 different entries")) (|mathieu24| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu24 constructs} the mathieu group acting on the integers 1,{}...,{}24.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu24(\\spad{li})} constructs the mathieu group acting on the 24 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. Error: if {\\em \\spad{li}} has less or more than 24 different entries.")) (|mathieu23| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu23 constructs} the mathieu group acting on the integers 1,{}...,{}23.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu23(\\spad{li})} constructs the mathieu group acting on the 23 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. Error: if {\\em \\spad{li}} has less or more than 23 different entries.")) (|mathieu22| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu22 constructs} the mathieu group acting on the integers 1,{}...,{}22.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu22(\\spad{li})} constructs the mathieu group acting on the 22 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. Error: if {\\em \\spad{li}} has less or more than 22 different entries.")) (|mathieu12| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu12 constructs} the mathieu group acting on the integers 1,{}...,{}12.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu12(\\spad{li})} constructs the mathieu group acting on the 12 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed Error: if {\\em \\spad{li}} has less or more than 12 different entries.")) (|mathieu11| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu11 constructs} the mathieu group acting on the integers 1,{}...,{}11.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu11(\\spad{li})} constructs the mathieu group acting on the 11 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. error,{} if {\\em \\spad{li}} has less or more than 11 different entries.")) (|dihedralGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{dihedralGroup([i1,{}...,{}ik])} constructs the dihedral group of order 2k acting on the integers out of {\\em i1},{}...,{}{\\em ik}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{dihedralGroup(n)} constructs the dihedral group of order 2n acting on integers 1,{}...,{}\\spad{N}.")) (|cyclicGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{cyclicGroup([i1,{}...,{}ik])} constructs the cyclic group of order \\spad{k} acting on the integers {\\em i1},{}...,{}{\\em ik}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{cyclicGroup(n)} constructs the cyclic group of order \\spad{n} acting on the integers 1,{}...,{}\\spad{n}.")) (|abelianGroup| (((|PermutationGroup| (|Integer|)) (|List| (|PositiveInteger|))) "\\spad{abelianGroup([n1,{}...,{}nk])} constructs the abelian group that is the direct product of cyclic groups with order {\\em \\spad{ni}}.")) (|alternatingGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{alternatingGroup(\\spad{li})} constructs the alternating group acting on the integers in the list {\\em \\spad{li}},{} generators are in general the {\\em n-2}-cycle {\\em (\\spad{li}.3,{}...,{}\\spad{li}.n)} and the 3-cycle {\\em (\\spad{li}.1,{}\\spad{li}.2,{}\\spad{li}.3)},{} if \\spad{n} is odd and product of the 2-cycle {\\em (\\spad{li}.1,{}\\spad{li}.2)} with {\\em n-2}-cycle {\\em (\\spad{li}.3,{}...,{}\\spad{li}.n)} and the 3-cycle {\\em (\\spad{li}.1,{}\\spad{li}.2,{}\\spad{li}.3)},{} if \\spad{n} is even. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{alternatingGroup(n)} constructs the alternating group {\\em An} acting on the integers 1,{}...,{}\\spad{n},{} generators are in general the {\\em n-2}-cycle {\\em (3,{}...,{}n)} and the 3-cycle {\\em (1,{}2,{}3)} if \\spad{n} is odd and the product of the 2-cycle {\\em (1,{}2)} with {\\em n-2}-cycle {\\em (3,{}...,{}n)} and the 3-cycle {\\em (1,{}2,{}3)} if \\spad{n} is even.")) (|symmetricGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{symmetricGroup(\\spad{li})} constructs the symmetric group acting on the integers in the list {\\em \\spad{li}},{} generators are the cycle given by {\\em \\spad{li}} and the 2-cycle {\\em (\\spad{li}.1,{}\\spad{li}.2)}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{symmetricGroup(n)} constructs the symmetric group {\\em Sn} acting on the integers 1,{}...,{}\\spad{n},{} generators are the {\\em n}-cycle {\\em (1,{}...,{}n)} and the 2-cycle {\\em (1,{}2)}."))) NIL NIL -(-918 -2382) +(-918 -2386) ((|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 @@ -3610,17 +3610,17 @@ NIL NIL (-920) ((|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| $)) "\\spad{principalIdeal([f1,{}...,{}fn])} returns a record whose generator component is a generator of the ideal generated by \\spad{[f1,{}...,{}fn]} whose coef component satisfies \\spad{generator = sum (input.i * coef.i)}"))) -((-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) +((-4407 . T) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) NIL (-921) ((|constructor| (NIL "\\spadtype{PositiveInteger} provides functions for \\indented{2}{positive integers.}")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} means multiplication is commutative : x*y = \\spad{y*x}")) (|gcd| (($ $ $) "\\spad{gcd(a,{}b)} computes the greatest common divisor of two positive integers \\spad{a} and \\spad{b}."))) -(((-4419 "*") . T)) +(((-4416 "*") . T)) NIL -(-922 -2382 P) +(-922 -2386 P) ((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,{}l2)} \\undocumented"))) NIL NIL -(-923 |xx| -2382) +(-923 |xx| -2386) ((|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 @@ -3644,7 +3644,7 @@ NIL ((|constructor| (NIL "This package exports plotting tools")) (|calcRanges| (((|List| (|Segment| (|DoubleFloat|))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{calcRanges(l)} \\undocumented"))) NIL NIL -(-929 R -2382) +(-929 R -2386) ((|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 @@ -3656,7 +3656,7 @@ NIL ((|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 -(-932 S R -2382) +(-932 S R -2386) ((|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 @@ -3676,11 +3676,11 @@ NIL ((|constructor| (NIL "This package provides pattern matching functions on polynomials.")) (|patternMatch| (((|PatternMatchResult| |#1| |#5|) |#5| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|)) "\\spad{patternMatch(p,{} pat,{} res)} matches the pattern \\spad{pat} to the polynomial \\spad{p}; res contains the variables of \\spad{pat} which are already matched and their matches.") (((|PatternMatchResult| |#1| |#5|) |#5| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|) (|Mapping| (|PatternMatchResult| |#1| |#5|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|))) "\\spad{patternMatch(p,{} pat,{} res,{} vmatch)} matches the pattern \\spad{pat} to the polynomial \\spad{p}. \\spad{res} contains the variables of \\spad{pat} which are already matched and their matches; vmatch is the matching function to use on the variables."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -886) (|devaluate| |#1|)))) -(-937 R -2382 -2840) +(-937 R -2386 -2876) ((|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 -(-938 -2840) +(-938 -2876) ((|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 @@ -3702,7 +3702,7 @@ NIL NIL (-943 R) ((|constructor| (NIL "This domain implements points in coordinate space"))) -((-4418 . T) (-4417 . T)) +((-4415 . T) (-4414 . T)) ((-2805 (-12 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538)))) (-2805 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099)))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| (-566) (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-726))) (|HasCategory| |#1| (QUOTE (-1049))) (-12 (|HasCategory| |#1| (QUOTE (-1002))) (|HasCategory| |#1| (QUOTE (-1049)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-944 |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}."))) @@ -3723,12 +3723,12 @@ NIL (-948 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 (-909))) (|HasAttribute| |#2| (QUOTE -4415)) (|HasCategory| |#2| (QUOTE (-454))) (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#4| (LIST (QUOTE -886) (QUOTE (-381)))) (|HasCategory| |#2| (LIST (QUOTE -886) (QUOTE (-381)))) (|HasCategory| |#4| (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| |#2| (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| |#4| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (|HasCategory| |#2| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (|HasCategory| |#4| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| |#2| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| |#4| (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-538))))) +((|HasCategory| |#2| (QUOTE (-909))) (|HasAttribute| |#2| (QUOTE -4412)) (|HasCategory| |#2| (QUOTE (-454))) (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#4| (LIST (QUOTE -886) (QUOTE (-381)))) (|HasCategory| |#2| (LIST (QUOTE -886) (QUOTE (-381)))) (|HasCategory| |#4| (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| |#2| (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| |#4| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (|HasCategory| |#2| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (|HasCategory| |#4| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| |#2| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| |#4| (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-538))))) (-949 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}."))) -(((-4419 "*") |has| |#1| (-172)) (-4410 |has| |#1| (-558)) (-4415 |has| |#1| (-6 -4415)) (-4412 . T) (-4411 . T) (-4414 . T)) +(((-4416 "*") |has| |#1| (-172)) (-4407 |has| |#1| (-558)) (-4412 |has| |#1| (-6 -4412)) (-4409 . T) (-4408 . T) (-4411 . T)) NIL -(-950 E V R P -2382) +(-950 E V R P -2386) ((|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 @@ -3738,9 +3738,9 @@ NIL NIL (-952 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}."))) -(((-4419 "*") |has| |#1| (-172)) (-4410 |has| |#1| (-558)) (-4415 |has| |#1| (-6 -4415)) (-4412 . T) (-4411 . T) (-4414 . T)) -((|HasCategory| |#1| (QUOTE (-909))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-909)))) (-2805 (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-909)))) (-2805 (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-172))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (-12 (|HasCategory| (-1175) (LIST (QUOTE -886) (QUOTE (-381)))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-381))))) (-12 (|HasCategory| (-1175) (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-566))))) (-12 (|HasCategory| (-1175) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381)))))) (-12 (|HasCategory| (-1175) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566)))))) (-12 (|HasCategory| (-1175) (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))) (-2805 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566)))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-365))) (|HasAttribute| |#1| (QUOTE -4415)) (|HasCategory| |#1| (QUOTE (-454))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-909)))) (-2805 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-145))))) -(-953 E V R P -2382) +(((-4416 "*") |has| |#1| (-172)) (-4407 |has| |#1| (-558)) (-4412 |has| |#1| (-6 -4412)) (-4409 . T) (-4408 . T) (-4411 . T)) +((|HasCategory| |#1| (QUOTE (-909))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-909)))) (-2805 (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-909)))) (-2805 (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-172))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (-12 (|HasCategory| (-1175) (LIST (QUOTE -886) (QUOTE (-381)))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-381))))) (-12 (|HasCategory| (-1175) (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-566))))) (-12 (|HasCategory| (-1175) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381)))))) (-12 (|HasCategory| (-1175) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566)))))) (-12 (|HasCategory| (-1175) (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))) (-2805 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566)))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-365))) (|HasAttribute| |#1| (QUOTE -4412)) (|HasCategory| |#1| (QUOTE (-454))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-909)))) (-2805 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-145))))) +(-953 E V R P -2386) ((|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| $) "\\spad{numer(x)} \\undocumented"))) NIL ((|HasCategory| |#3| (QUOTE (-454)))) @@ -3762,13 +3762,13 @@ NIL NIL (-958 S) ((|constructor| (NIL "\\indented{1}{This provides a fast array type with no bound checking on elt\\spad{'s}.} Minimum index is 0 in this type,{} cannot be changed"))) -((-4418 . T) (-4417 . T)) +((-4415 . T) (-4414 . T)) ((-2805 (-12 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538)))) (-2805 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099)))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| (-566) (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-959) ((|constructor| (NIL "Category for the functions defined by integrals.")) (|integral| (($ $ (|SegmentBinding| $)) "\\spad{integral(f,{} x = a..b)} returns the formal definite integral of \\spad{f} \\spad{dx} for \\spad{x} between \\spad{a} and \\spad{b}.") (($ $ (|Symbol|)) "\\spad{integral(f,{} x)} returns the formal integral of \\spad{f} \\spad{dx}."))) NIL NIL -(-960 -2382) +(-960 -2386) ((|constructor| (NIL "PrimitiveElement provides functions to compute primitive elements in algebraic extensions.")) (|primitiveElement| (((|Record| (|:| |coef| (|List| (|Integer|))) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#1|))) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|)) (|Symbol|)) "\\spad{primitiveElement([p1,{}...,{}pn],{} [a1,{}...,{}an],{} a)} returns \\spad{[[c1,{}...,{}cn],{} [q1,{}...,{}qn],{} q]} such that then \\spad{k(a1,{}...,{}an) = k(a)},{} where \\spad{a = a1 c1 + ... + an cn},{} \\spad{\\spad{ai} = \\spad{qi}(a)},{} and \\spad{q(a) = 0}. The \\spad{pi}\\spad{'s} are the defining polynomials for the \\spad{ai}\\spad{'s}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}.") (((|Record| (|:| |coef| (|List| (|Integer|))) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#1|))) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{primitiveElement([p1,{}...,{}pn],{} [a1,{}...,{}an])} returns \\spad{[[c1,{}...,{}cn],{} [q1,{}...,{}qn],{} q]} such that then \\spad{k(a1,{}...,{}an) = k(a)},{} where \\spad{a = a1 c1 + ... + an cn},{} \\spad{\\spad{ai} = \\spad{qi}(a)},{} and \\spad{q(a) = 0}. The \\spad{pi}\\spad{'s} are the defining polynomials for the \\spad{ai}\\spad{'s}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}.") (((|Record| (|:| |coef1| (|Integer|)) (|:| |coef2| (|Integer|)) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|Polynomial| |#1|) (|Symbol|) (|Polynomial| |#1|) (|Symbol|)) "\\spad{primitiveElement(p1,{} a1,{} p2,{} a2)} returns \\spad{[c1,{} c2,{} q]} such that \\spad{k(a1,{} a2) = k(a)} where \\spad{a = c1 a1 + c2 a2,{} and q(a) = 0}. The \\spad{pi}\\spad{'s} are the defining polynomials for the \\spad{ai}\\spad{'s}. The \\spad{p2} may involve \\spad{a1},{} but \\spad{p1} must not involve a2. This operation uses \\spadfun{resultant}."))) NIL NIL @@ -3782,11 +3782,11 @@ NIL NIL (-963 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}"))) -(((-4419 "*") |has| |#1| (-172)) (-4410 |has| |#1| (-558)) (-4415 |has| |#1| (-6 -4415)) (-4411 . T) (-4412 . T) (-4414 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-558))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-2805 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566)))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-454))) (-12 (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-131)))) (|HasAttribute| |#1| (QUOTE -4415))) +(((-4416 "*") |has| |#1| (-172)) (-4407 |has| |#1| (-558)) (-4412 |has| |#1| (-6 -4412)) (-4408 . T) (-4409 . T) (-4411 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-558))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-2805 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566)))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-454))) (-12 (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-131)))) (|HasAttribute| |#1| (QUOTE -4412))) (-964 A B) ((|constructor| (NIL "This domain implements cartesian product")) (|selectsecond| ((|#2| $) "\\spad{selectsecond(x)} \\undocumented")) (|selectfirst| ((|#1| $) "\\spad{selectfirst(x)} \\undocumented")) (|makeprod| (($ |#1| |#2|) "\\spad{makeprod(a,{}b)} \\undocumented"))) -((-4414 -12 (|has| |#2| (-475)) (|has| |#1| (-475)))) +((-4411 -12 (|has| |#2| (-475)) (|has| |#1| (-475)))) ((-2805 (-12 (|HasCategory| |#1| (QUOTE (-793))) (|HasCategory| |#2| (QUOTE (-793)))) (-12 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#2| (QUOTE (-850))))) (-12 (|HasCategory| |#1| (QUOTE (-793))) (|HasCategory| |#2| (QUOTE (-793)))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-793))) (|HasCategory| |#2| (QUOTE (-793))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-793))) (|HasCategory| |#2| (QUOTE (-793))))) (-12 (|HasCategory| |#1| (QUOTE (-475))) (|HasCategory| |#2| (QUOTE (-475)))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-475))) (|HasCategory| |#2| (QUOTE (-475)))) (-12 (|HasCategory| |#1| (QUOTE (-726))) (|HasCategory| |#2| (QUOTE (-726))))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (QUOTE (-370)))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-475))) (|HasCategory| |#2| (QUOTE (-475)))) (-12 (|HasCategory| |#1| (QUOTE (-726))) (|HasCategory| |#2| (QUOTE (-726)))) (-12 (|HasCategory| |#1| (QUOTE (-793))) (|HasCategory| |#2| (QUOTE (-793))))) (-12 (|HasCategory| |#1| (QUOTE (-726))) (|HasCategory| |#2| (QUOTE (-726)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#2| (QUOTE (-850))))) (-965) ((|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|) $) "\\spad{name(p)} returns the name of property \\spad{p}"))) @@ -3802,7 +3802,7 @@ NIL NIL (-968 S) ((|constructor| (NIL "A priority queue is a bag of items from an ordered set where the item extracted is always the maximum element.")) (|merge!| (($ $ $) "\\spad{merge!(q,{}q1)} destructively changes priority queue \\spad{q} to include the values from priority queue \\spad{q1}.")) (|merge| (($ $ $) "\\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}."))) -((-4417 . T) (-4418 . T)) +((-4414 . T) (-4415 . T)) NIL (-969 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}}"))) @@ -3822,7 +3822,7 @@ NIL NIL (-973 |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}."))) -(((-4419 "*") |has| |#1| (-172)) (-4410 |has| |#1| (-558)) (-4411 . T) (-4412 . T) (-4414 . T)) +(((-4416 "*") |has| |#1| (-172)) (-4407 |has| |#1| (-558)) (-4408 . T) (-4409 . T) (-4411 . T)) NIL (-974) ((|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}."))) @@ -3834,7 +3834,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-558)))) (-976 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."))) -((-4417 . T)) +((-4414 . T)) NIL (-977 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."))) @@ -3850,7 +3850,7 @@ NIL NIL (-980 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}."))) -((-4418 . T) (-4417 . T)) +((-4415 . T) (-4414 . T)) NIL (-981 R1 R2) ((|constructor| (NIL "This package \\undocumented")) (|map| (((|Point| |#2|) (|Mapping| |#2| |#1|) (|Point| |#1|)) "\\spad{map(f,{}p)} \\undocumented"))) @@ -3868,7 +3868,7 @@ NIL ((|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 -(-985 K R UP -2382) +(-985 K R UP -2386) ((|constructor| (NIL "In this package \\spad{K} is a finite field,{} \\spad{R} is a ring of univariate polynomials over \\spad{K},{} and \\spad{F} is a monogenic algebra over \\spad{R}. We require that \\spad{F} is monogenic,{} \\spadignore{i.e.} that \\spad{F = K[x,{}y]/(f(x,{}y))},{} because the integral basis algorithm used will factor the polynomial \\spad{f(x,{}y)}. The package provides a function to compute the integral closure of \\spad{R} in the quotient field of \\spad{F} as well as a function to compute a \"local integral basis\" at a specific prime.")) (|reducedDiscriminant| ((|#2| |#3|) "\\spad{reducedDiscriminant(up)} \\undocumented")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) |#2|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,{}basisDen,{}basisInv] } containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of the framed algebra \\spad{F}. \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If 'basis' is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix 'basisInv' contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if 'basisInv' is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,{}basisDen,{}basisInv] } containing information regarding the integral closure of \\spad{R} in the quotient field of the framed algebra \\spad{F}. \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If 'basis' is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix 'basisInv' contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if 'basisInv' is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}."))) NIL NIL @@ -3898,7 +3898,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-909))) (|HasCategory| |#2| (QUOTE (-547))) (|HasCategory| |#2| (QUOTE (-308))) (|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-1175)))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#2| (QUOTE (-1022))) (|HasCategory| |#2| (QUOTE (-820))) (|HasCategory| |#2| (QUOTE (-850))) (|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| |#2| (QUOTE (-1150)))) (-992 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}."))) -((-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) +((-4406 . T) (-4412 . T) (-4407 . T) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) NIL (-993 |n| K) ((|constructor| (NIL "This domain provides modest support for quadratic forms.")) (|elt| ((|#2| $ (|DirectProduct| |#1| |#2|)) "\\spad{elt(qf,{}v)} evaluates the quadratic form \\spad{qf} on the vector \\spad{v},{} producing a scalar.")) (|matrix| (((|SquareMatrix| |#1| |#2|) $) "\\spad{matrix(qf)} creates a square matrix from the quadratic form \\spad{qf}.")) (|quadraticForm| (($ (|SquareMatrix| |#1| |#2|)) "\\spad{quadraticForm(m)} creates a quadratic form from a symmetric,{} square matrix \\spad{m}."))) @@ -3910,7 +3910,7 @@ NIL NIL (-995 S) ((|constructor| (NIL "A queue is a bag where the first item inserted is the first item extracted.")) (|back| ((|#1| $) "\\spad{back(q)} returns the element at the back of the queue. The queue \\spad{q} is unchanged by this operation. Error: if \\spad{q} is empty.")) (|front| ((|#1| $) "\\spad{front(q)} returns the element at the front of the queue. The queue \\spad{q} is unchanged by this operation. Error: if \\spad{q} is empty.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length(q)} returns the number of elements in the queue. Note: \\axiom{length(\\spad{q}) = \\spad{#q}}.")) (|rotate!| (($ $) "\\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."))) -((-4417 . T) (-4418 . T)) +((-4414 . T) (-4415 . T)) NIL (-996 S R) ((|constructor| (NIL "\\spadtype{QuaternionCategory} describes the category of quaternions and implements functions that are not representation specific.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(q)} returns \\spad{q} as a rational number,{} or \"failed\" if this is not possible. Note: if \\spad{rational?(q)} is \\spad{true},{} the conversion can be done and the rational number will be returned.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(q)} tries to convert \\spad{q} into a rational number. Error: if this is not possible. If \\spad{rational?(q)} is \\spad{true},{} the conversion will be done and the rational number returned.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(q)} returns {\\it \\spad{true}} if all the imaginary parts of \\spad{q} are zero and the real part can be converted into a rational number,{} and {\\it \\spad{false}} otherwise.")) (|abs| ((|#2| $) "\\spad{abs(q)} computes the absolute value of quaternion \\spad{q} (sqrt of norm).")) (|real| ((|#2| $) "\\spad{real(q)} extracts the real part of quaternion \\spad{q}.")) (|quatern| (($ |#2| |#2| |#2| |#2|) "\\spad{quatern(r,{}i,{}j,{}k)} constructs a quaternion from scalars.")) (|norm| ((|#2| $) "\\spad{norm(q)} computes the norm of \\spad{q} (the sum of the squares of the components).")) (|imagK| ((|#2| $) "\\spad{imagK(q)} extracts the imaginary \\spad{k} part of quaternion \\spad{q}.")) (|imagJ| ((|#2| $) "\\spad{imagJ(q)} extracts the imaginary \\spad{j} part of quaternion \\spad{q}.")) (|imagI| ((|#2| $) "\\spad{imagI(q)} extracts the imaginary \\spad{i} part of quaternion \\spad{q}.")) (|conjugate| (($ $) "\\spad{conjugate(q)} negates the imaginary parts of quaternion \\spad{q}."))) @@ -3918,7 +3918,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-547))) (|HasCategory| |#2| (QUOTE (-1059))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#2| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-850))) (|HasCategory| |#2| (QUOTE (-291)))) (-997 R) ((|constructor| (NIL "\\spadtype{QuaternionCategory} describes the category of quaternions and implements functions that are not representation specific.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(q)} returns \\spad{q} as a rational number,{} or \"failed\" if this is not possible. Note: 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}."))) -((-4410 |has| |#1| (-291)) (-4411 . T) (-4412 . T) (-4414 . T)) +((-4407 |has| |#1| (-291)) (-4408 . T) (-4409 . T) (-4411 . T)) NIL (-998 QR R QS S) ((|constructor| (NIL "\\spadtype{QuaternionCategoryFunctions2} implements functions between two quaternion domains. The function \\spadfun{map} is used by the system interpreter to coerce between quaternion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,{}u)} maps \\spad{f} onto the component parts of the quaternion \\spad{u}."))) @@ -3926,11 +3926,11 @@ NIL NIL (-999 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.}"))) -((-4410 |has| |#1| (-291)) (-4411 . T) (-4412 . T) (-4414 . T)) +((-4407 |has| |#1| (-291)) (-4408 . T) (-4409 . T) (-4411 . T)) ((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#1| (QUOTE (-365))) (-2805 (|HasCategory| |#1| (QUOTE (-291))) (|HasCategory| |#1| (QUOTE (-365)))) (|HasCategory| |#1| (QUOTE (-291))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| |#1| (LIST (QUOTE -516) (QUOTE (-1175)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -287) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175)))) (-2805 (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-365)))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-1059))) (|HasCategory| |#1| (QUOTE (-547)))) (-1000 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}."))) -((-4417 . T) (-4418 . T)) +((-4414 . T) (-4415 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (-1001 S) ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|Fraction| (|Integer|))) "\\spad{x ** y} is the rational exponentiation of \\spad{x} by the power \\spad{y}.")) (|nthRoot| (($ $ (|Integer|)) "\\spad{nthRoot(x,{}n)} returns the \\spad{n}th root of \\spad{x}.")) (|sqrt| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) @@ -3940,13 +3940,13 @@ NIL ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|Fraction| (|Integer|))) "\\spad{x ** y} is the rational exponentiation of \\spad{x} by the power \\spad{y}.")) (|nthRoot| (($ $ (|Integer|)) "\\spad{nthRoot(x,{}n)} returns the \\spad{n}th root of \\spad{x}.")) (|sqrt| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) NIL NIL -(-1003 -2382 UP UPUP |radicnd| |n|) +(-1003 -2386 UP UPUP |radicnd| |n|) ((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x})."))) -((-4410 |has| (-409 |#2|) (-365)) (-4415 |has| (-409 |#2|) (-365)) (-4409 |has| (-409 |#2|) (-365)) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) +((-4407 |has| (-409 |#2|) (-365)) (-4412 |has| (-409 |#2|) (-365)) (-4406 |has| (-409 |#2|) (-365)) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) ((|HasCategory| (-409 |#2|) (QUOTE (-145))) (|HasCategory| (-409 |#2|) (QUOTE (-147))) (|HasCategory| (-409 |#2|) (QUOTE (-351))) (-2805 (|HasCategory| (-409 |#2|) (QUOTE (-365))) (|HasCategory| (-409 |#2|) (QUOTE (-351)))) (|HasCategory| (-409 |#2|) (QUOTE (-365))) (|HasCategory| (-409 |#2|) (QUOTE (-370))) (-2805 (-12 (|HasCategory| (-409 |#2|) (QUOTE (-233))) (|HasCategory| (-409 |#2|) (QUOTE (-365)))) (|HasCategory| (-409 |#2|) (QUOTE (-351)))) (-2805 (-12 (|HasCategory| (-409 |#2|) (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| (-409 |#2|) (QUOTE (-365)))) (-12 (|HasCategory| (-409 |#2|) (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| (-409 |#2|) (QUOTE (-351))))) (|HasCategory| (-409 |#2|) (LIST (QUOTE -639) (QUOTE (-566)))) (-2805 (|HasCategory| (-409 |#2|) (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| (-409 |#2|) (QUOTE (-365)))) (|HasCategory| (-409 |#2|) (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| (-409 |#2|) (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-370))) (-12 (|HasCategory| (-409 |#2|) (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| (-409 |#2|) (QUOTE (-365)))) (-12 (|HasCategory| (-409 |#2|) (QUOTE (-233))) (|HasCategory| (-409 |#2|) (QUOTE (-365))))) (-1004 |bb|) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating decimal expansions or more generally as repeating expansions in any base.")) (|fractRadix| (($ (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{fractRadix(pre,{}cyc)} creates a fractional radix expansion from a list of prefix ragits and a list of cyclic ragits. 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."))) -((-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) +((-4406 . T) (-4412 . T) (-4407 . T) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) ((|HasCategory| (-566) (QUOTE (-909))) (|HasCategory| (-566) (LIST (QUOTE -1038) (QUOTE (-1175)))) (|HasCategory| (-566) (QUOTE (-145))) (|HasCategory| (-566) (QUOTE (-147))) (|HasCategory| (-566) (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| (-566) (QUOTE (-1022))) (|HasCategory| (-566) (QUOTE (-820))) (-2805 (|HasCategory| (-566) (QUOTE (-820))) (|HasCategory| (-566) (QUOTE (-850)))) (|HasCategory| (-566) (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| (-566) (QUOTE (-1150))) (|HasCategory| (-566) (LIST (QUOTE -886) (QUOTE (-381)))) (|HasCategory| (-566) (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| (-566) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (|HasCategory| (-566) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| (-566) (QUOTE (-233))) (|HasCategory| (-566) (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| (-566) (LIST (QUOTE -516) (QUOTE (-1175)) (QUOTE (-566)))) (|HasCategory| (-566) (LIST (QUOTE -310) (QUOTE (-566)))) (|HasCategory| (-566) (LIST (QUOTE -287) (QUOTE (-566)) (QUOTE (-566)))) (|HasCategory| (-566) (QUOTE (-308))) (|HasCategory| (-566) (QUOTE (-547))) (|HasCategory| (-566) (QUOTE (-850))) (|HasCategory| (-566) (LIST (QUOTE -639) (QUOTE (-566)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-566) (QUOTE (-909)))) (-2805 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-566) (QUOTE (-909)))) (|HasCategory| (-566) (QUOTE (-145))))) (-1005) ((|constructor| (NIL "This package provides tools for creating radix expansions.")) (|radix| (((|Any|) (|Fraction| (|Integer|)) (|Integer|)) "\\spad{radix(x,{}b)} converts \\spad{x} to a radix expansion in base \\spad{b}."))) @@ -3967,7 +3967,7 @@ NIL (-1009 A S) ((|constructor| (NIL "A recursive aggregate over a type \\spad{S} is a model for a a directed graph containing values of type \\spad{S}. Recursively,{} a recursive aggregate is a {\\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 -4418)) (|HasCategory| |#2| (QUOTE (-1099)))) +((|HasAttribute| |#1| (QUOTE -4415)) (|HasCategory| |#2| (QUOTE (-1099)))) (-1010 S) ((|constructor| (NIL "A recursive aggregate over a type \\spad{S} is a model for a a directed graph containing values of type \\spad{S}. Recursively,{} a recursive aggregate is a {\\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 @@ -3978,21 +3978,21 @@ NIL NIL (-1012) ((|constructor| (NIL "\\axiomType{RealClosedField} provides common acces functions for all real closed fields.")) (|approximate| (((|Fraction| (|Integer|)) $ $) "\\axiom{approximate(\\spad{n},{}\\spad{p})} gives an approximation of \\axiom{\\spad{n}} that has precision \\axiom{\\spad{p}}")) (|rename| (($ $ (|OutputForm|)) "\\axiom{rename(\\spad{x},{}name)} gives a new number that prints as name")) (|rename!| (($ $ (|OutputForm|)) "\\axiom{rename!(\\spad{x},{}name)} changes the way \\axiom{\\spad{x}} is printed")) (|sqrt| (($ (|Integer|)) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ (|Fraction| (|Integer|))) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $ (|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}}"))) -((-4410 . T) (-4415 . T) (-4409 . T) (-4412 . T) (-4411 . T) ((-4419 "*") . T) (-4414 . T)) +((-4407 . T) (-4412 . T) (-4406 . T) (-4409 . T) (-4408 . T) ((-4416 "*") . T) (-4411 . T)) NIL -(-1013 R -2382) +(-1013 R -2386) ((|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 -(-1014 R -2382) +(-1014 R -2386) ((|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 -(-1015 -2382 UP) +(-1015 -2386 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 -(-1016 -2382 UP) +(-1016 -2386 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 @@ -4026,9 +4026,9 @@ NIL NIL (-1024 |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"))) -((-4410 . T) (-4415 . T) (-4409 . T) (-4412 . T) (-4411 . T) ((-4419 "*") . T) (-4414 . T)) +((-4407 . T) (-4412 . T) (-4406 . T) (-4409 . T) (-4408 . T) ((-4416 "*") . T) (-4411 . T)) ((-2805 (|HasCategory| (-409 (-566)) (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| (-409 (-566)) (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| (-409 (-566)) (LIST (QUOTE -1038) (QUOTE (-566))))) -(-1025 -2382 L) +(-1025 -2386 L) ((|constructor| (NIL "\\spadtype{ReductionOfOrder} provides functions for reducing the order of linear ordinary differential equations once some solutions are known.")) (|ReduceOrder| (((|Record| (|:| |eq| |#2|) (|:| |op| (|List| |#1|))) |#2| (|List| |#1|)) "\\spad{ReduceOrder(op,{} [f1,{}...,{}fk])} returns \\spad{[op1,{}[g1,{}...,{}gk]]} such that for any solution \\spad{z} of \\spad{op1 z = 0},{} \\spad{y = gk \\int(g_{k-1} \\int(... \\int(g1 \\int z)...)} is a solution of \\spad{op y = 0}. Each \\spad{\\spad{fi}} must satisfy \\spad{op \\spad{fi} = 0}.") ((|#2| |#2| |#1|) "\\spad{ReduceOrder(op,{} s)} returns \\spad{op1} such that for any solution \\spad{z} of \\spad{op1 z = 0},{} \\spad{y = s \\int z} is a solution of \\spad{op y = 0}. \\spad{s} must satisfy \\spad{op s = 0}."))) NIL NIL @@ -4038,12 +4038,12 @@ NIL ((|HasCategory| |#1| (QUOTE (-1099)))) (-1027 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."))) -((-4418 . T) (-4417 . T)) +((-4415 . T) (-4414 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1099))) (|HasCategory| |#4| (LIST (QUOTE -310) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#4| (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#3| (QUOTE (-370))) (|HasCategory| |#4| (LIST (QUOTE -613) (QUOTE (-862))))) (-1028 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(\\spad{pi},{}n)} returns the matrix {\\em (deltai,{}\\spad{pi}(i))} (Kronecker delta) if the permutation {\\em \\spad{pi}} is in list notation and permutes {\\em {1,{}2,{}...,{}n}}.") (((|Matrix| (|Integer|)) (|Permutation| (|Integer|)) (|Integer|)) "\\spad{permutationRepresentation(\\spad{pi},{}n)} returns the matrix {\\em (deltai,{}\\spad{pi}(i))} (Kronecker delta) for a permutation {\\em \\spad{pi}} of {\\em {1,{}2,{}...,{}n}}.")) (|tensorProduct| (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{tensorProduct([a1,{}...ak])} calculates the list of Kronecker products of each matrix {\\em \\spad{ai}} with itself for {1 \\spad{<=} \\spad{i} \\spad{<=} \\spad{k}}. Note: If the list of matrices corresponds to a group representation (repr. of generators) of one group,{} then these matrices correspond to the tensor product of the representation with itself.") (((|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{tensorProduct(a)} calculates the Kronecker product of the matrix {\\em a} with itself.") (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{tensorProduct([a1,{}...,{}ak],{}[b1,{}...,{}bk])} calculates the list of Kronecker products of the matrices {\\em \\spad{ai}} and {\\em \\spad{bi}} for {1 \\spad{<=} \\spad{i} \\spad{<=} \\spad{k}}. Note: If each list of matrices corresponds to a group representation (repr. of generators) of one group,{} then these matrices correspond to the tensor product of the two representations.") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{tensorProduct(a,{}b)} calculates the Kronecker product of the matrices {\\em a} and \\spad{b}. Note: if each matrix corresponds to a group representation (repr. of generators) of one group,{} then these matrices correspond to the tensor product of the two representations.")) (|symmetricTensors| (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|PositiveInteger|)) "\\spad{symmetricTensors(la,{}n)} applies to each \\spad{m}-by-\\spad{m} square matrix in the list {\\em la} the irreducible,{} polynomial representation of the general linear group {\\em GLm} which corresponds to the partition {\\em (n,{}0,{}...,{}0)} of \\spad{n}. Error: if the matrices in {\\em la} are not square matrices. Note: this corresponds to the symmetrization of the representation with the trivial representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the symmetric tensors of the \\spad{n}-fold tensor product.") (((|Matrix| |#1|) (|Matrix| |#1|) (|PositiveInteger|)) "\\spad{symmetricTensors(a,{}n)} applies to the \\spad{m}-by-\\spad{m} square matrix {\\em a} the irreducible,{} polynomial representation of the general linear group {\\em GLm} which corresponds to the partition {\\em (n,{}0,{}...,{}0)} of \\spad{n}. Error: if {\\em a} is not a square matrix. Note: this corresponds to the symmetrization of the representation with the trivial representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the symmetric tensors of the \\spad{n}-fold tensor product.")) (|createGenericMatrix| (((|Matrix| (|Polynomial| |#1|)) (|NonNegativeInteger|)) "\\spad{createGenericMatrix(m)} creates a square matrix of dimension \\spad{k} whose entry at the \\spad{i}-th row and \\spad{j}-th column is the indeterminate {\\em x[i,{}j]} (double subscripted).")) (|antisymmetricTensors| (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|PositiveInteger|)) "\\spad{antisymmetricTensors(la,{}n)} applies to each \\spad{m}-by-\\spad{m} square matrix in the list {\\em la} the irreducible,{} polynomial representation of the general linear group {\\em GLm} which corresponds to the partition {\\em (1,{}1,{}...,{}1,{}0,{}0,{}...,{}0)} of \\spad{n}. Error: if \\spad{n} is greater than \\spad{m}. Note: this corresponds to the symmetrization of the representation with the sign representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the antisymmetric tensors of the \\spad{n}-fold tensor product.") (((|Matrix| |#1|) (|Matrix| |#1|) (|PositiveInteger|)) "\\spad{antisymmetricTensors(a,{}n)} applies to the square matrix {\\em a} the irreducible,{} polynomial representation of the general linear group {\\em GLm},{} where \\spad{m} is the number of rows of {\\em a},{} which corresponds to the partition {\\em (1,{}1,{}...,{}1,{}0,{}0,{}...,{}0)} of \\spad{n}. Error: if \\spad{n} is greater than \\spad{m}. Note: this corresponds to the symmetrization of the representation with the sign representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the antisymmetric tensors of the \\spad{n}-fold tensor product."))) NIL -((|HasAttribute| |#1| (QUOTE (-4419 "*")))) +((|HasAttribute| |#1| (QUOTE (-4416 "*")))) (-1029 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 @@ -4064,14 +4064,14 @@ NIL ((|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 -(-1034 -2382 |Expon| |VarSet| |FPol| |LFPol|) +(-1034 -2386 |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"))) -(((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) +(((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) NIL (-1035) ((|constructor| (NIL "A domain used to return the results from a call to the NAG Library. It prints as a list of names and types,{} though the user may choose to display values automatically if he or she wishes.")) (|showArrayValues| (((|Boolean|) (|Boolean|)) "\\spad{showArrayValues(true)} forces the values of array components to be \\indented{1}{displayed rather than just their types.}")) (|showScalarValues| (((|Boolean|) (|Boolean|)) "\\spad{showScalarValues(true)} forces the values of scalar components to be \\indented{1}{displayed rather than just their types.}"))) -((-4417 . T) (-4418 . T)) -((-12 (|HasCategory| (-2 (|:| -2010 (-1175)) (|:| -2818 (-52))) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2010 (-1175)) (|:| -2818 (-52))) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2010) (QUOTE (-1175))) (LIST (QUOTE |:|) (QUOTE -2818) (QUOTE (-52))))))) (-2805 (|HasCategory| (-2 (|:| -2010 (-1175)) (|:| -2818 (-52))) (QUOTE (-1099))) (|HasCategory| (-52) (QUOTE (-1099)))) (-2805 (|HasCategory| (-2 (|:| -2010 (-1175)) (|:| -2818 (-52))) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2010 (-1175)) (|:| -2818 (-52))) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-52) (QUOTE (-1099))) (|HasCategory| (-52) (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-2 (|:| -2010 (-1175)) (|:| -2818 (-52))) (LIST (QUOTE -614) (QUOTE (-538)))) (-12 (|HasCategory| (-52) (QUOTE (-1099))) (|HasCategory| (-52) (LIST (QUOTE -310) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2010 (-1175)) (|:| -2818 (-52))) (QUOTE (-1099))) (|HasCategory| (-1175) (QUOTE (-850))) (|HasCategory| (-52) (QUOTE (-1099))) (-2805 (|HasCategory| (-2 (|:| -2010 (-1175)) (|:| -2818 (-52))) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-52) (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-52) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -2010 (-1175)) (|:| -2818 (-52))) (LIST (QUOTE -613) (QUOTE (-862))))) +((-4414 . T) (-4415 . T)) +((-12 (|HasCategory| (-2 (|:| -2050 (-1175)) (|:| -2849 (-52))) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2050 (-1175)) (|:| -2849 (-52))) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2050) (QUOTE (-1175))) (LIST (QUOTE |:|) (QUOTE -2849) (QUOTE (-52))))))) (-2805 (|HasCategory| (-2 (|:| -2050 (-1175)) (|:| -2849 (-52))) (QUOTE (-1099))) (|HasCategory| (-52) (QUOTE (-1099)))) (-2805 (|HasCategory| (-2 (|:| -2050 (-1175)) (|:| -2849 (-52))) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2050 (-1175)) (|:| -2849 (-52))) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-52) (QUOTE (-1099))) (|HasCategory| (-52) (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-2 (|:| -2050 (-1175)) (|:| -2849 (-52))) (LIST (QUOTE -614) (QUOTE (-538)))) (-12 (|HasCategory| (-52) (QUOTE (-1099))) (|HasCategory| (-52) (LIST (QUOTE -310) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2050 (-1175)) (|:| -2849 (-52))) (QUOTE (-1099))) (|HasCategory| (-1175) (QUOTE (-850))) (|HasCategory| (-52) (QUOTE (-1099))) (-2805 (|HasCategory| (-2 (|:| -2050 (-1175)) (|:| -2849 (-52))) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-52) (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-52) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -2050 (-1175)) (|:| -2849 (-52))) (LIST (QUOTE -613) (QUOTE (-862))))) (-1036) ((|constructor| (NIL "This domain represents `return' expressions.")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression returned by `e'."))) NIL @@ -4114,7 +4114,7 @@ NIL NIL (-1046 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}."))) -((-4418 . T) (-4417 . T)) +((-4415 . T) (-4414 . T)) ((-12 (|HasCategory| (-780 |#1| (-864 |#2|)) (QUOTE (-1099))) (|HasCategory| (-780 |#1| (-864 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -780) (|devaluate| |#1|) (LIST (QUOTE -864) (|devaluate| |#2|)))))) (|HasCategory| (-780 |#1| (-864 |#2|)) (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| (-780 |#1| (-864 |#2|)) (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| (-864 |#2|) (QUOTE (-370))) (|HasCategory| (-780 |#1| (-864 |#2|)) (LIST (QUOTE -613) (QUOTE (-862))))) (-1047) ((|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"))) @@ -4126,9 +4126,9 @@ NIL NIL (-1049) ((|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."))) -((-4414 . T)) +((-4411 . T)) NIL -(-1050 |xx| -2382) +(-1050 |xx| -2386) ((|constructor| (NIL "This package exports rational interpolation algorithms"))) NIL NIL @@ -4142,11 +4142,11 @@ NIL ((|HasCategory| |#4| (QUOTE (-308))) (|HasCategory| |#4| (QUOTE (-365))) (|HasCategory| |#4| (QUOTE (-558))) (|HasCategory| |#4| (QUOTE (-172)))) (-1053 |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"))) -((-4417 . T) (-4412 . T) (-4411 . T)) +((-4414 . T) (-4409 . T) (-4408 . T)) NIL (-1054 |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}."))) -((-4417 . T) (-4412 . T) (-4411 . T)) +((-4414 . T) (-4409 . T) (-4408 . T)) ((|HasCategory| |#3| (QUOTE (-172))) (-2805 (-12 (|HasCategory| |#3| (QUOTE (-172))) (|HasCategory| |#3| (LIST (QUOTE -310) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-365))) (|HasCategory| |#3| (LIST (QUOTE -310) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1099))) (|HasCategory| |#3| (LIST (QUOTE -310) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -614) (QUOTE (-538)))) (-2805 (|HasCategory| |#3| (QUOTE (-172))) (|HasCategory| |#3| (QUOTE (-365)))) (|HasCategory| |#3| (QUOTE (-365))) (|HasCategory| |#3| (QUOTE (-1099))) (|HasCategory| |#3| (QUOTE (-308))) (|HasCategory| |#3| (QUOTE (-558))) (-12 (|HasCategory| |#3| (QUOTE (-1099))) (|HasCategory| |#3| (LIST (QUOTE -310) (|devaluate| |#3|)))) (|HasCategory| |#3| (LIST (QUOTE -613) (QUOTE (-862))))) (-1055 |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}."))) @@ -4166,7 +4166,7 @@ NIL NIL (-1059) ((|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."))) -((-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) +((-4406 . T) (-4412 . T) (-4407 . T) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) NIL (-1060 |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| $) "\\axiom{left(rootChar)} is the left bound of the isolating interval"))) @@ -4174,19 +4174,19 @@ NIL NIL (-1061) ((|constructor| (NIL "\\spadtype{RomanNumeral} provides functions for converting \\indented{1}{integers to roman numerals.}")) (|roman| (($ (|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."))) -((-4405 . T) (-4409 . T) (-4404 . T) (-4415 . T) (-4416 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) +((-4402 . T) (-4406 . T) (-4401 . T) (-4412 . T) (-4413 . T) (-4407 . T) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) NIL (-1062) ((|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}"))) -((-4417 . T) (-4418 . T)) -((-12 (|HasCategory| (-2 (|:| -2010 (-1175)) (|:| -2818 (-52))) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2010 (-1175)) (|:| -2818 (-52))) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2010) (QUOTE (-1175))) (LIST (QUOTE |:|) (QUOTE -2818) (QUOTE (-52))))))) (-2805 (|HasCategory| (-2 (|:| -2010 (-1175)) (|:| -2818 (-52))) (QUOTE (-1099))) (|HasCategory| (-52) (QUOTE (-1099)))) (-2805 (|HasCategory| (-2 (|:| -2010 (-1175)) (|:| -2818 (-52))) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2010 (-1175)) (|:| -2818 (-52))) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-52) (QUOTE (-1099))) (|HasCategory| (-52) (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-2 (|:| -2010 (-1175)) (|:| -2818 (-52))) (LIST (QUOTE -614) (QUOTE (-538)))) (-12 (|HasCategory| (-52) (QUOTE (-1099))) (|HasCategory| (-52) (LIST (QUOTE -310) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2010 (-1175)) (|:| -2818 (-52))) (QUOTE (-1099))) (|HasCategory| (-1175) (QUOTE (-850))) (|HasCategory| (-52) (QUOTE (-1099))) (-2805 (|HasCategory| (-2 (|:| -2010 (-1175)) (|:| -2818 (-52))) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-52) (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-52) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -2010 (-1175)) (|:| -2818 (-52))) (LIST (QUOTE -613) (QUOTE (-862))))) +((-4414 . T) (-4415 . T)) +((-12 (|HasCategory| (-2 (|:| -2050 (-1175)) (|:| -2849 (-52))) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2050 (-1175)) (|:| -2849 (-52))) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2050) (QUOTE (-1175))) (LIST (QUOTE |:|) (QUOTE -2849) (QUOTE (-52))))))) (-2805 (|HasCategory| (-2 (|:| -2050 (-1175)) (|:| -2849 (-52))) (QUOTE (-1099))) (|HasCategory| (-52) (QUOTE (-1099)))) (-2805 (|HasCategory| (-2 (|:| -2050 (-1175)) (|:| -2849 (-52))) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2050 (-1175)) (|:| -2849 (-52))) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-52) (QUOTE (-1099))) (|HasCategory| (-52) (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-2 (|:| -2050 (-1175)) (|:| -2849 (-52))) (LIST (QUOTE -614) (QUOTE (-538)))) (-12 (|HasCategory| (-52) (QUOTE (-1099))) (|HasCategory| (-52) (LIST (QUOTE -310) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2050 (-1175)) (|:| -2849 (-52))) (QUOTE (-1099))) (|HasCategory| (-1175) (QUOTE (-850))) (|HasCategory| (-52) (QUOTE (-1099))) (-2805 (|HasCategory| (-2 (|:| -2050 (-1175)) (|:| -2849 (-52))) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-52) (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-52) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -2050 (-1175)) (|:| -2849 (-52))) (LIST (QUOTE -613) (QUOTE (-862))))) (-1063 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| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}."))) NIL ((|HasCategory| |#2| (QUOTE (-454))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| |#2| (QUOTE (-547))) (|HasCategory| |#2| (LIST (QUOTE -38) (QUOTE (-566)))) (|HasCategory| |#2| (LIST (QUOTE -992) (QUOTE (-566)))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#4| (LIST (QUOTE -614) (QUOTE (-1175))))) (-1064 R E V) ((|constructor| (NIL "A category for general multi-variate polynomials with coefficients in a ring,{} variables in an ordered set,{} and exponents from an ordered abelian monoid,{} with a \\axiomOp{sup} operation. When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\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}}."))) -(((-4419 "*") |has| |#1| (-172)) (-4410 |has| |#1| (-558)) (-4415 |has| |#1| (-6 -4415)) (-4412 . T) (-4411 . T) (-4414 . T)) +(((-4416 "*") |has| |#1| (-172)) (-4407 |has| |#1| (-558)) (-4412 |has| |#1| (-6 -4412)) (-4409 . T) (-4408 . T) (-4411 . T)) NIL (-1065) ((|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'."))) @@ -4210,7 +4210,7 @@ NIL NIL (-1070 R E V P) ((|constructor| (NIL "The category of regular triangular sets,{} introduced under the name regular chains in [1] (and other papers). In [3] it is proved that regular triangular sets and towers of simple extensions of a field are equivalent notions. In the following definitions,{} all polynomials and ideals are taken from the polynomial ring \\spad{k[x1,{}...,{}xn]} where \\spad{k} is the fraction field of \\spad{R}. The triangular set \\spad{[t1,{}...,{}tm]} is regular iff for every \\spad{i} the initial of \\spad{ti+1} is invertible in the tower of simple extensions associated with \\spad{[t1,{}...,{}\\spad{ti}]}. A family \\spad{[T1,{}...,{}Ts]} of regular triangular sets is a split of Kalkbrener of a given ideal \\spad{I} iff the radical of \\spad{I} is equal to the intersection of the radical ideals generated by the saturated ideals of the \\spad{[T1,{}...,{}\\spad{Ti}]}. A family \\spad{[T1,{}...,{}Ts]} of regular triangular sets is a split of Kalkbrener of a given triangular set \\spad{T} iff it is a split of Kalkbrener of the saturated ideal of \\spad{T}. Let \\spad{K} be an algebraic closure of \\spad{k}. Assume that \\spad{V} is finite with cardinality \\spad{n} and let \\spad{A} be the affine space \\spad{K^n}. For a regular triangular set \\spad{T} let denote by \\spad{W(T)} the set of regular zeros of \\spad{T}. A family \\spad{[T1,{}...,{}Ts]} of regular triangular sets is a split of Lazard of a given subset \\spad{S} of \\spad{A} iff the union of the \\spad{W(\\spad{Ti})} contains \\spad{S} and is contained in the closure of \\spad{S} (\\spad{w}.\\spad{r}.\\spad{t}. Zariski topology). A family \\spad{[T1,{}...,{}Ts]} of regular triangular sets is a split of Lazard of a given triangular set \\spad{T} if it is a split of Lazard of \\spad{W(T)}. Note that if \\spad{[T1,{}...,{}Ts]} is a split of Lazard of \\spad{T} then it is also a split of Kalkbrener of \\spad{T}. The converse is \\spad{false}. This category provides operations related to both kinds of splits,{} the former being related to ideals decomposition whereas the latter deals with varieties decomposition. See the example illustrating the \\spadtype{RegularTriangularSet} constructor for more explanations about decompositions by means of regular triangular sets. \\newline References : \\indented{1}{[1] \\spad{M}. KALKBRENER \"Three contributions to elimination theory\"} \\indented{5}{\\spad{Phd} Thesis,{} University of Linz,{} Austria,{} 1991.} \\indented{1}{[2] \\spad{M}. KALKBRENER \"Algorithmic properties of polynomial rings\"} \\indented{5}{Journal of Symbol. Comp. 1998} \\indented{1}{[3] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)} \\indented{1}{[4] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|zeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|)) "\\spad{zeroSetSplit(lp,{}clos?)} returns \\spad{lts} a split of Kalkbrener of the radical ideal associated with \\spad{lp}. If \\spad{clos?} is \\spad{false},{} it is also a decomposition of the variety associated with \\spad{lp} into the regular zero set of the \\spad{ts} in \\spad{lts} (or,{} in other words,{} a split of Lazard of this variety). See the example illustrating the \\spadtype{RegularTriangularSet} constructor for more explanations about decompositions by means of regular triangular sets.")) (|extend| (((|List| $) (|List| |#4|) (|List| $)) "\\spad{extend(lp,{}lts)} returns the same as \\spad{concat([extend(lp,{}ts) for ts in lts])|}") (((|List| $) (|List| |#4|) $) "\\spad{extend(lp,{}ts)} returns \\spad{ts} if \\spad{empty? lp} \\spad{extend(p,{}ts)} if \\spad{lp = [p]} else \\spad{extend(first lp,{} extend(rest lp,{} ts))}") (((|List| $) |#4| (|List| $)) "\\spad{extend(p,{}lts)} returns the same as \\spad{concat([extend(p,{}ts) for ts in lts])|}") (((|List| $) |#4| $) "\\spad{extend(p,{}ts)} assumes that \\spad{p} is a non-constant polynomial whose main variable is greater than any variable of \\spad{ts}. Then it returns a split of Kalkbrener of \\spad{ts+p}. This may not be \\spad{ts+p} itself,{} if for instance \\spad{ts+p} is not a regular triangular set.")) (|internalAugment| (($ (|List| |#4|) $) "\\spad{internalAugment(lp,{}ts)} returns \\spad{ts} if \\spad{lp} is empty otherwise returns \\spad{internalAugment(rest lp,{} internalAugment(first lp,{} ts))}") (($ |#4| $) "\\spad{internalAugment(p,{}ts)} assumes that \\spad{augment(p,{}ts)} returns a singleton and returns it.")) (|augment| (((|List| $) (|List| |#4|) (|List| $)) "\\spad{augment(lp,{}lts)} returns the same as \\spad{concat([augment(lp,{}ts) for ts in lts])}") (((|List| $) (|List| |#4|) $) "\\spad{augment(lp,{}ts)} returns \\spad{ts} if \\spad{empty? lp},{} \\spad{augment(p,{}ts)} if \\spad{lp = [p]},{} otherwise \\spad{augment(first lp,{} augment(rest lp,{} ts))}") (((|List| $) |#4| (|List| $)) "\\spad{augment(p,{}lts)} returns the same as \\spad{concat([augment(p,{}ts) for ts in lts])}") (((|List| $) |#4| $) "\\spad{augment(p,{}ts)} assumes that \\spad{p} is a non-constant polynomial whose main variable is greater than any variable of \\spad{ts}. This operation assumes also that if \\spad{p} is added to \\spad{ts} the resulting set,{} say \\spad{ts+p},{} is a regular triangular set. Then it returns a split of Kalkbrener of \\spad{ts+p}. This may not be \\spad{ts+p} itself,{} if for instance \\spad{ts+p} is required to be square-free.")) (|intersect| (((|List| $) |#4| (|List| $)) "\\spad{intersect(p,{}lts)} returns the same as \\spad{intersect([p],{}lts)}") (((|List| $) (|List| |#4|) (|List| $)) "\\spad{intersect(lp,{}lts)} returns the same as \\spad{concat([intersect(lp,{}ts) for ts in lts])|}") (((|List| $) (|List| |#4|) $) "\\spad{intersect(lp,{}ts)} returns \\spad{lts} a split of Lazard of the intersection of the affine variety associated with \\spad{lp} and the regular zero set of \\spad{ts}.") (((|List| $) |#4| $) "\\spad{intersect(p,{}ts)} returns the same as \\spad{intersect([p],{}ts)}")) (|squareFreePart| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| $))) |#4| $) "\\spad{squareFreePart(p,{}ts)} returns \\spad{lpwt} such that \\spad{lpwt.i.val} is a square-free polynomial \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower},{} this polynomial being associated with \\spad{p} modulo \\spad{lpwt.i.tower},{} for every \\spad{i}. Moreover,{} the list of the \\spad{lpwt.i.tower} is a split of Kalkbrener of \\spad{ts}. WARNING: This assumes that \\spad{p} is a non-constant polynomial such that if \\spad{p} is added to \\spad{ts},{} then the resulting set is a regular triangular set.")) (|lastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| $))) |#4| |#4| $) "\\spad{lastSubResultant(p1,{}p2,{}ts)} returns \\spad{lpwt} such that \\spad{lpwt.i.val} is a quasi-monic \\spad{gcd} of \\spad{p1} and \\spad{p2} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower},{} for every \\spad{i},{} and such that the list of the \\spad{lpwt.i.tower} is a split of Kalkbrener of \\spad{ts}. Moreover,{} if \\spad{p1} and \\spad{p2} do not have a non-trivial \\spad{gcd} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower} then \\spad{lpwt.i.val} is the resultant of these polynomials \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower}. This assumes that \\spad{p1} and \\spad{p2} have the same maim variable and that this variable is greater that any variable occurring in \\spad{ts}.")) (|lastSubResultantElseSplit| (((|Union| |#4| (|List| $)) |#4| |#4| $) "\\spad{lastSubResultantElseSplit(p1,{}p2,{}ts)} returns either \\spad{g} a quasi-monic \\spad{gcd} of \\spad{p1} and \\spad{p2} \\spad{w}.\\spad{r}.\\spad{t}. the \\spad{ts} or a split of Kalkbrener of \\spad{ts}. This assumes that \\spad{p1} and \\spad{p2} have the same maim variable and that this variable is greater that any variable occurring in \\spad{ts}.")) (|invertibleSet| (((|List| $) |#4| $) "\\spad{invertibleSet(p,{}ts)} returns a split of Kalkbrener of the quotient ideal of the ideal \\axiom{\\spad{I}} by \\spad{p} where \\spad{I} is the radical of saturated of \\spad{ts}.")) (|invertible?| (((|Boolean|) |#4| $) "\\spad{invertible?(p,{}ts)} returns \\spad{true} iff \\spad{p} is invertible in the tower associated with \\spad{ts}.") (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| $))) |#4| $) "\\spad{invertible?(p,{}ts)} returns \\spad{lbwt} where \\spad{lbwt.i} is the result of \\spad{invertibleElseSplit?(p,{}lbwt.i.tower)} and the list of the \\spad{(lqrwt.i).tower} is a split of Kalkbrener of \\spad{ts}.")) (|invertibleElseSplit?| (((|Union| (|Boolean|) (|List| $)) |#4| $) "\\spad{invertibleElseSplit?(p,{}ts)} returns \\spad{true} (resp. \\spad{false}) if \\spad{p} is invertible in the tower associated with \\spad{ts} or returns a split of Kalkbrener of \\spad{ts}.")) (|purelyAlgebraicLeadingMonomial?| (((|Boolean|) |#4| $) "\\spad{purelyAlgebraicLeadingMonomial?(p,{}ts)} returns \\spad{true} iff the main variable of any non-constant iterarted initial of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}.")) (|algebraicCoefficients?| (((|Boolean|) |#4| $) "\\spad{algebraicCoefficients?(p,{}ts)} returns \\spad{true} iff every variable of \\spad{p} which is not the main one of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}.")) (|purelyTranscendental?| (((|Boolean|) |#4| $) "\\spad{purelyTranscendental?(p,{}ts)} returns \\spad{true} iff every variable of \\spad{p} is not algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}")) (|purelyAlgebraic?| (((|Boolean|) $) "\\spad{purelyAlgebraic?(ts)} returns \\spad{true} iff for every algebraic variable \\spad{v} of \\spad{ts} we have \\spad{algebraicCoefficients?(t_v,{}ts_v_-)} where \\spad{ts_v} is \\axiomOpFrom{select}{TriangularSetCategory}(\\spad{ts},{}\\spad{v}) and \\spad{ts_v_-} is \\axiomOpFrom{collectUnder}{TriangularSetCategory}(\\spad{ts},{}\\spad{v}).") (((|Boolean|) |#4| $) "\\spad{purelyAlgebraic?(p,{}ts)} returns \\spad{true} iff every variable of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}."))) -((-4418 . T) (-4417 . T)) +((-4415 . T) (-4414 . T)) NIL (-1071 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."))) @@ -4228,11 +4228,11 @@ NIL ((|constructor| (NIL "This domain implements named rules")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) NIL NIL -(-1075 |Base| R -2382) +(-1075 |Base| R -2386) ((|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 -(-1076 |Base| R -2382) +(-1076 |Base| R -2386) ((|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 @@ -4246,7 +4246,7 @@ NIL NIL (-1079 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."))) -((-4410 |has| |#1| (-365)) (-4415 |has| |#1| (-365)) (-4409 |has| |#1| (-365)) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) +((-4407 |has| |#1| (-365)) (-4412 |has| |#1| (-365)) (-4406 |has| |#1| (-365)) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) ((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-351))) (-2805 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-351)))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-370))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (QUOTE (-365)))) (|HasCategory| |#1| (QUOTE (-351)))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175))))) (-12 (|HasCategory| |#1| (QUOTE (-351))) (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175)))))) (|HasCategory| |#1| (LIST (QUOTE -639) (QUOTE (-566)))) (-2805 (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-365)))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))) (-12 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175))))) (-12 (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (QUOTE (-365))))) (-1080 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}."))) @@ -4274,8 +4274,8 @@ NIL NIL (-1086 R) ((|constructor| (NIL "\\spadtype{SequentialDifferentialPolynomial} implements an ordinary differential polynomial ring in arbitrary number of differential indeterminates,{} with coefficients in a ring. The ranking on the differential indeterminate is sequential. \\blankline"))) -(((-4419 "*") |has| |#1| (-172)) (-4410 |has| |#1| (-558)) (-4415 |has| |#1| (-6 -4415)) (-4412 . T) (-4411 . T) (-4414 . T)) -((|HasCategory| |#1| (QUOTE (-909))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-909)))) (-2805 (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-909)))) (-2805 (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-172))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (-12 (|HasCategory| (-1087 (-1175)) (LIST (QUOTE -886) (QUOTE (-381)))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-381))))) (-12 (|HasCategory| (-1087 (-1175)) (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-566))))) (-12 (|HasCategory| (-1087 (-1175)) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381)))))) (-12 (|HasCategory| (-1087 (-1175)) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566)))))) (-12 (|HasCategory| (-1087 (-1175)) (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))) (-2805 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566)))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| |#1| (QUOTE (-365))) (|HasAttribute| |#1| (QUOTE -4415)) (|HasCategory| |#1| (QUOTE (-454))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-909)))) (-2805 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-145))))) +(((-4416 "*") |has| |#1| (-172)) (-4407 |has| |#1| (-558)) (-4412 |has| |#1| (-6 -4412)) (-4409 . T) (-4408 . T) (-4411 . T)) +((|HasCategory| |#1| (QUOTE (-909))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-909)))) (-2805 (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-909)))) (-2805 (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-172))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (-12 (|HasCategory| (-1087 (-1175)) (LIST (QUOTE -886) (QUOTE (-381)))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-381))))) (-12 (|HasCategory| (-1087 (-1175)) (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-566))))) (-12 (|HasCategory| (-1087 (-1175)) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381)))))) (-12 (|HasCategory| (-1087 (-1175)) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566)))))) (-12 (|HasCategory| (-1087 (-1175)) (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))) (-2805 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566)))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| |#1| (QUOTE (-365))) (|HasAttribute| |#1| (QUOTE -4412)) (|HasCategory| |#1| (QUOTE (-454))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-909)))) (-2805 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-145))))) (-1087 S) ((|constructor| (NIL "\\spadtype{OrderlyDifferentialVariable} adds a commonly used sequential ranking to the set of derivatives of an ordered list of differential indeterminates. A sequential ranking is a ranking \\spadfun{<} of the derivatives with the property that for any derivative \\spad{v},{} there are only a finite number of derivatives \\spad{u} with \\spad{u} \\spadfun{<} \\spad{v}. This domain belongs to \\spadtype{DifferentialVariableCategory}. It defines \\spadfun{weight} to be just \\spadfun{order},{} and it defines a sequential ranking \\spadfun{<} on derivatives \\spad{u} by the lexicographic order on the pair (\\spadfun{variable}(\\spad{u}),{} \\spadfun{order}(\\spad{u}))."))) NIL @@ -4318,7 +4318,7 @@ NIL NIL (-1097 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}."))) -((-4407 . T)) +((-4404 . T)) NIL (-1098 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{=}}")) (|before?| (((|Boolean|) $ $) "spad{before?(\\spad{x},{}\\spad{y})} holds if \\spad{x} comes before \\spad{y} in the internal total ordering used by OpenAxiom.")) (|latex| (((|String|) $) "\\spad{latex(s)} returns a LaTeX-printable output representation of \\spad{s}.")) (|hash| (((|SingleInteger|) $) "\\spad{hash(s)} calculates a hash code for \\spad{s}."))) @@ -4334,7 +4334,7 @@ NIL NIL (-1101 S) ((|constructor| (NIL "A set over a domain \\spad{D} models the usual mathematical notion of a finite set of elements from \\spad{D}. Sets are unordered collections of distinct elements (that is,{} order and duplication does not matter). The notation \\spad{set [a,{}b,{}c]} can be used to create a set and the usual operations such as union and intersection are available to form new sets. In our implementation,{} \\Language{} maintains the entries in sorted order. Specifically,{} the parts function returns the entries as a list in ascending order and the extract operation returns the maximum entry. Given two sets \\spad{s} and \\spad{t} where \\spad{\\#s = m} and \\spad{\\#t = n},{} the complexity of \\indented{2}{\\spad{s = t} is \\spad{O(min(n,{}m))}} \\indented{2}{\\spad{s < t} is \\spad{O(max(n,{}m))}} \\indented{2}{\\spad{union(s,{}t)},{} \\spad{intersect(s,{}t)},{} \\spad{minus(s,{}t)},{} \\spad{symmetricDifference(s,{}t)} is \\spad{O(max(n,{}m))}} \\indented{2}{\\spad{member(x,{}t)} is \\spad{O(n log n)}} \\indented{2}{\\spad{insert(x,{}t)} and \\spad{remove(x,{}t)} is \\spad{O(n)}}"))) -((-4417 . T) (-4407 . T) (-4418 . T)) +((-4414 . T) (-4404 . T) (-4415 . T)) ((-2805 (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-1102 |Str| |Sym| |Int| |Flt| |Expr|) ((|constructor| (NIL "This category allows the manipulation of Lisp values while keeping the grunge fairly localized.")) (|elt| (($ $ (|List| (|Integer|))) "\\spad{elt((a1,{}...,{}an),{} [i1,{}...,{}im])} returns \\spad{(a_i1,{}...,{}a_im)}.") (($ $ (|Integer|)) "\\spad{elt((a1,{}...,{}an),{} i)} returns \\spad{\\spad{ai}}.")) (|#| (((|Integer|) $) "\\spad{\\#((a1,{}...,{}an))} returns \\spad{n}.")) (|cdr| (($ $) "\\spad{cdr((a1,{}...,{}an))} returns \\spad{(a2,{}...,{}an)}.")) (|car| (($ $) "\\spad{car((a1,{}...,{}an))} returns 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 EQ(\\spad{s},{}\\spad{t}) is \\spad{true} in Lisp."))) @@ -4362,7 +4362,7 @@ NIL NIL (-1108 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.}"))) -((-4418 . T) (-4417 . T)) +((-4415 . T) (-4414 . T)) NIL (-1109) ((|constructor| (NIL "SymmetricGroupCombinatoricFunctions contains combinatoric functions concerning symmetric groups and representation theory: list young tableaus,{} improper partitions,{} subsets bijection of Coleman.")) (|unrankImproperPartitions1| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{unrankImproperPartitions1(n,{}m,{}k)} computes the {\\em k}\\spad{-}th improper partition of nonnegative \\spad{n} in at most \\spad{m} nonnegative parts ordered as follows: first,{} in reverse lexicographically according to their non-zero parts,{} then according to their positions (\\spadignore{i.e.} lexicographical order using {\\em subSet}: {\\em [3,{}0,{}0] < [0,{}3,{}0] < [0,{}0,{}3] < [2,{}1,{}0] < [2,{}0,{}1] < [0,{}2,{}1] < [1,{}2,{}0] < [1,{}0,{}2] < [0,{}1,{}2] < [1,{}1,{}1]}). Note: counting of subtrees is done by {\\em numberOfImproperPartitionsInternal}.")) (|unrankImproperPartitions0| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{unrankImproperPartitions0(n,{}m,{}k)} computes the {\\em k}\\spad{-}th improper partition of nonnegative \\spad{n} in \\spad{m} nonnegative parts in reverse lexicographical order. Example: {\\em [0,{}0,{}3] < [0,{}1,{}2] < [0,{}2,{}1] < [0,{}3,{}0] < [1,{}0,{}2] < [1,{}1,{}1] < [1,{}2,{}0] < [2,{}0,{}1] < [2,{}1,{}0] < [3,{}0,{}0]}. Error: if \\spad{k} is negative or too big. Note: counting of subtrees is done by \\spadfunFrom{numberOfImproperPartitions}{SymmetricGroupCombinatoricFunctions}.")) (|subSet| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{subSet(n,{}m,{}k)} calculates the {\\em k}\\spad{-}th {\\em m}-subset of the set {\\em 0,{}1,{}...,{}(n-1)} in the lexicographic order considered as a decreasing map from {\\em 0,{}...,{}(m-1)} into {\\em 0,{}...,{}(n-1)}. See \\spad{S}.\\spad{G}. Williamson: Theorem 1.60. Error: if not {\\em (0 <= m <= n and 0 < = k < (n choose m))}.")) (|numberOfImproperPartitions| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{numberOfImproperPartitions(n,{}m)} computes the number of partitions of the nonnegative integer \\spad{n} in \\spad{m} nonnegative parts with regarding the order (improper partitions). Example: {\\em numberOfImproperPartitions (3,{}3)} is 10,{} since {\\em [0,{}0,{}3],{} [0,{}1,{}2],{} [0,{}2,{}1],{} [0,{}3,{}0],{} [1,{}0,{}2],{} [1,{}1,{}1],{} [1,{}2,{}0],{} [2,{}0,{}1],{} [2,{}1,{}0],{} [3,{}0,{}0]} are the possibilities. Note: this operation has a recursive implementation.")) (|nextPartition| (((|Vector| (|Integer|)) (|List| (|Integer|)) (|Vector| (|Integer|)) (|Integer|)) "\\spad{nextPartition(gamma,{}part,{}number)} generates the partition of {\\em number} which follows {\\em part} according to the right-to-left lexicographical order. The partition has the property that its components do not exceed the corresponding components of {\\em gamma}. the first partition is achieved by {\\em part=[]}. Also,{} {\\em []} indicates that {\\em part} is the last partition.") (((|Vector| (|Integer|)) (|Vector| (|Integer|)) (|Vector| (|Integer|)) (|Integer|)) "\\spad{nextPartition(gamma,{}part,{}number)} generates the partition of {\\em number} which follows {\\em part} according to the right-to-left lexicographical order. The partition has the property that its components do not exceed the corresponding components of {\\em gamma}. The first partition is achieved by {\\em part=[]}. Also,{} {\\em []} indicates that {\\em part} is the last partition.")) (|nextLatticePermutation| (((|List| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|Boolean|)) "\\spad{nextLatticePermutation(lambda,{}lattP,{}constructNotFirst)} generates the lattice permutation according to the proper partition {\\em lambda} succeeding the lattice permutation {\\em lattP} in lexicographical order as long as {\\em constructNotFirst} is \\spad{true}. If {\\em constructNotFirst} is \\spad{false},{} the first lattice permutation is returned. The result {\\em nil} indicates that {\\em lattP} has no successor.")) (|nextColeman| (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|Matrix| (|Integer|))) "\\spad{nextColeman(alpha,{}beta,{}C)} generates the next Coleman matrix of column sums {\\em alpha} and row sums {\\em beta} according to the lexicographical order from bottom-to-top. The first Coleman matrix is achieved by {\\em C=new(1,{}1,{}0)}. Also,{} {\\em new(1,{}1,{}0)} indicates that \\spad{C} is the last Coleman matrix.")) (|makeYoungTableau| (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{makeYoungTableau(lambda,{}gitter)} computes for a given lattice permutation {\\em gitter} and for an improper partition {\\em lambda} the corresponding standard tableau of shape {\\em lambda}. Notes: see {\\em listYoungTableaus}. The entries are from {\\em 0,{}...,{}n-1}.")) (|listYoungTableaus| (((|List| (|Matrix| (|Integer|))) (|List| (|Integer|))) "\\spad{listYoungTableaus(lambda)} where {\\em lambda} is a proper partition generates the list of all standard tableaus of shape {\\em lambda} by means of lattice permutations. The numbers of the lattice permutation are interpreted as column labels. Hence the contents of these lattice permutations are the conjugate of {\\em lambda}. Notes: the functions {\\em nextLatticePermutation} and {\\em makeYoungTableau} are used. The entries are from {\\em 0,{}...,{}n-1}.")) (|inverseColeman| (((|List| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|Matrix| (|Integer|))) "\\spad{inverseColeman(alpha,{}beta,{}C)}: there is a bijection from the set of matrices having nonnegative entries and row sums {\\em alpha},{} column sums {\\em beta} to the set of {\\em Salpha - Sbeta} double cosets of the symmetric group {\\em Sn}. ({\\em Salpha} is the Young subgroup corresponding to the improper partition {\\em alpha}). For such a matrix \\spad{C},{} inverseColeman(\\spad{alpha},{}\\spad{beta},{}\\spad{C}) calculates the lexicographical smallest {\\em \\spad{pi}} in the corresponding double coset. Note: the resulting permutation {\\em \\spad{pi}} of {\\em {1,{}2,{}...,{}n}} is given in list form. Notes: the inverse of this map is {\\em coleman}. For details,{} see James/Kerber.")) (|coleman| (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{coleman(alpha,{}beta,{}\\spad{pi})}: there is a bijection from the set of matrices having nonnegative entries and row sums {\\em alpha},{} column sums {\\em beta} to the set of {\\em Salpha - Sbeta} double cosets of the symmetric group {\\em Sn}. ({\\em Salpha} is the Young subgroup corresponding to the improper partition {\\em alpha}). For a representing element {\\em \\spad{pi}} of such a double coset,{} coleman(\\spad{alpha},{}\\spad{beta},{}\\spad{pi}) generates the Coleman-matrix corresponding to {\\em alpha,{} beta,{} \\spad{pi}}. Note: The permutation {\\em \\spad{pi}} of {\\em {1,{}2,{}...,{}n}} has to be given in list form. Note: the inverse of this map is {\\em inverseColeman} (if {\\em \\spad{pi}} is the lexicographical smallest permutation in the coset). For details see James/Kerber."))) @@ -4378,8 +4378,8 @@ NIL NIL (-1112 |dimtot| |dim1| S) ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying ordered component type. The vectors are ordered as if they were split into two blocks. The dim1 parameter specifies the length of the first block. The ordering is lexicographic between the blocks but acts like \\spadtype{HomogeneousDirectProduct} within each block. 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(LIST (QUOTE -1038) (QUOTE (-566))))) (-12 (|HasCategory| |#3| (QUOTE (-365))) (|HasCategory| |#3| (LIST (QUOTE -1038) (QUOTE (-566))))) (-12 (|HasCategory| |#3| (QUOTE (-370))) (|HasCategory| |#3| (LIST (QUOTE -1038) (QUOTE (-566))))) (-12 (|HasCategory| |#3| (QUOTE (-726))) (|HasCategory| |#3| (LIST (QUOTE -1038) (QUOTE (-566))))) (-12 (|HasCategory| |#3| (QUOTE (-793))) (|HasCategory| |#3| (LIST (QUOTE -1038) (QUOTE (-566))))) (-12 (|HasCategory| |#3| (QUOTE (-848))) (|HasCategory| |#3| (LIST (QUOTE -1038) (QUOTE (-566))))) (-12 (|HasCategory| |#3| (QUOTE (-1049))) (|HasCategory| |#3| (LIST (QUOTE -1038) (QUOTE (-566))))) (-12 (|HasCategory| |#3| (QUOTE (-1099))) (|HasCategory| |#3| (LIST (QUOTE -1038) (QUOTE (-566)))))) (|HasCategory| (-566) (QUOTE (-850))) (-12 (|HasCategory| |#3| (QUOTE (-1049))) (|HasCategory| |#3| (LIST (QUOTE -639) (QUOTE (-566))))) (-12 (|HasCategory| |#3| (QUOTE (-233))) (|HasCategory| |#3| (QUOTE (-1049)))) (-12 (|HasCategory| |#3| (QUOTE (-1049))) (|HasCategory| |#3| (LIST (QUOTE -900) (QUOTE (-1175))))) (-2805 (|HasCategory| |#3| (QUOTE (-1049))) (-12 (|HasCategory| |#3| (QUOTE (-1099))) (|HasCategory| |#3| (LIST (QUOTE -1038) (QUOTE (-566)))))) (-12 (|HasCategory| |#3| (QUOTE (-1099))) (|HasCategory| |#3| (LIST (QUOTE -1038) (QUOTE (-566))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#3| (QUOTE (-1099)))) (|HasAttribute| |#3| (QUOTE -4411)) (|HasCategory| |#3| (QUOTE (-131))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| |#3| (QUOTE (-1099))) (|HasCategory| |#3| (LIST (QUOTE -310) (|devaluate| |#3|))))) (-1113 R |x|) ((|constructor| (NIL "This package produces functions for counting etc. real roots of univariate polynomials in \\spad{x} over \\spad{R},{} which must be an OrderedIntegralDomain")) (|countRealRootsMultiple| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{countRealRootsMultiple(p)} says how many real roots \\spad{p} has,{} counted with multiplicity")) (|SturmHabichtMultiple| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtMultiple(p1,{}p2)} computes \\spad{c_}{+}\\spad{-c_}{-} where \\spad{c_}{+} is the number of real roots of \\spad{p1} with 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 @@ -4388,7 +4388,7 @@ NIL ((|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 -(-1115 R -2382) +(-1115 R -2386) ((|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 @@ -4406,19 +4406,19 @@ NIL NIL (-1119) ((|constructor| (NIL "SingleInteger is intended to support machine integer arithmetic.")) (|Or| (($ $ $) "\\spad{Or(n,{}m)} returns the bit-by-bit logical {\\em or} of the single integers \\spad{n} and \\spad{m}.")) (|And| (($ $ $) "\\spad{And(n,{}m)} returns the bit-by-bit logical {\\em and} of the single integers \\spad{n} and \\spad{m}.")) (|Not| (($ $) "\\spad{Not(n)} returns the bit-by-bit logical {\\em not} of the single integer \\spad{n}.")) (|xor| (($ $ $) "\\spad{xor(n,{}m)} returns the bit-by-bit logical {\\em xor} of the single integers \\spad{n} and \\spad{m}.")) (|not| (($ $) "\\spad{not(n)} returns the bit-by-bit logical {\\em not} of the single integer \\spad{n}.")) (|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."))) -((-4405 . T) (-4409 . T) (-4404 . T) (-4415 . T) (-4416 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) +((-4402 . T) (-4406 . T) (-4401 . T) (-4412 . T) (-4413 . T) (-4407 . T) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) NIL (-1120 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| $) "\\spad{push!(x,{}s)} pushes \\spad{x} onto stack \\spad{s},{} \\spadignore{i.e.} destructively changing \\spad{s} so as to have a new first (top) element \\spad{x}. Afterwards,{} pop!(\\spad{s}) produces \\spad{x} and pop!(\\spad{s}) produces the original \\spad{s}."))) -((-4417 . T) (-4418 . T)) +((-4414 . T) (-4415 . T)) NIL (-1121 S |ndim| R |Row| |Col|) ((|constructor| (NIL "\\spadtype{SquareMatrixCategory} is a general square matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if the matrix is not invertible.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m},{} if that matrix is invertible and returns \"failed\" otherwise.")) (|minordet| ((|#3| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors.")) (|determinant| ((|#3| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}.")) (* ((|#4| |#4| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#5| $ |#5|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.")) (|diagonalProduct| ((|#3| $) "\\spad{diagonalProduct(m)} returns the product of the elements on the diagonal of the matrix \\spad{m}.")) (|trace| ((|#3| $) "\\spad{trace(m)} returns the trace of the matrix \\spad{m}. this is the sum of the elements on the diagonal of the matrix \\spad{m}.")) (|diagonal| ((|#4| $) "\\spad{diagonal(m)} returns a row consisting of the elements on the diagonal of the matrix \\spad{m}.")) (|diagonalMatrix| (($ (|List| |#3|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ |#3|) "\\spad{scalarMatrix(r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}\\spad{'s} on the diagonal and zeroes elsewhere."))) NIL -((|HasCategory| |#3| (QUOTE (-365))) (|HasAttribute| |#3| (QUOTE (-4419 "*"))) (|HasCategory| |#3| (QUOTE (-172)))) +((|HasCategory| |#3| (QUOTE (-365))) (|HasAttribute| |#3| (QUOTE (-4416 "*"))) (|HasCategory| |#3| (QUOTE (-172)))) (-1122 |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."))) -((-4417 . T) (-4411 . T) (-4412 . T) (-4414 . T)) +((-4414 . T) (-4408 . T) (-4409 . T) (-4411 . T)) NIL (-1123 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}."))) @@ -4426,17 +4426,17 @@ NIL NIL (-1124 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."))) -(((-4419 "*") |has| |#1| (-172)) (-4410 |has| |#1| (-558)) (-4415 |has| |#1| (-6 -4415)) (-4412 . T) (-4411 . T) (-4414 . T)) -((|HasCategory| |#1| (QUOTE (-909))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-909)))) (-2805 (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-909)))) (-2805 (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-172))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-381)))) (|HasCategory| |#2| (LIST (QUOTE -886) (QUOTE (-381))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| |#2| (LIST (QUOTE -886) (QUOTE (-566))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (|HasCategory| |#2| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| |#2| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))) (-2805 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566)))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-365))) (|HasAttribute| |#1| (QUOTE -4415)) (|HasCategory| |#1| (QUOTE (-454))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-909)))) (-2805 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-145))))) +(((-4416 "*") |has| |#1| (-172)) (-4407 |has| |#1| (-558)) (-4412 |has| |#1| (-6 -4412)) (-4409 . T) (-4408 . T) (-4411 . T)) +((|HasCategory| |#1| (QUOTE (-909))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-909)))) (-2805 (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-909)))) (-2805 (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-172))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-381)))) (|HasCategory| |#2| (LIST (QUOTE -886) (QUOTE (-381))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| |#2| (LIST (QUOTE -886) (QUOTE (-566))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (|HasCategory| |#2| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| |#2| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))) (-2805 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566)))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-365))) (|HasAttribute| |#1| (QUOTE -4412)) (|HasCategory| |#1| (QUOTE (-454))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-909)))) (-2805 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-145))))) (-1125 |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}."))) -(((-4419 "*") |has| |#1| (-172)) (-4410 |has| |#1| (-558)) (-4412 . T) (-4411 . T) (-4414 . T)) +(((-4416 "*") |has| |#1| (-172)) (-4407 |has| |#1| (-558)) (-4409 . T) (-4408 . T) (-4411 . T)) ((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-365)))) (-1126 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}"))) -((-4418 . T) (-4417 . T)) +((-4415 . T) (-4414 . T)) NIL -(-1127 UP -2382) +(-1127 UP -2386) ((|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 @@ -4490,19 +4490,19 @@ NIL NIL (-1140 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") $) "\\axiom{extractSplittingLeaf(a)} returns the left most leaf (as a tree) whose status is \\spad{false} if any,{} else \"failed\" is returned."))) -((-4417 . T) (-4418 . T)) +((-4414 . T) (-4415 . T)) ((-12 (|HasCategory| (-1139 |#1| |#2|) (LIST (QUOTE -310) (LIST (QUOTE -1139) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1139 |#1| |#2|) (QUOTE (-1099)))) (|HasCategory| (-1139 |#1| |#2|) (QUOTE (-1099))) (-2805 (|HasCategory| (-1139 |#1| |#2|) (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| (-1139 |#1| |#2|) (LIST (QUOTE -310) (LIST (QUOTE -1139) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1139 |#1| |#2|) (QUOTE (-1099))))) (|HasCategory| (-1139 |#1| |#2|) (LIST (QUOTE -613) (QUOTE (-862))))) (-1141 |ndim| R) ((|constructor| (NIL "\\spadtype{SquareMatrix} is a matrix domain of square matrices,{} where the number of rows (= number of columns) is a parameter of the type.")) (|unitsKnown| ((|attribute|) "the invertible matrices are simply the matrices whose determinants are units in the Ring \\spad{R}.")) (|central| ((|attribute|) "the elements of the Ring \\spad{R},{} viewed as diagonal matrices,{} commute with all matrices and,{} indeed,{} are the only matrices which commute with all matrices.")) (|squareMatrix| (($ (|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}."))) -((-4414 . T) (-4406 |has| |#2| (-6 (-4419 "*"))) (-4417 . T) (-4411 . T) (-4412 . T)) -((|HasCategory| |#2| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasAttribute| |#2| (QUOTE (-4419 "*"))) (|HasCategory| |#2| (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| |#2| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-566)))) (-2805 (-12 (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -639) (QUOTE (-566))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -900) (QUOTE (-1175)))))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#2| (QUOTE (-308))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (QUOTE (-365))) (-2805 (|HasAttribute| |#2| (QUOTE (-4419 "*"))) (|HasCategory| |#2| (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| |#2| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| |#2| (QUOTE (-233)))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-172)))) +((-4411 . T) (-4403 |has| |#2| (-6 (-4416 "*"))) (-4414 . T) (-4408 . T) (-4409 . T)) +((|HasCategory| |#2| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasAttribute| |#2| (QUOTE (-4416 "*"))) (|HasCategory| |#2| (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| |#2| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-566)))) (-2805 (-12 (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -639) (QUOTE (-566))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -900) (QUOTE (-1175)))))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#2| (QUOTE (-308))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (QUOTE (-365))) (-2805 (|HasAttribute| |#2| (QUOTE (-4416 "*"))) (|HasCategory| |#2| (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| |#2| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| |#2| (QUOTE (-233)))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-172)))) (-1142 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|) $ $) "\\spad{prefix?(s,{}t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) NIL NIL (-1143) ((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,{}t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|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."))) -((-4418 . T) (-4417 . T)) +((-4415 . T) (-4414 . T)) NIL (-1144 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.}"))) @@ -4510,11 +4510,11 @@ NIL NIL (-1145 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."))) -((-4418 . T) (-4417 . T)) +((-4415 . T) (-4414 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1099))) (|HasCategory| |#4| (LIST (QUOTE -310) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#4| (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#3| (QUOTE (-370))) (|HasCategory| |#4| (LIST (QUOTE -613) (QUOTE (-862))))) (-1146 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}."))) -((-4417 . T) (-4418 . T)) +((-4414 . T) (-4415 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (-1147 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})}."))) @@ -4526,8 +4526,8 @@ NIL NIL (-1149 |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."))) -((-4418 . T)) -((-12 (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2010) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2818) (|devaluate| |#2|)))))) (-2805 (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (QUOTE (-1099))) (|HasCategory| |#2| (QUOTE (-1099)))) (-2805 (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (LIST (QUOTE -614) (QUOTE (-538)))) (-12 (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-850))) (-2805 (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (QUOTE (-1099)))) +((-4415 . T)) +((-12 (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2050) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2849) (|devaluate| |#2|)))))) (-2805 (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (QUOTE (-1099))) (|HasCategory| |#2| (QUOTE (-1099)))) (-2805 (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (LIST (QUOTE -614) (QUOTE (-538)))) (-12 (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-850))) (-2805 (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (QUOTE (-1099)))) (-1150) ((|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 @@ -4550,20 +4550,20 @@ NIL NIL (-1155 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."))) -((-4418 . T)) +((-4415 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| (-566) (QUOTE (-850))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (-1156) ((|constructor| (NIL "A category for string-like objects")) (|string| (($ (|Integer|)) "\\spad{string(i)} returns the decimal representation of \\spad{i} in a string"))) -((-4418 . T) (-4417 . T)) +((-4415 . T) (-4414 . T)) NIL (-1157) NIL -((-4418 . T) (-4417 . T)) +((-4415 . T) (-4414 . T)) ((-2805 (-12 (|HasCategory| (-144) (QUOTE (-850))) (|HasCategory| (-144) (LIST (QUOTE -310) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1099))) (|HasCategory| (-144) (LIST (QUOTE -310) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| (-144) (QUOTE (-850))) (|HasCategory| (-566) (QUOTE (-850))) (|HasCategory| (-144) (QUOTE (-1099))) (|HasCategory| (-144) (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| (-144) (QUOTE (-1099))) (|HasCategory| (-144) (LIST (QUOTE -310) (QUOTE (-144)))))) (-1158 |Entry|) ((|constructor| (NIL "This domain provides tables where the keys are strings. A specialized hash function for strings is used."))) -((-4417 . T) (-4418 . T)) -((-12 (|HasCategory| (-2 (|:| -2010 (-1157)) (|:| -2818 |#1|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2010 (-1157)) (|:| -2818 |#1|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2010) (QUOTE (-1157))) (LIST (QUOTE |:|) (QUOTE -2818) (|devaluate| |#1|)))))) (-2805 (|HasCategory| (-2 (|:| -2010 (-1157)) (|:| -2818 |#1|)) (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-1099)))) (-2805 (|HasCategory| (-2 (|:| -2010 (-1157)) (|:| -2818 |#1|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2010 (-1157)) (|:| -2818 |#1|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-2 (|:| -2010 (-1157)) (|:| -2818 |#1|)) (LIST (QUOTE -614) (QUOTE (-538)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -2010 (-1157)) (|:| -2818 |#1|)) (QUOTE (-1099))) (|HasCategory| (-1157) (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099))) (-2805 (|HasCategory| (-2 (|:| -2010 (-1157)) (|:| -2818 |#1|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -2010 (-1157)) (|:| -2818 |#1|)) (LIST (QUOTE -613) (QUOTE (-862))))) +((-4414 . T) (-4415 . 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(|power| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{power(a,{}f)} returns the power series \\spad{f} raised to the power \\spad{a}.")) (|lazyGintegrate| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyGintegrate(f,{}r,{}g)} is used for fixed point computations.")) (|mapdiv| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapdiv([a0,{}a1,{}..],{}[b0,{}b1,{}..])} returns \\spad{[a0/b0,{}a1/b1,{}..]}.")) (|powern| (((|Stream| |#1|) (|Fraction| (|Integer|)) (|Stream| |#1|)) "\\spad{powern(r,{}f)} raises power series \\spad{f} to the power \\spad{r}.")) (|nlde| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{nlde(u)} solves a first order non-linear differential equation described by \\spad{u} of the form \\spad{[[b<0,{}0>,{}b<0,{}1>,{}...],{}[b<1,{}0>,{}b<1,{}1>,{}.],{}...]}. the differential equation has the form \\spad{y' = sum(i=0 to infinity,{}j=0 to infinity,{}b*(x**i)*(y**j))}.")) (|lazyIntegrate| (((|Stream| |#1|) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyIntegrate(r,{}f)} is a local function used for fixed point computations.")) (|integrate| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{integrate(r,{}a)} returns the integral of the power series \\spad{a} with respect to the power series variableintegration where \\spad{r} denotes the constant of integration. Thus \\spad{integrate(a,{}[a0,{}a1,{}a2,{}...]) = [a,{}a0,{}a1/2,{}a2/3,{}...]}.")) (|invmultisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{invmultisect(a,{}b,{}st)} substitutes \\spad{x**((a+b)*n)} for \\spad{x**n} and multiplies by \\spad{x**b}.")) (|multisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{multisect(a,{}b,{}st)} selects the coefficients of \\spad{x**((a+b)*n+a)},{} and changes them to \\spad{x**n}.")) (|generalLambert| (((|Stream| |#1|) (|Stream| |#1|) (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),{}a,{}d)} returns \\spad{f(x**a) + f(x**(a + d)) + f(x**(a + 2 d)) + ...}. \\spad{f(x)} should have zero constant coefficient and \\spad{a} and \\spad{d} should be positive.")) (|evenlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{evenlambert(st)} computes \\spad{f(x**2) + f(x**4) + f(x**6) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1,{} then \\spad{prod(f(x**(2*n)),{}n=1..infinity) = exp(evenlambert(log(f(x))))}.")) (|oddlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{oddlambert(st)} computes \\spad{f(x) + f(x**3) + f(x**5) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f}(\\spad{x}) is a power series with constant coefficient 1 then \\spad{prod(f(x**(2*n-1)),{}n=1..infinity) = exp(oddlambert(log(f(x))))}.")) (|lambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lambert(st)} computes \\spad{f(x) + f(x**2) + f(x**3) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1 then \\spad{prod(f(x**n),{}n = 1..infinity) = exp(lambert(log(f(x))))}.")) (|addiag| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{addiag(x)} performs diagonal addition of a stream of streams. if \\spad{x} = \\spad{[[a<0,{}0>,{}a<0,{}1>,{}..],{}[a<1,{}0>,{}a<1,{}1>,{}..],{}[a<2,{}0>,{}a<2,{}1>,{}..],{}..]} and \\spad{addiag(x) = [b<0,{}b<1>,{}...],{} then b = sum(i+j=k,{}a)}.")) (|revert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{revert(a)} computes the inverse of a power series \\spad{a} with respect to composition. the series should have constant coefficient 0 and first order coefficient 1.")) (|lagrange| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lagrange(g)} produces the power series for \\spad{f} where \\spad{f} is implicitly defined as \\spad{f(z) = z*g(f(z))}.")) (|compose| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{compose(a,{}b)} composes the power series \\spad{a} with the power series \\spad{b}.")) (|eval| (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{eval(a,{}r)} returns a stream of partial sums of the power series \\spad{a} evaluated at the power series variable equal to \\spad{r}.")) (|coerce| (((|Stream| |#1|) |#1|) "\\spad{coerce(r)} converts a ring element \\spad{r} to a stream with one element.")) (|gderiv| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) (|Stream| |#1|)) "\\spad{gderiv(f,{}[a0,{}a1,{}a2,{}..])} returns \\spad{[f(0)*a0,{}f(1)*a1,{}f(2)*a2,{}..]}.")) (|deriv| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{deriv(a)} returns the derivative of the power series with respect to the power series variable. Thus \\spad{deriv([a0,{}a1,{}a2,{}...])} returns \\spad{[a1,{}2 a2,{}3 a3,{}...]}.")) (|mapmult| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapmult([a0,{}a1,{}..],{}[b0,{}b1,{}..])} returns \\spad{[a0*b0,{}a1*b1,{}..]}.")) (|int| (((|Stream| |#1|) |#1|) "\\spad{int(r)} returns [\\spad{r},{}\\spad{r+1},{}\\spad{r+2},{}...],{} where \\spad{r} is a ring element.")) (|oddintegers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{oddintegers(n)} returns \\spad{[n,{}n+2,{}n+4,{}...]}.")) (|integers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{integers(n)} returns \\spad{[n,{}n+1,{}n+2,{}...]}.")) (|monom| (((|Stream| |#1|) |#1| (|Integer|)) "\\spad{monom(deg,{}coef)} is a monomial of degree \\spad{deg} with coefficient \\spad{coef}.")) (|recip| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|)) "\\spad{recip(a)} returns the power series reciprocal of \\spad{a},{} or \"failed\" if not possible.")) (/ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a / b} returns the power series quotient of \\spad{a} by \\spad{b}. An error message is returned if \\spad{b} is not invertible. This function is used in fixed point computations.")) (|exquo| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|) (|Stream| |#1|)) "\\spad{exquo(a,{}b)} returns the power series quotient of \\spad{a} by \\spad{b},{} if the quotient exists,{} and \"failed\" otherwise")) (* (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{a * r} returns the power series scalar multiplication of \\spad{a} by \\spad{r:} \\spad{[a0,{}a1,{}...] * r = [a0 * r,{}a1 * r,{}...]}") (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{r * a} returns the power series scalar multiplication of \\spad{r} by \\spad{a}: \\spad{r * [a0,{}a1,{}...] = [r * a0,{}r * a1,{}...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a * b} returns the power series (Cauchy) product of \\spad{a} and \\spad{b:} \\spad{[a0,{}a1,{}...] * [b0,{}b1,{}...] = [c0,{}c1,{}...]} where \\spad{ck = sum(i + j = k,{}\\spad{ai} * bk)}.")) (- (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{- a} returns the power series negative of \\spad{a}: \\spad{- [a0,{}a1,{}...] = [- a0,{}- a1,{}...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a - b} returns the power series difference of \\spad{a} and \\spad{b}: \\spad{[a0,{}a1,{}..] - [b0,{}b1,{}..] = [a0 - b0,{}a1 - b1,{}..]}")) (+ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a + b} returns the power series sum of \\spad{a} and \\spad{b}: \\spad{[a0,{}a1,{}..] + [b0,{}b1,{}..] = [a0 + b0,{}a1 + b1,{}..]}"))) NIL @@ -4594,9 +4594,9 @@ NIL NIL (-1166 |Coef| |var| |cen|) ((|constructor| (NIL "Sparse Laurent series in one variable \\indented{2}{\\spadtype{SparseUnivariateLaurentSeries} is a domain representing Laurent} \\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{SparseUnivariateLaurentSeries(Integer,{}x,{}3)} represents Laurent} \\indented{2}{series in \\spad{(x - 3)} with integer coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. 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T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-172))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-566))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-566))) (|devaluate| |#1|)))) (|HasCategory| (-409 (-566)) (QUOTE (-1111))) (|HasCategory| |#1| (QUOTE (-365))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-558)))) (-2805 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-558)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-566)))))) (|HasSignature| |#1| (LIST (QUOTE -2512) (LIST (|devaluate| |#1|) (QUOTE (-1175)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-566)))))) (-2805 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-959))) (|HasCategory| |#1| (QUOTE (-1199))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasSignature| |#1| (LIST (QUOTE -4117) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1175))))) (|HasSignature| |#1| (LIST (QUOTE -2540) (LIST (LIST (QUOTE -644) (QUOTE (-1175))) (|devaluate| |#1|))))))) +(((-4416 "*") |has| |#1| (-172)) (-4407 |has| |#1| (-558)) (-4412 |has| |#1| (-365)) (-4406 |has| |#1| (-365)) (-4408 . T) (-4409 . T) (-4411 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-172))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-566))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-566))) (|devaluate| |#1|)))) (|HasCategory| (-409 (-566)) (QUOTE (-1111))) (|HasCategory| |#1| (QUOTE (-365))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-558)))) (-2805 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-558)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-566)))))) (|HasSignature| |#1| (LIST (QUOTE -3780) (LIST (|devaluate| |#1|) (QUOTE (-1175)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-566)))))) (-2805 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-959))) (|HasCategory| |#1| (QUOTE (-1199))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasSignature| |#1| (LIST (QUOTE -3921) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1175))))) (|HasSignature| |#1| (LIST (QUOTE -2608) (LIST (LIST (QUOTE -644) (QUOTE (-1175))) (|devaluate| |#1|))))))) (-1173 |Coef| |var| |cen|) ((|constructor| (NIL "Sparse Taylor series in one variable \\indented{2}{\\spadtype{SparseUnivariateTaylorSeries} is a domain representing Taylor} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spadtype{SparseUnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor} \\indented{2}{series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x),{}x)} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} computes the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|univariatePolynomial| (((|UnivariatePolynomial| |#2| |#1|) $ (|NonNegativeInteger|)) "\\spad{univariatePolynomial(f,{}k)} returns a univariate polynomial \\indented{1}{consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.}")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a \\indented{1}{Taylor series.}") (($ (|UnivariatePolynomial| |#2| |#1|)) "\\spad{coerce(p)} converts a univariate polynomial \\spad{p} in the variable \\spad{var} to a univariate Taylor series in \\spad{var}."))) -(((-4419 "*") |has| |#1| (-172)) (-4410 |has| |#1| (-558)) (-4411 . T) (-4412 . T) (-4414 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-558))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-771)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-771)) (|devaluate| |#1|)))) (|HasCategory| (-771) (QUOTE (-1111))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-771))))) (|HasSignature| |#1| (LIST (QUOTE -2512) (LIST (|devaluate| |#1|) (QUOTE (-1175)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-771))))) (|HasCategory| |#1| (QUOTE (-365))) (-2805 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-959))) (|HasCategory| |#1| (QUOTE (-1199))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasSignature| |#1| (LIST (QUOTE -4117) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1175))))) (|HasSignature| |#1| (LIST (QUOTE -2540) (LIST (LIST (QUOTE -644) (QUOTE (-1175))) (|devaluate| |#1|))))))) +(((-4416 "*") |has| |#1| (-172)) (-4407 |has| |#1| (-558)) (-4408 . T) (-4409 . T) (-4411 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-558))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-771)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-771)) (|devaluate| |#1|)))) (|HasCategory| (-771) (QUOTE (-1111))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-771))))) (|HasSignature| |#1| (LIST (QUOTE -3780) (LIST (|devaluate| |#1|) (QUOTE (-1175)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-771))))) (|HasCategory| |#1| (QUOTE (-365))) (-2805 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-959))) (|HasCategory| |#1| (QUOTE (-1199))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasSignature| |#1| (LIST (QUOTE -3921) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1175))))) (|HasSignature| |#1| (LIST (QUOTE -2608) (LIST (LIST (QUOTE -644) (QUOTE (-1175))) (|devaluate| |#1|))))))) (-1174) ((|constructor| (NIL "This domain builds representations of boolean expressions for use with the \\axiomType{FortranCode} domain.")) (NOT (($ $) "\\spad{NOT(x)} returns the \\axiomType{Switch} expression representing \\spad{\\~~x}.") (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{NOT(x)} returns the \\axiomType{Switch} expression representing \\spad{\\~~x}.")) (AND (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{AND(x,{}y)} returns the \\axiomType{Switch} expression representing \\spad{x and y}.")) (EQ (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{EQ(x,{}y)} returns the \\axiomType{Switch} expression representing \\spad{x = y}.")) (OR (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{OR(x,{}y)} returns the \\axiomType{Switch} expression representing \\spad{x or y}.")) (GE (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{GE(x,{}y)} returns the \\axiomType{Switch} expression representing \\spad{x>=y}.")) (LE (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{LE(x,{}y)} returns the \\axiomType{Switch} expression representing \\spad{x<=y}.")) (GT (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{GT(x,{}y)} returns the \\axiomType{Switch} expression representing \\spad{x>y}.")) (LT (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{LT(x,{}y)} returns the \\axiomType{Switch} expression representing \\spad{x} Entry}. The result of such operations can be stored and retrieved with this package by using a hash-table. The user does not need to worry about the management of this hash-table. However,{} onnly one hash-table is built by calling \\axiom{TabulatedComputationPackage(Key ,{}Entry)}.")) (|insert!| (((|Void|) |#1| |#2|) "\\axiom{insert!(\\spad{x},{}\\spad{y})} stores the item whose key is \\axiom{\\spad{x}} and whose entry is \\axiom{\\spad{y}}.")) (|extractIfCan| (((|Union| |#2| "failed") |#1|) "\\axiom{extractIfCan(\\spad{x})} searches the item whose key is \\axiom{\\spad{x}}.")) (|makingStats?| (((|Boolean|)) "\\axiom{makingStats?()} returns \\spad{true} iff the statisitics process is running.")) (|printingInfo?| (((|Boolean|)) "\\axiom{printingInfo?()} returns \\spad{true} iff messages are printed when manipulating items from the hash-table.")) (|usingTable?| (((|Boolean|)) "\\axiom{usingTable?()} returns \\spad{true} iff the hash-table is used")) (|clearTable!| (((|Void|)) "\\axiom{clearTable!()} clears the hash-table and assumes that it will no longer be used.")) (|printStats!| (((|Void|)) "\\axiom{printStats!()} prints the statistics.")) (|startStats!| (((|Void|) (|String|)) "\\axiom{startStats!(\\spad{x})} initializes the statisitics process and sets the comments to display when statistics are printed")) (|printInfo!| (((|Void|) (|String|) (|String|)) "\\axiom{printInfo!(\\spad{x},{}\\spad{y})} initializes the mesages to be printed when manipulating items from the hash-table. If a key is retrieved then \\axiom{\\spad{x}} is displayed. If an item is stored then \\axiom{\\spad{y}} is displayed.")) (|initTable!| (((|Void|)) "\\axiom{initTable!()} initializes the hash-table."))) @@ -4730,7 +4730,7 @@ NIL NIL (-1200 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| $)) "\\spad{tree(nd,{}ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}."))) -((-4418 . T) (-4417 . T)) +((-4415 . T) (-4414 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (-1201 S) ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) @@ -4740,7 +4740,7 @@ NIL ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL NIL -(-1203 R -2382) +(-1203 R -2386) ((|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 @@ -4748,7 +4748,7 @@ NIL ((|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 -(-1205 R -2382) +(-1205 R -2386) ((|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 -614) (LIST (QUOTE -892) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -886) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -614) (LIST (QUOTE -892) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -886) (|devaluate| |#1|))))) @@ -4758,11 +4758,11 @@ NIL ((|HasCategory| |#4| (QUOTE (-370)))) (-1207 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|) $ $) "\\axiom{infRittWu?(\\spad{ts1},{}\\spad{ts2})} returns \\spad{true} iff \\axiom{\\spad{ts2}} has higher rank than \\axiom{\\spad{ts1}} in Wu Wen Tsun sense."))) -((-4418 . T) (-4417 . T)) +((-4415 . T) (-4414 . T)) NIL (-1208 |Coef|) ((|constructor| (NIL "\\spadtype{TaylorSeries} is a general multivariate Taylor series domain over the ring Coef and with variables of type Symbol.")) (|fintegrate| (($ (|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}."))) -(((-4419 "*") |has| |#1| (-172)) (-4410 |has| |#1| (-558)) (-4412 . T) (-4411 . T) (-4414 . T)) +(((-4416 "*") |has| |#1| (-172)) (-4407 |has| |#1| (-558)) (-4409 . T) (-4408 . T) (-4411 . T)) ((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-365)))) (-1209 |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}."))) @@ -4776,7 +4776,7 @@ NIL ((|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 (-1099))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) -(-1212 -2382) +(-1212 -2386) ((|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 @@ -4802,7 +4802,7 @@ NIL NIL (-1218) ((|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|) $) "\\spad{prime?(x)} tests if \\spad{x} can never be written as the product of two non-units of the ring,{} \\spadignore{i.e.} \\spad{x} is an irreducible element."))) -((-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) +((-4407 . T) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) NIL (-1219) ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 16 bits."))) @@ -4826,7 +4826,7 @@ NIL NIL (-1224 |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateLaurentSeriesCategory} is the category of Laurent series in one variable.")) (|integrate| (($ $ (|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."))) -(((-4419 "*") |has| |#1| (-172)) (-4410 |has| |#1| (-558)) (-4415 |has| |#1| (-365)) (-4409 |has| |#1| (-365)) (-4411 . T) (-4412 . T) (-4414 . T)) +(((-4416 "*") |has| |#1| (-172)) (-4407 |has| |#1| (-558)) (-4412 |has| |#1| (-365)) (-4406 |has| |#1| (-365)) (-4408 . T) (-4409 . T) (-4411 . T)) NIL (-1225 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)}."))) @@ -4834,16 +4834,16 @@ NIL ((|HasCategory| |#2| (QUOTE (-365)))) (-1226 |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)}."))) -(((-4419 "*") |has| |#1| (-172)) (-4410 |has| |#1| (-558)) (-4415 |has| |#1| (-365)) (-4409 |has| |#1| (-365)) (-4411 . T) (-4412 . T) (-4414 . T)) +(((-4416 "*") |has| |#1| (-172)) (-4407 |has| |#1| (-558)) (-4412 |has| |#1| (-365)) (-4406 |has| |#1| (-365)) (-4408 . T) (-4409 . T) (-4411 . T)) NIL (-1227 |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)}."))) -(((-4419 "*") |has| |#1| (-172)) (-4410 |has| |#1| (-558)) (-4415 |has| |#1| (-365)) (-4409 |has| |#1| (-365)) (-4411 . T) (-4412 . T) (-4414 . T)) -((-2805 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (-12 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#2| (LIST (QUOTE -287) (|devaluate| |#2|) (|devaluate| |#2|)))) (-12 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#2| (LIST (QUOTE -516) (QUOTE (-1175)) (|devaluate| |#2|)))) (-12 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-820)))) (-12 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-850)))) (-12 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-909)))) (-12 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-1022)))) (-12 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-1150)))) (-12 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-538))))) (-12 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (-12 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-566))))) (-12 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-1175)))))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-172))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (-2805 (|HasCategory| |#1| (QUOTE (-145))) (-12 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-145))))) (-2805 (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-147))))) (-2805 (-12 (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-566)) (|devaluate| |#1|))))) (-12 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#2| (LIST (QUOTE -900) (QUOTE (-1175)))))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-233)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-566)) (|devaluate| |#1|))))) (|HasCategory| (-566) (QUOTE 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T)) +((|HasCategory| |#2| (QUOTE (-909))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-172))) (-2805 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-558)))) (-12 (|HasCategory| (-1081) (LIST (QUOTE -886) (QUOTE (-381)))) (|HasCategory| |#2| (LIST (QUOTE -886) (QUOTE (-381))))) (-12 (|HasCategory| (-1081) (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| |#2| (LIST (QUOTE -886) (QUOTE (-566))))) (-12 (|HasCategory| (-1081) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (|HasCategory| |#2| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381)))))) (-12 (|HasCategory| (-1081) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| |#2| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566)))))) (-12 (|HasCategory| (-1081) (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-538))))) (|HasCategory| |#2| (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-566)))) (-2805 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#2| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566)))))) (|HasCategory| |#2| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (-2805 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-454))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-909)))) (-2805 (|HasCategory| |#2| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-454))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-909)))) (-2805 (|HasCategory| |#2| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-454))) (|HasCategory| |#2| (QUOTE (-909)))) (|HasCategory| |#2| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-1150))) (|HasCategory| |#2| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasAttribute| |#2| (QUOTE -4412)) (|HasCategory| |#2| (QUOTE (-454))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-909)))) (-2805 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-909)))) (|HasCategory| |#2| (QUOTE (-145))))) (-1238 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 @@ -4890,15 +4890,15 @@ NIL ((|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#2| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-454))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-1150)))) (-1240 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}."))) -(((-4419 "*") |has| |#1| (-172)) (-4410 |has| |#1| (-558)) (-4413 |has| |#1| (-365)) (-4415 |has| |#1| (-6 -4415)) (-4412 . T) (-4411 . T) (-4414 . T)) +(((-4416 "*") |has| |#1| (-172)) (-4407 |has| |#1| (-558)) (-4410 |has| |#1| (-365)) (-4412 |has| |#1| (-6 -4412)) (-4409 . T) (-4408 . T) (-4411 . T)) NIL (-1241 S |Coef| |Expon|) ((|constructor| (NIL "\\spadtype{UnivariatePowerSeriesCategory} is the most general univariate power series category with exponents in an ordered abelian monoid. Note: this category exports a substitution function if it is possible to multiply exponents. Note: this category exports a derivative operation if it is possible to multiply coefficients by exponents.")) (|eval| (((|Stream| |#2|) $ |#2|) "\\spad{eval(f,{}a)} evaluates a power series at a value in the ground ring by returning a stream of partial sums.")) (|extend| (($ $ |#3|) "\\spad{extend(f,{}n)} causes all terms of \\spad{f} of degree \\spad{<=} \\spad{n} to be computed.")) (|approximate| ((|#2| $ |#3|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#3| |#3|) "\\spad{truncate(f,{}k1,{}k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#3|) "\\spad{truncate(f,{}k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#3| $ |#3|) "\\spad{order(f,{}n) = min(m,{}n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#3| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,{}n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#2| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|elt| ((|#2| $ |#3|) "\\spad{elt(f(x),{}r)} returns the coefficient of the term of degree \\spad{r} in \\spad{f(x)}. This is the same as the function \\spadfun{coefficient}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#3|) (|:| |c| |#2|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1111))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -2512) (LIST (|devaluate| |#2|) (QUOTE (-1175)))))) +((|HasCategory| |#2| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1111))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -3780) (LIST (|devaluate| |#2|) (QUOTE (-1175)))))) (-1242 |Coef| |Expon|) ((|constructor| (NIL "\\spadtype{UnivariatePowerSeriesCategory} is the most general univariate power series category with exponents in an ordered abelian monoid. Note: this category exports a substitution function if it is possible to multiply exponents. Note: this category exports a derivative operation if it is possible to multiply coefficients by exponents.")) (|eval| (((|Stream| |#1|) $ |#1|) "\\spad{eval(f,{}a)} evaluates a power series at a value in the ground ring by returning a stream of partial sums.")) (|extend| (($ $ |#2|) "\\spad{extend(f,{}n)} causes all terms of \\spad{f} of degree \\spad{<=} \\spad{n} to be computed.")) (|approximate| ((|#1| $ |#2|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#2| |#2|) "\\spad{truncate(f,{}k1,{}k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#2|) "\\spad{truncate(f,{}k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#2| $ |#2|) "\\spad{order(f,{}n) = min(m,{}n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#2| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,{}n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#1| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|elt| ((|#1| $ |#2|) "\\spad{elt(f(x),{}r)} returns the coefficient of the term of degree \\spad{r} in \\spad{f(x)}. This is the same as the function \\spadfun{coefficient}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#2|) (|:| |c| |#1|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) -(((-4419 "*") |has| |#1| (-172)) (-4410 |has| |#1| (-558)) (-4411 . T) (-4412 . T) (-4414 . T)) +(((-4416 "*") |has| |#1| (-172)) (-4407 |has| |#1| (-558)) (-4408 . T) (-4409 . T) (-4411 . T)) NIL (-1243 RC P) ((|constructor| (NIL "This package provides for square-free decomposition of univariate polynomials over arbitrary rings,{} \\spadignore{i.e.} a partial factorization such that each factor is a product of irreducibles with multiplicity one and the factors are pairwise relatively prime. If the ring has characteristic zero,{} the result is guaranteed to satisfy this condition. If the ring is an infinite ring of finite characteristic,{} then it may not be possible to decide when polynomials contain factors which are \\spad{p}th powers. In this case,{} the flag associated with that polynomial is set to \"nil\" (meaning that that polynomials are not guaranteed to be square-free).")) (|BumInSepFFE| (((|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|))) (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|)))) "\\spad{BumInSepFFE(f)} is a local function,{} exported only because it has multiple conditional definitions.")) (|squareFreePart| ((|#2| |#2|) "\\spad{squareFreePart(p)} returns a polynomial which has the same irreducible factors as the univariate polynomial \\spad{p},{} but each factor has multiplicity one.")) (|squareFree| (((|Factored| |#2|) |#2|) "\\spad{squareFree(p)} computes the square-free factorization of the univariate polynomial \\spad{p}. Each factor has no repeated roots,{} and the factors are pairwise relatively prime.")) (|gcd| (($ $ $) "\\spad{gcd(p,{}q)} computes the greatest-common-divisor of \\spad{p} and \\spad{q}."))) @@ -4910,7 +4910,7 @@ NIL NIL (-1245 |Coef|) ((|constructor| (NIL "\\spadtype{UnivariatePuiseuxSeriesCategory} is the category of Puiseux series in one variable.")) (|integrate| (($ $ (|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."))) -(((-4419 "*") |has| |#1| (-172)) (-4410 |has| |#1| (-558)) (-4415 |has| |#1| (-365)) (-4409 |has| |#1| (-365)) (-4411 . T) (-4412 . T) (-4414 . T)) +(((-4416 "*") |has| |#1| (-172)) (-4407 |has| |#1| (-558)) (-4412 |has| |#1| (-365)) (-4406 |has| |#1| (-365)) (-4408 . T) (-4409 . T) (-4411 . T)) NIL (-1246 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)}."))) @@ -4918,24 +4918,24 @@ NIL NIL (-1247 |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)}."))) -(((-4419 "*") |has| |#1| (-172)) (-4410 |has| |#1| (-558)) (-4415 |has| |#1| (-365)) (-4409 |has| |#1| (-365)) (-4411 . T) (-4412 . T) (-4414 . T)) +(((-4416 "*") |has| |#1| (-172)) (-4407 |has| |#1| (-558)) (-4412 |has| |#1| (-365)) (-4406 |has| |#1| (-365)) (-4408 . T) (-4409 . T) (-4411 . T)) NIL (-1248 |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)}."))) -(((-4419 "*") |has| |#1| (-172)) (-4410 |has| |#1| (-558)) (-4415 |has| |#1| (-365)) (-4409 |has| |#1| (-365)) (-4411 . T) (-4412 . T) (-4414 . T)) -((|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-172))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-566))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-566))) (|devaluate| |#1|)))) (|HasCategory| (-409 (-566)) (QUOTE (-1111))) (|HasCategory| |#1| (QUOTE (-365))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-558)))) (-2805 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-558)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-566)))))) (|HasSignature| |#1| (LIST (QUOTE -2512) (LIST (|devaluate| |#1|) (QUOTE (-1175)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-566)))))) (-2805 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-959))) (|HasCategory| |#1| (QUOTE (-1199))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasSignature| |#1| (LIST (QUOTE -4117) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1175))))) (|HasSignature| |#1| (LIST (QUOTE -2540) (LIST (LIST (QUOTE -644) (QUOTE (-1175))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566)))))) +(((-4416 "*") |has| |#1| (-172)) (-4407 |has| |#1| (-558)) (-4412 |has| |#1| (-365)) (-4406 |has| |#1| (-365)) (-4408 . T) (-4409 . T) (-4411 . T)) +((|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-172))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-566))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-566))) (|devaluate| |#1|)))) (|HasCategory| (-409 (-566)) (QUOTE (-1111))) (|HasCategory| |#1| (QUOTE (-365))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-558)))) (-2805 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-558)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-566)))))) (|HasSignature| |#1| (LIST (QUOTE -3780) (LIST (|devaluate| |#1|) (QUOTE (-1175)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-566)))))) (-2805 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-959))) (|HasCategory| |#1| (QUOTE (-1199))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasSignature| |#1| (LIST (QUOTE -3921) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1175))))) (|HasSignature| |#1| (LIST (QUOTE -2608) (LIST (LIST (QUOTE -644) (QUOTE (-1175))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566)))))) (-1249 |Coef| |var| |cen|) ((|constructor| (NIL "Dense Puiseux series in one variable \\indented{2}{\\spadtype{UnivariatePuiseuxSeries} is a domain representing Puiseux} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{UnivariatePuiseuxSeries(Integer,{}x,{}3)} represents Puiseux series in} \\indented{2}{\\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}."))) -(((-4419 "*") |has| |#1| (-172)) (-4410 |has| |#1| (-558)) (-4415 |has| |#1| (-365)) (-4409 |has| |#1| (-365)) (-4411 . T) (-4412 . T) (-4414 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-172))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-566))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-566))) (|devaluate| |#1|)))) (|HasCategory| (-409 (-566)) (QUOTE (-1111))) (|HasCategory| |#1| (QUOTE (-365))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-558)))) (-2805 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-558)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-566)))))) (|HasSignature| |#1| (LIST (QUOTE -2512) (LIST (|devaluate| |#1|) (QUOTE (-1175)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-566)))))) (-2805 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-959))) (|HasCategory| |#1| (QUOTE (-1199))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasSignature| |#1| (LIST (QUOTE -4117) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1175))))) (|HasSignature| |#1| (LIST (QUOTE -2540) (LIST (LIST (QUOTE -644) (QUOTE (-1175))) (|devaluate| |#1|))))))) +(((-4416 "*") |has| |#1| (-172)) (-4407 |has| |#1| (-558)) (-4412 |has| |#1| (-365)) (-4406 |has| |#1| (-365)) (-4408 . T) (-4409 . T) (-4411 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-172))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-566))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-566))) (|devaluate| |#1|)))) (|HasCategory| (-409 (-566)) (QUOTE (-1111))) (|HasCategory| |#1| (QUOTE (-365))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-558)))) (-2805 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-558)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-566)))))) (|HasSignature| |#1| (LIST (QUOTE -3780) (LIST (|devaluate| |#1|) (QUOTE (-1175)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-566)))))) (-2805 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-959))) (|HasCategory| |#1| (QUOTE (-1199))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasSignature| |#1| (LIST (QUOTE -3921) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1175))))) (|HasSignature| |#1| (LIST (QUOTE -2608) (LIST (LIST (QUOTE -644) (QUOTE (-1175))) (|devaluate| |#1|))))))) (-1250 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") $) "\\spad{limitPlus(f(var))} returns \\spad{limit(var -> cen+,{}f(var))}."))) -(((-4419 "*") |has| (-1249 |#2| |#3| |#4|) (-172)) (-4410 |has| (-1249 |#2| |#3| |#4|) (-558)) (-4411 . T) (-4412 . T) (-4414 . T)) +(((-4416 "*") |has| (-1249 |#2| |#3| |#4|) (-172)) (-4407 |has| (-1249 |#2| |#3| |#4|) (-558)) (-4408 . T) (-4409 . T) (-4411 . T)) ((|HasCategory| (-1249 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| (-1249 |#2| |#3| |#4|) (QUOTE (-145))) (|HasCategory| (-1249 |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1249 |#2| |#3| |#4|) (QUOTE (-172))) (-2805 (|HasCategory| (-1249 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| (-1249 |#2| |#3| |#4|) (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566)))))) (|HasCategory| (-1249 |#2| |#3| |#4|) (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| (-1249 |#2| |#3| |#4|) (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| (-1249 |#2| |#3| |#4|) (QUOTE (-365))) (|HasCategory| (-1249 |#2| |#3| |#4|) (QUOTE (-454))) (|HasCategory| (-1249 |#2| |#3| |#4|) (QUOTE (-558)))) (-1251 A S) ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|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| $) "\\spad{concat(x,{}u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL -((|HasAttribute| |#1| (QUOTE -4418))) +((|HasAttribute| |#1| (QUOTE -4415))) (-1252 S) ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|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| $) "\\spad{concat(x,{}u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL @@ -4947,20 +4947,20 @@ NIL (-1254 S |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|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 (-566)))) (|HasCategory| |#2| (QUOTE (-959))) (|HasCategory| |#2| (QUOTE (-1199))) (|HasSignature| |#2| (LIST (QUOTE -2540) (LIST (LIST (QUOTE -644) (QUOTE (-1175))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -4117) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1175))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#2| (QUOTE (-365)))) +((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-566)))) (|HasCategory| |#2| (QUOTE (-959))) (|HasCategory| |#2| (QUOTE (-1199))) (|HasSignature| |#2| (LIST (QUOTE -2608) (LIST (LIST (QUOTE -644) (QUOTE (-1175))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -3921) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1175))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#2| (QUOTE (-365)))) (-1255 |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."))) -(((-4419 "*") |has| |#1| (-172)) (-4410 |has| |#1| (-558)) (-4411 . T) (-4412 . T) (-4414 . T)) +(((-4416 "*") |has| |#1| (-172)) (-4407 |has| |#1| (-558)) (-4408 . T) (-4409 . T) (-4411 . T)) NIL (-1256 |Coef| |var| |cen|) ((|constructor| (NIL "Dense Taylor series in one variable \\spadtype{UnivariateTaylorSeries} is a domain representing Taylor series in one variable with coefficients in an arbitrary ring. The parameters of the type specify the coefficient ring,{} the power series variable,{} and the center of the power series expansion. For example,{} \\spadtype{UnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x),{}x)} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|invmultisect| (($ (|Integer|) (|Integer|) $) "\\spad{invmultisect(a,{}b,{}f(x))} substitutes \\spad{x^((a+b)*n)} \\indented{1}{for \\spad{x^n} and multiples by \\spad{x^b}.}")) (|multisect| (($ (|Integer|) (|Integer|) $) "\\spad{multisect(a,{}b,{}f(x))} selects the coefficients of \\indented{1}{\\spad{x^((a+b)*n+a)},{} and changes this monomial to \\spad{x^n}.}")) (|revert| (($ $) "\\spad{revert(f(x))} returns a Taylor series \\spad{g(x)} such that \\spad{f(g(x)) = g(f(x)) = x}. Series \\spad{f(x)} should have constant coefficient 0 and 1st order coefficient 1.")) (|generalLambert| (($ $ (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),{}a,{}d)} returns \\spad{f(x^a) + f(x^(a + d)) + \\indented{1}{f(x^(a + 2 d)) + ... }. \\spad{f(x)} should have zero constant} \\indented{1}{coefficient and \\spad{a} and \\spad{d} should be positive.}")) (|evenlambert| (($ $) "\\spad{evenlambert(f(x))} returns \\spad{f(x^2) + f(x^4) + f(x^6) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,{}f(x^(2*n))) = exp(log(evenlambert(f(x))))}.}")) (|oddlambert| (($ $) "\\spad{oddlambert(f(x))} returns \\spad{f(x) + f(x^3) + f(x^5) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,{}f(x^(2*n-1)))=exp(log(oddlambert(f(x))))}.}")) (|lambert| (($ $) "\\spad{lambert(f(x))} returns \\spad{f(x) + f(x^2) + f(x^3) + ...}. \\indented{1}{This function is used for computing infinite products.} \\indented{1}{\\spad{f(x)} should have zero constant coefficient.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n = 1..infinity,{}f(x^n)) = exp(log(lambert(f(x))))}.}")) (|lagrange| (($ $) "\\spad{lagrange(g(x))} produces the Taylor series for \\spad{f(x)} \\indented{1}{where \\spad{f(x)} is implicitly defined as \\spad{f(x) = x*g(f(x))}.}")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} computes the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|univariatePolynomial| (((|UnivariatePolynomial| |#2| |#1|) $ (|NonNegativeInteger|)) "\\spad{univariatePolynomial(f,{}k)} returns a univariate polynomial \\indented{1}{consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.}")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a \\indented{1}{Taylor series.}") (($ (|UnivariatePolynomial| |#2| |#1|)) "\\spad{coerce(p)} converts a univariate polynomial \\spad{p} in the variable \\spad{var} to a univariate Taylor series in \\spad{var}."))) -(((-4419 "*") |has| |#1| (-172)) (-4410 |has| |#1| (-558)) (-4411 . T) (-4412 . T) (-4414 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-558))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-771)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-771)) (|devaluate| |#1|)))) (|HasCategory| (-771) (QUOTE (-1111))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-771))))) (|HasSignature| |#1| (LIST (QUOTE -2512) (LIST (|devaluate| |#1|) (QUOTE (-1175)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-771))))) (|HasCategory| |#1| (QUOTE (-365))) (-2805 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-959))) (|HasCategory| |#1| (QUOTE (-1199))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasSignature| |#1| (LIST (QUOTE -4117) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1175))))) (|HasSignature| |#1| (LIST (QUOTE -2540) (LIST (LIST (QUOTE -644) (QUOTE (-1175))) (|devaluate| |#1|))))))) +(((-4416 "*") |has| |#1| (-172)) (-4407 |has| |#1| (-558)) (-4408 . T) (-4409 . T) (-4411 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-558))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-771)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-771)) (|devaluate| |#1|)))) (|HasCategory| (-771) (QUOTE (-1111))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-771))))) (|HasSignature| |#1| (LIST (QUOTE -3780) (LIST (|devaluate| |#1|) (QUOTE (-1175)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-771))))) (|HasCategory| |#1| (QUOTE (-365))) (-2805 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-959))) (|HasCategory| |#1| (QUOTE (-1199))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasSignature| |#1| (LIST (QUOTE -3921) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1175))))) (|HasSignature| |#1| (LIST (QUOTE -2608) (LIST (LIST (QUOTE -644) (QUOTE (-1175))) (|devaluate| |#1|))))))) (-1257 |Coef| UTS) ((|constructor| (NIL "\\indented{1}{This package provides Taylor series solutions to regular} linear or non-linear ordinary differential equations of arbitrary order.")) (|mpsode| (((|List| |#2|) (|List| |#1|) (|List| (|Mapping| |#2| (|List| |#2|)))) "\\spad{mpsode(r,{}f)} solves the system of differential equations \\spad{dy[i]/dx =f[i] [x,{}y[1],{}y[2],{}...,{}y[n]]},{} \\spad{y[i](a) = r[i]} for \\spad{i} in 1..\\spad{n}.")) (|ode| ((|#2| (|Mapping| |#2| (|List| |#2|)) (|List| |#1|)) "\\spad{ode(f,{}cl)} is the solution to \\spad{y=f(y,{}y',{}..,{}y)} such that \\spad{y(a) = cl.i} for \\spad{i} in 1..\\spad{n}.")) (|ode2| ((|#2| (|Mapping| |#2| |#2| |#2|) |#1| |#1|) "\\spad{ode2(f,{}c0,{}c1)} is the solution to \\spad{y'' = f(y,{}y')} such that \\spad{y(a) = c0} and \\spad{y'(a) = c1}.")) (|ode1| ((|#2| (|Mapping| |#2| |#2|) |#1|) "\\spad{ode1(f,{}c)} is the solution to \\spad{y' = f(y)} such that \\spad{y(a) = c}.")) (|fixedPointExquo| ((|#2| |#2| |#2|) "\\spad{fixedPointExquo(f,{}g)} computes the exact quotient of \\spad{f} and \\spad{g} using a fixed point computation.")) (|stFuncN| (((|Mapping| (|Stream| |#1|) (|List| (|Stream| |#1|))) (|Mapping| |#2| (|List| |#2|))) "\\spad{stFuncN(f)} is a local function xported due to compiler problem. This function is of no interest to the top-level user.")) (|stFunc2| (((|Mapping| (|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) (|Mapping| |#2| |#2| |#2|)) "\\spad{stFunc2(f)} is a local function exported due to compiler problem. This function is of no interest to the top-level user.")) (|stFunc1| (((|Mapping| (|Stream| |#1|) (|Stream| |#1|)) (|Mapping| |#2| |#2|)) "\\spad{stFunc1(f)} is a local function exported due to compiler problem. This function is of no interest to the top-level user."))) NIL NIL -(-1258 -2382 UP L UTS) +(-1258 -2386 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 (-558)))) @@ -4978,7 +4978,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-1002))) (|HasCategory| |#2| (QUOTE (-1049))) (|HasCategory| |#2| (QUOTE (-726))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25)))) (-1262 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}.")) (+ (($ $ $) "\\spad{x + y} returns the component-wise sum of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length."))) -((-4418 . T) (-4417 . T)) +((-4415 . T) (-4414 . T)) NIL (-1263 A B) ((|constructor| (NIL "\\indented{2}{This package provides operations which all take as arguments} vectors of elements of some type \\spad{A} and functions from \\spad{A} to another of type \\spad{B}. The operations all iterate over their vector argument and either return a value of type \\spad{B} or a vector over \\spad{B}.")) (|map| (((|Union| (|Vector| |#2|) "failed") (|Mapping| (|Union| |#2| "failed") |#1|) (|Vector| |#1|)) "\\spad{map(f,{} v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values or \\spad{\"failed\"}.") (((|Vector| |#2|) (|Mapping| |#2| |#1|) (|Vector| |#1|)) "\\spad{map(f,{} v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{reduce(func,{}vec,{}ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if \\spad{vec} is empty.")) (|scan| (((|Vector| |#2|) (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{scan(func,{}vec,{}ident)} creates a new vector whose elements are the result of applying reduce to the binary function \\spad{func},{} increasing initial subsequences of the vector \\spad{vec},{} and the element \\spad{ident}."))) @@ -4986,7 +4986,7 @@ NIL NIL (-1264 R) ((|constructor| (NIL "This type represents vector like objects with varying lengths and indexed by a finite segment of integers starting at 1.")) (|vector| (($ (|List| |#1|)) "\\spad{vector(l)} converts the list \\spad{l} to a vector."))) -((-4418 . T) (-4417 . T)) +((-4415 . T) (-4414 . T)) ((-2805 (-12 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538)))) (-2805 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099)))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| (-566) (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-726))) (|HasCategory| |#1| (QUOTE (-1049))) (-12 (|HasCategory| |#1| (QUOTE (-1002))) (|HasCategory| |#1| (QUOTE (-1049)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-1265) ((|constructor| (NIL "TwoDimensionalViewport creates viewports to display graphs.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(v)} returns the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport} as output of the domain \\spadtype{OutputForm}.")) (|key| (((|Integer|) $) "\\spad{key(v)} returns the process ID number of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport}.")) (|reset| (((|Void|) $) "\\spad{reset(v)} sets the current state of the graph characteristics of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} back to their initial settings.")) (|write| (((|String|) $ (|String|) (|List| (|String|))) "\\spad{write(v,{}s,{}lf)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v} and the optional file types indicated by the list \\spad{lf}.") (((|String|) $ (|String|) (|String|)) "\\spad{write(v,{}s,{}f)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v} and an optional file type \\spad{f}.") (((|String|) $ (|String|)) "\\spad{write(v,{}s)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v}.")) (|resize| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{resize(v,{}w,{}h)} displays the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with a width of \\spad{w} and a height of \\spad{h},{} keeping the upper left-hand corner position unchanged.")) (|update| (((|Void|) $ (|GraphImage|) (|PositiveInteger|)) "\\spad{update(v,{}gr,{}n)} drops the graph \\spad{gr} in slot \\spad{n} of viewport \\spad{v}. The graph \\spad{gr} must have been transmitted already and acquired an integer key.")) (|move| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{move(v,{}x,{}y)} displays the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the upper left-hand corner of the viewport window at the screen coordinate position \\spad{x},{} \\spad{y}.")) (|show| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{show(v,{}n,{}s)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the graph if \\spad{s} is \"off\".")) (|translate| (((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|)) "\\spad{translate(v,{}n,{}dx,{}dy)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} translated by \\spad{dx} in the \\spad{x}-coordinate direction from the center of the viewport,{} and by \\spad{dy} in the \\spad{y}-coordinate direction from the center. Setting \\spad{dx} and \\spad{dy} to \\spad{0} places the center of the graph at the center of the viewport.")) (|scale| (((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|)) "\\spad{scale(v,{}n,{}sx,{}sy)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} scaled by the factor \\spad{sx} in the \\spad{x}-coordinate direction and by the factor \\spad{sy} in the \\spad{y}-coordinate direction.")) (|dimensions| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{dimensions(v,{}x,{}y,{}width,{}height)} sets the position of the upper left-hand corner of the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} to the window coordinate \\spad{x},{} \\spad{y},{} and sets the dimensions of the window to that of \\spad{width},{} \\spad{height}. The new dimensions are not displayed until the function \\spadfun{makeViewport2D} is executed again for \\spad{v}.")) (|close| (((|Void|) $) "\\spad{close(v)} closes the viewport window of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and terminates the corresponding process ID.")) (|controlPanel| (((|Void|) $ (|String|)) "\\spad{controlPanel(v,{}s)} displays the control panel of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or hides the control panel if \\spad{s} is \"off\".")) (|connect| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{connect(v,{}n,{}s)} displays the lines connecting the graph points in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the lines if \\spad{s} is \"off\".")) (|region| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{region(v,{}n,{}s)} displays the bounding box of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the bounding box if \\spad{s} is \"off\".")) (|points| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{points(v,{}n,{}s)} displays the points of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the points if \\spad{s} is \"off\".")) (|units| (((|Void|) $ (|PositiveInteger|) (|Palette|)) "\\spad{units(v,{}n,{}c)} displays the units of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the units color set to the given palette color \\spad{c}.") (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{units(v,{}n,{}s)} displays the units of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the units if \\spad{s} is \"off\".")) (|axes| (((|Void|) $ (|PositiveInteger|) (|Palette|)) "\\spad{axes(v,{}n,{}c)} displays the axes of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the axes color set to the given palette color \\spad{c}.") (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{axes(v,{}n,{}s)} displays the axes of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the axes if \\spad{s} is \"off\".")) (|getGraph| (((|GraphImage|) $ (|PositiveInteger|)) "\\spad{getGraph(v,{}n)} returns the graph which is of the domain \\spadtype{GraphImage} which is located in graph field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of the domain \\spadtype{TwoDimensionalViewport}.")) (|putGraph| (((|Void|) $ (|GraphImage|) (|PositiveInteger|)) "\\spad{putGraph(v,{}\\spad{gi},{}n)} sets the graph field indicated by \\spad{n},{} of the indicated two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} to be the graph,{} \\spad{\\spad{gi}} of domain \\spadtype{GraphImage}. The contents of viewport,{} \\spad{v},{} will contain \\spad{\\spad{gi}} when the function \\spadfun{makeViewport2D} is called to create the an updated viewport \\spad{v}.")) (|title| (((|Void|) $ (|String|)) "\\spad{title(v,{}s)} changes the title which is shown in the two-dimensional viewport window,{} \\spad{v} of domain \\spadtype{TwoDimensionalViewport}.")) (|graphs| (((|Vector| (|Union| (|GraphImage|) "undefined")) $) "\\spad{graphs(v)} returns a vector,{} or list,{} which is a union of all the graphs,{} of the domain \\spadtype{GraphImage},{} which are allocated for the two-dimensional viewport,{} \\spad{v},{} of domain \\spadtype{TwoDimensionalViewport}. Those graphs which have no data are labeled \"undefined\",{} otherwise their contents are shown.")) (|graphStates| (((|Vector| (|Record| (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)) (|:| |points| (|Integer|)) (|:| |connect| (|Integer|)) (|:| |spline| (|Integer|)) (|:| |axes| (|Integer|)) (|:| |axesColor| (|Palette|)) (|:| |units| (|Integer|)) (|:| |unitsColor| (|Palette|)) (|:| |showing| (|Integer|)))) $) "\\spad{graphStates(v)} returns and shows a listing of a record containing the current state of the characteristics of each of the ten graph records in the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport}.")) (|graphState| (((|Void|) $ (|PositiveInteger|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Palette|) (|Integer|) (|Palette|) (|Integer|)) "\\spad{graphState(v,{}num,{}sX,{}sY,{}dX,{}dY,{}pts,{}lns,{}box,{}axes,{}axesC,{}un,{}unC,{}cP)} sets the state of the characteristics for the graph indicated by \\spad{num} in the given two-dimensional viewport \\spad{v},{} of domain \\spadtype{TwoDimensionalViewport},{} to the values given as parameters. The scaling of the graph in the \\spad{x} and \\spad{y} component directions is set to be \\spad{sX} and \\spad{sY}; the window translation in the \\spad{x} and \\spad{y} component directions is set to be \\spad{dX} and \\spad{dY}; The graph points,{} lines,{} bounding \\spad{box},{} \\spad{axes},{} or units will be shown in the viewport if their given parameters \\spad{pts},{} \\spad{lns},{} \\spad{box},{} \\spad{axes} or \\spad{un} are set to be \\spad{1},{} but will not be shown if they are set to \\spad{0}. The color of the \\spad{axes} and the color of the units are indicated by the palette colors \\spad{axesC} and \\spad{unC} respectively. To display the control panel when the viewport window is displayed,{} set \\spad{cP} to \\spad{1},{} otherwise set it to \\spad{0}.")) (|options| (($ $ (|List| (|DrawOption|))) "\\spad{options(v,{}lopt)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and returns \\spad{v} with it\\spad{'s} draw options modified to be those which are indicated in the given list,{} \\spad{lopt} of domain \\spadtype{DrawOption}.") (((|List| (|DrawOption|)) $) "\\spad{options(v)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and returns a list containing the draw options from the domain \\spadtype{DrawOption} for \\spad{v}.")) (|makeViewport2D| (($ (|GraphImage|) (|List| (|DrawOption|))) "\\spad{makeViewport2D(\\spad{gi},{}lopt)} creates and displays a viewport window of the domain \\spadtype{TwoDimensionalViewport} whose graph field is assigned to be the given graph,{} \\spad{\\spad{gi}},{} of domain \\spadtype{GraphImage},{} and whose options field is set to be the list of options,{} \\spad{lopt} of domain \\spadtype{DrawOption}.") (($ $) "\\spad{makeViewport2D(v)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and displays a viewport window on the screen which contains the contents of \\spad{v}.")) (|viewport2D| (($) "\\spad{viewport2D()} returns an undefined two-dimensional viewport of the domain \\spadtype{TwoDimensionalViewport} whose contents are empty.")) (|getPickedPoints| (((|List| (|Point| (|DoubleFloat|))) $) "\\spad{getPickedPoints(x)} returns a list of small floats for the points the user interactively picked on the viewport for full integration into the system,{} some design issues need to be addressed: \\spadignore{e.g.} how to go through the GraphImage interface,{} how to default to graphs,{} etc."))) @@ -5014,13 +5014,13 @@ NIL NIL (-1271 S) ((|constructor| (NIL "Vector Spaces (not necessarily finite dimensional) over a field.")) (|dimension| (((|CardinalNumber|)) "\\spad{dimension()} returns the dimensionality of the vector space.")) (/ (($ $ |#1|) "\\spad{x/y} divides the vector \\spad{x} by the scalar \\spad{y}."))) -((-4412 . T) (-4411 . T)) +((-4409 . T) (-4408 . T)) NIL (-1272 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 -(-1273 K R UP -2382) +(-1273 K R UP -2386) ((|constructor| (NIL "In this package \\spad{K} is a finite field,{} \\spad{R} is a ring of univariate polynomials over \\spad{K},{} and \\spad{F} is a framed algebra over \\spad{R}. The package provides a function to compute the integral closure of \\spad{R} in the quotient field of \\spad{F} as well as a function to compute a \"local integral basis\" at a specific prime.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) |#2|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the integral closure of \\spad{R} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}."))) NIL NIL @@ -5034,56 +5034,56 @@ NIL NIL (-1276 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)"))) -((-4412 |has| |#1| (-172)) (-4411 |has| |#1| (-172)) (-4414 . T)) +((-4409 |has| |#1| (-172)) (-4408 |has| |#1| (-172)) (-4411 . T)) ((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365)))) (-1277 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}}."))) -((-4418 . T) (-4417 . T)) +((-4415 . T) (-4414 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1099))) (|HasCategory| |#4| (LIST (QUOTE -310) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#4| (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#3| (QUOTE (-370))) (|HasCategory| |#4| (LIST (QUOTE -613) (QUOTE (-862))))) (-1278 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})"))) -((-4411 . T) (-4412 . T) (-4414 . T)) +((-4408 . T) (-4409 . T) (-4411 . T)) NIL (-1279 |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."))) -((-4414 . T) (-4410 |has| |#2| (-6 -4410)) (-4412 . T) (-4411 . T)) -((|HasCategory| |#2| (QUOTE (-172))) (|HasAttribute| |#2| (QUOTE -4410))) +((-4411 . T) (-4407 |has| |#2| (-6 -4407)) (-4409 . T) (-4408 . T)) +((|HasCategory| |#2| (QUOTE (-172))) (|HasAttribute| |#2| (QUOTE -4407))) (-1280 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 (-1281 |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| $) "\\spad{v * x} returns the product of a variable \\spad{x} by \\spad{x}."))) -((-4410 |has| |#2| (-6 -4410)) (-4412 . T) (-4411 . T) (-4414 . T)) +((-4407 |has| |#2| (-6 -4407)) (-4409 . T) (-4408 . T) (-4411 . T)) NIL -(-1282 S -2382) +(-1282 S -2386) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) NIL ((|HasCategory| |#2| (QUOTE (-370))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147)))) -(-1283 -2382) +(-1283 -2386) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) -((-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) +((-4406 . T) (-4412 . T) (-4407 . T) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) NIL (-1284 |VarSet| R) ((|constructor| (NIL "This domain constructor implements polynomials in non-commutative variables written in the Poincare-Birkhoff-Witt basis from the Lyndon basis. These polynomials can be used to compute Baker-Campbell-Hausdorff relations. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|log| (($ $ (|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}}."))) -((-4410 |has| |#2| (-6 -4410)) (-4412 . T) (-4411 . T) (-4414 . T)) -((|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (LIST (QUOTE -717) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasAttribute| |#2| (QUOTE -4410))) +((-4407 |has| |#2| (-6 -4407)) (-4409 . T) (-4408 . T) (-4411 . T)) +((|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (LIST (QUOTE -717) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasAttribute| |#2| (QUOTE -4407))) (-1285 |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|) $) "\\spad{maxdeg(p)} returns the greatest leading word in the support of \\spad{p}."))) -((-4410 |has| |#2| (-6 -4410)) (-4412 . T) (-4411 . T) (-4414 . T)) +((-4407 |has| |#2| (-6 -4407)) (-4409 . T) (-4408 . T) (-4411 . T)) NIL (-1286 R) ((|constructor| (NIL "\\indented{2}{This type supports multivariate polynomials} whose set of variables is \\spadtype{Symbol}. The representation is recursive. The coefficient ring may be non-commutative and the variables do not commute. However,{} coefficients and variables commute."))) -((-4410 |has| |#1| (-6 -4410)) (-4412 . T) (-4411 . T) (-4414 . T)) -((|HasCategory| |#1| (QUOTE (-172))) (|HasAttribute| |#1| (QUOTE -4410))) +((-4407 |has| |#1| (-6 -4407)) (-4409 . T) (-4408 . T) (-4411 . T)) +((|HasCategory| |#1| (QUOTE (-172))) (|HasAttribute| |#1| (QUOTE -4407))) (-1287 R E) ((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and words belonging to an arbitrary \\spadtype{OrderedMonoid}. This type is used,{} for instance,{} by the \\spadtype{XDistributedPolynomial} domain constructor where the Monoid is free.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (/ (($ $ |#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}."))) -((-4414 . T) (-4415 |has| |#1| (-6 -4415)) (-4410 |has| |#1| (-6 -4410)) (-4412 . T) (-4411 . T)) -((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365))) (|HasAttribute| |#1| (QUOTE -4414)) (|HasAttribute| |#1| (QUOTE -4415)) (|HasAttribute| |#1| (QUOTE -4410))) +((-4411 . T) (-4412 |has| |#1| (-6 -4412)) (-4407 |has| |#1| (-6 -4407)) (-4409 . T) (-4408 . T)) +((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365))) (|HasAttribute| |#1| (QUOTE -4411)) (|HasAttribute| |#1| (QUOTE -4412)) (|HasAttribute| |#1| (QUOTE -4407))) (-1288 |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."))) -((-4410 |has| |#2| (-6 -4410)) (-4412 . T) (-4411 . T) (-4414 . T)) -((|HasCategory| |#2| (QUOTE (-172))) (|HasAttribute| |#2| (QUOTE -4410))) +((-4407 |has| |#2| (-6 -4407)) (-4409 . T) (-4408 . T) (-4411 . T)) +((|HasCategory| |#2| (QUOTE (-172))) (|HasAttribute| |#2| (QUOTE -4407))) (-1289 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 @@ -5098,7 +5098,7 @@ NIL NIL (-1292 |p|) ((|constructor| (NIL "IntegerMod(\\spad{n}) creates the ring of integers reduced modulo the integer \\spad{n}."))) -(((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) +(((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) NIL NIL NIL @@ -5116,4 +5116,4 @@ NIL NIL NIL NIL -((-3 NIL 2285477 2285482 2285487 2285492) (-2 NIL 2285457 2285462 2285467 2285472) (-1 NIL 2285437 2285442 2285447 2285452) (0 NIL 2285417 2285422 2285427 2285432) (-1292 "ZMOD.spad" 2285226 2285239 2285355 2285412) (-1291 "ZLINDEP.spad" 2284270 2284281 2285216 2285221) (-1290 "ZDSOLVE.spad" 2274119 2274141 2284260 2284265) (-1289 "YSTREAM.spad" 2273612 2273623 2274109 2274114) (-1288 "XRPOLY.spad" 2272832 2272852 2273468 2273537) (-1287 "XPR.spad" 2270623 2270636 2272550 2272649) (-1286 "XPOLY.spad" 2270178 2270189 2270479 2270548) (-1285 "XPOLYC.spad" 2269495 2269511 2270104 2270173) (-1284 "XPBWPOLY.spad" 2267932 2267952 2269275 2269344) (-1283 "XF.spad" 2266393 2266408 2267834 2267927) (-1282 "XF.spad" 2264834 2264851 2266277 2266282) (-1281 "XFALG.spad" 2261858 2261874 2264760 2264829) (-1280 "XEXPPKG.spad" 2261109 2261135 2261848 2261853) (-1279 "XDPOLY.spad" 2260723 2260739 2260965 2261034) (-1278 "XALG.spad" 2260383 2260394 2260679 2260718) (-1277 "WUTSET.spad" 2256222 2256239 2260029 2260056) (-1276 "WP.spad" 2255421 2255465 2256080 2256147) (-1275 "WHILEAST.spad" 2255219 2255228 2255411 2255416) (-1274 "WHEREAST.spad" 2254890 2254899 2255209 2255214) (-1273 "WFFINTBS.spad" 2252453 2252475 2254880 2254885) (-1272 "WEIER.spad" 2250667 2250678 2252443 2252448) (-1271 "VSPACE.spad" 2250340 2250351 2250635 2250662) (-1270 "VSPACE.spad" 2250033 2250046 2250330 2250335) (-1269 "VOID.spad" 2249710 2249719 2250023 2250028) (-1268 "VIEW.spad" 2247332 2247341 2249700 2249705) (-1267 "VIEWDEF.spad" 2242529 2242538 2247322 2247327) (-1266 "VIEW3D.spad" 2226364 2226373 2242519 2242524) (-1265 "VIEW2D.spad" 2214101 2214110 2226354 2226359) (-1264 "VECTOR.spad" 2212775 2212786 2213026 2213053) (-1263 "VECTOR2.spad" 2211402 2211415 2212765 2212770) (-1262 "VECTCAT.spad" 2209302 2209313 2211370 2211397) (-1261 "VECTCAT.spad" 2207009 2207022 2209079 2209084) (-1260 "VARIABLE.spad" 2206789 2206804 2206999 2207004) (-1259 "UTYPE.spad" 2206433 2206442 2206779 2206784) (-1258 "UTSODETL.spad" 2205726 2205750 2206389 2206394) (-1257 "UTSODE.spad" 2203914 2203934 2205716 2205721) (-1256 "UTS.spad" 2198703 2198731 2202381 2202478) (-1255 "UTSCAT.spad" 2196154 2196170 2198601 2198698) (-1254 "UTSCAT.spad" 2193249 2193267 2195698 2195703) (-1253 "UTS2.spad" 2192842 2192877 2193239 2193244) (-1252 "URAGG.spad" 2187475 2187486 2192832 2192837) (-1251 "URAGG.spad" 2182072 2182085 2187431 2187436) (-1250 "UPXSSING.spad" 2179715 2179741 2181153 2181286) (-1249 "UPXS.spad" 2176863 2176891 2177847 2177996) (-1248 "UPXSCONS.spad" 2174620 2174640 2174995 2175144) (-1247 "UPXSCCA.spad" 2173185 2173205 2174466 2174615) (-1246 "UPXSCCA.spad" 2171892 2171914 2173175 2173180) (-1245 "UPXSCAT.spad" 2170473 2170489 2171738 2171887) (-1244 "UPXS2.spad" 2170014 2170067 2170463 2170468) (-1243 "UPSQFREE.spad" 2168426 2168440 2170004 2170009) (-1242 "UPSCAT.spad" 2166019 2166043 2168324 2168421) (-1241 "UPSCAT.spad" 2163318 2163344 2165625 2165630) (-1240 "UPOLYC.spad" 2158296 2158307 2163160 2163313) (-1239 "UPOLYC.spad" 2153166 2153179 2158032 2158037) (-1238 "UPOLYC2.spad" 2152635 2152654 2153156 2153161) (-1237 "UP.spad" 2149828 2149843 2150221 2150374) (-1236 "UPMP.spad" 2148718 2148731 2149818 2149823) (-1235 "UPDIVP.spad" 2148281 2148295 2148708 2148713) (-1234 "UPDECOMP.spad" 2146518 2146532 2148271 2148276) (-1233 "UPCDEN.spad" 2145725 2145741 2146508 2146513) (-1232 "UP2.spad" 2145087 2145108 2145715 2145720) (-1231 "UNISEG.spad" 2144440 2144451 2145006 2145011) (-1230 "UNISEG2.spad" 2143933 2143946 2144396 2144401) (-1229 "UNIFACT.spad" 2143034 2143046 2143923 2143928) (-1228 "ULS.spad" 2133586 2133614 2134679 2135108) (-1227 "ULSCONS.spad" 2125980 2126000 2126352 2126501) (-1226 "ULSCCAT.spad" 2123709 2123729 2125826 2125975) (-1225 "ULSCCAT.spad" 2121546 2121568 2123665 2123670) (-1224 "ULSCAT.spad" 2119762 2119778 2121392 2121541) (-1223 "ULS2.spad" 2119274 2119327 2119752 2119757) (-1222 "UINT8.spad" 2119151 2119160 2119264 2119269) (-1221 "UINT64.spad" 2119027 2119036 2119141 2119146) (-1220 "UINT32.spad" 2118903 2118912 2119017 2119022) (-1219 "UINT16.spad" 2118779 2118788 2118893 2118898) (-1218 "UFD.spad" 2117844 2117853 2118705 2118774) (-1217 "UFD.spad" 2116971 2116982 2117834 2117839) (-1216 "UDVO.spad" 2115818 2115827 2116961 2116966) (-1215 "UDPO.spad" 2113245 2113256 2115774 2115779) (-1214 "TYPE.spad" 2113177 2113186 2113235 2113240) (-1213 "TYPEAST.spad" 2113096 2113105 2113167 2113172) (-1212 "TWOFACT.spad" 2111746 2111761 2113086 2113091) (-1211 "TUPLE.spad" 2111230 2111241 2111645 2111650) (-1210 "TUBETOOL.spad" 2108067 2108076 2111220 2111225) (-1209 "TUBE.spad" 2106708 2106725 2108057 2108062) (-1208 "TS.spad" 2105297 2105313 2106273 2106370) (-1207 "TSETCAT.spad" 2092424 2092441 2105265 2105292) (-1206 "TSETCAT.spad" 2079537 2079556 2092380 2092385) (-1205 "TRMANIP.spad" 2073903 2073920 2079243 2079248) (-1204 "TRIMAT.spad" 2072862 2072887 2073893 2073898) (-1203 "TRIGMNIP.spad" 2071379 2071396 2072852 2072857) (-1202 "TRIGCAT.spad" 2070891 2070900 2071369 2071374) (-1201 "TRIGCAT.spad" 2070401 2070412 2070881 2070886) (-1200 "TREE.spad" 2068972 2068983 2070008 2070035) (-1199 "TRANFUN.spad" 2068803 2068812 2068962 2068967) (-1198 "TRANFUN.spad" 2068632 2068643 2068793 2068798) (-1197 "TOPSP.spad" 2068306 2068315 2068622 2068627) (-1196 "TOOLSIGN.spad" 2067969 2067980 2068296 2068301) (-1195 "TEXTFILE.spad" 2066526 2066535 2067959 2067964) (-1194 "TEX.spad" 2063658 2063667 2066516 2066521) (-1193 "TEX1.spad" 2063214 2063225 2063648 2063653) (-1192 "TEMUTL.spad" 2062769 2062778 2063204 2063209) (-1191 "TBCMPPK.spad" 2060862 2060885 2062759 2062764) (-1190 "TBAGG.spad" 2059898 2059921 2060842 2060857) (-1189 "TBAGG.spad" 2058942 2058967 2059888 2059893) (-1188 "TANEXP.spad" 2058318 2058329 2058932 2058937) (-1187 "TABLE.spad" 2056729 2056752 2056999 2057026) (-1186 "TABLEAU.spad" 2056210 2056221 2056719 2056724) (-1185 "TABLBUMP.spad" 2052993 2053004 2056200 2056205) (-1184 "SYSTEM.spad" 2052221 2052230 2052983 2052988) (-1183 "SYSSOLP.spad" 2049694 2049705 2052211 2052216) (-1182 "SYSNNI.spad" 2048874 2048885 2049684 2049689) (-1181 "SYSINT.spad" 2048278 2048289 2048864 2048869) (-1180 "SYNTAX.spad" 2044472 2044481 2048268 2048273) (-1179 "SYMTAB.spad" 2042528 2042537 2044462 2044467) (-1178 "SYMS.spad" 2038513 2038522 2042518 2042523) (-1177 "SYMPOLY.spad" 2037520 2037531 2037602 2037729) (-1176 "SYMFUNC.spad" 2036995 2037006 2037510 2037515) (-1175 "SYMBOL.spad" 2034422 2034431 2036985 2036990) (-1174 "SWITCH.spad" 2031179 2031188 2034412 2034417) (-1173 "SUTS.spad" 2028078 2028106 2029646 2029743) (-1172 "SUPXS.spad" 2025213 2025241 2026210 2026359) (-1171 "SUP.spad" 2022018 2022029 2022799 2022952) (-1170 "SUPFRACF.spad" 2021123 2021141 2022008 2022013) (-1169 "SUP2.spad" 2020513 2020526 2021113 2021118) (-1168 "SUMRF.spad" 2019479 2019490 2020503 2020508) (-1167 "SUMFS.spad" 2019112 2019129 2019469 2019474) (-1166 "SULS.spad" 2009651 2009679 2010757 2011186) (-1165 "SUCHTAST.spad" 2009420 2009429 2009641 2009646) (-1164 "SUCH.spad" 2009100 2009115 2009410 2009415) (-1163 "SUBSPACE.spad" 2001107 2001122 2009090 2009095) (-1162 "SUBRESP.spad" 2000267 2000281 2001063 2001068) (-1161 "STTF.spad" 1996366 1996382 2000257 2000262) (-1160 "STTFNC.spad" 1992834 1992850 1996356 1996361) (-1159 "STTAYLOR.spad" 1985232 1985243 1992715 1992720) (-1158 "STRTBL.spad" 1983737 1983754 1983886 1983913) (-1157 "STRING.spad" 1983146 1983155 1983160 1983187) (-1156 "STRICAT.spad" 1982934 1982943 1983114 1983141) (-1155 "STREAM.spad" 1979792 1979803 1982459 1982474) (-1154 "STREAM3.spad" 1979337 1979352 1979782 1979787) (-1153 "STREAM2.spad" 1978405 1978418 1979327 1979332) (-1152 "STREAM1.spad" 1978109 1978120 1978395 1978400) (-1151 "STINPROD.spad" 1977015 1977031 1978099 1978104) (-1150 "STEP.spad" 1976216 1976225 1977005 1977010) (-1149 "STBL.spad" 1974742 1974770 1974909 1974924) (-1148 "STAGG.spad" 1973817 1973828 1974732 1974737) (-1147 "STAGG.spad" 1972890 1972903 1973807 1973812) (-1146 "STACK.spad" 1972241 1972252 1972497 1972524) (-1145 "SREGSET.spad" 1969945 1969962 1971887 1971914) (-1144 "SRDCMPK.spad" 1968490 1968510 1969935 1969940) (-1143 "SRAGG.spad" 1963587 1963596 1968458 1968485) (-1142 "SRAGG.spad" 1958704 1958715 1963577 1963582) (-1141 "SQMATRIX.spad" 1956320 1956338 1957236 1957323) (-1140 "SPLTREE.spad" 1950872 1950885 1955756 1955783) (-1139 "SPLNODE.spad" 1947460 1947473 1950862 1950867) (-1138 "SPFCAT.spad" 1946237 1946246 1947450 1947455) (-1137 "SPECOUT.spad" 1944787 1944796 1946227 1946232) (-1136 "SPADXPT.spad" 1936926 1936935 1944777 1944782) (-1135 "spad-parser.spad" 1936391 1936400 1936916 1936921) (-1134 "SPADAST.spad" 1936092 1936101 1936381 1936386) (-1133 "SPACEC.spad" 1920105 1920116 1936082 1936087) (-1132 "SPACE3.spad" 1919881 1919892 1920095 1920100) (-1131 "SORTPAK.spad" 1919426 1919439 1919837 1919842) (-1130 "SOLVETRA.spad" 1917183 1917194 1919416 1919421) (-1129 "SOLVESER.spad" 1915703 1915714 1917173 1917178) (-1128 "SOLVERAD.spad" 1911713 1911724 1915693 1915698) (-1127 "SOLVEFOR.spad" 1910133 1910151 1911703 1911708) (-1126 "SNTSCAT.spad" 1909733 1909750 1910101 1910128) (-1125 "SMTS.spad" 1907993 1908019 1909298 1909395) (-1124 "SMP.spad" 1905468 1905488 1905858 1905985) (-1123 "SMITH.spad" 1904311 1904336 1905458 1905463) (-1122 "SMATCAT.spad" 1902421 1902451 1904255 1904306) (-1121 "SMATCAT.spad" 1900463 1900495 1902299 1902304) (-1120 "SKAGG.spad" 1899424 1899435 1900431 1900458) (-1119 "SINT.spad" 1898250 1898259 1899290 1899419) (-1118 "SIMPAN.spad" 1897978 1897987 1898240 1898245) (-1117 "SIG.spad" 1897306 1897315 1897968 1897973) (-1116 "SIGNRF.spad" 1896414 1896425 1897296 1897301) (-1115 "SIGNEF.spad" 1895683 1895700 1896404 1896409) (-1114 "SIGAST.spad" 1895064 1895073 1895673 1895678) (-1113 "SHP.spad" 1892982 1892997 1895020 1895025) (-1112 "SHDP.spad" 1882693 1882720 1883202 1883333) (-1111 "SGROUP.spad" 1882301 1882310 1882683 1882688) (-1110 "SGROUP.spad" 1881907 1881918 1882291 1882296) (-1109 "SGCF.spad" 1874788 1874797 1881897 1881902) (-1108 "SFRTCAT.spad" 1873716 1873733 1874756 1874783) (-1107 "SFRGCD.spad" 1872779 1872799 1873706 1873711) (-1106 "SFQCMPK.spad" 1867416 1867436 1872769 1872774) (-1105 "SFORT.spad" 1866851 1866865 1867406 1867411) (-1104 "SEXOF.spad" 1866694 1866734 1866841 1866846) (-1103 "SEX.spad" 1866586 1866595 1866684 1866689) (-1102 "SEXCAT.spad" 1864137 1864177 1866576 1866581) (-1101 "SET.spad" 1862437 1862448 1863558 1863597) (-1100 "SETMN.spad" 1860871 1860888 1862427 1862432) (-1099 "SETCAT.spad" 1860193 1860202 1860861 1860866) (-1098 "SETCAT.spad" 1859513 1859524 1860183 1860188) (-1097 "SETAGG.spad" 1856034 1856045 1859493 1859508) (-1096 "SETAGG.spad" 1852563 1852576 1856024 1856029) (-1095 "SEQAST.spad" 1852266 1852275 1852553 1852558) (-1094 "SEGXCAT.spad" 1851388 1851401 1852256 1852261) (-1093 "SEG.spad" 1851201 1851212 1851307 1851312) (-1092 "SEGCAT.spad" 1850108 1850119 1851191 1851196) (-1091 "SEGBIND.spad" 1849180 1849191 1850063 1850068) (-1090 "SEGBIND2.spad" 1848876 1848889 1849170 1849175) (-1089 "SEGAST.spad" 1848590 1848599 1848866 1848871) (-1088 "SEG2.spad" 1848015 1848028 1848546 1848551) (-1087 "SDVAR.spad" 1847291 1847302 1848005 1848010) (-1086 "SDPOL.spad" 1844717 1844728 1845008 1845135) (-1085 "SCPKG.spad" 1842796 1842807 1844707 1844712) (-1084 "SCOPE.spad" 1841945 1841954 1842786 1842791) (-1083 "SCACHE.spad" 1840627 1840638 1841935 1841940) (-1082 "SASTCAT.spad" 1840536 1840545 1840617 1840622) (-1081 "SAOS.spad" 1840408 1840417 1840526 1840531) (-1080 "SAERFFC.spad" 1840121 1840141 1840398 1840403) (-1079 "SAE.spad" 1838296 1838312 1838907 1839042) (-1078 "SAEFACT.spad" 1837997 1838017 1838286 1838291) (-1077 "RURPK.spad" 1835638 1835654 1837987 1837992) (-1076 "RULESET.spad" 1835079 1835103 1835628 1835633) (-1075 "RULE.spad" 1833283 1833307 1835069 1835074) (-1074 "RULECOLD.spad" 1833135 1833148 1833273 1833278) (-1073 "RTVALUE.spad" 1832868 1832877 1833125 1833130) (-1072 "RSTRCAST.spad" 1832585 1832594 1832858 1832863) (-1071 "RSETGCD.spad" 1828963 1828983 1832575 1832580) (-1070 "RSETCAT.spad" 1818747 1818764 1828931 1828958) (-1069 "RSETCAT.spad" 1808551 1808570 1818737 1818742) (-1068 "RSDCMPK.spad" 1807003 1807023 1808541 1808546) (-1067 "RRCC.spad" 1805387 1805417 1806993 1806998) (-1066 "RRCC.spad" 1803769 1803801 1805377 1805382) (-1065 "RPTAST.spad" 1803471 1803480 1803759 1803764) (-1064 "RPOLCAT.spad" 1782831 1782846 1803339 1803466) (-1063 "RPOLCAT.spad" 1761905 1761922 1782415 1782420) (-1062 "ROUTINE.spad" 1757768 1757777 1760552 1760579) (-1061 "ROMAN.spad" 1757096 1757105 1757634 1757763) (-1060 "ROIRC.spad" 1756176 1756208 1757086 1757091) (-1059 "RNS.spad" 1755079 1755088 1756078 1756171) (-1058 "RNS.spad" 1754068 1754079 1755069 1755074) (-1057 "RNG.spad" 1753803 1753812 1754058 1754063) (-1056 "RMODULE.spad" 1753568 1753579 1753793 1753798) (-1055 "RMCAT2.spad" 1752976 1753033 1753558 1753563) (-1054 "RMATRIX.spad" 1751800 1751819 1752143 1752182) (-1053 "RMATCAT.spad" 1747333 1747364 1751756 1751795) (-1052 "RMATCAT.spad" 1742756 1742789 1747181 1747186) (-1051 "RLINSET.spad" 1742150 1742161 1742746 1742751) (-1050 "RINTERP.spad" 1742038 1742058 1742140 1742145) (-1049 "RING.spad" 1741508 1741517 1742018 1742033) (-1048 "RING.spad" 1740986 1740997 1741498 1741503) (-1047 "RIDIST.spad" 1740370 1740379 1740976 1740981) (-1046 "RGCHAIN.spad" 1738949 1738965 1739855 1739882) (-1045 "RGBCSPC.spad" 1738730 1738742 1738939 1738944) (-1044 "RGBCMDL.spad" 1738260 1738272 1738720 1738725) (-1043 "RF.spad" 1735874 1735885 1738250 1738255) (-1042 "RFFACTOR.spad" 1735336 1735347 1735864 1735869) (-1041 "RFFACT.spad" 1735071 1735083 1735326 1735331) (-1040 "RFDIST.spad" 1734059 1734068 1735061 1735066) (-1039 "RETSOL.spad" 1733476 1733489 1734049 1734054) (-1038 "RETRACT.spad" 1732904 1732915 1733466 1733471) (-1037 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1643864) (-981 "PTFUNC2.spad" 1640778 1640792 1640947 1640952) (-980 "PTCAT.spad" 1640027 1640037 1640746 1640773) (-979 "PSQFR.spad" 1639334 1639358 1640017 1640022) (-978 "PSEUDLIN.spad" 1638192 1638202 1639324 1639329) (-977 "PSETPK.spad" 1623625 1623641 1638070 1638075) (-976 "PSETCAT.spad" 1617545 1617568 1623605 1623620) (-975 "PSETCAT.spad" 1611439 1611464 1617501 1617506) (-974 "PSCURVE.spad" 1610422 1610430 1611429 1611434) (-973 "PSCAT.spad" 1609189 1609218 1610320 1610417) (-972 "PSCAT.spad" 1608046 1608077 1609179 1609184) (-971 "PRTITION.spad" 1606991 1606999 1608036 1608041) (-970 "PRTDAST.spad" 1606710 1606718 1606981 1606986) (-969 "PRS.spad" 1596272 1596289 1606666 1606671) (-968 "PRQAGG.spad" 1595703 1595713 1596240 1596267) (-967 "PROPLOG.spad" 1594998 1595006 1595693 1595698) (-966 "PROPFRML.spad" 1593806 1593817 1594988 1594993) (-965 "PROPERTY.spad" 1593292 1593300 1593796 1593801) (-964 "PRODUCT.spad" 1590972 1590984 1591258 1591313) (-963 "PR.spad" 1589358 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(-906 "PFBR.spad" 1492243 1492266 1494695 1494700) (-905 "PERM.spad" 1487924 1487934 1492073 1492088) (-904 "PERMGRP.spad" 1482660 1482670 1487914 1487919) (-903 "PERMCAT.spad" 1481212 1481222 1482640 1482655) (-902 "PERMAN.spad" 1479744 1479758 1481202 1481207) (-901 "PENDTREE.spad" 1479083 1479093 1479373 1479378) (-900 "PDRING.spad" 1477574 1477584 1479063 1479078) (-899 "PDRING.spad" 1476073 1476085 1477564 1477569) (-898 "PDEPROB.spad" 1475088 1475096 1476063 1476068) (-897 "PDEPACK.spad" 1469090 1469098 1475078 1475083) (-896 "PDECOMP.spad" 1468552 1468569 1469080 1469085) (-895 "PDECAT.spad" 1466906 1466914 1468542 1468547) (-894 "PCOMP.spad" 1466757 1466770 1466896 1466901) (-893 "PBWLB.spad" 1465339 1465356 1466747 1466752) (-892 "PATTERN.spad" 1459770 1459780 1465329 1465334) (-891 "PATTERN2.spad" 1459506 1459518 1459760 1459765) (-890 "PATTERN1.spad" 1457808 1457824 1459496 1459501) (-889 "PATRES.spad" 1455355 1455367 1457798 1457803) (-888 "PATRES2.spad" 1455017 1455031 1455345 1455350) (-887 "PATMATCH.spad" 1453174 1453205 1454725 1454730) (-886 "PATMAB.spad" 1452599 1452609 1453164 1453169) (-885 "PATLRES.spad" 1451683 1451697 1452589 1452594) (-884 "PATAB.spad" 1451447 1451457 1451673 1451678) (-883 "PARTPERM.spad" 1448809 1448817 1451437 1451442) (-882 "PARSURF.spad" 1448237 1448265 1448799 1448804) (-881 "PARSU2.spad" 1448032 1448048 1448227 1448232) (-880 "script-parser.spad" 1447552 1447560 1448022 1448027) (-879 "PARSCURV.spad" 1446980 1447008 1447542 1447547) (-878 "PARSC2.spad" 1446769 1446785 1446970 1446975) (-877 "PARPCURV.spad" 1446227 1446255 1446759 1446764) (-876 "PARPC2.spad" 1446016 1446032 1446217 1446222) (-875 "PAN2EXPR.spad" 1445428 1445436 1446006 1446011) (-874 "PALETTE.spad" 1444398 1444406 1445418 1445423) (-873 "PAIR.spad" 1443381 1443394 1443986 1443991) (-872 "PADICRC.spad" 1440711 1440729 1441886 1441979) (-871 "PADICRAT.spad" 1438726 1438738 1438947 1439040) (-870 "PADIC.spad" 1438421 1438433 1438652 1438721) (-869 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(-850 "ORDSET.spad" 1400362 1400370 1401186 1401191) (-849 "ORDSET.spad" 1399526 1399536 1400352 1400357) (-848 "ORDRING.spad" 1398916 1398924 1399506 1399521) (-847 "ORDRING.spad" 1398314 1398324 1398906 1398911) (-846 "ORDMON.spad" 1398169 1398177 1398304 1398309) (-845 "ORDFUNS.spad" 1397295 1397311 1398159 1398164) (-844 "ORDFIN.spad" 1397115 1397123 1397285 1397290) (-843 "ORDCOMP.spad" 1395580 1395590 1396662 1396691) (-842 "ORDCOMP2.spad" 1394865 1394877 1395570 1395575) (-841 "OPTPROB.spad" 1393503 1393511 1394855 1394860) (-840 "OPTPACK.spad" 1385888 1385896 1393493 1393498) (-839 "OPTCAT.spad" 1383563 1383571 1385878 1385883) (-838 "OPSIG.spad" 1383215 1383223 1383553 1383558) (-837 "OPQUERY.spad" 1382764 1382772 1383205 1383210) (-836 "OP.spad" 1382506 1382516 1382586 1382653) (-835 "OPERCAT.spad" 1381970 1381980 1382496 1382501) (-834 "OPERCAT.spad" 1381432 1381444 1381960 1381965) (-833 "ONECOMP.spad" 1380177 1380187 1380979 1381008) (-832 "ONECOMP2.spad" 1379595 1379607 1380167 1380172) (-831 "OMSERVER.spad" 1378597 1378605 1379585 1379590) (-830 "OMSAGG.spad" 1378385 1378395 1378553 1378592) (-829 "OMPKG.spad" 1376997 1377005 1378375 1378380) (-828 "OM.spad" 1375962 1375970 1376987 1376992) (-827 "OMLO.spad" 1375387 1375399 1375848 1375887) (-826 "OMEXPR.spad" 1375221 1375231 1375377 1375382) (-825 "OMERR.spad" 1374764 1374772 1375211 1375216) (-824 "OMERRK.spad" 1373798 1373806 1374754 1374759) (-823 "OMENC.spad" 1373142 1373150 1373788 1373793) (-822 "OMDEV.spad" 1367431 1367439 1373132 1373137) (-821 "OMCONN.spad" 1366840 1366848 1367421 1367426) (-820 "OINTDOM.spad" 1366603 1366611 1366766 1366835) (-819 "OFMONOID.spad" 1362790 1362800 1366593 1366598) (-818 "ODVAR.spad" 1362051 1362061 1362780 1362785) (-817 "ODR.spad" 1361695 1361721 1361863 1362012) (-816 "ODPOL.spad" 1359077 1359087 1359417 1359544) (-815 "ODP.spad" 1348924 1348944 1349297 1349428) (-814 "ODETOOLS.spad" 1347507 1347526 1348914 1348919) (-813 "ODESYS.spad" 1345157 1345174 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"MSET.spad" 1153422 1153432 1155186 1155225) (-736 "MSETAGG.spad" 1153267 1153277 1153390 1153417) (-735 "MRING.spad" 1150238 1150250 1152975 1153042) (-734 "MRF2.spad" 1149806 1149820 1150228 1150233) (-733 "MRATFAC.spad" 1149352 1149369 1149796 1149801) (-732 "MPRFF.spad" 1147382 1147401 1149342 1149347) (-731 "MPOLY.spad" 1144853 1144868 1145212 1145339) (-730 "MPCPF.spad" 1144117 1144136 1144843 1144848) (-729 "MPC3.spad" 1143932 1143972 1144107 1144112) (-728 "MPC2.spad" 1143574 1143607 1143922 1143927) (-727 "MONOTOOL.spad" 1141909 1141926 1143564 1143569) (-726 "MONOID.spad" 1141228 1141236 1141899 1141904) (-725 "MONOID.spad" 1140545 1140555 1141218 1141223) (-724 "MONOGEN.spad" 1139291 1139304 1140405 1140540) (-723 "MONOGEN.spad" 1138059 1138074 1139175 1139180) (-722 "MONADWU.spad" 1136073 1136081 1138049 1138054) (-721 "MONADWU.spad" 1134085 1134095 1136063 1136068) (-720 "MONAD.spad" 1133229 1133237 1134075 1134080) (-719 "MONAD.spad" 1132371 1132381 1133219 1133224) (-718 "MOEBIUS.spad" 1131057 1131071 1132351 1132366) (-717 "MODULE.spad" 1130927 1130937 1131025 1131052) (-716 "MODULE.spad" 1130817 1130829 1130917 1130922) (-715 "MODRING.spad" 1130148 1130187 1130797 1130812) (-714 "MODOP.spad" 1128807 1128819 1129970 1130037) (-713 "MODMONOM.spad" 1128536 1128554 1128797 1128802) (-712 "MODMON.spad" 1125331 1125347 1126050 1126203) (-711 "MODFIELD.spad" 1124689 1124728 1125233 1125326) (-710 "MMLFORM.spad" 1123549 1123557 1124679 1124684) (-709 "MMAP.spad" 1123289 1123323 1123539 1123544) (-708 "MLO.spad" 1121716 1121726 1123245 1123284) (-707 "MLIFT.spad" 1120288 1120305 1121706 1121711) (-706 "MKUCFUNC.spad" 1119821 1119839 1120278 1120283) (-705 "MKRECORD.spad" 1119423 1119436 1119811 1119816) (-704 "MKFUNC.spad" 1118804 1118814 1119413 1119418) (-703 "MKFLCFN.spad" 1117760 1117770 1118794 1118799) (-702 "MKBCFUNC.spad" 1117245 1117263 1117750 1117755) (-701 "MINT.spad" 1116684 1116692 1117147 1117240) (-700 "MHROWRED.spad" 1115185 1115195 1116674 1116679) (-699 "MFLOAT.spad" 1113701 1113709 1115075 1115180) (-698 "MFINFACT.spad" 1113101 1113123 1113691 1113696) (-697 "MESH.spad" 1110833 1110841 1113091 1113096) (-696 "MDDFACT.spad" 1109026 1109036 1110823 1110828) (-695 "MDAGG.spad" 1108313 1108323 1109006 1109021) (-694 "MCMPLX.spad" 1104324 1104332 1104938 1105139) (-693 "MCDEN.spad" 1103532 1103544 1104314 1104319) (-692 "MCALCFN.spad" 1100634 1100660 1103522 1103527) (-691 "MAYBE.spad" 1099918 1099929 1100624 1100629) (-690 "MATSTOR.spad" 1097194 1097204 1099908 1099913) (-689 "MATRIX.spad" 1095898 1095908 1096382 1096409) (-688 "MATLIN.spad" 1093224 1093248 1095782 1095787) (-687 "MATCAT.spad" 1084809 1084831 1093192 1093219) (-686 "MATCAT.spad" 1076266 1076290 1084651 1084656) (-685 "MATCAT2.spad" 1075534 1075582 1076256 1076261) (-684 "MAPPKG3.spad" 1074433 1074447 1075524 1075529) (-683 "MAPPKG2.spad" 1073767 1073779 1074423 1074428) (-682 "MAPPKG1.spad" 1072585 1072595 1073757 1073762) (-681 "MAPPAST.spad" 1071898 1071906 1072575 1072580) (-680 "MAPHACK3.spad" 1071706 1071720 1071888 1071893) (-679 "MAPHACK2.spad" 1071471 1071483 1071696 1071701) (-678 "MAPHACK1.spad" 1071101 1071111 1071461 1071466) (-677 "MAGMA.spad" 1068891 1068908 1071091 1071096) (-676 "MACROAST.spad" 1068470 1068478 1068881 1068886) (-675 "M3D.spad" 1066166 1066176 1067848 1067853) (-674 "LZSTAGG.spad" 1063394 1063404 1066156 1066161) (-673 "LZSTAGG.spad" 1060620 1060632 1063384 1063389) (-672 "LWORD.spad" 1057325 1057342 1060610 1060615) (-671 "LSTAST.spad" 1057109 1057117 1057315 1057320) (-670 "LSQM.spad" 1055335 1055349 1055733 1055784) (-669 "LSPP.spad" 1054868 1054885 1055325 1055330) (-668 "LSMP.spad" 1053708 1053736 1054858 1054863) (-667 "LSMP1.spad" 1051512 1051526 1053698 1053703) (-666 "LSAGG.spad" 1051181 1051191 1051480 1051507) (-665 "LSAGG.spad" 1050870 1050882 1051171 1051176) (-664 "LPOLY.spad" 1049824 1049843 1050726 1050795) (-663 "LPEFRAC.spad" 1049081 1049091 1049814 1049819) (-662 "LO.spad" 1048482 1048496 1049015 1049042) (-661 "LOGIC.spad" 1048084 1048092 1048472 1048477) (-660 "LOGIC.spad" 1047684 1047694 1048074 1048079) (-659 "LODOOPS.spad" 1046602 1046614 1047674 1047679) (-658 "LODO.spad" 1045986 1046002 1046282 1046321) (-657 "LODOF.spad" 1045030 1045047 1045943 1045948) (-656 "LODOCAT.spad" 1043688 1043698 1044986 1045025) (-655 "LODOCAT.spad" 1042344 1042356 1043644 1043649) (-654 "LODO2.spad" 1041617 1041629 1042024 1042063) (-653 "LODO1.spad" 1041017 1041027 1041297 1041336) (-652 "LODEEF.spad" 1039789 1039807 1041007 1041012) (-651 "LNAGG.spad" 1035591 1035601 1039779 1039784) (-650 "LNAGG.spad" 1031357 1031369 1035547 1035552) (-649 "LMOPS.spad" 1028093 1028110 1031347 1031352) (-648 "LMODULE.spad" 1027861 1027871 1028083 1028088) (-647 "LMDICT.spad" 1027144 1027154 1027412 1027439) (-646 "LLINSET.spad" 1026541 1026551 1027134 1027139) (-645 "LITERAL.spad" 1026447 1026458 1026531 1026536) (-644 "LIST.spad" 1024165 1024175 1025594 1025621) (-643 "LIST3.spad" 1023456 1023470 1024155 1024160) (-642 "LIST2.spad" 1022096 1022108 1023446 1023451) (-641 "LIST2MAP.spad" 1018973 1018985 1022086 1022091) (-640 "LINSET.spad" 1018595 1018605 1018963 1018968) (-639 "LINEXP.spad" 1018027 1018037 1018575 1018590) (-638 "LINDEP.spad" 1016804 1016816 1017939 1017944) (-637 "LIMITRF.spad" 1014718 1014728 1016794 1016799) (-636 "LIMITPS.spad" 1013601 1013614 1014708 1014713) (-635 "LIE.spad" 1011615 1011627 1012891 1013036) (-634 "LIECAT.spad" 1011091 1011101 1011541 1011610) (-633 "LIECAT.spad" 1010595 1010607 1011047 1011052) (-632 "LIB.spad" 1008643 1008651 1009254 1009269) (-631 "LGROBP.spad" 1005996 1006015 1008633 1008638) (-630 "LF.spad" 1004915 1004931 1005986 1005991) (-629 "LFCAT.spad" 1003934 1003942 1004905 1004910) (-628 "LEXTRIPK.spad" 999437 999452 1003924 1003929) (-627 "LEXP.spad" 997440 997467 999417 999432) (-626 "LETAST.spad" 997139 997147 997430 997435) (-625 "LEADCDET.spad" 995523 995540 997129 997134) (-624 "LAZM3PK.spad" 994227 994249 995513 995518) (-623 "LAUPOL.spad" 992916 992929 993820 993889) (-622 "LAPLACE.spad" 992489 992505 992906 992911) (-621 "LA.spad" 991929 991943 992411 992450) (-620 "LALG.spad" 991705 991715 991909 991924) (-619 "LALG.spad" 991489 991501 991695 991700) (-618 "KVTFROM.spad" 991224 991234 991479 991484) (-617 "KTVLOGIC.spad" 990736 990744 991214 991219) (-616 "KRCFROM.spad" 990474 990484 990726 990731) (-615 "KOVACIC.spad" 989187 989204 990464 990469) (-614 "KONVERT.spad" 988909 988919 989177 989182) (-613 "KOERCE.spad" 988646 988656 988899 988904) (-612 "KERNEL.spad" 987265 987275 988430 988435) (-611 "KERNEL2.spad" 986968 986980 987255 987260) (-610 "KDAGG.spad" 986071 986093 986948 986963) (-609 "KDAGG.spad" 985182 985206 986061 986066) (-608 "KAFILE.spad" 984145 984161 984380 984407) (-607 "JORDAN.spad" 981972 981984 983435 983580) (-606 "JOINAST.spad" 981666 981674 981962 981967) (-605 "JAVACODE.spad" 981532 981540 981656 981661) (-604 "IXAGG.spad" 979655 979679 981522 981527) (-603 "IXAGG.spad" 977633 977659 979502 979507) (-602 "IVECTOR.spad" 976403 976418 976558 976585) (-601 "ITUPLE.spad" 975548 975558 976393 976398) (-600 "ITRIGMNP.spad" 974359 974378 975538 975543) (-599 "ITFUN3.spad" 973853 973867 974349 974354) (-598 "ITFUN2.spad" 973583 973595 973843 973848) (-597 "ITAYLOR.spad" 971375 971390 973419 973544) (-596 "ISUPS.spad" 963786 963801 970349 970446) (-595 "ISUMP.spad" 963283 963299 963776 963781) (-594 "ISTRING.spad" 962286 962299 962452 962479) (-593 "ISAST.spad" 962005 962013 962276 962281) (-592 "IRURPK.spad" 960718 960737 961995 962000) (-591 "IRSN.spad" 958678 958686 960708 960713) (-590 "IRRF2F.spad" 957153 957163 958634 958639) (-589 "IRREDFFX.spad" 956754 956765 957143 957148) (-588 "IROOT.spad" 955085 955095 956744 956749) (-587 "IR.spad" 952874 952888 954940 954967) (-586 "IR2.spad" 951894 951910 952864 952869) (-585 "IR2F.spad" 951094 951110 951884 951889) (-584 "IPRNTPK.spad" 950854 950862 951084 951089) (-583 "IPF.spad" 950419 950431 950659 950752) (-582 "IPADIC.spad" 950180 950206 950345 950414) (-581 "IP4ADDR.spad" 949737 949745 950170 950175) (-580 "IOMODE.spad" 949358 949366 949727 949732) (-579 "IOBFILE.spad" 948719 948727 949348 949353) (-578 "IOBCON.spad" 948584 948592 948709 948714) (-577 "INVLAPLA.spad" 948229 948245 948574 948579) (-576 "INTTR.spad" 941475 941492 948219 948224) (-575 "INTTOOLS.spad" 939186 939202 941049 941054) (-574 "INTSLPE.spad" 938492 938500 939176 939181) (-573 "INTRVL.spad" 938058 938068 938406 938487) (-572 "INTRF.spad" 936422 936436 938048 938053) (-571 "INTRET.spad" 935854 935864 936412 936417) (-570 "INTRAT.spad" 934529 934546 935844 935849) (-569 "INTPM.spad" 932892 932908 934172 934177) (-568 "INTPAF.spad" 930660 930678 932824 932829) (-567 "INTPACK.spad" 920970 920978 930650 930655) (-566 "INT.spad" 920331 920339 920824 920965) (-565 "INTHERTR.spad" 919597 919614 920321 920326) (-564 "INTHERAL.spad" 919263 919287 919587 919592) (-563 "INTHEORY.spad" 915676 915684 919253 919258) (-562 "INTG0.spad" 909139 909157 915608 915613) (-561 "INTFTBL.spad" 903168 903176 909129 909134) (-560 "INTFACT.spad" 902227 902237 903158 903163) (-559 "INTEF.spad" 900542 900558 902217 902222) (-558 "INTDOM.spad" 899157 899165 900468 900537) (-557 "INTDOM.spad" 897834 897844 899147 899152) (-556 "INTCAT.spad" 896087 896097 897748 897829) (-555 "INTBIT.spad" 895590 895598 896077 896082) (-554 "INTALG.spad" 894772 894799 895580 895585) (-553 "INTAF.spad" 894264 894280 894762 894767) (-552 "INTABL.spad" 892782 892813 892945 892972) (-551 "INT8.spad" 892662 892670 892772 892777) (-550 "INT64.spad" 892541 892549 892652 892657) (-549 "INT32.spad" 892420 892428 892531 892536) (-548 "INT16.spad" 892299 892307 892410 892415) (-547 "INS.spad" 889766 889774 892201 892294) (-546 "INS.spad" 887319 887329 889756 889761) (-545 "INPSIGN.spad" 886753 886766 887309 887314) (-544 "INPRODPF.spad" 885819 885838 886743 886748) (-543 "INPRODFF.spad" 884877 884901 885809 885814) (-542 "INNMFACT.spad" 883848 883865 884867 884872) (-541 "INMODGCD.spad" 883332 883362 883838 883843) (-540 "INFSP.spad" 881617 881639 883322 883327) (-539 "INFPROD0.spad" 880667 880686 881607 881612) (-538 "INFORM.spad" 877828 877836 880657 880662) (-537 "INFORM1.spad" 877453 877463 877818 877823) (-536 "INFINITY.spad" 877005 877013 877443 877448) (-535 "INETCLTS.spad" 876982 876990 876995 877000) (-534 "INEP.spad" 875514 875536 876972 876977) (-533 "INDE.spad" 875243 875260 875504 875509) (-532 "INCRMAPS.spad" 874664 874674 875233 875238) (-531 "INBFILE.spad" 873736 873744 874654 874659) (-530 "INBFF.spad" 869506 869517 873726 873731) (-529 "INBCON.spad" 867794 867802 869496 869501) (-528 "INBCON.spad" 866080 866090 867784 867789) (-527 "INAST.spad" 865741 865749 866070 866075) (-526 "IMPTAST.spad" 865449 865457 865731 865736) (-525 "IMATRIX.spad" 864394 864420 864906 864933) (-524 "IMATQF.spad" 863488 863532 864350 864355) (-523 "IMATLIN.spad" 862093 862117 863444 863449) (-522 "ILIST.spad" 860749 860764 861276 861303) (-521 "IIARRAY2.spad" 860137 860175 860356 860383) (-520 "IFF.spad" 859547 859563 859818 859911) (-519 "IFAST.spad" 859161 859169 859537 859542) (-518 "IFARRAY.spad" 856648 856663 858344 858371) (-517 "IFAMON.spad" 856510 856527 856604 856609) (-516 "IEVALAB.spad" 855899 855911 856500 856505) (-515 "IEVALAB.spad" 855286 855300 855889 855894) (-514 "IDPO.spad" 855084 855096 855276 855281) (-513 "IDPOAMS.spad" 854840 854852 855074 855079) (-512 "IDPOAM.spad" 854560 854572 854830 854835) (-511 "IDPC.spad" 853494 853506 854550 854555) (-510 "IDPAM.spad" 853239 853251 853484 853489) (-509 "IDPAG.spad" 852986 852998 853229 853234) (-508 "IDENT.spad" 852636 852644 852976 852981) (-507 "IDECOMP.spad" 849873 849891 852626 852631) (-506 "IDEAL.spad" 844796 844835 849808 849813) (-505 "ICDEN.spad" 843947 843963 844786 844791) (-504 "ICARD.spad" 843136 843144 843937 843942) (-503 "IBPTOOLS.spad" 841729 841746 843126 843131) (-502 "IBITS.spad" 840928 840941 841365 841392) (-501 "IBATOOL.spad" 837803 837822 840918 840923) (-500 "IBACHIN.spad" 836290 836305 837793 837798) (-499 "IARRAY2.spad" 835278 835304 835897 835924) (-498 "IARRAY1.spad" 834323 834338 834461 834488) (-497 "IAN.spad" 832536 832544 834139 834232) (-496 "IALGFACT.spad" 832137 832170 832526 832531) (-495 "HYPCAT.spad" 831561 831569 832127 832132) (-494 "HYPCAT.spad" 830983 830993 831551 831556) (-493 "HOSTNAME.spad" 830791 830799 830973 830978) (-492 "HOMOTOP.spad" 830534 830544 830781 830786) (-491 "HOAGG.spad" 827802 827812 830524 830529) (-490 "HOAGG.spad" 824845 824857 827569 827574) (-489 "HEXADEC.spad" 822947 822955 823312 823405) (-488 "HEUGCD.spad" 821962 821973 822937 822942) (-487 "HELLFDIV.spad" 821552 821576 821952 821957) (-486 "HEAP.spad" 820944 820954 821159 821186) (-485 "HEADAST.spad" 820475 820483 820934 820939) (-484 "HDP.spad" 810318 810334 810695 810826) (-483 "HDMP.spad" 807530 807545 808148 808275) (-482 "HB.spad" 805767 805775 807520 807525) (-481 "HASHTBL.spad" 804237 804268 804448 804475) (-480 "HASAST.spad" 803953 803961 804227 804232) (-479 "HACKPI.spad" 803436 803444 803855 803948) (-478 "GTSET.spad" 802375 802391 803082 803109) (-477 "GSTBL.spad" 800894 800929 801068 801083) (-476 "GSERIES.spad" 798061 798088 799026 799175) (-475 "GROUP.spad" 797330 797338 798041 798056) (-474 "GROUP.spad" 796607 796617 797320 797325) (-473 "GROEBSOL.spad" 795095 795116 796597 796602) (-472 "GRMOD.spad" 793666 793678 795085 795090) (-471 "GRMOD.spad" 792235 792249 793656 793661) (-470 "GRIMAGE.spad" 784840 784848 792225 792230) (-469 "GRDEF.spad" 783219 783227 784830 784835) (-468 "GRAY.spad" 781678 781686 783209 783214) (-467 "GRALG.spad" 780725 780737 781668 781673) (-466 "GRALG.spad" 779770 779784 780715 780720) (-465 "GPOLSET.spad" 779224 779247 779452 779479) (-464 "GOSPER.spad" 778489 778507 779214 779219) (-463 "GMODPOL.spad" 777627 777654 778457 778484) (-462 "GHENSEL.spad" 776696 776710 777617 777622) (-461 "GENUPS.spad" 772797 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621069 621084) (-378 "FLINEXP.spad" 620467 620479 620737 620742) (-377 "FLASORT.spad" 619787 619799 620457 620462) (-376 "FLALG.spad" 617433 617452 619713 619782) (-375 "FLAGG.spad" 614451 614461 617413 617428) (-374 "FLAGG.spad" 611370 611382 614334 614339) (-373 "FLAGG2.spad" 610051 610067 611360 611365) (-372 "FINRALG.spad" 608080 608093 610007 610046) (-371 "FINRALG.spad" 606035 606050 607964 607969) (-370 "FINITE.spad" 605187 605195 606025 606030) (-369 "FINAALG.spad" 594168 594178 605129 605182) (-368 "FINAALG.spad" 583161 583173 594124 594129) (-367 "FILE.spad" 582744 582754 583151 583156) (-366 "FILECAT.spad" 581262 581279 582734 582739) (-365 "FIELD.spad" 580668 580676 581164 581257) (-364 "FIELD.spad" 580160 580170 580658 580663) (-363 "FGROUP.spad" 578769 578779 580140 580155) (-362 "FGLMICPK.spad" 577556 577571 578759 578764) (-361 "FFX.spad" 576931 576946 577272 577365) (-360 "FFSLPE.spad" 576420 576441 576921 576926) (-359 "FFPOLY.spad" 567672 567683 576410 576415) (-358 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523207) (-337 "FDIVCAT.spad" 520696 520720 522644 522649) (-336 "FDIVCAT.spad" 518736 518762 520686 520691) (-335 "FDIV2.spad" 518390 518430 518726 518731) (-334 "FCTRDATA.spad" 517422 517430 518380 518385) (-333 "FCPAK1.spad" 515975 515983 517412 517417) (-332 "FCOMP.spad" 515354 515364 515965 515970) (-331 "FC.spad" 505269 505277 515344 515349) (-330 "FAXF.spad" 498204 498218 505171 505264) (-329 "FAXF.spad" 491191 491207 498160 498165) (-328 "FARRAY.spad" 489337 489347 490374 490401) (-327 "FAMR.spad" 487457 487469 489235 489332) (-326 "FAMR.spad" 485561 485575 487341 487346) (-325 "FAMONOID.spad" 485211 485221 485515 485520) (-324 "FAMONC.spad" 483433 483445 485201 485206) (-323 "FAGROUP.spad" 483039 483049 483329 483356) (-322 "FACUTIL.spad" 481235 481252 483029 483034) (-321 "FACTFUNC.spad" 480411 480421 481225 481230) (-320 "EXPUPXS.spad" 477244 477267 478543 478692) (-319 "EXPRTUBE.spad" 474472 474480 477234 477239) (-318 "EXPRODE.spad" 471344 471360 474462 474467) (-317 "EXPR.spad" 466619 466629 467333 467740) (-316 "EXPR2UPS.spad" 462711 462724 466609 466614) (-315 "EXPR2.spad" 462414 462426 462701 462706) (-314 "EXPEXPAN.spad" 459352 459377 459986 460079) (-313 "EXIT.spad" 459023 459031 459342 459347) (-312 "EXITAST.spad" 458759 458767 459013 459018) (-311 "EVALCYC.spad" 458217 458231 458749 458754) (-310 "EVALAB.spad" 457781 457791 458207 458212) (-309 "EVALAB.spad" 457343 457355 457771 457776) (-308 "EUCDOM.spad" 454885 454893 457269 457338) (-307 "EUCDOM.spad" 452489 452499 454875 454880) (-306 "ESTOOLS.spad" 444329 444337 452479 452484) (-305 "ESTOOLS2.spad" 443930 443944 444319 444324) (-304 "ESTOOLS1.spad" 443615 443626 443920 443925) (-303 "ES.spad" 436162 436170 443605 443610) (-302 "ES.spad" 428615 428625 436060 436065) (-301 "ESCONT.spad" 425388 425396 428605 428610) (-300 "ESCONT1.spad" 425137 425149 425378 425383) (-299 "ES2.spad" 424632 424648 425127 425132) (-298 "ES1.spad" 424198 424214 424622 424627) (-297 "ERROR.spad" 421519 421527 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382344 384050 384055) (-275 "E04UCFA.spad" 381872 381880 382326 382331) (-274 "E04NAFA.spad" 381449 381457 381862 381867) (-273 "E04MBFA.spad" 381029 381037 381439 381444) (-272 "E04JAFA.spad" 380565 380573 381019 381024) (-271 "E04GCFA.spad" 380101 380109 380555 380560) (-270 "E04FDFA.spad" 379637 379645 380091 380096) (-269 "E04DGFA.spad" 379173 379181 379627 379632) (-268 "E04AGNT.spad" 375015 375023 379163 379168) (-267 "DVARCAT.spad" 371700 371710 375005 375010) (-266 "DVARCAT.spad" 368383 368395 371690 371695) (-265 "DSMP.spad" 365850 365864 366155 366282) (-264 "DROPT.spad" 359795 359803 365840 365845) (-263 "DROPT1.spad" 359458 359468 359785 359790) (-262 "DROPT0.spad" 354285 354293 359448 359453) (-261 "DRAWPT.spad" 352440 352448 354275 354280) (-260 "DRAW.spad" 345040 345053 352430 352435) (-259 "DRAWHACK.spad" 344348 344358 345030 345035) (-258 "DRAWCX.spad" 341790 341798 344338 344343) (-257 "DRAWCURV.spad" 341327 341342 341780 341785) (-256 "DRAWCFUN.spad" 330499 330507 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"CONTOUR.spad" 202318 202326 202901 202906) (-174 "CONTFRAC.spad" 197930 197940 202220 202313) (-173 "CONDUIT.spad" 197688 197696 197920 197925) (-172 "COMRING.spad" 197362 197370 197626 197683) (-171 "COMPPROP.spad" 196876 196884 197352 197357) (-170 "COMPLPAT.spad" 196643 196658 196866 196871) (-169 "COMPLEX.spad" 190780 190790 191024 191285) (-168 "COMPLEX2.spad" 190493 190505 190770 190775) (-167 "COMPFACT.spad" 190095 190109 190483 190488) (-166 "COMPCAT.spad" 188163 188173 189829 190090) (-165 "COMPCAT.spad" 185959 185971 187627 187632) (-164 "COMMUPC.spad" 185705 185723 185949 185954) (-163 "COMMONOP.spad" 185238 185246 185695 185700) (-162 "COMM.spad" 185047 185055 185228 185233) (-161 "COMMAAST.spad" 184810 184818 185037 185042) (-160 "COMBOPC.spad" 183715 183723 184800 184805) (-159 "COMBINAT.spad" 182460 182470 183705 183710) (-158 "COMBF.spad" 179828 179844 182450 182455) (-157 "COLOR.spad" 178665 178673 179818 179823) (-156 "COLONAST.spad" 178331 178339 178655 178660) (-155 "CMPLXRT.spad" 178040 178057 178321 178326) (-154 "CLLCTAST.spad" 177702 177710 178030 178035) (-153 "CLIP.spad" 173794 173802 177692 177697) (-152 "CLIF.spad" 172433 172449 173750 173789) (-151 "CLAGG.spad" 168918 168928 172423 172428) (-150 "CLAGG.spad" 165274 165286 168781 168786) (-149 "CINTSLPE.spad" 164599 164612 165264 165269) (-148 "CHVAR.spad" 162677 162699 164589 164594) (-147 "CHARZ.spad" 162592 162600 162657 162672) (-146 "CHARPOL.spad" 162100 162110 162582 162587) (-145 "CHARNZ.spad" 161853 161861 162080 162095) (-144 "CHAR.spad" 159721 159729 161843 161848) (-143 "CFCAT.spad" 159037 159045 159711 159716) (-142 "CDEN.spad" 158195 158209 159027 159032) (-141 "CCLASS.spad" 156344 156352 157606 157645) (-140 "CATEGORY.spad" 155434 155442 156334 156339) (-139 "CATCTOR.spad" 155325 155333 155424 155429) (-138 "CATAST.spad" 154943 154951 155315 155320) (-137 "CASEAST.spad" 154657 154665 154933 154938) (-136 "CARTEN.spad" 149760 149784 154647 154652) (-135 "CARTEN2.spad" 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129855) (-114 "BOP.spad" 124640 124648 129506 129511) (-113 "BOP1.spad" 122060 122070 124630 124635) (-112 "BOOLEAN.spad" 121492 121500 122050 122055) (-111 "BMODULE.spad" 121204 121216 121460 121487) (-110 "BITS.spad" 120623 120631 120840 120867) (-109 "BINDING.spad" 120034 120042 120613 120618) (-108 "BINARY.spad" 118145 118153 118501 118594) (-107 "BGAGG.spad" 117342 117352 118125 118140) (-106 "BGAGG.spad" 116547 116559 117332 117337) (-105 "BFUNCT.spad" 116111 116119 116527 116542) (-104 "BEZOUT.spad" 115245 115272 116061 116066) (-103 "BBTREE.spad" 112064 112074 114852 114879) (-102 "BASTYPE.spad" 111736 111744 112054 112059) (-101 "BASTYPE.spad" 111406 111416 111726 111731) (-100 "BALFACT.spad" 110845 110858 111396 111401) (-99 "AUTOMOR.spad" 110292 110301 110825 110840) (-98 "ATTREG.spad" 107011 107018 110044 110287) (-97 "ATTRBUT.spad" 103034 103041 106991 107006) (-96 "ATTRAST.spad" 102751 102758 103024 103029) (-95 "ATRIG.spad" 102221 102228 102741 102746) (-94 "ATRIG.spad" 101689 101698 102211 102216) (-93 "ASTCAT.spad" 101593 101600 101679 101684) (-92 "ASTCAT.spad" 101495 101504 101583 101588) (-91 "ASTACK.spad" 100828 100837 101102 101129) (-90 "ASSOCEQ.spad" 99628 99639 100784 100789) (-89 "ASP9.spad" 98709 98722 99618 99623) (-88 "ASP8.spad" 97752 97765 98699 98704) (-87 "ASP80.spad" 97074 97087 97742 97747) (-86 "ASP7.spad" 96234 96247 97064 97069) (-85 "ASP78.spad" 95685 95698 96224 96229) (-84 "ASP77.spad" 95054 95067 95675 95680) (-83 "ASP74.spad" 94146 94159 95044 95049) (-82 "ASP73.spad" 93417 93430 94136 94141) (-81 "ASP6.spad" 92284 92297 93407 93412) (-80 "ASP55.spad" 90793 90806 92274 92279) (-79 "ASP50.spad" 88610 88623 90783 90788) (-78 "ASP4.spad" 87905 87918 88600 88605) (-77 "ASP49.spad" 86904 86917 87895 87900) (-76 "ASP42.spad" 85311 85350 86894 86899) (-75 "ASP41.spad" 83890 83929 85301 85306) (-74 "ASP35.spad" 82878 82891 83880 83885) (-73 "ASP34.spad" 82179 82192 82868 82873) (-72 "ASP33.spad" 81739 81752 82169 82174) (-71 "ASP31.spad" 80879 80892 81729 81734) (-70 "ASP30.spad" 79771 79784 80869 80874) (-69 "ASP29.spad" 79237 79250 79761 79766) (-68 "ASP28.spad" 70510 70523 79227 79232) (-67 "ASP27.spad" 69407 69420 70500 70505) (-66 "ASP24.spad" 68494 68507 69397 69402) (-65 "ASP20.spad" 67958 67971 68484 68489) (-64 "ASP1.spad" 67339 67352 67948 67953) (-63 "ASP19.spad" 62025 62038 67329 67334) (-62 "ASP12.spad" 61439 61452 62015 62020) (-61 "ASP10.spad" 60710 60723 61429 61434) (-60 "ARRAY2.spad" 60070 60079 60317 60344) (-59 "ARRAY1.spad" 58905 58914 59253 59280) (-58 "ARRAY12.spad" 57574 57585 58895 58900) (-57 "ARR2CAT.spad" 53236 53257 57542 57569) (-56 "ARR2CAT.spad" 48918 48941 53226 53231) (-55 "ARITY.spad" 48290 48297 48908 48913) (-54 "APPRULE.spad" 47534 47556 48280 48285) (-53 "APPLYORE.spad" 47149 47162 47524 47529) (-52 "ANY.spad" 45491 45498 47139 47144) (-51 "ANY1.spad" 44562 44571 45481 45486) (-50 "ANTISYM.spad" 43001 43017 44542 44557) (-49 "ANON.spad" 42694 42701 42991 42996) (-48 "AN.spad" 40995 41002 42510 42603) (-47 "AMR.spad" 39174 39185 40893 40990) (-46 "AMR.spad" 37190 37203 38911 38916) (-45 "ALIST.spad" 34602 34623 34952 34979) (-44 "ALGSC.spad" 33725 33751 34474 34527) (-43 "ALGPKG.spad" 29434 29445 33681 33686) (-42 "ALGMFACT.spad" 28623 28637 29424 29429) (-41 "ALGMANIP.spad" 26079 26094 28456 28461) (-40 "ALGFF.spad" 24394 24421 24611 24767) (-39 "ALGFACT.spad" 23515 23525 24384 24389) (-38 "ALGEBRA.spad" 23348 23357 23471 23510) (-37 "ALGEBRA.spad" 23213 23224 23338 23343) (-36 "ALAGG.spad" 22723 22744 23181 23208) (-35 "AHYP.spad" 22104 22111 22713 22718) (-34 "AGG.spad" 20413 20420 22094 22099) (-33 "AGG.spad" 18686 18695 20369 20374) (-32 "AF.spad" 17111 17126 18621 18626) (-31 "ADDAST.spad" 16789 16796 17101 17106) (-30 "ACPLOT.spad" 15360 15367 16779 16784) (-29 "ACFS.spad" 13111 13120 15262 15355) (-28 "ACFS.spad" 10948 10959 13101 13106) (-27 "ACF.spad" 7550 7557 10850 10943) (-26 "ACF.spad" 4238 4247 7540 7545) (-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 2284962 2284967 2284972 2284977) (-2 NIL 2284942 2284947 2284952 2284957) (-1 NIL 2284922 2284927 2284932 2284937) (0 NIL 2284902 2284907 2284912 2284917) (-1292 "ZMOD.spad" 2284711 2284724 2284840 2284897) (-1291 "ZLINDEP.spad" 2283755 2283766 2284701 2284706) (-1290 "ZDSOLVE.spad" 2273604 2273626 2283745 2283750) (-1289 "YSTREAM.spad" 2273097 2273108 2273594 2273599) (-1288 "XRPOLY.spad" 2272317 2272337 2272953 2273022) (-1287 "XPR.spad" 2270108 2270121 2272035 2272134) (-1286 "XPOLY.spad" 2269663 2269674 2269964 2270033) (-1285 "XPOLYC.spad" 2268980 2268996 2269589 2269658) (-1284 "XPBWPOLY.spad" 2267417 2267437 2268760 2268829) (-1283 "XF.spad" 2265878 2265893 2267319 2267412) (-1282 "XF.spad" 2264319 2264336 2265762 2265767) (-1281 "XFALG.spad" 2261343 2261359 2264245 2264314) (-1280 "XEXPPKG.spad" 2260594 2260620 2261333 2261338) (-1279 "XDPOLY.spad" 2260208 2260224 2260450 2260519) (-1278 "XALG.spad" 2259868 2259879 2260164 2260203) (-1277 "WUTSET.spad" 2255707 2255724 2259514 2259541) (-1276 "WP.spad" 2254906 2254950 2255565 2255632) (-1275 "WHILEAST.spad" 2254704 2254713 2254896 2254901) (-1274 "WHEREAST.spad" 2254375 2254384 2254694 2254699) (-1273 "WFFINTBS.spad" 2251938 2251960 2254365 2254370) (-1272 "WEIER.spad" 2250152 2250163 2251928 2251933) (-1271 "VSPACE.spad" 2249825 2249836 2250120 2250147) (-1270 "VSPACE.spad" 2249518 2249531 2249815 2249820) (-1269 "VOID.spad" 2249195 2249204 2249508 2249513) (-1268 "VIEW.spad" 2246817 2246826 2249185 2249190) (-1267 "VIEWDEF.spad" 2242014 2242023 2246807 2246812) (-1266 "VIEW3D.spad" 2225849 2225858 2242004 2242009) (-1265 "VIEW2D.spad" 2213586 2213595 2225839 2225844) (-1264 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2107547) (-1208 "TS.spad" 2104782 2104798 2105758 2105855) (-1207 "TSETCAT.spad" 2091909 2091926 2104750 2104777) (-1206 "TSETCAT.spad" 2079022 2079041 2091865 2091870) (-1205 "TRMANIP.spad" 2073388 2073405 2078728 2078733) (-1204 "TRIMAT.spad" 2072347 2072372 2073378 2073383) (-1203 "TRIGMNIP.spad" 2070864 2070881 2072337 2072342) (-1202 "TRIGCAT.spad" 2070376 2070385 2070854 2070859) (-1201 "TRIGCAT.spad" 2069886 2069897 2070366 2070371) (-1200 "TREE.spad" 2068457 2068468 2069493 2069520) (-1199 "TRANFUN.spad" 2068288 2068297 2068447 2068452) (-1198 "TRANFUN.spad" 2068117 2068128 2068278 2068283) (-1197 "TOPSP.spad" 2067791 2067800 2068107 2068112) (-1196 "TOOLSIGN.spad" 2067454 2067465 2067781 2067786) (-1195 "TEXTFILE.spad" 2066011 2066020 2067444 2067449) (-1194 "TEX.spad" 2063143 2063152 2066001 2066006) (-1193 "TEX1.spad" 2062699 2062710 2063133 2063138) (-1192 "TEMUTL.spad" 2062254 2062263 2062689 2062694) (-1191 "TBCMPPK.spad" 2060347 2060370 2062244 2062249) (-1190 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2025695 2025844) (-1171 "SUP.spad" 2021503 2021514 2022284 2022437) (-1170 "SUPFRACF.spad" 2020608 2020626 2021493 2021498) (-1169 "SUP2.spad" 2019998 2020011 2020598 2020603) (-1168 "SUMRF.spad" 2018964 2018975 2019988 2019993) (-1167 "SUMFS.spad" 2018597 2018614 2018954 2018959) (-1166 "SULS.spad" 2009136 2009164 2010242 2010671) (-1165 "SUCHTAST.spad" 2008905 2008914 2009126 2009131) (-1164 "SUCH.spad" 2008585 2008600 2008895 2008900) (-1163 "SUBSPACE.spad" 2000592 2000607 2008575 2008580) (-1162 "SUBRESP.spad" 1999752 1999766 2000548 2000553) (-1161 "STTF.spad" 1995851 1995867 1999742 1999747) (-1160 "STTFNC.spad" 1992319 1992335 1995841 1995846) (-1159 "STTAYLOR.spad" 1984717 1984728 1992200 1992205) (-1158 "STRTBL.spad" 1983222 1983239 1983371 1983398) (-1157 "STRING.spad" 1982631 1982640 1982645 1982672) (-1156 "STRICAT.spad" 1982419 1982428 1982599 1982626) (-1155 "STREAM.spad" 1979277 1979288 1981944 1981959) (-1154 "STREAM3.spad" 1978822 1978837 1979267 1979272) (-1153 "STREAM2.spad" 1977890 1977903 1978812 1978817) (-1152 "STREAM1.spad" 1977594 1977605 1977880 1977885) (-1151 "STINPROD.spad" 1976500 1976516 1977584 1977589) (-1150 "STEP.spad" 1975701 1975710 1976490 1976495) (-1149 "STBL.spad" 1974227 1974255 1974394 1974409) (-1148 "STAGG.spad" 1973302 1973313 1974217 1974222) (-1147 "STAGG.spad" 1972375 1972388 1973292 1973297) (-1146 "STACK.spad" 1971726 1971737 1971982 1972009) (-1145 "SREGSET.spad" 1969430 1969447 1971372 1971399) (-1144 "SRDCMPK.spad" 1967975 1967995 1969420 1969425) (-1143 "SRAGG.spad" 1963072 1963081 1967943 1967970) (-1142 "SRAGG.spad" 1958189 1958200 1963062 1963067) (-1141 "SQMATRIX.spad" 1955805 1955823 1956721 1956808) (-1140 "SPLTREE.spad" 1950357 1950370 1955241 1955268) (-1139 "SPLNODE.spad" 1946945 1946958 1950347 1950352) (-1138 "SPFCAT.spad" 1945722 1945731 1946935 1946940) (-1137 "SPECOUT.spad" 1944272 1944281 1945712 1945717) (-1136 "SPADXPT.spad" 1936411 1936420 1944262 1944267) (-1135 "spad-parser.spad" 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1897458) (-1116 "SIGNRF.spad" 1895899 1895910 1896781 1896786) (-1115 "SIGNEF.spad" 1895168 1895185 1895889 1895894) (-1114 "SIGAST.spad" 1894549 1894558 1895158 1895163) (-1113 "SHP.spad" 1892467 1892482 1894505 1894510) (-1112 "SHDP.spad" 1882178 1882205 1882687 1882818) (-1111 "SGROUP.spad" 1881786 1881795 1882168 1882173) (-1110 "SGROUP.spad" 1881392 1881403 1881776 1881781) (-1109 "SGCF.spad" 1874273 1874282 1881382 1881387) (-1108 "SFRTCAT.spad" 1873201 1873218 1874241 1874268) (-1107 "SFRGCD.spad" 1872264 1872284 1873191 1873196) (-1106 "SFQCMPK.spad" 1866901 1866921 1872254 1872259) (-1105 "SFORT.spad" 1866336 1866350 1866891 1866896) (-1104 "SEXOF.spad" 1866179 1866219 1866326 1866331) (-1103 "SEX.spad" 1866071 1866080 1866169 1866174) (-1102 "SEXCAT.spad" 1863622 1863662 1866061 1866066) (-1101 "SET.spad" 1861922 1861933 1863043 1863082) (-1100 "SETMN.spad" 1860356 1860373 1861912 1861917) (-1099 "SETCAT.spad" 1859678 1859687 1860346 1860351) (-1098 "SETCAT.spad" 1858998 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"NARNG.spad" 1234671 1234679 1235317 1235322) (-760 "NARNG.spad" 1234013 1234023 1234661 1234666) (-759 "NAGSP.spad" 1233086 1233094 1234003 1234008) (-758 "NAGS.spad" 1222611 1222619 1233076 1233081) (-757 "NAGF07.spad" 1221004 1221012 1222601 1222606) (-756 "NAGF04.spad" 1215236 1215244 1220994 1220999) (-755 "NAGF02.spad" 1209045 1209053 1215226 1215231) (-754 "NAGF01.spad" 1204648 1204656 1209035 1209040) (-753 "NAGE04.spad" 1198108 1198116 1204638 1204643) (-752 "NAGE02.spad" 1188450 1188458 1198098 1198103) (-751 "NAGE01.spad" 1184334 1184342 1188440 1188445) (-750 "NAGD03.spad" 1182254 1182262 1184324 1184329) (-749 "NAGD02.spad" 1174785 1174793 1182244 1182249) (-748 "NAGD01.spad" 1168898 1168906 1174775 1174780) (-747 "NAGC06.spad" 1164685 1164693 1168888 1168893) (-746 "NAGC05.spad" 1163154 1163162 1164675 1164680) (-745 "NAGC02.spad" 1162409 1162417 1163144 1163149) (-744 "NAALG.spad" 1161944 1161954 1162377 1162404) (-743 "NAALG.spad" 1161499 1161511 1161934 1161939) (-742 "MULTSQFR.spad" 1158457 1158474 1161489 1161494) (-741 "MULTFACT.spad" 1157840 1157857 1158447 1158452) (-740 "MTSCAT.spad" 1155874 1155895 1157738 1157835) (-739 "MTHING.spad" 1155531 1155541 1155864 1155869) (-738 "MSYSCMD.spad" 1154965 1154973 1155521 1155526) (-737 "MSET.spad" 1152907 1152917 1154671 1154710) (-736 "MSETAGG.spad" 1152752 1152762 1152875 1152902) (-735 "MRING.spad" 1149723 1149735 1152460 1152527) (-734 "MRF2.spad" 1149291 1149305 1149713 1149718) (-733 "MRATFAC.spad" 1148837 1148854 1149281 1149286) (-732 "MPRFF.spad" 1146867 1146886 1148827 1148832) (-731 "MPOLY.spad" 1144338 1144353 1144697 1144824) (-730 "MPCPF.spad" 1143602 1143621 1144328 1144333) (-729 "MPC3.spad" 1143417 1143457 1143592 1143597) (-728 "MPC2.spad" 1143059 1143092 1143407 1143412) (-727 "MONOTOOL.spad" 1141394 1141411 1143049 1143054) (-726 "MONOID.spad" 1140713 1140721 1141384 1141389) (-725 "MONOID.spad" 1140030 1140040 1140703 1140708) (-724 "MONOGEN.spad" 1138776 1138789 1139890 1140025) (-723 "MONOGEN.spad" 1137544 1137559 1138660 1138665) (-722 "MONADWU.spad" 1135558 1135566 1137534 1137539) (-721 "MONADWU.spad" 1133570 1133580 1135548 1135553) (-720 "MONAD.spad" 1132714 1132722 1133560 1133565) (-719 "MONAD.spad" 1131856 1131866 1132704 1132709) (-718 "MOEBIUS.spad" 1130542 1130556 1131836 1131851) (-717 "MODULE.spad" 1130412 1130422 1130510 1130537) (-716 "MODULE.spad" 1130302 1130314 1130402 1130407) (-715 "MODRING.spad" 1129633 1129672 1130282 1130297) (-714 "MODOP.spad" 1128292 1128304 1129455 1129522) (-713 "MODMONOM.spad" 1128021 1128039 1128282 1128287) (-712 "MODMON.spad" 1124816 1124832 1125535 1125688) (-711 "MODFIELD.spad" 1124174 1124213 1124718 1124811) (-710 "MMLFORM.spad" 1123034 1123042 1124164 1124169) (-709 "MMAP.spad" 1122774 1122808 1123024 1123029) (-708 "MLO.spad" 1121201 1121211 1122730 1122769) (-707 "MLIFT.spad" 1119773 1119790 1121191 1121196) (-706 "MKUCFUNC.spad" 1119306 1119324 1119763 1119768) (-705 "MKRECORD.spad" 1118908 1118921 1119296 1119301) (-704 "MKFUNC.spad" 1118289 1118299 1118898 1118903) (-703 "MKFLCFN.spad" 1117245 1117255 1118279 1118284) (-702 "MKBCFUNC.spad" 1116730 1116748 1117235 1117240) (-701 "MINT.spad" 1116169 1116177 1116632 1116725) (-700 "MHROWRED.spad" 1114670 1114680 1116159 1116164) (-699 "MFLOAT.spad" 1113186 1113194 1114560 1114665) (-698 "MFINFACT.spad" 1112586 1112608 1113176 1113181) (-697 "MESH.spad" 1110318 1110326 1112576 1112581) (-696 "MDDFACT.spad" 1108511 1108521 1110308 1110313) (-695 "MDAGG.spad" 1107798 1107808 1108491 1108506) (-694 "MCMPLX.spad" 1103809 1103817 1104423 1104624) (-693 "MCDEN.spad" 1103017 1103029 1103799 1103804) (-692 "MCALCFN.spad" 1100119 1100145 1103007 1103012) (-691 "MAYBE.spad" 1099403 1099414 1100109 1100114) (-690 "MATSTOR.spad" 1096679 1096689 1099393 1099398) (-689 "MATRIX.spad" 1095383 1095393 1095867 1095894) (-688 "MATLIN.spad" 1092709 1092733 1095267 1095272) (-687 "MATCAT.spad" 1084294 1084316 1092677 1092704) (-686 "MATCAT.spad" 1075751 1075775 1084136 1084141) (-685 "MATCAT2.spad" 1075019 1075067 1075741 1075746) (-684 "MAPPKG3.spad" 1073918 1073932 1075009 1075014) (-683 "MAPPKG2.spad" 1073252 1073264 1073908 1073913) (-682 "MAPPKG1.spad" 1072070 1072080 1073242 1073247) (-681 "MAPPAST.spad" 1071383 1071391 1072060 1072065) (-680 "MAPHACK3.spad" 1071191 1071205 1071373 1071378) (-679 "MAPHACK2.spad" 1070956 1070968 1071181 1071186) (-678 "MAPHACK1.spad" 1070586 1070596 1070946 1070951) (-677 "MAGMA.spad" 1068376 1068393 1070576 1070581) (-676 "MACROAST.spad" 1067955 1067963 1068366 1068371) (-675 "M3D.spad" 1065651 1065661 1067333 1067338) (-674 "LZSTAGG.spad" 1062879 1062889 1065641 1065646) (-673 "LZSTAGG.spad" 1060105 1060117 1062869 1062874) (-672 "LWORD.spad" 1056810 1056827 1060095 1060100) (-671 "LSTAST.spad" 1056594 1056602 1056800 1056805) (-670 "LSQM.spad" 1054820 1054834 1055218 1055269) (-669 "LSPP.spad" 1054353 1054370 1054810 1054815) (-668 "LSMP.spad" 1053193 1053221 1054343 1054348) (-667 "LSMP1.spad" 1050997 1051011 1053183 1053188) (-666 "LSAGG.spad" 1050666 1050676 1050965 1050992) (-665 "LSAGG.spad" 1050355 1050367 1050656 1050661) (-664 "LPOLY.spad" 1049309 1049328 1050211 1050280) (-663 "LPEFRAC.spad" 1048566 1048576 1049299 1049304) (-662 "LO.spad" 1047967 1047981 1048500 1048527) (-661 "LOGIC.spad" 1047569 1047577 1047957 1047962) (-660 "LOGIC.spad" 1047169 1047179 1047559 1047564) (-659 "LODOOPS.spad" 1046087 1046099 1047159 1047164) (-658 "LODO.spad" 1045471 1045487 1045767 1045806) (-657 "LODOF.spad" 1044515 1044532 1045428 1045433) (-656 "LODOCAT.spad" 1043173 1043183 1044471 1044510) (-655 "LODOCAT.spad" 1041829 1041841 1043129 1043134) (-654 "LODO2.spad" 1041102 1041114 1041509 1041548) (-653 "LODO1.spad" 1040502 1040512 1040782 1040821) (-652 "LODEEF.spad" 1039274 1039292 1040492 1040497) (-651 "LNAGG.spad" 1035076 1035086 1039264 1039269) (-650 "LNAGG.spad" 1030842 1030854 1035032 1035037) (-649 "LMOPS.spad" 1027578 1027595 1030832 1030837) (-648 "LMODULE.spad" 1027346 1027356 1027568 1027573) (-647 "LMDICT.spad" 1026629 1026639 1026897 1026924) (-646 "LLINSET.spad" 1026026 1026036 1026619 1026624) (-645 "LITERAL.spad" 1025932 1025943 1026016 1026021) (-644 "LIST.spad" 1023650 1023660 1025079 1025106) (-643 "LIST3.spad" 1022941 1022955 1023640 1023645) (-642 "LIST2.spad" 1021581 1021593 1022931 1022936) (-641 "LIST2MAP.spad" 1018458 1018470 1021571 1021576) (-640 "LINSET.spad" 1018080 1018090 1018448 1018453) (-639 "LINEXP.spad" 1017512 1017522 1018060 1018075) (-638 "LINDEP.spad" 1016289 1016301 1017424 1017429) (-637 "LIMITRF.spad" 1014203 1014213 1016279 1016284) (-636 "LIMITPS.spad" 1013086 1013099 1014193 1014198) (-635 "LIE.spad" 1011100 1011112 1012376 1012521) (-634 "LIECAT.spad" 1010576 1010586 1011026 1011095) (-633 "LIECAT.spad" 1010080 1010092 1010532 1010537) (-632 "LIB.spad" 1008128 1008136 1008739 1008754) (-631 "LGROBP.spad" 1005481 1005500 1008118 1008123) (-630 "LF.spad" 1004400 1004416 1005471 1005476) (-629 "LFCAT.spad" 1003419 1003427 1004390 1004395) (-628 "LEXTRIPK.spad" 998922 998937 1003409 1003414) (-627 "LEXP.spad" 996925 996952 998902 998917) (-626 "LETAST.spad" 996624 996632 996915 996920) (-625 "LEADCDET.spad" 995008 995025 996614 996619) (-624 "LAZM3PK.spad" 993712 993734 994998 995003) (-623 "LAUPOL.spad" 992401 992414 993305 993374) (-622 "LAPLACE.spad" 991974 991990 992391 992396) (-621 "LA.spad" 991414 991428 991896 991935) (-620 "LALG.spad" 991190 991200 991394 991409) (-619 "LALG.spad" 990974 990986 991180 991185) (-618 "KVTFROM.spad" 990709 990719 990964 990969) (-617 "KTVLOGIC.spad" 990221 990229 990699 990704) (-616 "KRCFROM.spad" 989959 989969 990211 990216) (-615 "KOVACIC.spad" 988672 988689 989949 989954) (-614 "KONVERT.spad" 988394 988404 988662 988667) (-613 "KOERCE.spad" 988131 988141 988384 988389) (-612 "KERNEL.spad" 986750 986760 987915 987920) (-611 "KERNEL2.spad" 986453 986465 986740 986745) (-610 "KDAGG.spad" 985556 985578 986433 986448) (-609 "KDAGG.spad" 984667 984691 985546 985551) (-608 "KAFILE.spad" 983630 983646 983865 983892) (-607 "JORDAN.spad" 981457 981469 982920 983065) (-606 "JOINAST.spad" 981151 981159 981447 981452) (-605 "JAVACODE.spad" 981017 981025 981141 981146) (-604 "IXAGG.spad" 979140 979164 981007 981012) (-603 "IXAGG.spad" 977118 977144 978987 978992) (-602 "IVECTOR.spad" 975888 975903 976043 976070) (-601 "ITUPLE.spad" 975033 975043 975878 975883) (-600 "ITRIGMNP.spad" 973844 973863 975023 975028) (-599 "ITFUN3.spad" 973338 973352 973834 973839) (-598 "ITFUN2.spad" 973068 973080 973328 973333) (-597 "ITAYLOR.spad" 970860 970875 972904 973029) (-596 "ISUPS.spad" 963271 963286 969834 969931) (-595 "ISUMP.spad" 962768 962784 963261 963266) (-594 "ISTRING.spad" 961771 961784 961937 961964) (-593 "ISAST.spad" 961490 961498 961761 961766) (-592 "IRURPK.spad" 960203 960222 961480 961485) (-591 "IRSN.spad" 958163 958171 960193 960198) (-590 "IRRF2F.spad" 956638 956648 958119 958124) (-589 "IRREDFFX.spad" 956239 956250 956628 956633) (-588 "IROOT.spad" 954570 954580 956229 956234) (-587 "IR.spad" 952359 952373 954425 954452) (-586 "IR2.spad" 951379 951395 952349 952354) (-585 "IR2F.spad" 950579 950595 951369 951374) (-584 "IPRNTPK.spad" 950339 950347 950569 950574) (-583 "IPF.spad" 949904 949916 950144 950237) (-582 "IPADIC.spad" 949665 949691 949830 949899) (-581 "IP4ADDR.spad" 949222 949230 949655 949660) (-580 "IOMODE.spad" 948843 948851 949212 949217) (-579 "IOBFILE.spad" 948204 948212 948833 948838) (-578 "IOBCON.spad" 948069 948077 948194 948199) (-577 "INVLAPLA.spad" 947714 947730 948059 948064) (-576 "INTTR.spad" 940960 940977 947704 947709) (-575 "INTTOOLS.spad" 938671 938687 940534 940539) (-574 "INTSLPE.spad" 937977 937985 938661 938666) (-573 "INTRVL.spad" 937543 937553 937891 937972) (-572 "INTRF.spad" 935907 935921 937533 937538) (-571 "INTRET.spad" 935339 935349 935897 935902) (-570 "INTRAT.spad" 934014 934031 935329 935334) (-569 "INTPM.spad" 932377 932393 933657 933662) (-568 "INTPAF.spad" 930145 930163 932309 932314) (-567 "INTPACK.spad" 920455 920463 930135 930140) (-566 "INT.spad" 919816 919824 920309 920450) (-565 "INTHERTR.spad" 919082 919099 919806 919811) (-564 "INTHERAL.spad" 918748 918772 919072 919077) (-563 "INTHEORY.spad" 915161 915169 918738 918743) (-562 "INTG0.spad" 908624 908642 915093 915098) (-561 "INTFTBL.spad" 902653 902661 908614 908619) (-560 "INTFACT.spad" 901712 901722 902643 902648) (-559 "INTEF.spad" 900027 900043 901702 901707) (-558 "INTDOM.spad" 898642 898650 899953 900022) (-557 "INTDOM.spad" 897319 897329 898632 898637) (-556 "INTCAT.spad" 895572 895582 897233 897314) (-555 "INTBIT.spad" 895075 895083 895562 895567) (-554 "INTALG.spad" 894257 894284 895065 895070) (-553 "INTAF.spad" 893749 893765 894247 894252) (-552 "INTABL.spad" 892267 892298 892430 892457) (-551 "INT8.spad" 892147 892155 892257 892262) (-550 "INT64.spad" 892026 892034 892137 892142) (-549 "INT32.spad" 891905 891913 892016 892021) (-548 "INT16.spad" 891784 891792 891895 891900) (-547 "INS.spad" 889251 889259 891686 891779) (-546 "INS.spad" 886804 886814 889241 889246) (-545 "INPSIGN.spad" 886238 886251 886794 886799) (-544 "INPRODPF.spad" 885304 885323 886228 886233) (-543 "INPRODFF.spad" 884362 884386 885294 885299) (-542 "INNMFACT.spad" 883333 883350 884352 884357) (-541 "INMODGCD.spad" 882817 882847 883323 883328) (-540 "INFSP.spad" 881102 881124 882807 882812) (-539 "INFPROD0.spad" 880152 880171 881092 881097) (-538 "INFORM.spad" 877313 877321 880142 880147) (-537 "INFORM1.spad" 876938 876948 877303 877308) (-536 "INFINITY.spad" 876490 876498 876928 876933) (-535 "INETCLTS.spad" 876467 876475 876480 876485) (-534 "INEP.spad" 874999 875021 876457 876462) (-533 "INDE.spad" 874728 874745 874989 874994) (-532 "INCRMAPS.spad" 874149 874159 874718 874723) (-531 "INBFILE.spad" 873221 873229 874139 874144) (-530 "INBFF.spad" 868991 869002 873211 873216) (-529 "INBCON.spad" 867279 867287 868981 868986) (-528 "INBCON.spad" 865565 865575 867269 867274) (-527 "INAST.spad" 865226 865234 865555 865560) (-526 "IMPTAST.spad" 864934 864942 865216 865221) (-525 "IMATRIX.spad" 863879 863905 864391 864418) (-524 "IMATQF.spad" 862973 863017 863835 863840) (-523 "IMATLIN.spad" 861578 861602 862929 862934) (-522 "ILIST.spad" 860234 860249 860761 860788) (-521 "IIARRAY2.spad" 859622 859660 859841 859868) (-520 "IFF.spad" 859032 859048 859303 859396) (-519 "IFAST.spad" 858646 858654 859022 859027) (-518 "IFARRAY.spad" 856133 856148 857829 857856) (-517 "IFAMON.spad" 855995 856012 856089 856094) (-516 "IEVALAB.spad" 855384 855396 855985 855990) (-515 "IEVALAB.spad" 854771 854785 855374 855379) (-514 "IDPO.spad" 854569 854581 854761 854766) (-513 "IDPOAMS.spad" 854325 854337 854559 854564) (-512 "IDPOAM.spad" 854045 854057 854315 854320) (-511 "IDPC.spad" 852979 852991 854035 854040) (-510 "IDPAM.spad" 852724 852736 852969 852974) (-509 "IDPAG.spad" 852471 852483 852714 852719) (-508 "IDENT.spad" 852121 852129 852461 852466) (-507 "IDECOMP.spad" 849358 849376 852111 852116) (-506 "IDEAL.spad" 844281 844320 849293 849298) (-505 "ICDEN.spad" 843432 843448 844271 844276) (-504 "ICARD.spad" 842621 842629 843422 843427) (-503 "IBPTOOLS.spad" 841214 841231 842611 842616) (-502 "IBITS.spad" 840413 840426 840850 840877) (-501 "IBATOOL.spad" 837288 837307 840403 840408) (-500 "IBACHIN.spad" 835775 835790 837278 837283) (-499 "IARRAY2.spad" 834763 834789 835382 835409) (-498 "IARRAY1.spad" 833808 833823 833946 833973) (-497 "IAN.spad" 832021 832029 833624 833717) (-496 "IALGFACT.spad" 831622 831655 832011 832016) (-495 "HYPCAT.spad" 831046 831054 831612 831617) (-494 "HYPCAT.spad" 830468 830478 831036 831041) (-493 "HOSTNAME.spad" 830276 830284 830458 830463) (-492 "HOMOTOP.spad" 830019 830029 830266 830271) (-491 "HOAGG.spad" 827287 827297 830009 830014) (-490 "HOAGG.spad" 824330 824342 827054 827059) (-489 "HEXADEC.spad" 822432 822440 822797 822890) (-488 "HEUGCD.spad" 821447 821458 822422 822427) (-487 "HELLFDIV.spad" 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(|:| -2818 |#2|)) (-310 (-2 (|:| -2010 |#1|) (|:| -2818 |#2|))))) +(188029 . 3453990502) +(((|#2| |#2|) -12 (|has| |#2| (-310 |#2|)) (|has| |#2| (-1099))) ((#0=(-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) #0#) |has| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (-310 (-2 (|:| -2050 |#1|) (|:| -2849 |#2|))))) ((((-566)) . T) (($) -2805 (|has| |#1| (-308)) (|has| |#1| (-365)) (|has| |#1| (-351)) (|has| |#1| (-558))) (((-409 (-566))) -2805 (|has| |#1| (-365)) (|has| |#1| (-351)) (|has| |#1| (-1038 (-409 (-566))))) ((|#1|) . T)) (((|#2| |#2|) . T)) ((((-566)) . T)) @@ -51,12 +51,12 @@ (((|#1|) . T) (((-566)) |has| |#1| (-1038 (-566))) (((-409 (-566))) |has| |#1| (-1038 (-409 (-566))))) (-2805 (|has| |#2| (-172)) (|has| |#2| (-454)) (|has| |#2| (-558)) (|has| |#2| (-909))) (-2805 (|has| |#1| (-172)) (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) -(((|#2| (-484 (-2997 |#1|) (-771))) . T)) +(((|#2| (-484 (-3020 |#1|) (-771))) . T)) (((|#1| (-533 (-1175))) . T)) (((#0=(-870 |#1|) #0#) . T) ((#1=(-409 (-566)) #1#) . T) (($ $) . T)) ((((-1157)) . T) (((-958 (-129))) . T) (((-862)) . T)) ((((-862)) . T)) -((((-2 (|:| -2010 |#1|) (|:| -2818 |#2|))) . T)) +((((-2 (|:| -2050 |#1|) (|:| -2849 |#2|))) . T)) (|has| |#4| (-370)) (|has| |#3| (-370)) (((|#1|) . T)) @@ -73,7 +73,7 @@ ((((-566)) . T) (((-409 (-566))) -2805 (|has| |#2| (-38 (-409 (-566)))) (|has| |#2| (-1038 (-409 (-566))))) ((|#2|) . T) (($) -2805 (|has| |#2| (-454)) (|has| |#2| (-558)) (|has| |#2| (-909))) (((-864 |#1|)) . T)) (-2805 (|has| |#1| (-365)) (|has| |#1| (-558))) (-2805 (|has| |#1| (-365)) (|has| |#1| (-558))) -((((-2 (|:| -2168 |#1|) (|:| -3250 |#2|))) . T)) +((((-2 (|:| -2208 |#1|) (|:| -2456 |#2|))) . T)) ((($) . T)) ((((-566)) . T) (((-409 (-566))) -2805 (|has| |#1| (-38 (-409 (-566)))) (|has| |#1| (-1038 (-409 (-566))))) ((|#1|) . T) (($) -2805 (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) (((-1175)) . T)) ((((-862)) -2805 (|has| |#1| (-613 (-862))) (|has| |#1| (-850)) (|has| |#1| (-1099)))) @@ -129,7 +129,7 @@ (((|#1|) . T) (((-409 (-566))) |has| |#1| (-38 (-409 (-566)))) (($) . T)) (-2805 (|has| |#1| (-850)) (|has| |#1| (-1099))) (((|#1|) . T)) -((((-2 (|:| -2010 |#1|) (|:| -2818 |#2|))) . T)) +((((-2 (|:| -2050 |#1|) (|:| -2849 |#2|))) . T)) ((((-566)) . T)) ((((-862)) . T)) (((|#1| |#2|) . T)) @@ -268,8 +268,8 @@ (((|#1|) . T)) ((((-409 (-566))) |has| |#1| (-1038 (-409 (-566)))) (((-566)) |has| |#1| (-1038 (-566))) ((|#1|) . T)) (((|#1|) . T) (((-566)) |has| |#1| (-639 (-566)))) -(((|#2|) . T) (((-2 (|:| -2010 |#1|) (|:| -2818 |#2|))) . T)) -(((|#1|) . T) (((-2 (|:| -2010 (-1157)) (|:| -2818 |#1|))) . T)) +(((|#2|) . T) (((-2 (|:| -2050 |#1|) (|:| -2849 |#2|))) . T)) +(((|#1|) . T) (((-2 (|:| -2050 (-1157)) (|:| -2849 |#1|))) . T)) (|has| |#1| (-558)) ((((-566)) -2805 (|has| |#4| (-172)) (|has| |#4| (-848)) (-12 (|has| |#4| (-1038 (-566))) (|has| |#4| (-1099))) (|has| |#4| (-1049))) ((|#4|) -2805 (|has| |#4| (-172)) (|has| |#4| (-1099))) (((-409 (-566))) -12 (|has| |#4| (-1038 (-409 (-566)))) (|has| |#4| (-1099)))) ((((-566)) -2805 (|has| |#3| (-172)) (|has| |#3| (-848)) (-12 (|has| |#3| (-1038 (-566))) (|has| |#3| (-1099))) (|has| |#3| (-1049))) ((|#3|) -2805 (|has| |#3| (-172)) (|has| |#3| (-1099))) (((-409 (-566))) -12 (|has| |#3| (-1038 (-409 (-566)))) (|has| |#3| (-1099)))) @@ -298,11 +298,11 @@ ((((-538)) |has| |#2| (-614 (-538))) (((-892 (-381))) |has| |#2| (-614 (-892 (-381)))) (((-892 (-566))) |has| |#2| (-614 (-892 (-566))))) ((((-862)) . T)) (((|#1| |#2| |#3| |#4|) . T)) -((((-2 (|:| -2168 |#1|) (|:| -3250 |#2|))) . T) (((-862)) . T)) +((((-2 (|:| -2208 |#1|) (|:| -2456 |#2|))) . T) (((-862)) . T)) ((((-538)) |has| |#1| (-614 (-538))) (((-892 (-381))) |has| |#1| (-614 (-892 (-381)))) (((-892 (-566))) |has| |#1| (-614 (-892 (-566))))) (((|#4|) -2805 (|has| |#4| (-172)) (|has| |#4| (-365)) (|has| |#4| (-1049))) (($) |has| |#4| (-172))) (((|#3|) -2805 (|has| |#3| (-172)) (|has| |#3| (-365)) (|has| |#3| (-1049))) (($) |has| |#3| (-172))) -((((-2 (|:| -2168 |#1|) (|:| -3250 |#2|))) . T)) +((((-2 (|:| -2208 |#1|) (|:| -2456 |#2|))) . T)) ((((-862)) . T)) ((((-862)) . T)) ((((-538)) . T) (((-566)) . T) (((-892 (-566))) . T) (((-381)) . T) (((-225)) . T)) @@ -310,7 +310,7 @@ (((|#1|) . T) (((-566)) |has| |#1| (-1038 (-566))) (((-409 (-566))) |has| |#1| (-1038 (-409 (-566))))) ((($) . T) (((-409 (-566))) |has| |#2| (-38 (-409 (-566)))) ((|#2|) . T)) ((((-409 $) (-409 $)) |has| |#2| (-558)) (($ $) . T) ((|#2| |#2|) . T)) -((((-2 (|:| -2010 (-1157)) (|:| -2818 (-52)))) . T)) +((((-2 (|:| -2050 (-1157)) (|:| -2849 (-52)))) . T)) (((|#1|) . T)) (|has| |#2| (-909)) ((((-1157) (-52)) . T)) @@ -349,7 +349,7 @@ (((|#1|) . T)) (((|#2| |#2|) . T)) (|has| |#1| (-1150)) -((((-2 (|:| -2010 (-1157)) (|:| -2818 |#1|))) . T)) +((((-2 (|:| -2050 (-1157)) (|:| -2849 |#1|))) . T)) (|has| (-1250 |#1| |#2| |#3| |#4|) (-145)) (|has| (-1250 |#1| |#2| |#3| |#4|) (-147)) (|has| |#1| (-145)) @@ -367,10 +367,10 @@ ((($) . T) ((|#1|) . T)) (((|#2|) |has| |#2| (-1049))) ((((-862)) . T)) -(((|#2| |#2|) -12 (|has| |#2| (-310 |#2|)) (|has| |#2| (-1099))) ((#0=(-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) #0#) |has| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (-310 (-2 (|:| -2010 |#1|) (|:| -2818 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-310 |#2|)) (|has| |#2| (-1099))) ((#0=(-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) #0#) |has| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (-310 (-2 (|:| -2050 |#1|) (|:| -2849 |#2|))))) (((|#1|) . T)) -((((-1264 (-341 (-2523) (-2523 (QUOTE X)) (-699)))) . T)) -(((|#1| |#1|) -12 (|has| |#1| (-310 |#1|)) (|has| |#1| (-1099))) ((#0=(-2 (|:| -2010 (-1157)) (|:| -2818 |#1|)) #0#) |has| (-2 (|:| -2010 (-1157)) (|:| -2818 |#1|)) (-310 (-2 (|:| -2010 (-1157)) (|:| -2818 |#1|))))) +((((-1264 (-341 (-3791) (-3791 (QUOTE X)) (-699)))) . T)) +(((|#1| |#1|) -12 (|has| |#1| (-310 |#1|)) (|has| |#1| (-1099))) ((#0=(-2 (|:| -2050 (-1157)) (|:| -2849 |#1|)) #0#) |has| (-2 (|:| -2050 (-1157)) (|:| -2849 |#1|)) (-310 (-2 (|:| -2050 (-1157)) (|:| -2849 |#1|))))) ((((-862)) . T)) ((((-566) |#1|) . T)) ((((-538)) -12 (|has| |#1| (-614 (-538))) (|has| |#2| (-614 (-538)))) (((-892 (-381))) -12 (|has| |#1| (-614 (-892 (-381)))) (|has| |#2| (-614 (-892 (-381))))) (((-892 (-566))) -12 (|has| |#1| (-614 (-892 (-566)))) (|has| |#2| (-614 (-892 (-566)))))) @@ -488,12 +488,12 @@ ((((-144)) . T)) (((|#3|) |has| |#3| (-1099)) (((-566)) -12 (|has| |#3| (-1038 (-566))) (|has| |#3| (-1099))) (((-409 (-566))) -12 (|has| |#3| (-1038 (-409 (-566)))) (|has| |#3| (-1099)))) ((((-862)) . T)) -((((-2 (|:| -2010 |#1|) (|:| -2818 |#2|))) . T)) +((((-2 (|:| -2050 |#1|) (|:| -2849 |#2|))) . T)) (((|#1|) . T)) ((((-862)) -2805 (|has| |#1| (-613 (-862))) (|has| |#1| (-850)) (|has| |#1| (-1099)))) ((((-538)) |has| |#1| (-614 (-538)))) (((|#1|) |has| |#1| (-172))) -((((-2 (|:| -2010 (-1175)) (|:| -2818 (-52)))) . T)) +((((-2 (|:| -2050 (-1175)) (|:| -2849 (-52)))) . T)) (|has| |#1| (-365)) ((((-1180)) . T)) (((|#1|) . T)) @@ -504,13 +504,13 @@ (|has| |#1| (-848)) (-2805 (|has| |#1| (-850)) (|has| |#1| (-1099))) ((((-862)) . T)) -((((-2 (|:| -2010 |#1|) (|:| -2818 |#2|))) . T)) +((((-2 (|:| -2050 |#1|) (|:| -2849 |#2|))) . T)) ((((-538)) |has| |#1| (-614 (-538)))) (((|#1| |#2|) . T)) ((((-1175)) -12 (|has| |#1| (-365)) (|has| |#1| (-900 (-1175))))) ((((-1157) |#1|) . T)) (((|#1| |#2| |#3| (-533 |#3|)) . T)) -((((-2 (|:| -2010 |#1|) (|:| -2818 |#2|))) . T)) +((((-2 (|:| -2050 |#1|) (|:| -2849 |#2|))) . T)) (|has| |#1| (-370)) (|has| |#1| (-370)) (|has| |#1| (-370)) @@ -726,7 +726,7 @@ ((((-1139 |#1| |#2|)) |has| (-1139 |#1| |#2|) (-310 (-1139 |#1| |#2|)))) (((|#4| |#4|) -12 (|has| |#4| (-310 |#4|)) (|has| |#4| (-1099)))) (((|#3| |#3|) -12 (|has| |#3| (-310 |#3|)) (|has| |#3| (-1099)))) -(((|#2|) -12 (|has| |#2| (-310 |#2|)) (|has| |#2| (-1099))) (((-2 (|:| -2010 |#1|) (|:| -2818 |#2|))) |has| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (-310 (-2 (|:| -2010 |#1|) (|:| -2818 |#2|))))) +(((|#2|) -12 (|has| |#2| (-310 |#2|)) (|has| |#2| (-1099))) (((-2 (|:| -2050 |#1|) (|:| -2849 |#2|))) |has| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (-310 (-2 (|:| -2050 |#1|) (|:| -2849 |#2|))))) (((|#2|) . T) (((-566)) |has| |#2| (-1038 (-566))) (((-409 (-566))) |has| |#2| (-1038 (-409 (-566))))) (((|#1|) . T)) (((|#1| |#2|) . T)) @@ -735,7 +735,7 @@ (((|#2|) . T)) (((|#3|) . T)) (-2805 (|has| |#1| (-850)) (|has| |#1| (-1099))) -(((|#2|) -12 (|has| |#2| (-310 |#2|)) (|has| |#2| (-1099))) (((-2 (|:| -2010 |#1|) (|:| -2818 |#2|))) |has| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (-310 (-2 (|:| -2010 |#1|) (|:| -2818 |#2|))))) +(((|#2|) -12 (|has| |#2| (-310 |#2|)) (|has| |#2| (-1099))) (((-2 (|:| -2050 |#1|) (|:| -2849 |#2|))) |has| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (-310 (-2 (|:| -2050 |#1|) (|:| -2849 |#2|))))) (((|#2|) . T)) ((((-862)) -2805 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-613 (-862))) (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-370)) (|has| |#2| (-726)) (|has| |#2| (-793)) (|has| |#2| (-848)) (|has| |#2| (-1049)) (|has| |#2| (-1099))) (((-1264 |#2|)) . T)) ((((-409 (-566))) |has| |#1| (-1038 (-409 (-566)))) ((|#1|) . T) (((-566)) . T) (($) . T)) @@ -834,9 +834,9 @@ (-2805 (|has| |#1| (-454)) (|has| |#1| (-909))) ((((-566) |#2|) . T)) ((((-862)) . T)) -((((-2 (|:| -2010 |#1|) (|:| -2818 |#2|))) . T)) -((((-2 (|:| -2010 |#1|) (|:| -2818 |#2|))) . T)) -((((-2 (|:| -2010 |#1|) (|:| -2818 |#2|))) . T)) +((((-2 (|:| -2050 |#1|) (|:| -2849 |#2|))) . T)) +((((-2 (|:| -2050 |#1|) (|:| -2849 |#2|))) . T)) +((((-2 (|:| -2050 |#1|) (|:| -2849 |#2|))) . T)) (((|#1|) -12 (|has| |#1| (-310 |#1|)) (|has| |#1| (-1099)))) ((($) -2805 (|has| |#3| (-172)) (|has| |#3| (-848)) (|has| |#3| (-1049))) ((|#3|) -2805 (|has| |#3| (-172)) (|has| |#3| (-365)) (|has| |#3| (-1049)))) ((((-566) |#1|) . T)) @@ -851,11 +851,11 @@ (|has| |#1| (-558)) (|has| |#1| (-38 (-409 (-566)))) (|has| |#1| (-38 (-409 (-566)))) -((((-2 (|:| -2010 |#1|) (|:| -2818 |#2|))) . T)) +((((-2 (|:| -2050 |#1|) (|:| -2849 |#2|))) . T)) ((((-862)) . T)) -((((-2 (|:| -2010 (-1157)) (|:| -2818 |#1|))) . T)) +((((-2 (|:| -2050 (-1157)) (|:| -2849 |#1|))) . T)) (|has| |#1| (-38 (-409 (-566)))) -((((-390) (-2 (|:| -2010 (-1157)) (|:| -2818 |#1|))) . T)) +((((-390) (-2 (|:| -2050 (-1157)) (|:| -2849 |#1|))) . T)) (|has| |#1| (-38 (-409 (-566)))) (|has| |#2| (-1150)) (-2805 (|has| |#1| (-365)) (|has| |#1| (-558))) @@ -1070,7 +1070,7 @@ (|has| |#1| (-147)) (|has| |#1| (-145)) (|has| |#4| (-848)) -(((|#2| (-240 (-2997 |#1|) (-771)) (-864 |#1|)) . T)) +(((|#2| (-240 (-3020 |#1|) (-771)) (-864 |#1|)) . T)) (|has| |#3| (-848)) (((|#1| (-533 |#3|) |#3|) . T)) (|has| |#1| (-147)) @@ -1091,7 +1091,7 @@ (|has| |#2| (-172)) (((|#1| |#2|) . T)) (-12 (|has| |#2| (-233)) (|has| |#2| (-1049))) -(((|#2|) . T) (((-2 (|:| -2010 |#1|) (|:| -2818 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -2050 |#1|) (|:| -2849 |#2|))) . T)) (-2805 (|has| |#3| (-793)) (|has| |#3| (-848))) (-2805 (|has| |#3| (-793)) (|has| |#3| (-848))) ((((-862)) . T)) @@ -1122,10 +1122,10 @@ (((|#1| (-409 (-566))) . T)) (((|#3|) . T) (((-612 $)) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -2010 |#1|) (|:| -2818 |#2|))) . T)) +((((-2 (|:| -2050 |#1|) (|:| -2849 |#2|))) . T)) (((|#1|) . T)) (((|#1|) -12 (|has| |#1| (-310 |#1|)) (|has| |#1| (-1099)))) -((((-2 (|:| -2010 |#1|) (|:| -2818 |#2|))) . T)) +((((-2 (|:| -2050 |#1|) (|:| -2849 |#2|))) . T)) ((((-566)) -2805 (|has| |#2| (-172)) (|has| |#2| (-848)) (-12 (|has| |#2| (-1038 (-566))) (|has| |#2| (-1099))) (|has| |#2| (-1049))) ((|#2|) -2805 (|has| |#2| (-172)) (|has| |#2| (-1099))) (((-409 (-566))) -12 (|has| |#2| (-1038 (-409 (-566)))) (|has| |#2| (-1099)))) (((|#1|) . T) (((-409 (-566))) . T) (($) . T)) ((($ $) . T) ((|#2| $) . T)) @@ -1134,8 +1134,8 @@ ((((-862)) . T)) ((((-862)) . T)) (((|#1| |#1|) . T)) -(((|#2|) -12 (|has| |#2| (-310 |#2|)) (|has| |#2| (-1099))) (((-2 (|:| -2010 |#1|) (|:| -2818 |#2|))) |has| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (-310 (-2 (|:| -2010 |#1|) (|:| -2818 |#2|))))) -(((|#1|) -12 (|has| |#1| (-310 |#1|)) (|has| |#1| (-1099))) (((-2 (|:| -2010 (-1157)) (|:| -2818 |#1|))) |has| (-2 (|:| -2010 (-1157)) (|:| -2818 |#1|)) (-310 (-2 (|:| -2010 (-1157)) (|:| -2818 |#1|))))) +(((|#2|) -12 (|has| |#2| (-310 |#2|)) (|has| |#2| (-1099))) (((-2 (|:| -2050 |#1|) (|:| -2849 |#2|))) |has| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (-310 (-2 (|:| -2050 |#1|) (|:| -2849 |#2|))))) +(((|#1|) -12 (|has| |#1| (-310 |#1|)) (|has| |#1| (-1099))) (((-2 (|:| -2050 (-1157)) (|:| -2849 |#1|))) |has| (-2 (|:| -2050 (-1157)) (|:| -2849 |#1|)) (-310 (-2 (|:| -2050 (-1157)) (|:| -2849 |#1|))))) ((((-862)) . T)) (((|#1|) . T)) (((|#3| |#3|) . T)) @@ -1151,7 +1151,7 @@ (|has| |#1| (-1099)) (((|#2| |#2|) -2805 (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-1049))) (($ $) |has| |#2| (-172))) (((|#2|) -2805 (|has| |#2| (-172)) (|has| |#2| (-365)))) -((((-566) (-2 (|:| -2010 |#1|) (|:| -2818 |#2|))) . T) ((|#1| |#2|) . T)) +((((-566) (-2 (|:| -2050 |#1|) (|:| -2849 |#2|))) . T) ((|#1| |#2|) . T)) (((|#2|) -2805 (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-1049))) (($) |has| |#2| (-172))) ((((-566)) . T)) ((((-1180)) . T)) @@ -1195,7 +1195,7 @@ (-2805 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-370)) (|has| |#2| (-726)) (|has| |#2| (-793)) (|has| |#2| (-848)) (|has| |#2| (-1049)) (|has| |#2| (-1099))) (-12 (|has| |#3| (-233)) (|has| |#3| (-1049))) (|has| |#2| (-1150)) -(((#0=(-52)) . T) (((-2 (|:| -2010 (-1175)) (|:| -2818 #0#))) . T)) +(((#0=(-52)) . T) (((-2 (|:| -2050 (-1175)) (|:| -2849 #0#))) . T)) (((|#1| |#2|) . T)) (-2805 (|has| |#3| (-172)) (|has| |#3| (-848)) (|has| |#3| (-1049))) (((|#1| (-566) (-1081)) . T)) @@ -1224,7 +1224,7 @@ (((|#4|) . T) (((-862)) . T)) (((|#3|) . T) ((|#2|) . T) (($) -2805 (|has| |#4| (-172)) (|has| |#4| (-848)) (|has| |#4| (-1049))) (((-566)) . T) ((|#4|) -2805 (|has| |#4| (-172)) (|has| |#4| (-365)) (|has| |#4| (-1049)))) (((|#2|) . T) (($) -2805 (|has| |#3| (-172)) (|has| |#3| (-848)) (|has| |#3| (-1049))) (((-566)) . T) ((|#3|) -2805 (|has| |#3| (-172)) (|has| |#3| (-365)) (|has| |#3| (-1049)))) -(((|#2| |#2|) -12 (|has| |#2| (-310 |#2|)) (|has| |#2| (-1099))) ((#0=(-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) #0#) |has| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (-310 (-2 (|:| -2010 |#1|) (|:| -2818 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-310 |#2|)) (|has| |#2| (-1099))) ((#0=(-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) #0#) |has| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (-310 (-2 (|:| -2050 |#1|) (|:| -2849 |#2|))))) (|has| |#1| (-558)) (((|#1| |#1|) -12 (|has| |#1| (-310 |#1|)) (|has| |#1| (-1099)))) ((((-862)) . T)) @@ -1284,7 +1284,7 @@ (-12 (|has| |#1| (-793)) (|has| |#2| (-793))) (-2805 (|has| |#2| (-172)) (|has| |#2| (-848)) (|has| |#2| (-1049))) ((($) . T) (((-566)) . T) ((|#2|) . T)) -(((|#2|) . T) (((-2 (|:| -2010 |#1|) (|:| -2818 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -2050 |#1|) (|:| -2849 |#2|))) . T)) (((|#2|) . T) (($) . T)) (|has| |#1| (-1199)) (((#0=(-566) #0#) . T) ((#1=(-409 (-566)) #1#) . T) (($ $) . T)) @@ -1315,7 +1315,7 @@ ((($) . T) (((-409 (-566))) -2805 (|has| |#1| (-365)) (|has| |#1| (-351))) ((|#1|) . T)) (-2805 (|has| |#1| (-172)) (|has| |#1| (-558))) ((($) . T)) -(((#0=(-2 (|:| -2010 (-1175)) (|:| -2818 (-52))) #0#) |has| (-2 (|:| -2010 (-1175)) (|:| -2818 (-52))) (-310 (-2 (|:| -2010 (-1175)) (|:| -2818 (-52)))))) +(((#0=(-2 (|:| -2050 (-1175)) (|:| -2849 (-52))) #0#) |has| (-2 (|:| -2050 (-1175)) (|:| -2849 (-52))) (-310 (-2 (|:| -2050 (-1175)) (|:| -2849 (-52)))))) ((($) . T)) ((($) . T)) (((|#2|) |has| |#2| (-1099))) @@ -1331,10 +1331,10 @@ ((((-566)) |has| #0=(-409 |#2|) (-639 (-566))) ((#0#) . T)) ((($) . T) (((-566)) . T)) ((((-566) (-144)) . T)) -((((-566) (-2 (|:| -2010 |#1|) (|:| -2818 |#2|))) . T) ((|#1| |#2|) . T)) +((((-566) (-2 (|:| -2050 |#1|) (|:| -2849 |#2|))) . T) ((|#1| |#2|) . T)) ((((-409 (-566))) . T) (($) . T)) (((|#1|) . T)) -((((-2 (|:| -2010 |#1|) (|:| -2818 |#2|))) . T)) +((((-2 (|:| -2050 |#1|) (|:| -2849 |#2|))) . T)) ((((-862)) . T)) ((((-910 |#1|)) . T)) (|has| |#1| (-365)) @@ -1363,7 +1363,7 @@ ((((-862)) . T)) ((($) . T)) (((|#2|) . T) (($) . T)) -((((-566) (-2 (|:| -2010 |#1|) (|:| -2818 |#2|))) . T) ((|#1| |#2|) . T)) +((((-566) (-2 (|:| -2050 |#1|) (|:| -2849 |#2|))) . T) ((|#1| |#2|) . T)) (((|#1|) . T)) (((|#1|) |has| |#1| (-172))) ((($) |has| |#1| (-558)) ((|#1|) |has| |#1| (-172)) (((-409 (-566))) |has| |#1| (-38 (-409 (-566))))) @@ -1378,7 +1378,7 @@ ((((-538)) |has| |#1| (-614 (-538))) (((-892 (-381))) |has| |#1| (-614 (-892 (-381)))) (((-892 (-566))) |has| |#1| (-614 (-892 (-566))))) ((((-862)) . T)) ((((-870 |#1|)) . T) (($) . T) (((-409 (-566))) . T)) -(((|#2|) . T) (((-2 (|:| -2010 |#1|) (|:| -2818 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -2050 |#1|) (|:| -2849 |#2|))) . T)) ((((-508)) . T)) (|has| |#2| (-848)) ((((-508)) . T)) @@ -1413,7 +1413,7 @@ (((|#1|) . T)) ((((-1175)) |has| (-409 |#2|) (-900 (-1175)))) (((|#2|) . T)) -(((|#2| |#2|) -12 (|has| |#2| (-310 |#2|)) (|has| |#2| (-1099))) ((#0=(-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) #0#) |has| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (-310 (-2 (|:| -2010 |#1|) (|:| -2818 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-310 |#2|)) (|has| |#2| (-1099))) ((#0=(-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) #0#) |has| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (-310 (-2 (|:| -2050 |#1|) (|:| -2849 |#2|))))) ((((-409 (-566))) |has| |#2| (-38 (-409 (-566)))) ((|#2|) |has| |#2| (-172)) (($) -2805 (|has| |#2| (-454)) (|has| |#2| (-558)) (|has| |#2| (-909)))) ((((-409 (-566))) |has| |#2| (-38 (-409 (-566)))) ((|#2|) . T) (($) -2805 (|has| |#2| (-172)) (|has| |#2| (-454)) (|has| |#2| (-558)) (|has| |#2| (-909)))) ((((-409 (-566))) |has| |#1| (-38 (-409 (-566)))) ((|#1|) |has| |#1| (-172)) (($) -2805 (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909)))) @@ -1430,7 +1430,7 @@ (((|#2|) . T) (((-566)) . T)) ((((-862)) . T)) ((((-862)) . T)) -((((-2 (|:| -2010 |#1|) (|:| -2818 |#2|))) . T) ((|#2|) . T)) +((((-2 (|:| -2050 |#1|) (|:| -2849 |#2|))) . T) ((|#2|) . T)) ((((-862)) . T)) ((((-862)) . T)) ((((-1157) (-1175) (-566) (-225) (-862)) . T)) @@ -1521,7 +1521,7 @@ ((((-999 |#1|)) . T) ((|#1|) . T)) ((((-862)) . T)) ((((-862)) . T)) -((((-2 (|:| -2010 |#1|) (|:| -2818 |#2|))) . T)) +((((-2 (|:| -2050 |#1|) (|:| -2849 |#2|))) . T)) ((((-409 (-566))) . T) (((-409 |#1|)) . T) ((|#1|) . T) (($) . T)) (((|#1| (-1171 |#1|)) . T)) ((((-566)) . T) (($) . T) (((-409 (-566))) . T)) @@ -1530,7 +1530,7 @@ (((|#1|) . T) (((-566)) . T) (($) . T)) (((|#2|) . T)) ((((-566)) . T) (($) . T) (((-409 (-566))) . T)) -((((-2 (|:| -2010 (-1157)) (|:| -2818 |#1|))) . T)) +((((-2 (|:| -2050 (-1157)) (|:| -2849 |#1|))) . T)) ((((-862)) -2805 (|has| |#1| (-613 (-862))) (|has| |#1| (-1099)))) ((((-566) |#2|) . T)) (((|#1|) . T) (((-409 (-566))) . T) (((-566)) . T) (($) . T)) @@ -1544,7 +1544,7 @@ (|has| |#1| (-38 (-409 (-566)))) (|has| |#1| (-38 (-409 (-566)))) ((((-1256 |#1| |#2| |#3|)) |has| |#1| (-365))) -(((|#2| |#2|) -12 (|has| |#2| (-310 |#2|)) (|has| |#2| (-1099))) ((#0=(-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) #0#) |has| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (-310 (-2 (|:| -2010 |#1|) (|:| -2818 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-310 |#2|)) (|has| |#2| (-1099))) ((#0=(-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) #0#) |has| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (-310 (-2 (|:| -2050 |#1|) (|:| -2849 |#2|))))) (((|#2| |#2|) . T)) (|has| |#1| (-1099)) (|has| |#1| (-38 (-409 (-566)))) @@ -1589,7 +1589,7 @@ (((|#1|) -12 (|has| |#1| (-310 |#1|)) (|has| |#1| (-1099)))) (((|#1| |#2|) . T)) ((((-566) (-144)) . T)) -(((#0=(-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) #0#) |has| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (-310 (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-310 |#2|)) (|has| |#2| (-1099)))) +(((#0=(-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) #0#) |has| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (-310 (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-310 |#2|)) (|has| |#2| (-1099)))) ((($) -2805 (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) ((|#1|) |has| |#1| (-172)) (((-409 (-566))) |has| |#1| (-38 (-409 (-566))))) (|has| |#1| (-850)) (((|#2| (-771) (-1081)) . T)) @@ -1642,7 +1642,7 @@ ((((-390) (-1157)) . T)) ((($) |has| |#1| (-558)) ((|#1|) |has| |#1| (-172)) (((-409 (-566))) |has| |#1| (-38 (-409 (-566))))) ((((-862)) -2805 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-613 (-862))) (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-370)) (|has| |#2| (-726)) (|has| |#2| (-793)) (|has| |#2| (-848)) (|has| |#2| (-1049)) (|has| |#2| (-1099))) (((-1264 |#2|)) . T)) -(((#0=(-52)) . T) (((-2 (|:| -2010 (-1157)) (|:| -2818 #0#))) . T)) +(((#0=(-52)) . T) (((-2 (|:| -2050 (-1157)) (|:| -2849 #0#))) . T)) (((|#1|) . T)) ((((-862)) . T)) (((|#2| |#2|) -12 (|has| |#2| (-310 |#2|)) (|has| |#2| (-1099)))) @@ -1672,7 +1672,7 @@ ((((-862)) . T)) ((((-862)) . T)) (|has| |#1| (-1099)) -(((|#2| (-484 (-2997 |#1|) (-771)) (-864 |#1|)) . T)) +(((|#2| (-484 (-3020 |#1|) (-771)) (-864 |#1|)) . T)) ((((-409 (-566))) . #0=(|has| |#2| (-365))) (($) . #0#)) (((|#1| (-533 (-1175)) (-1175)) . T)) (((|#1|) . T)) @@ -1693,12 +1693,12 @@ (((|#2|) |has| |#2| (-172))) (((|#1|) . T)) (((|#2|) . T)) -(((|#1|) . T) (((-2 (|:| -2010 (-1157)) (|:| -2818 |#1|))) . T)) -((((-2 (|:| -2010 |#1|) (|:| -2818 |#2|))) . T)) +(((|#1|) . T) (((-2 (|:| -2050 (-1157)) (|:| -2849 |#1|))) . T)) +((((-2 (|:| -2050 |#1|) (|:| -2849 |#2|))) . T)) (((|#2|) . T)) -((((-2 (|:| -2010 (-1175)) (|:| -2818 (-52)))) . T)) +((((-2 (|:| -2050 (-1175)) (|:| -2849 (-52)))) . T)) ((((-1173 |#1| |#2| |#3|)) |has| |#1| (-365))) -((((-2 (|:| -2010 |#1|) (|:| -2818 |#2|))) . T)) +((((-2 (|:| -2050 |#1|) (|:| -2849 |#2|))) . T)) ((((-1175) (-52)) . T)) ((($ $) . T)) (((|#1| (-566)) . T)) @@ -1748,11 +1748,11 @@ (-2805 (|has| |#1| (-365)) (|has| |#1| (-351))) (|has| |#1| (-38 (-409 (-566)))) (|has| |#1| (-38 (-409 (-566)))) -((((-2 (|:| -2010 |#1|) (|:| -2818 |#2|))) . T)) +((((-2 (|:| -2050 |#1|) (|:| -2849 |#2|))) . T)) ((((-1175)) |has| |#1| (-900 (-1175))) (((-1081)) . T)) (((|#1|) . T)) (|has| |#1| (-848)) -(((#0=(-2 (|:| -2010 (-1157)) (|:| -2818 (-52))) #0#) |has| (-2 (|:| -2010 (-1157)) (|:| -2818 (-52))) (-310 (-2 (|:| -2010 (-1157)) (|:| -2818 (-52)))))) +(((#0=(-2 (|:| -2050 (-1157)) (|:| -2849 (-52))) #0#) |has| (-2 (|:| -2050 (-1157)) (|:| -2849 (-52))) (-310 (-2 (|:| -2050 (-1157)) (|:| -2849 (-52)))))) (((|#1| |#1|) -12 (|has| |#1| (-310 |#1|)) (|has| |#1| (-1099)))) (|has| |#1| (-1099)) ((((-862)) . T) (((-1180)) . T)) @@ -1812,7 +1812,7 @@ (((|#1| |#1|) -12 (|has| |#1| (-310 |#1|)) (|has| |#1| (-1099)))) (((|#1|) . T)) (((|#1| |#2|) . T)) -(((|#1| |#1|) -12 (|has| |#1| (-310 |#1|)) (|has| |#1| (-1099))) ((#0=(-2 (|:| -2010 (-1157)) (|:| -2818 |#1|)) #0#) |has| (-2 (|:| -2010 (-1157)) (|:| -2818 |#1|)) (-310 (-2 (|:| -2010 (-1157)) (|:| -2818 |#1|))))) +(((|#1| |#1|) -12 (|has| |#1| (-310 |#1|)) (|has| |#1| (-1099))) ((#0=(-2 (|:| -2050 (-1157)) (|:| -2849 |#1|)) #0#) |has| (-2 (|:| -2050 (-1157)) (|:| -2849 |#1|)) (-310 (-2 (|:| -2050 (-1157)) (|:| -2849 |#1|))))) (-2805 (|has| |#2| (-454)) (|has| |#2| (-909))) (-2805 (|has| |#1| (-454)) (|has| |#1| (-909))) (((|#1|) . T) (($) . T)) @@ -1837,7 +1837,7 @@ ((((-409 (-566))) -2805 (|has| |#1| (-38 (-409 (-566)))) (|has| |#1| (-365))) (($) -2805 (|has| |#1| (-365)) (|has| |#1| (-558))) (((-1173 |#1| |#2| |#3|)) |has| |#1| (-365)) ((|#1|) |has| |#1| (-172))) (((|#1|) |has| |#1| (-172)) (((-409 (-566))) -2805 (|has| |#1| (-38 (-409 (-566)))) (|has| |#1| (-365))) (($) -2805 (|has| |#1| (-365)) (|has| |#1| (-558)))) ((($) |has| |#1| (-558)) ((|#1|) |has| |#1| (-172)) (((-409 (-566))) |has| |#1| (-38 (-409 (-566))))) -((((-2 (|:| -2010 (-1175)) (|:| -2818 (-52)))) . T)) +((((-2 (|:| -2050 (-1175)) (|:| -2849 (-52)))) . T)) ((((-409 |#2|)) . T) (((-409 (-566))) . T) (($) . T)) ((((-672 |#1|)) . T)) (((|#1| |#2| |#3| |#4|) . T)) @@ -1915,7 +1915,7 @@ ((((-862)) . T)) ((((-862)) . T)) ((($ $) . T)) -((((-2 (|:| -2010 |#1|) (|:| -2818 |#2|))) . T)) +((((-2 (|:| -2050 |#1|) (|:| -2849 |#2|))) . T)) ((($ $) . T)) ((((-566) (-112)) . T)) ((($) . T)) @@ -1944,7 +1944,7 @@ (((|#1| (-1228 |#1| |#2| |#3|)) . T)) (((|#1| (-771)) . T)) (((|#1|) . T)) -((((-2 (|:| -2010 |#1|) (|:| -2818 |#2|))) . T)) +((((-2 (|:| -2050 |#1|) (|:| -2849 |#2|))) . T)) ((((-862)) . T)) (|has| |#1| (-1099)) ((((-1157) |#1|) . T)) @@ -1991,7 +1991,7 @@ ((($) -2805 (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-558))) (((-409 (-566))) -2805 (|has| |#1| (-38 (-409 (-566)))) (|has| |#1| (-365))) (((-1173 |#1| |#2| |#3|)) |has| |#1| (-365)) ((|#1|) . T)) (((|#1|) . T) (($) -2805 (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-558))) (((-409 (-566))) -2805 (|has| |#1| (-38 (-409 (-566)))) (|has| |#1| (-365)))) ((($) -2805 (|has| |#1| (-172)) (|has| |#1| (-558))) ((|#1|) . T) (((-409 (-566))) |has| |#1| (-38 (-409 (-566))))) -(((|#2|) -12 (|has| |#2| (-310 |#2|)) (|has| |#2| (-1099))) (((-2 (|:| -2010 |#1|) (|:| -2818 |#2|))) |has| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (-310 (-2 (|:| -2010 |#1|) (|:| -2818 |#2|))))) +(((|#2|) -12 (|has| |#2| (-310 |#2|)) (|has| |#2| (-1099))) (((-2 (|:| -2050 |#1|) (|:| -2849 |#2|))) |has| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (-310 (-2 (|:| -2050 |#1|) (|:| -2849 |#2|))))) (((|#1|) |has| |#1| (-172))) ((((-862)) . T)) ((($) |has| |#1| (-558)) ((|#1|) |has| |#1| (-172)) (((-409 (-566))) |has| |#1| (-38 (-409 (-566))))) @@ -2015,7 +2015,7 @@ (|has| |#1| (-848)) (((|#1| (-566) (-1081)) . T)) (-2805 (|has| |#1| (-900 (-1175))) (|has| |#1| (-1049))) -((((-2 (|:| -2010 |#1|) (|:| -2818 |#2|))) . T)) +((((-2 (|:| -2050 |#1|) (|:| -2849 |#2|))) . T)) (((|#1| (-409 (-566)) (-1081)) . T)) (((|#1| (-771) (-1081)) . T)) (|has| |#1| (-850)) @@ -2034,11 +2034,11 @@ (|has| |#1| (-1099)) ((((-566)) -12 (|has| |#1| (-365)) (|has| |#2| (-639 (-566)))) ((|#2|) |has| |#1| (-365))) (-2805 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-370)) (|has| |#2| (-726)) (|has| |#2| (-793)) (|has| |#2| (-848)) (|has| |#2| (-1049)) (|has| |#2| (-1099))) -((((-689 (-341 (-2523) (-2523 (QUOTE X) (QUOTE HESS)) (-699)))) . T)) +((((-689 (-341 (-3791) (-3791 (QUOTE X) (QUOTE HESS)) (-699)))) . T)) (((|#2|) |has| |#2| (-172))) (((|#1|) |has| |#1| (-172))) -((((-2 (|:| -2010 |#1|) (|:| -2818 |#2|))) . T)) -((((-2 (|:| -2010 (-1157)) (|:| -2818 |#1|))) . T)) +((((-2 (|:| -2050 |#1|) (|:| -2849 |#2|))) . T)) +((((-2 (|:| -2050 (-1157)) (|:| -2849 |#1|))) . T)) ((((-862)) . T)) (|has| |#3| (-848)) ((((-862)) . T)) @@ -2054,11 +2054,11 @@ ((($) . T) ((|#1|) . T) (((-409 (-566))) |has| |#1| (-365))) (|has| |#1| (-850)) (((|#1|) . T)) -((((-2 (|:| -2010 |#1|) (|:| -2818 |#2|))) . T)) +((((-2 (|:| -2050 |#1|) (|:| -2849 |#2|))) . T)) (((|#1|) . T) (((-566)) . T)) (((|#2|) . T)) ((((-566)) . T) ((|#3|) . T)) -((((-2 (|:| -2010 (-1175)) (|:| -2818 (-52)))) |has| (-2 (|:| -2010 (-1175)) (|:| -2818 (-52))) (-310 (-2 (|:| -2010 (-1175)) (|:| -2818 (-52)))))) +((((-2 (|:| -2050 (-1175)) (|:| -2849 (-52)))) |has| (-2 (|:| -2050 (-1175)) (|:| -2849 (-52))) (-310 (-2 (|:| -2050 (-1175)) (|:| -2849 (-52)))))) (-2805 (|has| |#1| (-454)) (|has| |#1| (-909))) (((|#2|) . T) (((-566)) |has| |#2| (-639 (-566)))) ((((-862)) . T)) @@ -2117,7 +2117,7 @@ ((((-644 |#1|)) . T)) (|has| |#1| (-909)) (((|#2|) |has| |#2| (-1049))) -(((|#2|) -12 (|has| |#2| (-310 |#2|)) (|has| |#2| (-1099))) (((-2 (|:| -2010 |#1|) (|:| -2818 |#2|))) |has| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (-310 (-2 (|:| -2010 |#1|) (|:| -2818 |#2|))))) +(((|#2|) -12 (|has| |#2| (-310 |#2|)) (|has| |#2| (-1099))) (((-2 (|:| -2050 |#1|) (|:| -2849 |#2|))) |has| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (-310 (-2 (|:| -2050 |#1|) (|:| -2849 |#2|))))) (|has| |#1| (-365)) (((|#1|) |has| |#1| (-172))) (((|#1| |#1|) . T)) @@ -2169,7 +2169,7 @@ (((|#1| |#2|) . T)) ((($) . T) (((-566)) . T) (((-409 (-566))) . T)) ((((-566)) . T) (($) . T) (((-409 (-566))) . T)) -((((-2 (|:| -2010 (-1157)) (|:| -2818 (-52)))) . T)) +((((-2 (|:| -2050 (-1157)) (|:| -2849 (-52)))) . T)) (((|#1|) . T) (((-409 (-566))) . T) (((-566)) . T) (($) . T)) (((|#1|) . T) (((-409 (-566))) . T) (((-566)) . T) (($) . T)) (((|#1|) . T) (((-409 (-566))) . T) (((-566)) . T) (($) . T)) @@ -2183,7 +2183,7 @@ (((|#2|) . T)) ((($) . T) (((-566)) . T) (((-409 (-566))) -2805 (|has| |#1| (-365)) (|has| |#1| (-351))) ((|#1|) . T)) ((((-566) |#1|) . T)) -(((|#2|) -12 (|has| |#2| (-310 |#2|)) (|has| |#2| (-1099))) (((-2 (|:| -2010 |#1|) (|:| -2818 |#2|))) |has| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (-310 (-2 (|:| -2010 |#1|) (|:| -2818 |#2|))))) +(((|#2|) -12 (|has| |#2| (-310 |#2|)) (|has| |#2| (-1099))) (((-2 (|:| -2050 |#1|) (|:| -2849 |#2|))) |has| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (-310 (-2 (|:| -2050 |#1|) (|:| -2849 |#2|))))) ((((-381)) . T)) ((((-699)) . T)) ((((-409 (-566))) . #0=(|has| |#2| (-365))) (($) . #0#)) @@ -2200,7 +2200,7 @@ (|has| |#1| (-365)) ((((-1175)) |has| |#2| (-900 (-1175)))) ((((-862)) . T)) -((((-2 (|:| -2010 |#1|) (|:| -2818 |#2|))) . T)) +((((-2 (|:| -2050 |#1|) (|:| -2849 |#2|))) . T)) ((((-409 (-566))) . T) (($) . T)) (|has| |#1| (-475)) (|has| |#1| (-370)) @@ -2228,12 +2228,12 @@ (|has| |#1| (-38 (-409 (-566)))) (|has| |#1| (-38 (-409 (-566)))) (|has| |#1| (-850)) -((((-2 (|:| -2010 (-1157)) (|:| -2818 |#1|))) . T)) +((((-2 (|:| -2050 (-1157)) (|:| -2849 |#1|))) . T)) (((|#1| |#2|) . T)) ((($) . T) (((-566)) . T)) (|has| |#1| (-147)) (|has| |#1| (-145)) -((((-2 (|:| -2010 |#1|) (|:| -2818 |#2|))) |has| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (-310 (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)))) ((|#2|) -12 (|has| |#2| (-310 |#2|)) (|has| |#2| (-1099)))) +((((-2 (|:| -2050 |#1|) (|:| -2849 |#2|))) |has| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (-310 (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)))) ((|#2|) -12 (|has| |#2| (-310 |#2|)) (|has| |#2| (-1099)))) (((|#2|) . T)) (((|#3|) . T)) ((((-116 |#1|)) . T)) @@ -2253,7 +2253,7 @@ ((((-538)) |has| |#1| (-614 (-538))) (((-892 (-566))) |has| |#1| (-614 (-892 (-566)))) (((-892 (-381))) |has| |#1| (-614 (-892 (-381)))) (((-381)) . #0=(|has| |#1| (-1022))) (((-225)) . #0#)) (((|#1|) |has| |#1| (-365))) ((((-862)) . T)) -((((-2 (|:| -2010 |#1|) (|:| -2818 |#2|))) . T)) +((((-2 (|:| -2050 |#1|) (|:| -2849 |#2|))) . T)) ((($ $) . T) (((-612 $) $) . T)) (-2805 (|has| |#1| (-365)) (|has| |#1| (-558))) ((($) . T) (((-1250 |#1| |#2| |#3| |#4|)) . T) (((-409 (-566))) . T)) @@ -2326,7 +2326,7 @@ ((((-952 |#1|)) . T) (((-862)) . T)) (((|#3|) . T)) (((|#1| |#1|) . T) (($ $) -2805 (|has| |#1| (-291)) (|has| |#1| (-365))) ((#0=(-409 (-566)) #0#) |has| |#1| (-365))) -((((-2 (|:| -2010 (-1175)) (|:| -2818 (-52)))) . T)) +((((-2 (|:| -2050 (-1175)) (|:| -2849 (-52)))) . T)) ((((-952 |#1|)) . T)) ((($) . T)) ((((-566) |#1|) . T)) @@ -2373,7 +2373,7 @@ ((($) -2805 (|has| |#1| (-365)) (|has| |#1| (-351))) (((-409 (-566))) -2805 (|has| |#1| (-365)) (|has| |#1| (-351))) ((|#1|) . T)) ((((-566)) . T)) (|has| |#1| (-38 (-409 (-566)))) -((((-2 (|:| -2010 (-1157)) (|:| -2818 (-52)))) |has| (-2 (|:| -2010 (-1157)) (|:| -2818 (-52))) (-310 (-2 (|:| -2010 (-1157)) (|:| -2818 (-52)))))) +((((-2 (|:| -2050 (-1157)) (|:| -2849 (-52)))) |has| (-2 (|:| -2050 (-1157)) (|:| -2849 (-52))) (-310 (-2 (|:| -2050 (-1157)) (|:| -2849 (-52)))))) (((|#1|) -12 (|has| |#1| (-310 |#1|)) (|has| |#1| (-1099)))) (|has| |#1| (-848)) (|has| |#1| (-38 (-409 (-566)))) @@ -2416,10 +2416,10 @@ ((($) -2805 (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) ((|#1|) . T) (((-409 (-566))) |has| |#1| (-38 (-409 (-566))))) ((((-538)) |has| |#4| (-614 (-538)))) ((((-862)) . T) (((-644 |#4|)) . T)) -((((-2 (|:| -2010 |#1|) (|:| -2818 |#2|))) . T)) +((((-2 (|:| -2050 |#1|) (|:| -2849 |#2|))) . T)) (((|#1|) . T)) (|has| |#1| (-848)) -(((|#1|) -12 (|has| |#1| (-310 |#1|)) (|has| |#1| (-1099))) (((-2 (|:| -2010 (-1157)) (|:| -2818 |#1|))) |has| (-2 (|:| -2010 (-1157)) (|:| -2818 |#1|)) (-310 (-2 (|:| -2010 (-1157)) (|:| -2818 |#1|))))) +(((|#1|) -12 (|has| |#1| (-310 |#1|)) (|has| |#1| (-1099))) (((-2 (|:| -2050 (-1157)) (|:| -2849 |#1|))) |has| (-2 (|:| -2050 (-1157)) (|:| -2849 |#1|)) (-310 (-2 (|:| -2050 (-1157)) (|:| -2849 |#1|))))) (|has| |#1| (-1099)) (|has| |#1| (-365)) (((|#1|) . T)) @@ -2464,7 +2464,7 @@ ((((-862)) . T)) ((((-862)) . T)) ((((-538)) |has| |#1| (-614 (-538)))) -((((-2 (|:| -2010 |#1|) (|:| -2818 |#2|))) . T)) +((((-2 (|:| -2050 |#1|) (|:| -2849 |#2|))) . T)) ((((-566)) . T) (($) . T) (((-409 (-566))) . T)) ((((-1175) |#1|) |has| |#1| (-516 (-1175) |#1|)) ((|#1| |#1|) |has| |#1| (-310 |#1|))) (((|#1|) -2805 (|has| |#1| (-172)) (|has| |#1| (-365)))) @@ -2503,7 +2503,7 @@ (|has| |#1| (-558)) (((|#2|) . T)) ((((-566)) . T)) -((((-2 (|:| -2010 |#1|) (|:| -2818 |#2|))) . T)) +((((-2 (|:| -2050 |#1|) (|:| -2849 |#2|))) . T)) (((|#1|) . T)) (-2805 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-558)) (|has| |#1| (-1049))) (((|#1| (-59 |#1|) (-59 |#1|)) . T)) @@ -2514,7 +2514,7 @@ ((($) . T)) (((|#1|) . T)) ((((-862)) . T)) -(((|#2|) |has| |#2| (-6 (-4419 "*")))) +(((|#2|) |has| |#2| (-6 (-4416 "*")))) (((|#1|) . T)) (((|#1|) . T)) ((($) . T)) @@ -2636,22 +2636,22 @@ (((|#2|) . T)) (((|#4| |#4|) -12 (|has| |#4| (-310 |#4|)) (|has| |#4| (-1099)))) (((|#2|) . T)) -(((|#2|) -2805 (|has| |#2| (-6 (-4419 "*"))) (|has| |#2| (-172)))) +(((|#2|) -2805 (|has| |#2| (-6 (-4416 "*"))) (|has| |#2| (-172)))) (-2805 (|has| |#2| (-454)) (|has| |#2| (-558)) (|has| |#2| (-909))) (-2805 (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) (|has| |#2| (-909)) (|has| |#1| (-909)) (((|#2|) |has| |#2| (-172))) -((((-2 (|:| -2010 |#1|) (|:| -2818 |#2|))) . T)) +((((-2 (|:| -2050 |#1|) (|:| -2849 |#2|))) . T)) ((((-1256 |#1| |#2| |#3|)) |has| |#1| (-365))) ((((-862)) . T)) ((((-862)) . T)) ((((-538)) . T) (((-566)) . T) (((-892 (-566))) . T) (((-381)) . T) (((-225)) . T)) (((|#1| |#2|) . T)) ((($) . T) (((-566)) . T)) -((((-2 (|:| -2010 (-1157)) (|:| -2818 (-52)))) . T)) +((((-2 (|:| -2050 (-1157)) (|:| -2849 (-52)))) . T)) (((|#1|) . T)) -((((-2 (|:| -2010 |#1|) (|:| -2818 |#2|))) . T)) +((((-2 (|:| -2050 |#1|) (|:| -2849 |#2|))) . T)) ((((-862)) . T)) (((|#1| |#2|) . T)) ((($) . T) (((-566)) . T)) @@ -2673,7 +2673,7 @@ ((((-862)) . T)) ((((-862)) . T)) ((((-187)) . T) (((-862)) . T)) -((((-2 (|:| -2010 |#1|) (|:| -2818 |#2|))) . T)) +((((-2 (|:| -2050 |#1|) (|:| -2849 |#2|))) . T)) (((|#2| |#2|) . T) ((|#1| |#1|) . T)) ((((-862)) . T)) ((((-862)) . T)) @@ -2686,7 +2686,7 @@ ((((-862)) . T)) ((((-1157)) . T)) ((((-1175) |#1|) |has| |#1| (-516 (-1175) |#1|)) ((|#1| |#1|) |has| |#1| (-310 |#1|))) -((((-2 (|:| -2010 (-1157)) (|:| -2818 |#1|))) . T)) +((((-2 (|:| -2050 (-1157)) (|:| -2849 |#1|))) . T)) (|has| |#1| (-850)) ((((-862)) . T)) ((((-538)) |has| |#1| (-614 (-538)))) @@ -2748,8 +2748,8 @@ (-2805 (|has| |#1| (-145)) (|has| |#1| (-370))) (-2805 (|has| |#1| (-145)) (|has| |#1| (-370))) (-2805 (|has| |#1| (-145)) (|has| |#1| (-370))) -((((-2 (|:| -2010 (-1175)) (|:| -2818 (-52)))) . T)) -(((#0=(-52)) . T) (((-2 (|:| -2010 (-1175)) (|:| -2818 #0#))) . T)) +((((-2 (|:| -2050 (-1175)) (|:| -2849 (-52)))) . T)) +(((#0=(-52)) . T) (((-2 (|:| -2050 (-1175)) (|:| -2849 #0#))) . T)) (|has| |#1| (-351)) ((((-566)) . T)) ((((-862)) . T)) @@ -2835,7 +2835,7 @@ (|has| |#2| (-1022)) ((($) . T)) (|has| |#1| (-909)) -((((-2 (|:| -2010 |#1|) (|:| -2818 |#2|))) . T)) +((((-2 (|:| -2050 |#1|) (|:| -2849 |#2|))) . T)) ((($) . T)) (((|#2|) . T)) (((|#1|) . T)) @@ -2858,12 +2858,12 @@ ((((-566)) . T) (($) . T)) ((((-566)) . T) (($) . T)) ((((-771) |#1|) . T)) -(((|#2| (-240 (-2997 |#1|) (-771))) . T)) +(((|#2| (-240 (-3020 |#1|) (-771))) . T)) (((|#1| (-533 |#3|)) . T)) ((((-409 (-566))) . T)) (-2805 (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) ((((-1157)) . T) (((-862)) . T)) -(((#0=(-2 (|:| -2010 (-1175)) (|:| -2818 (-52))) #0#) |has| (-2 (|:| -2010 (-1175)) (|:| -2818 (-52))) (-310 (-2 (|:| -2010 (-1175)) (|:| -2818 (-52)))))) +(((#0=(-2 (|:| -2050 (-1175)) (|:| -2849 (-52))) #0#) |has| (-2 (|:| -2050 (-1175)) (|:| -2849 (-52))) (-310 (-2 (|:| -2050 (-1175)) (|:| -2849 (-52)))))) ((((-1157)) . T)) (|has| |#1| (-909)) (|has| |#2| (-365)) @@ -2901,7 +2901,7 @@ (((|#2|) |has| |#1| (-365))) (((|#2|) |has| |#1| (-365))) ((((-566)) . T) (($) . T)) -((((-2 (|:| -2010 |#1|) (|:| -2818 |#2|))) . T)) +((((-2 (|:| -2050 |#1|) (|:| -2849 |#2|))) . T)) (((|#1|) . T)) (((|#1|) |has| |#1| (-172))) (((|#1|) . T)) @@ -2947,9 +2947,9 @@ (((|#2|) . T)) (((|#2|) . T)) (-2805 (|has| |#2| (-172)) (|has| |#2| (-726)) (|has| |#2| (-848)) (|has| |#2| (-1049))) -((((-2 (|:| -2010 |#1|) (|:| -2818 |#2|))) . T)) -((((-2 (|:| -2010 (-1157)) (|:| -2818 |#1|))) . T)) -((((-2 (|:| -2010 |#1|) (|:| -2818 |#2|))) . T)) +((((-2 (|:| -2050 |#1|) (|:| -2849 |#2|))) . T)) +((((-2 (|:| -2050 (-1157)) (|:| -2849 |#1|))) . T)) +((((-2 (|:| -2050 |#1|) (|:| -2849 |#2|))) . T)) (|has| |#1| (-38 (-409 (-566)))) (((|#1| |#2|) . T)) (|has| |#1| (-38 (-409 (-566)))) @@ -3081,7 +3081,7 @@ (|has| |#2| (-365)) ((((-583 |#1|)) . T) (((-409 (-566))) . T) (($) . T) (((-566)) . T)) ((((-566)) . T) (((-409 (-566))) . T) (($) . T)) -((((-2 (|:| -2010 (-1157)) (|:| -2818 (-52)))) . T)) +((((-2 (|:| -2050 (-1157)) (|:| -2849 (-52)))) . T)) (((|#1|) . T)) (((|#1|) . T) (((-566)) . T)) (((|#1|) -12 (|has| |#1| (-310 |#1|)) (|has| |#1| (-1099)))) @@ -3115,7 +3115,7 @@ (((|#1|) . T)) (((|#1|) . T)) ((($) . T) (((-409 (-566))) . T)) -(((|#2|) |has| |#2| (-6 (-4419 "*")))) +(((|#2|) |has| |#2| (-6 (-4416 "*")))) (((|#1|) . T)) ((((-409 (-566))) |has| |#1| (-1038 (-409 (-566)))) ((|#1|) . T) (((-566)) . T)) (((|#1|) . T)) @@ -3143,7 +3143,7 @@ ((($) -2805 (|has| |#1| (-172)) (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) ((|#1|) . T) (((-409 (-566))) |has| |#1| (-38 (-409 (-566))))) ((((-862)) . T)) (((|#1|) . T)) -((((-2 (|:| -2010 (-1157)) (|:| -2818 |#1|))) . T)) +((((-2 (|:| -2050 (-1157)) (|:| -2849 |#1|))) . T)) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -3228,7 +3228,7 @@ (((|#1|) . T)) (((|#1|) |has| |#1| (-172))) (((|#4|) -12 (|has| |#4| (-310 |#4|)) (|has| |#4| (-1099)))) -(((|#2|) -2805 (|has| |#2| (-6 (-4419 "*"))) (|has| |#2| (-172)))) +(((|#2|) -2805 (|has| |#2| (-6 (-4416 "*"))) (|has| |#2| (-172)))) (((|#2|) . T)) (|has| |#1| (-365)) (((|#2|) . T)) @@ -3274,7 +3274,7 @@ (((|#1|) . T)) ((((-862)) . T)) (|has| |#2| (-909)) -((((-2 (|:| -2010 (-1175)) (|:| -2818 (-52)))) . T)) +((((-2 (|:| -2050 (-1175)) (|:| -2849 (-52)))) . T)) ((((-538)) |has| |#2| (-614 (-538))) (((-892 (-381))) |has| |#2| (-614 (-892 (-381)))) (((-892 (-566))) |has| |#2| (-614 (-892 (-566))))) ((((-862)) . T)) ((((-862)) . T)) @@ -3317,7 +3317,7 @@ ((((-409 |#2|) |#3|) . T)) (((|#1|) . T)) (|has| |#1| (-1099)) -(((|#2| (-484 (-2997 |#1|) (-771))) . T)) +(((|#2| (-484 (-3020 |#1|) (-771))) . T)) ((((-566) |#1|) . T)) ((((-1157)) . T) (((-862)) . T)) (((|#2| |#2|) . T)) @@ -3376,7 +3376,7 @@ ((((-1175)) -12 (|has| |#3| (-900 (-1175))) (|has| |#3| (-1049)))) (((|#1|) . T)) (|has| |#1| (-233)) -(((|#2| (-240 (-2997 |#1|) (-771))) . T)) +(((|#2| (-240 (-3020 |#1|) (-771))) . T)) (((|#1| (-533 |#3|)) . T)) (|has| |#1| (-370)) (|has| |#1| (-370)) @@ -3465,7 +3465,7 @@ ((((-1213)) . T) (((-862)) . T) (((-1180)) . T)) ((((-1180)) . T)) ((((-1180)) . T)) -((((-2 (|:| -2010 (-1175)) (|:| -2818 (-52)))) |has| (-2 (|:| -2010 (-1175)) (|:| -2818 (-52))) (-310 (-2 (|:| -2010 (-1175)) (|:| -2818 (-52)))))) +((((-2 (|:| -2050 (-1175)) (|:| -2849 (-52)))) |has| (-2 (|:| -2050 (-1175)) (|:| -2849 (-52))) (-310 (-2 (|:| -2050 (-1175)) (|:| -2849 (-52)))))) (-2805 (|has| |#2| (-454)) (|has| |#2| (-558)) (|has| |#2| (-909))) ((((-566) |#1|) . T)) ((((-566) |#1|) . T)) @@ -3672,7 +3672,7 @@ (-2805 (-12 (|has| |#1| (-21)) (|has| |#2| (-21))) (-12 (|has| |#1| (-23)) (|has| |#2| (-23))) (-12 (|has| |#1| (-131)) (|has| |#2| (-131))) (-12 (|has| |#1| (-793)) (|has| |#2| (-793)))) ((((-566)) . T)) ((((-566)) . T)) -((((-2 (|:| -2010 |#1|) (|:| -2818 |#2|))) . T)) +((((-2 (|:| -2050 |#1|) (|:| -2849 |#2|))) . T)) (((|#1| |#2|) . T)) (((|#1|) . T)) (-2805 (|has| |#2| (-172)) (|has| |#2| (-726)) (|has| |#2| (-848)) (|has| |#2| (-1049))) @@ -3779,11 +3779,11 @@ ((((-1173 |#1| |#2| |#3|)) |has| |#1| (-365))) ((((-1139 |#1| |#2|)) . T)) ((((-1173 |#1| |#2| |#3|)) |has| |#1| (-365))) -(((|#2|) . T) (((-2 (|:| -2010 |#1|) (|:| -2818 |#2|))) . T)) -((((-2 (|:| -2010 (-1175)) (|:| -2818 (-52)))) . T)) +(((|#2|) . T) (((-2 (|:| -2050 |#1|) (|:| -2849 |#2|))) . T)) +((((-2 (|:| -2050 (-1175)) (|:| -2849 (-52)))) . T)) ((($) . T)) (|has| |#1| (-1022)) -(((|#2|) . T) (((-2 (|:| -2010 |#1|) (|:| -2818 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -2050 |#1|) (|:| -2849 |#2|))) . T)) ((((-862)) . T)) ((((-538)) |has| |#2| (-614 (-538))) (((-892 (-566))) |has| |#2| (-614 (-892 (-566)))) (((-892 (-381))) |has| |#2| (-614 (-892 (-381)))) (((-381)) . #0=(|has| |#2| (-1022))) (((-225)) . #0#)) ((((-295 |#3|)) . T)) @@ -3838,7 +3838,7 @@ ((((-862)) . T)) ((((-862)) . T)) (((|#1| (-533 |#2|)) . T)) -((((-2 (|:| -2010 (-1175)) (|:| -2818 (-52)))) . T)) +((((-2 (|:| -2050 (-1175)) (|:| -2849 (-52)))) . T)) ((((-566) (-129)) . T)) (((|#1| (-566)) . T)) (((|#1| (-409 (-566))) . T)) @@ -3875,7 +3875,7 @@ (((|#1| |#2|) . T)) ((((-1157) |#1|) . T)) ((((-409 |#2|)) . T)) -((((-2 (|:| -2010 |#1|) (|:| -2818 |#2|))) . T)) +((((-2 (|:| -2050 |#1|) (|:| -2849 |#2|))) . T)) (|has| |#1| (-558)) (|has| |#1| (-558)) ((($) . T) ((|#2|) . T)) @@ -3909,7 +3909,7 @@ (((|#1| |#2| |#3| |#4|) . T)) (((#0=(-1139 |#1| |#2|) #0#) |has| (-1139 |#1| |#2|) (-310 (-1139 |#1| |#2|)))) (((|#1|) . T)) -(((|#2| |#2|) -12 (|has| |#2| (-310 |#2|)) (|has| |#2| (-1099))) ((#0=(-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) #0#) |has| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (-310 (-2 (|:| -2010 |#1|) (|:| -2818 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-310 |#2|)) (|has| |#2| (-1099))) ((#0=(-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) #0#) |has| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (-310 (-2 (|:| -2050 |#1|) (|:| -2849 |#2|))))) (((#0=(-116 |#1|)) |has| #0# (-310 #0#))) ((($ $) . T)) (-2805 (|has| |#1| (-850)) (|has| |#1| (-1099))) diff --git a/src/share/algebra/compress.daase b/src/share/algebra/compress.daase index 3d47dfeb..e3dfad8b 100644 --- a/src/share/algebra/compress.daase +++ b/src/share/algebra/compress.daase @@ -1,6 +1,6 @@ -(30 . 3453749791) -(4420 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| +(30 . 3453990493) +(4417 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| ATTRIBUTE |package| |domain| |category| CATEGORY |nobranch| AND |Join| |ofType| SIGNATURE "failed" "algebra" |OneDimensionalArrayAggregate&| |OneDimensionalArrayAggregate| |AbelianGroup&| |AbelianGroup| @@ -478,664 +478,661 @@ |XPolynomial| |XPolynomialRing| |XRecursivePolynomial| |ParadoxicalCombinatorsForStreams| |ZeroDimensionalSolvePackage| |IntegerLinearDependence| |IntegerMod| |Enumeration| |Mapping| - |Record| |Union| |leftTraceMatrix| |pr2dmp| |minordet| |d01akf| - |monicLeftDivide| |shellSort| |baseRDE| |iicos| |printStats!| - |tubePoints| |internalDecompose| |qqq| |module| |hasHi| - |limitedIntegrate| |zRange| |cyclic?| |numberOfFactors| |minus!| - |expr| |numberOfComputedEntries| |musserTrials| - |monicCompleteDecompose| |nextPrimitiveNormalPoly| |addPoint| - |prinshINFO| |map!| |constantLeft| |double?| |redPo| - |basisOfLeftAnnihilator| |approxNthRoot| |lazyVariations| |localAbs| - |getOperator| |qsetelt!| |fractionFreeGauss!| |Lazard2| - |explicitlyFinite?| |eyeDistance| |taylorIfCan| |dn| |iiGamma| - |copies| |OMputObject| |hermiteH| |refine| |predicates| |sqfrFactor| - |abs| |shrinkable| |solveLinearPolynomialEquation| |nthExponent| - |tensorProduct| |e01sff| |generalLambert| |variable| |squareMatrix| - |s17dgf| |patternMatch| |coerceS| |finite?| |d01gbf| |errorKind| - |symbol| |restorePrecision| |monomials| |byte| |iterators| |ord| - |halfExtendedResultant2| |algebraicDecompose| |algebraic?| - |squareFree| |certainlySubVariety?| |point| |eigenMatrix| |expression| - |nextPrimitivePoly| |reduceLODE| |resize| |someBasis| - |setScreenResolution3D| |mat| |primlimintfrac| |acsch| |integer| - |option?| |acotIfCan| |findConstructor| |coefChoose| |lquo| |dark| - |semiIndiceSubResultantEuclidean| |readInt16!| |iteratedInitials| - |reverseLex| |hasTopPredicate?| |int| |expenseOfEvaluation| - |exprHasAlgebraicWeight| |collectUnder| |cylindrical| |wrregime| - |series| |dmp2rfi| |csch2sinh| |reindex| |acscIfCan| |cothIfCan| - |iicot| |stoseInvertibleSetsqfreg| |basisOfRightAnnihilator| |split!| - |OMputEndAttr| |outputBinaryFile| |lprop| |balancedFactorisation| - |e04ycf| |iiasin| |extendedint| ** |equality| |resultantEuclidean| - |doubleResultant| |radicalSimplify| |expenseOfEvaluationIF| |delete!| - |changeBase| |cCsch| |algebraicVariables| |clipWithRanges| - |quadratic?| |complexSolve| |problemPoints| |port| |symmetricProduct| - |cAcot| |orbits| |failed?| |KrullNumber| |padecf| |min| - |cyclicSubmodule| |fmecg| |distance| |commonDenominator| |s17akf| - |chebyshevT| |preprocess| |aQuartic| |children| |colorFunction| - |realRoots| |LagrangeInterpolation| |dot| |gcdcofactprim| |t| - |torsionIfCan| |label| |error| |makeFR| |close!| |chineseRemainder| - |Lazard| |particularSolution| |innerEigenvectors| |complexLimit| - |interpretString| |f02xef| |triangularSystems| |heapSort| - |setProperties| |principalIdeal| |selectsecond| - |semiResultantEuclidean1| |s18acf| |assert| |showTypeInOutput| - |generators| |integral?| |pastel| |removeCosSq| |connect| - |rightRegularRepresentation| |lowerCase| |s17aff| |numberOfCycles| - |makeResult| |stoseLastSubResultant| |dflist| - |semiDiscriminantEuclidean| |nativeModuleExtension| |numberOfHues| - |attributeData| |reorder| |substring?| |errorInfo| |sylvesterMatrix| - |differentialVariables| |karatsubaDivide| |concat!| |psolve| - |fractRagits| |quasiMonic?| |mkcomm| |rightUnits| |tubeRadiusDefault| - |coth2tanh| |mainContent| |noKaratsuba| |sayLength| |vark| |power!| - |optional?| |pushdown| |swap| |credPol| |zerosOf| |suffix?| - |subscript| |bringDown| |radicalEigenvalues| |sumOfSquares| - |ListOfTerms| |e04mbf| |binomial| |primitivePart!| |listBranches| - |idealSimplify| |OMclose| |iiacos| |createPrimitivePoly| |terms| - |drawCurves| |makeSketch| |mainSquareFreePart| |constructor| - |linearPart| |createPrimitiveElement| |swap!| |cLog| |fractionPart| - |prefix?| |graphCurves| |singularitiesOf| |copy!| |maxIndex| |hspace| - |antiCommutative?| |represents| |complexZeros| |s21bcf| |adjoint| - |normDeriv2| |resultant| |sub| |option| |rk4| |palglimint0| - |laguerreL| |explimitedint| |norm| |polar| |sizeLess?| |palgLODE0| - |iomode| |solveInField| |complexExpand| |pleskenSplit| - |polarCoordinates| |s15adf| |outputGeneral| |createRandomElement| - |nthExpon| |OMParseError?| |viewSizeDefault| |absolutelyIrreducible?| - |solveLinear| |roughEqualIdeals?| |OMgetBVar| |negative?| |recip| - |subMatrix| |setMaxPoints| |c06frf| |extendIfCan| |lagrange| - |checkRur| |supersub| |setlast!| |rombergo| |pToDmp| |seed| |d01asf| - |lazyGintegrate| |iibinom| |mvar| |determinant| |rightTrim| |addiag| - |clearTheSymbolTable| |setPoly| |e02bef| |s14abf| |purelyAlgebraic?| - |quote| |ceiling| |noncommutativeJordanAlgebra?| |permutations| - |outputAsScript| |leftTrim| |curveColor| |sortConstraints| |infix?| - |atom?| |bubbleSort!| |thenBranch| |f02abf| |setFieldInfo| |increment| - |nextIrreduciblePoly| |nthRootIfCan| |karatsubaOnce| |cCosh| - |countRealRootsMultiple| |mask| |lastSubResultant| |curveColorPalette| - |ridHack1| |stopTableInvSet!| |reducedSystem| |pointSizeDefault| - |readInt32!| |OMputVariable| |irreducibleFactors| |sparsityIF| - |associates?| |generic?| |cycleTail| |hexDigit?| |rangePascalTriangle| - |univariatePolynomials| |condition| |integralBasisAtInfinity| - |jordanAdmissible?| |euclideanNormalForm| |remainder| |superscript| - |compiledFunction| |factorSquareFreePolynomial| |hue| - |numberOfPrimitivePoly| |constantIfCan| |OMsetEncoding| |randomLC| - |create3Space| |comment| |constant| |multMonom| 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|entry?| |linearlyDependent?| |hMonic| |probablyZeroDim?| |divisor| - |jacobiIdentity?| |LowTriBddDenomInv| |leftRegularRepresentation| - |paren| |f02fjf| |primes| |inHallBasis?| |imagk| |denomRicDE| |rspace| - |head| |OMputApp| |invertibleElseSplit?| |range| |evenInfiniteProduct| - |listexp| |besselK| |decrease| |exponential1| |lift| - |intermediateResultsIF| |coth2trigh| |retractable?| |void| - |companionBlocks| |mapdiv| |left| |bezoutMatrix| |s21bbf| - |clipBoolean| |completeEchelonBasis| |reduce| - |semiResultantEuclideannaif| |mapCoef| |s13aaf| - |getMultiplicationTable| |monomial?| |right| |cyclicGroup| - |infiniteProduct| |expintegrate| |countRealRoots| |f02bbf| - |stopTable!| |groebner| |deepCopy| |singleFactorBound| - |listRepresentation| |palgint| |round| |morphism| |forLoop| - |OMgetAttr| |powers| |maxRowIndex| |elt| |LyndonWordsList1| - |defineProperty| |iicsch| |stronglyReduced?| |setStatus!| - |safeCeiling| |f02aff| |variable?| |front| |internalSubPolSet?| - |laurentIfCan| |nil| |infinite| |arbitraryExponent| |approximate| - |complex| |shallowMutable| |canonical| |noetherian| |central| + |Record| |Union| |arity| |rightLcm| |lookup| |squareTop| + |intermediateResultsIF| |option?| |wordInStrongGenerators| |c06fuf| + |getOperands| |functionIsOscillatory| |cCos| |f01mcf| |bracket| + |LazardQuotient2| |incrementKthElement| |coth2trigh| |mpsode| |addmod| + |OMreceive| |categoryFrame| |Ci| |generate| |symmetricTensors| + |parametersOf| |lieAdmissible?| |critT| |retractable?| |parameters| + |extendedEuclidean| |createNormalPoly| |perfectSqrt| |leadingSupport| + |imagJ| |clipParametric| |writable?| |leftRankPolynomial| |realZeros| + |companionBlocks| |makeSin| |outputMeasure| |quasiRegular| + |monicRightDivide| |lighting| |incrementBy| |generalizedEigenvectors| + |e01bef| |rowEch| |f04mbf| |mapdiv| |atrapezoidal| |distdfact| + |normalForm| |primextintfrac| |showScalarValues| |expand| |linGenPos| + |f04arf| |midpoint| |expr| |rational?| |bezoutMatrix| |firstDenom| + |completeSmith| |collectQuasiMonic| |isAnd| |shiftRight| |filterWhile| + |highCommonTerms| |hostByteOrder| |mathieu24| |zCoord| |s21bbf| + |stack| |removeZeroes| |OMputString| |sturmVariationsOf| |binding| + |green| |filterUntil| |normalizedAssociate| |complete| |iiacot| + |critMonD1| |clipBoolean| |iiacsch| |indiceSubResultantEuclidean| + |controlPanel| |makeFloatFunction| |showRegion| |select| + |inverseIntegralMatrixAtInfinity| |monicDecomposeIfCan| + |complementaryBasis| |trivialIdeal?| |completeEchelonBasis| RF2UTS + |style| |leadingExponent| |singularAtInfinity?| + |removeRedundantFactors| |normalDeriv| |body| + |createMultiplicationMatrix| |e02daf| |variable| |stFunc1| + |semiResultantEuclideannaif| |lifting1| |ScanRoman| |legendreP| + |shiftLeft| |clearTheIFTable| |squareMatrix| |symbol| |primlimitedint| + |unrankImproperPartitions1| |polygon| |iterators| |showTheIFTable| + |mapCoef| |bipolarCylindrical| |edf2ef| |d02ejf| |cAcoth| + |systemCommand| |sizeMultiplication| |s17dgf| |expression| |f02adf| + |redmat| |interval| |OMputEndError| |s13aaf| |changeNameToObjf| + |denominator| |nodes| |firstSubsetGray| |romberg| |integer| |sqfree| + |extractProperty| |laurentRep| UP2UTS |getMultiplicationTable| |sum| + |box| |ffactor| |eisensteinIrreducible?| |lfinfieldint| |OMgetEndBVar| + |infinite?| ** |whitePoint| |remove!| |pointColor| |getGraph| + |monomial?| |expandTrigProducts| |degreePartition| + |factorSquareFreeByRecursion| |reducedQPowers| |createGenericMatrix| + |makeRecord| |OMgetSymbol| |typeLists| |c05adf| |e02aef| |cyclicGroup| + |linearlyDependentOverZ?| |reopen!| |eulerPhi| |invertibleSet| + |makingStats?| |port| |freeOf?| |cycleLength| |OMunhandledSymbol| + |evaluateInverse| |infiniteProduct| |printCode| |parabolic| + |transcendent?| |f2st| |hasPredicate?| |e01sef| |monicModulo| + |critMTonD1| |selectOptimizationRoutines| |expintegrate| |initial| + |genericRightDiscriminant| |lowerCase?| |mix| |getMatch| + |lazyIrreducibleFactors| |lp| |t| |denominators| |rowEchelon| |c05nbf| + |d02bhf| |countRealRoots| |error| |elseBranch| |outputArgs| + |direction| |OMgetEndAtp| |nextPrime| + |functionIsContinuousAtEndPoints| |s14baf| |d03edf| |chiSquare1| + |f02bbf| |bindings| |assert| |getConstant| |splitSquarefree| + |BasicMethod| |extendedIntegrate| |clearTheFTable| |UnVectorise| + |light| |s17aef| |label| |stopTable!| |rootNormalize| |lepol| + |explicitlyEmpty?| |patternMatch| |d01amf| |d03eef| |float?| |htrigs| + |normalizedDivide| |newSubProgram| |groebner| |positive?| |readByte!| + |purelyTranscendental?| |ratDsolve| |cycleRagits| |rule| |sdf2lst| + |aQuadratic| |f01rdf| |definingInequation| |deepCopy| |cn| |delta| + |orthonormalBasis| |leastPower| |stosePrepareSubResAlgo| |writeBytes!| + |sh| |exteriorDifferential| |complexElementary| |aspFilename| |diff| + |singleFactorBound| |subPolSet?| |infieldIntegrate| + |extendedSubResultantGcd| |logGamma| |wholeRadix| |basisOfNucleus| + |tubePoints| |encodingDirectory| |bombieriNorm| |bivariate?| + |listRepresentation| |lift| |sort| |initiallyReduce| |sort!| + |returnTypeOf| |goodnessOfFit| |numberOfChildren| |size?| |basis| + |curryRight| |internalDecompose| |semiResultantEuclidean2| |palgint| + |reduce| |genericLeftTraceForm| |rootPower| |any?| + |getMultiplicationMatrix| |sumSquares| |bits| |movedPoints| |qqq| + |simpsono| |hostPlatform| |round| |constructor| + |primPartElseUnitCanonical!| |rightUnit| |makeUnit| |integerIfCan| + |square?| |module| |lazyPseudoDivide| |endOfFile?| |writeLine!| + |mindegTerm| |morphism| |drawToScale| |swapColumns!| |patternVariable| + |coerceListOfPairs| |multisect| |basisOfCentroid| |option| |nullary| + |squareFreePrim| |hasHi| |OMbindTCP| |forLoop| |void| |c06eaf| + |random| |testModulus| |cot2trig| |column| |mapSolve| |central?| + |sPol| |removeRedundantFactorsInContents| |limitedIntegrate| + |invertible?| |OMgetAttr| |lambda| |even?| |zeroVector| |sequences| + |coercePreimagesImages| |lazyResidueClass| |pr2dmp| |Vectorise| + |setvalue!| |cyclic?| |fixPredicate| |subQuasiComponent?| |powers| + |cExp| |belong?| |multiplyExponents| |createLowComplexityTable| + |exprToUPS| |minordet| |df2ef| |hclf| |Gamma| |raisePolynomial| + |numberOfFactors| |maxRowIndex| |say| |legendre| |genericRightNorm| + |intensity| |normInvertible?| |curve?| |rightTrim| |minus!| |ptFunc| + |s13adf| |diagonalMatrix| |delay| |LyndonWordsList1| |f02awf| + |squareFreeLexTriangular| |listLoops| |limitedint| |headReduce| + |leftTrim| |biRank| |numberOfComputedEntries| |coleman| + |primitiveElement| |depth| |quadraticForm| |defineProperty| + |changeVar| |leftOne| |rightDiscriminant| |orbit| |fintegrate| + |byteBuffer| |musserTrials| |overlap| |readUInt16!| |exprex| |iicsch| + |result| |s17ajf| |pascalTriangle| |palgextint0| |setProperty| + |eigenvector| |fi2df| |pmintegrate| |f04faf| |insertionSort!| + |monicCompleteDecompose| |stronglyReduced?| |minPoints| |pdct| + |lazyPremWithDefault| |iisqrt3| |logical?| |setProperties!| |rightOne| + |nextPrimitiveNormalPoly| |mainVariables| |OMgetObject| |close| + |setStatus!| |ranges| |reset| |meshFun2Var| |lowerCase!| + |rectangularMatrix| |medialSet| |rootKerSimp| |evaluate| + |extensionDegree| |characteristicSet| |addPoint| |safeCeiling| |recur| + |d01gaf| |integralAtInfinity?| |hasSolution?| |kind| + |powerAssociative?| |prinshINFO| |makeTerm| |cot2tan| |display| + |inGroundField?| |f02aff| |subMatrix| |write| |infinityNorm| + |factorFraction| |repeatUntilLoop| |slex| |constantLeft| |op| |c02aff| + |characteristicSerie| |f07adf| |viewPosDefault| |variable?| + |setMaxPoints| |save| |rootProduct| |modularGcdPrimitive| |tanNa| + |sec2cos| |internalIntegrate0| |f04asf| |bat| |double?| |low| |front| + |c06frf| |rootRadius| |iflist2Result| |numerators| |llprop| + |precision| |redPo| |normal?| |partition| |pattern| + |internalSubPolSet?| |extendIfCan| |moebiusMu| |logpart| + |genericLeftDiscriminant| |OMread| |laguerre| |endSubProgram| + |basisOfLeftAnnihilator| |commutator| |prime?| |laurentIfCan| + |lagrange| |leftRecip| |pushNewContour| |selectAndPolynomials| + |selectIntegrationRoutines| |mantissa| |exponential| |empty| |input| + |approxNthRoot| |normFactors| |satisfy?| |checkRur| + |setLegalFortranSourceExtensions| |aLinear| |rarrow| + |bivariatePolynomials| |leadingIdeal| |modifyPointData| |library| + |e04ucf| |totalLex| |lazyVariations| |supersub| |hexDigit| + |nextNormalPrimitivePoly| |perfectNthRoot| |f07fef| |union| |localAbs| + |d01apf| |message| |fixedPointExquo| |setlast!| |extractTop!| + |zeroDimPrime?| |selectNonFiniteRoutines| |tube| |varList| + |getProperties| |deref| |curry| |univariate?| |getOperator| |rombergo| + |setleaves!| |f2df| |lyndon| |sts2stst| |minimize| |froot| + |principalAncestors| |fractionFreeGauss!| |ParCondList| |pToDmp| + |identitySquareMatrix| |cAcsch| |startTableGcd!| |extractPoint| + |level| |testDim| |heap| |computeCycleEntry| |seed| |imagI| |mr| + |sumOfDivisors| |expintfldpoly| |qPot| |rowEchLocal| |factorials| + |frst| |d01asf| |LyndonWordsList| |quasiMonicPolynomials| |subNodeOf?| + |stripCommentsAndBlanks| |leftTrace| |maxrank| |components| |part?| + |retract| |lazyGintegrate| F2FG |stoseIntegralLastSubResultant| + |UP2ifCan| |cotIfCan| |cons| |divergence| |c06gcf| |point| |mapDown!| + |lflimitedint| |iibinom| |alternating| |fillPascalTriangle| + |binaryTree| |matrix| |trim| |invmod| |d01ajf| |mvar| |iisin| + |dAndcExp| |radicalRoots| |expandPower| |coerceP| |closedCurve?| + |makeVariable| |quartic| |determinant| |imports| + |stoseInternalLastSubResultant| |radicalOfLeftTraceForm| + |setMinPoints3D| |any| |toScale| |series| |changeWeightLevel| |fTable| + |OMencodingBinary| |addiag| |external?| |d01fcf| |ref| + |subResultantGcd| |setFormula!| |prevPrime| |notelem| + |LyndonCoordinates| |Lazard2| |clearTheSymbolTable| |hconcat| + |subResultantChain| |Is| |setfirst!| |exponents| |linearAssociatedExp| + |increasePrecision| |usingTable?| |fortranDouble| |explicitlyFinite?| + |categories| |setPoly| |iCompose| |colorDef| |has?| |functorData| + |lifting| |possiblyInfinite?| |lfextendedint| |s14aaf| |setrest!| + |e02bef| |setelt!| |pseudoQuotient| |qfactor| |bitCoef| |moduleSum| + |min| |acosIfCan| |multiEuclidean| |OMreadStr| |fortranDoubleComplex| + |s14abf| |unravel| |lazyPseudoQuotient| |ratPoly| |contractSolve| + |plus| |s18dcf| |cycleEntry| |harmonic| |divideIfCan| |completeHensel| + |purelyAlgebraic?| |ef2edf| |integers| |leftDiscriminant| + |insertMatch| |minColIndex| |externalList| |unitCanonical| + |OMmakeConn| |composite| |quote| |yellow| |s19acf| |weakBiRank| + |stoseInvertibleSet| |coefChoose| |maxint| |diagonal| |sncndn| |back| + |ipow| |ceiling| |var1Steps| |mainVariable| |consnewpol| |nthRoot| + |lquo| |linearAssociatedOrder| |showTheFTable| |asechIfCan| |reduced?| + GF2FG |noncommutativeJordanAlgebra?| |fortranLiteralLine| |signAround| + |stirling1| |henselFact| |dark| |times| |polyPart| + |showTheRoutinesTable| |eigenvectors| |changeMeasure| + |numberOfComposites| |permutations| |OMputAttr| |parent| + |fortranLogical| |pToHdmp| |semiIndiceSubResultantEuclidean| + |rightAlternative?| |dimension| |myDegree| |isPower| |taylorRep| + |outputAsScript| |linears| |rename!| |qinterval| |thetaCoord| + |applyRules| |matrixGcd| |read!| |setPrologue!| |limit| |curveColor| + |halfExtendedResultant2| |toseLastSubResultant| |magnitude| + |nextSubsetGray| |patternMatchTimes| |iterationVar| |readInt8!| + |asinIfCan| |rename| |messagePrint| |sortConstraints| |airyBi| + |monicDivide| |algebraicDecompose| |leftMinimalPolynomial| + |relationsIdeal| |node| |monom| |e02adf| |monic?| |component| + |identityMatrix| |plotPolar| |key| |atom?| |setTopPredicate| + |mainCoefficients| |lintgcd| |rightRemainder| |callForm?| + |sumOfKthPowerDivisors| |enterInCache| |cyclicEqual?| + |numberOfComponents| |bubbleSort!| |bfEntry| |measure2Result| |hex| + |phiCoord| |parabolicCylindrical| |polyRDE| |explogs2trigs| |dequeue!| + |filename| |selectFiniteRoutines| |thenBranch| |sin?| |critBonD| + |pdf2ef| |f02aef| |common| |bit?| |shufflein| + |dimensionOfIrreducibleRepresentation| |setOrder| |outputSpacing| + |f02abf| |cAcosh| |drawStyle| |deriv| |rquo| |oddintegers| |points| + |prepareDecompose| |separate| |zeroMatrix| |parse| |setFieldInfo| + |eval| |normalizeIfCan| |npcoef| |summation| + |internalSubQuasiComponent?| |coord| |Hausdorff| |inputBinaryFile| + |leftQuotient| |increment| |powerSum| |dioSolve| |upperCase!| |degree| + |groebgen| |splitDenominator| |iicosh| |rootBound| |rdregime| EQ + |nextIrreduciblePoly| |mainKernel| |algintegrate| |elementary| + |contract| |plenaryPower| |d01alf| |conjug| |addBadValue| + |knownInfBasis| |nthRootIfCan| |elColumn2!| |cycleSplit!| |intChoose| + |showAll?| |brillhartTrials| |exactQuotient!| |innerSolve1| |nextItem| + |nlde| |karatsubaOnce| |conditionsForIdempotents| |unexpand| |isList| + |contours| |indices| |tan2trig| |divisors| |viewDeltaYDefault| + |rootOfIrreduciblePoly| |cCosh| |zag| |fixedPoints| |escape| + |addMatchRestricted| |relativeApprox| |twoFactor| |RittWuCompare| + |dimensions| |numberOfVariables| |countRealRootsMultiple| |c06ebf| + |subresultantSequence| |mapExpon| |vconcat| |axesColorDefault| + |integralBasis| |operators| |scaleRoots| |var2StepsDefault| + |lastSubResultant| |s17adf| |complexNumericIfCan| |charClass| + |minGbasis| |cyclotomicDecomposition| |trapezoidalo| + |doublyTransitive?| |explicitEntries?| |iicsc| |equation| + |curveColorPalette| |zeroDimPrimary?| |OMconnectTCP| |squareFreePart| + |viewWriteAvailable| |zero| |factorsOfDegree| |member?| |varselect| + |hessian| |f01maf| |ridHack1| |nullary?| |elliptic?| |basisOfCenter| + |rightFactorCandidate| |nonSingularModel| |makeViewport2D| |elRow2!| + |e01sbf| |functionIsFracPolynomial?| |lcm| |stopTableInvSet!| + |setRealSteps| |fortranInteger| |pointColorPalette| + |complexEigenvalues| |And| |alphanumeric| |regularRepresentation| + |setMinPoints| |totalDegree| |index| |floor| |reducedSystem| |rk4f| + |monomRDEsys| |iidprod| |semiLastSubResultantEuclidean| |delete| |Or| + |resetAttributeButtons| |bernoulliB| |equiv| |selectODEIVPRoutines| + |gcdPolynomial| |append| |pointSizeDefault| |argument| |OMgetBind| + |iiacosh| |numerator| |Not| |c06gbf| |leftDivide| |linearMatrix| + |compactFraction| |branchIfCan| |readInt32!| |gcd| |setsubMatrix!| + |setAdaptive3D| |gbasis| |scale| |OMputEndObject| |continuedFraction| + |stiffnessAndStabilityFactor| |resultantEuclideannaif| |infix| |pair| + |OMputVariable| |false| |f01rcf| |fractRadix| |divisorCascade| + |routines| |value| |processTemplate| |permanent| |computeInt| + |partitions| |sincos| |irreducibleFactors| |repSq| |meshPar1Var| + |iiacoth| |cAtanh| |exprHasLogarithmicWeights| |times!| |expint| + |bumptab1| |UpTriBddDenomInv| |sparsityIF| |rational| |nodeOf?| + |accuracyIF| |f02aaf| |specialTrigs| |mainDefiningPolynomial| |prem| + |cyclicCopy| |tableForDiscreteLogarithm| |associates?| |outputAsTex| + |diagonals| |regime| |maxdeg| |flexible?| |internalAugment| + |getIdentifier| |nextSublist| |doubleFloatFormat| |generic?| + |partialQuotients| |boundOfCauchy| |simplifyPower| |btwFact| |sn| + |charpol| |extend| |f04axf| |univariateSolve| |entry?| |cycleTail| + |iisech| |mapUnivariate| |hermite| |invmultisect| + |createIrreduciblePoly| |graphImage| |polygamma| |substring?| + |PDESolve| |linearlyDependent?| |hexDigit?| |LyndonBasis| + |nextsubResultant2| |cardinality| |overset?| |plus!| |addPoint2| + |idealiserMatrix| |sechIfCan| |shellSort| |hMonic| + |rangePascalTriangle| |tValues| |implies| |nilFactor| + |stoseInvertible?reg| |drawComplexVectorField| |tower| |leftMult| + |suffix?| |monomials| |alternatingGroup| |tan2cot| |probablyZeroDim?| + |baseRDE| |univariatePolynomials| |overlabel| |initiallyReduced?| + |trueEqual| |ScanFloatIgnoreSpaces| |ord| |wholeRagits| |expt| + |createNormalPrimitivePoly| |inverse| |divisor| |setImagSteps| + |discreteLog| |createNormalElement| |findBinding| |cup| |connectTo| + |sinhcosh| |prefix?| |OMUnknownSymbol?| |jacobiIdentity?| + |ListOfTerms| |nary?| |cosSinInfo| |associative?| + |currentCategoryFrame| |log10| |pile| |collectUpper| |OMputAtp| + |moduloP| |LowTriBddDenomInv| |e04mbf| |bitTruth| |lazyIntegrate| + |push| |parametric?| |bitand| |symmetricPower| |powern| + |nonLinearPart| |lastSubResultantEuclidean| + |leftRegularRepresentation| |binomial| |fortranReal| |inR?| + |mapUnivariateIfCan| |largest| |complexNumeric| |bitior| + |positiveRemainder| F |untab| |paren| |primitivePart!| |rotatey| + |closedCurve| |indicialEquations| |child| |nextsousResultant2| |clip| + |symbolTable| |viewDefaults| |f02fjf| |listBranches| |rightPower| + |quotientByP| |latex| |tubePointsDefault| |kernels| |shade| + |ellipticCylindrical| |traverse| |primes| |idealSimplify| |setnext!| + |prologue| |ideal| |list?| |wreath| |operator| + |pushFortranOutputStack| |infix?| |conjugates| |complexNormalize| + |inHallBasis?| |OMclose| |null| |frobenius| |linearDependenceOverZ| + |rotate| |rationalApproximation| |popFortranOutputStack| |mask| + |readLineIfCan!| |imagk| |iiacos| |brillhartIrreducible?| + |complexForm| |xn| |zeroDimensional?| |not| |algSplitSimple| + |univariate| |curryLeft| |outputAsFortran| |vspace| |denomRicDE| + |mapExponents| |createPrimitivePoly| |condition| |OMgetEndObject| + |and| |nextPartition| |resetVariableOrder| |search| |quadratic| + |lexGroebner| |scalarMatrix| |rspace| |terms| |exponent| |prod| |ran| + |quickSort| |constant| |or| |startTableInvSet!| |subst| |head| + |drawCurves| |minimumDegree| |airyAi| |modulus| |odd?| |xor| + |operation| |symFunc| |factor| |associatorDependence| |perspective| + |OMputApp| |makeSketch| |cyclotomic| |selectfirst| + |genericLeftMinimalPolynomial| |tablePow| |case| |elRow1!| |sqrt| + |OMgetAtp| |wholePart| |invertibleElseSplit?| |mainSquareFreePart| + |s19abf| |curve| |algint| |s20acf| |Zero| |maximumExponent| |real| + |plot| |setTex!| |range| |linearPart| |alphabetic| |clearTable!| + |deleteProperty!| |imag| |twist| |csc2sin| |evenInfiniteProduct| + |createPrimitiveElement| |extension| |OMputEndBVar| |cycle| |lllip| + |directProduct| |mulmod| |getlo| |hitherPlane| |parents| |listexp| + |swap!| Y |SFunction| |unprotectedRemoveRedundantFactors| |ScanArabic| + |subset?| |backOldPos| |leftZero| |physicalLength| |objects| |besselK| + |cLog| |mathieu11| |headReduced?| |kroneckerDelta| |showAllElements| + |oddlambert| |brace| |rightMinimalPolynomial| |groebnerIdeal| + |findConstructor| |fractionPart| |expandLog| |transcendenceDegree| + |hyperelliptic| |coordinates| |subResultantGcdEuclidean| |destruct| + |bigEndian| |rotate!| |dfRange| |graphCurves| |constantKernel| + |mathieu23| |lookupFunction| |showFortranOutputStack| |comment| + |componentUpperBound| |select!| |bumprow| |e01bhf| |singularitiesOf| + |optpair| |areEquivalent?| |OMencodingXML| |extractIfCan| |trunc| + |mapUp!| |iiexp| |cAcsc| |vector| |copy!| |generalPosition| + |mainPrimitivePart| |goto| |scanOneDimSubspaces| |clipSurface| + |branchPointAtInfinity?| |pol| |c05pbf| |differentiate| |maxIndex| + |factorsOfCyclicGroupSize| |evenlambert| |element?| |setref| + |leftCharacteristicPolynomial| |monomial| |host| |ddFact| |shiftRoots| + |showSummary| |compile| |hspace| |palgRDE0| |localIntegralBasis| + |integralMatrixAtInfinity| |deepestInitial| |s13acf| |multivariate| + |generalizedInverse| |f02axf| |isOr| |zeroOf| |antiCommutative?| |obj| + |genericLeftNorm| |shallowExpand| |primintfldpoly| |augment| + |variables| |putColorInfo| |headAst| |computePowers| |att2Result| + |represents| |youngGroup| |minRowIndex| |cache| |showAttributes| + |schema| |userOrdered?| |approxSqrt| |numberOfFractionalTerms| + |addMatch| |complexZeros| |dmpToHdmp| |pushup| |nor| |mergeFactors| + |constantOpIfCan| |binomThmExpt| |leftNorm| |toseInvertibleSet| + |s21bcf| |s20adf| |pquo| |e04fdf| |crest| |inc| |OMgetType| |name| + |d02kef| |OMencodingSGML| |f01qdf| |adjoint| |unit?| |mainExpression| + |adaptive3D?| |isImplies| |e02zaf| |updatF| |fortranLinkerArgs| + |tanh2trigh| |normDeriv2| |getZechTable| |multiplyCoefficients| + |whatInfinity| |viewDeltaXDefault| |isPlus| |weights| |cscIfCan| + |setleft!| |remove| |resultant| |fibonacci| |conditionP| + |indicialEquation| |nonQsign| |moebius| |rischNormalize| |rroot| + |factors| |sub| |palgextint| |resetBadValues| |scalarTypeOf| |leaf?| + |chebyshevU| |integerBound| |showTheSymbolTable| |d02bbf| |last| |rk4| + |bottom!| |setMaxPoints3D| |entries| |ReduceOrder| |sinIfCan| + |rewriteIdealWithQuasiMonicGenerators| |outlineRender| + |removeRedundantFactorsInPols| |assoc| |palglimint0| |newReduc| + |LazardQuotient| |numberOfIrreduciblePoly| |padicallyExpand| + |flagFactor| |startPolynomial| |seriesToOutputForm| |identification| + |laguerreL| |genericRightMinimalPolynomial| + |semiSubResultantGcdEuclidean2| |OMconnOutDevice| |rootDirectory| + |rdHack1| |bitLength| |c06fpf| |whileLoop| |max| |explimitedint| + |factorial| |minIndex| |jacobi| |leftFactorIfCan| + |numberOfImproperPartitions| |lexico| |OMserve| |closeComponent| + |norm| |complexIntegrate| |d02gbf| |useEisensteinCriterion| |randomR| + |nthCoef| |setPosition| |hasoln| |in?| |polar| |cyclic| + |sylvesterSequence| |decompose| |df2st| BY |SturmHabicht| |rightMult| + |nullity| |d02gaf| |sizeLess?| |neglist| |cAsinh| |makeYoungTableau| + |generalInfiniteProduct| |fortranCharacter| |updatD| |zeroDim?| + |inverseColeman| |palgLODE0| |reflect| |isExpt| |minimalPolynomial| + |s17def| |solveLinearPolynomialEquationByRecursion| |acothIfCan| + |subTriSet?| |primitivePart| |iomode| |convergents| |corrPoly| + |optAttributes| |prime| |merge!| |imaginary| |f04mcf| |anticoord| + |taylorQuoByVar| |solveInField| |arg1| |stoseInvertible?| + |integralRepresents| |cPower| |OMputFloat| |elliptic| + |groebnerFactorize| |realSolve| |newLine| |complexExpand| |arg2| + |rootOf| |leftRank| |complex?| |mirror| |genericRightTraceForm| + |contains?| |OMgetApp| |pleskenSplit| |bandedJacobian| + |realEigenvectors| |const| |removeRoughlyRedundantFactorsInPols| + |digit?| |pureLex| |removeSuperfluousQuasiComponents| |graphStates| + |subCase?| NOT |polarCoordinates| |totalfract| |allRootsOf| + |conditions| |seriesSolve| |lyndon?| |cSin| |prinpolINFO| |leftFactor| + OR |generalSqFr| |perfectNthPower?| |s15adf| |numFunEvals3D| |match| + |rightNorm| |stoseSquareFreePart| |decreasePrecision| |matrixConcat3D| + |acoshIfCan| |eyeDistance| |asimpson| AND |outputGeneral| + |stopMusserTrials| |s17dhf| |createPrimitiveNormalPoly| + |diophantineSystem| |leastAffineMultiple| |mindeg| |dimensionsOf| + |taylorIfCan| |resultantReduit| |sizePascalTriangle| + |createRandomElement| |pow| |OMgetFloat| |makeGraphImage| |acsc| + |trailingCoefficient| |insertRoot!| |univariatePolynomialsGcds| + |iifact| |identity| |nthExpon| |bandedHessian| |deleteRoutine!| |sinh| + |hdmpToDmp| |ode2| |linkToFortran| |euclideanGroebner| |normalized?| + |entry| |getProperty| |OMParseError?| |OMwrite| |cosh| + |semicolonSeparate| |polyred| |bipolar| |removeCoshSq| |putGraph| + |ocf2ocdf| |iiperm| |reciprocalPolynomial| |viewSizeDefault| + |safetyMargin| |debug| |tanh| |quotedOperators| |divideExponents| + |OMgetVariable| |blue| |figureUnits| |pomopo!| + |absolutelyIrreducible?| |readable?| |unparse| |lfextlimint| D |coth| + |d01akf| |var1StepsDefault| |setLength!| |distFact| |setAdaptive| + |ratpart| |solveLinear| |is?| |getMeasure| |jacobian| |sech| + |monicLeftDivide| |setRow!| |antiAssociative?| |null?| |omError| + |eulerE| |roughEqualIdeals?| |changeThreshhold| |csch| |red| |sign| + |assign| |primeFrobenius| |c06gsf| |insert!| |sequence| |OMgetBVar| + |f02ajf| |asinh| |padicFraction| |argscript| |compdegd| |polCase| + |abelianGroup| |mkIntegral| * |rootSimp| |char| |negative?| + |removeSinSq| |revert| |acosh| |printTypes| |truncate| + |normalizeAtInfinity| |lastSubResultantElseSplit| |scopes| |bag| + |properties| |recip| |subscriptedVariables| |exptMod| |atanh| + |structuralConstants| |plusInfinity| |leftScalarTimes!| + |exprHasWeightCosWXorSinWX| |chiSquare| |readUInt32!| |comparison| + |translate| |distribute| |OMputError| |mapMatrixIfCan| |acoth| + |minusInfinity| |randnum| |meshPar2Var| |listOfLists| |swapRows!| + |rem| = |particularSolution| |innerint| |toseSquareFreePart| |asech| + |blankSeparate| |redpps| |topFortranOutputStack| |polyRicDE| |pair?| + |quo| |calcRanges| |innerEigenvectors| |cAcos| |setEpilogue!| + |traceMatrix| |roughBasicSet| |lineColorDefault| + |stiffnessAndStabilityOfODEIF| |cyclicEntries| + |selectSumOfSquaresRoutines| |complexLimit| < + |basisOfCommutingElements| |primaryDecomp| |pushdterm| + |purelyAlgebraicLeadingMonomial?| |multiple| |print| |radPoly| + |stirling2| |e01saf| |tubePlot| |div| > |interpretString| |applyQuote| + |float| |beauzamyBound| |OMputBVar| |resolve| |tab| + |fortranCarriageReturn| |stop| |reduceBasisAtInfinity| |directSum| + |leadingIndex| |exquo| |f02xef| <= |permutationRepresentation| + |gderiv| |jordanAlgebra?| |e02bcf| |type| |getBadValues| |f02wef| + |partialFraction| |f04qaf| ~= >= |triangularSystems| |changeName| + |inf| |basisOfLeftNucloid| |zero?| |showArrayValues| |arbitrary| + |fullDisplay| |fglmIfCan| |#| |heapSort| |f04atf| |ruleset| + |viewPhiDefault| |deepExpand| |virtualDegree| |moreAlgebraic?| ~ + |expIfCan| |setProperties| |quadraticNorm| |f01ref| |interpret| + |cycleElt| |antiCommutator| |lllp| |generalizedEigenvector| |getCurve| + |unary?| + |principalIdeal| |content| + |zeroSetSplitIntoTriangularSystems| |every?| |point?| |cos2sec| + |unitVector| |pseudoDivide| |signature| |leftGcd| - |selectsecond| + |setStatus| |pointColorDefault| |suchThat| |bivariateSLPEBR| |create| + |space| |qelt| |useSingleFactorBound| |/\\| / + |semiResultantEuclidean1| |gcdprim| |midpoints| |retractIfCan| + |unaryFunction| |string?| |s18aef| |sorted?| |transcendentalDecompose| + |arguments| |qsetelt| |\\/| |readIfCan!| |transform| |s18acf| + |besselI| GE |integralDerivationMatrix| |factorSFBRlcUnit| |push!| + |tryFunctionalDecomposition| |HermiteIntegrate| |xRange| |qroot| + |eof?| |numer| |leadingCoefficientRicDE| GT |e04jaf| + |listYoungTableaus| |crushedSet| |factor1| |normalise| |yRange| + |elem?| |cosh2sech| |generators| |denom| |e02bdf| LE |integer?| + |solve1| |sech2cosh| |zRange| |basicSet| |integral?| |typeList| + |removeSinhSq| LT |critM| |atoms| |anfactor| |topPredicate| + |printInfo!| |map!| |nsqfree| |pastel| |pi| |rightTrace| |f04maf| + |exists?| |rightExactQuotient| |fortranLiteral| |d03faf| |rk4qc| + |qsetelt!| |shift| |collect| |infinity| |removeCosSq| |palgLODE| + |d01anf| |leadingBasisTerm| |opeval| |redPol| |prolateSpheroidal| + |iiasech| |connect| |totolex| |printHeader| |interactiveEnv| |leftLcm| + |numericalIntegration| |cCot| |intersect| |ode1| |iiacsc| + |rightRegularRepresentation| |makeCos| |map| |OMgetEndAttr| + |outputForm| UTS2UP |relerror| |viewThetaDefault| |outputFloating| + |kernel| |lowerCase| |OMlistSymbols| |Beta| |setVariableOrder| + |viewpoint| |property| |separateFactors| |f02akf| + |possiblyNewVariety?| |gradient| |chvar| |draw| |s17aff| + |factorSquareFree| |center| |makeSeries| |over| |palgRDE| |cSech| + |subHeight| |irreducibleRepresentation| |acsch| |cond| + |numberOfCycles| |bezoutDiscriminant| |e02dcf| |OMopenString| + |BumInSepFFE| |finiteBound| |cAtan| |s17dcf| |internalZeroSetSplit| + |makeResult| |prefixRagits| |symmetric?| |infieldint| |ParCond| + |units| |useNagFunctions| |OMputInteger| |viewZoomDefault| |constant?| + |lieAlgebra?| |stoseLastSubResultant| |convert| |createThreeSpace| + |coerceImages| |makeSUP| |tanQ| |e04naf| |nthr| |minPoints3D| + |makeObject| |dflist| |e01bgf| |clikeUniv| |currentSubProgram| + |weierstrass| |unrankImproperPartitions0| |roughBase?| |unmakeSUP| + |secIfCan| |semiDiscriminantEuclidean| |coef| |just| |f04adf| + |charthRoot| |order| |checkForZero| |computeCycleLength| |algebraicOf| + |leftPower| |nativeModuleExtension| |e01daf| |rubiksGroup| + |hypergeometric0F1| |internalLastSubResultant| |imagi| |bright| + |irreducibleFactor| |rationalFunction| |dn| |e02gaf| |numberOfHues| + |alphanumeric?| |measure| |rootsOf| |complement| |code| |nil?| + |readBytes!| |mainMonomial| |iiGamma| |fortranCompilerName| |status| + |arrayStack| |attributeData| |binaryFunction| |algebraic?| + |setClipValue| LODO2FUN |failed| |adaptive?| |minrank| |scan| |copies| + |B1solve| |setright!| |datalist| |reorder| |graphState| |squareFree| + |modularFactor| |OMlistCDs| |fortran| |tanh2coth| |members| + |buildSyntax| |bat1| |OMputObject| |rightRankPolynomial| |errorInfo| + |function| |OMconnInDevice| |combineFeatureCompatibility| |graphs| + |multiEuclideanTree| |inconsistent?| |totalDifferential| |cfirst| |lo| + |hermiteH| |sylvesterMatrix| |var2Steps| |baseRDEsys| |e04gcf| + |f01bsf| |universe| |listOfMonoms| |asecIfCan| |localReal?| |refine| + |differentialVariables| |kmax| |difference| |OMreadFile| |meatAxe| + |genericRightTrace| |mesh?| |discriminant| |roughUnitIdeal?| + |predicates| |karatsubaDivide| |fixedDivisor| |elements| |spherical| + |qualifier| |dom| |leaves| |horizConcat| |createZechTable| + |inputOutputBinaryFile| |sqfrFactor| |rur| |concat!| |iroot| |diag| + |makeMulti| |radix| |initials| |s17acf| |headRemainder| |conical| + |abs| |psolve| |initializeGroupForWordProblem| |addPointLast| + |getExplanations| |stFuncN| |mappingAst| |decimal| + |standardBasisOfCyclicSubmodule| |schwerpunkt| |shrinkable| + |basisOfLeftNucleus| |fractRagits| |ldf2vmf| |makeCrit| |lazyPrem| + |lhs| |skewSFunction| |roman| |makeViewport3D| |cTanh| + |solveLinearPolynomialEquation| |inverseIntegralMatrix| + |factorGroebnerBasis| |quasiMonic?| |slash| |antisymmetric?| |coerceS| + |rhs| |normal| |ODESolve| |extractClosed| |triangSolve| |nthExponent| + |roughSubIdeal?| |mkcomm| |numberOfNormalPoly| + |semiResultantReduitEuclidean| |s17ahf| |commaSeparate| |title| + |compose| |iidsum| |simpleBounds?| |variationOfParameters| + |tensorProduct| |rightUnits| |divideIfCan!| |child?| + |primPartElseUnitCanonical| |resetNew| |LiePoly| |pack!| + |indiceSubResultant| |e01sff| |subResultantsChain| |tubeRadiusDefault| + |isOpen?| |composites| |minPoly| |safeFloor| |c06gqf| |doubleComplex?| + |OMputEndApp| |normal01| |generalLambert| |coth2tanh| |true| |janko2| + |xCoord| |deepestTail| |argumentList!| |e| |script| |cartesian| + |mkAnswer| |selectPolynomials| |reducedContinuedFraction| |unknown| + |mainContent| |compBound| |s19adf| |systemSizeIF| |reverse!| + |paraboloidal| |reduction| |unitsColorDefault| |fortranTypeOf| + |noKaratsuba| |key?| |duplicates| |yCoord| |enterPointData| |df2fi| + |PollardSmallFactor| |associator| |position!| |sayLength| + |commutative?| |signatureAst| |linearAssociatedLog| |isNot| |nothing| + |tex| |palginfieldint| |firstUncouplingMatrix| |SturmHabichtSequence| + |iExquo| |vark| |setprevious!| |normalDenom| |open?| |showClipRegion| + |readInt16!| |gcdPrimitive| |reify| |tubeRadius| |replaceKthElement| + |power!| |isConnected?| |finite?| |sinh2csch| |triangular?| + |coefficients| |iteratedInitials| |power| |ramifiedAtInfinity?| + |invertIfCan| |empty?| |isMult| |optional?| |d01gbf| |poisson| |one?| + |limitPlus| |reverseLex| |outputList| |euclideanSize| |d02cjf| |queue| + |bumptab| |pushdown| |rootPoly| |radicalEigenvectors| |permutation| + |diagonal?| |hasTopPredicate?| |OMgetInteger| |critpOrder| + |radicalEigenvector| |rk4a| |swap| |saturate| |monomialIntPoly| + |SturmHabichtCoefficients| |birth| |printInfo| |currentEnv| + |expenseOfEvaluation| |rightExtendedGcd| |solveid| |generalTwoFactor| + |uniform| |width| |credPol| |setLabelValue| |f02bjf| + |generalizedContinuumHypothesisAssumed| |more?| + |exprHasAlgebraicWeight| |wordsForStrongGenerators| |factorList| + |cyclePartition| |iitanh| |reverse| |zerosOf| + |degreeSubResultantEuclidean| |completeHermite| |constantRight| + |normalize| |collectUnder| |trigs| |cyclotomicFactorization| |ldf2lst| + |reduceByQuasiMonic| |localUnquote| |subscript| |call| |OMputSymbol| + |linearPolynomials| |interReduce| |se2rfi| |OMcloseConn| |move| + |quasiAlgebraicSet| |bringDown| |OMsend| |getDatabase| |pointPlot| + |algebraicSort| |adaptive| |getStream| |aCubic| |GospersMethod| |open| + |radicalEigenvalues| |constDsolve| |rightDivide| |matrixDimensions| + |coHeight| |taylor| |Nul| |Si| |euler| |c02agf| |sumOfSquares| + |modularGcd| |tRange| |dictionary| |exprToXXP| |laurent| |e02akf| + |s21baf| |coshIfCan| |expextendedint| |f01qcf| |f04jgf| + |numberOfOperations| |leftAlternative?| |puiseux| |partialNumerators| + |dihedral| |kovacic| |singRicDE| |cylindrical| |optional| + |permutationGroup| |rischDE| |leftUnits| |debug3D| + |removeRoughlyRedundantFactorsInContents| + |tryFunctionalDecomposition?| |iprint| |edf2fi| |incr| |wrregime| + |operations| |block| |s18adf| |less?| |Frobenius| |inv| + |constantToUnaryFunction| |nullSpace| |RemainderList| |ricDsolve| |hi| + |dmp2rfi| |find| |realEigenvalues| |rootSplit| |product| |ground?| + |aromberg| |splitNodeOf!| |drawComplex| |csch2sinh| |nand| + |definingPolynomial| |setAttributeButtonStep| |high| |ground| |f02agf| + |octon| |numericalOptimization| |toseInvertible?| |reindex| + |copyInto!| |stopTableGcd!| |prinb| |c06ekf| |leadingMonomial| |iisec| + |leviCivitaSymbol| |currentScope| |nil| |OMUnknownCD?| |acscIfCan| + |returns| |parseString| |recoverAfterFail| |screenResolution| |init| + |leadingCoefficient| |intPatternMatch| |separateDegrees| |optimize| + |newTypeLists| |physicalLength!| |cothIfCan| |symbolTableOf| + |quasiRegular?| |primitiveMonomials| |getGoodPrime| |e01bff| + |diagonalProduct| |wronskianMatrix| |iicot| |extractBottom!| |cAsech| + |realElementary| |quotient| |reductum| SEGMENT |makeprod| |ode| + |subspace| |countable?| |approximate| |stoseInvertibleSetsqfreg| + |commutativeEquality| |hcrf| |representationType| |cSinh| |rules| + |isAbsolutelyIrreducible?| |ratDenom| + |generalizedContinuumHypothesisAssumed?| |complex| |loopPoints| + |basisOfRightAnnihilator| |principal?| |rightScalarTimes!| |vedf2vef| + |pseudoRemainder| |setchildren!| |factorByRecursion| |split!| |log| + |e02baf| |rCoord| |primeFactor| |lambert| |packageCall| |innerSolve| + |interpolate| |getVariableOrder| |factorOfDegree| |OMputEndAttr| + |denomLODE| |certainlySubVariety?| |lowerPolynomial| |cyclicParents| + |ignore?| |edf2df| |setEmpty!| |flatten| |reseed| |lexTriangular| + |outputBinaryFile| |makeop| |eigenMatrix| |rangeIsFinite| |write!| + |complexEigenvectors| |primitive?| |OMencodingUnknown| |cubic| |lprop| + |multiple?| |uniform01| |fixedPoint| |c06ecf| + |constantCoefficientRicDE| |Aleph| |balancedFactorisation| + |completeEval| |sturmSequence| |definingEquations| |set| + |stronglyReduce| |simplifyExp| |OMReadError?| |viewWriteDefault| + |gcdcofact| |e04ycf| |mathieu22| |mainMonomials| |bfKeys| + |reducedForm| |palgintegrate| |palgint0| |getRef| |e02ajf| |concat| + |iiasin| |nextColeman| |tab1| |OMgetString| |linear?| |byte| |cCsc| + |rightTraceMatrix| |logIfCan| |extendedint| |OMputEndBind| + |rationalPower| |bothWays| |linearDependence| |e02ddf| |dualSignature| + |multiset| |e02bbf| |equality| |unvectorise| |simpson| |nthFactor| + |fill!| |strongGenerators| |printingInfo?| |lfintegrate| + |resultantEuclidean| |iiasec| |coefficient| |associatedEquations| + |fullPartialFraction| |separant| |simplifyLog| |unitNormal| |int| + |minset| |doubleResultant| |inspect| |computeBasis| |acschIfCan| + |besselJ| |category| |presub| |OMgetEndError| |torsion?| |f01brf| + |outerProduct| |radicalSimplify| |Ei| |d01aqf| |monomialIntegrate| + |chainSubResultants| |coerce| |domain| |karatsuba| |e04dgf| + |startTable!| |setCondition!| |expenseOfEvaluationIF| |bounds| + |vectorise| |droot| |rewriteSetWithReduction| |construct| |package| + |mightHaveRoots| |polynomialZeros| |minimumExponent| |mapGen| |source| + |delete!| |parts| |groebner?| |before?| |critB| |rightQuotient| + |zeroSetSplit| |leftExtendedGcd| |extractIndex| |maxColIndex| + |goodPoint| |changeBase| |vertConcat| |sinhIfCan| |clearDenominator| + |show| |isobaric?| |yCoordinates| |bernoulli| |univcase| |ptree| + |base| |cCsch| |generic| |FormatArabic| |noLinearFactor?| |setOfMinN| + |d01bbf| |intcompBasis| |pop!| |screenResolution3D| |coerceL| + |algebraicVariables| |pushuconst| |writeByte!| |symmetricGroup| + |trace| |f07fdf| |lazy?| |nthFractionalTerm| |basisOfRightNucleus| + |clipWithRanges| |leadingTerm| |inverseLaplace| |primintegrate| + |bsolve| |OMputBind| |recolor| |integralLastSubResultant| + |discriminantEuclidean| |target| |quadratic?| |conjugate| |real?| + |extract!| |binarySearchTree| |pade| |isQuotient| |weight| |color| + |ksec| |complexSolve| |genericPosition| |region| |removeConstantTerm| + |setClosed| |df2mf| |build| |mergeDifference| |tanhIfCan| + |problemPoints| |isOp| |autoReduced?| |po| |atanIfCan| |next| |erf| + |wordInGenerators| |unitNormalize| |sample| |e02ahf| + |symmetricProduct| |hdmpToP| |selectPDERoutines| |basisOfRightNucloid| + |trapezoidal| |writeInt8!| |cycles| |infRittWu?| |oneDimensionalArray| + |ravel| |cAcot| |ScanFloatIgnoreSpacesIfCan| |merge| |bezoutResultant| + |polygon?| |enqueue!| |alphabetic?| |compound?| |lSpaceBasis| + |reshape| |orbits| FG2F |imagE| |bytes| |withPredicates| |dilog| + |laplacian| |height| |iisinh| |d02raf| |setPredicates| |failed?| + |s21bdf| |SturmHabichtMultiple| |factorset| |removeSuperfluousCases| + |sin| |setelt| |algebraicCoefficients?| |top| |divide| |split| + |integrate| |KrullNumber| |argumentListOf| |startStats!| |mainValue| + |scripted?| |cos| |dmpToP| |character?| |idealiser| |lazyEvaluate| + |previous| |comp| |padecf| |index?| |OMsupportsCD?| |solid| + |duplicates?| |tan| |copy| |symbol?| |solveRetract| |positiveSolve| + |mathieu12| |length| |cyclicSubmodule| |clearFortranOutputStack| + |internal?| |iilog| |cRationalPower| |cot| |continue| |badValues| + |multinomial| |mapmult| |replace| |scripts| |update| |fmecg| + |presuper| |zoom| |toroidal| |removeZero| |sec| |badNum| |postfix| + |readLine!| |choosemon| |distance| |imagK| |tanSum| |root| |integral| + |csc| |autoCoerce| |modifyPoint| |list| |digit| |gethi| + |solveLinearPolynomialEquationByFractions| |commonDenominator| + |tableau| |epilogue| |setErrorBound| |getOrder| |asin| |splitLinear| + |car| |prindINFO| |OMgetEndApp| |rst| |s17akf| |lazyPseudoRemainder| + |reducedDiscriminant| |quoted?| |characteristic| |acos| |OMgetEndBind| + |cdr| |iiabs| |supRittWu?| |OMopenFile| |acotIfCan| |chebyshevT| + |iisqrt2| |smith| |exponentialOrder| |gramschmidt| |atan| + |setDifference| |cschIfCan| |powmod| |surface| |subtractIfCan| + |position| |preprocess| |pointLists| |besselY| |rationalPoints| + |e01baf| |acot| |rotatez| |setIntersection| |selectOrPolynomials| + |quatern| |genus| |declare| |aQuartic| |rightRecip| |overbar| + |rotatex| |internalInfRittWu?| |asec| |eigenvalues| |setUnion| + |splitConstant| |tanIfCan| |isTerm| |match?| |partialDenominators| + |children| |pdf2df| |tail| |insertTop!| |rationalIfCan| |apply| + |digamma| |laplace| |csubst| |node?| |colorFunction| + |oblateSpheroidal| |atanhIfCan| |appendPoint| |imagj| |hash| |iiatan| + |s19aaf| |squareFreeFactors| |removeDuplicates!| |iicos| |realRoots| + |factorAndSplit| |stoseInvertible?sqfreg| |unit| |maxrow| |count| + |double| |maxPoints| |size| |shanksDiscLogAlgorithm| |cCoth| |mesh| + |printStats!| |LagrangeInterpolation| |indicialEquationAtInfinity| + |squareFreePolynomial| |transpose| |viewport3D| |setButtonValue| + |iFTable| |stoseInvertibleSetreg| |repeating| |associatedSystem| + |digits| |dot| |dominantTerm| |tree| |zeroSquareMatrix| |dec| + |printStatement| |rightRank| |e02agf| |rightGcd| |gcdcofactprim| + |integralCoordinates| |supDimElseRittWu?| |number?| |triangulate| + |clipPointsDefault| |first| |irreducible?| |cTan| |row| + |leftTraceMatrix| |torsionIfCan| |FormatRoman| |simplify| + |generateIrredPoly| |prepareSubResAlgo| |increase| |rest| + |mainVariable?| |setValue!| |An| |makeFR| |solid?| |rightFactorIfCan| + |pmComplexintegrate| |showIntensityFunctions| |resize| |substitute| + |resultantnaif| |groebSolve| |s18aff| |complexRoots| |close!| + |leftUnit| |mainCharacterization| |mapBivariate| |cSec| |someBasis| + |removeDuplicates| |symmetricDifference| |symmetricSquare| |closed?| + |factorPolynomial| |normalElement| |chineseRemainder| |li| |s17agf| + |alternative?| |quasiComponent| |leader| |declare!| |upperCase| + |derivative| |algDsolve| |getSyntaxFormsFromFile| |doubleRank| + |Lazard| |generator| |s17dlf| |internalIntegrate| + |halfExtendedSubResultantGcd2| |linSolve| |rank| |pushucoef| |solve| + |extractSplittingLeaf| |ip4Address| |OMgetError| |setProperty!| + |finiteBasis| |resultantReduitEuclidean| |basisOfMiddleNucleus| + |nthFlag| |expPot| |nextPrimitivePoly| |integralMatrix| |subSet| + |submod| |cross| |c06fqf| |top!| |useSingleFactorBound?| |edf2efi| + |reduceLODE| |constantOperator| |updateStatus!| + |rightCharacteristicPolynomial| |minPol| |setScreenResolution3D| + |middle| |gensym| |infLex?| |extendedResultant| + |createMultiplicationTable| |shallowCopy| |removeSquaresIfCan| + |cosIfCan| |super| |mat| |cap| |iitan| |subresultantVector| |linear| + |useEisensteinCriterion?| |genericLeftTrace| |exprToGenUPS| |isTimes| + |integralBasisAtInfinity| |fortranComplex| |nextLatticePermutation| + |singular?| |lyndonIfCan| |initTable!| |expressIdealMember| |check| + |segment| |jordanAdmissible?| |modTree| |tanintegrate| |exQuo| + |polynomial| |radicalSolve| |sin2csc| |lazyPquo| |getPickedPoints| + |euclideanNormalForm| |lists| |degreeSubResultant| + |univariatePolynomial| |weighted| |dim| |tracePowMod| |asinhIfCan| + |remainder| |test| |numberOfMonomials| |numFunEvals| |iiatanh| + |firstNumer| |repeating?| |homogeneous?| |pointData| |superscript| + |loadNativeModule| |rewriteIdealWithRemainder| |LiePolyIfCan| + |isEquiv| |semiSubResultantGcdEuclidean1| + |halfExtendedSubResultantGcd1| |upperCase?| |s01eaf| + |compiledFunction| |HenselLift| |rischDEsys| |id| + |antisymmetricTensors| |littleEndian| |findCycle| |f07aef| |geometric| + |factorSquareFreePolynomial| |enumerate| |eq| |inrootof| + |numericIfCan| |cAsec| |dihedralGroup| |formula| |hue| |flexibleArray| + |maxPoints3D| |table| |upDateBranches| |iter| |exportedOperators| + |binary| |prefix| |makeEq| |writeUInt8!| |numberOfPrimitivePoly| + |shuffle| |decomposeFunc| |inRadical?| |new| |mkPrim| |e02dff| + |rightZero| |subNode?| |constantIfCan| |fracPart| |rowEchelonLocal| + |insert| |setScreenResolution| |symbolIfCan| |root?| |OMsetEncoding| + |iicoth| |getCode| |setColumn!| |checkPrecision| |uncouplingMatrices| + |insertBottom!| |mainForm| |quoByVar| |clearCache| |randomLC| |nrows| + |s18def| |totalGroebner| |options| |nextNormalPoly| |validExponential| + |superHeight| |palglimint| |OMsupportsSymbol?| |unknownEndian| + |create3Space| |output| |ncols| |keys| + |selectMultiDimensionalRoutines| |approximants| |rationalPoint?| + |returnType!| |e02def| |monomRDE| |directory| |multMonom| |log2| + |leftExactQuotient| |perfectSquare?| |oddInfiniteProduct| |socf2socdf| + |f01qef| |trace2PowMod| |predicate| |fprindINFO| |symmetricRemainder| + |One| |removeIrreducibleRedundantFactors| + |semiDegreeSubResultantEuclidean| |string| |exp| |balancedBinaryTree| + |tanAn| |outputFixed| |exactQuotient| |leftRemainder| |lfunc| + |rewriteIdealWithHeadRemainder| |removeRoughlyRedundantFactorsInPol| + |monicRightFactorIfCan| |exp1| |mdeg| |leastMonomial| |axes| + |errorKind| |doubleDisc| |dequeue| |readUInt8!| |domainTemplate| + |ramified?| |createLowComplexityNormalBasis| |second| + |derivationCoordinates| |restorePrecision| |OMputEndAtp| |coordinate| + |rewriteSetByReducingWithParticularGenerators| + |halfExtendedResultant1| |viewport2D| |primextendedint| |stFunc2| + |numberOfDivisors| |third| |characteristicPolynomial| |numeric| |eq?| + |capacity| |decrease| |cAsin| |graeffe| |lex| |getButtonValue| + |branchPoint?| |left| |listConjugateBases| |radical| |s15aef| + |binaryTournament| |sup| |exponential1| |iipow| |iiasinh| + |primlimintfrac| |trigs2explogs| |solveLinearlyOverQ| |pole?| |elt| + |right| |nil| |infinite| |arbitraryExponent| |approximate| |complex| + |shallowMutable| |canonical| |noetherian| |central| |partiallyOrderedSet| |arbitraryPrecision| |canonicalsClosed| |noZeroDivisors| |rightUnitary| |leftUnitary| |additiveValuation| |unitsKnown| |canonicalUnitNormal| |multiplicativeValuation| diff --git a/src/share/algebra/interp.daase b/src/share/algebra/interp.daase index 6e1e9464..5b70fb9d 100644 --- a/src/share/algebra/interp.daase +++ b/src/share/algebra/interp.daase @@ -1,5319 +1,5319 @@ -(3221336 . 3453749814) -((-2383 (((-112) (-1 (-112) |#2| |#2|) $) 87) (((-112) $) NIL)) (-3426 (($ (-1 (-112) |#2| |#2|) $) 18) (($ $) NIL)) (-3874 ((|#2| $ (-566) |#2|) NIL) ((|#2| $ (-1231 (-566)) |#2|) 44)) (-2736 (($ $) 81)) (-4362 ((|#2| 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T) ((-38 |#2|) |has| |#2| (-172)) ((-102) -2805 (|has| |#2| (-1099)) (|has| |#2| (-1049)) (|has| |#2| (-848)) (|has| |#2| (-793)) (|has| |#2| (-726)) (|has| |#2| (-370)) (|has| |#2| (-365)) (|has| |#2| (-172)) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-111 |#2| |#2|) -2805 (|has| |#2| (-1049)) (|has| |#2| (-365)) (|has| |#2| (-172))) ((-111 $ $) |has| |#2| (-172)) ((-131) -2805 (|has| |#2| (-1049)) (|has| |#2| (-848)) (|has| |#2| (-793)) (|has| |#2| (-365)) (|has| |#2| (-172)) (|has| |#2| (-131))) ((-616 #0=(-409 (-566))) -12 (|has| |#2| (-1038 (-409 (-566)))) (|has| |#2| (-1099))) ((-616 (-566)) -2805 (|has| |#2| (-1049)) (-12 (|has| |#2| (-1038 (-566))) (|has| |#2| (-1099))) (|has| |#2| (-848)) (|has| |#2| (-172))) ((-616 |#2|) -2805 (|has| |#2| (-1099)) (|has| |#2| (-172))) ((-613 (-862)) -2805 (|has| |#2| (-1099)) (|has| |#2| (-1049)) (|has| |#2| (-848)) (|has| |#2| (-793)) (|has| |#2| (-726)) (|has| |#2| (-370)) (|has| |#2| (-365)) (|has| |#2| (-172)) (|has| |#2| (-613 (-862))) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-613 (-1264 |#2|)) . T) ((-172) |has| |#2| (-172)) ((-231 |#2|) |has| |#2| (-1049)) ((-233) -12 (|has| |#2| (-233)) (|has| |#2| (-1049))) ((-287 #1=(-566) |#2|) . T) ((-289 #1# |#2|) . T) ((-310 |#2|) -12 (|has| |#2| (-310 |#2|)) (|has| |#2| (-1099))) ((-370) |has| |#2| (-370)) ((-379 |#2|) |has| |#2| (-1049)) ((-413 |#2|) |has| |#2| (-1099)) ((-491 |#2|) . T) ((-604 #1# |#2|) . T) ((-516 |#2| |#2|) -12 (|has| |#2| (-310 |#2|)) (|has| |#2| (-1099))) ((-646 (-566)) -2805 (|has| |#2| (-1049)) (|has| |#2| (-848)) (|has| |#2| (-365)) (|has| |#2| (-172))) ((-646 |#2|) -2805 (|has| |#2| (-1049)) (|has| |#2| (-365)) (|has| |#2| (-172))) ((-646 $) -2805 (|has| |#2| (-1049)) (|has| |#2| (-848)) (|has| |#2| (-172))) ((-648 |#2|) -2805 (|has| |#2| (-1049)) (|has| |#2| (-365)) (|has| |#2| (-172))) ((-648 $) -2805 (|has| |#2| (-1049)) (|has| |#2| (-848)) (|has| |#2| (-172))) ((-640 |#2|) -2805 (|has| |#2| (-365)) (|has| |#2| (-172))) ((-639 (-566)) -12 (|has| |#2| (-639 (-566))) (|has| |#2| (-1049))) ((-639 |#2|) |has| |#2| (-1049)) ((-717 |#2|) -2805 (|has| |#2| (-365)) (|has| |#2| (-172))) ((-726) -2805 (|has| |#2| (-1049)) (|has| |#2| (-848)) (|has| |#2| (-726)) (|has| |#2| (-172))) ((-791) |has| |#2| (-848)) ((-792) -2805 (|has| |#2| (-848)) (|has| |#2| (-793))) ((-793) |has| |#2| (-793)) ((-794) -2805 (|has| |#2| (-848)) (|has| |#2| (-793))) ((-795) -2805 (|has| |#2| (-848)) (|has| |#2| (-793))) ((-848) |has| |#2| (-848)) ((-850) -2805 (|has| |#2| (-848)) (|has| |#2| (-793))) ((-900 (-1175)) -12 (|has| |#2| (-900 (-1175))) (|has| |#2| (-1049))) ((-1038 #0#) -12 (|has| |#2| (-1038 (-409 (-566)))) (|has| |#2| (-1099))) ((-1038 (-566)) -12 (|has| |#2| (-1038 (-566))) (|has| |#2| (-1099))) ((-1038 |#2|) |has| |#2| (-1099)) ((-1051 |#2|) -2805 (|has| |#2| (-1049)) (|has| |#2| (-365)) (|has| |#2| (-172))) ((-1051 $) |has| |#2| (-172)) ((-1056 |#2|) -2805 (|has| |#2| (-1049)) (|has| |#2| (-365)) (|has| |#2| (-172))) ((-1056 $) |has| |#2| (-172)) ((-1049) -2805 (|has| |#2| (-1049)) (|has| |#2| (-848)) (|has| |#2| (-172))) ((-1057) -2805 (|has| |#2| (-1049)) (|has| |#2| (-848)) (|has| |#2| (-172))) ((-1111) -2805 (|has| |#2| (-1049)) (|has| |#2| (-848)) (|has| |#2| (-726)) (|has| |#2| (-172))) ((-1099) -2805 (|has| |#2| (-1099)) (|has| |#2| (-1049)) (|has| |#2| (-848)) (|has| |#2| (-793)) (|has| |#2| (-726)) (|has| |#2| (-370)) (|has| |#2| (-365)) (|has| |#2| (-172)) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-1214) . T) ((-1271 |#2|) |has| |#2| (-365))) -((-2403 (((-240 |#1| |#3|) (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|) 21)) (-4362 ((|#3| (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|) 23)) (-3077 (((-240 |#1| |#3|) (-1 |#3| |#2|) (-240 |#1| |#2|)) 18))) -(((-239 |#1| |#2| |#3|) (-10 -7 (-15 -2403 ((-240 |#1| |#3|) (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|)) (-15 -4362 (|#3| (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|)) (-15 -3077 ((-240 |#1| |#3|) (-1 |#3| |#2|) (-240 |#1| |#2|)))) (-771) (-1214) (-1214)) (T -239)) -((-3077 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-240 *5 *6)) (-14 *5 (-771)) (-4 *6 (-1214)) (-4 *7 (-1214)) (-5 *2 (-240 *5 *7)) (-5 *1 (-239 *5 *6 *7)))) (-4362 (*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *6 *2)) (-5 *4 (-240 *5 *6)) (-14 *5 (-771)) (-4 *6 (-1214)) (-4 *2 (-1214)) (-5 *1 (-239 *5 *6 *2)))) (-2403 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *5 *7 *5)) (-5 *4 (-240 *6 *7)) (-14 *6 (-771)) (-4 *7 (-1214)) (-4 *5 (-1214)) (-5 *2 (-240 *6 *5)) (-5 *1 (-239 *6 *7 *5))))) -(-10 -7 (-15 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T) ((-646 |#1|) . T) ((-646 |#2|) |has| |#1| (-365)) ((-646 $) . T) ((-648 #1#) -2805 (|has| |#1| (-365)) (|has| |#1| (-38 (-409 (-566))))) ((-648 |#1|) . T) ((-648 |#2|) |has| |#1| (-365)) ((-648 $) . T) ((-640 #1#) -2805 (|has| |#1| (-365)) (|has| |#1| (-38 (-409 (-566))))) ((-640 |#1|) |has| |#1| (-172)) ((-640 |#2|) |has| |#1| (-365)) ((-640 $) -2805 (|has| |#1| (-558)) (|has| |#1| (-365))) ((-639 (-566)) -12 (|has| |#1| (-365)) (|has| |#2| (-639 (-566)))) ((-639 |#2|) |has| |#1| (-365)) ((-717 #1#) -2805 (|has| |#1| (-365)) (|has| |#1| (-38 (-409 (-566))))) ((-717 |#1|) |has| |#1| (-172)) ((-717 |#2|) |has| |#1| (-365)) ((-717 $) -2805 (|has| |#1| (-558)) (|has| |#1| (-365))) ((-726) . 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(-3040 (($ $ $) 35)) (** (($ $ (-921)) NIL) (($ $ (-771)) 54)) (* (($ (-921) $) NIL) (($ (-771) $) NIL) (($ (-566) $) 44) (($ $ $) 43))) (((-1292 |#1|) (-13 (-172) (-370) (-614 (-566)) (-1150)) (-921)) (T -1292)) NIL (-13 (-172) (-370) (-614 (-566)) (-1150)) @@ -5329,4 +5329,4 @@ NIL NIL NIL NIL -((-3 3221321 3221326 3221331 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-2 3221306 3221311 3221316 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1 3221291 3221296 3221301 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (0 3221276 3221281 3221286 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1292 3220419 3221151 3221228 "ZMOD" 3221233 NIL ZMOD (NIL NIL) -8 NIL NIL NIL) (-1291 3219529 3219693 3219902 "ZLINDEP" 3220251 NIL ZLINDEP (NIL T) -7 NIL NIL NIL) (-1290 3208829 3210597 3212569 "ZDSOLVE" 3217659 NIL ZDSOLVE (NIL T NIL NIL) -7 NIL NIL NIL) (-1289 3208075 3208216 3208405 "YSTREAM" 3208675 NIL YSTREAM (NIL T) -7 NIL NIL NIL) (-1288 3205849 3207376 3207580 "XRPOLY" 3207918 NIL XRPOLY (NIL T T) -8 NIL NIL NIL) (-1287 3202402 3203720 3204295 "XPR" 3205321 NIL XPR (NIL T T) -8 NIL NIL NIL) (-1286 3200123 3201733 3201937 "XPOLY" 3202233 NIL XPOLY (NIL T) -8 NIL NIL NIL) (-1285 3197776 3199144 3199199 "XPOLYC" 3199487 NIL XPOLYC (NIL T T) -9 NIL 3199600 NIL) (-1284 3194151 3196293 3196681 "XPBWPOLY" 3197434 NIL XPBWPOLY (NIL T T) -8 NIL NIL NIL) (-1283 3189846 3192141 3192183 "XF" 3192804 NIL XF (NIL T) -9 NIL 3193204 NIL) (-1282 3189467 3189555 3189724 "XF-" 3189729 NIL XF- (NIL T T) -8 NIL NIL NIL) (-1281 3184663 3185952 3186007 "XFALG" 3188179 NIL XFALG (NIL T T) -9 NIL 3188968 NIL) (-1280 3183796 3183900 3184105 "XEXPPKG" 3184555 NIL XEXPPKG (NIL T T T) -7 NIL NIL NIL) (-1279 3181905 3183646 3183742 "XDPOLY" 3183747 NIL XDPOLY (NIL T T) -8 NIL NIL NIL) (-1278 3180712 3181312 3181355 "XALG" 3181360 NIL XALG (NIL T) -9 NIL 3181471 NIL) (-1277 3174154 3178689 3179183 "WUTSET" 3180304 NIL WUTSET (NIL T T T T) -8 NIL NIL NIL) (-1276 3172410 3173206 3173529 "WP" 3173965 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL NIL) (-1275 3172012 3172232 3172302 "WHILEAST" 3172362 T WHILEAST (NIL) -8 NIL NIL NIL) (-1274 3171484 3171729 3171823 "WHEREAST" 3171940 T WHEREAST (NIL) -8 NIL NIL NIL) (-1273 3170370 3170568 3170863 "WFFINTBS" 3171281 NIL WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1272 3168274 3168701 3169163 "WEIER" 3169942 NIL WEIER (NIL T) -7 NIL NIL NIL) (-1271 3167320 3167770 3167812 "VSPACE" 3167948 NIL VSPACE (NIL T) -9 NIL 3168022 NIL) (-1270 3167158 3167185 3167276 "VSPACE-" 3167281 NIL VSPACE- (NIL T T) -8 NIL NIL NIL) (-1269 3166966 3167009 3167077 "VOID" 3167112 T VOID (NIL) -8 NIL NIL NIL) (-1268 3165102 3165461 3165867 "VIEW" 3166582 T VIEW (NIL) -7 NIL NIL NIL) (-1267 3161526 3162165 3162902 "VIEWDEF" 3164387 T VIEWDEF (NIL) -7 NIL NIL NIL) (-1266 3150830 3153074 3155247 "VIEW3D" 3159375 T VIEW3D (NIL) -8 NIL NIL NIL) (-1265 3143081 3144741 3146320 "VIEW2D" 3149273 T VIEW2D (NIL) -8 NIL NIL NIL) (-1264 3138433 3142851 3142943 "VECTOR" 3143024 NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1263 3137010 3137269 3137587 "VECTOR2" 3138163 NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1262 3130484 3134791 3134834 "VECTCAT" 3135829 NIL VECTCAT (NIL T) -9 NIL 3136416 NIL) (-1261 3129498 3129752 3130142 "VECTCAT-" 3130147 NIL VECTCAT- (NIL T T) -8 NIL NIL NIL) (-1260 3128952 3129149 3129269 "VARIABLE" 3129413 NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1259 3128885 3128890 3128920 "UTYPE" 3128925 T UTYPE (NIL) -9 NIL NIL NIL) (-1258 3127715 3127869 3128131 "UTSODETL" 3128711 NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1257 3125155 3125615 3126139 "UTSODE" 3127256 NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1256 3116992 3122781 3123270 "UTS" 3124724 NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1255 3107866 3113233 3113276 "UTSCAT" 3114388 NIL UTSCAT (NIL T) -9 NIL 3115146 NIL) (-1254 3105213 3105936 3106925 "UTSCAT-" 3106930 NIL UTSCAT- (NIL T T) -8 NIL NIL NIL) (-1253 3104840 3104883 3105016 "UTS2" 3105164 NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1252 3099066 3101678 3101721 "URAGG" 3103791 NIL URAGG (NIL T) -9 NIL 3104514 NIL) (-1251 3096005 3096868 3097991 "URAGG-" 3097996 NIL URAGG- (NIL T T) -8 NIL NIL NIL) (-1250 3091714 3094640 3095105 "UPXSSING" 3095669 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1249 3083780 3090961 3091234 "UPXS" 3091499 NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1248 3076853 3083684 3083756 "UPXSCONS" 3083761 NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1247 3066598 3073391 3073453 "UPXSCCA" 3074027 NIL UPXSCCA (NIL T T) -9 NIL 3074260 NIL) (-1246 3066236 3066321 3066495 "UPXSCCA-" 3066500 NIL UPXSCCA- (NIL T T T) -8 NIL NIL NIL) (-1245 3055833 3062399 3062442 "UPXSCAT" 3063090 NIL UPXSCAT (NIL T) -9 NIL 3063699 NIL) (-1244 3055263 3055342 3055521 "UPXS2" 3055748 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1243 3053917 3054170 3054521 "UPSQFREE" 3055006 NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1242 3047338 3050395 3050450 "UPSCAT" 3051611 NIL UPSCAT (NIL T T) -9 NIL 3052385 NIL) (-1241 3046542 3046749 3047076 "UPSCAT-" 3047081 NIL UPSCAT- (NIL T T T) -8 NIL NIL NIL) (-1240 3032197 3039965 3040008 "UPOLYC" 3042109 NIL UPOLYC (NIL T) -9 NIL 3043330 NIL) (-1239 3023525 3025951 3029098 "UPOLYC-" 3029103 NIL UPOLYC- (NIL T T) -8 NIL NIL NIL) (-1238 3023152 3023195 3023328 "UPOLYC2" 3023476 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1237 3014963 3022835 3022964 "UP" 3023071 NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1236 3014302 3014409 3014573 "UPMP" 3014852 NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1235 3013855 3013936 3014075 "UPDIVP" 3014215 NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1234 3012423 3012672 3012988 "UPDECOMP" 3013604 NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1233 3011658 3011770 3011955 "UPCDEN" 3012307 NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1232 3011177 3011246 3011395 "UP2" 3011583 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1231 3009644 3010381 3010658 "UNISEG" 3010935 NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1230 3008859 3008986 3009191 "UNISEG2" 3009487 NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1229 3007919 3008099 3008325 "UNIFACT" 3008675 NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1228 2991851 3007096 3007347 "ULS" 3007726 NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1227 2979849 2991755 2991827 "ULSCONS" 2991832 NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1226 2961868 2973853 2973915 "ULSCCAT" 2974553 NIL ULSCCAT (NIL T T) -9 NIL 2974841 NIL) (-1225 2960918 2961163 2961551 "ULSCCAT-" 2961556 NIL ULSCCAT- (NIL T T T) -8 NIL NIL NIL) (-1224 2950292 2956772 2956815 "ULSCAT" 2957678 NIL ULSCAT (NIL T) -9 NIL 2958409 NIL) (-1223 2949722 2949801 2949980 "ULS2" 2950207 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1222 2948849 2949359 2949466 "UINT8" 2949577 T UINT8 (NIL) -8 NIL NIL 2949662) (-1221 2947975 2948485 2948592 "UINT64" 2948703 T UINT64 (NIL) -8 NIL NIL 2948788) (-1220 2947101 2947611 2947718 "UINT32" 2947829 T UINT32 (NIL) -8 NIL NIL 2947914) (-1219 2946227 2946737 2946844 "UINT16" 2946955 T UINT16 (NIL) -8 NIL NIL 2947040) (-1218 2944530 2945487 2945517 "UFD" 2945729 T UFD (NIL) -9 NIL 2945843 NIL) (-1217 2944324 2944370 2944465 "UFD-" 2944470 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1216 2943406 2943589 2943805 "UDVO" 2944130 T UDVO (NIL) -7 NIL NIL NIL) (-1215 2941222 2941631 2942102 "UDPO" 2942970 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1214 2941155 2941160 2941190 "TYPE" 2941195 T TYPE (NIL) -9 NIL NIL NIL) (-1213 2940915 2941110 2941141 "TYPEAST" 2941146 T TYPEAST (NIL) -8 NIL NIL NIL) (-1212 2939886 2940088 2940328 "TWOFACT" 2940709 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1211 2938909 2939295 2939530 "TUPLE" 2939686 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1210 2936600 2937119 2937658 "TUBETOOL" 2938392 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1209 2935449 2935654 2935895 "TUBE" 2936393 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1208 2930178 2934421 2934704 "TS" 2935201 NIL TS (NIL T) -8 NIL NIL NIL) (-1207 2918818 2922937 2923034 "TSETCAT" 2928303 NIL TSETCAT (NIL T T T T) -9 NIL 2929834 NIL) (-1206 2913550 2915150 2917041 "TSETCAT-" 2917046 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1205 2908189 2909036 2909965 "TRMANIP" 2912686 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1204 2907630 2907693 2907856 "TRIMAT" 2908121 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1203 2905496 2905733 2906090 "TRIGMNIP" 2907379 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1202 2905016 2905129 2905159 "TRIGCAT" 2905372 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1201 2904685 2904764 2904905 "TRIGCAT-" 2904910 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1200 2901530 2903543 2903824 "TREE" 2904439 NIL TREE (NIL T) -8 NIL NIL NIL) (-1199 2900804 2901332 2901362 "TRANFUN" 2901397 T TRANFUN (NIL) -9 NIL 2901463 NIL) (-1198 2900083 2900274 2900554 "TRANFUN-" 2900559 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1197 2899887 2899919 2899980 "TOPSP" 2900044 T TOPSP (NIL) -7 NIL NIL NIL) (-1196 2899235 2899350 2899504 "TOOLSIGN" 2899768 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1195 2897869 2898412 2898651 "TEXTFILE" 2899018 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1194 2895781 2896322 2896751 "TEX" 2897462 T TEX (NIL) -8 NIL NIL NIL) (-1193 2895562 2895593 2895665 "TEX1" 2895744 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1192 2895210 2895273 2895363 "TEMUTL" 2895494 T TEMUTL (NIL) -7 NIL NIL NIL) (-1191 2893364 2893644 2893969 "TBCMPPK" 2894933 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1190 2885141 2891524 2891580 "TBAGG" 2891980 NIL TBAGG (NIL T T) -9 NIL 2892191 NIL) (-1189 2880211 2881699 2883453 "TBAGG-" 2883458 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1188 2879595 2879702 2879847 "TANEXP" 2880100 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1187 2872985 2879452 2879545 "TABLE" 2879550 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1186 2872397 2872496 2872634 "TABLEAU" 2872882 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1185 2867005 2868225 2869473 "TABLBUMP" 2871183 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1184 2866227 2866374 2866555 "SYSTEM" 2866846 T SYSTEM (NIL) -8 NIL NIL NIL) (-1183 2862686 2863385 2864168 "SYSSOLP" 2865478 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1182 2861730 2862235 2862354 "SYSNNI" 2862540 NIL SYSNNI (NIL NIL) -8 NIL NIL 2862625) (-1181 2861037 2861496 2861575 "SYSINT" 2861635 NIL SYSINT (NIL NIL) -8 NIL NIL 2861680) (-1180 2857369 2858315 2859025 "SYNTAX" 2860349 T SYNTAX (NIL) -8 NIL NIL NIL) (-1179 2854527 2855129 2855761 "SYMTAB" 2856759 T SYMTAB (NIL) -8 NIL NIL NIL) (-1178 2849776 2850678 2851661 "SYMS" 2853566 T SYMS (NIL) -8 NIL NIL NIL) (-1177 2847011 2849234 2849464 "SYMPOLY" 2849581 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1176 2846528 2846603 2846726 "SYMFUNC" 2846923 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1175 2842547 2843840 2844653 "SYMBOL" 2845737 T SYMBOL (NIL) -8 NIL NIL NIL) (-1174 2836086 2837775 2839495 "SWITCH" 2840849 T SWITCH (NIL) -8 NIL NIL NIL) (-1173 2829320 2834907 2835210 "SUTS" 2835841 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1172 2821386 2828567 2828840 "SUPXS" 2829105 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1171 2813145 2821004 2821130 "SUP" 2821295 NIL SUP (NIL T) -8 NIL NIL NIL) (-1170 2812304 2812431 2812648 "SUPFRACF" 2813013 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1169 2811925 2811984 2812097 "SUP2" 2812239 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1168 2810373 2810647 2811003 "SUMRF" 2811624 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1167 2809708 2809774 2809966 "SUMFS" 2810294 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1166 2793675 2808885 2809136 "SULS" 2809515 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1165 2793277 2793497 2793567 "SUCHTAST" 2793627 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1164 2792572 2792802 2792942 "SUCH" 2793185 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1163 2786438 2787478 2788437 "SUBSPACE" 2791660 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1162 2785868 2785958 2786122 "SUBRESP" 2786326 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1161 2779233 2780533 2781844 "STTF" 2784604 NIL STTF (NIL T) -7 NIL NIL NIL) (-1160 2773406 2774526 2775673 "STTFNC" 2778133 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1159 2764716 2766588 2768382 "STTAYLOR" 2771647 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1158 2757846 2764580 2764663 "STRTBL" 2764668 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1157 2753210 2757801 2757832 "STRING" 2757837 T STRING (NIL) -8 NIL NIL NIL) (-1156 2748071 2752583 2752613 "STRICAT" 2752672 T STRICAT (NIL) -9 NIL 2752734 NIL) (-1155 2740824 2745690 2746301 "STREAM" 2747495 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1154 2740334 2740411 2740555 "STREAM3" 2740741 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1153 2739316 2739499 2739734 "STREAM2" 2740147 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1152 2739004 2739056 2739149 "STREAM1" 2739258 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1151 2738020 2738201 2738432 "STINPROD" 2738820 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1150 2737572 2737782 2737812 "STEP" 2737892 T STEP (NIL) -9 NIL 2737970 NIL) (-1149 2731004 2737471 2737548 "STBL" 2737553 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1148 2726130 2730225 2730268 "STAGG" 2730421 NIL STAGG (NIL T) -9 NIL 2730510 NIL) (-1147 2723832 2724434 2725306 "STAGG-" 2725311 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1146 2721979 2723602 2723694 "STACK" 2723775 NIL STACK (NIL T) -8 NIL NIL NIL) (-1145 2714674 2720120 2720576 "SREGSET" 2721609 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1144 2707099 2708468 2709981 "SRDCMPK" 2713280 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1143 2700016 2704539 2704569 "SRAGG" 2705872 T SRAGG (NIL) -9 NIL 2706480 NIL) (-1142 2699033 2699288 2699667 "SRAGG-" 2699672 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1141 2693493 2697980 2698401 "SQMATRIX" 2698659 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1140 2687178 2690211 2690938 "SPLTREE" 2692838 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1139 2683141 2683834 2684480 "SPLNODE" 2686604 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1138 2682188 2682421 2682451 "SPFCAT" 2682895 T SPFCAT (NIL) -9 NIL NIL NIL) (-1137 2680925 2681135 2681399 "SPECOUT" 2681946 T SPECOUT (NIL) -7 NIL NIL NIL) (-1136 2672551 2674321 2674351 "SPADXPT" 2678743 T SPADXPT (NIL) -9 NIL 2680777 NIL) (-1135 2672312 2672352 2672421 "SPADPRSR" 2672504 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1134 2670467 2672267 2672298 "SPADAST" 2672303 T SPADAST (NIL) -8 NIL NIL NIL) (-1133 2662412 2664185 2664228 "SPACEC" 2668601 NIL SPACEC (NIL T) -9 NIL 2670417 NIL) (-1132 2660542 2662344 2662393 "SPACE3" 2662398 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1131 2659294 2659465 2659756 "SORTPAK" 2660347 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1130 2657386 2657689 2658101 "SOLVETRA" 2658958 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1129 2656436 2656658 2656919 "SOLVESER" 2657159 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1128 2651740 2652628 2653623 "SOLVERAD" 2655488 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1127 2647555 2648164 2648893 "SOLVEFOR" 2651107 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1126 2641825 2646904 2647001 "SNTSCAT" 2647006 NIL SNTSCAT (NIL T T T T) -9 NIL 2647076 NIL) (-1125 2635931 2640148 2640539 "SMTS" 2641515 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1124 2630615 2635819 2635896 "SMP" 2635901 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1123 2628774 2629075 2629473 "SMITH" 2630312 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1122 2621487 2625683 2625786 "SMATCAT" 2627137 NIL SMATCAT (NIL NIL T T T) -9 NIL 2627687 NIL) (-1121 2618427 2619250 2620428 "SMATCAT-" 2620433 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1120 2616093 2617663 2617706 "SKAGG" 2617967 NIL SKAGG (NIL T) -9 NIL 2618102 NIL) (-1119 2612404 2615509 2615704 "SINT" 2615891 T SINT (NIL) -8 NIL NIL 2616064) (-1118 2612176 2612214 2612280 "SIMPAN" 2612360 T SIMPAN (NIL) -7 NIL NIL NIL) (-1117 2611455 2611711 2611851 "SIG" 2612058 T SIG (NIL) -8 NIL NIL NIL) (-1116 2610293 2610514 2610789 "SIGNRF" 2611214 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1115 2609126 2609277 2609561 "SIGNEF" 2610122 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1114 2608432 2608709 2608833 "SIGAST" 2609024 T SIGAST (NIL) -8 NIL NIL NIL) (-1113 2606121 2606576 2607082 "SHP" 2607973 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1112 2599973 2606022 2606098 "SHDP" 2606103 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1111 2599546 2599738 2599768 "SGROUP" 2599861 T SGROUP (NIL) -9 NIL 2599923 NIL) (-1110 2599404 2599430 2599503 "SGROUP-" 2599508 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1109 2596239 2596937 2597660 "SGCF" 2598703 T SGCF (NIL) -7 NIL NIL NIL) (-1108 2590607 2595686 2595783 "SFRTCAT" 2595788 NIL SFRTCAT (NIL T T T T) -9 NIL 2595827 NIL) (-1107 2584028 2585046 2586182 "SFRGCD" 2589590 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1106 2577154 2578227 2579413 "SFQCMPK" 2582961 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1105 2576774 2576863 2576974 "SFORT" 2577095 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1104 2575892 2576614 2576735 "SEXOF" 2576740 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1103 2574999 2575773 2575841 "SEX" 2575846 T SEX (NIL) -8 NIL NIL NIL) (-1102 2570512 2571227 2571322 "SEXCAT" 2574259 NIL SEXCAT (NIL T T T T T) -9 NIL 2574837 NIL) (-1101 2567665 2570446 2570494 "SET" 2570499 NIL SET (NIL T) -8 NIL NIL NIL) (-1100 2565889 2566378 2566683 "SETMN" 2567406 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1099 2565385 2565537 2565567 "SETCAT" 2565743 T SETCAT (NIL) -9 NIL 2565853 NIL) (-1098 2565077 2565155 2565285 "SETCAT-" 2565290 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1097 2561438 2563538 2563581 "SETAGG" 2564451 NIL SETAGG (NIL T) -9 NIL 2564791 NIL) (-1096 2560896 2561012 2561249 "SETAGG-" 2561254 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1095 2560339 2560592 2560693 "SEQAST" 2560817 T SEQAST (NIL) -8 NIL NIL NIL) (-1094 2559538 2559832 2559893 "SEGXCAT" 2560179 NIL SEGXCAT (NIL T T) -9 NIL 2560299 NIL) (-1093 2558544 2559204 2559386 "SEG" 2559391 NIL SEG (NIL T) -8 NIL NIL NIL) (-1092 2557523 2557737 2557780 "SEGCAT" 2558302 NIL SEGCAT (NIL T) -9 NIL 2558523 NIL) (-1091 2556524 2556902 2557102 "SEGBIND" 2557358 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1090 2556145 2556204 2556317 "SEGBIND2" 2556459 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1089 2555718 2555946 2556023 "SEGAST" 2556090 T SEGAST (NIL) -8 NIL NIL NIL) (-1088 2554937 2555063 2555267 "SEG2" 2555562 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1087 2554347 2554872 2554919 "SDVAR" 2554924 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1086 2546874 2554117 2554247 "SDPOL" 2554252 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1085 2545467 2545733 2546052 "SCPKG" 2546589 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1084 2544631 2544803 2544995 "SCOPE" 2545297 T SCOPE (NIL) -8 NIL NIL NIL) (-1083 2543851 2543985 2544164 "SCACHE" 2544486 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1082 2543497 2543683 2543713 "SASTCAT" 2543718 T SASTCAT (NIL) -9 NIL 2543731 NIL) (-1081 2542984 2543332 2543408 "SAOS" 2543443 T SAOS (NIL) -8 NIL NIL NIL) (-1080 2542549 2542584 2542757 "SAERFFC" 2542943 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1079 2536488 2542446 2542526 "SAE" 2542531 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1078 2536081 2536116 2536275 "SAEFACT" 2536447 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1077 2534402 2534716 2535117 "RURPK" 2535747 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1076 2533039 2533345 2533650 "RULESET" 2534236 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1075 2530262 2530792 2531250 "RULE" 2532720 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1074 2529874 2530056 2530139 "RULECOLD" 2530214 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1073 2529664 2529692 2529763 "RTVALUE" 2529825 T RTVALUE (NIL) -8 NIL NIL NIL) (-1072 2529135 2529381 2529475 "RSTRCAST" 2529592 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1071 2523983 2524778 2525698 "RSETGCD" 2528334 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1070 2513213 2518292 2518389 "RSETCAT" 2522508 NIL RSETCAT (NIL T T T T) -9 NIL 2523605 NIL) (-1069 2511140 2511679 2512503 "RSETCAT-" 2512508 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1068 2503525 2504902 2506422 "RSDCMPK" 2509739 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1067 2501504 2501971 2502045 "RRCC" 2503131 NIL RRCC (NIL T T) -9 NIL 2503475 NIL) (-1066 2500855 2501029 2501308 "RRCC-" 2501313 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1065 2500298 2500551 2500652 "RPTAST" 2500776 T RPTAST (NIL) -8 NIL NIL NIL) (-1064 2474149 2483506 2483573 "RPOLCAT" 2494237 NIL RPOLCAT (NIL T T T) -9 NIL 2497396 NIL) (-1063 2465647 2467987 2471109 "RPOLCAT-" 2471114 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1062 2456578 2463858 2464340 "ROUTINE" 2465187 T ROUTINE (NIL) -8 NIL NIL NIL) (-1061 2453376 2456204 2456344 "ROMAN" 2456460 T ROMAN (NIL) -8 NIL NIL NIL) (-1060 2451620 2452236 2452496 "ROIRC" 2453181 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1059 2447852 2450136 2450166 "RNS" 2450470 T RNS (NIL) -9 NIL 2450744 NIL) (-1058 2446361 2446744 2447278 "RNS-" 2447353 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1057 2445764 2446172 2446202 "RNG" 2446207 T RNG (NIL) -9 NIL 2446228 NIL) (-1056 2445163 2445551 2445594 "RMODULE" 2445599 NIL RMODULE (NIL T) -9 NIL 2445626 NIL) (-1055 2443999 2444093 2444429 "RMCAT2" 2445064 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1054 2440849 2443345 2443642 "RMATRIX" 2443761 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1053 2433676 2435936 2436051 "RMATCAT" 2439410 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2440392 NIL) (-1052 2433051 2433198 2433505 "RMATCAT-" 2433510 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1051 2432452 2432673 2432716 "RLINSET" 2432910 NIL RLINSET (NIL T) -9 NIL 2433001 NIL) (-1050 2432019 2432094 2432222 "RINTERP" 2432371 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1049 2431077 2431631 2431661 "RING" 2431717 T RING (NIL) -9 NIL 2431809 NIL) (-1048 2430869 2430913 2431010 "RING-" 2431015 NIL RING- (NIL T) -8 NIL NIL NIL) (-1047 2429710 2429947 2430205 "RIDIST" 2430633 T RIDIST (NIL) -7 NIL NIL NIL) (-1046 2420999 2429178 2429384 "RGCHAIN" 2429558 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1045 2420349 2420755 2420796 "RGBCSPC" 2420854 NIL RGBCSPC (NIL T) -9 NIL 2420906 NIL) (-1044 2419507 2419888 2419929 "RGBCMDL" 2420161 NIL RGBCMDL (NIL T) -9 NIL 2420275 NIL) (-1043 2416501 2417115 2417785 "RF" 2418871 NIL RF (NIL T) -7 NIL NIL NIL) (-1042 2416147 2416210 2416313 "RFFACTOR" 2416432 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1041 2415872 2415907 2416004 "RFFACT" 2416106 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1040 2413989 2414353 2414735 "RFDIST" 2415512 T RFDIST (NIL) -7 NIL NIL NIL) (-1039 2413442 2413534 2413697 "RETSOL" 2413891 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1038 2413078 2413158 2413201 "RETRACT" 2413334 NIL RETRACT (NIL T) -9 NIL 2413421 NIL) (-1037 2412927 2412952 2413039 "RETRACT-" 2413044 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1036 2412529 2412749 2412819 "RETAST" 2412879 T RETAST (NIL) -8 NIL NIL NIL) (-1035 2405267 2412182 2412309 "RESULT" 2412424 T RESULT (NIL) -8 NIL NIL NIL) (-1034 2403858 2404536 2404735 "RESRING" 2405170 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1033 2403494 2403543 2403641 "RESLATC" 2403795 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1032 2403199 2403234 2403341 "REPSQ" 2403453 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1031 2400621 2401201 2401803 "REP" 2402619 T REP (NIL) -7 NIL NIL NIL) (-1030 2400318 2400353 2400464 "REPDB" 2400580 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1029 2394218 2395607 2396830 "REP2" 2399130 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1028 2390595 2391276 2392084 "REP1" 2393445 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1027 2383291 2388736 2389192 "REGSET" 2390225 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1026 2382056 2382439 2382689 "REF" 2383076 NIL REF (NIL T) -8 NIL NIL NIL) (-1025 2381433 2381536 2381703 "REDORDER" 2381940 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1024 2377401 2380646 2380873 "RECLOS" 2381261 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1023 2376453 2376634 2376849 "REALSOLV" 2377208 T REALSOLV (NIL) -7 NIL NIL NIL) (-1022 2376299 2376340 2376370 "REAL" 2376375 T REAL (NIL) -9 NIL 2376410 NIL) (-1021 2372782 2373584 2374468 "REAL0Q" 2375464 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1020 2368383 2369371 2370432 "REAL0" 2371763 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1019 2367854 2368100 2368194 "RDUCEAST" 2368311 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1018 2367259 2367331 2367538 "RDIV" 2367776 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1017 2366327 2366501 2366714 "RDIST" 2367081 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1016 2364924 2365211 2365583 "RDETRS" 2366035 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1015 2362736 2363190 2363728 "RDETR" 2364466 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1014 2361361 2361639 2362036 "RDEEFS" 2362452 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1013 2359870 2360176 2360601 "RDEEF" 2361049 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1012 2353931 2356851 2356881 "RCFIELD" 2358176 T RCFIELD (NIL) -9 NIL 2358907 NIL) (-1011 2351995 2352499 2353195 "RCFIELD-" 2353270 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1010 2348264 2350096 2350139 "RCAGG" 2351223 NIL RCAGG (NIL T) -9 NIL 2351688 NIL) (-1009 2347892 2347986 2348149 "RCAGG-" 2348154 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1008 2347227 2347339 2347504 "RATRET" 2347776 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1007 2346780 2346847 2346968 "RATFACT" 2347155 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1006 2346088 2346208 2346360 "RANDSRC" 2346650 T RANDSRC (NIL) -7 NIL NIL NIL) (-1005 2345822 2345866 2345939 "RADUTIL" 2346037 T RADUTIL (NIL) -7 NIL NIL NIL) (-1004 2338938 2344655 2344965 "RADIX" 2345546 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-1003 2330557 2338780 2338910 "RADFF" 2338915 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-1002 2330204 2330279 2330309 "RADCAT" 2330469 T RADCAT (NIL) -9 NIL NIL NIL) (-1001 2329986 2330034 2330134 "RADCAT-" 2330139 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-1000 2328086 2329758 2329849 "QUEUE" 2329930 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-999 2324627 2328023 2328068 "QUAT" 2328073 NIL QUAT (NIL T) -8 NIL NIL NIL) (-998 2324265 2324308 2324435 "QUATCT2" 2324578 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-997 2317727 2321072 2321112 "QUATCAT" 2321892 NIL QUATCAT (NIL T) -9 NIL 2322658 NIL) (-996 2313871 2314908 2316295 "QUATCAT-" 2316389 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-995 2311344 2312955 2312996 "QUAGG" 2313371 NIL QUAGG (NIL T) -9 NIL 2313546 NIL) (-994 2310949 2311169 2311237 "QQUTAST" 2311296 T QQUTAST (NIL) -8 NIL NIL NIL) (-993 2309847 2310347 2310519 "QFORM" 2310821 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-992 2300852 2306091 2306131 "QFCAT" 2306789 NIL QFCAT (NIL T) -9 NIL 2307790 NIL) (-991 2296424 2297625 2299216 "QFCAT-" 2299310 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-990 2296062 2296105 2296232 "QFCAT2" 2296375 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-989 2295522 2295632 2295762 "QEQUAT" 2295952 T QEQUAT (NIL) -8 NIL NIL NIL) (-988 2288668 2289741 2290925 "QCMPACK" 2294455 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-987 2286217 2286665 2287093 "QALGSET" 2288323 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-986 2285462 2285636 2285868 "QALGSET2" 2286037 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-985 2284152 2284376 2284693 "PWFFINTB" 2285235 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-984 2282334 2282502 2282856 "PUSHVAR" 2283966 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-983 2278252 2279306 2279347 "PTRANFN" 2281231 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-982 2276654 2276945 2277267 "PTPACK" 2277963 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-981 2276286 2276343 2276452 "PTFUNC2" 2276591 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-980 2270763 2275158 2275199 "PTCAT" 2275495 NIL PTCAT (NIL T) -9 NIL 2275648 NIL) (-979 2270421 2270456 2270580 "PSQFR" 2270722 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-978 2269016 2269314 2269648 "PSEUDLIN" 2270119 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-977 2255779 2258150 2260474 "PSETPK" 2266776 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-976 2248797 2251537 2251633 "PSETCAT" 2254654 NIL PSETCAT (NIL T T T T) -9 NIL 2255468 NIL) (-975 2246633 2247267 2248088 "PSETCAT-" 2248093 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-974 2245982 2246147 2246175 "PSCURVE" 2246443 T PSCURVE (NIL) -9 NIL 2246610 NIL) (-973 2241980 2243496 2243561 "PSCAT" 2244405 NIL PSCAT (NIL T T T) -9 NIL 2244645 NIL) (-972 2241043 2241259 2241659 "PSCAT-" 2241664 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-971 2239748 2240408 2240613 "PRTITION" 2240858 T PRTITION (NIL) -8 NIL NIL NIL) (-970 2239223 2239469 2239561 "PRTDAST" 2239676 T PRTDAST (NIL) -8 NIL NIL NIL) (-969 2228312 2230527 2232715 "PRS" 2237085 NIL PRS (NIL T T) -7 NIL NIL NIL) (-968 2226123 2227662 2227702 "PRQAGG" 2227885 NIL PRQAGG (NIL T) -9 NIL 2227987 NIL) (-967 2225327 2225632 2225660 "PROPLOG" 2225907 T PROPLOG (NIL) -9 NIL 2226073 NIL) (-966 2223757 2224278 2224535 "PROPFRML" 2225103 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-965 2223226 2223333 2223461 "PROPERTY" 2223649 T PROPERTY (NIL) -8 NIL NIL NIL) (-964 2217284 2221392 2222212 "PRODUCT" 2222452 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-963 2214562 2216742 2216976 "PR" 2217095 NIL PR (NIL T T) -8 NIL NIL NIL) (-962 2214358 2214390 2214449 "PRINT" 2214523 T PRINT (NIL) -7 NIL NIL NIL) (-961 2213698 2213815 2213967 "PRIMES" 2214238 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-960 2211763 2212164 2212630 "PRIMELT" 2213277 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-959 2211492 2211541 2211569 "PRIMCAT" 2211693 T PRIMCAT (NIL) -9 NIL NIL NIL) (-958 2207607 2211430 2211475 "PRIMARR" 2211480 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-957 2206614 2206792 2207020 "PRIMARR2" 2207425 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-956 2206257 2206313 2206424 "PREASSOC" 2206552 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-955 2205732 2205865 2205893 "PPCURVE" 2206098 T PPCURVE (NIL) -9 NIL 2206234 NIL) (-954 2205327 2205527 2205610 "PORTNUM" 2205669 T PORTNUM (NIL) -8 NIL NIL NIL) (-953 2202686 2203085 2203677 "POLYROOT" 2204908 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-952 2196868 2202290 2202450 "POLY" 2202559 NIL POLY (NIL T) -8 NIL NIL NIL) (-951 2196251 2196309 2196543 "POLYLIFT" 2196804 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-950 2192526 2192975 2193604 "POLYCATQ" 2195796 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-949 2179238 2184366 2184431 "POLYCAT" 2187945 NIL POLYCAT (NIL T T T) -9 NIL 2189823 NIL) (-948 2172687 2174549 2176933 "POLYCAT-" 2176938 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-947 2172274 2172342 2172462 "POLY2UP" 2172613 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-946 2171906 2171963 2172072 "POLY2" 2172211 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-945 2170591 2170830 2171106 "POLUTIL" 2171680 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-944 2168946 2169223 2169554 "POLTOPOL" 2170313 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-943 2164411 2168882 2168928 "POINT" 2168933 NIL POINT (NIL T) -8 NIL NIL NIL) (-942 2162598 2162955 2163330 "PNTHEORY" 2164056 T PNTHEORY (NIL) -7 NIL NIL NIL) (-941 2161056 2161353 2161752 "PMTOOLS" 2162296 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-940 2160649 2160727 2160844 "PMSYM" 2160972 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-939 2160159 2160228 2160402 "PMQFCAT" 2160574 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-938 2159514 2159624 2159780 "PMPRED" 2160036 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-937 2158907 2158993 2159155 "PMPREDFS" 2159415 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-936 2157571 2157779 2158157 "PMPLCAT" 2158669 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-935 2157103 2157182 2157334 "PMLSAGG" 2157486 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-934 2156576 2156652 2156834 "PMKERNEL" 2157021 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-933 2156193 2156268 2156381 "PMINS" 2156495 NIL PMINS (NIL T) -7 NIL NIL NIL) (-932 2155635 2155704 2155913 "PMFS" 2156118 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-931 2154863 2154981 2155186 "PMDOWN" 2155512 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-930 2154030 2154188 2154369 "PMASS" 2154702 T PMASS (NIL) -7 NIL NIL NIL) (-929 2153303 2153413 2153576 "PMASSFS" 2153917 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-928 2152958 2153026 2153120 "PLOTTOOL" 2153229 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-927 2147565 2148769 2149917 "PLOT" 2151830 T PLOT (NIL) -8 NIL NIL NIL) (-926 2143369 2144413 2145334 "PLOT3D" 2146664 T PLOT3D (NIL) -8 NIL NIL NIL) (-925 2142281 2142458 2142693 "PLOT1" 2143173 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-924 2117670 2122347 2127198 "PLEQN" 2137547 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-923 2116988 2117110 2117290 "PINTERP" 2117535 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-922 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"PF" 2098344 NIL PF (NIL NIL) -8 NIL NIL NIL) (-909 2092268 2093539 2093567 "PFECAT" 2094152 T PFECAT (NIL) -9 NIL 2094536 NIL) (-908 2091713 2091867 2092081 "PFECAT-" 2092086 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-907 2090316 2090568 2090869 "PFBRU" 2091462 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-906 2088182 2088534 2088966 "PFBR" 2089967 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-905 2084064 2085558 2086234 "PERM" 2087539 NIL PERM (NIL T) -8 NIL NIL NIL) (-904 2079298 2080271 2081141 "PERMGRP" 2083227 NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-903 2077404 2078361 2078402 "PERMCAT" 2078848 NIL PERMCAT (NIL T) -9 NIL 2079153 NIL) (-902 2077057 2077098 2077222 "PERMAN" 2077357 NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-901 2074545 2076722 2076844 "PENDTREE" 2076968 NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-900 2072569 2073337 2073378 "PDRING" 2074035 NIL PDRING (NIL T) -9 NIL 2074321 NIL) (-899 2071672 2071890 2072252 "PDRING-" 2072257 NIL PDRING- (NIL T T) -8 NIL NIL NIL) (-898 2068887 2069665 2070333 "PDEPROB" 2071024 T PDEPROB (NIL) -8 NIL NIL NIL) (-897 2066432 2066936 2067491 "PDEPACK" 2068352 T PDEPACK (NIL) -7 NIL NIL NIL) (-896 2065344 2065534 2065785 "PDECOMP" 2066231 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-895 2062923 2063766 2063794 "PDECAT" 2064581 T PDECAT (NIL) -9 NIL 2065294 NIL) (-894 2062674 2062707 2062797 "PCOMP" 2062884 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-893 2060852 2061475 2061772 "PBWLB" 2062403 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-892 2053325 2054925 2056263 "PATTERN" 2059535 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-891 2052957 2053014 2053123 "PATTERN2" 2053262 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-890 2050714 2051102 2051559 "PATTERN1" 2052546 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-889 2048082 2048663 2049144 "PATRES" 2050279 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-888 2047646 2047713 2047845 "PATRES2" 2048009 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-887 2045529 2045934 2046341 "PATMATCH" 2047313 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-886 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NIL) (-874 2036422 2036766 2036994 "PALETTE" 2037437 T PALETTE (NIL) -8 NIL NIL NIL) (-873 2034815 2035427 2035787 "PAIR" 2036108 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-872 2028685 2034074 2034268 "PADICRC" 2034670 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-871 2021914 2028031 2028215 "PADICRAT" 2028533 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-870 2020229 2021851 2021896 "PADIC" 2021901 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-869 2017339 2018903 2018943 "PADICCT" 2019524 NIL PADICCT (NIL NIL) -9 NIL 2019806 NIL) (-868 2016296 2016496 2016764 "PADEPAC" 2017126 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-867 2015508 2015641 2015847 "PADE" 2016158 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-866 2013895 2014716 2014996 "OWP" 2015312 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-865 2013388 2013601 2013698 "OVERSET" 2013818 T OVERSET (NIL) -8 NIL NIL NIL) (-864 2012434 2012993 2013165 "OVAR" 2013256 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-863 2011698 2011819 2011980 "OUT" 2012293 T OUT (NIL) -7 NIL NIL NIL) (-862 2000570 2002807 2005007 "OUTFORM" 2009518 T OUTFORM (NIL) -8 NIL NIL NIL) (-861 1999906 2000167 2000294 "OUTBFILE" 2000463 T OUTBFILE (NIL) -8 NIL NIL NIL) (-860 1999213 1999378 1999406 "OUTBCON" 1999724 T OUTBCON (NIL) -9 NIL 1999890 NIL) (-859 1998814 1998926 1999083 "OUTBCON-" 1999088 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-858 1998194 1998543 1998632 "OSI" 1998745 T OSI (NIL) -8 NIL NIL NIL) (-857 1997724 1998062 1998090 "OSGROUP" 1998095 T OSGROUP (NIL) -9 NIL 1998117 NIL) (-856 1996469 1996696 1996981 "ORTHPOL" 1997471 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-855 1994020 1996304 1996425 "OREUP" 1996430 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-854 1991423 1993711 1993838 "ORESUP" 1993962 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-853 1988951 1989451 1990012 "OREPCTO" 1990912 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-852 1982637 1984838 1984879 "OREPCAT" 1987227 NIL OREPCAT (NIL T) -9 NIL 1988331 NIL) (-851 1979784 1980566 1981624 "OREPCAT-" 1981629 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-850 1978935 1979233 1979261 "ORDSET" 1979570 T ORDSET (NIL) -9 NIL 1979734 NIL) (-849 1978366 1978514 1978738 "ORDSET-" 1978743 NIL ORDSET- (NIL T) -8 NIL NIL NIL) (-848 1976931 1977722 1977750 "ORDRING" 1977952 T ORDRING (NIL) -9 NIL 1978077 NIL) (-847 1976576 1976670 1976814 "ORDRING-" 1976819 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-846 1975956 1976419 1976447 "ORDMON" 1976452 T ORDMON (NIL) -9 NIL 1976473 NIL) (-845 1975118 1975265 1975460 "ORDFUNS" 1975805 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-844 1974456 1974875 1974903 "ORDFIN" 1974968 T ORDFIN (NIL) -9 NIL 1975042 NIL) (-843 1971015 1973042 1973451 "ORDCOMP" 1974080 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-842 1970281 1970408 1970594 "ORDCOMP2" 1970875 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-841 1966862 1967772 1968586 "OPTPROB" 1969487 T OPTPROB (NIL) -8 NIL NIL NIL) (-840 1963664 1964303 1965007 "OPTPACK" 1966178 T OPTPACK (NIL) -7 NIL NIL NIL) (-839 1961351 1962117 1962145 "OPTCAT" 1962964 T OPTCAT (NIL) -9 NIL 1963614 NIL) (-838 1960735 1961028 1961133 "OPSIG" 1961266 T OPSIG (NIL) -8 NIL NIL NIL) (-837 1960503 1960542 1960608 "OPQUERY" 1960689 T OPQUERY (NIL) -7 NIL NIL NIL) (-836 1957634 1958814 1959318 "OP" 1960032 NIL OP (NIL T) -8 NIL NIL NIL) (-835 1957008 1957234 1957275 "OPERCAT" 1957487 NIL OPERCAT (NIL T) -9 NIL 1957584 NIL) (-834 1956763 1956819 1956936 "OPERCAT-" 1956941 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-833 1953576 1955560 1955929 "ONECOMP" 1956427 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-832 1952881 1952996 1953170 "ONECOMP2" 1953448 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-831 1952300 1952406 1952536 "OMSERVER" 1952771 T OMSERVER (NIL) -7 NIL NIL NIL) (-830 1949162 1951740 1951780 "OMSAGG" 1951841 NIL OMSAGG (NIL T) -9 NIL 1951905 NIL) (-829 1947785 1948048 1948330 "OMPKG" 1948900 T OMPKG (NIL) -7 NIL NIL NIL) (-828 1947215 1947318 1947346 "OM" 1947645 T OM (NIL) -9 NIL NIL NIL) (-827 1945762 1946764 1946933 "OMLO" 1947096 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-826 1944722 1944869 1945089 "OMEXPR" 1945588 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-825 1944013 1944268 1944404 "OMERR" 1944606 T OMERR (NIL) -8 NIL NIL NIL) (-824 1943164 1943434 1943594 "OMERRK" 1943873 T OMERRK (NIL) -8 NIL NIL NIL) (-823 1942615 1942841 1942949 "OMENC" 1943076 T OMENC (NIL) -8 NIL NIL NIL) (-822 1936510 1937695 1938866 "OMDEV" 1941464 T OMDEV (NIL) -8 NIL NIL NIL) (-821 1935579 1935750 1935944 "OMCONN" 1936336 T OMCONN (NIL) -8 NIL NIL NIL) (-820 1934100 1935076 1935104 "OINTDOM" 1935109 T OINTDOM (NIL) -9 NIL 1935130 NIL) (-819 1929879 1931090 1931806 "OFMONOID" 1933416 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-818 1929290 1929816 1929861 "ODVAR" 1929866 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-817 1926713 1929035 1929190 "ODR" 1929195 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-816 1919294 1926489 1926615 "ODPOL" 1926620 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-815 1913116 1919166 1919271 "ODP" 1919276 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-814 1911882 1912097 1912372 "ODETOOLS" 1912890 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-813 1908849 1909507 1910223 "ODESYS" 1911215 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-812 1903731 1904639 1905664 "ODERTRIC" 1907924 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-811 1903157 1903239 1903433 "ODERED" 1903643 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-810 1900045 1900593 1901270 "ODERAT" 1902580 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-809 1897002 1897469 1898066 "ODEPRRIC" 1899574 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-808 1894945 1895541 1896027 "ODEPROB" 1896536 T ODEPROB (NIL) -8 NIL NIL NIL) (-807 1891465 1891950 1892597 "ODEPRIM" 1894424 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-806 1890714 1890816 1891076 "ODEPAL" 1891357 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-805 1886876 1887667 1888531 "ODEPACK" 1889870 T ODEPACK (NIL) -7 NIL NIL NIL) (-804 1885937 1886044 1886266 "ODEINT" 1886765 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-803 1880038 1881463 1882910 "ODEIFTBL" 1884510 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-802 1875436 1876222 1877174 "ODEEF" 1879197 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-801 1874785 1874874 1875097 "ODECONST" 1875341 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-800 1872910 1873571 1873599 "ODECAT" 1874204 T ODECAT (NIL) -9 NIL 1874735 NIL) (-799 1869782 1872622 1872741 "OCT" 1872823 NIL OCT (NIL T) -8 NIL NIL NIL) (-798 1869420 1869463 1869590 "OCTCT2" 1869733 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-797 1864069 1866504 1866544 "OC" 1867641 NIL OC (NIL T) -9 NIL 1868499 NIL) (-796 1861296 1862044 1863034 "OC-" 1863128 NIL OC- (NIL T T) -8 NIL NIL NIL) (-795 1860648 1861116 1861144 "OCAMON" 1861149 T OCAMON (NIL) -9 NIL 1861170 NIL) (-794 1860179 1860520 1860548 "OASGP" 1860553 T OASGP (NIL) -9 NIL 1860573 NIL) (-793 1859440 1859929 1859957 "OAMONS" 1859997 T OAMONS (NIL) -9 NIL 1860040 NIL) (-792 1858854 1859287 1859315 "OAMON" 1859320 T OAMON (NIL) -9 NIL 1859340 NIL) (-791 1858112 1858630 1858658 "OAGROUP" 1858663 T OAGROUP (NIL) -9 NIL 1858683 NIL) (-790 1857802 1857852 1857940 "NUMTUBE" 1858056 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-789 1851375 1852893 1854429 "NUMQUAD" 1856286 T NUMQUAD (NIL) -7 NIL NIL NIL) (-788 1847131 1848119 1849144 "NUMODE" 1850370 T NUMODE (NIL) -7 NIL NIL NIL) (-787 1844486 1845366 1845394 "NUMINT" 1846317 T NUMINT (NIL) -9 NIL 1847081 NIL) (-786 1843434 1843631 1843849 "NUMFMT" 1844288 T NUMFMT (NIL) -7 NIL NIL NIL) (-785 1829793 1832738 1835270 "NUMERIC" 1840941 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-784 1824163 1829242 1829337 "NTSCAT" 1829342 NIL NTSCAT (NIL T T T T) -9 NIL 1829381 NIL) (-783 1823357 1823522 1823715 "NTPOLFN" 1824002 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-782 1811434 1820182 1820994 "NSUP" 1822578 NIL NSUP (NIL T) -8 NIL NIL NIL) (-781 1811066 1811123 1811232 "NSUP2" 1811371 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-780 1801294 1810840 1810973 "NSMP" 1810978 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-779 1799726 1800027 1800384 "NREP" 1800982 NIL NREP (NIL T) -7 NIL NIL NIL) (-778 1798317 1798569 1798927 "NPCOEF" 1799469 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-777 1797383 1797498 1797714 "NORMRETR" 1798198 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-776 1795424 1795714 1796123 "NORMPK" 1797091 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-775 1795109 1795137 1795261 "NORMMA" 1795390 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-774 1794909 1795066 1795095 "NONE" 1795100 T NONE (NIL) -8 NIL NIL NIL) (-773 1794698 1794727 1794796 "NONE1" 1794873 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-772 1794195 1794257 1794436 "NODE1" 1794630 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-771 1792480 1793331 1793586 "NNI" 1793933 T NNI (NIL) -8 NIL NIL 1794168) (-770 1790900 1791213 1791577 "NLINSOL" 1792148 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-769 1787141 1788136 1789035 "NIPROB" 1790021 T NIPROB (NIL) -8 NIL NIL NIL) (-768 1785898 1786132 1786434 "NFINTBAS" 1786903 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-767 1785072 1785548 1785589 "NETCLT" 1785761 NIL NETCLT (NIL T) -9 NIL 1785843 NIL) (-766 1783780 1784011 1784292 "NCODIV" 1784840 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-765 1783542 1783579 1783654 "NCNTFRAC" 1783737 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-764 1781722 1782086 1782506 "NCEP" 1783167 NIL NCEP (NIL T) -7 NIL NIL NIL) (-763 1780573 1781346 1781374 "NASRING" 1781484 T NASRING (NIL) -9 NIL 1781564 NIL) (-762 1780368 1780412 1780506 "NASRING-" 1780511 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-761 1779475 1780000 1780028 "NARNG" 1780145 T NARNG (NIL) -9 NIL 1780236 NIL) (-760 1779167 1779234 1779368 "NARNG-" 1779373 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-759 1778046 1778253 1778488 "NAGSP" 1778952 T NAGSP (NIL) -7 NIL NIL NIL) (-758 1769318 1771002 1772675 "NAGS" 1776393 T NAGS (NIL) -7 NIL NIL NIL) (-757 1767866 1768174 1768505 "NAGF07" 1769007 T NAGF07 (NIL) -7 NIL NIL NIL) (-756 1762404 1763695 1765002 "NAGF04" 1766579 T NAGF04 (NIL) -7 NIL NIL NIL) (-755 1755372 1756986 1758619 "NAGF02" 1760791 T NAGF02 (NIL) -7 NIL NIL NIL) (-754 1750596 1751696 1752813 "NAGF01" 1754275 T NAGF01 (NIL) -7 NIL NIL NIL) (-753 1744224 1745790 1747375 "NAGE04" 1749031 T NAGE04 (NIL) -7 NIL NIL NIL) (-752 1735393 1737514 1739644 "NAGE02" 1742114 T NAGE02 (NIL) -7 NIL NIL NIL) (-751 1731346 1732293 1733257 "NAGE01" 1734449 T NAGE01 (NIL) -7 NIL NIL NIL) (-750 1729141 1729675 1730233 "NAGD03" 1730808 T NAGD03 (NIL) -7 NIL NIL NIL) (-749 1720891 1722819 1724773 "NAGD02" 1727207 T NAGD02 (NIL) -7 NIL NIL NIL) (-748 1714702 1716127 1717567 "NAGD01" 1719471 T NAGD01 (NIL) -7 NIL NIL NIL) (-747 1710911 1711733 1712570 "NAGC06" 1713885 T NAGC06 (NIL) -7 NIL NIL NIL) (-746 1709376 1709708 1710064 "NAGC05" 1710575 T NAGC05 (NIL) -7 NIL NIL NIL) (-745 1708752 1708871 1709015 "NAGC02" 1709252 T NAGC02 (NIL) -7 NIL NIL NIL) (-744 1707711 1708294 1708334 "NAALG" 1708413 NIL NAALG (NIL T) -9 NIL 1708474 NIL) (-743 1707546 1707575 1707665 "NAALG-" 1707670 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-742 1701496 1702604 1703791 "MULTSQFR" 1706442 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-741 1700815 1700890 1701074 "MULTFACT" 1701408 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-740 1693539 1697452 1697505 "MTSCAT" 1698575 NIL MTSCAT (NIL T T) -9 NIL 1699090 NIL) (-739 1693251 1693305 1693397 "MTHING" 1693479 NIL MTHING (NIL T) -7 NIL NIL NIL) (-738 1693043 1693076 1693136 "MSYSCMD" 1693211 T MSYSCMD (NIL) -7 NIL NIL NIL) (-737 1689125 1691798 1692118 "MSET" 1692756 NIL MSET (NIL T) -8 NIL NIL NIL) (-736 1686194 1688686 1688727 "MSETAGG" 1688732 NIL MSETAGG (NIL T) -9 NIL 1688766 NIL) (-735 1682035 1683573 1684318 "MRING" 1685494 NIL MRING (NIL T T) -8 NIL NIL NIL) (-734 1681601 1681668 1681799 "MRF2" 1681962 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-733 1681219 1681254 1681398 "MRATFAC" 1681560 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-732 1678831 1679126 1679557 "MPRFF" 1680924 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-731 1673128 1678685 1678782 "MPOLY" 1678787 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-730 1672618 1672653 1672861 "MPCPF" 1673087 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-729 1672132 1672175 1672359 "MPC3" 1672569 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-728 1671327 1671408 1671629 "MPC2" 1672047 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-727 1669628 1669965 1670355 "MONOTOOL" 1670987 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-726 1668853 1669170 1669198 "MONOID" 1669417 T MONOID (NIL) -9 NIL 1669564 NIL) (-725 1668399 1668518 1668699 "MONOID-" 1668704 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-724 1658874 1664825 1664884 "MONOGEN" 1665558 NIL MONOGEN (NIL T T) -9 NIL 1666014 NIL) (-723 1656092 1656827 1657827 "MONOGEN-" 1657946 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-722 1654925 1655371 1655399 "MONADWU" 1655791 T MONADWU (NIL) -9 NIL 1656029 NIL) (-721 1654297 1654456 1654704 "MONADWU-" 1654709 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-720 1653656 1653900 1653928 "MONAD" 1654135 T MONAD (NIL) -9 NIL 1654247 NIL) (-719 1653341 1653419 1653551 "MONAD-" 1653556 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-718 1651630 1652254 1652533 "MOEBIUS" 1653094 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-717 1650908 1651312 1651352 "MODULE" 1651357 NIL MODULE (NIL T) -9 NIL 1651396 NIL) (-716 1650476 1650572 1650762 "MODULE-" 1650767 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-715 1648156 1648840 1649167 "MODRING" 1650300 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-714 1645100 1646261 1646782 "MODOP" 1647685 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-713 1643688 1644167 1644444 "MODMONOM" 1644963 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-712 1633729 1641979 1642393 "MODMON" 1643325 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-711 1630885 1632573 1632849 "MODFIELD" 1633604 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-710 1629862 1630166 1630356 "MMLFORM" 1630715 T MMLFORM (NIL) -8 NIL NIL NIL) (-709 1629388 1629431 1629610 "MMAP" 1629813 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-708 1627467 1628234 1628275 "MLO" 1628698 NIL MLO (NIL T) -9 NIL 1628940 NIL) (-707 1624833 1625349 1625951 "MLIFT" 1626948 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-706 1624224 1624308 1624462 "MKUCFUNC" 1624744 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-705 1623823 1623893 1624016 "MKRECORD" 1624147 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-704 1622870 1623032 1623260 "MKFUNC" 1623634 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-703 1622258 1622362 1622518 "MKFLCFN" 1622753 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-702 1621535 1621637 1621822 "MKBCFUNC" 1622151 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-701 1618242 1621089 1621225 "MINT" 1621419 T MINT (NIL) -8 NIL NIL NIL) (-700 1617054 1617297 1617574 "MHROWRED" 1617997 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-699 1612433 1615589 1615994 "MFLOAT" 1616669 T MFLOAT (NIL) -8 NIL NIL NIL) (-698 1611790 1611866 1612037 "MFINFACT" 1612345 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-697 1608105 1608953 1609837 "MESH" 1610926 T MESH (NIL) -7 NIL NIL NIL) (-696 1606495 1606807 1607160 "MDDFACT" 1607792 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-695 1603290 1605654 1605695 "MDAGG" 1605950 NIL MDAGG (NIL T) -9 NIL 1606093 NIL) (-694 1593030 1602583 1602790 "MCMPLX" 1603103 T MCMPLX (NIL) -8 NIL NIL NIL) (-693 1592171 1592317 1592517 "MCDEN" 1592879 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-692 1590061 1590331 1590711 "MCALCFN" 1591901 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-691 1588986 1589226 1589459 "MAYBE" 1589867 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-690 1586598 1587121 1587683 "MATSTOR" 1588457 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-689 1582555 1585970 1586218 "MATRIX" 1586383 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-688 1578319 1579028 1579764 "MATLIN" 1581912 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-687 1568425 1571611 1571688 "MATCAT" 1576568 NIL MATCAT (NIL T T T) -9 NIL 1577985 NIL) (-686 1564781 1565802 1567158 "MATCAT-" 1567163 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-685 1563375 1563528 1563861 "MATCAT2" 1564616 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-684 1561487 1561811 1562195 "MAPPKG3" 1563050 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-683 1560468 1560641 1560863 "MAPPKG2" 1561311 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-682 1558967 1559251 1559578 "MAPPKG1" 1560174 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-681 1558046 1558373 1558550 "MAPPAST" 1558810 T MAPPAST (NIL) -8 NIL NIL NIL) (-680 1557657 1557715 1557838 "MAPHACK3" 1557982 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-679 1557249 1557310 1557424 "MAPHACK2" 1557589 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-678 1556686 1556790 1556932 "MAPHACK1" 1557140 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-677 1554765 1555386 1555690 "MAGMA" 1556414 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-676 1554244 1554489 1554580 "MACROAST" 1554694 T MACROAST (NIL) -8 NIL NIL NIL) (-675 1550662 1552483 1552944 "M3D" 1553816 NIL M3D (NIL T) -8 NIL NIL NIL) (-674 1544768 1549031 1549072 "LZSTAGG" 1549854 NIL LZSTAGG (NIL T) -9 NIL 1550149 NIL) (-673 1540725 1541899 1543356 "LZSTAGG-" 1543361 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-672 1537812 1538616 1539103 "LWORD" 1540270 NIL LWORD (NIL T) -8 NIL NIL NIL) (-671 1537388 1537616 1537691 "LSTAST" 1537757 T LSTAST (NIL) -8 NIL NIL NIL) (-670 1530554 1537159 1537293 "LSQM" 1537298 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-669 1529778 1529917 1530145 "LSPP" 1530409 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-668 1527590 1527891 1528347 "LSMP" 1529467 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-667 1524369 1525043 1525773 "LSMP1" 1526892 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-666 1518246 1523536 1523577 "LSAGG" 1523639 NIL LSAGG (NIL T) -9 NIL 1523717 NIL) (-665 1514941 1515865 1517078 "LSAGG-" 1517083 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-664 1512540 1514085 1514334 "LPOLY" 1514736 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-663 1512122 1512207 1512330 "LPEFRAC" 1512449 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-662 1510443 1511216 1511469 "LO" 1511954 NIL LO (NIL T T T) -8 NIL NIL NIL) (-661 1510095 1510207 1510235 "LOGIC" 1510346 T LOGIC (NIL) -9 NIL 1510427 NIL) (-660 1509957 1509980 1510051 "LOGIC-" 1510056 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-659 1509150 1509290 1509483 "LODOOPS" 1509813 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-658 1506573 1509066 1509132 "LODO" 1509137 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-657 1505111 1505346 1505699 "LODOF" 1506320 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-656 1501329 1503760 1503801 "LODOCAT" 1504239 NIL LODOCAT (NIL T) -9 NIL 1504450 NIL) (-655 1501062 1501120 1501247 "LODOCAT-" 1501252 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-654 1498382 1500903 1501021 "LODO2" 1501026 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-653 1495817 1498319 1498364 "LODO1" 1498369 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-652 1494698 1494863 1495168 "LODEEF" 1495640 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-651 1489937 1492828 1492869 "LNAGG" 1493816 NIL LNAGG (NIL T) -9 NIL 1494260 NIL) (-650 1489084 1489298 1489640 "LNAGG-" 1489645 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-649 1485220 1486009 1486648 "LMOPS" 1488499 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-648 1484623 1485011 1485052 "LMODULE" 1485057 NIL LMODULE (NIL T) -9 NIL 1485083 NIL) (-647 1481821 1484268 1484391 "LMDICT" 1484533 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-646 1481227 1481448 1481489 "LLINSET" 1481680 NIL LLINSET (NIL T) -9 NIL 1481771 NIL) (-645 1480926 1481135 1481195 "LITERAL" 1481200 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-644 1474109 1479872 1480170 "LIST" 1480661 NIL LIST (NIL T) -8 NIL NIL NIL) (-643 1473634 1473708 1473847 "LIST3" 1474029 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-642 1472641 1472819 1473047 "LIST2" 1473452 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-641 1470775 1471087 1471486 "LIST2MAP" 1472288 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-640 1470371 1470608 1470649 "LINSET" 1470654 NIL LINSET (NIL T) -9 NIL 1470688 NIL) (-639 1469032 1469702 1469743 "LINEXP" 1469998 NIL LINEXP (NIL T) -9 NIL 1470147 NIL) (-638 1467679 1467939 1468236 "LINDEP" 1468784 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-637 1464446 1465165 1465942 "LIMITRF" 1466934 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-636 1462749 1463045 1463454 "LIMITPS" 1464141 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-635 1457177 1462260 1462488 "LIE" 1462570 NIL LIE (NIL T T) -8 NIL NIL NIL) (-634 1456125 1456594 1456634 "LIECAT" 1456774 NIL LIECAT (NIL T) -9 NIL 1456925 NIL) (-633 1455966 1455993 1456081 "LIECAT-" 1456086 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-632 1448462 1455415 1455580 "LIB" 1455821 T LIB (NIL) -8 NIL NIL NIL) (-631 1444097 1444980 1445915 "LGROBP" 1447579 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-630 1442095 1442369 1442719 "LF" 1443818 NIL LF (NIL T T) -7 NIL NIL NIL) (-629 1440935 1441627 1441655 "LFCAT" 1441862 T LFCAT (NIL) -9 NIL 1442001 NIL) (-628 1437837 1438467 1439155 "LEXTRIPK" 1440299 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-627 1434581 1435407 1435910 "LEXP" 1437417 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-626 1434057 1434302 1434394 "LETAST" 1434509 T LETAST (NIL) -8 NIL NIL NIL) (-625 1432455 1432768 1433169 "LEADCDET" 1433739 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-624 1431645 1431719 1431948 "LAZM3PK" 1432376 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-623 1426562 1429722 1430260 "LAUPOL" 1431157 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-622 1426141 1426185 1426346 "LAPLACE" 1426512 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-621 1424080 1425242 1425493 "LA" 1425974 NIL LA (NIL T T T) -8 NIL NIL NIL) (-620 1423074 1423658 1423699 "LALG" 1423761 NIL LALG (NIL T) -9 NIL 1423820 NIL) (-619 1422788 1422847 1422983 "LALG-" 1422988 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-618 1422623 1422647 1422688 "KVTFROM" 1422750 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-617 1421546 1421990 1422175 "KTVLOGIC" 1422458 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-616 1421381 1421405 1421446 "KRCFROM" 1421508 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-615 1420285 1420472 1420771 "KOVACIC" 1421181 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-614 1420120 1420144 1420185 "KONVERT" 1420247 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-613 1419955 1419979 1420020 "KOERCE" 1420082 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-612 1417785 1418548 1418925 "KERNEL" 1419611 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-611 1417281 1417362 1417494 "KERNEL2" 1417699 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-610 1411051 1415820 1415874 "KDAGG" 1416251 NIL KDAGG (NIL T T) -9 NIL 1416457 NIL) (-609 1410580 1410704 1410909 "KDAGG-" 1410914 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-608 1403728 1410241 1410396 "KAFILE" 1410458 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-607 1398156 1403239 1403467 "JORDAN" 1403549 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-606 1397535 1397805 1397926 "JOINAST" 1398055 T JOINAST (NIL) -8 NIL NIL NIL) (-605 1397381 1397440 1397495 "JAVACODE" 1397500 T JAVACODE (NIL) -8 NIL NIL NIL) (-604 1393633 1395586 1395640 "IXAGG" 1396569 NIL IXAGG (NIL T T) -9 NIL 1397028 NIL) (-603 1392552 1392858 1393277 "IXAGG-" 1393282 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-602 1388082 1392474 1392533 "IVECTOR" 1392538 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-601 1386848 1387085 1387351 "ITUPLE" 1387849 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-600 1385350 1385527 1385822 "ITRIGMNP" 1386670 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-599 1384095 1384299 1384582 "ITFUN3" 1385126 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-598 1383727 1383784 1383893 "ITFUN2" 1384032 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-597 1381529 1382589 1382888 "ITAYLOR" 1383461 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-596 1370474 1375666 1376829 "ISUPS" 1380399 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-595 1369578 1369718 1369954 "ISUMP" 1370321 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-594 1364792 1369379 1369458 "ISTRING" 1369531 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-593 1364268 1364513 1364605 "ISAST" 1364720 T ISAST (NIL) -8 NIL NIL NIL) (-592 1363477 1363559 1363775 "IRURPK" 1364182 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-591 1362413 1362614 1362854 "IRSN" 1363257 T IRSN (NIL) -7 NIL NIL NIL) (-590 1360484 1360839 1361268 "IRRF2F" 1362051 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-589 1360231 1360269 1360345 "IRREDFFX" 1360440 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-588 1358846 1359105 1359404 "IROOT" 1359964 NIL IROOT (NIL T) -7 NIL NIL NIL) (-587 1355450 1356530 1357222 "IR" 1358186 NIL IR (NIL T) -8 NIL NIL NIL) (-586 1353063 1353558 1354124 "IR2" 1354928 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-585 1352163 1352276 1352490 "IR2F" 1352946 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-584 1351954 1351988 1352048 "IPRNTPK" 1352123 T IPRNTPK (NIL) -7 NIL NIL NIL) (-583 1348533 1351843 1351912 "IPF" 1351917 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-582 1346860 1348458 1348515 "IPADIC" 1348520 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-581 1346172 1346420 1346550 "IP4ADDR" 1346750 T IP4ADDR (NIL) -8 NIL NIL NIL) (-580 1345645 1345876 1345986 "IOMODE" 1346082 T IOMODE (NIL) -8 NIL NIL NIL) (-579 1344718 1345242 1345369 "IOBFILE" 1345538 T IOBFILE (NIL) -8 NIL NIL NIL) (-578 1344206 1344622 1344650 "IOBCON" 1344655 T IOBCON (NIL) -9 NIL 1344676 NIL) (-577 1343717 1343775 1343958 "INVLAPLA" 1344142 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-576 1333365 1335719 1338105 "INTTR" 1341381 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-575 1329700 1330442 1331307 "INTTOOLS" 1332550 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-574 1329286 1329377 1329494 "INTSLPE" 1329603 T INTSLPE (NIL) -7 NIL NIL NIL) (-573 1327239 1329209 1329268 "INTRVL" 1329273 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-572 1324841 1325353 1325928 "INTRF" 1326724 NIL INTRF (NIL T) -7 NIL NIL NIL) (-571 1324252 1324349 1324491 "INTRET" 1324739 NIL INTRET (NIL T) -7 NIL NIL NIL) (-570 1322249 1322638 1323108 "INTRAT" 1323860 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-569 1319512 1320095 1320714 "INTPM" 1321734 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-568 1316257 1316856 1317594 "INTPAF" 1318898 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-567 1311436 1312398 1313449 "INTPACK" 1315226 T INTPACK (NIL) -7 NIL NIL NIL) (-566 1308316 1311165 1311292 "INT" 1311329 T INT (NIL) -8 NIL NIL NIL) (-565 1307568 1307720 1307928 "INTHERTR" 1308158 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-564 1307007 1307087 1307275 "INTHERAL" 1307482 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-563 1304853 1305296 1305753 "INTHEORY" 1306570 T INTHEORY (NIL) -7 NIL NIL NIL) (-562 1296259 1297880 1299652 "INTG0" 1303205 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-561 1276832 1281622 1286432 "INTFTBL" 1291469 T INTFTBL (NIL) -8 NIL NIL NIL) (-560 1276081 1276219 1276392 "INTFACT" 1276691 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-559 1273508 1273954 1274511 "INTEF" 1275635 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-558 1271875 1272614 1272642 "INTDOM" 1272943 T INTDOM (NIL) -9 NIL 1273150 NIL) (-557 1271244 1271418 1271660 "INTDOM-" 1271665 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-556 1267632 1269560 1269614 "INTCAT" 1270413 NIL INTCAT (NIL T) -9 NIL 1270734 NIL) (-555 1267104 1267207 1267335 "INTBIT" 1267524 T INTBIT (NIL) -7 NIL NIL NIL) (-554 1265803 1265957 1266264 "INTALG" 1266949 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-553 1265286 1265376 1265533 "INTAF" 1265707 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-552 1258629 1265096 1265236 "INTABL" 1265241 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-551 1257970 1258436 1258501 "INT8" 1258535 T INT8 (NIL) -8 NIL NIL 1258580) (-550 1257310 1257776 1257841 "INT64" 1257875 T INT64 (NIL) -8 NIL NIL 1257920) (-549 1256650 1257116 1257181 "INT32" 1257215 T INT32 (NIL) -8 NIL NIL 1257260) (-548 1255990 1256456 1256521 "INT16" 1256555 T INT16 (NIL) -8 NIL NIL 1256600) (-547 1250900 1253613 1253641 "INS" 1254575 T INS (NIL) -9 NIL 1255240 NIL) (-546 1248140 1248911 1249885 "INS-" 1249958 NIL INS- (NIL T) -8 NIL NIL NIL) (-545 1246915 1247142 1247440 "INPSIGN" 1247893 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-544 1246033 1246150 1246347 "INPRODPF" 1246795 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-543 1244927 1245044 1245281 "INPRODFF" 1245913 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-542 1243927 1244079 1244339 "INNMFACT" 1244763 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-541 1243124 1243221 1243409 "INMODGCD" 1243826 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-540 1241632 1241877 1242201 "INFSP" 1242869 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-539 1240816 1240933 1241116 "INFPROD0" 1241512 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-538 1237671 1238881 1239396 "INFORM" 1240309 T INFORM (NIL) -8 NIL NIL NIL) (-537 1237281 1237341 1237439 "INFORM1" 1237606 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-536 1236804 1236893 1237007 "INFINITY" 1237187 T INFINITY (NIL) -7 NIL NIL NIL) (-535 1235980 1236524 1236625 "INETCLTS" 1236723 T INETCLTS (NIL) -8 NIL NIL NIL) (-534 1234596 1234846 1235167 "INEP" 1235728 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-533 1233845 1234493 1234558 "INDE" 1234563 NIL INDE (NIL T) -8 NIL NIL NIL) (-532 1233409 1233477 1233594 "INCRMAPS" 1233772 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-531 1232227 1232678 1232884 "INBFILE" 1233223 T INBFILE (NIL) -8 NIL NIL NIL) (-530 1227526 1228463 1229407 "INBFF" 1231315 NIL INBFF (NIL T) -7 NIL NIL NIL) (-529 1226434 1226703 1226731 "INBCON" 1227244 T INBCON (NIL) -9 NIL 1227510 NIL) (-528 1225686 1225909 1226185 "INBCON-" 1226190 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-527 1225165 1225410 1225501 "INAST" 1225615 T INAST (NIL) -8 NIL NIL NIL) (-526 1224592 1224844 1224950 "IMPTAST" 1225079 T IMPTAST (NIL) -8 NIL NIL NIL) (-525 1221038 1224436 1224540 "IMATRIX" 1224545 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-524 1219750 1219873 1220188 "IMATQF" 1220894 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-523 1217970 1218197 1218534 "IMATLIN" 1219506 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-522 1212548 1217894 1217952 "ILIST" 1217957 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-521 1210453 1212408 1212521 "IIARRAY2" 1212526 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-520 1205851 1210364 1210428 "IFF" 1210433 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-519 1205198 1205468 1205584 "IFAST" 1205755 T IFAST (NIL) -8 NIL NIL NIL) (-518 1200193 1204490 1204678 "IFARRAY" 1205055 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-517 1199373 1200097 1200170 "IFAMON" 1200175 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-516 1198957 1199022 1199076 "IEVALAB" 1199283 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-515 1198632 1198700 1198860 "IEVALAB-" 1198865 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-514 1198263 1198546 1198609 "IDPO" 1198614 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-513 1197513 1198152 1198227 "IDPOAMS" 1198232 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-512 1196820 1197402 1197477 "IDPOAM" 1197482 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-511 1195879 1196155 1196208 "IDPC" 1196621 NIL IDPC (NIL T T) -9 NIL 1196770 NIL) (-510 1195348 1195771 1195844 "IDPAM" 1195849 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-509 1194724 1195240 1195313 "IDPAG" 1195318 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-508 1194369 1194560 1194635 "IDENT" 1194669 T IDENT (NIL) -8 NIL NIL NIL) (-507 1190624 1191472 1192367 "IDECOMP" 1193526 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-506 1183462 1184547 1185594 "IDEAL" 1189660 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-505 1182626 1182738 1182937 "ICDEN" 1183346 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-504 1181697 1182106 1182253 "ICARD" 1182499 T ICARD (NIL) -8 NIL NIL NIL) (-503 1179757 1180070 1180475 "IBPTOOLS" 1181374 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-502 1175364 1179377 1179490 "IBITS" 1179676 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-501 1172087 1172663 1173358 "IBATOOL" 1174781 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-500 1169866 1170328 1170861 "IBACHIN" 1171622 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-499 1167695 1169712 1169815 "IARRAY2" 1169820 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-498 1163801 1167621 1167678 "IARRAY1" 1167683 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-497 1157910 1162213 1162694 "IAN" 1163340 T IAN (NIL) -8 NIL NIL NIL) (-496 1157421 1157478 1157651 "IALGFACT" 1157847 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-495 1156949 1157062 1157090 "HYPCAT" 1157297 T HYPCAT (NIL) -9 NIL NIL NIL) (-494 1156487 1156604 1156790 "HYPCAT-" 1156795 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-493 1156082 1156282 1156365 "HOSTNAME" 1156424 T HOSTNAME (NIL) -8 NIL NIL NIL) (-492 1155927 1155964 1156005 "HOMOTOP" 1156010 NIL HOMOTOP (NIL T) -9 NIL 1156043 NIL) (-491 1152559 1153937 1153978 "HOAGG" 1154959 NIL HOAGG (NIL T) -9 NIL 1155638 NIL) (-490 1151153 1151552 1152078 "HOAGG-" 1152083 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-489 1145157 1150748 1150897 "HEXADEC" 1151024 T HEXADEC (NIL) -8 NIL NIL NIL) (-488 1143904 1144127 1144390 "HEUGCD" 1144934 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-487 1142980 1143741 1143871 "HELLFDIV" 1143876 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-486 1141159 1142757 1142845 "HEAP" 1142924 NIL HEAP (NIL T) -8 NIL NIL NIL) (-485 1140422 1140711 1140845 "HEADAST" 1141045 T HEADAST (NIL) -8 NIL NIL NIL) (-484 1134288 1140337 1140399 "HDP" 1140404 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-483 1128276 1133923 1134075 "HDMP" 1134189 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-482 1127600 1127740 1127904 "HB" 1128132 T HB (NIL) -7 NIL NIL NIL) (-481 1120986 1127446 1127550 "HASHTBL" 1127555 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-480 1120462 1120707 1120799 "HASAST" 1120914 T HASAST (NIL) -8 NIL NIL NIL) (-479 1118240 1120084 1120266 "HACKPI" 1120300 T HACKPI (NIL) -8 NIL NIL NIL) (-478 1113908 1118093 1118206 "GTSET" 1118211 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-477 1107323 1113786 1113884 "GSTBL" 1113889 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-476 1099601 1106354 1106619 "GSERIES" 1107114 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-475 1098742 1099159 1099187 "GROUP" 1099390 T GROUP (NIL) -9 NIL 1099524 NIL) (-474 1098108 1098267 1098518 "GROUP-" 1098523 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-473 1096475 1096796 1097183 "GROEBSOL" 1097785 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-472 1095389 1095677 1095728 "GRMOD" 1096257 NIL GRMOD (NIL T T) -9 NIL 1096425 NIL) (-471 1095157 1095193 1095321 "GRMOD-" 1095326 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-470 1090447 1091511 1092511 "GRIMAGE" 1094177 T GRIMAGE (NIL) -8 NIL NIL NIL) (-469 1088913 1089174 1089498 "GRDEF" 1090143 T GRDEF (NIL) -7 NIL NIL NIL) (-468 1088357 1088473 1088614 "GRAY" 1088792 T GRAY (NIL) -7 NIL NIL NIL) (-467 1087544 1087950 1088001 "GRALG" 1088154 NIL GRALG (NIL T T) -9 NIL 1088247 NIL) (-466 1087205 1087278 1087441 "GRALG-" 1087446 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-465 1083982 1086790 1086968 "GPOLSET" 1087112 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-464 1083336 1083393 1083651 "GOSPER" 1083919 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-463 1079068 1079774 1080300 "GMODPOL" 1083035 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-462 1078073 1078257 1078495 "GHENSEL" 1078880 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-461 1072229 1073072 1074092 "GENUPS" 1077157 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-460 1071926 1071977 1072066 "GENUFACT" 1072172 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-459 1071338 1071415 1071580 "GENPGCD" 1071844 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-458 1070812 1070847 1071060 "GENMFACT" 1071297 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-457 1069378 1069635 1069942 "GENEEZ" 1070555 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-456 1063524 1068989 1069151 "GDMP" 1069301 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-455 1052866 1057295 1058401 "GCNAALG" 1062507 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-454 1051193 1052055 1052083 "GCDDOM" 1052338 T GCDDOM (NIL) -9 NIL 1052495 NIL) (-453 1050663 1050790 1051005 "GCDDOM-" 1051010 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-452 1049335 1049520 1049824 "GB" 1050442 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-451 1037951 1040281 1042673 "GBINTERN" 1047026 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-450 1035788 1036080 1036501 "GBF" 1037626 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-449 1034569 1034734 1035001 "GBEUCLID" 1035604 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-448 1033918 1034043 1034192 "GAUSSFAC" 1034440 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-447 1032285 1032587 1032901 "GALUTIL" 1033637 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-446 1030593 1030867 1031191 "GALPOLYU" 1032012 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-445 1027958 1028248 1028655 "GALFACTU" 1030290 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-444 1019763 1021263 1022871 "GALFACT" 1026390 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-443 1017151 1017809 1017837 "FVFUN" 1018993 T FVFUN (NIL) -9 NIL 1019713 NIL) (-442 1016417 1016599 1016627 "FVC" 1016918 T FVC (NIL) -9 NIL 1017101 NIL) (-441 1016060 1016242 1016310 "FUNDESC" 1016369 T FUNDESC (NIL) -8 NIL NIL NIL) (-440 1015675 1015857 1015938 "FUNCTION" 1016012 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-439 1013419 1013997 1014463 "FT" 1015229 T FT (NIL) -8 NIL NIL NIL) (-438 1012210 1012720 1012923 "FTEM" 1013236 T FTEM (NIL) -8 NIL NIL NIL) (-437 1010501 1010790 1011187 "FSUPFACT" 1011901 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-436 1008898 1009187 1009519 "FST" 1010189 T FST (NIL) -8 NIL NIL NIL) (-435 1008097 1008203 1008391 "FSRED" 1008780 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-434 1006796 1007052 1007399 "FSPRMELT" 1007812 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-433 1004102 1004540 1005026 "FSPECF" 1006359 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-432 985740 994071 994112 "FS" 997996 NIL FS (NIL T) -9 NIL 1000285 NIL) (-431 974383 977376 981433 "FS-" 981733 NIL FS- (NIL T T) -8 NIL NIL NIL) (-430 973911 973965 974135 "FSINT" 974324 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-429 972203 972904 973207 "FSERIES" 973690 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-428 971245 971361 971585 "FSCINT" 972083 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-427 967453 970189 970230 "FSAGG" 970600 NIL FSAGG (NIL T) -9 NIL 970859 NIL) (-426 965215 965816 966612 "FSAGG-" 966707 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-425 964257 964400 964627 "FSAGG2" 965068 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-424 961939 962219 962766 "FS2UPS" 963975 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-423 961573 961616 961745 "FS2" 961890 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-422 960451 960622 960924 "FS2EXPXP" 961398 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-421 959877 959992 960144 "FRUTIL" 960331 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-420 951290 955372 956730 "FR" 958551 NIL FR (NIL T) -8 NIL NIL NIL) (-419 946259 948933 948973 "FRNAALG" 950369 NIL FRNAALG (NIL T) -9 NIL 950976 NIL) (-418 941932 943008 944283 "FRNAALG-" 945033 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-417 941570 941613 941740 "FRNAAF2" 941883 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-416 939950 940424 940719 "FRMOD" 941382 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-415 937701 938333 938650 "FRIDEAL" 939741 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-414 936896 936983 937272 "FRIDEAL2" 937608 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-413 936029 936443 936484 "FRETRCT" 936489 NIL FRETRCT (NIL T) -9 NIL 936665 NIL) (-412 935141 935372 935723 "FRETRCT-" 935728 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-411 932229 933439 933498 "FRAMALG" 934380 NIL FRAMALG (NIL T T) -9 NIL 934672 NIL) (-410 930363 930818 931448 "FRAMALG-" 931671 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-409 924284 929838 930114 "FRAC" 930119 NIL FRAC (NIL T) -8 NIL NIL NIL) (-408 923920 923977 924084 "FRAC2" 924221 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-407 923556 923613 923720 "FR2" 923857 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-406 918069 920962 920990 "FPS" 922109 T FPS (NIL) -9 NIL 922666 NIL) (-405 917518 917627 917791 "FPS-" 917937 NIL FPS- (NIL T) -8 NIL NIL NIL) (-404 914820 916489 916517 "FPC" 916742 T FPC (NIL) -9 NIL 916884 NIL) (-403 914613 914653 914750 "FPC-" 914755 NIL FPC- (NIL T) -8 NIL NIL NIL) (-402 913403 914101 914142 "FPATMAB" 914147 NIL FPATMAB (NIL T) -9 NIL 914299 NIL) (-401 911076 911579 912005 "FPARFRAC" 913040 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-400 906469 906968 907650 "FORTRAN" 910508 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-399 904185 904685 905224 "FORT" 905950 T FORT (NIL) -7 NIL NIL NIL) (-398 901861 902423 902451 "FORTFN" 903511 T FORTFN (NIL) -9 NIL 904135 NIL) (-397 901625 901675 901703 "FORTCAT" 901762 T FORTCAT (NIL) -9 NIL 901824 NIL) (-396 899731 900241 900631 "FORMULA" 901255 T FORMULA (NIL) -8 NIL NIL NIL) (-395 899519 899549 899618 "FORMULA1" 899695 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-394 899042 899094 899267 "FORDER" 899461 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-393 898138 898302 898495 "FOP" 898869 T FOP (NIL) -7 NIL NIL NIL) (-392 896719 897418 897592 "FNLA" 898020 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-391 895448 895863 895891 "FNCAT" 896351 T FNCAT (NIL) -9 NIL 896611 NIL) (-390 894987 895407 895435 "FNAME" 895440 T FNAME (NIL) -8 NIL NIL NIL) (-389 893550 894513 894541 "FMTC" 894546 T FMTC (NIL) -9 NIL 894582 NIL) (-388 889883 891073 891702 "FMONOID" 892954 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-387 889075 889625 889774 "FM" 889779 NIL FM (NIL T T) -8 NIL NIL NIL) (-386 886499 887145 887173 "FMFUN" 888317 T FMFUN (NIL) -9 NIL 889025 NIL) (-385 885768 885949 885977 "FMC" 886267 T FMC (NIL) -9 NIL 886449 NIL) (-384 882847 883707 883761 "FMCAT" 884956 NIL FMCAT (NIL T T) -9 NIL 885451 NIL) (-383 881713 882613 882713 "FM1" 882792 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-382 879487 879903 880397 "FLOATRP" 881264 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-381 873062 877216 877837 "FLOAT" 878886 T FLOAT (NIL) -8 NIL NIL NIL) (-380 870500 871000 871578 "FLOATCP" 872529 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-379 869240 870078 870119 "FLINEXP" 870124 NIL FLINEXP (NIL T) -9 NIL 870217 NIL) (-378 868394 868629 868957 "FLINEXP-" 868962 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-377 867470 867614 867838 "FLASORT" 868246 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-376 864586 865454 865506 "FLALG" 866733 NIL FLALG (NIL T T) -9 NIL 867200 NIL) (-375 858322 862072 862113 "FLAGG" 863375 NIL FLAGG (NIL T) -9 NIL 864027 NIL) (-374 857048 857387 857877 "FLAGG-" 857882 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-373 856090 856233 856460 "FLAGG2" 856901 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-372 852941 853949 854008 "FINRALG" 855136 NIL FINRALG (NIL T T) -9 NIL 855644 NIL) (-371 852101 852330 852669 "FINRALG-" 852674 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-370 851481 851720 851748 "FINITE" 851944 T FINITE (NIL) -9 NIL 852051 NIL) (-369 843838 846025 846065 "FINAALG" 849732 NIL FINAALG (NIL T) -9 NIL 851185 NIL) (-368 839170 840220 841364 "FINAALG-" 842743 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-367 838538 838925 839028 "FILE" 839100 NIL FILE (NIL T) -8 NIL NIL NIL) (-366 837196 837534 837588 "FILECAT" 838272 NIL FILECAT (NIL T T) -9 NIL 838488 NIL) (-365 834912 836440 836468 "FIELD" 836508 T FIELD (NIL) -9 NIL 836588 NIL) (-364 833532 833917 834428 "FIELD-" 834433 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-363 831382 832167 832514 "FGROUP" 833218 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-362 830472 830636 830856 "FGLMICPK" 831214 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-361 826304 830397 830454 "FFX" 830459 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-360 825905 825966 826101 "FFSLPE" 826237 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-359 821894 822677 823473 "FFPOLY" 825141 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-358 821398 821434 821643 "FFPOLY2" 821852 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-357 817241 821317 821380 "FFP" 821385 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-356 812639 817152 817216 "FF" 817221 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-355 807765 811982 812172 "FFNBX" 812493 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-354 802694 806900 807158 "FFNBP" 807619 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-353 797327 801978 802189 "FFNB" 802527 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-352 796159 796357 796672 "FFINTBAS" 797124 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-351 792228 794448 794476 "FFIELDC" 795096 T FFIELDC (NIL) -9 NIL 795472 NIL) (-350 790890 791261 791758 "FFIELDC-" 791763 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-349 790459 790505 790629 "FFHOM" 790832 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-348 788154 788641 789158 "FFF" 789974 NIL FFF (NIL T) -7 NIL NIL NIL) (-347 783772 787896 787997 "FFCGX" 788097 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-346 779393 783504 783611 "FFCGP" 783715 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-345 774576 779120 779228 "FFCG" 779329 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-344 755972 765053 765139 "FFCAT" 770304 NIL FFCAT (NIL T T T) -9 NIL 771755 NIL) (-343 751170 752217 753531 "FFCAT-" 754761 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-342 750581 750624 750859 "FFCAT2" 751121 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-341 739902 743553 744773 "FEXPR" 749433 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-340 738902 739337 739378 "FEVALAB" 739462 NIL FEVALAB (NIL T) -9 NIL 739723 NIL) (-339 738061 738271 738609 "FEVALAB-" 738614 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-338 736627 737444 737647 "FDIV" 737960 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-337 733647 734388 734503 "FDIVCAT" 736071 NIL FDIVCAT (NIL T T T T) -9 NIL 736508 NIL) (-336 733409 733436 733606 "FDIVCAT-" 733611 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-335 732629 732716 732993 "FDIV2" 733316 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-334 731631 731945 732140 "FCTRDATA" 732454 T FCTRDATA (NIL) -8 NIL NIL NIL) (-333 730317 730576 730865 "FCPAK1" 731362 T FCPAK1 (NIL) -7 NIL NIL NIL) (-332 729416 729817 729958 "FCOMP" 730208 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-331 713118 716566 720104 "FC" 725898 T FC (NIL) -8 NIL NIL NIL) (-330 705481 709509 709549 "FAXF" 711351 NIL FAXF (NIL T) -9 NIL 712043 NIL) (-329 702757 703415 704240 "FAXF-" 704705 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-328 697809 702133 702309 "FARRAY" 702614 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-327 692703 694770 694823 "FAMR" 695846 NIL FAMR (NIL T T) -9 NIL 696306 NIL) (-326 691593 691895 692330 "FAMR-" 692335 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-325 690762 691515 691568 "FAMONOID" 691573 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-324 688548 689258 689311 "FAMONC" 690252 NIL FAMONC (NIL T T) -9 NIL 690638 NIL) (-323 687212 688302 688439 "FAGROUP" 688444 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-322 685007 685326 685729 "FACUTIL" 686893 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-321 684106 684291 684513 "FACTFUNC" 684817 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-320 676528 683409 683608 "EXPUPXS" 683962 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-319 674011 674551 675137 "EXPRTUBE" 675962 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-318 670282 670874 671604 "EXPRODE" 673350 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-317 655767 668931 669360 "EXPR" 669886 NIL EXPR (NIL T) -8 NIL NIL NIL) (-316 650321 650908 651714 "EXPR2UPS" 655065 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-315 649953 650010 650119 "EXPR2" 650258 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-314 641343 649106 649396 "EXPEXPAN" 649790 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-313 641143 641300 641329 "EXIT" 641334 T EXIT (NIL) -8 NIL NIL NIL) (-312 640623 640867 640958 "EXITAST" 641072 T EXITAST (NIL) -8 NIL NIL NIL) (-311 640250 640312 640425 "EVALCYC" 640555 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-310 639791 639909 639950 "EVALAB" 640120 NIL EVALAB (NIL T) -9 NIL 640224 NIL) (-309 639272 639394 639615 "EVALAB-" 639620 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-308 636640 637942 637970 "EUCDOM" 638525 T EUCDOM (NIL) -9 NIL 638875 NIL) (-307 635045 635487 636077 "EUCDOM-" 636082 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-306 622583 625343 628093 "ESTOOLS" 632315 T ESTOOLS (NIL) -7 NIL NIL NIL) (-305 622215 622272 622381 "ESTOOLS2" 622520 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-304 621966 622008 622088 "ESTOOLS1" 622167 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-303 616003 617611 617639 "ES" 620407 T ES (NIL) -9 NIL 621817 NIL) (-302 610950 612237 614054 "ES-" 614218 NIL ES- (NIL T) -8 NIL NIL NIL) (-301 607324 608085 608865 "ESCONT" 610190 T ESCONT (NIL) -7 NIL NIL NIL) (-300 607069 607101 607183 "ESCONT1" 607286 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-299 606744 606794 606894 "ES2" 607013 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-298 606374 606432 606541 "ES1" 606680 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-297 605590 605719 605895 "ERROR" 606218 T ERROR (NIL) -7 NIL NIL NIL) (-296 598982 605449 605540 "EQTBL" 605545 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-295 591485 594296 595745 "EQ" 597566 NIL -2097 (NIL T) -8 NIL NIL NIL) (-294 591117 591174 591283 "EQ2" 591422 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-293 586406 587455 588548 "EP" 590056 NIL EP (NIL T) -7 NIL NIL NIL) (-292 585006 585297 585603 "ENV" 586120 T ENV (NIL) -8 NIL NIL NIL) (-291 584100 584654 584682 "ENTIRER" 584687 T ENTIRER (NIL) -9 NIL 584733 NIL) (-290 580567 582055 582425 "EMR" 583899 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-289 579711 579896 579950 "ELTAGG" 580330 NIL ELTAGG (NIL T T) -9 NIL 580541 NIL) (-288 579430 579492 579633 "ELTAGG-" 579638 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-287 579219 579248 579302 "ELTAB" 579386 NIL ELTAB (NIL T T) -9 NIL NIL NIL) (-286 578345 578491 578690 "ELFUTS" 579070 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-285 578087 578143 578171 "ELEMFUN" 578276 T ELEMFUN (NIL) -9 NIL NIL NIL) (-284 577957 577978 578046 "ELEMFUN-" 578051 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-283 572801 576057 576098 "ELAGG" 577038 NIL ELAGG (NIL T) -9 NIL 577501 NIL) (-282 571086 571520 572183 "ELAGG-" 572188 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-281 569751 570029 570322 "ELABEXPR" 570813 T ELABEXPR (NIL) -8 NIL NIL NIL) (-280 562615 564418 565245 "EFUPXS" 569027 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-279 556065 557866 558676 "EFULS" 561891 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-278 553550 553908 554380 "EFSTRUC" 555697 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-277 543341 544907 546455 "EF" 552065 NIL EF (NIL T T) -7 NIL NIL NIL) (-276 542415 542826 542975 "EAB" 543212 T EAB (NIL) -8 NIL NIL NIL) (-275 541597 542374 542402 "E04UCFA" 542407 T E04UCFA (NIL) -8 NIL NIL NIL) (-274 540779 541556 541584 "E04NAFA" 541589 T E04NAFA (NIL) -8 NIL NIL NIL) (-273 539961 540738 540766 "E04MBFA" 540771 T E04MBFA (NIL) -8 NIL NIL NIL) (-272 539143 539920 539948 "E04JAFA" 539953 T E04JAFA (NIL) -8 NIL NIL NIL) (-271 538327 539102 539130 "E04GCFA" 539135 T E04GCFA (NIL) -8 NIL NIL NIL) (-270 537511 538286 538314 "E04FDFA" 538319 T E04FDFA (NIL) -8 NIL NIL NIL) (-269 536693 537470 537498 "E04DGFA" 537503 T E04DGFA (NIL) -8 NIL NIL NIL) (-268 530866 532218 533582 "E04AGNT" 535349 T E04AGNT (NIL) -7 NIL NIL NIL) (-267 529546 530052 530092 "DVARCAT" 530567 NIL DVARCAT (NIL T) -9 NIL 530766 NIL) (-266 528750 528962 529276 "DVARCAT-" 529281 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-265 521887 528549 528678 "DSMP" 528683 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-264 516668 517832 518900 "DROPT" 520839 T DROPT (NIL) -8 NIL NIL NIL) (-263 516333 516392 516490 "DROPT1" 516603 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-262 511448 512574 513711 "DROPT0" 515216 T DROPT0 (NIL) -7 NIL NIL NIL) (-261 509793 510118 510504 "DRAWPT" 511082 T DRAWPT (NIL) -7 NIL NIL NIL) (-260 504380 505303 506382 "DRAW" 508767 NIL DRAW (NIL T) -7 NIL NIL NIL) (-259 504013 504066 504184 "DRAWHACK" 504321 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-258 502744 503013 503304 "DRAWCX" 503742 T DRAWCX (NIL) -7 NIL NIL NIL) (-257 502259 502328 502479 "DRAWCURV" 502670 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-256 492727 494689 496804 "DRAWCFUN" 500164 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-255 489493 491422 491463 "DQAGG" 492092 NIL DQAGG (NIL T) -9 NIL 492365 NIL) (-254 477617 484086 484169 "DPOLCAT" 486021 NIL DPOLCAT (NIL T T T T) -9 NIL 486566 NIL) (-253 472453 473802 475760 "DPOLCAT-" 475765 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-252 465575 472314 472412 "DPMO" 472417 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-251 458600 465355 465522 "DPMM" 465527 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-250 458078 458292 458390 "DOMTMPLT" 458522 T DOMTMPLT (NIL) -8 NIL NIL NIL) (-249 457511 457880 457960 "DOMCTOR" 458018 T DOMCTOR (NIL) -8 NIL NIL NIL) (-248 456779 457033 457170 "DOMAIN" 457394 T DOMAIN (NIL) -8 NIL NIL NIL) (-247 450767 456414 456566 "DMP" 456680 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-246 450367 450423 450567 "DLP" 450705 NIL DLP (NIL T) -7 NIL NIL NIL) (-245 444189 449694 449884 "DLIST" 450209 NIL DLIST (NIL T) -8 NIL NIL NIL) (-244 440986 443042 443083 "DLAGG" 443633 NIL DLAGG (NIL T) -9 NIL 443863 NIL) (-243 439662 440326 440354 "DIVRING" 440446 T DIVRING (NIL) -9 NIL 440529 NIL) (-242 438899 439089 439389 "DIVRING-" 439394 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-241 437001 437358 437764 "DISPLAY" 438513 T DISPLAY (NIL) -7 NIL NIL NIL) (-240 430889 436915 436978 "DIRPROD" 436983 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-239 429737 429940 430205 "DIRPROD2" 430682 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-238 418512 424518 424571 "DIRPCAT" 424981 NIL DIRPCAT (NIL NIL T) -9 NIL 425821 NIL) (-237 415838 416480 417361 "DIRPCAT-" 417698 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-236 415125 415285 415471 "DIOSP" 415672 T DIOSP (NIL) -7 NIL NIL NIL) (-235 411780 414037 414078 "DIOPS" 414512 NIL DIOPS (NIL T) -9 NIL 414741 NIL) (-234 411329 411443 411634 "DIOPS-" 411639 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-233 410152 410780 410808 "DIFRING" 410995 T DIFRING (NIL) -9 NIL 411105 NIL) (-232 409798 409875 410027 "DIFRING-" 410032 NIL DIFRING- (NIL T) -8 NIL NIL NIL) (-231 407534 408806 408847 "DIFEXT" 409210 NIL DIFEXT (NIL T) -9 NIL 409504 NIL) (-230 405819 406247 406913 "DIFEXT-" 406918 NIL DIFEXT- (NIL T T) -8 NIL NIL NIL) (-229 403094 405351 405392 "DIAGG" 405397 NIL DIAGG (NIL T) -9 NIL 405417 NIL) (-228 402478 402635 402887 "DIAGG-" 402892 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-227 397895 401437 401714 "DHMATRIX" 402247 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-226 393507 394416 395426 "DFSFUN" 396905 T DFSFUN (NIL) -7 NIL NIL NIL) (-225 388585 392438 392750 "DFLOAT" 393215 T DFLOAT (NIL) -8 NIL NIL NIL) (-224 386848 387129 387518 "DFINTTLS" 388293 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-223 383877 384869 385269 "DERHAM" 386514 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-222 381678 383652 383741 "DEQUEUE" 383821 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-221 380932 381065 381248 "DEGRED" 381540 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-220 377362 378107 378953 "DEFINTRF" 380160 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-219 374917 375386 375978 "DEFINTEF" 376881 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-218 374267 374537 374652 "DEFAST" 374822 T DEFAST (NIL) -8 NIL NIL NIL) (-217 368271 373862 374011 "DECIMAL" 374138 T DECIMAL (NIL) -8 NIL NIL NIL) (-216 365783 366241 366747 "DDFACT" 367815 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-215 365379 365422 365573 "DBLRESP" 365734 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-214 363251 363612 363972 "DBASE" 365146 NIL DBASE (NIL T) -8 NIL NIL NIL) (-213 362493 362731 362877 "DATAARY" 363150 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-212 361599 362452 362480 "D03FAFA" 362485 T D03FAFA (NIL) -8 NIL NIL NIL) (-211 360706 361558 361586 "D03EEFA" 361591 T D03EEFA (NIL) -8 NIL NIL NIL) (-210 358656 359122 359611 "D03AGNT" 360237 T D03AGNT (NIL) -7 NIL NIL NIL) (-209 357945 358615 358643 "D02EJFA" 358648 T D02EJFA (NIL) -8 NIL NIL NIL) (-208 357234 357904 357932 "D02CJFA" 357937 T D02CJFA (NIL) -8 NIL NIL NIL) (-207 356523 357193 357221 "D02BHFA" 357226 T D02BHFA (NIL) -8 NIL NIL NIL) (-206 355812 356482 356510 "D02BBFA" 356515 T D02BBFA (NIL) -8 NIL NIL NIL) (-205 349009 350598 352204 "D02AGNT" 354226 T D02AGNT (NIL) -7 NIL NIL NIL) (-204 346777 347300 347846 "D01WGTS" 348483 T D01WGTS (NIL) -7 NIL NIL NIL) (-203 345844 346736 346764 "D01TRNS" 346769 T D01TRNS (NIL) -8 NIL NIL NIL) (-202 344912 345803 345831 "D01GBFA" 345836 T D01GBFA (NIL) -8 NIL NIL NIL) (-201 343980 344871 344899 "D01FCFA" 344904 T D01FCFA (NIL) -8 NIL NIL NIL) (-200 343048 343939 343967 "D01ASFA" 343972 T D01ASFA (NIL) -8 NIL NIL NIL) (-199 342116 343007 343035 "D01AQFA" 343040 T D01AQFA (NIL) -8 NIL NIL NIL) (-198 341184 342075 342103 "D01APFA" 342108 T D01APFA (NIL) -8 NIL NIL NIL) (-197 340252 341143 341171 "D01ANFA" 341176 T D01ANFA (NIL) -8 NIL NIL NIL) (-196 339320 340211 340239 "D01AMFA" 340244 T D01AMFA (NIL) -8 NIL NIL NIL) (-195 338388 339279 339307 "D01ALFA" 339312 T D01ALFA (NIL) -8 NIL NIL NIL) (-194 337456 338347 338375 "D01AKFA" 338380 T D01AKFA (NIL) -8 NIL NIL NIL) (-193 336524 337415 337443 "D01AJFA" 337448 T D01AJFA (NIL) -8 NIL NIL NIL) (-192 329819 331372 332933 "D01AGNT" 334983 T D01AGNT (NIL) -7 NIL NIL NIL) (-191 329156 329284 329436 "CYCLOTOM" 329687 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-190 325890 326604 327331 "CYCLES" 328449 T CYCLES (NIL) -7 NIL NIL NIL) (-189 325202 325336 325507 "CVMP" 325751 NIL CVMP (NIL T) -7 NIL NIL NIL) (-188 323043 323301 323670 "CTRIGMNP" 324930 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-187 322479 322837 322910 "CTOR" 322990 T CTOR (NIL) -8 NIL NIL NIL) (-186 321988 322210 322311 "CTORKIND" 322398 T CTORKIND (NIL) -8 NIL NIL NIL) (-185 321279 321595 321623 "CTORCAT" 321805 T CTORCAT (NIL) -9 NIL 321918 NIL) (-184 320877 320988 321147 "CTORCAT-" 321152 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-183 320366 320580 320678 "CTORCALL" 320799 T CTORCALL (NIL) -8 NIL NIL NIL) (-182 319740 319839 319992 "CSTTOOLS" 320263 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-181 315539 316196 316954 "CRFP" 319052 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-180 315014 315260 315352 "CRCEAST" 315467 T CRCEAST (NIL) -8 NIL NIL NIL) (-179 314061 314246 314474 "CRAPACK" 314818 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-178 313445 313546 313750 "CPMATCH" 313937 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-177 313170 313198 313304 "CPIMA" 313411 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-176 309518 310190 310909 "COORDSYS" 312505 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-175 308930 309051 309193 "CONTOUR" 309396 T CONTOUR (NIL) -8 NIL NIL NIL) (-174 304821 306933 307425 "CONTFRAC" 308470 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-173 304701 304722 304750 "CONDUIT" 304787 T CONDUIT (NIL) -9 NIL NIL NIL) (-172 303789 304343 304371 "COMRING" 304376 T COMRING (NIL) -9 NIL 304428 NIL) (-171 302843 303147 303331 "COMPPROP" 303625 T COMPPROP (NIL) -8 NIL NIL NIL) (-170 302504 302539 302667 "COMPLPAT" 302802 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-169 292795 302313 302422 "COMPLEX" 302427 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-168 292431 292488 292595 "COMPLEX2" 292732 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-167 292149 292184 292282 "COMPFACT" 292390 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-166 276229 286223 286263 "COMPCAT" 287267 NIL COMPCAT (NIL T) -9 NIL 288615 NIL) (-165 265741 268668 272295 "COMPCAT-" 272651 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-164 265470 265498 265601 "COMMUPC" 265707 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-163 265264 265298 265357 "COMMONOP" 265431 T COMMONOP (NIL) -7 NIL NIL NIL) (-162 264820 265015 265102 "COMM" 265197 T COMM (NIL) -8 NIL NIL NIL) (-161 264396 264624 264699 "COMMAAST" 264765 T COMMAAST (NIL) -8 NIL NIL NIL) (-160 263645 263839 263867 "COMBOPC" 264205 T COMBOPC (NIL) -9 NIL 264380 NIL) (-159 262541 262751 262993 "COMBINAT" 263435 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-158 258998 259572 260199 "COMBF" 261963 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-157 257756 258114 258349 "COLOR" 258783 T COLOR (NIL) -8 NIL NIL NIL) (-156 257232 257477 257569 "COLONAST" 257684 T COLONAST (NIL) -8 NIL NIL NIL) (-155 256872 256919 257044 "CMPLXRT" 257179 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-154 256320 256572 256671 "CLLCTAST" 256793 T CLLCTAST (NIL) -8 NIL NIL NIL) (-153 251818 252850 253930 "CLIP" 255260 T CLIP (NIL) -7 NIL NIL NIL) (-152 250164 250924 251163 "CLIF" 251645 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-151 246339 248310 248351 "CLAGG" 249280 NIL CLAGG (NIL T) -9 NIL 249816 NIL) (-150 244761 245218 245801 "CLAGG-" 245806 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-149 244305 244390 244530 "CINTSLPE" 244670 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-148 241806 242277 242825 "CHVAR" 243833 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-147 240980 241534 241562 "CHARZ" 241567 T CHARZ (NIL) -9 NIL 241582 NIL) (-146 240734 240774 240852 "CHARPOL" 240934 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-145 239792 240379 240407 "CHARNZ" 240454 T CHARNZ (NIL) -9 NIL 240510 NIL) (-144 237758 238482 238817 "CHAR" 239477 T CHAR (NIL) -8 NIL NIL NIL) (-143 237484 237545 237573 "CFCAT" 237684 T CFCAT (NIL) -9 NIL NIL NIL) (-142 236729 236840 237022 "CDEN" 237368 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-141 232694 235882 236162 "CCLASS" 236469 T CCLASS (NIL) -8 NIL NIL NIL) (-140 232001 232144 232307 "CATEGORY" 232551 T -10 (NIL) -8 NIL NIL NIL) (-139 231574 231920 231968 "CATCTOR" 231973 T CATCTOR (NIL) -8 NIL NIL NIL) (-138 231025 231277 231375 "CATAST" 231496 T CATAST (NIL) -8 NIL NIL NIL) (-137 230501 230746 230838 "CASEAST" 230953 T CASEAST (NIL) -8 NIL NIL NIL) (-136 225510 226530 227283 "CARTEN" 229804 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-135 224618 224766 224987 "CARTEN2" 225357 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-134 222934 223768 224025 "CARD" 224381 T CARD (NIL) -8 NIL NIL NIL) (-133 222510 222738 222813 "CAPSLAST" 222879 T CAPSLAST (NIL) -8 NIL NIL NIL) (-132 222014 222222 222250 "CACHSET" 222382 T CACHSET (NIL) -9 NIL 222460 NIL) (-131 221484 221806 221834 "CABMON" 221884 T CABMON (NIL) -9 NIL 221940 NIL) (-130 220957 221188 221298 "BYTEORD" 221394 T BYTEORD (NIL) -8 NIL NIL NIL) (-129 219936 220491 220633 "BYTE" 220796 T BYTE (NIL) -8 NIL NIL 220918) (-128 215286 219441 219613 "BYTEBUF" 219784 T BYTEBUF (NIL) -8 NIL NIL NIL) (-127 212795 214978 215085 "BTREE" 215212 NIL BTREE (NIL T) -8 NIL NIL NIL) (-126 210244 212443 212565 "BTOURN" 212705 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-125 207614 209714 209755 "BTCAT" 209823 NIL BTCAT (NIL T) -9 NIL 209900 NIL) (-124 207281 207361 207510 "BTCAT-" 207515 NIL BTCAT- (NIL T T) -8 NIL NIL NIL) (-123 202546 206424 206452 "BTAGG" 206674 T BTAGG (NIL) -9 NIL 206835 NIL) (-122 202036 202161 202367 "BTAGG-" 202372 NIL BTAGG- (NIL T) -8 NIL NIL NIL) (-121 199031 201314 201529 "BSTREE" 201853 NIL BSTREE (NIL T) -8 NIL NIL NIL) (-120 198169 198295 198479 "BRILL" 198887 NIL BRILL (NIL T) -7 NIL NIL NIL) (-119 194821 196895 196936 "BRAGG" 197585 NIL BRAGG (NIL T) -9 NIL 197843 NIL) (-118 193350 193756 194311 "BRAGG-" 194316 NIL BRAGG- (NIL T T) -8 NIL NIL NIL) (-117 186579 192696 192880 "BPADICRT" 193198 NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-116 184894 186516 186561 "BPADIC" 186566 NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-115 184592 184622 184736 "BOUNDZRO" 184858 NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-114 179820 181018 181930 "BOP" 183700 T BOP (NIL) -8 NIL NIL NIL) (-113 177601 178005 178480 "BOP1" 179378 NIL BOP1 (NIL T) -7 NIL NIL NIL) (-112 176426 177175 177324 "BOOLEAN" 177472 T BOOLEAN (NIL) -8 NIL NIL NIL) (-111 175705 176109 176163 "BMODULE" 176168 NIL BMODULE (NIL T T) -9 NIL 176233 NIL) (-110 171506 175503 175576 "BITS" 175652 T BITS (NIL) -8 NIL NIL NIL) (-109 170927 171046 171186 "BINDING" 171386 T BINDING (NIL) -8 NIL NIL NIL) (-108 164934 170524 170672 "BINARY" 170799 T BINARY (NIL) -8 NIL NIL NIL) (-107 162714 164189 164230 "BGAGG" 164490 NIL BGAGG (NIL T) -9 NIL 164627 NIL) (-106 162545 162577 162668 "BGAGG-" 162673 NIL BGAGG- (NIL T T) -8 NIL NIL NIL) (-105 161616 161929 162134 "BFUNCT" 162360 T BFUNCT (NIL) -8 NIL NIL NIL) (-104 160306 160484 160772 "BEZOUT" 161440 NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 156775 159158 159488 "BBTREE" 160009 NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 156509 156562 156590 "BASTYPE" 156709 T BASTYPE (NIL) -9 NIL NIL NIL) (-101 156361 156390 156463 "BASTYPE-" 156468 NIL BASTYPE- (NIL T) -8 NIL NIL NIL) (-100 155795 155871 156023 "BALFACT" 156272 NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 154651 155210 155396 "AUTOMOR" 155640 NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-98 154377 154382 154408 "ATTREG" 154413 T ATTREG (NIL) -9 NIL NIL NIL) (-97 152629 153074 153426 "ATTRBUT" 154043 T ATTRBUT (NIL) -8 NIL NIL NIL) (-96 152237 152457 152523 "ATTRAST" 152581 T ATTRAST (NIL) -8 NIL NIL NIL) (-95 151773 151886 151912 "ATRIG" 152113 T ATRIG (NIL) -9 NIL NIL NIL) (-94 151582 151623 151710 "ATRIG-" 151715 NIL ATRIG- (NIL T) -8 NIL NIL NIL) (-93 151227 151413 151439 "ASTCAT" 151444 T ASTCAT (NIL) -9 NIL 151474 NIL) (-92 150954 151013 151132 "ASTCAT-" 151137 NIL ASTCAT- (NIL T) -8 NIL NIL NIL) (-91 149103 150730 150818 "ASTACK" 150897 NIL ASTACK (NIL T) -8 NIL NIL NIL) (-90 147608 147905 148270 "ASSOCEQ" 148785 NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-89 146640 147267 147391 "ASP9" 147515 NIL ASP9 (NIL NIL) -8 NIL NIL NIL) (-88 146403 146588 146627 "ASP8" 146632 NIL ASP8 (NIL NIL) -8 NIL NIL NIL) (-87 145271 146008 146150 "ASP80" 146292 NIL ASP80 (NIL NIL) -8 NIL NIL NIL) (-86 144169 144906 145038 "ASP7" 145170 NIL ASP7 (NIL NIL) -8 NIL NIL NIL) (-85 143123 143846 143964 "ASP78" 144082 NIL ASP78 (NIL NIL) -8 NIL NIL NIL) (-84 142092 142803 142920 "ASP77" 143037 NIL ASP77 (NIL NIL) -8 NIL NIL NIL) (-83 141004 141730 141861 "ASP74" 141992 NIL ASP74 (NIL NIL) -8 NIL NIL NIL) (-82 139904 140639 140771 "ASP73" 140903 NIL ASP73 (NIL NIL) -8 NIL NIL NIL) (-81 139008 139730 139830 "ASP6" 139835 NIL ASP6 (NIL NIL) -8 NIL NIL NIL) (-80 137952 138685 138803 "ASP55" 138921 NIL ASP55 (NIL NIL) -8 NIL NIL NIL) (-79 136901 137626 137745 "ASP50" 137864 NIL ASP50 (NIL NIL) -8 NIL NIL NIL) (-78 135989 136602 136712 "ASP4" 136822 NIL ASP4 (NIL NIL) -8 NIL NIL NIL) (-77 135077 135690 135800 "ASP49" 135910 NIL ASP49 (NIL NIL) -8 NIL NIL NIL) (-76 133861 134616 134784 "ASP42" 134966 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-75 132637 133394 133564 "ASP41" 133748 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-74 131587 132314 132432 "ASP35" 132550 NIL ASP35 (NIL NIL) -8 NIL NIL NIL) (-73 131352 131535 131574 "ASP34" 131579 NIL ASP34 (NIL NIL) -8 NIL NIL NIL) (-72 131089 131156 131232 "ASP33" 131307 NIL ASP33 (NIL NIL) -8 NIL NIL NIL) (-71 129982 130724 130856 "ASP31" 130988 NIL ASP31 (NIL NIL) -8 NIL NIL NIL) (-70 129747 129930 129969 "ASP30" 129974 NIL ASP30 (NIL NIL) -8 NIL NIL NIL) (-69 129482 129551 129627 "ASP29" 129702 NIL ASP29 (NIL NIL) -8 NIL NIL NIL) (-68 129247 129430 129469 "ASP28" 129474 NIL ASP28 (NIL NIL) -8 NIL NIL NIL) (-67 129012 129195 129234 "ASP27" 129239 NIL ASP27 (NIL NIL) -8 NIL NIL NIL) (-66 128096 128710 128821 "ASP24" 128932 NIL ASP24 (NIL NIL) -8 NIL NIL NIL) (-65 127172 127898 128010 "ASP20" 128015 NIL ASP20 (NIL NIL) -8 NIL NIL NIL) (-64 126260 126873 126983 "ASP1" 127093 NIL ASP1 (NIL NIL) -8 NIL NIL NIL) (-63 125202 125934 126053 "ASP19" 126172 NIL ASP19 (NIL NIL) -8 NIL NIL NIL) (-62 124939 125006 125082 "ASP12" 125157 NIL ASP12 (NIL NIL) -8 NIL NIL NIL) (-61 123791 124538 124682 "ASP10" 124826 NIL ASP10 (NIL NIL) -8 NIL NIL NIL) (-60 121642 123635 123726 "ARRAY2" 123731 NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 117407 121290 121404 "ARRAY1" 121559 NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-58 116439 116612 116833 "ARRAY12" 117230 NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-57 110751 112669 112744 "ARR2CAT" 115374 NIL ARR2CAT (NIL T T T) -9 NIL 116132 NIL) (-56 108185 108929 109883 "ARR2CAT-" 109888 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL NIL) (-55 107502 107812 107937 "ARITY" 108078 T ARITY (NIL) -8 NIL NIL NIL) (-54 106278 106430 106729 "APPRULE" 107338 NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 105929 105977 106096 "APPLYORE" 106224 NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 104876 105194 105389 "ANY" 105752 T ANY (NIL) -8 NIL NIL NIL) (-51 104154 104277 104434 "ANY1" 104750 NIL ANY1 (NIL T) -7 NIL NIL NIL) (-50 101684 102591 102918 "ANTISYM" 103878 NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 101176 101391 101487 "ANON" 101606 T ANON (NIL) -8 NIL NIL NIL) (-48 95425 99715 100169 "AN" 100740 T AN (NIL) -8 NIL NIL NIL) (-47 91323 92711 92762 "AMR" 93510 NIL AMR (NIL T T) -9 NIL 94110 NIL) (-46 90435 90656 91019 "AMR-" 91024 NIL AMR- (NIL T T T) -8 NIL NIL NIL) (-45 74874 90352 90413 "ALIST" 90418 NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 71676 74468 74637 "ALGSC" 74792 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 68231 68786 69393 "ALGPKG" 71116 NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 67508 67609 67793 "ALGMFACT" 68117 NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 63543 64122 64716 "ALGMANIP" 67092 NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 54913 63169 63319 "ALGFF" 63476 NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 54109 54240 54419 "ALGFACT" 54771 NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 53050 53650 53688 "ALGEBRA" 53693 NIL ALGEBRA (NIL T) -9 NIL 53734 NIL) (-37 52768 52827 52959 "ALGEBRA-" 52964 NIL ALGEBRA- (NIL T T) -8 NIL NIL NIL) (-36 34861 50770 50822 "ALAGG" 50958 NIL ALAGG (NIL T T) -9 NIL 51119 NIL) (-35 34397 34510 34536 "AHYP" 34737 T AHYP (NIL) -9 NIL NIL NIL) (-34 33328 33576 33602 "AGG" 34101 T AGG (NIL) -9 NIL 34380 NIL) (-33 32762 32924 33138 "AGG-" 33143 NIL AGG- (NIL T) -8 NIL NIL NIL) (-32 30568 30991 31396 "AF" 32404 NIL AF (NIL T T) -7 NIL NIL NIL) (-31 30048 30293 30383 "ADDAST" 30496 T ADDAST (NIL) -8 NIL NIL NIL) (-30 29316 29575 29731 "ACPLOT" 29910 T ACPLOT (NIL) -8 NIL NIL NIL) (-29 18639 26443 26481 "ACFS" 27088 NIL ACFS (NIL T) -9 NIL 27327 NIL) (-28 16666 17156 17918 "ACFS-" 17923 NIL ACFS- (NIL T T) -8 NIL NIL NIL) (-27 12784 14713 14739 "ACF" 15618 T ACF (NIL) -9 NIL 16031 NIL) (-26 11488 11822 12315 "ACF-" 12320 NIL ACF- (NIL T) -8 NIL NIL NIL) (-25 11060 11255 11281 "ABELSG" 11373 T ABELSG (NIL) -9 NIL 11438 NIL) (-24 10927 10952 11018 "ABELSG-" 11023 NIL ABELSG- (NIL T) -8 NIL NIL NIL) (-23 10270 10557 10583 "ABELMON" 10753 T ABELMON (NIL) -9 NIL 10865 NIL) (-22 9934 10018 10156 "ABELMON-" 10161 NIL ABELMON- (NIL T) -8 NIL NIL NIL) (-21 9282 9654 9680 "ABELGRP" 9752 T ABELGRP (NIL) -9 NIL 9827 NIL) (-20 8745 8874 9090 "ABELGRP-" 9095 NIL ABELGRP- (NIL T) -8 NIL NIL NIL) (-19 4334 8084 8123 "A1AGG" 8128 NIL A1AGG (NIL T) -9 NIL 8168 NIL) (-18 30 1252 2814 "A1AGG-" 2819 NIL A1AGG- (NIL T T) -8 NIL NIL NIL)) \ No newline at end of file +((-3 3220914 3220919 3220924 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-2 3220899 3220904 3220909 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1 3220884 3220889 3220894 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (0 3220869 3220874 3220879 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1292 3220012 3220744 3220821 "ZMOD" 3220826 NIL ZMOD (NIL NIL) -8 NIL NIL NIL) (-1291 3219122 3219286 3219495 "ZLINDEP" 3219844 NIL ZLINDEP (NIL T) -7 NIL NIL NIL) (-1290 3208422 3210190 3212162 "ZDSOLVE" 3217252 NIL ZDSOLVE (NIL T NIL NIL) -7 NIL NIL NIL) (-1289 3207668 3207809 3207998 "YSTREAM" 3208268 NIL YSTREAM (NIL T) -7 NIL NIL NIL) (-1288 3205442 3206969 3207173 "XRPOLY" 3207511 NIL XRPOLY (NIL T T) -8 NIL NIL NIL) (-1287 3201995 3203313 3203888 "XPR" 3204914 NIL XPR (NIL T T) -8 NIL NIL NIL) (-1286 3199716 3201326 3201530 "XPOLY" 3201826 NIL XPOLY (NIL T) -8 NIL NIL NIL) (-1285 3197369 3198737 3198792 "XPOLYC" 3199080 NIL XPOLYC (NIL T T) -9 NIL 3199193 NIL) (-1284 3193744 3195886 3196274 "XPBWPOLY" 3197027 NIL XPBWPOLY (NIL T T) -8 NIL NIL NIL) (-1283 3189439 3191734 3191776 "XF" 3192397 NIL XF (NIL T) -9 NIL 3192797 NIL) (-1282 3189060 3189148 3189317 "XF-" 3189322 NIL XF- (NIL T T) -8 NIL NIL NIL) (-1281 3184256 3185545 3185600 "XFALG" 3187772 NIL XFALG (NIL T T) -9 NIL 3188561 NIL) (-1280 3183389 3183493 3183698 "XEXPPKG" 3184148 NIL XEXPPKG (NIL T T T) -7 NIL NIL NIL) (-1279 3181498 3183239 3183335 "XDPOLY" 3183340 NIL XDPOLY (NIL T T) -8 NIL NIL NIL) (-1278 3180305 3180905 3180948 "XALG" 3180953 NIL XALG (NIL T) -9 NIL 3181064 NIL) (-1277 3173747 3178282 3178776 "WUTSET" 3179897 NIL WUTSET (NIL T T T T) -8 NIL NIL NIL) (-1276 3172003 3172799 3173122 "WP" 3173558 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL NIL) (-1275 3171605 3171825 3171895 "WHILEAST" 3171955 T WHILEAST (NIL) -8 NIL NIL NIL) (-1274 3171077 3171322 3171416 "WHEREAST" 3171533 T WHEREAST (NIL) -8 NIL NIL NIL) (-1273 3169963 3170161 3170456 "WFFINTBS" 3170874 NIL WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1272 3167867 3168294 3168756 "WEIER" 3169535 NIL WEIER (NIL T) -7 NIL NIL NIL) (-1271 3166913 3167363 3167405 "VSPACE" 3167541 NIL VSPACE (NIL T) -9 NIL 3167615 NIL) (-1270 3166751 3166778 3166869 "VSPACE-" 3166874 NIL VSPACE- (NIL T T) -8 NIL NIL NIL) (-1269 3166559 3166602 3166670 "VOID" 3166705 T VOID (NIL) -8 NIL NIL NIL) (-1268 3164695 3165054 3165460 "VIEW" 3166175 T VIEW (NIL) -7 NIL NIL NIL) (-1267 3161119 3161758 3162495 "VIEWDEF" 3163980 T VIEWDEF (NIL) -7 NIL NIL NIL) (-1266 3150423 3152667 3154840 "VIEW3D" 3158968 T VIEW3D (NIL) -8 NIL NIL NIL) (-1265 3142674 3144334 3145913 "VIEW2D" 3148866 T VIEW2D (NIL) -8 NIL NIL NIL) (-1264 3138026 3142444 3142536 "VECTOR" 3142617 NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1263 3136603 3136862 3137180 "VECTOR2" 3137756 NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1262 3130077 3134384 3134427 "VECTCAT" 3135422 NIL VECTCAT (NIL T) -9 NIL 3136009 NIL) (-1261 3129091 3129345 3129735 "VECTCAT-" 3129740 NIL VECTCAT- (NIL T T) -8 NIL NIL NIL) (-1260 3128545 3128742 3128862 "VARIABLE" 3129006 NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1259 3128478 3128483 3128513 "UTYPE" 3128518 T UTYPE (NIL) -9 NIL NIL NIL) (-1258 3127308 3127462 3127724 "UTSODETL" 3128304 NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1257 3124748 3125208 3125732 "UTSODE" 3126849 NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1256 3116585 3122374 3122863 "UTS" 3124317 NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1255 3107459 3112826 3112869 "UTSCAT" 3113981 NIL UTSCAT (NIL T) -9 NIL 3114739 NIL) (-1254 3104806 3105529 3106518 "UTSCAT-" 3106523 NIL UTSCAT- (NIL T T) -8 NIL NIL NIL) (-1253 3104433 3104476 3104609 "UTS2" 3104757 NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1252 3098659 3101271 3101314 "URAGG" 3103384 NIL URAGG (NIL T) -9 NIL 3104107 NIL) (-1251 3095598 3096461 3097584 "URAGG-" 3097589 NIL URAGG- (NIL T T) -8 NIL NIL NIL) (-1250 3091307 3094233 3094698 "UPXSSING" 3095262 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1249 3083373 3090554 3090827 "UPXS" 3091092 NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1248 3076446 3083277 3083349 "UPXSCONS" 3083354 NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1247 3066191 3072984 3073046 "UPXSCCA" 3073620 NIL UPXSCCA (NIL T T) -9 NIL 3073853 NIL) (-1246 3065829 3065914 3066088 "UPXSCCA-" 3066093 NIL UPXSCCA- (NIL T T T) -8 NIL NIL NIL) (-1245 3055426 3061992 3062035 "UPXSCAT" 3062683 NIL UPXSCAT (NIL T) -9 NIL 3063292 NIL) (-1244 3054856 3054935 3055114 "UPXS2" 3055341 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1243 3053510 3053763 3054114 "UPSQFREE" 3054599 NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1242 3046931 3049988 3050043 "UPSCAT" 3051204 NIL UPSCAT (NIL T T) -9 NIL 3051978 NIL) (-1241 3046135 3046342 3046669 "UPSCAT-" 3046674 NIL UPSCAT- (NIL T T T) -8 NIL NIL NIL) (-1240 3031790 3039558 3039601 "UPOLYC" 3041702 NIL UPOLYC (NIL T) -9 NIL 3042923 NIL) (-1239 3023118 3025544 3028691 "UPOLYC-" 3028696 NIL UPOLYC- (NIL T T) -8 NIL NIL NIL) (-1238 3022745 3022788 3022921 "UPOLYC2" 3023069 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1237 3014556 3022428 3022557 "UP" 3022664 NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1236 3013895 3014002 3014166 "UPMP" 3014445 NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1235 3013448 3013529 3013668 "UPDIVP" 3013808 NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1234 3012016 3012265 3012581 "UPDECOMP" 3013197 NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1233 3011251 3011363 3011548 "UPCDEN" 3011900 NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1232 3010770 3010839 3010988 "UP2" 3011176 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1231 3009237 3009974 3010251 "UNISEG" 3010528 NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1230 3008452 3008579 3008784 "UNISEG2" 3009080 NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1229 3007512 3007692 3007918 "UNIFACT" 3008268 NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1228 2991444 3006689 3006940 "ULS" 3007319 NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1227 2979442 2991348 2991420 "ULSCONS" 2991425 NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1226 2961461 2973446 2973508 "ULSCCAT" 2974146 NIL ULSCCAT (NIL T T) -9 NIL 2974434 NIL) (-1225 2960511 2960756 2961144 "ULSCCAT-" 2961149 NIL ULSCCAT- (NIL T T T) -8 NIL NIL NIL) (-1224 2949885 2956365 2956408 "ULSCAT" 2957271 NIL ULSCAT (NIL T) -9 NIL 2958002 NIL) (-1223 2949315 2949394 2949573 "ULS2" 2949800 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1222 2948442 2948952 2949059 "UINT8" 2949170 T UINT8 (NIL) -8 NIL NIL 2949255) (-1221 2947568 2948078 2948185 "UINT64" 2948296 T UINT64 (NIL) -8 NIL NIL 2948381) (-1220 2946694 2947204 2947311 "UINT32" 2947422 T UINT32 (NIL) -8 NIL NIL 2947507) (-1219 2945820 2946330 2946437 "UINT16" 2946548 T UINT16 (NIL) -8 NIL NIL 2946633) (-1218 2944123 2945080 2945110 "UFD" 2945322 T UFD (NIL) -9 NIL 2945436 NIL) (-1217 2943917 2943963 2944058 "UFD-" 2944063 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1216 2942999 2943182 2943398 "UDVO" 2943723 T UDVO (NIL) -7 NIL NIL NIL) (-1215 2940815 2941224 2941695 "UDPO" 2942563 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1214 2940748 2940753 2940783 "TYPE" 2940788 T TYPE (NIL) -9 NIL NIL NIL) (-1213 2940508 2940703 2940734 "TYPEAST" 2940739 T TYPEAST (NIL) -8 NIL NIL NIL) (-1212 2939479 2939681 2939921 "TWOFACT" 2940302 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1211 2938502 2938888 2939123 "TUPLE" 2939279 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1210 2936193 2936712 2937251 "TUBETOOL" 2937985 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1209 2935042 2935247 2935488 "TUBE" 2935986 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1208 2929771 2934014 2934297 "TS" 2934794 NIL TS (NIL T) -8 NIL NIL NIL) (-1207 2918411 2922530 2922627 "TSETCAT" 2927896 NIL TSETCAT (NIL T T T T) -9 NIL 2929427 NIL) (-1206 2913143 2914743 2916634 "TSETCAT-" 2916639 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1205 2907782 2908629 2909558 "TRMANIP" 2912279 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1204 2907223 2907286 2907449 "TRIMAT" 2907714 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1203 2905089 2905326 2905683 "TRIGMNIP" 2906972 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1202 2904609 2904722 2904752 "TRIGCAT" 2904965 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1201 2904278 2904357 2904498 "TRIGCAT-" 2904503 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1200 2901123 2903136 2903417 "TREE" 2904032 NIL TREE (NIL T) -8 NIL NIL NIL) (-1199 2900397 2900925 2900955 "TRANFUN" 2900990 T TRANFUN (NIL) -9 NIL 2901056 NIL) (-1198 2899676 2899867 2900147 "TRANFUN-" 2900152 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1197 2899480 2899512 2899573 "TOPSP" 2899637 T TOPSP (NIL) -7 NIL NIL NIL) (-1196 2898828 2898943 2899097 "TOOLSIGN" 2899361 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1195 2897462 2898005 2898244 "TEXTFILE" 2898611 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1194 2895374 2895915 2896344 "TEX" 2897055 T TEX (NIL) -8 NIL NIL NIL) (-1193 2895155 2895186 2895258 "TEX1" 2895337 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1192 2894803 2894866 2894956 "TEMUTL" 2895087 T TEMUTL (NIL) -7 NIL NIL NIL) (-1191 2892957 2893237 2893562 "TBCMPPK" 2894526 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1190 2884734 2891117 2891173 "TBAGG" 2891573 NIL TBAGG (NIL T T) -9 NIL 2891784 NIL) (-1189 2879804 2881292 2883046 "TBAGG-" 2883051 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1188 2879188 2879295 2879440 "TANEXP" 2879693 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1187 2872578 2879045 2879138 "TABLE" 2879143 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1186 2871990 2872089 2872227 "TABLEAU" 2872475 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1185 2866598 2867818 2869066 "TABLBUMP" 2870776 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1184 2865820 2865967 2866148 "SYSTEM" 2866439 T SYSTEM (NIL) -8 NIL NIL NIL) (-1183 2862279 2862978 2863761 "SYSSOLP" 2865071 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1182 2861323 2861828 2861947 "SYSNNI" 2862133 NIL SYSNNI (NIL NIL) -8 NIL NIL 2862218) (-1181 2860630 2861089 2861168 "SYSINT" 2861228 NIL SYSINT (NIL NIL) -8 NIL NIL 2861273) (-1180 2856962 2857908 2858618 "SYNTAX" 2859942 T SYNTAX (NIL) -8 NIL NIL NIL) (-1179 2854120 2854722 2855354 "SYMTAB" 2856352 T SYMTAB (NIL) -8 NIL NIL NIL) (-1178 2849369 2850271 2851254 "SYMS" 2853159 T SYMS (NIL) -8 NIL NIL NIL) (-1177 2846604 2848827 2849057 "SYMPOLY" 2849174 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1176 2846121 2846196 2846319 "SYMFUNC" 2846516 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1175 2842140 2843433 2844246 "SYMBOL" 2845330 T SYMBOL (NIL) -8 NIL NIL NIL) (-1174 2835679 2837368 2839088 "SWITCH" 2840442 T SWITCH (NIL) -8 NIL NIL NIL) (-1173 2828913 2834500 2834803 "SUTS" 2835434 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1172 2820979 2828160 2828433 "SUPXS" 2828698 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1171 2812738 2820597 2820723 "SUP" 2820888 NIL SUP (NIL T) -8 NIL NIL NIL) (-1170 2811897 2812024 2812241 "SUPFRACF" 2812606 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1169 2811518 2811577 2811690 "SUP2" 2811832 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1168 2809966 2810240 2810596 "SUMRF" 2811217 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1167 2809301 2809367 2809559 "SUMFS" 2809887 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1166 2793268 2808478 2808729 "SULS" 2809108 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1165 2792870 2793090 2793160 "SUCHTAST" 2793220 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1164 2792165 2792395 2792535 "SUCH" 2792778 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1163 2786031 2787071 2788030 "SUBSPACE" 2791253 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1162 2785461 2785551 2785715 "SUBRESP" 2785919 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1161 2778826 2780126 2781437 "STTF" 2784197 NIL STTF (NIL T) -7 NIL NIL NIL) (-1160 2772999 2774119 2775266 "STTFNC" 2777726 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1159 2764309 2766181 2767975 "STTAYLOR" 2771240 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1158 2757439 2764173 2764256 "STRTBL" 2764261 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1157 2752803 2757394 2757425 "STRING" 2757430 T STRING (NIL) -8 NIL NIL NIL) (-1156 2747664 2752176 2752206 "STRICAT" 2752265 T STRICAT (NIL) -9 NIL 2752327 NIL) (-1155 2740417 2745283 2745894 "STREAM" 2747088 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1154 2739927 2740004 2740148 "STREAM3" 2740334 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1153 2738909 2739092 2739327 "STREAM2" 2739740 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1152 2738597 2738649 2738742 "STREAM1" 2738851 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1151 2737613 2737794 2738025 "STINPROD" 2738413 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1150 2737165 2737375 2737405 "STEP" 2737485 T STEP (NIL) -9 NIL 2737563 NIL) (-1149 2730597 2737064 2737141 "STBL" 2737146 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1148 2725723 2729818 2729861 "STAGG" 2730014 NIL STAGG (NIL T) -9 NIL 2730103 NIL) (-1147 2723425 2724027 2724899 "STAGG-" 2724904 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1146 2721572 2723195 2723287 "STACK" 2723368 NIL STACK (NIL T) -8 NIL NIL NIL) (-1145 2714267 2719713 2720169 "SREGSET" 2721202 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1144 2706692 2708061 2709574 "SRDCMPK" 2712873 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1143 2699609 2704132 2704162 "SRAGG" 2705465 T SRAGG (NIL) -9 NIL 2706073 NIL) (-1142 2698626 2698881 2699260 "SRAGG-" 2699265 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1141 2693086 2697573 2697994 "SQMATRIX" 2698252 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1140 2686771 2689804 2690531 "SPLTREE" 2692431 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1139 2682734 2683427 2684073 "SPLNODE" 2686197 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1138 2681781 2682014 2682044 "SPFCAT" 2682488 T SPFCAT (NIL) -9 NIL NIL NIL) (-1137 2680518 2680728 2680992 "SPECOUT" 2681539 T SPECOUT (NIL) -7 NIL NIL NIL) (-1136 2672144 2673914 2673944 "SPADXPT" 2678336 T SPADXPT (NIL) -9 NIL 2680370 NIL) (-1135 2671905 2671945 2672014 "SPADPRSR" 2672097 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1134 2670060 2671860 2671891 "SPADAST" 2671896 T SPADAST (NIL) -8 NIL NIL NIL) (-1133 2662005 2663778 2663821 "SPACEC" 2668194 NIL SPACEC (NIL T) -9 NIL 2670010 NIL) (-1132 2660135 2661937 2661986 "SPACE3" 2661991 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1131 2658887 2659058 2659349 "SORTPAK" 2659940 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1130 2656979 2657282 2657694 "SOLVETRA" 2658551 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1129 2656029 2656251 2656512 "SOLVESER" 2656752 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1128 2651333 2652221 2653216 "SOLVERAD" 2655081 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1127 2647148 2647757 2648486 "SOLVEFOR" 2650700 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1126 2641418 2646497 2646594 "SNTSCAT" 2646599 NIL SNTSCAT (NIL T T T T) -9 NIL 2646669 NIL) (-1125 2635524 2639741 2640132 "SMTS" 2641108 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1124 2630208 2635412 2635489 "SMP" 2635494 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1123 2628367 2628668 2629066 "SMITH" 2629905 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1122 2621080 2625276 2625379 "SMATCAT" 2626730 NIL SMATCAT (NIL NIL T T T) -9 NIL 2627280 NIL) (-1121 2618020 2618843 2620021 "SMATCAT-" 2620026 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1120 2615686 2617256 2617299 "SKAGG" 2617560 NIL SKAGG (NIL T) -9 NIL 2617695 NIL) (-1119 2611997 2615102 2615297 "SINT" 2615484 T SINT (NIL) -8 NIL NIL 2615657) (-1118 2611769 2611807 2611873 "SIMPAN" 2611953 T SIMPAN (NIL) -7 NIL NIL NIL) (-1117 2611048 2611304 2611444 "SIG" 2611651 T SIG (NIL) -8 NIL NIL NIL) (-1116 2609886 2610107 2610382 "SIGNRF" 2610807 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1115 2608719 2608870 2609154 "SIGNEF" 2609715 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1114 2608025 2608302 2608426 "SIGAST" 2608617 T SIGAST (NIL) -8 NIL NIL NIL) (-1113 2605714 2606169 2606675 "SHP" 2607566 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1112 2599566 2605615 2605691 "SHDP" 2605696 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1111 2599139 2599331 2599361 "SGROUP" 2599454 T SGROUP (NIL) -9 NIL 2599516 NIL) (-1110 2598997 2599023 2599096 "SGROUP-" 2599101 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1109 2595832 2596530 2597253 "SGCF" 2598296 T SGCF (NIL) -7 NIL NIL NIL) (-1108 2590200 2595279 2595376 "SFRTCAT" 2595381 NIL SFRTCAT (NIL T T T T) -9 NIL 2595420 NIL) (-1107 2583621 2584639 2585775 "SFRGCD" 2589183 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1106 2576747 2577820 2579006 "SFQCMPK" 2582554 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1105 2576367 2576456 2576567 "SFORT" 2576688 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1104 2575485 2576207 2576328 "SEXOF" 2576333 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1103 2574592 2575366 2575434 "SEX" 2575439 T SEX (NIL) -8 NIL NIL NIL) (-1102 2570105 2570820 2570915 "SEXCAT" 2573852 NIL SEXCAT (NIL T T T T T) -9 NIL 2574430 NIL) (-1101 2567258 2570039 2570087 "SET" 2570092 NIL SET (NIL T) -8 NIL NIL NIL) (-1100 2565482 2565971 2566276 "SETMN" 2566999 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1099 2564978 2565130 2565160 "SETCAT" 2565336 T SETCAT (NIL) -9 NIL 2565446 NIL) (-1098 2564670 2564748 2564878 "SETCAT-" 2564883 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1097 2561031 2563131 2563174 "SETAGG" 2564044 NIL SETAGG (NIL T) -9 NIL 2564384 NIL) (-1096 2560489 2560605 2560842 "SETAGG-" 2560847 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1095 2559932 2560185 2560286 "SEQAST" 2560410 T SEQAST (NIL) -8 NIL NIL NIL) (-1094 2559131 2559425 2559486 "SEGXCAT" 2559772 NIL SEGXCAT (NIL T T) -9 NIL 2559892 NIL) (-1093 2558137 2558797 2558979 "SEG" 2558984 NIL SEG (NIL T) -8 NIL NIL NIL) (-1092 2557116 2557330 2557373 "SEGCAT" 2557895 NIL SEGCAT (NIL T) -9 NIL 2558116 NIL) (-1091 2556117 2556495 2556695 "SEGBIND" 2556951 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1090 2555738 2555797 2555910 "SEGBIND2" 2556052 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1089 2555311 2555539 2555616 "SEGAST" 2555683 T SEGAST (NIL) -8 NIL NIL NIL) (-1088 2554530 2554656 2554860 "SEG2" 2555155 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1087 2553940 2554465 2554512 "SDVAR" 2554517 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1086 2546467 2553710 2553840 "SDPOL" 2553845 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1085 2545060 2545326 2545645 "SCPKG" 2546182 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1084 2544224 2544396 2544588 "SCOPE" 2544890 T SCOPE (NIL) -8 NIL NIL NIL) (-1083 2543444 2543578 2543757 "SCACHE" 2544079 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1082 2543090 2543276 2543306 "SASTCAT" 2543311 T SASTCAT (NIL) -9 NIL 2543324 NIL) (-1081 2542577 2542925 2543001 "SAOS" 2543036 T SAOS (NIL) -8 NIL NIL NIL) (-1080 2542142 2542177 2542350 "SAERFFC" 2542536 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1079 2536081 2542039 2542119 "SAE" 2542124 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1078 2535674 2535709 2535868 "SAEFACT" 2536040 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1077 2533995 2534309 2534710 "RURPK" 2535340 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1076 2532632 2532938 2533243 "RULESET" 2533829 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1075 2529855 2530385 2530843 "RULE" 2532313 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1074 2529467 2529649 2529732 "RULECOLD" 2529807 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1073 2529257 2529285 2529356 "RTVALUE" 2529418 T RTVALUE (NIL) -8 NIL NIL NIL) (-1072 2528728 2528974 2529068 "RSTRCAST" 2529185 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1071 2523576 2524371 2525291 "RSETGCD" 2527927 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1070 2512806 2517885 2517982 "RSETCAT" 2522101 NIL RSETCAT (NIL T T T T) -9 NIL 2523198 NIL) (-1069 2510733 2511272 2512096 "RSETCAT-" 2512101 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1068 2503118 2504495 2506015 "RSDCMPK" 2509332 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1067 2501097 2501564 2501638 "RRCC" 2502724 NIL RRCC (NIL T T) -9 NIL 2503068 NIL) (-1066 2500448 2500622 2500901 "RRCC-" 2500906 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1065 2499891 2500144 2500245 "RPTAST" 2500369 T RPTAST (NIL) -8 NIL NIL NIL) (-1064 2473742 2483099 2483166 "RPOLCAT" 2493830 NIL RPOLCAT (NIL T T T) -9 NIL 2496989 NIL) (-1063 2465240 2467580 2470702 "RPOLCAT-" 2470707 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1062 2456171 2463451 2463933 "ROUTINE" 2464780 T ROUTINE (NIL) -8 NIL NIL NIL) (-1061 2452969 2455797 2455937 "ROMAN" 2456053 T ROMAN (NIL) -8 NIL NIL NIL) (-1060 2451213 2451829 2452089 "ROIRC" 2452774 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1059 2447445 2449729 2449759 "RNS" 2450063 T RNS (NIL) -9 NIL 2450337 NIL) (-1058 2445954 2446337 2446871 "RNS-" 2446946 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1057 2445357 2445765 2445795 "RNG" 2445800 T RNG (NIL) -9 NIL 2445821 NIL) (-1056 2444756 2445144 2445187 "RMODULE" 2445192 NIL RMODULE (NIL T) -9 NIL 2445219 NIL) (-1055 2443592 2443686 2444022 "RMCAT2" 2444657 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1054 2440442 2442938 2443235 "RMATRIX" 2443354 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1053 2433269 2435529 2435644 "RMATCAT" 2439003 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2439985 NIL) (-1052 2432644 2432791 2433098 "RMATCAT-" 2433103 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1051 2432045 2432266 2432309 "RLINSET" 2432503 NIL RLINSET (NIL T) -9 NIL 2432594 NIL) (-1050 2431612 2431687 2431815 "RINTERP" 2431964 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1049 2430670 2431224 2431254 "RING" 2431310 T RING (NIL) -9 NIL 2431402 NIL) (-1048 2430462 2430506 2430603 "RING-" 2430608 NIL RING- (NIL T) -8 NIL NIL NIL) (-1047 2429303 2429540 2429798 "RIDIST" 2430226 T RIDIST (NIL) -7 NIL NIL NIL) (-1046 2420592 2428771 2428977 "RGCHAIN" 2429151 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1045 2419942 2420348 2420389 "RGBCSPC" 2420447 NIL RGBCSPC (NIL T) -9 NIL 2420499 NIL) (-1044 2419100 2419481 2419522 "RGBCMDL" 2419754 NIL RGBCMDL (NIL T) -9 NIL 2419868 NIL) (-1043 2416094 2416708 2417378 "RF" 2418464 NIL RF (NIL T) -7 NIL NIL NIL) (-1042 2415740 2415803 2415906 "RFFACTOR" 2416025 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1041 2415465 2415500 2415597 "RFFACT" 2415699 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1040 2413582 2413946 2414328 "RFDIST" 2415105 T RFDIST (NIL) -7 NIL NIL NIL) (-1039 2413035 2413127 2413290 "RETSOL" 2413484 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1038 2412671 2412751 2412794 "RETRACT" 2412927 NIL RETRACT (NIL T) -9 NIL 2413014 NIL) (-1037 2412520 2412545 2412632 "RETRACT-" 2412637 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1036 2412122 2412342 2412412 "RETAST" 2412472 T RETAST (NIL) -8 NIL NIL NIL) (-1035 2404860 2411775 2411902 "RESULT" 2412017 T RESULT (NIL) -8 NIL NIL NIL) (-1034 2403451 2404129 2404328 "RESRING" 2404763 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1033 2403087 2403136 2403234 "RESLATC" 2403388 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1032 2402792 2402827 2402934 "REPSQ" 2403046 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1031 2400214 2400794 2401396 "REP" 2402212 T REP (NIL) -7 NIL NIL NIL) (-1030 2399911 2399946 2400057 "REPDB" 2400173 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1029 2393811 2395200 2396423 "REP2" 2398723 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1028 2390188 2390869 2391677 "REP1" 2393038 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1027 2382884 2388329 2388785 "REGSET" 2389818 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1026 2381649 2382032 2382282 "REF" 2382669 NIL REF (NIL T) -8 NIL NIL NIL) (-1025 2381026 2381129 2381296 "REDORDER" 2381533 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1024 2376994 2380239 2380466 "RECLOS" 2380854 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1023 2376046 2376227 2376442 "REALSOLV" 2376801 T REALSOLV (NIL) -7 NIL NIL NIL) (-1022 2375892 2375933 2375963 "REAL" 2375968 T REAL (NIL) -9 NIL 2376003 NIL) (-1021 2372375 2373177 2374061 "REAL0Q" 2375057 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1020 2367976 2368964 2370025 "REAL0" 2371356 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1019 2367447 2367693 2367787 "RDUCEAST" 2367904 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1018 2366852 2366924 2367131 "RDIV" 2367369 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1017 2365920 2366094 2366307 "RDIST" 2366674 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1016 2364517 2364804 2365176 "RDETRS" 2365628 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1015 2362329 2362783 2363321 "RDETR" 2364059 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1014 2360954 2361232 2361629 "RDEEFS" 2362045 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1013 2359463 2359769 2360194 "RDEEF" 2360642 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1012 2353524 2356444 2356474 "RCFIELD" 2357769 T RCFIELD (NIL) -9 NIL 2358500 NIL) (-1011 2351588 2352092 2352788 "RCFIELD-" 2352863 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1010 2347857 2349689 2349732 "RCAGG" 2350816 NIL RCAGG (NIL T) -9 NIL 2351281 NIL) (-1009 2347485 2347579 2347742 "RCAGG-" 2347747 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1008 2346820 2346932 2347097 "RATRET" 2347369 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1007 2346373 2346440 2346561 "RATFACT" 2346748 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1006 2345681 2345801 2345953 "RANDSRC" 2346243 T RANDSRC (NIL) -7 NIL NIL NIL) (-1005 2345415 2345459 2345532 "RADUTIL" 2345630 T RADUTIL (NIL) -7 NIL NIL NIL) (-1004 2338531 2344248 2344558 "RADIX" 2345139 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-1003 2330150 2338373 2338503 "RADFF" 2338508 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-1002 2329797 2329872 2329902 "RADCAT" 2330062 T RADCAT (NIL) -9 NIL NIL NIL) (-1001 2329579 2329627 2329727 "RADCAT-" 2329732 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-1000 2327679 2329351 2329442 "QUEUE" 2329523 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-999 2324220 2327616 2327661 "QUAT" 2327666 NIL QUAT (NIL T) -8 NIL NIL NIL) (-998 2323858 2323901 2324028 "QUATCT2" 2324171 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-997 2317320 2320665 2320705 "QUATCAT" 2321485 NIL QUATCAT (NIL T) -9 NIL 2322251 NIL) (-996 2313464 2314501 2315888 "QUATCAT-" 2315982 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-995 2310937 2312548 2312589 "QUAGG" 2312964 NIL QUAGG (NIL T) -9 NIL 2313139 NIL) (-994 2310542 2310762 2310830 "QQUTAST" 2310889 T QQUTAST (NIL) -8 NIL NIL NIL) (-993 2309440 2309940 2310112 "QFORM" 2310414 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-992 2300445 2305684 2305724 "QFCAT" 2306382 NIL QFCAT (NIL T) -9 NIL 2307383 NIL) (-991 2296017 2297218 2298809 "QFCAT-" 2298903 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-990 2295655 2295698 2295825 "QFCAT2" 2295968 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-989 2295115 2295225 2295355 "QEQUAT" 2295545 T QEQUAT (NIL) -8 NIL NIL NIL) (-988 2288261 2289334 2290518 "QCMPACK" 2294048 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-987 2285810 2286258 2286686 "QALGSET" 2287916 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-986 2285055 2285229 2285461 "QALGSET2" 2285630 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-985 2283745 2283969 2284286 "PWFFINTB" 2284828 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-984 2281927 2282095 2282449 "PUSHVAR" 2283559 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-983 2277845 2278899 2278940 "PTRANFN" 2280824 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-982 2276247 2276538 2276860 "PTPACK" 2277556 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-981 2275879 2275936 2276045 "PTFUNC2" 2276184 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-980 2270356 2274751 2274792 "PTCAT" 2275088 NIL PTCAT (NIL T) -9 NIL 2275241 NIL) (-979 2270014 2270049 2270173 "PSQFR" 2270315 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-978 2268609 2268907 2269241 "PSEUDLIN" 2269712 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-977 2255372 2257743 2260067 "PSETPK" 2266369 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-976 2248390 2251130 2251226 "PSETCAT" 2254247 NIL PSETCAT (NIL T T T T) -9 NIL 2255061 NIL) (-975 2246226 2246860 2247681 "PSETCAT-" 2247686 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-974 2245575 2245740 2245768 "PSCURVE" 2246036 T PSCURVE (NIL) -9 NIL 2246203 NIL) (-973 2241573 2243089 2243154 "PSCAT" 2243998 NIL PSCAT (NIL T T T) -9 NIL 2244238 NIL) (-972 2240636 2240852 2241252 "PSCAT-" 2241257 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-971 2239341 2240001 2240206 "PRTITION" 2240451 T PRTITION (NIL) -8 NIL NIL NIL) (-970 2238816 2239062 2239154 "PRTDAST" 2239269 T PRTDAST (NIL) -8 NIL NIL NIL) (-969 2227905 2230120 2232308 "PRS" 2236678 NIL PRS (NIL T T) -7 NIL NIL NIL) (-968 2225716 2227255 2227295 "PRQAGG" 2227478 NIL PRQAGG (NIL T) -9 NIL 2227580 NIL) (-967 2224920 2225225 2225253 "PROPLOG" 2225500 T PROPLOG (NIL) -9 NIL 2225666 NIL) (-966 2223350 2223871 2224128 "PROPFRML" 2224696 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-965 2222819 2222926 2223054 "PROPERTY" 2223242 T PROPERTY (NIL) -8 NIL NIL NIL) (-964 2216877 2220985 2221805 "PRODUCT" 2222045 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-963 2214155 2216335 2216569 "PR" 2216688 NIL PR (NIL T T) -8 NIL NIL NIL) (-962 2213951 2213983 2214042 "PRINT" 2214116 T PRINT (NIL) -7 NIL NIL NIL) (-961 2213291 2213408 2213560 "PRIMES" 2213831 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-960 2211356 2211757 2212223 "PRIMELT" 2212870 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-959 2211085 2211134 2211162 "PRIMCAT" 2211286 T PRIMCAT (NIL) -9 NIL NIL NIL) (-958 2207200 2211023 2211068 "PRIMARR" 2211073 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-957 2206207 2206385 2206613 "PRIMARR2" 2207018 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-956 2205850 2205906 2206017 "PREASSOC" 2206145 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-955 2205325 2205458 2205486 "PPCURVE" 2205691 T PPCURVE (NIL) -9 NIL 2205827 NIL) (-954 2204920 2205120 2205203 "PORTNUM" 2205262 T PORTNUM (NIL) -8 NIL NIL NIL) (-953 2202279 2202678 2203270 "POLYROOT" 2204501 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-952 2196461 2201883 2202043 "POLY" 2202152 NIL POLY (NIL T) -8 NIL NIL NIL) (-951 2195844 2195902 2196136 "POLYLIFT" 2196397 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-950 2192119 2192568 2193197 "POLYCATQ" 2195389 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-949 2178831 2183959 2184024 "POLYCAT" 2187538 NIL POLYCAT (NIL T T T) -9 NIL 2189416 NIL) (-948 2172280 2174142 2176526 "POLYCAT-" 2176531 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-947 2171867 2171935 2172055 "POLY2UP" 2172206 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-946 2171499 2171556 2171665 "POLY2" 2171804 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-945 2170184 2170423 2170699 "POLUTIL" 2171273 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-944 2168539 2168816 2169147 "POLTOPOL" 2169906 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-943 2164004 2168475 2168521 "POINT" 2168526 NIL POINT (NIL T) -8 NIL NIL NIL) (-942 2162191 2162548 2162923 "PNTHEORY" 2163649 T PNTHEORY (NIL) -7 NIL NIL NIL) (-941 2160649 2160946 2161345 "PMTOOLS" 2161889 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-940 2160242 2160320 2160437 "PMSYM" 2160565 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-939 2159752 2159821 2159995 "PMQFCAT" 2160167 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-938 2159107 2159217 2159373 "PMPRED" 2159629 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-937 2158500 2158586 2158748 "PMPREDFS" 2159008 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-936 2157164 2157372 2157750 "PMPLCAT" 2158262 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-935 2156696 2156775 2156927 "PMLSAGG" 2157079 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-934 2156169 2156245 2156427 "PMKERNEL" 2156614 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-933 2155786 2155861 2155974 "PMINS" 2156088 NIL PMINS (NIL T) -7 NIL NIL NIL) (-932 2155228 2155297 2155506 "PMFS" 2155711 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-931 2154456 2154574 2154779 "PMDOWN" 2155105 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-930 2153623 2153781 2153962 "PMASS" 2154295 T PMASS (NIL) -7 NIL NIL NIL) (-929 2152896 2153006 2153169 "PMASSFS" 2153510 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-928 2152551 2152619 2152713 "PLOTTOOL" 2152822 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-927 2147158 2148362 2149510 "PLOT" 2151423 T PLOT (NIL) -8 NIL NIL NIL) (-926 2142962 2144006 2144927 "PLOT3D" 2146257 T PLOT3D (NIL) -8 NIL NIL NIL) (-925 2141874 2142051 2142286 "PLOT1" 2142766 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-924 2117263 2121940 2126791 "PLEQN" 2137140 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-923 2116581 2116703 2116883 "PINTERP" 2117128 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-922 2116274 2116321 2116424 "PINTERPA" 2116528 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-921 2115495 2116043 2116130 "PI" 2116170 T PI (NIL) -8 NIL NIL 2116237) (-920 2113792 2114767 2114795 "PID" 2114977 T PID (NIL) -9 NIL 2115111 NIL) (-919 2113543 2113580 2113655 "PICOERCE" 2113749 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-918 2112863 2113002 2113178 "PGROEB" 2113399 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-917 2108450 2109264 2110169 "PGE" 2111978 T PGE (NIL) -7 NIL NIL NIL) (-916 2106573 2106820 2107186 "PGCD" 2108167 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-915 2105911 2106014 2106175 "PFRPAC" 2106457 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-914 2102551 2104459 2104812 "PFR" 2105590 NIL PFR (NIL T) -8 NIL NIL NIL) (-913 2100940 2101184 2101509 "PFOTOOLS" 2102298 NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-912 2099473 2099712 2100063 "PFOQ" 2100697 NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-911 2097974 2098186 2098542 "PFO" 2099257 NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-910 2094527 2097863 2097932 "PF" 2097937 NIL PF (NIL NIL) -8 NIL NIL NIL) (-909 2091861 2093132 2093160 "PFECAT" 2093745 T PFECAT (NIL) -9 NIL 2094129 NIL) (-908 2091306 2091460 2091674 "PFECAT-" 2091679 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-907 2089909 2090161 2090462 "PFBRU" 2091055 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-906 2087775 2088127 2088559 "PFBR" 2089560 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-905 2083657 2085151 2085827 "PERM" 2087132 NIL PERM (NIL T) -8 NIL NIL NIL) (-904 2078891 2079864 2080734 "PERMGRP" 2082820 NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-903 2076997 2077954 2077995 "PERMCAT" 2078441 NIL PERMCAT (NIL T) -9 NIL 2078746 NIL) (-902 2076650 2076691 2076815 "PERMAN" 2076950 NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-901 2074138 2076315 2076437 "PENDTREE" 2076561 NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-900 2072162 2072930 2072971 "PDRING" 2073628 NIL PDRING (NIL T) -9 NIL 2073914 NIL) (-899 2071265 2071483 2071845 "PDRING-" 2071850 NIL PDRING- (NIL T T) -8 NIL NIL NIL) (-898 2068480 2069258 2069926 "PDEPROB" 2070617 T PDEPROB (NIL) -8 NIL NIL NIL) (-897 2066025 2066529 2067084 "PDEPACK" 2067945 T PDEPACK (NIL) -7 NIL NIL NIL) (-896 2064937 2065127 2065378 "PDECOMP" 2065824 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-895 2062516 2063359 2063387 "PDECAT" 2064174 T PDECAT (NIL) -9 NIL 2064887 NIL) (-894 2062267 2062300 2062390 "PCOMP" 2062477 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-893 2060445 2061068 2061365 "PBWLB" 2061996 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-892 2052918 2054518 2055856 "PATTERN" 2059128 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-891 2052550 2052607 2052716 "PATTERN2" 2052855 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-890 2050307 2050695 2051152 "PATTERN1" 2052139 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-889 2047675 2048256 2048737 "PATRES" 2049872 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-888 2047239 2047306 2047438 "PATRES2" 2047602 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-887 2045122 2045527 2045934 "PATMATCH" 2046906 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-886 2044632 2044841 2044882 "PATMAB" 2044989 NIL PATMAB (NIL T) -9 NIL 2045072 NIL) (-885 2043150 2043486 2043744 "PATLRES" 2044437 NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-884 2042696 2042819 2042860 "PATAB" 2042865 NIL PATAB (NIL T) -9 NIL 2043037 NIL) (-883 2040177 2040709 2041282 "PARTPERM" 2042143 T PARTPERM (NIL) -7 NIL NIL NIL) (-882 2039798 2039861 2039963 "PARSURF" 2040108 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-881 2039430 2039487 2039596 "PARSU2" 2039735 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-880 2039194 2039234 2039301 "PARSER" 2039383 T PARSER (NIL) -7 NIL NIL NIL) (-879 2038815 2038878 2038980 "PARSCURV" 2039125 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-878 2038447 2038504 2038613 "PARSC2" 2038752 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-877 2038086 2038144 2038241 "PARPCURV" 2038383 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-876 2037718 2037775 2037884 "PARPC2" 2038023 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-875 2037238 2037324 2037443 "PAN2EXPR" 2037619 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-874 2036015 2036359 2036587 "PALETTE" 2037030 T PALETTE (NIL) -8 NIL NIL NIL) (-873 2034408 2035020 2035380 "PAIR" 2035701 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-872 2028278 2033667 2033861 "PADICRC" 2034263 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-871 2021507 2027624 2027808 "PADICRAT" 2028126 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-870 2019822 2021444 2021489 "PADIC" 2021494 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-869 2016932 2018496 2018536 "PADICCT" 2019117 NIL PADICCT (NIL NIL) -9 NIL 2019399 NIL) (-868 2015889 2016089 2016357 "PADEPAC" 2016719 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-867 2015101 2015234 2015440 "PADE" 2015751 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-866 2013488 2014309 2014589 "OWP" 2014905 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-865 2012981 2013194 2013291 "OVERSET" 2013411 T OVERSET (NIL) -8 NIL NIL NIL) (-864 2012027 2012586 2012758 "OVAR" 2012849 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-863 2011291 2011412 2011573 "OUT" 2011886 T OUT (NIL) -7 NIL NIL NIL) (-862 2000163 2002400 2004600 "OUTFORM" 2009111 T OUTFORM (NIL) -8 NIL NIL NIL) (-861 1999499 1999760 1999887 "OUTBFILE" 2000056 T OUTBFILE (NIL) -8 NIL NIL NIL) (-860 1998806 1998971 1998999 "OUTBCON" 1999317 T OUTBCON (NIL) -9 NIL 1999483 NIL) (-859 1998407 1998519 1998676 "OUTBCON-" 1998681 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-858 1997787 1998136 1998225 "OSI" 1998338 T OSI (NIL) -8 NIL NIL NIL) (-857 1997317 1997655 1997683 "OSGROUP" 1997688 T OSGROUP (NIL) -9 NIL 1997710 NIL) (-856 1996062 1996289 1996574 "ORTHPOL" 1997064 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-855 1993613 1995897 1996018 "OREUP" 1996023 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-854 1991016 1993304 1993431 "ORESUP" 1993555 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-853 1988544 1989044 1989605 "OREPCTO" 1990505 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-852 1982230 1984431 1984472 "OREPCAT" 1986820 NIL OREPCAT (NIL T) -9 NIL 1987924 NIL) (-851 1979377 1980159 1981217 "OREPCAT-" 1981222 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-850 1978528 1978826 1978854 "ORDSET" 1979163 T ORDSET (NIL) -9 NIL 1979327 NIL) (-849 1977959 1978107 1978331 "ORDSET-" 1978336 NIL ORDSET- (NIL T) -8 NIL NIL NIL) (-848 1976524 1977315 1977343 "ORDRING" 1977545 T ORDRING (NIL) -9 NIL 1977670 NIL) (-847 1976169 1976263 1976407 "ORDRING-" 1976412 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-846 1975549 1976012 1976040 "ORDMON" 1976045 T ORDMON (NIL) -9 NIL 1976066 NIL) (-845 1974711 1974858 1975053 "ORDFUNS" 1975398 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-844 1974049 1974468 1974496 "ORDFIN" 1974561 T ORDFIN (NIL) -9 NIL 1974635 NIL) (-843 1970608 1972635 1973044 "ORDCOMP" 1973673 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-842 1969874 1970001 1970187 "ORDCOMP2" 1970468 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-841 1966455 1967365 1968179 "OPTPROB" 1969080 T OPTPROB (NIL) -8 NIL NIL NIL) (-840 1963257 1963896 1964600 "OPTPACK" 1965771 T OPTPACK (NIL) -7 NIL NIL NIL) (-839 1960944 1961710 1961738 "OPTCAT" 1962557 T OPTCAT (NIL) -9 NIL 1963207 NIL) (-838 1960328 1960621 1960726 "OPSIG" 1960859 T OPSIG (NIL) -8 NIL NIL NIL) (-837 1960096 1960135 1960201 "OPQUERY" 1960282 T OPQUERY (NIL) -7 NIL NIL NIL) (-836 1957227 1958407 1958911 "OP" 1959625 NIL OP (NIL T) -8 NIL NIL NIL) (-835 1956601 1956827 1956868 "OPERCAT" 1957080 NIL OPERCAT (NIL T) -9 NIL 1957177 NIL) (-834 1956356 1956412 1956529 "OPERCAT-" 1956534 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-833 1953169 1955153 1955522 "ONECOMP" 1956020 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-832 1952474 1952589 1952763 "ONECOMP2" 1953041 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-831 1951893 1951999 1952129 "OMSERVER" 1952364 T OMSERVER (NIL) -7 NIL NIL NIL) (-830 1948755 1951333 1951373 "OMSAGG" 1951434 NIL OMSAGG (NIL T) -9 NIL 1951498 NIL) (-829 1947378 1947641 1947923 "OMPKG" 1948493 T OMPKG (NIL) -7 NIL NIL NIL) (-828 1946808 1946911 1946939 "OM" 1947238 T OM (NIL) -9 NIL NIL NIL) (-827 1945355 1946357 1946526 "OMLO" 1946689 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-826 1944315 1944462 1944682 "OMEXPR" 1945181 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-825 1943606 1943861 1943997 "OMERR" 1944199 T OMERR (NIL) -8 NIL NIL NIL) (-824 1942757 1943027 1943187 "OMERRK" 1943466 T OMERRK (NIL) -8 NIL NIL NIL) (-823 1942208 1942434 1942542 "OMENC" 1942669 T OMENC (NIL) -8 NIL NIL NIL) (-822 1936103 1937288 1938459 "OMDEV" 1941057 T OMDEV (NIL) -8 NIL NIL NIL) (-821 1935172 1935343 1935537 "OMCONN" 1935929 T OMCONN (NIL) -8 NIL NIL NIL) (-820 1933693 1934669 1934697 "OINTDOM" 1934702 T OINTDOM (NIL) -9 NIL 1934723 NIL) (-819 1929472 1930683 1931399 "OFMONOID" 1933009 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-818 1928883 1929409 1929454 "ODVAR" 1929459 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-817 1926306 1928628 1928783 "ODR" 1928788 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-816 1918887 1926082 1926208 "ODPOL" 1926213 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-815 1912709 1918759 1918864 "ODP" 1918869 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-814 1911475 1911690 1911965 "ODETOOLS" 1912483 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-813 1908442 1909100 1909816 "ODESYS" 1910808 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-812 1903324 1904232 1905257 "ODERTRIC" 1907517 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-811 1902750 1902832 1903026 "ODERED" 1903236 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-810 1899638 1900186 1900863 "ODERAT" 1902173 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-809 1896595 1897062 1897659 "ODEPRRIC" 1899167 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-808 1894538 1895134 1895620 "ODEPROB" 1896129 T ODEPROB (NIL) -8 NIL NIL NIL) (-807 1891058 1891543 1892190 "ODEPRIM" 1894017 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-806 1890307 1890409 1890669 "ODEPAL" 1890950 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-805 1886469 1887260 1888124 "ODEPACK" 1889463 T ODEPACK (NIL) -7 NIL NIL NIL) (-804 1885530 1885637 1885859 "ODEINT" 1886358 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-803 1879631 1881056 1882503 "ODEIFTBL" 1884103 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-802 1875029 1875815 1876767 "ODEEF" 1878790 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-801 1874378 1874467 1874690 "ODECONST" 1874934 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-800 1872503 1873164 1873192 "ODECAT" 1873797 T ODECAT (NIL) -9 NIL 1874328 NIL) (-799 1869375 1872215 1872334 "OCT" 1872416 NIL OCT (NIL T) -8 NIL NIL NIL) (-798 1869013 1869056 1869183 "OCTCT2" 1869326 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-797 1863662 1866097 1866137 "OC" 1867234 NIL OC (NIL T) -9 NIL 1868092 NIL) (-796 1860889 1861637 1862627 "OC-" 1862721 NIL OC- (NIL T T) -8 NIL NIL NIL) (-795 1860241 1860709 1860737 "OCAMON" 1860742 T OCAMON (NIL) -9 NIL 1860763 NIL) (-794 1859772 1860113 1860141 "OASGP" 1860146 T OASGP (NIL) -9 NIL 1860166 NIL) (-793 1859033 1859522 1859550 "OAMONS" 1859590 T OAMONS (NIL) -9 NIL 1859633 NIL) (-792 1858447 1858880 1858908 "OAMON" 1858913 T OAMON (NIL) -9 NIL 1858933 NIL) (-791 1857705 1858223 1858251 "OAGROUP" 1858256 T OAGROUP (NIL) -9 NIL 1858276 NIL) (-790 1857395 1857445 1857533 "NUMTUBE" 1857649 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-789 1850968 1852486 1854022 "NUMQUAD" 1855879 T NUMQUAD (NIL) -7 NIL NIL NIL) (-788 1846724 1847712 1848737 "NUMODE" 1849963 T NUMODE (NIL) -7 NIL NIL NIL) (-787 1844079 1844959 1844987 "NUMINT" 1845910 T NUMINT (NIL) -9 NIL 1846674 NIL) (-786 1843027 1843224 1843442 "NUMFMT" 1843881 T NUMFMT (NIL) -7 NIL NIL NIL) (-785 1829386 1832331 1834863 "NUMERIC" 1840534 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-784 1823756 1828835 1828930 "NTSCAT" 1828935 NIL NTSCAT (NIL T T T T) -9 NIL 1828974 NIL) (-783 1822950 1823115 1823308 "NTPOLFN" 1823595 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-782 1811027 1819775 1820587 "NSUP" 1822171 NIL NSUP (NIL T) -8 NIL NIL NIL) (-781 1810659 1810716 1810825 "NSUP2" 1810964 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-780 1800887 1810433 1810566 "NSMP" 1810571 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-779 1799319 1799620 1799977 "NREP" 1800575 NIL NREP (NIL T) -7 NIL NIL NIL) (-778 1797910 1798162 1798520 "NPCOEF" 1799062 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-777 1796976 1797091 1797307 "NORMRETR" 1797791 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-776 1795017 1795307 1795716 "NORMPK" 1796684 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-775 1794702 1794730 1794854 "NORMMA" 1794983 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-774 1794502 1794659 1794688 "NONE" 1794693 T NONE (NIL) -8 NIL NIL NIL) (-773 1794291 1794320 1794389 "NONE1" 1794466 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-772 1793788 1793850 1794029 "NODE1" 1794223 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-771 1792073 1792924 1793179 "NNI" 1793526 T NNI (NIL) -8 NIL NIL 1793761) (-770 1790493 1790806 1791170 "NLINSOL" 1791741 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-769 1786734 1787729 1788628 "NIPROB" 1789614 T NIPROB (NIL) -8 NIL NIL NIL) (-768 1785491 1785725 1786027 "NFINTBAS" 1786496 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-767 1784665 1785141 1785182 "NETCLT" 1785354 NIL NETCLT (NIL T) -9 NIL 1785436 NIL) (-766 1783373 1783604 1783885 "NCODIV" 1784433 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-765 1783135 1783172 1783247 "NCNTFRAC" 1783330 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-764 1781315 1781679 1782099 "NCEP" 1782760 NIL NCEP (NIL T) -7 NIL NIL NIL) (-763 1780166 1780939 1780967 "NASRING" 1781077 T NASRING (NIL) -9 NIL 1781157 NIL) (-762 1779961 1780005 1780099 "NASRING-" 1780104 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-761 1779068 1779593 1779621 "NARNG" 1779738 T NARNG (NIL) -9 NIL 1779829 NIL) (-760 1778760 1778827 1778961 "NARNG-" 1778966 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-759 1777639 1777846 1778081 "NAGSP" 1778545 T NAGSP (NIL) -7 NIL NIL NIL) (-758 1768911 1770595 1772268 "NAGS" 1775986 T NAGS (NIL) -7 NIL NIL NIL) (-757 1767459 1767767 1768098 "NAGF07" 1768600 T NAGF07 (NIL) -7 NIL NIL NIL) (-756 1761997 1763288 1764595 "NAGF04" 1766172 T NAGF04 (NIL) -7 NIL NIL NIL) (-755 1754965 1756579 1758212 "NAGF02" 1760384 T NAGF02 (NIL) -7 NIL NIL NIL) (-754 1750189 1751289 1752406 "NAGF01" 1753868 T NAGF01 (NIL) -7 NIL NIL NIL) (-753 1743817 1745383 1746968 "NAGE04" 1748624 T NAGE04 (NIL) -7 NIL NIL NIL) (-752 1734986 1737107 1739237 "NAGE02" 1741707 T NAGE02 (NIL) -7 NIL NIL NIL) (-751 1730939 1731886 1732850 "NAGE01" 1734042 T NAGE01 (NIL) -7 NIL NIL NIL) (-750 1728734 1729268 1729826 "NAGD03" 1730401 T NAGD03 (NIL) -7 NIL NIL NIL) (-749 1720484 1722412 1724366 "NAGD02" 1726800 T NAGD02 (NIL) -7 NIL NIL NIL) (-748 1714295 1715720 1717160 "NAGD01" 1719064 T NAGD01 (NIL) -7 NIL NIL NIL) (-747 1710504 1711326 1712163 "NAGC06" 1713478 T NAGC06 (NIL) -7 NIL NIL NIL) (-746 1708969 1709301 1709657 "NAGC05" 1710168 T NAGC05 (NIL) -7 NIL NIL NIL) (-745 1708345 1708464 1708608 "NAGC02" 1708845 T NAGC02 (NIL) -7 NIL NIL NIL) (-744 1707304 1707887 1707927 "NAALG" 1708006 NIL NAALG (NIL T) -9 NIL 1708067 NIL) (-743 1707139 1707168 1707258 "NAALG-" 1707263 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-742 1701089 1702197 1703384 "MULTSQFR" 1706035 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-741 1700408 1700483 1700667 "MULTFACT" 1701001 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-740 1693132 1697045 1697098 "MTSCAT" 1698168 NIL MTSCAT (NIL T T) -9 NIL 1698683 NIL) (-739 1692844 1692898 1692990 "MTHING" 1693072 NIL MTHING (NIL T) -7 NIL NIL NIL) (-738 1692636 1692669 1692729 "MSYSCMD" 1692804 T MSYSCMD (NIL) -7 NIL NIL NIL) (-737 1688718 1691391 1691711 "MSET" 1692349 NIL MSET (NIL T) -8 NIL NIL NIL) (-736 1685787 1688279 1688320 "MSETAGG" 1688325 NIL MSETAGG (NIL T) -9 NIL 1688359 NIL) (-735 1681628 1683166 1683911 "MRING" 1685087 NIL MRING (NIL T T) -8 NIL NIL NIL) (-734 1681194 1681261 1681392 "MRF2" 1681555 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-733 1680812 1680847 1680991 "MRATFAC" 1681153 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-732 1678424 1678719 1679150 "MPRFF" 1680517 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-731 1672721 1678278 1678375 "MPOLY" 1678380 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-730 1672211 1672246 1672454 "MPCPF" 1672680 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-729 1671725 1671768 1671952 "MPC3" 1672162 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-728 1670920 1671001 1671222 "MPC2" 1671640 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-727 1669221 1669558 1669948 "MONOTOOL" 1670580 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-726 1668446 1668763 1668791 "MONOID" 1669010 T MONOID (NIL) -9 NIL 1669157 NIL) (-725 1667992 1668111 1668292 "MONOID-" 1668297 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-724 1658467 1664418 1664477 "MONOGEN" 1665151 NIL MONOGEN (NIL T T) -9 NIL 1665607 NIL) (-723 1655685 1656420 1657420 "MONOGEN-" 1657539 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-722 1654518 1654964 1654992 "MONADWU" 1655384 T MONADWU (NIL) -9 NIL 1655622 NIL) (-721 1653890 1654049 1654297 "MONADWU-" 1654302 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-720 1653249 1653493 1653521 "MONAD" 1653728 T MONAD (NIL) -9 NIL 1653840 NIL) (-719 1652934 1653012 1653144 "MONAD-" 1653149 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-718 1651223 1651847 1652126 "MOEBIUS" 1652687 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-717 1650501 1650905 1650945 "MODULE" 1650950 NIL MODULE (NIL T) -9 NIL 1650989 NIL) (-716 1650069 1650165 1650355 "MODULE-" 1650360 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-715 1647749 1648433 1648760 "MODRING" 1649893 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-714 1644693 1645854 1646375 "MODOP" 1647278 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-713 1643281 1643760 1644037 "MODMONOM" 1644556 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-712 1633322 1641572 1641986 "MODMON" 1642918 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-711 1630478 1632166 1632442 "MODFIELD" 1633197 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-710 1629455 1629759 1629949 "MMLFORM" 1630308 T MMLFORM (NIL) -8 NIL NIL NIL) (-709 1628981 1629024 1629203 "MMAP" 1629406 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-708 1627060 1627827 1627868 "MLO" 1628291 NIL MLO (NIL T) -9 NIL 1628533 NIL) (-707 1624426 1624942 1625544 "MLIFT" 1626541 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-706 1623817 1623901 1624055 "MKUCFUNC" 1624337 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-705 1623416 1623486 1623609 "MKRECORD" 1623740 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-704 1622463 1622625 1622853 "MKFUNC" 1623227 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-703 1621851 1621955 1622111 "MKFLCFN" 1622346 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-702 1621128 1621230 1621415 "MKBCFUNC" 1621744 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-701 1617835 1620682 1620818 "MINT" 1621012 T MINT (NIL) -8 NIL NIL NIL) (-700 1616647 1616890 1617167 "MHROWRED" 1617590 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-699 1612026 1615182 1615587 "MFLOAT" 1616262 T MFLOAT (NIL) -8 NIL NIL NIL) (-698 1611383 1611459 1611630 "MFINFACT" 1611938 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-697 1607698 1608546 1609430 "MESH" 1610519 T MESH (NIL) -7 NIL NIL NIL) (-696 1606088 1606400 1606753 "MDDFACT" 1607385 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-695 1602883 1605247 1605288 "MDAGG" 1605543 NIL MDAGG (NIL T) -9 NIL 1605686 NIL) (-694 1592623 1602176 1602383 "MCMPLX" 1602696 T MCMPLX (NIL) -8 NIL NIL NIL) (-693 1591764 1591910 1592110 "MCDEN" 1592472 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-692 1589654 1589924 1590304 "MCALCFN" 1591494 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-691 1588579 1588819 1589052 "MAYBE" 1589460 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-690 1586191 1586714 1587276 "MATSTOR" 1588050 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-689 1582148 1585563 1585811 "MATRIX" 1585976 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-688 1577912 1578621 1579357 "MATLIN" 1581505 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-687 1568018 1571204 1571281 "MATCAT" 1576161 NIL MATCAT (NIL T T T) -9 NIL 1577578 NIL) (-686 1564374 1565395 1566751 "MATCAT-" 1566756 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-685 1562968 1563121 1563454 "MATCAT2" 1564209 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-684 1561080 1561404 1561788 "MAPPKG3" 1562643 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-683 1560061 1560234 1560456 "MAPPKG2" 1560904 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-682 1558560 1558844 1559171 "MAPPKG1" 1559767 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-681 1557639 1557966 1558143 "MAPPAST" 1558403 T MAPPAST (NIL) -8 NIL NIL NIL) (-680 1557250 1557308 1557431 "MAPHACK3" 1557575 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-679 1556842 1556903 1557017 "MAPHACK2" 1557182 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-678 1556279 1556383 1556525 "MAPHACK1" 1556733 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-677 1554358 1554979 1555283 "MAGMA" 1556007 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-676 1553837 1554082 1554173 "MACROAST" 1554287 T MACROAST (NIL) -8 NIL NIL NIL) (-675 1550255 1552076 1552537 "M3D" 1553409 NIL M3D (NIL T) -8 NIL NIL NIL) (-674 1544361 1548624 1548665 "LZSTAGG" 1549447 NIL LZSTAGG (NIL T) -9 NIL 1549742 NIL) (-673 1540318 1541492 1542949 "LZSTAGG-" 1542954 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-672 1537405 1538209 1538696 "LWORD" 1539863 NIL LWORD (NIL T) -8 NIL NIL NIL) (-671 1536981 1537209 1537284 "LSTAST" 1537350 T LSTAST (NIL) -8 NIL NIL NIL) (-670 1530147 1536752 1536886 "LSQM" 1536891 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-669 1529371 1529510 1529738 "LSPP" 1530002 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-668 1527183 1527484 1527940 "LSMP" 1529060 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-667 1523962 1524636 1525366 "LSMP1" 1526485 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-666 1517839 1523129 1523170 "LSAGG" 1523232 NIL LSAGG (NIL T) -9 NIL 1523310 NIL) (-665 1514534 1515458 1516671 "LSAGG-" 1516676 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-664 1512133 1513678 1513927 "LPOLY" 1514329 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-663 1511715 1511800 1511923 "LPEFRAC" 1512042 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-662 1510036 1510809 1511062 "LO" 1511547 NIL LO (NIL T T T) -8 NIL NIL NIL) (-661 1509688 1509800 1509828 "LOGIC" 1509939 T LOGIC (NIL) -9 NIL 1510020 NIL) (-660 1509550 1509573 1509644 "LOGIC-" 1509649 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-659 1508743 1508883 1509076 "LODOOPS" 1509406 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-658 1506166 1508659 1508725 "LODO" 1508730 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-657 1504704 1504939 1505292 "LODOF" 1505913 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-656 1500922 1503353 1503394 "LODOCAT" 1503832 NIL LODOCAT (NIL T) -9 NIL 1504043 NIL) (-655 1500655 1500713 1500840 "LODOCAT-" 1500845 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-654 1497975 1500496 1500614 "LODO2" 1500619 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-653 1495410 1497912 1497957 "LODO1" 1497962 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-652 1494291 1494456 1494761 "LODEEF" 1495233 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-651 1489530 1492421 1492462 "LNAGG" 1493409 NIL LNAGG (NIL T) -9 NIL 1493853 NIL) (-650 1488677 1488891 1489233 "LNAGG-" 1489238 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-649 1484813 1485602 1486241 "LMOPS" 1488092 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-648 1484216 1484604 1484645 "LMODULE" 1484650 NIL LMODULE (NIL T) -9 NIL 1484676 NIL) (-647 1481414 1483861 1483984 "LMDICT" 1484126 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-646 1480820 1481041 1481082 "LLINSET" 1481273 NIL LLINSET (NIL T) -9 NIL 1481364 NIL) (-645 1480519 1480728 1480788 "LITERAL" 1480793 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-644 1473702 1479465 1479763 "LIST" 1480254 NIL LIST (NIL T) -8 NIL NIL NIL) (-643 1473227 1473301 1473440 "LIST3" 1473622 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-642 1472234 1472412 1472640 "LIST2" 1473045 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-641 1470368 1470680 1471079 "LIST2MAP" 1471881 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-640 1469964 1470201 1470242 "LINSET" 1470247 NIL LINSET (NIL T) -9 NIL 1470281 NIL) (-639 1468625 1469295 1469336 "LINEXP" 1469591 NIL LINEXP (NIL T) -9 NIL 1469740 NIL) (-638 1467272 1467532 1467829 "LINDEP" 1468377 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-637 1464039 1464758 1465535 "LIMITRF" 1466527 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-636 1462342 1462638 1463047 "LIMITPS" 1463734 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-635 1456770 1461853 1462081 "LIE" 1462163 NIL LIE (NIL T T) -8 NIL NIL NIL) (-634 1455718 1456187 1456227 "LIECAT" 1456367 NIL LIECAT (NIL T) -9 NIL 1456518 NIL) (-633 1455559 1455586 1455674 "LIECAT-" 1455679 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-632 1448055 1455008 1455173 "LIB" 1455414 T LIB (NIL) -8 NIL NIL NIL) (-631 1443690 1444573 1445508 "LGROBP" 1447172 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-630 1441688 1441962 1442312 "LF" 1443411 NIL LF (NIL T T) -7 NIL NIL NIL) (-629 1440528 1441220 1441248 "LFCAT" 1441455 T LFCAT (NIL) -9 NIL 1441594 NIL) (-628 1437430 1438060 1438748 "LEXTRIPK" 1439892 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-627 1434174 1435000 1435503 "LEXP" 1437010 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-626 1433650 1433895 1433987 "LETAST" 1434102 T LETAST (NIL) -8 NIL NIL NIL) (-625 1432048 1432361 1432762 "LEADCDET" 1433332 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-624 1431238 1431312 1431541 "LAZM3PK" 1431969 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-623 1426155 1429315 1429853 "LAUPOL" 1430750 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-622 1425734 1425778 1425939 "LAPLACE" 1426105 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-621 1423673 1424835 1425086 "LA" 1425567 NIL LA (NIL T T T) -8 NIL NIL NIL) (-620 1422667 1423251 1423292 "LALG" 1423354 NIL LALG (NIL T) -9 NIL 1423413 NIL) (-619 1422381 1422440 1422576 "LALG-" 1422581 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-618 1422216 1422240 1422281 "KVTFROM" 1422343 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-617 1421139 1421583 1421768 "KTVLOGIC" 1422051 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-616 1420974 1420998 1421039 "KRCFROM" 1421101 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-615 1419878 1420065 1420364 "KOVACIC" 1420774 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-614 1419713 1419737 1419778 "KONVERT" 1419840 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-613 1419548 1419572 1419613 "KOERCE" 1419675 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-612 1417378 1418141 1418518 "KERNEL" 1419204 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-611 1416874 1416955 1417087 "KERNEL2" 1417292 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-610 1410644 1415413 1415467 "KDAGG" 1415844 NIL KDAGG (NIL T T) -9 NIL 1416050 NIL) (-609 1410173 1410297 1410502 "KDAGG-" 1410507 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-608 1403321 1409834 1409989 "KAFILE" 1410051 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-607 1397749 1402832 1403060 "JORDAN" 1403142 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-606 1397128 1397398 1397519 "JOINAST" 1397648 T JOINAST (NIL) -8 NIL NIL NIL) (-605 1396974 1397033 1397088 "JAVACODE" 1397093 T JAVACODE (NIL) -8 NIL NIL NIL) (-604 1393226 1395179 1395233 "IXAGG" 1396162 NIL IXAGG (NIL T T) -9 NIL 1396621 NIL) (-603 1392145 1392451 1392870 "IXAGG-" 1392875 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-602 1387675 1392067 1392126 "IVECTOR" 1392131 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-601 1386441 1386678 1386944 "ITUPLE" 1387442 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-600 1384943 1385120 1385415 "ITRIGMNP" 1386263 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-599 1383688 1383892 1384175 "ITFUN3" 1384719 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-598 1383320 1383377 1383486 "ITFUN2" 1383625 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-597 1381122 1382182 1382481 "ITAYLOR" 1383054 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-596 1370067 1375259 1376422 "ISUPS" 1379992 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-595 1369171 1369311 1369547 "ISUMP" 1369914 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-594 1364385 1368972 1369051 "ISTRING" 1369124 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-593 1363861 1364106 1364198 "ISAST" 1364313 T ISAST (NIL) -8 NIL NIL NIL) (-592 1363070 1363152 1363368 "IRURPK" 1363775 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-591 1362006 1362207 1362447 "IRSN" 1362850 T IRSN (NIL) -7 NIL NIL NIL) (-590 1360077 1360432 1360861 "IRRF2F" 1361644 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-589 1359824 1359862 1359938 "IRREDFFX" 1360033 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-588 1358439 1358698 1358997 "IROOT" 1359557 NIL IROOT (NIL T) -7 NIL NIL NIL) (-587 1355043 1356123 1356815 "IR" 1357779 NIL IR (NIL T) -8 NIL NIL NIL) (-586 1352656 1353151 1353717 "IR2" 1354521 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-585 1351756 1351869 1352083 "IR2F" 1352539 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-584 1351547 1351581 1351641 "IPRNTPK" 1351716 T IPRNTPK (NIL) -7 NIL NIL NIL) (-583 1348126 1351436 1351505 "IPF" 1351510 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-582 1346453 1348051 1348108 "IPADIC" 1348113 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-581 1345765 1346013 1346143 "IP4ADDR" 1346343 T IP4ADDR (NIL) -8 NIL NIL NIL) (-580 1345238 1345469 1345579 "IOMODE" 1345675 T IOMODE (NIL) -8 NIL NIL NIL) (-579 1344311 1344835 1344962 "IOBFILE" 1345131 T IOBFILE (NIL) -8 NIL NIL NIL) (-578 1343799 1344215 1344243 "IOBCON" 1344248 T IOBCON (NIL) -9 NIL 1344269 NIL) (-577 1343310 1343368 1343551 "INVLAPLA" 1343735 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-576 1332958 1335312 1337698 "INTTR" 1340974 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-575 1329293 1330035 1330900 "INTTOOLS" 1332143 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-574 1328879 1328970 1329087 "INTSLPE" 1329196 T INTSLPE (NIL) -7 NIL NIL NIL) (-573 1326832 1328802 1328861 "INTRVL" 1328866 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-572 1324434 1324946 1325521 "INTRF" 1326317 NIL INTRF (NIL T) -7 NIL NIL NIL) (-571 1323845 1323942 1324084 "INTRET" 1324332 NIL INTRET (NIL T) -7 NIL NIL NIL) (-570 1321842 1322231 1322701 "INTRAT" 1323453 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-569 1319105 1319688 1320307 "INTPM" 1321327 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-568 1315850 1316449 1317187 "INTPAF" 1318491 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-567 1311029 1311991 1313042 "INTPACK" 1314819 T INTPACK (NIL) -7 NIL NIL NIL) (-566 1307909 1310758 1310885 "INT" 1310922 T INT (NIL) -8 NIL NIL NIL) (-565 1307161 1307313 1307521 "INTHERTR" 1307751 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-564 1306600 1306680 1306868 "INTHERAL" 1307075 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-563 1304446 1304889 1305346 "INTHEORY" 1306163 T INTHEORY (NIL) -7 NIL NIL NIL) (-562 1295852 1297473 1299245 "INTG0" 1302798 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-561 1276425 1281215 1286025 "INTFTBL" 1291062 T INTFTBL (NIL) -8 NIL NIL NIL) (-560 1275674 1275812 1275985 "INTFACT" 1276284 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-559 1273101 1273547 1274104 "INTEF" 1275228 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-558 1271468 1272207 1272235 "INTDOM" 1272536 T INTDOM (NIL) -9 NIL 1272743 NIL) (-557 1270837 1271011 1271253 "INTDOM-" 1271258 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-556 1267225 1269153 1269207 "INTCAT" 1270006 NIL INTCAT (NIL T) -9 NIL 1270327 NIL) (-555 1266697 1266800 1266928 "INTBIT" 1267117 T INTBIT (NIL) -7 NIL NIL NIL) (-554 1265396 1265550 1265857 "INTALG" 1266542 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-553 1264879 1264969 1265126 "INTAF" 1265300 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-552 1258222 1264689 1264829 "INTABL" 1264834 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-551 1257563 1258029 1258094 "INT8" 1258128 T INT8 (NIL) -8 NIL NIL 1258173) (-550 1256903 1257369 1257434 "INT64" 1257468 T INT64 (NIL) -8 NIL NIL 1257513) (-549 1256243 1256709 1256774 "INT32" 1256808 T INT32 (NIL) -8 NIL NIL 1256853) (-548 1255583 1256049 1256114 "INT16" 1256148 T INT16 (NIL) -8 NIL NIL 1256193) (-547 1250493 1253206 1253234 "INS" 1254168 T INS (NIL) -9 NIL 1254833 NIL) (-546 1247733 1248504 1249478 "INS-" 1249551 NIL INS- (NIL T) -8 NIL NIL NIL) (-545 1246508 1246735 1247033 "INPSIGN" 1247486 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-544 1245626 1245743 1245940 "INPRODPF" 1246388 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-543 1244520 1244637 1244874 "INPRODFF" 1245506 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-542 1243520 1243672 1243932 "INNMFACT" 1244356 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-541 1242717 1242814 1243002 "INMODGCD" 1243419 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-540 1241225 1241470 1241794 "INFSP" 1242462 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-539 1240409 1240526 1240709 "INFPROD0" 1241105 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-538 1237264 1238474 1238989 "INFORM" 1239902 T INFORM (NIL) -8 NIL NIL NIL) (-537 1236874 1236934 1237032 "INFORM1" 1237199 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-536 1236397 1236486 1236600 "INFINITY" 1236780 T INFINITY (NIL) -7 NIL NIL NIL) (-535 1235573 1236117 1236218 "INETCLTS" 1236316 T INETCLTS (NIL) -8 NIL NIL NIL) (-534 1234189 1234439 1234760 "INEP" 1235321 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-533 1233438 1234086 1234151 "INDE" 1234156 NIL INDE (NIL T) -8 NIL NIL NIL) (-532 1233002 1233070 1233187 "INCRMAPS" 1233365 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-531 1231820 1232271 1232477 "INBFILE" 1232816 T INBFILE (NIL) -8 NIL NIL NIL) (-530 1227119 1228056 1229000 "INBFF" 1230908 NIL INBFF (NIL T) -7 NIL NIL NIL) (-529 1226027 1226296 1226324 "INBCON" 1226837 T INBCON (NIL) -9 NIL 1227103 NIL) (-528 1225279 1225502 1225778 "INBCON-" 1225783 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-527 1224758 1225003 1225094 "INAST" 1225208 T INAST (NIL) -8 NIL NIL NIL) (-526 1224185 1224437 1224543 "IMPTAST" 1224672 T IMPTAST (NIL) -8 NIL NIL NIL) (-525 1220631 1224029 1224133 "IMATRIX" 1224138 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-524 1219343 1219466 1219781 "IMATQF" 1220487 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-523 1217563 1217790 1218127 "IMATLIN" 1219099 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-522 1212141 1217487 1217545 "ILIST" 1217550 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-521 1210046 1212001 1212114 "IIARRAY2" 1212119 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-520 1205444 1209957 1210021 "IFF" 1210026 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-519 1204791 1205061 1205177 "IFAST" 1205348 T IFAST (NIL) -8 NIL NIL NIL) (-518 1199786 1204083 1204271 "IFARRAY" 1204648 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-517 1198966 1199690 1199763 "IFAMON" 1199768 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-516 1198550 1198615 1198669 "IEVALAB" 1198876 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-515 1198225 1198293 1198453 "IEVALAB-" 1198458 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-514 1197856 1198139 1198202 "IDPO" 1198207 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-513 1197106 1197745 1197820 "IDPOAMS" 1197825 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-512 1196413 1196995 1197070 "IDPOAM" 1197075 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-511 1195472 1195748 1195801 "IDPC" 1196214 NIL IDPC (NIL T T) -9 NIL 1196363 NIL) (-510 1194941 1195364 1195437 "IDPAM" 1195442 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-509 1194317 1194833 1194906 "IDPAG" 1194911 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-508 1193962 1194153 1194228 "IDENT" 1194262 T IDENT (NIL) -8 NIL NIL NIL) (-507 1190217 1191065 1191960 "IDECOMP" 1193119 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-506 1183055 1184140 1185187 "IDEAL" 1189253 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-505 1182219 1182331 1182530 "ICDEN" 1182939 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-504 1181290 1181699 1181846 "ICARD" 1182092 T ICARD (NIL) -8 NIL NIL NIL) (-503 1179350 1179663 1180068 "IBPTOOLS" 1180967 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-502 1174957 1178970 1179083 "IBITS" 1179269 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-501 1171680 1172256 1172951 "IBATOOL" 1174374 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-500 1169459 1169921 1170454 "IBACHIN" 1171215 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-499 1167288 1169305 1169408 "IARRAY2" 1169413 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-498 1163394 1167214 1167271 "IARRAY1" 1167276 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-497 1157503 1161806 1162287 "IAN" 1162933 T IAN (NIL) -8 NIL NIL NIL) (-496 1157014 1157071 1157244 "IALGFACT" 1157440 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-495 1156542 1156655 1156683 "HYPCAT" 1156890 T HYPCAT (NIL) -9 NIL NIL NIL) (-494 1156080 1156197 1156383 "HYPCAT-" 1156388 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-493 1155675 1155875 1155958 "HOSTNAME" 1156017 T HOSTNAME (NIL) -8 NIL NIL NIL) (-492 1155520 1155557 1155598 "HOMOTOP" 1155603 NIL HOMOTOP (NIL T) -9 NIL 1155636 NIL) (-491 1152152 1153530 1153571 "HOAGG" 1154552 NIL HOAGG (NIL T) -9 NIL 1155231 NIL) (-490 1150746 1151145 1151671 "HOAGG-" 1151676 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-489 1144750 1150341 1150490 "HEXADEC" 1150617 T HEXADEC (NIL) -8 NIL NIL NIL) (-488 1143497 1143720 1143983 "HEUGCD" 1144527 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-487 1142573 1143334 1143464 "HELLFDIV" 1143469 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-486 1140752 1142350 1142438 "HEAP" 1142517 NIL HEAP (NIL T) -8 NIL NIL NIL) (-485 1140015 1140304 1140438 "HEADAST" 1140638 T HEADAST (NIL) -8 NIL NIL NIL) (-484 1133881 1139930 1139992 "HDP" 1139997 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-483 1127869 1133516 1133668 "HDMP" 1133782 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-482 1127193 1127333 1127497 "HB" 1127725 T HB (NIL) -7 NIL NIL NIL) (-481 1120579 1127039 1127143 "HASHTBL" 1127148 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-480 1120055 1120300 1120392 "HASAST" 1120507 T HASAST (NIL) -8 NIL NIL NIL) (-479 1117833 1119677 1119859 "HACKPI" 1119893 T HACKPI (NIL) -8 NIL NIL NIL) (-478 1113501 1117686 1117799 "GTSET" 1117804 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-477 1106916 1113379 1113477 "GSTBL" 1113482 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-476 1099194 1105947 1106212 "GSERIES" 1106707 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-475 1098335 1098752 1098780 "GROUP" 1098983 T GROUP (NIL) -9 NIL 1099117 NIL) (-474 1097701 1097860 1098111 "GROUP-" 1098116 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-473 1096068 1096389 1096776 "GROEBSOL" 1097378 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-472 1094982 1095270 1095321 "GRMOD" 1095850 NIL GRMOD (NIL T T) -9 NIL 1096018 NIL) (-471 1094750 1094786 1094914 "GRMOD-" 1094919 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-470 1090040 1091104 1092104 "GRIMAGE" 1093770 T GRIMAGE (NIL) -8 NIL NIL NIL) (-469 1088506 1088767 1089091 "GRDEF" 1089736 T GRDEF (NIL) -7 NIL NIL NIL) (-468 1087950 1088066 1088207 "GRAY" 1088385 T GRAY (NIL) -7 NIL NIL NIL) (-467 1087137 1087543 1087594 "GRALG" 1087747 NIL GRALG (NIL T T) -9 NIL 1087840 NIL) (-466 1086798 1086871 1087034 "GRALG-" 1087039 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-465 1083575 1086383 1086561 "GPOLSET" 1086705 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-464 1082929 1082986 1083244 "GOSPER" 1083512 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-463 1078661 1079367 1079893 "GMODPOL" 1082628 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-462 1077666 1077850 1078088 "GHENSEL" 1078473 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-461 1071822 1072665 1073685 "GENUPS" 1076750 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-460 1071519 1071570 1071659 "GENUFACT" 1071765 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-459 1070931 1071008 1071173 "GENPGCD" 1071437 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-458 1070405 1070440 1070653 "GENMFACT" 1070890 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-457 1068971 1069228 1069535 "GENEEZ" 1070148 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-456 1063117 1068582 1068744 "GDMP" 1068894 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-455 1052459 1056888 1057994 "GCNAALG" 1062100 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-454 1050786 1051648 1051676 "GCDDOM" 1051931 T GCDDOM (NIL) -9 NIL 1052088 NIL) (-453 1050256 1050383 1050598 "GCDDOM-" 1050603 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-452 1048928 1049113 1049417 "GB" 1050035 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-451 1037544 1039874 1042266 "GBINTERN" 1046619 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-450 1035381 1035673 1036094 "GBF" 1037219 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-449 1034162 1034327 1034594 "GBEUCLID" 1035197 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-448 1033511 1033636 1033785 "GAUSSFAC" 1034033 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-447 1031878 1032180 1032494 "GALUTIL" 1033230 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-446 1030186 1030460 1030784 "GALPOLYU" 1031605 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-445 1027551 1027841 1028248 "GALFACTU" 1029883 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-444 1019356 1020856 1022464 "GALFACT" 1025983 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-443 1016744 1017402 1017430 "FVFUN" 1018586 T FVFUN (NIL) -9 NIL 1019306 NIL) (-442 1016010 1016192 1016220 "FVC" 1016511 T FVC (NIL) -9 NIL 1016694 NIL) (-441 1015653 1015835 1015903 "FUNDESC" 1015962 T FUNDESC (NIL) -8 NIL NIL NIL) (-440 1015268 1015450 1015531 "FUNCTION" 1015605 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-439 1013012 1013590 1014056 "FT" 1014822 T FT (NIL) -8 NIL NIL NIL) (-438 1011803 1012313 1012516 "FTEM" 1012829 T FTEM (NIL) -8 NIL NIL NIL) (-437 1010094 1010383 1010780 "FSUPFACT" 1011494 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-436 1008491 1008780 1009112 "FST" 1009782 T FST (NIL) -8 NIL NIL NIL) (-435 1007690 1007796 1007984 "FSRED" 1008373 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-434 1006389 1006645 1006992 "FSPRMELT" 1007405 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-433 1003695 1004133 1004619 "FSPECF" 1005952 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-432 985333 993664 993705 "FS" 997589 NIL FS (NIL T) -9 NIL 999878 NIL) (-431 973976 976969 981026 "FS-" 981326 NIL FS- (NIL T T) -8 NIL NIL NIL) (-430 973504 973558 973728 "FSINT" 973917 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-429 971796 972497 972800 "FSERIES" 973283 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-428 970838 970954 971178 "FSCINT" 971676 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-427 967046 969782 969823 "FSAGG" 970193 NIL FSAGG (NIL T) -9 NIL 970452 NIL) (-426 964808 965409 966205 "FSAGG-" 966300 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-425 963850 963993 964220 "FSAGG2" 964661 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-424 961532 961812 962359 "FS2UPS" 963568 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-423 961166 961209 961338 "FS2" 961483 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-422 960044 960215 960517 "FS2EXPXP" 960991 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-421 959470 959585 959737 "FRUTIL" 959924 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-420 950883 954965 956323 "FR" 958144 NIL FR (NIL T) -8 NIL NIL NIL) (-419 945852 948526 948566 "FRNAALG" 949962 NIL FRNAALG (NIL T) -9 NIL 950569 NIL) (-418 941525 942601 943876 "FRNAALG-" 944626 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-417 941163 941206 941333 "FRNAAF2" 941476 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-416 939543 940017 940312 "FRMOD" 940975 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-415 937294 937926 938243 "FRIDEAL" 939334 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-414 936489 936576 936865 "FRIDEAL2" 937201 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-413 935622 936036 936077 "FRETRCT" 936082 NIL FRETRCT (NIL T) -9 NIL 936258 NIL) (-412 934734 934965 935316 "FRETRCT-" 935321 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-411 931822 933032 933091 "FRAMALG" 933973 NIL FRAMALG (NIL T T) -9 NIL 934265 NIL) (-410 929956 930411 931041 "FRAMALG-" 931264 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-409 923877 929431 929707 "FRAC" 929712 NIL FRAC (NIL T) -8 NIL NIL NIL) (-408 923513 923570 923677 "FRAC2" 923814 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-407 923149 923206 923313 "FR2" 923450 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-406 917662 920555 920583 "FPS" 921702 T FPS (NIL) -9 NIL 922259 NIL) (-405 917111 917220 917384 "FPS-" 917530 NIL FPS- (NIL T) -8 NIL NIL NIL) (-404 914413 916082 916110 "FPC" 916335 T FPC (NIL) -9 NIL 916477 NIL) (-403 914206 914246 914343 "FPC-" 914348 NIL FPC- (NIL T) -8 NIL NIL NIL) (-402 912996 913694 913735 "FPATMAB" 913740 NIL FPATMAB (NIL T) -9 NIL 913892 NIL) (-401 910669 911172 911598 "FPARFRAC" 912633 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-400 906062 906561 907243 "FORTRAN" 910101 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-399 903778 904278 904817 "FORT" 905543 T FORT (NIL) -7 NIL NIL NIL) (-398 901454 902016 902044 "FORTFN" 903104 T FORTFN (NIL) -9 NIL 903728 NIL) (-397 901218 901268 901296 "FORTCAT" 901355 T FORTCAT (NIL) -9 NIL 901417 NIL) (-396 899324 899834 900224 "FORMULA" 900848 T FORMULA (NIL) -8 NIL NIL NIL) (-395 899112 899142 899211 "FORMULA1" 899288 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-394 898635 898687 898860 "FORDER" 899054 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-393 897731 897895 898088 "FOP" 898462 T FOP (NIL) -7 NIL NIL NIL) (-392 896312 897011 897185 "FNLA" 897613 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-391 895041 895456 895484 "FNCAT" 895944 T FNCAT (NIL) -9 NIL 896204 NIL) (-390 894580 895000 895028 "FNAME" 895033 T FNAME (NIL) -8 NIL NIL NIL) (-389 893143 894106 894134 "FMTC" 894139 T FMTC (NIL) -9 NIL 894175 NIL) (-388 889476 890666 891295 "FMONOID" 892547 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-387 888668 889218 889367 "FM" 889372 NIL FM (NIL T T) -8 NIL NIL NIL) (-386 886092 886738 886766 "FMFUN" 887910 T FMFUN (NIL) -9 NIL 888618 NIL) (-385 885361 885542 885570 "FMC" 885860 T FMC (NIL) -9 NIL 886042 NIL) (-384 882440 883300 883354 "FMCAT" 884549 NIL FMCAT (NIL T T) -9 NIL 885044 NIL) (-383 881306 882206 882306 "FM1" 882385 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-382 879080 879496 879990 "FLOATRP" 880857 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-381 872655 876809 877430 "FLOAT" 878479 T FLOAT (NIL) -8 NIL NIL NIL) (-380 870093 870593 871171 "FLOATCP" 872122 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-379 868833 869671 869712 "FLINEXP" 869717 NIL FLINEXP (NIL T) -9 NIL 869810 NIL) (-378 867987 868222 868550 "FLINEXP-" 868555 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-377 867063 867207 867431 "FLASORT" 867839 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-376 864179 865047 865099 "FLALG" 866326 NIL FLALG (NIL T T) -9 NIL 866793 NIL) (-375 857915 861665 861706 "FLAGG" 862968 NIL FLAGG (NIL T) -9 NIL 863620 NIL) (-374 856641 856980 857470 "FLAGG-" 857475 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-373 855683 855826 856053 "FLAGG2" 856494 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-372 852534 853542 853601 "FINRALG" 854729 NIL FINRALG (NIL T T) -9 NIL 855237 NIL) (-371 851694 851923 852262 "FINRALG-" 852267 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-370 851074 851313 851341 "FINITE" 851537 T FINITE (NIL) -9 NIL 851644 NIL) (-369 843431 845618 845658 "FINAALG" 849325 NIL FINAALG (NIL T) -9 NIL 850778 NIL) (-368 838763 839813 840957 "FINAALG-" 842336 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-367 838131 838518 838621 "FILE" 838693 NIL FILE (NIL T) -8 NIL NIL NIL) (-366 836789 837127 837181 "FILECAT" 837865 NIL FILECAT (NIL T T) -9 NIL 838081 NIL) (-365 834505 836033 836061 "FIELD" 836101 T FIELD (NIL) -9 NIL 836181 NIL) (-364 833125 833510 834021 "FIELD-" 834026 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-363 830975 831760 832107 "FGROUP" 832811 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-362 830065 830229 830449 "FGLMICPK" 830807 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-361 825897 829990 830047 "FFX" 830052 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-360 825498 825559 825694 "FFSLPE" 825830 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-359 821487 822270 823066 "FFPOLY" 824734 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-358 820991 821027 821236 "FFPOLY2" 821445 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-357 816834 820910 820973 "FFP" 820978 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-356 812232 816745 816809 "FF" 816814 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-355 807358 811575 811765 "FFNBX" 812086 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-354 802287 806493 806751 "FFNBP" 807212 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-353 796920 801571 801782 "FFNB" 802120 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-352 795752 795950 796265 "FFINTBAS" 796717 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-351 791821 794041 794069 "FFIELDC" 794689 T FFIELDC (NIL) -9 NIL 795065 NIL) (-350 790483 790854 791351 "FFIELDC-" 791356 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-349 790052 790098 790222 "FFHOM" 790425 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-348 787747 788234 788751 "FFF" 789567 NIL FFF (NIL T) -7 NIL NIL NIL) (-347 783365 787489 787590 "FFCGX" 787690 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-346 778986 783097 783204 "FFCGP" 783308 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-345 774169 778713 778821 "FFCG" 778922 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-344 755565 764646 764732 "FFCAT" 769897 NIL FFCAT (NIL T T T) -9 NIL 771348 NIL) (-343 750763 751810 753124 "FFCAT-" 754354 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-342 750174 750217 750452 "FFCAT2" 750714 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-341 739495 743146 744366 "FEXPR" 749026 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-340 738495 738930 738971 "FEVALAB" 739055 NIL FEVALAB (NIL T) -9 NIL 739316 NIL) (-339 737654 737864 738202 "FEVALAB-" 738207 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-338 736220 737037 737240 "FDIV" 737553 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-337 733240 733981 734096 "FDIVCAT" 735664 NIL FDIVCAT (NIL T T T T) -9 NIL 736101 NIL) (-336 733002 733029 733199 "FDIVCAT-" 733204 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-335 732222 732309 732586 "FDIV2" 732909 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-334 731224 731538 731733 "FCTRDATA" 732047 T FCTRDATA (NIL) -8 NIL NIL NIL) (-333 729910 730169 730458 "FCPAK1" 730955 T FCPAK1 (NIL) -7 NIL NIL NIL) (-332 729009 729410 729551 "FCOMP" 729801 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-331 712711 716159 719697 "FC" 725491 T FC (NIL) -8 NIL NIL NIL) (-330 705074 709102 709142 "FAXF" 710944 NIL FAXF (NIL T) -9 NIL 711636 NIL) (-329 702350 703008 703833 "FAXF-" 704298 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-328 697402 701726 701902 "FARRAY" 702207 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-327 692296 694363 694416 "FAMR" 695439 NIL FAMR (NIL T T) -9 NIL 695899 NIL) (-326 691186 691488 691923 "FAMR-" 691928 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-325 690355 691108 691161 "FAMONOID" 691166 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-324 688141 688851 688904 "FAMONC" 689845 NIL FAMONC (NIL T T) -9 NIL 690231 NIL) (-323 686805 687895 688032 "FAGROUP" 688037 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-322 684600 684919 685322 "FACUTIL" 686486 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-321 683699 683884 684106 "FACTFUNC" 684410 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-320 676121 683002 683201 "EXPUPXS" 683555 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-319 673604 674144 674730 "EXPRTUBE" 675555 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-318 669875 670467 671197 "EXPRODE" 672943 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-317 655360 668524 668953 "EXPR" 669479 NIL EXPR (NIL T) -8 NIL NIL NIL) (-316 649914 650501 651307 "EXPR2UPS" 654658 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-315 649546 649603 649712 "EXPR2" 649851 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-314 640936 648699 648989 "EXPEXPAN" 649383 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-313 640736 640893 640922 "EXIT" 640927 T EXIT (NIL) -8 NIL NIL NIL) (-312 640216 640460 640551 "EXITAST" 640665 T EXITAST (NIL) -8 NIL NIL NIL) (-311 639843 639905 640018 "EVALCYC" 640148 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-310 639384 639502 639543 "EVALAB" 639713 NIL EVALAB (NIL T) -9 NIL 639817 NIL) (-309 638865 638987 639208 "EVALAB-" 639213 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-308 636233 637535 637563 "EUCDOM" 638118 T EUCDOM (NIL) -9 NIL 638468 NIL) (-307 634638 635080 635670 "EUCDOM-" 635675 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-306 622176 624936 627686 "ESTOOLS" 631908 T ESTOOLS (NIL) -7 NIL NIL NIL) (-305 621808 621865 621974 "ESTOOLS2" 622113 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-304 621559 621601 621681 "ESTOOLS1" 621760 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-303 615596 617204 617232 "ES" 620000 T ES (NIL) -9 NIL 621410 NIL) (-302 610543 611830 613647 "ES-" 613811 NIL ES- (NIL T) -8 NIL NIL NIL) (-301 606917 607678 608458 "ESCONT" 609783 T ESCONT (NIL) -7 NIL NIL NIL) (-300 606662 606694 606776 "ESCONT1" 606879 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-299 606337 606387 606487 "ES2" 606606 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-298 605967 606025 606134 "ES1" 606273 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-297 605183 605312 605488 "ERROR" 605811 T ERROR (NIL) -7 NIL NIL NIL) (-296 598575 605042 605133 "EQTBL" 605138 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-295 591078 593889 595338 "EQ" 597159 NIL -2114 (NIL T) -8 NIL NIL NIL) (-294 590710 590767 590876 "EQ2" 591015 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-293 585999 587048 588141 "EP" 589649 NIL EP (NIL T) -7 NIL NIL NIL) (-292 584599 584890 585196 "ENV" 585713 T ENV (NIL) -8 NIL NIL NIL) (-291 583693 584247 584275 "ENTIRER" 584280 T ENTIRER (NIL) -9 NIL 584326 NIL) (-290 580160 581648 582018 "EMR" 583492 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-289 579304 579489 579543 "ELTAGG" 579923 NIL ELTAGG (NIL T T) -9 NIL 580134 NIL) (-288 579023 579085 579226 "ELTAGG-" 579231 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-287 578812 578841 578895 "ELTAB" 578979 NIL ELTAB (NIL T T) -9 NIL NIL NIL) (-286 577938 578084 578283 "ELFUTS" 578663 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-285 577680 577736 577764 "ELEMFUN" 577869 T ELEMFUN (NIL) -9 NIL NIL NIL) (-284 577550 577571 577639 "ELEMFUN-" 577644 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-283 572394 575650 575691 "ELAGG" 576631 NIL ELAGG (NIL T) -9 NIL 577094 NIL) (-282 570679 571113 571776 "ELAGG-" 571781 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-281 569344 569622 569915 "ELABEXPR" 570406 T ELABEXPR (NIL) -8 NIL NIL NIL) (-280 562208 564011 564838 "EFUPXS" 568620 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-279 555658 557459 558269 "EFULS" 561484 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-278 553143 553501 553973 "EFSTRUC" 555290 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-277 542934 544500 546048 "EF" 551658 NIL EF (NIL T T) -7 NIL NIL NIL) (-276 542008 542419 542568 "EAB" 542805 T EAB (NIL) -8 NIL NIL NIL) (-275 541190 541967 541995 "E04UCFA" 542000 T E04UCFA (NIL) -8 NIL NIL NIL) (-274 540372 541149 541177 "E04NAFA" 541182 T E04NAFA (NIL) -8 NIL NIL NIL) (-273 539554 540331 540359 "E04MBFA" 540364 T E04MBFA (NIL) -8 NIL NIL NIL) (-272 538736 539513 539541 "E04JAFA" 539546 T E04JAFA (NIL) -8 NIL NIL NIL) (-271 537920 538695 538723 "E04GCFA" 538728 T E04GCFA (NIL) -8 NIL NIL NIL) (-270 537104 537879 537907 "E04FDFA" 537912 T E04FDFA (NIL) -8 NIL NIL NIL) (-269 536286 537063 537091 "E04DGFA" 537096 T E04DGFA (NIL) -8 NIL NIL NIL) (-268 530459 531811 533175 "E04AGNT" 534942 T E04AGNT (NIL) -7 NIL NIL NIL) (-267 529139 529645 529685 "DVARCAT" 530160 NIL DVARCAT (NIL T) -9 NIL 530359 NIL) (-266 528343 528555 528869 "DVARCAT-" 528874 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-265 521480 528142 528271 "DSMP" 528276 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-264 516261 517425 518493 "DROPT" 520432 T DROPT (NIL) -8 NIL NIL NIL) (-263 515926 515985 516083 "DROPT1" 516196 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-262 511041 512167 513304 "DROPT0" 514809 T DROPT0 (NIL) -7 NIL NIL NIL) (-261 509386 509711 510097 "DRAWPT" 510675 T DRAWPT (NIL) -7 NIL NIL NIL) (-260 503973 504896 505975 "DRAW" 508360 NIL DRAW (NIL T) -7 NIL NIL NIL) (-259 503606 503659 503777 "DRAWHACK" 503914 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-258 502337 502606 502897 "DRAWCX" 503335 T DRAWCX (NIL) -7 NIL NIL NIL) (-257 501852 501921 502072 "DRAWCURV" 502263 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-256 492320 494282 496397 "DRAWCFUN" 499757 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-255 489086 491015 491056 "DQAGG" 491685 NIL DQAGG (NIL T) -9 NIL 491958 NIL) (-254 477210 483679 483762 "DPOLCAT" 485614 NIL DPOLCAT (NIL T T T T) -9 NIL 486159 NIL) (-253 472046 473395 475353 "DPOLCAT-" 475358 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-252 465168 471907 472005 "DPMO" 472010 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-251 458193 464948 465115 "DPMM" 465120 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-250 457671 457885 457983 "DOMTMPLT" 458115 T DOMTMPLT (NIL) -8 NIL NIL NIL) (-249 457104 457473 457553 "DOMCTOR" 457611 T DOMCTOR (NIL) -8 NIL NIL NIL) (-248 456372 456626 456763 "DOMAIN" 456987 T DOMAIN (NIL) -8 NIL NIL NIL) (-247 450360 456007 456159 "DMP" 456273 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-246 449960 450016 450160 "DLP" 450298 NIL DLP (NIL T) -7 NIL NIL NIL) (-245 443782 449287 449477 "DLIST" 449802 NIL DLIST (NIL T) -8 NIL NIL NIL) (-244 440579 442635 442676 "DLAGG" 443226 NIL DLAGG (NIL T) -9 NIL 443456 NIL) (-243 439255 439919 439947 "DIVRING" 440039 T DIVRING (NIL) -9 NIL 440122 NIL) (-242 438492 438682 438982 "DIVRING-" 438987 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-241 436594 436951 437357 "DISPLAY" 438106 T DISPLAY (NIL) -7 NIL NIL NIL) (-240 430482 436508 436571 "DIRPROD" 436576 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-239 429330 429533 429798 "DIRPROD2" 430275 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-238 418105 424111 424164 "DIRPCAT" 424574 NIL DIRPCAT (NIL NIL T) -9 NIL 425414 NIL) (-237 415431 416073 416954 "DIRPCAT-" 417291 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-236 414718 414878 415064 "DIOSP" 415265 T DIOSP (NIL) -7 NIL NIL NIL) (-235 411373 413630 413671 "DIOPS" 414105 NIL DIOPS (NIL T) -9 NIL 414334 NIL) (-234 410922 411036 411227 "DIOPS-" 411232 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-233 409745 410373 410401 "DIFRING" 410588 T DIFRING (NIL) -9 NIL 410698 NIL) (-232 409391 409468 409620 "DIFRING-" 409625 NIL DIFRING- (NIL T) -8 NIL NIL NIL) (-231 407127 408399 408440 "DIFEXT" 408803 NIL DIFEXT (NIL T) -9 NIL 409097 NIL) (-230 405412 405840 406506 "DIFEXT-" 406511 NIL DIFEXT- (NIL T T) -8 NIL NIL NIL) (-229 402687 404944 404985 "DIAGG" 404990 NIL DIAGG (NIL T) -9 NIL 405010 NIL) (-228 402071 402228 402480 "DIAGG-" 402485 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-227 397488 401030 401307 "DHMATRIX" 401840 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-226 393100 394009 395019 "DFSFUN" 396498 T DFSFUN (NIL) -7 NIL NIL NIL) (-225 388178 392031 392343 "DFLOAT" 392808 T DFLOAT (NIL) -8 NIL NIL NIL) (-224 386441 386722 387111 "DFINTTLS" 387886 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-223 383470 384462 384862 "DERHAM" 386107 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-222 381271 383245 383334 "DEQUEUE" 383414 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-221 380525 380658 380841 "DEGRED" 381133 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-220 376955 377700 378546 "DEFINTRF" 379753 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-219 374510 374979 375571 "DEFINTEF" 376474 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-218 373860 374130 374245 "DEFAST" 374415 T DEFAST (NIL) -8 NIL NIL NIL) (-217 367864 373455 373604 "DECIMAL" 373731 T DECIMAL (NIL) -8 NIL NIL NIL) (-216 365376 365834 366340 "DDFACT" 367408 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-215 364972 365015 365166 "DBLRESP" 365327 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-214 362844 363205 363565 "DBASE" 364739 NIL DBASE (NIL T) -8 NIL NIL NIL) (-213 362086 362324 362470 "DATAARY" 362743 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-212 361192 362045 362073 "D03FAFA" 362078 T D03FAFA (NIL) -8 NIL NIL NIL) (-211 360299 361151 361179 "D03EEFA" 361184 T D03EEFA (NIL) -8 NIL NIL NIL) (-210 358249 358715 359204 "D03AGNT" 359830 T D03AGNT (NIL) -7 NIL NIL NIL) (-209 357538 358208 358236 "D02EJFA" 358241 T D02EJFA (NIL) -8 NIL NIL NIL) (-208 356827 357497 357525 "D02CJFA" 357530 T D02CJFA (NIL) -8 NIL NIL NIL) (-207 356116 356786 356814 "D02BHFA" 356819 T D02BHFA (NIL) -8 NIL NIL NIL) (-206 355405 356075 356103 "D02BBFA" 356108 T D02BBFA (NIL) -8 NIL NIL NIL) (-205 348602 350191 351797 "D02AGNT" 353819 T D02AGNT (NIL) -7 NIL NIL NIL) (-204 346370 346893 347439 "D01WGTS" 348076 T D01WGTS (NIL) -7 NIL NIL NIL) (-203 345437 346329 346357 "D01TRNS" 346362 T D01TRNS (NIL) -8 NIL NIL NIL) (-202 344505 345396 345424 "D01GBFA" 345429 T D01GBFA (NIL) -8 NIL NIL NIL) (-201 343573 344464 344492 "D01FCFA" 344497 T D01FCFA (NIL) -8 NIL NIL NIL) (-200 342641 343532 343560 "D01ASFA" 343565 T D01ASFA (NIL) -8 NIL NIL NIL) (-199 341709 342600 342628 "D01AQFA" 342633 T D01AQFA (NIL) -8 NIL NIL NIL) (-198 340777 341668 341696 "D01APFA" 341701 T D01APFA (NIL) -8 NIL NIL NIL) (-197 339845 340736 340764 "D01ANFA" 340769 T D01ANFA (NIL) -8 NIL NIL NIL) (-196 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(-28 16666 17156 17918 "ACFS-" 17923 NIL ACFS- (NIL T T) -8 NIL NIL NIL) (-27 12784 14713 14739 "ACF" 15618 T ACF (NIL) -9 NIL 16031 NIL) (-26 11488 11822 12315 "ACF-" 12320 NIL ACF- (NIL T) -8 NIL NIL NIL) (-25 11060 11255 11281 "ABELSG" 11373 T ABELSG (NIL) -9 NIL 11438 NIL) (-24 10927 10952 11018 "ABELSG-" 11023 NIL ABELSG- (NIL T) -8 NIL NIL NIL) (-23 10270 10557 10583 "ABELMON" 10753 T ABELMON (NIL) -9 NIL 10865 NIL) (-22 9934 10018 10156 "ABELMON-" 10161 NIL ABELMON- (NIL T) -8 NIL NIL NIL) (-21 9282 9654 9680 "ABELGRP" 9752 T ABELGRP (NIL) -9 NIL 9827 NIL) (-20 8745 8874 9090 "ABELGRP-" 9095 NIL ABELGRP- (NIL T) -8 NIL NIL NIL) (-19 4334 8084 8123 "A1AGG" 8128 NIL A1AGG (NIL T) -9 NIL 8168 NIL) (-18 30 1252 2814 "A1AGG-" 2819 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 1beb7866..3f082283 100644 --- a/src/share/algebra/operation.daase +++ b/src/share/algebra/operation.daase @@ -1,41 +1,13 @@ -(732389 . 3453749794) -(((*1 *2 *1) - (|partial| -12 (-4 *1 (-1247 *3 *2)) (-4 *3 (-1049)) - (-4 *2 (-1224 *3))))) -(((*1 *2 *3 *3) - (-12 (-5 *3 (-644 *7)) (-4 *7 (-1064 *4 *5 *6)) (-4 *4 (-454)) - (-4 *5 (-793)) (-4 *6 (-850)) (-5 *2 (-112)) - (-5 *1 (-988 *4 *5 *6 *7 *8)) (-4 *8 (-1070 *4 *5 *6 *7)))) - ((*1 *2 *3 *3) - (-12 (-5 *3 (-644 *7)) (-4 *7 (-1064 *4 *5 *6)) (-4 *4 (-454)) - (-4 *5 (-793)) (-4 *6 (-850)) (-5 *2 (-112)) - (-5 *1 (-1106 *4 *5 *6 *7 *8)) (-4 *8 (-1070 *4 *5 *6 *7))))) -(((*1 *2 *1) (-12 (-4 *1 (-995 *2)) (-4 *2 (-1214))))) -(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-281))))) -(((*1 *2 *3 *3 *4 *3) - (-12 (-5 *3 (-566)) (-5 *4 (-689 (-225))) (-5 *2 (-1035)) - (-5 *1 (-755))))) -(((*1 *2 *3) - (-12 (-5 *2 (-566)) (-5 *1 (-447 *3)) (-4 *3 (-406)) (-4 *3 (-1049))))) -(((*1 *1 *1 *2) - (-12 (-5 *2 (-112)) (-5 *1 (-1139 *3 *4)) (-4 *3 (-13 (-1099) (-34))) - (-4 *4 (-13 (-1099) (-34)))))) -(((*1 *2 *1) - (-12 (-4 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(-566)) (-4 *1 (-57 *2 *4 *5)) (-4 *2 (-1214)) (-4 *4 (-375 *2)) (-4 *5 (-375 *2)))) @@ -67,14 +39,14 @@ (-12 (-5 *3 (-1175)) (-5 *2 (-245 (-1157))) (-5 *1 (-214 *4)) (-4 *4 (-13 (-850) - (-10 -8 (-15 -4386 ((-1157) $ *3)) (-15 -1697 ((-1269) $)) - (-15 -2509 ((-1269) $))))))) + (-10 -8 (-15 -4393 ((-1157) $ *3)) (-15 -1736 ((-1269) $)) + (-15 -3018 ((-1269) $))))))) ((*1 *1 *1 *2) (-12 (-5 *2 (-989)) (-5 *1 (-214 *3)) (-4 *3 (-13 (-850) - (-10 -8 (-15 -4386 ((-1157) $ (-1175))) (-15 -1697 ((-1269) $)) - (-15 -2509 ((-1269) $))))))) + (-10 -8 (-15 -4393 ((-1157) $ (-1175))) (-15 -1736 ((-1269) $)) + (-15 -3018 ((-1269) $))))))) ((*1 *2 *1 *3) (-12 (-5 *3 "count") (-5 *2 (-771)) (-5 *1 (-245 *4)) (-4 *4 (-850)))) ((*1 *1 *1 *2) (-12 (-5 *2 "sort") (-5 *1 (-245 *3)) (-4 *3 (-850)))) @@ -161,100 +133,54 @@ (-12 (-5 *2 "rest") (-4 *1 (-1252 *3)) (-4 *3 (-1214)))) ((*1 *2 *1 *3) (-12 (-5 *3 "first") (-4 *1 (-1252 *2)) (-4 *2 (-1214))))) -(((*1 *2 *1) - (-12 (-4 *1 (-57 *3 *4 *5)) (-4 *3 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