diff options
| author | dos-reis <gdr@axiomatics.org> | 2009-11-09 01:58:44 +0000 |
|---|---|---|
| committer | dos-reis <gdr@axiomatics.org> | 2009-11-09 01:58:44 +0000 |
| commit | beb923feadbabd89f92eb61dc6284d41eeccd540 (patch) | |
| tree | 01c1c0e0eb6a9c2ab0bfa0aed9250e1f3f99cfaa /src/share | |
| parent | 90e75eb56b50a8fb87dc241f5bba0c78aec8c973 (diff) | |
| download | open-axiom-beb923feadbabd89f92eb61dc6284d41eeccd540.tar.gz | |
Fix SF/2893009
* algebra/syntax.spad.pamphlet (ParameterAst): New.
(HeadAst): Use it.
* testsuite/interpreter/sf-2893009.input: Likewise.
* testsuite/interpreter/sf-2893009.spad: New.
Diffstat (limited to 'src/share')
| -rw-r--r-- | src/share/algebra/browse.daase | 2154 | ||||
| -rw-r--r-- | src/share/algebra/category.daase | 2853 | ||||
| -rw-r--r-- | src/share/algebra/compress.daase | 1336 | ||||
| -rw-r--r-- | src/share/algebra/interp.daase | 9974 | ||||
| -rw-r--r-- | src/share/algebra/operation.daase | 30826 |
5 files changed, 23579 insertions, 23564 deletions
diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase index 50bb40ed..ee6ecd1d 100644 --- a/src/share/algebra/browse.daase +++ b/src/share/algebra/browse.daase @@ -1,12 +1,12 @@ -(2262676 . 3465761899) +(2263553 . 3466723534) (-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)) +((-4419 . T) (-4418 . T)) NIL (-20 S) ((|constructor| (NIL "The class of abelian groups,{} \\spadignore{i.e.} additive monoids where each element has an additive inverse. \\blankline")) (- (($ $ $) "\\spad{x-y} is the difference of \\spad{x} and \\spad{y} \\spadignore{i.e.} \\spad{x + (-y)}.") (($ $) "\\spad{-x} is the additive inverse of \\spad{x}"))) @@ -38,7 +38,7 @@ NIL NIL (-27) ((|constructor| (NIL "Model for algebraically closed fields.")) (|zerosOf| (((|List| $) (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{zerosOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\spad{zerosOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) (|Polynomial| $)) "\\spad{zerosOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible. Otherwise they are implicit algebraic quantities. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|zeroOf| (($ (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{zeroOf(p, y)} returns \\spad{y} such that \\spad{p(y) = 0}; if possible,{} \\spad{y} is expressed in terms of radicals. Otherwise it is an implicit algebraic quantity which displays as \\spad{'y}.") (($ (|SparseUnivariatePolynomial| $)) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}; if possible,{} \\spad{y} is expressed in terms of radicals. Otherwise it is an implicit algebraic quantity.") (($ (|Polynomial| $)) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. If possible,{} \\spad{y} is expressed in terms of radicals. Otherwise it is an implicit algebraic quantity. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootsOf| (((|List| $) (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; The returned roots display as \\spad{'y1},{}...,{}\\spad{'yn}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\spad{rootsOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) (|Polynomial| $)) "\\spad{rootsOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{rootOf(p, y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ (|SparseUnivariatePolynomial| $)) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}.") (($ (|Polynomial| $)) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) -((-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) +((-4410 . T) (-4416 . T) (-4411 . T) ((-4420 "*") . T) (-4412 . T) (-4413 . T) (-4415 . T)) NIL (-28 S R) ((|constructor| (NIL "Model for algebraically closed function spaces.")) (|zerosOf| (((|List| $) $ (|Symbol|)) "\\spad{zerosOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{zerosOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable.")) (|zeroOf| (($ $ (|Symbol|)) "\\spad{zeroOf(p, y)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity which displays as \\spad{'y}.") (($ $) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity. Error: if \\spad{p} has more than one variable.")) (|rootsOf| (((|List| $) $ (|Symbol|)) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; The returned roots display as \\spad{'y1},{}...,{}\\spad{'yn}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ $ (|Symbol|)) "\\spad{rootOf(p,y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) @@ -46,7 +46,7 @@ NIL NIL (-29 R) ((|constructor| (NIL "Model for algebraically closed function spaces.")) (|zerosOf| (((|List| $) $ (|Symbol|)) "\\spad{zerosOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{zerosOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable.")) (|zeroOf| (($ $ (|Symbol|)) "\\spad{zeroOf(p, y)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity which displays as \\spad{'y}.") (($ $) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity. Error: if \\spad{p} has more than one variable.")) (|rootsOf| (((|List| $) $ (|Symbol|)) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; The returned roots display as \\spad{'y1},{}...,{}\\spad{'yn}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ $ (|Symbol|)) "\\spad{rootOf(p,y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) -((-4414 . T) (-4412 . T) (-4411 . T) ((-4419 "*") . T) (-4410 . T) (-4415 . T) (-4409 . T)) +((-4415 . T) (-4413 . T) (-4412 . T) ((-4420 "*") . T) (-4411 . T) (-4416 . T) (-4410 . T)) NIL (-30) ((|constructor| (NIL "\\indented{1}{Plot a NON-SINGULAR plane algebraic curve \\spad{p}(\\spad{x},{}\\spad{y}) = 0.} Author: Clifton \\spad{J}. Williamson Date Created: Fall 1988 Date Last Updated: 27 April 1990 Keywords: algebraic curve,{} non-singular,{} plot Examples: References:")) (|refine| (($ $ (|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 -3867) +(-32 R -3879) ((|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 -1039) (QUOTE (-567))))) +((|HasCategory| |#1| (LIST (QUOTE -1040) (QUOTE (-567))))) (-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 -4418))) (-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)) +((-4418 . T) (-4419 . T)) NIL (-37 S R) ((|constructor| (NIL "The category of associative algebras (modules which are themselves rings). \\blankline"))) @@ -82,20 +82,20 @@ NIL NIL (-38 R) ((|constructor| (NIL "The category of associative algebras (modules which are themselves rings). \\blankline"))) -((-4411 . T) (-4412 . T) (-4414 . T)) +((-4412 . T) (-4413 . T) (-4415 . 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 -3867 UP UPUP -2542) +(-40 -3879 UP UPUP -2211) ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) -((-4410 |has| (-410 |#2|) (-365)) (-4415 |has| (-410 |#2|) (-365)) (-4409 |has| (-410 |#2|) (-365)) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) -((|HasCategory| (-410 |#2|) (QUOTE (-145))) (|HasCategory| (-410 |#2|) (QUOTE (-147))) (|HasCategory| (-410 |#2|) (QUOTE (-351))) (-2797 (|HasCategory| (-410 |#2|) (QUOTE (-365))) (|HasCategory| (-410 |#2|) (QUOTE (-351)))) (|HasCategory| (-410 |#2|) (QUOTE (-365))) (|HasCategory| (-410 |#2|) (QUOTE (-370))) (-2797 (-12 (|HasCategory| (-410 |#2|) (QUOTE (-233))) (|HasCategory| (-410 |#2|) (QUOTE (-365)))) (|HasCategory| (-410 |#2|) (QUOTE (-351)))) (-2797 (-12 (|HasCategory| (-410 |#2|) (LIST (QUOTE -901) (QUOTE (-1177)))) (|HasCategory| (-410 |#2|) (QUOTE (-365)))) (-12 (|HasCategory| (-410 |#2|) (LIST (QUOTE -901) (QUOTE (-1177)))) (|HasCategory| (-410 |#2|) (QUOTE (-351))))) (|HasCategory| (-410 |#2|) (LIST (QUOTE -640) (QUOTE (-567)))) (-2797 (|HasCategory| (-410 |#2|) (LIST (QUOTE -1039) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| (-410 |#2|) (QUOTE (-365)))) (|HasCategory| (-410 |#2|) (LIST (QUOTE -1039) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| (-410 |#2|) (LIST (QUOTE -1039) (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-370))) (-12 (|HasCategory| (-410 |#2|) (LIST (QUOTE -901) (QUOTE (-1177)))) (|HasCategory| (-410 |#2|) (QUOTE (-365)))) (-12 (|HasCategory| (-410 |#2|) (QUOTE (-233))) (|HasCategory| (-410 |#2|) (QUOTE (-365))))) -(-41 R -3867) +((-4411 |has| (-410 |#2|) (-365)) (-4416 |has| (-410 |#2|) (-365)) (-4410 |has| (-410 |#2|) (-365)) ((-4420 "*") . T) (-4412 . T) (-4413 . T) (-4415 . T)) +((|HasCategory| (-410 |#2|) (QUOTE (-145))) (|HasCategory| (-410 |#2|) (QUOTE (-147))) (|HasCategory| (-410 |#2|) (QUOTE (-351))) (-2800 (|HasCategory| (-410 |#2|) (QUOTE (-365))) (|HasCategory| (-410 |#2|) (QUOTE (-351)))) (|HasCategory| (-410 |#2|) (QUOTE (-365))) (|HasCategory| (-410 |#2|) (QUOTE (-370))) (-2800 (-12 (|HasCategory| (-410 |#2|) (QUOTE (-233))) (|HasCategory| (-410 |#2|) (QUOTE (-365)))) (|HasCategory| (-410 |#2|) (QUOTE (-351)))) (-2800 (-12 (|HasCategory| (-410 |#2|) (LIST (QUOTE -902) (QUOTE (-1178)))) (|HasCategory| (-410 |#2|) (QUOTE (-365)))) (-12 (|HasCategory| (-410 |#2|) (LIST (QUOTE -902) (QUOTE (-1178)))) (|HasCategory| (-410 |#2|) (QUOTE (-351))))) (|HasCategory| (-410 |#2|) (LIST (QUOTE -640) (QUOTE (-567)))) (-2800 (|HasCategory| (-410 |#2|) (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| (-410 |#2|) (QUOTE (-365)))) (|HasCategory| (-410 |#2|) (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| (-410 |#2|) (LIST (QUOTE -1040) (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-370))) (-12 (|HasCategory| (-410 |#2|) (LIST (QUOTE -902) (QUOTE (-1178)))) (|HasCategory| (-410 |#2|) (QUOTE (-365)))) (-12 (|HasCategory| (-410 |#2|) (QUOTE (-233))) (|HasCategory| (-410 |#2|) (QUOTE (-365))))) +(-41 R -3879) ((|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| $)) $) "\\spad{numer(x)} \\undocumented"))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-455))) (|HasCategory| |#1| (LIST (QUOTE -1039) (QUOTE (-567)))) (|HasCategory| |#2| (LIST (QUOTE -433) (|devaluate| |#1|))))) +((-12 (|HasCategory| |#1| (QUOTE (-455))) (|HasCategory| |#1| (LIST (QUOTE -1040) (QUOTE (-567)))) (|HasCategory| |#2| (LIST (QUOTE -433) (|devaluate| |#1|))))) (-42 OV E P) ((|constructor| (NIL "This package factors multivariate polynomials over the domain of \\spadtype{AlgebraicNumber} by allowing the user to specify a list of algebraic numbers generating the particular extension to factor over.")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| |#3|)) (|SparseUnivariatePolynomial| |#3|) (|List| (|AlgebraicNumber|))) "\\spad{factor(p,lan)} factors the polynomial \\spad{p} over the extension generated by the algebraic numbers given by the list \\spad{lan}. \\spad{p} is presented as a univariate polynomial with multivariate coefficients.") (((|Factored| |#3|) |#3| (|List| (|AlgebraicNumber|))) "\\spad{factor(p,lan)} factors the polynomial \\spad{p} over the extension generated by the algebraic numbers given by the list \\spad{lan}."))) NIL @@ -106,31 +106,31 @@ NIL ((|HasCategory| |#1| (QUOTE (-308)))) (-44 R |n| |ls| |gamma|) ((|constructor| (NIL "AlgebraGivenByStructuralConstants implements finite rank algebras over a commutative ring,{} given by the structural constants \\spad{gamma} with respect to a fixed basis \\spad{[a1,..,an]},{} where \\spad{gamma} is an \\spad{n}-vector of \\spad{n} by \\spad{n} matrices \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{ai * aj = gammaij1 * a1 + ... + gammaijn * an}. The symbols for the fixed basis have to be given as a list of symbols.")) (|coerce| (($ (|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| (-559)) (-4412 . T) (-4411 . T)) +((-4415 |has| |#1| (-559)) (-4413 . T) (-4412 . T)) ((|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-559)))) (-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)) -((-2797 (-12 (|HasCategory| (-2 (|:| -1791 |#1|) (|:| -4232 |#2|)) (QUOTE (-851))) (|HasCategory| (-2 (|:| -1791 |#1|) (|:| -4232 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1791) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4232) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -1791 |#1|) (|:| -4232 |#2|)) (QUOTE (-1101))) (|HasCategory| (-2 (|:| -1791 |#1|) (|:| -4232 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1791) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4232) (|devaluate| |#2|))))))) (-2797 (|HasCategory| (-2 (|:| -1791 |#1|) (|:| -4232 |#2|)) (QUOTE (-851))) (|HasCategory| (-2 (|:| -1791 |#1|) (|:| -4232 |#2|)) (QUOTE (-1101))) (|HasCategory| (-2 (|:| -1791 |#1|) (|:| -4232 |#2|)) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| |#2| (QUOTE (-1101))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| (-2 (|:| -1791 |#1|) (|:| -4232 |#2|)) (LIST (QUOTE -615) (QUOTE (-539)))) (-12 (|HasCategory| |#2| (QUOTE (-1101))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (-2797 (|HasCategory| (-2 (|:| -1791 |#1|) (|:| -4232 |#2|)) (QUOTE (-851))) (|HasCategory| (-2 (|:| -1791 |#1|) (|:| -4232 |#2|)) (QUOTE (-1101))) (|HasCategory| |#2| (QUOTE (-1101)))) (|HasCategory| (-2 (|:| -1791 |#1|) (|:| -4232 |#2|)) (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#2| (QUOTE (-1101))) (|HasCategory| (-567) (QUOTE (-851))) (|HasCategory| (-2 (|:| -1791 |#1|) (|:| -4232 |#2|)) (QUOTE (-1101))) (-2797 (|HasCategory| (-2 (|:| -1791 |#1|) (|:| -4232 |#2|)) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863))))) (-2797 (|HasCategory| (-2 (|:| -1791 |#1|) (|:| -4232 |#2|)) (QUOTE (-1101))) (|HasCategory| |#2| (QUOTE (-1101)))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-2 (|:| -1791 |#1|) (|:| -4232 |#2|)) (LIST (QUOTE -614) (QUOTE (-863)))) (-12 (|HasCategory| (-2 (|:| -1791 |#1|) (|:| -4232 |#2|)) (QUOTE (-1101))) (|HasCategory| (-2 (|:| -1791 |#1|) (|:| -4232 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1791) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4232) (|devaluate| |#2|))))))) +((-4418 . T) (-4419 . T)) +((-2800 (-12 (|HasCategory| (-2 (|:| -1795 |#1|) (|:| -4237 |#2|)) (QUOTE (-851))) (|HasCategory| (-2 (|:| -1795 |#1|) (|:| -4237 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1795) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4237) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -1795 |#1|) (|:| -4237 |#2|)) (QUOTE (-1102))) (|HasCategory| (-2 (|:| -1795 |#1|) (|:| -4237 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1795) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4237) (|devaluate| |#2|))))))) (-2800 (|HasCategory| (-2 (|:| -1795 |#1|) (|:| -4237 |#2|)) (QUOTE (-851))) (|HasCategory| (-2 (|:| -1795 |#1|) (|:| -4237 |#2|)) (QUOTE (-1102))) (|HasCategory| (-2 (|:| -1795 |#1|) (|:| -4237 |#2|)) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| |#2| (QUOTE (-1102))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| (-2 (|:| -1795 |#1|) (|:| -4237 |#2|)) (LIST (QUOTE -615) (QUOTE (-539)))) (-12 (|HasCategory| |#2| (QUOTE (-1102))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (-2800 (|HasCategory| (-2 (|:| -1795 |#1|) (|:| -4237 |#2|)) (QUOTE (-851))) (|HasCategory| (-2 (|:| -1795 |#1|) (|:| -4237 |#2|)) (QUOTE (-1102))) (|HasCategory| |#2| (QUOTE (-1102)))) (|HasCategory| (-2 (|:| -1795 |#1|) (|:| -4237 |#2|)) (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#2| (QUOTE (-1102))) (|HasCategory| (-567) (QUOTE (-851))) (|HasCategory| (-2 (|:| -1795 |#1|) (|:| -4237 |#2|)) (QUOTE (-1102))) (-2800 (|HasCategory| (-2 (|:| -1795 |#1|) (|:| -4237 |#2|)) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863))))) (-2800 (|HasCategory| (-2 (|:| -1795 |#1|) (|:| -4237 |#2|)) (QUOTE (-1102))) (|HasCategory| |#2| (QUOTE (-1102)))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-2 (|:| -1795 |#1|) (|:| -4237 |#2|)) (LIST (QUOTE -614) (QUOTE (-863)))) (-12 (|HasCategory| (-2 (|:| -1795 |#1|) (|:| -4237 |#2|)) (QUOTE (-1102))) (|HasCategory| (-2 (|:| -1795 |#1|) (|:| -4237 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1795) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4237) (|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| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) NIL ((|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#2| (QUOTE (-559))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-365)))) (-47 R E) ((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#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| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) -(((-4419 "*") |has| |#1| (-172)) (-4410 |has| |#1| (-559)) (-4411 . T) (-4412 . T) (-4414 . T)) +(((-4420 "*") |has| |#1| (-172)) (-4411 |has| |#1| (-559)) (-4412 . T) (-4413 . T) (-4415 . T)) NIL (-48) ((|constructor| (NIL "Algebraic closure of the rational numbers,{} with mathematical =")) (|norm| (($ $ (|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)) -((|HasCategory| $ (QUOTE (-1050))) (|HasCategory| $ (LIST (QUOTE -1039) (QUOTE (-567))))) +((-4410 . T) (-4416 . T) (-4411 . T) ((-4420 "*") . T) (-4412 . T) (-4413 . T) (-4415 . T)) +((|HasCategory| $ (QUOTE (-1051))) (|HasCategory| $ (LIST (QUOTE -1040) (QUOTE (-567))))) (-49) ((|constructor| (NIL "This domain implements anonymous functions")) (|body| (((|Syntax|) $) "\\spad{body(f)} returns the body of the unnamed function \\spad{`f'}.")) (|parameters| (((|List| (|Identifier|)) $) "\\spad{parameters(f)} returns the list of parameters bound by \\spad{`f'}."))) NIL NIL (-50 R |lVar|) ((|constructor| (NIL "The domain of antisymmetric polynomials.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,p)} changes each coefficient of \\spad{p} by the application of \\spad{f}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(p)} returns the homogeneous degree of \\spad{p}.")) (|retractable?| (((|Boolean|) $) "\\spad{retractable?(p)} tests if \\spad{p} is a 0-form,{} \\spadignore{i.e.} if degree(\\spad{p}) = 0.")) (|homogeneous?| (((|Boolean|) $) "\\spad{homogeneous?(p)} tests if all of the terms of \\spad{p} have the same degree.")) (|exp| (($ (|List| (|Integer|))) "\\spad{exp([i1,...in])} returns \\spad{u_1\\^{i_1} ... u_n\\^{i_n}}")) (|generator| (($ (|NonNegativeInteger|)) "\\spad{generator(n)} returns the \\spad{n}th multiplicative generator,{} a basis term.")) (|coefficient| ((|#1| $ $) "\\spad{coefficient(p,u)} returns the coefficient of the term in \\spad{p} containing the basis term \\spad{u} if such a term exists,{} and 0 otherwise. Error: if the second argument \\spad{u} is not a basis element.")) (|reductum| (($ $) "\\spad{reductum(p)},{} where \\spad{p} is an antisymmetric polynomial,{} returns \\spad{p} minus the leading term of \\spad{p} if \\spad{p} has at least two terms,{} and 0 otherwise.")) (|leadingBasisTerm| (($ $) "\\spad{leadingBasisTerm(p)} returns the leading basis term of antisymmetric polynomial \\spad{p}.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(p)} returns the leading coefficient of antisymmetric polynomial \\spad{p}."))) -((-4414 . T)) +((-4415 . T)) NIL (-51 S) ((|constructor| (NIL "\\spadtype{AnyFunctions1} implements several utility functions for working with \\spadtype{Any}. These functions are used to go back and forth between objects of \\spadtype{Any} and objects of other types.")) (|retract| ((|#1| (|Any|)) "\\spad{retract(a)} tries to convert \\spad{a} into an object of type \\spad{S}. If possible,{} it returns the object. Error: if no such retraction is possible.")) (|retractable?| (((|Boolean|) (|Any|)) "\\spad{retractable?(a)} tests if \\spad{a} can be converted into an object of type \\spad{S}.")) (|retractIfCan| (((|Union| |#1| "failed") (|Any|)) "\\spad{retractIfCan(a)} tries change \\spad{a} into an object of type \\spad{S}. If it can,{} then such an object is returned. Otherwise,{} \"failed\" is returned.")) (|coerce| (((|Any|) |#1|) "\\spad{coerce(s)} creates an object of \\spadtype{Any} from the object \\spad{s} of type \\spad{S}."))) @@ -144,7 +144,7 @@ NIL ((|constructor| (NIL "\\spad{ApplyUnivariateSkewPolynomial} (internal) allows univariate skew polynomials to be applied to appropriate modules.")) (|apply| ((|#2| |#3| (|Mapping| |#2| |#2|) |#2|) "\\spad{apply(p, f, m)} returns \\spad{p(m)} where the action is given by \\spad{x m = f(m)}. \\spad{f} must be an \\spad{R}-pseudo linear map on \\spad{M}."))) NIL NIL -(-54 |Base| R -3867) +(-54 |Base| R -3879) ((|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)) +((-4418 . T) (-4419 . 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)) -((-2797 (-12 (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1101))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-1101))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539)))) (-2797 (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-1101)))) (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| (-567) (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-1101))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863)))) (-12 (|HasCategory| |#1| (QUOTE (-1101))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) +((-4419 . T) (-4418 . T)) +((-2800 (-12 (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2800 (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539)))) (-2800 (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-1102)))) (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| (-567) (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863)))) (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|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)) -((-12 (|HasCategory| |#1| (QUOTE (-1101))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1101))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-1101))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) -(-61 -1988) +((-4418 . T) (-4419 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1102))) (-2800 (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) +(-61 -1996) ((|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 -1988) +(-62 -1996) ((|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 -1988) +(-63 -1996) ((|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 -1988) +(-64 -1996) ((|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 -1988) +(-65 -1996) ((|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 -1988) +(-66 -1996) ((|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 -1988) +(-67 -1996) ((|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 -1988) +(-68 -1996) ((|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 -1988) +(-69 -1996) ((|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 -1988) +(-70 -1996) ((|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 -1988) +(-71 -1996) ((|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 -1988) +(-72 -1996) ((|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 -1988) +(-73 -1996) ((|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 -1988) +(-74 -1996) ((|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 -1988) +(-77 -1996) ((|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 -1988) +(-78 -1996) ((|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 -1988) +(-79 -1996) ((|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 -1988) +(-80 -1996) ((|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 -1988) +(-81 -1996) ((|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 -1988) +(-82 -1996) ((|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 -1988) +(-83 -1996) ((|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 -1988) +(-84 -1996) ((|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 -1988) +(-85 -1996) ((|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 -1988) +(-86 -1996) ((|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 -1988) +(-87 -1996) ((|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 -1988) +(-88 -1996) ((|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 -1988) +(-89 -1996) ((|constructor| (NIL "\\spadtype{Asp9} produces Fortran for Type 9 ASPs,{} needed for NAG routines \\axiomOpFrom{d02bhf}{d02Package},{} \\axiomOpFrom{d02cjf}{d02Package},{} \\axiomOpFrom{d02ejf}{d02Package}. These ASPs represent a function of a scalar \\spad{X} and a vector \\spad{Y},{} for example:\\begin{verbatim} DOUBLE PRECISION FUNCTION G(X,Y) DOUBLE PRECISION X,Y(*) G=X+Y(1) RETURN END\\end{verbatim} If the user provides a constant value for \\spad{G},{} then extra information is added via COMMON blocks used by certain routines. This specifies that the value returned by \\spad{G} in this case is to be ignored.")) (|coerce| (($ (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL @@ -294,8 +294,8 @@ NIL ((|HasCategory| |#1| (QUOTE (-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)) -((-12 (|HasCategory| |#1| (QUOTE (-1101))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1101))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-1101))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) +((-4418 . T) (-4419 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1102))) (-2800 (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (-92 S) ((|constructor| (NIL "This is the category of Spad abstract syntax trees."))) NIL @@ -318,15 +318,15 @@ NIL NIL (-97) ((|constructor| (NIL "\\axiomType{AttributeButtons} implements a database and associated adjustment mechanisms for a set of attributes. \\blankline For ODEs these attributes are \"stiffness\",{} \"stability\" (\\spadignore{i.e.} how much affect the cosine or sine component of the solution has on the stability of the result),{} \"accuracy\" and \"expense\" (\\spadignore{i.e.} how expensive is the evaluation of the ODE). All these have bearing on the cost of calculating the solution given that reducing the step-length to achieve greater accuracy requires considerable number of evaluations and calculations. \\blankline The effect of each of these attributes can be altered by increasing or decreasing the button value. \\blankline For Integration there is a button for increasing and decreasing the preset number of function evaluations for each method. This is automatically used by ANNA when a method fails due to insufficient workspace or where the limit of function evaluations has been reached before the required accuracy is achieved. \\blankline")) (|setButtonValue| (((|Float|) (|String|) (|String|) (|Float|)) "\\axiom{setButtonValue(attributeName,{}routineName,{}\\spad{n})} sets the value of the button of attribute \\spad{attributeName} to routine \\spad{routineName} to \\spad{n}. \\spad{n} must be in the range [0..1]. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".") (((|Float|) (|String|) (|Float|)) "\\axiom{setButtonValue(attributeName,{}\\spad{n})} sets the value of all buttons of attribute \\spad{attributeName} to \\spad{n}. \\spad{n} must be in the range [0..1]. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".")) (|setAttributeButtonStep| (((|Float|) (|Float|)) "\\axiom{setAttributeButtonStep(\\spad{n})} sets the value of the steps for increasing and decreasing the button values. \\axiom{\\spad{n}} must be greater than 0 and less than 1. The preset value is 0.5.")) (|resetAttributeButtons| (((|Void|)) "\\axiom{resetAttributeButtons()} resets the Attribute buttons to a neutral level.")) (|getButtonValue| (((|Float|) (|String|) (|String|)) "\\axiom{getButtonValue(routineName,{}attributeName)} returns the current value for the effect of the attribute \\axiom{attributeName} with routine \\axiom{routineName}. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".")) (|decrease| (((|Float|) (|String|)) "\\axiom{decrease(attributeName)} decreases the value for the effect of the attribute \\axiom{attributeName} with all routines. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".") (((|Float|) (|String|) (|String|)) "\\axiom{decrease(routineName,{}attributeName)} decreases the value for the effect of the attribute \\axiom{attributeName} with routine \\axiom{routineName}. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".")) (|increase| (((|Float|) (|String|)) "\\axiom{increase(attributeName)} increases the value for the effect of the attribute \\axiom{attributeName} with all routines. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".") (((|Float|) (|String|) (|String|)) "\\axiom{increase(routineName,{}attributeName)} increases the value for the effect of the attribute \\axiom{attributeName} with routine \\axiom{routineName}. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\"."))) -((-4417 . T)) +((-4418 . T)) NIL (-98) ((|constructor| (NIL "This category exports the attributes in the AXIOM Library")) (|canonical| ((|attribute|) "\\spad{canonical} is \\spad{true} if and only if distinct elements have distinct data structures. For example,{} a domain of mathematical objects which has the \\spad{canonical} attribute means that two objects are mathematically equal if and only if their data structures are equal.")) (|multiplicativeValuation| ((|attribute|) "\\spad{multiplicativeValuation} implies \\spad{euclideanSize(a*b)=euclideanSize(a)*euclideanSize(b)}.")) (|additiveValuation| ((|attribute|) "\\spad{additiveValuation} implies \\spad{euclideanSize(a*b)=euclideanSize(a)+euclideanSize(b)}.")) (|noetherian| ((|attribute|) "\\spad{noetherian} is \\spad{true} if all of its ideals are finitely generated.")) (|central| ((|attribute|) "\\spad{central} is \\spad{true} if,{} given an algebra over a ring \\spad{R},{} the image of \\spad{R} is the center of the algebra,{} \\spadignore{i.e.} the set of members of the algebra which commute with all others is precisely the image of \\spad{R} in the algebra.")) (|partiallyOrderedSet| ((|attribute|) "\\spad{partiallyOrderedSet} is \\spad{true} if a set with \\spadop{<} which is transitive,{} but \\spad{not(a < b or a = b)} does not necessarily imply \\spad{b<a}.")) (|arbitraryPrecision| ((|attribute|) "\\spad{arbitraryPrecision} means the user can set the precision for subsequent calculations.")) (|canonicalsClosed| ((|attribute|) "\\spad{canonicalsClosed} is \\spad{true} if \\spad{unitCanonical(a)*unitCanonical(b) = unitCanonical(a*b)}.")) (|canonicalUnitNormal| ((|attribute|) "\\spad{canonicalUnitNormal} is \\spad{true} if we can choose a canonical representative for each class of associate elements,{} that is \\spad{associates?(a,b)} returns \\spad{true} if and only if \\spad{unitCanonical(a) = unitCanonical(b)}.")) (|noZeroDivisors| ((|attribute|) "\\spad{noZeroDivisors} is \\spad{true} if \\spad{x * y \\~~= 0} implies both \\spad{x} and \\spad{y} are non-zero.")) (|rightUnitary| ((|attribute|) "\\spad{rightUnitary} is \\spad{true} if \\spad{x * 1 = x} for all \\spad{x}.")) (|leftUnitary| ((|attribute|) "\\spad{leftUnitary} is \\spad{true} if \\spad{1 * x = x} for all \\spad{x}.")) (|unitsKnown| ((|attribute|) "\\spad{unitsKnown} is \\spad{true} if a monoid (a multiplicative semigroup with a 1) has \\spad{unitsKnown} means that the operation \\spadfun{recip} can only return \"failed\" if its argument is not a unit.")) (|shallowlyMutable| ((|attribute|) "\\spad{shallowlyMutable} is \\spad{true} if its values have immediate components that are updateable (mutable). Note: the properties of any component domain are irrevelant to the \\spad{shallowlyMutable} proper.")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} is \\spad{true} if it has an operation \\spad{\"*\": (D,D) -> D} which is commutative.")) (|finiteAggregate| ((|attribute|) "\\spad{finiteAggregate} is \\spad{true} if it is an aggregate with a finite number of elements."))) -((-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)) +((-4418 . T) ((-4420 "*") . T) (-4419 . T) (-4415 . T) (-4413 . T) (-4412 . T) (-4411 . T) (-4416 . T) (-4410 . T) (-4409 . T) (-4408 . T) (-4407 . T) (-4406 . T) (-4414 . T) (-4417 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-4405 . 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)) +((-4415 . T)) NIL (-100 R UP) ((|constructor| (NIL "This package provides balanced factorisations of polynomials.")) (|balancedFactorisation| (((|Factored| |#2|) |#2| (|List| |#2|)) "\\spad{balancedFactorisation(a, [b1,...,bn])} returns a factorisation \\spad{a = p1^e1 ... pm^em} such that each \\spad{pi} is balanced with respect to \\spad{[b1,...,bm]}.") (((|Factored| |#2|) |#2| |#2|) "\\spad{balancedFactorisation(a, b)} returns a factorisation \\spad{a = p1^e1 ... pm^em} such that each \\spad{pi} is balanced with respect to \\spad{b}."))) @@ -342,15 +342,15 @@ NIL NIL (-103 S) ((|constructor| (NIL "\\spadtype{BalancedBinaryTree(S)} is the domain of balanced binary trees (bbtree). A balanced binary tree of \\spad{2**k} leaves,{} for some \\spad{k > 0},{} is symmetric,{} that is,{} the left and right subtree of each interior node have identical shape. In general,{} the left and right subtree of a given node can differ by at most leaf node.")) (|mapDown!| (($ $ |#1| (|Mapping| (|List| |#1|) |#1| |#1| |#1|)) "\\spad{mapDown!(t,p,f)} returns \\spad{t} after traversing \\spad{t} in \"preorder\" (node then left then right) fashion replacing the successive interior nodes as follows. Let \\spad{l} and \\spad{r} denote the left and right subtrees of \\spad{t}. The root value \\spad{x} of \\spad{t} is replaced by \\spad{p}. Then \\spad{f}(value \\spad{l},{} value \\spad{r},{} \\spad{p}),{} where \\spad{l} and \\spad{r} denote the left and right subtrees of \\spad{t},{} is evaluated producing two values \\spad{pl} and \\spad{pr}. Then \\spad{mapDown!(l,pl,f)} and \\spad{mapDown!(l,pr,f)} are evaluated.") (($ $ |#1| (|Mapping| |#1| |#1| |#1|)) "\\spad{mapDown!(t,p,f)} returns \\spad{t} after traversing \\spad{t} in \"preorder\" (node then left then right) fashion replacing the successive interior nodes as follows. The root value \\spad{x} is replaced by \\spad{q} \\spad{:=} \\spad{f}(\\spad{p},{}\\spad{x}). The mapDown!(\\spad{l},{}\\spad{q},{}\\spad{f}) and mapDown!(\\spad{r},{}\\spad{q},{}\\spad{f}) are evaluated for the left and right subtrees \\spad{l} and \\spad{r} of \\spad{t}.")) (|mapUp!| (($ $ $ (|Mapping| |#1| |#1| |#1| |#1| |#1|)) "\\spad{mapUp!(t,t1,f)} traverses \\spad{t} in an \"endorder\" (left then right then node) fashion returning \\spad{t} with the value at each successive interior node of \\spad{t} replaced by \\spad{f}(\\spad{l},{}\\spad{r},{}\\spad{l1},{}\\spad{r1}) where \\spad{l} and \\spad{r} are the values at the immediate left and right nodes. Values \\spad{l1} and \\spad{r1} are values at the corresponding nodes of a balanced binary tree \\spad{t1},{} of identical shape at \\spad{t}.") ((|#1| $ (|Mapping| |#1| |#1| |#1|)) "\\spad{mapUp!(t,f)} traverses balanced binary tree \\spad{t} in an \"endorder\" (left then right then node) fashion returning \\spad{t} with the value at each successive interior node of \\spad{t} replaced by \\spad{f}(\\spad{l},{}\\spad{r}) where \\spad{l} and \\spad{r} are the values at the immediate left and right nodes.")) (|setleaves!| (($ $ (|List| |#1|)) "\\spad{setleaves!(t, ls)} sets the leaves of \\spad{t} in left-to-right order to the elements of \\spad{ls}.")) (|balancedBinaryTree| (($ (|NonNegativeInteger|) |#1|) "\\spad{balancedBinaryTree(n, s)} creates a balanced binary tree with \\spad{n} nodes each with value \\spad{s}."))) -((-4417 . T) (-4418 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1101))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1101))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-1101))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) +((-4418 . T) (-4419 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1102))) (-2800 (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (-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 (-4420 "*")))) (-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)) +((-4418 . T)) NIL (-106 A S) ((|constructor| (NIL "A bag aggregate is an aggregate for which one can insert and extract objects,{} and where the order in which objects are inserted determines the order of extraction. Examples of bags are stacks,{} queues,{} and dequeues.")) (|inspect| ((|#2| $) "\\spad{inspect(u)} returns an (random) element from a bag.")) (|insert!| (($ |#2| $) "\\spad{insert!(x,u)} inserts item \\spad{x} into bag \\spad{u}.")) (|extract!| ((|#2| $) "\\spad{extract!(u)} destructively removes a (random) item from bag \\spad{u}.")) (|bag| (($ (|List| |#2|)) "\\spad{bag([x,y,...,z])} creates a bag with elements \\spad{x},{}\\spad{y},{}...,{}\\spad{z}.")) (|shallowlyMutable| ((|attribute|) "shallowlyMutable means that elements of bags may be destructively changed."))) @@ -358,23 +358,23 @@ NIL NIL (-107 S) ((|constructor| (NIL "A bag aggregate is an aggregate for which one can insert and extract objects,{} and where the order in which objects are inserted determines the order of extraction. Examples of bags are stacks,{} queues,{} and dequeues.")) (|inspect| ((|#1| $) "\\spad{inspect(u)} returns an (random) element from a bag.")) (|insert!| (($ |#1| $) "\\spad{insert!(x,u)} inserts item \\spad{x} into bag \\spad{u}.")) (|extract!| ((|#1| $) "\\spad{extract!(u)} destructively removes a (random) item from bag \\spad{u}.")) (|bag| (($ (|List| |#1|)) "\\spad{bag([x,y,...,z])} creates a bag with elements \\spad{x},{}\\spad{y},{}...,{}\\spad{z}.")) (|shallowlyMutable| ((|attribute|) "shallowlyMutable means that elements of bags may be destructively changed."))) -((-4418 . T)) +((-4419 . 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)) -((|HasCategory| (-567) (QUOTE (-910))) (|HasCategory| (-567) (LIST (QUOTE -1039) (QUOTE (-1177)))) (|HasCategory| (-567) (QUOTE (-145))) (|HasCategory| (-567) (QUOTE (-147))) (|HasCategory| (-567) (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| (-567) (QUOTE (-1023))) (|HasCategory| (-567) (QUOTE (-821))) (-2797 (|HasCategory| (-567) (QUOTE (-821))) (|HasCategory| (-567) (QUOTE (-851)))) (|HasCategory| (-567) (LIST (QUOTE -1039) (QUOTE (-567)))) (|HasCategory| (-567) (QUOTE (-1152))) (|HasCategory| (-567) (LIST (QUOTE -887) (QUOTE (-381)))) (|HasCategory| (-567) (LIST (QUOTE -887) (QUOTE (-567)))) (|HasCategory| (-567) (LIST (QUOTE -615) (LIST (QUOTE -893) (QUOTE (-381))))) (|HasCategory| (-567) (LIST (QUOTE -615) (LIST (QUOTE -893) (QUOTE (-567))))) (|HasCategory| (-567) (QUOTE (-233))) (|HasCategory| (-567) (LIST (QUOTE -901) (QUOTE (-1177)))) (|HasCategory| (-567) (LIST (QUOTE -517) (QUOTE (-1177)) (QUOTE (-567)))) (|HasCategory| (-567) (LIST (QUOTE -310) (QUOTE (-567)))) (|HasCategory| (-567) (LIST (QUOTE -287) (QUOTE (-567)) (QUOTE (-567)))) (|HasCategory| (-567) (QUOTE (-308))) (|HasCategory| (-567) (QUOTE (-548))) (|HasCategory| (-567) (QUOTE (-851))) (|HasCategory| (-567) (LIST (QUOTE -640) (QUOTE (-567)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-567) (QUOTE (-910)))) (-2797 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-567) (QUOTE (-910)))) (|HasCategory| (-567) (QUOTE (-145))))) +((-4410 . T) (-4416 . T) (-4411 . T) ((-4420 "*") . T) (-4412 . T) (-4413 . T) (-4415 . T)) +((|HasCategory| (-567) (QUOTE (-911))) (|HasCategory| (-567) (LIST (QUOTE -1040) (QUOTE (-1178)))) (|HasCategory| (-567) (QUOTE (-145))) (|HasCategory| (-567) (QUOTE (-147))) (|HasCategory| (-567) (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| (-567) (QUOTE (-1024))) (|HasCategory| (-567) (QUOTE (-821))) (-2800 (|HasCategory| (-567) (QUOTE (-821))) (|HasCategory| (-567) (QUOTE (-851)))) (|HasCategory| (-567) (LIST (QUOTE -1040) (QUOTE (-567)))) (|HasCategory| (-567) (QUOTE (-1153))) (|HasCategory| (-567) (LIST (QUOTE -888) (QUOTE (-381)))) (|HasCategory| (-567) (LIST (QUOTE -888) (QUOTE (-567)))) (|HasCategory| (-567) (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-381))))) (|HasCategory| (-567) (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567))))) (|HasCategory| (-567) (QUOTE (-233))) (|HasCategory| (-567) (LIST (QUOTE -902) (QUOTE (-1178)))) (|HasCategory| (-567) (LIST (QUOTE -517) (QUOTE (-1178)) (QUOTE (-567)))) (|HasCategory| (-567) (LIST (QUOTE -310) (QUOTE (-567)))) (|HasCategory| (-567) (LIST (QUOTE -287) (QUOTE (-567)) (QUOTE (-567)))) (|HasCategory| (-567) (QUOTE (-308))) (|HasCategory| (-567) (QUOTE (-548))) (|HasCategory| (-567) (QUOTE (-851))) (|HasCategory| (-567) (LIST (QUOTE -640) (QUOTE (-567)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-567) (QUOTE (-911)))) (-2800 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-567) (QUOTE (-911)))) (|HasCategory| (-567) (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|) $) "\\spad{name(b)} returns the name of binding \\spad{b}"))) NIL NIL (-110) ((|constructor| (NIL "\\spadtype{Bits} provides logical functions for Indexed Bits.")) (|bits| (($ (|NonNegativeInteger|) (|Boolean|)) "\\spad{bits(n,b)} creates bits with \\spad{n} values of \\spad{b}"))) -((-4418 . T) (-4417 . T)) -((-12 (|HasCategory| (-112) (QUOTE (-1101))) (|HasCategory| (-112) (LIST (QUOTE -310) (QUOTE (-112))))) (|HasCategory| (-112) (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| (-112) (QUOTE (-851))) (|HasCategory| (-567) (QUOTE (-851))) (|HasCategory| (-112) (QUOTE (-1101))) (|HasCategory| (-112) (LIST (QUOTE -614) (QUOTE (-863))))) +((-4419 . T) (-4418 . T)) +((-12 (|HasCategory| (-112) (QUOTE (-1102))) (|HasCategory| (-112) (LIST (QUOTE -310) (QUOTE (-112))))) (|HasCategory| (-112) (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| (-112) (QUOTE (-851))) (|HasCategory| (-567) (QUOTE (-851))) (|HasCategory| (-112) (QUOTE (-1102))) (|HasCategory| (-112) (LIST (QUOTE -614) (QUOTE (-863))))) (-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)) +((-4413 . T) (-4412 . 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 -3867 UP) +(-115 -3879 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)) +((-4411 . T) ((-4420 "*") . T) (-4412 . T) (-4413 . T) (-4415 . 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)) -((|HasCategory| (-116 |#1|) (QUOTE (-910))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1039) (QUOTE (-1177)))) (|HasCategory| (-116 |#1|) (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-147))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| (-116 |#1|) (QUOTE (-1023))) (|HasCategory| (-116 |#1|) (QUOTE (-821))) (-2797 (|HasCategory| (-116 |#1|) (QUOTE (-821))) (|HasCategory| (-116 |#1|) (QUOTE (-851)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1039) (QUOTE (-567)))) (|HasCategory| (-116 |#1|) (QUOTE (-1152))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -887) (QUOTE (-381)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -887) (QUOTE (-567)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -615) (LIST (QUOTE -893) (QUOTE (-381))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -615) (LIST (QUOTE -893) (QUOTE (-567))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -640) (QUOTE (-567)))) (|HasCategory| (-116 |#1|) (QUOTE (-233))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -901) (QUOTE (-1177)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -517) (QUOTE (-1177)) (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 (-548))) (|HasCategory| (-116 |#1|) (QUOTE (-851))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-910)))) (-2797 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-910)))) (|HasCategory| (-116 |#1|) (QUOTE (-145))))) +((-4410 . T) (-4416 . T) (-4411 . T) ((-4420 "*") . T) (-4412 . T) (-4413 . T) (-4415 . T)) +((|HasCategory| (-116 |#1|) (QUOTE (-911))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1040) (QUOTE (-1178)))) (|HasCategory| (-116 |#1|) (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-147))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| (-116 |#1|) (QUOTE (-1024))) (|HasCategory| (-116 |#1|) (QUOTE (-821))) (-2800 (|HasCategory| (-116 |#1|) (QUOTE (-821))) (|HasCategory| (-116 |#1|) (QUOTE (-851)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1040) (QUOTE (-567)))) (|HasCategory| (-116 |#1|) (QUOTE (-1153))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -888) (QUOTE (-381)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -888) (QUOTE (-567)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-381))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -640) (QUOTE (-567)))) (|HasCategory| (-116 |#1|) (QUOTE (-233))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -902) (QUOTE (-1178)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -517) (QUOTE (-1178)) (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 (-548))) (|HasCategory| (-116 |#1|) (QUOTE (-851))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-911)))) (-2800 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-911)))) (|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| (($ $) "\\spad{left(u)} returns the left child."))) NIL -((|HasAttribute| |#1| (QUOTE -4418))) +((|HasAttribute| |#1| (QUOTE -4419))) (-119 S) ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "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 @@ -414,15 +414,15 @@ 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)) -((-12 (|HasCategory| |#1| (QUOTE (-1101))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1101))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-1101))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) +((-4418 . T) (-4419 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1102))) (-2800 (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (-122 S) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|or| (($ $ $) "\\spad{a or b} returns the logical {\\em or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|and| (($ $ $) "\\spad{a and b} returns the logical {\\em and} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|not| (($ $) "\\spad{not(b)} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}."))) NIL NIL (-123) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|or| (($ $ $) "\\spad{a or b} returns the logical {\\em or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|and| (($ $ $) "\\spad{a and b} returns the logical {\\em and} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|not| (($ $) "\\spad{not(b)} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}."))) -((-4418 . T) (-4417 . T)) +((-4419 . T) (-4418 . T)) NIL (-124 A S) ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#2| $) "\\spad{node(left,v,right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) @@ -430,20 +430,20 @@ NIL NIL (-125 S) ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#1| $) "\\spad{node(left,v,right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) -((-4417 . T) (-4418 . T)) +((-4418 . T) (-4419 . T)) NIL (-126 S) ((|constructor| (NIL "\\spadtype{BinaryTournament(S)} is the domain of binary trees where elements are ordered down the tree. A binary search tree is either empty or is a node containing a \\spadfun{value} of type \\spad{S},{} and a \\spadfun{right} and a \\spadfun{left} which are both \\spadtype{BinaryTree(S)}")) (|insert!| (($ |#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)) -((-12 (|HasCategory| |#1| (QUOTE (-1101))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1101))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-1101))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) +((-4418 . T) (-4419 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1102))) (-2800 (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (-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)) -((-12 (|HasCategory| |#1| (QUOTE (-1101))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1101))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-1101))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) +((-4418 . T) (-4419 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1102))) (-2800 (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (-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)) -((-2797 (-12 (|HasCategory| (-129) (QUOTE (-851))) (|HasCategory| (-129) (LIST (QUOTE -310) (QUOTE (-129))))) (-12 (|HasCategory| (-129) (QUOTE (-1101))) (|HasCategory| (-129) (LIST (QUOTE -310) (QUOTE (-129)))))) (-2797 (-12 (|HasCategory| (-129) (QUOTE (-1101))) (|HasCategory| (-129) (LIST (QUOTE -310) (QUOTE (-129))))) (|HasCategory| (-129) (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| (-129) (LIST (QUOTE -615) (QUOTE (-539)))) (-2797 (|HasCategory| (-129) (QUOTE (-851))) (|HasCategory| (-129) (QUOTE (-1101)))) (|HasCategory| (-129) (QUOTE (-851))) (|HasCategory| (-567) (QUOTE (-851))) (|HasCategory| (-129) (QUOTE (-1101))) (|HasCategory| (-129) (LIST (QUOTE -614) (QUOTE (-863)))) (-12 (|HasCategory| (-129) (QUOTE (-1101))) (|HasCategory| (-129) (LIST (QUOTE -310) (QUOTE (-129)))))) +((-4419 . T) (-4418 . T)) +((-2800 (-12 (|HasCategory| (-129) (QUOTE (-851))) (|HasCategory| (-129) (LIST (QUOTE -310) (QUOTE (-129))))) (-12 (|HasCategory| (-129) (QUOTE (-1102))) (|HasCategory| (-129) (LIST (QUOTE -310) (QUOTE (-129)))))) (-2800 (-12 (|HasCategory| (-129) (QUOTE (-1102))) (|HasCategory| (-129) (LIST (QUOTE -310) (QUOTE (-129))))) (|HasCategory| (-129) (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| (-129) (LIST (QUOTE -615) (QUOTE (-539)))) (-2800 (|HasCategory| (-129) (QUOTE (-851))) (|HasCategory| (-129) (QUOTE (-1102)))) (|HasCategory| (-129) (QUOTE (-851))) (|HasCategory| (-567) (QUOTE (-851))) (|HasCategory| (-129) (QUOTE (-1102))) (|HasCategory| (-129) (LIST (QUOTE -614) (QUOTE (-863)))) (-12 (|HasCategory| (-129) (QUOTE (-1102))) (|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."))) NIL @@ -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") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,D) -> D} which is commutative."))) -(((-4419 "*") . T)) +(((-4420 "*") . T)) NIL -(-135 |minix| -2609 S T$) +(-135 |minix| -2612 S T$) ((|constructor| (NIL "This package provides functions to enable conversion of tensors given conversion of the components.")) (|map| (((|CartesianTensor| |#1| |#2| |#4|) (|Mapping| |#4| |#3|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{map(f,ts)} does a componentwise conversion of the tensor \\spad{ts} to a tensor with components of type \\spad{T}.")) (|reshape| (((|CartesianTensor| |#1| |#2| |#4|) (|List| |#4|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{reshape(lt,ts)} organizes the list of components \\spad{lt} into a tensor with the same shape as \\spad{ts}."))) NIL NIL -(-136 |minix| -2609 R) +(-136 |minix| -2612 R) ((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\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 @@ -494,8 +494,8 @@ 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)) -((-2797 (-12 (|HasCategory| (-144) (QUOTE (-370))) (|HasCategory| (-144) (LIST (QUOTE -310) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1101))) (|HasCategory| (-144) (LIST (QUOTE -310) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| (-144) (QUOTE (-370))) (|HasCategory| (-144) (QUOTE (-851))) (|HasCategory| (-144) (QUOTE (-1101))) (|HasCategory| (-144) (LIST (QUOTE -614) (QUOTE (-863)))) (-12 (|HasCategory| (-144) (QUOTE (-1101))) (|HasCategory| (-144) (LIST (QUOTE -310) (QUOTE (-144)))))) +((-4418 . T) (-4408 . T) (-4419 . T)) +((-2800 (-12 (|HasCategory| (-144) (QUOTE (-370))) (|HasCategory| (-144) (LIST (QUOTE -310) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1102))) (|HasCategory| (-144) (LIST (QUOTE -310) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| (-144) (QUOTE (-370))) (|HasCategory| (-144) (QUOTE (-851))) (|HasCategory| (-144) (QUOTE (-1102))) (|HasCategory| (-144) (LIST (QUOTE -614) (QUOTE (-863)))) (-12 (|HasCategory| (-144) (QUOTE (-1102))) (|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{qi = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|clearDenominator| ((|#3| |#3|) "\\spad{clearDenominator([q1,...,qn])} returns \\spad{[p1,...,pn]} such that \\spad{qi = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|commonDenominator| ((|#1| |#3|) "\\spad{commonDenominator([q1,...,qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}\\spad{qn}."))) NIL @@ -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)) +((-4415 . 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)) +((-4415 . T)) NIL -(-148 -3867 UP UPUP) +(-148 -3879 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 -615) (QUOTE (-539)))) (|HasCategory| |#2| (QUOTE (-1101))) (|HasAttribute| |#1| (QUOTE -4417))) +((|HasCategory| |#2| (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| |#2| (QUOTE (-1102))) (|HasAttribute| |#1| (QUOTE -4418))) (-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<i2<=n}),{}...,{}\\spad{e[1]*e[2]*..*e[n]} is a basis for the Clifford Algebra. \\blankline The algebra is defined by the relations \\indented{3}{\\spad{e[i]*e[j] = -e[j]*e[i]}\\space{2}(\\spad{i \\~~= j}),{}} \\indented{3}{\\spad{e[i]*e[i] = Q(e[i])}} \\blankline Examples of Clifford Algebras are: gaussians,{} quaternions,{} exterior algebras and spin algebras.")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} computes the multiplicative inverse of \\spad{x} or \"failed\" if \\spad{x} is not invertible.")) (|coefficient| ((|#2| $ (|List| (|PositiveInteger|))) "\\spad{coefficient(x,[i1,i2,...,iN])} extracts the coefficient of \\spad{e(i1)*e(i2)*...*e(iN)} in \\spad{x}.")) (|monomial| (($ |#2| (|List| (|PositiveInteger|))) "\\spad{monomial(c,[i1,i2,...,iN])} produces the value given by \\spad{c*e(i1)*e(i2)*...*e(iN)}.")) (|e| (($ (|PositiveInteger|)) "\\spad{e(n)} produces the appropriate unit element."))) -((-4412 . T) (-4411 . T) (-4414 . T)) +((-4413 . T) (-4412 . T) (-4415 . T)) NIL (-153) ((|constructor| (NIL "\\indented{1}{The purpose of this package is to provide reasonable plots of} functions with singularities.")) (|clipWithRanges| (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|List| (|List| (|Point| (|DoubleFloat|)))) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{clipWithRanges(pointLists,xMin,xMax,yMin,yMax)} performs clipping on a list of lists of points,{} \\spad{pointLists}. Clipping is done within the specified ranges of \\spad{xMin},{} \\spad{xMax} and \\spad{yMin},{} \\spad{yMax}. This function is used internally by the \\fakeAxiomFun{iClipParametric} subroutine in this package.")) (|clipParametric| (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|Plot|) (|Fraction| (|Integer|)) (|Fraction| (|Integer|))) "\\spad{clipParametric(p,frac,sc)} performs two-dimensional clipping on a plot,{} \\spad{p},{} from the domain \\spadtype{Plot} for the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)}; the fraction parameter is specified by \\spad{frac} and the scale parameter is specified by \\spad{sc} for use in the \\fakeAxiomFun{iClipParametric} subroutine,{} which is called by this function.") (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|Plot|)) "\\spad{clipParametric(p)} performs two-dimensional clipping on a plot,{} \\spad{p},{} from the domain \\spadtype{Plot} for the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)}; the default parameters \\spad{1/2} for the fraction and \\spad{5/1} for the scale are used in the \\fakeAxiomFun{iClipParametric} subroutine,{} which is called by this function.")) (|clip| (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{clip(ll)} performs two-dimensional clipping on a list of lists of points,{} \\spad{ll}; the default parameters \\spad{1/2} for the fraction and \\spad{5/1} for the scale are used in the \\fakeAxiomFun{iClipParametric} subroutine,{} which is called by this function.") (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|List| (|Point| (|DoubleFloat|)))) "\\spad{clip(l)} performs two-dimensional clipping on a curve \\spad{l},{} which is a list of points; the default parameters \\spad{1/2} for the fraction and \\spad{5/1} for the scale are used in the \\fakeAxiomFun{iClipParametric} subroutine,{} which is called by this function.") (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|Plot|) (|Fraction| (|Integer|)) (|Fraction| (|Integer|))) "\\spad{clip(p,frac,sc)} performs two-dimensional clipping on a plot,{} \\spad{p},{} from the domain \\spadtype{Plot} for the graph of one variable \\spad{y = f(x)}; the fraction parameter is specified by \\spad{frac} and the scale parameter is specified by \\spad{sc} for use in the \\spadfun{clip} function.") (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|Plot|)) "\\spad{clip(p)} performs two-dimensional clipping on a plot,{} \\spad{p},{} from the domain \\spadtype{Plot} for the graph of one variable,{} \\spad{y = f(x)}; the default parameters \\spad{1/4} for the fraction and \\spad{5/1} for the scale are used in the \\spadfun{clip} function."))) @@ -560,7 +560,7 @@ NIL ((|constructor| (NIL "Color() specifies a domain of 27 colors provided in the \\Language{} system (the colors mix additively).")) (|color| (($ (|Integer|)) "\\spad{color(i)} returns a color of the indicated hue \\spad{i}.")) (|numberOfHues| (((|PositiveInteger|)) "\\spad{numberOfHues()} returns the number of total hues,{} set in totalHues.")) (|hue| (((|Integer|) $) "\\spad{hue(c)} returns the hue index of the indicated color \\spad{c}.")) (|blue| (($) "\\spad{blue()} returns the position of the blue hue from total hues.")) (|green| (($) "\\spad{green()} returns the position of the green hue from total hues.")) (|yellow| (($) "\\spad{yellow()} returns the position of the yellow hue from total hues.")) (|red| (($) "\\spad{red()} returns the position of the red hue from total hues.")) (+ (($ $ $) "\\spad{c1 + c2} additively mixes the two colors \\spad{c1} and \\spad{c2}.")) (* (($ (|DoubleFloat|) $) "\\spad{s * c},{} returns the color \\spad{c},{} whose weighted shade has been scaled by \\spad{s}.") (($ (|PositiveInteger|) $) "\\spad{s * c},{} returns the color \\spad{c},{} whose weighted shade has been scaled by \\spad{s}."))) NIL NIL -(-158 R -3867) +(-158 R -3879) ((|constructor| (NIL "Provides combinatorial functions over an integral domain.")) (|ipow| ((|#2| (|List| |#2|)) "\\spad{ipow(l)} should be local but conditional.")) (|iidprod| ((|#2| (|List| |#2|)) "\\spad{iidprod(l)} should be local but conditional.")) (|iidsum| ((|#2| (|List| |#2|)) "\\spad{iidsum(l)} should be local but conditional.")) (|iipow| ((|#2| (|List| |#2|)) "\\spad{iipow(l)} should be local but conditional.")) (|iiperm| ((|#2| (|List| |#2|)) "\\spad{iiperm(l)} should be local but conditional.")) (|iibinom| ((|#2| (|List| |#2|)) "\\spad{iibinom(l)} should be local but conditional.")) (|iifact| ((|#2| |#2|) "\\spad{iifact(x)} should be local but conditional.")) (|product| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{product(f(n), n = a..b)} returns \\spad{f}(a) * ... * \\spad{f}(\\spad{b}) as a formal product.") ((|#2| |#2| (|Symbol|)) "\\spad{product(f(n), n)} returns the formal product \\spad{P}(\\spad{n}) which verifies \\spad{P}(\\spad{n+1})\\spad{/P}(\\spad{n}) = \\spad{f}(\\spad{n}).")) (|summation| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{summation(f(n), n = a..b)} returns \\spad{f}(a) + ... + \\spad{f}(\\spad{b}) as a formal sum.") ((|#2| |#2| (|Symbol|)) "\\spad{summation(f(n), n)} returns the formal sum \\spad{S}(\\spad{n}) which verifies \\spad{S}(\\spad{n+1}) - \\spad{S}(\\spad{n}) = \\spad{f}(\\spad{n}).")) (|factorials| ((|#2| |#2| (|Symbol|)) "\\spad{factorials(f, x)} rewrites the permutations and binomials in \\spad{f} involving \\spad{x} in terms of factorials.") ((|#2| |#2|) "\\spad{factorials(f)} rewrites the permutations and binomials in \\spad{f} in terms of factorials.")) (|factorial| ((|#2| |#2|) "\\spad{factorial(n)} returns the factorial of \\spad{n},{} \\spadignore{i.e.} \\spad{n!}.")) (|permutation| ((|#2| |#2| |#2|) "\\spad{permutation(n, r)} returns the number of permutations of \\spad{n} objects taken \\spad{r} at a time,{} \\spadignore{i.e.} \\spad{n!/}(\\spad{n}-\\spad{r})!.")) (|binomial| ((|#2| |#2| |#2|) "\\spad{binomial(n, r)} returns the number of subsets of \\spad{r} objects taken among \\spad{n} objects,{} \\spadignore{i.e.} \\spad{n!/}(\\spad{r!} * (\\spad{n}-\\spad{r})!).")) (** ((|#2| |#2| |#2|) "\\spad{a ** b} is the formal exponential a**b.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\spad{F}; error if \\spad{op} is not a combinatorial operator.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} is \\spad{true} if \\spad{op} is a combinatorial operator."))) NIL NIL @@ -591,10 +591,10 @@ NIL (-165 S R) ((|constructor| (NIL "This category represents the extension of a ring by a square root of \\spad{-1}.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a rational number,{} or \"failed\" if \\spad{x} is not a rational number.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a rational number. Error: if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a rational number.")) (|polarCoordinates| (((|Record| (|:| |r| |#2|) (|:| |phi| |#2|)) $) "\\spad{polarCoordinates(x)} returns (\\spad{r},{} phi) such that \\spad{x} = \\spad{r} * exp(\\%\\spad{i} * phi).")) (|argument| ((|#2| $) "\\spad{argument(x)} returns the angle made by (0,{}1) and (0,{}\\spad{x}).")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x} = sqrt(norm(\\spad{x})).")) (|exquo| (((|Union| $ "failed") $ |#2|) "\\spad{exquo(x, r)} returns the exact quotient of \\spad{x} by \\spad{r},{} or \"failed\" if \\spad{r} does not divide \\spad{x} exactly.")) (|norm| ((|#2| $) "\\spad{norm(x)} returns \\spad{x} * conjugate(\\spad{x})")) (|real| ((|#2| $) "\\spad{real(x)} returns real part of \\spad{x}.")) (|imag| ((|#2| $) "\\spad{imag(x)} returns imaginary part of \\spad{x}.")) (|conjugate| (($ $) "\\spad{conjugate(x + \\%i y)} returns \\spad{x} - \\%\\spad{i} \\spad{y}.")) (|imaginary| (($) "\\spad{imaginary()} = sqrt(\\spad{-1}) = \\%\\spad{i}.")) (|complex| (($ |#2| |#2|) "\\spad{complex(x,y)} constructs \\spad{x} + \\%i*y.") ((|attribute|) "indicates that \\% has sqrt(\\spad{-1})"))) NIL -((|HasCategory| |#2| (QUOTE (-910))) (|HasCategory| |#2| (QUOTE (-548))) (|HasCategory| |#2| (QUOTE (-1003))) (|HasCategory| |#2| (QUOTE (-1202))) (|HasCategory| |#2| (QUOTE (-1061))) (|HasCategory| |#2| (QUOTE (-1023))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| |#2| (QUOTE (-365))) (|HasAttribute| |#2| (QUOTE -4413)) (|HasAttribute| |#2| (QUOTE -4416)) (|HasCategory| |#2| (QUOTE (-308))) (|HasCategory| |#2| (QUOTE (-559)))) +((|HasCategory| |#2| (QUOTE (-911))) (|HasCategory| |#2| (QUOTE (-548))) (|HasCategory| |#2| (QUOTE (-1004))) (|HasCategory| |#2| (QUOTE (-1203))) (|HasCategory| |#2| (QUOTE (-1062))) (|HasCategory| |#2| (QUOTE (-1024))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| |#2| (QUOTE (-365))) (|HasAttribute| |#2| (QUOTE -4414)) (|HasAttribute| |#2| (QUOTE -4417)) (|HasCategory| |#2| (QUOTE (-308))) (|HasCategory| |#2| (QUOTE (-559)))) (-166 R) ((|constructor| (NIL "This category represents the extension of a ring by a square root of \\spad{-1}.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a rational number,{} or \"failed\" if \\spad{x} is not a rational number.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a rational number. Error: if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a rational number.")) (|polarCoordinates| (((|Record| (|:| |r| |#1|) (|:| |phi| |#1|)) $) "\\spad{polarCoordinates(x)} returns (\\spad{r},{} phi) such that \\spad{x} = \\spad{r} * exp(\\%\\spad{i} * phi).")) (|argument| ((|#1| $) "\\spad{argument(x)} returns the angle made by (0,{}1) and (0,{}\\spad{x}).")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x} = sqrt(norm(\\spad{x})).")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(x, r)} returns the exact quotient of \\spad{x} by \\spad{r},{} or \"failed\" if \\spad{r} does not divide \\spad{x} exactly.")) (|norm| ((|#1| $) "\\spad{norm(x)} returns \\spad{x} * conjugate(\\spad{x})")) (|real| ((|#1| $) "\\spad{real(x)} returns real part of \\spad{x}.")) (|imag| ((|#1| $) "\\spad{imag(x)} returns imaginary part of \\spad{x}.")) (|conjugate| (($ $) "\\spad{conjugate(x + \\%i y)} returns \\spad{x} - \\%\\spad{i} \\spad{y}.")) (|imaginary| (($) "\\spad{imaginary()} = sqrt(\\spad{-1}) = \\%\\spad{i}.")) (|complex| (($ |#1| |#1|) "\\spad{complex(x,y)} constructs \\spad{x} + \\%i*y.") ((|attribute|) "indicates that \\% has sqrt(\\spad{-1})"))) -((-4410 -2797 (|has| |#1| (-559)) (-12 (|has| |#1| (-308)) (|has| |#1| (-910)))) (-4415 |has| |#1| (-365)) (-4409 |has| |#1| (-365)) (-4413 |has| |#1| (-6 -4413)) (-4416 |has| |#1| (-6 -4416)) (-3046 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) +((-4411 -2800 (|has| |#1| (-559)) (-12 (|has| |#1| (-308)) (|has| |#1| (-911)))) (-4416 |has| |#1| (-365)) (-4410 |has| |#1| (-365)) (-4414 |has| |#1| (-6 -4414)) (-4417 |has| |#1| (-6 -4417)) (-3056 . T) ((-4420 "*") . T) (-4412 . T) (-4413 . T) (-4415 . T)) NIL (-167 RR PR) ((|constructor| (NIL "\\indented{1}{Author:} Date Created: Date Last Updated: Basic Functions: Related Constructors: Complex,{} UnivariatePolynomial Also See: AMS Classifications: Keywords: complex,{} polynomial factorization,{} factor References:")) (|factor| (((|Factored| |#2|) |#2|) "\\spad{factor(p)} factorizes the polynomial \\spad{p} with complex coefficients."))) @@ -606,8 +606,8 @@ NIL NIL (-169 R) ((|constructor| (NIL "\\spadtype {Complex(R)} creates the domain of elements of the form \\spad{a + b * i} where \\spad{a} and \\spad{b} come from the ring \\spad{R},{} and \\spad{i} is a new element such that \\spad{i**2 = -1}."))) -((-4410 -2797 (|has| |#1| (-559)) (-12 (|has| |#1| (-308)) (|has| |#1| (-910)))) (-4415 |has| |#1| (-365)) (-4409 |has| |#1| (-365)) (-4413 |has| |#1| (-6 -4413)) (-4416 |has| |#1| (-6 -4416)) (-3046 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) -((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-351))) (-2797 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-351)))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-370))) (-2797 (-12 (|HasCategory| |#1| (LIST (QUOTE -615) (LIST (QUOTE -893) (QUOTE (-381))))) (|HasCategory| |#1| (QUOTE (-351)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -615) (LIST (QUOTE -893) (QUOTE (-567))))) (|HasCategory| |#1| (QUOTE (-351)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -517) (QUOTE (-1177)) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-351)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -1039) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (QUOTE (-351)))) (-12 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-351)))) (-12 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-351)))) (|HasCategory| |#1| (QUOTE (-233))) (-12 (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-351)))) (-12 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-351)))) (-12 (|HasCategory| |#1| (QUOTE (-351))) (|HasCategory| |#1| (LIST (QUOTE -287) (|devaluate| |#1|) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-351))) (|HasCategory| |#1| (LIST (QUOTE -640) (QUOTE (-567))))) (-12 (|HasCategory| |#1| (QUOTE (-351))) (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-1177))))) (-12 (|HasCategory| |#1| (QUOTE (-351))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| |#1| (QUOTE (-351))) (|HasCategory| |#1| (QUOTE (-559)))) (-12 (|HasCategory| |#1| (QUOTE (-351))) (|HasCategory| |#1| (QUOTE (-829)))) (-12 (|HasCategory| |#1| (QUOTE (-351))) (|HasCategory| |#1| (QUOTE (-1023)))) (-12 (|HasCategory| |#1| (QUOTE (-351))) (|HasCategory| |#1| (QUOTE (-1202)))) (-12 (|HasCategory| |#1| (QUOTE (-351))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539))))) (-12 (|HasCategory| |#1| (QUOTE (-351))) (|HasCategory| |#1| 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(|HasCategory| |#1| (LIST (QUOTE -902) (QUOTE (-1178))))) (-2800 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-911)))) (|HasCategory| |#1| (QUOTE (-145)))) (-2800 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-911)))) (|HasCategory| |#1| (QUOTE (-351))))) (-170 R S CS) ((|constructor| (NIL "This package supports converting complex expressions to patterns")) (|convert| (((|Pattern| |#1|) |#3|) "\\spad{convert(cs)} converts the complex expression \\spad{cs} to a pattern"))) NIL @@ -618,7 +618,7 @@ NIL NIL (-172) ((|constructor| (NIL "The category of commutative rings with unity,{} \\spadignore{i.e.} rings where \\spadop{*} is commutative,{} and which have a multiplicative identity. element.")) (|commutative| ((|attribute| "*") "multiplication is commutative."))) -(((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) +(((-4420 "*") . T) (-4412 . T) (-4413 . T) (-4415 . T)) NIL (-173) ((|constructor| (NIL "This category is the root of the I/O conduits.")) (|close!| (($ $) "\\spad{close!(c)} closes the conduit \\spad{c},{} changing its state to one that is invalid for future read or write operations."))) @@ -626,7 +626,7 @@ NIL NIL (-174 R) ((|constructor| (NIL "\\spadtype{ContinuedFraction} implements general \\indented{1}{continued fractions.\\space{2}This version is not restricted to simple,{}} \\indented{1}{finite fractions and uses the \\spadtype{Stream} as a} \\indented{1}{representation.\\space{2}The arithmetic functions assume that the} \\indented{1}{approximants alternate below/above the convergence point.} \\indented{1}{This is enforced by ensuring the partial numerators and partial} \\indented{1}{denominators are greater than 0 in the Euclidean domain view of \\spad{R}} \\indented{1}{(\\spadignore{i.e.} \\spad{sizeLess?(0, x)}).}")) (|complete| (($ $) "\\spad{complete(x)} causes all entries in \\spadvar{\\spad{x}} to be computed. Normally entries are only computed as needed. If \\spadvar{\\spad{x}} is an infinite continued fraction,{} a user-initiated interrupt is necessary to stop the computation.")) (|extend| (($ $ (|Integer|)) "\\spad{extend(x,n)} causes the first \\spadvar{\\spad{n}} entries in the continued fraction \\spadvar{\\spad{x}} to be computed. Normally entries are only computed as needed.")) (|denominators| (((|Stream| |#1|) $) "\\spad{denominators(x)} returns the stream of denominators of the approximants of the continued fraction \\spadvar{\\spad{x}}. If the continued fraction is finite,{} then the stream will be finite.")) (|numerators| (((|Stream| |#1|) $) "\\spad{numerators(x)} returns the stream of numerators of the approximants of the continued fraction \\spadvar{\\spad{x}}. If the continued fraction is finite,{} then the stream will be finite.")) (|convergents| (((|Stream| (|Fraction| |#1|)) $) "\\spad{convergents(x)} returns the stream of the convergents of the continued fraction \\spadvar{\\spad{x}}. If the continued fraction is finite,{} then the stream will be finite.")) (|approximants| (((|Stream| (|Fraction| |#1|)) $) "\\spad{approximants(x)} returns the stream of approximants of the continued fraction \\spadvar{\\spad{x}}. If the continued fraction is finite,{} then the stream will be infinite and periodic with period 1.")) (|reducedForm| (($ $) "\\spad{reducedForm(x)} puts the continued fraction \\spadvar{\\spad{x}} in reduced form,{} \\spadignore{i.e.} the function returns an equivalent continued fraction of the form \\spad{continuedFraction(b0,[1,1,1,...],[b1,b2,b3,...])}.")) (|wholePart| ((|#1| $) "\\spad{wholePart(x)} extracts the whole part of \\spadvar{\\spad{x}}. That is,{} if \\spad{x = continuedFraction(b0, [a1,a2,a3,...], [b1,b2,b3,...])},{} then \\spad{wholePart(x) = b0}.")) (|partialQuotients| (((|Stream| |#1|) $) "\\spad{partialQuotients(x)} extracts the partial quotients in \\spadvar{\\spad{x}}. That is,{} if \\spad{x = continuedFraction(b0, [a1,a2,a3,...], [b1,b2,b3,...])},{} then \\spad{partialQuotients(x) = [b0,b1,b2,b3,...]}.")) (|partialDenominators| (((|Stream| |#1|) $) "\\spad{partialDenominators(x)} extracts the denominators in \\spadvar{\\spad{x}}. That is,{} if \\spad{x = continuedFraction(b0, [a1,a2,a3,...], [b1,b2,b3,...])},{} then \\spad{partialDenominators(x) = [b1,b2,b3,...]}.")) (|partialNumerators| (((|Stream| |#1|) $) "\\spad{partialNumerators(x)} extracts the numerators in \\spadvar{\\spad{x}}. That is,{} if \\spad{x = continuedFraction(b0, [a1,a2,a3,...], [b1,b2,b3,...])},{} then \\spad{partialNumerators(x) = [a1,a2,a3,...]}.")) (|reducedContinuedFraction| (($ |#1| (|Stream| |#1|)) "\\spad{reducedContinuedFraction(b0,b)} constructs a continued fraction in the following way: if \\spad{b = [b1,b2,...]} then the result is the continued fraction \\spad{b0 + 1/(b1 + 1/(b2 + ...))}. That is,{} the result is the same as \\spad{continuedFraction(b0,[1,1,1,...],[b1,b2,b3,...])}.")) (|continuedFraction| (($ |#1| (|Stream| |#1|) (|Stream| |#1|)) "\\spad{continuedFraction(b0,a,b)} constructs a continued fraction in the following way: if \\spad{a = [a1,a2,...]} and \\spad{b = [b1,b2,...]} then the result is the continued fraction \\spad{b0 + a1/(b1 + a2/(b2 + ...))}.") (($ (|Fraction| |#1|)) "\\spad{continuedFraction(r)} converts the fraction \\spadvar{\\spad{r}} with components of type \\spad{R} to a continued fraction over \\spad{R}."))) -(((-4419 "*") . T) (-4410 . T) (-4415 . T) (-4409 . T) (-4411 . T) (-4412 . T) (-4414 . T)) +(((-4420 "*") . T) (-4411 . T) (-4416 . T) (-4410 . T) (-4412 . T) (-4413 . T) (-4415 . T)) NIL (-175) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. A `Contour' a list of bindings making up a `virtual scope'.")) (|findBinding| (((|Maybe| (|Binding|)) (|Identifier|) $) "\\spad{findBinding(c,n)} returns the first binding associated with \\spad{`n'}. Otherwise `nothing.")) (|push| (($ (|Binding|) $) "\\spad{push(c,b)} augments the contour with binding \\spad{`b'}.")) (|bindings| (((|List| (|Binding|)) $) "\\spad{bindings(c)} returns the list of bindings in countour \\spad{c}."))) @@ -643,7 +643,7 @@ NIL (-178 R S CS) ((|constructor| (NIL "This package supports matching patterns involving complex expressions")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(cexpr, pat, res)} matches the pattern \\spad{pat} to the complex expression \\spad{cexpr}. res contains the variables of \\spad{pat} which are already matched and their matches."))) NIL -((|HasCategory| (-953 |#2|) (LIST (QUOTE -887) (|devaluate| |#1|)))) +((|HasCategory| (-954 |#2|) (LIST (QUOTE -888) (|devaluate| |#1|)))) (-179 R) ((|constructor| (NIL "This package \\undocumented{}")) (|multiEuclideanTree| (((|List| |#1|) (|List| |#1|) |#1|) "\\spad{multiEuclideanTree(l,r)} \\undocumented{}")) (|chineseRemainder| (((|List| |#1|) (|List| (|List| |#1|)) (|List| |#1|)) "\\spad{chineseRemainder(llv,lm)} returns a list of values,{} each of which corresponds to the Chinese remainder of the associated element of \\axiom{\\spad{llv}} and axiom{\\spad{lm}}. This is more efficient than applying chineseRemainder several times.") ((|#1| (|List| |#1|) (|List| |#1|)) "\\spad{chineseRemainder(lv,lm)} returns a value \\axiom{\\spad{v}} such that,{} if \\spad{x} is \\axiom{\\spad{lv}.\\spad{i}} modulo \\axiom{\\spad{lm}.\\spad{i}} for all \\axiom{\\spad{i}},{} then \\spad{x} is \\axiom{\\spad{v}} modulo \\axiom{\\spad{lm}(1)\\spad{*lm}(2)*...\\spad{*lm}(\\spad{n})}.")) (|modTree| (((|List| |#1|) |#1| (|List| |#1|)) "\\spad{modTree(r,l)} \\undocumented{}"))) NIL @@ -680,7 +680,7 @@ NIL ((|constructor| (NIL "This domain provides implementations for constructors.")) (|findConstructor| (((|Maybe| $) (|Identifier|)) "\\spad{findConstructor(s)} attempts to find a constructor named \\spad{s}. If successful,{} returns that constructor; otherwise,{} returns \\spad{nothing}."))) NIL NIL -(-188 R -3867) +(-188 R -3879) ((|constructor| (NIL "\\spadtype{ComplexTrigonometricManipulations} provides function that compute the real and imaginary parts of complex functions.")) (|complexForm| (((|Complex| (|Expression| |#1|)) |#2|) "\\spad{complexForm(f)} returns \\spad{[real f, imag f]}.")) (|trigs| ((|#2| |#2|) "\\spad{trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (|real?| (((|Boolean|) |#2|) "\\spad{real?(f)} returns \\spad{true} if \\spad{f = real f}.")) (|imag| (((|Expression| |#1|) |#2|) "\\spad{imag(f)} returns the imaginary part of \\spad{f} where \\spad{f} is a complex function.")) (|real| (((|Expression| |#1|) |#2|) "\\spad{real(f)} returns the real part of \\spad{f} where \\spad{f} is a complex function.")) (|complexElementary| ((|#2| |#2| (|Symbol|)) "\\spad{complexElementary(f, x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.") ((|#2| |#2|) "\\spad{complexElementary(f)} rewrites \\spad{f} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.")) (|complexNormalize| ((|#2| |#2| (|Symbol|)) "\\spad{complexNormalize(f, x)} rewrites \\spad{f} using the least possible number of complex independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{complexNormalize(f)} rewrites \\spad{f} using the least possible number of complex independent kernels."))) NIL NIL @@ -788,23 +788,23 @@ NIL ((|constructor| (NIL "\\indented{1}{This domain implements a simple view of a database whose fields are} indexed by symbols")) (- (($ $ $) "\\spad{db1-db2} returns the difference of databases \\spad{db1} and \\spad{db2} \\spadignore{i.e.} consisting of elements in \\spad{db1} but not in \\spad{db2}")) (+ (($ $ $) "\\spad{db1+db2} returns the merge of databases \\spad{db1} and \\spad{db2}")) (|fullDisplay| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{fullDisplay(db,start,end )} prints full details of entries in the range \\axiom{\\spad{start}..end} in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{fullDisplay(db)} prints full details of each entry in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{fullDisplay(x)} displays \\spad{x} in detail")) (|display| (((|Void|) $) "\\spad{display(db)} prints a summary line for each entry in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{display(x)} displays \\spad{x} in some form")) (|elt| (((|DataList| (|String|)) $ (|Symbol|)) "\\spad{elt(db,s)} returns the \\axiom{\\spad{s}} field of each element of \\axiom{\\spad{db}}.") (($ $ (|QueryEquation|)) "\\spad{elt(db,q)} returns all elements of \\axiom{\\spad{db}} which satisfy \\axiom{\\spad{q}}.") (((|String|) $ (|Symbol|)) "\\spad{elt(x,s)} returns an element of \\spad{x} indexed by \\spad{s}"))) NIL NIL -(-215 -3867 UP UPUP R) +(-215 -3879 UP UPUP R) ((|constructor| (NIL "This package provides functions for computing the residues of a function on an algebraic curve.")) (|doubleResultant| ((|#2| |#4| (|Mapping| |#2| |#2|)) "\\spad{doubleResultant(f, ')} returns \\spad{p}(\\spad{x}) whose roots are rational multiples of the residues of \\spad{f} at all its finite poles. Argument ' is the derivation to use."))) NIL NIL -(-216 -3867 FP) +(-216 -3879 FP) ((|constructor| (NIL "Package for the factorization of a univariate polynomial with coefficients in a finite field. The algorithm used is the \"distinct degree\" algorithm of Cantor-Zassenhaus,{} modified to use trace instead of the norm and a table for computing Frobenius as suggested by Naudin and Quitte .")) (|irreducible?| (((|Boolean|) |#2|) "\\spad{irreducible?(p)} tests whether the polynomial \\spad{p} is irreducible.")) (|tracePowMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{tracePowMod(u,k,v)} produces the sum of \\spad{u**(q**i)} for \\spad{i} running and \\spad{q=} size \\spad{F}")) (|trace2PowMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{trace2PowMod(u,k,v)} produces the sum of \\spad{u**(2**i)} for \\spad{i} running from 1 to \\spad{k} all computed modulo the polynomial \\spad{v}.")) (|exptMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{exptMod(u,k,v)} raises the polynomial \\spad{u} to the \\spad{k}th power modulo the polynomial \\spad{v}.")) (|separateFactors| (((|List| |#2|) (|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |prod| |#2|)))) "\\spad{separateFactors(lfact)} takes the list produced by \\spadfunFrom{separateDegrees}{DistinctDegreeFactorization} and produces the complete list of factors.")) (|separateDegrees| (((|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |prod| |#2|))) |#2|) "\\spad{separateDegrees(p)} splits the square free polynomial \\spad{p} into factors each of which is a product of irreducibles of the same degree.")) (|distdfact| (((|Record| (|:| |cont| |#1|) (|:| |factors| (|List| (|Record| (|:| |irr| |#2|) (|:| |pow| (|Integer|)))))) |#2| (|Boolean|)) "\\spad{distdfact(p,sqfrflag)} produces the complete factorization of the polynomial \\spad{p} returning an internal data structure. If argument \\spad{sqfrflag} is \\spad{true},{} the polynomial is assumed square free.")) (|factorSquareFree| (((|Factored| |#2|) |#2|) "\\spad{factorSquareFree(p)} produces the complete factorization of the square free polynomial \\spad{p}.")) (|factor| (((|Factored| |#2|) |#2|) "\\spad{factor(p)} produces the complete factorization of the polynomial \\spad{p}."))) NIL NIL (-217) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating decimal expansions.")) (|decimal| (($ (|Fraction| (|Integer|))) "\\spad{decimal(r)} converts a rational number to a decimal expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(d)} returns the fractional part of a decimal expansion."))) -((-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) -((|HasCategory| (-567) (QUOTE (-910))) (|HasCategory| (-567) (LIST (QUOTE -1039) (QUOTE (-1177)))) (|HasCategory| (-567) (QUOTE (-145))) (|HasCategory| (-567) (QUOTE (-147))) (|HasCategory| (-567) (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| (-567) (QUOTE (-1023))) (|HasCategory| (-567) (QUOTE (-821))) (-2797 (|HasCategory| (-567) (QUOTE (-821))) (|HasCategory| (-567) (QUOTE (-851)))) (|HasCategory| (-567) (LIST (QUOTE -1039) (QUOTE (-567)))) (|HasCategory| (-567) (QUOTE (-1152))) (|HasCategory| (-567) (LIST (QUOTE -887) (QUOTE (-381)))) (|HasCategory| (-567) (LIST (QUOTE -887) (QUOTE (-567)))) (|HasCategory| (-567) (LIST (QUOTE -615) (LIST (QUOTE -893) (QUOTE (-381))))) (|HasCategory| (-567) (LIST (QUOTE -615) (LIST (QUOTE -893) (QUOTE (-567))))) (|HasCategory| (-567) (QUOTE (-233))) (|HasCategory| (-567) (LIST (QUOTE -901) (QUOTE (-1177)))) (|HasCategory| (-567) (LIST (QUOTE -517) (QUOTE (-1177)) (QUOTE (-567)))) (|HasCategory| (-567) (LIST (QUOTE -310) (QUOTE (-567)))) (|HasCategory| (-567) (LIST (QUOTE -287) (QUOTE (-567)) (QUOTE (-567)))) (|HasCategory| (-567) (QUOTE (-308))) (|HasCategory| (-567) (QUOTE (-548))) (|HasCategory| (-567) (QUOTE (-851))) (|HasCategory| (-567) (LIST (QUOTE -640) (QUOTE (-567)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-567) (QUOTE (-910)))) (-2797 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-567) (QUOTE (-910)))) (|HasCategory| (-567) (QUOTE (-145))))) +((-4410 . T) (-4416 . T) (-4411 . T) ((-4420 "*") . T) (-4412 . T) (-4413 . T) (-4415 . T)) +((|HasCategory| (-567) (QUOTE (-911))) (|HasCategory| (-567) (LIST (QUOTE -1040) (QUOTE (-1178)))) (|HasCategory| (-567) (QUOTE (-145))) (|HasCategory| (-567) (QUOTE (-147))) (|HasCategory| (-567) (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| (-567) (QUOTE (-1024))) (|HasCategory| (-567) (QUOTE (-821))) (-2800 (|HasCategory| (-567) (QUOTE (-821))) (|HasCategory| (-567) (QUOTE (-851)))) (|HasCategory| (-567) (LIST (QUOTE -1040) (QUOTE (-567)))) (|HasCategory| (-567) (QUOTE (-1153))) (|HasCategory| (-567) (LIST (QUOTE -888) (QUOTE (-381)))) (|HasCategory| (-567) (LIST (QUOTE -888) (QUOTE (-567)))) (|HasCategory| (-567) (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-381))))) (|HasCategory| (-567) (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567))))) (|HasCategory| (-567) (QUOTE (-233))) (|HasCategory| (-567) (LIST (QUOTE -902) (QUOTE (-1178)))) (|HasCategory| (-567) (LIST (QUOTE -517) (QUOTE (-1178)) (QUOTE (-567)))) (|HasCategory| (-567) (LIST (QUOTE -310) (QUOTE (-567)))) (|HasCategory| (-567) (LIST (QUOTE -287) (QUOTE (-567)) (QUOTE (-567)))) (|HasCategory| (-567) (QUOTE (-308))) (|HasCategory| (-567) (QUOTE (-548))) (|HasCategory| (-567) (QUOTE (-851))) (|HasCategory| (-567) (LIST (QUOTE -640) (QUOTE (-567)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-567) (QUOTE (-911)))) (-2800 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-567) (QUOTE (-911)))) (|HasCategory| (-567) (QUOTE (-145))))) (-218) ((|constructor| (NIL "This domain represents the syntax of a definition.")) (|body| (((|SpadAst|) $) "\\spad{body(d)} returns the right hand side of the definition \\spad{`d'}.")) (|signature| (((|Signature|) $) "\\spad{signature(d)} returns the signature of the operation being defined. Note that this list may be partial in that it contains only the types actually specified in the definition.")) (|head| (((|HeadAst|) $) "\\spad{head(d)} returns the head of the definition \\spad{`d'}. This is a list of identifiers starting with the name of the operation followed by the name of the parameters,{} if any."))) NIL NIL -(-219 R -3867) +(-219 R -3879) ((|constructor| (NIL "\\spadtype{ElementaryFunctionDefiniteIntegration} provides functions to compute definite integrals of elementary functions.")) (|innerint| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{innerint(f, x, a, b, ignore?)} should be local but conditional")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|)) (|String|)) "\\spad{integrate(f, x = a..b, \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|))) "\\spad{integrate(f, x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}."))) NIL NIL @@ -818,19 +818,19 @@ NIL NIL (-222 S) ((|constructor| (NIL "Linked list implementation of a Dequeue")) (|dequeue| (($ (|List| |#1|)) "\\spad{dequeue([x,y,...,z])} creates a dequeue with first (top or front) element \\spad{x},{} second element \\spad{y},{}...,{}and last (bottom or back) element \\spad{z}."))) -((-4417 . T) (-4418 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1101))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1101))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-1101))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) +((-4418 . T) (-4419 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1102))) (-2800 (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (-223 |CoefRing| |listIndVar|) ((|constructor| (NIL "The deRham complex of Euclidean space,{} that is,{} the class of differential forms of arbitary degree over a coefficient ring. See Flanders,{} Harley,{} Differential Forms,{} With Applications to the Physical Sciences,{} New York,{} Academic Press,{} 1963.")) (|exteriorDifferential| (($ $) "\\spad{exteriorDifferential(df)} returns the exterior derivative (gradient,{} curl,{} divergence,{} ...) of the differential form \\spad{df}.")) (|totalDifferential| (($ (|Expression| |#1|)) "\\spad{totalDifferential(x)} returns the total differential (gradient) form for element \\spad{x}.")) (|map| (($ (|Mapping| (|Expression| |#1|) (|Expression| |#1|)) $) "\\spad{map(f,df)} replaces each coefficient \\spad{x} of differential form \\spad{df} by \\spad{f(x)}.")) (|degree| (((|Integer|) $) "\\spad{degree(df)} returns the homogeneous degree of differential form \\spad{df}.")) (|retractable?| (((|Boolean|) $) "\\spad{retractable?(df)} tests if differential form \\spad{df} is a 0-form,{} \\spadignore{i.e.} if degree(\\spad{df}) = 0.")) (|homogeneous?| (((|Boolean|) $) "\\spad{homogeneous?(df)} tests if all of the terms of differential form \\spad{df} have the same degree.")) (|generator| (($ (|NonNegativeInteger|)) "\\spad{generator(n)} returns the \\spad{n}th basis term for a differential form.")) (|coefficient| (((|Expression| |#1|) $ $) "\\spad{coefficient(df,u)},{} where \\spad{df} is a differential form,{} returns the coefficient of \\spad{df} containing the basis term \\spad{u} if such a term exists,{} and 0 otherwise.")) (|reductum| (($ $) "\\spad{reductum(df)},{} where \\spad{df} is a differential form,{} returns \\spad{df} minus the leading term of \\spad{df} if \\spad{df} has two or more terms,{} and 0 otherwise.")) (|leadingBasisTerm| (($ $) "\\spad{leadingBasisTerm(df)} returns the leading basis term of differential form \\spad{df}.")) (|leadingCoefficient| (((|Expression| |#1|) $) "\\spad{leadingCoefficient(df)} returns the leading coefficient of differential form \\spad{df}."))) -((-4414 . T)) +((-4415 . T)) NIL -(-224 R -3867) +(-224 R -3879) ((|constructor| (NIL "\\spadtype{DefiniteIntegrationTools} provides common tools used by the definite integration of both rational and elementary functions.")) (|checkForZero| (((|Union| (|Boolean|) "failed") (|SparseUnivariatePolynomial| |#2|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{checkForZero(p, a, b, incl?)} is \\spad{true} if \\spad{p} has a zero between a and \\spad{b},{} \\spad{false} otherwise,{} \"failed\" if this cannot be determined. Check for a and \\spad{b} inclusive if incl? is \\spad{true},{} exclusive otherwise.") (((|Union| (|Boolean|) "failed") (|Polynomial| |#1|) (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{checkForZero(p, x, a, b, incl?)} is \\spad{true} if \\spad{p} has a zero for \\spad{x} between a and \\spad{b},{} \\spad{false} otherwise,{} \"failed\" if this cannot be determined. Check for a and \\spad{b} inclusive if incl? is \\spad{true},{} exclusive otherwise.")) (|computeInt| (((|Union| (|OrderedCompletion| |#2|) "failed") (|Kernel| |#2|) |#2| (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{computeInt(x, g, a, b, eval?)} returns the integral of \\spad{f} for \\spad{x} between a and \\spad{b},{} assuming that \\spad{g} is an indefinite integral of \\spad{f} and \\spad{f} has no pole between a and \\spad{b}. If \\spad{eval?} is \\spad{true},{} then \\spad{g} can be evaluated safely at \\spad{a} and \\spad{b},{} provided that they are finite values. Otherwise,{} limits must be computed.")) (|ignore?| (((|Boolean|) (|String|)) "\\spad{ignore?(s)} is \\spad{true} if \\spad{s} is the string that tells the integrator to assume that the function has no pole in the integration interval."))) NIL NIL (-225) ((|constructor| (NIL "\\indented{1}{\\spadtype{DoubleFloat} is intended to make accessible} hardware floating point arithmetic in \\Language{},{} either native double precision,{} or IEEE. On most machines,{} there will be hardware support for the arithmetic operations: \\spadfunFrom{+}{DoubleFloat},{} \\spadfunFrom{*}{DoubleFloat},{} \\spadfunFrom{/}{DoubleFloat} and possibly also the \\spadfunFrom{sqrt}{DoubleFloat} operation. The operations \\spadfunFrom{exp}{DoubleFloat},{} \\spadfunFrom{log}{DoubleFloat},{} \\spadfunFrom{sin}{DoubleFloat},{} \\spadfunFrom{cos}{DoubleFloat},{} \\spadfunFrom{atan}{DoubleFloat} are normally coded in software based on minimax polynomial/rational approximations. Note that under Lisp/VM,{} \\spadfunFrom{atan}{DoubleFloat} is not available at this time. Some general comments about the accuracy of the operations: the operations \\spadfunFrom{+}{DoubleFloat},{} \\spadfunFrom{*}{DoubleFloat},{} \\spadfunFrom{/}{DoubleFloat} and \\spadfunFrom{sqrt}{DoubleFloat} are expected to be fully accurate. The operations \\spadfunFrom{exp}{DoubleFloat},{} \\spadfunFrom{log}{DoubleFloat},{} \\spadfunFrom{sin}{DoubleFloat},{} \\spadfunFrom{cos}{DoubleFloat} and \\spadfunFrom{atan}{DoubleFloat} are not expected to be fully accurate. In particular,{} \\spadfunFrom{sin}{DoubleFloat} and \\spadfunFrom{cos}{DoubleFloat} will lose all precision for large arguments. \\blankline The \\spadtype{Float} domain provides an alternative to the \\spad{DoubleFloat} domain. It provides an arbitrary precision model of floating point arithmetic. This means that accuracy problems like those above are eliminated by increasing the working precision where necessary. \\spadtype{Float} provides some special functions such as \\spadfunFrom{erf}{DoubleFloat},{} the error function in addition to the elementary functions. The disadvantage of \\spadtype{Float} is that it is much more expensive than small floats when the latter can be used.")) (|rationalApproximation| (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rationalApproximation(f, n, b)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< b**(-n)} (that is,{} \\spad{|(r-f)/f| < b**(-n)}).") (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|)) "\\spad{rationalApproximation(f, n)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< 10**(-n)}.")) (|Beta| (($ $ $) "\\spad{Beta(x,y)} is \\spad{Gamma(x) * Gamma(y)/Gamma(x+y)}.")) (|Gamma| (($ $) "\\spad{Gamma(x)} is the Euler Gamma function.")) (|atan| (($ $ $) "\\spad{atan(x,y)} computes the arc tangent from \\spad{x} with phase \\spad{y}.")) (|log10| (($ $) "\\spad{log10(x)} computes the logarithm with base 10 for \\spad{x}.")) (|log2| (($ $) "\\spad{log2(x)} computes the logarithm with base 2 for \\spad{x}.")) (|exp1| (($) "\\spad{exp1()} returns the natural log base \\spad{2.718281828...}.")) (** (($ $ $) "\\spad{x ** y} returns the \\spad{y}th power of \\spad{x} (equal to \\spad{exp(y log x)}).")) (/ (($ $ (|Integer|)) "\\spad{x / i} computes the division from \\spad{x} by an integer \\spad{i}."))) -((-3040 . T) (-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) +((-3050 . T) (-4410 . T) (-4416 . T) (-4411 . T) ((-4420 "*") . T) (-4412 . T) (-4413 . T) (-4415 . T)) NIL (-226) ((|constructor| (NIL "This package provides special functions for double precision real and complex floating point.")) (|hypergeometric0F1| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{hypergeometric0F1(c,z)} is the hypergeometric function \\spad{0F1(; c; z)}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{hypergeometric0F1(c,z)} is the hypergeometric function \\spad{0F1(; c; z)}.")) (|airyBi| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyBi(x)} is the Airy function \\spad{Bi(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Bi''(x) - x * Bi(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyBi(x)} is the Airy function \\spad{Bi(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Bi''(x) - x * Bi(x) = 0}.}")) (|airyAi| (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyAi(x)} is the Airy function \\spad{Ai(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Ai''(x) - x * Ai(x) = 0}.}") (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyAi(x)} is the Airy function \\spad{Ai(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Ai''(x) - x * Ai(x) = 0}.}")) (|besselK| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselK(v,x)} is the modified Bessel function of the first kind,{} \\spad{K(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{K(v,x) = \\%pi/2*(I(-v,x) - I(v,x))/sin(v*\\%pi)}} so is not valid for integer values of \\spad{v}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselK(v,x)} is the modified Bessel function of the first kind,{} \\spad{K(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{K(v,x) = \\%pi/2*(I(-v,x) - I(v,x))/sin(v*\\%pi)}.} so is not valid for integer values of \\spad{v}.")) (|besselI| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselI(v,x)} is the modified Bessel function of the first kind,{} \\spad{I(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselI(v,x)} is the modified Bessel function of the first kind,{} \\spad{I(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.}")) (|besselY| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselY(v,x)} is the Bessel function of the second kind,{} \\spad{Y(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{Y(v,x) = (J(v,x) cos(v*\\%pi) - J(-v,x))/sin(v*\\%pi)}} so is not valid for integer values of \\spad{v}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselY(v,x)} is the Bessel function of the second kind,{} \\spad{Y(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{Y(v,x) = (J(v,x) cos(v*\\%pi) - J(-v,x))/sin(v*\\%pi)}} so is not valid for integer values of \\spad{v}.")) (|besselJ| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselJ(v,x)} is the Bessel function of the first kind,{} \\spad{J(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselJ(v,x)} is the Bessel function of the first kind,{} \\spad{J(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.}")) (|polygamma| (((|Complex| (|DoubleFloat|)) (|NonNegativeInteger|) (|Complex| (|DoubleFloat|))) "\\spad{polygamma(n, x)} is the \\spad{n}-th derivative of \\spad{digamma(x)}.") (((|DoubleFloat|) (|NonNegativeInteger|) (|DoubleFloat|)) "\\spad{polygamma(n, x)} is the \\spad{n}-th derivative of \\spad{digamma(x)}.")) (|digamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{digamma(x)} is the function,{} \\spad{psi(x)},{} defined by \\indented{2}{\\spad{psi(x) = Gamma'(x)/Gamma(x)}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{digamma(x)} is the function,{} \\spad{psi(x)},{} defined by \\indented{2}{\\spad{psi(x) = Gamma'(x)/Gamma(x)}.}")) (|logGamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{logGamma(x)} is the natural log of \\spad{Gamma(x)}. This can often be computed even if \\spad{Gamma(x)} cannot.") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{logGamma(x)} is the natural log of \\spad{Gamma(x)}. This can often be computed even if \\spad{Gamma(x)} cannot.")) (|Beta| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{Beta(x, y)} is the Euler beta function,{} \\spad{B(x,y)},{} defined by \\indented{2}{\\spad{Beta(x,y) = integrate(t^(x-1)*(1-t)^(y-1), t=0..1)}.} This is related to \\spad{Gamma(x)} by \\indented{2}{\\spad{Beta(x,y) = Gamma(x)*Gamma(y) / Gamma(x + y)}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{Beta(x, y)} is the Euler beta function,{} \\spad{B(x,y)},{} defined by \\indented{2}{\\spad{Beta(x,y) = integrate(t^(x-1)*(1-t)^(y-1), t=0..1)}.} This is related to \\spad{Gamma(x)} by \\indented{2}{\\spad{Beta(x,y) = Gamma(x)*Gamma(y) / Gamma(x + y)}.}")) (|Gamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{Gamma(x)} is the Euler gamma function,{} \\spad{Gamma(x)},{} defined by \\indented{2}{\\spad{Gamma(x) = integrate(t^(x-1)*exp(-t), t=0..\\%infinity)}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{Gamma(x)} is the Euler gamma function,{} \\spad{Gamma(x)},{} defined by \\indented{2}{\\spad{Gamma(x) = integrate(t^(x-1)*exp(-t), t=0..\\%infinity)}.}"))) @@ -838,23 +838,23 @@ NIL NIL (-227 R) ((|constructor| (NIL "\\indented{1}{A Denavit-Hartenberg Matrix is a 4x4 Matrix of the form:} \\indented{1}{\\spad{nx ox ax px}} \\indented{1}{\\spad{ny oy ay py}} \\indented{1}{\\spad{nz oz az pz}} \\indented{2}{\\spad{0\\space{2}0\\space{2}0\\space{2}1}} (\\spad{n},{} \\spad{o},{} and a are the direction cosines)")) (|translate| (($ |#1| |#1| |#1|) "\\spad{translate(X,Y,Z)} returns a dhmatrix for translation by \\spad{X},{} \\spad{Y},{} and \\spad{Z}")) (|scale| (($ |#1| |#1| |#1|) "\\spad{scale(sx,sy,sz)} returns a dhmatrix for scaling in the \\spad{X},{} \\spad{Y} and \\spad{Z} directions")) (|rotatez| (($ |#1|) "\\spad{rotatez(r)} returns a dhmatrix for rotation about axis \\spad{Z} for \\spad{r} degrees")) (|rotatey| (($ |#1|) "\\spad{rotatey(r)} returns a dhmatrix for rotation about axis \\spad{Y} for \\spad{r} degrees")) (|rotatex| (($ |#1|) "\\spad{rotatex(r)} returns a dhmatrix for rotation about axis \\spad{X} for \\spad{r} degrees")) (|identity| (($) "\\spad{identity()} create the identity dhmatrix")) (* (((|Point| |#1|) $ (|Point| |#1|)) "\\spad{t*p} applies the dhmatrix \\spad{t} to point \\spad{p}"))) -((-4417 . T) (-4418 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1101))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1101))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-1101))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-559))) (|HasAttribute| |#1| (QUOTE (-4419 "*"))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) +((-4418 . T) (-4419 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1102))) (-2800 (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-559))) (|HasAttribute| |#1| (QUOTE (-4420 "*"))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (-228 A S) ((|constructor| (NIL "A dictionary is an aggregate in which entries can be inserted,{} searched for and removed. Duplicates are thrown away on insertion. This category models the usual notion of dictionary which involves large amounts of data where copying is impractical. Principal operations are thus destructive (non-copying) ones."))) NIL NIL (-229 S) ((|constructor| (NIL "A dictionary is an aggregate in which entries can be inserted,{} searched for and removed. Duplicates are thrown away on insertion. This category models the usual notion of dictionary which involves large amounts of data where copying is impractical. Principal operations are thus destructive (non-copying) ones."))) -((-4418 . T)) +((-4419 . T)) NIL (-230 S R) ((|constructor| (NIL "Differential extensions of a ring \\spad{R}. Given a differentiation on \\spad{R},{} extend it to a differentiation on \\%.")) (D (($ $ (|Mapping| |#2| |#2|) (|NonNegativeInteger|)) "\\spad{D(x, deriv, n)} differentiate \\spad{x} \\spad{n} times using a derivation which extends \\spad{deriv} on \\spad{R}.") (($ $ (|Mapping| |#2| |#2|)) "\\spad{D(x, deriv)} differentiates \\spad{x} extending the derivation deriv on \\spad{R}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|) (|NonNegativeInteger|)) "\\spad{differentiate(x, deriv, n)} differentiate \\spad{x} \\spad{n} times using a derivation which extends \\spad{deriv} on \\spad{R}.") (($ $ (|Mapping| |#2| |#2|)) "\\spad{differentiate(x, deriv)} differentiates \\spad{x} extending the derivation deriv on \\spad{R}."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -901) (QUOTE (-1177)))) (|HasCategory| |#2| (QUOTE (-233)))) +((|HasCategory| |#2| (LIST (QUOTE -902) (QUOTE (-1178)))) (|HasCategory| |#2| (QUOTE (-233)))) (-231 R) ((|constructor| (NIL "Differential extensions of a ring \\spad{R}. Given a differentiation on \\spad{R},{} extend it to a differentiation on \\%.")) (D (($ $ (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) "\\spad{D(x, deriv, n)} differentiate \\spad{x} \\spad{n} times using a derivation which extends \\spad{deriv} on \\spad{R}.") (($ $ (|Mapping| |#1| |#1|)) "\\spad{D(x, deriv)} differentiates \\spad{x} extending the derivation deriv on \\spad{R}.")) (|differentiate| (($ $ (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) "\\spad{differentiate(x, deriv, n)} differentiate \\spad{x} \\spad{n} times using a derivation which extends \\spad{deriv} on \\spad{R}.") (($ $ (|Mapping| |#1| |#1|)) "\\spad{differentiate(x, deriv)} differentiates \\spad{x} extending the derivation deriv on \\spad{R}."))) -((-4414 . T)) +((-4415 . T)) NIL (-232 S) ((|constructor| (NIL "An ordinary differential ring,{} that is,{} a ring with an operation \\spadfun{differentiate}. \\blankline")) (D (($ $ (|NonNegativeInteger|)) "\\spad{D(x, n)} returns the \\spad{n}-th derivative of \\spad{x}.") (($ $) "\\spad{D(x)} returns the derivative of \\spad{x}. This function is a simple differential operator where no variable needs to be specified.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(x, n)} returns the \\spad{n}-th derivative of \\spad{x}.") (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}. This function is a simple differential operator where no variable needs to be specified."))) @@ -862,36 +862,36 @@ NIL NIL (-233) ((|constructor| (NIL "An ordinary differential ring,{} that is,{} a ring with an operation \\spadfun{differentiate}. \\blankline")) (D (($ $ (|NonNegativeInteger|)) "\\spad{D(x, n)} returns the \\spad{n}-th derivative of \\spad{x}.") (($ $) "\\spad{D(x)} returns the derivative of \\spad{x}. This function is a simple differential operator where no variable needs to be specified.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(x, n)} returns the \\spad{n}-th derivative of \\spad{x}.") (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}. This function is a simple differential operator where no variable needs to be specified."))) -((-4414 . T)) +((-4415 . T)) NIL (-234 A S) ((|constructor| (NIL "This category is a collection of operations common to both categories \\spadtype{Dictionary} and \\spadtype{MultiDictionary}")) (|select!| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{select!(p,d)} destructively changes dictionary \\spad{d} by removing all entries \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is not \\spad{true}.")) (|remove!| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{remove!(p,d)} destructively changes dictionary \\spad{d} by removeing all entries \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}.") (($ |#2| $) "\\spad{remove!(x,d)} destructively changes dictionary \\spad{d} by removing all entries \\spad{y} such that \\axiom{\\spad{y} = \\spad{x}}.")) (|dictionary| (($ (|List| |#2|)) "\\spad{dictionary([x,y,...,z])} creates a dictionary consisting of entries \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}}.") (($) "\\spad{dictionary()}\\$\\spad{D} creates an empty dictionary of type \\spad{D}."))) NIL -((|HasAttribute| |#1| (QUOTE -4417))) +((|HasAttribute| |#1| (QUOTE -4418))) (-235 S) ((|constructor| (NIL "This category is a collection of operations common to both categories \\spadtype{Dictionary} and \\spadtype{MultiDictionary}")) (|select!| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select!(p,d)} destructively changes dictionary \\spad{d} by removing all entries \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is not \\spad{true}.")) (|remove!| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove!(p,d)} destructively changes dictionary \\spad{d} by removeing all entries \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}.") (($ |#1| $) "\\spad{remove!(x,d)} destructively changes dictionary \\spad{d} by removing all entries \\spad{y} such that \\axiom{\\spad{y} = \\spad{x}}.")) (|dictionary| (($ (|List| |#1|)) "\\spad{dictionary([x,y,...,z])} creates a dictionary consisting of entries \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}}.") (($) "\\spad{dictionary()}\\$\\spad{D} creates an empty dictionary of type \\spad{D}."))) -((-4418 . T)) +((-4419 . T)) NIL (-236) ((|constructor| (NIL "any solution of a homogeneous linear Diophantine equation can be represented as a sum of minimal solutions,{} which form a \"basis\" (a minimal solution cannot be represented as a nontrivial sum of solutions) in the case of an inhomogeneous linear Diophantine equation,{} each solution is the sum of a inhomogeneous solution and any number of homogeneous solutions therefore,{} it suffices to compute two sets: \\indented{3}{1. all minimal inhomogeneous solutions} \\indented{3}{2. all minimal homogeneous solutions} the algorithm implemented is a completion procedure,{} which enumerates all solutions in a recursive depth-first-search it can be seen as finding monotone paths in a graph for more details see Reference")) (|dioSolve| (((|Record| (|:| |varOrder| (|List| (|Symbol|))) (|:| |inhom| (|Union| (|List| (|Vector| (|NonNegativeInteger|))) "failed")) (|:| |hom| (|List| (|Vector| (|NonNegativeInteger|))))) (|Equation| (|Polynomial| (|Integer|)))) "\\spad{dioSolve(u)} computes a basis of all minimal solutions for linear homogeneous Diophantine equation \\spad{u},{} then all minimal solutions of inhomogeneous equation"))) NIL NIL -(-237 S -2609 R) +(-237 S -2612 R) ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (* (($ $ |#3|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#3| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.")) (|dot| ((|#3| $ $) "\\spad{dot(x,y)} computes the inner product of the vectors \\spad{x} and \\spad{y}.")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#3|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim.")) (|finiteAggregate| ((|attribute|) "attribute to indicate an aggregate of finite size"))) NIL -((|HasCategory| |#3| (QUOTE (-365))) (|HasCategory| |#3| (QUOTE (-794))) (|HasCategory| |#3| (QUOTE (-849))) (|HasAttribute| |#3| (QUOTE -4414)) (|HasCategory| |#3| (QUOTE (-172))) (|HasCategory| |#3| (QUOTE (-370))) (|HasCategory| |#3| (QUOTE (-727))) (|HasCategory| |#3| (QUOTE (-131))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1050))) (|HasCategory| |#3| (QUOTE (-1101)))) -(-238 -2609 R) +((|HasCategory| |#3| (QUOTE (-365))) (|HasCategory| |#3| (QUOTE (-794))) (|HasCategory| |#3| (QUOTE (-849))) (|HasAttribute| |#3| (QUOTE -4415)) (|HasCategory| |#3| (QUOTE (-172))) (|HasCategory| |#3| (QUOTE (-370))) (|HasCategory| |#3| (QUOTE (-727))) (|HasCategory| |#3| (QUOTE (-131))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1051))) (|HasCategory| |#3| (QUOTE (-1102)))) +(-238 -2612 R) ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (* (($ $ |#2|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#2| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.")) (|dot| ((|#2| $ $) "\\spad{dot(x,y)} computes the inner product of the vectors \\spad{x} and \\spad{y}.")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#2|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim.")) (|finiteAggregate| ((|attribute|) "attribute to indicate an aggregate of finite size"))) -((-4411 |has| |#2| (-1050)) (-4412 |has| |#2| (-1050)) (-4414 |has| |#2| (-6 -4414)) ((-4419 "*") |has| |#2| (-172)) (-4417 . T)) +((-4412 |has| |#2| (-1051)) (-4413 |has| |#2| (-1051)) (-4415 |has| |#2| (-6 -4415)) ((-4420 "*") |has| |#2| (-172)) (-4418 . T)) NIL -(-239 -2609 A B) +(-239 -2612 A B) ((|constructor| (NIL "\\indented{2}{This package provides operations which all take as arguments} direct products of elements of some type \\spad{A} and functions from \\spad{A} to another type \\spad{B}. The operations all iterate over their vector argument and either return a value of type \\spad{B} or a direct product over \\spad{B}.")) (|map| (((|DirectProduct| |#1| |#3|) (|Mapping| |#3| |#2|) (|DirectProduct| |#1| |#2|)) "\\spad{map(f, v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values.")) (|reduce| ((|#3| (|Mapping| |#3| |#2| |#3|) (|DirectProduct| |#1| |#2|) |#3|) "\\spad{reduce(func,vec,ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if the vector is empty.")) (|scan| (((|DirectProduct| |#1| |#3|) (|Mapping| |#3| |#2| |#3|) (|DirectProduct| |#1| |#2|) |#3|) "\\spad{scan(func,vec,ident)} creates a new vector whose elements are the result of applying reduce to the binary function \\spad{func},{} increasing initial subsequences of the vector \\spad{vec},{} and the element \\spad{ident}."))) NIL NIL -(-240 -2609 R) +(-240 -2612 R) ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying component type. This contrasts with simple vectors in that the members can be viewed as having constant length. Thus many categorical properties can by lifted from the underlying component type. Component extraction operations are provided but no updating operations. Thus new direct product elements can either be created by converting vector elements using the \\spadfun{directProduct} function or by taking appropriate linear combinations of basis vectors provided by the \\spad{unitVector} operation."))) -((-4411 |has| |#2| (-1050)) (-4412 |has| |#2| (-1050)) (-4414 |has| |#2| (-6 -4414)) ((-4419 "*") |has| |#2| (-172)) (-4417 . T)) -((-2797 (-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 (-727))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-794))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-849))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1050))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1101))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -640) (QUOTE (-567))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -901) (QUOTE (-1177)))))) (-2797 (-12 (|HasCategory| |#2| (LIST (QUOTE -1039) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#2| (QUOTE (-1101)))) (-12 (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (QUOTE (-1050)))) (-12 (|HasCategory| |#2| (QUOTE (-1050))) (|HasCategory| |#2| (LIST (QUOTE -640) (QUOTE (-567))))) (-12 (|HasCategory| |#2| (QUOTE (-1050))) (|HasCategory| |#2| (LIST (QUOTE -901) (QUOTE (-1177))))) (-12 (|HasCategory| |#2| (QUOTE (-1101))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1101))) (|HasCategory| |#2| (LIST (QUOTE -1039) (QUOTE (-567))))) 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(|sayLength| (((|Integer|) (|List| (|String|))) "\\spad{sayLength(l)} returns the length of a list of strings \\spad{l} as an integer.") (((|Integer|) (|String|)) "\\spad{sayLength(s)} returns the length of a string \\spad{s} as an integer.")) (|say| (((|Void|) (|List| (|String|))) "\\spad{say(l)} sends a list of strings \\spad{l} to output.") (((|Void|) (|String|)) "\\spad{say(s)} sends a string \\spad{s} to output.")) (|center| (((|List| (|String|)) (|List| (|String|)) (|Integer|) (|String|)) "\\spad{center(l,i,s)} takes a list of strings \\spad{l},{} and centers them within a list of strings which is \\spad{i} characters long,{} in which the remaining spaces are filled with strings composed of as many repetitions as possible of the last string parameter \\spad{s}.") (((|String|) (|String|) (|Integer|) (|String|)) "\\spad{center(s,i,s)} takes the first string \\spad{s},{} and centers it within a string of length \\spad{i},{} in which the other elements of the string are composed of as many replications as possible of the second indicated string,{} \\spad{s} which must have a length greater than that of an empty string.")) (|copies| (((|String|) (|Integer|) (|String|)) "\\spad{copies(i,s)} will take a string \\spad{s} and create a new string composed of \\spad{i} copies of \\spad{s}.")) (|newLine| (((|String|)) "\\spad{newLine()} sends a new line command to output.")) (|bright| (((|List| (|String|)) (|List| (|String|))) "\\spad{bright(l)} sets the font property of a list of strings,{} \\spad{l},{} to bold-face type.") (((|List| (|String|)) (|String|)) "\\spad{bright(s)} sets the font property of the string \\spad{s} to bold-face type."))) NIL @@ -902,7 +902,7 @@ NIL NIL (-243) ((|constructor| (NIL "A division ring (sometimes called a skew field),{} \\spadignore{i.e.} a not necessarily commutative ring where all non-zero elements have multiplicative inverses.")) (|inv| (($ $) "\\spad{inv x} returns the multiplicative inverse of \\spad{x}. Error: if \\spad{x} is 0.")) (** (($ $ (|Integer|)) "\\spad{x**n} returns \\spad{x} raised to the integer power \\spad{n}."))) -((-4410 . T) (-4411 . T) (-4412 . T) (-4414 . T)) +((-4411 . T) (-4412 . T) (-4413 . T) (-4415 . T)) NIL (-244 S) ((|constructor| (NIL "A doubly-linked aggregate serves as a model for a doubly-linked list,{} that is,{} a list which can has links to both next and previous nodes and thus can be efficiently traversed in both directions.")) (|setnext!| (($ $ $) "\\spad{setnext!(u,v)} destructively sets the next node of doubly-linked aggregate \\spad{u} to \\spad{v},{} returning \\spad{v}.")) (|setprevious!| (($ $ $) "\\spad{setprevious!(u,v)} destructively sets the previous node of doubly-linked aggregate \\spad{u} to \\spad{v},{} returning \\spad{v}.")) (|concat!| (($ $ $) "\\spad{concat!(u,v)} destructively concatenates doubly-linked aggregate \\spad{v} to the end of doubly-linked aggregate \\spad{u}.")) (|next| (($ $) "\\spad{next(l)} returns the doubly-linked aggregate beginning with its next element. Error: if \\spad{l} has no next element. Note: \\axiom{next(\\spad{l}) = rest(\\spad{l})} and \\axiom{previous(next(\\spad{l})) = \\spad{l}}.")) (|previous| (($ $) "\\spad{previous(l)} returns the doubly-link list beginning with its previous element. Error: if \\spad{l} has no previous element. Note: \\axiom{next(previous(\\spad{l})) = \\spad{l}}.")) (|tail| (($ $) "\\spad{tail(l)} returns the doubly-linked aggregate \\spad{l} starting at its second element. Error: if \\spad{l} is empty.")) (|head| (($ $) "\\spad{head(l)} returns the first element of a doubly-linked aggregate \\spad{l}. Error: if \\spad{l} is empty.")) (|last| ((|#1| $) "\\spad{last(l)} returns the last element of a doubly-linked aggregate \\spad{l}. Error: if \\spad{l} is empty."))) @@ -910,16 +910,16 @@ NIL NIL (-245 S) ((|constructor| (NIL "This domain provides some nice functions on lists")) (|elt| (((|NonNegativeInteger|) $ "count") "\\axiom{\\spad{l}.\"count\"} returns the number of elements in \\axiom{\\spad{l}}.") (($ $ "sort") "\\axiom{\\spad{l}.sort} returns \\axiom{\\spad{l}} with elements sorted. Note: \\axiom{\\spad{l}.sort = sort(\\spad{l})}") (($ $ "unique") "\\axiom{\\spad{l}.unique} returns \\axiom{\\spad{l}} with duplicates removed. Note: \\axiom{\\spad{l}.unique = removeDuplicates(\\spad{l})}.")) (|datalist| (($ (|List| |#1|)) "\\spad{datalist(l)} creates a datalist from \\spad{l}"))) -((-4418 . T) (-4417 . T)) -((-2797 (-12 (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1101))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-1101))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539)))) (-2797 (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-1101)))) (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| (-567) (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-1101))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863)))) (-12 (|HasCategory| |#1| (QUOTE (-1101))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) +((-4419 . T) (-4418 . T)) +((-2800 (-12 (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2800 (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539)))) (-2800 (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-1102)))) (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| (-567) (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863)))) (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-246 M) ((|constructor| (NIL "DiscreteLogarithmPackage implements help functions for discrete logarithms in monoids using small cyclic groups.")) (|shanksDiscLogAlgorithm| (((|Union| (|NonNegativeInteger|) "failed") |#1| |#1| (|NonNegativeInteger|)) "\\spad{shanksDiscLogAlgorithm(b,a,p)} computes \\spad{s} with \\spad{b**s = a} for assuming that \\spad{a} and \\spad{b} are elements in a 'small' cyclic group of order \\spad{p} by Shank\\spad{'s} algorithm. Note: this is a subroutine of the function \\spadfun{discreteLog}.")) (** ((|#1| |#1| (|Integer|)) "\\spad{x ** n} returns \\spad{x} raised to the integer power \\spad{n}"))) NIL NIL (-247 |vl| R) ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is lexicographic specified by the variable list parameter with the most significant variable first in the list.")) (|reorder| (($ $ (|List| (|Integer|))) "\\spad{reorder(p, perm)} applies the permutation perm to the variables in a polynomial and returns the new correctly ordered polynomial"))) -(((-4419 "*") |has| |#2| (-172)) (-4410 |has| |#2| (-559)) (-4415 |has| |#2| (-6 -4415)) (-4412 . T) (-4411 . T) (-4414 . T)) -((|HasCategory| |#2| (QUOTE (-910))) (-2797 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-455))) (|HasCategory| |#2| (QUOTE (-559))) (|HasCategory| |#2| (QUOTE (-910)))) (-2797 (|HasCategory| |#2| (QUOTE (-455))) (|HasCategory| |#2| (QUOTE (-559))) (|HasCategory| |#2| (QUOTE (-910)))) (-2797 (|HasCategory| |#2| (QUOTE (-455))) (|HasCategory| |#2| (QUOTE (-910)))) (|HasCategory| |#2| (QUOTE (-559))) (|HasCategory| |#2| (QUOTE (-172))) (-2797 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-559)))) (-12 (|HasCategory| (-865 |#1|) (LIST (QUOTE -887) (QUOTE (-381)))) (|HasCategory| |#2| (LIST (QUOTE -887) (QUOTE (-381))))) (-12 (|HasCategory| (-865 |#1|) (LIST (QUOTE -887) (QUOTE (-567)))) (|HasCategory| |#2| (LIST (QUOTE -887) (QUOTE (-567))))) (-12 (|HasCategory| (-865 |#1|) (LIST (QUOTE -615) (LIST (QUOTE -893) (QUOTE (-381))))) (|HasCategory| |#2| (LIST (QUOTE -615) (LIST (QUOTE -893) (QUOTE (-381)))))) (-12 (|HasCategory| (-865 |#1|) (LIST (QUOTE -615) (LIST (QUOTE -893) (QUOTE (-567))))) (|HasCategory| |#2| (LIST (QUOTE -615) (LIST (QUOTE -893) (QUOTE (-567)))))) (-12 (|HasCategory| (-865 |#1|) (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| |#2| (LIST (QUOTE -615) (QUOTE (-539))))) (|HasCategory| |#2| (LIST (QUOTE -640) (QUOTE (-567)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#2| (LIST (QUOTE -1039) (QUOTE (-567)))) (-2797 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#2| (LIST (QUOTE -1039) (LIST (QUOTE -410) (QUOTE (-567)))))) (|HasCategory| |#2| (LIST (QUOTE -1039) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#2| (QUOTE (-365))) (|HasAttribute| |#2| (QUOTE -4415)) (|HasCategory| |#2| (QUOTE (-455))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-910)))) (-2797 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-910)))) (|HasCategory| |#2| (QUOTE (-145))))) +(((-4420 "*") |has| |#2| (-172)) (-4411 |has| |#2| (-559)) (-4416 |has| |#2| (-6 -4416)) (-4413 . T) (-4412 . T) (-4415 . T)) +((|HasCategory| |#2| (QUOTE (-911))) (-2800 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-455))) (|HasCategory| |#2| (QUOTE (-559))) (|HasCategory| |#2| (QUOTE (-911)))) (-2800 (|HasCategory| |#2| (QUOTE (-455))) (|HasCategory| |#2| (QUOTE (-559))) (|HasCategory| |#2| (QUOTE (-911)))) (-2800 (|HasCategory| |#2| (QUOTE (-455))) (|HasCategory| |#2| (QUOTE (-911)))) (|HasCategory| |#2| (QUOTE (-559))) (|HasCategory| |#2| (QUOTE (-172))) (-2800 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-559)))) (-12 (|HasCategory| (-865 |#1|) (LIST (QUOTE -888) (QUOTE (-381)))) (|HasCategory| |#2| (LIST (QUOTE -888) (QUOTE (-381))))) (-12 (|HasCategory| (-865 |#1|) (LIST (QUOTE -888) (QUOTE (-567)))) (|HasCategory| |#2| (LIST (QUOTE -888) (QUOTE (-567))))) (-12 (|HasCategory| (-865 |#1|) (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-381))))) (|HasCategory| |#2| (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-381)))))) (-12 (|HasCategory| (-865 |#1|) (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567))))) (|HasCategory| |#2| (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567)))))) (-12 (|HasCategory| (-865 |#1|) (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| |#2| (LIST (QUOTE -615) (QUOTE (-539))))) (|HasCategory| |#2| (LIST (QUOTE -640) (QUOTE (-567)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#2| (LIST (QUOTE -1040) (QUOTE (-567)))) (-2800 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#2| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567)))))) (|HasCategory| |#2| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#2| (QUOTE (-365))) (|HasAttribute| |#2| (QUOTE -4416)) (|HasCategory| |#2| (QUOTE (-455))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-911)))) (-2800 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-911)))) (|HasCategory| |#2| (QUOTE (-145))))) (-248) ((|showSummary| (((|Void|) $) "\\spad{showSummary(d)} prints out implementation detail information of domain \\spad{`d'}.")) (|reflect| (($ (|ConstructorCall| (|DomainConstructor|))) "\\spad{reflect cc} returns the domain object designated by the ConstructorCall syntax `cc'. The constructor implied by `cc' must be known to the system since it is instantiated.")) (|reify| (((|ConstructorCall| (|DomainConstructor|)) $) "\\spad{reify(d)} returns the abstract syntax for the domain \\spad{`x'}.")) (|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Create: October 18,{} 2007. Date Last Updated: December 20,{} 2008. Basic Operations: coerce,{} reify Related Constructors: Type,{} Syntax,{} OutputForm Also See: Type,{} ConstructorCall") (((|DomainConstructor|) $) "\\spad{constructor(d)} returns the domain constructor that is instantiated to the domain object \\spad{`d'}."))) NIL @@ -934,23 +934,23 @@ NIL NIL (-251 |n| R M S) ((|constructor| (NIL "This constructor provides a direct product type with a left matrix-module view."))) -((-4414 -2797 (-1664 (|has| |#4| (-1050)) (|has| |#4| (-233))) (-1664 (|has| |#4| (-1050)) (|has| |#4| (-901 (-1177)))) (|has| |#4| (-6 -4414)) (-1664 (|has| |#4| (-1050)) (|has| |#4| (-640 (-567))))) (-4411 |has| |#4| (-1050)) (-4412 |has| |#4| (-1050)) ((-4419 "*") |has| |#4| (-172)) (-4417 . T)) -((-2797 (-12 (|HasCategory| |#4| (QUOTE (-172))) (|HasCategory| |#4| (LIST (QUOTE -310) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-233))) (|HasCategory| |#4| (LIST (QUOTE -310) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-365))) (|HasCategory| |#4| (LIST (QUOTE -310) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-370))) (|HasCategory| |#4| (LIST (QUOTE -310) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-727))) (|HasCategory| |#4| (LIST (QUOTE -310) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-794))) (|HasCategory| |#4| (LIST (QUOTE -310) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-849))) (|HasCategory| |#4| (LIST (QUOTE -310) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-1050))) (|HasCategory| |#4| (LIST (QUOTE -310) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-1101))) (|HasCategory| |#4| (LIST (QUOTE -310) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (LIST (QUOTE -310) (|devaluate| |#4|))) (|HasCategory| |#4| (LIST (QUOTE -640) (QUOTE (-567))))) (-12 (|HasCategory| |#4| (LIST (QUOTE -310) (|devaluate| |#4|))) (|HasCategory| |#4| (LIST (QUOTE -901) (QUOTE (-1177)))))) (|HasCategory| |#4| (QUOTE (-365))) (-2797 (|HasCategory| |#4| (QUOTE (-172))) (|HasCategory| |#4| (QUOTE (-365))) (|HasCategory| |#4| (QUOTE (-1050)))) (-2797 (|HasCategory| |#4| (QUOTE (-172))) (|HasCategory| |#4| (QUOTE (-365)))) (|HasCategory| |#4| (QUOTE (-1050))) (|HasCategory| |#4| (QUOTE (-172))) (|HasCategory| |#4| (QUOTE (-794))) (-2797 (|HasCategory| |#4| (QUOTE (-794))) (|HasCategory| |#4| (QUOTE (-849)))) (|HasCategory| |#4| (QUOTE (-849))) (|HasCategory| |#4| (QUOTE (-727))) (-2797 (|HasCategory| |#4| (QUOTE (-172))) (|HasCategory| |#4| (QUOTE (-1050)))) (|HasCategory| |#4| (QUOTE (-370))) (|HasCategory| |#4| (LIST (QUOTE -640) (QUOTE (-567)))) (|HasCategory| |#4| (LIST (QUOTE -901) (QUOTE (-1177)))) (-2797 (|HasCategory| |#4| (LIST (QUOTE -640) (QUOTE (-567)))) (|HasCategory| |#4| (LIST (QUOTE 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(|HasCategory| |#3| (QUOTE (-233))) (|HasCategory| |#3| (LIST (QUOTE -1040) (QUOTE (-567))))) (-12 (|HasCategory| |#3| (QUOTE (-365))) (|HasCategory| |#3| (LIST (QUOTE -1040) (QUOTE (-567))))) (-12 (|HasCategory| |#3| (QUOTE (-370))) (|HasCategory| |#3| (LIST (QUOTE -1040) (QUOTE (-567))))) (-12 (|HasCategory| |#3| (QUOTE (-727))) (|HasCategory| |#3| (LIST (QUOTE -1040) (QUOTE (-567))))) (-12 (|HasCategory| |#3| (QUOTE (-794))) (|HasCategory| |#3| (LIST (QUOTE -1040) (QUOTE (-567))))) (-12 (|HasCategory| |#3| (QUOTE (-849))) (|HasCategory| |#3| (LIST (QUOTE -1040) (QUOTE (-567))))) (-12 (|HasCategory| |#3| (QUOTE (-1051))) (|HasCategory| |#3| (LIST (QUOTE -1040) (QUOTE (-567))))) (-12 (|HasCategory| |#3| (QUOTE (-1102))) (|HasCategory| |#3| (LIST (QUOTE -1040) (QUOTE (-567)))))) (|HasCategory| (-567) (QUOTE (-851))) (-12 (|HasCategory| |#3| (QUOTE (-1051))) (|HasCategory| |#3| (LIST (QUOTE -640) (QUOTE (-567))))) (-12 (|HasCategory| |#3| (QUOTE (-1051))) (|HasCategory| |#3| (LIST (QUOTE -902) (QUOTE (-1178))))) (-12 (|HasCategory| |#3| (QUOTE (-233))) (|HasCategory| |#3| (QUOTE (-1051)))) (-2800 (-12 (|HasCategory| |#3| (QUOTE (-233))) (|HasCategory| |#3| (QUOTE (-1051)))) (|HasCategory| |#3| (QUOTE (-727))) (-12 (|HasCategory| |#3| (QUOTE (-1051))) (|HasCategory| |#3| (LIST (QUOTE -640) (QUOTE (-567))))) (-12 (|HasCategory| |#3| (QUOTE (-1051))) (|HasCategory| |#3| (LIST (QUOTE -902) (QUOTE (-1178)))))) (-12 (|HasCategory| |#3| (QUOTE (-1102))) (|HasCategory| |#3| (LIST (QUOTE -1040) (QUOTE (-567))))) (-2800 (|HasCategory| |#3| (QUOTE (-1051))) (-12 (|HasCategory| |#3| (QUOTE (-1102))) (|HasCategory| |#3| (LIST (QUOTE -1040) (QUOTE (-567)))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#3| (QUOTE (-1102)))) (-2800 (|HasAttribute| |#3| (QUOTE -4415)) (-12 (|HasCategory| |#3| (QUOTE (-233))) (|HasCategory| |#3| (QUOTE (-1051)))) (-12 (|HasCategory| |#3| (QUOTE (-1051))) (|HasCategory| |#3| (LIST (QUOTE -640) (QUOTE (-567))))) (-12 (|HasCategory| |#3| (QUOTE (-1051))) (|HasCategory| |#3| (LIST (QUOTE -902) (QUOTE (-1178)))))) (|HasCategory| |#3| (QUOTE (-131))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -614) (QUOTE (-863)))) (-12 (|HasCategory| |#3| (QUOTE (-1102))) (|HasCategory| |#3| (LIST (QUOTE -310) (|devaluate| |#3|))))) (-253 A R S V E) ((|constructor| (NIL "\\spadtype{DifferentialPolynomialCategory} is a category constructor specifying basic functions in an ordinary differential polynomial ring with a given ordered set of differential indeterminates. In addition,{} it implements defaults for the basic functions. The functions \\spadfun{order} and \\spadfun{weight} are extended from the set of derivatives of differential indeterminates to the set of differential polynomials. Other operations provided on differential polynomials are \\spadfun{leader},{} \\spadfun{initial},{} \\spadfun{separant},{} \\spadfun{differentialVariables},{} and \\spadfun{isobaric?}. Furthermore,{} if the ground ring is a differential ring,{} then evaluation (substitution of differential indeterminates by elements of the ground ring or by differential polynomials) is provided by \\spadfun{eval}. A convenient way of referencing derivatives is provided by the functions \\spadfun{makeVariable}. \\blankline To construct a domain using this constructor,{} one needs to provide a ground ring \\spad{R},{} an ordered set \\spad{S} of differential indeterminates,{} a ranking \\spad{V} on the set of derivatives of the differential indeterminates,{} and a set \\spad{E} of exponents in bijection with the set of differential monomials in the given differential indeterminates. \\blankline")) (|separant| (($ $) "\\spad{separant(p)} returns the partial derivative of the differential polynomial \\spad{p} with respect to its leader.")) (|initial| (($ $) "\\spad{initial(p)} returns the leading coefficient when the differential polynomial \\spad{p} is written as a univariate polynomial in its leader.")) (|leader| ((|#4| $) "\\spad{leader(p)} returns the derivative of the highest rank appearing in the differential polynomial \\spad{p} Note: an error occurs if \\spad{p} is in the ground ring.")) (|isobaric?| (((|Boolean|) $) "\\spad{isobaric?(p)} returns \\spad{true} if every differential monomial appearing in the differential polynomial \\spad{p} has same weight,{} and returns \\spad{false} otherwise.")) (|weight| (((|NonNegativeInteger|) $ |#3|) "\\spad{weight(p, s)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|NonNegativeInteger|) $) "\\spad{weight(p)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p}.")) (|weights| (((|List| (|NonNegativeInteger|)) $ |#3|) "\\spad{weights(p, s)} returns a list of weights of differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|List| (|NonNegativeInteger|)) $) "\\spad{weights(p)} returns a list of weights of differential monomials appearing in differential polynomial \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $ |#3|) "\\spad{degree(p, s)} returns the maximum degree of the differential polynomial \\spad{p} viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of the differential polynomial \\spad{p},{} which is the maximum number of differentiations of a differential indeterminate,{} among all those appearing in \\spad{p}.") (((|NonNegativeInteger|) $ |#3|) "\\spad{order(p,s)} returns the order of the differential polynomial \\spad{p} in differential indeterminate \\spad{s}.")) (|differentialVariables| (((|List| |#3|) $) "\\spad{differentialVariables(p)} returns a list of differential indeterminates occurring in a differential polynomial \\spad{p}.")) (|makeVariable| (((|Mapping| $ (|NonNegativeInteger|)) $) "\\spad{makeVariable(p)} views \\spad{p} as an element of a differential ring,{} in such a way that the \\spad{n}-th derivative of \\spad{p} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} \\spad{:=} makeVariable(\\spad{p}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored.") (((|Mapping| $ (|NonNegativeInteger|)) |#3|) "\\spad{makeVariable(s)} views \\spad{s} as a differential indeterminate,{} in such a way that the \\spad{n}-th derivative of \\spad{s} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} :=makeVariable(\\spad{s}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored."))) NIL ((|HasCategory| |#2| (QUOTE (-233)))) (-254 R S V E) ((|constructor| (NIL "\\spadtype{DifferentialPolynomialCategory} is a category constructor specifying basic functions in an ordinary differential polynomial ring with a given ordered set of differential indeterminates. In addition,{} it implements defaults for the basic functions. The functions \\spadfun{order} and \\spadfun{weight} are extended from the set of derivatives of differential indeterminates to the set of differential polynomials. Other operations provided on differential polynomials are \\spadfun{leader},{} \\spadfun{initial},{} \\spadfun{separant},{} \\spadfun{differentialVariables},{} and \\spadfun{isobaric?}. Furthermore,{} if the ground ring is a differential ring,{} then evaluation (substitution of differential indeterminates by elements of the ground ring or by differential polynomials) is provided by \\spadfun{eval}. A convenient way of referencing derivatives is provided by the functions \\spadfun{makeVariable}. \\blankline To construct a domain using this constructor,{} one needs to provide a ground ring \\spad{R},{} an ordered set \\spad{S} of differential indeterminates,{} a ranking \\spad{V} on the set of derivatives of the differential indeterminates,{} and a set \\spad{E} of exponents in bijection with the set of differential monomials in the given differential indeterminates. \\blankline")) (|separant| (($ $) "\\spad{separant(p)} returns the partial derivative of the differential polynomial \\spad{p} with respect to its leader.")) (|initial| (($ $) "\\spad{initial(p)} returns the leading coefficient when the differential polynomial \\spad{p} is written as a univariate polynomial in its leader.")) (|leader| ((|#3| $) "\\spad{leader(p)} returns the derivative of the highest rank appearing in the differential polynomial \\spad{p} Note: an error occurs if \\spad{p} is in the ground ring.")) (|isobaric?| (((|Boolean|) $) "\\spad{isobaric?(p)} returns \\spad{true} if every differential monomial appearing in the differential polynomial \\spad{p} has same weight,{} and returns \\spad{false} otherwise.")) (|weight| (((|NonNegativeInteger|) $ |#2|) "\\spad{weight(p, s)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|NonNegativeInteger|) $) "\\spad{weight(p)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p}.")) (|weights| (((|List| (|NonNegativeInteger|)) $ |#2|) "\\spad{weights(p, s)} returns a list of weights of differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|List| (|NonNegativeInteger|)) $) "\\spad{weights(p)} returns a list of weights of differential monomials appearing in differential polynomial \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $ |#2|) "\\spad{degree(p, s)} returns the maximum degree of the differential polynomial \\spad{p} viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of the differential polynomial \\spad{p},{} which is the maximum number of differentiations of a differential indeterminate,{} among all those appearing in \\spad{p}.") (((|NonNegativeInteger|) $ |#2|) "\\spad{order(p,s)} returns the order of the differential polynomial \\spad{p} in differential indeterminate \\spad{s}.")) (|differentialVariables| (((|List| |#2|) $) "\\spad{differentialVariables(p)} returns a list of differential indeterminates occurring in a differential polynomial \\spad{p}.")) (|makeVariable| (((|Mapping| $ (|NonNegativeInteger|)) $) "\\spad{makeVariable(p)} views \\spad{p} as an element of a differential ring,{} in such a way that the \\spad{n}-th derivative of \\spad{p} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} \\spad{:=} makeVariable(\\spad{p}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored.") (((|Mapping| $ (|NonNegativeInteger|)) |#2|) "\\spad{makeVariable(s)} views \\spad{s} as a differential indeterminate,{} in such a way that the \\spad{n}-th derivative of \\spad{s} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} :=makeVariable(\\spad{s}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored."))) -(((-4419 "*") |has| |#1| (-172)) (-4410 |has| |#1| (-559)) (-4415 |has| |#1| (-6 -4415)) (-4412 . T) (-4411 . T) (-4414 . T)) +(((-4420 "*") |has| |#1| (-172)) (-4411 |has| |#1| (-559)) (-4416 |has| |#1| (-6 -4416)) (-4413 . T) (-4412 . T) (-4415 . T)) NIL (-255 S) ((|constructor| (NIL "A dequeue is a doubly ended stack,{} that is,{} a bag where first items inserted are the first items extracted,{} at either the front or the back end of the data structure.")) (|reverse!| (($ $) "\\spad{reverse!(d)} destructively replaces \\spad{d} by its reverse dequeue,{} \\spadignore{i.e.} the top (front) element is now the bottom (back) element,{} and so on.")) (|extractBottom!| ((|#1| $) "\\spad{extractBottom!(d)} destructively extracts the bottom (back) element from the dequeue \\spad{d}. Error: if \\spad{d} is empty.")) (|extractTop!| ((|#1| $) "\\spad{extractTop!(d)} destructively extracts the top (front) element from the dequeue \\spad{d}. Error: if \\spad{d} is empty.")) (|insertBottom!| ((|#1| |#1| $) "\\spad{insertBottom!(x,d)} destructively inserts \\spad{x} into the dequeue \\spad{d} at the bottom (back) of the dequeue.")) (|insertTop!| ((|#1| |#1| $) "\\spad{insertTop!(x,d)} destructively inserts \\spad{x} into the dequeue \\spad{d},{} that is,{} at the top (front) of the dequeue. The element previously at the top of the dequeue becomes the second in the dequeue,{} and so on.")) (|bottom!| ((|#1| $) "\\spad{bottom!(d)} returns the element at the bottom (back) of the dequeue.")) (|top!| ((|#1| $) "\\spad{top!(d)} returns the element at the top (front) of the dequeue.")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(d)} returns the number of elements in dequeue \\spad{d}. Note: \\axiom{height(\\spad{d}) = \\# \\spad{d}}.")) (|dequeue| (($ (|List| |#1|)) "\\spad{dequeue([x,y,...,z])} creates a dequeue with first (top or front) element \\spad{x},{} second element \\spad{y},{}...,{}and last (bottom or back) element \\spad{z}.") (($) "\\spad{dequeue()}\\$\\spad{D} creates an empty dequeue of type \\spad{D}."))) -((-4417 . T) (-4418 . T)) +((-4418 . T) (-4419 . T)) NIL (-256) ((|constructor| (NIL "TopLevelDrawFunctionsForCompiledFunctions provides top level functions for drawing graphics of expressions.")) (|recolor| (((|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) "\\spad{recolor()},{} uninteresting to top level user; exported in order to compile package.")) (|makeObject| (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSurface| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{makeObject(surface(f,g,h),a..b,c..d,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{x = f(u,v)},{} \\spad{y = g(u,v)},{} \\spad{z = h(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSurface| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(surface(f,g,h),a..b,c..d,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{x = f(u,v)},{} \\spad{y = g(u,v)},{} \\spad{z = h(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{makeObject(f,a..b,c..d,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{f(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(f,a..b,c..d,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{f(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{makeObject(f,a..b,c..d)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of \\spad{z = f(x,y)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{y} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(f,a..b,c..d,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of \\spad{z = f(x,y)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{y} ranges from \\spad{min(c,d)} to \\spad{max(c,d)},{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|Float|))) "\\spad{makeObject(sp,curve(f,g,h),a..b)} returns the space \\spad{sp} of the domain \\spadtype{ThreeSpace} with the addition of the graph of the parametric curve \\spad{x = f(t), y = g(t), z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(curve(f,g,h),a..b,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric curve \\spad{x = f(t), y = g(t), z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|))) "\\spad{makeObject(sp,curve(f,g,h),a..b)} returns the space \\spad{sp} of the domain \\spadtype{ThreeSpace} with the addition of the graph of the parametric curve \\spad{x = f(t), y = g(t), z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(curve(f,g,h),a..b,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric curve \\spad{x = f(t), y = g(t), z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.")) (|draw| (((|ThreeDimensionalViewport|) (|ParametricSurface| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{draw(surface(f,g,h),a..b,c..d)} draws the graph of the parametric surface \\spad{x = f(u,v)},{} \\spad{y = g(u,v)},{} \\spad{z = h(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}.") (((|ThreeDimensionalViewport|) (|ParametricSurface| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(surface(f,g,h),a..b,c..d)} draws the graph of the parametric surface \\spad{x = f(u,v)},{} \\spad{y = g(u,v)},{} \\spad{z = h(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{draw(f,a..b,c..d)} draws the graph of the parametric surface \\spad{f(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)} The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f,a..b,c..d)} draws the graph of the parametric surface \\spad{f(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{draw(f,a..b,c..d)} draws the graph of \\spad{z = f(x,y)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{y} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}.") (((|ThreeDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f,a..b,c..d,l)} draws the graph of \\spad{z = f(x,y)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{y} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}. and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|Float|))) "\\spad{draw(f,a..b,l)} draws the graph of the parametric curve \\spad{f} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}.") (((|ThreeDimensionalViewport|) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f,a..b,l)} draws the graph of the parametric curve \\spad{f} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|))) "\\spad{draw(curve(f,g,h),a..b,l)} draws the graph of the parametric curve \\spad{x = f(t), y = g(t), z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}.") (((|ThreeDimensionalViewport|) (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(curve(f,g,h),a..b,l)} draws the graph of the parametric curve \\spad{x = f(t), y = g(t), z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) (|ParametricPlaneCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|))) "\\spad{draw(curve(f,g),a..b)} draws the graph of the parametric curve \\spad{x = f(t), y = g(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}.") (((|TwoDimensionalViewport|) (|ParametricPlaneCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(curve(f,g),a..b,l)} draws the graph of the parametric curve \\spad{x = f(t), y = g(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|))) "\\spad{draw(f,a..b)} draws the graph of \\spad{y = f(x)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}.") (((|TwoDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f,a..b,l)} draws the graph of \\spad{y = f(x)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied."))) @@ -990,8 +990,8 @@ NIL NIL (-265 R S V) ((|constructor| (NIL "\\spadtype{DifferentialSparseMultivariatePolynomial} implements an ordinary differential polynomial ring by combining a domain belonging to the category \\spadtype{DifferentialVariableCategory} with the domain \\spadtype{SparseMultivariatePolynomial}. \\blankline"))) -(((-4419 "*") |has| |#1| (-172)) (-4410 |has| |#1| (-559)) (-4415 |has| |#1| (-6 -4415)) (-4412 . T) (-4411 . T) (-4414 . T)) -((|HasCategory| |#1| (QUOTE (-910))) (-2797 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-455))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-910)))) (-2797 (|HasCategory| |#1| (QUOTE (-455))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-910)))) (-2797 (|HasCategory| |#1| (QUOTE (-455))) (|HasCategory| |#1| (QUOTE (-910)))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-172))) (-2797 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-559)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -887) (QUOTE (-381)))) (|HasCategory| |#3| (LIST (QUOTE -887) (QUOTE (-381))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -887) (QUOTE (-567)))) (|HasCategory| |#3| (LIST (QUOTE -887) (QUOTE (-567))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -615) (LIST (QUOTE -893) (QUOTE (-381))))) (|HasCategory| |#3| (LIST (QUOTE -615) (LIST (QUOTE -893) (QUOTE (-381)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -615) (LIST (QUOTE -893) (QUOTE (-567))))) (|HasCategory| |#3| (LIST (QUOTE -615) (LIST (QUOTE -893) (QUOTE (-567)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| |#3| (LIST (QUOTE -615) (QUOTE (-539))))) (|HasCategory| |#1| (LIST (QUOTE -640) (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1039) (QUOTE (-567)))) (-2797 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1039) (LIST (QUOTE -410) (QUOTE (-567)))))) (|HasCategory| |#1| (LIST (QUOTE -1039) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-1177)))) (|HasCategory| |#1| (QUOTE (-365))) (|HasAttribute| |#1| (QUOTE -4415)) (|HasCategory| |#1| (QUOTE (-455))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-910)))) (-2797 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-910)))) (|HasCategory| |#1| (QUOTE (-145))))) +(((-4420 "*") |has| |#1| (-172)) (-4411 |has| |#1| (-559)) (-4416 |has| |#1| (-6 -4416)) (-4413 . T) (-4412 . T) (-4415 . T)) +((|HasCategory| |#1| (QUOTE (-911))) (-2800 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-455))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-911)))) (-2800 (|HasCategory| |#1| (QUOTE (-455))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-911)))) (-2800 (|HasCategory| |#1| (QUOTE (-455))) (|HasCategory| |#1| (QUOTE (-911)))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-172))) (-2800 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-559)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -888) (QUOTE (-381)))) (|HasCategory| |#3| (LIST (QUOTE -888) (QUOTE (-381))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -888) (QUOTE (-567)))) (|HasCategory| |#3| (LIST (QUOTE -888) (QUOTE (-567))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-381))))) (|HasCategory| |#3| (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-381)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567))))) (|HasCategory| |#3| (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| |#3| (LIST (QUOTE -615) (QUOTE (-539))))) (|HasCategory| |#1| (LIST (QUOTE -640) (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (QUOTE (-567)))) (-2800 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567)))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -902) (QUOTE (-1178)))) (|HasCategory| |#1| (QUOTE (-365))) (|HasAttribute| |#1| (QUOTE -4416)) (|HasCategory| |#1| (QUOTE (-455))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-911)))) (-2800 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-911)))) (|HasCategory| |#1| (QUOTE (-145))))) (-266 A S) ((|constructor| (NIL "\\spadtype{DifferentialVariableCategory} constructs the set of derivatives of a given set of (ordinary) differential indeterminates. If \\spad{x},{}...,{}\\spad{y} is an ordered set of differential indeterminates,{} and the prime notation is used for differentiation,{} then the set of derivatives (including zero-th order) of the differential indeterminates is \\spad{x},{}\\spad{x'},{}\\spad{x''},{}...,{} \\spad{y},{}\\spad{y'},{}\\spad{y''},{}... (Note: in the interpreter,{} the \\spad{n}-th derivative of \\spad{y} is displayed as \\spad{y} with a subscript \\spad{n}.) This set is viewed as a set of algebraic indeterminates,{} totally ordered in a way compatible with differentiation and the given order on the differential indeterminates. Such a total order is called a ranking of the differential indeterminates. \\blankline A domain in this category is needed to construct a differential polynomial domain. Differential polynomials are ordered by a ranking on the derivatives,{} and by an order (extending the ranking) on on the set of differential monomials. One may thus associate a domain in this category with a ranking of the differential indeterminates,{} just as one associates a domain in the category \\spadtype{OrderedAbelianMonoidSup} with an ordering of the set of monomials in a set of algebraic indeterminates. The ranking is specified through the binary relation \\spadfun{<}. For example,{} one may define one derivative to be less than another by lexicographically comparing first the \\spadfun{order},{} then the given order of the differential indeterminates appearing in the derivatives. This is the default implementation. \\blankline The notion of weight generalizes that of degree. A polynomial domain may be made into a graded ring if a weight function is given on the set of indeterminates,{} Very often,{} a grading is the first step in ordering the set of monomials. For differential polynomial domains,{} this constructor provides a function \\spadfun{weight},{} which allows the assignment of a non-negative number to each derivative of a differential indeterminate. For example,{} one may define the weight of a derivative to be simply its \\spadfun{order} (this is the default assignment). This weight function can then be extended to the set of all differential polynomials,{} providing a graded ring structure.")) (|coerce| (($ |#2|) "\\spad{coerce(s)} returns \\spad{s},{} viewed as the zero-th order derivative of \\spad{s}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(v, n)} returns the \\spad{n}-th derivative of \\spad{v}.") (($ $) "\\spad{differentiate(v)} returns the derivative of \\spad{v}.")) (|weight| (((|NonNegativeInteger|) $) "\\spad{weight(v)} returns the weight of the derivative \\spad{v}.")) (|variable| ((|#2| $) "\\spad{variable(v)} returns \\spad{s} if \\spad{v} is any derivative of the differential indeterminate \\spad{s}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(v)} returns \\spad{n} if \\spad{v} is the \\spad{n}-th derivative of any differential indeterminate.")) (|makeVariable| (($ |#2| (|NonNegativeInteger|)) "\\spad{makeVariable(s, n)} returns the \\spad{n}-th derivative of a differential indeterminate \\spad{s} as an algebraic indeterminate."))) NIL @@ -1036,11 +1036,11 @@ NIL ((|constructor| (NIL "A domain used in the construction of the exterior algebra on a set \\spad{X} over a ring \\spad{R}. This domain represents the set of all ordered subsets of the set \\spad{X},{} assumed to be in correspondance with {1,{}2,{}3,{} ...}. The ordered subsets are themselves ordered lexicographically and are in bijective correspondance with an ordered basis of the exterior algebra. In this domain we are dealing strictly with the exponents of basis elements which can only be 0 or 1. \\blankline The multiplicative identity element of the exterior algebra corresponds to the empty subset of \\spad{X}. A coerce from List Integer to an ordered basis element is provided to allow the convenient input of expressions. Another exported function forgets the ordered structure and simply returns the list corresponding to an ordered subset.")) (|Nul| (($ (|NonNegativeInteger|)) "\\spad{Nul()} gives the basis element 1 for the algebra generated by \\spad{n} generators.")) (|exponents| (((|List| (|Integer|)) $) "\\spad{exponents(x)} converts a domain element into a list of zeros and ones corresponding to the exponents in the basis element that \\spad{x} represents.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(x)} gives the numbers of 1\\spad{'s} in \\spad{x},{} \\spadignore{i.e.} the number of non-zero exponents in the basis element that \\spad{x} represents.")) (|coerce| (($ (|List| (|Integer|))) "\\spad{coerce(l)} converts a list of 0\\spad{'s} and 1\\spad{'s} into a basis element,{} where 1 (respectively 0) designates that the variable of the corresponding index of \\spad{l} is (respectively,{} is not) present. Error: if an element of \\spad{l} is not 0 or 1."))) NIL NIL -(-277 R -3867) +(-277 R -3879) ((|constructor| (NIL "Provides elementary functions over an integral domain.")) (|localReal?| (((|Boolean|) |#2|) "\\spad{localReal?(x)} should be local but conditional")) (|specialTrigs| (((|Union| |#2| "failed") |#2| (|List| (|Record| (|:| |func| |#2|) (|:| |pole| (|Boolean|))))) "\\spad{specialTrigs(x,l)} should be local but conditional")) (|iiacsch| ((|#2| |#2|) "\\spad{iiacsch(x)} should be local but conditional")) (|iiasech| ((|#2| |#2|) "\\spad{iiasech(x)} should be local but conditional")) (|iiacoth| ((|#2| |#2|) "\\spad{iiacoth(x)} should be local but conditional")) (|iiatanh| ((|#2| |#2|) "\\spad{iiatanh(x)} should be local but conditional")) (|iiacosh| ((|#2| |#2|) "\\spad{iiacosh(x)} should be local but conditional")) (|iiasinh| ((|#2| |#2|) "\\spad{iiasinh(x)} should be local but conditional")) (|iicsch| ((|#2| |#2|) "\\spad{iicsch(x)} should be local but conditional")) (|iisech| ((|#2| |#2|) "\\spad{iisech(x)} should be local but conditional")) (|iicoth| ((|#2| |#2|) "\\spad{iicoth(x)} should be local but conditional")) (|iitanh| ((|#2| |#2|) "\\spad{iitanh(x)} should be local but conditional")) (|iicosh| ((|#2| |#2|) "\\spad{iicosh(x)} should be local but conditional")) (|iisinh| ((|#2| |#2|) "\\spad{iisinh(x)} should be local but conditional")) (|iiacsc| ((|#2| |#2|) "\\spad{iiacsc(x)} should be local but conditional")) (|iiasec| ((|#2| |#2|) "\\spad{iiasec(x)} should be local but conditional")) (|iiacot| ((|#2| |#2|) "\\spad{iiacot(x)} should be local but conditional")) (|iiatan| ((|#2| |#2|) "\\spad{iiatan(x)} should be local but conditional")) (|iiacos| ((|#2| |#2|) "\\spad{iiacos(x)} should be local but conditional")) (|iiasin| ((|#2| |#2|) "\\spad{iiasin(x)} should be local but conditional")) (|iicsc| ((|#2| |#2|) "\\spad{iicsc(x)} should be local but conditional")) (|iisec| ((|#2| |#2|) "\\spad{iisec(x)} should be local but conditional")) (|iicot| ((|#2| |#2|) "\\spad{iicot(x)} should be local but conditional")) (|iitan| ((|#2| |#2|) "\\spad{iitan(x)} should be local but conditional")) (|iicos| ((|#2| |#2|) "\\spad{iicos(x)} should be local but conditional")) (|iisin| ((|#2| |#2|) "\\spad{iisin(x)} should be local but conditional")) (|iilog| ((|#2| |#2|) "\\spad{iilog(x)} should be local but conditional")) (|iiexp| ((|#2| |#2|) "\\spad{iiexp(x)} should be local but conditional")) (|iisqrt3| ((|#2|) "\\spad{iisqrt3()} should be local but conditional")) (|iisqrt2| ((|#2|) "\\spad{iisqrt2()} should be local but conditional")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(p)} returns an elementary operator with the same symbol as \\spad{p}")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(p)} returns \\spad{true} if operator \\spad{p} is elementary")) (|pi| ((|#2|) "\\spad{pi()} returns the \\spad{pi} operator")) (|acsch| ((|#2| |#2|) "\\spad{acsch(x)} applies the inverse hyperbolic cosecant operator to \\spad{x}")) (|asech| ((|#2| |#2|) "\\spad{asech(x)} applies the inverse hyperbolic secant operator to \\spad{x}")) (|acoth| ((|#2| |#2|) "\\spad{acoth(x)} applies the inverse hyperbolic cotangent operator to \\spad{x}")) (|atanh| ((|#2| |#2|) "\\spad{atanh(x)} applies the inverse hyperbolic tangent operator to \\spad{x}")) (|acosh| ((|#2| |#2|) "\\spad{acosh(x)} applies the inverse hyperbolic cosine operator to \\spad{x}")) (|asinh| ((|#2| |#2|) "\\spad{asinh(x)} applies the inverse hyperbolic sine operator to \\spad{x}")) (|csch| ((|#2| |#2|) "\\spad{csch(x)} applies the hyperbolic cosecant operator to \\spad{x}")) (|sech| ((|#2| |#2|) "\\spad{sech(x)} applies the hyperbolic secant operator to \\spad{x}")) (|coth| ((|#2| |#2|) "\\spad{coth(x)} applies the hyperbolic cotangent operator to \\spad{x}")) (|tanh| ((|#2| |#2|) "\\spad{tanh(x)} applies the hyperbolic tangent operator to \\spad{x}")) (|cosh| ((|#2| |#2|) "\\spad{cosh(x)} applies the hyperbolic cosine operator to \\spad{x}")) (|sinh| ((|#2| |#2|) "\\spad{sinh(x)} applies the hyperbolic sine operator to \\spad{x}")) (|acsc| ((|#2| |#2|) "\\spad{acsc(x)} applies the inverse cosecant operator to \\spad{x}")) (|asec| ((|#2| |#2|) "\\spad{asec(x)} applies the inverse secant operator to \\spad{x}")) (|acot| ((|#2| |#2|) "\\spad{acot(x)} applies the inverse cotangent operator to \\spad{x}")) (|atan| ((|#2| |#2|) "\\spad{atan(x)} applies the inverse tangent operator to \\spad{x}")) (|acos| ((|#2| |#2|) "\\spad{acos(x)} applies the inverse cosine operator to \\spad{x}")) (|asin| ((|#2| |#2|) "\\spad{asin(x)} applies the inverse sine operator to \\spad{x}")) (|csc| ((|#2| |#2|) "\\spad{csc(x)} applies the cosecant operator to \\spad{x}")) (|sec| ((|#2| |#2|) "\\spad{sec(x)} applies the secant operator to \\spad{x}")) (|cot| ((|#2| |#2|) "\\spad{cot(x)} applies the cotangent operator to \\spad{x}")) (|tan| ((|#2| |#2|) "\\spad{tan(x)} applies the tangent operator to \\spad{x}")) (|cos| ((|#2| |#2|) "\\spad{cos(x)} applies the cosine operator to \\spad{x}")) (|sin| ((|#2| |#2|) "\\spad{sin(x)} applies the sine operator to \\spad{x}")) (|log| ((|#2| |#2|) "\\spad{log(x)} applies the logarithm operator to \\spad{x}")) (|exp| ((|#2| |#2|) "\\spad{exp(x)} applies the exponential operator to \\spad{x}"))) NIL NIL -(-278 R -3867) +(-278 R -3879) ((|constructor| (NIL "ElementaryFunctionStructurePackage provides functions to test the algebraic independence of various elementary functions,{} using the Risch structure theorem (real and complex versions). It also provides transformations on elementary functions which are not considered simplifications.")) (|tanQ| ((|#2| (|Fraction| (|Integer|)) |#2|) "\\spad{tanQ(q,a)} is a local function with a conditional implementation.")) (|rootNormalize| ((|#2| |#2| (|Kernel| |#2|)) "\\spad{rootNormalize(f, k)} returns \\spad{f} rewriting either \\spad{k} which must be an \\spad{n}th-root in terms of radicals already in \\spad{f},{} or some radicals in \\spad{f} in terms of \\spad{k}.")) (|validExponential| (((|Union| |#2| "failed") (|List| (|Kernel| |#2|)) |#2| (|Symbol|)) "\\spad{validExponential([k1,...,kn],f,x)} returns \\spad{g} if \\spad{exp(f)=g} and \\spad{g} involves only \\spad{k1...kn},{} and \"failed\" otherwise.")) (|realElementary| ((|#2| |#2| (|Symbol|)) "\\spad{realElementary(f,x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 4 fundamental real transcendental elementary functions: \\spad{log, exp, tan, atan}.") ((|#2| |#2|) "\\spad{realElementary(f)} rewrites \\spad{f} in terms of the 4 fundamental real transcendental elementary functions: \\spad{log, exp, tan, atan}.")) (|rischNormalize| (((|Record| (|:| |func| |#2|) (|:| |kers| (|List| (|Kernel| |#2|))) (|:| |vals| (|List| |#2|))) |#2| (|Symbol|)) "\\spad{rischNormalize(f, x)} returns \\spad{[g, [k1,...,kn], [h1,...,hn]]} such that \\spad{g = normalize(f, x)} and each \\spad{ki} was rewritten as \\spad{hi} during the normalization.")) (|normalize| ((|#2| |#2| (|Symbol|)) "\\spad{normalize(f, x)} rewrites \\spad{f} using the least possible number of real algebraically independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{normalize(f)} rewrites \\spad{f} using the least possible number of real algebraically independent kernels."))) NIL NIL @@ -1059,10 +1059,10 @@ NIL (-282 A S) ((|constructor| (NIL "An extensible aggregate is one which allows insertion and deletion of entries. These aggregates are models of lists and streams which are represented by linked structures so as to make insertion,{} deletion,{} and concatenation efficient. However,{} access to elements of these extensible aggregates is generally slow since access is made from the end. See \\spadtype{FlexibleArray} for an exception.")) (|removeDuplicates!| (($ $) "\\spad{removeDuplicates!(u)} destructively removes duplicates from \\spad{u}.")) (|select!| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{select!(p,u)} destructively changes \\spad{u} by keeping only values \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})}.")) (|merge!| (($ $ $) "\\spad{merge!(u,v)} destructively merges \\spad{u} and \\spad{v} in ascending order.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $ $) "\\spad{merge!(p,u,v)} destructively merges \\spad{u} and \\spad{v} using predicate \\spad{p}.")) (|insert!| (($ $ $ (|Integer|)) "\\spad{insert!(v,u,i)} destructively inserts aggregate \\spad{v} into \\spad{u} at position \\spad{i}.") (($ |#2| $ (|Integer|)) "\\spad{insert!(x,u,i)} destructively inserts \\spad{x} into \\spad{u} at position \\spad{i}.")) (|remove!| (($ |#2| $) "\\spad{remove!(x,u)} destructively removes all values \\spad{x} from \\spad{u}.") (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{remove!(p,u)} destructively removes all elements \\spad{x} of \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}.")) (|delete!| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete!(u,i..j)} destructively deletes elements \\spad{u}.\\spad{i} through \\spad{u}.\\spad{j}.") (($ $ (|Integer|)) "\\spad{delete!(u,i)} destructively deletes the \\axiom{\\spad{i}}th element of \\spad{u}.")) (|concat!| (($ $ $) "\\spad{concat!(u,v)} destructively appends \\spad{v} to the end of \\spad{u}. \\spad{v} is unchanged") (($ $ |#2|) "\\spad{concat!(u,x)} destructively adds element \\spad{x} to the end of \\spad{u}."))) NIL -((|HasCategory| |#2| (QUOTE (-851))) (|HasCategory| |#2| (QUOTE (-1101)))) +((|HasCategory| |#2| (QUOTE (-851))) (|HasCategory| |#2| (QUOTE (-1102)))) (-283 S) ((|constructor| (NIL "An extensible aggregate is one which allows insertion and deletion of entries. These aggregates are models of lists and streams which are represented by linked structures so as to make insertion,{} deletion,{} and concatenation efficient. However,{} access to elements of these extensible aggregates is generally slow since access is made from the end. See \\spadtype{FlexibleArray} for an exception.")) (|removeDuplicates!| (($ $) "\\spad{removeDuplicates!(u)} destructively removes duplicates from \\spad{u}.")) (|select!| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select!(p,u)} destructively changes \\spad{u} by keeping only values \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})}.")) (|merge!| (($ $ $) "\\spad{merge!(u,v)} destructively merges \\spad{u} and \\spad{v} in ascending order.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $ $) "\\spad{merge!(p,u,v)} destructively merges \\spad{u} and \\spad{v} using predicate \\spad{p}.")) (|insert!| (($ $ $ (|Integer|)) "\\spad{insert!(v,u,i)} destructively inserts aggregate \\spad{v} into \\spad{u} at position \\spad{i}.") (($ |#1| $ (|Integer|)) "\\spad{insert!(x,u,i)} destructively inserts \\spad{x} into \\spad{u} at position \\spad{i}.")) (|remove!| (($ |#1| $) "\\spad{remove!(x,u)} destructively removes all values \\spad{x} from \\spad{u}.") (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove!(p,u)} destructively removes all elements \\spad{x} of \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}.")) (|delete!| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete!(u,i..j)} destructively deletes elements \\spad{u}.\\spad{i} through \\spad{u}.\\spad{j}.") (($ $ (|Integer|)) "\\spad{delete!(u,i)} destructively deletes the \\axiom{\\spad{i}}th element of \\spad{u}.")) (|concat!| (($ $ $) "\\spad{concat!(u,v)} destructively appends \\spad{v} to the end of \\spad{u}. \\spad{v} is unchanged") (($ $ |#1|) "\\spad{concat!(u,x)} destructively adds element \\spad{x} to the end of \\spad{u}."))) -((-4418 . T)) +((-4419 . T)) NIL (-284 S) ((|constructor| (NIL "Category for the elementary functions.")) (** (($ $ $) "\\spad{x**y} returns \\spad{x} to the power \\spad{y}.")) (|exp| (($ $) "\\spad{exp(x)} returns \\%\\spad{e} to the power \\spad{x}.")) (|log| (($ $) "\\spad{log(x)} returns the natural logarithm of \\spad{x}."))) @@ -1083,18 +1083,18 @@ NIL (-288 S |Dom| |Im|) ((|constructor| (NIL "An eltable aggregate is one which can be viewed as a function. For example,{} the list \\axiom{[1,{}7,{}4]} can applied to 0,{}1,{} and 2 respectively will return the integers 1,{}7,{} and 4; thus this list may be viewed as mapping 0 to 1,{} 1 to 7 and 2 to 4. In general,{} an aggregate can map members of a domain {\\em Dom} to an image domain {\\em Im}.")) (|qsetelt!| ((|#3| $ |#2| |#3|) "\\spad{qsetelt!(u,x,y)} sets the image of \\axiom{\\spad{x}} to be \\axiom{\\spad{y}} under \\axiom{\\spad{u}},{} without checking that \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If such a check is required use the function \\axiom{setelt}.")) (|setelt| ((|#3| $ |#2| |#3|) "\\spad{setelt(u,x,y)} sets the image of \\spad{x} to be \\spad{y} under \\spad{u},{} assuming \\spad{x} is in the domain of \\spad{u}. Error: if \\spad{x} is not in the domain of \\spad{u}.")) (|qelt| ((|#3| $ |#2|) "\\spad{qelt(u, x)} applies \\axiom{\\spad{u}} to \\axiom{\\spad{x}} without checking whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If \\axiom{\\spad{x}} is not in the domain of \\axiom{\\spad{u}} a memory-access violation may occur. If a check on whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}} is required,{} use the function \\axiom{elt}.")) (|elt| ((|#3| $ |#2| |#3|) "\\spad{elt(u, x, y)} applies \\spad{u} to \\spad{x} if \\spad{x} is in the domain of \\spad{u},{} and returns \\spad{y} otherwise. For example,{} if \\spad{u} is a polynomial in \\axiom{\\spad{x}} over the rationals,{} \\axiom{elt(\\spad{u},{}\\spad{n},{}0)} may define the coefficient of \\axiom{\\spad{x}} to the power \\spad{n},{} returning 0 when \\spad{n} is out of range."))) NIL -((|HasAttribute| |#1| (QUOTE -4418))) +((|HasAttribute| |#1| (QUOTE -4419))) (-289 |Dom| |Im|) ((|constructor| (NIL "An eltable aggregate is one which can be viewed as a function. For example,{} the list \\axiom{[1,{}7,{}4]} can applied to 0,{}1,{} and 2 respectively will return the integers 1,{}7,{} and 4; thus this list may be viewed as mapping 0 to 1,{} 1 to 7 and 2 to 4. In general,{} an aggregate can map members of a domain {\\em Dom} to an image domain {\\em Im}.")) (|qsetelt!| ((|#2| $ |#1| |#2|) "\\spad{qsetelt!(u,x,y)} sets the image of \\axiom{\\spad{x}} to be \\axiom{\\spad{y}} under \\axiom{\\spad{u}},{} without checking that \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If such a check is required use the function \\axiom{setelt}.")) (|setelt| ((|#2| $ |#1| |#2|) "\\spad{setelt(u,x,y)} sets the image of \\spad{x} to be \\spad{y} under \\spad{u},{} assuming \\spad{x} is in the domain of \\spad{u}. Error: if \\spad{x} is not in the domain of \\spad{u}.")) (|qelt| ((|#2| $ |#1|) "\\spad{qelt(u, x)} applies \\axiom{\\spad{u}} to \\axiom{\\spad{x}} without checking whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If \\axiom{\\spad{x}} is not in the domain of \\axiom{\\spad{u}} a memory-access violation may occur. If a check on whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}} is required,{} use the function \\axiom{elt}.")) (|elt| ((|#2| $ |#1| |#2|) "\\spad{elt(u, x, y)} applies \\spad{u} to \\spad{x} if \\spad{x} is in the domain of \\spad{u},{} and returns \\spad{y} otherwise. For example,{} if \\spad{u} is a polynomial in \\axiom{\\spad{x}} over the rationals,{} \\axiom{elt(\\spad{u},{}\\spad{n},{}0)} may define the coefficient of \\axiom{\\spad{x}} to the power \\spad{n},{} returning 0 when \\spad{n} is out of range."))) NIL NIL -(-290 S R |Mod| -3269 -3523 |exactQuo|) +(-290 S R |Mod| -1591 -4135 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{ModularRing},{} \\spadtype{ModularField}")) (|elt| ((|#2| $ |#2|) "\\spad{elt(x,r)} or \\spad{x}.\\spad{r} \\undocumented")) (|inv| (($ $) "\\spad{inv(x)} \\undocumented")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} \\undocumented")) (|exQuo| (((|Union| $ "failed") $ $) "\\spad{exQuo(x,y)} \\undocumented")) (|reduce| (($ |#2| |#3|) "\\spad{reduce(r,m)} \\undocumented")) (|coerce| ((|#2| $) "\\spad{coerce(x)} \\undocumented")) (|modulus| ((|#3| $) "\\spad{modulus(x)} \\undocumented"))) -((-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) +((-4411 . T) ((-4420 "*") . T) (-4412 . T) (-4413 . T) (-4415 . T)) NIL (-291) ((|constructor| (NIL "Entire Rings (non-commutative Integral Domains),{} \\spadignore{i.e.} a ring not necessarily commutative which has no zero divisors. \\blankline")) (|noZeroDivisors| ((|attribute|) "if a product is zero then one of the factors must be zero."))) -((-4410 . T) (-4411 . T) (-4412 . T) (-4414 . T)) +((-4411 . T) (-4412 . T) (-4413 . T) (-4415 . T)) NIL (-292) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 19,{} 2008. An `Environment' is a stack of scope.")) (|categoryFrame| (($) "the current category environment in the interpreter.")) (|interactiveEnv| (($) "the current interactive environment in effect.")) (|currentEnv| (($) "the current normal environment in effect.")) (|setProperties!| (($ (|Identifier|) (|List| (|Property|)) $) "setBinding!(\\spad{n},{}props,{}\\spad{e}) set the list of properties of \\spad{`n'} to `props' in `e'.")) (|getProperties| (((|List| (|Property|)) (|Identifier|) $) "getBinding(\\spad{n},{}\\spad{e}) returns the list of properties of \\spad{`n'} in \\spad{e}.")) (|setProperty!| (($ (|Identifier|) (|Identifier|) (|SExpression|) $) "\\spad{setProperty!(n,p,v,e)} binds the property `(\\spad{p},{}\\spad{v})' to \\spad{`n'} in the topmost scope of `e'.")) (|getProperty| (((|Maybe| (|SExpression|)) (|Identifier|) (|Identifier|) $) "\\spad{getProperty(n,p,e)} returns the value of property with name \\spad{`p'} for the symbol \\spad{`n'} in environment `e'. Otherwise,{} `nothing.")) (|scopes| (((|List| (|Scope|)) $) "\\spad{scopes(e)} returns the stack of scopes in environment \\spad{e}.")) (|empty| (($) "\\spad{empty()} constructs an empty environment"))) @@ -1110,21 +1110,21 @@ NIL NIL (-295 S) ((|constructor| (NIL "Equations as mathematical objects. All properties of the basis domain,{} \\spadignore{e.g.} being an abelian group are carried over the equation domain,{} by performing the structural operations on the left and on the right hand side.")) (|subst| (($ $ $) "\\spad{subst(eq1,eq2)} substitutes \\spad{eq2} into both sides of \\spad{eq1} the \\spad{lhs} of \\spad{eq2} should be a kernel")) (|inv| (($ $) "\\spad{inv(x)} returns the multiplicative inverse of \\spad{x}.")) (/ (($ $ $) "\\spad{e1/e2} produces a new equation by dividing the left and right hand sides of equations e1 and e2.")) (|factorAndSplit| (((|List| $) $) "\\spad{factorAndSplit(eq)} make the right hand side 0 and factors the new left hand side. Each factor is equated to 0 and put into the resulting list without repetitions.")) (|rightOne| (((|Union| $ "failed") $) "\\spad{rightOne(eq)} divides by the right hand side.") (((|Union| $ "failed") $) "\\spad{rightOne(eq)} divides by the right hand side,{} if possible.")) (|leftOne| (((|Union| $ "failed") $) "\\spad{leftOne(eq)} divides by the left hand side.") (((|Union| $ "failed") $) "\\spad{leftOne(eq)} divides by the left hand side,{} if possible.")) (* (($ $ |#1|) "\\spad{eqn*x} produces a new equation by multiplying both sides of equation eqn by \\spad{x}.") (($ |#1| $) "\\spad{x*eqn} produces a new equation by multiplying both sides of equation eqn by \\spad{x}.")) (- (($ $ |#1|) "\\spad{eqn-x} produces a new equation by subtracting \\spad{x} from both sides of equation eqn.") (($ |#1| $) "\\spad{x-eqn} produces a new equation by subtracting both sides of equation eqn from \\spad{x}.")) (|rightZero| (($ $) "\\spad{rightZero(eq)} subtracts the right hand side.")) (|leftZero| (($ $) "\\spad{leftZero(eq)} subtracts the left hand side.")) (+ (($ $ |#1|) "\\spad{eqn+x} produces a new equation by adding \\spad{x} to both sides of equation eqn.") (($ |#1| $) "\\spad{x+eqn} produces a new equation by adding \\spad{x} to both sides of equation eqn.")) (|eval| (($ $ (|List| $)) "\\spad{eval(eqn, [x1=v1, ... xn=vn])} replaces \\spad{xi} by \\spad{vi} in equation \\spad{eqn}.") (($ $ $) "\\spad{eval(eqn, x=f)} replaces \\spad{x} by \\spad{f} in equation \\spad{eqn}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,eqn)} constructs a new equation by applying \\spad{f} to both sides of \\spad{eqn}.")) (|rhs| ((|#1| $) "\\spad{rhs(eqn)} returns the right hand side of equation \\spad{eqn}.")) (|lhs| ((|#1| $) "\\spad{lhs(eqn)} returns the left hand side of equation \\spad{eqn}.")) (|swap| (($ $) "\\spad{swap(eq)} interchanges left and right hand side of equation \\spad{eq}.")) (|equation| (($ |#1| |#1|) "\\spad{equation(a,b)} creates an equation.")) 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Thus keys are considered equal only if they are the same instance of a structure."))) -((-4417 . T) (-4418 . T)) -((-12 (|HasCategory| (-2 (|:| -1791 |#1|) (|:| -4232 |#2|)) (QUOTE (-1101))) (|HasCategory| (-2 (|:| -1791 |#1|) (|:| -4232 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1791) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4232) (|devaluate| |#2|)))))) (-2797 (|HasCategory| (-2 (|:| -1791 |#1|) (|:| -4232 |#2|)) (QUOTE (-1101))) (|HasCategory| |#2| (QUOTE (-1101)))) (-2797 (|HasCategory| (-2 (|:| -1791 |#1|) (|:| -4232 |#2|)) (QUOTE (-1101))) (|HasCategory| (-2 (|:| -1791 |#1|) (|:| -4232 |#2|)) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| |#2| (QUOTE (-1101))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| (-2 (|:| -1791 |#1|) (|:| -4232 |#2|)) (LIST (QUOTE -615) (QUOTE (-539)))) (-12 (|HasCategory| |#2| (QUOTE (-1101))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1791 |#1|) (|:| -4232 |#2|)) (QUOTE (-1101))) (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#2| (QUOTE (-1101))) (-2797 (|HasCategory| (-2 (|:| -1791 |#1|) (|:| -4232 |#2|)) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-2 (|:| -1791 |#1|) (|:| -4232 |#2|)) (LIST (QUOTE -614) (QUOTE (-863))))) +((-4418 . T) (-4419 . T)) +((-12 (|HasCategory| (-2 (|:| -1795 |#1|) (|:| -4237 |#2|)) (QUOTE (-1102))) (|HasCategory| (-2 (|:| -1795 |#1|) (|:| -4237 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1795) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4237) (|devaluate| |#2|)))))) (-2800 (|HasCategory| (-2 (|:| -1795 |#1|) (|:| -4237 |#2|)) (QUOTE (-1102))) (|HasCategory| |#2| (QUOTE (-1102)))) (-2800 (|HasCategory| (-2 (|:| -1795 |#1|) (|:| -4237 |#2|)) (QUOTE (-1102))) (|HasCategory| (-2 (|:| -1795 |#1|) (|:| -4237 |#2|)) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| |#2| (QUOTE (-1102))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| (-2 (|:| -1795 |#1|) (|:| -4237 |#2|)) (LIST (QUOTE -615) (QUOTE (-539)))) (-12 (|HasCategory| |#2| (QUOTE (-1102))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1795 |#1|) (|:| -4237 |#2|)) (QUOTE (-1102))) (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#2| (QUOTE (-1102))) (-2800 (|HasCategory| (-2 (|:| -1795 |#1|) (|:| -4237 |#2|)) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-2 (|:| -1795 |#1|) (|:| -4237 |#2|)) (LIST (QUOTE -614) (QUOTE (-863))))) (-297) ((|constructor| (NIL "ErrorFunctions implements error functions callable from the system interpreter. Typically,{} these functions would be called in user functions. The simple forms of the functions take one argument which is either a string (an error message) or a list of strings which all together make up a message. The list can contain formatting codes (see below). The more sophisticated versions takes two arguments where the first argument is the name of the function from which the error was invoked and the second argument is either a string or a list of strings,{} as above. When you use the one argument version in an interpreter function,{} the system will automatically insert the name of the function as the new first argument. Thus in the user interpreter function \\indented{2}{\\spad{f x == if x < 0 then error \"negative argument\" else x}} the call to error will actually be of the form \\indented{2}{\\spad{error(\"f\",\"negative argument\")}} because the interpreter will have created a new first argument. \\blankline Formatting codes: error messages may contain the following formatting codes (they should either start or end a string or else have blanks around them): \\indented{3}{\\spad{\\%l}\\space{6}start a new line} \\indented{3}{\\spad{\\%b}\\space{6}start printing in a bold font (where available)} \\indented{3}{\\spad{\\%d}\\space{6}stop\\space{2}printing in a bold font (where available)} \\indented{3}{\\spad{ \\%ceon}\\space{2}start centering message lines} \\indented{3}{\\spad{\\%ceoff}\\space{2}stop\\space{2}centering message lines} \\indented{3}{\\spad{\\%rjon}\\space{3}start displaying lines \"ragged left\"} \\indented{3}{\\spad{\\%rjoff}\\space{2}stop\\space{2}displaying lines \"ragged left\"} \\indented{3}{\\spad{\\%i}\\space{6}indent\\space{3}following lines 3 additional spaces} \\indented{3}{\\spad{\\%u}\\space{6}unindent following lines 3 additional spaces} \\indented{3}{\\spad{\\%xN}\\space{5}insert \\spad{N} blanks (eg,{} \\spad{\\%x10} inserts 10 blanks)} \\blankline")) (|error| (((|Exit|) (|String|) (|List| (|String|))) "\\spad{error(nam,lmsg)} displays error messages \\spad{lmsg} preceded by a message containing the name \\spad{nam} of the function in which the error is contained.") (((|Exit|) (|String|) (|String|)) "\\spad{error(nam,msg)} displays error message \\spad{msg} preceded by a message containing the name \\spad{nam} of the function in which the error is contained.") (((|Exit|) (|List| (|String|))) "\\spad{error(lmsg)} displays error message \\spad{lmsg} and terminates.") (((|Exit|) (|String|)) "\\spad{error(msg)} displays error message \\spad{msg} and terminates."))) NIL NIL -(-298 -3867 S) +(-298 -3879 S) ((|constructor| (NIL "This package allows a map from any expression space into any object to be lifted to a kernel over the expression set,{} using a given property of the operator of the kernel.")) (|map| ((|#2| (|Mapping| |#2| |#1|) (|String|) (|Kernel| |#1|)) "\\spad{map(f, p, k)} uses the property \\spad{p} of the operator of \\spad{k},{} in order to lift \\spad{f} and apply it to \\spad{k}."))) NIL NIL -(-299 E -3867) +(-299 E -3879) ((|constructor| (NIL "This package allows a mapping \\spad{E} \\spad{->} \\spad{F} to be lifted to a kernel over \\spad{E}; This lifting can fail if the operator of the kernel cannot be applied in \\spad{F}; Do not use this package with \\spad{E} = \\spad{F},{} since this may drop some properties of the operators.")) (|map| ((|#2| (|Mapping| |#2| |#1|) (|Kernel| |#1|)) "\\spad{map(f, k)} returns \\spad{g = op(f(a1),...,f(an))} where \\spad{k = op(a1,...,an)}."))) NIL NIL @@ -1139,7 +1139,7 @@ NIL (-302 S) ((|constructor| (NIL "An expression space is a set which is closed under certain operators.")) (|odd?| (((|Boolean|) $) "\\spad{odd? x} is \\spad{true} if \\spad{x} is an odd integer.")) (|even?| (((|Boolean|) $) "\\spad{even? x} is \\spad{true} if \\spad{x} is an even integer.")) (|definingPolynomial| (($ $) "\\spad{definingPolynomial(x)} returns an expression \\spad{p} such that \\spad{p(x) = 0}.")) (|minPoly| (((|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{minPoly(k)} returns \\spad{p} such that \\spad{p(k) = 0}.")) (|eval| (($ $ (|BasicOperator|) (|Mapping| $ $)) "\\spad{eval(x, s, f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|BasicOperator|) (|Mapping| $ (|List| $))) "\\spad{eval(x, s, f)} replaces every \\spad{s(a1,..,am)} in \\spad{x} by \\spad{f(a1,..,am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ $)) "\\spad{eval(x, s, f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ (|List| $))) "\\spad{eval(x, s, f)} replaces every \\spad{s(a1,..,am)} in \\spad{x} by \\spad{f(a1,..,am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.")) (|freeOf?| (((|Boolean|) $ (|Symbol|)) "\\spad{freeOf?(x, s)} tests if \\spad{x} does not contain any operator whose name is \\spad{s}.") (((|Boolean|) $ $) "\\spad{freeOf?(x, y)} tests if \\spad{x} does not contain any occurrence of \\spad{y},{} where \\spad{y} is a single kernel.")) (|map| (($ (|Mapping| $ $) (|Kernel| $)) "\\spad{map(f, k)} returns \\spad{op(f(x1),...,f(xn))} where \\spad{k = op(x1,...,xn)}.")) (|kernel| (($ (|BasicOperator|) (|List| $)) "\\spad{kernel(op, [f1,...,fn])} constructs \\spad{op(f1,...,fn)} without evaluating it.") (($ (|BasicOperator|) $) "\\spad{kernel(op, x)} constructs \\spad{op}(\\spad{x}) without evaluating it.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(x, s)} tests if \\spad{x} is a kernel and is the name of its operator is \\spad{s}.") (((|Boolean|) $ (|BasicOperator|)) "\\spad{is?(x, op)} tests if \\spad{x} is a kernel and is its operator is op.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} tests if \\% accepts \\spad{op} as applicable to its elements.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\%.")) (|operators| (((|List| (|BasicOperator|)) $) "\\spad{operators(f)} returns all the basic operators appearing in \\spad{f},{} no matter what their levels are.")) (|tower| (((|List| (|Kernel| $)) $) "\\spad{tower(f)} returns all the kernels appearing in \\spad{f},{} no matter what their levels are.")) (|kernels| (((|List| (|Kernel| $)) $) "\\spad{kernels(f)} returns the list of all the top-level kernels appearing in \\spad{f},{} but not the ones appearing in the arguments of the top-level kernels.")) (|mainKernel| (((|Union| (|Kernel| $) "failed") $) "\\spad{mainKernel(f)} returns a kernel of \\spad{f} with maximum nesting level,{} or if \\spad{f} has no kernels (\\spadignore{i.e.} \\spad{f} is a constant).")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(f)} returns the highest nesting level appearing in \\spad{f}. Constants have height 0. Symbols have height 1. For any operator op and expressions \\spad{f1},{}...,{}\\spad{fn},{} \\spad{op(f1,...,fn)} has height equal to \\spad{1 + max(height(f1),...,height(fn))}.")) (|distribute| (($ $ $) "\\spad{distribute(f, g)} expands all the kernels in \\spad{f} that contain \\spad{g} in their arguments and that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or a \\spadfunFrom{paren}{ExpressionSpace} expression.") (($ $) "\\spad{distribute(f)} expands all the kernels in \\spad{f} that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or \\spadfunFrom{paren}{ExpressionSpace} expression.")) (|paren| (($ (|List| $)) "\\spad{paren([f1,...,fn])} returns \\spad{(f1,...,fn)}. This prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(paren [x, 2])} returns the formal kernel \\spad{atan((x, 2))}.") (($ $) "\\spad{paren(f)} returns (\\spad{f}). This prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(paren 1)} returns the formal kernel log((1)).")) (|box| (($ (|List| $)) "\\spad{box([f1,...,fn])} returns \\spad{(f1,...,fn)} with a 'box' around them that prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(box [x, 2])} returns the formal kernel \\spad{atan(x, 2)}.") (($ $) "\\spad{box(f)} returns \\spad{f} with a 'box' around it that prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(box 1)} returns the formal kernel log(1).")) (|subst| (($ $ (|List| (|Kernel| $)) (|List| $)) "\\spad{subst(f, [k1...,kn], [g1,...,gn])} replaces the kernels \\spad{k1},{}...,{}\\spad{kn} by \\spad{g1},{}...,{}\\spad{gn} formally in \\spad{f}.") (($ $ (|List| (|Equation| $))) "\\spad{subst(f, [k1 = g1,...,kn = gn])} replaces the kernels \\spad{k1},{}...,{}\\spad{kn} by \\spad{g1},{}...,{}\\spad{gn} formally in \\spad{f}.") (($ $ (|Equation| $)) "\\spad{subst(f, k = g)} replaces the kernel \\spad{k} by \\spad{g} formally in \\spad{f}.")) (|elt| (($ (|BasicOperator|) (|List| $)) "\\spad{elt(op,[x1,...,xn])} or \\spad{op}([\\spad{x1},{}...,{}\\spad{xn}]) applies the \\spad{n}-ary operator \\spad{op} to \\spad{x1},{}...,{}\\spad{xn}.") (($ (|BasicOperator|) $ $ $ $) "\\spad{elt(op,x,y,z,t)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z},{} \\spad{t}) applies the 4-ary operator \\spad{op} to \\spad{x},{} \\spad{y},{} \\spad{z} and \\spad{t}.") (($ (|BasicOperator|) $ $ $) "\\spad{elt(op,x,y,z)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z}) applies the ternary operator \\spad{op} to \\spad{x},{} \\spad{y} and \\spad{z}.") (($ (|BasicOperator|) $ $) "\\spad{elt(op,x,y)} or \\spad{op}(\\spad{x},{} \\spad{y}) applies the binary operator \\spad{op} to \\spad{x} and \\spad{y}.") (($ (|BasicOperator|) $) "\\spad{elt(op,x)} or \\spad{op}(\\spad{x}) applies the unary operator \\spad{op} to \\spad{x}."))) NIL -((|HasCategory| |#1| (LIST (QUOTE -1039) (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-1050)))) +((|HasCategory| |#1| (LIST (QUOTE -1040) (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-1051)))) (-303) ((|constructor| (NIL "An expression space is a set which is closed under certain operators.")) (|odd?| (((|Boolean|) $) "\\spad{odd? x} is \\spad{true} if \\spad{x} is an odd integer.")) (|even?| (((|Boolean|) $) "\\spad{even? x} is \\spad{true} if \\spad{x} is an even integer.")) (|definingPolynomial| (($ $) "\\spad{definingPolynomial(x)} returns an expression \\spad{p} such that \\spad{p(x) = 0}.")) (|minPoly| (((|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{minPoly(k)} returns \\spad{p} such that \\spad{p(k) = 0}.")) (|eval| (($ $ (|BasicOperator|) (|Mapping| $ $)) "\\spad{eval(x, s, f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|BasicOperator|) (|Mapping| $ (|List| $))) "\\spad{eval(x, s, f)} replaces every \\spad{s(a1,..,am)} in \\spad{x} by \\spad{f(a1,..,am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ $)) "\\spad{eval(x, s, f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ (|List| $))) "\\spad{eval(x, s, f)} replaces every \\spad{s(a1,..,am)} in \\spad{x} by \\spad{f(a1,..,am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.")) (|freeOf?| (((|Boolean|) $ (|Symbol|)) "\\spad{freeOf?(x, s)} tests if \\spad{x} does not contain any operator whose name is \\spad{s}.") (((|Boolean|) $ $) "\\spad{freeOf?(x, y)} tests if \\spad{x} does not contain any occurrence of \\spad{y},{} where \\spad{y} is a single kernel.")) (|map| (($ (|Mapping| $ $) (|Kernel| $)) "\\spad{map(f, k)} returns \\spad{op(f(x1),...,f(xn))} where \\spad{k = op(x1,...,xn)}.")) (|kernel| (($ (|BasicOperator|) (|List| $)) "\\spad{kernel(op, [f1,...,fn])} constructs \\spad{op(f1,...,fn)} without evaluating it.") (($ (|BasicOperator|) $) "\\spad{kernel(op, x)} constructs \\spad{op}(\\spad{x}) without evaluating it.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(x, s)} tests if \\spad{x} is a kernel and is the name of its operator is \\spad{s}.") (((|Boolean|) $ (|BasicOperator|)) "\\spad{is?(x, op)} tests if \\spad{x} is a kernel and is its operator is op.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} tests if \\% accepts \\spad{op} as applicable to its elements.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\%.")) (|operators| (((|List| (|BasicOperator|)) $) "\\spad{operators(f)} returns all the basic operators appearing in \\spad{f},{} no matter what their levels are.")) (|tower| (((|List| (|Kernel| $)) $) "\\spad{tower(f)} returns all the kernels appearing in \\spad{f},{} no matter what their levels are.")) (|kernels| (((|List| (|Kernel| $)) $) "\\spad{kernels(f)} returns the list of all the top-level kernels appearing in \\spad{f},{} but not the ones appearing in the arguments of the top-level kernels.")) (|mainKernel| (((|Union| (|Kernel| $) "failed") $) "\\spad{mainKernel(f)} returns a kernel of \\spad{f} with maximum nesting level,{} or if \\spad{f} has no kernels (\\spadignore{i.e.} \\spad{f} is a constant).")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(f)} returns the highest nesting level appearing in \\spad{f}. Constants have height 0. Symbols have height 1. For any operator op and expressions \\spad{f1},{}...,{}\\spad{fn},{} \\spad{op(f1,...,fn)} has height equal to \\spad{1 + max(height(f1),...,height(fn))}.")) (|distribute| (($ $ $) "\\spad{distribute(f, g)} expands all the kernels in \\spad{f} that contain \\spad{g} in their arguments and that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or a \\spadfunFrom{paren}{ExpressionSpace} expression.") (($ $) "\\spad{distribute(f)} expands all the kernels in \\spad{f} that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or \\spadfunFrom{paren}{ExpressionSpace} expression.")) (|paren| (($ (|List| $)) "\\spad{paren([f1,...,fn])} returns \\spad{(f1,...,fn)}. This prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(paren [x, 2])} returns the formal kernel \\spad{atan((x, 2))}.") (($ $) "\\spad{paren(f)} returns (\\spad{f}). This prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(paren 1)} returns the formal kernel log((1)).")) (|box| (($ (|List| $)) "\\spad{box([f1,...,fn])} returns \\spad{(f1,...,fn)} with a 'box' around them that prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(box [x, 2])} returns the formal kernel \\spad{atan(x, 2)}.") (($ $) "\\spad{box(f)} returns \\spad{f} with a 'box' around it that prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(box 1)} returns the formal kernel log(1).")) (|subst| (($ $ (|List| (|Kernel| $)) (|List| $)) "\\spad{subst(f, [k1...,kn], [g1,...,gn])} replaces the kernels \\spad{k1},{}...,{}\\spad{kn} by \\spad{g1},{}...,{}\\spad{gn} formally in \\spad{f}.") (($ $ (|List| (|Equation| $))) "\\spad{subst(f, [k1 = g1,...,kn = gn])} replaces the kernels \\spad{k1},{}...,{}\\spad{kn} by \\spad{g1},{}...,{}\\spad{gn} formally in \\spad{f}.") (($ $ (|Equation| $)) "\\spad{subst(f, k = g)} replaces the kernel \\spad{k} by \\spad{g} formally in \\spad{f}.")) (|elt| (($ (|BasicOperator|) (|List| $)) "\\spad{elt(op,[x1,...,xn])} or \\spad{op}([\\spad{x1},{}...,{}\\spad{xn}]) applies the \\spad{n}-ary operator \\spad{op} to \\spad{x1},{}...,{}\\spad{xn}.") (($ (|BasicOperator|) $ $ $ $) "\\spad{elt(op,x,y,z,t)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z},{} \\spad{t}) applies the 4-ary operator \\spad{op} to \\spad{x},{} \\spad{y},{} \\spad{z} and \\spad{t}.") (($ (|BasicOperator|) $ $ $) "\\spad{elt(op,x,y,z)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z}) applies the ternary operator \\spad{op} to \\spad{x},{} \\spad{y} and \\spad{z}.") (($ (|BasicOperator|) $ $) "\\spad{elt(op,x,y)} or \\spad{op}(\\spad{x},{} \\spad{y}) applies the binary operator \\spad{op} to \\spad{x} and \\spad{y}.") (($ (|BasicOperator|) $) "\\spad{elt(op,x)} or \\spad{op}(\\spad{x}) applies the unary operator \\spad{op} to \\spad{x}."))) NIL @@ -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 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|) $ $) "\\spad{sizeLess?(x,y)} tests whether \\spad{x} is strictly smaller than \\spad{y} with respect to the \\spadfunFrom{euclideanSize}{EuclideanDomain}."))) -((-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) +((-4411 . T) ((-4420 "*") . T) (-4412 . T) (-4413 . T) (-4415 . T)) NIL (-309 S R) ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation\\spad{''} substitutions.")) (|eval| (($ $ (|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 -3867) +(-311 -3879) ((|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 @@ -1186,8 +1186,8 @@ 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)) -((|HasCategory| (-1253 |#1| |#2| |#3| |#4|) (QUOTE (-910))) (|HasCategory| (-1253 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1039) (QUOTE (-1177)))) (|HasCategory| (-1253 |#1| |#2| |#3| |#4|) (QUOTE (-145))) (|HasCategory| (-1253 |#1| |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1253 |#1| |#2| |#3| |#4|) (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| (-1253 |#1| |#2| |#3| |#4|) (QUOTE (-1023))) (|HasCategory| (-1253 |#1| |#2| |#3| |#4|) (QUOTE (-821))) (-2797 (|HasCategory| (-1253 |#1| |#2| |#3| |#4|) (QUOTE (-821))) (|HasCategory| (-1253 |#1| |#2| |#3| |#4|) (QUOTE (-851)))) (|HasCategory| (-1253 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1039) (QUOTE (-567)))) (|HasCategory| (-1253 |#1| |#2| |#3| |#4|) (QUOTE (-1152))) (|HasCategory| (-1253 |#1| |#2| |#3| |#4|) (LIST (QUOTE -887) (QUOTE (-381)))) (|HasCategory| (-1253 |#1| |#2| |#3| |#4|) (LIST (QUOTE -887) (QUOTE (-567)))) (|HasCategory| (-1253 |#1| |#2| |#3| |#4|) (LIST (QUOTE -615) (LIST (QUOTE -893) (QUOTE (-381))))) (|HasCategory| (-1253 |#1| |#2| |#3| |#4|) (LIST (QUOTE -615) (LIST (QUOTE -893) (QUOTE (-567))))) (|HasCategory| (-1253 |#1| |#2| |#3| |#4|) (LIST (QUOTE -640) (QUOTE (-567)))) (|HasCategory| (-1253 |#1| |#2| |#3| |#4|) (QUOTE (-233))) (|HasCategory| (-1253 |#1| |#2| |#3| |#4|) (LIST (QUOTE -901) (QUOTE (-1177)))) (|HasCategory| (-1253 |#1| |#2| |#3| |#4|) (LIST (QUOTE -517) (QUOTE (-1177)) (LIST (QUOTE -1253) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1253 |#1| |#2| |#3| |#4|) (LIST (QUOTE -310) (LIST (QUOTE -1253) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1253 |#1| |#2| |#3| |#4|) (LIST (QUOTE -287) (LIST (QUOTE -1253) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1253) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1253 |#1| |#2| |#3| |#4|) (QUOTE (-308))) (|HasCategory| (-1253 |#1| |#2| |#3| |#4|) (QUOTE (-548))) (|HasCategory| (-1253 |#1| |#2| |#3| |#4|) (QUOTE (-851))) (-12 (|HasCategory| (-1253 |#1| |#2| |#3| |#4|) (QUOTE (-910))) (|HasCategory| $ (QUOTE (-145)))) (-2797 (|HasCategory| (-1253 |#1| |#2| |#3| |#4|) (QUOTE (-145))) (-12 (|HasCategory| (-1253 |#1| |#2| |#3| |#4|) (QUOTE (-910))) (|HasCategory| $ (QUOTE (-145)))))) +((-4410 . T) (-4416 . T) (-4411 . T) ((-4420 "*") . T) (-4412 . T) (-4413 . T) (-4415 . T)) +((|HasCategory| (-1254 |#1| |#2| |#3| |#4|) (QUOTE (-911))) (|HasCategory| (-1254 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1040) (QUOTE (-1178)))) (|HasCategory| (-1254 |#1| |#2| |#3| |#4|) (QUOTE (-145))) (|HasCategory| (-1254 |#1| |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1254 |#1| |#2| |#3| |#4|) (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| (-1254 |#1| |#2| |#3| |#4|) (QUOTE (-1024))) (|HasCategory| (-1254 |#1| |#2| |#3| |#4|) (QUOTE (-821))) (-2800 (|HasCategory| (-1254 |#1| |#2| |#3| |#4|) (QUOTE (-821))) (|HasCategory| (-1254 |#1| |#2| |#3| |#4|) (QUOTE (-851)))) (|HasCategory| (-1254 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1040) (QUOTE (-567)))) (|HasCategory| (-1254 |#1| |#2| |#3| |#4|) (QUOTE (-1153))) (|HasCategory| (-1254 |#1| |#2| |#3| |#4|) (LIST (QUOTE -888) (QUOTE (-381)))) (|HasCategory| (-1254 |#1| |#2| |#3| |#4|) (LIST (QUOTE -888) (QUOTE (-567)))) (|HasCategory| (-1254 |#1| |#2| |#3| |#4|) (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-381))))) (|HasCategory| (-1254 |#1| |#2| |#3| |#4|) (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567))))) (|HasCategory| (-1254 |#1| |#2| |#3| |#4|) (LIST (QUOTE -640) (QUOTE (-567)))) (|HasCategory| (-1254 |#1| |#2| |#3| |#4|) (QUOTE (-233))) (|HasCategory| (-1254 |#1| |#2| |#3| |#4|) (LIST (QUOTE -902) (QUOTE (-1178)))) (|HasCategory| (-1254 |#1| |#2| |#3| |#4|) (LIST (QUOTE -517) (QUOTE (-1178)) (LIST (QUOTE -1254) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1254 |#1| |#2| |#3| |#4|) (LIST (QUOTE -310) (LIST (QUOTE -1254) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1254 |#1| |#2| |#3| |#4|) (LIST (QUOTE -287) (LIST (QUOTE -1254) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1254) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1254 |#1| |#2| |#3| |#4|) (QUOTE (-308))) (|HasCategory| (-1254 |#1| |#2| |#3| |#4|) (QUOTE (-548))) (|HasCategory| (-1254 |#1| |#2| |#3| |#4|) (QUOTE (-851))) (-12 (|HasCategory| (-1254 |#1| |#2| |#3| |#4|) (QUOTE (-911))) (|HasCategory| $ (QUOTE (-145)))) (-2800 (|HasCategory| (-1254 |#1| |#2| |#3| |#4|) (QUOTE (-145))) (-12 (|HasCategory| (-1254 |#1| |#2| |#3| |#4|) (QUOTE (-911))) (|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}."))) NIL @@ -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 -2797 (-1664 (|has| |#1| (-1050)) (|has| |#1| (-640 (-567)))) (-12 (|has| |#1| (-559)) (-2797 (-1664 (|has| |#1| (-1050)) (|has| |#1| (-640 (-567)))) (|has| |#1| (-1050)) (|has| |#1| (-476)))) (|has| |#1| (-1050)) (|has| |#1| (-476))) (-4412 |has| |#1| (-172)) (-4411 |has| |#1| (-172)) ((-4419 "*") |has| |#1| (-559)) (-4410 |has| |#1| (-559)) (-4415 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(-1114)))) (-2800 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1051))) (|HasCategory| |#1| (LIST (QUOTE -640) (QUOTE (-567)))))) (-2800 (|HasCategory| |#1| (QUOTE (-476))) (|HasCategory| |#1| (QUOTE (-1051)))) (-2800 (-12 (|HasCategory| |#1| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (QUOTE (-559)))) (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (LIST (QUOTE -1040) (QUOTE (-567)))))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1114))) (|HasCategory| |#1| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| $ (QUOTE (-1051))) (|HasCategory| $ (LIST (QUOTE -1040) (QUOTE (-567))))) +(-318 R -3879) ((|constructor| (NIL "Taylor series solutions of explicit ODE\\spad{'s}.")) (|seriesSolve| (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq, y, x = a, [b0,...,bn])} is equivalent to \\spad{seriesSolve(eq = 0, y, x = a, [b0,...,b(n-1)])}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq, y, x = a, y a = b)} is equivalent to \\spad{seriesSolve(eq=0, y, x=a, y a = b)}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq, y, x = a, b)} is equivalent to \\spad{seriesSolve(eq = 0, y, x = a, y a = b)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq,y, x=a, b)} is equivalent to \\spad{seriesSolve(eq, y, x=a, y a = b)}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x = a,[y1 a = b1,..., yn a = bn])} is equivalent to \\spad{seriesSolve([eq1=0,...,eqn=0], [y1,...,yn], x = a, [y1 a = b1,..., yn a = bn])}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x=a, [b1,...,bn])} is equivalent to \\spad{seriesSolve([eq1=0,...,eqn=0], [y1,...,yn], x=a, [b1,...,bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x=a, [b1,...,bn])} is equivalent to \\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x = a, [y1 a = b1,..., yn a = bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,...,eqn],[y1,...,yn],x = a,[y1 a = b1,...,yn a = bn])} returns a taylor series solution of \\spad{[eq1,...,eqn]} around \\spad{x = a} with initial conditions \\spad{yi(a) = bi}. Note: eqi must be of the form \\spad{fi(x, y1 x, y2 x,..., yn x) y1'(x) + gi(x, y1 x, y2 x,..., yn x) = h(x, y1 x, y2 x,..., yn x)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq,y,x=a,[b0,...,b(n-1)])} returns a Taylor series solution of \\spad{eq} around \\spad{x = a} with initial conditions \\spad{y(a) = b0},{} \\spad{y'(a) = b1},{} \\spad{y''(a) = b2},{} ...,{}\\spad{y(n-1)(a) = b(n-1)} \\spad{eq} must be of the form \\spad{f(x, y x, y'(x),..., y(n-1)(x)) y(n)(x) + g(x,y x,y'(x),...,y(n-1)(x)) = h(x,y x, y'(x),..., y(n-1)(x))}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq,y,x=a, y a = b)} returns a Taylor series solution of \\spad{eq} around \\spad{x} = a with initial condition \\spad{y(a) = b}. Note: \\spad{eq} must be of the form \\spad{f(x, y x) y'(x) + g(x, y x) = h(x, y x)}."))) NIL NIL @@ -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| (-559)) (-4415 |has| |#1| (-365)) (-4409 |has| |#1| (-365)) (-4411 . T) (-4412 . T) (-4414 . 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(|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(+,[ni * 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)) +((-4413 . T) (-4412 . T)) ((|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| (-567) (QUOTE (-793)))) (-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(+,[ni * si])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are in a given abelian monoid. The operation is commutative.")) (|highCommonTerms| (($ $ $) "\\spad{highCommonTerms(e1 a1 + ... + en an, f1 b1 + ... + fm bm)} returns \\indented{2}{\\spad{reduce(+,[max(ei, fi) ci])}} where \\spad{ci} ranges in the intersection of \\spad{{a1,...,an}} and \\spad{{b1,...,bm}}.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f, e1 a1 +...+ en an)} returns \\spad{e1 f(a1) +...+ en f(an)}.")) (|mapCoef| (($ (|Mapping| |#2| |#2|) $) "\\spad{mapCoef(f, e1 a1 +...+ en an)} returns \\spad{f(e1) a1 +...+ f(en) an}.")) (|coefficient| ((|#2| |#1| $) "\\spad{coefficient(s, e1 a1 + ... + en an)} returns \\spad{ei} such that \\spad{ai} = \\spad{s},{} or 0 if \\spad{s} is not one of the \\spad{ai}\\spad{'s}.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(x, n)} returns the factor of the n^th term of \\spad{x}.")) (|nthCoef| ((|#2| $ (|Integer|)) "\\spad{nthCoef(x, n)} returns the coefficient of the n^th term of \\spad{x}.")) (|terms| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| |#2|))) $) "\\spad{terms(e1 a1 + ... + en an)} returns \\spad{[[a1, e1],...,[an, en]]}.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(x)} returns the number of terms in \\spad{x}. mapGen(\\spad{f},{} a1\\spad{\\^}e1 ... an\\spad{\\^}en) returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (* (($ |#2| |#1|) "\\spad{e * s} returns \\spad{e} times \\spad{s}.")) (+ (($ |#1| $) "\\spad{s + x} returns the sum of \\spad{s} and \\spad{x}."))) @@ -1238,19 +1238,19 @@ NIL ((|HasCategory| |#2| (QUOTE (-455))) (|HasCategory| |#2| (QUOTE (-559))) (|HasCategory| |#2| (QUOTE (-172)))) (-327 R E) ((|constructor| (NIL "This category is similar to AbelianMonoidRing,{} except that the sum is assumed to be finite. It is a useful model for polynomials,{} but is somewhat more general.")) (|primitivePart| (($ $) "\\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| (-559)) (-4411 . T) (-4412 . T) (-4414 . T)) +(((-4420 "*") |has| |#1| (-172)) (-4411 |has| |#1| (-559)) (-4412 . T) (-4413 . T) (-4415 . 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)) -((-2797 (-12 (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1101))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-1101))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539)))) (-2797 (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-1101)))) (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| (-567) (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-1101))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863)))) (-12 (|HasCategory| |#1| (QUOTE (-1101))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) -(-329 S -3867) +((-4419 . T) (-4418 . T)) +((-2800 (-12 (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2800 (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539)))) (-2800 (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-1102)))) (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| (-567) (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863)))) (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) +(-329 S -3879) ((|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 -3867) +(-330 -3879) ((|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)) +((-4410 . T) (-4416 . T) (-4411 . T) ((-4420 "*") . T) (-4412 . T) (-4413 . T) (-4415 . 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."))) @@ -1272,54 +1272,54 @@ NIL ((|constructor| (NIL "\\indented{1}{Lift a map to finite divisors.} Author: Manuel Bronstein Date Created: 1988 Date Last Updated: 19 May 1993")) (|map| (((|FiniteDivisor| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FiniteDivisor| |#1| |#2| |#3| |#4|)) "\\spad{map(f,d)} \\undocumented{}"))) NIL NIL -(-336 S -3867 UP UPUP R) +(-336 S -3879 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 -3867 UP UPUP R) +(-337 -3879 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 -3867 UP UPUP R) +(-338 -3879 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|) $) "\\spad{finiteBasis(d)} returns a basis for \\spad{d} as a module over {\\em K[x]}."))) NIL NIL (-339 S R) ((|constructor| (NIL "This category provides a selection of evaluation operations depending on what the argument type \\spad{R} provides.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(f, ex)} evaluates ex,{} applying \\spad{f} to values of type \\spad{R} in ex."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -517) (QUOTE (-1177)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -287) (|devaluate| |#2|) (|devaluate| |#2|)))) +((|HasCategory| |#2| (LIST (QUOTE -517) (QUOTE (-1178)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -287) (|devaluate| |#2|) (|devaluate| |#2|)))) (-340 R) ((|constructor| (NIL "This category provides a selection of evaluation operations depending on what the argument type \\spad{R} provides.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f, ex)} evaluates ex,{} applying \\spad{f} to values of type \\spad{R} in ex."))) NIL NIL (-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{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)) -((|HasCategory| |#3| (LIST (QUOTE -1039) (QUOTE (-567)))) (|HasCategory| |#3| (LIST (QUOTE -1039) (QUOTE (-381)))) (|HasCategory| $ (QUOTE (-1050))) (|HasCategory| $ (LIST (QUOTE -1039) (QUOTE (-567))))) +((-4412 . T) (-4413 . T) (-4415 . T)) +((|HasCategory| |#3| (LIST (QUOTE -1040) (QUOTE (-567)))) (|HasCategory| |#3| (LIST (QUOTE -1040) (QUOTE (-381)))) (|HasCategory| $ (QUOTE (-1051))) (|HasCategory| $ (LIST (QUOTE -1040) (QUOTE (-567))))) (-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 -3867 UP UPUP) +(-343 S -3879 UP UPUP) ((|constructor| (NIL "This category is a model for the function field of a plane algebraic curve.")) (|rationalPoints| (((|List| (|List| |#2|))) "\\spad{rationalPoints()} returns the list of all the affine rational points.")) (|nonSingularModel| (((|List| (|Polynomial| |#2|)) (|Symbol|)) "\\spad{nonSingularModel(u)} returns the equations in u1,{}...,{}un of an affine non-singular model for the curve.")) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#3|) (|:| |derivden| |#3|) (|:| |gd| |#3|)) $ (|Mapping| |#3| |#3|)) "\\spad{algSplitSimple(f, D)} returns \\spad{[h,d,d',g]} such that \\spad{f=h/d},{} \\spad{h} is integral at all the normal places \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{d' = Dd},{} \\spad{g = gcd(d, discriminant())} and \\spad{D} is the derivation to use. \\spad{f} must have at most simple finite poles.")) (|hyperelliptic| (((|Union| |#3| "failed")) "\\spad{hyperelliptic()} returns \\spad{p(x)} if the curve is the hyperelliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elliptic| (((|Union| |#3| "failed")) "\\spad{elliptic()} returns \\spad{p(x)} if the curve is the elliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elt| ((|#2| $ |#2| |#2|) "\\spad{elt(f,a,b)} or \\spad{f}(a,{} \\spad{b}) returns the value of \\spad{f} at the point \\spad{(x = a, y = b)} if it is not singular.")) (|primitivePart| (($ $) "\\spad{primitivePart(f)} removes the content of the denominator and the common content of the numerator of \\spad{f}.")) (|differentiate| (($ $ (|Mapping| |#3| |#3|)) "\\spad{differentiate(x, d)} extends the derivation \\spad{d} from UP to \\$ and applies it to \\spad{x}.")) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#3|)) (|:| |den| |#3|)) (|Mapping| |#3| |#3|)) "\\spad{integralDerivationMatrix(d)} extends the derivation \\spad{d} from UP to \\$ and returns (\\spad{M},{} \\spad{Q}) such that the i^th row of \\spad{M} divided by \\spad{Q} form the coordinates of \\spad{d(wi)} with respect to \\spad{(w1,...,wn)} where \\spad{(w1,...,wn)} is the integral basis returned by integralBasis().")) (|integralRepresents| (($ (|Vector| |#3|) |#3|) "\\spad{integralRepresents([A1,...,An], D)} returns \\spad{(A1 w1+...+An wn)/D} where \\spad{(w1,...,wn)} is the integral basis of \\spad{integralBasis()}.")) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#3|)) (|:| |den| |#3|)) $) "\\spad{integralCoordinates(f)} returns \\spad{[[A1,...,An], D]} such that \\spad{f = (A1 w1 +...+ An wn) / D} where \\spad{(w1,...,wn)} is the integral basis returned by \\spad{integralBasis()}.")) (|represents| (($ (|Vector| |#3|) |#3|) "\\spad{represents([A0,...,A(n-1)],D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.")) (|yCoordinates| (((|Record| (|:| |num| (|Vector| |#3|)) (|:| |den| |#3|)) $) "\\spad{yCoordinates(f)} returns \\spad{[[A1,...,An], D]} such that \\spad{f = (A1 + A2 y +...+ An y**(n-1)) / D}.")) (|inverseIntegralMatrixAtInfinity| (((|Matrix| (|Fraction| |#3|))) "\\spad{inverseIntegralMatrixAtInfinity()} returns \\spad{M} such that \\spad{M (v1,...,vn) = (1, y, ..., y**(n-1))} where \\spad{(v1,...,vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|integralMatrixAtInfinity| (((|Matrix| (|Fraction| |#3|))) "\\spad{integralMatrixAtInfinity()} returns \\spad{M} such that \\spad{(v1,...,vn) = M (1, y, ..., y**(n-1))} where \\spad{(v1,...,vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|inverseIntegralMatrix| (((|Matrix| (|Fraction| |#3|))) "\\spad{inverseIntegralMatrix()} returns \\spad{M} such that \\spad{M (w1,...,wn) = (1, y, ..., y**(n-1))} where \\spad{(w1,...,wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|integralMatrix| (((|Matrix| (|Fraction| |#3|))) "\\spad{integralMatrix()} returns \\spad{M} such that \\spad{(w1,...,wn) = M (1, y, ..., y**(n-1))},{} where \\spad{(w1,...,wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|reduceBasisAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{reduceBasisAtInfinity(b1,...,bn)} returns \\spad{(x**i * bj)} for all \\spad{i},{}\\spad{j} such that \\spad{x**i*bj} is locally integral at infinity.")) (|normalizeAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{normalizeAtInfinity(v)} makes \\spad{v} normal at infinity.")) (|complementaryBasis| (((|Vector| $) (|Vector| $)) "\\spad{complementaryBasis(b1,...,bn)} returns the complementary basis \\spad{(b1',...,bn')} of \\spad{(b1,...,bn)}.")) (|integral?| (((|Boolean|) $ |#3|) "\\spad{integral?(f, p)} tests whether \\spad{f} is locally integral at \\spad{p(x) = 0}.") (((|Boolean|) $ |#2|) "\\spad{integral?(f, a)} tests whether \\spad{f} is locally integral at \\spad{x = a}.") (((|Boolean|) $) "\\spad{integral?()} tests if \\spad{f} is integral over \\spad{k[x]}.")) (|integralAtInfinity?| (((|Boolean|) $) "\\spad{integralAtInfinity?()} tests if \\spad{f} is locally integral at infinity.")) (|integralBasisAtInfinity| (((|Vector| $)) "\\spad{integralBasisAtInfinity()} returns the local integral basis at infinity.")) (|integralBasis| (((|Vector| $)) "\\spad{integralBasis()} returns the integral basis for the curve.")) (|ramified?| (((|Boolean|) |#3|) "\\spad{ramified?(p)} tests whether \\spad{p(x) = 0} is ramified.") (((|Boolean|) |#2|) "\\spad{ramified?(a)} tests whether \\spad{x = a} is ramified.")) (|ramifiedAtInfinity?| (((|Boolean|)) "\\spad{ramifiedAtInfinity?()} tests if infinity is ramified.")) (|singular?| (((|Boolean|) |#3|) "\\spad{singular?(p)} tests whether \\spad{p(x) = 0} is singular.") (((|Boolean|) |#2|) "\\spad{singular?(a)} tests whether \\spad{x = a} is singular.")) (|singularAtInfinity?| (((|Boolean|)) "\\spad{singularAtInfinity?()} tests if there is a singularity at infinity.")) (|branchPoint?| (((|Boolean|) |#3|) "\\spad{branchPoint?(p)} tests whether \\spad{p(x) = 0} is a branch point.") (((|Boolean|) |#2|) "\\spad{branchPoint?(a)} tests whether \\spad{x = a} is a branch point.")) (|branchPointAtInfinity?| (((|Boolean|)) "\\spad{branchPointAtInfinity?()} tests if there is a branch point at infinity.")) (|rationalPoint?| (((|Boolean|) |#2| |#2|) "\\spad{rationalPoint?(a, b)} tests if \\spad{(x=a,y=b)} is on the curve.")) (|absolutelyIrreducible?| (((|Boolean|)) "\\spad{absolutelyIrreducible?()} tests if the curve absolutely irreducible?")) (|genus| (((|NonNegativeInteger|)) "\\spad{genus()} returns the genus of one absolutely irreducible component")) (|numberOfComponents| (((|NonNegativeInteger|)) "\\spad{numberOfComponents()} returns the number of absolutely irreducible components."))) NIL ((|HasCategory| |#2| (QUOTE (-370))) (|HasCategory| |#2| (QUOTE (-365)))) -(-344 -3867 UP UPUP) +(-344 -3879 UP UPUP) ((|constructor| (NIL "This category is a model for the function field of a plane algebraic curve.")) (|rationalPoints| (((|List| (|List| |#1|))) "\\spad{rationalPoints()} returns the list of all the affine rational points.")) (|nonSingularModel| (((|List| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{nonSingularModel(u)} returns the equations in u1,{}...,{}un of an affine non-singular model for the curve.")) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#2|) (|:| |derivden| |#2|) (|:| |gd| |#2|)) $ (|Mapping| |#2| |#2|)) "\\spad{algSplitSimple(f, D)} returns \\spad{[h,d,d',g]} such that \\spad{f=h/d},{} \\spad{h} is integral at all the normal places \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{d' = Dd},{} \\spad{g = gcd(d, discriminant())} and \\spad{D} is the derivation to use. \\spad{f} must have at most simple finite poles.")) (|hyperelliptic| (((|Union| |#2| "failed")) "\\spad{hyperelliptic()} returns \\spad{p(x)} if the curve is the hyperelliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elliptic| (((|Union| |#2| "failed")) "\\spad{elliptic()} returns \\spad{p(x)} if the curve is the elliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elt| ((|#1| $ |#1| |#1|) "\\spad{elt(f,a,b)} or \\spad{f}(a,{} \\spad{b}) returns the value of \\spad{f} at the point \\spad{(x = a, y = b)} if it is not singular.")) (|primitivePart| (($ $) "\\spad{primitivePart(f)} removes the content of the denominator and the common content of the numerator of \\spad{f}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|)) "\\spad{differentiate(x, d)} extends the derivation \\spad{d} from UP to \\$ and applies it to \\spad{x}.")) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#2|)) (|:| |den| |#2|)) (|Mapping| |#2| |#2|)) "\\spad{integralDerivationMatrix(d)} extends the derivation \\spad{d} from UP to \\$ and returns (\\spad{M},{} \\spad{Q}) such that the i^th row of \\spad{M} divided by \\spad{Q} form the coordinates of \\spad{d(wi)} with respect to \\spad{(w1,...,wn)} where \\spad{(w1,...,wn)} is the integral basis returned by integralBasis().")) (|integralRepresents| (($ (|Vector| |#2|) |#2|) "\\spad{integralRepresents([A1,...,An], D)} returns \\spad{(A1 w1+...+An wn)/D} where \\spad{(w1,...,wn)} is the integral basis of \\spad{integralBasis()}.")) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) "\\spad{integralCoordinates(f)} returns \\spad{[[A1,...,An], D]} such that \\spad{f = (A1 w1 +...+ An wn) / D} where \\spad{(w1,...,wn)} is the integral basis returned by \\spad{integralBasis()}.")) (|represents| (($ (|Vector| |#2|) |#2|) "\\spad{represents([A0,...,A(n-1)],D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.")) (|yCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) "\\spad{yCoordinates(f)} returns \\spad{[[A1,...,An], D]} such that \\spad{f = (A1 + A2 y +...+ An y**(n-1)) / D}.")) (|inverseIntegralMatrixAtInfinity| (((|Matrix| (|Fraction| |#2|))) "\\spad{inverseIntegralMatrixAtInfinity()} returns \\spad{M} such that \\spad{M (v1,...,vn) = (1, y, ..., y**(n-1))} where \\spad{(v1,...,vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|integralMatrixAtInfinity| (((|Matrix| (|Fraction| |#2|))) "\\spad{integralMatrixAtInfinity()} returns \\spad{M} such that \\spad{(v1,...,vn) = M (1, y, ..., y**(n-1))} where \\spad{(v1,...,vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|inverseIntegralMatrix| (((|Matrix| (|Fraction| |#2|))) "\\spad{inverseIntegralMatrix()} returns \\spad{M} such that \\spad{M (w1,...,wn) = (1, y, ..., y**(n-1))} where \\spad{(w1,...,wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|integralMatrix| (((|Matrix| (|Fraction| |#2|))) "\\spad{integralMatrix()} returns \\spad{M} such that \\spad{(w1,...,wn) = M (1, y, ..., y**(n-1))},{} where \\spad{(w1,...,wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|reduceBasisAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{reduceBasisAtInfinity(b1,...,bn)} returns \\spad{(x**i * bj)} for all \\spad{i},{}\\spad{j} such that \\spad{x**i*bj} is locally integral at infinity.")) (|normalizeAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{normalizeAtInfinity(v)} makes \\spad{v} normal at infinity.")) (|complementaryBasis| (((|Vector| $) (|Vector| $)) "\\spad{complementaryBasis(b1,...,bn)} returns the complementary basis \\spad{(b1',...,bn')} of \\spad{(b1,...,bn)}.")) (|integral?| (((|Boolean|) $ |#2|) "\\spad{integral?(f, p)} tests whether \\spad{f} is locally integral at \\spad{p(x) = 0}.") (((|Boolean|) $ |#1|) "\\spad{integral?(f, a)} tests whether \\spad{f} is locally integral at \\spad{x = a}.") (((|Boolean|) $) "\\spad{integral?()} tests if \\spad{f} is integral over \\spad{k[x]}.")) (|integralAtInfinity?| (((|Boolean|) $) "\\spad{integralAtInfinity?()} tests if \\spad{f} is locally integral at infinity.")) (|integralBasisAtInfinity| (((|Vector| $)) "\\spad{integralBasisAtInfinity()} returns the local integral basis at infinity.")) (|integralBasis| (((|Vector| $)) "\\spad{integralBasis()} returns the integral basis for the curve.")) (|ramified?| (((|Boolean|) |#2|) "\\spad{ramified?(p)} tests whether \\spad{p(x) = 0} is ramified.") (((|Boolean|) |#1|) "\\spad{ramified?(a)} tests whether \\spad{x = a} is ramified.")) (|ramifiedAtInfinity?| (((|Boolean|)) "\\spad{ramifiedAtInfinity?()} tests if infinity is ramified.")) (|singular?| (((|Boolean|) |#2|) "\\spad{singular?(p)} tests whether \\spad{p(x) = 0} is singular.") (((|Boolean|) |#1|) "\\spad{singular?(a)} tests whether \\spad{x = a} is singular.")) (|singularAtInfinity?| (((|Boolean|)) "\\spad{singularAtInfinity?()} tests if there is a singularity at infinity.")) (|branchPoint?| (((|Boolean|) |#2|) "\\spad{branchPoint?(p)} tests whether \\spad{p(x) = 0} is a branch point.") (((|Boolean|) |#1|) "\\spad{branchPoint?(a)} tests whether \\spad{x = a} is a branch point.")) (|branchPointAtInfinity?| (((|Boolean|)) "\\spad{branchPointAtInfinity?()} tests if there is a branch point at infinity.")) (|rationalPoint?| (((|Boolean|) |#1| |#1|) "\\spad{rationalPoint?(a, b)} tests if \\spad{(x=a,y=b)} is on the curve.")) (|absolutelyIrreducible?| (((|Boolean|)) "\\spad{absolutelyIrreducible?()} tests if the curve absolutely irreducible?")) (|genus| (((|NonNegativeInteger|)) "\\spad{genus()} returns the genus of one absolutely irreducible component")) (|numberOfComponents| (((|NonNegativeInteger|)) "\\spad{numberOfComponents()} returns the number of absolutely irreducible components."))) -((-4410 |has| (-410 |#2|) (-365)) (-4415 |has| (-410 |#2|) (-365)) (-4409 |has| (-410 |#2|) (-365)) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) +((-4411 |has| (-410 |#2|) (-365)) (-4416 |has| (-410 |#2|) (-365)) (-4410 |has| (-410 |#2|) (-365)) ((-4420 "*") . T) (-4412 . T) (-4413 . T) (-4415 . 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)) -((-2797 (|HasCategory| (-911 |#1|) (QUOTE (-145))) (|HasCategory| (-911 |#1|) (QUOTE (-370)))) (|HasCategory| (-911 |#1|) (QUOTE (-147))) (|HasCategory| (-911 |#1|) (QUOTE (-370))) (|HasCategory| (-911 |#1|) (QUOTE (-145)))) +((-4410 . T) (-4416 . T) (-4411 . T) ((-4420 "*") . T) (-4412 . T) (-4413 . T) (-4415 . T)) +((-2800 (|HasCategory| (-912 |#1|) (QUOTE (-145))) (|HasCategory| (-912 |#1|) (QUOTE (-370)))) (|HasCategory| (-912 |#1|) (QUOTE (-147))) (|HasCategory| (-912 |#1|) (QUOTE (-370))) (|HasCategory| (-912 |#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)) -((-2797 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-145)))) +((-4410 . T) (-4416 . T) (-4411 . T) ((-4420 "*") . T) (-4412 . T) (-4413 . T) (-4415 . T)) +((-2800 (|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)) -((-2797 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-145)))) +((-4410 . T) (-4416 . T) (-4411 . T) ((-4420 "*") . T) (-4412 . T) (-4413 . T) (-4415 . T)) +((-2800 (|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}."))) NIL @@ -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)) +((-4410 . T) (-4416 . T) (-4411 . T) ((-4420 "*") . T) (-4412 . T) (-4413 . T) (-4415 . T)) NIL -(-352 R UP -3867) +(-352 R UP -3879) ((|constructor| (NIL "In this package \\spad{R} is a Euclidean domain and \\spad{F} is a framed algebra over \\spad{R}. The package provides functions to compute the integral closure of \\spad{R} in the quotient field of \\spad{F}. It is assumed that \\spad{char(R/P) = char(R)} for any prime \\spad{P} of \\spad{R}. A typical instance of this is when \\spad{R = K[x]} and \\spad{F} is a function field over \\spad{R}.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) |#1|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the integral closure of \\spad{R} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL (-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)) -((-2797 (|HasCategory| (-911 |#1|) (QUOTE (-145))) (|HasCategory| (-911 |#1|) (QUOTE (-370)))) (|HasCategory| (-911 |#1|) (QUOTE (-147))) (|HasCategory| (-911 |#1|) (QUOTE (-370))) (|HasCategory| (-911 |#1|) (QUOTE (-145)))) +((-4410 . T) (-4416 . T) (-4411 . T) ((-4420 "*") . T) (-4412 . T) (-4413 . T) (-4415 . T)) +((-2800 (|HasCategory| (-912 |#1|) (QUOTE (-145))) (|HasCategory| (-912 |#1|) (QUOTE (-370)))) (|HasCategory| (-912 |#1|) (QUOTE (-147))) (|HasCategory| (-912 |#1|) (QUOTE (-370))) (|HasCategory| (-912 |#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)) -((-2797 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-145)))) +((-4410 . T) (-4416 . T) (-4411 . T) ((-4420 "*") . T) (-4412 . T) (-4413 . T) (-4415 . T)) +((-2800 (|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)) -((-2797 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-145)))) +((-4410 . T) (-4416 . T) (-4411 . T) ((-4420 "*") . T) (-4412 . T) (-4413 . T) (-4415 . T)) +((-2800 (|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)) -((-2797 (|HasCategory| (-911 |#1|) (QUOTE (-145))) (|HasCategory| (-911 |#1|) (QUOTE (-370)))) (|HasCategory| (-911 |#1|) (QUOTE (-147))) (|HasCategory| (-911 |#1|) (QUOTE (-370))) (|HasCategory| (-911 |#1|) (QUOTE (-145)))) +((-4410 . T) (-4416 . T) (-4411 . T) ((-4420 "*") . T) (-4412 . T) (-4413 . T) (-4415 . T)) +((-2800 (|HasCategory| (-912 |#1|) (QUOTE (-145))) (|HasCategory| (-912 |#1|) (QUOTE (-370)))) (|HasCategory| (-912 |#1|) (QUOTE (-147))) (|HasCategory| (-912 |#1|) (QUOTE (-370))) (|HasCategory| (-912 |#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)) -((-2797 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-145)))) -(-358 -3867 GF) +((-4410 . T) (-4416 . T) (-4411 . T) ((-4420 "*") . T) (-4412 . T) (-4413 . T) (-4415 . T)) +((-2800 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-145)))) +(-358 -3879 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 @@ -1368,21 +1368,21 @@ NIL ((|constructor| (NIL "This package provides a number of functions for generating,{} counting and testing irreducible,{} normal,{} primitive,{} random polynomials over finite fields.")) (|reducedQPowers| (((|PrimitiveArray| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{reducedQPowers(f)} generates \\spad{[x,x**q,x**(q**2),...,x**(q**(n-1))]} reduced modulo \\spad{f} where \\spad{q = size()\\$GF} and \\spad{n = degree f}.")) (|leastAffineMultiple| (((|SparseUnivariatePolynomial| |#1|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{leastAffineMultiple(f)} computes the least affine polynomial which is divisible by the polynomial \\spad{f} over the finite field {\\em GF},{} \\spadignore{i.e.} a polynomial whose exponents are 0 or a power of \\spad{q},{} the size of {\\em GF}.")) (|random| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{random(m,n)}\\$FFPOLY(\\spad{GF}) generates a random monic polynomial of degree \\spad{d} over the finite field {\\em GF},{} \\spad{d} between \\spad{m} and \\spad{n}.") (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{random(n)}\\$FFPOLY(\\spad{GF}) generates a random monic polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|nextPrimitiveNormalPoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextPrimitiveNormalPoly(f)} yields the next primitive normal polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g} or,{} in case these numbers are equal,{} if the {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than this number for \\spad{g}. If these numbers are equals,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than that for \\spad{g},{} or if the lists of exponents for \\spad{f} are lexicographically less than those for \\spad{g}. If these lists are also equal,{} the lists of coefficients are coefficients according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}. This operation is equivalent to nextNormalPrimitivePoly(\\spad{f}).")) (|nextNormalPrimitivePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextNormalPrimitivePoly(f)} yields the next normal primitive polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g} or if {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than this number for \\spad{g}. Otherwise,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than that for \\spad{g} or if the lists of exponents for \\spad{f} are lexicographically less than those for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}. This operation is equivalent to nextPrimitiveNormalPoly(\\spad{f}).")) (|nextNormalPoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextNormalPoly(f)} yields the next normal polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than that for \\spad{g}. In case these numbers are equal,{} \\spad{f < g} if if the number of monomials of \\spad{f} is less that for \\spad{g} or if the list of exponents of \\spad{f} are lexicographically less than the corresponding list for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|nextPrimitivePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextPrimitivePoly(f)} yields the next primitive polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g}. If these values are equal,{} then \\spad{f < g} if if the number of monomials of \\spad{f} is less than that for \\spad{g} or if the lists of exponents of \\spad{f} are lexicographically less than the corresponding list for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|nextIrreduciblePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextIrreduciblePoly(f)} yields the next monic irreducible polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than this number for \\spad{g}. If \\spad{f} and \\spad{g} have the same number of monomials,{} the lists of exponents are compared lexicographically. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|createPrimitiveNormalPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createPrimitiveNormalPoly(n)}\\$FFPOLY(\\spad{GF}) generates a normal and primitive polynomial of degree \\spad{n} over the field {\\em GF}. polynomial of degree \\spad{n} over the field {\\em GF}.")) (|createNormalPrimitivePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createNormalPrimitivePoly(n)}\\$FFPOLY(\\spad{GF}) generates a normal and primitive polynomial of degree \\spad{n} over the field {\\em GF}. Note: this function is equivalent to createPrimitiveNormalPoly(\\spad{n})")) (|createNormalPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createNormalPoly(n)}\\$FFPOLY(\\spad{GF}) generates a normal polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|createPrimitivePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createPrimitivePoly(n)}\\$FFPOLY(\\spad{GF}) generates a primitive polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|createIrreduciblePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createIrreduciblePoly(n)}\\$FFPOLY(\\spad{GF}) generates a monic irreducible univariate polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfNormalPoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfNormalPoly(n)}\\$FFPOLY(\\spad{GF}) yields the number of normal polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfPrimitivePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfPrimitivePoly(n)}\\$FFPOLY(\\spad{GF}) yields the number of primitive polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfIrreduciblePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfIrreduciblePoly(n)}\\$FFPOLY(\\spad{GF}) yields the number of monic irreducible univariate polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|normal?| (((|Boolean|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{normal?(f)} tests whether the polynomial \\spad{f} over a finite field is normal,{} \\spadignore{i.e.} its roots are linearly independent over the field.")) (|primitive?| (((|Boolean|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{primitive?(f)} tests whether the polynomial \\spad{f} over a finite field is primitive,{} \\spadignore{i.e.} all its roots are primitive."))) NIL NIL -(-360 -3867 FP FPP) +(-360 -3879 FP FPP) ((|constructor| (NIL "This package solves linear diophantine equations for Bivariate polynomials over finite fields")) (|solveLinearPolynomialEquation| (((|Union| (|List| |#3|) "failed") (|List| |#3|) |#3|) "\\spad{solveLinearPolynomialEquation([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists."))) NIL NIL (-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)) -((-2797 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-145)))) +((-4410 . T) (-4416 . T) (-4411 . T) ((-4420 "*") . T) (-4412 . T) (-4413 . T) (-4415 . T)) +((-2800 (|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}}."))) 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(*,[si ** ni])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are integers. The multiplication is not commutative.")) (|factors| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| (|Integer|)))) $) "\\spad{factors(a1\\^e1,...,an\\^en)} returns \\spad{[[a1, e1],...,[an, en]]}.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f, a1\\^e1 ... an\\^en)} returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (|mapExpon| (($ (|Mapping| (|Integer|) (|Integer|)) $) "\\spad{mapExpon(f, a1\\^e1 ... an\\^en)} returns \\spad{a1\\^f(e1) ... an\\^f(en)}.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(x, n)} returns the factor of the n^th monomial of \\spad{x}.")) (|nthExpon| (((|Integer|) $ (|Integer|)) "\\spad{nthExpon(x, n)} returns the exponent of the n^th monomial of \\spad{x}.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(x)} returns the number of monomials in \\spad{x}.")) (** (($ |#1| (|Integer|)) "\\spad{s ** n} returns the product of \\spad{s} by itself \\spad{n} times.")) (* (($ $ |#1|) "\\spad{x * s} returns the product of \\spad{x} by \\spad{s} on the right.") (($ |#1| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) -((-4414 . T)) +((-4415 . T)) NIL (-364 S) ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) @@ -1390,7 +1390,7 @@ NIL NIL (-365) ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\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)) +((-4410 . T) (-4416 . T) (-4411 . T) ((-4420 "*") . T) (-4412 . T) (-4413 . T) (-4415 . 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 (-559)))) (-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{ai} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.") (((|Vector| |#1|) $ (|Vector| $)) "\\spad{coordinates(a,[v1,...,vn])} returns the coordinates of \\spad{a} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rightNorm| ((|#1| $) "\\spad{rightNorm(a)} returns the determinant of the right regular representation of \\spad{a}.")) (|leftNorm| ((|#1| $) "\\spad{leftNorm(a)} returns the determinant of the left regular representation of \\spad{a}.")) (|rightTrace| ((|#1| $) "\\spad{rightTrace(a)} returns the trace of the right regular representation of \\spad{a}.")) (|leftTrace| ((|#1| $) "\\spad{leftTrace(a)} returns the trace of the left regular representation of \\spad{a}.")) (|rightRegularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) "\\spad{rightRegularRepresentation(a,[v1,...,vn])} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,...,vn]}.")) (|leftRegularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) "\\spad{leftRegularRepresentation(a,[v1,...,vn])} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,...,vn]}.")) (|structuralConstants| (((|Vector| (|Matrix| |#1|)) (|Vector| $)) "\\spad{structuralConstants([v1,v2,...,vm])} calculates the structural constants \\spad{[(gammaijk) for k in 1..m]} defined by \\spad{vi * vj = gammaij1 * v1 + ... + gammaijm * vm},{} where \\spad{[v1,...,vm]} is an \\spad{R}-module basis of a subalgebra.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|)) (|Vector| $)) "\\spad{conditionsForIdempotents([v1,...,vn])} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra as \\spad{R}-module.")) (|someBasis| (((|Vector| $)) "\\spad{someBasis()} returns some \\spad{R}-module basis."))) -((-4414 |has| |#1| (-559)) (-4412 . T) (-4411 . T)) +((-4415 |has| |#1| (-559)) (-4413 . T) (-4412 . T)) NIL (-370) ((|constructor| (NIL "The category of domains composed of a finite set of elements. We include the functions \\spadfun{lookup} and \\spadfun{index} to give a bijection between the finite set and an initial segment of positive integers. \\blankline")) (|random| (($) "\\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| $)) "\\spad{regularRepresentation(a,basis)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra."))) -((-4411 . T) (-4412 . T) (-4414 . T)) +((-4412 . T) (-4413 . T) (-4415 . T)) NIL (-373 S A R B) ((|constructor| (NIL "FiniteLinearAggregateFunctions2 provides functions involving two FiniteLinearAggregates where the underlying domains might be different. An example of this might be creating a list of rational numbers by mapping a function across a list of integers where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-aggregates \\spad{x} of aggregrate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad{[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$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|) $ $) "\\spad{merge(p,a,b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) NIL -((|HasAttribute| |#1| (QUOTE -4418)) (|HasCategory| |#2| (QUOTE (-851))) (|HasCategory| |#2| (QUOTE (-1101)))) +((|HasAttribute| |#1| (QUOTE -4419)) (|HasCategory| |#2| (QUOTE (-851))) (|HasCategory| |#2| (QUOTE (-1102)))) (-375 S) ((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|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|) $ $) "\\spad{merge(p,a,b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) -((-4417 . T)) +((-4418 . T)) NIL (-376 |VarSet| R) ((|constructor| (NIL "The category of free Lie algebras. It is used by domains of non-commutative algebra: \\spadtype{LiePolynomial} and \\spadtype{XPBWPolynomial}. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr})")) (|eval| (($ $ (|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) (-4413 . T) (-4412 . 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 -640) (QUOTE (-567))))) (-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)) +((-4415 . 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{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) (-3040 . T) (-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) +((-4401 . T) (-4409 . T) (-3050 . T) (-4410 . T) (-4416 . T) (-4411 . T) ((-4420 "*") . T) (-4412 . T) (-4413 . T) (-4415 . 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)) +((-4413 . T) (-4412 . 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)) +((-4413 . T) (-4412 . 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)) +((-4413 . T) (-4412 . T)) ((|HasCategory| |#1| (QUOTE (-172)))) (-388 S) ((|constructor| (NIL "A free monoid on a set \\spad{S} is the monoid of finite products of the form \\spad{reduce(*,[si ** ni])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are nonnegative integers. The multiplication is not commutative.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f, a1\\^e1 ... an\\^en)} returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (|mapExpon| (($ (|Mapping| (|NonNegativeInteger|) (|NonNegativeInteger|)) $) "\\spad{mapExpon(f, a1\\^e1 ... an\\^en)} returns \\spad{a1\\^f(e1) ... an\\^f(en)}.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(x, n)} returns the factor of the n^th monomial of \\spad{x}.")) (|nthExpon| (((|NonNegativeInteger|) $ (|Integer|)) "\\spad{nthExpon(x, n)} returns the exponent of the n^th monomial of \\spad{x}.")) (|factors| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| (|NonNegativeInteger|)))) $) "\\spad{factors(a1\\^e1,...,an\\^en)} returns \\spad{[[a1, e1],...,[an, en]]}.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(x)} returns the number of monomials in \\spad{x}.")) (|overlap| (((|Record| (|:| |lm| $) (|:| |mm| $) (|:| |rm| $)) $ $) "\\spad{overlap(x, y)} returns \\spad{[l, m, r]} such that \\spad{x = l * m},{} \\spad{y = m * r} and \\spad{l} and \\spad{r} have no overlap,{} \\spadignore{i.e.} \\spad{overlap(l, r) = [l, 1, r]}.")) (|divide| (((|Union| (|Record| (|:| |lm| $) (|:| |rm| $)) "failed") $ $) "\\spad{divide(x, y)} returns the left and right exact quotients of \\spad{x} by \\spad{y},{} \\spadignore{i.e.} \\spad{[l, r]} such that \\spad{x = l * y * r},{} \"failed\" if \\spad{x} is not of the form \\spad{l * y * r}.")) (|rquo| (((|Union| $ "failed") $ $) "\\spad{rquo(x, y)} returns the exact right quotient of \\spad{x} by \\spad{y} \\spadignore{i.e.} \\spad{q} such that \\spad{x = q * y},{} \"failed\" if \\spad{x} is not of the form \\spad{q * y}.")) (|lquo| (((|Union| $ "failed") $ $) "\\spad{lquo(x, y)} returns the exact left quotient of \\spad{x} by \\spad{y} \\spadignore{i.e.} \\spad{q} such that \\spad{x = y * q},{} \"failed\" if \\spad{x} is not of the form \\spad{y * q}.")) (|hcrf| (($ $ $) "\\spad{hcrf(x, y)} returns the highest common right factor of \\spad{x} and \\spad{y},{} \\spadignore{i.e.} the largest \\spad{d} such that \\spad{x = a d} and \\spad{y = b d}.")) (|hclf| (($ $ $) "\\spad{hclf(x, y)} returns the highest common left factor of \\spad{x} and \\spad{y},{} \\spadignore{i.e.} the largest \\spad{d} such that \\spad{x = d a} and \\spad{y = d b}.")) (** (($ |#1| (|NonNegativeInteger|)) "\\spad{s ** n} returns the product of \\spad{s} by itself \\spad{n} times.")) (* (($ $ |#1|) "\\spad{x * s} returns the product of \\spad{x} by \\spad{s} on the right.") (($ |#1| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) @@ -1490,7 +1490,7 @@ NIL ((|HasCategory| |#1| (QUOTE (-851)))) (-390) ((|constructor| (NIL "A category of domains which model machine arithmetic used by machines in the AXIOM-NAG link."))) -((-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) +((-4411 . T) ((-4420 "*") . T) (-4412 . T) (-4413 . T) (-4415 . T)) NIL (-391) ((|constructor| (NIL "This domain provides an interface to names in the file system."))) @@ -1502,13 +1502,13 @@ NIL NIL (-393 |n| |class| R) ((|constructor| (NIL "Generate the Free Lie Algebra over a ring \\spad{R} with identity; A \\spad{P}. Hall basis is generated by a package call to HallBasis.")) (|generator| (($ (|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)) +((-4413 . T) (-4412 . T)) NIL (-394) ((|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 -(-395 -3867 UP UPUP R) +(-395 -3879 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 @@ -1532,11 +1532,11 @@ 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 -(-401 -1988 |returnType| -4187 |symbols|) +(-401 -1996 |returnType| -4165 |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 -(-402 -3867 UP) +(-402 -3879 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| $) "\\spad{p + x} returns the sum of \\spad{p} and \\spad{x}"))) NIL NIL @@ -1550,15 +1550,15 @@ NIL NIL (-405) ((|constructor| (NIL "FieldOfPrimeCharacteristic is the category of fields of prime characteristic,{} \\spadignore{e.g.} finite fields,{} algebraic closures of fields of prime characteristic,{} transcendental extensions of of fields of prime characteristic.")) (|primeFrobenius| (($ $ (|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|)) $) "\\spad{order(a)} computes the order of an element in the multiplicative group of the field. Error: if \\spad{a} is 0."))) -((-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) +((-4410 . T) (-4416 . T) (-4411 . T) ((-4420 "*") . T) (-4412 . T) (-4413 . T) (-4415 . T)) NIL (-406 S) ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\\spad{\"+\"}) does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\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 -4401)) (|HasAttribute| |#1| (QUOTE -4409))) (-407) ((|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\"."))) -((-3040 . T) (-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) +((-3050 . T) (-4410 . T) (-4416 . T) (-4411 . T) ((-4420 "*") . T) (-4412 . T) (-4413 . T) (-4415 . T)) NIL (-408 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."))) @@ -1570,20 +1570,20 @@ NIL NIL (-410 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| (-455)) (|has| |#1| (-6 -4404))) (-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) -((|HasCategory| |#1| (QUOTE (-910))) (|HasCategory| |#1| (LIST (QUOTE -1039) (QUOTE (-1177)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-548))) (|HasCategory| |#1| (QUOTE (-829)))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539))))) (|HasCategory| |#1| (QUOTE (-1023))) (|HasCategory| |#1| (QUOTE (-821))) (-2797 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-851)))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-548))) (|HasCategory| |#1| (QUOTE (-829)))) (|HasCategory| |#1| (LIST (QUOTE -1039) (QUOTE (-567))))) (|HasCategory| |#1| (QUOTE (-1152))) (|HasCategory| |#1| (LIST (QUOTE -887) (QUOTE (-381)))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-548))) (|HasCategory| |#1| (QUOTE (-829)))) (|HasCategory| |#1| (LIST (QUOTE -887) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -615) (LIST (QUOTE -893) (QUOTE (-381))))) (-2797 (|HasCategory| |#1| (LIST (QUOTE -615) (LIST (QUOTE -893) (QUOTE (-567))))) (-12 (|HasCategory| |#1| (QUOTE (-548))) (|HasCategory| |#1| (QUOTE (-829))))) (-2797 (|HasCategory| |#1| (LIST (QUOTE -640) (QUOTE (-567)))) (-12 (|HasCategory| |#1| (QUOTE (-548))) (|HasCategory| |#1| (QUOTE (-829))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-1177)))) (|HasCategory| |#1| (LIST (QUOTE -517) (QUOTE (-1177)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -287) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-548))) (|HasCategory| |#1| (QUOTE (-829)))) (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-548))) (-12 (|HasAttribute| |#1| (QUOTE -4415)) (|HasAttribute| |#1| (QUOTE -4404)) (|HasCategory| |#1| (QUOTE (-455)))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (LIST (QUOTE -1039) (QUOTE (-567)))) (|HasCategory| |#1| (LIST (QUOTE -887) (QUOTE (-567)))) (|HasCategory| |#1| (LIST (QUOTE -615) (LIST (QUOTE -893) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -640) (QUOTE (-567)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-910)))) (-2797 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-910)))) (|HasCategory| |#1| (QUOTE (-145))))) +((-4405 -12 (|has| |#1| (-6 -4416)) (|has| |#1| (-455)) (|has| |#1| (-6 -4405))) (-4410 . T) (-4416 . T) (-4411 . T) ((-4420 "*") . T) (-4412 . T) (-4413 . T) (-4415 . T)) +((|HasCategory| |#1| (QUOTE (-911))) (|HasCategory| |#1| (LIST (QUOTE -1040) (QUOTE (-1178)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-2800 (-12 (|HasCategory| |#1| (QUOTE (-548))) (|HasCategory| |#1| (QUOTE (-829)))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539))))) (|HasCategory| |#1| (QUOTE (-1024))) (|HasCategory| |#1| (QUOTE (-821))) (-2800 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-851)))) (-2800 (-12 (|HasCategory| |#1| (QUOTE (-548))) (|HasCategory| |#1| (QUOTE (-829)))) (|HasCategory| |#1| (LIST (QUOTE -1040) (QUOTE (-567))))) (|HasCategory| |#1| (QUOTE (-1153))) (|HasCategory| |#1| (LIST (QUOTE -888) (QUOTE (-381)))) (-2800 (-12 (|HasCategory| |#1| (QUOTE (-548))) (|HasCategory| |#1| (QUOTE (-829)))) (|HasCategory| |#1| (LIST (QUOTE -888) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-381))))) (-2800 (|HasCategory| |#1| (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567))))) (-12 (|HasCategory| |#1| (QUOTE (-548))) (|HasCategory| |#1| (QUOTE (-829))))) (-2800 (|HasCategory| |#1| (LIST (QUOTE -640) (QUOTE (-567)))) (-12 (|HasCategory| |#1| (QUOTE (-548))) (|HasCategory| |#1| (QUOTE (-829))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -902) (QUOTE (-1178)))) (|HasCategory| |#1| (LIST (QUOTE -517) (QUOTE (-1178)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -287) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-548))) (|HasCategory| |#1| (QUOTE (-829)))) (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-548))) (-12 (|HasAttribute| |#1| (QUOTE -4416)) (|HasAttribute| |#1| (QUOTE -4405)) (|HasCategory| |#1| (QUOTE (-455)))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (LIST (QUOTE -1040) (QUOTE (-567)))) (|HasCategory| |#1| (LIST (QUOTE -888) (QUOTE (-567)))) (|HasCategory| |#1| (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -640) (QUOTE (-567)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-911)))) (-2800 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-911)))) (|HasCategory| |#1| (QUOTE (-145))))) (-411 S R UP) ((|constructor| (NIL "A \\spadtype{FramedAlgebra} is a \\spadtype{FiniteRankAlgebra} together with a fixed \\spad{R}-module basis.")) (|regularRepresentation| (((|Matrix| |#2|) $) "\\spad{regularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed basis.")) (|discriminant| ((|#2|) "\\spad{discriminant()} = determinant(traceMatrix()).")) (|traceMatrix| (((|Matrix| |#2|)) "\\spad{traceMatrix()} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr(vi * vj)} ),{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|convert| (($ (|Vector| |#2|)) "\\spad{convert([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.") (((|Vector| |#2|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#2|)) "\\spad{represents([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $)) "\\spad{coordinates([v1,...,vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#2|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) NIL NIL (-412 R UP) ((|constructor| (NIL "A \\spadtype{FramedAlgebra} is a \\spadtype{FiniteRankAlgebra} together with a fixed \\spad{R}-module basis.")) (|regularRepresentation| (((|Matrix| |#1|) $) "\\spad{regularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed basis.")) (|discriminant| ((|#1|) "\\spad{discriminant()} = determinant(traceMatrix()).")) (|traceMatrix| (((|Matrix| |#1|)) "\\spad{traceMatrix()} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr(vi * vj)} ),{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|convert| (($ (|Vector| |#1|)) "\\spad{convert([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.") (((|Vector| |#1|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([v1,...,vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#1|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) -((-4411 . T) (-4412 . T) (-4414 . T)) +((-4412 . T) (-4413 . T) (-4415 . T)) NIL (-413 A S) ((|constructor| (NIL "\\indented{2}{A is fully retractable to \\spad{B} means that A is retractable to \\spad{B},{} and,{}} \\indented{2}{in addition,{} if \\spad{B} is retractable to the integers or rational} \\indented{2}{numbers then so is A.} \\indented{2}{In particular,{} what we are asserting is that there are no integers} \\indented{2}{(rationals) in A which don\\spad{'t} retract into \\spad{B}.} Date Created: March 1990 Date Last Updated: 9 April 1991"))) NIL -((|HasCategory| |#2| (LIST (QUOTE -1039) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#2| (LIST (QUOTE -1039) (QUOTE (-567))))) +((|HasCategory| |#2| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#2| (LIST (QUOTE -1040) (QUOTE (-567))))) (-414 S) ((|constructor| (NIL "\\indented{2}{A is fully retractable to \\spad{B} means that A is retractable to \\spad{B},{} and,{}} \\indented{2}{in addition,{} if \\spad{B} is retractable to the integers or rational} \\indented{2}{numbers then so is A.} \\indented{2}{In particular,{} what we are asserting is that there are no integers} \\indented{2}{(rationals) in A which don\\spad{'t} retract into \\spad{B}.} Date Created: March 1990 Date Last Updated: 9 April 1991"))) NIL @@ -1592,14 +1592,14 @@ NIL ((|constructor| (NIL "\\indented{1}{Lifting of morphisms to fractional ideals.} Author: Manuel Bronstein Date Created: 1 Feb 1989 Date Last Updated: 27 Feb 1990 Keywords: ideal,{} algebra,{} module.")) (|map| (((|FractionalIdeal| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FractionalIdeal| |#1| |#2| |#3| |#4|)) "\\spad{map(f,i)} \\undocumented{}"))) NIL NIL -(-416 R -3867 UP A) +(-416 R -3879 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)) +((-4415 . T)) NIL -(-417 R -3867 UP A |ibasis|) +(-417 R -3879 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|) $) "\\spad{basis((f1,...,fn))} = the vector \\spad{[f1,...,fn]}."))) NIL -((|HasCategory| |#4| (LIST (QUOTE -1039) (|devaluate| |#2|)))) +((|HasCategory| |#4| (LIST (QUOTE -1040) (|devaluate| |#2|)))) (-418 AR R AS S) ((|constructor| (NIL "FramedNonAssociativeAlgebraFunctions2 implements functions between two framed non associative algebra domains defined over different rings. The function map is used to coerce between algebras over different domains having the same structural constants.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,u)} maps \\spad{f} onto the coordinates of \\spad{u} to get an element in \\spad{AS} via identification of the basis of \\spad{AR} as beginning part of the basis of \\spad{AS}."))) NIL @@ -1610,12 +1610,12 @@ NIL ((|HasCategory| |#2| (QUOTE (-365)))) (-420 R) ((|constructor| (NIL "FramedNonAssociativeAlgebra(\\spad{R}) is a \\spadtype{FiniteRankNonAssociativeAlgebra} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank) over a commutative ring \\spad{R} together with a fixed \\spad{R}-module basis.")) (|apply| (($ (|Matrix| |#1|) $) "\\spad{apply(m,a)} defines a left operation of \\spad{n} by \\spad{n} matrices where \\spad{n} is the rank of the algebra in terms of matrix-vector multiplication,{} this is a substitute for a left module structure. Error: if shape of matrix doesn\\spad{'t} fit.")) (|rightRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#1|))) "\\spad{rightRankPolynomial()} calculates the right minimal polynomial of the generic element in the algebra,{} defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|leftRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#1|))) "\\spad{leftRankPolynomial()} calculates the left minimal polynomial of the generic element in the algebra,{} defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|rightRegularRepresentation| (((|Matrix| |#1|) $) "\\spad{rightRegularRepresentation(a)} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|leftRegularRepresentation| (((|Matrix| |#1|) $) "\\spad{leftRegularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|rightTraceMatrix| (((|Matrix| |#1|)) "\\spad{rightTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|leftTraceMatrix| (((|Matrix| |#1|)) "\\spad{leftTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|rightDiscriminant| ((|#1|) "\\spad{rightDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note: the same as \\spad{determinant(rightTraceMatrix())}.")) (|leftDiscriminant| ((|#1|) "\\spad{leftDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note: the same as \\spad{determinant(leftTraceMatrix())}.")) (|convert| (($ (|Vector| |#1|)) "\\spad{convert([a1,...,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed \\spad{R}-module basis.") (((|Vector| |#1|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,...,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|))) "\\spad{conditionsForIdempotents()} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the fixed \\spad{R}-module basis.")) (|structuralConstants| (((|Vector| (|Matrix| |#1|))) "\\spad{structuralConstants()} calculates the structural constants \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{vi * vj = gammaij1 * v1 + ... + gammaijn * vn},{} where \\spad{v1},{}...,{}\\spad{vn} is the fixed \\spad{R}-module basis.")) (|elt| ((|#1| $ (|Integer|)) "\\spad{elt(a,i)} returns the \\spad{i}-th coefficient of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([a1,...,am])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{ai} with respect to the fixed \\spad{R}-module basis.") (((|Vector| |#1|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) -((-4414 |has| |#1| (-559)) (-4412 . T) (-4411 . T)) +((-4415 |has| |#1| (-559)) (-4413 . T) (-4412 . T)) NIL (-421 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)) -((|HasCategory| |#1| (LIST (QUOTE -517) (QUOTE (-1177)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -310) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -287) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| |#1| (QUOTE (-1221))) (-2797 (|HasCategory| |#1| (QUOTE (-455))) (|HasCategory| |#1| (QUOTE (-1221)))) (|HasCategory| |#1| (QUOTE (-1023))) (|HasCategory| |#1| (LIST (QUOTE -1039) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1039) (QUOTE (-567)))) (|HasCategory| |#1| (LIST (QUOTE -517) (QUOTE (-1177)) (|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 -901) (QUOTE (-1177)))) (|HasCategory| |#1| (QUOTE (-548))) (|HasCategory| |#1| (QUOTE (-455)))) +((-4411 . T) ((-4420 "*") . T) (-4412 . T) (-4413 . T) (-4415 . T)) +((|HasCategory| |#1| (LIST (QUOTE -517) (QUOTE (-1178)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -310) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -287) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| |#1| (QUOTE (-1222))) (-2800 (|HasCategory| |#1| (QUOTE (-455))) (|HasCategory| |#1| (QUOTE (-1222)))) (|HasCategory| |#1| (QUOTE (-1024))) (|HasCategory| |#1| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (QUOTE (-567)))) (|HasCategory| |#1| (LIST (QUOTE -517) (QUOTE (-1178)) (|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 -902) (QUOTE (-1178)))) (|HasCategory| |#1| (QUOTE (-548))) (|HasCategory| |#1| (QUOTE (-455)))) (-422 R) ((|constructor| (NIL "\\spadtype{FactoredFunctionUtilities} implements some utility functions for manipulating factored objects.")) (|mergeFactors| (((|Factored| |#1|) (|Factored| |#1|) (|Factored| |#1|)) "\\spad{mergeFactors(u,v)} is used when the factorizations of \\spadvar{\\spad{u}} and \\spadvar{\\spad{v}} are known to be disjoint,{} \\spadignore{e.g.} resulting from a content/primitive part split. Essentially,{} it creates a new factored object by multiplying the units together and appending the lists of factors.")) (|refine| (((|Factored| |#1|) (|Factored| |#1|) (|Mapping| (|Factored| |#1|) |#1|)) "\\spad{refine(u,fn)} is used to apply the function \\userfun{\\spad{fn}} to each factor of \\spadvar{\\spad{u}} and then build a new factored object from the results. For example,{} if \\spadvar{\\spad{u}} were created by calling \\spad{nilFactor(10,2)} then \\spad{refine(u,factor)} would create a factored object equal to that created by \\spad{factor(100)} or \\spad{primeFactor(2,2) * primeFactor(5,2)}."))) NIL @@ -1642,37 +1642,37 @@ NIL ((|HasCategory| |#2| (QUOTE (-851))) (|HasCategory| |#2| (QUOTE (-370)))) (-428 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|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) -((-4417 . T) (-4407 . T) (-4418 . T)) +((-4418 . T) (-4408 . T) (-4419 . T)) NIL -(-429 R -3867) +(-429 R -3879) ((|constructor| (NIL "\\spadtype{FunctionSpaceComplexIntegration} provides functions for the indefinite integration of complex-valued functions.")) (|complexIntegrate| ((|#2| |#2| (|Symbol|)) "\\spad{complexIntegrate(f, x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable.")) (|internalIntegrate0| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate0 should} be a local function,{} but is conditional.")) (|internalIntegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate(f, x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable."))) NIL NIL (-430 R E) ((|constructor| (NIL "\\indented{1}{Author: James Davenport} Date Created: 17 April 1992 Date Last Updated: Basic Functions: Related Constructors: Also See: AMS Classifications: Keywords: References: Description:")) (|makeCos| (($ |#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)))) -(-431 R -3867) +((-4405 -12 (|has| |#1| (-6 -4405)) (|has| |#2| (-6 -4405))) (-4412 . T) (-4413 . T) (-4415 . T)) +((-12 (|HasAttribute| |#1| (QUOTE -4405)) (|HasAttribute| |#2| (QUOTE -4405)))) +(-431 R -3879) ((|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 (-432 S R) ((|constructor| (NIL "A space of formal functions with arguments in an arbitrary ordered set.")) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| $)) $ (|Kernel| $)) "\\spad{univariate(f, k)} returns \\spad{f} viewed as a univariate fraction in \\spad{k}.")) (/ (($ (|SparseMultivariatePolynomial| |#2| (|Kernel| $)) (|SparseMultivariatePolynomial| |#2| (|Kernel| $))) "\\spad{p1/p2} returns the quotient of \\spad{p1} and \\spad{p2} as an element of \\%.")) (|denominator| (($ $) "\\spad{denominator(f)} returns the denominator of \\spad{f} converted to \\%.")) (|denom| (((|SparseMultivariatePolynomial| |#2| (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|convert| (($ (|Factored| $)) "\\spad{convert(f1\\^e1 ... fm\\^em)} returns \\spad{(f1)\\^e1 ... (fm)\\^em} as an element of \\%,{} using formal kernels created using a \\spadfunFrom{paren}{ExpressionSpace}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isPower(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|numerator| (($ $) "\\spad{numerator(f)} returns the numerator of \\spad{f} converted to \\%.")) (|numer| (((|SparseMultivariatePolynomial| |#2| (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R} if \\spad{R} is an integral domain. If not,{} then numer(\\spad{f}) = \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|coerce| (($ (|Fraction| (|Polynomial| (|Fraction| |#2|)))) "\\spad{coerce(f)} returns \\spad{f} as an element of \\%.") (($ (|Polynomial| (|Fraction| |#2|))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.") (($ (|Fraction| |#2|)) "\\spad{coerce(q)} returns \\spad{q} as an element of \\%.") (($ (|SparseMultivariatePolynomial| |#2| (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.")) (|isMult| (((|Union| (|Record| (|:| |coef| (|Integer|)) (|:| |var| (|Kernel| $))) "failed") $) "\\spad{isMult(p)} returns \\spad{[n, x]} if \\spad{p = n * x} and \\spad{n <> 0}.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,...,mn]} if \\spad{p = m1 +...+ mn} and \\spad{n > 1}.")) (|isExpt| (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|Symbol|)) "\\spad{isExpt(p,f)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = f(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|BasicOperator|)) "\\spad{isExpt(p,op)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = op(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if \\spad{p = a1*...*an} and \\spad{n > 1}.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns \\spad{x} * \\spad{x} * \\spad{x} * ... * \\spad{x} (\\spad{n} times).")) (|eval| (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ $)) "\\spad{eval(x, s, n, f)} replaces every \\spad{s(a)**n} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ (|List| $))) "\\spad{eval(x, s, n, f)} replaces every \\spad{s(a1,...,am)**n} in \\spad{x} by \\spad{f(a1,...,am)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [n1,...,nm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)**ni} in \\spad{x} by \\spad{fi(a1,...,an)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [n1,...,nm], [f1,...,fm])} replaces every \\spad{si(a)**ni} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.") (($ $ (|List| (|BasicOperator|)) (|List| $) (|Symbol|)) "\\spad{eval(x, [s1,...,sm], [f1,...,fm], y)} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $ (|BasicOperator|) $ (|Symbol|)) "\\spad{eval(x, s, f, y)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $) "\\spad{eval(f)} unquotes all the quoted operators in \\spad{f}.") (($ $ (|List| (|Symbol|))) "\\spad{eval(f, [foo1,...,foon])} unquotes all the \\spad{fooi}\\spad{'s} in \\spad{f}.") (($ $ (|Symbol|)) "\\spad{eval(f, foo)} unquotes all the foo\\spad{'s} in \\spad{f}.")) (|applyQuote| (($ (|Symbol|) (|List| $)) "\\spad{applyQuote(foo, [x1,...,xn])} returns \\spad{'foo(x1,...,xn)}.") (($ (|Symbol|) $ $ $ $) "\\spad{applyQuote(foo, x, y, z, t)} returns \\spad{'foo(x,y,z,t)}.") (($ (|Symbol|) $ $ $) "\\spad{applyQuote(foo, x, y, z)} returns \\spad{'foo(x,y,z)}.") (($ (|Symbol|) $ $) "\\spad{applyQuote(foo, x, y)} returns \\spad{'foo(x,y)}.") (($ (|Symbol|) $) "\\spad{applyQuote(foo, x)} returns \\spad{'foo(x)}.")) (|variables| (((|List| (|Symbol|)) $) "\\spad{variables(f)} returns the list of all the variables of \\spad{f}.")) (|ground| ((|#2| $) "\\spad{ground(f)} returns \\spad{f} as an element of \\spad{R}. An error occurs if \\spad{f} is not an element of \\spad{R}.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(f)} tests if \\spad{f} is an element of \\spad{R}."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -1039) (QUOTE (-567)))) (|HasCategory| |#2| (QUOTE (-559))) (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-1050))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-476))) (|HasCategory| |#2| (QUOTE (-1113))) (|HasCategory| |#2| (LIST (QUOTE -615) (QUOTE (-539))))) +((|HasCategory| |#2| (LIST (QUOTE -1040) (QUOTE (-567)))) (|HasCategory| |#2| (QUOTE (-559))) (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-1051))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-476))) (|HasCategory| |#2| (QUOTE (-1114))) (|HasCategory| |#2| (LIST (QUOTE -615) (QUOTE (-539))))) (-433 R) ((|constructor| (NIL "A space of formal functions with arguments in an arbitrary ordered set.")) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| $)) $ (|Kernel| $)) "\\spad{univariate(f, k)} returns \\spad{f} viewed as a univariate fraction in \\spad{k}.")) (/ (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $)) (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{p1/p2} returns the quotient of \\spad{p1} and \\spad{p2} as an element of \\%.")) (|denominator| (($ $) "\\spad{denominator(f)} returns the denominator of \\spad{f} converted to \\%.")) (|denom| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|convert| (($ (|Factored| $)) "\\spad{convert(f1\\^e1 ... fm\\^em)} returns \\spad{(f1)\\^e1 ... (fm)\\^em} as an element of \\%,{} using formal kernels created using a \\spadfunFrom{paren}{ExpressionSpace}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isPower(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|numerator| (($ $) "\\spad{numerator(f)} returns the numerator of \\spad{f} converted to \\%.")) (|numer| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R} if \\spad{R} is an integral domain. If not,{} then numer(\\spad{f}) = \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|coerce| (($ (|Fraction| (|Polynomial| (|Fraction| |#1|)))) "\\spad{coerce(f)} returns \\spad{f} as an element of \\%.") (($ (|Polynomial| (|Fraction| |#1|))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.") (($ (|Fraction| |#1|)) "\\spad{coerce(q)} returns \\spad{q} as an element of \\%.") (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.")) (|isMult| (((|Union| (|Record| (|:| |coef| (|Integer|)) (|:| |var| (|Kernel| $))) "failed") $) "\\spad{isMult(p)} returns \\spad{[n, x]} if \\spad{p = n * x} and \\spad{n <> 0}.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,...,mn]} if \\spad{p = m1 +...+ mn} and \\spad{n > 1}.")) (|isExpt| (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|Symbol|)) "\\spad{isExpt(p,f)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = f(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|BasicOperator|)) "\\spad{isExpt(p,op)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = op(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if \\spad{p = a1*...*an} and \\spad{n > 1}.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns \\spad{x} * \\spad{x} * \\spad{x} * ... * \\spad{x} (\\spad{n} times).")) (|eval| (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ $)) "\\spad{eval(x, s, n, f)} replaces every \\spad{s(a)**n} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ (|List| $))) "\\spad{eval(x, s, n, f)} replaces every \\spad{s(a1,...,am)**n} in \\spad{x} by \\spad{f(a1,...,am)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [n1,...,nm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)**ni} in \\spad{x} by \\spad{fi(a1,...,an)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [n1,...,nm], [f1,...,fm])} replaces every \\spad{si(a)**ni} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.") (($ $ (|List| (|BasicOperator|)) (|List| $) (|Symbol|)) "\\spad{eval(x, [s1,...,sm], [f1,...,fm], y)} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $ (|BasicOperator|) $ (|Symbol|)) "\\spad{eval(x, s, f, y)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $) "\\spad{eval(f)} unquotes all the quoted operators in \\spad{f}.") (($ $ (|List| (|Symbol|))) "\\spad{eval(f, [foo1,...,foon])} unquotes all the \\spad{fooi}\\spad{'s} in \\spad{f}.") (($ $ (|Symbol|)) "\\spad{eval(f, foo)} unquotes all the foo\\spad{'s} in \\spad{f}.")) (|applyQuote| (($ (|Symbol|) (|List| $)) "\\spad{applyQuote(foo, [x1,...,xn])} returns \\spad{'foo(x1,...,xn)}.") (($ (|Symbol|) $ $ $ $) "\\spad{applyQuote(foo, x, y, z, t)} returns \\spad{'foo(x,y,z,t)}.") (($ (|Symbol|) $ $ $) "\\spad{applyQuote(foo, x, y, z)} returns \\spad{'foo(x,y,z)}.") (($ (|Symbol|) $ $) "\\spad{applyQuote(foo, x, y)} returns \\spad{'foo(x,y)}.") (($ (|Symbol|) $) "\\spad{applyQuote(foo, x)} returns \\spad{'foo(x)}.")) (|variables| (((|List| (|Symbol|)) $) "\\spad{variables(f)} returns the list of all the variables of \\spad{f}.")) (|ground| ((|#1| $) "\\spad{ground(f)} returns \\spad{f} as an element of \\spad{R}. An error occurs if \\spad{f} is not an element of \\spad{R}.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(f)} tests if \\spad{f} is an element of \\spad{R}."))) -((-4414 -2797 (|has| |#1| (-1050)) (|has| |#1| (-476))) (-4412 |has| |#1| (-172)) (-4411 |has| |#1| (-172)) ((-4419 "*") |has| |#1| (-559)) (-4410 |has| |#1| (-559)) (-4415 |has| |#1| (-559)) (-4409 |has| |#1| (-559))) +((-4415 -2800 (|has| |#1| (-1051)) (|has| |#1| (-476))) (-4413 |has| |#1| (-172)) (-4412 |has| |#1| (-172)) ((-4420 "*") |has| |#1| (-559)) (-4411 |has| |#1| (-559)) (-4416 |has| |#1| (-559)) (-4410 |has| |#1| (-559))) NIL -(-434 R -3867) +(-434 R -3879) ((|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 -(-435 R -3867) +(-435 R -3879) ((|constructor| (NIL "FunctionsSpacePrimitiveElement provides functions to compute primitive elements in functions spaces.")) (|primitiveElement| (((|Record| (|:| |primelt| |#2|) (|:| |pol1| (|SparseUnivariatePolynomial| |#2|)) (|:| |pol2| (|SparseUnivariatePolynomial| |#2|)) (|:| |prim| (|SparseUnivariatePolynomial| |#2|))) |#2| |#2|) "\\spad{primitiveElement(a1, a2)} returns \\spad{[a, q1, q2, q]} such that \\spad{k(a1, a2) = k(a)},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. The minimal polynomial for a2 may involve \\spad{a1},{} but the minimal polynomial for \\spad{a1} may not involve a2; This operations uses \\spadfun{resultant}.") (((|Record| (|:| |primelt| |#2|) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#2|))) (|:| |prim| (|SparseUnivariatePolynomial| |#2|))) (|List| |#2|)) "\\spad{primitiveElement([a1,...,an])} returns \\spad{[a, [q1,...,qn], q]} such that then \\spad{k(a1,...,an) = k(a)},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}."))) NIL ((|HasCategory| |#2| (QUOTE (-27)))) -(-436 R -3867) +(-436 R -3879) ((|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 @@ -1680,10 +1680,10 @@ NIL ((|constructor| (NIL "Creates and manipulates objects which correspond to the basic FORTRAN data types: REAL,{} INTEGER,{} COMPLEX,{} LOGICAL and CHARACTER")) (= (((|Boolean|) $ $) "\\spad{x=y} tests for equality")) (|logical?| (((|Boolean|) $) "\\spad{logical?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type LOGICAL.")) (|character?| (((|Boolean|) $) "\\spad{character?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type CHARACTER.")) (|doubleComplex?| (((|Boolean|) $) "\\spad{doubleComplex?(t)} tests whether \\spad{t} is equivalent to the (non-standard) FORTRAN type DOUBLE COMPLEX.")) (|complex?| (((|Boolean|) $) "\\spad{complex?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type COMPLEX.")) (|integer?| (((|Boolean|) $) "\\spad{integer?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type INTEGER.")) (|double?| (((|Boolean|) $) "\\spad{double?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type DOUBLE PRECISION")) (|real?| (((|Boolean|) $) "\\spad{real?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type REAL.")) (|coerce| (((|SExpression|) $) "\\spad{coerce(x)} returns the \\spad{s}-expression associated with \\spad{x}") (((|Symbol|) $) "\\spad{coerce(x)} returns the symbol associated with \\spad{x}") (($ (|Symbol|)) "\\spad{coerce(s)} transforms the symbol \\spad{s} into an element of FortranScalarType provided \\spad{s} is one of real,{} complex,{}double precision,{} logical,{} integer,{} character,{} REAL,{} COMPLEX,{} LOGICAL,{} INTEGER,{} CHARACTER,{} DOUBLE PRECISION") (($ (|String|)) "\\spad{coerce(s)} transforms the string \\spad{s} into an element of FortranScalarType provided \\spad{s} is one of \"real\",{} \"double precision\",{} \"complex\",{} \"logical\",{} \"integer\",{} \"character\",{} \"REAL\",{} \"COMPLEX\",{} \"LOGICAL\",{} \"INTEGER\",{} \"CHARACTER\",{} \"DOUBLE PRECISION\""))) NIL NIL -(-438 R -3867 UP) +(-438 R -3879 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 -1039) (QUOTE (-48))))) +((|HasCategory| |#2| (LIST (QUOTE -1040) (QUOTE (-48))))) (-439) ((|constructor| (NIL "Code to manipulate Fortran templates")) (|fortranCarriageReturn| (((|Void|)) "\\spad{fortranCarriageReturn()} produces a carriage return on the current Fortran output stream")) (|fortranLiteral| (((|Void|) (|String|)) "\\spad{fortranLiteral(s)} writes \\spad{s} to the current Fortran output stream")) (|fortranLiteralLine| (((|Void|) (|String|)) "\\spad{fortranLiteralLine(s)} writes \\spad{s} to the current Fortran output stream,{} followed by a carriage return")) (|processTemplate| (((|FileName|) (|FileName|)) "\\spad{processTemplate(tp)} processes the template \\spad{tp},{} writing the result to the current FORTRAN output stream.") (((|FileName|) (|FileName|) (|FileName|)) "\\spad{processTemplate(tp,fn)} processes the template \\spad{tp},{} writing the result out to \\spad{fn}."))) NIL @@ -1712,7 +1712,7 @@ 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 -(-446 R UP -3867) +(-446 R UP -3879) ((|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 @@ -1750,16 +1750,16 @@ NIL NIL (-455) ((|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)) +((-4411 . T) ((-4420 "*") . T) (-4412 . T) (-4413 . T) (-4415 . T)) NIL (-456 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| (-410 (-953 |#1|)) (-559)) (-4412 . T) (-4411 . T)) -((|HasCategory| (-410 (-953 |#1|)) (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| (-410 (-953 |#1|)) (QUOTE (-559)))) +((-4415 |has| (-410 (-954 |#1|)) (-559)) (-4413 . T) (-4412 . T)) +((|HasCategory| (-410 (-954 |#1|)) (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| (-410 (-954 |#1|)) (QUOTE (-559)))) (-457 |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| (-559)) (-4415 |has| |#2| (-6 -4415)) (-4412 . T) (-4411 . T) (-4414 . T)) -((|HasCategory| |#2| (QUOTE (-910))) (-2797 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-455))) (|HasCategory| |#2| (QUOTE (-559))) (|HasCategory| |#2| (QUOTE (-910)))) (-2797 (|HasCategory| |#2| (QUOTE (-455))) (|HasCategory| |#2| (QUOTE (-559))) (|HasCategory| |#2| (QUOTE (-910)))) (-2797 (|HasCategory| |#2| (QUOTE (-455))) (|HasCategory| |#2| (QUOTE (-910)))) (|HasCategory| |#2| (QUOTE (-559))) (|HasCategory| |#2| (QUOTE (-172))) (-2797 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-559)))) (-12 (|HasCategory| (-865 |#1|) (LIST (QUOTE -887) (QUOTE (-381)))) (|HasCategory| |#2| (LIST (QUOTE -887) (QUOTE (-381))))) (-12 (|HasCategory| (-865 |#1|) (LIST (QUOTE -887) (QUOTE (-567)))) (|HasCategory| |#2| (LIST (QUOTE -887) (QUOTE (-567))))) (-12 (|HasCategory| (-865 |#1|) (LIST (QUOTE -615) (LIST (QUOTE -893) (QUOTE (-381))))) (|HasCategory| |#2| (LIST (QUOTE -615) (LIST (QUOTE -893) (QUOTE (-381)))))) (-12 (|HasCategory| (-865 |#1|) (LIST (QUOTE -615) (LIST (QUOTE -893) (QUOTE (-567))))) (|HasCategory| |#2| (LIST (QUOTE -615) (LIST (QUOTE -893) (QUOTE (-567)))))) (-12 (|HasCategory| (-865 |#1|) (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| |#2| (LIST (QUOTE -615) (QUOTE (-539))))) (|HasCategory| |#2| (LIST (QUOTE -640) (QUOTE (-567)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#2| (LIST (QUOTE -1039) (QUOTE (-567)))) (-2797 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#2| (LIST (QUOTE -1039) (LIST (QUOTE -410) (QUOTE (-567)))))) (|HasCategory| |#2| (LIST (QUOTE -1039) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#2| (QUOTE (-365))) (|HasAttribute| |#2| (QUOTE -4415)) (|HasCategory| |#2| (QUOTE (-455))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-910)))) (-2797 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-910)))) (|HasCategory| |#2| (QUOTE (-145))))) +(((-4420 "*") |has| |#2| (-172)) (-4411 |has| |#2| (-559)) (-4416 |has| |#2| (-6 -4416)) (-4413 . T) (-4412 . T) (-4415 . T)) +((|HasCategory| |#2| (QUOTE (-911))) (-2800 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-455))) (|HasCategory| |#2| (QUOTE (-559))) (|HasCategory| |#2| (QUOTE (-911)))) (-2800 (|HasCategory| |#2| (QUOTE (-455))) (|HasCategory| |#2| (QUOTE (-559))) (|HasCategory| |#2| (QUOTE (-911)))) (-2800 (|HasCategory| |#2| (QUOTE (-455))) (|HasCategory| |#2| (QUOTE (-911)))) (|HasCategory| |#2| (QUOTE (-559))) (|HasCategory| |#2| (QUOTE (-172))) (-2800 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-559)))) (-12 (|HasCategory| (-865 |#1|) (LIST (QUOTE -888) (QUOTE (-381)))) (|HasCategory| |#2| (LIST (QUOTE -888) (QUOTE (-381))))) (-12 (|HasCategory| (-865 |#1|) (LIST (QUOTE -888) (QUOTE (-567)))) (|HasCategory| |#2| (LIST (QUOTE -888) (QUOTE (-567))))) (-12 (|HasCategory| (-865 |#1|) (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-381))))) (|HasCategory| |#2| (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-381)))))) (-12 (|HasCategory| (-865 |#1|) (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567))))) (|HasCategory| |#2| (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567)))))) (-12 (|HasCategory| (-865 |#1|) (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| |#2| (LIST (QUOTE -615) (QUOTE (-539))))) (|HasCategory| |#2| (LIST (QUOTE -640) (QUOTE (-567)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#2| (LIST (QUOTE -1040) (QUOTE (-567)))) (-2800 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#2| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567)))))) (|HasCategory| |#2| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#2| (QUOTE (-365))) (|HasAttribute| |#2| (QUOTE -4416)) (|HasCategory| |#2| (QUOTE (-455))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-911)))) (-2800 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-911)))) (|HasCategory| |#2| (QUOTE (-145))))) (-458 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 @@ -1786,7 +1786,7 @@ NIL NIL (-464 |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| $) "\\spad{leadingCoefficient(x)} \\undocumented"))) -((-4412 . T) (-4411 . T)) +((-4413 . T) (-4412 . T)) NIL (-465 E V R P Q) ((|constructor| (NIL "Gosper\\spad{'s} summation algorithm.")) (|GospersMethod| (((|Union| |#5| "failed") |#5| |#2| (|Mapping| |#2|)) "\\spad{GospersMethod(b, n, new)} returns a rational function \\spad{rf(n)} such that \\spad{a(n) * rf(n)} is the indefinite sum of \\spad{a(n)} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{a(n+1) * rf(n+1) - a(n) * rf(n) = a(n)},{} where \\spad{b(n) = a(n)/a(n-1)} is a rational function. Returns \"failed\" if no such rational function \\spad{rf(n)} exists. Note: \\spad{new} is a nullary function returning a new \\spad{V} every time. The condition on \\spad{a(n)} is that \\spad{a(n)/a(n-1)} is a rational function of \\spad{n}."))) @@ -1794,8 +1794,8 @@ NIL NIL (-466 R E |VarSet| P) ((|constructor| (NIL "A domain for polynomial sets.")) (|convert| (($ (|List| |#4|)) "\\axiom{convert(\\spad{lp})} returns the polynomial set whose members are the polynomials of \\axiom{\\spad{lp}}."))) -((-4418 . T) (-4417 . T)) -((-12 (|HasCategory| |#4| (QUOTE (-1101))) (|HasCategory| |#4| (LIST (QUOTE -310) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| |#4| (QUOTE (-1101))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#4| (LIST (QUOTE -614) (QUOTE (-863))))) +((-4419 . T) (-4418 . T)) +((-12 (|HasCategory| |#4| (QUOTE (-1102))) (|HasCategory| |#4| (LIST (QUOTE -310) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| |#4| (QUOTE (-1102))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#4| (LIST (QUOTE -614) (QUOTE (-863))))) (-467 S R E) ((|constructor| (NIL "GradedAlgebra(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-algebra\\spad{''}. A graded algebra is a graded module together with a degree preserving \\spad{R}-linear map,{} called the {\\em product}. \\blankline The name ``product\\spad{''} is written out in full so inner and outer products with the same mapping type can be distinguished by name.")) (|product| (($ $ $) "\\spad{product(a,b)} is the degree-preserving \\spad{R}-linear product: \\blankline \\indented{2}{\\spad{degree product(a,b) = degree a + degree b}} \\indented{2}{\\spad{product(a1+a2,b) = product(a1,b) + product(a2,b)}} \\indented{2}{\\spad{product(a,b1+b2) = product(a,b1) + product(a,b2)}} \\indented{2}{\\spad{product(r*a,b) = product(a,r*b) = r*product(a,b)}} \\indented{2}{\\spad{product(a,product(b,c)) = product(product(a,b),c)}}")) ((|One|) (($) "1 is the identity for \\spad{product}."))) NIL @@ -1824,7 +1824,7 @@ 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| $) "\\spad{degree(g)} names the degree of \\spad{g}. The set of all elements of a given degree form an \\spad{R}-module."))) NIL NIL -(-474 |lv| -3867 R) +(-474 |lv| -3879 R) ((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni,{} Summer \\spad{'88},{} revised November \\spad{'89}} Solve systems of polynomial equations using Groebner bases Total order Groebner bases are computed and then converted to lex ones This package is mostly intended for internal use.")) (|genericPosition| (((|Record| (|:| |dpolys| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |coords| (|List| (|Integer|)))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{genericPosition(lp,lv)} puts a radical zero dimensional ideal in general position,{} for system \\spad{lp} in variables \\spad{lv}.")) (|testDim| (((|Union| (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "failed") (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{testDim(lp,lv)} tests if the polynomial system \\spad{lp} in variables \\spad{lv} is zero dimensional.")) (|groebSolve| (((|List| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{groebSolve(lp,lv)} reduces the polynomial system \\spad{lp} in variables \\spad{lv} to triangular form. Algorithm based on groebner bases algorithm with linear algebra for change of ordering. Preprocessing for the general solver. The polynomials in input are of type \\spadtype{DMP}."))) NIL NIL @@ -1834,23 +1834,23 @@ NIL NIL (-476) ((|constructor| (NIL "The class of multiplicative groups,{} \\spadignore{i.e.} monoids with multiplicative inverses. \\blankline")) (|commutator| (($ $ $) "\\spad{commutator(p,q)} computes \\spad{inv(p) * inv(q) * p * q}.")) (|conjugate| (($ $ $) "\\spad{conjugate(p,q)} computes \\spad{inv(q) * p * q}; this is 'right action by conjugation'.")) (|unitsKnown| ((|attribute|) "unitsKnown asserts that recip only returns \"failed\" for non-units.")) (** (($ $ (|Integer|)) "\\spad{x**n} returns \\spad{x} raised to the integer power \\spad{n}.")) (/ (($ $ $) "\\spad{x/y} is the same as \\spad{x} times the inverse of \\spad{y}.")) (|inv| (($ $) "\\spad{inv(x)} returns the inverse of \\spad{x}."))) -((-4414 . T)) +((-4415 . T)) NIL (-477 |Coef| |var| |cen|) ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x\\^r)}.")) (|integrate| (($ $ (|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| (-559)) (-4415 |has| |#1| (-365)) (-4409 |has| |#1| (-365)) (-4411 . T) (-4412 . T) (-4414 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-172))) (-2797 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-559)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-1177)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -410) (QUOTE (-567))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -410) (QUOTE (-567))) (|devaluate| |#1|)))) (|HasCategory| (-410 (-567)) (QUOTE (-1113))) (|HasCategory| |#1| (QUOTE (-365))) (-2797 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-559)))) (-2797 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-559)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -410) (QUOTE (-567)))))) (|HasSignature| |#1| (LIST (QUOTE -4127) (LIST (|devaluate| |#1|) (QUOTE (-1177)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -410) (QUOTE (-567)))))) (-2797 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-960))) (|HasCategory| |#1| (QUOTE (-1202))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasSignature| |#1| (LIST (QUOTE -1576) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1177))))) (|HasSignature| |#1| (LIST (QUOTE -2845) (LIST (LIST (QUOTE -645) (QUOTE (-1177))) (|devaluate| |#1|))))))) +(((-4420 "*") |has| |#1| (-172)) (-4411 |has| |#1| (-559)) (-4416 |has| |#1| (-365)) (-4410 |has| |#1| (-365)) (-4412 . T) (-4413 . T) (-4415 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-172))) (-2800 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-559)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -902) (QUOTE (-1178)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -410) (QUOTE (-567))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -410) (QUOTE (-567))) (|devaluate| |#1|)))) (|HasCategory| (-410 (-567)) (QUOTE (-1114))) (|HasCategory| |#1| (QUOTE (-365))) (-2800 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-559)))) (-2800 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-559)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -410) (QUOTE (-567)))))) (|HasSignature| |#1| (LIST (QUOTE -4132) (LIST (|devaluate| |#1|) (QUOTE (-1178)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -410) (QUOTE (-567)))))) (-2800 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-961))) (|HasCategory| |#1| (QUOTE (-1203))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasSignature| |#1| (LIST (QUOTE -2416) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1178))))) (|HasSignature| |#1| (LIST (QUOTE -2847) (LIST (LIST (QUOTE -645) (QUOTE (-1178))) (|devaluate| |#1|))))))) (-478 |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 (|:| -1791 |#1|) (|:| -4232 |#2|)) (QUOTE (-1101))) (|HasCategory| (-2 (|:| -1791 |#1|) (|:| -4232 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1791) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4232) (|devaluate| |#2|)))))) (-2797 (|HasCategory| (-2 (|:| -1791 |#1|) (|:| -4232 |#2|)) (QUOTE (-1101))) (|HasCategory| |#2| (QUOTE (-1101)))) (-2797 (|HasCategory| (-2 (|:| -1791 |#1|) (|:| -4232 |#2|)) (QUOTE (-1101))) (|HasCategory| (-2 (|:| -1791 |#1|) (|:| -4232 |#2|)) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| |#2| (QUOTE (-1101))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| (-2 (|:| -1791 |#1|) (|:| -4232 |#2|)) (LIST (QUOTE -615) (QUOTE (-539)))) (-12 (|HasCategory| |#2| (QUOTE (-1101))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-851))) (-2797 (|HasCategory| (-2 (|:| -1791 |#1|) (|:| -4232 |#2|)) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#2| (QUOTE (-1101))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-2 (|:| -1791 |#1|) (|:| -4232 |#2|)) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-2 (|:| -1791 |#1|) (|:| -4232 |#2|)) (QUOTE (-1101)))) +((-4419 . T)) +((-12 (|HasCategory| (-2 (|:| -1795 |#1|) (|:| -4237 |#2|)) (QUOTE (-1102))) (|HasCategory| (-2 (|:| -1795 |#1|) (|:| -4237 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1795) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4237) (|devaluate| |#2|)))))) (-2800 (|HasCategory| (-2 (|:| -1795 |#1|) (|:| -4237 |#2|)) (QUOTE (-1102))) (|HasCategory| |#2| (QUOTE (-1102)))) (-2800 (|HasCategory| (-2 (|:| -1795 |#1|) (|:| -4237 |#2|)) (QUOTE (-1102))) (|HasCategory| (-2 (|:| -1795 |#1|) (|:| -4237 |#2|)) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| |#2| (QUOTE (-1102))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| (-2 (|:| -1795 |#1|) (|:| -4237 |#2|)) (LIST (QUOTE -615) (QUOTE (-539)))) (-12 (|HasCategory| |#2| (QUOTE (-1102))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-851))) (-2800 (|HasCategory| (-2 (|:| -1795 |#1|) (|:| -4237 |#2|)) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#2| (QUOTE (-1102))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-2 (|:| -1795 |#1|) (|:| -4237 |#2|)) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-2 (|:| -1795 |#1|) (|:| -4237 |#2|)) (QUOTE (-1102)))) (-479 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)) -((-12 (|HasCategory| |#4| (QUOTE (-1101))) (|HasCategory| |#4| (LIST (QUOTE -310) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| |#4| (QUOTE (-1101))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#3| (QUOTE (-370))) (|HasCategory| |#4| (LIST (QUOTE -614) (QUOTE (-863))))) +((-4419 . T) (-4418 . T)) +((-12 (|HasCategory| |#4| (QUOTE (-1102))) (|HasCategory| |#4| (LIST (QUOTE -310) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| |#4| (QUOTE (-1102))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#3| (QUOTE (-370))) (|HasCategory| |#4| (LIST (QUOTE -614) (QUOTE (-863))))) (-480) ((|constructor| (NIL "\\indented{1}{Symbolic fractions in \\%\\spad{pi} with integer coefficients;} \\indented{1}{The point for using \\spad{Pi} as the default domain for those fractions} \\indented{1}{is that \\spad{Pi} is coercible to the float types,{} and not Expression.} Date Created: 21 Feb 1990 Date Last Updated: 12 Mai 1992")) (|pi| (($) "\\spad{pi()} returns the symbolic \\%\\spad{pi}."))) -((-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) +((-4410 . T) (-4416 . T) (-4411 . T) ((-4420 "*") . T) (-4412 . T) (-4413 . T) (-4415 . T)) NIL (-481) ((|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'."))) @@ -1858,29 +1858,29 @@ NIL NIL (-482 |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 (|:| -1791 |#1|) (|:| -4232 |#2|)) (QUOTE (-1101))) (|HasCategory| (-2 (|:| -1791 |#1|) (|:| -4232 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1791) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4232) (|devaluate| |#2|)))))) (-2797 (|HasCategory| (-2 (|:| -1791 |#1|) (|:| -4232 |#2|)) (QUOTE (-1101))) (|HasCategory| |#2| (QUOTE (-1101)))) (-2797 (|HasCategory| (-2 (|:| -1791 |#1|) (|:| -4232 |#2|)) (QUOTE (-1101))) (|HasCategory| (-2 (|:| -1791 |#1|) (|:| -4232 |#2|)) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| |#2| (QUOTE (-1101))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| (-2 (|:| -1791 |#1|) (|:| -4232 |#2|)) (LIST (QUOTE -615) (QUOTE (-539)))) (-12 (|HasCategory| |#2| (QUOTE (-1101))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1791 |#1|) (|:| -4232 |#2|)) (QUOTE (-1101))) (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#2| (QUOTE (-1101))) (-2797 (|HasCategory| (-2 (|:| -1791 |#1|) (|:| -4232 |#2|)) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-2 (|:| -1791 |#1|) (|:| -4232 |#2|)) (LIST (QUOTE -614) (QUOTE (-863))))) +((-4418 . T) (-4419 . T)) +((-12 (|HasCategory| (-2 (|:| -1795 |#1|) (|:| -4237 |#2|)) (QUOTE (-1102))) (|HasCategory| (-2 (|:| -1795 |#1|) (|:| -4237 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1795) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4237) (|devaluate| |#2|)))))) (-2800 (|HasCategory| (-2 (|:| -1795 |#1|) (|:| -4237 |#2|)) (QUOTE (-1102))) (|HasCategory| |#2| (QUOTE (-1102)))) (-2800 (|HasCategory| (-2 (|:| -1795 |#1|) (|:| -4237 |#2|)) (QUOTE (-1102))) (|HasCategory| (-2 (|:| -1795 |#1|) (|:| -4237 |#2|)) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| |#2| (QUOTE (-1102))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| (-2 (|:| -1795 |#1|) (|:| -4237 |#2|)) (LIST (QUOTE -615) (QUOTE (-539)))) (-12 (|HasCategory| |#2| (QUOTE (-1102))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1795 |#1|) (|:| -4237 |#2|)) (QUOTE (-1102))) (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#2| (QUOTE (-1102))) (-2800 (|HasCategory| (-2 (|:| -1795 |#1|) (|:| -4237 |#2|)) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-2 (|:| -1795 |#1|) (|:| -4237 |#2|)) (LIST (QUOTE -614) (QUOTE (-863))))) (-483) ((|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 (-484 |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.")) (|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| (-559)) (-4415 |has| |#2| (-6 -4415)) (-4412 . T) (-4411 . T) (-4414 . 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(|HasCategory| |#2| (LIST (QUOTE -902) (QUOTE (-1178))))) (-2800 (|HasCategory| |#2| (QUOTE (-1051))) (-12 (|HasCategory| |#2| (QUOTE (-1102))) (|HasCategory| |#2| (LIST (QUOTE -1040) (QUOTE (-567)))))) (-12 (|HasCategory| |#2| (QUOTE (-1102))) (|HasCategory| |#2| (LIST (QUOTE -1040) (QUOTE (-567))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#2| (QUOTE (-1102)))) (|HasAttribute| |#2| (QUOTE -4415)) (|HasCategory| |#2| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863)))) (-12 (|HasCategory| |#2| (QUOTE (-1102))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|))))) (-486) -((|constructor| (NIL "This domain represents the header of a definition.")) (|parameters| (((|List| (|Identifier|)) $) "\\spad{parameters(h)} gives the parameters specified in the definition header \\spad{`h'}.")) (|name| (((|Identifier|) $) "\\spad{name(h)} returns the name of the operation defined defined.")) (|headAst| (($ (|Identifier|) (|List| (|Identifier|))) "\\spad{headAst(f,[x1,..,xn])} constructs a function definition header."))) +((|constructor| (NIL "This domain represents the header of a definition.")) (|parameters| (((|List| (|ParameterAst|)) $) "\\spad{parameters(h)} gives the parameters specified in the definition header \\spad{`h'}.")) (|name| (((|Identifier|) $) "\\spad{name(h)} returns the name of the operation defined defined.")) (|headAst| (($ (|Identifier|) (|List| (|ParameterAst|))) "\\spad{headAst(f,[x1,..,xn])} constructs a function definition header."))) NIL NIL (-487 S) ((|constructor| (NIL "Heap implemented in a flexible array to allow for insertions")) (|heap| (($ (|List| |#1|)) "\\spad{heap(ls)} creates a heap of elements consisting of the elements of \\spad{ls}."))) -((-4417 . T) (-4418 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1101))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1101))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-1101))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) -(-488 -3867 UP UPUP R) +((-4418 . T) (-4419 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1102))) (-2800 (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) +(-488 -3879 UP UPUP R) ((|constructor| (NIL "This domains implements finite rational divisors on an hyperelliptic curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}\\spad{'s} are integers and the \\spad{P}\\spad{'s} are finite rational points on the curve. The equation of the curve must be \\spad{y^2} = \\spad{f}(\\spad{x}) and \\spad{f} must have odd degree."))) NIL NIL @@ -1890,12 +1890,12 @@ NIL NIL (-490) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating hexadecimal expansions.")) (|hex| (($ (|Fraction| (|Integer|))) "\\spad{hex(r)} converts a rational number to a hexadecimal expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(h)} returns the fractional part of a hexadecimal expansion."))) -((-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) -((|HasCategory| (-567) (QUOTE (-910))) (|HasCategory| (-567) (LIST (QUOTE -1039) (QUOTE (-1177)))) (|HasCategory| (-567) (QUOTE (-145))) (|HasCategory| (-567) (QUOTE (-147))) (|HasCategory| (-567) (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| (-567) (QUOTE (-1023))) (|HasCategory| (-567) (QUOTE (-821))) (-2797 (|HasCategory| (-567) (QUOTE (-821))) (|HasCategory| (-567) (QUOTE (-851)))) (|HasCategory| (-567) (LIST (QUOTE -1039) (QUOTE (-567)))) (|HasCategory| (-567) (QUOTE (-1152))) (|HasCategory| (-567) (LIST (QUOTE -887) (QUOTE (-381)))) (|HasCategory| (-567) (LIST (QUOTE -887) (QUOTE (-567)))) (|HasCategory| (-567) (LIST (QUOTE -615) (LIST (QUOTE -893) (QUOTE (-381))))) (|HasCategory| (-567) (LIST (QUOTE -615) (LIST (QUOTE -893) (QUOTE (-567))))) (|HasCategory| (-567) (QUOTE (-233))) (|HasCategory| (-567) (LIST (QUOTE -901) (QUOTE (-1177)))) (|HasCategory| (-567) (LIST (QUOTE -517) (QUOTE (-1177)) (QUOTE (-567)))) (|HasCategory| (-567) (LIST (QUOTE -310) (QUOTE (-567)))) (|HasCategory| (-567) (LIST (QUOTE -287) (QUOTE (-567)) (QUOTE (-567)))) (|HasCategory| (-567) (QUOTE (-308))) (|HasCategory| (-567) (QUOTE (-548))) (|HasCategory| (-567) (QUOTE (-851))) (|HasCategory| (-567) (LIST (QUOTE -640) (QUOTE (-567)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-567) (QUOTE (-910)))) (-2797 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-567) (QUOTE (-910)))) (|HasCategory| (-567) (QUOTE (-145))))) +((-4410 . T) (-4416 . T) (-4411 . T) ((-4420 "*") . T) (-4412 . T) (-4413 . T) (-4415 . T)) +((|HasCategory| (-567) (QUOTE (-911))) (|HasCategory| (-567) (LIST (QUOTE -1040) (QUOTE (-1178)))) (|HasCategory| (-567) (QUOTE (-145))) (|HasCategory| (-567) (QUOTE (-147))) (|HasCategory| (-567) (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| (-567) (QUOTE (-1024))) (|HasCategory| (-567) (QUOTE (-821))) (-2800 (|HasCategory| (-567) (QUOTE (-821))) (|HasCategory| (-567) (QUOTE (-851)))) (|HasCategory| (-567) (LIST (QUOTE -1040) (QUOTE (-567)))) (|HasCategory| (-567) (QUOTE (-1153))) (|HasCategory| (-567) (LIST (QUOTE -888) (QUOTE (-381)))) (|HasCategory| (-567) (LIST (QUOTE -888) (QUOTE (-567)))) (|HasCategory| (-567) (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-381))))) (|HasCategory| (-567) (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567))))) (|HasCategory| (-567) (QUOTE (-233))) (|HasCategory| (-567) (LIST (QUOTE -902) (QUOTE (-1178)))) (|HasCategory| (-567) (LIST (QUOTE -517) (QUOTE (-1178)) (QUOTE (-567)))) (|HasCategory| (-567) (LIST (QUOTE -310) (QUOTE (-567)))) (|HasCategory| (-567) (LIST (QUOTE -287) (QUOTE (-567)) (QUOTE (-567)))) (|HasCategory| (-567) (QUOTE (-308))) (|HasCategory| (-567) (QUOTE (-548))) (|HasCategory| (-567) (QUOTE (-851))) (|HasCategory| (-567) (LIST (QUOTE -640) (QUOTE (-567)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-567) (QUOTE (-911)))) (-2800 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-567) (QUOTE (-911)))) (|HasCategory| (-567) (QUOTE (-145))))) (-491 A S) ((|constructor| (NIL "A homogeneous aggregate is an aggregate of elements all of the same type. In the current system,{} all aggregates are homogeneous. Two attributes characterize classes of aggregates. Aggregates from domains with attribute \\spadatt{finiteAggregate} have a finite number of members. Those with attribute \\spadatt{shallowlyMutable} allow an element to be modified or updated without changing its overall value.")) (|member?| (((|Boolean|) |#2| $) "\\spad{member?(x,u)} tests if \\spad{x} is a member of \\spad{u}. For collections,{} \\axiom{member?(\\spad{x},{}\\spad{u}) = reduce(or,{}[x=y for \\spad{y} in \\spad{u}],{}\\spad{false})}.")) (|members| (((|List| |#2|) $) "\\spad{members(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|parts| (((|List| |#2|) $) "\\spad{parts(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|count| (((|NonNegativeInteger|) |#2| $) "\\spad{count(x,u)} returns the number of occurrences of \\spad{x} in \\spad{u}. For collections,{} \\axiom{count(\\spad{x},{}\\spad{u}) = reduce(+,{}[x=y for \\spad{y} in \\spad{u}],{}0)}.") (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{count(p,u)} returns the number of elements \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. For collections,{} \\axiom{count(\\spad{p},{}\\spad{u}) = reduce(+,{}[1 for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})],{}0)}.")) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{every?(f,u)} tests if \\spad{p}(\\spad{x}) is \\spad{true} for all elements \\spad{x} of \\spad{u}. Note: 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 (-1101))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863))))) +((|HasAttribute| |#1| (QUOTE -4418)) (|HasAttribute| |#1| (QUOTE -4419)) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1102))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863))))) (-492 S) ((|constructor| (NIL "A homogeneous aggregate is an aggregate of elements all of the same type. In the current system,{} all aggregates are homogeneous. Two attributes characterize classes of aggregates. Aggregates from domains with attribute \\spadatt{finiteAggregate} have a finite number of members. Those with attribute \\spadatt{shallowlyMutable} allow an element to be modified or updated without changing its overall value.")) (|member?| (((|Boolean|) |#1| $) "\\spad{member?(x,u)} tests if \\spad{x} is a member of \\spad{u}. For collections,{} \\axiom{member?(\\spad{x},{}\\spad{u}) = reduce(or,{}[x=y for \\spad{y} in \\spad{u}],{}\\spad{false})}.")) (|members| (((|List| |#1|) $) "\\spad{members(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|parts| (((|List| |#1|) $) "\\spad{parts(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|count| (((|NonNegativeInteger|) |#1| $) "\\spad{count(x,u)} returns the number of occurrences of \\spad{x} in \\spad{u}. For collections,{} \\axiom{count(\\spad{x},{}\\spad{u}) = reduce(+,{}[x=y for \\spad{y} in \\spad{u}],{}0)}.") (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{count(p,u)} returns the number of elements \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. For collections,{} \\axiom{count(\\spad{p},{}\\spad{u}) = reduce(+,{}[1 for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})],{}0)}.")) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{every?(f,u)} tests if \\spad{p}(\\spad{x}) is \\spad{true} for all elements \\spad{x} of \\spad{u}. Note: 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|) $) "\\spad{map(f,u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) NIL @@ -1916,34 +1916,34 @@ NIL ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) NIL NIL -(-497 -3867 UP |AlExt| |AlPol|) +(-497 -3879 UP |AlExt| |AlPol|) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of a field over which we can factor UP\\spad{'s}.")) (|factor| (((|Factored| |#4|) |#4| (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{factor(p, f)} returns a prime factorisation of \\spad{p}; \\spad{f} is a factorisation map for elements of UP."))) NIL NIL (-498) ((|constructor| (NIL "Algebraic closure of the rational numbers.")) (|norm| (($ $ (|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)) -((|HasCategory| $ (QUOTE (-1050))) (|HasCategory| $ (LIST (QUOTE -1039) (QUOTE (-567))))) +((-4410 . T) (-4416 . T) (-4411 . T) ((-4420 "*") . T) (-4412 . T) (-4413 . T) (-4415 . T)) +((|HasCategory| $ (QUOTE (-1051))) (|HasCategory| $ (LIST (QUOTE -1040) (QUOTE (-567))))) (-499 S |mn|) ((|constructor| (NIL "\\indented{1}{Author Micheal Monagan Aug/87} This is the basic one dimensional array data type."))) -((-4418 . T) (-4417 . T)) -((-2797 (-12 (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1101))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-1101))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539)))) (-2797 (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-1101)))) (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| (-567) (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-1101))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863)))) (-12 (|HasCategory| |#1| (QUOTE (-1101))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) +((-4419 . T) (-4418 . T)) +((-2800 (-12 (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2800 (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539)))) (-2800 (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-1102)))) (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| (-567) (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863)))) (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-500 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)) -((-12 (|HasCategory| |#1| (QUOTE (-1101))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1101))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-1101))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) +((-4418 . T) (-4419 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1102))) (-2800 (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (-501 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 -(-502 R UP -3867) +(-502 R UP -3879) ((|constructor| (NIL "This package contains functions used in the packages FunctionFieldIntegralBasis and NumberFieldIntegralBasis.")) (|moduleSum| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) (|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) (|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|)))) "\\spad{moduleSum(m1,m2)} returns the sum of two modules in the framed algebra \\spad{F}. Each module \\spad{mi} is represented as follows: \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn} and \\spad{mi} is a record \\spad{[basis,basisDen,basisInv]}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then a basis \\spad{v1,...,vn} for \\spad{mi} is given by \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|idealiserMatrix| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{idealiserMatrix(m1, m2)} returns the matrix representing the linear conditions on the Ring associatied with an ideal defined by \\spad{m1} and \\spad{m2}.")) (|idealiser| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{idealiser(m1,m2,d)} computes the order of an ideal defined by \\spad{m1} and \\spad{m2} where \\spad{d} is the known part of the denominator") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{idealiser(m1,m2)} computes the order of an ideal defined by \\spad{m1} and \\spad{m2}")) (|leastPower| (((|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{leastPower(p,n)} returns \\spad{e},{} where \\spad{e} is the smallest integer such that \\spad{p **e >= n}")) (|divideIfCan!| ((|#1| (|Matrix| |#1|) (|Matrix| |#1|) |#1| (|Integer|)) "\\spad{divideIfCan!(matrix,matrixOut,prime,n)} attempts to divide the entries of \\spad{matrix} by \\spad{prime} and store the result in \\spad{matrixOut}. If it is successful,{} 1 is returned and if not,{} \\spad{prime} is returned. Here both \\spad{matrix} and \\spad{matrixOut} are \\spad{n}-by-\\spad{n} upper triangular matrices.")) (|matrixGcd| ((|#1| (|Matrix| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{matrixGcd(mat,sing,n)} is \\spad{gcd(sing,g)} where \\spad{g} is the \\spad{gcd} of the entries of the \\spad{n}-by-\\spad{n} upper-triangular matrix \\spad{mat}.")) (|diagonalProduct| ((|#1| (|Matrix| |#1|)) "\\spad{diagonalProduct(m)} returns the product of the elements on the diagonal of the matrix \\spad{m}")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL (-503 |mn|) ((|constructor| (NIL "\\spadtype{IndexedBits} is a domain to compactly represent large quantities of Boolean data.")) (|And| (($ $ $) "\\spad{And(n,m)} returns the bit-by-bit logical {\\em And} of \\spad{n} and \\spad{m}.")) (|Or| (($ $ $) "\\spad{Or(n,m)} returns the bit-by-bit logical {\\em Or} of \\spad{n} and \\spad{m}.")) (|Not| (($ $) "\\spad{Not(n)} returns the bit-by-bit logical {\\em Not} of \\spad{n}."))) -((-4418 . T) (-4417 . T)) -((-12 (|HasCategory| (-112) (QUOTE (-1101))) (|HasCategory| (-112) (LIST (QUOTE -310) (QUOTE (-112))))) (|HasCategory| (-112) (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| (-112) (QUOTE (-851))) (|HasCategory| (-567) (QUOTE (-851))) (|HasCategory| (-112) (QUOTE (-1101))) (|HasCategory| (-112) (LIST (QUOTE -614) (QUOTE (-863))))) +((-4419 . T) (-4418 . T)) +((-12 (|HasCategory| (-112) (QUOTE (-1102))) (|HasCategory| (-112) (LIST (QUOTE -310) (QUOTE (-112))))) (|HasCategory| (-112) (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| (-112) (QUOTE (-851))) (|HasCategory| (-567) (QUOTE (-851))) (|HasCategory| (-112) (QUOTE (-1102))) (|HasCategory| (-112) (LIST (QUOTE -614) (QUOTE (-863))))) (-504 K R UP L) ((|constructor| (NIL "IntegralBasisPolynomialTools provides functions for \\indented{1}{mapping functions on the coefficients of univariate and bivariate} \\indented{1}{polynomials.}")) (|mapBivariate| (((|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#4|)) (|Mapping| |#4| |#1|) |#3|) "\\spad{mapBivariate(f,p(x,y))} applies the function \\spad{f} to the coefficients of \\spad{p(x,y)}.")) (|mapMatrixIfCan| (((|Union| (|Matrix| |#2|) "failed") (|Mapping| (|Union| |#1| "failed") |#4|) (|Matrix| (|SparseUnivariatePolynomial| |#4|))) "\\spad{mapMatrixIfCan(f,mat)} applies the function \\spad{f} to the coefficients of the entries of \\spad{mat} if possible,{} and returns \\spad{\"failed\"} otherwise.")) (|mapUnivariateIfCan| (((|Union| |#2| "failed") (|Mapping| (|Union| |#1| "failed") |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{mapUnivariateIfCan(f,p(x))} applies the function \\spad{f} to the coefficients of \\spad{p(x)},{} if possible,{} and returns \\spad{\"failed\"} otherwise.")) (|mapUnivariate| (((|SparseUnivariatePolynomial| |#4|) (|Mapping| |#4| |#1|) |#2|) "\\spad{mapUnivariate(f,p(x))} applies the function \\spad{f} to the coefficients of \\spad{p(x)}.") ((|#2| (|Mapping| |#1| |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{mapUnivariate(f,p(x))} applies the function \\spad{f} to the coefficients of \\spad{p(x)}."))) NIL @@ -1956,10 +1956,10 @@ NIL ((|constructor| (NIL "InnerCommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#4|) "\\spad{splitDenominator([q1,...,qn])} returns \\spad{[[p1,...,pn], d]} such that \\spad{qi = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|clearDenominator| ((|#3| |#4|) "\\spad{clearDenominator([q1,...,qn])} returns \\spad{[p1,...,pn]} such that \\spad{qi = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|commonDenominator| ((|#1| |#4|) "\\spad{commonDenominator([q1,...,qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}\\spad{qn}."))) NIL NIL -(-507 -3867 |Expon| |VarSet| |DPoly|) +(-507 -3879 |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 -615) (QUOTE (-1177))))) +((|HasCategory| |#3| (LIST (QUOTE -615) (QUOTE (-1178))))) (-508 |vl| |nv|) ((|constructor| (NIL "\\indented{2}{This package provides functions for the primary decomposition of} polynomial ideals over the rational numbers. The ideals are members of the \\spadtype{PolynomialIdeals} domain,{} and the polynomial generators are required to be from the \\spadtype{DistributedMultivariatePolynomial} domain.")) (|contract| (((|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|)))) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|)))) (|List| (|OrderedVariableList| |#1|))) "\\spad{contract(I,lvar)} contracts the ideal \\spad{I} to the polynomial ring \\spad{F[lvar]}.")) (|primaryDecomp| (((|List| (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{primaryDecomp(I)} returns a list of primary ideals such that their intersection is the ideal \\spad{I}.")) (|radical| (((|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|)))) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{radical(I)} returns the radical of the ideal \\spad{I}.")) (|prime?| (((|Boolean|) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{prime?(I)} tests if the ideal \\spad{I} is prime.")) (|zeroDimPrimary?| (((|Boolean|) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{zeroDimPrimary?(I)} tests if the ideal \\spad{I} is 0-dimensional primary.")) (|zeroDimPrime?| (((|Boolean|) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{zeroDimPrime?(I)} tests if the ideal \\spad{I} is a 0-dimensional prime."))) NIL @@ -2006,36 +2006,36 @@ NIL ((|HasCategory| |#2| (QUOTE (-793)))) (-519 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)) -((-2797 (-12 (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1101))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-1101))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539)))) (-2797 (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-1101)))) (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| (-567) (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-1101))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863)))) (-12 (|HasCategory| |#1| (QUOTE (-1101))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) +((-4419 . T) (-4418 . T)) +((-2800 (-12 (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2800 (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539)))) (-2800 (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-1102)))) (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| (-567) (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863)))) (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-520) ((|constructor| (NIL "This domain represents AST for conditional expressions.")) (|elseBranch| (((|SpadAst|) $) "thenBranch(\\spad{e}) returns the `else-branch' of `e'.")) (|thenBranch| (((|SpadAst|) $) "\\spad{thenBranch(e)} returns the `then-branch' of `e'.")) (|condition| (((|SpadAst|) $) "\\spad{condition(e)} returns the condition of the if-expression `e'."))) NIL NIL (-521 |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)) -((-2797 (|HasCategory| (-584 |#1|) (QUOTE (-145))) (|HasCategory| (-584 |#1|) (QUOTE (-370)))) (|HasCategory| (-584 |#1|) (QUOTE (-147))) (|HasCategory| (-584 |#1|) (QUOTE (-370))) (|HasCategory| (-584 |#1|) (QUOTE (-145)))) +((-4410 . T) (-4416 . T) (-4411 . T) ((-4420 "*") . T) (-4412 . T) (-4413 . T) (-4415 . T)) +((-2800 (|HasCategory| (-584 |#1|) (QUOTE (-145))) (|HasCategory| (-584 |#1|) (QUOTE (-370)))) (|HasCategory| (-584 |#1|) (QUOTE (-147))) (|HasCategory| (-584 |#1|) (QUOTE (-370))) (|HasCategory| (-584 |#1|) (QUOTE (-145)))) (-522 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)) -((-12 (|HasCategory| |#1| (QUOTE (-1101))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1101))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-1101))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) +((-4418 . T) (-4419 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1102))) (-2800 (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (-523 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)) -((-2797 (-12 (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1101))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-1101))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539)))) (-2797 (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-1101)))) (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| (-567) (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-1101))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863)))) (-12 (|HasCategory| |#1| (QUOTE (-1101))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) +((-4419 . T) (-4418 . T)) +((-2800 (-12 (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2800 (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539)))) (-2800 (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-1102)))) (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| (-567) (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863)))) (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-524 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 -4419))) (-525 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 -4419))) (-526 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 (-1101))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1101))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-1101))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-559))) (|HasAttribute| |#1| (QUOTE (-4419 "*"))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) +((-4418 . T) (-4419 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1102))) (-2800 (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-559))) (|HasAttribute| |#1| (QUOTE (-4420 "*"))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (-527) ((|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 @@ -2068,7 +2068,7 @@ 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 -(-535 K -3867 |Par|) +(-535 K -3879 |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 @@ -2092,7 +2092,7 @@ 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 -(-541 K -3867 |Par|) +(-541 K -3879 |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 @@ -2122,7 +2122,7 @@ NIL NIL (-548) ((|constructor| (NIL "An \\spad{IntegerNumberSystem} is a model for the integers.")) (|invmod| (($ $ $) "\\spad{invmod(a,b)},{} \\spad{0<=a<b>1},{} \\spad{(a,b)=1} means \\spad{1/a mod b}.")) (|powmod| (($ $ $ $) "\\spad{powmod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a**b mod p}.")) (|mulmod| (($ $ $ $) "\\spad{mulmod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a*b mod p}.")) (|submod| (($ $ $ $) "\\spad{submod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a-b mod p}.")) (|addmod| (($ $ $ $) "\\spad{addmod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a+b mod p}.")) (|mask| (($ $) "\\spad{mask(n)} returns \\spad{2**n-1} (an \\spad{n} bit mask).")) (|dec| (($ $) "\\spad{dec(x)} returns \\spad{x - 1}.")) (|inc| (($ $) "\\spad{inc(x)} returns \\spad{x + 1}.")) (|copy| (($ $) "\\spad{copy(n)} gives a copy of \\spad{n}.")) (|random| (($ $) "\\spad{random(a)} creates a random element from 0 to \\spad{a-1}.") (($) "\\spad{random()} creates a random element.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(n)} creates a rational number,{} or returns \"failed\" if this is not possible.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(n)} creates a rational number (see \\spadtype{Fraction Integer})..")) (|rational?| (((|Boolean|) $) "\\spad{rational?(n)} tests if \\spad{n} is a rational number (see \\spadtype{Fraction Integer}).")) (|symmetricRemainder| (($ $ $) "\\spad{symmetricRemainder(a,b)} (where \\spad{b > 1}) yields \\spad{r} where \\spad{ -b/2 <= r < b/2 }.")) (|positiveRemainder| (($ $ $) "\\spad{positiveRemainder(a,b)} (where \\spad{b > 1}) yields \\spad{r} where \\spad{0 <= r < b} and \\spad{r == a rem b}.")) (|bit?| (((|Boolean|) $ $) "\\spad{bit?(n,i)} returns \\spad{true} if and only if \\spad{i}-th bit of \\spad{n} is a 1.")) (|shift| (($ $ $) "\\spad{shift(a,i)} shift \\spad{a} by \\spad{i} digits.")) (|length| (($ $) "\\spad{length(a)} length of \\spad{a} in digits.")) (|base| (($) "\\spad{base()} returns the base for the operations of \\spad{IntegerNumberSystem}.")) (|multiplicativeValuation| ((|attribute|) "euclideanSize(a*b) returns \\spad{euclideanSize(a)*euclideanSize(b)}.")) (|even?| (((|Boolean|) $) "\\spad{even?(n)} returns \\spad{true} if and only if \\spad{n} is even.")) (|odd?| (((|Boolean|) $) "\\spad{odd?(n)} returns \\spad{true} if and only if \\spad{n} is odd."))) -((-4415 . T) (-4416 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) +((-4416 . T) (-4417 . T) (-4411 . T) ((-4420 "*") . T) (-4412 . T) (-4413 . T) (-4415 . T)) NIL (-549) ((|constructor| (NIL "This domain is a datatype for (signed) integer values of precision 16 bits."))) @@ -2142,13 +2142,13 @@ NIL NIL (-553 |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 (|:| -1791 |#1|) (|:| -4232 |#2|)) (QUOTE (-1101))) (|HasCategory| (-2 (|:| -1791 |#1|) (|:| -4232 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1791) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4232) (|devaluate| |#2|)))))) (-2797 (|HasCategory| (-2 (|:| -1791 |#1|) (|:| -4232 |#2|)) (QUOTE (-1101))) (|HasCategory| |#2| (QUOTE (-1101)))) (-2797 (|HasCategory| (-2 (|:| -1791 |#1|) (|:| -4232 |#2|)) (QUOTE (-1101))) (|HasCategory| (-2 (|:| -1791 |#1|) (|:| -4232 |#2|)) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| |#2| (QUOTE (-1101))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| (-2 (|:| -1791 |#1|) (|:| -4232 |#2|)) (LIST (QUOTE -615) (QUOTE (-539)))) (-12 (|HasCategory| |#2| (QUOTE (-1101))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1791 |#1|) (|:| -4232 |#2|)) (QUOTE (-1101))) (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#2| (QUOTE (-1101))) (-2797 (|HasCategory| (-2 (|:| -1791 |#1|) (|:| -4232 |#2|)) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-2 (|:| -1791 |#1|) (|:| -4232 |#2|)) (LIST (QUOTE -614) (QUOTE (-863))))) -(-554 R -3867) +((-4418 . T) (-4419 . T)) +((-12 (|HasCategory| (-2 (|:| -1795 |#1|) (|:| -4237 |#2|)) (QUOTE (-1102))) (|HasCategory| (-2 (|:| -1795 |#1|) (|:| -4237 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1795) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4237) (|devaluate| |#2|)))))) (-2800 (|HasCategory| (-2 (|:| -1795 |#1|) (|:| -4237 |#2|)) (QUOTE (-1102))) (|HasCategory| |#2| (QUOTE (-1102)))) (-2800 (|HasCategory| (-2 (|:| -1795 |#1|) (|:| -4237 |#2|)) (QUOTE (-1102))) (|HasCategory| (-2 (|:| -1795 |#1|) (|:| -4237 |#2|)) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| |#2| (QUOTE (-1102))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| (-2 (|:| -1795 |#1|) (|:| -4237 |#2|)) (LIST (QUOTE -615) (QUOTE (-539)))) (-12 (|HasCategory| |#2| (QUOTE (-1102))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1795 |#1|) (|:| -4237 |#2|)) (QUOTE (-1102))) (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#2| (QUOTE (-1102))) (-2800 (|HasCategory| (-2 (|:| -1795 |#1|) (|:| -4237 |#2|)) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-2 (|:| -1795 |#1|) (|:| -4237 |#2|)) (LIST (QUOTE -614) (QUOTE (-863))))) +(-554 R -3879) ((|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 -(-555 R0 -3867 UP UPUP R) +(-555 R0 -3879 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 @@ -2158,7 +2158,7 @@ NIL NIL (-557 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."))) -((-3040 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) +((-3050 . T) (-4411 . T) ((-4420 "*") . T) (-4412 . T) (-4413 . T) (-4415 . T)) NIL (-558 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."))) @@ -2166,9 +2166,9 @@ NIL NIL (-559) ((|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)) +((-4411 . T) ((-4420 "*") . T) (-4412 . T) (-4413 . T) (-4415 . T)) NIL -(-560 R -3867) +(-560 R -3879) ((|constructor| (NIL "This package provides functions for integration,{} limited integration,{} extended integration and the risch differential equation for elemntary functions.")) (|lfextlimint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Symbol|) (|Kernel| |#2|) (|List| (|Kernel| |#2|))) "\\spad{lfextlimint(f,x,k,[k1,...,kn])} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f - c dk/dx}. Value \\spad{h} is looked for in a field containing \\spad{f} and \\spad{k1},{}...,{}\\spad{kn} (the \\spad{ki}\\spad{'s} must be logs).")) (|lfintegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{lfintegrate(f, x)} = \\spad{g} such that \\spad{dg/dx = f}.")) (|lfinfieldint| (((|Union| |#2| "failed") |#2| (|Symbol|)) "\\spad{lfinfieldint(f, x)} returns a function \\spad{g} such that \\spad{dg/dx = f} if \\spad{g} exists,{} \"failed\" otherwise.")) (|lflimitedint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Symbol|) (|List| |#2|)) "\\spad{lflimitedint(f,x,[g1,...,gn])} returns functions \\spad{[h,[[ci, gi]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,...,gn]},{} and \\spad{d(h+sum(ci log(gi)))/dx = f},{} if possible,{} \"failed\" otherwise.")) (|lfextendedint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Symbol|) |#2|) "\\spad{lfextendedint(f, x, g)} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f - cg},{} if (\\spad{h},{} \\spad{c}) exist,{} \"failed\" otherwise."))) NIL NIL @@ -2180,7 +2180,7 @@ 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 -(-563 R -3867 L) +(-563 R -3879 L) ((|constructor| (NIL "This internal package rationalises integrands on curves of the form: \\indented{2}{\\spad{y\\^2 = a x\\^2 + b x + c}} \\indented{2}{\\spad{y\\^2 = (a x + b) / (c x + d)}} \\indented{2}{\\spad{f(x, y) = 0} where \\spad{f} has degree 1 in \\spad{x}} The rationalization is done for integration,{} limited integration,{} extended integration and the risch differential equation.")) (|palgLODE0| (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgLODE0(op,g,x,y,z,t,c)} returns the solution of \\spad{op f = g} Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}.") (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgLODE0(op, g, x, y, d, p)} returns the solution of \\spad{op f = g}. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}.")) (|lift| (((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|SparseUnivariatePolynomial| |#2|) (|Kernel| |#2|)) "\\spad{lift(u,k)} \\undocumented")) (|multivariate| ((|#2| (|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|Kernel| |#2|) |#2|) "\\spad{multivariate(u,k,f)} \\undocumented")) (|univariate| (((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|SparseUnivariatePolynomial| |#2|)) "\\spad{univariate(f,k,k,p)} \\undocumented")) (|palgRDE0| (((|Union| |#2| "failed") |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|)) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgRDE0(f, g, x, y, foo, t, c)} returns a function \\spad{z(x,y)} such that \\spad{dz/dx + n * df/dx z(x,y) = g(x,y)} if such a \\spad{z} exists,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{foo},{} called by \\spad{foo(a, b, x)},{} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}.") (((|Union| |#2| "failed") |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|)) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgRDE0(f, g, x, y, foo, d, p)} returns a function \\spad{z(x,y)} such that \\spad{dz/dx + n * df/dx z(x,y) = g(x,y)} if such a \\spad{z} exists,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}. Argument \\spad{foo},{} called by \\spad{foo(a, b, x)},{} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}.")) (|palglimint0| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palglimint0(f, x, y, [u1,...,un], z, t, c)} returns functions \\spad{[h,[[ci, ui]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,...,un]} and \\spad{d(h + sum(ci log(ui)))/dx = f(x,y)} if such functions exist,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}.") (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palglimint0(f, x, y, [u1,...,un], d, p)} returns functions \\spad{[h,[[ci, ui]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,...,un]} and \\spad{d(h + sum(ci log(ui)))/dx = f(x,y)} if such functions exist,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}.")) (|palgextint0| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgextint0(f, x, y, g, z, t, c)} returns functions \\spad{[h, d]} such that \\spad{dh/dx = f(x,y) - d g},{} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy},{} and \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{z} is a dummy variable not appearing in \\spad{f(x,y)}. The operation returns \"failed\" if no such functions exist.") (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgextint0(f, x, y, g, d, p)} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f(x,y) - c g},{} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2 y(x)\\^2 = P(x)},{} or \"failed\" if no such functions exist.")) (|palgint0| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgint0(f, x, y, z, t, c)} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{z} is a dummy variable not appearing in \\spad{f(x,y)}.") (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgint0(f, x, y, d, p)} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2 y(x)\\^2 = P(x)}."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -657) (|devaluate| |#2|)))) @@ -2188,31 +2188,31 @@ 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 -(-565 -3867 UP UPUP R) +(-565 -3879 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 -(-566 -3867 UP) +(-566 -3879 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 (-567) ((|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."))) -((-4399 . T) (-4405 . T) (-4409 . T) (-4404 . T) (-4415 . T) (-4416 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) +((-4400 . T) (-4406 . T) (-4410 . T) (-4405 . T) (-4416 . T) (-4417 . T) (-4411 . T) ((-4420 "*") . T) (-4412 . T) (-4413 . T) (-4415 . T)) NIL (-568) ((|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 -(-569 R -3867 L) +(-569 R -3879 L) ((|constructor| (NIL "This package provides functions for integration,{} limited integration,{} extended integration and the risch differential equation for pure algebraic integrands.")) (|palgLODE| (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Symbol|)) "\\spad{palgLODE(op, g, kx, y, x)} returns the solution of \\spad{op f = g}. \\spad{y} is an algebraic function of \\spad{x}.")) (|palgRDE| (((|Union| |#2| "failed") |#2| |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|))) "\\spad{palgRDE(nfp, f, g, x, y, foo)} returns a function \\spad{z(x,y)} such that \\spad{dz/dx + n * df/dx z(x,y) = g(x,y)} if such a \\spad{z} exists,{} \"failed\" otherwise; \\spad{y} is an algebraic function of \\spad{x}; \\spad{foo(a, b, x)} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}. \\spad{nfp} is \\spad{n * df/dx}.")) (|palglimint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|)) "\\spad{palglimint(f, x, y, [u1,...,un])} returns functions \\spad{[h,[[ci, ui]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,...,un]} and \\spad{d(h + sum(ci log(ui)))/dx = f(x,y)} if such functions exist,{} \"failed\" otherwise; \\spad{y} is an algebraic function of \\spad{x}.")) (|palgextint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2|) "\\spad{palgextint(f, x, y, g)} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f(x,y) - c g},{} where \\spad{y} is an algebraic function of \\spad{x}; returns \"failed\" if no such functions exist.")) (|palgint| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|)) "\\spad{palgint(f, x, y)} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x}."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -657) (|devaluate| |#2|)))) -(-570 R -3867) +(-570 R -3879) ((|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 -615) (LIST (QUOTE -893) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -887) (QUOTE (-567)))) (|HasCategory| |#2| (QUOTE (-1140)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -615) (LIST (QUOTE -893) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -887) (QUOTE (-567)))) (|HasCategory| |#2| (QUOTE (-630))))) -(-571 -3867 UP) +((-12 (|HasCategory| |#1| (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -888) (QUOTE (-567)))) (|HasCategory| |#2| (QUOTE (-1141)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -888) (QUOTE (-567)))) (|HasCategory| |#2| (QUOTE (-630))))) +(-571 -3879 UP) ((|constructor| (NIL "This package provides functions for the base case of the Risch algorithm.")) (|limitedint| (((|Union| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|)))))) "failed") (|Fraction| |#2|) (|List| (|Fraction| |#2|))) "\\spad{limitedint(f, [g1,...,gn])} returns fractions \\spad{[h,[[ci, gi]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,...,gn]},{} \\spad{ci' = 0},{} and \\spad{(h+sum(ci log(gi)))' = f},{} if possible,{} \"failed\" otherwise.")) (|extendedint| (((|Union| (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{extendedint(f, g)} returns fractions \\spad{[h, c]} such that \\spad{c' = 0} and \\spad{h' = f - cg},{} if \\spad{(h, c)} exist,{} \"failed\" otherwise.")) (|infieldint| (((|Union| (|Fraction| |#2|) "failed") (|Fraction| |#2|)) "\\spad{infieldint(f)} returns \\spad{g} such that \\spad{g' = f} or \"failed\" if the integral of \\spad{f} is not a rational function.")) (|integrate| (((|IntegrationResult| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{integrate(f)} returns \\spad{g} such that \\spad{g' = f}."))) NIL NIL @@ -2220,27 +2220,27 @@ 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 -(-573 -3867) +(-573 -3879) ((|constructor| (NIL "This package provides functions for the integration of rational functions.")) (|extendedIntegrate| (((|Union| (|Record| (|:| |ratpart| (|Fraction| (|Polynomial| |#1|))) (|:| |coeff| (|Fraction| (|Polynomial| |#1|)))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|))) "\\spad{extendedIntegrate(f, x, g)} returns fractions \\spad{[h, c]} such that \\spad{dc/dx = 0} and \\spad{dh/dx = f - cg},{} if \\spad{(h, c)} exist,{} \"failed\" otherwise.")) (|limitedIntegrate| (((|Union| (|Record| (|:| |mainpart| (|Fraction| (|Polynomial| |#1|))) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| (|Polynomial| |#1|))) (|:| |logand| (|Fraction| (|Polynomial| |#1|))))))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|List| (|Fraction| (|Polynomial| |#1|)))) "\\spad{limitedIntegrate(f, x, [g1,...,gn])} returns fractions \\spad{[h, [[ci,gi]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,...,gn]},{} \\spad{dci/dx = 0},{} and \\spad{d(h + sum(ci log(gi)))/dx = f} if possible,{} \"failed\" otherwise.")) (|infieldIntegrate| (((|Union| (|Fraction| (|Polynomial| |#1|)) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{infieldIntegrate(f, x)} returns a fraction \\spad{g} such that \\spad{dg/dx = f} if \\spad{g} exists,{} \"failed\" otherwise.")) (|internalIntegrate| (((|IntegrationResult| (|Fraction| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{internalIntegrate(f, x)} returns \\spad{g} such that \\spad{dg/dx = f}."))) NIL NIL (-574 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."))) -((-3040 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) +((-3050 . T) (-4411 . T) ((-4420 "*") . T) (-4412 . T) (-4413 . T) (-4415 . T)) NIL (-575) ((|constructor| (NIL "This package provides the implementation for the \\spadfun{solveLinearPolynomialEquation} operation over the integers. It uses a lifting technique from the package GenExEuclid")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| (|Integer|))) "failed") (|List| (|SparseUnivariatePolynomial| (|Integer|))) (|SparseUnivariatePolynomial| (|Integer|))) "\\spad{solveLinearPolynomialEquation([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists."))) NIL NIL -(-576 R -3867) +(-576 R -3879) ((|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 -615) (LIST (QUOTE -893) (QUOTE (-567))))) (|HasCategory| |#1| (QUOTE (-455))) (|HasCategory| |#1| (LIST (QUOTE -887) (QUOTE (-567)))) (|HasCategory| |#2| (QUOTE (-285))) (|HasCategory| |#2| (QUOTE (-630))) (|HasCategory| |#2| (LIST (QUOTE -1039) (QUOTE (-1177))))) (-12 (|HasCategory| |#1| (QUOTE (-455))) (|HasCategory| |#2| (QUOTE (-285)))) (|HasCategory| |#1| (QUOTE (-559)))) -(-577 -3867 UP) +((-12 (|HasCategory| |#1| (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567))))) (|HasCategory| |#1| (QUOTE (-455))) (|HasCategory| |#1| (LIST (QUOTE -888) (QUOTE (-567)))) (|HasCategory| |#2| (QUOTE (-285))) (|HasCategory| |#2| (QUOTE (-630))) (|HasCategory| |#2| (LIST (QUOTE -1040) (QUOTE (-1178))))) (-12 (|HasCategory| |#1| (QUOTE (-455))) (|HasCategory| |#2| (QUOTE (-285)))) (|HasCategory| |#1| (QUOTE (-559)))) +(-577 -3879 UP) ((|constructor| (NIL "This package provides functions for the transcendental case of the Risch algorithm.")) (|monomialIntPoly| (((|Record| (|:| |answer| |#2|) (|:| |polypart| |#2|)) |#2| (|Mapping| |#2| |#2|)) "\\spad{monomialIntPoly(p, ')} returns [\\spad{q},{} \\spad{r}] such that \\spad{p = q' + r} and \\spad{degree(r) < degree(t')}. Error if \\spad{degree(t') < 2}.")) (|monomialIntegrate| (((|Record| (|:| |ir| (|IntegrationResult| (|Fraction| |#2|))) (|:| |specpart| (|Fraction| |#2|)) (|:| |polypart| |#2|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{monomialIntegrate(f, ')} returns \\spad{[ir, s, p]} such that \\spad{f = ir' + s + p} and all the squarefree factors of the denominator of \\spad{s} are special \\spad{w}.\\spad{r}.\\spad{t} the derivation '.")) (|expintfldpoly| (((|Union| (|LaurentPolynomial| |#1| |#2|) "failed") (|LaurentPolynomial| |#1| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|)) "\\spad{expintfldpoly(p, foo)} returns \\spad{q} such that \\spad{p' = q} or \"failed\" if no such \\spad{q} exists. Argument foo is a Risch differential equation function on \\spad{F}.")) (|primintfldpoly| (((|Union| |#2| "failed") |#2| (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) |#1|) "\\spad{primintfldpoly(p, ', t')} returns \\spad{q} such that \\spad{p' = q} or \"failed\" if no such \\spad{q} exists. Argument \\spad{t'} is the derivative of the primitive generating the extension.")) (|primlimintfrac| (((|Union| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|)))))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|List| (|Fraction| |#2|))) "\\spad{primlimintfrac(f, ', [u1,...,un])} returns \\spad{[v, [c1,...,cn]]} such that \\spad{ci' = 0} and \\spad{f = v' + +/[ci * ui'/ui]}. Error: if \\spad{degree numer f >= degree denom f}.")) (|primextintfrac| (((|Union| (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Fraction| |#2|)) "\\spad{primextintfrac(f, ', g)} returns \\spad{[v, c]} such that \\spad{f = v' + c g} and \\spad{c' = 0}. Error: if \\spad{degree numer f >= degree denom f} or if \\spad{degree numer g >= degree denom g} or if \\spad{denom g} is not squarefree.")) (|explimitedint| (((|Union| (|Record| (|:| |answer| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|))))))) (|:| |a0| |#1|)) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|) (|List| (|Fraction| |#2|))) "\\spad{explimitedint(f, ', foo, [u1,...,un])} returns \\spad{[v, [c1,...,cn], a]} such that \\spad{ci' = 0},{} \\spad{f = v' + a + reduce(+,[ci * ui'/ui])},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}. Returns \"failed\" if no such \\spad{v},{} \\spad{ci},{} a exist. Argument \\spad{foo} is a Risch differential equation function on \\spad{F}.")) (|primlimitedint| (((|Union| (|Record| (|:| |answer| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|))))))) (|:| |a0| |#1|)) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) (|List| (|Fraction| |#2|))) "\\spad{primlimitedint(f, ', foo, [u1,...,un])} returns \\spad{[v, [c1,...,cn], a]} such that \\spad{ci' = 0},{} \\spad{f = v' + a + reduce(+,[ci * ui'/ui])},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Returns \"failed\" if no such \\spad{v},{} \\spad{ci},{} a exist. Argument \\spad{foo} is an extended integration function on \\spad{F}.")) (|expextendedint| (((|Union| (|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |a0| |#1|)) (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|) (|Fraction| |#2|)) "\\spad{expextendedint(f, ', foo, g)} returns either \\spad{[v, c]} such that \\spad{f = v' + c g} and \\spad{c' = 0},{} or \\spad{[v, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}. Returns \"failed\" if neither case can hold. Argument \\spad{foo} is a Risch differential equation function on \\spad{F}.")) (|primextendedint| (((|Union| (|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |a0| |#1|)) (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) (|Fraction| |#2|)) "\\spad{primextendedint(f, ', foo, g)} returns either \\spad{[v, c]} such that \\spad{f = v' + c g} and \\spad{c' = 0},{} or \\spad{[v, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Returns \"failed\" if neither case can hold. Argument \\spad{foo} is an extended integration function on \\spad{F}.")) (|tanintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|List| |#1|) "failed") (|Integer|) |#1| |#1|)) "\\spad{tanintegrate(f, ', foo)} returns \\spad{[g, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}; Argument foo is a Risch differential system solver on \\spad{F}.")) (|expintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|)) "\\spad{expintegrate(f, ', foo)} returns \\spad{[g, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}; Argument foo is a Risch differential equation solver on \\spad{F}.")) (|primintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|)) "\\spad{primintegrate(f, ', foo)} returns \\spad{[g, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Argument foo is an extended integration function on \\spad{F}."))) NIL NIL -(-578 R -3867) +(-578 R -3879) ((|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 @@ -2262,28 +2262,28 @@ NIL NIL (-583 |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)) +((-4411 . T) ((-4420 "*") . T) (-4412 . T) (-4413 . T) (-4415 . T)) NIL (-584 |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)) +((-4410 . T) (-4416 . T) (-4411 . T) ((-4420 "*") . T) (-4412 . T) (-4413 . T) (-4415 . T)) ((|HasCategory| $ (QUOTE (-147))) (|HasCategory| $ (QUOTE (-145))) (|HasCategory| $ (QUOTE (-370)))) (-585) ((|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 -(-586 R -3867) +(-586 R -3879) ((|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 -(-587 E -3867) +(-587 E -3879) ((|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 -(-588 -3867) +(-588 -3879) ((|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)) -((|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-1177)))) (|HasCategory| |#1| (LIST (QUOTE -1039) (QUOTE (-1177))))) +((-4413 . T) (-4412 . T)) +((|HasCategory| |#1| (LIST (QUOTE -902) (QUOTE (-1178)))) (|HasCategory| |#1| (LIST (QUOTE -1040) (QUOTE (-1178))))) (-589 I) ((|constructor| (NIL "The \\spadtype{IntegerRoots} package computes square roots and \\indented{2}{\\spad{n}th roots of integers efficiently.}")) (|approxSqrt| ((|#1| |#1|) "\\spad{approxSqrt(n)} returns an approximation \\spad{x} to \\spad{sqrt(n)} such that \\spad{-1 < x - sqrt(n) < 1}. Compute an approximation \\spad{s} to \\spad{sqrt(n)} such that \\indented{10}{\\spad{-1 < s - sqrt(n) < 1}} A variable precision Newton iteration is used. The running time is \\spad{O( log(n)**2 )}.")) (|perfectSqrt| (((|Union| |#1| "failed") |#1|) "\\spad{perfectSqrt(n)} returns the square root of \\spad{n} if \\spad{n} is a perfect square and returns \"failed\" otherwise")) (|perfectSquare?| (((|Boolean|) |#1|) "\\spad{perfectSquare?(n)} returns \\spad{true} if \\spad{n} is a perfect square and \\spad{false} otherwise")) (|approxNthRoot| ((|#1| |#1| (|NonNegativeInteger|)) "\\spad{approxRoot(n,r)} returns an approximation \\spad{x} to \\spad{n**(1/r)} such that \\spad{-1 < x - n**(1/r) < 1}")) (|perfectNthRoot| (((|Record| (|:| |base| |#1|) (|:| |exponent| (|NonNegativeInteger|))) |#1|) "\\spad{perfectNthRoot(n)} returns \\spad{[x,r]},{} where \\spad{n = x\\^r} and \\spad{r} is the largest integer such that \\spad{n} is a perfect \\spad{r}th power") (((|Union| |#1| "failed") |#1| (|NonNegativeInteger|)) "\\spad{perfectNthRoot(n,r)} returns the \\spad{r}th root of \\spad{n} if \\spad{n} is an \\spad{r}th power and returns \"failed\" otherwise")) (|perfectNthPower?| (((|Boolean|) |#1| (|NonNegativeInteger|)) "\\spad{perfectNthPower?(n,r)} returns \\spad{true} if \\spad{n} is an \\spad{r}th power and \\spad{false} otherwise"))) NIL @@ -2310,19 +2310,19 @@ NIL NIL (-595 |mn|) ((|constructor| (NIL "This domain implements low-level strings"))) -((-4418 . T) (-4417 . T)) -((-2797 (-12 (|HasCategory| (-144) (QUOTE (-851))) (|HasCategory| (-144) (LIST (QUOTE -310) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1101))) (|HasCategory| (-144) (LIST (QUOTE -310) (QUOTE (-144)))))) (-2797 (|HasCategory| (-144) (LIST (QUOTE -614) (QUOTE (-863)))) (-12 (|HasCategory| (-144) (QUOTE (-1101))) (|HasCategory| (-144) (LIST (QUOTE -310) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -615) (QUOTE (-539)))) (-2797 (|HasCategory| (-144) (QUOTE (-851))) (|HasCategory| (-144) (QUOTE (-1101)))) (|HasCategory| (-144) (QUOTE (-851))) (|HasCategory| (-567) (QUOTE (-851))) (|HasCategory| (-144) (QUOTE (-1101))) (|HasCategory| (-144) (LIST (QUOTE -614) (QUOTE (-863)))) (-12 (|HasCategory| (-144) (QUOTE (-1101))) (|HasCategory| (-144) (LIST (QUOTE -310) (QUOTE (-144)))))) +((-4419 . T) (-4418 . T)) +((-2800 (-12 (|HasCategory| (-144) (QUOTE (-851))) (|HasCategory| (-144) (LIST (QUOTE -310) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1102))) (|HasCategory| (-144) (LIST (QUOTE -310) (QUOTE (-144)))))) (-2800 (|HasCategory| (-144) (LIST (QUOTE -614) (QUOTE (-863)))) (-12 (|HasCategory| (-144) (QUOTE (-1102))) (|HasCategory| (-144) (LIST (QUOTE -310) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -615) (QUOTE (-539)))) (-2800 (|HasCategory| (-144) (QUOTE (-851))) (|HasCategory| (-144) (QUOTE (-1102)))) (|HasCategory| (-144) (QUOTE (-851))) (|HasCategory| (-567) (QUOTE (-851))) (|HasCategory| (-144) (QUOTE (-1102))) (|HasCategory| (-144) (LIST (QUOTE -614) (QUOTE (-863)))) (-12 (|HasCategory| (-144) (QUOTE (-1102))) (|HasCategory| (-144) (LIST (QUOTE -310) (QUOTE (-144)))))) (-596 E V R P) ((|constructor| (NIL "tools for the summation packages.")) (|sum| (((|Record| (|:| |num| |#4|) (|:| |den| (|Integer|))) |#4| |#2|) "\\spad{sum(p(n), n)} returns \\spad{P(n)},{} the indefinite sum of \\spad{p(n)} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{P(n+1) - P(n) = a(n)}.") (((|Record| (|:| |num| |#4|) (|:| |den| (|Integer|))) |#4| |#2| (|Segment| |#4|)) "\\spad{sum(p(n), n = a..b)} returns \\spad{p(a) + p(a+1) + ... + p(b)}."))) NIL NIL (-597 |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| (-559)) (-4411 . T) (-4412 . T) (-4414 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (QUOTE (-559))) (-2797 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-559)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-1177)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-567)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-567)) (|devaluate| |#1|)))) (|HasCategory| (-567) (QUOTE (-1113))) (|HasCategory| |#1| (QUOTE (-365))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-567))))) (|HasSignature| |#1| (LIST (QUOTE -4127) (LIST (|devaluate| |#1|) (QUOTE (-1177)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-567)))))) +(((-4420 "*") |has| |#1| (-172)) (-4411 |has| |#1| (-559)) (-4412 . T) (-4413 . T) (-4415 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (QUOTE (-559))) (-2800 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-559)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -902) (QUOTE (-1178)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-567)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-567)) (|devaluate| |#1|)))) (|HasCategory| (-567) (QUOTE (-1114))) (|HasCategory| |#1| (QUOTE (-365))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-567))))) (|HasSignature| |#1| (LIST (QUOTE -4132) (LIST (|devaluate| |#1|) (QUOTE (-1178)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-567)))))) (-598 |Coef|) ((|constructor| (NIL "Internal package for dense Taylor series. This is an internal Taylor series type in which Taylor series are represented by a \\spadtype{Stream} of \\spadtype{Ring} elements. For univariate series,{} the \\spad{Stream} elements are the Taylor coefficients. For multivariate series,{} the \\spad{n}th Stream element is a form of degree \\spad{n} in the power series variables.")) (* (($ $ (|Integer|)) "\\spad{x*i} returns the product of integer \\spad{i} and the series \\spad{x}.")) (|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.}"))) -(((-4419 "*") |has| |#1| (-559)) (-4410 |has| |#1| (-559)) (-4411 . T) (-4412 . T) (-4414 . T)) +(((-4420 "*") |has| |#1| (-559)) (-4411 |has| |#1| (-559)) (-4412 . T) (-4413 . T) (-4415 . T)) ((|HasCategory| |#1| (QUOTE (-559)))) (-599 A B) ((|constructor| (NIL "Functions defined on streams with entries in two sets.")) (|map| (((|InfiniteTuple| |#2|) (|Mapping| |#2| |#1|) (|InfiniteTuple| |#1|)) "\\spad{map(f,[x0,x1,x2,...])} returns \\spad{[f(x0),f(x1),f(x2),..]}."))) @@ -2332,7 +2332,7 @@ 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 -(-601 R -3867 FG) +(-601 R -3879 FG) ((|constructor| (NIL "This package provides transformations from trigonometric functions to exponentials and logarithms,{} and back. \\spad{F} and \\spad{FG} should be the same type of function space.")) (|trigs2explogs| ((|#3| |#3| (|List| (|Kernel| |#3|)) (|List| (|Symbol|))) "\\spad{trigs2explogs(f, [k1,...,kn], [x1,...,xm])} rewrites all the trigonometric functions appearing in \\spad{f} and involving one of the \\spad{xi's} in terms of complex logarithms and exponentials. A kernel of the form \\spad{tan(u)} is expressed using \\spad{exp(u)**2} if it is one of the \\spad{ki's},{} in terms of \\spad{exp(2*u)} otherwise.")) (|explogs2trigs| (((|Complex| |#2|) |#3|) "\\spad{explogs2trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (F2FG ((|#3| |#2|) "\\spad{F2FG(a + sqrt(-1) b)} returns \\spad{a + i b}.")) (FG2F ((|#2| |#3|) "\\spad{FG2F(a + i b)} returns \\spad{a + sqrt(-1) b}.")) (GF2FG ((|#3| (|Complex| |#2|)) "\\spad{GF2FG(a + i b)} returns \\spad{a + i b} viewed as a function with the \\spad{i} pushed down into the coefficient domain."))) NIL NIL @@ -2342,12 +2342,12 @@ NIL NIL (-603 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)) -((-2797 (-12 (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1101))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-1101))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539)))) (-2797 (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-1101)))) (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| (-567) (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-1101))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-727))) (|HasCategory| |#1| (QUOTE (-1050))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (QUOTE (-1050)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863)))) (-12 (|HasCategory| |#1| (QUOTE (-1101))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) +((-4419 . T) (-4418 . T)) +((-2800 (-12 (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2800 (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539)))) (-2800 (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-1102)))) (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| (-567) (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-727))) (|HasCategory| |#1| (QUOTE (-1051))) (-12 (|HasCategory| |#1| (QUOTE (-1004))) (|HasCategory| |#1| (QUOTE (-1051)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863)))) (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-604 S |Index| |Entry|) ((|constructor| (NIL "An indexed aggregate is a many-to-one mapping of indices to entries. For example,{} a one-dimensional-array is an indexed aggregate where the index is an integer. Also,{} a table is an indexed aggregate where the indices and entries may have any type.")) (|swap!| (((|Void|) $ |#2| |#2|) "\\spad{swap!(u,i,j)} interchanges elements \\spad{i} and \\spad{j} of aggregate \\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 (-851))) (|HasAttribute| |#1| (QUOTE -4417)) (|HasCategory| |#3| (QUOTE (-1101)))) +((|HasAttribute| |#1| (QUOTE -4419)) (|HasCategory| |#2| (QUOTE (-851))) (|HasAttribute| |#1| (QUOTE -4418)) (|HasCategory| |#3| (QUOTE (-1102)))) (-605 |Index| |Entry|) ((|constructor| (NIL "An indexed aggregate is a many-to-one mapping of indices to entries. For example,{} a one-dimensional-array is an indexed aggregate where the index is an integer. Also,{} a table is an indexed aggregate where the indices and entries may have any type.")) (|swap!| (((|Void|) $ |#1| |#1|) "\\spad{swap!(u,i,j)} interchanges elements \\spad{i} and \\spad{j} of aggregate \\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|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) NIL @@ -2362,19 +2362,19 @@ NIL NIL (-608 R A) ((|constructor| (NIL "\\indented{1}{AssociatedJordanAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$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 -2797 (-1664 (|has| |#2| (-369 |#1|)) (|has| |#1| (-559))) (-12 (|has| |#2| (-420 |#1|)) (|has| |#1| (-559)))) (-4412 . T) (-4411 . T)) -((-2797 (|HasCategory| |#2| (LIST (QUOTE -369) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -420) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -420) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#2| (LIST (QUOTE -420) (|devaluate| |#1|)))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#2| (LIST (QUOTE -369) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#2| (LIST (QUOTE -420) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -369) (|devaluate| |#1|)))) +((-4415 -2800 (-1667 (|has| |#2| (-369 |#1|)) (|has| |#1| (-559))) (-12 (|has| |#2| (-420 |#1|)) (|has| |#1| (-559)))) (-4413 . T) (-4412 . T)) +((-2800 (|HasCategory| |#2| (LIST (QUOTE -369) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -420) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -420) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#2| (LIST (QUOTE -420) (|devaluate| |#1|)))) (-2800 (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#2| (LIST (QUOTE -369) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#2| (LIST (QUOTE -420) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -369) (|devaluate| |#1|)))) (-609 |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 (|:| -1791 (-1159)) (|:| -4232 |#1|)) (QUOTE (-1101))) (|HasCategory| (-2 (|:| -1791 (-1159)) (|:| -4232 |#1|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1791) (QUOTE (-1159))) (LIST (QUOTE |:|) (QUOTE -4232) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -1791 (-1159)) (|:| -4232 |#1|)) (LIST (QUOTE -615) (QUOTE (-539)))) (-12 (|HasCategory| |#1| (QUOTE (-1101))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1101))) (|HasCategory| (-1159) (QUOTE (-851))) (|HasCategory| (-2 (|:| -1791 (-1159)) (|:| -4232 |#1|)) (QUOTE (-1101))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-2 (|:| -1791 (-1159)) (|:| -4232 |#1|)) (LIST (QUOTE -614) (QUOTE (-863))))) +((-4418 . T) (-4419 . T)) +((-12 (|HasCategory| (-2 (|:| -1795 (-1160)) (|:| -4237 |#1|)) (QUOTE (-1102))) (|HasCategory| (-2 (|:| -1795 (-1160)) (|:| -4237 |#1|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1795) (QUOTE (-1160))) (LIST (QUOTE |:|) (QUOTE -4237) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -1795 (-1160)) (|:| -4237 |#1|)) (LIST (QUOTE -615) (QUOTE (-539)))) (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| (-1160) (QUOTE (-851))) (|HasCategory| (-2 (|:| -1795 (-1160)) (|:| -4237 |#1|)) (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-2 (|:| -1795 (-1160)) (|:| -4237 |#1|)) (LIST (QUOTE -614) (QUOTE (-863))))) (-610 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 (-611 |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)) +((-4419 . T)) NIL (-612 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"))) @@ -2383,7 +2383,7 @@ NIL (-613 S) ((|constructor| (NIL "A kernel over a set \\spad{S} is an operator applied to a given list of arguments from \\spad{S}.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(op(a1,...,an), s)} tests if the name of op is \\spad{s}.") (((|Boolean|) $ (|BasicOperator|)) "\\spad{is?(op(a1,...,an), f)} tests if op = \\spad{f}.")) (|symbolIfCan| (((|Union| (|Symbol|) "failed") $) "\\spad{symbolIfCan(k)} returns \\spad{k} viewed as a symbol if \\spad{k} is a symbol,{} and \"failed\" otherwise.")) (|kernel| (($ (|Symbol|)) "\\spad{kernel(x)} returns \\spad{x} viewed as a kernel.") (($ (|BasicOperator|) (|List| |#1|) (|NonNegativeInteger|)) "\\spad{kernel(op, [a1,...,an], m)} returns the kernel \\spad{op(a1,...,an)} of nesting level \\spad{m}. Error: if \\spad{op} is \\spad{k}-ary for some \\spad{k} not equal to \\spad{m}.")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(k)} returns the nesting level of \\spad{k}.")) (|argument| (((|List| |#1|) $) "\\spad{argument(op(a1,...,an))} returns \\spad{[a1,...,an]}.")) (|operator| (((|BasicOperator|) $) "\\spad{operator(op(a1,...,an))} returns the operator op."))) NIL -((|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| |#1| (LIST (QUOTE -615) (LIST (QUOTE -893) (QUOTE (-381))))) (|HasCategory| |#1| (LIST (QUOTE -615) (LIST (QUOTE -893) (QUOTE (-567)))))) +((|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| |#1| (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-381))))) (|HasCategory| |#1| (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567)))))) (-614 S) ((|constructor| (NIL "A is coercible to \\spad{B} means any element of A can automatically be converted into an element of \\spad{B} by the interpreter.")) (|coerce| ((|#1| $) "\\spad{coerce(a)} transforms a into an element of \\spad{S}."))) NIL @@ -2392,7 +2392,7 @@ 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| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}."))) NIL NIL -(-616 -3867 UP) +(-616 -3879 UP) ((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic\\spad{'s} algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,a_1,a_2,ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$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 @@ -2414,20 +2414,20 @@ NIL NIL (-621 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)) +((-4415 . T)) NIL (-622 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)) +((-4412 . T) (-4413 . T) (-4415 . T)) ((|HasCategory| |#1| (QUOTE (-849)))) -(-623 R -3867) +(-623 R -3879) ((|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 (-624 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)) -((|HasCategory| |#2| (LIST (QUOTE -901) (QUOTE (-1177)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -1039) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1039) (QUOTE (-567))))) +((-4413 . T) (-4412 . T) ((-4420 "*") . T) (-4411 . T) (-4415 . T)) +((|HasCategory| |#2| (LIST (QUOTE -902) (QUOTE (-1178)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (QUOTE (-567))))) (-625 R E V P TS ST) ((|constructor| (NIL "A package for solving polynomial systems by means of Lazard triangular sets [1]. This package provides two operations. One for solving in the sense of the regular zeros,{} and the other for solving in the sense of the Zariski closure. Both produce square-free regular sets. Moreover,{} the decompositions do not contain any redundant component. However,{} only zero-dimensional regular sets are normalized,{} since normalization may be time consumming in positive dimension. The decomposition process is that of [2].\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|zeroSetSplit| (((|List| |#6|) (|List| |#4|) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{}clos?)} has the same specifications as \\axiomOpFrom{zeroSetSplit(\\spad{lp},{}clos?)}{RegularTriangularSetCategory}.")) (|normalizeIfCan| ((|#6| |#6|) "\\axiom{normalizeIfCan(\\spad{ts})} returns \\axiom{\\spad{ts}} in an normalized shape if \\axiom{\\spad{ts}} is zero-dimensional."))) NIL @@ -2442,7 +2442,7 @@ NIL NIL (-628 |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)) +((-4415 . T)) NIL (-629 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}}."))) @@ -2452,30 +2452,30 @@ NIL ((|constructor| (NIL "Category for the transcendental Liouvillian functions.")) (|erf| (($ $) "\\spad{erf(x)} returns the error function of \\spad{x},{} \\spadignore{i.e.} \\spad{2 / sqrt(\\%pi)} times the integral of \\spad{exp(-x**2) dx}.")) (|dilog| (($ $) "\\spad{dilog(x)} returns the dilogarithm of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{log(x) / (1 - x) dx}.")) (|li| (($ $) "\\spad{li(x)} returns the logarithmic integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{dx / log(x)}.")) (|Ci| (($ $) "\\spad{Ci(x)} returns the cosine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{cos(x) / x dx}.")) (|Si| (($ $) "\\spad{Si(x)} returns the sine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{sin(x) / x dx}.")) (|Ei| (($ $) "\\spad{Ei(x)} returns the exponential integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{exp(x)/x dx}."))) NIL NIL -(-631 R -3867) +(-631 R -3879) ((|constructor| (NIL "This package provides liouvillian functions over an integral domain.")) (|integral| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{integral(f,x = a..b)} denotes the definite integral of \\spad{f} with respect to \\spad{x} from \\spad{a} to \\spad{b}.") ((|#2| |#2| (|Symbol|)) "\\spad{integral(f,x)} indefinite integral of \\spad{f} with respect to \\spad{x}.")) (|dilog| ((|#2| |#2|) "\\spad{dilog(f)} denotes the dilogarithm")) (|erf| ((|#2| |#2|) "\\spad{erf(f)} denotes the error function")) (|li| ((|#2| |#2|) "\\spad{li(f)} denotes the logarithmic integral")) (|Ci| ((|#2| |#2|) "\\spad{Ci(f)} denotes the cosine integral")) (|Si| ((|#2| |#2|) "\\spad{Si(f)} denotes the sine integral")) (|Ei| ((|#2| |#2|) "\\spad{Ei(f)} denotes the exponential integral")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns the Liouvillian operator based on \\spad{op}")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} checks if \\spad{op} is Liouvillian"))) NIL NIL -(-632 |lv| -3867) +(-632 |lv| -3879) ((|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 (-633) ((|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 (|:| -1791 (-1159)) (|:| -4232 (-52))) (QUOTE (-1101))) (|HasCategory| (-2 (|:| -1791 (-1159)) (|:| -4232 (-52))) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1791) (QUOTE (-1159))) (LIST (QUOTE |:|) (QUOTE -4232) (QUOTE (-52))))))) (-2797 (|HasCategory| (-2 (|:| -1791 (-1159)) (|:| -4232 (-52))) (QUOTE (-1101))) (|HasCategory| (-52) (QUOTE (-1101)))) (-2797 (|HasCategory| (-2 (|:| -1791 (-1159)) (|:| -4232 (-52))) (QUOTE (-1101))) (|HasCategory| (-2 (|:| -1791 (-1159)) (|:| -4232 (-52))) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-52) (QUOTE (-1101))) (|HasCategory| (-52) (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| (-2 (|:| -1791 (-1159)) (|:| -4232 (-52))) (LIST (QUOTE -615) (QUOTE (-539)))) (-12 (|HasCategory| (-52) (QUOTE (-1101))) (|HasCategory| (-52) (LIST (QUOTE -310) (QUOTE (-52))))) (|HasCategory| (-1159) (QUOTE (-851))) (-2797 (|HasCategory| (-2 (|:| -1791 (-1159)) (|:| -4232 (-52))) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-52) (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| (-52) (QUOTE (-1101))) (|HasCategory| (-52) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-2 (|:| -1791 (-1159)) (|:| -4232 (-52))) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-2 (|:| -1791 (-1159)) (|:| -4232 (-52))) (QUOTE (-1101)))) +((-4419 . T)) +((-12 (|HasCategory| (-2 (|:| -1795 (-1160)) (|:| -4237 (-52))) (QUOTE (-1102))) (|HasCategory| (-2 (|:| -1795 (-1160)) (|:| -4237 (-52))) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1795) (QUOTE (-1160))) (LIST (QUOTE |:|) (QUOTE -4237) (QUOTE (-52))))))) (-2800 (|HasCategory| (-2 (|:| -1795 (-1160)) (|:| -4237 (-52))) (QUOTE (-1102))) (|HasCategory| (-52) (QUOTE (-1102)))) (-2800 (|HasCategory| (-2 (|:| -1795 (-1160)) (|:| -4237 (-52))) (QUOTE (-1102))) (|HasCategory| (-2 (|:| -1795 (-1160)) (|:| -4237 (-52))) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-52) (QUOTE (-1102))) (|HasCategory| (-52) (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| (-2 (|:| -1795 (-1160)) (|:| -4237 (-52))) (LIST (QUOTE -615) (QUOTE (-539)))) (-12 (|HasCategory| (-52) (QUOTE (-1102))) (|HasCategory| (-52) (LIST (QUOTE -310) (QUOTE (-52))))) (|HasCategory| (-1160) (QUOTE (-851))) (-2800 (|HasCategory| (-2 (|:| -1795 (-1160)) (|:| -4237 (-52))) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-52) (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| (-52) (QUOTE (-1102))) (|HasCategory| (-52) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-2 (|:| -1795 (-1160)) (|:| -4237 (-52))) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-2 (|:| -1795 (-1160)) (|:| -4237 (-52))) (QUOTE (-1102)))) (-634 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| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) NIL ((|HasCategory| |#2| (QUOTE (-365)))) (-635 R) ((|constructor| (NIL "\\axiom{JacobiIdentity} means that \\axiom{[\\spad{x},{}[\\spad{y},{}\\spad{z}]]+[\\spad{y},{}[\\spad{z},{}\\spad{x}]]+[\\spad{z},{}[\\spad{x},{}\\spad{y}]] = 0} holds.")) (/ (($ $ |#1|) "\\axiom{\\spad{x/r}} returns the division of \\axiom{\\spad{x}} by \\axiom{\\spad{r}}.")) (|construct| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) -((|JacobiIdentity| . T) (|NullSquare| . T) (-4412 . T) (-4411 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-4413 . T) (-4412 . T)) NIL (-636 R A) ((|constructor| (NIL "AssociatedLieAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$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 -2797 (-1664 (|has| |#2| (-369 |#1|)) (|has| |#1| (-559))) (-12 (|has| |#2| (-420 |#1|)) (|has| |#1| (-559)))) (-4412 . T) (-4411 . T)) -((-2797 (|HasCategory| |#2| (LIST (QUOTE -369) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -420) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -420) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#2| (LIST (QUOTE -420) (|devaluate| |#1|)))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#2| (LIST (QUOTE -369) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#2| (LIST (QUOTE -420) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -369) (|devaluate| |#1|)))) +((-4415 -2800 (-1667 (|has| |#2| (-369 |#1|)) (|has| |#1| (-559))) (-12 (|has| |#2| (-420 |#1|)) (|has| |#1| (-559)))) (-4413 . T) (-4412 . T)) +((-2800 (|HasCategory| |#2| (LIST (QUOTE -369) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -420) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -420) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#2| (LIST (QUOTE -420) (|devaluate| |#1|)))) (-2800 (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#2| (LIST (QUOTE -369) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#2| (LIST (QUOTE -420) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -369) (|devaluate| |#1|)))) (-637 R FE) ((|constructor| (NIL "PowerSeriesLimitPackage implements limits of expressions in one or more variables as one of the variables approaches a limiting value. Included are two-sided limits,{} left- and right- hand limits,{} and limits at plus or minus infinity.")) (|complexLimit| (((|Union| (|OnePointCompletion| |#2|) "failed") |#2| (|Equation| (|OnePointCompletion| |#2|))) "\\spad{complexLimit(f(x),x = a)} computes the complex limit \\spad{lim(x -> a,f(x))}.")) (|limit| (((|Union| (|OrderedCompletion| |#2|) "failed") |#2| (|Equation| |#2|) (|String|)) "\\spad{limit(f(x),x=a,\"left\")} computes the left hand real limit \\spad{lim(x -> a-,f(x))}; \\spad{limit(f(x),x=a,\"right\")} computes the right hand real limit \\spad{lim(x -> a+,f(x))}.") (((|Union| (|OrderedCompletion| |#2|) (|Record| (|:| |leftHandLimit| (|Union| (|OrderedCompletion| |#2|) "failed")) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| |#2|) "failed"))) "failed") |#2| (|Equation| (|OrderedCompletion| |#2|))) "\\spad{limit(f(x),x = a)} computes the real limit \\spad{lim(x -> a,f(x))}."))) NIL @@ -2487,10 +2487,10 @@ NIL (-639 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 -((-1653 (|HasCategory| |#1| (QUOTE (-365)))) (|HasCategory| |#1| (QUOTE (-365)))) +((-1657 (|HasCategory| |#1| (QUOTE (-365)))) (|HasCategory| |#1| (QUOTE (-365)))) (-640 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| $)) "\\spad{reducedSystem(A)} returns a matrix \\spad{B} such that \\spad{A x = 0} and \\spad{B x = 0} have the same solutions in \\spad{R}."))) -((-4414 . T)) +((-4415 . T)) NIL (-641 R) ((|constructor| (NIL "\\indented{2}{A set is an \\spad{R}-linear set if it is stable by dilation} \\indented{2}{by elements in the ring \\spad{R}.\\space{2}This category differs from} \\indented{2}{\\spad{Module} in that no other assumption (such as addition)} \\indented{2}{is made about the underlying set.} See Also: LeftLinearSet,{} RightLinearSet."))) @@ -2510,8 +2510,8 @@ NIL NIL (-645 S) ((|constructor| (NIL "\\spadtype{List} implements singly-linked lists that are addressable by indices; the index of the first element is 1. In addition to the operations provided by \\spadtype{IndexedList},{} this constructor provides some LISP-like functions such as \\spadfun{null} and \\spadfun{cons}.")) (|setDifference| (($ $ $) "\\spad{setDifference(u1,u2)} returns a list of the elements of \\spad{u1} that are not also in \\spad{u2}. The order of elements in the resulting list is unspecified.")) (|setIntersection| (($ $ $) "\\spad{setIntersection(u1,u2)} returns a list of the elements that lists \\spad{u1} and \\spad{u2} have in common. The order of elements in the resulting list is unspecified.")) (|setUnion| (($ $ $) "\\spad{setUnion(u1,u2)} appends the two lists \\spad{u1} and \\spad{u2},{} then removes all duplicates. The order of elements in the resulting list is unspecified.")) (|append| (($ $ $) "\\spad{append(u1,u2)} appends the elements of list \\spad{u1} onto the front of list \\spad{u2}. This new list and \\spad{u2} will share some structure.")) (|cons| (($ |#1| $) "\\spad{cons(element,u)} appends \\spad{element} onto the front of list \\spad{u} and returns the new list. This new list and the old one will share some structure.")) (|null| (((|Boolean|) $) "\\spad{null(u)} tests if list \\spad{u} is the empty list.")) (|nil| (($) "\\spad{nil} is the empty list."))) -((-4418 . T) (-4417 . T)) -((-2797 (-12 (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1101))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-1101))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539)))) (-2797 (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-1101)))) (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-829))) (|HasCategory| (-567) (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-1101))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863)))) (-12 (|HasCategory| |#1| (QUOTE (-1101))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) +((-4419 . T) (-4418 . T)) +((-2800 (-12 (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2800 (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539)))) (-2800 (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-1102)))) (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-829))) (|HasCategory| (-567) (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863)))) (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-646 T$) ((|constructor| (NIL "This domain represents AST for Spad literals."))) NIL @@ -2522,8 +2522,8 @@ NIL NIL (-648 S) ((|substitute| (($ |#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)) -((-12 (|HasCategory| |#1| (QUOTE (-1101))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1101))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-1101))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) +((-4418 . T) (-4419 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1102))) (-2800 (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (-649 R) ((|constructor| (NIL "The category of left modules over an \\spad{rng} (ring not necessarily with unit). This is an abelian group which supports left multiplation by elements of the \\spad{rng}. \\blankline"))) NIL @@ -2535,39 +2535,39 @@ NIL (-651 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 -4419))) (-652 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 -(-653 R -3867 L) +(-653 R -3879 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 (-654 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)) -((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (LIST (QUOTE -1039) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1039) (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-455))) (|HasCategory| |#1| (QUOTE (-365)))) +((-4412 . T) (-4413 . T) (-4415 . T)) +((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-455))) (|HasCategory| |#1| (QUOTE (-365)))) (-655 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| (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}"))) -((-4411 . T) (-4412 . T) (-4414 . T)) -((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (LIST (QUOTE -1039) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1039) (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-455))) (|HasCategory| |#1| (QUOTE (-365)))) +((-4412 . T) (-4413 . T) (-4415 . T)) +((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-455))) (|HasCategory| |#1| (QUOTE (-365)))) (-656 S A) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorCategory} is the category of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|directSum| (($ $ $) "\\spad{directSum(a,b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}.")) (|symmetricSquare| (($ $) "\\spad{symmetricSquare(a)} computes \\spad{symmetricProduct(a,a)} using a more efficient method.")) (|symmetricPower| (($ $ (|NonNegativeInteger|)) "\\spad{symmetricPower(a,n)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of \\spad{n} solutions of \\spad{a}.")) (|symmetricProduct| (($ $ $) "\\spad{symmetricProduct(a,b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of a solution of \\spad{a} by a solution of \\spad{b}.")) (|adjoint| (($ $) "\\spad{adjoint(a)} returns the adjoint operator of a.")) (D (($) "\\spad{D()} provides the operator corresponding to a derivation in the ring \\spad{A}."))) NIL ((|HasCategory| |#2| (QUOTE (-365)))) (-657 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)) +((-4412 . T) (-4413 . T) (-4415 . T)) NIL -(-658 -3867 UP) +(-658 -3879 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)))) -(-659 A -2167) +(-659 A -4074) ((|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)) -((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (LIST (QUOTE -1039) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1039) (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-455))) (|HasCategory| |#1| (QUOTE (-365)))) +((-4412 . T) (-4413 . T) (-4415 . T)) +((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-455))) (|HasCategory| |#1| (QUOTE (-365)))) (-660 A L) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorsOps} provides symmetric products and sums for linear ordinary differential operators.")) (|directSum| ((|#2| |#2| |#2| (|Mapping| |#1| |#1|)) "\\spad{directSum(a,b,D)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}. \\spad{D} is the derivation to use.")) (|symmetricPower| ((|#2| |#2| (|NonNegativeInteger|) (|Mapping| |#1| |#1|)) "\\spad{symmetricPower(a,n,D)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of \\spad{n} solutions of \\spad{a}. \\spad{D} is the derivation to use.")) (|symmetricProduct| ((|#2| |#2| |#2| (|Mapping| |#1| |#1|)) "\\spad{symmetricProduct(a,b,D)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of a solution of \\spad{a} by a solution of \\spad{b}. \\spad{D} is the derivation to use."))) NIL @@ -2582,7 +2582,7 @@ NIL NIL (-663 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)) +((-4413 . T) (-4412 . T)) ((|HasCategory| |#1| (QUOTE (-792)))) (-664 R) ((|constructor| (NIL "Given a PolynomialFactorizationExplicit ring,{} this package provides a defaulting rule for the \\spad{solveLinearPolynomialEquation} operation,{} by moving into the field of fractions,{} and solving it there via the \\spad{multiEuclidean} operation.")) (|solveLinearPolynomialEquationByFractions| (((|Union| (|List| (|SparseUnivariatePolynomial| |#1|)) "failed") (|List| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{solveLinearPolynomialEquationByFractions([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such exists."))) @@ -2590,7 +2590,7 @@ NIL NIL (-665 |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) (-4413 . T) (-4412 . T)) ((|HasCategory| |#2| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-172)))) (-666 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}."))) @@ -2598,13 +2598,13 @@ NIL NIL (-667 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)) +((-4419 . T) (-4418 . T)) NIL -(-668 -3867) +(-668 -3879) ((|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 -(-669 -3867 |Row| |Col| M) +(-669 -3879 |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 @@ -2614,8 +2614,8 @@ NIL NIL (-671 |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 -901) (QUOTE (-1177)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasAttribute| |#2| (QUOTE (-4419 "*"))) (|HasCategory| |#2| (LIST (QUOTE -640) (QUOTE (-567)))) (|HasCategory| |#2| (LIST (QUOTE -1039) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#2| (LIST (QUOTE -1039) (QUOTE (-567)))) (-2797 (-12 (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1101))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -640) (QUOTE (-567))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -901) (QUOTE (-1177)))))) (|HasCategory| |#2| (QUOTE (-308))) (|HasCategory| |#2| (QUOTE (-1101))) (|HasCategory| |#2| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-559))) (-2797 (|HasAttribute| |#2| (QUOTE (-4419 "*"))) (|HasCategory| |#2| (LIST (QUOTE -640) (QUOTE (-567)))) (|HasCategory| |#2| (LIST (QUOTE -901) (QUOTE (-1177)))) (|HasCategory| |#2| (QUOTE (-233)))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863)))) (-12 (|HasCategory| |#2| (QUOTE (-1101))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-172)))) +((-4415 . T) (-4418 . T) (-4412 . T) (-4413 . T)) +((|HasCategory| |#2| (LIST (QUOTE -902) (QUOTE (-1178)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasAttribute| |#2| (QUOTE (-4420 "*"))) (|HasCategory| |#2| (LIST (QUOTE -640) (QUOTE (-567)))) (|HasCategory| |#2| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#2| (LIST (QUOTE -1040) (QUOTE (-567)))) (-2800 (-12 (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1102))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -640) (QUOTE (-567))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -902) (QUOTE (-1178)))))) (|HasCategory| |#2| (QUOTE (-308))) (|HasCategory| |#2| (QUOTE (-1102))) (|HasCategory| |#2| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-559))) (-2800 (|HasAttribute| |#2| (QUOTE (-4420 "*"))) (|HasCategory| |#2| (LIST (QUOTE -640) (QUOTE (-567)))) (|HasCategory| |#2| (LIST (QUOTE -902) (QUOTE (-1178)))) (|HasCategory| |#2| (QUOTE (-233)))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863)))) (-12 (|HasCategory| |#2| (QUOTE (-1102))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-172)))) (-672) ((|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 @@ -2635,7 +2635,7 @@ NIL (-676 R) ((|constructor| (NIL "This domain represents three dimensional matrices over a general object type")) (|matrixDimensions| (((|Vector| (|NonNegativeInteger|)) $) "\\spad{matrixDimensions(x)} returns the dimensions of a matrix")) (|matrixConcat3D| (($ (|Symbol|) $ $) "\\spad{matrixConcat3D(s,x,y)} concatenates two 3-\\spad{D} matrices along a specified axis")) (|coerce| (((|PrimitiveArray| (|PrimitiveArray| (|PrimitiveArray| |#1|))) $) "\\spad{coerce(x)} moves from the domain to the representation type") (($ (|PrimitiveArray| (|PrimitiveArray| (|PrimitiveArray| |#1|)))) "\\spad{coerce(p)} moves from the representation type (PrimitiveArray PrimitiveArray PrimitiveArray \\spad{R}) to the domain")) (|setelt!| ((|#1| $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|) "\\spad{setelt!(x,i,j,k,s)} (or \\spad{x}.\\spad{i}.\\spad{j}.k:=s) sets a specific element of the array to some value of type \\spad{R}")) (|elt| ((|#1| $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{elt(x,i,j,k)} extract an element from the matrix \\spad{x}")) (|construct| (($ (|List| (|List| (|List| |#1|)))) "\\spad{construct(lll)} creates a 3-\\spad{D} matrix from a List List List \\spad{R} \\spad{lll}")) (|plus| (($ $ $) "\\spad{plus(x,y)} adds two matrices,{} term by term we note that they must be the same size")) (|identityMatrix| (($ (|NonNegativeInteger|)) "\\spad{identityMatrix(n)} create an identity matrix we note that this must be square")) (|zeroMatrix| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{zeroMatrix(i,j,k)} create a matrix with all zero terms"))) NIL -((-2797 (-12 (|HasCategory| |#1| (QUOTE (-1050))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1101))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1101))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-1101))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (QUOTE (-1050))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863)))) (-12 (|HasCategory| |#1| (QUOTE (-1101))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) +((-2800 (-12 (|HasCategory| |#1| (QUOTE (-1051))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1102))) (-2800 (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (QUOTE (-1051))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863)))) (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-677) ((|constructor| (NIL "This domain represents the syntax of a macro definition.")) (|body| (((|SpadAst|) $) "\\spad{body(m)} returns the right hand side of the definition \\spad{`m'}.")) (|head| (((|HeadAst|) $) "\\spad{head(m)} returns the head of the macro definition \\spad{`m'}. This is a list of identifiers starting with the name of the macro followed by the name of the parameters,{} if any."))) NIL @@ -2679,10 +2679,10 @@ NIL (-687 S R |Row| |Col|) ((|constructor| (NIL "\\spadtype{MatrixCategory} is a general matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col. A domain belonging to this category will be shallowly mutable. The index of the 'first' row may be obtained by calling the function \\spadfun{minRowIndex}. The index of the 'first' column may be obtained by calling the function \\spadfun{minColIndex}. The index of the first element of a Row is the same as the index of the first column in a matrix and vice versa.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|minordet| ((|#2| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors. Error: if the matrix is not square.")) (|determinant| ((|#2| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. Error: if the matrix is not square.")) (|nullSpace| (((|List| |#4|) $) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#2|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#2|) "\\spad{exquo(m,r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if matrix is not square or if the matrix is square but not invertible.") (($ $ (|NonNegativeInteger|)) "\\spad{x ** n} computes a non-negative integral power of the matrix \\spad{x}. Error: if the matrix is not square.")) (* ((|#3| |#3| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#4| $ |#4|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.") (($ (|Integer|) $) "\\spad{n * x} is an integer multiple.") (($ $ |#2|) "\\spad{x * r} is the right scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ |#2| $) "\\spad{r*x} is the left scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ $ $) "\\spad{x * y} is the product of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (- (($ $) "\\spad{-x} returns the negative of the matrix \\spad{x}.") (($ $ $) "\\spad{x - y} is the difference of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (+ (($ $ $) "\\spad{x + y} is the sum of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (|setsubMatrix!| (($ $ (|Integer|) (|Integer|) $) "\\spad{setsubMatrix(x,i1,j1,y)} destructively alters the matrix \\spad{x}. Here \\spad{x(i,j)} is set to \\spad{y(i-i1+1,j-j1+1)} for \\spad{i = i1,...,i1-1+nrows y} and \\spad{j = j1,...,j1-1+ncols y}.")) (|subMatrix| (($ $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{subMatrix(x,i1,i2,j1,j2)} extracts the submatrix \\spad{[x(i,j)]} where the index \\spad{i} ranges from \\spad{i1} to \\spad{i2} and the index \\spad{j} ranges from \\spad{j1} to \\spad{j2}.")) (|swapColumns!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapColumns!(m,i,j)} interchanges the \\spad{i}th and \\spad{j}th columns of \\spad{m}. This destructively alters the matrix.")) (|swapRows!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapRows!(m,i,j)} interchanges the \\spad{i}th and \\spad{j}th rows of \\spad{m}. This destructively alters the matrix.")) (|setelt| (($ $ (|List| (|Integer|)) (|List| (|Integer|)) $) "\\spad{setelt(x,rowList,colList,y)} destructively alters the matrix \\spad{x}. If \\spad{y} is \\spad{m}-by-\\spad{n},{} \\spad{rowList = [i<1>,i<2>,...,i<m>]} and \\spad{colList = [j<1>,j<2>,...,j<n>]},{} then \\spad{x(i<k>,j<l>)} is set to \\spad{y(k,l)} for \\spad{k = 1,...,m} and \\spad{l = 1,...,n}.")) (|elt| (($ $ (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{elt(x,rowList,colList)} returns an \\spad{m}-by-\\spad{n} matrix consisting of elements of \\spad{x},{} where \\spad{m = \\# rowList} and \\spad{n = \\# colList}. If \\spad{rowList = [i<1>,i<2>,...,i<m>]} and \\spad{colList = [j<1>,j<2>,...,j<n>]},{} then the \\spad{(k,l)}th entry of \\spad{elt(x,rowList,colList)} is \\spad{x(i<k>,j<l>)}.")) (|listOfLists| (((|List| (|List| |#2|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|vertConcat| (($ $ $) "\\spad{vertConcat(x,y)} vertically concatenates two matrices with an equal number of columns. The entries of \\spad{y} appear below of the entries of \\spad{x}. Error: if the matrices do not have the same number of columns.")) (|horizConcat| (($ $ $) "\\spad{horizConcat(x,y)} horizontally concatenates two matrices with an equal number of rows. The entries of \\spad{y} appear to the right of the entries of \\spad{x}. Error: if the matrices do not have the same number of rows.")) (|squareTop| (($ $) "\\spad{squareTop(m)} returns an \\spad{n}-by-\\spad{n} matrix consisting of the first \\spad{n} rows of the \\spad{m}-by-\\spad{n} matrix \\spad{m}. Error: if \\spad{m < n}.")) (|transpose| (($ $) "\\spad{transpose(m)} returns the transpose of the matrix \\spad{m}.") (($ |#3|) "\\spad{transpose(r)} converts the row \\spad{r} to a row matrix.")) (|coerce| (($ |#4|) "\\spad{coerce(col)} converts the column \\spad{col} to a column matrix.")) (|diagonalMatrix| (($ (|List| $)) "\\spad{diagonalMatrix([m1,...,mk])} creates a block diagonal matrix \\spad{M} with block matrices {\\em m1},{}...,{}{\\em mk} down the diagonal,{} with 0 block matrices elsewhere. More precisly: if \\spad{ri := nrows mi},{} \\spad{ci := ncols mi},{} then \\spad{m} is an (\\spad{r1+}..\\spad{+rk}) by (\\spad{c1+}..\\spad{+ck}) - matrix with entries \\spad{m.i.j = ml.(i-r1-..-r(l-1)).(j-n1-..-n(l-1))},{} if \\spad{(r1+..+r(l-1)) < i <= r1+..+rl} and \\spad{(c1+..+c(l-1)) < i <= c1+..+cl},{} \\spad{m.i.j} = 0 otherwise.") (($ (|List| |#2|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ (|NonNegativeInteger|) |#2|) "\\spad{scalarMatrix(n,r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}\\spad{'s} on the diagonal and zeroes elsewhere.")) (|matrix| (($ (|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 (-559)))) +((|HasAttribute| |#2| (QUOTE (-4420 "*"))) (|HasCategory| |#2| (QUOTE (-308))) (|HasCategory| |#2| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-559)))) (-688 R |Row| |Col|) ((|constructor| (NIL "\\spadtype{MatrixCategory} is a general matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col. A domain belonging to this category will be shallowly mutable. The index of the 'first' row may be obtained by calling the function \\spadfun{minRowIndex}. The index of the 'first' column may be obtained by calling the function \\spadfun{minColIndex}. The index of the first element of a Row is the same as the index of the first column in a matrix and vice versa.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|minordet| ((|#1| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors. Error: if the matrix is not square.")) (|determinant| ((|#1| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. Error: if the matrix is not square.")) (|nullSpace| (((|List| |#3|) $) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#1|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(m,r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if matrix is not square or if the matrix is square but not invertible.") (($ $ (|NonNegativeInteger|)) "\\spad{x ** n} computes a non-negative integral power of the matrix \\spad{x}. Error: if the matrix is not square.")) (* ((|#2| |#2| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#3| $ |#3|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.") (($ (|Integer|) $) "\\spad{n * x} is an integer multiple.") (($ $ |#1|) "\\spad{x * r} is the right scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ |#1| $) "\\spad{r*x} is the left scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ $ $) "\\spad{x * y} is the product of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (- (($ $) "\\spad{-x} returns the negative of the matrix \\spad{x}.") (($ $ $) "\\spad{x - y} is the difference of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (+ (($ $ $) "\\spad{x + y} is the sum of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (|setsubMatrix!| (($ $ (|Integer|) (|Integer|) $) "\\spad{setsubMatrix(x,i1,j1,y)} destructively alters the matrix \\spad{x}. Here \\spad{x(i,j)} is set to \\spad{y(i-i1+1,j-j1+1)} for \\spad{i = i1,...,i1-1+nrows y} and \\spad{j = j1,...,j1-1+ncols y}.")) (|subMatrix| (($ $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{subMatrix(x,i1,i2,j1,j2)} extracts the submatrix \\spad{[x(i,j)]} where the index \\spad{i} ranges from \\spad{i1} to \\spad{i2} and the index \\spad{j} ranges from \\spad{j1} to \\spad{j2}.")) (|swapColumns!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapColumns!(m,i,j)} interchanges the \\spad{i}th and \\spad{j}th columns of \\spad{m}. This destructively alters the matrix.")) (|swapRows!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapRows!(m,i,j)} interchanges the \\spad{i}th and \\spad{j}th rows of \\spad{m}. This destructively alters the matrix.")) (|setelt| (($ $ (|List| (|Integer|)) (|List| (|Integer|)) $) "\\spad{setelt(x,rowList,colList,y)} destructively alters the matrix \\spad{x}. If \\spad{y} is \\spad{m}-by-\\spad{n},{} \\spad{rowList = [i<1>,i<2>,...,i<m>]} and \\spad{colList = [j<1>,j<2>,...,j<n>]},{} then \\spad{x(i<k>,j<l>)} is set to \\spad{y(k,l)} for \\spad{k = 1,...,m} and \\spad{l = 1,...,n}.")) (|elt| (($ $ (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{elt(x,rowList,colList)} returns an \\spad{m}-by-\\spad{n} matrix consisting of elements of \\spad{x},{} where \\spad{m = \\# rowList} and \\spad{n = \\# colList}. If \\spad{rowList = [i<1>,i<2>,...,i<m>]} and \\spad{colList = [j<1>,j<2>,...,j<n>]},{} then the \\spad{(k,l)}th entry of \\spad{elt(x,rowList,colList)} is \\spad{x(i<k>,j<l>)}.")) (|listOfLists| (((|List| (|List| |#1|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|vertConcat| (($ $ $) "\\spad{vertConcat(x,y)} vertically concatenates two matrices with an equal number of columns. The entries of \\spad{y} appear below of the entries of \\spad{x}. Error: if the matrices do not have the same number of columns.")) (|horizConcat| (($ $ $) "\\spad{horizConcat(x,y)} horizontally concatenates two matrices with an equal number of rows. The entries of \\spad{y} appear to the right of the entries of \\spad{x}. Error: if the matrices do not have the same number of rows.")) (|squareTop| (($ $) "\\spad{squareTop(m)} returns an \\spad{n}-by-\\spad{n} matrix consisting of the first \\spad{n} rows of the \\spad{m}-by-\\spad{n} matrix \\spad{m}. Error: if \\spad{m < n}.")) (|transpose| (($ $) "\\spad{transpose(m)} returns the transpose of the matrix \\spad{m}.") (($ |#2|) "\\spad{transpose(r)} converts the row \\spad{r} to a row matrix.")) (|coerce| (($ |#3|) "\\spad{coerce(col)} converts the column \\spad{col} to a column matrix.")) (|diagonalMatrix| (($ (|List| $)) "\\spad{diagonalMatrix([m1,...,mk])} creates a block diagonal matrix \\spad{M} with block matrices {\\em m1},{}...,{}{\\em mk} down the diagonal,{} with 0 block matrices elsewhere. More precisly: if \\spad{ri := nrows mi},{} \\spad{ci := ncols mi},{} then \\spad{m} is an (\\spad{r1+}..\\spad{+rk}) by (\\spad{c1+}..\\spad{+ck}) - matrix with entries \\spad{m.i.j = ml.(i-r1-..-r(l-1)).(j-n1-..-n(l-1))},{} if \\spad{(r1+..+r(l-1)) < i <= r1+..+rl} and \\spad{(c1+..+c(l-1)) < i <= c1+..+cl},{} \\spad{m.i.j} = 0 otherwise.") (($ (|List| |#1|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ (|NonNegativeInteger|) |#1|) "\\spad{scalarMatrix(n,r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}\\spad{'s} on the diagonal and zeroes elsewhere.")) (|matrix| (($ (|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)) +((-4418 . T) (-4419 . T)) NIL (-689 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."))) @@ -2690,8 +2690,8 @@ NIL ((|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-559)))) (-690 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)) -((-2797 (-12 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1101))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1101))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-1101))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-559))) (|HasAttribute| |#1| (QUOTE (-4419 "*"))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863)))) (-12 (|HasCategory| |#1| (QUOTE (-1101))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) +((-4418 . T) (-4419 . T)) +((-2800 (-12 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1102))) (-2800 (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-559))) (|HasAttribute| |#1| (QUOTE (-4420 "*"))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863)))) (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-691 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 @@ -2700,7 +2700,7 @@ 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 -(-693 S -3867 FLAF FLAS) +(-693 S -3879 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 @@ -2710,11 +2710,11 @@ NIL NIL (-695) ((|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| (-700) (-365)) (-4409 |has| (-700) (-365)) (-3046 . T) (-4416 |has| (-700) (-6 -4416)) (-4413 |has| (-700) (-6 -4413)) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) -((|HasCategory| (-700) (QUOTE (-147))) (|HasCategory| (-700) (QUOTE (-145))) (|HasCategory| (-700) (LIST (QUOTE -1039) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| (-700) (LIST (QUOTE -640) (QUOTE (-567)))) (|HasCategory| (-700) (QUOTE (-370))) (|HasCategory| (-700) (QUOTE (-365))) (-2797 (|HasCategory| (-700) (LIST (QUOTE -1039) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| (-700) (QUOTE (-365)))) (|HasCategory| (-700) (LIST (QUOTE -901) (QUOTE (-1177)))) (|HasCategory| (-700) (QUOTE (-233))) (-2797 (|HasCategory| (-700) (QUOTE (-365))) (|HasCategory| (-700) (QUOTE (-351)))) (|HasCategory| (-700) (QUOTE (-351))) (|HasCategory| (-700) (LIST (QUOTE -287) (QUOTE (-700)) (QUOTE (-700)))) (|HasCategory| (-700) (LIST (QUOTE -310) (QUOTE (-700)))) (|HasCategory| (-700) (LIST (QUOTE -517) (QUOTE (-1177)) (QUOTE (-700)))) (|HasCategory| (-700) (LIST (QUOTE -887) (QUOTE (-567)))) (|HasCategory| (-700) (LIST (QUOTE -887) (QUOTE (-381)))) (|HasCategory| (-700) (LIST (QUOTE -615) (LIST (QUOTE -893) (QUOTE (-567))))) (|HasCategory| (-700) (LIST (QUOTE -615) (LIST (QUOTE -893) (QUOTE (-381))))) (-2797 (|HasCategory| (-700) (QUOTE (-308))) (|HasCategory| (-700) (QUOTE (-365))) (|HasCategory| (-700) (QUOTE (-351)))) (|HasCategory| (-700) (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| (-700) (QUOTE (-1023))) (|HasCategory| (-700) (QUOTE (-1202))) (-12 (|HasCategory| (-700) (QUOTE (-1003))) (|HasCategory| (-700) (QUOTE (-1202)))) (-2797 (-12 (|HasCategory| (-700) (QUOTE (-308))) (|HasCategory| (-700) (QUOTE (-910)))) (|HasCategory| (-700) (QUOTE (-365))) (-12 (|HasCategory| (-700) (QUOTE (-351))) (|HasCategory| (-700) (QUOTE (-910))))) (-2797 (-12 (|HasCategory| (-700) (QUOTE (-308))) (|HasCategory| (-700) (QUOTE (-910)))) (-12 (|HasCategory| (-700) (QUOTE (-365))) (|HasCategory| (-700) (QUOTE (-910)))) (-12 (|HasCategory| (-700) (QUOTE (-351))) (|HasCategory| (-700) (QUOTE (-910))))) (|HasCategory| (-700) (QUOTE (-548))) (-12 (|HasCategory| (-700) (QUOTE (-1061))) (|HasCategory| (-700) (QUOTE (-1202)))) (|HasCategory| (-700) (QUOTE (-1061))) (|HasCategory| (-700) (QUOTE (-308))) (|HasCategory| (-700) (QUOTE (-910))) (-2797 (-12 (|HasCategory| (-700) (QUOTE (-308))) (|HasCategory| (-700) (QUOTE (-910)))) (|HasCategory| (-700) (QUOTE (-365)))) (-2797 (-12 (|HasCategory| (-700) (QUOTE (-308))) (|HasCategory| (-700) (QUOTE (-910)))) (|HasCategory| (-700) (QUOTE (-559)))) (-12 (|HasCategory| (-700) (QUOTE (-233))) (|HasCategory| (-700) (QUOTE (-365)))) (-12 (|HasCategory| (-700) (LIST (QUOTE -901) (QUOTE (-1177)))) (|HasCategory| (-700) (QUOTE (-365)))) (|HasCategory| (-700) (LIST (QUOTE -1039) (QUOTE (-567)))) (|HasCategory| (-700) (QUOTE (-559))) (|HasAttribute| (-700) (QUOTE -4416)) (|HasAttribute| (-700) (QUOTE -4413)) (-12 (|HasCategory| (-700) (QUOTE (-308))) (|HasCategory| (-700) (QUOTE (-910)))) (-2797 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-700) (QUOTE (-308))) (|HasCategory| (-700) (QUOTE (-910)))) (|HasCategory| (-700) (QUOTE (-145)))) (-2797 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-700) (QUOTE (-308))) (|HasCategory| (-700) (QUOTE (-910)))) (|HasCategory| (-700) (QUOTE (-351))))) +((-4411 . T) (-4416 |has| (-700) (-365)) (-4410 |has| (-700) (-365)) (-3056 . T) (-4417 |has| (-700) (-6 -4417)) (-4414 |has| (-700) (-6 -4414)) ((-4420 "*") . T) (-4412 . T) (-4413 . T) (-4415 . T)) +((|HasCategory| (-700) (QUOTE (-147))) (|HasCategory| (-700) (QUOTE (-145))) (|HasCategory| (-700) (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| (-700) (LIST (QUOTE -640) (QUOTE (-567)))) (|HasCategory| (-700) (QUOTE (-370))) (|HasCategory| (-700) (QUOTE (-365))) (-2800 (|HasCategory| (-700) (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| (-700) (QUOTE (-365)))) (|HasCategory| (-700) (LIST (QUOTE -902) (QUOTE (-1178)))) (|HasCategory| (-700) (QUOTE (-233))) (-2800 (|HasCategory| (-700) (QUOTE (-365))) (|HasCategory| (-700) (QUOTE (-351)))) (|HasCategory| (-700) (QUOTE (-351))) (|HasCategory| (-700) (LIST (QUOTE -287) (QUOTE (-700)) (QUOTE (-700)))) (|HasCategory| (-700) (LIST (QUOTE -310) (QUOTE (-700)))) (|HasCategory| (-700) (LIST (QUOTE -517) (QUOTE (-1178)) (QUOTE (-700)))) (|HasCategory| (-700) (LIST (QUOTE -888) (QUOTE (-567)))) (|HasCategory| (-700) (LIST (QUOTE -888) (QUOTE (-381)))) (|HasCategory| (-700) (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567))))) (|HasCategory| (-700) (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-381))))) (-2800 (|HasCategory| (-700) (QUOTE (-308))) (|HasCategory| (-700) (QUOTE (-365))) (|HasCategory| (-700) (QUOTE (-351)))) (|HasCategory| (-700) (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| (-700) (QUOTE (-1024))) (|HasCategory| (-700) (QUOTE (-1203))) (-12 (|HasCategory| (-700) (QUOTE (-1004))) (|HasCategory| (-700) (QUOTE (-1203)))) (-2800 (-12 (|HasCategory| (-700) (QUOTE (-308))) (|HasCategory| (-700) (QUOTE (-911)))) (|HasCategory| (-700) (QUOTE (-365))) (-12 (|HasCategory| (-700) (QUOTE (-351))) (|HasCategory| (-700) (QUOTE (-911))))) (-2800 (-12 (|HasCategory| (-700) (QUOTE (-308))) (|HasCategory| (-700) (QUOTE (-911)))) (-12 (|HasCategory| (-700) (QUOTE (-365))) (|HasCategory| (-700) (QUOTE (-911)))) (-12 (|HasCategory| (-700) (QUOTE (-351))) (|HasCategory| (-700) (QUOTE (-911))))) (|HasCategory| (-700) (QUOTE (-548))) (-12 (|HasCategory| (-700) (QUOTE (-1062))) (|HasCategory| (-700) (QUOTE (-1203)))) (|HasCategory| (-700) (QUOTE (-1062))) (|HasCategory| (-700) (QUOTE (-308))) (|HasCategory| (-700) (QUOTE (-911))) (-2800 (-12 (|HasCategory| (-700) (QUOTE (-308))) (|HasCategory| (-700) (QUOTE (-911)))) (|HasCategory| (-700) (QUOTE (-365)))) (-2800 (-12 (|HasCategory| (-700) (QUOTE (-308))) (|HasCategory| (-700) (QUOTE (-911)))) (|HasCategory| (-700) (QUOTE (-559)))) (-12 (|HasCategory| (-700) (QUOTE (-233))) (|HasCategory| (-700) (QUOTE (-365)))) (-12 (|HasCategory| (-700) (LIST (QUOTE -902) (QUOTE (-1178)))) (|HasCategory| (-700) (QUOTE (-365)))) (|HasCategory| (-700) (LIST (QUOTE -1040) (QUOTE (-567)))) (|HasCategory| (-700) (QUOTE (-559))) (|HasAttribute| (-700) (QUOTE -4417)) (|HasAttribute| (-700) (QUOTE -4414)) (-12 (|HasCategory| (-700) (QUOTE (-308))) (|HasCategory| (-700) (QUOTE (-911)))) (-2800 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-700) (QUOTE (-308))) (|HasCategory| (-700) (QUOTE (-911)))) (|HasCategory| (-700) (QUOTE (-145)))) (-2800 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-700) (QUOTE (-308))) (|HasCategory| (-700) (QUOTE (-911)))) (|HasCategory| (-700) (QUOTE (-351))))) (-696 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)) +((-4419 . T)) NIL (-697 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}."))) @@ -2724,13 +2724,13 @@ NIL ((|constructor| (NIL "\\indented{1}{<description of package>} Author: Jim Wen Date Created: \\spad{??} Date Last Updated: October 1991 by Jon Steinbach Keywords: Examples: References:")) (|ptFunc| (((|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) "\\spad{ptFunc(a,b,c,d)} is an internal function exported in order to compile packages.")) (|meshPar1Var| (((|ThreeSpace| (|DoubleFloat|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar1Var(s,t,u,f,s1,l)} \\undocumented")) (|meshFun2Var| (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Union| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "undefined") (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshFun2Var(f,g,s1,s2,l)} \\undocumented")) (|meshPar2Var| (((|ThreeSpace| (|DoubleFloat|)) (|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(sp,f,s1,s2,l)} \\undocumented") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(f,s1,s2,l)} \\undocumented") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Union| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "undefined") (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(f,g,h,j,s1,s2,l)} \\undocumented"))) NIL NIL -(-699 OV E -3867 PG) +(-699 OV E -3879 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 (-700) ((|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}"))) -((-3040 . T) (-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) +((-3050 . T) (-4410 . T) (-4416 . T) (-4411 . T) ((-4420 "*") . T) (-4412 . T) (-4413 . T) (-4415 . T)) NIL (-701 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."))) @@ -2738,7 +2738,7 @@ NIL NIL (-702) ((|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)) +((-4417 . T) (-4416 . T) (-4411 . T) ((-4420 "*") . T) (-4412 . T) (-4413 . T) (-4415 . T)) NIL (-703 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"))) @@ -2756,7 +2756,7 @@ 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 -(-707 S -2636 I) +(-707 S -2637 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 @@ -2766,7 +2766,7 @@ NIL NIL (-709 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)) +((-4412 . T) (-4413 . T) (-4415 . T)) NIL (-710 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}."))) @@ -2776,25 +2776,25 @@ NIL ((|constructor| (NIL "\\spadtype{MathMLFormat} provides a coercion from \\spadtype{OutputForm} to MathML format.")) (|display| (((|Void|) (|String|)) "prints the string returned by coerce,{} adding <math ...> tags.")) (|exprex| (((|String|) (|OutputForm|)) "coverts \\spadtype{OutputForm} to \\spadtype{String} with the structure preserved with braces. Actually this is not quite accurate. The function \\spadfun{precondition} is first applied to the \\spadtype{OutputForm} expression before \\spadfun{exprex}. The raw \\spadtype{OutputForm} and the nature of the \\spadfun{precondition} function is still obscure to me at the time of this writing (2007-02-14).")) (|coerceL| (((|String|) (|OutputForm|)) "coerceS(\\spad{o}) changes \\spad{o} in the standard output format to MathML format and displays result as one long string.")) (|coerceS| (((|String|) (|OutputForm|)) "\\spad{coerceS(o)} changes \\spad{o} in the standard output format to MathML format and displays formatted result.")) (|coerce| (((|String|) (|OutputForm|)) "coerceS(\\spad{o}) changes \\spad{o} in the standard output format to MathML format."))) NIL NIL -(-712 R |Mod| -3269 -3523 |exactQuo|) +(-712 R |Mod| -1591 -4135 |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| $) "\\spad{modulus(x)} \\undocumented"))) -((-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) +((-4410 . T) (-4416 . T) (-4411 . T) ((-4420 "*") . T) (-4412 . T) (-4413 . T) (-4415 . T)) NIL (-713 R |Rep|) ((|constructor| (NIL "This package \\undocumented")) (|frobenius| (($ $) "\\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| (-559)) (-4413 |has| |#1| (-365)) (-4415 |has| |#1| (-6 -4415)) (-4412 . T) (-4411 . T) (-4414 . T)) -((|HasCategory| |#1| (QUOTE (-910))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-172))) (-2797 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-559)))) (-12 (|HasCategory| (-1083) (LIST (QUOTE -887) (QUOTE (-381)))) (|HasCategory| |#1| (LIST (QUOTE -887) (QUOTE (-381))))) (-12 (|HasCategory| (-1083) (LIST (QUOTE -887) (QUOTE (-567)))) (|HasCategory| |#1| (LIST (QUOTE -887) (QUOTE (-567))))) (-12 (|HasCategory| (-1083) (LIST (QUOTE -615) (LIST (QUOTE -893) (QUOTE (-381))))) (|HasCategory| |#1| (LIST (QUOTE -615) (LIST (QUOTE -893) (QUOTE (-381)))))) (-12 (|HasCategory| (-1083) (LIST (QUOTE -615) (LIST (QUOTE -893) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -615) (LIST (QUOTE -893) (QUOTE (-567)))))) (-12 (|HasCategory| (-1083) (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539))))) (|HasCategory| |#1| (LIST (QUOTE -640) (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1039) (QUOTE (-567)))) (-2797 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1039) (LIST (QUOTE -410) (QUOTE (-567)))))) (|HasCategory| |#1| (LIST (QUOTE -1039) (LIST (QUOTE -410) (QUOTE (-567))))) (-2797 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-455))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-910)))) (-2797 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-455))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-910)))) (-2797 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-455))) (|HasCategory| |#1| (QUOTE (-910)))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-1152))) (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-1177)))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-351))) (|HasCategory| |#1| (QUOTE (-233))) (|HasAttribute| |#1| (QUOTE -4415)) (|HasCategory| |#1| (QUOTE (-455))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-910)))) (-2797 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-910)))) (|HasCategory| |#1| (QUOTE (-145))))) +(((-4420 "*") |has| |#1| (-172)) (-4411 |has| |#1| (-559)) (-4414 |has| |#1| (-365)) (-4416 |has| |#1| (-6 -4416)) (-4413 . T) (-4412 . T) (-4415 . T)) +((|HasCategory| |#1| (QUOTE (-911))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-172))) (-2800 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-559)))) (-12 (|HasCategory| (-1084) (LIST (QUOTE -888) (QUOTE (-381)))) (|HasCategory| |#1| (LIST (QUOTE -888) (QUOTE (-381))))) (-12 (|HasCategory| (-1084) (LIST (QUOTE -888) (QUOTE (-567)))) (|HasCategory| |#1| (LIST (QUOTE -888) (QUOTE (-567))))) (-12 (|HasCategory| (-1084) (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-381))))) (|HasCategory| |#1| (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-381)))))) (-12 (|HasCategory| (-1084) (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567)))))) (-12 (|HasCategory| (-1084) (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539))))) (|HasCategory| |#1| (LIST (QUOTE -640) (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (QUOTE (-567)))) (-2800 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567)))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (-2800 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-455))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-911)))) (-2800 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-455))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-911)))) (-2800 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-455))) (|HasCategory| |#1| (QUOTE (-911)))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-1153))) (|HasCategory| |#1| (LIST (QUOTE -902) (QUOTE (-1178)))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-351))) (|HasCategory| |#1| (QUOTE (-233))) (|HasAttribute| |#1| (QUOTE -4416)) (|HasCategory| |#1| (QUOTE (-455))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-911)))) (-2800 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-911)))) (|HasCategory| |#1| (QUOTE (-145))))) (-714 IS E |ff|) ((|constructor| (NIL "This package \\undocumented")) (|construct| (($ |#1| |#2|) "\\spad{construct(i,e)} \\undocumented")) (|index| ((|#1| $) "\\spad{index(x)} \\undocumented")) (|exponent| ((|#2| $) "\\spad{exponent(x)} \\undocumented"))) NIL NIL (-715 R M) ((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#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| (($ $ $) "\\spad{adjoint(op1, op2)} sets the adjoint of \\spad{op1} to be op2. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) -((-4412 |has| |#1| (-172)) (-4411 |has| |#1| (-172)) (-4414 . T)) +((-4413 |has| |#1| (-172)) (-4412 |has| |#1| (-172)) (-4415 . T)) ((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147)))) -(-716 R |Mod| -3269 -3523 |exactQuo|) +(-716 R |Mod| -1591 -4135 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\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)) +((-4415 . T)) NIL (-717 S R) ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) @@ -2802,11 +2802,11 @@ NIL NIL (-718 R) ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) -((-4412 . T) (-4411 . T)) +((-4413 . T) (-4412 . T)) NIL -(-719 -3867) +(-719 -3879) ((|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)) +((-4415 . T)) NIL (-720 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."))) @@ -2830,7 +2830,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-351))) (|HasCategory| |#2| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-370)))) (-725 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)) +((-4411 |has| |#1| (-365)) (-4416 |has| |#1| (-365)) (-4410 |has| |#1| (-365)) ((-4420 "*") . T) (-4412 . T) (-4413 . T) (-4415 . T)) NIL (-726 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."))) @@ -2840,7 +2840,7 @@ 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 -(-728 -3867 UP) +(-728 -3879 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 @@ -2858,8 +2858,8 @@ NIL NIL (-732 |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| (-559)) (-4415 |has| |#2| (-6 -4415)) (-4412 . T) (-4411 . T) (-4414 . T)) -((|HasCategory| |#2| (QUOTE (-910))) (-2797 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-455))) (|HasCategory| |#2| (QUOTE (-559))) (|HasCategory| |#2| (QUOTE (-910)))) (-2797 (|HasCategory| |#2| (QUOTE (-455))) (|HasCategory| |#2| (QUOTE (-559))) (|HasCategory| |#2| (QUOTE (-910)))) (-2797 (|HasCategory| |#2| (QUOTE (-455))) (|HasCategory| |#2| (QUOTE (-910)))) (|HasCategory| |#2| (QUOTE (-559))) (|HasCategory| |#2| (QUOTE (-172))) (-2797 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-559)))) (-12 (|HasCategory| (-865 |#1|) (LIST (QUOTE -887) (QUOTE (-381)))) (|HasCategory| |#2| (LIST (QUOTE -887) (QUOTE (-381))))) (-12 (|HasCategory| (-865 |#1|) (LIST (QUOTE -887) (QUOTE (-567)))) (|HasCategory| |#2| (LIST (QUOTE -887) (QUOTE (-567))))) (-12 (|HasCategory| (-865 |#1|) (LIST (QUOTE -615) (LIST (QUOTE -893) (QUOTE (-381))))) (|HasCategory| |#2| (LIST (QUOTE -615) (LIST (QUOTE -893) (QUOTE (-381)))))) (-12 (|HasCategory| (-865 |#1|) (LIST (QUOTE -615) (LIST (QUOTE -893) (QUOTE (-567))))) (|HasCategory| |#2| (LIST (QUOTE -615) (LIST (QUOTE -893) (QUOTE (-567)))))) (-12 (|HasCategory| (-865 |#1|) (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| |#2| (LIST (QUOTE -615) (QUOTE (-539))))) (|HasCategory| |#2| (LIST (QUOTE -640) (QUOTE (-567)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#2| (LIST (QUOTE -1039) (QUOTE (-567)))) (-2797 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#2| (LIST (QUOTE -1039) (LIST (QUOTE -410) (QUOTE (-567)))))) (|HasCategory| |#2| (LIST (QUOTE -1039) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#2| (QUOTE (-365))) (|HasAttribute| |#2| (QUOTE -4415)) (|HasCategory| |#2| (QUOTE (-455))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-910)))) (-2797 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-910)))) (|HasCategory| |#2| (QUOTE (-145))))) +(((-4420 "*") |has| |#2| (-172)) (-4411 |has| |#2| (-559)) (-4416 |has| |#2| (-6 -4416)) (-4413 . T) (-4412 . T) (-4415 . T)) +((|HasCategory| |#2| (QUOTE (-911))) (-2800 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-455))) (|HasCategory| |#2| (QUOTE (-559))) (|HasCategory| |#2| (QUOTE (-911)))) (-2800 (|HasCategory| |#2| (QUOTE (-455))) (|HasCategory| |#2| (QUOTE (-559))) (|HasCategory| |#2| (QUOTE (-911)))) (-2800 (|HasCategory| |#2| (QUOTE (-455))) (|HasCategory| |#2| (QUOTE (-911)))) (|HasCategory| |#2| (QUOTE (-559))) (|HasCategory| |#2| (QUOTE (-172))) (-2800 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-559)))) (-12 (|HasCategory| (-865 |#1|) (LIST (QUOTE -888) (QUOTE (-381)))) (|HasCategory| |#2| (LIST (QUOTE -888) (QUOTE (-381))))) (-12 (|HasCategory| (-865 |#1|) (LIST (QUOTE -888) (QUOTE (-567)))) (|HasCategory| |#2| (LIST (QUOTE -888) (QUOTE (-567))))) (-12 (|HasCategory| (-865 |#1|) (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-381))))) (|HasCategory| |#2| (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-381)))))) (-12 (|HasCategory| (-865 |#1|) (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567))))) (|HasCategory| |#2| (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567)))))) (-12 (|HasCategory| (-865 |#1|) (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| |#2| (LIST (QUOTE -615) (QUOTE (-539))))) (|HasCategory| |#2| (LIST (QUOTE -640) (QUOTE (-567)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#2| (LIST (QUOTE -1040) (QUOTE (-567)))) (-2800 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#2| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567)))))) (|HasCategory| |#2| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#2| (QUOTE (-365))) (|HasAttribute| |#2| (QUOTE -4416)) (|HasCategory| |#2| (QUOTE (-455))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-911)))) (-2800 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-911)))) (|HasCategory| |#2| (QUOTE (-145))))) (-733 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|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) NIL @@ -2874,16 +2874,16 @@ NIL NIL (-736 R M) ((|constructor| (NIL "\\spadtype{MonoidRing}(\\spad{R},{}\\spad{M}),{} implements the algebra of all maps from the monoid \\spad{M} to the commutative ring \\spad{R} with finite support. Multiplication of two maps \\spad{f} and \\spad{g} is defined to map an element \\spad{c} of \\spad{M} to the (convolution) sum over {\\em f(a)g(b)} such that {\\em ab = c}. Thus \\spad{M} can be identified with a canonical basis and the maps can also be considered as formal linear combinations of the elements in \\spad{M}. Scalar multiples of a basis element are called monomials. A prominent example is the class of polynomials where the monoid is a direct product of the natural numbers with pointwise addition. When \\spad{M} is \\spadtype{FreeMonoid Symbol},{} one gets polynomials in infinitely many non-commuting variables. Another application area is representation theory of finite groups \\spad{G},{} where modules over \\spadtype{MonoidRing}(\\spad{R},{}\\spad{G}) are studied.")) (|reductum| (($ $) "\\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)) +((-4413 |has| |#1| (-172)) (-4412 |has| |#1| (-172)) (-4415 . 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 (-851)))) (-737 S) ((|constructor| (NIL "A multi-set aggregate is a set which keeps track of the multiplicity of its elements."))) -((-4407 . T) (-4418 . T)) +((-4408 . T) (-4419 . T)) NIL (-738 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)) -((-12 (|HasCategory| |#1| (QUOTE (-1101))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| |#1| (QUOTE (-1101))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) +((-4418 . T) (-4408 . T) (-4419 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (-739) ((|constructor| (NIL "\\spadtype{MoreSystemCommands} implements an interface with the system command facility. These are the commands that are issued from source files or the system interpreter and they start with a close parenthesis,{} \\spadignore{e.g.} \\spadsyscom{what} commands.")) (|systemCommand| (((|Void|) (|String|)) "\\spad{systemCommand(cmd)} takes the string \\spadvar{\\spad{cmd}} and passes it to the runtime environment for execution as a system command. Although various things may be printed,{} no usable value is returned."))) NIL @@ -2894,7 +2894,7 @@ NIL NIL (-741 |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| (-559)) (-4412 . T) (-4411 . T) (-4414 . T)) +(((-4420 "*") |has| |#1| (-172)) (-4411 |has| |#1| (-559)) (-4413 . T) (-4412 . T) (-4415 . T)) NIL (-742 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"))) @@ -2910,7 +2910,7 @@ NIL NIL (-745 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)) +((-4413 . T) (-4412 . T)) NIL (-746) ((|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}."))) @@ -2992,11 +2992,11 @@ 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 -(-766 -3867) +(-766 -3879) ((|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 -(-767 P -3867) +(-767 P -3879) ((|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 @@ -3004,7 +3004,7 @@ NIL NIL NIL NIL -(-769 UP -3867) +(-769 UP -3879) ((|constructor| (NIL "In this package \\spad{F} is a framed algebra over the integers (typically \\spad{F = Z[a]} for some algebraic integer a). The package provides functions to compute the integral closure of \\spad{Z} in the quotient quotient field of \\spad{F}.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| (|Integer|))) (|:| |basisDen| (|Integer|)) (|:| |basisInv| (|Matrix| (|Integer|)))) (|Integer|)) "\\spad{integralBasis(p)} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the local integral closure of \\spad{Z} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{Z}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| (|Integer|))) (|:| |basisDen| (|Integer|)) (|:| |basisInv| (|Matrix| (|Integer|))))) "\\spad{integralBasis()} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the integral closure of \\spad{Z} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{Z}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|discriminant| (((|Integer|)) "\\spad{discriminant()} returns the discriminant of the integral closure of \\spad{Z} in the quotient field of the framed algebra \\spad{F}."))) NIL NIL @@ -3018,9 +3018,9 @@ NIL NIL (-772) ((|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)) +(((-4420 "*") . T)) NIL -(-773 R -3867) +(-773 R -3879) ((|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 @@ -3040,7 +3040,7 @@ 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 -(-778 -3867 |ExtF| |SUEx| |ExtP| |n|) +(-778 -3879 |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 @@ -3054,28 +3054,28 @@ NIL NIL (-781 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| (-559)) (-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 (-783 R) ((|constructor| (NIL "A post-facto extension for \\axiomType{SUP} in order to speed up operations related to pseudo-division and \\spad{gcd} for both \\axiomType{SUP} and,{} consequently,{} \\axiomType{NSMP}.")) (|halfExtendedResultant2| (((|Record| (|:| |resultant| |#1|) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedResultant2(a,{}\\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.")) 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(|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 -410) (QUOTE (-567)))))) (-785 R E V P) ((|constructor| (NIL "The category of normalized triangular sets. A triangular set \\spad{ts} is said normalized if for every algebraic variable \\spad{v} of \\spad{ts} the polynomial \\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)) +((-4419 . T) (-4418 . T)) NIL (-786 S) ((|constructor| (NIL "Numeric provides real and complex numerical evaluation functions for various symbolic types.")) (|numericIfCan| (((|Union| (|Float|) "failed") (|Expression| |#1|) (|PositiveInteger|)) "\\spad{numericIfCan(x, n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Expression| |#1|)) "\\spad{numericIfCan(x)} returns a real approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{numericIfCan(x,n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Fraction| (|Polynomial| |#1|))) "\\spad{numericIfCan(x)} returns a real approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{numericIfCan(x,n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Polynomial| |#1|)) "\\spad{numericIfCan(x)} returns a real approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.")) (|complexNumericIfCan| (((|Union| (|Complex| (|Float|)) "failed") (|Expression| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Expression| (|Complex| |#1|))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Expression| |#1|) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Expression| |#1|)) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| (|Complex| |#1|))) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| (|Complex| |#1|)))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x, n)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| |#1|))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| |#1|)) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| (|Complex| |#1|))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not constant.")) (|complexNumeric| (((|Complex| (|Float|)) (|Expression| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Expression| (|Complex| |#1|))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Expression| |#1|) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Expression| |#1|)) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| (|Complex| |#1|))) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| (|Complex| |#1|)))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x}") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| |#1|))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Polynomial| |#1|)) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Polynomial| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Polynomial| (|Complex| |#1|))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Complex| |#1|) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Complex| |#1|)) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) |#1| (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) |#1|) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.")) (|numeric| (((|Float|) (|Expression| |#1|) (|PositiveInteger|)) "\\spad{numeric(x, n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) (|Expression| |#1|)) "\\spad{numeric(x)} returns a real approximation of \\spad{x}.") (((|Float|) (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{numeric(x,n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) (|Fraction| (|Polynomial| |#1|))) "\\spad{numeric(x)} returns a real approximation of \\spad{x}.") (((|Float|) (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{numeric(x,n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) (|Polynomial| |#1|)) "\\spad{numeric(x)} returns a real approximation of \\spad{x}.") (((|Float|) |#1| (|PositiveInteger|)) "\\spad{numeric(x, n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) |#1|) "\\spad{numeric(x)} returns a real approximation of \\spad{x}."))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-851)))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-1050))) (|HasCategory| |#1| (QUOTE (-172)))) +((-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-851)))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-1051))) (|HasCategory| |#1| (QUOTE (-172)))) (-787) ((|constructor| (NIL "NumberFormats provides function to format and read arabic and roman numbers,{} to convert numbers to strings and to read floating-point numbers.")) (|ScanFloatIgnoreSpacesIfCan| (((|Union| (|Float|) "failed") (|String|)) "\\spad{ScanFloatIgnoreSpacesIfCan(s)} tries to form a floating point number from the string \\spad{s} ignoring any spaces.")) (|ScanFloatIgnoreSpaces| (((|Float|) (|String|)) "\\spad{ScanFloatIgnoreSpaces(s)} forms a floating point number from the string \\spad{s} ignoring any spaces. Error is generated if the string is not recognised as a floating point number.")) (|ScanRoman| (((|PositiveInteger|) (|String|)) "\\spad{ScanRoman(s)} forms an integer from a Roman numeral string \\spad{s}.")) (|FormatRoman| (((|String|) (|PositiveInteger|)) "\\spad{FormatRoman(n)} forms a Roman numeral string from an integer \\spad{n}.")) (|ScanArabic| (((|PositiveInteger|) (|String|)) "\\spad{ScanArabic(s)} forms an integer from an Arabic numeral string \\spad{s}.")) (|FormatArabic| (((|String|) (|PositiveInteger|)) "\\spad{FormatArabic(n)} forms an Arabic numeral string from an integer \\spad{n}."))) NIL @@ -3119,28 +3119,28 @@ NIL (-797 S R) ((|constructor| (NIL "OctonionCategory gives the categorial frame for the octonions,{} and eight-dimensional non-associative algebra,{} doubling the the quaternions in the same way as doubling the Complex numbers to get the quaternions.")) (|inv| (($ $) "\\spad{inv(o)} returns the inverse of \\spad{o} if it exists.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(o)} returns the real part if all seven imaginary parts are 0,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(o)} returns the real part if all seven imaginary parts are 0. Error: if \\spad{o} is not rational.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(o)} tests if \\spad{o} is rational,{} \\spadignore{i.e.} that all seven imaginary parts are 0.")) (|abs| ((|#2| $) "\\spad{abs(o)} computes the absolute value of an octonion,{} equal to the square root of the \\spadfunFrom{norm}{Octonion}.")) (|octon| (($ |#2| |#2| |#2| |#2| |#2| |#2| |#2| |#2|) "\\spad{octon(re,ri,rj,rk,rE,rI,rJ,rK)} constructs an octonion from scalars.")) (|norm| ((|#2| $) "\\spad{norm(o)} returns the norm of an octonion,{} equal to the sum of the squares of its coefficients.")) (|imagK| ((|#2| $) "\\spad{imagK(o)} extracts the imaginary \\spad{K} part of octonion \\spad{o}.")) (|imagJ| ((|#2| $) "\\spad{imagJ(o)} extracts the imaginary \\spad{J} part of octonion \\spad{o}.")) (|imagI| ((|#2| $) "\\spad{imagI(o)} extracts the imaginary \\spad{I} part of octonion \\spad{o}.")) (|imagE| ((|#2| $) "\\spad{imagE(o)} extracts the imaginary \\spad{E} part of octonion \\spad{o}.")) (|imagk| ((|#2| $) "\\spad{imagk(o)} extracts the \\spad{k} part of octonion \\spad{o}.")) (|imagj| ((|#2| $) "\\spad{imagj(o)} extracts the \\spad{j} part of octonion \\spad{o}.")) (|imagi| ((|#2| $) "\\spad{imagi(o)} extracts the \\spad{i} part of octonion \\spad{o}.")) (|real| ((|#2| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) NIL -((|HasCategory| |#2| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-548))) (|HasCategory| |#2| (QUOTE (-1061))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| |#2| (QUOTE (-851))) (|HasCategory| |#2| (QUOTE (-370)))) +((|HasCategory| |#2| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-548))) (|HasCategory| |#2| (QUOTE (-1062))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| |#2| (QUOTE (-851))) (|HasCategory| |#2| (QUOTE (-370)))) (-798 R) ((|constructor| (NIL "OctonionCategory gives the categorial frame for the octonions,{} and eight-dimensional non-associative algebra,{} doubling the the quaternions in the same way as doubling the Complex numbers to get the quaternions.")) (|inv| (($ $) "\\spad{inv(o)} returns the inverse of \\spad{o} if it exists.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(o)} returns the real part if all seven imaginary parts are 0,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(o)} returns the real part if all seven imaginary parts are 0. Error: if \\spad{o} is not rational.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(o)} tests if \\spad{o} is rational,{} \\spadignore{i.e.} that all seven imaginary parts are 0.")) (|abs| ((|#1| $) "\\spad{abs(o)} computes the absolute value of an octonion,{} equal to the square root of the \\spadfunFrom{norm}{Octonion}.")) (|octon| (($ |#1| |#1| |#1| |#1| |#1| |#1| |#1| |#1|) "\\spad{octon(re,ri,rj,rk,rE,rI,rJ,rK)} constructs an octonion from scalars.")) (|norm| ((|#1| $) "\\spad{norm(o)} returns the norm of an octonion,{} equal to the sum of the squares of its coefficients.")) (|imagK| ((|#1| $) "\\spad{imagK(o)} extracts the imaginary \\spad{K} part of octonion \\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| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) -((-4411 . T) (-4412 . T) (-4414 . T)) +((-4412 . T) (-4413 . T) (-4415 . T)) NIL -(-799 -2797 R OS S) +(-799 -2800 R OS S) ((|constructor| (NIL "OctonionCategoryFunctions2 implements functions between two octonion domains defined over different rings. The function map is used to coerce between octonion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,u)} maps \\spad{f} onto the component parts of the octonion \\spad{u}."))) NIL NIL (-800 R) ((|constructor| (NIL "Octonion implements octonions (Cayley-Dixon algebra) over a commutative ring,{} an eight-dimensional non-associative algebra,{} doubling the quaternions in the same way as doubling the complex numbers to get the quaternions the main constructor function is {\\em octon} which takes 8 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j} imaginary part,{} the \\spad{k} imaginary part,{} (as with quaternions) and in addition the imaginary parts \\spad{E},{} \\spad{I},{} \\spad{J},{} \\spad{K}.")) (|octon| (($ (|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)) -((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (LIST (QUOTE -517) (QUOTE (-1177)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -287) (|devaluate| |#1|) (|devaluate| |#1|))) (-2797 (|HasCategory| (-1000 |#1|) (LIST (QUOTE -1039) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1039) (LIST (QUOTE -410) (QUOTE (-567)))))) (-2797 (|HasCategory| (-1000 |#1|) (LIST (QUOTE -1039) (QUOTE (-567)))) (|HasCategory| |#1| (LIST (QUOTE -1039) (QUOTE (-567))))) (|HasCategory| |#1| (QUOTE (-1061))) (|HasCategory| |#1| (QUOTE (-548))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| (-1000 |#1|) (LIST (QUOTE -1039) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| (-1000 |#1|) (LIST (QUOTE -1039) (QUOTE (-567)))) (|HasCategory| |#1| (LIST (QUOTE -1039) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1039) (QUOTE (-567))))) +((-4412 . T) (-4413 . T) (-4415 . T)) +((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (LIST (QUOTE -517) (QUOTE (-1178)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -287) (|devaluate| |#1|) (|devaluate| |#1|))) (-2800 (|HasCategory| (-1001 |#1|) (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567)))))) (-2800 (|HasCategory| (-1001 |#1|) (LIST (QUOTE -1040) (QUOTE (-567)))) (|HasCategory| |#1| (LIST (QUOTE -1040) (QUOTE (-567))))) (|HasCategory| |#1| (QUOTE (-1062))) (|HasCategory| |#1| (QUOTE (-548))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| (-1001 |#1|) (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| (-1001 |#1|) (LIST (QUOTE -1040) (QUOTE (-567)))) (|HasCategory| |#1| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (QUOTE (-567))))) (-801) ((|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 -(-802 R -3867 L) +(-802 R -3879 L) ((|constructor| (NIL "Solution of linear ordinary differential equations,{} constant coefficient case.")) (|constDsolve| (((|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Symbol|)) "\\spad{constDsolve(op, g, x)} returns \\spad{[f, [y1,...,ym]]} where \\spad{f} is a particular solution of the equation \\spad{op y = g},{} and the \\spad{yi}\\spad{'s} form a basis for the solutions of \\spad{op y = 0}."))) NIL NIL -(-803 R -3867) +(-803 R -3879) ((|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 @@ -3148,7 +3148,7 @@ 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 -(-805 R -3867) +(-805 R -3879) ((|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 @@ -3156,11 +3156,11 @@ 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 -(-807 -3867 UP UPUP R) +(-807 -3879 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 -(-808 -3867 UP L LQ) +(-808 -3879 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 @@ -3168,41 +3168,41 @@ 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 -(-810 -3867 UP L LQ) +(-810 -3879 UP L LQ) ((|constructor| (NIL "In-field solution of Riccati equations,{} primitive case.")) (|changeVar| ((|#3| |#3| (|Fraction| |#2|)) "\\spad{changeVar(+/[ai D^i], a)} returns the operator \\spad{+/[ai (D+a)^i]}.") ((|#3| |#3| |#2|) "\\spad{changeVar(+/[ai D^i], a)} returns the operator \\spad{+/[ai (D+a)^i]}.")) (|singRicDE| (((|List| (|Record| (|:| |frac| (|Fraction| |#2|)) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{singRicDE(op, zeros, ezfactor)} returns \\spad{[[f1, L1], [f2, L2], ... , [fk, Lk]]} such that the singular part of any rational solution of the associated Riccati equation of \\spad{op y=0} must be one of the \\spad{fi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z=y e^{-int p}} is \\spad{Li z=0}. \\spad{zeros(C(x),H(x,y))} returns all the \\spad{P_i(x)}\\spad{'s} such that \\spad{H(x,P_i(x)) = 0 modulo C(x)}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.")) (|polyRicDE| (((|List| (|Record| (|:| |poly| |#2|) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#1|) |#2|)) "\\spad{polyRicDE(op, zeros)} returns \\spad{[[p1, L1], [p2, L2], ... , [pk, Lk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y=0} must be one of the \\spad{pi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z=y e^{-int p}} is \\spad{Li z =0}. \\spad{zeros} is a zero finder in \\spad{UP}.")) (|constantCoefficientRicDE| (((|List| (|Record| (|:| |constant| |#1|) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#1|) |#2|)) "\\spad{constantCoefficientRicDE(op, ric)} returns \\spad{[[a1, L1], [a2, L2], ... , [ak, Lk]]} such that any rational solution with no polynomial part of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{ai}\\spad{'s} in which case the equation for \\spad{z = y e^{-int ai}} is \\spad{Li z = 0}. \\spad{ric} is a Riccati equation solver over \\spad{F},{} whose input is the associated linear equation.")) (|leadingCoefficientRicDE| (((|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |eq| |#2|))) |#3|) "\\spad{leadingCoefficientRicDE(op)} returns \\spad{[[m1, p1], [m2, p2], ... , [mk, pk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must have degree \\spad{mj} for some \\spad{j},{} and its leading coefficient is then a zero of \\spad{pj}. In addition,{}\\spad{m1>m2> ... >mk}.")) (|denomRicDE| ((|#2| |#3|) "\\spad{denomRicDE(op)} returns a polynomial \\spad{d} such that any rational solution of the associated Riccati equation of \\spad{op y = 0} is of the form \\spad{p/d + q'/q + r} for some polynomials \\spad{p} and \\spad{q} and a reduced \\spad{r}. Also,{} \\spad{deg(p) < deg(d)} and {\\spad{gcd}(\\spad{d},{}\\spad{q}) = 1}."))) NIL NIL -(-811 -3867 UP) +(-811 -3879 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 -(-812 -3867 L UP A LO) +(-812 -3879 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 -(-813 -3867 UP) +(-813 -3879 UP) ((|constructor| (NIL "In-field solution of Riccati equations,{} rational case.")) (|polyRicDE| (((|List| (|Record| (|:| |poly| |#2|) (|:| |eq| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{polyRicDE(op, zeros)} returns \\spad{[[p1, L1], [p2, L2], ... , [pk,Lk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{pi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z = y e^{-int p}} is \\spad{Li z = 0}. \\spad{zeros} is a zero finder in \\spad{UP}.")) (|singRicDE| (((|List| (|Record| (|:| |frac| (|Fraction| |#2|)) (|:| |eq| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{singRicDE(op, ezfactor)} returns \\spad{[[f1,L1], [f2,L2],..., [fk,Lk]]} such that the singular \\spad{++} part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{fi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z = y e^{-int ai}} is \\spad{Li z = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.")) (|ricDsolve| (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))) "\\spad{ricDsolve(op)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{ricDsolve(op)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, zeros, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{ricDsolve(op, zeros)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, zeros, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{ricDsolve(op, zeros)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}."))) NIL ((|HasCategory| |#1| (QUOTE (-27)))) -(-814 -3867 LO) +(-814 -3879 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 -(-815 -3867 LODO) +(-815 -3879 LODO) ((|constructor| (NIL "\\spad{ODETools} provides tools for the linear ODE solver.")) (|particularSolution| (((|Union| |#1| "failed") |#2| |#1| (|List| |#1|) (|Mapping| |#1| |#1|)) "\\spad{particularSolution(op, g, [f1,...,fm], I)} returns a particular solution \\spad{h} of the equation \\spad{op y = g} where \\spad{[f1,...,fm]} are linearly independent and \\spad{op(fi)=0}. The value \"failed\" is returned if no particular solution is found. Note: the method of variations of parameters is used.")) (|variationOfParameters| (((|Union| (|Vector| |#1|) "failed") |#2| |#1| (|List| |#1|)) "\\spad{variationOfParameters(op, g, [f1,...,fm])} returns \\spad{[u1,...,um]} such that a particular solution of the equation \\spad{op y = g} is \\spad{f1 int(u1) + ... + fm int(um)} where \\spad{[f1,...,fm]} are linearly independent and \\spad{op(fi)=0}. The value \"failed\" is returned if \\spad{m < n} and no particular solution is found.")) (|wronskianMatrix| (((|Matrix| |#1|) (|List| |#1|) (|NonNegativeInteger|)) "\\spad{wronskianMatrix([f1,...,fn], q, D)} returns the \\spad{q x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),...,fn^(i-1)]}.") (((|Matrix| |#1|) (|List| |#1|)) "\\spad{wronskianMatrix([f1,...,fn])} returns the \\spad{n x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),...,fn^(i-1)]}."))) NIL NIL -(-816 -2609 S |f|) +(-816 -2612 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| (-1050)) (-4412 |has| |#2| (-1050)) (-4414 |has| |#2| (-6 -4414)) ((-4419 "*") |has| |#2| (-172)) (-4417 . T)) -((-2797 (-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 (-727))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-794))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-849))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1050))) (|HasCategory| |#2| (LIST 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T)) -((|HasCategory| |#1| (QUOTE (-910))) (-2797 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-455))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-910)))) (-2797 (|HasCategory| |#1| (QUOTE (-455))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-910)))) (-2797 (|HasCategory| |#1| (QUOTE (-455))) (|HasCategory| |#1| (QUOTE (-910)))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-172))) (-2797 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-559)))) (-12 (|HasCategory| (-819 (-1177)) (LIST (QUOTE -887) (QUOTE (-381)))) (|HasCategory| |#1| (LIST (QUOTE -887) (QUOTE (-381))))) (-12 (|HasCategory| (-819 (-1177)) (LIST (QUOTE -887) (QUOTE (-567)))) (|HasCategory| |#1| (LIST (QUOTE -887) (QUOTE (-567))))) (-12 (|HasCategory| (-819 (-1177)) (LIST (QUOTE -615) (LIST (QUOTE -893) (QUOTE (-381))))) (|HasCategory| |#1| (LIST (QUOTE -615) (LIST (QUOTE -893) (QUOTE (-381)))))) (-12 (|HasCategory| (-819 (-1177)) (LIST (QUOTE -615) (LIST (QUOTE -893) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -615) (LIST (QUOTE -893) (QUOTE (-567)))))) (-12 (|HasCategory| (-819 (-1177)) (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539))))) (|HasCategory| |#1| (LIST (QUOTE -640) (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1039) (QUOTE (-567)))) (-2797 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1039) (LIST (QUOTE -410) (QUOTE (-567)))))) (|HasCategory| |#1| (LIST (QUOTE -1039) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-1177)))) (|HasCategory| |#1| (QUOTE (-365))) (|HasAttribute| |#1| (QUOTE -4415)) (|HasCategory| |#1| (QUOTE (-455))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-910)))) (-2797 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-910)))) (|HasCategory| |#1| (QUOTE (-145))))) +(((-4420 "*") |has| |#1| (-172)) (-4411 |has| |#1| (-559)) (-4416 |has| |#1| (-6 -4416)) (-4413 . T) (-4412 . T) (-4415 . T)) +((|HasCategory| |#1| (QUOTE (-911))) (-2800 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-455))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-911)))) (-2800 (|HasCategory| |#1| (QUOTE (-455))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-911)))) (-2800 (|HasCategory| |#1| (QUOTE (-455))) (|HasCategory| |#1| (QUOTE (-911)))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-172))) (-2800 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-559)))) (-12 (|HasCategory| (-819 (-1178)) (LIST (QUOTE -888) (QUOTE (-381)))) (|HasCategory| |#1| (LIST (QUOTE -888) (QUOTE (-381))))) (-12 (|HasCategory| (-819 (-1178)) (LIST (QUOTE -888) (QUOTE (-567)))) (|HasCategory| |#1| (LIST (QUOTE -888) (QUOTE (-567))))) (-12 (|HasCategory| (-819 (-1178)) (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-381))))) (|HasCategory| |#1| (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-381)))))) (-12 (|HasCategory| (-819 (-1178)) (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567)))))) (-12 (|HasCategory| (-819 (-1178)) (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539))))) (|HasCategory| |#1| (LIST (QUOTE -640) (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (QUOTE (-567)))) (-2800 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567)))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -902) (QUOTE (-1178)))) (|HasCategory| |#1| (QUOTE (-365))) (|HasAttribute| |#1| (QUOTE -4416)) (|HasCategory| |#1| (QUOTE (-455))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-911)))) (-2800 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-911)))) (|HasCategory| |#1| (QUOTE (-145))))) (-818 |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)) +(((-4420 "*") |has| |#2| (-365)) (-4411 |has| |#2| (-365)) (-4416 |has| |#2| (-365)) (-4410 |has| |#2| (-365)) (-4415 . T) (-4413 . T) (-4412 . T)) ((|HasCategory| |#2| (QUOTE (-365)))) (-819 S) ((|constructor| (NIL "\\spadtype{OrderlyDifferentialVariable} adds a commonly used orderly ranking to the set of derivatives of an ordered list of differential indeterminates. An orderly ranking is a ranking \\spadfun{<} of the derivatives with the property that for two derivatives \\spad{u} and \\spad{v},{} \\spad{u} \\spadfun{<} \\spad{v} if the \\spadfun{order} of \\spad{u} is less than that of \\spad{v}. This domain belongs to \\spadtype{DifferentialVariableCategory}. It defines \\spadfun{weight} to be just \\spadfun{order},{} and it defines an orderly ranking \\spadfun{<} on derivatives \\spad{u} via the lexicographic order on the pair (\\spadfun{order}(\\spad{u}),{} \\spadfun{variable}(\\spad{u}))."))) @@ -3214,7 +3214,7 @@ NIL ((|HasCategory| |#1| (QUOTE (-851)))) (-821) ((|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)) +((-4411 . T) ((-4420 "*") . T) (-4412 . T) (-4413 . T) (-4415 . T)) NIL (-822) ((|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}"))) @@ -3242,7 +3242,7 @@ NIL NIL (-828 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)) +((-4412 . T) (-4413 . T) (-4415 . T)) ((|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-233)))) (-829) ((|constructor| (NIL "\\spadtype{OpenMath} provides operations for exporting an object in OpenMath format.")) (|OMwrite| (((|Void|) (|OpenMathDevice|) $ (|Boolean|)) "\\spad{OMwrite(dev, u, true)} writes the OpenMath form of \\axiom{\\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."))) @@ -3254,7 +3254,7 @@ NIL NIL (-831 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)) +((-4418 . T) (-4408 . T) (-4419 . T)) NIL (-832) ((|constructor| (NIL "\\spadtype{OpenMathServerPackage} provides the necessary operations to run AXIOM as an OpenMath server,{} reading/writing objects to/from a port. Please note the facilities available here are very basic. The idea is that a user calls \\spadignore{e.g.} \\axiom{Omserve(4000,{}60)} and then another process sends OpenMath objects to port 4000 and reads the result.")) (|OMserve| (((|Void|) (|SingleInteger|) (|SingleInteger|)) "\\spad{OMserve(portnum,timeout)} puts AXIOM into server mode on port number \\axiom{\\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."))) @@ -3266,8 +3266,8 @@ NIL NIL (-834 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| (-849))) -((|HasCategory| |#1| (QUOTE (-849))) (|HasCategory| |#1| (QUOTE (-21))) (-2797 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-849)))) (|HasCategory| |#1| (LIST (QUOTE -1039) (LIST (QUOTE -410) (QUOTE (-567))))) (-2797 (|HasCategory| |#1| (QUOTE (-849))) (|HasCategory| |#1| (LIST (QUOTE -1039) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1039) (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-548)))) +((-4415 |has| |#1| (-849))) +((|HasCategory| |#1| (QUOTE (-849))) (|HasCategory| |#1| (QUOTE (-21))) (-2800 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-849)))) (|HasCategory| |#1| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (-2800 (|HasCategory| |#1| (QUOTE (-849))) (|HasCategory| |#1| (LIST (QUOTE -1040) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-548)))) (-835 A S) ((|constructor| (NIL "This category specifies the interface for operators used to build terms,{} in the sense of Universal Algebra. The domain parameter \\spad{S} provides representation for the `external name' of an operator.")) (|is?| (((|Boolean|) $ |#2|) "\\spad{is?(op,n)} holds if the name of the operator \\spad{op} is \\spad{n}.")) (|arity| (((|Arity|) $) "\\spad{arity(op)} returns the arity of the operator \\spad{op}.")) (|name| ((|#2| $) "\\spad{name(op)} returns the externam name of \\spad{op}."))) NIL @@ -3278,7 +3278,7 @@ NIL NIL (-837 R) ((|constructor| (NIL "Algebra of ADDITIVE operators over a ring."))) -((-4412 |has| |#1| (-172)) (-4411 |has| |#1| (-172)) (-4414 . T)) +((-4413 |has| |#1| (-172)) (-4412 |has| |#1| (-172)) (-4415 . T)) ((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147)))) (-838) ((|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)."))) @@ -3306,13 +3306,13 @@ NIL NIL (-844 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| (($) "\\spad{plusInfinity()} returns +infinity."))) -((-4414 |has| |#1| (-849))) -((|HasCategory| |#1| (QUOTE (-849))) (|HasCategory| |#1| (QUOTE (-21))) (-2797 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-849)))) (|HasCategory| |#1| (LIST (QUOTE -1039) (LIST (QUOTE -410) (QUOTE (-567))))) (-2797 (|HasCategory| |#1| (QUOTE (-849))) (|HasCategory| |#1| (LIST (QUOTE -1039) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1039) (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-548)))) +((-4415 |has| |#1| (-849))) +((|HasCategory| |#1| (QUOTE (-849))) (|HasCategory| |#1| (QUOTE (-21))) (-2800 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-849)))) (|HasCategory| |#1| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (-2800 (|HasCategory| |#1| (QUOTE (-849))) (|HasCategory| |#1| (LIST (QUOTE -1040) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-548)))) (-845) ((|constructor| (NIL "Ordered finite sets.")) (|max| (($) "\\spad{max} is the maximum value of \\%.")) (|min| (($) "\\spad{min} is the minimum value of \\%."))) NIL NIL -(-846 -2609 S) +(-846 -2612 S) ((|constructor| (NIL "\\indented{3}{This package provides ordering functions on vectors which} are suitable parameters for OrderedDirectProduct.")) (|reverseLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{reverseLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by the reverse lexicographic ordering.")) (|totalLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{totalLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by lexicographic ordering.")) (|pureLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{pureLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the lexicographic ordering."))) NIL NIL @@ -3326,7 +3326,7 @@ NIL NIL (-849) ((|constructor| (NIL "Ordered sets which are also rings,{} that is,{} domains where the ring operations are compatible with the ordering. \\blankline")) (|abs| (($ $) "\\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|) $) "\\spad{positive?(x)} tests whether \\spad{x} is strictly greater than 0."))) -((-4414 . T)) +((-4415 . T)) NIL (-850 S) ((|constructor| (NIL "The class of totally ordered sets,{} that is,{} sets such that for each pair of elements \\spad{(a,b)} exactly one of the following relations holds \\spad{a<b or a=b or b<a} and the relation is transitive,{} \\spadignore{i.e.} \\spad{a<b and b<c => a<c}.")) (|min| (($ $ $) "\\spad{min(x,y)} returns the minimum of \\spad{x} and \\spad{y} relative to \\spad{\"<\"}.")) (|max| (($ $ $) "\\spad{max(x,y)} returns the maximum of \\spad{x} and \\spad{y} relative to \\spad{\"<\"}.")) (<= (((|Boolean|) $ $) "\\spad{x <= y} is a less than or equal test.")) (>= (((|Boolean|) $ $) "\\spad{x >= y} is a greater than or equal test.")) (> (((|Boolean|) $ $) "\\spad{x > y} is a greater than test.")) (< (((|Boolean|) $ $) "\\spad{x < y} is a strict total ordering on the elements of the set."))) @@ -3342,20 +3342,20 @@ NIL ((|HasCategory| |#2| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-455))) (|HasCategory| |#2| (QUOTE (-559))) (|HasCategory| |#2| (QUOTE (-172)))) (-853 R) ((|constructor| (NIL "This is the category of univariate skew polynomials over an Ore coefficient ring. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}. This category is an evolution of the types \\indented{2}{MonogenicLinearOperator,{} OppositeMonogenicLinearOperator,{} and} \\indented{2}{NonCommutativeOperatorDivision} developped by Jean Della Dora and Stephen \\spad{M}. Watt.")) (|leftLcm| (($ $ $) "\\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)) +((-4412 . T) (-4413 . T) (-4415 . T)) NIL (-854 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 (-559)))) -(-855 R |sigma| -3120) +(-855 R |sigma| -1781) ((|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)) -((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (LIST (QUOTE -1039) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1039) (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-455))) (|HasCategory| |#1| (QUOTE (-365)))) -(-856 |x| R |sigma| -3120) +((-4412 . T) (-4413 . T) (-4415 . T)) +((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-455))) (|HasCategory| |#1| (QUOTE (-365)))) +(-856 |x| R |sigma| -1781) ((|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)) -((|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (LIST (QUOTE -1039) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#2| (LIST (QUOTE -1039) (QUOTE (-567)))) (|HasCategory| |#2| (QUOTE (-559))) (|HasCategory| |#2| (QUOTE (-455))) (|HasCategory| |#2| (QUOTE (-365)))) +((-4412 . T) (-4413 . T) (-4415 . T)) +((|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#2| (LIST (QUOTE -1040) (QUOTE (-567)))) (|HasCategory| |#2| (QUOTE (-559))) (|HasCategory| |#2| (QUOTE (-455))) (|HasCategory| |#2| (QUOTE (-365)))) (-857 R) ((|constructor| (NIL "This package provides orthogonal polynomials as functions on a ring.")) (|legendreP| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{legendreP(n,x)} is the \\spad{n}-th Legendre polynomial,{} \\spad{P[n](x)}. These are defined by \\spad{1/sqrt(1-2*x*t+t**2) = sum(P[n](x)*t**n, n = 0..)}.")) (|laguerreL| ((|#1| (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|) "\\spad{laguerreL(m,n,x)} is the associated Laguerre polynomial,{} \\spad{L<m>[n](x)}. This is the \\spad{m}-th derivative of \\spad{L[n](x)}.") ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{laguerreL(n,x)} is the \\spad{n}-th Laguerre polynomial,{} \\spad{L[n](x)}. These are defined by \\spad{exp(-t*x/(1-t))/(1-t) = sum(L[n](x)*t**n/n!, n = 0..)}.")) (|hermiteH| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{hermiteH(n,x)} is the \\spad{n}-th Hermite polynomial,{} \\spad{H[n](x)}. These are defined by \\spad{exp(2*t*x-t**2) = sum(H[n](x)*t**n/n!, n = 0..)}.")) (|chebyshevU| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{chebyshevU(n,x)} is the \\spad{n}-th Chebyshev polynomial of the second kind,{} \\spad{U[n](x)}. These are defined by \\spad{1/(1-2*t*x+t**2) = sum(T[n](x) *t**n, n = 0..)}.")) (|chebyshevT| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{chebyshevT(n,x)} is the \\spad{n}-th Chebyshev polynomial of the first kind,{} \\spad{T[n](x)}. These are defined by \\spad{(1-t*x)/(1-2*t*x+t**2) = sum(T[n](x) *t**n, n = 0..)}."))) NIL @@ -3398,7 +3398,7 @@ NIL NIL (-867 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") $ $) "\\spad{x/y} division (only works if minimum weight of divisor is zero,{} and if \\spad{R} is a Field)"))) -((-4412 |has| |#1| (-172)) (-4411 |has| |#1| (-172)) (-4414 . T)) +((-4413 |has| |#1| (-172)) (-4412 |has| |#1| (-172)) (-4415 . T)) ((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365)))) (-868 R PS UP) ((|constructor| (NIL "\\indented{1}{This package computes reliable Pad&ea. approximants using} a generalized Viskovatov continued fraction algorithm. Authors: Burge,{} Hassner & Watt. Date Created: April 1987 Date Last Updated: 12 April 1990 Keywords: Pade,{} series Examples: References: \\indented{2}{\"Pade Approximants,{} Part I: Basic Theory\",{} Baker & Graves-Morris.}")) (|padecf| (((|Union| (|ContinuedFraction| |#3|) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) |#2| |#2|) "\\spad{padecf(nd,dd,ns,ds)} computes the approximant as a continued fraction of polynomials (if it exists) for arguments \\spad{nd} (numerator degree of approximant),{} \\spad{dd} (denominator degree of approximant),{} \\spad{ns} (numerator series of function),{} and \\spad{ds} (denominator series of function).")) (|pade| (((|Union| (|Fraction| |#3|) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) |#2| |#2|) "\\spad{pade(nd,dd,ns,ds)} computes the approximant as a quotient of polynomials (if it exists) for arguments \\spad{nd} (numerator degree of approximant),{} \\spad{dd} (denominator degree of approximant),{} \\spad{ns} (numerator series of function),{} and \\spad{ds} (denominator series of function)."))) @@ -3410,24 +3410,24 @@ NIL NIL (-870 |p|) ((|constructor| (NIL "This is the catefory of stream-based representations of \\indented{2}{the \\spad{p}-adic integers.}")) (|root| (($ (|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)) +((-4411 . T) ((-4420 "*") . T) (-4412 . T) (-4413 . T) (-4415 . T)) NIL (-871 |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)) +((-4411 . T) ((-4420 "*") . T) (-4412 . T) (-4413 . T) (-4415 . T)) NIL (-872 |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)) -((|HasCategory| (-871 |#1|) (QUOTE (-910))) (|HasCategory| (-871 |#1|) (LIST (QUOTE -1039) (QUOTE (-1177)))) (|HasCategory| (-871 |#1|) (QUOTE (-145))) (|HasCategory| (-871 |#1|) (QUOTE (-147))) (|HasCategory| (-871 |#1|) (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| (-871 |#1|) (QUOTE (-1023))) (|HasCategory| (-871 |#1|) (QUOTE (-821))) (-2797 (|HasCategory| (-871 |#1|) (QUOTE (-821))) (|HasCategory| (-871 |#1|) (QUOTE (-851)))) (|HasCategory| (-871 |#1|) (LIST (QUOTE -1039) (QUOTE (-567)))) (|HasCategory| (-871 |#1|) (QUOTE (-1152))) (|HasCategory| (-871 |#1|) (LIST (QUOTE -887) (QUOTE (-381)))) (|HasCategory| (-871 |#1|) (LIST (QUOTE -887) (QUOTE (-567)))) (|HasCategory| (-871 |#1|) (LIST (QUOTE -615) (LIST (QUOTE -893) (QUOTE (-381))))) (|HasCategory| (-871 |#1|) (LIST (QUOTE -615) (LIST (QUOTE -893) (QUOTE (-567))))) (|HasCategory| (-871 |#1|) (LIST (QUOTE -640) (QUOTE (-567)))) (|HasCategory| (-871 |#1|) (QUOTE (-233))) (|HasCategory| (-871 |#1|) (LIST (QUOTE -901) (QUOTE (-1177)))) (|HasCategory| (-871 |#1|) (LIST (QUOTE -517) (QUOTE (-1177)) (LIST (QUOTE -871) (|devaluate| |#1|)))) (|HasCategory| (-871 |#1|) (LIST (QUOTE -310) (LIST (QUOTE -871) (|devaluate| |#1|)))) (|HasCategory| (-871 |#1|) (LIST (QUOTE -287) (LIST (QUOTE -871) (|devaluate| |#1|)) (LIST (QUOTE -871) (|devaluate| |#1|)))) (|HasCategory| (-871 |#1|) (QUOTE (-308))) (|HasCategory| (-871 |#1|) (QUOTE (-548))) (|HasCategory| (-871 |#1|) (QUOTE (-851))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-871 |#1|) (QUOTE (-910)))) (-2797 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-871 |#1|) (QUOTE (-910)))) (|HasCategory| (-871 |#1|) (QUOTE (-145))))) +((-4410 . T) (-4416 . T) (-4411 . T) ((-4420 "*") . T) (-4412 . T) (-4413 . T) (-4415 . T)) +((|HasCategory| (-871 |#1|) (QUOTE (-911))) (|HasCategory| (-871 |#1|) (LIST (QUOTE -1040) (QUOTE (-1178)))) (|HasCategory| (-871 |#1|) (QUOTE (-145))) (|HasCategory| (-871 |#1|) (QUOTE (-147))) (|HasCategory| (-871 |#1|) (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| (-871 |#1|) (QUOTE (-1024))) (|HasCategory| (-871 |#1|) (QUOTE (-821))) (-2800 (|HasCategory| (-871 |#1|) (QUOTE (-821))) (|HasCategory| (-871 |#1|) (QUOTE (-851)))) (|HasCategory| (-871 |#1|) (LIST (QUOTE -1040) (QUOTE (-567)))) (|HasCategory| (-871 |#1|) (QUOTE (-1153))) (|HasCategory| (-871 |#1|) (LIST (QUOTE -888) (QUOTE (-381)))) (|HasCategory| (-871 |#1|) (LIST (QUOTE -888) (QUOTE (-567)))) (|HasCategory| (-871 |#1|) (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-381))))) (|HasCategory| (-871 |#1|) (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567))))) (|HasCategory| (-871 |#1|) (LIST (QUOTE -640) (QUOTE (-567)))) (|HasCategory| (-871 |#1|) (QUOTE (-233))) (|HasCategory| (-871 |#1|) (LIST (QUOTE -902) (QUOTE (-1178)))) (|HasCategory| (-871 |#1|) (LIST (QUOTE -517) (QUOTE (-1178)) (LIST (QUOTE -871) (|devaluate| |#1|)))) (|HasCategory| (-871 |#1|) (LIST (QUOTE -310) (LIST (QUOTE -871) (|devaluate| |#1|)))) (|HasCategory| (-871 |#1|) (LIST (QUOTE -287) (LIST (QUOTE -871) (|devaluate| |#1|)) (LIST (QUOTE -871) (|devaluate| |#1|)))) (|HasCategory| (-871 |#1|) (QUOTE (-308))) (|HasCategory| (-871 |#1|) (QUOTE (-548))) (|HasCategory| (-871 |#1|) (QUOTE (-851))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-871 |#1|) (QUOTE (-911)))) (-2800 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-871 |#1|) (QUOTE (-911)))) (|HasCategory| (-871 |#1|) (QUOTE (-145))))) (-873 |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)) -((|HasCategory| |#2| (QUOTE (-910))) (|HasCategory| |#2| (LIST (QUOTE -1039) (QUOTE (-1177)))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| |#2| (QUOTE (-1023))) (|HasCategory| |#2| (QUOTE (-821))) (-2797 (|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| |#2| (QUOTE (-851)))) (|HasCategory| |#2| (LIST (QUOTE -1039) (QUOTE (-567)))) (|HasCategory| |#2| (QUOTE (-1152))) (|HasCategory| |#2| (LIST (QUOTE -887) (QUOTE (-381)))) (|HasCategory| |#2| (LIST (QUOTE -887) (QUOTE (-567)))) (|HasCategory| |#2| (LIST (QUOTE -615) (LIST (QUOTE -893) (QUOTE (-381))))) (|HasCategory| |#2| (LIST (QUOTE -615) (LIST (QUOTE -893) (QUOTE (-567))))) (|HasCategory| |#2| (LIST (QUOTE -640) (QUOTE (-567)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -901) (QUOTE (-1177)))) (|HasCategory| |#2| (LIST (QUOTE -517) (QUOTE (-1177)) (|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 (-548))) (|HasCategory| |#2| (QUOTE (-851))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-910)))) (-2797 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-910)))) (|HasCategory| |#2| (QUOTE (-145))))) +((-4410 . T) (-4416 . T) (-4411 . T) ((-4420 "*") . T) (-4412 . T) (-4413 . T) (-4415 . T)) +((|HasCategory| |#2| (QUOTE (-911))) (|HasCategory| |#2| (LIST (QUOTE -1040) (QUOTE (-1178)))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| |#2| (QUOTE (-1024))) (|HasCategory| |#2| (QUOTE (-821))) (-2800 (|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| |#2| (QUOTE (-851)))) (|HasCategory| |#2| (LIST (QUOTE -1040) (QUOTE (-567)))) (|HasCategory| |#2| (QUOTE (-1153))) (|HasCategory| |#2| (LIST (QUOTE -888) (QUOTE (-381)))) (|HasCategory| |#2| (LIST (QUOTE -888) (QUOTE (-567)))) (|HasCategory| |#2| (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-381))))) (|HasCategory| |#2| (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567))))) (|HasCategory| |#2| (LIST (QUOTE -640) (QUOTE (-567)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -902) (QUOTE (-1178)))) (|HasCategory| |#2| (LIST (QUOTE -517) (QUOTE (-1178)) (|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 (-548))) (|HasCategory| |#2| (QUOTE (-851))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-911)))) (-2800 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-911)))) (|HasCategory| |#2| (QUOTE (-145))))) (-874 S T$) ((|constructor| (NIL "\\indented{1}{This domain provides a very simple representation} of the notion of `pair of objects'. It does not try to achieve all possible imaginable things.")) (|second| ((|#2| $) "\\spad{second(p)} extracts the second components of \\spad{`p'}.")) (|first| ((|#1| $) "\\spad{first(p)} extracts the first component of \\spad{`p'}.")) (|construct| (($ |#1| |#2|) "\\spad{construct(s,t)} is same as pair(\\spad{s},{}\\spad{t}),{} with syntactic sugar.")) (|pair| (($ |#1| |#2|) "\\spad{pair(s,t)} returns a pair object composed of \\spad{`s'} and \\spad{`t'}."))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1101))) (|HasCategory| |#2| (QUOTE (-1101)))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-1101))) (|HasCategory| |#2| (QUOTE (-1101)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863)))))) +((-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#2| (QUOTE (-1102)))) (-2800 (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#2| (QUOTE (-1102)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863)))))) (-875) ((|constructor| (NIL "This domain describes four groups of color shades (palettes).")) (|coerce| (($ (|Color|)) "\\spad{coerce(c)} sets the average shade for the palette to that of the indicated color \\spad{c}.")) (|shade| (((|Integer|) $) "\\spad{shade(p)} returns the shade index of the indicated palette \\spad{p}.")) (|hue| (((|Color|) $) "\\spad{hue(p)} returns the hue field of the indicated palette \\spad{p}.")) (|light| (($ (|Color|)) "\\spad{light(c)} sets the shade of a hue,{} \\spad{c},{} to it\\spad{'s} highest value.")) (|pastel| (($ (|Color|)) "\\spad{pastel(c)} sets the shade of a hue,{} \\spad{c},{} above bright,{} but below light.")) (|bright| (($ (|Color|)) "\\spad{bright(c)} sets the shade of a hue,{} \\spad{c},{} above dim,{} but below pastel.")) (|dim| (($ (|Color|)) "\\spad{dim(c)} sets the shade of a hue,{} \\spad{c},{} above dark,{} but below bright.")) (|dark| (($ (|Color|)) "\\spad{dark(c)} sets the shade of the indicated hue of \\spad{c} to it\\spad{'s} lowest value."))) NIL @@ -3436,1681 +3436,1685 @@ NIL ((|constructor| (NIL "This package provides a coerce from polynomials over algebraic numbers to \\spadtype{Expression AlgebraicNumber}.")) (|coerce| (((|Expression| (|Integer|)) (|Fraction| (|Polynomial| (|AlgebraicNumber|)))) "\\spad{coerce(rf)} converts \\spad{rf},{} a fraction of polynomial \\spad{p} with algebraic number coefficients to \\spadtype{Expression Integer}.") (((|Expression| (|Integer|)) (|Polynomial| (|AlgebraicNumber|))) "\\spad{coerce(p)} converts the polynomial \\spad{p} with algebraic number coefficients to \\spadtype{Expression Integer}."))) NIL NIL -(-877 CF1 CF2) +(-877) +((|constructor| (NIL "Representation of parameters to functions or constructors. For the most part,{} they are Identifiers. However,{} in very cases,{} they are \"flags\",{} \\spadignore{e.g.} string literals.")) (|autoCoerce| (((|String|) $) "\\spad{autoCoerce(x)@String} implicitly coerce the object \\spad{x} to \\spadtype{String}. This function is left at the discretion of the compiler.") (((|Identifier|) $) "\\spad{autoCoerce(x)@Identifier} implicitly coerce the object \\spad{x} to \\spadtype{Identifier}. This function is left at the discretion of the compiler.")) (|case| (((|Boolean|) $ (|[\|\|]| (|String|))) "\\spad{x case String} if the parameter AST object \\spad{x} designates a flag.") (((|Boolean|) $ (|[\|\|]| (|Identifier|))) "\\spad{x case Identifier} if the parameter AST object \\spad{x} designates an \\spadtype{Identifier}."))) +NIL +NIL +(-878 CF1 CF2) ((|constructor| (NIL "This package \\undocumented")) (|map| (((|ParametricPlaneCurve| |#2|) (|Mapping| |#2| |#1|) (|ParametricPlaneCurve| |#1|)) "\\spad{map(f,x)} \\undocumented"))) NIL NIL -(-878 |ComponentFunction|) +(-879 |ComponentFunction|) ((|constructor| (NIL "ParametricPlaneCurve is used for plotting parametric plane curves in the affine plane.")) (|coordinate| ((|#1| $ (|NonNegativeInteger|)) "\\spad{coordinate(c,i)} returns a coordinate function for \\spad{c} using 1-based indexing according to \\spad{i}. This indicates what the function for the coordinate component \\spad{i} of the plane curve is.")) (|curve| (($ |#1| |#1|) "\\spad{curve(c1,c2)} creates a plane curve from 2 component functions \\spad{c1} and \\spad{c2}."))) NIL NIL -(-879 CF1 CF2) +(-880 CF1 CF2) ((|constructor| (NIL "This package \\undocumented")) (|map| (((|ParametricSpaceCurve| |#2|) (|Mapping| |#2| |#1|) (|ParametricSpaceCurve| |#1|)) "\\spad{map(f,x)} \\undocumented"))) NIL NIL -(-880 |ComponentFunction|) +(-881 |ComponentFunction|) ((|constructor| (NIL "ParametricSpaceCurve is used for plotting parametric space curves in affine 3-space.")) (|coordinate| ((|#1| $ (|NonNegativeInteger|)) "\\spad{coordinate(c,i)} returns a coordinate function of \\spad{c} using 1-based indexing according to \\spad{i}. This indicates what the function for the coordinate component,{} \\spad{i},{} of the space curve is.")) (|curve| (($ |#1| |#1| |#1|) "\\spad{curve(c1,c2,c3)} creates a space curve from 3 component functions \\spad{c1},{} \\spad{c2},{} and \\spad{c3}."))) NIL NIL -(-881) +(-882) ((|constructor| (NIL "\\indented{1}{This package provides a simple Spad script parser.} Related Constructors: Syntax. See Also: Syntax.")) (|getSyntaxFormsFromFile| (((|List| (|Syntax|)) (|String|)) "\\spad{getSyntaxFormsFromFile(f)} parses the source file \\spad{f} (supposedly containing Spad scripts) and returns a List Syntax. The filename \\spad{f} is supposed to have the proper extension. Note that source location information is not part of result."))) NIL NIL -(-882 CF1 CF2) +(-883 CF1 CF2) ((|constructor| (NIL "This package \\undocumented")) (|map| (((|ParametricSurface| |#2|) (|Mapping| |#2| |#1|) (|ParametricSurface| |#1|)) "\\spad{map(f,x)} \\undocumented"))) NIL NIL -(-883 |ComponentFunction|) +(-884 |ComponentFunction|) ((|constructor| (NIL "ParametricSurface is used for plotting parametric surfaces in affine 3-space.")) (|coordinate| ((|#1| $ (|NonNegativeInteger|)) "\\spad{coordinate(s,i)} returns a coordinate function of \\spad{s} using 1-based indexing according to \\spad{i}. This indicates what the function for the coordinate component,{} \\spad{i},{} of the surface is.")) (|surface| (($ |#1| |#1| |#1|) "\\spad{surface(c1,c2,c3)} creates a surface from 3 parametric component functions \\spad{c1},{} \\spad{c2},{} and \\spad{c3}."))) NIL NIL -(-884) +(-885) ((|constructor| (NIL "PartitionsAndPermutations contains functions for generating streams of integer partitions,{} and streams of sequences of integers composed from a multi-set.")) (|permutations| (((|Stream| (|List| (|Integer|))) (|Integer|)) "\\spad{permutations(n)} is the stream of permutations \\indented{1}{formed from \\spad{1,2,3,...,n}.}")) (|sequences| (((|Stream| (|List| (|Integer|))) (|List| (|Integer|))) "\\spad{sequences([l0,l1,l2,..,ln])} is the set of \\indented{1}{all sequences formed from} \\spad{l0} 0\\spad{'s},{}\\spad{l1} 1\\spad{'s},{}\\spad{l2} 2\\spad{'s},{}...,{}\\spad{ln} \\spad{n}\\spad{'s}.") (((|Stream| (|List| (|Integer|))) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{sequences(l1,l2)} is the stream of all sequences that \\indented{1}{can be composed from the multiset defined from} \\indented{1}{two lists of integers \\spad{l1} and \\spad{l2}.} \\indented{1}{For example,{}the pair \\spad{([1,2,4],[2,3,5])} represents} \\indented{1}{multi-set with 1 \\spad{2},{} 2 \\spad{3}\\spad{'s},{} and 4 \\spad{5}\\spad{'s}.}")) (|shufflein| (((|Stream| (|List| (|Integer|))) (|List| (|Integer|)) (|Stream| (|List| (|Integer|)))) "\\spad{shufflein(l,st)} maps shuffle(\\spad{l},{}\\spad{u}) on to all \\indented{1}{members \\spad{u} of \\spad{st},{} concatenating the results.}")) (|shuffle| (((|Stream| (|List| (|Integer|))) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{shuffle(l1,l2)} forms the stream of all shuffles of \\spad{l1} \\indented{1}{and \\spad{l2},{} \\spadignore{i.e.} all sequences that can be formed from} \\indented{1}{merging \\spad{l1} and \\spad{l2}.}")) (|conjugates| (((|Stream| (|List| (|Integer|))) (|Stream| (|List| (|Integer|)))) "\\spad{conjugates(lp)} is the stream of conjugates of a stream \\indented{1}{of partitions \\spad{lp}.}")) (|conjugate| (((|List| (|Integer|)) (|List| (|Integer|))) "\\spad{conjugate(pt)} is the conjugate of the partition \\spad{pt}.")) (|partitions| (((|Stream| (|List| (|Integer|))) (|Integer|) (|Integer|)) "\\spad{partitions(p,l)} is the stream of all \\indented{1}{partitions whose number of} \\indented{1}{parts and largest part are no greater than \\spad{p} and \\spad{l}.}") (((|Stream| (|List| (|Integer|))) (|Integer|)) "\\spad{partitions(n)} is the stream of all partitions of \\spad{n}.") (((|Stream| (|List| (|Integer|))) (|Integer|) (|Integer|) (|Integer|)) "\\spad{partitions(p,l,n)} is the stream of partitions \\indented{1}{of \\spad{n} whose number of parts is no greater than \\spad{p}} \\indented{1}{and whose largest part is no greater than \\spad{l}.}"))) NIL NIL -(-885 R) +(-886 R) ((|constructor| (NIL "An object \\spad{S} is Patternable over an object \\spad{R} if \\spad{S} can lift the conversions from \\spad{R} into \\spadtype{Pattern(Integer)} and \\spadtype{Pattern(Float)} to itself."))) NIL NIL -(-886 R S L) +(-887 R S L) ((|constructor| (NIL "A PatternMatchListResult is an object internally returned by the pattern matcher when matching on lists. It is either a failed match,{} or a pair of PatternMatchResult,{} one for atoms (elements of the list),{} and one for lists.")) (|lists| (((|PatternMatchResult| |#1| |#3|) $) "\\spad{lists(r)} returns the list of matches that match lists.")) (|atoms| (((|PatternMatchResult| |#1| |#2|) $) "\\spad{atoms(r)} returns the list of matches that match atoms (elements of the lists).")) (|makeResult| (($ (|PatternMatchResult| |#1| |#2|) (|PatternMatchResult| |#1| |#3|)) "\\spad{makeResult(r1,r2)} makes the combined result [\\spad{r1},{}\\spad{r2}].")) (|new| (($) "\\spad{new()} returns a new empty match result.")) (|failed| (($) "\\spad{failed()} returns a failed match.")) (|failed?| (((|Boolean|) $) "\\spad{failed?(r)} tests if \\spad{r} is a failed match."))) NIL NIL -(-887 S) +(-888 S) ((|constructor| (NIL "A set \\spad{R} is PatternMatchable over \\spad{S} if elements of \\spad{R} can be matched to patterns over \\spad{S}.")) (|patternMatch| (((|PatternMatchResult| |#1| $) $ (|Pattern| |#1|) (|PatternMatchResult| |#1| $)) "\\spad{patternMatch(expr, pat, res)} matches the pattern \\spad{pat} to the expression \\spad{expr}. res contains the variables of \\spad{pat} which are already matched and their matches (necessary for recursion). Initially,{} res is just the result of \\spadfun{new} which is an empty list of matches."))) NIL NIL -(-888 |Base| |Subject| |Pat|) +(-889 |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 (-1653 (|HasCategory| |#2| (QUOTE (-1050)))) (-1653 (|HasCategory| |#2| (LIST (QUOTE -1039) (QUOTE (-1177)))))) (-12 (|HasCategory| |#2| (QUOTE (-1050))) (-1653 (|HasCategory| |#2| (LIST (QUOTE -1039) (QUOTE (-1177)))))) (|HasCategory| |#2| (LIST (QUOTE -1039) (QUOTE (-1177))))) -(-889 R A B) +((-12 (-1657 (|HasCategory| |#2| (QUOTE (-1051)))) (-1657 (|HasCategory| |#2| (LIST (QUOTE -1040) (QUOTE (-1178)))))) (-12 (|HasCategory| |#2| (QUOTE (-1051))) (-1657 (|HasCategory| |#2| (LIST (QUOTE -1040) (QUOTE (-1178)))))) (|HasCategory| |#2| (LIST (QUOTE -1040) (QUOTE (-1178))))) +(-890 R A B) ((|constructor| (NIL "Lifts maps to pattern matching results.")) (|map| (((|PatternMatchResult| |#1| |#3|) (|Mapping| |#3| |#2|) (|PatternMatchResult| |#1| |#2|)) "\\spad{map(f, [(v1,a1),...,(vn,an)])} returns the matching result [(\\spad{v1},{}\\spad{f}(a1)),{}...,{}(\\spad{vn},{}\\spad{f}(an))]."))) NIL NIL -(-890 R S) +(-891 R S) ((|constructor| (NIL "A PatternMatchResult is an object internally returned by the pattern matcher; It is either a failed match,{} or a list of matches of the form (var,{} expr) meaning that the variable var matches the expression expr.")) (|satisfy?| (((|Union| (|Boolean|) "failed") $ (|Pattern| |#1|)) "\\spad{satisfy?(r, p)} returns \\spad{true} if the matches satisfy the top-level predicate of \\spad{p},{} \\spad{false} if they don\\spad{'t},{} and \"failed\" if not enough variables of \\spad{p} are matched in \\spad{r} to decide.")) (|construct| (($ (|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| |#2|)))) "\\spad{construct([v1,e1],...,[vn,en])} returns the match result containing the matches (\\spad{v1},{}e1),{}...,{}(\\spad{vn},{}en).")) (|destruct| (((|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| |#2|))) $) "\\spad{destruct(r)} returns the list of matches (var,{} expr) in \\spad{r}. Error: if \\spad{r} is a failed match.")) (|addMatchRestricted| (($ (|Pattern| |#1|) |#2| $ |#2|) "\\spad{addMatchRestricted(var, expr, r, val)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} provided that \\spad{expr} satisfies the predicates attached to \\spad{var},{} that \\spad{var} is not matched to another expression already,{} and that either \\spad{var} is an optional pattern variable or that \\spad{expr} is not equal to val (usually an identity).")) (|insertMatch| (($ (|Pattern| |#1|) |#2| $) "\\spad{insertMatch(var, expr, r)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} without checking predicates or previous matches for \\spad{var}.")) (|addMatch| (($ (|Pattern| |#1|) |#2| $) "\\spad{addMatch(var, expr, r)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} provided that \\spad{expr} satisfies the predicates attached to \\spad{var},{} and that \\spad{var} is not matched to another expression already.")) (|getMatch| (((|Union| |#2| "failed") (|Pattern| |#1|) $) "\\spad{getMatch(var, r)} returns the expression that \\spad{var} matches in the result \\spad{r},{} and \"failed\" if \\spad{var} is not matched in \\spad{r}.")) (|union| (($ $ $) "\\spad{union(a, b)} makes the set-union of two match results.")) (|new| (($) "\\spad{new()} returns a new empty match result.")) (|failed| (($) "\\spad{failed()} returns a failed match.")) (|failed?| (((|Boolean|) $) "\\spad{failed?(r)} tests if \\spad{r} is a failed match."))) NIL NIL -(-891 R -2636) +(-892 R -2637) ((|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 -(-892 R S) +(-893 R S) ((|constructor| (NIL "Lifts maps to patterns.")) (|map| (((|Pattern| |#2|) (|Mapping| |#2| |#1|) (|Pattern| |#1|)) "\\spad{map(f, p)} applies \\spad{f} to all the leaves of \\spad{p} and returns the result as a pattern over \\spad{S}."))) NIL NIL -(-893 R) +(-894 R) ((|constructor| (NIL "Patterns for use by the pattern matcher.")) (|optpair| (((|Union| (|List| $) "failed") (|List| $)) "\\spad{optpair(l)} returns \\spad{l} has the form \\spad{[a, b]} and a is optional,{} and \"failed\" otherwise.")) (|variables| (((|List| $) $) "\\spad{variables(p)} returns the list of matching variables appearing in \\spad{p}.")) (|getBadValues| (((|List| (|Any|)) $) "\\spad{getBadValues(p)} returns the list of \"bad values\" for \\spad{p}. Note: \\spad{p} is not allowed to match any of its \"bad values\".")) (|addBadValue| (($ $ (|Any|)) "\\spad{addBadValue(p, v)} adds \\spad{v} to the list of \"bad values\" for \\spad{p}. Note: \\spad{p} is not allowed to match any of its \"bad values\".")) (|resetBadValues| (($ $) "\\spad{resetBadValues(p)} initializes the list of \"bad values\" for \\spad{p} to \\spad{[]}. Note: \\spad{p} is not allowed to match any of its \"bad values\".")) (|hasTopPredicate?| (((|Boolean|) $) "\\spad{hasTopPredicate?(p)} tests if \\spad{p} has a top-level predicate.")) (|topPredicate| (((|Record| (|:| |var| (|List| (|Symbol|))) (|:| |pred| (|Any|))) $) "\\spad{topPredicate(x)} returns \\spad{[[a1,...,an], f]} where the top-level predicate of \\spad{x} is \\spad{f(a1,...,an)}. Note: \\spad{n} is 0 if \\spad{x} has no top-level predicate.")) (|setTopPredicate| (($ $ (|List| (|Symbol|)) (|Any|)) "\\spad{setTopPredicate(x, [a1,...,an], f)} returns \\spad{x} with the top-level predicate set to \\spad{f(a1,...,an)}.")) (|patternVariable| (($ (|Symbol|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\spad{patternVariable(x, c?, o?, m?)} creates a pattern variable \\spad{x},{} which is constant if \\spad{c? = true},{} optional if \\spad{o? = true},{} and multiple if \\spad{m? = true}.")) (|withPredicates| (($ $ (|List| (|Any|))) "\\spad{withPredicates(p, [p1,...,pn])} makes a copy of \\spad{p} and attaches the predicate \\spad{p1} and ... and \\spad{pn} to the copy,{} which is returned.")) (|setPredicates| (($ $ (|List| (|Any|))) "\\spad{setPredicates(p, [p1,...,pn])} attaches the predicate \\spad{p1} and ... and \\spad{pn} to \\spad{p}.")) (|predicates| (((|List| (|Any|)) $) "\\spad{predicates(p)} returns \\spad{[p1,...,pn]} such that the predicate attached to \\spad{p} is \\spad{p1} and ... and \\spad{pn}.")) (|hasPredicate?| (((|Boolean|) $) "\\spad{hasPredicate?(p)} tests if \\spad{p} has predicates attached to it.")) (|optional?| (((|Boolean|) $) "\\spad{optional?(p)} tests if \\spad{p} is a single matching variable which can match an identity.")) (|multiple?| (((|Boolean|) $) "\\spad{multiple?(p)} tests if \\spad{p} is a single matching variable allowing list matching or multiple term matching in a sum or product.")) (|generic?| (((|Boolean|) $) "\\spad{generic?(p)} tests if \\spad{p} is a single matching variable.")) (|constant?| (((|Boolean|) $) "\\spad{constant?(p)} tests if \\spad{p} contains no matching variables.")) (|symbol?| (((|Boolean|) $) "\\spad{symbol?(p)} tests if \\spad{p} is a symbol.")) (|quoted?| (((|Boolean|) $) "\\spad{quoted?(p)} tests if \\spad{p} is of the form \\spad{'s} for a symbol \\spad{s}.")) (|inR?| (((|Boolean|) $) "\\spad{inR?(p)} tests if \\spad{p} is an atom (\\spadignore{i.e.} an element of \\spad{R}).")) (|copy| (($ $) "\\spad{copy(p)} returns a recursive copy of \\spad{p}.")) (|convert| (($ (|List| $)) "\\spad{convert([a1,...,an])} returns the pattern \\spad{[a1,...,an]}.")) (|depth| (((|NonNegativeInteger|) $) "\\spad{depth(p)} returns the nesting level of \\spad{p}.")) (/ (($ $ $) "\\spad{a / b} returns the pattern \\spad{a / b}.")) (** (($ $ $) "\\spad{a ** b} returns the pattern \\spad{a ** b}.") (($ $ (|NonNegativeInteger|)) "\\spad{a ** n} returns the pattern \\spad{a ** n}.")) (* (($ $ $) "\\spad{a * b} returns the pattern \\spad{a * b}.")) (+ (($ $ $) "\\spad{a + b} returns the pattern \\spad{a + b}.")) (|elt| (($ (|BasicOperator|) (|List| $)) "\\spad{elt(op, [a1,...,an])} returns \\spad{op(a1,...,an)}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| $)) "failed") $) "\\spad{isPower(p)} returns \\spad{[a, b]} if \\spad{p = a ** b},{} and \"failed\" otherwise.")) (|isList| (((|Union| (|List| $) "failed") $) "\\spad{isList(p)} returns \\spad{[a1,...,an]} if \\spad{p = [a1,...,an]},{} \"failed\" otherwise.")) (|isQuotient| (((|Union| (|Record| (|:| |num| $) (|:| |den| $)) "failed") $) "\\spad{isQuotient(p)} returns \\spad{[a, b]} if \\spad{p = a / b},{} and \"failed\" otherwise.")) (|isExpt| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|NonNegativeInteger|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[q, n]} if \\spad{n > 0} and \\spad{p = q ** n},{} and \"failed\" otherwise.")) (|isOp| (((|Union| (|Record| (|:| |op| (|BasicOperator|)) (|:| |arg| (|List| $))) "failed") $) "\\spad{isOp(p)} returns \\spad{[op, [a1,...,an]]} if \\spad{p = op(a1,...,an)},{} and \"failed\" otherwise.") (((|Union| (|List| $) "failed") $ (|BasicOperator|)) "\\spad{isOp(p, op)} returns \\spad{[a1,...,an]} if \\spad{p = op(a1,...,an)},{} and \"failed\" otherwise.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if \\spad{n > 1} and \\spad{p = a1 * ... * an},{} and \"failed\" otherwise.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[a1,...,an]} if \\spad{n > 1} \\indented{1}{and \\spad{p = a1 + ... + an},{}} and \"failed\" otherwise.")) ((|One|) (($) "1")) ((|Zero|) (($) "0"))) NIL NIL -(-894 |VarSet|) +(-895 |VarSet|) ((|constructor| (NIL "This domain provides the internal representation of polynomials in non-commutative variables written over the Poincare-Birkhoff-Witt basis. See the \\spadtype{XPBWPolynomial} domain constructor. See Free Lie Algebras by \\spad{C}. Reutenauer (Oxford science publications). \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|varList| (((|List| |#1|) $) "\\spad{varList([l1]*[l2]*...[ln])} returns the list of variables in the word \\spad{l1*l2*...*ln}.")) (|retractable?| (((|Boolean|) $) "\\spad{retractable?([l1]*[l2]*...[ln])} returns \\spad{true} iff \\spad{n} equals \\spad{1}.")) (|rest| (($ $) "\\spad{rest([l1]*[l2]*...[ln])} returns the list \\spad{l2, .... ln}.")) (|ListOfTerms| (((|List| (|LyndonWord| |#1|)) $) "\\spad{ListOfTerms([l1]*[l2]*...[ln])} returns the list of words \\spad{l1, l2, .... ln}.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length([l1]*[l2]*...[ln])} returns the length of the word \\spad{l1*l2*...*ln}.")) (|first| (((|LyndonWord| |#1|) $) "\\spad{first([l1]*[l2]*...[ln])} returns the Lyndon word \\spad{l1}.")) (|coerce| (($ |#1|) "\\spad{coerce(v)} return \\spad{v}") (((|OrderedFreeMonoid| |#1|) $) "\\spad{coerce([l1]*[l2]*...[ln])} returns the word \\spad{l1*l2*...*ln},{} where \\spad{[l_i]} is the backeted form of the Lyndon word \\spad{l_i}.")) ((|One|) (($) "\\spad{1} returns the empty list."))) NIL NIL -(-895 UP R) +(-896 UP R) ((|constructor| (NIL "This package \\undocumented")) (|compose| ((|#1| |#1| |#1|) "\\spad{compose(p,q)} \\undocumented"))) NIL NIL -(-896) +(-897) ((|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 -(-897 UP -3867) +(-898 UP -3879) ((|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 -(-898) +(-899) ((|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalPDEProblem|) (|RoutinesTable|)) "\\spad{measure(prob,R)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical PDE problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} listed in \\axiom{\\spad{R}} of \\axiom{category} \\axiomType{PartialDifferentialEquationsSolverCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information. It predicts the likely most effective NAG numerical Library routine to solve the input set of PDEs by checking various attributes of the system of PDEs and calculating a measure of compatibility of each routine to these attributes.") (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalPDEProblem|)) "\\spad{measure(prob)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical PDE problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} of \\axiom{category} \\axiomType{PartialDifferentialEquationsSolverCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information. It predicts the likely most effective NAG numerical Library routine to solve the input set of PDEs by checking various attributes of the system of PDEs and calculating a measure of compatibility of each routine to these attributes.")) (|solve| (((|Result|) (|Float|) (|Float|) (|Float|) (|Float|) (|NonNegativeInteger|) (|NonNegativeInteger|) (|List| (|Expression| (|Float|))) (|List| (|List| (|Expression| (|Float|)))) (|String|)) "\\spad{solve(xmin,ymin,xmax,ymax,ngx,ngy,pde,bounds,st)} is a top level ANNA function to solve numerically a system of partial differential equations. This is defined as a list of coefficients (\\axiom{\\spad{pde}}),{} a grid (\\axiom{\\spad{xmin}},{} \\axiom{\\spad{ymin}},{} \\axiom{\\spad{xmax}},{} \\axiom{\\spad{ymax}},{} \\axiom{\\spad{ngx}},{} \\axiom{\\spad{ngy}}) and the boundary values (\\axiom{\\spad{bounds}}). A default value for tolerance is used. There is also a parameter (\\axiom{\\spad{st}}) which should contain the value \"elliptic\" if the PDE is known to be elliptic,{} or \"unknown\" if it is uncertain. This causes the routine to check whether the PDE is elliptic. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of PDE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine. \\blankline \\spad{**} At the moment,{} only Second Order Elliptic Partial Differential Equations are solved \\spad{**}") (((|Result|) (|Float|) (|Float|) (|Float|) (|Float|) (|NonNegativeInteger|) (|NonNegativeInteger|) (|List| (|Expression| (|Float|))) (|List| (|List| (|Expression| (|Float|)))) (|String|) (|DoubleFloat|)) "\\spad{solve(xmin,ymin,xmax,ymax,ngx,ngy,pde,bounds,st,tol)} is a top level ANNA function to solve numerically a system of partial differential equations. This is defined as a list of coefficients (\\axiom{\\spad{pde}}),{} a grid (\\axiom{\\spad{xmin}},{} \\axiom{\\spad{ymin}},{} \\axiom{\\spad{xmax}},{} \\axiom{\\spad{ymax}},{} \\axiom{\\spad{ngx}},{} \\axiom{\\spad{ngy}}),{} the boundary values (\\axiom{\\spad{bounds}}) and a tolerance requirement (\\axiom{\\spad{tol}}). There is also a parameter (\\axiom{\\spad{st}}) which should contain the value \"elliptic\" if the PDE is known to be elliptic,{} or \"unknown\" if it is uncertain. This causes the routine to check whether the PDE is elliptic. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of PDE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine. \\blankline \\spad{**} At the moment,{} only Second Order Elliptic Partial Differential Equations are solved \\spad{**}") (((|Result|) (|NumericalPDEProblem|) (|RoutinesTable|)) "\\spad{solve(PDEProblem,routines)} is a top level ANNA function to solve numerically a system of partial differential equations. \\blankline The method used to perform the numerical process will be one of the \\spad{routines} contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of PDE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine. \\blankline \\spad{**} At the moment,{} only Second Order Elliptic Partial Differential Equations are solved \\spad{**}") (((|Result|) (|NumericalPDEProblem|)) "\\spad{solve(PDEProblem)} is a top level ANNA function to solve numerically a system of partial differential equations. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of PDE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine. \\blankline \\spad{**} At the moment,{} only Second Order Elliptic Partial Differential Equations are solved \\spad{**}"))) NIL NIL -(-899) +(-900) ((|retract| (((|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|))) $) "\\spad{retract(x)} \\undocumented{}")) (|coerce| (($ (|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|)))) "\\spad{coerce(x)} \\undocumented{}"))) NIL NIL -(-900 A S) +(-901 A S) ((|constructor| (NIL "A partial differential ring with differentiations indexed by a parameter type \\spad{S}. \\blankline")) (D (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) "\\spad{D(x, [s1,...,sn], [n1,...,nn])} computes multiple partial derivatives,{} \\spadignore{i.e.} \\spad{D(...D(x, s1, n1)..., sn, nn)}.") (($ $ |#2| (|NonNegativeInteger|)) "\\spad{D(x, s, n)} computes multiple partial derivatives,{} \\spadignore{i.e.} \\spad{n}-th derivative of \\spad{x} with respect to \\spad{s}.") (($ $ (|List| |#2|)) "\\spad{D(x,[s1,...sn])} computes successive partial derivatives,{} \\spadignore{i.e.} \\spad{D(...D(x, s1)..., sn)}.") (($ $ |#2|) "\\spad{D(x,v)} computes the partial derivative of \\spad{x} with respect to \\spad{v}.")) (|differentiate| (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) "\\spad{differentiate(x, [s1,...,sn], [n1,...,nn])} computes multiple partial derivatives,{} \\spadignore{i.e.}") (($ $ |#2| (|NonNegativeInteger|)) "\\spad{differentiate(x, s, n)} computes multiple partial derivatives,{} \\spadignore{i.e.} \\spad{n}-th derivative of \\spad{x} with respect to \\spad{s}.") (($ $ (|List| |#2|)) "\\spad{differentiate(x,[s1,...sn])} computes successive partial derivatives,{} \\spadignore{i.e.} \\spad{differentiate(...differentiate(x, s1)..., sn)}.") (($ $ |#2|) "\\spad{differentiate(x,v)} computes the partial derivative of \\spad{x} with respect to \\spad{v}."))) NIL NIL -(-901 S) +(-902 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)) +((-4415 . T)) NIL -(-902 S) +(-903 S) ((|constructor| (NIL "\\indented{1}{A PendantTree(\\spad{S})is either a leaf? and is an \\spad{S} or has} a left and a right both PendantTree(\\spad{S})\\spad{'s}")) (|ptree| (($ $ $) "\\spad{ptree(x,y)} \\undocumented") (($ |#1|) "\\spad{ptree(s)} is a leaf? pendant tree"))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1101))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1101))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-1101))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) -(-903 |n| R) +((-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1102))) (-2800 (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) +(-904 |n| R) ((|constructor| (NIL "Permanent implements the functions {\\em permanent},{} the permanent for square matrices.")) (|permanent| ((|#2| (|SquareMatrix| |#1| |#2|)) "\\spad{permanent(x)} computes the permanent of a square matrix \\spad{x}. The {\\em permanent} is equivalent to the \\spadfun{determinant} except that coefficients have no change of sign. This function is much more difficult to compute than the {\\em determinant}. The formula used is by \\spad{H}.\\spad{J}. Ryser,{} improved by [Nijenhuis and Wilf,{} \\spad{Ch}. 19]. Note: permanent(\\spad{x}) choose one of three algorithms,{} depending on the underlying ring \\spad{R} and on \\spad{n},{} the number of rows (and columns) of \\spad{x:}\\begin{items} \\item 1. if 2 has an inverse in \\spad{R} we can use the algorithm of \\indented{3}{[Nijenhuis and Wilf,{} \\spad{ch}.19,{}\\spad{p}.158]; if 2 has no inverse,{}} \\indented{3}{some modifications are necessary:} \\item 2. if {\\em n > 6} and \\spad{R} is an integral domain with characteristic \\indented{3}{different from 2 (the algorithm works if and only 2 is not a} \\indented{3}{zero-divisor of \\spad{R} and {\\em characteristic()\\$R ~= 2},{}} \\indented{3}{but how to check that for any given \\spad{R} ?),{}} \\indented{3}{the local function {\\em permanent2} is called;} \\item 3. else,{} the local function {\\em permanent3} is called \\indented{3}{(works for all commutative rings \\spad{R}).} \\end{items}"))) NIL NIL -(-904 S) +(-905 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)) +((-4415 . T)) NIL -(-905 S) +(-906 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|)) $) "\\spad{coerce(gp)} returns the generators of the group {\\em gp}."))) NIL NIL -(-906 S) +(-907 S) ((|constructor| (NIL "Permutation(\\spad{S}) implements the group of all bijections \\indented{2}{on a set \\spad{S},{} which move only a finite number of points.} \\indented{2}{A permutation is considered as a map from \\spad{S} into \\spad{S}. In particular} \\indented{2}{multiplication is defined as composition of maps:} \\indented{2}{{\\em pi1 * pi2 = pi1 o pi2}.} \\indented{2}{The internal representation of permuatations are two lists} \\indented{2}{of equal length representing preimages and images.}")) (|coerceImages| (($ (|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)) -((-2797 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-851)))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-851)))) -(-907 R E |VarSet| S) +((-4415 . T)) +((-2800 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-851)))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-851)))) +(-908 R E |VarSet| S) ((|constructor| (NIL "PolynomialFactorizationByRecursion(\\spad{R},{}\\spad{E},{}\\spad{VarSet},{}\\spad{S}) is used for factorization of sparse univariate polynomials over a domain \\spad{S} of multivariate polynomials over \\spad{R}.")) (|factorSFBRlcUnit| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|List| |#3|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorSFBRlcUnit(p)} returns the square free factorization of polynomial \\spad{p} (see \\spadfun{factorSquareFreeByRecursion}{PolynomialFactorizationByRecursionUnivariate}) in the case where the leading coefficient of \\spad{p} is a unit.")) (|bivariateSLPEBR| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|List| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|) |#3|) "\\spad{bivariateSLPEBR(lp,p,v)} implements the bivariate case of \\spadfunFrom{solveLinearPolynomialEquationByRecursion}{PolynomialFactorizationByRecursionUnivariate}; its implementation depends on \\spad{R}")) (|randomR| ((|#1|) "\\spad{randomR produces} a random element of \\spad{R}")) (|factorSquareFreeByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorSquareFreeByRecursion(p)} returns the square free factorization of \\spad{p}. This functions performs the recursion step for factorSquareFreePolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorSquareFreePolynomial}).")) (|factorByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorByRecursion(p)} factors polynomial \\spad{p}. This function performs the recursion step for factorPolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorPolynomial})")) (|solveLinearPolynomialEquationByRecursion| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|List| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{solveLinearPolynomialEquationByRecursion([p1,...,pn],p)} returns the list of polynomials \\spad{[q1,...,qn]} such that \\spad{sum qi/pi = p / prod pi},{} a recursion step for solveLinearPolynomialEquation as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{solveLinearPolynomialEquation}). If no such list of \\spad{qi} exists,{} then \"failed\" is returned."))) NIL NIL -(-908 R S) +(-909 R S) ((|constructor| (NIL "\\indented{1}{PolynomialFactorizationByRecursionUnivariate} \\spad{R} is a \\spadfun{PolynomialFactorizationExplicit} domain,{} \\spad{S} is univariate polynomials over \\spad{R} We are interested in handling SparseUnivariatePolynomials over \\spad{S},{} is a variable we shall call \\spad{z}")) (|factorSFBRlcUnit| (((|Factored| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|)) "\\spad{factorSFBRlcUnit(p)} returns the square free factorization of polynomial \\spad{p} (see \\spadfun{factorSquareFreeByRecursion}{PolynomialFactorizationByRecursionUnivariate}) in the case where the leading coefficient of \\spad{p} is a unit.")) (|randomR| ((|#1|) "\\spad{randomR()} produces a random element of \\spad{R}")) (|factorSquareFreeByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|)) "\\spad{factorSquareFreeByRecursion(p)} returns the square free factorization of \\spad{p}. This functions performs the recursion step for factorSquareFreePolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorSquareFreePolynomial}).")) (|factorByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|)) "\\spad{factorByRecursion(p)} factors polynomial \\spad{p}. This function performs the recursion step for factorPolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorPolynomial})")) (|solveLinearPolynomialEquationByRecursion| (((|Union| (|List| (|SparseUnivariatePolynomial| |#2|)) "failed") (|List| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|)) "\\spad{solveLinearPolynomialEquationByRecursion([p1,...,pn],p)} returns the list of polynomials \\spad{[q1,...,qn]} such that \\spad{sum qi/pi = p / prod pi},{} a recursion step for solveLinearPolynomialEquation as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{solveLinearPolynomialEquation}). If no such list of \\spad{qi} exists,{} then \"failed\" is returned."))) NIL NIL -(-909 S) +(-910 S) ((|constructor| (NIL "This is the category of domains that know \"enough\" about themselves in order to factor univariate polynomials over themselves. This will be used in future releases for supporting factorization over finitely generated coefficient fields,{} it is not yet available in the current release of axiom.")) (|charthRoot| (((|Union| $ "failed") $) "\\spad{charthRoot(r)} returns the \\spad{p}\\spad{-}th root of \\spad{r},{} or \"failed\" if none exists in the domain.")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(m)} returns a vector of elements,{} not all zero,{} whose \\spad{p}\\spad{-}th powers (\\spad{p} is the characteristic of the domain) are a solution of the homogenous linear system represented by \\spad{m},{} or \"failed\" is there is no such vector.")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| $)) "failed") (|List| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{solveLinearPolynomialEquation([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists.")) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) "\\spad{gcdPolynomial(p,q)} returns the \\spad{gcd} of the univariate polynomials \\spad{p} \\spad{qnd} \\spad{q}.")) (|factorSquareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorSquareFreePolynomial(p)} factors the univariate polynomial \\spad{p} into irreducibles where \\spad{p} is known to be square free and primitive with respect to its main variable.")) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorPolynomial(p)} returns the factorization into irreducibles of the univariate polynomial \\spad{p}.")) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{squareFreePolynomial(p)} returns the square-free factorization of the univariate polynomial \\spad{p}."))) NIL ((|HasCategory| |#1| (QUOTE (-145)))) -(-910) +(-911) ((|constructor| (NIL "This is the category of domains that know \"enough\" about themselves in order to factor univariate polynomials over themselves. This will be used in future releases for supporting factorization over finitely generated coefficient fields,{} it is not yet available in the current release of axiom.")) (|charthRoot| (((|Union| $ "failed") $) "\\spad{charthRoot(r)} returns the \\spad{p}\\spad{-}th root of \\spad{r},{} or \"failed\" if none exists in the domain.")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(m)} returns a vector of elements,{} not all zero,{} whose \\spad{p}\\spad{-}th powers (\\spad{p} is the characteristic of the domain) are a solution of the homogenous linear system represented by \\spad{m},{} or \"failed\" is there is no such vector.")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| $)) "failed") (|List| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{solveLinearPolynomialEquation([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists.")) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) "\\spad{gcdPolynomial(p,q)} returns the \\spad{gcd} of the univariate polynomials \\spad{p} \\spad{qnd} \\spad{q}.")) (|factorSquareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorSquareFreePolynomial(p)} factors the univariate polynomial \\spad{p} into irreducibles where \\spad{p} is known to be square free and primitive with respect to its main variable.")) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorPolynomial(p)} returns the factorization into irreducibles of the univariate polynomial \\spad{p}.")) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{squareFreePolynomial(p)} returns the square-free factorization of the univariate polynomial \\spad{p}."))) -((-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) +((-4411 . T) ((-4420 "*") . T) (-4412 . T) (-4413 . T) (-4415 . T)) NIL -(-911 |p|) +(-912 |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)) +((-4410 . T) (-4416 . T) (-4411 . T) ((-4420 "*") . T) (-4412 . T) (-4413 . T) (-4415 . T)) ((|HasCategory| $ (QUOTE (-147))) (|HasCategory| $ (QUOTE (-145))) (|HasCategory| $ (QUOTE (-370)))) -(-912 R0 -3867 UP UPUP R) +(-913 R0 -3879 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 -(-913 UP UPUP R) +(-914 UP UPUP R) ((|constructor| (NIL "This package provides function for testing whether a divisor on a curve is a torsion divisor.")) (|torsionIfCan| (((|Union| (|Record| (|:| |order| (|NonNegativeInteger|)) (|:| |function| |#3|)) "failed") (|FiniteDivisor| (|Fraction| (|Integer|)) |#1| |#2| |#3|)) "\\spad{torsionIfCan(f)} \\undocumented")) (|torsion?| (((|Boolean|) (|FiniteDivisor| (|Fraction| (|Integer|)) |#1| |#2| |#3|)) "\\spad{torsion?(f)} \\undocumented")) (|order| (((|Union| (|NonNegativeInteger|) "failed") (|FiniteDivisor| (|Fraction| (|Integer|)) |#1| |#2| |#3|)) "\\spad{order(f)} \\undocumented"))) NIL NIL -(-914 UP UPUP) +(-915 UP UPUP) ((|constructor| (NIL "\\indented{1}{Utilities for PFOQ and PFO} Author: Manuel Bronstein Date Created: 25 Aug 1988 Date Last Updated: 11 Jul 1990")) (|polyred| ((|#2| |#2|) "\\spad{polyred(u)} \\undocumented")) (|doubleDisc| (((|Integer|) |#2|) "\\spad{doubleDisc(u)} \\undocumented")) (|mix| (((|Integer|) (|List| (|Record| (|:| |den| (|Integer|)) (|:| |gcdnum| (|Integer|))))) "\\spad{mix(l)} \\undocumented")) (|badNum| (((|Integer|) |#2|) "\\spad{badNum(u)} \\undocumented") (((|Record| (|:| |den| (|Integer|)) (|:| |gcdnum| (|Integer|))) |#1|) "\\spad{badNum(p)} \\undocumented")) (|getGoodPrime| (((|PositiveInteger|) (|Integer|)) "\\spad{getGoodPrime n} returns the smallest prime not dividing \\spad{n}"))) NIL NIL -(-915 R) +(-916 R) ((|constructor| (NIL "The domain \\spadtype{PartialFraction} implements partial fractions over a euclidean domain \\spad{R}. This requirement on the argument domain allows us to normalize the fractions. Of particular interest are the 2 forms for these fractions. The ``compact\\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)) +((-4410 . T) (-4416 . T) (-4411 . T) ((-4420 "*") . T) (-4412 . T) (-4413 . T) (-4415 . T)) NIL -(-916 R) +(-917 R) ((|constructor| (NIL "The package \\spadtype{PartialFractionPackage} gives an easier to use interfact the domain \\spadtype{PartialFraction}. The user gives a fraction of polynomials,{} and a variable and the package converts it to the proper datatype for the \\spadtype{PartialFraction} domain.")) (|partialFraction| (((|Any|) (|Polynomial| |#1|) (|Factored| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{partialFraction(num, facdenom, var)} returns the partial fraction decomposition of the rational function whose numerator is \\spad{num} and whose factored denominator is \\spad{facdenom} with respect to the variable var.") (((|Any|) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{partialFraction(rf, var)} returns the partial fraction decomposition of the rational function \\spad{rf} with respect to the variable var."))) NIL NIL -(-917 E OV R P) +(-918 E OV R P) ((|gcdPrimitive| ((|#4| (|List| |#4|)) "\\spad{gcdPrimitive lp} computes the \\spad{gcd} of the list of primitive polynomials \\spad{lp}.") (((|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{gcdPrimitive(p,q)} computes the \\spad{gcd} of the primitive polynomials \\spad{p} and \\spad{q}.") ((|#4| |#4| |#4|) "\\spad{gcdPrimitive(p,q)} computes the \\spad{gcd} of the primitive polynomials \\spad{p} and \\spad{q}.")) (|gcd| (((|SparseUnivariatePolynomial| |#4|) (|List| (|SparseUnivariatePolynomial| |#4|))) "\\spad{gcd(lp)} computes the \\spad{gcd} of the list of polynomials \\spad{lp}.") (((|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{gcd(p,q)} computes the \\spad{gcd} of the two polynomials \\spad{p} and \\spad{q}.") ((|#4| (|List| |#4|)) "\\spad{gcd(lp)} computes the \\spad{gcd} of the list of polynomials \\spad{lp}.") ((|#4| |#4| |#4|) "\\spad{gcd(p,q)} computes the \\spad{gcd} of the two polynomials \\spad{p} and \\spad{q}."))) NIL NIL -(-918) +(-919) ((|constructor| (NIL "PermutationGroupExamples provides permutation groups for some classes of groups: symmetric,{} alternating,{} dihedral,{} cyclic,{} direct products of cyclic,{} which are in fact the finite abelian groups of symmetric groups called Young subgroups. Furthermore,{} Rubik\\spad{'s} group as permutation group of 48 integers and a list of sporadic simple groups derived from the atlas of finite groups.")) (|youngGroup| (((|PermutationGroup| (|Integer|)) (|Partition|)) "\\spad{youngGroup(lambda)} constructs the direct product of the symmetric groups given by the parts of the partition {\\em lambda}.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{youngGroup([n1,...,nk])} constructs the direct product of the symmetric groups {\\em Sn1},{}...,{}{\\em Snk}.")) (|rubiksGroup| (((|PermutationGroup| (|Integer|))) "\\spad{rubiksGroup constructs} the permutation group representing Rubic\\spad{'s} Cube acting on integers {\\em 10*i+j} for {\\em 1 <= i <= 6},{} {\\em 1 <= j <= 8}. The faces of Rubik\\spad{'s} Cube are labelled in the obvious way Front,{} Right,{} Up,{} Down,{} Left,{} Back and numbered from 1 to 6 in this given ordering,{} the pieces on each face (except the unmoveable center piece) are clockwise numbered from 1 to 8 starting with the piece in the upper left corner. The moves of the cube are represented as permutations on these pieces,{} represented as a two digit integer {\\em ij} where \\spad{i} is the numer of theface (1 to 6) and \\spad{j} is the number of the piece on this face. The remaining ambiguities are resolved by looking at the 6 generators,{} which represent a 90 degree turns of the faces,{} or from the following pictorial description. Permutation group representing Rubic\\spad{'s} Cube acting on integers 10*i+j for 1 \\spad{<=} \\spad{i} \\spad{<=} 6,{} 1 \\spad{<=} \\spad{j} \\spad{<=8}. \\blankline\\begin{verbatim}Rubik's Cube: +-----+ +-- B where: marks Side # : / U /|/ / / | F(ront) <-> 1 L --> +-----+ R| R(ight) <-> 2 | | + U(p) <-> 3 | F | / D(own) <-> 4 | |/ L(eft) <-> 5 +-----+ B(ack) <-> 6 ^ | DThe Cube's surface: The pieces on each side +---+ (except the unmoveable center |567| piece) are clockwise numbered |4U8| from 1 to 8 starting with the |321| piece in the upper left +---+---+---+ corner (see figure on the |781|123|345| left). The moves of the cube |6L2|8F4|2R6| are represented as |543|765|187| permutations on these pieces. +---+---+---+ Each of the pieces is |123| represented as a two digit |8D4| integer ij where i is the |765| # of the side ( 1 to 6 for +---+ F to B (see table above )) |567| and j is the # of the piece. |4B8| |321| +---+\\end{verbatim}")) (|janko2| (((|PermutationGroup| (|Integer|))) "\\spad{janko2 constructs} the janko group acting on the integers 1,{}...,{}100.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{janko2(li)} constructs the janko group acting on the 100 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 100 different entries")) (|mathieu24| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu24 constructs} the mathieu group acting on the integers 1,{}...,{}24.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu24(li)} constructs the mathieu group acting on the 24 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 24 different entries.")) (|mathieu23| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu23 constructs} the mathieu group acting on the integers 1,{}...,{}23.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu23(li)} constructs the mathieu group acting on the 23 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 23 different entries.")) (|mathieu22| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu22 constructs} the mathieu group acting on the integers 1,{}...,{}22.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu22(li)} constructs the mathieu group acting on the 22 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 22 different entries.")) (|mathieu12| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu12 constructs} the mathieu group acting on the integers 1,{}...,{}12.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu12(li)} constructs the mathieu group acting on the 12 integers given in the list {\\em li}. Note: duplicates in the list will be removed Error: if {\\em li} has less or more than 12 different entries.")) (|mathieu11| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu11 constructs} the mathieu group acting on the integers 1,{}...,{}11.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu11(li)} constructs the mathieu group acting on the 11 integers given in the list {\\em li}. Note: duplicates in the list will be removed. error,{} if {\\em li} has less or more than 11 different entries.")) (|dihedralGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{dihedralGroup([i1,...,ik])} constructs the dihedral group of order 2k acting on the integers out of {\\em i1},{}...,{}{\\em ik}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{dihedralGroup(n)} constructs the dihedral group of order 2n acting on integers 1,{}...,{}\\spad{N}.")) (|cyclicGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{cyclicGroup([i1,...,ik])} constructs the cyclic group of order \\spad{k} acting on the integers {\\em i1},{}...,{}{\\em ik}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{cyclicGroup(n)} constructs the cyclic group of order \\spad{n} acting on the integers 1,{}...,{}\\spad{n}.")) (|abelianGroup| (((|PermutationGroup| (|Integer|)) (|List| (|PositiveInteger|))) "\\spad{abelianGroup([n1,...,nk])} constructs the abelian group that is the direct product of cyclic groups with order {\\em ni}.")) (|alternatingGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{alternatingGroup(li)} constructs the alternating group acting on the integers in the list {\\em li},{} generators are in general the {\\em n-2}-cycle {\\em (li.3,...,li.n)} and the 3-cycle {\\em (li.1,li.2,li.3)},{} if \\spad{n} is odd and product of the 2-cycle {\\em (li.1,li.2)} with {\\em n-2}-cycle {\\em (li.3,...,li.n)} and the 3-cycle {\\em (li.1,li.2,li.3)},{} if \\spad{n} is even. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{alternatingGroup(n)} constructs the alternating group {\\em An} acting on the integers 1,{}...,{}\\spad{n},{} generators are in general the {\\em n-2}-cycle {\\em (3,...,n)} and the 3-cycle {\\em (1,2,3)} if \\spad{n} is odd and the product of the 2-cycle {\\em (1,2)} with {\\em n-2}-cycle {\\em (3,...,n)} and the 3-cycle {\\em (1,2,3)} if \\spad{n} is even.")) (|symmetricGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{symmetricGroup(li)} constructs the symmetric group acting on the integers in the list {\\em li},{} generators are the cycle given by {\\em li} and the 2-cycle {\\em (li.1,li.2)}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{symmetricGroup(n)} constructs the symmetric group {\\em Sn} acting on the integers 1,{}...,{}\\spad{n},{} generators are the {\\em n}-cycle {\\em (1,...,n)} and the 2-cycle {\\em (1,2)}."))) NIL NIL -(-919 -3867) +(-920 -3879) ((|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 -(-920 R) +(-921 R) ((|constructor| (NIL "\\indented{1}{Provides a coercion from the symbolic fractions in \\%\\spad{pi} with} integer coefficients to any Expression type. Date Created: 21 Feb 1990 Date Last Updated: 21 Feb 1990")) (|coerce| (((|Expression| |#1|) (|Pi|)) "\\spad{coerce(f)} returns \\spad{f} as an Expression(\\spad{R})."))) NIL NIL -(-921) +(-922) ((|constructor| (NIL "The category of constructive principal ideal domains,{} \\spadignore{i.e.} where a single generator can be constructively found for any ideal given by a finite set of generators. Note that this constructive definition only implies that finitely generated ideals are principal. It is not clear what we would mean by an infinitely generated ideal.")) (|expressIdealMember| (((|Union| (|List| $) "failed") (|List| $) $) "\\spad{expressIdealMember([f1,...,fn],h)} returns a representation of \\spad{h} as a linear combination of the \\spad{fi} or \"failed\" if \\spad{h} is not in the ideal generated by the \\spad{fi}.")) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) "\\spad{principalIdeal([f1,...,fn])} returns a record whose generator component is a generator of the ideal generated by \\spad{[f1,...,fn]} whose coef component satisfies \\spad{generator = sum (input.i * coef.i)}"))) -((-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) +((-4411 . T) ((-4420 "*") . T) (-4412 . T) (-4413 . T) (-4415 . T)) NIL -(-922) +(-923) ((|constructor| (NIL "\\spadtype{PositiveInteger} provides functions for \\indented{2}{positive integers.}")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} means multiplication is commutative : x*y = \\spad{y*x}")) (|gcd| (($ $ $) "\\spad{gcd(a,b)} computes the greatest common divisor of two positive integers \\spad{a} and \\spad{b}."))) -(((-4419 "*") . T)) +(((-4420 "*") . T)) NIL -(-923 -3867 P) +(-924 -3879 P) ((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,l2)} \\undocumented"))) NIL NIL -(-924 |xx| -3867) +(-925 |xx| -3879) ((|constructor| (NIL "This package exports interpolation algorithms")) (|interpolate| (((|SparseUnivariatePolynomial| |#2|) (|List| |#2|) (|List| |#2|)) "\\spad{interpolate(lf,lg)} \\undocumented") (((|UnivariatePolynomial| |#1| |#2|) (|UnivariatePolynomial| |#1| |#2|) (|List| |#2|) (|List| |#2|)) "\\spad{interpolate(u,lf,lg)} \\undocumented"))) NIL NIL -(-925 R |Var| |Expon| GR) +(-926 R |Var| |Expon| GR) ((|constructor| (NIL "Author: William Sit,{} spring 89")) (|inconsistent?| (((|Boolean|) (|List| (|Polynomial| |#1|))) "inconsistant?(\\spad{pl}) returns \\spad{true} if the system of equations \\spad{p} = 0 for \\spad{p} in \\spad{pl} is inconsistent. It is assumed that \\spad{pl} is a groebner basis.") (((|Boolean|) (|List| |#4|)) "inconsistant?(\\spad{pl}) returns \\spad{true} if the system of equations \\spad{p} = 0 for \\spad{p} in \\spad{pl} is inconsistent. It is assumed that \\spad{pl} is a groebner basis.")) (|sqfree| ((|#4| |#4|) "\\spad{sqfree(p)} returns the product of square free factors of \\spad{p}")) (|regime| (((|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))))) (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))) (|Matrix| |#4|) (|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|List| |#4|)) (|NonNegativeInteger|) (|NonNegativeInteger|) (|Integer|)) "\\spad{regime(y,c, w, p, r, rm, m)} returns a regime,{} a list of polynomials specifying the consistency conditions,{} a particular solution and basis representing the general solution of the parametric linear system \\spad{c} \\spad{z} = \\spad{w} on that regime. The regime returned depends on the subdeterminant \\spad{y}.det and the row and column indices. The solutions are simplified using the assumption that the system has rank \\spad{r} and maximum rank \\spad{rm}. The list \\spad{p} represents a list of list of factors of polynomials in a groebner basis of the ideal generated by higher order subdeterminants,{} and ius used for the simplification. The mode \\spad{m} distinguishes the cases when the system is homogeneous,{} or the right hand side is arbitrary,{} or when there is no new right hand side variables.")) (|redmat| (((|Matrix| |#4|) (|Matrix| |#4|) (|List| |#4|)) "\\spad{redmat(m,g)} returns a matrix whose entries are those of \\spad{m} modulo the ideal generated by the groebner basis \\spad{g}")) (|ParCond| (((|List| (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|))))) (|Matrix| |#4|) (|NonNegativeInteger|)) "\\spad{ParCond(m,k)} returns the list of all \\spad{k} by \\spad{k} subdeterminants in the matrix \\spad{m}")) (|overset?| (((|Boolean|) (|List| |#4|) (|List| (|List| |#4|))) "\\spad{overset?(s,sl)} returns \\spad{true} if \\spad{s} properly a sublist of a member of \\spad{sl}; otherwise it returns \\spad{false}")) (|nextSublist| (((|List| (|List| (|Integer|))) (|Integer|) (|Integer|)) "\\spad{nextSublist(n,k)} returns a list of \\spad{k}-subsets of {1,{} ...,{} \\spad{n}}.")) (|minset| (((|List| (|List| |#4|)) (|List| (|List| |#4|))) "\\spad{minset(sl)} returns the sublist of \\spad{sl} consisting of the minimal lists (with respect to inclusion) in the list \\spad{sl} of lists")) (|minrank| (((|NonNegativeInteger|) (|List| (|Record| (|:| |rank| (|NonNegativeInteger|)) (|:| |eqns| (|List| (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))))) (|:| |fgb| (|List| |#4|))))) "\\spad{minrank(r)} returns the minimum rank in the list \\spad{r} of regimes")) (|maxrank| (((|NonNegativeInteger|) (|List| (|Record| (|:| |rank| (|NonNegativeInteger|)) (|:| |eqns| (|List| (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))))) (|:| |fgb| (|List| |#4|))))) "\\spad{maxrank(r)} returns the maximum rank in the list \\spad{r} of regimes")) (|factorset| (((|List| |#4|) |#4|) "\\spad{factorset(p)} returns the set of irreducible factors of \\spad{p}.")) (|B1solve| (((|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))) (|Record| (|:| |mat| (|Matrix| (|Fraction| (|Polynomial| |#1|)))) (|:| |vec| (|List| (|Fraction| (|Polynomial| |#1|)))) (|:| |rank| (|NonNegativeInteger|)) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|))))) "\\spad{B1solve(s)} solves the system (\\spad{s}.mat) \\spad{z} = \\spad{s}.vec for the variables given by the column indices of \\spad{s}.cols in terms of the other variables and the right hand side \\spad{s}.vec by assuming that the rank is \\spad{s}.rank,{} that the system is consistent,{} with the linearly independent equations indexed by the given row indices \\spad{s}.rows; the coefficients in \\spad{s}.mat involving parameters are treated as polynomials. B1solve(\\spad{s}) returns a particular solution to the system and a basis of the homogeneous system (\\spad{s}.mat) \\spad{z} = 0.")) (|redpps| (((|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))) (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))) (|List| |#4|)) "\\spad{redpps(s,g)} returns the simplified form of \\spad{s} after reducing modulo a groebner basis \\spad{g}")) (|ParCondList| (((|List| (|Record| (|:| |rank| (|NonNegativeInteger|)) (|:| |eqns| (|List| (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))))) (|:| |fgb| (|List| |#4|)))) (|Matrix| |#4|) (|NonNegativeInteger|)) "\\spad{ParCondList(c,r)} computes a list of subdeterminants of each rank \\spad{>=} \\spad{r} of the matrix \\spad{c} and returns a groebner basis for the ideal they generate")) (|hasoln| (((|Record| (|:| |sysok| (|Boolean|)) (|:| |z0| (|List| |#4|)) (|:| |n0| (|List| |#4|))) (|List| |#4|) (|List| |#4|)) "\\spad{hasoln(g, l)} tests whether the quasi-algebraic set defined by \\spad{p} = 0 for \\spad{p} in \\spad{g} and \\spad{q} \\spad{~=} 0 for \\spad{q} in \\spad{l} is empty or not and returns a simplified definition of the quasi-algebraic set")) (|pr2dmp| ((|#4| (|Polynomial| |#1|)) "\\spad{pr2dmp(p)} converts \\spad{p} to target domain")) (|se2rfi| (((|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|Symbol|))) "\\spad{se2rfi(l)} converts \\spad{l} to target domain")) (|dmp2rfi| (((|List| (|Fraction| (|Polynomial| |#1|))) (|List| |#4|)) "\\spad{dmp2rfi(l)} converts \\spad{l} to target domain") (((|Matrix| (|Fraction| (|Polynomial| |#1|))) (|Matrix| |#4|)) "\\spad{dmp2rfi(m)} converts \\spad{m} to target domain") (((|Fraction| (|Polynomial| |#1|)) |#4|) "\\spad{dmp2rfi(p)} converts \\spad{p} to target domain")) (|bsolve| (((|Record| (|:| |rgl| (|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))))))) (|:| |rgsz| (|Integer|))) (|Matrix| |#4|) (|List| (|Fraction| (|Polynomial| |#1|))) (|NonNegativeInteger|) (|String|) (|Integer|)) "\\spad{bsolve(c, w, r, s, m)} returns a list of regimes and solutions of the system \\spad{c} \\spad{z} = \\spad{w} for ranks at least \\spad{r}; depending on the mode \\spad{m} chosen,{} it writes the output to a file given by the string \\spad{s}.")) (|rdregime| (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|String|)) "\\spad{rdregime(s)} reads in a list from a file with name \\spad{s}")) (|wrregime| (((|Integer|) (|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|String|)) "\\spad{wrregime(l,s)} writes a list of regimes to a file named \\spad{s} and returns the number of regimes written")) (|psolve| (((|Integer|) (|Matrix| |#4|) (|PositiveInteger|) (|String|)) "\\spad{psolve(c,k,s)} solves \\spad{c} \\spad{z} = 0 for all possible ranks \\spad{>=} \\spad{k} of the matrix \\spad{c},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|List| (|Symbol|)) (|PositiveInteger|) (|String|)) "\\spad{psolve(c,w,k,s)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks \\spad{>=} \\spad{k} of the matrix \\spad{c} and indeterminate right hand side \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|List| |#4|) (|PositiveInteger|) (|String|)) "\\spad{psolve(c,w,k,s)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks \\spad{>=} \\spad{k} of the matrix \\spad{c} and given right hand side \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|String|)) "\\spad{psolve(c,s)} solves \\spad{c} \\spad{z} = 0 for all possible ranks of the matrix \\spad{c} and given right hand side vector \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|List| (|Symbol|)) (|String|)) "\\spad{psolve(c,w,s)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks of the matrix \\spad{c} and indeterminate right hand side \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|List| |#4|) (|String|)) "\\spad{psolve(c,w,s)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks of the matrix \\spad{c} and given right hand side vector \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|PositiveInteger|)) "\\spad{psolve(c)} solves the homogeneous linear system \\spad{c} \\spad{z} = 0 for all possible ranks \\spad{>=} \\spad{k} of the matrix \\spad{c}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|List| (|Symbol|)) (|PositiveInteger|)) "\\spad{psolve(c,w,k)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks \\spad{>=} \\spad{k} of the matrix \\spad{c} and indeterminate right hand side \\spad{w}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|List| |#4|) (|PositiveInteger|)) "\\spad{psolve(c,w,k)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks \\spad{>=} \\spad{k} of the matrix \\spad{c} and given right hand side vector \\spad{w}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|)) "\\spad{psolve(c)} solves the homogeneous linear system \\spad{c} \\spad{z} = 0 for all possible ranks of the matrix \\spad{c}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|List| (|Symbol|))) "\\spad{psolve(c,w)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks of the matrix \\spad{c} and indeterminate right hand side \\spad{w}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|List| |#4|)) "\\spad{psolve(c,w)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks of the matrix \\spad{c} and given right hand side vector \\spad{w}"))) NIL NIL -(-926 S) +(-927 S) ((|constructor| (NIL "PlotFunctions1 provides facilities for plotting curves where functions \\spad{SF} \\spad{->} \\spad{SF} are specified by giving an expression")) (|plotPolar| (((|Plot|) |#1| (|Symbol|)) "\\spad{plotPolar(f,theta)} plots the graph of \\spad{r = f(theta)} as \\spad{theta} ranges from 0 to 2 \\spad{pi}") (((|Plot|) |#1| (|Symbol|) (|Segment| (|DoubleFloat|))) "\\spad{plotPolar(f,theta,seg)} plots the graph of \\spad{r = f(theta)} as \\spad{theta} ranges over an interval")) (|plot| (((|Plot|) |#1| |#1| (|Symbol|) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,g,t,seg)} plots the graph of \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over an interval.") (((|Plot|) |#1| (|Symbol|) (|Segment| (|DoubleFloat|))) "\\spad{plot(fcn,x,seg)} plots the graph of \\spad{y = f(x)} on a interval"))) NIL NIL -(-927) +(-928) ((|constructor| (NIL "Plot3D supports parametric plots defined over a real number system. A real number system is a model for the real numbers and as such may be an approximation. For example,{} floating point numbers and infinite continued fractions are real number systems. The facilities at this point are limited to 3-dimensional parametric plots.")) (|debug3D| (((|Boolean|) (|Boolean|)) "\\spad{debug3D(true)} turns debug mode on; debug3D(\\spad{false}) turns debug mode off.")) (|numFunEvals3D| (((|Integer|)) "\\spad{numFunEvals3D()} returns the number of points computed.")) (|setAdaptive3D| (((|Boolean|) (|Boolean|)) "\\spad{setAdaptive3D(true)} turns adaptive plotting on; setAdaptive3D(\\spad{false}) turns adaptive plotting off.")) (|adaptive3D?| (((|Boolean|)) "\\spad{adaptive3D?()} determines whether plotting be done adaptively.")) (|setScreenResolution3D| (((|Integer|) (|Integer|)) "\\spad{setScreenResolution3D(i)} sets the screen resolution for a 3d graph to \\spad{i}.")) (|screenResolution3D| (((|Integer|)) "\\spad{screenResolution3D()} returns the screen resolution for a 3d graph.")) (|setMaxPoints3D| (((|Integer|) (|Integer|)) "\\spad{setMaxPoints3D(i)} sets the maximum number of points in a plot to \\spad{i}.")) (|maxPoints3D| (((|Integer|)) "\\spad{maxPoints3D()} returns the maximum number of points in a plot.")) (|setMinPoints3D| (((|Integer|) (|Integer|)) "\\spad{setMinPoints3D(i)} sets the minimum number of points in a plot to \\spad{i}.")) (|minPoints3D| (((|Integer|)) "\\spad{minPoints3D()} returns the minimum number of points in a plot.")) (|tValues| (((|List| (|List| (|DoubleFloat|))) $) "\\spad{tValues(p)} returns a list of lists of the values of the parameter for which a point is computed,{} one list for each curve in the plot \\spad{p}.")) (|tRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{tRange(p)} returns the range of the parameter in a parametric plot \\spad{p}.")) (|refine| (($ $) "\\spad{refine(x)} \\undocumented") (($ $ (|Segment| (|DoubleFloat|))) "\\spad{refine(x,r)} \\undocumented")) (|zoom| (($ $ (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{zoom(x,r,s,t)} \\undocumented")) (|plot| (($ $ (|Segment| (|DoubleFloat|))) "\\spad{plot(x,r)} \\undocumented") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f1,f2,f3,f4,x,y,z,w)} \\undocumented") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,g,h,a..b)} plots {/emx = \\spad{f}(\\spad{t}),{} \\spad{y} = \\spad{g}(\\spad{t}),{} \\spad{z} = \\spad{h}(\\spad{t})} as \\spad{t} ranges over {/em[a,{}\\spad{b}]}.")) (|pointPlot| (($ (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{pointPlot(f,x,y,z,w)} \\undocumented") (($ (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{pointPlot(f,g,h,a..b)} plots {/emx = \\spad{f}(\\spad{t}),{} \\spad{y} = \\spad{g}(\\spad{t}),{} \\spad{z} = \\spad{h}(\\spad{t})} as \\spad{t} ranges over {/em[a,{}\\spad{b}]}."))) NIL NIL -(-928) +(-929) ((|constructor| (NIL "The Plot domain supports plotting of functions defined over a real number system. A real number system is a model for the real numbers and as such may be an approximation. For example floating point numbers and infinite continued fractions. The facilities at this point are limited to 2-dimensional plots or either a single function or a parametric function.")) (|debug| (((|Boolean|) (|Boolean|)) "\\spad{debug(true)} turns debug mode on \\spad{debug(false)} turns debug mode off")) (|numFunEvals| (((|Integer|)) "\\spad{numFunEvals()} returns the number of points computed")) (|setAdaptive| (((|Boolean|) (|Boolean|)) "\\spad{setAdaptive(true)} turns adaptive plotting on \\spad{setAdaptive(false)} turns adaptive plotting off")) (|adaptive?| (((|Boolean|)) "\\spad{adaptive?()} determines whether plotting be done adaptively")) (|setScreenResolution| (((|Integer|) (|Integer|)) "\\spad{setScreenResolution(i)} sets the screen resolution to \\spad{i}")) (|screenResolution| (((|Integer|)) "\\spad{screenResolution()} returns the screen resolution")) (|setMaxPoints| (((|Integer|) (|Integer|)) "\\spad{setMaxPoints(i)} sets the maximum number of points in a plot to \\spad{i}")) (|maxPoints| (((|Integer|)) "\\spad{maxPoints()} returns the maximum number of points in a plot")) (|setMinPoints| (((|Integer|) (|Integer|)) "\\spad{setMinPoints(i)} sets the minimum number of points in a plot to \\spad{i}")) (|minPoints| (((|Integer|)) "\\spad{minPoints()} returns the minimum number of points in a plot")) (|tRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{tRange(p)} returns the range of the parameter in a parametric plot \\spad{p}")) (|refine| (($ $) "\\spad{refine(p)} performs a refinement on the plot \\spad{p}") (($ $ (|Segment| (|DoubleFloat|))) "\\spad{refine(x,r)} \\undocumented")) (|zoom| (($ $ (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{zoom(x,r,s)} \\undocumented") (($ $ (|Segment| (|DoubleFloat|))) "\\spad{zoom(x,r)} \\undocumented")) (|parametric?| (((|Boolean|) $) "\\spad{parametric? determines} whether it is a parametric plot?")) (|plotPolar| (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) "\\spad{plotPolar(f)} plots the polar curve \\spad{r = f(theta)} as theta ranges over the interval \\spad{[0,2*\\%pi]}; this is the same as the parametric curve \\spad{x = f(t) * cos(t)},{} \\spad{y = f(t) * sin(t)}.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plotPolar(f,a..b)} plots the polar curve \\spad{r = f(theta)} as theta ranges over the interval \\spad{[a,b]}; this is the same as the parametric curve \\spad{x = f(t) * cos(t)},{} \\spad{y = f(t) * sin(t)}.")) (|pointPlot| (($ (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{pointPlot(t +-> (f(t),g(t)),a..b,c..d,e..f)} plots the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over the interval \\spad{[a,b]}; \\spad{x}-range of \\spad{[c,d]} and \\spad{y}-range of \\spad{[e,f]} are noted in Plot object.") (($ (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{pointPlot(t +-> (f(t),g(t)),a..b)} plots the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over the interval \\spad{[a,b]}.")) (|plot| (($ $ (|Segment| (|DoubleFloat|))) "\\spad{plot(x,r)} \\undocumented") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,g,a..b,c..d,e..f)} plots the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over the interval \\spad{[a,b]}; \\spad{x}-range of \\spad{[c,d]} and \\spad{y}-range of \\spad{[e,f]} are noted in Plot object.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,g,a..b)} plots the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over the interval \\spad{[a,b]}.") (($ (|List| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot([f1,...,fm],a..b,c..d)} plots the functions \\spad{y = f1(x)},{}...,{} \\spad{y = fm(x)} on the interval \\spad{a..b}; \\spad{y}-range of \\spad{[c,d]} is noted in Plot object.") (($ (|List| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|DoubleFloat|))) "\\spad{plot([f1,...,fm],a..b)} plots the functions \\spad{y = f1(x)},{}...,{} \\spad{y = fm(x)} on the interval \\spad{a..b}.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,a..b,c..d)} plots the function \\spad{f(x)} on the interval \\spad{[a,b]}; \\spad{y}-range of \\spad{[c,d]} is noted in Plot object.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,a..b)} plots the function \\spad{f(x)} on the interval \\spad{[a,b]}."))) NIL NIL -(-929) +(-930) ((|constructor| (NIL "This package exports plotting tools")) (|calcRanges| (((|List| (|Segment| (|DoubleFloat|))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{calcRanges(l)} \\undocumented"))) NIL NIL -(-930 R -3867) +(-931 R -3879) ((|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 -(-931) +(-932) ((|constructor| (NIL "Attaching assertions to symbols for pattern matching. Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|multiple| (((|Expression| (|Integer|)) (|Symbol|)) "\\spad{multiple(x)} tells the pattern matcher that \\spad{x} should preferably match a multi-term quantity in a sum or product. For matching on lists,{} multiple(\\spad{x}) tells the pattern matcher that \\spad{x} should match a list instead of an element of a list.")) (|optional| (((|Expression| (|Integer|)) (|Symbol|)) "\\spad{optional(x)} tells the pattern matcher that \\spad{x} can match an identity (0 in a sum,{} 1 in a product or exponentiation)..")) (|constant| (((|Expression| (|Integer|)) (|Symbol|)) "\\spad{constant(x)} tells the pattern matcher that \\spad{x} should match only the symbol \\spad{'x} and no other quantity.")) (|assert| (((|Expression| (|Integer|)) (|Symbol|) (|Identifier|)) "\\spad{assert(x, s)} makes the assertion \\spad{s} about \\spad{x}."))) NIL NIL -(-932 S A B) +(-933 S A B) ((|constructor| (NIL "This packages provides tools for matching recursively in type towers.")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#2| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(expr, pat, res)} matches the pattern \\spad{pat} to the expression \\spad{expr}; res contains the variables of \\spad{pat} which are already matched and their matches. Note: this function handles type towers by changing the predicates and calling the matching function provided by \\spad{A}.")) (|fixPredicate| (((|Mapping| (|Boolean|) |#2|) (|Mapping| (|Boolean|) |#3|)) "\\spad{fixPredicate(f)} returns \\spad{g} defined by \\spad{g}(a) = \\spad{f}(a::B)."))) NIL NIL -(-933 S R -3867) +(-934 S R -3879) ((|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 -(-934 I) +(-935 I) ((|constructor| (NIL "This package provides pattern matching functions on integers.")) (|patternMatch| (((|PatternMatchResult| (|Integer|) |#1|) |#1| (|Pattern| (|Integer|)) (|PatternMatchResult| (|Integer|) |#1|)) "\\spad{patternMatch(n, pat, res)} matches the pattern \\spad{pat} to the integer \\spad{n}; res contains the variables of \\spad{pat} which are already matched and their matches."))) NIL NIL -(-935 S E) +(-936 S E) ((|constructor| (NIL "This package provides pattern matching functions on kernels.")) (|patternMatch| (((|PatternMatchResult| |#1| |#2|) (|Kernel| |#2|) (|Pattern| |#1|) (|PatternMatchResult| |#1| |#2|)) "\\spad{patternMatch(f(e1,...,en), pat, res)} matches the pattern \\spad{pat} to \\spad{f(e1,...,en)}; res contains the variables of \\spad{pat} which are already matched and their matches."))) NIL NIL -(-936 S R L) +(-937 S R L) ((|constructor| (NIL "This package provides pattern matching functions on lists.")) (|patternMatch| (((|PatternMatchListResult| |#1| |#2| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchListResult| |#1| |#2| |#3|)) "\\spad{patternMatch(l, pat, res)} matches the pattern \\spad{pat} to the list \\spad{l}; res contains the variables of \\spad{pat} which are already matched and their matches."))) NIL NIL -(-937 S E V R P) +(-938 S E V R P) ((|constructor| (NIL "This package provides pattern matching functions on polynomials.")) (|patternMatch| (((|PatternMatchResult| |#1| |#5|) |#5| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|)) "\\spad{patternMatch(p, pat, res)} matches the pattern \\spad{pat} to the polynomial \\spad{p}; res contains the variables of \\spad{pat} which are already matched and their matches.") (((|PatternMatchResult| |#1| |#5|) |#5| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|) (|Mapping| (|PatternMatchResult| |#1| |#5|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|))) "\\spad{patternMatch(p, pat, res, vmatch)} matches the pattern \\spad{pat} to the polynomial \\spad{p}. \\spad{res} contains the variables of \\spad{pat} which are already matched and their matches; vmatch is the matching function to use on the variables."))) NIL -((|HasCategory| |#3| (LIST (QUOTE -887) (|devaluate| |#1|)))) -(-938 R -3867 -2636) +((|HasCategory| |#3| (LIST (QUOTE -888) (|devaluate| |#1|)))) +(-939 R -3879 -2637) ((|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 -(-939 -2636) +(-940 -2637) ((|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 -(-940 S R Q) +(-941 S R Q) ((|constructor| (NIL "This package provides pattern matching functions on quotients.")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(a/b, pat, res)} matches the pattern \\spad{pat} to the quotient \\spad{a/b}; res contains the variables of \\spad{pat} which are already matched and their matches."))) NIL NIL -(-941 S) +(-942 S) ((|constructor| (NIL "This package provides pattern matching functions on symbols.")) (|patternMatch| (((|PatternMatchResult| |#1| (|Symbol|)) (|Symbol|) (|Pattern| |#1|) (|PatternMatchResult| |#1| (|Symbol|))) "\\spad{patternMatch(expr, pat, res)} matches the pattern \\spad{pat} to the expression \\spad{expr}; res contains the variables of \\spad{pat} which are already matched and their matches (necessary for recursion)."))) NIL NIL -(-942 S R P) +(-943 S R P) ((|constructor| (NIL "This package provides tools for the pattern matcher.")) (|patternMatchTimes| (((|PatternMatchResult| |#1| |#3|) (|List| |#3|) (|List| (|Pattern| |#1|)) (|PatternMatchResult| |#1| |#3|) (|Mapping| (|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|))) "\\spad{patternMatchTimes(lsubj, lpat, res, match)} matches the product of patterns \\spad{reduce(*,lpat)} to the product of subjects \\spad{reduce(*,lsubj)}; \\spad{r} contains the previous matches and match is a pattern-matching function on \\spad{P}.")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) (|List| |#3|) (|List| (|Pattern| |#1|)) (|Mapping| |#3| (|List| |#3|)) (|PatternMatchResult| |#1| |#3|) (|Mapping| (|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|))) "\\spad{patternMatch(lsubj, lpat, op, res, match)} matches the list of patterns \\spad{lpat} to the list of subjects \\spad{lsubj},{} allowing for commutativity; \\spad{op} is the operator such that \\spad{op}(\\spad{lpat}) should match \\spad{op}(\\spad{lsubj}) at the end,{} \\spad{r} contains the previous matches,{} and match is a pattern-matching function on \\spad{P}."))) NIL NIL -(-943) +(-944) ((|constructor| (NIL "This package provides various polynomial number theoretic functions over the integers.")) (|legendre| (((|SparseUnivariatePolynomial| (|Fraction| (|Integer|))) (|Integer|)) "\\spad{legendre(n)} returns the \\spad{n}th Legendre polynomial \\spad{P[n](x)}. Note: Legendre polynomials,{} denoted \\spad{P[n](x)},{} are computed from the two term recurrence. The generating function is: \\spad{1/sqrt(1-2*t*x+t**2) = sum(P[n](x)*t**n, n=0..infinity)}.")) (|laguerre| (((|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{laguerre(n)} returns the \\spad{n}th Laguerre polynomial \\spad{L[n](x)}. Note: Laguerre polynomials,{} denoted \\spad{L[n](x)},{} are computed from the two term recurrence. The generating function is: \\spad{exp(x*t/(t-1))/(1-t) = sum(L[n](x)*t**n/n!, n=0..infinity)}.")) (|hermite| (((|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{hermite(n)} returns the \\spad{n}th Hermite polynomial \\spad{H[n](x)}. Note: Hermite polynomials,{} denoted \\spad{H[n](x)},{} are computed from the two term recurrence. The generating function is: \\spad{exp(2*t*x-t**2) = sum(H[n](x)*t**n/n!, n=0..infinity)}.")) (|fixedDivisor| (((|Integer|) (|SparseUnivariatePolynomial| (|Integer|))) "\\spad{fixedDivisor(a)} for \\spad{a(x)} in \\spad{Z[x]} is the largest integer \\spad{f} such that \\spad{f} divides \\spad{a(x=k)} for all integers \\spad{k}. Note: fixed divisor of \\spad{a} is \\spad{reduce(gcd,[a(x=k) for k in 0..degree(a)])}.")) (|euler| (((|SparseUnivariatePolynomial| (|Fraction| (|Integer|))) (|Integer|)) "\\spad{euler(n)} returns the \\spad{n}th Euler polynomial \\spad{E[n](x)}. Note: Euler polynomials denoted \\spad{E(n,x)} computed by solving the differential equation \\spad{differentiate(E(n,x),x) = n E(n-1,x)} where \\spad{E(0,x) = 1} and initial condition comes from \\spad{E(n) = 2**n E(n,1/2)}.")) (|cyclotomic| (((|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{cyclotomic(n)} returns the \\spad{n}th cyclotomic polynomial \\spad{phi[n](x)}. Note: \\spad{phi[n](x)} is the factor of \\spad{x**n - 1} whose roots are the primitive \\spad{n}th roots of unity.")) (|chebyshevU| (((|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{chebyshevU(n)} returns the \\spad{n}th Chebyshev polynomial \\spad{U[n](x)}. Note: Chebyshev polynomials of the second kind,{} denoted \\spad{U[n](x)},{} computed from the two term recurrence. The generating function \\spad{1/(1-2*t*x+t**2) = sum(T[n](x)*t**n, n=0..infinity)}.")) (|chebyshevT| (((|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{chebyshevT(n)} returns the \\spad{n}th Chebyshev polynomial \\spad{T[n](x)}. Note: Chebyshev polynomials of the first kind,{} denoted \\spad{T[n](x)},{} computed from the two term recurrence. The generating function \\spad{(1-t*x)/(1-2*t*x+t**2) = sum(T[n](x)*t**n, n=0..infinity)}.")) (|bernoulli| (((|SparseUnivariatePolynomial| (|Fraction| (|Integer|))) (|Integer|)) "\\spad{bernoulli(n)} returns the \\spad{n}th Bernoulli polynomial \\spad{B[n](x)}. Note: Bernoulli polynomials denoted \\spad{B(n,x)} computed by solving the differential equation \\spad{differentiate(B(n,x),x) = n B(n-1,x)} where \\spad{B(0,x) = 1} and initial condition comes from \\spad{B(n) = B(n,0)}."))) NIL NIL -(-944 R) +(-945 R) ((|constructor| (NIL "This domain implements points in coordinate space"))) -((-4418 . T) (-4417 . T)) -((-2797 (-12 (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1101))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-1101))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539)))) (-2797 (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-1101)))) (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| (-567) (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-1101))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-727))) (|HasCategory| |#1| (QUOTE (-1050))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (QUOTE (-1050)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863)))) (-12 (|HasCategory| |#1| (QUOTE (-1101))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) -(-945 |lv| R) +((-4419 . T) (-4418 . T)) +((-2800 (-12 (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2800 (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539)))) (-2800 (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-1102)))) (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| (-567) (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-727))) (|HasCategory| |#1| (QUOTE (-1051))) (-12 (|HasCategory| |#1| (QUOTE (-1004))) (|HasCategory| |#1| (QUOTE (-1051)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863)))) (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) +(-946 |lv| R) ((|constructor| (NIL "Package with the conversion functions among different kind of polynomials")) (|pToDmp| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|Polynomial| |#2|)) "\\spad{pToDmp(p)} converts \\spad{p} from a \\spadtype{POLY} to a \\spadtype{DMP}.")) (|dmpToP| (((|Polynomial| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{dmpToP(p)} converts \\spad{p} from a \\spadtype{DMP} to a \\spadtype{POLY}.")) (|hdmpToP| (((|Polynomial| |#2|) (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{hdmpToP(p)} converts \\spad{p} from a \\spadtype{HDMP} to a \\spadtype{POLY}.")) (|pToHdmp| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|Polynomial| |#2|)) "\\spad{pToHdmp(p)} converts \\spad{p} from a \\spadtype{POLY} to a \\spadtype{HDMP}.")) (|hdmpToDmp| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{hdmpToDmp(p)} converts \\spad{p} from a \\spadtype{HDMP} to a \\spadtype{DMP}.")) (|dmpToHdmp| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{dmpToHdmp(p)} converts \\spad{p} from a \\spadtype{DMP} to a \\spadtype{HDMP}."))) NIL NIL -(-946 |TheField| |ThePols|) +(-947 |TheField| |ThePols|) ((|constructor| (NIL "\\axiomType{RealPolynomialUtilitiesPackage} provides common functions used by interval coding.")) (|lazyVariations| (((|NonNegativeInteger|) (|List| |#1|) (|Integer|) (|Integer|)) "\\axiom{lazyVariations(\\spad{l},{}\\spad{s1},{}\\spad{sn})} is the number of sign variations in the list of non null numbers [s1::l]\\spad{@sn},{}")) (|sturmVariationsOf| (((|NonNegativeInteger|) (|List| |#1|)) "\\axiom{sturmVariationsOf(\\spad{l})} is the number of sign variations in the list of numbers \\spad{l},{} note that the first term counts as a sign")) (|boundOfCauchy| ((|#1| |#2|) "\\axiom{boundOfCauchy(\\spad{p})} bounds the roots of \\spad{p}")) (|sturmSequence| (((|List| |#2|) |#2|) "\\axiom{sturmSequence(\\spad{p}) = sylvesterSequence(\\spad{p},{}\\spad{p'})}")) (|sylvesterSequence| (((|List| |#2|) |#2| |#2|) "\\axiom{sylvesterSequence(\\spad{p},{}\\spad{q})} is the negated remainder sequence of \\spad{p} and \\spad{q} divided by the last computed term"))) NIL ((|HasCategory| |#1| (QUOTE (-849)))) -(-947 R S) +(-948 R S) ((|constructor| (NIL "\\indented{2}{This package takes a mapping between coefficient rings,{} and lifts} it to a mapping between polynomials over those rings.")) (|map| (((|Polynomial| |#2|) (|Mapping| |#2| |#1|) (|Polynomial| |#1|)) "\\spad{map(f, p)} produces a new polynomial as a result of applying the function \\spad{f} to every coefficient of the polynomial \\spad{p}."))) NIL NIL -(-948 |x| R) +(-949 |x| R) ((|constructor| (NIL "This package is primarily to help the interpreter do coercions. It allows you to view a polynomial as a univariate polynomial in one of its variables with coefficients which are again a polynomial in all the other variables.")) (|univariate| (((|UnivariatePolynomial| |#1| (|Polynomial| |#2|)) (|Polynomial| |#2|) (|Variable| |#1|)) "\\spad{univariate(p, x)} converts the polynomial \\spad{p} to a one of type \\spad{UnivariatePolynomial(x,Polynomial(R))},{} ie. as a member of \\spad{R[...][x]}."))) NIL NIL -(-949 S R E |VarSet|) +(-950 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 (-910))) (|HasAttribute| |#2| (QUOTE -4415)) (|HasCategory| |#2| (QUOTE (-455))) (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#4| (LIST (QUOTE -887) (QUOTE (-381)))) (|HasCategory| |#2| (LIST (QUOTE -887) (QUOTE (-381)))) (|HasCategory| |#4| (LIST (QUOTE -887) (QUOTE (-567)))) (|HasCategory| |#2| (LIST (QUOTE -887) (QUOTE (-567)))) (|HasCategory| |#4| (LIST (QUOTE -615) (LIST (QUOTE -893) (QUOTE (-381))))) (|HasCategory| |#2| (LIST (QUOTE -615) (LIST (QUOTE -893) (QUOTE (-381))))) (|HasCategory| |#4| (LIST (QUOTE -615) (LIST (QUOTE -893) (QUOTE (-567))))) (|HasCategory| |#2| (LIST (QUOTE -615) (LIST (QUOTE -893) (QUOTE (-567))))) (|HasCategory| |#4| (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| |#2| (LIST (QUOTE -615) (QUOTE (-539))))) -(-950 R E |VarSet|) +((|HasCategory| |#2| (QUOTE (-911))) (|HasAttribute| |#2| (QUOTE -4416)) (|HasCategory| |#2| (QUOTE (-455))) (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#4| (LIST (QUOTE -888) (QUOTE (-381)))) (|HasCategory| |#2| (LIST (QUOTE -888) (QUOTE (-381)))) (|HasCategory| |#4| (LIST (QUOTE -888) (QUOTE (-567)))) (|HasCategory| |#2| (LIST (QUOTE -888) (QUOTE (-567)))) (|HasCategory| |#4| (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-381))))) (|HasCategory| |#2| (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-381))))) (|HasCategory| |#4| (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567))))) (|HasCategory| |#2| (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567))))) (|HasCategory| |#4| (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| |#2| (LIST (QUOTE -615) (QUOTE (-539))))) +(-951 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| (-559)) (-4415 |has| |#1| (-6 -4415)) (-4412 . T) (-4411 . T) (-4414 . T)) +(((-4420 "*") |has| |#1| (-172)) (-4411 |has| |#1| (-559)) (-4416 |has| |#1| (-6 -4416)) (-4413 . T) (-4412 . T) (-4415 . T)) NIL -(-951 E V R P -3867) +(-952 E V R P -3879) ((|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 -(-952 E |Vars| R P S) +(-953 E |Vars| R P S) ((|constructor| (NIL "This package provides a very general map function,{} which given a set \\spad{S} and polynomials over \\spad{R} with maps from the variables into \\spad{S} and the coefficients into \\spad{S},{} maps polynomials into \\spad{S}. \\spad{S} is assumed to support \\spad{+},{} \\spad{*} and \\spad{**}.")) (|map| ((|#5| (|Mapping| |#5| |#2|) (|Mapping| |#5| |#3|) |#4|) "\\spad{map(varmap, coefmap, p)} takes a \\spad{varmap},{} a mapping from the variables of polynomial \\spad{p} into \\spad{S},{} \\spad{coefmap},{} a mapping from coefficients of \\spad{p} into \\spad{S},{} and \\spad{p},{} and produces a member of \\spad{S} using the corresponding arithmetic. in \\spad{S}"))) NIL NIL -(-953 R) +(-954 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| (-559)) (-4415 |has| |#1| (-6 -4415)) (-4412 . T) (-4411 . T) (-4414 . T)) -((|HasCategory| |#1| (QUOTE (-910))) (-2797 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-455))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-910)))) (-2797 (|HasCategory| |#1| (QUOTE (-455))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-910)))) (-2797 (|HasCategory| |#1| (QUOTE (-455))) (|HasCategory| |#1| (QUOTE (-910)))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-172))) (-2797 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-559)))) (-12 (|HasCategory| (-1177) (LIST (QUOTE -887) (QUOTE (-381)))) (|HasCategory| |#1| (LIST (QUOTE -887) (QUOTE (-381))))) (-12 (|HasCategory| (-1177) (LIST (QUOTE -887) (QUOTE (-567)))) (|HasCategory| |#1| (LIST (QUOTE -887) (QUOTE (-567))))) (-12 (|HasCategory| (-1177) (LIST (QUOTE -615) (LIST (QUOTE -893) (QUOTE (-381))))) (|HasCategory| |#1| (LIST (QUOTE -615) (LIST (QUOTE -893) (QUOTE (-381)))))) (-12 (|HasCategory| (-1177) (LIST (QUOTE -615) (LIST (QUOTE -893) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -615) (LIST (QUOTE -893) (QUOTE (-567)))))) (-12 (|HasCategory| (-1177) (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539))))) (|HasCategory| |#1| (LIST (QUOTE -640) (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1039) (QUOTE (-567)))) (-2797 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1039) (LIST (QUOTE -410) (QUOTE (-567)))))) (|HasCategory| |#1| (LIST (QUOTE -1039) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (QUOTE (-365))) (|HasAttribute| |#1| (QUOTE -4415)) (|HasCategory| |#1| (QUOTE (-455))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-910)))) (-2797 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-910)))) (|HasCategory| |#1| (QUOTE (-145))))) -(-954 E V R P -3867) +(((-4420 "*") |has| |#1| (-172)) (-4411 |has| |#1| (-559)) (-4416 |has| |#1| (-6 -4416)) (-4413 . T) (-4412 . T) (-4415 . T)) +((|HasCategory| |#1| (QUOTE (-911))) (-2800 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-455))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-911)))) (-2800 (|HasCategory| |#1| (QUOTE (-455))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-911)))) (-2800 (|HasCategory| |#1| (QUOTE (-455))) (|HasCategory| |#1| (QUOTE (-911)))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-172))) (-2800 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-559)))) (-12 (|HasCategory| (-1178) (LIST (QUOTE -888) (QUOTE (-381)))) (|HasCategory| |#1| (LIST (QUOTE -888) (QUOTE (-381))))) (-12 (|HasCategory| (-1178) (LIST (QUOTE -888) (QUOTE (-567)))) (|HasCategory| |#1| (LIST (QUOTE -888) (QUOTE (-567))))) (-12 (|HasCategory| (-1178) (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-381))))) (|HasCategory| |#1| (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-381)))))) (-12 (|HasCategory| (-1178) (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567)))))) (-12 (|HasCategory| (-1178) (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539))))) (|HasCategory| |#1| (LIST (QUOTE -640) (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (QUOTE (-567)))) (-2800 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567)))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (QUOTE (-365))) (|HasAttribute| |#1| (QUOTE -4416)) (|HasCategory| |#1| (QUOTE (-455))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-911)))) (-2800 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-911)))) (|HasCategory| |#1| (QUOTE (-145))))) +(-955 E V R P -3879) ((|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| $) "\\spad{numer(x)} \\undocumented"))) NIL ((|HasCategory| |#3| (QUOTE (-455)))) -(-955) +(-956) ((|constructor| (NIL "This domain represents network port numbers (notable \\spad{TCP} and UDP).")) (|port| (($ (|SingleInteger|)) "\\spad{port(n)} constructs a PortNumber from the integer \\spad{`n'}."))) NIL NIL -(-956) +(-957) ((|constructor| (NIL "PlottablePlaneCurveCategory is the category of curves in the plane which may be plotted via the graphics facilities. Functions are provided for obtaining lists of lists of points,{} representing the branches of the curve,{} and for determining the ranges of the \\spad{x}-coordinates and \\spad{y}-coordinates of the points on the curve.")) (|yRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{yRange(c)} returns the range of the \\spad{y}-coordinates of the points on the curve \\spad{c}.")) (|xRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{xRange(c)} returns the range of the \\spad{x}-coordinates of the points on the curve \\spad{c}.")) (|listBranches| (((|List| (|List| (|Point| (|DoubleFloat|)))) $) "\\spad{listBranches(c)} returns a list of lists of points,{} representing the branches of the curve \\spad{c}."))) NIL NIL -(-957 R L) +(-958 R L) ((|constructor| (NIL "\\spadtype{PrecomputedAssociatedEquations} stores some generic precomputations which speed up the computations of the associated equations needed for factoring operators.")) (|firstUncouplingMatrix| (((|Union| (|Matrix| |#1|) "failed") |#2| (|PositiveInteger|)) "\\spad{firstUncouplingMatrix(op, m)} returns the matrix A such that \\spad{A w = (W',W'',...,W^N)} in the corresponding associated equations for right-factors of order \\spad{m} of \\spad{op}. Returns \"failed\" if the matrix A has not been precomputed for the particular combination \\spad{degree(L), m}."))) NIL NIL -(-958 A B) +(-959 A B) ((|constructor| (NIL "\\indented{1}{This package provides tools for operating on primitive arrays} with unary and binary functions involving different underlying types")) (|map| (((|PrimitiveArray| |#2|) (|Mapping| |#2| |#1|) (|PrimitiveArray| |#1|)) "\\spad{map(f,a)} applies function \\spad{f} to each member of primitive array \\spad{a} resulting in a new primitive array over a possibly different underlying domain.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|PrimitiveArray| |#1|) |#2|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the primitive array \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,[1,2,3],0)} does \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as the identity element for the function \\spad{f}.")) (|scan| (((|PrimitiveArray| |#2|) (|Mapping| |#2| |#1| |#2|) (|PrimitiveArray| |#1|) |#2|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-arrays \\spad{x} of primitive array \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad{[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}."))) NIL NIL -(-959 S) +(-960 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)) -((-2797 (-12 (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1101))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-1101))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539)))) (-2797 (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-1101)))) (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| (-567) (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-1101))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863)))) (-12 (|HasCategory| |#1| (QUOTE (-1101))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) -(-960) +((-4419 . T) (-4418 . T)) +((-2800 (-12 (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2800 (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539)))) (-2800 (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-1102)))) (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| (-567) (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863)))) (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) +(-961) ((|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 -(-961 -3867) +(-962 -3879) ((|constructor| (NIL "PrimitiveElement provides functions to compute primitive elements in algebraic extensions.")) (|primitiveElement| (((|Record| (|:| |coef| (|List| (|Integer|))) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#1|))) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|)) (|Symbol|)) "\\spad{primitiveElement([p1,...,pn], [a1,...,an], a)} returns \\spad{[[c1,...,cn], [q1,...,qn], q]} such that then \\spad{k(a1,...,an) = k(a)},{} where \\spad{a = a1 c1 + ... + an cn},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. The \\spad{pi}\\spad{'s} are the defining polynomials for the \\spad{ai}\\spad{'s}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}.") (((|Record| (|:| |coef| (|List| (|Integer|))) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#1|))) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{primitiveElement([p1,...,pn], [a1,...,an])} returns \\spad{[[c1,...,cn], [q1,...,qn], q]} such that then \\spad{k(a1,...,an) = k(a)},{} where \\spad{a = a1 c1 + ... + an cn},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. The \\spad{pi}\\spad{'s} are the defining polynomials for the \\spad{ai}\\spad{'s}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}.") (((|Record| (|:| |coef1| (|Integer|)) (|:| |coef2| (|Integer|)) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|Polynomial| |#1|) (|Symbol|) (|Polynomial| |#1|) (|Symbol|)) "\\spad{primitiveElement(p1, a1, p2, a2)} returns \\spad{[c1, c2, q]} such that \\spad{k(a1, a2) = k(a)} where \\spad{a = c1 a1 + c2 a2, and q(a) = 0}. The \\spad{pi}\\spad{'s} are the defining polynomials for the \\spad{ai}\\spad{'s}. The \\spad{p2} may involve \\spad{a1},{} but \\spad{p1} must not involve a2. This operation uses \\spadfun{resultant}."))) NIL NIL -(-962 I) +(-963 I) ((|constructor| (NIL "The \\spadtype{IntegerPrimesPackage} implements a modification of Rabin\\spad{'s} probabilistic primality test and the utility functions \\spadfun{nextPrime},{} \\spadfun{prevPrime} and \\spadfun{primes}.")) (|primes| (((|List| |#1|) |#1| |#1|) "\\spad{primes(a,b)} returns a list of all primes \\spad{p} with \\spad{a <= p <= b}")) (|prevPrime| ((|#1| |#1|) "\\spad{prevPrime(n)} returns the largest prime strictly smaller than \\spad{n}")) (|nextPrime| ((|#1| |#1|) "\\spad{nextPrime(n)} returns the smallest prime strictly larger than \\spad{n}")) (|prime?| (((|Boolean|) |#1|) "\\spad{prime?(n)} returns \\spad{true} if \\spad{n} is prime and \\spad{false} if not. The algorithm used is Rabin\\spad{'s} probabilistic primality test (reference: Knuth Volume 2 Semi Numerical Algorithms). If \\spad{prime? n} returns \\spad{false},{} \\spad{n} is proven composite. If \\spad{prime? n} returns \\spad{true},{} prime? may be in error however,{} the probability of error is very low. and is zero below 25*10**9 (due to a result of Pomerance et al),{} below 10**12 and 10**13 due to results of Pinch,{} and below 341550071728321 due to a result of Jaeschke. Specifically,{} this implementation does at least 10 pseudo prime tests and so the probability of error is \\spad{< 4**(-10)}. The running time of this method is cubic in the length of the input \\spad{n},{} that is \\spad{O( (log n)**3 )},{} for n<10**20. beyond that,{} the algorithm is quartic,{} \\spad{O( (log n)**4 )}. Two improvements due to Davenport have been incorporated which catches some trivial strong pseudo-primes,{} such as [Jaeschke,{} 1991] 1377161253229053 * 413148375987157,{} which the original algorithm regards as prime"))) NIL NIL -(-963) +(-964) ((|constructor| (NIL "PrintPackage provides a print function for output forms.")) (|print| (((|Void|) (|OutputForm|)) "\\spad{print(o)} writes the output form \\spad{o} on standard output using the two-dimensional formatter."))) NIL NIL -(-964 R E) +(-965 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| (-559)) (-4415 |has| |#1| (-6 -4415)) (-4411 . T) (-4412 . T) (-4414 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (QUOTE (-559))) (-2797 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-559)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-2797 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1039) (LIST (QUOTE -410) (QUOTE (-567)))))) (|HasCategory| |#1| (LIST (QUOTE -1039) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1039) (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-455))) (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#2| (QUOTE (-131)))) (|HasAttribute| |#1| (QUOTE -4415))) -(-965 A B) +(((-4420 "*") |has| |#1| (-172)) (-4411 |has| |#1| (-559)) (-4416 |has| |#1| (-6 -4416)) (-4412 . T) (-4413 . T) (-4415 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (QUOTE (-559))) (-2800 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-559)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-2800 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567)))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-455))) (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#2| (QUOTE (-131)))) (|HasAttribute| |#1| (QUOTE -4416))) +(-966 A B) ((|constructor| (NIL "This domain implements cartesian product")) (|selectsecond| ((|#2| $) "\\spad{selectsecond(x)} \\undocumented")) (|selectfirst| ((|#1| $) "\\spad{selectfirst(x)} \\undocumented")) 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(-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#2| (QUOTE (-851))))) +(-967) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. An `Property' is a pair of name and value.")) (|property| (($ (|Identifier|) (|SExpression|)) "\\spad{property(n,val)} constructs a property with name \\spad{`n'} and value `val'.")) (|value| (((|SExpression|) $) "\\spad{value(p)} returns value of property \\spad{p}")) (|name| (((|Identifier|) $) "\\spad{name(p)} returns the name of property \\spad{p}"))) NIL NIL -(-967 T$) +(-968 T$) ((|constructor| (NIL "This domain implements propositional formula build over a term domain,{} that itself belongs to PropositionalLogic")) (|isEquiv| (((|Maybe| (|Pair| $ $)) $) "\\spad{isEquiv f} returns a value \\spad{v} such that \\spad{v case Pair(\\%,\\%)} holds if the formula \\spad{f} is an equivalence formula.")) (|isImplies| (((|Maybe| (|Pair| $ $)) $) "\\spad{isImplies f} returns a value \\spad{v} such that \\spad{v case Pair(\\%,\\%)} holds if the formula \\spad{f} is an implication formula.")) (|isOr| (((|Maybe| (|Pair| $ $)) $) "\\spad{isOr f} returns a value \\spad{v} such that \\spad{v case Pair(\\%,\\%)} holds if the formula \\spad{f} is a disjunction formula.")) (|isAnd| (((|Maybe| (|Pair| $ $)) $) "\\spad{isAnd f} returns a value \\spad{v} such that \\spad{v case Pair(\\%,\\%)} holds if the formula \\spad{f} is a conjunction formula.")) (|isNot| (((|Maybe| $) $) "\\spad{isNot f} returns a value \\spad{v} such that \\spad{v case \\%} holds if the formula \\spad{f} is a negation.")) (|isTerm| (((|Maybe| |#1|) $) "\\spad{isTerm f} returns a value \\spad{v} such that \\spad{v case T} holds if the formula \\spad{f} is a term."))) NIL NIL -(-968) +(-969) ((|constructor| (NIL "This category declares the connectives of Propositional Logic.")) (|equiv| (($ $ $) "\\spad{equiv(p,q)} returns the logical equivalence of \\spad{`p'},{} \\spad{`q'}.")) (|implies| (($ $ $) "\\spad{implies(p,q)} returns the logical implication of \\spad{`q'} by \\spad{`p'}.")) (|or| (($ $ $) "\\spad{p or q} returns the logical disjunction of \\spad{`p'},{} \\spad{`q'}.")) (|and| (($ $ $) "\\spad{p and q} returns the logical conjunction of \\spad{`p'},{} \\spad{`q'}.")) (|not| (($ $) "\\spad{not p} returns the logical negation of \\spad{`p'}.")) (|false| (($) "\\spad{false} is a logical constant.")) (|true| (($) "\\spad{true} is a logical constant."))) NIL NIL -(-969 S) +(-970 S) ((|constructor| (NIL "A priority queue is a bag of items from an ordered set where the item extracted is always the maximum element.")) (|merge!| (($ $ $) "\\spad{merge!(q,q1)} destructively changes priority queue \\spad{q} to include the values from priority queue \\spad{q1}.")) (|merge| (($ $ $) "\\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)) +((-4418 . T) (-4419 . T)) NIL -(-970 R |polR|) +(-971 R |polR|) ((|constructor| (NIL "This package contains some functions: \\axiomOpFrom{discriminant}{PseudoRemainderSequence},{} \\axiomOpFrom{resultant}{PseudoRemainderSequence},{} \\axiomOpFrom{subResultantGcd}{PseudoRemainderSequence},{} \\axiomOpFrom{chainSubResultants}{PseudoRemainderSequence},{} \\axiomOpFrom{degreeSubResultant}{PseudoRemainderSequence},{} \\axiomOpFrom{lastSubResultant}{PseudoRemainderSequence},{} \\axiomOpFrom{resultantEuclidean}{PseudoRemainderSequence},{} \\axiomOpFrom{subResultantGcdEuclidean}{PseudoRemainderSequence},{} \\axiomOpFrom{semiSubResultantGcdEuclidean1}{PseudoRemainderSequence},{} \\axiomOpFrom{semiSubResultantGcdEuclidean2}{PseudoRemainderSequence},{} etc. This procedures are coming from improvements of the subresultants algorithm. \\indented{2}{Version : 7} \\indented{2}{References : Lionel Ducos \"Optimizations of the subresultant algorithm\"} \\indented{2}{to appear in the Journal of Pure and Applied Algebra.} \\indented{2}{Author : Ducos Lionel \\axiom{Lionel.Ducos@mathlabo.univ-poitiers.\\spad{fr}}}")) (|semiResultantEuclideannaif| (((|Record| (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{resultantEuclidean_naif(\\spad{P},{}\\spad{Q})} returns the semi-extended resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}} computed by means of the naive algorithm.")) (|resultantEuclideannaif| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{resultantEuclidean_naif(\\spad{P},{}\\spad{Q})} returns the extended resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}} computed by means of the naive algorithm.")) (|resultantnaif| ((|#1| |#2| |#2|) "\\axiom{resultantEuclidean_naif(\\spad{P},{}\\spad{Q})} returns the resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}} computed by means of the naive algorithm.")) (|nextsousResultant2| ((|#2| |#2| |#2| |#2| |#1|) "\\axiom{nextsousResultant2(\\spad{P},{} \\spad{Q},{} \\spad{Z},{} \\spad{s})} returns the subresultant \\axiom{\\spad{S_}{\\spad{e}-1}} where \\axiom{\\spad{P} ~ \\spad{S_d},{} \\spad{Q} = \\spad{S_}{\\spad{d}-1},{} \\spad{Z} = S_e,{} \\spad{s} = \\spad{lc}(\\spad{S_d})}")) (|Lazard2| ((|#2| |#2| |#1| |#1| (|NonNegativeInteger|)) "\\axiom{Lazard2(\\spad{F},{} \\spad{x},{} \\spad{y},{} \\spad{n})} computes \\axiom{(x/y)\\spad{**}(\\spad{n}-1) * \\spad{F}}")) (|Lazard| ((|#1| |#1| |#1| (|NonNegativeInteger|)) "\\axiom{Lazard(\\spad{x},{} \\spad{y},{} \\spad{n})} computes \\axiom{x**n/y**(\\spad{n}-1)}")) (|divide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2|) "\\axiom{divide(\\spad{F},{}\\spad{G})} computes quotient and rest of the exact euclidean division of \\axiom{\\spad{F}} by \\axiom{\\spad{G}}.")) (|pseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2|) "\\axiom{pseudoDivide(\\spad{P},{}\\spad{Q})} computes the pseudoDivide of \\axiom{\\spad{P}} by \\axiom{\\spad{Q}}.")) (|exquo| (((|Vector| |#2|) (|Vector| |#2|) |#1|) "\\axiom{\\spad{v} exquo \\spad{r}} computes the exact quotient of \\axiom{\\spad{v}} by \\axiom{\\spad{r}}")) (* (((|Vector| |#2|) |#1| (|Vector| |#2|)) "\\axiom{\\spad{r} * \\spad{v}} computes the product of \\axiom{\\spad{r}} and \\axiom{\\spad{v}}")) (|gcd| ((|#2| |#2| |#2|) "\\axiom{\\spad{gcd}(\\spad{P},{} \\spad{Q})} returns the \\spad{gcd} of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiResultantReduitEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |resultantReduit| |#1|)) |#2| |#2|) "\\axiom{semiResultantReduitEuclidean(\\spad{P},{}\\spad{Q})} returns the \"reduce resultant\" and carries out the equality \\axiom{...\\spad{P} + coef2*Q = resultantReduit(\\spad{P},{}\\spad{Q})}.")) (|resultantReduitEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |resultantReduit| |#1|)) |#2| |#2|) "\\axiom{resultantReduitEuclidean(\\spad{P},{}\\spad{Q})} returns the \"reduce resultant\" and carries out the equality \\axiom{coef1*P + coef2*Q = resultantReduit(\\spad{P},{}\\spad{Q})}.")) (|resultantReduit| ((|#1| |#2| |#2|) "\\axiom{resultantReduit(\\spad{P},{}\\spad{Q})} returns the \"reduce resultant\" of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|schema| (((|List| (|NonNegativeInteger|)) |#2| |#2|) "\\axiom{schema(\\spad{P},{}\\spad{Q})} returns the list of degrees of non zero subresultants of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|chainSubResultants| (((|List| |#2|) |#2| |#2|) "\\axiom{chainSubResultants(\\spad{P},{} \\spad{Q})} computes the list of non zero subresultants of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiDiscriminantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |discriminant| |#1|)) |#2|) "\\axiom{discriminantEuclidean(\\spad{P})} carries out the equality \\axiom{...\\spad{P} + coef2 * \\spad{D}(\\spad{P}) = discriminant(\\spad{P})}. Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|discriminantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |discriminant| |#1|)) |#2|) "\\axiom{discriminantEuclidean(\\spad{P})} carries out the equality \\axiom{coef1 * \\spad{P} + coef2 * \\spad{D}(\\spad{P}) = discriminant(\\spad{P})}.")) (|discriminant| ((|#1| |#2|) "\\axiom{discriminant(\\spad{P},{} \\spad{Q})} returns the discriminant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiSubResultantGcdEuclidean1| (((|Record| (|:| |coef1| |#2|) (|:| |gcd| |#2|)) |#2| |#2|) "\\axiom{semiSubResultantGcdEuclidean1(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1*P + ? \\spad{Q} = \\spad{+/-} S_i(\\spad{P},{}\\spad{Q})} where the degree (not the indice) of the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} is the smaller as possible.")) (|semiSubResultantGcdEuclidean2| (((|Record| (|:| |coef2| |#2|) (|:| |gcd| |#2|)) |#2| |#2|) "\\axiom{semiSubResultantGcdEuclidean2(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{...\\spad{P} + coef2*Q = \\spad{+/-} S_i(\\spad{P},{}\\spad{Q})} where the degree (not the indice) of the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} is the smaller as possible. Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|subResultantGcdEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |gcd| |#2|)) |#2| |#2|) "\\axiom{subResultantGcdEuclidean(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1*P + coef2*Q = \\spad{+/-} S_i(\\spad{P},{}\\spad{Q})} where the degree (not the indice) of the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} is the smaller as possible.")) (|subResultantGcd| ((|#2| |#2| |#2|) "\\axiom{subResultantGcd(\\spad{P},{} \\spad{Q})} returns the \\spad{gcd} of two primitive polynomials \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiLastSubResultantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2|) "\\axiom{semiLastSubResultantEuclidean(\\spad{P},{} \\spad{Q})} computes the last non zero subresultant \\axiom{\\spad{S}} and carries out the equality \\axiom{...\\spad{P} + coef2*Q = \\spad{S}}. Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|lastSubResultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2|) "\\axiom{lastSubResultantEuclidean(\\spad{P},{} \\spad{Q})} computes the last non zero subresultant \\axiom{\\spad{S}} and carries out the equality \\axiom{coef1*P + coef2*Q = \\spad{S}}.")) (|lastSubResultant| ((|#2| |#2| |#2|) "\\axiom{lastSubResultant(\\spad{P},{} \\spad{Q})} computes the last non zero subresultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}")) (|semiDegreeSubResultantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns a subresultant \\axiom{\\spad{S}} of degree \\axiom{\\spad{d}} and carries out the equality \\axiom{...\\spad{P} + coef2*Q = S_i}. Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|degreeSubResultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns a subresultant \\axiom{\\spad{S}} of degree \\axiom{\\spad{d}} and carries out the equality \\axiom{coef1*P + coef2*Q = S_i}.")) (|degreeSubResultant| ((|#2| |#2| |#2| (|NonNegativeInteger|)) "\\axiom{degreeSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{d})} computes a subresultant of degree \\axiom{\\spad{d}}.")) (|semiIndiceSubResultantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{semiIndiceSubResultantEuclidean(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} and carries out the equality \\axiom{...\\spad{P} + coef2*Q = S_i(\\spad{P},{}\\spad{Q})} Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|indiceSubResultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} and carries out the equality \\axiom{coef1*P + coef2*Q = S_i(\\spad{P},{}\\spad{Q})}")) (|indiceSubResultant| ((|#2| |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns the subresultant of indice \\axiom{\\spad{i}}")) (|semiResultantEuclidean1| (((|Record| (|:| |coef1| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{semiResultantEuclidean1(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1.\\spad{P} + ? \\spad{Q} = resultant(\\spad{P},{}\\spad{Q})}.")) (|semiResultantEuclidean2| (((|Record| (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{semiResultantEuclidean2(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{...\\spad{P} + coef2*Q = resultant(\\spad{P},{}\\spad{Q})}. Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|resultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{resultantEuclidean(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1*P + coef2*Q = resultant(\\spad{P},{}\\spad{Q})}")) (|resultant| ((|#1| |#2| |#2|) "\\axiom{resultant(\\spad{P},{} \\spad{Q})} returns the resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}"))) NIL ((|HasCategory| |#1| (QUOTE (-455)))) -(-971) +(-972) ((|constructor| (NIL "This domain represents `pretend' expressions.")) (|target| (((|TypeAst|) $) "\\spad{target(e)} returns the target type of the conversion..")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression being converted."))) NIL NIL -(-972) +(-973) ((|constructor| (NIL "\\indented{1}{Partition is an OrderedCancellationAbelianMonoid which is used} as the basis for symmetric polynomial representation of the sums of powers in SymmetricPolynomial. Thus,{} \\spad{(5 2 2 1)} will represent \\spad{s5 * s2**2 * s1}.")) (|conjugate| (($ $) "\\spad{conjugate(p)} returns the conjugate partition of a partition \\spad{p}")) (|pdct| (((|Integer|) $) "\\spad{pdct(a1**n1 a2**n2 ...)} returns \\spad{n1! * a1**n1 * n2! * a2**n2 * ...}. This function is used in the package \\spadtype{CycleIndicators}.")) (|powers| (((|List| (|List| (|Integer|))) (|List| (|Integer|))) "\\spad{powers(li)} returns a list of 2-element lists. For each 2-element list,{} the first element is an entry of \\spad{li} and the second element is the multiplicity with which the first element occurs in \\spad{li}. There is a 2-element list for each value occurring in \\spad{l}.")) (|partition| (($ (|List| (|Integer|))) "\\spad{partition(li)} converts a list of integers \\spad{li} to a partition"))) NIL NIL -(-973 S |Coef| |Expon| |Var|) +(-974 S |Coef| |Expon| |Var|) ((|constructor| (NIL "\\spadtype{PowerSeriesCategory} is the most general power series category with exponents in an ordered abelian monoid.")) (|complete| (($ $) "\\spad{complete(f)} causes all terms of \\spad{f} to be computed. Note: this results in an infinite loop if \\spad{f} has infinitely many terms.")) (|pole?| (((|Boolean|) $) "\\spad{pole?(f)} determines if the power series \\spad{f} has a pole.")) (|variables| (((|List| |#4|) $) "\\spad{variables(f)} returns a list of the variables occuring in the power series \\spad{f}.")) (|degree| ((|#3| $) "\\spad{degree(f)} returns the exponent of the lowest order term of \\spad{f}.")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(f)} returns the coefficient of the lowest order term of \\spad{f}")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(f)} returns the monomial of \\spad{f} of lowest order.")) (|monomial| (($ $ (|List| |#4|) (|List| |#3|)) "\\spad{monomial(a,[x1,..,xk],[n1,..,nk])} computes \\spad{a * x1**n1 * .. * xk**nk}.") (($ $ |#4| |#3|) "\\spad{monomial(a,x,n)} computes \\spad{a*x**n}."))) NIL NIL -(-974 |Coef| |Expon| |Var|) +(-975 |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| (-559)) (-4411 . T) (-4412 . T) (-4414 . T)) +(((-4420 "*") |has| |#1| (-172)) (-4411 |has| |#1| (-559)) (-4412 . T) (-4413 . T) (-4415 . T)) NIL -(-975) +(-976) ((|constructor| (NIL "PlottableSpaceCurveCategory is the category of curves in 3-space which may be plotted via the graphics facilities. Functions are provided for obtaining lists of lists of points,{} representing the branches of the curve,{} and for determining the ranges of the \\spad{x-},{} \\spad{y-},{} and \\spad{z}-coordinates of the points on the curve.")) (|zRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{zRange(c)} returns the range of the \\spad{z}-coordinates of the points on the curve \\spad{c}.")) (|yRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{yRange(c)} returns the range of the \\spad{y}-coordinates of the points on the curve \\spad{c}.")) (|xRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{xRange(c)} returns the range of the \\spad{x}-coordinates of the points on the curve \\spad{c}.")) (|listBranches| (((|List| (|List| (|Point| (|DoubleFloat|)))) $) "\\spad{listBranches(c)} returns a list of lists of points,{} representing the branches of the curve \\spad{c}."))) NIL NIL -(-976 S R E |VarSet| P) +(-977 S R E |VarSet| P) ((|constructor| (NIL "A category for finite subsets of a polynomial ring. Such a set is only regarded as a set of polynomials and not identified to the ideal it generates. So two distinct sets may generate the same the ideal. Furthermore,{} for \\spad{R} being an integral domain,{} a set of polynomials may be viewed as a representation of the ideal it generates in the polynomial ring \\spad{(R)^(-1) P},{} or the set of its zeros (described for instance by the radical of the previous ideal,{} or a split of the associated affine variety) and so on. So this category provides operations about those different notions.")) (|triangular?| (((|Boolean|) $) "\\axiom{triangular?(\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{ps}} is a triangular set,{} \\spadignore{i.e.} two distinct polynomials have distinct main variables and no constant lies in \\axiom{\\spad{ps}}.")) (|rewriteIdealWithRemainder| (((|List| |#5|) (|List| |#5|) $) "\\axiom{rewriteIdealWithRemainder(\\spad{lp},{}\\spad{cs})} returns \\axiom{\\spad{lr}} such that every polynomial in \\axiom{\\spad{lr}} is fully reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{cs}} and \\axiom{(\\spad{lp},{}\\spad{cs})} and \\axiom{(\\spad{lr},{}\\spad{cs})} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}.")) (|rewriteIdealWithHeadRemainder| (((|List| |#5|) (|List| |#5|) $) "\\axiom{rewriteIdealWithHeadRemainder(\\spad{lp},{}\\spad{cs})} returns \\axiom{\\spad{lr}} such that the leading monomial of every polynomial in \\axiom{\\spad{lr}} is reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{cs}} and \\axiom{(\\spad{lp},{}\\spad{cs})} and \\axiom{(\\spad{lr},{}\\spad{cs})} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}.")) (|remainder| (((|Record| (|:| |rnum| |#2|) (|:| |polnum| |#5|) (|:| |den| |#2|)) |#5| $) "\\axiom{remainder(a,{}\\spad{ps})} returns \\axiom{[\\spad{c},{}\\spad{b},{}\\spad{r}]} such that \\axiom{\\spad{b}} is fully reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ps}},{} \\axiom{r*a - \\spad{c*b}} lies in the ideal generated by \\axiom{\\spad{ps}}. Furthermore,{} if \\axiom{\\spad{R}} is a \\spad{gcd}-domain,{} \\axiom{\\spad{b}} is primitive.")) (|headRemainder| (((|Record| (|:| |num| |#5|) (|:| |den| |#2|)) |#5| $) "\\axiom{headRemainder(a,{}\\spad{ps})} returns \\axiom{[\\spad{b},{}\\spad{r}]} such that the leading monomial of \\axiom{\\spad{b}} is reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ps}} and \\axiom{r*a - \\spad{b}} lies in the ideal generated by \\axiom{\\spad{ps}}.")) (|roughUnitIdeal?| (((|Boolean|) $) "\\axiom{roughUnitIdeal?(\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{ps}} contains some non null element lying in the base ring \\axiom{\\spad{R}}.")) (|roughEqualIdeals?| (((|Boolean|) $ $) "\\axiom{roughEqualIdeals?(\\spad{ps1},{}\\spad{ps2})} returns \\spad{true} iff it can proved that \\axiom{\\spad{ps1}} and \\axiom{\\spad{ps2}} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}} without computing Groebner bases.")) (|roughSubIdeal?| (((|Boolean|) $ $) "\\axiom{roughSubIdeal?(\\spad{ps1},{}\\spad{ps2})} returns \\spad{true} iff it can proved that all polynomials in \\axiom{\\spad{ps1}} lie in the ideal generated by \\axiom{\\spad{ps2}} in \\axiom{\\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}} without computing Groebner bases.")) (|roughBase?| (((|Boolean|) $) "\\axiom{roughBase?(\\spad{ps})} returns \\spad{true} iff for every pair \\axiom{{\\spad{p},{}\\spad{q}}} of polynomials in \\axiom{\\spad{ps}} their leading monomials are relatively prime.")) (|trivialIdeal?| (((|Boolean|) $) "\\axiom{trivialIdeal?(\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{ps}} does not contain non-zero elements.")) (|sort| (((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |#4|) "\\axiom{sort(\\spad{v},{}\\spad{ps})} returns \\axiom{us,{}\\spad{vs},{}\\spad{ws}} such that \\axiom{us} is \\axiom{collectUnder(\\spad{ps},{}\\spad{v})},{} \\axiom{\\spad{vs}} is \\axiom{collect(\\spad{ps},{}\\spad{v})} and \\axiom{\\spad{ws}} is \\axiom{collectUpper(\\spad{ps},{}\\spad{v})}.")) (|collectUpper| (($ $ |#4|) "\\axiom{collectUpper(\\spad{ps},{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{\\spad{ps}} with main variable greater than \\axiom{\\spad{v}}.")) (|collect| (($ $ |#4|) "\\axiom{collect(\\spad{ps},{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{\\spad{ps}} with \\axiom{\\spad{v}} as main variable.")) (|collectUnder| (($ $ |#4|) "\\axiom{collectUnder(\\spad{ps},{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{\\spad{ps}} with main variable less than \\axiom{\\spad{v}}.")) (|mainVariable?| (((|Boolean|) |#4| $) "\\axiom{mainVariable?(\\spad{v},{}\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{\\spad{ps}}.")) (|mainVariables| (((|List| |#4|) $) "\\axiom{mainVariables(\\spad{ps})} returns the decreasingly sorted list of the variables which are main variables of some polynomial in \\axiom{\\spad{ps}}.")) (|variables| (((|List| |#4|) $) "\\axiom{variables(\\spad{ps})} returns the decreasingly sorted list of the variables which are variables of some polynomial in \\axiom{\\spad{ps}}.")) (|mvar| ((|#4| $) "\\axiom{mvar(\\spad{ps})} returns the main variable of the non constant polynomial with the greatest main variable,{} if any,{} else an error is returned.")) (|retract| (($ (|List| |#5|)) "\\axiom{retract(\\spad{lp})} returns an element of the domain whose elements are the members of \\axiom{\\spad{lp}} if such an element exists,{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|List| |#5|)) "\\axiom{retractIfCan(\\spad{lp})} returns an element of the domain whose elements are the members of \\axiom{\\spad{lp}} if such an element exists,{} otherwise \\axiom{\"failed\"} is returned."))) NIL ((|HasCategory| |#2| (QUOTE (-559)))) -(-977 R E |VarSet| P) +(-978 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)) +((-4418 . T)) NIL -(-978 R E V P) +(-979 R E V P) ((|constructor| (NIL "This package provides modest routines for polynomial system solving. The aim of many of the operations of this package is to remove certain factors in some polynomials in order to avoid unnecessary computations in algorithms involving splitting techniques by partial factorization.")) (|removeIrreducibleRedundantFactors| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeIrreducibleRedundantFactors(\\spad{lp},{}\\spad{lq})} returns the same as \\axiom{irreducibleFactors(concat(\\spad{lp},{}\\spad{lq}))} assuming that \\axiom{irreducibleFactors(\\spad{lp})} returns \\axiom{\\spad{lp}} up to replacing some polynomial \\axiom{\\spad{pj}} in \\axiom{\\spad{lp}} by some polynomial \\axiom{\\spad{qj}} associated to \\axiom{\\spad{pj}}.")) (|lazyIrreducibleFactors| (((|List| |#4|) (|List| |#4|)) "\\axiom{lazyIrreducibleFactors(\\spad{lp})} returns \\axiom{\\spad{lf}} such that if \\axiom{\\spad{lp} = [\\spad{p1},{}...,{}\\spad{pn}]} and \\axiom{\\spad{lf} = [\\spad{f1},{}...,{}\\spad{fm}]} then \\axiom{p1*p2*...*pn=0} means \\axiom{f1*f2*...*fm=0},{} and the \\axiom{\\spad{fi}} are irreducible over \\axiom{\\spad{R}} and are pairwise distinct. The algorithm tries to avoid factorization into irreducible factors as far as possible and makes previously use of \\spad{gcd} techniques over \\axiom{\\spad{R}}.")) (|irreducibleFactors| (((|List| |#4|) (|List| |#4|)) "\\axiom{irreducibleFactors(\\spad{lp})} returns \\axiom{\\spad{lf}} such that if \\axiom{\\spad{lp} = [\\spad{p1},{}...,{}\\spad{pn}]} and \\axiom{\\spad{lf} = [\\spad{f1},{}...,{}\\spad{fm}]} then \\axiom{p1*p2*...*pn=0} means \\axiom{f1*f2*...*fm=0},{} and the \\axiom{\\spad{fi}} are irreducible over \\axiom{\\spad{R}} and are pairwise distinct.")) (|removeRedundantFactorsInPols| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactorsInPols(\\spad{lp},{}\\spad{lf})} returns \\axiom{newlp} where \\axiom{newlp} is obtained from \\axiom{\\spad{lp}} by removing in every polynomial \\axiom{\\spad{p}} of \\axiom{\\spad{lp}} any non trivial factor of any polynomial \\axiom{\\spad{f}} in \\axiom{\\spad{lf}}. Moreover,{} squares over \\axiom{\\spad{R}} are first removed in every polynomial \\axiom{\\spad{lp}}.")) (|removeRedundantFactorsInContents| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactorsInContents(\\spad{lp},{}\\spad{lf})} returns \\axiom{newlp} where \\axiom{newlp} is obtained from \\axiom{\\spad{lp}} by removing in the content of every polynomial of \\axiom{\\spad{lp}} any non trivial factor of any polynomial \\axiom{\\spad{f}} in \\axiom{\\spad{lf}}. Moreover,{} squares over \\axiom{\\spad{R}} are first removed in the content of every polynomial of \\axiom{\\spad{lp}}.")) (|removeRoughlyRedundantFactorsInContents| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRoughlyRedundantFactorsInContents(\\spad{lp},{}\\spad{lf})} returns \\axiom{newlp}where \\axiom{newlp} is obtained from \\axiom{\\spad{lp}} by removing in the content of every polynomial of \\axiom{\\spad{lp}} any occurence of a polynomial \\axiom{\\spad{f}} in \\axiom{\\spad{lf}}. Moreover,{} squares over \\axiom{\\spad{R}} are first removed in the content of every polynomial of \\axiom{\\spad{lp}}.")) (|univariatePolynomialsGcds| (((|List| |#4|) (|List| |#4|) (|Boolean|)) "\\axiom{univariatePolynomialsGcds(\\spad{lp},{}opt)} returns the same as \\axiom{univariatePolynomialsGcds(\\spad{lp})} if \\axiom{opt} is \\axiom{\\spad{false}} and if the previous operation does not return any non null and constant polynomial,{} else return \\axiom{[1]}.") (((|List| |#4|) (|List| |#4|)) "\\axiom{univariatePolynomialsGcds(\\spad{lp})} returns \\axiom{\\spad{lg}} where \\axiom{\\spad{lg}} is a list of the gcds of every pair in \\axiom{\\spad{lp}} of univariate polynomials in the same main variable.")) (|squareFreeFactors| (((|List| |#4|) |#4|) "\\axiom{squareFreeFactors(\\spad{p})} returns the square-free factors of \\axiom{\\spad{p}} over \\axiom{\\spad{R}}")) (|rewriteIdealWithQuasiMonicGenerators| (((|List| |#4|) (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{rewriteIdealWithQuasiMonicGenerators(\\spad{lp},{}redOp?,{}redOp)} returns \\axiom{\\spad{lq}} where \\axiom{\\spad{lq}} and \\axiom{\\spad{lp}} generate the same ideal in \\axiom{\\spad{R^}(\\spad{-1}) \\spad{P}} and \\axiom{\\spad{lq}} has rank not higher than the one of \\axiom{\\spad{lp}}. Moreover,{} \\axiom{\\spad{lq}} is computed by reducing \\axiom{\\spad{lp}} \\spad{w}.\\spad{r}.\\spad{t}. some basic set of the ideal generated by the quasi-monic polynomials in \\axiom{\\spad{lp}}.")) (|rewriteSetByReducingWithParticularGenerators| (((|List| |#4|) (|List| |#4|) (|Mapping| (|Boolean|) |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{rewriteSetByReducingWithParticularGenerators(\\spad{lp},{}pred?,{}redOp?,{}redOp)} returns \\axiom{\\spad{lq}} where \\axiom{\\spad{lq}} is computed by the following algorithm. Chose a basic set \\spad{w}.\\spad{r}.\\spad{t}. the reduction-test \\axiom{redOp?} among the polynomials satisfying property \\axiom{pred?},{} if it is empty then leave,{} else reduce the other polynomials by this basic set \\spad{w}.\\spad{r}.\\spad{t}. the reduction-operation \\axiom{redOp}. Repeat while another basic set with smaller rank can be computed. See code. If \\axiom{pred?} is \\axiom{quasiMonic?} the ideal is unchanged.")) (|crushedSet| (((|List| |#4|) (|List| |#4|)) "\\axiom{crushedSet(\\spad{lp})} returns \\axiom{\\spad{lq}} such that \\axiom{\\spad{lp}} and and \\axiom{\\spad{lq}} generate the same ideal and no rough basic sets reduce (in the sense of Groebner bases) the other polynomials in \\axiom{\\spad{lq}}.")) (|roughBasicSet| (((|Union| (|Record| (|:| |bas| (|GeneralTriangularSet| |#1| |#2| |#3| |#4|)) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|)) "\\axiom{roughBasicSet(\\spad{lp})} returns the smallest (with Ritt-Wu ordering) triangular set contained in \\axiom{\\spad{lp}}.")) (|interReduce| (((|List| |#4|) (|List| |#4|)) "\\axiom{interReduce(\\spad{lp})} returns \\axiom{\\spad{lq}} such that \\axiom{\\spad{lp}} and \\axiom{\\spad{lq}} generate the same ideal and no polynomial in \\axiom{\\spad{lq}} is reducuble by the others in the sense of Groebner bases. Since no assumptions are required the result may depend on the ordering the reductions are performed.")) (|removeRoughlyRedundantFactorsInPol| ((|#4| |#4| (|List| |#4|)) "\\axiom{removeRoughlyRedundantFactorsInPol(\\spad{p},{}\\spad{lf})} returns the same as removeRoughlyRedundantFactorsInPols([\\spad{p}],{}\\spad{lf},{}\\spad{true})")) (|removeRoughlyRedundantFactorsInPols| (((|List| |#4|) (|List| |#4|) (|List| |#4|) (|Boolean|)) "\\axiom{removeRoughlyRedundantFactorsInPols(\\spad{lp},{}\\spad{lf},{}opt)} returns the same as \\axiom{removeRoughlyRedundantFactorsInPols(\\spad{lp},{}\\spad{lf})} if \\axiom{opt} is \\axiom{\\spad{false}} and if the previous operation does not return any non null and constant polynomial,{} else return \\axiom{[1]}.") (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRoughlyRedundantFactorsInPols(\\spad{lp},{}\\spad{lf})} returns \\axiom{newlp}where \\axiom{newlp} is obtained from \\axiom{\\spad{lp}} by removing in every polynomial \\axiom{\\spad{p}} of \\axiom{\\spad{lp}} any occurence of a polynomial \\axiom{\\spad{f}} in \\axiom{\\spad{lf}}. This may involve a lot of exact-quotients computations.")) (|bivariatePolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{bivariatePolynomials(\\spad{lp})} returns \\axiom{\\spad{bps},{}nbps} where \\axiom{\\spad{bps}} is a list of the bivariate polynomials,{} and \\axiom{nbps} are the other ones.")) (|bivariate?| (((|Boolean|) |#4|) "\\axiom{bivariate?(\\spad{p})} returns \\spad{true} iff \\axiom{\\spad{p}} involves two and only two variables.")) (|linearPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{linearPolynomials(\\spad{lp})} returns \\axiom{\\spad{lps},{}nlps} where \\axiom{\\spad{lps}} is a list of the linear polynomials in \\spad{lp},{} and \\axiom{nlps} are the other ones.")) (|linear?| (((|Boolean|) |#4|) "\\axiom{linear?(\\spad{p})} returns \\spad{true} iff \\axiom{\\spad{p}} does not lie in the base ring \\axiom{\\spad{R}} and has main degree \\axiom{1}.")) (|univariatePolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{univariatePolynomials(\\spad{lp})} returns \\axiom{ups,{}nups} where \\axiom{ups} is a list of the univariate polynomials,{} and \\axiom{nups} are the other ones.")) (|univariate?| (((|Boolean|) |#4|) "\\axiom{univariate?(\\spad{p})} returns \\spad{true} iff \\axiom{\\spad{p}} involves one and only one variable.")) (|quasiMonicPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{quasiMonicPolynomials(\\spad{lp})} returns \\axiom{qmps,{}nqmps} where \\axiom{qmps} is a list of the quasi-monic polynomials in \\axiom{\\spad{lp}} and \\axiom{nqmps} are the other ones.")) (|selectAndPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| (|Mapping| (|Boolean|) |#4|)) (|List| |#4|)) "\\axiom{selectAndPolynomials(lpred?,{}\\spad{ps})} returns \\axiom{\\spad{gps},{}\\spad{bps}} where \\axiom{\\spad{gps}} is a list of the polynomial \\axiom{\\spad{p}} in \\axiom{\\spad{ps}} such that \\axiom{pred?(\\spad{p})} holds for every \\axiom{pred?} in \\axiom{lpred?} and \\axiom{\\spad{bps}} are the other ones.")) (|selectOrPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| (|Mapping| (|Boolean|) |#4|)) (|List| |#4|)) "\\axiom{selectOrPolynomials(lpred?,{}\\spad{ps})} returns \\axiom{\\spad{gps},{}\\spad{bps}} where \\axiom{\\spad{gps}} is a list of the polynomial \\axiom{\\spad{p}} in \\axiom{\\spad{ps}} such that \\axiom{pred?(\\spad{p})} holds for some \\axiom{pred?} in \\axiom{lpred?} and \\axiom{\\spad{bps}} are the other ones.")) (|selectPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|Mapping| (|Boolean|) |#4|) (|List| |#4|)) "\\axiom{selectPolynomials(pred?,{}\\spad{ps})} returns \\axiom{\\spad{gps},{}\\spad{bps}} where \\axiom{\\spad{gps}} is a list of the polynomial \\axiom{\\spad{p}} in \\axiom{\\spad{ps}} such that \\axiom{pred?(\\spad{p})} holds and \\axiom{\\spad{bps}} are the other ones.")) (|probablyZeroDim?| (((|Boolean|) (|List| |#4|)) "\\axiom{probablyZeroDim?(\\spad{lp})} returns \\spad{true} iff the number of polynomials in \\axiom{\\spad{lp}} is not smaller than the number of variables occurring in these polynomials.")) (|possiblyNewVariety?| (((|Boolean|) (|List| |#4|) (|List| (|List| |#4|))) "\\axiom{possiblyNewVariety?(newlp,{}\\spad{llp})} returns \\spad{true} iff for every \\axiom{\\spad{lp}} in \\axiom{\\spad{llp}} certainlySubVariety?(newlp,{}\\spad{lp}) does not hold.")) (|certainlySubVariety?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{certainlySubVariety?(newlp,{}\\spad{lp})} returns \\spad{true} iff for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}} the remainder of \\axiom{\\spad{p}} by \\axiom{newlp} using the division algorithm of Groebner techniques is zero.")) (|unprotectedRemoveRedundantFactors| (((|List| |#4|) |#4| |#4|) "\\axiom{unprotectedRemoveRedundantFactors(\\spad{p},{}\\spad{q})} returns the same as \\axiom{removeRedundantFactors(\\spad{p},{}\\spad{q})} but does assume that neither \\axiom{\\spad{p}} nor \\axiom{\\spad{q}} lie in the base ring \\axiom{\\spad{R}} and assumes that \\axiom{infRittWu?(\\spad{p},{}\\spad{q})} holds. Moreover,{} if \\axiom{\\spad{R}} is \\spad{gcd}-domain,{} then \\axiom{\\spad{p}} and \\axiom{\\spad{q}} are assumed to be square free.")) (|removeSquaresIfCan| (((|List| |#4|) (|List| |#4|)) "\\axiom{removeSquaresIfCan(\\spad{lp})} returns \\axiom{removeDuplicates [squareFreePart(\\spad{p})\\$\\spad{P} for \\spad{p} in \\spad{lp}]} if \\axiom{\\spad{R}} is \\spad{gcd}-domain else returns \\axiom{\\spad{lp}}.")) (|removeRedundantFactors| (((|List| |#4|) (|List| |#4|) (|List| |#4|) (|Mapping| (|List| |#4|) (|List| |#4|))) "\\axiom{removeRedundantFactors(\\spad{lp},{}\\spad{lq},{}remOp)} returns the same as \\axiom{concat(remOp(removeRoughlyRedundantFactorsInPols(\\spad{lp},{}\\spad{lq})),{}\\spad{lq})} assuming that \\axiom{remOp(\\spad{lq})} returns \\axiom{\\spad{lq}} up to similarity.") (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactors(\\spad{lp},{}\\spad{lq})} returns the same as \\axiom{removeRedundantFactors(concat(\\spad{lp},{}\\spad{lq}))} assuming that \\axiom{removeRedundantFactors(\\spad{lp})} returns \\axiom{\\spad{lp}} up to replacing some polynomial \\axiom{\\spad{pj}} in \\axiom{\\spad{lp}} by some polynomial \\axiom{\\spad{qj}} associated to \\axiom{\\spad{pj}}.") (((|List| |#4|) (|List| |#4|) |#4|) "\\axiom{removeRedundantFactors(\\spad{lp},{}\\spad{q})} returns the same as \\axiom{removeRedundantFactors(cons(\\spad{q},{}\\spad{lp}))} assuming that \\axiom{removeRedundantFactors(\\spad{lp})} returns \\axiom{\\spad{lp}} up to replacing some polynomial \\axiom{\\spad{pj}} in \\axiom{\\spad{lp}} by some some polynomial \\axiom{\\spad{qj}} associated to \\axiom{\\spad{pj}}.") (((|List| |#4|) |#4| |#4|) "\\axiom{removeRedundantFactors(\\spad{p},{}\\spad{q})} returns the same as \\axiom{removeRedundantFactors([\\spad{p},{}\\spad{q}])}") (((|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactors(\\spad{lp})} returns \\axiom{\\spad{lq}} such that if \\axiom{\\spad{lp} = [\\spad{p1},{}...,{}\\spad{pn}]} and \\axiom{\\spad{lq} = [\\spad{q1},{}...,{}\\spad{qm}]} then the product \\axiom{p1*p2*...\\spad{*pn}} vanishes iff the product \\axiom{q1*q2*...\\spad{*qm}} vanishes,{} and the product of degrees of the \\axiom{\\spad{qi}} is not greater than the one of the \\axiom{\\spad{pj}},{} and no polynomial in \\axiom{\\spad{lq}} divides another polynomial in \\axiom{\\spad{lq}}. In particular,{} polynomials lying in the base ring \\axiom{\\spad{R}} are removed. Moreover,{} \\axiom{\\spad{lq}} is sorted \\spad{w}.\\spad{r}.\\spad{t} \\axiom{infRittWu?}. Furthermore,{} if \\spad{R} is \\spad{gcd}-domain,{} the polynomials in \\axiom{\\spad{lq}} are pairwise without common non trivial factor."))) NIL ((-12 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-308)))) (|HasCategory| |#1| (QUOTE (-455)))) -(-979 K) +(-980 K) ((|constructor| (NIL "PseudoLinearNormalForm provides a function for computing a block-companion form for pseudo-linear operators.")) (|companionBlocks| (((|List| (|Record| (|:| C (|Matrix| |#1|)) (|:| |g| (|Vector| |#1|)))) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{companionBlocks(m, v)} returns \\spad{[[C_1, g_1],...,[C_k, g_k]]} such that each \\spad{C_i} is a companion block and \\spad{m = diagonal(C_1,...,C_k)}.")) (|changeBase| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{changeBase(M, A, sig, der)}: computes the new matrix of a pseudo-linear transform given by the matrix \\spad{M} under the change of base A")) (|normalForm| (((|Record| (|:| R (|Matrix| |#1|)) (|:| A (|Matrix| |#1|)) (|:| |Ainv| (|Matrix| |#1|))) (|Matrix| |#1|) (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{normalForm(M, sig, der)} returns \\spad{[R, A, A^{-1}]} such that the pseudo-linear operator whose matrix in the basis \\spad{y} is \\spad{M} had matrix \\spad{R} in the basis \\spad{z = A y}. \\spad{der} is a \\spad{sig}-derivation."))) NIL NIL -(-980 |VarSet| E RC P) +(-981 |VarSet| E RC P) ((|constructor| (NIL "This package computes square-free decomposition of multivariate polynomials over a coefficient ring which is an arbitrary \\spad{gcd} domain. The requirement on the coefficient domain guarantees that the \\spadfun{content} can be removed so that factors will be primitive as well as square-free. Over an infinite ring of finite characteristic,{}it may not be possible to guarantee that the factors are square-free.")) (|squareFree| (((|Factored| |#4|) |#4|) "\\spad{squareFree(p)} returns the square-free factorization of the polynomial \\spad{p}. Each factor has no repeated roots,{} and the factors are pairwise relatively prime."))) NIL NIL -(-981 R) +(-982 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)) +((-4419 . T) (-4418 . T)) NIL -(-982 R1 R2) +(-983 R1 R2) ((|constructor| (NIL "This package \\undocumented")) (|map| (((|Point| |#2|) (|Mapping| |#2| |#1|) (|Point| |#1|)) "\\spad{map(f,p)} \\undocumented"))) NIL NIL -(-983 R) +(-984 R) ((|constructor| (NIL "This package \\undocumented")) (|shade| ((|#1| (|Point| |#1|)) "\\spad{shade(pt)} returns the fourth element of the two dimensional point,{} \\spad{pt},{} although no assumptions are made with regards as to how the components of higher dimensional points are interpreted. This function is defined for the convenience of the user using specifically,{} shade to express a fourth dimension.")) (|hue| ((|#1| (|Point| |#1|)) "\\spad{hue(pt)} returns the third element of the two dimensional point,{} \\spad{pt},{} although no assumptions are made with regards as to how the components of higher dimensional points are interpreted. This function is defined for the convenience of the user using specifically,{} hue to express a third dimension.")) (|color| ((|#1| (|Point| |#1|)) "\\spad{color(pt)} returns the fourth element of the point,{} \\spad{pt},{} although no assumptions are made with regards as to how the components of higher dimensional points are interpreted. This function is defined for the convenience of the user using specifically,{} color to express a fourth dimension.")) (|phiCoord| ((|#1| (|Point| |#1|)) "\\spad{phiCoord(pt)} returns the third element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a spherical coordinate system.")) (|thetaCoord| ((|#1| (|Point| |#1|)) "\\spad{thetaCoord(pt)} returns the second element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a spherical or a cylindrical coordinate system.")) (|rCoord| ((|#1| (|Point| |#1|)) "\\spad{rCoord(pt)} returns the first element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a spherical or a cylindrical coordinate system.")) (|zCoord| ((|#1| (|Point| |#1|)) "\\spad{zCoord(pt)} returns the third element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a Cartesian or a cylindrical coordinate system.")) (|yCoord| ((|#1| (|Point| |#1|)) "\\spad{yCoord(pt)} returns the second element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a Cartesian coordinate system.")) (|xCoord| ((|#1| (|Point| |#1|)) "\\spad{xCoord(pt)} returns the first element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a Cartesian coordinate system."))) NIL NIL -(-984 K) +(-985 K) ((|constructor| (NIL "This is the description of any package which provides partial functions on a domain belonging to TranscendentalFunctionCategory.")) (|acschIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acschIfCan(z)} returns acsch(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|asechIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{asechIfCan(z)} returns asech(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|acothIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acothIfCan(z)} returns acoth(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|atanhIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{atanhIfCan(z)} returns atanh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|acoshIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acoshIfCan(z)} returns acosh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|asinhIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{asinhIfCan(z)} returns asinh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|cschIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cschIfCan(z)} returns csch(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|sechIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{sechIfCan(z)} returns sech(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|cothIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cothIfCan(z)} returns coth(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|tanhIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{tanhIfCan(z)} returns tanh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|coshIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{coshIfCan(z)} returns cosh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|sinhIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{sinhIfCan(z)} returns sinh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|acscIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acscIfCan(z)} returns acsc(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|asecIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{asecIfCan(z)} returns asec(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|acotIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acotIfCan(z)} returns acot(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|atanIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{atanIfCan(z)} returns atan(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|acosIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acosIfCan(z)} returns acos(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|asinIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{asinIfCan(z)} returns asin(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|cscIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cscIfCan(z)} returns \\spad{csc}(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|secIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{secIfCan(z)} returns sec(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|cotIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cotIfCan(z)} returns cot(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|tanIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{tanIfCan(z)} returns tan(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|cosIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cosIfCan(z)} returns cos(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|sinIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{sinIfCan(z)} returns sin(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|logIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{logIfCan(z)} returns log(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|expIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{expIfCan(z)} returns exp(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|nthRootIfCan| (((|Union| |#1| "failed") |#1| (|NonNegativeInteger|)) "\\spad{nthRootIfCan(z,n)} returns the \\spad{n}th root of \\spad{z} if possible,{} and \"failed\" otherwise."))) NIL NIL -(-985 R E OV PPR) +(-986 R E OV PPR) ((|constructor| (NIL "This package \\undocumented{}")) (|map| ((|#4| (|Mapping| |#4| (|Polynomial| |#1|)) |#4|) "\\spad{map(f,p)} \\undocumented{}")) (|pushup| ((|#4| |#4| (|List| |#3|)) "\\spad{pushup(p,lv)} \\undocumented{}") ((|#4| |#4| |#3|) "\\spad{pushup(p,v)} \\undocumented{}")) (|pushdown| ((|#4| |#4| (|List| |#3|)) "\\spad{pushdown(p,lv)} \\undocumented{}") ((|#4| |#4| |#3|) "\\spad{pushdown(p,v)} \\undocumented{}")) (|variable| (((|Union| $ "failed") (|Symbol|)) "\\spad{variable(s)} makes an element from symbol \\spad{s} or fails")) (|convert| (((|Symbol|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) NIL NIL -(-986 K R UP -3867) +(-987 K R UP -3879) ((|constructor| (NIL "In this package \\spad{K} is a finite field,{} \\spad{R} is a ring of univariate polynomials over \\spad{K},{} and \\spad{F} is a monogenic algebra over \\spad{R}. We require that \\spad{F} is monogenic,{} \\spadignore{i.e.} that \\spad{F = K[x,y]/(f(x,y))},{} because the integral basis algorithm used will factor the polynomial \\spad{f(x,y)}. The package provides a function to compute the integral closure of \\spad{R} in the quotient field of \\spad{F} as well as a function to compute a \"local integral basis\" at a specific prime.")) (|reducedDiscriminant| ((|#2| |#3|) "\\spad{reducedDiscriminant(up)} \\undocumented")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) |#2|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,basisDen,basisInv] } containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of the framed algebra \\spad{F}. \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If 'basis' is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix 'basisInv' contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if 'basisInv' is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,basisDen,basisInv] } containing information regarding the integral closure of \\spad{R} in the quotient field of the framed algebra \\spad{F}. \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If 'basis' is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix 'basisInv' contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if 'basisInv' is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}."))) NIL NIL -(-987 |vl| |nv|) +(-988 |vl| |nv|) ((|constructor| (NIL "\\spadtype{QuasiAlgebraicSet2} adds a function \\spadfun{radicalSimplify} which uses \\spadtype{IdealDecompositionPackage} to simplify the representation of a quasi-algebraic set. A quasi-algebraic set is the intersection of a Zariski closed set,{} defined as the common zeros of a given list of polynomials (the defining polynomials for equations),{} and a principal Zariski open set,{} defined as the complement of the common zeros of a polynomial \\spad{f} (the defining polynomial for the inequation). Quasi-algebraic sets are implemented in the domain \\spadtype{QuasiAlgebraicSet},{} where two simplification routines are provided: \\spadfun{idealSimplify} and \\spadfun{simplify}. The function \\spadfun{radicalSimplify} is added for comparison study only. Because the domain \\spadtype{IdealDecompositionPackage} provides facilities for computing with radical ideals,{} it is necessary to restrict the ground ring to the domain \\spadtype{Fraction Integer},{} and the polynomial ring to be of type \\spadtype{DistributedMultivariatePolynomial}. The routine \\spadfun{radicalSimplify} uses these to compute groebner basis of radical ideals and is inefficient and restricted when compared to the two in \\spadtype{QuasiAlgebraicSet}.")) (|radicalSimplify| (((|QuasiAlgebraicSet| (|Fraction| (|Integer|)) (|OrderedVariableList| |#1|) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|)))) (|QuasiAlgebraicSet| (|Fraction| (|Integer|)) (|OrderedVariableList| |#1|) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{radicalSimplify(s)} returns a different and presumably simpler representation of \\spad{s} with the defining polynomials for the equations forming a groebner basis,{} and the defining polynomial for the inequation reduced with respect to the basis,{} using using groebner basis of radical ideals"))) NIL NIL -(-988 R |Var| |Expon| |Dpoly|) +(-989 R |Var| |Expon| |Dpoly|) ((|constructor| (NIL "\\spadtype{QuasiAlgebraicSet} constructs a domain representing quasi-algebraic sets,{} which is the intersection of a Zariski closed set,{} defined as the common zeros of a given list of polynomials (the defining polynomials for equations),{} and a principal Zariski open set,{} defined as the complement of the common zeros of a polynomial \\spad{f} (the defining polynomial for the inequation). This domain provides simplification of a user-given representation using groebner basis computations. There are two simplification routines: the first function \\spadfun{idealSimplify} uses groebner basis of ideals alone,{} while the second,{} \\spadfun{simplify} uses both groebner basis and factorization. The resulting defining equations \\spad{L} always form a groebner basis,{} and the resulting defining inequation \\spad{f} is always reduced. The function \\spadfun{simplify} may be applied several times if desired. A third simplification routine \\spadfun{radicalSimplify} is provided in \\spadtype{QuasiAlgebraicSet2} for comparison study only,{} as it is inefficient compared to the other two,{} as well as is restricted to only certain coefficient domains. For detail analysis and a comparison of the three methods,{} please consult the reference cited. \\blankline A polynomial function \\spad{q} defined on the quasi-algebraic set is equivalent to its reduced form with respect to \\spad{L}. While this may be obtained using the usual normal form algorithm,{} there is no canonical form for \\spad{q}. \\blankline The ordering in groebner basis computation is determined by the data type of the input polynomials. If it is possible we suggest to use refinements of total degree orderings.")) (|simplify| (($ $) "\\spad{simplify(s)} returns a different and presumably simpler representation of \\spad{s} with the defining polynomials for the equations forming a groebner basis,{} and the defining polynomial for the inequation reduced with respect to the basis,{} using a heuristic algorithm based on factoring.")) (|idealSimplify| (($ $) "\\spad{idealSimplify(s)} returns a different and presumably simpler representation of \\spad{s} with the defining polynomials for the equations forming a groebner basis,{} and the defining polynomial for the inequation reduced with respect to the basis,{} using Buchberger\\spad{'s} algorithm.")) (|definingInequation| ((|#4| $) "\\spad{definingInequation(s)} returns a single defining polynomial for the inequation,{} that is,{} the Zariski open part of \\spad{s}.")) (|definingEquations| (((|List| |#4|) $) "\\spad{definingEquations(s)} returns a list of defining polynomials for equations,{} that is,{} for the Zariski closed part of \\spad{s}.")) (|empty?| (((|Boolean|) $) "\\spad{empty?(s)} returns \\spad{true} if the quasialgebraic set \\spad{s} has no points,{} and \\spad{false} otherwise.")) (|setStatus| (($ $ (|Union| (|Boolean|) "failed")) "\\spad{setStatus(s,t)} returns the same representation for \\spad{s},{} but asserts the following: if \\spad{t} is \\spad{true},{} then \\spad{s} is empty,{} if \\spad{t} is \\spad{false},{} then \\spad{s} is non-empty,{} and if \\spad{t} = \"failed\",{} then no assertion is made (that is,{} \"don\\spad{'t} know\"). Note: for internal use only,{} with care.")) (|status| (((|Union| (|Boolean|) "failed") $) "\\spad{status(s)} returns \\spad{true} if the quasi-algebraic set is empty,{} \\spad{false} if it is not,{} and \"failed\" if not yet known")) (|quasiAlgebraicSet| (($ (|List| |#4|) |#4|) "\\spad{quasiAlgebraicSet(pl,q)} returns the quasi-algebraic set with defining equations \\spad{p} = 0 for \\spad{p} belonging to the list \\spad{pl},{} and defining inequation \\spad{q} \\spad{~=} 0.")) (|empty| (($) "\\spad{empty()} returns the empty quasi-algebraic set"))) NIL ((-12 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-308))))) -(-989 R E V P TS) +(-990 R E V P TS) ((|constructor| (NIL "A package for removing redundant quasi-components and redundant branches when decomposing a variety by means of quasi-components of regular triangular sets. \\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|branchIfCan| (((|Union| (|Record| (|:| |eq| (|List| |#4|)) (|:| |tower| |#5|) (|:| |ineq| (|List| |#4|))) "failed") (|List| |#4|) |#5| (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{branchIfCan(leq,{}\\spad{ts},{}lineq,{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement.")) (|prepareDecompose| (((|List| (|Record| (|:| |eq| (|List| |#4|)) (|:| |tower| |#5|) (|:| |ineq| (|List| |#4|)))) (|List| |#4|) (|List| |#5|) (|Boolean|) (|Boolean|)) "\\axiom{prepareDecompose(\\spad{lp},{}\\spad{lts},{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|removeSuperfluousCases| (((|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|)))) "\\axiom{removeSuperfluousCases(llpwt)} is an internal subroutine,{} exported only for developement.")) (|subCase?| (((|Boolean|) (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|)) (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) "\\axiom{subCase?(lpwt1,{}lpwt2)} is an internal subroutine,{} exported only for developement.")) (|removeSuperfluousQuasiComponents| (((|List| |#5|) (|List| |#5|)) "\\axiom{removeSuperfluousQuasiComponents(\\spad{lts})} removes from \\axiom{\\spad{lts}} any \\spad{ts} such that \\axiom{subQuasiComponent?(\\spad{ts},{}us)} holds for another \\spad{us} in \\axiom{\\spad{lts}}.")) (|subQuasiComponent?| (((|Boolean|) |#5| (|List| |#5|)) "\\axiom{subQuasiComponent?(\\spad{ts},{}lus)} returns \\spad{true} iff \\axiom{subQuasiComponent?(\\spad{ts},{}us)} holds for one \\spad{us} in \\spad{lus}.") (((|Boolean|) |#5| |#5|) "\\axiom{subQuasiComponent?(\\spad{ts},{}us)} returns \\spad{true} iff \\axiomOpFrom{internalSubQuasiComponent?}{QuasiComponentPackage} returs \\spad{true}.")) (|internalSubQuasiComponent?| (((|Union| (|Boolean|) "failed") |#5| |#5|) "\\axiom{internalSubQuasiComponent?(\\spad{ts},{}us)} returns a boolean \\spad{b} value if the fact that the regular zero set of \\axiom{us} contains that of \\axiom{\\spad{ts}} can be decided (and in that case \\axiom{\\spad{b}} gives this inclusion) otherwise returns \\axiom{\"failed\"}.")) (|infRittWu?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{infRittWu?(\\spad{lp1},{}\\spad{lp2})} is an internal subroutine,{} exported only for developement.")) (|internalInfRittWu?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{internalInfRittWu?(\\spad{lp1},{}\\spad{lp2})} is an internal subroutine,{} exported only for developement.")) (|internalSubPolSet?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{internalSubPolSet?(\\spad{lp1},{}\\spad{lp2})} returns \\spad{true} iff \\axiom{\\spad{lp1}} is a sub-set of \\axiom{\\spad{lp2}} assuming that these lists are sorted increasingly \\spad{w}.\\spad{r}.\\spad{t}. \\axiomOpFrom{infRittWu?}{RecursivePolynomialCategory}.")) (|subPolSet?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{subPolSet?(\\spad{lp1},{}\\spad{lp2})} returns \\spad{true} iff \\axiom{\\spad{lp1}} is a sub-set of \\axiom{\\spad{lp2}}.")) (|subTriSet?| (((|Boolean|) |#5| |#5|) "\\axiom{subTriSet?(\\spad{ts},{}us)} returns \\spad{true} iff \\axiom{\\spad{ts}} is a sub-set of \\axiom{us}.")) (|moreAlgebraic?| (((|Boolean|) |#5| |#5|) "\\axiom{moreAlgebraic?(\\spad{ts},{}us)} returns \\spad{false} iff \\axiom{\\spad{ts}} and \\axiom{us} are both empty,{} or \\axiom{\\spad{ts}} has less elements than \\axiom{us},{} or some variable is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{us} and is not \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ts}}.")) (|algebraicSort| (((|List| |#5|) (|List| |#5|)) "\\axiom{algebraicSort(\\spad{lts})} sorts \\axiom{\\spad{lts}} \\spad{w}.\\spad{r}.\\spad{t} \\axiomOpFrom{supDimElseRittWu?}{QuasiComponentPackage}.")) (|supDimElseRittWu?| (((|Boolean|) |#5| |#5|) "\\axiom{supDimElseRittWu(\\spad{ts},{}us)} returns \\spad{true} iff \\axiom{\\spad{ts}} has less elements than \\axiom{us} otherwise if \\axiom{\\spad{ts}} has higher rank than \\axiom{us} \\spad{w}.\\spad{r}.\\spad{t}. Riit and Wu ordering.")) (|stopTable!| (((|Void|)) "\\axiom{stopTableGcd!()} is an internal subroutine,{} exported only for developement.")) (|startTable!| (((|Void|) (|String|) (|String|) (|String|)) "\\axiom{startTableGcd!(\\spad{s1},{}\\spad{s2},{}\\spad{s3})} is an internal subroutine,{} exported only for developement."))) NIL NIL -(-990) +(-991) ((|constructor| (NIL "This domain implements simple database queries")) (|value| (((|String|) $) "\\spad{value(q)} returns the value (\\spadignore{i.e.} right hand side) of \\axiom{\\spad{q}}.")) (|variable| (((|Symbol|) $) "\\spad{variable(q)} returns the variable (\\spadignore{i.e.} left hand side) of \\axiom{\\spad{q}}.")) (|equation| (($ (|Symbol|) (|String|)) "\\spad{equation(s,\"a\")} creates a new equation."))) NIL NIL -(-991 A B R S) +(-992 A B R S) ((|constructor| (NIL "This package extends a function between integral domains to a mapping between their quotient fields.")) (|map| ((|#4| (|Mapping| |#2| |#1|) |#3|) "\\spad{map(func,frac)} applies the function \\spad{func} to the numerator and denominator of \\spad{frac}."))) NIL NIL -(-992 A S) +(-993 A S) ((|constructor| (NIL "QuotientField(\\spad{S}) is the category of fractions of an Integral Domain \\spad{S}.")) (|floor| ((|#2| $) "\\spad{floor(x)} returns the largest integral element below \\spad{x}.")) (|ceiling| ((|#2| $) "\\spad{ceiling(x)} returns the smallest integral element above \\spad{x}.")) (|random| (($) "\\spad{random()} returns a random fraction.")) (|fractionPart| (($ $) "\\spad{fractionPart(x)} returns the fractional part of \\spad{x}. \\spad{x} = wholePart(\\spad{x}) + fractionPart(\\spad{x})")) (|wholePart| ((|#2| $) "\\spad{wholePart(x)} returns the whole part of the fraction \\spad{x} \\spadignore{i.e.} the truncated quotient of the numerator by the denominator.")) (|denominator| (($ $) "\\spad{denominator(x)} is the denominator of the fraction \\spad{x} converted to \\%.")) (|numerator| (($ $) "\\spad{numerator(x)} is the numerator of the fraction \\spad{x} converted to \\%.")) (|denom| ((|#2| $) "\\spad{denom(x)} returns the denominator of the fraction \\spad{x}.")) (|numer| ((|#2| $) "\\spad{numer(x)} returns the numerator of the fraction \\spad{x}.")) (/ (($ |#2| |#2|) "\\spad{d1 / d2} returns the fraction \\spad{d1} divided by \\spad{d2}."))) NIL -((|HasCategory| |#2| (QUOTE (-910))) (|HasCategory| |#2| (QUOTE (-548))) (|HasCategory| |#2| (QUOTE (-308))) (|HasCategory| |#2| (LIST (QUOTE -1039) (QUOTE (-1177)))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| |#2| (QUOTE (-1023))) (|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| |#2| (QUOTE (-851))) (|HasCategory| |#2| (LIST (QUOTE -1039) (QUOTE (-567)))) (|HasCategory| |#2| (QUOTE (-1152)))) -(-993 S) +((|HasCategory| |#2| (QUOTE (-911))) (|HasCategory| |#2| (QUOTE (-548))) (|HasCategory| |#2| (QUOTE (-308))) (|HasCategory| |#2| (LIST (QUOTE -1040) (QUOTE (-1178)))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| |#2| (QUOTE (-1024))) (|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| |#2| (QUOTE (-851))) (|HasCategory| |#2| (LIST (QUOTE -1040) (QUOTE (-567)))) (|HasCategory| |#2| (QUOTE (-1153)))) +(-994 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)) +((-4410 . T) (-4416 . T) (-4411 . T) ((-4420 "*") . T) (-4412 . T) (-4413 . T) (-4415 . T)) NIL -(-994 |n| K) +(-995 |n| K) ((|constructor| (NIL "This domain provides modest support for quadratic forms.")) (|elt| ((|#2| $ (|DirectProduct| |#1| |#2|)) "\\spad{elt(qf,v)} evaluates the quadratic form \\spad{qf} on the vector \\spad{v},{} producing a scalar.")) (|matrix| (((|SquareMatrix| |#1| |#2|) $) "\\spad{matrix(qf)} creates a square matrix from the quadratic form \\spad{qf}.")) (|quadraticForm| (($ (|SquareMatrix| |#1| |#2|)) "\\spad{quadraticForm(m)} creates a quadratic form from a symmetric,{} square matrix \\spad{m}."))) NIL NIL -(-995) +(-996) ((|constructor| (NIL "This domain represents the syntax of a quasiquote \\indented{2}{expression.}")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the syntax for the expression being quoted."))) NIL NIL -(-996 S) +(-997 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)) +((-4418 . T) (-4419 . T)) NIL -(-997 S R) +(-998 S R) ((|constructor| (NIL "\\spadtype{QuaternionCategory} describes the category of quaternions and implements functions that are not representation specific.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(q)} returns \\spad{q} as a rational number,{} or \"failed\" if this is not possible. Note: if \\spad{rational?(q)} is \\spad{true},{} the conversion can be done and the rational number will be returned.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(q)} tries to convert \\spad{q} into a rational number. Error: if this is not possible. If \\spad{rational?(q)} is \\spad{true},{} the conversion will be done and the rational number returned.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(q)} returns {\\it \\spad{true}} if all the imaginary parts of \\spad{q} are zero and the real part can be converted into a rational number,{} and {\\it \\spad{false}} otherwise.")) (|abs| ((|#2| $) "\\spad{abs(q)} computes the absolute value of quaternion \\spad{q} (sqrt of norm).")) (|real| ((|#2| $) "\\spad{real(q)} extracts the real part of quaternion \\spad{q}.")) (|quatern| (($ |#2| |#2| |#2| |#2|) "\\spad{quatern(r,i,j,k)} constructs a quaternion from scalars.")) (|norm| ((|#2| $) "\\spad{norm(q)} computes the norm of \\spad{q} (the sum of the squares of the components).")) (|imagK| ((|#2| $) "\\spad{imagK(q)} extracts the imaginary \\spad{k} part of quaternion \\spad{q}.")) (|imagJ| ((|#2| $) "\\spad{imagJ(q)} extracts the imaginary \\spad{j} part of quaternion \\spad{q}.")) (|imagI| ((|#2| $) "\\spad{imagI(q)} extracts the imaginary \\spad{i} part of quaternion \\spad{q}.")) (|conjugate| (($ $) "\\spad{conjugate(q)} negates the imaginary parts of quaternion \\spad{q}."))) NIL -((|HasCategory| |#2| (QUOTE (-548))) (|HasCategory| |#2| (QUOTE (-1061))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| |#2| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-851))) (|HasCategory| |#2| (QUOTE (-291)))) -(-998 R) +((|HasCategory| |#2| (QUOTE (-548))) (|HasCategory| |#2| (QUOTE (-1062))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| |#2| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-851))) (|HasCategory| |#2| (QUOTE (-291)))) +(-999 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)) +((-4411 |has| |#1| (-291)) (-4412 . T) (-4413 . T) (-4415 . T)) NIL -(-999 QR R QS S) +(-1000 QR R QS S) ((|constructor| (NIL "\\spadtype{QuaternionCategoryFunctions2} implements functions between two quaternion domains. The function \\spadfun{map} is used by the system interpreter to coerce between quaternion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,u)} maps \\spad{f} onto the component parts of the quaternion \\spad{u}."))) NIL NIL -(-1000 R) +(-1001 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)) -((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| |#1| (QUOTE (-365))) (-2797 (|HasCategory| |#1| (QUOTE (-291))) (|HasCategory| |#1| (QUOTE (-365)))) (|HasCategory| |#1| (QUOTE (-291))) (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (LIST (QUOTE -640) (QUOTE (-567)))) (|HasCategory| |#1| (LIST (QUOTE -517) (QUOTE (-1177)) (|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 -901) (QUOTE (-1177)))) (-2797 (|HasCategory| |#1| (LIST (QUOTE -1039) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (QUOTE (-365)))) (|HasCategory| |#1| (LIST (QUOTE -1039) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1039) (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-1061))) (|HasCategory| |#1| (QUOTE (-548)))) -(-1001 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)) -((-12 (|HasCategory| |#1| (QUOTE (-1101))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1101))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-1101))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) +((-4411 |has| |#1| (-291)) (-4412 . T) (-4413 . T) (-4415 . T)) +((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| |#1| (QUOTE (-365))) (-2800 (|HasCategory| |#1| (QUOTE (-291))) (|HasCategory| |#1| (QUOTE (-365)))) (|HasCategory| |#1| (QUOTE (-291))) (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (LIST (QUOTE -640) (QUOTE (-567)))) (|HasCategory| |#1| (LIST (QUOTE -517) (QUOTE (-1178)) (|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 -902) (QUOTE (-1178)))) (-2800 (|HasCategory| |#1| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (QUOTE (-365)))) (|HasCategory| |#1| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-1062))) (|HasCategory| |#1| (QUOTE (-548)))) (-1002 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}."))) +((-4418 . T) (-4419 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1102))) (-2800 (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) +(-1003 S) ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|Fraction| (|Integer|))) "\\spad{x ** y} is the rational exponentiation of \\spad{x} by the power \\spad{y}.")) (|nthRoot| (($ $ (|Integer|)) "\\spad{nthRoot(x,n)} returns the \\spad{n}th root of \\spad{x}.")) (|sqrt| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) NIL NIL -(-1003) +(-1004) ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|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 -(-1004 -3867 UP UPUP |radicnd| |n|) +(-1005 -3879 UP UPUP |radicnd| |n|) ((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x})."))) -((-4410 |has| (-410 |#2|) (-365)) (-4415 |has| (-410 |#2|) (-365)) (-4409 |has| (-410 |#2|) (-365)) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) -((|HasCategory| (-410 |#2|) (QUOTE (-145))) (|HasCategory| (-410 |#2|) (QUOTE (-147))) (|HasCategory| (-410 |#2|) (QUOTE (-351))) (-2797 (|HasCategory| (-410 |#2|) (QUOTE (-365))) (|HasCategory| (-410 |#2|) (QUOTE (-351)))) (|HasCategory| (-410 |#2|) (QUOTE (-365))) (|HasCategory| (-410 |#2|) (QUOTE (-370))) (-2797 (-12 (|HasCategory| (-410 |#2|) (QUOTE (-233))) (|HasCategory| (-410 |#2|) (QUOTE (-365)))) (|HasCategory| (-410 |#2|) (QUOTE (-351)))) (-2797 (-12 (|HasCategory| (-410 |#2|) (LIST (QUOTE -901) (QUOTE (-1177)))) (|HasCategory| (-410 |#2|) (QUOTE (-365)))) (-12 (|HasCategory| (-410 |#2|) (LIST (QUOTE -901) (QUOTE (-1177)))) (|HasCategory| (-410 |#2|) (QUOTE (-351))))) (|HasCategory| (-410 |#2|) (LIST (QUOTE -640) (QUOTE (-567)))) (-2797 (|HasCategory| (-410 |#2|) (LIST (QUOTE -1039) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| (-410 |#2|) (QUOTE (-365)))) (|HasCategory| (-410 |#2|) (LIST (QUOTE -1039) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| (-410 |#2|) (LIST (QUOTE -1039) (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-370))) (-12 (|HasCategory| (-410 |#2|) (LIST (QUOTE -901) (QUOTE (-1177)))) (|HasCategory| (-410 |#2|) (QUOTE (-365)))) (-12 (|HasCategory| (-410 |#2|) (QUOTE (-233))) (|HasCategory| (-410 |#2|) (QUOTE (-365))))) -(-1005 |bb|) +((-4411 |has| (-410 |#2|) (-365)) (-4416 |has| (-410 |#2|) (-365)) (-4410 |has| (-410 |#2|) (-365)) ((-4420 "*") . T) (-4412 . T) (-4413 . T) (-4415 . T)) +((|HasCategory| (-410 |#2|) (QUOTE (-145))) (|HasCategory| (-410 |#2|) (QUOTE (-147))) (|HasCategory| (-410 |#2|) (QUOTE (-351))) (-2800 (|HasCategory| (-410 |#2|) (QUOTE (-365))) (|HasCategory| (-410 |#2|) (QUOTE (-351)))) (|HasCategory| (-410 |#2|) (QUOTE (-365))) (|HasCategory| (-410 |#2|) (QUOTE (-370))) (-2800 (-12 (|HasCategory| (-410 |#2|) (QUOTE (-233))) (|HasCategory| (-410 |#2|) (QUOTE (-365)))) (|HasCategory| (-410 |#2|) (QUOTE (-351)))) (-2800 (-12 (|HasCategory| (-410 |#2|) (LIST (QUOTE -902) (QUOTE (-1178)))) (|HasCategory| (-410 |#2|) (QUOTE (-365)))) (-12 (|HasCategory| (-410 |#2|) (LIST (QUOTE -902) (QUOTE (-1178)))) (|HasCategory| (-410 |#2|) (QUOTE (-351))))) (|HasCategory| (-410 |#2|) (LIST (QUOTE -640) (QUOTE (-567)))) (-2800 (|HasCategory| (-410 |#2|) (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| (-410 |#2|) (QUOTE (-365)))) (|HasCategory| (-410 |#2|) (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| (-410 |#2|) (LIST (QUOTE -1040) (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-370))) (-12 (|HasCategory| (-410 |#2|) (LIST (QUOTE -902) (QUOTE (-1178)))) (|HasCategory| (-410 |#2|) (QUOTE (-365)))) (-12 (|HasCategory| (-410 |#2|) (QUOTE (-233))) (|HasCategory| (-410 |#2|) (QUOTE (-365))))) +(-1006 |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)) -((|HasCategory| (-567) (QUOTE (-910))) (|HasCategory| (-567) (LIST (QUOTE -1039) (QUOTE (-1177)))) (|HasCategory| (-567) (QUOTE (-145))) (|HasCategory| (-567) (QUOTE (-147))) (|HasCategory| (-567) (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| (-567) (QUOTE (-1023))) (|HasCategory| (-567) (QUOTE (-821))) (-2797 (|HasCategory| (-567) (QUOTE (-821))) (|HasCategory| (-567) (QUOTE (-851)))) (|HasCategory| (-567) (LIST (QUOTE -1039) (QUOTE (-567)))) (|HasCategory| (-567) (QUOTE (-1152))) (|HasCategory| (-567) (LIST (QUOTE -887) (QUOTE (-381)))) (|HasCategory| (-567) (LIST (QUOTE -887) (QUOTE (-567)))) (|HasCategory| (-567) (LIST (QUOTE -615) (LIST (QUOTE -893) (QUOTE (-381))))) (|HasCategory| (-567) (LIST (QUOTE -615) (LIST (QUOTE -893) (QUOTE (-567))))) (|HasCategory| (-567) (QUOTE (-233))) (|HasCategory| (-567) (LIST (QUOTE -901) (QUOTE (-1177)))) (|HasCategory| (-567) (LIST (QUOTE -517) (QUOTE (-1177)) (QUOTE (-567)))) (|HasCategory| (-567) (LIST (QUOTE -310) (QUOTE (-567)))) (|HasCategory| (-567) (LIST (QUOTE -287) (QUOTE (-567)) (QUOTE (-567)))) (|HasCategory| (-567) (QUOTE (-308))) (|HasCategory| (-567) (QUOTE (-548))) (|HasCategory| (-567) (QUOTE (-851))) (|HasCategory| (-567) (LIST (QUOTE -640) (QUOTE (-567)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-567) (QUOTE (-910)))) (-2797 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-567) (QUOTE (-910)))) (|HasCategory| (-567) (QUOTE (-145))))) -(-1006) +((-4410 . T) (-4416 . T) (-4411 . T) ((-4420 "*") . T) (-4412 . T) (-4413 . T) (-4415 . T)) +((|HasCategory| (-567) (QUOTE (-911))) (|HasCategory| (-567) (LIST (QUOTE -1040) (QUOTE (-1178)))) (|HasCategory| (-567) (QUOTE (-145))) (|HasCategory| (-567) (QUOTE (-147))) (|HasCategory| (-567) (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| (-567) (QUOTE (-1024))) (|HasCategory| (-567) (QUOTE (-821))) (-2800 (|HasCategory| (-567) (QUOTE (-821))) (|HasCategory| (-567) (QUOTE (-851)))) (|HasCategory| (-567) (LIST (QUOTE -1040) (QUOTE (-567)))) (|HasCategory| (-567) (QUOTE (-1153))) (|HasCategory| (-567) (LIST (QUOTE -888) (QUOTE (-381)))) (|HasCategory| (-567) (LIST (QUOTE -888) (QUOTE (-567)))) (|HasCategory| (-567) (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-381))))) (|HasCategory| (-567) (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567))))) (|HasCategory| (-567) (QUOTE (-233))) (|HasCategory| (-567) (LIST (QUOTE -902) (QUOTE (-1178)))) (|HasCategory| (-567) (LIST (QUOTE -517) (QUOTE (-1178)) (QUOTE (-567)))) (|HasCategory| (-567) (LIST (QUOTE -310) (QUOTE (-567)))) (|HasCategory| (-567) (LIST (QUOTE -287) (QUOTE (-567)) (QUOTE (-567)))) (|HasCategory| (-567) (QUOTE (-308))) (|HasCategory| (-567) (QUOTE (-548))) (|HasCategory| (-567) (QUOTE (-851))) (|HasCategory| (-567) (LIST (QUOTE -640) (QUOTE (-567)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-567) (QUOTE (-911)))) (-2800 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-567) (QUOTE (-911)))) (|HasCategory| (-567) (QUOTE (-145))))) +(-1007) ((|constructor| (NIL "This package provides tools for creating radix expansions.")) (|radix| (((|Any|) (|Fraction| (|Integer|)) (|Integer|)) "\\spad{radix(x,b)} converts \\spad{x} to a radix expansion in base \\spad{b}."))) NIL NIL -(-1007) +(-1008) ((|constructor| (NIL "Random number generators \\indented{2}{All random numbers used in the system should originate from} \\indented{2}{the same generator.\\space{2}This package is intended to be the source.}")) (|seed| (((|Integer|)) "\\spad{seed()} returns the current seed value.")) (|reseed| (((|Void|) (|Integer|)) "\\spad{reseed(n)} restarts the random number generator at \\spad{n}.")) (|size| (((|Integer|)) "\\spad{size()} is the base of the random number generator")) (|randnum| (((|Integer|) (|Integer|)) "\\spad{randnum(n)} is a random number between 0 and \\spad{n}.") (((|Integer|)) "\\spad{randnum()} is a random number between 0 and size()."))) NIL NIL -(-1008 RP) +(-1009 RP) ((|factorSquareFree| (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(p)} factors an extended squareFree polynomial \\spad{p} over the rational numbers.")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(p)} factors an extended polynomial \\spad{p} over the rational numbers."))) NIL NIL -(-1009 S) +(-1010 S) ((|constructor| (NIL "rational number testing and retraction functions. Date Created: March 1990 Date Last Updated: 9 April 1991")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") |#1|) "\\spad{rationalIfCan(x)} returns \\spad{x} as a rational number,{} \"failed\" if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) |#1|) "\\spad{rational?(x)} returns \\spad{true} if \\spad{x} is a rational number,{} \\spad{false} otherwise.")) (|rational| (((|Fraction| (|Integer|)) |#1|) "\\spad{rational(x)} returns \\spad{x} as a rational number; error if \\spad{x} is not a rational number."))) NIL NIL -(-1010 A S) +(-1011 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 (-1101)))) -(-1011 S) +((|HasAttribute| |#1| (QUOTE -4419)) (|HasCategory| |#2| (QUOTE (-1102)))) +(-1012 S) ((|constructor| (NIL "A recursive aggregate over a type \\spad{S} is a model for a a directed graph containing values of type \\spad{S}. Recursively,{} a recursive aggregate is a {\\em node} consisting of a \\spadfun{value} from \\spad{S} and 0 or more \\spadfun{children} which are recursive aggregates. A node with no children is called a \\spadfun{leaf} node. A recursive aggregate may be cyclic for which some operations as noted may go into an infinite loop.")) (|setvalue!| ((|#1| $ |#1|) "\\spad{setvalue!(u,x)} sets the value of node \\spad{u} to \\spad{x}.")) (|setelt| ((|#1| $ "value" |#1|) "\\spad{setelt(a,\"value\",x)} (also written \\axiom{a . value \\spad{:=} \\spad{x}}) is equivalent to \\axiom{setvalue!(a,{}\\spad{x})}")) (|setchildren!| (($ $ (|List| $)) "\\spad{setchildren!(u,v)} replaces the current children of node \\spad{u} with the members of \\spad{v} in left-to-right order.")) (|node?| (((|Boolean|) $ $) "\\spad{node?(u,v)} tests if node \\spad{u} is contained in node \\spad{v} (either as a child,{} a child of a child,{} etc.).")) (|child?| (((|Boolean|) $ $) "\\spad{child?(u,v)} tests if node \\spad{u} is a child of node \\spad{v}.")) (|distance| (((|Integer|) $ $) "\\spad{distance(u,v)} returns the path length (an integer) from node \\spad{u} to \\spad{v}.")) (|leaves| (((|List| |#1|) $) "\\spad{leaves(t)} returns the list of values in obtained by visiting the nodes of tree \\axiom{\\spad{t}} in left-to-right order.")) (|cyclic?| (((|Boolean|) $) "\\spad{cyclic?(u)} tests if \\spad{u} has a cycle.")) (|elt| ((|#1| $ "value") "\\spad{elt(u,\"value\")} (also written: \\axiom{a. value}) is equivalent to \\axiom{value(a)}.")) (|value| ((|#1| $) "\\spad{value(u)} returns the value of the node \\spad{u}.")) (|leaf?| (((|Boolean|) $) "\\spad{leaf?(u)} tests if \\spad{u} is a terminal node.")) (|nodes| (((|List| $) $) "\\spad{nodes(u)} returns a list of all of the nodes of aggregate \\spad{u}.")) (|children| (((|List| $) $) "\\spad{children(u)} returns a list of the children of aggregate \\spad{u}."))) NIL NIL -(-1012 S) +(-1013 S) ((|constructor| (NIL "\\axiomType{RealClosedField} provides common acces functions for all real closed fields.")) (|approximate| (((|Fraction| (|Integer|)) $ $) "\\axiom{approximate(\\spad{n},{}\\spad{p})} gives an approximation of \\axiom{\\spad{n}} that has precision \\axiom{\\spad{p}}")) (|rename| (($ $ (|OutputForm|)) "\\axiom{rename(\\spad{x},{}name)} gives a new number that prints as name")) (|rename!| (($ $ (|OutputForm|)) "\\axiom{rename!(\\spad{x},{}name)} changes the way \\axiom{\\spad{x}} is printed")) (|sqrt| (($ (|Integer|)) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ (|Fraction| (|Integer|))) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $ (|PositiveInteger|)) "\\axiom{sqrt(\\spad{x},{}\\spad{n})} is \\axiom{\\spad{x} \\spad{**} (1/n)}")) (|allRootsOf| (((|List| $) (|Polynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely")) (|rootOf| (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|)) "\\axiom{rootOf(pol,{}\\spad{n})} creates the \\spad{n}th root for the order of \\axiom{pol} and gives it unique name") (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|) (|OutputForm|)) "\\axiom{rootOf(pol,{}\\spad{n},{}name)} creates the \\spad{n}th root for the order of \\axiom{pol} and names it \\axiom{name}")) (|mainValue| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainValue(\\spad{x})} is the expression of \\axiom{\\spad{x}} in terms of \\axiom{SparseUnivariatePolynomial(\\$)}")) (|mainDefiningPolynomial| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainDefiningPolynomial(\\spad{x})} is the defining polynomial for the main algebraic quantity of \\axiom{\\spad{x}}")) (|mainForm| (((|Union| (|OutputForm|) "failed") $) "\\axiom{mainForm(\\spad{x})} is the main algebraic quantity name of \\axiom{\\spad{x}}"))) NIL NIL -(-1013) +(-1014) ((|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)) +((-4411 . T) (-4416 . T) (-4410 . T) (-4413 . T) (-4412 . T) ((-4420 "*") . T) (-4415 . T)) NIL -(-1014 R -3867) +(-1015 R -3879) ((|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 -(-1015 R -3867) +(-1016 R -3879) ((|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 -(-1016 -3867 UP) +(-1017 -3879 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 -(-1017 -3867 UP) +(-1018 -3879 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 -(-1018 S) +(-1019 S) ((|constructor| (NIL "This package exports random distributions")) (|rdHack1| (((|Mapping| |#1|) (|Vector| |#1|) (|Vector| (|Integer|)) (|Integer|)) "\\spad{rdHack1(v,u,n)} \\undocumented")) (|weighted| (((|Mapping| |#1|) (|List| (|Record| (|:| |value| |#1|) (|:| |weight| (|Integer|))))) "\\spad{weighted(l)} \\undocumented")) (|uniform| (((|Mapping| |#1|) (|Set| |#1|)) "\\spad{uniform(s)} \\undocumented"))) NIL NIL -(-1019 F1 UP UPUP R F2) +(-1020 F1 UP UPUP R F2) ((|constructor| (NIL "\\indented{1}{Finds the order of a divisor over a finite field} Author: Manuel Bronstein Date Created: 1988 Date Last Updated: 8 November 1994")) (|order| (((|NonNegativeInteger|) (|FiniteDivisor| |#1| |#2| |#3| |#4|) |#3| (|Mapping| |#5| |#1|)) "\\spad{order(f,u,g)} \\undocumented"))) NIL NIL -(-1020) +(-1021) ((|constructor| (NIL "This domain represents list reduction syntax.")) (|body| (((|SpadAst|) $) "\\spad{body(e)} return the list of expressions being redcued.")) (|operator| (((|SpadAst|) $) "\\spad{operator(e)} returns the magma operation being applied."))) NIL NIL -(-1021 |Pol|) +(-1022 |Pol|) ((|constructor| (NIL "\\indented{2}{This package provides functions for finding the real zeros} of univariate polynomials over the integers to arbitrary user-specified precision. The results are returned as a list of isolating intervals which are expressed as records with \"left\" and \"right\" rational number components.")) (|midpoints| (((|List| (|Fraction| (|Integer|))) (|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))))) "\\spad{midpoints(isolist)} returns the list of midpoints for the list of intervals \\spad{isolist}.")) (|midpoint| (((|Fraction| (|Integer|)) (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{midpoint(int)} returns the midpoint of the interval \\spad{int}.")) (|refine| (((|Union| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) "failed") |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{refine(pol, int, range)} takes a univariate polynomial \\spad{pol} and and isolating interval \\spad{int} containing exactly one real root of \\spad{pol}; the operation returns an isolating interval which is contained within range,{} or \"failed\" if no such isolating interval exists.") (((|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|))) "\\spad{refine(pol, int, eps)} refines the interval \\spad{int} containing exactly one root of the univariate polynomial \\spad{pol} to size less than the rational number eps.")) (|realZeros| (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|))) "\\spad{realZeros(pol, int, eps)} returns a list of intervals of length less than the rational number eps for all the real roots of the polynomial \\spad{pol} which lie in the interval expressed by the record \\spad{int}.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Fraction| (|Integer|))) "\\spad{realZeros(pol, eps)} returns a list of intervals of length less than the rational number eps for all the real roots of the polynomial \\spad{pol}.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{realZeros(pol, range)} returns a list of isolating intervals for all the real zeros of the univariate polynomial \\spad{pol} which lie in the interval expressed by the record range.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1|) "\\spad{realZeros(pol)} returns a list of isolating intervals for all the real zeros of the univariate polynomial \\spad{pol}."))) NIL NIL -(-1022 |Pol|) +(-1023 |Pol|) ((|constructor| (NIL "\\indented{2}{This package provides functions for finding the real zeros} of univariate polynomials over the rational numbers to arbitrary user-specified precision. The results are returned as a list of isolating intervals,{} expressed as records with \"left\" and \"right\" rational number components.")) (|refine| (((|Union| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) "failed") |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{refine(pol, int, range)} takes a univariate polynomial \\spad{pol} and and isolating interval \\spad{int} which must contain exactly one real root of \\spad{pol},{} and returns an isolating interval which is contained within range,{} or \"failed\" if no such isolating interval exists.") (((|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|))) "\\spad{refine(pol, int, eps)} refines the interval \\spad{int} containing exactly one root of the univariate polynomial \\spad{pol} to size less than the rational number eps.")) (|realZeros| (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|))) "\\spad{realZeros(pol, int, eps)} returns a list of intervals of length less than the rational number eps for all the real roots of the polynomial \\spad{pol} which lie in the interval expressed by the record \\spad{int}.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Fraction| (|Integer|))) "\\spad{realZeros(pol, eps)} returns a list of intervals of length less than the rational number eps for all the real roots of the polynomial \\spad{pol}.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{realZeros(pol, range)} returns a list of isolating intervals for all the real zeros of the univariate polynomial \\spad{pol} which lie in the interval expressed by the record range.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1|) "\\spad{realZeros(pol)} returns a list of isolating intervals for all the real zeros of the univariate polynomial \\spad{pol}."))) NIL NIL -(-1023) +(-1024) ((|constructor| (NIL "The category of real numeric domains,{} \\spadignore{i.e.} convertible to floats."))) NIL NIL -(-1024) +(-1025) ((|constructor| (NIL "\\indented{1}{This package provides numerical solutions of systems of polynomial} equations for use in ACPLOT.")) (|realSolve| (((|List| (|List| (|Float|))) (|List| (|Polynomial| (|Integer|))) (|List| (|Symbol|)) (|Float|)) "\\spad{realSolve(lp,lv,eps)} = compute the list of the real solutions of the list \\spad{lp} of polynomials with integer coefficients with respect to the variables in \\spad{lv},{} with precision \\spad{eps}.")) (|solve| (((|List| (|Float|)) (|Polynomial| (|Integer|)) (|Float|)) "\\spad{solve(p,eps)} finds the real zeroes of a univariate integer polynomial \\spad{p} with precision \\spad{eps}.") (((|List| (|Float|)) (|Polynomial| (|Fraction| (|Integer|))) (|Float|)) "\\spad{solve(p,eps)} finds the real zeroes of a univariate rational polynomial \\spad{p} with precision \\spad{eps}."))) NIL NIL -(-1025 |TheField|) +(-1026 |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)) -((-2797 (|HasCategory| (-410 (-567)) (LIST (QUOTE -1039) (QUOTE (-567)))) (|HasCategory| |#1| (LIST (QUOTE -1039) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1039) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1039) (QUOTE (-567)))) (|HasCategory| (-410 (-567)) (LIST (QUOTE -1039) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| (-410 (-567)) (LIST (QUOTE -1039) (QUOTE (-567))))) -(-1026 -3867 L) +((-4411 . T) (-4416 . T) (-4410 . T) (-4413 . T) (-4412 . T) ((-4420 "*") . T) (-4415 . T)) +((-2800 (|HasCategory| (-410 (-567)) (LIST (QUOTE -1040) (QUOTE (-567)))) (|HasCategory| |#1| (LIST (QUOTE -1040) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (QUOTE (-567)))) (|HasCategory| (-410 (-567)) (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| (-410 (-567)) (LIST (QUOTE -1040) (QUOTE (-567))))) +(-1027 -3879 L) ((|constructor| (NIL "\\spadtype{ReductionOfOrder} provides functions for reducing the order of linear ordinary differential equations once some solutions are known.")) (|ReduceOrder| (((|Record| (|:| |eq| |#2|) (|:| |op| (|List| |#1|))) |#2| (|List| |#1|)) "\\spad{ReduceOrder(op, [f1,...,fk])} returns \\spad{[op1,[g1,...,gk]]} such that for any solution \\spad{z} of \\spad{op1 z = 0},{} \\spad{y = gk \\int(g_{k-1} \\int(... \\int(g1 \\int z)...)} is a solution of \\spad{op y = 0}. Each \\spad{fi} must satisfy \\spad{op fi = 0}.") ((|#2| |#2| |#1|) "\\spad{ReduceOrder(op, s)} returns \\spad{op1} such that for any solution \\spad{z} of \\spad{op1 z = 0},{} \\spad{y = s \\int z} is a solution of \\spad{op y = 0}. \\spad{s} must satisfy \\spad{op s = 0}."))) NIL NIL -(-1027 S) +(-1028 S) ((|constructor| (NIL "\\indented{1}{\\spadtype{Reference} is for making a changeable instance} of something.")) (= (((|Boolean|) $ $) "\\spad{a=b} tests if \\spad{a} and \\spad{b} are equal.")) (|setref| ((|#1| $ |#1|) "\\spad{setref(n,m)} same as \\spad{setelt(n,m)}.")) (|deref| ((|#1| $) "\\spad{deref(n)} is equivalent to \\spad{elt(n)}.")) (|setelt| ((|#1| $ |#1|) "\\spad{setelt(n,m)} changes the value of the object \\spad{n} to \\spad{m}.")) (|elt| ((|#1| $) "\\spad{elt(n)} returns the object \\spad{n}.")) (|ref| (($ |#1|) "\\spad{ref(n)} creates a pointer (reference) to the object \\spad{n}."))) NIL -((|HasCategory| |#1| (QUOTE (-1101)))) -(-1028 R E V P) +((|HasCategory| |#1| (QUOTE (-1102)))) +(-1029 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)) -((-12 (|HasCategory| |#4| (QUOTE (-1101))) (|HasCategory| |#4| (LIST (QUOTE -310) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| |#4| (QUOTE (-1101))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#3| (QUOTE (-370))) (|HasCategory| |#4| (LIST (QUOTE -614) (QUOTE (-863))))) -(-1029 R) +((-4419 . T) (-4418 . T)) +((-12 (|HasCategory| |#4| (QUOTE (-1102))) (|HasCategory| |#4| (LIST (QUOTE -310) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| |#4| (QUOTE (-1102))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#3| (QUOTE (-370))) (|HasCategory| |#4| (LIST (QUOTE -614) (QUOTE (-863))))) +(-1030 R) ((|constructor| (NIL "RepresentationPackage1 provides functions for representation theory for finite groups and algebras. The package creates permutation representations and uses tensor products and its symmetric and antisymmetric components to create new representations of larger degree from given ones. Note: instead of having parameters from \\spadtype{Permutation} this package allows list notation of permutations as well: \\spadignore{e.g.} \\spad{[1,4,3,2]} denotes permutes 2 and 4 and fixes 1 and 3.")) (|permutationRepresentation| (((|List| (|Matrix| (|Integer|))) (|List| (|List| (|Integer|)))) "\\spad{permutationRepresentation([pi1,...,pik],n)} returns the list of matrices {\\em [(deltai,pi1(i)),...,(deltai,pik(i))]} if the permutations {\\em pi1},{}...,{}{\\em pik} are in list notation and are permuting {\\em {1,2,...,n}}.") (((|List| (|Matrix| (|Integer|))) (|List| (|Permutation| (|Integer|))) (|Integer|)) "\\spad{permutationRepresentation([pi1,...,pik],n)} returns the list of matrices {\\em [(deltai,pi1(i)),...,(deltai,pik(i))]} (Kronecker delta) for the permutations {\\em pi1,...,pik} of {\\em {1,2,...,n}}.") (((|Matrix| (|Integer|)) (|List| (|Integer|))) "\\spad{permutationRepresentation(pi,n)} returns the matrix {\\em (deltai,pi(i))} (Kronecker delta) if the permutation {\\em pi} is in list notation and permutes {\\em {1,2,...,n}}.") (((|Matrix| (|Integer|)) (|Permutation| (|Integer|)) (|Integer|)) "\\spad{permutationRepresentation(pi,n)} returns the matrix {\\em (deltai,pi(i))} (Kronecker delta) for a permutation {\\em pi} of {\\em {1,2,...,n}}.")) (|tensorProduct| (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{tensorProduct([a1,...ak])} calculates the list of Kronecker products of each matrix {\\em ai} with itself for {1 \\spad{<=} \\spad{i} \\spad{<=} \\spad{k}}. Note: If the list of matrices corresponds to a group representation (repr. of generators) of one group,{} then these matrices correspond to the tensor product of the representation with itself.") (((|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{tensorProduct(a)} calculates the Kronecker product of the matrix {\\em a} with itself.") (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{tensorProduct([a1,...,ak],[b1,...,bk])} calculates the list of Kronecker products of the matrices {\\em ai} and {\\em bi} for {1 \\spad{<=} \\spad{i} \\spad{<=} \\spad{k}}. Note: If each list of matrices corresponds to a group representation (repr. of generators) of one group,{} then these matrices correspond to the tensor product of the two representations.") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{tensorProduct(a,b)} calculates the Kronecker product of the matrices {\\em a} and \\spad{b}. Note: if each matrix corresponds to a group representation (repr. of generators) of one group,{} then these matrices correspond to the tensor product of the two representations.")) (|symmetricTensors| (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|PositiveInteger|)) "\\spad{symmetricTensors(la,n)} applies to each \\spad{m}-by-\\spad{m} square matrix in the list {\\em la} the irreducible,{} polynomial representation of the general linear group {\\em GLm} which corresponds to the partition {\\em (n,0,...,0)} of \\spad{n}. Error: if the matrices in {\\em la} are not square matrices. Note: this corresponds to the symmetrization of the representation with the trivial representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the symmetric tensors of the \\spad{n}-fold tensor product.") (((|Matrix| |#1|) (|Matrix| |#1|) (|PositiveInteger|)) "\\spad{symmetricTensors(a,n)} applies to the \\spad{m}-by-\\spad{m} square matrix {\\em a} the irreducible,{} polynomial representation of the general linear group {\\em GLm} which corresponds to the partition {\\em (n,0,...,0)} of \\spad{n}. Error: if {\\em a} is not a square matrix. Note: this corresponds to the symmetrization of the representation with the trivial representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the symmetric tensors of the \\spad{n}-fold tensor product.")) (|createGenericMatrix| (((|Matrix| (|Polynomial| |#1|)) (|NonNegativeInteger|)) "\\spad{createGenericMatrix(m)} creates a square matrix of dimension \\spad{k} whose entry at the \\spad{i}-th row and \\spad{j}-th column is the indeterminate {\\em x[i,j]} (double subscripted).")) (|antisymmetricTensors| (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|PositiveInteger|)) "\\spad{antisymmetricTensors(la,n)} applies to each \\spad{m}-by-\\spad{m} square matrix in the list {\\em la} the irreducible,{} polynomial representation of the general linear group {\\em GLm} which corresponds to the partition {\\em (1,1,...,1,0,0,...,0)} of \\spad{n}. Error: if \\spad{n} is greater than \\spad{m}. Note: this corresponds to the symmetrization of the representation with the sign representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the antisymmetric tensors of the \\spad{n}-fold tensor product.") (((|Matrix| |#1|) (|Matrix| |#1|) (|PositiveInteger|)) "\\spad{antisymmetricTensors(a,n)} applies to the square matrix {\\em a} the irreducible,{} polynomial representation of the general linear group {\\em GLm},{} where \\spad{m} is the number of rows of {\\em a},{} which corresponds to the partition {\\em (1,1,...,1,0,0,...,0)} of \\spad{n}. Error: if \\spad{n} is greater than \\spad{m}. Note: this corresponds to the symmetrization of the representation with the sign representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the antisymmetric tensors of the \\spad{n}-fold tensor product."))) NIL -((|HasAttribute| |#1| (QUOTE (-4419 "*")))) -(-1030 R) +((|HasAttribute| |#1| (QUOTE (-4420 "*")))) +(-1031 R) ((|constructor| (NIL "RepresentationPackage2 provides functions for working with modular representations of finite groups and algebra. The routines in this package are created,{} using ideas of \\spad{R}. Parker,{} (the meat-Axe) to get smaller representations from bigger ones,{} \\spadignore{i.e.} finding sub- and factormodules,{} or to show,{} that such the representations are irreducible. Note: most functions are randomized functions of Las Vegas type \\spadignore{i.e.} every answer is correct,{} but with small probability the algorithm fails to get an answer.")) (|scanOneDimSubspaces| (((|Vector| |#1|) (|List| (|Vector| |#1|)) (|Integer|)) "\\spad{scanOneDimSubspaces(basis,n)} gives a canonical representative of the {\\em n}\\spad{-}th one-dimensional subspace of the vector space generated by the elements of {\\em basis},{} all from {\\em R**n}. The coefficients of the representative are of shape {\\em (0,...,0,1,*,...,*)},{} {\\em *} in \\spad{R}. If the size of \\spad{R} is \\spad{q},{} then there are {\\em (q**n-1)/(q-1)} of them. We first reduce \\spad{n} modulo this number,{} then find the largest \\spad{i} such that {\\em +/[q**i for i in 0..i-1] <= n}. Subtracting this sum of powers from \\spad{n} results in an \\spad{i}-digit number to \\spad{basis} \\spad{q}. This fills the positions of the stars.")) (|meatAxe| (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|PositiveInteger|)) "\\spad{meatAxe(aG, numberOfTries)} calls {\\em meatAxe(aG,true,numberOfTries,7)}. Notes: 7 covers the case of three-dimensional kernels over the field with 2 elements.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Boolean|)) "\\spad{meatAxe(aG, randomElements)} calls {\\em meatAxe(aG,false,6,7)},{} only using Parker\\spad{'s} fingerprints,{} if {\\em randomElemnts} is \\spad{false}. If it is \\spad{true},{} it calls {\\em meatAxe(aG,true,25,7)},{} only using random elements. Note: the choice of 25 was rather arbitrary. Also,{} 7 covers the case of three-dimensional kernels over the field with 2 elements.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|))) "\\spad{meatAxe(aG)} calls {\\em meatAxe(aG,false,25,7)} returns a 2-list of representations as follows. All matrices of argument \\spad{aG} are assumed to be square and of equal size. Then \\spad{aG} generates a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an A-module in the usual way. meatAxe(\\spad{aG}) creates at most 25 random elements of the algebra,{} tests them for singularity. If singular,{} it tries at most 7 elements of its kernel to generate a proper submodule. If successful a list which contains first the list of the representations of the submodule,{} then a list of the representations of the factor module is returned. Otherwise,{} if we know that all the kernel is already scanned,{} Norton\\spad{'s} irreducibility test can be used either to prove irreducibility or to find the splitting. Notes: the first 6 tries use Parker\\spad{'s} fingerprints. Also,{} 7 covers the case of three-dimensional kernels over the field with 2 elements.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Boolean|) (|Integer|) (|Integer|)) "\\spad{meatAxe(aG,randomElements,numberOfTries, maxTests)} returns a 2-list of representations as follows. All matrices of argument \\spad{aG} are assumed to be square and of equal size. Then \\spad{aG} generates a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an A-module in the usual way. meatAxe(\\spad{aG},{}\\spad{numberOfTries},{} maxTests) creates at most {\\em numberOfTries} random elements of the algebra,{} tests them for singularity. If singular,{} it tries at most {\\em maxTests} elements of its kernel to generate a proper submodule. If successful,{} a 2-list is returned: first,{} a list containing first the list of the representations of the submodule,{} then a list of the representations of the factor module. Otherwise,{} if we know that all the kernel is already scanned,{} Norton\\spad{'s} irreducibility test can be used either to prove irreducibility or to find the splitting. If {\\em randomElements} is {\\em false},{} the first 6 tries use Parker\\spad{'s} fingerprints.")) (|split| (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Vector| (|Vector| |#1|))) "\\spad{split(aG,submodule)} uses a proper \\spad{submodule} of {\\em R**n} to create the representations of the \\spad{submodule} and of the factor module.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Vector| |#1|)) "\\spad{split(aG, vector)} returns a subalgebra \\spad{A} of all square matrix of dimension \\spad{n} as a list of list of matrices,{} generated by the list of matrices \\spad{aG},{} where \\spad{n} denotes both the size of vector as well as the dimension of each of the square matrices. {\\em V R} is an A-module in the natural way. split(\\spad{aG},{} vector) then checks whether the cyclic submodule generated by {\\em vector} is a proper submodule of {\\em V R}. If successful,{} it returns a two-element list,{} which contains first the list of the representations of the submodule,{} then the list of the representations of the factor module. If the vector generates the whole module,{} a one-element list of the old representation is given. Note: a later version this should call the other split.")) (|isAbsolutelyIrreducible?| (((|Boolean|) (|List| (|Matrix| |#1|))) "\\spad{isAbsolutelyIrreducible?(aG)} calls {\\em isAbsolutelyIrreducible?(aG,25)}. Note: the choice of 25 was rather arbitrary.") (((|Boolean|) (|List| (|Matrix| |#1|)) (|Integer|)) "\\spad{isAbsolutelyIrreducible?(aG, numberOfTries)} uses Norton\\spad{'s} irreducibility test to check for absolute irreduciblity,{} assuming if a one-dimensional kernel is found. As no field extension changes create \"new\" elements in a one-dimensional space,{} the criterium stays \\spad{true} for every extension. The method looks for one-dimensionals only by creating random elements (no fingerprints) since a run of {\\em meatAxe} would have proved absolute irreducibility anyway.")) (|areEquivalent?| (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|Integer|)) "\\spad{areEquivalent?(aG0,aG1,numberOfTries)} calls {\\em areEquivalent?(aG0,aG1,true,25)}. Note: the choice of 25 was rather arbitrary.") (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{areEquivalent?(aG0,aG1)} calls {\\em areEquivalent?(aG0,aG1,true,25)}. Note: the choice of 25 was rather arbitrary.") (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|Boolean|) (|Integer|)) "\\spad{areEquivalent?(aG0,aG1,randomelements,numberOfTries)} tests whether the two lists of matrices,{} all assumed of same square shape,{} can be simultaneously conjugated by a non-singular matrix. If these matrices represent the same group generators,{} the representations are equivalent. The algorithm tries {\\em numberOfTries} times to create elements in the generated algebras in the same fashion. If their ranks differ,{} they are not equivalent. If an isomorphism is assumed,{} then the kernel of an element of the first algebra is mapped to the kernel of the corresponding element in the second algebra. Now consider the one-dimensional ones. If they generate the whole space (\\spadignore{e.g.} irreducibility !) we use {\\em standardBasisOfCyclicSubmodule} to create the only possible transition matrix. The method checks whether the matrix conjugates all corresponding matrices from {\\em aGi}. The way to choose the singular matrices is as in {\\em meatAxe}. If the two representations are equivalent,{} this routine returns the transformation matrix {\\em TM} with {\\em aG0.i * TM = TM * aG1.i} for all \\spad{i}. If the representations are not equivalent,{} a small 0-matrix is returned. Note: the case with different sets of group generators cannot be handled.")) (|standardBasisOfCyclicSubmodule| (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|Vector| |#1|)) "\\spad{standardBasisOfCyclicSubmodule(lm,v)} returns a matrix as follows. It is assumed that the size \\spad{n} of the vector equals the number of rows and columns of the matrices. Then the matrices generate a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an \\spad{A}-module in the natural way. standardBasisOfCyclicSubmodule(\\spad{lm},{}\\spad{v}) calculates a matrix whose non-zero column vectors are the \\spad{R}-Basis of {\\em Av} achieved in the way as described in section 6 of \\spad{R}. A. Parker\\spad{'s} \"The Meat-Axe\". Note: in contrast to {\\em cyclicSubmodule},{} the result is not in echelon form.")) (|cyclicSubmodule| (((|Vector| (|Vector| |#1|)) (|List| (|Matrix| |#1|)) (|Vector| |#1|)) "\\spad{cyclicSubmodule(lm,v)} generates a basis as follows. It is assumed that the size \\spad{n} of the vector equals the number of rows and columns of the matrices. Then the matrices generate a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an \\spad{A}-module in the natural way. cyclicSubmodule(\\spad{lm},{}\\spad{v}) generates the \\spad{R}-Basis of {\\em Av} as described in section 6 of \\spad{R}. A. Parker\\spad{'s} \"The Meat-Axe\". Note: in contrast to the description in \"The Meat-Axe\" and to {\\em standardBasisOfCyclicSubmodule} the result is in echelon form.")) (|createRandomElement| (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|Matrix| |#1|)) "\\spad{createRandomElement(aG,x)} creates a random element of the group algebra generated by {\\em aG}.")) (|completeEchelonBasis| (((|Matrix| |#1|) (|Vector| (|Vector| |#1|))) "\\spad{completeEchelonBasis(lv)} completes the basis {\\em lv} assumed to be in echelon form of a subspace of {\\em R**n} (\\spad{n} the length of all the vectors in {\\em lv}) with unit vectors to a basis of {\\em R**n}. It is assumed that the argument is not an empty vector and that it is not the basis of the 0-subspace. Note: the rows of the result correspond to the vectors of the basis."))) NIL ((-12 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-308)))) -(-1031 S) +(-1032 S) ((|constructor| (NIL "Implements multiplication by repeated addition")) (|double| ((|#1| (|PositiveInteger|) |#1|) "\\spad{double(i, r)} multiplies \\spad{r} by \\spad{i} using repeated doubling.")) (+ (($ $ $) "\\spad{x+y} returns the sum of \\spad{x} and \\spad{y}"))) NIL NIL -(-1032) +(-1033) ((|constructor| (NIL "Package for the computation of eigenvalues and eigenvectors. This package works for matrices with coefficients which are rational functions over the integers. (see \\spadtype{Fraction Polynomial Integer}). The eigenvalues and eigenvectors are expressed in terms of radicals.")) (|orthonormalBasis| (((|List| (|Matrix| (|Expression| (|Integer|)))) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{orthonormalBasis(m)} returns the orthogonal matrix \\spad{b} such that \\spad{b*m*(inverse b)} is diagonal. Error: if \\spad{m} is not a symmetric matrix.")) (|gramschmidt| (((|List| (|Matrix| (|Expression| (|Integer|)))) (|List| (|Matrix| (|Expression| (|Integer|))))) "\\spad{gramschmidt(lv)} converts the list of column vectors \\spad{lv} into a set of orthogonal column vectors of euclidean length 1 using the Gram-Schmidt algorithm.")) (|normalise| (((|Matrix| (|Expression| (|Integer|))) (|Matrix| (|Expression| (|Integer|)))) "\\spad{normalise(v)} returns the column vector \\spad{v} divided by its euclidean norm; when possible,{} the vector \\spad{v} is expressed in terms of radicals.")) (|eigenMatrix| (((|Union| (|Matrix| (|Expression| (|Integer|))) "failed") (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{eigenMatrix(m)} returns the matrix \\spad{b} such that \\spad{b*m*(inverse b)} is diagonal,{} or \"failed\" if no such \\spad{b} exists.")) (|radicalEigenvalues| (((|List| (|Expression| (|Integer|))) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{radicalEigenvalues(m)} computes the eigenvalues of the matrix \\spad{m}; when possible,{} the eigenvalues are expressed in terms of radicals.")) (|radicalEigenvector| (((|List| (|Matrix| (|Expression| (|Integer|)))) (|Expression| (|Integer|)) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{radicalEigenvector(c,m)} computes the eigenvector(\\spad{s}) of the matrix \\spad{m} corresponding to the eigenvalue \\spad{c}; when possible,{} values are expressed in terms of radicals.")) (|radicalEigenvectors| (((|List| (|Record| (|:| |radval| (|Expression| (|Integer|))) (|:| |radmult| (|Integer|)) (|:| |radvect| (|List| (|Matrix| (|Expression| (|Integer|))))))) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{radicalEigenvectors(m)} computes the eigenvalues and the corresponding eigenvectors of the matrix \\spad{m}; when possible,{} values are expressed in terms of radicals."))) NIL NIL -(-1033 S) +(-1034 S) ((|constructor| (NIL "Implements exponentiation by repeated squaring")) (|expt| ((|#1| |#1| (|PositiveInteger|)) "\\spad{expt(r, i)} computes r**i by repeated squaring")) (* (($ $ $) "\\spad{x*y} returns the product of \\spad{x} and \\spad{y}"))) NIL NIL -(-1034 S) +(-1035 S) ((|constructor| (NIL "This package provides coercions for the special types \\spadtype{Exit} and \\spadtype{Void}.")) (|coerce| ((|#1| (|Exit|)) "\\spad{coerce(e)} is never really evaluated. This coercion is used for formal type correctness when a function will not return directly to its caller.") (((|Void|) |#1|) "\\spad{coerce(s)} throws all information about \\spad{s} away. This coercion allows values of any type to appear in contexts where they will not be used. For example,{} it allows the resolution of different types in the \\spad{then} and \\spad{else} branches when an \\spad{if} is in a context where the resulting value is not used."))) NIL NIL -(-1035 -3867 |Expon| |VarSet| |FPol| |LFPol|) +(-1036 -3879 |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)) +(((-4420 "*") . T) (-4412 . T) (-4413 . T) (-4415 . T)) NIL -(-1036) -((|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 (|:| -1791 (-1177)) (|:| -4232 (-52))) (QUOTE (-1101))) (|HasCategory| (-2 (|:| -1791 (-1177)) (|:| -4232 (-52))) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1791) (QUOTE (-1177))) (LIST (QUOTE |:|) (QUOTE -4232) (QUOTE (-52))))))) (-2797 (|HasCategory| (-2 (|:| -1791 (-1177)) (|:| -4232 (-52))) (QUOTE (-1101))) (|HasCategory| (-52) (QUOTE (-1101)))) (-2797 (|HasCategory| (-2 (|:| -1791 (-1177)) (|:| -4232 (-52))) (QUOTE (-1101))) (|HasCategory| (-2 (|:| -1791 (-1177)) (|:| -4232 (-52))) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-52) (QUOTE (-1101))) (|HasCategory| (-52) (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| (-2 (|:| -1791 (-1177)) (|:| -4232 (-52))) (LIST (QUOTE -615) (QUOTE (-539)))) (-12 (|HasCategory| (-52) (QUOTE (-1101))) (|HasCategory| (-52) (LIST (QUOTE -310) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -1791 (-1177)) (|:| -4232 (-52))) (QUOTE (-1101))) (|HasCategory| (-1177) (QUOTE (-851))) (|HasCategory| (-52) (QUOTE (-1101))) (-2797 (|HasCategory| (-2 (|:| -1791 (-1177)) (|:| -4232 (-52))) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-52) (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| (-52) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-2 (|:| -1791 (-1177)) (|:| -4232 (-52))) (LIST (QUOTE -614) (QUOTE (-863))))) (-1037) +((|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.}"))) +((-4418 . T) (-4419 . T)) +((-12 (|HasCategory| (-2 (|:| -1795 (-1178)) (|:| -4237 (-52))) (QUOTE (-1102))) (|HasCategory| (-2 (|:| -1795 (-1178)) (|:| -4237 (-52))) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1795) (QUOTE (-1178))) (LIST (QUOTE |:|) (QUOTE -4237) (QUOTE (-52))))))) (-2800 (|HasCategory| (-2 (|:| -1795 (-1178)) (|:| -4237 (-52))) (QUOTE (-1102))) (|HasCategory| (-52) (QUOTE (-1102)))) (-2800 (|HasCategory| (-2 (|:| -1795 (-1178)) (|:| -4237 (-52))) (QUOTE (-1102))) (|HasCategory| (-2 (|:| -1795 (-1178)) (|:| -4237 (-52))) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-52) (QUOTE (-1102))) (|HasCategory| (-52) (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| (-2 (|:| -1795 (-1178)) (|:| -4237 (-52))) (LIST (QUOTE -615) (QUOTE (-539)))) (-12 (|HasCategory| (-52) (QUOTE (-1102))) (|HasCategory| (-52) (LIST (QUOTE -310) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -1795 (-1178)) (|:| -4237 (-52))) (QUOTE (-1102))) (|HasCategory| (-1178) (QUOTE (-851))) (|HasCategory| (-52) (QUOTE (-1102))) (-2800 (|HasCategory| (-2 (|:| -1795 (-1178)) (|:| -4237 (-52))) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-52) (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| (-52) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-2 (|:| -1795 (-1178)) (|:| -4237 (-52))) (LIST (QUOTE -614) (QUOTE (-863))))) +(-1038) ((|constructor| (NIL "This domain represents `return' expressions.")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression returned by `e'."))) NIL NIL -(-1038 A S) +(-1039 A S) ((|constructor| (NIL "A is retractable to \\spad{B} means that some elementsif A can be converted into elements of \\spad{B} and any element of \\spad{B} can be converted into an element of A.")) (|retract| ((|#2| $) "\\spad{retract(a)} transforms a into an element of \\spad{S} if possible. Error: if a cannot be made into an element of \\spad{S}.")) (|retractIfCan| (((|Union| |#2| "failed") $) "\\spad{retractIfCan(a)} transforms a into an element of \\spad{S} if possible. Returns \"failed\" if a cannot be made into an element of \\spad{S}."))) NIL NIL -(-1039 S) +(-1040 S) ((|constructor| (NIL "A is retractable to \\spad{B} means that some elementsif A can be converted into elements of \\spad{B} and any element of \\spad{B} can be converted into an element of A.")) (|retract| ((|#1| $) "\\spad{retract(a)} transforms a into an element of \\spad{S} if possible. Error: if a cannot be made into an element of \\spad{S}.")) (|retractIfCan| (((|Union| |#1| "failed") $) "\\spad{retractIfCan(a)} transforms a into an element of \\spad{S} if possible. Returns \"failed\" if a cannot be made into an element of \\spad{S}."))) NIL NIL -(-1040 Q R) +(-1041 Q R) ((|constructor| (NIL "RetractSolvePackage is an interface to \\spadtype{SystemSolvePackage} that attempts to retract the coefficients of the equations before solving.")) (|solveRetract| (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#2|))))) (|List| (|Polynomial| |#2|)) (|List| (|Symbol|))) "\\spad{solveRetract(lp,lv)} finds the solutions of the list \\spad{lp} of rational functions with respect to the list of symbols \\spad{lv}. The function tries to retract all the coefficients of the equations to \\spad{Q} before solving if possible."))) NIL NIL -(-1041) +(-1042) ((|t| (((|Mapping| (|Float|)) (|NonNegativeInteger|)) "\\spad{t(n)} \\undocumented")) (F (((|Mapping| (|Float|)) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{F(n,m)} \\undocumented")) (|Beta| (((|Mapping| (|Float|)) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{Beta(n,m)} \\undocumented")) (|chiSquare| (((|Mapping| (|Float|)) (|NonNegativeInteger|)) "\\spad{chiSquare(n)} \\undocumented")) (|exponential| (((|Mapping| (|Float|)) (|Float|)) "\\spad{exponential(f)} \\undocumented")) (|normal| (((|Mapping| (|Float|)) (|Float|) (|Float|)) "\\spad{normal(f,g)} \\undocumented")) (|uniform| (((|Mapping| (|Float|)) (|Float|) (|Float|)) "\\spad{uniform(f,g)} \\undocumented")) (|chiSquare1| (((|Float|) (|NonNegativeInteger|)) "\\spad{chiSquare1(n)} \\undocumented")) (|exponential1| (((|Float|)) "\\spad{exponential1()} \\undocumented")) (|normal01| (((|Float|)) "\\spad{normal01()} \\undocumented")) (|uniform01| (((|Float|)) "\\spad{uniform01()} \\undocumented"))) NIL NIL -(-1042 UP) +(-1043 UP) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients which are rational functions with integer coefficients.")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p}."))) NIL NIL -(-1043 R) +(-1044 R) ((|constructor| (NIL "\\spadtype{RationalFunctionFactorizer} contains the factor function (called factorFraction) which factors fractions of polynomials by factoring the numerator and denominator. Since any non zero fraction is a unit the usual factor operation will just return the original fraction.")) (|factorFraction| (((|Fraction| (|Factored| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|))) "\\spad{factorFraction(r)} factors the numerator and the denominator of the polynomial fraction \\spad{r}."))) NIL NIL -(-1044 R) +(-1045 R) ((|constructor| (NIL "Utilities that provide the same top-level manipulations on fractions than on polynomials.")) (|coerce| (((|Fraction| (|Polynomial| |#1|)) |#1|) "\\spad{coerce(r)} returns \\spad{r} viewed as a rational function over \\spad{R}.")) (|eval| (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) "\\spad{eval(f, [v1 = g1,...,vn = gn])} returns \\spad{f} with each \\spad{vi} replaced by \\spad{gi} in parallel,{} \\spadignore{i.e.} \\spad{vi}\\spad{'s} appearing inside the \\spad{gi}\\spad{'s} are not replaced. Error: if any \\spad{vi} is not a symbol.") (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|)))) "\\spad{eval(f, v = g)} returns \\spad{f} with \\spad{v} replaced by \\spad{g}. Error: if \\spad{v} is not a symbol.") (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|List| (|Symbol|)) (|List| (|Fraction| (|Polynomial| |#1|)))) "\\spad{eval(f, [v1,...,vn], [g1,...,gn])} returns \\spad{f} with each \\spad{vi} replaced by \\spad{gi} in parallel,{} \\spadignore{i.e.} \\spad{vi}\\spad{'s} appearing inside the \\spad{gi}\\spad{'s} are not replaced.") (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|))) "\\spad{eval(f, v, g)} returns \\spad{f} with \\spad{v} replaced by \\spad{g}.")) (|multivariate| (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|)))) (|Symbol|)) "\\spad{multivariate(f, v)} applies both the numerator and denominator of \\spad{f} to \\spad{v}.")) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|)))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{univariate(f, v)} returns \\spad{f} viewed as a univariate rational function in \\spad{v}.")) (|mainVariable| (((|Union| (|Symbol|) "failed") (|Fraction| (|Polynomial| |#1|))) "\\spad{mainVariable(f)} returns the highest variable appearing in the numerator or the denominator of \\spad{f},{} \"failed\" if \\spad{f} has no variables.")) (|variables| (((|List| (|Symbol|)) (|Fraction| (|Polynomial| |#1|))) "\\spad{variables(f)} returns the list of variables appearing in the numerator or the denominator of \\spad{f}."))) NIL NIL -(-1045 T$) +(-1046 T$) ((|constructor| (NIL "This category defines the common interface for \\spad{RGB} color models.")) (|componentUpperBound| ((|#1|) "componentUpperBound is an upper bound for all component values.")) (|blue| ((|#1| $) "\\spad{blue(c)} returns the `blue' component of \\spad{`c'}.")) (|green| ((|#1| $) "\\spad{green(c)} returns the `green' component of \\spad{`c'}.")) (|red| ((|#1| $) "\\spad{red(c)} returns the `red' component of \\spad{`c'}."))) NIL NIL -(-1046 T$) +(-1047 T$) ((|constructor| (NIL "This category defines the common interface for \\spad{RGB} color spaces.")) (|whitePoint| (($) "whitePoint is the contant indicating the white point of this color space."))) NIL NIL -(-1047 R |ls|) +(-1048 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)) -((-12 (|HasCategory| (-781 |#1| (-865 |#2|)) (QUOTE (-1101))) (|HasCategory| (-781 |#1| (-865 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -781) (|devaluate| |#1|) (LIST (QUOTE -865) (|devaluate| |#2|)))))) (|HasCategory| (-781 |#1| (-865 |#2|)) (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| (-781 |#1| (-865 |#2|)) (QUOTE (-1101))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| (-865 |#2|) (QUOTE (-370))) (|HasCategory| (-781 |#1| (-865 |#2|)) (LIST (QUOTE -614) (QUOTE (-863))))) -(-1048) +((-4419 . T) (-4418 . T)) +((-12 (|HasCategory| (-781 |#1| (-865 |#2|)) (QUOTE (-1102))) (|HasCategory| (-781 |#1| (-865 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -781) (|devaluate| |#1|) (LIST (QUOTE -865) (|devaluate| |#2|)))))) (|HasCategory| (-781 |#1| (-865 |#2|)) (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| (-781 |#1| (-865 |#2|)) (QUOTE (-1102))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| (-865 |#2|) (QUOTE (-370))) (|HasCategory| (-781 |#1| (-865 |#2|)) (LIST (QUOTE -614) (QUOTE (-863))))) +(-1049) ((|constructor| (NIL "This package exports integer distributions")) (|ridHack1| (((|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{ridHack1(i,j,k,l)} \\undocumented")) (|geometric| (((|Mapping| (|Integer|)) |RationalNumber|) "\\spad{geometric(f)} \\undocumented")) (|poisson| (((|Mapping| (|Integer|)) |RationalNumber|) "\\spad{poisson(f)} \\undocumented")) (|binomial| (((|Mapping| (|Integer|)) (|Integer|) |RationalNumber|) "\\spad{binomial(n,f)} \\undocumented")) (|uniform| (((|Mapping| (|Integer|)) (|Segment| (|Integer|))) "\\spad{uniform(s)} \\undocumented"))) NIL NIL -(-1049 S) +(-1050 S) ((|constructor| (NIL "The category of rings with unity,{} always associative,{} but not necessarily commutative.")) (|unitsKnown| ((|attribute|) "recip truly yields reciprocal or \"failed\" if not a unit. Note: \\spad{recip(0) = \"failed\"}.")) (|characteristic| (((|NonNegativeInteger|)) "\\spad{characteristic()} returns the characteristic of the ring this is the smallest positive integer \\spad{n} such that \\spad{n*x=0} for all \\spad{x} in the ring,{} or zero if no such \\spad{n} exists."))) NIL NIL -(-1050) +(-1051) ((|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)) +((-4415 . T)) NIL -(-1051 |xx| -3867) +(-1052 |xx| -3879) ((|constructor| (NIL "This package exports rational interpolation algorithms"))) NIL NIL -(-1052 R) +(-1053 R) ((|constructor| (NIL "\\indented{2}{A set is an \\spad{R}-right linear set if it is stable by right-dilation} \\indented{2}{by elements in the ring \\spad{R}.\\space{2}This category differs from} \\indented{2}{\\spad{RightModule} in that no other assumption (such as addition)} \\indented{2}{is made about the underlying set.} See Also: LeftLinearSet.")) (* (($ $ |#1|) "\\spad{r*x} is the left-dilation of \\spad{x} by \\spad{r}.")) (|zero?| (((|Boolean|) $) "\\spad{zero? x} holds is \\spad{x} is the origin.")) ((|Zero|) (($) "\\spad{0} represents the origin of the linear set"))) NIL NIL -(-1053 S |m| |n| R |Row| |Col|) +(-1054 S |m| |n| R |Row| |Col|) ((|constructor| (NIL "\\spadtype{RectangularMatrixCategory} is a category of matrices of fixed dimensions. The dimensions of the matrix will be parameters of the domain. Domains in this category will be \\spad{R}-modules and will be non-mutable.")) (|nullSpace| (((|List| |#6|) $) "\\spad{nullSpace(m)}+ returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#4|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#4|) "\\spad{exquo(m,r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (|map| (($ (|Mapping| |#4| |#4| |#4|) $ $) "\\spad{map(f,a,b)} returns \\spad{c},{} where \\spad{c} is such that \\spad{c(i,j) = f(a(i,j),b(i,j))} for all \\spad{i},{} \\spad{j}.") (($ (|Mapping| |#4| |#4|) $) "\\spad{map(f,a)} returns \\spad{b},{} where \\spad{b(i,j) = a(i,j)} for all \\spad{i},{} \\spad{j}.")) (|column| ((|#6| $ (|Integer|)) "\\spad{column(m,j)} returns the \\spad{j}th column of the matrix \\spad{m}. Error: if the index outside the proper range.")) (|row| ((|#5| $ (|Integer|)) "\\spad{row(m,i)} returns the \\spad{i}th row of the matrix \\spad{m}. Error: if the index is outside the proper range.")) (|qelt| ((|#4| $ (|Integer|) (|Integer|)) "\\spad{qelt(m,i,j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m}. Note: there is NO error check to determine if indices are in the proper ranges.")) (|elt| ((|#4| $ (|Integer|) (|Integer|) |#4|) "\\spad{elt(m,i,j,r)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m},{} if \\spad{m} has an \\spad{i}th row and a \\spad{j}th column,{} and returns \\spad{r} otherwise.") ((|#4| $ (|Integer|) (|Integer|)) "\\spad{elt(m,i,j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m}. Error: if indices are outside the proper ranges.")) (|listOfLists| (((|List| (|List| |#4|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|ncols| (((|NonNegativeInteger|) $) "\\spad{ncols(m)} returns the number of columns in the matrix \\spad{m}.")) (|nrows| (((|NonNegativeInteger|) $) "\\spad{nrows(m)} returns the number of rows in the matrix \\spad{m}.")) (|maxColIndex| (((|Integer|) $) "\\spad{maxColIndex(m)} returns the index of the 'last' column of the matrix \\spad{m}.")) (|minColIndex| (((|Integer|) $) "\\spad{minColIndex(m)} returns the index of the 'first' column of the matrix \\spad{m}.")) (|maxRowIndex| (((|Integer|) $) "\\spad{maxRowIndex(m)} returns the index of the 'last' row of the matrix \\spad{m}.")) (|minRowIndex| (((|Integer|) $) "\\spad{minRowIndex(m)} returns the index of the 'first' row of the matrix \\spad{m}.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,j] = -m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,j] = m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.")) (|matrix| (($ (|List| (|List| |#4|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix.")) (|finiteAggregate| ((|attribute|) "matrices are finite"))) NIL ((|HasCategory| |#4| (QUOTE (-308))) (|HasCategory| |#4| (QUOTE (-365))) (|HasCategory| |#4| (QUOTE (-559))) (|HasCategory| |#4| (QUOTE (-172)))) -(-1054 |m| |n| R |Row| |Col|) +(-1055 |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)) +((-4418 . T) (-4413 . T) (-4412 . T)) NIL -(-1055 |m| |n| R) +(-1056 |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)) -((|HasCategory| |#3| (QUOTE (-172))) (-2797 (-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 (-1101))) (|HasCategory| |#3| (LIST (QUOTE -310) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -615) (QUOTE (-539)))) (-2797 (|HasCategory| |#3| (QUOTE (-172))) (|HasCategory| |#3| (QUOTE (-365)))) (|HasCategory| |#3| (QUOTE (-365))) (|HasCategory| |#3| (QUOTE (-1101))) (|HasCategory| |#3| (QUOTE (-308))) (|HasCategory| |#3| (QUOTE (-559))) (-12 (|HasCategory| |#3| (QUOTE (-1101))) (|HasCategory| |#3| (LIST (QUOTE -310) (|devaluate| |#3|)))) (|HasCategory| |#3| (LIST (QUOTE -614) (QUOTE (-863))))) -(-1056 |m| |n| R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2) +((-4418 . T) (-4413 . T) (-4412 . T)) +((|HasCategory| |#3| (QUOTE (-172))) (-2800 (-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 (-1102))) (|HasCategory| |#3| (LIST (QUOTE -310) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -615) (QUOTE (-539)))) (-2800 (|HasCategory| |#3| (QUOTE (-172))) (|HasCategory| |#3| (QUOTE (-365)))) (|HasCategory| |#3| (QUOTE (-365))) (|HasCategory| |#3| (QUOTE (-1102))) (|HasCategory| |#3| (QUOTE (-308))) (|HasCategory| |#3| (QUOTE (-559))) (-12 (|HasCategory| |#3| (QUOTE (-1102))) (|HasCategory| |#3| (LIST (QUOTE -310) (|devaluate| |#3|)))) (|HasCategory| |#3| (LIST (QUOTE -614) (QUOTE (-863))))) +(-1057 |m| |n| R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2) ((|constructor| (NIL "\\spadtype{RectangularMatrixCategoryFunctions2} provides functions between two matrix domains. The functions provided are \\spadfun{map} and \\spadfun{reduce}.")) (|reduce| ((|#7| (|Mapping| |#7| |#3| |#7|) |#6| |#7|) "\\spad{reduce(f,m,r)} returns a matrix \\spad{n} where \\spad{n[i,j] = f(m[i,j],r)} for all indices spad{\\spad{i}} and \\spad{j}.")) (|map| ((|#10| (|Mapping| |#7| |#3|) |#6|) "\\spad{map(f,m)} applies the function \\spad{f} to the elements of the matrix \\spad{m}."))) NIL NIL -(-1057 R) +(-1058 R) ((|constructor| (NIL "The category of right modules over an \\spad{rng} (ring not necessarily with unit). This is an abelian group which supports right multiplation by elements of the \\spad{rng}. \\blankline"))) NIL NIL -(-1058 S T$) +(-1059 S T$) ((|constructor| (NIL "This domain represents the notion of binding a variable to range over a specific segment (either bounded,{} or half bounded).")) (|segment| ((|#1| $) "\\spad{segment(x)} returns the segment from the right hand side of the \\spadtype{RangeBinding}. For example,{} if \\spad{x} is \\spad{v=s},{} then \\spad{segment(x)} returns \\spad{s}.")) (|variable| (((|Symbol|) $) "\\spad{variable(x)} returns the variable from the left hand side of the \\spadtype{RangeBinding}. For example,{} if \\spad{x} is \\spad{v=s},{} then \\spad{variable(x)} returns \\spad{v}.")) (|equation| (($ (|Symbol|) |#1|) "\\spad{equation(v,s)} creates a segment binding value with variable \\spad{v} and segment \\spad{s}. Note that the interpreter parses \\spad{v=s} to this form."))) NIL -((|HasCategory| |#1| (QUOTE (-1101)))) -(-1059) +((|HasCategory| |#1| (QUOTE (-1102)))) +(-1060) ((|constructor| (NIL "The category of associative rings,{} not necessarily commutative,{} and not necessarily with a 1. This is a combination of an abelian group and a semigroup,{} with multiplication distributing over addition. \\blankline"))) NIL NIL -(-1060 S) +(-1061 S) ((|constructor| (NIL "The real number system category is intended as a model for the real numbers. The real numbers form an ordered normed field. Note that we have purposely not included \\spadtype{DifferentialRing} or the elementary functions (see \\spadtype{TranscendentalFunctionCategory}) in the definition.")) (|abs| (($ $) "\\spad{abs x} returns the absolute value of \\spad{x}.")) (|round| (($ $) "\\spad{round x} computes the integer closest to \\spad{x}.")) (|truncate| (($ $) "\\spad{truncate x} returns the integer between \\spad{x} and 0 closest to \\spad{x}.")) (|fractionPart| (($ $) "\\spad{fractionPart x} returns the fractional part of \\spad{x}.")) (|wholePart| (((|Integer|) $) "\\spad{wholePart x} returns the integer part of \\spad{x}.")) (|floor| (($ $) "\\spad{floor x} returns the largest integer \\spad{<= x}.")) (|ceiling| (($ $) "\\spad{ceiling x} returns the small integer \\spad{>= x}.")) (|norm| (($ $) "\\spad{norm x} returns the same as absolute value."))) NIL NIL -(-1061) +(-1062) ((|constructor| (NIL "The real number system category is intended as a model for the real numbers. The real numbers form an ordered normed field. Note that we have purposely not included \\spadtype{DifferentialRing} or the elementary functions (see \\spadtype{TranscendentalFunctionCategory}) in the definition.")) (|abs| (($ $) "\\spad{abs x} returns the absolute value of \\spad{x}.")) (|round| (($ $) "\\spad{round x} computes the integer closest to \\spad{x}.")) (|truncate| (($ $) "\\spad{truncate x} returns the integer between \\spad{x} and 0 closest to \\spad{x}.")) (|fractionPart| (($ $) "\\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)) +((-4410 . T) (-4416 . T) (-4411 . T) ((-4420 "*") . T) (-4412 . T) (-4413 . T) (-4415 . T)) NIL -(-1062 |TheField| |ThePolDom|) +(-1063 |TheField| |ThePolDom|) ((|constructor| (NIL "\\axiomType{RightOpenIntervalRootCharacterization} provides work with interval root coding.")) (|relativeApprox| ((|#1| |#2| $ |#1|) "\\axiom{relativeApprox(exp,{}\\spad{c},{}\\spad{p}) = a} is relatively close to exp as a polynomial in \\spad{c} ip to precision \\spad{p}")) (|mightHaveRoots| (((|Boolean|) |#2| $) "\\axiom{mightHaveRoots(\\spad{p},{}\\spad{r})} is \\spad{false} if \\axiom{\\spad{p}.\\spad{r}} is not 0")) (|refine| (($ $) "\\axiom{refine(rootChar)} shrinks isolating interval around \\axiom{rootChar}")) (|middle| ((|#1| $) "\\axiom{middle(rootChar)} is the middle of the isolating interval")) (|size| ((|#1| $) "The size of the isolating interval")) (|right| ((|#1| $) "\\axiom{right(rootChar)} is the right bound of the isolating interval")) (|left| ((|#1| $) "\\axiom{left(rootChar)} is the left bound of the isolating interval"))) NIL NIL -(-1063) +(-1064) ((|constructor| (NIL "\\spadtype{RomanNumeral} provides functions for converting \\indented{1}{integers to roman numerals.}")) (|roman| (($ (|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)) +((-4406 . T) (-4410 . T) (-4405 . T) (-4416 . T) (-4417 . T) (-4411 . T) ((-4420 "*") . T) (-4412 . T) (-4413 . T) (-4415 . T)) NIL -(-1064) +(-1065) ((|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 (|:| -1791 (-1177)) (|:| -4232 (-52))) (QUOTE (-1101))) (|HasCategory| (-2 (|:| -1791 (-1177)) (|:| -4232 (-52))) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1791) (QUOTE (-1177))) (LIST (QUOTE |:|) (QUOTE -4232) (QUOTE (-52))))))) (-2797 (|HasCategory| (-2 (|:| -1791 (-1177)) (|:| -4232 (-52))) (QUOTE (-1101))) (|HasCategory| (-52) (QUOTE (-1101)))) (-2797 (|HasCategory| (-2 (|:| -1791 (-1177)) (|:| -4232 (-52))) (QUOTE (-1101))) (|HasCategory| (-2 (|:| -1791 (-1177)) (|:| -4232 (-52))) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-52) (QUOTE (-1101))) (|HasCategory| (-52) (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| (-2 (|:| -1791 (-1177)) (|:| -4232 (-52))) (LIST (QUOTE -615) (QUOTE (-539)))) (-12 (|HasCategory| (-52) (QUOTE (-1101))) (|HasCategory| (-52) (LIST (QUOTE -310) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -1791 (-1177)) (|:| -4232 (-52))) (QUOTE (-1101))) (|HasCategory| (-1177) (QUOTE (-851))) (|HasCategory| (-52) (QUOTE (-1101))) (-2797 (|HasCategory| (-2 (|:| -1791 (-1177)) (|:| -4232 (-52))) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-52) (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| (-52) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-2 (|:| -1791 (-1177)) (|:| -4232 (-52))) (LIST (QUOTE -614) (QUOTE (-863))))) -(-1065 S R E V) +((-4418 . T) (-4419 . T)) +((-12 (|HasCategory| (-2 (|:| -1795 (-1178)) (|:| -4237 (-52))) (QUOTE (-1102))) (|HasCategory| (-2 (|:| -1795 (-1178)) (|:| -4237 (-52))) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1795) (QUOTE (-1178))) (LIST (QUOTE |:|) (QUOTE -4237) (QUOTE (-52))))))) (-2800 (|HasCategory| (-2 (|:| -1795 (-1178)) (|:| -4237 (-52))) (QUOTE (-1102))) (|HasCategory| (-52) (QUOTE (-1102)))) (-2800 (|HasCategory| (-2 (|:| -1795 (-1178)) (|:| -4237 (-52))) (QUOTE (-1102))) (|HasCategory| (-2 (|:| -1795 (-1178)) (|:| -4237 (-52))) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-52) (QUOTE (-1102))) (|HasCategory| (-52) (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| (-2 (|:| -1795 (-1178)) (|:| -4237 (-52))) (LIST (QUOTE -615) (QUOTE (-539)))) (-12 (|HasCategory| (-52) (QUOTE (-1102))) (|HasCategory| (-52) (LIST (QUOTE -310) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -1795 (-1178)) (|:| -4237 (-52))) (QUOTE (-1102))) (|HasCategory| (-1178) (QUOTE (-851))) (|HasCategory| (-52) (QUOTE (-1102))) (-2800 (|HasCategory| (-2 (|:| -1795 (-1178)) (|:| -4237 (-52))) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-52) (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| (-52) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-2 (|:| -1795 (-1178)) (|:| -4237 (-52))) (LIST (QUOTE -614) (QUOTE (-863))))) +(-1066 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| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}."))) NIL -((|HasCategory| |#2| (QUOTE (-455))) (|HasCategory| |#2| (QUOTE (-559))) (|HasCategory| |#2| (LIST (QUOTE -1039) (QUOTE (-567)))) (|HasCategory| |#2| (QUOTE (-548))) (|HasCategory| |#2| (LIST (QUOTE -38) (QUOTE (-567)))) (|HasCategory| |#2| (LIST (QUOTE -993) (QUOTE (-567)))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#4| (LIST (QUOTE -615) (QUOTE (-1177))))) -(-1066 R E V) +((|HasCategory| |#2| (QUOTE (-455))) (|HasCategory| |#2| (QUOTE (-559))) (|HasCategory| |#2| (LIST (QUOTE -1040) (QUOTE (-567)))) (|HasCategory| |#2| (QUOTE (-548))) (|HasCategory| |#2| (LIST (QUOTE -38) (QUOTE (-567)))) (|HasCategory| |#2| (LIST (QUOTE -994) (QUOTE (-567)))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#4| (LIST (QUOTE -615) (QUOTE (-1178))))) +(-1067 R E V) ((|constructor| (NIL "A category for general multi-variate polynomials with coefficients in a ring,{} variables in an ordered set,{} and exponents from an ordered abelian monoid,{} with a \\axiomOp{sup} operation. When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\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| (-559)) (-4415 |has| |#1| (-6 -4415)) (-4412 . T) (-4411 . T) (-4414 . T)) +(((-4420 "*") |has| |#1| (-172)) (-4411 |has| |#1| (-559)) (-4416 |has| |#1| (-6 -4416)) (-4413 . T) (-4412 . T) (-4415 . T)) NIL -(-1067) +(-1068) ((|constructor| (NIL "This domain represents the `repeat' iterator syntax.")) (|body| (((|SpadAst|) $) "\\spad{body(e)} returns the body of the loop `e'.")) (|iterators| (((|List| (|SpadAst|)) $) "\\spad{iterators(e)} returns the list of iterators controlling the loop `e'."))) NIL NIL -(-1068 S |TheField| |ThePols|) +(-1069 S |TheField| |ThePols|) ((|constructor| (NIL "\\axiomType{RealRootCharacterizationCategory} provides common acces functions for all real root codings.")) (|relativeApprox| ((|#2| |#3| $ |#2|) "\\axiom{approximate(term,{}root,{}prec)} gives an approximation of \\axiom{term} over \\axiom{root} with precision \\axiom{prec}")) (|approximate| ((|#2| |#3| $ |#2|) "\\axiom{approximate(term,{}root,{}prec)} gives an approximation of \\axiom{term} over \\axiom{root} with precision \\axiom{prec}")) (|rootOf| (((|Union| $ "failed") |#3| (|PositiveInteger|)) "\\axiom{rootOf(pol,{}\\spad{n})} gives the \\spad{n}th root for the order of the Real Closure")) (|allRootsOf| (((|List| $) |#3|) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} in the Real Closure,{} assumed in order.")) (|definingPolynomial| ((|#3| $) "\\axiom{definingPolynomial(aRoot)} gives a polynomial such that \\axiom{definingPolynomial(aRoot).aRoot = 0}")) (|recip| (((|Union| |#3| "failed") |#3| $) "\\axiom{recip(pol,{}aRoot)} tries to inverse \\axiom{pol} interpreted as \\axiom{aRoot}")) (|positive?| (((|Boolean|) |#3| $) "\\axiom{positive?(pol,{}aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is positive")) (|negative?| (((|Boolean|) |#3| $) "\\axiom{negative?(pol,{}aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is negative")) (|zero?| (((|Boolean|) |#3| $) "\\axiom{zero?(pol,{}aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is \\axiom{0}")) (|sign| (((|Integer|) |#3| $) "\\axiom{sign(pol,{}aRoot)} gives the sign of \\axiom{pol} interpreted as \\axiom{aRoot}"))) NIL NIL -(-1069 |TheField| |ThePols|) +(-1070 |TheField| |ThePols|) ((|constructor| (NIL "\\axiomType{RealRootCharacterizationCategory} provides common acces functions for all real root codings.")) (|relativeApprox| ((|#1| |#2| $ |#1|) "\\axiom{approximate(term,{}root,{}prec)} gives an approximation of \\axiom{term} over \\axiom{root} with precision \\axiom{prec}")) (|approximate| ((|#1| |#2| $ |#1|) "\\axiom{approximate(term,{}root,{}prec)} gives an approximation of \\axiom{term} over \\axiom{root} with precision \\axiom{prec}")) (|rootOf| (((|Union| $ "failed") |#2| (|PositiveInteger|)) "\\axiom{rootOf(pol,{}\\spad{n})} gives the \\spad{n}th root for the order of the Real Closure")) (|allRootsOf| (((|List| $) |#2|) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} in the Real Closure,{} assumed in order.")) (|definingPolynomial| ((|#2| $) "\\axiom{definingPolynomial(aRoot)} gives a polynomial such that \\axiom{definingPolynomial(aRoot).aRoot = 0}")) (|recip| (((|Union| |#2| "failed") |#2| $) "\\axiom{recip(pol,{}aRoot)} tries to inverse \\axiom{pol} interpreted as \\axiom{aRoot}")) (|positive?| (((|Boolean|) |#2| $) "\\axiom{positive?(pol,{}aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is positive")) (|negative?| (((|Boolean|) |#2| $) "\\axiom{negative?(pol,{}aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is negative")) (|zero?| (((|Boolean|) |#2| $) "\\axiom{zero?(pol,{}aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is \\axiom{0}")) (|sign| (((|Integer|) |#2| $) "\\axiom{sign(pol,{}aRoot)} gives the sign of \\axiom{pol} interpreted as \\axiom{aRoot}"))) NIL NIL -(-1070 R E V P TS) +(-1071 R E V P TS) ((|constructor| (NIL "A package providing a new algorithm for solving polynomial systems by means of regular chains. Two ways of solving are proposed: in the sense of Zariski closure (like in Kalkbrener\\spad{'s} algorithm) or in the sense of the regular zeros (like in Wu,{} Wang or Lazard methods). This algorithm is valid for nay type of regular set. It does not care about the way a polynomial is added in an regular set,{} or how two quasi-components are compared (by an inclusion-test),{} or how the invertibility test is made in the tower of simple extensions associated with a regular set. These operations are realized respectively by the domain \\spad{TS} and the packages \\axiomType{QCMPACK}(\\spad{R},{}\\spad{E},{}\\spad{V},{}\\spad{P},{}\\spad{TS}) and \\axiomType{RSETGCD}(\\spad{R},{}\\spad{E},{}\\spad{V},{}\\spad{P},{}\\spad{TS}). The same way it does not care about the way univariate polynomial \\spad{gcd} (with coefficients in the tower of simple extensions associated with a regular set) are computed. The only requirement is that these \\spad{gcd} need to have invertible initials (normalized or not). WARNING. There is no need for a user to call diectly any operation of this package since they can be accessed by the domain \\axiom{\\spad{TS}}. Thus,{} the operations of this package are not documented.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}"))) NIL NIL -(-1071 S R E V P) +(-1072 S R E V P) ((|constructor| (NIL "The category of regular triangular sets,{} introduced under the name regular chains in [1] (and other papers). In [3] it is proved that regular triangular sets and towers of simple extensions of a field are equivalent notions. In the following definitions,{} all polynomials and ideals are taken from the polynomial ring \\spad{k[x1,...,xn]} where \\spad{k} is the fraction field of \\spad{R}. The triangular set \\spad{[t1,...,tm]} is regular iff for every \\spad{i} the initial of \\spad{ti+1} is invertible in the tower of simple extensions associated with \\spad{[t1,...,ti]}. A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Kalkbrener of a given ideal \\spad{I} iff the radical of \\spad{I} is equal to the intersection of the radical ideals generated by the saturated ideals of the \\spad{[T1,...,Ti]}. A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Kalkbrener of a given triangular set \\spad{T} iff it is a split of Kalkbrener of the saturated ideal of \\spad{T}. Let \\spad{K} be an algebraic closure of \\spad{k}. Assume that \\spad{V} is finite with cardinality \\spad{n} and let \\spad{A} be the affine space \\spad{K^n}. For a regular triangular set \\spad{T} let denote by \\spad{W(T)} the set of regular zeros of \\spad{T}. A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Lazard of a given subset \\spad{S} of \\spad{A} iff the union of the \\spad{W(Ti)} contains \\spad{S} and is contained in the closure of \\spad{S} (\\spad{w}.\\spad{r}.\\spad{t}. Zariski topology). A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Lazard of a given triangular set \\spad{T} if it is a split of Lazard of \\spad{W(T)}. Note that if \\spad{[T1,...,Ts]} is a split of Lazard of \\spad{T} then it is also a split of Kalkbrener of \\spad{T}. The converse is \\spad{false}. This category provides operations related to both kinds of splits,{} the former being related to ideals decomposition whereas the latter deals with varieties decomposition. See the example illustrating the \\spadtype{RegularTriangularSet} constructor for more explanations about decompositions by means of regular triangular sets. \\newline References : \\indented{1}{[1] \\spad{M}. KALKBRENER \"Three contributions to elimination theory\"} \\indented{5}{\\spad{Phd} Thesis,{} University of Linz,{} Austria,{} 1991.} \\indented{1}{[2] \\spad{M}. KALKBRENER \"Algorithmic properties of polynomial rings\"} \\indented{5}{Journal of Symbol. Comp. 1998} \\indented{1}{[3] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)} \\indented{1}{[4] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|zeroSetSplit| (((|List| $) (|List| |#5|) (|Boolean|)) "\\spad{zeroSetSplit(lp,clos?)} returns \\spad{lts} a split of Kalkbrener of the radical ideal associated with \\spad{lp}. If \\spad{clos?} is \\spad{false},{} it is also a decomposition of the variety associated with \\spad{lp} into the regular zero set of the \\spad{ts} in \\spad{lts} (or,{} in other words,{} a split of Lazard of this variety). See the example illustrating the \\spadtype{RegularTriangularSet} constructor for more explanations about decompositions by means of regular triangular sets.")) (|extend| (((|List| $) (|List| |#5|) (|List| $)) "\\spad{extend(lp,lts)} returns the same as \\spad{concat([extend(lp,ts) for ts in lts])|}") (((|List| $) (|List| |#5|) $) "\\spad{extend(lp,ts)} returns \\spad{ts} if \\spad{empty? lp} \\spad{extend(p,ts)} if \\spad{lp = [p]} else \\spad{extend(first lp, extend(rest lp, ts))}") (((|List| $) |#5| (|List| $)) "\\spad{extend(p,lts)} returns the same as \\spad{concat([extend(p,ts) for ts in lts])|}") (((|List| $) |#5| $) "\\spad{extend(p,ts)} assumes that \\spad{p} is a non-constant polynomial whose main variable is greater than any variable of \\spad{ts}. Then it returns a split of Kalkbrener of \\spad{ts+p}. This may not be \\spad{ts+p} itself,{} if for instance \\spad{ts+p} is not a regular triangular set.")) (|internalAugment| (($ (|List| |#5|) $) "\\spad{internalAugment(lp,ts)} returns \\spad{ts} if \\spad{lp} is empty otherwise returns \\spad{internalAugment(rest lp, internalAugment(first lp, ts))}") (($ |#5| $) "\\spad{internalAugment(p,ts)} assumes that \\spad{augment(p,ts)} returns a singleton and returns it.")) (|augment| (((|List| $) (|List| |#5|) (|List| $)) "\\spad{augment(lp,lts)} returns the same as \\spad{concat([augment(lp,ts) for ts in lts])}") (((|List| $) (|List| |#5|) $) "\\spad{augment(lp,ts)} returns \\spad{ts} if \\spad{empty? lp},{} \\spad{augment(p,ts)} if \\spad{lp = [p]},{} otherwise \\spad{augment(first lp, augment(rest lp, ts))}") (((|List| $) |#5| (|List| $)) "\\spad{augment(p,lts)} returns the same as \\spad{concat([augment(p,ts) for ts in lts])}") (((|List| $) |#5| $) "\\spad{augment(p,ts)} assumes that \\spad{p} is a non-constant polynomial whose main variable is greater than any variable of \\spad{ts}. This operation assumes also that if \\spad{p} is added to \\spad{ts} the resulting set,{} say \\spad{ts+p},{} is a regular triangular set. Then it returns a split of Kalkbrener of \\spad{ts+p}. This may not be \\spad{ts+p} itself,{} if for instance \\spad{ts+p} is required to be square-free.")) (|intersect| (((|List| $) |#5| (|List| $)) "\\spad{intersect(p,lts)} returns the same as \\spad{intersect([p],lts)}") (((|List| $) (|List| |#5|) (|List| $)) "\\spad{intersect(lp,lts)} returns the same as \\spad{concat([intersect(lp,ts) for ts in lts])|}") (((|List| $) (|List| |#5|) $) "\\spad{intersect(lp,ts)} returns \\spad{lts} a split of Lazard of the intersection of the affine variety associated with \\spad{lp} and the regular zero set of \\spad{ts}.") (((|List| $) |#5| $) "\\spad{intersect(p,ts)} returns the same as \\spad{intersect([p],ts)}")) (|squareFreePart| (((|List| (|Record| (|:| |val| |#5|) (|:| |tower| $))) |#5| $) "\\spad{squareFreePart(p,ts)} returns \\spad{lpwt} such that \\spad{lpwt.i.val} is a square-free polynomial \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower},{} this polynomial being associated with \\spad{p} modulo \\spad{lpwt.i.tower},{} for every \\spad{i}. Moreover,{} the list of the \\spad{lpwt.i.tower} is a split of Kalkbrener of \\spad{ts}. WARNING: This assumes that \\spad{p} is a non-constant polynomial such that if \\spad{p} is added to \\spad{ts},{} then the resulting set is a regular triangular set.")) (|lastSubResultant| (((|List| (|Record| (|:| |val| |#5|) (|:| |tower| $))) |#5| |#5| $) "\\spad{lastSubResultant(p1,p2,ts)} returns \\spad{lpwt} such that \\spad{lpwt.i.val} is a quasi-monic \\spad{gcd} of \\spad{p1} and \\spad{p2} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower},{} for every \\spad{i},{} and such that the list of the \\spad{lpwt.i.tower} is a split of Kalkbrener of \\spad{ts}. Moreover,{} if \\spad{p1} and \\spad{p2} do not have a non-trivial \\spad{gcd} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower} then \\spad{lpwt.i.val} is the resultant of these polynomials \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower}. This assumes that \\spad{p1} and \\spad{p2} have the same maim variable and that this variable is greater that any variable occurring in \\spad{ts}.")) (|lastSubResultantElseSplit| (((|Union| |#5| (|List| $)) |#5| |#5| $) "\\spad{lastSubResultantElseSplit(p1,p2,ts)} returns either \\spad{g} a quasi-monic \\spad{gcd} of \\spad{p1} and \\spad{p2} \\spad{w}.\\spad{r}.\\spad{t}. the \\spad{ts} or a split of Kalkbrener of \\spad{ts}. This assumes that \\spad{p1} and \\spad{p2} have the same maim variable and that this variable is greater that any variable occurring in \\spad{ts}.")) (|invertibleSet| (((|List| $) |#5| $) "\\spad{invertibleSet(p,ts)} returns a split of Kalkbrener of the quotient ideal of the ideal \\axiom{\\spad{I}} by \\spad{p} where \\spad{I} is the radical of saturated of \\spad{ts}.")) (|invertible?| (((|Boolean|) |#5| $) "\\spad{invertible?(p,ts)} returns \\spad{true} iff \\spad{p} is invertible in the tower associated with \\spad{ts}.") (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| $))) |#5| $) "\\spad{invertible?(p,ts)} returns \\spad{lbwt} where \\spad{lbwt.i} is the result of \\spad{invertibleElseSplit?(p,lbwt.i.tower)} and the list of the \\spad{(lqrwt.i).tower} is a split of Kalkbrener of \\spad{ts}.")) (|invertibleElseSplit?| (((|Union| (|Boolean|) (|List| $)) |#5| $) "\\spad{invertibleElseSplit?(p,ts)} returns \\spad{true} (resp. \\spad{false}) if \\spad{p} is invertible in the tower associated with \\spad{ts} or returns a split of Kalkbrener of \\spad{ts}.")) (|purelyAlgebraicLeadingMonomial?| (((|Boolean|) |#5| $) "\\spad{purelyAlgebraicLeadingMonomial?(p,ts)} returns \\spad{true} iff the main variable of any non-constant iterarted initial of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}.")) (|algebraicCoefficients?| (((|Boolean|) |#5| $) "\\spad{algebraicCoefficients?(p,ts)} returns \\spad{true} iff every variable of \\spad{p} which is not the main one of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}.")) (|purelyTranscendental?| (((|Boolean|) |#5| $) "\\spad{purelyTranscendental?(p,ts)} returns \\spad{true} iff every variable of \\spad{p} is not algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}")) (|purelyAlgebraic?| (((|Boolean|) $) "\\spad{purelyAlgebraic?(ts)} returns \\spad{true} iff for every algebraic variable \\spad{v} of \\spad{ts} we have \\spad{algebraicCoefficients?(t_v,ts_v_-)} where \\spad{ts_v} is \\axiomOpFrom{select}{TriangularSetCategory}(\\spad{ts},{}\\spad{v}) and \\spad{ts_v_-} is \\axiomOpFrom{collectUnder}{TriangularSetCategory}(\\spad{ts},{}\\spad{v}).") (((|Boolean|) |#5| $) "\\spad{purelyAlgebraic?(p,ts)} returns \\spad{true} iff every variable of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}."))) NIL NIL -(-1072 R E V P) +(-1073 R E V P) ((|constructor| (NIL "The category of regular triangular sets,{} introduced under the name regular chains in [1] (and other papers). In [3] it is proved that regular triangular sets and towers of simple extensions of a field are equivalent notions. In the following definitions,{} all polynomials and ideals are taken from the polynomial ring \\spad{k[x1,...,xn]} where \\spad{k} is the fraction field of \\spad{R}. The triangular set \\spad{[t1,...,tm]} is regular iff for every \\spad{i} the initial of \\spad{ti+1} is invertible in the tower of simple extensions associated with \\spad{[t1,...,ti]}. A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Kalkbrener of a given ideal \\spad{I} iff the radical of \\spad{I} is equal to the intersection of the radical ideals generated by the saturated ideals of the \\spad{[T1,...,Ti]}. A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Kalkbrener of a given triangular set \\spad{T} iff it is a split of Kalkbrener of the saturated ideal of \\spad{T}. Let \\spad{K} be an algebraic closure of \\spad{k}. Assume that \\spad{V} is finite with cardinality \\spad{n} and let \\spad{A} be the affine space \\spad{K^n}. For a regular triangular set \\spad{T} let denote by \\spad{W(T)} the set of regular zeros of \\spad{T}. A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Lazard of a given subset \\spad{S} of \\spad{A} iff the union of the \\spad{W(Ti)} contains \\spad{S} and is contained in the closure of \\spad{S} (\\spad{w}.\\spad{r}.\\spad{t}. Zariski topology). A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Lazard of a given triangular set \\spad{T} if it is a split of Lazard of \\spad{W(T)}. Note that if \\spad{[T1,...,Ts]} is a split of Lazard of \\spad{T} then it is also a split of Kalkbrener of \\spad{T}. The converse is \\spad{false}. This category provides operations related to both kinds of splits,{} the former being related to ideals decomposition whereas the latter deals with varieties decomposition. See the example illustrating the \\spadtype{RegularTriangularSet} constructor for more explanations about decompositions by means of regular triangular sets. \\newline References : \\indented{1}{[1] \\spad{M}. KALKBRENER \"Three contributions to elimination theory\"} \\indented{5}{\\spad{Phd} Thesis,{} University of Linz,{} Austria,{} 1991.} \\indented{1}{[2] \\spad{M}. KALKBRENER \"Algorithmic properties of polynomial rings\"} \\indented{5}{Journal of Symbol. Comp. 1998} \\indented{1}{[3] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)} \\indented{1}{[4] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|zeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|)) "\\spad{zeroSetSplit(lp,clos?)} returns \\spad{lts} a split of Kalkbrener of the radical ideal associated with \\spad{lp}. If \\spad{clos?} is \\spad{false},{} it is also a decomposition of the variety associated with \\spad{lp} into the regular zero set of the \\spad{ts} in \\spad{lts} (or,{} in other words,{} a split of Lazard of this variety). See the example illustrating the \\spadtype{RegularTriangularSet} constructor for more explanations about decompositions by means of regular triangular sets.")) (|extend| (((|List| $) (|List| |#4|) (|List| $)) "\\spad{extend(lp,lts)} returns the same as \\spad{concat([extend(lp,ts) for ts in lts])|}") (((|List| $) (|List| |#4|) $) "\\spad{extend(lp,ts)} returns \\spad{ts} if \\spad{empty? lp} \\spad{extend(p,ts)} if \\spad{lp = [p]} else \\spad{extend(first lp, extend(rest lp, ts))}") (((|List| $) |#4| (|List| $)) "\\spad{extend(p,lts)} returns the same as \\spad{concat([extend(p,ts) for ts in lts])|}") (((|List| $) |#4| $) "\\spad{extend(p,ts)} assumes that \\spad{p} is a non-constant polynomial whose main variable is greater than any variable of \\spad{ts}. Then it returns a split of Kalkbrener of \\spad{ts+p}. This may not be \\spad{ts+p} itself,{} if for instance \\spad{ts+p} is not a regular triangular set.")) (|internalAugment| (($ (|List| |#4|) $) "\\spad{internalAugment(lp,ts)} returns \\spad{ts} if \\spad{lp} is empty otherwise returns \\spad{internalAugment(rest lp, internalAugment(first lp, ts))}") (($ |#4| $) "\\spad{internalAugment(p,ts)} assumes that \\spad{augment(p,ts)} returns a singleton and returns it.")) (|augment| (((|List| $) (|List| |#4|) (|List| $)) "\\spad{augment(lp,lts)} returns the same as \\spad{concat([augment(lp,ts) for ts in lts])}") (((|List| $) (|List| |#4|) $) "\\spad{augment(lp,ts)} returns \\spad{ts} if \\spad{empty? lp},{} \\spad{augment(p,ts)} if \\spad{lp = [p]},{} otherwise \\spad{augment(first lp, augment(rest lp, ts))}") (((|List| $) |#4| (|List| $)) "\\spad{augment(p,lts)} returns the same as \\spad{concat([augment(p,ts) for ts in lts])}") (((|List| $) |#4| $) "\\spad{augment(p,ts)} assumes that \\spad{p} is a non-constant polynomial whose main variable is greater than any variable of \\spad{ts}. This operation assumes also that if \\spad{p} is added to \\spad{ts} the resulting set,{} say \\spad{ts+p},{} is a regular triangular set. Then it returns a split of Kalkbrener of \\spad{ts+p}. This may not be \\spad{ts+p} itself,{} if for instance \\spad{ts+p} is required to be square-free.")) (|intersect| (((|List| $) |#4| (|List| $)) "\\spad{intersect(p,lts)} returns the same as \\spad{intersect([p],lts)}") (((|List| $) (|List| |#4|) (|List| $)) "\\spad{intersect(lp,lts)} returns the same as \\spad{concat([intersect(lp,ts) for ts in lts])|}") (((|List| $) (|List| |#4|) $) "\\spad{intersect(lp,ts)} returns \\spad{lts} a split of Lazard of the intersection of the affine variety associated with \\spad{lp} and the regular zero set of \\spad{ts}.") (((|List| $) |#4| $) "\\spad{intersect(p,ts)} returns the same as \\spad{intersect([p],ts)}")) (|squareFreePart| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| $))) |#4| $) "\\spad{squareFreePart(p,ts)} returns \\spad{lpwt} such that \\spad{lpwt.i.val} is a square-free polynomial \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower},{} this polynomial being associated with \\spad{p} modulo \\spad{lpwt.i.tower},{} for every \\spad{i}. Moreover,{} the list of the \\spad{lpwt.i.tower} is a split of Kalkbrener of \\spad{ts}. WARNING: This assumes that \\spad{p} is a non-constant polynomial such that if \\spad{p} is added to \\spad{ts},{} then the resulting set is a regular triangular set.")) (|lastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| $))) |#4| |#4| $) "\\spad{lastSubResultant(p1,p2,ts)} returns \\spad{lpwt} such that \\spad{lpwt.i.val} is a quasi-monic \\spad{gcd} of \\spad{p1} and \\spad{p2} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower},{} for every \\spad{i},{} and such that the list of the \\spad{lpwt.i.tower} is a split of Kalkbrener of \\spad{ts}. Moreover,{} if \\spad{p1} and \\spad{p2} do not have a non-trivial \\spad{gcd} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower} then \\spad{lpwt.i.val} is the resultant of these polynomials \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower}. This assumes that \\spad{p1} and \\spad{p2} have the same maim variable and that this variable is greater that any variable occurring in \\spad{ts}.")) (|lastSubResultantElseSplit| (((|Union| |#4| (|List| $)) |#4| |#4| $) "\\spad{lastSubResultantElseSplit(p1,p2,ts)} returns either \\spad{g} a quasi-monic \\spad{gcd} of \\spad{p1} and \\spad{p2} \\spad{w}.\\spad{r}.\\spad{t}. the \\spad{ts} or a split of Kalkbrener of \\spad{ts}. This assumes that \\spad{p1} and \\spad{p2} have the same maim variable and that this variable is greater that any variable occurring in \\spad{ts}.")) (|invertibleSet| (((|List| $) |#4| $) "\\spad{invertibleSet(p,ts)} returns a split of Kalkbrener of the quotient ideal of the ideal \\axiom{\\spad{I}} by \\spad{p} where \\spad{I} is the radical of saturated of \\spad{ts}.")) (|invertible?| (((|Boolean|) |#4| $) "\\spad{invertible?(p,ts)} returns \\spad{true} iff \\spad{p} is invertible in the tower associated with \\spad{ts}.") (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| $))) |#4| $) "\\spad{invertible?(p,ts)} returns \\spad{lbwt} where \\spad{lbwt.i} is the result of \\spad{invertibleElseSplit?(p,lbwt.i.tower)} and the list of the \\spad{(lqrwt.i).tower} is a split of Kalkbrener of \\spad{ts}.")) (|invertibleElseSplit?| (((|Union| (|Boolean|) (|List| $)) |#4| $) "\\spad{invertibleElseSplit?(p,ts)} returns \\spad{true} (resp. \\spad{false}) if \\spad{p} is invertible in the tower associated with \\spad{ts} or returns a split of Kalkbrener of \\spad{ts}.")) (|purelyAlgebraicLeadingMonomial?| (((|Boolean|) |#4| $) "\\spad{purelyAlgebraicLeadingMonomial?(p,ts)} returns \\spad{true} iff the main variable of any non-constant iterarted initial of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}.")) (|algebraicCoefficients?| (((|Boolean|) |#4| $) "\\spad{algebraicCoefficients?(p,ts)} returns \\spad{true} iff every variable of \\spad{p} which is not the main one of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}.")) (|purelyTranscendental?| (((|Boolean|) |#4| $) "\\spad{purelyTranscendental?(p,ts)} returns \\spad{true} iff every variable of \\spad{p} is not algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}")) (|purelyAlgebraic?| (((|Boolean|) $) "\\spad{purelyAlgebraic?(ts)} returns \\spad{true} iff for every algebraic variable \\spad{v} of \\spad{ts} we have \\spad{algebraicCoefficients?(t_v,ts_v_-)} where \\spad{ts_v} is \\axiomOpFrom{select}{TriangularSetCategory}(\\spad{ts},{}\\spad{v}) and \\spad{ts_v_-} is \\axiomOpFrom{collectUnder}{TriangularSetCategory}(\\spad{ts},{}\\spad{v}).") (((|Boolean|) |#4| $) "\\spad{purelyAlgebraic?(p,ts)} returns \\spad{true} iff every variable of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}."))) -((-4418 . T) (-4417 . T)) +((-4419 . T) (-4418 . T)) NIL -(-1073 R E V P TS) +(-1074 R E V P TS) ((|constructor| (NIL "An internal package for computing gcds and resultants of univariate polynomials with coefficients in a tower of simple extensions of a field.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA and \\spad{R}. RIOBOO \"Computations of \\spad{gcd} over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of AAECC11} \\indented{5}{Paris,{} 1995.} \\indented{1}{[2] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|toseSquareFreePart| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{toseSquareFreePart(\\spad{p},{}\\spad{ts})} has the same specifications as \\axiomOpFrom{squareFreePart}{RegularTriangularSetCategory}.")) (|toseInvertibleSet| (((|List| |#5|) |#4| |#5|) "\\axiom{toseInvertibleSet(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} has the same specifications as \\axiomOpFrom{invertibleSet}{RegularTriangularSetCategory}.")) (|toseInvertible?| (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{toseInvertible?(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} has the same specifications as \\axiomOpFrom{invertible?}{RegularTriangularSetCategory}.") (((|Boolean|) |#4| |#5|) "\\axiom{toseInvertible?(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} has the same specifications as \\axiomOpFrom{invertible?}{RegularTriangularSetCategory}.")) (|toseLastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#4| |#5|) "\\axiom{toseLastSubResultant(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} has the same specifications as \\axiomOpFrom{lastSubResultant}{RegularTriangularSetCategory}.")) (|integralLastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#4| |#5|) "\\axiom{integralLastSubResultant(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} is an internal subroutine,{} exported only for developement.")) (|internalLastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) |#3| (|Boolean|)) "\\axiom{internalLastSubResultant(lpwt,{}\\spad{v},{}flag)} is an internal subroutine,{} exported only for developement.") (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#4| |#5| (|Boolean|) (|Boolean|)) "\\axiom{internalLastSubResultant(\\spad{p1},{}\\spad{p2},{}\\spad{ts},{}inv?,{}break?)} is an internal subroutine,{} exported only for developement.")) (|prepareSubResAlgo| (((|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) |#4| |#4| |#5|) "\\axiom{prepareSubResAlgo(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} is an internal subroutine,{} exported only for developement.")) (|stopTableInvSet!| (((|Void|)) "\\axiom{stopTableInvSet!()} is an internal subroutine,{} exported only for developement.")) (|startTableInvSet!| (((|Void|) (|String|) (|String|) (|String|)) "\\axiom{startTableInvSet!(\\spad{s1},{}\\spad{s2},{}\\spad{s3})} is an internal subroutine,{} exported only for developement.")) (|stopTableGcd!| (((|Void|)) "\\axiom{stopTableGcd!()} is an internal subroutine,{} exported only for developement.")) (|startTableGcd!| (((|Void|) (|String|) (|String|) (|String|)) "\\axiom{startTableGcd!(\\spad{s1},{}\\spad{s2},{}\\spad{s3})} is an internal subroutine,{} exported only for developement."))) NIL NIL -(-1074) +(-1075) ((|constructor| (NIL "This domain represents `restrict' expressions.")) (|target| (((|TypeAst|) $) "\\spad{target(e)} returns the target type of the conversion..")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression being converted."))) NIL NIL -(-1075) +(-1076) ((|constructor| (NIL "This is the datatype of OpenAxiom runtime values. It exists solely for internal purposes.")) (|eq| (((|Boolean|) $ $) "\\spad{eq(x,y)} holds if both values \\spad{x} and \\spad{y} resides at the same address in memory."))) NIL NIL -(-1076 |f|) +(-1077 |f|) ((|constructor| (NIL "This domain implements named rules")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) NIL NIL -(-1077 |Base| R -3867) +(-1078 |Base| R -3879) ((|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 -(-1078 |Base| R -3867) +(-1079 |Base| R -3879) ((|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 -(-1079 R |ls|) +(-1080 R |ls|) ((|constructor| (NIL "\\indented{1}{A package for computing the rational univariate representation} \\indented{1}{of a zero-dimensional algebraic variety given by a regular} \\indented{1}{triangular set. This package is essentially an interface for the} \\spadtype{InternalRationalUnivariateRepresentationPackage} constructor. It is used in the \\spadtype{ZeroDimensionalSolvePackage} for solving polynomial systems with finitely many solutions.")) (|rur| (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{rur(lp,univ?,check?)} returns the same as \\spad{rur(lp,true)}. Moreover,{} if \\spad{check?} is \\spad{true} then the result is checked.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|))) "\\spad{rur(lp)} returns the same as \\spad{rur(lp,true)}") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{rur(lp,univ?)} returns a rational univariate representation of \\spad{lp}. This assumes that \\spad{lp} defines a regular triangular \\spad{ts} whose associated variety is zero-dimensional over \\spad{R}. \\spad{rur(lp,univ?)} returns a list of items \\spad{[u,lc]} where \\spad{u} is an irreducible univariate polynomial and each \\spad{c} in \\spad{lc} involves two variables: one from \\spad{ls},{} called the coordinate of \\spad{c},{} and an extra variable which represents any root of \\spad{u}. Every root of \\spad{u} leads to a tuple of values for the coordinates of \\spad{lc}. Moreover,{} a point \\spad{x} belongs to the variety associated with \\spad{lp} iff there exists an item \\spad{[u,lc]} in \\spad{rur(lp,univ?)} and a root \\spad{r} of \\spad{u} such that \\spad{x} is given by the tuple of values for the coordinates of \\spad{lc} evaluated at \\spad{r}. If \\spad{univ?} is \\spad{true} then each polynomial \\spad{c} will have a constant leading coefficient \\spad{w}.\\spad{r}.\\spad{t}. its coordinate. See the example which illustrates the \\spadtype{ZeroDimensionalSolvePackage} package constructor."))) NIL NIL -(-1080 UP SAE UPA) +(-1081 UP SAE UPA) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of the rational numbers (\\spadtype{Fraction Integer}).")) (|factor| (((|Factored| |#3|) |#3|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p}."))) NIL NIL -(-1081 R UP M) +(-1082 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)) -((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-351))) (-2797 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-351)))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-370))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (QUOTE (-365)))) (|HasCategory| |#1| (QUOTE (-351)))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-1177))))) (-12 (|HasCategory| |#1| (QUOTE (-351))) (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-1177)))))) (|HasCategory| |#1| (LIST (QUOTE -640) (QUOTE (-567)))) (-2797 (|HasCategory| |#1| (LIST (QUOTE -1039) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (QUOTE (-365)))) (|HasCategory| |#1| (LIST (QUOTE -1039) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1039) (QUOTE (-567)))) (-12 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-1177))))) (-12 (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (QUOTE (-365))))) -(-1082 UP SAE UPA) +((-4411 |has| |#1| (-365)) (-4416 |has| |#1| (-365)) (-4410 |has| |#1| (-365)) ((-4420 "*") . T) (-4412 . T) (-4413 . T) (-4415 . T)) +((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-351))) (-2800 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-351)))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-370))) (-2800 (-12 (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (QUOTE (-365)))) (|HasCategory| |#1| (QUOTE (-351)))) (-2800 (-12 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (LIST (QUOTE -902) (QUOTE (-1178))))) (-12 (|HasCategory| |#1| (QUOTE (-351))) (|HasCategory| |#1| (LIST (QUOTE -902) (QUOTE (-1178)))))) (|HasCategory| |#1| (LIST (QUOTE -640) (QUOTE (-567)))) (-2800 (|HasCategory| |#1| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (QUOTE (-365)))) (|HasCategory| |#1| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (QUOTE (-567)))) (-12 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (LIST (QUOTE -902) (QUOTE (-1178))))) (-12 (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (QUOTE (-365))))) +(-1083 UP SAE UPA) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of \\spadtype{Fraction Polynomial Integer}.")) (|factor| (((|Factored| |#3|) |#3|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p}."))) NIL NIL -(-1083) +(-1084) ((|constructor| (NIL "This trivial domain lets us build Univariate Polynomials in an anonymous variable"))) NIL NIL -(-1084) +(-1085) ((|constructor| (NIL "This is the category of Spad syntax objects."))) NIL NIL -(-1085 S) +(-1086 S) ((|constructor| (NIL "\\indented{1}{Cache of elements in a set} Author: Manuel Bronstein Date Created: 31 Oct 1988 Date Last Updated: 14 May 1991 \\indented{2}{A sorted cache of a cachable set \\spad{S} is a dynamic structure that} \\indented{2}{keeps the elements of \\spad{S} sorted and assigns an integer to each} \\indented{2}{element of \\spad{S} once it is in the cache. This way,{} equality and ordering} \\indented{2}{on \\spad{S} are tested directly on the integers associated with the elements} \\indented{2}{of \\spad{S},{} once they have been entered in the cache.}")) (|enterInCache| ((|#1| |#1| (|Mapping| (|Integer|) |#1| |#1|)) "\\spad{enterInCache(x, f)} enters \\spad{x} in the cache,{} calling \\spad{f(x, y)} to determine whether \\spad{x < y (f(x,y) < 0), x = y (f(x,y) = 0)},{} or \\spad{x > y (f(x,y) > 0)}. It returns \\spad{x} with an integer associated with it.") ((|#1| |#1| (|Mapping| (|Boolean|) |#1|)) "\\spad{enterInCache(x, f)} enters \\spad{x} in the cache,{} calling \\spad{f(y)} to determine whether \\spad{x} is equal to \\spad{y}. It returns \\spad{x} with an integer associated with it.")) (|cache| (((|List| |#1|)) "\\spad{cache()} returns the current cache as a list.")) (|clearCache| (((|Void|)) "\\spad{clearCache()} empties the cache."))) NIL NIL -(-1086) +(-1087) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. A `Scope' is a sequence of contours.")) (|currentCategoryFrame| (($) "\\spad{currentCategoryFrame()} returns the category frame currently in effect.")) (|currentScope| (($) "\\spad{currentScope()} returns the scope currently in effect")) (|pushNewContour| (($ (|Binding|) $) "\\spad{pushNewContour(b,s)} pushs a new contour with sole binding \\spad{`b'}.")) (|findBinding| (((|Maybe| (|Binding|)) (|Identifier|) $) "\\spad{findBinding(n,s)} returns the first binding of \\spad{`n'} in \\spad{`s'}; otherwise `nothing'.")) (|contours| (((|List| (|Contour|)) $) "\\spad{contours(s)} returns the list of contours in scope \\spad{s}.")) (|empty| (($) "\\spad{empty()} returns an empty scope."))) NIL NIL -(-1087 R) +(-1088 R) ((|constructor| (NIL "StructuralConstantsPackage provides functions creating structural constants from a multiplication tables or a basis of a matrix algebra and other useful functions in this context.")) (|coordinates| (((|Vector| |#1|) (|Matrix| |#1|) (|List| (|Matrix| |#1|))) "\\spad{coordinates(a,[v1,...,vn])} returns the coordinates of \\spad{a} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|structuralConstants| (((|Vector| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{structuralConstants(basis)} takes the \\spad{basis} of a matrix algebra,{} \\spadignore{e.g.} the result of \\spadfun{basisOfCentroid} and calculates the structural constants. Note,{} that the it is not checked,{} whether \\spad{basis} really is a \\spad{basis} of a matrix algebra.") (((|Vector| (|Matrix| (|Polynomial| |#1|))) (|List| (|Symbol|)) (|Matrix| (|Polynomial| |#1|))) "\\spad{structuralConstants(ls,mt)} determines the structural constants of an algebra with generators \\spad{ls} and multiplication table \\spad{mt},{} the entries of which must be given as linear polynomials in the indeterminates given by \\spad{ls}. The result is in particular useful \\indented{1}{as fourth argument for \\spadtype{AlgebraGivenByStructuralConstants}} \\indented{1}{and \\spadtype{GenericNonAssociativeAlgebra}.}") (((|Vector| (|Matrix| (|Fraction| (|Polynomial| |#1|)))) (|List| (|Symbol|)) (|Matrix| (|Fraction| (|Polynomial| |#1|)))) "\\spad{structuralConstants(ls,mt)} determines the structural constants of an algebra with generators \\spad{ls} and multiplication table \\spad{mt},{} the entries of which must be given as linear polynomials in the indeterminates given by \\spad{ls}. The result is in particular useful \\indented{1}{as fourth argument for \\spadtype{AlgebraGivenByStructuralConstants}} \\indented{1}{and \\spadtype{GenericNonAssociativeAlgebra}.}"))) NIL NIL -(-1088 R) +(-1089 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| (-559)) (-4415 |has| |#1| (-6 -4415)) (-4412 . T) (-4411 . T) (-4414 . T)) -((|HasCategory| |#1| (QUOTE (-910))) (-2797 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-455))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-910)))) (-2797 (|HasCategory| |#1| (QUOTE (-455))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-910)))) (-2797 (|HasCategory| |#1| (QUOTE (-455))) (|HasCategory| |#1| (QUOTE (-910)))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-172))) (-2797 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-559)))) (-12 (|HasCategory| (-1089 (-1177)) (LIST (QUOTE -887) (QUOTE (-381)))) (|HasCategory| |#1| (LIST (QUOTE -887) (QUOTE (-381))))) (-12 (|HasCategory| (-1089 (-1177)) (LIST (QUOTE -887) (QUOTE (-567)))) (|HasCategory| |#1| (LIST (QUOTE -887) (QUOTE (-567))))) (-12 (|HasCategory| (-1089 (-1177)) (LIST (QUOTE -615) (LIST (QUOTE -893) (QUOTE (-381))))) (|HasCategory| |#1| (LIST (QUOTE -615) (LIST (QUOTE -893) (QUOTE (-381)))))) (-12 (|HasCategory| (-1089 (-1177)) (LIST (QUOTE -615) (LIST (QUOTE -893) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -615) (LIST (QUOTE -893) (QUOTE (-567)))))) (-12 (|HasCategory| (-1089 (-1177)) (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539))))) (|HasCategory| |#1| (LIST (QUOTE -640) (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1039) (QUOTE (-567)))) (-2797 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1039) (LIST (QUOTE -410) (QUOTE (-567)))))) (|HasCategory| |#1| (LIST (QUOTE -1039) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-1177)))) (|HasCategory| |#1| (QUOTE (-365))) (|HasAttribute| |#1| (QUOTE -4415)) (|HasCategory| |#1| (QUOTE (-455))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-910)))) (-2797 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-910)))) (|HasCategory| |#1| (QUOTE (-145))))) -(-1089 S) +(((-4420 "*") |has| |#1| (-172)) (-4411 |has| |#1| (-559)) (-4416 |has| |#1| (-6 -4416)) (-4413 . T) (-4412 . T) (-4415 . T)) +((|HasCategory| |#1| (QUOTE (-911))) (-2800 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-455))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-911)))) (-2800 (|HasCategory| |#1| (QUOTE (-455))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-911)))) (-2800 (|HasCategory| |#1| (QUOTE (-455))) (|HasCategory| |#1| (QUOTE (-911)))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-172))) (-2800 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-559)))) (-12 (|HasCategory| (-1090 (-1178)) (LIST (QUOTE -888) (QUOTE (-381)))) (|HasCategory| |#1| (LIST (QUOTE -888) (QUOTE (-381))))) (-12 (|HasCategory| (-1090 (-1178)) (LIST (QUOTE -888) (QUOTE (-567)))) (|HasCategory| |#1| (LIST (QUOTE -888) (QUOTE (-567))))) (-12 (|HasCategory| (-1090 (-1178)) (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-381))))) (|HasCategory| |#1| (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-381)))))) (-12 (|HasCategory| (-1090 (-1178)) (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567)))))) (-12 (|HasCategory| (-1090 (-1178)) (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539))))) (|HasCategory| |#1| (LIST (QUOTE -640) (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (QUOTE (-567)))) (-2800 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567)))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -902) (QUOTE (-1178)))) (|HasCategory| |#1| (QUOTE (-365))) (|HasAttribute| |#1| (QUOTE -4416)) (|HasCategory| |#1| (QUOTE (-455))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-911)))) (-2800 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-911)))) (|HasCategory| |#1| (QUOTE (-145))))) +(-1090 S) ((|constructor| (NIL "\\spadtype{OrderlyDifferentialVariable} adds a commonly used sequential ranking to the set of derivatives of an ordered list of differential indeterminates. A sequential ranking is a ranking \\spadfun{<} of the derivatives with the property that for any derivative \\spad{v},{} there are only a finite number of derivatives \\spad{u} with \\spad{u} \\spadfun{<} \\spad{v}. This domain belongs to \\spadtype{DifferentialVariableCategory}. It defines \\spadfun{weight} to be just \\spadfun{order},{} and it defines a sequential ranking \\spadfun{<} on derivatives \\spad{u} by the lexicographic order on the pair (\\spadfun{variable}(\\spad{u}),{} \\spadfun{order}(\\spad{u}))."))) NIL NIL -(-1090 R S) +(-1091 R S) ((|constructor| (NIL "This package provides operations for mapping functions onto segments.")) (|map| (((|List| |#2|) (|Mapping| |#2| |#1|) (|Segment| |#1|)) "\\spad{map(f,s)} expands the segment \\spad{s},{} applying \\spad{f} to each value. For example,{} if \\spad{s = l..h by k},{} then the list \\spad{[f(l), f(l+k),..., f(lN)]} is computed,{} where \\spad{lN <= h < lN+k}.") (((|Segment| |#2|) (|Mapping| |#2| |#1|) (|Segment| |#1|)) "\\spad{map(f,l..h)} returns a new segment \\spad{f(l)..f(h)}."))) NIL ((|HasCategory| |#1| (QUOTE (-849)))) -(-1091) +(-1092) ((|constructor| (NIL "This domain represents segement expressions.")) (|bounds| (((|List| (|SpadAst|)) $) "\\spad{bounds(s)} returns the bounds of the segment \\spad{`s'}. If \\spad{`s'} designates an infinite interval,{} then the returns list a singleton list."))) NIL NIL -(-1092 R S) +(-1093 R S) ((|constructor| (NIL "This package provides operations for mapping functions onto \\spadtype{SegmentBinding}\\spad{s}.")) (|map| (((|SegmentBinding| |#2|) (|Mapping| |#2| |#1|) (|SegmentBinding| |#1|)) "\\spad{map(f,v=a..b)} returns the value given by \\spad{v=f(a)..f(b)}."))) NIL NIL -(-1093 S) +(-1094 S) ((|constructor| (NIL "This domain is used to provide the function argument syntax \\spad{v=a..b}. This is used,{} for example,{} by the top-level \\spadfun{draw} functions."))) NIL -((|HasCategory| (-1095 |#1|) (QUOTE (-1101)))) -(-1094 S) +((|HasCategory| (-1096 |#1|) (QUOTE (-1102)))) +(-1095 S) ((|constructor| (NIL "This category provides operations on ranges,{} or {\\em segments} as they are called.")) (|segment| (($ |#1| |#1|) "\\spad{segment(i,j)} is an alternate way to create the segment \\spad{i..j}.")) (|incr| (((|Integer|) $) "\\spad{incr(s)} returns \\spad{n},{} where \\spad{s} is a segment in which every \\spad{n}\\spad{-}th element is used. Note: \\spad{incr(l..h by n) = n}.")) (|high| ((|#1| $) "\\spad{high(s)} returns the second endpoint of \\spad{s}. Note: \\spad{high(l..h) = h}.")) (|low| ((|#1| $) "\\spad{low(s)} returns the first endpoint of \\spad{s}. Note: \\spad{low(l..h) = l}.")) (|hi| ((|#1| $) "\\spad{hi(s)} returns the second endpoint of \\spad{s}. Note: \\spad{hi(l..h) = h}.")) (|lo| ((|#1| $) "\\spad{lo(s)} returns the first endpoint of \\spad{s}. Note: \\spad{lo(l..h) = l}.")) (BY (($ $ (|Integer|)) "\\spad{s by n} creates a new segment in which only every \\spad{n}\\spad{-}th element is used.")) (SEGMENT (($ |#1| |#1|) "\\spad{l..h} creates a segment with \\spad{l} and \\spad{h} as the endpoints."))) NIL NIL -(-1095 S) +(-1096 S) ((|constructor| (NIL "This type is used to specify a range of values from type \\spad{S}."))) NIL -((|HasCategory| |#1| (QUOTE (-849))) (|HasCategory| |#1| (QUOTE (-1101)))) -(-1096 S L) +((|HasCategory| |#1| (QUOTE (-849))) (|HasCategory| |#1| (QUOTE (-1102)))) +(-1097 S L) ((|constructor| (NIL "This category provides an interface for expanding segments to a stream of elements.")) (|map| ((|#2| (|Mapping| |#1| |#1|) $) "\\spad{map(f,l..h by k)} produces a value of type \\spad{L} by applying \\spad{f} to each of the succesive elements of the segment,{} that is,{} \\spad{[f(l), f(l+k), ..., f(lN)]},{} where \\spad{lN <= h < lN+k}.")) (|expand| ((|#2| $) "\\spad{expand(l..h by k)} creates value of type \\spad{L} with elements \\spad{l, l+k, ... lN} where \\spad{lN <= h < lN+k}. For example,{} \\spad{expand(1..5 by 2) = [1,3,5]}.") ((|#2| (|List| $)) "\\spad{expand(l)} creates a new value of type \\spad{L} in which each segment \\spad{l..h by k} is replaced with \\spad{l, l+k, ... lN},{} where \\spad{lN <= h < lN+k}. For example,{} \\spad{expand [1..4, 7..9] = [1,2,3,4,7,8,9]}."))) NIL NIL -(-1097) +(-1098) ((|constructor| (NIL "This domain represents a block of expressions.")) (|last| (((|SpadAst|) $) "\\spad{last(e)} returns the last instruction in `e'.")) (|body| (((|List| (|SpadAst|)) $) "\\spad{body(e)} returns the list of expressions in the sequence of instruction `e'."))) NIL NIL -(-1098 A S) +(-1099 A S) ((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#2| $) "\\spad{union(x,u)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{x},{}\\spad{u})} returns a copy of \\spad{u}.") (($ $ |#2|) "\\spad{union(u,x)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{u},{}\\spad{x})} returns a copy of \\spad{u}.") (($ $ $) "\\spad{union(u,v)} returns the set aggregate of elements which are members of either set aggregate \\spad{u} or \\spad{v}.")) (|subset?| (((|Boolean|) $ $) "\\spad{subset?(u,v)} tests if \\spad{u} is a subset of \\spad{v}. Note: equivalent to \\axiom{reduce(and,{}{member?(\\spad{x},{}\\spad{v}) for \\spad{x} in \\spad{u}},{}\\spad{true},{}\\spad{false})}.")) (|symmetricDifference| (($ $ $) "\\spad{symmetricDifference(u,v)} returns the set aggregate of elements \\spad{x} which are members of set aggregate \\spad{u} or set aggregate \\spad{v} but not both. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{symmetricDifference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: \\axiom{symmetricDifference(\\spad{u},{}\\spad{v}) = union(difference(\\spad{u},{}\\spad{v}),{}difference(\\spad{v},{}\\spad{u}))}")) (|difference| (($ $ |#2|) "\\spad{difference(u,x)} returns the set aggregate \\spad{u} with element \\spad{x} removed. If \\spad{u} does not contain \\spad{x},{} a copy of \\spad{u} is returned. Note: \\axiom{difference(\\spad{s},{} \\spad{x}) = difference(\\spad{s},{} {\\spad{x}})}.") (($ $ $) "\\spad{difference(u,v)} returns the set aggregate \\spad{w} consisting of elements in set aggregate \\spad{u} but not in set aggregate \\spad{v}. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{difference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: equivalent to the notation (not currently supported) \\axiom{{\\spad{x} for \\spad{x} in \\spad{u} | not member?(\\spad{x},{}\\spad{v})}}.")) (|intersect| (($ $ $) "\\spad{intersect(u,v)} returns the set aggregate \\spad{w} consisting of elements common to both set aggregates \\spad{u} and \\spad{v}. Note: equivalent to the notation (not currently supported) {\\spad{x} for \\spad{x} in \\spad{u} | member?(\\spad{x},{}\\spad{v})}.")) (|set| (($ (|List| |#2|)) "\\spad{set([x,y,...,z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}.") (($) "\\spad{set()}\\$\\spad{D} creates an empty set aggregate of type \\spad{D}.")) (|brace| (($ (|List| |#2|)) "\\spad{brace([x,y,...,z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}. This form is considered obsolete. Use \\axiomFun{set} instead.") (($) "\\spad{brace()}\\$\\spad{D} (otherwise written {}\\$\\spad{D}) creates an empty set aggregate of type \\spad{D}. This form is considered obsolete. Use \\axiomFun{set} instead.")) (|part?| (((|Boolean|) $ $) "\\spad{s} < \\spad{t} returns \\spad{true} if all elements of set aggregate \\spad{s} are also elements of set aggregate \\spad{t}."))) NIL NIL -(-1099 S) +(-1100 S) ((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#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)) +((-4408 . T)) NIL -(-1100 S) +(-1101 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}."))) NIL NIL -(-1101) +(-1102) ((|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}."))) NIL NIL -(-1102 |m| |n|) +(-1103 |m| |n|) ((|constructor| (NIL "\\spadtype{SetOfMIntegersInOneToN} implements the subsets of \\spad{M} integers in the interval \\spad{[1..n]}")) (|delta| (((|NonNegativeInteger|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{delta(S,k,p)} returns the number of elements of \\spad{S} which are strictly between \\spad{p} and the \\spad{k^}{th} element of \\spad{S}.")) (|member?| (((|Boolean|) (|PositiveInteger|) $) "\\spad{member?(p, s)} returns \\spad{true} is \\spad{p} is in \\spad{s},{} \\spad{false} otherwise.")) (|enumerate| (((|Vector| $)) "\\spad{enumerate()} returns a vector of all the sets of \\spad{M} integers in \\spad{1..n}.")) (|setOfMinN| (($ (|List| (|PositiveInteger|))) "\\spad{setOfMinN([a_1,...,a_m])} returns the set {a_1,{}...,{}a_m}. Error if {a_1,{}...,{}a_m} is not a set of \\spad{M} integers in \\spad{1..n}.")) (|elements| (((|List| (|PositiveInteger|)) $) "\\spad{elements(S)} returns the list of the elements of \\spad{S} in increasing order.")) (|replaceKthElement| (((|Union| $ "failed") $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{replaceKthElement(S,k,p)} replaces the \\spad{k^}{th} element of \\spad{S} by \\spad{p},{} and returns \"failed\" if the result is not a set of \\spad{M} integers in \\spad{1..n} any more.")) (|incrementKthElement| (((|Union| $ "failed") $ (|PositiveInteger|)) "\\spad{incrementKthElement(S,k)} increments the \\spad{k^}{th} element of \\spad{S},{} and returns \"failed\" if the result is not a set of \\spad{M} integers in \\spad{1..n} any more."))) NIL NIL -(-1103 S) +(-1104 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)) -((-2797 (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1101))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-1101))) (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863)))) (-12 (|HasCategory| |#1| (QUOTE (-1101))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) -(-1104 |Str| |Sym| |Int| |Flt| |Expr|) +((-4418 . T) (-4408 . T) (-4419 . T)) +((-2800 (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863)))) (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) +(-1105 |Str| |Sym| |Int| |Flt| |Expr|) ((|constructor| (NIL "This category allows the manipulation of Lisp values while keeping the grunge fairly localized.")) (|elt| (($ $ (|List| (|Integer|))) "\\spad{elt((a1,...,an), [i1,...,im])} returns \\spad{(a_i1,...,a_im)}.") (($ $ (|Integer|)) "\\spad{elt((a1,...,an), i)} returns \\spad{ai}.")) (|#| (((|Integer|) $) "\\spad{\\#((a1,...,an))} returns \\spad{n}.")) (|cdr| (($ $) "\\spad{cdr((a1,...,an))} returns \\spad{(a2,...,an)}.")) (|car| (($ $) "\\spad{car((a1,...,an))} returns a1.")) (|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|) $ $) "\\spad{eq(s, t)} is \\spad{true} if EQ(\\spad{s},{}\\spad{t}) is \\spad{true} in Lisp."))) NIL NIL -(-1105) +(-1106) ((|constructor| (NIL "This domain allows the manipulation of the usual Lisp values."))) NIL NIL -(-1106 |Str| |Sym| |Int| |Flt| |Expr|) +(-1107 |Str| |Sym| |Int| |Flt| |Expr|) ((|constructor| (NIL "This domain allows the manipulation of Lisp values over arbitrary atomic types."))) NIL NIL -(-1107 R FS) +(-1108 R FS) ((|constructor| (NIL "\\axiomType{SimpleFortranProgram(\\spad{f},{}type)} provides a simple model of some FORTRAN subprograms,{} making it possible to coerce objects of various domains into a FORTRAN subprogram called \\axiom{\\spad{f}}. These can then be translated into legal FORTRAN code.")) (|fortran| (($ (|Symbol|) (|FortranScalarType|) |#2|) "\\spad{fortran(fname,ftype,body)} builds an object of type \\axiomType{FortranProgramCategory}. The three arguments specify the name,{} the type and the \\spad{body} of the program."))) NIL NIL -(-1108 R E V P TS) +(-1109 R E V P TS) ((|constructor| (NIL "\\indented{2}{A internal package for removing redundant quasi-components and redundant} \\indented{2}{branches when decomposing a variety by means of quasi-components} \\indented{2}{of regular triangular sets. \\newline} References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{5}{Tech. Report (PoSSo project)} \\indented{1}{[2] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|branchIfCan| (((|Union| (|Record| (|:| |eq| (|List| |#4|)) (|:| |tower| |#5|) (|:| |ineq| (|List| |#4|))) "failed") (|List| |#4|) |#5| (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{branchIfCan(leq,{}\\spad{ts},{}lineq,{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement.")) (|prepareDecompose| (((|List| (|Record| (|:| |eq| (|List| |#4|)) (|:| |tower| |#5|) (|:| |ineq| (|List| |#4|)))) (|List| |#4|) (|List| |#5|) (|Boolean|) (|Boolean|)) "\\axiom{prepareDecompose(\\spad{lp},{}\\spad{lts},{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|removeSuperfluousCases| (((|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|)))) "\\axiom{removeSuperfluousCases(llpwt)} is an internal subroutine,{} exported only for developement.")) (|subCase?| (((|Boolean|) (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|)) (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) "\\axiom{subCase?(lpwt1,{}lpwt2)} is an internal subroutine,{} exported only for developement.")) (|removeSuperfluousQuasiComponents| (((|List| |#5|) (|List| |#5|)) "\\axiom{removeSuperfluousQuasiComponents(\\spad{lts})} removes from \\axiom{\\spad{lts}} any \\spad{ts} such that \\axiom{subQuasiComponent?(\\spad{ts},{}us)} holds for another \\spad{us} in \\axiom{\\spad{lts}}.")) (|subQuasiComponent?| (((|Boolean|) |#5| (|List| |#5|)) "\\axiom{subQuasiComponent?(\\spad{ts},{}lus)} returns \\spad{true} iff \\axiom{subQuasiComponent?(\\spad{ts},{}us)} holds for one \\spad{us} in \\spad{lus}.") (((|Boolean|) |#5| |#5|) "\\axiom{subQuasiComponent?(\\spad{ts},{}us)} returns \\spad{true} iff \\axiomOpFrom{internalSubQuasiComponent?(\\spad{ts},{}us)}{QuasiComponentPackage} returs \\spad{true}.")) (|internalSubQuasiComponent?| (((|Union| (|Boolean|) "failed") |#5| |#5|) "\\axiom{internalSubQuasiComponent?(\\spad{ts},{}us)} returns a boolean \\spad{b} value if the fact the regular zero set of \\axiom{us} contains that of \\axiom{\\spad{ts}} can be decided (and in that case \\axiom{\\spad{b}} gives this inclusion) otherwise returns \\axiom{\"failed\"}.")) (|infRittWu?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{infRittWu?(\\spad{lp1},{}\\spad{lp2})} is an internal subroutine,{} exported only for developement.")) (|internalInfRittWu?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{internalInfRittWu?(\\spad{lp1},{}\\spad{lp2})} is an internal subroutine,{} exported only for developement.")) (|internalSubPolSet?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{internalSubPolSet?(\\spad{lp1},{}\\spad{lp2})} returns \\spad{true} iff \\axiom{\\spad{lp1}} is a sub-set of \\axiom{\\spad{lp2}} assuming that these lists are sorted increasingly \\spad{w}.\\spad{r}.\\spad{t}. \\axiomOpFrom{infRittWu?}{RecursivePolynomialCategory}.")) (|subPolSet?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{subPolSet?(\\spad{lp1},{}\\spad{lp2})} returns \\spad{true} iff \\axiom{\\spad{lp1}} is a sub-set of \\axiom{\\spad{lp2}}.")) (|subTriSet?| (((|Boolean|) |#5| |#5|) "\\axiom{subTriSet?(\\spad{ts},{}us)} returns \\spad{true} iff \\axiom{\\spad{ts}} is a sub-set of \\axiom{us}.")) (|moreAlgebraic?| (((|Boolean|) |#5| |#5|) "\\axiom{moreAlgebraic?(\\spad{ts},{}us)} returns \\spad{false} iff \\axiom{\\spad{ts}} and \\axiom{us} are both empty,{} or \\axiom{\\spad{ts}} has less elements than \\axiom{us},{} or some variable is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{us} and is not \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ts}}.")) (|algebraicSort| (((|List| |#5|) (|List| |#5|)) "\\axiom{algebraicSort(\\spad{lts})} sorts \\axiom{\\spad{lts}} \\spad{w}.\\spad{r}.\\spad{t} \\axiomOpFrom{supDimElseRittWu}{QuasiComponentPackage}.")) (|supDimElseRittWu?| (((|Boolean|) |#5| |#5|) "\\axiom{supDimElseRittWu(\\spad{ts},{}us)} returns \\spad{true} iff \\axiom{\\spad{ts}} has less elements than \\axiom{us} otherwise if \\axiom{\\spad{ts}} has higher rank than \\axiom{us} \\spad{w}.\\spad{r}.\\spad{t}. Riit and Wu ordering.")) (|stopTable!| (((|Void|)) "\\axiom{stopTableGcd!()} is an internal subroutine,{} exported only for developement.")) (|startTable!| (((|Void|) (|String|) (|String|) (|String|)) "\\axiom{startTableGcd!(\\spad{s1},{}\\spad{s2},{}\\spad{s3})} is an internal subroutine,{} exported only for developement."))) NIL NIL -(-1109 R E V P TS) +(-1110 R E V P TS) ((|constructor| (NIL "A internal package for computing gcds and resultants of univariate polynomials with coefficients in a tower of simple extensions of a field. There is no need to use directly this package since its main operations are available from \\spad{TS}. \\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA and \\spad{R}. RIOBOO \"Computations of \\spad{gcd} over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of AAECC11} \\indented{5}{Paris,{} 1995.} \\indented{1}{[2] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}"))) NIL NIL -(-1110 R E V P) +(-1111 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)) +((-4419 . T) (-4418 . T)) NIL -(-1111) +(-1112) ((|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 pi} in the corresponding double coset. Note: the resulting permutation {\\em pi} of {\\em {1,2,...,n}} is given in list form. Notes: the inverse of this map is {\\em coleman}. For details,{} see James/Kerber.")) (|coleman| (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{coleman(alpha,beta,pi)}: there is a bijection from the set of matrices having nonnegative entries and row sums {\\em alpha},{} column sums {\\em beta} to the set of {\\em Salpha - Sbeta} double cosets of the symmetric group {\\em Sn}. ({\\em Salpha} is the Young subgroup corresponding to the improper partition {\\em alpha}). For a representing element {\\em pi} of such a double coset,{} coleman(\\spad{alpha},{}\\spad{beta},{}\\spad{pi}) generates the Coleman-matrix corresponding to {\\em alpha, beta, pi}. Note: The permutation {\\em pi} of {\\em {1,2,...,n}} has to be given in list form. Note: the inverse of this map is {\\em inverseColeman} (if {\\em pi} is the lexicographical smallest permutation in the coset). For details see James/Kerber."))) NIL NIL -(-1112 S) +(-1113 S) ((|constructor| (NIL "the class of all multiplicative semigroups,{} \\spadignore{i.e.} a set with an associative operation \\spadop{*}. \\blankline")) (** (($ $ (|PositiveInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (* (($ $ $) "\\spad{x*y} returns the product of \\spad{x} and \\spad{y}."))) NIL NIL -(-1113) +(-1114) ((|constructor| (NIL "the class of all multiplicative semigroups,{} \\spadignore{i.e.} a set with an associative operation \\spadop{*}. \\blankline")) (** (($ $ (|PositiveInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) 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(LIST (QUOTE -1040) (QUOTE (-567))))) (-12 (|HasCategory| |#3| (QUOTE (-365))) (|HasCategory| |#3| (LIST (QUOTE -1040) (QUOTE (-567))))) (-12 (|HasCategory| |#3| (QUOTE (-370))) (|HasCategory| |#3| (LIST (QUOTE -1040) (QUOTE (-567))))) (-12 (|HasCategory| |#3| (QUOTE (-727))) (|HasCategory| |#3| (LIST (QUOTE -1040) (QUOTE (-567))))) (-12 (|HasCategory| |#3| (QUOTE (-794))) (|HasCategory| |#3| (LIST (QUOTE -1040) (QUOTE (-567))))) (-12 (|HasCategory| |#3| (QUOTE (-849))) (|HasCategory| |#3| (LIST (QUOTE -1040) (QUOTE (-567))))) (-12 (|HasCategory| |#3| (QUOTE (-1051))) (|HasCategory| |#3| (LIST (QUOTE -1040) (QUOTE (-567))))) (-12 (|HasCategory| |#3| (QUOTE (-1102))) (|HasCategory| |#3| (LIST (QUOTE -1040) (QUOTE (-567)))))) (|HasCategory| (-567) (QUOTE (-851))) (-12 (|HasCategory| |#3| (QUOTE (-1051))) (|HasCategory| |#3| (LIST (QUOTE -640) (QUOTE (-567))))) (-12 (|HasCategory| |#3| (QUOTE (-233))) (|HasCategory| |#3| (QUOTE (-1051)))) (-12 (|HasCategory| |#3| (QUOTE (-1051))) (|HasCategory| |#3| (LIST (QUOTE -902) (QUOTE (-1178))))) (-2800 (|HasCategory| |#3| (QUOTE (-1051))) (-12 (|HasCategory| |#3| (QUOTE (-1102))) (|HasCategory| |#3| (LIST (QUOTE -1040) (QUOTE (-567)))))) (-12 (|HasCategory| |#3| (QUOTE (-1102))) (|HasCategory| |#3| (LIST (QUOTE -1040) (QUOTE (-567))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#3| (QUOTE (-1102)))) (|HasAttribute| |#3| (QUOTE -4415)) (|HasCategory| |#3| (QUOTE (-131))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -614) (QUOTE (-863)))) (-12 (|HasCategory| |#3| (QUOTE (-1102))) (|HasCategory| |#3| (LIST (QUOTE -310) (|devaluate| |#3|))))) +(-1116 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 ((|HasCategory| |#1| (QUOTE (-455)))) -(-1116) +(-1117) ((|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 -(-1117 R -3867) +(-1118 R -3879) ((|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 -(-1118 R) +(-1119 R) ((|constructor| (NIL "Find the sign of a rational function around a point or infinity.")) (|sign| (((|Union| (|Integer|) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|)) (|String|)) "\\spad{sign(f, x, a, s)} returns the sign of \\spad{f} as \\spad{x} nears \\spad{a} from the left (below) if \\spad{s} is the string \\spad{\"left\"},{} or from the right (above) if \\spad{s} is the string \\spad{\"right\"}.") (((|Union| (|Integer|) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|)))) "\\spad{sign(f, x, a)} returns the sign of \\spad{f} as \\spad{x} approaches \\spad{a},{} from both sides if \\spad{a} is finite.") (((|Union| (|Integer|) "failed") (|Fraction| (|Polynomial| |#1|))) "\\spad{sign f} returns the sign of \\spad{f} if it is constant everywhere."))) NIL NIL -(-1119) +(-1120) ((|constructor| (NIL "This is the datatype for operation signatures as \\indented{2}{used by the compiler and the interpreter.\\space{2}Note that this domain} \\indented{2}{differs from SignatureAst.} See also: ConstructorCall,{} Domain.")) (|source| (((|List| (|Syntax|)) $) "\\spad{source(s)} returns the list of parameter types of \\spad{`s'}.")) (|target| (((|Syntax|) $) "\\spad{target(s)} returns the target type of the signature \\spad{`s'}.")) (|signature| (($ (|List| (|Syntax|)) (|Syntax|)) "\\spad{signature(s,t)} constructs a Signature object with parameter types indicaded by \\spad{`s'},{} and return type indicated by \\spad{`t'}."))) NIL NIL -(-1120) +(-1121) ((|constructor| (NIL "\\indented{1}{Package to allow simplify to be called on AlgebraicNumbers} by converting to EXPR(INT)")) (|simplify| (((|Expression| (|Integer|)) (|AlgebraicNumber|)) "\\spad{simplify(an)} applies simplifications to \\spad{an}"))) NIL NIL -(-1121) +(-1122) ((|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)) +((-4406 . T) (-4410 . T) (-4405 . T) (-4416 . T) (-4417 . T) (-4411 . T) ((-4420 "*") . T) (-4412 . T) (-4413 . T) (-4415 . T)) NIL -(-1122 S) +(-1123 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| $) "\\spad{push!(x,s)} pushes \\spad{x} onto stack \\spad{s},{} \\spadignore{i.e.} destructively changing \\spad{s} so as to have a new first (top) element \\spad{x}. Afterwards,{} pop!(\\spad{s}) produces \\spad{x} and pop!(\\spad{s}) produces the original \\spad{s}."))) -((-4417 . T) (-4418 . T)) +((-4418 . T) (-4419 . T)) NIL -(-1123 S |ndim| R |Row| |Col|) +(-1124 S |ndim| R |Row| |Col|) ((|constructor| (NIL "\\spadtype{SquareMatrixCategory} is a general square matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col.")) (** (($ $ (|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)))) -(-1124 |ndim| R |Row| |Col|) +((|HasCategory| |#3| (QUOTE (-365))) (|HasAttribute| |#3| (QUOTE (-4420 "*"))) (|HasCategory| |#3| (QUOTE (-172)))) +(-1125 |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)) +((-4418 . T) (-4412 . T) (-4413 . T) (-4415 . T)) NIL -(-1125 R |Row| |Col| M) +(-1126 R |Row| |Col| M) ((|constructor| (NIL "\\spadtype{SmithNormalForm} is a package which provides some standard canonical forms for matrices.")) (|diophantineSystem| (((|Record| (|:| |particular| (|Union| |#3| "failed")) (|:| |basis| (|List| |#3|))) |#4| |#3|) "\\spad{diophantineSystem(A,B)} returns a particular integer solution and an integer basis of the equation \\spad{AX = B}.")) (|completeSmith| (((|Record| (|:| |Smith| |#4|) (|:| |leftEqMat| |#4|) (|:| |rightEqMat| |#4|)) |#4|) "\\spad{completeSmith} returns a record that contains the Smith normal form \\spad{H} of the matrix and the left and right equivalence matrices \\spad{U} and \\spad{V} such that U*m*v = \\spad{H}")) (|smith| ((|#4| |#4|) "\\spad{smith(m)} returns the Smith Normal form of the matrix \\spad{m}.")) (|completeHermite| (((|Record| (|:| |Hermite| |#4|) (|:| |eqMat| |#4|)) |#4|) "\\spad{completeHermite} returns a record that contains the Hermite normal form \\spad{H} of the matrix and the equivalence matrix \\spad{U} such that U*m = \\spad{H}")) (|hermite| ((|#4| |#4|) "\\spad{hermite(m)} returns the Hermite normal form of the matrix \\spad{m}."))) NIL NIL -(-1126 R |VarSet|) +(-1127 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| (-559)) (-4415 |has| |#1| (-6 -4415)) (-4412 . T) (-4411 . T) (-4414 . T)) -((|HasCategory| |#1| (QUOTE (-910))) (-2797 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-455))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-910)))) (-2797 (|HasCategory| |#1| (QUOTE (-455))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-910)))) (-2797 (|HasCategory| |#1| (QUOTE (-455))) (|HasCategory| |#1| (QUOTE (-910)))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-172))) (-2797 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-559)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -887) (QUOTE (-381)))) (|HasCategory| |#2| (LIST (QUOTE -887) (QUOTE (-381))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -887) (QUOTE (-567)))) (|HasCategory| |#2| (LIST (QUOTE -887) (QUOTE (-567))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -615) (LIST (QUOTE -893) (QUOTE (-381))))) (|HasCategory| |#2| (LIST (QUOTE -615) (LIST (QUOTE -893) (QUOTE (-381)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -615) (LIST (QUOTE -893) (QUOTE (-567))))) (|HasCategory| |#2| (LIST (QUOTE -615) (LIST (QUOTE -893) (QUOTE (-567)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| |#2| (LIST (QUOTE -615) (QUOTE (-539))))) (|HasCategory| |#1| (LIST (QUOTE -640) (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1039) (QUOTE (-567)))) (-2797 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1039) (LIST (QUOTE -410) (QUOTE (-567)))))) (|HasCategory| |#1| (LIST (QUOTE -1039) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (QUOTE (-365))) (|HasAttribute| |#1| (QUOTE -4415)) (|HasCategory| |#1| (QUOTE (-455))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-910)))) (-2797 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-910)))) (|HasCategory| |#1| (QUOTE (-145))))) -(-1127 |Coef| |Var| SMP) +(((-4420 "*") |has| |#1| (-172)) (-4411 |has| |#1| (-559)) (-4416 |has| |#1| (-6 -4416)) (-4413 . T) (-4412 . T) (-4415 . T)) +((|HasCategory| |#1| (QUOTE (-911))) (-2800 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-455))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-911)))) (-2800 (|HasCategory| |#1| (QUOTE (-455))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-911)))) (-2800 (|HasCategory| |#1| (QUOTE (-455))) (|HasCategory| |#1| (QUOTE (-911)))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-172))) (-2800 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-559)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -888) (QUOTE (-381)))) (|HasCategory| |#2| (LIST (QUOTE -888) (QUOTE (-381))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -888) (QUOTE (-567)))) (|HasCategory| |#2| (LIST (QUOTE -888) (QUOTE (-567))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-381))))) (|HasCategory| |#2| (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-381)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567))))) (|HasCategory| |#2| (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| |#2| (LIST (QUOTE -615) (QUOTE (-539))))) (|HasCategory| |#1| (LIST (QUOTE -640) (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (QUOTE (-567)))) (-2800 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567)))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (QUOTE (-365))) (|HasAttribute| |#1| (QUOTE -4416)) (|HasCategory| |#1| (QUOTE (-455))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-911)))) (-2800 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-911)))) (|HasCategory| |#1| (QUOTE (-145))))) +(-1128 |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| (-559)) (-4412 . T) (-4411 . T) (-4414 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (-2797 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-559)))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-365)))) -(-1128 R E V P) +(((-4420 "*") |has| |#1| (-172)) (-4411 |has| |#1| (-559)) (-4413 . T) (-4412 . T) (-4415 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (-2800 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-559)))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-365)))) +(-1129 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)) +((-4419 . T) (-4418 . T)) NIL -(-1129 UP -3867) +(-1130 UP -3879) ((|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 -(-1130 R) +(-1131 R) ((|constructor| (NIL "This package tries to find solutions expressed in terms of radicals for systems of equations of rational functions with coefficients in an integral domain \\spad{R}.")) (|contractSolve| (((|SuchThat| (|List| (|Expression| |#1|)) (|List| (|Equation| (|Expression| |#1|)))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{contractSolve(rf,x)} finds the solutions expressed in terms of radicals of the equation \\spad{rf} = 0 with respect to the symbol \\spad{x},{} where \\spad{rf} is a rational function. The result contains new symbols for common subexpressions in order to reduce the size of the output.") (((|SuchThat| (|List| (|Expression| |#1|)) (|List| (|Equation| (|Expression| |#1|)))) (|Equation| (|Fraction| (|Polynomial| |#1|))) (|Symbol|)) "\\spad{contractSolve(eq,x)} finds the solutions expressed in terms of radicals of the equation of rational functions \\spad{eq} with respect to the symbol \\spad{x}. The result contains new symbols for common subexpressions in order to reduce the size of the output.")) (|radicalRoots| (((|List| (|List| (|Expression| |#1|))) (|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|Symbol|))) "\\spad{radicalRoots(lrf,lvar)} finds the roots expressed in terms of radicals of the list of rational functions \\spad{lrf} with respect to the list of symbols \\spad{lvar}.") (((|List| (|Expression| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{radicalRoots(rf,x)} finds the roots expressed in terms of radicals of the rational function \\spad{rf} with respect to the symbol \\spad{x}.")) (|radicalSolve| (((|List| (|List| (|Equation| (|Expression| |#1|)))) (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) "\\spad{radicalSolve(leq)} finds the solutions expressed in terms of radicals of the system of equations of rational functions \\spad{leq} with respect to the unique symbol \\spad{x} appearing in \\spad{leq}.") (((|List| (|List| (|Equation| (|Expression| |#1|)))) (|List| (|Equation| (|Fraction| (|Polynomial| |#1|)))) (|List| (|Symbol|))) "\\spad{radicalSolve(leq,lvar)} finds the solutions expressed in terms of radicals of the system of equations of rational functions \\spad{leq} with respect to the list of symbols \\spad{lvar}.") (((|List| (|List| (|Equation| (|Expression| |#1|)))) (|List| (|Fraction| (|Polynomial| |#1|)))) "\\spad{radicalSolve(lrf)} finds the solutions expressed in terms of radicals of the system of equations \\spad{lrf} = 0,{} where \\spad{lrf} is a system of univariate rational functions.") (((|List| (|List| (|Equation| (|Expression| |#1|)))) (|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|Symbol|))) "\\spad{radicalSolve(lrf,lvar)} finds the solutions expressed in terms of radicals of the system of equations \\spad{lrf} = 0 with respect to the list of symbols \\spad{lvar},{} where \\spad{lrf} is a list of rational functions.") (((|List| (|Equation| (|Expression| |#1|))) (|Equation| (|Fraction| (|Polynomial| |#1|)))) "\\spad{radicalSolve(eq)} finds the solutions expressed in terms of radicals of the equation of rational functions \\spad{eq} with respect to the unique symbol \\spad{x} appearing in \\spad{eq}.") (((|List| (|Equation| (|Expression| |#1|))) (|Equation| (|Fraction| (|Polynomial| |#1|))) (|Symbol|)) "\\spad{radicalSolve(eq,x)} finds the solutions expressed in terms of radicals of the equation of rational functions \\spad{eq} with respect to the symbol \\spad{x}.") (((|List| (|Equation| (|Expression| |#1|))) (|Fraction| (|Polynomial| |#1|))) "\\spad{radicalSolve(rf)} finds the solutions expressed in terms of radicals of the equation \\spad{rf} = 0,{} where \\spad{rf} is a univariate rational function.") (((|List| (|Equation| (|Expression| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{radicalSolve(rf,x)} finds the solutions expressed in terms of radicals of the equation \\spad{rf} = 0 with respect to the symbol \\spad{x},{} where \\spad{rf} is a rational function."))) NIL NIL -(-1131 R) +(-1132 R) ((|constructor| (NIL "This package finds the function func3 where func1 and func2 \\indented{1}{are given and\\space{2}func1 = func3(func2) .\\space{2}If there is no solution then} \\indented{1}{function func1 will be returned.} \\indented{1}{An example would be\\space{2}\\spad{func1:= 8*X**3+32*X**2-14*X ::EXPR INT} and} \\indented{1}{\\spad{func2:=2*X ::EXPR INT} convert them via univariate} \\indented{1}{to FRAC SUP EXPR INT and then the solution is \\spad{func3:=X**3+X**2-X}} \\indented{1}{of type FRAC SUP EXPR INT}")) (|unvectorise| (((|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Vector| (|Expression| |#1|)) (|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Integer|)) "\\spad{unvectorise(vect, var, n)} returns \\spad{vect(1) + vect(2)*var + ... + vect(n+1)*var**(n)} where \\spad{vect} is the vector of the coefficients of the polynomail ,{} \\spad{var} the new variable and \\spad{n} the degree.")) (|decomposeFunc| (((|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|)))) "\\spad{decomposeFunc(func1, func2, newvar)} returns a function func3 where \\spad{func1} = func3(\\spad{func2}) and expresses it in the new variable newvar. If there is no solution then \\spad{func1} will be returned."))) NIL NIL -(-1132 R) +(-1133 R) ((|constructor| (NIL "This package tries to find solutions of equations of type Expression(\\spad{R}). This means expressions involving transcendental,{} exponential,{} logarithmic and nthRoot functions. After trying to transform different kernels to one kernel by applying several rules,{} it calls zerosOf for the SparseUnivariatePolynomial in the remaining kernel. For example the expression \\spad{sin(x)*cos(x)-2} will be transformed to \\indented{3}{\\spad{-2 tan(x/2)**4 -2 tan(x/2)**3 -4 tan(x/2)**2 +2 tan(x/2) -2}} by using the function normalize and then to \\indented{3}{\\spad{-2 tan(x)**2 + tan(x) -2}} with help of subsTan. This function tries to express the given function in terms of \\spad{tan(x/2)} to express in terms of \\spad{tan(x)} . Other examples are the expressions \\spad{sqrt(x+1)+sqrt(x+7)+1} or \\indented{1}{\\spad{sqrt(sin(x))+1} .}")) (|solve| (((|List| (|List| (|Equation| (|Expression| |#1|)))) (|List| (|Equation| (|Expression| |#1|))) (|List| (|Symbol|))) "\\spad{solve(leqs, lvar)} returns a list of solutions to the list of equations \\spad{leqs} with respect to the list of symbols lvar.") (((|List| (|Equation| (|Expression| |#1|))) (|Expression| |#1|) (|Symbol|)) "\\spad{solve(expr,x)} finds the solutions of the equation \\spad{expr} = 0 with respect to the symbol \\spad{x} where \\spad{expr} is a function of type Expression(\\spad{R}).") (((|List| (|Equation| (|Expression| |#1|))) (|Equation| (|Expression| |#1|)) (|Symbol|)) "\\spad{solve(eq,x)} finds the solutions of the equation \\spad{eq} where \\spad{eq} is an equation of functions of type Expression(\\spad{R}) with respect to the symbol \\spad{x}.") (((|List| (|Equation| (|Expression| |#1|))) (|Equation| (|Expression| |#1|))) "\\spad{solve(eq)} finds the solutions of the equation \\spad{eq} where \\spad{eq} is an equation of functions of type Expression(\\spad{R}) with respect to the unique symbol \\spad{x} appearing in \\spad{eq}.") (((|List| (|Equation| (|Expression| |#1|))) (|Expression| |#1|)) "\\spad{solve(expr)} finds the solutions of the equation \\spad{expr} = 0 where \\spad{expr} is a function of type Expression(\\spad{R}) with respect to the unique symbol \\spad{x} appearing in eq."))) NIL NIL -(-1133 S A) +(-1134 S A) ((|constructor| (NIL "This package exports sorting algorithnms")) (|insertionSort!| ((|#2| |#2|) "\\spad{insertionSort! }\\undocumented") ((|#2| |#2| (|Mapping| (|Boolean|) |#1| |#1|)) "\\spad{insertionSort!(a,f)} \\undocumented")) (|bubbleSort!| ((|#2| |#2|) "\\spad{bubbleSort!(a)} \\undocumented") ((|#2| |#2| (|Mapping| (|Boolean|) |#1| |#1|)) "\\spad{bubbleSort!(a,f)} \\undocumented"))) NIL ((|HasCategory| |#1| (QUOTE (-851)))) -(-1134 R) +(-1135 R) ((|constructor| (NIL "The domain ThreeSpace is used for creating three dimensional objects using functions for defining points,{} curves,{} polygons,{} constructs and the subspaces containing them."))) NIL NIL -(-1135 R) +(-1136 R) ((|constructor| (NIL "The category ThreeSpaceCategory is used for creating three dimensional objects using functions for defining points,{} curves,{} polygons,{} constructs and the subspaces containing them.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(s)} returns the \\spadtype{ThreeSpace} \\spad{s} to Output format.")) (|subspace| (((|SubSpace| 3 |#1|) $) "\\spad{subspace(s)} returns the \\spadtype{SubSpace} which holds all the point information in the \\spadtype{ThreeSpace},{} \\spad{s}.")) (|check| (($ $) "\\spad{check(s)} returns lllpt,{} list of lists of lists of point information about the \\spadtype{ThreeSpace} \\spad{s}.")) (|objects| (((|Record| (|:| |points| (|NonNegativeInteger|)) (|:| |curves| (|NonNegativeInteger|)) (|:| |polygons| (|NonNegativeInteger|)) (|:| |constructs| (|NonNegativeInteger|))) $) "\\spad{objects(s)} returns the \\spadtype{ThreeSpace},{} \\spad{s},{} in the form of a 3D object record containing information on the number of points,{} curves,{} polygons and constructs comprising the \\spadtype{ThreeSpace}..")) (|lprop| (((|List| (|SubSpaceComponentProperty|)) $) "\\spad{lprop(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a list of subspace component properties,{} and if so,{} returns the list; An error is signaled otherwise.")) (|llprop| (((|List| (|List| (|SubSpaceComponentProperty|))) $) "\\spad{llprop(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a list of curves which are lists of the subspace component properties of the curves,{} and if so,{} returns the list of lists; An error is signaled otherwise.")) (|lllp| (((|List| (|List| (|List| (|Point| |#1|)))) $) "\\spad{lllp(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a list of components,{} which are lists of curves,{} which are lists of points,{} and if so,{} returns the list of lists of lists; An error is signaled otherwise.")) (|lllip| (((|List| (|List| (|List| (|NonNegativeInteger|)))) $) "\\spad{lllip(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a list of components,{} which are lists of curves,{} which are lists of indices to points,{} and if so,{} returns the list of lists of lists; An error is signaled otherwise.")) (|lp| (((|List| (|Point| |#1|)) $) "\\spad{lp(s)} returns the list of points component which the \\spadtype{ThreeSpace},{} \\spad{s},{} contains; these points are used by reference,{} \\spadignore{i.e.} the component holds indices referring to the points rather than the points themselves. This allows for sharing of the points.")) (|mesh?| (((|Boolean|) $) "\\spad{mesh?(s)} returns \\spad{true} if the \\spadtype{ThreeSpace} \\spad{s} is composed of one component,{} a mesh comprising a list of curves which are lists of points,{} or returns \\spad{false} if otherwise")) (|mesh| (((|List| (|List| (|Point| |#1|))) $) "\\spad{mesh(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single surface component defined by a list curves which contain lists of points,{} and if so,{} returns the list of lists of points; An error is signaled otherwise.") (($ (|List| (|List| (|Point| |#1|))) (|Boolean|) (|Boolean|)) "\\spad{mesh([[p0],[p1],...,[pn]], close1, close2)} creates a surface defined over a list of curves,{} \\spad{p0} through \\spad{pn},{} which are lists of points; the booleans \\spad{close1} and close2 indicate how the surface is to be closed: \\spad{close1} set to \\spad{true} means that each individual list (a curve) is to be closed (that is,{} the last point of the list is to be connected to the first point); close2 set to \\spad{true} means that the boundary at one end of the surface is to be connected to the boundary at the other end (the boundaries are defined as the first list of points (curve) and the last list of points (curve)); the \\spadtype{ThreeSpace} containing this surface is returned.") (($ (|List| (|List| (|Point| |#1|)))) "\\spad{mesh([[p0],[p1],...,[pn]])} creates a surface defined by a list of curves which are lists,{} \\spad{p0} through \\spad{pn},{} of points,{} and returns a \\spadtype{ThreeSpace} whose component is the surface.") (($ $ (|List| (|List| (|List| |#1|))) (|Boolean|) (|Boolean|)) "\\spad{mesh(s,[ [[r10]...,[r1m]], [[r20]...,[r2m]],..., [[rn0]...,[rnm]] ], close1, close2)} adds a surface component to the \\spadtype{ThreeSpace} \\spad{s},{} which is defined over a rectangular domain of size \\spad{WxH} where \\spad{W} is the number of lists of points from the domain \\spad{PointDomain(R)} and \\spad{H} is the number of elements in each of those lists; the booleans \\spad{close1} and close2 indicate how the surface is to be closed: if \\spad{close1} is \\spad{true} this means that each individual list (a curve) is to be closed (\\spadignore{i.e.} the last point of the list is to be connected to the first point); if close2 is \\spad{true},{} this means that the boundary at one end of the surface is to be connected to the boundary at the other end (the boundaries are defined as the first list of points (curve) and the last list of points (curve)).") (($ $ (|List| (|List| (|Point| |#1|))) (|Boolean|) (|Boolean|)) "\\spad{mesh(s,[[p0],[p1],...,[pn]], close1, close2)} adds a surface component to the \\spadtype{ThreeSpace},{} which is defined over a list of curves,{} in which each of these curves is a list of points. The boolean arguments \\spad{close1} and close2 indicate how the surface is to be closed. Argument \\spad{close1} equal \\spad{true} means that each individual list (a curve) is to be closed,{} \\spadignore{i.e.} the last point of the list is to be connected to the first point. Argument close2 equal \\spad{true} means that the boundary at one end of the surface is to be connected to the boundary at the other end,{} \\spadignore{i.e.} the boundaries are defined as the first list of points (curve) and the last list of points (curve).") (($ $ (|List| (|List| (|List| |#1|))) (|List| (|SubSpaceComponentProperty|)) (|SubSpaceComponentProperty|)) "\\spad{mesh(s,[ [[r10]...,[r1m]], [[r20]...,[r2m]],..., [[rn0]...,[rnm]] ], [props], prop)} adds a surface component to the \\spadtype{ThreeSpace} \\spad{s},{} which is defined over a rectangular domain of size \\spad{WxH} where \\spad{W} is the number of lists of points from the domain \\spad{PointDomain(R)} and \\spad{H} is the number of elements in each of those lists; lprops is the list of the subspace component properties for each curve list,{} and prop is the subspace component property by which the points are defined.") (($ $ (|List| (|List| (|Point| |#1|))) (|List| (|SubSpaceComponentProperty|)) (|SubSpaceComponentProperty|)) "\\spad{mesh(s,[[p0],[p1],...,[pn]],[props],prop)} adds a surface component,{} defined over a list curves which contains lists of points,{} to the \\spadtype{ThreeSpace} \\spad{s}; props is a list which contains the subspace component properties for each surface parameter,{} and \\spad{prop} is the subspace component property by which the points are defined.")) (|polygon?| (((|Boolean|) $) "\\spad{polygon?(s)} returns \\spad{true} if the \\spadtype{ThreeSpace} \\spad{s} contains a single polygon component,{} or \\spad{false} otherwise.")) (|polygon| (((|List| (|Point| |#1|)) $) "\\spad{polygon(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single polygon component defined by a list of points,{} and if so,{} returns the list of points; An error is signaled otherwise.") (($ (|List| (|Point| |#1|))) "\\spad{polygon([p0,p1,...,pn])} creates a polygon defined by a list of points,{} \\spad{p0} through \\spad{pn},{} and returns a \\spadtype{ThreeSpace} whose component is the polygon.") (($ $ (|List| (|List| |#1|))) "\\spad{polygon(s,[[r0],[r1],...,[rn]])} adds a polygon component defined by a list of points \\spad{r0} through \\spad{rn},{} which are lists of elements from the domain \\spad{PointDomain(m,R)} to the \\spadtype{ThreeSpace} \\spad{s},{} where \\spad{m} is the dimension of the points and \\spad{R} is the \\spadtype{Ring} over which the points are defined.") (($ $ (|List| (|Point| |#1|))) "\\spad{polygon(s,[p0,p1,...,pn])} adds a polygon component defined by a list of points,{} \\spad{p0} throught \\spad{pn},{} to the \\spadtype{ThreeSpace} \\spad{s}.")) (|closedCurve?| (((|Boolean|) $) "\\spad{closedCurve?(s)} returns \\spad{true} if the \\spadtype{ThreeSpace} \\spad{s} contains a single closed curve component,{} \\spadignore{i.e.} the first element of the curve is also the last element,{} or \\spad{false} otherwise.")) (|closedCurve| (((|List| (|Point| |#1|)) $) "\\spad{closedCurve(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single closed curve component defined by a list of points in which the first point is also the last point,{} all of which are from the domain \\spad{PointDomain(m,R)} and if so,{} returns the list of points. An error is signaled otherwise.") (($ (|List| (|Point| |#1|))) "\\spad{closedCurve(lp)} sets a list of points defined by the first element of \\spad{lp} through the last element of \\spad{lp} and back to the first elelment again and returns a \\spadtype{ThreeSpace} whose component is the closed curve defined by \\spad{lp}.") (($ $ (|List| (|List| |#1|))) "\\spad{closedCurve(s,[[lr0],[lr1],...,[lrn],[lr0]])} adds a closed curve component defined by a list of points \\spad{lr0} through \\spad{lrn},{} which are lists of elements from the domain \\spad{PointDomain(m,R)},{} where \\spad{R} is the \\spadtype{Ring} over which the point elements are defined and \\spad{m} is the dimension of the points,{} in which the last element of the list of points contains a copy of the first element list,{} \\spad{lr0}. The closed curve is added to the \\spadtype{ThreeSpace},{} \\spad{s}.") (($ $ (|List| (|Point| |#1|))) "\\spad{closedCurve(s,[p0,p1,...,pn,p0])} adds a closed curve component which is a list of points defined by the first element \\spad{p0} through the last element \\spad{pn} and back to the first element \\spad{p0} again,{} to the \\spadtype{ThreeSpace} \\spad{s}.")) (|curve?| (((|Boolean|) $) "\\spad{curve?(s)} queries whether the \\spadtype{ThreeSpace},{} \\spad{s},{} is a curve,{} \\spadignore{i.e.} has one component,{} a list of list of points,{} and returns \\spad{true} if it is,{} or \\spad{false} otherwise.")) (|curve| (((|List| (|Point| |#1|)) $) "\\spad{curve(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single curve defined by a list of points and if so,{} returns the curve,{} \\spadignore{i.e.} list of points. An error is signaled otherwise.") (($ (|List| (|Point| |#1|))) "\\spad{curve([p0,p1,p2,...,pn])} creates a space curve defined by the list of points \\spad{p0} through \\spad{pn},{} and returns the \\spadtype{ThreeSpace} whose component is the curve.") (($ $ (|List| (|List| |#1|))) "\\spad{curve(s,[[p0],[p1],...,[pn]])} adds a space curve which is a list of points \\spad{p0} through \\spad{pn} defined by lists of elements from the domain \\spad{PointDomain(m,R)},{} where \\spad{R} is the \\spadtype{Ring} over which the point elements are defined and \\spad{m} is the dimension of the points,{} to the \\spadtype{ThreeSpace} \\spad{s}.") (($ $ (|List| (|Point| |#1|))) "\\spad{curve(s,[p0,p1,...,pn])} adds a space curve component defined by a list of points \\spad{p0} through \\spad{pn},{} to the \\spadtype{ThreeSpace} \\spad{s}.")) (|point?| (((|Boolean|) $) "\\spad{point?(s)} queries whether the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single component which is a point and returns the boolean result.")) (|point| (((|Point| |#1|) $) "\\spad{point(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of only a single point and if so,{} returns the point. An error is signaled otherwise.") (($ (|Point| |#1|)) "\\spad{point(p)} returns a \\spadtype{ThreeSpace} object which is composed of one component,{} the point \\spad{p}.") (($ $ (|NonNegativeInteger|)) "\\spad{point(s,i)} adds a point component which is placed into a component list of the \\spadtype{ThreeSpace},{} \\spad{s},{} at the index given by \\spad{i}.") (($ $ (|List| |#1|)) "\\spad{point(s,[x,y,z])} adds a point component defined by a list of elements which are from the \\spad{PointDomain(R)} to the \\spadtype{ThreeSpace},{} \\spad{s},{} where \\spad{R} is the \\spadtype{Ring} over which the point elements are defined.") (($ $ (|Point| |#1|)) "\\spad{point(s,p)} adds a point component defined by the point,{} \\spad{p},{} specified as a list from \\spad{List(R)},{} to the \\spadtype{ThreeSpace},{} \\spad{s},{} where \\spad{R} is the \\spadtype{Ring} over which the point is defined.")) (|modifyPointData| (($ $ (|NonNegativeInteger|) (|Point| |#1|)) "\\spad{modifyPointData(s,i,p)} changes the point at the indexed location \\spad{i} in the \\spadtype{ThreeSpace},{} \\spad{s},{} to that of point \\spad{p}. This is useful for making changes to a point which has been transformed.")) (|enterPointData| (((|NonNegativeInteger|) $ (|List| (|Point| |#1|))) "\\spad{enterPointData(s,[p0,p1,...,pn])} adds a list of points from \\spad{p0} through \\spad{pn} to the \\spadtype{ThreeSpace},{} \\spad{s},{} and returns the index,{} to the starting point of the list.")) (|copy| (($ $) "\\spad{copy(s)} returns a new \\spadtype{ThreeSpace} that is an exact copy of \\spad{s}.")) (|composites| (((|List| $) $) "\\spad{composites(s)} takes the \\spadtype{ThreeSpace} \\spad{s},{} and creates a list containing a unique \\spadtype{ThreeSpace} for each single composite of \\spad{s}. If \\spad{s} has no composites defined (composites need to be explicitly created),{} the list returned is empty. Note that not all the components need to be part of a composite.")) (|components| (((|List| $) $) "\\spad{components(s)} takes the \\spadtype{ThreeSpace} \\spad{s},{} and creates a list containing a unique \\spadtype{ThreeSpace} for each single component of \\spad{s}. If \\spad{s} has no components defined,{} the list returned is empty.")) (|composite| (($ (|List| $)) "\\spad{composite([s1,s2,...,sn])} will create a new \\spadtype{ThreeSpace} that is a union of all the components from each \\spadtype{ThreeSpace} in the parameter list,{} grouped as a composite.")) (|merge| (($ $ $) "\\spad{merge(s1,s2)} will create a new \\spadtype{ThreeSpace} that has the components of \\spad{s1} and \\spad{s2}; Groupings of components into composites are maintained.") (($ (|List| $)) "\\spad{merge([s1,s2,...,sn])} will create a new \\spadtype{ThreeSpace} that has the components of all the ones in the list; Groupings of components into composites are maintained.")) (|numberOfComposites| (((|NonNegativeInteger|) $) "\\spad{numberOfComposites(s)} returns the number of supercomponents,{} or composites,{} in the \\spadtype{ThreeSpace},{} \\spad{s}; Composites are arbitrary groupings of otherwise distinct and unrelated components; A \\spadtype{ThreeSpace} need not have any composites defined at all and,{} outside of the requirement that no component can belong to more than one composite at a time,{} the definition and interpretation of composites are unrestricted.")) (|numberOfComponents| (((|NonNegativeInteger|) $) "\\spad{numberOfComponents(s)} returns the number of distinct object components in the indicated \\spadtype{ThreeSpace},{} \\spad{s},{} such as points,{} curves,{} polygons,{} and constructs.")) (|create3Space| (($ (|SubSpace| 3 |#1|)) "\\spad{create3Space(s)} creates a \\spadtype{ThreeSpace} object containing objects pre-defined within some \\spadtype{SubSpace} \\spad{s}.") (($) "\\spad{create3Space()} creates a \\spadtype{ThreeSpace} object capable of holding point,{} curve,{} mesh components and any combination."))) NIL NIL -(-1136) +(-1137) ((|constructor| (NIL "This domain represents a kind of base domain \\indented{2}{for Spad syntax domain.\\space{2}It merely exists as a kind of} \\indented{2}{of abstract base in object-oriented programming language.} \\indented{2}{However,{} this is not an abstract class.}"))) NIL NIL -(-1137) +(-1138) ((|constructor| (NIL "\\indented{1}{This package provides a simple Spad algebra parser.} Related Constructors: Syntax. See Also: Syntax.")) (|parse| (((|List| (|Syntax|)) (|String|)) "\\spad{parse(f)} parses the source file \\spad{f} (supposedly containing Spad algebras) and returns a List Syntax. The filename \\spad{f} is supposed to have the proper extension. Note that this function has the side effect of executing any system command contained in the file \\spad{f},{} even if it might not be meaningful."))) NIL NIL -(-1138) +(-1139) ((|constructor| (NIL "This category describes the exported \\indented{2}{signatures of the SpadAst domain.}")) (|autoCoerce| (((|Integer|) $) "\\spad{autoCoerce(s)} returns the Integer view of \\spad{`s'}. Left at the discretion of the compiler.") (((|String|) $) "\\spad{autoCoerce(s)} returns the String view of \\spad{`s'}. Left at the discretion of the compiler.") (((|Identifier|) $) "\\spad{autoCoerce(s)} returns the Identifier view of \\spad{`s'}. Left at the discretion of the compiler.") (((|IsAst|) $) "\\spad{autoCoerce(s)} returns the IsAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|HasAst|) $) "\\spad{autoCoerce(s)} returns the HasAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|CaseAst|) $) "\\spad{autoCoerce(s)} returns the CaseAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|ColonAst|) $) "\\spad{autoCoerce(s)} returns the ColoonAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|SuchThatAst|) $) "\\spad{autoCoerce(s)} returns the SuchThatAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|LetAst|) $) "\\spad{autoCoerce(s)} returns the LetAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|SequenceAst|) $) "\\spad{autoCoerce(s)} returns the SequenceAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|SegmentAst|) $) "\\spad{autoCoerce(s)} returns the SegmentAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|RestrictAst|) $) "\\spad{autoCoerce(s)} returns the RestrictAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|PretendAst|) $) "\\spad{autoCoerce(s)} returns the PretendAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|CoerceAst|) $) "\\spad{autoCoerce(s)} returns the CoerceAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|ReturnAst|) $) "\\spad{autoCoerce(s)} returns the ReturnAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|ExitAst|) $) "\\spad{autoCoerce(s)} returns the ExitAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|ConstructAst|) $) "\\spad{autoCoerce(s)} returns the ConstructAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|CollectAst|) $) "\\spad{autoCoerce(s)} returns the CollectAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|InAst|) $) "\\spad{autoCoerce(s)} returns the InAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|WhileAst|) $) "\\spad{autoCoerce(s)} returns the WhileAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|RepeatAst|) $) "\\spad{autoCoerce(s)} returns the RepeatAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|IfAst|) $) "\\spad{autoCoerce(s)} returns the IfAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|MappingAst|) $) "\\spad{autoCoerce(s)} returns the MappingAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|AttributeAst|) $) "\\spad{autoCoerce(s)} returns the AttributeAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|SignatureAst|) $) "\\spad{autoCoerce(s)} returns the SignatureAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|CapsuleAst|) $) "\\spad{autoCoerce(s)} returns the CapsuleAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|CategoryAst|) $) "\\spad{autoCoerce(s)} returns the CategoryAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|WhereAst|) $) "\\spad{autoCoerce(s)} returns the WhereAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|MacroAst|) $) "\\spad{autoCoerce(s)} returns the MacroAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|DefinitionAst|) $) "\\spad{autoCoerce(s)} returns the DefinitionAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|ImportAst|) $) "\\spad{autoCoerce(s)} returns the ImportAst view of \\spad{`s'}. Left at the discretion of the compiler.")) (|case| (((|Boolean|) $ (|[\|\|]| (|Integer|))) "\\spad{s case Integer} holds if \\spad{`s'} represents an integer literal.") (((|Boolean|) $ (|[\|\|]| (|String|))) "\\spad{s case String} holds if \\spad{`s'} represents a string literal.") (((|Boolean|) $ (|[\|\|]| (|Identifier|))) "\\spad{s case Identifier} holds if \\spad{`s'} represents an identifier.") (((|Boolean|) $ (|[\|\|]| (|IsAst|))) "\\spad{s case IsAst} holds if \\spad{`s'} represents an is-expression.") (((|Boolean|) $ (|[\|\|]| (|HasAst|))) "\\spad{s case HasAst} holds if \\spad{`s'} represents a has-expression.") (((|Boolean|) $ (|[\|\|]| (|CaseAst|))) "\\spad{s case CaseAst} holds if \\spad{`s'} represents a case-expression.") (((|Boolean|) $ (|[\|\|]| (|ColonAst|))) "\\spad{s case ColonAst} holds if \\spad{`s'} represents a colon-expression.") (((|Boolean|) $ (|[\|\|]| (|SuchThatAst|))) "\\spad{s case SuchThatAst} holds if \\spad{`s'} represents a qualified-expression.") (((|Boolean|) $ (|[\|\|]| (|LetAst|))) "\\spad{s case LetAst} holds if \\spad{`s'} represents an assignment-expression.") (((|Boolean|) $ (|[\|\|]| (|SequenceAst|))) "\\spad{s case SequenceAst} holds if \\spad{`s'} represents a sequence-of-statements.") (((|Boolean|) $ (|[\|\|]| (|SegmentAst|))) "\\spad{s case SegmentAst} holds if \\spad{`s'} represents a segment-expression.") (((|Boolean|) $ (|[\|\|]| (|RestrictAst|))) "\\spad{s case RestrictAst} holds if \\spad{`s'} represents a restrict-expression.") (((|Boolean|) $ (|[\|\|]| (|PretendAst|))) "\\spad{s case PretendAst} holds if \\spad{`s'} represents a pretend-expression.") (((|Boolean|) $ (|[\|\|]| (|CoerceAst|))) "\\spad{s case ReturnAst} holds if \\spad{`s'} represents a coerce-expression.") (((|Boolean|) $ (|[\|\|]| (|ReturnAst|))) "\\spad{s case ReturnAst} holds if \\spad{`s'} represents a return-statement.") (((|Boolean|) $ (|[\|\|]| (|ExitAst|))) "\\spad{s case ExitAst} holds if \\spad{`s'} represents an exit-expression.") (((|Boolean|) $ (|[\|\|]| (|ConstructAst|))) "\\spad{s case ConstructAst} holds if \\spad{`s'} represents a list-expression.") (((|Boolean|) $ (|[\|\|]| (|CollectAst|))) "\\spad{s case CollectAst} holds if \\spad{`s'} represents a list-comprehension.") (((|Boolean|) $ (|[\|\|]| (|InAst|))) "\\spad{s case InAst} holds if \\spad{`s'} represents a in-iterator") (((|Boolean|) $ (|[\|\|]| (|WhileAst|))) "\\spad{s case WhileAst} holds if \\spad{`s'} represents a while-iterator") (((|Boolean|) $ (|[\|\|]| (|RepeatAst|))) "\\spad{s case RepeatAst} holds if \\spad{`s'} represents an repeat-loop.") (((|Boolean|) $ (|[\|\|]| (|IfAst|))) "\\spad{s case IfAst} holds if \\spad{`s'} represents an if-statement.") (((|Boolean|) $ (|[\|\|]| (|MappingAst|))) "\\spad{s case MappingAst} holds if \\spad{`s'} represents a mapping type.") (((|Boolean|) $ (|[\|\|]| (|AttributeAst|))) "\\spad{s case AttributeAst} holds if \\spad{`s'} represents an attribute.") (((|Boolean|) $ (|[\|\|]| (|SignatureAst|))) "\\spad{s case SignatureAst} holds if \\spad{`s'} represents a signature export.") (((|Boolean|) $ (|[\|\|]| (|CapsuleAst|))) "\\spad{s case CapsuleAst} holds if \\spad{`s'} represents a domain capsule.") (((|Boolean|) $ (|[\|\|]| (|CategoryAst|))) "\\spad{s case CategoryAst} holds if \\spad{`s'} represents an unnamed category.") (((|Boolean|) $ (|[\|\|]| (|WhereAst|))) "\\spad{s case WhereAst} holds if \\spad{`s'} represents an expression with local definitions.") (((|Boolean|) $ (|[\|\|]| (|MacroAst|))) "\\spad{s case MacroAst} holds if \\spad{`s'} represents a macro definition.") (((|Boolean|) $ (|[\|\|]| (|DefinitionAst|))) "\\spad{s case DefinitionAst} holds if \\spad{`s'} represents a definition.") (((|Boolean|) $ (|[\|\|]| (|ImportAst|))) "\\spad{s case ImportAst} holds if \\spad{`s'} represents an `import' statement."))) NIL NIL -(-1139) +(-1140) ((|constructor| (NIL "SpecialOutputPackage allows FORTRAN,{} Tex and \\indented{2}{Script Formula Formatter output from programs.}")) (|outputAsTex| (((|Void|) (|List| (|OutputForm|))) "\\spad{outputAsTex(l)} sends (for each expression in the list \\spad{l}) output in Tex format to the destination as defined by \\spadsyscom{set output tex}.") (((|Void|) (|OutputForm|)) "\\spad{outputAsTex(o)} sends output \\spad{o} in Tex format to the destination defined by \\spadsyscom{set output tex}.")) (|outputAsScript| (((|Void|) (|List| (|OutputForm|))) "\\spad{outputAsScript(l)} sends (for each expression in the list \\spad{l}) output in Script Formula Formatter format to the destination defined. by \\spadsyscom{set output forumula}.") (((|Void|) (|OutputForm|)) "\\spad{outputAsScript(o)} sends output \\spad{o} in Script Formula Formatter format to the destination defined by \\spadsyscom{set output formula}.")) (|outputAsFortran| (((|Void|) (|List| (|OutputForm|))) "\\spad{outputAsFortran(l)} sends (for each expression in the list \\spad{l}) output in FORTRAN format to the destination defined by \\spadsyscom{set output fortran}.") (((|Void|) (|OutputForm|)) "\\spad{outputAsFortran(o)} sends output \\spad{o} in FORTRAN format.") (((|Void|) (|String|) (|OutputForm|)) "\\spad{outputAsFortran(v,o)} sends output \\spad{v} = \\spad{o} in FORTRAN format to the destination defined by \\spadsyscom{set output fortran}."))) NIL NIL -(-1140) +(-1141) ((|constructor| (NIL "Category for the other special functions.")) (|airyBi| (($ $) "\\spad{airyBi(x)} is the Airy function \\spad{Bi(x)}.")) (|airyAi| (($ $) "\\spad{airyAi(x)} is the Airy function \\spad{Ai(x)}.")) (|besselK| (($ $ $) "\\spad{besselK(v,z)} is the modified Bessel function of the second kind.")) (|besselI| (($ $ $) "\\spad{besselI(v,z)} is the modified Bessel function of the first kind.")) (|besselY| (($ $ $) "\\spad{besselY(v,z)} is the Bessel function of the second kind.")) (|besselJ| (($ $ $) "\\spad{besselJ(v,z)} is the Bessel function of the first kind.")) (|polygamma| (($ $ $) "\\spad{polygamma(k,x)} is the \\spad{k-th} derivative of \\spad{digamma(x)},{} (often written \\spad{psi(k,x)} in the literature).")) (|digamma| (($ $) "\\spad{digamma(x)} is the logarithmic derivative of \\spad{Gamma(x)} (often written \\spad{psi(x)} in the literature).")) (|Beta| (($ $ $) "\\spad{Beta(x,y)} is \\spad{Gamma(x) * Gamma(y)/Gamma(x+y)}.")) (|Gamma| (($ $ $) "\\spad{Gamma(a,x)} is the incomplete Gamma function.") (($ $) "\\spad{Gamma(x)} is the Euler Gamma function.")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x}."))) NIL NIL -(-1141 V C) +(-1142 V C) ((|constructor| (NIL "This domain exports a modest implementation for the vertices of splitting trees. These vertices are called here splitting nodes. Every of these nodes store 3 informations. The first one is its value,{} that is the current expression to evaluate. The second one is its condition,{} that is the hypothesis under which the value has to be evaluated. The last one is its status,{} that is a boolean flag which is \\spad{true} iff the value is the result of its evaluation under its condition. Two splitting vertices are equal iff they have the sane values and the same conditions (so their status do not matter).")) (|subNode?| (((|Boolean|) $ $ (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{subNode?(\\spad{n1},{}\\spad{n2},{}o2)} returns \\spad{true} iff \\axiom{value(\\spad{n1}) = value(\\spad{n2})} and \\axiom{o2(condition(\\spad{n1}),{}condition(\\spad{n2}))}")) (|infLex?| (((|Boolean|) $ $ (|Mapping| (|Boolean|) |#1| |#1|) (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{infLex?(\\spad{n1},{}\\spad{n2},{}o1,{}o2)} returns \\spad{true} iff \\axiom{o1(value(\\spad{n1}),{}value(\\spad{n2}))} or \\axiom{value(\\spad{n1}) = value(\\spad{n2})} and \\axiom{o2(condition(\\spad{n1}),{}condition(\\spad{n2}))}.")) (|setEmpty!| (($ $) "\\axiom{setEmpty!(\\spad{n})} replaces \\spad{n} by \\axiom{empty()\\$\\%}.")) (|setStatus!| (($ $ (|Boolean|)) "\\axiom{setStatus!(\\spad{n},{}\\spad{b})} returns \\spad{n} whose status has been replaced by \\spad{b} if it is not empty,{} else an error is produced.")) (|setCondition!| (($ $ |#2|) "\\axiom{setCondition!(\\spad{n},{}\\spad{t})} returns \\spad{n} whose condition has been replaced by \\spad{t} if it is not empty,{} else an error is produced.")) (|setValue!| (($ $ |#1|) "\\axiom{setValue!(\\spad{n},{}\\spad{v})} returns \\spad{n} whose value has been replaced by \\spad{v} if it is not empty,{} else an error is produced.")) (|copy| (($ $) "\\axiom{copy(\\spad{n})} returns a copy of \\spad{n}.")) (|construct| (((|List| $) |#1| (|List| |#2|)) "\\axiom{construct(\\spad{v},{}\\spad{lt})} returns the same as \\axiom{[construct(\\spad{v},{}\\spad{t}) for \\spad{t} in \\spad{lt}]}") (((|List| $) (|List| (|Record| (|:| |val| |#1|) (|:| |tower| |#2|)))) "\\axiom{construct(\\spad{lvt})} returns the same as \\axiom{[construct(\\spad{vt}.val,{}\\spad{vt}.tower) for \\spad{vt} in \\spad{lvt}]}") (($ (|Record| (|:| |val| |#1|) (|:| |tower| |#2|))) "\\axiom{construct(\\spad{vt})} returns the same as \\axiom{construct(\\spad{vt}.val,{}\\spad{vt}.tower)}") (($ |#1| |#2|) "\\axiom{construct(\\spad{v},{}\\spad{t})} returns the same as \\axiom{construct(\\spad{v},{}\\spad{t},{}\\spad{false})}") (($ |#1| |#2| (|Boolean|)) "\\axiom{construct(\\spad{v},{}\\spad{t},{}\\spad{b})} returns the non-empty node with value \\spad{v},{} condition \\spad{t} and flag \\spad{b}")) (|status| (((|Boolean|) $) "\\axiom{status(\\spad{n})} returns the status of the node \\spad{n}.")) (|condition| ((|#2| $) "\\axiom{condition(\\spad{n})} returns the condition of the node \\spad{n}.")) (|value| ((|#1| $) "\\axiom{value(\\spad{n})} returns the value of the node \\spad{n}.")) (|empty?| (((|Boolean|) $) "\\axiom{empty?(\\spad{n})} returns \\spad{true} iff the node \\spad{n} is \\axiom{empty()\\$\\%}.")) (|empty| (($) "\\axiom{empty()} returns the same as \\axiom{[empty()\\$\\spad{V},{}empty()\\$\\spad{C},{}\\spad{false}]\\$\\%}"))) NIL NIL -(-1142 V C) +(-1143 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") $) "\\axiom{extractSplittingLeaf(a)} returns the left most leaf (as a tree) whose status is \\spad{false} if any,{} else \"failed\" is returned."))) -((-4417 . T) (-4418 . T)) -((-12 (|HasCategory| (-1141 |#1| |#2|) (LIST (QUOTE -310) (LIST (QUOTE -1141) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1141 |#1| |#2|) (QUOTE (-1101)))) (|HasCategory| (-1141 |#1| |#2|) (QUOTE (-1101))) (-2797 (|HasCategory| (-1141 |#1| |#2|) (LIST (QUOTE -614) (QUOTE (-863)))) (-12 (|HasCategory| (-1141 |#1| |#2|) (LIST (QUOTE -310) (LIST (QUOTE -1141) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1141 |#1| |#2|) (QUOTE (-1101))))) (|HasCategory| (-1141 |#1| |#2|) (LIST (QUOTE -614) (QUOTE (-863))))) -(-1143 |ndim| R) +((-4418 . T) (-4419 . T)) +((-12 (|HasCategory| (-1142 |#1| |#2|) (LIST (QUOTE -310) (LIST (QUOTE -1142) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1142 |#1| |#2|) (QUOTE (-1102)))) (|HasCategory| (-1142 |#1| |#2|) (QUOTE (-1102))) (-2800 (|HasCategory| (-1142 |#1| |#2|) (LIST (QUOTE -614) (QUOTE (-863)))) (-12 (|HasCategory| (-1142 |#1| |#2|) (LIST (QUOTE -310) (LIST (QUOTE -1142) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1142 |#1| |#2|) (QUOTE (-1102))))) (|HasCategory| (-1142 |#1| |#2|) (LIST (QUOTE -614) (QUOTE (-863))))) +(-1144 |ndim| R) ((|constructor| (NIL "\\spadtype{SquareMatrix} is a matrix domain of square matrices,{} where the number of rows (= number of columns) is a parameter of the type.")) (|unitsKnown| ((|attribute|) "the invertible matrices are simply the matrices whose determinants are units in the Ring \\spad{R}.")) (|central| ((|attribute|) "the elements of the Ring \\spad{R},{} viewed as diagonal matrices,{} commute with all matrices and,{} indeed,{} are the only matrices which commute with all matrices.")) (|squareMatrix| (($ (|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 -901) (QUOTE (-1177)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasAttribute| |#2| (QUOTE (-4419 "*"))) (|HasCategory| |#2| (LIST (QUOTE -640) (QUOTE (-567)))) (|HasCategory| |#2| (LIST (QUOTE -1039) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#2| (LIST (QUOTE -1039) (QUOTE (-567)))) (-2797 (-12 (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1101))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -640) (QUOTE (-567))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -901) (QUOTE (-1177)))))) (|HasCategory| |#2| (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| |#2| (QUOTE (-308))) (|HasCategory| |#2| (QUOTE (-559))) (|HasCategory| |#2| (QUOTE (-1101))) (|HasCategory| |#2| (QUOTE (-365))) (-2797 (|HasAttribute| |#2| (QUOTE (-4419 "*"))) (|HasCategory| |#2| (LIST (QUOTE -640) (QUOTE (-567)))) (|HasCategory| |#2| (LIST (QUOTE -901) (QUOTE (-1177)))) (|HasCategory| |#2| (QUOTE (-233)))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863)))) (-12 (|HasCategory| |#2| (QUOTE (-1101))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-172)))) -(-1144 S) +((-4415 . T) (-4407 |has| |#2| (-6 (-4420 "*"))) (-4418 . T) (-4412 . T) (-4413 . T)) +((|HasCategory| |#2| (LIST (QUOTE -902) (QUOTE (-1178)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasAttribute| |#2| (QUOTE (-4420 "*"))) (|HasCategory| |#2| (LIST (QUOTE -640) (QUOTE (-567)))) (|HasCategory| |#2| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#2| (LIST (QUOTE -1040) (QUOTE (-567)))) (-2800 (-12 (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1102))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -640) (QUOTE (-567))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -902) (QUOTE (-1178)))))) (|HasCategory| |#2| (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| |#2| (QUOTE (-308))) (|HasCategory| |#2| (QUOTE (-559))) (|HasCategory| |#2| (QUOTE (-1102))) (|HasCategory| |#2| (QUOTE (-365))) (-2800 (|HasAttribute| |#2| (QUOTE (-4420 "*"))) (|HasCategory| |#2| (LIST (QUOTE -640) (QUOTE (-567)))) (|HasCategory| |#2| (LIST (QUOTE -902) (QUOTE (-1178)))) (|HasCategory| |#2| (QUOTE (-233)))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863)))) (-12 (|HasCategory| |#2| (QUOTE (-1102))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-172)))) +(-1145 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|) $ $) "\\spad{prefix?(s,t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) NIL NIL -(-1145) +(-1146) ((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|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)) +((-4419 . T) (-4418 . T)) NIL -(-1146 R E V P TS) +(-1147 R E V P TS) ((|constructor| (NIL "A package providing a new algorithm for solving polynomial systems by means of regular chains. Two ways of solving are provided: in the sense of Zariski closure (like in Kalkbrener\\spad{'s} algorithm) or in the sense of the regular zeros (like in Wu,{} Wang or Lazard- Moreno methods). This algorithm is valid for nay type of regular set. It does not care about the way a polynomial is added in an regular set,{} or how two quasi-components are compared (by an inclusion-test),{} or how the invertibility test is made in the tower of simple extensions associated with a regular set. These operations are realized respectively by the domain \\spad{TS} and the packages \\spad{QCMPPK(R,E,V,P,TS)} and \\spad{RSETGCD(R,E,V,P,TS)}. The same way it does not care about the way univariate polynomial gcds (with coefficients in the tower of simple extensions associated with a regular set) are computed. The only requirement is that these gcds need to have invertible initials (normalized or not). WARNING. There is no need for a user to call diectly any operation of this package since they can be accessed by the domain \\axiomType{\\spad{TS}}. Thus,{} the operations of this package are not documented.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}"))) NIL NIL -(-1147 R E V P) +(-1148 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)) -((-12 (|HasCategory| |#4| (QUOTE (-1101))) (|HasCategory| |#4| (LIST (QUOTE -310) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| |#4| (QUOTE (-1101))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#3| (QUOTE (-370))) (|HasCategory| |#4| (LIST (QUOTE -614) (QUOTE (-863))))) -(-1148 S) +((-4419 . T) (-4418 . T)) +((-12 (|HasCategory| |#4| (QUOTE (-1102))) (|HasCategory| |#4| (LIST (QUOTE -310) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| |#4| (QUOTE (-1102))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#3| (QUOTE (-370))) (|HasCategory| |#4| (LIST (QUOTE -614) (QUOTE (-863))))) +(-1149 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)) -((-12 (|HasCategory| |#1| (QUOTE (-1101))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1101))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-1101))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) -(-1149 A S) +((-4418 . T) (-4419 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1102))) (-2800 (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) +(-1150 A S) ((|constructor| (NIL "A stream aggregate is a linear aggregate which possibly has an infinite number of elements. A basic domain constructor which builds stream aggregates is \\spadtype{Stream}. From streams,{} a number of infinite structures such power series can be built. A stream aggregate may also be infinite since it may be cyclic. For example,{} see \\spadtype{DecimalExpansion}.")) (|possiblyInfinite?| (((|Boolean|) $) "\\spad{possiblyInfinite?(s)} tests if the stream \\spad{s} could possibly have an infinite number of elements. Note: for many datatypes,{} \\axiom{possiblyInfinite?(\\spad{s}) = not explictlyFinite?(\\spad{s})}.")) (|explicitlyFinite?| (((|Boolean|) $) "\\spad{explicitlyFinite?(s)} tests if the stream has a finite number of elements,{} and \\spad{false} otherwise. Note: for many datatypes,{} \\axiom{explicitlyFinite?(\\spad{s}) = not possiblyInfinite?(\\spad{s})}."))) NIL NIL -(-1150 S) +(-1151 S) ((|constructor| (NIL "A stream aggregate is a linear aggregate which possibly has an infinite number of elements. A basic domain constructor which builds stream aggregates is \\spadtype{Stream}. From streams,{} a number of infinite structures such power series can be built. A stream aggregate may also be infinite since it may be cyclic. For example,{} see \\spadtype{DecimalExpansion}.")) (|possiblyInfinite?| (((|Boolean|) $) "\\spad{possiblyInfinite?(s)} tests if the stream \\spad{s} could possibly have an infinite number of elements. Note: for many datatypes,{} \\axiom{possiblyInfinite?(\\spad{s}) = not explictlyFinite?(\\spad{s})}.")) (|explicitlyFinite?| (((|Boolean|) $) "\\spad{explicitlyFinite?(s)} tests if the stream has a finite number of elements,{} and \\spad{false} otherwise. Note: for many datatypes,{} \\axiom{explicitlyFinite?(\\spad{s}) = not possiblyInfinite?(\\spad{s})}."))) NIL NIL -(-1151 |Key| |Ent| |dent|) +(-1152 |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 (|:| -1791 |#1|) (|:| -4232 |#2|)) (QUOTE (-1101))) (|HasCategory| (-2 (|:| -1791 |#1|) (|:| -4232 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1791) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4232) (|devaluate| |#2|)))))) (-2797 (|HasCategory| (-2 (|:| -1791 |#1|) (|:| -4232 |#2|)) (QUOTE (-1101))) (|HasCategory| |#2| (QUOTE (-1101)))) (-2797 (|HasCategory| (-2 (|:| -1791 |#1|) (|:| -4232 |#2|)) (QUOTE (-1101))) (|HasCategory| (-2 (|:| -1791 |#1|) (|:| -4232 |#2|)) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| |#2| (QUOTE (-1101))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| (-2 (|:| -1791 |#1|) (|:| -4232 |#2|)) (LIST (QUOTE -615) (QUOTE (-539)))) (-12 (|HasCategory| |#2| (QUOTE (-1101))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-851))) (-2797 (|HasCategory| (-2 (|:| -1791 |#1|) (|:| -4232 |#2|)) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#2| (QUOTE (-1101))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-2 (|:| -1791 |#1|) (|:| -4232 |#2|)) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-2 (|:| -1791 |#1|) (|:| -4232 |#2|)) (QUOTE (-1101)))) -(-1152) +((-4419 . T)) +((-12 (|HasCategory| (-2 (|:| -1795 |#1|) (|:| -4237 |#2|)) (QUOTE (-1102))) (|HasCategory| (-2 (|:| -1795 |#1|) (|:| -4237 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1795) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4237) (|devaluate| |#2|)))))) (-2800 (|HasCategory| (-2 (|:| -1795 |#1|) (|:| -4237 |#2|)) (QUOTE (-1102))) (|HasCategory| |#2| (QUOTE (-1102)))) (-2800 (|HasCategory| (-2 (|:| -1795 |#1|) (|:| -4237 |#2|)) (QUOTE (-1102))) (|HasCategory| (-2 (|:| -1795 |#1|) (|:| -4237 |#2|)) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| |#2| (QUOTE (-1102))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| (-2 (|:| -1795 |#1|) (|:| -4237 |#2|)) (LIST (QUOTE -615) (QUOTE (-539)))) (-12 (|HasCategory| |#2| (QUOTE (-1102))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-851))) (-2800 (|HasCategory| (-2 (|:| -1795 |#1|) (|:| -4237 |#2|)) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#2| (QUOTE (-1102))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-2 (|:| -1795 |#1|) (|:| -4237 |#2|)) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-2 (|:| -1795 |#1|) (|:| -4237 |#2|)) (QUOTE (-1102)))) +(-1153) ((|constructor| (NIL "A class of objects which can be 'stepped through'. Repeated applications of \\spadfun{nextItem} is guaranteed never to return duplicate items and only return \"failed\" after exhausting all elements of the domain. This assumes that the sequence starts with \\spad{init()}. For infinite domains,{} repeated application of \\spadfun{nextItem} is not required to reach all possible domain elements starting from any initial element. \\blankline Conditional attributes: \\indented{2}{infinite\\tab{15}repeated \\spad{nextItem}\\spad{'s} are never \"failed\".}")) (|nextItem| (((|Union| $ "failed") $) "\\spad{nextItem(x)} returns the next item,{} or \"failed\" if domain is exhausted.")) (|init| (($) "\\spad{init()} chooses an initial object for stepping."))) NIL NIL -(-1153 |Coef|) +(-1154 |Coef|) ((|constructor| (NIL "This package computes infinite products of Taylor series over an integral domain of characteristic 0. Here Taylor series are represented by streams of Taylor coefficients.")) (|generalInfiniteProduct| (((|Stream| |#1|) (|Stream| |#1|) (|Integer|) (|Integer|)) "\\spad{generalInfiniteProduct(f(x),a,d)} computes \\spad{product(n=a,a+d,a+2*d,...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|oddInfiniteProduct| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{oddInfiniteProduct(f(x))} computes \\spad{product(n=1,3,5...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|evenInfiniteProduct| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{evenInfiniteProduct(f(x))} computes \\spad{product(n=2,4,6...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|infiniteProduct| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{infiniteProduct(f(x))} computes \\spad{product(n=1,2,3...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1."))) NIL NIL -(-1154 S) +(-1155 S) ((|constructor| (NIL "Functions defined on streams with entries in one set.")) (|concat| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{concat(u)} returns the left-to-right concatentation of the streams in \\spad{u}. Note: \\spad{concat(u) = reduce(concat,u)}."))) NIL NIL -(-1155 A B) +(-1156 A B) ((|constructor| (NIL "Functions defined on streams with entries in two sets.")) (|reduce| ((|#2| |#2| (|Mapping| |#2| |#1| |#2|) (|Stream| |#1|)) "\\spad{reduce(b,f,u)},{} where \\spad{u} is a finite stream \\spad{[x0,x1,...,xn]},{} returns the value \\spad{r(n)} computed as follows: \\spad{r0 = f(x0,b), r1 = f(x1,r0),..., r(n) = f(xn,r(n-1))}.")) (|scan| (((|Stream| |#2|) |#2| (|Mapping| |#2| |#1| |#2|) (|Stream| |#1|)) "\\spad{scan(b,h,[x0,x1,x2,...])} returns \\spad{[y0,y1,y2,...]},{} where \\spad{y0 = h(x0,b)},{} \\spad{y1 = h(x1,y0)},{}\\spad{...} \\spad{yn = h(xn,y(n-1))}.")) (|map| (((|Stream| |#2|) (|Mapping| |#2| |#1|) (|Stream| |#1|)) "\\spad{map(f,s)} returns a stream whose elements are the function \\spad{f} applied to the corresponding elements of \\spad{s}. Note: \\spad{map(f,[x0,x1,x2,...]) = [f(x0),f(x1),f(x2),..]}."))) NIL NIL -(-1156 A B C) +(-1157 A B C) ((|constructor| (NIL "Functions defined on streams with entries in three sets.")) (|map| (((|Stream| |#3|) (|Mapping| |#3| |#1| |#2|) (|Stream| |#1|) (|Stream| |#2|)) "\\spad{map(f,st1,st2)} returns the stream whose elements are the function \\spad{f} applied to the corresponding elements of \\spad{st1} and \\spad{st2}. Note: \\spad{map(f,[x0,x1,x2,..],[y0,y1,y2,..]) = [f(x0,y0),f(x1,y1),..]}."))) NIL NIL -(-1157 S) +(-1158 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)) -((-12 (|HasCategory| |#1| (QUOTE (-1101))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1101))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-1101))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| (-567) (QUOTE (-851))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) -(-1158) +((-4419 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1102))) (-2800 (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| (-567) (QUOTE (-851))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) +(-1159) ((|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)) +((-4419 . T) (-4418 . T)) NIL -(-1159) +(-1160) NIL -((-4418 . T) (-4417 . T)) -((-2797 (-12 (|HasCategory| (-144) (QUOTE (-851))) (|HasCategory| (-144) (LIST (QUOTE -310) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1101))) (|HasCategory| (-144) (LIST (QUOTE -310) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| (-144) (QUOTE (-851))) (|HasCategory| (-567) (QUOTE (-851))) (|HasCategory| (-144) (QUOTE (-1101))) (|HasCategory| (-144) (LIST (QUOTE -614) (QUOTE (-863)))) (-12 (|HasCategory| (-144) (QUOTE (-1101))) (|HasCategory| (-144) (LIST (QUOTE -310) (QUOTE (-144)))))) -(-1160 |Entry|) +((-4419 . T) (-4418 . T)) +((-2800 (-12 (|HasCategory| (-144) (QUOTE (-851))) (|HasCategory| (-144) (LIST (QUOTE -310) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1102))) (|HasCategory| (-144) (LIST (QUOTE -310) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| (-144) (QUOTE (-851))) (|HasCategory| (-567) (QUOTE (-851))) (|HasCategory| (-144) (QUOTE (-1102))) (|HasCategory| (-144) (LIST (QUOTE -614) (QUOTE (-863)))) (-12 (|HasCategory| (-144) (QUOTE (-1102))) (|HasCategory| (-144) (LIST (QUOTE -310) (QUOTE (-144)))))) +(-1161 |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 (|:| -1791 (-1159)) (|:| -4232 |#1|)) (QUOTE (-1101))) (|HasCategory| (-2 (|:| -1791 (-1159)) (|:| -4232 |#1|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1791) (QUOTE (-1159))) (LIST (QUOTE |:|) (QUOTE -4232) (|devaluate| |#1|)))))) (-2797 (|HasCategory| (-2 (|:| -1791 (-1159)) (|:| -4232 |#1|)) (QUOTE (-1101))) (|HasCategory| |#1| (QUOTE (-1101)))) (-2797 (|HasCategory| (-2 (|:| -1791 (-1159)) (|:| -4232 |#1|)) (QUOTE (-1101))) (|HasCategory| (-2 (|:| -1791 (-1159)) (|:| -4232 |#1|)) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| |#1| (QUOTE (-1101))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| (-2 (|:| -1791 (-1159)) (|:| -4232 |#1|)) (LIST (QUOTE -615) (QUOTE (-539)))) (-12 (|HasCategory| |#1| (QUOTE (-1101))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -1791 (-1159)) (|:| -4232 |#1|)) (QUOTE (-1101))) (|HasCategory| (-1159) (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-1101))) (-2797 (|HasCategory| (-2 (|:| -1791 (-1159)) (|:| -4232 |#1|)) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-2 (|:| -1791 (-1159)) (|:| -4232 |#1|)) (LIST (QUOTE -614) (QUOTE (-863))))) -(-1161 A) +((-4418 . T) (-4419 . T)) +((-12 (|HasCategory| (-2 (|:| -1795 (-1160)) (|:| -4237 |#1|)) (QUOTE (-1102))) (|HasCategory| (-2 (|:| -1795 (-1160)) (|:| -4237 |#1|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1795) (QUOTE (-1160))) (LIST (QUOTE |:|) (QUOTE -4237) (|devaluate| |#1|)))))) (-2800 (|HasCategory| (-2 (|:| -1795 (-1160)) (|:| -4237 |#1|)) (QUOTE (-1102))) (|HasCategory| |#1| (QUOTE (-1102)))) (-2800 (|HasCategory| (-2 (|:| -1795 (-1160)) (|:| -4237 |#1|)) (QUOTE (-1102))) (|HasCategory| (-2 (|:| -1795 (-1160)) (|:| -4237 |#1|)) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| (-2 (|:| -1795 (-1160)) (|:| -4237 |#1|)) (LIST (QUOTE -615) (QUOTE (-539)))) (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -1795 (-1160)) (|:| -4237 |#1|)) (QUOTE (-1102))) (|HasCategory| (-1160) (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-1102))) (-2800 (|HasCategory| (-2 (|:| -1795 (-1160)) (|:| -4237 |#1|)) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-2 (|:| -1795 (-1160)) (|:| -4237 |#1|)) (LIST (QUOTE -614) (QUOTE (-863))))) +(-1162 A) ((|constructor| (NIL "StreamTaylorSeriesOperations implements Taylor series arithmetic,{} where a Taylor series is represented by a stream of its coefficients.")) (|power| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{power(a,f)} returns the power series \\spad{f} raised to the power \\spad{a}.")) (|lazyGintegrate| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyGintegrate(f,r,g)} is used for fixed point computations.")) (|mapdiv| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapdiv([a0,a1,..],[b0,b1,..])} returns \\spad{[a0/b0,a1/b1,..]}.")) (|powern| (((|Stream| |#1|) (|Fraction| (|Integer|)) (|Stream| |#1|)) "\\spad{powern(r,f)} raises power series \\spad{f} to the power \\spad{r}.")) (|nlde| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{nlde(u)} solves a first order non-linear differential equation described by \\spad{u} of the form \\spad{[[b<0,0>,b<0,1>,...],[b<1,0>,b<1,1>,.],...]}. the differential equation has the form \\spad{y' = sum(i=0 to infinity,j=0 to infinity,b<i,j>*(x**i)*(y**j))}.")) (|lazyIntegrate| (((|Stream| |#1|) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyIntegrate(r,f)} is a local function used for fixed point computations.")) (|integrate| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{integrate(r,a)} returns the integral of the power series \\spad{a} with respect to the power series variableintegration where \\spad{r} denotes the constant of integration. Thus \\spad{integrate(a,[a0,a1,a2,...]) = [a,a0,a1/2,a2/3,...]}.")) (|invmultisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{invmultisect(a,b,st)} substitutes \\spad{x**((a+b)*n)} for \\spad{x**n} and multiplies by \\spad{x**b}.")) (|multisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{multisect(a,b,st)} selects the coefficients of \\spad{x**((a+b)*n+a)},{} and changes them to \\spad{x**n}.")) (|generalLambert| (((|Stream| |#1|) (|Stream| |#1|) (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),a,d)} returns \\spad{f(x**a) + f(x**(a + d)) + f(x**(a + 2 d)) + ...}. \\spad{f(x)} should have zero constant coefficient and \\spad{a} and \\spad{d} should be positive.")) (|evenlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{evenlambert(st)} computes \\spad{f(x**2) + f(x**4) + f(x**6) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1,{} then \\spad{prod(f(x**(2*n)),n=1..infinity) = exp(evenlambert(log(f(x))))}.")) (|oddlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{oddlambert(st)} computes \\spad{f(x) + f(x**3) + f(x**5) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f}(\\spad{x}) is a power series with constant coefficient 1 then \\spad{prod(f(x**(2*n-1)),n=1..infinity) = exp(oddlambert(log(f(x))))}.")) (|lambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lambert(st)} computes \\spad{f(x) + f(x**2) + f(x**3) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1 then \\spad{prod(f(x**n),n = 1..infinity) = exp(lambert(log(f(x))))}.")) (|addiag| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{addiag(x)} performs diagonal addition of a stream of streams. if \\spad{x} = \\spad{[[a<0,0>,a<0,1>,..],[a<1,0>,a<1,1>,..],[a<2,0>,a<2,1>,..],..]} and \\spad{addiag(x) = [b<0,b<1>,...], then b<k> = sum(i+j=k,a<i,j>)}.")) (|revert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{revert(a)} computes the inverse of a power series \\spad{a} with respect to composition. the series should have constant coefficient 0 and first order coefficient 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,ai * bk)}.")) (- (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{- a} returns the power series negative of \\spad{a}: \\spad{- [a0,a1,...] = [- a0,- a1,...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a - b} returns the power series difference of \\spad{a} and \\spad{b}: \\spad{[a0,a1,..] - [b0,b1,..] = [a0 - b0,a1 - b1,..]}")) (+ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a + b} returns the power series sum of \\spad{a} and \\spad{b}: \\spad{[a0,a1,..] + [b0,b1,..] = [a0 + b0,a1 + b1,..]}"))) NIL ((|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567)))))) -(-1162 |Coef|) +(-1163 |Coef|) ((|constructor| (NIL "StreamTranscendentalFunctionsNonCommutative implements transcendental functions on Taylor series over a non-commutative ring,{} where a Taylor series is represented by a stream of its coefficients.")) (|acsch| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acsch(st)} computes the inverse hyperbolic cosecant of a power series \\spad{st}.")) (|asech| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asech(st)} computes the inverse hyperbolic secant of a power series \\spad{st}.")) (|acoth| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acoth(st)} computes the inverse hyperbolic cotangent of a power series \\spad{st}.")) (|atanh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{atanh(st)} computes the inverse hyperbolic tangent of a power series \\spad{st}.")) (|acosh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acosh(st)} computes the inverse hyperbolic cosine of a power series \\spad{st}.")) (|asinh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asinh(st)} computes the inverse hyperbolic sine of a power series \\spad{st}.")) (|csch| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{csch(st)} computes the hyperbolic cosecant of a power series \\spad{st}.")) (|sech| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sech(st)} computes the hyperbolic secant of a power series \\spad{st}.")) (|coth| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{coth(st)} computes the hyperbolic cotangent of a power series \\spad{st}.")) (|tanh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{tanh(st)} computes the hyperbolic tangent of a power series \\spad{st}.")) (|cosh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cosh(st)} computes the hyperbolic cosine of a power series \\spad{st}.")) (|sinh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sinh(st)} computes the hyperbolic sine of a power series \\spad{st}.")) (|acsc| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acsc(st)} computes arccosecant of a power series \\spad{st}.")) (|asec| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asec(st)} computes arcsecant of a power series \\spad{st}.")) (|acot| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acot(st)} computes arccotangent of a power series \\spad{st}.")) (|atan| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{atan(st)} computes arctangent of a power series \\spad{st}.")) (|acos| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acos(st)} computes arccosine of a power series \\spad{st}.")) (|asin| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asin(st)} computes arcsine of a power series \\spad{st}.")) (|csc| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{csc(st)} computes cosecant of a power series \\spad{st}.")) (|sec| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sec(st)} computes secant of a power series \\spad{st}.")) (|cot| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cot(st)} computes cotangent of a power series \\spad{st}.")) (|tan| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{tan(st)} computes tangent of a power series \\spad{st}.")) (|cos| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cos(st)} computes cosine of a power series \\spad{st}.")) (|sin| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sin(st)} computes sine of a power series \\spad{st}.")) (** (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{st1 ** st2} computes the power of a power series \\spad{st1} by another power series \\spad{st2}.")) (|log| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{log(st)} computes the log of a power series.")) (|exp| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{exp(st)} computes the exponential of a power series \\spad{st}."))) NIL NIL -(-1163 |Coef|) +(-1164 |Coef|) ((|constructor| (NIL "StreamTranscendentalFunctions implements transcendental functions on Taylor series,{} where a Taylor series is represented by a stream of its coefficients.")) (|acsch| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acsch(st)} computes the inverse hyperbolic cosecant of a power series \\spad{st}.")) (|asech| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asech(st)} computes the inverse hyperbolic secant of a power series \\spad{st}.")) (|acoth| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acoth(st)} computes the inverse hyperbolic cotangent of a power series \\spad{st}.")) (|atanh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{atanh(st)} computes the inverse hyperbolic tangent of a power series \\spad{st}.")) (|acosh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acosh(st)} computes the inverse hyperbolic cosine of a power series \\spad{st}.")) (|asinh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asinh(st)} computes the inverse hyperbolic sine of a power series \\spad{st}.")) (|csch| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{csch(st)} computes the hyperbolic cosecant of a power series \\spad{st}.")) (|sech| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sech(st)} computes the hyperbolic secant of a power series \\spad{st}.")) (|coth| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{coth(st)} computes the hyperbolic cotangent of a power series \\spad{st}.")) (|tanh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{tanh(st)} computes the hyperbolic tangent of a power series \\spad{st}.")) (|cosh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cosh(st)} computes the hyperbolic cosine of a power series \\spad{st}.")) (|sinh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sinh(st)} computes the hyperbolic sine of a power series \\spad{st}.")) (|sinhcosh| (((|Record| (|:| |sinh| (|Stream| |#1|)) (|:| |cosh| (|Stream| |#1|))) (|Stream| |#1|)) "\\spad{sinhcosh(st)} returns a record containing the hyperbolic sine and cosine of a power series \\spad{st}.")) (|acsc| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acsc(st)} computes arccosecant of a power series \\spad{st}.")) (|asec| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asec(st)} computes arcsecant of a power series \\spad{st}.")) (|acot| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acot(st)} computes arccotangent of a power series \\spad{st}.")) (|atan| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{atan(st)} computes arctangent of a power series \\spad{st}.")) (|acos| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acos(st)} computes arccosine of a power series \\spad{st}.")) (|asin| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asin(st)} computes arcsine of a power series \\spad{st}.")) (|csc| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{csc(st)} computes cosecant of a power series \\spad{st}.")) (|sec| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sec(st)} computes secant of a power series \\spad{st}.")) (|cot| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cot(st)} computes cotangent of a power series \\spad{st}.")) (|tan| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{tan(st)} computes tangent of a power series \\spad{st}.")) (|cos| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cos(st)} computes cosine of a power series \\spad{st}.")) (|sin| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sin(st)} computes sine of a power series \\spad{st}.")) (|sincos| (((|Record| (|:| |sin| (|Stream| |#1|)) (|:| |cos| (|Stream| |#1|))) (|Stream| |#1|)) "\\spad{sincos(st)} returns a record containing the sine and cosine of a power series \\spad{st}.")) (** (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{st1 ** st2} computes the power of a power series \\spad{st1} by another power series \\spad{st2}.")) (|log| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{log(st)} computes the log of a power series.")) (|exp| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{exp(st)} computes the exponential of a power series \\spad{st}."))) NIL NIL -(-1164 R UP) +(-1165 R UP) ((|constructor| (NIL "This package computes the subresultants of two polynomials which is needed for the `Lazard Rioboo' enhancement to Tragers integrations formula For efficiency reasons this has been rewritten to call Lionel Ducos package which is currently the best one. \\blankline")) (|primitivePart| ((|#2| |#2| |#1|) "\\spad{primitivePart(p, q)} reduces the coefficient of \\spad{p} modulo \\spad{q},{} takes the primitive part of the result,{} and ensures that the leading coefficient of that result is monic.")) (|subresultantVector| (((|PrimitiveArray| |#2|) |#2| |#2|) "\\spad{subresultantVector(p, q)} returns \\spad{[p0,...,pn]} where \\spad{pi} is the \\spad{i}-th subresultant of \\spad{p} and \\spad{q}. In particular,{} \\spad{p0 = resultant(p, q)}."))) NIL ((|HasCategory| |#1| (QUOTE (-308)))) -(-1165 |n| R) +(-1166 |n| R) ((|constructor| (NIL "This domain \\undocumented")) (|pointData| (((|List| (|Point| |#2|)) $) "\\spad{pointData(s)} returns the list of points from the point data field of the 3 dimensional subspace \\spad{s}.")) (|parent| (($ $) "\\spad{parent(s)} returns the subspace which is the parent of the indicated 3 dimensional subspace \\spad{s}. If \\spad{s} is the top level subspace an error message is returned.")) (|level| (((|NonNegativeInteger|) $) "\\spad{level(s)} returns a non negative integer which is the current level field of the indicated 3 dimensional subspace \\spad{s}.")) (|extractProperty| (((|SubSpaceComponentProperty|) $) "\\spad{extractProperty(s)} returns the property of domain \\spadtype{SubSpaceComponentProperty} of the indicated 3 dimensional subspace \\spad{s}.")) (|extractClosed| (((|Boolean|) $) "\\spad{extractClosed(s)} returns the \\spadtype{Boolean} value of the closed property for the indicated 3 dimensional subspace \\spad{s}. If the property is closed,{} \\spad{True} is returned,{} otherwise \\spad{False} is returned.")) (|extractIndex| (((|NonNegativeInteger|) $) "\\spad{extractIndex(s)} returns a non negative integer which is the current index of the 3 dimensional subspace \\spad{s}.")) (|extractPoint| (((|Point| |#2|) $) "\\spad{extractPoint(s)} returns the point which is given by the current index location into the point data field of the 3 dimensional subspace \\spad{s}.")) (|traverse| (($ $ (|List| (|NonNegativeInteger|))) "\\spad{traverse(s,li)} follows the branch list of the 3 dimensional subspace,{} \\spad{s},{} along the path dictated by the list of non negative integers,{} \\spad{li},{} which points to the component which has been traversed to. The subspace,{} \\spad{s},{} is returned,{} where \\spad{s} is now the subspace pointed to by \\spad{li}.")) (|defineProperty| (($ $ (|List| (|NonNegativeInteger|)) (|SubSpaceComponentProperty|)) "\\spad{defineProperty(s,li,p)} defines the component property in the 3 dimensional subspace,{} \\spad{s},{} to be that of \\spad{p},{} where \\spad{p} is of the domain \\spadtype{SubSpaceComponentProperty}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component whose property is being defined. The subspace,{} \\spad{s},{} is returned with the component property definition.")) (|closeComponent| (($ $ (|List| (|NonNegativeInteger|)) (|Boolean|)) "\\spad{closeComponent(s,li,b)} sets the property of the component in the 3 dimensional subspace,{} \\spad{s},{} to be closed if \\spad{b} is \\spad{true},{} or open if \\spad{b} is \\spad{false}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component whose closed property is to be set. The subspace,{} \\spad{s},{} is returned with the component property modification.")) (|modifyPoint| (($ $ (|NonNegativeInteger|) (|Point| |#2|)) "\\spad{modifyPoint(s,ind,p)} modifies the point referenced by the index location,{} \\spad{ind},{} by replacing it with the point,{} \\spad{p} in the 3 dimensional subspace,{} \\spad{s}. An error message occurs if \\spad{s} is empty,{} otherwise the subspace \\spad{s} is returned with the point modification.") (($ $ (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{modifyPoint(s,li,i)} replaces an existing point in the 3 dimensional subspace,{} \\spad{s},{} with the 4 dimensional point indicated by the index location,{} \\spad{i}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component in which the existing point is to be modified. An error message occurs if \\spad{s} is empty,{} otherwise the subspace \\spad{s} is returned with the point modification.") (($ $ (|List| (|NonNegativeInteger|)) (|Point| |#2|)) "\\spad{modifyPoint(s,li,p)} replaces an existing point in the 3 dimensional subspace,{} \\spad{s},{} with the 4 dimensional point,{} \\spad{p}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component in which the existing point is to be modified. An error message occurs if \\spad{s} is empty,{} otherwise the subspace \\spad{s} is returned with the point modification.")) (|addPointLast| (($ $ $ (|Point| |#2|) (|NonNegativeInteger|)) "\\spad{addPointLast(s,s2,li,p)} adds the 4 dimensional point,{} \\spad{p},{} to the 3 dimensional subspace,{} \\spad{s}. \\spad{s2} point to the end of the subspace \\spad{s}. \\spad{n} is the path in the \\spad{s2} component. The subspace \\spad{s} is returned with the additional point.")) (|addPoint2| (($ $ (|Point| |#2|)) "\\spad{addPoint2(s,p)} adds the 4 dimensional point,{} \\spad{p},{} to the 3 dimensional subspace,{} \\spad{s}. The subspace \\spad{s} is returned with the additional point.")) (|addPoint| (((|NonNegativeInteger|) $ (|Point| |#2|)) "\\spad{addPoint(s,p)} adds the point,{} \\spad{p},{} to the 3 dimensional subspace,{} \\spad{s},{} and returns the new total number of points in \\spad{s}.") (($ $ (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{addPoint(s,li,i)} adds the 4 dimensional point indicated by the index location,{} \\spad{i},{} to the 3 dimensional subspace,{} \\spad{s}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component in which the point is to be added. It\\spad{'s} length should range from 0 to \\spad{n - 1} where \\spad{n} is the dimension of the subspace. If the length is \\spad{n - 1},{} then a specific lowest level component is being referenced. If it is less than \\spad{n - 1},{} then some higher level component (0 indicates top level component) is being referenced and a component of that level with the desired point is created. The subspace \\spad{s} is returned with the additional point.") (($ $ (|List| (|NonNegativeInteger|)) (|Point| |#2|)) "\\spad{addPoint(s,li,p)} adds the 4 dimensional point,{} \\spad{p},{} to the 3 dimensional subspace,{} \\spad{s}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component in which the point is to be added. It\\spad{'s} length should range from 0 to \\spad{n - 1} where \\spad{n} is the dimension of the subspace. If the length is \\spad{n - 1},{} then a specific lowest level component is being referenced. If it is less than \\spad{n - 1},{} then some higher level component (0 indicates top level component) is being referenced and a component of that level with the desired point is created. The subspace \\spad{s} is returned with the additional point.")) (|separate| (((|List| $) $) "\\spad{separate(s)} makes each of the components of the \\spadtype{SubSpace},{} \\spad{s},{} into a list of separate and distinct subspaces and returns the list.")) (|merge| (($ (|List| $)) "\\spad{merge(ls)} a list of subspaces,{} \\spad{ls},{} into one subspace.") (($ $ $) "\\spad{merge(s1,s2)} the subspaces \\spad{s1} and \\spad{s2} into a single subspace.")) 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(|sum| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{sum(f(n), n = a..b)} returns \\spad{f}(a) + \\spad{f}(a+1) + ... + \\spad{f}(\\spad{b}).") ((|#2| |#2| (|Symbol|)) "\\spad{sum(a(n), n)} returns A(\\spad{n}) such that A(\\spad{n+1}) - A(\\spad{n}) = a(\\spad{n})."))) NIL NIL -(-1170 R) +(-1171 R) ((|constructor| (NIL "Computes sums of rational functions.")) (|sum| (((|Union| (|Fraction| (|Polynomial| |#1|)) (|Expression| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|Fraction| (|Polynomial| |#1|)))) "\\spad{sum(f(n), n = a..b)} returns \\spad{f(a) + f(a+1) + ... f(b)}.") (((|Fraction| (|Polynomial| |#1|)) (|Polynomial| |#1|) (|SegmentBinding| (|Polynomial| |#1|))) "\\spad{sum(f(n), n = a..b)} returns \\spad{f(a) + f(a+1) + ... f(b)}.") 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(|sample| (($) "\\spad{sample()} returns a sample of \\%")) (|list| (((|List| $) $) "\\spad{list(sy)} takes a scripted symbol and produces a list of the name followed by the scripts.")) (|string| (((|String|) $) "\\spad{string(s)} converts the symbol \\spad{s} to a string. Error: if the symbol is subscripted.")) (|elt| (($ $ (|List| (|OutputForm|))) "\\spad{elt(s,[a1,...,an])} or \\spad{s}([a1,{}...,{}an]) returns \\spad{s} subscripted by \\spad{[a1,...,an]}.")) (|argscript| (($ $ (|List| (|OutputForm|))) "\\spad{argscript(s, [a1,...,an])} returns \\spad{s} arg-scripted by \\spad{[a1,...,an]}.")) (|superscript| (($ $ (|List| (|OutputForm|))) "\\spad{superscript(s, [a1,...,an])} returns \\spad{s} superscripted by \\spad{[a1,...,an]}.")) (|subscript| (($ $ (|List| (|OutputForm|))) "\\spad{subscript(s, [a1,...,an])} returns \\spad{s} subscripted by \\spad{[a1,...,an]}.")) (|script| (($ $ (|Record| (|:| |sub| (|List| (|OutputForm|))) (|:| |sup| (|List| (|OutputForm|))) (|:| |presup| (|List| (|OutputForm|))) (|:| |presub| (|List| (|OutputForm|))) (|:| |args| (|List| (|OutputForm|))))) "\\spad{script(s, [a,b,c,d,e])} returns \\spad{s} with subscripts a,{} superscripts \\spad{b},{} pre-superscripts \\spad{c},{} pre-subscripts \\spad{d},{} and argument-scripts \\spad{e}.") (($ $ (|List| (|List| (|OutputForm|)))) "\\spad{script(s, [a,b,c,d,e])} returns \\spad{s} with subscripts a,{} superscripts \\spad{b},{} pre-superscripts \\spad{c},{} pre-subscripts \\spad{d},{} and argument-scripts \\spad{e}. Omitted components are taken to be empty. For example,{} \\spad{script(s, [a,b,c])} is equivalent to \\spad{script(s,[a,b,c,[],[]])}.")) (|scripts| (((|Record| (|:| |sub| (|List| (|OutputForm|))) (|:| |sup| (|List| (|OutputForm|))) (|:| |presup| (|List| (|OutputForm|))) (|:| |presub| (|List| (|OutputForm|))) (|:| |args| (|List| (|OutputForm|)))) $) "\\spad{scripts(s)} returns all the scripts of \\spad{s}.")) (|scripted?| (((|Boolean|) $) "\\spad{scripted?(s)} is \\spad{true} if \\spad{s} has been given any scripts.")) (|name| (($ $) "\\spad{name(s)} returns \\spad{s} without its scripts.")) (|resetNew| (((|Void|)) "\\spad{resetNew()} resets the internals counters that new() and new(\\spad{s}) use to return distinct symbols every time.")) (|new| (($ $) "\\spad{new(s)} returns a new symbol whose name starts with \\%\\spad{s}.") (($) "\\spad{new()} returns a new symbol whose name starts with \\%."))) NIL NIL -(-1178 R) +(-1179 R) ((|constructor| (NIL "Computes all the symmetric functions in \\spad{n} variables.")) (|symFunc| (((|Vector| |#1|) |#1| (|PositiveInteger|)) "\\spad{symFunc(r, n)} returns the vector of the elementary symmetric functions in \\spad{[r,r,...,r]} \\spad{n} times.") (((|Vector| |#1|) (|List| |#1|)) "\\spad{symFunc([r1,...,rn])} returns the vector of the elementary symmetric functions in the \\spad{ri's}: \\spad{[r1 + ... + rn, r1 r2 + ... + r(n-1) rn, ..., r1 r2 ... rn]}."))) NIL NIL -(-1179 R) +(-1180 R) ((|constructor| (NIL "This domain implements symmetric polynomial"))) -(((-4419 "*") |has| |#1| (-172)) (-4410 |has| |#1| (-559)) (-4415 |has| |#1| (-6 -4415)) (-4411 . T) (-4412 . T) (-4414 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (QUOTE (-559))) (-2797 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-559)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-2797 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1039) (LIST (QUOTE -410) (QUOTE (-567)))))) (|HasCategory| |#1| (LIST (QUOTE -1039) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1039) (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-455))) (-12 (|HasCategory| (-972) (QUOTE (-131))) (|HasCategory| |#1| (QUOTE (-559)))) (|HasAttribute| |#1| (QUOTE -4415))) -(-1180) +(((-4420 "*") |has| |#1| (-172)) (-4411 |has| |#1| (-559)) (-4416 |has| |#1| (-6 -4416)) (-4412 . T) (-4413 . T) (-4415 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (QUOTE (-559))) (-2800 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-559)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-2800 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567)))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (LIST (QUOTE -1040) (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-455))) (-12 (|HasCategory| (-973) (QUOTE (-131))) (|HasCategory| |#1| (QUOTE (-559)))) (|HasAttribute| |#1| (QUOTE -4416))) +(-1181) ((|constructor| (NIL "Creates and manipulates one global symbol table for FORTRAN code generation,{} containing details of types,{} dimensions,{} and argument lists.")) (|symbolTableOf| (((|SymbolTable|) (|Symbol|) $) "\\spad{symbolTableOf(f,tab)} returns the symbol table of \\spad{f}")) (|argumentListOf| (((|List| (|Symbol|)) (|Symbol|) $) "\\spad{argumentListOf(f,tab)} returns the argument list of \\spad{f}")) (|returnTypeOf| (((|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) (|Symbol|) $) "\\spad{returnTypeOf(f,tab)} returns the type of the object returned by \\spad{f}")) (|empty| (($) "\\spad{empty()} creates a new,{} empty symbol table.")) (|printTypes| (((|Void|) (|Symbol|)) "\\spad{printTypes(tab)} produces FORTRAN type declarations from \\spad{tab},{} on the current FORTRAN output stream")) (|printHeader| (((|Void|)) "\\spad{printHeader()} produces the FORTRAN header for the current subprogram in the global symbol table on the current FORTRAN output stream.") (((|Void|) (|Symbol|)) "\\spad{printHeader(f)} produces the FORTRAN header for subprogram \\spad{f} in the global symbol table on the current FORTRAN output stream.") (((|Void|) (|Symbol|) $) "\\spad{printHeader(f,tab)} produces the FORTRAN header for subprogram \\spad{f} in symbol table \\spad{tab} on the current FORTRAN output stream.")) (|returnType!| (((|Void|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void"))) "\\spad{returnType!(t)} declares that the return type of he current subprogram in the global symbol table is \\spad{t}.") (((|Void|) (|Symbol|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void"))) "\\spad{returnType!(f,t)} declares that the return type of subprogram \\spad{f} in the global symbol table is \\spad{t}.") (((|Void|) (|Symbol|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) $) "\\spad{returnType!(f,t,tab)} declares that the return type of subprogram \\spad{f} in symbol table \\spad{tab} is \\spad{t}.")) (|argumentList!| (((|Void|) (|List| (|Symbol|))) "\\spad{argumentList!(l)} declares that the argument list for the current subprogram in the global symbol table is \\spad{l}.") (((|Void|) (|Symbol|) (|List| (|Symbol|))) "\\spad{argumentList!(f,l)} declares that the argument list for subprogram \\spad{f} in the global symbol table is \\spad{l}.") (((|Void|) (|Symbol|) (|List| (|Symbol|)) $) "\\spad{argumentList!(f,l,tab)} declares that the argument list for subprogram \\spad{f} in symbol table \\spad{tab} is \\spad{l}.")) (|endSubProgram| (((|Symbol|)) "\\spad{endSubProgram()} asserts that we are no longer processing the current subprogram.")) (|currentSubProgram| (((|Symbol|)) "\\spad{currentSubProgram()} returns the name of the current subprogram being processed")) (|newSubProgram| (((|Void|) (|Symbol|)) "\\spad{newSubProgram(f)} asserts that from now on type declarations are part of subprogram \\spad{f}.")) (|declare!| (((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|)) "\\spad{declare!(u,t,asp)} declares the parameter \\spad{u} to have type \\spad{t} in \\spad{asp}.") (((|FortranType|) (|Symbol|) (|FortranType|)) "\\spad{declare!(u,t)} declares the parameter \\spad{u} to have type \\spad{t} in the current level of the symbol table.") (((|FortranType|) (|List| (|Symbol|)) (|FortranType|) (|Symbol|) $) "\\spad{declare!(u,t,asp,tab)} declares the parameters \\spad{u} of subprogram \\spad{asp} to have type \\spad{t} in symbol table \\spad{tab}.") (((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|) $) "\\spad{declare!(u,t,asp,tab)} declares the parameter \\spad{u} of subprogram \\spad{asp} to have type \\spad{t} in symbol table \\spad{tab}.")) (|clearTheSymbolTable| (((|Void|) (|Symbol|)) "\\spad{clearTheSymbolTable(x)} removes the symbol \\spad{x} from the table") (((|Void|)) "\\spad{clearTheSymbolTable()} clears the current symbol table.")) (|showTheSymbolTable| (($) "\\spad{showTheSymbolTable()} returns the current symbol table."))) NIL NIL -(-1181) +(-1182) ((|constructor| (NIL "Create and manipulate a symbol table for generated FORTRAN code")) (|symbolTable| (($ (|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| (|FortranType|))))) "\\spad{symbolTable(l)} creates a symbol table from the elements of \\spad{l}.")) (|printTypes| (((|Void|) $) "\\spad{printTypes(tab)} produces FORTRAN type declarations from \\spad{tab},{} on the current FORTRAN output stream")) (|newTypeLists| (((|SExpression|) $) "\\spad{newTypeLists(x)} \\undocumented")) (|typeLists| (((|List| (|List| (|Union| (|:| |name| (|Symbol|)) (|:| |bounds| (|List| (|Union| (|:| S (|Symbol|)) (|:| P (|Polynomial| (|Integer|))))))))) $) "\\spad{typeLists(tab)} returns a list of lists of types of objects in \\spad{tab}")) (|externalList| (((|List| (|Symbol|)) $) "\\spad{externalList(tab)} returns a list of all the external symbols in \\spad{tab}")) (|typeList| (((|List| (|Union| (|:| |name| (|Symbol|)) (|:| |bounds| (|List| (|Union| (|:| S (|Symbol|)) (|:| P (|Polynomial| (|Integer|)))))))) (|FortranScalarType|) $) "\\spad{typeList(t,tab)} returns a list of all the objects of type \\spad{t} in \\spad{tab}")) (|parametersOf| (((|List| (|Symbol|)) $) "\\spad{parametersOf(tab)} returns a list of all the symbols declared in \\spad{tab}")) (|fortranTypeOf| (((|FortranType|) (|Symbol|) $) "\\spad{fortranTypeOf(u,tab)} returns the type of \\spad{u} in \\spad{tab}")) (|declare!| (((|FortranType|) (|Symbol|) (|FortranType|) $) "\\spad{declare!(u,t,tab)} creates a new entry in \\spad{tab},{} declaring \\spad{u} to be of type \\spad{t}") (((|FortranType|) (|List| (|Symbol|)) (|FortranType|) $) "\\spad{declare!(l,t,tab)} creates new entrys in \\spad{tab},{} declaring each of \\spad{l} to be of type \\spad{t}")) (|empty| (($) "\\spad{empty()} returns a new,{} empty symbol table")) (|coerce| (((|Table| (|Symbol|) (|FortranType|)) $) "\\spad{coerce(x)} returns a table view of \\spad{x}"))) NIL NIL -(-1182) +(-1183) ((|constructor| (NIL "\\indented{1}{This domain provides a simple domain,{} general enough for} \\indented{2}{building complete representation of Spad programs as objects} \\indented{2}{of a term algebra built from ground terms of type integers,{} foats,{}} \\indented{2}{identifiers,{} and strings.} \\indented{2}{This domain differs from InputForm in that it represents} \\indented{2}{any entity in a Spad program,{} not just expressions.\\space{2}Furthermore,{}} \\indented{2}{while InputForm may contain atoms like vectors and other Lisp} \\indented{2}{objects,{} the Syntax domain is supposed to contain only that} \\indented{2}{initial algebra build from the primitives listed above.} Related Constructors: \\indented{2}{Integer,{} DoubleFloat,{} Identifier,{} String,{} SExpression.} See Also: SExpression,{} InputForm. The equality supported by this domain is structural.")) (|case| (((|Boolean|) $ (|[\|\|]| (|String|))) "\\spad{x case String} is \\spad{true} if \\spad{`x'} really is a String") (((|Boolean|) $ (|[\|\|]| (|Identifier|))) "\\spad{x case Identifier} is \\spad{true} if \\spad{`x'} really is an Identifier") (((|Boolean|) $ (|[\|\|]| (|DoubleFloat|))) "\\spad{x case DoubleFloat} is \\spad{true} if \\spad{`x'} really is a DoubleFloat") (((|Boolean|) $ (|[\|\|]| (|Integer|))) "\\spad{x case Integer} is \\spad{true} if \\spad{`x'} really is an Integer")) (|compound?| (((|Boolean|) $) "\\spad{compound? x} is \\spad{true} when \\spad{`x'} is not an atomic syntax.")) (|getOperands| (((|List| $) $) "\\spad{getOperands(x)} returns the list of operands to the operator in \\spad{`x'}.")) (|getOperator| (((|Union| (|Integer|) (|DoubleFloat|) (|Identifier|) (|String|) $) $) "\\spad{getOperator(x)} returns the operator,{} or tag,{} of the syntax \\spad{`x'}. The value returned is itself a syntax if \\spad{`x'} really is an application of a function symbol as opposed to being an atomic ground term.")) (|nil?| (((|Boolean|) $) "\\spad{nil?(s)} is \\spad{true} when \\spad{`s'} is a syntax for the constant nil.")) (|buildSyntax| (($ $ (|List| $)) "\\spad{buildSyntax(op, [a1, ..., an])} builds a syntax object for \\spad{op}(a1,{}...,{}an).") (($ (|Identifier|) (|List| $)) "\\spad{buildSyntax(op, [a1, ..., an])} builds a syntax object for \\spad{op}(a1,{}...,{}an).")) (|autoCoerce| (((|String|) $) "\\spad{autoCoerce(s)} forcibly extracts a string value from the syntax \\spad{`s'}; no check performed. To be called only at the discretion of the compiler.") (((|Identifier|) $) "\\spad{autoCoerce(s)} forcibly extracts an identifier from the Syntax domain \\spad{`s'}; no check performed. To be called only at at the discretion of the compiler.") (((|DoubleFloat|) $) "\\spad{autoCoerce(s)} forcibly extracts a float value from the syntax \\spad{`s'}; no check performed. To be called only at the discretion of the compiler") (((|Integer|) $) "\\spad{autoCoerce(s)} forcibly extracts an integer value from the syntax \\spad{`s'}; no check performed. To be called only at the discretion of the compiler.")) (|coerce| (((|String|) $) "\\spad{coerce(s)} extracts a string value from the syntax \\spad{`s'}.") (((|Identifier|) $) "\\spad{coerce(s)} extracts an identifier from the syntax \\spad{`s'}.") (((|DoubleFloat|) $) "\\spad{coerce(s)} extracts a float value from the syntax \\spad{`s'}.") (((|Integer|) $) "\\spad{coerce(s)} extracts and integer value from the syntax \\spad{`s'}")) (|convert| (($ (|SExpression|)) "\\spad{convert(s)} converts an \\spad{s}-expression to Syntax. Note,{} when \\spad{`s'} is not an atom,{} it is expected that it designates a proper list,{} \\spadignore{e.g.} a sequence of cons cells ending with nil.") (((|SExpression|) $) "\\spad{convert(s)} returns the \\spad{s}-expression representation of a syntax."))) NIL NIL -(-1183 N) +(-1184 N) ((|constructor| (NIL "This domain implements sized (signed) integer datatypes parameterized by the precision (or width) of the underlying representation. The intent is that they map directly to the hosting hardware natural integer datatypes. Consequently,{} natural values for \\spad{N} are: 8,{} 16,{} 32,{} 64,{} etc. These datatypes are mostly useful for system programming tasks,{} \\spadignore{i.e.} interfacting with the hosting operating system,{} reading/writing external binary format files.")) (|sample| (($) "\\spad{sample} gives a sample datum of this type."))) NIL NIL -(-1184 N) +(-1185 N) ((|constructor| (NIL "This domain implements sized (unsigned) integer datatypes parameterized by the precision (or width) of the underlying representation. The intent is that they map directly to the hosting hardware natural integer datatypes. Consequently,{} natural values for \\spad{N} are: 8,{} 16,{} 32,{} 64,{} etc. These datatypes are mostly useful for system programming tasks,{} \\spadignore{i.e.} interfacting with the hosting operating system,{} reading/writing external binary format files.")) (|sample| (($) "\\spad{sample} gives a sample datum of type Byte.")) (|bitior| (($ $ $) "bitor(\\spad{x},{}\\spad{y}) returns the bitwise `inclusive or' of \\spad{`x'} and \\spad{`y'}.")) (|bitand| (($ $ $) "\\spad{bitand(x,y)} returns the bitwise `and' of \\spad{`x'} and \\spad{`y'}."))) NIL NIL -(-1185) +(-1186) ((|constructor| (NIL "This domain is a datatype system-level pointer values."))) NIL NIL -(-1186 R) +(-1187 R) ((|triangularSystems| (((|List| (|List| (|Polynomial| |#1|))) (|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|Symbol|))) "\\spad{triangularSystems(lf,lv)} solves the system of equations defined by \\spad{lf} with respect to the list of symbols \\spad{lv}; the system of equations is obtaining by equating to zero the list of rational functions \\spad{lf}. The output is a list of solutions where each solution is expressed as a \"reduced\" triangular system of polynomials.")) (|solve| (((|List| (|Equation| (|Fraction| (|Polynomial| |#1|)))) (|Equation| (|Fraction| (|Polynomial| |#1|)))) "\\spad{solve(eq)} finds the solutions of the equation \\spad{eq} with respect to the unique variable appearing in \\spad{eq}.") (((|List| (|Equation| (|Fraction| (|Polynomial| |#1|)))) (|Fraction| (|Polynomial| |#1|))) "\\spad{solve(p)} finds the solution of a rational function \\spad{p} = 0 with respect to the unique variable appearing in \\spad{p}.") (((|List| (|Equation| (|Fraction| (|Polynomial| |#1|)))) (|Equation| (|Fraction| (|Polynomial| |#1|))) (|Symbol|)) "\\spad{solve(eq,v)} finds the solutions of the equation \\spad{eq} with respect to the variable \\spad{v}.") (((|List| (|Equation| (|Fraction| (|Polynomial| |#1|)))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{solve(p,v)} solves the equation \\spad{p=0},{} where \\spad{p} is a rational function with respect to the variable \\spad{v}.") (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) "\\spad{solve(le)} finds the solutions of the list \\spad{le} of equations of rational functions with respect to all symbols appearing in \\spad{le}.") (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Fraction| (|Polynomial| |#1|)))) "\\spad{solve(lp)} finds the solutions of the list \\spad{lp} of rational functions with respect to all symbols appearing in \\spad{lp}.") (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Equation| (|Fraction| (|Polynomial| |#1|)))) (|List| (|Symbol|))) "\\spad{solve(le,lv)} finds the solutions of the list \\spad{le} of equations of rational functions with respect to the list of symbols \\spad{lv}.") (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|Symbol|))) "\\spad{solve(lp,lv)} finds the solutions of the list \\spad{lp} of rational functions with respect to the list of symbols \\spad{lv}."))) NIL NIL -(-1187) +(-1188) ((|constructor| (NIL "The package \\spadtype{System} provides information about the runtime system and its characteristics.")) (|loadNativeModule| (((|Void|) (|String|)) "\\spad{loadNativeModule(path)} loads the native modile designated by \\spadvar{\\spad{path}}.")) (|nativeModuleExtension| (((|String|)) "\\spad{nativeModuleExtension} is a string representation of a filename extension for native modules.")) (|hostByteOrder| (((|ByteOrder|)) "\\sapd{hostByteOrder}")) (|hostPlatform| (((|String|)) "\\spad{hostPlatform} is a string `triplet' description of the platform hosting the running OpenAxiom system.")) (|rootDirectory| (((|String|)) "\\spad{rootDirectory()} returns the pathname of the root directory for the running OpenAxiom system."))) NIL NIL -(-1188 S) +(-1189 S) ((|constructor| (NIL "TableauBumpers implements the Schenstead-Knuth correspondence between sequences and pairs of Young tableaux. The 2 Young tableaux are represented as a single tableau with pairs as components.")) (|mr| (((|Record| (|:| |f1| (|List| |#1|)) (|:| |f2| (|List| (|List| (|List| |#1|)))) (|:| |f3| (|List| (|List| |#1|))) (|:| |f4| (|List| (|List| (|List| |#1|))))) (|List| (|List| (|List| |#1|)))) "\\spad{mr(t)} is an auxiliary function which finds the position of the maximum element of a tableau \\spad{t} which is in the lowest row,{} producing a record of results")) (|maxrow| (((|Record| (|:| |f1| (|List| |#1|)) (|:| |f2| (|List| (|List| (|List| |#1|)))) (|:| |f3| (|List| (|List| |#1|))) (|:| |f4| (|List| (|List| (|List| |#1|))))) (|List| |#1|) (|List| (|List| (|List| |#1|))) (|List| (|List| |#1|)) (|List| (|List| (|List| |#1|))) (|List| (|List| (|List| |#1|))) (|List| (|List| (|List| |#1|)))) "\\spad{maxrow(a,b,c,d,e)} is an auxiliary function for \\spad{mr}")) (|inverse| (((|List| |#1|) (|List| |#1|)) "\\spad{inverse(ls)} forms the inverse of a sequence \\spad{ls}")) (|slex| (((|List| (|List| |#1|)) (|List| |#1|)) "\\spad{slex(ls)} sorts the argument sequence \\spad{ls},{} then zips (see \\spadfunFrom{map}{ListFunctions3}) the original argument sequence with the sorted result to a list of pairs")) (|lex| (((|List| (|List| |#1|)) (|List| (|List| |#1|))) "\\spad{lex(ls)} sorts a list of pairs to lexicographic order")) (|tab| (((|Tableau| (|List| |#1|)) (|List| |#1|)) "\\spad{tab(ls)} creates a tableau from \\spad{ls} by first creating a list of pairs using \\spadfunFrom{slex}{TableauBumpers},{} then creating a tableau using \\spadfunFrom{tab1}{TableauBumpers}.")) (|tab1| (((|List| (|List| (|List| |#1|))) (|List| (|List| |#1|))) "\\spad{tab1(lp)} creates a tableau from a list of pairs \\spad{lp}")) (|bat| (((|List| (|List| |#1|)) (|Tableau| (|List| |#1|))) "\\spad{bat(ls)} unbumps a tableau \\spad{ls}")) (|bat1| (((|List| (|List| |#1|)) (|List| (|List| (|List| |#1|)))) "\\spad{bat1(llp)} unbumps a tableau \\spad{llp}. Operation bat1 is the inverse of tab1.")) (|untab| (((|List| (|List| |#1|)) (|List| (|List| |#1|)) (|List| (|List| (|List| |#1|)))) "\\spad{untab(lp,llp)} is an auxiliary function which unbumps a tableau \\spad{llp},{} using \\spad{lp} to accumulate pairs")) (|bumptab1| (((|List| (|List| (|List| |#1|))) (|List| |#1|) (|List| (|List| (|List| |#1|)))) "\\spad{bumptab1(pr,t)} bumps a tableau \\spad{t} with a pair \\spad{pr} using comparison function \\spadfun{<},{} returning a new tableau")) (|bumptab| (((|List| (|List| (|List| |#1|))) (|Mapping| (|Boolean|) |#1| |#1|) (|List| |#1|) (|List| (|List| (|List| |#1|)))) "\\spad{bumptab(cf,pr,t)} bumps a tableau \\spad{t} with a pair \\spad{pr} using comparison function \\spad{cf},{} returning a new tableau")) (|bumprow| (((|Record| (|:| |fs| (|Boolean|)) (|:| |sd| (|List| |#1|)) (|:| |td| (|List| (|List| |#1|)))) (|Mapping| (|Boolean|) |#1| |#1|) (|List| |#1|) (|List| (|List| |#1|))) "\\spad{bumprow(cf,pr,r)} is an auxiliary function which bumps a row \\spad{r} with a pair \\spad{pr} using comparison function \\spad{cf},{} and returns a record"))) NIL NIL -(-1189 S) +(-1190 S) ((|constructor| (NIL "\\indented{1}{The tableau domain is for printing Young tableaux,{} and} coercions to and from List List \\spad{S} where \\spad{S} is a set.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(t)} converts a tableau \\spad{t} to an output form.")) (|listOfLists| (((|List| (|List| |#1|)) $) "\\spad{listOfLists t} converts a tableau \\spad{t} to a list of lists.")) (|tableau| (($ (|List| (|List| |#1|))) "\\spad{tableau(ll)} converts a list of lists \\spad{ll} to a tableau."))) NIL NIL -(-1190 |Key| |Entry|) +(-1191 |Key| |Entry|) ((|constructor| (NIL "This is the general purpose table type. The keys are hashed to look up the entries. This creates a \\spadtype{HashTable} if equal for the Key domain is consistent with Lisp EQUAL otherwise an \\spadtype{AssociationList}"))) -((-4417 . T) (-4418 . T)) -((-12 (|HasCategory| (-2 (|:| -1791 |#1|) (|:| -4232 |#2|)) (QUOTE (-1101))) (|HasCategory| (-2 (|:| -1791 |#1|) (|:| -4232 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1791) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4232) (|devaluate| |#2|)))))) (-2797 (|HasCategory| (-2 (|:| -1791 |#1|) (|:| -4232 |#2|)) (QUOTE (-1101))) (|HasCategory| |#2| (QUOTE (-1101)))) (-2797 (|HasCategory| (-2 (|:| -1791 |#1|) (|:| -4232 |#2|)) (QUOTE (-1101))) (|HasCategory| (-2 (|:| -1791 |#1|) (|:| -4232 |#2|)) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| |#2| (QUOTE (-1101))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| (-2 (|:| -1791 |#1|) (|:| -4232 |#2|)) (LIST (QUOTE -615) (QUOTE (-539)))) (-12 (|HasCategory| |#2| (QUOTE (-1101))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1791 |#1|) (|:| -4232 |#2|)) (QUOTE (-1101))) (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#2| (QUOTE (-1101))) (-2797 (|HasCategory| (-2 (|:| -1791 |#1|) (|:| -4232 |#2|)) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-2 (|:| -1791 |#1|) (|:| -4232 |#2|)) (LIST (QUOTE -614) (QUOTE (-863))))) -(-1191 R) +((-4418 . T) (-4419 . T)) +((-12 (|HasCategory| (-2 (|:| -1795 |#1|) (|:| -4237 |#2|)) (QUOTE (-1102))) (|HasCategory| (-2 (|:| -1795 |#1|) (|:| -4237 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1795) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -4237) (|devaluate| |#2|)))))) (-2800 (|HasCategory| (-2 (|:| -1795 |#1|) (|:| -4237 |#2|)) (QUOTE (-1102))) (|HasCategory| |#2| (QUOTE (-1102)))) (-2800 (|HasCategory| (-2 (|:| -1795 |#1|) (|:| -4237 |#2|)) (QUOTE (-1102))) (|HasCategory| (-2 (|:| -1795 |#1|) (|:| -4237 |#2|)) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| |#2| (QUOTE (-1102))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| (-2 (|:| -1795 |#1|) (|:| -4237 |#2|)) (LIST (QUOTE -615) (QUOTE (-539)))) (-12 (|HasCategory| |#2| (QUOTE (-1102))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1795 |#1|) (|:| -4237 |#2|)) (QUOTE (-1102))) (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#2| (QUOTE (-1102))) (-2800 (|HasCategory| (-2 (|:| -1795 |#1|) (|:| -4237 |#2|)) (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-863)))) (|HasCategory| (-2 (|:| -1795 |#1|) (|:| -4237 |#2|)) (LIST (QUOTE -614) (QUOTE (-863))))) +(-1192 R) ((|constructor| (NIL "Expands tangents of sums and scalar products.")) (|tanNa| ((|#1| |#1| (|Integer|)) "\\spad{tanNa(a, n)} returns \\spad{f(a)} such that if \\spad{a = tan(u)} then \\spad{f(a) = tan(n * u)}.")) (|tanAn| (((|SparseUnivariatePolynomial| |#1|) |#1| (|PositiveInteger|)) "\\spad{tanAn(a, n)} returns \\spad{P(x)} such that if \\spad{a = tan(u)} then \\spad{P(tan(u/n)) = 0}.")) (|tanSum| ((|#1| (|List| |#1|)) "\\spad{tanSum([a1,...,an])} returns \\spad{f(a1,...,an)} such that if \\spad{ai = tan(ui)} then \\spad{f(a1,...,an) = tan(u1 + ... + un)}."))) NIL NIL -(-1192 S |Key| |Entry|) +(-1193 S |Key| |Entry|) ((|constructor| (NIL "A table aggregate is a model of a table,{} \\spadignore{i.e.} a discrete many-to-one mapping from keys to entries.")) (|map| (($ (|Mapping| |#3| |#3| |#3|) $ $) "\\spad{map(fn,t1,t2)} creates a new table \\spad{t} from given tables \\spad{t1} and \\spad{t2} with elements \\spad{fn}(\\spad{x},{}\\spad{y}) where \\spad{x} and \\spad{y} are corresponding elements from \\spad{t1} and \\spad{t2} respectively.")) (|table| (($ (|List| (|Record| (|:| |key| |#2|) (|:| |entry| |#3|)))) "\\spad{table([x,y,...,z])} creates a table consisting of entries \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}}.") (($) "\\spad{table()}\\$\\spad{T} creates an empty table of type \\spad{T}.")) (|setelt| ((|#3| $ |#2| |#3|) "\\spad{setelt(t,k,e)} (also written \\axiom{\\spad{t}.\\spad{k} \\spad{:=} \\spad{e}}) is equivalent to \\axiom{(insert([\\spad{k},{}\\spad{e}],{}\\spad{t}); \\spad{e})}."))) NIL NIL -(-1193 |Key| |Entry|) +(-1194 |Key| |Entry|) ((|constructor| (NIL "A table aggregate is a model of a table,{} \\spadignore{i.e.} a discrete many-to-one mapping from keys to entries.")) (|map| (($ (|Mapping| |#2| |#2| |#2|) $ $) "\\spad{map(fn,t1,t2)} creates a new table \\spad{t} from given tables \\spad{t1} and \\spad{t2} with elements \\spad{fn}(\\spad{x},{}\\spad{y}) where \\spad{x} and \\spad{y} are corresponding elements from \\spad{t1} and \\spad{t2} respectively.")) (|table| (($ (|List| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) "\\spad{table([x,y,...,z])} creates a table consisting of entries \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}}.") (($) "\\spad{table()}\\$\\spad{T} creates an empty table of type \\spad{T}.")) (|setelt| ((|#2| $ |#1| |#2|) "\\spad{setelt(t,k,e)} (also written \\axiom{\\spad{t}.\\spad{k} \\spad{:=} \\spad{e}}) is equivalent to \\axiom{(insert([\\spad{k},{}\\spad{e}],{}\\spad{t}); \\spad{e})}."))) -((-4418 . T)) +((-4419 . T)) NIL -(-1194 |Key| |Entry|) +(-1195 |Key| |Entry|) ((|constructor| (NIL "\\axiom{TabulatedComputationPackage(Key ,{}Entry)} provides some modest support for dealing with operations with type \\axiom{Key \\spad{->} Entry}. The result of such operations can be stored and retrieved with this package by using a hash-table. The user does not need to worry about the management of this hash-table. However,{} onnly one hash-table is built by calling \\axiom{TabulatedComputationPackage(Key ,{}Entry)}.")) (|insert!| (((|Void|) |#1| |#2|) "\\axiom{insert!(\\spad{x},{}\\spad{y})} stores the item whose key is \\axiom{\\spad{x}} and whose entry is \\axiom{\\spad{y}}.")) (|extractIfCan| (((|Union| |#2| "failed") |#1|) "\\axiom{extractIfCan(\\spad{x})} searches the item whose key is \\axiom{\\spad{x}}.")) (|makingStats?| (((|Boolean|)) "\\axiom{makingStats?()} returns \\spad{true} iff the statisitics process is running.")) (|printingInfo?| (((|Boolean|)) "\\axiom{printingInfo?()} returns \\spad{true} iff messages are printed when manipulating items from the hash-table.")) (|usingTable?| (((|Boolean|)) "\\axiom{usingTable?()} returns \\spad{true} iff the hash-table is used")) (|clearTable!| (((|Void|)) "\\axiom{clearTable!()} clears the hash-table and assumes that it will no longer be used.")) (|printStats!| (((|Void|)) "\\axiom{printStats!()} prints the statistics.")) (|startStats!| (((|Void|) (|String|)) "\\axiom{startStats!(\\spad{x})} initializes the statisitics process and sets the comments to display when statistics are printed")) (|printInfo!| (((|Void|) (|String|) (|String|)) "\\axiom{printInfo!(\\spad{x},{}\\spad{y})} initializes the mesages to be printed when manipulating items from the hash-table. If a key is retrieved then \\axiom{\\spad{x}} is displayed. If an item is stored then \\axiom{\\spad{y}} is displayed.")) (|initTable!| (((|Void|)) "\\axiom{initTable!()} initializes the hash-table."))) NIL NIL -(-1195) +(-1196) ((|constructor| (NIL "This package provides functions for template manipulation")) (|stripCommentsAndBlanks| (((|String|) (|String|)) "\\spad{stripCommentsAndBlanks(s)} treats \\spad{s} as a piece of AXIOM input,{} and removes comments,{} and leading and trailing blanks.")) (|interpretString| (((|Any|) (|String|)) "\\spad{interpretString(s)} treats a string as a piece of AXIOM input,{} by parsing and interpreting it."))) NIL NIL -(-1196 S) +(-1197 S) ((|constructor| (NIL "\\spadtype{TexFormat1} provides a utility coercion for changing to TeX format anything that has a coercion to the standard output format.")) (|coerce| (((|TexFormat|) |#1|) "\\spad{coerce(s)} provides a direct coercion from a domain \\spad{S} to TeX format. This allows the user to skip the step of first manually coercing the object to standard output format before it is coerced to TeX format."))) NIL NIL -(-1197) +(-1198) ((|constructor| (NIL "\\spadtype{TexFormat} provides a coercion from \\spadtype{OutputForm} to \\TeX{} format. The particular dialect of \\TeX{} used is \\LaTeX{}. The basic object consists of three parts: a prologue,{} a tex part and an epilogue. The functions \\spadfun{prologue},{} \\spadfun{tex} and \\spadfun{epilogue} extract these parts,{} respectively. The main guts of the expression go into the tex part. The other parts can be set (\\spadfun{setPrologue!},{} \\spadfun{setEpilogue!}) so that contain the appropriate tags for printing. For example,{} the prologue and epilogue might simply contain \\spad{``}\\verb+\\spad{\\[}+\\spad{''} and \\spad{``}\\verb+\\spad{\\]}+\\spad{''},{} respectively,{} so that the TeX section will be printed in LaTeX display math mode.")) (|setPrologue!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setPrologue!(t,strings)} sets the prologue section of a TeX form \\spad{t} to \\spad{strings}.")) (|setTex!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setTex!(t,strings)} sets the TeX section of a TeX form \\spad{t} to \\spad{strings}.")) (|setEpilogue!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setEpilogue!(t,strings)} sets the epilogue section of a TeX form \\spad{t} to \\spad{strings}.")) (|prologue| (((|List| (|String|)) $) "\\spad{prologue(t)} extracts the prologue section of a TeX form \\spad{t}.")) (|new| (($) "\\spad{new()} create a new,{} empty object. Use \\spadfun{setPrologue!},{} \\spadfun{setTex!} and \\spadfun{setEpilogue!} to set the various components of this object.")) (|tex| (((|List| (|String|)) $) "\\spad{tex(t)} extracts the TeX section of a TeX form \\spad{t}.")) (|epilogue| (((|List| (|String|)) $) "\\spad{epilogue(t)} extracts the epilogue section of a TeX form \\spad{t}.")) (|display| (((|Void|) $) "\\spad{display(t)} outputs the TeX formatted code \\spad{t} so that each line has length less than or equal to the value set by the system command \\spadsyscom{set output length}.") (((|Void|) $ (|Integer|)) "\\spad{display(t,width)} outputs the TeX formatted code \\spad{t} so that each line has length less than or equal to \\spadvar{\\spad{width}}.")) (|convert| (($ (|OutputForm|) (|Integer|) (|OutputForm|)) "\\spad{convert(o,step,type)} changes \\spad{o} in standard output format to TeX format and also adds the given \\spad{step} number and \\spad{type}. This is useful if you want to create equations with given numbers or have the equation numbers correspond to the interpreter \\spad{step} numbers.") (($ (|OutputForm|) (|Integer|)) "\\spad{convert(o,step)} changes \\spad{o} in standard output format to TeX format and also adds the given \\spad{step} number. This is useful if you want to create equations with given numbers or have the equation numbers correspond to the interpreter \\spad{step} numbers."))) NIL NIL -(-1198) +(-1199) ((|constructor| (NIL "This domain provides an implementation of text files. Text is stored in these files using the native character set of the computer.")) (|endOfFile?| (((|Boolean|) $) "\\spad{endOfFile?(f)} tests whether the file \\spad{f} is positioned after the end of all text. If the file is open for output,{} then this test is always \\spad{true}.")) (|readIfCan!| (((|Union| (|String|) "failed") $) "\\spad{readIfCan!(f)} returns a string of the contents of a line from file \\spad{f},{} if possible. If \\spad{f} is not readable or if it is positioned at the end of file,{} then \\spad{\"failed\"} is returned.")) (|readLineIfCan!| (((|Union| (|String|) "failed") $) "\\spad{readLineIfCan!(f)} returns a string of the contents of a line from file \\spad{f},{} if possible. If \\spad{f} is not readable or if it is positioned at the end of file,{} then \\spad{\"failed\"} is returned.")) (|readLine!| (((|String|) $) "\\spad{readLine!(f)} returns a string of the contents of a line from the file \\spad{f}.")) (|writeLine!| (((|String|) $) "\\spad{writeLine!(f)} finishes the current line in the file \\spad{f}. An empty string is returned. The call \\spad{writeLine!(f)} is equivalent to \\spad{writeLine!(f,\"\")}.") (((|String|) $ (|String|)) "\\spad{writeLine!(f,s)} writes the contents of the string \\spad{s} and finishes the current line in the file \\spad{f}. The value of \\spad{s} is returned."))) NIL NIL -(-1199 R) +(-1200 R) ((|constructor| (NIL "Tools for the sign finding utilities.")) (|direction| (((|Integer|) (|String|)) "\\spad{direction(s)} \\undocumented")) (|nonQsign| (((|Union| (|Integer|) "failed") |#1|) "\\spad{nonQsign(r)} \\undocumented")) (|sign| (((|Union| (|Integer|) "failed") |#1|) "\\spad{sign(r)} \\undocumented"))) NIL NIL -(-1200) +(-1201) ((|constructor| (NIL "This package exports a function for making a \\spadtype{ThreeSpace}")) (|createThreeSpace| (((|ThreeSpace| (|DoubleFloat|))) "\\spad{createThreeSpace()} creates a \\spadtype{ThreeSpace(DoubleFloat)} object capable of holding point,{} curve,{} mesh components and any combination."))) NIL NIL -(-1201 S) +(-1202 S) ((|constructor| (NIL "Category for the transcendental elementary functions.")) (|pi| (($) "\\spad{pi()} returns the constant \\spad{pi}."))) NIL NIL -(-1202) +(-1203) ((|constructor| (NIL "Category for the transcendental elementary functions.")) (|pi| (($) "\\spad{pi()} returns the constant \\spad{pi}."))) NIL NIL -(-1203 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)) -((-12 (|HasCategory| |#1| (QUOTE (-1101))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1101))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-1101))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (-1204 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| $)) "\\spad{tree(nd,ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}."))) +((-4419 . T) (-4418 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1102))) (-2800 (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) +(-1205 S) ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL NIL -(-1205) +(-1206) ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL NIL -(-1206 R -3867) +(-1207 R -3879) ((|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 -(-1207 R |Row| |Col| M) +(-1208 R |Row| |Col| M) ((|constructor| (NIL "This package provides functions that compute \"fraction-free\" inverses of upper and lower triangular matrices over a integral domain. By \"fraction-free inverses\" we mean the following: given a matrix \\spad{B} with entries in \\spad{R} and an element \\spad{d} of \\spad{R} such that \\spad{d} * inv(\\spad{B}) also has entries in \\spad{R},{} we return \\spad{d} * inv(\\spad{B}). Thus,{} it is not necessary to pass to the quotient field in any of our computations.")) (|LowTriBddDenomInv| ((|#4| |#4| |#1|) "\\spad{LowTriBddDenomInv(B,d)} returns \\spad{M},{} where \\spad{B} is a non-singular lower triangular matrix and \\spad{d} is an element of \\spad{R} such that \\spad{M = d * inv(B)} has entries in \\spad{R}.")) (|UpTriBddDenomInv| ((|#4| |#4| |#1|) "\\spad{UpTriBddDenomInv(B,d)} returns \\spad{M},{} where \\spad{B} is a non-singular upper triangular matrix and \\spad{d} is an element of \\spad{R} such that \\spad{M = d * inv(B)} has entries in \\spad{R}."))) NIL NIL -(-1208 R -3867) +(-1209 R -3879) ((|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 -615) (LIST (QUOTE -893) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -887) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -615) (LIST (QUOTE -893) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -887) (|devaluate| |#1|))))) -(-1209 S R E V P) +((-12 (|HasCategory| |#1| (LIST (QUOTE -615) (LIST (QUOTE -894) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -888) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -615) (LIST (QUOTE -894) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -888) (|devaluate| |#1|))))) +(-1210 S R E V P) ((|constructor| (NIL "The category of triangular sets of multivariate polynomials with coefficients in an integral domain. Let \\axiom{\\spad{R}} be an integral domain and \\axiom{\\spad{V}} a finite ordered set of variables,{} say \\axiom{\\spad{X1} < \\spad{X2} < ... < \\spad{Xn}}. A set \\axiom{\\spad{S}} of polynomials in \\axiom{\\spad{R}[\\spad{X1},{}\\spad{X2},{}...,{}\\spad{Xn}]} is triangular if no elements of \\axiom{\\spad{S}} lies in \\axiom{\\spad{R}},{} and if two distinct elements of \\axiom{\\spad{S}} have distinct main variables. Note that the empty set is a triangular set. A triangular set is not necessarily a (lexicographical) Groebner basis and the notion of reduction related to triangular sets is based on the recursive view of polynomials. We recall this notion here and refer to [1] for more details. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a non-constant polynomial \\axiom{\\spad{Q}} if the degree of \\axiom{\\spad{P}} in the main variable of \\axiom{\\spad{Q}} is less than the main degree of \\axiom{\\spad{Q}}. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a triangular set \\axiom{\\spad{T}} if it is reduced \\spad{w}.\\spad{r}.\\spad{t}. every polynomial of \\axiom{\\spad{T}}. \\newline References : \\indented{1}{[1] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)}")) (|coHeight| (((|NonNegativeInteger|) $) "\\axiom{coHeight(\\spad{ts})} returns \\axiom{size()\\spad{\\$}\\spad{V}} minus \\axiom{\\spad{\\#}\\spad{ts}}.")) (|extend| (($ $ |#5|) "\\axiom{extend(\\spad{ts},{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{\\spad{ts}},{} according to the properties of triangular sets of the current category If the required properties do not hold an error is returned.")) (|extendIfCan| (((|Union| $ "failed") $ |#5|) "\\axiom{extendIfCan(\\spad{ts},{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{\\spad{ts}},{} according to the properties of triangular sets of the current domain. If the required properties do not hold then \"failed\" is returned. This operation encodes in some sense the properties of the triangular sets of the current category. Is is used to implement the \\axiom{construct} operation to guarantee that every triangular set build from a list of polynomials has the required properties.")) (|select| (((|Union| |#5| "failed") $ |#4|) "\\axiom{select(\\spad{ts},{}\\spad{v})} returns the polynomial of \\axiom{\\spad{ts}} with \\axiom{\\spad{v}} as main variable,{} if any.")) (|algebraic?| (((|Boolean|) |#4| $) "\\axiom{algebraic?(\\spad{v},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{\\spad{ts}}.")) (|algebraicVariables| (((|List| |#4|) $) "\\axiom{algebraicVariables(\\spad{ts})} returns the decreasingly sorted list of the main variables of the polynomials of \\axiom{\\spad{ts}}.")) (|rest| (((|Union| $ "failed") $) "\\axiom{rest(\\spad{ts})} returns the polynomials of \\axiom{\\spad{ts}} with smaller main variable than \\axiom{mvar(\\spad{ts})} if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \"failed\"")) (|last| (((|Union| |#5| "failed") $) "\\axiom{last(\\spad{ts})} returns the polynomial of \\axiom{\\spad{ts}} with smallest main variable if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|first| (((|Union| |#5| "failed") $) "\\axiom{first(\\spad{ts})} returns the polynomial of \\axiom{\\spad{ts}} with greatest main variable if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) (|:| |open| (|List| |#5|)))) (|List| |#5|)) "\\axiom{zeroSetSplitIntoTriangularSystems(\\spad{lp})} returns a list of triangular systems \\axiom{[[\\spad{ts1},{}\\spad{qs1}],{}...,{}[\\spad{tsn},{}\\spad{qsn}]]} such that the zero set of \\axiom{\\spad{lp}} is the union of the closures of the \\axiom{W_i} where \\axiom{W_i} consists of the zeros of \\axiom{\\spad{ts}} which do not cancel any polynomial in \\axiom{qsi}.")) (|zeroSetSplit| (((|List| $) (|List| |#5|)) "\\axiom{zeroSetSplit(\\spad{lp})} returns a list \\axiom{\\spad{lts}} of triangular sets such that the zero set of \\axiom{\\spad{lp}} is the union of the closures of the regular zero sets of the members of \\axiom{\\spad{lts}}.")) (|reduceByQuasiMonic| ((|#5| |#5| $) "\\axiom{reduceByQuasiMonic(\\spad{p},{}\\spad{ts})} returns the same as \\axiom{remainder(\\spad{p},{}collectQuasiMonic(\\spad{ts})).polnum}.")) (|collectQuasiMonic| (($ $) "\\axiom{collectQuasiMonic(\\spad{ts})} returns the subset of \\axiom{\\spad{ts}} consisting of the polynomials with initial in \\axiom{\\spad{R}}.")) (|removeZero| ((|#5| |#5| $) "\\axiom{removeZero(\\spad{p},{}\\spad{ts})} returns \\axiom{0} if \\axiom{\\spad{p}} reduces to \\axiom{0} by pseudo-division \\spad{w}.\\spad{r}.\\spad{t} \\axiom{\\spad{ts}} otherwise returns a polynomial \\axiom{\\spad{q}} computed from \\axiom{\\spad{p}} by removing any coefficient in \\axiom{\\spad{p}} reducing to \\axiom{0}.")) (|initiallyReduce| ((|#5| |#5| $) "\\axiom{initiallyReduce(\\spad{p},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|headReduce| ((|#5| |#5| $) "\\axiom{headReduce(\\spad{p},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduce?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|stronglyReduce| ((|#5| |#5| $) "\\axiom{stronglyReduce(\\spad{p},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{stronglyReduced?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|rewriteSetWithReduction| (((|List| |#5|) (|List| |#5|) $ (|Mapping| |#5| |#5| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{rewriteSetWithReduction(\\spad{lp},{}\\spad{ts},{}redOp,{}redOp?)} returns a list \\axiom{\\spad{lq}} of polynomials such that \\axiom{[reduce(\\spad{p},{}\\spad{ts},{}redOp,{}redOp?) for \\spad{p} in \\spad{lp}]} and \\axiom{\\spad{lp}} have the same zeros inside the regular zero set of \\axiom{\\spad{ts}}. Moreover,{} for every polynomial \\axiom{\\spad{q}} in \\axiom{\\spad{lq}} and every polynomial \\axiom{\\spad{t}} in \\axiom{\\spad{ts}} \\axiom{redOp?(\\spad{q},{}\\spad{t})} holds and there exists a polynomial \\axiom{\\spad{p}} in the ideal generated by \\axiom{\\spad{lp}} and a product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = \\spad{f*q} + redOp(\\spad{p},{}\\spad{q})}.")) (|reduce| ((|#5| |#5| $ (|Mapping| |#5| |#5| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{reduce(\\spad{p},{}\\spad{ts},{}redOp,{}redOp?)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{redOp?(\\spad{r},{}\\spad{p})} holds for every \\axiom{\\spad{p}} of \\axiom{\\spad{ts}} and there exists some product \\axiom{\\spad{h}} of the initials of the members of \\axiom{\\spad{ts}} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = \\spad{f*q} + redOp(\\spad{p},{}\\spad{q})}.")) (|autoReduced?| (((|Boolean|) $ (|Mapping| (|Boolean|) |#5| (|List| |#5|))) "\\axiom{autoReduced?(\\spad{ts},{}redOp?)} returns \\spad{true} iff every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to every other in the sense of \\axiom{redOp?}")) (|initiallyReduced?| (((|Boolean|) $) "\\spad{initiallyReduced?(ts)} returns \\spad{true} iff for every element \\axiom{\\spad{p}} of \\axiom{\\spad{ts}} \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the other elements of \\axiom{\\spad{ts}} with the same main variable.") (((|Boolean|) |#5| $) "\\axiom{initiallyReduced?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the elements of \\axiom{\\spad{ts}} with the same main variable.")) (|headReduced?| (((|Boolean|) $) "\\spad{headReduced?(ts)} returns \\spad{true} iff the head of every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{\\spad{ts}}.") (((|Boolean|) |#5| $) "\\axiom{headReduced?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff the head of \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ts}}.")) (|stronglyReduced?| (((|Boolean|) $) "\\axiom{stronglyReduced?(\\spad{ts})} returns \\spad{true} iff every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{\\spad{ts}}.") (((|Boolean|) |#5| $) "\\axiom{stronglyReduced?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ts}}.")) (|reduced?| (((|Boolean|) |#5| $ (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{reduced?(\\spad{p},{}\\spad{ts},{}redOp?)} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. in the sense of the operation \\axiom{redOp?},{} that is if for every \\axiom{\\spad{t}} in \\axiom{\\spad{ts}} \\axiom{redOp?(\\spad{p},{}\\spad{t})} holds.")) (|normalized?| (((|Boolean|) $) "\\axiom{normalized?(\\spad{ts})} returns \\spad{true} iff for every axiom{\\spad{p}} in axiom{\\spad{ts}} we have \\axiom{normalized?(\\spad{p},{}us)} where \\axiom{us} is \\axiom{collectUnder(\\spad{ts},{}mvar(\\spad{p}))}.") (((|Boolean|) |#5| $) "\\axiom{normalized?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variables of the polynomials of \\axiom{\\spad{ts}}")) (|quasiComponent| (((|Record| (|:| |close| (|List| |#5|)) (|:| |open| (|List| |#5|))) $) "\\axiom{quasiComponent(\\spad{ts})} returns \\axiom{[\\spad{lp},{}\\spad{lq}]} where \\axiom{\\spad{lp}} is the list of the members of \\axiom{\\spad{ts}} and \\axiom{\\spad{lq}}is \\axiom{initials(\\spad{ts})}.")) (|degree| (((|NonNegativeInteger|) $) "\\axiom{degree(\\spad{ts})} returns the product of main degrees of the members of \\axiom{\\spad{ts}}.")) (|initials| (((|List| |#5|) $) "\\axiom{initials(\\spad{ts})} returns the list of the non-constant initials of the members of \\axiom{\\spad{ts}}.")) (|basicSet| (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#5|))) "failed") (|List| |#5|) (|Mapping| (|Boolean|) |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{basicSet(\\spad{ps},{}pred?,{}redOp?)} returns the same as \\axiom{basicSet(\\spad{qs},{}redOp?)} where \\axiom{\\spad{qs}} consists of the polynomials of \\axiom{\\spad{ps}} satisfying property \\axiom{pred?}.") (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#5|))) "failed") (|List| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{basicSet(\\spad{ps},{}redOp?)} returns \\axiom{[\\spad{bs},{}\\spad{ts}]} where \\axiom{concat(\\spad{bs},{}\\spad{ts})} is \\axiom{\\spad{ps}} and \\axiom{\\spad{bs}} is a basic set in Wu Wen Tsun sense of \\axiom{\\spad{ps}} \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?},{} if no non-zero constant polynomial lie in \\axiom{\\spad{ps}},{} otherwise \\axiom{\"failed\"} is returned.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(\\spad{ts1},{}\\spad{ts2})} returns \\spad{true} iff \\axiom{\\spad{ts2}} has higher rank than \\axiom{\\spad{ts1}} in Wu Wen Tsun sense."))) NIL ((|HasCategory| |#4| (QUOTE (-370)))) -(-1210 R E V P) +(-1211 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|) $ $) "\\axiom{infRittWu?(\\spad{ts1},{}\\spad{ts2})} returns \\spad{true} iff \\axiom{\\spad{ts2}} has higher rank than \\axiom{\\spad{ts1}} in Wu Wen Tsun sense."))) -((-4418 . T) (-4417 . T)) +((-4419 . T) (-4418 . T)) NIL -(-1211 |Coef|) +(-1212 |Coef|) ((|constructor| (NIL "\\spadtype{TaylorSeries} is a general multivariate Taylor series domain over the ring Coef and with variables of type Symbol.")) (|fintegrate| (($ (|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| (-559)) (-4412 . T) (-4411 . T) (-4414 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (-2797 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-559)))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-365)))) -(-1212 |Curve|) +(((-4420 "*") |has| |#1| (-172)) (-4411 |has| |#1| (-559)) (-4413 . T) (-4412 . T) (-4415 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (-2800 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-559)))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-365)))) +(-1213 |Curve|) ((|constructor| (NIL "\\indented{2}{Package for constructing tubes around 3-dimensional parametric curves.} Domain of tubes around 3-dimensional parametric curves.")) (|tube| (($ |#1| (|List| (|List| (|Point| (|DoubleFloat|)))) (|Boolean|)) "\\spad{tube(c,ll,b)} creates a tube of the domain \\spadtype{TubePlot} from a space curve \\spad{c} of the category \\spadtype{PlottableSpaceCurveCategory},{} a list of lists of points (loops) \\spad{ll} and a boolean \\spad{b} which if \\spad{true} indicates a closed tube,{} or if \\spad{false} an open tube.")) (|setClosed| (((|Boolean|) $ (|Boolean|)) "\\spad{setClosed(t,b)} declares the given tube plot \\spad{t} to be closed if \\spad{b} is \\spad{true},{} or if \\spad{b} is \\spad{false},{} \\spad{t} is set to be open.")) (|open?| (((|Boolean|) $) "\\spad{open?(t)} tests whether the given tube plot \\spad{t} is open.")) (|closed?| (((|Boolean|) $) "\\spad{closed?(t)} tests whether the given tube plot \\spad{t} is closed.")) (|listLoops| (((|List| (|List| (|Point| (|DoubleFloat|)))) $) "\\spad{listLoops(t)} returns the list of lists of points,{} or the 'loops',{} of the given tube plot \\spad{t}.")) (|getCurve| ((|#1| $) "\\spad{getCurve(t)} returns the \\spadtype{PlottableSpaceCurveCategory} representing the parametric curve of the given tube plot \\spad{t}."))) NIL NIL -(-1213) +(-1214) ((|constructor| (NIL "Tools for constructing tubes around 3-dimensional parametric curves.")) (|loopPoints| (((|List| (|Point| (|DoubleFloat|))) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|List| (|List| (|DoubleFloat|)))) "\\spad{loopPoints(p,n,b,r,lls)} creates and returns a list of points which form the loop with radius \\spad{r},{} around the center point indicated by the point \\spad{p},{} with the principal normal vector of the space curve at point \\spad{p} given by the point(vector) \\spad{n},{} and the binormal vector given by the point(vector) \\spad{b},{} and a list of lists,{} \\spad{lls},{} which is the \\spadfun{cosSinInfo} of the number of points defining the loop.")) (|cosSinInfo| (((|List| (|List| (|DoubleFloat|))) (|Integer|)) "\\spad{cosSinInfo(n)} returns the list of lists of values for \\spad{n},{} in the form: \\spad{[[cos(n - 1) a,sin(n - 1) a],...,[cos 2 a,sin 2 a],[cos a,sin a]]} where \\spad{a = 2 pi/n}. Note: \\spad{n} should be greater than 2.")) (|unitVector| (((|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))) "\\spad{unitVector(p)} creates the unit vector of the point \\spad{p} and returns the result as a point. Note: \\spad{unitVector(p) = p/|p|}.")) (|cross| (((|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))) "\\spad{cross(p,q)} computes the cross product of the two points \\spad{p} and \\spad{q} using only the first three coordinates,{} and keeping the color of the first point \\spad{p}. The result is returned as a point.")) (|dot| (((|DoubleFloat|) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))) "\\spad{dot(p,q)} computes the dot product of the two points \\spad{p} and \\spad{q} using only the first three coordinates,{} and returns the resulting \\spadtype{DoubleFloat}.")) (- (((|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))) "\\spad{p - q} computes and returns a point whose coordinates are the differences of the coordinates of two points \\spad{p} and \\spad{q},{} using the color,{} or fourth coordinate,{} of the first point \\spad{p} as the color also of the point \\spad{q}.")) (+ (((|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))) "\\spad{p + q} computes and returns a point whose coordinates are the sums of the coordinates of the two points \\spad{p} and \\spad{q},{} using the color,{} or fourth coordinate,{} of the first point \\spad{p} as the color also of the point \\spad{q}.")) (* (((|Point| (|DoubleFloat|)) (|DoubleFloat|) (|Point| (|DoubleFloat|))) "\\spad{s * p} returns a point whose coordinates are the scalar multiple of the point \\spad{p} by the scalar \\spad{s},{} preserving the color,{} or fourth coordinate,{} of \\spad{p}.")) (|point| (((|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{point(x1,x2,x3,c)} creates and returns a point from the three specified coordinates \\spad{x1},{} \\spad{x2},{} \\spad{x3},{} and also a fourth coordinate,{} \\spad{c},{} which is generally used to specify the color of the point."))) NIL NIL -(-1214 S) +(-1215 S) ((|constructor| (NIL "\\indented{1}{This domain is used to interface with the interpreter\\spad{'s} notion} of comma-delimited sequences of values.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length(x)} returns the number of elements in tuple \\spad{x}")) (|select| ((|#1| $ (|NonNegativeInteger|)) "\\spad{select(x,n)} returns the \\spad{n}-th element of tuple \\spad{x}. tuples are 0-based"))) NIL -((|HasCategory| |#1| (QUOTE (-1101))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) -(-1215 -3867) +((|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) +(-1216 -3879) ((|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 -(-1216) +(-1217) ((|constructor| (NIL "This domain represents a type AST."))) NIL NIL -(-1217) +(-1218) ((|constructor| (NIL "The fundamental Type."))) NIL NIL -(-1218 S) +(-1219 S) ((|constructor| (NIL "Provides functions to force a partial ordering on any set.")) (|more?| (((|Boolean|) |#1| |#1|) "\\spad{more?(a, b)} compares \\spad{a} and \\spad{b} in the partial ordering induced by setOrder,{} and uses the ordering on \\spad{S} if \\spad{a} and \\spad{b} are not comparable in the partial ordering.")) (|userOrdered?| (((|Boolean|)) "\\spad{userOrdered?()} tests if the partial ordering induced by \\spadfunFrom{setOrder}{UserDefinedPartialOrdering} is not empty.")) (|largest| ((|#1| (|List| |#1|)) "\\spad{largest l} returns the largest element of \\spad{l} where the partial ordering induced by setOrder is completed into a total one by the ordering on \\spad{S}.") ((|#1| (|List| |#1|) (|Mapping| (|Boolean|) |#1| |#1|)) "\\spad{largest(l, fn)} returns the largest element of \\spad{l} where the partial ordering induced by setOrder is completed into a total one by \\spad{fn}.")) (|less?| (((|Boolean|) |#1| |#1| (|Mapping| (|Boolean|) |#1| |#1|)) "\\spad{less?(a, b, fn)} compares \\spad{a} and \\spad{b} in the partial ordering induced by setOrder,{} and returns \\spad{fn(a, b)} if \\spad{a} and \\spad{b} are not comparable in that ordering.") (((|Union| (|Boolean|) "failed") |#1| |#1|) "\\spad{less?(a, b)} compares \\spad{a} and \\spad{b} in the partial ordering induced by setOrder.")) (|getOrder| (((|Record| (|:| |low| (|List| |#1|)) (|:| |high| (|List| |#1|)))) "\\spad{getOrder()} returns \\spad{[[b1,...,bm], [a1,...,an]]} such that the partial ordering on \\spad{S} was given by \\spad{setOrder([b1,...,bm],[a1,...,an])}.")) (|setOrder| (((|Void|) (|List| |#1|) (|List| |#1|)) "\\spad{setOrder([b1,...,bm], [a1,...,an])} defines a partial ordering on \\spad{S} given \\spad{by:} \\indented{3}{(1)\\space{2}\\spad{b1 < b2 < ... < bm < a1 < a2 < ... < an}.} \\indented{3}{(2)\\space{2}\\spad{bj < c < ai}\\space{2}for \\spad{c} not among the \\spad{ai}\\spad{'s} and \\spad{bj}\\spad{'s}.} \\indented{3}{(3)\\space{2}undefined on \\spad{(c,d)} if neither is among the \\spad{ai}\\spad{'s},{}\\spad{bj}\\spad{'s}.}") (((|Void|) (|List| |#1|)) "\\spad{setOrder([a1,...,an])} defines a partial ordering on \\spad{S} given \\spad{by:} \\indented{3}{(1)\\space{2}\\spad{a1 < a2 < ... < an}.} \\indented{3}{(2)\\space{2}\\spad{b < ai\\space{3}for i = 1..n} and \\spad{b} not among the \\spad{ai}\\spad{'s}.} \\indented{3}{(3)\\space{2}undefined on \\spad{(b, c)} if neither is among the \\spad{ai}\\spad{'s}.}"))) NIL ((|HasCategory| |#1| (QUOTE (-851)))) -(-1219) +(-1220) ((|constructor| (NIL "This packages provides functions to allow the user to select the ordering on the variables and operators for displaying polynomials,{} fractions and expressions. The ordering affects the display only and not the computations.")) (|resetVariableOrder| (((|Void|)) "\\spad{resetVariableOrder()} cancels any previous use of setVariableOrder and returns to the default system ordering.")) (|getVariableOrder| (((|Record| (|:| |high| (|List| (|Symbol|))) (|:| |low| (|List| (|Symbol|))))) "\\spad{getVariableOrder()} returns \\spad{[[b1,...,bm], [a1,...,an]]} such that the ordering on the variables was given by \\spad{setVariableOrder([b1,...,bm], [a1,...,an])}.")) (|setVariableOrder| (((|Void|) (|List| (|Symbol|)) (|List| (|Symbol|))) "\\spad{setVariableOrder([b1,...,bm], [a1,...,an])} defines an ordering on the variables given by \\spad{b1 > b2 > ... > bm >} other variables \\spad{> a1 > a2 > ... > an}.") (((|Void|) (|List| (|Symbol|))) "\\spad{setVariableOrder([a1,...,an])} defines an ordering on the variables given by \\spad{a1 > a2 > ... > an > other variables}."))) NIL NIL -(-1220 S) +(-1221 S) ((|constructor| (NIL "A constructive unique factorization domain,{} \\spadignore{i.e.} where we can constructively factor members into a product of a finite number of irreducible elements.")) (|factor| (((|Factored| $) $) "\\spad{factor(x)} returns the factorization of \\spad{x} into irreducibles.")) (|squareFreePart| (($ $) "\\spad{squareFreePart(x)} returns a product of prime factors of \\spad{x} each taken with multiplicity one.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns the square-free factorization of \\spad{x} \\spadignore{i.e.} such that the factors are pairwise relatively prime and each has multiple prime factors.")) (|prime?| (((|Boolean|) $) "\\spad{prime?(x)} tests if \\spad{x} can never be written as the product of two non-units of the ring,{} \\spadignore{i.e.} \\spad{x} is an irreducible element."))) NIL NIL -(-1221) +(-1222) ((|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|) $) "\\spad{prime?(x)} tests if \\spad{x} can never be written as the product of two non-units of the ring,{} \\spadignore{i.e.} \\spad{x} is an irreducible element."))) -((-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) +((-4411 . T) ((-4420 "*") . T) (-4412 . T) (-4413 . T) (-4415 . T)) NIL -(-1222) +(-1223) ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 16 bits."))) NIL NIL -(-1223) +(-1224) ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 32 bits."))) NIL NIL -(-1224) +(-1225) ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 64 bits."))) NIL NIL -(-1225) +(-1226) ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 8 bits."))) NIL NIL -(-1226 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) +(-1227 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) ((|constructor| (NIL "Mapping package for univariate Laurent series \\indented{2}{This package allows one to apply a function to the coefficients of} \\indented{2}{a univariate Laurent series.}")) (|map| (((|UnivariateLaurentSeries| |#2| |#4| |#6|) (|Mapping| |#2| |#1|) (|UnivariateLaurentSeries| |#1| |#3| |#5|)) "\\spad{map(f,g(x))} applies the map \\spad{f} to the coefficients of the Laurent series \\spad{g(x)}."))) NIL NIL -(-1227 |Coef|) +(-1228 |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateLaurentSeriesCategory} is the category of Laurent series in one variable.")) (|integrate| (($ $ (|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| (-559)) (-4415 |has| |#1| (-365)) (-4409 |has| |#1| (-365)) (-4411 . T) (-4412 . T) (-4414 . T)) +(((-4420 "*") |has| |#1| (-172)) (-4411 |has| |#1| (-559)) (-4416 |has| |#1| (-365)) (-4410 |has| |#1| (-365)) (-4412 . T) (-4413 . T) (-4415 . T)) NIL -(-1228 S |Coef| UTS) +(-1229 S |Coef| UTS) ((|constructor| (NIL "This is a category of univariate Laurent series constructed from univariate Taylor series. A Laurent series is represented by a pair \\spad{[n,f(x)]},{} where \\spad{n} is an arbitrary integer and \\spad{f(x)} is a Taylor series. This pair represents the Laurent series \\spad{x**n * f(x)}.")) (|taylorIfCan| (((|Union| |#3| "failed") $) "\\spad{taylorIfCan(f(x))} converts the Laurent series \\spad{f(x)} to a Taylor series,{} if possible. If this is not possible,{} \"failed\" is returned.")) (|taylor| ((|#3| $) "\\spad{taylor(f(x))} converts the Laurent series \\spad{f}(\\spad{x}) to a Taylor series,{} if possible. Error: if this is not possible.")) (|removeZeroes| (($ (|Integer|) $) "\\spad{removeZeroes(n,f(x))} removes up to \\spad{n} leading zeroes from the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable.") (($ $) "\\spad{removeZeroes(f(x))} removes leading zeroes from the representation of the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable. Note: \\spad{removeZeroes(f)} removes all leading zeroes from \\spad{f}")) (|taylorRep| ((|#3| $) "\\spad{taylorRep(f(x))} returns \\spad{g(x)},{} where \\spad{f = x**n * g(x)} is represented by \\spad{[n,g(x)]}.")) (|degree| (((|Integer|) $) "\\spad{degree(f(x))} returns the degree of the lowest order term of \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurent| (($ (|Integer|) |#3|) "\\spad{laurent(n,f(x))} returns \\spad{x**n * f(x)}."))) NIL ((|HasCategory| |#2| (QUOTE (-365)))) -(-1229 |Coef| UTS) +(-1230 |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| (-559)) (-4415 |has| |#1| (-365)) (-4409 |has| |#1| (-365)) (-4411 . T) (-4412 . T) (-4414 . T)) +(((-4420 "*") |has| |#1| (-172)) (-4411 |has| |#1| (-559)) (-4416 |has| |#1| (-365)) (-4410 |has| |#1| (-365)) (-4412 . T) (-4413 . T) (-4415 . T)) NIL -(-1230 |Coef| UTS) +(-1231 |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| (-559)) (-4415 |has| |#1| (-365)) (-4409 |has| |#1| (-365)) (-4411 . T) (-4412 . T) (-4414 . T)) -((-2797 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (-12 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#2| (LIST (QUOTE -287) (|devaluate| |#2|) (|devaluate| |#2|)))) (-12 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#2| (LIST (QUOTE -517) (QUOTE (-1177)) (|devaluate| |#2|)))) (-12 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-821)))) (-12 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-851)))) (-12 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-910)))) (-12 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-1023)))) (-12 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-1152)))) (-12 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#2| (LIST (QUOTE -615) (QUOTE (-539))))) (-12 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (-12 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#2| (LIST (QUOTE -1039) 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for the factorization of univariate polynomials with integer coefficients. The factorization is done by \"lifting\" (HENSEL) the factorization over a finite field.")) (|henselFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|)) "\\spad{henselFact(m,flag)} returns the factorization of \\spad{m},{} FinalFact is a Record \\spad{s}.\\spad{t}. FinalFact.contp=content \\spad{m},{} FinalFact.factors=List of irreducible factors of \\spad{m} with exponent ,{} if \\spad{flag} =true the polynomial is assumed square free.")) (|factorSquareFree| (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(m)} returns the factorization of \\spad{m} square free polynomial")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(m)} returns the factorization of \\spad{m}"))) NIL NIL -(-1233 R S) +(-1234 R S) ((|constructor| (NIL "This package provides operations for mapping functions onto segments.")) 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NIL NIL -(-1236 R Q UP) +(-1237 R Q UP) ((|constructor| (NIL "UnivariatePolynomialCommonDenominator provides functions to compute the common denominator of the coefficients of univariate polynomials over the quotient field of a \\spad{gcd} domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#3|) "\\spad{splitDenominator(q)} returns \\spad{[p, d]} such that \\spad{q = p/d} and \\spad{d} is a common denominator for the coefficients of \\spad{q}.")) (|clearDenominator| ((|#3| |#3|) "\\spad{clearDenominator(q)} returns \\spad{p} such that \\spad{q = p/d} where \\spad{d} is a common denominator for the coefficients of \\spad{q}.")) (|commonDenominator| ((|#1| |#3|) "\\spad{commonDenominator(q)} returns a common denominator \\spad{d} for the coefficients of \\spad{q}."))) NIL NIL -(-1237 R UP) +(-1238 R UP) ((|constructor| (NIL "UnivariatePolynomialDecompositionPackage implements functional decomposition of univariate polynomial with coefficients in an \\spad{IntegralDomain} of \\spad{CharacteristicZero}.")) (|monicCompleteDecompose| (((|List| |#2|) |#2|) "\\spad{monicCompleteDecompose(f)} returns a list of factors of \\spad{f} for the functional decomposition ([ \\spad{f1},{} ...,{} \\spad{fn} ] means \\spad{f} = \\spad{f1} \\spad{o} ... \\spad{o} \\spad{fn}).")) (|monicDecomposeIfCan| (((|Union| (|Record| (|:| |left| |#2|) (|:| |right| |#2|)) "failed") |#2|) "\\spad{monicDecomposeIfCan(f)} returns a functional decomposition of the monic polynomial \\spad{f} of \"failed\" if it has not found any.")) (|leftFactorIfCan| (((|Union| |#2| "failed") |#2| |#2|) "\\spad{leftFactorIfCan(f,h)} returns the left factor (\\spad{g} in \\spad{f} = \\spad{g} \\spad{o} \\spad{h}) of the functional decomposition of the polynomial \\spad{f} with given \\spad{h} or \\spad{\"failed\"} if \\spad{g} does not exist.")) (|rightFactorIfCan| (((|Union| |#2| "failed") |#2| (|NonNegativeInteger|) |#1|) "\\spad{rightFactorIfCan(f,d,c)} returns a candidate to be the right factor (\\spad{h} in \\spad{f} = \\spad{g} \\spad{o} \\spad{h}) of degree \\spad{d} with leading coefficient \\spad{c} of a functional decomposition of the polynomial \\spad{f} or \\spad{\"failed\"} if no such candidate.")) (|monicRightFactorIfCan| (((|Union| |#2| "failed") |#2| (|NonNegativeInteger|)) "\\spad{monicRightFactorIfCan(f,d)} returns a candidate to be the monic right factor (\\spad{h} in \\spad{f} = \\spad{g} \\spad{o} \\spad{h}) of degree \\spad{d} of a functional decomposition of the polynomial \\spad{f} or \\spad{\"failed\"} if no such candidate."))) NIL NIL -(-1238 R UP) +(-1239 R UP) ((|constructor| (NIL "UnivariatePolynomialDivisionPackage provides a division for non monic univarite polynomials with coefficients in an \\spad{IntegralDomain}.")) (|divideIfCan| (((|Union| (|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) "failed") |#2| |#2|) "\\spad{divideIfCan(f,g)} returns quotient and remainder of the division of \\spad{f} by \\spad{g} or \"failed\" if it has not succeeded."))) NIL NIL -(-1239 R U) +(-1240 R U) ((|constructor| (NIL "This package implements Karatsuba\\spad{'s} trick for multiplying (large) univariate polynomials. It could be improved with a version doing the work on place and also with a special case for squares. We've done this in Basicmath,{} but we believe that this out of the scope of AXIOM.")) (|karatsuba| ((|#2| |#2| |#2| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{karatsuba(a,b,l,k)} returns \\spad{a*b} by applying Karatsuba\\spad{'s} trick provided that both \\spad{a} and \\spad{b} have at least \\spad{l} terms and \\spad{k > 0} holds and by calling \\spad{noKaratsuba} otherwise. The other multiplications are performed by recursive calls with the same third argument and \\spad{k-1} as fourth argument.")) (|karatsubaOnce| ((|#2| |#2| |#2|) "\\spad{karatsuba(a,b)} returns \\spad{a*b} by applying Karatsuba\\spad{'s} trick once. The other multiplications are performed by calling \\spad{*} from \\spad{U}.")) (|noKaratsuba| ((|#2| |#2| |#2|) "\\spad{noKaratsuba(a,b)} returns \\spad{a*b} without using Karatsuba\\spad{'s} trick at all."))) NIL NIL -(-1240 |x| R) +(-1241 |x| R) ((|constructor| (NIL "This domain represents univariate polynomials in some symbol over arbitrary (not necessarily commutative) coefficient rings. The representation is sparse in the sense that only non-zero terms are represented.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#2| $) "\\spad{fmecg(p1,e,r,p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}"))) -(((-4419 "*") |has| |#2| (-172)) (-4410 |has| |#2| (-559)) (-4413 |has| |#2| (-365)) (-4415 |has| |#2| (-6 -4415)) (-4412 . T) (-4411 . T) (-4414 . T)) -((|HasCategory| |#2| (QUOTE (-910))) (|HasCategory| |#2| (QUOTE (-559))) (|HasCategory| |#2| (QUOTE (-172))) (-2797 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-559)))) (-12 (|HasCategory| (-1083) (LIST (QUOTE -887) (QUOTE (-381)))) (|HasCategory| |#2| (LIST (QUOTE -887) (QUOTE (-381))))) (-12 (|HasCategory| (-1083) (LIST (QUOTE -887) (QUOTE (-567)))) (|HasCategory| |#2| (LIST (QUOTE -887) (QUOTE (-567))))) (-12 (|HasCategory| (-1083) (LIST (QUOTE -615) (LIST (QUOTE -893) (QUOTE (-381))))) (|HasCategory| |#2| (LIST (QUOTE -615) (LIST (QUOTE -893) (QUOTE (-381)))))) (-12 (|HasCategory| (-1083) (LIST (QUOTE -615) (LIST (QUOTE -893) (QUOTE (-567))))) (|HasCategory| |#2| (LIST (QUOTE -615) (LIST (QUOTE -893) (QUOTE (-567)))))) (-12 (|HasCategory| (-1083) (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| |#2| (LIST (QUOTE -615) (QUOTE (-539))))) (|HasCategory| |#2| (LIST (QUOTE -640) (QUOTE (-567)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#2| (LIST (QUOTE -1039) (QUOTE (-567)))) (-2797 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#2| (LIST (QUOTE -1039) (LIST (QUOTE -410) (QUOTE (-567)))))) (|HasCategory| |#2| (LIST (QUOTE -1039) (LIST (QUOTE -410) (QUOTE (-567))))) (-2797 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-455))) (|HasCategory| |#2| (QUOTE (-559))) (|HasCategory| |#2| (QUOTE (-910)))) (-2797 (|HasCategory| |#2| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-455))) (|HasCategory| |#2| (QUOTE (-559))) (|HasCategory| |#2| (QUOTE (-910)))) (-2797 (|HasCategory| |#2| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-455))) (|HasCategory| |#2| (QUOTE (-910)))) (|HasCategory| |#2| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-1152))) (|HasCategory| |#2| (LIST (QUOTE -901) (QUOTE (-1177)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasAttribute| |#2| (QUOTE -4415)) (|HasCategory| |#2| (QUOTE (-455))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-910)))) (-2797 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-910)))) (|HasCategory| |#2| (QUOTE (-145))))) -(-1241 R PR S PS) +(((-4420 "*") |has| |#2| (-172)) (-4411 |has| |#2| (-559)) (-4414 |has| |#2| (-365)) (-4416 |has| |#2| (-6 -4416)) (-4413 . T) (-4412 . T) (-4415 . T)) +((|HasCategory| |#2| (QUOTE (-911))) (|HasCategory| |#2| (QUOTE (-559))) (|HasCategory| |#2| (QUOTE (-172))) (-2800 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-559)))) (-12 (|HasCategory| (-1084) (LIST (QUOTE -888) (QUOTE (-381)))) (|HasCategory| |#2| (LIST (QUOTE -888) (QUOTE (-381))))) (-12 (|HasCategory| (-1084) (LIST (QUOTE -888) (QUOTE (-567)))) (|HasCategory| |#2| (LIST (QUOTE -888) (QUOTE (-567))))) (-12 (|HasCategory| (-1084) (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-381))))) (|HasCategory| |#2| (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-381)))))) (-12 (|HasCategory| (-1084) (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567))))) (|HasCategory| |#2| (LIST (QUOTE -615) (LIST (QUOTE -894) (QUOTE (-567)))))) (-12 (|HasCategory| (-1084) (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| |#2| (LIST (QUOTE -615) (QUOTE (-539))))) (|HasCategory| |#2| (LIST (QUOTE -640) (QUOTE (-567)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#2| (LIST (QUOTE -1040) (QUOTE (-567)))) (-2800 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#2| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567)))))) (|HasCategory| |#2| (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (-2800 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-455))) (|HasCategory| |#2| (QUOTE (-559))) (|HasCategory| |#2| (QUOTE (-911)))) (-2800 (|HasCategory| |#2| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-455))) (|HasCategory| |#2| (QUOTE (-559))) (|HasCategory| |#2| (QUOTE (-911)))) (-2800 (|HasCategory| |#2| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-455))) (|HasCategory| |#2| (QUOTE (-911)))) (|HasCategory| |#2| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-1153))) (|HasCategory| |#2| (LIST (QUOTE -902) (QUOTE (-1178)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasAttribute| |#2| (QUOTE -4416)) (|HasCategory| |#2| (QUOTE (-455))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-911)))) (-2800 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-911)))) (|HasCategory| |#2| (QUOTE (-145))))) +(-1242 R PR S PS) ((|constructor| (NIL "Mapping from polynomials over \\spad{R} to polynomials over \\spad{S} given a map from \\spad{R} to \\spad{S} assumed to send zero to zero.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f, p)} takes a function \\spad{f} from \\spad{R} to \\spad{S},{} and applies it to each (non-zero) coefficient of a polynomial \\spad{p} over \\spad{R},{} getting a new polynomial over \\spad{S}. Note: since the map is not applied to zero elements,{} it may map zero to zero."))) NIL NIL -(-1242 S R) +(-1243 S R) ((|constructor| (NIL "The category of univariate polynomials over a ring \\spad{R}. No particular model is assumed - implementations can be either sparse or dense.")) (|integrate| (($ $) "\\spad{integrate(p)} integrates the univariate polynomial \\spad{p} with respect to its distinguished variable.")) (|additiveValuation| ((|attribute|) "euclideanSize(a*b) = euclideanSize(a) + euclideanSize(\\spad{b})")) (|separate| (((|Record| (|:| |primePart| $) (|:| |commonPart| $)) $ $) "\\spad{separate(p, q)} returns \\spad{[a, b]} such that polynomial \\spad{p = a b} and \\spad{a} is relatively prime to \\spad{q}.")) (|pseudoDivide| (((|Record| (|:| |coef| |#2|) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{pseudoDivide(p,q)} returns \\spad{[c, q, r]},{} when \\spad{p' := p*lc(q)**(deg p - deg q + 1) = c * p} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|pseudoQuotient| (($ $ $) "\\spad{pseudoQuotient(p,q)} returns \\spad{r},{} the quotient when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|composite| (((|Union| (|Fraction| $) "failed") (|Fraction| $) $) "\\spad{composite(f, q)} returns \\spad{h} if \\spad{f} = \\spad{h}(\\spad{q}),{} and \"failed\" is no such \\spad{h} exists.") (((|Union| $ "failed") $ $) "\\spad{composite(p, q)} returns \\spad{h} if \\spad{p = h(q)},{} and \"failed\" no such \\spad{h} exists.")) (|subResultantGcd| (($ $ $) "\\spad{subResultantGcd(p,q)} computes the \\spad{gcd} of the polynomials \\spad{p} and \\spad{q} using the SubResultant \\spad{GCD} algorithm.")) (|order| (((|NonNegativeInteger|) $ $) "\\spad{order(p, q)} returns the largest \\spad{n} such that \\spad{q**n} divides polynomial \\spad{p} \\spadignore{i.e.} the order of \\spad{p(x)} at \\spad{q(x)=0}.")) (|elt| ((|#2| (|Fraction| $) |#2|) "\\spad{elt(a,r)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by the constant \\spad{r}.") (((|Fraction| $) (|Fraction| $) (|Fraction| $)) "\\spad{elt(a,b)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by \\spad{b}.")) (|resultant| ((|#2| $ $) "\\spad{resultant(p,q)} returns the resultant of the polynomials \\spad{p} and \\spad{q}.")) (|discriminant| ((|#2| $) "\\spad{discriminant(p)} returns the discriminant of the polynomial \\spad{p}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|) $) "\\spad{differentiate(p, d, x')} extends the \\spad{R}-derivation \\spad{d} to an extension \\spad{D} in \\spad{R[x]} where \\spad{Dx} is given by \\spad{x'},{} and returns \\spad{Dp}.")) (|pseudoRemainder| (($ $ $) "\\spad{pseudoRemainder(p,q)} = \\spad{r},{} for polynomials \\spad{p} and \\spad{q},{} returns the remainder when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|shiftLeft| (($ $ (|NonNegativeInteger|)) "\\spad{shiftLeft(p,n)} returns \\spad{p * monomial(1,n)}")) (|shiftRight| (($ $ (|NonNegativeInteger|)) "\\spad{shiftRight(p,n)} returns \\spad{monicDivide(p,monomial(1,n)).quotient}")) (|karatsubaDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ (|NonNegativeInteger|)) "\\spad{karatsubaDivide(p,n)} returns the same as \\spad{monicDivide(p,monomial(1,n))}")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicDivide(p,q)} divide the polynomial \\spad{p} by the monic polynomial \\spad{q},{} returning the pair \\spad{[quotient, remainder]}. Error: if \\spad{q} isn\\spad{'t} monic.")) (|divideExponents| (((|Union| $ "failed") $ (|NonNegativeInteger|)) "\\spad{divideExponents(p,n)} returns a new polynomial resulting from dividing all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n},{} or \"failed\" if some exponent is not exactly divisible by \\spad{n}.")) (|multiplyExponents| (($ $ (|NonNegativeInteger|)) "\\spad{multiplyExponents(p,n)} returns a new polynomial resulting from multiplying all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n}.")) (|unmakeSUP| (($ (|SparseUnivariatePolynomial| |#2|)) "\\spad{unmakeSUP(sup)} converts \\spad{sup} of type \\spadtype{SparseUnivariatePolynomial(R)} to be a member of the given type. Note: converse of makeSUP.")) (|makeSUP| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{makeSUP(p)} converts the polynomial \\spad{p} to be of type SparseUnivariatePolynomial over the same coefficients.")) (|vectorise| (((|Vector| |#2|) $ (|NonNegativeInteger|)) "\\spad{vectorise(p, n)} returns \\spad{[a0,...,a(n-1)]} where \\spad{p = a0 + a1*x + ... + a(n-1)*x**(n-1)} + higher order terms. The degree of polynomial \\spad{p} can be different from \\spad{n-1}."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#2| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-455))) (|HasCategory| |#2| (QUOTE (-559))) (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-1152)))) -(-1243 R) +((|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#2| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-455))) (|HasCategory| |#2| (QUOTE (-559))) (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-1153)))) +(-1244 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| (-559)) (-4413 |has| |#1| (-365)) (-4415 |has| |#1| (-6 -4415)) (-4412 . T) (-4411 . T) (-4414 . T)) +(((-4420 "*") |has| |#1| (-172)) (-4411 |has| |#1| (-559)) (-4414 |has| |#1| (-365)) (-4416 |has| |#1| (-6 -4416)) (-4413 . T) (-4412 . T) (-4415 . T)) NIL -(-1244 S |Coef| |Expon|) +(-1245 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 -901) (QUOTE (-1177)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1113))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -4127) (LIST (|devaluate| |#2|) (QUOTE (-1177)))))) -(-1245 |Coef| |Expon|) +((|HasCategory| |#2| (LIST (QUOTE -902) (QUOTE (-1178)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1114))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -4132) (LIST (|devaluate| |#2|) (QUOTE (-1178)))))) +(-1246 |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|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) -(((-4419 "*") |has| |#1| (-172)) (-4410 |has| |#1| (-559)) (-4411 . T) (-4412 . T) (-4414 . T)) +(((-4420 "*") |has| |#1| (-172)) (-4411 |has| |#1| (-559)) (-4412 . T) (-4413 . T) (-4415 . T)) NIL -(-1246 RC P) +(-1247 RC P) ((|constructor| (NIL "This package provides for square-free decomposition of univariate polynomials over arbitrary rings,{} \\spadignore{i.e.} a partial factorization such that each factor is a product of irreducibles with multiplicity one and the factors are pairwise relatively prime. If the ring has characteristic zero,{} the result is guaranteed to satisfy this condition. If the ring is an infinite ring of finite characteristic,{} then it may not be possible to decide when polynomials contain factors which are \\spad{p}th powers. In this case,{} the flag associated with that polynomial is set to \"nil\" (meaning that that polynomials are not guaranteed to be square-free).")) (|BumInSepFFE| (((|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|))) (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|)))) "\\spad{BumInSepFFE(f)} is a local function,{} exported only because it has multiple conditional definitions.")) (|squareFreePart| ((|#2| |#2|) "\\spad{squareFreePart(p)} returns a polynomial which has the same irreducible factors as the univariate polynomial \\spad{p},{} but each factor has multiplicity one.")) (|squareFree| (((|Factored| |#2|) |#2|) "\\spad{squareFree(p)} computes the square-free factorization of the univariate polynomial \\spad{p}. Each factor has no repeated roots,{} and the factors are pairwise relatively prime.")) (|gcd| (($ $ $) "\\spad{gcd(p,q)} computes the greatest-common-divisor of \\spad{p} and \\spad{q}."))) NIL NIL -(-1247 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) +(-1248 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) ((|constructor| (NIL "Mapping package for univariate Puiseux series. This package allows one to apply a function to the coefficients of a univariate Puiseux series.")) (|map| (((|UnivariatePuiseuxSeries| |#2| |#4| |#6|) (|Mapping| |#2| |#1|) (|UnivariatePuiseuxSeries| |#1| |#3| |#5|)) "\\spad{map(f,g(x))} applies the map \\spad{f} to the coefficients of the Puiseux series \\spad{g(x)}."))) NIL NIL -(-1248 |Coef|) +(-1249 |Coef|) ((|constructor| (NIL "\\spadtype{UnivariatePuiseuxSeriesCategory} is the category of Puiseux series in one variable.")) (|integrate| (($ $ (|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| (-559)) (-4415 |has| |#1| (-365)) (-4409 |has| |#1| (-365)) (-4411 . T) (-4412 . T) (-4414 . T)) +(((-4420 "*") |has| |#1| (-172)) (-4411 |has| |#1| (-559)) (-4416 |has| |#1| (-365)) (-4410 |has| |#1| (-365)) (-4412 . T) (-4413 . T) (-4415 . T)) NIL -(-1249 S |Coef| ULS) +(-1250 S |Coef| ULS) ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x^r)}.")) (|laurentIfCan| (((|Union| |#3| "failed") $) "\\spad{laurentIfCan(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. If this is not possible,{} \"failed\" is returned.")) (|laurent| ((|#3| $) "\\spad{laurent(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. Error: if this is not possible.")) (|degree| (((|Fraction| (|Integer|)) $) "\\spad{degree(f(x))} returns the degree of the leading term of the Puiseux series \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurentRep| ((|#3| $) "\\spad{laurentRep(f(x))} returns \\spad{g(x)} where the Puiseux series \\spad{f(x) = g(x^r)} is represented by \\spad{[r,g(x)]}.")) (|rationalPower| (((|Fraction| (|Integer|)) $) "\\spad{rationalPower(f(x))} returns \\spad{r} where the Puiseux series \\spad{f(x) = g(x^r)}.")) (|puiseux| (($ (|Fraction| (|Integer|)) |#3|) "\\spad{puiseux(r,f(x))} returns \\spad{f(x^r)}."))) NIL NIL -(-1250 |Coef| ULS) +(-1251 |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| (-559)) (-4415 |has| |#1| (-365)) (-4409 |has| |#1| (-365)) (-4411 . T) (-4412 . T) (-4414 . T)) +(((-4420 "*") |has| |#1| (-172)) (-4411 |has| |#1| (-559)) (-4416 |has| |#1| (-365)) (-4410 |has| |#1| (-365)) (-4412 . T) (-4413 . T) (-4415 . T)) NIL -(-1251 |Coef| ULS) +(-1252 |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| (-559)) (-4415 |has| |#1| (-365)) (-4409 |has| |#1| (-365)) (-4411 . T) (-4412 . T) (-4414 . T)) -((|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-172))) (-2797 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-559)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-1177)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -410) (QUOTE (-567))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -410) (QUOTE (-567))) (|devaluate| |#1|)))) (|HasCategory| (-410 (-567)) (QUOTE (-1113))) (|HasCategory| |#1| (QUOTE (-365))) (-2797 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-559)))) (-2797 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-559)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -410) (QUOTE (-567)))))) (|HasSignature| |#1| (LIST (QUOTE -4127) (LIST (|devaluate| |#1|) (QUOTE (-1177)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -410) (QUOTE (-567)))))) (-2797 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-960))) (|HasCategory| |#1| (QUOTE (-1202))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasSignature| |#1| (LIST (QUOTE -1576) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1177))))) (|HasSignature| |#1| (LIST (QUOTE -2845) (LIST (LIST (QUOTE -645) (QUOTE (-1177))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567)))))) -(-1252 |Coef| |var| |cen|) +(((-4420 "*") |has| |#1| (-172)) (-4411 |has| |#1| (-559)) (-4416 |has| |#1| (-365)) (-4410 |has| |#1| (-365)) (-4412 . T) (-4413 . T) (-4415 . T)) +((|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-172))) (-2800 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-559)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -902) (QUOTE (-1178)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -410) (QUOTE (-567))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -410) (QUOTE (-567))) (|devaluate| |#1|)))) (|HasCategory| (-410 (-567)) (QUOTE (-1114))) (|HasCategory| |#1| (QUOTE (-365))) (-2800 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-559)))) (-2800 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-559)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -410) (QUOTE (-567)))))) (|HasSignature| |#1| (LIST (QUOTE -4132) (LIST (|devaluate| |#1|) (QUOTE (-1178)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -410) (QUOTE (-567)))))) (-2800 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-961))) (|HasCategory| |#1| (QUOTE (-1203))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasSignature| |#1| (LIST (QUOTE -2416) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1178))))) (|HasSignature| |#1| (LIST (QUOTE -2847) (LIST (LIST (QUOTE -645) (QUOTE (-1178))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567)))))) +(-1253 |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| (-559)) (-4415 |has| |#1| (-365)) (-4409 |has| |#1| (-365)) (-4411 . T) (-4412 . T) (-4414 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-172))) (-2797 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-559)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-1177)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -410) (QUOTE (-567))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -410) (QUOTE (-567))) (|devaluate| |#1|)))) (|HasCategory| (-410 (-567)) (QUOTE (-1113))) (|HasCategory| |#1| (QUOTE (-365))) (-2797 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-559)))) (-2797 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-559)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -410) (QUOTE (-567)))))) (|HasSignature| |#1| (LIST (QUOTE -4127) (LIST (|devaluate| |#1|) (QUOTE (-1177)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -410) (QUOTE (-567)))))) (-2797 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-960))) (|HasCategory| |#1| (QUOTE (-1202))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasSignature| |#1| (LIST (QUOTE -1576) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1177))))) (|HasSignature| |#1| (LIST (QUOTE -2845) (LIST (LIST (QUOTE -645) (QUOTE (-1177))) (|devaluate| |#1|))))))) -(-1253 R FE |var| |cen|) +(((-4420 "*") |has| |#1| (-172)) (-4411 |has| |#1| (-559)) (-4416 |has| |#1| (-365)) (-4410 |has| |#1| (-365)) (-4412 . T) (-4413 . T) (-4415 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-172))) (-2800 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-559)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -902) (QUOTE (-1178)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -410) (QUOTE (-567))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -410) (QUOTE (-567))) (|devaluate| |#1|)))) (|HasCategory| (-410 (-567)) (QUOTE (-1114))) (|HasCategory| |#1| (QUOTE (-365))) (-2800 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-559)))) (-2800 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-559)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -410) (QUOTE (-567)))))) (|HasSignature| |#1| (LIST (QUOTE -4132) (LIST (|devaluate| |#1|) (QUOTE (-1178)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -410) (QUOTE (-567)))))) (-2800 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-961))) (|HasCategory| |#1| (QUOTE (-1203))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasSignature| |#1| (LIST (QUOTE -2416) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1178))))) (|HasSignature| |#1| (LIST (QUOTE -2847) (LIST (LIST (QUOTE -645) (QUOTE (-1178))) (|devaluate| |#1|))))))) +(-1254 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| (-1252 |#2| |#3| |#4|) (-172)) (-4410 |has| (-1252 |#2| |#3| |#4|) (-559)) (-4411 . T) (-4412 . T) (-4414 . T)) -((|HasCategory| (-1252 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| (-1252 |#2| |#3| |#4|) (QUOTE (-145))) (|HasCategory| (-1252 |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1252 |#2| |#3| |#4|) (QUOTE (-172))) (-2797 (|HasCategory| (-1252 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| (-1252 |#2| |#3| |#4|) (LIST (QUOTE -1039) (LIST (QUOTE -410) (QUOTE (-567)))))) (|HasCategory| (-1252 |#2| |#3| |#4|) (LIST (QUOTE -1039) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| (-1252 |#2| |#3| |#4|) (LIST (QUOTE -1039) (QUOTE (-567)))) (|HasCategory| (-1252 |#2| |#3| |#4|) (QUOTE (-365))) (|HasCategory| (-1252 |#2| |#3| |#4|) (QUOTE (-455))) (|HasCategory| (-1252 |#2| |#3| |#4|) (QUOTE (-559)))) -(-1254 A S) +(((-4420 "*") |has| (-1253 |#2| |#3| |#4|) (-172)) (-4411 |has| (-1253 |#2| |#3| |#4|) (-559)) (-4412 . T) (-4413 . T) (-4415 . T)) +((|HasCategory| (-1253 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| (-1253 |#2| |#3| |#4|) (QUOTE (-145))) (|HasCategory| (-1253 |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1253 |#2| |#3| |#4|) (QUOTE (-172))) (-2800 (|HasCategory| (-1253 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| (-1253 |#2| |#3| |#4|) (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567)))))) (|HasCategory| (-1253 |#2| |#3| |#4|) (LIST (QUOTE -1040) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| (-1253 |#2| |#3| |#4|) (LIST (QUOTE -1040) (QUOTE (-567)))) (|HasCategory| (-1253 |#2| |#3| |#4|) (QUOTE (-365))) (|HasCategory| (-1253 |#2| |#3| |#4|) (QUOTE (-455))) (|HasCategory| (-1253 |#2| |#3| |#4|) (QUOTE (-559)))) +(-1255 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| $) "\\spad{concat(x,u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL -((|HasAttribute| |#1| (QUOTE -4418))) -(-1255 S) +((|HasAttribute| |#1| (QUOTE -4419))) +(-1256 S) ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|Integer|)) "\\spad{split!(u,n)} splits \\spad{u} into two aggregates: \\axiom{\\spad{v} = rest(\\spad{u},{}\\spad{n})} and \\axiom{\\spad{w} = first(\\spad{u},{}\\spad{n})},{} returning \\axiom{\\spad{v}}. Note: afterwards \\axiom{rest(\\spad{u},{}\\spad{n})} returns \\axiom{empty()}.")) (|setlast!| ((|#1| $ |#1|) "\\spad{setlast!(u,x)} destructively changes the last element of \\spad{u} to \\spad{x}.")) (|setrest!| (($ $ $) "\\spad{setrest!(u,v)} destructively changes the rest of \\spad{u} to \\spad{v}.")) (|setelt| ((|#1| $ "last" |#1|) "\\spad{setelt(u,\"last\",x)} (also written: \\axiom{\\spad{u}.last \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setlast!(\\spad{u},{}\\spad{v})}.") (($ $ "rest" $) "\\spad{setelt(u,\"rest\",v)} (also written: \\axiom{\\spad{u}.rest \\spad{:=} \\spad{v}}) is equivalent to \\axiom{setrest!(\\spad{u},{}\\spad{v})}.") ((|#1| $ "first" |#1|) "\\spad{setelt(u,\"first\",x)} (also written: \\axiom{\\spad{u}.first \\spad{:=} \\spad{x}}) is equivalent to \\axiom{setfirst!(\\spad{u},{}\\spad{x})}.")) (|setfirst!| ((|#1| $ |#1|) "\\spad{setfirst!(u,x)} destructively changes the first element of a to \\spad{x}.")) (|cycleSplit!| (($ $) "\\spad{cycleSplit!(u)} splits the aggregate by dropping off the cycle. The value returned is the cycle entry,{} or nil if none exists. For example,{} if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} is the cyclic list where \\spad{v} is the head of the cycle,{} \\axiom{cycleSplit!(\\spad{w})} will drop \\spad{v} off \\spad{w} thus destructively changing \\spad{w} to \\spad{u},{} and returning \\spad{v}.")) (|concat!| (($ $ |#1|) "\\spad{concat!(u,x)} destructively adds element \\spad{x} to the end of \\spad{u}. Note: \\axiom{concat!(a,{}\\spad{x}) = setlast!(a,{}[\\spad{x}])}.") (($ $ $) "\\spad{concat!(u,v)} destructively concatenates \\spad{v} to the end of \\spad{u}. Note: \\axiom{concat!(\\spad{u},{}\\spad{v}) = setlast!(\\spad{u},{}\\spad{v})}.")) (|cycleTail| (($ $) "\\spad{cycleTail(u)} returns the last node in the cycle,{} or empty if none exists.")) (|cycleLength| (((|NonNegativeInteger|) $) "\\spad{cycleLength(u)} returns the length of a top-level cycle contained in aggregate \\spad{u},{} or 0 is \\spad{u} has no such cycle.")) (|cycleEntry| (($ $) "\\spad{cycleEntry(u)} returns the head of a top-level cycle contained in aggregate \\spad{u},{} or \\axiom{empty()} if none exists.")) (|third| ((|#1| $) "\\spad{third(u)} returns the third element of \\spad{u}. Note: \\axiom{third(\\spad{u}) = first(rest(rest(\\spad{u})))}.")) (|second| ((|#1| $) "\\spad{second(u)} returns the second element of \\spad{u}. Note: \\axiom{second(\\spad{u}) = first(rest(\\spad{u}))}.")) (|tail| (($ $) "\\spad{tail(u)} returns the last node of \\spad{u}. Note: if \\spad{u} is \\axiom{shallowlyMutable},{} \\axiom{setrest(tail(\\spad{u}),{}\\spad{v}) = concat(\\spad{u},{}\\spad{v})}.")) (|last| (($ $ (|NonNegativeInteger|)) "\\spad{last(u,n)} returns a copy of the last \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) nodes of \\spad{u}. Note: \\axiom{last(\\spad{u},{}\\spad{n})} is a list of \\spad{n} elements.") ((|#1| $) "\\spad{last(u)} resturn the last element of \\spad{u}. Note: for lists,{} \\axiom{last(\\spad{u}) = \\spad{u} . (maxIndex \\spad{u}) = \\spad{u} . (\\# \\spad{u} - 1)}.")) (|rest| (($ $ (|NonNegativeInteger|)) "\\spad{rest(u,n)} returns the \\axiom{\\spad{n}}th (\\spad{n} \\spad{>=} 0) node of \\spad{u}. Note: \\axiom{rest(\\spad{u},{}0) = \\spad{u}}.") (($ $) "\\spad{rest(u)} returns an aggregate consisting of all but the first element of \\spad{u} (equivalently,{} the next node of \\spad{u}).")) (|elt| ((|#1| $ "last") "\\spad{elt(u,\"last\")} (also written: \\axiom{\\spad{u} . last}) is equivalent to last \\spad{u}.") (($ $ "rest") "\\spad{elt(\\%,\"rest\")} (also written: \\axiom{\\spad{u}.rest}) is equivalent to \\axiom{rest \\spad{u}}.") ((|#1| $ "first") "\\spad{elt(u,\"first\")} (also written: \\axiom{\\spad{u} . first}) is equivalent to first \\spad{u}.")) (|first| (($ $ (|NonNegativeInteger|)) "\\spad{first(u,n)} returns a copy of the first \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) elements of \\spad{u}.") ((|#1| $) "\\spad{first(u)} returns the first element of \\spad{u} (equivalently,{} the value at the current node).")) (|concat| (($ |#1| $) "\\spad{concat(x,u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL NIL -(-1256 |Coef1| |Coef2| UTS1 UTS2) +(-1257 |Coef1| |Coef2| UTS1 UTS2) ((|constructor| (NIL "Mapping package for univariate Taylor series. \\indented{2}{This package allows one to apply a function to the coefficients of} \\indented{2}{a univariate Taylor series.}")) (|map| ((|#4| (|Mapping| |#2| |#1|) |#3|) "\\spad{map(f,g(x))} applies the map \\spad{f} to the coefficients of \\indented{1}{the Taylor series \\spad{g(x)}.}"))) NIL NIL -(-1257 S |Coef|) +(-1258 S |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|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 (-567)))) (|HasCategory| |#2| (QUOTE (-960))) (|HasCategory| |#2| (QUOTE (-1202))) (|HasSignature| |#2| (LIST (QUOTE -2845) (LIST (LIST (QUOTE -645) (QUOTE (-1177))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -1576) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1177))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#2| (QUOTE (-365)))) -(-1258 |Coef|) +((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-567)))) (|HasCategory| |#2| (QUOTE (-961))) (|HasCategory| |#2| (QUOTE (-1203))) (|HasSignature| |#2| (LIST (QUOTE -2847) (LIST (LIST (QUOTE -645) (QUOTE (-1178))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -2416) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1178))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#2| (QUOTE (-365)))) +(-1259 |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| (-559)) (-4411 . T) (-4412 . T) (-4414 . T)) +(((-4420 "*") |has| |#1| (-172)) (-4411 |has| |#1| (-559)) (-4412 . T) (-4413 . T) (-4415 . T)) NIL -(-1259 |Coef| |var| |cen|) +(-1260 |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| (-559)) (-4411 . T) (-4412 . T) (-4414 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (QUOTE (-559))) (-2797 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-559)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -901) (QUOTE (-1177)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-772)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-772)) (|devaluate| |#1|)))) (|HasCategory| (-772) (QUOTE (-1113))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-772))))) (|HasSignature| |#1| (LIST (QUOTE -4127) (LIST (|devaluate| |#1|) (QUOTE (-1177)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-772))))) (|HasCategory| |#1| (QUOTE (-365))) (-2797 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-960))) (|HasCategory| |#1| (QUOTE (-1202))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasSignature| |#1| (LIST (QUOTE -1576) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1177))))) (|HasSignature| |#1| (LIST (QUOTE -2845) (LIST (LIST (QUOTE -645) (QUOTE (-1177))) (|devaluate| |#1|))))))) -(-1260 |Coef| UTS) +(((-4420 "*") |has| |#1| (-172)) (-4411 |has| |#1| (-559)) (-4412 . T) (-4413 . T) (-4415 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasCategory| |#1| (QUOTE (-559))) (-2800 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-559)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -902) (QUOTE (-1178)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-772)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-772)) (|devaluate| |#1|)))) (|HasCategory| (-772) (QUOTE (-1114))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-772))))) (|HasSignature| |#1| (LIST (QUOTE -4132) (LIST (|devaluate| |#1|) (QUOTE (-1178)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-772))))) (|HasCategory| |#1| (QUOTE (-365))) (-2800 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-567)))) (|HasCategory| |#1| (QUOTE (-961))) (|HasCategory| |#1| (QUOTE (-1203))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasSignature| |#1| (LIST (QUOTE -2416) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1178))))) (|HasSignature| |#1| (LIST (QUOTE -2847) (LIST (LIST (QUOTE -645) (QUOTE (-1178))) (|devaluate| |#1|))))))) +(-1261 |Coef| UTS) ((|constructor| (NIL "\\indented{1}{This package provides Taylor series solutions to regular} linear or non-linear ordinary differential equations of arbitrary order.")) (|mpsode| (((|List| |#2|) (|List| |#1|) (|List| (|Mapping| |#2| (|List| |#2|)))) "\\spad{mpsode(r,f)} solves the system of differential equations \\spad{dy[i]/dx =f[i] [x,y[1],y[2],...,y[n]]},{} \\spad{y[i](a) = r[i]} for \\spad{i} in 1..\\spad{n}.")) (|ode| ((|#2| (|Mapping| |#2| (|List| |#2|)) (|List| |#1|)) "\\spad{ode(f,cl)} is the solution to \\spad{y<n>=f(y,y',..,y<n-1>)} such that \\spad{y<i>(a) = cl.i} for \\spad{i} in 1..\\spad{n}.")) (|ode2| ((|#2| (|Mapping| |#2| |#2| |#2|) |#1| |#1|) "\\spad{ode2(f,c0,c1)} is the solution to \\spad{y'' = f(y,y')} such that \\spad{y(a) = c0} and \\spad{y'(a) = c1}.")) (|ode1| ((|#2| (|Mapping| |#2| |#2|) |#1|) "\\spad{ode1(f,c)} is the solution to \\spad{y' = f(y)} such that \\spad{y(a) = c}.")) (|fixedPointExquo| ((|#2| |#2| |#2|) "\\spad{fixedPointExquo(f,g)} computes the exact quotient of \\spad{f} and \\spad{g} using a fixed point computation.")) (|stFuncN| (((|Mapping| (|Stream| |#1|) (|List| (|Stream| |#1|))) (|Mapping| |#2| (|List| |#2|))) "\\spad{stFuncN(f)} is a local function xported due to compiler problem. This function is of no interest to the top-level user.")) (|stFunc2| (((|Mapping| (|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) (|Mapping| |#2| |#2| |#2|)) "\\spad{stFunc2(f)} is a local function exported due to compiler problem. This function is of no interest to the top-level user.")) (|stFunc1| (((|Mapping| (|Stream| |#1|) (|Stream| |#1|)) (|Mapping| |#2| |#2|)) "\\spad{stFunc1(f)} is a local function exported due to compiler problem. This function is of no interest to the top-level user."))) NIL NIL -(-1261 -3867 UP L UTS) +(-1262 -3879 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 (-559)))) -(-1262) +(-1263) ((|constructor| (NIL "The category of domains that act like unions. UnionType,{} like Type or Category,{} acts mostly as a take that communicates `union-like' intended semantics to the compiler. A domain \\spad{D} that satifies UnionType should provide definitions for `case' operators,{} with corresponding `autoCoerce' operators."))) NIL NIL -(-1263 |sym|) +(-1264 |sym|) ((|constructor| (NIL "This domain implements variables")) (|variable| (((|Symbol|)) "\\spad{variable()} returns the symbol")) (|coerce| (((|Symbol|) $) "\\spad{coerce(x)} returns the symbol"))) NIL NIL -(-1264 S R) +(-1265 S R) ((|constructor| (NIL "\\spadtype{VectorCategory} represents the type of vector like objects,{} \\spadignore{i.e.} finite sequences indexed by some finite segment of the integers. The operations available on vectors depend on the structure of the underlying components. Many operations from the component domain are defined for vectors componentwise. It can by assumed that extraction or updating components can be done in constant time.")) (|magnitude| ((|#2| $) "\\spad{magnitude(v)} computes the sqrt(dot(\\spad{v},{}\\spad{v})),{} \\spadignore{i.e.} the length")) (|length| ((|#2| $) "\\spad{length(v)} computes the sqrt(dot(\\spad{v},{}\\spad{v})),{} \\spadignore{i.e.} the magnitude")) (|cross| (($ $ $) "vectorProduct(\\spad{u},{}\\spad{v}) constructs the cross product of \\spad{u} and \\spad{v}. Error: if \\spad{u} and \\spad{v} are not of length 3.")) (|outerProduct| (((|Matrix| |#2|) $ $) "\\spad{outerProduct(u,v)} constructs the matrix whose (\\spad{i},{}\\spad{j})\\spad{'}th element is \\spad{u}(\\spad{i})\\spad{*v}(\\spad{j}).")) (|dot| ((|#2| $ $) "\\spad{dot(x,y)} computes the inner product of the two vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.")) (* (($ $ |#2|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#2| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.") (($ (|Integer|) $) "\\spad{n * y} multiplies each component of the vector \\spad{y} by the integer \\spad{n}.")) (- (($ $ $) "\\spad{x - y} returns the component-wise difference of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.") (($ $) "\\spad{-x} negates all components of the vector \\spad{x}.")) (|zero| (($ (|NonNegativeInteger|)) "\\spad{zero(n)} creates a zero vector of length \\spad{n}.")) (+ (($ $ $) "\\spad{x + y} returns the component-wise sum of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length."))) NIL -((|HasCategory| |#2| (QUOTE (-1003))) (|HasCategory| |#2| (QUOTE (-1050))) (|HasCategory| |#2| (QUOTE (-727))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25)))) -(-1265 R) +((|HasCategory| |#2| (QUOTE (-1004))) (|HasCategory| |#2| (QUOTE (-1051))) (|HasCategory| |#2| (QUOTE (-727))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25)))) +(-1266 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}.")) (+ (($ $ $) "\\spad{x + y} returns the component-wise sum of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length."))) -((-4418 . T) (-4417 . T)) +((-4419 . T) (-4418 . T)) NIL -(-1266 A B) +(-1267 A B) ((|constructor| (NIL "\\indented{2}{This package provides operations which all take as arguments} vectors of elements of some type \\spad{A} and functions from \\spad{A} to another of type \\spad{B}. The operations all iterate over their vector argument and either return a value of type \\spad{B} or a vector over \\spad{B}.")) (|map| (((|Union| (|Vector| |#2|) "failed") (|Mapping| (|Union| |#2| "failed") |#1|) (|Vector| |#1|)) "\\spad{map(f, v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values or \\spad{\"failed\"}.") (((|Vector| |#2|) (|Mapping| |#2| |#1|) (|Vector| |#1|)) "\\spad{map(f, v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{reduce(func,vec,ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if \\spad{vec} is empty.")) (|scan| (((|Vector| |#2|) (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{scan(func,vec,ident)} creates a new vector whose elements are the result of applying reduce to the binary function \\spad{func},{} increasing initial subsequences of the vector \\spad{vec},{} and the element \\spad{ident}."))) NIL NIL -(-1267 R) +(-1268 R) ((|constructor| (NIL "This type represents vector like objects with varying lengths and indexed by a finite segment of integers starting at 1.")) (|vector| (($ (|List| |#1|)) "\\spad{vector(l)} converts the list \\spad{l} to a vector."))) -((-4418 . T) (-4417 . T)) -((-2797 (-12 (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1101))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-1101))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539)))) (-2797 (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-1101)))) (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| (-567) (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-1101))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-727))) (|HasCategory| |#1| (QUOTE (-1050))) (-12 (|HasCategory| |#1| (QUOTE (-1003))) (|HasCategory| |#1| (QUOTE (-1050)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863)))) (-12 (|HasCategory| |#1| (QUOTE (-1101))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) -(-1268) +((-4419 . T) (-4418 . T)) +((-2800 (-12 (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2800 (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863))))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-539)))) (-2800 (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-1102)))) (|HasCategory| |#1| (QUOTE (-851))) (|HasCategory| (-567) (QUOTE (-851))) (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-727))) (|HasCategory| |#1| (QUOTE (-1051))) (-12 (|HasCategory| |#1| (QUOTE (-1004))) (|HasCategory| |#1| (QUOTE (-1051)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-863)))) (-12 (|HasCategory| |#1| (QUOTE (-1102))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) +(-1269) ((|constructor| (NIL "TwoDimensionalViewport creates viewports to display graphs.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(v)} returns the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport} as output of the domain \\spadtype{OutputForm}.")) (|key| (((|Integer|) $) "\\spad{key(v)} returns the process ID number of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport}.")) (|reset| (((|Void|) $) "\\spad{reset(v)} sets the current state of the graph characteristics of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} back to their initial settings.")) (|write| (((|String|) $ (|String|) (|List| (|String|))) "\\spad{write(v,s,lf)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v} and the optional file types indicated by the list \\spad{lf}.") (((|String|) $ (|String|) (|String|)) "\\spad{write(v,s,f)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v} and an optional file type \\spad{f}.") (((|String|) $ (|String|)) "\\spad{write(v,s)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v}.")) (|resize| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{resize(v,w,h)} displays the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with a width of \\spad{w} and a height of \\spad{h},{} keeping the upper left-hand corner position unchanged.")) (|update| (((|Void|) $ (|GraphImage|) (|PositiveInteger|)) "\\spad{update(v,gr,n)} drops the graph \\spad{gr} in slot \\spad{n} of viewport \\spad{v}. The graph \\spad{gr} must have been transmitted already and acquired an integer key.")) (|move| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{move(v,x,y)} displays the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the upper left-hand corner of the viewport window at the screen coordinate position \\spad{x},{} \\spad{y}.")) (|show| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{show(v,n,s)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the graph if \\spad{s} is \"off\".")) (|translate| (((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|)) "\\spad{translate(v,n,dx,dy)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} translated by \\spad{dx} in the \\spad{x}-coordinate direction from the center of the viewport,{} and by \\spad{dy} in the \\spad{y}-coordinate direction from the center. Setting \\spad{dx} and \\spad{dy} to \\spad{0} places the center of the graph at the center of the viewport.")) (|scale| (((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|)) "\\spad{scale(v,n,sx,sy)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} scaled by the factor \\spad{sx} in the \\spad{x}-coordinate direction and by the factor \\spad{sy} in the \\spad{y}-coordinate direction.")) (|dimensions| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{dimensions(v,x,y,width,height)} sets the position of the upper left-hand corner of the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} to the window coordinate \\spad{x},{} \\spad{y},{} and sets the dimensions of the window to that of \\spad{width},{} \\spad{height}. The new dimensions are not displayed until the function \\spadfun{makeViewport2D} is executed again for \\spad{v}.")) (|close| (((|Void|) $) "\\spad{close(v)} closes the viewport window of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and terminates the corresponding process ID.")) (|controlPanel| (((|Void|) $ (|String|)) "\\spad{controlPanel(v,s)} displays the control panel of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or hides the control panel if \\spad{s} is \"off\".")) (|connect| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{connect(v,n,s)} displays the lines connecting the graph points in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the lines if \\spad{s} is \"off\".")) (|region| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{region(v,n,s)} displays the bounding box of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the bounding box if \\spad{s} is \"off\".")) (|points| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{points(v,n,s)} displays the points of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the points if \\spad{s} is \"off\".")) (|units| (((|Void|) $ (|PositiveInteger|) (|Palette|)) "\\spad{units(v,n,c)} displays the units of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the units color set to the given palette color \\spad{c}.") (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{units(v,n,s)} displays the units of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the units if \\spad{s} is \"off\".")) (|axes| (((|Void|) $ (|PositiveInteger|) (|Palette|)) "\\spad{axes(v,n,c)} displays the axes of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the axes color set to the given palette color \\spad{c}.") (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{axes(v,n,s)} displays the axes of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the axes if \\spad{s} is \"off\".")) (|getGraph| (((|GraphImage|) $ (|PositiveInteger|)) "\\spad{getGraph(v,n)} returns the graph which is of the domain \\spadtype{GraphImage} which is located in graph field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of the domain \\spadtype{TwoDimensionalViewport}.")) (|putGraph| (((|Void|) $ (|GraphImage|) (|PositiveInteger|)) "\\spad{putGraph(v,gi,n)} sets the graph field indicated by \\spad{n},{} of the indicated two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} to be the graph,{} \\spad{gi} of domain \\spadtype{GraphImage}. The contents of viewport,{} \\spad{v},{} will contain \\spad{gi} when the function \\spadfun{makeViewport2D} is called to create the an updated viewport \\spad{v}.")) (|title| (((|Void|) $ (|String|)) "\\spad{title(v,s)} changes the title which is shown in the two-dimensional viewport window,{} \\spad{v} of domain \\spadtype{TwoDimensionalViewport}.")) (|graphs| (((|Vector| (|Union| (|GraphImage|) "undefined")) $) "\\spad{graphs(v)} returns a vector,{} or list,{} which is a union of all the graphs,{} of the domain \\spadtype{GraphImage},{} which are allocated for the two-dimensional viewport,{} \\spad{v},{} of domain \\spadtype{TwoDimensionalViewport}. Those graphs which have no data are labeled \"undefined\",{} otherwise their contents are shown.")) (|graphStates| (((|Vector| (|Record| (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)) (|:| |points| (|Integer|)) (|:| |connect| (|Integer|)) (|:| |spline| (|Integer|)) (|:| |axes| (|Integer|)) (|:| |axesColor| (|Palette|)) (|:| |units| (|Integer|)) (|:| |unitsColor| (|Palette|)) (|:| |showing| (|Integer|)))) $) "\\spad{graphStates(v)} returns and shows a listing of a record containing the current state of the characteristics of each of the ten graph records in the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport}.")) (|graphState| (((|Void|) $ (|PositiveInteger|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Palette|) (|Integer|) (|Palette|) (|Integer|)) "\\spad{graphState(v,num,sX,sY,dX,dY,pts,lns,box,axes,axesC,un,unC,cP)} sets the state of the characteristics for the graph indicated by \\spad{num} in the given two-dimensional viewport \\spad{v},{} of domain \\spadtype{TwoDimensionalViewport},{} to the values given as parameters. The scaling of the graph in the \\spad{x} and \\spad{y} component directions is set to be \\spad{sX} and \\spad{sY}; the window translation in the \\spad{x} and \\spad{y} component directions is set to be \\spad{dX} and \\spad{dY}; The graph points,{} lines,{} bounding \\spad{box},{} \\spad{axes},{} or units will be shown in the viewport if their given parameters \\spad{pts},{} \\spad{lns},{} \\spad{box},{} \\spad{axes} or \\spad{un} are set to be \\spad{1},{} but will not be shown if they are set to \\spad{0}. The color of the \\spad{axes} and the color of the units are indicated by the palette colors \\spad{axesC} and \\spad{unC} respectively. To display the control panel when the viewport window is displayed,{} set \\spad{cP} to \\spad{1},{} otherwise set it to \\spad{0}.")) (|options| (($ $ (|List| (|DrawOption|))) "\\spad{options(v,lopt)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and returns \\spad{v} with it\\spad{'s} draw options modified to be those which are indicated in the given list,{} \\spad{lopt} of domain \\spadtype{DrawOption}.") (((|List| (|DrawOption|)) $) "\\spad{options(v)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and returns a list containing the draw options from the domain \\spadtype{DrawOption} for \\spad{v}.")) (|makeViewport2D| (($ (|GraphImage|) (|List| (|DrawOption|))) "\\spad{makeViewport2D(gi,lopt)} creates and displays a viewport window of the domain \\spadtype{TwoDimensionalViewport} whose graph field is assigned to be the given graph,{} \\spad{gi},{} of domain \\spadtype{GraphImage},{} and whose options field is set to be the list of options,{} \\spad{lopt} of domain \\spadtype{DrawOption}.") (($ $) "\\spad{makeViewport2D(v)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and displays a viewport window on the screen which contains the contents of \\spad{v}.")) (|viewport2D| (($) "\\spad{viewport2D()} returns an undefined two-dimensional viewport of the domain \\spadtype{TwoDimensionalViewport} whose contents are empty.")) (|getPickedPoints| (((|List| (|Point| (|DoubleFloat|))) $) "\\spad{getPickedPoints(x)} returns a list of small floats for the points the user interactively picked on the viewport for full integration into the system,{} some design issues need to be addressed: \\spadignore{e.g.} how to go through the GraphImage interface,{} how to default to graphs,{} etc."))) NIL NIL -(-1269) +(-1270) ((|key| (((|Integer|) $) "\\spad{key(v)} returns the process ID number of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|close| (((|Void|) $) "\\spad{close(v)} closes the viewport window of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} and terminates the corresponding process ID.")) (|write| (((|String|) $ (|String|) (|List| (|String|))) "\\spad{write(v,s,lf)} takes the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data file for \\spad{v} and the optional file types indicated by the list \\spad{lf}.") (((|String|) $ (|String|) (|String|)) "\\spad{write(v,s,f)} takes the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data file for \\spad{v} and an optional file type \\spad{f}.") (((|String|) $ (|String|)) "\\spad{write(v,s)} takes the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data file for \\spad{v}.")) (|colorDef| (((|Void|) $ (|Color|) (|Color|)) "\\spad{colorDef(v,c1,c2)} sets the range of colors along the colormap so that the lower end of the colormap is defined by \\spad{c1} and the top end of the colormap is defined by \\spad{c2},{} for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|reset| (((|Void|) $) "\\spad{reset(v)} sets the current state of the graph characteristics of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} back to their initial settings.")) (|intensity| (((|Void|) $ (|Float|)) "\\spad{intensity(v,i)} sets the intensity of the light source to \\spad{i},{} for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|lighting| (((|Void|) $ (|Float|) (|Float|) (|Float|)) "\\spad{lighting(v,x,y,z)} sets the position of the light source to the coordinates \\spad{x},{} \\spad{y},{} and \\spad{z} and displays the graph for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|clipSurface| (((|Void|) $ (|String|)) "\\spad{clipSurface(v,s)} displays the graph with the specified clipping region removed if \\spad{s} is \"on\",{} or displays the graph without clipping implemented if \\spad{s} is \"off\",{} for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|showClipRegion| (((|Void|) $ (|String|)) "\\spad{showClipRegion(v,s)} displays the clipping region of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the region if \\spad{s} is \"off\".")) (|showRegion| (((|Void|) $ (|String|)) "\\spad{showRegion(v,s)} displays the bounding box of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the box if \\spad{s} is \"off\".")) (|hitherPlane| (((|Void|) $ (|Float|)) "\\spad{hitherPlane(v,h)} sets the hither clipping plane of the graph to \\spad{h},{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|eyeDistance| (((|Void|) $ (|Float|)) "\\spad{eyeDistance(v,d)} sets the distance of the observer from the center of the graph to \\spad{d},{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|perspective| (((|Void|) $ (|String|)) "\\spad{perspective(v,s)} displays the graph in perspective if \\spad{s} is \"on\",{} or does not display perspective if \\spad{s} is \"off\" for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|translate| (((|Void|) $ (|Float|) (|Float|)) "\\spad{translate(v,dx,dy)} sets the horizontal viewport offset to \\spad{dx} and the vertical viewport offset to \\spad{dy},{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|zoom| (((|Void|) $ (|Float|) (|Float|) (|Float|)) "\\spad{zoom(v,sx,sy,sz)} sets the graph scaling factors for the \\spad{x}-coordinate axis to \\spad{sx},{} the \\spad{y}-coordinate axis to \\spad{sy} and the \\spad{z}-coordinate axis to \\spad{sz} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.") (((|Void|) $ (|Float|)) "\\spad{zoom(v,s)} sets the graph scaling factor to \\spad{s},{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|rotate| (((|Void|) $ (|Integer|) (|Integer|)) "\\spad{rotate(v,th,phi)} rotates the graph to the longitudinal view angle \\spad{th} degrees and the latitudinal view angle \\spad{phi} degrees for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}. The new rotation position is not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.") (((|Void|) $ (|Float|) (|Float|)) "\\spad{rotate(v,th,phi)} rotates the graph to the longitudinal view angle \\spad{th} radians and the latitudinal view angle \\spad{phi} radians for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|drawStyle| (((|Void|) $ (|String|)) "\\spad{drawStyle(v,s)} displays the surface for the given three-dimensional viewport \\spad{v} which is of domain \\spadtype{ThreeDimensionalViewport} in the style of drawing indicated by \\spad{s}. If \\spad{s} is not a valid drawing style the style is wireframe by default. Possible styles are \\spad{\"shade\"},{} \\spad{\"solid\"} or \\spad{\"opaque\"},{} \\spad{\"smooth\"},{} and \\spad{\"wireMesh\"}.")) (|outlineRender| (((|Void|) $ (|String|)) "\\spad{outlineRender(v,s)} displays the polygon outline showing either triangularized surface or a quadrilateral surface outline depending on the whether the \\spadfun{diagonals} function has been set,{} for the given three-dimensional viewport \\spad{v} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the polygon outline if \\spad{s} is \"off\".")) (|diagonals| (((|Void|) $ (|String|)) "\\spad{diagonals(v,s)} displays the diagonals of the polygon outline showing a triangularized surface instead of a quadrilateral surface outline,{} for the given three-dimensional viewport \\spad{v} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the diagonals if \\spad{s} is \"off\".")) (|axes| (((|Void|) $ (|String|)) "\\spad{axes(v,s)} displays the axes of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the axes if \\spad{s} is \"off\".")) (|controlPanel| (((|Void|) $ (|String|)) "\\spad{controlPanel(v,s)} displays the control panel of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or hides the control panel if \\spad{s} is \"off\".")) (|viewpoint| (((|Void|) $ (|Float|) (|Float|) (|Float|)) "\\spad{viewpoint(v,rotx,roty,rotz)} sets the rotation about the \\spad{x}-axis to be \\spad{rotx} radians,{} sets the rotation about the \\spad{y}-axis to be \\spad{roty} radians,{} and sets the rotation about the \\spad{z}-axis to be \\spad{rotz} radians,{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport} and displays \\spad{v} with the new view position.") (((|Void|) $ (|Float|) (|Float|)) "\\spad{viewpoint(v,th,phi)} sets the longitudinal view angle to \\spad{th} radians and the latitudinal view angle to \\spad{phi} radians for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}. The new viewpoint position is not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.") (((|Void|) $ (|Integer|) (|Integer|) (|Float|) (|Float|) (|Float|)) "\\spad{viewpoint(v,th,phi,s,dx,dy)} sets the longitudinal view angle to \\spad{th} degrees,{} the latitudinal view angle to \\spad{phi} degrees,{} the scale factor to \\spad{s},{} the horizontal viewport offset to \\spad{dx},{} and the vertical viewport offset to \\spad{dy} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}. The new viewpoint position is not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.") (((|Void|) $ (|Record| (|:| |theta| (|DoubleFloat|)) (|:| |phi| (|DoubleFloat|)) (|:| |scale| (|DoubleFloat|)) (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |scaleZ| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)))) "\\spad{viewpoint(v,viewpt)} sets the viewpoint for the viewport. The viewport record consists of the latitudal and longitudal angles,{} the zoom factor,{} the \\spad{X},{} \\spad{Y},{} and \\spad{Z} scales,{} and the \\spad{X} and \\spad{Y} displacements.") (((|Record| (|:| |theta| (|DoubleFloat|)) (|:| |phi| (|DoubleFloat|)) (|:| |scale| (|DoubleFloat|)) (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |scaleZ| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|))) $) "\\spad{viewpoint(v)} returns the current viewpoint setting of the given viewport,{} \\spad{v}. This function is useful in the situation where the user has created a viewport,{} proceeded to interact with it via the control panel and desires to save the values of the viewpoint as the default settings for another viewport to be created using the system.") (((|Void|) $ (|Float|) (|Float|) (|Float|) (|Float|) (|Float|)) "\\spad{viewpoint(v,th,phi,s,dx,dy)} sets the longitudinal view angle to \\spad{th} radians,{} the latitudinal view angle to \\spad{phi} radians,{} the scale factor to \\spad{s},{} the horizontal viewport offset to \\spad{dx},{} and the vertical viewport offset to \\spad{dy} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}. The new viewpoint position is not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.")) (|dimensions| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{dimensions(v,x,y,width,height)} sets the position of the upper left-hand corner of the three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} to the window coordinate \\spad{x},{} \\spad{y},{} and sets the dimensions of the window to that of \\spad{width},{} \\spad{height}. The new dimensions are not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.")) (|title| (((|Void|) $ (|String|)) "\\spad{title(v,s)} changes the title which is shown in the three-dimensional viewport window,{} \\spad{v} of domain \\spadtype{ThreeDimensionalViewport}.")) (|resize| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{resize(v,w,h)} displays the three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} with a width of \\spad{w} and a height of \\spad{h},{} keeping the upper left-hand corner position unchanged.")) (|move| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{move(v,x,y)} displays the three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} with the upper left-hand corner of the viewport window at the screen coordinate position \\spad{x},{} \\spad{y}.")) (|options| (($ $ (|List| (|DrawOption|))) "\\spad{options(v,lopt)} takes the viewport,{} \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport} and sets the draw options being used by \\spad{v} to those indicated in the list,{} \\spad{lopt},{} which is a list of options from the domain \\spad{DrawOption}.") (((|List| (|DrawOption|)) $) "\\spad{options(v)} takes the viewport,{} \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport} and returns a list of all the draw options from the domain \\spad{DrawOption} which are being used by \\spad{v}.")) (|modifyPointData| (((|Void|) $ (|NonNegativeInteger|) (|Point| (|DoubleFloat|))) "\\spad{modifyPointData(v,ind,pt)} takes the viewport,{} \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport},{} and places the data point,{} \\spad{pt} into the list of points database of \\spad{v} at the index location given by \\spad{ind}.")) (|subspace| (($ $ (|ThreeSpace| (|DoubleFloat|))) "\\spad{subspace(v,sp)} places the contents of the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport},{} in the subspace \\spad{sp},{} which is of the domain \\spad{ThreeSpace}.") (((|ThreeSpace| (|DoubleFloat|)) $) "\\spad{subspace(v)} returns the contents of the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport},{} as a subspace of the domain \\spad{ThreeSpace}.")) (|makeViewport3D| (($ (|ThreeSpace| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{makeViewport3D(sp,lopt)} takes the given space,{} \\spad{sp} which is of the domain \\spadtype{ThreeSpace} and displays a viewport window on the screen which contains the contents of \\spad{sp},{} and whose draw options are indicated by the list \\spad{lopt},{} which is a list of options from the domain \\spad{DrawOption}.") (($ (|ThreeSpace| (|DoubleFloat|)) (|String|)) "\\spad{makeViewport3D(sp,s)} takes the given space,{} \\spad{sp} which is of the domain \\spadtype{ThreeSpace} and displays a viewport window on the screen which contains the contents of \\spad{sp},{} and whose title is given by \\spad{s}.") (($ $) "\\spad{makeViewport3D(v)} takes the given three-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{ThreeDimensionalViewport} and displays a viewport window on the screen which contains the contents of \\spad{v}.")) (|viewport3D| (($) "\\spad{viewport3D()} returns an undefined three-dimensional viewport of the domain \\spadtype{ThreeDimensionalViewport} whose contents are empty.")) (|viewDeltaYDefault| (((|Float|) (|Float|)) "\\spad{viewDeltaYDefault(dy)} sets the current default vertical offset from the center of the viewport window to be \\spad{dy} and returns \\spad{dy}.") (((|Float|)) "\\spad{viewDeltaYDefault()} returns the current default vertical offset from the center of the viewport window.")) (|viewDeltaXDefault| (((|Float|) (|Float|)) "\\spad{viewDeltaXDefault(dx)} sets the current default horizontal offset from the center of the viewport window to be \\spad{dx} and returns \\spad{dx}.") (((|Float|)) "\\spad{viewDeltaXDefault()} returns the current default horizontal offset from the center of the viewport window.")) (|viewZoomDefault| (((|Float|) (|Float|)) "\\spad{viewZoomDefault(s)} sets the current default graph scaling value to \\spad{s} and returns \\spad{s}.") (((|Float|)) "\\spad{viewZoomDefault()} returns the current default graph scaling value.")) (|viewPhiDefault| (((|Float|) (|Float|)) "\\spad{viewPhiDefault(p)} sets the current default latitudinal view angle in radians to the value \\spad{p} and returns \\spad{p}.") (((|Float|)) "\\spad{viewPhiDefault()} returns the current default latitudinal view angle in radians.")) (|viewThetaDefault| (((|Float|) (|Float|)) "\\spad{viewThetaDefault(t)} sets the current default longitudinal view angle in radians to the value \\spad{t} and returns \\spad{t}.") (((|Float|)) "\\spad{viewThetaDefault()} returns the current default longitudinal view angle in radians."))) NIL NIL -(-1270) +(-1271) ((|constructor| (NIL "ViewportDefaultsPackage describes default and user definable values for graphics")) (|tubeRadiusDefault| (((|DoubleFloat|)) "\\spad{tubeRadiusDefault()} returns the radius used for a 3D tube plot.") (((|DoubleFloat|) (|Float|)) "\\spad{tubeRadiusDefault(r)} sets the default radius for a 3D tube plot to \\spad{r}.")) (|tubePointsDefault| (((|PositiveInteger|)) "\\spad{tubePointsDefault()} returns the number of points to be used when creating the circle to be used in creating a 3D tube plot.") (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{tubePointsDefault(i)} sets the number of points to use when creating the circle to be used in creating a 3D tube plot to \\spad{i}.")) (|var2StepsDefault| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{var2StepsDefault(i)} sets the number of steps to take when creating a 3D mesh in the direction of the first defined free variable to \\spad{i} (a free variable is considered defined when its range is specified (\\spadignore{e.g.} \\spad{x=0}..10)).") (((|PositiveInteger|)) "\\spad{var2StepsDefault()} is the current setting for the number of steps to take when creating a 3D mesh in the direction of the first defined free variable (a free variable is considered defined when its range is specified (\\spadignore{e.g.} \\spad{x=0}..10)).")) (|var1StepsDefault| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{var1StepsDefault(i)} sets the number of steps to take when creating a 3D mesh in the direction of the first defined free variable to \\spad{i} (a free variable is considered defined when its range is specified (\\spadignore{e.g.} \\spad{x=0}..10)).") (((|PositiveInteger|)) "\\spad{var1StepsDefault()} is the current setting for the number of steps to take when creating a 3D mesh in the direction of the first defined free variable (a free variable is considered defined when its range is specified (\\spadignore{e.g.} \\spad{x=0}..10)).")) (|viewWriteAvailable| (((|List| (|String|))) "\\spad{viewWriteAvailable()} returns a list of available methods for writing,{} such as BITMAP,{} POSTSCRIPT,{} etc.")) (|viewWriteDefault| (((|List| (|String|)) (|List| (|String|))) "\\spad{viewWriteDefault(l)} sets the default list of things to write in a viewport data file to the strings in \\spad{l}; a viewAlone file is always genereated.") (((|List| (|String|))) "\\spad{viewWriteDefault()} returns the list of things to write in a viewport data file; a viewAlone file is always generated.")) (|viewDefaults| (((|Void|)) "\\spad{viewDefaults()} resets all the default graphics settings.")) (|viewSizeDefault| (((|List| (|PositiveInteger|)) (|List| (|PositiveInteger|))) "\\spad{viewSizeDefault([w,h])} sets the default viewport width to \\spad{w} and height to \\spad{h}.") (((|List| (|PositiveInteger|))) "\\spad{viewSizeDefault()} returns the default viewport width and height.")) (|viewPosDefault| (((|List| (|NonNegativeInteger|)) (|List| (|NonNegativeInteger|))) "\\spad{viewPosDefault([x,y])} sets the default \\spad{X} and \\spad{Y} position of a viewport window unless overriden explicityly,{} newly created viewports will have th \\spad{X} and \\spad{Y} coordinates \\spad{x},{} \\spad{y}.") (((|List| (|NonNegativeInteger|))) "\\spad{viewPosDefault()} returns the default \\spad{X} and \\spad{Y} position of a viewport window unless overriden explicityly,{} newly created viewports will have this \\spad{X} and \\spad{Y} coordinate.")) (|pointSizeDefault| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{pointSizeDefault(i)} sets the default size of the points in a 2D viewport to \\spad{i}.") (((|PositiveInteger|)) "\\spad{pointSizeDefault()} returns the default size of the points in a 2D viewport.")) (|unitsColorDefault| (((|Palette|) (|Palette|)) "\\spad{unitsColorDefault(p)} sets the default color of the unit ticks in a 2D viewport to the palette \\spad{p}.") (((|Palette|)) "\\spad{unitsColorDefault()} returns the default color of the unit ticks in a 2D viewport.")) (|axesColorDefault| (((|Palette|) (|Palette|)) "\\spad{axesColorDefault(p)} sets the default color of the axes in a 2D viewport to the palette \\spad{p}.") (((|Palette|)) "\\spad{axesColorDefault()} returns the default color of the axes in a 2D viewport.")) (|lineColorDefault| (((|Palette|) (|Palette|)) "\\spad{lineColorDefault(p)} sets the default color of lines connecting points in a 2D viewport to the palette \\spad{p}.") (((|Palette|)) "\\spad{lineColorDefault()} returns the default color of lines connecting points in a 2D viewport.")) (|pointColorDefault| (((|Palette|) (|Palette|)) "\\spad{pointColorDefault(p)} sets the default color of points in a 2D viewport to the palette \\spad{p}.") (((|Palette|)) "\\spad{pointColorDefault()} returns the default color of points in a 2D viewport."))) NIL NIL -(-1271) +(-1272) ((|constructor| (NIL "ViewportPackage provides functions for creating GraphImages and TwoDimensionalViewports from lists of lists of points.")) (|coerce| (((|TwoDimensionalViewport|) (|GraphImage|)) "\\spad{coerce(gi)} converts the indicated \\spadtype{GraphImage},{} \\spad{gi},{} into the \\spadtype{TwoDimensionalViewport} form.")) (|drawCurves| (((|TwoDimensionalViewport|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|DrawOption|))) "\\spad{drawCurves([[p0],[p1],...,[pn]],[options])} creates a \\spadtype{TwoDimensionalViewport} from the list of lists of points,{} \\spad{p0} throught \\spad{pn},{} using the options specified in the list \\spad{options}.") (((|TwoDimensionalViewport|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|Palette|) (|Palette|) (|PositiveInteger|) (|List| (|DrawOption|))) "\\spad{drawCurves([[p0],[p1],...,[pn]],ptColor,lineColor,ptSize,[options])} creates a \\spadtype{TwoDimensionalViewport} from the list of lists of points,{} \\spad{p0} throught \\spad{pn},{} using the options specified in the list \\spad{options}. The point color is specified by \\spad{ptColor},{} the line color is specified by \\spad{lineColor},{} and the point size is specified by \\spad{ptSize}.")) (|graphCurves| (((|GraphImage|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|DrawOption|))) "\\spad{graphCurves([[p0],[p1],...,[pn]],[options])} creates a \\spadtype{GraphImage} from the list of lists of points,{} \\spad{p0} throught \\spad{pn},{} using the options specified in the list \\spad{options}.") (((|GraphImage|) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{graphCurves([[p0],[p1],...,[pn]])} creates a \\spadtype{GraphImage} from the list of lists of points indicated by \\spad{p0} through \\spad{pn}.") (((|GraphImage|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|Palette|) (|Palette|) (|PositiveInteger|) (|List| (|DrawOption|))) "\\spad{graphCurves([[p0],[p1],...,[pn]],ptColor,lineColor,ptSize,[options])} creates a \\spadtype{GraphImage} from the list of lists of points,{} \\spad{p0} throught \\spad{pn},{} using the options specified in the list \\spad{options}. The graph point color is specified by \\spad{ptColor},{} the graph line color is specified by \\spad{lineColor},{} and the size of the points is specified by \\spad{ptSize}."))) NIL NIL -(-1272) +(-1273) ((|constructor| (NIL "This type is used when no value is needed,{} \\spadignore{e.g.} in the \\spad{then} part of a one armed \\spad{if}. All values can be coerced to type Void. Once a value has been coerced to Void,{} it cannot be recovered.")) (|void| (($) "\\spad{void()} produces a void object."))) NIL NIL -(-1273 A S) +(-1274 A S) ((|constructor| (NIL "Vector Spaces (not necessarily finite dimensional) over a field.")) (|dimension| (((|CardinalNumber|)) "\\spad{dimension()} returns the dimensionality of the vector space.")) (/ (($ $ |#2|) "\\spad{x/y} divides the vector \\spad{x} by the scalar \\spad{y}."))) NIL NIL -(-1274 S) +(-1275 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)) +((-4413 . T) (-4412 . T)) NIL -(-1275 R) +(-1276 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 -(-1276 K R UP -3867) +(-1277 K R UP -3879) ((|constructor| (NIL "In this package \\spad{K} is a finite field,{} \\spad{R} is a ring of univariate polynomials over \\spad{K},{} and \\spad{F} is a framed algebra over \\spad{R}. The package provides a function to compute the integral closure of \\spad{R} in the quotient field of \\spad{F} as well as a function to compute a \"local integral basis\" at a specific prime.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) |#2|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the integral closure of \\spad{R} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}."))) NIL NIL -(-1277) +(-1278) ((|constructor| (NIL "This domain represents the syntax of a `where' expression.")) (|qualifier| (((|SpadAst|) $) "\\spad{qualifier(e)} returns the qualifier of the expression `e'.")) (|mainExpression| (((|SpadAst|) $) "\\spad{mainExpression(e)} returns the main expression of the `where' expression `e'."))) NIL NIL -(-1278) +(-1279) ((|constructor| (NIL "This domain represents the `while' iterator syntax.")) (|condition| (((|SpadAst|) $) "\\spad{condition(i)} returns the condition of the while iterator `i'."))) NIL NIL -(-1279 R |VarSet| E P |vl| |wl| |wtlevel|) +(-1280 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)) +((-4413 |has| |#1| (-172)) (-4412 |has| |#1| (-172)) (-4415 . T)) ((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365)))) -(-1280 R E V P) +(-1281 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)) -((-12 (|HasCategory| |#4| (QUOTE (-1101))) (|HasCategory| |#4| (LIST (QUOTE -310) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| |#4| (QUOTE (-1101))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#3| (QUOTE (-370))) (|HasCategory| |#4| (LIST (QUOTE -614) (QUOTE (-863))))) -(-1281 R) +((-4419 . T) (-4418 . T)) +((-12 (|HasCategory| |#4| (QUOTE (-1102))) (|HasCategory| |#4| (LIST (QUOTE -310) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -615) (QUOTE (-539)))) (|HasCategory| |#4| (QUOTE (-1102))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#3| (QUOTE (-370))) (|HasCategory| |#4| (LIST (QUOTE -614) (QUOTE (-863))))) +(-1282 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)) +((-4412 . T) (-4413 . T) (-4415 . T)) NIL -(-1282 |vl| R) +(-1283 |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))) -(-1283 R |VarSet| XPOLY) +((-4415 . T) (-4411 |has| |#2| (-6 -4411)) (-4413 . T) (-4412 . T)) +((|HasCategory| |#2| (QUOTE (-172))) (|HasAttribute| |#2| (QUOTE -4411))) +(-1284 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 -(-1284 |vl| R) +(-1285 |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| $) "\\spad{v * x} returns the product of a variable \\spad{x} by \\spad{x}."))) -((-4410 |has| |#2| (-6 -4410)) (-4412 . T) (-4411 . T) (-4414 . T)) +((-4411 |has| |#2| (-6 -4411)) (-4413 . T) (-4412 . T) (-4415 . T)) NIL -(-1285 S -3867) +(-1286 S -3879) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) NIL ((|HasCategory| |#2| (QUOTE (-370))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147)))) -(-1286 -3867) +(-1287 -3879) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) -((-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) +((-4410 . T) (-4416 . T) (-4411 . T) ((-4420 "*") . T) (-4412 . T) (-4413 . T) (-4415 . T)) NIL -(-1287 |VarSet| R) +(-1288 |VarSet| R) ((|constructor| (NIL "This domain constructor implements polynomials in non-commutative variables written in the Poincare-Birkhoff-Witt basis from the Lyndon basis. These polynomials can be used to compute Baker-Campbell-Hausdorff relations. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|log| (($ $ (|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 -718) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasAttribute| |#2| (QUOTE -4410))) -(-1288 |vl| R) +((-4411 |has| |#2| (-6 -4411)) (-4413 . T) (-4412 . T) (-4415 . T)) +((|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (LIST (QUOTE -718) (LIST (QUOTE -410) (QUOTE (-567))))) (|HasAttribute| |#2| (QUOTE -4411))) +(-1289 |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|) $) "\\spad{maxdeg(p)} returns the greatest leading word in the support of \\spad{p}."))) -((-4410 |has| |#2| (-6 -4410)) (-4412 . T) (-4411 . T) (-4414 . T)) +((-4411 |has| |#2| (-6 -4411)) (-4413 . T) (-4412 . T) (-4415 . T)) NIL -(-1289 R) +(-1290 R) ((|constructor| (NIL "\\indented{2}{This type supports multivariate polynomials} whose set of variables is \\spadtype{Symbol}. The representation is recursive. The coefficient ring may be non-commutative and the variables do not commute. However,{} coefficients and variables commute."))) -((-4410 |has| |#1| (-6 -4410)) (-4412 . T) (-4411 . T) (-4414 . T)) -((|HasCategory| |#1| (QUOTE (-172))) (|HasAttribute| |#1| (QUOTE -4410))) -(-1290 R E) +((-4411 |has| |#1| (-6 -4411)) (-4413 . T) (-4412 . T) (-4415 . T)) +((|HasCategory| |#1| (QUOTE (-172))) (|HasAttribute| |#1| (QUOTE -4411))) +(-1291 R E) ((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and words belonging to an arbitrary \\spadtype{OrderedMonoid}. This type is used,{} for instance,{} by the \\spadtype{XDistributedPolynomial} domain constructor where the Monoid is free.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (/ (($ $ |#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))) -(-1291 |VarSet| R) +((-4415 . T) (-4416 |has| |#1| (-6 -4416)) (-4411 |has| |#1| (-6 -4411)) (-4413 . T) (-4412 . T)) +((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365))) (|HasAttribute| |#1| (QUOTE -4415)) (|HasAttribute| |#1| (QUOTE -4416)) (|HasAttribute| |#1| (QUOTE -4411))) +(-1292 |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))) -(-1292 A) +((-4411 |has| |#2| (-6 -4411)) (-4413 . T) (-4412 . T) (-4415 . T)) +((|HasCategory| |#2| (QUOTE (-172))) (|HasAttribute| |#2| (QUOTE -4411))) +(-1293 A) ((|constructor| (NIL "This package implements fixed-point computations on streams.")) (Y (((|List| (|Stream| |#1|)) (|Mapping| (|List| (|Stream| |#1|)) (|List| (|Stream| |#1|))) (|Integer|)) "\\spad{Y(g,n)} computes a fixed point of the function \\spad{g},{} where \\spad{g} takes a list of \\spad{n} streams and returns a list of \\spad{n} streams.") (((|Stream| |#1|) (|Mapping| (|Stream| |#1|) (|Stream| |#1|))) "\\spad{Y(f)} computes a fixed point of the function \\spad{f}."))) NIL NIL -(-1293 R |ls| |ls2|) +(-1294 R |ls| |ls2|) ((|constructor| (NIL "A package for computing symbolically the complex and real roots of zero-dimensional algebraic systems over the integer or rational numbers. Complex roots are given by means of univariate representations of irreducible regular chains. Real roots are given by means of tuples of coordinates lying in the \\spadtype{RealClosure} of the coefficient ring. This constructor takes three arguments. The first one \\spad{R} is the coefficient ring. The second one \\spad{ls} is the list of variables involved in the systems to solve. The third one must be \\spad{concat(ls,s)} where \\spad{s} is an additional symbol used for the univariate representations. WARNING: The third argument is not checked. All operations are based on triangular decompositions. The default is to compute these decompositions directly from the input system by using the \\spadtype{RegularChain} domain constructor. The lexTriangular algorithm can also be used for computing these decompositions (see the \\spadtype{LexTriangularPackage} package constructor). For that purpose,{} the operations \\axiomOpFrom{univariateSolve}{ZeroDimensionalSolvePackage},{} \\axiomOpFrom{realSolve}{ZeroDimensionalSolvePackage} and \\axiomOpFrom{positiveSolve}{ZeroDimensionalSolvePackage} admit an optional argument. \\newline Author: Marc Moreno Maza.")) (|convert| (((|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|))) (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#3|)) (|OrderedVariableList| |#3|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|)))) "\\spad{convert(st)} returns the members of \\spad{st}.") (((|SparseUnivariatePolynomial| (|RealClosure| (|Fraction| |#1|))) (|SparseUnivariatePolynomial| |#1|)) "\\spad{convert(u)} converts \\spad{u}.") (((|Polynomial| (|RealClosure| (|Fraction| |#1|))) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|))) "\\spad{convert(q)} converts \\spad{q}.") (((|Polynomial| (|RealClosure| (|Fraction| |#1|))) (|Polynomial| |#1|)) "\\spad{convert(p)} converts \\spad{p}.") (((|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|)) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) "\\spad{convert(q)} converts \\spad{q}.")) (|squareFree| (((|List| (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#3|)) (|OrderedVariableList| |#3|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|)))) (|RegularChain| |#1| |#2|)) "\\spad{squareFree(ts)} returns the square-free factorization of \\spad{ts}. Moreover,{} each factor is a Lazard triangular set and the decomposition is a Kalkbrener split of \\spad{ts},{} which is enough here for the matter of solving zero-dimensional algebraic systems. WARNING: \\spad{ts} is not checked to be zero-dimensional.")) (|positiveSolve| (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|))) "\\spad{positiveSolve(lp)} returns the same as \\spad{positiveSolve(lp,false,false)}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{positiveSolve(lp)} returns the same as \\spad{positiveSolve(lp,info?,false)}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{positiveSolve(lp,info?,lextri?)} returns the set of the points in the variety associated with \\spad{lp} whose coordinates are (real) strictly positive. Moreover,{} if \\spad{info?} is \\spad{true} then some information is displayed during decomposition into regular chains. If \\spad{lextri?} is \\spad{true} then the lexTriangular algorithm is called from the \\spadtype{LexTriangularPackage} constructor (see \\axiomOpFrom{zeroSetSplit}{LexTriangularPackage}(\\spad{lp},{}\\spad{false})). Otherwise,{} the triangular decomposition is computed directly from the input system by using the \\axiomOpFrom{zeroSetSplit}{RegularChain} from \\spadtype{RegularChain}. WARNING: For each set of coordinates given by \\spad{positiveSolve(lp,info?,lextri?)} the ordering of the indeterminates is reversed \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ls}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|RegularChain| |#1| |#2|)) "\\spad{positiveSolve(ts)} returns the points of the regular set of \\spad{ts} with (real) strictly positive coordinates.")) (|realSolve| (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|))) "\\spad{realSolve(lp)} returns the same as \\spad{realSolve(ts,false,false,false)}") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{realSolve(ts,info?)} returns the same as \\spad{realSolve(ts,info?,false,false)}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{realSolve(ts,info?,check?)} returns the same as \\spad{realSolve(ts,info?,check?,false)}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|) (|Boolean|)) "\\spad{realSolve(ts,info?,check?,lextri?)} returns the set of the points in the variety associated with \\spad{lp} whose coordinates are all real. Moreover,{} if \\spad{info?} is \\spad{true} then some information is displayed during decomposition into regular chains. If \\spad{check?} is \\spad{true} then the result is checked. If \\spad{lextri?} is \\spad{true} then the lexTriangular algorithm is called from the \\spadtype{LexTriangularPackage} constructor (see \\axiomOpFrom{zeroSetSplit}{LexTriangularPackage}(\\spad{lp},{}\\spad{false})). Otherwise,{} the triangular decomposition is computed directly from the input system by using the \\axiomOpFrom{zeroSetSplit}{RegularChain} from \\spadtype{RegularChain}. WARNING: For each set of coordinates given by \\spad{realSolve(ts,info?,check?,lextri?)} the ordering of the indeterminates is reversed \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ls}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|RegularChain| |#1| |#2|)) "\\spad{realSolve(ts)} returns the set of the points in the regular zero set of \\spad{ts} whose coordinates are all real. WARNING: For each set of coordinates given by \\spad{realSolve(ts)} the ordering of the indeterminates is reversed \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ls}.")) (|univariateSolve| (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|))) "\\spad{univariateSolve(lp)} returns the same as \\spad{univariateSolve(lp,false,false,false)}.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{univariateSolve(lp,info?)} returns the same as \\spad{univariateSolve(lp,info?,false,false)}.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{univariateSolve(lp,info?,check?)} returns the same as \\spad{univariateSolve(lp,info?,check?,false)}.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|) (|Boolean|)) "\\spad{univariateSolve(lp,info?,check?,lextri?)} returns a univariate representation of the variety associated with \\spad{lp}. Moreover,{} if \\spad{info?} is \\spad{true} then some information is displayed during the decomposition into regular chains. If \\spad{check?} is \\spad{true} then the result is checked. See \\axiomOpFrom{rur}{RationalUnivariateRepresentationPackage}(\\spad{lp},{}\\spad{true}). If \\spad{lextri?} is \\spad{true} then the lexTriangular algorithm is called from the \\spadtype{LexTriangularPackage} constructor (see \\axiomOpFrom{zeroSetSplit}{LexTriangularPackage}(\\spad{lp},{}\\spad{false})). Otherwise,{} the triangular decomposition is computed directly from the input system by using the \\axiomOpFrom{zeroSetSplit}{RegularChain} from \\spadtype{RegularChain}.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|RegularChain| |#1| |#2|)) "\\spad{univariateSolve(ts)} returns a univariate representation of \\spad{ts}. See \\axiomOpFrom{rur}{RationalUnivariateRepresentationPackage}(\\spad{lp},{}\\spad{true}).")) (|triangSolve| (((|List| (|RegularChain| |#1| |#2|)) (|List| (|Polynomial| |#1|))) "\\spad{triangSolve(lp)} returns the same as \\spad{triangSolve(lp,false,false)}") (((|List| (|RegularChain| |#1| |#2|)) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{triangSolve(lp,info?)} returns the same as \\spad{triangSolve(lp,false)}") (((|List| (|RegularChain| |#1| |#2|)) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{triangSolve(lp,info?,lextri?)} decomposes the variety associated with \\axiom{\\spad{lp}} into regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{\\spad{lp}} needs to generate a zero-dimensional ideal. If \\axiom{\\spad{lp}} is not zero-dimensional then the result is only a decomposition of its zero-set in the sense of the closure (\\spad{w}.\\spad{r}.\\spad{t}. Zarisky topology). Moreover,{} if \\spad{info?} is \\spad{true} then some information is displayed during the computations. See \\axiomOpFrom{zeroSetSplit}{RegularTriangularSetCategory}(\\spad{lp},{}\\spad{true},{}\\spad{info?}). If \\spad{lextri?} is \\spad{true} then the lexTriangular algorithm is called from the \\spadtype{LexTriangularPackage} constructor (see \\axiomOpFrom{zeroSetSplit}{LexTriangularPackage}(\\spad{lp},{}\\spad{false})). Otherwise,{} the triangular decomposition is computed directly from the input system by using the \\axiomOpFrom{zeroSetSplit}{RegularChain} from \\spadtype{RegularChain}."))) NIL NIL -(-1294 R) +(-1295 R) ((|constructor| (NIL "Test for linear dependence over the integers.")) (|solveLinearlyOverQ| (((|Union| (|Vector| (|Fraction| (|Integer|))) "failed") (|Vector| |#1|) |#1|) "\\spad{solveLinearlyOverQ([v1,...,vn], u)} returns \\spad{[c1,...,cn]} such that \\spad{c1*v1 + ... + cn*vn = u},{} \"failed\" if no such rational numbers \\spad{ci}\\spad{'s} exist.")) (|linearDependenceOverZ| (((|Union| (|Vector| (|Integer|)) "failed") (|Vector| |#1|)) "\\spad{linearlyDependenceOverZ([v1,...,vn])} returns \\spad{[c1,...,cn]} if \\spad{c1*v1 + ... + cn*vn = 0} and not all the \\spad{ci}\\spad{'s} are 0,{} \"failed\" if the \\spad{vi}\\spad{'s} are linearly independent over the integers.")) (|linearlyDependentOverZ?| (((|Boolean|) (|Vector| |#1|)) "\\spad{linearlyDependentOverZ?([v1,...,vn])} returns \\spad{true} if the \\spad{vi}\\spad{'s} are linearly dependent over the integers,{} \\spad{false} otherwise."))) NIL NIL -(-1295 |p|) +(-1296 |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)) +(((-4420 "*") . T) (-4412 . T) (-4413 . T) (-4415 . T)) NIL NIL NIL @@ -5128,4 +5132,4 @@ NIL NIL NIL NIL -((-3 NIL 2262656 2262661 2262666 2262671) (-2 NIL 2262636 2262641 2262646 2262651) (-1 NIL 2262616 2262621 2262626 2262631) (0 NIL 2262596 2262601 2262606 2262611) (-1295 "ZMOD.spad" 2262405 2262418 2262534 2262591) (-1294 "ZLINDEP.spad" 2261471 2261482 2262395 2262400) (-1293 "ZDSOLVE.spad" 2251416 2251438 2261461 2261466) (-1292 "YSTREAM.spad" 2250911 2250922 2251406 2251411) (-1291 "XRPOLY.spad" 2250131 2250151 2250767 2250836) (-1290 "XPR.spad" 2247926 2247939 2249849 2249948) (-1289 "XPOLY.spad" 2247481 2247492 2247782 2247851) (-1288 "XPOLYC.spad" 2246800 2246816 2247407 2247476) (-1287 "XPBWPOLY.spad" 2245237 2245257 2246580 2246649) (-1286 "XF.spad" 2243700 2243715 2245139 2245232) (-1285 "XF.spad" 2242143 2242160 2243584 2243589) (-1284 "XFALG.spad" 2239191 2239207 2242069 2242138) (-1283 "XEXPPKG.spad" 2238442 2238468 2239181 2239186) (-1282 "XDPOLY.spad" 2238056 2238072 2238298 2238367) (-1281 "XALG.spad" 2237716 2237727 2238012 2238051) (-1280 "WUTSET.spad" 2233555 2233572 2237362 2237389) (-1279 "WP.spad" 2232754 2232798 2233413 2233480) (-1278 "WHILEAST.spad" 2232552 2232561 2232744 2232749) (-1277 "WHEREAST.spad" 2232223 2232232 2232542 2232547) (-1276 "WFFINTBS.spad" 2229886 2229908 2232213 2232218) (-1275 "WEIER.spad" 2228108 2228119 2229876 2229881) (-1274 "VSPACE.spad" 2227781 2227792 2228076 2228103) (-1273 "VSPACE.spad" 2227474 2227487 2227771 2227776) (-1272 "VOID.spad" 2227151 2227160 2227464 2227469) (-1271 "VIEW.spad" 2224831 2224840 2227141 2227146) (-1270 "VIEWDEF.spad" 2220032 2220041 2224821 2224826) (-1269 "VIEW3D.spad" 2203993 2204002 2220022 2220027) (-1268 "VIEW2D.spad" 2191884 2191893 2203983 2203988) (-1267 "VECTOR.spad" 2190558 2190569 2190809 2190836) (-1266 "VECTOR2.spad" 2189197 2189210 2190548 2190553) (-1265 "VECTCAT.spad" 2187101 2187112 2189165 2189192) (-1264 "VECTCAT.spad" 2184812 2184825 2186878 2186883) (-1263 "VARIABLE.spad" 2184592 2184607 2184802 2184807) (-1262 "UTYPE.spad" 2184236 2184245 2184582 2184587) (-1261 "UTSODETL.spad" 2183531 2183555 2184192 2184197) (-1260 "UTSODE.spad" 2181747 2181767 2183521 2183526) (-1259 "UTS.spad" 2176560 2176588 2180214 2180311) (-1258 "UTSCAT.spad" 2174039 2174055 2176458 2176555) (-1257 "UTSCAT.spad" 2171162 2171180 2173583 2173588) (-1256 "UTS2.spad" 2170757 2170792 2171152 2171157) (-1255 "URAGG.spad" 2165430 2165441 2170747 2170752) (-1254 "URAGG.spad" 2160067 2160080 2165386 2165391) (-1253 "UPXSSING.spad" 2157712 2157738 2159148 2159281) (-1252 "UPXS.spad" 2154866 2154894 2155844 2155993) (-1251 "UPXSCONS.spad" 2152625 2152645 2152998 2153147) (-1250 "UPXSCCA.spad" 2151196 2151216 2152471 2152620) (-1249 "UPXSCCA.spad" 2149909 2149931 2151186 2151191) (-1248 "UPXSCAT.spad" 2148498 2148514 2149755 2149904) (-1247 "UPXS2.spad" 2148041 2148094 2148488 2148493) (-1246 "UPSQFREE.spad" 2146455 2146469 2148031 2148036) (-1245 "UPSCAT.spad" 2144066 2144090 2146353 2146450) (-1244 "UPSCAT.spad" 2141383 2141409 2143672 2143677) (-1243 "UPOLYC.spad" 2136423 2136434 2141225 2141378) (-1242 "UPOLYC.spad" 2131355 2131368 2136159 2136164) (-1241 "UPOLYC2.spad" 2130826 2130845 2131345 2131350) (-1240 "UP.spad" 2128025 2128040 2128412 2128565) (-1239 "UPMP.spad" 2126925 2126938 2128015 2128020) (-1238 "UPDIVP.spad" 2126490 2126504 2126915 2126920) (-1237 "UPDECOMP.spad" 2124735 2124749 2126480 2126485) (-1236 "UPCDEN.spad" 2123944 2123960 2124725 2124730) (-1235 "UP2.spad" 2123308 2123329 2123934 2123939) (-1234 "UNISEG.spad" 2122661 2122672 2123227 2123232) (-1233 "UNISEG2.spad" 2122158 2122171 2122617 2122622) (-1232 "UNIFACT.spad" 2121261 2121273 2122148 2122153) (-1231 "ULS.spad" 2111819 2111847 2112906 2113335) (-1230 "ULSCONS.spad" 2104215 2104235 2104585 2104734) (-1229 "ULSCCAT.spad" 2101952 2101972 2104061 2104210) (-1228 "ULSCCAT.spad" 2099797 2099819 2101908 2101913) (-1227 "ULSCAT.spad" 2098029 2098045 2099643 2099792) (-1226 "ULS2.spad" 2097543 2097596 2098019 2098024) (-1225 "UINT8.spad" 2097420 2097429 2097533 2097538) (-1224 "UINT64.spad" 2097296 2097305 2097410 2097415) (-1223 "UINT32.spad" 2097172 2097181 2097286 2097291) (-1222 "UINT16.spad" 2097048 2097057 2097162 2097167) (-1221 "UFD.spad" 2096113 2096122 2096974 2097043) (-1220 "UFD.spad" 2095240 2095251 2096103 2096108) (-1219 "UDVO.spad" 2094121 2094130 2095230 2095235) (-1218 "UDPO.spad" 2091614 2091625 2094077 2094082) (-1217 "TYPE.spad" 2091546 2091555 2091604 2091609) (-1216 "TYPEAST.spad" 2091465 2091474 2091536 2091541) (-1215 "TWOFACT.spad" 2090117 2090132 2091455 2091460) (-1214 "TUPLE.spad" 2089603 2089614 2090016 2090021) (-1213 "TUBETOOL.spad" 2086470 2086479 2089593 2089598) (-1212 "TUBE.spad" 2085117 2085134 2086460 2086465) (-1211 "TS.spad" 2083716 2083732 2084682 2084779) (-1210 "TSETCAT.spad" 2070843 2070860 2083684 2083711) (-1209 "TSETCAT.spad" 2057956 2057975 2070799 2070804) (-1208 "TRMANIP.spad" 2052322 2052339 2057662 2057667) (-1207 "TRIMAT.spad" 2051285 2051310 2052312 2052317) (-1206 "TRIGMNIP.spad" 2049812 2049829 2051275 2051280) (-1205 "TRIGCAT.spad" 2049324 2049333 2049802 2049807) (-1204 "TRIGCAT.spad" 2048834 2048845 2049314 2049319) (-1203 "TREE.spad" 2047409 2047420 2048441 2048468) (-1202 "TRANFUN.spad" 2047248 2047257 2047399 2047404) (-1201 "TRANFUN.spad" 2047085 2047096 2047238 2047243) (-1200 "TOPSP.spad" 2046759 2046768 2047075 2047080) (-1199 "TOOLSIGN.spad" 2046422 2046433 2046749 2046754) (-1198 "TEXTFILE.spad" 2044983 2044992 2046412 2046417) (-1197 "TEX.spad" 2042129 2042138 2044973 2044978) (-1196 "TEX1.spad" 2041685 2041696 2042119 2042124) (-1195 "TEMUTL.spad" 2041240 2041249 2041675 2041680) (-1194 "TBCMPPK.spad" 2039333 2039356 2041230 2041235) (-1193 "TBAGG.spad" 2038383 2038406 2039313 2039328) (-1192 "TBAGG.spad" 2037441 2037466 2038373 2038378) (-1191 "TANEXP.spad" 2036849 2036860 2037431 2037436) (-1190 "TABLE.spad" 2035260 2035283 2035530 2035557) (-1189 "TABLEAU.spad" 2034741 2034752 2035250 2035255) (-1188 "TABLBUMP.spad" 2031544 2031555 2034731 2034736) (-1187 "SYSTEM.spad" 2030772 2030781 2031534 2031539) (-1186 "SYSSOLP.spad" 2028255 2028266 2030762 2030767) (-1185 "SYSPTR.spad" 2028154 2028163 2028245 2028250) (-1184 "SYSNNI.spad" 2027336 2027347 2028144 2028149) (-1183 "SYSINT.spad" 2026740 2026751 2027326 2027331) (-1182 "SYNTAX.spad" 2022946 2022955 2026730 2026735) (-1181 "SYMTAB.spad" 2021014 2021023 2022936 2022941) (-1180 "SYMS.spad" 2017037 2017046 2021004 2021009) (-1179 "SYMPOLY.spad" 2016044 2016055 2016126 2016253) (-1178 "SYMFUNC.spad" 2015545 2015556 2016034 2016039) (-1177 "SYMBOL.spad" 2013048 2013057 2015535 2015540) (-1176 "SWITCH.spad" 2009819 2009828 2013038 2013043) (-1175 "SUTS.spad" 2006724 2006752 2008286 2008383) (-1174 "SUPXS.spad" 2003865 2003893 2004856 2005005) (-1173 "SUP.spad" 2000678 2000689 2001451 2001604) (-1172 "SUPFRACF.spad" 1999783 1999801 2000668 2000673) (-1171 "SUP2.spad" 1999175 1999188 1999773 1999778) (-1170 "SUMRF.spad" 1998149 1998160 1999165 1999170) (-1169 "SUMFS.spad" 1997786 1997803 1998139 1998144) (-1168 "SULS.spad" 1988331 1988359 1989431 1989860) (-1167 "SUCHTAST.spad" 1988100 1988109 1988321 1988326) (-1166 "SUCH.spad" 1987782 1987797 1988090 1988095) (-1165 "SUBSPACE.spad" 1979897 1979912 1987772 1987777) (-1164 "SUBRESP.spad" 1979067 1979081 1979853 1979858) (-1163 "STTF.spad" 1975166 1975182 1979057 1979062) (-1162 "STTFNC.spad" 1971634 1971650 1975156 1975161) (-1161 "STTAYLOR.spad" 1964288 1964299 1971515 1971520) (-1160 "STRTBL.spad" 1962793 1962810 1962942 1962969) (-1159 "STRING.spad" 1962202 1962211 1962216 1962243) (-1158 "STRICAT.spad" 1961990 1961999 1962170 1962197) (-1157 "STREAM.spad" 1958908 1958919 1961515 1961530) (-1156 "STREAM3.spad" 1958481 1958496 1958898 1958903) (-1155 "STREAM2.spad" 1957609 1957622 1958471 1958476) (-1154 "STREAM1.spad" 1957315 1957326 1957599 1957604) (-1153 "STINPROD.spad" 1956251 1956267 1957305 1957310) (-1152 "STEP.spad" 1955452 1955461 1956241 1956246) (-1151 "STBL.spad" 1953978 1954006 1954145 1954160) (-1150 "STAGG.spad" 1953053 1953064 1953968 1953973) (-1149 "STAGG.spad" 1952126 1952139 1953043 1953048) (-1148 "STACK.spad" 1951483 1951494 1951733 1951760) (-1147 "SREGSET.spad" 1949187 1949204 1951129 1951156) (-1146 "SRDCMPK.spad" 1947748 1947768 1949177 1949182) (-1145 "SRAGG.spad" 1942891 1942900 1947716 1947743) (-1144 "SRAGG.spad" 1938054 1938065 1942881 1942886) (-1143 "SQMATRIX.spad" 1935670 1935688 1936586 1936673) (-1142 "SPLTREE.spad" 1930222 1930235 1935106 1935133) (-1141 "SPLNODE.spad" 1926810 1926823 1930212 1930217) (-1140 "SPFCAT.spad" 1925619 1925628 1926800 1926805) (-1139 "SPECOUT.spad" 1924171 1924180 1925609 1925614) (-1138 "SPADXPT.spad" 1916310 1916319 1924161 1924166) (-1137 "spad-parser.spad" 1915775 1915784 1916300 1916305) (-1136 "SPADAST.spad" 1915476 1915485 1915765 1915770) (-1135 "SPACEC.spad" 1899675 1899686 1915466 1915471) (-1134 "SPACE3.spad" 1899451 1899462 1899665 1899670) (-1133 "SORTPAK.spad" 1899000 1899013 1899407 1899412) (-1132 "SOLVETRA.spad" 1896763 1896774 1898990 1898995) (-1131 "SOLVESER.spad" 1895291 1895302 1896753 1896758) (-1130 "SOLVERAD.spad" 1891317 1891328 1895281 1895286) (-1129 "SOLVEFOR.spad" 1889779 1889797 1891307 1891312) (-1128 "SNTSCAT.spad" 1889379 1889396 1889747 1889774) (-1127 "SMTS.spad" 1887651 1887677 1888944 1889041) (-1126 "SMP.spad" 1885126 1885146 1885516 1885643) (-1125 "SMITH.spad" 1883971 1883996 1885116 1885121) (-1124 "SMATCAT.spad" 1882081 1882111 1883915 1883966) (-1123 "SMATCAT.spad" 1880123 1880155 1881959 1881964) (-1122 "SKAGG.spad" 1879086 1879097 1880091 1880118) (-1121 "SINT.spad" 1877918 1877927 1878952 1879081) (-1120 "SIMPAN.spad" 1877646 1877655 1877908 1877913) (-1119 "SIG.spad" 1876976 1876985 1877636 1877641) (-1118 "SIGNRF.spad" 1876094 1876105 1876966 1876971) (-1117 "SIGNEF.spad" 1875373 1875390 1876084 1876089) (-1116 "SIGAST.spad" 1874758 1874767 1875363 1875368) (-1115 "SHP.spad" 1872686 1872701 1874714 1874719) (-1114 "SHDP.spad" 1862397 1862424 1862906 1863037) (-1113 "SGROUP.spad" 1862005 1862014 1862387 1862392) (-1112 "SGROUP.spad" 1861611 1861622 1861995 1862000) (-1111 "SGCF.spad" 1854774 1854783 1861601 1861606) (-1110 "SFRTCAT.spad" 1853704 1853721 1854742 1854769) (-1109 "SFRGCD.spad" 1852767 1852787 1853694 1853699) (-1108 "SFQCMPK.spad" 1847404 1847424 1852757 1852762) (-1107 "SFORT.spad" 1846843 1846857 1847394 1847399) (-1106 "SEXOF.spad" 1846686 1846726 1846833 1846838) (-1105 "SEX.spad" 1846578 1846587 1846676 1846681) (-1104 "SEXCAT.spad" 1844179 1844219 1846568 1846573) (-1103 "SET.spad" 1842503 1842514 1843600 1843639) (-1102 "SETMN.spad" 1840953 1840970 1842493 1842498) (-1101 "SETCAT.spad" 1840275 1840284 1840943 1840948) (-1100 "SETCAT.spad" 1839595 1839606 1840265 1840270) (-1099 "SETAGG.spad" 1836144 1836155 1839575 1839590) (-1098 "SETAGG.spad" 1832701 1832714 1836134 1836139) (-1097 "SEQAST.spad" 1832404 1832413 1832691 1832696) (-1096 "SEGXCAT.spad" 1831560 1831573 1832394 1832399) (-1095 "SEG.spad" 1831373 1831384 1831479 1831484) (-1094 "SEGCAT.spad" 1830298 1830309 1831363 1831368) (-1093 "SEGBIND.spad" 1830056 1830067 1830245 1830250) (-1092 "SEGBIND2.spad" 1829754 1829767 1830046 1830051) (-1091 "SEGAST.spad" 1829468 1829477 1829744 1829749) (-1090 "SEG2.spad" 1828903 1828916 1829424 1829429) (-1089 "SDVAR.spad" 1828179 1828190 1828893 1828898) (-1088 "SDPOL.spad" 1825605 1825616 1825896 1826023) (-1087 "SCPKG.spad" 1823694 1823705 1825595 1825600) (-1086 "SCOPE.spad" 1822847 1822856 1823684 1823689) (-1085 "SCACHE.spad" 1821543 1821554 1822837 1822842) (-1084 "SASTCAT.spad" 1821452 1821461 1821533 1821538) (-1083 "SAOS.spad" 1821324 1821333 1821442 1821447) (-1082 "SAERFFC.spad" 1821037 1821057 1821314 1821319) (-1081 "SAE.spad" 1819212 1819228 1819823 1819958) (-1080 "SAEFACT.spad" 1818913 1818933 1819202 1819207) (-1079 "RURPK.spad" 1816572 1816588 1818903 1818908) (-1078 "RULESET.spad" 1816025 1816049 1816562 1816567) (-1077 "RULE.spad" 1814265 1814289 1816015 1816020) (-1076 "RULECOLD.spad" 1814117 1814130 1814255 1814260) (-1075 "RTVALUE.spad" 1813852 1813861 1814107 1814112) (-1074 "RSTRCAST.spad" 1813569 1813578 1813842 1813847) (-1073 "RSETGCD.spad" 1809947 1809967 1813559 1813564) (-1072 "RSETCAT.spad" 1799883 1799900 1809915 1809942) (-1071 "RSETCAT.spad" 1789839 1789858 1799873 1799878) (-1070 "RSDCMPK.spad" 1788291 1788311 1789829 1789834) (-1069 "RRCC.spad" 1786675 1786705 1788281 1788286) (-1068 "RRCC.spad" 1785057 1785089 1786665 1786670) (-1067 "RPTAST.spad" 1784759 1784768 1785047 1785052) (-1066 "RPOLCAT.spad" 1764119 1764134 1784627 1784754) (-1065 "RPOLCAT.spad" 1743193 1743210 1763703 1763708) (-1064 "ROUTINE.spad" 1739076 1739085 1741840 1741867) (-1063 "ROMAN.spad" 1738404 1738413 1738942 1739071) (-1062 "ROIRC.spad" 1737484 1737516 1738394 1738399) (-1061 "RNS.spad" 1736387 1736396 1737386 1737479) (-1060 "RNS.spad" 1735376 1735387 1736377 1736382) (-1059 "RNG.spad" 1735111 1735120 1735366 1735371) (-1058 "RNGBIND.spad" 1734271 1734285 1735066 1735071) (-1057 "RMODULE.spad" 1734036 1734047 1734261 1734266) (-1056 "RMCAT2.spad" 1733456 1733513 1734026 1734031) (-1055 "RMATRIX.spad" 1732280 1732299 1732623 1732662) (-1054 "RMATCAT.spad" 1727859 1727890 1732236 1732275) (-1053 "RMATCAT.spad" 1723328 1723361 1727707 1727712) (-1052 "RLINSET.spad" 1722722 1722733 1723318 1723323) (-1051 "RINTERP.spad" 1722610 1722630 1722712 1722717) (-1050 "RING.spad" 1722080 1722089 1722590 1722605) (-1049 "RING.spad" 1721558 1721569 1722070 1722075) (-1048 "RIDIST.spad" 1720950 1720959 1721548 1721553) (-1047 "RGCHAIN.spad" 1719533 1719549 1720435 1720462) (-1046 "RGBCSPC.spad" 1719314 1719326 1719523 1719528) (-1045 "RGBCMDL.spad" 1718844 1718856 1719304 1719309) (-1044 "RF.spad" 1716486 1716497 1718834 1718839) (-1043 "RFFACTOR.spad" 1715948 1715959 1716476 1716481) (-1042 "RFFACT.spad" 1715683 1715695 1715938 1715943) (-1041 "RFDIST.spad" 1714679 1714688 1715673 1715678) (-1040 "RETSOL.spad" 1714098 1714111 1714669 1714674) (-1039 "RETRACT.spad" 1713526 1713537 1714088 1714093) (-1038 "RETRACT.spad" 1712952 1712965 1713516 1713521) (-1037 "RETAST.spad" 1712764 1712773 1712942 1712947) (-1036 "RESULT.spad" 1710824 1710833 1711411 1711438) (-1035 "RESRING.spad" 1710171 1710218 1710762 1710819) (-1034 "RESLATC.spad" 1709495 1709506 1710161 1710166) (-1033 "REPSQ.spad" 1709226 1709237 1709485 1709490) (-1032 "REP.spad" 1706780 1706789 1709216 1709221) (-1031 "REPDB.spad" 1706487 1706498 1706770 1706775) (-1030 "REP2.spad" 1696145 1696156 1706329 1706334) (-1029 "REP1.spad" 1690341 1690352 1696095 1696100) (-1028 "REGSET.spad" 1688138 1688155 1689987 1690014) (-1027 "REF.spad" 1687473 1687484 1688093 1688098) (-1026 "REDORDER.spad" 1686679 1686696 1687463 1687468) (-1025 "RECLOS.spad" 1685462 1685482 1686166 1686259) (-1024 "REALSOLV.spad" 1684602 1684611 1685452 1685457) (-1023 "REAL.spad" 1684474 1684483 1684592 1684597) (-1022 "REAL0Q.spad" 1681772 1681787 1684464 1684469) (-1021 "REAL0.spad" 1678616 1678631 1681762 1681767) (-1020 "RDUCEAST.spad" 1678337 1678346 1678606 1678611) (-1019 "RDIV.spad" 1677992 1678017 1678327 1678332) (-1018 "RDIST.spad" 1677559 1677570 1677982 1677987) (-1017 "RDETRS.spad" 1676423 1676441 1677549 1677554) (-1016 "RDETR.spad" 1674562 1674580 1676413 1676418) (-1015 "RDEEFS.spad" 1673661 1673678 1674552 1674557) (-1014 "RDEEF.spad" 1672671 1672688 1673651 1673656) (-1013 "RCFIELD.spad" 1669857 1669866 1672573 1672666) (-1012 "RCFIELD.spad" 1667129 1667140 1669847 1669852) (-1011 "RCAGG.spad" 1665057 1665068 1667119 1667124) (-1010 "RCAGG.spad" 1662912 1662925 1664976 1664981) (-1009 "RATRET.spad" 1662272 1662283 1662902 1662907) (-1008 "RATFACT.spad" 1661964 1661976 1662262 1662267) (-1007 "RANDSRC.spad" 1661283 1661292 1661954 1661959) (-1006 "RADUTIL.spad" 1661039 1661048 1661273 1661278) (-1005 "RADIX.spad" 1657960 1657974 1659506 1659599) (-1004 "RADFF.spad" 1656373 1656410 1656492 1656648) (-1003 "RADCAT.spad" 1655968 1655977 1656363 1656368) (-1002 "RADCAT.spad" 1655561 1655572 1655958 1655963) (-1001 "QUEUE.spad" 1654909 1654920 1655168 1655195) (-1000 "QUAT.spad" 1653490 1653501 1653833 1653898) (-999 "QUATCT2.spad" 1653111 1653129 1653480 1653485) (-998 "QUATCAT.spad" 1651282 1651292 1653041 1653106) (-997 "QUATCAT.spad" 1649204 1649216 1650965 1650970) (-996 "QUAGG.spad" 1648032 1648042 1649172 1649199) (-995 "QQUTAST.spad" 1647801 1647809 1648022 1648027) (-994 "QFORM.spad" 1647266 1647280 1647791 1647796) (-993 "QFCAT.spad" 1645969 1645979 1647168 1647261) (-992 "QFCAT.spad" 1644263 1644275 1645464 1645469) (-991 "QFCAT2.spad" 1643956 1643972 1644253 1644258) (-990 "QEQUAT.spad" 1643515 1643523 1643946 1643951) (-989 "QCMPACK.spad" 1638262 1638281 1643505 1643510) (-988 "QALGSET.spad" 1634341 1634373 1638176 1638181) (-987 "QALGSET2.spad" 1632337 1632355 1634331 1634336) (-986 "PWFFINTB.spad" 1629753 1629774 1632327 1632332) (-985 "PUSHVAR.spad" 1629092 1629111 1629743 1629748) (-984 "PTRANFN.spad" 1625220 1625230 1629082 1629087) (-983 "PTPACK.spad" 1622308 1622318 1625210 1625215) (-982 "PTFUNC2.spad" 1622131 1622145 1622298 1622303) (-981 "PTCAT.spad" 1621386 1621396 1622099 1622126) (-980 "PSQFR.spad" 1620693 1620717 1621376 1621381) (-979 "PSEUDLIN.spad" 1619579 1619589 1620683 1620688) (-978 "PSETPK.spad" 1605012 1605028 1619457 1619462) (-977 "PSETCAT.spad" 1598932 1598955 1604992 1605007) (-976 "PSETCAT.spad" 1592826 1592851 1598888 1598893) (-975 "PSCURVE.spad" 1591809 1591817 1592816 1592821) (-974 "PSCAT.spad" 1590592 1590621 1591707 1591804) (-973 "PSCAT.spad" 1589465 1589496 1590582 1590587) (-972 "PRTITION.spad" 1588426 1588434 1589455 1589460) (-971 "PRTDAST.spad" 1588145 1588153 1588416 1588421) (-970 "PRS.spad" 1577707 1577724 1588101 1588106) (-969 "PRQAGG.spad" 1577142 1577152 1577675 1577702) (-968 "PROPLOG.spad" 1576441 1576449 1577132 1577137) (-967 "PROPFRML.spad" 1575257 1575268 1576431 1576436) (-966 "PROPERTY.spad" 1574745 1574753 1575247 1575252) (-965 "PRODUCT.spad" 1572427 1572439 1572711 1572766) (-964 "PR.spad" 1570819 1570831 1571518 1571645) (-963 "PRINT.spad" 1570571 1570579 1570809 1570814) (-962 "PRIMES.spad" 1568824 1568834 1570561 1570566) (-961 "PRIMELT.spad" 1566905 1566919 1568814 1568819) (-960 "PRIMCAT.spad" 1566532 1566540 1566895 1566900) (-959 "PRIMARR.spad" 1565537 1565547 1565715 1565742) (-958 "PRIMARR2.spad" 1564304 1564316 1565527 1565532) (-957 "PREASSOC.spad" 1563686 1563698 1564294 1564299) (-956 "PPCURVE.spad" 1562823 1562831 1563676 1563681) (-955 "PORTNUM.spad" 1562598 1562606 1562813 1562818) (-954 "POLYROOT.spad" 1561447 1561469 1562554 1562559) (-953 "POLY.spad" 1558782 1558792 1559297 1559424) (-952 "POLYLIFT.spad" 1558047 1558070 1558772 1558777) (-951 "POLYCATQ.spad" 1556165 1556187 1558037 1558042) (-950 "POLYCAT.spad" 1549635 1549656 1556033 1556160) (-949 "POLYCAT.spad" 1542443 1542466 1548843 1548848) (-948 "POLY2UP.spad" 1541895 1541909 1542433 1542438) (-947 "POLY2.spad" 1541492 1541504 1541885 1541890) (-946 "POLUTIL.spad" 1540433 1540462 1541448 1541453) (-945 "POLTOPOL.spad" 1539181 1539196 1540423 1540428) (-944 "POINT.spad" 1538019 1538029 1538106 1538133) (-943 "PNTHEORY.spad" 1534721 1534729 1538009 1538014) (-942 "PMTOOLS.spad" 1533496 1533510 1534711 1534716) (-941 "PMSYM.spad" 1533045 1533055 1533486 1533491) (-940 "PMQFCAT.spad" 1532636 1532650 1533035 1533040) (-939 "PMPRED.spad" 1532115 1532129 1532626 1532631) (-938 "PMPREDFS.spad" 1531569 1531591 1532105 1532110) (-937 "PMPLCAT.spad" 1530649 1530667 1531501 1531506) (-936 "PMLSAGG.spad" 1530234 1530248 1530639 1530644) (-935 "PMKERNEL.spad" 1529813 1529825 1530224 1530229) (-934 "PMINS.spad" 1529393 1529403 1529803 1529808) (-933 "PMFS.spad" 1528970 1528988 1529383 1529388) (-932 "PMDOWN.spad" 1528260 1528274 1528960 1528965) (-931 "PMASS.spad" 1527270 1527278 1528250 1528255) (-930 "PMASSFS.spad" 1526237 1526253 1527260 1527265) (-929 "PLOTTOOL.spad" 1526017 1526025 1526227 1526232) (-928 "PLOT.spad" 1520940 1520948 1526007 1526012) (-927 "PLOT3D.spad" 1517404 1517412 1520930 1520935) (-926 "PLOT1.spad" 1516561 1516571 1517394 1517399) (-925 "PLEQN.spad" 1503851 1503878 1516551 1516556) (-924 "PINTERP.spad" 1503473 1503492 1503841 1503846) (-923 "PINTERPA.spad" 1503257 1503273 1503463 1503468) (-922 "PI.spad" 1502866 1502874 1503231 1503252) (-921 "PID.spad" 1501836 1501844 1502792 1502861) (-920 "PICOERCE.spad" 1501493 1501503 1501826 1501831) (-919 "PGROEB.spad" 1500094 1500108 1501483 1501488) (-918 "PGE.spad" 1491711 1491719 1500084 1500089) (-917 "PGCD.spad" 1490601 1490618 1491701 1491706) (-916 "PFRPAC.spad" 1489750 1489760 1490591 1490596) (-915 "PFR.spad" 1486413 1486423 1489652 1489745) (-914 "PFOTOOLS.spad" 1485671 1485687 1486403 1486408) (-913 "PFOQ.spad" 1485041 1485059 1485661 1485666) (-912 "PFO.spad" 1484460 1484487 1485031 1485036) (-911 "PF.spad" 1484034 1484046 1484265 1484358) (-910 "PFECAT.spad" 1481716 1481724 1483960 1484029) (-909 "PFECAT.spad" 1479426 1479436 1481672 1481677) (-908 "PFBRU.spad" 1477314 1477326 1479416 1479421) (-907 "PFBR.spad" 1474874 1474897 1477304 1477309) (-906 "PERM.spad" 1470559 1470569 1474704 1474719) (-905 "PERMGRP.spad" 1465321 1465331 1470549 1470554) (-904 "PERMCAT.spad" 1463879 1463889 1465301 1465316) (-903 "PERMAN.spad" 1462411 1462425 1463869 1463874) (-902 "PENDTREE.spad" 1461752 1461762 1462040 1462045) (-901 "PDRING.spad" 1460303 1460313 1461732 1461747) (-900 "PDRING.spad" 1458862 1458874 1460293 1460298) (-899 "PDEPROB.spad" 1457877 1457885 1458852 1458857) (-898 "PDEPACK.spad" 1451917 1451925 1457867 1457872) (-897 "PDECOMP.spad" 1451387 1451404 1451907 1451912) (-896 "PDECAT.spad" 1449743 1449751 1451377 1451382) (-895 "PCOMP.spad" 1449596 1449609 1449733 1449738) (-894 "PBWLB.spad" 1448184 1448201 1449586 1449591) (-893 "PATTERN.spad" 1442723 1442733 1448174 1448179) (-892 "PATTERN2.spad" 1442461 1442473 1442713 1442718) (-891 "PATTERN1.spad" 1440797 1440813 1442451 1442456) (-890 "PATRES.spad" 1438372 1438384 1440787 1440792) (-889 "PATRES2.spad" 1438044 1438058 1438362 1438367) (-888 "PATMATCH.spad" 1436241 1436272 1437752 1437757) (-887 "PATMAB.spad" 1435670 1435680 1436231 1436236) (-886 "PATLRES.spad" 1434756 1434770 1435660 1435665) (-885 "PATAB.spad" 1434520 1434530 1434746 1434751) (-884 "PARTPERM.spad" 1431920 1431928 1434510 1434515) (-883 "PARSURF.spad" 1431354 1431382 1431910 1431915) (-882 "PARSU2.spad" 1431151 1431167 1431344 1431349) (-881 "script-parser.spad" 1430671 1430679 1431141 1431146) (-880 "PARSCURV.spad" 1430105 1430133 1430661 1430666) (-879 "PARSC2.spad" 1429896 1429912 1430095 1430100) (-878 "PARPCURV.spad" 1429358 1429386 1429886 1429891) (-877 "PARPC2.spad" 1429149 1429165 1429348 1429353) (-876 "PAN2EXPR.spad" 1428561 1428569 1429139 1429144) (-875 "PALETTE.spad" 1427531 1427539 1428551 1428556) (-874 "PAIR.spad" 1426518 1426531 1427119 1427124) (-873 "PADICRC.spad" 1423852 1423870 1425023 1425116) (-872 "PADICRAT.spad" 1421867 1421879 1422088 1422181) (-871 "PADIC.spad" 1421562 1421574 1421793 1421862) (-870 "PADICCT.spad" 1420111 1420123 1421488 1421557) (-869 "PADEPAC.spad" 1418800 1418819 1420101 1420106) (-868 "PADE.spad" 1417552 1417568 1418790 1418795) (-867 "OWP.spad" 1416792 1416822 1417410 1417477) (-866 "OVERSET.spad" 1416365 1416373 1416782 1416787) (-865 "OVAR.spad" 1416146 1416169 1416355 1416360) (-864 "OUT.spad" 1415232 1415240 1416136 1416141) (-863 "OUTFORM.spad" 1404624 1404632 1415222 1415227) (-862 "OUTBFILE.spad" 1404042 1404050 1404614 1404619) (-861 "OUTBCON.spad" 1403048 1403056 1404032 1404037) (-860 "OUTBCON.spad" 1402052 1402062 1403038 1403043) (-859 "OSI.spad" 1401527 1401535 1402042 1402047) (-858 "OSGROUP.spad" 1401445 1401453 1401517 1401522) (-857 "ORTHPOL.spad" 1399930 1399940 1401362 1401367) (-856 "OREUP.spad" 1399383 1399411 1399610 1399649) (-855 "ORESUP.spad" 1398684 1398708 1399063 1399102) (-854 "OREPCTO.spad" 1396541 1396553 1398604 1398609) (-853 "OREPCAT.spad" 1390688 1390698 1396497 1396536) (-852 "OREPCAT.spad" 1384725 1384737 1390536 1390541) (-851 "ORDSET.spad" 1383897 1383905 1384715 1384720) (-850 "ORDSET.spad" 1383067 1383077 1383887 1383892) (-849 "ORDRING.spad" 1382457 1382465 1383047 1383062) (-848 "ORDRING.spad" 1381855 1381865 1382447 1382452) (-847 "ORDMON.spad" 1381710 1381718 1381845 1381850) (-846 "ORDFUNS.spad" 1380842 1380858 1381700 1381705) (-845 "ORDFIN.spad" 1380662 1380670 1380832 1380837) (-844 "ORDCOMP.spad" 1379127 1379137 1380209 1380238) (-843 "ORDCOMP2.spad" 1378420 1378432 1379117 1379122) (-842 "OPTPROB.spad" 1377058 1377066 1378410 1378415) (-841 "OPTPACK.spad" 1369467 1369475 1377048 1377053) (-840 "OPTCAT.spad" 1367146 1367154 1369457 1369462) (-839 "OPSIG.spad" 1366800 1366808 1367136 1367141) (-838 "OPQUERY.spad" 1366349 1366357 1366790 1366795) (-837 "OP.spad" 1366091 1366101 1366171 1366238) (-836 "OPERCAT.spad" 1365557 1365567 1366081 1366086) (-835 "OPERCAT.spad" 1365021 1365033 1365547 1365552) (-834 "ONECOMP.spad" 1363766 1363776 1364568 1364597) (-833 "ONECOMP2.spad" 1363190 1363202 1363756 1363761) (-832 "OMSERVER.spad" 1362196 1362204 1363180 1363185) (-831 "OMSAGG.spad" 1361984 1361994 1362152 1362191) (-830 "OMPKG.spad" 1360600 1360608 1361974 1361979) (-829 "OM.spad" 1359573 1359581 1360590 1360595) (-828 "OMLO.spad" 1358998 1359010 1359459 1359498) (-827 "OMEXPR.spad" 1358832 1358842 1358988 1358993) (-826 "OMERR.spad" 1358377 1358385 1358822 1358827) (-825 "OMERRK.spad" 1357411 1357419 1358367 1358372) (-824 "OMENC.spad" 1356755 1356763 1357401 1357406) (-823 "OMDEV.spad" 1351064 1351072 1356745 1356750) (-822 "OMCONN.spad" 1350473 1350481 1351054 1351059) (-821 "OINTDOM.spad" 1350236 1350244 1350399 1350468) (-820 "OFMONOID.spad" 1348359 1348369 1350192 1350197) (-819 "ODVAR.spad" 1347620 1347630 1348349 1348354) (-818 "ODR.spad" 1347264 1347290 1347432 1347581) (-817 "ODPOL.spad" 1344646 1344656 1344986 1345113) (-816 "ODP.spad" 1334493 1334513 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1107055 1107060) (-702 "MINT.spad" 1105999 1106007 1106462 1106555) (-701 "MHROWRED.spad" 1104510 1104520 1105989 1105994) (-700 "MFLOAT.spad" 1103030 1103038 1104400 1104505) (-699 "MFINFACT.spad" 1102430 1102452 1103020 1103025) (-698 "MESH.spad" 1100212 1100220 1102420 1102425) (-697 "MDDFACT.spad" 1098423 1098433 1100202 1100207) (-696 "MDAGG.spad" 1097714 1097724 1098403 1098418) (-695 "MCMPLX.spad" 1093725 1093733 1094339 1094540) (-694 "MCDEN.spad" 1092935 1092947 1093715 1093720) (-693 "MCALCFN.spad" 1090057 1090083 1092925 1092930) (-692 "MAYBE.spad" 1089341 1089352 1090047 1090052) (-691 "MATSTOR.spad" 1086649 1086659 1089331 1089336) (-690 "MATRIX.spad" 1085353 1085363 1085837 1085864) (-689 "MATLIN.spad" 1082697 1082721 1085237 1085242) (-688 "MATCAT.spad" 1074426 1074448 1082665 1082692) (-687 "MATCAT.spad" 1066027 1066051 1074268 1074273) (-686 "MATCAT2.spad" 1065309 1065357 1066017 1066022) (-685 "MAPPKG3.spad" 1064224 1064238 1065299 1065304) (-684 "MAPPKG2.spad" 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(-606 "JAVACODE.spad" 971966 971974 972090 972095) (-605 "IXAGG.spad" 970099 970123 971956 971961) (-604 "IXAGG.spad" 968087 968113 969946 969951) (-603 "IVECTOR.spad" 966857 966872 967012 967039) (-602 "ITUPLE.spad" 966018 966028 966847 966852) (-601 "ITRIGMNP.spad" 964857 964876 966008 966013) (-600 "ITFUN3.spad" 964363 964377 964847 964852) (-599 "ITFUN2.spad" 964107 964119 964353 964358) (-598 "ITAYLOR.spad" 962101 962116 963971 964068) (-597 "ISUPS.spad" 954538 954553 961075 961172) (-596 "ISUMP.spad" 954039 954055 954528 954533) (-595 "ISTRING.spad" 953127 953140 953208 953235) (-594 "ISAST.spad" 952846 952854 953117 953122) (-593 "IRURPK.spad" 951563 951582 952836 952841) (-592 "IRSN.spad" 949567 949575 951553 951558) (-591 "IRRF2F.spad" 948052 948062 949523 949528) (-590 "IRREDFFX.spad" 947653 947664 948042 948047) (-589 "IROOT.spad" 945992 946002 947643 947648) (-588 "IR.spad" 943793 943807 945847 945874) (-587 "IR2.spad" 942821 942837 943783 943788) (-586 "IR2F.spad" 942027 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911838) (-565 "INTHERAL.spad" 910787 910811 911107 911112) (-564 "INTHEORY.spad" 907226 907234 910777 910782) (-563 "INTG0.spad" 900959 900977 907158 907163) (-562 "INTFTBL.spad" 894988 894996 900949 900954) (-561 "INTFACT.spad" 894047 894057 894978 894983) (-560 "INTEF.spad" 892432 892448 894037 894042) (-559 "INTDOM.spad" 891055 891063 892358 892427) (-558 "INTDOM.spad" 889740 889750 891045 891050) (-557 "INTCAT.spad" 887999 888009 889654 889735) (-556 "INTBIT.spad" 887506 887514 887989 887994) (-555 "INTALG.spad" 886694 886721 887496 887501) (-554 "INTAF.spad" 886194 886210 886684 886689) (-553 "INTABL.spad" 884712 884743 884875 884902) (-552 "INT8.spad" 884592 884600 884702 884707) (-551 "INT64.spad" 884471 884479 884582 884587) (-550 "INT32.spad" 884350 884358 884461 884466) (-549 "INT16.spad" 884229 884237 884340 884345) (-548 "INS.spad" 881732 881740 884131 884224) (-547 "INS.spad" 879321 879331 881722 881727) (-546 "INPSIGN.spad" 878769 878782 879311 879316) (-545 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(-218 "DEFAST.spad" 248731 248739 249353 249358) (-217 "DECIMAL.spad" 246837 246845 247198 247291) (-216 "DDFACT.spad" 244650 244667 246827 246832) (-215 "DBLRESP.spad" 244250 244274 244640 244645) (-214 "DBASE.spad" 242914 242924 244240 244245) (-213 "DATAARY.spad" 242376 242389 242904 242909) (-212 "D03FAFA.spad" 242204 242212 242366 242371) (-211 "D03EEFA.spad" 242024 242032 242194 242199) (-210 "D03AGNT.spad" 241110 241118 242014 242019) (-209 "D02EJFA.spad" 240572 240580 241100 241105) (-208 "D02CJFA.spad" 240050 240058 240562 240567) (-207 "D02BHFA.spad" 239540 239548 240040 240045) (-206 "D02BBFA.spad" 239030 239038 239530 239535) (-205 "D02AGNT.spad" 233844 233852 239020 239025) (-204 "D01WGTS.spad" 232163 232171 233834 233839) (-203 "D01TRNS.spad" 232140 232148 232153 232158) (-202 "D01GBFA.spad" 231662 231670 232130 232135) (-201 "D01FCFA.spad" 231184 231192 231652 231657) (-200 "D01ASFA.spad" 230652 230660 231174 231179) (-199 "D01AQFA.spad" 230098 230106 230642 230647) (-198 "D01APFA.spad" 229522 229530 230088 230093) (-197 "D01ANFA.spad" 229016 229024 229512 229517) (-196 "D01AMFA.spad" 228526 228534 229006 229011) (-195 "D01ALFA.spad" 228066 228074 228516 228521) (-194 "D01AKFA.spad" 227592 227600 228056 228061) (-193 "D01AJFA.spad" 227115 227123 227582 227587) (-192 "D01AGNT.spad" 223182 223190 227105 227110) (-191 "CYCLOTOM.spad" 222688 222696 223172 223177) (-190 "CYCLES.spad" 219544 219552 222678 222683) (-189 "CVMP.spad" 218961 218971 219534 219539) (-188 "CTRIGMNP.spad" 217461 217477 218951 218956) (-187 "CTOR.spad" 217152 217160 217451 217456) (-186 "CTORKIND.spad" 216755 216763 217142 217147) (-185 "CTORCAT.spad" 216004 216012 216745 216750) (-184 "CTORCAT.spad" 215251 215261 215994 215999) (-183 "CTORCALL.spad" 214840 214850 215241 215246) (-182 "CSTTOOLS.spad" 214085 214098 214830 214835) (-181 "CRFP.spad" 207809 207822 214075 214080) (-180 "CRCEAST.spad" 207529 207537 207799 207804) (-179 "CRAPACK.spad" 206580 206590 207519 207524) (-178 "CPMATCH.spad" 206084 206099 206505 206510) (-177 "CPIMA.spad" 205789 205808 206074 206079) (-176 "COORDSYS.spad" 200798 200808 205779 205784) (-175 "CONTOUR.spad" 200209 200217 200788 200793) (-174 "CONTFRAC.spad" 195959 195969 200111 200204) (-173 "CONDUIT.spad" 195717 195725 195949 195954) (-172 "COMRING.spad" 195391 195399 195655 195712) (-171 "COMPPROP.spad" 194909 194917 195381 195386) (-170 "COMPLPAT.spad" 194676 194691 194899 194904) (-169 "COMPLEX.spad" 188813 188823 189057 189318) (-168 "COMPLEX2.spad" 188528 188540 188803 188808) (-167 "COMPFACT.spad" 188130 188144 188518 188523) (-166 "COMPCAT.spad" 186202 186212 187864 188125) (-165 "COMPCAT.spad" 184002 184014 185666 185671) (-164 "COMMUPC.spad" 183750 183768 183992 183997) (-163 "COMMONOP.spad" 183283 183291 183740 183745) (-162 "COMM.spad" 183094 183102 183273 183278) (-161 "COMMAAST.spad" 182857 182865 183084 183089) (-160 "COMBOPC.spad" 181772 181780 182847 182852) (-159 "COMBINAT.spad" 180539 180549 181762 181767) (-158 "COMBF.spad" 177921 177937 180529 180534) (-157 "COLOR.spad" 176758 176766 177911 177916) (-156 "COLONAST.spad" 176424 176432 176748 176753) (-155 "CMPLXRT.spad" 176135 176152 176414 176419) (-154 "CLLCTAST.spad" 175797 175805 176125 176130) (-153 "CLIP.spad" 171905 171913 175787 175792) (-152 "CLIF.spad" 170560 170576 171861 171900) (-151 "CLAGG.spad" 167065 167075 170550 170555) (-150 "CLAGG.spad" 163441 163453 166928 166933) (-149 "CINTSLPE.spad" 162772 162785 163431 163436) (-148 "CHVAR.spad" 160910 160932 162762 162767) (-147 "CHARZ.spad" 160825 160833 160890 160905) (-146 "CHARPOL.spad" 160335 160345 160815 160820) (-145 "CHARNZ.spad" 160088 160096 160315 160330) (-144 "CHAR.spad" 157962 157970 160078 160083) (-143 "CFCAT.spad" 157290 157298 157952 157957) (-142 "CDEN.spad" 156486 156500 157280 157285) (-141 "CCLASS.spad" 154635 154643 155897 155936) (-140 "CATEGORY.spad" 153677 153685 154625 154630) (-139 "CATCTOR.spad" 153568 153576 153667 153672) (-138 "CATAST.spad" 153186 153194 153558 153563) (-137 "CASEAST.spad" 152900 152908 153176 153181) (-136 "CARTEN.spad" 148187 148211 152890 152895) (-135 "CARTEN2.spad" 147577 147604 148177 148182) (-134 "CARD.spad" 144872 144880 147551 147572) (-133 "CAPSLAST.spad" 144646 144654 144862 144867) (-132 "CACHSET.spad" 144270 144278 144636 144641) (-131 "CABMON.spad" 143825 143833 144260 144265) (-130 "BYTEORD.spad" 143500 143508 143815 143820) (-129 "BYTE.spad" 142927 142935 143490 143495) (-128 "BYTEBUF.spad" 140786 140794 142096 142123) (-127 "BTREE.spad" 139859 139869 140393 140420) (-126 "BTOURN.spad" 138864 138874 139466 139493) (-125 "BTCAT.spad" 138256 138266 138832 138859) (-124 "BTCAT.spad" 137668 137680 138246 138251) (-123 "BTAGG.spad" 136796 136804 137636 137663) (-122 "BTAGG.spad" 135944 135954 136786 136791) (-121 "BSTREE.spad" 134685 134695 135551 135578) (-120 "BRILL.spad" 132882 132893 134675 134680) (-119 "BRAGG.spad" 131822 131832 132872 132877) (-118 "BRAGG.spad" 130726 130738 131778 131783) (-117 "BPADICRT.spad" 128707 128719 128962 129055) (-116 "BPADIC.spad" 128371 128383 128633 128702) (-115 "BOUNDZRO.spad" 128027 128044 128361 128366) (-114 "BOP.spad" 123209 123217 128017 128022) (-113 "BOP1.spad" 120675 120685 123199 123204) (-112 "BOOLEAN.spad" 120113 120121 120665 120670) (-111 "BMODULE.spad" 119825 119837 120081 120108) (-110 "BITS.spad" 119246 119254 119461 119488) (-109 "BINDING.spad" 118659 118667 119236 119241) (-108 "BINARY.spad" 116770 116778 117126 117219) (-107 "BGAGG.spad" 115975 115985 116750 116765) (-106 "BGAGG.spad" 115188 115200 115965 115970) (-105 "BFUNCT.spad" 114752 114760 115168 115183) (-104 "BEZOUT.spad" 113892 113919 114702 114707) (-103 "BBTREE.spad" 110737 110747 113499 113526) (-102 "BASTYPE.spad" 110409 110417 110727 110732) (-101 "BASTYPE.spad" 110079 110089 110399 110404) (-100 "BALFACT.spad" 109538 109551 110069 110074) (-99 "AUTOMOR.spad" 108989 108998 109518 109533) (-98 "ATTREG.spad" 105712 105719 108741 108984) (-97 "ATTRBUT.spad" 101735 101742 105692 105707) (-96 "ATTRAST.spad" 101452 101459 101725 101730) (-95 "ATRIG.spad" 100922 100929 101442 101447) (-94 "ATRIG.spad" 100390 100399 100912 100917) (-93 "ASTCAT.spad" 100294 100301 100380 100385) (-92 "ASTCAT.spad" 100196 100205 100284 100289) (-91 "ASTACK.spad" 99535 99544 99803 99830) (-90 "ASSOCEQ.spad" 98361 98372 99491 99496) (-89 "ASP9.spad" 97442 97455 98351 98356) (-88 "ASP8.spad" 96485 96498 97432 97437) (-87 "ASP80.spad" 95807 95820 96475 96480) (-86 "ASP7.spad" 94967 94980 95797 95802) (-85 "ASP78.spad" 94418 94431 94957 94962) (-84 "ASP77.spad" 93787 93800 94408 94413) (-83 "ASP74.spad" 92879 92892 93777 93782) (-82 "ASP73.spad" 92150 92163 92869 92874) (-81 "ASP6.spad" 91017 91030 92140 92145) (-80 "ASP55.spad" 89526 89539 91007 91012) (-79 "ASP50.spad" 87343 87356 89516 89521) (-78 "ASP4.spad" 86638 86651 87333 87338) (-77 "ASP49.spad" 85637 85650 86628 86633) (-76 "ASP42.spad" 84044 84083 85627 85632) (-75 "ASP41.spad" 82623 82662 84034 84039) (-74 "ASP35.spad" 81611 81624 82613 82618) (-73 "ASP34.spad" 80912 80925 81601 81606) (-72 "ASP33.spad" 80472 80485 80902 80907) (-71 "ASP31.spad" 79612 79625 80462 80467) (-70 "ASP30.spad" 78504 78517 79602 79607) (-69 "ASP29.spad" 77970 77983 78494 78499) (-68 "ASP28.spad" 69243 69256 77960 77965) (-67 "ASP27.spad" 68140 68153 69233 69238) (-66 "ASP24.spad" 67227 67240 68130 68135) (-65 "ASP20.spad" 66691 66704 67217 67222) (-64 "ASP1.spad" 66072 66085 66681 66686) (-63 "ASP19.spad" 60758 60771 66062 66067) (-62 "ASP12.spad" 60172 60185 60748 60753) (-61 "ASP10.spad" 59443 59456 60162 60167) (-60 "ARRAY2.spad" 58803 58812 59050 59077) (-59 "ARRAY1.spad" 57640 57649 57986 58013) (-58 "ARRAY12.spad" 56353 56364 57630 57635) (-57 "ARR2CAT.spad" 52127 52148 56321 56348) (-56 "ARR2CAT.spad" 47921 47944 52117 52122) (-55 "ARITY.spad" 47293 47300 47911 47916) (-54 "APPRULE.spad" 46553 46575 47283 47288) (-53 "APPLYORE.spad" 46172 46185 46543 46548) (-52 "ANY.spad" 45031 45038 46162 46167) (-51 "ANY1.spad" 44102 44111 45021 45026) (-50 "ANTISYM.spad" 42547 42563 44082 44097) (-49 "ANON.spad" 42240 42247 42537 42542) (-48 "AN.spad" 40549 40556 42056 42149) (-47 "AMR.spad" 38734 38745 40447 40544) (-46 "AMR.spad" 36756 36769 38471 38476) (-45 "ALIST.spad" 34168 34189 34518 34545) (-44 "ALGSC.spad" 33303 33329 34040 34093) (-43 "ALGPKG.spad" 29086 29097 33259 33264) (-42 "ALGMFACT.spad" 28279 28293 29076 29081) (-41 "ALGMANIP.spad" 25753 25768 28112 28117) (-40 "ALGFF.spad" 24068 24095 24285 24441) (-39 "ALGFACT.spad" 23195 23205 24058 24063) (-38 "ALGEBRA.spad" 23028 23037 23151 23190) (-37 "ALGEBRA.spad" 22893 22904 23018 23023) (-36 "ALAGG.spad" 22405 22426 22861 22888) (-35 "AHYP.spad" 21786 21793 22395 22400) (-34 "AGG.spad" 20103 20110 21776 21781) (-33 "AGG.spad" 18384 18393 20059 20064) (-32 "AF.spad" 16815 16830 18319 18324) (-31 "ADDAST.spad" 16493 16500 16805 16810) (-30 "ACPLOT.spad" 15084 15091 16483 16488) (-29 "ACFS.spad" 12893 12902 14986 15079) (-28 "ACFS.spad" 10788 10799 12883 12888) (-27 "ACF.spad" 7470 7477 10690 10783) (-26 "ACF.spad" 4238 4247 7460 7465) (-25 "ABELSG.spad" 3779 3786 4228 4233) (-24 "ABELSG.spad" 3318 3327 3769 3774) (-23 "ABELMON.spad" 2861 2868 3308 3313) (-22 "ABELMON.spad" 2402 2411 2851 2856) (-21 "ABELGRP.spad" 2067 2074 2392 2397) (-20 "ABELGRP.spad" 1730 1739 2057 2062) (-19 "A1AGG.spad" 870 879 1698 1725) (-18 "A1AGG.spad" 30 41 860 865))
\ No newline at end of file +((-3 NIL 2263533 2263538 2263543 2263548) (-2 NIL 2263513 2263518 2263523 2263528) (-1 NIL 2263493 2263498 2263503 2263508) (0 NIL 2263473 2263478 2263483 2263488) (-1296 "ZMOD.spad" 2263282 2263295 2263411 2263468) (-1295 "ZLINDEP.spad" 2262348 2262359 2263272 2263277) (-1294 "ZDSOLVE.spad" 2252293 2252315 2262338 2262343) (-1293 "YSTREAM.spad" 2251788 2251799 2252283 2252288) (-1292 "XRPOLY.spad" 2251008 2251028 2251644 2251713) (-1291 "XPR.spad" 2248803 2248816 2250726 2250825) (-1290 "XPOLY.spad" 2248358 2248369 2248659 2248728) (-1289 "XPOLYC.spad" 2247677 2247693 2248284 2248353) (-1288 "XPBWPOLY.spad" 2246114 2246134 2247457 2247526) (-1287 "XF.spad" 2244577 2244592 2246016 2246109) (-1286 "XF.spad" 2243020 2243037 2244461 2244466) (-1285 "XFALG.spad" 2240068 2240084 2242946 2243015) (-1284 "XEXPPKG.spad" 2239319 2239345 2240058 2240063) (-1283 "XDPOLY.spad" 2238933 2238949 2239175 2239244) (-1282 "XALG.spad" 2238593 2238604 2238889 2238928) (-1281 "WUTSET.spad" 2234432 2234449 2238239 2238266) (-1280 "WP.spad" 2233631 2233675 2234290 2234357) (-1279 "WHILEAST.spad" 2233429 2233438 2233621 2233626) (-1278 "WHEREAST.spad" 2233100 2233109 2233419 2233424) (-1277 "WFFINTBS.spad" 2230763 2230785 2233090 2233095) (-1276 "WEIER.spad" 2228985 2228996 2230753 2230758) (-1275 "VSPACE.spad" 2228658 2228669 2228953 2228980) (-1274 "VSPACE.spad" 2228351 2228364 2228648 2228653) (-1273 "VOID.spad" 2228028 2228037 2228341 2228346) (-1272 "VIEW.spad" 2225708 2225717 2228018 2228023) (-1271 "VIEWDEF.spad" 2220909 2220918 2225698 2225703) (-1270 "VIEW3D.spad" 2204870 2204879 2220899 2220904) (-1269 "VIEW2D.spad" 2192761 2192770 2204860 2204865) (-1268 "VECTOR.spad" 2191435 2191446 2191686 2191713) (-1267 "VECTOR2.spad" 2190074 2190087 2191425 2191430) (-1266 "VECTCAT.spad" 2187978 2187989 2190042 2190069) (-1265 "VECTCAT.spad" 2185689 2185702 2187755 2187760) (-1264 "VARIABLE.spad" 2185469 2185484 2185679 2185684) (-1263 "UTYPE.spad" 2185113 2185122 2185459 2185464) (-1262 "UTSODETL.spad" 2184408 2184432 2185069 2185074) (-1261 "UTSODE.spad" 2182624 2182644 2184398 2184403) (-1260 "UTS.spad" 2177437 2177465 2181091 2181188) (-1259 "UTSCAT.spad" 2174916 2174932 2177335 2177432) (-1258 "UTSCAT.spad" 2172039 2172057 2174460 2174465) (-1257 "UTS2.spad" 2171634 2171669 2172029 2172034) (-1256 "URAGG.spad" 2166307 2166318 2171624 2171629) (-1255 "URAGG.spad" 2160944 2160957 2166263 2166268) (-1254 "UPXSSING.spad" 2158589 2158615 2160025 2160158) (-1253 "UPXS.spad" 2155743 2155771 2156721 2156870) (-1252 "UPXSCONS.spad" 2153502 2153522 2153875 2154024) (-1251 "UPXSCCA.spad" 2152073 2152093 2153348 2153497) (-1250 "UPXSCCA.spad" 2150786 2150808 2152063 2152068) (-1249 "UPXSCAT.spad" 2149375 2149391 2150632 2150781) (-1248 "UPXS2.spad" 2148918 2148971 2149365 2149370) (-1247 "UPSQFREE.spad" 2147332 2147346 2148908 2148913) (-1246 "UPSCAT.spad" 2144943 2144967 2147230 2147327) (-1245 "UPSCAT.spad" 2142260 2142286 2144549 2144554) (-1244 "UPOLYC.spad" 2137300 2137311 2142102 2142255) (-1243 "UPOLYC.spad" 2132232 2132245 2137036 2137041) (-1242 "UPOLYC2.spad" 2131703 2131722 2132222 2132227) (-1241 "UP.spad" 2128902 2128917 2129289 2129442) (-1240 "UPMP.spad" 2127802 2127815 2128892 2128897) (-1239 "UPDIVP.spad" 2127367 2127381 2127792 2127797) (-1238 "UPDECOMP.spad" 2125612 2125626 2127357 2127362) (-1237 "UPCDEN.spad" 2124821 2124837 2125602 2125607) (-1236 "UP2.spad" 2124185 2124206 2124811 2124816) (-1235 "UNISEG.spad" 2123538 2123549 2124104 2124109) (-1234 "UNISEG2.spad" 2123035 2123048 2123494 2123499) (-1233 "UNIFACT.spad" 2122138 2122150 2123025 2123030) (-1232 "ULS.spad" 2112696 2112724 2113783 2114212) (-1231 "ULSCONS.spad" 2105092 2105112 2105462 2105611) (-1230 "ULSCCAT.spad" 2102829 2102849 2104938 2105087) (-1229 "ULSCCAT.spad" 2100674 2100696 2102785 2102790) (-1228 "ULSCAT.spad" 2098906 2098922 2100520 2100669) (-1227 "ULS2.spad" 2098420 2098473 2098896 2098901) (-1226 "UINT8.spad" 2098297 2098306 2098410 2098415) (-1225 "UINT64.spad" 2098173 2098182 2098287 2098292) (-1224 "UINT32.spad" 2098049 2098058 2098163 2098168) (-1223 "UINT16.spad" 2097925 2097934 2098039 2098044) (-1222 "UFD.spad" 2096990 2096999 2097851 2097920) (-1221 "UFD.spad" 2096117 2096128 2096980 2096985) (-1220 "UDVO.spad" 2094998 2095007 2096107 2096112) (-1219 "UDPO.spad" 2092491 2092502 2094954 2094959) (-1218 "TYPE.spad" 2092423 2092432 2092481 2092486) (-1217 "TYPEAST.spad" 2092342 2092351 2092413 2092418) (-1216 "TWOFACT.spad" 2090994 2091009 2092332 2092337) (-1215 "TUPLE.spad" 2090480 2090491 2090893 2090898) (-1214 "TUBETOOL.spad" 2087347 2087356 2090470 2090475) (-1213 "TUBE.spad" 2085994 2086011 2087337 2087342) (-1212 "TS.spad" 2084593 2084609 2085559 2085656) (-1211 "TSETCAT.spad" 2071720 2071737 2084561 2084588) (-1210 "TSETCAT.spad" 2058833 2058852 2071676 2071681) (-1209 "TRMANIP.spad" 2053199 2053216 2058539 2058544) (-1208 "TRIMAT.spad" 2052162 2052187 2053189 2053194) (-1207 "TRIGMNIP.spad" 2050689 2050706 2052152 2052157) (-1206 "TRIGCAT.spad" 2050201 2050210 2050679 2050684) (-1205 "TRIGCAT.spad" 2049711 2049722 2050191 2050196) (-1204 "TREE.spad" 2048286 2048297 2049318 2049345) (-1203 "TRANFUN.spad" 2048125 2048134 2048276 2048281) (-1202 "TRANFUN.spad" 2047962 2047973 2048115 2048120) (-1201 "TOPSP.spad" 2047636 2047645 2047952 2047957) (-1200 "TOOLSIGN.spad" 2047299 2047310 2047626 2047631) (-1199 "TEXTFILE.spad" 2045860 2045869 2047289 2047294) (-1198 "TEX.spad" 2043006 2043015 2045850 2045855) (-1197 "TEX1.spad" 2042562 2042573 2042996 2043001) (-1196 "TEMUTL.spad" 2042117 2042126 2042552 2042557) (-1195 "TBCMPPK.spad" 2040210 2040233 2042107 2042112) (-1194 "TBAGG.spad" 2039260 2039283 2040190 2040205) (-1193 "TBAGG.spad" 2038318 2038343 2039250 2039255) (-1192 "TANEXP.spad" 2037726 2037737 2038308 2038313) (-1191 "TABLE.spad" 2036137 2036160 2036407 2036434) (-1190 "TABLEAU.spad" 2035618 2035629 2036127 2036132) (-1189 "TABLBUMP.spad" 2032421 2032432 2035608 2035613) (-1188 "SYSTEM.spad" 2031649 2031658 2032411 2032416) (-1187 "SYSSOLP.spad" 2029132 2029143 2031639 2031644) (-1186 "SYSPTR.spad" 2029031 2029040 2029122 2029127) (-1185 "SYSNNI.spad" 2028213 2028224 2029021 2029026) (-1184 "SYSINT.spad" 2027617 2027628 2028203 2028208) (-1183 "SYNTAX.spad" 2023823 2023832 2027607 2027612) (-1182 "SYMTAB.spad" 2021891 2021900 2023813 2023818) (-1181 "SYMS.spad" 2017914 2017923 2021881 2021886) (-1180 "SYMPOLY.spad" 2016921 2016932 2017003 2017130) (-1179 "SYMFUNC.spad" 2016422 2016433 2016911 2016916) (-1178 "SYMBOL.spad" 2013925 2013934 2016412 2016417) (-1177 "SWITCH.spad" 2010696 2010705 2013915 2013920) (-1176 "SUTS.spad" 2007601 2007629 2009163 2009260) (-1175 "SUPXS.spad" 2004742 2004770 2005733 2005882) (-1174 "SUP.spad" 2001555 2001566 2002328 2002481) (-1173 "SUPFRACF.spad" 2000660 2000678 2001545 2001550) (-1172 "SUP2.spad" 2000052 2000065 2000650 2000655) (-1171 "SUMRF.spad" 1999026 1999037 2000042 2000047) (-1170 "SUMFS.spad" 1998663 1998680 1999016 1999021) (-1169 "SULS.spad" 1989208 1989236 1990308 1990737) (-1168 "SUCHTAST.spad" 1988977 1988986 1989198 1989203) (-1167 "SUCH.spad" 1988659 1988674 1988967 1988972) (-1166 "SUBSPACE.spad" 1980774 1980789 1988649 1988654) (-1165 "SUBRESP.spad" 1979944 1979958 1980730 1980735) (-1164 "STTF.spad" 1976043 1976059 1979934 1979939) (-1163 "STTFNC.spad" 1972511 1972527 1976033 1976038) (-1162 "STTAYLOR.spad" 1965165 1965176 1972392 1972397) (-1161 "STRTBL.spad" 1963670 1963687 1963819 1963846) (-1160 "STRING.spad" 1963079 1963088 1963093 1963120) (-1159 "STRICAT.spad" 1962867 1962876 1963047 1963074) (-1158 "STREAM.spad" 1959785 1959796 1962392 1962407) (-1157 "STREAM3.spad" 1959358 1959373 1959775 1959780) (-1156 "STREAM2.spad" 1958486 1958499 1959348 1959353) (-1155 "STREAM1.spad" 1958192 1958203 1958476 1958481) (-1154 "STINPROD.spad" 1957128 1957144 1958182 1958187) (-1153 "STEP.spad" 1956329 1956338 1957118 1957123) (-1152 "STBL.spad" 1954855 1954883 1955022 1955037) (-1151 "STAGG.spad" 1953930 1953941 1954845 1954850) (-1150 "STAGG.spad" 1953003 1953016 1953920 1953925) (-1149 "STACK.spad" 1952360 1952371 1952610 1952637) (-1148 "SREGSET.spad" 1950064 1950081 1952006 1952033) (-1147 "SRDCMPK.spad" 1948625 1948645 1950054 1950059) (-1146 "SRAGG.spad" 1943768 1943777 1948593 1948620) (-1145 "SRAGG.spad" 1938931 1938942 1943758 1943763) (-1144 "SQMATRIX.spad" 1936547 1936565 1937463 1937550) (-1143 "SPLTREE.spad" 1931099 1931112 1935983 1936010) (-1142 "SPLNODE.spad" 1927687 1927700 1931089 1931094) (-1141 "SPFCAT.spad" 1926496 1926505 1927677 1927682) (-1140 "SPECOUT.spad" 1925048 1925057 1926486 1926491) (-1139 "SPADXPT.spad" 1917187 1917196 1925038 1925043) (-1138 "spad-parser.spad" 1916652 1916661 1917177 1917182) (-1137 "SPADAST.spad" 1916353 1916362 1916642 1916647) (-1136 "SPACEC.spad" 1900552 1900563 1916343 1916348) (-1135 "SPACE3.spad" 1900328 1900339 1900542 1900547) (-1134 "SORTPAK.spad" 1899877 1899890 1900284 1900289) (-1133 "SOLVETRA.spad" 1897640 1897651 1899867 1899872) (-1132 "SOLVESER.spad" 1896168 1896179 1897630 1897635) (-1131 "SOLVERAD.spad" 1892194 1892205 1896158 1896163) (-1130 "SOLVEFOR.spad" 1890656 1890674 1892184 1892189) (-1129 "SNTSCAT.spad" 1890256 1890273 1890624 1890651) (-1128 "SMTS.spad" 1888528 1888554 1889821 1889918) (-1127 "SMP.spad" 1886003 1886023 1886393 1886520) (-1126 "SMITH.spad" 1884848 1884873 1885993 1885998) (-1125 "SMATCAT.spad" 1882958 1882988 1884792 1884843) (-1124 "SMATCAT.spad" 1881000 1881032 1882836 1882841) (-1123 "SKAGG.spad" 1879963 1879974 1880968 1880995) (-1122 "SINT.spad" 1878795 1878804 1879829 1879958) (-1121 "SIMPAN.spad" 1878523 1878532 1878785 1878790) (-1120 "SIG.spad" 1877853 1877862 1878513 1878518) (-1119 "SIGNRF.spad" 1876971 1876982 1877843 1877848) (-1118 "SIGNEF.spad" 1876250 1876267 1876961 1876966) (-1117 "SIGAST.spad" 1875635 1875644 1876240 1876245) (-1116 "SHP.spad" 1873563 1873578 1875591 1875596) (-1115 "SHDP.spad" 1863274 1863301 1863783 1863914) (-1114 "SGROUP.spad" 1862882 1862891 1863264 1863269) (-1113 "SGROUP.spad" 1862488 1862499 1862872 1862877) (-1112 "SGCF.spad" 1855651 1855660 1862478 1862483) (-1111 "SFRTCAT.spad" 1854581 1854598 1855619 1855646) (-1110 "SFRGCD.spad" 1853644 1853664 1854571 1854576) (-1109 "SFQCMPK.spad" 1848281 1848301 1853634 1853639) (-1108 "SFORT.spad" 1847720 1847734 1848271 1848276) (-1107 "SEXOF.spad" 1847563 1847603 1847710 1847715) (-1106 "SEX.spad" 1847455 1847464 1847553 1847558) (-1105 "SEXCAT.spad" 1845056 1845096 1847445 1847450) (-1104 "SET.spad" 1843380 1843391 1844477 1844516) (-1103 "SETMN.spad" 1841830 1841847 1843370 1843375) (-1102 "SETCAT.spad" 1841152 1841161 1841820 1841825) (-1101 "SETCAT.spad" 1840472 1840483 1841142 1841147) (-1100 "SETAGG.spad" 1837021 1837032 1840452 1840467) (-1099 "SETAGG.spad" 1833578 1833591 1837011 1837016) (-1098 "SEQAST.spad" 1833281 1833290 1833568 1833573) (-1097 "SEGXCAT.spad" 1832437 1832450 1833271 1833276) (-1096 "SEG.spad" 1832250 1832261 1832356 1832361) (-1095 "SEGCAT.spad" 1831175 1831186 1832240 1832245) (-1094 "SEGBIND.spad" 1830933 1830944 1831122 1831127) (-1093 "SEGBIND2.spad" 1830631 1830644 1830923 1830928) (-1092 "SEGAST.spad" 1830345 1830354 1830621 1830626) (-1091 "SEG2.spad" 1829780 1829793 1830301 1830306) (-1090 "SDVAR.spad" 1829056 1829067 1829770 1829775) (-1089 "SDPOL.spad" 1826482 1826493 1826773 1826900) (-1088 "SCPKG.spad" 1824571 1824582 1826472 1826477) (-1087 "SCOPE.spad" 1823724 1823733 1824561 1824566) (-1086 "SCACHE.spad" 1822420 1822431 1823714 1823719) (-1085 "SASTCAT.spad" 1822329 1822338 1822410 1822415) (-1084 "SAOS.spad" 1822201 1822210 1822319 1822324) (-1083 "SAERFFC.spad" 1821914 1821934 1822191 1822196) (-1082 "SAE.spad" 1820089 1820105 1820700 1820835) (-1081 "SAEFACT.spad" 1819790 1819810 1820079 1820084) (-1080 "RURPK.spad" 1817449 1817465 1819780 1819785) (-1079 "RULESET.spad" 1816902 1816926 1817439 1817444) (-1078 "RULE.spad" 1815142 1815166 1816892 1816897) (-1077 "RULECOLD.spad" 1814994 1815007 1815132 1815137) (-1076 "RTVALUE.spad" 1814729 1814738 1814984 1814989) (-1075 "RSTRCAST.spad" 1814446 1814455 1814719 1814724) (-1074 "RSETGCD.spad" 1810824 1810844 1814436 1814441) (-1073 "RSETCAT.spad" 1800760 1800777 1810792 1810819) (-1072 "RSETCAT.spad" 1790716 1790735 1800750 1800755) (-1071 "RSDCMPK.spad" 1789168 1789188 1790706 1790711) (-1070 "RRCC.spad" 1787552 1787582 1789158 1789163) (-1069 "RRCC.spad" 1785934 1785966 1787542 1787547) (-1068 "RPTAST.spad" 1785636 1785645 1785924 1785929) (-1067 "RPOLCAT.spad" 1764996 1765011 1785504 1785631) (-1066 "RPOLCAT.spad" 1744070 1744087 1764580 1764585) (-1065 "ROUTINE.spad" 1739953 1739962 1742717 1742744) (-1064 "ROMAN.spad" 1739281 1739290 1739819 1739948) (-1063 "ROIRC.spad" 1738361 1738393 1739271 1739276) (-1062 "RNS.spad" 1737264 1737273 1738263 1738356) (-1061 "RNS.spad" 1736253 1736264 1737254 1737259) (-1060 "RNG.spad" 1735988 1735997 1736243 1736248) (-1059 "RNGBIND.spad" 1735148 1735162 1735943 1735948) (-1058 "RMODULE.spad" 1734913 1734924 1735138 1735143) (-1057 "RMCAT2.spad" 1734333 1734390 1734903 1734908) (-1056 "RMATRIX.spad" 1733157 1733176 1733500 1733539) (-1055 "RMATCAT.spad" 1728736 1728767 1733113 1733152) (-1054 "RMATCAT.spad" 1724205 1724238 1728584 1728589) (-1053 "RLINSET.spad" 1723599 1723610 1724195 1724200) (-1052 "RINTERP.spad" 1723487 1723507 1723589 1723594) (-1051 "RING.spad" 1722957 1722966 1723467 1723482) (-1050 "RING.spad" 1722435 1722446 1722947 1722952) (-1049 "RIDIST.spad" 1721827 1721836 1722425 1722430) (-1048 "RGCHAIN.spad" 1720410 1720426 1721312 1721339) (-1047 "RGBCSPC.spad" 1720191 1720203 1720400 1720405) (-1046 "RGBCMDL.spad" 1719721 1719733 1720181 1720186) (-1045 "RF.spad" 1717363 1717374 1719711 1719716) (-1044 "RFFACTOR.spad" 1716825 1716836 1717353 1717358) (-1043 "RFFACT.spad" 1716560 1716572 1716815 1716820) (-1042 "RFDIST.spad" 1715556 1715565 1716550 1716555) (-1041 "RETSOL.spad" 1714975 1714988 1715546 1715551) (-1040 "RETRACT.spad" 1714403 1714414 1714965 1714970) (-1039 "RETRACT.spad" 1713829 1713842 1714393 1714398) (-1038 "RETAST.spad" 1713641 1713650 1713819 1713824) (-1037 "RESULT.spad" 1711701 1711710 1712288 1712315) (-1036 "RESRING.spad" 1711048 1711095 1711639 1711696) (-1035 "RESLATC.spad" 1710372 1710383 1711038 1711043) (-1034 "REPSQ.spad" 1710103 1710114 1710362 1710367) (-1033 "REP.spad" 1707657 1707666 1710093 1710098) (-1032 "REPDB.spad" 1707364 1707375 1707647 1707652) (-1031 "REP2.spad" 1697022 1697033 1707206 1707211) (-1030 "REP1.spad" 1691218 1691229 1696972 1696977) (-1029 "REGSET.spad" 1689015 1689032 1690864 1690891) (-1028 "REF.spad" 1688350 1688361 1688970 1688975) (-1027 "REDORDER.spad" 1687556 1687573 1688340 1688345) (-1026 "RECLOS.spad" 1686339 1686359 1687043 1687136) (-1025 "REALSOLV.spad" 1685479 1685488 1686329 1686334) (-1024 "REAL.spad" 1685351 1685360 1685469 1685474) (-1023 "REAL0Q.spad" 1682649 1682664 1685341 1685346) (-1022 "REAL0.spad" 1679493 1679508 1682639 1682644) (-1021 "RDUCEAST.spad" 1679214 1679223 1679483 1679488) (-1020 "RDIV.spad" 1678869 1678894 1679204 1679209) (-1019 "RDIST.spad" 1678436 1678447 1678859 1678864) (-1018 "RDETRS.spad" 1677300 1677318 1678426 1678431) (-1017 "RDETR.spad" 1675439 1675457 1677290 1677295) (-1016 "RDEEFS.spad" 1674538 1674555 1675429 1675434) (-1015 "RDEEF.spad" 1673548 1673565 1674528 1674533) (-1014 "RCFIELD.spad" 1670734 1670743 1673450 1673543) (-1013 "RCFIELD.spad" 1668006 1668017 1670724 1670729) (-1012 "RCAGG.spad" 1665934 1665945 1667996 1668001) (-1011 "RCAGG.spad" 1663789 1663802 1665853 1665858) (-1010 "RATRET.spad" 1663149 1663160 1663779 1663784) (-1009 "RATFACT.spad" 1662841 1662853 1663139 1663144) (-1008 "RANDSRC.spad" 1662160 1662169 1662831 1662836) (-1007 "RADUTIL.spad" 1661916 1661925 1662150 1662155) (-1006 "RADIX.spad" 1658837 1658851 1660383 1660476) (-1005 "RADFF.spad" 1657250 1657287 1657369 1657525) (-1004 "RADCAT.spad" 1656845 1656854 1657240 1657245) (-1003 "RADCAT.spad" 1656438 1656449 1656835 1656840) (-1002 "QUEUE.spad" 1655786 1655797 1656045 1656072) (-1001 "QUAT.spad" 1654367 1654378 1654710 1654775) (-1000 "QUATCT2.spad" 1653987 1654006 1654357 1654362) (-999 "QUATCAT.spad" 1652158 1652168 1653917 1653982) (-998 "QUATCAT.spad" 1650080 1650092 1651841 1651846) (-997 "QUAGG.spad" 1648908 1648918 1650048 1650075) (-996 "QQUTAST.spad" 1648677 1648685 1648898 1648903) (-995 "QFORM.spad" 1648142 1648156 1648667 1648672) (-994 "QFCAT.spad" 1646845 1646855 1648044 1648137) (-993 "QFCAT.spad" 1645139 1645151 1646340 1646345) (-992 "QFCAT2.spad" 1644832 1644848 1645129 1645134) (-991 "QEQUAT.spad" 1644391 1644399 1644822 1644827) (-990 "QCMPACK.spad" 1639138 1639157 1644381 1644386) (-989 "QALGSET.spad" 1635217 1635249 1639052 1639057) (-988 "QALGSET2.spad" 1633213 1633231 1635207 1635212) (-987 "PWFFINTB.spad" 1630629 1630650 1633203 1633208) (-986 "PUSHVAR.spad" 1629968 1629987 1630619 1630624) (-985 "PTRANFN.spad" 1626096 1626106 1629958 1629963) (-984 "PTPACK.spad" 1623184 1623194 1626086 1626091) (-983 "PTFUNC2.spad" 1623007 1623021 1623174 1623179) (-982 "PTCAT.spad" 1622262 1622272 1622975 1623002) (-981 "PSQFR.spad" 1621569 1621593 1622252 1622257) (-980 "PSEUDLIN.spad" 1620455 1620465 1621559 1621564) (-979 "PSETPK.spad" 1605888 1605904 1620333 1620338) (-978 "PSETCAT.spad" 1599808 1599831 1605868 1605883) (-977 "PSETCAT.spad" 1593702 1593727 1599764 1599769) (-976 "PSCURVE.spad" 1592685 1592693 1593692 1593697) (-975 "PSCAT.spad" 1591468 1591497 1592583 1592680) (-974 "PSCAT.spad" 1590341 1590372 1591458 1591463) (-973 "PRTITION.spad" 1589302 1589310 1590331 1590336) (-972 "PRTDAST.spad" 1589021 1589029 1589292 1589297) (-971 "PRS.spad" 1578583 1578600 1588977 1588982) (-970 "PRQAGG.spad" 1578018 1578028 1578551 1578578) (-969 "PROPLOG.spad" 1577317 1577325 1578008 1578013) (-968 "PROPFRML.spad" 1576133 1576144 1577307 1577312) (-967 "PROPERTY.spad" 1575621 1575629 1576123 1576128) (-966 "PRODUCT.spad" 1573303 1573315 1573587 1573642) (-965 "PR.spad" 1571695 1571707 1572394 1572521) (-964 "PRINT.spad" 1571447 1571455 1571685 1571690) (-963 "PRIMES.spad" 1569700 1569710 1571437 1571442) (-962 "PRIMELT.spad" 1567781 1567795 1569690 1569695) (-961 "PRIMCAT.spad" 1567408 1567416 1567771 1567776) (-960 "PRIMARR.spad" 1566413 1566423 1566591 1566618) (-959 "PRIMARR2.spad" 1565180 1565192 1566403 1566408) (-958 "PREASSOC.spad" 1564562 1564574 1565170 1565175) (-957 "PPCURVE.spad" 1563699 1563707 1564552 1564557) (-956 "PORTNUM.spad" 1563474 1563482 1563689 1563694) (-955 "POLYROOT.spad" 1562323 1562345 1563430 1563435) (-954 "POLY.spad" 1559658 1559668 1560173 1560300) (-953 "POLYLIFT.spad" 1558923 1558946 1559648 1559653) (-952 "POLYCATQ.spad" 1557041 1557063 1558913 1558918) (-951 "POLYCAT.spad" 1550511 1550532 1556909 1557036) (-950 "POLYCAT.spad" 1543319 1543342 1549719 1549724) (-949 "POLY2UP.spad" 1542771 1542785 1543309 1543314) (-948 "POLY2.spad" 1542368 1542380 1542761 1542766) (-947 "POLUTIL.spad" 1541309 1541338 1542324 1542329) (-946 "POLTOPOL.spad" 1540057 1540072 1541299 1541304) (-945 "POINT.spad" 1538895 1538905 1538982 1539009) (-944 "PNTHEORY.spad" 1535597 1535605 1538885 1538890) (-943 "PMTOOLS.spad" 1534372 1534386 1535587 1535592) (-942 "PMSYM.spad" 1533921 1533931 1534362 1534367) (-941 "PMQFCAT.spad" 1533512 1533526 1533911 1533916) (-940 "PMPRED.spad" 1532991 1533005 1533502 1533507) (-939 "PMPREDFS.spad" 1532445 1532467 1532981 1532986) (-938 "PMPLCAT.spad" 1531525 1531543 1532377 1532382) (-937 "PMLSAGG.spad" 1531110 1531124 1531515 1531520) (-936 "PMKERNEL.spad" 1530689 1530701 1531100 1531105) (-935 "PMINS.spad" 1530269 1530279 1530679 1530684) (-934 "PMFS.spad" 1529846 1529864 1530259 1530264) (-933 "PMDOWN.spad" 1529136 1529150 1529836 1529841) (-932 "PMASS.spad" 1528146 1528154 1529126 1529131) (-931 "PMASSFS.spad" 1527113 1527129 1528136 1528141) (-930 "PLOTTOOL.spad" 1526893 1526901 1527103 1527108) (-929 "PLOT.spad" 1521816 1521824 1526883 1526888) (-928 "PLOT3D.spad" 1518280 1518288 1521806 1521811) (-927 "PLOT1.spad" 1517437 1517447 1518270 1518275) (-926 "PLEQN.spad" 1504727 1504754 1517427 1517432) (-925 "PINTERP.spad" 1504349 1504368 1504717 1504722) (-924 "PINTERPA.spad" 1504133 1504149 1504339 1504344) (-923 "PI.spad" 1503742 1503750 1504107 1504128) (-922 "PID.spad" 1502712 1502720 1503668 1503737) (-921 "PICOERCE.spad" 1502369 1502379 1502702 1502707) (-920 "PGROEB.spad" 1500970 1500984 1502359 1502364) (-919 "PGE.spad" 1492587 1492595 1500960 1500965) (-918 "PGCD.spad" 1491477 1491494 1492577 1492582) (-917 "PFRPAC.spad" 1490626 1490636 1491467 1491472) (-916 "PFR.spad" 1487289 1487299 1490528 1490621) (-915 "PFOTOOLS.spad" 1486547 1486563 1487279 1487284) (-914 "PFOQ.spad" 1485917 1485935 1486537 1486542) (-913 "PFO.spad" 1485336 1485363 1485907 1485912) (-912 "PF.spad" 1484910 1484922 1485141 1485234) (-911 "PFECAT.spad" 1482592 1482600 1484836 1484905) (-910 "PFECAT.spad" 1480302 1480312 1482548 1482553) (-909 "PFBRU.spad" 1478190 1478202 1480292 1480297) (-908 "PFBR.spad" 1475750 1475773 1478180 1478185) (-907 "PERM.spad" 1471435 1471445 1475580 1475595) (-906 "PERMGRP.spad" 1466197 1466207 1471425 1471430) (-905 "PERMCAT.spad" 1464755 1464765 1466177 1466192) (-904 "PERMAN.spad" 1463287 1463301 1464745 1464750) (-903 "PENDTREE.spad" 1462628 1462638 1462916 1462921) (-902 "PDRING.spad" 1461179 1461189 1462608 1462623) (-901 "PDRING.spad" 1459738 1459750 1461169 1461174) (-900 "PDEPROB.spad" 1458753 1458761 1459728 1459733) (-899 "PDEPACK.spad" 1452793 1452801 1458743 1458748) (-898 "PDECOMP.spad" 1452263 1452280 1452783 1452788) (-897 "PDECAT.spad" 1450619 1450627 1452253 1452258) (-896 "PCOMP.spad" 1450472 1450485 1450609 1450614) (-895 "PBWLB.spad" 1449060 1449077 1450462 1450467) (-894 "PATTERN.spad" 1443599 1443609 1449050 1449055) (-893 "PATTERN2.spad" 1443337 1443349 1443589 1443594) (-892 "PATTERN1.spad" 1441673 1441689 1443327 1443332) (-891 "PATRES.spad" 1439248 1439260 1441663 1441668) (-890 "PATRES2.spad" 1438920 1438934 1439238 1439243) (-889 "PATMATCH.spad" 1437117 1437148 1438628 1438633) (-888 "PATMAB.spad" 1436546 1436556 1437107 1437112) (-887 "PATLRES.spad" 1435632 1435646 1436536 1436541) (-886 "PATAB.spad" 1435396 1435406 1435622 1435627) (-885 "PARTPERM.spad" 1432796 1432804 1435386 1435391) (-884 "PARSURF.spad" 1432230 1432258 1432786 1432791) (-883 "PARSU2.spad" 1432027 1432043 1432220 1432225) (-882 "script-parser.spad" 1431547 1431555 1432017 1432022) (-881 "PARSCURV.spad" 1430981 1431009 1431537 1431542) (-880 "PARSC2.spad" 1430772 1430788 1430971 1430976) (-879 "PARPCURV.spad" 1430234 1430262 1430762 1430767) (-878 "PARPC2.spad" 1430025 1430041 1430224 1430229) (-877 "PARAMAST.spad" 1429153 1429161 1430015 1430020) (-876 "PAN2EXPR.spad" 1428565 1428573 1429143 1429148) (-875 "PALETTE.spad" 1427535 1427543 1428555 1428560) (-874 "PAIR.spad" 1426522 1426535 1427123 1427128) (-873 "PADICRC.spad" 1423856 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T)) -(|has| |#1| (-1101)) +(((|#1| (-410 (-567)) (-1084)) . T)) +(|has| |#1| (-1102)) (|has| |#1| (-559)) (|has| |#1| (-38 (-410 (-567)))) (|has| |#1| (-38 (-410 (-567)))) (|has| |#1| (-38 (-410 (-567)))) -(-2797 (|has| |#1| (-365)) (|has| |#1| (-455)) (|has| |#1| (-559)) (|has| |#1| (-910))) +(-2800 (|has| |#1| (-365)) (|has| |#1| (-455)) (|has| |#1| (-559)) (|has| |#1| (-911))) (|has| |#1| (-821)) -(((#0=(-911 |#1|) #0#) . T) (($ $) . T) ((#1=(-410 (-567)) #1#) . T)) +(((#0=(-912 |#1|) #0#) . T) (($ $) . T) ((#1=(-410 (-567)) #1#) . T)) ((((-410 |#2|)) . T)) (|has| |#1| (-849)) -((((-1203 |#1|)) . T) (((-863)) -2797 (|has| |#1| (-614 (-863))) (|has| |#1| (-1101)))) +((((-1204 |#1|)) . T) (((-863)) -2800 (|has| |#1| (-614 (-863))) (|has| |#1| (-1102)))) (((|#1| |#1|) . T) ((#0=(-410 (-567)) #0#) . T) ((#1=(-567) #1#) . T) (($ $) . T)) -((((-911 |#1|)) . T) (($) . T) (((-410 (-567))) . T)) -(((|#2|) |has| |#2| (-1050)) (((-567)) -12 (|has| |#2| (-640 (-567))) (|has| |#2| (-1050)))) -((((-911 |#1|)) . T) (((-410 (-567))) . T) (((-567)) . T) (($) . T)) +((((-912 |#1|)) . T) (($) . T) (((-410 (-567))) . T)) +(((|#2|) |has| |#2| (-1051)) (((-567)) -12 (|has| |#2| (-640 (-567))) (|has| |#2| (-1051)))) +((((-912 |#1|)) . T) (((-410 (-567))) . T) (((-567)) . T) (($) . T)) (((|#1|) . T) (((-410 (-567))) . T) (((-567)) . T) (($) . T)) (((|#1| |#2| |#3| |#4|) . T)) (|has| |#1| (-147)) @@ -2750,39 +2750,39 @@ (((|#2|) |has| |#2| (-172))) (((|#1|) . T)) (((|#2|) . T)) -(-2797 (|has| |#1| (-145)) (|has| |#1| (-370))) -(-2797 (|has| |#1| (-145)) (|has| |#1| (-370))) -(-2797 (|has| |#1| (-145)) (|has| |#1| (-370))) -((((-2 (|:| -1791 (-1177)) (|:| -4232 (-52)))) . T)) -(((#0=(-52)) . T) (((-2 (|:| -1791 (-1177)) (|:| -4232 #0#))) . 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T)) (((|#3| |#3|) . T)) (|has| |#2| (-233)) ((((-865 |#1|)) . T)) -((((-1177)) |has| |#1| (-901 (-1177))) ((|#3|) . T)) +((((-1178)) |has| |#1| (-902 (-1178))) ((|#3|) . T)) ((((-645 $)) . T) ((|#1|) . T) ((|#2|) . T) ((|#3|) . T) ((|#4|) . T) ((|#5|) . T)) -(-12 (|has| |#1| (-365)) (|has| |#2| (-1023))) +(-12 (|has| |#1| (-365)) (|has| |#2| (-1024))) ((((-410 (-567))) . T) (($) . T)) -((((-1175 |#1| |#2| |#3|)) |has| |#1| (-365))) +((((-1176 |#1| |#2| |#3|)) |has| |#1| (-365))) ((($) . T) (((-410 (-567))) . T)) ((((-863)) . T)) (|has| |#1| (-365)) @@ -2791,12 +2791,12 @@ ((((-567)) . T) (((-116 |#1|)) . T) (($) . T) (((-410 (-567))) . T)) ((((-567)) . T)) (((|#3|) . T)) -(|has| |#1| (-1101)) +(|has| |#1| (-1102)) (((|#2|) . T)) (((|#1|) . T)) ((((-567)) . T)) -(((|#2|) . T) (((-410 (-567))) |has| |#1| (-1039 (-410 (-567)))) ((|#1|) . T) (($) . T) (((-567)) . T)) -(-2797 (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-455)) (|has| |#1| (-559)) (|has| |#1| (-910))) +(((|#2|) . T) (((-410 (-567))) |has| |#1| (-1040 (-410 (-567)))) ((|#1|) . T) (($) . T) (((-567)) . T)) +(-2800 (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-455)) (|has| |#1| (-559)) (|has| |#1| (-911))) (((|#2|) . T) (((-567)) |has| |#2| (-640 (-567)))) (((|#1| |#2|) . T)) ((($) . T)) @@ -2806,7 +2806,7 @@ (((|#1|) . T) (($) . T)) (((|#1|) . T) (((-567)) . T)) (((|#1|) . T) (((-567)) . T)) -(((|#1| (-1267 |#1|) (-1267 |#1|)) . T)) +(((|#1| (-1268 |#1|) (-1268 |#1|)) . T)) (((|#1| |#2| |#3| |#4|) . T)) (((|#2|) . T)) ((((-863)) . T)) @@ -2814,8 +2814,8 @@ (((|#2|) . T)) (((|#3|) . T)) (((#0=(-116 |#1|) #0#) . T) ((#1=(-410 (-567)) #1#) . T) (($ $) . T)) -((((-410 (-567))) |has| |#2| (-1039 (-410 (-567)))) (((-567)) |has| |#2| (-1039 (-567))) ((|#2|) . T) (((-865 |#1|)) . T)) -((((-1126 |#1| |#2|)) . T) ((|#3|) . T) ((|#1|) . T) (((-567)) |has| |#1| (-1039 (-567))) (((-410 (-567))) |has| |#1| (-1039 (-410 (-567)))) ((|#2|) . T)) +((((-410 (-567))) |has| |#2| (-1040 (-410 (-567)))) (((-567)) |has| |#2| (-1040 (-567))) ((|#2|) . T) (((-865 |#1|)) . T)) +((((-1127 |#1| |#2|)) . T) ((|#3|) . T) ((|#1|) . T) (((-567)) |has| |#1| (-1040 (-567))) (((-410 (-567))) |has| |#1| (-1040 (-410 (-567)))) ((|#2|) . T)) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -2824,7 +2824,7 @@ ((((-673 |#1|)) . T)) ((($) . T) (((-410 (-567))) |has| |#2| (-38 (-410 (-567)))) ((|#2|) . T)) ((((-116 |#1|)) . T) (((-410 (-567))) . T) (($) . T)) -((((-567)) -12 (|has| |#1| (-887 (-567))) (|has| |#3| (-887 (-567)))) (((-381)) -12 (|has| |#1| (-887 (-381))) (|has| |#3| (-887 (-381))))) +((((-567)) -12 (|has| |#1| (-888 (-567))) (|has| |#3| (-888 (-567)))) (((-381)) -12 (|has| |#1| (-888 (-381))) (|has| |#3| (-888 (-381))))) (((|#2|) . T) ((|#6|) . T)) (((|#1|) . T) (((-410 (-567))) |has| |#1| (-38 (-410 (-567)))) (($) . T)) ((((-144)) . T)) @@ -2833,47 +2833,47 @@ ((((-381)) . T) (((-410 (-567))) . T) (($) . T) (((-567)) . T)) ((($) . 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. -1050) T) ((-1289 . -1281) 131576) ((-1287 . -1281) 131560) ((-1036 . -605) 131535) ((-317 . -615) 131396) ((-317 . -614) 131378) ((-314 . -615) NIL) ((-314 . -614) 131360) ((-48 . -243) T) ((-48 . -233) T) ((-655 . -287) 131321) ((-553 . -235) 131271) ((-139 . -614) 131238) ((-136 . -614) 131220) ((-114 . -614) 131202) ((-480 . -38) 131167) ((-1291 . -1288) 131146) ((-1282 . -131) T) ((-1290 . -1059) T) ((-1083 . -102) T) ((-88 . -1217) T) ((-503 . -310) NIL) ((-1001 . -107) 131130) ((-890 . -1101) T) ((-886 . -1101) T) ((-1267 . -652) 131114) ((-1267 . -375) 131098) ((-328 . -1217) T) ((-595 . -851) T) ((-1143 . -1101) T) ((-1143 . -1054) 131038) ((-103 . -517) 130971) ((-928 . -614) 130953) ((-345 . -727) T) ((-30 . -614) 130935) ((-867 . -1101) T) ((-844 . -1059) 130914) ((-40 . -649) 130859) ((-225 . -1221) T) ((-410 . -1059) T) ((-1159 . -151) 130841) ((-1000 . -291) 130792) ((-618 . -1101) T) ((-225 . -559) T) ((-320 . -1248) 130776) ((-320 . -1245) 130746) ((-702 . -647) 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. -1274) 129245) ((-44 . -641) 129229) ((-347 . -1274) 129213) ((-551 . -102) T) ((-523 . -851) 129192) ((-1047 . -1101) T) ((-818 . -455) 129171) ((-152 . -1052) 129155) ((-1047 . -1072) 129084) ((-1028 . -977) 129053) ((-820 . -1113) T) ((-1004 . -718) 128998) ((-152 . -641) 128982) ((-389 . -1113) T) ((-479 . -977) 128951) ((-466 . -977) 128920) ((-110 . -151) 128902) ((-73 . -614) 128884) ((-894 . -614) 128866) ((-1081 . -725) 128845) ((-1295 . -1050) T) ((-817 . -640) 128793) ((-295 . -1059) 128735) ((-169 . -1221) 128640) ((-225 . -1113) T) ((-325 . -23) T) ((-1168 . -993) 128592) ((-844 . -1101) T) ((-1253 . -1057) 128497) ((-1127 . -741) 128476) ((-1251 . -921) 128455) ((-1230 . -921) 128434) ((-871 . -727) T) ((-169 . -559) 128345) ((-583 . -649) 128332) ((-567 . -649) 128319) ((-410 . -1101) T) ((-264 . -1101) T) ((-213 . -614) 128301) ((-498 . -649) 128266) ((-225 . -23) T) ((-1230 . -821) 128219) ((-1289 . -102) T) ((-356 . -1286) 128196) ((-1287 . -102) T) ((-1253 . -111) 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. -1039) 124927) ((-317 . -617) 124491) ((-314 . -617) 124374) ((-393 . -647) 124343) ((-650 . -1039) 124327) ((-628 . -102) T) ((-222 . -492) 124311) ((-1267 . -34) T) ((-622 . -647) 124270) ((-290 . -1052) 124257) ((-136 . -617) 124241) ((-290 . -641) 124228) ((-636 . -718) 124212) ((-608 . -718) 124196) ((-671 . -38) 124156) ((-320 . -102) T) ((-85 . -614) 124138) ((-50 . -1039) 124122) ((-1121 . -1057) 124109) ((-1088 . -379) 124093) ((-783 . -379) 124077) ((-700 . -727) T) ((-700 . -795) T) ((-700 . -792) T) ((-584 . -1039) 124064) ((-521 . -1039) 124041) ((-60 . -57) 124003) ((-325 . -131) T) ((-317 . -1050) 123893) ((-314 . -1050) T) ((-169 . -1113) T) ((-781 . -379) 123877) ((-45 . -151) 123827) ((-1005 . -993) 123809) ((-457 . -379) 123793) ((-410 . -172) T) ((-317 . -243) 123772) ((-314 . -243) T) ((-314 . -233) NIL) ((-295 . -1101) 123554) ((-225 . -131) T) ((-1121 . -111) 123539) ((-169 . -23) T) ((-800 . -147) 123518) ((-800 . -145) 123497) ((-252 . -640) 123403) ((-251 . 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. -559) T) ((-490 . -647) 95099) ((-430 . -1052) 95083) ((-430 . -641) 95067) ((-361 . -718) 95019) ((-355 . -718) 94971) ((-341 . -1057) 94955) ((-347 . -718) 94907) ((-341 . -111) 94886) ((-174 . -1057) 94818) ((-217 . -647) 94768) ((-174 . -111) 94679) ((-108 . -718) 94629) ((-275 . -1101) T) ((-274 . -1101) T) ((-273 . -1101) T) ((-272 . -1101) T) ((-271 . -1101) T) ((-270 . -1101) T) ((-269 . -1101) T) ((-212 . -1101) T) ((-211 . -1101) T) ((-169 . -1205) 94607) ((-169 . -1202) 94585) ((-209 . -1101) T) ((-208 . -1101) T) ((-116 . -1050) T) ((-207 . -1101) T) ((-206 . -1101) T) ((-203 . -1101) T) ((-202 . -1101) T) ((-201 . -1101) T) ((-200 . -1101) T) ((-199 . -1101) T) ((-198 . -1101) T) ((-197 . -1101) T) ((-196 . -1101) T) ((-195 . -1101) T) ((-194 . -1101) T) ((-193 . -1101) T) ((-240 . -102) 94375) ((-169 . -35) 94353) ((-169 . -95) 94331) ((-655 . -1039) 94227) ((-485 . -1059) 94157) ((-1114 . -1101) 93947) ((-1143 . -34) T) ((-671 . -492) 93931) ((-73 . -1217) T) ((-105 . 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. -1101) T) ((-387 . -1101) T) ((-312 . -614) 88836) ((-227 . -1101) 88814) ((-648 . -517) 88747) ((-633 . -517) 88591) ((-834 . -1050) 88570) ((-645 . -151) 88554) ((-345 . -559) T) ((-713 . -901) 88497) ((-553 . -229) 88447) ((-1259 . -285) 88413) ((-1252 . -285) 88379) ((-1081 . -291) 88330) ((-490 . -849) T) ((-223 . -1113) T) ((-1231 . -285) 88296) ((-1211 . -496) 88262) ((-1005 . -38) 88212) ((-217 . -849) T) ((-421 . -647) 88171) ((-915 . -38) 88123) ((-844 . -795) 88102) ((-844 . -792) 88081) ((-844 . -727) 88060) ((-361 . -291) T) ((-355 . -291) T) ((-347 . -291) T) ((-169 . -455) 87991) ((-430 . -38) 87975) ((-108 . -291) T) ((-223 . -23) T) ((-410 . -795) 87954) ((-410 . -792) 87933) ((-410 . -727) T) ((-503 . -289) 87908) ((-480 . -1057) 87873) ((-659 . -131) T) ((-622 . -617) 87842) ((-1114 . -517) 87775) ((-338 . -131) T) ((-169 . -405) 87754) ((-485 . -718) 87696) ((-816 . -287) 87673) ((-480 . -111) 87629) ((-654 . -1059) T) ((-817 . -1052) 87472) ((-1278 . -1084) T) 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161618) ((-346 . -243) T) ((-265 . -327) 161590) ((-247 . -327) 161547) ((-265 . -233) 161526) ((-1158 . -151) 161510) ((-252 . -902) 161442) ((-251 . -902) 161374) ((-1084 . -851) T) ((-417 . -1114) T) ((-1056 . -23) T) ((-912 . -1051) T) ((-323 . -649) 161356) ((-1026 . -849) T) ((-1212 . -1004) 161322) ((-1175 . -922) 161301) ((-1169 . -922) 161280) ((-1169 . -821) NIL) ((-1001 . -1053) 161176) ((-912 . -243) T) ((-818 . -365) 161155) ((-387 . -23) T) ((-127 . -1102) 161133) ((-121 . -1102) 161111) ((-912 . -233) T) ((-128 . -34) T) ((-381 . -649) 161076) ((-1001 . -641) 161024) ((-871 . -718) 161011) ((-1296 . -647) 160983) ((-1048 . -151) 160948) ((-40 . -172) T) ((-695 . -414) 160930) ((-713 . -310) 160917) ((-837 . -649) 160877) ((-828 . -649) 160851) ((-320 . -25) T) ((-320 . -21) T) ((-659 . -287) 160830) ((-583 . -1102) T) ((-567 . -1102) T) ((-498 . -1102) T) ((-245 . -289) 160807) ((-314 . -231) 160768) ((-1174 . -888) NIL) ((-55 . -1102) T) ((-1127 . -888) 160627) ((-129 . 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. -25) T) ((-712 . -649) 140475) ((-456 . -21) T) ((-456 . -25) T) ((-341 . -102) T) ((-174 . -102) T) ((-1001 . -1060) T) ((-871 . -1051) T) ((-775 . -102) T) ((-1253 . -365) 140454) ((-1252 . -902) 140360) ((-1232 . -365) 140339) ((-1231 . -902) 140190) ((-1026 . -614) 140172) ((-410 . -829) 140125) ((-1176 . -496) 140091) ((-169 . -922) 140022) ((-1175 . -496) 139988) ((-1169 . -496) 139954) ((-713 . -1102) T) ((-1128 . -496) 139920) ((-583 . -1058) 139907) ((-567 . -1058) 139894) ((-498 . -1058) 139859) ((-317 . -291) 139838) ((-314 . -291) T) ((-356 . -614) 139820) ((-421 . -25) T) ((-421 . -21) T) ((-99 . -287) 139799) ((-583 . -111) 139784) ((-567 . -111) 139769) ((-498 . -111) 139725) ((-1178 . -888) 139692) ((-903 . -492) 139676) ((-48 . -614) 139658) ((-48 . -615) 139603) ((-240 . -131) 139473) ((-1291 . -647) 139432) ((-1241 . -922) 139411) ((-817 . -1222) 139390) ((-391 . -493) 139371) ((-1037 . -517) 139215) ((-391 . -614) 139181) ((-817 . -559) 139112) ((-588 . -649) 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. -649) 128266) ((-225 . -23) T) ((-1231 . -821) 128219) ((-1290 . -102) T) ((-356 . -1287) 128196) ((-1288 . -102) T) ((-1254 . -111) 128088) ((-816 . -1053) 127985) ((-816 . -641) 127927) ((-144 . -614) 127909) ((-995 . -131) T) ((-44 . -102) T) ((-240 . -851) 127860) ((-1241 . -1222) 127839) ((-103 . -492) 127823) ((-1291 . -718) 127793) ((-1089 . -47) 127754) ((-1064 . -1114) T) ((-954 . -1114) T) ((-127 . -34) T) ((-121 . -34) T) ((-783 . -47) 127731) ((-781 . -47) 127703) ((-1241 . -559) 127614) ((-356 . -370) T) ((-484 . -1114) T) ((-1174 . -131) T) ((-1127 . -131) T) ((-457 . -47) 127593) ((-872 . -365) T) ((-855 . -131) T) ((-152 . -102) T) ((-1064 . -23) T) ((-954 . -23) T) ((-574 . -559) T) ((-817 . -25) T) ((-817 . -21) T) ((-1144 . -517) 127526) ((-594 . -1085) T) ((-588 . -1040) 127510) ((-1254 . -617) 127384) ((-484 . -23) T) ((-353 . -1060) T) ((-1212 . -902) 127365) ((-671 . -310) 127303) ((-1115 . -1275) 127273) ((-700 . -649) 127238) ((-1005 . -172) T) ((-965 . -145) 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. -1102) T) ((-1036 . -25) T) ((-1036 . -21) T) ((-1005 . -1058) 107710) ((-907 . -102) T) ((-867 . -1051) T) ((-695 . -902) NIL) ((-357 . -330) 107694) ((-357 . -365) T) ((-354 . -330) 107678) ((-354 . -365) T) ((-346 . -330) 107662) ((-346 . -365) T) ((-490 . -102) T) ((-1280 . -38) 107632) ((-549 . -851) T) ((-526 . -688) 107582) ((-217 . -102) T) ((-1026 . -1040) 107462) ((-1005 . -111) 107391) ((-1176 . -975) 107360) ((-523 . -151) 107344) ((-1082 . -372) 107323) ((-353 . -614) 107305) ((-323 . -21) T) ((-356 . -1040) 107282) ((-323 . -25) T) ((-1175 . -975) 107244) ((-1169 . -975) 107213) ((-76 . -614) 107195) ((-1128 . -975) 107162) ((-700 . -308) T) ((-129 . -845) T) ((-912 . -365) T) ((-381 . -25) T) ((-381 . -21) T) ((-912 . -330) 107149) ((-86 . -614) 107131) ((-700 . -1024) T) ((-678 . -851) T) ((-1252 . -131) T) ((-1231 . -131) T) ((-903 . -1012) 107115) ((-837 . -21) T) ((-48 . -1040) 107058) ((-837 . -25) T) ((-828 . -25) T) ((-828 . -21) T) ((-1115 . -647) 106808) 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. -849) T) ((-227 . -688) 70432) ((-695 . -1114) T) ((-1212 . -741) 70408) ((-1026 . -365) T) ((-839 . -836) 70390) ((-834 . -795) 70369) ((-410 . -902) 70328) ((-320 . -1051) T) ((-345 . -25) T) ((-345 . -21) T) ((-169 . -1053) 70238) ((-68 . -1218) T) ((-834 . -792) 70217) ((-421 . -718) 70191) ((-800 . -1102) T) ((-713 . -922) 70170) ((-700 . -131) T) ((-169 . -641) 69998) ((-695 . -23) T) ((-490 . -291) T) ((-834 . -727) 69977) ((-320 . -233) 69929) ((-320 . -243) 69908) ((-217 . -291) T) ((-129 . -370) T) ((-1252 . -455) 69887) ((-1231 . -455) 69866) ((-356 . -330) 69843) ((-356 . -365) T) ((-1142 . -614) 69825) ((-45 . -1256) 69775) ((-872 . -102) T) ((-645 . -283) 69759) ((-700 . -1062) T) ((-1279 . -102) T) ((-1278 . -102) T) ((-480 . -649) 69724) ((-471 . -1102) T) ((-45 . -605) 69649) ((-1160 . -289) 69624) ((-290 . -617) 69596) ((-40 . -640) 69535) ((-1241 . -1053) 69358) ((-856 . -1053) 69342) ((-48 . -365) T) ((-1108 . -614) 69324) ((-1241 . -641) 69153) ((-856 . -641) 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\ No newline at end of file diff --git a/src/share/algebra/compress.daase b/src/share/algebra/compress.daase index 018c1c11..5bf50190 100644 --- a/src/share/algebra/compress.daase +++ b/src/share/algebra/compress.daase @@ -1,6 +1,6 @@ -(30 . 3465761897) -(4420 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| +(30 . 3466723533) +(4421 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| ATTRIBUTE |package| |domain| |category| CATEGORY |nobranch| AND |Join| |ofType| SIGNATURE "failed" "algebra" |OneDimensionalArrayAggregate&| |OneDimensionalArrayAggregate| |AbelianGroup&| |AbelianGroup| @@ -318,13 +318,13 @@ |OrderedVariableList| |OverloadSet| |OrdinaryWeightedPolynomials| |PadeApproximants| |PadeApproximantPackage| |PAdicIntegerCategory| |PAdicInteger| |PAdicRational| |PAdicRationalConstructor| |Pair| - |Palette| |PolynomialAN2Expression| |ParametricPlaneCurveFunctions2| - |ParametricPlaneCurve| |ParametricSpaceCurveFunctions2| - |ParametricSpaceCurve| |Parser| |ParametricSurfaceFunctions2| - 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|Record| |Union| |changeName| |bombieriNorm| |sumOfSquares| - |clipPointsDefault| |Aleph| |useEisensteinCriterion| |shallowExpand| - |pseudoQuotient| |c06ekf| |OMsupportsCD?| |leftExtendedGcd| - |parabolicCylindrical| |unitCanonical| |reset| |zero| |double?| - |hconcat| |makeSUP| |coercePreimagesImages| |dioSolve| |seed| |prime| - |viewport3D| |bfKeys| |cTanh| |setRealSteps| |selectfirst| |s18acf| - |stoseInvertible?reg| |semiDegreeSubResultantEuclidean| |insert!| - |box| |sort| |outputFloating| |pmintegrate| |att2Result| |e01bgf| - |write| |And| |sequence| |imagJ| |pointColorDefault| |stFuncN| - |moduleSum| |logpart| |bandedJacobian| |infiniteProduct| |save| - |taylorQuoByVar| |pointSizeDefault| |Or| |figureUnits| |f07adf| - |f02fjf| |clearTheIFTable| |setMaxPoints| |printStats!| |iiasinh| - |linGenPos| |midpoints| |mathieu23| |f01rdf| |Not| |OMgetSymbol| - |aspFilename| |oneDimensionalArray| |jacobi| |clipParametric| - |taylorRep| |chvar| |complementaryBasis| |mainPrimitivePart| - |primextintfrac| |normFactors| |s17def| |fortranCompilerName| - |OMgetEndBind| |hspace| |random| |inHallBasis?| |indicialEquations| - |duplicates?| |var2StepsDefault| |s18aff| |viewport2D| - |rightRemainder| |OMgetVariable| |constantKernel| - |selectOptimizationRoutines| |prolateSpheroidal| |clipBoolean| - |readUInt8!| |ref| |closedCurve?| |generator| |bat| - |radicalEigenvectors| |laurentRep| |sqfrFactor| |drawToScale| - |tracePowMod| |isOp| |primes| |lo| |shiftRight| |positiveSolve| - |resultantEuclidean| |ParCond| |quasiRegular| |algebraicOf| - |parametersOf| |positiveRemainder| |getExplanations| |droot| - |extendedEuclidean| |paraboloidal| |semiDiscriminantEuclidean| - |unravel| |stoseInvertible?sqfreg| |push| |vertConcat| |sumSquares| - |keys| |quotientByP| |invertibleSet| |incr| |rational?| |nthCoef| - |drawStyle| |evenlambert| |makeViewport3D| |squareFreePolynomial| - |symbolTable| |reducedForm| |df2fi| |hi| |yCoord| |stoseInvertible?| - |flatten| |d02bhf| |isMult| |numer| ** |realElementary| |singRicDE| - |genus| |conjugates| |tanintegrate| |argumentListOf| |diagonalMatrix| - 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|categoryFrame| |numberOfDivisors| |atoms| |print| - |irreducibleRepresentation| |indices| |sh| |simpleBounds?| |lcm| - |imag| |distFact| |triangulate| |Nul| |setelt!| |palginfieldint| - |resolve| |OMgetInteger| |nlde| |reflect| |directProduct| |rightUnits| - |forLoop| |anfactor| |algint| |stFunc1| |minimumDegree| |mapExpon| - |resultantReduit| |edf2ef| |declare!| |append| |mappingAst| - |constantLeft| |An| |OMserve| |roughSubIdeal?| |solveid| - |OMconnectTCP| |maxdeg| |isConnected?| |boundOfCauchy| |brace| - |mainExpression| |SturmHabichtSequence| |gcd| |linearAssociatedLog| - |simplifyLog| |remove!| |strongGenerators| |invmultisect| - |monicDivide| |nonLinearPart| |d02raf| |destruct| |nthr| |false| - |listexp| |quote| |schema| NOT |uncouplingMatrices| |exp1| - |useSingleFactorBound?| |setProperty| |lazyEvaluate| |rangeIsFinite| - |center| |normalElement| |vark| |selectPDERoutines| OR |s17aff| - |even?| |adaptive?| |screenResolution| |goodnessOfFit| |retractable?| - |f04jgf| |inconsistent?| |d01alf| AND |approxSqrt| |patternMatchTimes| - |Is| |copyInto!| |principal?| |gcdprim| - |removeIrreducibleRedundantFactors| |initiallyReduced?| |setOrder| - |iiacot| |explogs2trigs| |coth2tanh| |gradient| |monomial| - |zeroDimPrimary?| |OMconnOutDevice| |f2df| |sup| |stack| - |normalizedDivide| |iiexp| |s17acf| |light| |table| |multivariate| - |squareFree| |computeBasis| |opeval| |multiEuclideanTree| |OMgetType| - |rowEchelon| |rationalApproximation| |zero?| |ratDenom| |insert| - |one?| |new| |variables| |nextSubsetGray| |normalized?| |swap!| - |moebius| |numericIfCan| |functionIsContinuousAtEndPoints| - |rightRankPolynomial| |s15aef| |s21bbf| - |createLowComplexityNormalBasis| |getRef| |surface| |polyred| |cache| - |lllip| |branchPoint?| |autoReduced?| |reduceLODE| - |unprotectedRemoveRedundantFactors| |OMputError| - |initializeGroupForWordProblem| |f02adf| |composite| |f01qdf| - |trace2PowMod| |sorted?| |rootKerSimp| |totalfract| |optAttributes| - |isAnd| |lSpaceBasis| |linearlyDependentOverZ?| |iidsum| - |integralBasisAtInfinity| |determinant| |character?| |firstDenom| - |leftRank| |rootNormalize| |f02bjf| |minPoints| |separate| |reopen!| - |besselI| |polyRicDE| |option?| |taylor| |idealiserMatrix| |contains?| - |hex| |norm| |f02akf| * |messagePrint| |expIfCan| |exactQuotient!| - |isAbsolutelyIrreducible?| |laurent| |odd?| |aLinear| |symFunc| - |generalSqFr| |movedPoints| |setnext!| |localIntegralBasis| - |approxNthRoot| |processTemplate| |puiseux| |getBadValues| |leaf?| - |approximants| |primextendedint| |certainlySubVariety?| |littleEndian| - |plus!| |rischDE| |groebgen| |showTheRoutinesTable| |headReduced?| - |associatorDependence| |s17dgf| |d01aqf| |variationOfParameters| = - |completeEchelonBasis| |shanksDiscLogAlgorithm| |PollardSmallFactor| - |inv| |minimumExponent| |f07aef| |maxrank| |order| |status| - |SturmHabicht| |infinityNorm| |leftPower| |rightTraceMatrix| |ground?| - |left| |acotIfCan| |decimal| |Beta| |badNum| |complexForm| - |alternative?| |physicalLength!| < |perspective| |updatD| |ground| - |right| |tab1| |factorials| |reducedQPowers| |UP2ifCan| - |collectQuasiMonic| |iroot| |reduceBasisAtInfinity| > - |halfExtendedSubResultantGcd2| |physicalLength| |erf| |rightPower| - |leadingMonomial| |minColIndex| |minRowIndex| |jordanAlgebra?| - |setref| |rootPoly| |nextNormalPrimitivePoly| - |tryFunctionalDecomposition?| <= |nullity| |imagK| - |leadingCoefficient| |traceMatrix| |supersub| - |createLowComplexityTable| |definingInequation| |fullDisplay| - |checkRur| |f04mbf| >= |subst| |close!| |entry?| |primitiveMonomials| - |rule| |iExquo| |quadratic| |fortranLiteralLine| |deref| |max| |clip| - |expextendedint| |swap| |dilog| |nil| |normalize| |primitiveElement| - |reductum| |universe| |triangular?| |push!| |controlPanel| |argument| - |rowEchLocal| |rationalPower| |selectIntegrationRoutines| |sin| - |brillhartTrials| |trailingCoefficient| |subresultantVector| - |topFortranOutputStack| |c06gbf| |eulerE| |nthFractionalTerm| - |OMputEndAttr| + |c06fuf| |cos| |power!| |iiGamma| |dmpToP| - |integralCoordinates| |B1solve| |next| |iiacoth| |loadNativeModule| - |singleFactorBound| |internalDecompose| - |squareFreeFactors| |tan| - |approximate| |tablePow| |semiSubResultantGcdEuclidean2| - |toseInvertible?| |anticoord| |list?| |complex| |internalIntegrate| - |setPredicates| |coshIfCan| / |definingEquations| |cot| |log| - |groebnerIdeal| |basisOfCentroid| |setRow!| |createPrimitiveElement| - |wordInGenerators| |dom| |extract!| |integers| |ramifiedAtInfinity?| - |frobenius| |objects| |sec| |totolex| |explicitEntries?| |plotPolar| - |numericalIntegration| |rootOf| |numerators| |quasiAlgebraicSet| - |randomLC| |base| |coleman| |csc| |symbol| |OMgetFloat| |iiacsc| - |unitNormalize| |squareFreePart| |solveLinearlyOverQ| |signAround| - |cAcoth| |rightFactorIfCan| |cotIfCan| |asin| |validExponential| - |expression| |rightMinimalPolynomial| |roman| |segment| |tanh2coth| - |top!| |iprint| |withPredicates| |SFunction| |acos| |integer| - |backOldPos| |prefixRagits| |euclideanNormalForm| |swapRows!| |say| - |atom?| |lyndonIfCan| |rightLcm| |critpOrder| |atan| |s17dcf| - |fixedDivisor| |high| |algebraic?| |fglmIfCan| |title| - |characteristicPolynomial| |splitNodeOf!| - |semiSubResultantGcdEuclidean1| |acot| |delta| |headRemainder| - |selectOrPolynomials| |linears| LODO2FUN |lookupFunction| - |symmetricSquare| |modTree| |asec| |parents| |csubst| - |showTheSymbolTable| |squareTop| |pade| |tanAn| |torsion?| |member?| - |acsc| |listLoops| |outputList| |e02ahf| |asecIfCan| |bubbleSort!| - |readLine!| |iCompose| |exportedOperators| |head| |changeNameToObjf| - |sinh| |leastPower| |readInt16!| |lieAdmissible?| |initTable!| |recip| - |reindex| |f02axf| |corrPoly| |cosh| |OMmakeConn| |presub| |label| - |sort!| |roughUnitIdeal?| |quasiComponent| |atrapezoidal| |tanh| - |constantOperator| |fortranReal| |denominator| - |generalInfiniteProduct| |e01bhf| |genericRightDiscriminant| - |aQuadratic| |iicos| |coth| |augment| |clearTheSymbolTable| |solid| - |nonSingularModel| |OMputApp| |doubleRank| |startPolynomial| - |gcdcofactprim| |previous| |sech| |lambda| |integralMatrix| |saturate| - |tubeRadius| |nextPrime| |symmetricTensors| |hasSolution?| |csch| - |f04atf| |doubleDisc| |cAcot| |getMeasure| |cAtanh| |cosIfCan| - |algebraicSort| |irreducibleFactor| |asinh| |recolor| - |LyndonWordsList1| |squareFreeLexTriangular| - |indiceSubResultantEuclidean| |monicRightDivide| |rightZero| |rarrow| - |s17dhf| |acosh| |freeOf?| |pureLex| |e01sff| |digamma| |dihedral| - |super| |whileLoop| |standardBasisOfCyclicSubmodule| |charClass| - |atanh| |constructor| |absolutelyIrreducible?| |fortranLogical| - |reverse!| |Vectorise| |permutationRepresentation| |numFunEvals| - |acoth| |shiftLeft| |remove| |elRow2!| |roughEqualIdeals?| - |encodingDirectory| |redmat| |option| |ldf2lst| |elliptic| |closed?| - |asinhIfCan| |empty?| |asech| |gensym| |OMputVariable| - |LowTriBddDenomInv| |simplify| |dot| |iisinh| |c06fpf| - |univariateSolve| |last| |OMunhandledSymbol| |removeCosSq| - |dictionary| |mainVariables| |alphabetic?| |every?| |limitedint| - |assoc| |varList| |s19adf| |htrigs| |submod| |sturmVariationsOf| - |printInfo| |cSin| |cAsin| |mergeDifference| |exponential1| - |reduction| |generate| |isList| |rightTrim| |addBadValue| - |internalSubPolSet?| |multiplyExponents| |groebSolve| |rotatey| - |bivariate?| |allRootsOf| |constant| |leadingIndex| - |semiIndiceSubResultantEuclidean| |subQuasiComponent?| |leftTrim| - |pointColorPalette| |fortranDoubleComplex| |rootProduct| |readByte!| - |setMaxPoints3D| |lazyIrreducibleFactors| |numberOfComposites| - |neglist| |deepExpand| |genericLeftNorm| |trivialIdeal?| |incrementBy| - |infix| |depth| |subTriSet?| |OMputBVar| |prod| |realRoots| - |perfectNthPower?| |expand| |subResultantGcdEuclidean| - |orthonormalBasis| |stoseIntegralLastSubResultant| |leftRemainder| - |pastel| |points| |rowEch| |move| |repeating| |iicoth| - |createNormalPrimitivePoly| |structuralConstants| |s18adf| - |filterWhile| |ratPoly| |cosh2sech| |mapUnivariateIfCan| |bounds| - |rquo| |deleteRoutine!| |computeCycleEntry| |complexSolve| |f07fdf| - |f02wef| |filterUntil| |getZechTable| |regime| |rightRank| - |lineColorDefault| |curve| |factorOfDegree| |palgextint| - |derivationCoordinates| |select| |unrankImproperPartitions1| |cyclic?| - |color| |d01anf| |intensity| |ode2| |mapExponents| |safetyMargin| - |empty| |axes| |decompose| |element?| |wholeRagits| - |SturmHabichtMultiple| |getMultiplicationMatrix| |prepareSubResAlgo| - |henselFact| |leftTraceMatrix| |zeroDimensional?| |tanhIfCan| - |exprHasWeightCosWXorSinWX| |c06fqf| |mapmult| |acothIfCan| |d02cjf| - |cschIfCan| |radicalSimplify| |dimensions| |position!| |pattern| - |OMgetEndAtp| |dfRange| |mapGen| |lprop| |primintegrate| - |expandTrigProducts| |qfactor| |trunc| |mainVariable?| |complex?| - |d03faf| |e04fdf| |nextColeman| |invmod| |mulmod| |signature| |cAtan| - |symbolTableOf| |commutator| |subResultantsChain| |showScalarValues| - |blue| |lex| |meshPar2Var| |ParCondList| |possiblyNewVariety?| - |makeRecord| |hasHi| |parts| |lazyPseudoQuotient| |number?| - |weakBiRank| |permutationGroup| |areEquivalent?| |node| |iisec| - |pdf2df| |adjoint| |expressIdealMember| |assign| |message| |pdct| - |antiCommutator| |subResultantGcd| |buildSyntax| |operation| - |permanent| |radix| |genericLeftMinimalPolynomial| |lyndon?| |trim| - |resultantEuclideannaif| |lowerCase?| |ran| |subscript| |find| - |lookup| |degreeSubResultantEuclidean| |ptree| |Lazard2| - |rischNormalize| |hash| |d01amf| |numberOfComputedEntries| - |torsionIfCan| |e04jaf| |digits| |tanSum| |degreePartition| |addPoint| - |count| |cyclicGroup| |hypergeometric0F1| |twist| |bat1| |concat!| - |sumOfKthPowerDivisors| |monomialIntPoly| |curryLeft| |OMopenFile| - |sign| |OMputEndApp| |palglimint| |listRepresentation| - |getPickedPoints| |extendIfCan| |vectorise| |getConstant| |unitVector| - |pushdterm| |hdmpToP| |subtractIfCan| |pdf2ef| |d01ajf| |cons| - |OMgetObject| |selectMultiDimensionalRoutines| |sayLength| |nthFlag| - |coefficients| |currentSubProgram| |laplacian| - |internalLastSubResultant| |ode1| |tan2trig| |viewSizeDefault| - |factorSquareFreePolynomial| |bivariatePolynomials| |variable?| - |completeEval| |stiffnessAndStabilityFactor| |OMputBind| - |incrementKthElement| |drawComplexVectorField| |e02aef| - |lazyIntegrate| |magnitude| |reducedContinuedFraction| - |normalizeAtInfinity| |packageCall| |patternMatch| |newSubProgram| - |denominators| |lifting1| |nextIrreduciblePoly| |numberOfVariables| - |ramified?| |mkcomm| |lfinfieldint| |setEmpty!| |yellow| - |generalizedEigenvector| |createMultiplicationTable| |select!| - |realZeros| |fortranLiteral| |checkPrecision| |recur| - |increasePrecision| |errorKind| |trigs2explogs| |iiatanh| |scripted?| - |wrregime| |polyRDE| |c06frf| |reseed| |polygon?| |setClosed| - |typeList| |source| |d01asf| |removeSuperfluousQuasiComponents| - |iitanh| |merge| |OMputInteger| |exponentialOrder| |multinomial| - |finite?| |getSyntaxFormsFromFile| |basisOfNucleus| |LyndonWordsList| - |s01eaf| |s14aaf| |dmpToHdmp| |hue| |makeTerm| |invertibleElseSplit?| - |addiag| |powerSum| |polarCoordinates| |leftScalarTimes!| - |fortranCharacter| |nil?| |sub| |roughBase?| |idealSimplify| - |completeHermite| |partialQuotients| |LagrangeInterpolation| |e01saf| - |createNormalPoly| |blankSeparate| |stopTableGcd!| |e01bff| - |repeating?| |viewPhiDefault| |bezoutMatrix| |laguerre| |mdeg| - |cycleElt| |contract| |nextPartition| |polynomialZeros| |fractRadix| - |entries| |extractIndex| |limitPlus| |Ci| |target| |shellSort| - |d01gaf| |antiAssociative?| |extractPoint| |expintegrate| |newLine| - |rename| |linear?| |mapUp!| |scalarTypeOf| |roughBasicSet| - |explicitlyFinite?| |tableForDiscreteLogarithm| |hessian| |reverse| - |SturmHabichtCoefficients| |lowerCase| |mapMatrixIfCan| - |completeSmith| |bringDown| |bytes| |toroidal| |fortranComplex| - |myDegree| |sum| |removeCoshSq| |gethi| |algSplitSimple| |Ei| - |FormatArabic| |expr| |outputSpacing| |normal?| |children| - |nextLatticePermutation| |rightScalarTimes!| |monicModulo| - |convergents| |fTable| |mkPrim| |homogeneous?| |setCondition!| - |f04arf| |makeSketch| |ravel| |leadingCoefficientRicDE| - |hyperelliptic| |optional?| |in?| |options| |mathieu22| - |algebraicCoefficients?| |resultant| |reshape| |realEigenvectors| - |debug3D| |divideIfCan| |lquo| |kernel| |bindings| |doublyTransitive?| - |flexible?| |coerceS| |draw| |host| |divisors| |factorSFBRlcUnit| - |triangularSystems| |lp| |variable| |extension| |s15adf| |nextItem| - |coerceImages| |splitSquarefree| |outputAsScript| |zeroSetSplit| - |multisect| |iterators| |iiperm| |optpair| |rightUnit| |string| - |rightFactorCandidate| |currentEnv| |sin?| |cCoth| - |stiffnessAndStabilityOfODEIF| |jordanAdmissible?| - |radicalOfLeftTraceForm| |cycle| |leftNorm| |failed| |duplicates| - |complexZeros| |substring?| |dominantTerm| |exptMod| |npcoef| - |argumentList!| |localUnquote| |reduceByQuasiMonic| |removeZeroes| - |df2st| |write!| |update| |attributeData| |decreasePrecision| - |makeObject| |mapDown!| |logGamma| |laguerreL| |d01gbf| |algDsolve| - |suffix?| |showIntensityFunctions| |delay| |coef| |calcRanges| |nand| - |zerosOf| |generalTwoFactor| |iidprod| |weighted| |lazyPseudoDivide| - |normInvertible?| |wordsForStrongGenerators| |returnType!| - |zeroVector| |quadraticNorm| |modularGcdPrimitive| |rk4| |s19acf| - |qelt| |prefix?| |birth| |evaluateInverse| |replace| - |genericRightNorm| |LyndonCoordinates| |plenaryPower| |btwFact| - |qsetelt| |collect| |baseRDE| |leader| |rotate!| |redPo| |prinb| - |linear| |scale| |iipow| |linearPart| |binaryTournament| |ScanArabic| - |xRange| |cardinality| |basisOfRightAnnihilator| |symmetricGroup| - |wreath| |fprindINFO| |stoseInvertibleSet| |sumOfDivisors| |yRange| - |hasPredicate?| |linearlyDependent?| |precision| |polynomial| - |cyclicEntries| |changeWeightLevel| |latex| |c06gsf| |f02aaf| |redPol| - |zRange| |endSubProgram| |removeRoughlyRedundantFactorsInPol| - |seriesSolve| |retractIfCan| |leadingSupport| |besselK| - |branchPointAtInfinity?| |map!| |resultantReduitEuclidean| |setfirst!| - |coerceL| |stopTable!| |stirling2| |clearTheFTable| |OMputEndBVar| - |qsetelt!| |readInt8!| |lfintegrate| |factorsOfCyclicGroupSize| - |index| |integralMatrixAtInfinity| |s17ahf| |OMsend| |e04mbf| - |partition| |ScanFloatIgnoreSpacesIfCan| - |halfExtendedSubResultantGcd1| |bernoulliB| - |removeRedundantFactorsInContents| |decomposeFunc| - |removeSuperfluousCases| |ef2edf| |badValues| |antisymmetric?| - |bfEntry| |mainCharacterization| |sec2cos| |leaves| |genericPosition| - |semiResultantReduitEuclidean| |cCosh| |setvalue!| |pair| - |monicRightFactorIfCan| |Si| |taylorIfCan| |chebyshevT| |test| - |combineFeatureCompatibility| |iicosh| |value| |d01akf| |routines| - |sn| |rightCharacteristicPolynomial| |complexLimit| |imagE| - |fortranCarriageReturn| |rules| |f01qef| |setMinPoints3D| - |numberOfOperations| |algintegrate| |acsch| |startTableInvSet!| - |noncommutativeJordanAlgebra?| |mkAnswer| |knownInfBasis| |dAndcExp| - |bitTruth| |sinhcosh| |open| |powmod| |iisqrt3| |mirror| - |leftQuotient| |cyclicParents| |OMencodingUnknown| |map| - |computeCycleLength| |OMgetApp| |extractIfCan| |mpsode| |eq| - |rewriteIdealWithHeadRemainder| |stopMusserTrials| |check| - |OMputString| |redpps| |OMUnknownCD?| |part?| |fi2df| |showClipRegion| - |iicot| |iter| |directory| |slash| |c06ebf| |prefix| |innerSolve| - |mainForm| |ffactor| |shiftRoots| |createPrimitiveNormalPoly| |updatF| - |unknown| |setchildren!| |ord| |complexEigenvectors| |prologue| - |csch2sinh| |setErrorBound| |setAdaptive| |iomode| |f02aef| - |complexRoots| |any| |operations| |semiResultantEuclidean1| |expint| - |alternatingGroup| |pointLists| |nthExpon| F |elliptic?| |tanh2trigh| - |testModulus| |factorPolynomial| |palglimint0| |quasiRegular?| - |f02aff| |basisOfRightNucleus| |cyclicSubmodule| |iiabs| - |swapColumns!| |mergeFactors| |convert| |leadingExponent| |s13aaf| - |indicialEquation| |subPolSet?| |po| |constantCoefficientRicDE| - |digit| |useSingleFactorBound| |headAst| |infinite?| |outputArgs| - |linearPolynomials| |qroot| |rectangularMatrix| |hasTopPredicate?| - |resize| |resetVariableOrder| |tRange| |resetAttributeButtons| - |numeric| |coerceListOfPairs| |subresultantSequence| |aCubic| - |removeRoughlyRedundantFactorsInContents| |zCoord| - |balancedBinaryTree| |cap| |divergence| |charpol| |PDESolve| |bag| - |sincos| |ldf2vmf| |createNormalElement| |radical| |nodeOf?| |csc2sin| - |FormatRoman| |pointData| |getButtonValue| |operators| |infLex?| - |raisePolynomial| |bernoulli| |isTerm| |abelianGroup| |exp| |lazy?| - |fixPredicate| |e02bdf| |satisfy?| UP2UTS |curve?| |splitLinear| - |pile| |trapezoidalo| |viewDeltaXDefault| |inrootof| |d01fcf| - |basisOfLeftNucloid| |binarySearchTree| |discreteLog| |musserTrials| - |cSinh| |deepestTail| |iisech| |associative?| |s13adf| |s21bcf| - |e04gcf| |acosIfCan| |reify| |colorFunction| FG2F |s13acf| - |lfextendedint| |preprocess| |numberOfNormalPoly| |numberOfChildren| - |compactFraction| |firstUncouplingMatrix| |setLabelValue| |product| - |pascalTriangle| |fractionFreeGauss!| |s18def| - |primPartElseUnitCanonical!| |qinterval| |sequences| |id| - |maxPoints3D| |float?| |rk4f| |readIfCan!| |besselY| |constant?| - |second| |morphism| |gderiv| |components| |extend| |e02akf| - |RemainderList| |sparsityIF| |s17aef| |symbol?| - |extendedSubResultantGcd| |close| |goodPoint| - |genericLeftDiscriminant| |third| |bipolarCylindrical| |minIndex| - |diag| |OMreadFile| |maxPoints| |exactQuotient| |OMgetBind| |lighting| - |e04dgf| |twoFactor| |cAsinh| |quatern| |binding| |bumptab| - |limitedIntegrate| |minrank| |representationType| |bits| |makeCrit| - |readUInt32!| |ratpart| |search| |OMParseError?| |display| - |highCommonTerms| |f02xef| |obj| |cAcosh| |symmetricDifference| |cSec| - |OMputAtp| |cyclotomic| |failed?| |represents| |isExpt| |countable?| - |alphabetic| |eisensteinIrreducible?| |enqueue!| |byteBuffer| UTS2UP - |numberOfHues| |cRationalPower| |antisymmetricTensors| - |internalZeroSetSplit| |rightAlternative?| |e02baf| |schwerpunkt| - |univariatePolynomial| |compBound| |removeZero| |setright!| |fracPart| - |rotatez| |integralLastSubResultant| |finiteBasis| - |fullPartialFraction| |minPol| |setVariableOrder| |critM| |pquo| - |frst| |transcendentalDecompose| |f2st| |makingStats?| - |groebnerFactorize| |extendedIntegrate| |coord| |queue| |isQuotient| - |nextPrimitivePoly| |OMopenString| |sizePascalTriangle| - |componentUpperBound| |logIfCan| |midpoint| |iiacos| - |listConjugateBases| |OMputEndAtp| |powern| |selectNonFiniteRoutines| - |normalForm| |GospersMethod| |input| |setScreenResolution| - |unitsColorDefault| |stosePrepareSubResAlgo| |airyBi| |nextSublist| - |eigenMatrix| |heap| |factor1| |lhs| |f02awf| |pushdown| |cycles| - |green| |associatedSystem| |category| |linearAssociatedOrder| - |complement| |pair?| |library| |currentCategoryFrame| |notelem| - |leftExactQuotient| |extractBottom!| |qPot| |rhs| |quasiMonic?| - |simplifyExp| |sinhIfCan| |before?| |domain| |nary?| - |constantToUnaryFunction| |nextNormalPoly| |palgLODE0| - |rootOfIrreduciblePoly| |tValues| |primeFrobenius| |create| - |gcdcofact| |eulerPhi| |diagonal?| |getOperator| |package| |sPol| - |slex| |cPower| |imagj| |printCode| |stronglyReduce| |shift| - |distance| |coerce| |makeCos| |crest| |makeMulti| |normalise| - |systemCommand| |height| |internalInfRittWu?| |realSolve| - |purelyAlgebraic?| |abs| |mat| |changeMeasure| |cAcsch| |arg1| - |construct| |palgRDE| |oddlambert| |continuedFraction| |mvar| |cAcsc| - |Gamma| |equiv| |set| |region| |useNagFunctions| |readLineIfCan!| - |integralDerivationMatrix| |arg2| |sinIfCan| |radicalRoots| - |makeFloatFunction| |rewriteSetWithReduction| |comparison| |kind| - |isobaric?| |tab| |startStats!| |getGraph| |euler| - |stoseInvertibleSetreg| |shufflein| |createPrimitivePoly| - |putColorInfo| |readBytes!| |pushuconst| |genericRightTraceForm| |op| - |asimpson| |normal| |halfExtendedResultant2| |setScreenResolution3D| - |tubePoints| |tubePlot| |scaleRoots| |conditions| |numberOfMonomials| - |pole?| |critMonD1| |getMatch| |arguments| |leftGcd| |clikeUniv| - |symbolIfCan| |coHeight| |pmComplexintegrate| |psolve| |match| - |c05adf| |fmecg| |euclideanSize| |pointPlot| |callForm?| |unparse| - |LyndonBasis| |subset?| |leastMonomial| |accuracyIF| |insertTop!| - |nthExponent| |exQuo| |s17ajf| |matrixConcat3D| |curryRight| |e02agf| - |romberg| |expandLog| |pop!| |dimensionsOf| |largest| |imagI| |node?| - |partialDenominators| |stopTableInvSet!| |socf2socdf| |e01baf| |block| - |OMwrite| |separateDegrees| |consnewpol| |thenBranch| |sts2stst| - |edf2efi| |safeCeiling| |makeResult| |entry| |e02ajf| |sin2csc| - |OMlistCDs| |bipolar| |antiCommutative?| |s17dlf| |OMUnknownSymbol?| - |union| |iiacsch| |cycleRagits| |d03eef| |selectSumOfSquaresRoutines| - |fixedPoints| |iisqrt2| |expPot| |modifyPoint| |multMonom| |exponent| - |appendPoint| |tanNa| |elColumn2!| |mainSquareFreePart| - |contractSolve| |closedCurve| |palgint0| |characteristicSet| - |divisorCascade| |c02agf| |rootRadius| |matrixGcd| |cycleEntry| - |poisson| |show| |formula| |rewriteIdealWithRemainder| |terms| |mix| - |quotedOperators| |fill!| |mesh?| |factorFraction| |replaceKthElement| - |minPoly| |e02adf| |squareMatrix| |call| |nsqfree| |tail| |setelt| - |polyPart| |deepestInitial| |primitive?| |writeInt8!| |toScale| - |vedf2vef| |credPol| |maxRowIndex| |trace| |basicSet| |cos2sec| - |expandPower| |colorDef| |prinshINFO| |string?| |OMcloseConn| - |hostPlatform| |clearFortranOutputStack| |xn| |extractSplittingLeaf| - |errorInfo| |copy| |dequeue| |setClipValue| |rootBound| |lowerCase!| - |someBasis| |setStatus| |fortranDouble| |OMgetBVar| |scopes| |nrows| - |viewWriteDefault| |particularSolution| |makeViewport2D| - |outputGeneral| |solveLinearPolynomialEquationByRecursion| |void| - |perfectSqrt| |irreducibleFactors| |partitions| |radicalSolve| |imagi| - |ncols| |commutativeEquality| |parabolic| |leadingBasisTerm| - |setleft!| |RittWuCompare| |lexTriangular| |qualifier| |ODESolve| - |primitivePart| |constDsolve| |normalDenom| |coefChoose| |cAsech| - |parametric?| |semiResultantEuclidean2| |prime?| |rightExactQuotient| - |nodes| |multiplyCoefficients| |eof?| |pushucoef| - |createRandomElement| |commutative?| |thetaCoord| |dualSignature| - |indiceSubResultant| |unary?| |integer?| |lazyPremWithDefault| - |directSum| |binary| |positive?| |fixedPoint| |elRow1!| - |rewriteSetByReducingWithParticularGenerators| |oddInfiniteProduct| - |domainTemplate| |setMinPoints| |fixedPointExquo| |s17akf| - |inverseIntegralMatrixAtInfinity| |cycleSplit!| |arrayStack| - |summation| |sdf2lst| |d02gaf| |totalDifferential| |rischDEsys| - |lfextlimint| |commaSeparate| |superHeight| |viewPosDefault| - |isImplies| |expt| |associates?| |rubiksGroup| |setProperties!| - |generalizedContinuumHypothesisAssumed| |adaptive3D?| |content| - |showTheIFTable| |cycleLength| |result| |setleaves!| |lambert| - |univariatePolynomials| |baseRDEsys| |writable?| - |genericRightMinimalPolynomial| |beauzamyBound| |extendedint| - |selectAndPolynomials| |nil| |infinite| |arbitraryExponent| - |approximate| |complex| |shallowMutable| |canonical| |noetherian| - |central| |partiallyOrderedSet| |arbitraryPrecision| - |canonicalsClosed| |noZeroDivisors| |rightUnitary| |leftUnitary| - |additiveValuation| |unitsKnown| |canonicalUnitNormal| - |multiplicativeValuation| |finiteAggregate| |shallowlyMutable| - |commutative|)
\ No newline at end of file + |Record| |Union| |setchildren!| |hasHi| |cylindrical| |result| + |solve1| |series| |expPot| |plot| |semiLastSubResultantEuclidean| + |connect| |OMlistSymbols| |movedPoints| |c06gbf| |finite?| |reset| + |zero| |df2fi| |dmpToP| |constantIfCan| |ratDenom| |ideal| + |numberOfCycles| |multinomial| |getExplanations| |nullSpace| + |stronglyReduced?| |complexForm| |mkAnswer| |e02def| + |changeWeightLevel| |singularAtInfinity?| FG2F |sumOfKthPowerDivisors| + |box| |plotPolar| |leftFactorIfCan| |iroot| |makeFloatFunction| + |dominantTerm| |write| |And| |OMputApp| |generalLambert| |fixedPoint| + |fullDisplay| |reducedDiscriminant| |limitPlus| |random| |sechIfCan| + |radicalRoots| |save| |colorDef| |modifyPointData| |min| |Or| + |nilFactor| |addPoint2| |sizePascalTriangle| |leastMonomial| |makeEq| + |evaluateInverse| |rootKerSimp| |push| |genericLeftTrace| |variable?| + |Not| |subHeight| |normalizeIfCan| |makeVariable| |clearTheFTable| + |whileLoop| |inverseColeman| |minGbasis| + |standardBasisOfCyclicSubmodule| |perfectNthPower?| |predicates| + |Lazard2| |coerceS| |powerAssociative?| |linears| |rationalPoints| + |logpart| |categoryFrame| |c06fqf| |qPot| |pushNewContour| + |fullPartialFraction| |matrixGcd| |mergeDifference| |karatsuba| |keys| + |s17agf| |complexEigenvectors| |sort!| |copyInto!| |LyndonWordsList1| + |SturmHabicht| |generator| |possiblyInfinite?| |hasTopPredicate?| + |inverse| |viewDeltaYDefault| |symbolTable| |singular?| |double?| + |lazy?| |lo| |legendre| |e02ddf| |resetNew| |lfextlimint| + |strongGenerators| |normInvertible?| |selectODEIVPRoutines| + |getSyntaxFormsFromFile| |RemainderList| |iicosh| |horizConcat| + |latex| |insertBottom!| |lineColorDefault| |randomR| |ceiling| + |pushFortranOutputStack| |indicialEquationAtInfinity| |normal?| |cExp| + |LiePolyIfCan| |transform| |incr| |setButtonValue| |fi2df| |one?| + |outputFloating| |monomialIntPoly| |popFortranOutputStack| |infix?| + |clipWithRanges| |completeEval| |eulerE| |rewriteSetWithReduction| + |realEigenvalues| |hi| |rightAlternative?| |flatten| |mask| |s13acf| + |numer| ** |Ci| |lazyResidueClass| |partitions| |outputAsFortran| + |exptMod| |subspace| |rombergo| |OMlistCDs| |validExponential| + |checkRur| |denom| |accuracyIF| |componentUpperBound| |makeCrit| + |reorder| |charClass| |factorset| |vertConcat| |totalDegree| + |printingInfo?| |coth2trigh| |stoseInternalLastSubResultant| + |bumptab1| |c06frf| |s19abf| |prinshINFO| |connectTo| |true| + |squareFreePrim| |quasiMonic?| |cardinality| |host| |pi| + |palgintegrate| LODO2FUN |commutator| |oddlambert| |stirling1| + |numberOfDivisors| |subResultantGcdEuclidean| |roughUnitIdeal?| + |lazyPrem| |loopPoints| |infinity| |OMputEndBVar| |exponential1| + |f01qcf| |cfirst| |sparsityIF| |prologue| |principal?| |rotate| + |commutative?| |cycleEntry| |UpTriBddDenomInv| |invmultisect| + |squareFreeLexTriangular| |messagePrint| |basisOfNucleus| |mapmult| + |d01akf| |fixPredicate| |choosemon| |rightOne| |commaSeparate| + |resize| |shiftRight| |lagrange| |totalfract| |argscript| + |skewSFunction| |zag| |genericLeftMinimalPolynomial| |nextSubsetGray| + |normDeriv2| |radicalEigenvectors| |setPosition| + |createPrimitiveElement| |overbar| |hconcat| |OMputFloat| |children| + |intChoose| |curve| |setProperties| |s18aef| |imagk| |showClipRegion| + |categories| |comparison| |primlimintfrac| |bipolar| + |stiffnessAndStabilityFactor| |e02baf| |outerProduct| |returnTypeOf| + |shellSort| |curryLeft| |fillPascalTriangle| |f07fef| |eigenvalues| + |nthFractionalTerm| |space| |sumSquares| |s17dgf| |lfextendedint| + |OMgetEndAttr| |logIfCan| |wordsForStrongGenerators| |reseed| |delete| + |cyclotomicDecomposition| |absolutelyIrreducible?| |bitCoef| + |simplifyExp| |basisOfRightAnnihilator| |inspect| |insertTop!| + |lookupFunction| |pmintegrate| |usingTable?| |minimize| |npcoef| + |coerceP| |orthonormalBasis| |rightMinimalPolynomial| |factorial| + |f04mbf| |readInt8!| |continuedFraction| |radicalSolve| |vector| + |atoms| |string?| |gcdprim| |quasiComponent| |comment| |generators| + |identitySquareMatrix| |genericLeftTraceForm| |innerSolve1| + |reduction| |sizeMultiplication| |differentiate| |getlo| |csch2sinh| + |e02bdf| |routines| |cubic| |divisors| |perfectNthRoot| |leftMult| + |OMputObject| |listOfLists| |range| |LyndonWordsList| |getCode| + |linearDependenceOverZ| |thetaCoord| |poisson| |superHeight| + |resetVariableOrder| |readUInt32!| |indiceSubResultantEuclidean| + |optAttributes| |ode| |degreeSubResultant| |exponential| |e02zaf| + |factorOfDegree| |c05pbf| |monicDivide| |iicot| |subResultantsChain| + |monicLeftDivide| |acothIfCan| |functorData| |nextLatticePermutation| + |iiatan| |pseudoRemainder| |OMopenFile| |setPrologue!| |expIfCan| + |hitherPlane| |isobaric?| |s17aef| |antiCommutative?| |OMputBind| + |lyndon?| |reduceBasisAtInfinity| |getIdentifier| |univariate?| |null| + |numFunEvals3D| |cycleTail| |positiveSolve| |discriminantEuclidean| + |makeSUP| |quotientByP| |sinhIfCan| |schwerpunkt| |addMatch| |module| + |preprocess| |d01gaf| |midpoint| GF2FG |not| |fortranLogical| + |OMputEndAttr| |extractTop!| |enumerate| |d01aqf| |nthExponent| + |normalized?| |lfintegrate| |wordInGenerators| |and| |polygon?| + |rightMult| |sqfree| |atrapezoidal| |stoseIntegralLastSubResultant| + |roman| |alphanumeric| |close!| |symmetricSquare| |or| + |univariatePolynomialsGcds| |mvar| |setErrorBound| |argumentList!| + |rightCharacteristicPolynomial| |satisfy?| |real?| |OMreceive| + |listYoungTableaus| |karatsubaOnce| |Lazard| |xor| |returnType!| + |irreducibleRepresentation| |tube| |OMread| + |removeIrreducibleRedundantFactors| |symmetricGroup| |att2Result| + |setsubMatrix!| |factorSFBRlcUnit| |length| |isList| + |monicRightDivide| |case| |log10| |property| |OMcloseConn| + |wordInStrongGenerators| |completeHensel| |getVariableOrder| + |monomials| |nonLinearPart| |scripts| |hasoln| |viewPosDefault| + |imagi| |overset?| |Zero| |bitand| |finiteBound| |s01eaf| |prindINFO| + |monic?| |dualSignature| |style| |rewriteIdealWithRemainder| + |multiEuclidean| |tRange| |slash| |One| |bitior| |exprex| + |stoseLastSubResultant| |rightScalarTimes!| |incrementKthElement| + |subResultantChain| |rightTraceMatrix| |subMatrix| + |numberOfIrreduciblePoly| |topPredicate| |leftLcm| |tubeRadiusDefault| + |units| |d02cjf| |tab| |s17dlf| |before?| |s14baf| |critM| + |palgextint| |antiAssociative?| |sign| |primaryDecomp| |ratpart| + |ocf2ocdf| |isAnd| |constantOperator| |invertibleSet| |trim| |iiacos| + |f01brf| |redPol| |orbits| |repSq| |showScalarValues| |reverse!| + |symbol?| |quickSort| |generalizedInverse| |variationOfParameters| + |modTree| |numberOfNormalPoly| |exQuo| |exactQuotient!| |setClosed| + |padicFraction| |coercePreimagesImages| |closeComponent| + |complexLimit| |leftRemainder| |univariatePolynomial| |systemSizeIF| + |delta| |domainTemplate| |swap!| |readInt32!| |cAcsc| + |resultantEuclidean| |elt| |rootSimp| |indices| |rroot| + |initiallyReduced?| |wreath| |extract!| |entry?| |key| + |factorsOfCyclicGroupSize| |gbasis| |newTypeLists| |makeprod| |code| + |c06fuf| |setAdaptive| |drawComplexVectorField| UP2UTS + |measure2Result| |cn| |rightZero| |subNode?| |ScanRoman| |addBadValue| + |regularRepresentation| |acotIfCan| |localUnquote| |wholeRadix| + |lintgcd| |jacobian| |tanh2coth| |resetAttributeButtons| |filename| + |triangularSystems| |zeroVector| |isImplies| |conjugate| |pquo| + |c05nbf| |s14aaf| |s17def| |sylvesterSequence| + |purelyAlgebraicLeadingMonomial?| |factorials| |cot2trig| |d02raf| + |branchIfCan| |interactiveEnv| |leadingIdeal| |algebraicDecompose| + |hostPlatform| |monicModulo| |rur| |indiceSubResultant| + |exprHasAlgebraicWeight| |parse| |terms| |zeroSquareMatrix| + |ip4Address| |commutativeEquality| |c06ebf| |iibinom| |startStats!| + |nary?| |OMUnknownSymbol?| |unrankImproperPartitions0| |any?| |is?| + |e01bgf| |OMputEndApp| |point?| |hdmpToDmp| |component| + |lazyPseudoRemainder| |polar| |rational?| |digit?| + |resultantEuclideannaif| |curveColorPalette| |derivationCoordinates| + |listConjugateBases| |extractPoint| |typeList| |endSubProgram| + |Vectorise| |cschIfCan| |fortranReal| |curve?| |LazardQuotient| + |s17ajf| |diagonalProduct| |eyeDistance| |dimension| |setMinPoints| + |lSpaceBasis| |e02dff| |rightNorm| |setOrder| |compBound| |asechIfCan| + |iiasin| |csubst| |OMParseError?| |Gamma| |rootDirectory| |iomode| + |extendedSubResultantGcd| |imagE| |conditionP| |completeEchelonBasis| + |computeCycleEntry| Y |eigenvector| |integralMatrixAtInfinity| + |leadingTerm| |li| |charthRoot| |blue| |datalist| |bandedHessian| |sh| + |convergents| |showTheFTable| |top!| |omError| |isPower| + |internalSubPolSet?| |overlap| |isAbsolutelyIrreducible?| |cAsec| + |e02aef| |substring?| |quadraticForm| |s13adf| |coerceListOfPairs| + |expt| |rarrow| |ParCond| |initializeGroupForWordProblem| |iiacsch| + |fortranCompilerName| |integralAtInfinity?| |opeval| |showSummary| + |nthr| |monicDecomposeIfCan| |quadraticNorm| |innerSolve| |constant?| + |nthCoef| |quasiMonicPolynomials| |suffix?| |fprindINFO| |nullity| + |factorGroebnerBasis| |palglimint| |compdegd| |row| |e| + |pseudoQuotient| |constantToUnaryFunction| |square?| |unary?| + |truncate| |showAttributes| |integers| |extensionDegree| |rank| + |deleteProperty!| |fortranCarriageReturn| |aQuadratic| |prefix?| + |const| |makeSin| |setColumn!| |s18dcf| |d01asf| |f01maf| + |selectIntegrationRoutines| |splitLinear| |denominator| + |sylvesterMatrix| |debug3D| |degreePartition| |contract| |parabolic| + |iFTable| |homogeneous?| |radicalOfLeftTraceForm| |iiacot| |mapdiv| + |lowerCase?| |closedCurve| |HenselLift| |symmetric?| |sequence| + |equiv| |pastel| |e01bef| |nothing| |monomRDE| + |shanksDiscLogAlgorithm| |splitDenominator| |euclideanSize| + |symbolIfCan| |decimal| |highCommonTerms| |s19aaf| |credPol| |name| + |thenBranch| |laplacian| |removeZero| |complexSolve| |identityMatrix| + |s19adf| |harmonic| |makeUnit| |rootsOf| |body| |relationsIdeal| + |s17adf| |alternating| |printInfo!| |OMgetEndError| |algebraic?| + |s17dhf| |updateStatus!| |morphism| |linearAssociatedOrder| + |trivialIdeal?| |iprint| |multiEuclideanTree| |setFormula!| + |stoseSquareFreePart| |lists| |computeInt| |lazyGintegrate| + |findBinding| |clearCache| |OMputAttr| |s21bcf| |headAst| |besselK| + |minordet| |realSolve| |henselFact| |operators| |initTable!| |e02dcf| + |stoseInvertibleSet| |retract| |width| |boundOfCauchy| + |characteristicSerie| |selectfirst| |weierstrass| |c06ekf| |cCosh| + |f04jgf| |integer?| |imagK| |listBranches| |repeating| + |inGroundField?| |numberOfFractionalTerms| |makeViewport2D| |f02adf| + |condition| |isTimes| |changeBase| |error| |alternative?| |e01daf| + |supRittWu?| |addPoint| |idealiserMatrix| |getMeasure| |stop| + |brillhartTrials| |port| |paren| |mindeg| |prinb| |divideIfCan| + |nextPartition| |coHeight| |assert| |stopMusserTrials| + |halfExtendedResultant1| |more?| |factorSquareFreeByRecursion| + |removeCoshSq| |rightExactQuotient| |ruleset| |palgint0| |fglmIfCan| + |pointPlot| |rationalIfCan| |axesColorDefault| |t| |cycle| + |internalLastSubResultant| |sts2stst| |mainContent| |meshPar1Var| + |quoted?| |countRealRoots| |dflist| |nextColeman| |LazardQuotient2| EQ + |complement| |cCos| |setAttributeButtonStep| |f07fdf| + |leviCivitaSymbol| |branchPointAtInfinity?| |readUInt16!| |bumptab| + |maxRowIndex| |infix| |recip| |pdct| |suchThat| |e04ucf| + |setTopPredicate| |matrix| |optional| |htrigs| |outputGeneral| + |errorKind| |leftTraceMatrix| |collectUnder| |setEpilogue!| |plus!| + |e04gcf| |arity| |infinite?| |setPoly| |purelyAlgebraic?| |graphState| + |critT| |inconsistent?| UTS2UP |OMgetType| |removeDuplicates!| + |mainExpression| |cAtanh| |coshIfCan| |e02bef| |setvalue!| |infLex?| + |medialSet| |traceMatrix| |parseString| |restorePrecision| + |cyclicGroup| |generalTwoFactor| |fortran| |exteriorDifferential| + |mantissa| |gderiv| |printTypes| |move| |solveLinearlyOverQ| + |associator| |polynomialZeros| |characteristicPolynomial| |mathieu12| + |rationalFunction| |gethi| |composite| |defineProperty| |makingStats?| + |fortranInteger| |getDatabase| |mesh| |trigs| |center| |readable?| + |readUInt8!| |OMsupportsCD?| |makeGraphImage| |ode1| |scale| |lquo| + |iitan| |callForm?| |s18acf| |check| |trailingCoefficient| SEGMENT + |edf2efi| |pair?| |nodes| |operation| |characteristicSet| |cCsc| + |resultantReduitEuclidean| |OMbindTCP| |mainDefiningPolynomial| + |structuralConstants| |interpolate| |reindex| |complete| |innerint| + |pointColor| |getProperties| |invmod| |makeYoungTableau| + |trigs2explogs| |comp| |leftNorm| |compile| |expenseOfEvaluation| + |subTriSet?| |makeFR| |plus| |f02wef| |hypergeometric0F1| |submod| + |rightRecip| |rightQuotient| |modulus| |c06eaf| |diagonal| + |antiCommutator| |OMputEndBind| |infieldIntegrate| |outputArgs| + |contains?| |abs| |basicSet| |raisePolynomial| |monicRightFactorIfCan| + |numberOfHues| |acosIfCan| |coord| |SturmHabichtSequence| + |limitedIntegrate| |monomialIntegrate| |moebiusMu| |graphImage| + |d01alf| |rischDE| |rowEchelon| |dequeue!| |splitNodeOf!| |root| + |column| |parameters| |noKaratsuba| |var2Steps| |linearDependence| + |iipow| |times| |ddFact| |compiledFunction| |BumInSepFFE| |cosIfCan| + |definingEquations| |frst| |algSplitSimple| |zeroDimensional?| + |optimize| |tan2trig| |signAround| |char| |supersub| + |getMultiplicationTable| |fractRadix| |iidprod| |OMputString| + |iiasinh| |top| |f01qdf| |measure| |currentCategoryFrame| |maxIndex| + |bindings| |sortConstraints| |concat| |unparse| |setfirst!| + |lastSubResultant| |script| |components| |safeCeiling| |f02axf| |dec| + |times!| |members| |linearAssociatedLog| |tableau| |rootPower| + |stoseInvertible?reg| |list| |leftExtendedGcd| |linearAssociatedExp| + |acoshIfCan| |multiplyCoefficients| |inc| |monom| |divisorCascade| + |removeConstantTerm| |partialFraction| |iiatanh| + |solveLinearPolynomialEquationByRecursion| |car| |basisOfLeftNucloid| + |refine| |Si| |iteratedInitials| |nonQsign| |direction| |twist| + |sturmVariationsOf| |secIfCan| |create3Space| |cdr| |sdf2lst| + |subresultantVector| |approxSqrt| |OMconnInDevice| |printStatement| + |decrease| |queue| |setlast!| |mat| |mulmod| |setDifference| + |plusInfinity| |pomopo!| |kroneckerDelta| |OMputBVar| + |subResultantGcd| |common| |cond| |getZechTable| |float| |fibonacci| + |linearPolynomials| |complexEigenvalues| |rational| |setIntersection| + |minusInfinity| |duplicates| |s14abf| |rightRemainder| + |cRationalPower| |reify| |entries| |semiSubResultantGcdEuclidean1| + |insertRoot!| |hex| |setUnion| |initial| |cos2sec| |bernoulli| + |viewSizeDefault| |groebgen| |rem| |rationalApproximation| |bumprow| + |stripCommentsAndBlanks| |minrank| |algebraicSort| |apply| + |parabolicCylindrical| |notelem| |OMsupportsSymbol?| |cAcoth| |quo| + |createLowComplexityTable| |coerceL| |atanIfCan| |singularitiesOf| + |groebnerIdeal| |split!| |Ei| |corrPoly| |viewpoint| |intersect| + |makeop| |setMaxPoints| |kmax| |redpps| |size| |tanhIfCan| + |rewriteIdealWithQuasiMonicGenerators| |changeThreshhold| + |partialNumerators| |div| |doublyTransitive?| |LyndonBasis| |lifting| + |divide| |algebraicVariables| |type| |polygamma| |rootSplit| + |makeResult| |linearPart| |exquo| |innerEigenvectors| |output| |tree| + |differentialVariables| |bat1| |collectUpper| |weighted| + |trace2PowMod| |intPatternMatch| |taylorIfCan| |eof?| ~= |c02agf| + |nextPrimitivePoly| |bitLength| |perfectSqrt| |scripted?| |first| + |extend| |inputOutputBinaryFile| |OMgetVariable| |patternVariable| |#| + GE |integrate| |cSin| |explicitlyEmpty?| + |semiDegreeSubResultantEuclidean| |changeMeasure| |rest| + |topFortranOutputStack| |safeFloor| |prod| ~ |buildSyntax| + |dimensionOfIrreducibleRepresentation| GT |qroot| |headRemainder| + |noLinearFactor?| |setAdaptive3D| |substitute| |exprToGenUPS| + |factorSquareFreePolynomial| |patternMatchTimes| |graphStates| LE + |regime| |asinIfCan| |simplifyLog| |cartesian| |representationType| + |removeDuplicates| |complexZeros| |leftExactQuotient| |isTerm| + |antisymmetricTensors| |colorFunction| LT |radPoly| |stopTable!| + |irreducibleFactor| |cAtan| |rk4qc| |central?| |whitePoint| |/\\| + |showTheRoutinesTable| |zero?| |endOfFile?| |cot2tan| |capacity| + |getOrder| |lift| |expandPower| |interval| |OMmakeConn| + |binaryTournament| |\\/| |tryFunctionalDecomposition| + |definingInequation| |OMUnknownCD?| |extractIndex| |norm| |compose| + |reduce| |exprHasWeightCosWXorSinWX| |s21baf| |FormatArabic| + |typeLists| |createNormalPrimitivePoly| |printStats!| |concat!| + |f01mcf| |isOp| |hMonic| |e02ajf| |chebyshevT| |rightFactorIfCan| + |discreteLog| |OMopenString| |subset?| |basisOfCentroid| + |numberOfPrimitivePoly| |sorted?| |fractRagits| + |stoseInvertible?sqfreg| |simplifyPower| |normalizedDivide| + |binaryTree| |complexExpand| |wrregime| |low| |lazyVariations| + |elementary| |totalLex| |pushucoef| |localAbs| |screenResolution3D| + |selectOrPolynomials| |exprHasLogarithmicWeights| |cAcsch| |realRoots| + |bivariatePolynomials| |interReduce| |pol| |cAsin| |startTable!| + |normal01| |lazyPseudoDivide| |rename!| |autoCoerce| |extractBottom!| + |Is| |permanent| |minRowIndex| |stirling2| |rectangularMatrix| + |recolor| |insert!| |decompose| |presub| |abelianGroup| |round| + |optional?| |equation| |rischDEsys| |remove!| |cyclePartition| + |irreducibleFactors| |branchPoint?| |setTex!| |zoom| + |internalZeroSetSplit| |iiexp| |bits| |part?| |continue| |properties| + |maxPoints3D| |combineFeatureCompatibility| |outputSpacing| + |headReduced?| |extractClosed| |f02aff| |s13aaf| |flexibleArray| + |elements| |subSet| |extractProperty| |intermediateResultsIF| + |translate| |makeSeries| |cyclicEqual?| |tower| |fortranLinkerArgs| + |OMgetAttr| |position| |outputForm| |stFunc1| |physicalLength| + |symbolTableOf| |tan2cot| |f2df| |push!| |signatureAst| |sin2csc| + |cotIfCan| |match?| |cosh2sech| |setprevious!| |rightTrace| |rst| + |sample| |rightPower| |d02gbf| |ScanArabic| |musserTrials| + |partialQuotients| |repeating?| |f02akf| |polyRDE| |byte| + |upDateBranches| |rightFactorCandidate| |bright| |exportedOperators| + |reciprocalPolynomial| |solveRetract| |iifact| |iilog| + |viewWriteDefault| |palgRDE| |primes| |deepestInitial| + |mapMatrixIfCan| |recoverAfterFail| |jordanAlgebra?| + |createRandomElement| |scaleRoots| |dim| |setFieldInfo| |function| + |setRow!| |firstSubsetGray| |bombieriNorm| |socf2socdf| + |antisymmetric?| |ellipticCylindrical| |internalIntegrate0| + |complexNumeric| |basis| |jacobi| |pow| |debug| |bothWays| + |viewThetaDefault| |radix| |reducedSystem| |eval| |currentScope| + |atom?| |generalizedEigenvector| |qfactor| |read!| D |writable?| + |virtualDegree| |open?| |kernels| |in?| |basisOfRightNucleus| + |removeCosSq| |maximumExponent| |maxColIndex| |setCondition!| + |element?| |interpret| |setMaxPoints3D| |nthRoot| + |associatorDependence| |appendPoint| |operator| |indicialEquation| + |minimumDegree| |generateIrredPoly| |distance| |arrayStack| |float?| + |createNormalElement| |curry| |mapUnivariateIfCan| |OMserve| |conjug| + |genus| |semiSubResultantGcdEuclidean2| |autoReduced?| |int| |s17aff| + |selectMultiDimensionalRoutines| |init| |power| |cSinh| |univariate| + |rightDiscriminant| |limit| |algDsolve| |nextPrime| |rightGcd| + |f02awf| |acschIfCan| |btwFact| |level| |double| |OMencodingBinary| + |LagrangeInterpolation| |factorSquareFree| |nextsubResultant2| + |triangSolve| |controlPanel| |bfEntry| |completeSmith| + |outputBinaryFile| |numberOfMonomials| |s17acf| |viewPhiDefault| |mr| + |rotatex| |mainKernel| |sin?| |leftRegularRepresentation| |unmakeSUP| + |figureUnits| |semicolonSeparate| |factor| |clipParametric| + |lyndonIfCan| |trapezoidal| |OMencodingUnknown| |writeLine!| + |genericRightMinimalPolynomial| |e01baf| |coefChoose| BY |sqrt| + |setref| |dictionary| |mainCoefficients| |leftDivide| |trunc| + |primitive?| |leftFactor| |head| |OMputEndObject| |leftTrace| |real| + |mapExpon| |composites| |createMultiplicationTable| |e04dgf| |Aleph| + |print| |d01apf| |f01rcf| |iisec| |iisin| |mathieu22| |imag| |lcm| + |cyclicSubmodule| |dmp2rfi| |separate| |resolve| |f04axf| |f01rdf| + |lazyIrreducibleFactors| |nextsousResultant2| |directProduct| |tanNa| + |iiasec| |roughSubIdeal?| |makeCos| |toseInvertible?| + |findConstructor| |inHallBasis?| |even?| |countable?| |declare!| + |append| |ListOfTerms| |pole?| |subPolSet?| |conjugates| |removeSinSq| + |wholeRagits| |lazyPquo| |nodeOf?| |leaf?| |linSolve| + |removeRedundantFactors| |brace| |chebyshevU| |gcd| |groebner?| + |showIntensityFunctions| |parts| |rk4f| |sayLength| |floor| + |doubleResultant| |bezoutMatrix| |bounds| |destruct| |rightLcm| + |false| |symmetricTensors| |scan| |reduceLODE| NOT |mkIntegral| + |f04faf| |coleman| |light| |iiabs| |showAll?| |computeCycleLength| + |OMreadStr| |argument| OR |bringDown| |pushdown| |padecf| + |deepestTail| |pmComplexintegrate| |resultantReduit| |copies| + |mainVariable?| AND |nativeModuleExtension| |changeNameToObjf| |block| + |collect| |rootPoly| |outputFixed| |f02agf| |janko2| |aQuartic| + |cCoth| |numberOfFactors| |taylorRep| |cAsech| |constantRight| + |monomial| |imaginary| |mainVariables| |linearMatrix| |reopen!| + |stack| |gcdPrimitive| |integerIfCan| + |solveLinearPolynomialEquationByFractions| |f07adf| |f04mcf| |table| + |multivariate| |torsionIfCan| |setValue!| |select!| |twoFactor| + |writeInt8!| |numberOfComposites| |monomial?| |just| |insert| |new| + |variables| |algebraicCoefficients?| |critMonD1| |solveid| |anticoord| + |crest| |useEisensteinCriterion| |OMgetSymbol| |adaptive?| |pdf2df| + |elColumn2!| |s18aff| |po| |tanintegrate| |viewDefaults| |cache| + |less?| |mainCharacterization| |csc2sin| |removeSinhSq| |build| + |outputMeasure| |critpOrder| |primlimitedint| |sturmSequence| + |primitivePart!| |beauzamyBound| |cscIfCan| |alphabetic| + |chineseRemainder| |changeVar| |laguerre| |hasSolution?| |delay| + |SturmHabichtMultiple| |symmetricRemainder| |indicialEquations| + |approximants| |rquo| |edf2ef| |coordinates| |bfKeys| |OMgetApp| + |unprotectedRemoveRedundantFactors| |bytes| |subCase?| |d01bbf| + |basisOfRightNucloid| |iisech| |taylor| |swapColumns!| |psolve| |tab1| + |revert| |readIfCan!| * |oblateSpheroidal| |OMwrite| |d02bbf| + |nullary?| |laurent| |squareFree| |f04adf| |oddintegers| |maxint| + |complexElementary| |status| |principalAncestors| |nthFlag| + |getOperands| |OMgetFloat| |df2mf| |puiseux| |associatedEquations| + |alphabetic?| |complex?| |cSech| |rowEchLocal| |neglist| |cycles| + |baseRDE| |nextNormalPrimitivePoly| |drawComplex| |e04jaf| |cAsinh| + |realZeros| |chvar| |stiffnessAndStabilityOfODEIF| |laplace| = |erf| + |f02fjf| |inv| |integral| |constantCoefficientRicDE| |getMatch| + |makeMulti| |besselI| |powers| |bezoutResultant| |FormatRoman| + |parametric?| |ground?| |left| |resultant| |OMconnectTCP| |viewport2D| + |constantOpIfCan| |argumentListOf| |toScale| |leastPower| < + |screenResolution| |subst| |vspace| |ground| |right| + |mainSquareFreePart| |arbitrary| |merge!| |permutation| |list?| + |getMultiplicationMatrix| |s20adf| > |sec2cos| |dilog| |adjoint| F2FG + |leadingMonomial| |setLength!| |s17dcf| |idealiser| |f04atf| |max| + |toroidal| |shallowExpand| <= |qqq| |companionBlocks| |sin| + |deleteRoutine!| |leadingCoefficient| |mergeFactors| |mdeg| + |calcRanges| |supDimElseRittWu?| |generalPosition| |extendedint| + |index?| >= |eisensteinIrreducible?| |cos| |primitiveMonomials| |rule| + |findCycle| |mappingAst| |c05adf| |prolateSpheroidal| |extractIfCan| + |separateDegrees| |hermiteH| |ksec| |primextendedint| |nil| |tan| + |associative?| |reductum| |relerror| |f02ajf| |cTanh| |solve| + |OMputError| |f01bsf| |externalList| |iiacsc| |cot| |computeBasis| + |every?| |wronskianMatrix| |unknownEndian| |epilogue| |heapSort| + |deepExpand| |besselY| |coefficients| + |objects| |sec| + |tryFunctionalDecomposition?| |rightExtendedGcd| |digits| + |fortranLiteral| |d03faf| |next| |leftDiscriminant| |green| + |loadNativeModule| - |mainVariable| |base| |pToHdmp| |csc| + |approximate| |fortranTypeOf| |digit| |leftGcd| |normalise| |uniform| + |complex| |readInt16!| |rationalPower| |goodnessOfFit| / |rotate!| + |asin| |log| |realEigenvectors| |fixedDivisor| |maxdeg| |polyRicDE| + |diagonalMatrix| |dom| |jordanAdmissible?| |ratDsolve| |pointData| + |semiResultantEuclidean2| |acos| |gramschmidt| |llprop| |degree| + |doubleDisc| |quatern| |leftRecip| |genericPosition| |middle| + |clearTheIFTable| |atan| |symbol| |contractSolve| |cycleElt| + |inverseLaplace| |internalIntegrate| |back| |vedf2vef| |eq?| + |wholePart| |transpose| |acot| |vconcat| |expression| |tanSum| + |segment| |aromberg| |internalAugment| |quotient| |fortranComplex| + |selectAndPolynomials| |applyRules| |asec| |nand| |integer| + |sinh2csch| |fmecg| |parents| |mpsode| |say| |cothIfCan| |consnewpol| + |c02aff| |expressIdealMember| |acsc| |spherical| |clikeUniv| + |radicalEigenvalues| |hermite| |prepareSubResAlgo| |title| + |intcompBasis| |prevPrime| |certainlySubVariety?| |sinh| |outputList| + |limitedint| |high| |setRealSteps| |elseBranch| |genericLeftNorm| + |currentSubProgram| |enqueue!| |cosh| |se2rfi| |karatsubaDivide| + |recur| |particularSolution| |expextendedint| |associatedSystem| + |randnum| |unitNormalize| |tanh| |useSingleFactorBound| + |leadingSupport| |binding| |internalInfRittWu?| |leader| + |genericRightTrace| |getButtonValue| |lieAdmissible?| |froot| |coth| + |isConnected?| |clearTable!| |initiallyReduce| |outlineRender| + |outputAsScript| |previous| |exprToUPS| |retractable?| |redPo| |sech| + |lambda| |cAcot| |e04fdf| |label| |replaceKthElement| |quadratic?| + |flagFactor| |rdHack1| |csch| |readBytes!| |c06ecf| |binaryFunction| + |principalIdeal| |generalizedEigenvectors| |normalDeriv| + |semiResultantReduitEuclidean| |asinh| |prime?| |divideIfCan!| + |LowTriBddDenomInv| |option?| |explimitedint| |Hausdorff| |iicsc| + |myDegree| |createGenericMatrix| |acosh| |leftRank| |redmat| + |clipBoolean| |rewriteIdealWithHeadRemainder| + |createLowComplexityNormalBasis| |createIrreduciblePoly| |atanh| + |dioSolve| |nthExpon| |OMputSymbol| |mapSolve| |ode2| |super| + |meshFun2Var| |dihedralGroup| |assign| |firstNumer| |acoth| + |OMgetInteger| |maxPoints| |increasePrecision| |setPredicates| + |fractionFreeGauss!| |escape| |listLoops| |byteBuffer| |summation| + |asech| |pack!| |mathieu23| |zerosOf| |e02bcf| |swap| |bernoulliB| + |roughBasicSet| |littleEndian| |constructor| |hcrf| + |lastSubResultantElseSplit| |e04ycf| |dimensionsOf| |insertMatch| + |multiple| |addPointLast| |remove| |leftScalarTimes!| |lowerCase!| + |distribute| |OMgetError| |option| |zeroSetSplit| |external?| + |showTheIFTable| |applyQuote| |squareFreePart| |zeroDim?| |pushuconst| + |eulerPhi| |numberOfVariables| |Frobenius| |isOpen?| + |semiIndiceSubResultantEuclidean| |euclideanGroebner| |last| |ldf2lst| + |minset| |lowerPolynomial| |monicCompleteDecompose| |printInfo| + |minPoly| |inverseIntegralMatrix| |graphCurves| |assoc| |varList| + |isNot| |simplify| |integralCoordinates| |modifyPoint| |depth| + |mapExponents| |setProperty| |pushdterm| |qualifier| |elliptic?| + |rootNormalize| |rightTrim| |knownInfBasis| |doubleRank| + |rationalPoint?| |divergence| |stosePrepareSubResAlgo| |droot| + |constant| |cTan| |exactQuotient| |leftTrim| |nlde| |generate| + |yCoord| |getRef| |e02ahf| |closedCurve?| |pToDmp| |moduloP| |seed| + |aspFilename| |internalSubQuasiComponent?| |f04qaf| |ricDsolve| + |front| |lazyPseudoQuotient| |fortranCharacter| |incrementBy| + |primintfldpoly| |perfectSquare?| |univcase| |elRow1!| |s18def| + |lexGroebner| |enterInCache| |uniform01| |palgextint0| |e01saf| + |expand| |OMgetEndAtp| |sinhcosh| |ranges| |normalize| + |removeRedundantFactorsInContents| |explicitlyFinite?| |setnext!| + |genericRightTraceForm| |filterWhile| |rightDivide| |rdregime| + |cyclicCopy| |rischNormalize| |OMgetEndApp| |OMgetEndBind| |largest| + |OMputAtp| |weights| |functionIsFracPolynomial?| |someBasis| + |filterUntil| |diagonal?| |critMTonD1| |definingPolynomial| + |predicate| |logical?| |cycleLength| |leftUnit| |elliptic| |ramified?| + |lastSubResultantEuclidean| |prinpolINFO| |select| |infinityNorm| + |multisect| |basisOfLeftNucleus| |commonDenominator| + |numericalIntegration| |reflect| |enterPointData| |multMonom| + |B1solve| |minPol| |e02adf| |rangePascalTriangle| |subQuasiComponent?| + |replace| |tanh2trigh| |dot| |oneDimensionalArray| |stoseInvertible?| + |removeRedundantFactorsInPols| |pattern| |safetyMargin| |charpol| + |hdmpToP| |putGraph| |lieAlgebra?| |f02bjf| |startPolynomial| + |dAndcExp| |perspective| |isOr| |lazyEvaluate| |airyBi| + |bandedJacobian| |OMgetBind| |nil?| |signature| + |semiResultantEuclideannaif| |mainMonomials| |functionIsOscillatory| + |resetBadValues| |asecIfCan| |infRittWu?| |ODESolve| |asimpson| + |primPartElseUnitCanonical| |leftAlternative?| |zeroDimPrime?| + |c06gsf| |surface| |tableForDiscreteLogarithm| |toseLastSubResultant| + |extendedEuclidean| |node| |dfRange| |createNormalPoly| |whatInfinity| + |powmod| |makeRecord| |rewriteSetByReducingWithParticularGenerators| + |message| |primPartElseUnitCanonical!| |leftUnits| |compound?| + |OMReadError?| |setOfMinN| |closed?| |palgLODE| |primextintfrac| + |transcendent?| |f02abf| |imagI| |decomposeFunc| |number?| |mkcomm| + |rightUnits| |setStatus| |ptree| |getOperator| |eigenvectors| |hash| + |primitiveElement| |setleaves!| |useEisensteinCriterion?| + |selectPolynomials| |testModulus| |palgRDE0| |iiacoth| |leftOne| + |count| |d01amf| |iiperm| |pointColorPalette| |hspace| |cyclotomic| + |size?| |setLegalFortranSourceExtensions| |phiCoord| |mainValue| + |iicoth| |leftPower| |sech2cosh| |permutations| |diagonals| + |localIntegralBasis| |iisinh| |evaluate| |bitTruth| |exponent| + |physicalLength!| |setVariableOrder| |squareMatrix| + |basisOfCommutingElements| |rangeIsFinite| |factorAndSplit| |cons| + |sub| |minPoints| |d02bhf| |superscript| |updatD| |qinterval| + |subtractIfCan| |PDESolve| |tensorProduct| |halfExtendedResultant2| + |lighting| |divisor| |gcdcofactprim| |mightHaveRoots| |unvectorise| + |newReduc| |nextSublist| |rootOf| |asinhIfCan| + |numberOfImproperPartitions| |iicsch| + |zeroSetSplitIntoTriangularSystems| |iterationVar| |shuffle| |df2ef| + |mathieu11| |genericRightNorm| |critBonD| |negative?| |iisqrt3| + |mapGen| |f02aaf| |empty| |hessian| |bubbleSort!| |primitivePart| + |forLoop| |sPol| |extendedIntegrate| |blankSeparate| |e02gaf| + |OMencodingSGML| |checkPrecision| |oddInfiniteProduct| |polyred| + |lfunc| |node?| |infiniteProduct| |fortranDouble| |groebnerFactorize| + |singleFactorBound| |factorPolynomial| |normFactors| |cycleSplit!| + |trueEqual| |halfExtendedSubResultantGcd2| |basisOfMiddleNucleus| + |showArrayValues| |removeSuperfluousCases| |weakBiRank| |dn| |source| + |rightRegularRepresentation| |mathieu24| |numerator| |deriv| + |numberOfComputedEntries| |universe| |fortranDoubleComplex| |lambert| + |scalarMatrix| |localReal?| |exprToXXP| |lfinfieldint| |outputAsTex| + |graphs| |doubleComplex?| |increment| |copy!| |paraboloidal| |c06fpf| + |roughBase?| |cCot| |solveInField| |optpair| |bag| |pdf2ef| |bracket| + |ptFunc| |setScreenResolution3D| |isMult| |lprop| |nsqfree| + |normalElement| |d03edf| |approxNthRoot| |iflist2Result| + |userOrdered?| |integralMatrix| |slex| RF2UTS + |leftCharacteristicPolynomial| |eigenMatrix| |failed?| |target| + |stopTableGcd!| |empty?| |invertible?| |internalDecompose| + |hostByteOrder| |expenseOfEvaluationIF| |SturmHabichtCoefficients| + |numerators| |sum| |anfactor| |OMgetBVar| |null?| |fintegrate| + |reverse| |axes| |lllp| |readLine!| |LyndonCoordinates| |inf| + |palglimint0| |logGamma| |mirror| |formula| |sequences| + |partialDenominators| |ef2edf| |writeBytes!| |basisOfLeftAnnihilator| + |tanIfCan| |shrinkable| |infieldint| |expr| |lllip| + |balancedFactorisation| |postfix| |child?| |identification| + |univariateSolve| |sizeLess?| |createMultiplicationMatrix| |lp| + |increase| |rootProduct| |univariatePolynomials| |taylorQuoByVar| + |ravel| |leadingExponent| |idealSimplify| |primintegrate| |setEmpty!| + |declare| |f04maf| |triangular?| |options| |prepareDecompose| + |constDsolve| |tubePoints| |constantLeft| |reshape| |printCode| + |c06gcf| |kernel| |nrows| |separant| |vark| |d01ajf| |setProperty!| + |draw| |algint| |seriesToOutputForm| |realElementary| |cPower| |ncols| + |variable| |rightUnit| |coordinate| |sincos| |exists?| |e01bff| + |quasiRegular?| |saturate| |squareFreeFactors| |iterators| |polyPart| + |heap| |splitConstant| |string| |represents| |currentEnv| + |OMgetEndObject| |implies| |simpson| |numberOfComponents| |changeName| + |critB| |unitNormal| |iCompose| |failed| |permutationGroup| |delete!| + |isPlus| |showFortranOutputStack| |c06gqf| |integerBound| + |integralBasis| |e01sbf| |lowerCase| |processTemplate| |scopes| |qelt| + |completeHermite| |update| |leftQuotient| |laguerreL| |makeObject| + |over| |stopTableInvSet!| |semiDiscriminantEuclidean| |qsetelt| + |tubePlot| |f02bbf| |invertIfCan| |crushedSet| |coef| |red| + |repeatUntilLoop| |linear| |badValues| |quasiAlgebraicSet| |yellow| + |identity| |OMunhandledSymbol| |xRange| |getGoodPrime| |moebius| + |readByte!| |baseRDEsys| |pseudoDivide| |swapRows!| |An| |yRange| + |expandTrigProducts| |mindegTerm| |upperCase| |numberOfChildren| + |groebner| |polynomial| |resultantnaif| |plenaryPower| |zRange| + |imagj| |stronglyReduce| |f04arf| |iExquo| |precision| |ldf2vmf| + |cAcos| |stoseInvertibleSetsqfreg| |weight| |reduceByQuasiMonic| + |map!| |singRicDE| |bat| |simpsono| |OMgetObject| |selectPDERoutines| + |normalDenom| |clearFortranOutputStack| |unaryFunction| |tubeRadius| + |qsetelt!| |generic| |derivative| |factor1| |totalGroebner| + |pointSizeDefault| |minPoints3D| |dmpToHdmp| |tablePow| + |gcdPolynomial| |extension| |unravel| |retractIfCan| |radicalSimplify| + |getGraph| |iiacosh| |traverse| |internal?| |mix| |cyclic| |maxrow| + |normalizedAssociate| |printHeader| |untab| |mapBivariate| |d01gbf| + |cyclicParents| |index| |nthRootIfCan| |expintegrate| |OMputEndAtp| + |legendreP| |leaves| |goodPoint| |permutationRepresentation| |sn| + |rk4a| |overlabel| |unrankImproperPartitions1| |matrixConcat3D| + |showTheSymbolTable| |areEquivalent?| |purelyTranscendental?| + |linearlyDependentOverZ?| |acsch| |reduced?| |selectsecond| + |discriminant| |getBadValues| |simpleBounds?| |computePowers| + |factorList| |constantKernel| |numericIfCan| |pair| |tanQ| |belong?| + |isExpt| |test| |imports| |f02aef| |value| |bezoutDiscriminant| + |laurentRep| |compactFraction| |s17ahf| |multiplyExponents| + |hexDigit?| |randomLC| |rules| |hue| |removeZeroes| |var1Steps| + |lazyIntegrate| |solveLinearPolynomialEquation| |associates?| + |listexp| |directory| |xn| |child| |nextNormalPoly| |fTable| |open| + |quadratic| |inRadical?| |subresultantSequence| |hclf| |lex| |map| + |modularFactor| |pr2dmp| |rowEchelonLocal| |generalInfiniteProduct| + |brillhartIrreducible?| |writeUInt8!| |showAllElements| |odd?| + |mainForm| |denomLODE| |euler| |iicos| |quoByVar| |reducedQPowers| + |any| |eq| |newLine| |s15adf| |prefix| |listRepresentation| + |chiSquare1| |quasiRegular| |yCoordinates| |dimensions| |f01qef| + |cycleRagits| |OMgetString| |generic?| |unknown| |iter| + |quotedOperators| |powern| |transcendenceDegree| |ramifiedAtInfinity?| + |removeSuperfluousQuasiComponents| |iidsum| |numFunEvals| + |bivariateSLPEBR| |drawStyle| |alphanumeric?| |mapCoef| |operations| + |curveColor| |var1StepsDefault| |curryRight| |numeric| |pushup| + |clipSurface| |makeSketch| F |genericLeftDiscriminant| |binomial| + |nextPrimitiveNormalPoly| |e01sef| |ran| + |removeRoughlyRedundantFactorsInPol| |edf2fi| |writeByte!| |squareTop| + |chiSquare| |radical| |region| |complexRoots| |convert| + |explogs2trigs| |dark| |polCase| |toseInvertibleSet| |fixedPointExquo| + |octon| |cyclic?| |groebSolve| |OMsend| |sumOfSquares| + |modularGcdPrimitive| |df2st| |distFact| |pile| |magnitude| + |setright!| |distdfact| |functionIsContinuousAtEndPoints| + |numericalOptimization| |besselJ| |leadingBasisTerm| |padicallyExpand| + |createZechTable| |doubleFloatFormat| |palgLODE0| + |selectOptimizationRoutines| |factors| |PollardSmallFactor| |freeOf?| + |firstUncouplingMatrix| |quote| |rubiksGroup| |imagJ| + |leadingCoefficientRicDE| |nullary| |extractSplittingLeaf| + |sqfrFactor| |symmetricPower| |points| |withPredicates| |upperCase?| + |fortranLiteralLine| |removeSquaresIfCan| |aCubic| |listOfMonoms| + |multiple?| |makeTerm| |polygon| |BasicMethod| |e01bhf| |Beta| + |isEquiv| |exp| |problemPoints| |OMgetEndBVar| |unit?| |prime| |unit| + |d02gaf| |position!| |stoseInvertibleSetreg| |mkPrim| |setMinPoints3D| + |sumOfDivisors| |transcendentalDecompose| |ipow| + |leftMinimalPolynomial| |ffactor| |getPickedPoints| |mapUnivariate| + |meshPar2Var| |UnVectorise| |ridHack1| |monomRDEsys| |subNodeOf?| + |UP2ifCan| |separateFactors| |log2| |nextItem| + |selectNonFiniteRoutines| |unexpand| |f02xef| |s18adf| |hexDigit| + |bipolarCylindrical| |id| |lflimitedint| |d03eef| |linGenPos| + |lazyPremWithDefault| |second| |iitanh| |fill!| |goto| |rename| + |aLinear| |rspace| |reducedContinuedFraction| + |integralBasisAtInfinity| |shiftLeft| |evenlambert| |close| |e02daf| + |divideExponents| |third| |binarySearchTree| |complementaryBasis| + |e02agf| |pade| |cCsch| |algebraicOf| |nor| |triangulate| + |subscriptedVariables| |solveLinear| |seriesSolve| + |leastAffineMultiple| |bigEndian| |setLabelValue| + |conditionsForIdempotents| |symmetricProduct| |useNagFunctions| |sup| + |cup| |rootOfIrreduciblePoly| |search| |semiResultantEuclidean1| + |augment| |display| |airyAi| |subscript| |obj| |rotatey| |varselect| + |edf2df| |e04mbf| |shiftRoots| |frobenius| |write!| |denomRicDE| + |generalizedContinuumHypothesisAssumed?| |trapezoidalo| |fracPart| + |s17akf| |setProperties!| |color| |mainMonomial| |viewZoomDefault| + |setStatus!| |minColIndex| |errorInfo| |scanOneDimSubspaces| + |numberOfOperations| |coth2tanh| |minimumExponent| |complexNormalize| + |hyperelliptic| |initials| |schema| |getCurve| |rk4| |pureLex| + |e02bbf| |invertibleElseSplit?| |genericRightDiscriminant| + |drawToScale| |SFunction| |rowEch| |setleft!| |rightRankPolynomial| + |specialTrigs| |removeRoughlyRedundantFactorsInContents| |geometric| + |youngGroup| |isQuotient| |minIndex| |shufflein| |difference| + |insertionSort!| |returns| |diff| |pleskenSplit| |totalDifferential| + |extendIfCan| |viewport3D| |clipPointsDefault| |pointColorDefault| + |input| |multiset| |determinant| |duplicates?| + |selectSumOfSquaresRoutines| |f2st| |hasPredicate?| |ratPoly| |lhs| + |deref| |d02ejf| |normalForm| |lepol| |fractionPart| |category| + |irreducible?| |expintfldpoly| |library| |ScanFloatIgnoreSpaces| + |makeViewport3D| |stFunc2| |badNum| |zeroOf| |rhs| |coerceImages| + |cAcosh| |extendedResultant| |nthFactor| |acscIfCan| |domain| + |attributeData| |elRow2!| |setImagSteps| |meatAxe| |equality| + |directSum| |zeroMatrix| |showRegion| |linear?| |tanAn| |ParCondList| + |relativeApprox| |package| |Nul| |getStream| |normalizeAtInfinity| + |clearTheSymbolTable| |find| |collectQuasiMonic| |shift| |mesh?| + |coerce| |romberg| |inR?| |merge| |coefficient| |dequeue| |height| + |systemCommand| |expint| |gradient| |tValues| + |inverseIntegralMatrixAtInfinity| |laurentIfCan| |arg1| + |mainPrimitivePart| |construct| |uncouplingMatrices| |partition| + |symFunc| |readLineIfCan!| |linkToFortran| |factorByRecursion| + |deepCopy| |set| |viewDeltaXDefault| |rotatez| |bottom!| |elem?| + |arg2| |generalizedContinuumHypothesisAssumed| |leftRankPolynomial| + |parametersOf| |headReduce| |arguments| |kind| |gensym| + |selectFiniteRoutines| |tracePowMod| |algintegrate| |f07aef| + |upperCase!| |d01anf| |solid?| |lexico| |binomThmExpt| |totolex| + |matrixDimensions| |op| |normal| |addiag| |cLog| |var2StepsDefault| + |backOldPos| |s15aef| |conditions| |bivariate?| |toseSquareFreePart| + |e01sff| |f04asf| |createPrimitivePoly| |character?| |denominators| + |remainder| |moreAlgebraic?| |OMclose| |match| |zCoord| |vectorise| + |createPrimitiveNormalPoly| |palgint| |diag| |countRealRootsMultiple| + |packageCall| |prem| |minimalPolynomial| |product| |GospersMethod| + |setrest!| |bit?| |s19acf| |chainSubResultants| |atanhIfCan| |tex| + |OMgetAtp| |fixedPoints| |linearlyDependent?| |clip| |mapUp!| + |torsion?| |characteristic| |RittWuCompare| |decreasePrecision| + |roughEqualIdeals?| |primeFrobenius| |squareFreePolynomial| |binary| + |iiasech| |contours| |KrullNumber| |has?| |stFuncN| |biRank| |setelt!| + |tubePointsDefault| |integralRepresents| |entry| |f01ref| |exponents| + |ScanFloatIgnoreSpacesIfCan| |expandLog| |modularGcd| |OMputInteger| + |union| |setClipValue| |alternatingGroup| |solid| |power!| |lookup| + |splitSquarefree| |key?| |viewWriteAvailable| + |integralDerivationMatrix| |positiveRemainder| |integral?| + |probablyZeroDim?| |inrootof| |inputBinaryFile| |OMencodingXML| + |factorFraction| |adaptive3D?| |allRootsOf| |OMputEndError| |presuper| + |powerSum| |zeroDimPrimary?| |OMputVariable| |startTableInvSet!| + |show| |maxrank| |pascalTriangle| |rCoord| |diophantineSystem| + |possiblyNewVariety?| |digamma| |orbit| |evenInfiniteProduct| + |ignore?| |reverseLex| |integralLastSubResultant| |call| |kovacic| + |tail| |setelt| |balancedBinaryTree| |getConstant| + |symmetricDifference| |drawCurves| |cyclotomicFactorization| + |putColorInfo| |OMreadFile| |lifting1| |trace| |prefixRagits| |cross| + |sncndn| |exp1| |updatF| |generalSqFr| |encodingDirectory| + |firstDenom| |s21bdf| |patternMatch| |clearDenominator| |copy| + |intensity| |adaptive| |setScreenResolution| |addmod| |root?| + |pointLists| |midpoints| |reducedForm| |create| |shade| |s21bbf| + |scalarTypeOf| |e04naf| |conical| |explicitEntries?| |void| + |OMsetEncoding| |split| |iisqrt2| |iiGamma| |cyclicEntries| + |checkForZero| |complexNumericIfCan| |shallowCopy| |leftZero| + |interpretString| |mapDown!| |palginfieldint| |nonSingularModel| + |quartic| |positive?| |member?| |pop!| |exponentialOrder| |birth| + |jacobiIdentity?| |d02kef| |getProperty| |minus!| |radicalEigenvector| + |parent| |lyndon| |halfExtendedSubResultantGcd1| |moduleSum| + |sinIfCan| |polarCoordinates| |rootBound| + |noncommutativeJordanAlgebra?| |d01fcf| |degreeSubResultantEuclidean| + |flexible?| |leadingIndex| |content| |lexTriangular| + |removeRoughlyRedundantFactorsInPols| |bsolve| |smith| |LiePoly| + |OMconnOutDevice| |ReduceOrder| |xCoord| |testDim| |s20acf| |dihedral| + |factorsOfDegree| |point| |graeffe| |addMatchRestricted| |finiteBasis| + |rootRadius| |cap| |HermiteIntegrate| |startTableGcd!| + |createThreeSpace| |ord| |unitCanonical| |nextIrreduciblePoly| + |newSubProgram| |order| |basisOfCenter| |useSingleFactorBound?| + |unitVector| |primeFactor| |cSec| |e02akf| |cosSinInfo| |gcdcofact| + |complexIntegrate| |euclideanNormalForm| |rightRank| |sort| |ref| + |unitsColorDefault| |nil| |infinite| |arbitraryExponent| |approximate| + |complex| |shallowMutable| |canonical| |noetherian| |central| + |partiallyOrderedSet| |arbitraryPrecision| |canonicalsClosed| + |noZeroDivisors| |rightUnitary| |leftUnitary| |additiveValuation| + |unitsKnown| |canonicalUnitNormal| |multiplicativeValuation| + |finiteAggregate| |shallowlyMutable| |commutative|)
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T) ((-23) . T) ((-25) . T) ((-38 #0=(-410 (-567))) -2800 (|has| |#1| (-351)) (|has| |#1| (-365))) ((-38 |#1|) . T) ((-38 $) -2800 (|has| |#1| (-559)) (|has| |#1| (-351)) (|has| |#1| (-365)) (|has| |#1| (-308))) ((-35) |has| |#1| (-1203)) ((-95) |has| |#1| (-1203)) ((-102) . T) ((-111 #0# #0#) -2800 (|has| |#1| (-351)) (|has| |#1| (-365))) ((-111 |#1| |#1|) . T) ((-111 $ $) . T) ((-131) . T) ((-145) -2800 (|has| |#1| (-351)) (|has| |#1| (-145))) ((-147) |has| |#1| (-147)) ((-617 #0#) -2800 (|has| |#1| (-1040 (-410 (-567)))) (|has| |#1| (-351)) (|has| |#1| (-365))) ((-617 (-567)) . T) ((-617 |#1|) . T) ((-617 $) -2800 (|has| |#1| (-559)) (|has| |#1| (-351)) (|has| |#1| (-365)) (|has| |#1| (-308))) ((-614 (-863)) . T) ((-172) . T) ((-615 (-169 (-225))) |has| |#1| (-1024)) ((-615 (-169 (-381))) |has| |#1| (-1024)) ((-615 (-539)) |has| |#1| (-615 (-539))) ((-615 (-894 (-381))) |has| |#1| (-615 (-894 (-381)))) ((-615 (-894 (-567))) |has| |#1| (-615 (-894 (-567)))) ((-615 #1=(-1174 |#1|)) . 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T) ((-455) -2800 (|has| |#1| (-351)) (|has| |#1| (-365)) (|has| |#1| (-308))) ((-496) |has| |#1| (-1203)) ((-517 (-1178) |#1|) |has| |#1| (-517 (-1178) |#1|)) ((-517 |#1| |#1|) |has| |#1| (-310 |#1|)) ((-559) -2800 (|has| |#1| (-559)) (|has| |#1| (-351)) (|has| |#1| (-365)) (|has| |#1| (-308))) ((-647 #0#) -2800 (|has| |#1| (-351)) (|has| |#1| (-365))) ((-647 (-567)) . T) ((-647 |#1|) . T) ((-647 $) . T) ((-649 #0#) -2800 (|has| |#1| (-351)) (|has| |#1| (-365))) ((-649 |#1|) . T) ((-649 $) . T) ((-641 #0#) -2800 (|has| |#1| (-351)) (|has| |#1| (-365))) ((-641 |#1|) . T) ((-641 $) -2800 (|has| |#1| (-559)) (|has| |#1| (-351)) (|has| |#1| (-365)) (|has| |#1| (-308))) ((-640 (-567)) |has| |#1| (-640 (-567))) ((-640 |#1|) . T) ((-718 #0#) -2800 (|has| |#1| (-351)) (|has| |#1| (-365))) ((-718 |#1|) . T) ((-718 $) -2800 (|has| |#1| (-559)) (|has| |#1| (-351)) (|has| |#1| (-365)) (|has| |#1| (-308))) ((-725 |#1| #1#) . T) ((-727) . T) ((-902 (-1178)) |has| |#1| (-902 (-1178))) ((-888 (-381)) |has| |#1| (-888 (-381))) ((-888 (-567)) |has| |#1| (-888 (-567))) ((-886 |#1|) . T) ((-911) -12 (|has| |#1| (-308)) (|has| |#1| (-911))) ((-922) -2800 (|has| |#1| (-351)) (|has| |#1| (-365)) (|has| |#1| (-308))) ((-1004) -12 (|has| |#1| (-1004)) (|has| |#1| (-1203))) ((-1040 (-410 (-567))) |has| |#1| (-1040 (-410 (-567)))) ((-1040 (-567)) |has| |#1| (-1040 (-567))) ((-1040 |#1|) . T) ((-1053 #0#) -2800 (|has| |#1| (-351)) (|has| |#1| (-365))) ((-1053 |#1|) . T) ((-1053 $) . T) ((-1058 #0#) -2800 (|has| |#1| (-351)) (|has| |#1| (-365))) ((-1058 |#1|) . T) ((-1058 $) . T) ((-1051) . T) ((-1060) . T) ((-1114) . T) ((-1102) . T) ((-1153) |has| |#1| (-351)) ((-1203) |has| |#1| (-1203)) ((-1206) |has| |#1| (-1203)) ((-1218) . 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are infinite") (|:| |notEvaluated| "Range not yet evaluated"))) (-5 *1 (-192))))) +(-10 -7 (-15 -3463 ((-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")) (-2 (|:| |var| (-1178)) (|:| |fn| (-317 (-225))) (|:| -1604 (-1096 (-844 (-225)))) (|:| |abserr| (-225)) (|:| |relerr| (-225))))) (-15 -3911 ((-3 (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated")) (-2 (|:| |var| (-1178)) (|:| |fn| (-317 (-225))) (|:| -1604 (-1096 (-844 (-225)))) (|:| |abserr| (-225)) (|:| |relerr| (-225))))) (-15 -1594 ((-225) (-1096 (-844 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(-849)) (|has| |#2| (-794)) (|has| |#2| (-365)) (|has| |#2| (-172)) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-34) . T) ((-38 |#2|) |has| |#2| (-172)) ((-102) -2797 (|has| |#2| (-1101)) (|has| |#2| (-1050)) (|has| |#2| (-849)) (|has| |#2| (-794)) (|has| |#2| (-727)) (|has| |#2| (-370)) (|has| |#2| (-365)) (|has| |#2| (-172)) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-111 |#2| |#2|) -2797 (|has| |#2| (-1050)) (|has| |#2| (-365)) (|has| |#2| (-172))) ((-111 $ $) |has| |#2| (-172)) ((-131) -2797 (|has| |#2| (-1050)) (|has| |#2| (-849)) (|has| |#2| (-794)) (|has| |#2| (-365)) (|has| |#2| (-172)) (|has| |#2| (-131))) ((-617 #0=(-410 (-567))) -12 (|has| |#2| (-1039 (-410 (-567)))) (|has| |#2| (-1101))) ((-617 (-567)) -2797 (|has| |#2| (-1050)) (-12 (|has| |#2| (-1039 (-567))) (|has| |#2| (-1101))) (|has| |#2| (-849)) (|has| |#2| (-172))) ((-617 |#2|) -2797 (|has| |#2| (-1101)) (|has| |#2| (-172))) ((-614 (-863)) -2797 (|has| |#2| (-1101)) (|has| |#2| (-1050)) (|has| |#2| (-849)) (|has| |#2| (-794)) (|has| |#2| (-727)) (|has| |#2| (-370)) (|has| |#2| (-365)) (|has| |#2| (-172)) (|has| |#2| (-614 (-863))) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-614 (-1267 |#2|)) . T) ((-172) |has| |#2| (-172)) ((-231 |#2|) |has| |#2| (-1050)) ((-233) -12 (|has| |#2| (-233)) (|has| |#2| (-1050))) ((-287 #1=(-567) |#2|) . T) ((-289 #1# |#2|) . T) ((-310 |#2|) -12 (|has| |#2| (-310 |#2|)) (|has| |#2| (-1101))) ((-370) |has| |#2| (-370)) ((-379 |#2|) |has| |#2| (-1050)) ((-414 |#2|) |has| |#2| (-1101)) ((-492 |#2|) . T) ((-605 #1# |#2|) . T) ((-517 |#2| |#2|) -12 (|has| |#2| (-310 |#2|)) (|has| |#2| (-1101))) ((-647 (-567)) -2797 (|has| |#2| (-1050)) (|has| |#2| (-849)) (|has| |#2| (-365)) (|has| |#2| (-172))) ((-647 |#2|) -2797 (|has| |#2| (-1050)) (|has| |#2| (-365)) (|has| |#2| (-172))) ((-647 $) -2797 (|has| |#2| (-1050)) (|has| |#2| (-849)) (|has| |#2| (-172))) ((-649 |#2|) -2797 (|has| |#2| (-1050)) (|has| |#2| (-365)) (|has| |#2| (-172))) ((-649 $) -2797 (|has| |#2| (-1050)) (|has| |#2| (-849)) (|has| |#2| (-172))) ((-641 |#2|) -2797 (|has| |#2| (-365)) (|has| |#2| (-172))) ((-640 (-567)) -12 (|has| |#2| (-640 (-567))) (|has| |#2| (-1050))) ((-640 |#2|) |has| |#2| (-1050)) ((-718 |#2|) -2797 (|has| |#2| (-365)) (|has| |#2| (-172))) ((-727) -2797 (|has| |#2| (-1050)) (|has| |#2| (-849)) (|has| |#2| (-727)) (|has| |#2| (-172))) ((-792) |has| |#2| (-849)) ((-793) -2797 (|has| |#2| (-849)) (|has| |#2| (-794))) ((-794) |has| |#2| (-794)) ((-795) -2797 (|has| |#2| (-849)) (|has| |#2| (-794))) ((-796) -2797 (|has| |#2| (-849)) (|has| |#2| (-794))) ((-849) |has| |#2| (-849)) ((-851) -2797 (|has| |#2| (-849)) (|has| |#2| (-794))) ((-901 (-1177)) -12 (|has| |#2| (-901 (-1177))) (|has| |#2| (-1050))) ((-1039 #0#) -12 (|has| |#2| (-1039 (-410 (-567)))) (|has| |#2| (-1101))) ((-1039 (-567)) -12 (|has| |#2| (-1039 (-567))) (|has| |#2| (-1101))) ((-1039 |#2|) |has| |#2| (-1101)) ((-1052 |#2|) -2797 (|has| |#2| (-1050)) (|has| |#2| (-365)) (|has| |#2| (-172))) ((-1052 $) |has| |#2| (-172)) ((-1057 |#2|) -2797 (|has| |#2| (-1050)) (|has| |#2| (-365)) (|has| |#2| (-172))) ((-1057 $) |has| |#2| (-172)) ((-1050) -2797 (|has| |#2| (-1050)) (|has| |#2| (-849)) (|has| |#2| (-172))) ((-1059) -2797 (|has| |#2| (-1050)) (|has| |#2| (-849)) (|has| |#2| (-172))) ((-1113) -2797 (|has| |#2| (-1050)) (|has| |#2| (-849)) (|has| |#2| (-727)) (|has| |#2| (-172))) ((-1101) -2797 (|has| |#2| (-1101)) (|has| |#2| (-1050)) (|has| |#2| (-849)) (|has| |#2| (-794)) (|has| |#2| (-727)) (|has| |#2| (-370)) (|has| |#2| (-365)) (|has| |#2| (-172)) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-1217) . T) ((-1274 |#2|) |has| |#2| (-365))) -((-2565 (((-240 |#1| |#3|) (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|) 21)) (-2499 ((|#3| (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|) 23)) (-3822 (((-240 |#1| |#3|) (-1 |#3| |#2|) (-240 |#1| |#2|)) 18))) -(((-239 |#1| |#2| |#3|) (-10 -7 (-15 -2565 ((-240 |#1| |#3|) (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|)) (-15 -2499 (|#3| (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|)) (-15 -3822 ((-240 |#1| |#3|) (-1 |#3| |#2|) (-240 |#1| |#2|)))) (-772) (-1217) (-1217)) (T -239)) -((-3822 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-240 *5 *6)) (-14 *5 (-772)) (-4 *6 (-1217)) (-4 *7 (-1217)) (-5 *2 (-240 *5 *7)) (-5 *1 (-239 *5 *6 *7)))) (-2499 (*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *6 *2)) (-5 *4 (-240 *5 *6)) (-14 *5 (-772)) (-4 *6 (-1217)) (-4 *2 (-1217)) (-5 *1 (-239 *5 *6 *2)))) (-2565 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *5 *7 *5)) (-5 *4 (-240 *6 *7)) (-14 *6 (-772)) (-4 *7 (-1217)) (-4 *5 (-1217)) (-5 *2 (-240 *6 *5)) (-5 *1 (-239 *6 *7 *5))))) -(-10 -7 (-15 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(|has| |#2| (-1051)))) (-3033 (($ $ $) 70 (|has| |#2| (-25)))) (** (($ $ (-772)) 81 (|has| |#2| (-727))) (($ $ (-923)) 78 (|has| |#2| (-727)))) (* (($ (-567) $) 100 (|has| |#2| (-1051))) (($ $ $) 79 (|has| |#2| (-727))) (($ $ |#2|) 77 (|has| |#2| (-727))) (($ |#2| $) 76 (|has| |#2| (-727))) (($ (-772) $) 74 (|has| |#2| (-131))) (($ (-923) $) 71 (|has| |#2| (-25)))) (-2414 (((-772) $) 6 (|has| $ (-6 -4418))))) +(((-238 |#1| |#2|) (-140) (-772) (-1218)) (T -238)) +((-2749 (*1 *1 *2) (-12 (-5 *2 (-1268 *4)) (-4 *4 (-1218)) (-4 *1 (-238 *3 *4)))) (-4387 (*1 *1 *2) (-12 (-5 *2 (-923)) (-4 *1 (-238 *3 *4)) (-4 *4 (-1051)) (-4 *4 (-1218)))) (-3366 (*1 *2 *1 *1) (-12 (-4 *1 (-238 *3 *2)) (-4 *2 (-1218)) (-4 *2 (-1051)))) (* (*1 *1 *1 *2) (-12 (-4 *1 (-238 *3 *2)) (-4 *2 (-1218)) (-4 *2 (-727)))) (* (*1 *1 *2 *1) (-12 (-4 *1 (-238 *3 *2)) (-4 *2 (-1218)) (-4 *2 (-727))))) +(-13 (-605 (-567) |t#2|) (-614 (-1268 |t#2|)) (-10 -8 (-6 -4418) (-15 -2749 ($ (-1268 |t#2|))) (IF (|has| |t#2| (-1102)) 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(-849)) (|has| |#2| (-794)) (|has| |#2| (-365)) (|has| |#2| (-172)) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-34) . T) ((-38 |#2|) |has| |#2| (-172)) ((-102) -2800 (|has| |#2| (-1102)) (|has| |#2| (-1051)) (|has| |#2| (-849)) (|has| |#2| (-794)) (|has| |#2| (-727)) (|has| |#2| (-370)) (|has| |#2| (-365)) (|has| |#2| (-172)) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-111 |#2| |#2|) -2800 (|has| |#2| (-1051)) (|has| |#2| (-365)) (|has| |#2| (-172))) ((-111 $ $) |has| |#2| (-172)) ((-131) -2800 (|has| |#2| (-1051)) (|has| |#2| (-849)) (|has| |#2| (-794)) (|has| |#2| (-365)) (|has| |#2| (-172)) (|has| |#2| (-131))) ((-617 #0=(-410 (-567))) -12 (|has| |#2| (-1040 (-410 (-567)))) (|has| |#2| (-1102))) ((-617 (-567)) -2800 (|has| |#2| (-1051)) (-12 (|has| |#2| (-1040 (-567))) (|has| |#2| (-1102))) (|has| |#2| (-849)) (|has| |#2| (-172))) ((-617 |#2|) -2800 (|has| |#2| (-1102)) (|has| |#2| (-172))) ((-614 (-863)) -2800 (|has| |#2| (-1102)) (|has| |#2| (-1051)) (|has| |#2| (-849)) (|has| |#2| (-794)) (|has| |#2| (-727)) (|has| |#2| (-370)) (|has| |#2| (-365)) (|has| |#2| (-172)) (|has| |#2| (-614 (-863))) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-614 (-1268 |#2|)) . T) ((-172) |has| |#2| (-172)) ((-231 |#2|) |has| |#2| (-1051)) ((-233) -12 (|has| |#2| (-233)) (|has| |#2| (-1051))) ((-287 #1=(-567) |#2|) . T) ((-289 #1# |#2|) . T) ((-310 |#2|) -12 (|has| |#2| (-310 |#2|)) (|has| |#2| (-1102))) ((-370) |has| |#2| (-370)) ((-379 |#2|) |has| |#2| (-1051)) ((-414 |#2|) |has| |#2| (-1102)) ((-492 |#2|) . T) ((-605 #1# |#2|) . T) ((-517 |#2| |#2|) -12 (|has| |#2| (-310 |#2|)) (|has| |#2| (-1102))) ((-647 (-567)) -2800 (|has| |#2| (-1051)) (|has| |#2| (-849)) (|has| |#2| (-365)) (|has| |#2| (-172))) ((-647 |#2|) -2800 (|has| |#2| (-1051)) (|has| |#2| (-365)) (|has| |#2| (-172))) ((-647 $) -2800 (|has| |#2| (-1051)) (|has| |#2| (-849)) (|has| |#2| (-172))) ((-649 |#2|) -2800 (|has| |#2| (-1051)) (|has| |#2| (-365)) (|has| |#2| (-172))) ((-649 $) -2800 (|has| |#2| (-1051)) (|has| |#2| (-849)) (|has| |#2| (-172))) ((-641 |#2|) -2800 (|has| |#2| (-365)) (|has| |#2| (-172))) ((-640 (-567)) -12 (|has| |#2| (-640 (-567))) (|has| |#2| (-1051))) ((-640 |#2|) |has| |#2| (-1051)) ((-718 |#2|) -2800 (|has| |#2| (-365)) (|has| |#2| (-172))) ((-727) -2800 (|has| |#2| (-1051)) (|has| |#2| (-849)) (|has| |#2| (-727)) (|has| |#2| (-172))) ((-792) |has| |#2| (-849)) ((-793) -2800 (|has| |#2| (-849)) (|has| |#2| (-794))) ((-794) |has| |#2| (-794)) ((-795) -2800 (|has| |#2| (-849)) (|has| |#2| (-794))) ((-796) -2800 (|has| |#2| (-849)) (|has| |#2| (-794))) ((-849) |has| |#2| (-849)) ((-851) -2800 (|has| |#2| (-849)) (|has| |#2| (-794))) ((-902 (-1178)) -12 (|has| |#2| (-902 (-1178))) (|has| |#2| (-1051))) ((-1040 #0#) -12 (|has| |#2| (-1040 (-410 (-567)))) (|has| |#2| (-1102))) ((-1040 (-567)) -12 (|has| |#2| (-1040 (-567))) (|has| |#2| (-1102))) ((-1040 |#2|) |has| |#2| (-1102)) ((-1053 |#2|) -2800 (|has| |#2| (-1051)) (|has| |#2| (-365)) (|has| |#2| (-172))) ((-1053 $) |has| |#2| (-172)) ((-1058 |#2|) -2800 (|has| |#2| (-1051)) (|has| |#2| (-365)) (|has| |#2| (-172))) ((-1058 $) |has| |#2| (-172)) ((-1051) -2800 (|has| |#2| (-1051)) (|has| |#2| (-849)) (|has| |#2| (-172))) ((-1060) -2800 (|has| |#2| (-1051)) (|has| |#2| (-849)) (|has| |#2| (-172))) ((-1114) -2800 (|has| |#2| (-1051)) (|has| |#2| (-849)) (|has| |#2| (-727)) (|has| |#2| (-172))) ((-1102) -2800 (|has| |#2| (-1102)) (|has| |#2| (-1051)) (|has| |#2| (-849)) (|has| |#2| (-794)) (|has| |#2| (-727)) (|has| |#2| (-370)) (|has| |#2| (-365)) (|has| |#2| (-172)) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-1218) . T) ((-1275 |#2|) |has| |#2| (-365))) +((-2788 (((-240 |#1| |#3|) (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|) 21)) (-2477 ((|#3| (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|) 23)) (-3829 (((-240 |#1| |#3|) (-1 |#3| |#2|) (-240 |#1| |#2|)) 18))) +(((-239 |#1| |#2| |#3|) (-10 -7 (-15 -2788 ((-240 |#1| |#3|) (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|)) (-15 -2477 (|#3| (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|)) (-15 -3829 ((-240 |#1| |#3|) (-1 |#3| |#2|) (-240 |#1| |#2|)))) (-772) (-1218) (-1218)) (T -239)) +((-3829 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-240 *5 *6)) (-14 *5 (-772)) (-4 *6 (-1218)) (-4 *7 (-1218)) (-5 *2 (-240 *5 *7)) (-5 *1 (-239 *5 *6 *7)))) (-2477 (*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *6 *2)) (-5 *4 (-240 *5 *6)) (-14 *5 (-772)) (-4 *6 (-1218)) (-4 *2 (-1218)) (-5 *1 (-239 *5 *6 *2)))) (-2788 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *5 *7 *5)) (-5 *4 (-240 *6 *7)) (-14 *6 (-772)) (-4 *7 (-1218)) (-4 *5 (-1218)) (-5 *2 (-240 *6 *5)) (-5 *1 (-239 *6 *7 *5))))) +(-10 -7 (-15 -2788 ((-240 |#1| |#3|) (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|)) (-15 -2477 (|#3| (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|)) (-15 -3829 ((-240 |#1| |#3|) (-1 |#3| |#2|) (-240 |#1| |#2|)))) +((-2403 (((-112) $ $) NIL (|has| |#2| (-1102)))) (-2460 (((-112) $) NIL (|has| |#2| (-131)))) (-4387 (($ (-923)) 65 (|has| |#2| (-1051)))) (-1783 (((-1273) $ (-567) (-567)) NIL (|has| $ (-6 -4419)))) (-4016 (($ $ $) 70 (|has| |#2| (-794)))) (-3472 (((-3 $ "failed") $ $) 57 (|has| |#2| (-131)))) (-3445 (((-112) $ (-772)) 17)) (-2375 (((-772)) NIL (|has| |#2| (-370)))) (-1750 (((-567) $) NIL (|has| |#2| (-849)))) (-4284 ((|#2| $ (-567) |#2|) NIL (|has| $ (-6 -4419)))) (-2585 (($) NIL T CONST)) (-3753 (((-3 (-567) "failed") $) NIL (-12 (|has| |#2| (-1040 (-567))) (|has| |#2| (-1102)))) (((-3 (-410 (-567)) "failed") $) NIL (-12 (|has| |#2| (-1040 (-410 (-567)))) (|has| |#2| (-1102)))) (((-3 |#2| "failed") $) 34 (|has| |#2| (-1102)))) (-2038 (((-567) $) NIL (-12 (|has| |#2| (-1040 (-567))) (|has| 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T) ((-303) . T) ((-365) |has| |#1| (-559)) ((-379 |#1|) |has| |#1| (-1050)) ((-403 |#1|) . T) ((-414 |#1|) . T) ((-455) |has| |#1| (-559)) ((-476) |has| |#1| (-476)) ((-517 (-613 $) $) . T) ((-517 $ $) . 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T) ((-23) . T) ((-47 |#1| #0=(-567)) . T) ((-25) . T) ((-38 #1=(-410 (-567))) -2797 (|has| |#1| (-365)) (|has| |#1| (-38 (-410 (-567))))) ((-38 |#1|) |has| |#1| (-172)) ((-38 |#2|) |has| |#1| (-365)) ((-38 $) -2797 (|has| |#1| (-559)) (|has| |#1| (-365))) ((-35) |has| |#1| (-38 (-410 (-567)))) ((-95) |has| |#1| (-38 (-410 (-567)))) ((-102) . T) ((-111 #1# #1#) -2797 (|has| |#1| (-365)) (|has| |#1| (-38 (-410 (-567))))) ((-111 |#1| |#1|) . T) ((-111 |#2| |#2|) |has| |#1| (-365)) ((-111 $ $) -2797 (|has| |#1| (-559)) (|has| |#1| (-365)) (|has| |#1| (-172))) ((-131) . T) ((-145) -2797 (-12 (|has| |#1| (-365)) (|has| |#2| (-145))) (|has| |#1| (-145))) ((-147) -2797 (-12 (|has| |#1| (-365)) (|has| |#2| (-147))) (|has| |#1| (-147))) ((-617 #1#) -2797 (|has| |#1| (-365)) (|has| |#1| (-38 (-410 (-567))))) ((-617 (-567)) . T) ((-617 #2=(-1177)) -12 (|has| |#1| (-365)) (|has| |#2| (-1039 (-1177)))) ((-617 |#1|) |has| |#1| (-172)) ((-617 |#2|) . 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T) ((-172) -2797 (|has| |#1| (-559)) (|has| |#1| (-365)) (|has| |#1| (-172))) ((-615 (-225)) -12 (|has| |#1| (-365)) (|has| |#2| (-1023))) ((-615 (-381)) -12 (|has| |#1| (-365)) (|has| |#2| (-1023))) ((-615 (-539)) -12 (|has| |#1| (-365)) (|has| |#2| (-615 (-539)))) ((-615 (-893 (-381))) -12 (|has| |#1| (-365)) (|has| |#2| (-615 (-893 (-381))))) ((-615 (-893 (-567))) -12 (|has| |#1| (-365)) (|has| |#2| (-615 (-893 (-567))))) ((-231 |#2|) |has| |#1| (-365)) ((-233) -2797 (-12 (|has| |#1| (-365)) (|has| |#2| (-233))) (|has| |#1| (-15 * (|#1| (-567) |#1|)))) ((-243) |has| |#1| (-365)) ((-285) |has| |#1| (-38 (-410 (-567)))) ((-287 |#2| $) -12 (|has| |#1| (-365)) (|has| |#2| (-287 |#2| |#2|))) ((-287 $ $) |has| (-567) (-1113)) ((-291) -2797 (|has| |#1| (-559)) (|has| |#1| (-365))) ((-308) |has| |#1| (-365)) ((-310 |#2|) -12 (|has| |#1| (-365)) (|has| |#2| (-310 |#2|))) ((-365) |has| |#1| (-365)) ((-340 |#2|) |has| |#1| (-365)) ((-379 |#2|) |has| |#1| (-365)) ((-403 |#2|) |has| |#1| (-365)) ((-455) |has| |#1| (-365)) ((-496) |has| |#1| (-38 (-410 (-567)))) ((-517 (-1177) |#2|) -12 (|has| |#1| (-365)) (|has| |#2| (-517 (-1177) |#2|))) ((-517 |#2| |#2|) -12 (|has| |#1| (-365)) (|has| |#2| (-310 |#2|))) ((-559) -2797 (|has| |#1| (-559)) (|has| |#1| (-365))) ((-647 #1#) -2797 (|has| |#1| (-365)) (|has| |#1| (-38 (-410 (-567))))) ((-647 (-567)) . T) ((-647 |#1|) . T) ((-647 |#2|) |has| |#1| (-365)) ((-647 $) . T) ((-649 #1#) -2797 (|has| |#1| (-365)) (|has| |#1| (-38 (-410 (-567))))) ((-649 |#1|) . T) ((-649 |#2|) |has| |#1| (-365)) ((-649 $) . T) ((-641 #1#) -2797 (|has| |#1| (-365)) (|has| |#1| (-38 (-410 (-567))))) ((-641 |#1|) |has| |#1| (-172)) ((-641 |#2|) |has| |#1| (-365)) ((-641 $) -2797 (|has| |#1| (-559)) (|has| |#1| (-365))) ((-640 (-567)) -12 (|has| |#1| (-365)) (|has| |#2| (-640 (-567)))) ((-640 |#2|) |has| |#1| (-365)) ((-718 #1#) -2797 (|has| |#1| (-365)) (|has| |#1| (-38 (-410 (-567))))) ((-718 |#1|) |has| |#1| (-172)) ((-718 |#2|) |has| |#1| (-365)) ((-718 $) -2797 (|has| |#1| (-559)) (|has| |#1| (-365))) ((-727) . T) ((-792) -12 (|has| |#1| (-365)) (|has| |#2| (-821))) ((-793) -12 (|has| |#1| (-365)) (|has| |#2| (-821))) ((-795) -12 (|has| |#1| (-365)) (|has| |#2| (-821))) ((-796) -12 (|has| |#1| (-365)) (|has| |#2| (-821))) ((-821) -12 (|has| |#1| (-365)) (|has| |#2| (-821))) ((-849) -12 (|has| |#1| (-365)) (|has| |#2| (-821))) ((-851) -2797 (-12 (|has| |#1| (-365)) (|has| |#2| (-851))) (-12 (|has| |#1| (-365)) (|has| |#2| (-821)))) ((-901 (-1177)) -2797 (-12 (|has| |#1| (-365)) (|has| |#2| (-901 (-1177)))) (-12 (|has| |#1| (-15 * (|#1| (-567) |#1|))) (|has| |#1| (-901 (-1177))))) ((-887 (-381)) -12 (|has| |#1| (-365)) (|has| |#2| (-887 (-381)))) ((-887 (-567)) -12 (|has| |#1| (-365)) (|has| |#2| (-887 (-567)))) ((-885 |#2|) |has| |#1| (-365)) ((-910) -12 (|has| |#1| (-365)) (|has| |#2| (-910))) ((-974 |#1| #0# (-1083)) . T) ((-921) |has| |#1| (-365)) ((-993 |#2|) |has| |#1| (-365)) ((-1003) |has| |#1| (-38 (-410 (-567)))) ((-1023) -12 (|has| |#1| (-365)) (|has| |#2| (-1023))) ((-1039 (-410 (-567))) -12 (|has| |#1| (-365)) (|has| |#2| (-1039 (-567)))) ((-1039 (-567)) -12 (|has| |#1| (-365)) (|has| |#2| (-1039 (-567)))) ((-1039 #2#) -12 (|has| |#1| (-365)) (|has| |#2| (-1039 (-1177)))) ((-1039 |#2|) . T) ((-1052 #1#) -2797 (|has| |#1| (-365)) (|has| |#1| (-38 (-410 (-567))))) ((-1052 |#1|) . T) ((-1052 |#2|) |has| |#1| (-365)) ((-1052 $) -2797 (|has| |#1| (-559)) (|has| |#1| (-365)) (|has| |#1| (-172))) ((-1057 #1#) -2797 (|has| |#1| (-365)) (|has| |#1| (-38 (-410 (-567))))) ((-1057 |#1|) . T) ((-1057 |#2|) |has| |#1| (-365)) ((-1057 $) -2797 (|has| |#1| (-559)) (|has| |#1| (-365)) (|has| |#1| (-172))) ((-1050) . T) ((-1059) . T) ((-1113) . T) ((-1101) . T) ((-1152) -12 (|has| |#1| (-365)) (|has| |#2| (-1152))) ((-1202) |has| |#1| (-38 (-410 (-567)))) ((-1205) |has| |#1| (-38 (-410 (-567)))) ((-1217) |has| |#1| (-365)) ((-1221) |has| |#1| (-365)) ((-1227 |#1|) . T) ((-1245 |#1| #0#) . T)) -((-2399 (((-112) $ $) NIL)) (-2840 (((-112) $) 81)) (-2660 ((|#2| $) NIL (-12 (|has| |#2| (-308)) (|has| |#1| (-365))))) (-2845 (((-645 (-1083)) $) NIL)) (-3638 (((-1177) $) 100)) (-2474 (((-2 (|:| -2720 $) (|:| -4404 $) (|:| |associate| $)) $) NIL (|has| |#1| (-559)))) (-1312 (($ $) NIL (|has| |#1| (-559)))) (-2318 (((-112) $) NIL (|has| |#1| (-559)))) (-1873 (($ $ (-567)) 109) (($ $ (-567) (-567)) 111)) (-4268 (((-1157 (-2 (|:| |k| (-567)) (|:| |c| |#1|))) $) 51)) (-1368 ((|#2| $) 11)) (-3789 (((-3 |#2| "failed") $) 35)) (-2892 ((|#2| $) 36)) (-3165 (($ $) 206 (|has| |#1| (-38 (-410 (-567)))))) (-3039 (($ $) 182 (|has| |#1| (-38 (-410 (-567)))))) (-3460 (((-3 $ "failed") $ $) NIL)) (-1431 (((-421 (-1173 $)) (-1173 $)) NIL (-12 (|has| |#2| (-910)) (|has| |#1| (-365))))) (-3081 (($ $) NIL (|has| |#1| (-365)))) (-2833 (((-421 $) $) NIL (|has| |#1| (-365)))) (-2714 (($ $) NIL (|has| |#1| (-38 (-410 (-567)))))) (-1885 (((-3 (-645 (-1173 $)) "failed") (-645 (-1173 $)) (-1173 $)) NIL 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T) ((-647 |#1|) . T) ((-647 $) . T) ((-649 #1#) |has| |#1| (-38 (-410 (-567)))) ((-649 |#1|) . T) ((-649 $) . T) ((-641 #1#) |has| |#1| (-38 (-410 (-567)))) ((-641 |#1|) |has| |#1| (-172)) ((-641 $) -2797 (|has| |#1| (-910)) (|has| |#1| (-559)) (|has| |#1| (-455)) (|has| |#1| (-365))) ((-640 (-567)) |has| |#1| (-640 (-567))) ((-640 |#1|) . T) ((-718 #1#) |has| |#1| (-38 (-410 (-567)))) ((-718 |#1|) |has| |#1| (-172)) ((-718 $) -2797 (|has| |#1| (-910)) (|has| |#1| (-559)) (|has| |#1| (-455)) (|has| |#1| (-365))) ((-727) . T) ((-901 #2#) . T) ((-901 (-1177)) |has| |#1| (-901 (-1177))) ((-887 (-381)) -12 (|has| (-1083) (-887 (-381))) (|has| |#1| (-887 (-381)))) ((-887 (-567)) -12 (|has| (-1083) (-887 (-567))) (|has| |#1| (-887 (-567)))) ((-950 |#1| #0# #2#) . T) ((-910) |has| |#1| (-910)) ((-921) |has| |#1| (-365)) ((-1039 (-410 (-567))) |has| |#1| (-1039 (-410 (-567)))) ((-1039 (-567)) |has| |#1| (-1039 (-567))) ((-1039 #2#) . T) ((-1039 |#1|) . T) ((-1052 #1#) |has| |#1| (-38 (-410 (-567)))) ((-1052 |#1|) . T) ((-1052 $) -2797 (|has| |#1| (-910)) (|has| |#1| (-559)) (|has| |#1| (-455)) (|has| |#1| (-365)) (|has| |#1| (-172))) ((-1057 #1#) |has| |#1| (-38 (-410 (-567)))) ((-1057 |#1|) . T) ((-1057 $) -2797 (|has| |#1| (-910)) (|has| |#1| (-559)) (|has| |#1| (-455)) (|has| |#1| (-365)) (|has| |#1| (-172))) ((-1050) . T) ((-1059) . T) ((-1113) . T) ((-1101) . T) ((-1152) |has| |#1| (-1152)) ((-1221) |has| |#1| (-910))) -((-2845 (((-645 (-1083)) $) 34)) (-3006 (($ $) 31)) (-2821 (($ |#2| |#3|) NIL) (($ $ (-1083) |#3|) 28) (($ $ (-645 (-1083)) (-645 |#3|)) 27)) (-2969 (($ $) 14)) (-2980 ((|#2| $) 12)) (-1813 ((|#3| $) 10))) -(((-1244 |#1| |#2| |#3|) (-10 -8 (-15 -2845 ((-645 (-1083)) |#1|)) (-15 -2821 (|#1| |#1| (-645 (-1083)) (-645 |#3|))) (-15 -2821 (|#1| |#1| (-1083) |#3|)) (-15 -3006 (|#1| |#1|)) (-15 -2821 (|#1| |#2| |#3|)) (-15 -1813 (|#3| |#1|)) (-15 -2969 (|#1| |#1|)) (-15 -2980 (|#2| |#1|))) (-1245 |#2| |#3|) (-1050) (-793)) (T -1244)) -NIL -(-10 -8 (-15 -2845 ((-645 (-1083)) |#1|)) (-15 -2821 (|#1| |#1| (-645 (-1083)) (-645 |#3|))) (-15 -2821 (|#1| |#1| (-1083) |#3|)) (-15 -3006 (|#1| |#1|)) (-15 -2821 (|#1| |#2| |#3|)) (-15 -1813 (|#3| |#1|)) (-15 -2969 (|#1| |#1|)) (-15 -2980 (|#2| |#1|))) -((-2399 (((-112) $ $) 7)) (-2840 (((-112) $) 17)) (-2845 (((-645 (-1083)) $) 86)) (-3638 (((-1177) $) 115)) (-2474 (((-2 (|:| -2720 $) (|:| 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T) ((-23) . T) ((-47 |#1| |#2|) . T) ((-25) . T) ((-38 #0=(-410 (-567))) |has| |#1| (-38 (-410 (-567)))) ((-38 |#1|) |has| |#1| (-172)) ((-38 $) |has| |#1| (-559)) ((-102) . T) ((-111 #0# #0#) |has| |#1| (-38 (-410 (-567)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2797 (|has| |#1| (-559)) (|has| |#1| (-172))) ((-131) . T) ((-145) |has| |#1| (-145)) ((-147) |has| |#1| (-147)) ((-617 #0#) |has| |#1| (-38 (-410 (-567)))) ((-617 (-567)) . T) ((-617 |#1|) |has| |#1| (-172)) ((-617 $) |has| |#1| (-559)) ((-614 (-863)) . T) ((-172) -2797 (|has| |#1| (-559)) (|has| |#1| (-172))) ((-233) |has| |#1| (-15 * (|#1| |#2| |#1|))) ((-287 $ $) |has| |#2| (-1113)) ((-291) |has| |#1| (-559)) ((-559) |has| |#1| (-559)) ((-647 #0#) |has| |#1| (-38 (-410 (-567)))) ((-647 (-567)) . T) ((-647 |#1|) . T) ((-647 $) . T) ((-649 #0#) |has| |#1| (-38 (-410 (-567)))) ((-649 |#1|) . T) ((-649 $) . T) ((-641 #0#) |has| |#1| (-38 (-410 (-567)))) ((-641 |#1|) |has| |#1| (-172)) ((-641 $) |has| |#1| (-559)) ((-718 #0#) |has| |#1| (-38 (-410 (-567)))) ((-718 |#1|) |has| |#1| (-172)) ((-718 $) |has| |#1| (-559)) ((-727) . T) ((-901 (-1177)) -12 (|has| |#1| (-15 * (|#1| |#2| |#1|))) (|has| |#1| (-901 (-1177)))) ((-974 |#1| |#2| (-1083)) . T) ((-1052 #0#) |has| |#1| (-38 (-410 (-567)))) ((-1052 |#1|) . T) ((-1052 $) -2797 (|has| |#1| (-559)) (|has| |#1| (-172))) ((-1057 #0#) |has| |#1| (-38 (-410 (-567)))) ((-1057 |#1|) . T) ((-1057 $) -2797 (|has| |#1| (-559)) (|has| |#1| (-172))) ((-1050) . T) ((-1059) . T) ((-1113) . T) ((-1101) . T)) -((-3081 ((|#2| |#2|) 12)) (-2833 (((-421 |#2|) |#2|) 14)) (-1987 (((-2 (|:| |flg| (-3 "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (-567))) (-2 (|:| |flg| (-3 "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (-567)))) 30))) -(((-1246 |#1| |#2|) (-10 -7 (-15 -2833 ((-421 |#2|) |#2|)) (-15 -3081 (|#2| |#2|)) (-15 -1987 ((-2 (|:| |flg| (-3 "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (-567))) (-2 (|:| |flg| (-3 "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (-567)))))) (-559) (-13 (-1243 |#1|) (-559) (-10 -8 (-15 -2771 ($ $ $))))) (T -1246)) -((-1987 (*1 *2 *2) (-12 (-5 *2 (-2 (|:| |flg| (-3 "nil" "sqfr" "irred" "prime")) (|:| |fctr| *4) (|:| |xpnt| (-567)))) (-4 *4 (-13 (-1243 *3) (-559) (-10 -8 (-15 -2771 ($ $ $))))) (-4 *3 (-559)) (-5 *1 (-1246 *3 *4)))) (-3081 (*1 *2 *2) (-12 (-4 *3 (-559)) (-5 *1 (-1246 *3 *2)) (-4 *2 (-13 (-1243 *3) (-559) (-10 -8 (-15 -2771 ($ $ $))))))) (-2833 (*1 *2 *3) (-12 (-4 *4 (-559)) (-5 *2 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2944402 "UFD-" 2944407 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1219 2943343 2943526 2943742 "UDVO" 2944067 T UDVO (NIL) -7 NIL NIL NIL) (-1218 2941159 2941568 2942039 "UDPO" 2942907 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1217 2941092 2941097 2941127 "TYPE" 2941132 T TYPE (NIL) -9 NIL NIL NIL) (-1216 2940852 2941047 2941078 "TYPEAST" 2941083 T TYPEAST (NIL) -8 NIL NIL NIL) (-1215 2939823 2940025 2940265 "TWOFACT" 2940646 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1214 2938846 2939232 2939467 "TUPLE" 2939623 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1213 2936537 2937056 2937595 "TUBETOOL" 2938329 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1212 2935386 2935591 2935832 "TUBE" 2936330 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1211 2930115 2934358 2934641 "TS" 2935138 NIL TS (NIL T) -8 NIL NIL NIL) (-1210 2918755 2922874 2922971 "TSETCAT" 2928240 NIL TSETCAT (NIL T T T T) -9 NIL 2929771 NIL) (-1209 2913487 2915087 2916978 "TSETCAT-" 2916983 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1208 2908126 2908973 2909902 "TRMANIP" 2912623 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1207 2907567 2907630 2907793 "TRIMAT" 2908058 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1206 2905433 2905670 2906027 "TRIGMNIP" 2907316 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1205 2904953 2905066 2905096 "TRIGCAT" 2905309 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1204 2904622 2904701 2904842 "TRIGCAT-" 2904847 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1203 2901467 2903480 2903761 "TREE" 2904376 NIL TREE (NIL T) -8 NIL NIL NIL) (-1202 2900741 2901269 2901299 "TRANFUN" 2901334 T TRANFUN (NIL) -9 NIL 2901400 NIL) (-1201 2900020 2900211 2900491 "TRANFUN-" 2900496 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1200 2899824 2899856 2899917 "TOPSP" 2899981 T TOPSP (NIL) -7 NIL NIL NIL) (-1199 2899172 2899287 2899441 "TOOLSIGN" 2899705 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1198 2897806 2898349 2898588 "TEXTFILE" 2898955 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1197 2895718 2896259 2896688 "TEX" 2897399 T TEX (NIL) -8 NIL NIL NIL) (-1196 2895499 2895530 2895602 "TEX1" 2895681 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1195 2895147 2895210 2895300 "TEMUTL" 2895431 T TEMUTL (NIL) -7 NIL NIL NIL) (-1194 2893301 2893581 2893906 "TBCMPPK" 2894870 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1193 2885078 2891461 2891517 "TBAGG" 2891917 NIL TBAGG (NIL T T) -9 NIL 2892128 NIL) (-1192 2880148 2881636 2883390 "TBAGG-" 2883395 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1191 2879532 2879639 2879784 "TANEXP" 2880037 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1190 2872922 2879389 2879482 "TABLE" 2879487 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1189 2872334 2872433 2872571 "TABLEAU" 2872819 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1188 2866942 2868162 2869410 "TABLBUMP" 2871120 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1187 2866164 2866311 2866492 "SYSTEM" 2866783 T SYSTEM (NIL) -8 NIL NIL NIL) (-1186 2862623 2863322 2864105 "SYSSOLP" 2865415 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1185 2862421 2862578 2862609 "SYSPTR" 2862614 T SYSPTR (NIL) -8 NIL NIL NIL) (-1184 2861465 2861970 2862089 "SYSNNI" 2862275 NIL SYSNNI (NIL NIL) -8 NIL NIL 2862360) (-1183 2860772 2861231 2861310 "SYSINT" 2861370 NIL SYSINT (NIL NIL) -8 NIL NIL 2861415) (-1182 2857104 2858050 2858760 "SYNTAX" 2860084 T SYNTAX (NIL) -8 NIL NIL NIL) (-1181 2854262 2854864 2855496 "SYMTAB" 2856494 T SYMTAB (NIL) -8 NIL NIL NIL) (-1180 2849511 2850413 2851396 "SYMS" 2853301 T SYMS (NIL) -8 NIL NIL NIL) (-1179 2846746 2848969 2849199 "SYMPOLY" 2849316 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1178 2846263 2846338 2846461 "SYMFUNC" 2846658 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1177 2842282 2843575 2844388 "SYMBOL" 2845472 T SYMBOL (NIL) -8 NIL NIL NIL) (-1176 2835821 2837510 2839230 "SWITCH" 2840584 T SWITCH (NIL) -8 NIL NIL NIL) (-1175 2829055 2834642 2834945 "SUTS" 2835576 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1174 2821121 2828302 2828575 "SUPXS" 2828840 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1173 2812880 2820739 2820865 "SUP" 2821030 NIL SUP (NIL T) -8 NIL NIL NIL) (-1172 2812039 2812166 2812383 "SUPFRACF" 2812748 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1171 2811660 2811719 2811832 "SUP2" 2811974 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1170 2810108 2810382 2810738 "SUMRF" 2811359 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1169 2809443 2809509 2809701 "SUMFS" 2810029 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1168 2793410 2808620 2808871 "SULS" 2809250 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1167 2793012 2793232 2793302 "SUCHTAST" 2793362 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1166 2792307 2792537 2792677 "SUCH" 2792920 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1165 2786173 2787213 2788172 "SUBSPACE" 2791395 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1164 2785603 2785693 2785857 "SUBRESP" 2786061 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1163 2778968 2780268 2781579 "STTF" 2784339 NIL STTF (NIL T) -7 NIL NIL NIL) (-1162 2773141 2774261 2775408 "STTFNC" 2777868 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1161 2764451 2766323 2768117 "STTAYLOR" 2771382 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1160 2757581 2764315 2764398 "STRTBL" 2764403 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1159 2752945 2757536 2757567 "STRING" 2757572 T STRING (NIL) -8 NIL NIL NIL) (-1158 2747806 2752318 2752348 "STRICAT" 2752407 T STRICAT (NIL) -9 NIL 2752469 NIL) (-1157 2740559 2745425 2746036 "STREAM" 2747230 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1156 2740069 2740146 2740290 "STREAM3" 2740476 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1155 2739051 2739234 2739469 "STREAM2" 2739882 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1154 2738739 2738791 2738884 "STREAM1" 2738993 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1153 2737755 2737936 2738167 "STINPROD" 2738555 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1152 2737307 2737517 2737547 "STEP" 2737627 T STEP (NIL) -9 NIL 2737705 NIL) (-1151 2730739 2737206 2737283 "STBL" 2737288 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1150 2725865 2729960 2730003 "STAGG" 2730156 NIL STAGG (NIL T) -9 NIL 2730245 NIL) (-1149 2723567 2724169 2725041 "STAGG-" 2725046 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1148 2721714 2723337 2723429 "STACK" 2723510 NIL STACK (NIL T) -8 NIL NIL NIL) (-1147 2714409 2719855 2720311 "SREGSET" 2721344 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1146 2706834 2708203 2709716 "SRDCMPK" 2713015 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1145 2699751 2704274 2704304 "SRAGG" 2705607 T SRAGG (NIL) -9 NIL 2706215 NIL) (-1144 2698768 2699023 2699402 "SRAGG-" 2699407 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1143 2693228 2697715 2698136 "SQMATRIX" 2698394 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1142 2686913 2689946 2690673 "SPLTREE" 2692573 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1141 2682876 2683569 2684215 "SPLNODE" 2686339 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1140 2681923 2682156 2682186 "SPFCAT" 2682630 T SPFCAT (NIL) -9 NIL NIL NIL) (-1139 2680660 2680870 2681134 "SPECOUT" 2681681 T SPECOUT (NIL) -7 NIL NIL NIL) (-1138 2672286 2674056 2674086 "SPADXPT" 2678478 T SPADXPT (NIL) -9 NIL 2680512 NIL) (-1137 2672047 2672087 2672156 "SPADPRSR" 2672239 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1136 2670202 2672002 2672033 "SPADAST" 2672038 T SPADAST (NIL) -8 NIL NIL NIL) (-1135 2662147 2663920 2663963 "SPACEC" 2668336 NIL SPACEC (NIL T) -9 NIL 2670152 NIL) (-1134 2660277 2662079 2662128 "SPACE3" 2662133 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1133 2659029 2659200 2659491 "SORTPAK" 2660082 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1132 2657121 2657424 2657836 "SOLVETRA" 2658693 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1131 2656171 2656393 2656654 "SOLVESER" 2656894 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1130 2651475 2652363 2653358 "SOLVERAD" 2655223 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1129 2647290 2647899 2648628 "SOLVEFOR" 2650842 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1128 2641560 2646639 2646736 "SNTSCAT" 2646741 NIL SNTSCAT (NIL T T T T) -9 NIL 2646811 NIL) (-1127 2635666 2639883 2640274 "SMTS" 2641250 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1126 2630350 2635554 2635631 "SMP" 2635636 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1125 2628509 2628810 2629208 "SMITH" 2630047 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1124 2621222 2625418 2625521 "SMATCAT" 2626872 NIL SMATCAT (NIL NIL T T T) -9 NIL 2627422 NIL) (-1123 2618162 2618985 2620163 "SMATCAT-" 2620168 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1122 2615828 2617398 2617441 "SKAGG" 2617702 NIL SKAGG (NIL T) -9 NIL 2617837 NIL) (-1121 2612139 2615244 2615439 "SINT" 2615626 T SINT (NIL) -8 NIL NIL 2615799) (-1120 2611911 2611949 2612015 "SIMPAN" 2612095 T SIMPAN (NIL) -7 NIL NIL NIL) (-1119 2611190 2611446 2611586 "SIG" 2611793 T SIG (NIL) -8 NIL NIL NIL) (-1118 2610028 2610249 2610524 "SIGNRF" 2610949 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1117 2608861 2609012 2609296 "SIGNEF" 2609857 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1116 2608167 2608444 2608568 "SIGAST" 2608759 T SIGAST (NIL) -8 NIL NIL NIL) (-1115 2605856 2606311 2606817 "SHP" 2607708 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1114 2599708 2605757 2605833 "SHDP" 2605838 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1113 2599281 2599473 2599503 "SGROUP" 2599596 T SGROUP (NIL) -9 NIL 2599658 NIL) (-1112 2599139 2599165 2599238 "SGROUP-" 2599243 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1111 2595974 2596672 2597395 "SGCF" 2598438 T SGCF (NIL) -7 NIL NIL NIL) (-1110 2590342 2595421 2595518 "SFRTCAT" 2595523 NIL SFRTCAT (NIL T T T T) -9 NIL 2595562 NIL) (-1109 2583763 2584781 2585917 "SFRGCD" 2589325 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1108 2576889 2577962 2579148 "SFQCMPK" 2582696 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1107 2576509 2576598 2576709 "SFORT" 2576830 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1106 2575627 2576349 2576470 "SEXOF" 2576475 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1105 2574734 2575508 2575576 "SEX" 2575581 T SEX (NIL) -8 NIL NIL NIL) (-1104 2570247 2570962 2571057 "SEXCAT" 2573994 NIL SEXCAT (NIL T T T T T) -9 NIL 2574572 NIL) (-1103 2567400 2570181 2570229 "SET" 2570234 NIL SET (NIL T) -8 NIL NIL NIL) (-1102 2565624 2566113 2566418 "SETMN" 2567141 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1101 2565120 2565272 2565302 "SETCAT" 2565478 T SETCAT (NIL) -9 NIL 2565588 NIL) (-1100 2564812 2564890 2565020 "SETCAT-" 2565025 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1099 2561173 2563273 2563316 "SETAGG" 2564186 NIL SETAGG (NIL T) -9 NIL 2564526 NIL) (-1098 2560631 2560747 2560984 "SETAGG-" 2560989 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1097 2560074 2560327 2560428 "SEQAST" 2560552 T SEQAST (NIL) -8 NIL NIL NIL) (-1096 2559273 2559567 2559628 "SEGXCAT" 2559914 NIL SEGXCAT (NIL T T) -9 NIL 2560034 NIL) (-1095 2558279 2558939 2559121 "SEG" 2559126 NIL SEG (NIL T) -8 NIL NIL NIL) (-1094 2557258 2557472 2557515 "SEGCAT" 2558037 NIL SEGCAT (NIL T) -9 NIL 2558258 NIL) (-1093 2556190 2556621 2556829 "SEGBIND" 2557085 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1092 2555811 2555870 2555983 "SEGBIND2" 2556125 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1091 2555384 2555612 2555689 "SEGAST" 2555756 T SEGAST (NIL) -8 NIL NIL NIL) (-1090 2554603 2554729 2554933 "SEG2" 2555228 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1089 2554013 2554538 2554585 "SDVAR" 2554590 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1088 2546540 2553783 2553913 "SDPOL" 2553918 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1087 2545133 2545399 2545718 "SCPKG" 2546255 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1086 2544297 2544469 2544661 "SCOPE" 2544963 T SCOPE (NIL) -8 NIL NIL NIL) (-1085 2543517 2543651 2543830 "SCACHE" 2544152 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1084 2543163 2543349 2543379 "SASTCAT" 2543384 T SASTCAT (NIL) -9 NIL 2543397 NIL) (-1083 2542650 2542998 2543074 "SAOS" 2543109 T SAOS (NIL) -8 NIL NIL NIL) (-1082 2542215 2542250 2542423 "SAERFFC" 2542609 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1081 2536154 2542112 2542192 "SAE" 2542197 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1080 2535747 2535782 2535941 "SAEFACT" 2536113 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1079 2534068 2534382 2534783 "RURPK" 2535413 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1078 2532705 2533011 2533316 "RULESET" 2533902 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1077 2529928 2530458 2530916 "RULE" 2532386 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1076 2529540 2529722 2529805 "RULECOLD" 2529880 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1075 2529330 2529358 2529429 "RTVALUE" 2529491 T RTVALUE (NIL) -8 NIL NIL NIL) (-1074 2528801 2529047 2529141 "RSTRCAST" 2529258 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1073 2523649 2524444 2525364 "RSETGCD" 2528000 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1072 2512879 2517958 2518055 "RSETCAT" 2522174 NIL RSETCAT (NIL T T T T) -9 NIL 2523271 NIL) (-1071 2510806 2511345 2512169 "RSETCAT-" 2512174 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1070 2503191 2504568 2506088 "RSDCMPK" 2509405 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1069 2501170 2501637 2501711 "RRCC" 2502797 NIL RRCC (NIL T T) -9 NIL 2503141 NIL) (-1068 2500521 2500695 2500974 "RRCC-" 2500979 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1067 2499964 2500217 2500318 "RPTAST" 2500442 T RPTAST (NIL) -8 NIL NIL NIL) (-1066 2473815 2483172 2483239 "RPOLCAT" 2493903 NIL RPOLCAT (NIL T T T) -9 NIL 2497062 NIL) (-1065 2465313 2467653 2470775 "RPOLCAT-" 2470780 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1064 2456244 2463524 2464006 "ROUTINE" 2464853 T ROUTINE (NIL) -8 NIL NIL NIL) (-1063 2453042 2455870 2456010 "ROMAN" 2456126 T ROMAN (NIL) -8 NIL NIL NIL) (-1062 2451286 2451902 2452162 "ROIRC" 2452847 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1061 2447518 2449802 2449832 "RNS" 2450136 T RNS (NIL) -9 NIL 2450410 NIL) (-1060 2446027 2446410 2446944 "RNS-" 2447019 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1059 2445430 2445838 2445868 "RNG" 2445873 T RNG (NIL) -9 NIL 2445894 NIL) (-1058 2444433 2444795 2444997 "RNGBIND" 2445281 NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-1057 2443832 2444220 2444263 "RMODULE" 2444268 NIL RMODULE (NIL T) -9 NIL 2444295 NIL) (-1056 2442668 2442762 2443098 "RMCAT2" 2443733 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1055 2439518 2442014 2442311 "RMATRIX" 2442430 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1054 2432345 2434605 2434720 "RMATCAT" 2438079 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2439061 NIL) (-1053 2431720 2431867 2432174 "RMATCAT-" 2432179 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1052 2431121 2431342 2431385 "RLINSET" 2431579 NIL RLINSET (NIL T) -9 NIL 2431670 NIL) (-1051 2430688 2430763 2430891 "RINTERP" 2431040 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1050 2429746 2430300 2430330 "RING" 2430386 T RING (NIL) -9 NIL 2430478 NIL) (-1049 2429538 2429582 2429679 "RING-" 2429684 NIL RING- (NIL T) -8 NIL NIL NIL) (-1048 2428379 2428616 2428874 "RIDIST" 2429302 T RIDIST (NIL) -7 NIL NIL NIL) (-1047 2419668 2427847 2428053 "RGCHAIN" 2428227 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1046 2419018 2419424 2419465 "RGBCSPC" 2419523 NIL RGBCSPC (NIL T) -9 NIL 2419575 NIL) (-1045 2418176 2418557 2418598 "RGBCMDL" 2418830 NIL RGBCMDL (NIL T) -9 NIL 2418944 NIL) (-1044 2415170 2415784 2416454 "RF" 2417540 NIL RF (NIL T) -7 NIL NIL NIL) (-1043 2414816 2414879 2414982 "RFFACTOR" 2415101 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1042 2414541 2414576 2414673 "RFFACT" 2414775 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1041 2412658 2413022 2413404 "RFDIST" 2414181 T RFDIST (NIL) -7 NIL NIL NIL) (-1040 2412111 2412203 2412366 "RETSOL" 2412560 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1039 2411747 2411827 2411870 "RETRACT" 2412003 NIL RETRACT (NIL T) -9 NIL 2412090 NIL) (-1038 2411596 2411621 2411708 "RETRACT-" 2411713 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1037 2411198 2411418 2411488 "RETAST" 2411548 T RETAST (NIL) -8 NIL NIL NIL) (-1036 2403936 2410851 2410978 "RESULT" 2411093 T RESULT (NIL) -8 NIL NIL NIL) (-1035 2402527 2403205 2403404 "RESRING" 2403839 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1034 2402163 2402212 2402310 "RESLATC" 2402464 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1033 2401868 2401903 2402010 "REPSQ" 2402122 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1032 2399290 2399870 2400472 "REP" 2401288 T REP (NIL) -7 NIL NIL NIL) (-1031 2398987 2399022 2399133 "REPDB" 2399249 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1030 2392887 2394276 2395499 "REP2" 2397799 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1029 2389264 2389945 2390753 "REP1" 2392114 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1028 2381960 2387405 2387861 "REGSET" 2388894 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1027 2380725 2381108 2381358 "REF" 2381745 NIL REF (NIL T) -8 NIL NIL NIL) (-1026 2380102 2380205 2380372 "REDORDER" 2380609 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1025 2376070 2379315 2379542 "RECLOS" 2379930 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1024 2375122 2375303 2375518 "REALSOLV" 2375877 T REALSOLV (NIL) -7 NIL NIL NIL) (-1023 2374968 2375009 2375039 "REAL" 2375044 T REAL (NIL) -9 NIL 2375079 NIL) (-1022 2371451 2372253 2373137 "REAL0Q" 2374133 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1021 2367052 2368040 2369101 "REAL0" 2370432 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1020 2366523 2366769 2366863 "RDUCEAST" 2366980 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1019 2365928 2366000 2366207 "RDIV" 2366445 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1018 2364996 2365170 2365383 "RDIST" 2365750 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1017 2363593 2363880 2364252 "RDETRS" 2364704 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1016 2361405 2361859 2362397 "RDETR" 2363135 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1015 2360030 2360308 2360705 "RDEEFS" 2361121 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1014 2358539 2358845 2359270 "RDEEF" 2359718 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1013 2352600 2355520 2355550 "RCFIELD" 2356845 T RCFIELD (NIL) -9 NIL 2357576 NIL) (-1012 2350664 2351168 2351864 "RCFIELD-" 2351939 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1011 2346933 2348765 2348808 "RCAGG" 2349892 NIL RCAGG (NIL T) -9 NIL 2350357 NIL) (-1010 2346561 2346655 2346818 "RCAGG-" 2346823 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1009 2345896 2346008 2346173 "RATRET" 2346445 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1008 2345449 2345516 2345637 "RATFACT" 2345824 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1007 2344757 2344877 2345029 "RANDSRC" 2345319 T RANDSRC (NIL) -7 NIL NIL NIL) (-1006 2344491 2344535 2344608 "RADUTIL" 2344706 T RADUTIL (NIL) -7 NIL NIL NIL) (-1005 2337607 2343324 2343634 "RADIX" 2344215 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-1004 2329226 2337449 2337579 "RADFF" 2337584 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-1003 2328873 2328948 2328978 "RADCAT" 2329138 T RADCAT (NIL) -9 NIL NIL NIL) (-1002 2328655 2328703 2328803 "RADCAT-" 2328808 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-1001 2326755 2328427 2328518 "QUEUE" 2328599 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-1000 2323294 2326690 2326737 "QUAT" 2326742 NIL QUAT (NIL T) -8 NIL NIL NIL) (-999 2322932 2322975 2323102 "QUATCT2" 2323245 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-998 2316394 2319739 2319779 "QUATCAT" 2320559 NIL QUATCAT (NIL T) -9 NIL 2321325 NIL) (-997 2312538 2313575 2314962 "QUATCAT-" 2315056 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-996 2310011 2311622 2311663 "QUAGG" 2312038 NIL QUAGG (NIL T) -9 NIL 2312213 NIL) (-995 2309616 2309836 2309904 "QQUTAST" 2309963 T QQUTAST (NIL) -8 NIL NIL NIL) (-994 2308514 2309014 2309186 "QFORM" 2309488 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-993 2299519 2304758 2304798 "QFCAT" 2305456 NIL QFCAT (NIL T) -9 NIL 2306457 NIL) (-992 2295091 2296292 2297883 "QFCAT-" 2297977 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-991 2294729 2294772 2294899 "QFCAT2" 2295042 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-990 2294189 2294299 2294429 "QEQUAT" 2294619 T QEQUAT (NIL) -8 NIL NIL NIL) (-989 2287335 2288408 2289592 "QCMPACK" 2293122 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-988 2284884 2285332 2285760 "QALGSET" 2286990 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-987 2284129 2284303 2284535 "QALGSET2" 2284704 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-986 2282819 2283043 2283360 "PWFFINTB" 2283902 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-985 2281001 2281169 2281523 "PUSHVAR" 2282633 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-984 2276919 2277973 2278014 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NIL) (-865 2011101 2011660 2011832 "OVAR" 2011923 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-864 2010365 2010486 2010647 "OUT" 2010960 T OUT (NIL) -7 NIL NIL NIL) (-863 1999237 2001474 2003674 "OUTFORM" 2008185 T OUTFORM (NIL) -8 NIL NIL NIL) (-862 1998573 1998834 1998961 "OUTBFILE" 1999130 T OUTBFILE (NIL) -8 NIL NIL NIL) (-861 1997880 1998045 1998073 "OUTBCON" 1998391 T OUTBCON (NIL) -9 NIL 1998557 NIL) (-860 1997481 1997593 1997750 "OUTBCON-" 1997755 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-859 1996861 1997210 1997299 "OSI" 1997412 T OSI (NIL) -8 NIL NIL NIL) (-858 1996391 1996729 1996757 "OSGROUP" 1996762 T OSGROUP (NIL) -9 NIL 1996784 NIL) (-857 1995136 1995363 1995648 "ORTHPOL" 1996138 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-856 1992687 1994971 1995092 "OREUP" 1995097 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-855 1990090 1992378 1992505 "ORESUP" 1992629 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-854 1987618 1988118 1988679 "OREPCTO" 1989579 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-853 1981304 1983505 1983546 "OREPCAT" 1985894 NIL OREPCAT (NIL T) -9 NIL 1986998 NIL) (-852 1978451 1979233 1980291 "OREPCAT-" 1980296 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-851 1977602 1977900 1977928 "ORDSET" 1978237 T ORDSET (NIL) -9 NIL 1978401 NIL) (-850 1977033 1977181 1977405 "ORDSET-" 1977410 NIL ORDSET- (NIL T) -8 NIL NIL NIL) (-849 1975598 1976389 1976417 "ORDRING" 1976619 T ORDRING (NIL) -9 NIL 1976744 NIL) (-848 1975243 1975337 1975481 "ORDRING-" 1975486 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-847 1974623 1975086 1975114 "ORDMON" 1975119 T ORDMON (NIL) -9 NIL 1975140 NIL) (-846 1973785 1973932 1974127 "ORDFUNS" 1974472 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-845 1973123 1973542 1973570 "ORDFIN" 1973635 T ORDFIN (NIL) -9 NIL 1973709 NIL) (-844 1969682 1971709 1972118 "ORDCOMP" 1972747 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-843 1968948 1969075 1969261 "ORDCOMP2" 1969542 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-842 1965529 1966439 1967253 "OPTPROB" 1968154 T OPTPROB (NIL) -8 NIL NIL NIL) (-841 1962331 1962970 1963674 "OPTPACK" 1964845 T OPTPACK (NIL) -7 NIL NIL NIL) (-840 1960018 1960784 1960812 "OPTCAT" 1961631 T OPTCAT (NIL) -9 NIL 1962281 NIL) (-839 1959402 1959695 1959800 "OPSIG" 1959933 T OPSIG (NIL) -8 NIL NIL NIL) (-838 1959170 1959209 1959275 "OPQUERY" 1959356 T OPQUERY (NIL) -7 NIL NIL NIL) (-837 1956301 1957481 1957985 "OP" 1958699 NIL OP (NIL T) -8 NIL NIL NIL) (-836 1955675 1955901 1955942 "OPERCAT" 1956154 NIL OPERCAT (NIL T) -9 NIL 1956251 NIL) (-835 1955430 1955486 1955603 "OPERCAT-" 1955608 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-834 1952243 1954227 1954596 "ONECOMP" 1955094 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-833 1951548 1951663 1951837 "ONECOMP2" 1952115 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-832 1950967 1951073 1951203 "OMSERVER" 1951438 T OMSERVER (NIL) -7 NIL NIL NIL) (-831 1947829 1950407 1950447 "OMSAGG" 1950508 NIL OMSAGG (NIL T) -9 NIL 1950572 NIL) (-830 1946452 1946715 1946997 "OMPKG" 1947567 T OMPKG (NIL) -7 NIL NIL NIL) (-829 1945882 1945985 1946013 "OM" 1946312 T OM (NIL) -9 NIL NIL NIL) (-828 1944429 1945431 1945600 "OMLO" 1945763 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-827 1943389 1943536 1943756 "OMEXPR" 1944255 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-826 1942680 1942935 1943071 "OMERR" 1943273 T OMERR (NIL) -8 NIL NIL NIL) (-825 1941831 1942101 1942261 "OMERRK" 1942540 T OMERRK (NIL) -8 NIL NIL NIL) (-824 1941282 1941508 1941616 "OMENC" 1941743 T OMENC (NIL) -8 NIL NIL NIL) (-823 1935177 1936362 1937533 "OMDEV" 1940131 T OMDEV (NIL) -8 NIL NIL NIL) (-822 1934246 1934417 1934611 "OMCONN" 1935003 T OMCONN (NIL) -8 NIL NIL NIL) (-821 1932767 1933743 1933771 "OINTDOM" 1933776 T OINTDOM (NIL) -9 NIL 1933797 NIL) (-820 1930105 1931455 1931792 "OFMONOID" 1932462 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-819 1929516 1930042 1930087 "ODVAR" 1930092 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-818 1926939 1929261 1929416 "ODR" 1929421 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-817 1919520 1926715 1926841 "ODPOL" 1926846 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-816 1913342 1919392 1919497 "ODP" 1919502 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-815 1912108 1912323 1912598 "ODETOOLS" 1913116 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-814 1909075 1909733 1910449 "ODESYS" 1911441 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-813 1903957 1904865 1905890 "ODERTRIC" 1908150 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-812 1903383 1903465 1903659 "ODERED" 1903869 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-811 1900271 1900819 1901496 "ODERAT" 1902806 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-810 1897228 1897695 1898292 "ODEPRRIC" 1899800 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-809 1895171 1895767 1896253 "ODEPROB" 1896762 T ODEPROB (NIL) -8 NIL NIL NIL) (-808 1891691 1892176 1892823 "ODEPRIM" 1894650 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-807 1890940 1891042 1891302 "ODEPAL" 1891583 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-806 1887102 1887893 1888757 "ODEPACK" 1890096 T ODEPACK (NIL) -7 NIL NIL NIL) (-805 1886163 1886270 1886492 "ODEINT" 1886991 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-804 1880264 1881689 1883136 "ODEIFTBL" 1884736 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-803 1875662 1876448 1877400 "ODEEF" 1879423 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-802 1875011 1875100 1875323 "ODECONST" 1875567 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-801 1873136 1873797 1873825 "ODECAT" 1874430 T ODECAT (NIL) -9 NIL 1874961 NIL) (-800 1869991 1872841 1872963 "OCT" 1873046 NIL OCT (NIL T) -8 NIL NIL NIL) (-799 1869629 1869672 1869799 "OCTCT2" 1869942 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-798 1864278 1866713 1866753 "OC" 1867850 NIL OC (NIL T) -9 NIL 1868708 NIL) (-797 1861505 1862253 1863243 "OC-" 1863337 NIL OC- (NIL T T) -8 NIL NIL NIL) (-796 1860857 1861325 1861353 "OCAMON" 1861358 T OCAMON (NIL) -9 NIL 1861379 NIL) (-795 1860388 1860729 1860757 "OASGP" 1860762 T OASGP (NIL) -9 NIL 1860782 NIL) (-794 1859649 1860138 1860166 "OAMONS" 1860206 T OAMONS (NIL) -9 NIL 1860249 NIL) (-793 1859063 1859496 1859524 "OAMON" 1859529 T OAMON (NIL) -9 NIL 1859549 NIL) (-792 1858321 1858839 1858867 "OAGROUP" 1858872 T OAGROUP (NIL) -9 NIL 1858892 NIL) (-791 1858011 1858061 1858149 "NUMTUBE" 1858265 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-790 1851584 1853102 1854638 "NUMQUAD" 1856495 T NUMQUAD (NIL) -7 NIL NIL NIL) (-789 1847340 1848328 1849353 "NUMODE" 1850579 T NUMODE (NIL) -7 NIL NIL NIL) (-788 1844695 1845575 1845603 "NUMINT" 1846526 T NUMINT (NIL) -9 NIL 1847290 NIL) (-787 1843643 1843840 1844058 "NUMFMT" 1844497 T NUMFMT (NIL) -7 NIL NIL NIL) (-786 1830002 1832947 1835479 "NUMERIC" 1841150 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-785 1824372 1829451 1829546 "NTSCAT" 1829551 NIL NTSCAT (NIL T T T T) -9 NIL 1829590 NIL) (-784 1823566 1823731 1823924 "NTPOLFN" 1824211 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-783 1811643 1820391 1821203 "NSUP" 1822787 NIL NSUP (NIL T) -8 NIL NIL NIL) (-782 1811275 1811332 1811441 "NSUP2" 1811580 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-781 1801503 1811049 1811182 "NSMP" 1811187 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-780 1799935 1800236 1800593 "NREP" 1801191 NIL NREP (NIL T) -7 NIL NIL NIL) (-779 1798526 1798778 1799136 "NPCOEF" 1799678 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-778 1797592 1797707 1797923 "NORMRETR" 1798407 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-777 1795633 1795923 1796332 "NORMPK" 1797300 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-776 1795318 1795346 1795470 "NORMMA" 1795599 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-775 1795118 1795275 1795304 "NONE" 1795309 T NONE (NIL) -8 NIL NIL NIL) (-774 1794907 1794936 1795005 "NONE1" 1795082 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-773 1794404 1794466 1794645 "NODE1" 1794839 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-772 1792689 1793540 1793795 "NNI" 1794142 T NNI (NIL) -8 NIL NIL 1794377) (-771 1791109 1791422 1791786 "NLINSOL" 1792357 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-770 1787350 1788345 1789244 "NIPROB" 1790230 T NIPROB (NIL) -8 NIL NIL NIL) (-769 1786107 1786341 1786643 "NFINTBAS" 1787112 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-768 1785281 1785757 1785798 "NETCLT" 1785970 NIL NETCLT (NIL T) -9 NIL 1786052 NIL) (-767 1783989 1784220 1784501 "NCODIV" 1785049 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-766 1783751 1783788 1783863 "NCNTFRAC" 1783946 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-765 1781931 1782295 1782715 "NCEP" 1783376 NIL NCEP (NIL T) -7 NIL NIL NIL) (-764 1780782 1781555 1781583 "NASRING" 1781693 T NASRING (NIL) -9 NIL 1781773 NIL) (-763 1780577 1780621 1780715 "NASRING-" 1780720 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-762 1779684 1780209 1780237 "NARNG" 1780354 T NARNG (NIL) -9 NIL 1780445 NIL) (-761 1779376 1779443 1779577 "NARNG-" 1779582 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-760 1778255 1778462 1778697 "NAGSP" 1779161 T NAGSP (NIL) -7 NIL NIL NIL) (-759 1769527 1771211 1772884 "NAGS" 1776602 T NAGS (NIL) -7 NIL NIL NIL) (-758 1768075 1768383 1768714 "NAGF07" 1769216 T NAGF07 (NIL) -7 NIL NIL NIL) (-757 1762613 1763904 1765211 "NAGF04" 1766788 T NAGF04 (NIL) -7 NIL NIL NIL) (-756 1755581 1757195 1758828 "NAGF02" 1761000 T NAGF02 (NIL) -7 NIL NIL NIL) (-755 1750805 1751905 1753022 "NAGF01" 1754484 T NAGF01 (NIL) -7 NIL NIL NIL) (-754 1744433 1745999 1747584 "NAGE04" 1749240 T NAGE04 (NIL) -7 NIL NIL NIL) (-753 1735602 1737723 1739853 "NAGE02" 1742323 T NAGE02 (NIL) -7 NIL NIL NIL) (-752 1731555 1732502 1733466 "NAGE01" 1734658 T NAGE01 (NIL) -7 NIL NIL NIL) (-751 1729350 1729884 1730442 "NAGD03" 1731017 T NAGD03 (NIL) -7 NIL NIL NIL) (-750 1721100 1723028 1724982 "NAGD02" 1727416 T NAGD02 (NIL) -7 NIL NIL NIL) (-749 1714911 1716336 1717776 "NAGD01" 1719680 T NAGD01 (NIL) -7 NIL NIL NIL) (-748 1711120 1711942 1712779 "NAGC06" 1714094 T NAGC06 (NIL) -7 NIL NIL NIL) (-747 1709585 1709917 1710273 "NAGC05" 1710784 T NAGC05 (NIL) -7 NIL NIL NIL) (-746 1708961 1709080 1709224 "NAGC02" 1709461 T NAGC02 (NIL) -7 NIL NIL NIL) (-745 1707920 1708503 1708543 "NAALG" 1708622 NIL NAALG (NIL T) -9 NIL 1708683 NIL) (-744 1707755 1707784 1707874 "NAALG-" 1707879 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-743 1701705 1702813 1704000 "MULTSQFR" 1706651 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-742 1701024 1701099 1701283 "MULTFACT" 1701617 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-741 1693748 1697661 1697714 "MTSCAT" 1698784 NIL MTSCAT (NIL T T) -9 NIL 1699299 NIL) (-740 1693460 1693514 1693606 "MTHING" 1693688 NIL MTHING (NIL T) -7 NIL NIL NIL) (-739 1693252 1693285 1693345 "MSYSCMD" 1693420 T MSYSCMD (NIL) -7 NIL NIL NIL) (-738 1689334 1692007 1692327 "MSET" 1692965 NIL MSET (NIL T) -8 NIL NIL NIL) (-737 1686403 1688895 1688936 "MSETAGG" 1688941 NIL MSETAGG (NIL T) -9 NIL 1688975 NIL) (-736 1682244 1683782 1684527 "MRING" 1685703 NIL MRING (NIL T T) -8 NIL NIL NIL) (-735 1681810 1681877 1682008 "MRF2" 1682171 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-734 1681428 1681463 1681607 "MRATFAC" 1681769 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-733 1679040 1679335 1679766 "MPRFF" 1681133 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-732 1673337 1678894 1678991 "MPOLY" 1678996 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-731 1672827 1672862 1673070 "MPCPF" 1673296 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-730 1672341 1672384 1672568 "MPC3" 1672778 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-729 1671536 1671617 1671838 "MPC2" 1672256 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-728 1669837 1670174 1670564 "MONOTOOL" 1671196 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-727 1669062 1669379 1669407 "MONOID" 1669626 T MONOID (NIL) -9 NIL 1669773 NIL) (-726 1668608 1668727 1668908 "MONOID-" 1668913 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-725 1659083 1665034 1665093 "MONOGEN" 1665767 NIL MONOGEN (NIL T T) -9 NIL 1666223 NIL) (-724 1656301 1657036 1658036 "MONOGEN-" 1658155 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-723 1655134 1655580 1655608 "MONADWU" 1656000 T MONADWU (NIL) -9 NIL 1656238 NIL) (-722 1654506 1654665 1654913 "MONADWU-" 1654918 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-721 1653865 1654109 1654137 "MONAD" 1654344 T MONAD (NIL) -9 NIL 1654456 NIL) (-720 1653550 1653628 1653760 "MONAD-" 1653765 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-719 1651839 1652463 1652742 "MOEBIUS" 1653303 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-718 1651117 1651521 1651561 "MODULE" 1651566 NIL MODULE (NIL T) -9 NIL 1651605 NIL) (-717 1650685 1650781 1650971 "MODULE-" 1650976 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-716 1648365 1649049 1649376 "MODRING" 1650509 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-715 1645309 1646470 1646991 "MODOP" 1647894 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-714 1643897 1644376 1644653 "MODMONOM" 1645172 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-713 1633938 1642188 1642602 "MODMON" 1643534 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-712 1631094 1632782 1633058 "MODFIELD" 1633813 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-711 1630071 1630375 1630565 "MMLFORM" 1630924 T MMLFORM (NIL) -8 NIL NIL NIL) (-710 1629597 1629640 1629819 "MMAP" 1630022 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-709 1627676 1628443 1628484 "MLO" 1628907 NIL MLO (NIL T) -9 NIL 1629149 NIL) (-708 1625042 1625558 1626160 "MLIFT" 1627157 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-707 1624433 1624517 1624671 "MKUCFUNC" 1624953 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-706 1624032 1624102 1624225 "MKRECORD" 1624356 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-705 1623079 1623241 1623469 "MKFUNC" 1623843 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-704 1622467 1622571 1622727 "MKFLCFN" 1622962 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-703 1621744 1621846 1622031 "MKBCFUNC" 1622360 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-702 1618451 1621298 1621434 "MINT" 1621628 T MINT (NIL) -8 NIL NIL NIL) (-701 1617263 1617506 1617783 "MHROWRED" 1618206 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-700 1612642 1615798 1616203 "MFLOAT" 1616878 T MFLOAT (NIL) -8 NIL NIL NIL) (-699 1611999 1612075 1612246 "MFINFACT" 1612554 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-698 1608314 1609162 1610046 "MESH" 1611135 T MESH (NIL) -7 NIL NIL NIL) (-697 1606704 1607016 1607369 "MDDFACT" 1608001 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-696 1603499 1605863 1605904 "MDAGG" 1606159 NIL MDAGG (NIL T) -9 NIL 1606302 NIL) (-695 1593239 1602792 1602999 "MCMPLX" 1603312 T MCMPLX (NIL) -8 NIL NIL NIL) (-694 1592380 1592526 1592726 "MCDEN" 1593088 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-693 1590270 1590540 1590920 "MCALCFN" 1592110 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-692 1589195 1589435 1589668 "MAYBE" 1590076 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-691 1586807 1587330 1587892 "MATSTOR" 1588666 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-690 1582764 1586179 1586427 "MATRIX" 1586592 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-689 1578528 1579237 1579973 "MATLIN" 1582121 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-688 1568634 1571820 1571897 "MATCAT" 1576777 NIL MATCAT (NIL T T T) -9 NIL 1578194 NIL) (-687 1564990 1566011 1567367 "MATCAT-" 1567372 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-686 1563584 1563737 1564070 "MATCAT2" 1564825 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-685 1561696 1562020 1562404 "MAPPKG3" 1563259 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-684 1560677 1560850 1561072 "MAPPKG2" 1561520 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-683 1559176 1559460 1559787 "MAPPKG1" 1560383 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-682 1558255 1558582 1558759 "MAPPAST" 1559019 T MAPPAST (NIL) -8 NIL NIL NIL) (-681 1557866 1557924 1558047 "MAPHACK3" 1558191 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-680 1557458 1557519 1557633 "MAPHACK2" 1557798 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-679 1556895 1556999 1557141 "MAPHACK1" 1557349 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-678 1554974 1555595 1555899 "MAGMA" 1556623 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-677 1554453 1554698 1554789 "MACROAST" 1554903 T MACROAST (NIL) -8 NIL NIL NIL) (-676 1550871 1552692 1553153 "M3D" 1554025 NIL M3D (NIL T) -8 NIL NIL NIL) (-675 1544977 1549240 1549281 "LZSTAGG" 1550063 NIL LZSTAGG (NIL T) -9 NIL 1550358 NIL) (-674 1540934 1542108 1543565 "LZSTAGG-" 1543570 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-673 1538021 1538825 1539312 "LWORD" 1540479 NIL LWORD (NIL T) -8 NIL NIL NIL) (-672 1537597 1537825 1537900 "LSTAST" 1537966 T LSTAST (NIL) -8 NIL NIL NIL) (-671 1530763 1537368 1537502 "LSQM" 1537507 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-670 1529987 1530126 1530354 "LSPP" 1530618 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-669 1527799 1528100 1528556 "LSMP" 1529676 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-668 1524578 1525252 1525982 "LSMP1" 1527101 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-667 1518455 1523745 1523786 "LSAGG" 1523848 NIL LSAGG (NIL T) -9 NIL 1523926 NIL) (-666 1515150 1516074 1517287 "LSAGG-" 1517292 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-665 1512749 1514294 1514543 "LPOLY" 1514945 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-664 1512331 1512416 1512539 "LPEFRAC" 1512658 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-663 1510652 1511425 1511678 "LO" 1512163 NIL LO (NIL T T T) -8 NIL NIL NIL) (-662 1510304 1510416 1510444 "LOGIC" 1510555 T LOGIC (NIL) -9 NIL 1510636 NIL) (-661 1510166 1510189 1510260 "LOGIC-" 1510265 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-660 1509359 1509499 1509692 "LODOOPS" 1510022 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-659 1506782 1509275 1509341 "LODO" 1509346 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-658 1505320 1505555 1505908 "LODOF" 1506529 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-657 1501538 1503969 1504010 "LODOCAT" 1504448 NIL LODOCAT (NIL T) -9 NIL 1504659 NIL) (-656 1501271 1501329 1501456 "LODOCAT-" 1501461 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-655 1498591 1501112 1501230 "LODO2" 1501235 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-654 1496026 1498528 1498573 "LODO1" 1498578 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-653 1494907 1495072 1495377 "LODEEF" 1495849 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-652 1490146 1493037 1493078 "LNAGG" 1494025 NIL LNAGG (NIL T) -9 NIL 1494469 NIL) (-651 1489293 1489507 1489849 "LNAGG-" 1489854 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-650 1485429 1486218 1486857 "LMOPS" 1488708 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-649 1484832 1485220 1485261 "LMODULE" 1485266 NIL LMODULE (NIL T) -9 NIL 1485292 NIL) (-648 1482030 1484477 1484600 "LMDICT" 1484742 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-647 1481436 1481657 1481698 "LLINSET" 1481889 NIL LLINSET (NIL T) -9 NIL 1481980 NIL) (-646 1481135 1481344 1481404 "LITERAL" 1481409 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-645 1474298 1480069 1480373 "LIST" 1480864 NIL LIST (NIL T) -8 NIL NIL NIL) (-644 1473823 1473897 1474036 "LIST3" 1474218 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-643 1472830 1473008 1473236 "LIST2" 1473641 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-642 1470964 1471276 1471675 "LIST2MAP" 1472477 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-641 1470560 1470797 1470838 "LINSET" 1470843 NIL LINSET (NIL T) -9 NIL 1470877 NIL) (-640 1469221 1469891 1469932 "LINEXP" 1470187 NIL LINEXP (NIL T) -9 NIL 1470336 NIL) (-639 1467868 1468128 1468425 "LINDEP" 1468973 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-638 1464635 1465354 1466131 "LIMITRF" 1467123 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-637 1462938 1463234 1463643 "LIMITPS" 1464330 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-636 1457366 1462449 1462677 "LIE" 1462759 NIL LIE (NIL T T) -8 NIL NIL NIL) (-635 1456314 1456783 1456823 "LIECAT" 1456963 NIL LIECAT (NIL T) -9 NIL 1457114 NIL) (-634 1456155 1456182 1456270 "LIECAT-" 1456275 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-633 1448651 1455604 1455769 "LIB" 1456010 T LIB (NIL) -8 NIL NIL NIL) (-632 1444286 1445169 1446104 "LGROBP" 1447768 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-631 1442284 1442558 1442908 "LF" 1444007 NIL LF (NIL T T) -7 NIL NIL NIL) (-630 1441124 1441816 1441844 "LFCAT" 1442051 T LFCAT (NIL) -9 NIL 1442190 NIL) (-629 1438026 1438656 1439344 "LEXTRIPK" 1440488 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-628 1434770 1435596 1436099 "LEXP" 1437606 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-627 1434246 1434491 1434583 "LETAST" 1434698 T LETAST (NIL) -8 NIL NIL NIL) (-626 1432644 1432957 1433358 "LEADCDET" 1433928 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-625 1431834 1431908 1432137 "LAZM3PK" 1432565 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-624 1426751 1429911 1430449 "LAUPOL" 1431346 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-623 1426330 1426374 1426535 "LAPLACE" 1426701 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-622 1424269 1425431 1425682 "LA" 1426163 NIL LA (NIL T T T) -8 NIL NIL NIL) (-621 1423263 1423847 1423888 "LALG" 1423950 NIL LALG (NIL T) -9 NIL 1424009 NIL) (-620 1422977 1423036 1423172 "LALG-" 1423177 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-619 1422812 1422836 1422877 "KVTFROM" 1422939 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-618 1421735 1422179 1422364 "KTVLOGIC" 1422647 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-617 1421570 1421594 1421635 "KRCFROM" 1421697 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-616 1420474 1420661 1420960 "KOVACIC" 1421370 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-615 1420309 1420333 1420374 "KONVERT" 1420436 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-614 1420144 1420168 1420209 "KOERCE" 1420271 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-613 1417974 1418737 1419114 "KERNEL" 1419800 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-612 1417470 1417551 1417683 "KERNEL2" 1417888 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-611 1411240 1416009 1416063 "KDAGG" 1416440 NIL KDAGG (NIL T T) -9 NIL 1416646 NIL) (-610 1410769 1410893 1411098 "KDAGG-" 1411103 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-609 1403917 1410430 1410585 "KAFILE" 1410647 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-608 1398345 1403428 1403656 "JORDAN" 1403738 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-607 1397724 1397994 1398115 "JOINAST" 1398244 T JOINAST (NIL) -8 NIL NIL NIL) (-606 1397570 1397629 1397684 "JAVACODE" 1397689 T JAVACODE (NIL) -8 NIL NIL NIL) (-605 1393822 1395775 1395829 "IXAGG" 1396758 NIL IXAGG (NIL T T) -9 NIL 1397217 NIL) (-604 1392741 1393047 1393466 "IXAGG-" 1393471 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-603 1388271 1392663 1392722 "IVECTOR" 1392727 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-602 1387037 1387274 1387540 "ITUPLE" 1388038 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-601 1385539 1385716 1386011 "ITRIGMNP" 1386859 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-600 1384284 1384488 1384771 "ITFUN3" 1385315 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-599 1383916 1383973 1384082 "ITFUN2" 1384221 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-598 1381877 1382936 1383214 "ITAYLOR" 1383671 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-597 1370822 1376014 1377177 "ISUPS" 1380747 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-596 1369926 1370066 1370302 "ISUMP" 1370669 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-595 1365301 1369871 1369912 "ISTRING" 1369917 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-594 1364777 1365022 1365114 "ISAST" 1365229 T ISAST (NIL) -8 NIL NIL NIL) (-593 1363986 1364068 1364284 "IRURPK" 1364691 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-592 1362922 1363123 1363363 "IRSN" 1363766 T IRSN (NIL) -7 NIL NIL NIL) (-591 1360993 1361348 1361777 "IRRF2F" 1362560 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-590 1360740 1360778 1360854 "IRREDFFX" 1360949 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-589 1359355 1359614 1359913 "IROOT" 1360473 NIL IROOT (NIL T) -7 NIL NIL NIL) (-588 1355959 1357039 1357731 "IR" 1358695 NIL IR (NIL T) -8 NIL NIL NIL) (-587 1353572 1354067 1354633 "IR2" 1355437 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-586 1352672 1352785 1352999 "IR2F" 1353455 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-585 1352463 1352497 1352557 "IPRNTPK" 1352632 T IPRNTPK (NIL) -7 NIL NIL NIL) (-584 1349044 1352352 1352421 "IPF" 1352426 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-583 1347371 1348969 1349026 "IPADIC" 1349031 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-582 1346683 1346931 1347061 "IP4ADDR" 1347261 T IP4ADDR (NIL) -8 NIL NIL NIL) (-581 1346156 1346387 1346497 "IOMODE" 1346593 T IOMODE (NIL) -8 NIL NIL NIL) (-580 1345229 1345753 1345880 "IOBFILE" 1346049 T IOBFILE (NIL) -8 NIL NIL NIL) (-579 1344717 1345133 1345161 "IOBCON" 1345166 T IOBCON (NIL) -9 NIL 1345187 NIL) (-578 1344228 1344286 1344469 "INVLAPLA" 1344653 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-577 1333876 1336230 1338616 "INTTR" 1341892 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-576 1330211 1330953 1331818 "INTTOOLS" 1333061 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-575 1329797 1329888 1330005 "INTSLPE" 1330114 T INTSLPE (NIL) -7 NIL NIL NIL) (-574 1327750 1329720 1329779 "INTRVL" 1329784 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-573 1325352 1325864 1326439 "INTRF" 1327235 NIL INTRF (NIL T) -7 NIL NIL NIL) (-572 1324763 1324860 1325002 "INTRET" 1325250 NIL INTRET (NIL T) -7 NIL NIL NIL) (-571 1322760 1323149 1323619 "INTRAT" 1324371 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-570 1320023 1320606 1321225 "INTPM" 1322245 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-569 1316768 1317367 1318105 "INTPAF" 1319409 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-568 1311947 1312909 1313960 "INTPACK" 1315737 T INTPACK (NIL) -7 NIL NIL NIL) (-567 1308895 1311744 1311853 "INT" 1311858 T INT (NIL) -8 NIL NIL NIL) (-566 1308147 1308299 1308507 "INTHERTR" 1308737 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-565 1307586 1307666 1307854 "INTHERAL" 1308061 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-564 1305432 1305875 1306332 "INTHEORY" 1307149 T INTHEORY (NIL) -7 NIL NIL NIL) (-563 1296838 1298459 1300231 "INTG0" 1303784 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-562 1277411 1282201 1287011 "INTFTBL" 1292048 T INTFTBL (NIL) -8 NIL NIL NIL) (-561 1276660 1276798 1276971 "INTFACT" 1277270 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-560 1274087 1274533 1275090 "INTEF" 1276214 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-559 1272454 1273193 1273221 "INTDOM" 1273522 T INTDOM (NIL) -9 NIL 1273729 NIL) (-558 1271823 1271997 1272239 "INTDOM-" 1272244 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-557 1268211 1270139 1270193 "INTCAT" 1270992 NIL INTCAT (NIL T) -9 NIL 1271313 NIL) (-556 1267683 1267786 1267914 "INTBIT" 1268103 T INTBIT (NIL) -7 NIL NIL NIL) (-555 1266382 1266536 1266843 "INTALG" 1267528 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-554 1265865 1265955 1266112 "INTAF" 1266286 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-553 1259208 1265675 1265815 "INTABL" 1265820 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-552 1258549 1259015 1259080 "INT8" 1259114 T INT8 (NIL) -8 NIL NIL 1259159) (-551 1257889 1258355 1258420 "INT64" 1258454 T INT64 (NIL) -8 NIL NIL 1258499) (-550 1257229 1257695 1257760 "INT32" 1257794 T INT32 (NIL) -8 NIL NIL 1257839) (-549 1256569 1257035 1257100 "INT16" 1257134 T INT16 (NIL) -8 NIL NIL 1257179) (-548 1251479 1254192 1254220 "INS" 1255154 T INS (NIL) -9 NIL 1255819 NIL) (-547 1248719 1249490 1250464 "INS-" 1250537 NIL INS- (NIL T) -8 NIL NIL NIL) (-546 1247494 1247721 1248019 "INPSIGN" 1248472 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-545 1246612 1246729 1246926 "INPRODPF" 1247374 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-544 1245506 1245623 1245860 "INPRODFF" 1246492 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-543 1244506 1244658 1244918 "INNMFACT" 1245342 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-542 1243703 1243800 1243988 "INMODGCD" 1244405 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-541 1242211 1242456 1242780 "INFSP" 1243448 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-540 1241395 1241512 1241695 "INFPROD0" 1242091 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-539 1238250 1239460 1239975 "INFORM" 1240888 T INFORM (NIL) -8 NIL NIL NIL) (-538 1237860 1237920 1238018 "INFORM1" 1238185 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-537 1237383 1237472 1237586 "INFINITY" 1237766 T INFINITY (NIL) -7 NIL NIL NIL) (-536 1236559 1237103 1237204 "INETCLTS" 1237302 T INETCLTS (NIL) -8 NIL NIL NIL) (-535 1235175 1235425 1235746 "INEP" 1236307 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-534 1234424 1235072 1235137 "INDE" 1235142 NIL INDE (NIL T) -8 NIL NIL NIL) (-533 1233988 1234056 1234173 "INCRMAPS" 1234351 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-532 1232806 1233257 1233463 "INBFILE" 1233802 T INBFILE (NIL) -8 NIL NIL NIL) (-531 1228105 1229042 1229986 "INBFF" 1231894 NIL INBFF (NIL T) -7 NIL NIL NIL) (-530 1227013 1227282 1227310 "INBCON" 1227823 T INBCON (NIL) -9 NIL 1228089 NIL) (-529 1226265 1226488 1226764 "INBCON-" 1226769 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-528 1225744 1225989 1226080 "INAST" 1226194 T INAST (NIL) -8 NIL NIL NIL) (-527 1225171 1225423 1225529 "IMPTAST" 1225658 T IMPTAST (NIL) -8 NIL NIL NIL) (-526 1221617 1225015 1225119 "IMATRIX" 1225124 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-525 1220329 1220452 1220767 "IMATQF" 1221473 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-524 1218549 1218776 1219113 "IMATLIN" 1220085 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-523 1213127 1218473 1218531 "ILIST" 1218536 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-522 1211032 1212987 1213100 "IIARRAY2" 1213105 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-521 1206430 1210943 1211007 "IFF" 1211012 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-520 1205777 1206047 1206163 "IFAST" 1206334 T IFAST (NIL) -8 NIL NIL NIL) (-519 1200772 1205069 1205257 "IFARRAY" 1205634 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-518 1199952 1200676 1200749 "IFAMON" 1200754 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-517 1199536 1199601 1199655 "IEVALAB" 1199862 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-516 1199211 1199279 1199439 "IEVALAB-" 1199444 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-515 1198842 1199125 1199188 "IDPO" 1199193 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-514 1198092 1198731 1198806 "IDPOAMS" 1198811 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-513 1197399 1197981 1198056 "IDPOAM" 1198061 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-512 1196458 1196734 1196787 "IDPC" 1197200 NIL IDPC (NIL T T) -9 NIL 1197349 NIL) (-511 1195927 1196350 1196423 "IDPAM" 1196428 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-510 1195303 1195819 1195892 "IDPAG" 1195897 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-509 1194948 1195139 1195214 "IDENT" 1195248 T IDENT (NIL) -8 NIL NIL NIL) (-508 1191203 1192051 1192946 "IDECOMP" 1194105 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-507 1184041 1185126 1186173 "IDEAL" 1190239 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-506 1183205 1183317 1183516 "ICDEN" 1183925 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-505 1182276 1182685 1182832 "ICARD" 1183078 T ICARD (NIL) -8 NIL NIL NIL) (-504 1180336 1180649 1181054 "IBPTOOLS" 1181953 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-503 1175943 1179956 1180069 "IBITS" 1180255 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-502 1172666 1173242 1173937 "IBATOOL" 1175360 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-501 1170445 1170907 1171440 "IBACHIN" 1172201 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-500 1168274 1170291 1170394 "IARRAY2" 1170399 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-499 1164380 1168200 1168257 "IARRAY1" 1168262 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-498 1158489 1162792 1163273 "IAN" 1163919 T IAN (NIL) -8 NIL NIL NIL) (-497 1158000 1158057 1158230 "IALGFACT" 1158426 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-496 1157528 1157641 1157669 "HYPCAT" 1157876 T HYPCAT (NIL) -9 NIL NIL NIL) (-495 1157066 1157183 1157369 "HYPCAT-" 1157374 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-494 1156661 1156861 1156944 "HOSTNAME" 1157003 T HOSTNAME (NIL) -8 NIL NIL NIL) (-493 1156506 1156543 1156584 "HOMOTOP" 1156589 NIL HOMOTOP (NIL T) -9 NIL 1156622 NIL) (-492 1153138 1154516 1154557 "HOAGG" 1155538 NIL HOAGG (NIL T) -9 NIL 1156217 NIL) (-491 1151732 1152131 1152657 "HOAGG-" 1152662 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-490 1145736 1151327 1151476 "HEXADEC" 1151603 T HEXADEC (NIL) -8 NIL NIL NIL) (-489 1144483 1144706 1144969 "HEUGCD" 1145513 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-488 1143559 1144320 1144450 "HELLFDIV" 1144455 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-487 1141738 1143336 1143424 "HEAP" 1143503 NIL HEAP (NIL T) -8 NIL NIL NIL) (-486 1141001 1141290 1141424 "HEADAST" 1141624 T HEADAST (NIL) -8 NIL NIL NIL) (-485 1134867 1140916 1140978 "HDP" 1140983 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-484 1128855 1134502 1134654 "HDMP" 1134768 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-483 1128179 1128319 1128483 "HB" 1128711 T HB (NIL) -7 NIL NIL NIL) (-482 1121565 1128025 1128129 "HASHTBL" 1128134 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-481 1121041 1121286 1121378 "HASAST" 1121493 T HASAST (NIL) -8 NIL NIL NIL) (-480 1118819 1120663 1120845 "HACKPI" 1120879 T HACKPI (NIL) -8 NIL NIL NIL) (-479 1114487 1118672 1118785 "GTSET" 1118790 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-478 1107902 1114365 1114463 "GSTBL" 1114468 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-477 1100180 1106933 1107198 "GSERIES" 1107693 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-476 1099321 1099738 1099766 "GROUP" 1099969 T GROUP (NIL) -9 NIL 1100103 NIL) (-475 1098687 1098846 1099097 "GROUP-" 1099102 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-474 1097054 1097375 1097762 "GROEBSOL" 1098364 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-473 1095968 1096256 1096307 "GRMOD" 1096836 NIL GRMOD (NIL T T) -9 NIL 1097004 NIL) (-472 1095736 1095772 1095900 "GRMOD-" 1095905 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-471 1091026 1092090 1093090 "GRIMAGE" 1094756 T GRIMAGE (NIL) -8 NIL NIL NIL) (-470 1089492 1089753 1090077 "GRDEF" 1090722 T GRDEF (NIL) -7 NIL NIL NIL) (-469 1088936 1089052 1089193 "GRAY" 1089371 T GRAY (NIL) -7 NIL NIL NIL) (-468 1088123 1088529 1088580 "GRALG" 1088733 NIL GRALG (NIL T T) -9 NIL 1088826 NIL) (-467 1087784 1087857 1088020 "GRALG-" 1088025 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-466 1084561 1087369 1087547 "GPOLSET" 1087691 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-465 1083915 1083972 1084230 "GOSPER" 1084498 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-464 1079647 1080353 1080879 "GMODPOL" 1083614 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-463 1078652 1078836 1079074 "GHENSEL" 1079459 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-462 1072808 1073651 1074671 "GENUPS" 1077736 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-461 1072505 1072556 1072645 "GENUFACT" 1072751 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-460 1071917 1071994 1072159 "GENPGCD" 1072423 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-459 1071391 1071426 1071639 "GENMFACT" 1071876 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-458 1069957 1070214 1070521 "GENEEZ" 1071134 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-457 1064103 1069568 1069730 "GDMP" 1069880 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-456 1053445 1057874 1058980 "GCNAALG" 1063086 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-455 1051772 1052634 1052662 "GCDDOM" 1052917 T GCDDOM (NIL) -9 NIL 1053074 NIL) (-454 1051242 1051369 1051584 "GCDDOM-" 1051589 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-453 1049914 1050099 1050403 "GB" 1051021 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-452 1038530 1040860 1043252 "GBINTERN" 1047605 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-451 1036367 1036659 1037080 "GBF" 1038205 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-450 1035148 1035313 1035580 "GBEUCLID" 1036183 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-449 1034497 1034622 1034771 "GAUSSFAC" 1035019 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-448 1032864 1033166 1033480 "GALUTIL" 1034216 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-447 1031172 1031446 1031770 "GALPOLYU" 1032591 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-446 1028537 1028827 1029234 "GALFACTU" 1030869 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-445 1020342 1021842 1023450 "GALFACT" 1026969 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-444 1017730 1018388 1018416 "FVFUN" 1019572 T FVFUN (NIL) -9 NIL 1020292 NIL) (-443 1016996 1017178 1017206 "FVC" 1017497 T FVC (NIL) -9 NIL 1017680 NIL) (-442 1016639 1016821 1016889 "FUNDESC" 1016948 T FUNDESC (NIL) -8 NIL NIL NIL) (-441 1016254 1016436 1016517 "FUNCTION" 1016591 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-440 1013998 1014576 1015042 "FT" 1015808 T FT (NIL) -8 NIL NIL NIL) (-439 1012789 1013299 1013502 "FTEM" 1013815 T FTEM (NIL) -8 NIL NIL NIL) (-438 1011080 1011369 1011766 "FSUPFACT" 1012480 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-437 1009477 1009766 1010098 "FST" 1010768 T FST (NIL) -8 NIL NIL NIL) (-436 1008676 1008782 1008970 "FSRED" 1009359 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-435 1007375 1007631 1007978 "FSPRMELT" 1008391 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-434 1004681 1005119 1005605 "FSPECF" 1006938 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-433 986319 994650 994691 "FS" 998575 NIL FS (NIL T) -9 NIL 1000864 NIL) (-432 974962 977955 982012 "FS-" 982312 NIL FS- (NIL T T) -8 NIL NIL NIL) (-431 974490 974544 974714 "FSINT" 974903 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-430 972782 973483 973786 "FSERIES" 974269 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-429 971824 971940 972164 "FSCINT" 972662 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-428 968032 970768 970809 "FSAGG" 971179 NIL FSAGG (NIL T) -9 NIL 971438 NIL) (-427 965794 966395 967191 "FSAGG-" 967286 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-426 964836 964979 965206 "FSAGG2" 965647 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-425 962518 962798 963345 "FS2UPS" 964554 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-424 962152 962195 962324 "FS2" 962469 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-423 961030 961201 961503 "FS2EXPXP" 961977 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-422 960456 960571 960723 "FRUTIL" 960910 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-421 951869 955951 957309 "FR" 959130 NIL FR (NIL T) -8 NIL NIL NIL) (-420 946838 949512 949552 "FRNAALG" 950948 NIL FRNAALG (NIL T) -9 NIL 951555 NIL) (-419 942511 943587 944862 "FRNAALG-" 945612 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-418 942149 942192 942319 "FRNAAF2" 942462 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-417 940529 941003 941298 "FRMOD" 941961 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-416 938280 938912 939229 "FRIDEAL" 940320 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-415 937475 937562 937851 "FRIDEAL2" 938187 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-414 936608 937022 937063 "FRETRCT" 937068 NIL FRETRCT (NIL T) -9 NIL 937244 NIL) (-413 935720 935951 936302 "FRETRCT-" 936307 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-412 932808 934018 934077 "FRAMALG" 934959 NIL FRAMALG (NIL T T) -9 NIL 935251 NIL) (-411 930942 931397 932027 "FRAMALG-" 932250 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-410 924863 930417 930693 "FRAC" 930698 NIL FRAC (NIL T) -8 NIL NIL NIL) (-409 924499 924556 924663 "FRAC2" 924800 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-408 924135 924192 924299 "FR2" 924436 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-407 918648 921541 921569 "FPS" 922688 T FPS (NIL) -9 NIL 923245 NIL) (-406 918097 918206 918370 "FPS-" 918516 NIL FPS- (NIL T) -8 NIL NIL NIL) (-405 915399 917068 917096 "FPC" 917321 T FPC (NIL) -9 NIL 917463 NIL) (-404 915192 915232 915329 "FPC-" 915334 NIL FPC- (NIL T) -8 NIL NIL NIL) (-403 913982 914680 914721 "FPATMAB" 914726 NIL FPATMAB (NIL T) -9 NIL 914878 NIL) (-402 911655 912158 912584 "FPARFRAC" 913619 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-401 907048 907547 908229 "FORTRAN" 911087 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-400 904764 905264 905803 "FORT" 906529 T FORT (NIL) -7 NIL NIL NIL) (-399 902440 903002 903030 "FORTFN" 904090 T FORTFN (NIL) -9 NIL 904714 NIL) (-398 902204 902254 902282 "FORTCAT" 902341 T FORTCAT (NIL) -9 NIL 902403 NIL) (-397 900310 900820 901210 "FORMULA" 901834 T FORMULA (NIL) -8 NIL NIL NIL) (-396 900098 900128 900197 "FORMULA1" 900274 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-395 899621 899673 899846 "FORDER" 900040 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-394 898717 898881 899074 "FOP" 899448 T FOP (NIL) -7 NIL NIL NIL) (-393 897298 897997 898171 "FNLA" 898599 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-392 896027 896442 896470 "FNCAT" 896930 T FNCAT (NIL) -9 NIL 897190 NIL) (-391 895566 895986 896014 "FNAME" 896019 T FNAME (NIL) -8 NIL NIL NIL) (-390 894129 895092 895120 "FMTC" 895125 T FMTC (NIL) -9 NIL 895161 NIL) (-389 892875 894065 894111 "FMONOID" 894116 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-388 889703 890871 890912 "FMONCAT" 892129 NIL FMONCAT (NIL T) -9 NIL 892734 NIL) (-387 888895 889445 889594 "FM" 889599 NIL FM (NIL T T) -8 NIL NIL NIL) (-386 886319 886965 886993 "FMFUN" 888137 T FMFUN (NIL) -9 NIL 888845 NIL) (-385 885588 885769 885797 "FMC" 886087 T FMC (NIL) -9 NIL 886269 NIL) (-384 882667 883527 883581 "FMCAT" 884776 NIL FMCAT (NIL T T) -9 NIL 885271 NIL) (-383 881533 882433 882533 "FM1" 882612 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-382 879307 879723 880217 "FLOATRP" 881084 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-381 872882 877036 877657 "FLOAT" 878706 T FLOAT (NIL) -8 NIL NIL NIL) (-380 870320 870820 871398 "FLOATCP" 872349 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-379 869060 869898 869939 "FLINEXP" 869944 NIL FLINEXP (NIL T) -9 NIL 870037 NIL) (-378 868214 868449 868777 "FLINEXP-" 868782 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-377 867290 867434 867658 "FLASORT" 868066 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-376 864406 865274 865326 "FLALG" 866553 NIL FLALG (NIL T T) -9 NIL 867020 NIL) (-375 858142 861892 861933 "FLAGG" 863195 NIL FLAGG (NIL T) -9 NIL 863847 NIL) (-374 856868 857207 857697 "FLAGG-" 857702 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-373 855910 856053 856280 "FLAGG2" 856721 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-372 852761 853769 853828 "FINRALG" 854956 NIL FINRALG (NIL T T) -9 NIL 855464 NIL) (-371 851921 852150 852489 "FINRALG-" 852494 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-370 851301 851540 851568 "FINITE" 851764 T FINITE (NIL) -9 NIL 851871 NIL) (-369 843658 845845 845885 "FINAALG" 849552 NIL FINAALG (NIL T) -9 NIL 851005 NIL) (-368 838990 840040 841184 "FINAALG-" 842563 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-367 838358 838745 838848 "FILE" 838920 NIL FILE (NIL T) -8 NIL NIL NIL) (-366 837016 837354 837408 "FILECAT" 838092 NIL FILECAT (NIL T T) -9 NIL 838308 NIL) (-365 834732 836260 836288 "FIELD" 836328 T FIELD (NIL) -9 NIL 836408 NIL) (-364 833352 833737 834248 "FIELD-" 834253 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-363 831202 831987 832334 "FGROUP" 833038 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-362 830292 830456 830676 "FGLMICPK" 831034 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-361 826124 830217 830274 "FFX" 830279 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-360 825725 825786 825921 "FFSLPE" 826057 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-359 821714 822497 823293 "FFPOLY" 824961 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-358 821218 821254 821463 "FFPOLY2" 821672 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-357 817061 821137 821200 "FFP" 821205 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-356 812459 816972 817036 "FF" 817041 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-355 807585 811802 811992 "FFNBX" 812313 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-354 802514 806720 806978 "FFNBP" 807439 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-353 797147 801798 802009 "FFNB" 802347 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-352 795979 796177 796492 "FFINTBAS" 796944 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-351 792048 794268 794296 "FFIELDC" 794916 T FFIELDC (NIL) -9 NIL 795292 NIL) (-350 790710 791081 791578 "FFIELDC-" 791583 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-349 790279 790325 790449 "FFHOM" 790652 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-348 787974 788461 788978 "FFF" 789794 NIL FFF (NIL T) -7 NIL NIL NIL) (-347 783592 787716 787817 "FFCGX" 787917 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-346 779213 783324 783431 "FFCGP" 783535 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-345 774396 778940 779048 "FFCG" 779149 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-344 755792 764873 764959 "FFCAT" 770124 NIL FFCAT (NIL T T T) -9 NIL 771575 NIL) (-343 750990 752037 753351 "FFCAT-" 754581 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-342 750401 750444 750679 "FFCAT2" 750941 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-341 739722 743373 744593 "FEXPR" 749253 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-340 738722 739157 739198 "FEVALAB" 739282 NIL FEVALAB (NIL T) -9 NIL 739543 NIL) (-339 737881 738091 738429 "FEVALAB-" 738434 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-338 736447 737264 737467 "FDIV" 737780 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-337 733467 734208 734323 "FDIVCAT" 735891 NIL FDIVCAT (NIL T T T T) -9 NIL 736328 NIL) (-336 733229 733256 733426 "FDIVCAT-" 733431 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-335 732449 732536 732813 "FDIV2" 733136 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-334 731423 731744 731946 "FCTRDATA" 732267 T FCTRDATA (NIL) -8 NIL NIL NIL) (-333 730109 730368 730657 "FCPAK1" 731154 T FCPAK1 (NIL) -7 NIL NIL NIL) (-332 729208 729609 729750 "FCOMP" 730000 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-331 712910 716358 719896 "FC" 725690 T FC (NIL) -8 NIL NIL NIL) (-330 705273 709301 709341 "FAXF" 711143 NIL FAXF (NIL T) -9 NIL 711835 NIL) (-329 702549 703207 704032 "FAXF-" 704497 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-328 697601 701925 702101 "FARRAY" 702406 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-327 692495 694562 694615 "FAMR" 695638 NIL FAMR (NIL T T) -9 NIL 696098 NIL) (-326 691385 691687 692122 "FAMR-" 692127 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-325 690554 691307 691360 "FAMONOID" 691365 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-324 688340 689050 689103 "FAMONC" 690044 NIL FAMONC (NIL T T) -9 NIL 690430 NIL) (-323 687004 688094 688231 "FAGROUP" 688236 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-322 684799 685118 685521 "FACUTIL" 686685 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-321 683898 684083 684305 "FACTFUNC" 684609 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-320 676320 683201 683400 "EXPUPXS" 683754 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-319 673803 674343 674929 "EXPRTUBE" 675754 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-318 670074 670666 671396 "EXPRODE" 673142 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-317 655559 668723 669152 "EXPR" 669678 NIL EXPR (NIL T) -8 NIL NIL NIL) (-316 650113 650700 651506 "EXPR2UPS" 654857 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-315 649745 649802 649911 "EXPR2" 650050 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-314 641135 648898 649188 "EXPEXPAN" 649582 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-313 640935 641092 641121 "EXIT" 641126 T EXIT (NIL) -8 NIL NIL NIL) (-312 640415 640659 640750 "EXITAST" 640864 T EXITAST (NIL) -8 NIL NIL NIL) (-311 640042 640104 640217 "EVALCYC" 640347 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-310 639583 639701 639742 "EVALAB" 639912 NIL EVALAB (NIL T) -9 NIL 640016 NIL) (-309 639064 639186 639407 "EVALAB-" 639412 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-308 636432 637734 637762 "EUCDOM" 638317 T EUCDOM (NIL) -9 NIL 638667 NIL) (-307 634837 635279 635869 "EUCDOM-" 635874 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-306 622375 625135 627885 "ESTOOLS" 632107 T ESTOOLS (NIL) -7 NIL NIL NIL) (-305 622007 622064 622173 "ESTOOLS2" 622312 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-304 621758 621800 621880 "ESTOOLS1" 621959 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-303 615795 617403 617431 "ES" 620199 T ES (NIL) -9 NIL 621609 NIL) (-302 610742 612029 613846 "ES-" 614010 NIL ES- (NIL T) -8 NIL NIL NIL) (-301 607116 607877 608657 "ESCONT" 609982 T ESCONT (NIL) -7 NIL NIL NIL) (-300 606861 606893 606975 "ESCONT1" 607078 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-299 606536 606586 606686 "ES2" 606805 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-298 606166 606224 606333 "ES1" 606472 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-297 605382 605511 605687 "ERROR" 606010 T ERROR (NIL) -7 NIL NIL NIL) (-296 598774 605241 605332 "EQTBL" 605337 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-295 591277 594088 595537 "EQ" 597358 NIL -2093 (NIL T) -8 NIL NIL NIL) (-294 590909 590966 591075 "EQ2" 591214 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-293 586198 587247 588340 "EP" 589848 NIL EP (NIL T) -7 NIL NIL NIL) (-292 584798 585089 585395 "ENV" 585912 T ENV (NIL) -8 NIL NIL NIL) (-291 583892 584446 584474 "ENTIRER" 584479 T ENTIRER (NIL) -9 NIL 584525 NIL) (-290 580359 581847 582217 "EMR" 583691 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-289 579503 579688 579742 "ELTAGG" 580122 NIL ELTAGG (NIL T T) -9 NIL 580333 NIL) (-288 579222 579284 579425 "ELTAGG-" 579430 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-287 579011 579040 579094 "ELTAB" 579178 NIL ELTAB (NIL T T) -9 NIL NIL NIL) (-286 578137 578283 578482 "ELFUTS" 578862 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-285 577879 577935 577963 "ELEMFUN" 578068 T ELEMFUN (NIL) -9 NIL NIL NIL) (-284 577749 577770 577838 "ELEMFUN-" 577843 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-283 572593 575849 575890 "ELAGG" 576830 NIL ELAGG (NIL T) -9 NIL 577293 NIL) (-282 570878 571312 571975 "ELAGG-" 571980 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-281 569539 569818 570112 "ELABEXPR" 570604 T ELABEXPR (NIL) -8 NIL NIL NIL) (-280 562403 564206 565033 "EFUPXS" 568815 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-279 555853 557654 558464 "EFULS" 561679 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-278 553338 553696 554168 "EFSTRUC" 555485 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-277 543129 544695 546243 "EF" 551853 NIL EF (NIL T T) -7 NIL NIL NIL) (-276 542203 542614 542763 "EAB" 543000 T EAB (NIL) -8 NIL NIL NIL) (-275 541385 542162 542190 "E04UCFA" 542195 T E04UCFA (NIL) -8 NIL NIL NIL) (-274 540567 541344 541372 "E04NAFA" 541377 T E04NAFA (NIL) -8 NIL NIL NIL) (-273 539749 540526 540554 "E04MBFA" 540559 T E04MBFA (NIL) -8 NIL NIL NIL) (-272 538931 539708 539736 "E04JAFA" 539741 T E04JAFA (NIL) -8 NIL NIL NIL) (-271 538115 538890 538918 "E04GCFA" 538923 T E04GCFA (NIL) -8 NIL NIL NIL) (-270 537299 538074 538102 "E04FDFA" 538107 T E04FDFA (NIL) -8 NIL NIL NIL) (-269 536481 537258 537286 "E04DGFA" 537291 T E04DGFA (NIL) -8 NIL NIL NIL) (-268 530654 532006 533370 "E04AGNT" 535137 T E04AGNT (NIL) -7 NIL NIL NIL) (-267 529334 529840 529880 "DVARCAT" 530355 NIL DVARCAT (NIL T) -9 NIL 530554 NIL) (-266 528538 528750 529064 "DVARCAT-" 529069 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-265 521675 528337 528466 "DSMP" 528471 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-264 516456 517620 518688 "DROPT" 520627 T DROPT (NIL) -8 NIL NIL NIL) (-263 516121 516180 516278 "DROPT1" 516391 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-262 511236 512362 513499 "DROPT0" 515004 T DROPT0 (NIL) -7 NIL NIL NIL) (-261 509581 509906 510292 "DRAWPT" 510870 T DRAWPT (NIL) -7 NIL NIL NIL) (-260 504168 505091 506170 "DRAW" 508555 NIL DRAW (NIL T) -7 NIL NIL NIL) (-259 503801 503854 503972 "DRAWHACK" 504109 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-258 502532 502801 503092 "DRAWCX" 503530 T DRAWCX (NIL) -7 NIL NIL NIL) (-257 502047 502116 502267 "DRAWCURV" 502458 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-256 492515 494477 496592 "DRAWCFUN" 499952 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-255 489281 491210 491251 "DQAGG" 491880 NIL DQAGG (NIL T) -9 NIL 492153 NIL) (-254 477405 483874 483957 "DPOLCAT" 485809 NIL DPOLCAT (NIL T T T T) -9 NIL 486354 NIL) (-253 472241 473590 475548 "DPOLCAT-" 475553 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-252 465363 472102 472200 "DPMO" 472205 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-251 458388 465143 465310 "DPMM" 465315 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-250 457866 458080 458178 "DOMTMPLT" 458310 T DOMTMPLT (NIL) -8 NIL NIL NIL) (-249 457299 457668 457748 "DOMCTOR" 457806 T DOMCTOR (NIL) -8 NIL NIL NIL) (-248 456511 456779 456930 "DOMAIN" 457168 T DOMAIN (NIL) -8 NIL NIL NIL) (-247 450499 456146 456298 "DMP" 456412 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-246 450099 450155 450299 "DLP" 450437 NIL DLP (NIL T) -7 NIL NIL NIL) (-245 443921 449426 449616 "DLIST" 449941 NIL DLIST (NIL T) -8 NIL NIL NIL) (-244 440718 442774 442815 "DLAGG" 443365 NIL DLAGG (NIL T) -9 NIL 443595 NIL) (-243 439394 440058 440086 "DIVRING" 440178 T DIVRING (NIL) -9 NIL 440261 NIL) (-242 438631 438821 439121 "DIVRING-" 439126 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-241 436733 437090 437496 "DISPLAY" 438245 T DISPLAY (NIL) -7 NIL NIL NIL) (-240 430621 436647 436710 "DIRPROD" 436715 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-239 429469 429672 429937 "DIRPROD2" 430414 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-238 418244 424250 424303 "DIRPCAT" 424713 NIL DIRPCAT (NIL NIL T) -9 NIL 425553 NIL) (-237 415570 416212 417093 "DIRPCAT-" 417430 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-236 414857 415017 415203 "DIOSP" 415404 T DIOSP (NIL) -7 NIL NIL NIL) (-235 411512 413769 413810 "DIOPS" 414244 NIL DIOPS (NIL T) -9 NIL 414473 NIL) (-234 411061 411175 411366 "DIOPS-" 411371 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-233 409884 410512 410540 "DIFRING" 410727 T DIFRING (NIL) -9 NIL 410837 NIL) (-232 409530 409607 409759 "DIFRING-" 409764 NIL DIFRING- (NIL T) -8 NIL NIL NIL) (-231 407266 408538 408579 "DIFEXT" 408942 NIL DIFEXT (NIL T) -9 NIL 409236 NIL) (-230 405551 405979 406645 "DIFEXT-" 406650 NIL DIFEXT- (NIL T T) -8 NIL NIL NIL) (-229 402826 405083 405124 "DIAGG" 405129 NIL DIAGG (NIL T) -9 NIL 405149 NIL) (-228 402210 402367 402619 "DIAGG-" 402624 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-227 397627 401169 401446 "DHMATRIX" 401979 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-226 393239 394148 395158 "DFSFUN" 396637 T DFSFUN (NIL) -7 NIL NIL NIL) (-225 388317 392170 392482 "DFLOAT" 392947 T DFLOAT (NIL) -8 NIL NIL NIL) (-224 386580 386861 387250 "DFINTTLS" 388025 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-223 383609 384601 385001 "DERHAM" 386246 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-222 381410 383384 383473 "DEQUEUE" 383553 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-221 380664 380797 380980 "DEGRED" 381272 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-220 377094 377839 378685 "DEFINTRF" 379892 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-219 374649 375118 375710 "DEFINTEF" 376613 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-218 373999 374269 374384 "DEFAST" 374554 T DEFAST (NIL) -8 NIL NIL NIL) (-217 368003 373594 373743 "DECIMAL" 373870 T DECIMAL (NIL) -8 NIL NIL NIL) (-216 365515 365973 366479 "DDFACT" 367547 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-215 365111 365154 365305 "DBLRESP" 365466 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-214 362983 363344 363704 "DBASE" 364878 NIL DBASE (NIL T) -8 NIL NIL NIL) (-213 362225 362463 362609 "DATAARY" 362882 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-212 361331 362184 362212 "D03FAFA" 362217 T D03FAFA (NIL) -8 NIL NIL NIL) (-211 360438 361290 361318 "D03EEFA" 361323 T D03EEFA (NIL) -8 NIL NIL NIL) (-210 358388 358854 359343 "D03AGNT" 359969 T D03AGNT (NIL) -7 NIL NIL NIL) (-209 357677 358347 358375 "D02EJFA" 358380 T D02EJFA (NIL) -8 NIL NIL NIL) (-208 356966 357636 357664 "D02CJFA" 357669 T D02CJFA (NIL) -8 NIL NIL NIL) (-207 356255 356925 356953 "D02BHFA" 356958 T D02BHFA (NIL) -8 NIL NIL NIL) (-206 355544 356214 356242 "D02BBFA" 356247 T D02BBFA (NIL) -8 NIL NIL NIL) (-205 348741 350330 351936 "D02AGNT" 353958 T D02AGNT (NIL) -7 NIL NIL NIL) (-204 346509 347032 347578 "D01WGTS" 348215 T D01WGTS (NIL) -7 NIL NIL NIL) (-203 345576 346468 346496 "D01TRNS" 346501 T D01TRNS (NIL) -8 NIL NIL NIL) (-202 344644 345535 345563 "D01GBFA" 345568 T D01GBFA (NIL) -8 NIL NIL NIL) (-201 343712 344603 344631 "D01FCFA" 344636 T D01FCFA (NIL) -8 NIL NIL NIL) (-200 342780 343671 343699 "D01ASFA" 343704 T D01ASFA (NIL) -8 NIL NIL NIL) (-199 341848 342739 342767 "D01AQFA" 342772 T D01AQFA (NIL) -8 NIL NIL NIL) (-198 340916 341807 341835 "D01APFA" 341840 T D01APFA (NIL) -8 NIL NIL NIL) (-197 339984 340875 340903 "D01ANFA" 340908 T D01ANFA (NIL) -8 NIL NIL NIL) (-196 339052 339943 339971 "D01AMFA" 339976 T D01AMFA (NIL) -8 NIL NIL NIL) (-195 338120 339011 339039 "D01ALFA" 339044 T D01ALFA (NIL) -8 NIL NIL NIL) (-194 337188 338079 338107 "D01AKFA" 338112 T D01AKFA (NIL) -8 NIL NIL NIL) (-193 336256 337147 337175 "D01AJFA" 337180 T D01AJFA (NIL) -8 NIL NIL NIL) (-192 329551 331104 332665 "D01AGNT" 334715 T D01AGNT (NIL) -7 NIL NIL NIL) (-191 328888 329016 329168 "CYCLOTOM" 329419 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-190 325622 326336 327063 "CYCLES" 328181 T CYCLES (NIL) -7 NIL NIL NIL) (-189 324934 325068 325239 "CVMP" 325483 NIL CVMP (NIL T) -7 NIL NIL NIL) (-188 322775 323033 323402 "CTRIGMNP" 324662 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-187 322211 322569 322642 "CTOR" 322722 T CTOR (NIL) -8 NIL NIL NIL) (-186 321720 321942 322043 "CTORKIND" 322130 T CTORKIND (NIL) -8 NIL NIL NIL) (-185 321011 321327 321355 "CTORCAT" 321537 T CTORCAT (NIL) -9 NIL 321650 NIL) (-184 320609 320720 320879 "CTORCAT-" 320884 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-183 320071 320283 320391 "CTORCALL" 320533 NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-182 319445 319544 319697 "CSTTOOLS" 319968 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-181 315244 315901 316659 "CRFP" 318757 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-180 314719 314965 315057 "CRCEAST" 315172 T CRCEAST (NIL) -8 NIL NIL NIL) (-179 313766 313951 314179 "CRAPACK" 314523 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-178 313150 313251 313455 "CPMATCH" 313642 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-177 312875 312903 313009 "CPIMA" 313116 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-176 309223 309895 310614 "COORDSYS" 312210 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-175 308635 308756 308898 "CONTOUR" 309101 T CONTOUR (NIL) -8 NIL NIL NIL) (-174 304526 306638 307130 "CONTFRAC" 308175 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-173 304406 304427 304455 "CONDUIT" 304492 T CONDUIT (NIL) -9 NIL NIL NIL) (-172 303494 304048 304076 "COMRING" 304081 T COMRING (NIL) -9 NIL 304133 NIL) (-171 302548 302852 303036 "COMPPROP" 303330 T COMPPROP (NIL) -8 NIL NIL NIL) (-170 302209 302244 302372 "COMPLPAT" 302507 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-169 292500 302018 302127 "COMPLEX" 302132 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-168 292136 292193 292300 "COMPLEX2" 292437 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-167 291854 291889 291987 "COMPFACT" 292095 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-166 275934 285928 285968 "COMPCAT" 286972 NIL COMPCAT (NIL T) -9 NIL 288320 NIL) (-165 265446 268373 272000 "COMPCAT-" 272356 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-164 265175 265203 265306 "COMMUPC" 265412 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-163 264969 265003 265062 "COMMONOP" 265136 T COMMONOP (NIL) -7 NIL NIL NIL) (-162 264525 264720 264807 "COMM" 264902 T COMM (NIL) -8 NIL NIL NIL) (-161 264101 264329 264404 "COMMAAST" 264470 T COMMAAST (NIL) -8 NIL NIL NIL) (-160 263350 263544 263572 "COMBOPC" 263910 T COMBOPC (NIL) -9 NIL 264085 NIL) (-159 262246 262456 262698 "COMBINAT" 263140 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-158 258703 259277 259904 "COMBF" 261668 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-157 257461 257819 258054 "COLOR" 258488 T COLOR (NIL) -8 NIL NIL NIL) (-156 256937 257182 257274 "COLONAST" 257389 T COLONAST (NIL) -8 NIL NIL NIL) (-155 256577 256624 256749 "CMPLXRT" 256884 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-154 256025 256277 256376 "CLLCTAST" 256498 T CLLCTAST (NIL) -8 NIL NIL NIL) (-153 251523 252555 253635 "CLIP" 254965 T CLIP (NIL) -7 NIL NIL NIL) (-152 249869 250629 250868 "CLIF" 251350 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-151 246044 248015 248056 "CLAGG" 248985 NIL CLAGG (NIL T) -9 NIL 249521 NIL) (-150 244466 244923 245506 "CLAGG-" 245511 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-149 244010 244095 244235 "CINTSLPE" 244375 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-148 241511 241982 242530 "CHVAR" 243538 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-147 240685 241239 241267 "CHARZ" 241272 T CHARZ (NIL) -9 NIL 241287 NIL) (-146 240439 240479 240557 "CHARPOL" 240639 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-145 239497 240084 240112 "CHARNZ" 240159 T CHARNZ (NIL) -9 NIL 240215 NIL) (-144 237403 238151 238504 "CHAR" 239164 T CHAR (NIL) -8 NIL NIL NIL) (-143 237129 237190 237218 "CFCAT" 237329 T CFCAT (NIL) -9 NIL NIL NIL) (-142 236374 236485 236667 "CDEN" 237013 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-141 232339 235527 235807 "CCLASS" 236114 T CCLASS (NIL) -8 NIL NIL NIL) (-140 231590 231747 231924 "CATEGORY" 232182 T -10 (NIL) -8 NIL NIL NIL) (-139 231163 231509 231557 "CATCTOR" 231562 T CATCTOR (NIL) -8 NIL NIL NIL) (-138 230614 230866 230964 "CATAST" 231085 T CATAST (NIL) -8 NIL NIL NIL) (-137 230090 230335 230427 "CASEAST" 230542 T CASEAST (NIL) -8 NIL NIL NIL) (-136 225099 226119 226872 "CARTEN" 229393 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-135 224207 224355 224576 "CARTEN2" 224946 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-134 222523 223357 223614 "CARD" 223970 T CARD (NIL) -8 NIL NIL NIL) (-133 222099 222327 222402 "CAPSLAST" 222468 T CAPSLAST (NIL) -8 NIL NIL NIL) (-132 221603 221811 221839 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T) ((-23) . T) ((-47 |#1| #0=(-567)) . T) ((-25) . T) ((-38 #1=(-410 (-567))) -2800 (|has| |#1| (-365)) (|has| |#1| (-38 (-410 (-567))))) ((-38 |#1|) |has| |#1| (-172)) ((-38 |#2|) |has| |#1| (-365)) ((-38 $) -2800 (|has| |#1| (-559)) (|has| |#1| (-365))) ((-35) |has| |#1| (-38 (-410 (-567)))) ((-95) |has| |#1| (-38 (-410 (-567)))) ((-102) . T) ((-111 #1# #1#) -2800 (|has| |#1| (-365)) (|has| |#1| (-38 (-410 (-567))))) ((-111 |#1| |#1|) . T) ((-111 |#2| |#2|) |has| |#1| (-365)) ((-111 $ $) -2800 (|has| |#1| (-559)) (|has| |#1| (-365)) (|has| |#1| (-172))) ((-131) . T) ((-145) -2800 (-12 (|has| |#1| (-365)) (|has| |#2| (-145))) (|has| |#1| (-145))) ((-147) -2800 (-12 (|has| |#1| (-365)) (|has| |#2| (-147))) (|has| |#1| (-147))) ((-617 #1#) -2800 (|has| |#1| (-365)) (|has| |#1| (-38 (-410 (-567))))) ((-617 (-567)) . T) ((-617 #2=(-1178)) -12 (|has| |#1| (-365)) (|has| |#2| (-1040 (-1178)))) ((-617 |#1|) |has| |#1| (-172)) ((-617 |#2|) . 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T) ((-647 |#1|) . T) ((-647 |#2|) |has| |#1| (-365)) ((-647 $) . T) ((-649 #1#) -2800 (|has| |#1| (-365)) (|has| |#1| (-38 (-410 (-567))))) ((-649 |#1|) . T) ((-649 |#2|) |has| |#1| (-365)) ((-649 $) . T) ((-641 #1#) -2800 (|has| |#1| (-365)) (|has| |#1| (-38 (-410 (-567))))) ((-641 |#1|) |has| |#1| (-172)) ((-641 |#2|) |has| |#1| (-365)) ((-641 $) -2800 (|has| |#1| (-559)) (|has| |#1| (-365))) ((-640 (-567)) -12 (|has| |#1| (-365)) (|has| |#2| (-640 (-567)))) ((-640 |#2|) |has| |#1| (-365)) ((-718 #1#) -2800 (|has| |#1| (-365)) (|has| |#1| (-38 (-410 (-567))))) ((-718 |#1|) |has| |#1| (-172)) ((-718 |#2|) |has| |#1| (-365)) ((-718 $) -2800 (|has| |#1| (-559)) (|has| |#1| (-365))) ((-727) . 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T) ((-23) . T) ((-47 |#1| #0=(-772)) . T) ((-25) . T) ((-38 #1=(-410 (-567))) |has| |#1| (-38 (-410 (-567)))) ((-38 |#1|) |has| |#1| (-172)) ((-38 $) -2800 (|has| |#1| (-911)) (|has| |#1| (-559)) (|has| |#1| (-455)) (|has| |#1| (-365))) ((-102) . T) ((-111 #1# #1#) |has| |#1| (-38 (-410 (-567)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2800 (|has| |#1| (-911)) (|has| |#1| (-559)) (|has| |#1| (-455)) (|has| |#1| (-365)) (|has| |#1| (-172))) ((-131) . T) ((-145) |has| |#1| (-145)) ((-147) |has| |#1| (-147)) ((-617 #1#) -2800 (|has| |#1| (-1040 (-410 (-567)))) (|has| |#1| (-38 (-410 (-567))))) ((-617 (-567)) . T) ((-617 #2=(-1084)) . T) ((-617 |#1|) . T) ((-617 $) -2800 (|has| |#1| (-911)) (|has| |#1| (-559)) (|has| |#1| (-455)) (|has| |#1| (-365))) ((-614 (-863)) . 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T) ((-647 |#1|) . T) ((-647 $) . T) ((-649 #1#) |has| |#1| (-38 (-410 (-567)))) ((-649 |#1|) . T) ((-649 $) . T) ((-641 #1#) |has| |#1| (-38 (-410 (-567)))) ((-641 |#1|) |has| |#1| (-172)) ((-641 $) -2800 (|has| |#1| (-911)) (|has| |#1| (-559)) (|has| |#1| (-455)) (|has| |#1| (-365))) ((-640 (-567)) |has| |#1| (-640 (-567))) ((-640 |#1|) . T) ((-718 #1#) |has| |#1| (-38 (-410 (-567)))) ((-718 |#1|) |has| |#1| (-172)) ((-718 $) -2800 (|has| |#1| (-911)) (|has| |#1| (-559)) (|has| |#1| (-455)) (|has| |#1| (-365))) ((-727) . T) ((-902 #2#) . T) ((-902 (-1178)) |has| |#1| (-902 (-1178))) ((-888 (-381)) -12 (|has| (-1084) (-888 (-381))) (|has| |#1| (-888 (-381)))) ((-888 (-567)) -12 (|has| (-1084) (-888 (-567))) (|has| |#1| (-888 (-567)))) ((-951 |#1| #0# #2#) . T) ((-911) |has| |#1| (-911)) ((-922) |has| |#1| (-365)) ((-1040 (-410 (-567))) |has| |#1| (-1040 (-410 (-567)))) ((-1040 (-567)) |has| |#1| (-1040 (-567))) ((-1040 #2#) . T) ((-1040 |#1|) . T) ((-1053 #1#) |has| |#1| (-38 (-410 (-567)))) ((-1053 |#1|) . T) ((-1053 $) -2800 (|has| |#1| (-911)) (|has| |#1| (-559)) (|has| |#1| (-455)) (|has| |#1| (-365)) (|has| |#1| (-172))) ((-1058 #1#) |has| |#1| (-38 (-410 (-567)))) ((-1058 |#1|) . T) ((-1058 $) -2800 (|has| |#1| (-911)) (|has| |#1| (-559)) (|has| |#1| (-455)) (|has| |#1| (-365)) (|has| |#1| (-172))) ((-1051) . T) ((-1060) . T) ((-1114) . T) ((-1102) . T) ((-1153) |has| |#1| (-1153)) ((-1222) |has| |#1| (-911))) +((-2847 (((-645 (-1084)) $) 34)) (-3014 (($ $) 31)) (-2824 (($ |#2| |#3|) NIL) (($ $ (-1084) |#3|) 28) (($ $ (-645 (-1084)) (-645 |#3|)) 27)) (-2976 (($ $) 14)) (-2989 ((|#2| $) 12)) (-3077 ((|#3| $) 10))) +(((-1245 |#1| |#2| |#3|) (-10 -8 (-15 -2847 ((-645 (-1084)) |#1|)) (-15 -2824 (|#1| |#1| (-645 (-1084)) (-645 |#3|))) (-15 -2824 (|#1| |#1| (-1084) |#3|)) (-15 -3014 (|#1| |#1|)) (-15 -2824 (|#1| |#2| |#3|)) (-15 -3077 (|#3| |#1|)) (-15 -2976 (|#1| |#1|)) (-15 -2989 (|#2| |#1|))) (-1246 |#2| |#3|) (-1051) (-793)) (T -1245)) +NIL +(-10 -8 (-15 -2847 ((-645 (-1084)) |#1|)) (-15 -2824 (|#1| |#1| (-645 (-1084)) (-645 |#3|))) (-15 -2824 (|#1| |#1| (-1084) |#3|)) (-15 -3014 (|#1| |#1|)) (-15 -2824 (|#1| |#2| |#3|)) (-15 -3077 (|#3| |#1|)) (-15 -2976 (|#1| |#1|)) (-15 -2989 (|#2| |#1|))) +((-2403 (((-112) $ $) 7)) (-2460 (((-112) $) 17)) (-2847 (((-645 (-1084)) $) 86)) (-3644 (((-1178) $) 115)) (-3666 (((-2 (|:| -3951 $) (|:| 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T) ((-641 #0#) |has| |#1| (-38 (-410 (-567)))) ((-641 |#1|) |has| |#1| (-172)) ((-641 $) |has| |#1| (-559)) ((-718 #0#) |has| |#1| (-38 (-410 (-567)))) ((-718 |#1|) |has| |#1| (-172)) ((-718 $) |has| |#1| (-559)) ((-727) . T) ((-902 (-1178)) -12 (|has| |#1| (-15 * (|#1| |#2| |#1|))) (|has| |#1| (-902 (-1178)))) ((-975 |#1| |#2| (-1084)) . T) ((-1053 #0#) |has| |#1| (-38 (-410 (-567)))) ((-1053 |#1|) . T) ((-1053 $) -2800 (|has| |#1| (-559)) (|has| |#1| (-172))) ((-1058 #0#) |has| |#1| (-38 (-410 (-567)))) ((-1058 |#1|) . T) ((-1058 $) -2800 (|has| |#1| (-559)) (|has| |#1| (-172))) ((-1051) . T) ((-1060) . T) ((-1114) . T) ((-1102) . 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T) ((-23) . T) ((-47 |#1| #0=(-410 (-567))) . T) ((-25) . T) ((-38 #1=(-410 (-567))) -2800 (|has| |#1| (-365)) (|has| |#1| (-38 (-410 (-567))))) ((-38 |#1|) |has| |#1| (-172)) ((-38 $) -2800 (|has| |#1| (-559)) (|has| |#1| (-365))) ((-35) |has| |#1| (-38 (-410 (-567)))) ((-95) |has| |#1| (-38 (-410 (-567)))) ((-102) . T) ((-111 #1# #1#) -2800 (|has| |#1| (-365)) (|has| |#1| (-38 (-410 (-567))))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2800 (|has| |#1| (-559)) (|has| |#1| (-365)) (|has| |#1| (-172))) ((-131) . T) ((-145) |has| |#1| (-145)) ((-147) |has| |#1| (-147)) ((-617 #1#) -2800 (|has| |#1| (-365)) (|has| |#1| (-38 (-410 (-567))))) ((-617 (-567)) . T) ((-617 |#1|) |has| |#1| (-172)) ((-617 $) -2800 (|has| |#1| (-559)) (|has| |#1| (-365))) ((-614 (-863)) . 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"SUPFRACF" 2813690 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1172 2812602 2812661 2812774 "SUP2" 2812916 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1171 2811050 2811324 2811680 "SUMRF" 2812301 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1170 2810385 2810451 2810643 "SUMFS" 2810971 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1169 2794352 2809562 2809813 "SULS" 2810192 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1168 2793954 2794174 2794244 "SUCHTAST" 2794304 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1167 2793249 2793479 2793619 "SUCH" 2793862 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1166 2787115 2788155 2789114 "SUBSPACE" 2792337 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1165 2786545 2786635 2786799 "SUBRESP" 2787003 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1164 2779910 2781210 2782521 "STTF" 2785281 NIL STTF (NIL T) -7 NIL NIL NIL) (-1163 2774083 2775203 2776350 "STTFNC" 2778810 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1162 2765393 2767265 2769059 "STTAYLOR" 2772324 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1161 2758523 2765257 2765340 "STRTBL" 2765345 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1160 2753887 2758478 2758509 "STRING" 2758514 T STRING (NIL) -8 NIL NIL NIL) (-1159 2748748 2753260 2753290 "STRICAT" 2753349 T STRICAT (NIL) -9 NIL 2753411 NIL) (-1158 2741501 2746367 2746978 "STREAM" 2748172 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1157 2741011 2741088 2741232 "STREAM3" 2741418 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1156 2739993 2740176 2740411 "STREAM2" 2740824 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1155 2739681 2739733 2739826 "STREAM1" 2739935 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1154 2738697 2738878 2739109 "STINPROD" 2739497 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1153 2738249 2738459 2738489 "STEP" 2738569 T STEP (NIL) -9 NIL 2738647 NIL) (-1152 2731681 2738148 2738225 "STBL" 2738230 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1151 2726807 2730902 2730945 "STAGG" 2731098 NIL STAGG (NIL T) -9 NIL 2731187 NIL) (-1150 2724509 2725111 2725983 "STAGG-" 2725988 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1149 2722656 2724279 2724371 "STACK" 2724452 NIL STACK (NIL T) -8 NIL NIL NIL) (-1148 2715351 2720797 2721253 "SREGSET" 2722286 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1147 2707776 2709145 2710658 "SRDCMPK" 2713957 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1146 2700693 2705216 2705246 "SRAGG" 2706549 T SRAGG (NIL) -9 NIL 2707157 NIL) (-1145 2699710 2699965 2700344 "SRAGG-" 2700349 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1144 2694170 2698657 2699078 "SQMATRIX" 2699336 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1143 2687855 2690888 2691615 "SPLTREE" 2693515 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1142 2683818 2684511 2685157 "SPLNODE" 2687281 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1141 2682865 2683098 2683128 "SPFCAT" 2683572 T SPFCAT (NIL) -9 NIL NIL NIL) (-1140 2681602 2681812 2682076 "SPECOUT" 2682623 T SPECOUT (NIL) -7 NIL NIL NIL) (-1139 2673228 2674998 2675028 "SPADXPT" 2679420 T SPADXPT (NIL) -9 NIL 2681454 NIL) (-1138 2672989 2673029 2673098 "SPADPRSR" 2673181 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1137 2671144 2672944 2672975 "SPADAST" 2672980 T SPADAST (NIL) -8 NIL NIL NIL) (-1136 2663089 2664862 2664905 "SPACEC" 2669278 NIL SPACEC (NIL T) -9 NIL 2671094 NIL) (-1135 2661219 2663021 2663070 "SPACE3" 2663075 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1134 2659971 2660142 2660433 "SORTPAK" 2661024 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1133 2658063 2658366 2658778 "SOLVETRA" 2659635 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1132 2657113 2657335 2657596 "SOLVESER" 2657836 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1131 2652417 2653305 2654300 "SOLVERAD" 2656165 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1130 2648232 2648841 2649570 "SOLVEFOR" 2651784 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1129 2642502 2647581 2647678 "SNTSCAT" 2647683 NIL SNTSCAT (NIL T T T T) -9 NIL 2647753 NIL) (-1128 2636608 2640825 2641216 "SMTS" 2642192 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1127 2631292 2636496 2636573 "SMP" 2636578 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1126 2629451 2629752 2630150 "SMITH" 2630989 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1125 2622164 2626360 2626463 "SMATCAT" 2627814 NIL SMATCAT (NIL NIL T T T) -9 NIL 2628364 NIL) (-1124 2619104 2619927 2621105 "SMATCAT-" 2621110 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1123 2616770 2618340 2618383 "SKAGG" 2618644 NIL SKAGG (NIL T) -9 NIL 2618779 NIL) (-1122 2613081 2616186 2616381 "SINT" 2616568 T SINT (NIL) -8 NIL NIL 2616741) (-1121 2612853 2612891 2612957 "SIMPAN" 2613037 T SIMPAN (NIL) -7 NIL NIL NIL) (-1120 2612132 2612388 2612528 "SIG" 2612735 T SIG (NIL) -8 NIL NIL NIL) (-1119 2610970 2611191 2611466 "SIGNRF" 2611891 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1118 2609803 2609954 2610238 "SIGNEF" 2610799 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1117 2609109 2609386 2609510 "SIGAST" 2609701 T SIGAST (NIL) -8 NIL NIL NIL) (-1116 2606798 2607253 2607759 "SHP" 2608650 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1115 2600650 2606699 2606775 "SHDP" 2606780 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1114 2600223 2600415 2600445 "SGROUP" 2600538 T SGROUP (NIL) -9 NIL 2600600 NIL) (-1113 2600081 2600107 2600180 "SGROUP-" 2600185 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1112 2596916 2597614 2598337 "SGCF" 2599380 T SGCF (NIL) -7 NIL NIL NIL) (-1111 2591284 2596363 2596460 "SFRTCAT" 2596465 NIL SFRTCAT (NIL T T T T) -9 NIL 2596504 NIL) (-1110 2584705 2585723 2586859 "SFRGCD" 2590267 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1109 2577831 2578904 2580090 "SFQCMPK" 2583638 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1108 2577451 2577540 2577651 "SFORT" 2577772 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1107 2576569 2577291 2577412 "SEXOF" 2577417 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1106 2575676 2576450 2576518 "SEX" 2576523 T SEX (NIL) -8 NIL NIL NIL) (-1105 2571189 2571904 2571999 "SEXCAT" 2574936 NIL SEXCAT (NIL T T T T T) -9 NIL 2575514 NIL) (-1104 2568342 2571123 2571171 "SET" 2571176 NIL SET (NIL T) -8 NIL NIL NIL) (-1103 2566566 2567055 2567360 "SETMN" 2568083 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1102 2566062 2566214 2566244 "SETCAT" 2566420 T SETCAT (NIL) -9 NIL 2566530 NIL) (-1101 2565754 2565832 2565962 "SETCAT-" 2565967 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1100 2562115 2564215 2564258 "SETAGG" 2565128 NIL SETAGG (NIL T) -9 NIL 2565468 NIL) (-1099 2561573 2561689 2561926 "SETAGG-" 2561931 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1098 2561016 2561269 2561370 "SEQAST" 2561494 T SEQAST (NIL) -8 NIL NIL NIL) (-1097 2560215 2560509 2560570 "SEGXCAT" 2560856 NIL SEGXCAT (NIL T T) -9 NIL 2560976 NIL) (-1096 2559221 2559881 2560063 "SEG" 2560068 NIL SEG (NIL T) -8 NIL NIL NIL) (-1095 2558200 2558414 2558457 "SEGCAT" 2558979 NIL SEGCAT (NIL T) -9 NIL 2559200 NIL) (-1094 2557132 2557563 2557771 "SEGBIND" 2558027 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1093 2556753 2556812 2556925 "SEGBIND2" 2557067 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1092 2556326 2556554 2556631 "SEGAST" 2556698 T SEGAST (NIL) -8 NIL NIL NIL) (-1091 2555545 2555671 2555875 "SEG2" 2556170 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1090 2554955 2555480 2555527 "SDVAR" 2555532 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1089 2547482 2554725 2554855 "SDPOL" 2554860 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1088 2546075 2546341 2546660 "SCPKG" 2547197 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1087 2545239 2545411 2545603 "SCOPE" 2545905 T SCOPE (NIL) -8 NIL NIL NIL) (-1086 2544459 2544593 2544772 "SCACHE" 2545094 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1085 2544105 2544291 2544321 "SASTCAT" 2544326 T SASTCAT (NIL) -9 NIL 2544339 NIL) (-1084 2543592 2543940 2544016 "SAOS" 2544051 T SAOS (NIL) -8 NIL NIL NIL) (-1083 2543157 2543192 2543365 "SAERFFC" 2543551 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1082 2537096 2543054 2543134 "SAE" 2543139 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1081 2536689 2536724 2536883 "SAEFACT" 2537055 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1080 2535010 2535324 2535725 "RURPK" 2536355 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1079 2533647 2533953 2534258 "RULESET" 2534844 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1078 2530870 2531400 2531858 "RULE" 2533328 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1077 2530482 2530664 2530747 "RULECOLD" 2530822 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1076 2530272 2530300 2530371 "RTVALUE" 2530433 T RTVALUE (NIL) -8 NIL NIL NIL) (-1075 2529743 2529989 2530083 "RSTRCAST" 2530200 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1074 2524591 2525386 2526306 "RSETGCD" 2528942 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1073 2513821 2518900 2518997 "RSETCAT" 2523116 NIL RSETCAT (NIL T T T T) -9 NIL 2524213 NIL) (-1072 2511748 2512287 2513111 "RSETCAT-" 2513116 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1071 2504133 2505510 2507030 "RSDCMPK" 2510347 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1070 2502112 2502579 2502653 "RRCC" 2503739 NIL RRCC (NIL T T) -9 NIL 2504083 NIL) (-1069 2501463 2501637 2501916 "RRCC-" 2501921 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1068 2500906 2501159 2501260 "RPTAST" 2501384 T RPTAST (NIL) -8 NIL NIL NIL) (-1067 2474757 2484114 2484181 "RPOLCAT" 2494845 NIL RPOLCAT (NIL T T T) -9 NIL 2498004 NIL) (-1066 2466255 2468595 2471717 "RPOLCAT-" 2471722 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1065 2457186 2464466 2464948 "ROUTINE" 2465795 T ROUTINE (NIL) -8 NIL NIL NIL) (-1064 2453984 2456812 2456952 "ROMAN" 2457068 T ROMAN (NIL) -8 NIL NIL NIL) (-1063 2452228 2452844 2453104 "ROIRC" 2453789 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1062 2448460 2450744 2450774 "RNS" 2451078 T RNS (NIL) -9 NIL 2451352 NIL) (-1061 2446969 2447352 2447886 "RNS-" 2447961 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1060 2446372 2446780 2446810 "RNG" 2446815 T RNG (NIL) -9 NIL 2446836 NIL) (-1059 2445375 2445737 2445939 "RNGBIND" 2446223 NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-1058 2444774 2445162 2445205 "RMODULE" 2445210 NIL RMODULE (NIL T) -9 NIL 2445237 NIL) (-1057 2443610 2443704 2444040 "RMCAT2" 2444675 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1056 2440460 2442956 2443253 "RMATRIX" 2443372 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1055 2433287 2435547 2435662 "RMATCAT" 2439021 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2440003 NIL) (-1054 2432662 2432809 2433116 "RMATCAT-" 2433121 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1053 2432063 2432284 2432327 "RLINSET" 2432521 NIL RLINSET (NIL T) -9 NIL 2432612 NIL) (-1052 2431630 2431705 2431833 "RINTERP" 2431982 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1051 2430688 2431242 2431272 "RING" 2431328 T RING (NIL) -9 NIL 2431420 NIL) (-1050 2430480 2430524 2430621 "RING-" 2430626 NIL RING- (NIL T) -8 NIL NIL NIL) (-1049 2429321 2429558 2429816 "RIDIST" 2430244 T RIDIST (NIL) -7 NIL NIL NIL) (-1048 2420610 2428789 2428995 "RGCHAIN" 2429169 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1047 2419960 2420366 2420407 "RGBCSPC" 2420465 NIL RGBCSPC (NIL T) -9 NIL 2420517 NIL) (-1046 2419118 2419499 2419540 "RGBCMDL" 2419772 NIL RGBCMDL (NIL T) -9 NIL 2419886 NIL) (-1045 2416112 2416726 2417396 "RF" 2418482 NIL RF (NIL T) -7 NIL NIL NIL) (-1044 2415758 2415821 2415924 "RFFACTOR" 2416043 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1043 2415483 2415518 2415615 "RFFACT" 2415717 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1042 2413600 2413964 2414346 "RFDIST" 2415123 T RFDIST (NIL) -7 NIL NIL NIL) (-1041 2413053 2413145 2413308 "RETSOL" 2413502 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1040 2412689 2412769 2412812 "RETRACT" 2412945 NIL RETRACT (NIL T) -9 NIL 2413032 NIL) (-1039 2412538 2412563 2412650 "RETRACT-" 2412655 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1038 2412140 2412360 2412430 "RETAST" 2412490 T RETAST (NIL) -8 NIL NIL NIL) (-1037 2404878 2411793 2411920 "RESULT" 2412035 T RESULT (NIL) -8 NIL NIL NIL) (-1036 2403469 2404147 2404346 "RESRING" 2404781 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1035 2403105 2403154 2403252 "RESLATC" 2403406 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1034 2402810 2402845 2402952 "REPSQ" 2403064 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1033 2400232 2400812 2401414 "REP" 2402230 T REP (NIL) -7 NIL NIL NIL) (-1032 2399929 2399964 2400075 "REPDB" 2400191 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1031 2393829 2395218 2396441 "REP2" 2398741 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1030 2390206 2390887 2391695 "REP1" 2393056 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1029 2382902 2388347 2388803 "REGSET" 2389836 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1028 2381667 2382050 2382300 "REF" 2382687 NIL REF (NIL T) -8 NIL NIL NIL) (-1027 2381044 2381147 2381314 "REDORDER" 2381551 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1026 2377012 2380257 2380484 "RECLOS" 2380872 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1025 2376064 2376245 2376460 "REALSOLV" 2376819 T REALSOLV (NIL) -7 NIL NIL NIL) (-1024 2375910 2375951 2375981 "REAL" 2375986 T REAL (NIL) -9 NIL 2376021 NIL) (-1023 2372393 2373195 2374079 "REAL0Q" 2375075 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1022 2367994 2368982 2370043 "REAL0" 2371374 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1021 2367465 2367711 2367805 "RDUCEAST" 2367922 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1020 2366870 2366942 2367149 "RDIV" 2367387 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1019 2365938 2366112 2366325 "RDIST" 2366692 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1018 2364535 2364822 2365194 "RDETRS" 2365646 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1017 2362347 2362801 2363339 "RDETR" 2364077 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1016 2360972 2361250 2361647 "RDEEFS" 2362063 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1015 2359481 2359787 2360212 "RDEEF" 2360660 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1014 2353542 2356462 2356492 "RCFIELD" 2357787 T RCFIELD (NIL) -9 NIL 2358518 NIL) (-1013 2351606 2352110 2352806 "RCFIELD-" 2352881 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1012 2347875 2349707 2349750 "RCAGG" 2350834 NIL RCAGG (NIL T) -9 NIL 2351299 NIL) (-1011 2347503 2347597 2347760 "RCAGG-" 2347765 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1010 2346838 2346950 2347115 "RATRET" 2347387 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1009 2346391 2346458 2346579 "RATFACT" 2346766 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1008 2345699 2345819 2345971 "RANDSRC" 2346261 T RANDSRC (NIL) -7 NIL NIL NIL) (-1007 2345433 2345477 2345550 "RADUTIL" 2345648 T RADUTIL (NIL) -7 NIL NIL NIL) (-1006 2338549 2344266 2344576 "RADIX" 2345157 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-1005 2330168 2338391 2338521 "RADFF" 2338526 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-1004 2329815 2329890 2329920 "RADCAT" 2330080 T RADCAT (NIL) -9 NIL NIL NIL) (-1003 2329597 2329645 2329745 "RADCAT-" 2329750 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-1002 2327697 2329369 2329460 "QUEUE" 2329541 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-1001 2324236 2327632 2327679 "QUAT" 2327684 NIL QUAT (NIL T) -8 NIL NIL NIL) (-1000 2323871 2323914 2324043 "QUATCT2" 2324187 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-999 2317333 2320678 2320718 "QUATCAT" 2321498 NIL QUATCAT (NIL T) -9 NIL 2322264 NIL) (-998 2313477 2314514 2315901 "QUATCAT-" 2315995 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-997 2310950 2312561 2312602 "QUAGG" 2312977 NIL QUAGG (NIL T) -9 NIL 2313152 NIL) (-996 2310555 2310775 2310843 "QQUTAST" 2310902 T QQUTAST (NIL) -8 NIL NIL NIL) (-995 2309453 2309953 2310125 "QFORM" 2310427 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-994 2300458 2305697 2305737 "QFCAT" 2306395 NIL QFCAT (NIL T) -9 NIL 2307396 NIL) (-993 2296030 2297231 2298822 "QFCAT-" 2298916 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-992 2295668 2295711 2295838 "QFCAT2" 2295981 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-991 2295128 2295238 2295368 "QEQUAT" 2295558 T QEQUAT (NIL) -8 NIL NIL NIL) (-990 2288274 2289347 2290531 "QCMPACK" 2294061 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-989 2285823 2286271 2286699 "QALGSET" 2287929 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-988 2285068 2285242 2285474 "QALGSET2" 2285643 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-987 2283758 2283982 2284299 "PWFFINTB" 2284841 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-986 2281940 2282108 2282462 "PUSHVAR" 2283572 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-985 2277858 2278912 2278953 "PTRANFN" 2280837 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-984 2276260 2276551 2276873 "PTPACK" 2277569 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-983 2275892 2275949 2276058 "PTFUNC2" 2276197 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-982 2270369 2274764 2274805 "PTCAT" 2275101 NIL PTCAT (NIL T) -9 NIL 2275254 NIL) (-981 2270027 2270062 2270186 "PSQFR" 2270328 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-980 2268622 2268920 2269254 "PSEUDLIN" 2269725 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-979 2255385 2257756 2260080 "PSETPK" 2266382 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-978 2248403 2251143 2251239 "PSETCAT" 2254260 NIL PSETCAT (NIL T T T T) -9 NIL 2255074 NIL) (-977 2246239 2246873 2247694 "PSETCAT-" 2247699 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-976 2245588 2245753 2245781 "PSCURVE" 2246049 T PSCURVE (NIL) -9 NIL 2246216 NIL) (-975 2241586 2243102 2243167 "PSCAT" 2244011 NIL PSCAT (NIL T T T) -9 NIL 2244251 NIL) (-974 2240649 2240865 2241265 "PSCAT-" 2241270 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-973 2239354 2240014 2240219 "PRTITION" 2240464 T PRTITION (NIL) -8 NIL NIL NIL) (-972 2238829 2239075 2239167 "PRTDAST" 2239282 T PRTDAST (NIL) -8 NIL NIL NIL) (-971 2227918 2230133 2232321 "PRS" 2236691 NIL PRS (NIL T T) -7 NIL NIL NIL) (-970 2225729 2227268 2227308 "PRQAGG" 2227491 NIL PRQAGG (NIL T) -9 NIL 2227593 NIL) (-969 2224933 2225238 2225266 "PROPLOG" 2225513 T PROPLOG (NIL) -9 NIL 2225679 NIL) (-968 2223363 2223884 2224141 "PROPFRML" 2224709 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-967 2222832 2222939 2223067 "PROPERTY" 2223255 T PROPERTY (NIL) -8 NIL NIL NIL) (-966 2216890 2220998 2221818 "PRODUCT" 2222058 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-965 2214168 2216348 2216582 "PR" 2216701 NIL PR (NIL T T) -8 NIL NIL NIL) (-964 2213964 2213996 2214055 "PRINT" 2214129 T PRINT (NIL) -7 NIL NIL NIL) (-963 2213304 2213421 2213573 "PRIMES" 2213844 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-962 2211369 2211770 2212236 "PRIMELT" 2212883 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-961 2211098 2211147 2211175 "PRIMCAT" 2211299 T PRIMCAT (NIL) -9 NIL NIL NIL) (-960 2207213 2211036 2211081 "PRIMARR" 2211086 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-959 2206220 2206398 2206626 "PRIMARR2" 2207031 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-958 2205863 2205919 2206030 "PREASSOC" 2206158 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-957 2205338 2205471 2205499 "PPCURVE" 2205704 T PPCURVE (NIL) -9 NIL 2205840 NIL) (-956 2204933 2205133 2205216 "PORTNUM" 2205275 T PORTNUM (NIL) -8 NIL NIL NIL) (-955 2202292 2202691 2203283 "POLYROOT" 2204514 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-954 2196474 2201896 2202056 "POLY" 2202165 NIL POLY (NIL T) -8 NIL NIL NIL) (-953 2195857 2195915 2196149 "POLYLIFT" 2196410 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-952 2192132 2192581 2193210 "POLYCATQ" 2195402 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-951 2178844 2183972 2184037 "POLYCAT" 2187551 NIL POLYCAT (NIL T T T) -9 NIL 2189429 NIL) (-950 2172293 2174155 2176539 "POLYCAT-" 2176544 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-949 2171880 2171948 2172068 "POLY2UP" 2172219 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-948 2171512 2171569 2171678 "POLY2" 2171817 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-947 2170197 2170436 2170712 "POLUTIL" 2171286 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-946 2168552 2168829 2169160 "POLTOPOL" 2169919 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-945 2164017 2168488 2168534 "POINT" 2168539 NIL POINT (NIL T) -8 NIL NIL NIL) (-944 2162204 2162561 2162936 "PNTHEORY" 2163662 T PNTHEORY (NIL) -7 NIL NIL NIL) (-943 2160662 2160959 2161358 "PMTOOLS" 2161902 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-942 2160255 2160333 2160450 "PMSYM" 2160578 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-941 2159765 2159834 2160008 "PMQFCAT" 2160180 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-940 2159120 2159230 2159386 "PMPRED" 2159642 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-939 2158513 2158599 2158761 "PMPREDFS" 2159021 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-938 2157177 2157385 2157763 "PMPLCAT" 2158275 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-937 2156709 2156788 2156940 "PMLSAGG" 2157092 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-936 2156182 2156258 2156440 "PMKERNEL" 2156627 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-935 2155799 2155874 2155987 "PMINS" 2156101 NIL PMINS (NIL T) -7 NIL NIL NIL) (-934 2155241 2155310 2155519 "PMFS" 2155724 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-933 2154469 2154587 2154792 "PMDOWN" 2155118 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-932 2153636 2153794 2153975 "PMASS" 2154308 T PMASS (NIL) -7 NIL NIL NIL) (-931 2152909 2153019 2153182 "PMASSFS" 2153523 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-930 2152564 2152632 2152726 "PLOTTOOL" 2152835 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-929 2147171 2148375 2149523 "PLOT" 2151436 T PLOT (NIL) -8 NIL NIL NIL) (-928 2142975 2144019 2144940 "PLOT3D" 2146270 T PLOT3D (NIL) -8 NIL NIL NIL) (-927 2141887 2142064 2142299 "PLOT1" 2142779 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-926 2117276 2121953 2126804 "PLEQN" 2137153 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-925 2116594 2116716 2116896 "PINTERP" 2117141 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-924 2116287 2116334 2116437 "PINTERPA" 2116541 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-923 2115508 2116056 2116143 "PI" 2116183 T PI (NIL) -8 NIL NIL 2116250) (-922 2113805 2114780 2114808 "PID" 2114990 T PID (NIL) -9 NIL 2115124 NIL) (-921 2113556 2113593 2113668 "PICOERCE" 2113762 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-920 2112876 2113015 2113191 "PGROEB" 2113412 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-919 2108463 2109277 2110182 "PGE" 2111991 T PGE (NIL) -7 NIL NIL NIL) (-918 2106586 2106833 2107199 "PGCD" 2108180 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-917 2105924 2106027 2106188 "PFRPAC" 2106470 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-916 2102564 2104472 2104825 "PFR" 2105603 NIL PFR (NIL T) -8 NIL NIL NIL) (-915 2100953 2101197 2101522 "PFOTOOLS" 2102311 NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-914 2099486 2099725 2100076 "PFOQ" 2100710 NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-913 2097987 2098199 2098555 "PFO" 2099270 NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-912 2094540 2097876 2097945 "PF" 2097950 NIL PF (NIL NIL) -8 NIL NIL NIL) (-911 2091874 2093145 2093173 "PFECAT" 2093758 T PFECAT (NIL) -9 NIL 2094142 NIL) (-910 2091319 2091473 2091687 "PFECAT-" 2091692 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-909 2089922 2090174 2090475 "PFBRU" 2091068 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-908 2087788 2088140 2088572 "PFBR" 2089573 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-907 2083670 2085164 2085840 "PERM" 2087145 NIL PERM (NIL T) -8 NIL NIL NIL) (-906 2078904 2079877 2080747 "PERMGRP" 2082833 NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-905 2077010 2077967 2078008 "PERMCAT" 2078454 NIL PERMCAT (NIL T) -9 NIL 2078759 NIL) (-904 2076663 2076704 2076828 "PERMAN" 2076963 NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-903 2074151 2076328 2076450 "PENDTREE" 2076574 NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-902 2072175 2072943 2072984 "PDRING" 2073641 NIL PDRING (NIL T) -9 NIL 2073927 NIL) (-901 2071278 2071496 2071858 "PDRING-" 2071863 NIL PDRING- (NIL T T) -8 NIL NIL NIL) (-900 2068493 2069271 2069939 "PDEPROB" 2070630 T PDEPROB (NIL) -8 NIL NIL NIL) (-899 2066038 2066542 2067097 "PDEPACK" 2067958 T PDEPACK (NIL) -7 NIL NIL NIL) (-898 2064950 2065140 2065391 "PDECOMP" 2065837 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-897 2062529 2063372 2063400 "PDECAT" 2064187 T PDECAT (NIL) -9 NIL 2064900 NIL) (-896 2062280 2062313 2062403 "PCOMP" 2062490 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-895 2060458 2061081 2061378 "PBWLB" 2062009 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-894 2052931 2054531 2055869 "PATTERN" 2059141 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-893 2052563 2052620 2052729 "PATTERN2" 2052868 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-892 2050320 2050708 2051165 "PATTERN1" 2052152 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-891 2047688 2048269 2048750 "PATRES" 2049885 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-890 2047252 2047319 2047451 "PATRES2" 2047615 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-889 2045135 2045540 2045947 "PATMATCH" 2046919 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-888 2044645 2044854 2044895 "PATMAB" 2045002 NIL PATMAB (NIL T) -9 NIL 2045085 NIL) (-887 2043163 2043499 2043757 "PATLRES" 2044450 NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-886 2042709 2042832 2042873 "PATAB" 2042878 NIL PATAB (NIL T) -9 NIL 2043050 NIL) (-885 2040190 2040722 2041295 "PARTPERM" 2042156 T PARTPERM (NIL) -7 NIL NIL NIL) (-884 2039811 2039874 2039976 "PARSURF" 2040121 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-883 2039443 2039500 2039609 "PARSU2" 2039748 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-882 2039207 2039247 2039314 "PARSER" 2039396 T PARSER (NIL) -7 NIL NIL NIL) (-881 2038828 2038891 2038993 "PARSCURV" 2039138 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-880 2038460 2038517 2038626 "PARSC2" 2038765 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-879 2038099 2038157 2038254 "PARPCURV" 2038396 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-878 2037731 2037788 2037897 "PARPC2" 2038036 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-877 2036792 2037104 2037286 "PARAMAST" 2037569 T PARAMAST (NIL) -8 NIL NIL NIL) (-876 2036312 2036398 2036517 "PAN2EXPR" 2036693 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-875 2035089 2035433 2035661 "PALETTE" 2036104 T PALETTE (NIL) -8 NIL NIL NIL) (-874 2033482 2034094 2034454 "PAIR" 2034775 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-873 2027352 2032741 2032935 "PADICRC" 2033337 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-872 2020581 2026698 2026882 "PADICRAT" 2027200 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-871 2018896 2020518 2020563 "PADIC" 2020568 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-870 2016006 2017570 2017610 "PADICCT" 2018191 NIL PADICCT (NIL NIL) -9 NIL 2018473 NIL) (-869 2014963 2015163 2015431 "PADEPAC" 2015793 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-868 2014175 2014308 2014514 "PADE" 2014825 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-867 2012562 2013383 2013663 "OWP" 2013979 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-866 2012055 2012268 2012365 "OVERSET" 2012485 T OVERSET (NIL) -8 NIL NIL NIL) (-865 2011101 2011660 2011832 "OVAR" 2011923 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-864 2010365 2010486 2010647 "OUT" 2010960 T OUT (NIL) -7 NIL NIL NIL) (-863 1999237 2001474 2003674 "OUTFORM" 2008185 T OUTFORM (NIL) -8 NIL NIL NIL) (-862 1998573 1998834 1998961 "OUTBFILE" 1999130 T OUTBFILE (NIL) -8 NIL NIL NIL) (-861 1997880 1998045 1998073 "OUTBCON" 1998391 T OUTBCON (NIL) -9 NIL 1998557 NIL) (-860 1997481 1997593 1997750 "OUTBCON-" 1997755 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-859 1996861 1997210 1997299 "OSI" 1997412 T OSI (NIL) -8 NIL NIL NIL) (-858 1996391 1996729 1996757 "OSGROUP" 1996762 T OSGROUP (NIL) -9 NIL 1996784 NIL) (-857 1995136 1995363 1995648 "ORTHPOL" 1996138 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-856 1992687 1994971 1995092 "OREUP" 1995097 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-855 1990090 1992378 1992505 "ORESUP" 1992629 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-854 1987618 1988118 1988679 "OREPCTO" 1989579 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-853 1981304 1983505 1983546 "OREPCAT" 1985894 NIL OREPCAT (NIL T) -9 NIL 1986998 NIL) (-852 1978451 1979233 1980291 "OREPCAT-" 1980296 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-851 1977602 1977900 1977928 "ORDSET" 1978237 T ORDSET (NIL) -9 NIL 1978401 NIL) (-850 1977033 1977181 1977405 "ORDSET-" 1977410 NIL ORDSET- (NIL T) -8 NIL NIL NIL) (-849 1975598 1976389 1976417 "ORDRING" 1976619 T ORDRING (NIL) -9 NIL 1976744 NIL) (-848 1975243 1975337 1975481 "ORDRING-" 1975486 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-847 1974623 1975086 1975114 "ORDMON" 1975119 T ORDMON (NIL) -9 NIL 1975140 NIL) (-846 1973785 1973932 1974127 "ORDFUNS" 1974472 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-845 1973123 1973542 1973570 "ORDFIN" 1973635 T ORDFIN (NIL) -9 NIL 1973709 NIL) (-844 1969682 1971709 1972118 "ORDCOMP" 1972747 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-843 1968948 1969075 1969261 "ORDCOMP2" 1969542 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-842 1965529 1966439 1967253 "OPTPROB" 1968154 T OPTPROB (NIL) -8 NIL NIL NIL) (-841 1962331 1962970 1963674 "OPTPACK" 1964845 T OPTPACK (NIL) -7 NIL NIL NIL) (-840 1960018 1960784 1960812 "OPTCAT" 1961631 T OPTCAT (NIL) -9 NIL 1962281 NIL) (-839 1959402 1959695 1959800 "OPSIG" 1959933 T OPSIG (NIL) -8 NIL NIL NIL) (-838 1959170 1959209 1959275 "OPQUERY" 1959356 T OPQUERY (NIL) -7 NIL NIL NIL) (-837 1956301 1957481 1957985 "OP" 1958699 NIL OP (NIL T) -8 NIL NIL NIL) (-836 1955675 1955901 1955942 "OPERCAT" 1956154 NIL OPERCAT (NIL T) -9 NIL 1956251 NIL) (-835 1955430 1955486 1955603 "OPERCAT-" 1955608 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-834 1952243 1954227 1954596 "ONECOMP" 1955094 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-833 1951548 1951663 1951837 "ONECOMP2" 1952115 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-832 1950967 1951073 1951203 "OMSERVER" 1951438 T OMSERVER (NIL) -7 NIL NIL NIL) (-831 1947829 1950407 1950447 "OMSAGG" 1950508 NIL OMSAGG (NIL T) -9 NIL 1950572 NIL) (-830 1946452 1946715 1946997 "OMPKG" 1947567 T OMPKG (NIL) -7 NIL NIL NIL) (-829 1945882 1945985 1946013 "OM" 1946312 T OM (NIL) -9 NIL NIL NIL) (-828 1944429 1945431 1945600 "OMLO" 1945763 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-827 1943389 1943536 1943756 "OMEXPR" 1944255 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-826 1942680 1942935 1943071 "OMERR" 1943273 T OMERR (NIL) -8 NIL NIL NIL) (-825 1941831 1942101 1942261 "OMERRK" 1942540 T OMERRK (NIL) -8 NIL NIL NIL) (-824 1941282 1941508 1941616 "OMENC" 1941743 T OMENC (NIL) -8 NIL NIL NIL) (-823 1935177 1936362 1937533 "OMDEV" 1940131 T OMDEV (NIL) -8 NIL NIL NIL) (-822 1934246 1934417 1934611 "OMCONN" 1935003 T OMCONN (NIL) -8 NIL NIL NIL) (-821 1932767 1933743 1933771 "OINTDOM" 1933776 T OINTDOM (NIL) -9 NIL 1933797 NIL) (-820 1930105 1931455 1931792 "OFMONOID" 1932462 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-819 1929516 1930042 1930087 "ODVAR" 1930092 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-818 1926939 1929261 1929416 "ODR" 1929421 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-817 1919520 1926715 1926841 "ODPOL" 1926846 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-816 1913342 1919392 1919497 "ODP" 1919502 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-815 1912108 1912323 1912598 "ODETOOLS" 1913116 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-814 1909075 1909733 1910449 "ODESYS" 1911441 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-813 1903957 1904865 1905890 "ODERTRIC" 1908150 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-812 1903383 1903465 1903659 "ODERED" 1903869 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-811 1900271 1900819 1901496 "ODERAT" 1902806 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-810 1897228 1897695 1898292 "ODEPRRIC" 1899800 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-809 1895171 1895767 1896253 "ODEPROB" 1896762 T ODEPROB (NIL) -8 NIL NIL NIL) (-808 1891691 1892176 1892823 "ODEPRIM" 1894650 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-807 1890940 1891042 1891302 "ODEPAL" 1891583 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-806 1887102 1887893 1888757 "ODEPACK" 1890096 T ODEPACK (NIL) -7 NIL NIL NIL) (-805 1886163 1886270 1886492 "ODEINT" 1886991 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-804 1880264 1881689 1883136 "ODEIFTBL" 1884736 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-803 1875662 1876448 1877400 "ODEEF" 1879423 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-802 1875011 1875100 1875323 "ODECONST" 1875567 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-801 1873136 1873797 1873825 "ODECAT" 1874430 T ODECAT (NIL) -9 NIL 1874961 NIL) (-800 1869991 1872841 1872963 "OCT" 1873046 NIL OCT (NIL T) -8 NIL NIL NIL) (-799 1869629 1869672 1869799 "OCTCT2" 1869942 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-798 1864278 1866713 1866753 "OC" 1867850 NIL OC (NIL T) -9 NIL 1868708 NIL) (-797 1861505 1862253 1863243 "OC-" 1863337 NIL OC- (NIL T T) -8 NIL NIL NIL) (-796 1860857 1861325 1861353 "OCAMON" 1861358 T OCAMON (NIL) -9 NIL 1861379 NIL) (-795 1860388 1860729 1860757 "OASGP" 1860762 T OASGP (NIL) -9 NIL 1860782 NIL) (-794 1859649 1860138 1860166 "OAMONS" 1860206 T OAMONS (NIL) -9 NIL 1860249 NIL) (-793 1859063 1859496 1859524 "OAMON" 1859529 T OAMON (NIL) -9 NIL 1859549 NIL) (-792 1858321 1858839 1858867 "OAGROUP" 1858872 T OAGROUP (NIL) -9 NIL 1858892 NIL) (-791 1858011 1858061 1858149 "NUMTUBE" 1858265 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-790 1851584 1853102 1854638 "NUMQUAD" 1856495 T NUMQUAD (NIL) -7 NIL NIL NIL) (-789 1847340 1848328 1849353 "NUMODE" 1850579 T NUMODE (NIL) -7 NIL NIL NIL) (-788 1844695 1845575 1845603 "NUMINT" 1846526 T NUMINT (NIL) -9 NIL 1847290 NIL) (-787 1843643 1843840 1844058 "NUMFMT" 1844497 T NUMFMT (NIL) -7 NIL NIL NIL) (-786 1830002 1832947 1835479 "NUMERIC" 1841150 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-785 1824372 1829451 1829546 "NTSCAT" 1829551 NIL NTSCAT (NIL T T T T) -9 NIL 1829590 NIL) (-784 1823566 1823731 1823924 "NTPOLFN" 1824211 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-783 1811643 1820391 1821203 "NSUP" 1822787 NIL NSUP (NIL T) -8 NIL NIL NIL) (-782 1811275 1811332 1811441 "NSUP2" 1811580 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-781 1801503 1811049 1811182 "NSMP" 1811187 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-780 1799935 1800236 1800593 "NREP" 1801191 NIL NREP (NIL T) -7 NIL NIL NIL) (-779 1798526 1798778 1799136 "NPCOEF" 1799678 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-778 1797592 1797707 1797923 "NORMRETR" 1798407 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-777 1795633 1795923 1796332 "NORMPK" 1797300 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-776 1795318 1795346 1795470 "NORMMA" 1795599 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-775 1795118 1795275 1795304 "NONE" 1795309 T NONE (NIL) -8 NIL NIL NIL) (-774 1794907 1794936 1795005 "NONE1" 1795082 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-773 1794404 1794466 1794645 "NODE1" 1794839 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-772 1792689 1793540 1793795 "NNI" 1794142 T NNI (NIL) -8 NIL NIL 1794377) (-771 1791109 1791422 1791786 "NLINSOL" 1792357 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-770 1787350 1788345 1789244 "NIPROB" 1790230 T NIPROB (NIL) -8 NIL NIL NIL) (-769 1786107 1786341 1786643 "NFINTBAS" 1787112 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-768 1785281 1785757 1785798 "NETCLT" 1785970 NIL NETCLT (NIL T) -9 NIL 1786052 NIL) (-767 1783989 1784220 1784501 "NCODIV" 1785049 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-766 1783751 1783788 1783863 "NCNTFRAC" 1783946 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-765 1781931 1782295 1782715 "NCEP" 1783376 NIL NCEP (NIL T) -7 NIL NIL NIL) (-764 1780782 1781555 1781583 "NASRING" 1781693 T NASRING (NIL) -9 NIL 1781773 NIL) (-763 1780577 1780621 1780715 "NASRING-" 1780720 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-762 1779684 1780209 1780237 "NARNG" 1780354 T NARNG (NIL) -9 NIL 1780445 NIL) (-761 1779376 1779443 1779577 "NARNG-" 1779582 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-760 1778255 1778462 1778697 "NAGSP" 1779161 T NAGSP (NIL) -7 NIL NIL NIL) (-759 1769527 1771211 1772884 "NAGS" 1776602 T NAGS (NIL) -7 NIL NIL NIL) (-758 1768075 1768383 1768714 "NAGF07" 1769216 T NAGF07 (NIL) -7 NIL NIL NIL) (-757 1762613 1763904 1765211 "NAGF04" 1766788 T NAGF04 (NIL) -7 NIL NIL NIL) (-756 1755581 1757195 1758828 "NAGF02" 1761000 T NAGF02 (NIL) -7 NIL NIL NIL) (-755 1750805 1751905 1753022 "NAGF01" 1754484 T NAGF01 (NIL) -7 NIL NIL NIL) (-754 1744433 1745999 1747584 "NAGE04" 1749240 T NAGE04 (NIL) -7 NIL NIL NIL) (-753 1735602 1737723 1739853 "NAGE02" 1742323 T NAGE02 (NIL) -7 NIL NIL NIL) (-752 1731555 1732502 1733466 "NAGE01" 1734658 T NAGE01 (NIL) -7 NIL NIL NIL) (-751 1729350 1729884 1730442 "NAGD03" 1731017 T NAGD03 (NIL) -7 NIL NIL NIL) (-750 1721100 1723028 1724982 "NAGD02" 1727416 T NAGD02 (NIL) -7 NIL NIL NIL) (-749 1714911 1716336 1717776 "NAGD01" 1719680 T NAGD01 (NIL) -7 NIL NIL NIL) (-748 1711120 1711942 1712779 "NAGC06" 1714094 T NAGC06 (NIL) -7 NIL NIL NIL) (-747 1709585 1709917 1710273 "NAGC05" 1710784 T NAGC05 (NIL) -7 NIL NIL NIL) (-746 1708961 1709080 1709224 "NAGC02" 1709461 T NAGC02 (NIL) -7 NIL NIL NIL) (-745 1707920 1708503 1708543 "NAALG" 1708622 NIL NAALG (NIL T) -9 NIL 1708683 NIL) (-744 1707755 1707784 1707874 "NAALG-" 1707879 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-743 1701705 1702813 1704000 "MULTSQFR" 1706651 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-742 1701024 1701099 1701283 "MULTFACT" 1701617 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-741 1693748 1697661 1697714 "MTSCAT" 1698784 NIL MTSCAT (NIL T T) -9 NIL 1699299 NIL) (-740 1693460 1693514 1693606 "MTHING" 1693688 NIL MTHING (NIL T) -7 NIL NIL NIL) (-739 1693252 1693285 1693345 "MSYSCMD" 1693420 T MSYSCMD (NIL) -7 NIL NIL NIL) (-738 1689334 1692007 1692327 "MSET" 1692965 NIL MSET (NIL T) -8 NIL NIL NIL) (-737 1686403 1688895 1688936 "MSETAGG" 1688941 NIL MSETAGG (NIL T) -9 NIL 1688975 NIL) (-736 1682244 1683782 1684527 "MRING" 1685703 NIL MRING (NIL T T) -8 NIL NIL NIL) (-735 1681810 1681877 1682008 "MRF2" 1682171 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-734 1681428 1681463 1681607 "MRATFAC" 1681769 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-733 1679040 1679335 1679766 "MPRFF" 1681133 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-732 1673337 1678894 1678991 "MPOLY" 1678996 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-731 1672827 1672862 1673070 "MPCPF" 1673296 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-730 1672341 1672384 1672568 "MPC3" 1672778 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-729 1671536 1671617 1671838 "MPC2" 1672256 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-728 1669837 1670174 1670564 "MONOTOOL" 1671196 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-727 1669062 1669379 1669407 "MONOID" 1669626 T MONOID (NIL) -9 NIL 1669773 NIL) (-726 1668608 1668727 1668908 "MONOID-" 1668913 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-725 1659083 1665034 1665093 "MONOGEN" 1665767 NIL MONOGEN (NIL T T) -9 NIL 1666223 NIL) (-724 1656301 1657036 1658036 "MONOGEN-" 1658155 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-723 1655134 1655580 1655608 "MONADWU" 1656000 T MONADWU (NIL) -9 NIL 1656238 NIL) (-722 1654506 1654665 1654913 "MONADWU-" 1654918 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-721 1653865 1654109 1654137 "MONAD" 1654344 T MONAD (NIL) -9 NIL 1654456 NIL) (-720 1653550 1653628 1653760 "MONAD-" 1653765 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-719 1651839 1652463 1652742 "MOEBIUS" 1653303 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-718 1651117 1651521 1651561 "MODULE" 1651566 NIL MODULE (NIL T) -9 NIL 1651605 NIL) (-717 1650685 1650781 1650971 "MODULE-" 1650976 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-716 1648365 1649049 1649376 "MODRING" 1650509 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-715 1645309 1646470 1646991 "MODOP" 1647894 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-714 1643897 1644376 1644653 "MODMONOM" 1645172 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-713 1633938 1642188 1642602 "MODMON" 1643534 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-712 1631094 1632782 1633058 "MODFIELD" 1633813 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-711 1630071 1630375 1630565 "MMLFORM" 1630924 T MMLFORM (NIL) -8 NIL NIL NIL) (-710 1629597 1629640 1629819 "MMAP" 1630022 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-709 1627676 1628443 1628484 "MLO" 1628907 NIL MLO (NIL T) -9 NIL 1629149 NIL) (-708 1625042 1625558 1626160 "MLIFT" 1627157 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-707 1624433 1624517 1624671 "MKUCFUNC" 1624953 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-706 1624032 1624102 1624225 "MKRECORD" 1624356 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-705 1623079 1623241 1623469 "MKFUNC" 1623843 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-704 1622467 1622571 1622727 "MKFLCFN" 1622962 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-703 1621744 1621846 1622031 "MKBCFUNC" 1622360 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-702 1618451 1621298 1621434 "MINT" 1621628 T MINT (NIL) -8 NIL NIL NIL) (-701 1617263 1617506 1617783 "MHROWRED" 1618206 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-700 1612642 1615798 1616203 "MFLOAT" 1616878 T MFLOAT (NIL) -8 NIL NIL NIL) (-699 1611999 1612075 1612246 "MFINFACT" 1612554 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-698 1608314 1609162 1610046 "MESH" 1611135 T MESH (NIL) -7 NIL NIL NIL) (-697 1606704 1607016 1607369 "MDDFACT" 1608001 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-696 1603499 1605863 1605904 "MDAGG" 1606159 NIL MDAGG (NIL T) -9 NIL 1606302 NIL) (-695 1593239 1602792 1602999 "MCMPLX" 1603312 T MCMPLX (NIL) -8 NIL NIL NIL) (-694 1592380 1592526 1592726 "MCDEN" 1593088 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-693 1590270 1590540 1590920 "MCALCFN" 1592110 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-692 1589195 1589435 1589668 "MAYBE" 1590076 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-691 1586807 1587330 1587892 "MATSTOR" 1588666 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-690 1582764 1586179 1586427 "MATRIX" 1586592 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-689 1578528 1579237 1579973 "MATLIN" 1582121 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-688 1568634 1571820 1571897 "MATCAT" 1576777 NIL MATCAT (NIL T T T) -9 NIL 1578194 NIL) (-687 1564990 1566011 1567367 "MATCAT-" 1567372 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-686 1563584 1563737 1564070 "MATCAT2" 1564825 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-685 1561696 1562020 1562404 "MAPPKG3" 1563259 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-684 1560677 1560850 1561072 "MAPPKG2" 1561520 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-683 1559176 1559460 1559787 "MAPPKG1" 1560383 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-682 1558255 1558582 1558759 "MAPPAST" 1559019 T MAPPAST (NIL) -8 NIL NIL NIL) (-681 1557866 1557924 1558047 "MAPHACK3" 1558191 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-680 1557458 1557519 1557633 "MAPHACK2" 1557798 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-679 1556895 1556999 1557141 "MAPHACK1" 1557349 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-678 1554974 1555595 1555899 "MAGMA" 1556623 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-677 1554453 1554698 1554789 "MACROAST" 1554903 T MACROAST (NIL) -8 NIL NIL NIL) (-676 1550871 1552692 1553153 "M3D" 1554025 NIL M3D (NIL T) -8 NIL NIL NIL) (-675 1544977 1549240 1549281 "LZSTAGG" 1550063 NIL LZSTAGG (NIL T) -9 NIL 1550358 NIL) (-674 1540934 1542108 1543565 "LZSTAGG-" 1543570 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-673 1538021 1538825 1539312 "LWORD" 1540479 NIL LWORD (NIL T) -8 NIL NIL NIL) (-672 1537597 1537825 1537900 "LSTAST" 1537966 T LSTAST (NIL) -8 NIL NIL NIL) (-671 1530763 1537368 1537502 "LSQM" 1537507 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-670 1529987 1530126 1530354 "LSPP" 1530618 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-669 1527799 1528100 1528556 "LSMP" 1529676 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-668 1524578 1525252 1525982 "LSMP1" 1527101 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-667 1518455 1523745 1523786 "LSAGG" 1523848 NIL LSAGG (NIL T) -9 NIL 1523926 NIL) (-666 1515150 1516074 1517287 "LSAGG-" 1517292 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-665 1512749 1514294 1514543 "LPOLY" 1514945 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-664 1512331 1512416 1512539 "LPEFRAC" 1512658 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-663 1510652 1511425 1511678 "LO" 1512163 NIL LO (NIL T T T) -8 NIL NIL NIL) (-662 1510304 1510416 1510444 "LOGIC" 1510555 T LOGIC (NIL) -9 NIL 1510636 NIL) (-661 1510166 1510189 1510260 "LOGIC-" 1510265 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-660 1509359 1509499 1509692 "LODOOPS" 1510022 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-659 1506782 1509275 1509341 "LODO" 1509346 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-658 1505320 1505555 1505908 "LODOF" 1506529 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-657 1501538 1503969 1504010 "LODOCAT" 1504448 NIL LODOCAT (NIL T) -9 NIL 1504659 NIL) (-656 1501271 1501329 1501456 "LODOCAT-" 1501461 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-655 1498591 1501112 1501230 "LODO2" 1501235 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-654 1496026 1498528 1498573 "LODO1" 1498578 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-653 1494907 1495072 1495377 "LODEEF" 1495849 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-652 1490146 1493037 1493078 "LNAGG" 1494025 NIL LNAGG (NIL T) -9 NIL 1494469 NIL) (-651 1489293 1489507 1489849 "LNAGG-" 1489854 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-650 1485429 1486218 1486857 "LMOPS" 1488708 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-649 1484832 1485220 1485261 "LMODULE" 1485266 NIL LMODULE (NIL T) -9 NIL 1485292 NIL) (-648 1482030 1484477 1484600 "LMDICT" 1484742 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-647 1481436 1481657 1481698 "LLINSET" 1481889 NIL LLINSET (NIL T) -9 NIL 1481980 NIL) (-646 1481135 1481344 1481404 "LITERAL" 1481409 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-645 1474298 1480069 1480373 "LIST" 1480864 NIL LIST (NIL T) -8 NIL NIL NIL) (-644 1473823 1473897 1474036 "LIST3" 1474218 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-643 1472830 1473008 1473236 "LIST2" 1473641 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-642 1470964 1471276 1471675 "LIST2MAP" 1472477 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-641 1470560 1470797 1470838 "LINSET" 1470843 NIL LINSET (NIL T) -9 NIL 1470877 NIL) (-640 1469221 1469891 1469932 "LINEXP" 1470187 NIL LINEXP (NIL T) -9 NIL 1470336 NIL) (-639 1467868 1468128 1468425 "LINDEP" 1468973 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-638 1464635 1465354 1466131 "LIMITRF" 1467123 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-637 1462938 1463234 1463643 "LIMITPS" 1464330 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-636 1457366 1462449 1462677 "LIE" 1462759 NIL LIE (NIL T T) -8 NIL NIL NIL) (-635 1456314 1456783 1456823 "LIECAT" 1456963 NIL LIECAT (NIL T) -9 NIL 1457114 NIL) (-634 1456155 1456182 1456270 "LIECAT-" 1456275 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-633 1448651 1455604 1455769 "LIB" 1456010 T LIB (NIL) -8 NIL NIL NIL) (-632 1444286 1445169 1446104 "LGROBP" 1447768 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-631 1442284 1442558 1442908 "LF" 1444007 NIL LF (NIL T T) -7 NIL NIL NIL) (-630 1441124 1441816 1441844 "LFCAT" 1442051 T LFCAT (NIL) -9 NIL 1442190 NIL) (-629 1438026 1438656 1439344 "LEXTRIPK" 1440488 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-628 1434770 1435596 1436099 "LEXP" 1437606 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-627 1434246 1434491 1434583 "LETAST" 1434698 T LETAST (NIL) -8 NIL NIL NIL) (-626 1432644 1432957 1433358 "LEADCDET" 1433928 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-625 1431834 1431908 1432137 "LAZM3PK" 1432565 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-624 1426751 1429911 1430449 "LAUPOL" 1431346 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-623 1426330 1426374 1426535 "LAPLACE" 1426701 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-622 1424269 1425431 1425682 "LA" 1426163 NIL LA (NIL T T T) -8 NIL NIL NIL) (-621 1423263 1423847 1423888 "LALG" 1423950 NIL LALG (NIL T) -9 NIL 1424009 NIL) (-620 1422977 1423036 1423172 "LALG-" 1423177 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-619 1422812 1422836 1422877 "KVTFROM" 1422939 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-618 1421735 1422179 1422364 "KTVLOGIC" 1422647 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-617 1421570 1421594 1421635 "KRCFROM" 1421697 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-616 1420474 1420661 1420960 "KOVACIC" 1421370 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-615 1420309 1420333 1420374 "KONVERT" 1420436 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-614 1420144 1420168 1420209 "KOERCE" 1420271 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-613 1417974 1418737 1419114 "KERNEL" 1419800 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-612 1417470 1417551 1417683 "KERNEL2" 1417888 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-611 1411240 1416009 1416063 "KDAGG" 1416440 NIL KDAGG (NIL T T) -9 NIL 1416646 NIL) (-610 1410769 1410893 1411098 "KDAGG-" 1411103 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-609 1403917 1410430 1410585 "KAFILE" 1410647 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-608 1398345 1403428 1403656 "JORDAN" 1403738 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-607 1397724 1397994 1398115 "JOINAST" 1398244 T JOINAST (NIL) -8 NIL NIL NIL) (-606 1397570 1397629 1397684 "JAVACODE" 1397689 T JAVACODE (NIL) -8 NIL NIL NIL) (-605 1393822 1395775 1395829 "IXAGG" 1396758 NIL IXAGG (NIL T T) -9 NIL 1397217 NIL) (-604 1392741 1393047 1393466 "IXAGG-" 1393471 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-603 1388271 1392663 1392722 "IVECTOR" 1392727 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-602 1387037 1387274 1387540 "ITUPLE" 1388038 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-601 1385539 1385716 1386011 "ITRIGMNP" 1386859 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-600 1384284 1384488 1384771 "ITFUN3" 1385315 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-599 1383916 1383973 1384082 "ITFUN2" 1384221 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-598 1381877 1382936 1383214 "ITAYLOR" 1383671 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-597 1370822 1376014 1377177 "ISUPS" 1380747 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-596 1369926 1370066 1370302 "ISUMP" 1370669 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-595 1365301 1369871 1369912 "ISTRING" 1369917 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-594 1364777 1365022 1365114 "ISAST" 1365229 T ISAST (NIL) -8 NIL NIL NIL) (-593 1363986 1364068 1364284 "IRURPK" 1364691 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-592 1362922 1363123 1363363 "IRSN" 1363766 T IRSN (NIL) -7 NIL NIL NIL) (-591 1360993 1361348 1361777 "IRRF2F" 1362560 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-590 1360740 1360778 1360854 "IRREDFFX" 1360949 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-589 1359355 1359614 1359913 "IROOT" 1360473 NIL IROOT (NIL T) -7 NIL NIL NIL) (-588 1355959 1357039 1357731 "IR" 1358695 NIL IR (NIL T) -8 NIL NIL NIL) (-587 1353572 1354067 1354633 "IR2" 1355437 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-586 1352672 1352785 1352999 "IR2F" 1353455 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-585 1352463 1352497 1352557 "IPRNTPK" 1352632 T IPRNTPK (NIL) -7 NIL NIL NIL) (-584 1349044 1352352 1352421 "IPF" 1352426 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-583 1347371 1348969 1349026 "IPADIC" 1349031 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-582 1346683 1346931 1347061 "IP4ADDR" 1347261 T IP4ADDR (NIL) -8 NIL NIL NIL) (-581 1346156 1346387 1346497 "IOMODE" 1346593 T IOMODE (NIL) -8 NIL NIL NIL) (-580 1345229 1345753 1345880 "IOBFILE" 1346049 T IOBFILE (NIL) -8 NIL NIL NIL) (-579 1344717 1345133 1345161 "IOBCON" 1345166 T IOBCON (NIL) -9 NIL 1345187 NIL) (-578 1344228 1344286 1344469 "INVLAPLA" 1344653 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-577 1333876 1336230 1338616 "INTTR" 1341892 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-576 1330211 1330953 1331818 "INTTOOLS" 1333061 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-575 1329797 1329888 1330005 "INTSLPE" 1330114 T INTSLPE (NIL) -7 NIL NIL NIL) (-574 1327750 1329720 1329779 "INTRVL" 1329784 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-573 1325352 1325864 1326439 "INTRF" 1327235 NIL INTRF (NIL T) -7 NIL NIL NIL) (-572 1324763 1324860 1325002 "INTRET" 1325250 NIL INTRET (NIL T) -7 NIL NIL NIL) (-571 1322760 1323149 1323619 "INTRAT" 1324371 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-570 1320023 1320606 1321225 "INTPM" 1322245 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-569 1316768 1317367 1318105 "INTPAF" 1319409 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-568 1311947 1312909 1313960 "INTPACK" 1315737 T INTPACK (NIL) -7 NIL NIL NIL) (-567 1308895 1311744 1311853 "INT" 1311858 T INT (NIL) -8 NIL NIL NIL) (-566 1308147 1308299 1308507 "INTHERTR" 1308737 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-565 1307586 1307666 1307854 "INTHERAL" 1308061 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-564 1305432 1305875 1306332 "INTHEORY" 1307149 T INTHEORY (NIL) -7 NIL NIL NIL) (-563 1296838 1298459 1300231 "INTG0" 1303784 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-562 1277411 1282201 1287011 "INTFTBL" 1292048 T INTFTBL (NIL) -8 NIL NIL NIL) (-561 1276660 1276798 1276971 "INTFACT" 1277270 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-560 1274087 1274533 1275090 "INTEF" 1276214 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-559 1272454 1273193 1273221 "INTDOM" 1273522 T INTDOM (NIL) -9 NIL 1273729 NIL) (-558 1271823 1271997 1272239 "INTDOM-" 1272244 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-557 1268211 1270139 1270193 "INTCAT" 1270992 NIL INTCAT (NIL T) -9 NIL 1271313 NIL) (-556 1267683 1267786 1267914 "INTBIT" 1268103 T INTBIT (NIL) -7 NIL NIL NIL) (-555 1266382 1266536 1266843 "INTALG" 1267528 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-554 1265865 1265955 1266112 "INTAF" 1266286 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-553 1259208 1265675 1265815 "INTABL" 1265820 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-552 1258549 1259015 1259080 "INT8" 1259114 T INT8 (NIL) -8 NIL NIL 1259159) (-551 1257889 1258355 1258420 "INT64" 1258454 T INT64 (NIL) -8 NIL NIL 1258499) (-550 1257229 1257695 1257760 "INT32" 1257794 T INT32 (NIL) -8 NIL NIL 1257839) (-549 1256569 1257035 1257100 "INT16" 1257134 T INT16 (NIL) -8 NIL NIL 1257179) (-548 1251479 1254192 1254220 "INS" 1255154 T INS (NIL) -9 NIL 1255819 NIL) (-547 1248719 1249490 1250464 "INS-" 1250537 NIL INS- (NIL T) -8 NIL NIL NIL) (-546 1247494 1247721 1248019 "INPSIGN" 1248472 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-545 1246612 1246729 1246926 "INPRODPF" 1247374 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-544 1245506 1245623 1245860 "INPRODFF" 1246492 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-543 1244506 1244658 1244918 "INNMFACT" 1245342 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-542 1243703 1243800 1243988 "INMODGCD" 1244405 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-541 1242211 1242456 1242780 "INFSP" 1243448 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-540 1241395 1241512 1241695 "INFPROD0" 1242091 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-539 1238250 1239460 1239975 "INFORM" 1240888 T INFORM (NIL) -8 NIL NIL NIL) (-538 1237860 1237920 1238018 "INFORM1" 1238185 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-537 1237383 1237472 1237586 "INFINITY" 1237766 T INFINITY (NIL) -7 NIL NIL NIL) (-536 1236559 1237103 1237204 "INETCLTS" 1237302 T INETCLTS (NIL) -8 NIL NIL NIL) (-535 1235175 1235425 1235746 "INEP" 1236307 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-534 1234424 1235072 1235137 "INDE" 1235142 NIL INDE (NIL T) -8 NIL NIL NIL) (-533 1233988 1234056 1234173 "INCRMAPS" 1234351 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-532 1232806 1233257 1233463 "INBFILE" 1233802 T INBFILE (NIL) -8 NIL NIL NIL) (-531 1228105 1229042 1229986 "INBFF" 1231894 NIL INBFF (NIL T) -7 NIL NIL NIL) (-530 1227013 1227282 1227310 "INBCON" 1227823 T INBCON (NIL) -9 NIL 1228089 NIL) (-529 1226265 1226488 1226764 "INBCON-" 1226769 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-528 1225744 1225989 1226080 "INAST" 1226194 T INAST (NIL) -8 NIL NIL NIL) (-527 1225171 1225423 1225529 "IMPTAST" 1225658 T IMPTAST (NIL) -8 NIL NIL NIL) (-526 1221617 1225015 1225119 "IMATRIX" 1225124 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-525 1220329 1220452 1220767 "IMATQF" 1221473 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-524 1218549 1218776 1219113 "IMATLIN" 1220085 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-523 1213127 1218473 1218531 "ILIST" 1218536 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-522 1211032 1212987 1213100 "IIARRAY2" 1213105 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-521 1206430 1210943 1211007 "IFF" 1211012 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-520 1205777 1206047 1206163 "IFAST" 1206334 T IFAST (NIL) -8 NIL NIL NIL) (-519 1200772 1205069 1205257 "IFARRAY" 1205634 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-518 1199952 1200676 1200749 "IFAMON" 1200754 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-517 1199536 1199601 1199655 "IEVALAB" 1199862 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-516 1199211 1199279 1199439 "IEVALAB-" 1199444 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-515 1198842 1199125 1199188 "IDPO" 1199193 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-514 1198092 1198731 1198806 "IDPOAMS" 1198811 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-513 1197399 1197981 1198056 "IDPOAM" 1198061 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-512 1196458 1196734 1196787 "IDPC" 1197200 NIL IDPC (NIL T T) -9 NIL 1197349 NIL) (-511 1195927 1196350 1196423 "IDPAM" 1196428 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-510 1195303 1195819 1195892 "IDPAG" 1195897 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-509 1194948 1195139 1195214 "IDENT" 1195248 T IDENT (NIL) -8 NIL NIL NIL) (-508 1191203 1192051 1192946 "IDECOMP" 1194105 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-507 1184041 1185126 1186173 "IDEAL" 1190239 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-506 1183205 1183317 1183516 "ICDEN" 1183925 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-505 1182276 1182685 1182832 "ICARD" 1183078 T ICARD (NIL) -8 NIL NIL NIL) (-504 1180336 1180649 1181054 "IBPTOOLS" 1181953 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-503 1175943 1179956 1180069 "IBITS" 1180255 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-502 1172666 1173242 1173937 "IBATOOL" 1175360 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-501 1170445 1170907 1171440 "IBACHIN" 1172201 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-500 1168274 1170291 1170394 "IARRAY2" 1170399 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-499 1164380 1168200 1168257 "IARRAY1" 1168262 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-498 1158489 1162792 1163273 "IAN" 1163919 T IAN (NIL) -8 NIL NIL NIL) (-497 1158000 1158057 1158230 "IALGFACT" 1158426 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-496 1157528 1157641 1157669 "HYPCAT" 1157876 T HYPCAT (NIL) -9 NIL NIL NIL) (-495 1157066 1157183 1157369 "HYPCAT-" 1157374 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-494 1156661 1156861 1156944 "HOSTNAME" 1157003 T HOSTNAME (NIL) -8 NIL NIL NIL) (-493 1156506 1156543 1156584 "HOMOTOP" 1156589 NIL HOMOTOP (NIL T) -9 NIL 1156622 NIL) (-492 1153138 1154516 1154557 "HOAGG" 1155538 NIL HOAGG (NIL T) -9 NIL 1156217 NIL) (-491 1151732 1152131 1152657 "HOAGG-" 1152662 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-490 1145736 1151327 1151476 "HEXADEC" 1151603 T HEXADEC (NIL) -8 NIL NIL NIL) (-489 1144483 1144706 1144969 "HEUGCD" 1145513 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-488 1143559 1144320 1144450 "HELLFDIV" 1144455 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-487 1141738 1143336 1143424 "HEAP" 1143503 NIL HEAP (NIL T) -8 NIL NIL NIL) (-486 1141001 1141290 1141424 "HEADAST" 1141624 T HEADAST (NIL) -8 NIL NIL NIL) (-485 1134867 1140916 1140978 "HDP" 1140983 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-484 1128855 1134502 1134654 "HDMP" 1134768 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-483 1128179 1128319 1128483 "HB" 1128711 T HB (NIL) -7 NIL NIL NIL) (-482 1121565 1128025 1128129 "HASHTBL" 1128134 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-481 1121041 1121286 1121378 "HASAST" 1121493 T HASAST (NIL) -8 NIL NIL NIL) (-480 1118819 1120663 1120845 "HACKPI" 1120879 T HACKPI (NIL) -8 NIL NIL NIL) (-479 1114487 1118672 1118785 "GTSET" 1118790 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-478 1107902 1114365 1114463 "GSTBL" 1114468 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-477 1100180 1106933 1107198 "GSERIES" 1107693 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-476 1099321 1099738 1099766 "GROUP" 1099969 T GROUP (NIL) -9 NIL 1100103 NIL) (-475 1098687 1098846 1099097 "GROUP-" 1099102 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-474 1097054 1097375 1097762 "GROEBSOL" 1098364 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-473 1095968 1096256 1096307 "GRMOD" 1096836 NIL GRMOD (NIL T T) -9 NIL 1097004 NIL) (-472 1095736 1095772 1095900 "GRMOD-" 1095905 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-471 1091026 1092090 1093090 "GRIMAGE" 1094756 T GRIMAGE (NIL) -8 NIL NIL NIL) (-470 1089492 1089753 1090077 "GRDEF" 1090722 T GRDEF (NIL) -7 NIL NIL NIL) (-469 1088936 1089052 1089193 "GRAY" 1089371 T GRAY (NIL) -7 NIL NIL NIL) (-468 1088123 1088529 1088580 "GRALG" 1088733 NIL GRALG (NIL T T) -9 NIL 1088826 NIL) (-467 1087784 1087857 1088020 "GRALG-" 1088025 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-466 1084561 1087369 1087547 "GPOLSET" 1087691 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-465 1083915 1083972 1084230 "GOSPER" 1084498 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-464 1079647 1080353 1080879 "GMODPOL" 1083614 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-463 1078652 1078836 1079074 "GHENSEL" 1079459 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-462 1072808 1073651 1074671 "GENUPS" 1077736 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-461 1072505 1072556 1072645 "GENUFACT" 1072751 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-460 1071917 1071994 1072159 "GENPGCD" 1072423 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-459 1071391 1071426 1071639 "GENMFACT" 1071876 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-458 1069957 1070214 1070521 "GENEEZ" 1071134 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-457 1064103 1069568 1069730 "GDMP" 1069880 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-456 1053445 1057874 1058980 "GCNAALG" 1063086 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-455 1051772 1052634 1052662 "GCDDOM" 1052917 T GCDDOM (NIL) -9 NIL 1053074 NIL) (-454 1051242 1051369 1051584 "GCDDOM-" 1051589 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-453 1049914 1050099 1050403 "GB" 1051021 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-452 1038530 1040860 1043252 "GBINTERN" 1047605 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-451 1036367 1036659 1037080 "GBF" 1038205 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-450 1035148 1035313 1035580 "GBEUCLID" 1036183 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-449 1034497 1034622 1034771 "GAUSSFAC" 1035019 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-448 1032864 1033166 1033480 "GALUTIL" 1034216 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-447 1031172 1031446 1031770 "GALPOLYU" 1032591 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-446 1028537 1028827 1029234 "GALFACTU" 1030869 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-445 1020342 1021842 1023450 "GALFACT" 1026969 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-444 1017730 1018388 1018416 "FVFUN" 1019572 T FVFUN (NIL) -9 NIL 1020292 NIL) (-443 1016996 1017178 1017206 "FVC" 1017497 T FVC (NIL) -9 NIL 1017680 NIL) (-442 1016639 1016821 1016889 "FUNDESC" 1016948 T FUNDESC (NIL) -8 NIL NIL NIL) (-441 1016254 1016436 1016517 "FUNCTION" 1016591 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-440 1013998 1014576 1015042 "FT" 1015808 T FT (NIL) -8 NIL NIL NIL) (-439 1012789 1013299 1013502 "FTEM" 1013815 T FTEM (NIL) -8 NIL NIL NIL) (-438 1011080 1011369 1011766 "FSUPFACT" 1012480 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-437 1009477 1009766 1010098 "FST" 1010768 T FST (NIL) -8 NIL NIL NIL) (-436 1008676 1008782 1008970 "FSRED" 1009359 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-435 1007375 1007631 1007978 "FSPRMELT" 1008391 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-434 1004681 1005119 1005605 "FSPECF" 1006938 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-433 986319 994650 994691 "FS" 998575 NIL FS (NIL T) -9 NIL 1000864 NIL) (-432 974962 977955 982012 "FS-" 982312 NIL FS- (NIL T T) -8 NIL NIL NIL) (-431 974490 974544 974714 "FSINT" 974903 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-430 972782 973483 973786 "FSERIES" 974269 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-429 971824 971940 972164 "FSCINT" 972662 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-428 968032 970768 970809 "FSAGG" 971179 NIL FSAGG (NIL T) -9 NIL 971438 NIL) (-427 965794 966395 967191 "FSAGG-" 967286 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-426 964836 964979 965206 "FSAGG2" 965647 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-425 962518 962798 963345 "FS2UPS" 964554 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-424 962152 962195 962324 "FS2" 962469 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-423 961030 961201 961503 "FS2EXPXP" 961977 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-422 960456 960571 960723 "FRUTIL" 960910 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-421 951869 955951 957309 "FR" 959130 NIL FR (NIL T) -8 NIL NIL NIL) (-420 946838 949512 949552 "FRNAALG" 950948 NIL FRNAALG (NIL T) -9 NIL 951555 NIL) (-419 942511 943587 944862 "FRNAALG-" 945612 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-418 942149 942192 942319 "FRNAAF2" 942462 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-417 940529 941003 941298 "FRMOD" 941961 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-416 938280 938912 939229 "FRIDEAL" 940320 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-415 937475 937562 937851 "FRIDEAL2" 938187 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-414 936608 937022 937063 "FRETRCT" 937068 NIL FRETRCT (NIL T) -9 NIL 937244 NIL) (-413 935720 935951 936302 "FRETRCT-" 936307 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-412 932808 934018 934077 "FRAMALG" 934959 NIL FRAMALG (NIL T T) -9 NIL 935251 NIL) (-411 930942 931397 932027 "FRAMALG-" 932250 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-410 924863 930417 930693 "FRAC" 930698 NIL FRAC (NIL T) -8 NIL NIL NIL) (-409 924499 924556 924663 "FRAC2" 924800 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-408 924135 924192 924299 "FR2" 924436 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-407 918648 921541 921569 "FPS" 922688 T FPS (NIL) -9 NIL 923245 NIL) (-406 918097 918206 918370 "FPS-" 918516 NIL FPS- (NIL T) -8 NIL NIL NIL) (-405 915399 917068 917096 "FPC" 917321 T FPC (NIL) -9 NIL 917463 NIL) (-404 915192 915232 915329 "FPC-" 915334 NIL FPC- (NIL T) -8 NIL NIL NIL) (-403 913982 914680 914721 "FPATMAB" 914726 NIL FPATMAB (NIL T) -9 NIL 914878 NIL) (-402 911655 912158 912584 "FPARFRAC" 913619 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-401 907048 907547 908229 "FORTRAN" 911087 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-400 904764 905264 905803 "FORT" 906529 T FORT (NIL) -7 NIL NIL NIL) (-399 902440 903002 903030 "FORTFN" 904090 T FORTFN (NIL) -9 NIL 904714 NIL) (-398 902204 902254 902282 "FORTCAT" 902341 T FORTCAT (NIL) -9 NIL 902403 NIL) (-397 900310 900820 901210 "FORMULA" 901834 T FORMULA (NIL) -8 NIL NIL NIL) (-396 900098 900128 900197 "FORMULA1" 900274 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-395 899621 899673 899846 "FORDER" 900040 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-394 898717 898881 899074 "FOP" 899448 T FOP (NIL) -7 NIL NIL NIL) (-393 897298 897997 898171 "FNLA" 898599 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-392 896027 896442 896470 "FNCAT" 896930 T FNCAT (NIL) -9 NIL 897190 NIL) (-391 895566 895986 896014 "FNAME" 896019 T FNAME (NIL) -8 NIL NIL NIL) (-390 894129 895092 895120 "FMTC" 895125 T FMTC (NIL) -9 NIL 895161 NIL) (-389 892875 894065 894111 "FMONOID" 894116 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-388 889703 890871 890912 "FMONCAT" 892129 NIL FMONCAT (NIL T) -9 NIL 892734 NIL) (-387 888895 889445 889594 "FM" 889599 NIL FM (NIL T T) -8 NIL NIL NIL) (-386 886319 886965 886993 "FMFUN" 888137 T FMFUN (NIL) -9 NIL 888845 NIL) (-385 885588 885769 885797 "FMC" 886087 T FMC (NIL) -9 NIL 886269 NIL) (-384 882667 883527 883581 "FMCAT" 884776 NIL FMCAT (NIL T T) -9 NIL 885271 NIL) (-383 881533 882433 882533 "FM1" 882612 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-382 879307 879723 880217 "FLOATRP" 881084 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-381 872882 877036 877657 "FLOAT" 878706 T FLOAT (NIL) -8 NIL NIL NIL) (-380 870320 870820 871398 "FLOATCP" 872349 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-379 869060 869898 869939 "FLINEXP" 869944 NIL FLINEXP (NIL T) -9 NIL 870037 NIL) (-378 868214 868449 868777 "FLINEXP-" 868782 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-377 867290 867434 867658 "FLASORT" 868066 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-376 864406 865274 865326 "FLALG" 866553 NIL FLALG (NIL T T) -9 NIL 867020 NIL) (-375 858142 861892 861933 "FLAGG" 863195 NIL FLAGG (NIL T) -9 NIL 863847 NIL) (-374 856868 857207 857697 "FLAGG-" 857702 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-373 855910 856053 856280 "FLAGG2" 856721 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-372 852761 853769 853828 "FINRALG" 854956 NIL FINRALG (NIL T T) -9 NIL 855464 NIL) (-371 851921 852150 852489 "FINRALG-" 852494 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-370 851301 851540 851568 "FINITE" 851764 T FINITE (NIL) -9 NIL 851871 NIL) (-369 843658 845845 845885 "FINAALG" 849552 NIL FINAALG (NIL T) -9 NIL 851005 NIL) (-368 838990 840040 841184 "FINAALG-" 842563 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-367 838358 838745 838848 "FILE" 838920 NIL FILE (NIL T) -8 NIL NIL NIL) (-366 837016 837354 837408 "FILECAT" 838092 NIL FILECAT (NIL T T) -9 NIL 838308 NIL) (-365 834732 836260 836288 "FIELD" 836328 T FIELD (NIL) -9 NIL 836408 NIL) (-364 833352 833737 834248 "FIELD-" 834253 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-363 831202 831987 832334 "FGROUP" 833038 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-362 830292 830456 830676 "FGLMICPK" 831034 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-361 826124 830217 830274 "FFX" 830279 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-360 825725 825786 825921 "FFSLPE" 826057 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-359 821714 822497 823293 "FFPOLY" 824961 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-358 821218 821254 821463 "FFPOLY2" 821672 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-357 817061 821137 821200 "FFP" 821205 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-356 812459 816972 817036 "FF" 817041 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-355 807585 811802 811992 "FFNBX" 812313 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-354 802514 806720 806978 "FFNBP" 807439 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-353 797147 801798 802009 "FFNB" 802347 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-352 795979 796177 796492 "FFINTBAS" 796944 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-351 792048 794268 794296 "FFIELDC" 794916 T FFIELDC (NIL) -9 NIL 795292 NIL) (-350 790710 791081 791578 "FFIELDC-" 791583 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-349 790279 790325 790449 "FFHOM" 790652 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-348 787974 788461 788978 "FFF" 789794 NIL FFF (NIL T) -7 NIL NIL NIL) (-347 783592 787716 787817 "FFCGX" 787917 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-346 779213 783324 783431 "FFCGP" 783535 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-345 774396 778940 779048 "FFCG" 779149 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-344 755792 764873 764959 "FFCAT" 770124 NIL FFCAT (NIL T T T) -9 NIL 771575 NIL) (-343 750990 752037 753351 "FFCAT-" 754581 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-342 750401 750444 750679 "FFCAT2" 750941 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-341 739722 743373 744593 "FEXPR" 749253 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-340 738722 739157 739198 "FEVALAB" 739282 NIL FEVALAB (NIL T) -9 NIL 739543 NIL) (-339 737881 738091 738429 "FEVALAB-" 738434 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-338 736447 737264 737467 "FDIV" 737780 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-337 733467 734208 734323 "FDIVCAT" 735891 NIL FDIVCAT (NIL T T T T) -9 NIL 736328 NIL) (-336 733229 733256 733426 "FDIVCAT-" 733431 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-335 732449 732536 732813 "FDIV2" 733136 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-334 731423 731744 731946 "FCTRDATA" 732267 T FCTRDATA (NIL) -8 NIL NIL NIL) (-333 730109 730368 730657 "FCPAK1" 731154 T FCPAK1 (NIL) -7 NIL NIL NIL) (-332 729208 729609 729750 "FCOMP" 730000 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-331 712910 716358 719896 "FC" 725690 T FC (NIL) -8 NIL NIL NIL) (-330 705273 709301 709341 "FAXF" 711143 NIL FAXF (NIL T) -9 NIL 711835 NIL) (-329 702549 703207 704032 "FAXF-" 704497 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-328 697601 701925 702101 "FARRAY" 702406 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-327 692495 694562 694615 "FAMR" 695638 NIL FAMR (NIL T T) -9 NIL 696098 NIL) (-326 691385 691687 692122 "FAMR-" 692127 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-325 690554 691307 691360 "FAMONOID" 691365 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-324 688340 689050 689103 "FAMONC" 690044 NIL FAMONC (NIL T T) -9 NIL 690430 NIL) (-323 687004 688094 688231 "FAGROUP" 688236 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-322 684799 685118 685521 "FACUTIL" 686685 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-321 683898 684083 684305 "FACTFUNC" 684609 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-320 676320 683201 683400 "EXPUPXS" 683754 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-319 673803 674343 674929 "EXPRTUBE" 675754 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-318 670074 670666 671396 "EXPRODE" 673142 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-317 655559 668723 669152 "EXPR" 669678 NIL EXPR (NIL T) -8 NIL NIL NIL) (-316 650113 650700 651506 "EXPR2UPS" 654857 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-315 649745 649802 649911 "EXPR2" 650050 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-314 641135 648898 649188 "EXPEXPAN" 649582 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-313 640935 641092 641121 "EXIT" 641126 T EXIT (NIL) -8 NIL NIL NIL) (-312 640415 640659 640750 "EXITAST" 640864 T EXITAST (NIL) -8 NIL NIL NIL) (-311 640042 640104 640217 "EVALCYC" 640347 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-310 639583 639701 639742 "EVALAB" 639912 NIL EVALAB (NIL T) -9 NIL 640016 NIL) (-309 639064 639186 639407 "EVALAB-" 639412 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-308 636432 637734 637762 "EUCDOM" 638317 T EUCDOM (NIL) -9 NIL 638667 NIL) (-307 634837 635279 635869 "EUCDOM-" 635874 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-306 622375 625135 627885 "ESTOOLS" 632107 T ESTOOLS (NIL) -7 NIL NIL NIL) (-305 622007 622064 622173 "ESTOOLS2" 622312 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-304 621758 621800 621880 "ESTOOLS1" 621959 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-303 615795 617403 617431 "ES" 620199 T ES (NIL) -9 NIL 621609 NIL) (-302 610742 612029 613846 "ES-" 614010 NIL ES- (NIL T) -8 NIL NIL NIL) (-301 607116 607877 608657 "ESCONT" 609982 T ESCONT (NIL) -7 NIL NIL NIL) (-300 606861 606893 606975 "ESCONT1" 607078 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-299 606536 606586 606686 "ES2" 606805 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-298 606166 606224 606333 "ES1" 606472 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-297 605382 605511 605687 "ERROR" 606010 T ERROR (NIL) -7 NIL NIL NIL) (-296 598774 605241 605332 "EQTBL" 605337 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-295 591277 594088 595537 "EQ" 597358 NIL -2098 (NIL T) -8 NIL NIL NIL) (-294 590909 590966 591075 "EQ2" 591214 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-293 586198 587247 588340 "EP" 589848 NIL EP (NIL T) -7 NIL NIL NIL) (-292 584798 585089 585395 "ENV" 585912 T ENV (NIL) -8 NIL NIL NIL) (-291 583892 584446 584474 "ENTIRER" 584479 T ENTIRER (NIL) -9 NIL 584525 NIL) (-290 580359 581847 582217 "EMR" 583691 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-289 579503 579688 579742 "ELTAGG" 580122 NIL ELTAGG (NIL T T) -9 NIL 580333 NIL) (-288 579222 579284 579425 "ELTAGG-" 579430 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-287 579011 579040 579094 "ELTAB" 579178 NIL ELTAB (NIL T T) -9 NIL NIL NIL) (-286 578137 578283 578482 "ELFUTS" 578862 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-285 577879 577935 577963 "ELEMFUN" 578068 T ELEMFUN (NIL) -9 NIL NIL NIL) (-284 577749 577770 577838 "ELEMFUN-" 577843 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-283 572593 575849 575890 "ELAGG" 576830 NIL ELAGG (NIL T) -9 NIL 577293 NIL) (-282 570878 571312 571975 "ELAGG-" 571980 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-281 569539 569818 570112 "ELABEXPR" 570604 T ELABEXPR (NIL) -8 NIL NIL NIL) (-280 562403 564206 565033 "EFUPXS" 568815 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-279 555853 557654 558464 "EFULS" 561679 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-278 553338 553696 554168 "EFSTRUC" 555485 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-277 543129 544695 546243 "EF" 551853 NIL EF (NIL T T) -7 NIL NIL NIL) (-276 542203 542614 542763 "EAB" 543000 T EAB (NIL) -8 NIL NIL NIL) (-275 541385 542162 542190 "E04UCFA" 542195 T E04UCFA (NIL) -8 NIL NIL NIL) (-274 540567 541344 541372 "E04NAFA" 541377 T E04NAFA (NIL) -8 NIL NIL NIL) (-273 539749 540526 540554 "E04MBFA" 540559 T E04MBFA (NIL) -8 NIL NIL NIL) (-272 538931 539708 539736 "E04JAFA" 539741 T E04JAFA (NIL) -8 NIL NIL NIL) (-271 538115 538890 538918 "E04GCFA" 538923 T E04GCFA (NIL) -8 NIL NIL NIL) (-270 537299 538074 538102 "E04FDFA" 538107 T E04FDFA (NIL) -8 NIL NIL NIL) (-269 536481 537258 537286 "E04DGFA" 537291 T E04DGFA (NIL) -8 NIL NIL NIL) (-268 530654 532006 533370 "E04AGNT" 535137 T E04AGNT (NIL) -7 NIL NIL NIL) (-267 529334 529840 529880 "DVARCAT" 530355 NIL DVARCAT (NIL T) -9 NIL 530554 NIL) (-266 528538 528750 529064 "DVARCAT-" 529069 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-265 521675 528337 528466 "DSMP" 528471 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-264 516456 517620 518688 "DROPT" 520627 T DROPT (NIL) -8 NIL NIL NIL) (-263 516121 516180 516278 "DROPT1" 516391 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-262 511236 512362 513499 "DROPT0" 515004 T DROPT0 (NIL) -7 NIL NIL NIL) (-261 509581 509906 510292 "DRAWPT" 510870 T DRAWPT (NIL) -7 NIL NIL NIL) (-260 504168 505091 506170 "DRAW" 508555 NIL DRAW (NIL T) -7 NIL NIL NIL) (-259 503801 503854 503972 "DRAWHACK" 504109 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-258 502532 502801 503092 "DRAWCX" 503530 T DRAWCX (NIL) -7 NIL NIL NIL) (-257 502047 502116 502267 "DRAWCURV" 502458 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-256 492515 494477 496592 "DRAWCFUN" 499952 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-255 489281 491210 491251 "DQAGG" 491880 NIL DQAGG (NIL T) -9 NIL 492153 NIL) (-254 477405 483874 483957 "DPOLCAT" 485809 NIL DPOLCAT (NIL T T T T) -9 NIL 486354 NIL) (-253 472241 473590 475548 "DPOLCAT-" 475553 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-252 465363 472102 472200 "DPMO" 472205 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-251 458388 465143 465310 "DPMM" 465315 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-250 457866 458080 458178 "DOMTMPLT" 458310 T DOMTMPLT (NIL) -8 NIL NIL NIL) (-249 457299 457668 457748 "DOMCTOR" 457806 T DOMCTOR (NIL) -8 NIL NIL NIL) (-248 456511 456779 456930 "DOMAIN" 457168 T DOMAIN (NIL) -8 NIL NIL NIL) (-247 450499 456146 456298 "DMP" 456412 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-246 450099 450155 450299 "DLP" 450437 NIL DLP (NIL T) -7 NIL NIL NIL) (-245 443921 449426 449616 "DLIST" 449941 NIL DLIST (NIL T) -8 NIL NIL NIL) (-244 440718 442774 442815 "DLAGG" 443365 NIL DLAGG (NIL T) -9 NIL 443595 NIL) (-243 439394 440058 440086 "DIVRING" 440178 T DIVRING (NIL) -9 NIL 440261 NIL) (-242 438631 438821 439121 "DIVRING-" 439126 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-241 436733 437090 437496 "DISPLAY" 438245 T DISPLAY (NIL) -7 NIL NIL NIL) (-240 430621 436647 436710 "DIRPROD" 436715 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-239 429469 429672 429937 "DIRPROD2" 430414 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-238 418244 424250 424303 "DIRPCAT" 424713 NIL DIRPCAT (NIL NIL T) -9 NIL 425553 NIL) (-237 415570 416212 417093 "DIRPCAT-" 417430 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-236 414857 415017 415203 "DIOSP" 415404 T DIOSP (NIL) -7 NIL NIL NIL) (-235 411512 413769 413810 "DIOPS" 414244 NIL DIOPS (NIL T) -9 NIL 414473 NIL) (-234 411061 411175 411366 "DIOPS-" 411371 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-233 409884 410512 410540 "DIFRING" 410727 T DIFRING (NIL) -9 NIL 410837 NIL) (-232 409530 409607 409759 "DIFRING-" 409764 NIL DIFRING- (NIL T) -8 NIL NIL NIL) (-231 407266 408538 408579 "DIFEXT" 408942 NIL DIFEXT (NIL T) -9 NIL 409236 NIL) (-230 405551 405979 406645 "DIFEXT-" 406650 NIL DIFEXT- (NIL T T) -8 NIL NIL NIL) (-229 402826 405083 405124 "DIAGG" 405129 NIL DIAGG (NIL T) -9 NIL 405149 NIL) (-228 402210 402367 402619 "DIAGG-" 402624 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-227 397627 401169 401446 "DHMATRIX" 401979 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-226 393239 394148 395158 "DFSFUN" 396637 T DFSFUN (NIL) -7 NIL NIL NIL) (-225 388317 392170 392482 "DFLOAT" 392947 T DFLOAT (NIL) -8 NIL NIL NIL) (-224 386580 386861 387250 "DFINTTLS" 388025 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-223 383609 384601 385001 "DERHAM" 386246 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-222 381410 383384 383473 "DEQUEUE" 383553 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-221 380664 380797 380980 "DEGRED" 381272 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-220 377094 377839 378685 "DEFINTRF" 379892 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-219 374649 375118 375710 "DEFINTEF" 376613 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-218 373999 374269 374384 "DEFAST" 374554 T DEFAST (NIL) -8 NIL NIL NIL) (-217 368003 373594 373743 "DECIMAL" 373870 T DECIMAL (NIL) -8 NIL NIL NIL) (-216 365515 365973 366479 "DDFACT" 367547 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-215 365111 365154 365305 "DBLRESP" 365466 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-214 362983 363344 363704 "DBASE" 364878 NIL DBASE (NIL T) -8 NIL NIL NIL) (-213 362225 362463 362609 "DATAARY" 362882 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-212 361331 362184 362212 "D03FAFA" 362217 T D03FAFA (NIL) -8 NIL NIL NIL) (-211 360438 361290 361318 "D03EEFA" 361323 T D03EEFA (NIL) -8 NIL NIL NIL) (-210 358388 358854 359343 "D03AGNT" 359969 T D03AGNT (NIL) -7 NIL NIL NIL) (-209 357677 358347 358375 "D02EJFA" 358380 T D02EJFA (NIL) -8 NIL NIL NIL) (-208 356966 357636 357664 "D02CJFA" 357669 T D02CJFA (NIL) -8 NIL NIL NIL) (-207 356255 356925 356953 "D02BHFA" 356958 T D02BHFA (NIL) -8 NIL NIL NIL) (-206 355544 356214 356242 "D02BBFA" 356247 T D02BBFA (NIL) -8 NIL NIL NIL) (-205 348741 350330 351936 "D02AGNT" 353958 T D02AGNT (NIL) -7 NIL NIL NIL) (-204 346509 347032 347578 "D01WGTS" 348215 T D01WGTS (NIL) -7 NIL NIL NIL) (-203 345576 346468 346496 "D01TRNS" 346501 T D01TRNS (NIL) -8 NIL NIL NIL) (-202 344644 345535 345563 "D01GBFA" 345568 T D01GBFA (NIL) -8 NIL NIL NIL) (-201 343712 344603 344631 "D01FCFA" 344636 T D01FCFA (NIL) -8 NIL NIL NIL) (-200 342780 343671 343699 "D01ASFA" 343704 T D01ASFA (NIL) -8 NIL NIL NIL) (-199 341848 342739 342767 "D01AQFA" 342772 T D01AQFA (NIL) -8 NIL NIL NIL) (-198 340916 341807 341835 "D01APFA" 341840 T D01APFA (NIL) -8 NIL NIL NIL) (-197 339984 340875 340903 "D01ANFA" 340908 T D01ANFA (NIL) -8 NIL NIL NIL) (-196 339052 339943 339971 "D01AMFA" 339976 T D01AMFA (NIL) -8 NIL NIL NIL) (-195 338120 339011 339039 "D01ALFA" 339044 T D01ALFA (NIL) -8 NIL NIL NIL) (-194 337188 338079 338107 "D01AKFA" 338112 T D01AKFA (NIL) -8 NIL NIL NIL) (-193 336256 337147 337175 "D01AJFA" 337180 T D01AJFA (NIL) -8 NIL NIL NIL) (-192 329551 331104 332665 "D01AGNT" 334715 T D01AGNT (NIL) -7 NIL NIL NIL) (-191 328888 329016 329168 "CYCLOTOM" 329419 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-190 325622 326336 327063 "CYCLES" 328181 T CYCLES (NIL) -7 NIL NIL NIL) (-189 324934 325068 325239 "CVMP" 325483 NIL CVMP (NIL T) -7 NIL NIL NIL) (-188 322775 323033 323402 "CTRIGMNP" 324662 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-187 322211 322569 322642 "CTOR" 322722 T CTOR (NIL) -8 NIL NIL NIL) (-186 321720 321942 322043 "CTORKIND" 322130 T CTORKIND (NIL) -8 NIL NIL NIL) (-185 321011 321327 321355 "CTORCAT" 321537 T CTORCAT (NIL) -9 NIL 321650 NIL) (-184 320609 320720 320879 "CTORCAT-" 320884 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-183 320071 320283 320391 "CTORCALL" 320533 NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-182 319445 319544 319697 "CSTTOOLS" 319968 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-181 315244 315901 316659 "CRFP" 318757 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-180 314719 314965 315057 "CRCEAST" 315172 T CRCEAST (NIL) -8 NIL NIL NIL) (-179 313766 313951 314179 "CRAPACK" 314523 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-178 313150 313251 313455 "CPMATCH" 313642 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-177 312875 312903 313009 "CPIMA" 313116 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-176 309223 309895 310614 "COORDSYS" 312210 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-175 308635 308756 308898 "CONTOUR" 309101 T CONTOUR (NIL) -8 NIL NIL NIL) (-174 304526 306638 307130 "CONTFRAC" 308175 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-173 304406 304427 304455 "CONDUIT" 304492 T CONDUIT (NIL) -9 NIL NIL NIL) (-172 303494 304048 304076 "COMRING" 304081 T COMRING (NIL) -9 NIL 304133 NIL) (-171 302548 302852 303036 "COMPPROP" 303330 T COMPPROP (NIL) -8 NIL NIL NIL) (-170 302209 302244 302372 "COMPLPAT" 302507 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-169 292500 302018 302127 "COMPLEX" 302132 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-168 292136 292193 292300 "COMPLEX2" 292437 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-167 291854 291889 291987 "COMPFACT" 292095 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-166 275934 285928 285968 "COMPCAT" 286972 NIL COMPCAT (NIL T) -9 NIL 288320 NIL) (-165 265446 268373 272000 "COMPCAT-" 272356 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-164 265175 265203 265306 "COMMUPC" 265412 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-163 264969 265003 265062 "COMMONOP" 265136 T COMMONOP (NIL) -7 NIL NIL NIL) (-162 264525 264720 264807 "COMM" 264902 T COMM (NIL) -8 NIL NIL NIL) (-161 264101 264329 264404 "COMMAAST" 264470 T COMMAAST (NIL) -8 NIL NIL NIL) (-160 263350 263544 263572 "COMBOPC" 263910 T COMBOPC (NIL) -9 NIL 264085 NIL) (-159 262246 262456 262698 "COMBINAT" 263140 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-158 258703 259277 259904 "COMBF" 261668 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-157 257461 257819 258054 "COLOR" 258488 T COLOR (NIL) -8 NIL NIL NIL) (-156 256937 257182 257274 "COLONAST" 257389 T COLONAST (NIL) -8 NIL NIL NIL) (-155 256577 256624 256749 "CMPLXRT" 256884 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-154 256025 256277 256376 "CLLCTAST" 256498 T CLLCTAST (NIL) -8 NIL NIL NIL) (-153 251523 252555 253635 "CLIP" 254965 T CLIP (NIL) -7 NIL NIL NIL) (-152 249869 250629 250868 "CLIF" 251350 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-151 246044 248015 248056 "CLAGG" 248985 NIL CLAGG (NIL T) -9 NIL 249521 NIL) (-150 244466 244923 245506 "CLAGG-" 245511 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-149 244010 244095 244235 "CINTSLPE" 244375 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-148 241511 241982 242530 "CHVAR" 243538 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-147 240685 241239 241267 "CHARZ" 241272 T CHARZ (NIL) -9 NIL 241287 NIL) (-146 240439 240479 240557 "CHARPOL" 240639 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-145 239497 240084 240112 "CHARNZ" 240159 T CHARNZ (NIL) -9 NIL 240215 NIL) (-144 237403 238151 238504 "CHAR" 239164 T CHAR (NIL) -8 NIL NIL NIL) (-143 237129 237190 237218 "CFCAT" 237329 T CFCAT (NIL) -9 NIL NIL NIL) (-142 236374 236485 236667 "CDEN" 237013 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-141 232339 235527 235807 "CCLASS" 236114 T CCLASS (NIL) -8 NIL NIL NIL) (-140 231590 231747 231924 "CATEGORY" 232182 T -10 (NIL) -8 NIL NIL NIL) (-139 231163 231509 231557 "CATCTOR" 231562 T CATCTOR (NIL) -8 NIL NIL NIL) (-138 230614 230866 230964 "CATAST" 231085 T CATAST (NIL) -8 NIL NIL NIL) (-137 230090 230335 230427 "CASEAST" 230542 T CASEAST (NIL) -8 NIL NIL NIL) (-136 225099 226119 226872 "CARTEN" 229393 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-135 224207 224355 224576 "CARTEN2" 224946 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-134 222523 223357 223614 "CARD" 223970 T CARD (NIL) -8 NIL NIL NIL) (-133 222099 222327 222402 "CAPSLAST" 222468 T CAPSLAST (NIL) -8 NIL NIL NIL) (-132 221603 221811 221839 "CACHSET" 221971 T CACHSET (NIL) -9 NIL 222049 NIL) (-131 221073 221395 221423 "CABMON" 221473 T CABMON (NIL) -9 NIL 221529 NIL) (-130 220546 220777 220887 "BYTEORD" 220983 T BYTEORD (NIL) -8 NIL NIL NIL) (-129 219529 220080 220222 "BYTE" 220385 T BYTE (NIL) -8 NIL NIL 220507) (-128 214879 219034 219206 "BYTEBUF" 219377 T BYTEBUF (NIL) -8 NIL NIL NIL) (-127 212388 214571 214678 "BTREE" 214805 NIL BTREE (NIL T) -8 NIL NIL NIL) (-126 209837 212036 212158 "BTOURN" 212298 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-125 207207 209307 209348 "BTCAT" 209416 NIL BTCAT (NIL T) -9 NIL 209493 NIL) (-124 206874 206954 207103 "BTCAT-" 207108 NIL BTCAT- (NIL T T) -8 NIL NIL NIL) (-123 202139 206017 206045 "BTAGG" 206267 T BTAGG (NIL) -9 NIL 206428 NIL) (-122 201629 201754 201960 "BTAGG-" 201965 NIL BTAGG- (NIL T) -8 NIL NIL NIL) (-121 198624 200907 201122 "BSTREE" 201446 NIL BSTREE (NIL T) -8 NIL NIL NIL) (-120 197762 197888 198072 "BRILL" 198480 NIL BRILL (NIL T) -7 NIL NIL NIL) (-119 194414 196488 196529 "BRAGG" 197178 NIL BRAGG (NIL T) -9 NIL 197436 NIL) (-118 192943 193349 193904 "BRAGG-" 193909 NIL BRAGG- (NIL T T) -8 NIL NIL NIL) (-117 186172 192289 192473 "BPADICRT" 192791 NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-116 184487 186109 186154 "BPADIC" 186159 NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-115 184185 184215 184329 "BOUNDZRO" 184451 NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-114 179413 180611 181523 "BOP" 183293 T BOP (NIL) -8 NIL NIL NIL) (-113 177194 177598 178073 "BOP1" 178971 NIL BOP1 (NIL T) -7 NIL NIL NIL) (-112 176019 176768 176917 "BOOLEAN" 177065 T BOOLEAN (NIL) -8 NIL NIL NIL) (-111 175298 175702 175756 "BMODULE" 175761 NIL BMODULE (NIL T T) -9 NIL 175826 NIL) (-110 171099 175096 175169 "BITS" 175245 T BITS (NIL) -8 NIL NIL NIL) (-109 170520 170639 170779 "BINDING" 170979 T BINDING (NIL) -8 NIL NIL NIL) (-108 164527 170117 170265 "BINARY" 170392 T BINARY (NIL) -8 NIL NIL NIL) (-107 162307 163782 163823 "BGAGG" 164083 NIL BGAGG (NIL T) -9 NIL 164220 NIL) (-106 162138 162170 162261 "BGAGG-" 162266 NIL BGAGG- (NIL T T) -8 NIL NIL NIL) (-105 161209 161522 161727 "BFUNCT" 161953 T BFUNCT (NIL) -8 NIL NIL NIL) (-104 159899 160077 160365 "BEZOUT" 161033 NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 156368 158751 159081 "BBTREE" 159602 NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 156102 156155 156183 "BASTYPE" 156302 T BASTYPE (NIL) -9 NIL NIL NIL) (-101 155954 155983 156056 "BASTYPE-" 156061 NIL BASTYPE- (NIL T) -8 NIL NIL NIL) (-100 155388 155464 155616 "BALFACT" 155865 NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 154244 154803 154989 "AUTOMOR" 155233 NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-98 153970 153975 154001 "ATTREG" 154006 T ATTREG (NIL) -9 NIL NIL NIL) (-97 152222 152667 153019 "ATTRBUT" 153636 T ATTRBUT (NIL) -8 NIL NIL NIL) (-96 151830 152050 152116 "ATTRAST" 152174 T ATTRAST (NIL) -8 NIL NIL NIL) (-95 151366 151479 151505 "ATRIG" 151706 T ATRIG (NIL) -9 NIL NIL NIL) (-94 151175 151216 151303 "ATRIG-" 151308 NIL ATRIG- (NIL T) -8 NIL NIL NIL) (-93 150820 151006 151032 "ASTCAT" 151037 T ASTCAT (NIL) -9 NIL 151067 NIL) (-92 150547 150606 150725 "ASTCAT-" 150730 NIL ASTCAT- (NIL T) -8 NIL NIL NIL) (-91 148696 150323 150411 "ASTACK" 150490 NIL ASTACK (NIL T) -8 NIL NIL NIL) (-90 147201 147498 147863 "ASSOCEQ" 148378 NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-89 146233 146860 146984 "ASP9" 147108 NIL ASP9 (NIL NIL) -8 NIL NIL NIL) (-88 145996 146181 146220 "ASP8" 146225 NIL ASP8 (NIL NIL) -8 NIL NIL NIL) (-87 144864 145601 145743 "ASP80" 145885 NIL ASP80 (NIL NIL) -8 NIL NIL NIL) (-86 143762 144499 144631 "ASP7" 144763 NIL ASP7 (NIL NIL) -8 NIL NIL NIL) (-85 142716 143439 143557 "ASP78" 143675 NIL ASP78 (NIL NIL) -8 NIL NIL NIL) (-84 141685 142396 142513 "ASP77" 142630 NIL ASP77 (NIL NIL) -8 NIL NIL NIL) (-83 140597 141323 141454 "ASP74" 141585 NIL ASP74 (NIL NIL) -8 NIL NIL NIL) (-82 139497 140232 140364 "ASP73" 140496 NIL ASP73 (NIL NIL) -8 NIL NIL NIL) (-81 138601 139323 139423 "ASP6" 139428 NIL ASP6 (NIL NIL) -8 NIL NIL NIL) (-80 137545 138278 138396 "ASP55" 138514 NIL ASP55 (NIL NIL) -8 NIL NIL NIL) (-79 136494 137219 137338 "ASP50" 137457 NIL ASP50 (NIL NIL) -8 NIL NIL NIL) (-78 135582 136195 136305 "ASP4" 136415 NIL ASP4 (NIL NIL) -8 NIL NIL NIL) (-77 134670 135283 135393 "ASP49" 135503 NIL ASP49 (NIL NIL) -8 NIL NIL NIL) (-76 133454 134209 134377 "ASP42" 134559 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-75 132230 132987 133157 "ASP41" 133341 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-74 131180 131907 132025 "ASP35" 132143 NIL ASP35 (NIL NIL) -8 NIL NIL NIL) (-73 130945 131128 131167 "ASP34" 131172 NIL ASP34 (NIL NIL) -8 NIL NIL NIL) (-72 130682 130749 130825 "ASP33" 130900 NIL ASP33 (NIL NIL) -8 NIL NIL NIL) (-71 129575 130317 130449 "ASP31" 130581 NIL ASP31 (NIL NIL) -8 NIL NIL NIL) (-70 129340 129523 129562 "ASP30" 129567 NIL ASP30 (NIL NIL) -8 NIL NIL NIL) (-69 129075 129144 129220 "ASP29" 129295 NIL ASP29 (NIL NIL) -8 NIL NIL NIL) (-68 128840 129023 129062 "ASP28" 129067 NIL ASP28 (NIL NIL) -8 NIL NIL NIL) (-67 128605 128788 128827 "ASP27" 128832 NIL ASP27 (NIL NIL) -8 NIL NIL NIL) (-66 127689 128303 128414 "ASP24" 128525 NIL ASP24 (NIL NIL) -8 NIL NIL NIL) (-65 126765 127491 127603 "ASP20" 127608 NIL ASP20 (NIL NIL) -8 NIL NIL NIL) (-64 125853 126466 126576 "ASP1" 126686 NIL ASP1 (NIL NIL) -8 NIL NIL NIL) (-63 124795 125527 125646 "ASP19" 125765 NIL ASP19 (NIL NIL) -8 NIL NIL NIL) (-62 124532 124599 124675 "ASP12" 124750 NIL ASP12 (NIL NIL) -8 NIL NIL NIL) (-61 123384 124131 124275 "ASP10" 124419 NIL ASP10 (NIL NIL) -8 NIL NIL NIL) (-60 121235 123228 123319 "ARRAY2" 123324 NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 117000 120883 120997 "ARRAY1" 121152 NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-58 116032 116205 116426 "ARRAY12" 116823 NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-57 110344 112262 112337 "ARR2CAT" 114967 NIL ARR2CAT (NIL T T T) -9 NIL 115725 NIL) (-56 107778 108522 109476 "ARR2CAT-" 109481 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL NIL) (-55 107095 107405 107530 "ARITY" 107671 T ARITY (NIL) -8 NIL NIL NIL) (-54 105871 106023 106322 "APPRULE" 106931 NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 105522 105570 105689 "APPLYORE" 105817 NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 104876 105115 105235 "ANY" 105420 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 diff --git a/src/share/algebra/operation.daase b/src/share/algebra/operation.daase index 86edd3d5..b0ae6b74 100644 --- a/src/share/algebra/operation.daase +++ b/src/share/algebra/operation.daase @@ -1,707 +1,819 @@ -(731401 . 3465761901) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-645 (-1 (-112) *8))) (-4 *8 (-1066 *5 *6 *7)) - (-4 *5 (-559)) (-4 *6 (-794)) (-4 *7 (-851)) - (-5 *2 (-2 (|:| |goodPols| (-645 *8)) (|:| |badPols| (-645 *8)))) - (-5 *1 (-978 *5 *6 *7 *8)) (-5 *4 (-645 *8))))) -(((*1 *2 *3 *3) - (|partial| -12 (-4 *4 (-13 (-365) (-147) (-1039 (-567)))) - (-4 *5 (-1243 *4)) - (-5 *2 (-2 (|:| -4012 (-410 *5)) (|:| |coeff| (-410 *5)))) - (-5 *1 (-571 *4 *5)) (-5 *3 (-410 *5))))) +(731666 . 3466723536) +(((*1 *2) (-12 (-5 *2 (-875)) (-5 *1 (-1271)))) + ((*1 *2 *2) (-12 (-5 *2 (-875)) (-5 *1 (-1271))))) +(((*1 *1 *2) (-12 (-5 *1 (-1028 *2)) (-4 *2 (-1218))))) +(((*1 *1 *1) (-12 (-4 *1 (-375 *2)) (-4 *2 (-1218)) (-4 *2 (-851)))) + ((*1 *1 *2 *1) + (-12 (-5 *2 (-1 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