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authordos-reis <gdr@axiomatics.org>2013-05-10 09:21:22 +0000
committerdos-reis <gdr@axiomatics.org>2013-05-10 09:21:22 +0000
commit0f2fe8a37ab42191fa2b871e0ce8bd05c701eed7 (patch)
tree21351b5529ef766fc386e2103d6da0e249513220 /src/share
parent095dc531352b8055aa4ec355d8cf1157901377fa (diff)
downloadopen-axiom-0f2fe8a37ab42191fa2b871e0ce8bd05c701eed7.tar.gz
Add opposite? and annihilate? exports.
Diffstat (limited to 'src/share')
-rw-r--r--src/share/algebra/browse.daase3134
-rw-r--r--src/share/algebra/category.daase6422
-rw-r--r--src/share/algebra/compress.daase58
-rw-r--r--src/share/algebra/interp.daase7950
-rw-r--r--src/share/algebra/operation.daase20846
5 files changed, 19213 insertions, 19197 deletions
diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase
index c0908d72..a099c5fb 100644
--- a/src/share/algebra/browse.daase
+++ b/src/share/algebra/browse.daase
@@ -1,12 +1,12 @@
-(1962139 . 3577105535)
+(1963183 . 3577141751)
(-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.")))
-((-3993 . T) (-3992 . T))
+((-3997 . T) (-3996 . T))
NIL
(-20 S)
((|constructor| (NIL "The class of abelian groups,{} \\spadignore{i.e.} additive monoids where each element has an additive inverse. \\blankline")) (- (($ $ $) "\\spad{x-y} is the difference of \\spad{x} and \\spad{y} \\spadignore{i.e.} \\spad{x + (-y)}.") (($ $) "\\spad{-x} is the additive inverse of \\spad{x}")))
@@ -17,11 +17,11 @@ NIL
NIL
NIL
(-22 S)
-((|constructor| (NIL "The class of multiplicative monoids,{} \\spadignore{i.e.} semigroups with an additive identity element. \\blankline")) (* (($ (|NonNegativeInteger|) $) "\\spad{n * x} is left-multiplication by a non negative integer")) (|zero?| (((|Boolean|) $) "\\spad{zero?(x)} tests if \\spad{x} is equal to 0.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) (|Zero| (($) "0 is the additive identity element.")))
+((|constructor| (NIL "The class of multiplicative monoids,{} \\spadignore{i.e.} semigroups with an additive identity element. \\blankline")) (|opposite?| (((|Boolean|) $ $) "\\spad{opposite?(x,y)} holds if the sum of \\spad{x} and \\spad{y} is \\spad{0}.")) (* (($ (|NonNegativeInteger|) $) "\\spad{n * x} is left-multiplication by a non negative integer")) (|zero?| (((|Boolean|) $) "\\spad{zero?(x)} tests if \\spad{x} is equal to 0.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) (|Zero| (($) "0 is the additive identity element.")))
NIL
NIL
(-23)
-((|constructor| (NIL "The class of multiplicative monoids,{} \\spadignore{i.e.} semigroups with an additive identity element. \\blankline")) (* (($ (|NonNegativeInteger|) $) "\\spad{n * x} is left-multiplication by a non negative integer")) (|zero?| (((|Boolean|) $) "\\spad{zero?(x)} tests if \\spad{x} is equal to 0.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) (|Zero| (($) "0 is the additive identity element.")))
+((|constructor| (NIL "The class of multiplicative monoids,{} \\spadignore{i.e.} semigroups with an additive identity element. \\blankline")) (|opposite?| (((|Boolean|) $ $) "\\spad{opposite?(x,y)} holds if the sum of \\spad{x} and \\spad{y} is \\spad{0}.")) (* (($ (|NonNegativeInteger|) $) "\\spad{n * x} is left-multiplication by a non negative integer")) (|zero?| (((|Boolean|) $) "\\spad{zero?(x)} tests if \\spad{x} is equal to 0.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) (|Zero| (($) "0 is the additive identity element.")))
NIL
NIL
(-24 S)
@@ -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}'s are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}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}'s are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities. The returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values.") (((|List| $) (|Polynomial| $)) "\\spad{zerosOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}'s are expressed in radicals if possible. Otherwise they are implicit algebraic quantities. The returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|zeroOf| (($ (|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},{}...,{}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},{}...,{}yn are bound in the interpreter to respective root values.") (((|List| $) (|Polynomial| $)) "\\spad{rootsOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. Note: the returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ (|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}.")))
-((-3984 . T) (-3990 . T) (-3985 . T) ((-3994 "*") . T) (-3986 . T) (-3987 . T) (-3989 . T))
+((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . 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}'s are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{zerosOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}'s are expressed in radicals if possible. The returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable.")) (|zeroOf| (($ $ (|Symbol|)) "\\spad{zeroOf(p, 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},{}...,{}yn are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; Note: the returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ $ (|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}'s are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{zerosOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}'s are expressed in radicals if possible. The returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable.")) (|zeroOf| (($ $ (|Symbol|)) "\\spad{zeroOf(p, 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},{}...,{}yn are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; Note: the returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ $ (|Symbol|)) "\\spad{rootOf(p,y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}.")))
-((-3989 . T) (-3987 . T) (-3986 . T) ((-3994 "*") . T) (-3985 . T) (-3990 . T) (-3984 . T))
+((-3993 . T) (-3991 . T) (-3990 . T) ((-3998 "*") . T) (-3989 . T) (-3994 . T) (-3988 . T))
NIL
(-30)
((|refine| (($ $ (|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 `d'.")) (|base| (((|SpadAst|) $) "\\spad{base(d)} returns the base domain(\\spad{s}) of the add-domain expression.")))
NIL
NIL
-(-32 R -3091)
+(-32 R -3094)
((|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| (QUOTE (-951 (-484)))))
+((|HasCategory| |#1| (QUOTE (-952 (-485)))))
(-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 \\%")) (|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} := empty()}.")) (|copy| (($ $) "\\spad{copy(u)} returns a top-level (non-recursive) copy of \\spad{u}. Note: for collections,{} \\axiom{copy(\\spad{u}) == [\\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 -3992)))
+((|HasAttribute| |#1| (QUOTE -3996)))
(-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 \\%")) (|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} := empty()}.")) (|copy| (($ $) "\\spad{copy(u)} returns a top-level (non-recursive) copy of \\spad{u}. Note: for collections,{} \\axiom{copy(\\spad{u}) == [\\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}.")))
-((-3992 . T) (-3993 . T))
+((-3996 . T) (-3997 . 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")))
-((-3986 . T) (-3987 . T) (-3989 . T))
+((-3990 . T) (-3991 . T) (-3993 . 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 \\spad{a1},{}...,{}an.")))
NIL
NIL
-(-40 -3091 UP UPUP -2613)
+(-40 -3094 UP UPUP -2616)
((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}")))
-((-3985 |has| (-347 |#2|) (-311)) (-3990 |has| (-347 |#2|) (-311)) (-3984 |has| (-347 |#2|) (-311)) ((-3994 "*") . T) (-3986 . T) (-3987 . T) (-3989 . T))
-((|HasCategory| (-347 |#2|) (QUOTE (-118))) (|HasCategory| (-347 |#2|) (QUOTE (-120))) (|HasCategory| (-347 |#2|) (QUOTE (-298))) (OR (|HasCategory| (-347 |#2|) (QUOTE (-311))) (|HasCategory| (-347 |#2|) (QUOTE (-298)))) (|HasCategory| (-347 |#2|) (QUOTE (-311))) (|HasCategory| (-347 |#2|) (QUOTE (-317))) (OR (-12 (|HasCategory| (-347 |#2|) (QUOTE (-190))) (|HasCategory| (-347 |#2|) (QUOTE (-311)))) (|HasCategory| (-347 |#2|) (QUOTE (-298)))) (OR (-12 (|HasCategory| (-347 |#2|) (QUOTE (-190))) (|HasCategory| (-347 |#2|) (QUOTE (-311)))) (-12 (|HasCategory| (-347 |#2|) (QUOTE (-189))) (|HasCategory| (-347 |#2|) (QUOTE (-311)))) (|HasCategory| (-347 |#2|) (QUOTE (-298)))) (OR (-12 (|HasCategory| (-347 |#2|) (QUOTE (-311))) (|HasCategory| (-347 |#2|) (QUOTE (-810 (-1089))))) (-12 (|HasCategory| (-347 |#2|) (QUOTE (-298))) (|HasCategory| (-347 |#2|) (QUOTE (-810 (-1089)))))) (OR (-12 (|HasCategory| (-347 |#2|) (QUOTE (-311))) (|HasCategory| (-347 |#2|) (QUOTE (-810 (-1089))))) (-12 (|HasCategory| (-347 |#2|) (QUOTE (-311))) (|HasCategory| (-347 |#2|) (QUOTE (-812 (-1089)))))) (|HasCategory| (-347 |#2|) (QUOTE (-581 (-484)))) (OR (|HasCategory| (-347 |#2|) (QUOTE (-311))) (|HasCategory| (-347 |#2|) (QUOTE (-951 (-347 (-484)))))) (|HasCategory| (-347 |#2|) (QUOTE (-951 (-347 (-484))))) (|HasCategory| (-347 |#2|) (QUOTE (-951 (-484)))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-317))) (-12 (|HasCategory| (-347 |#2|) (QUOTE (-189))) (|HasCategory| (-347 |#2|) (QUOTE (-311)))) (-12 (|HasCategory| (-347 |#2|) (QUOTE (-311))) (|HasCategory| (-347 |#2|) (QUOTE (-812 (-1089))))) (-12 (|HasCategory| (-347 |#2|) (QUOTE (-190))) (|HasCategory| (-347 |#2|) (QUOTE (-311)))) (-12 (|HasCategory| (-347 |#2|) (QUOTE (-311))) (|HasCategory| (-347 |#2|) (QUOTE (-810 (-1089))))))
-(-41 R -3091)
+((-3989 |has| (-348 |#2|) (-312)) (-3994 |has| (-348 |#2|) (-312)) (-3988 |has| (-348 |#2|) (-312)) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T))
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+(-41 R -3094)
((|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}'s which are algebraic from the denominators in \\spad{f}.") ((|#2| |#2| (|List| |#2|)) "\\spad{ratDenom(f, [a1,...,an])} removes the \\spad{ai}'s which are algebraic kernels from the denominators in \\spad{f}.") ((|#2| |#2| |#2|) "\\spad{ratDenom(f, a)} removes \\spad{a} from the denominators in \\spad{f} if \\spad{a} is an algebraic kernel.") ((|#2| |#2|) "\\spad{ratDenom(f)} rationalizes the denominators appearing in \\spad{f} by moving all the algebraic quantities into the numerators.")) (|rootSplit| ((|#2| |#2|) "\\spad{rootSplit(f)} transforms every radical of the form \\spad{(a/b)**(1/n)} appearing in \\spad{f} into \\spad{a**(1/n) / b**(1/n)}. This transformation is not in general valid for all complex numbers \\spad{a} and \\spad{b}.")) (|coerce| (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{coerce(x)} \\undocumented")) (|denom| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{denom(x)} \\undocumented")) (|numer| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{numer(x)} \\undocumented")))
NIL
-((-12 (|HasCategory| |#1| (QUOTE (-389))) (|HasCategory| |#1| (QUOTE (-951 (-484)))) (|HasCategory| |#2| (|%list| (QUOTE -361) (|devaluate| |#1|)))))
+((-12 (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-952 (-485)))) (|HasCategory| |#2| (|%list| (QUOTE -362) (|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
@@ -103,34 +103,34 @@ NIL
(-43 R A)
((|constructor| (NIL "AlgebraPackage assembles a variety of useful functions for general algebras.")) (|basis| (((|Vector| |#2|) (|Vector| |#2|)) "\\spad{basis(va)} selects a basis from the elements of \\spad{va}.")) (|radicalOfLeftTraceForm| (((|List| |#2|)) "\\spad{radicalOfLeftTraceForm()} returns basis for null space of \\spad{leftTraceMatrix()},{} if the algebra is associative,{} alternative or a Jordan algebra,{} then this space equals the radical (maximal nil ideal) of the algebra.")) (|basisOfCentroid| (((|List| (|Matrix| |#1|))) "\\spad{basisOfCentroid()} returns a basis of the centroid,{} \\spadignore{i.e.} the endomorphism ring of \\spad{A} considered as \\spad{(A,A)}-bimodule.")) (|basisOfRightNucloid| (((|List| (|Matrix| |#1|))) "\\spad{basisOfRightNucloid()} returns a basis of the space of endomorphisms of \\spad{A} as left module. Note: right nucloid coincides with right nucleus if \\spad{A} has a unit.")) (|basisOfLeftNucloid| (((|List| (|Matrix| |#1|))) "\\spad{basisOfLeftNucloid()} returns a basis of the space of endomorphisms of \\spad{A} as right module. Note: left nucloid coincides with left nucleus if \\spad{A} has a unit.")) (|basisOfCenter| (((|List| |#2|)) "\\spad{basisOfCenter()} returns a basis of the space of all \\spad{x} of \\spad{A} satisfying \\spad{commutator(x,a) = 0} and \\spad{associator(x,a,b) = associator(a,x,b) = associator(a,b,x) = 0} for all \\spad{a},{}\\spad{b} in \\spad{A}.")) (|basisOfNucleus| (((|List| |#2|)) "\\spad{basisOfNucleus()} returns a basis of the space of all \\spad{x} of \\spad{A} satisfying \\spad{associator(x,a,b) = associator(a,x,b) = associator(a,b,x) = 0} for all \\spad{a},{}\\spad{b} in \\spad{A}.")) (|basisOfMiddleNucleus| (((|List| |#2|)) "\\spad{basisOfMiddleNucleus()} returns a basis of the space of all \\spad{x} of \\spad{A} satisfying \\spad{0 = associator(a,x,b)} for all \\spad{a},{}\\spad{b} in \\spad{A}.")) (|basisOfRightNucleus| (((|List| |#2|)) "\\spad{basisOfRightNucleus()} returns a basis of the space of all \\spad{x} of \\spad{A} satisfying \\spad{0 = associator(a,b,x)} for all \\spad{a},{}\\spad{b} in \\spad{A}.")) (|basisOfLeftNucleus| (((|List| |#2|)) "\\spad{basisOfLeftNucleus()} returns a basis of the space of all \\spad{x} of \\spad{A} satisfying \\spad{0 = associator(x,a,b)} for all \\spad{a},{}\\spad{b} in \\spad{A}.")) (|basisOfRightAnnihilator| (((|List| |#2|) |#2|) "\\spad{basisOfRightAnnihilator(a)} returns a basis of the space of all \\spad{x} of \\spad{A} satisfying \\spad{0 = a*x}.")) (|basisOfLeftAnnihilator| (((|List| |#2|) |#2|) "\\spad{basisOfLeftAnnihilator(a)} returns a basis of the space of all \\spad{x} of \\spad{A} satisfying \\spad{0 = x*a}.")) (|basisOfCommutingElements| (((|List| |#2|)) "\\spad{basisOfCommutingElements()} returns a basis of the space of all \\spad{x} of \\spad{A} satisfying \\spad{0 = commutator(x,a)} for all \\spad{a} in \\spad{A}.")) (|biRank| (((|NonNegativeInteger|) |#2|) "\\spad{biRank(x)} determines the number of linearly independent elements in \\spad{x},{} \\spad{x*bi},{} \\spad{bi*x},{} \\spad{bi*x*bj},{} \\spad{i,j=1,...,n},{} where \\spad{b=[b1,...,bn]} is a basis. Note: if \\spad{A} has a unit,{} then \\spadfunFrom{doubleRank}{AlgebraPackage},{} \\spadfunFrom{weakBiRank}{AlgebraPackage} and \\spadfunFrom{biRank}{AlgebraPackage} coincide.")) (|weakBiRank| (((|NonNegativeInteger|) |#2|) "\\spad{weakBiRank(x)} determines the number of linearly independent elements in the \\spad{bi*x*bj},{} \\spad{i,j=1,...,n},{} where \\spad{b=[b1,...,bn]} is a basis.")) (|doubleRank| (((|NonNegativeInteger|) |#2|) "\\spad{doubleRank(x)} determines the number of linearly independent elements in \\spad{b1*x},{}...,{}\\spad{x*bn},{} where \\spad{b=[b1,...,bn]} is a basis.")) (|rightRank| (((|NonNegativeInteger|) |#2|) "\\spad{rightRank(x)} determines the number of linearly independent elements in \\spad{b1*x},{}...,{}\\spad{bn*x},{} where \\spad{b=[b1,...,bn]} is a basis.")) (|leftRank| (((|NonNegativeInteger|) |#2|) "\\spad{leftRank(x)} determines the number of linearly independent elements in \\spad{x*b1},{}...,{}\\spad{x*bn},{} where \\spad{b=[b1,...,bn]} is a basis.")))
NIL
-((|HasCategory| |#1| (QUOTE (-257))))
+((|HasCategory| |#1| (QUOTE (-258))))
(-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.")))
-((-3989 |has| |#1| (-495)) (-3987 . T) (-3986 . T))
-((|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-495))))
+((-3993 |has| |#1| (-496)) (-3991 . T) (-3990 . T))
+((|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-496))))
(-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.")))
-((-3992 . T) (-3993 . T))
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+((-3996 . T) (-3997 . T))
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(-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| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}.")))
NIL
-((|HasCategory| |#2| (QUOTE (-38 (-347 (-484))))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-311))))
+((|HasCategory| |#2| (QUOTE (-38 (-348 (-485))))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-312))))
(-47 R E)
((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#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| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}.")))
-(((-3994 "*") |has| |#1| (-146)) (-3985 |has| |#1| (-495)) (-3986 . T) (-3987 . T) (-3989 . T))
+(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3990 . T) (-3991 . T) (-3993 . T))
NIL
(-48)
((|constructor| (NIL "Algebraic closure of the rational numbers,{} with mathematical =")) (|norm| (($ $ (|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}.")))
-((-3984 . T) (-3990 . T) (-3985 . T) ((-3994 "*") . T) (-3986 . T) (-3987 . T) (-3989 . T))
-((|HasCategory| $ (QUOTE (-962))) (|HasCategory| $ (QUOTE (-951 (-484)))))
+((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T))
+((|HasCategory| $ (QUOTE (-963))) (|HasCategory| $ (QUOTE (-952 (-485)))))
(-49)
((|constructor| (NIL "This domain implements anonymous functions")) (|body| (((|Syntax|) $) "\\spad{body(f)} returns the body of the unnamed function `f'.")) (|parameters| (((|List| (|Identifier|)) $) "\\spad{parameters(f)} returns the list of parameters bound by `f'.")))
NIL
NIL
(-50 R |lVar|)
((|constructor| (NIL "The domain of antisymmetric polynomials.")) (|map| (($ (|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}.")))
-((-3989 . T))
+((-3993 . T))
NIL
(-51)
((|constructor| (NIL "\\spadtype{Any} implements a type that packages up objects and their types in objects of \\spadtype{Any}. Roughly speaking that means that if \\spad{s : S} then when converted to \\spadtype{Any},{} the new object will include both the original object and its type. This is a way of converting arbitrary objects into a single type without losing any of the original information. Any object can be converted to one of \\spadtype{Any}. The original object can be recovered by `is-case' pattern matching as exemplified here and \\spad{AnyFunctions1}.")) (|obj| (((|None|) $) "\\spad{obj(a)} essentially returns the original object that was converted to \\spadtype{Any} except that the type is forced to be \\spadtype{None}.")) (|dom| (((|SExpression|) $) "\\spad{dom(a)} returns a \\spadgloss{LISP} form of the type of the original object that was converted to \\spadtype{Any}.")) (|any| (($ (|SExpression|) (|None|)) "\\spad{any(type,object)} is a technical function for creating an \\spad{object} of \\spadtype{Any}. Arugment \\spad{type} is a \\spadgloss{LISP} form for the \\spad{type} of \\spad{object}.")))
@@ -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 -3091)
+(-54 |Base| R -3094)
((|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},{}...,{}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},{}...,{}rn to \\spad{f} an unlimited number of times,{} \\spadignore{i.e.} until none of \\spad{r1},{}...,{}rn is applicable to the expression.")))
NIL
NIL
@@ -158,28 +158,28 @@ 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}'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")))
-((-3992 . T) (-3993 . T))
+((-3996 . T) (-3997 . T))
NIL
(-58 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}")))
-((-3993 . T) (-3992 . T))
-((OR (-12 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-554 (-473)))) (OR (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-757))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| (-484) (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))))
+((-3997 . T) (-3996 . T))
+((OR (-12 (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-554 (-774)))) (|HasCategory| |#1| (QUOTE (-555 (-474)))) (OR (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| |#1| (QUOTE (-758))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| (-485) (QUOTE (-758))) (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))))
(-59 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),...]}.")))
NIL
NIL
(-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's.")))
-((-3992 . T) (-3993 . T))
-((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1013))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-72))))
+((-3996 . T) (-3997 . T))
+((-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1015))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| |#1| (QUOTE (-554 (-774)))) (|HasCategory| |#1| (QUOTE (-72))))
(-61 R L)
((|constructor| (NIL "\\spadtype{AssociatedEquations} provides functions to compute the associated equations needed for factoring operators")) (|associatedEquations| (((|Record| (|:| |minor| (|List| (|PositiveInteger|))) (|:| |eq| |#2|) (|:| |minors| (|List| (|List| (|PositiveInteger|)))) (|:| |ops| (|List| |#2|))) |#2| (|PositiveInteger|)) "\\spad{associatedEquations(op, m)} returns \\spad{[w, eq, lw, lop]} such that \\spad{eq(w) = 0} where \\spad{w} is the given minor,{} and \\spad{lw_i = lop_i(w)} for all the other minors.")) (|uncouplingMatrices| (((|Vector| (|Matrix| |#1|)) (|Matrix| |#1|)) "\\spad{uncouplingMatrices(M)} returns \\spad{[A_1,...,A_n]} such that if \\spad{y = [y_1,...,y_n]} is a solution of \\spad{y' = M y},{} then \\spad{[\\$y_j',y_j'',...,y_j^{(n)}\\$] = \\$A_j y\\$} for all \\spad{j}'s.")) (|associatedSystem| (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| (|List| (|PositiveInteger|))))) |#2| (|PositiveInteger|)) "\\spad{associatedSystem(op, m)} returns \\spad{[M,w]} such that the \\spad{m}-th associated equation system to \\spad{L} is \\spad{w' = M w}.")))
NIL
-((|HasCategory| |#1| (QUOTE (-311))))
+((|HasCategory| |#1| (QUOTE (-312))))
(-62 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}.")))
-((-3992 . T) (-3993 . T))
-((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1013))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-72))))
+((-3996 . T) (-3997 . T))
+((-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1015))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| |#1| (QUOTE (-554 (-774)))) (|HasCategory| |#1| (QUOTE (-72))))
(-63 S)
((|constructor| (NIL "This is the category of Spad abstract syntax trees.")))
NIL
@@ -202,11 +202,11 @@ NIL
NIL
(-68)
((|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.")))
-((-3992 . T) ((-3994 "*") . T) (-3993 . T) (-3989 . T) (-3987 . T) (-3986 . T) (-3985 . T) (-3990 . T) (-3984 . T) (-3983 . T) (-3982 . T) (-3981 . T) (-3980 . T) (-3988 . T) (-3991 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-3979 . T))
+((-3996 . T) ((-3998 "*") . T) (-3997 . T) (-3993 . T) (-3991 . T) (-3990 . T) (-3989 . T) (-3994 . T) (-3988 . T) (-3987 . T) (-3986 . T) (-3985 . T) (-3984 . T) (-3992 . T) (-3995 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-3983 . T))
NIL
(-69 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}.")))
-((-3989 . T))
+((-3993 . T))
NIL
(-70 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}.")))
@@ -222,24 +222,24 @@ NIL
NIL
(-73 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 pl and 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{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 ls.")) (|balancedBinaryTree| (($ (|NonNegativeInteger|) |#1|) "\\spad{balancedBinaryTree(n, s)} creates a balanced binary tree with \\spad{n} nodes each with value \\spad{s}.")))
-((-3992 . T) (-3993 . T))
-((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1013))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-72))))
+((-3996 . T) (-3997 . T))
+((-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1015))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| |#1| (QUOTE (-554 (-774)))) (|HasCategory| |#1| (QUOTE (-72))))
(-74 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 (-3994 "*"))))
+((|HasAttribute| |#1| (QUOTE (-3998 "*"))))
(-75 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.")))
NIL
NIL
(-76 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.")))
-((-3993 . T))
+((-3997 . T))
NIL
(-77)
((|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.")))
-((-3984 . T) (-3990 . T) (-3985 . T) ((-3994 "*") . T) (-3986 . T) (-3987 . T) (-3989 . T))
-((|HasCategory| (-484) (QUOTE (-822))) (|HasCategory| (-484) (QUOTE (-951 (-1089)))) (|HasCategory| (-484) (QUOTE (-118))) (|HasCategory| (-484) (QUOTE (-120))) (|HasCategory| (-484) (QUOTE (-554 (-473)))) (|HasCategory| (-484) (QUOTE (-934))) (|HasCategory| (-484) (QUOTE (-741))) (|HasCategory| (-484) (QUOTE (-757))) (OR (|HasCategory| (-484) (QUOTE (-741))) (|HasCategory| (-484) (QUOTE (-757)))) (|HasCategory| (-484) (QUOTE (-951 (-484)))) (|HasCategory| (-484) (QUOTE (-1065))) (|HasCategory| (-484) (QUOTE (-797 (-327)))) (|HasCategory| (-484) (QUOTE (-797 (-484)))) (|HasCategory| (-484) (QUOTE (-554 (-801 (-327))))) (|HasCategory| (-484) (QUOTE (-554 (-801 (-484))))) (|HasCategory| (-484) (QUOTE (-189))) (|HasCategory| (-484) (QUOTE (-812 (-1089)))) (|HasCategory| (-484) (QUOTE (-190))) (|HasCategory| (-484) (QUOTE (-810 (-1089)))) (|HasCategory| (-484) (QUOTE (-453 (-1089) (-484)))) (|HasCategory| (-484) (QUOTE (-259 (-484)))) (|HasCategory| (-484) (QUOTE (-241 (-484) (-484)))) (|HasCategory| (-484) (QUOTE (-257))) (|HasCategory| (-484) (QUOTE (-483))) (|HasCategory| (-484) (QUOTE (-581 (-484)))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-484) (QUOTE (-822)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-484) (QUOTE (-822)))) (|HasCategory| (-484) (QUOTE (-118)))))
+((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T))
+((|HasCategory| (-485) (QUOTE (-823))) (|HasCategory| (-485) (QUOTE (-952 (-1091)))) (|HasCategory| (-485) (QUOTE (-118))) (|HasCategory| (-485) (QUOTE (-120))) (|HasCategory| (-485) (QUOTE (-555 (-474)))) (|HasCategory| (-485) (QUOTE (-935))) (|HasCategory| (-485) (QUOTE (-742))) (|HasCategory| (-485) (QUOTE (-758))) (OR (|HasCategory| (-485) (QUOTE (-742))) (|HasCategory| (-485) (QUOTE (-758)))) (|HasCategory| (-485) (QUOTE (-952 (-485)))) (|HasCategory| (-485) (QUOTE (-1067))) (|HasCategory| (-485) (QUOTE (-798 (-328)))) (|HasCategory| (-485) (QUOTE (-798 (-485)))) (|HasCategory| (-485) (QUOTE (-555 (-802 (-328))))) (|HasCategory| (-485) (QUOTE (-555 (-802 (-485))))) (|HasCategory| (-485) (QUOTE (-189))) (|HasCategory| (-485) (QUOTE (-813 (-1091)))) (|HasCategory| (-485) (QUOTE (-190))) (|HasCategory| (-485) (QUOTE (-811 (-1091)))) (|HasCategory| (-485) (QUOTE (-454 (-1091) (-485)))) (|HasCategory| (-485) (QUOTE (-260 (-485)))) (|HasCategory| (-485) (QUOTE (-241 (-485) (-485)))) (|HasCategory| (-485) (QUOTE (-258))) (|HasCategory| (-485) (QUOTE (-484))) (|HasCategory| (-485) (QUOTE (-582 (-485)))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-485) (QUOTE (-823)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-485) (QUOTE (-823)))) (|HasCategory| (-485) (QUOTE (-118)))))
(-78)
((|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 `n' and property list `props'.")) (|properties| (((|List| (|Property|)) $) "\\spad{properties(b)} returns the properties associated with binding \\spad{b}.")) (|name| (((|Identifier|) $) "\\spad{name(b)} returns the name of binding \\spad{b}")))
NIL
@@ -254,11 +254,11 @@ NIL
NIL
(-81)
((|constructor| (NIL "\\spadtype{Bits} provides logical functions for Indexed Bits.")) (|bits| (($ (|NonNegativeInteger|) (|Boolean|)) "\\spad{bits(n,b)} creates bits with \\spad{n} values of \\spad{b}")))
-((-3993 . T) (-3992 . T))
-((-12 (|HasCategory| (-85) (QUOTE (-259 (-85)))) (|HasCategory| (-85) (QUOTE (-1013)))) (|HasCategory| (-85) (QUOTE (-554 (-473)))) (|HasCategory| (-85) (QUOTE (-757))) (|HasCategory| (-484) (QUOTE (-757))) (|HasCategory| (-85) (QUOTE (-1013))) (|HasCategory| (-85) (QUOTE (-553 (-773)))) (|HasCategory| (-85) (QUOTE (-72))))
+((-3997 . T) (-3996 . T))
+((-12 (|HasCategory| (-85) (QUOTE (-260 (-85)))) (|HasCategory| (-85) (QUOTE (-1015)))) (|HasCategory| (-85) (QUOTE (-555 (-474)))) (|HasCategory| (-85) (QUOTE (-758))) (|HasCategory| (-485) (QUOTE (-758))) (|HasCategory| (-85) (QUOTE (-1015))) (|HasCategory| (-85) (QUOTE (-554 (-774)))) (|HasCategory| (-85) (QUOTE (-72))))
(-82 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}")))
-((-3987 . T) (-3986 . T))
+((-3991 . T) (-3990 . T))
NIL
(-83 S)
((|constructor| (NIL "This is the category of Boolean logic structures.")) (|or| (($ $ $) "\\spad{x or y} returns the disjunction of \\spad{x} and \\spad{y}.")) (|and| (($ $ $) "\\spad{x and y} returns the conjunction of \\spad{x} and \\spad{y}.")) (|not| (($ $) "\\spad{not x} returns the complement or negation of \\spad{x}.")))
@@ -280,22 +280,22 @@ NIL
((|constructor| (NIL "This package exports functions to set some commonly used properties of operators,{} including properties which contain functions.")) (|constantOpIfCan| (((|Union| |#1| "failed") (|BasicOperator|)) "\\spad{constantOpIfCan(op)} returns \\spad{a} if \\spad{op} is the constant nullary operator always returning \\spad{a},{} \"failed\" otherwise.")) (|constantOperator| (((|BasicOperator|) |#1|) "\\spad{constantOperator(a)} returns a nullary operator op such that \\spad{op()} always evaluate to \\spad{a}.")) (|derivative| (((|Union| (|List| (|Mapping| |#1| (|List| |#1|))) "failed") (|BasicOperator|)) "\\spad{derivative(op)} returns the value of the \"\\%diff\" property of \\spad{op} if it has one,{} and \"failed\" otherwise.") (((|BasicOperator|) (|BasicOperator|) (|Mapping| |#1| |#1|)) "\\spad{derivative(op, foo)} attaches foo as the \"\\%diff\" property of \\spad{op}. If \\spad{op} has an \"\\%diff\" property \\spad{f},{} then applying a derivation \\spad{D} to \\spad{op}(a) returns \\spad{f(a) * D(a)}. Argument \\spad{op} must be unary.") (((|BasicOperator|) (|BasicOperator|) (|List| (|Mapping| |#1| (|List| |#1|)))) "\\spad{derivative(op, [foo1,...,foon])} attaches [\\spad{foo1},{}...,{}foon] as the \"\\%diff\" property of \\spad{op}. If \\spad{op} has an \"\\%diff\" property \\spad{[f1,...,fn]} then applying a derivation \\spad{D} to \\spad{op(a1,...,an)} returns \\spad{f1(a1,...,an) * D(a1) + ... + fn(a1,...,an) * D(an)}.")) (|evaluate| (((|Union| (|Mapping| |#1| (|List| |#1|)) "failed") (|BasicOperator|)) "\\spad{evaluate(op)} returns the value of the \"\\%eval\" property of \\spad{op} if it has one,{} and \"failed\" otherwise.") (((|BasicOperator|) (|BasicOperator|) (|Mapping| |#1| |#1|)) "\\spad{evaluate(op, foo)} attaches foo as the \"\\%eval\" property of \\spad{op}. If \\spad{op} has an \"\\%eval\" property \\spad{f},{} then applying \\spad{op} to a returns the result of \\spad{f(a)}. Argument \\spad{op} must be unary.") (((|BasicOperator|) (|BasicOperator|) (|Mapping| |#1| (|List| |#1|))) "\\spad{evaluate(op, foo)} attaches foo as the \"\\%eval\" property of \\spad{op}. If \\spad{op} has an \"\\%eval\" property \\spad{f},{} then applying \\spad{op} to \\spad{(a1,...,an)} returns the result of \\spad{f(a1,...,an)}.") (((|Union| |#1| "failed") (|BasicOperator|) (|List| |#1|)) "\\spad{evaluate(op, [a1,...,an])} checks if \\spad{op} has an \"\\%eval\" property \\spad{f}. If it has,{} then \\spad{f(a1,...,an)} is returned,{} and \"failed\" otherwise.")))
NIL
NIL
-(-88 -3091 UP)
+(-88 -3094 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
(-89 |p|)
((|constructor| (NIL "Stream-based implementation of 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}.")))
-((-3985 . T) ((-3994 "*") . T) (-3986 . T) (-3987 . T) (-3989 . T))
+((-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T))
NIL
(-90 |p|)
((|constructor| (NIL "Stream-based implementation of 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}.")))
-((-3984 . T) (-3990 . T) (-3985 . T) ((-3994 "*") . T) (-3986 . T) (-3987 . T) (-3989 . T))
-((|HasCategory| (-89 |#1|) (QUOTE (-822))) (|HasCategory| (-89 |#1|) (QUOTE (-951 (-1089)))) (|HasCategory| (-89 |#1|) (QUOTE (-118))) (|HasCategory| (-89 |#1|) (QUOTE (-120))) (|HasCategory| (-89 |#1|) (QUOTE (-554 (-473)))) (|HasCategory| (-89 |#1|) (QUOTE (-934))) (|HasCategory| (-89 |#1|) (QUOTE (-741))) (|HasCategory| (-89 |#1|) (QUOTE (-757))) (OR (|HasCategory| (-89 |#1|) (QUOTE (-741))) (|HasCategory| (-89 |#1|) (QUOTE (-757)))) (|HasCategory| (-89 |#1|) (QUOTE (-951 (-484)))) (|HasCategory| (-89 |#1|) (QUOTE (-1065))) (|HasCategory| (-89 |#1|) (QUOTE (-797 (-327)))) (|HasCategory| (-89 |#1|) (QUOTE (-797 (-484)))) (|HasCategory| (-89 |#1|) (QUOTE (-554 (-801 (-327))))) (|HasCategory| (-89 |#1|) (QUOTE (-554 (-801 (-484))))) (|HasCategory| (-89 |#1|) (QUOTE (-581 (-484)))) (|HasCategory| (-89 |#1|) (QUOTE (-189))) (|HasCategory| (-89 |#1|) (QUOTE (-812 (-1089)))) (|HasCategory| (-89 |#1|) (QUOTE (-190))) (|HasCategory| (-89 |#1|) (QUOTE (-810 (-1089)))) (|HasCategory| (-89 |#1|) (|%list| (QUOTE -453) (QUOTE (-1089)) (|%list| (QUOTE -89) (|devaluate| |#1|)))) (|HasCategory| (-89 |#1|) (|%list| (QUOTE -259) (|%list| (QUOTE -89) (|devaluate| |#1|)))) (|HasCategory| (-89 |#1|) (|%list| (QUOTE -241) (|%list| (QUOTE -89) (|devaluate| |#1|)) (|%list| (QUOTE -89) (|devaluate| |#1|)))) (|HasCategory| (-89 |#1|) (QUOTE (-257))) (|HasCategory| (-89 |#1|) (QUOTE (-483))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-89 |#1|) (QUOTE (-822)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-89 |#1|) (QUOTE (-822)))) (|HasCategory| (-89 |#1|) (QUOTE (-118)))))
+((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T))
+((|HasCategory| (-89 |#1|) (QUOTE (-823))) (|HasCategory| (-89 |#1|) (QUOTE (-952 (-1091)))) (|HasCategory| (-89 |#1|) (QUOTE (-118))) (|HasCategory| (-89 |#1|) (QUOTE (-120))) (|HasCategory| (-89 |#1|) (QUOTE (-555 (-474)))) (|HasCategory| (-89 |#1|) (QUOTE (-935))) (|HasCategory| (-89 |#1|) (QUOTE (-742))) (|HasCategory| (-89 |#1|) (QUOTE (-758))) (OR (|HasCategory| (-89 |#1|) (QUOTE (-742))) (|HasCategory| (-89 |#1|) (QUOTE (-758)))) (|HasCategory| (-89 |#1|) (QUOTE (-952 (-485)))) (|HasCategory| (-89 |#1|) (QUOTE (-1067))) (|HasCategory| (-89 |#1|) (QUOTE (-798 (-328)))) (|HasCategory| (-89 |#1|) (QUOTE (-798 (-485)))) (|HasCategory| (-89 |#1|) (QUOTE (-555 (-802 (-328))))) (|HasCategory| (-89 |#1|) (QUOTE (-555 (-802 (-485))))) (|HasCategory| (-89 |#1|) (QUOTE (-582 (-485)))) (|HasCategory| (-89 |#1|) (QUOTE (-189))) (|HasCategory| (-89 |#1|) (QUOTE (-813 (-1091)))) (|HasCategory| (-89 |#1|) (QUOTE (-190))) (|HasCategory| (-89 |#1|) (QUOTE (-811 (-1091)))) (|HasCategory| (-89 |#1|) (|%list| (QUOTE -454) (QUOTE (-1091)) (|%list| (QUOTE -89) (|devaluate| |#1|)))) (|HasCategory| (-89 |#1|) (|%list| (QUOTE -260) (|%list| (QUOTE -89) (|devaluate| |#1|)))) (|HasCategory| (-89 |#1|) (|%list| (QUOTE -241) (|%list| (QUOTE -89) (|devaluate| |#1|)) (|%list| (QUOTE -89) (|devaluate| |#1|)))) (|HasCategory| (-89 |#1|) (QUOTE (-258))) (|HasCategory| (-89 |#1|) (QUOTE (-484))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-89 |#1|) (QUOTE (-823)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-89 |#1|) (QUOTE (-823)))) (|HasCategory| (-89 |#1|) (QUOTE (-118)))))
(-91 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" $) "\\spad{setelt(a,\"right\",b)} (also written \\axiom{\\spad{b} . right := \\spad{b}}) is equivalent to \\axiom{setright!(a,{}\\spad{b})}.") (($ $ "left" $) "\\spad{setelt(a,\"left\",b)} (also written \\axiom{a . left := \\spad{b}}) is equivalent to \\axiom{setleft!(a,{}\\spad{b})}.")) (|right| (($ $) "\\spad{right(a)} returns the right child.")) (|elt| (($ $ "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| (($ $) "\\spad{left(u)} returns the left child.")))
NIL
-((|HasAttribute| |#1| (QUOTE -3993)))
+((|HasAttribute| |#1| (QUOTE -3997)))
(-92 S)
((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "right" $) "\\spad{setelt(a,\"right\",b)} (also written \\axiom{\\spad{b} . right := \\spad{b}}) is equivalent to \\axiom{setright!(a,{}\\spad{b})}.") (($ $ "left" $) "\\spad{setelt(a,\"left\",b)} (also written \\axiom{a . left := \\spad{b}}) is equivalent to \\axiom{setleft!(a,{}\\spad{b})}.")) (|right| (($ $) "\\spad{right(a)} returns the right child.")) (|elt| (($ $ "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
@@ -306,15 +306,15 @@ NIL
NIL
(-94 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")))
-((-3992 . T) (-3993 . T))
-((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1013))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-72))))
+((-3996 . T) (-3997 . T))
+((-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1015))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| |#1| (QUOTE (-554 (-774)))) (|HasCategory| |#1| (QUOTE (-72))))
(-95 S)
((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")))
NIL
NIL
(-96)
((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")))
-((-3993 . T) (-3992 . T))
+((-3997 . T) (-3996 . T))
NIL
(-97 A S)
((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#2| $) "\\spad{node(left,v,right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components")))
@@ -322,24 +322,24 @@ NIL
NIL
(-98 S)
((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#1| $) "\\spad{node(left,v,right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components")))
-((-3992 . T) (-3993 . T))
+((-3996 . T) (-3997 . T))
NIL
(-99 S)
((|constructor| (NIL "\\spadtype{BinaryTournament(S)} is the domain of binary trees where elements are ordered down the tree. A binary search tree is either empty or is a node containing a \\spadfun{value} of type \\spad{S},{} and a \\spadfun{right} and a \\spadfun{left} which are both \\spadtype{BinaryTree(S)}")) (|insert!| (($ |#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.")))
-((-3992 . T) (-3993 . T))
-((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1013))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-72))))
+((-3996 . T) (-3997 . T))
+((-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1015))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| |#1| (QUOTE (-554 (-774)))) (|HasCategory| |#1| (QUOTE (-72))))
(-100 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.")))
-((-3992 . T) (-3993 . T))
-((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1013))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-72))))
+((-3996 . T) (-3997 . T))
+((-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1015))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| |#1| (QUOTE (-554 (-774)))) (|HasCategory| |#1| (QUOTE (-72))))
(-101)
((|constructor| (NIL "Byte is the datatype of 8-bit sized unsigned integer values.")) (|sample| (($) "\\spad{sample} gives a sample datum of type Byte.")) (|bitior| (($ $ $) "bitor(\\spad{x},{}\\spad{y}) returns the bitwise `inclusive or' of `x' and `y'.")) (|bitand| (($ $ $) "\\spad{bitand(x,y)} returns the bitwise `and' of `x' and `y'.")) (|byte| (($ (|NonNegativeInteger|)) "\\spad{byte(x)} injects the unsigned integer value `v' into the Byte algebra. `v' must be non-negative and less than 256.")))
NIL
NIL
(-102)
((|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 `n'. The array can then store up to `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 `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.")))
-((-3993 . T) (-3992 . T))
-((OR (-12 (|HasCategory| (-101) (QUOTE (-259 (-101)))) (|HasCategory| (-101) (QUOTE (-757)))) (-12 (|HasCategory| (-101) (QUOTE (-259 (-101)))) (|HasCategory| (-101) (QUOTE (-1013))))) (|HasCategory| (-101) (QUOTE (-553 (-773)))) (|HasCategory| (-101) (QUOTE (-554 (-473)))) (OR (|HasCategory| (-101) (QUOTE (-757))) (|HasCategory| (-101) (QUOTE (-1013)))) (|HasCategory| (-101) (QUOTE (-757))) (OR (|HasCategory| (-101) (QUOTE (-72))) (|HasCategory| (-101) (QUOTE (-757))) (|HasCategory| (-101) (QUOTE (-1013)))) (|HasCategory| (-484) (QUOTE (-757))) (|HasCategory| (-101) (QUOTE (-1013))) (|HasCategory| (-101) (QUOTE (-72))) (-12 (|HasCategory| (-101) (QUOTE (-259 (-101)))) (|HasCategory| (-101) (QUOTE (-1013)))))
+((-3997 . T) (-3996 . T))
+((OR (-12 (|HasCategory| (-101) (QUOTE (-260 (-101)))) (|HasCategory| (-101) (QUOTE (-758)))) (-12 (|HasCategory| (-101) (QUOTE (-260 (-101)))) (|HasCategory| (-101) (QUOTE (-1015))))) (|HasCategory| (-101) (QUOTE (-554 (-774)))) (|HasCategory| (-101) (QUOTE (-555 (-474)))) (OR (|HasCategory| (-101) (QUOTE (-758))) (|HasCategory| (-101) (QUOTE (-1015)))) (|HasCategory| (-101) (QUOTE (-758))) (OR (|HasCategory| (-101) (QUOTE (-72))) (|HasCategory| (-101) (QUOTE (-758))) (|HasCategory| (-101) (QUOTE (-1015)))) (|HasCategory| (-485) (QUOTE (-758))) (|HasCategory| (-101) (QUOTE (-1015))) (|HasCategory| (-101) (QUOTE (-72))) (-12 (|HasCategory| (-101) (QUOTE (-260 (-101)))) (|HasCategory| (-101) (QUOTE (-1015)))))
(-103)
((|constructor| (NIL "This datatype describes byte order of machine values stored memory.")) (|unknownEndian| (($) "\\spad{unknownEndian} for none of the above.")) (|bigEndian| (($) "\\spad{bigEndian} describes big endian host")) (|littleEndian| (($) "\\spad{littleEndian} describes little endian host")))
NIL
@@ -358,13 +358,13 @@ NIL
NIL
(-107)
((|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") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,D) -> D} which is commutative.")))
-(((-3994 "*") . T))
+(((-3998 "*") . T))
NIL
-(-108 |minix| -2620 R)
+(-108 |minix| -2623 R)
((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\spad{sample()} returns an object of type \\%.")) (|unravel| (($ (|List| |#3|)) "\\spad{unravel(t)} produces a tensor from a list of components such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|ravel| (((|List| |#3|) $) "\\spad{ravel(t)} produces a list of components from a tensor such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|leviCivitaSymbol| (($) "\\spad{leviCivitaSymbol()} is the rank \\spad{dim} tensor defined by \\spad{leviCivitaSymbol()(i1,...idim) = +1/0/-1} if \\spad{i1,...,idim} is an even/is nota /is an odd permutation of \\spad{minix,...,minix+dim-1}.")) (|kroneckerDelta| (($) "\\spad{kroneckerDelta()} is the rank 2 tensor defined by \\indented{3}{\\spad{kroneckerDelta()(i,j)}} \\indented{6}{\\spad{= 1\\space{2}if i = j}} \\indented{6}{\\spad{= 0 if\\space{2}i \\~= j}}")) (|reindex| (($ $ (|List| (|Integer|))) "\\spad{reindex(t,[i1,...,idim])} permutes the indices of \\spad{t}. For example,{} if \\spad{r = reindex(t, [4,1,2,3])} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank for tensor given by \\indented{4}{\\spad{r(i,j,k,l) = t(l,i,j,k)}.}")) (|transpose| (($ $ (|Integer|) (|Integer|)) "\\spad{transpose(t,i,j)} exchanges the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices of \\spad{t}. For example,{} if \\spad{r = transpose(t,2,3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,j,k,l) = t(i,k,j,l)}.}") (($ $) "\\spad{transpose(t)} exchanges the first and last indices of \\spad{t}. For example,{} if \\spad{r = transpose(t)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,j,k,l) = t(l,j,k,i)}.}")) (|contract| (($ $ (|Integer|) (|Integer|)) "\\spad{contract(t,i,j)} is the contraction of tensor \\spad{t} which sums along the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices. For example,{} if \\spad{r = contract(t,1,3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 2 \\spad{(= 4 - 2)} tensor given by \\indented{4}{\\spad{r(i,j) = sum(h=1..dim,t(h,i,h,j))}.}") (($ $ (|Integer|) $ (|Integer|)) "\\spad{contract(t,i,s,j)} is the inner product of tenors \\spad{s} and \\spad{t} which sums along the \\spad{k1}\\spad{-}th index of \\spad{t} and the \\spad{k2}\\spad{-}th index of \\spad{s}. For example,{} if \\spad{r = contract(s,2,t,1)} for rank 3 tensors rank 3 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is the rank 4 \\spad{(= 3 + 3 - 2)} tensor given by \\indented{4}{\\spad{r(i,j,k,l) = sum(h=1..dim,s(i,h,j)*t(h,k,l))}.}")) (* (($ $ $) "\\spad{s*t} is the inner product of the tensors \\spad{s} and \\spad{t} which contracts the last index of \\spad{s} with the first index of \\spad{t},{} \\spadignore{i.e.} \\indented{4}{\\spad{t*s = contract(t,rank t, s, 1)}} \\indented{4}{\\spad{t*s = sum(k=1..N, t[i1,..,iN,k]*s[k,j1,..,jM])}} This is compatible with the use of \\spad{M*v} to denote the matrix-vector inner product.")) (|product| (($ $ $) "\\spad{product(s,t)} is the outer product of the tensors \\spad{s} and \\spad{t}. For example,{} if \\spad{r = product(s,t)} for rank 2 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is a rank 4 tensor given by \\indented{4}{\\spad{r(i,j,k,l) = s(i,j)*t(k,l)}.}")) (|elt| ((|#3| $ (|List| (|Integer|))) "\\spad{elt(t,[i1,...,iN])} gives a component of a rank \\spad{N} tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,i,j,k,l)} gives a component of a rank 4 tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,i,j,k)} gives a component of a rank 3 tensor.") ((|#3| $ (|Integer|) (|Integer|)) "\\spad{elt(t,i,j)} gives a component of a rank 2 tensor.") ((|#3| $) "\\spad{elt(t)} gives the component of a rank 0 tensor.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(t)} returns the tensorial rank of \\spad{t} (that is,{} the number of indices). This is the same as the graded module degree.")))
NIL
NIL
-(-109 |minix| -2620 S T$)
+(-109 |minix| -2623 S T$)
((|constructor| (NIL "This package provides functions to enable conversion of tensors given conversion of the components.")) (|map| (((|CartesianTensor| |#1| |#2| |#4|) (|Mapping| |#4| |#3|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{map(f,ts)} does a componentwise conversion of the tensor \\spad{ts} to a tensor with components of type \\spad{T}.")) (|reshape| (((|CartesianTensor| |#1| |#2| |#4|) (|List| |#4|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{reshape(lt,ts)} organizes the list of components \\spad{lt} into a tensor with the same shape as \\spad{ts}.")))
NIL
NIL
@@ -386,8 +386,8 @@ NIL
NIL
(-114)
((|constructor| (NIL "This domain allows classes of characters to be defined and manipulated efficiently.")) (|alphanumeric| (($) "\\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}.")))
-((-3992 . T) (-3982 . T) (-3993 . T))
-((OR (-12 (|HasCategory| (-117) (QUOTE (-259 (-117)))) (|HasCategory| (-117) (QUOTE (-317)))) (-12 (|HasCategory| (-117) (QUOTE (-259 (-117)))) (|HasCategory| (-117) (QUOTE (-1013))))) (|HasCategory| (-117) (QUOTE (-554 (-473)))) (|HasCategory| (-117) (QUOTE (-317))) (|HasCategory| (-117) (QUOTE (-757))) (|HasCategory| (-117) (QUOTE (-1013))) (|HasCategory| (-117) (QUOTE (-553 (-773)))) (|HasCategory| (-117) (QUOTE (-72))) (-12 (|HasCategory| (-117) (QUOTE (-259 (-117)))) (|HasCategory| (-117) (QUOTE (-1013)))))
+((-3996 . T) (-3986 . T) (-3997 . T))
+((OR (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-318)))) (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-1015))))) (|HasCategory| (-117) (QUOTE (-555 (-474)))) (|HasCategory| (-117) (QUOTE (-318))) (|HasCategory| (-117) (QUOTE (-758))) (|HasCategory| (-117) (QUOTE (-1015))) (|HasCategory| (-117) (QUOTE (-554 (-774)))) (|HasCategory| (-117) (QUOTE (-72))) (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-1015)))))
(-115 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}'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}'s.")) (|commonDenominator| ((|#1| |#3|) "\\spad{commonDenominator([q1,...,qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}qn.")))
NIL
@@ -402,7 +402,7 @@ NIL
NIL
(-118)
((|constructor| (NIL "Rings of Characteristic Non Zero")) (|charthRoot| (((|Maybe| $) $) "\\spad{charthRoot(x)} returns the \\spad{p}th root of \\spad{x} where \\spad{p} is the characteristic of the ring.")))
-((-3989 . T))
+((-3993 . T))
NIL
(-119 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 'x,{} then it returns the characteristic polynomial expressed as a polynomial in 'x.")))
@@ -410,9 +410,9 @@ NIL
NIL
(-120)
((|constructor| (NIL "Rings of Characteristic Zero.")))
-((-3989 . T))
+((-3993 . T))
NIL
-(-121 -3091 UP UPUP)
+(-121 -3094 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
@@ -423,14 +423,14 @@ NIL
(-123 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|) $) "\\spad{select(p,u)} returns a copy of \\spad{u} containing only those elements such \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{select(\\spad{p},{}\\spad{u}) == [\\spad{x} for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})]}.")) (|remove| (($ |#2| $) "\\spad{remove(x,u)} returns a copy of \\spad{u} with all elements \\axiom{\\spad{y} = \\spad{x}} removed. Note: \\axiom{remove(\\spad{y},{}\\spad{c}) == [\\spad{x} for \\spad{x} in \\spad{c} | \\spad{x} ~= \\spad{y}]}.") (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{remove(p,u)} returns a copy of \\spad{u} removing all elements \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{remove(\\spad{p},{}\\spad{u}) == [\\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| (QUOTE (-554 (-473)))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasAttribute| |#1| (QUOTE -3992)))
+((|HasCategory| |#2| (QUOTE (-555 (-474)))) (|HasCategory| |#2| (QUOTE (-1015))) (|HasAttribute| |#1| (QUOTE -3996)))
(-124 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|) $) "\\spad{select(p,u)} returns a copy of \\spad{u} containing only those elements such \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{select(\\spad{p},{}\\spad{u}) == [\\spad{x} for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})]}.")) (|remove| (($ |#1| $) "\\spad{remove(x,u)} returns a copy of \\spad{u} with all elements \\axiom{\\spad{y} = \\spad{x}} removed. Note: \\axiom{remove(\\spad{y},{}\\spad{c}) == [\\spad{x} for \\spad{x} in \\spad{c} | \\spad{x} ~= \\spad{y}]}.") (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove(p,u)} returns a copy of \\spad{u} removing all elements \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{remove(\\spad{p},{}\\spad{u}) == [\\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
(-125 |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.")))
-((-3987 . T) (-3986 . T) (-3989 . T))
+((-3991 . T) (-3990 . T) (-3993 . T))
NIL
(-126)
((|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.")))
@@ -452,7 +452,7 @@ 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
-(-131 R -3091)
+(-131 R -3094)
((|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})/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.} 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.} 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.} n!/(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
@@ -483,10 +483,10 @@ NIL
(-138 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 (-822))) (|HasCategory| |#2| (QUOTE (-483))) (|HasCategory| |#2| (QUOTE (-916))) (|HasCategory| |#2| (QUOTE (-1114))) (|HasCategory| |#2| (QUOTE (-973))) (|HasCategory| |#2| (QUOTE (-934))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-554 (-473)))) (|HasCategory| |#2| (QUOTE (-311))) (|HasAttribute| |#2| (QUOTE -3988)) (|HasAttribute| |#2| (QUOTE -3991)) (|HasCategory| |#2| (QUOTE (-257))) (|HasCategory| |#2| (QUOTE (-495))))
+((|HasCategory| |#2| (QUOTE (-823))) (|HasCategory| |#2| (QUOTE (-484))) (|HasCategory| |#2| (QUOTE (-917))) (|HasCategory| |#2| (QUOTE (-1116))) (|HasCategory| |#2| (QUOTE (-975))) (|HasCategory| |#2| (QUOTE (-935))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-555 (-474)))) (|HasCategory| |#2| (QUOTE (-312))) (|HasAttribute| |#2| (QUOTE -3992)) (|HasAttribute| |#2| (QUOTE -3995)) (|HasCategory| |#2| (QUOTE (-258))) (|HasCategory| |#2| (QUOTE (-496))))
(-139 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})")))
-((-3985 OR (|has| |#1| (-495)) (-12 (|has| |#1| (-257)) (|has| |#1| (-822)))) (-3990 |has| |#1| (-311)) (-3984 |has| |#1| (-311)) (-3988 |has| |#1| (-6 -3988)) (-3991 |has| |#1| (-6 -3991)) (-1374 . T) ((-3994 "*") . T) (-3986 . T) (-3987 . T) (-3989 . T))
+((-3989 OR (|has| |#1| (-496)) (-12 (|has| |#1| (-258)) (|has| |#1| (-823)))) (-3994 |has| |#1| (-312)) (-3988 |has| |#1| (-312)) (-3992 |has| |#1| (-6 -3992)) (-3995 |has| |#1| (-6 -3995)) (-1377 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T))
NIL
(-140 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.")))
@@ -498,8 +498,8 @@ NIL
NIL
(-142 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}.")))
-((-3985 OR (|has| |#1| (-495)) (-12 (|has| |#1| (-257)) (|has| |#1| (-822)))) (-3990 |has| |#1| (-311)) (-3984 |has| |#1| (-311)) (-3988 |has| |#1| (-6 -3988)) (-3991 |has| |#1| (-6 -3991)) (-1374 . T) ((-3994 "*") . T) (-3986 . T) (-3987 . T) (-3989 . T))
-((|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-298))) (OR (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-298)))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-317))) (OR (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-298)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-311)))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-298)))) (|HasCategory| |#1| (QUOTE (-810 (-1089)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-810 (-1089))))) (|HasCategory| |#1| (QUOTE (-812 (-1089))))) (|HasCategory| |#1| (QUOTE (-581 (-484)))) (OR (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-951 (-347 (-484)))))) (|HasCategory| |#1| (QUOTE (-951 (-347 (-484))))) (|HasCategory| |#1| (QUOTE (-951 (-484)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-257))) (|HasCategory| |#1| (QUOTE (-822)))) (-12 (|HasCategory| |#1| (QUOTE (-298))) (|HasCategory| |#1| (QUOTE (-822)))) (|HasCategory| |#1| (QUOTE (-311)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-257))) (|HasCategory| |#1| (QUOTE (-822)))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-822)))) (-12 (|HasCategory| |#1| (QUOTE (-298))) (|HasCategory| |#1| (QUOTE (-822))))) (OR (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-495)))) (-12 (|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| |#1| (QUOTE (-1114)))) (|HasCategory| |#1| (QUOTE (-1114))) (|HasCategory| |#1| (QUOTE (-934))) (|HasCategory| |#1| (QUOTE (-554 (-473)))) (OR (|HasCategory| |#1| (QUOTE (-257))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-298))) (|HasCategory| |#1| (QUOTE (-495)))) (OR (|HasCategory| |#1| (QUOTE (-257))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-298)))) (|HasCategory| |#1| (QUOTE (-554 (-801 (-327))))) (|HasCategory| |#1| (QUOTE (-554 (-801 (-484))))) (|HasCategory| |#1| (QUOTE (-797 (-327)))) (|HasCategory| |#1| (QUOTE (-797 (-484)))) (|HasCategory| |#1| (|%list| (QUOTE -453) (QUOTE (-1089)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -241) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-973))) (-12 (|HasCategory| |#1| (QUOTE (-973))) (|HasCategory| |#1| (QUOTE (-1114)))) (|HasCategory| |#1| (QUOTE (-483))) (|HasCategory| |#1| (QUOTE (-257))) (|HasCategory| |#1| (QUOTE (-822))) (OR (-12 (|HasCategory| |#1| (QUOTE (-257))) (|HasCategory| |#1| (QUOTE (-822)))) (|HasCategory| |#1| (QUOTE (-311)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-257))) (|HasCategory| |#1| (QUOTE (-822)))) (|HasCategory| |#1| (QUOTE (-495)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-311)))) (|HasCategory| |#1| (QUOTE (-189)))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-812 (-1089)))) (|HasCategory| |#1| (QUOTE (-190))) (-12 (|HasCategory| |#1| (QUOTE (-257))) (|HasCategory| |#1| (QUOTE (-822)))) (|HasAttribute| |#1| (QUOTE -3988)) (|HasAttribute| |#1| (QUOTE -3991)) (-12 (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-311)))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-812 (-1089))))) (-12 (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-311)))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-810 (-1089))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-257))) (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-298)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-257))) (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118)))))
+((-3989 OR (|has| |#1| (-496)) (-12 (|has| |#1| (-258)) (|has| |#1| (-823)))) (-3994 |has| |#1| (-312)) (-3988 |has| |#1| (-312)) (-3992 |has| |#1| (-6 -3992)) (-3995 |has| |#1| (-6 -3995)) (-1377 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T))
+((|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-299))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-299)))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-318))) (OR (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-299)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-312)))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-299)))) (|HasCategory| |#1| (QUOTE (-811 (-1091)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-811 (-1091))))) (|HasCategory| |#1| (QUOTE (-813 (-1091))))) (|HasCategory| |#1| (QUOTE (-582 (-485)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-952 (-348 (-485)))))) (|HasCategory| |#1| (QUOTE (-952 (-348 (-485))))) (|HasCategory| |#1| (QUOTE (-952 (-485)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-823)))) (-12 (|HasCategory| |#1| (QUOTE (-299))) (|HasCategory| |#1| (QUOTE (-823)))) (|HasCategory| |#1| (QUOTE (-312)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-823)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-823)))) (-12 (|HasCategory| |#1| (QUOTE (-299))) (|HasCategory| |#1| (QUOTE (-823))))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-496)))) (-12 (|HasCategory| |#1| (QUOTE (-917))) (|HasCategory| |#1| (QUOTE (-1116)))) (|HasCategory| |#1| (QUOTE (-1116))) (|HasCategory| |#1| (QUOTE (-935))) (|HasCategory| |#1| (QUOTE (-555 (-474)))) (OR (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-299))) (|HasCategory| |#1| (QUOTE (-496)))) (OR (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-299)))) (|HasCategory| |#1| (QUOTE (-555 (-802 (-328))))) (|HasCategory| |#1| (QUOTE (-555 (-802 (-485))))) (|HasCategory| |#1| (QUOTE (-798 (-328)))) (|HasCategory| |#1| (QUOTE (-798 (-485)))) (|HasCategory| |#1| (|%list| (QUOTE -454) (QUOTE (-1091)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -241) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-975))) (-12 (|HasCategory| |#1| (QUOTE (-975))) (|HasCategory| |#1| (QUOTE (-1116)))) (|HasCategory| |#1| (QUOTE (-484))) (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-823))) (OR (-12 (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-823)))) (|HasCategory| |#1| (QUOTE (-312)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-823)))) (|HasCategory| |#1| (QUOTE (-496)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-312)))) (|HasCategory| |#1| (QUOTE (-189)))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-813 (-1091)))) (|HasCategory| |#1| (QUOTE (-190))) (-12 (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-823)))) (|HasAttribute| |#1| (QUOTE -3992)) (|HasAttribute| |#1| (QUOTE -3995)) (-12 (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-312)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-813 (-1091))))) (-12 (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-312)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-811 (-1091))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-299)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118)))))
(-143 R S)
((|constructor| (NIL "This package extends maps from underlying rings to maps between complex over those rings.")) (|map| (((|Complex| |#2|) (|Mapping| |#2| |#1|) (|Complex| |#1|)) "\\spad{map(f,u)} maps \\spad{f} onto real and imaginary parts of \\spad{u}.")))
NIL
@@ -514,7 +514,7 @@ NIL
NIL
(-146)
((|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.")))
-(((-3994 "*") . T) (-3986 . T) (-3987 . T) (-3989 . T))
+(((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T))
NIL
(-147)
((|constructor| (NIL "This category is the root of the I/O conduits.")) (|close!| (($ $) "\\spad{close!(c)} closes the conduit \\spad{c},{} changing its state to one that is invalid for future read or write operations.")))
@@ -522,7 +522,7 @@ NIL
NIL
(-148 R)
((|constructor| (NIL "\\spadtype{ContinuedFraction} implements general \\indented{1}{continued fractions.\\space{2}This version is not restricted to simple,{}} \\indented{1}{finite fractions and uses the \\spadtype{Stream} as a} \\indented{1}{representation.\\space{2}The arithmetic functions assume that the} \\indented{1}{approximants alternate below/above the convergence point.} \\indented{1}{This is enforced by ensuring the partial numerators and partial} \\indented{1}{denominators are greater than 0 in the Euclidean domain view of \\spad{R}} \\indented{1}{(\\spadignore{i.e.} \\spad{sizeLess?(0, x)}).}")) (|complete| (($ $) "\\spad{complete(x)} causes all entries in \\spadvar{\\spad{x}} to be computed. Normally entries are only computed as needed. If \\spadvar{\\spad{x}} is an infinite continued fraction,{} a user-initiated interrupt is necessary to stop the computation.")) (|extend| (($ $ (|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}.")))
-(((-3994 "*") . T) (-3985 . T) (-3990 . T) (-3984 . T) (-3986 . T) (-3987 . T) (-3989 . T))
+(((-3998 "*") . T) (-3989 . T) (-3994 . T) (-3988 . T) (-3990 . T) (-3991 . T) (-3993 . T))
NIL
(-149)
((|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|) $) "\\spad{findBinding(c,n)} returns the first binding associated with `n'. Otherwise `nothing.")) (|push| (($ (|Binding|) $) "\\spad{push(c,b)} augments the contour with binding `b'.")) (|bindings| (((|List| (|Binding|)) $) "\\spad{bindings(c)} returns the list of bindings in countour \\spad{c}.")))
@@ -539,7 +539,7 @@ NIL
(-152 R S CS)
((|constructor| (NIL "This package supports matching patterns involving complex expressions")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(cexpr, pat, res)} matches the pattern \\spad{pat} to the complex expression \\spad{cexpr}. res contains the variables of \\spad{pat} which are already matched and their matches.")))
NIL
-((|HasCategory| (-858 |#2|) (|%list| (QUOTE -797) (|devaluate| |#1|))))
+((|HasCategory| (-859 |#2|) (|%list| (QUOTE -798) (|devaluate| |#1|))))
(-153 R)
((|constructor| (NIL "This package \\undocumented{}")) (|multiEuclideanTree| (((|List| |#1|) (|List| |#1|) |#1|) "\\spad{multiEuclideanTree(l,r)} \\undocumented{}")) (|chineseRemainder| (((|List| |#1|) (|List| (|List| |#1|)) (|List| |#1|)) "\\spad{chineseRemainder(llv,lm)} returns a list of values,{} each of which corresponds to the Chinese remainder of the associated element of \\axiom{\\spad{llv}} and axiom{\\spad{lm}}. This is more efficient than applying chineseRemainder several times.") ((|#1| (|List| |#1|) (|List| |#1|)) "\\spad{chineseRemainder(lv,lm)} returns a value \\axiom{\\spad{v}} such that,{} if \\spad{x} is \\axiom{\\spad{lv}.\\spad{i}} modulo \\axiom{\\spad{lm}.\\spad{i}} for all \\axiom{\\spad{i}},{} then \\spad{x} is \\axiom{\\spad{v}} modulo \\axiom{\\spad{lm}(1)*lm(2)*...*lm(\\spad{n})}.")) (|modTree| (((|List| |#1|) |#1| (|List| |#1|)) "\\spad{modTree(r,l)} \\undocumented{}")))
NIL
@@ -576,7 +576,7 @@ NIL
((|constructor| (NIL "This domain enumerates the three kinds of constructors available in OpenAxiom: category constructors,{} domain constructors,{} and package constructors.")) (|package| (($) "`package' is the kind of package constructors.")) (|domain| (($) "`domain' is the kind of domain constructors")) (|category| (($) "`category' is the kind of category constructors")))
NIL
NIL
-(-162 R -3091)
+(-162 R -3094)
((|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
@@ -604,23 +604,23 @@ NIL
((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: July 2,{} 2010 Date Last Modified: July 2,{} 2010 Descrption: \\indented{2}{Representation of a dual vector space basis,{} given by symbols.}")) (|dual| (($ (|LinearBasis| |#1|)) "\\spad{dual x} constructs the dual vector of a linear element which is part of a basis.")))
NIL
NIL
-(-169 -3091 UP UPUP R)
+(-169 -3094 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
-(-170 -3091 FP)
+(-170 -3094 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 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
(-171)
((|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.")))
-((-3984 . T) (-3990 . T) (-3985 . T) ((-3994 "*") . T) (-3986 . T) (-3987 . T) (-3989 . T))
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+((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T))
+((|HasCategory| (-485) (QUOTE (-823))) (|HasCategory| (-485) (QUOTE (-952 (-1091)))) (|HasCategory| (-485) (QUOTE (-118))) (|HasCategory| (-485) (QUOTE (-120))) (|HasCategory| (-485) (QUOTE (-555 (-474)))) (|HasCategory| (-485) (QUOTE (-935))) (|HasCategory| (-485) (QUOTE (-742))) (|HasCategory| (-485) (QUOTE (-758))) (OR (|HasCategory| (-485) (QUOTE (-742))) (|HasCategory| (-485) (QUOTE (-758)))) (|HasCategory| (-485) (QUOTE (-952 (-485)))) (|HasCategory| (-485) (QUOTE (-1067))) (|HasCategory| (-485) (QUOTE (-798 (-328)))) (|HasCategory| (-485) (QUOTE (-798 (-485)))) (|HasCategory| (-485) (QUOTE (-555 (-802 (-328))))) (|HasCategory| (-485) (QUOTE (-555 (-802 (-485))))) (|HasCategory| (-485) (QUOTE (-189))) (|HasCategory| (-485) (QUOTE (-813 (-1091)))) (|HasCategory| (-485) (QUOTE (-190))) (|HasCategory| (-485) (QUOTE (-811 (-1091)))) (|HasCategory| (-485) (QUOTE (-454 (-1091) (-485)))) (|HasCategory| (-485) (QUOTE (-260 (-485)))) (|HasCategory| (-485) (QUOTE (-241 (-485) (-485)))) (|HasCategory| (-485) (QUOTE (-258))) (|HasCategory| (-485) (QUOTE (-484))) (|HasCategory| (-485) (QUOTE (-582 (-485)))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-485) (QUOTE (-823)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-485) (QUOTE (-823)))) (|HasCategory| (-485) (QUOTE (-118)))))
(-172)
((|constructor| (NIL "This domain represents the syntax of a definition.")) (|body| (((|SpadAst|) $) "\\spad{body(d)} returns the right hand side of the definition `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|) $) "\\spad{head(d)} returns the head of the definition `d'. This is a list of identifiers starting with the name of the operation followed by the name of the parameters,{} if any.")))
NIL
NIL
-(-173 R -3091)
+(-173 R -3094)
((|constructor| (NIL "\\spadtype{ElementaryFunctionDefiniteIntegration} provides functions to compute definite integrals of elementary functions.")) (|innerint| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| #1="failed") (|:| |pole| #2="potentialPole")) |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{innerint(f, x, a, b, ignore?)} should be local but conditional")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| #1#) (|:| |pole| #2#)) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|)) (|String|)) "\\spad{integrate(f, x = a..b, \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| #1#) (|:| |pole| #2#)) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|))) "\\spad{integrate(f, x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}.")))
NIL
NIL
@@ -634,19 +634,19 @@ NIL
NIL
(-176 S)
((|constructor| (NIL "Linked list implementation of a Dequeue")) (|dequeue| (($ (|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}.")))
-((-3992 . T) (-3993 . T))
-((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1013))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-72))))
+((-3996 . T) (-3997 . T))
+((-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1015))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| |#1| (QUOTE (-554 (-774)))) (|HasCategory| |#1| (QUOTE (-72))))
(-177 |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}.")))
-((-3989 . T))
+((-3993 . T))
NIL
-(-178 R -3091)
+(-178 R -3094)
((|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
(-179)
((|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.")) (|nan?| (((|Boolean|) $) "\\spad{nan? x} holds if \\spad{x} is a Not a Number floating point data in the IEEE 754 sense.")) (|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}.")))
-((-3767 . T) (-3984 . T) (-3990 . T) (-3985 . T) ((-3994 "*") . T) (-3986 . T) (-3987 . T) (-3989 . T))
+((-3771 . T) (-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T))
NIL
(-180)
((|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)}.}")))
@@ -654,19 +654,19 @@ NIL
NIL
(-181 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}")))
-((-3992 . T) (-3993 . T))
-((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1013))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-257))) (|HasCategory| |#1| (QUOTE (-495))) (|HasAttribute| |#1| (QUOTE (-3994 "*"))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-72))))
+((-3996 . T) (-3997 . T))
+((-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1015))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| |#1| (QUOTE (-554 (-774)))) (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-496))) (|HasAttribute| |#1| (QUOTE (-3998 "*"))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-72))))
(-182 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
(-183 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.")))
-((-3993 . T))
+((-3997 . T))
NIL
(-184 R)
((|constructor| (NIL "Differential extensions of a ring \\spad{R}. Given a differentiation on \\spad{R},{} extend it to a differentiation on \\%.")))
-((-3989 . T))
+((-3993 . T))
NIL
(-185 S T$)
((|constructor| (NIL "This category captures the interface of domains with a distinguished operation named \\spad{differentiate}. Usually,{} additional properties are wanted. For example,{} that it obeys the usual Leibniz identity of differentiation of product,{} in case of differential rings. One could also want \\spad{differentiate} to obey the chain rule when considering differential manifolds. The lack of specific requirement in this category is an implicit admission that currently \\Language{} is not expressive enough to express the most general notion of differentiation in an adequate manner,{} suitable for computational purposes.")) (D ((|#2| $) "\\spad{D x} is a shorthand for \\spad{differentiate x}")) (|differentiate| ((|#2| $) "\\spad{differentiate x} compute the derivative of \\spad{x}.")))
@@ -678,7 +678,7 @@ NIL
NIL
(-187 R)
((|constructor| (NIL "An \\spad{R}-module equipped with a distinguised differential operator. If \\spad{R} is a differential ring,{} then differentiation on the module should extend differentiation on the differential ring \\spad{R}. The latter can be the null operator. In that case,{} the differentiation operator on the module is just an \\spad{R}-linear operator. For that reason,{} we do not require that the ring \\spad{R} be a DifferentialRing; \\blankline")))
-((-3987 . T) (-3986 . T))
+((-3991 . T) (-3990 . T))
NIL
(-188 S)
((|constructor| (NIL "This category is like \\spadtype{DifferentialDomain} where the target of the differentiation operator is the same as its source.")) (D (($ $ (|NonNegativeInteger|)) "\\spad{D(x, n)} returns the \\spad{n}\\spad{-}th derivative of \\spad{x}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(x,n)} returns the \\spad{n}\\spad{-}th derivative of \\spad{x}.")))
@@ -690,7 +690,7 @@ NIL
NIL
(-190)
((|constructor| (NIL "An ordinary differential ring,{} that is,{} a ring with an operation \\spadfun{differentiate}. \\blankline")))
-((-3989 . T))
+((-3993 . T))
NIL
(-191)
((|constructor| (NIL "Dioid is the class of semirings where the addition operation induces a canonical order relation.")))
@@ -699,28 +699,28 @@ NIL
(-192 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 -3992)))
+((|HasAttribute| |#1| (QUOTE -3996)))
(-193 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}.")))
-((-3993 . T))
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NIL
(-194)
((|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
-(-195 S -2620 R)
+(-195 S -2623 R)
((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (|dot| ((|#3| $ $) "\\spad{dot(x,y)} computes the inner product of the vectors \\spad{x} and \\spad{y}.")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#3|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim.")) (|finiteAggregate| ((|attribute|) "attribute to indicate an aggregate of finite size")))
NIL
-((|HasCategory| |#3| (QUOTE (-311))) (|HasCategory| |#3| (QUOTE (-718))) (|HasCategory| |#3| (QUOTE (-757))) (|HasAttribute| |#3| (QUOTE -3989)) (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-317))) (|HasCategory| |#3| (QUOTE (-664))) (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-104))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-962))) (|HasCategory| |#3| (QUOTE (-1013))))
-(-196 -2620 R)
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+(-196 -2623 R)
((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (|dot| ((|#2| $ $) "\\spad{dot(x,y)} computes the inner product of the vectors \\spad{x} and \\spad{y}.")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#2|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim.")) (|finiteAggregate| ((|attribute|) "attribute to indicate an aggregate of finite size")))
-((-3986 |has| |#2| (-962)) (-3987 |has| |#2| (-962)) (-3989 |has| |#2| (-6 -3989)) (-3992 . T))
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NIL
-(-197 -2620 R)
+(-197 -2623 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.")))
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+(-198 -2623 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
@@ -734,7 +734,7 @@ NIL
NIL
(-201)
((|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}.")))
-((-3985 . T) (-3986 . T) (-3987 . T) (-3989 . T))
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NIL
(-202 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.")))
@@ -742,20 +742,20 @@ NIL
NIL
(-203 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}")))
-((-3993 . T) (-3992 . T))
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(-204 M)
((|constructor| (NIL "DiscreteLogarithmPackage implements help functions for discrete logarithms in monoids using small cyclic groups.")) (|shanksDiscLogAlgorithm| (((|Union| (|NonNegativeInteger|) "failed") |#1| |#1| (|NonNegativeInteger|)) "\\spad{shanksDiscLogAlgorithm(b,a,p)} computes \\spad{s} with \\spad{b**s = a} for assuming that \\spad{a} and \\spad{b} are elements in a 'small' cyclic group of order \\spad{p} by Shank's algorithm. Note: 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
(-205 R)
((|constructor| (NIL "Category of modules that extend differential rings. \\blankline")))
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NIL
(-206 |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")))
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(-207)
((|showSummary| (((|Void|) $) "\\spad{showSummary(d)} prints out implementation detail information of domain `d'.")) (|reflect| (($ (|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 `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 `d'.")))
NIL
@@ -770,23 +770,23 @@ NIL
NIL
(-210 |n| R M S)
((|constructor| (NIL "This constructor provides a direct product type with a left matrix-module view.")))
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(QUOTE (-1015)))) (OR (-12 (|HasCategory| |#3| (QUOTE (-952 (-485)))) (|HasCategory| |#3| (QUOTE (-1015)))) (|HasCategory| |#3| (QUOTE (-963)))) (-12 (|HasCategory| |#3| (QUOTE (-952 (-348 (-485))))) (|HasCategory| |#3| (QUOTE (-1015)))) (OR (-12 (|HasCategory| |#3| (QUOTE (-811 (-1091)))) (|HasCategory| |#3| (QUOTE (-963)))) (|HasAttribute| |#3| (QUOTE -3993)) (-12 (|HasCategory| |#3| (QUOTE (-190))) (|HasCategory| |#3| (QUOTE (-963))))) (-12 (|HasCategory| |#3| (QUOTE (-189))) (|HasCategory| |#3| (QUOTE (-963)))) (-12 (|HasCategory| |#3| (QUOTE (-813 (-1091)))) (|HasCategory| |#3| (QUOTE (-963)))) (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-104))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-554 (-774)))) (|HasCategory| |#3| (QUOTE (-72))) (-12 (|HasCategory| |#3| (QUOTE (-1015))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))))
(-212 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} := 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 (-190))))
(-213 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} := 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.")))
-(((-3994 "*") |has| |#1| (-146)) (-3985 |has| |#1| (-495)) (-3990 |has| |#1| (-6 -3990)) (-3987 . T) (-3986 . T) (-3989 . T))
+(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3994 |has| |#1| (-6 -3994)) (-3991 . T) (-3990 . T) (-3993 . T))
NIL
(-214 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}.")))
-((-3992 . T) (-3993 . T))
+((-3996 . T) (-3997 . T))
NIL
(-215 |Ex|)
((|constructor| (NIL "TopLevelDrawFunctions provides top level functions for drawing graphics of expressions.")) (|makeObject| (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSurface| |#1|) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|))) "\\spad{makeObject(surface(f(u,v),g(u,v),h(u,v)),u = a..b,v = c..d)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{x = f(u,v)},{} \\spad{y = g(u,v)},{} \\spad{z = h(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{h(t)} is the default title.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSurface| |#1|) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(surface(f(u,v),g(u,v),h(u,v)),u = a..b,v = c..d,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{x = f(u,v)},{} \\spad{y = g(u,v)},{} \\spad{z = h(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{h(t)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) |#1| (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|))) "\\spad{makeObject(f(x,y),x = a..b,y = c..d)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of \\spad{z = f(x,y)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{y} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{f(x,y)} appears as the default title.") (((|ThreeSpace| (|DoubleFloat|)) |#1| (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(f(x,y),x = a..b,y = c..d,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of \\spad{z = f(x,y)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{y} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{f(x,y)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSpaceCurve| |#1|) (|SegmentBinding| (|Float|))) "\\spad{makeObject(curve(f(t),g(t),h(t)),t = a..b)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{h(t)} is the default title.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSpaceCurve| |#1|) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(curve(f(t),g(t),h(t)),t = a..b,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{h(t)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.")) (|draw| (((|ThreeDimensionalViewport|) (|ParametricSurface| |#1|) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|))) "\\spad{draw(surface(f(u,v),g(u,v),h(u,v)),u = a..b,v = c..d)} draws the graph of the parametric surface \\spad{x = f(u,v)},{} \\spad{y = g(u,v)},{} \\spad{z = h(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{h(t)} is the default title.") (((|ThreeDimensionalViewport|) (|ParametricSurface| |#1|) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(surface(f(u,v),g(u,v),h(u,v)),u = a..b,v = c..d,l)} draws the graph of the parametric surface \\spad{x = f(u,v)},{} \\spad{y = g(u,v)},{} \\spad{z = h(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{h(t)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) |#1| (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|))) "\\spad{draw(f(x,y),x = a..b,y = c..d)} draws the graph of \\spad{z = f(x,y)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{y} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{f(x,y)} appears in the title bar.") (((|ThreeDimensionalViewport|) |#1| (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f(x,y),x = a..b,y = c..d,l)} draws the graph of \\spad{z = f(x,y)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{y} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{f(x,y)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|ParametricSpaceCurve| |#1|) (|SegmentBinding| (|Float|))) "\\spad{draw(curve(f(t),g(t),h(t)),t = a..b)} draws the graph of the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{h(t)} is the default title.") (((|ThreeDimensionalViewport|) (|ParametricSpaceCurve| |#1|) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(curve(f(t),g(t),h(t)),t = a..b,l)} draws the graph of the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{h(t)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) (|ParametricPlaneCurve| |#1|) (|SegmentBinding| (|Float|))) "\\spad{draw(curve(f(t),g(t)),t = a..b)} draws the graph of the parametric curve \\spad{x = f(t), y = g(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{(f(t),g(t))} appears in the title bar.") (((|TwoDimensionalViewport|) (|ParametricPlaneCurve| |#1|) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(curve(f(t),g(t)),t = a..b,l)} draws the graph of the parametric curve \\spad{x = f(t), y = g(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{(f(t),g(t))} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) |#1| (|SegmentBinding| (|Float|))) "\\spad{draw(f(x),x = a..b)} draws the graph of \\spad{y = f(x)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{f(x)} appears in the title bar.") (((|TwoDimensionalViewport|) |#1| (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f(x),x = a..b,l)} draws the graph of \\spad{y = f(x)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{f(x)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.")))
@@ -827,15 +827,15 @@ NIL
(-224 S R)
((|constructor| (NIL "Extension of a base differential space with a derivation. \\blankline")) (D (($ $ (|Mapping| |#2| |#2|) (|NonNegativeInteger|)) "\\spad{D(x,d,n)} is a shorthand for \\spad{differentiate(x,d,n)}.") (($ $ (|Mapping| |#2| |#2|)) "\\spad{D(x,d)} is a shorthand for \\spad{differentiate(x,d)}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|) (|NonNegativeInteger|)) "\\spad{differentiate(x,d,n)} computes the \\spad{n}\\spad{-}th derivative of \\spad{x} using a derivation extending \\spad{d} on \\spad{R}.") (($ $ (|Mapping| |#2| |#2|)) "\\spad{differentiate(x,d)} computes the derivative of \\spad{x},{} extending differentiation \\spad{d} on \\spad{R}.")))
NIL
-((|HasCategory| |#2| (QUOTE (-812 (-1089)))) (|HasCategory| |#2| (QUOTE (-189))))
+((|HasCategory| |#2| (QUOTE (-813 (-1091)))) (|HasCategory| |#2| (QUOTE (-189))))
(-225 R)
((|constructor| (NIL "Extension of a base differential space with a derivation. \\blankline")) (D (($ $ (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) "\\spad{D(x,d,n)} is a shorthand for \\spad{differentiate(x,d,n)}.") (($ $ (|Mapping| |#1| |#1|)) "\\spad{D(x,d)} is a shorthand for \\spad{differentiate(x,d)}.")) (|differentiate| (($ $ (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) "\\spad{differentiate(x,d,n)} computes the \\spad{n}\\spad{-}th derivative of \\spad{x} using a derivation extending \\spad{d} on \\spad{R}.") (($ $ (|Mapping| |#1| |#1|)) "\\spad{differentiate(x,d)} computes the derivative of \\spad{x},{} extending differentiation \\spad{d} on \\spad{R}.")))
NIL
NIL
(-226 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")))
-(((-3994 "*") |has| |#1| (-146)) (-3985 |has| |#1| (-495)) (-3990 |has| |#1| (-6 -3990)) (-3987 . T) (-3986 . T) (-3989 . T))
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(-227 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.")) (|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
@@ -848,22 +848,22 @@ 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|) $) "\\spad{degree(x)} gives the numbers of 1's in \\spad{x},{} \\spadignore{i.e.} the number of non-zero exponents in the basis element that \\spad{x} represents.")) (|coerce| (($ (|List| (|Integer|))) "\\spad{coerce(l)} converts a list of 0's and 1's into a basis element,{} where 1 (respectively 0) designates that the variable of the corresponding index of \\spad{l} is (respectively,{} is not) present. Error: if an element of \\spad{l} is not 0 or 1.")))
NIL
NIL
-(-230 R -3091)
+(-230 R -3094)
((|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
-(-231 R -3091)
+(-231 R -3094)
((|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
(-232 |Coef| UTS ULS)
((|constructor| (NIL "\\indented{1}{This package provides elementary functions on any Laurent series} domain over a field which was constructed from a Taylor series domain. These functions are implemented by calling the corresponding functions on the Taylor series domain. We also provide 'partial functions' which compute transcendental functions of Laurent series when possible and return \"failed\" when this is not possible.")) (|acsch| ((|#3| |#3|) "\\spad{acsch(z)} returns the inverse hyperbolic cosecant of Laurent series \\spad{z}.")) (|asech| ((|#3| |#3|) "\\spad{asech(z)} returns the inverse hyperbolic secant of Laurent series \\spad{z}.")) (|acoth| ((|#3| |#3|) "\\spad{acoth(z)} returns the inverse hyperbolic cotangent of Laurent series \\spad{z}.")) (|atanh| ((|#3| |#3|) "\\spad{atanh(z)} returns the inverse hyperbolic tangent of Laurent series \\spad{z}.")) (|acosh| ((|#3| |#3|) "\\spad{acosh(z)} returns the inverse hyperbolic cosine of Laurent series \\spad{z}.")) (|asinh| ((|#3| |#3|) "\\spad{asinh(z)} returns the inverse hyperbolic sine of Laurent series \\spad{z}.")) (|csch| ((|#3| |#3|) "\\spad{csch(z)} returns the hyperbolic cosecant of Laurent series \\spad{z}.")) (|sech| ((|#3| |#3|) "\\spad{sech(z)} returns the hyperbolic secant of Laurent series \\spad{z}.")) (|coth| ((|#3| |#3|) "\\spad{coth(z)} returns the hyperbolic cotangent of Laurent series \\spad{z}.")) (|tanh| ((|#3| |#3|) "\\spad{tanh(z)} returns the hyperbolic tangent of Laurent series \\spad{z}.")) (|cosh| ((|#3| |#3|) "\\spad{cosh(z)} returns the hyperbolic cosine of Laurent series \\spad{z}.")) (|sinh| ((|#3| |#3|) "\\spad{sinh(z)} returns the hyperbolic sine of Laurent series \\spad{z}.")) (|acsc| ((|#3| |#3|) "\\spad{acsc(z)} returns the arc-cosecant of Laurent series \\spad{z}.")) (|asec| ((|#3| |#3|) "\\spad{asec(z)} returns the arc-secant of Laurent series \\spad{z}.")) (|acot| ((|#3| |#3|) "\\spad{acot(z)} returns the arc-cotangent of Laurent series \\spad{z}.")) (|atan| ((|#3| |#3|) "\\spad{atan(z)} returns the arc-tangent of Laurent series \\spad{z}.")) (|acos| ((|#3| |#3|) "\\spad{acos(z)} returns the arc-cosine of Laurent series \\spad{z}.")) (|asin| ((|#3| |#3|) "\\spad{asin(z)} returns the arc-sine of Laurent series \\spad{z}.")) (|csc| ((|#3| |#3|) "\\spad{csc(z)} returns the cosecant of Laurent series \\spad{z}.")) (|sec| ((|#3| |#3|) "\\spad{sec(z)} returns the secant of Laurent series \\spad{z}.")) (|cot| ((|#3| |#3|) "\\spad{cot(z)} returns the cotangent of Laurent series \\spad{z}.")) (|tan| ((|#3| |#3|) "\\spad{tan(z)} returns the tangent of Laurent series \\spad{z}.")) (|cos| ((|#3| |#3|) "\\spad{cos(z)} returns the cosine of Laurent series \\spad{z}.")) (|sin| ((|#3| |#3|) "\\spad{sin(z)} returns the sine of Laurent series \\spad{z}.")) (|log| ((|#3| |#3|) "\\spad{log(z)} returns the logarithm of Laurent series \\spad{z}.")) (|exp| ((|#3| |#3|) "\\spad{exp(z)} returns the exponential of Laurent series \\spad{z}.")) (** ((|#3| |#3| (|Fraction| (|Integer|))) "\\spad{s ** r} raises a Laurent series \\spad{s} to a rational power \\spad{r}")))
NIL
-((|HasCategory| |#1| (QUOTE (-311))))
+((|HasCategory| |#1| (QUOTE (-312))))
(-233 |Coef| ULS UPXS EFULS)
((|constructor| (NIL "\\indented{1}{This package provides elementary functions on any Laurent series} domain over a field which was constructed from a Taylor series domain. These functions are implemented by calling the corresponding functions on the Taylor series domain. We also provide 'partial functions' which compute transcendental functions of Laurent series when possible and return \"failed\" when this is not possible.")) (|acsch| ((|#3| |#3|) "\\spad{acsch(z)} returns the inverse hyperbolic cosecant of a Puiseux series \\spad{z}.")) (|asech| ((|#3| |#3|) "\\spad{asech(z)} returns the inverse hyperbolic secant of a Puiseux series \\spad{z}.")) (|acoth| ((|#3| |#3|) "\\spad{acoth(z)} returns the inverse hyperbolic cotangent of a Puiseux series \\spad{z}.")) (|atanh| ((|#3| |#3|) "\\spad{atanh(z)} returns the inverse hyperbolic tangent of a Puiseux series \\spad{z}.")) (|acosh| ((|#3| |#3|) "\\spad{acosh(z)} returns the inverse hyperbolic cosine of a Puiseux series \\spad{z}.")) (|asinh| ((|#3| |#3|) "\\spad{asinh(z)} returns the inverse hyperbolic sine of a Puiseux series \\spad{z}.")) (|csch| ((|#3| |#3|) "\\spad{csch(z)} returns the hyperbolic cosecant of a Puiseux series \\spad{z}.")) (|sech| ((|#3| |#3|) "\\spad{sech(z)} returns the hyperbolic secant of a Puiseux series \\spad{z}.")) (|coth| ((|#3| |#3|) "\\spad{coth(z)} returns the hyperbolic cotangent of a Puiseux series \\spad{z}.")) (|tanh| ((|#3| |#3|) "\\spad{tanh(z)} returns the hyperbolic tangent of a Puiseux series \\spad{z}.")) (|cosh| ((|#3| |#3|) "\\spad{cosh(z)} returns the hyperbolic cosine of a Puiseux series \\spad{z}.")) (|sinh| ((|#3| |#3|) "\\spad{sinh(z)} returns the hyperbolic sine of a Puiseux series \\spad{z}.")) (|acsc| ((|#3| |#3|) "\\spad{acsc(z)} returns the arc-cosecant of a Puiseux series \\spad{z}.")) (|asec| ((|#3| |#3|) "\\spad{asec(z)} returns the arc-secant of a Puiseux series \\spad{z}.")) (|acot| ((|#3| |#3|) "\\spad{acot(z)} returns the arc-cotangent of a Puiseux series \\spad{z}.")) (|atan| ((|#3| |#3|) "\\spad{atan(z)} returns the arc-tangent of a Puiseux series \\spad{z}.")) (|acos| ((|#3| |#3|) "\\spad{acos(z)} returns the arc-cosine of a Puiseux series \\spad{z}.")) (|asin| ((|#3| |#3|) "\\spad{asin(z)} returns the arc-sine of a Puiseux series \\spad{z}.")) (|csc| ((|#3| |#3|) "\\spad{csc(z)} returns the cosecant of a Puiseux series \\spad{z}.")) (|sec| ((|#3| |#3|) "\\spad{sec(z)} returns the secant of a Puiseux series \\spad{z}.")) (|cot| ((|#3| |#3|) "\\spad{cot(z)} returns the cotangent of a Puiseux series \\spad{z}.")) (|tan| ((|#3| |#3|) "\\spad{tan(z)} returns the tangent of a Puiseux series \\spad{z}.")) (|cos| ((|#3| |#3|) "\\spad{cos(z)} returns the cosine of a Puiseux series \\spad{z}.")) (|sin| ((|#3| |#3|) "\\spad{sin(z)} returns the sine of a Puiseux series \\spad{z}.")) (|log| ((|#3| |#3|) "\\spad{log(z)} returns the logarithm of a Puiseux series \\spad{z}.")) (|exp| ((|#3| |#3|) "\\spad{exp(z)} returns the exponential of a Puiseux series \\spad{z}.")) (** ((|#3| |#3| (|Fraction| (|Integer|))) "\\spad{z ** r} raises a Puiseaux series \\spad{z} to a rational power \\spad{r}")))
NIL
-((|HasCategory| |#1| (QUOTE (-311))))
+((|HasCategory| |#1| (QUOTE (-312))))
(-234)
((|constructor| (NIL "This domains an expresion as elaborated by the interpreter. See Also:")) (|getOperands| (((|Union| (|List| $) "failed") $) "\\spad{getOperands(e)} returns the list of operands in `e',{} assuming it is a call form.")) (|getOperator| (((|Union| (|Identifier|) "failed") $) "\\spad{getOperator(e)} retrieves the operator being invoked in `e',{} when `e' is an expression.")) (|callForm?| (((|Boolean|) $) "\\spad{callForm?(e)} is \\spad{true} when `e' is a call expression.")) (|getIdentifier| (((|Union| (|Identifier|) "failed") $) "\\spad{getIdentifier(e)} retrieves the name of the variable `e'.")) (|variable?| (((|Boolean|) $) "\\spad{variable?(e)} returns \\spad{true} if `e' is a variable.")) (|getConstant| (((|Union| (|SExpression|) "failed") $) "\\spad{getConstant(e)} retrieves the constant value of `e'e.")) (|constant?| (((|Boolean|) $) "\\spad{constant?(e)} returns \\spad{true} if `e' is a constant.")) (|type| (((|Syntax|) $) "\\spad{type(e)} returns the type of the expression as computed by the interpreter.")))
NIL
@@ -875,10 +875,10 @@ NIL
(-236 A S)
((|constructor| (NIL "An extensible aggregate is one which allows insertion and deletion of entries. These aggregates are models of lists and streams which are represented by linked structures so as to make insertion,{} deletion,{} and concatenation efficient. However,{} access to elements of these extensible aggregates is generally slow since access is made from the end. See \\spadtype{FlexibleArray} for an exception.")) (|removeDuplicates!| (($ $) "\\spad{removeDuplicates!(u)} destructively removes duplicates from \\spad{u}.")) (|select!| (($ (|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 (-757))) (|HasCategory| |#2| (QUOTE (-1013))))
+((|HasCategory| |#2| (QUOTE (-758))) (|HasCategory| |#2| (QUOTE (-1015))))
(-237 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}.")))
-((-3993 . T))
+((-3997 . T))
NIL
(-238 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}.")))
@@ -899,3870 +899,3878 @@ NIL
(-242 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 -3993)))
+((|HasAttribute| |#1| (QUOTE -3997)))
(-243 |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
-(-244 S R |Mod| -2036 -3515 |exactQuo|)
+(-244 S R |Mod| -2039 -3519 |exactQuo|)
((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{ModularRing},{} \\spadtype{ModularField}")) (|inv| (($ $) "\\spad{inv(x)} \\undocumented")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} \\undocumented")) (|exQuo| (((|Union| $ "failed") $ $) "\\spad{exQuo(x,y)} \\undocumented")) (|reduce| (($ |#2| |#3|) "\\spad{reduce(r,m)} \\undocumented")) (|coerce| ((|#2| $) "\\spad{coerce(x)} \\undocumented")) (|modulus| ((|#3| $) "\\spad{modulus(x)} \\undocumented")))
-((-3985 . T) ((-3994 "*") . T) (-3986 . T) (-3987 . T) (-3989 . T))
+((-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T))
NIL
-(-245)
+(-245 S)
((|constructor| (NIL "Entire Rings (non-commutative Integral Domains),{} \\spadignore{i.e.} a ring not necessarily commutative which has no zero divisors. \\blankline")) (|noZeroDivisors| ((|attribute|) "if a product is zero then one of the factors must be zero.")))
-((-3985 . T) (-3986 . T) (-3987 . T) (-3989 . T))
+NIL
NIL
(-246)
+((|constructor| (NIL "Entire Rings (non-commutative Integral Domains),{} \\spadignore{i.e.} a ring not necessarily commutative which has no zero divisors. \\blankline")) (|noZeroDivisors| ((|attribute|) "if a product is zero then one of the factors must be zero.")))
+((-3989 . T) (-3990 . T) (-3991 . T) (-3993 . T))
+NIL
+(-247)
((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: March 18,{} 2010. An `Environment' is a stack of scope.")) (|categoryFrame| (($) "the current category environment in the interpreter.")) (|interactiveEnv| (($) "the current interactive environment in effect.")) (|currentEnv| (($) "the current normal environment in effect.")) (|putProperties| (($ (|Identifier|) (|List| (|Property|)) $) "\\spad{putProperties(n,props,e)} set the list of properties of \\spad{n} to \\spad{props} in \\spad{e}.")) (|getProperties| (((|List| (|Property|)) (|Identifier|) $) "\\spad{getBinding(n,e)} returns the list of properties of \\spad{n} in \\spad{e}.")) (|putProperty| (($ (|Identifier|) (|Identifier|) (|SExpression|) $) "\\spad{putProperty(n,p,v,e)} binds the property \\spad{(p,v)} to \\spad{n} in the topmost scope of \\spad{e}.")) (|getProperty| (((|Maybe| (|SExpression|)) (|Identifier|) (|Identifier|) $) "\\spad{getProperty(n,p,e)} returns the value of property with name \\spad{p} for the symbol \\spad{n} in environment \\spad{e}. Otherwise,{} \\spad{nothing}.")) (|scopes| (((|List| (|Scope|)) $) "\\spad{scopes(e)} returns the stack of scopes in environment \\spad{e}.")) (|empty| (($) "\\spad{empty()} constructs an empty environment")))
NIL
NIL
-(-247 R)
+(-248 R)
((|constructor| (NIL "This is a package for the exact computation of eigenvalues and eigenvectors. This package can be made to work for matrices with coefficients which are rational functions over a ring where we can factor polynomials. Rational eigenvalues are always explicitly computed while the non-rational ones are expressed in terms of their minimal polynomial.")) (|eigenvectors| (((|List| (|Record| (|:| |eigval| (|Union| (|Fraction| (|Polynomial| |#1|)) (|SuchThat| (|Symbol|) (|Polynomial| |#1|)))) (|:| |eigmult| (|NonNegativeInteger|)) (|:| |eigvec| (|List| (|Matrix| (|Fraction| (|Polynomial| |#1|))))))) (|Matrix| (|Fraction| (|Polynomial| |#1|)))) "\\spad{eigenvectors(m)} returns the eigenvalues and eigenvectors for the matrix \\spad{m}. The rational eigenvalues and the correspondent eigenvectors are explicitely computed,{} while the non rational ones are given via their minimal polynomial and the corresponding eigenvectors are expressed in terms of a \"generic\" root of such a polynomial.")) (|generalizedEigenvectors| (((|List| (|Record| (|:| |eigval| (|Union| (|Fraction| (|Polynomial| |#1|)) (|SuchThat| (|Symbol|) (|Polynomial| |#1|)))) (|:| |geneigvec| (|List| (|Matrix| (|Fraction| (|Polynomial| |#1|))))))) (|Matrix| (|Fraction| (|Polynomial| |#1|)))) "\\spad{generalizedEigenvectors(m)} returns the generalized eigenvectors of the matrix \\spad{m}.")) (|generalizedEigenvector| (((|List| (|Matrix| (|Fraction| (|Polynomial| |#1|)))) (|Record| (|:| |eigval| (|Union| (|Fraction| (|Polynomial| |#1|)) (|SuchThat| (|Symbol|) (|Polynomial| |#1|)))) (|:| |eigmult| (|NonNegativeInteger|)) (|:| |eigvec| (|List| (|Matrix| (|Fraction| (|Polynomial| |#1|)))))) (|Matrix| (|Fraction| (|Polynomial| |#1|)))) "\\spad{generalizedEigenvector(eigen,m)} returns the generalized eigenvectors of the matrix relative to the eigenvalue \\spad{eigen},{} as returned by the function eigenvectors.") (((|List| (|Matrix| (|Fraction| (|Polynomial| |#1|)))) (|Union| (|Fraction| (|Polynomial| |#1|)) (|SuchThat| (|Symbol|) (|Polynomial| |#1|))) (|Matrix| (|Fraction| (|Polynomial| |#1|))) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{generalizedEigenvector(alpha,m,k,g)} returns the generalized eigenvectors of the matrix relative to the eigenvalue \\spad{alpha}. The integers \\spad{k} and \\spad{g} are respectively the algebraic and the geometric multiplicity of tye eigenvalue \\spad{alpha}. \\spad{alpha} can be either rational or not. In the seconda case apha is the minimal polynomial of the eigenvalue.")) (|eigenvector| (((|List| (|Matrix| (|Fraction| (|Polynomial| |#1|)))) (|Union| (|Fraction| (|Polynomial| |#1|)) (|SuchThat| (|Symbol|) (|Polynomial| |#1|))) (|Matrix| (|Fraction| (|Polynomial| |#1|)))) "\\spad{eigenvector(eigval,m)} returns the eigenvectors belonging to the eigenvalue \\spad{eigval} for the matrix \\spad{m}.")) (|eigenvalues| (((|List| (|Union| (|Fraction| (|Polynomial| |#1|)) (|SuchThat| (|Symbol|) (|Polynomial| |#1|)))) (|Matrix| (|Fraction| (|Polynomial| |#1|)))) "\\spad{eigenvalues(m)} returns the eigenvalues of the matrix \\spad{m} which are expressible as rational functions over the rational numbers.")) (|characteristicPolynomial| (((|Polynomial| |#1|) (|Matrix| (|Fraction| (|Polynomial| |#1|)))) "\\spad{characteristicPolynomial(m)} returns the characteristicPolynomial of the matrix \\spad{m} using a new generated symbol symbol as the main variable.") (((|Polynomial| |#1|) (|Matrix| (|Fraction| (|Polynomial| |#1|))) (|Symbol|)) "\\spad{characteristicPolynomial(m,var)} returns the characteristicPolynomial of the matrix \\spad{m} using the symbol \\spad{var} as the main variable.")))
NIL
NIL
-(-248 S)
+(-249 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| (($ $ $) "\\spad{subst(eq1,eq2)} substitutes \\spad{eq2} into both sides of \\spad{eq1} the lhs of \\spad{eq2} should be a kernel")) (|inv| (($ $) "\\spad{inv(x)} returns the multiplicative inverse of \\spad{x}.")) (/ (($ $ $) "\\spad{e1/e2} produces a new equation by dividing the left and right hand sides of equations \\spad{e1} and \\spad{e2}.")) (|factorAndSplit| (((|List| $) $) "\\spad{factorAndSplit(eq)} make the right hand side 0 and factors the new left hand side. Each factor is equated to 0 and put into the resulting list without repetitions.")) (|rightOne| (((|Union| $ "failed") $) "\\spad{rightOne(eq)} divides by the right hand side.") (((|Union| $ "failed") $) "\\spad{rightOne(eq)} divides by the right hand side,{} if possible.")) (|leftOne| (((|Union| $ "failed") $) "\\spad{leftOne(eq)} divides by the left hand side.") (((|Union| $ "failed") $) "\\spad{leftOne(eq)} divides by the left hand side,{} if possible.")) (* (($ $ |#1|) "\\spad{eqn*x} produces a new equation by multiplying both sides of equation eqn by \\spad{x}.") (($ |#1| $) "\\spad{x*eqn} produces a new equation by multiplying both sides of equation eqn by \\spad{x}.")) (- (($ $ |#1|) "\\spad{eqn-x} produces a new equation by subtracting \\spad{x} from both sides of equation eqn.") (($ |#1| $) "\\spad{x-eqn} produces a new equation by subtracting both sides of equation eqn from \\spad{x}.")) (|rightZero| (($ $) "\\spad{rightZero(eq)} subtracts the right hand side.")) (|leftZero| (($ $) "\\spad{leftZero(eq)} subtracts the left hand side.")) (+ (($ $ |#1|) "\\spad{eqn+x} produces a new equation by adding \\spad{x} to both sides of equation eqn.") (($ |#1| $) "\\spad{x+eqn} produces a new equation by adding \\spad{x} to both sides of equation eqn.")) (|eval| (($ $ (|List| $)) "\\spad{eval(eqn, [x1=v1, ... xn=vn])} replaces \\spad{xi} by \\spad{vi} in equation \\spad{eqn}.") (($ $ $) "\\spad{eval(eqn, x=f)} replaces \\spad{x} by \\spad{f} in equation \\spad{eqn}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,eqn)} constructs a new equation by applying \\spad{f} to both sides of \\spad{eqn}.")) (|rhs| ((|#1| $) "\\spad{rhs(eqn)} returns the right hand side of equation \\spad{eqn}.")) (|lhs| ((|#1| $) "\\spad{lhs(eqn)} returns the left hand side of equation \\spad{eqn}.")) (|swap| (($ $) "\\spad{swap(eq)} interchanges left and right hand side of equation \\spad{eq}.")) (|equation| (($ |#1| |#1|) "\\spad{equation(a,b)} creates an equation.")) (= (($ |#1| |#1|) "\\spad{a=b} creates an equation.")))
-((-3989 OR (|has| |#1| (-962)) (|has| |#1| (-410))) (-3986 |has| |#1| (-962)) (-3987 |has| |#1| (-962)))
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((|constructor| (NIL "This package provides operations for mapping the sides of equations.")) (|map| (((|Equation| |#2|) (|Mapping| |#2| |#1|) (|Equation| |#1|)) "\\spad{map(f,eq)} returns an equation where \\spad{f} is applied to the sides of \\spad{eq}")))
NIL
NIL
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((|constructor| (NIL "This domain provides tables where the keys are compared using \\spadfun{eq?}. Thus keys are considered equal only if they are the same instance of a structure.")))
-((-3992 . T) (-3993 . T))
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((|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
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((|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|) $) "\\spad{height(f)} returns the highest nesting level appearing in \\spad{f}. Constants have height 0. Symbols have height 1. For any operator op and expressions \\spad{f1},{}...,{}fn,{} \\spad{op(f1,...,fn)} has height equal to \\spad{1 + max(height(f1),...,height(fn))}.")) (|distribute| (($ $ $) "\\spad{distribute(f, g)} expands all the kernels in \\spad{f} that contain \\spad{g} in their arguments and that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or a \\spadfunFrom{paren}{ExpressionSpace} expression.") (($ $) "\\spad{distribute(f)} expands all the kernels in \\spad{f} that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or \\spadfunFrom{paren}{ExpressionSpace} expression.")) (|paren| (($ (|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| $)) "\\spad{subst(f, [k1...,kn], [g1,...,gn])} replaces the kernels \\spad{k1},{}...,{}kn by \\spad{g1},{}...,{}gn formally in \\spad{f}.") (($ $ (|List| (|Equation| $))) "\\spad{subst(f, [k1 = g1,...,kn = gn])} replaces the kernels \\spad{k1},{}...,{}kn by \\spad{g1},{}...,{}gn formally in \\spad{f}.") (($ $ (|Equation| $)) "\\spad{subst(f, k = g)} replaces the kernel \\spad{k} by \\spad{g} formally in \\spad{f}.")) (|elt| (($ (|BasicOperator|) (|List| $)) "\\spad{elt(op,[x1,...,xn])} or \\spad{op}([\\spad{x1},{}...,{}xn]) applies the \\spad{n}-ary operator \\spad{op} to \\spad{x1},{}...,{}xn.") (($ (|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
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+((|HasCategory| |#1| (QUOTE (-952 (-485)))) (|HasCategory| |#1| (QUOTE (-963))))
+(-254)
((|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|) $) "\\spad{height(f)} returns the highest nesting level appearing in \\spad{f}. Constants have height 0. Symbols have height 1. For any operator op and expressions \\spad{f1},{}...,{}fn,{} \\spad{op(f1,...,fn)} has height equal to \\spad{1 + max(height(f1),...,height(fn))}.")) (|distribute| (($ $ $) "\\spad{distribute(f, g)} expands all the kernels in \\spad{f} that contain \\spad{g} in their arguments and that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or a \\spadfunFrom{paren}{ExpressionSpace} expression.") (($ $) "\\spad{distribute(f)} expands all the kernels in \\spad{f} that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or \\spadfunFrom{paren}{ExpressionSpace} expression.")) (|paren| (($ (|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| $)) "\\spad{subst(f, [k1...,kn], [g1,...,gn])} replaces the kernels \\spad{k1},{}...,{}kn by \\spad{g1},{}...,{}gn formally in \\spad{f}.") (($ $ (|List| (|Equation| $))) "\\spad{subst(f, [k1 = g1,...,kn = gn])} replaces the kernels \\spad{k1},{}...,{}kn by \\spad{g1},{}...,{}gn formally in \\spad{f}.") (($ $ (|Equation| $)) "\\spad{subst(f, k = g)} replaces the kernel \\spad{k} by \\spad{g} formally in \\spad{f}.")) (|elt| (($ (|BasicOperator|) (|List| $)) "\\spad{elt(op,[x1,...,xn])} or \\spad{op}([\\spad{x1},{}...,{}xn]) applies the \\spad{n}-ary operator \\spad{op} to \\spad{x1},{}...,{}xn.") (($ (|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
NIL
-(-254 -3091 S)
+(-255 -3094 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
-(-255 E -3091)
+(-256 E -3094)
((|constructor| (NIL "This package allows a mapping \\spad{E} -> \\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
-(-256 S)
+(-257 S)
((|constructor| (NIL "A constructive euclidean domain,{} \\spadignore{i.e.} one can divide producing a quotient and a remainder where the remainder is either zero or is smaller (\\spadfun{euclideanSize}) than the divisor. \\blankline Conditional attributes: \\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| $)) $ $) "\\spad{extendedEuclidean(x,y)} returns a record rec where \\spad{rec.coef1*x+rec.coef2*y = rec.generator} and rec.generator is a gcd of \\spad{x} and \\spad{y}. The gcd is unique only up to associates if \\spadatt{canonicalUnitNormal} is not asserted. \\spadfun{principalIdeal} provides a version of this operation which accepts an arbitrary length list of arguments.")) (|rem| (($ $ $) "\\spad{x rem y} is the same as \\spad{divide(x,y).remainder}. See \\spadfunFrom{divide}{EuclideanDomain}.")) (|quo| (($ $ $) "\\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}.")))
NIL
NIL
-(-257)
+(-258)
((|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| $)) $ $) "\\spad{extendedEuclidean(x,y)} returns a record rec where \\spad{rec.coef1*x+rec.coef2*y = rec.generator} and rec.generator is a gcd of \\spad{x} and \\spad{y}. The gcd is unique only up to associates if \\spadatt{canonicalUnitNormal} is not asserted. \\spadfun{principalIdeal} provides a version of this operation which accepts an arbitrary length list of arguments.")) (|rem| (($ $ $) "\\spad{x rem y} is the same as \\spad{divide(x,y).remainder}. See \\spadfunFrom{divide}{EuclideanDomain}.")) (|quo| (($ $ $) "\\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|) $ $) "\\spad{sizeLess?(x,y)} tests whether \\spad{x} is strictly smaller than \\spad{y} with respect to the \\spadfunFrom{euclideanSize}{EuclideanDomain}.")))
-((-3985 . T) ((-3994 "*") . T) (-3986 . T) (-3987 . T) (-3989 . T))
+((-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T))
NIL
-(-258 S R)
+(-259 S R)
((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation'' substitutions.")) (|eval| (($ $ (|List| (|Equation| |#2|))) "\\spad{eval(f, [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}.")))
NIL
NIL
-(-259 R)
+(-260 R)
((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation'' substitutions.")) (|eval| (($ $ (|List| (|Equation| |#1|))) "\\spad{eval(f, [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
-(-260 -3091)
+(-261 -3094)
((|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
-(-261)
+(-262)
((|constructor| (NIL "A function which does not return directly to its caller should have Exit as its return type. \\blankline Note: It is convenient to have a formal \\spad{coerce} into each type from type Exit. This allows,{} for example,{} errors to be raised in one half of a type-balanced \\spad{if}.")))
NIL
NIL
-(-262)
+(-263)
((|constructor| (NIL "This domain represents exit expressions.")) (|level| (((|Integer|) $) "\\spad{level(e)} returns the nesting exit level of `e'")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the exit expression of `e'.")))
NIL
NIL
-(-263 R FE |var| |cen|)
+(-264 R FE |var| |cen|)
((|constructor| (NIL "UnivariatePuiseuxSeriesWithExponentialSingularity is a domain used to represent essential singularities of functions. Objects in this domain are quotients of sums,{} where each term in the sum is a univariate Puiseux series times the exponential of a univariate Puiseux series.")) (|coerce| (($ (|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))}.")))
-((-3984 . T) (-3990 . T) (-3985 . T) ((-3994 "*") . T) (-3986 . T) (-3987 . T) (-3989 . T))
-((|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-822))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-951 (-1089)))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-118))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-120))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-554 (-473)))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-934))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-741))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-757))) (OR (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-741))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-757)))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-951 (-484)))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-1065))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-797 (-327)))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-797 (-484)))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-554 (-801 (-327))))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-554 (-801 (-484))))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-581 (-484)))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-189))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-812 (-1089)))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-190))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-810 (-1089)))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -453) (QUOTE (-1089)) (|%list| (QUOTE -1165) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -259) (|%list| (QUOTE -1165) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -241) (|%list| (QUOTE -1165) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (|%list| (QUOTE -1165) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-257))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-483))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-822)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-822)))) (|HasCategory| (-1165 |#1| |#2| |#3| |#4|) (QUOTE (-118)))))
-(-264 R)
+((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T))
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+(-265 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.")))
-((-3989 OR (-12 (|has| |#1| (-495)) (OR (|has| |#1| (-962)) (|has| |#1| (-410)))) (|has| |#1| (-962)) (|has| |#1| (-410))) (-3987 |has| |#1| (-146)) (-3986 |has| |#1| (-146)) ((-3994 "*") |has| |#1| (-495)) (-3985 |has| |#1| (-495)) (-3990 |has| |#1| (-495)) (-3984 |has| |#1| (-495)))
-((OR (-12 (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-951 (-484))))) (|HasCategory| |#1| (QUOTE (-951 (-347 (-484)))))) (|HasCategory| |#1| (QUOTE (-495))) (OR (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-962)))) (|HasCategory| |#1| (QUOTE (-962))) (|HasCategory| |#1| (QUOTE (-21))) (OR (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-951 (-347 (-484)))))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-962)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-581 (-484))))) (-12 (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-581 (-484))))) (-12 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-581 (-484))))) (-12 (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-581 (-484))))) (-12 (|HasCategory| |#1| (QUOTE (-581 (-484)))) (|HasCategory| |#1| (QUOTE (-962))))) (OR (|HasCategory| |#1| (QUOTE (-410))) (|HasCategory| |#1| (QUOTE (-1025)))) (|HasCategory| |#1| (QUOTE (-410))) (|HasCategory| |#1| (QUOTE (-554 (-473)))) (OR (|HasCategory| |#1| (QUOTE (-951 (-484)))) (|HasCategory| |#1| (QUOTE (-962)))) (|HasCategory| |#1| (QUOTE (-951 (-484)))) (|HasCategory| |#1| (QUOTE (-797 (-327)))) (|HasCategory| |#1| (QUOTE (-797 (-484)))) (|HasCategory| |#1| (QUOTE (-554 (-801 (-327))))) (|HasCategory| |#1| (QUOTE (-554 (-801 (-484))))) (-12 (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-951 (-484))))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-962)))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-962)))) (OR (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-962)))) (-12 (|HasCategory| |#1| (QUOTE (-389))) (|HasCategory| |#1| (QUOTE (-495)))) (OR (|HasCategory| |#1| (QUOTE (-410))) (|HasCategory| |#1| (QUOTE (-495)))) (-12 (|HasCategory| |#1| (QUOTE (-581 (-484)))) (|HasCategory| |#1| (QUOTE (-962)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-581 (-484)))) (|HasCategory| |#1| (QUOTE (-962)))) (|HasCategory| |#1| (QUOTE (-21)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-581 (-484)))) (|HasCategory| |#1| (QUOTE (-962)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1025)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-581 (-484)))) (|HasCategory| |#1| (QUOTE (-962)))) (|HasCategory| |#1| (QUOTE (-25)))) (OR (|HasCategory| |#1| (QUOTE (-410))) (|HasCategory| |#1| (QUOTE (-962)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-951 (-347 (-484)))))) (-12 (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-951 (-484)))))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1025))) (|HasCategory| |#1| (QUOTE (-951 (-347 (-484))))) (|HasCategory| $ (QUOTE (-962))) (|HasCategory| $ (QUOTE (-951 (-484)))))
-(-265 R S)
+((-3993 OR (-12 (|has| |#1| (-496)) (OR (|has| |#1| (-963)) (|has| |#1| (-411)))) (|has| |#1| (-963)) (|has| |#1| (-411))) (-3991 |has| |#1| (-146)) (-3990 |has| |#1| (-146)) ((-3998 "*") |has| |#1| (-496)) (-3989 |has| |#1| (-496)) (-3994 |has| |#1| (-496)) (-3988 |has| |#1| (-496)))
+((OR (-12 (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-952 (-485))))) (|HasCategory| |#1| (QUOTE (-952 (-348 (-485)))))) (|HasCategory| |#1| (QUOTE (-496))) (OR (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-963)))) (|HasCategory| |#1| (QUOTE (-963))) (|HasCategory| |#1| (QUOTE (-21))) (OR (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-952 (-348 (-485)))))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-963)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-582 (-485))))) (-12 (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-582 (-485))))) (-12 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-582 (-485))))) (-12 (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-582 (-485))))) (-12 (|HasCategory| |#1| (QUOTE (-582 (-485)))) (|HasCategory| |#1| (QUOTE (-963))))) (OR (|HasCategory| |#1| (QUOTE (-411))) (|HasCategory| |#1| (QUOTE (-1027)))) (|HasCategory| |#1| (QUOTE (-411))) (|HasCategory| |#1| (QUOTE (-555 (-474)))) (OR (|HasCategory| |#1| (QUOTE (-952 (-485)))) (|HasCategory| |#1| (QUOTE (-963)))) (|HasCategory| |#1| (QUOTE (-952 (-485)))) (|HasCategory| |#1| (QUOTE (-798 (-328)))) (|HasCategory| |#1| (QUOTE (-798 (-485)))) (|HasCategory| |#1| (QUOTE (-555 (-802 (-328))))) (|HasCategory| |#1| (QUOTE (-555 (-802 (-485))))) (-12 (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-952 (-485))))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-963)))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-963)))) (OR (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-963)))) (-12 (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-496)))) (OR (|HasCategory| |#1| (QUOTE (-411))) (|HasCategory| |#1| (QUOTE (-496)))) (-12 (|HasCategory| |#1| (QUOTE (-582 (-485)))) (|HasCategory| |#1| (QUOTE (-963)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-582 (-485)))) (|HasCategory| |#1| (QUOTE (-963)))) (|HasCategory| |#1| (QUOTE (-21)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-582 (-485)))) (|HasCategory| |#1| (QUOTE (-963)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1027)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-582 (-485)))) (|HasCategory| |#1| (QUOTE (-963)))) (|HasCategory| |#1| (QUOTE (-25)))) (OR (|HasCategory| |#1| (QUOTE (-411))) (|HasCategory| |#1| (QUOTE (-963)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-952 (-348 (-485)))))) (-12 (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-952 (-485)))))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (QUOTE (-952 (-348 (-485))))) (|HasCategory| $ (QUOTE (-963))) (|HasCategory| $ (QUOTE (-952 (-485)))))
+(-266 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
NIL
-(-266 R FE)
+(-267 R FE)
((|constructor| (NIL "This package provides functions to convert functional expressions to power series.")) (|series| (((|Any|) |#2| (|Equation| |#2|) (|Fraction| (|Integer|))) "\\spad{series(f,x = a,n)} expands the expression \\spad{f} as a series in powers of (\\spad{x} - a); terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{series(f,x = a)} expands the expression \\spad{f} as a series in powers of (\\spad{x} - a).") (((|Any|) |#2| (|Fraction| (|Integer|))) "\\spad{series(f,n)} returns a series expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2|) "\\spad{series(f)} returns a series expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{series(x)} returns \\spad{x} viewed as a series.")) (|puiseux| (((|Any|) |#2| (|Equation| |#2|) (|Fraction| (|Integer|))) "\\spad{puiseux(f,x = a,n)} expands the expression \\spad{f} as a Puiseux series in powers of \\spad{(x - a)}; terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{puiseux(f,x = a)} expands the expression \\spad{f} as a Puiseux series in powers of \\spad{(x - a)}.") (((|Any|) |#2| (|Fraction| (|Integer|))) "\\spad{puiseux(f,n)} returns a Puiseux expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2|) "\\spad{puiseux(f)} returns a Puiseux expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{puiseux(x)} returns \\spad{x} viewed as a Puiseux series.")) (|laurent| (((|Any|) |#2| (|Equation| |#2|) (|Integer|)) "\\spad{laurent(f,x = a,n)} expands the expression \\spad{f} as a Laurent series in powers of \\spad{(x - a)}; terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{laurent(f,x = a)} expands the expression \\spad{f} as a Laurent series in powers of \\spad{(x - a)}.") (((|Any|) |#2| (|Integer|)) "\\spad{laurent(f,n)} returns a Laurent expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2|) "\\spad{laurent(f)} returns a Laurent expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{laurent(x)} returns \\spad{x} viewed as a Laurent series.")) (|taylor| (((|Any|) |#2| (|Equation| |#2|) (|NonNegativeInteger|)) "\\spad{taylor(f,x = a)} expands the expression \\spad{f} as a Taylor series in powers of \\spad{(x - a)}; terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{taylor(f,x = a)} expands the expression \\spad{f} as a Taylor series in powers of \\spad{(x - a)}.") (((|Any|) |#2| (|NonNegativeInteger|)) "\\spad{taylor(f,n)} returns a Taylor expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2|) "\\spad{taylor(f)} returns a Taylor expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{taylor(x)} returns \\spad{x} viewed as a Taylor series.")))
NIL
NIL
-(-267 R -3091)
+(-268 R -3094)
((|constructor| (NIL "Taylor series solutions of explicit ODE'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
-(-268)
+(-269)
((|constructor| (NIL "\\indented{1}{Author: Clifton \\spad{J}. Williamson} Date Created: Bastille Day 1989 Date Last Updated: 5 June 1990 Keywords: Examples: Package for constructing tubes around 3-dimensional parametric curves.")) (|tubePlot| (((|TubePlot| (|Plot3D|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|String|)) "\\spad{tubePlot(f,g,h,colorFcn,a..b,r,n,s)} puts a tube of radius \\spad{r} with \\spad{n} points on each circle about the curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} for \\spad{t} in \\spad{[a,b]}. If \\spad{s} = \"closed\",{} the tube is considered to be closed; if \\spad{s} = \"open\",{} the tube is considered to be open.") (((|TubePlot| (|Plot3D|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|)) "\\spad{tubePlot(f,g,h,colorFcn,a..b,r,n)} puts a tube of radius \\spad{r} with \\spad{n} points on each circle about the curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} for \\spad{t} in \\spad{[a,b]}. The tube is considered to be open.") (((|TubePlot| (|Plot3D|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Integer|) (|String|)) "\\spad{tubePlot(f,g,h,colorFcn,a..b,r,n,s)} puts a tube of radius \\spad{r(t)} with \\spad{n} points on each circle about the curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} for \\spad{t} in \\spad{[a,b]}. If \\spad{s} = \"closed\",{} the tube is considered to be closed; if \\spad{s} = \"open\",{} the tube is considered to be open.") (((|TubePlot| (|Plot3D|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Integer|)) "\\spad{tubePlot(f,g,h,colorFcn,a..b,r,n)} puts a tube of radius \\spad{r}(\\spad{t}) with \\spad{n} points on each circle about the curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} for \\spad{t} in \\spad{[a,b]}. The tube is considered to be open.")) (|constantToUnaryFunction| (((|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|DoubleFloat|)) "\\spad{constantToUnaryFunction(s)} is a local function which takes the value of \\spad{s},{} which may be a function of a constant,{} and returns a function which always returns the value \\spadtype{DoubleFloat} \\spad{s}.")))
NIL
NIL
-(-269 FE |var| |cen|)
+(-270 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.")))
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((|constructor| (NIL "computes various functions on factored arguments.")) (|log| (((|List| (|Record| (|:| |coef| (|NonNegativeInteger|)) (|:| |logand| |#1|))) (|Factored| |#1|)) "\\spad{log(f)} returns \\spad{[(a1,b1),...,(am,bm)]} such that the logarithm of \\spad{f} is equal to \\spad{a1*log(b1) + ... + am*log(bm)}.")) (|nthRoot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#1|) (|:| |radicand| (|List| |#1|))) (|Factored| |#1|) (|NonNegativeInteger|)) "\\spad{nthRoot(f, n)} returns \\spad{(p, r, [r1,...,rm])} such that the \\spad{n}th-root of \\spad{f} is equal to \\spad{r * \\spad{p}th-root(r1 * ... * rm)},{} where \\spad{r1},{}...,{}rm are distinct factors of \\spad{f},{} each of which has an exponent smaller than \\spad{p} in \\spad{f}.")))
NIL
NIL
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((|constructor| (NIL "This package provides utilities used by the factorizers which operate on polynomials represented as univariate polynomials with multivariate coefficients.")) (|ran| ((|#3| (|Integer|)) "\\spad{ran(k)} computes a random integer between -k and \\spad{k} as a member of \\spad{R}.")) (|normalDeriv| (((|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|) (|Integer|)) "\\spad{normalDeriv(poly,i)} computes the \\spad{i}th derivative of \\spad{poly} divided by i!.")) (|raisePolynomial| (((|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#3|)) "\\spad{raisePolynomial(rpoly)} converts \\spad{rpoly} from a univariate polynomial over \\spad{r} to be a univariate polynomial with polynomial coefficients.")) (|lowerPolynomial| (((|SparseUnivariatePolynomial| |#3|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{lowerPolynomial(upoly)} converts \\spad{upoly} to be a univariate polynomial over \\spad{R}. An error if the coefficients contain variables.")) (|variables| (((|List| |#2|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{variables(upoly)} returns the list of variables for the coefficients of \\spad{upoly}.")) (|degree| (((|List| (|NonNegativeInteger|)) (|SparseUnivariatePolynomial| |#4|) (|List| |#2|)) "\\spad{degree(upoly, lvar)} returns a list containing the maximum degree for each variable in lvar.")) (|completeEval| (((|SparseUnivariatePolynomial| |#3|) (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|List| |#3|)) "\\spad{completeEval(upoly, lvar, lval)} evaluates the polynomial \\spad{upoly} with each variable in \\spad{lvar} replaced by the corresponding value in lval. Substitutions are done for all variables in \\spad{upoly} producing a univariate polynomial over \\spad{R}.")))
NIL
NIL
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((|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}'s are in \\spad{S},{} and the \\spad{ni}'s are integers. The operation is commutative.")))
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((|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}'s are in \\spad{S},{} and the \\spad{ni}'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}'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|) $) "\\spad{size(x)} returns the number of terms in \\spad{x}. mapGen(\\spad{f},{} \\spad{a1}\\^\\spad{e1} ... an\\^en) returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (* (($ |#2| |#1|) "\\spad{e * s} returns \\spad{e} times \\spad{s}.")) (+ (($ |#1| $) "\\spad{s + x} returns the sum of \\spad{s} and \\spad{x}.")))
NIL
NIL
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((|constructor| (NIL "The free abelian monoid on a set \\spad{S} is the monoid of finite sums of the form \\spad{reduce(+,[ni * si])} where the \\spad{si}'s are in \\spad{S},{} and the \\spad{ni}'s are non-negative integers. The operation is commutative.")))
NIL
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((|constructor| (NIL "This category is similar to AbelianMonoidRing,{} except that the sum is assumed to be finite. It is a useful model for polynomials,{} but is somewhat more general.")) (|primitivePart| (($ $) "\\spad{primitivePart(p)} returns the unit normalized form of polynomial \\spad{p} divided by the content of \\spad{p}.")) (|content| ((|#2| $) "\\spad{content(p)} gives the gcd of the coefficients of polynomial \\spad{p}.")) (|exquo| (((|Union| $ "failed") $ |#2|) "\\spad{exquo(p,r)} returns the exact quotient of polynomial \\spad{p} by \\spad{r},{} or \"failed\" if none exists.")) (|binomThmExpt| (($ $ $ (|NonNegativeInteger|)) "\\spad{binomThmExpt(p,q,n)} returns \\spad{(x+y)^n} by means of the binomial theorem trick.")) (|pomopo!| (($ $ |#2| |#3| $) "\\spad{pomopo!(p1,r,e,p2)} returns \\spad{p1 + monomial(e,r) * p2} and may use \\spad{p1} as workspace. The constaant \\spad{r} is assumed to be nonzero.")) (|mapExponents| (($ (|Mapping| |#3| |#3|) $) "\\spad{mapExponents(fn,u)} maps function \\spad{fn} onto the exponents of the non-zero monomials of polynomial \\spad{u}.")) (|minimumDegree| ((|#3| $) "\\spad{minimumDegree(p)} gives the least exponent of a non-zero term of polynomial \\spad{p}. Error: if applied to 0.")) (|numberOfMonomials| (((|NonNegativeInteger|) $) "\\spad{numberOfMonomials(p)} gives the number of non-zero monomials in polynomial \\spad{p}.")) (|coefficients| (((|List| |#2|) $) "\\spad{coefficients(p)} gives the list of non-zero coefficients of polynomial \\spad{p}.")) (|ground| ((|#2| $) "\\spad{ground(p)} retracts polynomial \\spad{p} to the coefficient ring.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(p)} tests if polynomial \\spad{p} is a member of the coefficient ring.")))
NIL
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((|constructor| (NIL "This category is similar to AbelianMonoidRing,{} except that the sum is assumed to be finite. It is a useful model for polynomials,{} but is somewhat more general.")) (|primitivePart| (($ $) "\\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 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.")))
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NIL
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((|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.")))
-((-3993 . T) (-3992 . T))
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-(-278 S -3091)
+((-3997 . T) (-3996 . T))
+((OR (-12 (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-554 (-774)))) (|HasCategory| |#1| (QUOTE (-555 (-474)))) (OR (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| |#1| (QUOTE (-758))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| (-485) (QUOTE (-758))) (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))))
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((|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})\\$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})\\$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**(q**(d*i)) for \\spad{i} in 0..n/d])") ((|#2| $) "\\spad{norm(a)} computes the norm of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|degree| (((|PositiveInteger|) $) "\\spad{degree(a)} returns the degree of the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|extensionDegree| (((|PositiveInteger|)) "\\spad{extensionDegree()} returns the degree of field extension.")) (|definingPolynomial| (((|SparseUnivariatePolynomial| |#2|)) "\\spad{definingPolynomial()} returns the polynomial used to define the field extension.")) (|minimalPolynomial| (((|SparseUnivariatePolynomial| $) $ (|PositiveInteger|)) "\\spad{minimalPolynomial(x,n)} computes the minimal polynomial of \\spad{x} over the field of extension degree \\spad{n} over the ground field \\spad{F}.") (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|represents| (($ (|Vector| |#2|)) "\\spad{represents([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{}...,{}vn are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $)) "\\spad{coordinates([v1,...,vm])} returns the coordinates of the \\spad{vi}'s with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#2|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{F}-vectorspace basis.")) (|basis| (((|Vector| $) (|PositiveInteger|)) "\\spad{basis(n)} returns a fixed basis of a subfield of \\$ as \\spad{F}-vectorspace.") (((|Vector| $)) "\\spad{basis()} returns a fixed basis of \\$ as \\spad{F}-vectorspace.")))
NIL
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((|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})\\$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})\\$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**(q**(d*i)) for \\spad{i} in 0..n/d])") ((|#1| $) "\\spad{norm(a)} computes the norm of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|degree| (((|PositiveInteger|) $) "\\spad{degree(a)} returns the degree of the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|extensionDegree| (((|PositiveInteger|)) "\\spad{extensionDegree()} returns the degree of field extension.")) (|definingPolynomial| (((|SparseUnivariatePolynomial| |#1|)) "\\spad{definingPolynomial()} returns the polynomial used to define the field extension.")) (|minimalPolynomial| (((|SparseUnivariatePolynomial| $) $ (|PositiveInteger|)) "\\spad{minimalPolynomial(x,n)} computes the minimal polynomial of \\spad{x} over the field of extension degree \\spad{n} over the ground field \\spad{F}.") (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{}...,{}vn are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([v1,...,vm])} returns the coordinates of the \\spad{vi}'s with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#1|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{F}-vectorspace basis.")) (|basis| (((|Vector| $) (|PositiveInteger|)) "\\spad{basis(n)} returns a fixed basis of a subfield of \\$ as \\spad{F}-vectorspace.") (((|Vector| $)) "\\spad{basis()} returns a fixed basis of \\$ as \\spad{F}-vectorspace.")))
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NIL
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((|constructor| (NIL "\\indented{1}{Author: James Davenport} Date Created: 17 April 1992 Date Last Updated: 12 June 1992 Basic Functions: Related Constructors: Also See: AMS Classifications: Keywords: References: Description:")) (|argument| ((|#1| $) "\\spad{argument(x)} returns the argument of a given sin/cos expressions")) (|sin?| (((|Boolean|) $) "\\spad{sin?(x)} returns \\spad{true} if term is a sin,{} otherwise \\spad{false}")) (|cos| (($ |#1|) "\\spad{cos(x)} makes a cos kernel for use in Fourier series")) (|sin| (($ |#1|) "\\spad{sin(x)} makes a sin kernel for use in Fourier series")))
NIL
NIL
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((|constructor| (NIL "Represntation of data needed to instantiate a domain constructor.")) (|lookupFunction| (((|Identifier|) $) "\\spad{lookupFunction x} returns the name of the lookup function associated with the functor data \\spad{x}.")) (|categories| (((|PrimitiveArray| (|ConstructorCall| (|CategoryConstructor|))) $) "\\spad{categories x} returns the list of categories forms each domain object obtained from the domain data \\spad{x} belongs to.")) (|encodingDirectory| (((|PrimitiveArray| (|NonNegativeInteger|)) $) "\\spad{encodintDirectory x} returns the directory of domain-wide entity description.")) (|attributeData| (((|List| (|Pair| (|Syntax|) (|NonNegativeInteger|))) $) "\\spad{attributeData x} returns the list of attribute-predicate bit vector index pair associated with the functor data \\spad{x}.")) (|domainTemplate| (((|DomainTemplate|) $) "\\spad{domainTemplate x} returns the domain template vector associated with the functor data \\spad{x}.")))
NIL
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((|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}'s are integers and the \\spad{P}'s are finite rational points on the curve.")) (|lSpaceBasis| (((|Vector| |#4|) $) "\\spad{lSpaceBasis(d)} returns a basis for \\spad{L(d) = {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
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((|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
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((|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}'s are integers and the \\spad{P}'s are finite rational points on the curve.")) (|generator| (((|Union| |#5| "failed") $) "\\spad{generator(d)} returns \\spad{f} if \\spad{(f) = 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 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 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
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((|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}'s are integers and the \\spad{P}'s are finite rational points on the curve.")) (|generator| (((|Union| |#4| "failed") $) "\\spad{generator(d)} returns \\spad{f} if \\spad{(f) = 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 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 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|) $) "\\spad{ideal(D)} returns the ideal corresponding to a divisor \\spad{D}.")))
NIL
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((|constructor| (NIL "This category provides a selection of evaluation operations depending on what the argument type \\spad{R} provides.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(f, ex)} evaluates ex,{} applying \\spad{f} to values of type \\spad{R} in ex.")))
NIL
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((|constructor| (NIL "This category provides a selection of evaluation operations depending on what the argument type \\spad{R} provides.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f, ex)} evaluates ex,{} applying \\spad{f} to values of type \\spad{R} in ex.")))
NIL
NIL
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((|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}.")))
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+((OR (|HasCategory| (-819 |#1|) (QUOTE (-118))) (|HasCategory| (-819 |#1|) (QUOTE (-318)))) (|HasCategory| (-819 |#1|) (QUOTE (-120))) (|HasCategory| (-819 |#1|) (QUOTE (-318))) (|HasCategory| (-819 |#1|) (QUOTE (-118))))
+(-290 S -3094 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 \\spad{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 (-317))) (|HasCategory| |#2| (QUOTE (-311))))
-(-290 -3091 UP UPUP)
+((|HasCategory| |#2| (QUOTE (-318))) (|HasCategory| |#2| (QUOTE (-312))))
+(-291 -3094 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 \\spad{u1},{}...,{}un of an affine non-singular model for the curve.")) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#2|) (|:| |derivden| |#2|) (|:| |gd| |#2|)) $ (|Mapping| |#2| |#2|)) "\\spad{algSplitSimple(f, D)} returns \\spad{[h,d,d',g]} such that \\spad{f=h/d},{} \\spad{h} is integral at all the normal places \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{d' = Dd},{} \\spad{g = gcd(d, discriminant())} and \\spad{D} is the derivation to use. \\spad{f} must have at most simple finite poles.")) (|hyperelliptic| (((|Union| |#2| "failed")) "\\spad{hyperelliptic()} returns \\spad{p(x)} if the curve is the hyperelliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elliptic| (((|Union| |#2| "failed")) "\\spad{elliptic()} returns \\spad{p(x)} if the curve is the elliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elt| ((|#1| $ |#1| |#1|) "\\spad{elt(f,a,b)} or \\spad{f}(a,{} \\spad{b}) returns the value of \\spad{f} at the point \\spad{(x = a, y = b)} if it is not singular.")) (|primitivePart| (($ $) "\\spad{primitivePart(f)} removes the content of the denominator and the common content of the numerator of \\spad{f}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|)) "\\spad{differentiate(x, d)} extends the derivation \\spad{d} from UP to \\$ and applies it to \\spad{x}.")) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#2|)) (|:| |den| |#2|)) (|Mapping| |#2| |#2|)) "\\spad{integralDerivationMatrix(d)} extends the derivation \\spad{d} from UP to \\$ and returns (\\spad{M},{} \\spad{Q}) such that the i^th row of \\spad{M} divided by \\spad{Q} form the coordinates of \\spad{d(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.")))
-((-3985 |has| (-347 |#2|) (-311)) (-3990 |has| (-347 |#2|) (-311)) (-3984 |has| (-347 |#2|) (-311)) ((-3994 "*") . T) (-3986 . T) (-3987 . T) (-3989 . T))
+((-3989 |has| (-348 |#2|) (-312)) (-3994 |has| (-348 |#2|) (-312)) (-3988 |has| (-348 |#2|) (-312)) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T))
NIL
-(-291 R1 UP1 UPUP1 F1 R2 UP2 UPUP2 F2)
+(-292 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
-(-292 |p| |extdeg|)
+(-293 |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.")))
-((-3984 . T) (-3990 . T) (-3985 . T) ((-3994 "*") . T) (-3986 . T) (-3987 . T) (-3989 . T))
-((OR (|HasCategory| (-818 |#1|) (QUOTE (-118))) (|HasCategory| (-818 |#1|) (QUOTE (-317)))) (|HasCategory| (-818 |#1|) (QUOTE (-120))) (|HasCategory| (-818 |#1|) (QUOTE (-317))) (|HasCategory| (-818 |#1|) (QUOTE (-118))))
-(-293 GF |defpol|)
+((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T))
+((OR (|HasCategory| (-819 |#1|) (QUOTE (-118))) (|HasCategory| (-819 |#1|) (QUOTE (-318)))) (|HasCategory| (-819 |#1|) (QUOTE (-120))) (|HasCategory| (-819 |#1|) (QUOTE (-318))) (|HasCategory| (-819 |#1|) (QUOTE (-118))))
+(-294 GF |defpol|)
((|constructor| (NIL "FiniteFieldCyclicGroupExtensionByPolynomial(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.")))
-((-3984 . T) (-3990 . T) (-3985 . T) ((-3994 "*") . T) (-3986 . T) (-3987 . T) (-3989 . T))
-((OR (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-317)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-118))))
-(-294 GF |extdeg|)
+((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T))
+((OR (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-318)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-118))))
+(-295 GF |extdeg|)
((|constructor| (NIL "FiniteFieldCyclicGroupExtension(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.")))
-((-3984 . T) (-3990 . T) (-3985 . T) ((-3994 "*") . T) (-3986 . T) (-3987 . T) (-3989 . T))
-((OR (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-317)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-118))))
-(-295 GF)
+((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T))
+((OR (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-318)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-118))))
+(-296 GF)
((|constructor| (NIL "FiniteFieldFunctions(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
NIL
-(-296 F1 GF F2)
+(-297 F1 GF F2)
((|constructor| (NIL "FiniteFieldHomomorphisms(\\spad{F1},{}GF,{}\\spad{F2}) exports coercion functions of elements between the fields {\\em F1} and {\\em F2},{} which both must be finite simple algebraic extensions of the finite ground field {\\em GF}.")) (|coerce| ((|#1| |#3|) "\\spad{coerce(x)} is the homomorphic image of \\spad{x} from {\\em F2} in {\\em F1},{} where {\\em coerce} is a field homomorphism between the fields extensions {\\em F2} and {\\em F1} both over ground field {\\em GF} (the second argument to the package). Error: if the extension degree of {\\em F2} doesn't divide the extension degree of {\\em F1}. Note that the other coercion function in the \\spadtype{FiniteFieldHomomorphisms} is a left inverse.") ((|#3| |#1|) "\\spad{coerce(x)} is the homomorphic image of \\spad{x} from {\\em F1} in {\\em F2}. Thus {\\em coerce} is a field homomorphism between the fields extensions {\\em F1} and {\\em F2} both over ground field {\\em GF} (the second argument to the package). Error: if the extension degree of {\\em F1} doesn't divide the extension degree of {\\em F2}. Note that the other coercion function in the \\spadtype{FiniteFieldHomomorphisms} is a left inverse.")))
NIL
NIL
-(-297 S)
+(-298 S)
((|constructor| (NIL "FiniteFieldCategory is the category of finite fields")) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) "\\spad{representationType()} returns the type of the representation,{} one of: \\spad{prime},{} \\spad{polynomial},{} \\spad{normal},{} or \\spad{cyclic}.")) (|order| (((|PositiveInteger|) $) "\\spad{order(b)} computes the order of an element \\spad{b} in the multiplicative group of the field. Error: if \\spad{b} equals 0.")) (|discreteLog| (((|NonNegativeInteger|) $) "\\spad{discreteLog(a)} computes the discrete logarithm of \\spad{a} with respect to \\spad{primitiveElement()} of the field.")) (|primitive?| (((|Boolean|) $) "\\spad{primitive?(b)} tests whether the element \\spad{b} is a generator of the (cyclic) multiplicative group of the field,{} \\spadignore{i.e.} is a primitive element. Implementation Note: see ch.IX.1.3,{} th.2 in \\spad{D}. Lipson.")) (|primitiveElement| (($) "\\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.")))
NIL
NIL
-(-298)
+(-299)
((|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|) $) "\\spad{primitive?(b)} tests whether the element \\spad{b} is a generator of the (cyclic) multiplicative group of the field,{} \\spadignore{i.e.} is a primitive element. Implementation Note: see ch.IX.1.3,{} th.2 in \\spad{D}. Lipson.")) (|primitiveElement| (($) "\\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.")))
-((-3984 . T) (-3990 . T) (-3985 . T) ((-3994 "*") . T) (-3986 . T) (-3987 . T) (-3989 . T))
+((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T))
NIL
-(-299 R UP -3091)
+(-300 R UP -3094)
((|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
-(-300 |p| |extdeg|)
+(-301 |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.")))
-((-3984 . T) (-3990 . T) (-3985 . T) ((-3994 "*") . T) (-3986 . T) (-3987 . T) (-3989 . T))
-((OR (|HasCategory| (-818 |#1|) (QUOTE (-118))) (|HasCategory| (-818 |#1|) (QUOTE (-317)))) (|HasCategory| (-818 |#1|) (QUOTE (-120))) (|HasCategory| (-818 |#1|) (QUOTE (-317))) (|HasCategory| (-818 |#1|) (QUOTE (-118))))
-(-301 GF |uni|)
+((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T))
+((OR (|HasCategory| (-819 |#1|) (QUOTE (-118))) (|HasCategory| (-819 |#1|) (QUOTE (-318)))) (|HasCategory| (-819 |#1|) (QUOTE (-120))) (|HasCategory| (-819 |#1|) (QUOTE (-318))) (|HasCategory| (-819 |#1|) (QUOTE (-118))))
+(-302 GF |uni|)
((|constructor| (NIL "FiniteFieldNormalBasisExtensionByPolynomial(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.")))
-((-3984 . T) (-3990 . T) (-3985 . T) ((-3994 "*") . T) (-3986 . T) (-3987 . T) (-3989 . T))
-((OR (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-317)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-118))))
-(-302 GF |extdeg|)
+((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T))
+((OR (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-318)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-118))))
+(-303 GF |extdeg|)
((|constructor| (NIL "FiniteFieldNormalBasisExtensionByPolynomial(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.")))
-((-3984 . T) (-3990 . T) (-3985 . T) ((-3994 "*") . T) (-3986 . T) (-3987 . T) (-3989 . T))
-((OR (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-317)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-118))))
-(-303 GF |defpol|)
+((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T))
+((OR (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-318)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-118))))
+(-304 GF |defpol|)
((|constructor| (NIL "FiniteFieldExtensionByPolynomial(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.")))
-((-3984 . T) (-3990 . T) (-3985 . T) ((-3994 "*") . T) (-3986 . T) (-3987 . T) (-3989 . T))
-((OR (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-317)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-118))))
-(-304 GF)
+((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T))
+((OR (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-318)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-118))))
+(-305 GF)
((|constructor| (NIL "This package provides a number of functions for generating,{} counting and testing irreducible,{} normal,{} primitive,{} random polynomials over finite fields.")) (|reducedQPowers| (((|PrimitiveArray| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{reducedQPowers(f)} generates \\spad{[x,x**q,x**(q**2),...,x**(q**(n-1))]} reduced modulo \\spad{f} where \\spad{q = size()\\$GF} and \\spad{n = degree 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(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(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(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(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(GF) generates a normal polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|createPrimitivePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createPrimitivePoly(n)}\\$FFPOLY(GF) generates a primitive polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|createIrreduciblePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createIrreduciblePoly(n)}\\$FFPOLY(GF) generates a monic irreducible univariate polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfNormalPoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfNormalPoly(n)}\\$FFPOLY(GF) yields the number of normal polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfPrimitivePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfPrimitivePoly(n)}\\$FFPOLY(GF) yields the number of primitive polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfIrreduciblePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfIrreduciblePoly(n)}\\$FFPOLY(GF) yields the number of monic irreducible univariate polynomials of degree \\spad{n} over the finite field {\\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
-(-305 -3091 GF)
+(-306 -3094 GF)
((|constructor| (NIL "\\spad{FiniteFieldPolynomialPackage2}(\\spad{F},{}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
-(-306 -3091 FP FPP)
+(-307 -3094 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}'s exists.")))
NIL
NIL
-(-307 GF |n|)
+(-308 GF |n|)
((|constructor| (NIL "FiniteFieldExtensionByPolynomial(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}.")))
-((-3984 . T) (-3990 . T) (-3985 . T) ((-3994 "*") . T) (-3986 . T) (-3987 . T) (-3989 . T))
-((OR (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-317)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-118))))
-(-308 R |ls|)
+((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T))
+((OR (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-318)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-118))))
+(-309 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{ls}.")))
NIL
NIL
-(-309 S)
+(-310 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}'s are in \\spad{S},{} and the \\spad{ni}'s are integers. The multiplication is not commutative.")) (|factors| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| (|Integer|)))) $) "\\spad{factors(a1\\^e1,...,an\\^en)} returns \\spad{[[a1, e1],...,[an, en]]}.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f, a1\\^e1 ... an\\^en)} returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (|mapExpon| (($ (|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| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left.")))
-((-3989 . T))
+((-3993 . T))
NIL
-(-310 S)
+(-311 S)
((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0.")))
NIL
NIL
-(-311)
+(-312)
((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0.")))
-((-3984 . T) (-3990 . T) (-3985 . T) ((-3994 "*") . T) (-3986 . T) (-3987 . T) (-3989 . T))
+((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T))
NIL
-(-312 S)
+(-313 S)
((|constructor| (NIL "This domain provides a basic model of files to save arbitrary values. The operations provide sequential access to the contents.")) (|readIfCan!| (((|Union| |#1| "failed") $) "\\spad{readIfCan!(f)} returns a value from the file \\spad{f},{} if possible. If \\spad{f} is not open for reading,{} or if \\spad{f} is at the end of file then \\spad{\"failed\"} is the result.")))
NIL
NIL
-(-313 |Name| S)
+(-314 |Name| S)
((|constructor| (NIL "This category provides an interface to operate on files in the computer's file system. The precise method of naming files is determined by the Name parameter. The type of the contents of the file is determined by \\spad{S}.")) (|write!| ((|#2| $ |#2|) "\\spad{write!(f,s)} puts the value \\spad{s} into the file \\spad{f}. The state of \\spad{f} is modified so subsequents call to \\spad{write!} will append one after another.")) (|read!| ((|#2| $) "\\spad{read!(f)} extracts a value from file \\spad{f}. The state of \\spad{f} is modified so a subsequent call to \\spadfun{read!} will return the next element.")) (|iomode| (((|String|) $) "\\spad{iomode(f)} returns the status of the file \\spad{f}. The input/output status of \\spad{f} may be \"input\",{} \"output\" or \"closed\" mode.")) (|name| ((|#1| $) "\\spad{name(f)} returns the external name of the file \\spad{f}.")) (|close!| (($ $) "\\spad{close!(f)} returns the file \\spad{f} closed to input and output.")) (|reopen!| (($ $ (|String|)) "\\spad{reopen!(f,mode)} returns a file \\spad{f} reopened for operation in the indicated mode: \"input\" or \"output\". \\spad{reopen!(f,\"input\")} will reopen the file \\spad{f} for input.")) (|open| (($ |#1| (|String|)) "\\spad{open(s,mode)} returns a file \\spad{s} open for operation in the indicated mode: \"input\" or \"output\".") (($ |#1|) "\\spad{open(s)} returns the file \\spad{s} open for input.")))
NIL
NIL
-(-314 S R)
+(-315 S R)
((|constructor| (NIL "A FiniteRankNonAssociativeAlgebra is a non associative algebra over a commutative ring \\spad{R} which is a free \\spad{R}-module of finite rank.")) (|unitsKnown| ((|attribute|) "unitsKnown means that \\spadfun{recip} truly yields reciprocal or \\spad{\"failed\"} if not a unit,{} similarly for \\spadfun{leftRecip} and \\spadfun{rightRecip}. The reason is that we use left,{} respectively right,{} minimal polynomials to decide this question.")) (|unit| (((|Union| $ "failed")) "\\spad{unit()} returns a unit of the algebra (necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnit| (((|Union| $ "failed")) "\\spad{rightUnit()} returns a right unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|leftUnit| (((|Union| $ "failed")) "\\spad{leftUnit()} returns a left unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{rightUnits()} returns the affine space of all right units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|leftUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{leftUnits()} returns the affine space of all left units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|rightMinimalPolynomial| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{rightMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of right powers of \\spad{a}. Note: the polynomial never has a constant term as in general the algebra has no unit.")) (|leftMinimalPolynomial| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{leftMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of left powers of \\spad{a}. Note: the polynomial never has a constant term as in general the algebra has no unit.")) (|associatorDependence| (((|List| (|Vector| |#2|))) "\\spad{associatorDependence()} looks for the associator identities,{} \\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't exist or cannot be determined (see unitsKnown).")) (|leftRecip| (((|Union| $ "failed") $) "\\spad{leftRecip(a)} returns an element,{} which is a left inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(a)} returns an element,{} which is both a left and a right inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (|lieAlgebra?| (((|Boolean|)) "\\spad{lieAlgebra?()} tests if the algebra is anticommutative and \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} for all \\spad{a},{}\\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(\"*\")} 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'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'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'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'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| |#2|) $) "\\spad{rightCharacteristicPolynomial(a)} returns the characteristic polynomial of the right regular representation of \\spad{a} with respect to any basis.")) (|leftCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{leftCharacteristicPolynomial(a)} returns the characteristic polynomial of the left regular representation of \\spad{a} with respect to any basis.")) (|rightTraceMatrix| (((|Matrix| |#2|) (|Vector| $)) "\\spad{rightTraceMatrix([v1,...,vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj}.")) (|leftTraceMatrix| (((|Matrix| |#2|) (|Vector| $)) "\\spad{leftTraceMatrix([v1,...,vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj}.")) (|rightDiscriminant| ((|#2| (|Vector| $)) "\\spad{rightDiscriminant([v1,...,vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\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| ((|#2| (|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| |#2|) (|Vector| $)) "\\spad{represents([a1,...,am],[v1,...,vm])} returns the linear combination \\spad{a1*vm + ... + an*vm}.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $) (|Vector| $)) "\\spad{coordinates([a1,...,am],[v1,...,vn])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{ai} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.") (((|Vector| |#2|) $ (|Vector| $)) "\\spad{coordinates(a,[v1,...,vn])} returns the coordinates of \\spad{a} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rightNorm| ((|#2| $) "\\spad{rightNorm(a)} returns the determinant of the right regular representation of \\spad{a}.")) (|leftNorm| ((|#2| $) "\\spad{leftNorm(a)} returns the determinant of the left regular representation of \\spad{a}.")) (|rightTrace| ((|#2| $) "\\spad{rightTrace(a)} returns the trace of the right regular representation of \\spad{a}.")) (|leftTrace| ((|#2| $) "\\spad{leftTrace(a)} returns the trace of the left regular representation of \\spad{a}.")) (|rightRegularRepresentation| (((|Matrix| |#2|) $ (|Vector| $)) "\\spad{rightRegularRepresentation(a,[v1,...,vn])} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,...,vn]}.")) (|leftRegularRepresentation| (((|Matrix| |#2|) $ (|Vector| $)) "\\spad{leftRegularRepresentation(a,[v1,...,vn])} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,...,vn]}.")) (|structuralConstants| (((|Vector| (|Matrix| |#2|)) (|Vector| $)) "\\spad{structuralConstants([v1,v2,...,vm])} calculates the structural constants \\spad{[(gammaijk) for 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| |#2|)) (|Vector| $)) "\\spad{conditionsForIdempotents([v1,...,vn])} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra as \\spad{R}-module.")) (|someBasis| (((|Vector| $)) "\\spad{someBasis()} returns some \\spad{R}-module basis.")))
NIL
-((|HasCategory| |#2| (QUOTE (-495))))
-(-315 R)
+((|HasCategory| |#2| (QUOTE (-496))))
+(-316 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't exist or cannot be determined (see unitsKnown).")) (|leftRecip| (((|Union| $ "failed") $) "\\spad{leftRecip(a)} returns an element,{} which is a left inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(a)} returns an element,{} which is both a left and a right inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (|lieAlgebra?| (((|Boolean|)) "\\spad{lieAlgebra?()} tests if the algebra is anticommutative and \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} for all \\spad{a},{}\\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(\"*\")} 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'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'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'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'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| $)) "\\spad{someBasis()} returns some \\spad{R}-module basis.")))
-((-3989 |has| |#1| (-495)) (-3987 . T) (-3986 . T))
+((-3993 |has| |#1| (-496)) (-3991 . T) (-3990 . T))
NIL
-(-316 S)
+(-317 S)
((|constructor| (NIL "The category of domains composed of a finite set of elements. We include the functions \\spadfun{lookup} and \\spadfun{index} to give a bijection between the finite set and an initial segment of positive integers. \\blankline")) (|random| (($) "\\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.")))
NIL
NIL
-(-317)
+(-318)
((|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.")))
NIL
NIL
-(-318 S R UP)
+(-319 S 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| ((|#3| $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of \\spad{a}.")) (|characteristicPolynomial| ((|#3| $) "\\spad{characteristicPolynomial(a)} returns the characteristic polynomial of the regular representation of \\spad{a} with respect to any basis.")) (|traceMatrix| (((|Matrix| |#2|) (|Vector| $)) "\\spad{traceMatrix([v1,..,vn])} is the \\spad{n}-by-\\spad{n} matrix ( Tr(\\spad{vi} * vj) )")) (|discriminant| ((|#2| (|Vector| $)) "\\spad{discriminant([v1,..,vn])} returns \\spad{determinant(traceMatrix([v1,..,vn]))}.")) (|represents| (($ (|Vector| |#2|) (|Vector| $)) "\\spad{represents([a1,..,an],[v1,..,vn])} returns \\spad{a1*v1 + ... + an*vn}.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $) (|Vector| $)) "\\spad{coordinates([v1,...,vm], basis)} returns the coordinates of the \\spad{vi}'s with to the basis \\spad{basis}. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#2|) $ (|Vector| $)) "\\spad{coordinates(a,basis)} returns the coordinates of \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|norm| ((|#2| $) "\\spad{norm(a)} returns the determinant of the regular representation of \\spad{a} with respect to any basis.")) (|trace| ((|#2| $) "\\spad{trace(a)} returns the trace of the regular representation of \\spad{a} with respect to any basis.")) (|regularRepresentation| (((|Matrix| |#2|) $ (|Vector| $)) "\\spad{regularRepresentation(a,basis)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra.")))
NIL
-((|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-311))))
-(-319 R UP)
+((|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-312))))
+(-320 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 ( Tr(\\spad{vi} * 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}'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| $)) "\\spad{regularRepresentation(a,basis)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra.")))
-((-3986 . T) (-3987 . T) (-3989 . T))
+((-3990 . T) (-3991 . T) (-3993 . T))
NIL
-(-320 A S)
+(-321 A S)
((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|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{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|) $) "\\spad{sorted?(p,a)} tests if \\axiom{a} is sorted according to predicate \\spad{p}.")) (|sort| (($ $) "\\spad{sort(u)} returns an \\spad{u} with elements in ascending order. Note: \\axiom{sort(\\spad{u}) = sort(<=,{}\\spad{u})}.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $) "\\spad{sort(p,a)} returns a copy of \\axiom{a} sorted using total ordering predicate \\spad{p}.")) (|reverse| (($ $) "\\spad{reverse(a)} returns a copy of \\axiom{a} with elements in reverse order.")) (|merge| (($ $ $) "\\spad{merge(u,v)} merges \\spad{u} and \\spad{v} in ascending order. Note: \\axiom{merge(\\spad{u},{}\\spad{v}) = merge(<=,{}\\spad{u},{}\\spad{v})}.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $ $) "\\spad{merge(p,a,b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}.")))
NIL
-((|HasAttribute| |#1| (QUOTE -3993)) (|HasCategory| |#2| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-1013))))
-(-321 S)
+((|HasAttribute| |#1| (QUOTE -3997)) (|HasCategory| |#2| (QUOTE (-758))) (|HasCategory| |#2| (QUOTE (-1015))))
+(-322 S)
((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|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{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|) $) "\\spad{sorted?(p,a)} tests if \\axiom{a} is sorted according to predicate \\spad{p}.")) (|sort| (($ $) "\\spad{sort(u)} returns an \\spad{u} with elements in ascending order. Note: \\axiom{sort(\\spad{u}) = sort(<=,{}\\spad{u})}.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $) "\\spad{sort(p,a)} returns a copy of \\axiom{a} sorted using total ordering predicate \\spad{p}.")) (|reverse| (($ $) "\\spad{reverse(a)} returns a copy of \\axiom{a} with elements in reverse order.")) (|merge| (($ $ $) "\\spad{merge(u,v)} merges \\spad{u} and \\spad{v} in ascending order. Note: \\axiom{merge(\\spad{u},{}\\spad{v}) = merge(<=,{}\\spad{u},{}\\spad{v})}.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $ $) "\\spad{merge(p,a,b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}.")))
-((-3992 . T))
+((-3996 . T))
NIL
-(-322 S A R B)
+(-323 S A R B)
((|constructor| (NIL "\\spad{FiniteLinearAggregateFunctions2} provides functions involving two FiniteLinearAggregates where the underlying domains might be different. An example of this might be creating a list of rational numbers by mapping a function across a list of integers where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-aggregates \\spad{x} of aggregrate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad{[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,[1,2,3],0)} does \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as the identity element for the function \\spad{f}.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f,a)} applies function \\spad{f} to each member of aggregate \\spad{a} resulting in a new aggregate over a possibly different underlying domain.")))
NIL
NIL
-(-323 |VarSet| R)
+(-324 |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.fr)")) (|eval| (($ $ (|List| |#1|) (|List| $)) "\\axiom{eval(\\spad{p},{} [\\spad{x1},{}...,{}xn],{} [\\spad{v1},{}...,{}vn])} replaces \\axiom{\\spad{xi}} by \\axiom{\\spad{vi}} in \\axiom{\\spad{p}}.") (($ $ |#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) (-3987 . T) (-3986 . T))
+((|JacobiIdentity| . T) (|NullSquare| . T) (-3991 . T) (-3990 . T))
NIL
-(-324 S V)
+(-325 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.")))
NIL
NIL
-(-325 S R)
+(-326 S 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}")))
NIL
-((|HasCategory| |#2| (QUOTE (-581 (-484)))))
-(-326 R)
+((|HasCategory| |#2| (QUOTE (-582 (-485)))))
+(-327 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}")))
NIL
NIL
-(-327)
+(-328)
((|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}.")))
-((-3975 . T) (-3983 . T) (-3767 . T) (-3984 . T) (-3990 . T) (-3985 . T) ((-3994 "*") . T) (-3986 . T) (-3987 . T) (-3989 . T))
+((-3979 . T) (-3987 . T) (-3771 . T) (-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T))
NIL
-(-328 |Par|)
+(-329 |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 lp.") (((|List| (|List| (|Equation| (|Polynomial| (|Complex| |#1|))))) (|List| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) |#1|) "\\spad{complexSolve(lp,eps)} finds all the complex solutions to precision \\spad{eps} of the system \\spad{lp} of rational functions over the complex rationals with respect to all the variables appearing in \\spad{lp}.")))
NIL
NIL
-(-329 |Par|)
+(-330 |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 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}.")))
NIL
NIL
-(-330 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.")))
-((-3987 . T) (-3986 . T))
-((|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-1013)))))
(-331 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.")))
+((-3991 . T) (-3990 . T))
+((|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#2| (QUOTE (-1015)))))
+(-332 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.fr)")) (* (($ |#2| |#1|) "\\spad{s*r} returns the product \\spad{r*s} used by \\spadtype{XRecursivePolynomial}")))
-((-3987 . T) (-3986 . T))
+((-3991 . T) (-3990 . T))
((|HasCategory| |#1| (QUOTE (-146))))
-(-332 R |Basis|)
+(-333 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.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}.")))
-((-3987 . T) (-3986 . T))
+((-3991 . T) (-3990 . T))
NIL
-(-333 S)
+(-334 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}'s are in \\spad{S},{} and the \\spad{ni}'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| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left.")))
NIL
NIL
-(-334 S)
+(-335 S)
((|constructor| (NIL "The free monoid on a set \\spad{S} is the monoid of finite products of the form \\spad{reduce(*,[si ** ni])} where the \\spad{si}'s are in \\spad{S},{} and the \\spad{ni}'s are nonnegative integers. The multiplication is not commutative.")))
NIL
-((|HasCategory| |#1| (QUOTE (-757))))
-(-335)
+((|HasCategory| |#1| (QUOTE (-758))))
+(-336)
((|constructor| (NIL "This domain provides an interface to names in the file system.")))
NIL
NIL
-(-336)
+(-337)
((|constructor| (NIL "This category provides an interface to names in the file system.")) (|new| (($ (|String|) (|String|) (|String|)) "\\spad{new(d,pref,e)} constructs the name of a new writable file with \\spad{d} as its directory,{} \\spad{pref} as a prefix of its name and \\spad{e} as its extension. When \\spad{d} or \\spad{t} is the empty string,{} a default is used. An error occurs if a new file cannot be written in the given directory.")) (|writable?| (((|Boolean|) $) "\\spad{writable?(f)} tests if the named file be opened for writing. The named file need not already exist.")) (|readable?| (((|Boolean|) $) "\\spad{readable?(f)} tests if the named file exist and can it be opened for reading.")) (|exists?| (((|Boolean|) $) "\\spad{exists?(f)} tests if the file exists in the file system.")) (|extension| (((|String|) $) "\\spad{extension(f)} returns the type part of the file name.")) (|name| (((|String|) $) "\\spad{name(f)} returns the name part of the file name.")) (|directory| (((|String|) $) "\\spad{directory(f)} returns the directory part of the file name.")) (|filename| (($ (|String|) (|String|) (|String|)) "\\spad{filename(d,n,e)} creates a file name with \\spad{d} as its directory,{} \\spad{n} as its name and \\spad{e} as its extension. This is a portable way to create file names. When \\spad{d} or \\spad{t} is the empty string,{} a default is used.")))
NIL
NIL
-(-337 |n| |class| R)
+(-338 |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|) $) "\\spad{deepExpand(x)} \\undocumented{}")) (|dimension| (((|NonNegativeInteger|)) "\\spad{dimension()} is the rank of this Lie algebra")))
-((-3987 . T) (-3986 . T))
+((-3991 . T) (-3990 . T))
NIL
-(-338 -3091 UP UPUP R)
+(-339 -3094 UP UPUP R)
((|constructor| (NIL "\\indented{1}{Finds the order of a divisor over a finite field} Author: Manuel Bronstein Date Created: 1988 Date Last Updated: 11 Jul 1990")) (|order| (((|NonNegativeInteger|) (|FiniteDivisor| |#1| |#2| |#3| |#4|)) "\\spad{order(x)} \\undocumented")))
NIL
NIL
-(-339 -3091 UP)
+(-340 -3094 UP)
((|constructor| (NIL "\\indented{1}{Full partial fraction expansion of rational functions} Author: Manuel Bronstein Date Created: 9 December 1992 Date Last Updated: June 18,{} 2010 References: \\spad{M}.Bronstein & \\spad{B}.Salvy,{} \\indented{12}{Full Partial Fraction Decomposition of Rational Functions,{}} \\indented{12}{in Proceedings of \\spad{ISSAC'93},{} Kiev,{} ACM Press.}")) (|construct| (($ (|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| |#2|) (|:| |num| |#2|)))) "\\spad{construct(l)} is the inverse of fracPart.")) (|fracPart| (((|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| |#2|) (|:| |num| |#2|))) $) "\\spad{fracPart(f)} returns the list of summands of the fractional part of \\spad{f}.")) (|polyPart| ((|#2| $) "\\spad{polyPart(f)} returns the polynomial part of \\spad{f}.")) (|fullPartialFraction| (($ (|Fraction| |#2|)) "\\spad{fullPartialFraction(f)} returns \\spad{[p, [[j, Dj, Hj]...]]} such that \\spad{f = p(x) + \\sum_{[j,Dj,Hj] in l} \\sum_{Dj(a)=0} Hj(a)/(x - a)\\^j}.")) (+ (($ |#2| $) "\\spad{p + x} returns the sum of \\spad{p} and \\spad{x}")))
NIL
NIL
-(-340 R)
+(-341 R)
((|constructor| (NIL "A set \\spad{S} is PatternMatchable over \\spad{R} if \\spad{S} can lift the pattern-matching functions of \\spad{S} over the integers and float to itself (necessary for matching in towers).")))
NIL
NIL
-(-341 S)
+(-342 S)
((|constructor| (NIL "FieldOfPrimeCharacteristic is the category of fields of prime characteristic,{} \\spadignore{e.g.} finite fields,{} algebraic closures of fields of prime characteristic,{} transcendental extensions of of fields of prime characteristic.")) (|primeFrobenius| (($ $ (|NonNegativeInteger|)) "\\spad{primeFrobenius(a,s)} returns \\spad{a**(p**s)} where \\spad{p} is the characteristic.") (($ $) "\\spad{primeFrobenius(a)} returns \\spad{a ** p} where \\spad{p} is the characteristic.")) (|discreteLog| (((|Union| (|NonNegativeInteger|) "failed") $ $) "\\spad{discreteLog(b,a)} computes \\spad{s} with \\spad{b**s = a} if such an \\spad{s} exists.")) (|order| (((|OnePointCompletion| (|PositiveInteger|)) $) "\\spad{order(a)} computes the order of an element in the multiplicative group of the field. Error: if \\spad{a} is 0.")))
NIL
NIL
-(-342)
+(-343)
((|constructor| (NIL "FieldOfPrimeCharacteristic is the category of fields of prime characteristic,{} \\spadignore{e.g.} finite fields,{} algebraic closures of fields of prime characteristic,{} transcendental extensions of of fields of prime characteristic.")) (|primeFrobenius| (($ $ (|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|)) $) "\\spad{order(a)} computes the order of an element in the multiplicative group of the field. Error: if \\spad{a} is 0.")))
-((-3984 . T) (-3990 . T) (-3985 . T) ((-3994 "*") . T) (-3986 . T) (-3987 . T) (-3989 . T))
+((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T))
NIL
-(-343 S)
+(-344 S)
((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\"+\") does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\spad{max()} returns the maximum floating point number.")) (|min| (($) "\\spad{min()} returns the minimum floating point number.")) (|decreasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{decreasePrecision(n)} decreases the current \\spadfunFrom{precision}{FloatingPointSystem} precision by \\spad{n} decimal digits.")) (|increasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{increasePrecision(n)} increases the current \\spadfunFrom{precision}{FloatingPointSystem} by \\spad{n} decimal digits.")) (|precision| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{precision(n)} set the precision in the base to \\spad{n} decimal digits.") (((|PositiveInteger|)) "\\spad{precision()} returns the precision in digits base.")) (|digits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{digits(d)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{d} digits.") (((|PositiveInteger|)) "\\spad{digits()} returns ceiling's precision in decimal digits.")) (|bits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{bits(n)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{n} bits.") (((|PositiveInteger|)) "\\spad{bits()} returns ceiling's precision in bits.")) (|mantissa| (((|Integer|) $) "\\spad{mantissa(x)} returns the mantissa part of \\spad{x}.")) (|exponent| (((|Integer|) $) "\\spad{exponent(x)} returns the \\spadfunFrom{exponent}{FloatingPointSystem} part of \\spad{x}.")) (|base| (((|PositiveInteger|)) "\\spad{base()} returns the base of the \\spadfunFrom{exponent}{FloatingPointSystem}.")) (|order| (((|Integer|) $) "\\spad{order x} is the order of magnitude of \\spad{x}. Note: \\spad{base ** order x <= |x| < base ** (1 + order x)}.")) (|float| (($ (|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 -3975)) (|HasAttribute| |#1| (QUOTE -3983)))
-(-344)
+((|HasAttribute| |#1| (QUOTE -3979)) (|HasAttribute| |#1| (QUOTE -3987)))
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((|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(\"+\") does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\spad{max()} returns the maximum floating point number.")) (|min| (($) "\\spad{min()} returns the minimum floating point number.")) (|decreasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{decreasePrecision(n)} decreases the current \\spadfunFrom{precision}{FloatingPointSystem} precision by \\spad{n} decimal digits.")) (|increasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{increasePrecision(n)} increases the current \\spadfunFrom{precision}{FloatingPointSystem} by \\spad{n} decimal digits.")) (|precision| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{precision(n)} set the precision in the base to \\spad{n} decimal digits.") (((|PositiveInteger|)) "\\spad{precision()} returns the precision in digits base.")) (|digits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{digits(d)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{d} digits.") (((|PositiveInteger|)) "\\spad{digits()} returns ceiling's precision in decimal digits.")) (|bits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{bits(n)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{n} bits.") (((|PositiveInteger|)) "\\spad{bits()} returns ceiling's precision in bits.")) (|mantissa| (((|Integer|) $) "\\spad{mantissa(x)} returns the mantissa part of \\spad{x}.")) (|exponent| (((|Integer|) $) "\\spad{exponent(x)} returns the \\spadfunFrom{exponent}{FloatingPointSystem} part of \\spad{x}.")) (|base| (((|PositiveInteger|)) "\\spad{base()} returns the base of the \\spadfunFrom{exponent}{FloatingPointSystem}.")) (|order| (((|Integer|) $) "\\spad{order x} is the order of magnitude of \\spad{x}. Note: \\spad{base ** order x <= |x| < base ** (1 + order x)}.")) (|float| (($ (|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\".")))
-((-3767 . T) (-3984 . T) (-3990 . T) (-3985 . T) ((-3994 "*") . T) (-3986 . T) (-3987 . T) (-3989 . T))
+((-3771 . T) (-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T))
NIL
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((|constructor| (NIL "\\spadtype{Factored} creates a domain whose objects are kept in factored form as long as possible. Thus certain operations like multiplication and 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| #1="nil" #2="sqfr" #3="irred" #4="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| #1# #2# #3# #4#) $ (|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| #1# #2# #3# #4#)) (|:| |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| #1# #2# #3# #4#)) (|:| |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.")))
-((-3985 . T) ((-3994 "*") . T) (-3986 . T) (-3987 . T) (-3989 . T))
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+((-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T))
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+(-347 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.")))
NIL
NIL
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((|constructor| (NIL "Fraction takes an IntegralDomain \\spad{S} and produces the domain of Fractions with numerators and denominators from \\spad{S}. If \\spad{S} is also a GcdDomain,{} then gcd's between numerator and denominator will be cancelled during all operations.")) (|canonical| ((|attribute|) "\\spad{canonical} means that equal elements are in fact identical.")))
-((-3979 -12 (|has| |#1| (-6 -3990)) (|has| |#1| (-389)) (|has| |#1| (-6 -3979))) (-3984 . T) (-3990 . T) (-3985 . T) ((-3994 "*") . T) (-3986 . T) (-3987 . T) (-3989 . T))
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((|constructor| (NIL "This package extends a map between integral domains to a map between Fractions over those domains by applying the map to the numerators and denominators.")) (|map| (((|Fraction| |#2|) (|Mapping| |#2| |#1|) (|Fraction| |#1|)) "\\spad{map(func,frac)} applies the function \\spad{func} to the numerator and denominator of the fraction \\spad{frac}.")))
NIL
NIL
-(-349 S R UP)
+(-350 S R UP)
((|constructor| (NIL "A \\spadtype{FramedAlgebra} is a \\spadtype{FiniteRankAlgebra} together with a fixed \\spad{R}-module basis.")) (|regularRepresentation| (((|Matrix| |#2|) $) "\\spad{regularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed basis.")) (|discriminant| ((|#2|) "\\spad{discriminant()} = determinant(traceMatrix()).")) (|traceMatrix| (((|Matrix| |#2|)) "\\spad{traceMatrix()} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr(vi * vj)} ),{} where \\spad{v1},{} ...,{} vn are the elements of the fixed basis.")) (|convert| (($ (|Vector| |#2|)) "\\spad{convert([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} 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},{} ...,{} vn are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $)) "\\spad{coordinates([v1,...,vm])} returns the coordinates of the \\spad{vi}'s with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#2|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis.")))
NIL
NIL
-(-350 R UP)
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((|constructor| (NIL "A \\spadtype{FramedAlgebra} is a \\spadtype{FiniteRankAlgebra} together with a fixed \\spad{R}-module basis.")) (|regularRepresentation| (((|Matrix| |#1|) $) "\\spad{regularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed basis.")) (|discriminant| ((|#1|) "\\spad{discriminant()} = determinant(traceMatrix()).")) (|traceMatrix| (((|Matrix| |#1|)) "\\spad{traceMatrix()} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr(vi * vj)} ),{} where \\spad{v1},{} ...,{} vn are the elements of the fixed basis.")) (|convert| (($ (|Vector| |#1|)) "\\spad{convert([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} 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},{} ...,{} vn are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([v1,...,vm])} returns the coordinates of the \\spad{vi}'s with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#1|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis.")))
-((-3986 . T) (-3987 . T) (-3989 . T))
+((-3990 . T) (-3991 . T) (-3993 . T))
NIL
-(-351 A S)
+(-352 A S)
((|constructor| (NIL "\\indented{2}{A is fully retractable to \\spad{B} means that A is retractable to \\spad{B},{} and,{}} \\indented{2}{in addition,{} if \\spad{B} is retractable to the integers or rational} \\indented{2}{numbers then so is A.} \\indented{2}{In particular,{} what we are asserting is that there are no integers} \\indented{2}{(rationals) in A which don't retract into \\spad{B}.} Date Created: March 1990 Date Last Updated: 9 April 1991")))
NIL
-((|HasCategory| |#2| (QUOTE (-951 (-347 (-484))))) (|HasCategory| |#2| (QUOTE (-951 (-484)))))
-(-352 S)
+((|HasCategory| |#2| (QUOTE (-952 (-348 (-485))))) (|HasCategory| |#2| (QUOTE (-952 (-485)))))
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((|constructor| (NIL "\\indented{2}{A is fully retractable to \\spad{B} means that A is retractable to \\spad{B},{} and,{}} \\indented{2}{in addition,{} if \\spad{B} is retractable to the integers or rational} \\indented{2}{numbers then so is A.} \\indented{2}{In particular,{} what we are asserting is that there are no integers} \\indented{2}{(rationals) in A which don't retract into \\spad{B}.} Date Created: March 1990 Date Last Updated: 9 April 1991")))
NIL
NIL
-(-353 R -3091 UP A)
+(-354 R -3094 UP A)
((|constructor| (NIL "Fractional ideals in a framed algebra.")) (|randomLC| ((|#4| (|NonNegativeInteger|) (|Vector| |#4|)) "\\spad{randomLC(n,x)} should be local but conditional.")) (|minimize| (($ $) "\\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)}.")))
-((-3989 . T))
+((-3993 . T))
NIL
-(-354 R1 F1 U1 A1 R2 F2 U2 A2)
+(-355 R1 F1 U1 A1 R2 F2 U2 A2)
((|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
-(-355 R -3091 UP A |ibasis|)
+(-356 R -3094 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|) $) "\\spad{basis((f1,...,fn))} = the vector \\spad{[f1,...,fn]}.")))
NIL
-((|HasCategory| |#4| (|%list| (QUOTE -951) (|devaluate| |#2|))))
-(-356 AR R AS S)
+((|HasCategory| |#4| (|%list| (QUOTE -952) (|devaluate| |#2|))))
+(-357 AR R AS S)
((|constructor| (NIL "\\spad{FramedNonAssociativeAlgebraFunctions2} implements functions between two framed non associative algebra domains defined over different rings. The function map is used to coerce between algebras over different domains having the same structural constants.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,u)} maps \\spad{f} onto the coordinates of \\spad{u} to get an element in \\spad{AS} via identification of the basis of \\spad{AR} as beginning part of the basis of \\spad{AS}.")))
NIL
NIL
-(-357 S R)
+(-358 S R)
((|constructor| (NIL "FramedNonAssociativeAlgebra(\\spad{R}) is a \\spadtype{FiniteRankNonAssociativeAlgebra} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank) over a commutative ring \\spad{R} together with a fixed \\spad{R}-module basis.")) (|apply| (($ (|Matrix| |#2|) $) "\\spad{apply(m,a)} defines a left operation of \\spad{n} by \\spad{n} matrices where \\spad{n} is the rank of the algebra in terms of matrix-vector multiplication,{} this is a substitute for a left module structure. Error: if shape of matrix doesn't fit.")) (|rightRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#2|))) "\\spad{rightRankPolynomial()} calculates the right minimal polynomial of the generic element in the algebra,{} defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|leftRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#2|))) "\\spad{leftRankPolynomial()} calculates the left minimal polynomial of the generic element in the algebra,{} defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|rightRegularRepresentation| (((|Matrix| |#2|) $) "\\spad{rightRegularRepresentation(a)} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|leftRegularRepresentation| (((|Matrix| |#2|) $) "\\spad{leftRegularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|rightTraceMatrix| (((|Matrix| |#2|)) "\\spad{rightTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|leftTraceMatrix| (((|Matrix| |#2|)) "\\spad{leftTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|rightDiscriminant| ((|#2|) "\\spad{rightDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note: the same as \\spad{determinant(rightTraceMatrix())}.")) (|leftDiscriminant| ((|#2|) "\\spad{leftDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note: the same as \\spad{determinant(leftTraceMatrix())}.")) (|convert| (($ (|Vector| |#2|)) "\\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| |#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 \\spad{R}-module basis.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#2|))) "\\spad{conditionsForIdempotents()} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the fixed \\spad{R}-module basis.")) (|structuralConstants| (((|Vector| (|Matrix| |#2|))) "\\spad{structuralConstants()} calculates the structural constants \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{vi * vj = gammaij1 * v1 + ... + gammaijn * vn},{} where \\spad{v1},{}...,{}\\spad{vn} is the fixed \\spad{R}-module basis.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $)) "\\spad{coordinates([a1,...,am])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{ai} with respect to the fixed \\spad{R}-module basis.") (((|Vector| |#2|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis.")))
NIL
-((|HasCategory| |#2| (QUOTE (-311))))
-(-358 R)
+((|HasCategory| |#2| (QUOTE (-312))))
+(-359 R)
((|constructor| (NIL "FramedNonAssociativeAlgebra(\\spad{R}) is a \\spadtype{FiniteRankNonAssociativeAlgebra} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank) over a commutative ring \\spad{R} together with a fixed \\spad{R}-module basis.")) (|apply| (($ (|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't fit.")) (|rightRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#1|))) "\\spad{rightRankPolynomial()} calculates the right minimal polynomial of the generic element in the algebra,{} defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|leftRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#1|))) "\\spad{leftRankPolynomial()} calculates the left minimal polynomial of the generic element in the algebra,{} defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|rightRegularRepresentation| (((|Matrix| |#1|) $) "\\spad{rightRegularRepresentation(a)} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|leftRegularRepresentation| (((|Matrix| |#1|) $) "\\spad{leftRegularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|rightTraceMatrix| (((|Matrix| |#1|)) "\\spad{rightTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|leftTraceMatrix| (((|Matrix| |#1|)) "\\spad{leftTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|rightDiscriminant| ((|#1|) "\\spad{rightDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note: the same as \\spad{determinant(rightTraceMatrix())}.")) (|leftDiscriminant| ((|#1|) "\\spad{leftDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note: the same as \\spad{determinant(leftTraceMatrix())}.")) (|convert| (($ (|Vector| |#1|)) "\\spad{convert([a1,...,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed \\spad{R}-module basis.") (((|Vector| |#1|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,...,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|))) "\\spad{conditionsForIdempotents()} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the fixed \\spad{R}-module basis.")) (|structuralConstants| (((|Vector| (|Matrix| |#1|))) "\\spad{structuralConstants()} calculates the structural constants \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{vi * vj = gammaij1 * v1 + ... + gammaijn * vn},{} where \\spad{v1},{}...,{}\\spad{vn} is the fixed \\spad{R}-module basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([a1,...,am])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{ai} with respect to the fixed \\spad{R}-module basis.") (((|Vector| |#1|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis.")))
-((-3989 |has| |#1| (-495)) (-3987 . T) (-3986 . T))
+((-3993 |has| |#1| (-496)) (-3991 . T) (-3990 . T))
NIL
-(-359 R)
+(-360 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
NIL
-(-360 S R)
+(-361 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| $))) "\\spad{eval(x, s, n, f)} replaces every \\spad{s(a1,...,am)**n} in \\spad{x} by \\spad{f(a1,...,am)} for any \\spad{a1},{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [n1,...,nm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)**ni} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},{}...,{}am.") (($ $ (|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}'s in \\spad{f}.") (($ $ (|Symbol|)) "\\spad{eval(f, foo)} unquotes all the foo's in \\spad{f}.")) (|applyQuote| (($ (|Symbol|) (|List| $)) "\\spad{applyQuote(foo, [x1,...,xn])} returns \\spad{'foo(x1,...,xn)}.") (($ (|Symbol|) $ $ $ $) "\\spad{applyQuote(foo, x, y, z, t)} returns \\spad{'foo(x,y,z,t)}.") (($ (|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| (QUOTE (-951 (-484)))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-962))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-410))) (|HasCategory| |#2| (QUOTE (-1025))) (|HasCategory| |#2| (QUOTE (-554 (-473)))))
-(-361 R)
+((|HasCategory| |#2| (QUOTE (-952 (-485)))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-963))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-411))) (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (QUOTE (-555 (-474)))))
+(-362 R)
((|constructor| (NIL "A space of formal functions with arguments in an arbitrary ordered set.")) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| $)) $ (|Kernel| $)) "\\spad{univariate(f, k)} returns \\spad{f} viewed as a univariate fraction in \\spad{k}.")) (/ (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $)) (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{p1/p2} returns the quotient of \\spad{p1} and \\spad{p2} as an element of \\%.")) (|denominator| (($ $) "\\spad{denominator(f)} returns the denominator of \\spad{f} converted to \\%.")) (|denom| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|convert| (($ (|Factored| $)) "\\spad{convert(f1\\^e1 ... fm\\^em)} returns \\spad{(f1)\\^e1 ... (fm)\\^em} as an element of \\%,{} using formal kernels created using a \\spadfunFrom{paren}{ExpressionSpace}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isPower(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|numerator| (($ $) "\\spad{numerator(f)} returns the numerator of \\spad{f} converted to \\%.")) (|numer| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R} if \\spad{R} is an integral domain. If not,{} then numer(\\spad{f}) = \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|coerce| (($ (|Fraction| (|Polynomial| (|Fraction| |#1|)))) "\\spad{coerce(f)} returns \\spad{f} as an element of \\%.") (($ (|Polynomial| (|Fraction| |#1|))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.") (($ (|Fraction| |#1|)) "\\spad{coerce(q)} returns \\spad{q} as an element of \\%.") (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.")) (|isMult| (((|Union| (|Record| (|:| |coef| (|Integer|)) (|:| |var| (|Kernel| $))) "failed") $) "\\spad{isMult(p)} returns \\spad{[n, x]} if \\spad{p = n * x} and \\spad{n <> 0}.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,...,mn]} if \\spad{p = m1 +...+ mn} and \\spad{n > 1}.")) (|isExpt| (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|Symbol|)) "\\spad{isExpt(p,f)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = f(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|BasicOperator|)) "\\spad{isExpt(p,op)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = op(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if \\spad{p = a1*...*an} and \\spad{n > 1}.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns \\spad{x} * \\spad{x} * \\spad{x} * ... * \\spad{x} (\\spad{n} times).")) (|eval| (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ $)) "\\spad{eval(x, s, n, f)} replaces every \\spad{s(a)**n} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ (|List| $))) "\\spad{eval(x, s, n, f)} replaces every \\spad{s(a1,...,am)**n} in \\spad{x} by \\spad{f(a1,...,am)} for any \\spad{a1},{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [n1,...,nm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)**ni} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [n1,...,nm], [f1,...,fm])} replaces every \\spad{si(a)**ni} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.") (($ $ (|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}'s in \\spad{f}.") (($ $ (|Symbol|)) "\\spad{eval(f, foo)} unquotes all the foo's in \\spad{f}.")) (|applyQuote| (($ (|Symbol|) (|List| $)) "\\spad{applyQuote(foo, [x1,...,xn])} returns \\spad{'foo(x1,...,xn)}.") (($ (|Symbol|) $ $ $ $) "\\spad{applyQuote(foo, x, y, z, t)} returns \\spad{'foo(x,y,z,t)}.") (($ (|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}.")))
-((-3989 OR (|has| |#1| (-962)) (|has| |#1| (-410))) (-3987 |has| |#1| (-146)) (-3986 |has| |#1| (-146)) ((-3994 "*") |has| |#1| (-495)) (-3985 |has| |#1| (-495)) (-3990 |has| |#1| (-495)) (-3984 |has| |#1| (-495)))
+((-3993 OR (|has| |#1| (-963)) (|has| |#1| (-411))) (-3991 |has| |#1| (-146)) (-3990 |has| |#1| (-146)) ((-3998 "*") |has| |#1| (-496)) (-3989 |has| |#1| (-496)) (-3994 |has| |#1| (-496)) (-3988 |has| |#1| (-496)))
NIL
-(-362 R A S B)
+(-363 R A S B)
((|constructor| (NIL "This package allows a mapping \\spad{R} -> \\spad{S} to be lifted to a mapping from a function space over \\spad{R} to a function space over \\spad{S}.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f, a)} applies \\spad{f} to all the constants in \\spad{R} appearing in \\spad{a}.")))
NIL
NIL
-(-363 R FE |x| |cen|)
+(-364 R FE |x| |cen|)
((|constructor| (NIL "This package converts expressions in some function space to exponential expansions.")) (|localAbs| ((|#2| |#2|) "\\spad{localAbs(fcn)} = \\spad{abs(fcn)} or \\spad{sqrt(fcn**2)} depending on whether or not FE has a function \\spad{abs}. This should be a local function,{} but the compiler won't allow it.")) (|exprToXXP| (((|Union| (|:| |%expansion| (|ExponentialExpansion| |#1| |#2| |#3| |#4|)) (|:| |%problem| (|Record| (|:| |func| (|String|)) (|:| |prob| (|String|))))) |#2| (|Boolean|)) "\\spad{exprToXXP(fcn,posCheck?)} converts the expression \\spad{fcn} to an exponential expansion. If \\spad{posCheck?} is \\spad{true},{} log's of negative numbers are not allowed nor are \\spad{n}th roots of negative numbers with \\spad{n} even. If \\spad{posCheck?} is \\spad{false},{} these are allowed.")))
NIL
NIL
-(-364 R FE |Expon| UPS TRAN |x|)
+(-365 R FE |Expon| UPS TRAN |x|)
((|constructor| (NIL "This package converts expressions in some function space to power series in a variable \\spad{x} with coefficients in that function space. The function \\spadfun{exprToUPS} converts expressions to power series whose coefficients do not contain the variable \\spad{x}. The function \\spadfun{exprToGenUPS} converts functional expressions to power series whose coefficients may involve functions of \\spad{log(x)}.")) (|localAbs| ((|#2| |#2|) "\\spad{localAbs(fcn)} = \\spad{abs(fcn)} or \\spad{sqrt(fcn**2)} depending on whether or not FE has a function \\spad{abs}. This should be a local function,{} but the compiler won't allow it.")) (|exprToGenUPS| (((|Union| (|:| |%series| |#4|) (|:| |%problem| (|Record| (|:| |func| (|String|)) (|:| |prob| (|String|))))) |#2| (|Boolean|) (|String|)) "\\spad{exprToGenUPS(fcn,posCheck?,atanFlag)} converts the expression \\spad{fcn} to a generalized power series. If \\spad{posCheck?} is \\spad{true},{} log's of negative numbers are not allowed nor are \\spad{n}th roots of negative numbers with \\spad{n} even. If \\spad{posCheck?} is \\spad{false},{} these are allowed. \\spad{atanFlag} determines how the case \\spad{atan(f(x))},{} where \\spad{f(x)} has a pole,{} will be treated. The possible values of \\spad{atanFlag} are \\spad{\"complex\"},{} \\spad{\"real: two sides\"},{} \\spad{\"real: left side\"},{} \\spad{\"real: right side\"},{} and \\spad{\"just do it\"}. If \\spad{atanFlag} is \\spad{\"complex\"},{} then no series expansion will be computed because,{} viewed as a function of a complex variable,{} \\spad{atan(f(x))} has an essential singularity. Otherwise,{} the sign of the leading coefficient of the series expansion of \\spad{f(x)} determines the constant coefficient in the series expansion of \\spad{atan(f(x))}. If this sign cannot be determined,{} a series expansion is computed only when \\spad{atanFlag} is \\spad{\"just do it\"}. When the leading term in the series expansion of \\spad{f(x)} is of odd degree (or is a rational degree with odd numerator),{} then the constant coefficient in the series expansion of \\spad{atan(f(x))} for values to the left differs from that for values to the right. If \\spad{atanFlag} is \\spad{\"real: two sides\"},{} no series expansion will be computed. If \\spad{atanFlag} is \\spad{\"real: left side\"} the constant coefficient for values to the left will be used and if \\spad{atanFlag} \\spad{\"real: right side\"} the constant coefficient for values to the right will be used. If there is a problem in converting the function to a power series,{} we return a record containing the name of the function that caused the problem and a brief description of the problem. When expanding the expression into a series it is assumed that the series is centered at 0. For a series centered at a,{} the user should perform the substitution \\spad{x -> x + a} before calling this function.")) (|exprToUPS| (((|Union| (|:| |%series| |#4|) (|:| |%problem| (|Record| (|:| |func| (|String|)) (|:| |prob| (|String|))))) |#2| (|Boolean|) (|String|)) "\\spad{exprToUPS(fcn,posCheck?,atanFlag)} converts the expression \\spad{fcn} to a power series. If \\spad{posCheck?} is \\spad{true},{} log's of negative numbers are not allowed nor are \\spad{n}th roots of negative numbers with \\spad{n} even. If \\spad{posCheck?} is \\spad{false},{} these are allowed. \\spad{atanFlag} determines how the case \\spad{atan(f(x))},{} where \\spad{f(x)} has a pole,{} will be treated. The possible values of \\spad{atanFlag} are \\spad{\"complex\"},{} \\spad{\"real: two sides\"},{} \\spad{\"real: left side\"},{} \\spad{\"real: right side\"},{} and \\spad{\"just do it\"}. If \\spad{atanFlag} is \\spad{\"complex\"},{} then no series expansion will be computed because,{} viewed as a function of a complex variable,{} \\spad{atan(f(x))} has an essential singularity. Otherwise,{} the sign of the leading coefficient of the series expansion of \\spad{f(x)} determines the constant coefficient in the series expansion of \\spad{atan(f(x))}. If this sign cannot be determined,{} a series expansion is computed only when \\spad{atanFlag} is \\spad{\"just do it\"}. When the leading term in the series expansion of \\spad{f(x)} is of odd degree (or is a rational degree with odd numerator),{} then the constant coefficient in the series expansion of \\spad{atan(f(x))} for values to the left differs from that for values to the right. If \\spad{atanFlag} is \\spad{\"real: two sides\"},{} no series expansion will be computed. If \\spad{atanFlag} is \\spad{\"real: left side\"} the constant coefficient for values to the left will be used and if \\spad{atanFlag} \\spad{\"real: right side\"} the constant coefficient for values to the right will be used. If there is a problem in converting the function to a power series,{} a record containing the name of the function that caused the problem and a brief description of the problem is returned. When expanding the expression into a series it is assumed that the series is centered at 0. For a series centered at a,{} the user should perform the substitution \\spad{x -> x + a} before calling this function.")) (|integrate| (($ $) "\\spad{integrate(x)} returns the integral of \\spad{x} since we need to be able to integrate a power series")) (|differentiate| (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x} since we need to be able to differentiate a power series")))
NIL
NIL
-(-365 A S)
+(-366 A S)
((|constructor| (NIL "A finite-set aggregate models the notion of a finite set,{} that is,{} a collection of elements characterized by membership,{} but not by order or multiplicity. See \\spadtype{Set} for an example.")) (|min| ((|#2| $) "\\spad{min(u)} returns the smallest element of aggregate \\spad{u}.")) (|max| ((|#2| $) "\\spad{max(u)} returns the largest element of aggregate \\spad{u}.")) (|universe| (($) "\\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}.")))
NIL
-((|HasCategory| |#2| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-317))))
-(-366 S)
+((|HasCategory| |#2| (QUOTE (-758))) (|HasCategory| |#2| (QUOTE (-318))))
+(-367 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|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}.")))
-((-3992 . T) (-3982 . T) (-3993 . T))
+((-3996 . T) (-3986 . T) (-3997 . T))
NIL
-(-367 S A R B)
+(-368 S A R B)
((|constructor| (NIL "\\spad{FiniteSetAggregateFunctions2} provides functions involving two finite set aggregates where the underlying domains might be different. An example of this is to create a set of rational numbers by mapping a function across a set of integers,{} where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-aggregates \\spad{x} of aggregate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad {[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialised to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,[1,2,3],0)} does a \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as an identity element for the function.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f,a)} applies function \\spad{f} to each member of aggregate \\spad{a},{} creating a new aggregate with a possibly different underlying domain.")))
NIL
NIL
-(-368 R -3091)
+(-369 R -3094)
((|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
-(-369 R E)
+(-370 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")))
-((-3979 -12 (|has| |#1| (-6 -3979)) (|has| |#2| (-6 -3979))) (-3986 . T) (-3987 . T) (-3989 . T))
-((-12 (|HasAttribute| |#1| (QUOTE -3979)) (|HasAttribute| |#2| (QUOTE -3979))))
-(-370 R -3091)
+((-3983 -12 (|has| |#1| (-6 -3983)) (|has| |#2| (-6 -3983))) (-3990 . T) (-3991 . T) (-3993 . T))
+((-12 (|HasAttribute| |#1| (QUOTE -3983)) (|HasAttribute| |#2| (QUOTE -3983))))
+(-371 R -3094)
((|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
-(-371 R -3091)
+(-372 R -3094)
((|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
-(-372 R -3091)
+(-373 R -3094)
((|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 \\spad{a2} may involve \\spad{a1},{} but the minimal polynomial for \\spad{a1} may not involve \\spad{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))))
-(-373 R -3091)
+(-374 R -3094)
((|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
-(-374)
+(-375)
((|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
-(-375 R -3091 UP)
+(-376 R -3094 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| (QUOTE (-951 (-48)))))
-(-376)
+((|HasCategory| |#2| (QUOTE (-952 (-48)))))
+(-377)
((|constructor| (NIL "Creates and manipulates objects which correspond to FORTRAN data types,{} including array dimensions.")) (|fortranCharacter| (($) "\\spad{fortranCharacter()} returns CHARACTER,{} an element of FortranType")) (|fortranDoubleComplex| (($) "\\spad{fortranDoubleComplex()} returns DOUBLE COMPLEX,{} an element of FortranType")) (|fortranComplex| (($) "\\spad{fortranComplex()} returns COMPLEX,{} an element of FortranType")) (|fortranLogical| (($) "\\spad{fortranLogical()} returns LOGICAL,{} an element of FortranType")) (|fortranInteger| (($) "\\spad{fortranInteger()} returns INTEGER,{} an element of FortranType")) (|fortranDouble| (($) "\\spad{fortranDouble()} returns DOUBLE PRECISION,{} an element of FortranType")) (|fortranReal| (($) "\\spad{fortranReal()} returns REAL,{} an element of FortranType")) (|construct| (($ (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| #1="void")) (|List| (|Polynomial| (|Integer|))) (|Boolean|)) "\\spad{construct(type,dims)} creates an element of FortranType") (($ (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| #1#)) (|List| (|Symbol|)) (|Boolean|)) "\\spad{construct(type,dims)} creates an element of FortranType")) (|external?| (((|Boolean|) $) "\\spad{external?(u)} returns \\spad{true} if \\spad{u} is declared to be EXTERNAL")) (|dimensionsOf| (((|List| (|Polynomial| (|Integer|))) $) "\\spad{dimensionsOf(t)} returns the dimensions of \\spad{t}")) (|scalarTypeOf| (((|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| #1#)) $) "\\spad{scalarTypeOf(t)} returns the FORTRAN data type of \\spad{t}")) (|coerce| (($ (|FortranScalarType|)) "\\spad{coerce(t)} creates an element from a scalar type")))
NIL
NIL
-(-377 |f|)
+(-378 |f|)
((|constructor| (NIL "This domain implements named functions")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol")))
NIL
NIL
-(-378)
+(-379)
((|constructor| (NIL "This is the datatype for exported function descriptor. A function descriptor consists of: (1) a signature; (2) a predicate; and (3) a slot into the scope object.")) (|signature| (((|Signature|) $) "\\spad{signature(x)} returns the signature of function described by \\spad{x}.")))
NIL
NIL
-(-379 UP)
+(-380 UP)
((|constructor| (NIL "\\spadtype{GaloisGroupFactorizer} provides functions to factor resolvents.")) (|btwFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|) (|Set| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{btwFact(p,sqf,pd,r)} returns the factorization of \\spad{p},{} the result is a Record such that \\spad{contp=}content \\spad{p},{} \\spad{factors=}List of irreducible factors of \\spad{p} with exponent. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors). \\spad{pd} is the \\spadtype{Set} of possible degrees. \\spad{r} is a lower bound for the number of factors of \\spad{p}. Please do not use this function in your code because its design may change.")) (|henselFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|)) "\\spad{henselFact(p,sqf)} returns the factorization of \\spad{p},{} the result is a Record such that \\spad{contp=}content \\spad{p},{} \\spad{factors=}List of irreducible factors of \\spad{p} with exponent. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors).")) (|factorOfDegree| (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|) (|Boolean|)) "\\spad{factorOfDegree(d,p,listOfDegrees,r,sqf)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\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's criterion,{} \\spad{false} is inconclusive.")) (|useEisensteinCriterion| (((|Boolean|) (|Boolean|)) "\\spad{useEisensteinCriterion(b)} chooses whether factorizers check Eisenstein's criterion before factoring: \\spad{true} for using it,{} \\spad{false} else. Returns the previous value.")) (|useEisensteinCriterion?| (((|Boolean|)) "\\spad{useEisensteinCriterion?()} returns \\spad{true} if factorizers check Eisenstein's criterion before factoring.")) (|useSingleFactorBound| (((|Boolean|) (|Boolean|)) "\\spad{useSingleFactorBound(b)} chooses the algorithm to be used by the factorizers: \\spad{true} for algorithm with single factor bound,{} \\spad{false} for algorithm with overall bound. Returns the previous value.")) (|useSingleFactorBound?| (((|Boolean|)) "\\spad{useSingleFactorBound?()} returns \\spad{true} if algorithm with single factor bound is used for factorization,{} \\spad{false} for algorithm with overall bound.")) (|modularFactor| (((|Record| (|:| |prime| (|Integer|)) (|:| |factors| (|List| |#1|))) |#1|) "\\spad{modularFactor(f)} chooses a \"good\" prime and returns the factorization of \\spad{f} modulo this prime in a form that may be used by \\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
-(-380 R UP -3091)
+(-381 R UP -3094)
((|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 lp norm of the polynomial \\spad{f}.")) (|singleFactorBound| (((|Integer|) |#2|) "\\spad{singleFactorBound(p,r)} returns a bound on the infinite norm of the factor of \\spad{p} with smallest Bombieri's norm. \\spad{p} shall be of degree higher or equal to 2.") (((|Integer|) |#2| (|NonNegativeInteger|)) "\\spad{singleFactorBound(p,r)} returns a bound on the infinite norm of the factor of \\spad{p} with smallest Bombieri's norm. \\spad{r} is a lower bound for the number of factors of \\spad{p}. \\spad{p} shall be of degree higher or equal to 2.")) (|rootBound| (((|Integer|) |#2|) "\\spad{rootBound(p)} returns a bound on the largest norm of the complex roots of \\spad{p}.")) (|bombieriNorm| ((|#3| |#2| (|PositiveInteger|)) "\\spad{bombieriNorm(p,n)} returns the \\spad{n}th Bombieri's norm of \\spad{p}.") ((|#3| |#2|) "\\spad{bombieriNorm(p)} returns quadratic Bombieri's norm of \\spad{p}.")) (|beauzamyBound| (((|Integer|) |#2|) "\\spad{beauzamyBound(p)} returns a bound on the larger coefficient of any factor of \\spad{p}.")))
NIL
NIL
-(-381 R UP)
+(-382 R UP)
((|constructor| (NIL "\\spadtype{GaloisGroupPolynomialUtilities} provides useful functions for univariate polynomials which should be added to \\spadtype{UnivariatePolynomialCategory} or to \\spadtype{Factored} (July 1994).")) (|factorsOfDegree| (((|List| |#2|) (|PositiveInteger|) (|Factored| |#2|)) "\\spad{factorsOfDegree(d,f)} returns the factors of degree \\spad{d} of the factored polynomial \\spad{f}.")) (|factorOfDegree| ((|#2| (|PositiveInteger|) (|Factored| |#2|)) "\\spad{factorOfDegree(d,f)} returns a factor of degree \\spad{d} of the factored polynomial \\spad{f}. Such a factor shall exist.")) (|degreePartition| (((|Multiset| (|NonNegativeInteger|)) (|Factored| |#2|)) "\\spad{degreePartition(f)} returns the degree partition (\\spadignore{i.e.} the multiset of the degrees of the irreducible factors) of the polynomial \\spad{f}.")) (|shiftRoots| ((|#2| |#2| |#1|) "\\spad{shiftRoots(p,c)} returns the polynomial which has for roots \\spad{c} added to the roots of \\spad{p}.")) (|scaleRoots| ((|#2| |#2| |#1|) "\\spad{scaleRoots(p,c)} returns the polynomial which has \\spad{c} times the roots of \\spad{p}.")) (|reverse| ((|#2| |#2|) "\\spad{reverse(p)} returns the reverse polynomial of \\spad{p}.")) (|unvectorise| ((|#2| (|Vector| |#1|)) "\\spad{unvectorise(v)} returns the polynomial which has for coefficients the entries of \\spad{v} in the increasing order.")) (|monic?| (((|Boolean|) |#2|) "\\spad{monic?(p)} tests if \\spad{p} is monic (\\spadignore{i.e.} leading coefficient equal to 1).")))
NIL
NIL
-(-382 R)
+(-383 R)
((|constructor| (NIL "\\spadtype{GaloisGroupUtilities} provides several useful functions.")) (|safetyMargin| (((|NonNegativeInteger|)) "\\spad{safetyMargin()} returns the number of low weight digits we do not trust in the floating point representation (used by \\spadfun{safeCeiling}).") (((|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{safetyMargin(n)} sets to \\spad{n} the number of low weight digits we do not trust in the floating point representation and returns the previous value (for use by \\spadfun{safeCeiling}).")) (|safeFloor| (((|Integer|) |#1|) "\\spad{safeFloor(x)} returns the integer which is lower or equal to the largest integer which has the same floating point number representation.")) (|safeCeiling| (((|Integer|) |#1|) "\\spad{safeCeiling(x)} returns the integer which is greater than any integer with the same floating point number representation.")) (|fillPascalTriangle| (((|Void|)) "\\spad{fillPascalTriangle()} fills the stored table.")) (|sizePascalTriangle| (((|NonNegativeInteger|)) "\\spad{sizePascalTriangle()} returns the number of entries currently stored in the table.")) (|rangePascalTriangle| (((|NonNegativeInteger|)) "\\spad{rangePascalTriangle()} returns the maximal number of lines stored.") (((|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rangePascalTriangle(n)} sets the maximal number of lines which are stored and returns the previous value.")) (|pascalTriangle| ((|#1| (|NonNegativeInteger|) (|Integer|)) "\\spad{pascalTriangle(n,r)} returns the binomial coefficient \\spad{C(n,r)=n!/(r! (n-r)!)} and stores it in a table to prevent recomputation.")))
NIL
-((|HasCategory| |#1| (QUOTE (-344))))
-(-383)
+((|HasCategory| |#1| (QUOTE (-345))))
+(-384)
((|constructor| (NIL "Package for the factorization of complex or gaussian integers.")) (|prime?| (((|Boolean|) (|Complex| (|Integer|))) "\\spad{prime?(zi)} tests if the complex integer \\spad{zi} is prime.")) (|sumSquares| (((|List| (|Integer|)) (|Integer|)) "\\spad{sumSquares(p)} construct \\spad{a} and \\spad{b} such that \\spad{a**2+b**2} is equal to the integer prime \\spad{p},{} and otherwise returns an error. It will succeed if the prime number \\spad{p} is 2 or congruent to 1 mod 4.")) (|factor| (((|Factored| (|Complex| (|Integer|))) (|Complex| (|Integer|))) "\\spad{factor(zi)} produces the complete factorization of the complex integer \\spad{zi}.")))
NIL
NIL
-(-384 |Dom| |Expon| |VarSet| |Dpol|)
+(-385 |Dom| |Expon| |VarSet| |Dpol|)
((|constructor| (NIL "\\spadtype{GroebnerPackage} computes groebner bases for polynomial ideals. The basic computation provides a distinguished set of generators for polynomial ideals over fields. This basis allows an easy test for membership: the operation \\spadfun{normalForm} returns zero on ideal members. When the provided coefficient domain,{} Dom,{} is not a field,{} the result is equivalent to considering the extended ideal with \\spadtype{Fraction(Dom)} as coefficients,{} but considerably more efficient since all calculations are performed in Dom. Additional argument \"info\" and \"redcrit\" can be given to provide incremental information during computation. Argument \"info\" produces a computational summary for each \\spad{s}-polynomial. Argument \"redcrit\" prints out the reduced critical pairs. The term ordering is determined by the polynomial type used. Suggested types include \\spadtype{DistributedMultivariatePolynomial},{} \\spadtype{HomogeneousDistributedMultivariatePolynomial},{} \\spadtype{GeneralDistributedMultivariatePolynomial}.")) (|normalForm| ((|#4| |#4| (|List| |#4|)) "\\spad{normalForm(poly,gb)} reduces the polynomial \\spad{poly} modulo the precomputed groebner basis \\spad{gb} giving a canonical representative of the residue class.")) (|groebner| (((|List| |#4|) (|List| |#4|) (|String|) (|String|)) "\\spad{groebner(lp, \"info\", \"redcrit\")} computes a groebner basis for a polynomial ideal generated by the list of polynomials \\spad{lp},{} displaying both a summary of the critical pairs considered (\\spad{\"info\"}) and the result of reducing each critical pair (\"redcrit\"). If the second or third arguments have any other string value,{} the indicated information is suppressed.") (((|List| |#4|) (|List| |#4|) (|String|)) "\\spad{groebner(lp, infoflag)} computes a groebner basis for a polynomial ideal generated by the list of polynomials \\spad{lp}. Argument infoflag is used to get information on the computation. If infoflag is \"info\",{} then summary information is displayed for each \\spad{s}-polynomial generated. If infoflag is \"redcrit\",{} the reduced critical pairs are displayed. If infoflag is any other string,{} no information is printed during computation.") (((|List| |#4|) (|List| |#4|)) "\\spad{groebner(lp)} computes a groebner basis for a polynomial ideal generated by the list of polynomials \\spad{lp}.")))
NIL
-((|HasCategory| |#1| (QUOTE (-311))))
-(-385 |Dom| |Expon| |VarSet| |Dpol|)
+((|HasCategory| |#1| (QUOTE (-312))))
+(-386 |Dom| |Expon| |VarSet| |Dpol|)
((|constructor| (NIL "\\spadtype{EuclideanGroebnerBasisPackage} computes groebner bases for polynomial ideals over euclidean domains. The basic computation provides a distinguished set of generators for these ideals. This basis allows an easy test for membership: the operation \\spadfun{euclideanNormalForm} returns zero on ideal members. The string \"info\" and \"redcrit\" can be given as additional args to provide incremental information during the computation. If \"info\" is given,{} \\indented{1}{a computational summary is given for each \\spad{s}-polynomial. If \"redcrit\"} is given,{} the reduced critical pairs are printed. The term ordering is determined by the polynomial type used. Suggested types include \\spadtype{DistributedMultivariatePolynomial},{} \\spadtype{HomogeneousDistributedMultivariatePolynomial},{} \\spadtype{GeneralDistributedMultivariatePolynomial}.")) (|euclideanGroebner| (((|List| |#4|) (|List| |#4|) (|String|) (|String|)) "\\spad{euclideanGroebner(lp, \"info\", \"redcrit\")} computes a groebner basis for a polynomial ideal generated by the list of polynomials \\spad{lp}. If the second argument is \\spad{\"info\"},{} a summary is given of the critical pairs. If the third argument is \"redcrit\",{} critical pairs are printed.") (((|List| |#4|) (|List| |#4|) (|String|)) "\\spad{euclideanGroebner(lp, infoflag)} computes a groebner basis for a polynomial ideal over a euclidean domain generated by the list of polynomials \\spad{lp}. During computation,{} additional information is printed out if infoflag is given as either \"info\" (for summary information) or \"redcrit\" (for reduced critical pairs)") (((|List| |#4|) (|List| |#4|)) "\\spad{euclideanGroebner(lp)} computes a groebner basis for a polynomial ideal over a euclidean domain generated by the list of polynomials \\spad{lp}.")) (|euclideanNormalForm| ((|#4| |#4| (|List| |#4|)) "\\spad{euclideanNormalForm(poly,gb)} reduces the polynomial \\spad{poly} modulo the precomputed groebner basis \\spad{gb} giving a canonical representative of the residue class.")))
NIL
NIL
-(-386 |Dom| |Expon| |VarSet| |Dpol|)
+(-387 |Dom| |Expon| |VarSet| |Dpol|)
((|constructor| (NIL "\\spadtype{GroebnerFactorizationPackage} provides the function groebnerFactor\" which uses the factorization routines of \\Language{} to factor each polynomial under consideration while doing the groebner basis algorithm. Then it writes the ideal as an intersection of ideals determined by the irreducible factors. Note that the whole ring may occur as well as other redundancies. We also use the fact,{} that from the second factor on we can assume that the preceding factors are not equal to 0 and we divide all polynomials under considerations by the elements of this list of \"nonZeroRestrictions\". The result is a list of groebner bases,{} whose union of solutions of the corresponding systems of equations is the solution of the system of equation corresponding to the input list. The term ordering is determined by the polynomial type used. Suggested types include \\spadtype{DistributedMultivariatePolynomial},{} \\spadtype{HomogeneousDistributedMultivariatePolynomial},{} \\spadtype{GeneralDistributedMultivariatePolynomial}.")) (|groebnerFactorize| (((|List| (|List| |#4|)) (|List| |#4|) (|Boolean|)) "\\spad{groebnerFactorize(listOfPolys, info)} returns a list of groebner bases. The union of their solutions is the solution of the system of equations given by {\\em listOfPolys}. At each stage the polynomial \\spad{p} under consideration (either from the given basis or obtained from a reduction of the next \\spad{S}-polynomial) is factorized. For each irreducible factors of \\spad{p},{} a new {\\em createGroebnerBasis} is started doing the usual updates with the factor in place of \\spad{p}. If {\\em info} is \\spad{true},{} information is printed about partial results.") (((|List| (|List| |#4|)) (|List| |#4|)) "\\spad{groebnerFactorize(listOfPolys)} returns a list of groebner bases. The union of their solutions is the solution of the system of equations given by {\\em listOfPolys}. At each stage the polynomial \\spad{p} under consideration (either from the given basis or obtained from a reduction of the next \\spad{S}-polynomial) is factorized. For each irreducible factors of \\spad{p},{} a new {\\em createGroebnerBasis} is started doing the usual updates with the factor in place of \\spad{p}.") (((|List| (|List| |#4|)) (|List| |#4|) (|List| |#4|) (|Boolean|)) "\\spad{groebnerFactorize(listOfPolys, nonZeroRestrictions, info)} returns a list of groebner basis. The union of their solutions is the solution of the system of equations given by {\\em listOfPolys} under the restriction that the polynomials of {\\em nonZeroRestrictions} don't vanish. At each stage the polynomial \\spad{p} under consideration (either from the given basis or obtained from a reduction of the next \\spad{S}-polynomial) is factorized. For each irreducible factors of \\spad{p} a new {\\em createGroebnerBasis} is started doing the usual updates with the factor in place of \\spad{p}. If argument {\\em info} is \\spad{true},{} information is printed about partial results.") (((|List| (|List| |#4|)) (|List| |#4|) (|List| |#4|)) "\\spad{groebnerFactorize(listOfPolys, nonZeroRestrictions)} returns a list of groebner basis. The union of their solutions is the solution of the system of equations given by {\\em listOfPolys} under the restriction that the polynomials of {\\em nonZeroRestrictions} don't vanish. At each stage the polynomial \\spad{p} under consideration (either from the given basis or obtained from a reduction of the next \\spad{S}-polynomial) is factorized. For each irreducible factors of \\spad{p},{} a new {\\em createGroebnerBasis} is started doing the usual updates with the factor in place of \\spad{p}.")) (|factorGroebnerBasis| (((|List| (|List| |#4|)) (|List| |#4|) (|Boolean|)) "\\spad{factorGroebnerBasis(basis,info)} checks whether the \\spad{basis} contains reducible polynomials and uses these to split the \\spad{basis}. If argument {\\em info} is \\spad{true},{} information is printed about partial results.") (((|List| (|List| |#4|)) (|List| |#4|)) "\\spad{factorGroebnerBasis(basis)} checks whether the \\spad{basis} contains reducible polynomials and uses these to split the \\spad{basis}.")))
NIL
NIL
-(-387 |Dom| |Expon| |VarSet| |Dpol|)
+(-388 |Dom| |Expon| |VarSet| |Dpol|)
((|constructor| (NIL "\\indented{1}{Author:} Date Created: Date Last Updated: Keywords: Description This package provides low level tools for Groebner basis computations")) (|virtualDegree| (((|NonNegativeInteger|) |#4|) "\\spad{virtualDegree }\\undocumented")) (|makeCrit| (((|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)) (|Record| (|:| |totdeg| (|NonNegativeInteger|)) (|:| |pol| |#4|)) |#4| (|NonNegativeInteger|)) "\\spad{makeCrit }\\undocumented")) (|critpOrder| (((|Boolean|) (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)) (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) "\\spad{critpOrder }\\undocumented")) (|prinb| (((|Void|) (|Integer|)) "\\spad{prinb }\\undocumented")) (|prinpolINFO| (((|Void|) (|List| |#4|)) "\\spad{prinpolINFO }\\undocumented")) (|fprindINFO| (((|Integer|) (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)) |#4| |#4| (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{fprindINFO }\\undocumented")) (|prindINFO| (((|Integer|) (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)) |#4| |#4| (|Integer|) (|Integer|) (|Integer|)) "\\spad{prindINFO }\\undocumented")) (|prinshINFO| (((|Void|) |#4|) "\\spad{prinshINFO }\\undocumented")) (|lepol| (((|Integer|) |#4|) "\\spad{lepol }\\undocumented")) (|minGbasis| (((|List| |#4|) (|List| |#4|)) "\\spad{minGbasis }\\undocumented")) (|updatD| (((|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) (|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) (|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)))) "\\spad{updatD }\\undocumented")) (|sPol| ((|#4| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) "\\spad{sPol }\\undocumented")) (|updatF| (((|List| (|Record| (|:| |totdeg| (|NonNegativeInteger|)) (|:| |pol| |#4|))) |#4| (|NonNegativeInteger|) (|List| (|Record| (|:| |totdeg| (|NonNegativeInteger|)) (|:| |pol| |#4|)))) "\\spad{updatF }\\undocumented")) (|hMonic| ((|#4| |#4|) "\\spad{hMonic }\\undocumented")) (|redPo| (((|Record| (|:| |poly| |#4|) (|:| |mult| |#1|)) |#4| (|List| |#4|)) "\\spad{redPo }\\undocumented")) (|critMonD1| (((|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) |#2| (|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)))) "\\spad{critMonD1 }\\undocumented")) (|critMTonD1| (((|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) (|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)))) "\\spad{critMTonD1 }\\undocumented")) (|critBonD| (((|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) |#4| (|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)))) "\\spad{critBonD }\\undocumented")) (|critB| (((|Boolean|) |#2| |#2| |#2| |#2|) "\\spad{critB }\\undocumented")) (|critM| (((|Boolean|) |#2| |#2|) "\\spad{critM }\\undocumented")) (|critT| (((|Boolean|) (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) "\\spad{critT }\\undocumented")) (|gbasis| (((|List| |#4|) (|List| |#4|) (|Integer|) (|Integer|)) "\\spad{gbasis }\\undocumented")) (|redPol| ((|#4| |#4| (|List| |#4|)) "\\spad{redPol }\\undocumented")) (|credPol| ((|#4| |#4| (|List| |#4|)) "\\spad{credPol }\\undocumented")))
NIL
NIL
-(-388 S)
+(-389 S)
((|constructor| (NIL "This category describes domains where \\spadfun{gcd} can be computed but where there is no guarantee of the existence of \\spadfun{factor} operation for factorisation into irreducibles. However,{} if such a \\spadfun{factor} operation exist,{} factorization will be unique up to order and units.")) (|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| $)) "\\spad{gcd(l)} returns the common gcd of the elements in the list \\spad{l}.") (($ $ $) "\\spad{gcd(x,y)} returns the greatest common divisor of \\spad{x} and \\spad{y}.")))
NIL
NIL
-(-389)
+(-390)
((|constructor| (NIL "This category describes domains where \\spadfun{gcd} can be computed but where there is no guarantee of the existence of \\spadfun{factor} operation for factorisation into irreducibles. However,{} if such a \\spadfun{factor} operation exist,{} factorization will be unique up to order and units.")) (|lcm| (($ (|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| $)) "\\spad{gcd(l)} returns the common gcd of the elements in the list \\spad{l}.") (($ $ $) "\\spad{gcd(x,y)} returns the greatest common divisor of \\spad{x} and \\spad{y}.")))
-((-3985 . T) ((-3994 "*") . T) (-3986 . T) (-3987 . T) (-3989 . T))
+((-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T))
NIL
-(-390 R |n| |ls| |gamma|)
+(-391 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")))
-((-3989 |has| (-347 (-858 |#1|)) (-495)) (-3987 . T) (-3986 . T))
-((|HasCategory| (-347 (-858 |#1|)) (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| (-347 (-858 |#1|)) (QUOTE (-495))))
-(-391 |vl| R E)
+((-3993 |has| (-348 (-859 |#1|)) (-496)) (-3991 . T) (-3990 . T))
+((|HasCategory| (-348 (-859 |#1|)) (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| (-348 (-859 |#1|)) (QUOTE (-496))))
+(-392 |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")))
-(((-3994 "*") |has| |#2| (-146)) (-3985 |has| |#2| (-495)) (-3990 |has| |#2| (-6 -3990)) (-3987 . T) (-3986 . T) (-3989 . T))
-((|HasCategory| |#2| (QUOTE (-822))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-389))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-822)))) (OR (|HasCategory| |#2| (QUOTE (-389))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-822)))) (OR (|HasCategory| |#2| (QUOTE (-389))) (|HasCategory| |#2| (QUOTE (-822)))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-146))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-495)))) (-12 (|HasCategory| |#2| (QUOTE (-797 (-327)))) (|HasCategory| (-774 |#1|) (QUOTE (-797 (-327))))) (-12 (|HasCategory| |#2| (QUOTE (-797 (-484)))) (|HasCategory| (-774 |#1|) (QUOTE (-797 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-554 (-801 (-327))))) (|HasCategory| (-774 |#1|) (QUOTE (-554 (-801 (-327)))))) (-12 (|HasCategory| |#2| (QUOTE (-554 (-801 (-484))))) (|HasCategory| (-774 |#1|) (QUOTE (-554 (-801 (-484)))))) (-12 (|HasCategory| |#2| (QUOTE (-554 (-473)))) (|HasCategory| (-774 |#1|) (QUOTE (-554 (-473))))) (|HasCategory| |#2| (QUOTE (-581 (-484)))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-38 (-347 (-484))))) (|HasCategory| |#2| (QUOTE (-951 (-484)))) (OR (|HasCategory| |#2| (QUOTE (-38 (-347 (-484))))) (|HasCategory| |#2| (QUOTE (-951 (-347 (-484)))))) (|HasCategory| |#2| (QUOTE (-951 (-347 (-484))))) (|HasCategory| |#2| (QUOTE (-311))) (|HasAttribute| |#2| (QUOTE -3990)) (|HasCategory| |#2| (QUOTE (-389))) (-12 (|HasCategory| |#2| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#2| (QUOTE (-118)))))
-(-392 R BP)
+(((-3998 "*") |has| |#2| (-146)) (-3989 |has| |#2| (-496)) (-3994 |has| |#2| (-6 -3994)) (-3991 . T) (-3990 . T) (-3993 . T))
+((|HasCategory| |#2| (QUOTE (-823))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-390))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-823)))) (OR (|HasCategory| |#2| (QUOTE (-390))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-823)))) (OR (|HasCategory| |#2| (QUOTE (-390))) (|HasCategory| |#2| (QUOTE (-823)))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-146))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-496)))) (-12 (|HasCategory| |#2| (QUOTE (-798 (-328)))) (|HasCategory| (-775 |#1|) (QUOTE (-798 (-328))))) (-12 (|HasCategory| |#2| (QUOTE (-798 (-485)))) (|HasCategory| (-775 |#1|) (QUOTE (-798 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-555 (-802 (-328))))) (|HasCategory| (-775 |#1|) (QUOTE (-555 (-802 (-328)))))) (-12 (|HasCategory| |#2| (QUOTE (-555 (-802 (-485))))) (|HasCategory| (-775 |#1|) (QUOTE (-555 (-802 (-485)))))) (-12 (|HasCategory| |#2| (QUOTE (-555 (-474)))) (|HasCategory| (-775 |#1|) (QUOTE (-555 (-474))))) (|HasCategory| |#2| (QUOTE (-582 (-485)))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-38 (-348 (-485))))) (|HasCategory| |#2| (QUOTE (-952 (-485)))) (OR (|HasCategory| |#2| (QUOTE (-38 (-348 (-485))))) (|HasCategory| |#2| (QUOTE (-952 (-348 (-485)))))) (|HasCategory| |#2| (QUOTE (-952 (-348 (-485))))) (|HasCategory| |#2| (QUOTE (-312))) (|HasAttribute| |#2| (QUOTE -3994)) (|HasCategory| |#2| (QUOTE (-390))) (-12 (|HasCategory| |#2| (QUOTE (-823))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-823))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#2| (QUOTE (-118)))))
+(-393 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's conditional.")))
NIL
NIL
-(-393 OV E S R P)
+(-394 OV E S 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| |#5|) |#5|) "\\spad{factor(p)} factors the multivariate polynomial \\spad{p} over its coefficient domain")) (|variable| (((|Union| $ "failed") (|Symbol|)) "\\spad{variable(s)} makes an element from symbol \\spad{s} or fails.")) (|convert| (((|Symbol|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol")))
NIL
NIL
-(-394 E OV R P)
+(-395 E OV R P)
((|constructor| (NIL "This package provides operations for GCD computations on polynomials")) (|randomR| ((|#3|) "\\spad{randomR()} should be local but conditional")) (|gcdPolynomial| (((|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{gcdPolynomial(p,q)} returns the GCD of \\spad{p} and \\spad{q}")))
NIL
NIL
-(-395 R)
+(-396 R)
((|constructor| (NIL "\\indented{1}{Description} This package provides operations for the factorization of univariate polynomials with integer coefficients. The factorization is done by \"lifting\" the finite \"berlekamp's\" factorization")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{factor(p)} returns the factorisation of \\spad{p}")))
NIL
NIL
-(-396 R FE)
+(-397 R FE)
((|constructor| (NIL "\\spadtype{GenerateUnivariatePowerSeries} provides functions that create power series from explicit formulas for their \\spad{n}th coefficient.")) (|series| (((|Any|) |#2| (|Symbol|) (|Equation| |#2|) (|UniversalSegment| (|Fraction| (|Integer|))) (|Fraction| (|Integer|))) "\\spad{series(a(n),n,x = a,r0..,r)} returns \\spad{sum(n = r0,r0 + r,r0 + 2*r..., a(n) * (x - a)**n)}; \\spad{series(a(n),n,x = a,r0..r1,r)} returns \\spad{sum(n = r0 + k*r while n <= r1, a(n) * (x - a)**n)}.") (((|Any|) (|Mapping| |#2| (|Fraction| (|Integer|))) (|Equation| |#2|) (|UniversalSegment| (|Fraction| (|Integer|))) (|Fraction| (|Integer|))) "\\spad{series(n +-> a(n),x = a,r0..,r)} returns \\spad{sum(n = r0,r0 + r,r0 + 2*r..., a(n) * (x - a)**n)}; \\spad{series(n +-> a(n),x = a,r0..r1,r)} returns \\spad{sum(n = r0 + k*r while n <= r1, a(n) * (x - a)**n)}.") (((|Any|) |#2| (|Symbol|) (|Equation| |#2|) (|UniversalSegment| (|Integer|))) "\\spad{series(a(n),n,x=a,n0..)} returns \\spad{sum(n = n0..,a(n) * (x - a)**n)}; \\spad{series(a(n),n,x=a,n0..n1)} returns \\spad{sum(n = n0..n1,a(n) * (x - a)**n)}.") (((|Any|) (|Mapping| |#2| (|Integer|)) (|Equation| |#2|) (|UniversalSegment| (|Integer|))) "\\spad{series(n +-> a(n),x = a,n0..)} returns \\spad{sum(n = n0..,a(n) * (x - a)**n)}; \\spad{series(n +-> a(n),x = a,n0..n1)} returns \\spad{sum(n = n0..n1,a(n) * (x - a)**n)}.") (((|Any|) |#2| (|Symbol|) (|Equation| |#2|)) "\\spad{series(a(n),n,x = a)} returns \\spad{sum(n = 0..,a(n)*(x-a)**n)}.") (((|Any|) (|Mapping| |#2| (|Integer|)) (|Equation| |#2|)) "\\spad{series(n +-> a(n),x = a)} returns \\spad{sum(n = 0..,a(n)*(x-a)**n)}.")) (|puiseux| (((|Any|) |#2| (|Symbol|) (|Equation| |#2|) (|UniversalSegment| (|Fraction| (|Integer|))) (|Fraction| (|Integer|))) "\\spad{puiseux(a(n),n,x = a,r0..,r)} returns \\spad{sum(n = r0,r0 + r,r0 + 2*r..., a(n) * (x - a)**n)}; \\spad{puiseux(a(n),n,x = a,r0..r1,r)} returns \\spad{sum(n = r0 + k*r while n <= r1, a(n) * (x - a)**n)}.") (((|Any|) (|Mapping| |#2| (|Fraction| (|Integer|))) (|Equation| |#2|) (|UniversalSegment| (|Fraction| (|Integer|))) (|Fraction| (|Integer|))) "\\spad{puiseux(n +-> a(n),x = a,r0..,r)} returns \\spad{sum(n = r0,r0 + r,r0 + 2*r..., a(n) * (x - a)**n)}; \\spad{puiseux(n +-> a(n),x = a,r0..r1,r)} returns \\spad{sum(n = r0 + k*r while n <= r1, a(n) * (x - a)**n)}.")) (|laurent| (((|Any|) |#2| (|Symbol|) (|Equation| |#2|) (|UniversalSegment| (|Integer|))) "\\spad{laurent(a(n),n,x=a,n0..)} returns \\spad{sum(n = n0..,a(n) * (x - a)**n)}; \\spad{laurent(a(n),n,x=a,n0..n1)} returns \\spad{sum(n = n0..n1,a(n) * (x - a)**n)}.") (((|Any|) (|Mapping| |#2| (|Integer|)) (|Equation| |#2|) (|UniversalSegment| (|Integer|))) "\\spad{laurent(n +-> a(n),x = a,n0..)} returns \\spad{sum(n = n0..,a(n) * (x - a)**n)}; \\spad{laurent(n +-> a(n),x = a,n0..n1)} returns \\spad{sum(n = n0..n1,a(n) * (x - a)**n)}.")) (|taylor| (((|Any|) |#2| (|Symbol|) (|Equation| |#2|) (|UniversalSegment| (|NonNegativeInteger|))) "\\spad{taylor(a(n),n,x = a,n0..)} returns \\spad{sum(n = n0..,a(n)*(x-a)**n)}; \\spad{taylor(a(n),n,x = a,n0..n1)} returns \\spad{sum(n = n0..,a(n)*(x-a)**n)}.") (((|Any|) (|Mapping| |#2| (|Integer|)) (|Equation| |#2|) (|UniversalSegment| (|NonNegativeInteger|))) "\\spad{taylor(n +-> a(n),x = a,n0..)} returns \\spad{sum(n=n0..,a(n)*(x-a)**n)}; \\spad{taylor(n +-> a(n),x = a,n0..n1)} returns \\spad{sum(n = n0..,a(n)*(x-a)**n)}.") (((|Any|) |#2| (|Symbol|) (|Equation| |#2|)) "\\spad{taylor(a(n),n,x = a)} returns \\spad{sum(n = 0..,a(n)*(x-a)**n)}.") (((|Any|) (|Mapping| |#2| (|Integer|)) (|Equation| |#2|)) "\\spad{taylor(n +-> a(n),x = a)} returns \\spad{sum(n = 0..,a(n)*(x-a)**n)}.")))
NIL
NIL
-(-397 RP TP)
+(-398 RP TP)
((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni} General Hensel Lifting Used for Factorization of bivariate polynomials over a finite field.")) (|reduction| ((|#2| |#2| |#1|) "\\spad{reduction(u,pol)} computes the symmetric reduction of \\spad{u} mod \\spad{pol}")) (|completeHensel| (((|List| |#2|) |#2| (|List| |#2|) |#1| (|PositiveInteger|)) "\\spad{completeHensel(pol,lfact,prime,bound)} lifts \\spad{lfact},{} the factorization mod \\spad{prime} of \\spad{pol},{} to the factorization mod prime**k>bound. Factors are recombined on the way.")) (|HenselLift| (((|Record| (|:| |plist| (|List| |#2|)) (|:| |modulo| |#1|)) |#2| (|List| |#2|) |#1| (|PositiveInteger|)) "\\spad{HenselLift(pol,lfacts,prime,bound)} lifts \\spad{lfacts},{} that are the factors of \\spad{pol} mod \\spad{prime},{} to factors of \\spad{pol} mod prime**k > \\spad{bound}. No recombining is done .")))
NIL
NIL
-(-398 |vl| R IS E |ff| P)
+(-399 |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| $) "\\spad{leadingCoefficient(x)} \\undocumented")))
-((-3987 . T) (-3986 . T))
+((-3991 . T) (-3990 . T))
NIL
-(-399 E V R P Q)
+(-400 E V R P Q)
((|constructor| (NIL "Gosper's summation algorithm.")) (|GospersMethod| (((|Union| |#5| "failed") |#5| |#2| (|Mapping| |#2|)) "\\spad{GospersMethod(b, n, new)} returns a rational function \\spad{rf(n)} such that \\spad{a(n) * rf(n)} is the indefinite sum of \\spad{a(n)} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{a(n+1) * rf(n+1) - a(n) * rf(n) = a(n)},{} where \\spad{b(n) = a(n)/a(n-1)} is a rational function. Returns \"failed\" if no such rational function \\spad{rf(n)} exists. Note: \\spad{new} is a nullary function returning a new \\spad{V} every time. The condition on \\spad{a(n)} is that \\spad{a(n)/a(n-1)} is a rational function of \\spad{n}.")))
NIL
NIL
-(-400 R E |VarSet| P)
+(-401 R E |VarSet| P)
((|constructor| (NIL "A domain for polynomial sets.")) (|convert| (($ (|List| |#4|)) "\\axiom{convert(lp)} returns the polynomial set whose members are the polynomials of \\axiom{lp}.")))
-((-3993 . T) (-3992 . T))
-((-12 (|HasCategory| |#4| (QUOTE (-1013))) (|HasCategory| |#4| (|%list| (QUOTE -259) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-554 (-473)))) (|HasCategory| |#4| (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#4| (QUOTE (-553 (-773)))) (|HasCategory| |#4| (QUOTE (-72))))
-(-401 S R E)
+((-3997 . T) (-3996 . T))
+((-12 (|HasCategory| |#4| (QUOTE (-1015))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-555 (-474)))) (|HasCategory| |#4| (QUOTE (-1015))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#4| (QUOTE (-554 (-774)))) (|HasCategory| |#4| (QUOTE (-72))))
+(-402 S R E)
((|constructor| (NIL "GradedAlgebra(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-algebra''. A graded algebra is a graded module together with a degree preserving \\spad{R}-linear map,{} called the {\\em product}. \\blankline The name ``product'' is written out in full so inner and outer products with the same mapping type can be distinguished by name.")) (|product| (($ $ $) "\\spad{product(a,b)} is the degree-preserving \\spad{R}-linear product: \\blankline \\indented{2}{\\spad{degree product(a,b) = degree a + degree b}} \\indented{2}{\\spad{product(a1+a2,b) = product(a1,b) + product(a2,b)}} \\indented{2}{\\spad{product(a,b1+b2) = product(a,b1) + product(a,b2)}} \\indented{2}{\\spad{product(r*a,b) = product(a,r*b) = r*product(a,b)}} \\indented{2}{\\spad{product(a,product(b,c)) = product(product(a,b),c)}}")) (|One| (($) "1 is the identity for \\spad{product}.")))
NIL
NIL
-(-402 R E)
+(-403 R E)
((|constructor| (NIL "GradedAlgebra(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-algebra''. A graded algebra is a graded module together with a degree preserving \\spad{R}-linear map,{} called the {\\em product}. \\blankline The name ``product'' is written out in full so inner and outer products with the same mapping type can be distinguished by name.")) (|product| (($ $ $) "\\spad{product(a,b)} is the degree-preserving \\spad{R}-linear product: \\blankline \\indented{2}{\\spad{degree product(a,b) = degree a + degree b}} \\indented{2}{\\spad{product(a1+a2,b) = product(a1,b) + product(a2,b)}} \\indented{2}{\\spad{product(a,b1+b2) = product(a,b1) + product(a,b2)}} \\indented{2}{\\spad{product(r*a,b) = product(a,r*b) = r*product(a,b)}} \\indented{2}{\\spad{product(a,product(b,c)) = product(product(a,b),c)}}")) (|One| (($) "1 is the identity for \\spad{product}.")))
NIL
NIL
-(-403)
+(-404)
((|constructor| (NIL "GrayCode provides a function for efficiently running through all subsets of a finite set,{} only changing one element by another one.")) (|firstSubsetGray| (((|Vector| (|Vector| (|Integer|))) (|PositiveInteger|)) "\\spad{firstSubsetGray(n)} creates the first vector {\\em ww} to start a loop using {\\em nextSubsetGray(ww,n)}")) (|nextSubsetGray| (((|Vector| (|Vector| (|Integer|))) (|Vector| (|Vector| (|Integer|))) (|PositiveInteger|)) "\\spad{nextSubsetGray(ww,n)} returns a vector {\\em vv} whose components have the following meanings:\\begin{items} \\item {\\em vv.1}: a vector of length \\spad{n} whose entries are 0 or 1. This \\indented{3}{can be interpreted as a code for a subset of the set 1,{}...,{}\\spad{n};} \\indented{3}{{\\em vv.1} differs from {\\em ww.1} by exactly one entry;} \\item {\\em vv.2.1} is the number of the entry of {\\em vv.1} which \\indented{3}{will be changed next time;} \\item {\\em vv.2.1 = n+1} means that {\\em vv.1} is the last subset; \\indented{3}{trying to compute nextSubsetGray(vv) if {\\em vv.2.1 = n+1}} \\indented{3}{will produce an error!} \\end{items} The other components of {\\em vv.2} are needed to compute nextSubsetGray efficiently. Note: this is an implementation of [Williamson,{} Topic II,{} 3.54,{} \\spad{p}. 112] for the special case {\\em r1 = r2 = ... = rn = 2}; Note: nextSubsetGray produces a side-effect,{} \\spadignore{i.e.} {\\em nextSubsetGray(vv)} and {\\em vv := nextSubsetGray(vv)} will have the same effect.")))
NIL
NIL
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((|constructor| (NIL "TwoDimensionalPlotSettings sets global flags and constants for 2-dimensional plotting.")) (|screenResolution| (((|Integer|) (|Integer|)) "\\spad{screenResolution(n)} sets the screen resolution to \\spad{n}.") (((|Integer|)) "\\spad{screenResolution()} returns the screen resolution \\spad{n}.")) (|minPoints| (((|Integer|) (|Integer|)) "\\spad{minPoints()} sets the minimum number of points in a plot.") (((|Integer|)) "\\spad{minPoints()} returns the minimum number of points in a plot.")) (|maxPoints| (((|Integer|) (|Integer|)) "\\spad{maxPoints()} sets the maximum number of points in a plot.") (((|Integer|)) "\\spad{maxPoints()} returns the maximum number of points in a plot.")) (|adaptive| (((|Boolean|) (|Boolean|)) "\\spad{adaptive(true)} turns adaptive plotting on; \\spad{adaptive(false)} turns adaptive plotting off.") (((|Boolean|)) "\\spad{adaptive()} determines whether plotting will be done adaptively.")) (|drawToScale| (((|Boolean|) (|Boolean|)) "\\spad{drawToScale(true)} causes plots to be drawn to scale. \\spad{drawToScale(false)} causes plots to be drawn so that they fill up the viewport window. The default setting is \\spad{false}.") (((|Boolean|)) "\\spad{drawToScale()} determines whether or not plots are to be drawn to scale.")) (|clipPointsDefault| (((|Boolean|) (|Boolean|)) "\\spad{clipPointsDefault(true)} turns on automatic clipping; \\spad{clipPointsDefault(false)} turns off automatic clipping. The default setting is \\spad{true}.") (((|Boolean|)) "\\spad{clipPointsDefault()} determines whether or not automatic clipping is to be done.")))
NIL
NIL
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+(-406)
((|constructor| (NIL "TwoDimensionalGraph creates virtual two dimensional graphs (to be displayed on TwoDimensionalViewports).")) (|putColorInfo| (((|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|Palette|))) "\\spad{putColorInfo(llp,lpal)} takes a list of list of points,{} \\spad{llp},{} and returns the points with their hue and shade components set according to the list of palette colors,{} \\spad{lpal}.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(gi)} returns the indicated graph,{} \\spad{gi},{} of domain \\spadtype{GraphImage} as output of the domain \\spadtype{OutputForm}.") (($ (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{coerce(llp)} component(\\spad{gi},{}pt) creates and returns a graph of the domain \\spadtype{GraphImage} which is composed of the list of list of points given by \\spad{llp},{} and whose point colors,{} line colors and point sizes are determined by the default functions \\spadfun{pointColorDefault},{} \\spadfun{lineColorDefault},{} and \\spadfun{pointSizeDefault}. The graph data is then sent to the viewport manager where it waits to be included in a two-dimensional viewport window.")) (|point| (((|Void|) $ (|Point| (|DoubleFloat|)) (|Palette|)) "\\spad{point(gi,pt,pal)} modifies the graph \\spad{gi} of the domain \\spadtype{GraphImage} to contain one point component,{} \\spad{pt} whose point color is set to be the palette color \\spad{pal},{} and whose line color and point size are determined by the default functions \\spadfun{lineColorDefault} and \\spadfun{pointSizeDefault}.")) (|appendPoint| (((|Void|) $ (|Point| (|DoubleFloat|))) "\\spad{appendPoint(gi,pt)} appends the point \\spad{pt} to the end of the list of points component for the graph,{} \\spad{gi},{} which is of the domain \\spadtype{GraphImage}.")) (|component| (((|Void|) $ (|Point| (|DoubleFloat|)) (|Palette|) (|Palette|) (|PositiveInteger|)) "\\spad{component(gi,pt,pal1,pal2,ps)} modifies the graph \\spad{gi} of the domain \\spadtype{GraphImage} to contain one point component,{} \\spad{pt} whose point color is set to the palette color \\spad{pal1},{} line color is set to the palette color \\spad{pal2},{} and point size is set to the positive integer \\spad{ps}.") (((|Void|) $ (|Point| (|DoubleFloat|))) "\\spad{component(gi,pt)} modifies the graph \\spad{gi} of the domain \\spadtype{GraphImage} to contain one point component,{} \\spad{pt} whose point color,{} line color and point size are determined by the default functions \\spadfun{pointColorDefault},{} \\spadfun{lineColorDefault},{} and \\spadfun{pointSizeDefault}.") (((|Void|) $ (|List| (|Point| (|DoubleFloat|))) (|Palette|) (|Palette|) (|PositiveInteger|)) "\\spad{component(gi,lp,pal1,pal2,p)} sets the components of the graph,{} \\spad{gi} of the domain \\spadtype{GraphImage},{} to the values given. The point list for \\spad{gi} is set to the list \\spad{lp},{} the color of the points in \\spad{lp} is set to the palette color \\spad{pal1},{} the color of the lines which connect the points \\spad{lp} is set to the palette color \\spad{pal2},{} and the size of the points in \\spad{lp} is given by the integer \\spad{p}.")) (|units| (((|List| (|Float|)) $ (|List| (|Float|))) "\\spad{units(gi,lu)} modifies the list of unit increments for the \\spad{x} and \\spad{y} axes of the given graph,{} \\spad{gi} of the domain \\spadtype{GraphImage},{} to be that of the list of unit increments,{} \\spad{lu},{} and returns the new list of units for \\spad{gi}.") (((|List| (|Float|)) $) "\\spad{units(gi)} returns the list of unit increments for the \\spad{x} and \\spad{y} axes of the indicated graph,{} \\spad{gi},{} of the domain \\spadtype{GraphImage}.")) (|ranges| (((|List| (|Segment| (|Float|))) $ (|List| (|Segment| (|Float|)))) "\\spad{ranges(gi,lr)} modifies the list of ranges for the given graph,{} \\spad{gi} of the domain \\spadtype{GraphImage},{} to be that of the list of range segments,{} \\spad{lr},{} and returns the new range list for \\spad{gi}.") (((|List| (|Segment| (|Float|))) $) "\\spad{ranges(gi)} returns the list of ranges of the point components from the indicated graph,{} \\spad{gi},{} of the domain \\spadtype{GraphImage}.")) (|key| (((|Integer|) $) "\\spad{key(gi)} returns the process ID of the given graph,{} \\spad{gi},{} of the domain \\spadtype{GraphImage}.")) (|pointLists| (((|List| (|List| (|Point| (|DoubleFloat|)))) $) "\\spad{pointLists(gi)} returns the list of lists of points which compose the given graph,{} \\spad{gi},{} of the domain \\spadtype{GraphImage}.")) (|makeGraphImage| (($ (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|Palette|)) (|List| (|Palette|)) (|List| (|PositiveInteger|)) (|List| (|DrawOption|))) "\\spad{makeGraphImage(llp,lpal1,lpal2,lp,lopt)} returns a graph of the domain \\spadtype{GraphImage} which is composed of the points and lines from the list of lists of points,{} \\spad{llp},{} whose point colors are indicated by the list of palette colors,{} \\spad{lpal1},{} and whose lines are colored according to the list of palette colors,{} \\spad{lpal2}. The paramater \\spad{lp} is a list of integers which denote the size of the data points,{} and \\spad{lopt} is the list of draw command options. The graph data is then sent to the viewport manager where it waits to be included in a two-dimensional viewport window.") (($ (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|Palette|)) (|List| (|Palette|)) (|List| (|PositiveInteger|))) "\\spad{makeGraphImage(llp,lpal1,lpal2,lp)} returns a graph of the domain \\spadtype{GraphImage} which is composed of the points and lines from the list of lists of points,{} \\spad{llp},{} whose point colors are indicated by the list of palette colors,{} \\spad{lpal1},{} and whose lines are colored according to the list of palette colors,{} \\spad{lpal2}. The paramater \\spad{lp} is a list of integers which denote the size of the data points. The graph data is then sent to the viewport manager where it waits to be included in a two-dimensional viewport window.") (($ (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{makeGraphImage(llp)} returns a graph of the domain \\spadtype{GraphImage} which is composed of the points and lines from the list of lists of points,{} \\spad{llp},{} with default point size and default point and line colours. The graph data is then sent to the viewport manager where it waits to be included in a two-dimensional viewport window.") (($ $) "\\spad{makeGraphImage(gi)} takes the given graph,{} \\spad{gi} of the domain \\spadtype{GraphImage},{} and sends it's data to the viewport manager where it waits to be included in a two-dimensional viewport window. \\spad{gi} cannot be an empty graph,{} and it's elements must have been created using the \\spadfun{point} or \\spadfun{component} functions,{} not by a previous \\spadfun{makeGraphImage}.")) (|graphImage| (($) "\\spad{graphImage()} returns an empty graph with 0 point lists of the domain \\spadtype{GraphImage}. A graph image contains the graph data component of a two dimensional viewport.")))
NIL
NIL
-(-406 S R E)
+(-407 S R E)
((|constructor| (NIL "GradedModule(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-module'',{} \\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.")) (+ (($ $ $) "\\spad{g+h} is the sum of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.")) (- (($ $ $) "\\spad{g-h} is the difference of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.") (($ $) "\\spad{-g} is the additive inverse of \\spad{g} in the module of elements of the same grade as \\spad{g}.")) (* (($ $ |#2|) "\\spad{g*r} is right module multiplication.") (($ |#2| $) "\\spad{r*g} is left module multiplication.")) (|Zero| (($) "0 denotes the zero of degree 0.")) (|degree| ((|#3| $) "\\spad{degree(g)} names the degree of \\spad{g}. The set of all elements of a given degree form an \\spad{R}-module.")))
NIL
NIL
-(-407 R E)
+(-408 R E)
((|constructor| (NIL "GradedModule(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-module'',{} \\spadignore{i.e.} collection of \\spad{R}-modules indexed by an abelian monoid \\spad{E}. An element \\spad{g} of \\spad{G[s]} for some specific \\spad{s} in \\spad{E} is said to be an element of \\spad{G} with {\\em degree} \\spad{s}. Sums are defined in each module \\spad{G[s]} so two elements of \\spad{G} have a sum if they have the same degree. \\blankline Morphisms can be defined and composed by degree to give the mathematical category of graded modules.")) (+ (($ $ $) "\\spad{g+h} is the sum of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.")) (- (($ $ $) "\\spad{g-h} is the difference of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.") (($ $) "\\spad{-g} is the additive inverse of \\spad{g} in the module of elements of the same grade as \\spad{g}.")) (* (($ $ |#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| $) "\\spad{degree(g)} names the degree of \\spad{g}. The set of all elements of a given degree form an \\spad{R}-module.")))
NIL
NIL
-(-408 |lv| -3091 R)
+(-409 |lv| -3094 R)
((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni,{} Summer \\spad{'88},{} revised November \\spad{'89}} Solve systems of polynomial equations using Groebner bases Total order Groebner bases are computed and then converted to lex ones This package is mostly intended for internal use.")) (|genericPosition| (((|Record| (|:| |dpolys| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |coords| (|List| (|Integer|)))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{genericPosition(lp,lv)} puts a radical zero dimensional ideal in general position,{} for system \\spad{lp} in variables \\spad{lv}.")) (|testDim| (((|Union| (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "failed") (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{testDim(lp,lv)} tests if the polynomial system \\spad{lp} in variables \\spad{lv} is zero dimensional.")) (|groebSolve| (((|List| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{groebSolve(lp,lv)} reduces the polynomial system \\spad{lp} in variables \\spad{lv} to triangular form. Algorithm based on groebner bases algorithm with linear algebra for change of ordering. Preprocessing for the general solver. The polynomials in input are of type \\spadtype{DMP}.")))
NIL
NIL
-(-409 S)
+(-410 S)
((|constructor| (NIL "The class of multiplicative groups,{} \\spadignore{i.e.} monoids with multiplicative inverses. \\blankline")) (|commutator| (($ $ $) "\\spad{commutator(p,q)} computes \\spad{inv(p) * inv(q) * p * q}.")) (|conjugate| (($ $ $) "\\spad{conjugate(p,q)} computes \\spad{inv(q) * p * q}; this is 'right action by conjugation'.")) (|unitsKnown| ((|attribute|) "unitsKnown asserts that recip only returns \"failed\" for non-units.")) (** (($ $ (|Integer|)) "\\spad{x**n} returns \\spad{x} raised to the integer power \\spad{n}.")) (/ (($ $ $) "\\spad{x/y} is the same as \\spad{x} times the inverse of \\spad{y}.")) (|inv| (($ $) "\\spad{inv(x)} returns the inverse of \\spad{x}.")))
NIL
NIL
-(-410)
+(-411)
((|constructor| (NIL "The class of multiplicative groups,{} \\spadignore{i.e.} monoids with multiplicative inverses. \\blankline")) (|commutator| (($ $ $) "\\spad{commutator(p,q)} computes \\spad{inv(p) * inv(q) * p * q}.")) (|conjugate| (($ $ $) "\\spad{conjugate(p,q)} computes \\spad{inv(q) * p * q}; this is 'right action by conjugation'.")) (|unitsKnown| ((|attribute|) "unitsKnown asserts that recip only returns \"failed\" for non-units.")) (** (($ $ (|Integer|)) "\\spad{x**n} returns \\spad{x} raised to the integer power \\spad{n}.")) (/ (($ $ $) "\\spad{x/y} is the same as \\spad{x} times the inverse of \\spad{y}.")) (|inv| (($ $) "\\spad{inv(x)} returns the inverse of \\spad{x}.")))
-((-3989 . T))
+((-3993 . T))
NIL
-(-411 |Coef| |var| |cen|)
+(-412 |Coef| |var| |cen|)
((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x\\^r)}.")) (|integrate| (($ $ (|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.")) (|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.")))
-(((-3994 "*") |has| |#1| (-146)) (-3985 |has| |#1| (-495)) (-3990 |has| |#1| (-311)) (-3984 |has| |#1| (-311)) (-3986 . T) (-3987 . T) (-3989 . T))
-((|HasCategory| |#1| (QUOTE (-38 (-347 (-484))))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-495)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-810 (-1089)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -347) (QUOTE (-484))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -347) (QUOTE (-484))) (|devaluate| |#1|)))) (|HasCategory| (-347 (-484)) (QUOTE (-1025))) (|HasCategory| |#1| (QUOTE (-311))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-495)))) (OR (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-495)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -347) (QUOTE (-484)))))) (|HasSignature| |#1| (|%list| (QUOTE -3943) (|%list| (|devaluate| |#1|) (QUOTE (-1089)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -347) (QUOTE (-484)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-347 (-484))))) (|HasCategory| |#1| (QUOTE (-29 (-484)))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1114)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-347 (-484))))) (|HasSignature| |#1| (|%list| (QUOTE -3809) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1089))))) (|HasSignature| |#1| (|%list| (QUOTE -3080) (|%list| (|%list| (QUOTE -584) (QUOTE (-1089))) (|devaluate| |#1|)))))))
-(-412 |Key| |Entry| |Tbl| |dent|)
+(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3994 |has| |#1| (-312)) (-3988 |has| |#1| (-312)) (-3990 . T) (-3991 . T) (-3993 . T))
+((|HasCategory| |#1| (QUOTE (-38 (-348 (-485))))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-811 (-1091)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -348) (QUOTE (-485))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -348) (QUOTE (-485))) (|devaluate| |#1|)))) (|HasCategory| (-348 (-485)) (QUOTE (-1027))) (|HasCategory| |#1| (QUOTE (-312))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-496)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-496)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -348) (QUOTE (-485)))))) (|HasSignature| |#1| (|%list| (QUOTE -3947) (|%list| (|devaluate| |#1|) (QUOTE (-1091)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -348) (QUOTE (-485)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-348 (-485))))) (|HasCategory| |#1| (QUOTE (-29 (-485)))) (|HasCategory| |#1| (QUOTE (-873))) (|HasCategory| |#1| (QUOTE (-1116)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-348 (-485))))) (|HasSignature| |#1| (|%list| (QUOTE -3813) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1091))))) (|HasSignature| |#1| (|%list| (QUOTE -3083) (|%list| (|%list| (QUOTE -585) (QUOTE (-1091))) (|devaluate| |#1|)))))))
+(-413 |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.")))
-((-3993 . T))
-((-12 (|HasCategory| (-2 (|:| -3857 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -259) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3857) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3857 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3857 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3857 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3857 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| (-2 (|:| -3857 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-553 (-773))))) (|HasCategory| (-2 (|:| -3857 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-473)))) (-12 (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (|%list| (QUOTE -259) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-757))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3857 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3857 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3857 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3857 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013))))
-(-413 R E V P)
+((-3997 . T))
+((-12 (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3861) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1015)))) (OR (|HasCategory| |#2| (QUOTE (-1015))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1015)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1015))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1015)))) (OR (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-774)))) (|HasCategory| |#2| (QUOTE (-554 (-774))))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-555 (-474)))) (-12 (|HasCategory| |#2| (QUOTE (-1015))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-758))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-1015))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-554 (-774)))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-774)))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1015))))
+(-414 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)}")))
-((-3993 . T) (-3992 . T))
-((-12 (|HasCategory| |#4| (QUOTE (-1013))) (|HasCategory| |#4| (|%list| (QUOTE -259) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-554 (-473)))) (|HasCategory| |#4| (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#3| (QUOTE (-317))) (|HasCategory| |#4| (QUOTE (-553 (-773)))) (|HasCategory| |#4| (QUOTE (-72))))
-(-414)
+((-3997 . T) (-3996 . T))
+((-12 (|HasCategory| |#4| (QUOTE (-1015))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-555 (-474)))) (|HasCategory| |#4| (QUOTE (-1015))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#3| (QUOTE (-318))) (|HasCategory| |#4| (QUOTE (-554 (-774)))) (|HasCategory| |#4| (QUOTE (-72))))
+(-415)
((|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}.")))
-((-3984 . T) (-3990 . T) (-3985 . T) ((-3994 "*") . T) (-3986 . T) (-3987 . T) (-3989 . T))
+((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T))
NIL
-(-415)
+(-416)
((|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'.")))
NIL
NIL
-(-416 |Key| |Entry| |hashfn|)
+(-417 |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.")))
-((-3992 . T) (-3993 . T))
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((|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's book Lie Groups -- 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{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
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((|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")))
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((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying ordered component type. The vectors are ordered first by the sum of their components,{} and then refined using a reverse lexicographic ordering. This type is a suitable third argument for \\spadtype{GeneralDistributedMultivariatePolynomial}.")))
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+(-421)
((|constructor| (NIL "This domain represents the header of a definition.")) (|parameters| (((|List| (|ParameterAst|)) $) "\\spad{parameters(h)} gives the parameters specified in the definition header `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
-(-421 S)
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((|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}.")))
-((-3992 . T) (-3993 . T))
-((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1013))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-72))))
-(-422 -3091 UP UPUP R)
+((-3996 . T) (-3997 . T))
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+(-423 -3094 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}'s are integers and the \\spad{P}'s are finite rational points on the curve. The equation of the curve must be \\spad{y^2} = \\spad{f}(\\spad{x}) and \\spad{f} must have odd degree.")))
NIL
NIL
-(-423 BP)
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((|constructor| (NIL "This package provides the functions for the heuristic integer gcd. Geddes's algorithm,{}for univariate polynomials with integer coefficients")) (|lintgcd| (((|Integer|) (|List| (|Integer|))) "\\spad{lintgcd([a1,..,ak])} = gcd of a list of integers")) (|content| (((|List| (|Integer|)) (|List| |#1|)) "\\spad{content([f1,..,fk])} = content of a list of univariate polynonials")) (|gcdcofactprim| (((|List| |#1|) (|List| |#1|)) "\\spad{gcdcofactprim([f1,..fk])} = gcd and cofactors of \\spad{k} primitive polynomials.")) (|gcdcofact| (((|List| |#1|) (|List| |#1|)) "\\spad{gcdcofact([f1,..fk])} = gcd and cofactors of \\spad{k} univariate polynomials.")) (|gcdprim| ((|#1| (|List| |#1|)) "\\spad{gcdprim([f1,..,fk])} = gcd of \\spad{k} PRIMITIVE univariate polynomials")) (|gcd| ((|#1| (|List| |#1|)) "\\spad{gcd([f1,..,fk])} = gcd of the polynomials \\spad{fi}.")))
NIL
NIL
-(-424)
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((|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.")))
-((-3984 . T) (-3990 . T) (-3985 . T) ((-3994 "*") . T) (-3986 . T) (-3987 . T) (-3989 . T))
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-(-425 A S)
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+(-426 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
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-(-426 S)
+((|HasAttribute| |#1| (QUOTE -3996)) (|HasAttribute| |#1| (QUOTE -3997)) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1015))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-554 (-774)))))
+(-427 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|) $) "\\spad{map(f,u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}.")))
NIL
NIL
-(-427 S)
+(-428 S)
((|constructor| (NIL "A is homotopic to \\spad{B} iff any element of domain \\spad{B} can be automically converted into an element of domain \\spad{B},{} and nay element of domain \\spad{B} can be automatically converted into an A.")))
NIL
NIL
-(-428)
+(-429)
((|constructor| (NIL "This domain represents hostnames on computer network.")) (|host| (($ (|String|)) "\\spad{host(n)} constructs a Hostname from the name `n'.")))
NIL
NIL
-(-429 S)
+(-430 S)
((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}.")))
NIL
NIL
-(-430)
+(-431)
((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}.")))
NIL
NIL
-(-431 -3091 UP |AlExt| |AlPol|)
+(-432 -3094 UP |AlExt| |AlPol|)
((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of a field over which we can factor UP's.")) (|factor| (((|Factored| |#4|) |#4| (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{factor(p, f)} returns a prime factorisation of \\spad{p}; \\spad{f} is a factorisation map for elements of UP.")))
NIL
NIL
-(-432)
+(-433)
((|constructor| (NIL "Algebraic closure of the rational numbers.")) (|norm| (($ $ (|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}.")))
-((-3984 . T) (-3990 . T) (-3985 . T) ((-3994 "*") . T) (-3986 . T) (-3987 . T) (-3989 . T))
-((|HasCategory| $ (QUOTE (-962))) (|HasCategory| $ (QUOTE (-951 (-484)))))
-(-433 S |mn|)
+((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T))
+((|HasCategory| $ (QUOTE (-963))) (|HasCategory| $ (QUOTE (-952 (-485)))))
+(-434 S |mn|)
((|constructor| (NIL "\\indented{1}{Author Micheal Monagan \\spad{Aug/87}} This is the basic one dimensional array data type.")))
-((-3993 . T) (-3992 . T))
-((OR (-12 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-554 (-473)))) (OR (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-757))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| (-484) (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))))
-(-434 R |mnRow| |mnCol|)
+((-3997 . T) (-3996 . T))
+((OR (-12 (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-554 (-774)))) (|HasCategory| |#1| (QUOTE (-555 (-474)))) (OR (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| |#1| (QUOTE (-758))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| (-485) (QUOTE (-758))) (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))))
+(-435 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'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.")))
-((-3992 . T) (-3993 . T))
-((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1013))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-72))))
-(-435 K R UP)
+((-3996 . T) (-3997 . T))
+((-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1015))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| |#1| (QUOTE (-554 (-774)))) (|HasCategory| |#1| (QUOTE (-72))))
+(-436 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
-(-436 R UP -3091)
+(-437 R UP -3094)
((|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 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
-(-437 |mn|)
+(-438 |mn|)
((|constructor| (NIL "\\spadtype{IndexedBits} is a domain to compactly represent large quantities of Boolean data.")))
-((-3993 . T) (-3992 . T))
-((-12 (|HasCategory| (-85) (QUOTE (-259 (-85)))) (|HasCategory| (-85) (QUOTE (-1013)))) (|HasCategory| (-85) (QUOTE (-554 (-473)))) (|HasCategory| (-85) (QUOTE (-757))) (|HasCategory| (-484) (QUOTE (-757))) (|HasCategory| (-85) (QUOTE (-1013))) (|HasCategory| (-85) (QUOTE (-553 (-773)))) (|HasCategory| (-85) (QUOTE (-72))))
-(-438 K R UP L)
+((-3997 . T) (-3996 . T))
+((-12 (|HasCategory| (-85) (QUOTE (-260 (-85)))) (|HasCategory| (-85) (QUOTE (-1015)))) (|HasCategory| (-85) (QUOTE (-555 (-474)))) (|HasCategory| (-85) (QUOTE (-758))) (|HasCategory| (-485) (QUOTE (-758))) (|HasCategory| (-85) (QUOTE (-1015))) (|HasCategory| (-85) (QUOTE (-554 (-774)))) (|HasCategory| (-85) (QUOTE (-72))))
+(-439 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
NIL
-(-439)
+(-440)
((|constructor| (NIL "\\indented{1}{This domain implements a container of information} about the AXIOM library")) (|fullDisplay| (((|Void|) $) "\\spad{fullDisplay(ic)} prints all of the information contained in \\axiom{\\spad{ic}}.")) (|display| (((|Void|) $) "\\spad{display(ic)} prints a summary of the information contained in \\axiom{\\spad{ic}}.")) (|elt| (((|String|) $ (|Symbol|)) "\\spad{elt(ic,s)} selects a particular field from \\axiom{\\spad{ic}}. Valid fields are \\axiom{name,{} nargs,{} exposed,{} type,{} abbreviation,{} kind,{} origin,{} params,{} condition,{} doc}.")))
NIL
NIL
-(-440 R Q A B)
+(-441 R Q A B)
((|constructor| (NIL "InnerCommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#4|) "\\spad{splitDenominator([q1,...,qn])} returns \\spad{[[p1,...,pn], d]} such that \\spad{qi = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}'s.")) (|clearDenominator| ((|#3| |#4|) "\\spad{clearDenominator([q1,...,qn])} returns \\spad{[p1,...,pn]} such that \\spad{qi = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}'s.")) (|commonDenominator| ((|#1| |#4|) "\\spad{commonDenominator([q1,...,qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}qn.")))
NIL
NIL
-(-441 -3091 |Expon| |VarSet| |DPoly|)
+(-442 -3094 |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| (QUOTE (-554 (-1089)))))
-(-442 |vl| |nv|)
+((|HasCategory| |#3| (QUOTE (-555 (-1091)))))
+(-443 |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
NIL
-(-443 T$)
+(-444 T$)
((|constructor| (NIL "This is the category of all domains that implement idempotent operations.")))
-(((|%Rule| |idempotence| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|)) (-3055 (|f| |x| |x|) |x|))) . T))
+(((|%Rule| |idempotence| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|)) (-3058 (|f| |x| |x|) |x|))) . T))
NIL
-(-444)
+(-445)
((|constructor| (NIL "This domain provides representation for plain identifiers. It differs from Symbol in that it does not support any form of scripting. It is a plain basic data structure. \\blankline")) (|gensym| (($) "\\spad{gensym()} returns a new identifier,{} different from any other identifier in the running system")))
NIL
NIL
-(-445 A S)
+(-446 A S)
((|constructor| (NIL "\\indented{1}{Indexed direct products of abelian groups over an abelian group \\spad{A} of} generators indexed by the ordered set \\spad{S}. All items have finite support: only non-zero terms are stored.")))
NIL
-((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-1013)))))
-(-446 A S)
+((-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#2| (QUOTE (-1015)))))
+(-447 A S)
((|constructor| (NIL "\\indented{1}{Indexed direct products of abelian monoids over an abelian monoid \\spad{A} of} generators indexed by the ordered set \\spad{S}. All items have finite support. Only non-zero terms are stored.")))
NIL
-((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-1013)))))
-(-447 A S)
+((-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#2| (QUOTE (-1015)))))
+(-448 A S)
((|constructor| (NIL "This category represents the direct product of some set with respect to an ordered indexing set.")) (|terms| (((|List| (|IndexedProductTerm| |#1| |#2|)) $) "\\spad{terms x} returns the list of terms in \\spad{x}. Each term is a pair of a support (the first component) and the corresponding value (the second component).")) (|reductum| (($ $) "\\spad{reductum(z)} returns a new element created by removing the leading coefficient/support pair from the element \\spad{z}. Error: if \\spad{z} has no support.")) (|leadingSupport| ((|#2| $) "\\spad{leadingSupport(z)} returns the index of leading (with respect to the ordering on the indexing set) monomial of \\spad{z}. Error: if \\spad{z} has no support.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(z)} returns the coefficient of the leading (with respect to the ordering on the indexing set) monomial of \\spad{z}. Error: if \\spad{z} has no support.")) (|monomial| (($ |#1| |#2|) "\\spad{monomial(a,s)} constructs a direct product element with the \\spad{s} component set to \\spad{a}")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,z)} returns the new element created by applying the function \\spad{f} to each component of the direct product element \\spad{z}.")))
NIL
NIL
-(-448 A S)
+(-449 A S)
((|constructor| (NIL "Indexed direct products of objects over a set \\spad{A} of generators indexed by an ordered set \\spad{S}. All items have finite support.")) (|combineWithIf| (($ $ $ (|Mapping| |#1| |#1| |#1|) (|Mapping| (|Boolean|) |#1| |#1|)) "\\spad{combineWithIf(u,v,f,p)} returns the result of combining index-wise,{} coefficients of \\spad{u} and \\spad{u} if when satisfy the predicate \\spad{p}. Those pairs of coefficients which fail\\spad{p} are implicitly ignored.")))
NIL
-((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-1013)))))
-(-449 A S)
+((-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#2| (QUOTE (-1015)))))
+(-450 A S)
((|constructor| (NIL "\\indented{1}{Indexed direct products of ordered abelian monoids \\spad{A} of} generators indexed by the ordered set \\spad{S}. The inherited order is lexicographical. All items have finite support: only non-zero terms are stored.")))
NIL
-((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-1013)))))
-(-450 A S)
+((-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#2| (QUOTE (-1015)))))
+(-451 A S)
((|constructor| (NIL "\\indented{1}{Indexed direct products of ordered abelian monoid sups \\spad{A},{}} generators indexed by the ordered set \\spad{S}. All items have finite support: only non-zero terms are stored.")))
NIL
-((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-1013)))))
-(-451 A S)
+((-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#2| (QUOTE (-1015)))))
+(-452 A S)
((|constructor| (NIL "An indexed product term is a utility domain used in the representation of indexed direct product objects.")) (|coefficient| ((|#1| $) "\\spad{coefficient t} returns the coefficient of the tern \\spad{t}.")) (|index| ((|#2| $) "\\spad{index t} returns the index of the term \\spad{t}.")) (|term| (($ |#2| |#1|) "\\spad{term(s,a)} constructs a term with index \\spad{s} and coefficient \\spad{a}.")))
NIL
NIL
-(-452 S A B)
+(-453 S A B)
((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation'' substitutions. The difference between this and \\spadtype{Evalable} is that the operations in this category specify the substitution as a pair of arguments rather than as an equation.")) (|eval| (($ $ (|List| |#2|) (|List| |#3|)) "\\spad{eval(f, [x1,...,xn], [v1,...,vn])} replaces \\spad{xi} by \\spad{vi} in \\spad{f}.") (($ $ |#2| |#3|) "\\spad{eval(f, x, v)} replaces \\spad{x} by \\spad{v} in \\spad{f}.")))
NIL
NIL
-(-453 A B)
+(-454 A B)
((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation'' substitutions. The difference between this and \\spadtype{Evalable} is that the operations in this category specify the substitution as a pair of arguments rather than as an equation.")) (|eval| (($ $ (|List| |#1|) (|List| |#2|)) "\\spad{eval(f, [x1,...,xn], [v1,...,vn])} replaces \\spad{xi} by \\spad{vi} in \\spad{f}.") (($ $ |#1| |#2|) "\\spad{eval(f, x, v)} replaces \\spad{x} by \\spad{v} in \\spad{f}.")))
NIL
NIL
-(-454 S E |un|)
+(-455 S E |un|)
((|constructor| (NIL "Internal implementation of a free abelian monoid.")))
NIL
-((|HasCategory| |#2| (QUOTE (-717))))
-(-455 S |mn|)
+((|HasCategory| |#2| (QUOTE (-718))))
+(-456 S |mn|)
((|constructor| (NIL "\\indented{1}{Author: Michael Monagan \\spad{July/87},{} modified SMW \\spad{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}")))
-((-3993 . T) (-3992 . T))
-((OR (-12 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-554 (-473)))) (OR (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-757))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| (-484) (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))))
-(-456)
+((-3997 . T) (-3996 . T))
+((OR (-12 (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-554 (-774)))) (|HasCategory| |#1| (QUOTE (-555 (-474)))) (OR (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| |#1| (QUOTE (-758))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| (-485) (QUOTE (-758))) (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))))
+(-457)
((|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
-(-457 |p| |n|)
+(-458 |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}.")))
-((-3984 . T) (-3990 . T) (-3985 . T) ((-3994 "*") . T) (-3986 . T) (-3987 . T) (-3989 . T))
-((OR (|HasCategory| (-517 |#1|) (QUOTE (-118))) (|HasCategory| (-517 |#1|) (QUOTE (-317)))) (|HasCategory| (-517 |#1|) (QUOTE (-120))) (|HasCategory| (-517 |#1|) (QUOTE (-317))) (|HasCategory| (-517 |#1|) (QUOTE (-118))))
-(-458 R |mnRow| |mnCol| |Row| |Col|)
+((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T))
+((OR (|HasCategory| (-518 |#1|) (QUOTE (-118))) (|HasCategory| (-518 |#1|) (QUOTE (-318)))) (|HasCategory| (-518 |#1|) (QUOTE (-120))) (|HasCategory| (-518 |#1|) (QUOTE (-318))) (|HasCategory| (-518 |#1|) (QUOTE (-118))))
+(-459 R |mnRow| |mnCol| |Row| |Col|)
((|constructor| (NIL "\\indented{1}{This is an internal type which provides an implementation of} 2-dimensional arrays as PrimitiveArray's of PrimitiveArray's.")))
-((-3992 . T) (-3993 . T))
-((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1013))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-72))))
-(-459 R |Row| |Col| M)
+((-3996 . T) (-3997 . T))
+((-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1015))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| |#1| (QUOTE (-554 (-774)))) (|HasCategory| |#1| (QUOTE (-72))))
+(-460 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,{} m*h and 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 -3993)))
-(-460 R |Row| |Col| M QF |Row2| |Col2| M2)
+((|HasAttribute| |#3| (QUOTE -3997)))
+(-461 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 -3993)))
-(-461 R |mnRow| |mnCol|)
+((|HasAttribute| |#7| (QUOTE -3997)))
+(-462 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.")))
-((-3992 . T) (-3993 . T))
-((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1013))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-257))) (|HasCategory| |#1| (QUOTE (-495))) (|HasAttribute| |#1| (QUOTE (-3994 "*"))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-72))))
-(-462)
+((-3996 . T) (-3997 . T))
+((-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1015))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| |#1| (QUOTE (-554 (-774)))) (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-496))) (|HasAttribute| |#1| (QUOTE (-3998 "*"))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-72))))
+(-463)
((|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
NIL
-(-463)
+(-464)
((|constructor| (NIL "This domain represents the `in' iterator syntax.")) (|sequence| (((|SpadAst|) $) "\\spad{sequence(i)} returns the sequence expression being iterated over by `i'.")) (|iterationVar| (((|Identifier|) $) "\\spad{iterationVar(i)} returns the name of the iterating variable of the `in' iterator 'i'")))
NIL
NIL
-(-464 S)
+(-465 S)
((|constructor| (NIL "This category describes input byte stream conduits.")) (|readBytes!| (((|NonNegativeInteger|) $ (|ByteBuffer|)) "\\spad{readBytes!(c,b)} reads byte sequences from conduit `c' into the byte buffer `b'. The actual number of bytes written is returned,{} and the length of `b' is set to that amount.")) (|readUInt32!| (((|Maybe| (|UInt32|)) $) "\\spad{readUInt32!(cond)} attempts to read a \\spad{UInt32} value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readInt32!| (((|Maybe| (|Int32|)) $) "\\spad{readInt32!(cond)} attempts to read an \\spad{Int32} value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readUInt16!| (((|Maybe| (|UInt16|)) $) "\\spad{readUInt16!(cond)} attempts to read a \\spad{UInt16} value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readInt16!| (((|Maybe| (|Int16|)) $) "\\spad{readInt16!(cond)} attempts to read an \\spad{Int16} value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readUInt8!| (((|Maybe| (|UInt8|)) $) "\\spad{readUInt8!(cond)} attempts to read a \\spad{UInt8} value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readInt8!| (((|Maybe| (|Int8|)) $) "\\spad{readInt8!(cond)} attempts to read an \\spad{Int8} value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readByte!| (((|Maybe| (|Byte|)) $) "\\spad{readByte!(cond)} attempts to read a byte from the input conduit `cond'. Returns the read byte if successful,{} otherwise \\spad{nothing}.")))
NIL
NIL
-(-465)
+(-466)
((|constructor| (NIL "This category describes input byte stream conduits.")) (|readBytes!| (((|NonNegativeInteger|) $ (|ByteBuffer|)) "\\spad{readBytes!(c,b)} reads byte sequences from conduit `c' into the byte buffer `b'. The actual number of bytes written is returned,{} and the length of `b' is set to that amount.")) (|readUInt32!| (((|Maybe| (|UInt32|)) $) "\\spad{readUInt32!(cond)} attempts to read a \\spad{UInt32} value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readInt32!| (((|Maybe| (|Int32|)) $) "\\spad{readInt32!(cond)} attempts to read an \\spad{Int32} value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readUInt16!| (((|Maybe| (|UInt16|)) $) "\\spad{readUInt16!(cond)} attempts to read a \\spad{UInt16} value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readInt16!| (((|Maybe| (|Int16|)) $) "\\spad{readInt16!(cond)} attempts to read an \\spad{Int16} value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readUInt8!| (((|Maybe| (|UInt8|)) $) "\\spad{readUInt8!(cond)} attempts to read a \\spad{UInt8} value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readInt8!| (((|Maybe| (|Int8|)) $) "\\spad{readInt8!(cond)} attempts to read an \\spad{Int8} value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readByte!| (((|Maybe| (|Byte|)) $) "\\spad{readByte!(cond)} attempts to read a byte from the input conduit `cond'. Returns the read byte if successful,{} otherwise \\spad{nothing}.")))
NIL
NIL
-(-466 GF)
+(-467 GF)
((|constructor| (NIL "InnerNormalBasisFieldFunctions(GF) (unexposed): This package has functions used by every normal basis finite field extension domain.")) (|minimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) (|Vector| |#1|)) "\\spad{minimalPolynomial(x)} \\undocumented{} See \\axiomFunFrom{minimalPolynomial}{FiniteAlgebraicExtensionField}")) (|normalElement| (((|Vector| |#1|) (|PositiveInteger|)) "\\spad{normalElement(n)} \\undocumented{} See \\axiomFunFrom{normalElement}{FiniteAlgebraicExtensionField}")) (|basis| (((|Vector| (|Vector| |#1|)) (|PositiveInteger|)) "\\spad{basis(n)} \\undocumented{} See \\axiomFunFrom{basis}{FiniteAlgebraicExtensionField}")) (|normal?| (((|Boolean|) (|Vector| |#1|)) "\\spad{normal?(x)} \\undocumented{} See \\axiomFunFrom{normal?}{FiniteAlgebraicExtensionField}")) (|lookup| (((|PositiveInteger|) (|Vector| |#1|)) "\\spad{lookup(x)} \\undocumented{} See \\axiomFunFrom{lookup}{Finite}")) (|inv| (((|Vector| |#1|) (|Vector| |#1|)) "\\spad{inv x} \\undocumented{} See \\axiomFunFrom{inv}{DivisionRing}")) (|trace| (((|Vector| |#1|) (|Vector| |#1|) (|PositiveInteger|)) "\\spad{trace(x,n)} \\undocumented{} See \\axiomFunFrom{trace}{FiniteAlgebraicExtensionField}")) (|norm| (((|Vector| |#1|) (|Vector| |#1|) (|PositiveInteger|)) "\\spad{norm(x,n)} \\undocumented{} See \\axiomFunFrom{norm}{FiniteAlgebraicExtensionField}")) (/ (((|Vector| |#1|) (|Vector| |#1|) (|Vector| |#1|)) "\\spad{x/y} \\undocumented{} See \\axiomFunFrom{/}{Field}")) (* (((|Vector| |#1|) (|Vector| |#1|) (|Vector| |#1|)) "\\spad{x*y} \\undocumented{} See \\axiomFunFrom{*}{SemiGroup}")) (** (((|Vector| |#1|) (|Vector| |#1|) (|Integer|)) "\\spad{x**n} \\undocumented{} See \\axiomFunFrom{**}{DivisionRing}")) (|qPot| (((|Vector| |#1|) (|Vector| |#1|) (|Integer|)) "\\spad{qPot(v,e)} computes \\spad{v**(q**e)},{} interpreting \\spad{v} as an element of normal basis field,{} \\spad{q} the size of the ground field. This is done by a cyclic \\spad{e}-shift of the vector \\spad{v}.")) (|expPot| (((|Vector| |#1|) (|Vector| |#1|) (|SingleInteger|) (|SingleInteger|)) "\\spad{expPot(v,e,d)} returns the sum from \\spad{i = 0} to \\spad{e - 1} of \\spad{v**(q**i*d)},{} interpreting \\spad{v} as an element of a normal basis field and where \\spad{q} is the size of the ground field. Note: for a description of the algorithm,{} see \\spad{T}.Itoh and \\spad{S}.Tsujii,{} \"A fast algorithm for computing multiplicative inverses in GF(2^m) using normal bases\",{} Information and Computation 78,{} pp.171-177,{} 1988.")) (|repSq| (((|Vector| |#1|) (|Vector| |#1|) (|NonNegativeInteger|)) "\\spad{repSq(v,e)} computes \\spad{v**e} by repeated squaring,{} interpreting \\spad{v} as an element of a normal basis field.")) (|dAndcExp| (((|Vector| |#1|) (|Vector| |#1|) (|NonNegativeInteger|) (|SingleInteger|)) "\\spad{dAndcExp(v,n,k)} computes \\spad{v**e} interpreting \\spad{v} as an element of normal basis field. A divide and conquer algorithm similar to the one from \\spad{D}.\\spad{R}.Stinson,{} \"Some observations on parallel Algorithms for fast exponentiation in GF(2^n)\",{} Siam \\spad{J}. Computation,{} Vol.19,{} No.4,{} pp.711-717,{} August 1990 is used. Argument \\spad{k} is a parameter of this algorithm.")) (|xn| (((|SparseUnivariatePolynomial| |#1|) (|NonNegativeInteger|)) "\\spad{xn(n)} returns the polynomial \\spad{x**n-1}.")) (|pol| (((|SparseUnivariatePolynomial| |#1|) (|Vector| |#1|)) "\\spad{pol(v)} turns the vector \\spad{[v0,...,vn]} into the polynomial \\spad{v0+v1*x+ ... + vn*x**n}.")) (|index| (((|Vector| |#1|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{index(n,m)} is a index function for vectors of length \\spad{n} over the ground field.")) (|random| (((|Vector| |#1|) (|PositiveInteger|)) "\\spad{random(n)} creates a vector over the ground field with random entries.")) (|setFieldInfo| (((|Void|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) |#1|) "\\spad{setFieldInfo(m,p)} initializes the field arithmetic,{} where \\spad{m} is the multiplication table and \\spad{p} is the respective normal element of the ground field GF.")))
NIL
NIL
-(-467)
+(-468)
((|constructor| (NIL "This domain provides representation for binary files open for input operations. `Binary' here means that the conduits do not interpret their contents.")) (|position!| (((|SingleInteger|) $ (|SingleInteger|)) "position(\\spad{f},{}\\spad{p}) sets the current byte-position to `i'.")) (|position| (((|SingleInteger|) $) "\\spad{position(f)} returns the current byte-position in the file `f'.")) (|isOpen?| (((|Boolean|) $) "\\spad{isOpen?(ifile)} holds if `ifile' is in open state.")) (|eof?| (((|Boolean|) $) "\\spad{eof?(ifile)} holds when the last read reached end of file.")) (|inputBinaryFile| (($ (|String|)) "\\spad{inputBinaryFile(f)} returns an input conduit obtained by opening the file named by `f' as a binary file.") (($ (|FileName|)) "\\spad{inputBinaryFile(f)} returns an input conduit obtained by opening the file named by `f' as a binary file.")))
NIL
NIL
-(-468 R)
+(-469 R)
((|constructor| (NIL "This package provides operations to create incrementing functions.")) (|incrementBy| (((|Mapping| |#1| |#1|) |#1|) "\\spad{incrementBy(n)} produces a function which adds \\spad{n} to whatever argument it is given. For example,{} if {\\spad{f} := increment(\\spad{n})} then \\spad{f x} is \\spad{x+n}.")) (|increment| (((|Mapping| |#1| |#1|)) "\\spad{increment()} produces a function which adds \\spad{1} to whatever argument it is given. For example,{} if {\\spad{f} := increment()} then \\spad{f x} is \\spad{x+1}.")))
NIL
NIL
-(-469 |Varset|)
+(-470 |Varset|)
((|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
-((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| (-695) (QUOTE (-1013)))))
-(-470 K -3091 |Par|)
+((-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| (-696) (QUOTE (-1015)))))
+(-471 K -3094 |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 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
-(-471)
+(-472)
NIL
NIL
NIL
-(-472)
+(-473)
((|constructor| (NIL "Default infinity signatures for the interpreter; Date Created: 4 Oct 1989 Date Last Updated: 4 Oct 1989")) (|minusInfinity| (((|OrderedCompletion| (|Integer|))) "\\spad{minusInfinity()} returns minusInfinity.")) (|plusInfinity| (((|OrderedCompletion| (|Integer|))) "\\spad{plusInfinity()} returns plusIinfinity.")) (|infinity| (((|OnePointCompletion| (|Integer|))) "\\spad{infinity()} returns infinity.")))
NIL
NIL
-(-473)
+(-474)
((|constructor| (NIL "Domain of parsed forms which can be passed to the interpreter. This is also the interface between algebra code and facilities in the interpreter.")) (|compile| (((|Symbol|) (|Symbol|) (|List| $)) "\\spad{compile(f, [t1,...,tn])} forces the interpreter to compile the function \\spad{f} with signature \\spad{(t1,...,tn) -> ?}. returns the symbol \\spad{f} if successful. Error: if \\spad{f} was not defined beforehand in the interpreter,{} or if the \\spad{ti}'s are not valid types,{} or if the compiler fails.")) (|declare| (((|Symbol|) (|List| $)) "\\spad{declare(t)} returns a name \\spad{f} such that \\spad{f} has been declared to the interpreter to be of type \\spad{t},{} but has not been assigned a value yet. Note: \\spad{t} should be created as \\spad{devaluate(T)\\$Lisp} where \\spad{T} is the actual type of \\spad{f} (this hack is required for the case where \\spad{T} is a mapping type).")) (|parseString| (($ (|String|)) "parseString is the inverse of unparse. It parses a string to InputForm.")) (|unparse| (((|String|) $) "\\spad{unparse(f)} returns a string \\spad{s} such that the parser would transform \\spad{s} to \\spad{f}. Error: if \\spad{f} is not the parsed form of a string.")) (|flatten| (($ $) "\\spad{flatten(s)} returns an input form corresponding to \\spad{s} with all the nested operations flattened to triples using new local variables. If \\spad{s} is a piece of code,{} this speeds up the compilation tremendously later on.")) (|One| (($) "\\spad{1} returns the input form corresponding to 1.")) (|Zero| (($) "\\spad{0} returns the input form corresponding to 0.")) (** (($ $ (|Integer|)) "\\spad{a ** b} returns the input form corresponding to \\spad{a ** b}.") (($ $ (|NonNegativeInteger|)) "\\spad{a ** b} returns the input form corresponding to \\spad{a ** b}.")) (/ (($ $ $) "\\spad{a / b} returns the input form corresponding to \\spad{a / b}.")) (* (($ $ $) "\\spad{a * b} returns the input form corresponding to \\spad{a * b}.")) (+ (($ $ $) "\\spad{a + b} returns the input form corresponding to \\spad{a + b}.")) (|lambda| (($ $ (|List| (|Symbol|))) "\\spad{lambda(code, [x1,...,xn])} returns the input form corresponding to \\spad{(x1,...,xn) +-> code} if \\spad{n > 1},{} or to \\spad{x1 +-> code} if \\spad{n = 1}.")) (|function| (($ $ (|List| (|Symbol|)) (|Symbol|)) "\\spad{function(code, [x1,...,xn], f)} returns the input form corresponding to \\spad{f(x1,...,xn) == code}.")) (|binary| (($ $ (|List| $)) "\\spad{binary(op, [a1,...,an])} returns the input form corresponding to \\spad{a1 op a2 op ... op an}.")) (|convert| (($ (|SExpression|)) "\\spad{convert(s)} makes \\spad{s} into an input form.")) (|interpret| (((|Any|) $) "\\spad{interpret(f)} passes \\spad{f} to the interpreter.")))
NIL
NIL
-(-474 R)
+(-475 R)
((|constructor| (NIL "Tools for manipulating input forms.")) (|interpret| ((|#1| (|InputForm|)) "\\spad{interpret(f)} passes \\spad{f} to the interpreter,{} and transforms the result into an object of type \\spad{R}.")) (|packageCall| (((|InputForm|) (|Symbol|)) "\\spad{packageCall(f)} returns the input form corresponding to \\spad{f}\\$\\spad{R}.")))
NIL
NIL
-(-475 |Coef| UTS)
+(-476 |Coef| UTS)
((|constructor| (NIL "This package computes infinite products of univariate Taylor series over an integral domain of characteristic 0.")) (|generalInfiniteProduct| ((|#2| |#2| (|Integer|) (|Integer|)) "\\spad{generalInfiniteProduct(f(x),a,d)} computes \\spad{product(n=a,a+d,a+2*d,...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|oddInfiniteProduct| ((|#2| |#2|) "\\spad{oddInfiniteProduct(f(x))} computes \\spad{product(n=1,3,5...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|evenInfiniteProduct| ((|#2| |#2|) "\\spad{evenInfiniteProduct(f(x))} computes \\spad{product(n=2,4,6...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|infiniteProduct| ((|#2| |#2|) "\\spad{infiniteProduct(f(x))} computes \\spad{product(n=1,2,3...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")))
NIL
NIL
-(-476 K -3091 |Par|)
+(-477 K -3094 |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
-(-477 R BP |pMod| |nextMod|)
+(-478 R BP |pMod| |nextMod|)
((|reduction| ((|#2| |#2| |#1|) "\\spad{reduction(f,p)} reduces the coefficients of the polynomial \\spad{f} modulo the prime \\spad{p}.")) (|modularGcd| ((|#2| (|List| |#2|)) "\\spad{modularGcd(listf)} computes the gcd of the list of polynomials \\spad{listf} by modular methods.")) (|modularGcdPrimitive| ((|#2| (|List| |#2|)) "\\spad{modularGcdPrimitive(f1,f2)} computes the gcd of the two polynomials \\spad{f1} and \\spad{f2} by modular methods.")))
NIL
NIL
-(-478 OV E R P)
+(-479 OV E R P)
((|constructor| (NIL "\\indented{2}{This is an inner package for factoring multivariate polynomials} over various coefficient domains in characteristic 0. The univariate factor operation is passed as a parameter. Multivariate hensel lifting is used to lift the univariate factorization")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|) (|Mapping| (|Factored| (|SparseUnivariatePolynomial| |#3|)) (|SparseUnivariatePolynomial| |#3|))) "\\spad{factor(p,ufact)} factors the multivariate polynomial \\spad{p} by specializing variables and calling the univariate factorizer \\spad{ufact}. \\spad{p} is represented as a univariate polynomial with multivariate coefficients.") (((|Factored| |#4|) |#4| (|Mapping| (|Factored| (|SparseUnivariatePolynomial| |#3|)) (|SparseUnivariatePolynomial| |#3|))) "\\spad{factor(p,ufact)} factors the multivariate polynomial \\spad{p} by specializing variables and calling the univariate factorizer \\spad{ufact}.")))
NIL
NIL
-(-479 K UP |Coef| UTS)
+(-480 K UP |Coef| UTS)
((|constructor| (NIL "This package computes infinite products of univariate Taylor series over an arbitrary finite field.")) (|generalInfiniteProduct| ((|#4| |#4| (|Integer|) (|Integer|)) "\\spad{generalInfiniteProduct(f(x),a,d)} computes \\spad{product(n=a,a+d,a+2*d,...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|oddInfiniteProduct| ((|#4| |#4|) "\\spad{oddInfiniteProduct(f(x))} computes \\spad{product(n=1,3,5...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|evenInfiniteProduct| ((|#4| |#4|) "\\spad{evenInfiniteProduct(f(x))} computes \\spad{product(n=2,4,6...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|infiniteProduct| ((|#4| |#4|) "\\spad{infiniteProduct(f(x))} computes \\spad{product(n=1,2,3...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")))
NIL
NIL
-(-480 |Coef| UTS)
+(-481 |Coef| UTS)
((|constructor| (NIL "This package computes infinite products of univariate Taylor series over a field of prime order.")) (|generalInfiniteProduct| ((|#2| |#2| (|Integer|) (|Integer|)) "\\spad{generalInfiniteProduct(f(x),a,d)} computes \\spad{product(n=a,a+d,a+2*d,...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|oddInfiniteProduct| ((|#2| |#2|) "\\spad{oddInfiniteProduct(f(x))} computes \\spad{product(n=1,3,5...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|evenInfiniteProduct| ((|#2| |#2|) "\\spad{evenInfiniteProduct(f(x))} computes \\spad{product(n=2,4,6...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|infiniteProduct| ((|#2| |#2|) "\\spad{infiniteProduct(f(x))} computes \\spad{product(n=1,2,3...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")))
NIL
NIL
-(-481 R UP)
+(-482 R UP)
((|constructor| (NIL "Find the sign of a polynomial around a point or infinity.")) (|signAround| (((|Union| (|Integer|) #1="failed") |#2| |#1| (|Mapping| (|Union| (|Integer|) #1#) |#1|)) "\\spad{signAround(u,r,f)} \\undocumented") (((|Union| (|Integer|) #1#) |#2| |#1| (|Integer|) (|Mapping| (|Union| (|Integer|) #1#) |#1|)) "\\spad{signAround(u,r,i,f)} \\undocumented") (((|Union| (|Integer|) #1#) |#2| (|Integer|) (|Mapping| (|Union| (|Integer|) #1#) |#1|)) "\\spad{signAround(u,i,f)} \\undocumented")))
NIL
NIL
-(-482 S)
+(-483 S)
((|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|) $) "\\spad{odd?(n)} returns \\spad{true} if and only if \\spad{n} is odd.")))
NIL
NIL
-(-483)
+(-484)
((|constructor| (NIL "An \\spad{IntegerNumberSystem} is a model for the integers.")) (|invmod| (($ $ $) "\\spad{invmod(a,b)},{} \\spad{0<=a<b>1},{} \\spad{(a,b)=1} means \\spad{1/a mod b}.")) (|powmod| (($ $ $ $) "\\spad{powmod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a**b mod p}.")) (|mulmod| (($ $ $ $) "\\spad{mulmod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a*b mod p}.")) (|submod| (($ $ $ $) "\\spad{submod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a-b mod p}.")) (|addmod| (($ $ $ $) "\\spad{addmod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a+b mod p}.")) (|mask| (($ $) "\\spad{mask(n)} returns \\spad{2**n-1} (an \\spad{n} bit mask).")) (|dec| (($ $) "\\spad{dec(x)} returns \\spad{x - 1}.")) (|inc| (($ $) "\\spad{inc(x)} returns \\spad{x + 1}.")) (|copy| (($ $) "\\spad{copy(n)} gives a copy of \\spad{n}.")) (|random| (($ $) "\\spad{random(a)} creates a random element from 0 to \\spad{a-1}.") (($) "\\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.")))
-((-3990 . T) (-3991 . T) (-3985 . T) ((-3994 "*") . T) (-3986 . T) (-3987 . T) (-3989 . T))
+((-3994 . T) (-3995 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T))
NIL
-(-484)
+(-485)
((|constructor| (NIL "\\spadtype{Integer} provides the domain of arbitrary precision integers.")) (|noetherian| ((|attribute|) "ascending chain condition on ideals.")) (|canonicalsClosed| ((|attribute|) "two positives multiply to give positive.")) (|canonical| ((|attribute|) "mathematical equality is data structure equality.")))
-((-3980 . T) (-3984 . T) (-3979 . T) (-3990 . T) (-3991 . T) (-3985 . T) ((-3994 "*") . T) (-3986 . T) (-3987 . T) (-3989 . T))
+((-3984 . T) (-3988 . T) (-3983 . T) (-3994 . T) (-3995 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T))
NIL
-(-485)
+(-486)
((|constructor| (NIL "This domain is a datatype for (signed) integer values of precision 16 bits.")))
NIL
NIL
-(-486)
+(-487)
((|constructor| (NIL "This domain is a datatype for (signed) integer values of precision 32 bits.")))
NIL
NIL
-(-487)
+(-488)
((|constructor| (NIL "This domain is a datatype for (signed) integer values of precision 64 bits.")))
NIL
NIL
-(-488)
+(-489)
((|constructor| (NIL "This domain is a datatype for (signed) integer values of precision 8 bits.")))
NIL
NIL
-(-489 |Key| |Entry| |addDom|)
+(-490 |Key| |Entry| |addDom|)
((|constructor| (NIL "This domain is used to provide a conditional \"add\" domain for the implementation of \\spadtype{Table}.")))
-((-3992 . T) (-3993 . T))
-((-12 (|HasCategory| (-2 (|:| -3857 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -259) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3857) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3857 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3857 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3857 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3857 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| (-2 (|:| -3857 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-553 (-773))))) (|HasCategory| (-2 (|:| -3857 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-473)))) (-12 (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (|%list| (QUOTE -259) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3857 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-1013))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3857 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3857 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3857 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))))
-(-490 R -3091)
+((-3996 . T) (-3997 . T))
+((-12 (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3861) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1015)))) (OR (|HasCategory| |#2| (QUOTE (-1015))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1015)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1015))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1015)))) (OR (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-774)))) (|HasCategory| |#2| (QUOTE (-554 (-774))))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-555 (-474)))) (-12 (|HasCategory| |#2| (QUOTE (-1015))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1015))) (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| |#2| (QUOTE (-1015))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-554 (-774)))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-774)))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))))
+(-491 R -3094)
((|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
-(-491 R0 -3091 UP UPUP R)
+(-492 R0 -3094 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
-(-492)
+(-493)
((|constructor| (NIL "This package provides functions to lookup bits in integers")) (|bitTruth| (((|Boolean|) (|Integer|) (|Integer|)) "\\spad{bitTruth(n,m)} returns \\spad{true} if coefficient of 2**m in abs(\\spad{n}) is 1")) (|bitCoef| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{bitCoef(n,m)} returns the coefficient of 2**m in abs(\\spad{n})")) (|bitLength| (((|Integer|) (|Integer|)) "\\spad{bitLength(n)} returns the number of bits to represent abs(\\spad{n})")))
NIL
NIL
-(-493 R)
+(-494 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{sup}} or \\axiom{[\\spad{sup},{}in]} otherwise.")))
-((-3767 . T) (-3985 . T) ((-3994 "*") . T) (-3986 . T) (-3987 . T) (-3989 . T))
+((-3771 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T))
NIL
-(-494 S)
+(-495 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.")))
NIL
NIL
-(-495)
+(-496)
((|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.")))
-((-3985 . T) ((-3994 "*") . T) (-3986 . T) (-3987 . T) (-3989 . T))
+((-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T))
NIL
-(-496 R -3091)
+(-497 R -3094)
((|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|)) #1="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},{}...,{}kn (the \\spad{ki}'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}'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|)) #1#) |#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
-(-497 I)
+(-498 I)
((|constructor| (NIL "\\indented{1}{This Package contains basic methods for integer factorization.} The factor operation employs trial division up to 10,{}000. It then tests to see if \\spad{n} is a perfect power before using Pollards rho method. Because Pollards method may fail,{} the result of factor may contain composite factors. We should also employ Lenstra's eliptic curve method.")) (|PollardSmallFactor| (((|Union| |#1| "failed") |#1|) "\\spad{PollardSmallFactor(n)} returns a factor of \\spad{n} or \"failed\" if no one is found")) (|BasicMethod| (((|Factored| |#1|) |#1|) "\\spad{BasicMethod(n)} returns the factorization of integer \\spad{n} by trial division")) (|squareFree| (((|Factored| |#1|) |#1|) "\\spad{squareFree(n)} returns the square free factorization of integer \\spad{n}")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(n)} returns the full factorization of integer \\spad{n}")))
NIL
NIL
-(-498 R -3091 L)
+(-499 R -3094 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| #1="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| #1#)) (|:| |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| #2="failed") |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| #2#) |#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| #2#) |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| #2#) |#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|))))) #3="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}'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|))))) #3#) |#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}'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|)) #4="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|)) #4#) |#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 -601) (|devaluate| |#2|))))
-(-499)
+((|HasCategory| |#3| (|%list| (QUOTE -602) (|devaluate| |#2|))))
+(-500)
((|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
-(-500 -3091 UP UPUP R)
+(-501 -3094 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
-(-501 -3091 UP)
+(-502 -3094 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
-(-502 R -3091 L)
+(-503 R -3094 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| #1="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| #1#) |#2| |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| #1#) |#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}'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 -601) (|devaluate| |#2|))))
-(-503 R -3091)
+((|HasCategory| |#3| (|%list| (QUOTE -602) (|devaluate| |#2|))))
+(-504 R -3094)
((|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| (QUOTE (-554 (-801 (-484))))) (|HasCategory| |#1| (QUOTE (-797 (-484)))) (|HasCategory| |#2| (QUOTE (-1052)))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-484))))) (|HasCategory| |#1| (QUOTE (-797 (-484)))) (|HasCategory| |#2| (QUOTE (-570)))))
-(-504 -3091 UP)
+((-12 (|HasCategory| |#1| (QUOTE (-555 (-802 (-485))))) (|HasCategory| |#1| (QUOTE (-798 (-485)))) (|HasCategory| |#2| (QUOTE (-1054)))) (-12 (|HasCategory| |#1| (QUOTE (-555 (-802 (-485))))) (|HasCategory| |#1| (QUOTE (-798 (-485)))) (|HasCategory| |#2| (QUOTE (-571)))))
+(-505 -3094 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}'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
-(-505 S)
+(-506 S)
((|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
-(-506 -3091)
+(-507 -3094)
((|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}'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
-(-507 R)
+(-508 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.")))
-((-3767 . T) (-3985 . T) ((-3994 "*") . T) (-3986 . T) (-3987 . T) (-3989 . T))
+((-3771 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T))
NIL
-(-508)
+(-509)
((|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}'s exists.")))
NIL
NIL
-(-509 R -3091)
+(-510 R -3094)
((|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| (QUOTE (-554 (-801 (-484))))) (|HasCategory| |#1| (QUOTE (-389))) (|HasCategory| |#1| (QUOTE (-797 (-484)))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (QUOTE (-570))) (|HasCategory| |#2| (QUOTE (-951 (-1089))))) (-12 (|HasCategory| |#1| (QUOTE (-389))) (|HasCategory| |#2| (QUOTE (-239)))) (|HasCategory| |#1| (QUOTE (-495))))
-(-510 -3091 UP)
+((-12 (|HasCategory| |#1| (QUOTE (-555 (-802 (-485))))) (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-798 (-485)))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-952 (-1091))))) (-12 (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#2| (QUOTE (-239)))) (|HasCategory| |#1| (QUOTE (-496))))
+(-511 -3094 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|)) #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|)) #1#) |#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|)) #1#) |#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|)) #1#) |#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
-(-511 R -3091)
+(-512 R -3094)
((|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
-(-512)
+(-513)
((|constructor| (NIL "This category describes byte stream conduits supporting both input and output operations.")))
NIL
NIL
-(-513)
+(-514)
((|constructor| (NIL "\\indented{2}{This domain provides representation for binary files open} \\indented{2}{for input and output operations.} See Also: InputBinaryFile,{} OutputBinaryFile")) (|isOpen?| (((|Boolean|) $) "\\spad{isOpen?(f)} holds if `f' is in open state.")) (|inputOutputBinaryFile| (($ (|String|)) "\\spad{inputOutputBinaryFile(f)} returns an input/output conduit obtained by opening the file named by `f' as a binary file.") (($ (|FileName|)) "\\spad{inputOutputBinaryFile(f)} returns an input/output conduit obtained by opening the file designated by `f' as a binary file.")))
NIL
NIL
-(-514)
+(-515)
((|constructor| (NIL "This domain provides constants to describe directions of IO conduits (file,{} etc) mode of operations.")) (|closed| (($) "\\spad{closed} indicates that the IO conduit has been closed.")) (|bothWays| (($) "\\spad{bothWays} indicates that an IO conduit is for both input and output.")) (|output| (($) "\\spad{output} indicates that an IO conduit is for output")) (|input| (($) "\\spad{input} indicates that an IO conduit is for input.")))
NIL
NIL
-(-515)
+(-516)
((|constructor| (NIL "This domain provides representation for ARPA Internet \\spad{IP4} addresses.")) (|resolve| (((|Maybe| $) (|Hostname|)) "\\spad{resolve(h)} returns the \\spad{IP4} address of host `h'.")) (|bytes| (((|DataArray| 4 (|Byte|)) $) "\\spad{bytes(x)} returns the bytes of the numeric address `x'.")) (|ip4Address| (($ (|String|)) "\\spad{ip4Address(a)} builds a numeric address out of the ASCII form `a'.")))
NIL
NIL
-(-516 |p| |unBalanced?|)
+(-517 |p| |unBalanced?|)
((|constructor| (NIL "This domain implements Zp,{} the \\spad{p}-adic completion of the integers. This is an internal domain.")))
-((-3985 . T) ((-3994 "*") . T) (-3986 . T) (-3987 . T) (-3989 . T))
+((-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T))
NIL
-(-517 |p|)
+(-518 |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.")))
-((-3984 . T) (-3990 . T) (-3985 . T) ((-3994 "*") . T) (-3986 . T) (-3987 . T) (-3989 . T))
-((|HasCategory| $ (QUOTE (-120))) (|HasCategory| $ (QUOTE (-118))) (|HasCategory| $ (QUOTE (-317))))
-(-518)
+((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T))
+((|HasCategory| $ (QUOTE (-120))) (|HasCategory| $ (QUOTE (-118))) (|HasCategory| $ (QUOTE (-318))))
+(-519)
((|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
-(-519 -3091)
+(-520 -3094)
((|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 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}.")))
-((-3987 . T) (-3986 . T))
-((|HasCategory| |#1| (QUOTE (-810 (-1089)))) (|HasCategory| |#1| (QUOTE (-951 (-1089)))))
-(-520 E -3091)
+((-3991 . T) (-3990 . T))
+((|HasCategory| |#1| (QUOTE (-811 (-1091)))) (|HasCategory| |#1| (QUOTE (-952 (-1091)))))
+(-521 E -3094)
((|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
-(-521 R -3091)
+(-522 R -3094)
((|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},{}...,{}Pn are the factors of \\spad{P}.")))
NIL
NIL
-(-522)
+(-523)
((|constructor| (NIL "This domain provides representations for the intermediate form data structure used by the Spad elaborator.")) (|irDef| (($ (|Identifier|) (|InternalTypeForm|) $) "\\spad{irDef(f,ts,e)} returns an IR representation for a definition of a function named \\spad{f},{} with signature \\spad{ts} and body \\spad{e}.")) (|irCtor| (($ (|Identifier|) (|InternalTypeForm|)) "\\spad{irCtor(n,t)} returns an IR for a constructor reference of type designated by the type form \\spad{t}")) (|irVar| (($ (|Identifier|) (|InternalTypeForm|)) "\\spad{irVar(x,t)} returns an IR for a variable reference of type designated by the type form \\spad{t}")))
NIL
NIL
-(-523 I)
+(-524 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
NIL
-(-524 GF)
+(-525 GF)
((|constructor| (NIL "This package exports the function generateIrredPoly that computes a monic irreducible polynomial of degree \\spad{n} over a finite field.")) (|generateIrredPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{generateIrredPoly(n)} generates an irreducible univariate polynomial of the given degree \\spad{n} over the finite field.")))
NIL
NIL
-(-525 R)
+(-526 R)
((|constructor| (NIL "\\indented{2}{This package allows a sum of logs over the roots of a polynomial} \\indented{2}{to be expressed as explicit logarithms and arc tangents,{} provided} \\indented{2}{that the indexing polynomial can be factored into quadratics.} Date Created: 21 August 1988 Date Last Updated: 4 October 1993")) (|complexIntegrate| (((|Expression| |#1|) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{complexIntegrate(f, x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable.")) (|integrate| (((|Union| (|Expression| |#1|) (|List| (|Expression| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{integrate(f, x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a real variable..")) (|complexExpand| (((|Expression| |#1|) (|IntegrationResult| (|Fraction| (|Polynomial| |#1|)))) "\\spad{complexExpand(i)} returns the expanded complex function corresponding to \\spad{i}.")) (|expand| (((|List| (|Expression| |#1|)) (|IntegrationResult| (|Fraction| (|Polynomial| |#1|)))) "\\spad{expand(i)} returns the list of possible real functions corresponding to \\spad{i}.")) (|split| (((|IntegrationResult| (|Fraction| (|Polynomial| |#1|))) (|IntegrationResult| (|Fraction| (|Polynomial| |#1|)))) "\\spad{split(u(x) + sum_{P(a)=0} Q(a,x))} returns \\spad{u(x) + sum_{P1(a)=0} Q(a,x) + ... + sum_{Pn(a)=0} Q(a,x)} where \\spad{P1},{}...,{}Pn are the factors of \\spad{P}.")))
NIL
((|HasCategory| |#1| (QUOTE (-120))))
-(-526)
+(-527)
((|constructor| (NIL "IrrRepSymNatPackage contains functions for computing the ordinary irreducible representations of symmetric groups on \\spad{n} letters {\\em {1,2,...,n}} in Young's natural form and their dimensions. These representations can be labelled by number partitions of \\spad{n},{} \\spadignore{i.e.} a weakly decreasing sequence of integers summing up to \\spad{n},{} \\spadignore{e.g.} {\\em [3,3,3,1]} labels an irreducible representation for \\spad{n} equals 10. Note: whenever a \\spadtype{List Integer} appears in a signature,{} a partition required.")) (|irreducibleRepresentation| (((|List| (|Matrix| (|Integer|))) (|List| (|PositiveInteger|)) (|List| (|Permutation| (|Integer|)))) "\\spad{irreducibleRepresentation(lambda,listOfPerm)} is the list of the irreducible representations corresponding to {\\em lambda} in Young's natural form for the list of permutations given by {\\em listOfPerm}.") (((|List| (|Matrix| (|Integer|))) (|List| (|PositiveInteger|))) "\\spad{irreducibleRepresentation(lambda)} is the list of the two irreducible representations corresponding to the partition {\\em lambda} in Young's natural form for the following two generators of the symmetric group,{} whose elements permute {\\em {1,2,...,n}},{} namely {\\em (1 2)} (2-cycle) and {\\em (1 2 ... n)} (\\spad{n}-cycle).") (((|Matrix| (|Integer|)) (|List| (|PositiveInteger|)) (|Permutation| (|Integer|))) "\\spad{irreducibleRepresentation(lambda,pi)} is the irreducible representation corresponding to partition {\\em lambda} in Young's natural form of the permutation {\\em pi} in the symmetric group,{} whose elements permute {\\em {1,2,...,n}}.")) (|dimensionOfIrreducibleRepresentation| (((|NonNegativeInteger|) (|List| (|PositiveInteger|))) "\\spad{dimensionOfIrreducibleRepresentation(lambda)} is the dimension of the ordinary irreducible representation of the symmetric group corresponding to {\\em lambda}. Note: the Robinson-Thrall hook formula is implemented.")))
NIL
NIL
-(-527 R E V P TS)
+(-528 R E V P TS)
((|constructor| (NIL "\\indented{1}{An internal package for computing the rational univariate representation} \\indented{1}{of a zero-dimensional algebraic variety given by a square-free} \\indented{1}{triangular set.} \\indented{1}{The main operation is \\axiomOpFrom{rur}{InternalRationalUnivariateRepresentationPackage}.} \\indented{1}{It is based on the {\\em generic} algorithm description in [1]. \\newline References:} [1] \\spad{D}. LAZARD \"Solving Zero-dimensional Algebraic Systems\" \\indented{4}{Journal of Symbolic Computation,{} 1992,{} 13,{} 117-131}")) (|checkRur| (((|Boolean|) |#5| (|List| |#5|)) "\\spad{checkRur(ts,lus)} returns \\spad{true} if \\spad{lus} is a rational univariate representation of \\spad{ts}.")) (|rur| (((|List| |#5|) |#5| (|Boolean|)) "\\spad{rur(ts,univ?)} returns a rational univariate representation of \\spad{ts}. This assumes that the lowest polynomial in \\spad{ts} is a variable \\spad{v} which does not occur in the other polynomials of \\spad{ts}. This variable will be used to define the simple algebraic extension over which these other polynomials will be rewritten as univariate polynomials with degree one. If \\spad{univ?} is \\spad{true} then these polynomials will have a constant initial.")))
NIL
NIL
-(-528)
+(-529)
((|constructor| (NIL "This domain represents a `has' expression.")) (|rhs| (((|SpadAst|) $) "\\spad{rhs(e)} returns the right hand side of the is expression `e'.")) (|lhs| (((|SpadAst|) $) "\\spad{lhs(e)} returns the left hand side of the is expression `e'.")))
NIL
NIL
-(-529 E V R P)
+(-530 E V R P)
((|constructor| (NIL "tools for the summation packages.")) (|sum| (((|Record| (|:| |num| |#4|) (|:| |den| (|Integer|))) |#4| |#2|) "\\spad{sum(p(n), n)} returns \\spad{P(n)},{} the indefinite sum of \\spad{p(n)} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{P(n+1) - P(n) = a(n)}.") (((|Record| (|:| |num| |#4|) (|:| |den| (|Integer|))) |#4| |#2| (|Segment| |#4|)) "\\spad{sum(p(n), n = a..b)} returns \\spad{p(a) + p(a+1) + ... + p(b)}.")))
NIL
NIL
-(-530 |Coef|)
-((|constructor| (NIL "InnerSparseUnivariatePowerSeries is an internal domain \\indented{2}{used for creating sparse Taylor and Laurent series.}")) (|cAcsch| (($ $) "\\spad{cAcsch(f)} computes the inverse hyperbolic cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsech| (($ $) "\\spad{cAsech(f)} computes the inverse hyperbolic secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcoth| (($ $) "\\spad{cAcoth(f)} computes the inverse hyperbolic cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAtanh| (($ $) "\\spad{cAtanh(f)} computes the inverse hyperbolic tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcosh| (($ $) "\\spad{cAcosh(f)} computes the inverse hyperbolic cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsinh| (($ $) "\\spad{cAsinh(f)} computes the inverse hyperbolic sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCsch| (($ $) "\\spad{cCsch(f)} computes the hyperbolic cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSech| (($ $) "\\spad{cSech(f)} computes the hyperbolic secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCoth| (($ $) "\\spad{cCoth(f)} computes the hyperbolic cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cTanh| (($ $) "\\spad{cTanh(f)} computes the hyperbolic tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCosh| (($ $) "\\spad{cCosh(f)} computes the hyperbolic cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSinh| (($ $) "\\spad{cSinh(f)} computes the hyperbolic sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcsc| (($ $) "\\spad{cAcsc(f)} computes the arccosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsec| (($ $) "\\spad{cAsec(f)} computes the arcsecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcot| (($ $) "\\spad{cAcot(f)} computes the arccotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAtan| (($ $) "\\spad{cAtan(f)} computes the arctangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcos| (($ $) "\\spad{cAcos(f)} computes the arccosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsin| (($ $) "\\spad{cAsin(f)} computes the arcsine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCsc| (($ $) "\\spad{cCsc(f)} computes the cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSec| (($ $) "\\spad{cSec(f)} computes the secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCot| (($ $) "\\spad{cCot(f)} computes the cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cTan| (($ $) "\\spad{cTan(f)} computes the tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCos| (($ $) "\\spad{cCos(f)} computes the cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSin| (($ $) "\\spad{cSin(f)} computes the sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cLog| (($ $) "\\spad{cLog(f)} computes the logarithm of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cExp| (($ $) "\\spad{cExp(f)} computes the exponential of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cRationalPower| (($ $ (|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}.")))
-(((-3994 "*") |has| |#1| (-146)) (-3985 |has| |#1| (-495)) (-3986 . T) (-3987 . T) (-3989 . T))
-((|HasCategory| |#1| (QUOTE (-38 (-347 (-484))))) (|HasCategory| |#1| (QUOTE (-495))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-495)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-810 (-1089)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-484)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-484)) (|devaluate| |#1|)))) (|HasCategory| (-484) (QUOTE (-1025))) (|HasCategory| |#1| (QUOTE (-311))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-484))))) (|HasSignature| |#1| (|%list| (QUOTE -3943) (|%list| (|devaluate| |#1|) (QUOTE (-1089)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-484))))))
(-531 |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}.")))
+(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3990 . T) (-3991 . T) (-3993 . T))
+((|HasCategory| |#1| (QUOTE (-38 (-348 (-485))))) (|HasCategory| |#1| (QUOTE (-496))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-811 (-1091)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-485)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-485)) (|devaluate| |#1|)))) (|HasCategory| (-485) (QUOTE (-1027))) (|HasCategory| |#1| (QUOTE (-312))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-485))))) (|HasSignature| |#1| (|%list| (QUOTE -3947) (|%list| (|devaluate| |#1|) (QUOTE (-1091)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-485))))))
+(-532 |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|) $) "\\spad{coefficients(x)} returns a stream of ring elements. \\indented{1}{When \\spad{x} is a univariate series,{} this is a stream of Taylor} \\indented{1}{coefficients. When \\spad{x} is a multivariate series,{} the} \\indented{1}{\\spad{n}th element of the stream is a form of} \\indented{1}{degree \\spad{n} in the power series variables.}")))
-(((-3994 "*") |has| |#1| (-495)) (-3985 |has| |#1| (-495)) (-3986 . T) (-3987 . T) (-3989 . T))
-((|HasCategory| |#1| (QUOTE (-495))))
-(-532)
+(((-3998 "*") |has| |#1| (-496)) (-3989 |has| |#1| (-496)) (-3990 . T) (-3991 . T) (-3993 . T))
+((|HasCategory| |#1| (QUOTE (-496))))
+(-533)
((|constructor| (NIL "This domain provides representations for internal type form.")) (|mappingMode| (($ $ (|List| $)) "\\spad{mappingMode(r,ts)} returns a mapping mode with return mode \\spad{r},{} and parameter modes \\spad{ts}.")) (|categoryMode| (($) "\\spad{categoryMode} is a constant mode denoting Category.")) (|voidMode| (($) "\\spad{voidMode} is a constant mode denoting Void.")) (|noValueMode| (($) "\\spad{noValueMode} is a constant mode that indicates that the value of an expression is to be ignored.")) (|jokerMode| (($) "\\spad{jokerMode} is a constant that stands for any mode in a type inference context")))
NIL
NIL
-(-533 A B)
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((|constructor| (NIL "Functions defined on streams with entries in two sets.")) (|map| (((|InfiniteTuple| |#2|) (|Mapping| |#2| |#1|) (|InfiniteTuple| |#1|)) "\\spad{map(f,[x0,x1,x2,...])} returns \\spad{[f(x0),f(x1),f(x2),..]}.")))
NIL
NIL
-(-534 A B C)
+(-535 A B C)
((|constructor| (NIL "Functions defined on streams with entries in two sets.")) (|map| (((|Stream| |#3|) (|Mapping| |#3| |#1| |#2|) (|InfiniteTuple| |#1|) (|Stream| |#2|)) "\\spad{map(f,a,b)} \\undocumented") (((|Stream| |#3|) (|Mapping| |#3| |#1| |#2|) (|Stream| |#1|) (|InfiniteTuple| |#2|)) "\\spad{map(f,a,b)} \\undocumented") (((|InfiniteTuple| |#3|) (|Mapping| |#3| |#1| |#2|) (|InfiniteTuple| |#1|) (|InfiniteTuple| |#2|)) "\\spad{map(f,a,b)} \\undocumented")))
NIL
NIL
-(-535 R -3091 FG)
+(-536 R -3094 FG)
((|constructor| (NIL "This package provides transformations from trigonometric functions to exponentials and logarithms,{} and back. \\spad{F} and 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
-(-536 S)
+(-537 S)
((|constructor| (NIL "This package implements 'infinite tuples' for the interpreter. The representation is a stream.")) (|construct| (((|Stream| |#1|) $) "\\spad{construct(t)} converts an infinite tuple to a stream.")) (|generate| (($ (|Mapping| |#1| |#1|) |#1|) "\\spad{generate(f,s)} returns \\spad{[s,f(s),f(f(s)),...]}.")) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select(p,t)} returns \\spad{[x for x in t | p(x)]}.")) (|filterUntil| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterUntil(p,t)} returns \\spad{[x for x in t while not p(x)]}.")) (|filterWhile| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterWhile(p,t)} returns \\spad{[x for x in t while p(x)]}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,t)} replaces the tuple \\spad{t} by \\spad{[f(x) for x in t]}.")))
NIL
NIL
-(-537 R |mn|)
+(-538 R |mn|)
((|constructor| (NIL "\\indented{2}{This type represents vector like objects with varying lengths} and a user-specified initial index.")))
-((-3993 . T) (-3992 . T))
-((OR (-12 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-554 (-473)))) (OR (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-757))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| (-484) (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-664))) (|HasCategory| |#1| (QUOTE (-962))) (-12 (|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| |#1| (QUOTE (-962)))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))))
-(-538 S |Index| |Entry|)
+((-3997 . T) (-3996 . T))
+((OR (-12 (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-554 (-774)))) (|HasCategory| |#1| (QUOTE (-555 (-474)))) (OR (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| |#1| (QUOTE (-758))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| (-485) (QUOTE (-758))) (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-665))) (|HasCategory| |#1| (QUOTE (-963))) (-12 (|HasCategory| |#1| (QUOTE (-917))) (|HasCategory| |#1| (QUOTE (-963)))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))))
+(-539 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 -3993)) (|HasCategory| |#2| (QUOTE (-757))) (|HasAttribute| |#1| (QUOTE -3992)) (|HasCategory| |#3| (QUOTE (-1013))))
-(-539 |Index| |Entry|)
+((|HasAttribute| |#1| (QUOTE -3997)) (|HasCategory| |#2| (QUOTE (-758))) (|HasAttribute| |#1| (QUOTE -3996)) (|HasCategory| |#3| (QUOTE (-1015))))
+(-540 |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
NIL
-(-540)
+(-541)
((|constructor| (NIL "This domain represents the join of categories ASTs.")) (|categories| (((|List| (|TypeAst|)) $) "catehories(\\spad{x}) returns the types in the join `x'.")) (|coerce| (($ (|List| (|TypeAst|))) "ts::JoinAst construct the AST for a join of the types `ts'.")))
NIL
NIL
-(-541 R A)
+(-542 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).")))
-((-3989 OR (-2561 (|has| |#2| (-315 |#1|)) (|has| |#1| (-495))) (-12 (|has| |#2| (-358 |#1|)) (|has| |#1| (-495)))) (-3987 . T) (-3986 . T))
-((OR (|HasCategory| |#2| (|%list| (QUOTE -315) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -358) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -358) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#2| (|%list| (QUOTE -358) (|devaluate| |#1|)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#2| (|%list| (QUOTE -315) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#2| (|%list| (QUOTE -358) (|devaluate| |#1|))))) (|HasCategory| |#2| (|%list| (QUOTE -315) (|devaluate| |#1|))))
-(-542)
+((-3993 OR (-2564 (|has| |#2| (-316 |#1|)) (|has| |#1| (-496))) (-12 (|has| |#2| (-359 |#1|)) (|has| |#1| (-496)))) (-3991 . T) (-3990 . T))
+((OR (|HasCategory| |#2| (|%list| (QUOTE -316) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -359) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -359) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (|%list| (QUOTE -359) (|devaluate| |#1|)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#2| (|%list| (QUOTE -316) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#2| (|%list| (QUOTE -359) (|devaluate| |#1|))))) (|HasCategory| |#2| (|%list| (QUOTE -316) (|devaluate| |#1|))))
+(-543)
((|constructor| (NIL "This is the datatype for the JVM bytecodes.")))
NIL
NIL
-(-543)
+(-544)
((|constructor| (NIL "JVM class file access bitmask and values.")) (|jvmAbstract| (($) "The class was declared abstract; therefore object of this class may not be created.")) (|jvmInterface| (($) "The class file represents an interface,{} not a class.")) (|jvmSuper| (($) "Instruct the JVM to treat base clss method invokation specially.")) (|jvmFinal| (($) "The class was declared final; therefore no derived class allowed.")) (|jvmPublic| (($) "The class was declared public,{} therefore may be accessed from outside its package")))
NIL
NIL
-(-544)
+(-545)
((|constructor| (NIL "JVM class file constant pool tags.")) (|jvmNameAndTypeConstantTag| (($) "The correspondong constant pool entry represents the name and type of a field or method info.")) (|jvmInterfaceMethodConstantTag| (($) "The correspondong constant pool entry represents an interface method info.")) (|jvmMethodrefConstantTag| (($) "The correspondong constant pool entry represents a class method info.")) (|jvmFieldrefConstantTag| (($) "The corresponding constant pool entry represents a class field info.")) (|jvmStringConstantTag| (($) "The corresponding constant pool entry is a string constant info.")) (|jvmClassConstantTag| (($) "The corresponding constant pool entry represents a class or and interface.")) (|jvmDoubleConstantTag| (($) "The corresponding constant pool entry is a double constant info.")) (|jvmLongConstantTag| (($) "The corresponding constant pool entry is a long constant info.")) (|jvmFloatConstantTag| (($) "The corresponding constant pool entry is a float constant info.")) (|jvmIntegerConstantTag| (($) "The corresponding constant pool entry is an integer constant info.")) (|jvmUTF8ConstantTag| (($) "The corresponding constant pool entry is sequence of bytes representing Java \\spad{UTF8} string constant.")))
NIL
NIL
-(-545)
+(-546)
((|constructor| (NIL "JVM class field access bitmask and values.")) (|jvmTransient| (($) "The field was declared transient.")) (|jvmVolatile| (($) "The field was declared volatile.")) (|jvmFinal| (($) "The field was declared final; therefore may not be modified after initialization.")) (|jvmStatic| (($) "The field was declared static.")) (|jvmProtected| (($) "The field was declared protected; therefore may be accessed withing derived classes.")) (|jvmPrivate| (($) "The field was declared private; threfore can be accessed only within the defining class.")) (|jvmPublic| (($) "The field was declared public; therefore mey accessed from outside its package.")))
NIL
NIL
-(-546)
+(-547)
((|constructor| (NIL "JVM class method access bitmask and values.")) (|jvmStrict| (($) "The method was declared fpstrict; therefore floating-point mode is FP-strict.")) (|jvmAbstract| (($) "The method was declared abstract; therefore no implementation is provided.")) (|jvmNative| (($) "The method was declared native; therefore implemented in a language other than Java.")) (|jvmSynchronized| (($) "The method was declared synchronized.")) (|jvmFinal| (($) "The method was declared final; therefore may not be overriden. in derived classes.")) (|jvmStatic| (($) "The method was declared static.")) (|jvmProtected| (($) "The method was declared protected; therefore may be accessed withing derived classes.")) (|jvmPrivate| (($) "The method was declared private; threfore can be accessed only within the defining class.")) (|jvmPublic| (($) "The method was declared public; therefore mey accessed from outside its package.")))
NIL
NIL
-(-547)
+(-548)
((|constructor| (NIL "This is the datatype for the JVM opcodes.")))
NIL
NIL
-(-548 |Entry|)
+(-549 |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.")))
-((-3992 . T) (-3993 . T))
-((-12 (|HasCategory| (-2 (|:| -3857 (-1072)) (|:| |entry| |#1|)) (|%list| (QUOTE -259) (|%list| (QUOTE -2) (QUOTE (|:| -3857 (-1072))) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -3857 (-1072)) (|:| |entry| |#1|)) (QUOTE (-1013)))) (|HasCategory| (-2 (|:| -3857 (-1072)) (|:| |entry| |#1|)) (QUOTE (-554 (-473)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| (-1072) (QUOTE (-757))) (|HasCategory| (-2 (|:| -3857 (-1072)) (|:| |entry| |#1|)) (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3857 (-1072)) (|:| |entry| |#1|)) (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3857 (-1072)) (|:| |entry| |#1|)) (QUOTE (-72))))
-(-549 S |Key| |Entry|)
+((-3996 . T) (-3997 . T))
+((-12 (|HasCategory| (-2 (|:| -3861 (-1074)) (|:| |entry| |#1|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (QUOTE (|:| -3861 (-1074))) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -3861 (-1074)) (|:| |entry| |#1|)) (QUOTE (-1015)))) (|HasCategory| (-2 (|:| -3861 (-1074)) (|:| |entry| |#1|)) (QUOTE (-555 (-474)))) (-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| (-1074) (QUOTE (-758))) (|HasCategory| (-2 (|:| -3861 (-1074)) (|:| |entry| |#1|)) (QUOTE (-1015))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-554 (-774)))) (|HasCategory| (-2 (|:| -3861 (-1074)) (|:| |entry| |#1|)) (QUOTE (-554 (-774)))) (|HasCategory| (-2 (|:| -3861 (-1074)) (|:| |entry| |#1|)) (QUOTE (-72))))
+(-550 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
-(-550 |Key| |Entry|)
+(-551 |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}.")))
-((-3993 . T))
+((-3997 . T))
NIL
-(-551 S)
+(-552 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| (QUOTE (-554 (-473)))) (|HasCategory| |#1| (QUOTE (-554 (-801 (-327))))) (|HasCategory| |#1| (QUOTE (-554 (-801 (-484))))))
-(-552 R S)
+((|HasCategory| |#1| (QUOTE (-555 (-474)))) (|HasCategory| |#1| (QUOTE (-555 (-802 (-328))))) (|HasCategory| |#1| (QUOTE (-555 (-802 (-485))))))
+(-553 R S)
((|constructor| (NIL "This package exports some auxiliary functions on kernels")) (|constantIfCan| (((|Union| |#1| "failed") (|Kernel| |#2|)) "\\spad{constantIfCan(k)} \\undocumented")) (|constantKernel| (((|Kernel| |#2|) |#1|) "\\spad{constantKernel(r)} \\undocumented")))
NIL
NIL
-(-553 S)
+(-554 S)
((|constructor| (NIL "A is coercible to \\spad{B} means any element of A can automatically be converted into an element of \\spad{B} by the interpreter.")) (|coerce| ((|#1| $) "\\spad{coerce(a)} transforms a into an element of \\spad{S}.")))
NIL
NIL
-(-554 S)
+(-555 S)
((|constructor| (NIL "A is convertible to \\spad{B} means any element of A can be converted into an element of \\spad{B},{} but not automatically by the interpreter.")) (|convert| ((|#1| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}.")))
NIL
NIL
-(-555 -3091 UP)
+(-556 -3094 UP)
((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic's algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,a_1,a_2,ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$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
-(-556 S)
+(-557 S)
((|constructor| (NIL "A is coercible from \\spad{B} iff any element of domain \\spad{B} can be automically converted into an element of domain A.")) (|coerce| (($ |#1|) "\\spad{coerce(s)} transforms `s' into an element of `\\%'.")))
NIL
NIL
-(-557)
+(-558)
((|constructor| (NIL "This domain implements Kleene's 3-valued propositional logic.")) (|case| (((|Boolean|) $ (|[\|\|]| |true|)) "\\spad{s case true} holds if the value of `x' is `true'.") (((|Boolean|) $ (|[\|\|]| |unknown|)) "\\spad{x case unknown} holds if the value of `x' is `unknown'") (((|Boolean|) $ (|[\|\|]| |false|)) "\\spad{x case false} holds if the value of `x' is `false'")) (|unknown| (($) "the indefinite `unknown'")))
NIL
NIL
-(-558 S)
+(-559 S)
((|constructor| (NIL "A is convertible from \\spad{B} iff any element of domain \\spad{B} can be explicitly converted into an element of domain A.")) (|convert| (($ |#1|) "\\spad{convert(s)} transforms `s' into an element of `\\%'.")))
NIL
NIL
-(-559 A R S)
+(-560 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}.")))
-((-3986 . T) (-3987 . T) (-3989 . T))
-((|HasCategory| |#1| (QUOTE (-756))))
-(-560 S R)
+((-3990 . T) (-3991 . T) (-3993 . T))
+((|HasCategory| |#1| (QUOTE (-757))))
+(-561 S R)
((|constructor| (NIL "The category of all left algebras over an arbitrary ring.")) (|coerce| (($ |#2|) "\\spad{coerce(r)} returns \\spad{r} * 1 where 1 is the identity of the left algebra.")))
NIL
NIL
-(-561 R)
+(-562 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.")))
-((-3989 . T))
+((-3993 . T))
NIL
-(-562 R -3091)
+(-563 R -3094)
((|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
-(-563 R UP)
+(-564 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")))
-((-3987 . T) (-3986 . T) ((-3994 "*") . T) (-3985 . T) (-3989 . T))
-((|HasCategory| |#2| (QUOTE (-810 (-1089)))) (|HasCategory| |#2| (QUOTE (-812 (-1089)))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-951 (-347 (-484))))) (|HasCategory| |#1| (QUOTE (-951 (-484)))))
-(-564 R E V P TS ST)
+((-3991 . T) (-3990 . T) ((-3998 "*") . T) (-3989 . T) (-3993 . T))
+((|HasCategory| |#2| (QUOTE (-811 (-1091)))) (|HasCategory| |#2| (QUOTE (-813 (-1091)))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-952 (-348 (-485))))) (|HasCategory| |#1| (QUOTE (-952 (-485)))))
+(-565 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(lp,{}clos?)} has the same specifications as \\axiomOpFrom{zeroSetSplit(lp,{}clos?)}{RegularTriangularSetCategory}.")) (|normalizeIfCan| ((|#6| |#6|) "\\axiom{normalizeIfCan(ts)} returns \\axiom{ts} in an normalized shape if \\axiom{ts} is zero-dimensional.")))
NIL
NIL
-(-565 OV E Z P)
+(-566 OV E Z P)
((|constructor| (NIL "Package for leading coefficient determination in the lifting step. Package working for every \\spad{R} euclidean with property \"F\".")) (|distFact| (((|Union| (|Record| (|:| |polfac| (|List| |#4|)) (|:| |correct| |#3|) (|:| |corrfact| (|List| (|SparseUnivariatePolynomial| |#3|)))) "failed") |#3| (|List| (|SparseUnivariatePolynomial| |#3|)) (|Record| (|:| |contp| |#3|) (|:| |factors| (|List| (|Record| (|:| |irr| |#4|) (|:| |pow| (|Integer|)))))) (|List| |#3|) (|List| |#1|) (|List| |#3|)) "\\spad{distFact(contm,unilist,plead,vl,lvar,lval)},{} where \\spad{contm} is the content of the evaluated polynomial,{} \\spad{unilist} is the list of factors of the evaluated polynomial,{} \\spad{plead} is the complete factorization of the leading coefficient,{} \\spad{vl} is the list of factors of the leading coefficient evaluated,{} \\spad{lvar} is the list of variables,{} \\spad{lval} is the list of values,{} returns a record giving the list of leading coefficients to impose on the univariate factors,{}")) (|polCase| (((|Boolean|) |#3| (|NonNegativeInteger|) (|List| |#3|)) "\\spad{polCase(contprod, numFacts, evallcs)},{} where \\spad{contprod} is the product of the content of the leading coefficient of the polynomial to be factored with the content of the evaluated polynomial,{} \\spad{numFacts} is the number of factors of the leadingCoefficient,{} and evallcs is the list of the evaluated factors of the leadingCoefficient,{} returns \\spad{true} if the factors of the leading Coefficient can be distributed with this valuation.")))
NIL
NIL
-(-566)
+(-567)
((|constructor| (NIL "This domain represents assignment expressions.")) (|rhs| (((|SpadAst|) $) "\\spad{rhs(e)} returns the right hand side of the assignment expression `e'.")) (|lhs| (((|SpadAst|) $) "\\spad{lhs(e)} returns the left hand side of the assignment expression `e'.")))
NIL
NIL
-(-567 |VarSet| R |Order|)
+(-568 |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.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(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}}.")))
-((-3989 . T))
+((-3993 . T))
NIL
-(-568 R |ls|)
+(-569 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(lp,{} norm?)} decomposes the variety associated with \\axiom{lp} into square-free regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{lp} needs to generate a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.") (((|List| (|RegularChain| |#1| |#2|)) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{zeroSetSplit(lp,{} norm?)} decomposes the variety associated with \\axiom{lp} into regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{lp} needs to generate a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\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(lp)} returns the lexicographical Groebner basis of \\axiom{lp}. If \\axiom{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(lp)} returns the lexicographical Groebner basis of \\axiom{lp} by using the {\\em FGLM} strategy,{} if \\axiom{zeroDimensional?(lp)} holds .")) (|zeroDimensional?| (((|Boolean|) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) "\\axiom{zeroDimensional?(lp)} returns \\spad{true} iff \\axiom{lp} generates a zero-dimensional ideal \\spad{w}.\\spad{r}.\\spad{t}. the variables involved in \\axiom{lp}.")))
NIL
NIL
-(-569 R -3091)
+(-570 R -3094)
((|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
-(-570)
+(-571)
((|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
-(-571 |lv| -3091)
+(-572 |lv| -3094)
((|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
-(-572)
+(-573)
((|constructor| (NIL "This domain provides a simple way to save values in files.")) (|setelt| (((|Any|) $ (|Symbol|) (|Any|)) "\\spad{lib.k := v} saves the value \\spad{v} in the library \\spad{lib}. It can later be extracted using the key \\spad{k}.")) (|pack!| (($ $) "\\spad{pack!(f)} reorganizes the file \\spad{f} on disk to recover unused space.")) (|library| (($ (|FileName|)) "\\spad{library(ln)} creates a new library file.")))
-((-3993 . T))
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+((-3997 . T))
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+(-574 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).")))
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((|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{x/r} returns the division of \\axiom{\\spad{x}} by \\axiom{\\spad{r}}.")) (|construct| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}.")))
NIL
-((|HasCategory| |#2| (QUOTE (-311))))
-(-575 R)
+((|HasCategory| |#2| (QUOTE (-312))))
+(-576 R)
((|constructor| (NIL "\\axiom{JacobiIdentity} means that \\axiom{[\\spad{x},{}[\\spad{y},{}\\spad{z}]]+[\\spad{y},{}[\\spad{z},{}\\spad{x}]]+[\\spad{z},{}[\\spad{x},{}\\spad{y}]] = 0} holds.")) (/ (($ $ |#1|) "\\axiom{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) (-3987 . T) (-3986 . T))
+((|JacobiIdentity| . T) (|NullSquare| . T) (-3991 . T) (-3990 . T))
NIL
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((|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|) #1="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|) #1#)) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| |#2|) #1#))) "failed") |#2| (|Equation| (|OrderedCompletion| |#2|))) "\\spad{limit(f(x),x = a)} computes the real limit \\spad{lim(x -> a,f(x))}.")))
NIL
NIL
-(-577 R)
+(-578 R)
((|constructor| (NIL "Computation of limits for rational functions.")) (|complexLimit| (((|OnePointCompletion| (|Fraction| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|)))) "\\spad{complexLimit(f(x),x = a)} computes the complex limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a}.") (((|OnePointCompletion| (|Fraction| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Equation| (|OnePointCompletion| (|Polynomial| |#1|)))) "\\spad{complexLimit(f(x),x = a)} computes the complex limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a}.")) (|limit| (((|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) #1="failed") (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|))) (|String|)) "\\spad{limit(f(x),x,a,\"left\")} computes the real limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a} from the left; limit(\\spad{f}(\\spad{x}),{}\\spad{x},{}a,{}\"right\") computes the corresponding limit as \\spad{x} approaches \\spad{a} from the right.") (((|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) (|Record| (|:| |leftHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) #1#)) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) #1#))) #2="failed") (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|)))) "\\spad{limit(f(x),x = a)} computes the real two-sided limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a}.") (((|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) (|Record| (|:| |leftHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) #1#)) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) #1#))) #2#) (|Fraction| (|Polynomial| |#1|)) (|Equation| (|OrderedCompletion| (|Polynomial| |#1|)))) "\\spad{limit(f(x),x = a)} computes the real two-sided limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a}.")))
NIL
NIL
-(-578 |vars|)
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((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: July 2,{} 2010 Date Last Modified: July 2,{} 2010 Descrption: \\indented{2}{Representation of a vector space basis,{} given by symbols.}")) (|dual| (($ (|DualBasis| |#1|)) "\\spad{dual f} constructs the dual vector of a linear form which is part of a basis.")))
NIL
NIL
-(-579 S R)
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((|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}'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}'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}'s are 0,{} \"failed\" if the \\spad{vi}'s are linearly independent over \\spad{S}.")) (|linearlyDependent?| (((|Boolean|) (|Vector| |#2|)) "\\spad{linearlyDependent?([v1,...,vn])} returns \\spad{true} if the \\spad{vi}'s are linearly dependent over \\spad{S},{} \\spad{false} otherwise.")))
NIL
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-(-580 K B)
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((|constructor| (NIL "A simple data structure for elements that form a vector space of finite dimension over a given field,{} with a given symbolic basis.")) (|coordinates| (((|Vector| |#1|) $) "\\spad{coordinates x} returns the coordinates of the linear element with respect to the basis \\spad{B}.")) (|linearElement| (($ (|List| |#1|)) "\\spad{linearElement [x1,..,xn]} returns a linear element \\indented{1}{with coordinates \\spad{[x1,..,xn]} with respect to} the basis elements \\spad{B}.")))
-((-3987 . T) (-3986 . T))
-((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| (-578 |#2|) (QUOTE (-1013)))))
-(-581 R)
+((-3991 . T) (-3990 . T))
+((-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| (-579 |#2|) (QUOTE (-1015)))))
+(-582 R)
((|constructor| (NIL "An extension of left-module with an explicit linear dependence test.")) (|reducedSystem| (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| $) (|Vector| $)) "\\spad{reducedSystem(A, v)} returns a matrix \\spad{B} and a vector \\spad{w} such that \\spad{A x = v} and \\spad{B x = w} have the same solutions in \\spad{R}.") (((|Matrix| |#1|) (|Matrix| $)) "\\spad{reducedSystem(A)} returns a matrix \\spad{B} such that \\spad{A x = 0} and \\spad{B x = 0} have the same solutions in \\spad{R}.")) (|leftReducedSystem| (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) (|Vector| $) $) "\\spad{reducedSystem([v1,...,vn],u)} returns a matrix \\spad{M} with coefficients in \\spad{R} and a vector \\spad{w} such that the system of equations \\spad{c1*v1 + ... + cn*vn = u} has the same solution as \\spad{c * M = w} where \\spad{c} is the row vector \\spad{[c1,...cn]}.") (((|Matrix| |#1|) (|Vector| $)) "\\spad{leftReducedSystem [v1,...,vn]} returns a matrix \\spad{M} with coefficients in \\spad{R} such that the system of equations \\spad{c1*v1 + ... + cn*vn = 0\\$\\%} has the same solution as \\spad{c * M = 0} where \\spad{c} is the row vector \\spad{[c1,...cn]}.")))
NIL
NIL
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((|constructor| (NIL "A simple data structure for linear forms on a vector space of finite dimension over a given field,{} with a given symbolic basis.")) (|coordinates| (((|Vector| |#1|) $) "\\spad{coordinates x} returns the coordinates of the linear form with respect to the basis \\spad{DualBasis B}.")) (|linearForm| (($ (|List| |#1|)) "\\spad{linearForm [x1,..,xn]} constructs a linear form with coordinates \\spad{[x1,..,xn]} with respect to the basis elements \\spad{DualBasis B}.")))
-((-3987 . T) (-3986 . T))
+((-3991 . T) (-3990 . T))
NIL
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((|constructor| (NIL "\\indented{2}{A set is an \\spad{S}-linear set if it is stable by dilation} \\indented{2}{by elements in the semigroup \\spad{S}.} See Also: LeftLinearSet,{} RightLinearSet.")))
NIL
NIL
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((|constructor| (NIL "\\spadtype{List} implements singly-linked lists that are addressable by indices; the index of the first element is 1. 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.")))
-((-3993 . T) (-3992 . T))
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-(-585 A B)
+((-3997 . T) (-3996 . T))
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((|constructor| (NIL "\\spadtype{ListFunctions2} implements utility functions that operate on two kinds of lists,{} each with a possibly different type of element.")) (|map| (((|List| |#2|) (|Mapping| |#2| |#1|) (|List| |#1|)) "\\spad{map(fn,u)} applies \\spad{fn} to each element of list \\spad{u} and returns a new list with the results. For example \\spad{map(square,[1,2,3]) = [1,4,9]}.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|List| |#1|) |#2|) "\\spad{reduce(fn,u,ident)} successively uses the binary function \\spad{fn} on the elements of list \\spad{u} and the result of previous applications. \\spad{ident} is returned if the \\spad{u} is empty. Note the order of application in the following examples: \\spad{reduce(fn,[1,2,3],0) = fn(3,fn(2,fn(1,0)))} and \\spad{reduce(*,[2,3],1) = 3 * (2 * 1)}.")) (|scan| (((|List| |#2|) (|Mapping| |#2| |#1| |#2|) (|List| |#1|) |#2|) "\\spad{scan(fn,u,ident)} successively uses the binary function \\spad{fn} to reduce more and more of list \\spad{u}. \\spad{ident} is returned if the \\spad{u} is empty. The result is a list of the reductions at each step. See \\spadfun{reduce} for more information. Examples: \\spad{scan(fn,[1,2],0) = [fn(2,fn(1,0)),fn(1,0)]} and \\spad{scan(*,[2,3],1) = [2 * 1, 3 * (2 * 1)]}.")))
NIL
NIL
-(-586 A B)
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((|constructor| (NIL "\\spadtype{ListToMap} allows mappings to be described by a pair of lists of equal lengths. The image of an element \\spad{x},{} which appears in position \\spad{n} in the first list,{} is then the \\spad{n}th element of the second list. A default value or default function can be specified to be used when \\spad{x} does not appear in the first list. In the absence of defaults,{} an error will occur in that case.")) (|match| ((|#2| (|List| |#1|) (|List| |#2|) |#1| (|Mapping| |#2| |#1|)) "\\spad{match(la, lb, a, f)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length. and applies this map to a. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Argument \\spad{f} is a default function to call if a is not in \\spad{la}. The value returned is then obtained by applying \\spad{f} to argument a.") (((|Mapping| |#2| |#1|) (|List| |#1|) (|List| |#2|) (|Mapping| |#2| |#1|)) "\\spad{match(la, lb, f)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Argument \\spad{f} is used as the function to call when the given function argument is not in \\spad{la}. The value returned is \\spad{f} applied to that argument.") ((|#2| (|List| |#1|) (|List| |#2|) |#1| |#2|) "\\spad{match(la, lb, a, b)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length. and applies this map to a. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Argument \\spad{b} is the default target value if a is not in \\spad{la}. Error: if \\spad{la} and \\spad{lb} are not of equal length.") (((|Mapping| |#2| |#1|) (|List| |#1|) (|List| |#2|) |#2|) "\\spad{match(la, lb, b)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length,{} where \\spad{b} is used as the default target value if the given function argument is not in \\spad{la}. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Error: if \\spad{la} and \\spad{lb} are not of equal length.") ((|#2| (|List| |#1|) (|List| |#2|) |#1|) "\\spad{match(la, lb, a)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length,{} where \\spad{a} is used as the default source value if the given one is not in \\spad{la}. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Error: if \\spad{la} and \\spad{lb} are not of equal length.") (((|Mapping| |#2| |#1|) (|List| |#1|) (|List| |#2|)) "\\spad{match(la, lb)} creates a map with no default source or target values defined by lists \\spad{la} and lb of equal length. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index lb. Error: if \\spad{la} and lb are not of equal length. Note: when this map is applied,{} an error occurs when applied to a value missing from \\spad{la}.")))
NIL
NIL
-(-587 A B C)
+(-588 A B C)
((|constructor| (NIL "\\spadtype{ListFunctions3} implements utility functions that operate on three kinds of lists,{} each with a possibly different type of element.")) (|map| (((|List| |#3|) (|Mapping| |#3| |#1| |#2|) (|List| |#1|) (|List| |#2|)) "\\spad{map(fn,list1, u2)} applies the binary function \\spad{fn} to corresponding elements of lists \\spad{u1} and \\spad{u2} and returns a list of the results (in the same order). Thus \\spad{map(/,[1,2,3],[4,5,6]) = [1/4,2/4,1/2]}. The computation terminates when the end of either list is reached. That is,{} the length of the result list is equal to the minimum of the lengths of \\spad{u1} and \\spad{u2}.")))
NIL
NIL
-(-588 T$)
+(-589 T$)
((|constructor| (NIL "This domain represents AST for Spad literals.")))
NIL
NIL
-(-589 S)
+(-590 S)
((|constructor| (NIL "\\indented{2}{A set is an \\spad{S}-left linear set if it is stable by left-dilation} \\indented{2}{by elements in the semigroup \\spad{S}.} See Also: RightLinearSet.")) (* (($ |#1| $) "\\spad{s*x} is the left-dilation of \\spad{x} by \\spad{s}.")))
NIL
NIL
-(-590 S)
+(-591 S)
((|substitute| (($ |#1| |#1| $) "\\spad{substitute(x,y,d)} replace \\spad{x}'s with \\spad{y}'s in dictionary \\spad{d}.")) (|duplicates?| (((|Boolean|) $) "\\spad{duplicates?(d)} tests if dictionary \\spad{d} has duplicate entries.")))
-((-3992 . T) (-3993 . T))
-((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1013))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-554 (-473)))) (|HasCategory| |#1| (QUOTE (-72))))
-(-591 R)
+((-3996 . T) (-3997 . T))
+((-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1015))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| |#1| (QUOTE (-554 (-774)))) (|HasCategory| |#1| (QUOTE (-555 (-474)))) (|HasCategory| |#1| (QUOTE (-72))))
+(-592 R)
((|constructor| (NIL "The category of left modules over an rng (ring not necessarily with unit). This is an abelian group which supports left multiplation by elements of the rng. \\blankline")))
NIL
NIL
-(-592 S E |un|)
+(-593 S E |un|)
((|constructor| (NIL "This internal package represents monoid (abelian or not,{} with or without inverses) as lists and provides some common operations to the various flavors of monoids.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f, a1\\^e1 ... an\\^en)} returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (|mapExpon| (($ (|Mapping| |#2| |#2|) $) "\\spad{mapExpon(f, a1\\^e1 ... an\\^en)} returns \\spad{a1\\^f(e1) ... an\\^f(en)}.")) (|commutativeEquality| (((|Boolean|) $ $) "\\spad{commutativeEquality(x,y)} returns \\spad{true} if \\spad{x} and \\spad{y} are equal assuming commutativity")) (|plus| (($ $ $) "\\spad{plus(x, y)} returns \\spad{x + y} where \\spad{+} is the monoid operation,{} which is assumed commutative.") (($ |#1| |#2| $) "\\spad{plus(s, e, x)} returns \\spad{e * s + x} where \\spad{+} is the monoid operation,{} which is assumed commutative.")) (|leftMult| (($ |#1| $) "\\spad{leftMult(s, a)} returns \\spad{s * a} where \\spad{*} is the monoid operation,{} which is assumed non-commutative.")) (|rightMult| (($ $ |#1|) "\\spad{rightMult(a, s)} returns \\spad{a * s} where \\spad{*} is the monoid operation,{} which is assumed non-commutative.")) (|makeUnit| (($) "\\spad{makeUnit()} returns the unit element of the monomial.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(l)} returns the number of monomials forming \\spad{l}.")) (|reverse!| (($ $) "\\spad{reverse!(l)} reverses the list of monomials forming \\spad{l},{} destroying the element \\spad{l}.")) (|reverse| (($ $) "\\spad{reverse(l)} reverses the list of monomials forming \\spad{l}. This has some effect if the monoid is non-abelian,{} \\spadignore{i.e.} \\spad{reverse(a1\\^e1 ... an\\^en) = an\\^en ... a1\\^e1} which is different.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(l, n)} returns the factor of the n^th monomial of \\spad{l}.")) (|nthExpon| ((|#2| $ (|Integer|)) "\\spad{nthExpon(l, n)} returns the exponent of the n^th monomial of \\spad{l}.")) (|makeMulti| (($ (|List| (|Record| (|:| |gen| |#1|) (|:| |exp| |#2|)))) "\\spad{makeMulti(l)} returns the element whose list of monomials is \\spad{l}.")) (|makeTerm| (($ |#1| |#2|) "\\spad{makeTerm(s, e)} returns the monomial \\spad{s} exponentiated by \\spad{e} (\\spadignore{e.g.} s^e or \\spad{e} * \\spad{s}).")) (|listOfMonoms| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| |#2|))) $) "\\spad{listOfMonoms(l)} returns the list of the monomials forming \\spad{l}.")) (|outputForm| (((|OutputForm|) $ (|Mapping| (|OutputForm|) (|OutputForm|) (|OutputForm|)) (|Mapping| (|OutputForm|) (|OutputForm|) (|OutputForm|)) (|Integer|)) "\\spad{outputForm(l, fop, fexp, unit)} converts the monoid element represented by \\spad{l} to an \\spadtype{OutputForm}. Argument unit is the output form for the \\spadignore{unit} of the monoid (\\spadignore{e.g.} 0 or 1),{} \\spad{fop(a, b)} is the output form for the monoid operation applied to \\spad{a} and \\spad{b} (\\spadignore{e.g.} \\spad{a + b},{} \\spad{a * b},{} \\spad{ab}),{} and \\spad{fexp(a, n)} is the output form for the exponentiation operation applied to \\spad{a} and \\spad{n} (\\spadignore{e.g.} \\spad{n a},{} \\spad{n * a},{} \\spad{a ** n},{} \\spad{a\\^n}).")))
NIL
NIL
-(-593 A S)
+(-594 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{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{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}) == concat(a(0..\\spad{i} - 1),{}a(\\spad{i} + 1,{}..))}.")) (|map| (($ (|Mapping| |#2| |#2| |#2|) $ $) "\\spad{map(f,u,v)} returns a new collection \\spad{w} with elements \\axiom{\\spad{z} = \\spad{f}(\\spad{x},{}\\spad{y})} for corresponding elements \\spad{x} and \\spad{y} from \\spad{u} and \\spad{v}. Note: for linear aggregates,{} \\axiom{\\spad{w}.\\spad{i} = \\spad{f}(\\spad{u}.\\spad{i},{}\\spad{v}.\\spad{i})}.")) (|concat| (($ (|List| $)) "\\spad{concat(u)},{} where \\spad{u} is a lists of aggregates \\axiom{[a,{}\\spad{b},{}...,{}\\spad{c}]},{} returns a single aggregate consisting of the elements of \\axiom{a} followed by those of \\spad{b} followed ... by the elements of \\spad{c}. Note: \\axiom{concat(a,{}\\spad{b},{}...,{}\\spad{c}) = concat(a,{}concat(\\spad{b},{}...,{}\\spad{c}))}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} then \\axiom{\\spad{w}.\\spad{i} = \\spad{u}.\\spad{i} for \\spad{i} in indices \\spad{u}} and \\axiom{\\spad{w}.(\\spad{j} + maxIndex \\spad{u}) = \\spad{v}.\\spad{j} for \\spad{j} in indices \\spad{v}}.") (($ |#2| $) "\\spad{concat(x,u)} returns aggregate \\spad{u} with additional element at the front. Note: for lists: \\axiom{concat(\\spad{x},{}\\spad{u}) == concat([\\spad{x}],{}\\spad{u})}.") (($ $ |#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}) == concat(\\spad{u},{}[\\spad{x}])}")) (|new| (($ (|NonNegativeInteger|) |#2|) "\\spad{new(n,x)} returns \\axiom{fill!(new \\spad{n},{}\\spad{x})}.")))
NIL
-((|HasAttribute| |#1| (QUOTE -3993)))
-(-594 S)
+((|HasAttribute| |#1| (QUOTE -3997)))
+(-595 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{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{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}) == concat(a(0..\\spad{i} - 1),{}a(\\spad{i} + 1,{}..))}.")) (|map| (($ (|Mapping| |#1| |#1| |#1|) $ $) "\\spad{map(f,u,v)} returns a new collection \\spad{w} with elements \\axiom{\\spad{z} = \\spad{f}(\\spad{x},{}\\spad{y})} for corresponding elements \\spad{x} and \\spad{y} from \\spad{u} and \\spad{v}. Note: for linear aggregates,{} \\axiom{\\spad{w}.\\spad{i} = \\spad{f}(\\spad{u}.\\spad{i},{}\\spad{v}.\\spad{i})}.")) (|concat| (($ (|List| $)) "\\spad{concat(u)},{} where \\spad{u} is a lists of aggregates \\axiom{[a,{}\\spad{b},{}...,{}\\spad{c}]},{} returns a single aggregate consisting of the elements of \\axiom{a} followed by those of \\spad{b} followed ... by the elements of \\spad{c}. Note: \\axiom{concat(a,{}\\spad{b},{}...,{}\\spad{c}) = concat(a,{}concat(\\spad{b},{}...,{}\\spad{c}))}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} then \\axiom{\\spad{w}.\\spad{i} = \\spad{u}.\\spad{i} for \\spad{i} in indices \\spad{u}} and \\axiom{\\spad{w}.(\\spad{j} + maxIndex \\spad{u}) = \\spad{v}.\\spad{j} for \\spad{j} in indices \\spad{v}}.") (($ |#1| $) "\\spad{concat(x,u)} returns aggregate \\spad{u} with additional element at the front. Note: for lists: \\axiom{concat(\\spad{x},{}\\spad{u}) == concat([\\spad{x}],{}\\spad{u})}.") (($ $ |#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}) == concat(\\spad{u},{}[\\spad{x}])}")) (|new| (($ (|NonNegativeInteger|) |#1|) "\\spad{new(n,x)} returns \\axiom{fill!(new \\spad{n},{}\\spad{x})}.")))
NIL
NIL
-(-595 M R S)
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((|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}.")))
-((-3987 . T) (-3986 . T))
-((|HasCategory| |#1| (QUOTE (-715))))
-(-596 R -3091 L)
+((-3991 . T) (-3990 . T))
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((|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
-(-597 A -2491)
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((|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}}")))
-((-3986 . T) (-3987 . T) (-3989 . T))
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-(-598 A)
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((|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}}")))
-((-3986 . T) (-3987 . T) (-3989 . T))
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-(-599 A M)
+((-3990 . T) (-3991 . T) (-3993 . T))
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((|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| (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}")))
-((-3986 . T) (-3987 . T) (-3989 . T))
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-(-600 S A)
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+((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-952 (-348 (-485))))) (|HasCategory| |#1| (QUOTE (-952 (-485)))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-312))))
+(-601 S A)
((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorCategory} is the category of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|directSum| (($ $ $) "\\spad{directSum(a,b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}.")) (|symmetricSquare| (($ $) "\\spad{symmetricSquare(a)} computes \\spad{symmetricProduct(a,a)} using a more efficient method.")) (|symmetricPower| (($ $ (|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 (-311))))
-(-601 A)
+((|HasCategory| |#2| (QUOTE (-312))))
+(-602 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}.")))
-((-3986 . T) (-3987 . T) (-3989 . T))
+((-3990 . T) (-3991 . T) (-3993 . T))
NIL
-(-602 -3091 UP)
+(-603 -3094 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))))
-(-603 A L)
+(-604 A L)
((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorsOps} provides symmetric products and sums for linear ordinary differential operators.")) (|directSum| ((|#2| |#2| |#2| (|Mapping| |#1| |#1|)) "\\spad{directSum(a,b,D)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}. \\spad{D} is the derivation to use.")) (|symmetricPower| ((|#2| |#2| (|NonNegativeInteger|) (|Mapping| |#1| |#1|)) "\\spad{symmetricPower(a,n,D)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of \\spad{n} solutions of \\spad{a}. \\spad{D} is the derivation to use.")) (|symmetricProduct| ((|#2| |#2| |#2| (|Mapping| |#1| |#1|)) "\\spad{symmetricProduct(a,b,D)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of a solution of \\spad{a} by a solution of \\spad{b}. \\spad{D} is the derivation to use.")))
NIL
NIL
-(-604 S)
+(-605 S)
((|constructor| (NIL "`Logic' provides the basic operations for lattices,{} \\spadignore{e.g.} boolean algebra.")) (|\\/| (($ $ $) "\\spadignore{ \\/ } returns the logical `join',{} \\spadignore{e.g.} `or'.")) (|/\\| (($ $ $) "\\spadignore { /\\ }returns the logical `meet',{} \\spadignore{e.g.} `and'.")) (~ (($ $) "\\spad{~(x)} returns the logical complement of \\spad{x}.")))
NIL
NIL
-(-605)
+(-606)
((|constructor| (NIL "`Logic' provides the basic operations for lattices,{} \\spadignore{e.g.} boolean algebra.")) (|\\/| (($ $ $) "\\spadignore{ \\/ } returns the logical `join',{} \\spadignore{e.g.} `or'.")) (|/\\| (($ $ $) "\\spadignore { /\\ }returns the logical `meet',{} \\spadignore{e.g.} `and'.")) (~ (($ $) "\\spad{~(x)} returns the logical complement of \\spad{x}.")))
NIL
NIL
-(-606 R)
+(-607 R)
((|constructor| (NIL "Given a PolynomialFactorizationExplicit ring,{} this package provides a defaulting rule for the \\spad{solveLinearPolynomialEquation} operation,{} by moving into the field of fractions,{} and solving it there via the \\spad{multiEuclidean} operation.")) (|solveLinearPolynomialEquationByFractions| (((|Union| (|List| (|SparseUnivariatePolynomial| |#1|)) "failed") (|List| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{solveLinearPolynomialEquationByFractions([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such exists.")))
NIL
NIL
-(-607 |VarSet| R)
+(-608 |VarSet| R)
((|constructor| (NIL "This type supports Lie polynomials in Lyndon basis see Free Lie Algebras by \\spad{C}. Reutenauer (Oxford science publications). \\newline Author: Michel Petitot (petitot@lifl.fr).")) (|construct| (($ $ (|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) (-3987 . T) (-3986 . T))
-((|HasCategory| |#2| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-146))))
-(-608 A S)
+((|JacobiIdentity| . T) (|NullSquare| . T) (-3991 . T) (-3990 . T))
+((|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-146))))
+(-609 A S)
((|constructor| (NIL "A list aggregate is a model for a linked list data structure. A linked list is a versatile data structure. Insertion and deletion are efficient and searching is a linear operation.")) (|list| (($ |#2|) "\\spad{list(x)} returns the list of one element \\spad{x}.")))
NIL
NIL
-(-609 S)
+(-610 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}.")))
-((-3993 . T) (-3992 . T))
+((-3997 . T) (-3996 . T))
NIL
-(-610 -3091 |Row| |Col| M)
+(-611 -3094 |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| #1="failed") |#4| |#3|) "\\spad{particularSolution(A,B)} finds a particular solution of the linear system \\spad{AX = B}.")) (|solve| (((|List| (|Record| (|:| |particular| (|Union| |#3| #1#)) (|:| |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| #1#)) (|:| |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
-(-611 -3091)
+(-612 -3094)
((|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'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|) #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|) #1#)) (|:| |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|) #1#)) (|:| |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|) #1#)) (|:| |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|) #1#)) (|:| |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
-(-612 R E OV P)
+(-613 R E OV P)
((|constructor| (NIL "this package finds the solutions of linear systems presented as a list of polynomials.")) (|linSolve| (((|Record| (|:| |particular| (|Union| (|Vector| (|Fraction| |#4|)) "failed")) (|:| |basis| (|List| (|Vector| (|Fraction| |#4|))))) (|List| |#4|) (|List| |#3|)) "\\spad{linSolve(lp,lvar)} finds the solutions of the linear system of polynomials \\spad{lp} = 0 with respect to the list of symbols \\spad{lvar}.")))
NIL
NIL
-(-613 |n| R)
+(-614 |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.")))
-((-3989 . T) (-3992 . T) (-3986 . T) (-3987 . T))
-((|HasCategory| |#2| (QUOTE (-810 (-1089)))) (|HasCategory| |#2| (QUOTE (-812 (-1089)))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-189))) (|HasAttribute| |#2| (QUOTE (-3994 #1="*"))) (|HasCategory| |#2| (QUOTE (-581 (-484)))) (|HasCategory| |#2| (QUOTE (-951 (-347 (-484))))) (|HasCategory| |#2| (QUOTE (-951 (-484)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (|%list| (QUOTE -259) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-581 (-484)))) (|HasCategory| |#2| (|%list| (QUOTE -259) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-810 (-1089)))) (|HasCategory| |#2| (|%list| (QUOTE -259) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (|%list| (QUOTE -259) (|devaluate| |#2|))))) (|HasCategory| |#2| (QUOTE (-257))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-495))) (OR (|HasAttribute| |#2| (QUOTE (-3994 #1#))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-810 (-1089))))) (|HasCategory| |#2| (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-72))) (-12 (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (|%list| (QUOTE -259) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-146))))
-(-614)
+((-3993 . T) (-3996 . T) (-3990 . T) (-3991 . T))
+((|HasCategory| |#2| (QUOTE (-811 (-1091)))) (|HasCategory| |#2| (QUOTE (-813 (-1091)))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-189))) (|HasAttribute| |#2| (QUOTE (-3998 #1="*"))) (|HasCategory| |#2| (QUOTE (-582 (-485)))) (|HasCategory| |#2| (QUOTE (-952 (-348 (-485))))) (|HasCategory| |#2| (QUOTE (-952 (-485)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-582 (-485)))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-811 (-1091)))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1015))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|))))) (|HasCategory| |#2| (QUOTE (-258))) (|HasCategory| |#2| (QUOTE (-1015))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-496))) (OR (|HasAttribute| |#2| (QUOTE (-3998 #1#))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-811 (-1091))))) (|HasCategory| |#2| (QUOTE (-554 (-774)))) (|HasCategory| |#2| (QUOTE (-72))) (-12 (|HasCategory| |#2| (QUOTE (-1015))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-146))))
+(-615)
((|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
NIL
-(-615 |VarSet|)
+(-616 |VarSet|)
((|constructor| (NIL "Lyndon words over arbitrary (ordered) symbols: see Free Lie Algebras by \\spad{C}. Reutenauer (Oxford science publications). A Lyndon word is a word which is smaller than any of its right factors \\spad{w}.\\spad{r}.\\spad{t}. the pure lexicographical ordering. If \\axiom{a} and \\axiom{\\spad{b}} are two Lyndon words such that \\axiom{a < \\spad{b}} holds \\spad{w}.\\spad{r}.\\spad{t} lexicographical ordering then \\axiom{a*b} is a Lyndon word. Parenthesized Lyndon words can be generated from symbols by using the following rule: \\axiom{[[a,{}\\spad{b}],{}\\spad{c}]} is a Lyndon word iff \\axiom{a*b < \\spad{c} <= \\spad{b}} holds. Lyndon words are internally represented by binary trees using the \\spadtype{Magma} domain constructor. Two ordering are provided: lexicographic and length-lexicographic. \\newline Author : Michel Petitot (petitot@lifl.fr).")) (|LyndonWordsList| (((|List| $) (|List| |#1|) (|PositiveInteger|)) "\\axiom{LyndonWordsList(vl,{} \\spad{n})} returns the list of Lyndon words over the alphabet \\axiom{vl},{} up to order \\axiom{\\spad{n}}.")) (|LyndonWordsList1| (((|OneDimensionalArray| (|List| $)) (|List| |#1|) (|PositiveInteger|)) "\\axiom{\\spad{LyndonWordsList1}(vl,{} \\spad{n})} returns an array of lists of Lyndon words over the alphabet \\axiom{vl},{} up to order \\axiom{\\spad{n}}.")) (|varList| (((|List| |#1|) $) "\\axiom{varList(\\spad{x})} returns the list of distinct entries of \\axiom{\\spad{x}}.")) (|lyndonIfCan| (((|Union| $ "failed") (|OrderedFreeMonoid| |#1|)) "\\axiom{lyndonIfCan(\\spad{w})} convert \\axiom{\\spad{w}} into a Lyndon word.")) (|lyndon| (($ (|OrderedFreeMonoid| |#1|)) "\\axiom{lyndon(\\spad{w})} convert \\axiom{\\spad{w}} into a Lyndon word,{} error if \\axiom{\\spad{w}} is not a Lyndon word.")) (|lyndon?| (((|Boolean|) (|OrderedFreeMonoid| |#1|)) "\\axiom{lyndon?(\\spad{w})} test if \\axiom{\\spad{w}} is a Lyndon word.")) (|factor| (((|List| $) (|OrderedFreeMonoid| |#1|)) "\\axiom{factor(\\spad{x})} returns the decreasing factorization into Lyndon words.")) (|coerce| (((|Magma| |#1|) $) "\\axiom{coerce(\\spad{x})} returns the element of \\axiomType{Magma}(VarSet) corresponding to \\axiom{\\spad{x}}.") (((|OrderedFreeMonoid| |#1|) $) "\\axiom{coerce(\\spad{x})} returns the element of \\axiomType{OrderedFreeMonoid}(VarSet) corresponding to \\axiom{\\spad{x}}.")) (|lexico| (((|Boolean|) $ $) "\\axiom{lexico(\\spad{x},{}\\spad{y})} returns \\axiom{\\spad{true}} iff \\axiom{\\spad{x}} is smaller than \\axiom{\\spad{y}} \\spad{w}.\\spad{r}.\\spad{t}. the lexicographical ordering induced by \\axiom{VarSet}.")) (|length| (((|PositiveInteger|) $) "\\axiom{length(\\spad{x})} returns the number of entries in \\axiom{\\spad{x}}.")) (|right| (($ $) "\\axiom{right(\\spad{x})} returns right subtree of \\axiom{\\spad{x}} or error if \\axiomOpFrom{retractable?}{LyndonWord}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|left| (($ $) "\\axiom{left(\\spad{x})} returns left subtree of \\axiom{\\spad{x}} or error if \\axiomOpFrom{retractable?}{LyndonWord}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|retractable?| (((|Boolean|) $) "\\axiom{retractable?(\\spad{x})} tests if \\axiom{\\spad{x}} is a tree with only one entry.")))
NIL
NIL
-(-616 A S)
+(-617 A S)
((|constructor| (NIL "LazyStreamAggregate is the category of streams with lazy evaluation. It is understood that the function 'empty?' will cause lazy evaluation if necessary to determine if there are entries. Functions which call 'empty?',{} \\spadignore{e.g.} 'first' and 'rest',{} will also cause lazy evaluation if necessary.")) (|complete| (($ $) "\\spad{complete(st)} causes all entries of 'st' to be computed. this function should only be called on streams which are known to be finite.")) (|extend| (($ $ (|Integer|)) "\\spad{extend(st,n)} causes entries to be computed,{} if necessary,{} so that 'st' will have at least 'n' explicit entries or so that all entries of 'st' will be computed if 'st' is finite with length <= \\spad{n}.")) (|numberOfComputedEntries| (((|NonNegativeInteger|) $) "\\spad{numberOfComputedEntries(st)} returns the number of explicitly computed entries of stream \\spad{st} which exist immediately prior to the time this function is called.")) (|rst| (($ $) "\\spad{rst(s)} returns a pointer to the next node of stream \\spad{s}. Caution: this function should only be called after a \\spad{empty?} test has been made since there no error check.")) (|frst| ((|#2| $) "\\spad{frst(s)} returns the first element of stream \\spad{s}. Caution: this function should only be called after a \\spad{empty?} test has been made since there no error check.")) (|lazyEvaluate| (($ $) "\\spad{lazyEvaluate(s)} causes one lazy evaluation of stream \\spad{s}. Caution: the first node must be a lazy evaluation mechanism (satisfies \\spad{lazy?(s) = true}) as there is no error check. Note: a call to this function may or may not produce an explicit first entry")) (|lazy?| (((|Boolean|) $) "\\spad{lazy?(s)} returns \\spad{true} if the first node of the stream \\spad{s} is a lazy evaluation mechanism which could produce an additional entry to \\spad{s}.")) (|explicitlyEmpty?| (((|Boolean|) $) "\\spad{explicitlyEmpty?(s)} returns \\spad{true} if the stream is an (explicitly) empty stream. Note: this is a null test which will not cause lazy evaluation.")) (|explicitEntries?| (((|Boolean|) $) "\\spad{explicitEntries?(s)} returns \\spad{true} if the stream \\spad{s} has explicitly computed entries,{} and \\spad{false} otherwise.")) (|select| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{select(f,st)} returns a stream consisting of those elements of stream \\spad{st} satisfying the predicate \\spad{f}. Note: \\spad{select(f,st) = [x for x in st | f(x)]}.")) (|remove| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{remove(f,st)} returns a stream consisting of those elements of stream \\spad{st} which do not satisfy the predicate \\spad{f}. Note: \\spad{remove(f,st) = [x for x in st | not f(x)]}.")))
NIL
NIL
-(-617 S)
+(-618 S)
((|constructor| (NIL "LazyStreamAggregate is the category of streams with lazy evaluation. It is understood that the function 'empty?' will cause lazy evaluation if necessary to determine if there are entries. Functions which call 'empty?',{} \\spadignore{e.g.} 'first' and 'rest',{} will also cause lazy evaluation if necessary.")) (|complete| (($ $) "\\spad{complete(st)} causes all entries of 'st' to be computed. this function should only be called on streams which are known to be finite.")) (|extend| (($ $ (|Integer|)) "\\spad{extend(st,n)} causes entries to be computed,{} if necessary,{} so that 'st' will have at least 'n' explicit entries or so that all entries of 'st' will be computed if 'st' is finite with length <= \\spad{n}.")) (|numberOfComputedEntries| (((|NonNegativeInteger|) $) "\\spad{numberOfComputedEntries(st)} returns the number of explicitly computed entries of stream \\spad{st} which exist immediately prior to the time this function is called.")) (|rst| (($ $) "\\spad{rst(s)} returns a pointer to the next node of stream \\spad{s}. Caution: this function should only be called after a \\spad{empty?} test has been made since there no error check.")) (|frst| ((|#1| $) "\\spad{frst(s)} returns the first element of stream \\spad{s}. Caution: this function should only be called after a \\spad{empty?} test has been made since there no error check.")) (|lazyEvaluate| (($ $) "\\spad{lazyEvaluate(s)} causes one lazy evaluation of stream \\spad{s}. Caution: the first node must be a lazy evaluation mechanism (satisfies \\spad{lazy?(s) = true}) as there is no error check. Note: a call to this function may or may not produce an explicit first entry")) (|lazy?| (((|Boolean|) $) "\\spad{lazy?(s)} returns \\spad{true} if the first node of the stream \\spad{s} is a lazy evaluation mechanism which could produce an additional entry to \\spad{s}.")) (|explicitlyEmpty?| (((|Boolean|) $) "\\spad{explicitlyEmpty?(s)} returns \\spad{true} if the stream is an (explicitly) empty stream. Note: this is a null test which will not cause lazy evaluation.")) (|explicitEntries?| (((|Boolean|) $) "\\spad{explicitEntries?(s)} returns \\spad{true} if the stream \\spad{s} has explicitly computed entries,{} and \\spad{false} otherwise.")) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select(f,st)} returns a stream consisting of those elements of stream \\spad{st} satisfying the predicate \\spad{f}. Note: \\spad{select(f,st) = [x for x in st | f(x)]}.")) (|remove| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove(f,st)} returns a stream consisting of those elements of stream \\spad{st} which do not satisfy the predicate \\spad{f}. Note: \\spad{remove(f,st) = [x for x in st | not f(x)]}.")))
NIL
NIL
-(-618)
+(-619)
((|constructor| (NIL "This domain represents the syntax of a macro definition.")) (|body| (((|SpadAst|) $) "\\spad{body(m)} returns the right hand side of the definition `m'.")) (|head| (((|HeadAst|) $) "\\spad{head(m)} returns the head of the macro definition `m'. This is a list of identifiers starting with the name of the macro followed by the name of the parameters,{} if any.")))
NIL
NIL
-(-619 |VarSet|)
+(-620 |VarSet|)
((|constructor| (NIL "This type is the basic representation of parenthesized words (binary trees over arbitrary symbols) useful in \\spadtype{LiePolynomial}. \\newline Author: Michel Petitot (petitot@lifl.fr).")) (|varList| (((|List| |#1|) $) "\\axiom{varList(\\spad{x})} returns the list of distinct entries of \\axiom{\\spad{x}}.")) (|right| (($ $) "\\axiom{right(\\spad{x})} returns right subtree of \\axiom{\\spad{x}} or error if \\axiomOpFrom{retractable?}{Magma}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|retractable?| (((|Boolean|) $) "\\axiom{retractable?(\\spad{x})} tests if \\axiom{\\spad{x}} is a tree with only one entry.")) (|rest| (($ $) "\\axiom{rest(\\spad{x})} return \\axiom{\\spad{x}} without the first entry or error if \\axiomOpFrom{retractable?}{Magma}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|mirror| (($ $) "\\axiom{mirror(\\spad{x})} returns the reversed word of \\axiom{\\spad{x}}. That is \\axiom{\\spad{x}} itself if \\axiomOpFrom{retractable?}{Magma}(\\axiom{\\spad{x}}) is \\spad{true} and \\axiom{mirror(\\spad{z}) * mirror(\\spad{y})} if \\axiom{\\spad{x}} is \\axiom{y*z}.")) (|lexico| (((|Boolean|) $ $) "\\axiom{lexico(\\spad{x},{}\\spad{y})} returns \\axiom{\\spad{true}} iff \\axiom{\\spad{x}} is smaller than \\axiom{\\spad{y}} \\spad{w}.\\spad{r}.\\spad{t}. the lexicographical ordering induced by \\axiom{VarSet}. \\spad{N}.\\spad{B}. This operation does not take into account the tree structure of its arguments. Thus this is not a total ordering.")) (|length| (((|PositiveInteger|) $) "\\axiom{length(\\spad{x})} returns the number of entries in \\axiom{\\spad{x}}.")) (|left| (($ $) "\\axiom{left(\\spad{x})} returns left subtree of \\axiom{\\spad{x}} or error if \\axiomOpFrom{retractable?}{Magma}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|first| ((|#1| $) "\\axiom{first(\\spad{x})} returns the first entry of the tree \\axiom{\\spad{x}}.")) (|coerce| (((|OrderedFreeMonoid| |#1|) $) "\\axiom{coerce(\\spad{x})} returns the element of \\axiomType{OrderedFreeMonoid}(VarSet) corresponding to \\axiom{\\spad{x}} by removing parentheses.")) (* (($ $ $) "\\axiom{x*y} returns the tree \\axiom{[\\spad{x},{}\\spad{y}]}.")))
NIL
NIL
-(-620 A)
+(-621 A)
((|constructor| (NIL "various Currying operations.")) (|recur| ((|#1| (|Mapping| |#1| (|NonNegativeInteger|) |#1|) (|NonNegativeInteger|) |#1|) "\\spad{recur(n,g,x)} is \\spad{g(n,g(n-1,..g(1,x)..))}.")) (|iter| ((|#1| (|Mapping| |#1| |#1|) (|NonNegativeInteger|) |#1|) "\\spad{iter(f,n,x)} applies \\spad{f n} times to \\spad{x}.")))
NIL
NIL
-(-621 A C)
+(-622 A C)
((|constructor| (NIL "various Currying operations.")) (|arg2| ((|#2| |#1| |#2|) "\\spad{arg2(a,c)} selects its second argument.")) (|arg1| ((|#1| |#1| |#2|) "\\spad{arg1(a,c)} selects its first argument.")))
NIL
NIL
-(-622 A B C)
+(-623 A B C)
((|constructor| (NIL "various Currying operations.")) (|comp| ((|#3| (|Mapping| |#3| |#2|) (|Mapping| |#2| |#1|) |#1|) "\\spad{comp(f,g,x)} is \\spad{f(g x)}.")))
NIL
NIL
-(-623)
+(-624)
((|constructor| (NIL "This domain represents a mapping type AST. A mapping AST \\indented{2}{is a syntactic description of a function type,{} \\spadignore{e.g.} its result} \\indented{2}{type and the list of its argument types.}")) (|target| (((|TypeAst|) $) "\\spad{target(s)} returns the result type AST for `s'.")) (|source| (((|List| (|TypeAst|)) $) "\\spad{source(s)} returns the parameter type AST list of `s'.")) (|mappingAst| (($ (|List| (|TypeAst|)) (|TypeAst|)) "\\spad{mappingAst(s,t)} builds the mapping AST \\spad{s} -> \\spad{t}")) (|coerce| (($ (|Signature|)) "sig::MappingAst builds a MappingAst from the Signature `sig'.")))
NIL
NIL
-(-624 A)
+(-625 A)
((|constructor| (NIL "various Currying operations.")) (|recur| (((|Mapping| |#1| (|NonNegativeInteger|) |#1|) (|Mapping| |#1| (|NonNegativeInteger|) |#1|)) "\\spad{recur(g)} is the function \\spad{h} such that \\indented{1}{\\spad{h(n,x)= g(n,g(n-1,..g(1,x)..))}.}")) (** (((|Mapping| |#1| |#1|) (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) "\\spad{f**n} is the function which is the \\spad{n}-fold application \\indented{1}{of \\spad{f}.}")) (|id| ((|#1| |#1|) "\\spad{id x} is \\spad{x}.")) (|fixedPoint| (((|List| |#1|) (|Mapping| (|List| |#1|) (|List| |#1|)) (|Integer|)) "\\spad{fixedPoint(f,n)} is the fixed point of function \\indented{1}{\\spad{f} which is assumed to transform a list of length} \\indented{1}{\\spad{n}.}") ((|#1| (|Mapping| |#1| |#1|)) "\\spad{fixedPoint f} is the fixed point of function \\spad{f}. \\indented{1}{\\spadignore{i.e.} such that \\spad{fixedPoint f = f(fixedPoint f)}.}")) (|coerce| (((|Mapping| |#1|) |#1|) "\\spad{coerce A} changes its argument into a \\indented{1}{nullary function.}")) (|nullary| (((|Mapping| |#1|) |#1|) "\\spad{nullary A} changes its argument into a \\indented{1}{nullary function.}")))
NIL
NIL
-(-625 A C)
+(-626 A C)
((|constructor| (NIL "various Currying operations.")) (|diag| (((|Mapping| |#2| |#1|) (|Mapping| |#2| |#1| |#1|)) "\\spad{diag(f)} is the function \\spad{g} \\indented{1}{such that \\spad{g a = f(a,a)}.}")) (|constant| (((|Mapping| |#2| |#1|) (|Mapping| |#2|)) "\\spad{vu(f)} is the function \\spad{g} \\indented{1}{such that \\spad{g a= f ()}.}")) (|curry| (((|Mapping| |#2|) (|Mapping| |#2| |#1|) |#1|) "\\spad{cu(f,a)} is the function \\spad{g} \\indented{1}{such that \\spad{g ()= f a}.}")) (|const| (((|Mapping| |#2| |#1|) |#2|) "\\spad{const c} is a function which produces \\spad{c} when \\indented{1}{applied to its argument.}")))
NIL
NIL
-(-626 A B C)
+(-627 A B C)
((|constructor| (NIL "various Currying operations.")) (* (((|Mapping| |#3| |#1|) (|Mapping| |#3| |#2|) (|Mapping| |#2| |#1|)) "\\spad{f*g} is the function \\spad{h} \\indented{1}{such that \\spad{h x= f(g x)}.}")) (|twist| (((|Mapping| |#3| |#2| |#1|) (|Mapping| |#3| |#1| |#2|)) "\\spad{twist(f)} is the function \\spad{g} \\indented{1}{such that \\spad{g (a,b)= f(b,a)}.}")) (|constantLeft| (((|Mapping| |#3| |#1| |#2|) (|Mapping| |#3| |#2|)) "\\spad{constantLeft(f)} is the function \\spad{g} \\indented{1}{such that \\spad{g (a,b)= f b}.}")) (|constantRight| (((|Mapping| |#3| |#1| |#2|) (|Mapping| |#3| |#1|)) "\\spad{constantRight(f)} is the function \\spad{g} \\indented{1}{such that \\spad{g (a,b)= f a}.}")) (|curryLeft| (((|Mapping| |#3| |#2|) (|Mapping| |#3| |#1| |#2|) |#1|) "\\spad{curryLeft(f,a)} is the function \\spad{g} \\indented{1}{such that \\spad{g b = f(a,b)}.}")) (|curryRight| (((|Mapping| |#3| |#1|) (|Mapping| |#3| |#1| |#2|) |#2|) "\\spad{curryRight(f,b)} is the function \\spad{g} such that \\indented{1}{\\spad{g a = f(a,b)}.}")))
NIL
NIL
-(-627 S R |Row| |Col|)
+(-628 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| $)) "\\spad{diagonalMatrix([m1,...,mk])} creates a block diagonal matrix \\spad{M} with block matrices {\\em m1},{}...,{}{\\em mk} down the diagonal,{} with 0 block matrices elsewhere. More precisly: if \\spad{ri := nrows mi},{} \\spad{ci := ncols mi},{} then \\spad{m} is an (r1+..+rk) by (c1+..+ck) - matrix with entries \\spad{m.i.j = ml.(i-r1-..-r(l-1)).(j-n1-..-n(l-1))},{} if \\spad{(r1+..+r(l-1)) < i <= r1+..+rl} and \\spad{(c1+..+c(l-1)) < i <= c1+..+cl},{} \\spad{m.i.j} = 0 otherwise.") (($ (|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}'s on the diagonal and zeroes elsewhere.")) (|matrix| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) (|Mapping| |#2| (|Integer|) (|Integer|))) "\\spad{matrix(n,m,f)} construcys and \\spad{n * m} matrix with the \\spad{(i,j)} entry equal to \\spad{f(i,j)}.") (($ (|List| (|List| |#2|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix.")) (|zero| (($ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{zero(m,n)} returns an \\spad{m}-by-\\spad{n} zero matrix.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,j] = -m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,j] = m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.")) (|finiteAggregate| ((|attribute|) "matrices are finite")) (|shallowlyMutable| ((|attribute|) "One may destructively alter matrices")))
NIL
-((|HasAttribute| |#2| (QUOTE (-3994 "*"))) (|HasCategory| |#2| (QUOTE (-257))) (|HasCategory| |#2| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-495))))
-(-628 R |Row| |Col|)
+((|HasAttribute| |#2| (QUOTE (-3998 "*"))) (|HasCategory| |#2| (QUOTE (-258))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-496))))
+(-629 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| $)) "\\spad{diagonalMatrix([m1,...,mk])} creates a block diagonal matrix \\spad{M} with block matrices {\\em m1},{}...,{}{\\em mk} down the diagonal,{} with 0 block matrices elsewhere. More precisly: if \\spad{ri := nrows mi},{} \\spad{ci := ncols mi},{} then \\spad{m} is an (r1+..+rk) by (c1+..+ck) - matrix with entries \\spad{m.i.j = ml.(i-r1-..-r(l-1)).(j-n1-..-n(l-1))},{} if \\spad{(r1+..+r(l-1)) < i <= r1+..+rl} and \\spad{(c1+..+c(l-1)) < i <= c1+..+cl},{} \\spad{m.i.j} = 0 otherwise.") (($ (|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}'s on the diagonal and zeroes elsewhere.")) (|matrix| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) (|Mapping| |#1| (|Integer|) (|Integer|))) "\\spad{matrix(n,m,f)} construcys and \\spad{n * m} matrix with the \\spad{(i,j)} entry equal to \\spad{f(i,j)}.") (($ (|List| (|List| |#1|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix.")) (|zero| (($ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{zero(m,n)} returns an \\spad{m}-by-\\spad{n} zero matrix.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,j] = -m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,j] = m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.")) (|finiteAggregate| ((|attribute|) "matrices are finite")) (|shallowlyMutable| ((|attribute|) "One may destructively alter matrices")))
-((-3992 . T) (-3993 . T))
+((-3996 . T) (-3997 . T))
NIL
-(-629 R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2)
+(-630 R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2)
((|constructor| (NIL "\\spadtype{MatrixCategoryFunctions2} provides functions between two matrix domains. The functions provided are \\spadfun{map} and \\spadfun{reduce}.")) (|reduce| ((|#5| (|Mapping| |#5| |#1| |#5|) |#4| |#5|) "\\spad{reduce(f,m,r)} returns a matrix \\spad{n} where \\spad{n[i,j] = f(m[i,j],r)} for all indices \\spad{i} and \\spad{j}.")) (|map| (((|Union| |#8| "failed") (|Mapping| (|Union| |#5| "failed") |#1|) |#4|) "\\spad{map(f,m)} applies the function \\spad{f} to the elements of the matrix \\spad{m}.") ((|#8| (|Mapping| |#5| |#1|) |#4|) "\\spad{map(f,m)} applies the function \\spad{f} to the elements of the matrix \\spad{m}.")))
NIL
NIL
-(-630 R |Row| |Col| M)
+(-631 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 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} ~=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} ~=j)")) (|elRow1!| ((|#4| |#4| (|Integer|) (|Integer|)) "\\spad{elRow1!(m,i,j)} swaps rows \\spad{i} and \\spad{j} of matrix \\spad{m} : elementary operation of first kind")) (|minordet| ((|#1| |#4|) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors. Error: if the matrix is not square.")) (|determinant| ((|#1| |#4|) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. an error message is returned if the matrix is not square.")))
NIL
-((|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-257))) (|HasCategory| |#1| (QUOTE (-495))))
-(-631 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.")))
-((-3992 . T) (-3993 . T))
-((OR (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1013))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-554 (-473)))) (|HasCategory| |#1| (QUOTE (-257))) (|HasCategory| |#1| (QUOTE (-495))) (|HasAttribute| |#1| (QUOTE (-3994 "*"))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))))
+((|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-496))))
(-632 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.")))
+((-3996 . T) (-3997 . T))
+((OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1015))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| |#1| (QUOTE (-554 (-774)))) (|HasCategory| |#1| (QUOTE (-555 (-474)))) (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-496))) (|HasAttribute| |#1| (QUOTE (-3998 "*"))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))))
+(-633 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{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
NIL
-(-633 T$)
+(-634 T$)
((|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 `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 `x' into \\%.")))
NIL
NIL
-(-634 R Q)
+(-635 R Q)
((|constructor| (NIL "MatrixCommonDenominator provides functions to compute the common denominator of a matrix of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| (|Matrix| |#1|)) (|:| |den| |#1|)) (|Matrix| |#2|)) "\\spad{splitDenominator(q)} returns \\spad{[p, d]} such that \\spad{q = p/d} and \\spad{d} is a common denominator for the elements of \\spad{q}.")) (|clearDenominator| (((|Matrix| |#1|) (|Matrix| |#2|)) "\\spad{clearDenominator(q)} returns \\spad{p} such that \\spad{q = p/d} where \\spad{d} is a common denominator for the elements of \\spad{q}.")) (|commonDenominator| ((|#1| (|Matrix| |#2|)) "\\spad{commonDenominator(q)} returns a common denominator \\spad{d} for the elements of \\spad{q}.")))
NIL
NIL
-(-635 S)
+(-636 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}.")))
-((-3993 . T))
+((-3997 . T))
NIL
-(-636 U)
+(-637 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 gcd of the univariate polynomials \\spad{f1} and \\spad{f2} modulo the integer prime \\spad{p}.")))
NIL
NIL
-(-637)
+(-638)
((|constructor| (NIL "\\indented{1}{<description of package>} Author: Jim Wen Date Created: ?? 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|)) #1="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|)) #1#) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(f,g,h,j,s1,s2,l)} \\undocumented")))
NIL
NIL
-(-638 OV E -3091 PG)
+(-639 OV E -3094 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
-(-639 R)
+(-640 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.")))
NIL
NIL
-(-640 S D1 D2 I)
+(-641 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")))
NIL
NIL
-(-641 S)
+(-642 S)
((|constructor| (NIL "MakeFloatCompiledFunction transforms top-level objects into compiled Lisp functions whose arguments are Lisp floats. This by-passes the \\Language{} compiler and interpreter,{} thereby gaining several orders of magnitude.")) (|makeFloatFunction| (((|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) |#1| (|Symbol|) (|Symbol|)) "\\spad{makeFloatFunction(expr, x, y)} returns a Lisp function \\spad{f: (\\axiomType{DoubleFloat}, \\axiomType{DoubleFloat}) -> \\axiomType{DoubleFloat}} defined by \\spad{f(x, y) == expr}. Function \\spad{f} is compiled and directly applicable to objects of type \\spad{(\\axiomType{DoubleFloat}, \\axiomType{DoubleFloat})}.") (((|Mapping| (|DoubleFloat|) (|DoubleFloat|)) |#1| (|Symbol|)) "\\spad{makeFloatFunction(expr, x)} returns a Lisp function \\spad{f: \\axiomType{DoubleFloat} -> \\axiomType{DoubleFloat}} defined by \\spad{f(x) == expr}. Function \\spad{f} is compiled and directly applicable to objects of type \\axiomType{DoubleFloat}.")))
NIL
NIL
-(-642 S)
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((|constructor| (NIL "transforms top-level objects into interpreter functions.")) (|function| (((|Symbol|) |#1| (|Symbol|) (|List| (|Symbol|))) "\\spad{function(e, foo, [x1,...,xn])} creates a function \\spad{foo(x1,...,xn) == e}.") (((|Symbol|) |#1| (|Symbol|) (|Symbol|) (|Symbol|)) "\\spad{function(e, foo, x, y)} creates a function \\spad{foo(x, y) = e}.") (((|Symbol|) |#1| (|Symbol|) (|Symbol|)) "\\spad{function(e, foo, x)} creates a function \\spad{foo(x) == e}.") (((|Symbol|) |#1| (|Symbol|)) "\\spad{function(e, foo)} creates a function \\spad{foo() == e}.")))
NIL
NIL
-(-643 S T$)
+(-644 S T$)
((|constructor| (NIL "MakeRecord is used internally by the interpreter to create record types which are used for doing parallel iterations on streams.")) (|makeRecord| (((|Record| (|:| |part1| |#1|) (|:| |part2| |#2|)) |#1| |#2|) "\\spad{makeRecord(a,b)} creates a record object with type Record(part1:S,{} part2:R),{} where \\spad{part1} is \\spad{a} and \\spad{part2} is \\spad{b}.")))
NIL
NIL
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((|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
-(-645 E OV R P)
+(-646 E OV R P)
((|constructor| (NIL "This package provides the functions for the multivariate \"lifting\",{} using an algorithm of Paul Wang. This package will work for every euclidean domain \\spad{R} which has property \\spad{F},{} \\spadignore{i.e.} there exists a factor operation in \\spad{R[x]}.")) (|lifting1| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|List| (|SparseUnivariatePolynomial| |#4|)) (|List| |#3|) (|List| |#4|) (|List| (|List| (|Record| (|:| |expt| (|NonNegativeInteger|)) (|:| |pcoef| |#4|)))) (|List| (|NonNegativeInteger|)) (|Vector| (|List| (|SparseUnivariatePolynomial| |#3|))) |#3|) "\\spad{lifting1(u,lv,lu,lr,lp,lt,ln,t,r)} \\undocumented")) (|lifting| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|List| (|SparseUnivariatePolynomial| |#3|)) (|List| |#3|) (|List| |#4|) (|List| (|NonNegativeInteger|)) |#3|) "\\spad{lifting(u,lv,lu,lr,lp,ln,r)} \\undocumented")) (|corrPoly| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|List| |#3|) (|List| (|NonNegativeInteger|)) (|List| (|SparseUnivariatePolynomial| |#4|)) (|Vector| (|List| (|SparseUnivariatePolynomial| |#3|))) |#3|) "\\spad{corrPoly(u,lv,lr,ln,lu,t,r)} \\undocumented")))
NIL
NIL
-(-646 R)
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((|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)}.}")))
-((-3986 . T) (-3987 . T) (-3989 . T))
+((-3990 . T) (-3991 . T) (-3993 . T))
NIL
-(-647 R1 UP1 UPUP1 R2 UP2 UPUP2)
+(-648 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}.")))
NIL
NIL
-(-648)
+(-649)
((|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
-(-649 R |Mod| -2036 -3515 |exactQuo|)
+(-650 R |Mod| -2039 -3519 |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| $) "\\spad{modulus(x)} \\undocumented")))
-((-3984 . T) (-3990 . T) (-3985 . T) ((-3994 "*") . T) (-3986 . T) (-3987 . T) (-3989 . T))
+((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T))
NIL
-(-650 R P)
+(-651 R P)
((|constructor| (NIL "This package \\undocumented")) (|frobenius| (($ $) "\\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")))
-(((-3994 "*") |has| |#1| (-146)) (-3985 |has| |#1| (-495)) (-3988 |has| |#1| (-311)) (-3990 |has| |#1| (-6 -3990)) (-3987 . T) (-3986 . T) (-3989 . T))
-((|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-495)))) (-12 (|HasCategory| |#1| (QUOTE (-797 (-327)))) (|HasCategory| (-994) (QUOTE (-797 (-327))))) (-12 (|HasCategory| |#1| (QUOTE (-797 (-484)))) (|HasCategory| (-994) (QUOTE (-797 (-484))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-327))))) (|HasCategory| (-994) (QUOTE (-554 (-801 (-327)))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-484))))) (|HasCategory| (-994) (QUOTE (-554 (-801 (-484)))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-473)))) (|HasCategory| (-994) (QUOTE (-554 (-473))))) (|HasCategory| |#1| (QUOTE (-581 (-484)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-347 (-484))))) (|HasCategory| |#1| (QUOTE (-951 (-484)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-347 (-484))))) (|HasCategory| |#1| (QUOTE (-951 (-347 (-484)))))) (|HasCategory| |#1| (QUOTE (-951 (-347 (-484))))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-389))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-822)))) (OR (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-389))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-822)))) (OR (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-389))) (|HasCategory| |#1| (QUOTE (-822)))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-1065))) (|HasCategory| |#1| (QUOTE (-812 (-1089)))) (|HasCategory| |#1| (QUOTE (-810 (-1089)))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-298))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-190))) (|HasAttribute| |#1| (QUOTE -3990)) (|HasCategory| |#1| (QUOTE (-389))) (-12 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118)))))
-(-651 IS E |ff|)
+(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3992 |has| |#1| (-312)) (-3994 |has| |#1| (-6 -3994)) (-3991 . T) (-3990 . T) (-3993 . T))
+((|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (-12 (|HasCategory| |#1| (QUOTE (-798 (-328)))) (|HasCategory| (-996) (QUOTE (-798 (-328))))) (-12 (|HasCategory| |#1| (QUOTE (-798 (-485)))) (|HasCategory| (-996) (QUOTE (-798 (-485))))) (-12 (|HasCategory| |#1| (QUOTE (-555 (-802 (-328))))) (|HasCategory| (-996) (QUOTE (-555 (-802 (-328)))))) (-12 (|HasCategory| |#1| (QUOTE (-555 (-802 (-485))))) (|HasCategory| (-996) (QUOTE (-555 (-802 (-485)))))) (-12 (|HasCategory| |#1| (QUOTE (-555 (-474)))) (|HasCategory| (-996) (QUOTE (-555 (-474))))) (|HasCategory| |#1| (QUOTE (-582 (-485)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-348 (-485))))) (|HasCategory| |#1| (QUOTE (-952 (-485)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-348 (-485))))) (|HasCategory| |#1| (QUOTE (-952 (-348 (-485)))))) (|HasCategory| |#1| (QUOTE (-952 (-348 (-485))))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-823)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-823)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-823)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (QUOTE (-813 (-1091)))) (|HasCategory| |#1| (QUOTE (-811 (-1091)))) (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-299))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-190))) (|HasAttribute| |#1| (QUOTE -3994)) (|HasCategory| |#1| (QUOTE (-390))) (-12 (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118)))))
+(-652 IS E |ff|)
((|constructor| (NIL "This package \\undocumented")) (|construct| (($ |#1| |#2|) "\\spad{construct(i,e)} \\undocumented")) (|index| ((|#1| $) "\\spad{index(x)} \\undocumented")) (|exponent| ((|#2| $) "\\spad{exponent(x)} \\undocumented")))
NIL
NIL
-(-652 R M)
+(-653 R M)
((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#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| (($ $ $) "\\spad{adjoint(op1, op2)} sets the adjoint of \\spad{op1} to be \\spad{op2}. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}.")))
-((-3987 |has| |#1| (-146)) (-3986 |has| |#1| (-146)) (-3989 . T))
+((-3991 |has| |#1| (-146)) (-3990 |has| |#1| (-146)) (-3993 . T))
((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))))
-(-653 R |Mod| -2036 -3515 |exactQuo|)
+(-654 R |Mod| -2039 -3519 |exactQuo|)
((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\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")))
-((-3989 . T))
+((-3993 . T))
NIL
-(-654 S R)
+(-655 S R)
((|constructor| (NIL "The category of modules over a commutative ring. \\blankline")))
NIL
NIL
-(-655 R)
+(-656 R)
((|constructor| (NIL "The category of modules over a commutative ring. \\blankline")))
-((-3987 . T) (-3986 . T))
+((-3991 . T) (-3990 . T))
NIL
-(-656 -3091)
+(-657 -3094)
((|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]]}.")))
-((-3989 . T))
+((-3993 . T))
NIL
-(-657 S)
+(-658 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}.")) (* (($ $ $) "\\spad{a*b} is the product of \\spad{a} and \\spad{b} in a set with a binary operation.")))
NIL
NIL
-(-658)
+(-659)
((|constructor| (NIL "Monad is the class of all multiplicative monads,{} \\spadignore{i.e.} sets with a binary operation.")) (** (($ $ (|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.")))
NIL
NIL
-(-659 S)
+(-660 S)
((|constructor| (NIL "\\indented{1}{MonadWithUnit is the class of multiplicative monads with unit,{}} \\indented{1}{\\spadignore{i.e.} sets with a binary operation and a unit element.} Axioms \\indented{3}{leftIdentity(\"*\":(\\%,{}\\%)->\\%,{}1)\\space{3}\\tab{30} 1*x=x} \\indented{3}{rightIdentity(\"*\":(\\%,{}\\%)->\\%,{}1)\\space{2}\\tab{30} x*1=x} Common Additional Axioms \\indented{3}{unitsKnown---if \"recip\" says \"failed\",{} that PROVES input wasn't a unit}")) (|rightRecip| (((|Union| $ "failed") $) "\\spad{rightRecip(a)} returns an element,{} which is a right inverse of \\spad{a},{} or \\spad{\"failed\"} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (|leftRecip| (((|Union| $ "failed") $) "\\spad{leftRecip(a)} returns an element,{} which is a left inverse of \\spad{a},{} or \\spad{\"failed\"} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(a)} returns an element,{} which is both a left and a right inverse of \\spad{a},{} or \\spad{\"failed\"} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (** (($ $ (|NonNegativeInteger|)) "\\spad{a**n} returns the \\spad{n}\\spad{-}th power of \\spad{a},{} defined by repeated squaring.")) (|leftPower| (($ $ (|NonNegativeInteger|)) "\\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,0) := 1}.")) (|rightPower| (($ $ (|NonNegativeInteger|)) "\\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,0) := 1}.")) (|one?| (((|Boolean|) $) "\\spad{one?(a)} tests whether \\spad{a} is the unit 1.")) (|One| (($) "1 returns the unit element,{} denoted by 1.")))
NIL
NIL
-(-660)
+(-661)
((|constructor| (NIL "\\indented{1}{MonadWithUnit is the class of multiplicative monads with unit,{}} \\indented{1}{\\spadignore{i.e.} sets with a binary operation and a unit element.} Axioms \\indented{3}{leftIdentity(\"*\":(\\%,{}\\%)->\\%,{}1)\\space{3}\\tab{30} 1*x=x} \\indented{3}{rightIdentity(\"*\":(\\%,{}\\%)->\\%,{}1)\\space{2}\\tab{30} x*1=x} Common Additional Axioms \\indented{3}{unitsKnown---if \"recip\" says \"failed\",{} that PROVES input wasn't a unit}")) (|rightRecip| (((|Union| $ "failed") $) "\\spad{rightRecip(a)} returns an element,{} which is a right inverse of \\spad{a},{} or \\spad{\"failed\"} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (|leftRecip| (((|Union| $ "failed") $) "\\spad{leftRecip(a)} returns an element,{} which is a left inverse of \\spad{a},{} or \\spad{\"failed\"} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(a)} returns an element,{} which is both a left and a right inverse of \\spad{a},{} or \\spad{\"failed\"} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (** (($ $ (|NonNegativeInteger|)) "\\spad{a**n} returns the \\spad{n}\\spad{-}th power of \\spad{a},{} defined by repeated squaring.")) (|leftPower| (($ $ (|NonNegativeInteger|)) "\\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,0) := 1}.")) (|rightPower| (($ $ (|NonNegativeInteger|)) "\\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,0) := 1}.")) (|one?| (((|Boolean|) $) "\\spad{one?(a)} tests whether \\spad{a} is the unit 1.")) (|One| (($) "1 returns the unit element,{} denoted by 1.")))
NIL
NIL
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+(-662 S R UP)
((|constructor| (NIL "A \\spadtype{MonogenicAlgebra} is an algebra of finite rank which can be generated by a single element.")) (|derivationCoordinates| (((|Matrix| |#2|) (|Vector| $) (|Mapping| |#2| |#2|)) "\\spad{derivationCoordinates(b, ')} returns \\spad{M} such that \\spad{b' = M b}.")) (|lift| ((|#3| $) "\\spad{lift(z)} returns a minimal degree univariate polynomial up such that \\spad{z=reduce up}.")) (|convert| (($ |#3|) "\\spad{convert(up)} converts the univariate polynomial \\spad{up} to an algebra element,{} reducing by the \\spad{definingPolynomial()} if necessary.")) (|reduce| (((|Union| $ "failed") (|Fraction| |#3|)) "\\spad{reduce(frac)} converts the fraction \\spad{frac} to an algebra element.") (($ |#3|) "\\spad{reduce(up)} converts the univariate polynomial \\spad{up} to an algebra element,{} reducing by the \\spad{definingPolynomial()} if necessary.")) (|definingPolynomial| ((|#3|) "\\spad{definingPolynomial()} returns the minimal polynomial which \\spad{generator()} satisfies.")) (|generator| (($) "\\spad{generator()} returns the generator for this domain.")))
NIL
-((|HasCategory| |#2| (QUOTE (-298))) (|HasCategory| |#2| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-317))))
-(-662 R UP)
+((|HasCategory| |#2| (QUOTE (-299))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-318))))
+(-663 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.")))
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NIL
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((|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
-(-664)
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((|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| (($) "1 is the multiplicative identity.")))
NIL
NIL
-(-665 T$)
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((|constructor| (NIL "This domain implements monoid operations.")) (|monoidOperation| (($ (|Mapping| |#1| |#1| |#1|) |#1|) "\\spad{monoidOperation(f,e)} constructs a operation from the binary mapping \\spad{f} with neutral value \\spad{e}.")))
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+(((|%Rule| |neutrality| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|)) (SEQ (-3058 (|f| |x| (-2414 |f|)) |x|) (|exit| 1 (-3058 (|f| (-2414 |f|) |x|) |x|))))) . T) ((|%Rule| |associativity| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|) (|:| |y| |#1|) (|:| |z| |#1|)) (-3058 (|f| (|f| |x| |y|) |z|) (|f| |x| (|f| |y| |z|))))) . T))
NIL
-(-666 T$)
+(-667 T$)
((|constructor| (NIL "This is the category of all domains that implement monoid operations")) (|neutralValue| ((|#1| $) "\\spad{neutralValue f} returns the neutral value of the monoid operation \\spad{f}.")))
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+(((|%Rule| |neutrality| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|)) (SEQ (-3058 (|f| |x| (-2414 |f|)) |x|) (|exit| 1 (-3058 (|f| (-2414 |f|) |x|) |x|))))) . T) ((|%Rule| |associativity| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|) (|:| |y| |#1|) (|:| |z| |#1|)) (-3058 (|f| (|f| |x| |y|) |z|) (|f| |x| (|f| |y| |z|))))) . T))
NIL
-(-667 -3091 UP)
+(-668 -3094 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
-(-668 |VarSet| E1 E2 R S PR PS)
+(-669 |VarSet| E1 E2 R S PR PS)
((|constructor| (NIL "\\indented{1}{Utilities for MPolyCat} Author: Manuel Bronstein Date Created: 1987 Date Last Updated: 28 March 1990 (PG)")) (|reshape| ((|#7| (|List| |#5|) |#6|) "\\spad{reshape(l,p)} \\undocumented")) (|map| ((|#7| (|Mapping| |#5| |#4|) |#6|) "\\spad{map(f,p)} \\undocumented")))
NIL
NIL
-(-669 |Vars1| |Vars2| E1 E2 R PR1 PR2)
+(-670 |Vars1| |Vars2| E1 E2 R PR1 PR2)
((|constructor| (NIL "This package \\undocumented")) (|map| ((|#7| (|Mapping| |#2| |#1|) |#6|) "\\spad{map(f,x)} \\undocumented")))
NIL
NIL
-(-670 E OV R PPR)
+(-671 E OV R PPR)
((|constructor| (NIL "\\indented{3}{This package exports a factor operation for multivariate polynomials} with coefficients which are polynomials over some ring \\spad{R} over which we can factor. It is used internally by packages such as the solve package which need to work with polynomials in a specific set of variables with coefficients which are polynomials in all the other variables.")) (|factor| (((|Factored| |#4|) |#4|) "\\spad{factor(p)} factors a polynomial with polynomial coefficients.")) (|variable| (((|Union| $ "failed") (|Symbol|)) "\\spad{variable(s)} makes an element from symbol \\spad{s} or fails.")) (|convert| (((|Symbol|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol")))
NIL
NIL
-(-671 |vl| R)
+(-672 |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.")))
-(((-3994 "*") |has| |#2| (-146)) (-3985 |has| |#2| (-495)) (-3990 |has| |#2| (-6 -3990)) (-3987 . T) (-3986 . T) (-3989 . T))
-((|HasCategory| |#2| (QUOTE (-822))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-389))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-822)))) (OR (|HasCategory| |#2| (QUOTE (-389))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-822)))) (OR (|HasCategory| |#2| (QUOTE (-389))) (|HasCategory| |#2| (QUOTE (-822)))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-146))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-495)))) (-12 (|HasCategory| |#2| (QUOTE (-797 (-327)))) (|HasCategory| (-774 |#1|) (QUOTE (-797 (-327))))) (-12 (|HasCategory| |#2| (QUOTE (-797 (-484)))) (|HasCategory| (-774 |#1|) (QUOTE (-797 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-554 (-801 (-327))))) (|HasCategory| (-774 |#1|) (QUOTE (-554 (-801 (-327)))))) (-12 (|HasCategory| |#2| (QUOTE (-554 (-801 (-484))))) (|HasCategory| (-774 |#1|) (QUOTE (-554 (-801 (-484)))))) (-12 (|HasCategory| |#2| (QUOTE (-554 (-473)))) (|HasCategory| (-774 |#1|) (QUOTE (-554 (-473))))) (|HasCategory| |#2| (QUOTE (-581 (-484)))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-38 (-347 (-484))))) (|HasCategory| |#2| (QUOTE (-951 (-484)))) (OR (|HasCategory| |#2| (QUOTE (-38 (-347 (-484))))) (|HasCategory| |#2| (QUOTE (-951 (-347 (-484)))))) (|HasCategory| |#2| (QUOTE (-951 (-347 (-484))))) (|HasCategory| |#2| (QUOTE (-311))) (|HasAttribute| |#2| (QUOTE -3990)) (|HasCategory| |#2| (QUOTE (-389))) (-12 (|HasCategory| |#2| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#2| (QUOTE (-118)))))
-(-672 E OV R PRF)
+(((-3998 "*") |has| |#2| (-146)) (-3989 |has| |#2| (-496)) (-3994 |has| |#2| (-6 -3994)) (-3991 . T) (-3990 . T) (-3993 . T))
+((|HasCategory| |#2| (QUOTE (-823))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-390))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-823)))) (OR (|HasCategory| |#2| (QUOTE (-390))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-823)))) (OR (|HasCategory| |#2| (QUOTE (-390))) (|HasCategory| |#2| (QUOTE (-823)))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-146))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-496)))) (-12 (|HasCategory| |#2| (QUOTE (-798 (-328)))) (|HasCategory| (-775 |#1|) (QUOTE (-798 (-328))))) (-12 (|HasCategory| |#2| (QUOTE (-798 (-485)))) (|HasCategory| (-775 |#1|) (QUOTE (-798 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-555 (-802 (-328))))) (|HasCategory| (-775 |#1|) (QUOTE (-555 (-802 (-328)))))) (-12 (|HasCategory| |#2| (QUOTE (-555 (-802 (-485))))) (|HasCategory| (-775 |#1|) (QUOTE (-555 (-802 (-485)))))) (-12 (|HasCategory| |#2| (QUOTE (-555 (-474)))) (|HasCategory| (-775 |#1|) (QUOTE (-555 (-474))))) (|HasCategory| |#2| (QUOTE (-582 (-485)))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-38 (-348 (-485))))) (|HasCategory| |#2| (QUOTE (-952 (-485)))) (OR (|HasCategory| |#2| (QUOTE (-38 (-348 (-485))))) (|HasCategory| |#2| (QUOTE (-952 (-348 (-485)))))) (|HasCategory| |#2| (QUOTE (-952 (-348 (-485))))) (|HasCategory| |#2| (QUOTE (-312))) (|HasAttribute| |#2| (QUOTE -3994)) (|HasCategory| |#2| (QUOTE (-390))) (-12 (|HasCategory| |#2| (QUOTE (-823))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-823))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#2| (QUOTE (-118)))))
+(-673 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
NIL
-(-673 E OV R P)
+(-674 E OV R P)
((|constructor| (NIL "\\indented{1}{MRationalFactorize contains the factor function for multivariate} polynomials over the quotient field of a ring \\spad{R} such that the package MultivariateFactorize can factor multivariate polynomials over \\spad{R}.")) (|factor| (((|Factored| |#4|) |#4|) "\\spad{factor(p)} factors the multivariate polynomial \\spad{p} with coefficients which are fractions of elements of \\spad{R}.")))
NIL
NIL
-(-674 R S M)
+(-675 R S M)
((|constructor| (NIL "\\spad{MonoidRingFunctions2} implements functions between two monoid rings defined with the same monoid over different rings.")) (|map| (((|MonoidRing| |#2| |#3|) (|Mapping| |#2| |#1|) (|MonoidRing| |#1| |#3|)) "\\spad{map(f,u)} maps \\spad{f} onto the coefficients \\spad{f} the element \\spad{u} of the monoid ring to create an element of a monoid ring with the same monoid \\spad{b}.")))
NIL
NIL
-(-675 R M)
+(-676 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}.")))
-((-3987 |has| |#1| (-146)) (-3986 |has| |#1| (-146)) (-3989 . T))
-((-12 (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#2| (QUOTE (-317)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-757))))
-(-676 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}.")))
-((-3992 . T) (-3982 . T) (-3993 . T))
-((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-554 (-473)))) (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-72))))
+((-3991 |has| |#1| (-146)) (-3990 |has| |#1| (-146)) (-3993 . T))
+((-12 (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#2| (QUOTE (-318)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-758))))
(-677 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}.")))
+((-3996 . T) (-3986 . T) (-3997 . T))
+((-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-555 (-474)))) (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (QUOTE (-554 (-774)))) (|HasCategory| |#1| (QUOTE (-72))))
+(-678 S)
((|constructor| (NIL "A multi-set aggregate is a set which keeps track of the multiplicity of its elements.")))
-((-3982 . T) (-3993 . T))
+((-3986 . T) (-3997 . T))
NIL
-(-678)
+(-679)
((|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
NIL
-(-679 S)
+(-680 S)
((|constructor| (NIL "This package exports tools for merging lists")) (|mergeDifference| (((|List| |#1|) (|List| |#1|) (|List| |#1|)) "\\spad{mergeDifference(l1,l2)} returns a list of elements in \\spad{l1} not present in \\spad{l2}. Assumes lists are ordered and all \\spad{x} in \\spad{l2} are also in \\spad{l1}.")))
NIL
NIL
-(-680 |Coef| |Var|)
+(-681 |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}.")))
-(((-3994 "*") |has| |#1| (-146)) (-3985 |has| |#1| (-495)) (-3987 . T) (-3986 . T) (-3989 . T))
+(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3991 . T) (-3990 . T) (-3993 . T))
NIL
-(-681 OV E R P)
+(-682 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")))
NIL
NIL
-(-682 E OV R P)
+(-683 E OV R P)
((|constructor| (NIL "Author : \\spad{P}.Gianni This package provides the functions for the computation of the square free decomposition of a multivariate polynomial. It uses the package GenExEuclid for the resolution of the equation \\spad{Af + Bg = h} and its generalization to \\spad{n} polynomials over an integral domain and the package \\spad{MultivariateLifting} for the \"multivariate\" lifting.")) (|normDeriv2| (((|SparseUnivariatePolynomial| |#3|) (|SparseUnivariatePolynomial| |#3|) (|Integer|)) "\\spad{normDeriv2 should} be local")) (|myDegree| (((|List| (|NonNegativeInteger|)) (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|NonNegativeInteger|)) "\\spad{myDegree should} be local")) (|lift| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#3|) (|SparseUnivariatePolynomial| |#3|) |#4| (|List| |#2|) (|List| (|NonNegativeInteger|)) (|List| |#3|)) "\\spad{lift should} be local")) (|check| (((|Boolean|) (|List| (|Record| (|:| |factor| (|SparseUnivariatePolynomial| |#3|)) (|:| |exponent| (|Integer|)))) (|List| (|Record| (|:| |factor| (|SparseUnivariatePolynomial| |#3|)) (|:| |exponent| (|Integer|))))) "\\spad{check should} be local")) (|coefChoose| ((|#4| (|Integer|) (|Factored| |#4|)) "\\spad{coefChoose should} be local")) (|intChoose| (((|Record| (|:| |upol| (|SparseUnivariatePolynomial| |#3|)) (|:| |Lval| (|List| |#3|)) (|:| |Lfact| (|List| (|Record| (|:| |factor| (|SparseUnivariatePolynomial| |#3|)) (|:| |exponent| (|Integer|))))) (|:| |ctpol| |#3|)) (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|List| (|List| |#3|))) "\\spad{intChoose should} be local")) (|nsqfree| (((|Record| (|:| |unitPart| |#4|) (|:| |suPart| (|List| (|Record| (|:| |factor| (|SparseUnivariatePolynomial| |#4|)) (|:| |exponent| (|Integer|)))))) (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|List| (|List| |#3|))) "\\spad{nsqfree should} be local")) (|consnewpol| (((|Record| (|:| |pol| (|SparseUnivariatePolynomial| |#4|)) (|:| |polval| (|SparseUnivariatePolynomial| |#3|))) (|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#3|) (|Integer|)) "\\spad{consnewpol should} be local")) (|univcase| (((|Factored| |#4|) |#4| |#2|) "\\spad{univcase should} be local")) (|compdegd| (((|Integer|) (|List| (|Record| (|:| |factor| (|SparseUnivariatePolynomial| |#3|)) (|:| |exponent| (|Integer|))))) "\\spad{compdegd should} be local")) (|squareFreePrim| (((|Factored| |#4|) |#4|) "\\spad{squareFreePrim(p)} compute the square free decomposition of a primitive multivariate polynomial \\spad{p}.")) (|squareFree| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{squareFree(p)} computes the square free decomposition of a multivariate polynomial \\spad{p} presented as a univariate polynomial with multivariate coefficients.") (((|Factored| |#4|) |#4|) "\\spad{squareFree(p)} computes the square free decomposition of a multivariate polynomial \\spad{p}.")))
NIL
NIL
-(-683 S R)
+(-684 S R)
((|constructor| (NIL "NonAssociativeAlgebra is the category of non associative algebras (modules which are themselves non associative rngs). Axioms \\indented{3}{r*(a*b) = (r*a)*b = a*(r*b)}")) (|plenaryPower| (($ $ (|PositiveInteger|)) "\\spad{plenaryPower(a,n)} is recursively defined to be \\spad{plenaryPower(a,n-1)*plenaryPower(a,n-1)} for \\spad{n>1} and \\spad{a} for \\spad{n=1}.")))
NIL
NIL
-(-684 R)
+(-685 R)
((|constructor| (NIL "NonAssociativeAlgebra is the category of non associative algebras (modules which are themselves non associative rngs). Axioms \\indented{3}{r*(a*b) = (r*a)*b = a*(r*b)}")) (|plenaryPower| (($ $ (|PositiveInteger|)) "\\spad{plenaryPower(a,n)} is recursively defined to be \\spad{plenaryPower(a,n-1)*plenaryPower(a,n-1)} for \\spad{n>1} and \\spad{a} for \\spad{n=1}.")))
-((-3987 . T) (-3986 . T))
+((-3991 . T) (-3990 . T))
NIL
-(-685 S)
+(-686 S)
((|constructor| (NIL "NonAssociativeRng is a basic ring-type structure,{} not necessarily commutative or associative,{} and not necessarily with unit. Axioms \\indented{2}{x*(y+z) = x*y + x*z} \\indented{2}{(x+y)*z = x*z + y*z} Common Additional Axioms \\indented{2}{noZeroDivisors\\space{2}ab = 0 => \\spad{a=0} or \\spad{b=0}}")) (|antiCommutator| (($ $ $) "\\spad{antiCommutator(a,b)} returns \\spad{a*b+b*a}.")) (|commutator| (($ $ $) "\\spad{commutator(a,b)} returns \\spad{a*b-b*a}.")) (|associator| (($ $ $ $) "\\spad{associator(a,b,c)} returns \\spad{(a*b)*c-a*(b*c)}.")))
NIL
NIL
-(-686)
+(-687)
((|constructor| (NIL "NonAssociativeRng is a basic ring-type structure,{} not necessarily commutative or associative,{} and not necessarily with unit. Axioms \\indented{2}{x*(y+z) = x*y + x*z} \\indented{2}{(x+y)*z = x*z + y*z} Common Additional Axioms \\indented{2}{noZeroDivisors\\space{2}ab = 0 => \\spad{a=0} or \\spad{b=0}}")) (|antiCommutator| (($ $ $) "\\spad{antiCommutator(a,b)} returns \\spad{a*b+b*a}.")) (|commutator| (($ $ $) "\\spad{commutator(a,b)} returns \\spad{a*b-b*a}.")) (|associator| (($ $ $ $) "\\spad{associator(a,b,c)} returns \\spad{(a*b)*c-a*(b*c)}.")))
NIL
NIL
-(-687 S)
+(-688 S)
((|constructor| (NIL "A NonAssociativeRing is a non associative rng which has a unit,{} the multiplication is not necessarily commutative or associative.")) (|coerce| (($ (|Integer|)) "\\spad{coerce(n)} coerces the integer \\spad{n} to an element of the ring.")) (|characteristic| (((|NonNegativeInteger|)) "\\spad{characteristic()} returns the characteristic of the ring.")))
NIL
NIL
-(-688)
+(-689)
((|constructor| (NIL "A NonAssociativeRing is a non associative rng which has a unit,{} the multiplication is not necessarily commutative or associative.")) (|coerce| (($ (|Integer|)) "\\spad{coerce(n)} coerces the integer \\spad{n} to an element of the ring.")) (|characteristic| (((|NonNegativeInteger|)) "\\spad{characteristic()} returns the characteristic of the ring.")))
NIL
NIL
-(-689 |Par|)
+(-690 |Par|)
((|constructor| (NIL "This package computes explicitly eigenvalues and eigenvectors of matrices with entries over the complex rational numbers. The results are expressed either as complex floating numbers or as complex rational numbers depending on the type of the precision parameter.")) (|complexEigenvectors| (((|List| (|Record| (|:| |outval| (|Complex| |#1|)) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| (|Complex| |#1|)))))) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) |#1|) "\\spad{complexEigenvectors(m,eps)} returns a list of records each one containing a complex eigenvalue,{} its algebraic multiplicity,{} and a list of associated eigenvectors. All these results are computed to precision \\spad{eps} and are expressed as complex floats or complex rational numbers depending on the type of \\spad{eps} (float or rational).")) (|complexEigenvalues| (((|List| (|Complex| |#1|)) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) |#1|) "\\spad{complexEigenvalues(m,eps)} computes the eigenvalues of the matrix \\spad{m} to precision \\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
-(-690 -3091)
+(-691 -3094)
((|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
-(-691 P -3091)
+(-692 P -3094)
((|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''.")))
NIL
NIL
-(-692 T$)
+(-693 T$)
NIL
NIL
NIL
-(-693 UP -3091)
+(-694 UP -3094)
((|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
-(-694 R)
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((|constructor| (NIL "NonLinearSolvePackage is an interface to \\spadtype{SystemSolvePackage} that attempts to retract the coefficients of the equations before solving. The solutions are given in the algebraic closure of \\spad{R} whenever possible.")) (|solve| (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|))) "\\spad{solve(lp)} finds the solution in the algebraic closure of \\spad{R} of the list \\spad{lp} of rational functions with respect to all the symbols appearing in \\spad{lp}.") (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{solve(lp,lv)} finds the solutions in the algebraic closure of \\spad{R} of the list \\spad{lp} of rational functions with respect to the list of symbols \\spad{lv}.")) (|solveInField| (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|))) "\\spad{solveInField(lp)} finds the solution of the list \\spad{lp} of rational functions with respect to all the symbols appearing in \\spad{lp}.") (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{solveInField(lp,lv)} finds the solutions of the list \\spad{lp} of rational functions with respect to the list of symbols \\spad{lv}.")))
NIL
NIL
-(-695)
+(-696)
((|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.")))
-(((-3994 "*") . T))
+(((-3998 "*") . T))
NIL
-(-696 R -3091)
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((|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
-(-697)
+(-698)
((|constructor| (NIL "\\spadtype{None} implements a type with no objects. It is mainly used in technical situations where such a thing is needed (\\spadignore{e.g.} the interpreter and some of the internal \\spadtype{Expression} code).")))
NIL
NIL
-(-698 S)
+(-699 S)
((|constructor| (NIL "\\spadtype{NoneFunctions1} implements functions on \\spadtype{None}. It particular it includes a particulary dangerous coercion from any other type to \\spadtype{None}.")) (|coerce| (((|None|) |#1|) "\\spad{coerce(x)} changes \\spad{x} into an object of type \\spadtype{None}.")))
NIL
NIL
-(-699 R |PolR| E |PolE|)
+(-700 R |PolR| E |PolE|)
((|constructor| (NIL "This package implements the norm of a polynomial with coefficients in a monogenic algebra (using resultants)")) (|norm| ((|#2| |#4|) "\\spad{norm q} returns the norm of \\spad{q},{} \\spadignore{i.e.} the product of all the conjugates of \\spad{q}.")))
NIL
NIL
-(-700 R E V P TS)
+(-701 R E V P TS)
((|constructor| (NIL "A package for computing normalized assocites of univariate polynomials with coefficients in a tower of simple extensions of a field.\\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 gcd over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of \\spad{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},{}ts)} is an internal subroutine,{} exported only for developement.")) (|outputArgs| (((|Void|) (|String|) (|String|) |#4| |#5|) "\\axiom{outputArgs(\\spad{s1},{}\\spad{s2},{}\\spad{p},{}ts)} is an internal subroutine,{} exported only for developement.")) (|normalize| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{normalize(\\spad{p},{}ts)} normalizes \\axiom{\\spad{p}} \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}.")) (|normalizedAssociate| ((|#4| |#4| |#5|) "\\axiom{normalizedAssociate(\\spad{p},{}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},{}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
-(-701 -3091 |ExtF| |SUEx| |ExtP| |n|)
+(-702 -3094 |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
-(-702 BP E OV R P)
+(-703 BP E OV R P)
((|constructor| (NIL "Package for the determination of the coefficients in the lifting process. Used by \\spadtype{MultivariateLifting}. This package will work for every euclidean domain \\spad{R} which has property \\spad{F},{} \\spadignore{i.e.} there exists a factor operation in \\spad{R[x]}.")) (|listexp| (((|List| (|NonNegativeInteger|)) |#1|) "\\spad{listexp }\\undocumented")) (|npcoef| (((|Record| (|:| |deter| (|List| (|SparseUnivariatePolynomial| |#5|))) (|:| |dterm| (|List| (|List| (|Record| (|:| |expt| (|NonNegativeInteger|)) (|:| |pcoef| |#5|))))) (|:| |nfacts| (|List| |#1|)) (|:| |nlead| (|List| |#5|))) (|SparseUnivariatePolynomial| |#5|) (|List| |#1|) (|List| |#5|)) "\\spad{npcoef }\\undocumented")))
NIL
NIL
-(-703 |Par|)
+(-704 |Par|)
((|constructor| (NIL "This package computes explicitly eigenvalues and eigenvectors of matrices with entries over the Rational Numbers. The results are expressed as floating numbers or as rational numbers depending on the type of the parameter Par.")) (|realEigenvectors| (((|List| (|Record| (|:| |outval| |#1|) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| |#1|))))) (|Matrix| (|Fraction| (|Integer|))) |#1|) "\\spad{realEigenvectors(m,eps)} returns a list of records each one containing a real eigenvalue,{} its algebraic multiplicity,{} and a list of associated eigenvectors. All these results are computed to precision \\spad{eps} as floats or rational numbers depending on the type of \\spad{eps} .")) (|realEigenvalues| (((|List| |#1|) (|Matrix| (|Fraction| (|Integer|))) |#1|) "\\spad{realEigenvalues(m,eps)} computes the eigenvalues of the matrix \\spad{m} to precision \\spad{eps}. The eigenvalues are expressed as floats or rational numbers depending on the type of \\spad{eps} (float or rational).")) (|characteristicPolynomial| (((|Polynomial| (|Fraction| (|Integer|))) (|Matrix| (|Fraction| (|Integer|))) (|Symbol|)) "\\spad{characteristicPolynomial(m,x)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over RN with variable \\spad{x}. Fraction \\spad{P} RN.") (((|Polynomial| (|Fraction| (|Integer|))) (|Matrix| (|Fraction| (|Integer|)))) "\\spad{characteristicPolynomial(m)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over RN with a new symbol as variable.")))
NIL
NIL
-(-704 R |VarSet|)
+(-705 R |VarSet|)
((|constructor| (NIL "A post-facto extension for \\axiomType{SMP} in order to speed up operations related to pseudo-division and gcd. This domain is based on the \\axiomType{NSUP} constructor which is itself a post-facto extension of the \\axiomType{SUP} constructor.")))
-(((-3994 "*") |has| |#1| (-146)) (-3985 |has| |#1| (-495)) (-3990 |has| |#1| (-6 -3990)) (-3987 . T) (-3986 . T) (-3989 . T))
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-(-705 R)
+(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3994 |has| |#1| (-6 -3994)) (-3991 . T) (-3990 . T) (-3993 . T))
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+(-706 R)
((|constructor| (NIL "A post-facto extension for \\axiomType{SUP} in order to speed up operations related to pseudo-division and gcd for both \\axiomType{SUP} and,{} consequently,{} \\axiomType{NSMP}.")) (|halfExtendedResultant2| (((|Record| (|:| |resultant| |#1|) (|:| |coef2| $)) $ $) "\\axiom{\\spad{halfExtendedResultant2}(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} cb]}")) (|halfExtendedResultant1| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $)) $ $) "\\axiom{\\spad{halfExtendedResultant1}(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} cb]}")) (|extendedResultant| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{}cb]} such that \\axiom{\\spad{r}} is the resultant of \\axiom{a} and \\axiom{\\spad{b}} and \\axiom{\\spad{r} = ca * a + cb * \\spad{b}}")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{\\spad{halfExtendedSubResultantGcd2}(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}cb]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} cb]}")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{\\spad{halfExtendedSubResultantGcd1}(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} cb]}")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} cb]} such that \\axiom{\\spad{g}} is a gcd of \\axiom{a} and \\axiom{\\spad{b}} in \\axiom{R^(\\spad{-1}) \\spad{P}} and \\axiom{\\spad{g} = ca * a + cb * \\spad{b}}")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns \\axiom{resultant(a,{}\\spad{b})} if \\axiom{a} and \\axiom{\\spad{b}} has no non-trivial gcd in \\axiom{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| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{c^n * a = q*b +r} and \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} where \\axiom{\\spad{n} + \\spad{g} = max(0,{} degree(\\spad{b}) - degree(a) + 1)}.")) (|lazyPseudoRemainder| (($ $ $) "\\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|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{c^n * a - \\spad{r}} where \\axiom{\\spad{c}} is \\axiom{leadingCoefficient(\\spad{b})} and \\axiom{\\spad{n}} is as small as possible with the previous properties.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} returns \\axiom{\\spad{r}} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{a -r} where \\axiom{\\spad{b}} is monic.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#1| $) "\\axiom{fmecg(\\spad{p1},{}\\spad{e},{}\\spad{r},{}\\spad{p2})} returns \\axiom{\\spad{p1} - \\spad{r} * X**e * \\spad{p2}} where \\axiom{\\spad{X}} is \\axiom{monomial(1,{}1)}")))
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-(-706 R S)
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+(-707 R S)
((|constructor| (NIL "This package lifts a mapping from coefficient rings \\spad{R} to \\spad{S} to a mapping from sparse univariate polynomial over \\spad{R} to a sparse univariate polynomial over \\spad{S}. Note that the mapping is assumed to send zero to zero,{} since it will only be applied to the non-zero coefficients of the polynomial.")) (|map| (((|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
-(-707 R)
+(-708 R)
((|constructor| (NIL "This package provides polynomials as functions on a ring.")) (|eulerE| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{eulerE(n,r)} \\undocumented")) (|bernoulliB| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{bernoulliB(n,r)} \\undocumented")) (|cyclotomic| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{cyclotomic(n,r)} \\undocumented")))
NIL
-((|HasCategory| |#1| (QUOTE (-38 (-347 (-484))))))
-(-708 R E V P)
+((|HasCategory| |#1| (QUOTE (-38 (-348 (-485))))))
+(-709 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 gcd over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of \\spad{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.}")))
-((-3993 . T) (-3992 . T))
+((-3997 . T) (-3996 . T))
NIL
-(-709 S)
+(-710 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 (-495))) (|HasCategory| |#1| (QUOTE (-757)))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-962))) (|HasCategory| |#1| (QUOTE (-146))))
-(-710)
+((-12 (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-758)))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-963))) (|HasCategory| |#1| (QUOTE (-146))))
+(-711)
((|constructor| (NIL "NumberFormats provides function to format and read arabic and roman numbers,{} to convert numbers to strings and to read floating-point numbers.")) (|ScanFloatIgnoreSpacesIfCan| (((|Union| (|Float|) "failed") (|String|)) "\\spad{ScanFloatIgnoreSpacesIfCan(s)} tries to form a floating point number from the string \\spad{s} ignoring any spaces.")) (|ScanFloatIgnoreSpaces| (((|Float|) (|String|)) "\\spad{ScanFloatIgnoreSpaces(s)} forms a floating point number from the string \\spad{s} ignoring any spaces. Error is generated if the string is not recognised as a floating point number.")) (|ScanRoman| (((|PositiveInteger|) (|String|)) "\\spad{ScanRoman(s)} forms an integer from a Roman numeral string \\spad{s}.")) (|FormatRoman| (((|String|) (|PositiveInteger|)) "\\spad{FormatRoman(n)} forms a Roman numeral string from an integer \\spad{n}.")) (|ScanArabic| (((|PositiveInteger|) (|String|)) "\\spad{ScanArabic(s)} forms an integer from an Arabic numeral string \\spad{s}.")) (|FormatArabic| (((|String|) (|PositiveInteger|)) "\\spad{FormatArabic(n)} forms an Arabic numeral string from an integer \\spad{n}.")))
NIL
NIL
-(-711)
+(-712)
((|constructor| (NIL "This package is a suite of functions for the numerical integration of an ordinary differential equation of \\spad{n} variables: \\blankline \\indented{8}{\\center{dy/dx = \\spad{f}(\\spad{y},{}\\spad{x})\\space{5}\\spad{y} is an \\spad{n}-vector}} \\blankline \\par All the routines are based on a 4-th order Runge-Kutta kernel. These routines generally have as arguments: \\spad{n},{} the number of dependent variables; \\spad{x1},{} the initial point; \\spad{h},{} the step size; \\spad{y},{} a vector of initial conditions of length \\spad{n} which upon exit contains the solution at \\spad{x1 + h}; \\spad{derivs},{} a function which computes the right hand side of the ordinary differential equation: \\spad{derivs(dydx,y,x)} computes \\spad{dydx},{} a vector which contains the derivative information. \\blankline \\par In order of increasing complexity:\\begin{items} \\blankline \\item \\spad{rk4(y,n,x1,h,derivs)} advances the solution vector to \\spad{x1 + h} and return the values in \\spad{y}. \\blankline \\item \\spad{rk4(y,n,x1,h,derivs,t1,t2,t3,t4)} is the same as \\spad{rk4(y,n,x1,h,derivs)} except that you must provide 4 scratch arrays \\spad{t1}-\\spad{t4} of size \\spad{n}. \\blankline \\item Starting with \\spad{y} at \\spad{x1},{} \\spad{rk4f(y,n,x1,x2,ns,derivs)} uses \\spad{ns} fixed steps of a 4-th order Runge-Kutta integrator to advance the solution vector to \\spad{x2} and return the values in \\spad{y}. Argument \\spad{x2},{} is the final point,{} and \\spad{ns},{} the number of steps to take. \\blankline \\item \\spad{rk4qc(y,n,x1,step,eps,yscal,derivs)} takes a 5-th order Runge-Kutta step with monitoring of local truncation to ensure accuracy and adjust stepsize. The function takes two half steps and one full step and scales the difference in solutions at the final point. If the error is within \\spad{eps},{} the step is taken and the result is returned. If the error is not within \\spad{eps},{} the stepsize if decreased and the procedure is tried again until the desired accuracy is reached. Upon input,{} an trial step size must be given and upon return,{} an estimate of the next step size to use is returned as well as the step size which produced the desired accuracy. The scaled error is computed as \\center{\\spad{error = MAX(ABS((y2steps(i) - y1step(i))/yscal(i)))}} and this is compared against \\spad{eps}. If this is greater than \\spad{eps},{} the step size is reduced accordingly to \\center{\\spad{hnew = 0.9 * hdid * (error/eps)**(-1/4)}} If the error criterion is satisfied,{} then we check if the step size was too fine and return a more efficient one. If \\spad{error > \\spad{eps} * (6.0E-04)} then the next step size should be \\center{\\spad{hnext = 0.9 * hdid * (error/\\spad{eps})**(\\spad{-1/5})}} Otherwise \\spad{hnext = 4.0 * hdid} is returned. A more detailed discussion of this and related topics can be found in the book \"Numerical Recipies\" by \\spad{W}.Press,{} \\spad{B}.\\spad{P}. Flannery,{} \\spad{S}.A. Teukolsky,{} \\spad{W}.\\spad{T}. Vetterling published by Cambridge University Press. Argument \\spad{step} is a record of 3 floating point numbers \\spad{(try , did , next)},{} \\spad{eps} is the required accuracy,{} \\spad{yscal} is the scaling vector for the difference in solutions. On input,{} \\spad{step.try} should be the guess at a step size to achieve the accuracy. On output,{} \\spad{step.did} contains the step size which achieved the accuracy and \\spad{step.next} is the next step size to use. \\blankline \\item \\spad{rk4qc(y,n,x1,step,eps,yscal,derivs,t1,t2,t3,t4,t5,t6,t7)} is the same as \\spad{rk4qc(y,n,x1,step,eps,yscal,derivs)} except that the user must provide the 7 scratch arrays \\spad{t1-t7} of size \\spad{n}. \\blankline \\item \\spad{rk4a(y,n,x1,x2,eps,h,ns,derivs)} is a driver program which uses \\spad{rk4qc} to integrate \\spad{n} ordinary differential equations starting at \\spad{x1} to \\spad{x2},{} keeping the local truncation error to within \\spad{eps} by changing the local step size. The scaling vector is defined as \\center{\\spad{yscal(i) = abs(y(i)) + abs(h*dydx(i)) + tiny}} where \\spad{y(i)} is the solution at location \\spad{x},{} \\spad{dydx} is the ordinary differential equation's right hand side,{} \\spad{h} is the current step size and \\spad{tiny} is 10 times the smallest positive number representable. The user must supply an estimate for a trial step size and the maximum number of calls to \\spad{rk4qc} to use. Argument \\spad{x2} is the final point,{} \\spad{eps} is local truncation,{} \\spad{ns} is the maximum number of call to \\spad{rk4qc} to use. \\end{items}")) (|rk4f| (((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Float|) (|Integer|) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|))) "\\spad{rk4f(y,n,x1,x2,ns,derivs)} uses a 4-th order Runge-Kutta method to numerically integrate the ordinary differential equation {\\em dy/dx = f(y,x)} of \\spad{n} variables,{} where \\spad{y} is an \\spad{n}-vector. Starting with \\spad{y} at \\spad{x1},{} this function uses \\spad{ns} fixed steps of a 4-th order Runge-Kutta integrator to advance the solution vector to \\spad{x2} and return the values in \\spad{y}. For details,{} see \\con{NumericalOrdinaryDifferentialEquations}.")) (|rk4qc| (((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Record| (|:| |tryValue| (|Float|)) (|:| |did| (|Float|)) (|:| |next| (|Float|))) (|Float|) (|Vector| (|Float|)) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|))) "\\spad{rk4qc(y,n,x1,step,eps,yscal,derivs,t1,t2,t3,t4,t5,t6,t7)} is a subfunction for the numerical integration of an ordinary differential equation {\\em dy/dx = f(y,x)} of \\spad{n} variables,{} where \\spad{y} is an \\spad{n}-vector using a 4-th order Runge-Kutta method. This function takes a 5-th order Runge-Kutta \\spad{step} with monitoring of local truncation to ensure accuracy and adjust stepsize. For details,{} see \\con{NumericalOrdinaryDifferentialEquations}.") (((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Record| (|:| |tryValue| (|Float|)) (|:| |did| (|Float|)) (|:| |next| (|Float|))) (|Float|) (|Vector| (|Float|)) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|))) "\\spad{rk4qc(y,n,x1,step,eps,yscal,derivs)} is a subfunction for the numerical integration of an ordinary differential equation {\\em dy/dx = f(y,x)} of \\spad{n} variables,{} where \\spad{y} is an \\spad{n}-vector using a 4-th order Runge-Kutta method. This function takes a 5-th order Runge-Kutta \\spad{step} with monitoring of local truncation to ensure accuracy and adjust stepsize. For details,{} see \\con{NumericalOrdinaryDifferentialEquations}.")) (|rk4a| (((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|))) "\\spad{rk4a(y,n,x1,x2,eps,h,ns,derivs)} is a driver function for the numerical integration of an ordinary differential equation {\\em dy/dx = f(y,x)} of \\spad{n} variables,{} where \\spad{y} is an \\spad{n}-vector using a 4-th order Runge-Kutta method. For details,{} see \\con{NumericalOrdinaryDifferentialEquations}.")) (|rk4| (((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Float|) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|))) "\\spad{rk4(y,n,x1,h,derivs,t1,t2,t3,t4)} is the same as \\spad{rk4(y,n,x1,h,derivs)} except that you must provide 4 scratch arrays \\spad{t1}-\\spad{t4} of size \\spad{n}. For details,{} see \\con{NumericalOrdinaryDifferentialEquations}.") (((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Float|) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|))) "\\spad{rk4(y,n,x1,h,derivs)} uses a 4-th order Runge-Kutta method to numerically integrate the ordinary differential equation {\\em dy/dx = f(y,x)} of \\spad{n} variables,{} where \\spad{y} is an \\spad{n}-vector. Argument \\spad{y} is a vector of initial conditions of length \\spad{n} which upon exit contains the solution at \\spad{x1 + h},{} \\spad{n} is the number of dependent variables,{} \\spad{x1} is the initial point,{} \\spad{h} is the step size,{} and \\spad{derivs} is a function which computes the right hand side of the ordinary differential equation. For details,{} see \\spadtype{NumericalOrdinaryDifferentialEquations}.")))
NIL
NIL
-(-712)
+(-713)
((|constructor| (NIL "This suite of routines performs numerical quadrature using algorithms derived from the basic trapezoidal rule. Because the error term of this rule contains only even powers of the step size (for open and closed versions),{} fast convergence can be obtained if the integrand is sufficiently smooth. \\blankline Each routine returns a Record of type TrapAns,{} which contains\\indent{3} \\newline value (\\spadtype{Float}):\\tab{20} estimate of the integral \\newline error (\\spadtype{Float}):\\tab{20} estimate of the error in the computation \\newline totalpts (\\spadtype{Integer}):\\tab{20} total number of function evaluations \\newline success (\\spadtype{Boolean}):\\tab{20} if the integral was computed within the user specified error criterion \\indent{0}\\indent{0} To produce this estimate,{} each routine generates an internal sequence of sub-estimates,{} denoted by {\\em S(i)},{} depending on the routine,{} to which the various convergence criteria are applied. The user must supply a relative accuracy,{} \\spad{eps_r},{} and an absolute accuracy,{} \\spad{eps_a}. Convergence is obtained when either \\center{\\spad{ABS(S(i) - S(i-1)) < eps_r * ABS(S(i-1))}} \\center{or \\spad{ABS(S(i) - S(i-1)) < eps_a}} are \\spad{true} statements. \\blankline The routines come in three families and three flavors: \\newline\\tab{3} closed:\\tab{20}romberg,{}\\tab{30}simpson,{}\\tab{42}trapezoidal \\newline\\tab{3} open: \\tab{20}rombergo,{}\\tab{30}simpsono,{}\\tab{42}trapezoidalo \\newline\\tab{3} adaptive closed:\\tab{20}aromberg,{}\\tab{30}asimpson,{}\\tab{42}atrapezoidal \\par The {\\em S(i)} for the trapezoidal family is the value of the integral using an equally spaced absicca trapezoidal rule for that level of refinement. \\par The {\\em S(i)} for the simpson family is the value of the integral using an equally spaced absicca simpson rule for that level of refinement. \\par The {\\em S(i)} for the romberg family is the estimate of the integral using an equally spaced absicca romberg method. For the \\spad{i}\\spad{-}th level,{} this is an appropriate combination of all the previous trapezodial estimates so that the error term starts with the \\spad{2*(i+1)} power only. \\par The three families come in a closed version,{} where the formulas include the endpoints,{} an open version where the formulas do not include the endpoints and an adaptive version,{} where the user is required to input the number of subintervals over which the appropriate closed family integrator will apply with the usual convergence parmeters for each subinterval. This is useful where a large number of points are needed only in a small fraction of the entire domain. \\par Each routine takes as arguments: \\newline \\spad{f}\\tab{10} integrand \\newline a\\tab{10} starting point \\newline \\spad{b}\\tab{10} ending point \\newline \\spad{eps_r}\\tab{10} relative error \\newline \\spad{eps_a}\\tab{10} absolute error \\newline \\spad{nmin} \\tab{10} refinement level when to start checking for convergence (> 1) \\newline \\spad{nmax} \\tab{10} maximum level of refinement \\par The adaptive routines take as an additional parameter \\newline \\spad{nint}\\tab{10} the number of independent intervals to apply a closed \\indented{1}{family integrator of the same name.} \\par Notes: \\newline Closed family level \\spad{i} uses \\spad{1 + 2**i} points. \\newline Open family level \\spad{i} uses \\spad{1 + 3**i} points.")) (|trapezoidalo| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|)) "\\spad{trapezoidalo(fn,a,b,epsrel,epsabs,nmin,nmax)} uses the trapezoidal method to numerically integrate function \\spad{fn} over the open interval from \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax}. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|simpsono| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|)) "\\spad{simpsono(fn,a,b,epsrel,epsabs,nmin,nmax)} uses the simpson method to numerically integrate function \\spad{fn} over the open interval from \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax}. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|rombergo| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|)) "\\spad{rombergo(fn,a,b,epsrel,epsabs,nmin,nmax)} uses the romberg method to numerically integrate function \\spad{fn} over the open interval from \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax}. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|trapezoidal| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|)) "\\spad{trapezoidal(fn,a,b,epsrel,epsabs,nmin,nmax)} uses the trapezoidal method to numerically integrate function \\spadvar{\\spad{fn}} over the closed interval \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax}. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|simpson| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|)) "\\spad{simpson(fn,a,b,epsrel,epsabs,nmin,nmax)} uses the simpson method to numerically integrate function \\spad{fn} over the closed interval \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax}. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|romberg| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|)) "\\spad{romberg(fn,a,b,epsrel,epsabs,nmin,nmax)} uses the romberg method to numerically integrate function \\spadvar{\\spad{fn}} over the closed interval \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax}. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|atrapezoidal| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{atrapezoidal(fn,a,b,epsrel,epsabs,nmin,nmax,nint)} uses the adaptive trapezoidal method to numerically integrate function \\spad{fn} over the closed interval from \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax},{} and where \\spad{nint} is the number of independent intervals to apply the integrator. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|asimpson| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{asimpson(fn,a,b,epsrel,epsabs,nmin,nmax,nint)} uses the adaptive simpson method to numerically integrate function \\spad{fn} over the closed interval from \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax},{} and where \\spad{nint} is the number of independent intervals to apply the integrator. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|aromberg| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{aromberg(fn,a,b,epsrel,epsabs,nmin,nmax,nint)} uses the adaptive romberg method to numerically integrate function \\spad{fn} over the closed interval from \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax},{} and where \\spad{nint} is the number of independent intervals to apply the integrator. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")))
NIL
NIL
-(-713 |Curve|)
+(-714 |Curve|)
((|constructor| (NIL "\\indented{1}{Author: Clifton \\spad{J}. Williamson} Date Created: Bastille Day 1989 Date Last Updated: 5 June 1990 Keywords: Examples: Package for constructing tubes around 3-dimensional parametric curves.")) (|tube| (((|TubePlot| |#1|) |#1| (|DoubleFloat|) (|Integer|)) "\\spad{tube(c,r,n)} creates a tube of radius \\spad{r} around the curve \\spad{c}.")))
NIL
NIL
-(-714 S)
+(-715 S)
((|constructor| (NIL "Ordered sets which are also abelian groups,{} such that the addition preserves the ordering.")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x}.")) (|sign| (((|Integer|) $) "\\spad{sign(x)} is \\spad{1} if \\spad{x} is positive,{} \\spad{-1} if \\spad{x} is negative,{} and \\spad{0} otherwise.")) (|negative?| (((|Boolean|) $) "\\spad{negative?(x)} holds when \\spad{x} is less than \\spad{0}.")))
NIL
NIL
-(-715)
+(-716)
((|constructor| (NIL "Ordered sets which are also abelian groups,{} such that the addition preserves the ordering.")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x}.")) (|sign| (((|Integer|) $) "\\spad{sign(x)} is \\spad{1} if \\spad{x} is positive,{} \\spad{-1} if \\spad{x} is negative,{} and \\spad{0} otherwise.")) (|negative?| (((|Boolean|) $) "\\spad{negative?(x)} holds when \\spad{x} is less than \\spad{0}.")))
NIL
NIL
-(-716 S)
+(-717 S)
((|constructor| (NIL "Ordered sets which are also abelian monoids,{} such that the addition preserves the ordering.")) (|positive?| (((|Boolean|) $) "\\spad{positive?(x)} holds when \\spad{x} is greater than \\spad{0}.")))
NIL
NIL
-(-717)
+(-718)
((|constructor| (NIL "Ordered sets which are also abelian monoids,{} such that the addition preserves the ordering.")) (|positive?| (((|Boolean|) $) "\\spad{positive?(x)} holds when \\spad{x} is greater than \\spad{0}.")))
NIL
NIL
-(-718)
+(-719)
((|constructor| (NIL "This domain is an OrderedAbelianMonoid with a \\spadfun{sup} operation added. The purpose of the \\spadfun{sup} operator in this domain is to act as a supremum with respect to the partial order imposed by \\spadop{-},{} rather than with respect to the total \\spad{>} order (since that is \"max\"). \\blankline")) (|sup| (($ $ $) "\\spad{sup(x,y)} returns the least element from which both \\spad{x} and \\spad{y} can be subtracted.")))
NIL
NIL
-(-719)
+(-720)
((|constructor| (NIL "Ordered sets which are also abelian semigroups,{} such that the addition preserves the ordering. \\indented{2}{\\spad{ x < y => x+z < y+z}}")))
NIL
NIL
-(-720 S R)
+(-721 S R)
((|constructor| (NIL "OctonionCategory gives the categorial frame for the octonions,{} and eight-dimensional non-associative algebra,{} doubling the the quaternions in the same way as doubling the Complex numbers to get the quaternions.")) (|inv| (($ $) "\\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| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}.")))
NIL
-((|HasCategory| |#2| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-483))) (|HasCategory| |#2| (QUOTE (-973))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-554 (-473)))) (|HasCategory| |#2| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-317))))
-(-721 R)
+((|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-484))) (|HasCategory| |#2| (QUOTE (-975))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-555 (-474)))) (|HasCategory| |#2| (QUOTE (-758))) (|HasCategory| |#2| (QUOTE (-318))))
+(-722 R)
((|constructor| (NIL "OctonionCategory gives the categorial frame for the octonions,{} and eight-dimensional non-associative algebra,{} doubling the the quaternions in the same way as doubling the Complex numbers to get the quaternions.")) (|inv| (($ $) "\\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| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}.")))
-((-3986 . T) (-3987 . T) (-3989 . T))
+((-3990 . T) (-3991 . T) (-3993 . T))
NIL
-(-722)
+(-723)
((|constructor| (NIL "Ordered sets which are also abelian cancellation monoids,{} such that the addition preserves the ordering.")))
NIL
NIL
-(-723 R)
+(-724 R)
((|constructor| (NIL "Octonion implements octonions (Cayley-Dixon algebra) over a commutative ring,{} an eight-dimensional non-associative algebra,{} doubling the quaternions in the same way as doubling the complex numbers to get the quaternions the main constructor function is {\\em octon} which takes 8 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j} imaginary part,{} the \\spad{k} imaginary part,{} (as with quaternions) and in addition the imaginary parts \\spad{E},{} \\spad{I},{} \\spad{J},{} \\spad{K}.")) (|octon| (($ (|Quaternion| |#1|) (|Quaternion| |#1|)) "\\spad{octon(qe,qE)} constructs an octonion from two quaternions using the relation {\\em O = Q + QE}.")))
-((-3986 . T) (-3987 . T) (-3989 . T))
-((|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-554 (-473)))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (|%list| (QUOTE -453) (QUOTE (-1089)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -241) (|devaluate| |#1|) (|devaluate| |#1|))) (OR (|HasCategory| |#1| (QUOTE (-951 (-347 (-484))))) (|HasCategory| (-910 |#1|) (QUOTE (-951 (-347 (-484)))))) (OR (|HasCategory| |#1| (QUOTE (-951 (-484)))) (|HasCategory| (-910 |#1|) (QUOTE (-951 (-484))))) (|HasCategory| |#1| (QUOTE (-973))) (|HasCategory| |#1| (QUOTE (-483))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| (-910 |#1|) (QUOTE (-951 (-347 (-484))))) (|HasCategory| (-910 |#1|) (QUOTE (-951 (-484)))) (|HasCategory| |#1| (QUOTE (-951 (-347 (-484))))) (|HasCategory| |#1| (QUOTE (-951 (-484)))))
-(-724 OR R OS S)
+((-3990 . T) (-3991 . T) (-3993 . T))
+((|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-555 (-474)))) (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (|%list| (QUOTE -454) (QUOTE (-1091)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -241) (|devaluate| |#1|) (|devaluate| |#1|))) (OR (|HasCategory| |#1| (QUOTE (-952 (-348 (-485))))) (|HasCategory| (-911 |#1|) (QUOTE (-952 (-348 (-485)))))) (OR (|HasCategory| |#1| (QUOTE (-952 (-485)))) (|HasCategory| (-911 |#1|) (QUOTE (-952 (-485))))) (|HasCategory| |#1| (QUOTE (-975))) (|HasCategory| |#1| (QUOTE (-484))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-911 |#1|) (QUOTE (-952 (-348 (-485))))) (|HasCategory| (-911 |#1|) (QUOTE (-952 (-485)))) (|HasCategory| |#1| (QUOTE (-952 (-348 (-485))))) (|HasCategory| |#1| (QUOTE (-952 (-485)))))
+(-725 OR R OS S)
((|constructor| (NIL "\\spad{OctonionCategoryFunctions2} implements functions between two octonion domains defined over different rings. The function map is used to coerce between octonion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,u)} maps \\spad{f} onto the component parts of the octonion \\spad{u}.")))
NIL
NIL
-(-725 R -3091 L)
+(-726 R -3094 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}'s form a basis for the solutions of \\spad{op y = 0}.")))
NIL
NIL
-(-726 R -3091)
+(-727 R -3094)
((|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| #1="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| #1#) (|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| #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| #2#) (|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
-(-727 R -3091)
+(-728 R -3094)
((|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
-(-728 -3091 UP UPUP R)
+(-729 -3094 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
-(-729 -3091 UP L LQ)
+(-730 -3094 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}'s are the affine singularities of \\spad{op} above the roots of \\spad{p},{} and the \\spad{e_i}'s are the indicial equations at each \\spad{d_i}.") (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#4|) "\\spad{indicialEquations op} returns \\spad{[[d1,e1],...,[dq,eq]]} where the \\spad{d_i}'s are the affine singularities of \\spad{op},{} and the \\spad{e_i}'s are the indicial equations at each \\spad{d_i}.") (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#3| |#2|) "\\spad{indicialEquations(op, p)} returns \\spad{[[d1,e1],...,[dq,eq]]} where the \\spad{d_i}'s are the affine singularities of \\spad{op} above the roots of \\spad{p},{} and the \\spad{e_i}'s are the indicial equations at each \\spad{d_i}.") (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#3|) "\\spad{indicialEquations op} returns \\spad{[[d1,e1],...,[dq,eq]]} where the \\spad{d_i}'s are the affine singularities of \\spad{op},{} and the \\spad{e_i}'s are the indicial equations at each \\spad{d_i}.")) (|denomLODE| ((|#2| |#3| (|List| (|Fraction| |#2|))) "\\spad{denomLODE(op, [g1,...,gm])} returns a polynomial \\spad{d} such that any rational solution of \\spad{op 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
-(-730 -3091 UP L LQ)
+(-731 -3094 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}'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)}'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}'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}'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 mj for some \\spad{j},{} and its leading coefficient is then a zero of 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 {gcd(\\spad{d},{}\\spad{q}) = 1}.")))
NIL
NIL
-(-731 -3091 UP)
+(-732 -3094 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|) #1="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}'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|) #1#)) (|:| |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}'s form a basis for the rational solutions of the homogeneous equation.")))
NIL
NIL
-(-732 -3091 L UP A LO)
+(-733 -3094 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
-(-733 -3091 UP)
+(-734 -3094 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}'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 ++ part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{fi}'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))))
-(-734 -3091 LO)
+(-735 -3094 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
-(-735 -3091 LODO)
+(-736 -3094 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
-(-736 -2620 S |f|)
+(-737 -2623 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}.")))
-((-3986 |has| |#2| (-962)) (-3987 |has| |#2| (-962)) (-3989 |has| |#2| (-6 -3989)) (-3992 . T))
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+(-739 |Kernels| R |var|)
((|constructor| (NIL "This constructor produces an ordinary differential ring from a partial differential ring by specifying a variable.")))
-(((-3994 "*") |has| |#2| (-311)) (-3985 |has| |#2| (-311)) (-3990 |has| |#2| (-311)) (-3984 |has| |#2| (-311)) (-3989 . T) (-3987 . T) (-3986 . T))
-((|HasCategory| |#2| (QUOTE (-311))))
-(-739 S)
+(((-3998 "*") |has| |#2| (-312)) (-3989 |has| |#2| (-312)) (-3994 |has| |#2| (-312)) (-3988 |has| |#2| (-312)) (-3993 . T) (-3991 . T) (-3990 . T))
+((|HasCategory| |#2| (QUOTE (-312))))
+(-740 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})).")))
NIL
NIL
-(-740 S)
+(-741 S)
((|constructor| (NIL "\\indented{3}{The free monoid on a set \\spad{S} is the monoid of finite products of} the form \\spad{reduce(*,[si ** ni])} where the \\spad{si}'s are in \\spad{S},{} and the \\spad{ni}'s are non-negative integers. The multiplication is not commutative. For two elements \\spad{x} and \\spad{y} the relation \\spad{x < y} holds if either \\spad{length(x) < length(y)} holds or if these lengths are equal and if \\spad{x} is smaller than \\spad{y} \\spad{w}.\\spad{r}.\\spad{t}. the lexicographical ordering induced by \\spad{S}. This domain inherits implementation from \\spadtype{FreeMonoid}.")) (|varList| (((|List| |#1|) $) "\\spad{varList(x)} returns the list of variables of \\spad{x}.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length(x)} returns the length of \\spad{x}.")) (|div| (((|Union| (|Record| (|:| |lm| $) (|:| |rm| $)) "failed") $ $) "\\spad{x div y} returns the left and right exact quotients of \\spad{x} by \\spad{y},{} that is \\spad{[l, r]} such that \\spad{x = l * y * r}. \"failed\" is returned iff \\spad{x} is not of the form \\spad{l * y * r}. monomial of \\spad{x}.")) (|rquo| (((|Union| $ "failed") $ |#1|) "\\spad{rquo(x, s)} returns the exact right quotient of \\spad{x} by \\spad{s}.")) (|lquo| (((|Union| $ "failed") $ |#1|) "\\spad{lquo(x, s)} returns the exact left quotient of \\spad{x} by \\spad{s}.")) (|lexico| (((|Boolean|) $ $) "\\spad{lexico(x,y)} returns \\spad{true} iff \\spad{x} is smaller than \\spad{y} \\spad{w}.\\spad{r}.\\spad{t}. the pure lexicographical ordering induced by \\spad{S}.")) (|mirror| (($ $) "\\spad{mirror(x)} returns the reversed word of \\spad{x}.")) (|rest| (($ $) "\\spad{rest(x)} returns \\spad{x} except the first letter.")) (|first| ((|#1| $) "\\spad{first(x)} returns the first letter of \\spad{x}.")))
NIL
-((|HasCategory| |#1| (QUOTE (-757))))
-(-741)
+((|HasCategory| |#1| (QUOTE (-758))))
+(-742)
((|constructor| (NIL "The category of ordered commutative integral domains,{} where ordering and the arithmetic operations are compatible \\blankline")))
-((-3985 . T) ((-3994 "*") . T) (-3986 . T) (-3987 . T) (-3989 . T))
+((-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T))
NIL
-(-742 P R)
+(-743 P R)
((|constructor| (NIL "This constructor creates the \\spadtype{MonogenicLinearOperator} domain which is ``opposite'' in the ring sense to \\spad{P}. That is,{} as sets \\spad{P = \\$} 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}.")))
-((-3986 . T) (-3987 . T) (-3989 . T))
+((-3990 . T) (-3991 . T) (-3993 . T))
((|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-190))))
-(-743 S)
+(-744 S)
((|constructor| (NIL "to become an in order iterator")) (|min| ((|#1| $) "\\spad{min(u)} returns the smallest entry in the multiset aggregate \\spad{u}.")))
-((-3992 . T) (-3982 . T) (-3993 . T))
+((-3996 . T) (-3986 . T) (-3997 . T))
NIL
-(-744 R)
+(-745 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.")))
-((-3989 |has| |#1| (-756)))
-((|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-21))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-756)))) (|HasCategory| |#1| (QUOTE (-951 (-347 (-484))))) (OR (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-951 (-484))))) (|HasCategory| |#1| (QUOTE (-951 (-484)))) (|HasCategory| |#1| (QUOTE (-483))))
-(-745 R S)
+((-3993 |has| |#1| (-757)))
+((|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-21))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-757)))) (|HasCategory| |#1| (QUOTE (-952 (-348 (-485))))) (OR (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-952 (-485))))) (|HasCategory| |#1| (QUOTE (-952 (-485)))) (|HasCategory| |#1| (QUOTE (-484))))
+(-746 R S)
((|constructor| (NIL "Lifting of maps to one-point completions. Date Created: 4 Oct 1989 Date Last Updated: 4 Oct 1989")) (|map| (((|OnePointCompletion| |#2|) (|Mapping| |#2| |#1|) (|OnePointCompletion| |#1|) (|OnePointCompletion| |#2|)) "\\spad{map(f, r, i)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(infinity) = \\spad{i}.") (((|OnePointCompletion| |#2|) (|Mapping| |#2| |#1|) (|OnePointCompletion| |#1|)) "\\spad{map(f, r)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(infinity) = infinity.")))
NIL
NIL
-(-746 R)
+(-747 R)
((|constructor| (NIL "Algebra of ADDITIVE operators over a ring.")))
-((-3987 |has| |#1| (-146)) (-3986 |has| |#1| (-146)) (-3989 . T))
+((-3991 |has| |#1| (-146)) (-3990 |has| |#1| (-146)) (-3993 . T))
((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))))
-(-747 A S)
+(-748 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
NIL
-(-748 S)
+(-749 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|) $ |#1|) "\\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| ((|#1| $) "\\spad{name(op)} returns the externam name of \\spad{op}.")))
NIL
NIL
-(-749)
+(-750)
((|constructor| (NIL "This package exports tools to create AXIOM Library information databases.")) (|getDatabase| (((|Database| (|IndexCard|)) (|String|)) "\\spad{getDatabase(\"char\")} returns a list of appropriate entries in the browser database. The legal values for \\spad{\"char\"} are \"o\" (operations),{} \"k\" (constructors),{} \"d\" (domains),{} \"c\" (categories) or \"p\" (packages).")))
NIL
NIL
-(-750)
+(-751)
((|constructor| (NIL "This the datatype for an operator-signature pair.")) (|construct| (($ (|Identifier|) (|Signature|)) "\\spad{construct(op,sig)} construct a signature-operator with operator name `op',{} and signature `sig'.")) (|signature| (((|Signature|) $) "\\spad{signature(x)} returns the signature of `x'.")))
NIL
NIL
-(-751 R)
+(-752 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| (($) "\\spad{plusInfinity()} returns +infinity.")))
-((-3989 |has| |#1| (-756)))
-((|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-21))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-756)))) (|HasCategory| |#1| (QUOTE (-951 (-347 (-484))))) (OR (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-951 (-484))))) (|HasCategory| |#1| (QUOTE (-951 (-484)))) (|HasCategory| |#1| (QUOTE (-483))))
-(-752 R S)
+((-3993 |has| |#1| (-757)))
+((|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-21))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-757)))) (|HasCategory| |#1| (QUOTE (-952 (-348 (-485))))) (OR (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-952 (-485))))) (|HasCategory| |#1| (QUOTE (-952 (-485)))) (|HasCategory| |#1| (QUOTE (-484))))
+(-753 R S)
((|constructor| (NIL "Lifting of maps to ordered completions. Date Created: 4 Oct 1989 Date Last Updated: 4 Oct 1989")) (|map| (((|OrderedCompletion| |#2|) (|Mapping| |#2| |#1|) (|OrderedCompletion| |#1|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|)) "\\spad{map(f, r, p, m)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(plusInfinity) = \\spad{p} and that \\spad{f}(minusInfinity) = \\spad{m}.") (((|OrderedCompletion| |#2|) (|Mapping| |#2| |#1|) (|OrderedCompletion| |#1|)) "\\spad{map(f, r)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(plusInfinity) = plusInfinity and that \\spad{f}(minusInfinity) = minusInfinity.")))
NIL
NIL
-(-753)
+(-754)
((|constructor| (NIL "Ordered finite sets.")) (|max| (($) "\\spad{max} is the maximum value of \\%.")) (|min| (($) "\\spad{min} is the minimum value of \\%.")))
NIL
NIL
-(-754 -2620 S)
+(-755 -2623 S)
((|constructor| (NIL "\\indented{3}{This package provides ordering functions on vectors which} are suitable parameters for OrderedDirectProduct.")) (|reverseLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{reverseLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by the reverse lexicographic ordering.")) (|totalLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{totalLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by lexicographic ordering.")) (|pureLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{pureLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the lexicographic ordering.")))
NIL
NIL
-(-755)
+(-756)
((|constructor| (NIL "Ordered sets which are also monoids,{} such that multiplication preserves the ordering. \\blankline")))
NIL
NIL
-(-756)
+(-757)
((|constructor| (NIL "Ordered sets which are also rings,{} that is,{} domains where the ring operations are compatible with the ordering. \\blankline")))
-((-3989 . T))
+((-3993 . T))
NIL
-(-757)
+(-758)
((|constructor| (NIL "The class of totally ordered sets,{} that is,{} sets such that for each pair of elements \\spad{(a,b)} exactly one of the following relations holds \\spad{a<b or a=b or b<a} and the relation is transitive,{} \\spadignore{i.e.} \\spad{a<b and b<c => a<c}.")))
NIL
NIL
-(-758 T$ |f|)
+(-759 T$ |f|)
((|constructor| (NIL "This domain turns any total ordering \\spad{f} on a type \\spad{T} into a model of the category \\spadtype{OrderedType}.")))
NIL
-((|HasCategory| |#1| (QUOTE (-553 (-773)))))
-(-759 S)
+((|HasCategory| |#1| (QUOTE (-554 (-774)))))
+(-760 S)
((|constructor| (NIL "Category of types equipped with a total ordering.")) (|min| (($ $ $) "\\spad{min(x,y)} returns the minimum of \\spad{x} and \\spad{y} relative to the ordering.")) (|max| (($ $ $) "\\spad{max(x,y)} returns the maximum of \\spad{x} and \\spad{y} relative to the ordering.")) (>= (((|Boolean|) $ $) "\\spad{x <= y} holds if \\spad{x} is greater or equal than \\spad{y} in the current domain.")) (<= (((|Boolean|) $ $) "\\spad{x <= y} holds if \\spad{x} is less or equal than \\spad{y} in the current domain.")) (> (((|Boolean|) $ $) "\\spad{x > y} holds if \\spad{x} is greater than \\spad{y} in the current domain.")) (< (((|Boolean|) $ $) "\\spad{x < y} holds if \\spad{x} is less than \\spad{y} in the current domain.")))
NIL
NIL
-(-760)
+(-761)
((|constructor| (NIL "Category of types equipped with a total ordering.")) (|min| (($ $ $) "\\spad{min(x,y)} returns the minimum of \\spad{x} and \\spad{y} relative to the ordering.")) (|max| (($ $ $) "\\spad{max(x,y)} returns the maximum of \\spad{x} and \\spad{y} relative to the ordering.")) (>= (((|Boolean|) $ $) "\\spad{x <= y} holds if \\spad{x} is greater or equal than \\spad{y} in the current domain.")) (<= (((|Boolean|) $ $) "\\spad{x <= y} holds if \\spad{x} is less or equal than \\spad{y} in the current domain.")) (> (((|Boolean|) $ $) "\\spad{x > y} holds if \\spad{x} is greater than \\spad{y} in the current domain.")) (< (((|Boolean|) $ $) "\\spad{x < y} holds if \\spad{x} is less than \\spad{y} in the current domain.")))
NIL
NIL
-(-761 S R)
+(-762 S R)
((|constructor| (NIL "This is the category of univariate skew polynomials over an Ore coefficient ring. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}. This category is an evolution of the types \\indented{2}{MonogenicLinearOperator,{} OppositeMonogenicLinearOperator,{} and} \\indented{2}{NonCommutativeOperatorDivision} developped by Jean Della Dora and Stephen \\spad{M}. Watt.")) (|leftLcm| (($ $ $) "\\spad{leftLcm(a,b)} computes the value \\spad{m} of lowest degree such that \\spad{m = aa*a = bb*b} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using right-division.")) (|rightExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{rightExtendedGcd(a,b)} returns \\spad{[c,d]} such that \\spad{g = c * a + d * b = rightGcd(a, b)}.")) (|rightGcd| (($ $ $) "\\spad{rightGcd(a,b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = aa*g}} \\indented{3}{\\spad{b = bb*g}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using right-division.")) (|rightExactQuotient| (((|Union| $ "failed") $ $) "\\spad{rightExactQuotient(a,b)} computes the value \\spad{q},{} if it exists such that \\spad{a = q*b}.")) (|rightRemainder| (($ $ $) "\\spad{rightRemainder(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|rightQuotient| (($ $ $) "\\spad{rightQuotient(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|rightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{rightDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``right division''.")) (|rightLcm| (($ $ $) "\\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| $)) $ $) "\\spad{leftDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division''.")) (|primitivePart| (($ $) "\\spad{primitivePart(l)} returns \\spad{l0} such that \\spad{l = a * l0} for some a in \\spad{R},{} and \\spad{content(l0) = 1}.")) (|content| ((|#2| $) "\\spad{content(l)} returns the 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''.")) (|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''.")) (|exquo| (((|Union| $ "failed") $ |#2|) "\\spad{exquo(l, a)} returns the exact quotient of \\spad{l} by a,{} returning \\axiom{\"failed\"} if this is not possible.")) (|apply| ((|#2| $ |#2| |#2|) "\\spad{apply(p, c, m)} returns \\spad{p(m)} where the action is given by \\spad{x m = c sigma(m) + delta(m)}.")) (|coefficients| (((|List| |#2|) $) "\\spad{coefficients(l)} returns the list of all the nonzero coefficients of \\spad{l}.")) (|monomial| (($ |#2| (|NonNegativeInteger|)) "\\spad{monomial(c,k)} produces \\spad{c} times the \\spad{k}-th power of the generating operator,{} \\spad{monomial(1,1)}.")) (|coefficient| ((|#2| $ (|NonNegativeInteger|)) "\\spad{coefficient(l,k)} is \\spad{a(k)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|reductum| (($ $) "\\spad{reductum(l)} is \\spad{l - monomial(a(n),n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(l)} is \\spad{a(n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|minimumDegree| (((|NonNegativeInteger|) $) "\\spad{minimumDegree(l)} is the smallest \\spad{k} such that \\spad{a(k) ~= 0} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(l)} is \\spad{n} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")))
NIL
-((|HasCategory| |#2| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-389))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-146))))
-(-762 R)
+((|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-390))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-146))))
+(-763 R)
((|constructor| (NIL "This is the category of univariate skew polynomials over an Ore coefficient ring. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}. This category is an evolution of the types \\indented{2}{MonogenicLinearOperator,{} OppositeMonogenicLinearOperator,{} and} \\indented{2}{NonCommutativeOperatorDivision} developped by Jean Della Dora and Stephen \\spad{M}. Watt.")) (|leftLcm| (($ $ $) "\\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| $)) $ $) "\\spad{rightDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``right division''.")) (|rightLcm| (($ $ $) "\\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| $)) $ $) "\\spad{leftDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division''.")) (|primitivePart| (($ $) "\\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 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''.")) (|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''.")) (|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)}.}")))
-((-3986 . T) (-3987 . T) (-3989 . T))
+((-3990 . T) (-3991 . T) (-3993 . T))
NIL
-(-763 R C)
+(-764 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{\\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{\\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{\\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{\\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 (-311))) (|HasCategory| |#1| (QUOTE (-495))))
-(-764 R |sigma| -3242)
+((|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-496))))
+(-765 R |sigma| -3246)
((|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.")))
-((-3986 . T) (-3987 . T) (-3989 . T))
-((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-951 (-347 (-484))))) (|HasCategory| |#1| (QUOTE (-951 (-484)))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-389))) (|HasCategory| |#1| (QUOTE (-311))))
-(-765 |x| R |sigma| -3242)
+((-3990 . T) (-3991 . T) (-3993 . T))
+((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-952 (-348 (-485))))) (|HasCategory| |#1| (QUOTE (-952 (-485)))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-312))))
+(-766 |x| R |sigma| -3246)
((|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}.")))
-((-3986 . T) (-3987 . T) (-3989 . T))
-((|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-951 (-347 (-484))))) (|HasCategory| |#2| (QUOTE (-951 (-484)))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-389))) (|HasCategory| |#2| (QUOTE (-311))))
-(-766 R)
+((-3990 . T) (-3991 . T) (-3993 . T))
+((|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-952 (-348 (-485))))) (|HasCategory| |#2| (QUOTE (-952 (-485)))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-390))) (|HasCategory| |#2| (QUOTE (-312))))
+(-767 R)
((|constructor| (NIL "This package provides orthogonal polynomials as functions on a ring.")) (|legendreP| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{legendreP(n,x)} is the \\spad{n}-th Legendre polynomial,{} \\spad{P[n](x)}. These are defined by \\spad{1/sqrt(1-2*x*t+t**2) = sum(P[n](x)*t**n, n = 0..)}.")) (|laguerreL| ((|#1| (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|) "\\spad{laguerreL(m,n,x)} is the associated Laguerre polynomial,{} \\spad{L<m>[n](x)}. This is the \\spad{m}-th derivative of \\spad{L[n](x)}.") ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{laguerreL(n,x)} is the \\spad{n}-th Laguerre polynomial,{} \\spad{L[n](x)}. These are defined by \\spad{exp(-t*x/(1-t))/(1-t) = sum(L[n](x)*t**n/n!, n = 0..)}.")) (|hermiteH| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{hermiteH(n,x)} is the \\spad{n}-th Hermite polynomial,{} \\spad{H[n](x)}. These are defined by \\spad{exp(2*t*x-t**2) = sum(H[n](x)*t**n/n!, n = 0..)}.")) (|chebyshevU| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{chebyshevU(n,x)} is the \\spad{n}-th Chebyshev polynomial of the second kind,{} \\spad{U[n](x)}. These are defined by \\spad{1/(1-2*t*x+t**2) = sum(T[n](x) *t**n, n = 0..)}.")) (|chebyshevT| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{chebyshevT(n,x)} is the \\spad{n}-th Chebyshev polynomial of the first kind,{} \\spad{T[n](x)}. These are defined by \\spad{(1-t*x)/(1-2*t*x+t**2) = sum(T[n](x) *t**n, n = 0..)}.")))
NIL
-((|HasCategory| |#1| (QUOTE (-38 (-347 (-484))))))
-(-767)
+((|HasCategory| |#1| (QUOTE (-38 (-348 (-485))))))
+(-768)
((|constructor| (NIL "Semigroups with compatible ordering.")))
NIL
NIL
-(-768)
+(-769)
((|constructor| (NIL "\\indented{1}{Author : Larry Lambe} Date created : 14 August 1988 Date Last Updated : 11 March 1991 Description : A domain used in order to take the free \\spad{R}-module on the Integers \\spad{I}. This is actually the forgetful functor from OrderedRings to OrderedSets applied to \\spad{I}")) (|value| (((|Integer|) $) "\\spad{value(x)} returns the integer associated with \\spad{x}")) (|coerce| (($ (|Integer|)) "\\spad{coerce(i)} returns the element corresponding to \\spad{i}")))
NIL
NIL
-(-769)
+(-770)
((|constructor| (NIL "OutPackage allows pretty-printing from programs.")) (|outputList| (((|Void|) (|List| (|Any|))) "\\spad{outputList(l)} displays the concatenated components of the list \\spad{l} on the ``algebra output'' stream,{} as defined by \\spadsyscom{set output algebra}; quotes are stripped from strings.")) (|output| (((|Void|) (|String|) (|OutputForm|)) "\\spad{output(s,x)} displays the string \\spad{s} followed by the form \\spad{x} on the ``algebra output'' stream,{} as defined by \\spadsyscom{set output algebra}.") (((|Void|) (|OutputForm|)) "\\spad{output(x)} displays the output form \\spad{x} on the ``algebra output'' stream,{} as defined by \\spadsyscom{set output algebra}.") (((|Void|) (|String|)) "\\spad{output(s)} displays the string \\spad{s} on the ``algebra output'' stream,{} as defined by \\spadsyscom{set output algebra}.")))
NIL
NIL
-(-770 S)
+(-771 S)
((|constructor| (NIL "This category describes output byte stream conduits.")) (|writeBytes!| (((|NonNegativeInteger|) $ (|ByteBuffer|)) "\\spad{writeBytes!(c,b)} write bytes from buffer `b' onto the conduit `c'. The actual number of written bytes is returned.")) (|writeUInt8!| (((|Maybe| (|UInt8|)) $ (|UInt8|)) "\\spad{writeUInt8!(c,b)} attempts to write the unsigned 8-bit value `v' on the conduit `c'. Returns the written value if successful,{} otherwise,{} returns \\spad{nothing}.")) (|writeInt8!| (((|Maybe| (|Int8|)) $ (|Int8|)) "\\spad{writeInt8!(c,b)} attempts to write the 8-bit value `v' on the conduit `c'. Returns the written value if successful,{} otherwise,{} returns \\spad{nothing}.")) (|writeByte!| (((|Maybe| (|Byte|)) $ (|Byte|)) "\\spad{writeByte!(c,b)} attempts to write the byte `b' on the conduit `c'. Returns the written byte if successful,{} otherwise,{} returns \\spad{nothing}.")))
NIL
NIL
-(-771)
+(-772)
((|constructor| (NIL "This category describes output byte stream conduits.")) (|writeBytes!| (((|NonNegativeInteger|) $ (|ByteBuffer|)) "\\spad{writeBytes!(c,b)} write bytes from buffer `b' onto the conduit `c'. The actual number of written bytes is returned.")) (|writeUInt8!| (((|Maybe| (|UInt8|)) $ (|UInt8|)) "\\spad{writeUInt8!(c,b)} attempts to write the unsigned 8-bit value `v' on the conduit `c'. Returns the written value if successful,{} otherwise,{} returns \\spad{nothing}.")) (|writeInt8!| (((|Maybe| (|Int8|)) $ (|Int8|)) "\\spad{writeInt8!(c,b)} attempts to write the 8-bit value `v' on the conduit `c'. Returns the written value if successful,{} otherwise,{} returns \\spad{nothing}.")) (|writeByte!| (((|Maybe| (|Byte|)) $ (|Byte|)) "\\spad{writeByte!(c,b)} attempts to write the byte `b' on the conduit `c'. Returns the written byte if successful,{} otherwise,{} returns \\spad{nothing}.")))
NIL
NIL
-(-772)
+(-773)
((|constructor| (NIL "This domain provides representation for binary files open for output operations. `Binary' here means that the conduits do not interpret their contents.")) (|isOpen?| (((|Boolean|) $) "open?(ifile) holds if `ifile' is in open state.")) (|outputBinaryFile| (($ (|String|)) "\\spad{outputBinaryFile(f)} returns an output conduit obtained by opening the file named by `f' as a binary file.") (($ (|FileName|)) "\\spad{outputBinaryFile(f)} returns an output conduit obtained by opening the file named by `f' as a binary file.")))
NIL
NIL
-(-773)
+(-774)
((|constructor| (NIL "This domain is used to create and manipulate mathematical expressions for output. It is intended to provide an insulating layer between the expression rendering software (\\spadignore{e.g.} TeX,{} or Script) and the output coercions in the various domains.")) (SEGMENT (($ $) "\\spad{SEGMENT(x)} creates the prefix form: \\spad{x..}.") (($ $ $) "\\spad{SEGMENT(x,y)} creates the infix form: \\spad{x..y}.")) (|not| (($ $) "\\spad{not f} creates the equivalent prefix form.")) (|or| (($ $ $) "\\spad{f or g} creates the equivalent infix form.")) (|and| (($ $ $) "\\spad{f and g} creates the equivalent infix form.")) (|exquo| (($ $ $) "\\spad{exquo(f,g)} creates the equivalent infix form.")) (|quo| (($ $ $) "\\spad{f quo g} creates the equivalent infix form.")) (|rem| (($ $ $) "\\spad{f rem g} creates the equivalent infix form.")) (|div| (($ $ $) "\\spad{f div g} creates the equivalent infix form.")) (** (($ $ $) "\\spad{f ** g} creates the equivalent infix form.")) (/ (($ $ $) "\\spad{f / g} creates the equivalent infix form.")) (* (($ $ $) "\\spad{f * g} creates the equivalent infix form.")) (- (($ $) "\\spad{- f} creates the equivalent prefix form.") (($ $ $) "\\spad{f - g} creates the equivalent infix form.")) (+ (($ $ $) "\\spad{f + g} creates the equivalent infix form.")) (>= (($ $ $) "\\spad{f >= g} creates the equivalent infix form.")) (<= (($ $ $) "\\spad{f <= g} creates the equivalent infix form.")) (> (($ $ $) "\\spad{f > g} creates the equivalent infix form.")) (< (($ $ $) "\\spad{f < g} creates the equivalent infix form.")) (~= (($ $ $) "\\spad{f ~= g} creates the equivalent infix form.")) (= (($ $ $) "\\spad{f = g} creates the equivalent infix form.")) (|blankSeparate| (($ (|List| $)) "\\spad{blankSeparate(l)} creates the form separating the elements of \\spad{l} by blanks.")) (|semicolonSeparate| (($ (|List| $)) "\\spad{semicolonSeparate(l)} creates the form separating the elements of \\spad{l} by semicolons.")) (|commaSeparate| (($ (|List| $)) "\\spad{commaSeparate(l)} creates the form separating the elements of \\spad{l} by commas.")) (|pile| (($ (|List| $)) "\\spad{pile(l)} creates the form consisting of the elements of \\spad{l} which displays as a pile,{} \\spadignore{i.e.} the elements begin on a new line and are indented right to the same margin.")) (|paren| (($ (|List| $)) "\\spad{paren(lf)} creates the form separating the elements of \\spad{lf} by commas and encloses the result in parentheses.") (($ $) "\\spad{paren(f)} creates the form enclosing \\spad{f} in parentheses.")) (|bracket| (($ (|List| $)) "\\spad{bracket(lf)} creates the form separating the elements of \\spad{lf} by commas and encloses the result in square brackets.") (($ $) "\\spad{bracket(f)} creates the form enclosing \\spad{f} in square brackets.")) (|brace| (($ (|List| $)) "\\spad{brace(lf)} creates the form separating the elements of \\spad{lf} by commas and encloses the result in curly brackets.") (($ $) "\\spad{brace(f)} creates the form enclosing \\spad{f} in braces (curly brackets).")) (|int| (($ $ $ $) "\\spad{int(expr,lowerlimit,upperlimit)} creates the form prefixing \\spad{expr} by an integral sign with both a \\spad{lowerlimit} and \\spad{upperlimit}.") (($ $ $) "\\spad{int(expr,lowerlimit)} creates the form prefixing \\spad{expr} by an integral sign with a \\spad{lowerlimit}.") (($ $) "\\spad{int(expr)} creates the form prefixing \\spad{expr} with an integral sign.")) (|prod| (($ $ $ $) "\\spad{prod(expr,lowerlimit,upperlimit)} creates the form prefixing \\spad{expr} by a capital \\spad{pi} with both a \\spad{lowerlimit} and \\spad{upperlimit}.") (($ $ $) "\\spad{prod(expr,lowerlimit)} creates the form prefixing \\spad{expr} by a capital \\spad{pi} with a \\spad{lowerlimit}.") (($ $) "\\spad{prod(expr)} creates the form prefixing \\spad{expr} by a capital \\spad{pi}.")) (|sum| (($ $ $ $) "\\spad{sum(expr,lowerlimit,upperlimit)} creates the form prefixing \\spad{expr} by a capital sigma with both a \\spad{lowerlimit} and \\spad{upperlimit}.") (($ $ $) "\\spad{sum(expr,lowerlimit)} creates the form prefixing \\spad{expr} by a capital sigma with a \\spad{lowerlimit}.") (($ $) "\\spad{sum(expr)} creates the form prefixing \\spad{expr} by a capital sigma.")) (|overlabel| (($ $ $) "\\spad{overlabel(x,f)} creates the form \\spad{f} with \"x overbar\" over the top.")) (|overbar| (($ $) "\\spad{overbar(f)} creates the form \\spad{f} with an overbar.")) (|prime| (($ $ (|NonNegativeInteger|)) "\\spad{prime(f,n)} creates the form \\spad{f} followed by \\spad{n} primes.") (($ $) "\\spad{prime(f)} creates the form \\spad{f} followed by a suffix prime (single quote).")) (|dot| (($ $ (|NonNegativeInteger|)) "\\spad{dot(f,n)} creates the form \\spad{f} with \\spad{n} dots overhead.") (($ $) "\\spad{dot(f)} creates the form with a one dot overhead.")) (|quote| (($ $) "\\spad{quote(f)} creates the form \\spad{f} with a prefix quote.")) (|supersub| (($ $ (|List| $)) "\\spad{supersub(a,[sub1,super1,sub2,super2,...])} creates a form with each subscript aligned under each superscript.")) (|scripts| (($ $ (|List| $)) "\\spad{scripts(f, [sub, super, presuper, presub])} \\indented{1}{creates a form for \\spad{f} with scripts on all 4 corners.}")) (|presuper| (($ $ $) "\\spad{presuper(f,n)} creates a form for \\spad{f} presuperscripted by \\spad{n}.")) (|presub| (($ $ $) "\\spad{presub(f,n)} creates a form for \\spad{f} presubscripted by \\spad{n}.")) (|super| (($ $ $) "\\spad{super(f,n)} creates a form for \\spad{f} superscripted by \\spad{n}.")) (|sub| (($ $ $) "\\spad{sub(f,n)} creates a form for \\spad{f} subscripted by \\spad{n}.")) (|binomial| (($ $ $) "\\spad{binomial(n,m)} creates a form for the binomial coefficient of \\spad{n} and \\spad{m}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(f,n)} creates a form for the \\spad{n}th derivative of \\spad{f},{} \\spadignore{e.g.} \\spad{f'},{} \\spad{f''},{} \\spad{f'''},{} \"f super \\spad{iv}\".")) (|rarrow| (($ $ $) "\\spad{rarrow(f,g)} creates a form for the mapping \\spad{f -> g}.")) (|assign| (($ $ $) "\\spad{assign(f,g)} creates a form for the assignment \\spad{f := g}.")) (|slash| (($ $ $) "\\spad{slash(f,g)} creates a form for the horizontal fraction of \\spad{f} over \\spad{g}.")) (|over| (($ $ $) "\\spad{over(f,g)} creates a form for the vertical fraction of \\spad{f} over \\spad{g}.")) (|root| (($ $ $) "\\spad{root(f,n)} creates a form for the \\spad{n}th root of form \\spad{f}.") (($ $) "\\spad{root(f)} creates a form for the square root of form \\spad{f}.")) (|zag| (($ $ $) "\\spad{zag(f,g)} creates a form for the continued fraction form for \\spad{f} over \\spad{g}.")) (|matrix| (($ (|List| (|List| $))) "\\spad{matrix(llf)} makes \\spad{llf} (a list of lists of forms) into a form which displays as a matrix.")) (|box| (($ $) "\\spad{box(f)} encloses \\spad{f} in a box.")) (|label| (($ $ $) "\\spad{label(n,f)} gives form \\spad{f} an equation label \\spad{n}.")) (|string| (($ $) "\\spad{string(f)} creates \\spad{f} with string quotes.")) (|elt| (($ $ (|List| $)) "\\spad{elt(op,l)} creates a form for application of \\spad{op} to list of arguments \\spad{l}.")) (|infix?| (((|Boolean|) $) "\\spad{infix?(op)} returns \\spad{true} if \\spad{op} is an infix operator,{} and \\spad{false} otherwise.")) (|postfix| (($ $ $) "\\spad{postfix(op, a)} creates a form which prints as: a \\spad{op}.")) (|infix| (($ $ $ $) "\\spad{infix(op, a, b)} creates a form which prints as: a \\spad{op} \\spad{b}.") (($ $ (|List| $)) "\\spad{infix(f,l)} creates a form depicting the \\spad{n}-ary application of infix operation \\spad{f} to a tuple of arguments \\spad{l}.")) (|prefix| (($ $ (|List| $)) "\\spad{prefix(f,l)} creates a form depicting the \\spad{n}-ary prefix application of \\spad{f} to a tuple of arguments given by list \\spad{l}.")) (|vconcat| (($ (|List| $)) "\\spad{vconcat(u)} vertically concatenates all forms in list \\spad{u}.") (($ $ $) "\\spad{vconcat(f,g)} vertically concatenates forms \\spad{f} and \\spad{g}.")) (|hconcat| (($ (|List| $)) "\\spad{hconcat(u)} horizontally concatenates all forms in list \\spad{u}.") (($ $ $) "\\spad{hconcat(f,g)} horizontally concatenate forms \\spad{f} and \\spad{g}.")) (|center| (($ $) "\\spad{center(f)} centers form \\spad{f} in total space.") (($ $ (|Integer|)) "\\spad{center(f,n)} centers form \\spad{f} within space of width \\spad{n}.")) (|right| (($ $) "\\spad{right(f)} right-justifies form \\spad{f} in total space.") (($ $ (|Integer|)) "\\spad{right(f,n)} right-justifies form \\spad{f} within space of width \\spad{n}.")) (|left| (($ $) "\\spad{left(f)} left-justifies form \\spad{f} in total space.") (($ $ (|Integer|)) "\\spad{left(f,n)} left-justifies form \\spad{f} within space of width \\spad{n}.")) (|rspace| (($ (|Integer|) (|Integer|)) "\\spad{rspace(n,m)} creates rectangular white space,{} \\spad{n} wide by \\spad{m} high.")) (|vspace| (($ (|Integer|)) "\\spad{vspace(n)} creates white space of height \\spad{n}.")) (|hspace| (($ (|Integer|)) "\\spad{hspace(n)} creates white space of width \\spad{n}.")) (|superHeight| (((|Integer|) $) "\\spad{superHeight(f)} returns the height of form \\spad{f} above the base line.")) (|subHeight| (((|Integer|) $) "\\spad{subHeight(f)} returns the height of form \\spad{f} below the base line.")) (|height| (((|Integer|)) "\\spad{height()} returns the height of the display area (an integer).") (((|Integer|) $) "\\spad{height(f)} returns the height of form \\spad{f} (an integer).")) (|width| (((|Integer|)) "\\spad{width()} returns the width of the display area (an integer).") (((|Integer|) $) "\\spad{width(f)} returns the width of form \\spad{f} (an integer).")) (|doubleFloatFormat| (((|String|) (|String|)) "change the output format for doublefloats using lisp format strings")) (|empty| (($) "\\spad{empty()} creates an empty form.")) (|outputForm| (($ (|DoubleFloat|)) "\\spad{outputForm(sf)} creates an form for small float \\spad{sf}.") (($ (|String|)) "\\spad{outputForm(s)} creates an form for string \\spad{s}.") (($ (|Symbol|)) "\\spad{outputForm(s)} creates an form for symbol \\spad{s}.") (($ (|Integer|)) "\\spad{outputForm(n)} creates an form for integer \\spad{n}.")) (|messagePrint| (((|Void|) (|String|)) "\\spad{messagePrint(s)} prints \\spad{s} without string quotes. Note: \\spad{messagePrint(s)} is equivalent to \\spad{print message(s)}.")) (|message| (($ (|String|)) "\\spad{message(s)} creates an form with no string quotes from string \\spad{s}.")) (|print| (((|Void|) $) "\\spad{print(u)} prints the form \\spad{u}.")))
NIL
NIL
-(-774 |VariableList|)
+(-775 |VariableList|)
((|constructor| (NIL "This domain implements ordered variables")) (|variable| (((|Union| $ "failed") (|Symbol|)) "\\spad{variable(s)} returns a member of the variable set or failed")))
NIL
NIL
-(-775)
+(-776)
((|constructor| (NIL "This domain represents set of overloaded operators (in fact operator descriptors).")) (|members| (((|List| (|FunctionDescriptor|)) $) "\\spad{members(x)} returns the list of operator descriptors,{} \\spadignore{e.g.} signature and implementation slots,{} of the overload set \\spad{x}.")) (|name| (((|Identifier|) $) "\\spad{name(x)} returns the name of the overload set \\spad{x}.")))
NIL
NIL
-(-776 R |vl| |wl| |wtlevel|)
+(-777 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: 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)")))
-((-3987 |has| |#1| (-146)) (-3986 |has| |#1| (-146)) (-3989 . T))
-((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-311))))
-(-777 R PS UP)
+((-3991 |has| |#1| (-146)) (-3990 |has| |#1| (-146)) (-3993 . T))
+((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))))
+(-778 R PS UP)
((|constructor| (NIL "\\indented{1}{This package computes reliable Pad&ea. approximants using} a generalized Viskovatov continued fraction algorithm. Authors: Burge,{} Hassner & Watt. Date Created: April 1987 Date Last Updated: 12 April 1990 Keywords: Pade,{} series Examples: References: \\indented{2}{\"Pade Approximants,{} Part I: Basic Theory\",{} Baker & Graves-Morris.}")) (|padecf| (((|Union| (|ContinuedFraction| |#3|) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) |#2| |#2|) "\\spad{padecf(nd,dd,ns,ds)} computes the approximant as a continued fraction of polynomials (if it exists) for arguments \\spad{nd} (numerator degree of approximant),{} \\spad{dd} (denominator degree of approximant),{} \\spad{ns} (numerator series of function),{} and \\spad{ds} (denominator series of function).")) (|pade| (((|Union| (|Fraction| |#3|) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) |#2| |#2|) "\\spad{pade(nd,dd,ns,ds)} computes the approximant as a quotient of polynomials (if it exists) for arguments \\spad{nd} (numerator degree of approximant),{} \\spad{dd} (denominator degree of approximant),{} \\spad{ns} (numerator series of function),{} and \\spad{ds} (denominator series of function).")))
NIL
NIL
-(-778 R |x| |pt|)
+(-779 R |x| |pt|)
((|constructor| (NIL "\\indented{1}{This package computes reliable Pad&ea. approximants using} a generalized Viskovatov continued fraction algorithm. Authors: Trager,{}Burge,{} Hassner & Watt. Date Created: April 1987 Date Last Updated: 12 April 1990 Keywords: Pade,{} series Examples: References: \\indented{2}{\"Pade Approximants,{} Part I: Basic Theory\",{} Baker & Graves-Morris.}")) (|pade| (((|Union| (|Fraction| (|UnivariatePolynomial| |#2| |#1|)) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) (|UnivariateTaylorSeries| |#1| |#2| |#3|)) "\\spad{pade(nd,dd,s)} computes the quotient of polynomials (if it exists) with numerator degree at most \\spad{nd} and denominator degree at most \\spad{dd} which matches the series \\spad{s} to order \\spad{nd + dd}.") (((|Union| (|Fraction| (|UnivariatePolynomial| |#2| |#1|)) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) (|UnivariateTaylorSeries| |#1| |#2| |#3|) (|UnivariateTaylorSeries| |#1| |#2| |#3|)) "\\spad{pade(nd,dd,ns,ds)} computes the approximant as a quotient of polynomials (if it exists) for arguments \\spad{nd} (numerator degree of approximant),{} \\spad{dd} (denominator degree of approximant),{} \\spad{ns} (numerator series of function),{} and \\spad{ds} (denominator series of function).")))
NIL
NIL
-(-779 |p|)
+(-780 |p|)
((|constructor| (NIL "Stream-based implementation of 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).")))
-((-3985 . T) ((-3994 "*") . T) (-3986 . T) (-3987 . T) (-3989 . T))
+((-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T))
NIL
-(-780 |p|)
+(-781 |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}.")))
-((-3985 . T) ((-3994 "*") . T) (-3986 . T) (-3987 . T) (-3989 . T))
+((-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T))
NIL
-(-781 |p|)
+(-782 |p|)
((|constructor| (NIL "Stream-based implementation of 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).")))
-((-3984 . T) (-3990 . T) (-3985 . T) ((-3994 "*") . T) (-3986 . T) (-3987 . T) (-3989 . T))
-((|HasCategory| (-779 |#1|) (QUOTE (-822))) (|HasCategory| (-779 |#1|) (QUOTE (-951 (-1089)))) (|HasCategory| (-779 |#1|) (QUOTE (-118))) (|HasCategory| (-779 |#1|) (QUOTE (-120))) (|HasCategory| (-779 |#1|) (QUOTE (-554 (-473)))) (|HasCategory| (-779 |#1|) (QUOTE (-934))) (|HasCategory| (-779 |#1|) (QUOTE (-741))) (|HasCategory| (-779 |#1|) (QUOTE (-757))) (OR (|HasCategory| (-779 |#1|) (QUOTE (-741))) (|HasCategory| (-779 |#1|) (QUOTE (-757)))) (|HasCategory| (-779 |#1|) (QUOTE (-951 (-484)))) (|HasCategory| (-779 |#1|) (QUOTE (-1065))) (|HasCategory| (-779 |#1|) (QUOTE (-797 (-327)))) (|HasCategory| (-779 |#1|) (QUOTE (-797 (-484)))) (|HasCategory| (-779 |#1|) (QUOTE (-554 (-801 (-327))))) (|HasCategory| (-779 |#1|) (QUOTE (-554 (-801 (-484))))) (|HasCategory| (-779 |#1|) (QUOTE (-581 (-484)))) (|HasCategory| (-779 |#1|) (QUOTE (-189))) (|HasCategory| (-779 |#1|) (QUOTE (-812 (-1089)))) (|HasCategory| (-779 |#1|) (QUOTE (-190))) (|HasCategory| (-779 |#1|) (QUOTE (-810 (-1089)))) (|HasCategory| (-779 |#1|) (|%list| (QUOTE -453) (QUOTE (-1089)) (|%list| (QUOTE -779) (|devaluate| |#1|)))) (|HasCategory| (-779 |#1|) (|%list| (QUOTE -259) (|%list| (QUOTE -779) (|devaluate| |#1|)))) (|HasCategory| (-779 |#1|) (|%list| (QUOTE -241) (|%list| (QUOTE -779) (|devaluate| |#1|)) (|%list| (QUOTE -779) (|devaluate| |#1|)))) (|HasCategory| (-779 |#1|) (QUOTE (-257))) (|HasCategory| (-779 |#1|) (QUOTE (-483))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-779 |#1|) (QUOTE (-822)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-779 |#1|) (QUOTE (-822)))) (|HasCategory| (-779 |#1|) (QUOTE (-118)))))
-(-782 |p| PADIC)
+((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T))
+((|HasCategory| (-780 |#1|) (QUOTE (-823))) (|HasCategory| (-780 |#1|) (QUOTE (-952 (-1091)))) (|HasCategory| (-780 |#1|) (QUOTE (-118))) (|HasCategory| (-780 |#1|) (QUOTE (-120))) (|HasCategory| (-780 |#1|) (QUOTE (-555 (-474)))) (|HasCategory| (-780 |#1|) (QUOTE (-935))) (|HasCategory| (-780 |#1|) (QUOTE (-742))) (|HasCategory| (-780 |#1|) (QUOTE (-758))) (OR (|HasCategory| (-780 |#1|) (QUOTE (-742))) (|HasCategory| (-780 |#1|) (QUOTE (-758)))) (|HasCategory| (-780 |#1|) (QUOTE (-952 (-485)))) (|HasCategory| (-780 |#1|) (QUOTE (-1067))) (|HasCategory| (-780 |#1|) (QUOTE (-798 (-328)))) (|HasCategory| (-780 |#1|) (QUOTE (-798 (-485)))) (|HasCategory| (-780 |#1|) (QUOTE (-555 (-802 (-328))))) (|HasCategory| (-780 |#1|) (QUOTE (-555 (-802 (-485))))) (|HasCategory| (-780 |#1|) (QUOTE (-582 (-485)))) (|HasCategory| (-780 |#1|) (QUOTE (-189))) (|HasCategory| (-780 |#1|) (QUOTE (-813 (-1091)))) (|HasCategory| (-780 |#1|) (QUOTE (-190))) (|HasCategory| (-780 |#1|) (QUOTE (-811 (-1091)))) (|HasCategory| (-780 |#1|) (|%list| (QUOTE -454) (QUOTE (-1091)) (|%list| (QUOTE -780) (|devaluate| |#1|)))) (|HasCategory| (-780 |#1|) (|%list| (QUOTE -260) (|%list| (QUOTE -780) (|devaluate| |#1|)))) (|HasCategory| (-780 |#1|) (|%list| (QUOTE -241) (|%list| (QUOTE -780) (|devaluate| |#1|)) (|%list| (QUOTE -780) (|devaluate| |#1|)))) (|HasCategory| (-780 |#1|) (QUOTE (-258))) (|HasCategory| (-780 |#1|) (QUOTE (-484))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-780 |#1|) (QUOTE (-823)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-780 |#1|) (QUOTE (-823)))) (|HasCategory| (-780 |#1|) (QUOTE (-118)))))
+(-783 |p| PADIC)
((|constructor| (NIL "This is the category of stream-based representations of 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)}.")))
-((-3984 . T) (-3990 . T) (-3985 . T) ((-3994 "*") . T) (-3986 . T) (-3987 . T) (-3989 . T))
-((|HasCategory| |#2| (QUOTE (-822))) (|HasCategory| |#2| (QUOTE (-951 (-1089)))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-554 (-473)))) (|HasCategory| |#2| (QUOTE (-934))) (|HasCategory| |#2| (QUOTE (-741))) (|HasCategory| |#2| (QUOTE (-757))) (OR (|HasCategory| |#2| (QUOTE (-741))) (|HasCategory| |#2| (QUOTE (-757)))) (|HasCategory| |#2| (QUOTE (-951 (-484)))) (|HasCategory| |#2| (QUOTE (-1065))) (|HasCategory| |#2| (QUOTE (-797 (-327)))) (|HasCategory| |#2| (QUOTE (-797 (-484)))) (|HasCategory| |#2| (QUOTE (-554 (-801 (-327))))) (|HasCategory| |#2| (QUOTE (-554 (-801 (-484))))) (|HasCategory| |#2| (QUOTE (-581 (-484)))) (|HasCategory| |#2| (QUOTE (-189))) (|HasCategory| |#2| (QUOTE (-812 (-1089)))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-810 (-1089)))) (|HasCategory| |#2| (|%list| (QUOTE -453) (QUOTE (-1089)) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -259) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -241) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-257))) (|HasCategory| |#2| (QUOTE (-483))) (-12 (|HasCategory| |#2| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#2| (QUOTE (-118)))))
-(-783 S T$)
+((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T))
+((|HasCategory| |#2| (QUOTE (-823))) (|HasCategory| |#2| (QUOTE (-952 (-1091)))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-555 (-474)))) (|HasCategory| |#2| (QUOTE (-935))) (|HasCategory| |#2| (QUOTE (-742))) (|HasCategory| |#2| (QUOTE (-758))) (OR (|HasCategory| |#2| (QUOTE (-742))) (|HasCategory| |#2| (QUOTE (-758)))) (|HasCategory| |#2| (QUOTE (-952 (-485)))) (|HasCategory| |#2| (QUOTE (-1067))) (|HasCategory| |#2| (QUOTE (-798 (-328)))) (|HasCategory| |#2| (QUOTE (-798 (-485)))) (|HasCategory| |#2| (QUOTE (-555 (-802 (-328))))) (|HasCategory| |#2| (QUOTE (-555 (-802 (-485))))) (|HasCategory| |#2| (QUOTE (-582 (-485)))) (|HasCategory| |#2| (QUOTE (-189))) (|HasCategory| |#2| (QUOTE (-813 (-1091)))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-811 (-1091)))) (|HasCategory| |#2| (|%list| (QUOTE -454) (QUOTE (-1091)) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -241) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-258))) (|HasCategory| |#2| (QUOTE (-484))) (-12 (|HasCategory| |#2| (QUOTE (-823))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-823))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#2| (QUOTE (-118)))))
+(-784 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 `p'.")) (|first| ((|#1| $) "\\spad{first(p)} extracts the first component of `p'.")) (|construct| (($ |#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 `s' and `t'.")))
NIL
-((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-1013)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-553 (-773))))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-1013))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-553 (-773))))))
-(-784)
+((-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#2| (QUOTE (-1015)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-554 (-774)))) (|HasCategory| |#2| (QUOTE (-554 (-774))))) (-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#2| (QUOTE (-1015))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-774)))) (|HasCategory| |#2| (QUOTE (-554 (-774))))))
+(-785)
((|constructor| (NIL "This domain describes four groups of color shades (palettes).")) (|shade| (((|Integer|) $) "\\spad{shade(p)} returns the shade index of the indicated palette \\spad{p}.")) (|hue| (((|Color|) $) "\\spad{hue(p)} returns the hue field of the indicated palette \\spad{p}.")) (|light| (($ (|Color|)) "\\spad{light(c)} sets the shade of a hue,{} \\spad{c},{} to it's highest value.")) (|pastel| (($ (|Color|)) "\\spad{pastel(c)} sets the shade of a hue,{} \\spad{c},{} above bright,{} but below light.")) (|bright| (($ (|Color|)) "\\spad{bright(c)} sets the shade of a hue,{} \\spad{c},{} above dim,{} but below pastel.")) (|dim| (($ (|Color|)) "\\spad{dim(c)} sets the shade of a hue,{} \\spad{c},{} above dark,{} but below bright.")) (|dark| (($ (|Color|)) "\\spad{dark(c)} sets the shade of the indicated hue of \\spad{c} to it's lowest value.")))
NIL
NIL
-(-785)
+(-786)
((|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
-(-786)
+(-787)
((|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
-(-787 CF1 CF2)
+(-788 CF1 CF2)
((|constructor| (NIL "This package \\undocumented")) (|map| (((|ParametricPlaneCurve| |#2|) (|Mapping| |#2| |#1|) (|ParametricPlaneCurve| |#1|)) "\\spad{map(f,x)} \\undocumented")))
NIL
NIL
-(-788 |ComponentFunction|)
+(-789 |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
-(-789 CF1 CF2)
+(-790 CF1 CF2)
((|constructor| (NIL "This package \\undocumented")) (|map| (((|ParametricSpaceCurve| |#2|) (|Mapping| |#2| |#1|) (|ParametricSpaceCurve| |#1|)) "\\spad{map(f,x)} \\undocumented")))
NIL
NIL
-(-790 |ComponentFunction|)
+(-791 |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
-(-791)
+(-792)
((|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
-(-792 CF1 CF2)
+(-793 CF1 CF2)
((|constructor| (NIL "This package \\undocumented")) (|map| (((|ParametricSurface| |#2|) (|Mapping| |#2| |#1|) (|ParametricSurface| |#1|)) "\\spad{map(f,x)} \\undocumented")))
NIL
NIL
-(-793 |ComponentFunction|)
+(-794 |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
-(-794)
+(-795)
((|constructor| (NIL "PartitionsAndPermutations contains functions for generating streams of integer partitions,{} and streams of sequences of integers composed from a multi-set.")) (|permutations| (((|Stream| (|List| (|Integer|))) (|Integer|)) "\\spad{permutations(n)} is the stream of permutations \\indented{1}{formed from \\spad{1,2,3,...,n}.}")) (|sequences| (((|Stream| (|List| (|Integer|))) (|List| (|Integer|))) "\\spad{sequences([l0,l1,l2,..,ln])} is the set of \\indented{1}{all sequences formed from} \\spad{l0} 0's,{}\\spad{l1} 1's,{}\\spad{l2} 2's,{}...,{}\\spad{ln} \\spad{n}'s.") (((|Stream| (|List| (|Integer|))) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{sequences(l1,l2)} is the stream of all sequences that \\indented{1}{can be composed from the multiset defined from} \\indented{1}{two lists of integers \\spad{l1} and \\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}'s,{} and 4 \\spad{5}'s.}")) (|shufflein| (((|Stream| (|List| (|Integer|))) (|List| (|Integer|)) (|Stream| (|List| (|Integer|)))) "\\spad{shufflein(l,st)} maps shuffle(\\spad{l},{}\\spad{u}) on to all \\indented{1}{members \\spad{u} of \\spad{st},{} concatenating the results.}")) (|shuffle| (((|Stream| (|List| (|Integer|))) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{shuffle(l1,l2)} forms the stream of all shuffles of \\spad{l1} \\indented{1}{and \\spad{l2},{} \\spadignore{i.e.} all sequences that can be formed from} \\indented{1}{merging \\spad{l1} and \\spad{l2}.}")) (|conjugates| (((|Stream| (|List| (|PositiveInteger|))) (|Stream| (|List| (|PositiveInteger|)))) "\\spad{conjugates(lp)} is the stream of conjugates of a stream \\indented{1}{of partitions \\spad{lp}.}")) (|conjugate| (((|List| (|PositiveInteger|)) (|List| (|PositiveInteger|))) "\\spad{conjugate(pt)} is the conjugate of the partition \\spad{pt}.")))
NIL
NIL
-(-795 R)
+(-796 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
-(-796 R S L)
+(-797 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
-(-797 S)
+(-798 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
-(-798 |Base| |Subject| |Pat|)
+(-799 |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 (-2559 (|HasCategory| |#2| (QUOTE (-951 (-1089))))) (-2559 (|HasCategory| |#2| (QUOTE (-962))))) (-12 (|HasCategory| |#2| (QUOTE (-962))) (-2559 (|HasCategory| |#2| (QUOTE (-951 (-1089)))))) (|HasCategory| |#2| (QUOTE (-951 (-1089)))))
-(-799 R S)
+((-12 (-2562 (|HasCategory| |#2| (QUOTE (-952 (-1091))))) (-2562 (|HasCategory| |#2| (QUOTE (-963))))) (-12 (|HasCategory| |#2| (QUOTE (-963))) (-2562 (|HasCategory| |#2| (QUOTE (-952 (-1091)))))) (|HasCategory| |#2| (QUOTE (-952 (-1091)))))
+(-800 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't,{} and \"failed\" if not enough variables of \\spad{p} are matched in \\spad{r} to decide.")) (|construct| (($ (|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| |#2|)))) "\\spad{construct([v1,e1],...,[vn,en])} returns the match result containing the matches (\\spad{v1},{}\\spad{e1}),{}...,{}(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
-(-800 R A B)
+(-801 R A B)
((|constructor| (NIL "Lifts maps to pattern matching results.")) (|map| (((|PatternMatchResult| |#1| |#3|) (|Mapping| |#3| |#2|) (|PatternMatchResult| |#1| |#2|)) "\\spad{map(f, [(v1,a1),...,(vn,an)])} returns the matching result [(\\spad{v1},{}\\spad{f}(\\spad{a1})),{}...,{}(vn,{}\\spad{f}(an))].")))
NIL
NIL
-(-801 R)
+(-802 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 pn to the copy,{} which is returned.")) (|setPredicates| (($ $ (|List| (|Any|))) "\\spad{setPredicates(p, [p1,...,pn])} attaches the predicate \\spad{p1} and ... and 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 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 '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
-(-802 R -2668)
+(-803 R -2671)
((|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 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
-(-803 R S)
+(-804 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
-(-804 |VarSet|)
+(-805 |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.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
-(-805 UP R)
+(-806 UP R)
((|constructor| (NIL "This package \\undocumented")) (|compose| ((|#1| |#1| |#1|) "\\spad{compose(p,q)} \\undocumented")))
NIL
NIL
-(-806 A T$ S)
+(-807 A T$ S)
((|constructor| (NIL "\\indented{2}{This category captures the interface of domains with a distinguished} \\indented{2}{operation named \\spad{differentiate} for partial differentiation with} \\indented{2}{respect to some domain of variables.} See Also: \\indented{2}{DifferentialDomain,{} PartialDifferentialSpace}")) (D ((|#2| $ |#3|) "\\spad{D(x,v)} is a shorthand for \\spad{differentiate(x,v)}")) (|differentiate| ((|#2| $ |#3|) "\\spad{differentiate(x,v)} computes the partial derivative of \\spad{x} with respect to \\spad{v}.")))
NIL
NIL
-(-807 T$ S)
+(-808 T$ S)
((|constructor| (NIL "\\indented{2}{This category captures the interface of domains with a distinguished} \\indented{2}{operation named \\spad{differentiate} for partial differentiation with} \\indented{2}{respect to some domain of variables.} See Also: \\indented{2}{DifferentialDomain,{} PartialDifferentialSpace}")) (D ((|#1| $ |#2|) "\\spad{D(x,v)} is a shorthand for \\spad{differentiate(x,v)}")) (|differentiate| ((|#1| $ |#2|) "\\spad{differentiate(x,v)} computes the partial derivative of \\spad{x} with respect to \\spad{v}.")))
NIL
NIL
-(-808 UP -3091)
+(-809 UP -3094)
((|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
-(-809 R S)
+(-810 R S)
((|constructor| (NIL "A partial differential \\spad{R}-module with differentiations indexed by a parameter type \\spad{S}. \\blankline")))
-((-3987 . T) (-3986 . T))
+((-3991 . T) (-3990 . T))
NIL
-(-810 S)
+(-811 S)
((|constructor| (NIL "A partial differential ring with differentiations indexed by a parameter type \\spad{S}. \\blankline")))
-((-3989 . T))
+((-3993 . T))
NIL
-(-811 A S)
+(-812 A S)
((|constructor| (NIL "\\indented{2}{This category captures the interface of domains stable by partial} \\indented{2}{differentiation with respect to variables from some domain.} See Also: \\indented{2}{PartialDifferentialDomain}")) (D (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) "\\spad{D(x,[s1,...,sn],[n1,...,nn])} is a shorthand for \\spad{differentiate(x,[s1,...,sn],[n1,...,nn])}.") (($ $ |#2| (|NonNegativeInteger|)) "\\spad{D(x,s,n)} is a shorthand for \\spad{differentiate(x,s,n)}.") (($ $ (|List| |#2|)) "\\spad{D(x,[s1,...sn])} is a shorthand for \\spad{differentiate(x,[s1,...sn])}.")) (|differentiate| (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) "\\spad{differentiate(x,[s1,...,sn],[n1,...,nn])} computes multiple partial derivatives,{} \\spadignore{i.e.}") (($ $ |#2| (|NonNegativeInteger|)) "\\spad{differentiate(x,s,n)} computes multiple partial derivatives,{} \\spadignore{i.e.} \\spad{n}\\spad{-}th derivative of \\spad{x} with respect to \\spad{s}.") (($ $ (|List| |#2|)) "\\spad{differentiate(x,[s1,...sn])} computes successive partial derivatives,{} \\spadignore{i.e.} \\spad{differentiate(...differentiate(x, s1)..., sn)}.")))
NIL
NIL
-(-812 S)
+(-813 S)
((|constructor| (NIL "\\indented{2}{This category captures the interface of domains stable by partial} \\indented{2}{differentiation with respect to variables from some domain.} See Also: \\indented{2}{PartialDifferentialDomain}")) (D (($ $ (|List| |#1|) (|List| (|NonNegativeInteger|))) "\\spad{D(x,[s1,...,sn],[n1,...,nn])} is a shorthand for \\spad{differentiate(x,[s1,...,sn],[n1,...,nn])}.") (($ $ |#1| (|NonNegativeInteger|)) "\\spad{D(x,s,n)} is a shorthand for \\spad{differentiate(x,s,n)}.") (($ $ (|List| |#1|)) "\\spad{D(x,[s1,...sn])} is a shorthand for \\spad{differentiate(x,[s1,...sn])}.")) (|differentiate| (($ $ (|List| |#1|) (|List| (|NonNegativeInteger|))) "\\spad{differentiate(x,[s1,...,sn],[n1,...,nn])} computes multiple partial derivatives,{} \\spadignore{i.e.}") (($ $ |#1| (|NonNegativeInteger|)) "\\spad{differentiate(x,s,n)} computes multiple partial derivatives,{} \\spadignore{i.e.} \\spad{n}\\spad{-}th derivative of \\spad{x} with respect to \\spad{s}.") (($ $ (|List| |#1|)) "\\spad{differentiate(x,[s1,...sn])} computes successive partial derivatives,{} \\spadignore{i.e.} \\spad{differentiate(...differentiate(x, s1)..., sn)}.")))
NIL
NIL
-(-813 S)
+(-814 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})'s")) (|ptree| (($ $ $) "\\spad{ptree(x,y)} \\undocumented") (($ |#1|) "\\spad{ptree(s)} is a leaf? pendant tree")))
NIL
-((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1013))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-72))))
-(-814 S)
+((-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1015))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| |#1| (QUOTE (-554 (-774)))) (|HasCategory| |#1| (QUOTE (-72))))
+(-815 S)
((|constructor| (NIL "Permutation(\\spad{S}) implements the group of all bijections \\indented{2}{on a set \\spad{S},{} which move only a finite number of points.} \\indented{2}{A permutation is considered as a map from \\spad{S} into \\spad{S}. In particular} \\indented{2}{multiplication is defined as composition of maps:} \\indented{2}{{\\em pi1 * pi2 = pi1 o pi2}.} \\indented{2}{The internal representation of permuatations are two lists} \\indented{2}{of equal length representing preimages and images.}")) (|coerceImages| (($ (|List| |#1|)) "\\spad{coerceImages(ls)} coerces the list {\\em ls} to a permutation whose image is given by {\\em ls} and the preimage is fixed to be {\\em [1,...,n]}. Note: {coerceImages(\\spad{ls})=coercePreimagesImages([1,{}...,{}\\spad{n}],{}\\spad{ls})}. We assume that both preimage and image do not contain repetitions.")) (|fixedPoints| (((|Set| |#1|) $) "\\spad{fixedPoints(p)} returns the points fixed by the permutation \\spad{p}.")) (|sort| (((|List| $) (|List| $)) "\\spad{sort(lp)} sorts a list of permutations {\\em lp} according to cycle structure first according to length of cycles,{} second,{} if \\spad{S} has \\spadtype{Finite} or \\spad{S} has \\spadtype{OrderedSet} according to lexicographical order of entries in cycles of equal length.")) (|odd?| (((|Boolean|) $) "\\spad{odd?(p)} returns \\spad{true} if and only if \\spad{p} is an odd permutation \\spadignore{i.e.} {\\em sign(p)} is {\\em -1}.")) (|even?| (((|Boolean|) $) "\\spad{even?(p)} returns \\spad{true} if and only if \\spad{p} is an even permutation,{} \\spadignore{i.e.} {\\em sign(p)} is 1.")) (|sign| (((|Integer|) $) "\\spad{sign(p)} returns the signum of the permutation \\spad{p},{} \\spad{+1} or \\spad{-1}.")) (|numberOfCycles| (((|NonNegativeInteger|) $) "\\spad{numberOfCycles(p)} returns the number of non-trivial cycles of the permutation \\spad{p}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of a permutation \\spad{p} as a group element.")) (|cyclePartition| (((|Partition|) $) "\\spad{cyclePartition(p)} returns the cycle structure of a permutation \\spad{p} including cycles of length 1 only if \\spad{S} is finite.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(p)} retuns the number of points moved by the permutation \\spad{p}.")) (|coerceListOfPairs| (($ (|List| (|List| |#1|))) "\\spad{coerceListOfPairs(lls)} coerces a list of pairs {\\em lls} to a permutation. Error: if not consistent,{} \\spadignore{i.e.} the set of the first elements coincides with the set of second elements. coerce(\\spad{p}) generates output of the permutation \\spad{p} with domain OutputForm.")) (|coerce| (($ (|List| |#1|)) "\\spad{coerce(ls)} coerces a cycle {\\em ls},{} \\spadignore{i.e.} a list with not repetitions to a permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list. Error: if repetitions occur.") (($ (|List| (|List| |#1|))) "\\spad{coerce(lls)} coerces a list of cycles {\\em lls} to a permutation,{} each cycle being a list with no repetitions,{} is coerced to the permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list,{} then these permutations are mutiplied. Error: if repetitions occur in one cycle.")) (|coercePreimagesImages| (($ (|List| (|List| |#1|))) "\\spad{coercePreimagesImages(lls)} coerces the representation {\\em lls} of a permutation as a list of preimages and images to a permutation. We assume that both preimage and image do not contain repetitions.")) (|listRepresentation| (((|Record| (|:| |preimage| (|List| |#1|)) (|:| |image| (|List| |#1|))) $) "\\spad{listRepresentation(p)} produces a representation {\\em rep} of the permutation \\spad{p} as a list of preimages and images,{} \\spad{i}.\\spad{e} \\spad{p} maps {\\em (rep.preimage).k} to {\\em (rep.image).k} for all indices \\spad{k}. Elements of \\spad{S} not in {\\em (rep.preimage).k} are fixed points,{} and these are the only fixed points of the permutation.")))
-((-3989 . T))
-((OR (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-757)))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-757))))
-(-815 |n| R)
+((-3993 . T))
+((OR (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-758)))) (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-758))))
+(-816 |n| R)
((|constructor| (NIL "Permanent implements the functions {\\em permanent},{} the permanent for square matrices.")) (|permanent| ((|#2| (|SquareMatrix| |#1| |#2|)) "\\spad{permanent(x)} computes the permanent of a square matrix \\spad{x}. The {\\em permanent} is equivalent to the \\spadfun{determinant} except that coefficients have no change of sign. This function is much more difficult to compute than the {\\em determinant}. The formula used is by \\spad{H}.\\spad{J}. Ryser,{} improved by [Nijenhuis and Wilf,{} Ch. 19]. Note: permanent(\\spad{x}) choose one of three algorithms,{} depending on the underlying ring \\spad{R} and on \\spad{n},{} the number of rows (and columns) of x:\\begin{items} \\item 1. if 2 has an inverse in \\spad{R} we can use the algorithm of \\indented{3}{[Nijenhuis and Wilf,{} ch.19,{}\\spad{p}.158]; if 2 has no inverse,{}} \\indented{3}{some modifications are necessary:} \\item 2. if {\\em n > 6} and \\spad{R} is an integral domain with characteristic \\indented{3}{different from 2 (the algorithm works if and only 2 is not a} \\indented{3}{zero-divisor of \\spad{R} and {\\em characteristic()\\$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
-(-816 S)
+(-817 S)
((|constructor| (NIL "PermutationCategory provides a categorial environment \\indented{1}{for subgroups of bijections of a set (\\spadignore{i.e.} permutations)}")) (< (((|Boolean|) $ $) "\\spad{p < q} is an order relation on permutations. Note: this order is only total if and only if \\spad{S} is totally ordered or \\spad{S} is finite.")) (|orbit| (((|Set| |#1|) $ |#1|) "\\spad{orbit(p, el)} returns the orbit of {\\em el} under the permutation \\spad{p},{} \\spadignore{i.e.} the set which is given by applications of the powers of \\spad{p} to {\\em el}.")) (|support| (((|Set| |#1|) $) "\\spad{support p} returns the set of points not fixed by the permutation \\spad{p}.")) (|cycles| (($ (|List| (|List| |#1|))) "\\spad{cycles(lls)} coerces a list list of cycles {\\em lls} to a permutation,{} each cycle being a list with not repetitions,{} is coerced to the permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list,{} then these permutations are mutiplied. Error: if repetitions occur in one cycle.")) (|cycle| (($ (|List| |#1|)) "\\spad{cycle(ls)} coerces a cycle {\\em ls},{} \\spadignore{i.e.} a list with not repetitions to a permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list. Error: if repetitions occur.")))
-((-3989 . T))
+((-3993 . T))
NIL
-(-817 S)
+(-818 S)
((|constructor| (NIL "PermutationGroup implements permutation groups acting on a set \\spad{S},{} \\spadignore{i.e.} all subgroups of the symmetric group of \\spad{S},{} represented as a list of permutations (generators). Note that therefore the objects are not members of the \\Language category \\spadtype{Group}. Using the idea of base and strong generators by Sims,{} basic routines and algorithms are implemented so that the word problem for permutation groups can be solved.")) (|initializeGroupForWordProblem| (((|Void|) $ (|Integer|) (|Integer|)) "\\spad{initializeGroupForWordProblem(gp,m,n)} initializes the group {\\em gp} for the word problem. Notes: (1) with a small integer you get shorter words,{} but the routine takes longer than the standard routine for longer words. (2) be careful: invoking this routine will destroy the possibly stored information about your group (but will recompute it again). (3) users need not call this function normally for the soultion of the word problem.") (((|Void|) $) "\\spad{initializeGroupForWordProblem(gp)} initializes the group {\\em gp} for the word problem. Notes: it calls the other function of this name with parameters 0 and 1: {\\em initializeGroupForWordProblem(gp,0,1)}. Notes: (1) be careful: invoking this routine will destroy the possibly information about your group (but will recompute it again) (2) users need not call this function normally for the soultion of the word problem.")) (<= (((|Boolean|) $ $) "\\spad{gp1 <= gp2} returns \\spad{true} if and only if {\\em gp1} is a subgroup of {\\em gp2}. Note: because of a bug in the parser you have to call this function explicitly by {\\em gp1 <=\\$(PERMGRP S) gp2}.")) (< (((|Boolean|) $ $) "\\spad{gp1 < gp2} returns \\spad{true} if and only if {\\em gp1} is a proper subgroup of {\\em gp2}.")) (|support| (((|Set| |#1|) $) "\\spad{support(gp)} returns the points moved by the group {\\em gp}.")) (|wordInGenerators| (((|List| (|NonNegativeInteger|)) (|Permutation| |#1|) $) "\\spad{wordInGenerators(p,gp)} returns the word for the permutation \\spad{p} in the original generators of the group {\\em gp},{} represented by the indices of the list,{} given by {\\em generators}.")) (|wordInStrongGenerators| (((|List| (|NonNegativeInteger|)) (|Permutation| |#1|) $) "\\spad{wordInStrongGenerators(p,gp)} returns the word for the permutation \\spad{p} in the strong generators of the group {\\em gp},{} represented by the indices of the list,{} given by {\\em strongGenerators}.")) (|member?| (((|Boolean|) (|Permutation| |#1|) $) "\\spad{member?(pp,gp)} answers the question,{} whether the permutation {\\em pp} is in the group {\\em gp} or not.")) (|orbits| (((|Set| (|Set| |#1|)) $) "\\spad{orbits(gp)} returns the orbits of the group {\\em gp},{} \\spadignore{i.e.} it partitions the (finite) of all moved points.")) (|orbit| (((|Set| (|List| |#1|)) $ (|List| |#1|)) "\\spad{orbit(gp,ls)} returns the orbit of the ordered list {\\em ls} under the group {\\em gp}. Note: return type is \\spad{L} \\spad{L} \\spad{S} temporarily because FSET \\spad{L} \\spad{S} has an error.") (((|Set| (|Set| |#1|)) $ (|Set| |#1|)) "\\spad{orbit(gp,els)} returns the orbit of the unordered set {\\em els} under the group {\\em gp}.") (((|Set| |#1|) $ |#1|) "\\spad{orbit(gp,el)} returns the orbit of the element {\\em el} under the group {\\em gp},{} \\spadignore{i.e.} the set of all points gained by applying each group element to {\\em el}.")) (|permutationGroup| (($ (|List| (|Permutation| |#1|))) "\\spad{permutationGroup(ls)} coerces a list of permutations {\\em ls} to the group generated by this list.")) (|wordsForStrongGenerators| (((|List| (|List| (|NonNegativeInteger|))) $) "\\spad{wordsForStrongGenerators(gp)} returns the words for the strong generators of the group {\\em gp} in the original generators of {\\em gp},{} represented by their indices in the list,{} given by {\\em generators}.")) (|strongGenerators| (((|List| (|Permutation| |#1|)) $) "\\spad{strongGenerators(gp)} returns strong generators for the group {\\em gp}.")) (|base| (((|List| |#1|) $) "\\spad{base(gp)} returns a base for the group {\\em gp}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(gp)} returns the number of points moved by all permutations of the group {\\em gp}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(gp)} returns the order of the group {\\em gp}.")) (|random| (((|Permutation| |#1|) $) "\\spad{random(gp)} returns a random product of maximal 20 generators of the group {\\em gp}. Note: {\\em random(gp)=random(gp,20)}.") (((|Permutation| |#1|) $ (|Integer|)) "\\spad{random(gp,i)} returns a random product of maximal \\spad{i} generators of the group {\\em gp}.")) (|elt| (((|Permutation| |#1|) $ (|NonNegativeInteger|)) "\\spad{elt(gp,i)} returns the \\spad{i}-th generator of the group {\\em gp}.")) (|generators| (((|List| (|Permutation| |#1|)) $) "\\spad{generators(gp)} returns the generators of the group {\\em gp}.")) (|coerce| (($ (|List| (|Permutation| |#1|))) "\\spad{coerce(ls)} coerces a list of permutations {\\em ls} to the group generated by this list.") (((|List| (|Permutation| |#1|)) $) "\\spad{coerce(gp)} returns the generators of the group {\\em gp}.")))
NIL
NIL
-(-818 |p|)
+(-819 |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.")))
-((-3984 . T) (-3990 . T) (-3985 . T) ((-3994 "*") . T) (-3986 . T) (-3987 . T) (-3989 . T))
-((|HasCategory| $ (QUOTE (-120))) (|HasCategory| $ (QUOTE (-118))) (|HasCategory| $ (QUOTE (-317))))
-(-819 R E |VarSet| S)
+((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T))
+((|HasCategory| $ (QUOTE (-120))) (|HasCategory| $ (QUOTE (-118))) (|HasCategory| $ (QUOTE (-318))))
+(-820 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
-(-820 R S)
+(-821 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
-(-821 S)
+(-822 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| (((|Maybe| $) $) "\\spad{charthRoot(r)} returns the \\spad{p}\\spad{-}th root of \\spad{r},{} or \\spad{nothing} 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}'s exists.")) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) "\\spad{gcdPolynomial(p,q)} returns the gcd of the univariate polynomials \\spad{p} 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 (-118))))
-(-822)
+(-823)
((|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| (((|Maybe| $) $) "\\spad{charthRoot(r)} returns the \\spad{p}\\spad{-}th root of \\spad{r},{} or \\spad{nothing} 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}'s exists.")) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) "\\spad{gcdPolynomial(p,q)} returns the gcd of the univariate polynomials \\spad{p} 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}.")))
-((-3985 . T) ((-3994 "*") . T) (-3986 . T) (-3987 . T) (-3989 . T))
+((-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T))
NIL
-(-823 R0 -3091 UP UPUP R)
+(-824 R0 -3094 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
-(-824 UP UPUP R)
+(-825 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
-(-825 UP UPUP)
+(-826 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
-(-826 R)
+(-827 R)
((|constructor| (NIL "The domain \\spadtype{PartialFraction} implements partial fractions over a euclidean domain \\spad{R}. This requirement on the argument domain allows us to normalize the fractions. Of particular interest are the 2 forms for these fractions. The ``compact'' form has only one fractional term per prime in the denominator,{} while the ``p-adic'' form expands each numerator \\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} ``p-adically'' 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.")))
-((-3984 . T) (-3990 . T) (-3985 . T) ((-3994 "*") . T) (-3986 . T) (-3987 . T) (-3989 . T))
+((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T))
NIL
-(-827 R)
+(-828 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
-(-828 E OV R P)
+(-829 E OV R P)
((|gcdPrimitive| ((|#4| (|List| |#4|)) "\\spad{gcdPrimitive lp} computes the gcd of the list of primitive polynomials lp.") (((|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{gcdPrimitive(p,q)} computes the gcd of the primitive polynomials \\spad{p} and \\spad{q}.") ((|#4| |#4| |#4|) "\\spad{gcdPrimitive(p,q)} computes the gcd of the primitive polynomials \\spad{p} and \\spad{q}.")) (|gcd| (((|SparseUnivariatePolynomial| |#4|) (|List| (|SparseUnivariatePolynomial| |#4|))) "\\spad{gcd(lp)} computes the gcd of the list of polynomials \\spad{lp}.") (((|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{gcd(p,q)} computes the gcd of the two polynomials \\spad{p} and \\spad{q}.") ((|#4| (|List| |#4|)) "\\spad{gcd(lp)} computes the gcd of the list of polynomials \\spad{lp}.") ((|#4| |#4| |#4|) "\\spad{gcd(p,q)} computes the gcd of the two polynomials \\spad{p} and \\spad{q}.")))
NIL
NIL
-(-829)
+(-830)
((|constructor| (NIL "PermutationGroupExamples provides permutation groups for some classes of groups: symmetric,{} alternating,{} dihedral,{} cyclic,{} direct products of cyclic,{} which are in fact the finite abelian groups of symmetric groups called Young subgroups. Furthermore,{} Rubik's group as permutation group of 48 integers and a list of sporadic simple groups derived from the atlas of finite groups.")) (|youngGroup| (((|PermutationGroup| (|Integer|)) (|Partition|)) "\\spad{youngGroup(lambda)} constructs the direct product of the symmetric groups given by the parts of the partition {\\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's Cube acting on integers {\\em 10*i+j} for {\\em 1 <= i <= 6},{} {\\em 1 <= j <= 8}. The faces of Rubik's Cube are labelled in the obvious way Front,{} Right,{} Up,{} Down,{} Left,{} Back and numbered from 1 to 6 in this given ordering,{} the pieces on each face (except the unmoveable center piece) are clockwise numbered from 1 to 8 starting with the piece in the upper left corner. The moves of the cube are represented as permutations on these pieces,{} represented as a two digit integer {\\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's Cube acting on integers 10*i+j for 1 <= \\spad{i} <= 6,{} 1 <= \\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
-(-830 -3091)
+(-831 -3094)
((|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 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
-(-831)
+(-832)
((|constructor| (NIL "\\spadtype{PositiveInteger} provides functions for \\indented{2}{positive integers.}")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} means multiplication is commutative : x*y = y*x")) (|gcd| (($ $ $) "\\spad{gcd(a,b)} computes the greatest common divisor of two positive integers \\spad{a} and \\spad{b}.")))
-(((-3994 "*") . T))
+(((-3998 "*") . T))
NIL
-(-832 R)
+(-833 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
-(-833)
+(-834)
((|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| (((|Maybe| (|List| $)) (|List| $) $) "\\spad{expressIdealMember([f1,...,fn],h)} returns a representation of \\spad{h} as a linear combination of the \\spad{fi} or \\spad{nothing} 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)}")))
-((-3985 . T) ((-3994 "*") . T) (-3986 . T) (-3987 . T) (-3989 . T))
+((-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T))
NIL
-(-834 |xx| -3091)
+(-835 |xx| -3094)
((|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
-(-835 -3091 P)
+(-836 -3094 P)
((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,l2)} \\undocumented")))
NIL
NIL
-(-836 R |Var| |Expon| GR)
+(-837 R |Var| |Expon| GR)
((|constructor| (NIL "Author: William Sit,{} spring 89")) (|inconsistent?| (((|Boolean|) (|List| (|Polynomial| |#1|))) "inconsistant?(pl) returns \\spad{true} if the system of equations \\spad{p} = 0 for \\spad{p} in pl is inconsistent. It is assumed that pl is a groebner basis.") (((|Boolean|) (|List| |#4|)) "inconsistant?(pl) returns \\spad{true} if the system of equations \\spad{p} = 0 for \\spad{p} in pl is inconsistent. It is assumed that 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{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} ~= 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{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{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{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{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{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{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
-(-837)
+(-838)
((|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
-(-838 S)
+(-839 S)
((|constructor| (NIL "\\spad{PlotFunctions1} provides facilities for plotting curves where functions SF -> 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
-(-839)
+(-840)
((|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
-(-840)
+(-841)
((|constructor| (NIL "This package exports plotting tools")) (|calcRanges| (((|List| (|Segment| (|DoubleFloat|))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{calcRanges(l)} \\undocumented")))
NIL
NIL
-(-841)
+(-842)
((|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 'x and no other quantity.")) (|assert| (((|Expression| (|Integer|)) (|Symbol|) (|Identifier|)) "\\spad{assert(x, s)} makes the assertion \\spad{s} about \\spad{x}.")))
NIL
NIL
-(-842 R -3091)
+(-843 R -3094)
((|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 '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
-(-843 S A B)
+(-844 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
-(-844 S R -3091)
+(-845 S R -3094)
((|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
-(-845 I)
+(-846 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
-(-846 S E)
+(-847 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
-(-847 S R L)
+(-848 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
-(-848 S E V R P)
+(-849 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 -797) (|devaluate| |#1|))))
-(-849 -2668)
+((|HasCategory| |#3| (|%list| (QUOTE -798) (|devaluate| |#1|))))
+(-850 -2671)
((|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 fn to \\spad{x}.") (((|Expression| (|Integer|)) (|Symbol|) (|Mapping| (|Boolean|) |#1|)) "\\spad{suchThat(x, foo)} attaches the predicate foo to \\spad{x}.")))
NIL
NIL
-(-850 R -3091 -2668)
+(-851 R -3094 -2671)
((|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 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
-(-851 S R Q)
+(-852 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
-(-852 S)
+(-853 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
-(-853 S R P)
+(-854 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
-(-854)
+(-855)
((|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
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((|constructor| (NIL "This domain implements points in coordinate space")))
-((-3993 . T) (-3992 . T))
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-(-856 |lv| R)
+((-3997 . T) (-3996 . T))
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+(-857 |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
-(-857 |TheField| |ThePols|)
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((|constructor| (NIL "\\axiomType{RealPolynomialUtilitiesPackage} provides common functions used by interval coding.")) (|lazyVariations| (((|NonNegativeInteger|) (|List| |#1|) (|Integer|) (|Integer|)) "\\axiom{lazyVariations(\\spad{l},{}\\spad{s1},{}sn)} is the number of sign variations in the list of non null numbers [s1::l]@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},{}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 (-756))))
-(-858 R)
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((|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}.")))
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-(-859 R S)
+(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3994 |has| |#1| (-6 -3994)) (-3991 . T) (-3990 . T) (-3993 . T))
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+(-860 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
-(-860 |x| R)
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((|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
-(-861 S R E |VarSet|)
+(-862 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 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 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 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 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
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-(-862 R E |VarSet|)
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+(-863 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 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 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 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 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}.")))
-(((-3994 "*") |has| |#1| (-146)) (-3985 |has| |#1| (-495)) (-3990 |has| |#1| (-6 -3990)) (-3987 . T) (-3986 . T) (-3989 . T))
+(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3994 |has| |#1| (-6 -3994)) (-3991 . T) (-3990 . T) (-3993 . T))
NIL
-(-863 E V R P -3091)
+(-864 E V R P -3094)
((|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},{}...,{}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
-(-864 E |Vars| R P S)
+(-865 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
-(-865 E V R P -3091)
+(-866 E V R P -3094)
((|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| $) "\\spad{numer(x)} \\undocumented")))
NIL
-((|HasCategory| |#3| (QUOTE (-389))))
-(-866)
+((|HasCategory| |#3| (QUOTE (-390))))
+(-867)
((|constructor| (NIL "This domain represents network port numbers (notable TCP and UDP).")) (|port| (($ (|SingleInteger|)) "\\spad{port(n)} constructs a PortNumber from the integer `n'.")))
NIL
NIL
-(-867)
+(-868)
((|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|)))) $) "\\spad{listBranches(c)} returns a list of lists of points,{} representing the branches of the curve \\spad{c}.")))
NIL
NIL
-(-868 R E)
+(-869 R E)
((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and terms indexed by their exponents (from an arbitrary ordered abelian monoid). This type is used,{} for example,{} by the \\spadtype{DistributedMultivariatePolynomial} domain where the exponent domain is a direct product of non negative integers.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (|fmecg| (($ $ |#2| |#1| $) "\\spad{fmecg(p1,e,r,p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}")))
-(((-3994 "*") |has| |#1| (-146)) (-3985 |has| |#1| (-495)) (-3990 |has| |#1| (-6 -3990)) (-3986 . T) (-3987 . T) (-3989 . T))
-((|HasCategory| |#1| (QUOTE (-38 (-347 (-484))))) (|HasCategory| |#1| (QUOTE (-495))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-495)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (OR (|HasCategory| |#1| (QUOTE (-38 (-347 (-484))))) (|HasCategory| |#1| (QUOTE (-951 (-347 (-484)))))) (|HasCategory| |#1| (QUOTE (-951 (-347 (-484))))) (|HasCategory| |#1| (QUOTE (-951 (-484)))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-389))) (-12 (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-104)))) (|HasAttribute| |#1| (QUOTE -3990)))
-(-869 R L)
+(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3994 |has| |#1| (-6 -3994)) (-3990 . T) (-3991 . T) (-3993 . T))
+((|HasCategory| |#1| (QUOTE (-38 (-348 (-485))))) (|HasCategory| |#1| (QUOTE (-496))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (OR (|HasCategory| |#1| (QUOTE (-38 (-348 (-485))))) (|HasCategory| |#1| (QUOTE (-952 (-348 (-485)))))) (|HasCategory| |#1| (QUOTE (-952 (-348 (-485))))) (|HasCategory| |#1| (QUOTE (-952 (-485)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-390))) (-12 (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-104)))) (|HasAttribute| |#1| (QUOTE -3994)))
+(-870 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
-(-870 S)
+(-871 S)
((|constructor| (NIL "\\indented{1}{This provides a fast array type with no bound checking on elt's.} Minimum index is 0 in this type,{} cannot be changed")))
-((-3993 . T) (-3992 . T))
-((OR (-12 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-554 (-473)))) (OR (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-757))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| (-484) (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))))
-(-871 A B)
+((-3997 . T) (-3996 . T))
+((OR (-12 (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-554 (-774)))) (|HasCategory| |#1| (QUOTE (-555 (-474)))) (OR (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| |#1| (QUOTE (-758))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| (-485) (QUOTE (-758))) (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))))
+(-872 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
-(-872)
+(-873)
((|constructor| (NIL "Category for the functions defined by integrals.")) (|integral| (($ $ (|SegmentBinding| $)) "\\spad{integral(f, x = a..b)} returns the formal definite integral of \\spad{f} dx for \\spad{x} between \\spad{a} and \\spad{b}.") (($ $ (|Symbol|)) "\\spad{integral(f, x)} returns the formal integral of \\spad{f} dx.")))
NIL
NIL
-(-873 -3091)
+(-874 -3094)
((|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}'s are the defining polynomials for the \\spad{ai}'s. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}.") (((|Record| (|:| |coef| (|List| (|Integer|))) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#1|))) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{primitiveElement([p1,...,pn], [a1,...,an])} returns \\spad{[[c1,...,cn], [q1,...,qn], 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}'s are the defining polynomials for the \\spad{ai}'s. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}.") (((|Record| (|:| |coef1| (|Integer|)) (|:| |coef2| (|Integer|)) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|Polynomial| |#1|) (|Symbol|) (|Polynomial| |#1|) (|Symbol|)) "\\spad{primitiveElement(p1, a1, 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}'s are the defining polynomials for the \\spad{ai}'s. The \\spad{p2} may involve \\spad{a1},{} but \\spad{p1} must not involve \\spad{a2}. This operation uses \\spadfun{resultant}.")))
NIL
NIL
-(-874 I)
+(-875 I)
((|constructor| (NIL "The \\spadtype{IntegerPrimesPackage} implements a modification of Rabin's probabilistic primality test and the utility functions \\spadfun{nextPrime},{} \\spadfun{prevPrime} and \\spadfun{primes}.")) (|primes| (((|List| |#1|) |#1| |#1|) "\\spad{primes(a,b)} returns a list of all primes \\spad{p} with \\spad{a <= 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'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 \\spad{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
-(-875)
+(-876)
((|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
-(-876 A B)
+(-877 A B)
((|constructor| (NIL "This domain implements cartesian product")) (|selectsecond| ((|#2| $) "\\spad{selectsecond(x)} \\undocumented")) (|selectfirst| ((|#1| $) "\\spad{selectfirst(x)} \\undocumented")) (|makeprod| (($ |#1| |#2|) "\\spad{makeprod(a,b)} \\undocumented")))
-((-3989 -12 (|has| |#2| (-410)) (|has| |#1| (-410))))
-((OR (-12 (|HasCategory| |#1| (QUOTE (-718))) (|HasCategory| |#2| (QUOTE (-718)))) (-12 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-757))))) (-12 (|HasCategory| |#1| (QUOTE (-718))) (|HasCategory| |#2| (QUOTE (-718)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-104)))) (-12 (|HasCategory| |#1| (QUOTE (-718))) (|HasCategory| |#2| (QUOTE (-718)))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-104)))) (-12 (|HasCategory| |#1| (QUOTE (-718))) (|HasCategory| |#2| (QUOTE (-718)))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23))))) (-12 (|HasCategory| |#1| (QUOTE (-410))) (|HasCategory| |#2| (QUOTE (-410)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-410))) (|HasCategory| |#2| (QUOTE (-410)))) (-12 (|HasCategory| |#1| (QUOTE (-664))) (|HasCategory| |#2| (QUOTE (-664))))) (-12 (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#2| (QUOTE (-317)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-104)))) (-12 (|HasCategory| |#1| (QUOTE (-718))) (|HasCategory| |#2| (QUOTE (-718)))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-410))) (|HasCategory| |#2| (QUOTE (-410)))) (-12 (|HasCategory| |#1| (QUOTE (-664))) (|HasCategory| |#2| (QUOTE (-664))))) (-12 (|HasCategory| |#1| (QUOTE (-664))) (|HasCategory| |#2| (QUOTE (-664)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-104)))) (-12 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-757)))))
-(-877)
+((-3993 -12 (|has| |#2| (-411)) (|has| |#1| (-411))))
+((OR (-12 (|HasCategory| |#1| (QUOTE (-719))) (|HasCategory| |#2| (QUOTE (-719)))) (-12 (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| |#2| (QUOTE (-758))))) (-12 (|HasCategory| |#1| (QUOTE (-719))) (|HasCategory| |#2| (QUOTE (-719)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-104)))) (-12 (|HasCategory| |#1| (QUOTE (-719))) (|HasCategory| |#2| (QUOTE (-719)))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-104)))) (-12 (|HasCategory| |#1| (QUOTE (-719))) (|HasCategory| |#2| (QUOTE (-719)))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23))))) (-12 (|HasCategory| |#1| (QUOTE (-411))) (|HasCategory| |#2| (QUOTE (-411)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-411))) (|HasCategory| |#2| (QUOTE (-411)))) (-12 (|HasCategory| |#1| (QUOTE (-665))) (|HasCategory| |#2| (QUOTE (-665))))) (-12 (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#2| (QUOTE (-318)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-104)))) (-12 (|HasCategory| |#1| (QUOTE (-719))) (|HasCategory| |#2| (QUOTE (-719)))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-411))) (|HasCategory| |#2| (QUOTE (-411)))) (-12 (|HasCategory| |#1| (QUOTE (-665))) (|HasCategory| |#2| (QUOTE (-665))))) (-12 (|HasCategory| |#1| (QUOTE (-665))) (|HasCategory| |#2| (QUOTE (-665)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-104)))) (-12 (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| |#2| (QUOTE (-758)))))
+(-878)
((|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 `n' and value `val'.")) (|value| (((|SExpression|) $) "\\spad{value(p)} returns value of property \\spad{p}")) (|name| (((|Identifier|) $) "\\spad{name(p)} returns the name of property \\spad{p}")))
NIL
NIL
-(-878 T$)
+(-879 T$)
((|constructor| (NIL "This domain implements propositional formula build over a term domain,{} that itself belongs to PropositionalLogic")) (|disjunction| (($ $ $) "\\spad{disjunction(p,q)} returns a formula denoting the disjunction of \\spad{p} and \\spad{q}.")) (|conjunction| (($ $ $) "\\spad{conjunction(p,q)} returns a formula denoting the conjunction of \\spad{p} and \\spad{q}.")) (|isEquiv| (((|Maybe| (|Pair| $ $)) $) "\\spad{isEquiv f} returns a value \\spad{v} such that \\spad{v case Pair(\\%,\\%)} holds if the formula \\spad{f} is an equivalence formula.")) (|isImplies| (((|Maybe| (|Pair| $ $)) $) "\\spad{isImplies f} returns a value \\spad{v} such that \\spad{v case Pair(\\%,\\%)} holds if the formula \\spad{f} is an implication formula.")) (|isOr| (((|Maybe| (|Pair| $ $)) $) "\\spad{isOr f} returns a value \\spad{v} such that \\spad{v case Pair(\\%,\\%)} holds if the formula \\spad{f} is a disjunction formula.")) (|isAnd| (((|Maybe| (|Pair| $ $)) $) "\\spad{isAnd f} returns a value \\spad{v} such that \\spad{v case Pair(\\%,\\%)} holds if the formula \\spad{f} is a conjunction formula.")) (|isNot| (((|Maybe| $) $) "\\spad{isNot f} returns a value \\spad{v} such that \\spad{v case \\%} holds if the formula \\spad{f} is a negation.")) (|isAtom| (((|Maybe| |#1|) $) "\\spad{isAtom f} returns a value \\spad{v} such that \\spad{v case T} holds if the formula \\spad{f} is a term.")))
NIL
NIL
-(-879 T$)
+(-880 T$)
((|constructor| (NIL "This package collects unary functions operating on propositional formulae.")) (|simplify| (((|PropositionalFormula| |#1|) (|PropositionalFormula| |#1|)) "\\spad{simplify f} returns a formula logically equivalent to \\spad{f} where obvious tautologies have been removed.")) (|atoms| (((|Set| |#1|) (|PropositionalFormula| |#1|)) "\\spad{atoms f} ++ returns the set of atoms appearing in the formula \\spad{f}.")) (|dual| (((|PropositionalFormula| |#1|) (|PropositionalFormula| |#1|)) "\\spad{dual f} returns the dual of the proposition \\spad{f}.")))
NIL
NIL
-(-880 S T$)
+(-881 S T$)
((|constructor| (NIL "This package collects binary functions operating on propositional formulae.")) (|map| (((|PropositionalFormula| |#2|) (|Mapping| |#2| |#1|) (|PropositionalFormula| |#1|)) "\\spad{map(f,x)} returns a propositional formula where all atoms in \\spad{x} have been replaced by the result of applying the function \\spad{f} to them.")))
NIL
NIL
-(-881)
+(-882)
((|constructor| (NIL "This category declares the connectives of Propositional Logic.")) (|equiv| (($ $ $) "\\spad{equiv(p,q)} returns the logical equivalence of `p',{} `q'.")) (|implies| (($ $ $) "\\spad{implies(p,q)} returns the logical implication of `q' by `p'.")) (|false| (($) "\\spad{false} is a logical constant.")) (|true| (($) "\\spad{true} is a logical constant.")))
NIL
NIL
-(-882 S)
+(-883 S)
((|constructor| (NIL "A priority queue is a bag of items from an ordered set where the item extracted is always the maximum element.")) (|merge!| (($ $ $) "\\spad{merge!(q,q1)} destructively changes priority queue \\spad{q} to include the values from priority queue \\spad{q1}.")) (|merge| (($ $ $) "\\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}.")))
-((-3992 . T) (-3993 . T))
+((-3996 . T) (-3997 . T))
NIL
-(-883 R |polR|)
+(-884 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{\\spad{semiSubResultantGcdEuclidean1}}{PseudoRemainderSequence},{} \\axiomOpFrom{\\spad{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.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{\\spad{nextsousResultant2}(\\spad{P},{} \\spad{Q},{} \\spad{Z},{} \\spad{s})} returns the subresultant \\axiom{S_{\\spad{e}-1}} where \\axiom{\\spad{P} ~ S_d,{} \\spad{Q} = S_{\\spad{d}-1},{} \\spad{Z} = S_e,{} \\spad{s} = lc(S_d)}")) (|Lazard2| ((|#2| |#2| |#1| |#1| (|NonNegativeInteger|)) "\\axiom{\\spad{Lazard2}(\\spad{F},{} \\spad{x},{} \\spad{y},{} \\spad{n})} computes \\axiom{(x/y)**(\\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{gcd(\\spad{P},{} \\spad{Q})} returns the gcd of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiResultantReduitEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |resultantReduit| |#1|)) |#2| |#2|) "\\axiom{semiResultantReduitEuclidean(\\spad{P},{}\\spad{Q})} returns the \"reduce resultant\" and carries out the equality \\axiom{...\\spad{P} + coef2*Q = resultantReduit(\\spad{P},{}\\spad{Q})}.")) (|resultantReduitEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |resultantReduit| |#1|)) |#2| |#2|) "\\axiom{resultantReduitEuclidean(\\spad{P},{}\\spad{Q})} returns the \"reduce resultant\" and carries out the equality \\axiom{coef1*P + coef2*Q = resultantReduit(\\spad{P},{}\\spad{Q})}.")) (|resultantReduit| ((|#1| |#2| |#2|) "\\axiom{resultantReduit(\\spad{P},{}\\spad{Q})} returns the \"reduce resultant\" of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|schema| (((|List| (|NonNegativeInteger|)) |#2| |#2|) "\\axiom{schema(\\spad{P},{}\\spad{Q})} returns the list of degrees of non zero subresultants of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|chainSubResultants| (((|List| |#2|) |#2| |#2|) "\\axiom{chainSubResultants(\\spad{P},{} \\spad{Q})} computes the list of non zero subresultants of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiDiscriminantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |discriminant| |#1|)) |#2|) "\\axiom{discriminantEuclidean(\\spad{P})} carries out the equality \\axiom{...\\spad{P} + \\spad{coef2} * \\spad{D}(\\spad{P}) = discriminant(\\spad{P})}. Warning: \\axiom{degree(\\spad{P}) >= degree(\\spad{Q})}.")) (|discriminantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |discriminant| |#1|)) |#2|) "\\axiom{discriminantEuclidean(\\spad{P})} carries out the equality \\axiom{\\spad{coef1} * \\spad{P} + \\spad{coef2} * \\spad{D}(\\spad{P}) = discriminant(\\spad{P})}.")) (|discriminant| ((|#1| |#2|) "\\axiom{discriminant(\\spad{P},{} \\spad{Q})} returns the discriminant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiSubResultantGcdEuclidean1| (((|Record| (|:| |coef1| |#2|) (|:| |gcd| |#2|)) |#2| |#2|) "\\axiom{\\spad{semiSubResultantGcdEuclidean1}(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1*P + ? \\spad{Q} = +/- S_i(\\spad{P},{}\\spad{Q})} where the degree (not the indice) of the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} is the smaller as possible.")) (|semiSubResultantGcdEuclidean2| (((|Record| (|:| |coef2| |#2|) (|:| |gcd| |#2|)) |#2| |#2|) "\\axiom{\\spad{semiSubResultantGcdEuclidean2}(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{...\\spad{P} + coef2*Q = +/- 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}) >= 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 = +/- 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 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}) >= 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}) >= 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}) >= degree(\\spad{Q})}.")) (|indiceSubResultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} and carries out the equality \\axiom{coef1*P + coef2*Q = S_i(\\spad{P},{}\\spad{Q})}")) (|indiceSubResultant| ((|#2| |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns the subresultant of indice \\axiom{\\spad{i}}")) (|semiResultantEuclidean1| (((|Record| (|:| |coef1| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{\\spad{semiResultantEuclidean1}(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{\\spad{coef1}.\\spad{P} + ? \\spad{Q} = resultant(\\spad{P},{}\\spad{Q})}.")) (|semiResultantEuclidean2| (((|Record| (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{\\spad{semiResultantEuclidean2}(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{...\\spad{P} + coef2*Q = resultant(\\spad{P},{}\\spad{Q})}. Warning: \\axiom{degree(\\spad{P}) >= 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 (-389))))
-(-884)
+((|HasCategory| |#1| (QUOTE (-390))))
+(-885)
((|constructor| (NIL "This domain represents `pretend' expressions.")) (|target| (((|TypeAst|) $) "\\spad{target(e)} returns the target type of the conversion..")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression being converted.")))
NIL
NIL
-(-885)
+(-886)
((|constructor| (NIL "Partition is an OrderedCancellationAbelianMonoid which is used as the basis for symmetric polynomial representation of the sums of powers in SymmetricPolynomial. Thus,{} \\spad{(5 2 2 1)} will represent \\spad{s5 * s2**2 * s1}.")) (|conjugate| (($ $) "\\spad{conjugate(p)} returns the conjugate partition of a partition \\spad{p}")) (|pdct| (((|PositiveInteger|) $) "\\spad{pdct(a1**n1 a2**n2 ...)} returns \\spad{n1! * a1**n1 * n2! * a2**n2 * ...}. This function is used in the package \\spadtype{CycleIndicators}.")) (|powers| (((|List| (|Pair| (|PositiveInteger|) (|PositiveInteger|))) $) "\\spad{powers(x)} returns a list of pairs. The second component of each pair is the multiplicity with which the first component occurs in \\spad{li}.")) (|partitions| (((|Stream| $) (|NonNegativeInteger|)) "\\spad{partitions n} returns the stream of all partitions of size \\spad{n}.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\#x} returns the sum of all parts of the partition \\spad{x}.")) (|parts| (((|List| (|PositiveInteger|)) $) "\\spad{parts x} returns the list of decreasing integer sequence making up the partition \\spad{x}.")) (|partition| (($ (|List| (|PositiveInteger|))) "\\spad{partition(li)} converts a list of integers \\spad{li} to a partition")))
NIL
NIL
-(-886 S |Coef| |Expon| |Var|)
+(-887 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
-(-887 |Coef| |Expon| |Var|)
+(-888 |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}.")))
-(((-3994 "*") |has| |#1| (-146)) (-3985 |has| |#1| (-495)) (-3986 . T) (-3987 . T) (-3989 . T))
+(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3990 . T) (-3991 . T) (-3993 . T))
NIL
-(-888)
+(-889)
((|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 x-,{} 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
-(-889 S R E |VarSet| P)
+(-890 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?(ps)} returns \\spad{true} iff \\axiom{ps} is a triangular set,{} \\spadignore{i.e.} two distinct polynomials have distinct main variables and no constant lies in \\axiom{ps}.")) (|rewriteIdealWithRemainder| (((|List| |#5|) (|List| |#5|) $) "\\axiom{rewriteIdealWithRemainder(lp,{}cs)} returns \\axiom{lr} such that every polynomial in \\axiom{lr} is fully reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{cs} and \\axiom{(lp,{}cs)} and \\axiom{(lr,{}cs)} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}.")) (|rewriteIdealWithHeadRemainder| (((|List| |#5|) (|List| |#5|) $) "\\axiom{rewriteIdealWithHeadRemainder(lp,{}cs)} returns \\axiom{lr} such that the leading monomial of every polynomial in \\axiom{lr} is reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{cs} and \\axiom{(lp,{}cs)} and \\axiom{(lr,{}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,{}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{ps},{} \\axiom{r*a - c*b} lies in the ideal generated by \\axiom{ps}. Furthermore,{} if \\axiom{\\spad{R}} is a gcd-domain,{} \\axiom{\\spad{b}} is primitive.")) (|headRemainder| (((|Record| (|:| |num| |#5|) (|:| |den| |#2|)) |#5| $) "\\axiom{headRemainder(a,{}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{ps} and \\axiom{r*a - \\spad{b}} lies in the ideal generated by \\axiom{ps}.")) (|roughUnitIdeal?| (((|Boolean|) $) "\\axiom{roughUnitIdeal?(ps)} returns \\spad{true} iff \\axiom{ps} contains 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?(ps)} returns \\spad{true} iff for every pair \\axiom{{\\spad{p},{}\\spad{q}}} of polynomials in \\axiom{ps} their leading monomials are relatively prime.")) (|trivialIdeal?| (((|Boolean|) $) "\\axiom{trivialIdeal?(ps)} returns \\spad{true} iff \\axiom{ps} does not contain non-zero elements.")) (|sort| (((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |#4|) "\\axiom{sort(\\spad{v},{}ps)} returns \\axiom{us,{}vs,{}ws} such that \\axiom{us} is \\axiom{collectUnder(ps,{}\\spad{v})},{} \\axiom{vs} is \\axiom{collect(ps,{}\\spad{v})} and \\axiom{ws} is \\axiom{collectUpper(ps,{}\\spad{v})}.")) (|collectUpper| (($ $ |#4|) "\\axiom{collectUpper(ps,{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{ps} with main variable greater than \\axiom{\\spad{v}}.")) (|collect| (($ $ |#4|) "\\axiom{collect(ps,{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{ps} with \\axiom{\\spad{v}} as main variable.")) (|collectUnder| (($ $ |#4|) "\\axiom{collectUnder(ps,{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{ps} with main variable less than \\axiom{\\spad{v}}.")) (|mainVariable?| (((|Boolean|) |#4| $) "\\axiom{mainVariable?(\\spad{v},{}ps)} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{ps}.")) (|mainVariables| (((|List| |#4|) $) "\\axiom{mainVariables(ps)} returns the decreasingly sorted list of the variables which are main variables of some polynomial in \\axiom{ps}.")) (|variables| (((|List| |#4|) $) "\\axiom{variables(ps)} returns the decreasingly sorted list of the variables which are variables of some polynomial in \\axiom{ps}.")) (|mvar| ((|#4| $) "\\axiom{mvar(ps)} returns the main variable of the non constant polynomial with the greatest main variable,{} if any,{} else an error is returned.")) (|retract| (($ (|List| |#5|)) "\\axiom{retract(lp)} returns an element of the domain whose elements are the members of \\axiom{lp} if such an element exists,{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|List| |#5|)) "\\axiom{retractIfCan(lp)} returns an element of the domain whose elements are the members of \\axiom{lp} if such an element exists,{} otherwise \\axiom{\"failed\"} is returned.")))
NIL
-((|HasCategory| |#2| (QUOTE (-495))))
-(-890 R E |VarSet| P)
+((|HasCategory| |#2| (QUOTE (-496))))
+(-891 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?(ps)} returns \\spad{true} iff \\axiom{ps} is a triangular set,{} \\spadignore{i.e.} two distinct polynomials have distinct main variables and no constant lies in \\axiom{ps}.")) (|rewriteIdealWithRemainder| (((|List| |#4|) (|List| |#4|) $) "\\axiom{rewriteIdealWithRemainder(lp,{}cs)} returns \\axiom{lr} such that every polynomial in \\axiom{lr} is fully reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{cs} and \\axiom{(lp,{}cs)} and \\axiom{(lr,{}cs)} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}.")) (|rewriteIdealWithHeadRemainder| (((|List| |#4|) (|List| |#4|) $) "\\axiom{rewriteIdealWithHeadRemainder(lp,{}cs)} returns \\axiom{lr} such that the leading monomial of every polynomial in \\axiom{lr} is reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{cs} and \\axiom{(lp,{}cs)} and \\axiom{(lr,{}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,{}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{ps},{} \\axiom{r*a - c*b} lies in the ideal generated by \\axiom{ps}. Furthermore,{} if \\axiom{\\spad{R}} is a gcd-domain,{} \\axiom{\\spad{b}} is primitive.")) (|headRemainder| (((|Record| (|:| |num| |#4|) (|:| |den| |#1|)) |#4| $) "\\axiom{headRemainder(a,{}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{ps} and \\axiom{r*a - \\spad{b}} lies in the ideal generated by \\axiom{ps}.")) (|roughUnitIdeal?| (((|Boolean|) $) "\\axiom{roughUnitIdeal?(ps)} returns \\spad{true} iff \\axiom{ps} contains 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?(ps)} returns \\spad{true} iff for every pair \\axiom{{\\spad{p},{}\\spad{q}}} of polynomials in \\axiom{ps} their leading monomials are relatively prime.")) (|trivialIdeal?| (((|Boolean|) $) "\\axiom{trivialIdeal?(ps)} returns \\spad{true} iff \\axiom{ps} does not contain non-zero elements.")) (|sort| (((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |#3|) "\\axiom{sort(\\spad{v},{}ps)} returns \\axiom{us,{}vs,{}ws} such that \\axiom{us} is \\axiom{collectUnder(ps,{}\\spad{v})},{} \\axiom{vs} is \\axiom{collect(ps,{}\\spad{v})} and \\axiom{ws} is \\axiom{collectUpper(ps,{}\\spad{v})}.")) (|collectUpper| (($ $ |#3|) "\\axiom{collectUpper(ps,{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{ps} with main variable greater than \\axiom{\\spad{v}}.")) (|collect| (($ $ |#3|) "\\axiom{collect(ps,{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{ps} with \\axiom{\\spad{v}} as main variable.")) (|collectUnder| (($ $ |#3|) "\\axiom{collectUnder(ps,{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{ps} with main variable less than \\axiom{\\spad{v}}.")) (|mainVariable?| (((|Boolean|) |#3| $) "\\axiom{mainVariable?(\\spad{v},{}ps)} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{ps}.")) (|mainVariables| (((|List| |#3|) $) "\\axiom{mainVariables(ps)} returns the decreasingly sorted list of the variables which are main variables of some polynomial in \\axiom{ps}.")) (|variables| (((|List| |#3|) $) "\\axiom{variables(ps)} returns the decreasingly sorted list of the variables which are variables of some polynomial in \\axiom{ps}.")) (|mvar| ((|#3| $) "\\axiom{mvar(ps)} returns the main variable of the non constant polynomial with the greatest main variable,{} if any,{} else an error is returned.")) (|retract| (($ (|List| |#4|)) "\\axiom{retract(lp)} returns an element of the domain whose elements are the members of \\axiom{lp} if such an element exists,{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|List| |#4|)) "\\axiom{retractIfCan(lp)} returns an element of the domain whose elements are the members of \\axiom{lp} if such an element exists,{} otherwise \\axiom{\"failed\"} is returned.")))
-((-3992 . T))
+((-3996 . T))
NIL
-(-891 R E V P)
+(-892 R E V P)
((|constructor| (NIL "This package provides modest routines for polynomial system solving. The aim of many of the operations of this package is to remove certain factors in some polynomials in order to avoid unnecessary computations in algorithms involving splitting techniques by partial factorization.")) (|removeIrreducibleRedundantFactors| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeIrreducibleRedundantFactors(lp,{}lq)} returns the same as \\axiom{irreducibleFactors(concat(lp,{}lq))} assuming that \\axiom{irreducibleFactors(lp)} returns \\axiom{lp} up to replacing some polynomial \\axiom{pj} in \\axiom{lp} by some polynomial \\axiom{qj} associated to \\axiom{pj}.")) (|lazyIrreducibleFactors| (((|List| |#4|) (|List| |#4|)) "\\axiom{lazyIrreducibleFactors(lp)} returns \\axiom{lf} such that if \\axiom{lp = [\\spad{p1},{}...,{}pn]} and \\axiom{lf = [\\spad{f1},{}...,{}fm]} then \\axiom{p1*p2*...\\spad{*pn=0}} means \\axiom{f1*f2*...\\spad{*fm=0}},{} and the \\axiom{\\spad{fi}} are irreducible over \\axiom{\\spad{R}} and are pairwise distinct. The algorithm tries to avoid factorization into irreducible factors as far as possible and makes previously use of gcd techniques over \\axiom{\\spad{R}}.")) (|irreducibleFactors| (((|List| |#4|) (|List| |#4|)) "\\axiom{irreducibleFactors(lp)} returns \\axiom{lf} such that if \\axiom{lp = [\\spad{p1},{}...,{}pn]} and \\axiom{lf = [\\spad{f1},{}...,{}fm]} then \\axiom{p1*p2*...\\spad{*pn=0}} means \\axiom{f1*f2*...\\spad{*fm=0}},{} and the \\axiom{\\spad{fi}} are irreducible over \\axiom{\\spad{R}} and are pairwise distinct.")) (|removeRedundantFactorsInPols| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactorsInPols(lp,{}lf)} returns \\axiom{newlp} where \\axiom{newlp} is obtained from \\axiom{lp} by removing in every polynomial \\axiom{\\spad{p}} of \\axiom{lp} any non trivial factor of any polynomial \\axiom{\\spad{f}} in \\axiom{lf}. Moreover,{} squares over \\axiom{\\spad{R}} are first removed in every polynomial \\axiom{lp}.")) (|removeRedundantFactorsInContents| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactorsInContents(lp,{}lf)} returns \\axiom{newlp} where \\axiom{newlp} is obtained from \\axiom{lp} by removing in the content of every polynomial of \\axiom{lp} any non trivial factor of any polynomial \\axiom{\\spad{f}} in \\axiom{lf}. Moreover,{} squares over \\axiom{\\spad{R}} are first removed in the content of every polynomial of \\axiom{lp}.")) (|removeRoughlyRedundantFactorsInContents| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRoughlyRedundantFactorsInContents(lp,{}lf)} returns \\axiom{newlp}where \\axiom{newlp} is obtained from \\axiom{lp} by removing in the content of every polynomial of \\axiom{lp} any occurence of a polynomial \\axiom{\\spad{f}} in \\axiom{lf}. Moreover,{} squares over \\axiom{\\spad{R}} are first removed in the content of every polynomial of \\axiom{lp}.")) (|univariatePolynomialsGcds| (((|List| |#4|) (|List| |#4|) (|Boolean|)) "\\axiom{univariatePolynomialsGcds(lp,{}opt)} returns the same as \\axiom{univariatePolynomialsGcds(lp)} if \\axiom{opt} is \\axiom{\\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(lp)} returns \\axiom{lg} where \\axiom{lg} is a list of the gcds of every pair in \\axiom{lp} of univariate polynomials in the same main variable.")) (|squareFreeFactors| (((|List| |#4|) |#4|) "\\axiom{squareFreeFactors(\\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(lp,{}redOp?,{}redOp)} returns \\axiom{lq} where \\axiom{lq} and \\axiom{lp} generate the same ideal in \\axiom{R^(\\spad{-1}) \\spad{P}} and \\axiom{lq} has rank not higher than the one of \\axiom{lp}. Moreover,{} \\axiom{lq} is computed by reducing \\axiom{lp} \\spad{w}.\\spad{r}.\\spad{t}. some basic set of the ideal generated by the quasi-monic polynomials in \\axiom{lp}.")) (|rewriteSetByReducingWithParticularGenerators| (((|List| |#4|) (|List| |#4|) (|Mapping| (|Boolean|) |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{rewriteSetByReducingWithParticularGenerators(lp,{}pred?,{}redOp?,{}redOp)} returns \\axiom{lq} where \\axiom{lq} is computed by the following algorithm. Chose a basic set \\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(lp)} returns \\axiom{lq} such that \\axiom{lp} and and \\axiom{lq} generate the same ideal and no rough basic sets reduce (in the sense of Groebner bases) the other polynomials in \\axiom{lq}.")) (|roughBasicSet| (((|Union| (|Record| (|:| |bas| (|GeneralTriangularSet| |#1| |#2| |#3| |#4|)) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|)) "\\axiom{roughBasicSet(lp)} returns the smallest (with Ritt-Wu ordering) triangular set contained in \\axiom{lp}.")) (|interReduce| (((|List| |#4|) (|List| |#4|)) "\\axiom{interReduce(lp)} returns \\axiom{lq} such that \\axiom{lp} and \\axiom{lq} generate the same ideal and no polynomial in \\axiom{lq} is reducuble by the others in the sense of Groebner bases. Since no assumptions are required the result may depend on the ordering the reductions are performed.")) (|removeRoughlyRedundantFactorsInPol| ((|#4| |#4| (|List| |#4|)) "\\axiom{removeRoughlyRedundantFactorsInPol(\\spad{p},{}lf)} returns the same as removeRoughlyRedundantFactorsInPols([\\spad{p}],{}lf,{}\\spad{true})")) (|removeRoughlyRedundantFactorsInPols| (((|List| |#4|) (|List| |#4|) (|List| |#4|) (|Boolean|)) "\\axiom{removeRoughlyRedundantFactorsInPols(lp,{}lf,{}opt)} returns the same as \\axiom{removeRoughlyRedundantFactorsInPols(lp,{}lf)} if \\axiom{opt} is \\axiom{\\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(lp,{}lf)} returns \\axiom{newlp}where \\axiom{newlp} is obtained from \\axiom{lp} by removing in every polynomial \\axiom{\\spad{p}} of \\axiom{lp} any occurence of a polynomial \\axiom{\\spad{f}} in \\axiom{lf}. This may involve a lot of exact-quotients computations.")) (|bivariatePolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{bivariatePolynomials(lp)} returns \\axiom{bps,{}nbps} where \\axiom{bps} is a list of the bivariate polynomials,{} and \\axiom{nbps} are the other ones.")) (|bivariate?| (((|Boolean|) |#4|) "\\axiom{bivariate?(\\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(lp)} returns \\axiom{lps,{}nlps} where \\axiom{lps} is a list of the linear polynomials in 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(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(lp)} returns \\axiom{qmps,{}nqmps} where \\axiom{qmps} is a list of the quasi-monic polynomials in \\axiom{lp} and \\axiom{nqmps} are the other ones.")) (|selectAndPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| (|Mapping| (|Boolean|) |#4|)) (|List| |#4|)) "\\axiom{selectAndPolynomials(lpred?,{}ps)} returns \\axiom{gps,{}bps} where \\axiom{gps} is a list of the polynomial \\axiom{\\spad{p}} in \\axiom{ps} such that \\axiom{pred?(\\spad{p})} holds for every \\axiom{pred?} in \\axiom{lpred?} and \\axiom{bps} are the other ones.")) (|selectOrPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| (|Mapping| (|Boolean|) |#4|)) (|List| |#4|)) "\\axiom{selectOrPolynomials(lpred?,{}ps)} returns \\axiom{gps,{}bps} where \\axiom{gps} is a list of the polynomial \\axiom{\\spad{p}} in \\axiom{ps} such that \\axiom{pred?(\\spad{p})} holds for some \\axiom{pred?} in \\axiom{lpred?} and \\axiom{bps} are the other ones.")) (|selectPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|Mapping| (|Boolean|) |#4|) (|List| |#4|)) "\\axiom{selectPolynomials(pred?,{}ps)} returns \\axiom{gps,{}bps} where \\axiom{gps} is a list of the polynomial \\axiom{\\spad{p}} in \\axiom{ps} such that \\axiom{pred?(\\spad{p})} holds and \\axiom{bps} are the other ones.")) (|probablyZeroDim?| (((|Boolean|) (|List| |#4|)) "\\axiom{probablyZeroDim?(lp)} returns \\spad{true} iff the number of polynomials in \\axiom{lp} is not smaller than the number of variables occurring in these polynomials.")) (|possiblyNewVariety?| (((|Boolean|) (|List| |#4|) (|List| (|List| |#4|))) "\\axiom{possiblyNewVariety?(newlp,{}llp)} returns \\spad{true} iff for every \\axiom{lp} in \\axiom{llp} certainlySubVariety?(newlp,{}lp) does not hold.")) (|certainlySubVariety?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{certainlySubVariety?(newlp,{}lp)} returns \\spad{true} iff for every \\axiom{\\spad{p}} in \\axiom{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 gcd-domain,{} then \\axiom{\\spad{p}} and \\axiom{\\spad{q}} are assumed to be square free.")) (|removeSquaresIfCan| (((|List| |#4|) (|List| |#4|)) "\\axiom{removeSquaresIfCan(lp)} returns \\axiom{removeDuplicates [squareFreePart(\\spad{p})\\$\\spad{P} for \\spad{p} in lp]} if \\axiom{\\spad{R}} is gcd-domain else returns \\axiom{lp}.")) (|removeRedundantFactors| (((|List| |#4|) (|List| |#4|) (|List| |#4|) (|Mapping| (|List| |#4|) (|List| |#4|))) "\\axiom{removeRedundantFactors(lp,{}lq,{}remOp)} returns the same as \\axiom{concat(remOp(removeRoughlyRedundantFactorsInPols(lp,{}lq)),{}lq)} assuming that \\axiom{remOp(lq)} returns \\axiom{lq} up to similarity.") (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactors(lp,{}lq)} returns the same as \\axiom{removeRedundantFactors(concat(lp,{}lq))} assuming that \\axiom{removeRedundantFactors(lp)} returns \\axiom{lp} up to replacing some polynomial \\axiom{pj} in \\axiom{lp} by some polynomial \\axiom{qj} associated to \\axiom{pj}.") (((|List| |#4|) (|List| |#4|) |#4|) "\\axiom{removeRedundantFactors(lp,{}\\spad{q})} returns the same as \\axiom{removeRedundantFactors(cons(\\spad{q},{}lp))} assuming that \\axiom{removeRedundantFactors(lp)} returns \\axiom{lp} up to replacing some polynomial \\axiom{pj} in \\axiom{lp} by some some polynomial \\axiom{qj} associated to \\axiom{pj}.") (((|List| |#4|) |#4| |#4|) "\\axiom{removeRedundantFactors(\\spad{p},{}\\spad{q})} returns the same as \\axiom{removeRedundantFactors([\\spad{p},{}\\spad{q}])}") (((|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactors(lp)} returns \\axiom{lq} such that if \\axiom{lp = [\\spad{p1},{}...,{}pn]} and \\axiom{lq = [\\spad{q1},{}...,{}qm]} then the product \\axiom{p1*p2*...*pn} vanishes iff the product \\axiom{q1*q2*...*qm} vanishes,{} and the product of degrees of the \\axiom{\\spad{qi}} is not greater than the one of the \\axiom{pj},{} and no polynomial in \\axiom{lq} divides another polynomial in \\axiom{lq}. In particular,{} polynomials lying in the base ring \\axiom{\\spad{R}} are removed. Moreover,{} \\axiom{lq} is sorted \\spad{w}.\\spad{r}.\\spad{t} \\axiom{infRittWu?}. Furthermore,{} if \\spad{R} is gcd-domain,{} the polynomials in \\axiom{lq} are pairwise without common non trivial factor.")))
NIL
-((-12 (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-257)))) (|HasCategory| |#1| (QUOTE (-389))))
-(-892 K)
+((-12 (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-258)))) (|HasCategory| |#1| (QUOTE (-390))))
+(-893 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
-(-893 |VarSet| E RC P)
+(-894 |VarSet| E RC P)
((|constructor| (NIL "This package computes square-free decomposition of multivariate polynomials over a coefficient ring which is an arbitrary 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
-(-894 R)
+(-895 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}.")))
-((-3993 . T) (-3992 . T))
+((-3997 . T) (-3996 . T))
NIL
-(-895 R1 R2)
+(-896 R1 R2)
((|constructor| (NIL "This package \\undocumented")) (|map| (((|Point| |#2|) (|Mapping| |#2| |#1|) (|Point| |#1|)) "\\spad{map(f,p)} \\undocumented")))
NIL
NIL
-(-896 R)
+(-897 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
-(-897 K)
+(-898 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 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
-(-898 R E OV PPR)
+(-899 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
-(-899 K R UP -3091)
+(-900 K R UP -3094)
((|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
-(-900 R |Var| |Expon| |Dpoly|)
+(-901 R |Var| |Expon| |Dpoly|)
((|constructor| (NIL "\\spadtype{QuasiAlgebraicSet} constructs a domain representing quasi-algebraic sets,{} which is the intersection of a Zariski closed set,{} defined as the common zeros of a given list of polynomials (the defining polynomials for equations),{} and a principal Zariski open set,{} defined as the complement of the common zeros of a polynomial \\spad{f} (the defining polynomial for the inequation). This domain provides simplification of a user-given representation using groebner basis computations. There are two simplification routines: the first function \\spadfun{idealSimplify} uses groebner basis of ideals alone,{} while the second,{} \\spadfun{simplify} uses both groebner basis and factorization. The resulting defining equations \\spad{L} always form a groebner basis,{} and the resulting defining inequation \\spad{f} is always reduced. The function \\spadfun{simplify} may be applied several times if desired. A third simplification routine \\spadfun{radicalSimplify} is provided in \\spadtype{QuasiAlgebraicSet2} for comparison study only,{} as it is inefficient compared to the other two,{} as well as is restricted to only certain coefficient domains. For detail analysis and a comparison of the three methods,{} please consult the reference cited. \\blankline A polynomial function \\spad{q} defined on the quasi-algebraic set is equivalent to its reduced form with respect to \\spad{L}. While this may be obtained using the usual normal form algorithm,{} there is no canonical form for \\spad{q}. \\blankline The ordering in groebner basis computation is determined by the data type of the input polynomials. If it is possible we suggest to use refinements of total degree orderings.")) (|simplify| (($ $) "\\spad{simplify(s)} returns a different and presumably simpler representation of \\spad{s} with the defining polynomials for the equations forming a groebner basis,{} and the defining polynomial for the inequation reduced with respect to the basis,{} using a heuristic algorithm based on factoring.")) (|idealSimplify| (($ $) "\\spad{idealSimplify(s)} returns a different and presumably simpler representation of \\spad{s} with the defining polynomials for the equations forming a groebner basis,{} and the defining polynomial for the inequation reduced with respect to the basis,{} using Buchberger's algorithm.")) (|definingInequation| ((|#4| $) "\\spad{definingInequation(s)} returns a single defining polynomial for the inequation,{} that is,{} the Zariski open part of \\spad{s}.")) (|definingEquations| (((|List| |#4|) $) "\\spad{definingEquations(s)} returns a list of defining polynomials for equations,{} that is,{} for the Zariski closed part of \\spad{s}.")) (|empty?| (((|Boolean|) $) "\\spad{empty?(s)} returns \\spad{true} if the quasialgebraic set \\spad{s} has no points,{} and \\spad{false} otherwise.")) (|setStatus| (($ $ (|Union| (|Boolean|) #1="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't know\"). Note: for internal use only,{} with care.")) (|status| (((|Union| (|Boolean|) #1#) $) "\\spad{status(s)} returns \\spad{true} if the quasi-algebraic set is empty,{} \\spad{false} if it is not,{} and \"failed\" if not yet known")) (|quasiAlgebraicSet| (($ (|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} ~= 0.")) (|empty| (($) "\\spad{empty()} returns the empty quasi-algebraic set")))
NIL
-((-12 (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-257)))))
-(-901 |vl| |nv|)
+((-12 (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-258)))))
+(-902 |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
-(-902 R E V P TS)
+(-903 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,{}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(lp,{}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?(\\spad{lpwt1},{}\\spad{lpwt2})} is an internal subroutine,{} exported only for developement.")) (|removeSuperfluousQuasiComponents| (((|List| |#5|) (|List| |#5|)) "\\axiom{removeSuperfluousQuasiComponents(lts)} removes from \\axiom{lts} any \\spad{ts} such that \\axiom{subQuasiComponent?(ts,{}us)} holds for another \\spad{us} in \\axiom{lts}.")) (|subQuasiComponent?| (((|Boolean|) |#5| (|List| |#5|)) "\\axiom{subQuasiComponent?(ts,{}lus)} returns \\spad{true} iff \\axiom{subQuasiComponent?(ts,{}us)} holds for one \\spad{us} in \\spad{lus}.") (((|Boolean|) |#5| |#5|) "\\axiom{subQuasiComponent?(ts,{}us)} returns \\spad{true} iff \\axiomOpFrom{internalSubQuasiComponent?}{QuasiComponentPackage} returs \\spad{true}.")) (|internalSubQuasiComponent?| (((|Union| (|Boolean|) "failed") |#5| |#5|) "\\axiom{internalSubQuasiComponent?(ts,{}us)} returns a boolean \\spad{b} value if the fact that the regular zero set of \\axiom{us} contains that of \\axiom{ts} can be decided (and in that case \\axiom{\\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?(ts,{}us)} returns \\spad{true} iff \\axiom{ts} is a sub-set of \\axiom{us}.")) (|moreAlgebraic?| (((|Boolean|) |#5| |#5|) "\\axiom{moreAlgebraic?(ts,{}us)} returns \\spad{false} iff \\axiom{ts} and \\axiom{us} are both empty,{} or \\axiom{ts} has less elements than \\axiom{us},{} or some variable is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{us} and is not \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ts}.")) (|algebraicSort| (((|List| |#5|) (|List| |#5|)) "\\axiom{algebraicSort(lts)} sorts \\axiom{lts} \\spad{w}.\\spad{r}.\\spad{t} \\axiomOpFrom{supDimElseRittWu?}{QuasiComponentPackage}.")) (|supDimElseRittWu?| (((|Boolean|) |#5| |#5|) "\\axiom{supDimElseRittWu(ts,{}us)} returns \\spad{true} iff \\axiom{ts} has less elements than \\axiom{us} otherwise if \\axiom{ts} has higher rank than \\axiom{us} \\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
-(-903)
+(-904)
((|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
-(-904 A S)
+(-905 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 (-822))) (|HasCategory| |#2| (QUOTE (-483))) (|HasCategory| |#2| (QUOTE (-257))) (|HasCategory| |#2| (QUOTE (-951 (-1089)))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-554 (-473)))) (|HasCategory| |#2| (QUOTE (-934))) (|HasCategory| |#2| (QUOTE (-741))) (|HasCategory| |#2| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-951 (-484)))) (|HasCategory| |#2| (QUOTE (-1065))))
-(-905 S)
+((|HasCategory| |#2| (QUOTE (-823))) (|HasCategory| |#2| (QUOTE (-484))) (|HasCategory| |#2| (QUOTE (-258))) (|HasCategory| |#2| (QUOTE (-952 (-1091)))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-555 (-474)))) (|HasCategory| |#2| (QUOTE (-935))) (|HasCategory| |#2| (QUOTE (-742))) (|HasCategory| |#2| (QUOTE (-758))) (|HasCategory| |#2| (QUOTE (-952 (-485)))) (|HasCategory| |#2| (QUOTE (-1067))))
+(-906 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}.")))
-((-3984 . T) (-3990 . T) (-3985 . T) ((-3994 "*") . T) (-3986 . T) (-3987 . T) (-3989 . T))
+((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T))
NIL
-(-906 A B R S)
+(-907 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
-(-907 |n| K)
+(-908 |n| K)
((|constructor| (NIL "This domain provides modest support for quadratic forms.")) (|matrix| (((|SquareMatrix| |#1| |#2|) $) "\\spad{matrix(qf)} creates a square matrix from the quadratic form \\spad{qf}.")) (|quadraticForm| (($ (|SquareMatrix| |#1| |#2|)) "\\spad{quadraticForm(m)} creates a quadratic form from a symmetric,{} square matrix \\spad{m}.")))
NIL
NIL
-(-908)
+(-909)
((|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
-(-909 S)
+(-910 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|) $) "\\spad{length(q)} returns the number of elements in the queue. Note: \\axiom{length(\\spad{q}) = \\#q}.")) (|rotate!| (($ $) "\\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.")))
-((-3992 . T) (-3993 . T))
+((-3996 . T) (-3997 . T))
NIL
-(-910 R)
+(-911 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.}")))
-((-3985 |has| |#1| (-245)) (-3986 . T) (-3987 . T) (-3989 . T))
-((|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-554 (-473)))) (|HasCategory| |#1| (QUOTE (-311))) (OR (|HasCategory| |#1| (QUOTE (-245))) (|HasCategory| |#1| (QUOTE (-311)))) (|HasCategory| |#1| (QUOTE (-245))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-581 (-484)))) (|HasCategory| |#1| (|%list| (QUOTE -453) (QUOTE (-1089)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -241) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-812 (-1089)))) (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-810 (-1089)))) (OR (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-951 (-347 (-484)))))) (|HasCategory| |#1| (QUOTE (-951 (-347 (-484))))) (|HasCategory| |#1| (QUOTE (-951 (-484)))) (|HasCategory| |#1| (QUOTE (-973))) (|HasCategory| |#1| (QUOTE (-483))))
-(-911 S R)
+((-3989 |has| |#1| (-246)) (-3990 . T) (-3991 . T) (-3993 . T))
+((|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-555 (-474)))) (|HasCategory| |#1| (QUOTE (-312))) (OR (|HasCategory| |#1| (QUOTE (-246))) (|HasCategory| |#1| (QUOTE (-312)))) (|HasCategory| |#1| (QUOTE (-246))) (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| |#1| (QUOTE (-582 (-485)))) (|HasCategory| |#1| (|%list| (QUOTE -454) (QUOTE (-1091)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -241) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-813 (-1091)))) (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-811 (-1091)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-952 (-348 (-485)))))) (|HasCategory| |#1| (QUOTE (-952 (-348 (-485))))) (|HasCategory| |#1| (QUOTE (-952 (-485)))) (|HasCategory| |#1| (QUOTE (-975))) (|HasCategory| |#1| (QUOTE (-484))))
+(-912 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 (-483))) (|HasCategory| |#2| (QUOTE (-973))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-554 (-473)))) (|HasCategory| |#2| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-245))))
-(-912 R)
+((|HasCategory| |#2| (QUOTE (-484))) (|HasCategory| |#2| (QUOTE (-975))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-555 (-474)))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-758))) (|HasCategory| |#2| (QUOTE (-246))))
+(-913 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| $) "\\spad{imagI(q)} extracts the imaginary \\spad{i} part of quaternion \\spad{q}.")) (|conjugate| (($ $) "\\spad{conjugate(q)} negates the imaginary parts of quaternion \\spad{q}.")))
-((-3985 |has| |#1| (-245)) (-3986 . T) (-3987 . T) (-3989 . T))
+((-3989 |has| |#1| (-246)) (-3990 . T) (-3991 . T) (-3993 . T))
NIL
-(-913 QR R QS S)
+(-914 QR R QS S)
((|constructor| (NIL "\\spadtype{QuaternionCategoryFunctions2} implements functions between two quaternion domains. The function \\spadfun{map} is used by the system interpreter to coerce between quaternion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,u)} maps \\spad{f} onto the component parts of the quaternion \\spad{u}.")))
NIL
NIL
-(-914 S)
-((|constructor| (NIL "Linked List implementation of a Queue")) (|queue| (($ (|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}.")))
-((-3992 . T) (-3993 . T))
-((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1013))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-72))))
(-915 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}.")))
+((-3996 . T) (-3997 . T))
+((-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1015))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| |#1| (QUOTE (-554 (-774)))) (|HasCategory| |#1| (QUOTE (-72))))
+(-916 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| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}.")))
NIL
NIL
-(-916)
+(-917)
((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|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
-(-917 -3091 UP UPUP |radicnd| |n|)
+(-918 -3094 UP UPUP |radicnd| |n|)
((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x}).")))
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-(-918 |bb|)
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+((|HasCategory| (-348 |#2|) (QUOTE (-118))) (|HasCategory| (-348 |#2|) (QUOTE (-120))) (|HasCategory| (-348 |#2|) (QUOTE (-299))) (OR (|HasCategory| (-348 |#2|) (QUOTE (-312))) (|HasCategory| (-348 |#2|) (QUOTE (-299)))) (|HasCategory| (-348 |#2|) (QUOTE (-312))) (|HasCategory| (-348 |#2|) (QUOTE (-318))) (OR (-12 (|HasCategory| (-348 |#2|) (QUOTE (-190))) (|HasCategory| (-348 |#2|) (QUOTE (-312)))) (|HasCategory| (-348 |#2|) (QUOTE (-299)))) (OR (-12 (|HasCategory| (-348 |#2|) (QUOTE (-190))) (|HasCategory| (-348 |#2|) (QUOTE (-312)))) (-12 (|HasCategory| (-348 |#2|) (QUOTE (-189))) (|HasCategory| (-348 |#2|) (QUOTE (-312)))) (|HasCategory| (-348 |#2|) (QUOTE (-299)))) (OR (-12 (|HasCategory| (-348 |#2|) (QUOTE (-312))) (|HasCategory| (-348 |#2|) (QUOTE (-811 (-1091))))) (-12 (|HasCategory| (-348 |#2|) (QUOTE (-299))) (|HasCategory| (-348 |#2|) (QUOTE (-811 (-1091)))))) (OR (-12 (|HasCategory| (-348 |#2|) (QUOTE (-312))) (|HasCategory| (-348 |#2|) (QUOTE (-811 (-1091))))) (-12 (|HasCategory| (-348 |#2|) (QUOTE (-312))) (|HasCategory| (-348 |#2|) (QUOTE (-813 (-1091)))))) (|HasCategory| (-348 |#2|) (QUOTE (-582 (-485)))) (OR (|HasCategory| (-348 |#2|) (QUOTE (-312))) (|HasCategory| (-348 |#2|) (QUOTE (-952 (-348 (-485)))))) (|HasCategory| (-348 |#2|) (QUOTE (-952 (-348 (-485))))) (|HasCategory| (-348 |#2|) (QUOTE (-952 (-485)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-318))) (-12 (|HasCategory| (-348 |#2|) (QUOTE (-189))) (|HasCategory| (-348 |#2|) (QUOTE (-312)))) (-12 (|HasCategory| (-348 |#2|) (QUOTE (-312))) (|HasCategory| (-348 |#2|) (QUOTE (-813 (-1091))))) (-12 (|HasCategory| (-348 |#2|) (QUOTE (-190))) (|HasCategory| (-348 |#2|) (QUOTE (-312)))) (-12 (|HasCategory| (-348 |#2|) (QUOTE (-312))) (|HasCategory| (-348 |#2|) (QUOTE (-811 (-1091))))))
+(-919 |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.")))
-((-3984 . T) (-3990 . T) (-3985 . T) ((-3994 "*") . T) (-3986 . T) (-3987 . T) (-3989 . T))
-((|HasCategory| (-484) (QUOTE (-822))) (|HasCategory| (-484) (QUOTE (-951 (-1089)))) (|HasCategory| (-484) (QUOTE (-118))) (|HasCategory| (-484) (QUOTE (-120))) (|HasCategory| (-484) (QUOTE (-554 (-473)))) (|HasCategory| (-484) (QUOTE (-934))) (|HasCategory| (-484) (QUOTE (-741))) (|HasCategory| (-484) (QUOTE (-757))) (OR (|HasCategory| (-484) (QUOTE (-741))) (|HasCategory| (-484) (QUOTE (-757)))) (|HasCategory| (-484) (QUOTE (-951 (-484)))) (|HasCategory| (-484) (QUOTE (-1065))) (|HasCategory| (-484) (QUOTE (-797 (-327)))) (|HasCategory| (-484) (QUOTE (-797 (-484)))) (|HasCategory| (-484) (QUOTE (-554 (-801 (-327))))) (|HasCategory| (-484) (QUOTE (-554 (-801 (-484))))) (|HasCategory| (-484) (QUOTE (-189))) (|HasCategory| (-484) (QUOTE (-812 (-1089)))) (|HasCategory| (-484) (QUOTE (-190))) (|HasCategory| (-484) (QUOTE (-810 (-1089)))) (|HasCategory| (-484) (QUOTE (-453 (-1089) (-484)))) (|HasCategory| (-484) (QUOTE (-259 (-484)))) (|HasCategory| (-484) (QUOTE (-241 (-484) (-484)))) (|HasCategory| (-484) (QUOTE (-257))) (|HasCategory| (-484) (QUOTE (-483))) (|HasCategory| (-484) (QUOTE (-581 (-484)))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-484) (QUOTE (-822)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-484) (QUOTE (-822)))) (|HasCategory| (-484) (QUOTE (-118)))))
-(-919)
+((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T))
+((|HasCategory| (-485) (QUOTE (-823))) (|HasCategory| (-485) (QUOTE (-952 (-1091)))) (|HasCategory| (-485) (QUOTE (-118))) (|HasCategory| (-485) (QUOTE (-120))) (|HasCategory| (-485) (QUOTE (-555 (-474)))) (|HasCategory| (-485) (QUOTE (-935))) (|HasCategory| (-485) (QUOTE (-742))) (|HasCategory| (-485) (QUOTE (-758))) (OR (|HasCategory| (-485) (QUOTE (-742))) (|HasCategory| (-485) (QUOTE (-758)))) (|HasCategory| (-485) (QUOTE (-952 (-485)))) (|HasCategory| (-485) (QUOTE (-1067))) (|HasCategory| (-485) (QUOTE (-798 (-328)))) (|HasCategory| (-485) (QUOTE (-798 (-485)))) (|HasCategory| (-485) (QUOTE (-555 (-802 (-328))))) (|HasCategory| (-485) (QUOTE (-555 (-802 (-485))))) (|HasCategory| (-485) (QUOTE (-189))) (|HasCategory| (-485) (QUOTE (-813 (-1091)))) (|HasCategory| (-485) (QUOTE (-190))) (|HasCategory| (-485) (QUOTE (-811 (-1091)))) (|HasCategory| (-485) (QUOTE (-454 (-1091) (-485)))) (|HasCategory| (-485) (QUOTE (-260 (-485)))) (|HasCategory| (-485) (QUOTE (-241 (-485) (-485)))) (|HasCategory| (-485) (QUOTE (-258))) (|HasCategory| (-485) (QUOTE (-484))) (|HasCategory| (-485) (QUOTE (-582 (-485)))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-485) (QUOTE (-823)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-485) (QUOTE (-823)))) (|HasCategory| (-485) (QUOTE (-118)))))
+(-920)
((|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
-(-920)
+(-921)
((|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
-(-921 RP)
+(-922 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
-(-922 S)
+(-923 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
-(-923 A S)
+(-924 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{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 -3993)) (|HasCategory| |#2| (QUOTE (-1013))))
-(-924 S)
+((|HasAttribute| |#1| (QUOTE -3997)) (|HasCategory| |#2| (QUOTE (-1015))))
+(-925 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{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
-(-925 S)
+(-926 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} ** (1/2)}") (($ (|Fraction| (|Integer|))) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} ** (1/2)}") (($ $) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} ** (1/2)}") (($ $ (|PositiveInteger|)) "\\axiom{sqrt(\\spad{x},{}\\spad{n})} is \\axiom{\\spad{x} ** (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
-(-926)
+(-927)
((|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} ** (1/2)}") (($ (|Fraction| (|Integer|))) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} ** (1/2)}") (($ $) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} ** (1/2)}") (($ $ (|PositiveInteger|)) "\\axiom{sqrt(\\spad{x},{}\\spad{n})} is \\axiom{\\spad{x} ** (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}}")))
-((-3985 . T) (-3990 . T) (-3984 . T) (-3987 . T) (-3986 . T) ((-3994 "*") . T) (-3989 . T))
+((-3989 . T) (-3994 . T) (-3988 . T) (-3991 . T) (-3990 . T) ((-3998 "*") . T) (-3993 . T))
NIL
-(-927 R -3091)
+(-928 R -3094)
((|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
-(-928 R -3091)
+(-929 R -3094)
((|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
-(-929 -3091 UP)
+(-930 -3094 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
-(-930 -3091 UP)
+(-931 -3094 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
-(-931 S)
+(-932 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
-(-932 F1 UP UPUP R F2)
+(-933 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
-(-933)
+(-934)
((|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
-(-934)
+(-935)
((|constructor| (NIL "The category of real numeric domains,{} \\spadignore{i.e.} convertible to floats.")))
NIL
NIL
-(-935 |Pol|)
+(-936 |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
-(-936 |Pol|)
+(-937 |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
-(-937)
+(-938)
((|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
-(-938 |TheField|)
+(-939 |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")))
-((-3985 . T) (-3990 . T) (-3984 . T) (-3987 . T) (-3986 . T) ((-3994 "*") . T) (-3989 . T))
-((OR (|HasCategory| |#1| (QUOTE (-951 (-484)))) (|HasCategory| (-347 (-484)) (QUOTE (-951 (-484))))) (|HasCategory| |#1| (QUOTE (-951 (-347 (-484))))) (|HasCategory| |#1| (QUOTE (-951 (-484)))) (|HasCategory| (-347 (-484)) (QUOTE (-951 (-347 (-484))))) (|HasCategory| (-347 (-484)) (QUOTE (-951 (-484)))))
-(-939 -3091 L)
+((-3989 . T) (-3994 . T) (-3988 . T) (-3991 . T) (-3990 . T) ((-3998 "*") . T) (-3993 . T))
+((OR (|HasCategory| |#1| (QUOTE (-952 (-485)))) (|HasCategory| (-348 (-485)) (QUOTE (-952 (-485))))) (|HasCategory| |#1| (QUOTE (-952 (-348 (-485))))) (|HasCategory| |#1| (QUOTE (-952 (-485)))) (|HasCategory| (-348 (-485)) (QUOTE (-952 (-348 (-485))))) (|HasCategory| (-348 (-485)) (QUOTE (-952 (-485)))))
+(-940 -3094 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
-(-940 S)
+(-941 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(r,s)} reset the reference \\spad{r} to refer to \\spad{s}")) (|deref| ((|#1| $) "\\spad{deref(r)} returns the object referenced by \\spad{r}")) (|ref| (($ |#1|) "\\spad{ref(s)} creates a reference to the object \\spad{s}.")))
NIL
NIL
-(-941 R E V P)
+(-942 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(lp,{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|internalZeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalZeroSetSplit(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(lp,{}\\spad{b1},{}\\spad{b2}.\\spad{b3},{}\\spad{b4})} is an internal subroutine,{} exported only for developement.") (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(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},{}ts,{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement.")))
-((-3993 . T) (-3992 . T))
-((-12 (|HasCategory| |#4| (QUOTE (-1013))) (|HasCategory| |#4| (|%list| (QUOTE -259) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-554 (-473)))) (|HasCategory| |#4| (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#3| (QUOTE (-317))) (|HasCategory| |#4| (QUOTE (-553 (-773)))) (|HasCategory| |#4| (QUOTE (-72))))
-(-942)
+((-3997 . T) (-3996 . T))
+((-12 (|HasCategory| |#4| (QUOTE (-1015))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-555 (-474)))) (|HasCategory| |#4| (QUOTE (-1015))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#3| (QUOTE (-318))) (|HasCategory| |#4| (QUOTE (-554 (-774)))) (|HasCategory| |#4| (QUOTE (-72))))
+(-943)
((|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
-(-943 R)
+(-944 R)
((|constructor| (NIL "\\spad{RepresentationPackage1} provides functions for representation theory for finite groups and algebras. The package creates permutation representations and uses tensor products and its symmetric and antisymmetric components to create new representations of larger degree from given ones. Note: 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{i} <= \\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{i} <= \\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 (-3994 "*"))))
-(-944 R)
+((|HasAttribute| |#1| (QUOTE (-3998 "*"))))
+(-945 R)
((|constructor| (NIL "\\spad{RepresentationPackage2} provides functions for working with modular representations of finite groups and algebra. The routines in this package are created,{} using ideas of \\spad{R}. Parker,{} (the meat-Axe) to get smaller representations from bigger ones,{} \\spadignore{i.e.} finding sub- and factormodules,{} or to show,{} that such the representations are irreducible. Note: 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'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's irreducibility test can be used either to prove irreducibility or to find the splitting. Notes: the first 6 tries use Parker's fingerprints. Also,{} 7 covers the case of three-dimensional kernels over the field with 2 elements.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Boolean|) (|Integer|) (|Integer|)) "\\spad{meatAxe(aG,randomElements,numberOfTries, maxTests)} returns a 2-list of representations as follows. All matrices of argument \\spad{aG} are assumed to be square and of equal size. Then \\spad{aG} generates a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\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'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'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'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'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'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 (-311))) (|HasCategory| |#1| (QUOTE (-317)))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-257))))
-(-945 S)
+((-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-318)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-258))))
+(-946 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.")) (+ (($ $ $) "\\spad{x+y} returns the sum of \\spad{x} and \\spad{y}")))
NIL
NIL
-(-946 S)
+(-947 S)
((|constructor| (NIL "Implements exponentiation by repeated squaring")) (|expt| ((|#1| |#1| (|PositiveInteger|)) "\\spad{expt(r, i)} computes r**i by repeated squaring")) (* (($ $ $) "\\spad{x*y} returns the product of \\spad{x} and \\spad{y}")))
NIL
NIL
-(-947 S)
+(-948 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
-(-948 -3091 |Expon| |VarSet| |FPol| |LFPol|)
+(-949 -3094 |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")))
-(((-3994 "*") . T) (-3986 . T) (-3987 . T) (-3989 . T))
+(((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T))
NIL
-(-949)
+(-950)
((|constructor| (NIL "This domain represents `return' expressions.")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression returned by `e'.")))
NIL
NIL
-(-950 A S)
+(-951 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
-(-951 S)
+(-952 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
-(-952 Q R)
+(-953 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
-(-953 R)
+(-954 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}'s appearing inside the \\spad{gi}'s are not replaced. Error: if any \\spad{vi} is not a symbol.") (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|)))) "\\spad{eval(f, 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}'s appearing inside the \\spad{gi}'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
-(-954)
+(-955)
((|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
-(-955 UP)
+(-956 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
-(-956 R)
+(-957 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
-(-957 T$)
+(-958 T$)
((|constructor| (NIL "This category defines the common interface for RGB color models.")) (|componentUpperBound| ((|#1|) "componentUpperBound is an upper bound for all component values.")) (|blue| ((|#1| $) "\\spad{blue(c)} returns the `blue' component of `c'.")) (|green| ((|#1| $) "\\spad{green(c)} returns the `green' component of `c'.")) (|red| ((|#1| $) "\\spad{red(c)} returns the `red' component of `c'.")))
NIL
NIL
-(-958 T$)
+(-959 T$)
((|constructor| (NIL "This category defines the common interface for RGB color spaces.")) (|whitePoint| (($) "whitePoint is the contant indicating the white point of this color space.")))
NIL
NIL
-(-959 R |ls|)
+(-960 R |ls|)
((|constructor| (NIL "A domain for regular chains (\\spadignore{i.e.} regular triangular sets) over a Gcd-Domain and with a fix list of variables. This is just a front-end for the \\spadtype{RegularTriangularSet} domain constructor.")) (|zeroSetSplit| (((|List| $) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|) (|Boolean|)) "\\spad{zeroSetSplit(lp,clos?,info?)} returns a list \\spad{lts} of regular chains such that the union of the closures of their regular zero sets equals the affine variety associated with \\spad{lp}. Moreover,{} if \\spad{clos?} is \\spad{false} then the union of the regular zero set of the \\spad{ts} (for \\spad{ts} in \\spad{lts}) equals this variety. If \\spad{info?} is \\spad{true} then some information is displayed during the computations. See \\axiomOpFrom{zeroSetSplit}{RegularTriangularSet}.")))
-((-3993 . T) (-3992 . T))
-((-12 (|HasCategory| (-704 |#1| (-774 |#2|)) (QUOTE (-1013))) (|HasCategory| (-704 |#1| (-774 |#2|)) (|%list| (QUOTE -259) (|%list| (QUOTE -704) (|devaluate| |#1|) (|%list| (QUOTE -774) (|devaluate| |#2|)))))) (|HasCategory| (-704 |#1| (-774 |#2|)) (QUOTE (-554 (-473)))) (|HasCategory| (-704 |#1| (-774 |#2|)) (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| (-774 |#2|) (QUOTE (-317))) (|HasCategory| (-704 |#1| (-774 |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| (-704 |#1| (-774 |#2|)) (QUOTE (-72))))
-(-960)
+((-3997 . T) (-3996 . T))
+((-12 (|HasCategory| (-705 |#1| (-775 |#2|)) (QUOTE (-1015))) (|HasCategory| (-705 |#1| (-775 |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -705) (|devaluate| |#1|) (|%list| (QUOTE -775) (|devaluate| |#2|)))))) (|HasCategory| (-705 |#1| (-775 |#2|)) (QUOTE (-555 (-474)))) (|HasCategory| (-705 |#1| (-775 |#2|)) (QUOTE (-1015))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| (-775 |#2|) (QUOTE (-318))) (|HasCategory| (-705 |#1| (-775 |#2|)) (QUOTE (-554 (-774)))) (|HasCategory| (-705 |#1| (-775 |#2|)) (QUOTE (-72))))
+(-961)
((|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
-(-961 S)
+(-962 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
-(-962)
+(-963)
((|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.")))
-((-3989 . T))
+((-3993 . T))
NIL
-(-963 |xx| -3091)
+(-964 |xx| -3094)
((|constructor| (NIL "This package exports rational interpolation algorithms")))
NIL
NIL
-(-964 S)
+(-965 S)
((|constructor| (NIL "\\indented{2}{A set is an \\spad{S}-right linear set if it is stable by right-dilation} \\indented{2}{by elements in the semigroup \\spad{S}.} See Also: LeftLinearSet.")) (* (($ $ |#1|) "\\spad{x*s} is the right-dilation of \\spad{x} by \\spad{s}.")))
NIL
NIL
-(-965 S |m| |n| R |Row| |Col|)
+(-966 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 (-257))) (|HasCategory| |#4| (QUOTE (-311))) (|HasCategory| |#4| (QUOTE (-495))) (|HasCategory| |#4| (QUOTE (-146))))
-(-966 |m| |n| R |Row| |Col|)
+((|HasCategory| |#4| (QUOTE (-258))) (|HasCategory| |#4| (QUOTE (-312))) (|HasCategory| |#4| (QUOTE (-496))) (|HasCategory| |#4| (QUOTE (-146))))
+(-967 |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")))
-((-3992 . T) (-3987 . T) (-3986 . T))
+((-3996 . T) (-3991 . T) (-3990 . T))
NIL
-(-967 |m| |n| R)
+(-968 |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}.")))
-((-3992 . T) (-3987 . T) (-3986 . T))
-((|HasCategory| |#3| (QUOTE (-146))) (OR (-12 (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (|%list| (QUOTE -259) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-311))) (|HasCategory| |#3| (|%list| (QUOTE -259) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1013))) (|HasCategory| |#3| (|%list| (QUOTE -259) (|devaluate| |#3|))))) (|HasCategory| |#3| (QUOTE (-554 (-473)))) (OR (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-311)))) (|HasCategory| |#3| (QUOTE (-311))) (|HasCategory| |#3| (QUOTE (-1013))) (|HasCategory| |#3| (QUOTE (-257))) (|HasCategory| |#3| (QUOTE (-495))) (-12 (|HasCategory| |#3| (QUOTE (-1013))) (|HasCategory| |#3| (|%list| (QUOTE -259) (|devaluate| |#3|)))) (|HasCategory| |#3| (QUOTE (-72))) (|HasCategory| |#3| (QUOTE (-553 (-773)))))
-(-968 |m| |n| R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2)
+((-3996 . T) (-3991 . T) (-3990 . T))
+((|HasCategory| |#3| (QUOTE (-146))) (OR (-12 (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1015))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|))))) (|HasCategory| |#3| (QUOTE (-555 (-474)))) (OR (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-312)))) (|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (QUOTE (-1015))) (|HasCategory| |#3| (QUOTE (-258))) (|HasCategory| |#3| (QUOTE (-496))) (-12 (|HasCategory| |#3| (QUOTE (-1015))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (|HasCategory| |#3| (QUOTE (-72))) (|HasCategory| |#3| (QUOTE (-554 (-774)))))
+(-969 |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
-(-969 R)
+(-970 R)
((|constructor| (NIL "The category of right modules over an rng (ring not necessarily with unit). This is an abelian group which supports right multiplation by elements of the rng. \\blankline")))
NIL
NIL
-(-970)
-((|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")))
+(-971 S)
+((|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")) (|annihilate?| (((|Boolean|) $ $) "\\spad{annihilate?(x,y)} holds when the product of \\spad{x} and \\spad{y} is \\spad{0}.")))
NIL
NIL
-(-971 S T$)
+(-972)
+((|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")) (|annihilate?| (((|Boolean|) $ $) "\\spad{annihilate?(x,y)} holds when the product of \\spad{x} and \\spad{y} is \\spad{0}.")))
+NIL
+NIL
+(-973 S T$)
((|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 (-1013))))
-(-972 S)
+((|HasCategory| |#1| (QUOTE (-1015))))
+(-974 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.")) (|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|) $) "\\spad{wholePart x} returns the integer part of \\spad{x}.")) (|floor| (($ $) "\\spad{floor x} returns the largest integer \\spad{<= x}.")) (|ceiling| (($ $) "\\spad{ceiling x} returns the small integer \\spad{>= x}.")) (|norm| (($ $) "\\spad{norm x} returns the same as absolute value.")))
NIL
NIL
-(-973)
+(-975)
((|constructor| (NIL "The real number system category is intended as a model for the real numbers. The real numbers form an ordered normed field. Note that we have purposely not included \\spadtype{DifferentialRing} or the elementary functions (see \\spadtype{TranscendentalFunctionCategory}) in the definition.")) (|round| (($ $) "\\spad{round x} computes the integer closest to \\spad{x}.")) (|truncate| (($ $) "\\spad{truncate x} returns the integer between \\spad{x} and 0 closest to \\spad{x}.")) (|fractionPart| (($ $) "\\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.")))
-((-3984 . T) (-3990 . T) (-3985 . T) ((-3994 "*") . T) (-3986 . T) (-3987 . T) (-3989 . T))
+((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T))
NIL
-(-974 |TheField| |ThePolDom|)
+(-976 |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| $) "\\axiom{left(rootChar)} is the left bound of the isolating interval")))
NIL
NIL
-(-975)
+(-977)
((|constructor| (NIL "\\spadtype{RomanNumeral} provides functions for converting \\indented{1}{integers to roman numerals.}")) (|roman| (($ (|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.")))
-((-3980 . T) (-3984 . T) (-3979 . T) (-3990 . T) (-3991 . T) (-3985 . T) ((-3994 "*") . T) (-3986 . T) (-3987 . T) (-3989 . T))
+((-3984 . T) (-3988 . T) (-3983 . T) (-3994 . T) (-3995 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T))
NIL
-(-976 S R E V)
+(-978 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| $) "\\axiom{gcd(\\spad{r},{}\\spad{p})} returns the gcd of \\axiom{\\spad{r}} and the content of \\axiom{\\spad{p}}.")) (|nextsubResultant2| (($ $ $ $ $) "\\axiom{\\spad{nextsubResultant2}(\\spad{p},{}\\spad{q},{}\\spad{z},{}\\spad{s})} is the multivariate version of the operation \\axiomOpFrom{\\spad{next_sousResultant2}}{PseudoRemainderSequence} from the \\axiomType{PseudoRemainderSequence} constructor.")) (|LazardQuotient2| (($ $ $ $ (|NonNegativeInteger|)) "\\axiom{\\spad{LazardQuotient2}(\\spad{p},{}a,{}\\spad{b},{}\\spad{n})} returns \\axiom{(a**(\\spad{n}-1) * \\spad{p}) exquo 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 b**(\\spad{n}-1)} assuming that this quotient does not fail.")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns the last non-zero subresultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|subResultantChain| (((|List| $) $ $) "\\axiom{subResultantChain(a,{}\\spad{b})},{} where \\axiom{a} and \\axiom{\\spad{b}} are not contant polynomials with the same main variable,{} returns the subresultant chain of \\axiom{a} and \\axiom{\\spad{b}}.")) (|resultant| (($ $ $) "\\axiom{resultant(a,{}\\spad{b})} computes the resultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{\\spad{halfExtendedSubResultantGcd2}(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}cb]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}cb]} otherwise produces an error.")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{\\spad{halfExtendedSubResultantGcd1}(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}cb]} otherwise produces an error.")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[ca,{}cb,{}\\spad{r}]} such that \\axiom{\\spad{r}} is \\axiom{subResultantGcd(a,{}\\spad{b})} and we have \\axiom{ca * a + cb * cb = \\spad{r}} .")) (|subResultantGcd| (($ $ $) "\\axiom{subResultantGcd(a,{}\\spad{b})} computes a gcd of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}} with coefficients in the fraction field of the polynomial ring generated by their other variables over \\axiom{\\spad{R}}.")) (|exactQuotient!| (($ $ $) "\\axiom{exactQuotient!(a,{}\\spad{b})} replaces \\axiom{a} by \\axiom{exactQuotient(a,{}\\spad{b})}") (($ $ |#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!| (($ $) "\\axiom{primPartElseUnitCanonical!(\\spad{p})} replaces \\axiom{\\spad{p}} by \\axiom{primPartElseUnitCanonical(\\spad{p})}.")) (|primPartElseUnitCanonical| (($ $) "\\axiom{primPartElseUnitCanonical(\\spad{p})} returns \\axiom{primitivePart(\\spad{p})} if \\axiom{\\spad{R}} is a gcd-domain,{} otherwise \\axiom{unitCanonical(\\spad{p})}.")) (|convert| (($ (|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)*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)*r = prem(a,{}\\spad{b},{}\\spad{v})}.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $) "\\axiom{lazyPremWithDefault(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b})} and \\axiom{(c**g)*r = prem(a,{}\\spad{b})}.")) (|lazyPquo| (($ $ $ |#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},{}lp)} returns \\spad{true} iff \\axiom{normalized?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{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},{}lp)} returns \\spad{true} iff \\axiom{initiallyReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{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},{}lp)} returns \\spad{true} iff \\axiom{headReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{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},{}lp)} returns \\spad{true} iff \\axiom{reduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{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| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}.")))
NIL
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-(-977 R E V)
+((|HasCategory| |#2| (QUOTE (-390))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-952 (-485)))) (|HasCategory| |#2| (QUOTE (-484))) (|HasCategory| |#2| (QUOTE (-38 (-485)))) (|HasCategory| |#2| (QUOTE (-906 (-485)))) (|HasCategory| |#2| (QUOTE (-38 (-348 (-485))))) (|HasCategory| |#4| (QUOTE (-555 (-1091)))))
+(-979 R E V)
((|constructor| (NIL "A category for general multi-variate polynomials with coefficients in a ring,{} variables in an ordered set,{} and exponents from an ordered abelian monoid,{} with a \\axiomOp{sup} operation. When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\axiom{primitivePart!(\\spad{p})} replaces \\axiom{\\spad{p}} by its primitive part.")) (|gcd| ((|#1| |#1| $) "\\axiom{gcd(\\spad{r},{}\\spad{p})} returns the gcd of \\axiom{\\spad{r}} and the content of \\axiom{\\spad{p}}.")) (|nextsubResultant2| (($ $ $ $ $) "\\axiom{\\spad{nextsubResultant2}(\\spad{p},{}\\spad{q},{}\\spad{z},{}\\spad{s})} is the multivariate version of the operation \\axiomOpFrom{\\spad{next_sousResultant2}}{PseudoRemainderSequence} from the \\axiomType{PseudoRemainderSequence} constructor.")) (|LazardQuotient2| (($ $ $ $ (|NonNegativeInteger|)) "\\axiom{\\spad{LazardQuotient2}(\\spad{p},{}a,{}\\spad{b},{}\\spad{n})} returns \\axiom{(a**(\\spad{n}-1) * \\spad{p}) exquo 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 b**(\\spad{n}-1)} assuming that this quotient does not fail.")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns the last non-zero subresultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|subResultantChain| (((|List| $) $ $) "\\axiom{subResultantChain(a,{}\\spad{b})},{} where \\axiom{a} and \\axiom{\\spad{b}} are not contant polynomials with the same main variable,{} returns the subresultant chain of \\axiom{a} and \\axiom{\\spad{b}}.")) (|resultant| (($ $ $) "\\axiom{resultant(a,{}\\spad{b})} computes the resultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{\\spad{halfExtendedSubResultantGcd2}(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}cb]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}cb]} otherwise produces an error.")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{\\spad{halfExtendedSubResultantGcd1}(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}cb]} otherwise produces an error.")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[ca,{}cb,{}\\spad{r}]} such that \\axiom{\\spad{r}} is \\axiom{subResultantGcd(a,{}\\spad{b})} and we have \\axiom{ca * a + cb * cb = \\spad{r}} .")) (|subResultantGcd| (($ $ $) "\\axiom{subResultantGcd(a,{}\\spad{b})} computes a gcd of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}} with coefficients in the fraction field of the polynomial ring generated by their other variables over \\axiom{\\spad{R}}.")) (|exactQuotient!| (($ $ $) "\\axiom{exactQuotient!(a,{}\\spad{b})} replaces \\axiom{a} by \\axiom{exactQuotient(a,{}\\spad{b})}") (($ $ |#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!| (($ $) "\\axiom{primPartElseUnitCanonical!(\\spad{p})} replaces \\axiom{\\spad{p}} by \\axiom{primPartElseUnitCanonical(\\spad{p})}.")) (|primPartElseUnitCanonical| (($ $) "\\axiom{primPartElseUnitCanonical(\\spad{p})} returns \\axiom{primitivePart(\\spad{p})} if \\axiom{\\spad{R}} is a gcd-domain,{} otherwise \\axiom{unitCanonical(\\spad{p})}.")) (|convert| (($ (|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)*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)*r = prem(a,{}\\spad{b},{}\\spad{v})}.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $) "\\axiom{lazyPremWithDefault(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b})} and \\axiom{(c**g)*r = prem(a,{}\\spad{b})}.")) (|lazyPquo| (($ $ $ |#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},{}lp)} returns \\spad{true} iff \\axiom{normalized?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{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},{}lp)} returns \\spad{true} iff \\axiom{initiallyReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{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},{}lp)} returns \\spad{true} iff \\axiom{headReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{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},{}lp)} returns \\spad{true} iff \\axiom{reduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{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}}.")))
-(((-3994 "*") |has| |#1| (-146)) (-3985 |has| |#1| (-495)) (-3990 |has| |#1| (-6 -3990)) (-3987 . T) (-3986 . T) (-3989 . T))
+(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3994 |has| |#1| (-6 -3994)) (-3991 . T) (-3990 . T) (-3993 . T))
NIL
-(-978)
+(-980)
((|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
-(-979 S |TheField| |ThePols|)
+(-981 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
-(-980 |TheField| |ThePols|)
+(-982 |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
-(-981 R E V P TS)
+(-983 R E V P TS)
((|constructor| (NIL "A package providing a new algorithm for solving polynomial systems by means of regular chains. Two ways of solving are proposed: in the sense of Zariski closure (like in Kalkbrener's algorithm) or in the sense of the regular zeros (like in Wu,{} Wang or Lazard methods). This algorithm is valid for 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},{}TS) and \\axiomType{RSETGCD}(\\spad{R},{}\\spad{E},{}\\spad{V},{}\\spad{P},{}TS). The same way it does not care about the way univariate polynomial gcd (with coefficients in the tower of simple extensions associated with a regular set) are computed. The only requirement is that these 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{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
-(-982 S R E V P)
+(-984 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}{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 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 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 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
-(-983 R E V P)
+(-985 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}{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 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 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 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}.")))
-((-3993 . T) (-3992 . T))
+((-3997 . T) (-3996 . T))
NIL
-(-984 R E V P TS)
+(-986 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 gcd over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of \\spad{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},{}ts)} has the same specifications as \\axiomOpFrom{squareFreePart}{RegularTriangularSetCategory}.")) (|toseInvertibleSet| (((|List| |#5|) |#4| |#5|) "\\axiom{toseInvertibleSet(\\spad{p1},{}\\spad{p2},{}ts)} has the same specifications as \\axiomOpFrom{invertibleSet}{RegularTriangularSetCategory}.")) (|toseInvertible?| (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{toseInvertible?(\\spad{p1},{}\\spad{p2},{}ts)} has the same specifications as \\axiomOpFrom{invertible?}{RegularTriangularSetCategory}.") (((|Boolean|) |#4| |#5|) "\\axiom{toseInvertible?(\\spad{p1},{}\\spad{p2},{}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},{}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},{}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},{}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},{}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
-(-985)
+(-987)
((|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
-(-986)
+(-988)
((|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
-(-987 |Base| R -3091)
+(-989 |Base| R -3094)
((|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},{}...,{}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
-(-988 |f|)
+(-990 |f|)
((|constructor| (NIL "This domain implements named rules")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol")))
NIL
NIL
-(-989 |Base| R -3091)
+(-991 |Base| R -3094)
((|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
-(-990 R |ls|)
+(-992 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
-(-991 R UP M)
+(-993 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.")))
-((-3985 |has| |#1| (-311)) (-3990 |has| |#1| (-311)) (-3984 |has| |#1| (-311)) ((-3994 "*") . T) (-3986 . T) (-3987 . T) (-3989 . T))
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-(-992 UP SAE UPA)
+((-3989 |has| |#1| (-312)) (-3994 |has| |#1| (-312)) (-3988 |has| |#1| (-312)) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T))
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+(-994 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
-(-993 UP SAE UPA)
+(-995 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
-(-994)
+(-996)
((|constructor| (NIL "This trivial domain lets us build Univariate Polynomials in an anonymous variable")))
NIL
NIL
-(-995)
+(-997)
((|constructor| (NIL "This is the category of Spad syntax objects.")))
NIL
NIL
-(-996 S)
+(-998 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
-(-997)
+(-999)
((|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 `b'.")) (|findBinding| (((|Maybe| (|Binding|)) (|Identifier|) $) "\\spad{findBinding(n,s)} returns the first binding of `n' in `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
-(-998 R)
+(-1000 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
-(-999 R)
+(-1001 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")))
-(((-3994 "*") |has| |#1| (-146)) (-3985 |has| |#1| (-495)) (-3990 |has| |#1| (-6 -3990)) (-3987 . T) (-3986 . T) (-3989 . T))
-((|HasCategory| |#1| (QUOTE (-822))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-389))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-822)))) (OR (|HasCategory| |#1| (QUOTE (-389))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-822)))) (OR (|HasCategory| |#1| (QUOTE (-389))) (|HasCategory| |#1| (QUOTE (-822)))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-495)))) (-12 (|HasCategory| |#1| (QUOTE (-797 (-327)))) (|HasCategory| (-1000 (-1089)) (QUOTE (-797 (-327))))) (-12 (|HasCategory| |#1| (QUOTE (-797 (-484)))) (|HasCategory| (-1000 (-1089)) (QUOTE (-797 (-484))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-327))))) (|HasCategory| (-1000 (-1089)) (QUOTE (-554 (-801 (-327)))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-484))))) (|HasCategory| (-1000 (-1089)) (QUOTE (-554 (-801 (-484)))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-473)))) (|HasCategory| (-1000 (-1089)) (QUOTE (-554 (-473))))) (|HasCategory| |#1| (QUOTE (-581 (-484)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-347 (-484))))) (|HasCategory| |#1| (QUOTE (-951 (-484)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-347 (-484))))) (|HasCategory| |#1| (QUOTE (-951 (-347 (-484)))))) (|HasCategory| |#1| (QUOTE (-951 (-347 (-484))))) (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-812 (-1089)))) (|HasCategory| |#1| (QUOTE (-810 (-1089)))) (|HasCategory| |#1| (QUOTE (-311))) (|HasAttribute| |#1| (QUOTE -3990)) (|HasCategory| |#1| (QUOTE (-389))) (-12 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118)))))
-(-1000 S)
+(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3994 |has| |#1| (-6 -3994)) (-3991 . T) (-3990 . T) (-3993 . T))
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+(-1002 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
-(-1001 S)
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((|constructor| (NIL "This type is used to specify a range of values from type \\spad{S}.")))
NIL
-((|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1013))))
-(-1002 R S)
+((|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1015))))
+(-1004 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 (-756))))
-(-1003)
+((|HasCategory| |#1| (QUOTE (-757))))
+(-1005)
((|constructor| (NIL "This domain represents segement expressions.")) (|bounds| (((|List| (|SpadAst|)) $) "\\spad{bounds(s)} returns the bounds of the segment `s'. If `s' designates an infinite interval,{} then the returns list a singleton list.")))
NIL
NIL
-(-1004 S)
+(-1006 S)
((|constructor| (NIL "This domain is used to provide the function argument syntax \\spad{v=a..b}. This is used,{} for example,{} by the top-level \\spadfun{draw} functions.")))
NIL
-((|HasCategory| (-1001 |#1|) (QUOTE (-1013))))
-(-1005 R S)
+((|HasCategory| (-1003 |#1|) (QUOTE (-1015))))
+(-1007 R S)
((|constructor| (NIL "This package provides operations for mapping functions onto \\spadtype{SegmentBinding}\\spad{s}.")) (|map| (((|SegmentBinding| |#2|) (|Mapping| |#2| |#1|) (|SegmentBinding| |#1|)) "\\spad{map(f,v=a..b)} returns the value given by \\spad{v=f(a)..f(b)}.")))
NIL
NIL
-(-1006 S)
+(-1008 S)
((|constructor| (NIL "This category provides operations on ranges,{} or {\\em segments} as they are called.")) (|segment| (($ |#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
-(-1007 S L)
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((|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
-(-1008)
+(-1010)
((|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
-(-1009 S)
+(-1011 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)}}")))
-((-3992 . T) (-3982 . T) (-3993 . T))
-((OR (-12 (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-554 (-473)))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))))
-(-1010 A S)
+((-3996 . T) (-3986 . T) (-3997 . T))
+((OR (-12 (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-555 (-474)))) (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| |#1| (QUOTE (-554 (-774)))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))))
+(-1012 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|) $ $) "\\spad{s} < \\spad{t} returns \\spad{true} if all elements of set aggregate \\spad{s} are also elements of set aggregate \\spad{t}.")))
NIL
NIL
-(-1011 S)
+(-1013 S)
((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#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}.")))
-((-3982 . T))
+((-3986 . T))
NIL
-(-1012 S)
+(-1014 S)
((|constructor| (NIL "\\spadtype{SetCategory} is the basic category for describing a collection of elements with \\spadop{=} (equality) and \\spadfun{coerce} to output form. \\blankline Conditional Attributes: \\indented{3}{canonical\\tab{15}data structure equality is the same as \\spadop{=}}")) (|latex| (((|String|) $) "\\spad{latex(s)} returns a LaTeX-printable output representation of \\spad{s}.")) (|hash| (((|SingleInteger|) $) "\\spad{hash(s)} calculates a hash code for \\spad{s}.")))
NIL
NIL
-(-1013)
+(-1015)
((|constructor| (NIL "\\spadtype{SetCategory} is the basic category for describing a collection of elements with \\spadop{=} (equality) and \\spadfun{coerce} to output form. \\blankline Conditional Attributes: \\indented{3}{canonical\\tab{15}data structure equality is the same as \\spadop{=}}")) (|latex| (((|String|) $) "\\spad{latex(s)} returns a LaTeX-printable output representation of \\spad{s}.")) (|hash| (((|SingleInteger|) $) "\\spad{hash(s)} calculates a hash code for \\spad{s}.")))
NIL
NIL
-(-1014 |m| |n|)
+(-1016 |m| |n|)
((|constructor| (NIL "\\spadtype{SetOfMIntegersInOneToN} implements the subsets of \\spad{M} integers in the interval \\spad{[1..n]}")) (|delta| (((|NonNegativeInteger|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{delta(S,k,p)} returns the number of elements of \\spad{S} which are strictly between \\spad{p} and the k^{th} element of \\spad{S}.")) (|member?| (((|Boolean|) (|PositiveInteger|) $) "\\spad{member?(p, 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 {\\spad{a_1},{}...,{}a_m}. Error if {\\spad{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| $ #1="failed") $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{replaceKthElement(S,k,p)} replaces the k^{th} element of \\spad{S} by \\spad{p},{} and returns \"failed\" if the result is not a set of \\spad{M} integers in \\spad{1..n} any more.")) (|incrementKthElement| (((|Union| $ #1#) $ (|PositiveInteger|)) "\\spad{incrementKthElement(S,k)} increments the k^{th} element of \\spad{S},{} and returns \"failed\" if the result is not a set of \\spad{M} integers in \\spad{1..n} any more.")))
NIL
NIL
-(-1015)
+(-1017)
((|constructor| (NIL "This domain allows the manipulation of the usual Lisp values.")))
NIL
NIL
-(-1016 |Str| |Sym| |Int| |Flt| |Expr|)
+(-1018 |Str| |Sym| |Int| |Flt| |Expr|)
((|constructor| (NIL "This category allows the manipulation of Lisp values while keeping the grunge fairly localized.")) (|#| (((|Integer|) $) "\\spad{\\#((a1,...,an))} returns \\spad{n}.")) (|cdr| (($ $) "\\spad{cdr((a1,...,an))} returns \\spad{(a2,...,an)}.")) (|car| (($ $) "\\spad{car((a1,...,an))} returns \\spad{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 Flt; Error: if \\spad{s} is not an atom that also belongs to Flt.")) (|integer| ((|#3| $) "\\spad{integer(s)} returns \\spad{s} as an element of Int. Error: if \\spad{s} is not an atom that also belongs to Int.")) (|symbol| ((|#2| $) "\\spad{symbol(s)} returns \\spad{s} as an element of Sym. Error: if \\spad{s} is not an atom that also belongs to Sym.")) (|string| ((|#1| $) "\\spad{string(s)} returns \\spad{s} as an element of Str. Error: if \\spad{s} is not an atom that also belongs to Str.")) (|destruct| (((|List| $) $) "\\spad{destruct((a1,...,an))} returns the list [\\spad{a1},{}...,{}an].")) (|float?| (((|Boolean|) $) "\\spad{float?(s)} is \\spad{true} if \\spad{s} is an atom and belong to Flt.")) (|integer?| (((|Boolean|) $) "\\spad{integer?(s)} is \\spad{true} if \\spad{s} is an atom and belong to Int.")) (|symbol?| (((|Boolean|) $) "\\spad{symbol?(s)} is \\spad{true} if \\spad{s} is an atom and belong to Sym.")) (|string?| (((|Boolean|) $) "\\spad{string?(s)} is \\spad{true} if \\spad{s} is an atom and belong to Str.")) (|list?| (((|Boolean|) $) "\\spad{list?(s)} is \\spad{true} if \\spad{s} is a Lisp list,{} possibly ().")) (|pair?| (((|Boolean|) $) "\\spad{pair?(s)} is \\spad{true} if \\spad{s} has is a non-null Lisp list.")) (|atom?| (((|Boolean|) $) "\\spad{atom?(s)} is \\spad{true} if \\spad{s} is a Lisp atom.")) (|null?| (((|Boolean|) $) "\\spad{null?(s)} is \\spad{true} if \\spad{s} is the \\spad{S}-expression ().")) (|eq| (((|Boolean|) $ $) "\\spad{eq(s, t)} is \\spad{true} if \\%peq(\\spad{s},{}\\spad{t}) is \\spad{true} for pointers.")))
NIL
NIL
-(-1017 |Str| |Sym| |Int| |Flt| |Expr|)
+(-1019 |Str| |Sym| |Int| |Flt| |Expr|)
((|constructor| (NIL "This domain allows the manipulation of Lisp values over arbitrary atomic types.")))
NIL
NIL
-(-1018 R E V P TS)
+(-1020 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,{}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(lp,{}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?(\\spad{lpwt1},{}\\spad{lpwt2})} is an internal subroutine,{} exported only for developement.")) (|removeSuperfluousQuasiComponents| (((|List| |#5|) (|List| |#5|)) "\\axiom{removeSuperfluousQuasiComponents(lts)} removes from \\axiom{lts} any \\spad{ts} such that \\axiom{subQuasiComponent?(ts,{}us)} holds for another \\spad{us} in \\axiom{lts}.")) (|subQuasiComponent?| (((|Boolean|) |#5| (|List| |#5|)) "\\axiom{subQuasiComponent?(ts,{}lus)} returns \\spad{true} iff \\axiom{subQuasiComponent?(ts,{}us)} holds for one \\spad{us} in \\spad{lus}.") (((|Boolean|) |#5| |#5|) "\\axiom{subQuasiComponent?(ts,{}us)} returns \\spad{true} iff \\axiomOpFrom{internalSubQuasiComponent?(ts,{}us)}{QuasiComponentPackage} returs \\spad{true}.")) (|internalSubQuasiComponent?| (((|Union| (|Boolean|) "failed") |#5| |#5|) "\\axiom{internalSubQuasiComponent?(ts,{}us)} returns a boolean \\spad{b} value if the fact the regular zero set of \\axiom{us} contains that of \\axiom{ts} can be decided (and in that case \\axiom{\\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?(ts,{}us)} returns \\spad{true} iff \\axiom{ts} is a sub-set of \\axiom{us}.")) (|moreAlgebraic?| (((|Boolean|) |#5| |#5|) "\\axiom{moreAlgebraic?(ts,{}us)} returns \\spad{false} iff \\axiom{ts} and \\axiom{us} are both empty,{} or \\axiom{ts} has less elements than \\axiom{us},{} or some variable is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{us} and is not \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ts}.")) (|algebraicSort| (((|List| |#5|) (|List| |#5|)) "\\axiom{algebraicSort(lts)} sorts \\axiom{lts} \\spad{w}.\\spad{r}.\\spad{t} \\axiomOpFrom{supDimElseRittWu}{QuasiComponentPackage}.")) (|supDimElseRittWu?| (((|Boolean|) |#5| |#5|) "\\axiom{supDimElseRittWu(ts,{}us)} returns \\spad{true} iff \\axiom{ts} has less elements than \\axiom{us} otherwise if \\axiom{ts} has higher rank than \\axiom{us} \\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
-(-1019 R E V P TS)
+(-1021 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 gcd over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of \\spad{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
-(-1020 R E V P)
+(-1022 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 gcd of any polynomial \\spad{p} in \\spad{ts} and \\spad{differentiate(p,mvar(p))} \\spad{w}.\\spad{r}.\\spad{t}. \\axiomOpFrom{collectUnder}{TriangularSetCategory}(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.}")))
-((-3993 . T) (-3992 . T))
+((-3997 . T) (-3996 . T))
NIL
-(-1021)
+(-1023)
((|constructor| (NIL "SymmetricGroupCombinatoricFunctions contains combinatoric functions concerning symmetric groups and representation theory: list young tableaus,{} improper partitions,{} subsets bijection of Coleman.")) (|unrankImproperPartitions1| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{unrankImproperPartitions1(n,m,k)} computes the {\\em k}\\spad{-}th improper partition of nonnegative \\spad{n} in at most \\spad{m} nonnegative parts ordered as follows: first,{} in reverse lexicographically according to their non-zero parts,{} then according to their positions (\\spadignore{i.e.} lexicographical order using {\\em subSet}: {\\em [3,0,0] < [0,3,0] < [0,0,3] < [2,1,0] < [2,0,1] < [0,2,1] < [1,2,0] < [1,0,2] < [0,1,2] < [1,1,1]}). Note: counting of subtrees is done by {\\em numberOfImproperPartitionsInternal}.")) (|unrankImproperPartitions0| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{unrankImproperPartitions0(n,m,k)} computes the {\\em k}\\spad{-}th improper partition of nonnegative \\spad{n} in \\spad{m} nonnegative parts in reverse lexicographical order. Example: {\\em [0,0,3] < [0,1,2] < [0,2,1] < [0,3,0] < [1,0,2] < [1,1,1] < [1,2,0] < [2,0,1] < [2,1,0] < [3,0,0]}. Error: if \\spad{k} is negative or too big. Note: counting of subtrees is done by \\spadfunFrom{numberOfImproperPartitions}{SymmetricGroupCombinatoricFunctions}.")) (|subSet| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{subSet(n,m,k)} calculates the {\\em k}\\spad{-}th {\\em m}-subset of the set {\\em 0,1,...,(n-1)} in the lexicographic order considered as a decreasing map from {\\em 0,...,(m-1)} into {\\em 0,...,(n-1)}. See \\spad{S}.\\spad{G}. Williamson: Theorem 1.60. Error: if not {\\em (0 <= m <= n and 0 < = k < (n choose m))}.")) (|numberOfImproperPartitions| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{numberOfImproperPartitions(n,m)} computes the number of partitions of the nonnegative integer \\spad{n} in \\spad{m} nonnegative parts with regarding the order (improper partitions). Example: {\\em numberOfImproperPartitions (3,3)} is 10,{} since {\\em [0,0,3], [0,1,2], [0,2,1], [0,3,0], [1,0,2], [1,1,1], [1,2,0], [2,0,1], [2,1,0], [3,0,0]} are the possibilities. Note: this operation has a recursive implementation.")) (|nextPartition| (((|Vector| (|Integer|)) (|List| (|Integer|)) (|Vector| (|Integer|)) (|Integer|)) "\\spad{nextPartition(gamma,part,number)} generates the partition of {\\em number} which follows {\\em part} according to the right-to-left lexicographical order. The partition has the property that its components do not exceed the corresponding components of {\\em gamma}. the first partition is achieved by {\\em part=[]}. Also,{} {\\em []} indicates that {\\em part} is the last partition.") (((|Vector| (|Integer|)) (|Vector| (|Integer|)) (|Vector| (|Integer|)) (|Integer|)) "\\spad{nextPartition(gamma,part,number)} generates the partition of {\\em number} which follows {\\em part} according to the right-to-left lexicographical order. The partition has the property that its components do not exceed the corresponding components of {\\em gamma}. The first partition is achieved by {\\em part=[]}. Also,{} {\\em []} indicates that {\\em part} is the last partition.")) (|nextLatticePermutation| (((|List| (|Integer|)) (|List| (|PositiveInteger|)) (|List| (|Integer|)) (|Boolean|)) "\\spad{nextLatticePermutation(lambda,lattP,constructNotFirst)} generates the lattice permutation according to the proper partition {\\em lambda} succeeding the lattice permutation {\\em lattP} in lexicographical order as long as {\\em constructNotFirst} is \\spad{true}. If {\\em constructNotFirst} is \\spad{false},{} the first lattice permutation is returned. The result {\\em nil} indicates that {\\em lattP} has no successor.")) (|nextColeman| (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|Matrix| (|Integer|))) "\\spad{nextColeman(alpha,beta,C)} generates the next Coleman matrix of column sums {\\em alpha} and row sums {\\em beta} according to the lexicographical order from bottom-to-top. The first Coleman matrix is achieved by {\\em C=new(1,1,0)}. Also,{} {\\em new(1,1,0)} indicates that \\spad{C} is the last Coleman matrix.")) (|makeYoungTableau| (((|Matrix| (|Integer|)) (|List| (|PositiveInteger|)) (|List| (|Integer|))) "\\spad{makeYoungTableau(lambda,gitter)} computes for a given lattice permutation {\\em gitter} and for an improper partition {\\em lambda} the corresponding standard tableau of shape {\\em lambda}. Notes: see {\\em listYoungTableaus}. The entries are from {\\em 0,...,n-1}.")) (|listYoungTableaus| (((|List| (|Matrix| (|Integer|))) (|List| (|PositiveInteger|))) "\\spad{listYoungTableaus(lambda)} where {\\em lambda} is a proper partition generates the list of all standard tableaus of shape {\\em lambda} by means of lattice permutations. The numbers of the lattice permutation are interpreted as column labels. Hence the contents of these lattice permutations are the conjugate of {\\em lambda}. Notes: the functions {\\em nextLatticePermutation} and {\\em makeYoungTableau} are used. The entries are from {\\em 0,...,n-1}.")) (|inverseColeman| (((|List| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|Matrix| (|Integer|))) "\\spad{inverseColeman(alpha,beta,C)}: there is a bijection from the set of matrices having nonnegative entries and row sums {\\em alpha},{} column sums {\\em beta} to the set of {\\em Salpha - Sbeta} double cosets of the symmetric group {\\em Sn}. ({\\em Salpha} is the Young subgroup corresponding to the improper partition {\\em alpha}). For such a matrix \\spad{C},{} inverseColeman(\\spad{alpha},{}\\spad{beta},{}\\spad{C}) calculates the lexicographical smallest {\\em pi} in the corresponding double coset. Note: the resulting permutation {\\em pi} of {\\em {1,2,...,n}} is given in list form. Notes: the inverse of this map is {\\em coleman}. For details,{} see James/Kerber.")) (|coleman| (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{coleman(alpha,beta,pi)}: there is a bijection from the set of matrices having nonnegative entries and row sums {\\em alpha},{} column sums {\\em beta} to the set of {\\em Salpha - Sbeta} double cosets of the symmetric group {\\em Sn}. ({\\em Salpha} is the Young subgroup corresponding to the improper partition {\\em alpha}). For a representing element {\\em pi} of such a double coset,{} coleman(\\spad{alpha},{}\\spad{beta},{}\\spad{pi}) generates the Coleman-matrix corresponding to {\\em alpha, beta, pi}. Note: The permutation {\\em pi} of {\\em {1,2,...,n}} has to be given in list form. Note: the inverse of this map is {\\em inverseColeman} (if {\\em pi} is the lexicographical smallest permutation in the coset). For details see James/Kerber.")))
NIL
NIL
-(-1022 T$)
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((|constructor| (NIL "This domain implements semigroup operations.")) (|semiGroupOperation| (($ (|Mapping| |#1| |#1| |#1|)) "\\spad{semiGroupOperation f} constructs a semigroup operation out of a binary homogeneous mapping known to be associative.")))
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NIL
-(-1023 T$)
+(-1025 T$)
((|constructor| (NIL "This is the category of all domains that implement semigroup operations")))
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NIL
-(-1024 S)
+(-1026 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.")) (* (($ $ $) "\\spad{x*y} returns the product of \\spad{x} and \\spad{y}.")))
NIL
NIL
-(-1025)
+(-1027)
((|constructor| (NIL "the class of all multiplicative semigroups,{} \\spadignore{i.e.} a set with an associative operation \\spadop{*}. \\blankline")) (** (($ $ (|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
-(-1026 |dimtot| |dim1| S)
+(-1028 |dimtot| |dim1| S)
((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying ordered component type. The vectors are ordered as if they were split into two blocks. The \\spad{dim1} parameter specifies the length of the first block. The ordering is lexicographic between the blocks but acts like \\spadtype{HomogeneousDirectProduct} within each block. This type is a suitable third argument for \\spadtype{GeneralDistributedMultivariatePolynomial}.")))
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-(-1027 R |x|)
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+(-1029 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 c_{+}-c_{-} where c_{+} is the number of real roots of \\spad{p1} with \\spad{p2>0} and c_{-} is the number of real roots of \\spad{p1} with \\spad{p2<0}. If \\spad{p2=1} what you get is the number of real roots of \\spad{p1}.")) (|countRealRoots| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{countRealRoots(p)} says how many real roots \\spad{p} has")) (|SturmHabicht| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabicht(p1,p2)} computes c_{+}-c_{-} where c_{+} is the number of real roots of \\spad{p1} with \\spad{p2>0} and c_{-} is the number of real roots of \\spad{p1} with \\spad{p2<0}. If \\spad{p2=1} what you get is the number of real roots of \\spad{p1}.")) (|SturmHabichtCoefficients| (((|List| |#1|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtCoefficients(p1,p2)} computes the principal Sturm-Habicht coefficients of \\spad{p1} and \\spad{p2}")) (|SturmHabichtSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtSequence(p1,p2)} computes the Sturm-Habicht sequence of \\spad{p1} and \\spad{p2}")) (|subresultantSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{subresultantSequence(p1,p2)} computes the (standard) subresultant sequence of \\spad{p1} and \\spad{p2}")))
NIL
-((|HasCategory| |#1| (QUOTE (-389))))
-(-1028)
+((|HasCategory| |#1| (QUOTE (-390))))
+(-1030)
((|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 `s'.")) (|target| (((|Syntax|) $) "\\spad{target(s)} returns the target type of the signature `s'.")) (|signature| (($ (|List| (|Syntax|)) (|Syntax|)) "\\spad{signature(s,t)} constructs a Signature object with parameter types indicaded by `s',{} and return type indicated by `t'.")))
NIL
NIL
-(-1029)
+(-1031)
((|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 `s'.")) (|name| (((|Identifier|) $) "\\spad{name(s)} returns the name of the signature `s'.")) (|signatureAst| (($ (|Identifier|) (|Signature|)) "\\spad{signatureAst(n,s,t)} builds the signature AST n: \\spad{s} -> \\spad{t}")))
NIL
NIL
-(-1030 R -3091)
+(-1032 R -3094)
((|constructor| (NIL "This package provides functions to determine the sign of an elementary function around a point or infinity.")) (|sign| (((|Union| (|Integer|) #1="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|) #1#) |#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|) #1#) |#2|) "\\spad{sign(f)} returns the sign of \\spad{f} if it is constant everywhere.")))
NIL
NIL
-(-1031 R)
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((|constructor| (NIL "Find the sign of a rational function around a point or infinity.")) (|sign| (((|Union| (|Integer|) #1="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|) #1#) (|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|) #1#) (|Fraction| (|Polynomial| |#1|))) "\\spad{sign f} returns the sign of \\spad{f} if it is constant everywhere.")))
NIL
NIL
-(-1032)
+(-1034)
((|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
-(-1033)
+(-1035)
((|constructor| (NIL "SingleInteger is intended to support machine integer arithmetic.")) (|xor| (($ $ $) "\\spad{xor(n,m)} returns the bit-by-bit logical {\\em xor} of the single integers \\spad{n} and \\spad{m}.")) (|noetherian| ((|attribute|) "\\spad{noetherian} all ideals are finitely generated (in fact principal).")) (|canonicalsClosed| ((|attribute|) "\\spad{canonicalClosed} means two positives multiply to give positive.")) (|canonical| ((|attribute|) "\\spad{canonical} means that mathematical equality is implied by data structure equality.")))
-((-3980 . T) (-3984 . T) (-3979 . T) (-3990 . T) (-3991 . T) (-3985 . T) ((-3994 "*") . T) (-3986 . T) (-3987 . T) (-3989 . T))
+((-3984 . T) (-3988 . T) (-3983 . T) (-3994 . T) (-3995 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T))
NIL
-(-1034 S)
+(-1036 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}) = \\#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| $) "\\spad{push!(x,s)} pushes \\spad{x} onto stack \\spad{s},{} \\spadignore{i.e.} destructively changing \\spad{s} so as to have a new first (top) element \\spad{x}. Afterwards,{} pop!(\\spad{s}) produces \\spad{x} and pop!(\\spad{s}) produces the original \\spad{s}.")))
-((-3992 . T) (-3993 . T))
+((-3996 . T) (-3997 . T))
NIL
-(-1035 S |ndim| R |Row| |Col|)
+(-1037 S |ndim| R |Row| |Col|)
((|constructor| (NIL "\\spadtype{SquareMatrixCategory} is a general square matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col.")) (** (($ $ (|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}'s on the diagonal and zeroes elsewhere.")))
NIL
-((|HasCategory| |#3| (QUOTE (-311))) (|HasAttribute| |#3| (QUOTE (-3994 "*"))) (|HasCategory| |#3| (QUOTE (-146))))
-(-1036 |ndim| R |Row| |Col|)
+((|HasCategory| |#3| (QUOTE (-312))) (|HasAttribute| |#3| (QUOTE (-3998 "*"))) (|HasCategory| |#3| (QUOTE (-146))))
+(-1038 |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}'s on the diagonal and zeroes elsewhere.")))
-((-3992 . T) (-3986 . T) (-3987 . T) (-3989 . T))
+((-3996 . T) (-3990 . T) (-3991 . T) (-3993 . T))
NIL
-(-1037 R |Row| |Col| M)
+(-1039 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
-(-1038 R |VarSet|)
+(-1040 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.")))
-(((-3994 "*") |has| |#1| (-146)) (-3985 |has| |#1| (-495)) (-3990 |has| |#1| (-6 -3990)) (-3987 . T) (-3986 . T) (-3989 . T))
-((|HasCategory| |#1| (QUOTE (-822))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-389))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-822)))) (OR (|HasCategory| |#1| (QUOTE (-389))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-822)))) (OR (|HasCategory| |#1| (QUOTE (-389))) (|HasCategory| |#1| (QUOTE (-822)))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-495)))) (-12 (|HasCategory| |#1| (QUOTE (-797 (-327)))) (|HasCategory| |#2| (QUOTE (-797 (-327))))) (-12 (|HasCategory| |#1| (QUOTE (-797 (-484)))) (|HasCategory| |#2| (QUOTE (-797 (-484))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-327))))) (|HasCategory| |#2| (QUOTE (-554 (-801 (-327)))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-484))))) (|HasCategory| |#2| (QUOTE (-554 (-801 (-484)))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-473)))) (|HasCategory| |#2| (QUOTE (-554 (-473))))) (|HasCategory| |#1| (QUOTE (-581 (-484)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-347 (-484))))) (|HasCategory| |#1| (QUOTE (-951 (-484)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-347 (-484))))) (|HasCategory| |#1| (QUOTE (-951 (-347 (-484)))))) (|HasCategory| |#1| (QUOTE (-951 (-347 (-484))))) (|HasCategory| |#1| (QUOTE (-311))) (|HasAttribute| |#1| (QUOTE -3990)) (|HasCategory| |#1| (QUOTE (-389))) (-12 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118)))))
-(-1039 |Coef| |Var| SMP)
+(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3994 |has| |#1| (-6 -3994)) (-3991 . T) (-3990 . T) (-3993 . T))
+((|HasCategory| |#1| (QUOTE (-823))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-823)))) (OR (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-823)))) (OR (|HasCategory| |#1| (QUOTE (-390))) (|HasCategory| |#1| (QUOTE (-823)))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (-12 (|HasCategory| |#1| (QUOTE (-798 (-328)))) (|HasCategory| |#2| (QUOTE (-798 (-328))))) (-12 (|HasCategory| |#1| (QUOTE (-798 (-485)))) (|HasCategory| |#2| (QUOTE (-798 (-485))))) (-12 (|HasCategory| |#1| (QUOTE (-555 (-802 (-328))))) (|HasCategory| |#2| (QUOTE (-555 (-802 (-328)))))) (-12 (|HasCategory| |#1| (QUOTE (-555 (-802 (-485))))) (|HasCategory| |#2| (QUOTE (-555 (-802 (-485)))))) (-12 (|HasCategory| |#1| (QUOTE (-555 (-474)))) (|HasCategory| |#2| (QUOTE (-555 (-474))))) (|HasCategory| |#1| (QUOTE (-582 (-485)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-348 (-485))))) (|HasCategory| |#1| (QUOTE (-952 (-485)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-348 (-485))))) (|HasCategory| |#1| (QUOTE (-952 (-348 (-485)))))) (|HasCategory| |#1| (QUOTE (-952 (-348 (-485))))) (|HasCategory| |#1| (QUOTE (-312))) (|HasAttribute| |#1| (QUOTE -3994)) (|HasCategory| |#1| (QUOTE (-390))) (-12 (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118)))))
+(-1041 |Coef| |Var| SMP)
((|constructor| (NIL "This domain provides multivariate Taylor series with variables from an arbitrary ordered set. A Taylor series is represented by a stream of polynomials from the polynomial domain SMP. The \\spad{n}th element of the stream is a form of degree \\spad{n}. SMTS is an internal domain.")) (|fintegrate| (($ (|Mapping| $) |#2| |#1|) "\\spad{fintegrate(f,v,c)} is the integral of \\spad{f()} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.} \\indented{1}{The evaluation of \\spad{f()} is delayed.}")) (|integrate| (($ $ |#2| |#1|) "\\spad{integrate(s,v,c)} is the integral of \\spad{s} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.}")) (|csubst| (((|Mapping| (|Stream| |#3|) |#3|) (|List| |#2|) (|List| (|Stream| |#3|))) "\\spad{csubst(a,b)} is for internal use only")) (* (($ |#3| $) "\\spad{smp*ts} multiplies a TaylorSeries by a monomial SMP.")) (|coerce| (($ |#3|) "\\spad{coerce(poly)} regroups the terms by total degree and forms a series.") (($ |#2|) "\\spad{coerce(var)} converts a variable to a Taylor series")) (|coefficient| ((|#3| $ (|NonNegativeInteger|)) "\\spad{coefficient(s, n)} gives the terms of total degree \\spad{n}.")))
-(((-3994 "*") |has| |#1| (-146)) (-3985 |has| |#1| (-495)) (-3987 . T) (-3986 . T) (-3989 . T))
-((|HasCategory| |#1| (QUOTE (-38 (-347 (-484))))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-495)))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-311))))
-(-1040 R E V P)
+(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3991 . T) (-3990 . T) (-3993 . T))
+((|HasCategory| |#1| (QUOTE (-38 (-348 (-485))))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-312))))
+(-1042 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}")))
-((-3993 . T) (-3992 . T))
+((-3997 . T) (-3996 . T))
NIL
-(-1041 UP -3091)
+(-1043 UP -3094)
((|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
-(-1042 R)
+(-1044 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
-(-1043 R)
+(-1045 R)
((|constructor| (NIL "This package finds the function \\spad{func3} where \\spad{func1} and \\spad{func2} \\indented{1}{are given and\\space{2}\\spad{func1} = \\spad{func3}(\\spad{func2}) .\\space{2}If there is no solution then} \\indented{1}{function \\spad{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 \\spad{func3} where \\spad{func1} = \\spad{func3}(\\spad{func2}) and expresses it in the new variable newvar. If there is no solution then \\spad{func1} will be returned.")))
NIL
NIL
-(-1044 R)
+(-1046 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
-(-1045 S A)
+(-1047 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 (-757))))
-(-1046 R)
+((|HasCategory| |#1| (QUOTE (-758))))
+(-1048 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
-(-1047 R)
+(-1049 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 pn,{} which are lists of points; the booleans \\spad{close1} and \\spad{close2} indicate how the surface is to be closed: \\spad{close1} set to \\spad{true} means that each individual list (a curve) is to be closed (that is,{} the last point of the list is to be connected to the first point); \\spad{close2} set to \\spad{true} means that the boundary at one end of the surface is to be connected to the boundary at the other end (the boundaries are defined as the first list of points (curve) and the last list of points (curve)); the \\spadtype{ThreeSpace} containing this surface is returned.") (($ (|List| (|List| (|Point| |#1|)))) "\\spad{mesh([[p0],[p1],...,[pn]])} creates a surface defined by a list of curves which are lists,{} \\spad{p0} through 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 WxH where \\spad{W} is the number of lists of points from the domain \\spad{PointDomain(R)} and \\spad{H} is the number of elements in each of those lists; the booleans \\spad{close1} and \\spad{close2} indicate how the surface is to be closed: if \\spad{close1} is \\spad{true} this means that each individual list (a curve) is to be closed (\\spadignore{i.e.} the last point of the list is to be connected to the first point); if \\spad{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 \\spad{close2} indicate how the surface is to be closed. Argument \\spad{close1} equal \\spad{true} means that each individual list (a curve) is to be closed,{} \\spadignore{i.e.} the last point of the list is to be connected to the first point. Argument \\spad{close2} equal \\spad{true} means that the boundary at one end of the surface is to be connected to the boundary at the other end,{} \\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 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 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 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 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 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
-(-1048)
+(-1050)
((|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
-(-1049)
+(-1051)
((|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
-(-1050)
+(-1052)
((|constructor| (NIL "This category describes the exported \\indented{2}{signatures of the SpadAst domain.}")) (|autoCoerce| (((|Integer|) $) "\\spad{autoCoerce(s)} returns the Integer view of `s'. Left at the discretion of the compiler.") (((|String|) $) "\\spad{autoCoerce(s)} returns the String view of `s'. Left at the discretion of the compiler.") (((|Identifier|) $) "\\spad{autoCoerce(s)} returns the Identifier view of `s'. Left at the discretion of the compiler.") (((|IsAst|) $) "\\spad{autoCoerce(s)} returns the IsAst view of `s'. Left at the discretion of the compiler.") (((|HasAst|) $) "\\spad{autoCoerce(s)} returns the HasAst view of `s'. Left at the discretion of the compiler.") (((|CaseAst|) $) "\\spad{autoCoerce(s)} returns the CaseAst view of `s'. Left at the discretion of the compiler.") (((|ColonAst|) $) "\\spad{autoCoerce(s)} returns the ColoonAst view of `s'. Left at the discretion of the compiler.") (((|SuchThatAst|) $) "\\spad{autoCoerce(s)} returns the SuchThatAst view of `s'. Left at the discretion of the compiler.") (((|LetAst|) $) "\\spad{autoCoerce(s)} returns the LetAst view of `s'. Left at the discretion of the compiler.") (((|SequenceAst|) $) "\\spad{autoCoerce(s)} returns the SequenceAst view of `s'. Left at the discretion of the compiler.") (((|SegmentAst|) $) "\\spad{autoCoerce(s)} returns the SegmentAst view of `s'. Left at the discretion of the compiler.") (((|RestrictAst|) $) "\\spad{autoCoerce(s)} returns the RestrictAst view of `s'. Left at the discretion of the compiler.") (((|PretendAst|) $) "\\spad{autoCoerce(s)} returns the PretendAst view of `s'. Left at the discretion of the compiler.") (((|CoerceAst|) $) "\\spad{autoCoerce(s)} returns the CoerceAst view of `s'. Left at the discretion of the compiler.") (((|ReturnAst|) $) "\\spad{autoCoerce(s)} returns the ReturnAst view of `s'. Left at the discretion of the compiler.") (((|ExitAst|) $) "\\spad{autoCoerce(s)} returns the ExitAst view of `s'. Left at the discretion of the compiler.") (((|ConstructAst|) $) "\\spad{autoCoerce(s)} returns the ConstructAst view of `s'. Left at the discretion of the compiler.") (((|CollectAst|) $) "\\spad{autoCoerce(s)} returns the CollectAst view of `s'. Left at the discretion of the compiler.") (((|StepAst|) $) "\\spad{autoCoerce(s)} returns the InAst view of \\spad{s}. Left at the discretion of the compiler.") (((|InAst|) $) "\\spad{autoCoerce(s)} returns the InAst view of `s'. Left at the discretion of the compiler.") (((|WhileAst|) $) "\\spad{autoCoerce(s)} returns the WhileAst view of `s'. Left at the discretion of the compiler.") (((|RepeatAst|) $) "\\spad{autoCoerce(s)} returns the RepeatAst view of `s'. Left at the discretion of the compiler.") (((|IfAst|) $) "\\spad{autoCoerce(s)} returns the IfAst view of `s'. Left at the discretion of the compiler.") (((|MappingAst|) $) "\\spad{autoCoerce(s)} returns the MappingAst view of `s'. Left at the discretion of the compiler.") (((|AttributeAst|) $) "\\spad{autoCoerce(s)} returns the AttributeAst view of `s'. Left at the discretion of the compiler.") (((|SignatureAst|) $) "\\spad{autoCoerce(s)} returns the SignatureAst view of `s'. Left at the discretion of the compiler.") (((|CapsuleAst|) $) "\\spad{autoCoerce(s)} returns the CapsuleAst view of `s'. Left at the discretion of the compiler.") (((|JoinAst|) $) "\\spad{autoCoerce(s)} returns the \\spadype{JoinAst} view of of the AST object \\spad{s}. Left at the discretion of the compiler.") (((|CategoryAst|) $) "\\spad{autoCoerce(s)} returns the CategoryAst view of `s'. Left at the discretion of the compiler.") (((|WhereAst|) $) "\\spad{autoCoerce(s)} returns the WhereAst view of `s'. Left at the discretion of the compiler.") (((|MacroAst|) $) "\\spad{autoCoerce(s)} returns the MacroAst view of `s'. Left at the discretion of the compiler.") (((|DefinitionAst|) $) "\\spad{autoCoerce(s)} returns the DefinitionAst view of `s'. Left at the discretion of the compiler.") (((|ImportAst|) $) "\\spad{autoCoerce(s)} returns the ImportAst view of `s'. Left at the discretion of the compiler.")) (|case| (((|Boolean|) $ (|[\|\|]| (|Integer|))) "\\spad{s case Integer} holds if `s' represents an integer literal.") (((|Boolean|) $ (|[\|\|]| (|String|))) "\\spad{s case String} holds if `s' represents a string literal.") (((|Boolean|) $ (|[\|\|]| (|Identifier|))) "\\spad{s case Identifier} holds if `s' represents an identifier.") (((|Boolean|) $ (|[\|\|]| (|IsAst|))) "\\spad{s case IsAst} holds if `s' represents an is-expression.") (((|Boolean|) $ (|[\|\|]| (|HasAst|))) "\\spad{s case HasAst} holds if `s' represents a has-expression.") (((|Boolean|) $ (|[\|\|]| (|CaseAst|))) "\\spad{s case CaseAst} holds if `s' represents a case-expression.") (((|Boolean|) $ (|[\|\|]| (|ColonAst|))) "\\spad{s case ColonAst} holds if `s' represents a colon-expression.") (((|Boolean|) $ (|[\|\|]| (|SuchThatAst|))) "\\spad{s case SuchThatAst} holds if `s' represents a qualified-expression.") (((|Boolean|) $ (|[\|\|]| (|LetAst|))) "\\spad{s case LetAst} holds if `s' represents an assignment-expression.") (((|Boolean|) $ (|[\|\|]| (|SequenceAst|))) "\\spad{s case SequenceAst} holds if `s' represents a sequence-of-statements.") (((|Boolean|) $ (|[\|\|]| (|SegmentAst|))) "\\spad{s case SegmentAst} holds if `s' represents a segment-expression.") (((|Boolean|) $ (|[\|\|]| (|RestrictAst|))) "\\spad{s case RestrictAst} holds if `s' represents a restrict-expression.") (((|Boolean|) $ (|[\|\|]| (|PretendAst|))) "\\spad{s case PretendAst} holds if `s' represents a pretend-expression.") (((|Boolean|) $ (|[\|\|]| (|CoerceAst|))) "\\spad{s case ReturnAst} holds if `s' represents a coerce-expression.") (((|Boolean|) $ (|[\|\|]| (|ReturnAst|))) "\\spad{s case ReturnAst} holds if `s' represents a return-statement.") (((|Boolean|) $ (|[\|\|]| (|ExitAst|))) "\\spad{s case ExitAst} holds if `s' represents an exit-expression.") (((|Boolean|) $ (|[\|\|]| (|ConstructAst|))) "\\spad{s case ConstructAst} holds if `s' represents a list-expression.") (((|Boolean|) $ (|[\|\|]| (|CollectAst|))) "\\spad{s case CollectAst} holds if `s' represents a list-comprehension.") (((|Boolean|) $ (|[\|\|]| (|StepAst|))) "\\spad{s case StepAst} holds if \\spad{s} represents an arithmetic progression iterator.") (((|Boolean|) $ (|[\|\|]| (|InAst|))) "\\spad{s case InAst} holds if `s' represents a in-iterator") (((|Boolean|) $ (|[\|\|]| (|WhileAst|))) "\\spad{s case WhileAst} holds if `s' represents a while-iterator") (((|Boolean|) $ (|[\|\|]| (|RepeatAst|))) "\\spad{s case RepeatAst} holds if `s' represents an repeat-loop.") (((|Boolean|) $ (|[\|\|]| (|IfAst|))) "\\spad{s case IfAst} holds if `s' represents an if-statement.") (((|Boolean|) $ (|[\|\|]| (|MappingAst|))) "\\spad{s case MappingAst} holds if `s' represents a mapping type.") (((|Boolean|) $ (|[\|\|]| (|AttributeAst|))) "\\spad{s case AttributeAst} holds if `s' represents an attribute.") (((|Boolean|) $ (|[\|\|]| (|SignatureAst|))) "\\spad{s case SignatureAst} holds if `s' represents a signature export.") (((|Boolean|) $ (|[\|\|]| (|CapsuleAst|))) "\\spad{s case CapsuleAst} holds if `s' represents a domain capsule.") (((|Boolean|) $ (|[\|\|]| (|JoinAst|))) "\\spad{s case JoinAst} holds is the syntax object \\spad{s} denotes the join of several categories.") (((|Boolean|) $ (|[\|\|]| (|CategoryAst|))) "\\spad{s case CategoryAst} holds if `s' represents an unnamed category.") (((|Boolean|) $ (|[\|\|]| (|WhereAst|))) "\\spad{s case WhereAst} holds if `s' represents an expression with local definitions.") (((|Boolean|) $ (|[\|\|]| (|MacroAst|))) "\\spad{s case MacroAst} holds if `s' represents a macro definition.") (((|Boolean|) $ (|[\|\|]| (|DefinitionAst|))) "\\spad{s case DefinitionAst} holds if `s' represents a definition.") (((|Boolean|) $ (|[\|\|]| (|ImportAst|))) "\\spad{s case ImportAst} holds if `s' represents an `import' statement.")))
NIL
NIL
-(-1051)
+(-1053)
((|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
-(-1052)
+(-1054)
((|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
-(-1053 V C)
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((|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},{}\\spad{o2})} returns \\spad{true} iff \\axiom{value(\\spad{n1}) = value(\\spad{n2})} and \\axiom{\\spad{o2}(condition(\\spad{n1}),{}condition(\\spad{n2}))}")) (|infLex?| (((|Boolean|) $ $ (|Mapping| (|Boolean|) |#1| |#1|) (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{infLex?(\\spad{n1},{}\\spad{n2},{}\\spad{o1},{}\\spad{o2})} returns \\spad{true} iff \\axiom{\\spad{o1}(value(\\spad{n1}),{}value(\\spad{n2}))} or \\axiom{value(\\spad{n1}) = value(\\spad{n2})} and \\axiom{\\spad{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},{}lt)} returns the same as \\axiom{[construct(\\spad{v},{}\\spad{t}) for \\spad{t} in lt]}") (((|List| $) (|List| (|Record| (|:| |val| |#1|) (|:| |tower| |#2|)))) "\\axiom{construct(lvt)} returns the same as \\axiom{[construct(vt.val,{}vt.tower) for vt in lvt]}") (($ (|Record| (|:| |val| |#1|) (|:| |tower| |#2|))) "\\axiom{construct(vt)} returns the same as \\axiom{construct(vt.val,{}vt.tower)}") (($ |#1| |#2|) "\\axiom{construct(\\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
-(-1054 V C)
+(-1056 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,{}ls,{}sub?)} returns \\axiom{a} where the children list of \\axiom{\\spad{l}} has been set to \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in 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,{}ls)} returns \\axiom{a} where the children list of \\axiom{\\spad{l}} has been set to \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in 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|))) $) "\\axiom{result(a)} where \\axiom{ls} is the leaves list of \\axiom{a} returns \\axiom{[[value(\\spad{s}),{}condition(\\spad{s})]\\$VT for \\spad{s} in ls]} if the computations are terminated in \\axiom{a} else an error is produced.")) (|conditions| (((|List| |#2|) $) "\\axiom{conditions(a)} returns the list of the conditions of the leaves of a")) (|construct| (($ |#1| |#2| |#1| (|List| |#2|)) "\\axiom{construct(\\spad{v1},{}\\spad{t},{}\\spad{v2},{}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 ls]}.") (($ |#1| |#2| (|List| (|SplittingNode| |#1| |#2|))) "\\axiom{construct(\\spad{v},{}\\spad{t},{}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 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") $) "\\axiom{extractSplittingLeaf(a)} returns the left most leaf (as a tree) whose status is \\spad{false} if any,{} else \"failed\" is returned.")))
-((-3992 . T) (-3993 . T))
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-(-1055 |ndim| R)
+((-3996 . T) (-3997 . T))
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+(-1057 |ndim| R)
((|constructor| (NIL "\\spadtype{SquareMatrix} is a matrix domain of square matrices,{} where the number of rows (= number of columns) is a parameter of the type.")) (|unitsKnown| ((|attribute|) "the invertible matrices are simply the matrices whose determinants are units in the Ring \\spad{R}.")) (|central| ((|attribute|) "the elements of the Ring \\spad{R},{} viewed as diagonal matrices,{} commute with all matrices and,{} indeed,{} are the only matrices which commute with all matrices.")) (|squareMatrix| (($ (|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}.")))
-((-3989 . T) (-3981 |has| |#2| (-6 (-3994 "*"))) (-3992 . T) (-3986 . T) (-3987 . T))
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-(-1056 S)
+((-3993 . T) (-3985 |has| |#2| (-6 (-3998 "*"))) (-3996 . T) (-3990 . T) (-3991 . T))
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+(-1058 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{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{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\",{}\"*\")} 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}) == 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|) $ $) "\\spad{prefix?(s,t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) == reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case.")))
NIL
NIL
-(-1057)
+(-1059)
((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|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{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{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\",{}\"*\")} 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}) == 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|) $ $) "\\spad{prefix?(s,t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) == reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case.")))
-((-3993 . T) (-3992 . T))
+((-3997 . T) (-3996 . T))
NIL
-(-1058 R E V P TS)
+(-1060 R E V P TS)
((|constructor| (NIL "A package providing a new algorithm for solving polynomial systems by means of regular chains. Two ways of solving are provided: in the sense of Zariski closure (like in Kalkbrener's algorithm) or in the sense of the regular zeros (like in Wu,{} Wang or Lazard- Moreno methods). This algorithm is valid for 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{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
-(-1059 R E V P)
+(-1061 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(lp,{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|internalZeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalZeroSetSplit(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(lp,{}\\spad{b1},{}\\spad{b2}.\\spad{b3},{}\\spad{b4})} is an internal subroutine,{} exported only for developement.") (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(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},{}ts,{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement.")))
-((-3993 . T) (-3992 . T))
-((-12 (|HasCategory| |#4| (QUOTE (-1013))) (|HasCategory| |#4| (|%list| (QUOTE -259) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-554 (-473)))) (|HasCategory| |#4| (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#3| (QUOTE (-317))) (|HasCategory| |#4| (QUOTE (-553 (-773)))) (|HasCategory| |#4| (QUOTE (-72))))
-(-1060)
+((-3997 . T) (-3996 . T))
+((-12 (|HasCategory| |#4| (QUOTE (-1015))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-555 (-474)))) (|HasCategory| |#4| (QUOTE (-1015))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#3| (QUOTE (-318))) (|HasCategory| |#4| (QUOTE (-554 (-774)))) (|HasCategory| |#4| (QUOTE (-72))))
+(-1062)
((|constructor| (NIL "The category of all semiring structures,{} \\spadignore{e.g.} triples (\\spad{D},{}+,{}*) such that (\\spad{D},{}+) is an Abelian monoid and (\\spad{D},{}*) is a monoid with the following laws:")))
NIL
NIL
-(-1061 S)
+(-1063 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}.")))
-((-3992 . T) (-3993 . T))
-((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1013))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-72))))
-(-1062 A S)
+((-3996 . T) (-3997 . T))
+((-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1015))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| |#1| (QUOTE (-554 (-774)))) (|HasCategory| |#1| (QUOTE (-72))))
+(-1064 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}.")) (|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.")) (|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
-(-1063 S)
+(-1065 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}.")) (|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.")) (|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
-(-1064 |Key| |Ent| |dent|)
+(-1066 |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.")))
-((-3993 . T))
-((-12 (|HasCategory| (-2 (|:| -3857 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -259) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3857) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3857 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3857 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3857 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3857 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| (-2 (|:| -3857 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-553 (-773))))) (|HasCategory| (-2 (|:| -3857 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-473)))) (-12 (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (|%list| (QUOTE -259) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-757))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3857 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3857 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3857 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3857 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013))))
-(-1065)
+((-3997 . T))
+((-12 (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3861) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1015)))) (OR (|HasCategory| |#2| (QUOTE (-1015))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1015)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1015))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1015)))) (OR (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-774)))) (|HasCategory| |#2| (QUOTE (-554 (-774))))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-555 (-474)))) (-12 (|HasCategory| |#2| (QUOTE (-1015))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-758))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-1015))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-554 (-774)))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-774)))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1015))))
+(-1067)
((|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 non-fiinite domains,{} repeated application of \\spadfun{nextItem} is not required to reach all possible domain elements starting from any initial element. \\blankline")) (|nextItem| (((|Maybe| $) $) "\\spad{nextItem(x)} returns the next item,{} or \\spad{failed} if domain is exhausted.")) (|init| (($) "\\spad{init()} chooses an initial object for stepping.")))
NIL
NIL
-(-1066)
+(-1068)
((|constructor| (NIL "This domain represents an arithmetic progression iterator syntax.")) (|step| (((|SpadAst|) $) "\\spad{step(i)} returns the Spad AST denoting the step of the arithmetic progression represented by the iterator \\spad{i}.")) (|upperBound| (((|Maybe| (|SpadAst|)) $) "If the set of values assumed by the iteration variable is bounded from above,{} \\spad{upperBound(i)} returns the upper bound. Otherwise,{} its returns \\spad{nothing}.")) (|lowerBound| (((|SpadAst|) $) "\\spad{lowerBound(i)} returns the lower bound on the values assumed by the iteration variable.")) (|iterationVar| (((|Identifier|) $) "\\spad{iterationVar(i)} returns the name of the iterating variable of the arithmetic progression iterator \\spad{i}.")))
NIL
NIL
-(-1067 |Coef|)
+(-1069 |Coef|)
((|constructor| (NIL "This package computes infinite products of Taylor series over an integral domain of characteristic 0. Here Taylor series are represented by streams of Taylor coefficients.")) (|generalInfiniteProduct| (((|Stream| |#1|) (|Stream| |#1|) (|Integer|) (|Integer|)) "\\spad{generalInfiniteProduct(f(x),a,d)} computes \\spad{product(n=a,a+d,a+2*d,...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|oddInfiniteProduct| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{oddInfiniteProduct(f(x))} computes \\spad{product(n=1,3,5...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|evenInfiniteProduct| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{evenInfiniteProduct(f(x))} computes \\spad{product(n=2,4,6...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|infiniteProduct| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{infiniteProduct(f(x))} computes \\spad{product(n=1,2,3...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")))
NIL
NIL
-(-1068 S)
+(-1070 S)
((|constructor| (NIL "A stream is an implementation of an infinite sequence using a list of terms that have been computed and a function closure to compute additional terms when needed.")) (|filterUntil| (($ (|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.")))
-((-3993 . T))
-((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1013))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-554 (-473)))) (|HasCategory| (-484) (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-72))))
-(-1069 S)
+((-3997 . T))
+((-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1015))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| |#1| (QUOTE (-554 (-774)))) (|HasCategory| |#1| (QUOTE (-555 (-474)))) (|HasCategory| (-485) (QUOTE (-758))) (|HasCategory| |#1| (QUOTE (-72))))
+(-1071 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
-(-1070 A B)
+(-1072 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
-(-1071 A B C)
+(-1073 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
-(-1072)
+(-1074)
((|constructor| (NIL "This is the domain of character strings.")) (|string| (($ (|Identifier|)) "\\spad{string id} is the string representation of the identifier \\spad{id}") (($ (|DoubleFloat|)) "\\spad{string f} returns the decimal representation of \\spad{f} in a string") (($ (|Integer|)) "\\spad{string i} returns the decimal representation of \\spad{i} in a string")))
-((-3993 . T) (-3992 . T))
-((OR (-12 (|HasCategory| (-117) (QUOTE (-259 (-117)))) (|HasCategory| (-117) (QUOTE (-757)))) (-12 (|HasCategory| (-117) (QUOTE (-259 (-117)))) (|HasCategory| (-117) (QUOTE (-1013))))) (|HasCategory| (-117) (QUOTE (-553 (-773)))) (|HasCategory| (-117) (QUOTE (-554 (-473)))) (OR (|HasCategory| (-117) (QUOTE (-757))) (|HasCategory| (-117) (QUOTE (-1013)))) (|HasCategory| (-117) (QUOTE (-757))) (OR (|HasCategory| (-117) (QUOTE (-72))) (|HasCategory| (-117) (QUOTE (-757))) (|HasCategory| (-117) (QUOTE (-1013)))) (|HasCategory| (-484) (QUOTE (-757))) (|HasCategory| (-117) (QUOTE (-1013))) (|HasCategory| (-117) (QUOTE (-72))) (-12 (|HasCategory| (-117) (QUOTE (-259 (-117)))) (|HasCategory| (-117) (QUOTE (-1013)))))
-(-1073 |Entry|)
+((-3997 . T) (-3996 . T))
+((OR (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-758)))) (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-1015))))) (|HasCategory| (-117) (QUOTE (-554 (-774)))) (|HasCategory| (-117) (QUOTE (-555 (-474)))) (OR (|HasCategory| (-117) (QUOTE (-758))) (|HasCategory| (-117) (QUOTE (-1015)))) (|HasCategory| (-117) (QUOTE (-758))) (OR (|HasCategory| (-117) (QUOTE (-72))) (|HasCategory| (-117) (QUOTE (-758))) (|HasCategory| (-117) (QUOTE (-1015)))) (|HasCategory| (-485) (QUOTE (-758))) (|HasCategory| (-117) (QUOTE (-1015))) (|HasCategory| (-117) (QUOTE (-72))) (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-1015)))))
+(-1075 |Entry|)
((|constructor| (NIL "This domain provides tables where the keys are strings. A specialized hash function for strings is used.")))
-((-3992 . T) (-3993 . T))
-((-12 (|HasCategory| (-2 (|:| -3857 (-1072)) (|:| |entry| |#1|)) (|%list| (QUOTE -259) (|%list| (QUOTE -2) (QUOTE (|:| -3857 (-1072))) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -3857 (-1072)) (|:| |entry| |#1|)) (QUOTE (-1013)))) (OR (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3857 (-1072)) (|:| |entry| |#1|)) (QUOTE (-1013)))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3857 (-1072)) (|:| |entry| |#1|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3857 (-1072)) (|:| |entry| |#1|)) (QUOTE (-1013)))) (OR (|HasCategory| (-2 (|:| -3857 (-1072)) (|:| |entry| |#1|)) (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-553 (-773))))) (|HasCategory| (-2 (|:| -3857 (-1072)) (|:| |entry| |#1|)) (QUOTE (-554 (-473)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -3857 (-1072)) (|:| |entry| |#1|)) (QUOTE (-1013))) (|HasCategory| (-1072) (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1013))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3857 (-1072)) (|:| |entry| |#1|)) (QUOTE (-72)))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3857 (-1072)) (|:| |entry| |#1|)) (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3857 (-1072)) (|:| |entry| |#1|)) (QUOTE (-72))))
-(-1074 A)
+((-3996 . T) (-3997 . T))
+((-12 (|HasCategory| (-2 (|:| -3861 (-1074)) (|:| |entry| |#1|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (QUOTE (|:| -3861 (-1074))) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -3861 (-1074)) (|:| |entry| |#1|)) (QUOTE (-1015)))) (OR (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| (-2 (|:| -3861 (-1074)) (|:| |entry| |#1|)) (QUOTE (-1015)))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| (-2 (|:| -3861 (-1074)) (|:| |entry| |#1|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 (-1074)) (|:| |entry| |#1|)) (QUOTE (-1015)))) (OR (|HasCategory| (-2 (|:| -3861 (-1074)) (|:| |entry| |#1|)) (QUOTE (-554 (-774)))) (|HasCategory| |#1| (QUOTE (-554 (-774))))) (|HasCategory| (-2 (|:| -3861 (-1074)) (|:| |entry| |#1|)) (QUOTE (-555 (-474)))) (-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -3861 (-1074)) (|:| |entry| |#1|)) (QUOTE (-1015))) (|HasCategory| (-1074) (QUOTE (-758))) (|HasCategory| |#1| (QUOTE (-1015))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 (-1074)) (|:| |entry| |#1|)) (QUOTE (-72)))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-554 (-774)))) (|HasCategory| (-2 (|:| -3861 (-1074)) (|:| |entry| |#1|)) (QUOTE (-554 (-774)))) (|HasCategory| (-2 (|:| -3861 (-1074)) (|:| |entry| |#1|)) (QUOTE (-72))))
+(-1076 A)
((|constructor| (NIL "StreamTaylorSeriesOperations implements Taylor series arithmetic,{} where a Taylor series is represented by a stream of its coefficients.")) (|power| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{power(a,f)} returns the power series \\spad{f} raised to the power \\spad{a}.")) (|lazyGintegrate| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyGintegrate(f,r,g)} is used for fixed point computations.")) (|mapdiv| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapdiv([a0,a1,..],[b0,b1,..])} returns \\spad{[a0/b0,a1/b1,..]}.")) (|powern| (((|Stream| |#1|) (|Fraction| (|Integer|)) (|Stream| |#1|)) "\\spad{powern(r,f)} raises power series \\spad{f} to the power \\spad{r}.")) (|nlde| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{nlde(u)} solves a first order non-linear differential equation described by \\spad{u} of the form \\spad{[[b<0,0>,b<0,1>,...],[b<1,0>,b<1,1>,.],...]}. the differential equation has the form \\spad{y' = sum(i=0 to infinity,j=0 to infinity,b<i,j>*(x**i)*(y**j))}.")) (|lazyIntegrate| (((|Stream| |#1|) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyIntegrate(r,f)} is a local function used for fixed point computations.")) (|integrate| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{integrate(r,a)} returns the integral of the power series \\spad{a} with respect to the power series variableintegration where \\spad{r} denotes the constant of integration. Thus \\spad{integrate(a,[a0,a1,a2,...]) = [a,a0,a1/2,a2/3,...]}.")) (|invmultisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{invmultisect(a,b,st)} substitutes \\spad{x**((a+b)*n)} for \\spad{x**n} and multiplies by \\spad{x**b}.")) (|multisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{multisect(a,b,st)} selects the coefficients of \\spad{x**((a+b)*n+a)},{} and changes them to \\spad{x**n}.")) (|generalLambert| (((|Stream| |#1|) (|Stream| |#1|) (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),a,d)} returns \\spad{f(x**a) + f(x**(a + d)) + f(x**(a + 2 d)) + ...}. \\spad{f(x)} should have zero constant coefficient and \\spad{a} and \\spad{d} should be positive.")) (|evenlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{evenlambert(st)} computes \\spad{f(x**2) + f(x**4) + f(x**6) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1,{} then \\spad{prod(f(x**(2*n)),n=1..infinity) = exp(evenlambert(log(f(x))))}.")) (|oddlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{oddlambert(st)} computes \\spad{f(x) + f(x**3) + f(x**5) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f}(\\spad{x}) is a power series with constant coefficient 1 then \\spad{prod(f(x**(2*n-1)),n=1..infinity) = exp(oddlambert(log(f(x))))}.")) (|lambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lambert(st)} computes \\spad{f(x) + f(x**2) + f(x**3) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1 then \\spad{prod(f(x**n),n = 1..infinity) = exp(lambert(log(f(x))))}.")) (|addiag| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{addiag(x)} performs diagonal addition of a stream of streams. if \\spad{x} = \\spad{[[a<0,0>,a<0,1>,..],[a<1,0>,a<1,1>,..],[a<2,0>,a<2,1>,..],..]} and \\spad{addiag(x) = [b<0,b<1>,...], then b<k> = sum(i+j=k,a<i,j>)}.")) (|revert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{revert(a)} computes the inverse of a power series \\spad{a} with respect to composition. the series should have constant coefficient 0 and first order coefficient should be invertible.")) (|lagrange| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lagrange(g)} produces the power series for \\spad{f} where \\spad{f} is implicitly defined as \\spad{f(z) = z*g(f(z))}.")) (|compose| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{compose(a,b)} composes the power series \\spad{a} with the power series \\spad{b}.")) (|eval| (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{eval(a,r)} returns a stream of partial sums of the power series \\spad{a} evaluated at the power series variable equal to \\spad{r}.")) (|coerce| (((|Stream| |#1|) |#1|) "\\spad{coerce(r)} converts a ring element \\spad{r} to a stream with one element.")) (|gderiv| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) (|Stream| |#1|)) "\\spad{gderiv(f,[a0,a1,a2,..])} returns \\spad{[f(0)*a0,f(1)*a1,f(2)*a2,..]}.")) (|deriv| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{deriv(a)} returns the derivative of the power series with respect to the power series variable. Thus \\spad{deriv([a0,a1,a2,...])} returns \\spad{[a1,2 a2,3 a3,...]}.")) (|mapmult| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapmult([a0,a1,..],[b0,b1,..])} returns \\spad{[a0*b0,a1*b1,..]}.")) (|int| (((|Stream| |#1|) |#1|) "\\spad{int(r)} returns [\\spad{r},{}\\spad{r+1},{}\\spad{r+2},{}...],{} where \\spad{r} is a ring element.")) (|oddintegers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{oddintegers(n)} returns \\spad{[n,n+2,n+4,...]}.")) (|integers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{integers(n)} returns \\spad{[n,n+1,n+2,...]}.")) (|monom| (((|Stream| |#1|) |#1| (|Integer|)) "\\spad{monom(deg,coef)} is a monomial of degree \\spad{deg} with coefficient \\spad{coef}.")) (|recip| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|)) "\\spad{recip(a)} returns the power series reciprocal of \\spad{a},{} or \"failed\" if not possible.")) (/ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a / b} returns the power series quotient of \\spad{a} by \\spad{b}. An error message is returned if \\spad{b} is not invertible. This function is used in fixed point computations.")) (|exquo| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|) (|Stream| |#1|)) "\\spad{exquo(a,b)} returns the power series quotient of \\spad{a} by \\spad{b},{} if the quotient exists,{} and \"failed\" otherwise")) (* (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{a * r} returns the power series scalar multiplication of \\spad{a} by 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 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 (-311))) (|HasCategory| |#1| (QUOTE (-38 (-347 (-484))))))
-(-1075 |Coef|)
+((|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-38 (-348 (-485))))))
+(-1077 |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
-(-1076 |Coef|)
+(-1078 |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
-(-1077 R UP)
+(-1079 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 (-257))))
-(-1078 |n| R)
+((|HasCategory| |#1| (QUOTE (-258))))
+(-1080 |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'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'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| $)) "\\spad{merge(ls)} a list of subspaces,{} \\spad{ls},{} into one subspace.") (($ $ $) "\\spad{merge(s1,s2)} the subspaces \\spad{s1} and \\spad{s2} into a single subspace.")) (|deepCopy| (($ $) "\\spad{deepCopy(x)} \\undocumented")) (|shallowCopy| (($ $) "\\spad{shallowCopy(x)} \\undocumented")) (|numberOfChildren| (((|NonNegativeInteger|) $) "\\spad{numberOfChildren(x)} \\undocumented")) (|children| (((|List| $) $) "\\spad{children(x)} \\undocumented")) (|child| (($ $ (|NonNegativeInteger|)) "\\spad{child(x,n)} \\undocumented")) (|birth| (($ $) "\\spad{birth(x)} \\undocumented")) (|subspace| (($) "\\spad{subspace()} \\undocumented")) (|new| (($) "\\spad{new()} \\undocumented")) (|internal?| (((|Boolean|) $) "\\spad{internal?(x)} \\undocumented")) (|root?| (((|Boolean|) $) "\\spad{root?(x)} \\undocumented")) (|leaf?| (((|Boolean|) $) "\\spad{leaf?(x)} \\undocumented")))
NIL
NIL
-(-1079 S1 S2)
+(-1081 S1 S2)
((|constructor| (NIL "This domain implements \"such that\" forms")) (|rhs| ((|#2| $) "\\spad{rhs(f)} returns the right side of \\spad{f}")) (|lhs| ((|#1| $) "\\spad{lhs(f)} returns the left side of \\spad{f}")) (|construct| (($ |#1| |#2|) "\\spad{construct(s,t)} makes a form s:t")))
NIL
NIL
-(-1080)
+(-1082)
((|constructor| (NIL "This domain represents the filter iterator syntax.")) (|predicate| (((|SpadAst|) $) "\\spad{predicate(e)} returns the syntax object for the predicate in the filter iterator syntax `e'.")))
NIL
NIL
-(-1081 |Coef| |var| |cen|)
+(-1083 |Coef| |var| |cen|)
((|constructor| (NIL "Sparse Laurent series in one variable \\indented{2}{\\spadtype{SparseUnivariateLaurentSeries} is a domain representing Laurent} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{SparseUnivariateLaurentSeries(Integer,x,3)} represents Laurent} \\indented{2}{series in \\spad{(x - 3)} with integer coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Laurent series.")))
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(QUOTE (-311))) (|HasCategory| (-1088 |#1| |#2| |#3|) (QUOTE (-257)))) (|HasCategory| (-1088 |#1| |#2| |#3|) (QUOTE (-822))) (|HasCategory| (-1088 |#1| |#2| |#3|) (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-118))) (OR (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| (-1088 |#1| |#2| |#3|) (QUOTE (-741)))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| (-1088 |#1| |#2| |#3|) (QUOTE (-822)))) (|HasCategory| |#1| (QUOTE (-495)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| (-1088 |#1| |#2| |#3|) (QUOTE (-741)))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| (-1088 |#1| |#2| |#3|) (QUOTE (-822)))) (|HasCategory| |#1| (QUOTE (-146)))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| (-1088 |#1| |#2| |#3|) (QUOTE (-812 (-1089))))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| (-1088 |#1| |#2| |#3|) (QUOTE (-189)))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| (-1088 |#1| |#2| |#3|) (QUOTE (-757)))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-1088 |#1| |#2| |#3|) (QUOTE (-822)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| (-1088 |#1| |#2| |#3|) (QUOTE (-118)))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-1088 |#1| |#2| |#3|) (QUOTE (-822)))) (|HasCategory| |#1| (QUOTE (-118)))))
-(-1082 R -3091)
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(QUOTE (-312))) (|HasCategory| (-1090 |#1| |#2| |#3|) (QUOTE (-258)))) (|HasCategory| (-1090 |#1| |#2| |#3|) (QUOTE (-823))) (|HasCategory| (-1090 |#1| |#2| |#3|) (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-118))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1090 |#1| |#2| |#3|) (QUOTE (-742)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1090 |#1| |#2| |#3|) (QUOTE (-823)))) (|HasCategory| |#1| (QUOTE (-496)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1090 |#1| |#2| |#3|) (QUOTE (-742)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1090 |#1| |#2| |#3|) (QUOTE (-823)))) (|HasCategory| |#1| (QUOTE (-146)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1090 |#1| |#2| |#3|) (QUOTE (-813 (-1091))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1090 |#1| |#2| |#3|) (QUOTE (-189)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1090 |#1| |#2| |#3|) (QUOTE (-758)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-1090 |#1| |#2| |#3|) (QUOTE (-823)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1090 |#1| |#2| |#3|) (QUOTE (-118)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-1090 |#1| |#2| |#3|) (QUOTE (-823)))) (|HasCategory| |#1| (QUOTE (-118)))))
+(-1084 R -3094)
((|constructor| (NIL "computes sums of top-level expressions.")) (|sum| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{sum(f(n), n = a..b)} returns \\spad{f}(a) + \\spad{f}(\\spad{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
-(-1083 R)
+(-1085 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)}.") (((|Union| (|Fraction| (|Polynomial| |#1|)) (|Expression| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{sum(a(n), n)} returns \\spad{A} which is the indefinite sum of \\spad{a} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{A(n+1) - A(n) = a(n)}.") (((|Fraction| (|Polynomial| |#1|)) (|Polynomial| |#1|) (|Symbol|)) "\\spad{sum(a(n), n)} returns \\spad{A} which is the indefinite sum of \\spad{a} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{A(n+1) - A(n) = a(n)}.")))
NIL
NIL
-(-1084 R)
+(-1086 R)
((|constructor| (NIL "This domain represents univariate polynomials over arbitrary (not necessarily commutative) coefficient rings. The variable is unspecified so that the variable displays as \\spad{?} on output. If it is necessary to specify the variable name,{} use type \\spadtype{UnivariatePolynomial}. The representation is sparse in the sense that only non-zero terms are represented.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#1| $) "\\spad{fmecg(p1,e,r,p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}")) (|outputForm| (((|OutputForm|) $ (|OutputForm|)) "\\spad{outputForm(p,var)} converts the SparseUnivariatePolynomial \\spad{p} to an output form (see \\spadtype{OutputForm}) printed as a polynomial in the output form variable.")))
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-(-1085 R S)
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+(-1087 R S)
((|constructor| (NIL "This package lifts a mapping from coefficient rings \\spad{R} to \\spad{S} to a mapping from sparse univariate polynomial over \\spad{R} to a sparse univariate polynomial over \\spad{S}. Note that the mapping is assumed to send zero to zero,{} since it will only be applied to the non-zero coefficients of the polynomial.")) (|map| (((|SparseUnivariatePolynomial| |#2|) (|Mapping| |#2| |#1|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{map(func, poly)} creates a new polynomial by applying \\spad{func} to every non-zero coefficient of the polynomial poly.")))
NIL
NIL
-(-1086 E OV R P)
+(-1088 E OV R P)
((|constructor| (NIL "\\indented{1}{SupFractionFactorize} contains the factor function for univariate polynomials over the quotient field of a ring \\spad{S} such that the package MultivariateFactorize works for \\spad{S}")) (|squareFree| (((|Factored| (|SparseUnivariatePolynomial| (|Fraction| |#4|))) (|SparseUnivariatePolynomial| (|Fraction| |#4|))) "\\spad{squareFree(p)} returns the square-free factorization of the univariate polynomial \\spad{p} with coefficients which are fractions of polynomials over \\spad{R}. Each factor has no repeated roots and the factors are pairwise relatively prime.")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| (|Fraction| |#4|))) (|SparseUnivariatePolynomial| (|Fraction| |#4|))) "\\spad{factor(p)} factors the univariate polynomial \\spad{p} with coefficients which are fractions of polynomials over \\spad{R}.")))
NIL
NIL
-(-1087 |Coef| |var| |cen|)
+(-1089 |Coef| |var| |cen|)
((|constructor| (NIL "Sparse Puiseux series in one variable \\indented{2}{\\spadtype{SparseUnivariatePuiseuxSeries} 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{SparseUnivariatePuiseuxSeries(Integer,x,3)} represents Puiseux} \\indented{2}{series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")))
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-(-1088 |Coef| |var| |cen|)
+(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3994 |has| |#1| (-312)) (-3988 |has| |#1| (-312)) (-3990 . T) (-3991 . T) (-3993 . T))
+((|HasCategory| |#1| (QUOTE (-38 (-348 (-485))))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-811 (-1091)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -348) (QUOTE (-485))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -348) (QUOTE (-485))) (|devaluate| |#1|)))) (|HasCategory| (-348 (-485)) (QUOTE (-1027))) (|HasCategory| |#1| (QUOTE (-312))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-496)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-496)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -348) (QUOTE (-485)))))) (|HasSignature| |#1| (|%list| (QUOTE -3947) (|%list| (|devaluate| |#1|) (QUOTE (-1091)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -348) (QUOTE (-485)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-348 (-485))))) (|HasCategory| |#1| (QUOTE (-29 (-485)))) (|HasCategory| |#1| (QUOTE (-873))) (|HasCategory| |#1| (QUOTE (-1116)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-348 (-485))))) (|HasSignature| |#1| (|%list| (QUOTE -3813) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1091))))) (|HasSignature| |#1| (|%list| (QUOTE -3083) (|%list| (|%list| (QUOTE -585) (QUOTE (-1091))) (|devaluate| |#1|)))))))
+(-1090 |Coef| |var| |cen|)
((|constructor| (NIL "Sparse Taylor series in one variable \\indented{2}{\\spadtype{SparseUnivariateTaylorSeries} is a domain representing Taylor} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spadtype{SparseUnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor} \\indented{2}{series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x),x)} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|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}.")))
-(((-3994 "*") |has| |#1| (-146)) (-3985 |has| |#1| (-495)) (-3986 . T) (-3987 . T) (-3989 . T))
-((|HasCategory| |#1| (QUOTE (-38 (-347 (-484))))) (|HasCategory| |#1| (QUOTE (-495))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-495)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-810 (-1089)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-695)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-695)) (|devaluate| |#1|)))) (|HasCategory| (-695) (QUOTE (-1025))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-695))))) (|HasSignature| |#1| (|%list| (QUOTE -3943) (|%list| (|devaluate| |#1|) (QUOTE (-1089)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-695))))) (|HasCategory| |#1| (QUOTE (-311))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-347 (-484))))) (|HasCategory| |#1| (QUOTE (-29 (-484)))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1114)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-347 (-484))))) (|HasSignature| |#1| (|%list| (QUOTE -3809) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1089))))) (|HasSignature| |#1| (|%list| (QUOTE -3080) (|%list| (|%list| (QUOTE -584) (QUOTE (-1089))) (|devaluate| |#1|)))))))
-(-1089)
+(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3990 . T) (-3991 . T) (-3993 . T))
+((|HasCategory| |#1| (QUOTE (-38 (-348 (-485))))) (|HasCategory| |#1| (QUOTE (-496))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-811 (-1091)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-696)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-696)) (|devaluate| |#1|)))) (|HasCategory| (-696) (QUOTE (-1027))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-696))))) (|HasSignature| |#1| (|%list| (QUOTE -3947) (|%list| (|devaluate| |#1|) (QUOTE (-1091)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-696))))) (|HasCategory| |#1| (QUOTE (-312))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-348 (-485))))) (|HasCategory| |#1| (QUOTE (-29 (-485)))) (|HasCategory| |#1| (QUOTE (-873))) (|HasCategory| |#1| (QUOTE (-1116)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-348 (-485))))) (|HasSignature| |#1| (|%list| (QUOTE -3813) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1091))))) (|HasSignature| |#1| (|%list| (QUOTE -3083) (|%list| (|%list| (QUOTE -585) (QUOTE (-1091))) (|devaluate| |#1|)))))))
+(-1091)
((|constructor| (NIL "Basic and scripted symbols.")) (|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}([\\spad{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
-(-1090 R)
+(-1092 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
-(-1091 R)
+(-1093 R)
((|constructor| (NIL "This domain implements symmetric polynomial")))
-(((-3994 "*") |has| |#1| (-146)) (-3985 |has| |#1| (-495)) (-3990 |has| |#1| (-6 -3990)) (-3986 . T) (-3987 . T) (-3989 . T))
-((|HasCategory| |#1| (QUOTE (-38 (-347 (-484))))) (|HasCategory| |#1| (QUOTE (-495))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-495)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (OR (|HasCategory| |#1| (QUOTE (-38 (-347 (-484))))) (|HasCategory| |#1| (QUOTE (-951 (-347 (-484)))))) (|HasCategory| |#1| (QUOTE (-951 (-347 (-484))))) (|HasCategory| |#1| (QUOTE (-951 (-484)))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-389))) (-12 (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| (-885) (QUOTE (-104)))) (|HasAttribute| |#1| (QUOTE -3990)))
-(-1092)
+(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3994 |has| |#1| (-6 -3994)) (-3990 . T) (-3991 . T) (-3993 . T))
+((|HasCategory| |#1| (QUOTE (-38 (-348 (-485))))) (|HasCategory| |#1| (QUOTE (-496))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (OR (|HasCategory| |#1| (QUOTE (-38 (-348 (-485))))) (|HasCategory| |#1| (QUOTE (-952 (-348 (-485)))))) (|HasCategory| |#1| (QUOTE (-952 (-348 (-485))))) (|HasCategory| |#1| (QUOTE (-952 (-485)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-390))) (-12 (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| (-886) (QUOTE (-104)))) (|HasAttribute| |#1| (QUOTE -3994)))
+(-1094)
((|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| #1="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| #1#))) "\\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| #1#))) "\\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| #1#)) $) "\\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
-(-1093)
+(-1095)
((|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
-(-1094)
+(-1096)
((|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 `x' really is a String") (((|Boolean|) $ (|[\|\|]| (|Identifier|))) "\\spad{x case Identifier} is \\spad{true} if `x' really is an Identifier") (((|Boolean|) $ (|[\|\|]| (|DoubleFloat|))) "\\spad{x case DoubleFloat} is \\spad{true} if `x' really is a DoubleFloat") (((|Boolean|) $ (|[\|\|]| (|Integer|))) "\\spad{x case Integer} is \\spad{true} if `x' really is an Integer")) (|compound?| (((|Boolean|) $) "\\spad{compound? x} is \\spad{true} when `x' is not an atomic syntax.")) (|getOperands| (((|List| $) $) "\\spad{getOperands(x)} returns the list of operands to the operator in `x'.")) (|getOperator| (((|Union| (|Integer|) (|DoubleFloat|) (|Identifier|) (|String|) $) $) "\\spad{getOperator(x)} returns the operator,{} or tag,{} of the syntax `x'. The value returned is itself a syntax if `x' really is an application of a function symbol as opposed to being an atomic ground term.")) (|nil?| (((|Boolean|) $) "\\spad{nil?(s)} is \\spad{true} when `s' is a syntax for the constant nil.")) (|buildSyntax| (($ $ (|List| $)) "\\spad{buildSyntax(op, [a1, ..., an])} builds a syntax object for \\spad{op}(\\spad{a1},{}...,{}an).") (($ (|Identifier|) (|List| $)) "\\spad{buildSyntax(op, [a1, ..., an])} builds a syntax object for \\spad{op}(\\spad{a1},{}...,{}an).")) (|autoCoerce| (((|String|) $) "\\spad{autoCoerce(s)} forcibly extracts a string value from the syntax `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 `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 `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 `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 `s'.") (((|Identifier|) $) "\\spad{coerce(s)} extracts an identifier from the syntax `s'.") (((|DoubleFloat|) $) "\\spad{coerce(s)} extracts a float value from the syntax `s'.") (((|Integer|) $) "\\spad{coerce(s)} extracts and integer value from the syntax `s'")) (|convert| (($ (|SExpression|)) "\\spad{convert(s)} converts an \\spad{s}-expression to Syntax. Note,{} when `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|) $) "\\spad{convert(s)} returns the \\spad{s}-expression representation of a syntax.")))
NIL
NIL
-(-1095 N)
+(-1097 N)
((|constructor| (NIL "This domain implements sized (signed) integer datatypes parameterized by the precision (or width) of the underlying representation. The intent is that they map directly to the hosting hardware natural integer datatypes. Consequently,{} natural values for \\spad{N} are: 8,{} 16,{} 32,{} 64,{} etc. These datatypes are mostly useful for system programming tasks,{} \\spadignore{i.e.} interfacting with the hosting operating system,{} reading/writing external binary format files.")) (|sample| (($) "\\spad{sample} gives a sample datum of this type.")))
NIL
NIL
-(-1096 N)
+(-1098 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| (($) "\\spad{sample} gives a sample datum of type Byte.")) (|bitior| (($ $ $) "\\spad{bitior(x,y)} returns the bitwise `inclusive or' of `x' and `y'.")) (|bitand| (($ $ $) "\\spad{bitand(x,y)} returns the bitwise `and' of `x' and `y'.")))
NIL
NIL
-(-1097)
+(-1099)
((|constructor| (NIL "This domain is a datatype system-level pointer values.")))
NIL
NIL
-(-1098 R)
+(-1100 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
-(-1099)
+(-1101)
((|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
-(-1100 S)
+(-1102 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 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}{\\spad{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{\\spad{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 \\spad{bat1} is the inverse of \\spad{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
-(-1101 |Key| |Entry|)
+(-1103 |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}")))
-((-3992 . T) (-3993 . T))
-((-12 (|HasCategory| (-2 (|:| -3857 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -259) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3857) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3857 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3857 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3857 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3857 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| (-2 (|:| -3857 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-553 (-773))))) (|HasCategory| (-2 (|:| -3857 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-473)))) (-12 (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (|%list| (QUOTE -259) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3857 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-1013))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3857 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3857 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3857 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))))
-(-1102 S)
+((-3996 . T) (-3997 . T))
+((-12 (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3861) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1015)))) (OR (|HasCategory| |#2| (QUOTE (-1015))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1015)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1015))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1015)))) (OR (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-774)))) (|HasCategory| |#2| (QUOTE (-554 (-774))))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-555 (-474)))) (-12 (|HasCategory| |#2| (QUOTE (-1015))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1015))) (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| |#2| (QUOTE (-1015))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-554 (-774)))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-774)))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))))
+(-1104 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
-(-1103 S)
+(-1105 S)
((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: April 17,{} 2010 Date Last Modified: April 17,{} 2010")) (|operator| (($ |#1| (|Arity|)) "\\spad{operator(n,a)} returns an operator named \\spad{n} and with arity \\spad{a}.")))
NIL
NIL
-(-1104 R)
+(-1106 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
-(-1105 S |Key| |Entry|)
+(-1107 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{e}}) is equivalent to \\axiom{(insert([\\spad{k},{}\\spad{e}],{}\\spad{t}); \\spad{e})}.")))
NIL
NIL
-(-1106 |Key| |Entry|)
+(-1108 |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{e}}) is equivalent to \\axiom{(insert([\\spad{k},{}\\spad{e}],{}\\spad{t}); \\spad{e})}.")))
-((-3993 . T))
+((-3997 . T))
NIL
-(-1107 |Key| |Entry|)
+(-1109 |Key| |Entry|)
((|constructor| (NIL "\\axiom{TabulatedComputationPackage(Key ,{}Entry)} provides some modest support for dealing with operations with type \\axiom{Key -> 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
-(-1108)
+(-1110)
((|constructor| (NIL "\\spadtype{TexFormat} provides a coercion from \\spadtype{OutputForm} to \\TeX{} format. The particular dialect of \\TeX{} used is \\LaTeX{}. The basic object consists of three parts: a prologue,{} a tex part and an epilogue. The functions \\spadfun{prologue},{} \\spadfun{tex} and \\spadfun{epilogue} extract these parts,{} respectively. The main guts of the expression go into the tex part. The other parts can be set (\\spadfun{setPrologue!},{} \\spadfun{setEpilogue!}) so that contain the appropriate tags for printing. For example,{} the prologue and epilogue might simply contain ``\\verb+\\[+'' and ``\\verb+\\]+'',{} respectively,{} so that the TeX section will be printed in LaTeX display math mode.")) (|setPrologue!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setPrologue!(t,strings)} sets the prologue section of a TeX form \\spad{t} to \\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
-(-1109 S)
+(-1111 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
-(-1110)
+(-1112)
((|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
-(-1111 R)
+(-1113 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
-(-1112)
+(-1114)
((|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
-(-1113 S)
+(-1115 S)
((|constructor| (NIL "Category for the transcendental elementary functions.")) (|pi| (($) "\\spad{pi()} returns the constant \\spad{pi}.")))
NIL
NIL
-(-1114)
+(-1116)
((|constructor| (NIL "Category for the transcendental elementary functions.")) (|pi| (($) "\\spad{pi()} returns the constant \\spad{pi}.")))
NIL
NIL
-(-1115 S)
+(-1117 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| $)) "\\spad{tree(nd,ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}.")))
-((-3993 . T) (-3992 . T))
-((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1013))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-72))))
-(-1116 S)
+((-3997 . T) (-3996 . T))
+((-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1015))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| |#1| (QUOTE (-554 (-774)))) (|HasCategory| |#1| (QUOTE (-72))))
+(-1118 S)
((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}.")))
NIL
NIL
-(-1117)
+(-1119)
((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}.")))
NIL
NIL
-(-1118 R -3091)
+(-1120 R -3094)
((|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
-(-1119 R |Row| |Col| M)
+(-1121 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
-(-1120 R -3091)
+(-1122 R -3094)
((|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 f:\\begin{items} \\item 1. rewrites trigs and hyperbolic trigs in terms of \\spad{sin} ,{}\\spad{cos},{} \\spad{sinh},{} \\spad{cosh}. \\item 2. rewrites \\spad{sin**2} and \\spad{sinh**2} in terms of \\spad{cos} and \\spad{cosh},{} \\item 3. rewrites \\spad{exp(a)*exp(b)} as \\spad{exp(a+b)}. \\item 4. rewrites \\spad{(a**(1/n))**m * (a**(1/s))**t} as a single power of a single radical of \\spad{a}. \\end{items}")) (|expand| ((|#2| |#2|) "\\spad{expand(f)} performs the following expansions on f:\\begin{items} \\item 1. logs of products are expanded into sums of logs,{} \\item 2. trigonometric and hyperbolic trigonometric functions of sums are expanded into sums of products of trigonometric and hyperbolic trigonometric functions. \\item 3. formal powers of the form \\spad{(a/b)**c} are expanded into \\spad{a**c * b**(-c)}. \\end{items}")))
NIL
-((-12 (|HasCategory| |#1| (|%list| (QUOTE -554) (|%list| (QUOTE -801) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -797) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -554) (|%list| (QUOTE -801) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -797) (|devaluate| |#1|)))))
-(-1121 |Coef|)
+((-12 (|HasCategory| |#1| (|%list| (QUOTE -555) (|%list| (QUOTE -802) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -798) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -555) (|%list| (QUOTE -802) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -798) (|devaluate| |#1|)))))
+(-1123 |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}.")))
-(((-3994 "*") |has| |#1| (-146)) (-3985 |has| |#1| (-495)) (-3987 . T) (-3986 . T) (-3989 . T))
-((|HasCategory| |#1| (QUOTE (-38 (-347 (-484))))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-495)))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-311))))
-(-1122 S R E V P)
+(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3991 . T) (-3990 . T) (-3993 . T))
+((|HasCategory| |#1| (QUOTE (-38 (-348 (-485))))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-312))))
+(-1124 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} < ... < Xn}. A set \\axiom{\\spad{S}} of polynomials in \\axiom{\\spad{R}[\\spad{X1},{}\\spad{X2},{}...,{}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|) $) "\\axiom{coHeight(ts)} returns \\axiom{size()\\$\\spad{V}} minus \\axiom{\\#ts}.")) (|extend| (($ $ |#5|) "\\axiom{extend(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{ts},{} according to the properties of triangular sets of the current category If the required properties do not hold an error is returned.")) (|extendIfCan| (((|Union| $ "failed") $ |#5|) "\\axiom{extendIfCan(ts,{}\\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{ts},{} according to the properties of triangular sets of the current domain. If the required properties do not hold then \"failed\" is returned. This operation encodes in some sense the properties of the triangular sets of the current category. Is is used to implement the \\axiom{construct} operation to guarantee that every triangular set build from a list of polynomials has the required properties.")) (|select| (((|Union| |#5| "failed") $ |#4|) "\\axiom{select(ts,{}\\spad{v})} returns the polynomial of \\axiom{ts} with \\axiom{\\spad{v}} as main variable,{} if any.")) (|algebraic?| (((|Boolean|) |#4| $) "\\axiom{algebraic?(\\spad{v},{}ts)} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{ts}.")) (|algebraicVariables| (((|List| |#4|) $) "\\axiom{algebraicVariables(ts)} returns the decreasingly sorted list of the main variables of the polynomials of \\axiom{ts}.")) (|rest| (((|Union| $ "failed") $) "\\axiom{rest(ts)} returns the polynomials of \\axiom{ts} with smaller main variable than \\axiom{mvar(ts)} if \\axiom{ts} is not empty,{} otherwise returns \"failed\"")) (|last| (((|Union| |#5| "failed") $) "\\axiom{last(ts)} returns the polynomial of \\axiom{ts} with smallest main variable if \\axiom{ts} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|first| (((|Union| |#5| "failed") $) "\\axiom{first(ts)} returns the polynomial of \\axiom{ts} with greatest main variable if \\axiom{ts} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) (|:| |open| (|List| |#5|)))) (|List| |#5|)) "\\axiom{zeroSetSplitIntoTriangularSystems(lp)} returns a list of triangular systems \\axiom{[[\\spad{ts1},{}\\spad{qs1}],{}...,{}[tsn,{}qsn]]} such that the zero set of \\axiom{lp} is the union of the closures of the \\axiom{W_i} where \\axiom{W_i} consists of the zeros of \\axiom{ts} which do not cancel any polynomial in \\axiom{qsi}.")) (|zeroSetSplit| (((|List| $) (|List| |#5|)) "\\axiom{zeroSetSplit(lp)} returns a list \\axiom{lts} of triangular sets such that the zero set of \\axiom{lp} is the union of the closures of the regular zero sets of the members of \\axiom{lts}.")) (|reduceByQuasiMonic| ((|#5| |#5| $) "\\axiom{reduceByQuasiMonic(\\spad{p},{}ts)} returns the same as \\axiom{remainder(\\spad{p},{}collectQuasiMonic(ts)).polnum}.")) (|collectQuasiMonic| (($ $) "\\axiom{collectQuasiMonic(ts)} returns the subset of \\axiom{ts} consisting of the polynomials with initial in \\axiom{\\spad{R}}.")) (|removeZero| ((|#5| |#5| $) "\\axiom{removeZero(\\spad{p},{}ts)} returns \\axiom{0} if \\axiom{\\spad{p}} reduces to \\axiom{0} by pseudo-division \\spad{w}.\\spad{r}.\\spad{t} \\axiom{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},{}ts)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}ts)} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}.")) (|headReduce| ((|#5| |#5| $) "\\axiom{headReduce(\\spad{p},{}ts)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduce?(\\spad{r},{}ts)} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}.")) (|stronglyReduce| ((|#5| |#5| $) "\\axiom{stronglyReduce(\\spad{p},{}ts)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{stronglyReduced?(\\spad{r},{}ts)} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}.")) (|rewriteSetWithReduction| (((|List| |#5|) (|List| |#5|) $ (|Mapping| |#5| |#5| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{rewriteSetWithReduction(lp,{}ts,{}redOp,{}redOp?)} returns a list \\axiom{lq} of polynomials such that \\axiom{[reduce(\\spad{p},{}ts,{}redOp,{}redOp?) for \\spad{p} in lp]} and \\axiom{lp} have the same zeros inside the regular zero set of \\axiom{ts}. Moreover,{} for every polynomial \\axiom{\\spad{q}} in \\axiom{lq} and every polynomial \\axiom{\\spad{t}} in \\axiom{ts} \\axiom{redOp?(\\spad{q},{}\\spad{t})} holds and there exists a polynomial \\axiom{\\spad{p}} in the ideal generated by \\axiom{lp} and a product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\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 = f*q + redOp(\\spad{p},{}\\spad{q})}.")) (|reduce| ((|#5| |#5| $ (|Mapping| |#5| |#5| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{reduce(\\spad{p},{}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{ts} and there exists some product \\axiom{\\spad{h}} of the initials of the members of \\axiom{ts} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\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 = f*q + redOp(\\spad{p},{}\\spad{q})}.")) (|autoReduced?| (((|Boolean|) $ (|Mapping| (|Boolean|) |#5| (|List| |#5|))) "\\axiom{autoReduced?(ts,{}redOp?)} returns \\spad{true} iff every element of \\axiom{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},{}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{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},{}ts)} returns \\spad{true} iff the head of \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ts}.")) (|stronglyReduced?| (((|Boolean|) $) "\\axiom{stronglyReduced?(ts)} returns \\spad{true} iff every element of \\axiom{ts} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{ts}.") (((|Boolean|) |#5| $) "\\axiom{stronglyReduced?(\\spad{p},{}ts)} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ts}.")) (|reduced?| (((|Boolean|) |#5| $ (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{reduced?(\\spad{p},{}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{ts} \\axiom{redOp?(\\spad{p},{}\\spad{t})} holds.")) (|normalized?| (((|Boolean|) $) "\\axiom{normalized?(ts)} returns \\spad{true} iff for every axiom{\\spad{p}} in axiom{ts} we have \\axiom{normalized?(\\spad{p},{}us)} where \\axiom{us} is \\axiom{collectUnder(ts,{}mvar(\\spad{p}))}.") (((|Boolean|) |#5| $) "\\axiom{normalized?(\\spad{p},{}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{ts}")) (|quasiComponent| (((|Record| (|:| |close| (|List| |#5|)) (|:| |open| (|List| |#5|))) $) "\\axiom{quasiComponent(ts)} returns \\axiom{[lp,{}lq]} where \\axiom{lp} is the list of the members of \\axiom{ts} and \\axiom{lq}is \\axiom{initials(ts)}.")) (|degree| (((|NonNegativeInteger|) $) "\\axiom{degree(ts)} returns the product of main degrees of the members of \\axiom{ts}.")) (|initials| (((|List| |#5|) $) "\\axiom{initials(ts)} returns the list of the non-constant initials of the members of \\axiom{ts}.")) (|basicSet| (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#5|))) "failed") (|List| |#5|) (|Mapping| (|Boolean|) |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{basicSet(ps,{}pred?,{}redOp?)} returns the same as \\axiom{basicSet(qs,{}redOp?)} where \\axiom{qs} consists of the polynomials of \\axiom{ps} satisfying property \\axiom{pred?}.") (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#5|))) "failed") (|List| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{basicSet(ps,{}redOp?)} returns \\axiom{[bs,{}ts]} where \\axiom{concat(bs,{}ts)} is \\axiom{ps} and \\axiom{bs} is a basic set in Wu Wen Tsun sense of \\axiom{ps} \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?},{} if no non-zero constant polynomial lie in \\axiom{ps},{} otherwise \\axiom{\"failed\"} is returned.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(\\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 (-317))))
-(-1123 R E V P)
+((|HasCategory| |#4| (QUOTE (-318))))
+(-1125 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} < ... < Xn}. A set \\axiom{\\spad{S}} of polynomials in \\axiom{\\spad{R}[\\spad{X1},{}\\spad{X2},{}...,{}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|) $) "\\axiom{coHeight(ts)} returns \\axiom{size()\\$\\spad{V}} minus \\axiom{\\#ts}.")) (|extend| (($ $ |#4|) "\\axiom{extend(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{ts},{} according to the properties of triangular sets of the current category If the required properties do not hold an error is returned.")) (|extendIfCan| (((|Union| $ "failed") $ |#4|) "\\axiom{extendIfCan(ts,{}\\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{ts},{} according to the properties of triangular sets of the current domain. If the required properties do not hold then \"failed\" is returned. This operation encodes in some sense the properties of the triangular sets of the current category. Is is used to implement the \\axiom{construct} operation to guarantee that every triangular set build from a list of polynomials has the required properties.")) (|select| (((|Union| |#4| "failed") $ |#3|) "\\axiom{select(ts,{}\\spad{v})} returns the polynomial of \\axiom{ts} with \\axiom{\\spad{v}} as main variable,{} if any.")) (|algebraic?| (((|Boolean|) |#3| $) "\\axiom{algebraic?(\\spad{v},{}ts)} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{ts}.")) (|algebraicVariables| (((|List| |#3|) $) "\\axiom{algebraicVariables(ts)} returns the decreasingly sorted list of the main variables of the polynomials of \\axiom{ts}.")) (|rest| (((|Union| $ "failed") $) "\\axiom{rest(ts)} returns the polynomials of \\axiom{ts} with smaller main variable than \\axiom{mvar(ts)} if \\axiom{ts} is not empty,{} otherwise returns \"failed\"")) (|last| (((|Union| |#4| "failed") $) "\\axiom{last(ts)} returns the polynomial of \\axiom{ts} with smallest main variable if \\axiom{ts} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|first| (((|Union| |#4| "failed") $) "\\axiom{first(ts)} returns the polynomial of \\axiom{ts} with greatest main variable if \\axiom{ts} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) (|:| |open| (|List| |#4|)))) (|List| |#4|)) "\\axiom{zeroSetSplitIntoTriangularSystems(lp)} returns a list of triangular systems \\axiom{[[\\spad{ts1},{}\\spad{qs1}],{}...,{}[tsn,{}qsn]]} such that the zero set of \\axiom{lp} is the union of the closures of the \\axiom{W_i} where \\axiom{W_i} consists of the zeros of \\axiom{ts} which do not cancel any polynomial in \\axiom{qsi}.")) (|zeroSetSplit| (((|List| $) (|List| |#4|)) "\\axiom{zeroSetSplit(lp)} returns a list \\axiom{lts} of triangular sets such that the zero set of \\axiom{lp} is the union of the closures of the regular zero sets of the members of \\axiom{lts}.")) (|reduceByQuasiMonic| ((|#4| |#4| $) "\\axiom{reduceByQuasiMonic(\\spad{p},{}ts)} returns the same as \\axiom{remainder(\\spad{p},{}collectQuasiMonic(ts)).polnum}.")) (|collectQuasiMonic| (($ $) "\\axiom{collectQuasiMonic(ts)} returns the subset of \\axiom{ts} consisting of the polynomials with initial in \\axiom{\\spad{R}}.")) (|removeZero| ((|#4| |#4| $) "\\axiom{removeZero(\\spad{p},{}ts)} returns \\axiom{0} if \\axiom{\\spad{p}} reduces to \\axiom{0} by pseudo-division \\spad{w}.\\spad{r}.\\spad{t} \\axiom{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},{}ts)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}ts)} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}.")) (|headReduce| ((|#4| |#4| $) "\\axiom{headReduce(\\spad{p},{}ts)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduce?(\\spad{r},{}ts)} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}.")) (|stronglyReduce| ((|#4| |#4| $) "\\axiom{stronglyReduce(\\spad{p},{}ts)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{stronglyReduced?(\\spad{r},{}ts)} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}.")) (|rewriteSetWithReduction| (((|List| |#4|) (|List| |#4|) $ (|Mapping| |#4| |#4| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{rewriteSetWithReduction(lp,{}ts,{}redOp,{}redOp?)} returns a list \\axiom{lq} of polynomials such that \\axiom{[reduce(\\spad{p},{}ts,{}redOp,{}redOp?) for \\spad{p} in lp]} and \\axiom{lp} have the same zeros inside the regular zero set of \\axiom{ts}. Moreover,{} for every polynomial \\axiom{\\spad{q}} in \\axiom{lq} and every polynomial \\axiom{\\spad{t}} in \\axiom{ts} \\axiom{redOp?(\\spad{q},{}\\spad{t})} holds and there exists a polynomial \\axiom{\\spad{p}} in the ideal generated by \\axiom{lp} and a product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\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 = f*q + redOp(\\spad{p},{}\\spad{q})}.")) (|reduce| ((|#4| |#4| $ (|Mapping| |#4| |#4| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{reduce(\\spad{p},{}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{ts} and there exists some product \\axiom{\\spad{h}} of the initials of the members of \\axiom{ts} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\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 = f*q + redOp(\\spad{p},{}\\spad{q})}.")) (|autoReduced?| (((|Boolean|) $ (|Mapping| (|Boolean|) |#4| (|List| |#4|))) "\\axiom{autoReduced?(ts,{}redOp?)} returns \\spad{true} iff every element of \\axiom{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},{}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{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},{}ts)} returns \\spad{true} iff the head of \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ts}.")) (|stronglyReduced?| (((|Boolean|) $) "\\axiom{stronglyReduced?(ts)} returns \\spad{true} iff every element of \\axiom{ts} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{ts}.") (((|Boolean|) |#4| $) "\\axiom{stronglyReduced?(\\spad{p},{}ts)} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ts}.")) (|reduced?| (((|Boolean|) |#4| $ (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{reduced?(\\spad{p},{}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{ts} \\axiom{redOp?(\\spad{p},{}\\spad{t})} holds.")) (|normalized?| (((|Boolean|) $) "\\axiom{normalized?(ts)} returns \\spad{true} iff for every axiom{\\spad{p}} in axiom{ts} we have \\axiom{normalized?(\\spad{p},{}us)} where \\axiom{us} is \\axiom{collectUnder(ts,{}mvar(\\spad{p}))}.") (((|Boolean|) |#4| $) "\\axiom{normalized?(\\spad{p},{}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{ts}")) (|quasiComponent| (((|Record| (|:| |close| (|List| |#4|)) (|:| |open| (|List| |#4|))) $) "\\axiom{quasiComponent(ts)} returns \\axiom{[lp,{}lq]} where \\axiom{lp} is the list of the members of \\axiom{ts} and \\axiom{lq}is \\axiom{initials(ts)}.")) (|degree| (((|NonNegativeInteger|) $) "\\axiom{degree(ts)} returns the product of main degrees of the members of \\axiom{ts}.")) (|initials| (((|List| |#4|) $) "\\axiom{initials(ts)} returns the list of the non-constant initials of the members of \\axiom{ts}.")) (|basicSet| (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{basicSet(ps,{}pred?,{}redOp?)} returns the same as \\axiom{basicSet(qs,{}redOp?)} where \\axiom{qs} consists of the polynomials of \\axiom{ps} satisfying property \\axiom{pred?}.") (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{basicSet(ps,{}redOp?)} returns \\axiom{[bs,{}ts]} where \\axiom{concat(bs,{}ts)} is \\axiom{ps} and \\axiom{bs} is a basic set in Wu Wen Tsun sense of \\axiom{ps} \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?},{} if no non-zero constant polynomial lie in \\axiom{ps},{} otherwise \\axiom{\"failed\"} is returned.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(\\spad{ts1},{}\\spad{ts2})} returns \\spad{true} iff \\axiom{\\spad{ts2}} has higher rank than \\axiom{\\spad{ts1}} in Wu Wen Tsun sense.")))
-((-3993 . T) (-3992 . T))
+((-3997 . T) (-3996 . T))
NIL
-(-1124 |Curve|)
+(-1126 |Curve|)
((|constructor| (NIL "\\indented{2}{Package for constructing tubes around 3-dimensional parametric curves.} Domain of tubes around 3-dimensional parametric curves.")) (|tube| (($ |#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
-(-1125)
+(-1127)
((|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
-(-1126 S)
+(-1128 S)
((|constructor| (NIL "\\indented{1}{This domain is used to interface with the interpreter'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 (-1013))) (|HasCategory| |#1| (QUOTE (-553 (-773)))))
-(-1127 -3091)
+((|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (QUOTE (-554 (-774)))))
+(-1129 -3094)
((|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
-(-1128)
+(-1130)
((|constructor| (NIL "The fundamental Type.")))
NIL
NIL
-(-1129)
+(-1131)
((|constructor| (NIL "This domain represents a type AST.")))
NIL
NIL
-(-1130 S)
+(-1132 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 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 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}'s and bj's.} \\indented{3}{(3)\\space{2}undefined on \\spad{(c,d)} if neither is among the \\spad{ai}'s,{}bj's.}") (((|Void|) (|List| |#1|)) "\\spad{setOrder([a1,...,an])} defines a partial ordering on \\spad{S} given 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}'s.} \\indented{3}{(3)\\space{2}undefined on \\spad{(b, c)} if neither is among the \\spad{ai}'s.}")))
NIL
-((|HasCategory| |#1| (QUOTE (-757))))
-(-1131)
+((|HasCategory| |#1| (QUOTE (-758))))
+(-1133)
((|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
-(-1132 S)
+(-1134 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
-(-1133)
+(-1135)
((|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|) $) "\\spad{prime?(x)} tests if \\spad{x} can never be written as the product of two non-units of the ring,{} \\spadignore{i.e.} \\spad{x} is an irreducible element.")))
-((-3985 . T) ((-3994 "*") . T) (-3986 . T) (-3987 . T) (-3989 . T))
+((-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T))
NIL
-(-1134)
+(-1136)
((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 16 bits.")))
NIL
NIL
-(-1135)
+(-1137)
((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 32 bits.")))
NIL
NIL
-(-1136)
+(-1138)
((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 64 bits.")))
NIL
NIL
-(-1137)
+(-1139)
((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 8 bits.")))
NIL
NIL
-(-1138 |Coef| |var| |cen|)
+(-1140 |Coef| |var| |cen|)
((|constructor| (NIL "Dense Laurent series in one variable \\indented{2}{\\spadtype{UnivariateLaurentSeries} is a domain representing Laurent} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{UnivariateLaurentSeries(Integer,x,3)} represents Laurent series in} \\indented{2}{\\spad{(x - 3)} with integer coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Laurent series.")))
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(|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-484)) (|devaluate| |#1|)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| (-1168 |#1| |#2| |#3|) (QUOTE (-190)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-484)) (|devaluate| |#1|))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| (-1168 |#1| |#2| |#3|) (QUOTE (-190)))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| (-1168 |#1| |#2| |#3|) (QUOTE (-189)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-484)) (|devaluate| |#1|))))) (|HasCategory| (-484) (QUOTE (-1025))) (OR (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-495)))) (|HasCategory| |#1| (QUOTE (-311))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| (-1168 |#1| |#2| |#3|) (QUOTE (-822)))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| (-1168 |#1| |#2| |#3|) (QUOTE (-951 (-1089))))) (-12 (|HasCategory| |#1| (QUOTE 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|#2| |#3|) (|%list| (QUOTE -241) (|%list| (QUOTE -1168) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|)) (|%list| (QUOTE -1168) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|))))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| (-1168 |#1| |#2| |#3|) (|%list| (QUOTE -259) (|%list| (QUOTE -1168) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|))))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| (-1168 |#1| |#2| |#3|) (|%list| (QUOTE -453) (QUOTE (-1089)) (|%list| (QUOTE -1168) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|))))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| (-1168 |#1| |#2| |#3|) (QUOTE (-581 (-484))))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| (-1168 |#1| |#2| |#3|) (QUOTE (-554 (-801 (-484)))))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| (-1168 |#1| |#2| |#3|) (QUOTE (-554 (-801 (-327)))))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| (-1168 |#1| |#2| |#3|) (QUOTE (-797 (-484))))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| (-1168 |#1| |#2| |#3|) (QUOTE (-797 (-327))))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-484))))) (|HasSignature| |#1| (|%list| (QUOTE -3943) (|%list| (|devaluate| |#1|) (QUOTE (-1089)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-484))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-347 (-484))))) (|HasCategory| |#1| (QUOTE (-29 (-484)))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1114)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-347 (-484))))) (|HasSignature| |#1| (|%list| (QUOTE -3809) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1089))))) (|HasSignature| |#1| (|%list| (QUOTE -3080) (|%list| (|%list| (QUOTE -584) (QUOTE (-1089))) (|devaluate| |#1|)))))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| (-1168 |#1| |#2| |#3|) (QUOTE (-483)))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| (-1168 |#1| |#2| |#3|) (QUOTE (-257)))) (|HasCategory| (-1168 |#1| |#2| |#3|) (QUOTE (-822))) (|HasCategory| (-1168 |#1| |#2| |#3|) (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-118))) (OR (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| (-1168 |#1| |#2| |#3|) (QUOTE (-822)))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| (-1168 |#1| |#2| |#3|) (QUOTE (-741)))) (|HasCategory| |#1| (QUOTE (-495)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| (-1168 |#1| |#2| |#3|) (QUOTE (-822)))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| (-1168 |#1| |#2| |#3|) (QUOTE (-741)))) (|HasCategory| |#1| (QUOTE (-146)))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| (-1168 |#1| |#2| |#3|) (QUOTE (-812 (-1089))))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| (-1168 |#1| |#2| |#3|) (QUOTE (-189)))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| (-1168 |#1| |#2| |#3|) (QUOTE (-757)))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-1168 |#1| |#2| |#3|) (QUOTE (-822)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| (-1168 |#1| |#2| |#3|) (QUOTE (-118)))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-1168 |#1| |#2| |#3|) (QUOTE (-822)))) (|HasCategory| |#1| (QUOTE (-118)))))
-(-1139 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|)
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(QUOTE (-312))) (|HasCategory| (-1170 |#1| |#2| |#3|) (QUOTE (-258)))) (|HasCategory| (-1170 |#1| |#2| |#3|) (QUOTE (-823))) (|HasCategory| (-1170 |#1| |#2| |#3|) (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-118))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1170 |#1| |#2| |#3|) (QUOTE (-823)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1170 |#1| |#2| |#3|) (QUOTE (-742)))) (|HasCategory| |#1| (QUOTE (-496)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1170 |#1| |#2| |#3|) (QUOTE (-823)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1170 |#1| |#2| |#3|) (QUOTE (-742)))) (|HasCategory| |#1| (QUOTE (-146)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1170 |#1| |#2| |#3|) (QUOTE (-813 (-1091))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1170 |#1| |#2| |#3|) (QUOTE (-189)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1170 |#1| |#2| |#3|) (QUOTE (-758)))) (-12 (|HasCategory| 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+(-1141 |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
-(-1140 |Coef|)
+(-1142 |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{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.")))
-(((-3994 "*") |has| |#1| (-146)) (-3985 |has| |#1| (-495)) (-3990 |has| |#1| (-311)) (-3984 |has| |#1| (-311)) (-3986 . T) (-3987 . T) (-3989 . T))
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NIL
-(-1141 S |Coef| UTS)
+(-1143 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 (-311))))
-(-1142 |Coef| UTS)
+((|HasCategory| |#2| (QUOTE (-312))))
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((|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)}.")))
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NIL
-(-1143 |Coef| UTS)
+(-1145 |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)}.")))
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-(-1144 ZP)
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(|devaluate| |#1|)))))) (OR (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-485)) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-190))))) (OR (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-485)) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-190)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-189))))) (|HasCategory| (-485) (QUOTE (-1027))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-496)))) (|HasCategory| |#1| (QUOTE (-312))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-823)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-952 (-1091))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-555 (-474))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-935)))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-496)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-742)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-742)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-758))))) (OR (|HasCategory| |#1| (QUOTE (-38 (-348 (-485))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-952 (-485)))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-952 (-485))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-1067)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (|%list| (QUOTE -241) (|devaluate| |#2|) (|devaluate| |#2|)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (|%list| (QUOTE -454) (QUOTE (-1091)) (|devaluate| |#2|)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-582 (-485))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-555 (-802 (-485)))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-555 (-802 (-328)))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-798 (-485))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-798 (-328))))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-485))))) (|HasSignature| |#1| (|%list| (QUOTE -3947) (|%list| (|devaluate| |#1|) (QUOTE (-1091)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-485))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-348 (-485))))) (|HasCategory| |#1| (QUOTE (-29 (-485)))) (|HasCategory| |#1| (QUOTE (-873))) (|HasCategory| |#1| (QUOTE (-1116)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-348 (-485))))) (|HasSignature| |#1| (|%list| (QUOTE -3813) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1091))))) (|HasSignature| |#1| (|%list| (QUOTE -3083) (|%list| (|%list| (QUOTE -585) (QUOTE (-1091))) (|devaluate| |#1|)))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-758)))) (|HasCategory| |#2| (QUOTE (-823))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-484)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-258)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-118))) (OR (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-485)) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-189))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-813 (-1091))))) (-12 (|HasCategory| |#1| (QUOTE (-811 (-1091)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-485)) (|devaluate| |#1|)))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-813 (-1091))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-189)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-823))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-823))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-118))))))
+(-1146 ZP)
((|constructor| (NIL "Package 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
-(-1145 S)
+(-1147 S)
((|constructor| (NIL "This domain provides segments which may be half open. That is,{} ranges of the form \\spad{a..} or \\spad{a..b}.")) (|hasHi| (((|Boolean|) $) "\\spad{hasHi(s)} tests whether the segment \\spad{s} has an upper bound.")) (|coerce| (($ (|Segment| |#1|)) "\\spad{coerce(x)} allows \\spadtype{Segment} values to be used as \\%.")) (|segment| (($ |#1|) "\\spad{segment(l)} is an alternate way to construct the segment \\spad{l..}.")) (SEGMENT (($ |#1|) "\\spad{l..} produces a half open segment,{} that is,{} one with no upper bound.")))
NIL
-((|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1013))))
-(-1146 R S)
+((|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1015))))
+(-1148 R S)
((|constructor| (NIL "This package provides operations for mapping functions onto segments.")) (|map| (((|Stream| |#2|) (|Mapping| |#2| |#1|) (|UniversalSegment| |#1|)) "\\spad{map(f,s)} expands the segment \\spad{s},{} applying \\spad{f} to each value.") (((|UniversalSegment| |#2|) (|Mapping| |#2| |#1|) (|UniversalSegment| |#1|)) "\\spad{map(f,seg)} returns the new segment obtained by applying \\spad{f} to the endpoints of \\spad{seg}.")))
NIL
-((|HasCategory| |#1| (QUOTE (-756))))
-(-1147 |x| R)
+((|HasCategory| |#1| (QUOTE (-757))))
+(-1149 |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}")))
-(((-3994 "*") |has| |#2| (-146)) (-3985 |has| |#2| (-495)) (-3988 |has| |#2| (-311)) (-3990 |has| |#2| (-6 -3990)) (-3987 . T) (-3986 . T) (-3989 . T))
-((|HasCategory| |#2| (QUOTE (-822))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-146))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-495)))) (-12 (|HasCategory| |#2| (QUOTE (-797 (-327)))) (|HasCategory| (-994) (QUOTE (-797 (-327))))) (-12 (|HasCategory| |#2| (QUOTE (-797 (-484)))) (|HasCategory| (-994) (QUOTE (-797 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-554 (-801 (-327))))) (|HasCategory| (-994) (QUOTE (-554 (-801 (-327)))))) (-12 (|HasCategory| |#2| (QUOTE (-554 (-801 (-484))))) (|HasCategory| (-994) (QUOTE (-554 (-801 (-484)))))) (-12 (|HasCategory| |#2| (QUOTE (-554 (-473)))) (|HasCategory| (-994) (QUOTE (-554 (-473))))) (|HasCategory| |#2| (QUOTE (-581 (-484)))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-38 (-347 (-484))))) (|HasCategory| |#2| (QUOTE (-951 (-484)))) (OR (|HasCategory| |#2| (QUOTE (-38 (-347 (-484))))) (|HasCategory| |#2| (QUOTE (-951 (-347 (-484)))))) (|HasCategory| |#2| (QUOTE (-951 (-347 (-484))))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-389))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-822)))) (OR (|HasCategory| |#2| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-389))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-822)))) (OR (|HasCategory| |#2| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-389))) (|HasCategory| |#2| (QUOTE (-822)))) (|HasCategory| |#2| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-1065))) (|HasCategory| |#2| (QUOTE (-812 (-1089)))) (|HasCategory| |#2| (QUOTE (-810 (-1089)))) (|HasCategory| |#2| (QUOTE (-189))) (|HasCategory| |#2| (QUOTE (-190))) (|HasAttribute| |#2| (QUOTE -3990)) (|HasCategory| |#2| (QUOTE (-389))) (-12 (|HasCategory| |#2| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#2| (QUOTE (-118)))))
-(-1148 |x| R |y| S)
+(((-3998 "*") |has| |#2| (-146)) (-3989 |has| |#2| (-496)) (-3992 |has| |#2| (-312)) (-3994 |has| |#2| (-6 -3994)) (-3991 . T) (-3990 . T) (-3993 . T))
+((|HasCategory| |#2| (QUOTE (-823))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-146))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-496)))) (-12 (|HasCategory| |#2| (QUOTE (-798 (-328)))) (|HasCategory| (-996) (QUOTE (-798 (-328))))) (-12 (|HasCategory| |#2| (QUOTE (-798 (-485)))) (|HasCategory| (-996) (QUOTE (-798 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-555 (-802 (-328))))) (|HasCategory| (-996) (QUOTE (-555 (-802 (-328)))))) (-12 (|HasCategory| |#2| (QUOTE (-555 (-802 (-485))))) (|HasCategory| (-996) (QUOTE (-555 (-802 (-485)))))) (-12 (|HasCategory| |#2| (QUOTE (-555 (-474)))) (|HasCategory| (-996) (QUOTE (-555 (-474))))) (|HasCategory| |#2| (QUOTE (-582 (-485)))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-38 (-348 (-485))))) (|HasCategory| |#2| (QUOTE (-952 (-485)))) (OR (|HasCategory| |#2| (QUOTE (-38 (-348 (-485))))) (|HasCategory| |#2| (QUOTE (-952 (-348 (-485)))))) (|HasCategory| |#2| (QUOTE (-952 (-348 (-485))))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-390))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-823)))) (OR (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-390))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-823)))) (OR (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-390))) (|HasCategory| |#2| (QUOTE (-823)))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-1067))) (|HasCategory| |#2| (QUOTE (-813 (-1091)))) (|HasCategory| |#2| (QUOTE (-811 (-1091)))) (|HasCategory| |#2| (QUOTE (-189))) (|HasCategory| |#2| (QUOTE (-190))) (|HasAttribute| |#2| (QUOTE -3994)) (|HasCategory| |#2| (QUOTE (-390))) (-12 (|HasCategory| |#2| (QUOTE (-823))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-823))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#2| (QUOTE (-118)))))
+(-1150 |x| R |y| S)
((|constructor| (NIL "This package lifts a mapping from coefficient rings \\spad{R} to \\spad{S} to a mapping from \\spadtype{UnivariatePolynomial}(\\spad{x},{}\\spad{R}) to \\spadtype{UnivariatePolynomial}(\\spad{y},{}\\spad{S}). Note that the mapping is assumed to send zero to zero,{} since it will only be applied to the non-zero coefficients of the polynomial.")) (|map| (((|UnivariatePolynomial| |#3| |#4|) (|Mapping| |#4| |#2|) (|UnivariatePolynomial| |#1| |#2|)) "\\spad{map(func, poly)} creates a new polynomial by applying \\spad{func} to every non-zero coefficient of the polynomial poly.")))
NIL
NIL
-(-1149 R Q UP)
+(-1151 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 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
-(-1150 R UP)
+(-1152 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},{} ...,{} fn ] means \\spad{f} = \\spad{f1} \\spad{o} ... \\spad{o} fn).")) (|monicDecomposeIfCan| (((|Union| (|Record| (|:| |left| |#2|) (|:| |right| |#2|)) "failed") |#2|) "\\spad{monicDecomposeIfCan(f)} returns a functional decomposition of the monic polynomial \\spad{f} of \"failed\" if it has not found any.")) (|leftFactorIfCan| (((|Union| |#2| "failed") |#2| |#2|) "\\spad{leftFactorIfCan(f,h)} returns the left factor (\\spad{g} in \\spad{f} = \\spad{g} \\spad{o} \\spad{h}) of the functional decomposition of the polynomial \\spad{f} with given \\spad{h} or \\spad{\"failed\"} if \\spad{g} does not exist.")) (|rightFactorIfCan| (((|Union| |#2| "failed") |#2| (|NonNegativeInteger|) |#1|) "\\spad{rightFactorIfCan(f,d,c)} returns a candidate to be the right factor (\\spad{h} in \\spad{f} = \\spad{g} \\spad{o} \\spad{h}) of degree \\spad{d} with leading coefficient \\spad{c} of a functional decomposition of the polynomial \\spad{f} or \\spad{\"failed\"} if no such candidate.")) (|monicRightFactorIfCan| (((|Union| |#2| "failed") |#2| (|NonNegativeInteger|)) "\\spad{monicRightFactorIfCan(f,d)} returns a candidate to be the monic right factor (\\spad{h} in \\spad{f} = \\spad{g} \\spad{o} \\spad{h}) of degree \\spad{d} of a functional decomposition of the polynomial \\spad{f} or \\spad{\"failed\"} if no such candidate.")))
NIL
NIL
-(-1151 R UP)
+(-1153 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
-(-1152 R U)
+(-1154 R U)
((|constructor| (NIL "This package implements Karatsuba's trick for multiplying (large) univariate polynomials. It could be improved with a version doing the work on place and also with a special case for squares. We've done this in Basicmath,{} but we believe that this out of the scope of AXIOM.")) (|karatsuba| ((|#2| |#2| |#2| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{karatsuba(a,b,l,k)} returns \\spad{a*b} by applying Karatsuba's trick provided that both \\spad{a} and \\spad{b} have at least \\spad{l} terms and \\spad{k > 0} holds and by calling \\spad{noKaratsuba} otherwise. The other multiplications are performed by recursive calls with the same third argument and \\spad{k-1} as fourth argument.")) (|karatsubaOnce| ((|#2| |#2| |#2|) "\\spad{karatsuba(a,b)} returns \\spad{a*b} by applying Karatsuba's trick once. The other multiplications are performed by calling \\spad{*} from \\spad{U}.")) (|noKaratsuba| ((|#2| |#2| |#2|) "\\spad{noKaratsuba(a,b)} returns \\spad{a*b} without using Karatsuba's trick at all.")))
NIL
NIL
-(-1153 S R)
+(-1155 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 gcd of the polynomials \\spad{p} and \\spad{q} using the SubResultant 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|) $) "\\spad{differentiate(p, d, x')} extends the \\spad{R}-derivation \\spad{d} to an extension \\spad{D} in \\spad{R[x]} where Dx is given by x',{} and returns \\spad{Dp}.")) (|pseudoRemainder| (($ $ $) "\\spad{pseudoRemainder(p,q)} = \\spad{r},{} for polynomials \\spad{p} and \\spad{q},{} returns the remainder when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|shiftLeft| (($ $ (|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'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| (QUOTE (-38 (-347 (-484))))) (|HasCategory| |#2| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-389))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-1065))))
-(-1154 R)
+((|HasCategory| |#2| (QUOTE (-38 (-348 (-485))))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-390))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-1067))))
+(-1156 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 gcd of the polynomials \\spad{p} and \\spad{q} using the SubResultant 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|) $) "\\spad{differentiate(p, d, x')} extends the \\spad{R}-derivation \\spad{d} to an extension \\spad{D} in \\spad{R[x]} where Dx is given by x',{} and returns \\spad{Dp}.")) (|pseudoRemainder| (($ $ $) "\\spad{pseudoRemainder(p,q)} = \\spad{r},{} for polynomials \\spad{p} and \\spad{q},{} returns the remainder when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|shiftLeft| (($ $ (|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'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}.")))
-(((-3994 "*") |has| |#1| (-146)) (-3985 |has| |#1| (-495)) (-3988 |has| |#1| (-311)) (-3990 |has| |#1| (-6 -3990)) (-3987 . T) (-3986 . T) (-3989 . T))
+(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3992 |has| |#1| (-312)) (-3994 |has| |#1| (-6 -3994)) (-3991 . T) (-3990 . T) (-3993 . T))
NIL
-(-1155 R PR S PS)
+(-1157 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
-(-1156 S |Coef| |Expon|)
+(-1158 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{n} to be computed.")) (|approximate| ((|#2| $ |#3|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#3| |#3|) "\\spad{truncate(f,k1,k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#3|) "\\spad{truncate(f,k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#3| $ |#3|) "\\spad{order(f,n) = min(m,n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#3| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#2| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#3|) (|:| |c| |#2|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents.")))
NIL
-((|HasCategory| |#2| (QUOTE (-810 (-1089)))) (|HasSignature| |#2| (|%list| (QUOTE *) (|%list| (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1025))) (|HasSignature| |#2| (|%list| (QUOTE **) (|%list| (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (|%list| (QUOTE -3943) (|%list| (|devaluate| |#2|) (QUOTE (-1089))))))
-(-1157 |Coef| |Expon|)
+((|HasCategory| |#2| (QUOTE (-811 (-1091)))) (|HasSignature| |#2| (|%list| (QUOTE *) (|%list| (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1027))) (|HasSignature| |#2| (|%list| (QUOTE **) (|%list| (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (|%list| (QUOTE -3947) (|%list| (|devaluate| |#2|) (QUOTE (-1091))))))
+(-1159 |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{n} to be computed.")) (|approximate| ((|#1| $ |#2|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#2| |#2|) "\\spad{truncate(f,k1,k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#2|) "\\spad{truncate(f,k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#2| $ |#2|) "\\spad{order(f,n) = min(m,n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#2| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#1| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#2|) (|:| |c| |#1|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents.")))
-(((-3994 "*") |has| |#1| (-146)) (-3985 |has| |#1| (-495)) (-3986 . T) (-3987 . T) (-3989 . T))
+(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3990 . T) (-3991 . T) (-3993 . T))
NIL
-(-1158 RC P)
+(-1160 RC P)
((|constructor| (NIL "This package provides for square-free decomposition of univariate polynomials over arbitrary rings,{} \\spadignore{i.e.} a partial factorization such that each factor is a product of irreducibles with multiplicity one and the factors are pairwise relatively prime. If the ring has characteristic zero,{} the result is guaranteed to satisfy this condition. If the ring is an infinite ring of finite characteristic,{} then it may not be possible to decide when polynomials contain factors which are \\spad{p}th powers. In this case,{} the flag associated with that polynomial is set to \"nil\" (meaning that that polynomials are not guaranteed to be square-free).")) (|BumInSepFFE| (((|Record| (|:| |flg| (|Union| #1="nil" #2="sqfr" #3="irred" #4="prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|))) (|Record| (|:| |flg| (|Union| #1# #2# #3# #4#)) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|)))) "\\spad{BumInSepFFE(f)} is a local function,{} exported only because it has multiple conditional definitions.")) (|squareFreePart| ((|#2| |#2|) "\\spad{squareFreePart(p)} returns a polynomial which has the same irreducible factors as the univariate polynomial \\spad{p},{} but each factor has multiplicity one.")) (|squareFree| (((|Factored| |#2|) |#2|) "\\spad{squareFree(p)} computes the square-free factorization of the univariate polynomial \\spad{p}. Each factor has no repeated roots,{} and the factors are pairwise relatively prime.")) (|gcd| (($ $ $) "\\spad{gcd(p,q)} computes the greatest-common-divisor of \\spad{p} and \\spad{q}.")))
NIL
NIL
-(-1159 |Coef| |var| |cen|)
+(-1161 |Coef| |var| |cen|)
((|constructor| (NIL "Dense Puiseux series in one variable \\indented{2}{\\spadtype{UnivariatePuiseuxSeries} is a domain representing Puiseux} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{UnivariatePuiseuxSeries(Integer,x,3)} represents Puiseux series in} \\indented{2}{\\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|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.")))
-(((-3994 "*") |has| |#1| (-146)) (-3985 |has| |#1| (-495)) (-3990 |has| |#1| (-311)) (-3984 |has| |#1| (-311)) (-3986 . T) (-3987 . T) (-3989 . T))
-((|HasCategory| |#1| (QUOTE (-38 (-347 (-484))))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-495)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-810 (-1089)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -347) (QUOTE (-484))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -347) (QUOTE (-484))) (|devaluate| |#1|)))) (|HasCategory| (-347 (-484)) (QUOTE (-1025))) (|HasCategory| |#1| (QUOTE (-311))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-495)))) (OR (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-495)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -347) (QUOTE (-484)))))) (|HasSignature| |#1| (|%list| (QUOTE -3943) (|%list| (|devaluate| |#1|) (QUOTE (-1089)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -347) (QUOTE (-484)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-347 (-484))))) (|HasCategory| |#1| (QUOTE (-29 (-484)))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1114)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-347 (-484))))) (|HasSignature| |#1| (|%list| (QUOTE -3809) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1089))))) (|HasSignature| |#1| (|%list| (QUOTE -3080) (|%list| (|%list| (QUOTE -584) (QUOTE (-1089))) (|devaluate| |#1|)))))))
-(-1160 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|)
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+(-1162 |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
-(-1161 |Coef|)
+(-1163 |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.")))
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+(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3994 |has| |#1| (-312)) (-3988 |has| |#1| (-312)) (-3990 . T) (-3991 . T) (-3993 . T))
NIL
-(-1162 S |Coef| ULS)
+(-1164 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
-(-1163 |Coef| ULS)
+(-1165 |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)}.")))
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+(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3994 |has| |#1| (-312)) (-3988 |has| |#1| (-312)) (-3990 . T) (-3991 . T) (-3993 . T))
NIL
-(-1164 |Coef| ULS)
+(-1166 |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)}.")))
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-(-1165 R FE |var| |cen|)
+(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3994 |has| |#1| (-312)) (-3988 |has| |#1| (-312)) (-3990 . T) (-3991 . T) (-3993 . T))
+((|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-811 (-1091)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -348) (QUOTE (-485))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -348) (QUOTE (-485))) (|devaluate| |#1|)))) (|HasCategory| (-348 (-485)) (QUOTE (-1027))) (|HasCategory| |#1| (QUOTE (-312))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-496)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-496)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -348) (QUOTE (-485)))))) (|HasSignature| |#1| (|%list| (QUOTE -3947) (|%list| (|devaluate| |#1|) (QUOTE (-1091)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -348) (QUOTE (-485)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-348 (-485))))) (|HasCategory| |#1| (QUOTE (-29 (-485)))) (|HasCategory| |#1| (QUOTE (-873))) (|HasCategory| |#1| (QUOTE (-1116)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-348 (-485))))) (|HasSignature| |#1| (|%list| (QUOTE -3813) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1091))))) (|HasSignature| |#1| (|%list| (QUOTE -3083) (|%list| (|%list| (QUOTE -585) (QUOTE (-1091))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (QUOTE (-38 (-348 (-485))))))
+(-1167 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") $) "\\spad{limitPlus(f(var))} returns \\spad{limit(var -> cen+,f(var))}.")))
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-(-1166 A S)
+(((-3998 "*") |has| (-1161 |#2| |#3| |#4|) (-146)) (-3989 |has| (-1161 |#2| |#3| |#4|) (-496)) (-3990 . T) (-3991 . T) (-3993 . T))
+((|HasCategory| (-1161 |#2| |#3| |#4|) (QUOTE (-38 (-348 (-485))))) (|HasCategory| (-1161 |#2| |#3| |#4|) (QUOTE (-118))) (|HasCategory| (-1161 |#2| |#3| |#4|) (QUOTE (-120))) (|HasCategory| (-1161 |#2| |#3| |#4|) (QUOTE (-146))) (OR (|HasCategory| (-1161 |#2| |#3| |#4|) (QUOTE (-38 (-348 (-485))))) (|HasCategory| (-1161 |#2| |#3| |#4|) (QUOTE (-952 (-348 (-485)))))) (|HasCategory| (-1161 |#2| |#3| |#4|) (QUOTE (-952 (-348 (-485))))) (|HasCategory| (-1161 |#2| |#3| |#4|) (QUOTE (-952 (-485)))) (|HasCategory| (-1161 |#2| |#3| |#4|) (QUOTE (-312))) (|HasCategory| (-1161 |#2| |#3| |#4|) (QUOTE (-390))) (|HasCategory| (-1161 |#2| |#3| |#4|) (QUOTE (-496))))
+(-1168 A S)
((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|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{b}}) is equivalent to \\axiom{setlast!(\\spad{u},{}\\spad{v})}.") (($ $ "rest" $) "\\spad{setelt(u,\"rest\",v)} (also written: \\axiom{\\spad{u}.rest := \\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{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} >= 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} >= 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} >= 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| $) "\\spad{concat(x,u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}.")))
NIL
-((|HasAttribute| |#1| (QUOTE -3993)))
-(-1167 S)
+((|HasAttribute| |#1| (QUOTE -3997)))
+(-1169 S)
((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|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{b}}) is equivalent to \\axiom{setlast!(\\spad{u},{}\\spad{v})}.") (($ $ "rest" $) "\\spad{setelt(u,\"rest\",v)} (also written: \\axiom{\\spad{u}.rest := \\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{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} >= 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} >= 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} >= 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| $) "\\spad{concat(x,u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}.")))
NIL
NIL
-(-1168 |Coef| |var| |cen|)
+(-1170 |Coef| |var| |cen|)
((|constructor| (NIL "Dense Taylor series in one variable \\spadtype{UnivariateTaylorSeries} is a domain representing Taylor series in one variable with coefficients in an arbitrary ring. The parameters of the type specify the coefficient ring,{} the power series variable,{} and the center of the power series expansion. For example,{} \\spadtype{UnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x),x)} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|invmultisect| (($ (|Integer|) (|Integer|) $) "\\spad{invmultisect(a,b,f(x))} substitutes \\spad{x^((a+b)*n)} \\indented{1}{for \\spad{x^n} and multiples by \\spad{x^b}.}")) (|multisect| (($ (|Integer|) (|Integer|) $) "\\spad{multisect(a,b,f(x))} selects the coefficients of \\indented{1}{\\spad{x^((a+b)*n+a)},{} and changes this monomial to \\spad{x^n}.}")) (|revert| (($ $) "\\spad{revert(f(x))} returns a Taylor series \\spad{g(x)} such that \\spad{f(g(x)) = g(f(x)) = x}. Series \\spad{f(x)} should have constant coefficient 0 and invertible 1st order coefficient.")) (|generalLambert| (($ $ (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),a,d)} returns \\spad{f(x^a) + f(x^(a + d)) + \\indented{1}{f(x^(a + 2 d)) + ... }. \\spad{f(x)} should have zero constant} \\indented{1}{coefficient and \\spad{a} and \\spad{d} should be positive.}")) (|evenlambert| (($ $) "\\spad{evenlambert(f(x))} returns \\spad{f(x^2) + f(x^4) + f(x^6) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,f(x^(2*n))) = exp(log(evenlambert(f(x))))}.}")) (|oddlambert| (($ $) "\\spad{oddlambert(f(x))} returns \\spad{f(x) + f(x^3) + f(x^5) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,f(x^(2*n-1)))=exp(log(oddlambert(f(x))))}.}")) (|lambert| (($ $) "\\spad{lambert(f(x))} returns \\spad{f(x) + f(x^2) + f(x^3) + ...}. \\indented{1}{This function is used for computing infinite products.} \\indented{1}{\\spad{f(x)} should have zero constant coefficient.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n = 1..infinity,f(x^n)) = exp(log(lambert(f(x))))}.}")) (|lagrange| (($ $) "\\spad{lagrange(g(x))} produces the Taylor series for \\spad{f(x)} \\indented{1}{where \\spad{f(x)} is implicitly defined as \\spad{f(x) = x*g(f(x))}.}")) (|univariatePolynomial| (((|UnivariatePolynomial| |#2| |#1|) $ (|NonNegativeInteger|)) "\\spad{univariatePolynomial(f,k)} returns a univariate polynomial \\indented{1}{consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.}")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a \\indented{1}{Taylor series.}") (($ (|UnivariatePolynomial| |#2| |#1|)) "\\spad{coerce(p)} converts a univariate polynomial \\spad{p} in the variable \\spad{var} to a univariate Taylor series in \\spad{var}.")))
-(((-3994 "*") |has| |#1| (-146)) (-3985 |has| |#1| (-495)) (-3986 . T) (-3987 . T) (-3989 . T))
-((|HasCategory| |#1| (QUOTE (-38 (-347 (-484))))) (|HasCategory| |#1| (QUOTE (-495))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-495)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-810 (-1089)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-695)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-695)) (|devaluate| |#1|)))) (|HasCategory| (-695) (QUOTE (-1025))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-695))))) (|HasSignature| |#1| (|%list| (QUOTE -3943) (|%list| (|devaluate| |#1|) (QUOTE (-1089)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-695))))) (|HasCategory| |#1| (QUOTE (-311))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-347 (-484))))) (|HasCategory| |#1| (QUOTE (-29 (-484)))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1114)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-347 (-484))))) (|HasSignature| |#1| (|%list| (QUOTE -3809) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1089))))) (|HasSignature| |#1| (|%list| (QUOTE -3080) (|%list| (|%list| (QUOTE -584) (QUOTE (-1089))) (|devaluate| |#1|)))))))
-(-1169 |Coef1| |Coef2| UTS1 UTS2)
+(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3990 . T) (-3991 . T) (-3993 . T))
+((|HasCategory| |#1| (QUOTE (-38 (-348 (-485))))) (|HasCategory| |#1| (QUOTE (-496))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-811 (-1091)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-696)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-696)) (|devaluate| |#1|)))) (|HasCategory| (-696) (QUOTE (-1027))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-696))))) (|HasSignature| |#1| (|%list| (QUOTE -3947) (|%list| (|devaluate| |#1|) (QUOTE (-1091)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-696))))) (|HasCategory| |#1| (QUOTE (-312))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-348 (-485))))) (|HasCategory| |#1| (QUOTE (-29 (-485)))) (|HasCategory| |#1| (QUOTE (-873))) (|HasCategory| |#1| (QUOTE (-1116)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-348 (-485))))) (|HasSignature| |#1| (|%list| (QUOTE -3813) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1091))))) (|HasSignature| |#1| (|%list| (QUOTE -3083) (|%list| (|%list| (QUOTE -585) (QUOTE (-1091))) (|devaluate| |#1|)))))))
+(-1171 |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
-(-1170 S |Coef|)
+(-1172 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| (QUOTE (-29 (-484)))) (|HasCategory| |#2| (QUOTE (-872))) (|HasCategory| |#2| (QUOTE (-1114))) (|HasSignature| |#2| (|%list| (QUOTE -3080) (|%list| (|%list| (QUOTE -584) (QUOTE (-1089))) (|devaluate| |#2|)))) (|HasSignature| |#2| (|%list| (QUOTE -3809) (|%list| (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1089))))) (|HasCategory| |#2| (QUOTE (-38 (-347 (-484))))) (|HasCategory| |#2| (QUOTE (-311))))
-(-1171 |Coef|)
+((|HasCategory| |#2| (QUOTE (-29 (-485)))) (|HasCategory| |#2| (QUOTE (-873))) (|HasCategory| |#2| (QUOTE (-1116))) (|HasSignature| |#2| (|%list| (QUOTE -3083) (|%list| (|%list| (QUOTE -585) (QUOTE (-1091))) (|devaluate| |#2|)))) (|HasSignature| |#2| (|%list| (QUOTE -3813) (|%list| (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1091))))) (|HasCategory| |#2| (QUOTE (-38 (-348 (-485))))) (|HasCategory| |#2| (QUOTE (-312))))
+(-1173 |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.")))
-(((-3994 "*") |has| |#1| (-146)) (-3985 |has| |#1| (-495)) (-3986 . T) (-3987 . T) (-3989 . T))
+(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3990 . T) (-3991 . T) (-3993 . T))
NIL
-(-1172 |Coef| UTS)
+(-1174 |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
-(-1173 -3091 UP L UTS)
+(-1175 -3094 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 (-495))))
-(-1174)
+((|HasCategory| |#1| (QUOTE (-496))))
+(-1176)
((|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
-(-1175 |sym|)
+(-1177 |sym|)
((|constructor| (NIL "This domain implements variables")) (|variable| (((|Symbol|)) "\\spad{variable()} returns the symbol")) (|coerce| (((|Symbol|) $) "\\spad{coerce(x)} returns the symbol")))
NIL
NIL
-(-1176 S R)
+(-1178 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})*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 (-916))) (|HasCategory| |#2| (QUOTE (-962))) (|HasCategory| |#2| (QUOTE (-664))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25))))
-(-1177 R)
+((|HasCategory| |#2| (QUOTE (-917))) (|HasCategory| |#2| (QUOTE (-963))) (|HasCategory| |#2| (QUOTE (-665))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25))))
+(-1179 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})*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}.")) (+ (($ $ $) "\\spad{x + y} returns the component-wise sum of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.")))
-((-3993 . T) (-3992 . T))
+((-3997 . T) (-3996 . T))
NIL
-(-1178 R)
+(-1180 R)
((|constructor| (NIL "This type represents vector like objects with varying lengths and indexed by a finite segment of integers starting at 1.")) (|vector| (($ (|List| |#1|)) "\\spad{vector(l)} converts the list \\spad{l} to a vector.")))
-((-3993 . T) (-3992 . T))
-((OR (-12 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-554 (-473)))) (OR (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-757))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| (-484) (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-664))) (|HasCategory| |#1| (QUOTE (-962))) (-12 (|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| |#1| (QUOTE (-962)))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))))
-(-1179 A B)
+((-3997 . T) (-3996 . T))
+((OR (-12 (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-554 (-774)))) (|HasCategory| |#1| (QUOTE (-555 (-474)))) (OR (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| |#1| (QUOTE (-758))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-758))) (|HasCategory| |#1| (QUOTE (-1015)))) (|HasCategory| (-485) (QUOTE (-758))) (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-665))) (|HasCategory| |#1| (QUOTE (-963))) (-12 (|HasCategory| |#1| (QUOTE (-917))) (|HasCategory| |#1| (QUOTE (-963)))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))))
+(-1181 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
-(-1180)
+(-1182)
((|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 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 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 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 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 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
-(-1181)
+(-1183)
((|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'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
-(-1182)
+(-1184)
((|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
-(-1183)
+(-1185)
((|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
-(-1184)
+(-1186)
((|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| (($) "\\spad{void()} produces a void object.")))
NIL
NIL
-(-1185 A S)
+(-1187 A S)
((|constructor| (NIL "Vector Spaces (not necessarily finite dimensional) over a field.")) (|dimension| (((|CardinalNumber|)) "\\spad{dimension()} returns the dimensionality of the vector space.")) (/ (($ $ |#2|) "\\spad{x/y} divides the vector \\spad{x} by the scalar \\spad{y}.")))
NIL
NIL
-(-1186 S)
+(-1188 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}.")))
-((-3987 . T) (-3986 . T))
+((-3991 . T) (-3990 . T))
NIL
-(-1187 R)
+(-1189 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]*v + A[2]\\spad{*v**2} + ... + A[\\spad{s}-1]*v**(\\spad{s}-1) + v**s such that p=A*B ,{} \\spad{B} being a TaylorSeries of minimum degree 0")) (|qqq| (((|Mapping| (|Stream| (|TaylorSeries| |#1|)) (|Stream| (|TaylorSeries| |#1|))) (|NonNegativeInteger|) (|TaylorSeries| |#1|) (|Stream| (|TaylorSeries| |#1|))) "\\spad{qqq(n,s,st)} is used internally.")) (|weierstrass| (((|List| (|TaylorSeries| |#1|)) (|Symbol|) (|TaylorSeries| |#1|)) "\\spad{weierstrass(v,ts)} where \\spad{v} is a variable and \\spad{ts} is \\indented{1}{a TaylorSeries,{} impements the Weierstrass Preparation} \\indented{1}{Theorem. The result is a list of TaylorSeries that} \\indented{1}{are the coefficients of the equivalent series.}")) (|clikeUniv| (((|Mapping| (|SparseUnivariatePolynomial| (|Polynomial| |#1|)) (|Polynomial| |#1|)) (|Symbol|)) "\\spad{clikeUniv(v)} is used internally.")) (|sts2stst| (((|Stream| (|Stream| (|Polynomial| |#1|))) (|Symbol|) (|Stream| (|Polynomial| |#1|))) "\\spad{sts2stst(v,s)} is used internally.")) (|cfirst| (((|Mapping| (|Stream| (|Polynomial| |#1|)) (|Stream| (|Polynomial| |#1|))) (|NonNegativeInteger|)) "\\spad{cfirst n} is used internally.")) (|crest| (((|Mapping| (|Stream| (|Polynomial| |#1|)) (|Stream| (|Polynomial| |#1|))) (|NonNegativeInteger|)) "\\spad{crest n} is used internally.")))
NIL
NIL
-(-1188 K R UP -3091)
+(-1190 K R UP -3094)
((|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
-(-1189)
+(-1191)
((|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
-(-1190)
+(-1192)
((|constructor| (NIL "This domain represents the `while' iterator syntax.")) (|condition| (((|SpadAst|) $) "\\spad{condition(i)} returns the condition of the while iterator `i'.")))
NIL
NIL
-(-1191 R |VarSet| E P |vl| |wl| |wtlevel|)
+(-1193 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: 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)")))
-((-3987 |has| |#1| (-146)) (-3986 |has| |#1| (-146)) (-3989 . T))
-((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-311))))
-(-1192 R E V P)
+((-3991 |has| |#1| (-146)) (-3990 |has| |#1| (-146)) (-3993 . T))
+((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))))
+(-1194 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}{MM Research Preprints,{} 1987.} \\indented{1}{[2] \\spad{D}. \\spad{M}. WANG \"An implementation of the characteristic set method in Maple\"} \\indented{6}{Proc. \\spad{DISCO'92}. Bath,{} England.}")) (|characteristicSerie| (((|List| $) (|List| |#4|)) "\\axiom{characteristicSerie(ps)} returns the same as \\axiom{characteristicSerie(ps,{}initiallyReduced?,{}initiallyReduce)}.") (((|List| $) (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{characteristicSerie(ps,{}redOp?,{}redOp)} returns a list \\axiom{lts} of triangular sets such that the zero set of \\axiom{ps} is the union of the regular zero sets of the members of \\axiom{lts}. This is made by the Ritt and Wu Wen Tsun process applying the operation \\axiom{characteristicSet(ps,{}redOp?,{}redOp)} to compute characteristic sets in Wu Wen Tsun sense.")) (|characteristicSet| (((|Union| $ "failed") (|List| |#4|)) "\\axiom{characteristicSet(ps)} returns the same as \\axiom{characteristicSet(ps,{}initiallyReduced?,{}initiallyReduce)}.") (((|Union| $ "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{characteristicSet(ps,{}redOp?,{}redOp)} returns a non-contradictory characteristic set of \\axiom{ps} in Wu Wen Tsun sense \\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 = f*q + redOp(\\spad{p},{}\\spad{q})}.")) (|medialSet| (((|Union| $ "failed") (|List| |#4|)) "\\axiom{medial(ps)} returns the same as \\axiom{medialSet(ps,{}initiallyReduced?,{}initiallyReduce)}.") (((|Union| $ "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{medialSet(ps,{}redOp?,{}redOp)} returns \\axiom{bs} a basic set (in Wu Wen Tsun sense \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?}) of some set generating the same ideal as \\axiom{ps} (with rank not higher than any basic set of \\axiom{ps}),{} if no non-zero constant polynomials appear during the computatioms,{} else \\axiom{\"failed\"} is returned. In the former case,{} \\axiom{bs} has to be understood as a candidate for being a characteristic set of \\axiom{ps}. In the original algorithm,{} \\axiom{bs} is simply a basic set of \\axiom{ps}.")))
-((-3993 . T) (-3992 . T))
-((-12 (|HasCategory| |#4| (QUOTE (-1013))) (|HasCategory| |#4| (|%list| (QUOTE -259) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-554 (-473)))) (|HasCategory| |#4| (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#3| (QUOTE (-317))) (|HasCategory| |#4| (QUOTE (-553 (-773)))) (|HasCategory| |#4| (QUOTE (-72))))
-(-1193 R)
+((-3997 . T) (-3996 . T))
+((-12 (|HasCategory| |#4| (QUOTE (-1015))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-555 (-474)))) (|HasCategory| |#4| (QUOTE (-1015))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#3| (QUOTE (-318))) (|HasCategory| |#4| (QUOTE (-554 (-774)))) (|HasCategory| |#4| (QUOTE (-72))))
+(-1195 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.fr)")))
-((-3986 . T) (-3987 . T) (-3989 . T))
+((-3990 . T) (-3991 . T) (-3993 . T))
NIL
-(-1194 |vl| R)
+(-1196 |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.")))
-((-3989 . T) (-3985 |has| |#2| (-6 -3985)) (-3987 . T) (-3986 . T))
-((|HasCategory| |#2| (QUOTE (-146))) (|HasAttribute| |#2| (QUOTE -3985)))
-(-1195 R |VarSet| XPOLY)
+((-3993 . T) (-3989 |has| |#2| (-6 -3989)) (-3991 . T) (-3990 . T))
+((|HasCategory| |#2| (QUOTE (-146))) (|HasAttribute| |#2| (QUOTE -3989)))
+(-1197 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.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
-(-1196 S -3091)
+(-1198 S -3094)
((|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}.")))
NIL
-((|HasCategory| |#2| (QUOTE (-317))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))))
-(-1197 -3091)
+((|HasCategory| |#2| (QUOTE (-318))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))))
+(-1199 -3094)
((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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}.")))
-((-3984 . T) (-3990 . T) (-3985 . T) ((-3994 "*") . T) (-3986 . T) (-3987 . T) (-3989 . T))
+((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T))
NIL
-(-1198 |vl| R)
+(-1200 |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| $) "\\spad{v * x} returns the product of a variable \\spad{x} by \\spad{x}.")))
-((-3985 |has| |#2| (-6 -3985)) (-3987 . T) (-3986 . T) (-3989 . T))
+((-3989 |has| |#2| (-6 -3989)) (-3991 . T) (-3990 . T) (-3993 . T))
NIL
-(-1199 |VarSet| R)
+(-1201 |VarSet| R)
((|constructor| (NIL "This domain constructor implements polynomials in non-commutative variables written in the Poincare-Birkhoff-Witt basis from the Lyndon basis. These polynomials can be used to compute Baker-Campbell-Hausdorff relations. \\newline Author: Michel Petitot (petitot@lifl.fr).")) (|log| (($ $ (|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}}.")))
-((-3985 |has| |#2| (-6 -3985)) (-3987 . T) (-3986 . T) (-3989 . T))
-((|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-655 (-347 (-484))))) (|HasAttribute| |#2| (QUOTE -3985)))
-(-1200 R)
+((-3989 |has| |#2| (-6 -3989)) (-3991 . T) (-3990 . T) (-3993 . T))
+((|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-656 (-348 (-485))))) (|HasAttribute| |#2| (QUOTE -3989)))
+(-1202 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.")))
-((-3985 |has| |#1| (-6 -3985)) (-3987 . T) (-3986 . T) (-3989 . T))
-((|HasCategory| |#1| (QUOTE (-146))) (|HasAttribute| |#1| (QUOTE -3985)))
-(-1201 |vl| R)
+((-3989 |has| |#1| (-6 -3989)) (-3991 . T) (-3990 . T) (-3993 . T))
+((|HasCategory| |#1| (QUOTE (-146))) (|HasAttribute| |#1| (QUOTE -3989)))
+(-1203 |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|) $) "\\spad{maxdeg(p)} returns the greatest leading word in the support of \\spad{p}.")))
-((-3985 |has| |#2| (-6 -3985)) (-3987 . T) (-3986 . T) (-3989 . T))
+((-3989 |has| |#2| (-6 -3989)) (-3991 . T) (-3990 . T) (-3993 . T))
NIL
-(-1202 R E)
+(-1204 R E)
((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and words belonging to an arbitrary \\spadtype{OrderedMonoid}. This type is used,{} for instance,{} by the \\spadtype{XDistributedPolynomial} domain constructor where the Monoid is free.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (/ (($ $ |#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}.")))
-((-3989 . T) (-3990 |has| |#1| (-6 -3990)) (-3985 |has| |#1| (-6 -3985)) (-3987 . T) (-3986 . T))
-((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-311))) (|HasAttribute| |#1| (QUOTE -3989)) (|HasAttribute| |#1| (QUOTE -3990)) (|HasAttribute| |#1| (QUOTE -3985)))
-(-1203 |VarSet| R)
+((-3993 . T) (-3994 |has| |#1| (-6 -3994)) (-3989 |has| |#1| (-6 -3989)) (-3991 . T) (-3990 . T))
+((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasAttribute| |#1| (QUOTE -3993)) (|HasAttribute| |#1| (QUOTE -3994)) (|HasAttribute| |#1| (QUOTE -3989)))
+(-1205 |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.")))
-((-3985 |has| |#2| (-6 -3985)) (-3987 . T) (-3986 . T) (-3989 . T))
-((|HasCategory| |#2| (QUOTE (-146))) (|HasAttribute| |#2| (QUOTE -3985)))
-(-1204)
+((-3989 |has| |#2| (-6 -3989)) (-3991 . T) (-3990 . T) (-3993 . T))
+((|HasCategory| |#2| (QUOTE (-146))) (|HasAttribute| |#2| (QUOTE -3989)))
+(-1206)
((|constructor| (NIL "This domain provides representations of Young diagrams.")) (|shape| (((|Partition|) $) "\\spad{shape x} returns the partition shaping \\spad{x}.")) (|youngDiagram| (($ (|List| (|PositiveInteger|))) "\\spad{youngDiagram l} returns an object representing a Young diagram with shape given by the list of integers \\spad{l}")))
NIL
NIL
-(-1205 A)
+(-1207 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
-(-1206 R |ls| |ls2|)
+(-1208 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}(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}(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
-(-1207 R)
+(-1209 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}'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}'s are 0,{} \"failed\" if the \\spad{vi}'s are linearly independent over the integers.")) (|linearlyDependentOverZ?| (((|Boolean|) (|Vector| |#1|)) "\\spad{linearlyDependentOverZ?([v1,...,vn])} returns \\spad{true} if the \\spad{vi}'s are linearly dependent over the integers,{} \\spad{false} otherwise.")))
NIL
NIL
-(-1208 |p|)
+(-1210 |p|)
((|constructor| (NIL "IntegerMod(\\spad{n}) creates the ring of integers reduced modulo the integer \\spad{n}.")))
-(((-3994 "*") . T) (-3986 . T) (-3987 . T) (-3989 . T))
+(((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T))
NIL
NIL
NIL
@@ -4780,4 +4788,4 @@ NIL
NIL
NIL
NIL
-((-3 NIL 1962119 1962124 1962129 1962134) (-2 NIL 1962099 1962104 1962109 1962114) (-1 NIL 1962079 1962084 1962089 1962094) (0 NIL 1962059 1962064 1962069 1962074) (-1208 "ZMOD.spad" 1961868 1961881 1961997 1962054) (-1207 "ZLINDEP.spad" 1960966 1960977 1961858 1961863) (-1206 "ZDSOLVE.spad" 1950927 1950949 1960956 1960961) (-1205 "YSTREAM.spad" 1950422 1950433 1950917 1950922) (-1204 "YDIAGRAM.spad" 1950056 1950065 1950412 1950417) (-1203 "XRPOLY.spad" 1949276 1949296 1949912 1949981) (-1202 "XPR.spad" 1947071 1947084 1948994 1949093) (-1201 "XPOLYC.spad" 1946390 1946406 1946997 1947066) (-1200 "XPOLY.spad" 1945945 1945956 1946246 1946315) (-1199 "XPBWPOLY.spad" 1944416 1944436 1945751 1945820) (-1198 "XFALG.spad" 1941464 1941480 1944342 1944411) (-1197 "XF.spad" 1939927 1939942 1941366 1941459) (-1196 "XF.spad" 1938370 1938387 1939811 1939816) (-1195 "XEXPPKG.spad" 1937629 1937655 1938360 1938365) (-1194 "XDPOLY.spad" 1937243 1937259 1937485 1937554) (-1193 "XALG.spad" 1936911 1936922 1937199 1937238) (-1192 "WUTSET.spad" 1932914 1932931 1936545 1936572) (-1191 "WP.spad" 1932121 1932165 1932772 1932839) (-1190 "WHILEAST.spad" 1931919 1931928 1932111 1932116) (-1189 "WHEREAST.spad" 1931590 1931599 1931909 1931914) (-1188 "WFFINTBS.spad" 1929253 1929275 1931580 1931585) (-1187 "WEIER.spad" 1927475 1927486 1929243 1929248) (-1186 "VSPACE.spad" 1927148 1927159 1927443 1927470) (-1185 "VSPACE.spad" 1926841 1926854 1927138 1927143) (-1184 "VOID.spad" 1926518 1926527 1926831 1926836) (-1183 "VIEWDEF.spad" 1921719 1921728 1926508 1926513) (-1182 "VIEW3D.spad" 1905680 1905689 1921709 1921714) (-1181 "VIEW2D.spad" 1893579 1893588 1905670 1905675) (-1180 "VIEW.spad" 1891299 1891308 1893569 1893574) (-1179 "VECTOR2.spad" 1889938 1889951 1891289 1891294) (-1178 "VECTOR.spad" 1888657 1888668 1888908 1888935) (-1177 "VECTCAT.spad" 1886569 1886580 1888625 1888652) (-1176 "VECTCAT.spad" 1884290 1884303 1886348 1886353) (-1175 "VARIABLE.spad" 1884070 1884085 1884280 1884285) (-1174 "UTYPE.spad" 1883714 1883723 1884060 1884065) (-1173 "UTSODETL.spad" 1883009 1883033 1883670 1883675) (-1172 "UTSODE.spad" 1881225 1881245 1882999 1883004) (-1171 "UTSCAT.spad" 1878704 1878720 1881123 1881220) (-1170 "UTSCAT.spad" 1875851 1875869 1878272 1878277) (-1169 "UTS2.spad" 1875446 1875481 1875841 1875846) (-1168 "UTS.spad" 1870458 1870486 1873978 1874075) (-1167 "URAGG.spad" 1865179 1865190 1870448 1870453) (-1166 "URAGG.spad" 1859864 1859877 1865135 1865140) (-1165 "UPXSSING.spad" 1857632 1857658 1859068 1859201) (-1164 "UPXSCONS.spad" 1855450 1855470 1855823 1855972) (-1163 "UPXSCCA.spad" 1854021 1854041 1855296 1855445) (-1162 "UPXSCCA.spad" 1852734 1852756 1854011 1854016) (-1161 "UPXSCAT.spad" 1851323 1851339 1852580 1852729) (-1160 "UPXS2.spad" 1850866 1850919 1851313 1851318) (-1159 "UPXS.spad" 1848221 1848249 1849057 1849206) (-1158 "UPSQFREE.spad" 1846636 1846650 1848211 1848216) (-1157 "UPSCAT.spad" 1844431 1844455 1846534 1846631) (-1156 "UPSCAT.spad" 1841927 1841953 1844032 1844037) (-1155 "UPOLYC2.spad" 1841398 1841417 1841917 1841922) (-1154 "UPOLYC.spad" 1836478 1836489 1841240 1841393) (-1153 "UPOLYC.spad" 1831476 1831489 1836240 1836245) (-1152 "UPMP.spad" 1830408 1830421 1831466 1831471) (-1151 "UPDIVP.spad" 1829973 1829987 1830398 1830403) (-1150 "UPDECOMP.spad" 1828234 1828248 1829963 1829968) (-1149 "UPCDEN.spad" 1827451 1827467 1828224 1828229) (-1148 "UP2.spad" 1826815 1826836 1827441 1827446) (-1147 "UP.spad" 1824285 1824300 1824672 1824825) (-1146 "UNISEG2.spad" 1823782 1823795 1824241 1824246) (-1145 "UNISEG.spad" 1823135 1823146 1823701 1823706) (-1144 "UNIFACT.spad" 1822238 1822250 1823125 1823130) (-1143 "ULSCONS.spad" 1816281 1816301 1816651 1816800) (-1142 "ULSCCAT.spad" 1814018 1814038 1816127 1816276) (-1141 "ULSCCAT.spad" 1811863 1811885 1813974 1813979) (-1140 "ULSCAT.spad" 1810103 1810119 1811709 1811858) (-1139 "ULS2.spad" 1809617 1809670 1810093 1810098) (-1138 "ULS.spad" 1801883 1801911 1802828 1803251) (-1137 "UINT8.spad" 1801760 1801769 1801873 1801878) (-1136 "UINT64.spad" 1801636 1801645 1801750 1801755) (-1135 "UINT32.spad" 1801512 1801521 1801626 1801631) (-1134 "UINT16.spad" 1801388 1801397 1801502 1801507) (-1133 "UFD.spad" 1800453 1800462 1801314 1801383) (-1132 "UFD.spad" 1799580 1799591 1800443 1800448) (-1131 "UDVO.spad" 1798461 1798470 1799570 1799575) (-1130 "UDPO.spad" 1796042 1796053 1798417 1798422) (-1129 "TYPEAST.spad" 1795961 1795970 1796032 1796037) (-1128 "TYPE.spad" 1795893 1795902 1795951 1795956) (-1127 "TWOFACT.spad" 1794545 1794560 1795883 1795888) (-1126 "TUPLE.spad" 1794052 1794063 1794457 1794462) (-1125 "TUBETOOL.spad" 1790919 1790928 1794042 1794047) (-1124 "TUBE.spad" 1789566 1789583 1790909 1790914) (-1123 "TSETCAT.spad" 1777637 1777654 1789534 1789561) (-1122 "TSETCAT.spad" 1765694 1765713 1777593 1777598) (-1121 "TS.spad" 1764322 1764338 1765288 1765385) (-1120 "TRMANIP.spad" 1758686 1758703 1764010 1764015) (-1119 "TRIMAT.spad" 1757649 1757674 1758676 1758681) (-1118 "TRIGMNIP.spad" 1756176 1756193 1757639 1757644) (-1117 "TRIGCAT.spad" 1755688 1755697 1756166 1756171) (-1116 "TRIGCAT.spad" 1755198 1755209 1755678 1755683) (-1115 "TREE.spad" 1753838 1753849 1754870 1754897) (-1114 "TRANFUN.spad" 1753677 1753686 1753828 1753833) (-1113 "TRANFUN.spad" 1753514 1753525 1753667 1753672) (-1112 "TOPSP.spad" 1753188 1753197 1753504 1753509) (-1111 "TOOLSIGN.spad" 1752851 1752862 1753178 1753183) (-1110 "TEXTFILE.spad" 1751412 1751421 1752841 1752846) (-1109 "TEX1.spad" 1750968 1750979 1751402 1751407) (-1108 "TEX.spad" 1748162 1748171 1750958 1750963) (-1107 "TBCMPPK.spad" 1746263 1746286 1748152 1748157) (-1106 "TBAGG.spad" 1745321 1745344 1746243 1746258) (-1105 "TBAGG.spad" 1744387 1744412 1745311 1745316) (-1104 "TANEXP.spad" 1743795 1743806 1744377 1744382) (-1103 "TALGOP.spad" 1743519 1743530 1743785 1743790) (-1102 "TABLEAU.spad" 1743000 1743011 1743509 1743514) (-1101 "TABLE.spad" 1741275 1741298 1741545 1741572) (-1100 "TABLBUMP.spad" 1738054 1738065 1741265 1741270) (-1099 "SYSTEM.spad" 1737282 1737291 1738044 1738049) (-1098 "SYSSOLP.spad" 1734765 1734776 1737272 1737277) (-1097 "SYSPTR.spad" 1734664 1734673 1734755 1734760) (-1096 "SYSNNI.spad" 1733887 1733898 1734654 1734659) (-1095 "SYSINT.spad" 1733291 1733302 1733877 1733882) (-1094 "SYNTAX.spad" 1729625 1729634 1733281 1733286) (-1093 "SYMTAB.spad" 1727693 1727702 1729615 1729620) (-1092 "SYMS.spad" 1723722 1723731 1727683 1727688) (-1091 "SYMPOLY.spad" 1722855 1722866 1722937 1723064) (-1090 "SYMFUNC.spad" 1722356 1722367 1722845 1722850) (-1089 "SYMBOL.spad" 1719851 1719860 1722346 1722351) (-1088 "SUTS.spad" 1716964 1716992 1718383 1718480) (-1087 "SUPXS.spad" 1714306 1714334 1715155 1715304) (-1086 "SUPFRACF.spad" 1713411 1713429 1714296 1714301) (-1085 "SUP2.spad" 1712803 1712816 1713401 1713406) (-1084 "SUP.spad" 1709887 1709898 1710660 1710813) (-1083 "SUMRF.spad" 1708861 1708872 1709877 1709882) (-1082 "SUMFS.spad" 1708490 1708507 1708851 1708856) (-1081 "SULS.spad" 1700743 1700771 1701701 1702124) (-1080 "syntax.spad" 1700512 1700521 1700733 1700738) (-1079 "SUCH.spad" 1700202 1700217 1700502 1700507) (-1078 "SUBSPACE.spad" 1692333 1692348 1700192 1700197) (-1077 "SUBRESP.spad" 1691503 1691517 1692289 1692294) (-1076 "STTFNC.spad" 1687971 1687987 1691493 1691498) (-1075 "STTF.spad" 1684070 1684086 1687961 1687966) (-1074 "STTAYLOR.spad" 1676747 1676758 1683977 1683982) (-1073 "STRTBL.spad" 1675134 1675151 1675283 1675310) (-1072 "STRING.spad" 1674002 1674011 1674387 1674414) (-1071 "STREAM3.spad" 1673575 1673590 1673992 1673997) (-1070 "STREAM2.spad" 1672703 1672716 1673565 1673570) (-1069 "STREAM1.spad" 1672409 1672420 1672693 1672698) (-1068 "STREAM.spad" 1669405 1669416 1672012 1672027) (-1067 "STINPROD.spad" 1668341 1668357 1669395 1669400) (-1066 "STEPAST.spad" 1667575 1667584 1668331 1668336) (-1065 "STEP.spad" 1666892 1666901 1667565 1667570) (-1064 "STBL.spad" 1665282 1665310 1665449 1665464) (-1063 "STAGG.spad" 1663981 1663992 1665272 1665277) (-1062 "STAGG.spad" 1662678 1662691 1663971 1663976) (-1061 "STACK.spad" 1662100 1662111 1662350 1662377) (-1060 "SRING.spad" 1661860 1661869 1662090 1662095) (-1059 "SREGSET.spad" 1659592 1659609 1661494 1661521) (-1058 "SRDCMPK.spad" 1658169 1658189 1659582 1659587) (-1057 "SRAGG.spad" 1653352 1653361 1658137 1658164) (-1056 "SRAGG.spad" 1648555 1648566 1653342 1653347) (-1055 "SQMATRIX.spad" 1646232 1646250 1647148 1647235) (-1054 "SPLTREE.spad" 1640974 1640987 1645770 1645797) (-1053 "SPLNODE.spad" 1637594 1637607 1640964 1640969) (-1052 "SPFCAT.spad" 1636403 1636412 1637584 1637589) (-1051 "SPECOUT.spad" 1634955 1634964 1636393 1636398) (-1050 "SPADXPT.spad" 1627046 1627055 1634945 1634950) (-1049 "spad-parser.spad" 1626511 1626520 1627036 1627041) (-1048 "SPADAST.spad" 1626212 1626221 1626501 1626506) (-1047 "SPACEC.spad" 1610427 1610438 1626202 1626207) (-1046 "SPACE3.spad" 1610203 1610214 1610417 1610422) (-1045 "SORTPAK.spad" 1609752 1609765 1610159 1610164) (-1044 "SOLVETRA.spad" 1607515 1607526 1609742 1609747) (-1043 "SOLVESER.spad" 1605971 1605982 1607505 1607510) (-1042 "SOLVERAD.spad" 1601997 1602008 1605961 1605966) (-1041 "SOLVEFOR.spad" 1600459 1600477 1601987 1601992) (-1040 "SNTSCAT.spad" 1600059 1600076 1600427 1600454) (-1039 "SMTS.spad" 1598376 1598402 1599653 1599750) (-1038 "SMP.spad" 1596184 1596204 1596574 1596701) (-1037 "SMITH.spad" 1595029 1595054 1596174 1596179) (-1036 "SMATCAT.spad" 1593147 1593177 1594973 1595024) (-1035 "SMATCAT.spad" 1591197 1591229 1593025 1593030) (-1034 "SKAGG.spad" 1590166 1590177 1591165 1591192) (-1033 "SINT.spad" 1589465 1589474 1590032 1590161) (-1032 "SIMPAN.spad" 1589193 1589202 1589455 1589460) (-1031 "SIGNRF.spad" 1588318 1588329 1589183 1589188) (-1030 "SIGNEF.spad" 1587604 1587621 1588308 1588313) (-1029 "syntax.spad" 1587021 1587030 1587594 1587599) (-1028 "SIG.spad" 1586383 1586392 1587011 1587016) (-1027 "SHP.spad" 1584327 1584342 1586339 1586344) (-1026 "SHDP.spad" 1573820 1573847 1574337 1574434) (-1025 "SGROUP.spad" 1573428 1573437 1573810 1573815) (-1024 "SGROUP.spad" 1573034 1573045 1573418 1573423) (-1023 "catdef.spad" 1572744 1572756 1572855 1573029) (-1022 "catdef.spad" 1572300 1572312 1572565 1572739) (-1021 "SGCF.spad" 1565439 1565448 1572290 1572295) (-1020 "SFRTCAT.spad" 1564385 1564402 1565407 1565434) (-1019 "SFRGCD.spad" 1563448 1563468 1564375 1564380) (-1018 "SFQCMPK.spad" 1558261 1558281 1563438 1563443) (-1017 "SEXOF.spad" 1558104 1558144 1558251 1558256) (-1016 "SEXCAT.spad" 1555932 1555972 1558094 1558099) (-1015 "SEX.spad" 1555824 1555833 1555922 1555927) (-1014 "SETMN.spad" 1554284 1554301 1555814 1555819) (-1013 "SETCAT.spad" 1553769 1553778 1554274 1554279) (-1012 "SETCAT.spad" 1553252 1553263 1553759 1553764) (-1011 "SETAGG.spad" 1549801 1549812 1553232 1553247) (-1010 "SETAGG.spad" 1546358 1546371 1549791 1549796) (-1009 "SET.spad" 1544667 1544678 1545764 1545803) (-1008 "syntax.spad" 1544370 1544379 1544657 1544662) (-1007 "SEGXCAT.spad" 1543526 1543539 1544360 1544365) (-1006 "SEGCAT.spad" 1542451 1542462 1543516 1543521) (-1005 "SEGBIND2.spad" 1542149 1542162 1542441 1542446) (-1004 "SEGBIND.spad" 1541907 1541918 1542096 1542101) (-1003 "SEGAST.spad" 1541637 1541646 1541897 1541902) (-1002 "SEG2.spad" 1541072 1541085 1541593 1541598) (-1001 "SEG.spad" 1540885 1540896 1540991 1540996) (-1000 "SDVAR.spad" 1540161 1540172 1540875 1540880) (-999 "SDPOL.spad" 1537854 1537864 1538144 1538271) (-998 "SCPKG.spad" 1535944 1535954 1537844 1537849) (-997 "SCOPE.spad" 1535122 1535130 1535934 1535939) (-996 "SCACHE.spad" 1533819 1533829 1535112 1535117) (-995 "SASTCAT.spad" 1533729 1533737 1533809 1533814) (-994 "SAOS.spad" 1533602 1533610 1533719 1533724) (-993 "SAERFFC.spad" 1533316 1533335 1533592 1533597) (-992 "SAEFACT.spad" 1533018 1533037 1533306 1533311) (-991 "SAE.spad" 1530669 1530684 1531279 1531414) (-990 "RURPK.spad" 1528329 1528344 1530659 1530664) (-989 "RULESET.spad" 1527783 1527806 1528319 1528324) (-988 "RULECOLD.spad" 1527636 1527648 1527773 1527778) (-987 "RULE.spad" 1525885 1525908 1527626 1527631) (-986 "RTVALUE.spad" 1525621 1525629 1525875 1525880) (-985 "syntax.spad" 1525339 1525347 1525611 1525616) (-984 "RSETGCD.spad" 1521782 1521801 1525329 1525334) (-983 "RSETCAT.spad" 1511751 1511767 1521750 1521777) (-982 "RSETCAT.spad" 1501740 1501758 1511741 1511746) (-981 "RSDCMPK.spad" 1500241 1500260 1501730 1501735) (-980 "RRCC.spad" 1498626 1498655 1500231 1500236) (-979 "RRCC.spad" 1497009 1497040 1498616 1498621) (-978 "RPTAST.spad" 1496712 1496720 1496999 1497004) (-977 "RPOLCAT.spad" 1476217 1476231 1496580 1496707) (-976 "RPOLCAT.spad" 1455515 1455531 1475880 1475885) (-975 "ROMAN.spad" 1454844 1454852 1455381 1455510) (-974 "ROIRC.spad" 1453925 1453956 1454834 1454839) (-973 "RNS.spad" 1452902 1452910 1453827 1453920) (-972 "RNS.spad" 1451965 1451975 1452892 1452897) (-971 "RNGBIND.spad" 1451126 1451139 1451920 1451925) (-970 "RNG.spad" 1450862 1450870 1451116 1451121) (-969 "RMODULE.spad" 1450644 1450654 1450852 1450857) (-968 "RMCAT2.spad" 1450065 1450121 1450634 1450639) (-967 "RMATRIX.spad" 1448875 1448893 1449217 1449256) (-966 "RMATCAT.spad" 1444455 1444485 1448831 1448870) (-965 "RMATCAT.spad" 1439925 1439957 1444303 1444308) (-964 "RLINSET.spad" 1439630 1439640 1439915 1439920) (-963 "RINTERP.spad" 1439519 1439538 1439620 1439625) (-962 "RING.spad" 1438990 1438998 1439499 1439514) (-961 "RING.spad" 1438469 1438479 1438980 1438985) (-960 "RIDIST.spad" 1437862 1437870 1438459 1438464) (-959 "RGCHAIN.spad" 1436417 1436432 1437310 1437337) (-958 "RGBCSPC.spad" 1436207 1436218 1436407 1436412) (-957 "RGBCMDL.spad" 1435770 1435781 1436197 1436202) (-956 "RFFACTOR.spad" 1435233 1435243 1435760 1435765) (-955 "RFFACT.spad" 1434969 1434980 1435223 1435228) (-954 "RFDIST.spad" 1433966 1433974 1434959 1434964) (-953 "RF.spad" 1431641 1431651 1433956 1433961) (-952 "RETSOL.spad" 1431061 1431073 1431631 1431636) (-951 "RETRACT.spad" 1430490 1430500 1431051 1431056) (-950 "RETRACT.spad" 1429917 1429929 1430480 1430485) (-949 "RETAST.spad" 1429730 1429738 1429907 1429912) (-948 "RESRING.spad" 1429078 1429124 1429668 1429725) (-947 "RESLATC.spad" 1428403 1428413 1429068 1429073) (-946 "REPSQ.spad" 1428135 1428145 1428393 1428398) (-945 "REPDB.spad" 1427843 1427853 1428125 1428130) (-944 "REP2.spad" 1417558 1417568 1427685 1427690) (-943 "REP1.spad" 1411779 1411789 1417508 1417513) (-942 "REP.spad" 1409334 1409342 1411769 1411774) (-941 "REGSET.spad" 1407160 1407176 1408968 1408995) (-940 "REF.spad" 1406679 1406689 1407150 1407155) (-939 "REDORDER.spad" 1405886 1405902 1406669 1406674) (-938 "RECLOS.spad" 1404783 1404802 1405486 1405579) (-937 "REALSOLV.spad" 1403924 1403932 1404773 1404778) (-936 "REAL0Q.spad" 1401223 1401237 1403914 1403919) (-935 "REAL0.spad" 1398068 1398082 1401213 1401218) (-934 "REAL.spad" 1397941 1397949 1398058 1398063) (-933 "RDUCEAST.spad" 1397663 1397671 1397931 1397936) (-932 "RDIV.spad" 1397319 1397343 1397653 1397658) (-931 "RDIST.spad" 1396887 1396897 1397309 1397314) (-930 "RDETRS.spad" 1395752 1395769 1396877 1396882) (-929 "RDETR.spad" 1393892 1393909 1395742 1395747) (-928 "RDEEFS.spad" 1392992 1393008 1393882 1393887) (-927 "RDEEF.spad" 1392003 1392019 1392982 1392987) (-926 "RCFIELD.spad" 1389222 1389230 1391905 1391998) (-925 "RCFIELD.spad" 1386527 1386537 1389212 1389217) (-924 "RCAGG.spad" 1384464 1384474 1386517 1386522) (-923 "RCAGG.spad" 1382328 1382340 1384383 1384388) (-922 "RATRET.spad" 1381689 1381699 1382318 1382323) (-921 "RATFACT.spad" 1381382 1381393 1381679 1381684) (-920 "RANDSRC.spad" 1380702 1380710 1381372 1381377) (-919 "RADUTIL.spad" 1380459 1380467 1380692 1380697) (-918 "RADIX.spad" 1377504 1377517 1379049 1379142) (-917 "RADFF.spad" 1375421 1375457 1375539 1375695) (-916 "RADCAT.spad" 1375017 1375025 1375411 1375416) (-915 "RADCAT.spad" 1374611 1374621 1375007 1375012) (-914 "QUEUE.spad" 1374025 1374035 1374283 1374310) (-913 "QUATCT2.spad" 1373646 1373664 1374015 1374020) (-912 "QUATCAT.spad" 1371817 1371827 1373576 1373641) (-911 "QUATCAT.spad" 1369753 1369765 1371514 1371519) (-910 "QUAT.spad" 1368360 1368370 1368702 1368767) (-909 "QUAGG.spad" 1367194 1367204 1368328 1368355) (-908 "QQUTAST.spad" 1366963 1366971 1367184 1367189) (-907 "QFORM.spad" 1366582 1366596 1366953 1366958) (-906 "QFCAT2.spad" 1366275 1366291 1366572 1366577) (-905 "QFCAT.spad" 1364978 1364988 1366177 1366270) (-904 "QFCAT.spad" 1363314 1363326 1364515 1364520) (-903 "QEQUAT.spad" 1362873 1362881 1363304 1363309) (-902 "QCMPACK.spad" 1357788 1357807 1362863 1362868) (-901 "QALGSET2.spad" 1355784 1355802 1357778 1357783) (-900 "QALGSET.spad" 1351889 1351921 1355698 1355703) (-899 "PWFFINTB.spad" 1349305 1349326 1351879 1351884) (-898 "PUSHVAR.spad" 1348644 1348663 1349295 1349300) (-897 "PTRANFN.spad" 1344780 1344790 1348634 1348639) (-896 "PTPACK.spad" 1341868 1341878 1344770 1344775) (-895 "PTFUNC2.spad" 1341691 1341705 1341858 1341863) (-894 "PTCAT.spad" 1340946 1340956 1341659 1341686) (-893 "PSQFR.spad" 1340261 1340285 1340936 1340941) (-892 "PSEUDLIN.spad" 1339147 1339157 1340251 1340256) (-891 "PSETPK.spad" 1325852 1325868 1339025 1339030) (-890 "PSETCAT.spad" 1320252 1320275 1325832 1325847) (-889 "PSETCAT.spad" 1314626 1314651 1320208 1320213) (-888 "PSCURVE.spad" 1313625 1313633 1314616 1314621) (-887 "PSCAT.spad" 1312408 1312437 1313523 1313620) (-886 "PSCAT.spad" 1311281 1311312 1312398 1312403) (-885 "PRTITION.spad" 1309979 1309987 1311271 1311276) (-884 "PRTDAST.spad" 1309698 1309706 1309969 1309974) (-883 "PRS.spad" 1299316 1299333 1309654 1309659) (-882 "PRQAGG.spad" 1298751 1298761 1299284 1299311) (-881 "PROPLOG.spad" 1298355 1298363 1298741 1298746) (-880 "PROPFUN2.spad" 1297978 1297991 1298345 1298350) (-879 "PROPFUN1.spad" 1297384 1297395 1297968 1297973) (-878 "PROPFRML.spad" 1295952 1295963 1297374 1297379) (-877 "PROPERTY.spad" 1295448 1295456 1295942 1295947) (-876 "PRODUCT.spad" 1293145 1293157 1293429 1293484) (-875 "PRINT.spad" 1292897 1292905 1293135 1293140) (-874 "PRIMES.spad" 1291158 1291168 1292887 1292892) (-873 "PRIMELT.spad" 1289279 1289293 1291148 1291153) (-872 "PRIMCAT.spad" 1288922 1288930 1289269 1289274) (-871 "PRIMARR2.spad" 1287689 1287701 1288912 1288917) (-870 "PRIMARR.spad" 1286744 1286754 1286914 1286941) (-869 "PREASSOC.spad" 1286126 1286138 1286734 1286739) (-868 "PR.spad" 1284644 1284656 1285343 1285470) (-867 "PPCURVE.spad" 1283781 1283789 1284634 1284639) (-866 "PORTNUM.spad" 1283572 1283580 1283771 1283776) (-865 "POLYROOT.spad" 1282421 1282443 1283528 1283533) (-864 "POLYLIFT.spad" 1281686 1281709 1282411 1282416) (-863 "POLYCATQ.spad" 1279812 1279834 1281676 1281681) (-862 "POLYCAT.spad" 1273314 1273335 1279680 1279807) (-861 "POLYCAT.spad" 1266336 1266359 1272704 1272709) (-860 "POLY2UP.spad" 1265788 1265802 1266326 1266331) (-859 "POLY2.spad" 1265385 1265397 1265778 1265783) (-858 "POLY.spad" 1263053 1263063 1263568 1263695) (-857 "POLUTIL.spad" 1262018 1262047 1263009 1263014) (-856 "POLTOPOL.spad" 1260766 1260781 1262008 1262013) (-855 "POINT.spad" 1259649 1259659 1259736 1259763) (-854 "PNTHEORY.spad" 1256351 1256359 1259639 1259644) (-853 "PMTOOLS.spad" 1255126 1255140 1256341 1256346) (-852 "PMSYM.spad" 1254675 1254685 1255116 1255121) (-851 "PMQFCAT.spad" 1254266 1254280 1254665 1254670) (-850 "PMPREDFS.spad" 1253728 1253750 1254256 1254261) (-849 "PMPRED.spad" 1253215 1253229 1253718 1253723) (-848 "PMPLCAT.spad" 1252292 1252310 1253144 1253149) (-847 "PMLSAGG.spad" 1251877 1251891 1252282 1252287) (-846 "PMKERNEL.spad" 1251456 1251468 1251867 1251872) (-845 "PMINS.spad" 1251036 1251046 1251446 1251451) (-844 "PMFS.spad" 1250613 1250631 1251026 1251031) (-843 "PMDOWN.spad" 1249903 1249917 1250603 1250608) (-842 "PMASSFS.spad" 1248878 1248894 1249893 1249898) (-841 "PMASS.spad" 1247896 1247904 1248868 1248873) (-840 "PLOTTOOL.spad" 1247676 1247684 1247886 1247891) (-839 "PLOT3D.spad" 1244140 1244148 1247666 1247671) (-838 "PLOT1.spad" 1243313 1243323 1244130 1244135) (-837 "PLOT.spad" 1238236 1238244 1243303 1243308) (-836 "PLEQN.spad" 1225638 1225665 1238226 1238231) (-835 "PINTERPA.spad" 1225422 1225438 1225628 1225633) (-834 "PINTERP.spad" 1225044 1225063 1225412 1225417) (-833 "PID.spad" 1224018 1224026 1224970 1225039) (-832 "PICOERCE.spad" 1223675 1223685 1224008 1224013) (-831 "PI.spad" 1223292 1223300 1223649 1223670) (-830 "PGROEB.spad" 1221901 1221915 1223282 1223287) (-829 "PGE.spad" 1213574 1213582 1221891 1221896) (-828 "PGCD.spad" 1212528 1212545 1213564 1213569) (-827 "PFRPAC.spad" 1211677 1211687 1212518 1212523) (-826 "PFR.spad" 1208380 1208390 1211579 1211672) (-825 "PFOTOOLS.spad" 1207638 1207654 1208370 1208375) (-824 "PFOQ.spad" 1207008 1207026 1207628 1207633) (-823 "PFO.spad" 1206427 1206454 1206998 1207003) (-822 "PFECAT.spad" 1204137 1204145 1206353 1206422) (-821 "PFECAT.spad" 1201875 1201885 1204093 1204098) (-820 "PFBRU.spad" 1199763 1199775 1201865 1201870) (-819 "PFBR.spad" 1197323 1197346 1199753 1199758) (-818 "PF.spad" 1196897 1196909 1197128 1197221) (-817 "PERMGRP.spad" 1191667 1191677 1196887 1196892) (-816 "PERMCAT.spad" 1190328 1190338 1191647 1191662) (-815 "PERMAN.spad" 1188884 1188898 1190318 1190323) (-814 "PERM.spad" 1184694 1184704 1188717 1188732) (-813 "PENDTREE.spad" 1184108 1184118 1184388 1184393) (-812 "PDSPC.spad" 1182921 1182931 1184098 1184103) (-811 "PDSPC.spad" 1181732 1181744 1182911 1182916) (-810 "PDRING.spad" 1181574 1181584 1181712 1181727) (-809 "PDMOD.spad" 1181390 1181402 1181542 1181569) (-808 "PDECOMP.spad" 1180860 1180877 1181380 1181385) (-807 "PDDOM.spad" 1180298 1180311 1180850 1180855) (-806 "PDDOM.spad" 1179734 1179749 1180288 1180293) (-805 "PCOMP.spad" 1179587 1179600 1179724 1179729) (-804 "PBWLB.spad" 1178185 1178202 1179577 1179582) (-803 "PATTERN2.spad" 1177923 1177935 1178175 1178180) (-802 "PATTERN1.spad" 1176267 1176283 1177913 1177918) (-801 "PATTERN.spad" 1170842 1170852 1176257 1176262) (-800 "PATRES2.spad" 1170514 1170528 1170832 1170837) (-799 "PATRES.spad" 1168097 1168109 1170504 1170509) (-798 "PATMATCH.spad" 1166338 1166369 1167849 1167854) (-797 "PATMAB.spad" 1165767 1165777 1166328 1166333) (-796 "PATLRES.spad" 1164853 1164867 1165757 1165762) (-795 "PATAB.spad" 1164617 1164627 1164843 1164848) (-794 "PARTPERM.spad" 1162673 1162681 1164607 1164612) (-793 "PARSURF.spad" 1162107 1162135 1162663 1162668) (-792 "PARSU2.spad" 1161904 1161920 1162097 1162102) (-791 "script-parser.spad" 1161424 1161432 1161894 1161899) (-790 "PARSCURV.spad" 1160858 1160886 1161414 1161419) (-789 "PARSC2.spad" 1160649 1160665 1160848 1160853) (-788 "PARPCURV.spad" 1160111 1160139 1160639 1160644) (-787 "PARPC2.spad" 1159902 1159918 1160101 1160106) (-786 "PARAMAST.spad" 1159030 1159038 1159892 1159897) (-785 "PAN2EXPR.spad" 1158442 1158450 1159020 1159025) (-784 "PALETTE.spad" 1157556 1157564 1158432 1158437) (-783 "PAIR.spad" 1156630 1156643 1157199 1157204) (-782 "PADICRC.spad" 1154035 1154053 1155198 1155291) (-781 "PADICRAT.spad" 1152095 1152107 1152308 1152401) (-780 "PADICCT.spad" 1150644 1150656 1152021 1152090) (-779 "PADIC.spad" 1150347 1150359 1150570 1150639) (-778 "PADEPAC.spad" 1149036 1149055 1150337 1150342) (-777 "PADE.spad" 1147788 1147804 1149026 1149031) (-776 "OWP.spad" 1147036 1147066 1147646 1147713) (-775 "OVERSET.spad" 1146609 1146617 1147026 1147031) (-774 "OVAR.spad" 1146390 1146413 1146599 1146604) (-773 "OUTFORM.spad" 1135798 1135806 1146380 1146385) (-772 "OUTBFILE.spad" 1135232 1135240 1135788 1135793) (-771 "OUTBCON.spad" 1134302 1134310 1135222 1135227) (-770 "OUTBCON.spad" 1133370 1133380 1134292 1134297) (-769 "OUT.spad" 1132488 1132496 1133360 1133365) (-768 "OSI.spad" 1131963 1131971 1132478 1132483) (-767 "OSGROUP.spad" 1131881 1131889 1131953 1131958) (-766 "ORTHPOL.spad" 1130392 1130402 1131824 1131829) (-765 "OREUP.spad" 1129886 1129914 1130113 1130152) (-764 "ORESUP.spad" 1129228 1129252 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"HEXADEC.spad" 685620 685628 685985 686078) (-423 "HEUGCD.spad" 684711 684722 685610 685615) (-422 "HELLFDIV.spad" 684317 684341 684701 684706) (-421 "HEAP.spad" 683774 683784 683989 684016) (-420 "HEADAST.spad" 683315 683323 683764 683769) (-419 "HDP.spad" 672948 672964 673325 673422) (-418 "HDMP.spad" 670495 670510 671111 671238) (-417 "HB.spad" 668770 668778 670485 670490) (-416 "HASHTBL.spad" 667104 667135 667315 667342) (-415 "HASAST.spad" 666820 666828 667094 667099) (-414 "HACKPI.spad" 666311 666319 666722 666815) (-413 "GTSET.spad" 665238 665254 665945 665972) (-412 "GSTBL.spad" 663621 663656 663795 663810) (-411 "GSERIES.spad" 660993 661020 661812 661961) (-410 "GROUP.spad" 660266 660274 660973 660988) (-409 "GROUP.spad" 659547 659557 660256 660261) (-408 "GROEBSOL.spad" 658041 658062 659537 659542) (-407 "GRMOD.spad" 656622 656634 658031 658036) (-406 "GRMOD.spad" 655201 655215 656612 656617) (-405 "GRIMAGE.spad" 648114 648122 655191 655196) (-404 "GRDEF.spad" 646493 646501 648104 648109) (-403 "GRAY.spad" 644964 644972 646483 646488) (-402 "GRALG.spad" 644059 644071 644954 644959) (-401 "GRALG.spad" 643152 643166 644049 644054) (-400 "GPOLSET.spad" 642610 642633 642822 642849) (-399 "GOSPER.spad" 641887 641905 642600 642605) (-398 "GMODPOL.spad" 641035 641062 641855 641882) (-397 "GHENSEL.spad" 640118 640132 641025 641030) (-396 "GENUPS.spad" 636411 636424 640108 640113) (-395 "GENUFACT.spad" 635988 635998 636401 636406) (-394 "GENPGCD.spad" 635590 635607 635978 635983) (-393 "GENMFACT.spad" 635042 635061 635580 635585) (-392 "GENEEZ.spad" 633001 633014 635032 635037) (-391 "GDMP.spad" 630390 630407 631164 631291) (-390 "GCNAALG.spad" 624313 624340 630184 630251) (-389 "GCDDOM.spad" 623505 623513 624239 624308) (-388 "GCDDOM.spad" 622759 622769 623495 623500) (-387 "GBINTERN.spad" 618779 618817 622749 622754) (-386 "GBF.spad" 614562 614600 618769 618774) (-385 "GBEUCLID.spad" 612444 612482 614552 614557) (-384 "GB.spad" 609970 610008 612400 612405) (-383 "GAUSSFAC.spad" 609283 609291 609960 609965) (-382 "GALUTIL.spad" 607609 607619 609239 609244) (-381 "GALPOLYU.spad" 606063 606076 607599 607604) (-380 "GALFACTU.spad" 604276 604295 606053 606058) (-379 "GALFACT.spad" 594489 594500 604266 604271) (-378 "FUNDESC.spad" 594167 594175 594479 594484) (-377 "FUNCTION.spad" 594016 594028 594157 594162) (-376 "FT.spad" 592316 592324 594006 594011) (-375 "FSUPFACT.spad" 591230 591249 592266 592271) (-374 "FST.spad" 589316 589324 591220 591225) (-373 "FSRED.spad" 588796 588812 589306 589311) (-372 "FSPRMELT.spad" 587662 587678 588753 588758) (-371 "FSPECF.spad" 585753 585769 587652 587657) (-370 "FSINT.spad" 585413 585429 585743 585748) (-369 "FSERIES.spad" 584604 584616 585233 585332) (-368 "FSCINT.spad" 583921 583937 584594 584599) (-367 "FSAGG2.spad" 582656 582672 583911 583916) (-366 "FSAGG.spad" 581773 581783 582612 582651) (-365 "FSAGG.spad" 580852 580864 581693 581698) (-364 "FS2UPS.spad" 575367 575401 580842 580847) (-363 "FS2EXPXP.spad" 574508 574531 575357 575362) (-362 "FS2.spad" 574163 574179 574498 574503) (-361 "FS.spad" 568435 568445 573942 574158) (-360 "FS.spad" 562509 562521 568018 568023) (-359 "FRUTIL.spad" 561463 561473 562499 562504) (-358 "FRNAALG.spad" 556740 556750 561405 561458) (-357 "FRNAALG.spad" 552029 552041 556696 556701) (-356 "FRNAAF2.spad" 551477 551495 552019 552024) (-355 "FRMOD.spad" 550885 550915 551406 551411) (-354 "FRIDEAL2.spad" 550489 550521 550875 550880) (-353 "FRIDEAL.spad" 549714 549735 550469 550484) (-352 "FRETRCT.spad" 549233 549243 549704 549709) (-351 "FRETRCT.spad" 548659 548671 549132 549137) (-350 "FRAMALG.spad" 547039 547052 548615 548654) (-349 "FRAMALG.spad" 545451 545466 547029 547034) (-348 "FRAC2.spad" 545056 545068 545441 545446) (-347 "FRAC.spad" 543043 543053 543430 543603) (-346 "FR2.spad" 542379 542391 543033 543038) (-345 "FR.spad" 536167 536177 541440 541509) (-344 "FPS.spad" 533006 533014 536057 536162) (-343 "FPS.spad" 529873 529883 532926 532931) (-342 "FPC.spad" 528919 528927 529775 529868) (-341 "FPC.spad" 528051 528061 528909 528914) (-340 "FPATMAB.spad" 527813 527823 528041 528046) (-339 "FPARFRAC.spad" 526655 526672 527803 527808) (-338 "FORDER.spad" 526346 526370 526645 526650) (-337 "FNLA.spad" 525770 525792 526314 526341) (-336 "FNCAT.spad" 524365 524373 525760 525765) (-335 "FNAME.spad" 524257 524265 524355 524360) (-334 "FMONOID.spad" 523938 523948 524213 524218) (-333 "FMONCAT.spad" 521107 521117 523928 523933) (-332 "FMCAT.spad" 518783 518801 521075 521102) (-331 "FM1.spad" 518148 518160 518717 518744) (-330 "FM.spad" 517763 517775 518002 518029) (-329 "FLOATRP.spad" 515506 515520 517753 517758) (-328 "FLOATCP.spad" 512945 512959 515496 515501) (-327 "FLOAT.spad" 510036 510044 512811 512940) (-326 "FLINEXP.spad" 509758 509768 510026 510031) (-325 "FLINEXP.spad" 509437 509449 509707 509712) (-324 "FLASORT.spad" 508763 508775 509427 509432) (-323 "FLALG.spad" 506433 506452 508689 508758) (-322 "FLAGG2.spad" 505150 505166 506423 506428) (-321 "FLAGG.spad" 502216 502226 505130 505145) (-320 "FLAGG.spad" 499183 499195 502099 502104) (-319 "FINRALG.spad" 497268 497281 499139 499178) (-318 "FINRALG.spad" 495279 495294 497152 497157) (-317 "FINITE.spad" 494431 494439 495269 495274) (-316 "FINITE.spad" 493581 493591 494421 494426) (-315 "FINAALG.spad" 482766 482776 493523 493576) (-314 "FINAALG.spad" 471963 471975 482722 482727) (-313 "FILECAT.spad" 470497 470514 471953 471958) (-312 "FILE.spad" 470080 470090 470487 470492) (-311 "FIELD.spad" 469486 469494 469982 470075) (-310 "FIELD.spad" 468978 468988 469476 469481) (-309 "FGROUP.spad" 467641 467651 468958 468973) (-308 "FGLMICPK.spad" 466436 466451 467631 467636) (-307 "FFX.spad" 465822 465837 466155 466248) (-306 "FFSLPE.spad" 465333 465354 465812 465817) (-305 "FFPOLY2.spad" 464393 464410 465323 465328) (-304 "FFPOLY.spad" 455735 455746 464383 464388) (-303 "FFP.spad" 455143 455163 455454 455547) (-302 "FFNBX.spad" 453666 453686 454862 454955) (-301 "FFNBP.spad" 452190 452207 453385 453478) (-300 "FFNB.spad" 450658 450679 451874 451967) (-299 "FFINTBAS.spad" 448172 448191 450648 450653) (-298 "FFIELDC.spad" 445757 445765 448074 448167) (-297 "FFIELDC.spad" 443428 443438 445747 445752) (-296 "FFHOM.spad" 442200 442217 443418 443423) (-295 "FFF.spad" 439643 439654 442190 442195) (-294 "FFCGX.spad" 438501 438521 439362 439455) (-293 "FFCGP.spad" 437401 437421 438220 438313) (-292 "FFCG.spad" 436196 436217 437085 437178) (-291 "FFCAT2.spad" 435943 435983 436186 436191) (-290 "FFCAT.spad" 429108 429130 435782 435938) (-289 "FFCAT.spad" 422352 422376 429028 429033) (-288 "FF.spad" 421803 421819 422036 422129) (-287 "FEVALAB.spad" 421511 421521 421793 421798) (-286 "FEVALAB.spad" 420995 421007 421279 421284) (-285 "FDIVCAT.spad" 419091 419115 420985 420990) (-284 "FDIVCAT.spad" 417185 417211 419081 419086) (-283 "FDIV2.spad" 416841 416881 417175 417180) (-282 "FDIV.spad" 416299 416323 416831 416836) (-281 "FCTRDATA.spad" 415307 415315 416289 416294) (-280 "FCOMP.spad" 414686 414696 415297 415302) (-279 "FAXF.spad" 407721 407735 414588 414681) (-278 "FAXF.spad" 400808 400824 407677 407682) (-277 "FARRAY.spad" 399000 399010 400033 400060) (-276 "FAMR.spad" 397144 397156 398898 398995) (-275 "FAMR.spad" 395272 395286 397028 397033) (-274 "FAMONOID.spad" 394956 394966 395226 395231) (-273 "FAMONC.spad" 393276 393288 394946 394951) (-272 "FAGROUP.spad" 392916 392926 393172 393199) (-271 "FACUTIL.spad" 391128 391145 392906 392911) (-270 "FACTFUNC.spad" 390330 390340 391118 391123) (-269 "EXPUPXS.spad" 387222 387245 388521 388670) (-268 "EXPRTUBE.spad" 384510 384518 387212 387217) (-267 "EXPRODE.spad" 381678 381694 384500 384505) (-266 "EXPR2UPS.spad" 377800 377813 381668 381673) (-265 "EXPR2.spad" 377505 377517 377790 377795) (-264 "EXPR.spad" 373150 373160 373864 374151) (-263 "EXPEXPAN.spad" 370095 370120 370727 370820) (-262 "EXITAST.spad" 369831 369839 370085 370090) (-261 "EXIT.spad" 369502 369510 369821 369826) (-260 "EVALCYC.spad" 368962 368976 369492 369497) (-259 "EVALAB.spad" 368542 368552 368952 368957) (-258 "EVALAB.spad" 368120 368132 368532 368537) (-257 "EUCDOM.spad" 365710 365718 368046 368115) (-256 "EUCDOM.spad" 363362 363372 365700 365705) (-255 "ES2.spad" 362875 362891 363352 363357) (-254 "ES1.spad" 362445 362461 362865 362870) (-253 "ES.spad" 355316 355324 362435 362440) (-252 "ES.spad" 348108 348118 355229 355234) (-251 "ERROR.spad" 345435 345443 348098 348103) (-250 "EQTBL.spad" 343771 343793 343980 344007) (-249 "EQ2.spad" 343489 343501 343761 343766) (-248 "EQ.spad" 338395 338405 341190 341296) (-247 "EP.spad" 334721 334731 338385 338390) (-246 "ENV.spad" 333399 333407 334711 334716) (-245 "ENTIRER.spad" 333067 333075 333343 333394) (-244 "EMR.spad" 332355 332396 332993 333062) (-243 "ELTAGG.spad" 330609 330628 332345 332350) (-242 "ELTAGG.spad" 328827 328848 330565 330570) (-241 "ELTAB.spad" 328302 328315 328817 328822) (-240 "ELFUTS.spad" 327737 327756 328292 328297) (-239 "ELEMFUN.spad" 327426 327434 327727 327732) (-238 "ELEMFUN.spad" 327113 327123 327416 327421) (-237 "ELAGG.spad" 325084 325094 327093 327108) (-236 "ELAGG.spad" 322992 323004 325003 325008) (-235 "ELABOR.spad" 322338 322346 322982 322987) (-234 "ELABEXPR.spad" 321270 321278 322328 322333) (-233 "EFUPXS.spad" 318046 318076 321226 321231) (-232 "EFULS.spad" 314882 314905 318002 318007) (-231 "EFSTRUC.spad" 312897 312913 314872 314877) (-230 "EF.spad" 307673 307689 312887 312892) (-229 "EAB.spad" 305973 305981 307663 307668) (-228 "DVARCAT.spad" 302979 302989 305963 305968) (-227 "DVARCAT.spad" 299983 299995 302969 302974) (-226 "DSMP.spad" 297716 297730 298021 298148) (-225 "DSEXT.spad" 297018 297028 297706 297711) (-224 "DSEXT.spad" 296240 296252 296930 296935) (-223 "DROPT1.spad" 295905 295915 296230 296235) (-222 "DROPT0.spad" 290770 290778 295895 295900) (-221 "DROPT.spad" 284729 284737 290760 290765) (-220 "DRAWPT.spad" 282902 282910 284719 284724) (-219 "DRAWHACK.spad" 282210 282220 282892 282897) (-218 "DRAWCX.spad" 279688 279696 282200 282205) (-217 "DRAWCURV.spad" 279235 279250 279678 279683) (-216 "DRAWCFUN.spad" 268767 268775 279225 279230) (-215 "DRAW.spad" 261643 261656 268757 268762) (-214 "DQAGG.spad" 259821 259831 261611 261638) (-213 "DPOLCAT.spad" 255178 255194 259689 259816) (-212 "DPOLCAT.spad" 250621 250639 255134 255139) (-211 "DPMO.spad" 243324 243340 243462 243668) (-210 "DPMM.spad" 236040 236058 236165 236371) (-209 "DOMTMPLT.spad" 235811 235819 236030 236035) (-208 "DOMCTOR.spad" 235566 235574 235801 235806) (-207 "DOMAIN.spad" 234677 234685 235556 235561) (-206 "DMP.spad" 232270 232285 232840 232967) (-205 "DMEXT.spad" 232137 232147 232238 232265) (-204 "DLP.spad" 231497 231507 232127 232132) (-203 "DLIST.spad" 230118 230128 230722 230749) (-202 "DLAGG.spad" 228535 228545 230108 230113) (-201 "DIVRING.spad" 228077 228085 228479 228530) (-200 "DIVRING.spad" 227663 227673 228067 228072) (-199 "DISPLAY.spad" 225853 225861 227653 227658) (-198 "DIRPROD2.spad" 224671 224689 225843 225848) (-197 "DIRPROD.spad" 214041 214057 214681 214778) (-196 "DIRPCAT.spad" 213236 213252 213939 214036) (-195 "DIRPCAT.spad" 212057 212075 212762 212767) (-194 "DIOSP.spad" 210882 210890 212047 212052) (-193 "DIOPS.spad" 209878 209888 210862 210877) (-192 "DIOPS.spad" 208848 208860 209834 209839) (-191 "catdef.spad" 208706 208714 208838 208843) (-190 "DIFRING.spad" 208544 208552 208686 208701) (-189 "DIFFSPC.spad" 208123 208131 208534 208539) (-188 "DIFFSPC.spad" 207700 207710 208113 208118) (-187 "DIFFMOD.spad" 207189 207199 207668 207695) (-186 "DIFFDOM.spad" 206354 206365 207179 207184) (-185 "DIFFDOM.spad" 205517 205530 206344 206349) (-184 "DIFEXT.spad" 205336 205346 205497 205512) (-183 "DIAGG.spad" 204966 204976 205316 205331) (-182 "DIAGG.spad" 204604 204616 204956 204961) (-181 "DHMATRIX.spad" 202981 202991 204126 204153) (-180 "DFSFUN.spad" 196621 196629 202971 202976) (-179 "DFLOAT.spad" 193228 193236 196511 196616) (-178 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"CTORCALL.spad" 169196 169206 169597 169602) (-157 "CTOR.spad" 168887 168895 169186 169191) (-156 "CSTTOOLS.spad" 168132 168145 168877 168882) (-155 "CRFP.spad" 161904 161917 168122 168127) (-154 "CRCEAST.spad" 161624 161632 161894 161899) (-153 "CRAPACK.spad" 160691 160701 161614 161619) (-152 "CPMATCH.spad" 160192 160207 160613 160618) (-151 "CPIMA.spad" 159897 159916 160182 160187) (-150 "COORDSYS.spad" 154906 154916 159887 159892) (-149 "CONTOUR.spad" 154333 154341 154896 154901) (-148 "CONTFRAC.spad" 150083 150093 154235 154328) (-147 "CONDUIT.spad" 149841 149849 150073 150078) (-146 "COMRING.spad" 149515 149523 149779 149836) (-145 "COMPPROP.spad" 149033 149041 149505 149510) (-144 "COMPLPAT.spad" 148800 148815 149023 149028) (-143 "COMPLEX2.spad" 148515 148527 148790 148795) (-142 "COMPLEX.spad" 144221 144231 144465 144723) (-141 "COMPILER.spad" 143770 143778 144211 144216) (-140 "COMPFACT.spad" 143372 143386 143760 143765) (-139 "COMPCAT.spad" 141447 141457 143109 143367) (-138 "COMPCAT.spad" 139263 139275 140927 140932) (-137 "COMMUPC.spad" 139011 139029 139253 139258) (-136 "COMMONOP.spad" 138544 138552 139001 139006) (-135 "COMMAAST.spad" 138307 138315 138534 138539) (-134 "COMM.spad" 138118 138126 138297 138302) (-133 "COMBOPC.spad" 137041 137049 138108 138113) (-132 "COMBINAT.spad" 135808 135818 137031 137036) (-131 "COMBF.spad" 133230 133246 135798 135803) (-130 "COLOR.spad" 132067 132075 133220 133225) (-129 "COLONAST.spad" 131733 131741 132057 132062) (-128 "CMPLXRT.spad" 131444 131461 131723 131728) (-127 "CLLCTAST.spad" 131106 131114 131434 131439) (-126 "CLIP.spad" 127214 127222 131096 131101) (-125 "CLIF.spad" 125869 125885 127170 127209) (-124 "CLAGG.spad" 122406 122416 125859 125864) (-123 "CLAGG.spad" 118827 118839 122282 122287) (-122 "CINTSLPE.spad" 118182 118195 118817 118822) (-121 "CHVAR.spad" 116320 116342 118172 118177) (-120 "CHARZ.spad" 116235 116243 116300 116315) (-119 "CHARPOL.spad" 115761 115771 116225 116230) (-118 "CHARNZ.spad" 115523 115531 115741 115756) (-117 "CHAR.spad" 112891 112899 115513 115518) (-116 "CFCAT.spad" 112219 112227 112881 112886) (-115 "CDEN.spad" 111439 111453 112209 112214) (-114 "CCLASS.spad" 109619 109627 110881 110920) (-113 "CATEGORY.spad" 108693 108701 109609 109614) (-112 "CATCTOR.spad" 108584 108592 108683 108688) (-111 "CATAST.spad" 108210 108218 108574 108579) (-110 "CASEAST.spad" 107924 107932 108200 108205) (-109 "CARTEN2.spad" 107314 107341 107914 107919) (-108 "CARTEN.spad" 103066 103090 107304 107309) (-107 "CARD.spad" 100361 100369 103040 103061) (-106 "CAPSLAST.spad" 100143 100151 100351 100356) (-105 "CACHSET.spad" 99767 99775 100133 100138) (-104 "CABMON.spad" 99322 99330 99757 99762) (-103 "BYTEORD.spad" 98997 99005 99312 99317) (-102 "BYTEBUF.spad" 96964 96972 98250 98277) (-101 "BYTE.spad" 96439 96447 96954 96959) (-100 "BTREE.spad" 95577 95587 96111 96138) (-99 "BTOURN.spad" 94648 94657 95249 95276) (-98 "BTCAT.spad" 94041 94050 94616 94643) (-97 "BTCAT.spad" 93454 93465 94031 94036) (-96 "BTAGG.spad" 92921 92928 93422 93449) (-95 "BTAGG.spad" 92408 92417 92911 92916) (-94 "BSTREE.spad" 91215 91224 92080 92107) (-93 "BRILL.spad" 89421 89431 91205 91210) (-92 "BRAGG.spad" 88378 88387 89411 89416) (-91 "BRAGG.spad" 87299 87310 88334 88339) (-90 "BPADICRT.spad" 85359 85370 85605 85698) (-89 "BPADIC.spad" 85032 85043 85285 85354) (-88 "BOUNDZRO.spad" 84689 84705 85022 85027) (-87 "BOP1.spad" 82148 82157 84679 84684) (-86 "BOP.spad" 77291 77298 82138 82143) (-85 "BOOLEAN.spad" 76840 76847 77281 77286) (-84 "BOOLE.spad" 76491 76498 76830 76835) (-83 "BOOLE.spad" 76140 76149 76481 76486) (-82 "BMODULE.spad" 75853 75864 76108 76135) (-81 "BITS.spad" 75285 75292 75499 75526) (-80 "catdef.spad" 75168 75178 75275 75280) (-79 "catdef.spad" 74919 74929 75158 75163) (-78 "BINDING.spad" 74341 74348 74909 74914) (-77 "BINARY.spad" 72576 72583 72931 73024) (-76 "BGAGG.spad" 71782 71791 72556 72571) (-75 "BGAGG.spad" 70996 71007 71772 71777) (-74 "BEZOUT.spad" 70137 70163 70946 70951) (-73 "BBTREE.spad" 67080 67089 69809 69836) (-72 "BASTYPE.spad" 66580 66587 67070 67075) (-71 "BASTYPE.spad" 66078 66087 66570 66575) (-70 "BALFACT.spad" 65538 65550 66068 66073) (-69 "AUTOMOR.spad" 64989 64998 65518 65533) (-68 "ATTREG.spad" 61712 61719 64741 64984) (-67 "ATTRAST.spad" 61429 61436 61702 61707) (-66 "ATRIG.spad" 60899 60906 61419 61424) (-65 "ATRIG.spad" 60367 60376 60889 60894) (-64 "ASTCAT.spad" 60271 60278 60357 60362) (-63 "ASTCAT.spad" 60173 60182 60261 60266) (-62 "ASTACK.spad" 59577 59586 59845 59872) (-61 "ASSOCEQ.spad" 58411 58422 59533 59538) (-60 "ARRAY2.spad" 57844 57853 58083 58110) (-59 "ARRAY12.spad" 56557 56568 57834 57839) (-58 "ARRAY1.spad" 55436 55445 55782 55809) (-57 "ARR2CAT.spad" 51218 51239 55404 55431) (-56 "ARR2CAT.spad" 47020 47043 51208 51213) (-55 "ARITY.spad" 46392 46399 47010 47015) (-54 "APPRULE.spad" 45676 45698 46382 46387) (-53 "APPLYORE.spad" 45295 45308 45666 45671) (-52 "ANY1.spad" 44366 44375 45285 45290) (-51 "ANY.spad" 43217 43224 44356 44361) (-50 "ANTISYM.spad" 41662 41678 43197 43212) (-49 "ANON.spad" 41371 41378 41652 41657) (-48 "AN.spad" 39839 39846 41202 41295) (-47 "AMR.spad" 38024 38035 39737 39834) (-46 "AMR.spad" 36072 36085 37787 37792) (-45 "ALIST.spad" 33310 33331 33660 33687) (-44 "ALGSC.spad" 32445 32471 33182 33235) (-43 "ALGPKG.spad" 28228 28239 32401 32406) (-42 "ALGMFACT.spad" 27421 27435 28218 28223) (-41 "ALGMANIP.spad" 24922 24937 27265 27270) (-40 "ALGFF.spad" 22740 22767 22957 23113) (-39 "ALGFACT.spad" 21859 21869 22730 22735) (-38 "ALGEBRA.spad" 21692 21701 21815 21854) (-37 "ALGEBRA.spad" 21557 21568 21682 21687) (-36 "ALAGG.spad" 21069 21090 21525 21552) (-35 "AHYP.spad" 20450 20457 21059 21064) (-34 "AGG.spad" 19159 19166 20440 20445) (-33 "AGG.spad" 17832 17841 19115 19120) (-32 "AF.spad" 16277 16292 17781 17786) (-31 "ADDAST.spad" 15963 15970 16267 16272) (-30 "ACPLOT.spad" 14840 14847 15953 15958) (-29 "ACFS.spad" 12697 12706 14742 14835) (-28 "ACFS.spad" 10640 10651 12687 12692) (-27 "ACF.spad" 7394 7401 10542 10635) (-26 "ACF.spad" 4234 4243 7384 7389) (-25 "ABELSG.spad" 3775 3782 4224 4229) (-24 "ABELSG.spad" 3314 3323 3765 3770) (-23 "ABELMON.spad" 2859 2866 3304 3309) (-22 "ABELMON.spad" 2402 2411 2849 2854) (-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 1963163 1963168 1963173 1963178) (-2 NIL 1963143 1963148 1963153 1963158) (-1 NIL 1963123 1963128 1963133 1963138) (0 NIL 1963103 1963108 1963113 1963118) (-1210 "ZMOD.spad" 1962912 1962925 1963041 1963098) (-1209 "ZLINDEP.spad" 1962010 1962021 1962902 1962907) (-1208 "ZDSOLVE.spad" 1951971 1951993 1962000 1962005) (-1207 "YSTREAM.spad" 1951466 1951477 1951961 1951966) (-1206 "YDIAGRAM.spad" 1951100 1951109 1951456 1951461) (-1205 "XRPOLY.spad" 1950320 1950340 1950956 1951025) (-1204 "XPR.spad" 1948115 1948128 1950038 1950137) (-1203 "XPOLYC.spad" 1947434 1947450 1948041 1948110) (-1202 "XPOLY.spad" 1946989 1947000 1947290 1947359) (-1201 "XPBWPOLY.spad" 1945460 1945480 1946795 1946864) (-1200 "XFALG.spad" 1942508 1942524 1945386 1945455) (-1199 "XF.spad" 1940971 1940986 1942410 1942503) (-1198 "XF.spad" 1939414 1939431 1940855 1940860) (-1197 "XEXPPKG.spad" 1938673 1938699 1939404 1939409) (-1196 "XDPOLY.spad" 1938287 1938303 1938529 1938598) (-1195 "XALG.spad" 1937955 1937966 1938243 1938282) (-1194 "WUTSET.spad" 1933958 1933975 1937589 1937616) (-1193 "WP.spad" 1933165 1933209 1933816 1933883) (-1192 "WHILEAST.spad" 1932963 1932972 1933155 1933160) (-1191 "WHEREAST.spad" 1932634 1932643 1932953 1932958) (-1190 "WFFINTBS.spad" 1930297 1930319 1932624 1932629) (-1189 "WEIER.spad" 1928519 1928530 1930287 1930292) (-1188 "VSPACE.spad" 1928192 1928203 1928487 1928514) (-1187 "VSPACE.spad" 1927885 1927898 1928182 1928187) (-1186 "VOID.spad" 1927562 1927571 1927875 1927880) (-1185 "VIEWDEF.spad" 1922763 1922772 1927552 1927557) (-1184 "VIEW3D.spad" 1906724 1906733 1922753 1922758) (-1183 "VIEW2D.spad" 1894623 1894632 1906714 1906719) (-1182 "VIEW.spad" 1892343 1892352 1894613 1894618) (-1181 "VECTOR2.spad" 1890982 1890995 1892333 1892338) (-1180 "VECTOR.spad" 1889701 1889712 1889952 1889979) (-1179 "VECTCAT.spad" 1887613 1887624 1889669 1889696) (-1178 "VECTCAT.spad" 1885334 1885347 1887392 1887397) (-1177 "VARIABLE.spad" 1885114 1885129 1885324 1885329) (-1176 "UTYPE.spad" 1884758 1884767 1885104 1885109) (-1175 "UTSODETL.spad" 1884053 1884077 1884714 1884719) (-1174 "UTSODE.spad" 1882269 1882289 1884043 1884048) (-1173 "UTSCAT.spad" 1879748 1879764 1882167 1882264) (-1172 "UTSCAT.spad" 1876895 1876913 1879316 1879321) (-1171 "UTS2.spad" 1876490 1876525 1876885 1876890) (-1170 "UTS.spad" 1871502 1871530 1875022 1875119) (-1169 "URAGG.spad" 1866223 1866234 1871492 1871497) (-1168 "URAGG.spad" 1860908 1860921 1866179 1866184) (-1167 "UPXSSING.spad" 1858676 1858702 1860112 1860245) (-1166 "UPXSCONS.spad" 1856494 1856514 1856867 1857016) (-1165 "UPXSCCA.spad" 1855065 1855085 1856340 1856489) (-1164 "UPXSCCA.spad" 1853778 1853800 1855055 1855060) (-1163 "UPXSCAT.spad" 1852367 1852383 1853624 1853773) (-1162 "UPXS2.spad" 1851910 1851963 1852357 1852362) (-1161 "UPXS.spad" 1849265 1849293 1850101 1850250) (-1160 "UPSQFREE.spad" 1847680 1847694 1849255 1849260) (-1159 "UPSCAT.spad" 1845475 1845499 1847578 1847675) (-1158 "UPSCAT.spad" 1842971 1842997 1845076 1845081) (-1157 "UPOLYC2.spad" 1842442 1842461 1842961 1842966) (-1156 "UPOLYC.spad" 1837522 1837533 1842284 1842437) (-1155 "UPOLYC.spad" 1832520 1832533 1837284 1837289) (-1154 "UPMP.spad" 1831452 1831465 1832510 1832515) (-1153 "UPDIVP.spad" 1831017 1831031 1831442 1831447) (-1152 "UPDECOMP.spad" 1829278 1829292 1831007 1831012) (-1151 "UPCDEN.spad" 1828495 1828511 1829268 1829273) (-1150 "UP2.spad" 1827859 1827880 1828485 1828490) (-1149 "UP.spad" 1825329 1825344 1825716 1825869) (-1148 "UNISEG2.spad" 1824826 1824839 1825285 1825290) (-1147 "UNISEG.spad" 1824179 1824190 1824745 1824750) (-1146 "UNIFACT.spad" 1823282 1823294 1824169 1824174) (-1145 "ULSCONS.spad" 1817325 1817345 1817695 1817844) (-1144 "ULSCCAT.spad" 1815062 1815082 1817171 1817320) (-1143 "ULSCCAT.spad" 1812907 1812929 1815018 1815023) (-1142 "ULSCAT.spad" 1811147 1811163 1812753 1812902) (-1141 "ULS2.spad" 1810661 1810714 1811137 1811142) (-1140 "ULS.spad" 1802927 1802955 1803872 1804295) (-1139 "UINT8.spad" 1802804 1802813 1802917 1802922) (-1138 "UINT64.spad" 1802680 1802689 1802794 1802799) (-1137 "UINT32.spad" 1802556 1802565 1802670 1802675) (-1136 "UINT16.spad" 1802432 1802441 1802546 1802551) (-1135 "UFD.spad" 1801497 1801506 1802358 1802427) (-1134 "UFD.spad" 1800624 1800635 1801487 1801492) (-1133 "UDVO.spad" 1799505 1799514 1800614 1800619) (-1132 "UDPO.spad" 1797086 1797097 1799461 1799466) (-1131 "TYPEAST.spad" 1797005 1797014 1797076 1797081) (-1130 "TYPE.spad" 1796937 1796946 1796995 1797000) (-1129 "TWOFACT.spad" 1795589 1795604 1796927 1796932) (-1128 "TUPLE.spad" 1795096 1795107 1795501 1795506) (-1127 "TUBETOOL.spad" 1791963 1791972 1795086 1795091) (-1126 "TUBE.spad" 1790610 1790627 1791953 1791958) (-1125 "TSETCAT.spad" 1778681 1778698 1790578 1790605) (-1124 "TSETCAT.spad" 1766738 1766757 1778637 1778642) (-1123 "TS.spad" 1765366 1765382 1766332 1766429) (-1122 "TRMANIP.spad" 1759730 1759747 1765054 1765059) (-1121 "TRIMAT.spad" 1758693 1758718 1759720 1759725) (-1120 "TRIGMNIP.spad" 1757220 1757237 1758683 1758688) (-1119 "TRIGCAT.spad" 1756732 1756741 1757210 1757215) (-1118 "TRIGCAT.spad" 1756242 1756253 1756722 1756727) (-1117 "TREE.spad" 1754882 1754893 1755914 1755941) (-1116 "TRANFUN.spad" 1754721 1754730 1754872 1754877) (-1115 "TRANFUN.spad" 1754558 1754569 1754711 1754716) (-1114 "TOPSP.spad" 1754232 1754241 1754548 1754553) (-1113 "TOOLSIGN.spad" 1753895 1753906 1754222 1754227) (-1112 "TEXTFILE.spad" 1752456 1752465 1753885 1753890) (-1111 "TEX1.spad" 1752012 1752023 1752446 1752451) (-1110 "TEX.spad" 1749206 1749215 1752002 1752007) (-1109 "TBCMPPK.spad" 1747307 1747330 1749196 1749201) (-1108 "TBAGG.spad" 1746365 1746388 1747287 1747302) (-1107 "TBAGG.spad" 1745431 1745456 1746355 1746360) (-1106 "TANEXP.spad" 1744839 1744850 1745421 1745426) (-1105 "TALGOP.spad" 1744563 1744574 1744829 1744834) (-1104 "TABLEAU.spad" 1744044 1744055 1744553 1744558) (-1103 "TABLE.spad" 1742319 1742342 1742589 1742616) (-1102 "TABLBUMP.spad" 1739098 1739109 1742309 1742314) (-1101 "SYSTEM.spad" 1738326 1738335 1739088 1739093) (-1100 "SYSSOLP.spad" 1735809 1735820 1738316 1738321) (-1099 "SYSPTR.spad" 1735708 1735717 1735799 1735804) (-1098 "SYSNNI.spad" 1734931 1734942 1735698 1735703) (-1097 "SYSINT.spad" 1734335 1734346 1734921 1734926) (-1096 "SYNTAX.spad" 1730669 1730678 1734325 1734330) (-1095 "SYMTAB.spad" 1728737 1728746 1730659 1730664) (-1094 "SYMS.spad" 1724766 1724775 1728727 1728732) (-1093 "SYMPOLY.spad" 1723899 1723910 1723981 1724108) (-1092 "SYMFUNC.spad" 1723400 1723411 1723889 1723894) (-1091 "SYMBOL.spad" 1720895 1720904 1723390 1723395) (-1090 "SUTS.spad" 1718008 1718036 1719427 1719524) (-1089 "SUPXS.spad" 1715350 1715378 1716199 1716348) (-1088 "SUPFRACF.spad" 1714455 1714473 1715340 1715345) (-1087 "SUP2.spad" 1713847 1713860 1714445 1714450) (-1086 "SUP.spad" 1710931 1710942 1711704 1711857) (-1085 "SUMRF.spad" 1709905 1709916 1710921 1710926) (-1084 "SUMFS.spad" 1709534 1709551 1709895 1709900) (-1083 "SULS.spad" 1701787 1701815 1702745 1703168) (-1082 "syntax.spad" 1701556 1701565 1701777 1701782) (-1081 "SUCH.spad" 1701246 1701261 1701546 1701551) (-1080 "SUBSPACE.spad" 1693377 1693392 1701236 1701241) (-1079 "SUBRESP.spad" 1692547 1692561 1693333 1693338) (-1078 "STTFNC.spad" 1689015 1689031 1692537 1692542) (-1077 "STTF.spad" 1685114 1685130 1689005 1689010) (-1076 "STTAYLOR.spad" 1677791 1677802 1685021 1685026) (-1075 "STRTBL.spad" 1676178 1676195 1676327 1676354) (-1074 "STRING.spad" 1675046 1675055 1675431 1675458) (-1073 "STREAM3.spad" 1674619 1674634 1675036 1675041) (-1072 "STREAM2.spad" 1673747 1673760 1674609 1674614) (-1071 "STREAM1.spad" 1673453 1673464 1673737 1673742) (-1070 "STREAM.spad" 1670449 1670460 1673056 1673071) (-1069 "STINPROD.spad" 1669385 1669401 1670439 1670444) (-1068 "STEPAST.spad" 1668619 1668628 1669375 1669380) (-1067 "STEP.spad" 1667936 1667945 1668609 1668614) (-1066 "STBL.spad" 1666326 1666354 1666493 1666508) (-1065 "STAGG.spad" 1665025 1665036 1666316 1666321) (-1064 "STAGG.spad" 1663722 1663735 1665015 1665020) (-1063 "STACK.spad" 1663144 1663155 1663394 1663421) (-1062 "SRING.spad" 1662904 1662913 1663134 1663139) (-1061 "SREGSET.spad" 1660636 1660653 1662538 1662565) (-1060 "SRDCMPK.spad" 1659213 1659233 1660626 1660631) (-1059 "SRAGG.spad" 1654396 1654405 1659181 1659208) (-1058 "SRAGG.spad" 1649599 1649610 1654386 1654391) (-1057 "SQMATRIX.spad" 1647276 1647294 1648192 1648279) (-1056 "SPLTREE.spad" 1642018 1642031 1646814 1646841) (-1055 "SPLNODE.spad" 1638638 1638651 1642008 1642013) (-1054 "SPFCAT.spad" 1637447 1637456 1638628 1638633) (-1053 "SPECOUT.spad" 1635999 1636008 1637437 1637442) (-1052 "SPADXPT.spad" 1628090 1628099 1635989 1635994) (-1051 "spad-parser.spad" 1627555 1627564 1628080 1628085) (-1050 "SPADAST.spad" 1627256 1627265 1627545 1627550) (-1049 "SPACEC.spad" 1611471 1611482 1627246 1627251) (-1048 "SPACE3.spad" 1611247 1611258 1611461 1611466) (-1047 "SORTPAK.spad" 1610796 1610809 1611203 1611208) (-1046 "SOLVETRA.spad" 1608559 1608570 1610786 1610791) (-1045 "SOLVESER.spad" 1607015 1607026 1608549 1608554) (-1044 "SOLVERAD.spad" 1603041 1603052 1607005 1607010) (-1043 "SOLVEFOR.spad" 1601503 1601521 1603031 1603036) (-1042 "SNTSCAT.spad" 1601103 1601120 1601471 1601498) (-1041 "SMTS.spad" 1599420 1599446 1600697 1600794) (-1040 "SMP.spad" 1597228 1597248 1597618 1597745) (-1039 "SMITH.spad" 1596073 1596098 1597218 1597223) (-1038 "SMATCAT.spad" 1594191 1594221 1596017 1596068) (-1037 "SMATCAT.spad" 1592241 1592273 1594069 1594074) (-1036 "SKAGG.spad" 1591210 1591221 1592209 1592236) (-1035 "SINT.spad" 1590509 1590518 1591076 1591205) (-1034 "SIMPAN.spad" 1590237 1590246 1590499 1590504) (-1033 "SIGNRF.spad" 1589362 1589373 1590227 1590232) (-1032 "SIGNEF.spad" 1588648 1588665 1589352 1589357) (-1031 "syntax.spad" 1588065 1588074 1588638 1588643) (-1030 "SIG.spad" 1587427 1587436 1588055 1588060) (-1029 "SHP.spad" 1585371 1585386 1587383 1587388) (-1028 "SHDP.spad" 1574864 1574891 1575381 1575478) (-1027 "SGROUP.spad" 1574472 1574481 1574854 1574859) (-1026 "SGROUP.spad" 1574078 1574089 1574462 1574467) (-1025 "catdef.spad" 1573788 1573800 1573899 1574073) (-1024 "catdef.spad" 1573344 1573356 1573609 1573783) (-1023 "SGCF.spad" 1566483 1566492 1573334 1573339) (-1022 "SFRTCAT.spad" 1565429 1565446 1566451 1566478) (-1021 "SFRGCD.spad" 1564492 1564512 1565419 1565424) (-1020 "SFQCMPK.spad" 1559305 1559325 1564482 1564487) (-1019 "SEXOF.spad" 1559148 1559188 1559295 1559300) (-1018 "SEXCAT.spad" 1556976 1557016 1559138 1559143) (-1017 "SEX.spad" 1556868 1556877 1556966 1556971) (-1016 "SETMN.spad" 1555328 1555345 1556858 1556863) (-1015 "SETCAT.spad" 1554813 1554822 1555318 1555323) (-1014 "SETCAT.spad" 1554296 1554307 1554803 1554808) (-1013 "SETAGG.spad" 1550845 1550856 1554276 1554291) (-1012 "SETAGG.spad" 1547402 1547415 1550835 1550840) (-1011 "SET.spad" 1545711 1545722 1546808 1546847) (-1010 "syntax.spad" 1545414 1545423 1545701 1545706) (-1009 "SEGXCAT.spad" 1544570 1544583 1545404 1545409) (-1008 "SEGCAT.spad" 1543495 1543506 1544560 1544565) (-1007 "SEGBIND2.spad" 1543193 1543206 1543485 1543490) (-1006 "SEGBIND.spad" 1542951 1542962 1543140 1543145) (-1005 "SEGAST.spad" 1542681 1542690 1542941 1542946) (-1004 "SEG2.spad" 1542116 1542129 1542637 1542642) (-1003 "SEG.spad" 1541929 1541940 1542035 1542040) (-1002 "SDVAR.spad" 1541205 1541216 1541919 1541924) (-1001 "SDPOL.spad" 1538897 1538908 1539188 1539315) (-1000 "SCPKG.spad" 1536986 1536997 1538887 1538892) (-999 "SCOPE.spad" 1536164 1536172 1536976 1536981) (-998 "SCACHE.spad" 1534861 1534871 1536154 1536159) (-997 "SASTCAT.spad" 1534771 1534779 1534851 1534856) (-996 "SAOS.spad" 1534644 1534652 1534761 1534766) (-995 "SAERFFC.spad" 1534358 1534377 1534634 1534639) (-994 "SAEFACT.spad" 1534060 1534079 1534348 1534353) (-993 "SAE.spad" 1531711 1531726 1532321 1532456) (-992 "RURPK.spad" 1529371 1529386 1531701 1531706) (-991 "RULESET.spad" 1528825 1528848 1529361 1529366) (-990 "RULECOLD.spad" 1528678 1528690 1528815 1528820) (-989 "RULE.spad" 1526927 1526950 1528668 1528673) (-988 "RTVALUE.spad" 1526663 1526671 1526917 1526922) (-987 "syntax.spad" 1526381 1526389 1526653 1526658) (-986 "RSETGCD.spad" 1522824 1522843 1526371 1526376) (-985 "RSETCAT.spad" 1512793 1512809 1522792 1522819) (-984 "RSETCAT.spad" 1502782 1502800 1512783 1512788) (-983 "RSDCMPK.spad" 1501283 1501302 1502772 1502777) (-982 "RRCC.spad" 1499668 1499697 1501273 1501278) (-981 "RRCC.spad" 1498051 1498082 1499658 1499663) (-980 "RPTAST.spad" 1497754 1497762 1498041 1498046) (-979 "RPOLCAT.spad" 1477259 1477273 1497622 1497749) (-978 "RPOLCAT.spad" 1456557 1456573 1476922 1476927) (-977 "ROMAN.spad" 1455886 1455894 1456423 1456552) (-976 "ROIRC.spad" 1454967 1454998 1455876 1455881) (-975 "RNS.spad" 1453944 1453952 1454869 1454962) (-974 "RNS.spad" 1453007 1453017 1453934 1453939) (-973 "RNGBIND.spad" 1452168 1452181 1452962 1452967) (-972 "RNG.spad" 1451777 1451785 1452158 1452163) (-971 "RNG.spad" 1451384 1451394 1451767 1451772) (-970 "RMODULE.spad" 1451166 1451176 1451374 1451379) (-969 "RMCAT2.spad" 1450587 1450643 1451156 1451161) (-968 "RMATRIX.spad" 1449397 1449415 1449739 1449778) (-967 "RMATCAT.spad" 1444977 1445007 1449353 1449392) (-966 "RMATCAT.spad" 1440447 1440479 1444825 1444830) (-965 "RLINSET.spad" 1440152 1440162 1440437 1440442) (-964 "RINTERP.spad" 1440041 1440060 1440142 1440147) (-963 "RING.spad" 1439512 1439520 1440021 1440036) (-962 "RING.spad" 1438991 1439001 1439502 1439507) (-961 "RIDIST.spad" 1438384 1438392 1438981 1438986) (-960 "RGCHAIN.spad" 1436939 1436954 1437832 1437859) (-959 "RGBCSPC.spad" 1436729 1436740 1436929 1436934) (-958 "RGBCMDL.spad" 1436292 1436303 1436719 1436724) (-957 "RFFACTOR.spad" 1435755 1435765 1436282 1436287) (-956 "RFFACT.spad" 1435491 1435502 1435745 1435750) (-955 "RFDIST.spad" 1434488 1434496 1435481 1435486) (-954 "RF.spad" 1432163 1432173 1434478 1434483) (-953 "RETSOL.spad" 1431583 1431595 1432153 1432158) (-952 "RETRACT.spad" 1431012 1431022 1431573 1431578) (-951 "RETRACT.spad" 1430439 1430451 1431002 1431007) (-950 "RETAST.spad" 1430252 1430260 1430429 1430434) (-949 "RESRING.spad" 1429600 1429646 1430190 1430247) (-948 "RESLATC.spad" 1428925 1428935 1429590 1429595) (-947 "REPSQ.spad" 1428657 1428667 1428915 1428920) (-946 "REPDB.spad" 1428365 1428375 1428647 1428652) (-945 "REP2.spad" 1418080 1418090 1428207 1428212) (-944 "REP1.spad" 1412301 1412311 1418030 1418035) (-943 "REP.spad" 1409856 1409864 1412291 1412296) (-942 "REGSET.spad" 1407682 1407698 1409490 1409517) (-941 "REF.spad" 1407201 1407211 1407672 1407677) (-940 "REDORDER.spad" 1406408 1406424 1407191 1407196) (-939 "RECLOS.spad" 1405305 1405324 1406008 1406101) (-938 "REALSOLV.spad" 1404446 1404454 1405295 1405300) (-937 "REAL0Q.spad" 1401745 1401759 1404436 1404441) (-936 "REAL0.spad" 1398590 1398604 1401735 1401740) (-935 "REAL.spad" 1398463 1398471 1398580 1398585) (-934 "RDUCEAST.spad" 1398185 1398193 1398453 1398458) (-933 "RDIV.spad" 1397841 1397865 1398175 1398180) (-932 "RDIST.spad" 1397409 1397419 1397831 1397836) (-931 "RDETRS.spad" 1396274 1396291 1397399 1397404) (-930 "RDETR.spad" 1394414 1394431 1396264 1396269) (-929 "RDEEFS.spad" 1393514 1393530 1394404 1394409) (-928 "RDEEF.spad" 1392525 1392541 1393504 1393509) (-927 "RCFIELD.spad" 1389744 1389752 1392427 1392520) (-926 "RCFIELD.spad" 1387049 1387059 1389734 1389739) (-925 "RCAGG.spad" 1384986 1384996 1387039 1387044) (-924 "RCAGG.spad" 1382850 1382862 1384905 1384910) (-923 "RATRET.spad" 1382211 1382221 1382840 1382845) (-922 "RATFACT.spad" 1381904 1381915 1382201 1382206) (-921 "RANDSRC.spad" 1381224 1381232 1381894 1381899) (-920 "RADUTIL.spad" 1380981 1380989 1381214 1381219) (-919 "RADIX.spad" 1378026 1378039 1379571 1379664) (-918 "RADFF.spad" 1375943 1375979 1376061 1376217) (-917 "RADCAT.spad" 1375539 1375547 1375933 1375938) (-916 "RADCAT.spad" 1375133 1375143 1375529 1375534) (-915 "QUEUE.spad" 1374547 1374557 1374805 1374832) (-914 "QUATCT2.spad" 1374168 1374186 1374537 1374542) (-913 "QUATCAT.spad" 1372339 1372349 1374098 1374163) (-912 "QUATCAT.spad" 1370275 1370287 1372036 1372041) (-911 "QUAT.spad" 1368882 1368892 1369224 1369289) (-910 "QUAGG.spad" 1367716 1367726 1368850 1368877) (-909 "QQUTAST.spad" 1367485 1367493 1367706 1367711) (-908 "QFORM.spad" 1367104 1367118 1367475 1367480) (-907 "QFCAT2.spad" 1366797 1366813 1367094 1367099) (-906 "QFCAT.spad" 1365500 1365510 1366699 1366792) (-905 "QFCAT.spad" 1363836 1363848 1365037 1365042) (-904 "QEQUAT.spad" 1363395 1363403 1363826 1363831) (-903 "QCMPACK.spad" 1358310 1358329 1363385 1363390) (-902 "QALGSET2.spad" 1356306 1356324 1358300 1358305) (-901 "QALGSET.spad" 1352411 1352443 1356220 1356225) (-900 "PWFFINTB.spad" 1349827 1349848 1352401 1352406) (-899 "PUSHVAR.spad" 1349166 1349185 1349817 1349822) (-898 "PTRANFN.spad" 1345302 1345312 1349156 1349161) (-897 "PTPACK.spad" 1342390 1342400 1345292 1345297) (-896 "PTFUNC2.spad" 1342213 1342227 1342380 1342385) (-895 "PTCAT.spad" 1341468 1341478 1342181 1342208) (-894 "PSQFR.spad" 1340783 1340807 1341458 1341463) (-893 "PSEUDLIN.spad" 1339669 1339679 1340773 1340778) (-892 "PSETPK.spad" 1326374 1326390 1339547 1339552) (-891 "PSETCAT.spad" 1320774 1320797 1326354 1326369) (-890 "PSETCAT.spad" 1315148 1315173 1320730 1320735) (-889 "PSCURVE.spad" 1314147 1314155 1315138 1315143) (-888 "PSCAT.spad" 1312930 1312959 1314045 1314142) (-887 "PSCAT.spad" 1311803 1311834 1312920 1312925) (-886 "PRTITION.spad" 1310501 1310509 1311793 1311798) (-885 "PRTDAST.spad" 1310220 1310228 1310491 1310496) (-884 "PRS.spad" 1299838 1299855 1310176 1310181) (-883 "PRQAGG.spad" 1299273 1299283 1299806 1299833) (-882 "PROPLOG.spad" 1298877 1298885 1299263 1299268) (-881 "PROPFUN2.spad" 1298500 1298513 1298867 1298872) (-880 "PROPFUN1.spad" 1297906 1297917 1298490 1298495) (-879 "PROPFRML.spad" 1296474 1296485 1297896 1297901) (-878 "PROPERTY.spad" 1295970 1295978 1296464 1296469) (-877 "PRODUCT.spad" 1293667 1293679 1293951 1294006) (-876 "PRINT.spad" 1293419 1293427 1293657 1293662) (-875 "PRIMES.spad" 1291680 1291690 1293409 1293414) (-874 "PRIMELT.spad" 1289801 1289815 1291670 1291675) (-873 "PRIMCAT.spad" 1289444 1289452 1289791 1289796) (-872 "PRIMARR2.spad" 1288211 1288223 1289434 1289439) (-871 "PRIMARR.spad" 1287266 1287276 1287436 1287463) (-870 "PREASSOC.spad" 1286648 1286660 1287256 1287261) (-869 "PR.spad" 1285166 1285178 1285865 1285992) (-868 "PPCURVE.spad" 1284303 1284311 1285156 1285161) (-867 "PORTNUM.spad" 1284094 1284102 1284293 1284298) (-866 "POLYROOT.spad" 1282943 1282965 1284050 1284055) (-865 "POLYLIFT.spad" 1282208 1282231 1282933 1282938) (-864 "POLYCATQ.spad" 1280334 1280356 1282198 1282203) (-863 "POLYCAT.spad" 1273836 1273857 1280202 1280329) (-862 "POLYCAT.spad" 1266858 1266881 1273226 1273231) (-861 "POLY2UP.spad" 1266310 1266324 1266848 1266853) (-860 "POLY2.spad" 1265907 1265919 1266300 1266305) (-859 "POLY.spad" 1263575 1263585 1264090 1264217) (-858 "POLUTIL.spad" 1262540 1262569 1263531 1263536) (-857 "POLTOPOL.spad" 1261288 1261303 1262530 1262535) (-856 "POINT.spad" 1260171 1260181 1260258 1260285) (-855 "PNTHEORY.spad" 1256873 1256881 1260161 1260166) (-854 "PMTOOLS.spad" 1255648 1255662 1256863 1256868) (-853 "PMSYM.spad" 1255197 1255207 1255638 1255643) (-852 "PMQFCAT.spad" 1254788 1254802 1255187 1255192) (-851 "PMPREDFS.spad" 1254250 1254272 1254778 1254783) (-850 "PMPRED.spad" 1253737 1253751 1254240 1254245) (-849 "PMPLCAT.spad" 1252814 1252832 1253666 1253671) (-848 "PMLSAGG.spad" 1252399 1252413 1252804 1252809) (-847 "PMKERNEL.spad" 1251978 1251990 1252389 1252394) (-846 "PMINS.spad" 1251558 1251568 1251968 1251973) (-845 "PMFS.spad" 1251135 1251153 1251548 1251553) (-844 "PMDOWN.spad" 1250425 1250439 1251125 1251130) (-843 "PMASSFS.spad" 1249400 1249416 1250415 1250420) (-842 "PMASS.spad" 1248418 1248426 1249390 1249395) (-841 "PLOTTOOL.spad" 1248198 1248206 1248408 1248413) (-840 "PLOT3D.spad" 1244662 1244670 1248188 1248193) (-839 "PLOT1.spad" 1243835 1243845 1244652 1244657) (-838 "PLOT.spad" 1238758 1238766 1243825 1243830) (-837 "PLEQN.spad" 1226160 1226187 1238748 1238753) (-836 "PINTERPA.spad" 1225944 1225960 1226150 1226155) (-835 "PINTERP.spad" 1225566 1225585 1225934 1225939) (-834 "PID.spad" 1224540 1224548 1225492 1225561) (-833 "PICOERCE.spad" 1224197 1224207 1224530 1224535) (-832 "PI.spad" 1223814 1223822 1224171 1224192) (-831 "PGROEB.spad" 1222423 1222437 1223804 1223809) (-830 "PGE.spad" 1214096 1214104 1222413 1222418) (-829 "PGCD.spad" 1213050 1213067 1214086 1214091) (-828 "PFRPAC.spad" 1212199 1212209 1213040 1213045) (-827 "PFR.spad" 1208902 1208912 1212101 1212194) (-826 "PFOTOOLS.spad" 1208160 1208176 1208892 1208897) (-825 "PFOQ.spad" 1207530 1207548 1208150 1208155) (-824 "PFO.spad" 1206949 1206976 1207520 1207525) (-823 "PFECAT.spad" 1204659 1204667 1206875 1206944) (-822 "PFECAT.spad" 1202397 1202407 1204615 1204620) (-821 "PFBRU.spad" 1200285 1200297 1202387 1202392) (-820 "PFBR.spad" 1197845 1197868 1200275 1200280) (-819 "PF.spad" 1197419 1197431 1197650 1197743) (-818 "PERMGRP.spad" 1192189 1192199 1197409 1197414) (-817 "PERMCAT.spad" 1190850 1190860 1192169 1192184) (-816 "PERMAN.spad" 1189406 1189420 1190840 1190845) (-815 "PERM.spad" 1185216 1185226 1189239 1189254) (-814 "PENDTREE.spad" 1184630 1184640 1184910 1184915) (-813 "PDSPC.spad" 1183443 1183453 1184620 1184625) (-812 "PDSPC.spad" 1182254 1182266 1183433 1183438) (-811 "PDRING.spad" 1182096 1182106 1182234 1182249) (-810 "PDMOD.spad" 1181912 1181924 1182064 1182091) (-809 "PDECOMP.spad" 1181382 1181399 1181902 1181907) (-808 "PDDOM.spad" 1180820 1180833 1181372 1181377) (-807 "PDDOM.spad" 1180256 1180271 1180810 1180815) (-806 "PCOMP.spad" 1180109 1180122 1180246 1180251) (-805 "PBWLB.spad" 1178707 1178724 1180099 1180104) (-804 "PATTERN2.spad" 1178445 1178457 1178697 1178702) (-803 "PATTERN1.spad" 1176789 1176805 1178435 1178440) (-802 "PATTERN.spad" 1171364 1171374 1176779 1176784) (-801 "PATRES2.spad" 1171036 1171050 1171354 1171359) (-800 "PATRES.spad" 1168619 1168631 1171026 1171031) (-799 "PATMATCH.spad" 1166860 1166891 1168371 1168376) (-798 "PATMAB.spad" 1166289 1166299 1166850 1166855) (-797 "PATLRES.spad" 1165375 1165389 1166279 1166284) (-796 "PATAB.spad" 1165139 1165149 1165365 1165370) (-795 "PARTPERM.spad" 1163195 1163203 1165129 1165134) (-794 "PARSURF.spad" 1162629 1162657 1163185 1163190) (-793 "PARSU2.spad" 1162426 1162442 1162619 1162624) (-792 "script-parser.spad" 1161946 1161954 1162416 1162421) (-791 "PARSCURV.spad" 1161380 1161408 1161936 1161941) (-790 "PARSC2.spad" 1161171 1161187 1161370 1161375) (-789 "PARPCURV.spad" 1160633 1160661 1161161 1161166) (-788 "PARPC2.spad" 1160424 1160440 1160623 1160628) (-787 "PARAMAST.spad" 1159552 1159560 1160414 1160419) (-786 "PAN2EXPR.spad" 1158964 1158972 1159542 1159547) (-785 "PALETTE.spad" 1158078 1158086 1158954 1158959) (-784 "PAIR.spad" 1157152 1157165 1157721 1157726) (-783 "PADICRC.spad" 1154557 1154575 1155720 1155813) (-782 "PADICRAT.spad" 1152617 1152629 1152830 1152923) (-781 "PADICCT.spad" 1151166 1151178 1152543 1152612) (-780 "PADIC.spad" 1150869 1150881 1151092 1151161) (-779 "PADEPAC.spad" 1149558 1149577 1150859 1150864) (-778 "PADE.spad" 1148310 1148326 1149548 1149553) (-777 "OWP.spad" 1147558 1147588 1148168 1148235) (-776 "OVERSET.spad" 1147131 1147139 1147548 1147553) (-775 "OVAR.spad" 1146912 1146935 1147121 1147126) (-774 "OUTFORM.spad" 1136320 1136328 1146902 1146907) (-773 "OUTBFILE.spad" 1135754 1135762 1136310 1136315) (-772 "OUTBCON.spad" 1134824 1134832 1135744 1135749) (-771 "OUTBCON.spad" 1133892 1133902 1134814 1134819) (-770 "OUT.spad" 1133010 1133018 1133882 1133887) (-769 "OSI.spad" 1132485 1132493 1133000 1133005) (-768 "OSGROUP.spad" 1132403 1132411 1132475 1132480) (-767 "ORTHPOL.spad" 1130914 1130924 1132346 1132351) (-766 "OREUP.spad" 1130408 1130436 1130635 1130674) (-765 "ORESUP.spad" 1129750 1129774 1130129 1130168) (-764 "OREPCTO.spad" 1127639 1127651 1129670 1129675) (-763 "OREPCAT.spad" 1121826 1121836 1127595 1127634) (-762 "OREPCAT.spad" 1115903 1115915 1121674 1121679) (-761 "ORDTYPE.spad" 1115140 1115148 1115893 1115898) (-760 "ORDTYPE.spad" 1114375 1114385 1115130 1115135) (-759 "ORDSTRCT.spad" 1114161 1114176 1114324 1114329) (-758 "ORDSET.spad" 1113861 1113869 1114151 1114156) (-757 "ORDRING.spad" 1113678 1113686 1113841 1113856) (-756 "ORDMON.spad" 1113533 1113541 1113668 1113673) (-755 "ORDFUNS.spad" 1112665 1112681 1113523 1113528) (-754 "ORDFIN.spad" 1112485 1112493 1112655 1112660) (-753 "ORDCOMP2.spad" 1111778 1111790 1112475 1112480) (-752 "ORDCOMP.spad" 1110304 1110314 1111386 1111415) (-751 "OPSIG.spad" 1109966 1109974 1110294 1110299) (-750 "OPQUERY.spad" 1109547 1109555 1109956 1109961) (-749 "OPERCAT.spad" 1109013 1109023 1109537 1109542) (-748 "OPERCAT.spad" 1108477 1108489 1109003 1109008) (-747 "OP.spad" 1108219 1108229 1108299 1108366) (-746 "ONECOMP2.spad" 1107643 1107655 1108209 1108214) (-745 "ONECOMP.spad" 1106449 1106459 1107251 1107280) (-744 "OMSAGG.spad" 1106237 1106247 1106405 1106444) (-743 "OMLO.spad" 1105670 1105682 1106123 1106162) (-742 "OINTDOM.spad" 1105433 1105441 1105596 1105665) (-741 "OFMONOID.spad" 1103572 1103582 1105389 1105394) (-740 "ODVAR.spad" 1102833 1102843 1103562 1103567) (-739 "ODR.spad" 1102477 1102503 1102645 1102794) (-738 "ODPOL.spad" 1100125 1100135 1100465 1100592) (-737 "ODP.spad" 1089762 1089782 1090135 1090232) (-736 "ODETOOLS.spad" 1088411 1088430 1089752 1089757) (-735 "ODESYS.spad" 1086105 1086122 1088401 1088406) (-734 "ODERTRIC.spad" 1082138 1082155 1086062 1086067) (-733 "ODERED.spad" 1081537 1081561 1082128 1082133) (-732 "ODERAT.spad" 1079170 1079187 1081527 1081532) (-731 "ODEPRRIC.spad" 1076263 1076285 1079160 1079165) (-730 "ODEPRIM.spad" 1073661 1073683 1076253 1076258) (-729 "ODEPAL.spad" 1073047 1073071 1073651 1073656) (-728 "ODEINT.spad" 1072482 1072498 1073037 1073042) (-727 "ODEEF.spad" 1067977 1067993 1072472 1072477) (-726 "ODECONST.spad" 1067522 1067540 1067967 1067972) (-725 "OCTCT2.spad" 1067163 1067181 1067512 1067517) (-724 "OCT.spad" 1065478 1065488 1066192 1066231) (-723 "OCAMON.spad" 1065326 1065334 1065468 1065473) (-722 "OC.spad" 1063122 1063132 1065282 1065321) (-721 "OC.spad" 1060657 1060669 1062819 1062824) (-720 "OASGP.spad" 1060472 1060480 1060647 1060652) (-719 "OAMONS.spad" 1059994 1060002 1060462 1060467) (-718 "OAMON.spad" 1059752 1059760 1059984 1059989) (-717 "OAMON.spad" 1059508 1059518 1059742 1059747) (-716 "OAGROUP.spad" 1059046 1059054 1059498 1059503) (-715 "OAGROUP.spad" 1058582 1058592 1059036 1059041) (-714 "NUMTUBE.spad" 1058173 1058189 1058572 1058577) (-713 "NUMQUAD.spad" 1046149 1046157 1058163 1058168) (-712 "NUMODE.spad" 1037501 1037509 1046139 1046144) (-711 "NUMFMT.spad" 1036341 1036349 1037491 1037496) (-710 "NUMERIC.spad" 1028456 1028466 1036147 1036152) (-709 "NTSCAT.spad" 1026964 1026980 1028424 1028451) (-708 "NTPOLFN.spad" 1026541 1026551 1026907 1026912) (-707 "NSUP2.spad" 1025933 1025945 1026531 1026536) (-706 "NSUP.spad" 1019370 1019380 1023790 1023943) (-705 "NSMP.spad" 1016282 1016301 1016574 1016701) (-704 "NREP.spad" 1014684 1014698 1016272 1016277) (-703 "NPCOEF.spad" 1013930 1013950 1014674 1014679) (-702 "NORMRETR.spad" 1013528 1013567 1013920 1013925) (-701 "NORMPK.spad" 1011470 1011489 1013518 1013523) (-700 "NORMMA.spad" 1011158 1011184 1011460 1011465) (-699 "NONE1.spad" 1010834 1010844 1011148 1011153) (-698 "NONE.spad" 1010575 1010583 1010824 1010829) (-697 "NODE1.spad" 1010062 1010078 1010565 1010570) (-696 "NNI.spad" 1008957 1008965 1010036 1010057) (-695 "NLINSOL.spad" 1007583 1007593 1008947 1008952) (-694 "NFINTBAS.spad" 1005143 1005160 1007573 1007578) (-693 "NETCLT.spad" 1005117 1005128 1005133 1005138) (-692 "NCODIV.spad" 1003341 1003357 1005107 1005112) (-691 "NCNTFRAC.spad" 1002983 1002997 1003331 1003336) (-690 "NCEP.spad" 1001149 1001163 1002973 1002978) (-689 "NASRING.spad" 1000753 1000761 1001139 1001144) (-688 "NASRING.spad" 1000355 1000365 1000743 1000748) (-687 "NARNG.spad" 999755 999763 1000345 1000350) (-686 "NARNG.spad" 999153 999163 999745 999750) (-685 "NAALG.spad" 998718 998728 999121 999148) (-684 "NAALG.spad" 998303 998315 998708 998713) (-683 "MULTSQFR.spad" 995261 995278 998293 998298) (-682 "MULTFACT.spad" 994644 994661 995251 995256) (-681 "MTSCAT.spad" 992738 992759 994542 994639) (-680 "MTHING.spad" 992397 992407 992728 992733) (-679 "MSYSCMD.spad" 991831 991839 992387 992392) (-678 "MSETAGG.spad" 991676 991686 991799 991826) (-677 "MSET.spad" 989622 989632 991370 991409) (-676 "MRING.spad" 986599 986611 989330 989397) (-675 "MRF2.spad" 986161 986175 986589 986594) (-674 "MRATFAC.spad" 985707 985724 986151 986156) (-673 "MPRFF.spad" 983747 983766 985697 985702) (-672 "MPOLY.spad" 981551 981566 981910 982037) (-671 "MPCPF.spad" 980815 980834 981541 981546) (-670 "MPC3.spad" 980632 980672 980805 980810) (-669 "MPC2.spad" 980286 980319 980622 980627) (-668 "MONOTOOL.spad" 978637 978654 980276 980281) (-667 "catdef.spad" 978070 978081 978291 978632) (-666 "catdef.spad" 977468 977479 977724 978065) (-665 "MONOID.spad" 976789 976797 977458 977463) (-664 "MONOID.spad" 976108 976118 976779 976784) (-663 "MONOGEN.spad" 974856 974869 975968 976103) (-662 "MONOGEN.spad" 973626 973641 974740 974745) (-661 "MONADWU.spad" 971706 971714 973616 973621) (-660 "MONADWU.spad" 969784 969794 971696 971701) (-659 "MONAD.spad" 968944 968952 969774 969779) (-658 "MONAD.spad" 968102 968112 968934 968939) (-657 "MOEBIUS.spad" 966838 966852 968082 968097) (-656 "MODULE.spad" 966708 966718 966806 966833) (-655 "MODULE.spad" 966598 966610 966698 966703) (-654 "MODRING.spad" 965933 965972 966578 966593) (-653 "MODOP.spad" 964590 964602 965755 965822) (-652 "MODMONOM.spad" 964321 964339 964580 964585) (-651 "MODMON.spad" 961391 961403 962106 962259) (-650 "MODFIELD.spad" 960753 960792 961293 961386) (-649 "MMLFORM.spad" 959613 959621 960743 960748) (-648 "MMAP.spad" 959355 959389 959603 959608) (-647 "MLO.spad" 957814 957824 959311 959350) (-646 "MLIFT.spad" 956426 956443 957804 957809) (-645 "MKUCFUNC.spad" 955961 955979 956416 956421) (-644 "MKRECORD.spad" 955549 955562 955951 955956) (-643 "MKFUNC.spad" 954956 954966 955539 955544) (-642 "MKFLCFN.spad" 953924 953934 954946 954951) (-641 "MKBCFUNC.spad" 953419 953437 953914 953919) (-640 "MHROWRED.spad" 951930 951940 953409 953414) (-639 "MFINFACT.spad" 951330 951352 951920 951925) (-638 "MESH.spad" 949125 949133 951320 951325) (-637 "MDDFACT.spad" 947344 947354 949115 949120) (-636 "MDAGG.spad" 946635 946645 947324 947339) (-635 "MCDEN.spad" 945845 945857 946625 946630) (-634 "MAYBE.spad" 945145 945156 945835 945840) (-633 "MATSTOR.spad" 942461 942471 945135 945140) (-632 "MATRIX.spad" 941240 941250 941724 941751) (-631 "MATLIN.spad" 938608 938632 941124 941129) (-630 "MATCAT2.spad" 937890 937938 938598 938603) (-629 "MATCAT.spad" 929452 929474 937858 937885) (-628 "MATCAT.spad" 920886 920910 929294 929299) (-627 "MAPPKG3.spad" 919801 919815 920876 920881) (-626 "MAPPKG2.spad" 919139 919151 919791 919796) (-625 "MAPPKG1.spad" 917967 917977 919129 919134) (-624 "MAPPAST.spad" 917306 917314 917957 917962) (-623 "MAPHACK3.spad" 917118 917132 917296 917301) (-622 "MAPHACK2.spad" 916887 916899 917108 917113) (-621 "MAPHACK1.spad" 916531 916541 916877 916882) (-620 "MAGMA.spad" 914337 914354 916521 916526) (-619 "MACROAST.spad" 913932 913940 914327 914332) (-618 "LZSTAGG.spad" 911186 911196 913922 913927) (-617 "LZSTAGG.spad" 908438 908450 911176 911181) (-616 "LWORD.spad" 905183 905200 908428 908433) (-615 "LSTAST.spad" 904967 904975 905173 905178) (-614 "LSQM.spad" 903245 903259 903639 903690) (-613 "LSPP.spad" 902780 902797 903235 903240) (-612 "LSMP1.spad" 900623 900637 902770 902775) (-611 "LSMP.spad" 899480 899508 900613 900618) (-610 "LSAGG.spad" 899149 899159 899448 899475) (-609 "LSAGG.spad" 898838 898850 899139 899144) (-608 "LPOLY.spad" 897800 897819 898694 898763) (-607 "LPEFRAC.spad" 897071 897081 897790 897795) (-606 "LOGIC.spad" 896673 896681 897061 897066) (-605 "LOGIC.spad" 896273 896283 896663 896668) (-604 "LODOOPS.spad" 895203 895215 896263 896268) (-603 "LODOF.spad" 894249 894266 895160 895165) (-602 "LODOCAT.spad" 892915 892925 894205 894244) (-601 "LODOCAT.spad" 891579 891591 892871 892876) (-600 "LODO2.spad" 890893 890905 891300 891339) (-599 "LODO1.spad" 890334 890344 890614 890653) (-598 "LODO.spad" 889759 889775 890055 890094) (-597 "LODEEF.spad" 888561 888579 889749 889754) (-596 "LO.spad" 887962 887976 888495 888522) (-595 "LNAGG.spad" 884149 884159 887952 887957) (-594 "LNAGG.spad" 880300 880312 884105 884110) (-593 "LMOPS.spad" 877068 877085 880290 880295) (-592 "LMODULE.spad" 876852 876862 877058 877063) (-591 "LMDICT.spad" 876233 876243 876481 876508) (-590 "LLINSET.spad" 875940 875950 876223 876228) (-589 "LITERAL.spad" 875846 875857 875930 875935) (-588 "LIST3.spad" 875157 875171 875836 875841) (-587 "LIST2MAP.spad" 872084 872096 875147 875152) (-586 "LIST2.spad" 870786 870798 872074 872079) (-585 "LIST.spad" 868668 868678 870011 870038) (-584 "LINSET.spad" 868447 868457 868658 868663) (-583 "LINFORM.spad" 867910 867922 868415 868442) (-582 "LINEXP.spad" 866653 866663 867900 867905) (-581 "LINELT.spad" 866024 866036 866536 866563) (-580 "LINDEP.spad" 864873 864885 865936 865941) (-579 "LINBASIS.spad" 864509 864524 864863 864868) (-578 "LIMITRF.spad" 862456 862466 864499 864504) (-577 "LIMITPS.spad" 861366 861379 862446 862451) (-576 "LIECAT.spad" 860850 860860 861292 861361) (-575 "LIECAT.spad" 860362 860374 860806 860811) (-574 "LIE.spad" 858366 858378 859640 859782) (-573 "LIB.spad" 856537 856545 856983 856998) (-572 "LGROBP.spad" 853890 853909 856527 856532) (-571 "LFCAT.spad" 852949 852957 853880 853885) (-570 "LF.spad" 851904 851920 852939 852944) (-569 "LEXTRIPK.spad" 847527 847542 851894 851899) (-568 "LEXP.spad" 845546 845573 847507 847522) (-567 "LETAST.spad" 845245 845253 845536 845541) (-566 "LEADCDET.spad" 843651 843668 845235 845240) (-565 "LAZM3PK.spad" 842395 842417 843641 843646) (-564 "LAUPOL.spad" 841062 841075 841962 842031) (-563 "LAPLACE.spad" 840645 840661 841052 841057) (-562 "LALG.spad" 840421 840431 840625 840640) (-561 "LALG.spad" 840205 840217 840411 840416) (-560 "LA.spad" 839645 839659 840127 840166) (-559 "KVTFROM.spad" 839388 839398 839635 839640) (-558 "KTVLOGIC.spad" 838932 838940 839378 839383) (-557 "KRCFROM.spad" 838678 838688 838922 838927) (-556 "KOVACIC.spad" 837409 837426 838668 838673) (-555 "KONVERT.spad" 837131 837141 837399 837404) (-554 "KOERCE.spad" 836868 836878 837121 837126) (-553 "KERNEL2.spad" 836571 836583 836858 836863) (-552 "KERNEL.spad" 835291 835301 836420 836425) (-551 "KDAGG.spad" 834400 834422 835271 835286) (-550 "KDAGG.spad" 833517 833541 834390 834395) (-549 "KAFILE.spad" 832407 832423 832642 832669) (-548 "JVMOP.spad" 832320 832328 832397 832402) (-547 "JVMMDACC.spad" 831374 831382 832310 832315) (-546 "JVMFDACC.spad" 830690 830698 831364 831369) (-545 "JVMCSTTG.spad" 829419 829427 830680 830685) (-544 "JVMCFACC.spad" 828865 828873 829409 829414) (-543 "JVMBCODE.spad" 828776 828784 828855 828860) (-542 "JORDAN.spad" 826593 826605 828054 828196) (-541 "JOINAST.spad" 826295 826303 826583 826588) (-540 "IXAGG.spad" 824428 824452 826285 826290) (-539 "IXAGG.spad" 822416 822442 824275 824280) (-538 "IVECTOR.spad" 821231 821246 821386 821413) (-537 "ITUPLE.spad" 820407 820417 821221 821226) (-536 "ITRIGMNP.spad" 819254 819273 820397 820402) (-535 "ITFUN3.spad" 818760 818774 819244 819249) (-534 "ITFUN2.spad" 818504 818516 818750 818755) (-533 "ITFORM.spad" 817859 817867 818494 818499) (-532 "ITAYLOR.spad" 815853 815868 817723 817820) (-531 "ISUPS.spad" 808302 808317 814839 814936) (-530 "ISUMP.spad" 807803 807819 808292 808297) (-529 "ISAST.spad" 807522 807530 807793 807798) (-528 "IRURPK.spad" 806239 806258 807512 807517) (-527 "IRSN.spad" 804243 804251 806229 806234) (-526 "IRRF2F.spad" 802736 802746 804199 804204) (-525 "IRREDFFX.spad" 802337 802348 802726 802731) (-524 "IROOT.spad" 800676 800686 802327 802332) (-523 "IRFORM.spad" 800000 800008 800666 800671) (-522 "IR2F.spad" 799214 799230 799990 799995) (-521 "IR2.spad" 798242 798258 799204 799209) (-520 "IR.spad" 796078 796092 798124 798151) (-519 "IPRNTPK.spad" 795838 795846 796068 796073) (-518 "IPF.spad" 795403 795415 795643 795736) (-517 "IPADIC.spad" 795172 795198 795329 795398) (-516 "IP4ADDR.spad" 794729 794737 795162 795167) (-515 "IOMODE.spad" 794251 794259 794719 794724) (-514 "IOBFILE.spad" 793636 793644 794241 794246) (-513 "IOBCON.spad" 793501 793509 793626 793631) (-512 "INVLAPLA.spad" 793150 793166 793491 793496) (-511 "INTTR.spad" 786544 786561 793140 793145) (-510 "INTTOOLS.spad" 784352 784368 786171 786176) (-509 "INTSLPE.spad" 783680 783688 784342 784347) (-508 "INTRVL.spad" 783246 783256 783594 783675) (-507 "INTRF.spad" 781678 781692 783236 783241) (-506 "INTRET.spad" 781110 781120 781668 781673) (-505 "INTRAT.spad" 779845 779862 781100 781105) (-504 "INTPM.spad" 778308 778324 779566 779571) (-503 "INTPAF.spad" 776184 776202 778237 778242) (-502 "INTHERTR.spad" 775458 775475 776174 776179) (-501 "INTHERAL.spad" 775128 775152 775448 775453) (-500 "INTHEORY.spad" 771567 771575 775118 775123) (-499 "INTG0.spad" 765331 765349 771496 771501) (-498 "INTFACT.spad" 764398 764408 765321 765326) (-497 "INTEF.spad" 762809 762825 764388 764393) (-496 "INTDOM.spad" 761432 761440 762735 762804) (-495 "INTDOM.spad" 760117 760127 761422 761427) (-494 "INTCAT.spad" 758384 758394 760031 760112) (-493 "INTBIT.spad" 757891 757899 758374 758379) (-492 "INTALG.spad" 757079 757106 757881 757886) (-491 "INTAF.spad" 756579 756595 757069 757074) (-490 "INTABL.spad" 754961 754992 755124 755151) (-489 "INT8.spad" 754841 754849 754951 754956) (-488 "INT64.spad" 754720 754728 754831 754836) (-487 "INT32.spad" 754599 754607 754710 754715) (-486 "INT16.spad" 754478 754486 754589 754594) (-485 "INT.spad" 754004 754012 754344 754473) (-484 "INS.spad" 751507 751515 753906 753999) (-483 "INS.spad" 749096 749106 751497 751502) (-482 "INPSIGN.spad" 748566 748579 749086 749091) (-481 "INPRODPF.spad" 747662 747681 748556 748561) (-480 "INPRODFF.spad" 746750 746774 747652 747657) (-479 "INNMFACT.spad" 745725 745742 746740 746745) (-478 "INMODGCD.spad" 745229 745259 745715 745720) (-477 "INFSP.spad" 743526 743548 745219 745224) (-476 "INFPROD0.spad" 742606 742625 743516 743521) (-475 "INFORM1.spad" 742231 742241 742596 742601) (-474 "INFORM.spad" 739442 739450 742221 742226) (-473 "INFINITY.spad" 738994 739002 739432 739437) (-472 "INETCLTS.spad" 738971 738979 738984 738989) (-471 "INEP.spad" 737517 737539 738961 738966) (-470 "INDE.spad" 737166 737183 737427 737432) (-469 "INCRMAPS.spad" 736603 736613 737156 737161) (-468 "INBFILE.spad" 735699 735707 736593 736598) (-467 "INBFF.spad" 731549 731560 735689 735694) (-466 "INBCON.spad" 729815 729823 731539 731544) (-465 "INBCON.spad" 728079 728089 729805 729810) (-464 "INAST.spad" 727740 727748 728069 728074) (-463 "IMPTAST.spad" 727448 727456 727730 727735) (-462 "IMATRIX.spad" 726458 726484 726970 726997) (-461 "IMATQF.spad" 725552 725596 726414 726419) (-460 "IMATLIN.spad" 724173 724197 725508 725513) (-459 "IIARRAY2.spad" 723642 723680 723845 723872) (-458 "IFF.spad" 723055 723071 723326 723419) (-457 "IFAST.spad" 722669 722677 723045 723050) (-456 "IFARRAY.spad" 720196 720211 721894 721921) (-455 "IFAMON.spad" 720058 720075 720152 720157) (-454 "IEVALAB.spad" 719471 719483 720048 720053) (-453 "IEVALAB.spad" 718882 718896 719461 719466) (-452 "indexedp.spad" 718438 718450 718872 718877) (-451 "IDPOAMS.spad" 718116 718128 718350 718355) (-450 "IDPOAM.spad" 717758 717770 718028 718033) (-449 "IDPO.spad" 717172 717184 717670 717675) (-448 "IDPC.spad" 715887 715899 717162 717167) (-447 "IDPAM.spad" 715554 715566 715799 715804) (-446 "IDPAG.spad" 715223 715235 715466 715471) (-445 "IDENT.spad" 714875 714883 715213 715218) (-444 "catdef.spad" 714646 714657 714758 714870) (-443 "IDECOMP.spad" 711885 711903 714636 714641) (-442 "IDEAL.spad" 706847 706886 711833 711838) (-441 "ICDEN.spad" 706060 706076 706837 706842) (-440 "ICARD.spad" 705453 705461 706050 706055) (-439 "IBPTOOLS.spad" 704060 704077 705443 705448) (-438 "IBITS.spad" 703573 703586 703706 703733) (-437 "IBATOOL.spad" 700558 700577 703563 703568) (-436 "IBACHIN.spad" 699065 699080 700548 700553) (-435 "IARRAY2.spad" 698126 698152 698737 698764) (-434 "IARRAY1.spad" 697205 697220 697351 697378) (-433 "IAN.spad" 695587 695595 697036 697129) (-432 "IALGFACT.spad" 695198 695231 695577 695582) (-431 "HYPCAT.spad" 694622 694630 695188 695193) (-430 "HYPCAT.spad" 694044 694054 694612 694617) (-429 "HOSTNAME.spad" 693860 693868 694034 694039) (-428 "HOMOTOP.spad" 693603 693613 693850 693855) (-427 "HOAGG.spad" 690885 690895 693593 693598) (-426 "HOAGG.spad" 687917 687929 690627 690632) (-425 "HEXADEC.spad" 686142 686150 686507 686600) (-424 "HEUGCD.spad" 685233 685244 686132 686137) (-423 "HELLFDIV.spad" 684839 684863 685223 685228) (-422 "HEAP.spad" 684296 684306 684511 684538) (-421 "HEADAST.spad" 683837 683845 684286 684291) (-420 "HDP.spad" 673470 673486 673847 673944) (-419 "HDMP.spad" 671017 671032 671633 671760) (-418 "HB.spad" 669292 669300 671007 671012) (-417 "HASHTBL.spad" 667626 667657 667837 667864) (-416 "HASAST.spad" 667342 667350 667616 667621) (-415 "HACKPI.spad" 666833 666841 667244 667337) (-414 "GTSET.spad" 665760 665776 666467 666494) (-413 "GSTBL.spad" 664143 664178 664317 664332) (-412 "GSERIES.spad" 661515 661542 662334 662483) (-411 "GROUP.spad" 660788 660796 661495 661510) (-410 "GROUP.spad" 660069 660079 660778 660783) (-409 "GROEBSOL.spad" 658563 658584 660059 660064) (-408 "GRMOD.spad" 657144 657156 658553 658558) (-407 "GRMOD.spad" 655723 655737 657134 657139) (-406 "GRIMAGE.spad" 648636 648644 655713 655718) (-405 "GRDEF.spad" 647015 647023 648626 648631) (-404 "GRAY.spad" 645486 645494 647005 647010) (-403 "GRALG.spad" 644581 644593 645476 645481) (-402 "GRALG.spad" 643674 643688 644571 644576) (-401 "GPOLSET.spad" 643132 643155 643344 643371) (-400 "GOSPER.spad" 642409 642427 643122 643127) (-399 "GMODPOL.spad" 641557 641584 642377 642404) (-398 "GHENSEL.spad" 640640 640654 641547 641552) (-397 "GENUPS.spad" 636933 636946 640630 640635) (-396 "GENUFACT.spad" 636510 636520 636923 636928) (-395 "GENPGCD.spad" 636112 636129 636500 636505) (-394 "GENMFACT.spad" 635564 635583 636102 636107) (-393 "GENEEZ.spad" 633523 633536 635554 635559) (-392 "GDMP.spad" 630912 630929 631686 631813) (-391 "GCNAALG.spad" 624835 624862 630706 630773) (-390 "GCDDOM.spad" 624027 624035 624761 624830) (-389 "GCDDOM.spad" 623281 623291 624017 624022) (-388 "GBINTERN.spad" 619301 619339 623271 623276) (-387 "GBF.spad" 615084 615122 619291 619296) (-386 "GBEUCLID.spad" 612966 613004 615074 615079) (-385 "GB.spad" 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"EXIT.spad" 370024 370032 370343 370348) (-261 "EVALCYC.spad" 369484 369498 370014 370019) (-260 "EVALAB.spad" 369064 369074 369474 369479) (-259 "EVALAB.spad" 368642 368654 369054 369059) (-258 "EUCDOM.spad" 366232 366240 368568 368637) (-257 "EUCDOM.spad" 363884 363894 366222 366227) (-256 "ES2.spad" 363397 363413 363874 363879) (-255 "ES1.spad" 362967 362983 363387 363392) (-254 "ES.spad" 355838 355846 362957 362962) (-253 "ES.spad" 348630 348640 355751 355756) (-252 "ERROR.spad" 345957 345965 348620 348625) (-251 "EQTBL.spad" 344293 344315 344502 344529) (-250 "EQ2.spad" 344011 344023 344283 344288) (-249 "EQ.spad" 338917 338927 341712 341818) (-248 "EP.spad" 335243 335253 338907 338912) (-247 "ENV.spad" 333921 333929 335233 335238) (-246 "ENTIRER.spad" 333589 333597 333865 333916) (-245 "ENTIRER.spad" 333301 333311 333579 333584) (-244 "EMR.spad" 332589 332630 333227 333296) (-243 "ELTAGG.spad" 330843 330862 332579 332584) (-242 "ELTAGG.spad" 329061 329082 330799 330804) (-241 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diff --git a/src/share/algebra/category.daase b/src/share/algebra/category.daase
index c54e7356..81203204 100644
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193114) ((-1165 . -1128) T) ((-1165 . -13) T) ((-1165 . -72) T) ((-1165 . -25) T) ((-1165 . -104) T) ((-1165 . -583) 192971) ((-1165 . -655) 192828) ((-1165 . -118) 192789) ((-1165 . -120) 192750) ((-1165 . -146) T) ((-1165 . -495) T) ((-1165 . -245) T) ((-1165 . -47) 192694) ((-1164 . -1163) 192673) ((-1164 . -311) 192652) ((-1164 . -1133) 192631) ((-1164 . -833) 192610) ((-1164 . -495) 192564) ((-1164 . -146) 192498) ((-1164 . -556) 192317) ((-1164 . -655) 192164) ((-1164 . -583) 192011) ((-1164 . -38) 191858) ((-1164 . -389) 191837) ((-1164 . -257) 191816) ((-1164 . -591) 191716) ((-1164 . -589) 191601) ((-1164 . -970) T) ((-1164 . -1025) T) ((-1164 . -1060) T) ((-1164 . -664) T) ((-1164 . -962) T) ((-1164 . -82) 191421) ((-1164 . -964) 191262) ((-1164 . -969) 191103) ((-1164 . -21) T) ((-1164 . -23) T) ((-1164 . -1013) T) ((-1164 . -553) 191085) ((-1164 . -1128) T) ((-1164 . -13) T) ((-1164 . -72) T) ((-1164 . -25) T) ((-1164 . -104) T) ((-1164 . -245) 191039) ((-1164 . -201) 191018) ((-1164 . -916) 190984) ((-1164 . -1114) 190950) ((-1164 . -1117) 190916) ((-1164 . -430) 190882) ((-1164 . -239) 190848) ((-1164 . -66) 190814) ((-1164 . -35) 190780) ((-1164 . -1157) 190750) ((-1164 . -47) 190720) ((-1164 . -120) 190699) ((-1164 . -118) 190678) ((-1164 . -887) 190641) ((-1164 . -812) 190547) ((-1164 . -807) 190451) ((-1164 . -810) 190357) ((-1164 . -241) 190315) ((-1164 . -189) 190267) ((-1164 . -186) 190213) ((-1164 . -190) 190165) ((-1164 . -1161) 190149) ((-1164 . -951) 190133) ((-1159 . -1163) 190094) ((-1159 . -311) 190073) ((-1159 . -1133) 190052) ((-1159 . -833) 190031) ((-1159 . -495) 189985) ((-1159 . -146) 189919) ((-1159 . -556) 189668) ((-1159 . -655) 189515) ((-1159 . -583) 189362) ((-1159 . -38) 189209) ((-1159 . -389) 189188) ((-1159 . -257) 189167) ((-1159 . -591) 189067) ((-1159 . -589) 188952) ((-1159 . -970) T) ((-1159 . -1025) T) ((-1159 . -1060) T) ((-1159 . -664) T) ((-1159 . -962) T) ((-1159 . -82) 188772) ((-1159 . -964) 188613) ((-1159 . -969) 188454) ((-1159 . -21) T) ((-1159 . -23) T) ((-1159 . -1013) T) ((-1159 . -553) 188436) ((-1159 . -1128) T) ((-1159 . -13) T) ((-1159 . -72) T) ((-1159 . -25) T) ((-1159 . -104) T) ((-1159 . -245) 188390) ((-1159 . -201) 188369) ((-1159 . -916) 188335) ((-1159 . -1114) 188301) ((-1159 . -1117) 188267) ((-1159 . -430) 188233) ((-1159 . -239) 188199) ((-1159 . -66) 188165) ((-1159 . -35) 188131) ((-1159 . -1157) 188101) ((-1159 . -47) 188071) ((-1159 . -120) 188050) ((-1159 . -118) 188029) ((-1159 . -887) 187992) ((-1159 . -812) 187898) ((-1159 . -807) 187779) ((-1159 . -810) 187685) ((-1159 . -241) 187643) ((-1159 . -189) 187595) ((-1159 . -186) 187541) ((-1159 . -190) 187493) ((-1159 . -1161) 187477) ((-1159 . -951) 187412) ((-1147 . -1154) 187396) ((-1147 . -1065) 187374) ((-1147 . -554) NIL) ((-1147 . -259) 187361) ((-1147 . -453) 187309) ((-1147 . -276) 187286) ((-1147 . -951) 187169) ((-1147 . -352) 187153) ((-1147 . -38) 186985) ((-1147 . -82) 186790) ((-1147 . -964) 186616) ((-1147 . -969) 186442) ((-1147 . -589) 186352) ((-1147 . -591) 186241) ((-1147 . -583) 186073) ((-1147 . -655) 185905) ((-1147 . -556) 185661) ((-1147 . -118) 185640) ((-1147 . -120) 185619) ((-1147 . -47) 185596) ((-1147 . -326) 185580) ((-1147 . -581) 185528) ((-1147 . -810) 185472) ((-1147 . -807) 185379) ((-1147 . -812) 185290) ((-1147 . -797) NIL) ((-1147 . -822) 185269) ((-1147 . -1133) 185248) ((-1147 . -862) 185218) ((-1147 . -833) 185197) ((-1147 . -495) 185111) ((-1147 . -245) 185025) ((-1147 . -146) 184919) ((-1147 . -389) 184853) ((-1147 . -257) 184832) ((-1147 . -241) 184759) ((-1147 . -190) T) ((-1147 . -104) T) ((-1147 . -25) T) ((-1147 . -72) T) ((-1147 . -553) 184741) ((-1147 . -1013) T) ((-1147 . -23) T) ((-1147 . -21) T) ((-1147 . -970) T) ((-1147 . -1025) T) ((-1147 . -1060) T) ((-1147 . -664) T) ((-1147 . -962) T) ((-1147 . -186) 184728) ((-1147 . -13) T) ((-1147 . -1128) T) ((-1147 . -189) T) ((-1147 . -225) 184712) ((-1147 . -184) 184696) ((-1145 . -1006) 184680) ((-1145 . -558) 184664) ((-1145 . -1013) 184642) ((-1145 . -553) 184609) ((-1145 . -1128) 184587) ((-1145 . -13) 184565) ((-1145 . -72) 184543) ((-1145 . -1007) 184500) ((-1143 . -1142) 184479) ((-1143 . -916) 184445) ((-1143 . -1114) 184411) ((-1143 . -1117) 184377) ((-1143 . -430) 184343) ((-1143 . -239) 184309) ((-1143 . -66) 184275) ((-1143 . -35) 184241) ((-1143 . -1157) 184218) ((-1143 . -47) 184195) ((-1143 . -556) 183950) ((-1143 . -655) 183770) ((-1143 . -583) 183590) ((-1143 . -591) 183401) ((-1143 . -589) 183259) ((-1143 . -969) 183073) ((-1143 . -964) 182887) ((-1143 . -82) 182675) ((-1143 . -38) 182495) ((-1143 . -887) 182465) ((-1143 . -241) 182365) ((-1143 . -1140) 182349) ((-1143 . -970) T) ((-1143 . -1025) T) ((-1143 . -1060) T) ((-1143 . -664) T) ((-1143 . -962) T) ((-1143 . -21) T) ((-1143 . -23) T) ((-1143 . -1013) T) ((-1143 . -553) 182331) ((-1143 . -1128) T) ((-1143 . -13) T) ((-1143 . -72) T) ((-1143 . -25) T) ((-1143 . -104) T) ((-1143 . -118) 182259) ((-1143 . -120) 182187) ((-1143 . -554) 181860) ((-1143 . -184) 181830) ((-1143 . -810) 181684) ((-1143 . -812) 181484) ((-1143 . -807) 181282) ((-1143 . -225) 181252) ((-1143 . -189) 181114) ((-1143 . -186) 180970) ((-1143 . -190) 180878) ((-1143 . -311) 180857) ((-1143 . -1133) 180836) ((-1143 . -833) 180815) ((-1143 . -495) 180769) ((-1143 . -146) 180703) ((-1143 . -389) 180682) ((-1143 . -257) 180661) ((-1143 . -245) 180615) ((-1143 . -201) 180594) ((-1143 . -287) 180564) ((-1143 . -453) 180424) ((-1143 . -259) 180363) ((-1143 . -326) 180333) ((-1143 . -581) 180241) ((-1143 . -340) 180211) ((-1143 . -797) 180084) ((-1143 . -741) 180037) ((-1143 . -715) 179990) ((-1143 . -717) 179943) ((-1143 . -757) 179845) ((-1143 . -760) 179747) ((-1143 . -719) 179700) ((-1143 . -722) 179653) ((-1143 . -756) 179606) ((-1143 . -795) 179576) ((-1143 . -822) 179529) ((-1143 . -934) 179482) ((-1143 . -951) 179271) ((-1143 . -1065) 179223) ((-1143 . -905) 179193) ((-1138 . -1142) 179154) ((-1138 . -916) 179120) ((-1138 . -1114) 179086) ((-1138 . -1117) 179052) ((-1138 . -430) 179018) ((-1138 . -239) 178984) ((-1138 . -66) 178950) ((-1138 . -35) 178916) ((-1138 . -1157) 178893) ((-1138 . -47) 178870) ((-1138 . -556) 178671) ((-1138 . -655) 178473) ((-1138 . -583) 178275) ((-1138 . -591) 178130) ((-1138 . -589) 177970) ((-1138 . -969) 177766) ((-1138 . -964) 177562) ((-1138 . -82) 177314) ((-1138 . -38) 177116) ((-1138 . -887) 177086) ((-1138 . -241) 176914) ((-1138 . -1140) 176898) ((-1138 . -970) T) ((-1138 . -1025) T) ((-1138 . -1060) T) ((-1138 . -664) T) ((-1138 . -962) T) ((-1138 . -21) T) ((-1138 . -23) T) ((-1138 . -1013) T) ((-1138 . -553) 176880) ((-1138 . -1128) T) ((-1138 . -13) T) ((-1138 . -72) T) ((-1138 . -25) T) ((-1138 . -104) T) ((-1138 . -118) 176790) ((-1138 . -120) 176700) ((-1138 . -554) NIL) ((-1138 . -184) 176652) ((-1138 . -810) 176488) ((-1138 . -812) 176252) ((-1138 . -807) 175991) ((-1138 . -225) 175943) ((-1138 . -189) 175769) ((-1138 . -186) 175589) ((-1138 . -190) 175479) ((-1138 . -311) 175458) ((-1138 . -1133) 175437) ((-1138 . -833) 175416) ((-1138 . -495) 175370) ((-1138 . -146) 175304) ((-1138 . -389) 175283) ((-1138 . -257) 175262) ((-1138 . -245) 175216) ((-1138 . -201) 175195) ((-1138 . -287) 175147) ((-1138 . -453) 174881) ((-1138 . -259) 174766) ((-1138 . -326) 174718) ((-1138 . -581) 174670) ((-1138 . -340) 174622) ((-1138 . -797) NIL) ((-1138 . -741) NIL) ((-1138 . -715) NIL) ((-1138 . -717) NIL) ((-1138 . -757) NIL) ((-1138 . -760) NIL) ((-1138 . -719) NIL) ((-1138 . -722) NIL) ((-1138 . -756) NIL) ((-1138 . -795) 174574) ((-1138 . -822) NIL) ((-1138 . -934) NIL) ((-1138 . -951) 174540) ((-1138 . -1065) NIL) ((-1138 . -905) 174492) ((-1137 . -753) T) ((-1137 . -760) T) ((-1137 . -757) T) ((-1137 . -1013) T) ((-1137 . -553) 174474) ((-1137 . -1128) T) ((-1137 . -13) T) ((-1137 . -72) T) ((-1137 . -317) T) ((-1137 . -605) T) ((-1136 . -753) T) ((-1136 . -760) T) ((-1136 . -757) T) ((-1136 . -1013) T) ((-1136 . -553) 174456) ((-1136 . -1128) T) ((-1136 . -13) T) ((-1136 . -72) T) ((-1136 . -317) T) ((-1136 . -605) T) ((-1135 . -753) T) ((-1135 . -760) T) ((-1135 . -757) T) ((-1135 . -1013) T) ((-1135 . -553) 174438) ((-1135 . -1128) T) ((-1135 . -13) T) ((-1135 . -72) T) ((-1135 . -317) T) ((-1135 . -605) T) ((-1134 . -753) T) ((-1134 . -760) T) ((-1134 . -757) T) ((-1134 . -1013) T) ((-1134 . -553) 174420) ((-1134 . -1128) T) ((-1134 . -13) T) ((-1134 . -72) T) ((-1134 . -317) T) ((-1134 . -605) T) ((-1129 . -995) T) ((-1129 . -427) 174401) ((-1129 . -553) 174367) ((-1129 . -556) 174348) ((-1129 . -1013) T) ((-1129 . -1128) T) ((-1129 . -13) T) ((-1129 . -72) T) ((-1129 . -64) T) ((-1126 . -427) 174325) ((-1126 . -553) 174266) ((-1126 . -556) 174243) ((-1126 . -1013) 174221) ((-1126 . -1128) 174199) ((-1126 . -13) 174177) ((-1126 . -72) 174155) ((-1121 . -680) 174131) ((-1121 . -35) 174097) ((-1121 . -66) 174063) ((-1121 . -239) 174029) ((-1121 . -430) 173995) ((-1121 . -1117) 173961) ((-1121 . -1114) 173927) ((-1121 . -916) 173893) ((-1121 . -47) 173862) ((-1121 . -38) 173759) ((-1121 . -583) 173656) ((-1121 . -655) 173553) ((-1121 . -556) 173435) ((-1121 . -245) 173414) ((-1121 . -495) 173393) ((-1121 . -82) 173258) ((-1121 . -964) 173144) ((-1121 . -969) 173030) ((-1121 . -146) 172984) ((-1121 . -120) 172963) ((-1121 . -118) 172942) ((-1121 . -591) 172867) ((-1121 . -589) 172777) ((-1121 . -887) 172738) ((-1121 . -812) 172719) ((-1121 . -1128) T) ((-1121 . -13) T) ((-1121 . -807) 172698) ((-1121 . -962) T) ((-1121 . -664) T) ((-1121 . -1060) T) ((-1121 . -1025) T) ((-1121 . -970) T) ((-1121 . -21) T) ((-1121 . -23) T) ((-1121 . -1013) T) ((-1121 . -553) 172680) ((-1121 . -72) T) ((-1121 . -25) T) ((-1121 . -104) T) ((-1121 . -810) 172661) ((-1121 . -453) 172628) ((-1121 . -259) 172615) ((-1115 . -924) 172599) ((-1115 . -34) T) ((-1115 . -13) T) ((-1115 . -1128) T) ((-1115 . -72) 172553) ((-1115 . -553) 172488) ((-1115 . -259) 172426) ((-1115 . -453) 172359) ((-1115 . -1013) 172337) ((-1115 . -426) 172321) ((-1110 . -313) 172295) ((-1110 . -72) T) ((-1110 . -13) T) ((-1110 . -1128) T) ((-1110 . -553) 172277) ((-1110 . -1013) T) ((-1108 . -1013) T) ((-1108 . -553) 172259) ((-1108 . -1128) T) ((-1108 . -13) T) ((-1108 . -72) T) ((-1108 . -556) 172241) ((-1103 . -748) 172225) ((-1103 . -72) T) ((-1103 . -13) T) ((-1103 . -1128) T) ((-1103 . -553) 172207) ((-1103 . -1013) T) ((-1101 . -1106) 172186) ((-1101 . -183) 172134) ((-1101 . -76) 172082) ((-1101 . -259) 171880) ((-1101 . -453) 171632) ((-1101 . -426) 171567) ((-1101 . -124) 171515) ((-1101 . -554) NIL) ((-1101 . -193) 171463) ((-1101 . -550) 171442) ((-1101 . -243) 171421) ((-1101 . -1128) T) ((-1101 . -13) T) ((-1101 . -241) 171400) ((-1101 . -1013) T) ((-1101 . -553) 171382) ((-1101 . -72) T) ((-1101 . -34) T) ((-1101 . -539) 171361) ((-1097 . -1013) T) ((-1097 . -553) 171343) ((-1097 . -1128) T) ((-1097 . -13) T) ((-1097 . -72) T) ((-1096 . -753) T) ((-1096 . -760) T) ((-1096 . -757) T) ((-1096 . -1013) T) ((-1096 . -553) 171325) ((-1096 . -1128) T) ((-1096 . -13) T) ((-1096 . -72) T) ((-1096 . -317) T) ((-1096 . -605) T) ((-1095 . -753) T) ((-1095 . -760) T) ((-1095 . -757) T) ((-1095 . -1013) T) ((-1095 . -553) 171307) ((-1095 . -1128) T) ((-1095 . -13) T) ((-1095 . -72) T) ((-1095 . -317) T) ((-1094 . -1174) T) ((-1094 . -1013) T) ((-1094 . -553) 171274) ((-1094 . -1128) T) ((-1094 . -13) T) ((-1094 . -72) T) ((-1094 . -951) 171210) ((-1094 . -556) 171146) ((-1093 . -553) 171128) ((-1092 . -553) 171110) ((-1091 . -276) 171087) ((-1091 . -951) 170985) ((-1091 . -352) 170969) ((-1091 . -38) 170866) ((-1091 . -556) 170723) ((-1091 . -591) 170648) ((-1091 . -589) 170558) ((-1091 . -970) T) ((-1091 . -1025) T) ((-1091 . -1060) T) ((-1091 . -664) T) ((-1091 . -962) T) ((-1091 . -82) 170423) ((-1091 . -964) 170309) ((-1091 . -969) 170195) ((-1091 . -21) T) ((-1091 . -23) T) ((-1091 . -1013) T) ((-1091 . -553) 170177) ((-1091 . -1128) T) ((-1091 . -13) T) ((-1091 . -72) T) ((-1091 . -25) T) ((-1091 . -104) T) ((-1091 . -583) 170074) ((-1091 . -655) 169971) ((-1091 . -118) 169950) ((-1091 . -120) 169929) ((-1091 . -146) 169883) ((-1091 . -495) 169862) ((-1091 . -245) 169841) ((-1091 . -47) 169818) ((-1089 . -757) T) ((-1089 . -553) 169800) ((-1089 . -1013) T) ((-1089 . -72) T) ((-1089 . -13) T) ((-1089 . -1128) T) ((-1089 . -760) T) ((-1089 . -554) 169722) ((-1089 . -556) 169688) ((-1089 . -951) 169670) ((-1089 . -797) 169637) ((-1088 . -1171) 169621) ((-1088 . -190) 169580) ((-1088 . -556) 169462) ((-1088 . -591) 169387) ((-1088 . -589) 169297) ((-1088 . -104) T) ((-1088 . -25) T) ((-1088 . -72) T) ((-1088 . -553) 169279) ((-1088 . -1013) T) ((-1088 . -23) T) ((-1088 . -21) T) ((-1088 . -970) T) ((-1088 . -1025) T) ((-1088 . -1060) T) ((-1088 . -664) T) ((-1088 . -962) T) ((-1088 . -186) 169232) ((-1088 . -13) T) ((-1088 . -1128) T) ((-1088 . -189) 169191) ((-1088 . -241) 169156) ((-1088 . -810) 169069) ((-1088 . -807) 168957) ((-1088 . -812) 168870) ((-1088 . -887) 168840) ((-1088 . -38) 168737) ((-1088 . -82) 168602) ((-1088 . -964) 168488) ((-1088 . -969) 168374) ((-1088 . -583) 168271) ((-1088 . -655) 168168) ((-1088 . -118) 168147) ((-1088 . -120) 168126) ((-1088 . -146) 168080) ((-1088 . -495) 168059) ((-1088 . -245) 168038) ((-1088 . -47) 168015) ((-1088 . -1157) 167992) ((-1088 . -35) 167958) ((-1088 . -66) 167924) ((-1088 . -239) 167890) ((-1088 . -430) 167856) ((-1088 . -1117) 167822) ((-1088 . -1114) 167788) ((-1088 . -916) 167754) ((-1087 . -1163) 167715) ((-1087 . -311) 167694) ((-1087 . -1133) 167673) ((-1087 . -833) 167652) ((-1087 . -495) 167606) ((-1087 . -146) 167540) ((-1087 . -556) 167289) ((-1087 . -655) 167136) ((-1087 . -583) 166983) ((-1087 . -38) 166830) ((-1087 . -389) 166809) ((-1087 . -257) 166788) ((-1087 . -591) 166688) ((-1087 . -589) 166573) ((-1087 . -970) T) ((-1087 . -1025) T) ((-1087 . -1060) T) ((-1087 . -664) T) ((-1087 . -962) T) ((-1087 . -82) 166393) ((-1087 . -964) 166234) ((-1087 . -969) 166075) ((-1087 . -21) T) ((-1087 . -23) T) ((-1087 . -1013) T) ((-1087 . -553) 166057) ((-1087 . -1128) T) ((-1087 . -13) T) ((-1087 . -72) T) ((-1087 . -25) T) ((-1087 . -104) T) ((-1087 . -245) 166011) ((-1087 . -201) 165990) ((-1087 . -916) 165956) ((-1087 . -1114) 165922) ((-1087 . -1117) 165888) ((-1087 . -430) 165854) ((-1087 . -239) 165820) ((-1087 . -66) 165786) ((-1087 . -35) 165752) ((-1087 . -1157) 165722) ((-1087 . -47) 165692) ((-1087 . -120) 165671) ((-1087 . -118) 165650) ((-1087 . -887) 165613) ((-1087 . -812) 165519) ((-1087 . -807) 165400) ((-1087 . -810) 165306) ((-1087 . -241) 165264) ((-1087 . -189) 165216) ((-1087 . -186) 165162) ((-1087 . -190) 165114) ((-1087 . -1161) 165098) ((-1087 . -951) 165033) ((-1084 . -1154) 165017) ((-1084 . -1065) 164995) ((-1084 . -554) NIL) ((-1084 . -259) 164982) ((-1084 . -453) 164930) ((-1084 . -276) 164907) ((-1084 . -951) 164790) ((-1084 . -352) 164774) ((-1084 . -38) 164606) ((-1084 . -82) 164411) ((-1084 . -964) 164237) ((-1084 . -969) 164063) ((-1084 . -589) 163973) ((-1084 . -591) 163862) ((-1084 . -583) 163694) ((-1084 . -655) 163526) ((-1084 . -556) 163303) ((-1084 . -118) 163282) ((-1084 . -120) 163261) ((-1084 . -47) 163238) ((-1084 . -326) 163222) ((-1084 . -581) 163170) ((-1084 . -810) 163114) ((-1084 . -807) 163021) ((-1084 . -812) 162932) ((-1084 . -797) NIL) ((-1084 . -822) 162911) ((-1084 . -1133) 162890) ((-1084 . -862) 162860) ((-1084 . -833) 162839) ((-1084 . -495) 162753) ((-1084 . -245) 162667) ((-1084 . -146) 162561) ((-1084 . -389) 162495) ((-1084 . -257) 162474) ((-1084 . -241) 162401) ((-1084 . -190) T) ((-1084 . -104) T) ((-1084 . -25) T) ((-1084 . -72) T) ((-1084 . -553) 162383) ((-1084 . -1013) T) ((-1084 . -23) T) ((-1084 . -21) T) ((-1084 . -970) T) ((-1084 . -1025) T) ((-1084 . -1060) T) ((-1084 . -664) T) ((-1084 . -962) T) ((-1084 . -186) 162370) ((-1084 . -13) T) ((-1084 . -1128) T) ((-1084 . -189) T) ((-1084 . -225) 162354) ((-1084 . -184) 162338) ((-1081 . -1142) 162299) ((-1081 . -916) 162265) ((-1081 . -1114) 162231) ((-1081 . -1117) 162197) ((-1081 . -430) 162163) ((-1081 . -239) 162129) ((-1081 . -66) 162095) ((-1081 . -35) 162061) ((-1081 . -1157) 162038) ((-1081 . -47) 162015) ((-1081 . -556) 161816) ((-1081 . -655) 161618) ((-1081 . -583) 161420) ((-1081 . -591) 161275) ((-1081 . -589) 161115) ((-1081 . -969) 160911) ((-1081 . -964) 160707) ((-1081 . -82) 160459) ((-1081 . -38) 160261) ((-1081 . -887) 160231) ((-1081 . -241) 160059) ((-1081 . -1140) 160043) ((-1081 . -970) T) ((-1081 . -1025) T) ((-1081 . -1060) T) ((-1081 . -664) T) ((-1081 . -962) T) ((-1081 . -21) T) ((-1081 . -23) T) ((-1081 . -1013) T) ((-1081 . -553) 160025) ((-1081 . -1128) T) ((-1081 . -13) T) ((-1081 . -72) T) ((-1081 . -25) T) ((-1081 . -104) T) ((-1081 . -118) 159935) ((-1081 . -120) 159845) ((-1081 . -554) NIL) ((-1081 . -184) 159797) ((-1081 . -810) 159633) ((-1081 . -812) 159397) ((-1081 . -807) 159136) ((-1081 . -225) 159088) ((-1081 . -189) 158914) ((-1081 . -186) 158734) ((-1081 . -190) 158624) ((-1081 . -311) 158603) ((-1081 . -1133) 158582) ((-1081 . -833) 158561) ((-1081 . -495) 158515) ((-1081 . -146) 158449) ((-1081 . -389) 158428) ((-1081 . -257) 158407) ((-1081 . -245) 158361) ((-1081 . -201) 158340) ((-1081 . -287) 158292) ((-1081 . -453) 158026) ((-1081 . -259) 157911) ((-1081 . -326) 157863) ((-1081 . -581) 157815) ((-1081 . -340) 157767) ((-1081 . -797) NIL) ((-1081 . -741) NIL) ((-1081 . -715) NIL) ((-1081 . -717) NIL) ((-1081 . -757) NIL) ((-1081 . -760) NIL) ((-1081 . -719) NIL) ((-1081 . -722) NIL) ((-1081 . -756) NIL) ((-1081 . -795) 157719) ((-1081 . -822) NIL) ((-1081 . -934) NIL) ((-1081 . -951) 157685) ((-1081 . -1065) NIL) ((-1081 . -905) 157637) ((-1080 . -995) T) ((-1080 . -427) 157618) ((-1080 . -553) 157584) ((-1080 . -556) 157565) ((-1080 . -1013) T) ((-1080 . -1128) T) ((-1080 . -13) T) ((-1080 . -72) T) ((-1080 . -64) T) ((-1079 . -1013) T) ((-1079 . -553) 157547) ((-1079 . -1128) T) ((-1079 . -13) T) ((-1079 . -72) T) ((-1078 . -1013) T) ((-1078 . -553) 157529) ((-1078 . -1128) T) ((-1078 . -13) T) ((-1078 . -72) T) ((-1073 . -1106) 157505) ((-1073 . -183) 157450) ((-1073 . -76) 157395) ((-1073 . -259) 157184) ((-1073 . -453) 156924) ((-1073 . -426) 156856) ((-1073 . -124) 156801) ((-1073 . -554) NIL) ((-1073 . -193) 156746) ((-1073 . -550) 156722) ((-1073 . -243) 156698) ((-1073 . -1128) T) ((-1073 . -13) T) ((-1073 . -241) 156674) ((-1073 . -1013) T) ((-1073 . -553) 156656) ((-1073 . -72) T) ((-1073 . -34) T) ((-1073 . -539) 156632) ((-1072 . -1057) T) ((-1072 . -321) 156614) ((-1072 . -760) T) ((-1072 . -757) T) ((-1072 . -124) 156596) ((-1072 . -34) T) ((-1072 . -13) T) ((-1072 . -1128) T) ((-1072 . -72) T) ((-1072 . -553) 156578) ((-1072 . -259) NIL) ((-1072 . -453) NIL) ((-1072 . -1013) T) ((-1072 . -426) 156560) ((-1072 . -554) NIL) ((-1072 . -241) 156510) ((-1072 . -539) 156485) ((-1072 . -243) 156460) ((-1072 . -594) 156442) ((-1072 . -19) 156424) ((-1068 . -617) 156408) ((-1068 . -594) 156392) ((-1068 . -243) 156369) ((-1068 . -241) 156321) ((-1068 . -539) 156298) ((-1068 . -554) 156259) ((-1068 . -426) 156243) ((-1068 . -1013) 156221) ((-1068 . -453) 156154) ((-1068 . -259) 156092) ((-1068 . -553) 156027) ((-1068 . -72) 155981) ((-1068 . -1128) T) ((-1068 . -13) T) ((-1068 . -34) T) ((-1068 . -124) 155965) ((-1068 . -1167) 155949) ((-1068 . -924) 155933) ((-1068 . -1063) 155917) ((-1068 . -556) 155894) ((-1066 . -995) T) ((-1066 . -427) 155875) ((-1066 . -553) 155841) ((-1066 . -556) 155822) ((-1066 . -1013) T) ((-1066 . -1128) T) ((-1066 . -13) T) ((-1066 . -72) T) ((-1066 . -64) T) ((-1064 . -1106) 155801) ((-1064 . -183) 155749) ((-1064 . -76) 155697) ((-1064 . -259) 155495) ((-1064 . -453) 155247) ((-1064 . -426) 155182) ((-1064 . -124) 155130) ((-1064 . -554) NIL) ((-1064 . -193) 155078) ((-1064 . -550) 155057) ((-1064 . -243) 155036) ((-1064 . -1128) T) ((-1064 . -13) T) ((-1064 . -241) 155015) ((-1064 . -1013) T) ((-1064 . -553) 154997) ((-1064 . -72) T) ((-1064 . -34) T) ((-1064 . -539) 154976) ((-1061 . -1034) 154960) ((-1061 . -426) 154944) ((-1061 . -1013) 154922) ((-1061 . -453) 154855) ((-1061 . -259) 154793) ((-1061 . -553) 154728) ((-1061 . -72) 154682) ((-1061 . -1128) T) ((-1061 . -13) T) ((-1061 . -34) T) ((-1061 . -76) 154666) ((-1059 . -1020) 154635) ((-1059 . -1123) 154604) ((-1059 . -553) 154566) ((-1059 . -124) 154550) ((-1059 . -34) T) ((-1059 . -13) T) ((-1059 . -1128) T) ((-1059 . -72) T) ((-1059 . -259) 154488) ((-1059 . -453) 154421) ((-1059 . -1013) T) ((-1059 . -426) 154405) ((-1059 . -554) 154366) ((-1059 . -890) 154335) ((-1059 . -983) 154304) ((-1055 . -1036) 154249) ((-1055 . -426) 154233) ((-1055 . -453) 154166) ((-1055 . -259) 154104) ((-1055 . -34) T) ((-1055 . -966) 154044) ((-1055 . -951) 153942) ((-1055 . -556) 153861) ((-1055 . -352) 153845) ((-1055 . -581) 153793) ((-1055 . -591) 153731) ((-1055 . -326) 153715) ((-1055 . -190) 153694) ((-1055 . -186) 153642) ((-1055 . -189) 153596) ((-1055 . -225) 153580) ((-1055 . -807) 153504) ((-1055 . -812) 153430) ((-1055 . -810) 153389) ((-1055 . -184) 153373) ((-1055 . -655) 153308) ((-1055 . -583) 153243) ((-1055 . -589) 153202) ((-1055 . -104) T) ((-1055 . -25) T) ((-1055 . -72) T) ((-1055 . -13) T) ((-1055 . -1128) T) ((-1055 . -553) 153164) ((-1055 . -1013) T) ((-1055 . -23) T) ((-1055 . -21) T) ((-1055 . -969) 153148) ((-1055 . -964) 153132) ((-1055 . -82) 153111) ((-1055 . -962) T) ((-1055 . -664) T) ((-1055 . -1060) T) ((-1055 . -1025) T) ((-1055 . -970) T) ((-1055 . -38) 153071) ((-1055 . -554) 153032) ((-1054 . -924) 153003) ((-1054 . -34) T) ((-1054 . -13) T) ((-1054 . -1128) T) ((-1054 . -72) T) ((-1054 . -553) 152985) ((-1054 . -259) 152911) ((-1054 . -453) 152819) ((-1054 . -1013) T) ((-1054 . -426) 152790) ((-1053 . -1013) T) ((-1053 . -553) 152772) ((-1053 . -1128) T) ((-1053 . -13) T) ((-1053 . -72) T) ((-1048 . -1050) T) ((-1048 . -1174) T) ((-1048 . -64) T) ((-1048 . -72) T) ((-1048 . -13) T) ((-1048 . -1128) T) ((-1048 . -553) 152738) ((-1048 . -1013) T) ((-1048 . -556) 152719) ((-1048 . -427) 152700) ((-1048 . -995) T) ((-1046 . -1047) 152684) ((-1046 . -72) T) ((-1046 . -13) T) ((-1046 . -1128) T) ((-1046 . -553) 152666) ((-1046 . -1013) T) ((-1039 . -680) 152645) ((-1039 . -35) 152611) ((-1039 . -66) 152577) ((-1039 . -239) 152543) ((-1039 . -430) 152509) ((-1039 . -1117) 152475) ((-1039 . -1114) 152441) ((-1039 . -916) 152407) ((-1039 . -47) 152379) ((-1039 . -38) 152276) ((-1039 . -583) 152173) ((-1039 . -655) 152070) ((-1039 . -556) 151952) ((-1039 . -245) 151931) ((-1039 . -495) 151910) ((-1039 . -82) 151775) ((-1039 . -964) 151661) ((-1039 . -969) 151547) ((-1039 . -146) 151501) ((-1039 . -120) 151480) ((-1039 . -118) 151459) ((-1039 . -591) 151384) ((-1039 . -589) 151294) ((-1039 . -887) 151261) ((-1039 . -812) 151245) ((-1039 . -1128) T) ((-1039 . -13) T) ((-1039 . -807) 151227) ((-1039 . -962) T) ((-1039 . -664) T) ((-1039 . -1060) T) ((-1039 . -1025) T) ((-1039 . -970) T) ((-1039 . -21) T) ((-1039 . -23) T) ((-1039 . -1013) T) ((-1039 . -553) 151209) ((-1039 . -72) T) ((-1039 . -25) T) ((-1039 . -104) T) ((-1039 . -810) 151193) ((-1039 . -453) 151163) ((-1039 . -259) 151150) ((-1038 . -862) 151117) ((-1038 . -556) 150916) ((-1038 . -951) 150801) ((-1038 . -1133) 150780) ((-1038 . -822) 150759) ((-1038 . -797) 150618) ((-1038 . -812) 150602) ((-1038 . -807) 150584) ((-1038 . -810) 150568) ((-1038 . -453) 150520) ((-1038 . -389) 150474) ((-1038 . -581) 150422) ((-1038 . -591) 150311) ((-1038 . -326) 150295) ((-1038 . -47) 150267) ((-1038 . -38) 150119) ((-1038 . -583) 149971) ((-1038 . -655) 149823) ((-1038 . -245) 149757) ((-1038 . -495) 149691) ((-1038 . -82) 149516) ((-1038 . -964) 149362) ((-1038 . -969) 149208) ((-1038 . -146) 149122) ((-1038 . -120) 149101) ((-1038 . -118) 149080) ((-1038 . -589) 148990) ((-1038 . -104) T) ((-1038 . -25) T) ((-1038 . -72) T) ((-1038 . -13) T) ((-1038 . -1128) T) ((-1038 . -553) 148972) ((-1038 . -1013) T) ((-1038 . -23) T) ((-1038 . -21) T) ((-1038 . -962) T) ((-1038 . -664) T) ((-1038 . -1060) T) ((-1038 . -1025) T) ((-1038 . -970) T) ((-1038 . -352) 148956) ((-1038 . -276) 148928) ((-1038 . -259) 148915) ((-1038 . -554) 148663) ((-1033 . -483) T) ((-1033 . -1133) T) ((-1033 . -1065) T) ((-1033 . -951) 148645) ((-1033 . -554) 148560) ((-1033 . -934) T) ((-1033 . -797) 148542) ((-1033 . -756) T) ((-1033 . -722) T) ((-1033 . -719) T) ((-1033 . -760) T) ((-1033 . -757) T) ((-1033 . -717) T) ((-1033 . -715) T) ((-1033 . -741) T) ((-1033 . -591) 148514) ((-1033 . -581) 148496) ((-1033 . -833) T) ((-1033 . -495) T) ((-1033 . -245) T) ((-1033 . -146) T) ((-1033 . -556) 148468) ((-1033 . -655) 148455) ((-1033 . -583) 148442) ((-1033 . -969) 148429) ((-1033 . -964) 148416) ((-1033 . -82) 148401) ((-1033 . -38) 148388) ((-1033 . -389) T) ((-1033 . -257) T) ((-1033 . -189) T) ((-1033 . -186) 148375) ((-1033 . -190) T) ((-1033 . -116) T) ((-1033 . -962) T) ((-1033 . -664) T) ((-1033 . -1060) T) ((-1033 . -1025) T) ((-1033 . -970) T) ((-1033 . -21) T) ((-1033 . -589) 148347) ((-1033 . -23) T) ((-1033 . -1013) T) ((-1033 . -553) 148329) ((-1033 . -1128) T) ((-1033 . -13) T) ((-1033 . -72) T) ((-1033 . -25) T) ((-1033 . -104) T) ((-1033 . -120) T) ((-1033 . -753) T) ((-1033 . -317) T) ((-1033 . -84) T) ((-1033 . -605) T) ((-1029 . -995) T) ((-1029 . -427) 148310) ((-1029 . -553) 148276) ((-1029 . -556) 148257) ((-1029 . -1013) T) ((-1029 . -1128) T) ((-1029 . -13) T) ((-1029 . -72) T) ((-1029 . -64) T) ((-1028 . -1013) T) ((-1028 . -553) 148239) ((-1028 . -1128) T) ((-1028 . -13) T) ((-1028 . -72) T) ((-1026 . -196) 148218) ((-1026 . -1186) 148188) ((-1026 . -722) 148167) ((-1026 . -719) 148146) ((-1026 . -760) 148100) ((-1026 . -757) 148054) ((-1026 . -717) 148033) ((-1026 . -718) 148012) ((-1026 . -655) 147957) ((-1026 . -583) 147882) ((-1026 . -243) 147859) ((-1026 . -241) 147836) ((-1026 . -426) 147820) ((-1026 . -453) 147753) ((-1026 . -259) 147691) ((-1026 . -34) T) ((-1026 . -539) 147668) ((-1026 . -951) 147497) ((-1026 . -556) 147301) ((-1026 . -352) 147270) ((-1026 . -581) 147178) ((-1026 . -591) 147017) ((-1026 . -326) 146987) ((-1026 . -317) 146966) ((-1026 . -190) 146919) ((-1026 . -589) 146707) ((-1026 . -970) 146686) ((-1026 . -1025) 146665) ((-1026 . -1060) 146644) ((-1026 . -664) 146623) ((-1026 . -962) 146602) ((-1026 . -186) 146498) ((-1026 . -189) 146400) ((-1026 . -225) 146370) ((-1026 . -807) 146242) ((-1026 . -812) 146116) ((-1026 . -810) 146049) ((-1026 . -184) 146019) ((-1026 . -553) 145716) ((-1026 . -969) 145641) ((-1026 . -964) 145546) ((-1026 . -82) 145466) ((-1026 . -104) 145341) ((-1026 . -25) 145178) ((-1026 . -72) 144915) ((-1026 . -13) T) ((-1026 . -1128) T) ((-1026 . -1013) 144671) ((-1026 . -23) 144527) ((-1026 . -21) 144442) ((-1022 . -1023) 144426) ((-1022 . |MappingCategory|) 144400) ((-1022 . -1128) T) ((-1022 . -80) 144384) ((-1022 . -1013) T) ((-1022 . -553) 144366) ((-1022 . -13) T) ((-1022 . -72) T) ((-1017 . -1016) 144330) ((-1017 . -72) T) ((-1017 . -553) 144312) ((-1017 . -1013) T) ((-1017 . -241) 144268) ((-1017 . -1128) T) ((-1017 . -13) T) ((-1017 . -558) 144183) ((-1015 . -1016) 144135) ((-1015 . -72) T) ((-1015 . -553) 144117) ((-1015 . -1013) T) ((-1015 . -241) 144073) ((-1015 . -1128) T) ((-1015 . -13) T) ((-1015 . -558) 143976) ((-1014 . -317) T) ((-1014 . -72) T) ((-1014 . -13) T) ((-1014 . -1128) T) ((-1014 . -553) 143958) ((-1014 . -1013) T) ((-1009 . -366) 143942) ((-1009 . -1011) 143926) ((-1009 . -317) 143905) ((-1009 . -193) 143889) ((-1009 . -554) 143850) ((-1009 . -124) 143834) ((-1009 . -426) 143818) ((-1009 . -1013) T) ((-1009 . -453) 143751) ((-1009 . -259) 143689) ((-1009 . -553) 143671) ((-1009 . -72) T) ((-1009 . -1128) T) ((-1009 . -13) T) ((-1009 . -34) T) ((-1009 . -76) 143655) ((-1009 . -183) 143639) ((-1008 . -995) T) ((-1008 . -427) 143620) ((-1008 . -553) 143586) ((-1008 . -556) 143567) ((-1008 . -1013) T) ((-1008 . -1128) T) ((-1008 . -13) T) ((-1008 . -72) T) ((-1008 . -64) T) ((-1004 . -1128) T) ((-1004 . -13) T) ((-1004 . -1013) 143537) ((-1004 . -553) 143496) ((-1004 . -72) 143466) ((-1003 . -995) T) ((-1003 . -427) 143447) ((-1003 . -553) 143413) ((-1003 . -556) 143394) ((-1003 . -1013) T) ((-1003 . -1128) T) ((-1003 . -13) T) ((-1003 . -72) T) ((-1003 . -64) T) ((-1001 . -1006) 143378) ((-1001 . -558) 143362) ((-1001 . -1013) 143340) ((-1001 . -553) 143307) ((-1001 . -1128) 143285) ((-1001 . -13) 143263) ((-1001 . -72) 143241) ((-1001 . -1007) 143199) ((-1000 . -228) 143183) ((-1000 . -556) 143167) ((-1000 . -951) 143151) ((-1000 . -760) T) ((-1000 . -72) T) ((-1000 . -1013) T) ((-1000 . -553) 143133) ((-1000 . -757) T) ((-1000 . -186) 143120) ((-1000 . -13) T) ((-1000 . -1128) T) ((-1000 . -189) T) ((-999 . -213) 143057) ((-999 . -556) 142800) ((-999 . -951) 142629) ((-999 . -554) NIL) ((-999 . -276) 142590) ((-999 . -352) 142574) ((-999 . -38) 142426) ((-999 . -82) 142251) ((-999 . -964) 142097) ((-999 . -969) 141943) ((-999 . -589) 141853) ((-999 . -591) 141742) ((-999 . -583) 141594) ((-999 . -655) 141446) ((-999 . -118) 141425) ((-999 . -120) 141404) ((-999 . -146) 141318) ((-999 . -495) 141252) ((-999 . -245) 141186) ((-999 . -47) 141147) ((-999 . -326) 141131) ((-999 . -581) 141079) ((-999 . -389) 141033) ((-999 . -453) 140896) ((-999 . -810) 140831) ((-999 . -807) 140729) ((-999 . -812) 140631) ((-999 . -797) NIL) ((-999 . -822) 140610) ((-999 . -1133) 140589) ((-999 . -862) 140534) ((-999 . -259) 140521) ((-999 . -190) 140500) ((-999 . -104) T) ((-999 . -25) T) ((-999 . -72) T) ((-999 . -553) 140482) ((-999 . -1013) T) ((-999 . -23) T) ((-999 . -21) T) ((-999 . -970) T) ((-999 . -1025) T) ((-999 . -1060) T) ((-999 . -664) T) ((-999 . -962) T) ((-999 . -186) 140430) ((-999 . -13) T) ((-999 . -1128) T) ((-999 . -189) 140384) ((-999 . -225) 140368) ((-999 . -184) 140352) ((-997 . -553) 140334) ((-994 . -757) T) ((-994 . -553) 140316) ((-994 . -1013) T) ((-994 . -72) T) ((-994 . -13) T) ((-994 . -1128) T) ((-994 . -760) T) ((-994 . -554) 140297) ((-991 . -662) 140276) ((-991 . -951) 140174) ((-991 . -352) 140158) ((-991 . -581) 140106) ((-991 . -591) 139983) ((-991 . -326) 139967) ((-991 . -319) 139946) ((-991 . -120) 139925) ((-991 . -556) 139750) ((-991 . -655) 139624) ((-991 . -583) 139498) ((-991 . -589) 139396) ((-991 . -969) 139309) ((-991 . -964) 139222) ((-991 . -82) 139114) ((-991 . -38) 138988) ((-991 . -350) 138967) ((-991 . -342) 138946) ((-991 . -118) 138900) ((-991 . -1065) 138879) ((-991 . -298) 138858) ((-991 . -317) 138812) ((-991 . -201) 138766) ((-991 . -245) 138720) ((-991 . -257) 138674) ((-991 . -389) 138628) ((-991 . -495) 138582) ((-991 . -833) 138536) ((-991 . -1133) 138490) ((-991 . -311) 138444) ((-991 . -190) 138372) ((-991 . -186) 138248) ((-991 . -189) 138130) ((-991 . -225) 138100) ((-991 . -807) 137972) ((-991 . -812) 137846) ((-991 . -810) 137779) ((-991 . -184) 137749) ((-991 . -554) 137733) ((-991 . -21) T) ((-991 . -23) T) ((-991 . -1013) T) ((-991 . -553) 137715) ((-991 . -1128) T) ((-991 . -13) T) ((-991 . -72) T) ((-991 . -25) T) ((-991 . -104) T) ((-991 . -962) T) ((-991 . -664) T) ((-991 . -1060) T) ((-991 . -1025) T) ((-991 . -970) T) ((-991 . -146) T) ((-989 . -1013) T) ((-989 . -553) 137697) ((-989 . -1128) T) ((-989 . -13) T) ((-989 . -72) T) ((-989 . -241) 137676) ((-988 . -1013) T) ((-988 . -553) 137658) ((-988 . -1128) T) ((-988 . -13) T) ((-988 . -72) T) ((-987 . -1013) T) ((-987 . -553) 137640) ((-987 . -1128) T) ((-987 . -13) T) ((-987 . -72) T) ((-987 . -241) 137619) ((-987 . -951) 137596) ((-987 . -556) 137573) ((-986 . -1128) T) ((-986 . -13) T) ((-985 . -995) T) ((-985 . -427) 137554) ((-985 . -553) 137520) ((-985 . -556) 137501) ((-985 . -1013) T) ((-985 . -1128) T) ((-985 . -13) T) ((-985 . -72) T) ((-985 . -64) T) ((-978 . -995) T) ((-978 . -427) 137482) ((-978 . -553) 137448) ((-978 . -556) 137429) ((-978 . -1013) T) ((-978 . -1128) T) ((-978 . -13) T) ((-978 . -72) T) ((-978 . -64) T) ((-975 . -483) T) 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137055) ((-974 . -72) T) ((-974 . -13) T) ((-974 . -1128) T) ((-974 . -553) 137037) ((-974 . -1013) T) ((-971 . -1128) T) ((-971 . -13) T) ((-971 . -1013) 137015) ((-971 . -553) 136982) ((-971 . -72) 136960) ((-967 . -966) 136900) ((-967 . -583) 136845) ((-967 . -655) 136790) ((-967 . -34) T) ((-967 . -259) 136728) ((-967 . -453) 136661) ((-967 . -426) 136645) ((-967 . -591) 136629) ((-967 . -589) 136598) ((-967 . -104) T) ((-967 . -25) T) ((-967 . -72) T) ((-967 . -13) T) ((-967 . -1128) T) ((-967 . -553) 136560) ((-967 . -1013) T) ((-967 . -23) T) ((-967 . -21) T) ((-967 . -969) 136544) ((-967 . -964) 136528) ((-967 . -82) 136507) ((-967 . -1186) 136477) ((-967 . -554) 136438) ((-959 . -983) 136367) ((-959 . -890) 136296) ((-959 . -554) 136238) ((-959 . -426) 136203) ((-959 . -1013) T) ((-959 . -453) 136087) ((-959 . -259) 135995) ((-959 . -553) 135938) ((-959 . -72) T) ((-959 . -1128) T) ((-959 . -13) T) ((-959 . -34) T) ((-959 . -124) 135903) ((-959 . -1123) 135832) ((-949 . -995) T) ((-949 . -427) 135813) ((-949 . -553) 135779) ((-949 . -556) 135760) ((-949 . -1013) T) ((-949 . -1128) T) ((-949 . -13) T) ((-949 . -72) T) ((-949 . -64) T) ((-948 . -146) T) ((-948 . -556) 135729) ((-948 . -970) T) ((-948 . -1025) T) ((-948 . -1060) T) ((-948 . -664) T) ((-948 . -962) T) ((-948 . -591) 135703) ((-948 . -589) 135662) ((-948 . -104) T) ((-948 . -25) T) ((-948 . -72) T) ((-948 . -13) T) ((-948 . -1128) T) ((-948 . -553) 135644) ((-948 . -1013) T) ((-948 . -23) T) ((-948 . -21) T) ((-948 . -969) 135618) ((-948 . -964) 135592) ((-948 . -82) 135559) ((-948 . -38) 135543) ((-948 . -583) 135527) ((-948 . -655) 135511) ((-941 . -983) 135480) ((-941 . -890) 135449) ((-941 . -554) 135410) ((-941 . -426) 135394) ((-941 . -1013) T) ((-941 . -453) 135327) ((-941 . -259) 135265) ((-941 . -553) 135227) ((-941 . -72) T) ((-941 . -1128) T) ((-941 . -13) T) ((-941 . -34) T) ((-941 . -124) 135211) ((-941 . -1123) 135180) ((-940 . -1013) T) ((-940 . -553) 135162) ((-940 . -1128) T) 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T) ((-907 . -553) 129957) ((-907 . -1128) T) ((-907 . -13) T) ((-907 . -72) T) ((-907 . -25) T) ((-907 . -104) T) ((-907 . -241) 129924) ((-903 . -553) 129906) ((-900 . -1013) T) ((-900 . -553) 129888) ((-900 . -1128) T) ((-900 . -13) T) ((-900 . -72) T) ((-885 . -722) T) ((-885 . -719) T) ((-885 . -760) T) ((-885 . -757) T) ((-885 . -717) T) ((-885 . -23) T) ((-885 . -1013) T) ((-885 . -553) 129848) ((-885 . -1128) T) ((-885 . -13) T) ((-885 . -72) T) ((-885 . -25) T) ((-885 . -104) T) ((-884 . -995) T) ((-884 . -427) 129829) ((-884 . -553) 129795) ((-884 . -556) 129776) ((-884 . -1013) T) ((-884 . -1128) T) ((-884 . -13) T) ((-884 . -72) T) ((-884 . -64) T) ((-878 . -881) T) ((-878 . -72) T) ((-878 . -553) 129758) ((-878 . -1013) T) ((-878 . -605) T) ((-878 . -13) T) ((-878 . -1128) T) ((-878 . -84) T) ((-878 . -556) 129742) ((-877 . -553) 129724) ((-876 . -1013) T) ((-876 . -553) 129706) ((-876 . -1128) T) ((-876 . -13) T) ((-876 . -72) T) ((-876 . -317) 129659) ((-876 . -664) 129561) ((-876 . -1025) 129463) ((-876 . -23) 129277) ((-876 . -25) 129091) ((-876 . -104) 128949) ((-876 . -410) 128902) ((-876 . -21) 128857) ((-876 . -589) 128801) ((-876 . -718) 128754) ((-876 . -717) 128707) ((-876 . -757) 128609) ((-876 . -760) 128511) ((-876 . -719) 128464) ((-876 . -722) 128417) ((-870 . -19) 128401) ((-870 . -594) 128385) ((-870 . -243) 128362) ((-870 . -241) 128314) ((-870 . -539) 128291) ((-870 . -554) 128252) ((-870 . -426) 128236) ((-870 . -1013) 128189) ((-870 . -453) 128122) ((-870 . -259) 128060) ((-870 . -553) 127975) ((-870 . -72) 127909) ((-870 . -1128) T) ((-870 . -13) T) ((-870 . -34) T) ((-870 . -124) 127893) ((-870 . -757) 127872) ((-870 . -760) 127851) ((-870 . -321) 127835) ((-868 . -276) 127814) ((-868 . -951) 127712) ((-868 . -352) 127696) ((-868 . -38) 127593) ((-868 . -556) 127450) ((-868 . -591) 127375) ((-868 . -589) 127285) ((-868 . -970) T) ((-868 . -1025) T) ((-868 . -1060) T) ((-868 . -664) T) ((-868 . -962) T) ((-868 . -82) 127150) 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T) ((-837 . -553) 123499) ((-831 . -719) T) ((-831 . -760) T) ((-831 . -757) T) ((-831 . -1013) T) ((-831 . -553) 123481) ((-831 . -1128) T) ((-831 . -13) T) ((-831 . -72) T) ((-831 . -25) T) ((-831 . -664) T) ((-831 . -1025) T) ((-826 . -311) T) ((-826 . -1133) T) ((-826 . -833) T) ((-826 . -495) T) ((-826 . -146) T) ((-826 . -556) 123418) ((-826 . -655) 123370) ((-826 . -583) 123322) ((-826 . -38) 123274) ((-826 . -389) T) ((-826 . -257) T) ((-826 . -591) 123226) ((-826 . -589) 123163) ((-826 . -970) T) ((-826 . -1025) T) ((-826 . -1060) T) ((-826 . -664) T) ((-826 . -962) T) ((-826 . -82) 123094) ((-826 . -964) 123046) ((-826 . -969) 122998) ((-826 . -21) T) ((-826 . -23) T) ((-826 . -1013) T) ((-826 . -553) 122980) ((-826 . -1128) T) ((-826 . -13) T) ((-826 . -72) T) ((-826 . -25) T) ((-826 . -104) T) ((-826 . -245) T) ((-826 . -201) T) ((-818 . -298) T) ((-818 . -1065) T) ((-818 . -317) T) ((-818 . -118) T) ((-818 . -311) T) ((-818 . -1133) T) ((-818 . -833) T) ((-818 . -495) T) ((-818 . -146) T) ((-818 . -556) 122930) ((-818 . -655) 122895) ((-818 . -583) 122860) ((-818 . -38) 122825) ((-818 . -389) T) ((-818 . -257) T) ((-818 . -82) 122774) ((-818 . -964) 122739) ((-818 . -969) 122704) ((-818 . -589) 122654) ((-818 . -591) 122619) ((-818 . -245) T) ((-818 . -201) T) ((-818 . -342) T) ((-818 . -189) T) ((-818 . -1128) T) ((-818 . -13) T) ((-818 . -186) 122606) ((-818 . -962) T) ((-818 . -664) T) ((-818 . -1060) T) ((-818 . -1025) T) ((-818 . -970) T) ((-818 . -21) T) ((-818 . -23) T) ((-818 . -1013) T) ((-818 . -553) 122588) ((-818 . -72) T) ((-818 . -25) T) ((-818 . -104) T) ((-818 . -190) T) ((-818 . -279) 122575) ((-818 . -120) 122557) ((-818 . -951) 122544) ((-818 . -1186) 122531) ((-818 . -1197) 122518) ((-818 . -554) 122500) ((-817 . -1013) T) ((-817 . -553) 122482) ((-817 . -1128) T) ((-817 . -13) T) ((-817 . -72) T) ((-814 . -816) 122466) ((-814 . -760) 122420) ((-814 . -757) 122374) ((-814 . -664) T) ((-814 . -1013) T) ((-814 . -553) 122356) ((-814 . -72) T) ((-814 . -1025) T) ((-814 . -410) T) ((-814 . -1128) T) ((-814 . -13) T) ((-814 . -241) 122335) ((-813 . -92) 122319) ((-813 . -426) 122303) ((-813 . -1013) 122281) ((-813 . -453) 122214) ((-813 . -259) 122152) ((-813 . -553) 122066) ((-813 . -72) 122020) ((-813 . -1128) T) ((-813 . -13) T) ((-813 . -34) T) ((-813 . -924) 122004) ((-804 . -757) T) ((-804 . -553) 121986) ((-804 . -1013) T) ((-804 . -72) T) ((-804 . -13) T) ((-804 . -1128) T) ((-804 . -760) T) ((-804 . -951) 121963) ((-804 . -556) 121940) ((-801 . -1013) T) ((-801 . -553) 121922) ((-801 . -1128) T) ((-801 . -13) T) ((-801 . -72) T) ((-801 . -951) 121890) ((-801 . -556) 121858) ((-799 . -1013) T) ((-799 . -553) 121840) ((-799 . -1128) T) ((-799 . -13) T) ((-799 . -72) T) ((-796 . -1013) T) ((-796 . -553) 121822) ((-796 . -1128) T) ((-796 . -13) T) ((-796 . -72) T) ((-786 . -995) T) ((-786 . -427) 121803) ((-786 . -553) 121769) ((-786 . -556) 121750) ((-786 . -1013) T) ((-786 . -1128) T) ((-786 . -13) T) ((-786 . -72) T) ((-786 . -64) T) ((-786 . -1174) T) ((-784 . -1013) T) ((-784 . -553) 121732) ((-784 . -1128) T) ((-784 . -13) T) ((-784 . -72) T) ((-784 . -556) 121714) ((-783 . -1128) T) ((-783 . -13) T) ((-783 . -553) 121589) ((-783 . -1013) 121540) ((-783 . -72) 121491) ((-782 . -905) 121475) ((-782 . -1065) 121453) ((-782 . -951) 121320) ((-782 . -556) 121219) ((-782 . -554) 121022) ((-782 . -934) 121001) ((-782 . -822) 120980) ((-782 . -795) 120964) ((-782 . -756) 120943) ((-782 . -722) 120922) ((-782 . -719) 120901) ((-782 . -760) 120855) ((-782 . -757) 120809) ((-782 . -717) 120788) ((-782 . -715) 120767) ((-782 . -741) 120746) ((-782 . -797) 120671) ((-782 . -340) 120655) ((-782 . -581) 120603) ((-782 . -591) 120519) ((-782 . -326) 120503) ((-782 . -241) 120461) ((-782 . -259) 120426) ((-782 . -453) 120338) ((-782 . -287) 120322) ((-782 . -201) T) ((-782 . -82) 120253) ((-782 . -964) 120205) ((-782 . -969) 120157) ((-782 . -245) T) ((-782 . -655) 120109) ((-782 . -583) 120061) ((-782 . -589) 119998) ((-782 . -38) 119950) ((-782 . -257) T) ((-782 . -389) T) ((-782 . -146) T) ((-782 . -495) T) ((-782 . -833) T) ((-782 . -1133) T) ((-782 . -311) T) ((-782 . -190) 119929) ((-782 . -186) 119877) ((-782 . -189) 119831) ((-782 . -225) 119815) ((-782 . -807) 119739) ((-782 . -812) 119665) ((-782 . -810) 119624) ((-782 . -184) 119608) ((-782 . -120) 119587) ((-782 . -118) 119566) ((-782 . -104) T) ((-782 . -25) T) ((-782 . -72) T) ((-782 . -13) T) ((-782 . -1128) T) ((-782 . -553) 119548) ((-782 . -1013) T) ((-782 . -23) T) ((-782 . -21) T) ((-782 . -962) T) ((-782 . -664) T) ((-782 . -1060) T) ((-782 . -1025) T) ((-782 . -970) T) ((-781 . -905) 119525) ((-781 . -1065) NIL) ((-781 . -951) 119502) ((-781 . -556) 119432) ((-781 . -554) NIL) ((-781 . -934) NIL) ((-781 . -822) NIL) ((-781 . -795) 119409) ((-781 . -756) NIL) ((-781 . -722) NIL) ((-781 . -719) NIL) ((-781 . -760) NIL) ((-781 . -757) NIL) ((-781 . -717) NIL) ((-781 . -715) NIL) ((-781 . -741) NIL) ((-781 . -797) NIL) ((-781 . -340) 119386) ((-781 . -581) 119363) ((-781 . -591) 119308) ((-781 . -326) 119285) ((-781 . -241) 119215) ((-781 . -259) 119159) ((-781 . -453) 119022) ((-781 . -287) 118999) ((-781 . -201) T) ((-781 . -82) 118916) ((-781 . -964) 118861) ((-781 . -969) 118806) ((-781 . -245) T) ((-781 . -655) 118751) ((-781 . -583) 118696) ((-781 . -589) 118626) ((-781 . -38) 118571) ((-781 . -257) T) ((-781 . -389) T) ((-781 . -146) T) ((-781 . -495) T) ((-781 . -833) T) ((-781 . -1133) T) ((-781 . -311) T) ((-781 . -190) NIL) ((-781 . -186) NIL) ((-781 . -189) NIL) ((-781 . -225) 118548) ((-781 . -807) NIL) ((-781 . -812) NIL) ((-781 . -810) NIL) ((-781 . -184) 118525) ((-781 . -120) T) ((-781 . -118) NIL) ((-781 . -104) T) ((-781 . -25) T) ((-781 . -72) T) ((-781 . -13) T) ((-781 . -1128) T) ((-781 . -553) 118507) ((-781 . -1013) T) ((-781 . -23) T) ((-781 . -21) T) ((-781 . -962) T) ((-781 . -664) T) ((-781 . -1060) T) ((-781 . -1025) T) ((-781 . -970) T) ((-779 . -780) 118491) ((-779 . -833) T) ((-779 . -495) T) ((-779 . -245) T) ((-779 . -146) T) ((-779 . -556) 118463) ((-779 . -655) 118450) ((-779 . -583) 118437) ((-779 . -969) 118424) ((-779 . -964) 118411) ((-779 . -82) 118396) ((-779 . -38) 118383) ((-779 . -389) T) ((-779 . -257) T) ((-779 . -962) T) ((-779 . -664) T) ((-779 . -1060) T) ((-779 . -1025) T) ((-779 . -970) T) ((-779 . -21) T) ((-779 . -589) 118355) ((-779 . -23) T) ((-779 . -1013) T) ((-779 . -553) 118337) ((-779 . -1128) T) ((-779 . -13) T) ((-779 . -72) T) ((-779 . -25) T) ((-779 . -104) T) ((-779 . -591) 118324) ((-779 . -120) T) ((-776 . -962) T) ((-776 . -664) T) ((-776 . -1060) T) ((-776 . -1025) T) ((-776 . -970) T) ((-776 . -21) T) ((-776 . -589) 118269) ((-776 . -23) T) ((-776 . -1013) T) ((-776 . -553) 118231) ((-776 . -1128) T) ((-776 . -13) T) ((-776 . -72) T) ((-776 . -25) T) ((-776 . -104) T) ((-776 . -591) 118191) ((-776 . -556) 118126) ((-776 . -427) 118103) ((-776 . -38) 118073) ((-776 . -82) 118038) ((-776 . -964) 118008) ((-776 . -969) 117978) ((-776 . -583) 117948) ((-776 . -655) 117918) ((-775 . -1013) T) ((-775 . -553) 117900) ((-775 . -1128) T) ((-775 . -13) T) ((-775 . -72) T) ((-774 . -753) T) ((-774 . -760) T) ((-774 . -757) T) ((-774 . -1013) T) ((-774 . -553) 117882) ((-774 . -1128) T) ((-774 . -13) T) ((-774 . -72) T) ((-774 . -317) T) ((-774 . -554) 117804) ((-773 . -1013) T) ((-773 . -553) 117786) ((-773 . -1128) T) ((-773 . -13) T) ((-773 . -72) T) ((-772 . -771) T) ((-772 . -147) T) ((-772 . -553) 117768) ((-768 . -757) T) ((-768 . -553) 117750) ((-768 . -1013) T) ((-768 . -72) T) ((-768 . -13) T) ((-768 . -1128) T) ((-768 . -760) T) ((-765 . -762) 117734) ((-765 . -951) 117632) ((-765 . -556) 117530) ((-765 . -352) 117514) ((-765 . -655) 117484) ((-765 . -583) 117454) ((-765 . -591) 117428) ((-765 . -589) 117387) ((-765 . -104) T) ((-765 . -25) T) ((-765 . -72) T) ((-765 . -13) T) ((-765 . -1128) T) ((-765 . -553) 117369) ((-765 . -1013) T) ((-765 . -23) T) ((-765 . -21) T) ((-765 . -969) 117353) ((-765 . -964) 117337) ((-765 . -82) 117316) ((-765 . -962) T) ((-765 . -664) T) ((-765 . -1060) T) ((-765 . -1025) T) ((-765 . -970) T) ((-765 . -38) 117286) ((-764 . -762) 117270) ((-764 . -951) 117168) ((-764 . -556) 117087) ((-764 . -352) 117071) ((-764 . -655) 117041) ((-764 . -583) 117011) ((-764 . -591) 116985) ((-764 . -589) 116944) ((-764 . -104) T) ((-764 . -25) T) ((-764 . -72) T) ((-764 . -13) T) ((-764 . -1128) T) ((-764 . -553) 116926) ((-764 . -1013) T) ((-764 . -23) T) ((-764 . -21) T) ((-764 . -969) 116910) ((-764 . -964) 116894) ((-764 . -82) 116873) ((-764 . -962) T) ((-764 . -664) T) ((-764 . -1060) T) ((-764 . -1025) T) ((-764 . -970) T) ((-764 . -38) 116843) ((-758 . -760) T) ((-758 . -1128) T) ((-758 . -13) T) ((-758 . -72) T) ((-758 . -427) 116827) ((-758 . -553) 116775) ((-758 . -556) 116759) ((-751 . -1013) T) ((-751 . -553) 116741) ((-751 . -1128) T) ((-751 . -13) T) ((-751 . -72) T) ((-751 . -352) 116725) ((-751 . -556) 116598) ((-751 . -951) 116496) ((-751 . -21) 116451) ((-751 . -589) 116371) ((-751 . -23) 116326) ((-751 . -25) 116281) ((-751 . -104) 116236) ((-751 . -756) 116215) ((-751 . -591) 116188) ((-751 . -970) 116167) ((-751 . -1060) 116146) ((-751 . -962) 116125) ((-751 . -722) 116104) ((-751 . -719) 116083) ((-751 . -760) 116062) ((-751 . -757) 116041) ((-751 . -717) 116020) ((-751 . -715) 115999) ((-751 . -1025) 115978) ((-751 . -664) 115957) ((-750 . -748) 115939) ((-750 . -72) T) ((-750 . -13) T) ((-750 . -1128) T) ((-750 . -553) 115921) ((-750 . -1013) T) ((-746 . -962) T) ((-746 . -664) T) ((-746 . -1060) T) ((-746 . -1025) T) ((-746 . -970) T) ((-746 . -21) T) ((-746 . -589) 115866) ((-746 . -23) T) ((-746 . -1013) T) ((-746 . -553) 115848) ((-746 . -1128) T) ((-746 . -13) T) ((-746 . -72) T) ((-746 . -25) T) ((-746 . -104) T) ((-746 . -591) 115808) ((-746 . -556) 115763) ((-746 . -951) 115733) ((-746 . -241) 115712) ((-746 . -120) 115691) ((-746 . -118) 115670) ((-746 . -38) 115640) ((-746 . -82) 115605) ((-746 . -964) 115575) ((-746 . -969) 115545) ((-746 . -583) 115515) ((-746 . -655) 115485) ((-744 . -1013) T) ((-744 . -553) 115467) ((-744 . -1128) T) ((-744 . -13) T) ((-744 . -72) T) ((-744 . -352) 115451) ((-744 . -556) 115324) ((-744 . -951) 115222) ((-744 . -21) 115177) ((-744 . -589) 115097) ((-744 . -23) 115052) ((-744 . -25) 115007) ((-744 . -104) 114962) ((-744 . -756) 114941) ((-744 . -591) 114914) ((-744 . -970) 114893) ((-744 . -1060) 114872) ((-744 . -962) 114851) ((-744 . -722) 114830) ((-744 . -719) 114809) ((-744 . -760) 114788) ((-744 . -757) 114767) ((-744 . -717) 114746) ((-744 . -715) 114725) ((-744 . -1025) 114704) ((-744 . -664) 114683) ((-742 . -646) 114667) ((-742 . -556) 114622) ((-742 . -655) 114592) ((-742 . -583) 114562) ((-742 . -591) 114536) ((-742 . -589) 114495) ((-742 . -104) T) ((-742 . -25) T) ((-742 . -72) T) ((-742 . -13) T) ((-742 . -1128) T) ((-742 . -553) 114477) ((-742 . -1013) T) ((-742 . -23) T) ((-742 . -21) T) ((-742 . -969) 114461) ((-742 . -964) 114445) ((-742 . -82) 114424) ((-742 . -962) T) ((-742 . -664) T) ((-742 . -1060) T) ((-742 . -1025) T) ((-742 . -970) T) ((-742 . -38) 114394) ((-742 . -190) 114373) ((-742 . -186) 114346) ((-742 . -189) 114325) ((-740 . -333) 114309) ((-740 . -556) 114293) ((-740 . -951) 114277) ((-740 . -760) T) ((-740 . -757) T) ((-740 . -1025) T) ((-740 . -72) T) ((-740 . -13) T) ((-740 . -1128) T) ((-740 . -553) 114259) ((-740 . -1013) T) ((-740 . -664) T) ((-740 . -755) T) ((-740 . -767) T) ((-739 . -228) 114243) ((-739 . -556) 114227) ((-739 . -951) 114211) ((-739 . -760) T) ((-739 . -72) T) ((-739 . -1013) T) ((-739 . -553) 114193) ((-739 . -757) T) ((-739 . -186) 114180) ((-739 . -13) T) ((-739 . -1128) T) ((-739 . -189) T) ((-738 . -82) 114115) ((-738 . -964) 114066) ((-738 . -969) 114017) ((-738 . -21) T) ((-738 . -589) 113953) ((-738 . -23) T) ((-738 . -1013) T) ((-738 . -553) 113922) ((-738 . -1128) T) ((-738 . -13) T) ((-738 . -72) T) ((-738 . -25) T) ((-738 . -104) T) ((-738 . -591) 113873) ((-738 . -190) T) ((-738 . -556) 113782) ((-738 . -970) T) ((-738 . -1025) T) ((-738 . -1060) T) ((-738 . -664) T) ((-738 . -962) T) ((-738 . -186) 113769) ((-738 . -189) T) ((-738 . -427) 113753) ((-738 . -311) 113732) ((-738 . -1133) 113711) ((-738 . -833) 113690) ((-738 . -495) 113669) ((-738 . -146) 113648) ((-738 . -655) 113585) ((-738 . -583) 113522) ((-738 . -38) 113459) ((-738 . -389) 113438) ((-738 . -257) 113417) ((-738 . -245) 113396) ((-738 . -201) 113375) ((-737 . -213) 113314) ((-737 . -556) 113058) ((-737 . -951) 112888) ((-737 . -554) NIL) ((-737 . -276) 112850) ((-737 . -352) 112834) ((-737 . -38) 112686) ((-737 . -82) 112511) ((-737 . -964) 112357) ((-737 . -969) 112203) ((-737 . -589) 112113) ((-737 . -591) 112002) ((-737 . -583) 111854) ((-737 . -655) 111706) ((-737 . -118) 111685) ((-737 . -120) 111664) ((-737 . -146) 111578) ((-737 . -495) 111512) ((-737 . -245) 111446) ((-737 . -47) 111408) ((-737 . -326) 111392) ((-737 . -581) 111340) ((-737 . -389) 111294) ((-737 . -453) 111159) ((-737 . -810) 111095) ((-737 . -807) 110994) ((-737 . -812) 110897) ((-737 . -797) NIL) ((-737 . -822) 110876) ((-737 . -1133) 110855) ((-737 . -862) 110802) ((-737 . -259) 110789) ((-737 . -190) 110768) ((-737 . -104) T) ((-737 . -25) T) ((-737 . -72) T) ((-737 . -553) 110750) ((-737 . -1013) T) ((-737 . -23) T) ((-737 . -21) T) ((-737 . -970) T) ((-737 . -1025) T) ((-737 . -1060) T) ((-737 . -664) T) ((-737 . -962) T) ((-737 . -186) 110698) ((-737 . -13) T) ((-737 . -1128) T) ((-737 . -189) 110652) ((-737 . -225) 110636) ((-737 . -184) 110620) ((-736 . -196) 110599) ((-736 . -1186) 110569) ((-736 . -722) 110548) ((-736 . -719) 110527) ((-736 . -760) 110481) ((-736 . -757) 110435) ((-736 . -717) 110414) ((-736 . -718) 110393) ((-736 . -655) 110338) ((-736 . -583) 110263) ((-736 . -243) 110240) ((-736 . -241) 110217) ((-736 . -426) 110201) ((-736 . -453) 110134) ((-736 . -259) 110072) ((-736 . -34) T) ((-736 . -539) 110049) ((-736 . -951) 109878) ((-736 . -556) 109682) ((-736 . -352) 109651) ((-736 . -581) 109559) ((-736 . -591) 109398) ((-736 . -326) 109368) ((-736 . -317) 109347) ((-736 . -190) 109300) ((-736 . -589) 109088) ((-736 . -970) 109067) ((-736 . -1025) 109046) ((-736 . -1060) 109025) ((-736 . -664) 109004) ((-736 . -962) 108983) ((-736 . -186) 108879) ((-736 . -189) 108781) ((-736 . -225) 108751) ((-736 . -807) 108623) ((-736 . -812) 108497) ((-736 . -810) 108430) ((-736 . -184) 108400) ((-736 . -553) 108097) ((-736 . -969) 108022) ((-736 . -964) 107927) ((-736 . -82) 107847) ((-736 . -104) 107722) ((-736 . -25) 107559) ((-736 . -72) 107296) ((-736 . -13) T) ((-736 . -1128) T) ((-736 . -1013) 107052) ((-736 . -23) 106908) ((-736 . -21) 106823) ((-723 . -721) 106807) ((-723 . -760) 106786) ((-723 . -757) 106765) ((-723 . -951) 106558) ((-723 . -556) 106411) ((-723 . -352) 106375) ((-723 . -241) 106333) ((-723 . -259) 106298) ((-723 . -453) 106210) ((-723 . -287) 106194) ((-723 . -317) 106173) ((-723 . -554) 106134) ((-723 . -120) 106113) ((-723 . -118) 106092) ((-723 . -655) 106076) ((-723 . -583) 106060) ((-723 . -591) 106034) ((-723 . -589) 105993) ((-723 . -104) T) ((-723 . -25) T) ((-723 . -72) T) ((-723 . -13) T) ((-723 . -1128) T) ((-723 . -553) 105975) ((-723 . -1013) T) ((-723 . -23) T) ((-723 . -21) T) ((-723 . -969) 105959) ((-723 . -964) 105943) ((-723 . -82) 105922) ((-723 . -962) T) ((-723 . -664) T) ((-723 . -1060) T) ((-723 . -1025) T) ((-723 . -970) T) ((-723 . -38) 105906) ((-705 . -1154) 105890) ((-705 . -1065) 105868) ((-705 . -554) NIL) ((-705 . -259) 105855) ((-705 . -453) 105803) ((-705 . -276) 105780) ((-705 . -951) 105642) ((-705 . -352) 105626) ((-705 . -38) 105458) ((-705 . -82) 105263) ((-705 . -964) 105089) ((-705 . -969) 104915) ((-705 . -589) 104825) ((-705 . -591) 104714) ((-705 . -583) 104546) ((-705 . -655) 104378) ((-705 . -556) 104134) ((-705 . -118) 104113) ((-705 . -120) 104092) ((-705 . -47) 104069) ((-705 . -326) 104053) ((-705 . -581) 104001) ((-705 . -810) 103945) ((-705 . -807) 103852) ((-705 . -812) 103763) ((-705 . -797) NIL) ((-705 . -822) 103742) ((-705 . -1133) 103721) ((-705 . -862) 103691) ((-705 . -833) 103670) ((-705 . -495) 103584) ((-705 . -245) 103498) ((-705 . -146) 103392) ((-705 . -389) 103326) ((-705 . -257) 103305) ((-705 . -241) 103232) ((-705 . -190) T) ((-705 . -104) T) ((-705 . -25) T) ((-705 . -72) T) ((-705 . -553) 103193) ((-705 . -1013) T) ((-705 . -23) T) ((-705 . -21) T) ((-705 . -970) T) ((-705 . -1025) T) ((-705 . -1060) T) ((-705 . -664) T) ((-705 . -962) T) ((-705 . -186) 103180) ((-705 . -13) T) ((-705 . -1128) T) ((-705 . -189) T) ((-705 . -225) 103164) ((-705 . -184) 103148) ((-704 . -977) 103115) ((-704 . -554) 102750) ((-704 . -259) 102737) ((-704 . -453) 102689) ((-704 . -276) 102661) ((-704 . -951) 102520) ((-704 . -352) 102504) ((-704 . -38) 102356) ((-704 . -556) 102129) ((-704 . -591) 102018) ((-704 . -589) 101928) ((-704 . -970) T) ((-704 . -1025) T) ((-704 . -1060) T) ((-704 . -664) T) ((-704 . -962) T) ((-704 . -82) 101753) ((-704 . -964) 101599) ((-704 . -969) 101445) ((-704 . -21) T) ((-704 . -23) T) ((-704 . -1013) T) ((-704 . -553) 101359) ((-704 . -1128) T) ((-704 . -13) T) ((-704 . -72) T) ((-704 . -25) T) ((-704 . -104) T) ((-704 . -583) 101211) ((-704 . -655) 101063) ((-704 . -118) 101042) ((-704 . -120) 101021) ((-704 . -146) 100935) ((-704 . -495) 100869) ((-704 . -245) 100803) ((-704 . -47) 100775) ((-704 . -326) 100759) ((-704 . -581) 100707) ((-704 . -389) 100661) ((-704 . -810) 100645) ((-704 . -807) 100627) ((-704 . -812) 100611) ((-704 . -797) 100470) ((-704 . -822) 100449) ((-704 . -1133) 100428) ((-704 . -862) 100395) ((-697 . -1013) T) ((-697 . -553) 100377) ((-697 . -1128) T) ((-697 . -13) T) ((-697 . -72) T) ((-695 . -718) T) ((-695 . -104) T) ((-695 . -25) T) ((-695 . -72) T) ((-695 . -13) T) ((-695 . -1128) T) ((-695 . -553) 100359) ((-695 . -1013) T) ((-695 . -23) T) ((-695 . -717) T) ((-695 . -757) T) ((-695 . -760) T) ((-695 . -719) T) ((-695 . 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. -1133) 99203) ((-671 . -822) 99182) ((-671 . -797) NIL) ((-671 . -812) 99159) ((-671 . -807) 99134) ((-671 . -810) 99111) ((-671 . -453) 99049) ((-671 . -389) 99003) ((-671 . -581) 98951) ((-671 . -591) 98840) ((-671 . -326) 98824) ((-671 . -47) 98789) ((-671 . -38) 98641) ((-671 . -583) 98493) ((-671 . -655) 98345) ((-671 . -245) 98279) ((-671 . -495) 98213) ((-671 . -82) 98038) ((-671 . -964) 97884) ((-671 . -969) 97730) ((-671 . -146) 97644) ((-671 . -120) 97623) ((-671 . -118) 97602) ((-671 . -589) 97512) ((-671 . -104) T) ((-671 . -25) T) ((-671 . -72) T) ((-671 . -13) T) ((-671 . -1128) T) ((-671 . -553) 97494) ((-671 . -1013) T) ((-671 . -23) T) ((-671 . -21) T) ((-671 . -962) T) ((-671 . -664) T) ((-671 . -1060) T) ((-671 . -1025) T) ((-671 . -970) T) ((-671 . -352) 97478) ((-671 . -276) 97443) ((-671 . -259) 97430) ((-671 . -554) 97291) ((-665 . -666) 97275) ((-665 . -80) 97259) ((-665 . -1128) T) ((-665 . |MappingCategory|) 97233) ((-665 . -1023) 97217) ((-665 . -1013) T) 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91515) ((-613 . -964) 91499) ((-613 . -82) 91478) ((-613 . -962) T) ((-613 . -664) T) ((-613 . -1060) T) ((-613 . -1025) T) ((-613 . -970) T) ((-613 . -38) 91438) ((-613 . -358) 91422) ((-613 . -684) 91406) ((-613 . -658) T) ((-613 . -686) T) ((-613 . -315) 91390) ((-613 . -241) 91367) ((-607 . -323) 91346) ((-607 . -655) 91330) ((-607 . -583) 91314) ((-607 . -591) 91298) ((-607 . -589) 91267) ((-607 . -104) T) ((-607 . -25) T) ((-607 . -72) T) ((-607 . -13) T) ((-607 . -1128) T) ((-607 . -553) 91249) ((-607 . -1013) T) ((-607 . -23) T) ((-607 . -21) T) ((-607 . -969) 91233) ((-607 . -964) 91217) ((-607 . -82) 91196) ((-607 . -575) 91180) ((-607 . -332) 91152) ((-607 . -556) 91129) ((-607 . -951) 91106) ((-599 . -601) 91090) ((-599 . -38) 91060) ((-599 . -556) 90979) ((-599 . -591) 90953) ((-599 . -589) 90912) ((-599 . -970) T) ((-599 . -1025) T) ((-599 . -1060) T) ((-599 . -664) T) ((-599 . -962) T) ((-599 . -82) 90891) ((-599 . -964) 90875) ((-599 . -969) 90859) ((-599 . -21) T) 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T) ((-597 . -664) T) ((-597 . -962) T) ((-597 . -82) 89913) ((-597 . -964) 89897) ((-597 . -969) 89881) ((-597 . -21) T) ((-597 . -23) T) ((-597 . -1013) T) ((-597 . -553) 89863) ((-597 . -72) T) ((-597 . -25) T) ((-597 . -104) T) ((-597 . -583) 89833) ((-597 . -655) 89803) ((-597 . -352) 89787) ((-597 . -951) 89685) ((-597 . -762) 89669) ((-597 . -1128) T) ((-597 . -13) T) ((-597 . -241) 89648) ((-595 . -655) 89632) ((-595 . -583) 89616) ((-595 . -591) 89600) ((-595 . -589) 89569) ((-595 . -104) T) ((-595 . -25) T) ((-595 . -72) T) ((-595 . -13) T) ((-595 . -1128) T) ((-595 . -553) 89551) ((-595 . -1013) T) ((-595 . -23) T) ((-595 . -21) T) ((-595 . -969) 89535) ((-595 . -964) 89519) ((-595 . -82) 89498) ((-595 . -715) 89477) ((-595 . -717) 89456) ((-595 . -757) 89435) ((-595 . -760) 89414) ((-595 . -719) 89393) ((-595 . -722) 89372) ((-592 . -1013) T) ((-592 . -553) 89354) ((-592 . -1128) T) ((-592 . -13) T) ((-592 . -72) T) ((-592 . -951) 89338) ((-592 . -556) 89322) ((-590 . -635) 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87658) ((-573 . -969) 87642) ((-573 . -21) T) ((-573 . -589) 87611) ((-573 . -23) T) ((-573 . -1013) T) ((-573 . -553) 87580) ((-573 . -1128) T) ((-573 . -13) T) ((-573 . -72) T) ((-573 . -25) T) ((-573 . -104) T) ((-573 . -591) 87564) ((-573 . -583) 87548) ((-573 . -655) 87532) ((-573 . -358) 87497) ((-573 . -315) 87432) ((-573 . -241) 87390) ((-572 . -1106) 87365) ((-572 . -183) 87309) ((-572 . -76) 87253) ((-572 . -259) 87098) ((-572 . -453) 86898) ((-572 . -426) 86828) ((-572 . -124) 86772) ((-572 . -554) NIL) ((-572 . -193) 86716) ((-572 . -550) 86691) ((-572 . -243) 86666) ((-572 . -1128) T) ((-572 . -13) T) ((-572 . -241) 86619) ((-572 . -1013) T) ((-572 . -553) 86601) ((-572 . -72) T) ((-572 . -34) T) ((-572 . -539) 86576) ((-567 . -410) T) ((-567 . -1025) T) ((-567 . -72) T) ((-567 . -13) T) ((-567 . -1128) T) ((-567 . -553) 86558) ((-567 . -1013) T) ((-567 . -664) T) ((-566 . -995) T) ((-566 . -427) 86539) ((-566 . -553) 86505) ((-566 . -556) 86486) ((-566 . -1013) T) ((-566 . -1128) T) ((-566 . -13) T) ((-566 . -72) T) ((-566 . -64) T) ((-563 . -184) 86470) ((-563 . -810) 86429) ((-563 . -812) 86355) ((-563 . -807) 86279) ((-563 . -225) 86263) ((-563 . -189) 86217) ((-563 . -1128) T) ((-563 . -13) T) ((-563 . -186) 86165) ((-563 . -962) T) ((-563 . -664) T) ((-563 . -1060) T) ((-563 . -1025) T) ((-563 . -970) T) ((-563 . -21) T) ((-563 . -589) 86137) ((-563 . -23) T) ((-563 . -1013) T) ((-563 . -553) 86119) ((-563 . -72) T) ((-563 . -25) T) ((-563 . -104) T) ((-563 . -591) 86106) ((-563 . -556) 86002) ((-563 . -190) 85981) ((-563 . -495) T) ((-563 . -245) T) ((-563 . -146) T) ((-563 . -655) 85968) ((-563 . -583) 85955) ((-563 . -969) 85942) ((-563 . -964) 85929) ((-563 . -82) 85914) ((-563 . -38) 85901) ((-563 . -554) 85878) ((-563 . -352) 85862) ((-563 . -951) 85747) ((-563 . -120) 85726) ((-563 . -118) 85705) ((-563 . -257) 85684) ((-563 . -389) 85663) ((-563 . -833) 85642) ((-559 . -38) 85626) ((-559 . -556) 85595) ((-559 . -591) 85569) ((-559 . -589) 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72584) ((-424 . -589) 72534) ((-424 . -38) 72484) ((-424 . -257) T) ((-424 . -389) T) ((-424 . -146) T) ((-424 . -495) T) ((-424 . -833) T) ((-424 . -1133) T) ((-424 . -311) T) ((-424 . -190) T) ((-424 . -186) 72471) ((-424 . -189) T) ((-424 . -225) 72453) ((-424 . -807) NIL) ((-424 . -812) NIL) ((-424 . -810) NIL) ((-424 . -184) 72435) ((-424 . -120) T) ((-424 . -118) NIL) ((-424 . -104) T) ((-424 . -25) T) ((-424 . -72) T) ((-424 . -13) T) ((-424 . -1128) T) ((-424 . -553) 72377) ((-424 . -1013) T) ((-424 . -23) T) ((-424 . -21) T) ((-424 . -962) T) ((-424 . -664) T) ((-424 . -1060) T) ((-424 . -1025) T) ((-424 . -970) T) ((-422 . -285) 72346) ((-422 . -104) T) ((-422 . -25) T) ((-422 . -72) T) ((-422 . -13) T) ((-422 . -1128) T) ((-422 . -553) 72328) ((-422 . -1013) T) ((-422 . -23) T) ((-422 . -589) 72310) ((-422 . -21) T) ((-421 . -882) 72294) ((-421 . -426) 72278) ((-421 . -1013) 72256) ((-421 . -453) 72189) ((-421 . -259) 72127) ((-421 . -553) 72062) ((-421 . -72) 72016) ((-421 . -1128) T) ((-421 . -13) T) ((-421 . -34) T) ((-421 . -76) 72000) ((-420 . -995) T) ((-420 . -427) 71981) ((-420 . -553) 71947) ((-420 . -556) 71928) ((-420 . -1013) T) ((-420 . -1128) T) ((-420 . -13) T) ((-420 . -72) T) ((-420 . -64) T) ((-419 . -196) 71907) ((-419 . -1186) 71877) ((-419 . -722) 71856) ((-419 . -719) 71835) ((-419 . -760) 71789) ((-419 . -757) 71743) ((-419 . -717) 71722) ((-419 . -718) 71701) ((-419 . -655) 71646) ((-419 . -583) 71571) ((-419 . -243) 71548) ((-419 . -241) 71525) ((-419 . -426) 71509) ((-419 . -453) 71442) ((-419 . -259) 71380) ((-419 . -34) T) ((-419 . -539) 71357) ((-419 . -951) 71186) ((-419 . -556) 70990) ((-419 . -352) 70959) ((-419 . -581) 70867) ((-419 . -591) 70706) ((-419 . -326) 70676) ((-419 . -317) 70655) ((-419 . -190) 70608) ((-419 . -589) 70396) ((-419 . -970) 70375) ((-419 . -1025) 70354) ((-419 . -1060) 70333) ((-419 . -664) 70312) ((-419 . -962) 70291) ((-419 . -186) 70187) ((-419 . -189) 70089) ((-419 . -225) 70059) ((-419 . -807) 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T) ((-418 . -553) 66008) ((-418 . -1013) T) ((-418 . -23) T) ((-418 . -21) T) ((-418 . -962) T) ((-418 . -664) T) ((-418 . -1060) T) ((-418 . -1025) T) ((-418 . -970) T) ((-418 . -352) 65992) ((-418 . -276) 65949) ((-418 . -259) 65936) ((-418 . -554) 65797) ((-416 . -1106) 65776) ((-416 . -183) 65724) ((-416 . -76) 65672) ((-416 . -259) 65470) ((-416 . -453) 65222) ((-416 . -426) 65157) ((-416 . -124) 65105) ((-416 . -554) NIL) ((-416 . -193) 65053) ((-416 . -550) 65032) ((-416 . -243) 65011) ((-416 . -1128) T) ((-416 . -13) T) ((-416 . -241) 64990) ((-416 . -1013) T) ((-416 . -553) 64972) ((-416 . -72) T) ((-416 . -34) T) ((-416 . -539) 64951) ((-415 . -995) T) ((-415 . -427) 64932) ((-415 . -553) 64898) ((-415 . -556) 64879) ((-415 . -1013) T) ((-415 . -1128) T) ((-415 . -13) T) ((-415 . -72) T) ((-415 . -64) T) ((-414 . -311) T) ((-414 . -1133) T) ((-414 . -833) T) ((-414 . -495) T) ((-414 . -146) T) ((-414 . -556) 64829) ((-414 . -655) 64794) ((-414 . -583) 64759) ((-414 . -38) 64724) ((-414 . -389) T) ((-414 . -257) T) ((-414 . -591) 64689) ((-414 . -589) 64639) ((-414 . -970) T) ((-414 . -1025) T) ((-414 . -1060) T) ((-414 . -664) T) ((-414 . -962) T) ((-414 . -82) 64588) ((-414 . -964) 64553) ((-414 . -969) 64518) ((-414 . -21) T) ((-414 . -23) T) ((-414 . -1013) T) ((-414 . -553) 64470) ((-414 . -1128) T) ((-414 . -13) T) ((-414 . -72) T) ((-414 . -25) T) ((-414 . -104) T) ((-414 . -245) T) ((-414 . -201) T) ((-414 . -120) T) ((-414 . -951) 64430) ((-414 . -934) T) ((-414 . -554) 64352) ((-413 . -1123) 64321) ((-413 . -553) 64283) ((-413 . -124) 64267) ((-413 . -34) T) ((-413 . -13) T) ((-413 . -1128) T) ((-413 . -72) T) ((-413 . -259) 64205) ((-413 . -453) 64138) ((-413 . -1013) T) ((-413 . -426) 64122) ((-413 . -554) 64083) ((-413 . -890) 64052) ((-412 . -1106) 64031) ((-412 . -183) 63979) ((-412 . -76) 63927) ((-412 . -259) 63725) ((-412 . -453) 63477) ((-412 . -426) 63412) ((-412 . -124) 63360) ((-412 . -554) NIL) ((-412 . -193) 63308) ((-412 . -550) 63287) ((-412 . -243) 63266) ((-412 . -1128) T) ((-412 . -13) T) ((-412 . -241) 63245) ((-412 . -1013) T) ((-412 . -553) 63227) ((-412 . -72) T) ((-412 . -34) T) ((-412 . -539) 63206) ((-411 . -1161) 63190) ((-411 . -190) 63142) ((-411 . -186) 63088) ((-411 . -189) 63040) ((-411 . -241) 62998) ((-411 . -810) 62904) ((-411 . -807) 62785) ((-411 . -812) 62691) ((-411 . -887) 62654) ((-411 . -38) 62501) ((-411 . -82) 62321) ((-411 . -964) 62162) ((-411 . -969) 62003) ((-411 . -589) 61888) ((-411 . -591) 61788) ((-411 . -583) 61635) ((-411 . -655) 61482) ((-411 . -556) 61314) ((-411 . -118) 61293) ((-411 . -120) 61272) ((-411 . -47) 61242) ((-411 . -1157) 61212) ((-411 . -35) 61178) ((-411 . -66) 61144) ((-411 . -239) 61110) ((-411 . -430) 61076) ((-411 . -1117) 61042) ((-411 . -1114) 61008) ((-411 . -916) 60974) ((-411 . -201) 60953) ((-411 . -245) 60907) ((-411 . -104) T) ((-411 . -25) T) ((-411 . -72) T) ((-411 . -13) T) ((-411 . -1128) T) ((-411 . -553) 60889) ((-411 . -1013) T) ((-411 . -23) T) ((-411 . -21) T) ((-411 . -962) T) ((-411 . -664) T) ((-411 . -1060) T) ((-411 . -1025) T) ((-411 . -970) T) ((-411 . -257) 60868) ((-411 . -389) 60847) ((-411 . -146) 60781) ((-411 . -495) 60735) ((-411 . -833) 60714) ((-411 . -1133) 60693) ((-411 . -311) 60672) ((-405 . -1013) T) ((-405 . -553) 60654) ((-405 . -1128) T) ((-405 . -13) T) ((-405 . -72) T) ((-400 . -890) 60623) ((-400 . -554) 60584) ((-400 . -426) 60568) ((-400 . -1013) T) ((-400 . -453) 60501) ((-400 . -259) 60439) ((-400 . -553) 60401) ((-400 . -72) T) ((-400 . -1128) T) ((-400 . -13) T) ((-400 . -34) T) ((-400 . -124) 60385) ((-398 . -655) 60356) ((-398 . -583) 60327) ((-398 . -591) 60298) ((-398 . -589) 60254) ((-398 . -104) T) ((-398 . -25) T) ((-398 . -72) T) ((-398 . -13) T) ((-398 . -1128) T) ((-398 . -553) 60236) ((-398 . -1013) T) ((-398 . -23) T) ((-398 . -21) T) ((-398 . -969) 60207) ((-398 . -964) 60178) ((-398 . -82) 60139) ((-391 . -862) 60106) ((-391 . -556) 59898) ((-391 . -951) 59776) ((-391 . -1133) 59755) ((-391 . -822) 59734) ((-391 . -797) NIL) ((-391 . -812) 59711) ((-391 . -807) 59686) ((-391 . -810) 59663) ((-391 . -453) 59601) ((-391 . -389) 59555) ((-391 . -581) 59503) ((-391 . -591) 59392) ((-391 . -326) 59376) ((-391 . -47) 59355) ((-391 . -38) 59207) ((-391 . -583) 59059) ((-391 . -655) 58911) ((-391 . -245) 58845) ((-391 . -495) 58779) ((-391 . -82) 58604) ((-391 . -964) 58450) ((-391 . -969) 58296) ((-391 . -146) 58210) ((-391 . -120) 58189) ((-391 . -118) 58168) ((-391 . -589) 58078) ((-391 . -104) T) ((-391 . -25) T) ((-391 . -72) T) ((-391 . -13) T) ((-391 . -1128) T) ((-391 . -553) 58060) ((-391 . -1013) T) ((-391 . -23) T) ((-391 . -21) T) ((-391 . -962) T) ((-391 . -664) T) ((-391 . -1060) T) ((-391 . -1025) T) ((-391 . -970) T) ((-391 . -352) 58044) ((-391 . -276) 58023) ((-391 . -259) 58010) ((-391 . -554) 57871) ((-390 . -358) 57841) ((-390 . -684) 57811) ((-390 . -658) T) ((-390 . -686) T) ((-390 . -82) 57762) ((-390 . -964) 57732) ((-390 . -969) 57702) ((-390 . -21) T) ((-390 . -589) 57617) ((-390 . -23) T) ((-390 . -1013) T) ((-390 . -553) 57599) ((-390 . -72) T) ((-390 . -25) T) ((-390 . -104) T) ((-390 . -591) 57529) ((-390 . -583) 57499) ((-390 . -655) 57469) ((-390 . -315) 57439) ((-390 . -1128) T) ((-390 . -13) T) ((-390 . -241) 57402) ((-378 . -1013) T) ((-378 . -553) 57384) ((-378 . -1128) T) ((-378 . -13) T) ((-378 . -72) T) ((-377 . -1013) T) ((-377 . -553) 57366) ((-377 . -1128) T) ((-377 . -13) T) ((-377 . -72) T) ((-376 . -1013) T) ((-376 . -553) 57348) ((-376 . -1128) T) ((-376 . -13) T) ((-376 . -72) T) ((-374 . -553) 57330) ((-369 . -38) 57314) ((-369 . -556) 57283) ((-369 . -591) 57257) ((-369 . -589) 57216) ((-369 . -970) T) ((-369 . -1025) T) ((-369 . -1060) T) ((-369 . -664) T) ((-369 . -962) T) ((-369 . -82) 57195) ((-369 . -964) 57179) ((-369 . -969) 57163) ((-369 . -21) T) ((-369 . -23) T) ((-369 . -1013) T) ((-369 . -553) 57145) ((-369 . -1128) T) ((-369 . -13) T) ((-369 . -72) T) ((-369 . -25) T) 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. -655) 55695) ((-347 . -583) 55647) ((-347 . -589) 55584) ((-347 . -38) 55536) ((-347 . -257) T) ((-347 . -389) T) ((-347 . -146) T) ((-347 . -495) T) ((-347 . -833) T) ((-347 . -1133) T) ((-347 . -311) T) ((-347 . -190) 55515) ((-347 . -186) 55463) ((-347 . -189) 55417) ((-347 . -225) 55401) ((-347 . -807) 55325) ((-347 . -812) 55251) ((-347 . -810) 55210) ((-347 . -184) 55194) ((-347 . -120) 55173) ((-347 . -118) 55152) ((-347 . -104) T) ((-347 . -25) T) ((-347 . -72) T) ((-347 . -13) T) ((-347 . -1128) T) ((-347 . -553) 55134) ((-347 . -1013) T) ((-347 . -23) T) ((-347 . -21) T) ((-347 . -962) T) ((-347 . -664) T) ((-347 . -1060) T) ((-347 . -1025) T) ((-347 . -970) T) ((-345 . -495) T) ((-345 . -245) T) ((-345 . -146) T) ((-345 . -556) 55043) ((-345 . -655) 55017) ((-345 . -583) 54991) ((-345 . -591) 54965) ((-345 . -589) 54924) ((-345 . -104) T) ((-345 . -25) T) ((-345 . -72) T) ((-345 . -13) T) ((-345 . -1128) T) ((-345 . -553) 54906) ((-345 . -1013) T) ((-345 . -23) T) ((-345 . -21) T) ((-345 . -969) 54880) ((-345 . -964) 54854) ((-345 . -82) 54821) ((-345 . -962) T) ((-345 . -664) T) ((-345 . -1060) T) ((-345 . -1025) T) ((-345 . -970) T) ((-345 . -38) 54795) ((-345 . -184) 54779) ((-345 . -810) 54738) ((-345 . -812) 54664) ((-345 . -807) 54588) ((-345 . -225) 54572) ((-345 . -189) 54526) ((-345 . -186) 54474) ((-345 . -190) 54453) ((-345 . -287) 54437) ((-345 . -453) 54279) ((-345 . -259) 54218) ((-345 . -241) 54146) ((-345 . -352) 54130) ((-345 . -951) 54028) ((-345 . -389) 53981) ((-345 . -934) 53960) ((-345 . -554) 53863) ((-345 . -1133) 53841) ((-339 . -1013) T) ((-339 . -553) 53823) ((-339 . -1128) T) ((-339 . -13) T) ((-339 . -72) T) ((-339 . -189) T) ((-339 . -186) 53810) ((-339 . -554) 53787) ((-337 . -684) 53771) ((-337 . -658) T) ((-337 . -686) T) ((-337 . -82) 53750) ((-337 . -964) 53734) ((-337 . -969) 53718) ((-337 . -21) T) ((-337 . -589) 53687) ((-337 . -23) T) ((-337 . -1013) T) ((-337 . -553) 53669) ((-337 . -1128) T) ((-337 . -13) T) ((-337 . -72) T) ((-337 . -25) T) ((-337 . -104) T) ((-337 . -591) 53653) ((-337 . -583) 53637) ((-337 . -655) 53621) ((-335 . -336) T) ((-335 . -72) T) ((-335 . -13) T) ((-335 . -1128) T) ((-335 . -553) 53587) ((-335 . -1013) T) ((-335 . -556) 53568) ((-335 . -427) 53549) ((-334 . -333) 53533) ((-334 . -556) 53517) ((-334 . -951) 53501) ((-334 . -760) 53480) ((-334 . -757) 53459) ((-334 . -1025) T) ((-334 . -72) T) ((-334 . -13) T) ((-334 . -1128) T) ((-334 . -553) 53441) ((-334 . -1013) T) ((-334 . -664) T) ((-331 . -332) 53420) ((-331 . -556) 53404) ((-331 . -951) 53388) ((-331 . -583) 53358) ((-331 . -655) 53328) ((-331 . -591) 53312) ((-331 . -589) 53281) ((-331 . -104) T) ((-331 . -25) T) ((-331 . -72) T) ((-331 . -13) T) ((-331 . -1128) T) ((-331 . -553) 53263) ((-331 . -1013) T) ((-331 . -23) T) ((-331 . -21) T) ((-331 . -969) 53247) ((-331 . -964) 53231) ((-331 . -82) 53210) ((-330 . -82) 53189) ((-330 . -964) 53173) ((-330 . -969) 53157) ((-330 . -21) T) ((-330 . -589) 53126) 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. -453) 21539) ((-203 . -259) 21477) ((-203 . -553) 21372) ((-203 . -72) 21306) ((-203 . -1128) T) ((-203 . -13) T) ((-203 . -34) T) ((-203 . -124) 21290) ((-203 . -237) 21274) ((-203 . -427) 21251) ((-203 . -556) 21228) ((-197 . -196) 21207) ((-197 . -1186) 21177) ((-197 . -722) 21156) ((-197 . -719) 21135) ((-197 . -760) 21089) ((-197 . -757) 21043) ((-197 . -717) 21022) ((-197 . -718) 21001) ((-197 . -655) 20946) ((-197 . -583) 20871) ((-197 . -243) 20848) ((-197 . -241) 20825) ((-197 . -426) 20809) ((-197 . -453) 20742) ((-197 . -259) 20680) ((-197 . -34) T) ((-197 . -539) 20657) ((-197 . -951) 20486) ((-197 . -556) 20290) ((-197 . -352) 20259) ((-197 . -581) 20167) ((-197 . -591) 20006) ((-197 . -326) 19976) ((-197 . -317) 19955) ((-197 . -190) 19908) ((-197 . -589) 19696) ((-197 . -970) 19675) ((-197 . -1025) 19654) ((-197 . -1060) 19633) ((-197 . -664) 19612) ((-197 . -962) 19591) ((-197 . -186) 19487) ((-197 . -189) 19389) ((-197 . -225) 19359) ((-197 . -807) 19231) ((-197 . 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-553) 15059) ((-166 . -1128) T) ((-166 . -13) T) ((-166 . -72) T) ((-161 . -1013) T) ((-161 . -553) 15041) ((-161 . -1128) T) ((-161 . -13) T) ((-161 . -72) T) ((-158 . -1013) T) ((-158 . -553) 15023) ((-158 . -1128) T) ((-158 . -13) T) ((-158 . -72) T) ((-157 . -160) T) ((-157 . -1013) T) ((-157 . -553) 15005) ((-157 . -1128) T) ((-157 . -13) T) ((-157 . -72) T) ((-157 . -748) 14987) ((-154 . -995) T) ((-154 . -427) 14968) ((-154 . -553) 14934) ((-154 . -556) 14915) ((-154 . -1013) T) ((-154 . -1128) T) ((-154 . -13) T) ((-154 . -72) T) ((-154 . -64) T) ((-149 . -553) 14897) ((-148 . -38) 14829) ((-148 . -556) 14746) ((-148 . -591) 14678) ((-148 . -589) 14595) ((-148 . -970) T) ((-148 . -1025) T) ((-148 . -1060) T) ((-148 . -664) T) ((-148 . -962) T) ((-148 . -82) 14494) ((-148 . -964) 14426) ((-148 . -969) 14358) ((-148 . -21) T) ((-148 . -23) T) ((-148 . -1013) T) ((-148 . -553) 14340) ((-148 . -1128) T) ((-148 . -13) T) ((-148 . -72) T) ((-148 . -25) T) ((-148 . -104) T) ((-148 . 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. -1128) T) ((-134 . -13) T) ((-134 . -72) T) ((-130 . -25) T) ((-130 . -72) T) ((-130 . -13) T) ((-130 . -1128) T) ((-130 . -553) 10667) ((-130 . -1013) T) ((-129 . -995) T) ((-129 . -427) 10648) ((-129 . -553) 10614) ((-129 . -556) 10595) ((-129 . -1013) T) ((-129 . -1128) T) ((-129 . -13) T) ((-129 . -72) T) ((-129 . -64) T) ((-127 . -995) T) ((-127 . -427) 10576) ((-127 . -553) 10542) ((-127 . -556) 10523) ((-127 . -1013) T) ((-127 . -1128) T) ((-127 . -13) T) ((-127 . -72) T) ((-127 . -64) T) ((-125 . -962) T) ((-125 . -664) T) ((-125 . -1060) T) ((-125 . -1025) T) ((-125 . -970) T) ((-125 . -21) T) ((-125 . -589) 10482) ((-125 . -23) T) ((-125 . -1013) T) ((-125 . -553) 10464) ((-125 . -1128) T) ((-125 . -13) T) ((-125 . -72) T) ((-125 . -25) T) ((-125 . -104) T) ((-125 . -591) 10438) ((-125 . -556) 10407) ((-125 . -38) 10391) ((-125 . -82) 10370) ((-125 . -964) 10354) ((-125 . -969) 10338) ((-125 . -583) 10322) ((-125 . -655) 10306) ((-125 . -1186) 10290) ((-117 . -753) T) 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. -590) 197177) ((-1193 . -23) T) ((-1193 . -1015) T) ((-1193 . -554) 197146) ((-1193 . -1130) T) ((-1193 . -13) T) ((-1193 . -72) T) ((-1193 . -25) T) ((-1193 . -104) T) ((-1193 . -592) 197106) ((-1193 . -557) 197048) ((-1193 . -428) 197032) ((-1193 . -38) 197002) ((-1193 . -82) 196967) ((-1193 . -965) 196937) ((-1193 . -970) 196907) ((-1193 . -584) 196877) ((-1193 . -656) 196847) ((-1192 . -997) T) ((-1192 . -428) 196828) ((-1192 . -554) 196794) ((-1192 . -557) 196775) ((-1192 . -1015) T) ((-1192 . -1130) T) ((-1192 . -13) T) ((-1192 . -72) T) ((-1192 . -64) T) ((-1191 . -997) T) ((-1191 . -428) 196756) ((-1191 . -554) 196722) ((-1191 . -557) 196703) ((-1191 . -1015) T) ((-1191 . -1130) T) ((-1191 . -13) T) ((-1191 . -72) T) ((-1191 . -64) T) ((-1186 . -554) 196685) ((-1184 . -1015) T) ((-1184 . -554) 196667) ((-1184 . -1130) T) ((-1184 . -13) T) ((-1184 . -72) T) ((-1183 . -1015) T) ((-1183 . -554) 196649) ((-1183 . -1130) T) ((-1183 . -13) T) ((-1183 . -72) T) ((-1180 . -1179) 196633) ((-1180 . -322) 196617) ((-1180 . -761) 196596) ((-1180 . -758) 196575) ((-1180 . -124) 196559) ((-1180 . -34) T) ((-1180 . -13) T) ((-1180 . -1130) T) ((-1180 . -72) 196493) ((-1180 . -554) 196408) ((-1180 . -260) 196346) ((-1180 . -454) 196279) ((-1180 . -1015) 196232) ((-1180 . -427) 196216) ((-1180 . -555) 196177) ((-1180 . -241) 196129) ((-1180 . -540) 196106) ((-1180 . -243) 196083) ((-1180 . -595) 196067) ((-1180 . -19) 196051) ((-1177 . -1015) T) ((-1177 . -554) 196017) ((-1177 . -1130) T) ((-1177 . -13) T) ((-1177 . -72) T) ((-1170 . -1173) 196001) ((-1170 . -190) 195960) ((-1170 . -557) 195842) ((-1170 . -592) 195767) ((-1170 . -590) 195677) ((-1170 . -104) T) ((-1170 . -25) T) ((-1170 . -72) T) ((-1170 . -554) 195659) ((-1170 . -1015) T) ((-1170 . -23) T) ((-1170 . -21) T) ((-1170 . -972) T) ((-1170 . -1027) T) ((-1170 . -1062) T) ((-1170 . -665) T) ((-1170 . -963) T) ((-1170 . -186) 195612) ((-1170 . -13) T) ((-1170 . -1130) T) ((-1170 . -189) 195571) ((-1170 . -241) 195536) ((-1170 . -811) 195449) ((-1170 . -808) 195337) ((-1170 . -813) 195250) ((-1170 . -888) 195220) ((-1170 . -38) 195117) ((-1170 . -82) 194982) ((-1170 . -965) 194868) ((-1170 . -970) 194754) ((-1170 . -584) 194651) ((-1170 . -656) 194548) ((-1170 . -118) 194527) ((-1170 . -120) 194506) ((-1170 . -146) 194460) ((-1170 . -496) 194439) ((-1170 . -246) 194418) ((-1170 . -47) 194395) ((-1170 . -1159) 194372) ((-1170 . -35) 194338) ((-1170 . -66) 194304) ((-1170 . -239) 194270) ((-1170 . -431) 194236) ((-1170 . -1119) 194202) ((-1170 . -1116) 194168) ((-1170 . -917) 194134) ((-1167 . -277) 194078) ((-1167 . -952) 194044) ((-1167 . -353) 194010) ((-1167 . -38) 193867) ((-1167 . -557) 193741) ((-1167 . -592) 193630) ((-1167 . -590) 193504) ((-1167 . -972) T) ((-1167 . -1027) T) ((-1167 . -1062) T) ((-1167 . -665) T) ((-1167 . -963) T) ((-1167 . -82) 193354) ((-1167 . -965) 193243) ((-1167 . -970) 193132) ((-1167 . -21) T) ((-1167 . -23) T) ((-1167 . -1015) T) ((-1167 . -554) 193114) ((-1167 . -1130) T) ((-1167 . -13) T) ((-1167 . -72) T) ((-1167 . -25) T) ((-1167 . -104) T) ((-1167 . -584) 192971) ((-1167 . -656) 192828) ((-1167 . -118) 192789) ((-1167 . -120) 192750) ((-1167 . -146) T) ((-1167 . -496) T) ((-1167 . -246) T) ((-1167 . -47) 192694) ((-1166 . -1165) 192673) ((-1166 . -312) 192652) ((-1166 . -1135) 192631) ((-1166 . -834) 192610) ((-1166 . -496) 192564) ((-1166 . -146) 192498) ((-1166 . -557) 192317) ((-1166 . -656) 192164) ((-1166 . -584) 192011) ((-1166 . -38) 191858) ((-1166 . -390) 191837) ((-1166 . -258) 191816) ((-1166 . -592) 191716) ((-1166 . -590) 191601) ((-1166 . -972) T) ((-1166 . -1027) T) ((-1166 . -1062) T) ((-1166 . -665) T) ((-1166 . -963) T) ((-1166 . -82) 191421) ((-1166 . -965) 191262) ((-1166 . -970) 191103) ((-1166 . -21) T) ((-1166 . -23) T) ((-1166 . -1015) T) ((-1166 . -554) 191085) ((-1166 . -1130) T) ((-1166 . -13) T) ((-1166 . -72) T) ((-1166 . -25) T) ((-1166 . -104) T) ((-1166 . -246) 191039) ((-1166 . -201) 191018) ((-1166 . -917) 190984) ((-1166 . -1116) 190950) ((-1166 . -1119) 190916) ((-1166 . -431) 190882) ((-1166 . -239) 190848) ((-1166 . -66) 190814) ((-1166 . -35) 190780) ((-1166 . -1159) 190750) ((-1166 . -47) 190720) ((-1166 . -120) 190699) ((-1166 . -118) 190678) ((-1166 . -888) 190641) ((-1166 . -813) 190547) ((-1166 . -808) 190451) ((-1166 . -811) 190357) ((-1166 . -241) 190315) ((-1166 . -189) 190267) ((-1166 . -186) 190213) ((-1166 . -190) 190165) ((-1166 . -1163) 190149) ((-1166 . -952) 190133) ((-1161 . -1165) 190094) ((-1161 . -312) 190073) ((-1161 . -1135) 190052) ((-1161 . -834) 190031) ((-1161 . -496) 189985) ((-1161 . -146) 189919) ((-1161 . -557) 189668) ((-1161 . -656) 189515) ((-1161 . -584) 189362) ((-1161 . -38) 189209) ((-1161 . -390) 189188) ((-1161 . -258) 189167) ((-1161 . -592) 189067) ((-1161 . -590) 188952) ((-1161 . -972) T) ((-1161 . -1027) T) ((-1161 . -1062) T) ((-1161 . -665) T) ((-1161 . -963) T) ((-1161 . -82) 188772) ((-1161 . -965) 188613) ((-1161 . -970) 188454) ((-1161 . -21) T) ((-1161 . -23) T) ((-1161 . -1015) T) ((-1161 . -554) 188436) ((-1161 . -1130) T) ((-1161 . -13) T) ((-1161 . -72) T) ((-1161 . -25) T) ((-1161 . -104) T) ((-1161 . -246) 188390) ((-1161 . -201) 188369) ((-1161 . -917) 188335) ((-1161 . -1116) 188301) ((-1161 . -1119) 188267) ((-1161 . -431) 188233) ((-1161 . -239) 188199) ((-1161 . -66) 188165) ((-1161 . -35) 188131) ((-1161 . -1159) 188101) ((-1161 . -47) 188071) ((-1161 . -120) 188050) ((-1161 . -118) 188029) ((-1161 . -888) 187992) ((-1161 . -813) 187898) ((-1161 . -808) 187779) ((-1161 . -811) 187685) ((-1161 . -241) 187643) ((-1161 . -189) 187595) ((-1161 . -186) 187541) ((-1161 . -190) 187493) ((-1161 . -1163) 187477) ((-1161 . -952) 187412) ((-1149 . -1156) 187396) ((-1149 . -1067) 187374) ((-1149 . -555) NIL) ((-1149 . -260) 187361) ((-1149 . -454) 187309) ((-1149 . -277) 187286) ((-1149 . -952) 187169) ((-1149 . -353) 187153) ((-1149 . -38) 186985) ((-1149 . -82) 186790) ((-1149 . -965) 186616) ((-1149 . -970) 186442) ((-1149 . -590) 186352) ((-1149 . -592) 186241) ((-1149 . -584) 186073) ((-1149 . -656) 185905) ((-1149 . -557) 185661) ((-1149 . -118) 185640) ((-1149 . -120) 185619) ((-1149 . -47) 185596) ((-1149 . -327) 185580) ((-1149 . -582) 185528) ((-1149 . -811) 185472) ((-1149 . -808) 185379) ((-1149 . -813) 185290) ((-1149 . -798) NIL) ((-1149 . -823) 185269) ((-1149 . -1135) 185248) ((-1149 . -863) 185218) ((-1149 . -834) 185197) ((-1149 . -496) 185111) ((-1149 . -246) 185025) ((-1149 . -146) 184919) ((-1149 . -390) 184853) ((-1149 . -258) 184832) ((-1149 . -241) 184759) ((-1149 . -190) T) ((-1149 . -104) T) ((-1149 . -25) T) ((-1149 . -72) T) ((-1149 . -554) 184741) ((-1149 . -1015) T) ((-1149 . -23) T) ((-1149 . -21) T) ((-1149 . -972) T) ((-1149 . -1027) T) ((-1149 . -1062) T) ((-1149 . -665) T) ((-1149 . -963) T) ((-1149 . -186) 184728) ((-1149 . -13) T) ((-1149 . -1130) T) ((-1149 . -189) T) ((-1149 . -225) 184712) ((-1149 . -184) 184696) ((-1147 . -1008) 184680) ((-1147 . -559) 184664) ((-1147 . -1015) 184642) ((-1147 . -554) 184609) ((-1147 . -1130) 184587) ((-1147 . -13) 184565) ((-1147 . -72) 184543) ((-1147 . -1009) 184500) ((-1145 . -1144) 184479) ((-1145 . -917) 184445) ((-1145 . -1116) 184411) ((-1145 . -1119) 184377) ((-1145 . -431) 184343) ((-1145 . -239) 184309) ((-1145 . -66) 184275) ((-1145 . -35) 184241) ((-1145 . -1159) 184218) ((-1145 . -47) 184195) ((-1145 . -557) 183950) ((-1145 . -656) 183770) ((-1145 . -584) 183590) ((-1145 . -592) 183401) ((-1145 . -590) 183259) ((-1145 . -970) 183073) ((-1145 . -965) 182887) ((-1145 . -82) 182675) ((-1145 . -38) 182495) ((-1145 . -888) 182465) ((-1145 . -241) 182365) ((-1145 . -1142) 182349) ((-1145 . -972) T) ((-1145 . -1027) T) ((-1145 . -1062) T) ((-1145 . -665) T) ((-1145 . -963) T) ((-1145 . -21) T) ((-1145 . -23) T) ((-1145 . -1015) T) ((-1145 . -554) 182331) ((-1145 . -1130) T) ((-1145 . -13) T) ((-1145 . -72) T) ((-1145 . -25) T) ((-1145 . -104) T) ((-1145 . -118) 182259) ((-1145 . -120) 182187) ((-1145 . -555) 181860) ((-1145 . -184) 181830) ((-1145 . -811) 181684) ((-1145 . -813) 181484) ((-1145 . -808) 181282) ((-1145 . -225) 181252) ((-1145 . -189) 181114) ((-1145 . -186) 180970) ((-1145 . -190) 180878) ((-1145 . -312) 180857) ((-1145 . -1135) 180836) ((-1145 . -834) 180815) ((-1145 . -496) 180769) ((-1145 . -146) 180703) ((-1145 . -390) 180682) ((-1145 . -258) 180661) ((-1145 . -246) 180615) ((-1145 . -201) 180594) ((-1145 . -288) 180564) ((-1145 . -454) 180424) ((-1145 . -260) 180363) ((-1145 . -327) 180333) ((-1145 . -582) 180241) ((-1145 . -341) 180211) ((-1145 . -798) 180084) ((-1145 . -742) 180037) ((-1145 . -716) 179990) ((-1145 . -718) 179943) ((-1145 . -758) 179845) ((-1145 . -761) 179747) ((-1145 . -720) 179700) ((-1145 . -723) 179653) ((-1145 . -757) 179606) ((-1145 . -796) 179576) ((-1145 . -823) 179529) ((-1145 . -935) 179482) ((-1145 . -952) 179271) ((-1145 . -1067) 179223) ((-1145 . -906) 179193) ((-1140 . -1144) 179154) ((-1140 . -917) 179120) ((-1140 . -1116) 179086) ((-1140 . -1119) 179052) ((-1140 . -431) 179018) ((-1140 . -239) 178984) ((-1140 . -66) 178950) ((-1140 . -35) 178916) ((-1140 . -1159) 178893) ((-1140 . -47) 178870) ((-1140 . -557) 178671) ((-1140 . -656) 178473) ((-1140 . -584) 178275) ((-1140 . -592) 178130) ((-1140 . -590) 177970) ((-1140 . -970) 177766) ((-1140 . -965) 177562) ((-1140 . -82) 177314) ((-1140 . -38) 177116) ((-1140 . -888) 177086) ((-1140 . -241) 176914) ((-1140 . -1142) 176898) ((-1140 . -972) T) ((-1140 . -1027) T) ((-1140 . -1062) T) ((-1140 . -665) T) ((-1140 . -963) T) ((-1140 . -21) T) ((-1140 . -23) T) ((-1140 . -1015) T) ((-1140 . -554) 176880) ((-1140 . -1130) T) ((-1140 . -13) T) ((-1140 . -72) T) ((-1140 . -25) T) ((-1140 . -104) T) ((-1140 . -118) 176790) ((-1140 . -120) 176700) ((-1140 . -555) NIL) ((-1140 . -184) 176652) ((-1140 . -811) 176488) ((-1140 . -813) 176252) ((-1140 . -808) 175991) ((-1140 . -225) 175943) ((-1140 . -189) 175769) ((-1140 . -186) 175589) ((-1140 . -190) 175479) ((-1140 . -312) 175458) ((-1140 . -1135) 175437) ((-1140 . -834) 175416) ((-1140 . -496) 175370) ((-1140 . -146) 175304) ((-1140 . -390) 175283) ((-1140 . -258) 175262) ((-1140 . -246) 175216) ((-1140 . -201) 175195) ((-1140 . -288) 175147) ((-1140 . -454) 174881) ((-1140 . -260) 174766) ((-1140 . -327) 174718) ((-1140 . -582) 174670) ((-1140 . -341) 174622) ((-1140 . -798) NIL) ((-1140 . -742) NIL) ((-1140 . -716) NIL) ((-1140 . -718) NIL) ((-1140 . -758) NIL) ((-1140 . -761) NIL) ((-1140 . -720) NIL) ((-1140 . -723) NIL) ((-1140 . -757) NIL) ((-1140 . -796) 174574) ((-1140 . -823) NIL) ((-1140 . -935) NIL) ((-1140 . -952) 174540) ((-1140 . -1067) NIL) ((-1140 . -906) 174492) ((-1139 . -754) T) ((-1139 . -761) T) ((-1139 . -758) T) ((-1139 . -1015) T) ((-1139 . -554) 174474) ((-1139 . -1130) T) ((-1139 . -13) T) ((-1139 . -72) T) ((-1139 . -318) T) ((-1139 . -606) T) ((-1138 . -754) T) ((-1138 . -761) T) ((-1138 . -758) T) ((-1138 . -1015) T) ((-1138 . -554) 174456) ((-1138 . -1130) T) ((-1138 . -13) T) ((-1138 . -72) T) ((-1138 . -318) T) ((-1138 . -606) T) ((-1137 . -754) T) ((-1137 . -761) T) ((-1137 . -758) T) ((-1137 . -1015) T) ((-1137 . -554) 174438) ((-1137 . -1130) T) ((-1137 . -13) T) ((-1137 . -72) T) ((-1137 . -318) T) ((-1137 . -606) T) ((-1136 . -754) T) ((-1136 . -761) T) ((-1136 . -758) T) ((-1136 . -1015) T) ((-1136 . -554) 174420) ((-1136 . -1130) T) ((-1136 . -13) T) ((-1136 . -72) T) ((-1136 . -318) T) ((-1136 . -606) T) ((-1131 . -997) T) ((-1131 . -428) 174401) ((-1131 . -554) 174367) ((-1131 . -557) 174348) ((-1131 . -1015) T) ((-1131 . -1130) T) ((-1131 . -13) T) ((-1131 . -72) T) ((-1131 . -64) T) ((-1128 . -428) 174325) ((-1128 . -554) 174266) ((-1128 . -557) 174243) ((-1128 . -1015) 174221) ((-1128 . -1130) 174199) ((-1128 . -13) 174177) ((-1128 . -72) 174155) ((-1123 . -681) 174131) ((-1123 . -35) 174097) ((-1123 . -66) 174063) ((-1123 . -239) 174029) ((-1123 . -431) 173995) ((-1123 . -1119) 173961) ((-1123 . -1116) 173927) ((-1123 . -917) 173893) ((-1123 . -47) 173862) ((-1123 . -38) 173759) ((-1123 . -584) 173656) ((-1123 . -656) 173553) ((-1123 . -557) 173435) ((-1123 . -246) 173414) ((-1123 . -496) 173393) ((-1123 . -82) 173258) ((-1123 . -965) 173144) ((-1123 . -970) 173030) ((-1123 . -146) 172984) ((-1123 . -120) 172963) ((-1123 . -118) 172942) ((-1123 . -592) 172867) ((-1123 . -590) 172777) ((-1123 . -888) 172738) ((-1123 . -813) 172719) ((-1123 . -1130) T) ((-1123 . -13) T) ((-1123 . -808) 172698) ((-1123 . -963) T) ((-1123 . -665) T) ((-1123 . -1062) T) ((-1123 . -1027) T) ((-1123 . -972) T) ((-1123 . -21) T) ((-1123 . -23) T) ((-1123 . -1015) T) ((-1123 . -554) 172680) ((-1123 . -72) T) ((-1123 . -25) T) ((-1123 . -104) T) ((-1123 . -811) 172661) ((-1123 . -454) 172628) ((-1123 . -260) 172615) ((-1117 . -925) 172599) ((-1117 . -34) T) ((-1117 . -13) T) ((-1117 . -1130) T) ((-1117 . -72) 172553) ((-1117 . -554) 172488) ((-1117 . -260) 172426) ((-1117 . -454) 172359) ((-1117 . -1015) 172337) ((-1117 . -427) 172321) ((-1112 . -314) 172295) ((-1112 . -72) T) ((-1112 . -13) T) ((-1112 . -1130) T) ((-1112 . -554) 172277) ((-1112 . -1015) T) ((-1110 . -1015) T) ((-1110 . -554) 172259) ((-1110 . -1130) T) ((-1110 . -13) T) ((-1110 . -72) T) ((-1110 . -557) 172241) ((-1105 . -749) 172225) ((-1105 . -72) T) ((-1105 . -13) T) ((-1105 . -1130) T) ((-1105 . -554) 172207) ((-1105 . -1015) T) ((-1103 . -1108) 172186) ((-1103 . -183) 172134) ((-1103 . -76) 172082) ((-1103 . -260) 171880) ((-1103 . -454) 171632) ((-1103 . -427) 171567) ((-1103 . -124) 171515) ((-1103 . -555) NIL) ((-1103 . -193) 171463) ((-1103 . -551) 171442) ((-1103 . -243) 171421) ((-1103 . -1130) T) ((-1103 . -13) T) ((-1103 . -241) 171400) ((-1103 . -1015) T) ((-1103 . -554) 171382) ((-1103 . -72) T) ((-1103 . -34) T) ((-1103 . -540) 171361) ((-1099 . -1015) T) ((-1099 . -554) 171343) ((-1099 . -1130) T) ((-1099 . -13) T) ((-1099 . -72) T) ((-1098 . -754) T) ((-1098 . -761) T) ((-1098 . -758) T) ((-1098 . -1015) T) ((-1098 . -554) 171325) ((-1098 . -1130) T) ((-1098 . -13) T) ((-1098 . -72) T) ((-1098 . -318) T) ((-1098 . -606) T) ((-1097 . -754) T) ((-1097 . -761) T) ((-1097 . -758) T) ((-1097 . -1015) T) ((-1097 . -554) 171307) ((-1097 . -1130) T) ((-1097 . -13) T) ((-1097 . -72) T) ((-1097 . -318) T) ((-1096 . -1176) T) ((-1096 . -1015) T) ((-1096 . -554) 171274) ((-1096 . -1130) T) ((-1096 . -13) T) ((-1096 . -72) T) ((-1096 . -952) 171210) ((-1096 . -557) 171146) ((-1095 . -554) 171128) ((-1094 . -554) 171110) ((-1093 . -277) 171087) ((-1093 . -952) 170985) ((-1093 . -353) 170969) ((-1093 . -38) 170866) ((-1093 . -557) 170723) ((-1093 . -592) 170648) ((-1093 . -590) 170558) ((-1093 . -972) T) ((-1093 . -1027) T) ((-1093 . -1062) T) ((-1093 . -665) T) ((-1093 . -963) T) ((-1093 . -82) 170423) ((-1093 . -965) 170309) ((-1093 . -970) 170195) ((-1093 . -21) T) ((-1093 . -23) T) ((-1093 . -1015) T) ((-1093 . -554) 170177) ((-1093 . -1130) T) ((-1093 . -13) T) ((-1093 . -72) T) ((-1093 . -25) T) ((-1093 . -104) T) ((-1093 . -584) 170074) ((-1093 . -656) 169971) ((-1093 . -118) 169950) ((-1093 . -120) 169929) ((-1093 . -146) 169883) ((-1093 . -496) 169862) ((-1093 . -246) 169841) ((-1093 . -47) 169818) ((-1091 . -758) T) ((-1091 . -554) 169800) ((-1091 . -1015) T) ((-1091 . -72) T) ((-1091 . -13) T) ((-1091 . -1130) T) ((-1091 . -761) T) ((-1091 . -555) 169722) ((-1091 . -557) 169688) ((-1091 . -952) 169670) ((-1091 . -798) 169637) ((-1090 . -1173) 169621) ((-1090 . -190) 169580) ((-1090 . -557) 169462) ((-1090 . -592) 169387) ((-1090 . -590) 169297) ((-1090 . -104) T) ((-1090 . -25) T) ((-1090 . -72) T) ((-1090 . -554) 169279) ((-1090 . -1015) T) ((-1090 . -23) T) ((-1090 . -21) T) ((-1090 . -972) T) ((-1090 . -1027) T) ((-1090 . -1062) T) ((-1090 . -665) T) ((-1090 . -963) T) ((-1090 . -186) 169232) ((-1090 . -13) T) ((-1090 . -1130) T) ((-1090 . -189) 169191) ((-1090 . -241) 169156) ((-1090 . -811) 169069) ((-1090 . -808) 168957) ((-1090 . -813) 168870) ((-1090 . -888) 168840) ((-1090 . -38) 168737) ((-1090 . -82) 168602) ((-1090 . -965) 168488) ((-1090 . -970) 168374) ((-1090 . -584) 168271) ((-1090 . -656) 168168) ((-1090 . -118) 168147) ((-1090 . -120) 168126) ((-1090 . -146) 168080) ((-1090 . -496) 168059) ((-1090 . -246) 168038) ((-1090 . -47) 168015) ((-1090 . -1159) 167992) ((-1090 . -35) 167958) ((-1090 . -66) 167924) ((-1090 . -239) 167890) ((-1090 . -431) 167856) ((-1090 . -1119) 167822) ((-1090 . -1116) 167788) ((-1090 . -917) 167754) ((-1089 . -1165) 167715) ((-1089 . -312) 167694) ((-1089 . -1135) 167673) ((-1089 . -834) 167652) ((-1089 . -496) 167606) ((-1089 . -146) 167540) ((-1089 . -557) 167289) ((-1089 . -656) 167136) ((-1089 . -584) 166983) ((-1089 . -38) 166830) ((-1089 . -390) 166809) ((-1089 . -258) 166788) ((-1089 . -592) 166688) ((-1089 . -590) 166573) ((-1089 . -972) T) ((-1089 . -1027) T) ((-1089 . -1062) T) ((-1089 . -665) T) ((-1089 . -963) T) ((-1089 . -82) 166393) ((-1089 . -965) 166234) ((-1089 . -970) 166075) ((-1089 . -21) T) ((-1089 . -23) T) ((-1089 . -1015) T) ((-1089 . -554) 166057) ((-1089 . -1130) T) ((-1089 . -13) T) ((-1089 . -72) T) ((-1089 . -25) T) ((-1089 . -104) T) ((-1089 . -246) 166011) ((-1089 . -201) 165990) ((-1089 . -917) 165956) ((-1089 . -1116) 165922) ((-1089 . -1119) 165888) ((-1089 . -431) 165854) ((-1089 . -239) 165820) ((-1089 . -66) 165786) ((-1089 . -35) 165752) ((-1089 . -1159) 165722) ((-1089 . -47) 165692) ((-1089 . -120) 165671) ((-1089 . -118) 165650) ((-1089 . -888) 165613) ((-1089 . -813) 165519) ((-1089 . -808) 165400) ((-1089 . -811) 165306) ((-1089 . -241) 165264) ((-1089 . -189) 165216) ((-1089 . -186) 165162) ((-1089 . -190) 165114) ((-1089 . -1163) 165098) ((-1089 . -952) 165033) ((-1086 . -1156) 165017) ((-1086 . -1067) 164995) ((-1086 . -555) NIL) ((-1086 . -260) 164982) ((-1086 . -454) 164930) ((-1086 . -277) 164907) ((-1086 . -952) 164790) ((-1086 . -353) 164774) ((-1086 . -38) 164606) ((-1086 . -82) 164411) ((-1086 . -965) 164237) ((-1086 . -970) 164063) ((-1086 . -590) 163973) ((-1086 . -592) 163862) ((-1086 . -584) 163694) ((-1086 . -656) 163526) ((-1086 . -557) 163303) ((-1086 . -118) 163282) ((-1086 . -120) 163261) ((-1086 . -47) 163238) ((-1086 . -327) 163222) ((-1086 . -582) 163170) ((-1086 . -811) 163114) ((-1086 . -808) 163021) ((-1086 . -813) 162932) ((-1086 . -798) NIL) ((-1086 . -823) 162911) ((-1086 . -1135) 162890) ((-1086 . -863) 162860) ((-1086 . -834) 162839) ((-1086 . -496) 162753) ((-1086 . -246) 162667) ((-1086 . -146) 162561) ((-1086 . -390) 162495) ((-1086 . -258) 162474) ((-1086 . -241) 162401) ((-1086 . -190) T) ((-1086 . -104) T) ((-1086 . -25) T) ((-1086 . -72) T) ((-1086 . -554) 162383) ((-1086 . -1015) T) ((-1086 . -23) T) ((-1086 . -21) T) ((-1086 . -972) T) ((-1086 . -1027) T) ((-1086 . -1062) T) ((-1086 . -665) T) ((-1086 . -963) T) ((-1086 . -186) 162370) ((-1086 . -13) T) ((-1086 . -1130) T) ((-1086 . -189) T) ((-1086 . -225) 162354) ((-1086 . -184) 162338) 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-189) 158914) ((-1083 . -186) 158734) ((-1083 . -190) 158624) ((-1083 . -312) 158603) ((-1083 . -1135) 158582) ((-1083 . -834) 158561) ((-1083 . -496) 158515) ((-1083 . -146) 158449) ((-1083 . -390) 158428) ((-1083 . -258) 158407) ((-1083 . -246) 158361) ((-1083 . -201) 158340) ((-1083 . -288) 158292) ((-1083 . -454) 158026) ((-1083 . -260) 157911) ((-1083 . -327) 157863) ((-1083 . -582) 157815) ((-1083 . -341) 157767) ((-1083 . -798) NIL) ((-1083 . -742) NIL) ((-1083 . -716) NIL) ((-1083 . -718) NIL) ((-1083 . -758) NIL) ((-1083 . -761) NIL) ((-1083 . -720) NIL) ((-1083 . -723) NIL) ((-1083 . -757) NIL) ((-1083 . -796) 157719) ((-1083 . -823) NIL) ((-1083 . -935) NIL) ((-1083 . -952) 157685) ((-1083 . -1067) NIL) ((-1083 . -906) 157637) ((-1082 . -997) T) ((-1082 . -428) 157618) ((-1082 . -554) 157584) ((-1082 . -557) 157565) ((-1082 . -1015) T) ((-1082 . -1130) T) ((-1082 . -13) T) ((-1082 . -72) T) ((-1082 . -64) T) ((-1081 . -1015) T) ((-1081 . -554) 157547) ((-1081 . -1130) T) 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. -618) 156408) ((-1070 . -595) 156392) ((-1070 . -243) 156369) ((-1070 . -241) 156321) ((-1070 . -540) 156298) ((-1070 . -555) 156259) ((-1070 . -427) 156243) ((-1070 . -1015) 156221) ((-1070 . -454) 156154) ((-1070 . -260) 156092) ((-1070 . -554) 156027) ((-1070 . -72) 155981) ((-1070 . -1130) T) ((-1070 . -13) T) ((-1070 . -34) T) ((-1070 . -124) 155965) ((-1070 . -1169) 155949) ((-1070 . -925) 155933) ((-1070 . -1065) 155917) ((-1070 . -557) 155894) ((-1068 . -997) T) ((-1068 . -428) 155875) ((-1068 . -554) 155841) ((-1068 . -557) 155822) ((-1068 . -1015) T) ((-1068 . -1130) T) ((-1068 . -13) T) ((-1068 . -72) T) ((-1068 . -64) T) ((-1066 . -1108) 155801) ((-1066 . -183) 155749) ((-1066 . -76) 155697) ((-1066 . -260) 155495) ((-1066 . -454) 155247) ((-1066 . -427) 155182) ((-1066 . -124) 155130) ((-1066 . -555) NIL) ((-1066 . -193) 155078) ((-1066 . -551) 155057) ((-1066 . -243) 155036) ((-1066 . -1130) T) ((-1066 . -13) T) ((-1066 . -241) 155015) ((-1066 . -1015) T) ((-1066 . -554) 154997) ((-1066 . -72) T) ((-1066 . -34) T) ((-1066 . -540) 154976) ((-1063 . -1036) 154960) ((-1063 . -427) 154944) ((-1063 . -1015) 154922) ((-1063 . -454) 154855) ((-1063 . -260) 154793) ((-1063 . -554) 154728) ((-1063 . -72) 154682) ((-1063 . -1130) T) ((-1063 . -13) T) ((-1063 . -34) T) ((-1063 . -76) 154666) ((-1061 . -1022) 154635) ((-1061 . -1125) 154604) ((-1061 . -554) 154566) ((-1061 . -124) 154550) ((-1061 . -34) T) ((-1061 . -13) T) ((-1061 . -1130) T) ((-1061 . -72) T) ((-1061 . -260) 154488) ((-1061 . -454) 154421) ((-1061 . -1015) T) ((-1061 . -427) 154405) ((-1061 . -555) 154366) ((-1061 . -891) 154335) ((-1061 . -985) 154304) ((-1057 . -1038) 154249) ((-1057 . -427) 154233) ((-1057 . -454) 154166) ((-1057 . -260) 154104) ((-1057 . -34) T) ((-1057 . -967) 154044) ((-1057 . -952) 153942) ((-1057 . -557) 153861) ((-1057 . -353) 153845) ((-1057 . -582) 153793) ((-1057 . -592) 153731) ((-1057 . -327) 153715) ((-1057 . -190) 153694) ((-1057 . -186) 153642) ((-1057 . -189) 153596) ((-1057 . -225) 153580) ((-1057 . -808) 153504) ((-1057 . -813) 153430) ((-1057 . -811) 153389) ((-1057 . -184) 153373) ((-1057 . -656) 153308) ((-1057 . -584) 153243) ((-1057 . -590) 153202) ((-1057 . -104) T) ((-1057 . -25) T) ((-1057 . -72) T) ((-1057 . -13) T) ((-1057 . -1130) T) ((-1057 . -554) 153164) ((-1057 . -1015) T) ((-1057 . -23) T) ((-1057 . -21) T) ((-1057 . -970) 153148) ((-1057 . -965) 153132) ((-1057 . -82) 153111) ((-1057 . -963) T) ((-1057 . -665) T) ((-1057 . -1062) T) ((-1057 . -1027) T) ((-1057 . -972) T) ((-1057 . -38) 153071) ((-1057 . -555) 153032) ((-1056 . -925) 153003) ((-1056 . -34) T) ((-1056 . -13) T) ((-1056 . -1130) T) ((-1056 . -72) T) ((-1056 . -554) 152985) ((-1056 . -260) 152911) ((-1056 . -454) 152819) ((-1056 . -1015) T) ((-1056 . -427) 152790) ((-1055 . -1015) T) ((-1055 . -554) 152772) ((-1055 . -1130) T) ((-1055 . -13) T) ((-1055 . -72) T) ((-1050 . -1052) T) ((-1050 . -1176) T) ((-1050 . -64) T) ((-1050 . -72) T) ((-1050 . -13) T) ((-1050 . -1130) T) ((-1050 . -554) 152738) ((-1050 . -1015) T) ((-1050 . -557) 152719) ((-1050 . -428) 152700) ((-1050 . -997) T) ((-1048 . -1049) 152684) ((-1048 . -72) T) ((-1048 . -13) T) ((-1048 . -1130) T) ((-1048 . -554) 152666) ((-1048 . -1015) T) ((-1041 . -681) 152645) ((-1041 . -35) 152611) ((-1041 . -66) 152577) ((-1041 . -239) 152543) ((-1041 . -431) 152509) ((-1041 . -1119) 152475) ((-1041 . -1116) 152441) ((-1041 . -917) 152407) ((-1041 . -47) 152379) ((-1041 . -38) 152276) ((-1041 . -584) 152173) ((-1041 . -656) 152070) ((-1041 . -557) 151952) ((-1041 . -246) 151931) ((-1041 . -496) 151910) ((-1041 . -82) 151775) ((-1041 . -965) 151661) ((-1041 . -970) 151547) ((-1041 . -146) 151501) ((-1041 . -120) 151480) ((-1041 . -118) 151459) ((-1041 . -592) 151384) ((-1041 . -590) 151294) ((-1041 . -888) 151261) ((-1041 . -813) 151245) ((-1041 . -1130) T) ((-1041 . -13) T) ((-1041 . -808) 151227) ((-1041 . -963) T) ((-1041 . -665) T) ((-1041 . -1062) T) ((-1041 . -1027) T) 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-1015) T) ((-1040 . -23) T) ((-1040 . -21) T) ((-1040 . -963) T) ((-1040 . -665) T) ((-1040 . -1062) T) ((-1040 . -1027) T) ((-1040 . -972) T) ((-1040 . -353) 148956) ((-1040 . -277) 148928) ((-1040 . -260) 148915) ((-1040 . -555) 148663) ((-1035 . -484) T) ((-1035 . -1135) T) ((-1035 . -1067) T) ((-1035 . -952) 148645) ((-1035 . -555) 148560) ((-1035 . -935) T) ((-1035 . -798) 148542) ((-1035 . -757) T) ((-1035 . -723) T) ((-1035 . -720) T) ((-1035 . -761) T) ((-1035 . -758) T) ((-1035 . -718) T) ((-1035 . -716) T) ((-1035 . -742) T) ((-1035 . -592) 148514) ((-1035 . -582) 148496) ((-1035 . -834) T) ((-1035 . -496) T) ((-1035 . -246) T) ((-1035 . -146) T) ((-1035 . -557) 148468) ((-1035 . -656) 148455) ((-1035 . -584) 148442) ((-1035 . -970) 148429) ((-1035 . -965) 148416) ((-1035 . -82) 148401) ((-1035 . -38) 148388) ((-1035 . -390) T) ((-1035 . -258) T) ((-1035 . -189) T) ((-1035 . -186) 148375) ((-1035 . -190) T) ((-1035 . -116) T) ((-1035 . -963) T) ((-1035 . -665) T) ((-1035 . -1062) T) ((-1035 . -1027) T) ((-1035 . -972) T) ((-1035 . -21) T) ((-1035 . -590) 148347) ((-1035 . -23) T) ((-1035 . -1015) T) ((-1035 . -554) 148329) ((-1035 . -1130) T) ((-1035 . -13) T) ((-1035 . -72) T) ((-1035 . -25) T) ((-1035 . -104) T) ((-1035 . -120) T) ((-1035 . -754) T) ((-1035 . -318) T) ((-1035 . -84) T) ((-1035 . -606) T) ((-1031 . -997) T) ((-1031 . -428) 148310) ((-1031 . -554) 148276) ((-1031 . -557) 148257) ((-1031 . -1015) T) ((-1031 . -1130) T) ((-1031 . -13) T) ((-1031 . -72) T) ((-1031 . -64) T) ((-1030 . -1015) T) ((-1030 . -554) 148239) ((-1030 . -1130) T) ((-1030 . -13) T) ((-1030 . -72) T) ((-1028 . -196) 148218) ((-1028 . -1188) 148188) ((-1028 . -723) 148167) ((-1028 . -720) 148146) ((-1028 . -761) 148100) ((-1028 . -758) 148054) ((-1028 . -718) 148033) ((-1028 . -719) 148012) ((-1028 . -656) 147957) ((-1028 . -584) 147882) ((-1028 . -243) 147859) ((-1028 . -241) 147836) ((-1028 . -427) 147820) ((-1028 . -454) 147753) ((-1028 . -260) 147691) ((-1028 . -34) T) ((-1028 . -540) 147668) ((-1028 . -952) 147497) ((-1028 . -557) 147301) ((-1028 . -353) 147270) ((-1028 . -582) 147178) ((-1028 . -592) 147017) ((-1028 . -327) 146987) ((-1028 . -318) 146966) ((-1028 . -190) 146919) ((-1028 . -590) 146707) ((-1028 . -972) 146686) ((-1028 . -1027) 146665) ((-1028 . -1062) 146644) ((-1028 . -665) 146623) ((-1028 . -963) 146602) ((-1028 . -186) 146498) ((-1028 . -189) 146400) ((-1028 . -225) 146370) ((-1028 . -808) 146242) ((-1028 . -813) 146116) ((-1028 . -811) 146049) ((-1028 . -184) 146019) ((-1028 . -554) 145716) ((-1028 . -970) 145641) ((-1028 . -965) 145546) ((-1028 . -82) 145466) ((-1028 . -104) 145341) ((-1028 . -25) 145178) ((-1028 . -72) 144915) ((-1028 . -13) T) ((-1028 . -1130) T) ((-1028 . -1015) 144671) ((-1028 . -23) 144527) ((-1028 . -21) 144442) ((-1024 . -1025) 144426) ((-1024 . |MappingCategory|) 144400) ((-1024 . -1130) T) ((-1024 . -80) 144384) ((-1024 . -1015) T) ((-1024 . -554) 144366) ((-1024 . -13) T) ((-1024 . -72) T) ((-1019 . -1018) 144330) ((-1019 . -72) T) ((-1019 . -554) 144312) ((-1019 . -1015) T) ((-1019 . -241) 144268) ((-1019 . -1130) T) ((-1019 . -13) T) ((-1019 . -559) 144183) ((-1017 . -1018) 144135) ((-1017 . -72) T) ((-1017 . -554) 144117) ((-1017 . -1015) T) ((-1017 . -241) 144073) ((-1017 . -1130) T) ((-1017 . -13) T) ((-1017 . -559) 143976) ((-1016 . -318) T) ((-1016 . -72) T) ((-1016 . -13) T) ((-1016 . -1130) T) ((-1016 . -554) 143958) ((-1016 . -1015) T) ((-1011 . -367) 143942) ((-1011 . -1013) 143926) ((-1011 . -318) 143905) ((-1011 . -193) 143889) ((-1011 . -555) 143850) ((-1011 . -124) 143834) ((-1011 . -427) 143818) ((-1011 . -1015) T) ((-1011 . -454) 143751) ((-1011 . -260) 143689) ((-1011 . -554) 143671) ((-1011 . -72) T) ((-1011 . -1130) T) ((-1011 . -13) T) ((-1011 . -34) T) ((-1011 . -76) 143655) ((-1011 . -183) 143639) ((-1010 . -997) T) ((-1010 . -428) 143620) ((-1010 . -554) 143586) ((-1010 . -557) 143567) ((-1010 . -1015) T) ((-1010 . -1130) T) ((-1010 . -13) T) ((-1010 . -72) T) ((-1010 . -64) T) ((-1006 . -1130) T) ((-1006 . -13) T) ((-1006 . -1015) 143537) ((-1006 . -554) 143496) ((-1006 . -72) 143466) ((-1005 . -997) T) ((-1005 . -428) 143447) ((-1005 . -554) 143413) ((-1005 . -557) 143394) ((-1005 . -1015) T) ((-1005 . -1130) T) ((-1005 . -13) T) ((-1005 . -72) T) ((-1005 . -64) T) ((-1003 . -1008) 143378) ((-1003 . -559) 143362) ((-1003 . -1015) 143340) ((-1003 . -554) 143307) ((-1003 . -1130) 143285) ((-1003 . -13) 143263) ((-1003 . -72) 143241) ((-1003 . -1009) 143199) ((-1002 . -228) 143183) ((-1002 . -557) 143167) ((-1002 . -952) 143151) ((-1002 . -761) T) ((-1002 . -72) T) ((-1002 . -1015) T) ((-1002 . -554) 143133) ((-1002 . -758) T) ((-1002 . -186) 143120) ((-1002 . -13) T) ((-1002 . -1130) T) ((-1002 . -189) T) ((-1001 . -213) 143057) ((-1001 . -557) 142800) ((-1001 . -952) 142629) ((-1001 . -555) NIL) ((-1001 . -277) 142590) ((-1001 . -353) 142574) ((-1001 . -38) 142426) ((-1001 . -82) 142251) ((-1001 . -965) 142097) ((-1001 . -970) 141943) ((-1001 . -590) 141853) ((-1001 . -592) 141742) ((-1001 . -584) 141594) ((-1001 . -656) 141446) ((-1001 . -118) 141425) ((-1001 . -120) 141404) ((-1001 . -146) 141318) ((-1001 . -496) 141252) ((-1001 . -246) 141186) ((-1001 . -47) 141147) ((-1001 . -327) 141131) ((-1001 . -582) 141079) ((-1001 . -390) 141033) ((-1001 . -454) 140896) ((-1001 . -811) 140831) ((-1001 . -808) 140729) ((-1001 . -813) 140631) ((-1001 . -798) NIL) ((-1001 . -823) 140610) ((-1001 . -1135) 140589) ((-1001 . -863) 140534) ((-1001 . -260) 140521) ((-1001 . -190) 140500) ((-1001 . -104) T) ((-1001 . -25) T) ((-1001 . -72) T) ((-1001 . -554) 140482) ((-1001 . -1015) T) ((-1001 . -23) T) ((-1001 . -21) T) ((-1001 . -972) T) ((-1001 . -1027) T) ((-1001 . -1062) T) ((-1001 . -665) T) ((-1001 . -963) T) ((-1001 . -186) 140430) ((-1001 . -13) T) ((-1001 . -1130) T) ((-1001 . -189) 140384) ((-1001 . -225) 140368) ((-1001 . -184) 140352) ((-999 . -554) 140334) ((-996 . -758) T) ((-996 . -554) 140316) ((-996 . 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-13) T) ((-980 . -72) T) ((-980 . -64) T) ((-977 . -484) T) ((-977 . -1135) T) ((-977 . -1067) T) ((-977 . -952) 137411) ((-977 . -555) 137326) ((-977 . -935) T) ((-977 . -798) 137308) ((-977 . -757) T) ((-977 . -723) T) ((-977 . -720) T) ((-977 . -761) T) ((-977 . -758) T) ((-977 . -718) T) ((-977 . -716) T) ((-977 . -742) T) ((-977 . -592) 137280) ((-977 . -582) 137262) ((-977 . -834) T) ((-977 . -496) T) ((-977 . -246) T) ((-977 . -146) T) ((-977 . -557) 137234) ((-977 . -656) 137221) ((-977 . -584) 137208) ((-977 . -970) 137195) ((-977 . -965) 137182) ((-977 . -82) 137167) ((-977 . -38) 137154) ((-977 . -390) T) ((-977 . -258) T) ((-977 . -189) T) ((-977 . -186) 137141) ((-977 . -190) T) ((-977 . -116) T) ((-977 . -963) T) ((-977 . -665) T) ((-977 . -1062) T) ((-977 . -1027) T) ((-977 . -972) T) ((-977 . -21) T) ((-977 . -590) 137113) ((-977 . -23) T) ((-977 . -1015) T) ((-977 . -554) 137095) ((-977 . -1130) T) ((-977 . -13) T) ((-977 . -72) T) ((-977 . -25) T) ((-977 . -104) T) 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. -124) 135903) ((-960 . -1125) 135832) ((-950 . -997) T) ((-950 . -428) 135813) ((-950 . -554) 135779) ((-950 . -557) 135760) ((-950 . -1015) T) ((-950 . -1130) T) ((-950 . -13) T) ((-950 . -72) T) ((-950 . -64) T) ((-949 . -146) T) ((-949 . -557) 135729) ((-949 . -972) T) ((-949 . -1027) T) ((-949 . -1062) T) ((-949 . -665) T) ((-949 . -963) T) ((-949 . -592) 135703) ((-949 . -590) 135662) ((-949 . -104) T) ((-949 . -25) T) ((-949 . -72) T) ((-949 . -13) T) ((-949 . -1130) T) ((-949 . -554) 135644) ((-949 . -1015) T) ((-949 . -23) T) ((-949 . -21) T) ((-949 . -970) 135618) ((-949 . -965) 135592) ((-949 . -82) 135559) ((-949 . -38) 135543) ((-949 . -584) 135527) ((-949 . -656) 135511) ((-942 . -985) 135480) ((-942 . -891) 135449) ((-942 . -555) 135410) ((-942 . -427) 135394) ((-942 . -1015) T) ((-942 . -454) 135327) ((-942 . -260) 135265) ((-942 . -554) 135227) ((-942 . -72) T) ((-942 . -1130) T) ((-942 . -13) T) ((-942 . -34) T) ((-942 . -124) 135211) ((-942 . -1125) 135180) ((-941 . -1015) T) ((-941 . -554) 135162) ((-941 . -1130) T) ((-941 . -13) T) ((-941 . -72) T) ((-939 . -927) T) ((-939 . -917) T) ((-939 . -716) T) ((-939 . -718) T) ((-939 . -758) T) ((-939 . -761) T) ((-939 . -720) T) ((-939 . -723) T) ((-939 . -757) T) ((-939 . -952) 135047) ((-939 . -353) 135009) ((-939 . -201) T) ((-939 . -246) T) ((-939 . -258) T) ((-939 . -390) T) ((-939 . -38) 134946) ((-939 . -584) 134883) ((-939 . -656) 134820) ((-939 . -557) 134757) ((-939 . -496) T) ((-939 . -834) T) ((-939 . -1135) T) ((-939 . -312) T) ((-939 . -82) 134666) ((-939 . -965) 134603) ((-939 . -970) 134540) ((-939 . -146) T) ((-939 . -120) T) ((-939 . -592) 134477) ((-939 . -590) 134414) ((-939 . -104) T) ((-939 . -25) T) ((-939 . -72) T) ((-939 . -13) T) ((-939 . -1130) T) ((-939 . -554) 134396) ((-939 . -1015) T) ((-939 . -23) T) ((-939 . -21) T) ((-939 . -963) T) ((-939 . -665) T) ((-939 . -1062) T) ((-939 . -1027) T) ((-939 . -972) T) ((-934 . -997) T) ((-934 . -428) 134377) ((-934 . -554) 134343) 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-189) T) ((-919 . -225) 133584) ((-919 . -808) NIL) ((-919 . -813) NIL) ((-919 . -811) NIL) ((-919 . -184) 133566) ((-919 . -120) T) ((-919 . -118) NIL) ((-919 . -104) T) ((-919 . -25) T) ((-919 . -72) T) ((-919 . -13) T) ((-919 . -1130) T) ((-919 . -554) 133526) ((-919 . -1015) T) ((-919 . -23) T) ((-919 . -21) T) ((-919 . -963) T) ((-919 . -665) T) ((-919 . -1062) T) ((-919 . -1027) T) ((-919 . -972) T) ((-918 . -291) 133500) ((-918 . -146) T) ((-918 . -557) 133430) ((-918 . -972) T) ((-918 . -1027) T) ((-918 . -1062) T) ((-918 . -665) T) ((-918 . -963) T) ((-918 . -592) 133332) ((-918 . -590) 133262) ((-918 . -104) T) ((-918 . -25) T) ((-918 . -72) T) ((-918 . -13) T) ((-918 . -1130) T) ((-918 . -554) 133244) ((-918 . -1015) T) ((-918 . -23) T) ((-918 . -21) T) ((-918 . -970) 133189) ((-918 . -965) 133134) ((-918 . -82) 133051) ((-918 . -555) 133035) ((-918 . -184) 133012) ((-918 . -811) 132964) ((-918 . -813) 132876) ((-918 . -808) 132786) ((-918 . -225) 132763) ((-918 . -189) 132703) ((-918 . -186) 132637) ((-918 . -190) 132609) ((-918 . -312) T) ((-918 . -1135) T) ((-918 . -834) T) ((-918 . -496) T) ((-918 . -656) 132554) ((-918 . -584) 132499) ((-918 . -38) 132444) ((-918 . -390) T) ((-918 . -258) T) ((-918 . -246) T) ((-918 . -201) T) ((-918 . -318) NIL) ((-918 . -299) NIL) ((-918 . -1067) NIL) ((-918 . -118) 132416) ((-918 . -343) NIL) ((-918 . -351) 132388) ((-918 . -120) 132360) ((-918 . -320) 132332) ((-918 . -327) 132309) ((-918 . -582) 132243) ((-918 . -353) 132220) ((-918 . -952) 132097) ((-918 . -663) 132069) ((-915 . -910) 132053) ((-915 . -427) 132037) ((-915 . -1015) 132015) ((-915 . -454) 131948) ((-915 . -260) 131886) ((-915 . -554) 131821) ((-915 . -72) 131775) ((-915 . -1130) T) ((-915 . -13) T) ((-915 . -34) T) ((-915 . -76) 131759) ((-911 . -913) 131743) ((-911 . -761) 131722) ((-911 . -758) 131701) ((-911 . -952) 131599) ((-911 . -353) 131583) ((-911 . -582) 131531) ((-911 . -592) 131433) ((-911 . -327) 131417) ((-911 . -241) 131375) 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((-877 . -72) T) ((-877 . -318) 129659) ((-877 . -665) 129561) ((-877 . -1027) 129463) ((-877 . -23) 129277) ((-877 . -25) 129091) ((-877 . -104) 128949) ((-877 . -411) 128902) ((-877 . -21) 128857) ((-877 . -590) 128801) ((-877 . -719) 128754) ((-877 . -718) 128707) ((-877 . -758) 128609) ((-877 . -761) 128511) ((-877 . -720) 128464) ((-877 . -723) 128417) ((-871 . -19) 128401) ((-871 . -595) 128385) ((-871 . -243) 128362) ((-871 . -241) 128314) ((-871 . -540) 128291) ((-871 . -555) 128252) ((-871 . -427) 128236) ((-871 . -1015) 128189) ((-871 . -454) 128122) ((-871 . -260) 128060) ((-871 . -554) 127975) ((-871 . -72) 127909) ((-871 . -1130) T) ((-871 . -13) T) ((-871 . -34) T) ((-871 . -124) 127893) ((-871 . -758) 127872) ((-871 . -761) 127851) ((-871 . -322) 127835) ((-869 . -277) 127814) ((-869 . -952) 127712) ((-869 . -353) 127696) ((-869 . -38) 127593) ((-869 . -557) 127450) ((-869 . -592) 127375) ((-869 . -590) 127285) ((-869 . -972) T) ((-869 . -1027) T) ((-869 . -1062) T) 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125090) ((-859 . -82) 124915) ((-859 . -965) 124761) ((-859 . -970) 124607) ((-859 . -146) 124521) ((-859 . -120) 124500) ((-859 . -118) 124479) ((-859 . -590) 124389) ((-859 . -104) T) ((-859 . -25) T) ((-859 . -72) T) ((-859 . -13) T) ((-859 . -1130) T) ((-859 . -554) 124371) ((-859 . -1015) T) ((-859 . -23) T) ((-859 . -21) T) ((-859 . -963) T) ((-859 . -665) T) ((-859 . -1062) T) ((-859 . -1027) T) ((-859 . -972) T) ((-859 . -353) 124355) ((-859 . -277) 124324) ((-859 . -260) 124311) ((-859 . -555) 124172) ((-856 . -895) 124156) ((-856 . -19) 124140) ((-856 . -595) 124124) ((-856 . -243) 124101) ((-856 . -241) 124053) ((-856 . -540) 124030) ((-856 . -555) 123991) ((-856 . -427) 123975) ((-856 . -1015) 123928) ((-856 . -454) 123861) ((-856 . -260) 123799) ((-856 . -554) 123714) ((-856 . -72) 123648) ((-856 . -1130) T) ((-856 . -13) T) ((-856 . -34) T) ((-856 . -124) 123632) ((-856 . -758) 123611) ((-856 . -761) 123590) ((-856 . -322) 123574) ((-856 . -1179) 123558) ((-856 . -559) 123535) ((-840 . -889) T) ((-840 . -554) 123517) ((-838 . -868) T) ((-838 . -554) 123499) ((-832 . -720) T) ((-832 . -761) T) ((-832 . -758) T) ((-832 . -1015) T) ((-832 . -554) 123481) ((-832 . -1130) T) ((-832 . -13) T) ((-832 . -72) T) ((-832 . -25) T) ((-832 . -665) T) ((-832 . -1027) T) ((-827 . -312) T) ((-827 . -1135) T) ((-827 . -834) T) ((-827 . -496) T) ((-827 . -146) T) ((-827 . -557) 123418) ((-827 . -656) 123370) ((-827 . -584) 123322) ((-827 . -38) 123274) ((-827 . -390) T) ((-827 . -258) T) ((-827 . -592) 123226) ((-827 . -590) 123163) ((-827 . -972) T) ((-827 . -1027) T) ((-827 . -1062) T) ((-827 . -665) T) ((-827 . -963) T) ((-827 . -82) 123094) ((-827 . -965) 123046) ((-827 . -970) 122998) ((-827 . -21) T) ((-827 . -23) T) ((-827 . -1015) T) ((-827 . -554) 122980) ((-827 . -1130) T) ((-827 . -13) T) ((-827 . -72) T) ((-827 . -25) T) ((-827 . -104) T) ((-827 . -246) T) ((-827 . -201) T) ((-819 . -299) T) ((-819 . -1067) T) ((-819 . -318) T) ((-819 . -118) T) ((-819 . -312) T) ((-819 . -1135) T) ((-819 . -834) T) ((-819 . -496) T) ((-819 . -146) T) ((-819 . -557) 122930) ((-819 . -656) 122895) ((-819 . -584) 122860) ((-819 . -38) 122825) ((-819 . -390) T) ((-819 . -258) T) ((-819 . -82) 122774) ((-819 . -965) 122739) ((-819 . -970) 122704) ((-819 . -590) 122654) ((-819 . -592) 122619) ((-819 . -246) T) ((-819 . -201) T) ((-819 . -343) T) ((-819 . -189) T) ((-819 . -1130) T) ((-819 . -13) T) ((-819 . -186) 122606) ((-819 . -963) T) ((-819 . -665) T) ((-819 . -1062) T) ((-819 . -1027) T) ((-819 . -972) T) ((-819 . -21) T) ((-819 . -23) T) ((-819 . -1015) T) ((-819 . -554) 122588) ((-819 . -72) T) ((-819 . -25) T) ((-819 . -104) T) ((-819 . -190) T) ((-819 . -280) 122575) ((-819 . -120) 122557) ((-819 . -952) 122544) ((-819 . -1188) 122531) ((-819 . -1199) 122518) ((-819 . -555) 122500) ((-818 . -1015) T) ((-818 . -554) 122482) ((-818 . -1130) T) ((-818 . -13) T) ((-818 . -72) T) ((-815 . -817) 122466) ((-815 . -761) 122420) ((-815 . -758) 122374) 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121750) ((-787 . -1015) T) ((-787 . -1130) T) ((-787 . -13) T) ((-787 . -72) T) ((-787 . -64) T) ((-787 . -1176) T) ((-785 . -1015) T) ((-785 . -554) 121732) ((-785 . -1130) T) ((-785 . -13) T) ((-785 . -72) T) ((-785 . -557) 121714) ((-784 . -1130) T) ((-784 . -13) T) ((-784 . -554) 121589) ((-784 . -1015) 121540) ((-784 . -72) 121491) ((-783 . -906) 121475) ((-783 . -1067) 121453) ((-783 . -952) 121320) ((-783 . -557) 121219) ((-783 . -555) 121022) ((-783 . -935) 121001) ((-783 . -823) 120980) ((-783 . -796) 120964) ((-783 . -757) 120943) ((-783 . -723) 120922) ((-783 . -720) 120901) ((-783 . -761) 120855) ((-783 . -758) 120809) ((-783 . -718) 120788) ((-783 . -716) 120767) ((-783 . -742) 120746) ((-783 . -798) 120671) ((-783 . -341) 120655) ((-783 . -582) 120603) ((-783 . -592) 120519) ((-783 . -327) 120503) ((-783 . -241) 120461) ((-783 . -260) 120426) ((-783 . -454) 120338) ((-783 . -288) 120322) ((-783 . -201) T) ((-783 . -82) 120253) ((-783 . -965) 120205) ((-783 . -970) 120157) ((-783 . -246) T) ((-783 . -656) 120109) ((-783 . -584) 120061) ((-783 . -590) 119998) ((-783 . -38) 119950) ((-783 . -258) T) ((-783 . -390) T) ((-783 . -146) T) ((-783 . -496) T) ((-783 . -834) T) ((-783 . -1135) T) ((-783 . -312) T) ((-783 . -190) 119929) ((-783 . -186) 119877) ((-783 . -189) 119831) ((-783 . -225) 119815) ((-783 . -808) 119739) ((-783 . -813) 119665) ((-783 . -811) 119624) ((-783 . -184) 119608) ((-783 . -120) 119587) ((-783 . -118) 119566) ((-783 . -104) T) ((-783 . -25) T) ((-783 . -72) T) ((-783 . -13) T) ((-783 . -1130) T) ((-783 . -554) 119548) ((-783 . -1015) T) ((-783 . -23) T) ((-783 . -21) T) ((-783 . -963) T) ((-783 . -665) T) ((-783 . -1062) T) ((-783 . -1027) T) ((-783 . -972) T) ((-782 . -906) 119525) ((-782 . -1067) NIL) ((-782 . -952) 119502) ((-782 . -557) 119432) ((-782 . -555) NIL) ((-782 . -935) NIL) ((-782 . -823) NIL) ((-782 . -796) 119409) ((-782 . -757) NIL) ((-782 . -723) NIL) ((-782 . -720) NIL) ((-782 . -761) NIL) ((-782 . -758) NIL) 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-1062) T) ((-782 . -1027) T) ((-782 . -972) T) ((-780 . -781) 118491) ((-780 . -834) T) ((-780 . -496) T) ((-780 . -246) T) ((-780 . -146) T) ((-780 . -557) 118463) ((-780 . -656) 118450) ((-780 . -584) 118437) ((-780 . -970) 118424) ((-780 . -965) 118411) ((-780 . -82) 118396) ((-780 . -38) 118383) ((-780 . -390) T) ((-780 . -258) T) ((-780 . -963) T) ((-780 . -665) T) ((-780 . -1062) T) ((-780 . -1027) T) ((-780 . -972) T) ((-780 . -21) T) ((-780 . -590) 118355) ((-780 . -23) T) ((-780 . -1015) T) ((-780 . -554) 118337) ((-780 . -1130) T) ((-780 . -13) T) ((-780 . -72) T) ((-780 . -25) T) ((-780 . -104) T) ((-780 . -592) 118324) ((-780 . -120) T) ((-777 . -963) T) ((-777 . -665) T) ((-777 . -1062) T) ((-777 . -1027) T) ((-777 . -972) T) ((-777 . -21) T) ((-777 . -590) 118269) ((-777 . -23) T) ((-777 . -1015) T) ((-777 . -554) 118231) ((-777 . -1130) T) ((-777 . -13) T) ((-777 . -72) T) ((-777 . -25) T) ((-777 . -104) T) ((-777 . -592) 118191) ((-777 . -557) 118126) ((-777 . -428) 118103) ((-777 . -38) 118073) ((-777 . -82) 118038) ((-777 . -965) 118008) ((-777 . -970) 117978) ((-777 . -584) 117948) ((-777 . -656) 117918) ((-776 . -1015) T) ((-776 . -554) 117900) ((-776 . -1130) T) ((-776 . -13) T) ((-776 . -72) T) ((-775 . -754) T) ((-775 . -761) T) ((-775 . -758) T) ((-775 . -1015) T) ((-775 . -554) 117882) ((-775 . -1130) T) ((-775 . -13) T) ((-775 . -72) T) ((-775 . -318) T) ((-775 . -555) 117804) ((-774 . -1015) T) ((-774 . -554) 117786) ((-774 . -1130) T) ((-774 . -13) T) ((-774 . -72) T) ((-773 . -772) T) ((-773 . -147) T) ((-773 . -554) 117768) ((-769 . -758) T) ((-769 . -554) 117750) ((-769 . -1015) T) ((-769 . -72) T) ((-769 . -13) T) ((-769 . -1130) T) ((-769 . -761) T) ((-766 . -763) 117734) ((-766 . -952) 117632) ((-766 . -557) 117530) ((-766 . -353) 117514) ((-766 . -656) 117484) ((-766 . -584) 117454) ((-766 . -592) 117428) ((-766 . -590) 117387) ((-766 . -104) T) ((-766 . -25) T) ((-766 . -72) T) ((-766 . -13) T) ((-766 . -1130) T) ((-766 . -554) 117369) ((-766 . -1015) T) ((-766 . -23) T) ((-766 . -21) T) ((-766 . -970) 117353) ((-766 . -965) 117337) ((-766 . -82) 117316) ((-766 . -963) T) ((-766 . -665) T) ((-766 . -1062) T) ((-766 . -1027) T) ((-766 . -972) T) ((-766 . -38) 117286) ((-765 . -763) 117270) ((-765 . -952) 117168) ((-765 . -557) 117087) ((-765 . -353) 117071) ((-765 . -656) 117041) ((-765 . -584) 117011) ((-765 . -592) 116985) ((-765 . -590) 116944) ((-765 . -104) T) ((-765 . -25) T) ((-765 . -72) T) ((-765 . -13) T) ((-765 . -1130) T) ((-765 . -554) 116926) ((-765 . -1015) T) ((-765 . -23) T) ((-765 . -21) T) ((-765 . -970) 116910) ((-765 . -965) 116894) ((-765 . -82) 116873) ((-765 . -963) T) ((-765 . -665) T) ((-765 . -1062) T) ((-765 . -1027) T) ((-765 . -972) T) ((-765 . -38) 116843) ((-759 . -761) T) ((-759 . -1130) T) ((-759 . -13) T) ((-759 . -72) T) ((-759 . -428) 116827) ((-759 . -554) 116775) ((-759 . -557) 116759) ((-752 . -1015) T) ((-752 . -554) 116741) ((-752 . -1130) T) ((-752 . -13) T) ((-752 . -72) T) ((-752 . -353) 116725) ((-752 . -557) 116598) ((-752 . -952) 116496) ((-752 . -21) 116451) ((-752 . -590) 116371) ((-752 . -23) 116326) ((-752 . -25) 116281) ((-752 . -104) 116236) ((-752 . -757) 116215) ((-752 . -592) 116188) ((-752 . -972) 116167) ((-752 . -1062) 116146) ((-752 . -963) 116125) ((-752 . -723) 116104) ((-752 . -720) 116083) ((-752 . -761) 116062) ((-752 . -758) 116041) ((-752 . -718) 116020) ((-752 . -716) 115999) ((-752 . -1027) 115978) ((-752 . -665) 115957) ((-751 . -749) 115939) ((-751 . -72) T) ((-751 . -13) T) ((-751 . -1130) T) ((-751 . -554) 115921) ((-751 . -1015) T) ((-747 . -963) T) ((-747 . -665) T) ((-747 . -1062) T) ((-747 . -1027) T) ((-747 . -972) T) ((-747 . -21) T) ((-747 . -590) 115866) ((-747 . -23) T) ((-747 . -1015) T) ((-747 . -554) 115848) ((-747 . -1130) T) ((-747 . -13) T) ((-747 . -72) T) ((-747 . -25) T) ((-747 . -104) T) ((-747 . -592) 115808) ((-747 . -557) 115763) ((-747 . -952) 115733) ((-747 . -241) 115712) ((-747 . -120) 115691) ((-747 . -118) 115670) ((-747 . -38) 115640) ((-747 . -82) 115605) ((-747 . -965) 115575) ((-747 . -970) 115545) ((-747 . -584) 115515) ((-747 . -656) 115485) ((-745 . -1015) T) ((-745 . -554) 115467) ((-745 . -1130) T) ((-745 . -13) T) ((-745 . -72) T) ((-745 . -353) 115451) ((-745 . -557) 115324) ((-745 . -952) 115222) ((-745 . -21) 115177) ((-745 . -590) 115097) ((-745 . -23) 115052) ((-745 . -25) 115007) ((-745 . -104) 114962) ((-745 . -757) 114941) ((-745 . -592) 114914) ((-745 . -972) 114893) ((-745 . -1062) 114872) ((-745 . -963) 114851) ((-745 . -723) 114830) ((-745 . -720) 114809) ((-745 . -761) 114788) ((-745 . -758) 114767) ((-745 . -718) 114746) ((-745 . -716) 114725) ((-745 . -1027) 114704) ((-745 . -665) 114683) ((-743 . -647) 114667) ((-743 . -557) 114622) ((-743 . -656) 114592) ((-743 . -584) 114562) ((-743 . -592) 114536) ((-743 . -590) 114495) ((-743 . -104) T) ((-743 . -25) T) ((-743 . -72) T) ((-743 . -13) T) ((-743 . -1130) T) ((-743 . -554) 114477) ((-743 . -1015) T) ((-743 . -23) T) ((-743 . -21) T) ((-743 . -970) 114461) ((-743 . -965) 114445) ((-743 . -82) 114424) ((-743 . -963) T) ((-743 . -665) T) ((-743 . -1062) T) ((-743 . -1027) T) ((-743 . -972) T) ((-743 . -38) 114394) ((-743 . -190) 114373) ((-743 . -186) 114346) ((-743 . -189) 114325) ((-741 . -334) 114309) ((-741 . -557) 114293) ((-741 . -952) 114277) ((-741 . -761) T) ((-741 . -758) T) ((-741 . -1027) T) ((-741 . -72) T) ((-741 . -13) T) ((-741 . -1130) T) ((-741 . -554) 114259) ((-741 . -1015) T) ((-741 . -665) T) ((-741 . -756) T) ((-741 . -768) T) ((-740 . -228) 114243) ((-740 . -557) 114227) ((-740 . -952) 114211) ((-740 . -761) T) ((-740 . -72) T) ((-740 . -1015) T) ((-740 . -554) 114193) ((-740 . -758) T) ((-740 . -186) 114180) ((-740 . -13) T) ((-740 . -1130) T) ((-740 . -189) T) ((-739 . -82) 114115) ((-739 . -965) 114066) ((-739 . -970) 114017) ((-739 . -21) T) ((-739 . -590) 113953) ((-739 . -23) T) ((-739 . -1015) T) ((-739 . -554) 113922) ((-739 . -1130) T) ((-739 . -13) T) ((-739 . -72) T) ((-739 . -25) T) ((-739 . -104) T) ((-739 . -592) 113873) ((-739 . -190) T) ((-739 . -557) 113782) ((-739 . -972) T) ((-739 . -1027) T) ((-739 . -1062) T) ((-739 . -665) T) ((-739 . -963) T) ((-739 . -186) 113769) ((-739 . -189) T) ((-739 . -428) 113753) ((-739 . -312) 113732) ((-739 . -1135) 113711) ((-739 . -834) 113690) ((-739 . -496) 113669) ((-739 . -146) 113648) ((-739 . -656) 113585) ((-739 . -584) 113522) ((-739 . -38) 113459) ((-739 . -390) 113438) ((-739 . -258) 113417) ((-739 . -246) 113396) ((-739 . -201) 113375) ((-738 . -213) 113314) ((-738 . -557) 113058) ((-738 . -952) 112888) ((-738 . -555) NIL) ((-738 . -277) 112850) ((-738 . -353) 112834) ((-738 . -38) 112686) ((-738 . -82) 112511) ((-738 . -965) 112357) ((-738 . -970) 112203) ((-738 . -590) 112113) ((-738 . -592) 112002) ((-738 . -584) 111854) ((-738 . -656) 111706) ((-738 . -118) 111685) ((-738 . -120) 111664) ((-738 . -146) 111578) ((-738 . -496) 111512) ((-738 . -246) 111446) 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. -1130) T) ((-619 . -13) T) ((-619 . -72) T) ((-619 . -64) T) ((-616 . -758) T) ((-616 . -554) 92677) ((-616 . -1015) T) ((-616 . -72) T) ((-616 . -13) T) ((-616 . -1130) T) ((-616 . -761) T) ((-616 . -952) 92661) ((-616 . -557) 92645) ((-615 . -997) T) ((-615 . -428) 92626) ((-615 . -554) 92592) ((-615 . -557) 92573) ((-615 . -1015) T) ((-615 . -1130) T) ((-615 . -13) T) ((-615 . -72) T) ((-615 . -64) T) ((-614 . -1038) 92518) ((-614 . -427) 92502) ((-614 . -454) 92435) ((-614 . -260) 92373) ((-614 . -34) T) ((-614 . -967) 92313) ((-614 . -952) 92211) ((-614 . -557) 92130) ((-614 . -353) 92114) ((-614 . -582) 92062) ((-614 . -592) 92000) ((-614 . -327) 91984) ((-614 . -190) 91963) ((-614 . -186) 91911) ((-614 . -189) 91865) ((-614 . -225) 91849) ((-614 . -808) 91773) ((-614 . -813) 91699) ((-614 . -811) 91658) ((-614 . -184) 91642) ((-614 . -656) 91626) ((-614 . -584) 91610) ((-614 . -590) 91569) ((-614 . -104) T) ((-614 . -25) T) ((-614 . -72) T) ((-614 . -13) T) ((-614 . -1130) T) 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. -834) 85642) ((-560 . -38) 85626) ((-560 . -557) 85595) ((-560 . -592) 85569) ((-560 . -590) 85528) ((-560 . -972) T) ((-560 . -1027) T) ((-560 . -1062) T) ((-560 . -665) T) ((-560 . -963) T) ((-560 . -82) 85507) ((-560 . -965) 85491) ((-560 . -970) 85475) ((-560 . -21) T) ((-560 . -23) T) ((-560 . -1015) T) ((-560 . -554) 85457) ((-560 . -1130) T) ((-560 . -13) T) ((-560 . -72) T) ((-560 . -25) T) ((-560 . -104) T) ((-560 . -584) 85441) ((-560 . -656) 85425) ((-560 . -757) 85404) ((-560 . -723) 85383) ((-560 . -720) 85362) ((-560 . -761) 85341) ((-560 . -758) 85320) ((-560 . -718) 85299) ((-560 . -716) 85278) ((-558 . -882) T) ((-558 . -72) T) ((-558 . -554) 85260) ((-558 . -1015) T) ((-558 . -606) T) ((-558 . -13) T) ((-558 . -1130) T) ((-558 . -84) T) ((-558 . -318) T) ((-552 . -105) T) ((-552 . -72) T) ((-552 . -13) T) ((-552 . -1130) T) ((-552 . -554) 85242) ((-552 . -1015) T) ((-552 . -758) T) ((-552 . -761) T) ((-552 . -796) 85226) ((-552 . -555) 85087) ((-549 . -314) 85025) 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83894) ((-543 . -1130) T) ((-543 . -13) T) ((-543 . -72) T) ((-543 . -428) 83876) ((-543 . -557) 83858) ((-542 . -685) 83842) ((-542 . -659) T) ((-542 . -687) T) ((-542 . -82) 83821) ((-542 . -965) 83805) ((-542 . -970) 83789) ((-542 . -21) T) ((-542 . -590) 83758) ((-542 . -23) T) ((-542 . -1015) T) ((-542 . -554) 83727) ((-542 . -1130) T) ((-542 . -13) T) ((-542 . -72) T) ((-542 . -25) T) ((-542 . -104) T) ((-542 . -592) 83711) ((-542 . -584) 83695) ((-542 . -656) 83679) ((-542 . -359) 83644) ((-542 . -316) 83579) ((-542 . -241) 83537) ((-541 . -997) T) ((-541 . -428) 83518) ((-541 . -554) 83468) ((-541 . -557) 83449) ((-541 . -1015) T) ((-541 . -1130) T) ((-541 . -13) T) ((-541 . -72) T) ((-541 . -64) T) ((-538 . -1179) 83433) ((-538 . -322) 83417) ((-538 . -761) 83396) ((-538 . -758) 83375) ((-538 . -124) 83359) ((-538 . -34) T) ((-538 . -13) T) ((-538 . -1130) T) ((-538 . -72) 83293) ((-538 . -554) 83208) ((-538 . -260) 83146) ((-538 . -454) 83079) ((-538 . -1015) 83032) ((-538 . 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78676) ((-490 . -243) 78655) ((-490 . -1130) T) ((-490 . -13) T) ((-490 . -241) 78634) ((-490 . -1015) T) ((-490 . -554) 78616) ((-490 . -72) T) ((-490 . -34) T) ((-490 . -540) 78595) ((-489 . -754) T) ((-489 . -761) T) ((-489 . -758) T) ((-489 . -1015) T) ((-489 . -554) 78577) ((-489 . -1130) T) ((-489 . -13) T) ((-489 . -72) T) ((-489 . -318) T) ((-488 . -754) T) ((-488 . -761) T) ((-488 . -758) T) ((-488 . -1015) T) ((-488 . -554) 78559) ((-488 . -1130) T) ((-488 . -13) T) ((-488 . -72) T) ((-488 . -318) T) ((-487 . -754) T) ((-487 . -761) T) ((-487 . -758) T) ((-487 . -1015) T) ((-487 . -554) 78541) ((-487 . -1130) T) ((-487 . -13) T) ((-487 . -72) T) ((-487 . -318) T) ((-486 . -754) T) ((-486 . -761) T) ((-486 . -758) T) ((-486 . -1015) T) ((-486 . -554) 78523) ((-486 . -1130) T) ((-486 . -13) T) ((-486 . -72) T) ((-486 . -318) T) ((-485 . -484) T) ((-485 . -1135) T) ((-485 . -1067) T) ((-485 . -952) 78505) ((-485 . -555) 78420) ((-485 . -935) T) ((-485 . -798) 78402) ((-485 . -757) T) ((-485 . -723) T) ((-485 . -720) T) ((-485 . -761) T) ((-485 . -758) T) ((-485 . -718) T) ((-485 . -716) T) ((-485 . -742) T) ((-485 . -592) 78374) ((-485 . -582) 78356) ((-485 . -834) T) ((-485 . -496) T) ((-485 . -246) T) ((-485 . -146) T) ((-485 . -557) 78328) ((-485 . -656) 78315) ((-485 . -584) 78302) ((-485 . -970) 78289) ((-485 . -965) 78276) ((-485 . -82) 78261) ((-485 . -38) 78248) ((-485 . -390) T) ((-485 . -258) T) ((-485 . -189) T) ((-485 . -186) 78235) ((-485 . -190) T) ((-485 . -116) T) ((-485 . -963) T) ((-485 . -665) T) ((-485 . -1062) T) ((-485 . -1027) T) ((-485 . -972) T) ((-485 . -21) T) ((-485 . -590) 78207) ((-485 . -23) T) ((-485 . -1015) T) ((-485 . -554) 78189) ((-485 . -1130) T) ((-485 . -13) T) ((-485 . -72) T) ((-485 . -25) T) ((-485 . -104) T) ((-485 . -120) T) ((-474 . -1018) 78141) ((-474 . -72) T) ((-474 . -554) 78123) ((-474 . -1015) T) ((-474 . -241) 78079) ((-474 . -1130) T) ((-474 . -13) T) ((-474 . -559) 77982) ((-474 . -555) 77963) ((-472 . -693) 77945) ((-472 . -466) T) ((-472 . -147) T) ((-472 . -772) T) ((-472 . -513) T) ((-472 . -554) 77927) ((-470 . -719) T) ((-470 . -104) T) ((-470 . -25) T) ((-470 . -72) T) ((-470 . -13) T) ((-470 . -1130) T) ((-470 . -554) 77909) ((-470 . -1015) T) ((-470 . -23) T) ((-470 . -718) T) ((-470 . -758) T) ((-470 . -761) T) ((-470 . -720) T) ((-470 . -723) T) ((-470 . -448) 77886) ((-470 . -559) 77849) ((-468 . -466) T) ((-468 . -147) T) ((-468 . -554) 77831) ((-464 . -997) T) ((-464 . -428) 77812) ((-464 . -554) 77778) ((-464 . -557) 77759) ((-464 . -1015) T) ((-464 . -1130) T) ((-464 . -13) T) ((-464 . -72) T) ((-464 . -64) T) ((-463 . -997) T) ((-463 . -428) 77740) ((-463 . -554) 77706) ((-463 . -557) 77687) ((-463 . -1015) T) ((-463 . -1130) T) ((-463 . -13) T) ((-463 . -72) T) ((-463 . -64) T) ((-462 . -629) 77637) ((-462 . -427) 77621) ((-462 . -1015) 77599) ((-462 . -454) 77532) ((-462 . -260) 77470) ((-462 . -554) 77405) ((-462 . -72) 77359) ((-462 . -1130) T) ((-462 . -13) T) ((-462 . -34) T) ((-462 . -57) 77309) ((-459 . -57) 77283) ((-459 . -34) T) ((-459 . -13) T) ((-459 . -1130) T) ((-459 . -72) 77237) ((-459 . -554) 77172) ((-459 . -260) 77110) ((-459 . -454) 77043) ((-459 . -1015) 77021) ((-459 . -427) 77005) ((-458 . -280) 76982) ((-458 . -190) T) ((-458 . -186) 76969) ((-458 . -189) T) ((-458 . -318) T) ((-458 . -1067) T) ((-458 . -299) T) ((-458 . -120) 76951) ((-458 . -557) 76881) ((-458 . -592) 76826) ((-458 . -590) 76756) ((-458 . -104) T) ((-458 . -25) T) ((-458 . -72) T) ((-458 . -13) T) ((-458 . -1130) T) ((-458 . -554) 76738) ((-458 . -1015) T) ((-458 . -23) T) ((-458 . -21) T) ((-458 . -972) T) ((-458 . -1027) T) ((-458 . -1062) T) ((-458 . -665) T) ((-458 . -963) T) ((-458 . -312) T) ((-458 . -1135) T) ((-458 . -834) T) ((-458 . -496) T) ((-458 . -146) T) ((-458 . -656) 76683) ((-458 . -584) 76628) ((-458 . -38) 76593) ((-458 . -390) T) ((-458 . -258) T) ((-458 . -82) 76510) ((-458 . -965) 76455) ((-458 . -970) 76400) ((-458 . -246) T) 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72256) ((-422 . -454) 72189) ((-422 . -260) 72127) ((-422 . -554) 72062) ((-422 . -72) 72016) ((-422 . -1130) T) ((-422 . -13) T) ((-422 . -34) T) ((-422 . -76) 72000) ((-421 . -997) T) ((-421 . -428) 71981) ((-421 . -554) 71947) ((-421 . -557) 71928) ((-421 . -1015) T) ((-421 . -1130) T) ((-421 . -13) T) ((-421 . -72) T) ((-421 . -64) T) ((-420 . -196) 71907) ((-420 . -1188) 71877) ((-420 . -723) 71856) ((-420 . -720) 71835) ((-420 . -761) 71789) ((-420 . -758) 71743) ((-420 . -718) 71722) ((-420 . -719) 71701) ((-420 . -656) 71646) ((-420 . -584) 71571) ((-420 . -243) 71548) ((-420 . -241) 71525) ((-420 . -427) 71509) ((-420 . -454) 71442) ((-420 . -260) 71380) ((-420 . -34) T) ((-420 . -540) 71357) ((-420 . -952) 71186) ((-420 . -557) 70990) ((-420 . -353) 70959) ((-420 . -582) 70867) ((-420 . -592) 70706) ((-420 . -327) 70676) ((-420 . -318) 70655) ((-420 . -190) 70608) ((-420 . -590) 70396) ((-420 . -972) 70375) ((-420 . -1027) 70354) ((-420 . -1062) 70333) ((-420 . -665) 70312) 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. -965) 60178) ((-399 . -82) 60139) ((-392 . -863) 60106) ((-392 . -557) 59898) ((-392 . -952) 59776) ((-392 . -1135) 59755) ((-392 . -823) 59734) ((-392 . -798) NIL) ((-392 . -813) 59711) ((-392 . -808) 59686) ((-392 . -811) 59663) ((-392 . -454) 59601) ((-392 . -390) 59555) ((-392 . -582) 59503) ((-392 . -592) 59392) ((-392 . -327) 59376) ((-392 . -47) 59355) ((-392 . -38) 59207) ((-392 . -584) 59059) ((-392 . -656) 58911) ((-392 . -246) 58845) ((-392 . -496) 58779) ((-392 . -82) 58604) ((-392 . -965) 58450) ((-392 . -970) 58296) ((-392 . -146) 58210) ((-392 . -120) 58189) ((-392 . -118) 58168) ((-392 . -590) 58078) ((-392 . -104) T) ((-392 . -25) T) ((-392 . -72) T) ((-392 . -13) T) ((-392 . -1130) T) ((-392 . -554) 58060) ((-392 . -1015) T) ((-392 . -23) T) ((-392 . -21) T) ((-392 . -963) T) ((-392 . -665) T) ((-392 . -1062) T) ((-392 . -1027) T) ((-392 . -972) T) ((-392 . -353) 58044) ((-392 . -277) 58023) ((-392 . -260) 58010) ((-392 . -555) 57871) ((-391 . -359) 57841) ((-391 . 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T) ((-244 . -834) T) ((-244 . -241) 32396) ((-235 . -554) 32378) ((-234 . -554) 32360) ((-229 . -758) T) ((-229 . -554) 32342) ((-229 . -1015) T) ((-229 . -72) T) ((-229 . -13) T) ((-229 . -1130) T) ((-229 . -761) T) ((-226 . -213) 32304) ((-226 . -557) 32064) ((-226 . -952) 31910) ((-226 . -555) 31658) ((-226 . -277) 31630) ((-226 . -353) 31614) ((-226 . -38) 31466) ((-226 . -82) 31291) ((-226 . -965) 31137) ((-226 . -970) 30983) ((-226 . -590) 30893) ((-226 . -592) 30782) ((-226 . -584) 30634) ((-226 . -656) 30486) ((-226 . -118) 30465) ((-226 . -120) 30444) ((-226 . -146) 30358) ((-226 . -496) 30292) ((-226 . -246) 30226) ((-226 . -47) 30198) ((-226 . -327) 30182) ((-226 . -582) 30130) ((-226 . -390) 30084) ((-226 . -454) 29975) ((-226 . -811) 29921) ((-226 . -808) 29830) ((-226 . -813) 29743) ((-226 . -798) 29602) ((-226 . -823) 29581) ((-226 . -1135) 29560) ((-226 . -863) 29527) ((-226 . -260) 29514) ((-226 . -190) 29493) ((-226 . -104) T) ((-226 . -25) T) ((-226 . -72) T) ((-226 . -554) 29475) ((-226 . -1015) T) ((-226 . -23) T) ((-226 . -21) T) ((-226 . -972) T) ((-226 . -1027) T) ((-226 . -1062) T) ((-226 . -665) T) ((-226 . -963) T) ((-226 . -186) 29423) ((-226 . -13) T) ((-226 . -1130) T) ((-226 . -189) 29377) ((-226 . -225) 29361) ((-226 . -184) 29345) ((-221 . -1015) T) ((-221 . -554) 29327) ((-221 . -1130) T) ((-221 . -13) T) ((-221 . -72) T) ((-211 . -196) 29306) ((-211 . -1188) 29276) ((-211 . -723) 29255) ((-211 . -720) 29234) ((-211 . -761) 29188) ((-211 . -758) 29142) ((-211 . -718) 29121) ((-211 . -719) 29100) ((-211 . -656) 29045) ((-211 . -584) 28970) ((-211 . -243) 28947) ((-211 . -241) 28924) ((-211 . -427) 28908) ((-211 . -454) 28841) ((-211 . -260) 28779) ((-211 . -34) T) ((-211 . -540) 28756) ((-211 . -952) 28585) ((-211 . -557) 28389) ((-211 . -353) 28358) ((-211 . -582) 28266) ((-211 . -592) 28092) ((-211 . -327) 28062) ((-211 . -318) 28041) ((-211 . -190) 27994) ((-211 . -590) 27847) ((-211 . -972) 27826) ((-211 . -1027) 27805) ((-211 . 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25364) ((-210 . -972) 25343) ((-210 . -1027) 25322) ((-210 . -1062) 25301) ((-210 . -665) 25280) ((-210 . -963) 25259) ((-210 . -186) 25155) ((-210 . -189) 25057) ((-210 . -225) 25027) ((-210 . -808) 24899) ((-210 . -813) 24773) ((-210 . -811) 24706) ((-210 . -184) 24676) ((-210 . -554) 24637) ((-210 . -970) 24562) ((-210 . -965) 24467) ((-210 . -82) 24387) ((-210 . -104) T) ((-210 . -25) T) ((-210 . -72) T) ((-210 . -13) T) ((-210 . -1130) T) ((-210 . -1015) T) ((-210 . -23) T) ((-210 . -21) T) ((-209 . -1015) T) ((-209 . -554) 24369) ((-209 . -1130) T) ((-209 . -13) T) ((-209 . -72) T) ((-209 . -241) 24343) ((-208 . -160) T) ((-208 . -1015) T) ((-208 . -554) 24310) ((-208 . -1130) T) ((-208 . -13) T) ((-208 . -72) T) ((-208 . -749) 24292) ((-207 . -1015) T) ((-207 . -554) 24274) ((-207 . -1130) T) ((-207 . -13) T) ((-207 . -72) T) ((-206 . -863) 24219) ((-206 . -557) 24011) ((-206 . -952) 23889) ((-206 . -1135) 23868) ((-206 . -823) 23847) ((-206 . -798) NIL) ((-206 . -813) 23824) 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21731) ((-203 . -540) 21708) ((-203 . -555) 21669) ((-203 . -427) 21653) ((-203 . -1015) 21606) ((-203 . -454) 21539) ((-203 . -260) 21477) ((-203 . -554) 21372) ((-203 . -72) 21306) ((-203 . -1130) T) ((-203 . -13) T) ((-203 . -34) T) ((-203 . -124) 21290) ((-203 . -237) 21274) ((-203 . -428) 21251) ((-203 . -557) 21228) ((-197 . -196) 21207) ((-197 . -1188) 21177) ((-197 . -723) 21156) ((-197 . -720) 21135) ((-197 . -761) 21089) ((-197 . -758) 21043) ((-197 . -718) 21022) ((-197 . -719) 21001) ((-197 . -656) 20946) ((-197 . -584) 20871) ((-197 . -243) 20848) ((-197 . -241) 20825) ((-197 . -427) 20809) ((-197 . -454) 20742) ((-197 . -260) 20680) ((-197 . -34) T) ((-197 . -540) 20657) ((-197 . -952) 20486) ((-197 . -557) 20290) ((-197 . -353) 20259) ((-197 . -582) 20167) ((-197 . -592) 20006) ((-197 . -327) 19976) ((-197 . -318) 19955) ((-197 . -190) 19908) ((-197 . -590) 19696) ((-197 . -972) 19675) ((-197 . -1027) 19654) ((-197 . -1062) 19633) ((-197 . -665) 19612) ((-197 . -963) 19591) ((-197 . -186) 19487) ((-197 . -189) 19389) ((-197 . -225) 19359) ((-197 . -808) 19231) ((-197 . -813) 19105) ((-197 . -811) 19038) ((-197 . -184) 19008) ((-197 . -554) 18705) ((-197 . -970) 18630) ((-197 . -965) 18535) ((-197 . -82) 18455) ((-197 . -104) 18330) ((-197 . -25) 18167) ((-197 . -72) 17904) ((-197 . -13) T) ((-197 . -1130) T) ((-197 . -1015) 17660) ((-197 . -23) 17516) ((-197 . -21) 17431) ((-181 . -629) 17389) ((-181 . -427) 17373) ((-181 . -1015) 17351) ((-181 . -454) 17284) ((-181 . -260) 17222) ((-181 . -554) 17157) ((-181 . -72) 17111) ((-181 . -1130) T) ((-181 . -13) T) ((-181 . -34) T) ((-181 . -57) 17069) ((-179 . -345) T) ((-179 . -120) T) ((-179 . -557) 17019) ((-179 . -592) 16984) ((-179 . -590) 16934) ((-179 . -104) T) ((-179 . -25) T) ((-179 . -72) T) ((-179 . -13) T) ((-179 . -1130) T) ((-179 . -554) 16916) ((-179 . -1015) T) ((-179 . -23) T) ((-179 . -21) T) ((-179 . -972) T) ((-179 . -1027) T) ((-179 . -1062) T) ((-179 . -665) T) ((-179 . -963) T) ((-179 . -555) 16846) ((-179 . -312) T) ((-179 . -1135) T) ((-179 . -834) T) ((-179 . -496) T) ((-179 . -146) T) ((-179 . -656) 16811) ((-179 . -584) 16776) ((-179 . -38) 16741) ((-179 . -390) T) ((-179 . -258) T) ((-179 . -82) 16690) ((-179 . -965) 16655) ((-179 . -970) 16620) ((-179 . -246) T) ((-179 . -201) T) ((-179 . -757) T) ((-179 . -723) T) ((-179 . -720) T) ((-179 . -761) T) ((-179 . -758) T) ((-179 . -718) T) ((-179 . -716) T) ((-179 . -798) 16602) ((-179 . -917) T) ((-179 . -935) T) ((-179 . -952) 16562) ((-179 . -975) T) ((-179 . -190) T) ((-179 . -186) 16549) ((-179 . -189) T) ((-179 . -1116) T) ((-179 . -1119) T) ((-179 . -431) T) ((-179 . -239) T) ((-179 . -66) T) ((-179 . -35) T) ((-177 . -562) 16526) ((-177 . -557) 16488) ((-177 . -592) 16455) ((-177 . -590) 16407) ((-177 . -972) T) ((-177 . -1027) T) ((-177 . -1062) T) ((-177 . -665) T) ((-177 . -963) T) ((-177 . -21) T) ((-177 . -23) T) ((-177 . -1015) T) ((-177 . -554) 16389) ((-177 . -1130) T) ((-177 . -13) T) ((-177 . -72) T) ((-177 . -25) T) ((-177 . -104) T) ((-177 . -952) 16366) ((-176 . -214) 16350) ((-176 . -1036) 16334) ((-176 . -76) 16318) ((-176 . -34) T) ((-176 . -13) T) ((-176 . -1130) T) ((-176 . -72) 16272) ((-176 . -554) 16207) ((-176 . -260) 16145) ((-176 . -454) 16078) ((-176 . -1015) 16056) ((-176 . -427) 16040) ((-176 . -910) 16024) ((-172 . -997) T) ((-172 . -428) 16005) ((-172 . -554) 15971) ((-172 . -557) 15952) ((-172 . -1015) T) ((-172 . -1130) T) ((-172 . -13) T) ((-172 . -72) T) ((-172 . -64) T) ((-171 . -906) 15934) ((-171 . -1067) T) ((-171 . -557) 15884) ((-171 . -952) 15844) ((-171 . -555) 15774) ((-171 . -935) T) ((-171 . -823) NIL) ((-171 . -796) 15756) ((-171 . -757) T) ((-171 . -723) T) ((-171 . -720) T) ((-171 . -761) T) ((-171 . -758) T) ((-171 . -718) T) ((-171 . -716) T) ((-171 . -742) T) ((-171 . -798) 15738) ((-171 . -341) 15720) ((-171 . -582) 15702) ((-171 . -327) 15684) ((-171 . -241) NIL) ((-171 . -260) NIL) ((-171 . -454) NIL) ((-171 . -288) 15666) ((-171 . -201) T) ((-171 . -82) 15593) ((-171 . -965) 15543) ((-171 . -970) 15493) ((-171 . -246) T) ((-171 . -656) 15443) ((-171 . -584) 15393) ((-171 . -592) 15343) ((-171 . -590) 15293) ((-171 . -38) 15243) ((-171 . -258) T) ((-171 . -390) T) ((-171 . -146) T) ((-171 . -496) T) ((-171 . -834) T) ((-171 . -1135) T) ((-171 . -312) T) ((-171 . -190) T) ((-171 . -186) 15230) ((-171 . -189) T) ((-171 . -225) 15212) ((-171 . -808) NIL) ((-171 . -813) NIL) ((-171 . -811) NIL) ((-171 . -184) 15194) ((-171 . -120) T) ((-171 . -118) NIL) ((-171 . -104) T) ((-171 . -25) T) ((-171 . -72) T) ((-171 . -13) T) ((-171 . -1130) T) ((-171 . -554) 15136) ((-171 . -1015) T) ((-171 . -23) T) ((-171 . -21) T) ((-171 . -963) T) ((-171 . -665) T) ((-171 . -1062) T) ((-171 . -1027) T) ((-171 . -972) T) ((-168 . -754) T) ((-168 . -761) T) ((-168 . -758) T) ((-168 . -1015) T) ((-168 . -554) 15118) ((-168 . -1130) T) ((-168 . -13) T) ((-168 . -72) T) ((-168 . -318) T) ((-167 . -1015) T) ((-167 . -554) 15100) ((-167 . -1130) T) ((-167 . -13) T) ((-167 . -72) T) ((-167 . -557) 15077) ((-166 . -1015) T) ((-166 . -554) 15059) ((-166 . -1130) T) ((-166 . -13) T) ((-166 . -72) T) ((-161 . -1015) T) ((-161 . -554) 15041) ((-161 . -1130) T) ((-161 . -13) T) ((-161 . -72) T) ((-158 . -1015) T) ((-158 . -554) 15023) ((-158 . -1130) T) ((-158 . -13) T) ((-158 . -72) T) ((-157 . -160) T) ((-157 . -1015) T) ((-157 . -554) 15005) ((-157 . -1130) T) ((-157 . -13) T) ((-157 . -72) T) ((-157 . -749) 14987) ((-154 . -997) T) ((-154 . -428) 14968) ((-154 . -554) 14934) ((-154 . -557) 14915) ((-154 . -1015) T) ((-154 . -1130) T) ((-154 . -13) T) ((-154 . -72) T) ((-154 . -64) T) ((-149 . -554) 14897) ((-148 . -38) 14829) ((-148 . -557) 14746) ((-148 . -592) 14678) ((-148 . -590) 14595) ((-148 . -972) T) ((-148 . -1027) T) ((-148 . -1062) T) ((-148 . -665) T) ((-148 . -963) T) ((-148 . -82) 14494) ((-148 . -965) 14426) ((-148 . -970) 14358) ((-148 . -21) T) ((-148 . -23) T) ((-148 . -1015) T) ((-148 . -554) 14340) ((-148 . -1130) T) ((-148 . -13) T) ((-148 . -72) T) ((-148 . -25) T) ((-148 . -104) T) ((-148 . -584) 14272) ((-148 . -656) 14204) ((-148 . -312) T) ((-148 . -1135) T) ((-148 . -834) T) ((-148 . -496) T) ((-148 . -146) T) ((-148 . -390) T) ((-148 . -258) T) ((-148 . -246) T) ((-148 . -201) T) ((-145 . -1015) T) ((-145 . -554) 14186) ((-145 . -1130) T) ((-145 . -13) T) ((-145 . -72) T) ((-142 . -139) 14170) ((-142 . -35) 14148) ((-142 . -66) 14126) ((-142 . -239) 14104) ((-142 . -431) 14082) ((-142 . -1119) 14060) ((-142 . -1116) 14038) ((-142 . -917) 13990) ((-142 . -823) 13943) ((-142 . -555) 13711) ((-142 . -796) 13695) ((-142 . -318) 13649) ((-142 . -299) 13628) ((-142 . -1067) 13607) ((-142 . -343) 13586) ((-142 . -351) 13557) ((-142 . -38) 13391) ((-142 . -82) 13283) ((-142 . -965) 13196) ((-142 . -970) 13109) ((-142 . -584) 12943) ((-142 . -656) 12777) ((-142 . -320) 12748) ((-142 . -663) 12719) ((-142 . -952) 12617) ((-142 . -557) 12402) ((-142 . -353) 12386) ((-142 . 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T) ((-135 . -13) T) ((-135 . -72) T) ((-135 . -64) T) ((-134 . -1015) T) ((-134 . -554) 10685) ((-134 . -1130) T) ((-134 . -13) T) ((-134 . -72) T) ((-130 . -25) T) ((-130 . -72) T) ((-130 . -13) T) ((-130 . -1130) T) ((-130 . -554) 10667) ((-130 . -1015) T) ((-129 . -997) T) ((-129 . -428) 10648) ((-129 . -554) 10614) ((-129 . -557) 10595) ((-129 . -1015) T) ((-129 . -1130) T) ((-129 . -13) T) ((-129 . -72) T) ((-129 . -64) T) ((-127 . -997) T) ((-127 . -428) 10576) ((-127 . -554) 10542) ((-127 . -557) 10523) ((-127 . -1015) T) ((-127 . -1130) T) ((-127 . -13) T) ((-127 . -72) T) ((-127 . -64) T) ((-125 . -963) T) ((-125 . -665) T) ((-125 . -1062) T) ((-125 . -1027) T) ((-125 . -972) T) ((-125 . -21) T) ((-125 . -590) 10482) ((-125 . -23) T) ((-125 . -1015) T) ((-125 . -554) 10464) ((-125 . -1130) T) ((-125 . -13) T) ((-125 . -72) T) ((-125 . -25) T) ((-125 . -104) T) ((-125 . -592) 10438) ((-125 . -557) 10407) ((-125 . -38) 10391) ((-125 . -82) 10370) ((-125 . -965) 10354) ((-125 . -970) 10338) ((-125 . -584) 10322) ((-125 . -656) 10306) ((-125 . -1188) 10290) ((-117 . -754) T) ((-117 . -761) T) ((-117 . -758) T) ((-117 . -1015) T) ((-117 . -554) 10272) ((-117 . -1130) T) ((-117 . -13) T) ((-117 . -72) T) ((-117 . -318) T) ((-114 . -1015) T) ((-114 . -554) 10254) ((-114 . -1130) T) ((-114 . -13) T) ((-114 . -72) T) ((-114 . -555) 10213) ((-114 . -367) 10195) ((-114 . -1013) 10177) ((-114 . -318) T) ((-114 . -193) 10159) ((-114 . -124) 10141) ((-114 . -427) 10123) ((-114 . -454) NIL) ((-114 . -260) NIL) ((-114 . -34) T) ((-114 . -76) 10105) ((-114 . -183) 10087) ((-113 . -554) 10069) ((-112 . -160) T) ((-112 . -1015) T) ((-112 . -554) 10036) ((-112 . -1130) T) ((-112 . -13) T) ((-112 . -72) T) ((-112 . -749) 10018) ((-111 . -997) T) ((-111 . -428) 9999) ((-111 . -554) 9965) ((-111 . -557) 9946) ((-111 . -1015) T) ((-111 . -1130) T) ((-111 . -13) T) ((-111 . -72) T) ((-111 . -64) T) ((-110 . -997) T) ((-110 . -428) 9927) ((-110 . -554) 9893) ((-110 . -557) 9874) 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-1015) 8291) ((-94 . -427) 8275) ((-94 . -92) 8259) ((-90 . -906) 8237) ((-90 . -1067) NIL) ((-90 . -952) 8215) ((-90 . -557) 8146) ((-90 . -555) NIL) ((-90 . -935) NIL) ((-90 . -823) NIL) ((-90 . -796) 8124) ((-90 . -757) NIL) ((-90 . -723) NIL) ((-90 . -720) NIL) ((-90 . -761) NIL) ((-90 . -758) NIL) ((-90 . -718) NIL) ((-90 . -716) NIL) ((-90 . -742) NIL) ((-90 . -798) NIL) ((-90 . -341) 8102) ((-90 . -582) 8080) ((-90 . -592) 8026) ((-90 . -327) 8004) ((-90 . -241) 7938) ((-90 . -260) 7885) ((-90 . -454) 7755) ((-90 . -288) 7733) ((-90 . -201) T) ((-90 . -82) 7652) ((-90 . -965) 7598) ((-90 . -970) 7544) ((-90 . -246) T) ((-90 . -656) 7490) ((-90 . -584) 7436) ((-90 . -590) 7367) ((-90 . -38) 7313) ((-90 . -258) T) ((-90 . -390) T) ((-90 . -146) T) ((-90 . -496) T) ((-90 . -834) T) ((-90 . -1135) T) ((-90 . -312) T) ((-90 . -190) NIL) ((-90 . -186) NIL) ((-90 . -189) NIL) ((-90 . -225) 7291) ((-90 . -808) NIL) ((-90 . -813) NIL) ((-90 . -811) NIL) ((-90 . -184) 7269) ((-90 . -120) T) ((-90 . -118) NIL) ((-90 . -104) T) ((-90 . -25) T) ((-90 . -72) T) ((-90 . -13) T) ((-90 . -1130) T) ((-90 . -554) 7251) ((-90 . -1015) T) ((-90 . -23) T) ((-90 . -21) T) ((-90 . -963) T) ((-90 . -665) T) ((-90 . -1062) T) ((-90 . -1027) T) ((-90 . -972) T) ((-89 . -781) 7235) ((-89 . -834) T) ((-89 . -496) T) ((-89 . -246) T) ((-89 . -146) T) ((-89 . -557) 7207) ((-89 . -656) 7194) ((-89 . -584) 7181) ((-89 . -970) 7168) ((-89 . -965) 7155) ((-89 . -82) 7140) ((-89 . -38) 7127) ((-89 . -390) T) ((-89 . -258) T) ((-89 . -963) T) ((-89 . -665) T) ((-89 . -1062) T) ((-89 . -1027) T) ((-89 . -972) T) ((-89 . -21) T) ((-89 . -590) 7099) ((-89 . -23) T) ((-89 . -1015) T) ((-89 . -554) 7081) ((-89 . -1130) T) ((-89 . -13) T) ((-89 . -72) T) ((-89 . -25) T) ((-89 . -104) T) ((-89 . -592) 7068) ((-89 . -120) T) ((-86 . -758) T) ((-86 . -554) 7050) ((-86 . -1015) T) ((-86 . -72) T) ((-86 . -13) T) ((-86 . -1130) T) ((-86 . -761) T) ((-86 . -749) 7031) ((-85 . -754) T) ((-85 . -761) T) ((-85 . -758) T) ((-85 . -1015) T) ((-85 . -554) 7013) ((-85 . -1130) T) ((-85 . -13) T) ((-85 . -72) T) ((-85 . -318) T) ((-85 . -882) T) ((-85 . -606) T) ((-85 . -84) T) ((-85 . -555) 6995) ((-81 . -96) T) ((-81 . -322) 6978) ((-81 . -761) T) ((-81 . -758) T) ((-81 . -124) 6961) ((-81 . -34) T) ((-81 . -72) T) ((-81 . -554) 6943) ((-81 . -260) NIL) ((-81 . -454) NIL) ((-81 . -1015) T) ((-81 . -427) 6926) ((-81 . -555) 6908) ((-81 . -241) 6859) ((-81 . -540) 6835) ((-81 . -243) 6811) ((-81 . -595) 6794) ((-81 . -19) 6777) ((-81 . -606) T) ((-81 . -13) T) ((-81 . -1130) T) ((-81 . -84) T) ((-79 . -80) 6761) ((-79 . -1130) T) ((-79 . |MappingCategory|) 6735) ((-79 . -1015) T) ((-79 . -554) 6717) ((-79 . -13) T) ((-79 . -72) T) ((-78 . -554) 6699) ((-77 . -906) 6681) ((-77 . -1067) T) ((-77 . -557) 6631) ((-77 . -952) 6591) ((-77 . -555) 6521) ((-77 . -935) T) ((-77 . -823) NIL) ((-77 . -796) 6503) ((-77 . -757) T) ((-77 . -723) T) ((-77 . -720) T) ((-77 . -761) T) ((-77 . -758) T) ((-77 . -718) T) ((-77 . -716) T) ((-77 . -742) T) ((-77 . -798) 6485) ((-77 . -341) 6467) ((-77 . -582) 6449) ((-77 . -327) 6431) ((-77 . -241) NIL) ((-77 . -260) NIL) ((-77 . -454) NIL) ((-77 . -288) 6413) ((-77 . -201) T) ((-77 . -82) 6340) ((-77 . -965) 6290) ((-77 . -970) 6240) ((-77 . -246) T) ((-77 . -656) 6190) ((-77 . -584) 6140) ((-77 . -592) 6090) ((-77 . -590) 6040) ((-77 . -38) 5990) ((-77 . -258) T) ((-77 . -390) T) ((-77 . -146) T) ((-77 . -496) T) ((-77 . -834) T) ((-77 . -1135) T) ((-77 . -312) T) ((-77 . -190) T) ((-77 . -186) 5977) ((-77 . -189) T) ((-77 . -225) 5959) ((-77 . -808) NIL) ((-77 . -813) NIL) ((-77 . -811) NIL) ((-77 . -184) 5941) ((-77 . -120) T) ((-77 . -118) NIL) ((-77 . -104) T) ((-77 . -25) T) ((-77 . -72) T) ((-77 . -13) T) ((-77 . -1130) T) ((-77 . -554) 5884) ((-77 . -1015) T) ((-77 . -23) T) ((-77 . -21) T) ((-77 . -963) T) ((-77 . -665) T) ((-77 . -1062) T) ((-77 . -1027) T) ((-77 . -972) T) ((-73 . -98) 5868) ((-73 . -925) 5852) ((-73 . -34) T) ((-73 . -13) T) ((-73 . -1130) T) ((-73 . -72) 5806) ((-73 . -554) 5741) ((-73 . -260) 5679) ((-73 . -454) 5612) ((-73 . -1015) 5590) ((-73 . -427) 5574) ((-73 . -92) 5558) ((-69 . -411) T) ((-69 . -1027) T) ((-69 . -72) T) ((-69 . -13) T) ((-69 . -1130) T) ((-69 . -554) 5540) ((-69 . -1015) T) ((-69 . -665) T) ((-69 . -241) 5519) ((-67 . -997) T) ((-67 . -428) 5500) ((-67 . -554) 5466) ((-67 . -557) 5447) ((-67 . -1015) T) ((-67 . -1130) T) ((-67 . -13) T) ((-67 . -72) T) ((-67 . -64) T) ((-62 . -1036) 5431) ((-62 . -427) 5415) ((-62 . -1015) 5393) ((-62 . -454) 5326) ((-62 . -260) 5264) ((-62 . -554) 5199) ((-62 . -72) 5153) ((-62 . -1130) T) ((-62 . -13) T) ((-62 . -34) T) ((-62 . -76) 5137) ((-60 . -57) 5099) ((-60 . -34) T) ((-60 . -13) T) ((-60 . -1130) T) ((-60 . -72) 5053) ((-60 . -554) 4988) ((-60 . -260) 4926) ((-60 . -454) 4859) ((-60 . -1015) 4837) ((-60 . -427) 4821) ((-58 . -19) 4805) ((-58 . -595) 4789) ((-58 . -243) 4766) ((-58 . -241) 4718) ((-58 . -540) 4695) ((-58 . -555) 4656) ((-58 . -427) 4640) ((-58 . -1015) 4593) ((-58 . -454) 4526) ((-58 . -260) 4464) ((-58 . -554) 4379) ((-58 . -72) 4313) ((-58 . -1130) T) ((-58 . -13) T) ((-58 . -34) T) ((-58 . -124) 4297) ((-58 . -758) 4276) ((-58 . -761) 4255) ((-58 . -322) 4239) ((-55 . -1015) T) ((-55 . -554) 4221) ((-55 . -1130) T) ((-55 . -13) T) ((-55 . -72) T) ((-55 . -952) 4203) ((-55 . -557) 4185) ((-51 . -1015) T) ((-51 . -554) 4167) ((-51 . -1130) T) ((-51 . -13) T) ((-51 . -72) T) ((-50 . -562) 4151) ((-50 . -557) 4120) ((-50 . -592) 4094) ((-50 . -590) 4053) ((-50 . -972) T) ((-50 . -1027) T) ((-50 . -1062) T) ((-50 . -665) T) ((-50 . -963) T) ((-50 . -21) T) ((-50 . -23) T) ((-50 . -1015) T) ((-50 . -554) 4035) ((-50 . -1130) T) ((-50 . -13) T) ((-50 . -72) T) ((-50 . -25) T) ((-50 . -104) T) ((-50 . -952) 4019) ((-49 . -1015) T) ((-49 . -554) 4001) ((-49 . -1130) T) ((-49 . -13) T) ((-49 . -72) T) ((-48 . -254) T) ((-48 . -72) T) ((-48 . -13) T) ((-48 . -1130) T) ((-48 . -554) 3983) ((-48 . -1015) T) ((-48 . -557) 3884) ((-48 . -952) 3827) ((-48 . -454) 3793) ((-48 . -260) 3780) ((-48 . -27) T) ((-48 . -917) T) ((-48 . -201) T) ((-48 . -82) 3729) ((-48 . -965) 3694) ((-48 . -970) 3659) ((-48 . -246) T) ((-48 . -656) 3624) ((-48 . -584) 3589) ((-48 . -592) 3539) ((-48 . -590) 3489) ((-48 . -104) T) ((-48 . -25) T) ((-48 . -23) T) ((-48 . -21) T) ((-48 . -963) T) ((-48 . -665) T) ((-48 . -1062) T) ((-48 . -1027) T) ((-48 . -972) T) ((-48 . -38) 3454) ((-48 . -258) T) ((-48 . -390) T) ((-48 . -146) T) ((-48 . -496) T) ((-48 . -834) T) ((-48 . -1135) T) ((-48 . -312) T) ((-48 . -582) 3414) ((-48 . -935) T) ((-48 . -555) 3359) ((-48 . -120) T) ((-48 . -190) T) ((-48 . -186) 3346) ((-48 . -189) T) ((-45 . -36) 3325) ((-45 . -540) 3248) ((-45 . -260) 3046) ((-45 . -454) 2798) ((-45 . -427) 2733) ((-45 . -241) 2631) ((-45 . -243) 2554) ((-45 . -551) 2533) ((-45 . -193) 2481) ((-45 . -76) 2429) ((-45 . -183) 2377) ((-45 . -1108) 2356) ((-45 . -237) 2304) ((-45 . -124) 2252) ((-45 . -34) T) ((-45 . -13) T) ((-45 . -1130) T) ((-45 . -72) T) ((-45 . -554) 2234) ((-45 . -1015) T) ((-45 . -555) NIL) ((-45 . -595) 2182) ((-45 . -322) 2130) ((-45 . -761) NIL) ((-45 . -758) NIL) ((-45 . -1065) 2078) ((-45 . -925) 2026) ((-45 . -1169) 1974) ((-45 . -610) 1922) ((-44 . -359) 1906) ((-44 . -685) 1890) ((-44 . -659) T) ((-44 . -687) T) ((-44 . -82) 1869) ((-44 . -965) 1853) ((-44 . -970) 1837) ((-44 . -21) T) ((-44 . -590) 1780) ((-44 . -23) T) ((-44 . -1015) T) ((-44 . -554) 1762) ((-44 . -72) T) ((-44 . -25) T) ((-44 . -104) T) ((-44 . -592) 1720) ((-44 . -584) 1704) ((-44 . -656) 1688) ((-44 . -316) 1672) ((-44 . -1130) T) ((-44 . -13) T) ((-44 . -241) 1649) ((-40 . -291) 1623) ((-40 . -146) T) ((-40 . -557) 1553) ((-40 . -972) T) ((-40 . -1027) T) ((-40 . -1062) T) ((-40 . -665) T) ((-40 . -963) T) ((-40 . -592) 1455) ((-40 . -590) 1385) ((-40 . -104) T) ((-40 . -25) T) ((-40 . -72) T) ((-40 . -13) T) ((-40 . -1130) T) ((-40 . -554) 1367) ((-40 . -1015) T) ((-40 . -23) T) ((-40 . -21) T) ((-40 . -970) 1312) ((-40 . -965) 1257) ((-40 . -82) 1174) ((-40 . -555) 1158) ((-40 . -184) 1135) ((-40 . -811) 1087) ((-40 . -813) 999) ((-40 . -808) 909) ((-40 . -225) 886) ((-40 . -189) 826) ((-40 . -186) 760) ((-40 . -190) 732) ((-40 . -312) T) ((-40 . -1135) T) ((-40 . -834) T) ((-40 . -496) T) ((-40 . -656) 677) ((-40 . -584) 622) ((-40 . -38) 567) ((-40 . -390) T) ((-40 . -258) T) ((-40 . -246) T) ((-40 . -201) T) ((-40 . -318) NIL) ((-40 . -299) NIL) ((-40 . -1067) NIL) ((-40 . -118) 539) ((-40 . -343) NIL) ((-40 . -351) 511) ((-40 . -120) 483) ((-40 . -320) 455) ((-40 . -327) 432) ((-40 . -582) 366) ((-40 . -353) 343) ((-40 . -952) 220) ((-40 . -663) 192) ((-31 . -997) T) ((-31 . -428) 173) ((-31 . -554) 139) ((-31 . -557) 120) ((-31 . -1015) T) ((-31 . -1130) T) ((-31 . -13) T) ((-31 . -72) T) ((-31 . -64) T) ((-30 . -868) T) ((-30 . -554) 102) ((0 . |EnumerationCategory|) T) ((0 . -554) 84) ((0 . -1015) T) ((0 . -72) T) ((0 . -1130) T) ((-2 . |RecordCategory|) T) ((-2 . -554) 66) ((-2 . -1015) T) ((-2 . -72) T) ((-2 . -1130) T) ((-3 . |UnionCategory|) T) ((-3 . -554) 48) ((-3 . -1015) T) ((-3 . -72) T) ((-3 . -1130) T) ((-1 . -1015) T) ((-1 . -554) 30) ((-1 . -1130) T) ((-1 . -13) T) ((-1 . -72) T)) \ No newline at end of file
diff --git a/src/share/algebra/compress.daase b/src/share/algebra/compress.daase
index 269f49ab..3cbc5d9f 100644
--- a/src/share/algebra/compress.daase
+++ b/src/share/algebra/compress.daase
@@ -1,6 +1,6 @@
-(30 . 3577105534)
-(3995 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain|
+(30 . 3577141750)
+(3999 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain|
ATTRIBUTE |package| |domain| |category| CATEGORY |nobranch| AND |Join|
|ofType| SIGNATURE "failed" "algebra" |OneDimensionalArrayAggregate&|
|OneDimensionalArrayAggregate| |AbelianGroup&| |AbelianGroup| |AbelianMonoid&|
@@ -73,17 +73,17 @@
|Elaboration| |ExtensibleLinearAggregate&| |ExtensibleLinearAggregate|
|ElementaryFunctionCategory&| |ElementaryFunctionCategory|
|EllipticFunctionsUnivariateTaylorSeries| |Eltable| |EltableAggregate&|
- |EltableAggregate| |EuclideanModularRing| |EntireRing| |Environment|
- |EigenPackage| |Equation| |EquationFunctions2| |EqTable| |ErrorFunctions|
- |ExpressionSpace&| |ExpressionSpace| |ExpressionSpaceFunctions1|
- |ExpressionSpaceFunctions2| |EuclideanDomain&| |EuclideanDomain| |Evalable&|
- |Evalable| |EvaluateCycleIndicators| |Exit| |ExitAst| |ExponentialExpansion|
- |Expression| |ExpressionFunctions2| |ExpressionToUnivariatePowerSeries|
- |ExpressionSpaceODESolver| |ExpressionTubePlot|
- |ExponentialOfUnivariatePuiseuxSeries| |FactoredFunctions|
- |FactoringUtilities| |FreeAbelianGroup| |FreeAbelianMonoidCategory|
- |FreeAbelianMonoid| |FiniteAbelianMonoidRing&| |FiniteAbelianMonoidRing|
- |FlexibleArray| |FiniteAlgebraicExtensionField&|
+ |EltableAggregate| |EuclideanModularRing| |EntireRing&| |EntireRing|
+ |Environment| |EigenPackage| |Equation| |EquationFunctions2| |EqTable|
+ |ErrorFunctions| |ExpressionSpace&| |ExpressionSpace|
+ |ExpressionSpaceFunctions1| |ExpressionSpaceFunctions2| |EuclideanDomain&|
+ |EuclideanDomain| |Evalable&| |Evalable| |EvaluateCycleIndicators| |Exit|
+ |ExitAst| |ExponentialExpansion| |Expression| |ExpressionFunctions2|
+ |ExpressionToUnivariatePowerSeries| |ExpressionSpaceODESolver|
+ |ExpressionTubePlot| |ExponentialOfUnivariatePuiseuxSeries|
+ |FactoredFunctions| |FactoringUtilities| |FreeAbelianGroup|
+ |FreeAbelianMonoidCategory| |FreeAbelianMonoid| |FiniteAbelianMonoidRing&|
+ |FiniteAbelianMonoidRing| |FlexibleArray| |FiniteAlgebraicExtensionField&|
|FiniteAlgebraicExtensionField| |FourierComponent| |FunctorData|
|FiniteDivisor| |FiniteDivisorFunctions2| |FiniteDivisorCategory&|
|FiniteDivisorCategory| |FullyEvalableOver&| |FullyEvalableOver| |FiniteField|
@@ -312,8 +312,8 @@
|RationalFunctionFactorizer| |RGBColorModel| |RGBColorSpace| |RegularChain|
|RandomIntegerDistributions| |Ring&| |Ring| |RationalInterpolation|
|RightLinearSet| |RectangularMatrixCategory&| |RectangularMatrixCategory|
- |RectangularMatrix| |RectangularMatrixCategoryFunctions2| |RightModule| |Rng|
- |RangeBinding| |RealNumberSystem&| |RealNumberSystem|
+ |RectangularMatrix| |RectangularMatrixCategoryFunctions2| |RightModule| |Rng&|
+ |Rng| |RangeBinding| |RealNumberSystem&| |RealNumberSystem|
|RightOpenIntervalRootCharacterization| |RomanNumeral|
|RecursivePolynomialCategory&| |RecursivePolynomialCategory| |RepeatAst|
|RealRootCharacterizationCategory&| |RealRootCharacterizationCategory|
@@ -396,17 +396,17 @@
|XPolynomialsCat| |XPolynomialRing| |XRecursivePolynomial| |YoungDiagram|
|ParadoxicalCombinatorsForStreams| |ZeroDimensionalSolvePackage|
|IntegerLinearDependence| |IntegerMod| |Enumeration| |Mapping| |Record|
- |Union| |zerosOf| |zeroOf| |rootsOf| |makeSketch| |inrootof| |droot| |iroot|
- |eq?| |assoc| |doublyTransitive?| |knownInfBasis| |rootSplit| |ratDenom|
- |ratPoly| |rootPower| |rootProduct| |rootSimp| |rootKerSimp| |leftRank|
- |rightRank| |doubleRank| |weakBiRank| |biRank| |basisOfCommutingElements|
- |basisOfLeftAnnihilator| |basisOfRightAnnihilator| |basisOfLeftNucleus|
- |basisOfRightNucleus| |basisOfMiddleNucleus| |basisOfNucleus| |basisOfCenter|
- |basisOfLeftNucloid| |basisOfRightNucloid| |basisOfCentroid|
- |radicalOfLeftTraceForm| |obj| |dom| |any| |applyRules| |localUnquote|
- |arbitrary| |setColumn!| |setRow!| |oneDimensionalArray| |associatedSystem|
- |uncouplingMatrices| |associatedEquations| |arrayStack| |morphism|
- |balancedFactorisation| |before?| |mapDown!| |mapUp!| |setleaves!|
+ |Union| |opposite?| |zerosOf| |zeroOf| |rootsOf| |makeSketch| |inrootof|
+ |droot| |iroot| |eq?| |assoc| |doublyTransitive?| |knownInfBasis| |rootSplit|
+ |ratDenom| |ratPoly| |rootPower| |rootProduct| |rootSimp| |rootKerSimp|
+ |leftRank| |rightRank| |doubleRank| |weakBiRank| |biRank|
+ |basisOfCommutingElements| |basisOfLeftAnnihilator| |basisOfRightAnnihilator|
+ |basisOfLeftNucleus| |basisOfRightNucleus| |basisOfMiddleNucleus|
+ |basisOfNucleus| |basisOfCenter| |basisOfLeftNucloid| |basisOfRightNucloid|
+ |basisOfCentroid| |radicalOfLeftTraceForm| |obj| |dom| |any| |applyRules|
+ |localUnquote| |arbitrary| |setColumn!| |setRow!| |oneDimensionalArray|
+ |associatedSystem| |uncouplingMatrices| |associatedEquations| |arrayStack|
+ |morphism| |balancedFactorisation| |before?| |mapDown!| |mapUp!| |setleaves!|
|balancedBinaryTree| |sylvesterMatrix| |bezoutMatrix| |bezoutResultant|
|bezoutDiscriminant| |inspect| |extract!| |bag| |binding| |binaryOperation|
|setProperties| |setProperty| |deleteProperty!| |has?| |comparison| |equality|
@@ -769,9 +769,9 @@
|nullSpace| |nullity| |rank| |rowEchelon| |column| |row| |qelt| |ncols|
|nrows| |maxColIndex| |minColIndex| |maxRowIndex| |minRowIndex|
|antisymmetric?| |symmetric?| |diagonal?| |square?| |matrix|
- |rectangularMatrix| |characteristic| |round| |fractionPart| |wholePart|
- |floor| |ceiling| |norm| |mightHaveRoots| |refine| |middle| |size| |right|
- |left| |roman| |mainSquareFreePart| |mainPrimitivePart| |mainContent|
+ |rectangularMatrix| |annihilate?| |characteristic| |round| |fractionPart|
+ |wholePart| |floor| |ceiling| |norm| |mightHaveRoots| |refine| |middle| |size|
+ |right| |left| |roman| |mainSquareFreePart| |mainPrimitivePart| |mainContent|
|primitivePart!| |gcd| |nextsubResultant2| |LazardQuotient2| |LazardQuotient|
|subResultantChain| |halfExtendedSubResultantGcd2|
|halfExtendedSubResultantGcd1| |extendedSubResultantGcd| |exactQuotient!|
diff --git a/src/share/algebra/interp.daase b/src/share/algebra/interp.daase
index 4417a140..8b11d4e6 100644
--- a/src/share/algebra/interp.daase
+++ b/src/share/algebra/interp.daase
@@ -1,4042 +1,4048 @@
-(2806310 . 3577105543)
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+(2820677 . 3577141760)
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NIL
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-(((-19 |#1|) (-113) (-1128)) (T -19))
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+(((-19 |#1|) (-113) (-1130)) (T -19))
NIL
-(-13 (-321 |t#1|) (-10 -7 (-6 -3993)))
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NIL
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NIL
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NIL
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(((-25) (-113)) (T -25))
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NIL
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(((-38 |#1|) (-113) (-146)) (T -38))
NIL
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NIL
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-NIL
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-NIL
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+NIL
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NIL
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-NIL
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(((-147) . T))
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-NIL
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-NIL
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-(((-21) . T) ((-23) . T) ((-47 |#1| (-484)) . T) ((-25) . T) ((-38 (-347 (-484))) OR (|has| |#1| (-311)) (|has| |#1| (-38 (-347 (-484))))) ((-38 |#1|) |has| |#1| (-146)) ((-38 |#2|) |has| |#1| (-311)) ((-38 $) OR (|has| |#1| (-495)) (|has| |#1| (-311))) ((-35) |has| |#1| (-38 (-347 (-484)))) ((-66) |has| |#1| (-38 (-347 (-484)))) ((-72) . T) ((-82 (-347 (-484)) (-347 (-484))) OR (|has| |#1| (-311)) (|has| |#1| (-38 (-347 (-484))))) ((-82 |#1| |#1|) . T) ((-82 |#2| |#2|) |has| |#1| (-311)) ((-82 $ $) OR (|has| |#1| (-495)) (|has| |#1| (-311)) (|has| |#1| (-146))) ((-104) . T) ((-118) OR (-12 (|has| |#1| (-311)) (|has| |#2| (-118))) (|has| |#1| (-118))) ((-120) OR (-12 (|has| |#1| (-311)) (|has| |#2| (-120))) (|has| |#1| (-120))) ((-556 (-347 (-484))) OR (|has| |#1| (-311)) (|has| |#1| (-38 (-347 (-484))))) ((-556 (-484)) . T) ((-556 (-1089)) -12 (|has| |#1| (-311)) (|has| |#2| (-951 (-1089)))) ((-556 |#1|) |has| |#1| (-146)) ((-556 |#2|) . 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T) ((-241 |#2| $) -12 (|has| |#1| (-311)) (|has| |#2| (-241 |#2| |#2|))) ((-241 $ $) |has| (-484) (-1025)) ((-245) OR (|has| |#1| (-495)) (|has| |#1| (-311))) ((-257) |has| |#1| (-311)) ((-259 |#2|) -12 (|has| |#1| (-311)) (|has| |#2| (-259 |#2|))) ((-311) |has| |#1| (-311)) ((-287 |#2|) |has| |#1| (-311)) ((-326 |#2|) |has| |#1| (-311)) ((-340 |#2|) |has| |#1| (-311)) ((-389) |has| |#1| (-311)) ((-430) |has| |#1| (-38 (-347 (-484)))) ((-453 (-1089) |#2|) -12 (|has| |#1| (-311)) (|has| |#2| (-453 (-1089) |#2|))) ((-453 |#2| |#2|) -12 (|has| |#1| (-311)) (|has| |#2| (-259 |#2|))) ((-495) OR (|has| |#1| (-495)) (|has| |#1| (-311))) ((-13) . T) ((-589 (-347 (-484))) OR (|has| |#1| (-311)) (|has| |#1| (-38 (-347 (-484))))) ((-589 (-484)) . T) ((-589 |#1|) . T) ((-589 |#2|) |has| |#1| (-311)) ((-589 $) . T) ((-591 (-347 (-484))) OR (|has| |#1| (-311)) (|has| |#1| (-38 (-347 (-484))))) ((-591 (-484)) -12 (|has| |#1| (-311)) (|has| |#2| (-581 (-484)))) ((-591 |#1|) . T) ((-591 |#2|) |has| |#1| (-311)) ((-591 $) . T) ((-583 (-347 (-484))) OR (|has| |#1| (-311)) (|has| |#1| (-38 (-347 (-484))))) ((-583 |#1|) |has| |#1| (-146)) ((-583 |#2|) |has| |#1| (-311)) ((-583 $) OR (|has| |#1| (-495)) (|has| |#1| (-311))) ((-581 (-484)) -12 (|has| |#1| (-311)) (|has| |#2| (-581 (-484)))) ((-581 |#2|) |has| |#1| (-311)) ((-655 (-347 (-484))) OR (|has| |#1| (-311)) (|has| |#1| (-38 (-347 (-484))))) ((-655 |#1|) |has| |#1| (-146)) ((-655 |#2|) |has| |#1| (-311)) ((-655 $) OR (|has| |#1| (-495)) (|has| |#1| (-311))) ((-664) . 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T) ((-1065) -12 (|has| |#1| (-311)) (|has| |#2| (-1065))) ((-1114) |has| |#1| (-38 (-347 (-484)))) ((-1117) |has| |#1| (-38 (-347 (-484)))) ((-1128) . T) ((-1133) |has| |#1| (-311)) ((-1140 |#1|) . T) ((-1157 |#1| (-484)) . T))
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-(((-21) . T) ((-23) . T) ((-47 |#1| (-695)) . T) ((-25) . T) ((-38 (-347 (-484))) |has| |#1| (-38 (-347 (-484)))) ((-38 |#1|) |has| |#1| (-146)) ((-38 $) |has| |#1| (-495)) ((-35) |has| |#1| (-38 (-347 (-484)))) ((-66) |has| |#1| (-38 (-347 (-484)))) ((-72) . T) ((-82 (-347 (-484)) (-347 (-484))) |has| |#1| (-38 (-347 (-484)))) ((-82 |#1| |#1|) . T) ((-82 $ $) OR (|has| |#1| (-495)) (|has| |#1| (-146))) ((-104) . T) ((-118) |has| |#1| (-118)) ((-120) |has| |#1| (-120)) ((-556 (-347 (-484))) |has| |#1| (-38 (-347 (-484)))) ((-556 (-484)) . T) ((-556 |#1|) |has| |#1| (-146)) ((-556 $) |has| |#1| (-495)) ((-553 (-773)) . T) ((-146) OR (|has| |#1| (-495)) (|has| |#1| (-146))) ((-186 $) |has| |#1| (-15 * (|#1| (-695) |#1|))) ((-190) |has| |#1| (-15 * (|#1| (-695) |#1|))) ((-189) |has| |#1| (-15 * (|#1| (-695) |#1|))) ((-239) |has| |#1| (-38 (-347 (-484)))) ((-241 (-695) |#1|) . T) ((-241 $ $) |has| (-695) (-1025)) ((-245) |has| |#1| (-495)) ((-430) |has| |#1| (-38 (-347 (-484)))) ((-495) |has| |#1| (-495)) ((-13) . T) ((-589 (-347 (-484))) |has| |#1| (-38 (-347 (-484)))) ((-589 (-484)) . T) ((-589 |#1|) . T) ((-589 $) . T) ((-591 (-347 (-484))) |has| |#1| (-38 (-347 (-484)))) ((-591 |#1|) . T) ((-591 $) . T) ((-583 (-347 (-484))) |has| |#1| (-38 (-347 (-484)))) ((-583 |#1|) |has| |#1| (-146)) ((-583 $) |has| |#1| (-495)) ((-655 (-347 (-484))) |has| |#1| (-38 (-347 (-484)))) ((-655 |#1|) |has| |#1| (-146)) ((-655 $) |has| |#1| (-495)) ((-664) . T) ((-807 $ (-1089)) -12 (|has| |#1| (-810 (-1089))) (|has| |#1| (-15 * (|#1| (-695) |#1|)))) ((-810 (-1089)) -12 (|has| |#1| (-810 (-1089))) (|has| |#1| (-15 * (|#1| (-695) |#1|)))) ((-812 (-1089)) -12 (|has| |#1| (-810 (-1089))) (|has| |#1| (-15 * (|#1| (-695) |#1|)))) ((-887 |#1| (-695) (-994)) . T) ((-916) |has| |#1| (-38 (-347 (-484)))) ((-964 (-347 (-484))) |has| |#1| (-38 (-347 (-484)))) ((-964 |#1|) . T) ((-964 $) OR (|has| |#1| (-495)) (|has| |#1| (-146))) ((-969 (-347 (-484))) |has| |#1| (-38 (-347 (-484)))) ((-969 |#1|) . T) ((-969 $) OR (|has| |#1| (-495)) (|has| |#1| (-146))) ((-962) . T) ((-970) . T) ((-1025) . T) ((-1060) . T) ((-1013) . T) ((-1114) |has| |#1| (-38 (-347 (-484)))) ((-1117) |has| |#1| (-38 (-347 (-484)))) ((-1128) . T) ((-1157 |#1| (-695)) . T))
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-NIL
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-NIL
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-NIL
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(-257) (-120) (-934))) (-5 *2 (-584 (-2 (|:| -1745 (-1084 *5)) (|:| -3222 (-584 (-858 *5)))))) (-5 *1 (-1206 *5 *6 *7)) (-5 *3 (-584 (-858 *5))) (-14 *6 (-584 (-1089))) (-14 *7 (-584 (-1089))))) (-3965 (*1 *2 *3) (-12 (-5 *3 (-959 *4 *5)) (-4 *4 (-13 (-756) (-257) (-120) (-934))) (-14 *5 (-584 (-1089))) (-5 *2 (-584 (-2 (|:| -1745 (-1084 *4)) (|:| -3222 (-584 (-858 *4)))))) (-5 *1 (-1206 *4 *5 *6)) (-14 *6 (-584 (-1089))))) (-3964 (*1 *2 *3) (-12 (-5 *3 (-584 (-858 *4))) (-4 *4 (-13 (-756) (-257) (-120) (-934))) (-5 *2 (-584 (-959 *4 *5))) (-5 *1 (-1206 *4 *5 *6)) (-14 *5 (-584 (-1089))) (-14 *6 (-584 (-1089))))) (-3964 (*1 *2 *3 *4) (-12 (-5 *3 (-584 (-858 *5))) (-5 *4 (-85)) (-4 *5 (-13 (-756) (-257) (-120) (-934))) (-5 *2 (-584 (-959 *5 *6))) (-5 *1 (-1206 *5 *6 *7)) (-14 *6 (-584 (-1089))) (-14 *7 (-584 (-1089))))) (-3964 (*1 *2 *3 *4 *4) (-12 (-5 *3 (-584 (-858 *5))) (-5 *4 (-85)) (-4 *5 (-13 (-756) (-257) (-120) (-934))) (-5 *2 (-584 (-959 *5 *6))) (-5 *1 (-1206 *5 *6 *7)) (-14 *6 (-584 (-1089))) (-14 *7 (-584 (-1089))))))
-((-3972 (((-3 (-1178 (-347 (-484))) #1="failed") (-1178 |#1|) |#1|) 21 T ELT)) (-3970 (((-85) (-1178 |#1|)) 12 T ELT)) (-3971 (((-3 (-1178 (-484)) #1#) (-1178 |#1|)) 16 T ELT)))
-(((-1207 |#1|) (-10 -7 (-15 -3970 ((-85) (-1178 |#1|))) (-15 -3971 ((-3 (-1178 (-484)) #1="failed") (-1178 |#1|))) (-15 -3972 ((-3 (-1178 (-347 (-484))) #1#) (-1178 |#1|) |#1|))) (-13 (-962) (-581 (-484)))) (T -1207))
-((-3972 (*1 *2 *3 *4) (|partial| -12 (-5 *3 (-1178 *4)) (-4 *4 (-13 (-962) (-581 (-484)))) (-5 *2 (-1178 (-347 (-484)))) (-5 *1 (-1207 *4)))) (-3971 (*1 *2 *3) (|partial| -12 (-5 *3 (-1178 *4)) (-4 *4 (-13 (-962) (-581 (-484)))) (-5 *2 (-1178 (-484))) (-5 *1 (-1207 *4)))) (-3970 (*1 *2 *3) (-12 (-5 *3 (-1178 *4)) (-4 *4 (-13 (-962) (-581 (-484)))) (-5 *2 (-85)) (-5 *1 (-1207 *4)))))
-((-2567 (((-85) $ $) NIL T ELT)) (-3186 (((-85) $) 12 T ELT)) (-1310 (((-3 $ #1="failed") $ $) NIL T ELT)) (-3134 (((-695)) 9 T ELT)) (-3721 (($) NIL T CONST)) (-3464 (((-3 $ #1#) $) 57 T ELT)) (-2993 (($) 46 T ELT)) (-2409 (((-85) $) 38 T ELT)) (-3442 (((-633 $) $) 36 T ELT)) (-2009 (((-831) $) 14 T ELT)) (-3240 (((-1072) $) NIL T ELT)) (-3443 (($) 26 T CONST)) (-2399 (($ (-831)) 47 T ELT)) (-3241 (((-1033) $) NIL T ELT)) (-3969 (((-484) $) 16 T ELT)) (-3943 (((-773) $) 21 T ELT) (($ (-484)) 18 T ELT)) (-3124 (((-695)) 10 T CONST)) (-1263 (((-85) $ $) 59 T ELT)) (-2659 (($) 23 T CONST)) (-2665 (($) 25 T CONST)) (-3055 (((-85) $ $) 31 T ELT)) (-3834 (($ $) 50 T ELT) (($ $ $) 44 T ELT)) (-3836 (($ $ $) 29 T ELT)) (** (($ $ (-831)) NIL T ELT) (($ $ (-695)) 52 T ELT)) (* (($ (-831) $) NIL T ELT) (($ (-695) $) NIL T ELT) (($ (-484) $) 41 T ELT) (($ $ $) 40 T ELT)))
-(((-1208 |#1|) (-13 (-146) (-317) (-554 (-484)) (-1065)) (-831)) (T -1208))
-NIL
-NIL
-NIL
-NIL
-NIL
-NIL
-NIL
-NIL
-NIL
-NIL
-NIL
-NIL
-NIL
-((-3 2806295 2806300 2806305 NIL NIL NIL (NIL) -8 NIL NIL NIL) (-2 2806280 2806285 2806290 NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1 2806265 2806270 2806275 NIL NIL NIL (NIL) -8 NIL NIL NIL) (0 2806250 2806255 2806260 NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1208 2805293 2806168 2806245 "ZMOD" NIL ZMOD (NIL NIL) -8 NIL NIL NIL) (-1207 2804508 2804687 2804906 "ZLINDEP" NIL ZLINDEP (NIL T) -7 NIL NIL NIL) (-1206 2795667 2797536 2799470 "ZDSOLVE" NIL ZDSOLVE (NIL T NIL NIL) -7 NIL NIL NIL) (-1205 2795055 2795208 2795397 "YSTREAM" NIL YSTREAM (NIL T) -7 NIL NIL NIL) (-1204 2794517 2794820 2794933 "YDIAGRAM" NIL YDIAGRAM (NIL) -8 NIL NIL NIL) (-1203 2792141 2793979 2794182 "XRPOLY" NIL XRPOLY (NIL T T) -8 NIL NIL NIL) (-1202 2788969 2790558 2791129 "XPR" NIL XPR (NIL T T) -8 NIL NIL NIL) (-1201 2786288 2787956 2788010 "XPOLYC" 2788295 XPOLYC (NIL T T) -9 NIL 2788408 NIL) (-1200 2783871 2785792 2785995 "XPOLY" NIL XPOLY (NIL T) -8 NIL NIL NIL) (-1199 2780183 2782730 2783118 "XPBWPOLY" NIL XPBWPOLY (NIL T T) -8 NIL NIL NIL) (-1198 2775092 2776663 2776717 "XFALG" 2778862 XFALG (NIL T T) -9 NIL 2779646 NIL) (-1197 2770310 2772981 2773023 "XF" 2773641 XF (NIL T) -9 NIL 2774037 NIL) (-1196 2770028 2770138 2770305 "XF-" NIL XF- (NIL T T) -7 NIL NIL NIL) (-1195 2769255 2769377 2769581 "XEXPPKG" NIL XEXPPKG (NIL T T T) -7 NIL NIL NIL) (-1194 2767061 2769155 2769250 "XDPOLY" NIL XDPOLY (NIL T T) -8 NIL NIL NIL) (-1193 2765704 2766437 2766479 "XALG" 2766484 XALG (NIL T) -9 NIL 2766593 NIL) (-1192 2759261 2764114 2764592 "WUTSET" NIL WUTSET (NIL T T T T) -8 NIL NIL NIL) (-1191 2757568 2758506 2758827 "WP" NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL NIL) (-1190 2757167 2757439 2757508 "WHILEAST" NIL WHILEAST (NIL) -8 NIL NIL NIL) (-1189 2756654 2756957 2757050 "WHEREAST" NIL WHEREAST (NIL) -8 NIL NIL NIL) (-1188 2755731 2755941 2756236 "WFFINTBS" NIL WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1187 2754027 2754490 2754952 "WEIER" NIL WEIER (NIL T) -7 NIL NIL NIL) (-1186 2752947 2753501 2753543 "VSPACE" 2753679 VSPACE (NIL T) -9 NIL 2753753 NIL) (-1185 2752818 2752851 2752942 "VSPACE-" NIL VSPACE- (NIL T T) -7 NIL NIL NIL) (-1184 2752661 2752715 2752783 "VOID" NIL VOID (NIL) -8 NIL NIL NIL) (-1183 2749644 2750439 2751176 "VIEWDEF" NIL VIEWDEF (NIL) -7 NIL NIL NIL) (-1182 2740742 2743343 2745516 "VIEW3D" NIL VIEW3D (NIL) -8 NIL NIL NIL) (-1181 2734319 2736210 2737789 "VIEW2D" NIL VIEW2D (NIL) -8 NIL NIL NIL) (-1180 2732803 2733198 2733604 "VIEW" NIL VIEW (NIL) -7 NIL NIL NIL) (-1179 2731630 2731911 2732227 "VECTOR2" NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1178 2726744 2731457 2731549 "VECTOR" NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1177 2719846 2724454 2724497 "VECTCAT" 2725485 VECTCAT (NIL T) -9 NIL 2726069 NIL) (-1176 2719125 2719451 2719841 "VECTCAT-" NIL VECTCAT- (NIL T T) -7 NIL NIL NIL) (-1175 2718619 2718861 2718981 "VARIABLE" NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1174 2718552 2718557 2718587 "UTYPE" 2718592 UTYPE (NIL) -9 NIL NIL NIL) (-1173 2717539 2717715 2717976 "UTSODETL" NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1172 2715390 2715898 2716422 "UTSODE" NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1171 2705334 2711242 2711284 "UTSCAT" 2712382 UTSCAT (NIL T) -9 NIL 2713139 NIL) (-1170 2703399 2704342 2705329 "UTSCAT-" NIL UTSCAT- (NIL T T) -7 NIL NIL NIL) (-1169 2703073 2703122 2703253 "UTS2" NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1168 2694848 2701269 2701748 "UTS" NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1167 2688843 2691656 2691699 "URAGG" 2693769 URAGG (NIL T) -9 NIL 2694491 NIL) (-1166 2686858 2687820 2688838 "URAGG-" NIL URAGG- (NIL T T) -7 NIL NIL NIL) (-1165 2682629 2685834 2686296 "UPXSSING" NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1164 2675122 2682553 2682624 "UPXSCONS" NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1163 2663835 2671260 2671321 "UPXSCCA" 2671889 UPXSCCA (NIL T T) -9 NIL 2672121 NIL) (-1162 2663556 2663658 2663830 "UPXSCCA-" NIL UPXSCCA- (NIL T T T) -7 NIL NIL NIL) (-1161 2652170 2659320 2659362 "UPXSCAT" 2660002 UPXSCAT (NIL T) -9 NIL 2660610 NIL) (-1160 2651683 2651768 2651945 "UPXS2" NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1159 2643433 2651274 2651536 "UPXS" NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1158 2642328 2642598 2642948 "UPSQFREE" NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1157 2635093 2638516 2638570 "UPSCAT" 2639639 UPSCAT (NIL T T) -9 NIL 2640403 NIL) (-1156 2634513 2634765 2635088 "UPSCAT-" NIL UPSCAT- (NIL T T T) -7 NIL NIL NIL) (-1155 2634187 2634236 2634367 "UPOLYC2" NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1154 2618381 2627271 2627313 "UPOLYC" 2629391 UPOLYC (NIL T) -9 NIL 2630611 NIL) (-1153 2612436 2615284 2618376 "UPOLYC-" NIL UPOLYC- (NIL T T) -7 NIL NIL NIL) (-1152 2611872 2611997 2612160 "UPMP" NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1151 2611506 2611593 2611732 "UPDIVP" NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1150 2610319 2610586 2610890 "UPDECOMP" NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1149 2609652 2609782 2609967 "UPCDEN" NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1148 2609244 2609319 2609466 "UP2" NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1147 2600072 2609010 2609138 "UP" NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1146 2599434 2599571 2599776 "UNISEG2" NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1145 2598035 2598882 2599158 "UNISEG" NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1144 2597264 2597461 2597686 "UNIFACT" NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1143 2584138 2597188 2597259 "ULSCONS" NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1142 2564052 2577225 2577286 "ULSCCAT" 2577917 ULSCCAT (NIL T T) -9 NIL 2578204 NIL) (-1141 2563387 2563673 2564047 "ULSCCAT-" NIL ULSCCAT- (NIL T T T) -7 NIL NIL NIL) (-1140 2551821 2558893 2558935 "ULSCAT" 2559788 ULSCAT (NIL T) -9 NIL 2560518 NIL) (-1139 2551334 2551419 2551596 "ULS2" NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1138 2533515 2550833 2551074 "ULS" NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1137 2532549 2533242 2533356 "UINT8" NIL UINT8 (NIL) -8 NIL NIL 2533467) (-1136 2531582 2532275 2532389 "UINT64" NIL UINT64 (NIL) -8 NIL NIL 2532500) (-1135 2530615 2531308 2531422 "UINT32" NIL UINT32 (NIL) -8 NIL NIL 2531533) (-1134 2529648 2530341 2530455 "UINT16" NIL UINT16 (NIL) -8 NIL NIL 2530566) (-1133 2527717 2528876 2528906 "UFD" 2529117 UFD (NIL) -9 NIL 2529230 NIL) (-1132 2527561 2527618 2527712 "UFD-" NIL UFD- (NIL T) -7 NIL NIL NIL) (-1131 2526813 2527020 2527236 "UDVO" NIL UDVO (NIL) -7 NIL NIL NIL) (-1130 2525033 2525486 2525951 "UDPO" NIL UDPO (NIL T) -7 NIL NIL NIL) (-1129 2524758 2524998 2525028 "TYPEAST" NIL TYPEAST (NIL) -8 NIL NIL NIL) (-1128 2524696 2524701 2524731 "TYPE" 2524736 TYPE (NIL) -9 NIL 2524743 NIL) (-1127 2523855 2524075 2524315 "TWOFACT" NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1126 2523033 2523464 2523699 "TUPLE" NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1125 2521187 2521760 2522299 "TUBETOOL" NIL TUBETOOL (NIL) -7 NIL NIL NIL) (-1124 2520221 2520457 2520693 "TUBE" NIL TUBE (NIL T) -8 NIL NIL NIL) (-1123 2508575 2513043 2513139 "TSETCAT" 2518354 TSETCAT (NIL T T T T) -9 NIL 2519866 NIL) (-1122 2504912 2506728 2508570 "TSETCAT-" NIL TSETCAT- (NIL T T T T T) -7 NIL NIL NIL) (-1121 2499368 2504138 2504420 "TS" NIL TS (NIL T) -8 NIL NIL NIL) (-1120 2494705 2495718 2496647 "TRMANIP" NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1119 2494202 2494277 2494440 "TRIMAT" NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1118 2492278 2492568 2492923 "TRIGMNIP" NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1117 2491762 2491911 2491941 "TRIGCAT" 2492154 TRIGCAT (NIL) -9 NIL NIL NIL) (-1116 2491513 2491616 2491757 "TRIGCAT-" NIL TRIGCAT- (NIL T) -7 NIL NIL NIL) (-1115 2488509 2490622 2490900 "TREE" NIL TREE (NIL T) -8 NIL NIL NIL) (-1114 2487615 2488311 2488341 "TRANFUN" 2488376 TRANFUN (NIL) -9 NIL 2488442 NIL) (-1113 2487079 2487330 2487610 "TRANFUN-" NIL TRANFUN- (NIL T) -7 NIL NIL NIL) (-1112 2486916 2486954 2487015 "TOPSP" NIL TOPSP (NIL) -7 NIL NIL NIL) (-1111 2486373 2486504 2486655 "TOOLSIGN" NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1110 2485114 2485771 2486007 "TEXTFILE" NIL TEXTFILE (NIL) -8 NIL NIL NIL) (-1109 2484926 2484963 2485035 "TEX1" NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1108 2483140 2483786 2484215 "TEX" NIL TEX (NIL) -8 NIL NIL NIL) (-1107 2481520 2481857 2482179 "TBCMPPK" NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1106 2472578 2479321 2479377 "TBAGG" 2479779 TBAGG (NIL T T) -9 NIL 2479992 NIL) (-1105 2469109 2470801 2472573 "TBAGG-" NIL TBAGG- (NIL T T T) -7 NIL NIL NIL) (-1104 2468586 2468711 2468856 "TANEXP" NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1103 2468096 2468416 2468506 "TALGOP" NIL TALGOP (NIL T) -8 NIL NIL NIL) (-1102 2467593 2467710 2467848 "TABLEAU" NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1101 2460680 2467495 2467588 "TABLE" NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1100 2456433 2457728 2458973 "TABLBUMP" NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1099 2455802 2455961 2456142 "SYSTEM" NIL SYSTEM (NIL) -7 NIL NIL NIL) (-1098 2452956 2453709 2454492 "SYSSOLP" NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1097 2452730 2452920 2452951 "SYSPTR" NIL SYSPTR (NIL) -8 NIL NIL NIL) (-1096 2451684 2452369 2452495 "SYSNNI" NIL SYSNNI (NIL NIL) -8 NIL NIL 2452681) (-1095 2450948 2451496 2451575 "SYSINT" NIL SYSINT (NIL NIL) -8 NIL NIL 2451635) (-1094 2447771 2448930 2449630 "SYNTAX" NIL SYNTAX (NIL) -8 NIL NIL NIL) (-1093 2445454 2446137 2446771 "SYMTAB" NIL SYMTAB (NIL) -8 NIL NIL NIL) (-1092 2441532 2442578 2443555 "SYMS" NIL SYMS (NIL) -8 NIL NIL NIL) (-1091 2438695 2441187 2441416 "SYMPOLY" NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1090 2438291 2438378 2438500 "SYMFUNC" NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1089 2434915 2436389 2437208 "SYMBOL" NIL SYMBOL (NIL) -8 NIL NIL NIL) (-1088 2427939 2434112 2434405 "SUTS" NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1087 2419689 2427530 2427792 "SUPXS" NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1086 2418968 2419107 2419324 "SUPFRACF" NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1085 2418652 2418717 2418828 "SUP2" NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1084 2409439 2418364 2418489 "SUP" NIL SUP (NIL T) -8 NIL NIL NIL) (-1083 2408169 2408467 2408822 "SUMRF" NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1082 2407574 2407652 2407843 "SUMFS" NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1081 2389790 2407073 2407314 "SULS" NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1080 2389389 2389661 2389730 "SUCHTAST" NIL SUCHTAST (NIL) -8 NIL NIL NIL) (-1079 2388725 2389006 2389146 "SUCH" NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1078 2383327 2384586 2385539 "SUBSPACE" NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1077 2382859 2382959 2383123 "SUBRESP" NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1076 2377970 2379252 2380399 "STTFNC" NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1075 2372428 2373899 2375210 "STTF" NIL STTF (NIL T) -7 NIL NIL NIL) (-1074 2365343 2367407 2369198 "STTAYLOR" NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1073 2358173 2365255 2365338 "STRTBL" NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1072 2352867 2357887 2358002 "STRING" NIL STRING (NIL) -8 NIL NIL NIL) (-1071 2352454 2352537 2352681 "STREAM3" NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1070 2351605 2351806 2352041 "STREAM2" NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1069 2351345 2351403 2351496 "STREAM1" NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1068 2344083 2349550 2350156 "STREAM" NIL STREAM (NIL T) -8 NIL NIL NIL) (-1067 2343259 2343464 2343695 "STINPROD" NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1066 2342504 2342875 2343022 "STEPAST" NIL STEPAST (NIL) -8 NIL NIL NIL) (-1065 2341992 2342234 2342264 "STEP" 2342358 STEP (NIL) -9 NIL 2342429 NIL) (-1064 2335095 2341910 2341987 "STBL" NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1063 2329310 2333893 2333936 "STAGG" 2334363 STAGG (NIL T) -9 NIL 2334537 NIL) (-1062 2327689 2328437 2329305 "STAGG-" NIL STAGG- (NIL T T) -7 NIL NIL NIL) (-1061 2325846 2327516 2327608 "STACK" NIL STACK (NIL T) -8 NIL NIL NIL) (-1060 2325157 2325665 2325695 "SRING" 2325700 SRING (NIL) -9 NIL 2325720 NIL) (-1059 2317779 2323695 2324134 "SREGSET" NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1058 2311553 2312992 2314496 "SRDCMPK" NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1057 2303978 2308889 2308919 "SRAGG" 2310218 SRAGG (NIL) -9 NIL 2310822 NIL) (-1056 2303275 2303595 2303973 "SRAGG-" NIL SRAGG- (NIL T) -7 NIL NIL NIL) (-1055 2297394 2302597 2303020 "SQMATRIX" NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1054 2291607 2294776 2295498 "SPLTREE" NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1053 2288036 2288855 2289492 "SPLNODE" NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1052 2287011 2287316 2287346 "SPFCAT" 2287790 SPFCAT (NIL) -9 NIL NIL NIL) (-1051 2285948 2286200 2286464 "SPECOUT" NIL SPECOUT (NIL) -7 NIL NIL NIL) (-1050 2276706 2278980 2279010 "SPADXPT" 2283647 SPADXPT (NIL) -9 NIL 2285771 NIL) (-1049 2276508 2276554 2276623 "SPADPRSR" NIL SPADPRSR (NIL) -7 NIL NIL NIL) (-1048 2274164 2276472 2276503 "SPADAST" NIL SPADAST (NIL) -8 NIL NIL NIL) (-1047 2265838 2267927 2267969 "SPACEC" 2272284 SPACEC (NIL T) -9 NIL 2274089 NIL) (-1046 2263667 2265785 2265833 "SPACE3" NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1045 2262600 2262789 2263078 "SORTPAK" NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1044 2261004 2261337 2261748 "SOLVETRA" NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1043 2260269 2260503 2260764 "SOLVESER" NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1042 2256449 2257409 2258404 "SOLVERAD" NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1041 2252807 2253506 2254235 "SOLVEFOR" NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1040 2246593 2252147 2252243 "SNTSCAT" 2252248 SNTSCAT (NIL T T T T) -9 NIL 2252318 NIL) (-1039 2240478 2245234 2245624 "SMTS" NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1038 2234314 2240397 2240473 "SMP" NIL SMP (NIL T T) -8 NIL NIL NIL) (-1037 2232746 2233077 2233475 "SMITH" NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1036 2224415 2229330 2229432 "SMATCAT" 2230775 SMATCAT (NIL NIL T T T) -9 NIL 2231323 NIL) (-1035 2222256 2223240 2224410 "SMATCAT-" NIL SMATCAT- (NIL T NIL T T T) -7 NIL NIL NIL) (-1034 2219848 2221462 2221505 "SKAGG" 2221766 SKAGG (NIL T) -9 NIL 2221900 NIL) (-1033 2215958 2219668 2219779 "SINT" NIL SINT (NIL) -8 NIL NIL 2219820) (-1032 2215768 2215812 2215878 "SIMPAN" NIL SIMPAN (NIL) -7 NIL NIL NIL) (-1031 2214843 2215075 2215343 "SIGNRF" NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1030 2213847 2214009 2214285 "SIGNEF" NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1029 2213193 2213533 2213656 "SIGAST" NIL SIGAST (NIL) -8 NIL NIL NIL) (-1028 2212539 2212846 2212986 "SIG" NIL SIG (NIL) -8 NIL NIL NIL) (-1027 2210650 2211142 2211648 "SHP" NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1026 2204189 2210569 2210645 "SHDP" NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1025 2203692 2203929 2203959 "SGROUP" 2204052 SGROUP (NIL) -9 NIL 2204114 NIL) (-1024 2203582 2203614 2203687 "SGROUP-" NIL SGROUP- (NIL T) -7 NIL NIL NIL) (-1023 2203220 2203260 2203301 "SGPOPC" 2203306 SGPOPC (NIL T) -9 NIL 2203507 NIL) (-1022 2202754 2203031 2203137 "SGPOP" NIL SGPOP (NIL T) -8 NIL NIL NIL) (-1021 2200177 2200946 2201668 "SGCF" NIL SGCF (NIL) -7 NIL NIL NIL) (-1020 2194062 2199616 2199712 "SFRTCAT" 2199717 SFRTCAT (NIL T T T T) -9 NIL 2199755 NIL) (-1019 2188454 2189567 2190694 "SFRGCD" NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1018 2182630 2183791 2184955 "SFQCMPK" NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1017 2181602 2182504 2182625 "SEXOF" NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1016 2177210 2178105 2178200 "SEXCAT" 2180813 SEXCAT (NIL T T T T T) -9 NIL 2181364 NIL) (-1015 2176183 2177137 2177205 "SEX" NIL SEX (NIL) -8 NIL NIL NIL) (-1014 2174574 2175159 2175461 "SETMN" NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1013 2174097 2174282 2174312 "SETCAT" 2174429 SETCAT (NIL) -9 NIL 2174513 NIL) (-1012 2173929 2173993 2174092 "SETCAT-" NIL SETCAT- (NIL T) -7 NIL NIL NIL) (-1011 2170152 2172383 2172426 "SETAGG" 2173294 SETAGG (NIL T) -9 NIL 2173632 NIL) (-1010 2169758 2169910 2170147 "SETAGG-" NIL SETAGG- (NIL T T) -7 NIL NIL NIL) (-1009 2166712 2169705 2169753 "SET" NIL SET (NIL T) -8 NIL NIL NIL) (-1008 2166178 2166488 2166588 "SEQAST" NIL SEQAST (NIL) -8 NIL NIL NIL) (-1007 2165305 2165671 2165732 "SEGXCAT" 2166018 SEGXCAT (NIL T T) -9 NIL 2166138 NIL) (-1006 2164230 2164498 2164541 "SEGCAT" 2165063 SEGCAT (NIL T) -9 NIL 2165284 NIL) (-1005 2163910 2163975 2164088 "SEGBIND2" NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1004 2162976 2163446 2163654 "SEGBIND" NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1003 2162554 2162833 2162909 "SEGAST" NIL SEGAST (NIL) -8 NIL NIL NIL) (-1002 2161919 2162055 2162259 "SEG2" NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1001 2160985 2161732 2161914 "SEG" NIL SEG (NIL T) -8 NIL NIL NIL) (-1000 2160238 2160933 2160980 "SDVAR" NIL SDVAR (NIL T) -8 NIL NIL NIL) (-999 2151789 2160107 2160233 "SDPOL" NIL SDPOL (NIL T) -8 NIL NIL NIL) (-998 2150649 2150939 2151256 "SCPKG" NIL SCPKG (NIL T) -7 NIL NIL NIL) (-997 2149955 2150167 2150355 "SCOPE" NIL SCOPE (NIL) -8 NIL NIL NIL) (-996 2149305 2149462 2149638 "SCACHE" NIL SCACHE (NIL T) -7 NIL NIL NIL) (-995 2148878 2149109 2149137 "SASTCAT" 2149142 SASTCAT (NIL) -9 NIL 2149155 NIL) (-994 2148345 2148770 2148844 "SAOS" NIL SAOS (NIL) -8 NIL NIL NIL) (-993 2147948 2147989 2148160 "SAERFFC" NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-992 2147579 2147620 2147777 "SAEFACT" NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-991 2140724 2147496 2147574 "SAE" NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-990 2139374 2139703 2140099 "RURPK" NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-989 2138135 2138496 2138796 "RULESET" NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-988 2137759 2137980 2138061 "RULECOLD" NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-987 2135219 2135853 2136306 "RULE" NIL RULE (NIL T T T) -8 NIL NIL NIL) (-986 2135058 2135091 2135159 "RTVALUE" NIL RTVALUE (NIL) -8 NIL NIL NIL) (-985 2134549 2134852 2134943 "RSTRCAST" NIL RSTRCAST (NIL) -8 NIL NIL NIL) (-984 2130177 2131045 2131956 "RSETGCD" NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-983 2118996 2124550 2124644 "RSETCAT" 2128700 RSETCAT (NIL T T T T) -9 NIL 2129788 NIL) (-982 2117534 2118176 2118991 "RSETCAT-" NIL RSETCAT- (NIL T T T T T) -7 NIL NIL NIL) (-981 2111308 2112753 2114260 "RSDCMPK" NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-980 2109190 2109747 2109819 "RRCC" 2110892 RRCC (NIL T T) -9 NIL 2111233 NIL) (-979 2108715 2108914 2109185 "RRCC-" NIL RRCC- (NIL T T T) -7 NIL NIL NIL) (-978 2108185 2108495 2108593 "RPTAST" NIL RPTAST (NIL) -8 NIL NIL NIL) (-977 2080801 2091450 2091514 "RPOLCAT" 2101988 RPOLCAT (NIL T T T) -9 NIL 2105133 NIL) (-976 2074900 2077723 2080796 "RPOLCAT-" NIL RPOLCAT- (NIL T T T T) -7 NIL NIL NIL) (-975 2071131 2074648 2074786 "ROMAN" NIL ROMAN (NIL) -8 NIL NIL NIL) (-974 2069459 2070198 2070454 "ROIRC" NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-973 2065164 2067914 2067942 "RNS" 2068204 RNS (NIL) -9 NIL 2068456 NIL) (-972 2064067 2064554 2065091 "RNS-" NIL RNS- (NIL T) -7 NIL NIL NIL) (-971 2063185 2063586 2063786 "RNGBIND" NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-970 2062473 2062973 2063001 "RNG" 2063006 RNG (NIL) -9 NIL 2063027 NIL) (-969 2061766 2062240 2062280 "RMODULE" 2062285 RMODULE (NIL T) -9 NIL 2062311 NIL) (-968 2060705 2060811 2061141 "RMCAT2" NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-967 2057583 2060295 2060588 "RMATRIX" NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-966 2050263 2052724 2052836 "RMATCAT" 2056141 RMATCAT (NIL NIL NIL T T T) -9 NIL 2057118 NIL) (-965 2049780 2049959 2050258 "RMATCAT-" NIL RMATCAT- (NIL T NIL NIL T T T) -7 NIL NIL NIL) (-964 2049348 2049559 2049600 "RLINSET" 2049661 RLINSET (NIL T) -9 NIL 2049705 NIL) (-963 2048993 2049074 2049200 "RINTERP" NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-962 2047901 2048570 2048598 "RING" 2048653 RING (NIL) -9 NIL 2048745 NIL) (-961 2047746 2047802 2047896 "RING-" NIL RING- (NIL T) -7 NIL NIL NIL) (-960 2046800 2047067 2047323 "RIDIST" NIL RIDIST (NIL) -7 NIL NIL NIL) (-959 2037787 2046428 2046629 "RGCHAIN" NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-958 2037043 2037523 2037562 "RGBCSPC" 2037619 RGBCSPC (NIL T) -9 NIL 2037670 NIL) (-957 2036108 2036563 2036602 "RGBCMDL" 2036830 RGBCMDL (NIL T) -9 NIL 2036944 NIL) (-956 2035820 2035889 2035990 "RFFACTOR" NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-955 2035583 2035624 2035719 "RFFACT" NIL RFFACT (NIL T) -7 NIL NIL NIL) (-954 2034007 2034437 2034817 "RFDIST" NIL RFDIST (NIL) -7 NIL NIL NIL) (-953 2031594 2032262 2032930 "RF" NIL RF (NIL T) -7 NIL NIL NIL) (-952 2031144 2031242 2031402 "RETSOL" NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-951 2030766 2030864 2030905 "RETRACT" 2031036 RETRACT (NIL T) -9 NIL 2031123 NIL) (-950 2030646 2030677 2030761 "RETRACT-" NIL RETRACT- (NIL T T) -7 NIL NIL NIL) (-949 2030248 2030520 2030587 "RETAST" NIL RETAST (NIL) -8 NIL NIL NIL) (-948 2028792 2029619 2029816 "RESRING" NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-947 2028483 2028544 2028640 "RESLATC" NIL RESLATC (NIL T) -7 NIL NIL NIL) (-946 2028226 2028267 2028372 "REPSQ" NIL REPSQ (NIL T) -7 NIL NIL NIL) (-945 2027961 2028002 2028111 "REPDB" NIL REPDB (NIL T) -7 NIL NIL NIL) (-944 2023032 2024483 2025698 "REP2" NIL REP2 (NIL T) -7 NIL NIL NIL) (-943 2020131 2020889 2021697 "REP1" NIL REP1 (NIL T) -7 NIL NIL NIL) (-942 2018100 2018722 2019322 "REP" NIL REP (NIL) -7 NIL NIL NIL) (-941 2010735 2016651 2017087 "REGSET" NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-940 2010047 2010327 2010476 "REF" NIL REF (NIL T) -8 NIL NIL NIL) (-939 2009532 2009647 2009812 "REDORDER" NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-938 2005189 2008935 2009156 "RECLOS" NIL RECLOS (NIL T) -8 NIL NIL NIL) (-937 2004421 2004620 2004833 "REALSOLV" NIL REALSOLV (NIL) -7 NIL NIL NIL) (-936 2001711 2002549 2003431 "REAL0Q" NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-935 1998293 1999329 2000388 "REAL0" NIL REAL0 (NIL T) -7 NIL NIL NIL) (-934 1998129 1998182 1998210 "REAL" 1998215 REAL (NIL) -9 NIL 1998250 NIL) (-933 1997619 1997923 1998014 "RDUCEAST" NIL RDUCEAST (NIL) -8 NIL NIL NIL) (-932 1997099 1997177 1997382 "RDIV" NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-931 1996332 1996524 1996735 "RDIST" NIL RDIST (NIL T) -7 NIL NIL NIL) (-930 1995220 1995517 1995884 "RDETRS" NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-929 1993487 1993957 1994490 "RDETR" NIL RDETR (NIL T T) -7 NIL NIL NIL) (-928 1992409 1992686 1993073 "RDEEFS" NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-927 1991236 1991545 1991964 "RDEEF" NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-926 1984648 1988096 1988124 "RCFIELD" 1989401 RCFIELD (NIL) -9 NIL 1990131 NIL) (-925 1983266 1983878 1984575 "RCFIELD-" NIL RCFIELD- (NIL T) -7 NIL NIL NIL) (-924 1979466 1981358 1981399 "RCAGG" 1982466 RCAGG (NIL T) -9 NIL 1982927 NIL) (-923 1979193 1979303 1979461 "RCAGG-" NIL RCAGG- (NIL T T) -7 NIL NIL NIL) (-922 1978638 1978767 1978928 "RATRET" NIL RATRET (NIL T) -7 NIL NIL NIL) (-921 1978255 1978334 1978453 "RATFACT" NIL RATFACT (NIL T) -7 NIL NIL NIL) (-920 1977670 1977820 1977970 "RANDSRC" NIL RANDSRC (NIL) -7 NIL NIL NIL) (-919 1977452 1977502 1977573 "RADUTIL" NIL RADUTIL (NIL) -7 NIL NIL NIL) (-918 1969958 1976570 1976878 "RADIX" NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-917 1959724 1969825 1969953 "RADFF" NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-916 1959358 1959451 1959479 "RADCAT" 1959636 RADCAT (NIL) -9 NIL NIL NIL) (-915 1959196 1959256 1959353 "RADCAT-" NIL RADCAT- (NIL T) -7 NIL NIL NIL) (-914 1957296 1959027 1959116 "QUEUE" NIL QUEUE (NIL T) -8 NIL NIL NIL) (-913 1956977 1957026 1957153 "QUATCT2" NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-912 1949328 1953348 1953388 "QUATCAT" 1954166 QUATCAT (NIL T) -9 NIL 1954930 NIL) (-911 1946578 1947858 1949234 "QUATCAT-" NIL QUATCAT- (NIL T T) -7 NIL NIL NIL) (-910 1942482 1946528 1946573 "QUAT" NIL QUAT (NIL T) -8 NIL NIL NIL) (-909 1939869 1941536 1941577 "QUAGG" 1941952 QUAGG (NIL T) -9 NIL 1942126 NIL) (-908 1939471 1939743 1939810 "QQUTAST" NIL QQUTAST (NIL) -8 NIL NIL NIL) (-907 1938509 1939107 1939270 "QFORM" NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-906 1938190 1938239 1938366 "QFCAT2" NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-905 1927877 1933984 1934024 "QFCAT" 1934682 QFCAT (NIL T) -9 NIL 1935675 NIL) (-904 1924761 1926200 1927783 "QFCAT-" NIL QFCAT- (NIL T T) -7 NIL NIL NIL) (-903 1924307 1924441 1924571 "QEQUAT" NIL QEQUAT (NIL) -8 NIL NIL NIL) (-902 1918503 1919664 1920826 "QCMPACK" NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-901 1917922 1918102 1918334 "QALGSET2" NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-900 1915744 1916272 1916695 "QALGSET" NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-899 1914643 1914885 1915202 "PWFFINTB" NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-898 1913004 1913202 1913555 "PUSHVAR" NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-897 1908760 1909976 1910017 "PTRANFN" 1911901 PTRANFN (NIL T) -9 NIL NIL NIL) (-896 1907407 1907752 1908073 "PTPACK" NIL PTPACK (NIL T) -7 NIL NIL NIL) (-895 1907100 1907163 1907270 "PTFUNC2" NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-894 1901173 1905896 1905936 "PTCAT" 1906228 PTCAT (NIL T) -9 NIL 1906381 NIL) (-893 1900866 1900907 1901031 "PSQFR" NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-892 1899745 1900061 1900395 "PSEUDLIN" NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-891 1888624 1891185 1893494 "PSETPK" NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-890 1881531 1884427 1884521 "PSETCAT" 1887495 PSETCAT (NIL T T T T) -9 NIL 1888302 NIL) (-889 1879981 1880715 1881526 "PSETCAT-" NIL PSETCAT- (NIL T T T T T) -7 NIL NIL NIL) (-888 1879300 1879495 1879523 "PSCURVE" 1879791 PSCURVE (NIL) -9 NIL 1879958 NIL) (-887 1874964 1876722 1876786 "PSCAT" 1877621 PSCAT (NIL T T T) -9 NIL 1877860 NIL) (-886 1874278 1874560 1874959 "PSCAT-" NIL PSCAT- (NIL T T T T) -7 NIL NIL NIL) (-885 1872707 1873590 1873853 "PRTITION" NIL PRTITION (NIL) -8 NIL NIL NIL) (-884 1872198 1872501 1872592 "PRTDAST" NIL PRTDAST (NIL) -8 NIL NIL NIL) (-883 1863218 1865640 1867828 "PRS" NIL PRS (NIL T T) -7 NIL NIL NIL) (-882 1860961 1862538 1862578 "PRQAGG" 1862761 PRQAGG (NIL T) -9 NIL 1862862 NIL) (-881 1860134 1860580 1860608 "PROPLOG" 1860747 PROPLOG (NIL) -9 NIL 1860861 NIL) (-880 1859809 1859872 1859995 "PROPFUN2" NIL PROPFUN2 (NIL T T) -7 NIL NIL NIL) (-879 1859245 1859384 1859556 "PROPFUN1" NIL PROPFUN1 (NIL T) -7 NIL NIL NIL) (-878 1857493 1858256 1858553 "PROPFRML" NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-877 1857045 1857177 1857305 "PROPERTY" NIL PROPERTY (NIL) -8 NIL NIL NIL) (-876 1851701 1855985 1856805 "PRODUCT" NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-875 1851530 1851568 1851627 "PRINT" NIL PRINT (NIL) -7 NIL NIL NIL) (-874 1850969 1851109 1851260 "PRIMES" NIL PRIMES (NIL T) -7 NIL NIL NIL) (-873 1849437 1849856 1850322 "PRIMELT" NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-872 1849154 1849215 1849243 "PRIMCAT" 1849367 PRIMCAT (NIL) -9 NIL NIL NIL) (-871 1848325 1848521 1848749 "PRIMARR2" NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-870 1844203 1848275 1848320 "PRIMARR" NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-869 1843902 1843964 1844075 "PREASSOC" NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-868 1841102 1843551 1843784 "PR" NIL PR (NIL T T) -8 NIL NIL NIL) (-867 1840553 1840710 1840738 "PPCURVE" 1840943 PPCURVE (NIL) -9 NIL 1841079 NIL) (-866 1840166 1840411 1840494 "PORTNUM" NIL PORTNUM (NIL) -8 NIL NIL NIL) (-865 1837922 1838343 1838935 "POLYROOT" NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-864 1837365 1837429 1837662 "POLYLIFT" NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-863 1834085 1834571 1835182 "POLYCATQ" NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-862 1819740 1825805 1825869 "POLYCAT" 1829354 POLYCAT (NIL T T T) -9 NIL 1831231 NIL) (-861 1815250 1817397 1819735 "POLYCAT-" NIL POLYCAT- (NIL T T T T) -7 NIL NIL NIL) (-860 1814907 1814981 1815100 "POLY2UP" NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-859 1814600 1814663 1814770 "POLY2" NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-858 1808027 1814333 1814492 "POLY" NIL POLY (NIL T) -8 NIL NIL NIL) (-857 1806914 1807177 1807453 "POLUTIL" NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-856 1805518 1805831 1806161 "POLTOPOL" NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-855 1800680 1805468 1805513 "POINT" NIL POINT (NIL T) -8 NIL NIL NIL) (-854 1799168 1799579 1799954 "PNTHEORY" NIL PNTHEORY (NIL) -7 NIL NIL NIL) (-853 1797925 1798234 1798630 "PMTOOLS" NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-852 1797596 1797680 1797797 "PMSYM" NIL PMSYM (NIL T) -7 NIL NIL NIL) (-851 1797175 1797250 1797424 "PMQFCAT" NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-850 1796661 1796757 1796917 "PMPREDFS" NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-849 1796133 1796253 1796407 "PMPRED" NIL PMPRED (NIL T) -7 NIL NIL NIL) (-848 1795028 1795246 1795623 "PMPLCAT" NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-847 1794639 1794724 1794876 "PMLSAGG" NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-846 1794190 1794272 1794453 "PMKERNEL" NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-845 1793882 1793963 1794076 "PMINS" NIL PMINS (NIL T) -7 NIL NIL NIL) (-844 1793395 1793470 1793678 "PMFS" NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-843 1792743 1792871 1793073 "PMDOWN" NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-842 1792105 1792239 1792402 "PMASSFS" NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-841 1791409 1791591 1791772 "PMASS" NIL PMASS (NIL) -7 NIL NIL NIL) (-840 1791132 1791206 1791300 "PLOTTOOL" NIL PLOTTOOL (NIL) -7 NIL NIL NIL) (-839 1787700 1788889 1789805 "PLOT3D" NIL PLOT3D (NIL) -8 NIL NIL NIL) (-838 1786784 1786985 1787220 "PLOT1" NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-837 1782349 1783733 1784875 "PLOT" NIL PLOT (NIL) -8 NIL NIL NIL) (-836 1762270 1767157 1772004 "PLEQN" NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-835 1762010 1762063 1762166 "PINTERPA" NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-834 1761451 1761585 1761765 "PINTERP" NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-833 1759522 1760681 1760709 "PID" 1760906 PID (NIL) -9 NIL 1761033 NIL) (-832 1759310 1759353 1759428 "PICOERCE" NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-831 1758497 1759157 1759244 "PI" NIL PI (NIL) -8 NIL NIL 1759284) (-830 1757949 1758100 1758276 "PGROEB" NIL PGROEB (NIL T) -7 NIL NIL NIL) (-829 1754277 1755235 1756140 "PGE" NIL PGE (NIL) -7 NIL NIL NIL) (-828 1752641 1752930 1753296 "PGCD" NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-827 1752083 1752198 1752359 "PFRPAC" NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-826 1748688 1750952 1751305 "PFR" NIL PFR (NIL T) -8 NIL NIL NIL) (-825 1747294 1747574 1747899 "PFOTOOLS" NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-824 1746059 1746313 1746661 "PFOQ" NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-823 1744769 1744996 1745348 "PFO" NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-822 1741841 1743339 1743367 "PFECAT" 1743960 PFECAT (NIL) -9 NIL 1744337 NIL) (-821 1741464 1741629 1741836 "PFECAT-" NIL PFECAT- (NIL T) -7 NIL NIL NIL) (-820 1740288 1740570 1740871 "PFBRU" NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-819 1738470 1738857 1739287 "PFBR" NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-818 1734504 1738396 1738465 "PF" NIL PF (NIL NIL) -8 NIL NIL NIL) (-817 1730407 1731554 1732421 "PERMGRP" NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-816 1728339 1729428 1729469 "PERMCAT" 1729868 PERMCAT (NIL T) -9 NIL 1730165 NIL) (-815 1728035 1728082 1728205 "PERMAN" NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-814 1724484 1726165 1726810 "PERM" NIL PERM (NIL T) -8 NIL NIL NIL) (-813 1721949 1724239 1724360 "PENDTREE" NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-812 1720818 1721081 1721122 "PDSPC" 1721655 PDSPC (NIL T) -9 NIL 1721900 NIL) (-811 1720185 1720451 1720813 "PDSPC-" NIL PDSPC- (NIL T T) -7 NIL NIL NIL) (-810 1718882 1719813 1719854 "PDRING" 1719859 PDRING (NIL T) -9 NIL 1719886 NIL) (-809 1717623 1718381 1718434 "PDMOD" 1718439 PDMOD (NIL T T) -9 NIL 1718542 NIL) (-808 1716716 1716928 1717177 "PDECOMP" NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-807 1716321 1716388 1716442 "PDDOM" 1716607 PDDOM (NIL T T) -9 NIL 1716687 NIL) (-806 1716173 1716209 1716316 "PDDOM-" NIL PDDOM- (NIL T T T) -7 NIL NIL NIL) (-805 1715959 1715998 1716087 "PCOMP" NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-804 1714276 1715030 1715329 "PBWLB" NIL PBWLB (NIL T) -8 NIL NIL NIL) (-803 1713965 1714028 1714137 "PATTERN2" NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-802 1712103 1712533 1712984 "PATTERN1" NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-801 1705723 1707552 1708844 "PATTERN" NIL PATTERN (NIL T) -8 NIL NIL NIL) (-800 1705354 1705427 1705559 "PATRES2" NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-799 1703056 1703736 1704217 "PATRES" NIL PATRES (NIL T T) -8 NIL NIL NIL) (-798 1701260 1701688 1702091 "PATMATCH" NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-797 1700706 1700954 1700995 "PATMAB" 1701102 PATMAB (NIL T) -9 NIL 1701185 NIL) (-796 1699353 1699757 1700014 "PATLRES" NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-795 1698891 1699022 1699063 "PATAB" 1699068 PATAB (NIL T) -9 NIL 1699240 NIL) (-794 1697434 1697871 1698294 "PARTPERM" NIL PARTPERM (NIL) -7 NIL NIL NIL) (-793 1697112 1697187 1697289 "PARSURF" NIL PARSURF (NIL T) -8 NIL NIL NIL) (-792 1696801 1696864 1696973 "PARSU2" NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-791 1696606 1696652 1696719 "PARSER" NIL PARSER (NIL) -7 NIL NIL NIL) (-790 1696284 1696359 1696461 "PARSCURV" NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-789 1695973 1696036 1696145 "PARSC2" NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-788 1695664 1695734 1695831 "PARPCURV" NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-787 1695353 1695416 1695525 "PARPC2" NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-786 1694514 1694893 1695072 "PARAMAST" NIL PARAMAST (NIL) -8 NIL NIL NIL) (-785 1694121 1694219 1694338 "PAN2EXPR" NIL PAN2EXPR (NIL) -7 NIL NIL NIL) (-784 1693089 1693514 1693733 "PALETTE" NIL PALETTE (NIL) -8 NIL NIL NIL) (-783 1691754 1692408 1692768 "PAIR" NIL PAIR (NIL T T) -8 NIL NIL NIL) (-782 1684908 1691158 1691352 "PADICRC" NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-781 1677393 1684406 1684590 "PADICRAT" NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-780 1674180 1676033 1676073 "PADICCT" 1676654 PADICCT (NIL NIL) -9 NIL 1676936 NIL) (-779 1672234 1674130 1674175 "PADIC" NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-778 1671396 1671606 1671872 "PADEPAC" NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-777 1670738 1670881 1671085 "PADE" NIL PADE (NIL T T T) -7 NIL NIL NIL) (-776 1669183 1670146 1670424 "OWP" NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-775 1668707 1668966 1669063 "OVERSET" NIL OVERSET (NIL) -8 NIL NIL NIL) (-774 1667766 1668444 1668616 "OVAR" NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-773 1658188 1661057 1663256 "OUTFORM" NIL OUTFORM (NIL) -8 NIL NIL NIL) (-772 1657580 1657894 1658020 "OUTBFILE" NIL OUTBFILE (NIL) -8 NIL NIL NIL) (-771 1656857 1657052 1657080 "OUTBCON" 1657398 OUTBCON (NIL) -9 NIL 1657564 NIL) (-770 1656565 1656695 1656852 "OUTBCON-" NIL OUTBCON- (NIL T) -7 NIL NIL NIL) (-769 1655946 1656091 1656252 "OUT" NIL OUT (NIL) -7 NIL NIL NIL) (-768 1655317 1655744 1655833 "OSI" NIL OSI (NIL) -8 NIL NIL NIL) (-767 1654732 1655147 1655175 "OSGROUP" 1655180 OSGROUP (NIL) -9 NIL 1655202 NIL) (-766 1653696 1653957 1654242 "ORTHPOL" NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-765 1651029 1653571 1653691 "OREUP" NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-764 1648234 1650780 1650906 "ORESUP" NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-763 1646252 1646780 1647340 "OREPCTO" NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-762 1639656 1642134 1642174 "OREPCAT" 1644495 OREPCAT (NIL T) -9 NIL 1645597 NIL) (-761 1637682 1638616 1639651 "OREPCAT-" NIL OREPCAT- (NIL T T) -7 NIL NIL NIL) (-760 1636879 1637150 1637178 "ORDTYPE" 1637483 ORDTYPE (NIL) -9 NIL 1637641 NIL) (-759 1636413 1636624 1636874 "ORDTYPE-" NIL ORDTYPE- (NIL T) -7 NIL NIL NIL) (-758 1635875 1636251 1636408 "ORDSTRCT" NIL ORDSTRCT (NIL T NIL) -8 NIL NIL NIL) (-757 1635369 1635732 1635760 "ORDSET" 1635765 ORDSET (NIL) -9 NIL 1635787 NIL) (-756 1634009 1634969 1634997 "ORDRING" 1635002 ORDRING (NIL) -9 NIL 1635030 NIL) (-755 1633257 1633814 1633842 "ORDMON" 1633847 ORDMON (NIL) -9 NIL 1633868 NIL) (-754 1632561 1632723 1632915 "ORDFUNS" NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-753 1631772 1632280 1632308 "ORDFIN" 1632373 ORDFIN (NIL) -9 NIL 1632447 NIL) (-752 1631166 1631305 1631491 "ORDCOMP2" NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-751 1627940 1630134 1630540 "ORDCOMP" NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-750 1627347 1627702 1627807 "OPSIG" NIL OPSIG (NIL) -8 NIL NIL NIL) (-749 1627155 1627200 1627266 "OPQUERY" NIL OPQUERY (NIL) -7 NIL NIL NIL) (-748 1626456 1626732 1626773 "OPERCAT" 1626984 OPERCAT (NIL T) -9 NIL 1627080 NIL) (-747 1626268 1626335 1626451 "OPERCAT-" NIL OPERCAT- (NIL T T) -7 NIL NIL NIL) (-746 1623698 1625070 1625566 "OP" NIL OP (NIL T) -8 NIL NIL NIL) (-745 1623119 1623246 1623420 "ONECOMP2" NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-744 1620119 1622258 1622624 "ONECOMP" NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-743 1616750 1619549 1619589 "OMSAGG" 1619650 OMSAGG (NIL T) -9 NIL 1619714 NIL) (-742 1615226 1616421 1616589 "OMLO" NIL OMLO (NIL T T) -8 NIL NIL NIL) (-741 1613497 1614676 1614704 "OINTDOM" 1614709 OINTDOM (NIL) -9 NIL 1614730 NIL) (-740 1610927 1612499 1612828 "OFMONOID" NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-739 1610181 1610877 1610922 "ODVAR" NIL ODVAR (NIL T) -8 NIL NIL NIL) (-738 1607447 1610022 1610176 "ODR" NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-737 1599048 1607318 1607442 "ODPOL" NIL ODPOL (NIL T) -8 NIL NIL NIL) (-736 1592558 1598939 1599043 "ODP" NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-735 1591530 1591767 1592040 "ODETOOLS" NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-734 1589164 1589834 1590538 "ODESYS" NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-733 1584941 1585901 1586924 "ODERTRIC" NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-732 1584449 1584537 1584731 "ODERED" NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-731 1581898 1582480 1583153 "ODERAT" NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-730 1579293 1579801 1580397 "ODEPRRIC" NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-729 1576290 1576829 1577475 "ODEPRIM" NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-728 1575645 1575753 1576011 "ODEPAL" NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-727 1574803 1574928 1575149 "ODEINT" NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-726 1571087 1571883 1572796 "ODEEF" NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-725 1570527 1570622 1570844 "ODECONST" NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-724 1570208 1570257 1570384 "OCTCT2" NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-723 1566875 1570007 1570126 "OCT" NIL OCT (NIL T) -8 NIL NIL NIL) (-722 1566066 1566657 1566685 "OCAMON" 1566690 OCAMON (NIL) -9 NIL 1566711 NIL) (-721 1560342 1563092 1563132 "OC" 1564227 OC (NIL T) -9 NIL 1565083 NIL) (-720 1558342 1559268 1560248 "OC-" NIL OC- (NIL T T) -7 NIL NIL NIL) (-719 1557758 1558176 1558204 "OASGP" 1558209 OASGP (NIL) -9 NIL 1558229 NIL) (-718 1556852 1557470 1557498 "OAMONS" 1557538 OAMONS (NIL) -9 NIL 1557581 NIL) (-717 1556028 1556578 1556606 "OAMON" 1556663 OAMON (NIL) -9 NIL 1556714 NIL) (-716 1555924 1555956 1556023 "OAMON-" NIL OAMON- (NIL T) -7 NIL NIL NIL) (-715 1554706 1555449 1555477 "OAGROUP" 1555623 OAGROUP (NIL) -9 NIL 1555715 NIL) (-714 1554497 1554584 1554701 "OAGROUP-" NIL OAGROUP- (NIL T) -7 NIL NIL NIL) (-713 1554237 1554293 1554381 "NUMTUBE" NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-712 1549299 1550862 1552389 "NUMQUAD" NIL NUMQUAD (NIL) -7 NIL NIL NIL) (-711 1545994 1547028 1548063 "NUMODE" NIL NUMODE (NIL) -7 NIL NIL NIL) (-710 1545104 1545337 1545555 "NUMFMT" NIL NUMFMT (NIL) -7 NIL NIL NIL) (-709 1533965 1536993 1539441 "NUMERIC" NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-708 1527852 1533406 1533500 "NTSCAT" 1533505 NTSCAT (NIL T T T T) -9 NIL 1533543 NIL) (-707 1527193 1527372 1527565 "NTPOLFN" NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-706 1526886 1526949 1527056 "NSUP2" NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-705 1514617 1524506 1525316 "NSUP" NIL NSUP (NIL T) -8 NIL NIL NIL) (-704 1503690 1514482 1514612 "NSMP" NIL NSMP (NIL T T) -8 NIL NIL NIL) (-703 1502410 1502735 1503092 "NREP" NIL NREP (NIL T) -7 NIL NIL NIL) (-702 1501246 1501510 1501868 "NPCOEF" NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-701 1500413 1500546 1500762 "NORMRETR" NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-700 1498731 1499050 1499456 "NORMPK" NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-699 1498444 1498478 1498602 "NORMMA" NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-698 1498263 1498298 1498367 "NONE1" NIL NONE1 (NIL T) -7 NIL NIL NIL) (-697 1498039 1498229 1498258 "NONE" NIL NONE (NIL) -8 NIL NIL NIL) (-696 1497603 1497670 1497847 "NODE1" NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-695 1495921 1496966 1497221 "NNI" NIL NNI (NIL) -8 NIL NIL 1497568) (-694 1494649 1494986 1495350 "NLINSOL" NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-693 1493626 1493878 1494180 "NFINTBAS" NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-692 1492713 1493278 1493319 "NETCLT" 1493490 NETCLT (NIL T) -9 NIL 1493571 NIL) (-691 1491617 1491884 1492165 "NCODIV" NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-690 1491416 1491459 1491534 "NCNTFRAC" NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-689 1489947 1490335 1490755 "NCEP" NIL NCEP (NIL T) -7 NIL NIL NIL) (-688 1488611 1489546 1489574 "NASRING" 1489684 NASRING (NIL) -9 NIL 1489764 NIL) (-687 1488456 1488512 1488606 "NASRING-" NIL NASRING- (NIL T) -7 NIL NIL NIL) (-686 1487416 1488063 1488091 "NARNG" 1488208 NARNG (NIL) -9 NIL 1488299 NIL) (-685 1487192 1487277 1487411 "NARNG-" NIL NARNG- (NIL T) -7 NIL NIL NIL) (-684 1485989 1486712 1486752 "NAALG" 1486831 NAALG (NIL T) -9 NIL 1486892 NIL) (-683 1485859 1485894 1485984 "NAALG-" NIL NAALG- (NIL T T) -7 NIL NIL NIL) (-682 1480838 1482023 1483209 "MULTSQFR" NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-681 1480233 1480320 1480504 "MULTFACT" NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-680 1472307 1476737 1476789 "MTSCAT" 1477849 MTSCAT (NIL T T) -9 NIL 1478363 NIL) (-679 1472073 1472133 1472225 "MTHING" NIL MTHING (NIL T) -7 NIL NIL NIL) (-678 1471899 1471938 1471998 "MSYSCMD" NIL MSYSCMD (NIL) -7 NIL NIL NIL) (-677 1468761 1471450 1471491 "MSETAGG" 1471496 MSETAGG (NIL T) -9 NIL 1471530 NIL) (-676 1464898 1467807 1468125 "MSET" NIL MSET (NIL T) -8 NIL NIL NIL) (-675 1461236 1462995 1463735 "MRING" NIL MRING (NIL T T) -8 NIL NIL NIL) (-674 1460873 1460946 1461075 "MRF2" NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-673 1460526 1460567 1460711 "MRATFAC" NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-672 1458391 1458728 1459159 "MPRFF" NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-671 1451853 1458290 1458386 "MPOLY" NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-670 1451378 1451419 1451627 "MPCPF" NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-669 1450937 1450986 1451169 "MPC3" NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-668 1450211 1450304 1450523 "MPC2" NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-667 1448828 1449189 1449579 "MONOTOOL" NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-666 1448349 1448416 1448455 "MONOPC" 1448515 MONOPC (NIL T) -9 NIL 1448734 NIL) (-665 1447800 1448136 1448264 "MONOP" NIL MONOP (NIL T) -8 NIL NIL NIL) (-664 1446942 1447321 1447349 "MONOID" 1447567 MONOID (NIL) -9 NIL 1447711 NIL) (-663 1446601 1446751 1446937 "MONOID-" NIL MONOID- (NIL T) -7 NIL NIL NIL) (-662 1435601 1442409 1442468 "MONOGEN" 1443142 MONOGEN (NIL T T) -9 NIL 1443598 NIL) (-661 1433613 1434499 1435482 "MONOGEN-" NIL MONOGEN- (NIL T T T) -7 NIL NIL NIL) (-660 1432327 1432871 1432899 "MONADWU" 1433290 MONADWU (NIL) -9 NIL 1433525 NIL) (-659 1431875 1432075 1432322 "MONADWU-" NIL MONADWU- (NIL T) -7 NIL NIL NIL) (-658 1431152 1431453 1431481 "MONAD" 1431688 MONAD (NIL) -9 NIL 1431800 NIL) (-657 1430919 1431015 1431147 "MONAD-" NIL MONAD- (NIL T) -7 NIL NIL NIL) (-656 1429309 1430079 1430358 "MOEBIUS" NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-655 1428474 1428970 1429010 "MODULE" 1429015 MODULE (NIL T) -9 NIL 1429053 NIL) (-654 1428153 1428279 1428469 "MODULE-" NIL MODULE- (NIL T T) -7 NIL NIL NIL) (-653 1425928 1426750 1427064 "MODRING" NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-652 1423171 1424524 1425037 "MODOP" NIL MODOP (NIL T T) -8 NIL NIL NIL) (-651 1421805 1422379 1422655 "MODMONOM" NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-650 1411088 1420470 1420883 "MODMON" NIL MODMON (NIL T T) -8 NIL NIL NIL) (-649 1408108 1410088 1410357 "MODFIELD" NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-648 1407192 1407559 1407749 "MMLFORM" NIL MMLFORM (NIL) -8 NIL NIL NIL) (-647 1406761 1406810 1406989 "MMAP" NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-646 1404648 1405582 1405622 "MLO" 1406039 MLO (NIL T) -9 NIL 1406279 NIL) (-645 1402529 1403056 1403651 "MLIFT" NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-644 1401997 1402093 1402247 "MKUCFUNC" NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-643 1401667 1401743 1401866 "MKRECORD" NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-642 1400879 1401065 1401293 "MKFUNC" NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-641 1400372 1400488 1400644 "MKFLCFN" NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-640 1399744 1399858 1400043 "MKBCFUNC" NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-639 1398771 1399044 1399321 "MHROWRED" NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-638 1398204 1398292 1398463 "MFINFACT" NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-637 1395362 1396241 1397120 "MESH" NIL MESH (NIL) -7 NIL NIL NIL) (-636 1394029 1394377 1394730 "MDDFACT" NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-635 1390686 1393153 1393194 "MDAGG" 1393451 MDAGG (NIL T) -9 NIL 1393596 NIL) (-634 1389960 1390124 1390324 "MCDEN" NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-633 1389038 1389324 1389554 "MAYBE" NIL MAYBE (NIL T) -8 NIL NIL NIL) (-632 1387135 1387712 1388273 "MATSTOR" NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-631 1382906 1386725 1386972 "MATRIX" NIL MATRIX (NIL T) -8 NIL NIL NIL) (-630 1379255 1380024 1380758 "MATLIN" NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-629 1378008 1378177 1378506 "MATCAT2" NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-628 1367521 1371110 1371186 "MATCAT" 1376174 MATCAT (NIL T T T) -9 NIL 1377642 NIL) (-627 1364802 1366108 1367516 "MATCAT-" NIL MATCAT- (NIL T T T T) -7 NIL NIL NIL) (-626 1363203 1363563 1363947 "MAPPKG3" NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-625 1362336 1362533 1362755 "MAPPKG2" NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-624 1361087 1361413 1361740 "MAPPKG1" NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-623 1360249 1360651 1360827 "MAPPAST" NIL MAPPAST (NIL) -8 NIL NIL NIL) (-622 1359918 1359982 1360105 "MAPHACK3" NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-621 1359566 1359639 1359753 "MAPHACK2" NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-620 1359101 1359216 1359358 "MAPHACK1" NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-619 1357310 1358078 1358379 "MAGMA" NIL MAGMA (NIL T) -8 NIL NIL NIL) (-618 1356804 1357106 1357196 "MACROAST" NIL MACROAST (NIL) -8 NIL NIL NIL) (-617 1350313 1355119 1355160 "LZSTAGG" 1355937 LZSTAGG (NIL T) -9 NIL 1356227 NIL) (-616 1347432 1348866 1350308 "LZSTAGG-" NIL LZSTAGG- (NIL T T) -7 NIL NIL NIL) (-615 1344819 1345785 1346268 "LWORD" NIL LWORD (NIL T) -8 NIL NIL NIL) (-614 1344400 1344679 1344753 "LSTAST" NIL LSTAST (NIL) -8 NIL NIL NIL) (-613 1336628 1344261 1344395 "LSQM" NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-612 1335991 1336136 1336364 "LSPP" NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-611 1333475 1334173 1334885 "LSMP1" NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-610 1331587 1331910 1332358 "LSMP" NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-609 1324756 1330674 1330715 "LSAGG" 1330777 LSAGG (NIL T) -9 NIL 1330855 NIL) (-608 1322450 1323549 1324751 "LSAGG-" NIL LSAGG- (NIL T T) -7 NIL NIL NIL) (-607 1319962 1321799 1322048 "LPOLY" NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-606 1319629 1319720 1319843 "LPEFRAC" NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-605 1319300 1319379 1319407 "LOGIC" 1319518 LOGIC (NIL) -9 NIL 1319600 NIL) (-604 1319195 1319224 1319295 "LOGIC-" NIL LOGIC- (NIL T) -7 NIL NIL NIL) (-603 1318514 1318672 1318865 "LODOOPS" NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-602 1317299 1317548 1317899 "LODOF" NIL LODOF (NIL T T) -7 NIL NIL NIL) (-601 1313185 1315920 1315960 "LODOCAT" 1316392 LODOCAT (NIL T) -9 NIL 1316603 NIL) (-600 1312978 1313054 1313180 "LODOCAT-" NIL LODOCAT- (NIL T T) -7 NIL NIL NIL) (-599 1310042 1312855 1312973 "LODO2" NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-598 1307204 1309992 1310037 "LODO1" NIL LODO1 (NIL T) -8 NIL NIL NIL) (-597 1304355 1307134 1307199 "LODO" NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-596 1303408 1303583 1303885 "LODEEF" NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-595 1301572 1302670 1302923 "LO" NIL LO (NIL T T T) -8 NIL NIL NIL) (-594 1296667 1299731 1299772 "LNAGG" 1300634 LNAGG (NIL T) -9 NIL 1301069 NIL) (-593 1296054 1296321 1296662 "LNAGG-" NIL LNAGG- (NIL T T) -7 NIL NIL NIL) (-592 1292626 1293567 1294204 "LMOPS" NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-591 1291919 1292393 1292433 "LMODULE" 1292438 LMODULE (NIL T) -9 NIL 1292464 NIL) (-590 1289098 1291656 1291778 "LMDICT" NIL LMDICT (NIL T) -8 NIL NIL NIL) (-589 1288666 1288877 1288918 "LLINSET" 1288979 LLINSET (NIL T) -9 NIL 1289023 NIL) (-588 1288342 1288602 1288661 "LITERAL" NIL LITERAL (NIL T) -8 NIL NIL NIL) (-587 1287941 1288021 1288160 "LIST3" NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-586 1286392 1286740 1287139 "LIST2MAP" NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-585 1285563 1285759 1285987 "LIST2" NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-584 1278609 1284819 1285073 "LIST" NIL LIST (NIL T) -8 NIL NIL NIL) (-583 1278186 1278419 1278460 "LINSET" 1278465 LINSET (NIL T) -9 NIL 1278498 NIL) (-582 1277119 1277809 1277976 "LINFORM" NIL LINFORM (NIL T NIL) -8 NIL NIL NIL) (-581 1275416 1276140 1276180 "LINEXP" 1276666 LINEXP (NIL T) -9 NIL 1276939 NIL) (-580 1274070 1275025 1275206 "LINELT" NIL LINELT (NIL T NIL) -8 NIL NIL NIL) (-579 1272897 1273169 1273471 "LINDEP" NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-578 1272110 1272699 1272809 "LINBASIS" NIL LINBASIS (NIL NIL) -8 NIL NIL NIL) (-577 1269660 1270382 1271132 "LIMITRF" NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-576 1268290 1268587 1268978 "LIMITPS" NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-575 1267114 1267685 1267725 "LIECAT" 1267865 LIECAT (NIL T) -9 NIL 1268016 NIL) (-574 1266988 1267021 1267109 "LIECAT-" NIL LIECAT- (NIL T T) -7 NIL NIL NIL) (-573 1261276 1266678 1266906 "LIE" NIL LIE (NIL T T) -8 NIL NIL NIL) (-572 1253625 1260952 1261108 "LIB" NIL LIB (NIL) -8 NIL NIL NIL) (-571 1250077 1251026 1251961 "LGROBP" NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-570 1248701 1249609 1249637 "LFCAT" 1249844 LFCAT (NIL) -9 NIL 1249983 NIL) (-569 1246940 1247270 1247615 "LF" NIL LF (NIL T T) -7 NIL NIL NIL) (-568 1244457 1245122 1245803 "LEXTRIPK" NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-567 1241469 1242447 1242950 "LEXP" NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-566 1240960 1241263 1241354 "LETAST" NIL LETAST (NIL) -8 NIL NIL NIL) (-565 1239667 1239991 1240391 "LEADCDET" NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-564 1238933 1239018 1239244 "LAZM3PK" NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-563 1234000 1237501 1238037 "LAUPOL" NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-562 1233625 1233675 1233835 "LAPLACE" NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-561 1232458 1233169 1233209 "LALG" 1233270 LALG (NIL T) -9 NIL 1233328 NIL) (-560 1232241 1232318 1232453 "LALG-" NIL LALG- (NIL T T) -7 NIL NIL NIL) (-559 1230158 1231509 1231760 "LA" NIL LA (NIL T T T) -8 NIL NIL NIL) (-558 1229987 1230017 1230058 "KVTFROM" 1230120 KVTFROM (NIL T) -9 NIL NIL NIL) (-557 1228803 1229518 1229707 "KTVLOGIC" NIL KTVLOGIC (NIL) -8 NIL NIL NIL) (-556 1228632 1228662 1228703 "KRCFROM" 1228765 KRCFROM (NIL T) -9 NIL NIL NIL) (-555 1227734 1227931 1228226 "KOVACIC" NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-554 1227563 1227593 1227634 "KONVERT" 1227696 KONVERT (NIL T) -9 NIL NIL NIL) (-553 1227392 1227422 1227463 "KOERCE" 1227525 KOERCE (NIL T) -9 NIL NIL NIL) (-552 1226962 1227055 1227187 "KERNEL2" NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-551 1225015 1225909 1226281 "KERNEL" NIL KERNEL (NIL T) -8 NIL NIL NIL) (-550 1218192 1223207 1223261 "KDAGG" 1223637 KDAGG (NIL T T) -9 NIL 1223844 NIL) (-549 1217840 1217982 1218187 "KDAGG-" NIL KDAGG- (NIL T T T) -7 NIL NIL NIL) (-548 1210670 1217621 1217778 "KAFILE" NIL KAFILE (NIL T) -8 NIL NIL NIL) (-547 1210320 1210602 1210665 "JVMOP" NIL JVMOP (NIL) -8 NIL NIL NIL) (-546 1209290 1209789 1210038 "JVMMDACC" NIL JVMMDACC (NIL) -8 NIL NIL NIL) (-545 1208416 1208865 1209070 "JVMFDACC" NIL JVMFDACC (NIL) -8 NIL NIL NIL) (-544 1207280 1207772 1208072 "JVMCSTTG" NIL JVMCSTTG (NIL) -8 NIL NIL NIL) (-543 1206562 1206961 1207122 "JVMCFACC" NIL JVMCFACC (NIL) -8 NIL NIL NIL) (-542 1206272 1206508 1206557 "JVMBCODE" NIL JVMBCODE (NIL) -8 NIL NIL NIL) (-541 1200559 1205962 1206190 "JORDAN" NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-540 1199977 1200310 1200430 "JOINAST" NIL JOINAST (NIL) -8 NIL NIL NIL) (-539 1196139 1198154 1198208 "IXAGG" 1199135 IXAGG (NIL T T) -9 NIL 1199592 NIL) (-538 1195345 1195716 1196134 "IXAGG-" NIL IXAGG- (NIL T T T) -7 NIL NIL NIL) (-537 1190599 1195281 1195340 "IVECTOR" NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-536 1189566 1189841 1190104 "ITUPLE" NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-535 1188228 1188435 1188728 "ITRIGMNP" NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-534 1187179 1187401 1187684 "ITFUN3" NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-533 1186854 1186917 1187040 "ITFUN2" NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-532 1186116 1186488 1186662 "ITFORM" NIL ITFORM (NIL) -8 NIL NIL NIL) (-531 1184156 1185392 1185666 "ITAYLOR" NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-530 1173768 1179473 1180630 "ISUPS" NIL ISUPS (NIL T) -8 NIL NIL NIL) (-529 1173013 1173165 1173401 "ISUMP" NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-528 1172504 1172807 1172898 "ISAST" NIL ISAST (NIL) -8 NIL NIL NIL) (-527 1171797 1171888 1172101 "IRURPK" NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-526 1170929 1171154 1171394 "IRSN" NIL IRSN (NIL) -7 NIL NIL NIL) (-525 1169342 1169723 1170151 "IRRF2F" NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-524 1169127 1169171 1169247 "IRREDFFX" NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-523 1167977 1168274 1168569 "IROOT" NIL IROOT (NIL T) -7 NIL NIL NIL) (-522 1167250 1167601 1167752 "IRFORM" NIL IRFORM (NIL) -8 NIL NIL NIL) (-521 1166453 1166584 1166797 "IR2F" NIL IR2F (NIL T T) -7 NIL NIL NIL) (-520 1164608 1165105 1165649 "IR2" NIL IR2 (NIL T T) -7 NIL NIL NIL) (-519 1161721 1162957 1163646 "IR" NIL IR (NIL T) -8 NIL NIL NIL) (-518 1161546 1161586 1161646 "IPRNTPK" NIL IPRNTPK (NIL) -7 NIL NIL NIL) (-517 1157608 1161472 1161541 "IPF" NIL IPF (NIL NIL) -8 NIL NIL NIL) (-516 1155675 1157547 1157603 "IPADIC" NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-515 1155046 1155345 1155475 "IP4ADDR" NIL IP4ADDR (NIL) -8 NIL NIL NIL) (-514 1154499 1154787 1154919 "IOMODE" NIL IOMODE (NIL) -8 NIL NIL NIL) (-513 1153580 1154205 1154331 "IOBFILE" NIL IOBFILE (NIL) -8 NIL NIL NIL) (-512 1152990 1153484 1153512 "IOBCON" 1153517 IOBCON (NIL) -9 NIL 1153538 NIL) (-511 1152561 1152625 1152807 "INVLAPLA" NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-510 1144605 1146976 1149301 "INTTR" NIL INTTR (NIL T T) -7 NIL NIL NIL) (-509 1141716 1142499 1143363 "INTTOOLS" NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-508 1141393 1141490 1141607 "INTSLPE" NIL INTSLPE (NIL) -7 NIL NIL NIL) (-507 1138899 1141329 1141388 "INTRVL" NIL INTRVL (NIL T) -8 NIL NIL NIL) (-506 1137011 1137540 1138107 "INTRF" NIL INTRF (NIL T) -7 NIL NIL NIL) (-505 1136513 1136627 1136767 "INTRET" NIL INTRET (NIL T) -7 NIL NIL NIL) (-504 1134897 1135303 1135765 "INTRAT" NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-503 1132676 1133270 1133881 "INTPM" NIL INTPM (NIL T T) -7 NIL NIL NIL) (-502 1130049 1130659 1131379 "INTPAF" NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-501 1129453 1129611 1129819 "INTHERTR" NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-500 1128972 1129058 1129246 "INTHERAL" NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-499 1127177 1127698 1128155 "INTHEORY" NIL INTHEORY (NIL) -7 NIL NIL NIL) (-498 1120259 1121912 1123641 "INTG0" NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-497 1119625 1119787 1119960 "INTFACT" NIL INTFACT (NIL T) -7 NIL NIL NIL) (-496 1117498 1117962 1118506 "INTEF" NIL INTEF (NIL T T) -7 NIL NIL NIL) (-495 1115686 1116574 1116602 "INTDOM" 1116901 INTDOM (NIL) -9 NIL 1117106 NIL) (-494 1115239 1115441 1115681 "INTDOM-" NIL INTDOM- (NIL T) -7 NIL NIL NIL) (-493 1111110 1113518 1113572 "INTCAT" 1114368 INTCAT (NIL T) -9 NIL 1114684 NIL) (-492 1110675 1110795 1110922 "INTBIT" NIL INTBIT (NIL) -7 NIL NIL NIL) (-491 1109515 1109687 1109993 "INTALG" NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-490 1109088 1109184 1109341 "INTAF" NIL INTAF (NIL T T) -7 NIL NIL NIL) (-489 1102128 1108943 1109083 "INTABL" NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-488 1101426 1101981 1102046 "INT8" NIL INT8 (NIL) -8 NIL NIL 1102080) (-487 1100723 1101278 1101343 "INT64" NIL INT64 (NIL) -8 NIL NIL 1101377) (-486 1100020 1100575 1100640 "INT32" NIL INT32 (NIL) -8 NIL NIL 1100674) (-485 1099317 1099872 1099937 "INT16" NIL INT16 (NIL) -8 NIL NIL 1099971) (-484 1095844 1099236 1099312 "INT" NIL INT (NIL) -8 NIL NIL NIL) (-483 1089965 1093384 1093412 "INS" 1094342 INS (NIL) -9 NIL 1095001 NIL) (-482 1088027 1088945 1089892 "INS-" NIL INS- (NIL T) -7 NIL NIL NIL) (-481 1087086 1087309 1087584 "INPSIGN" NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-480 1086300 1086441 1086638 "INPRODPF" NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-479 1085290 1085431 1085668 "INPRODFF" NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-478 1084442 1084606 1084866 "INNMFACT" NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-477 1083722 1083837 1084025 "INMODGCD" NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-476 1082461 1082730 1083054 "INFSP" NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-475 1081741 1081882 1082065 "INFPROD0" NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-474 1081404 1081476 1081574 "INFORM1" NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-473 1078482 1079968 1080491 "INFORM" NIL INFORM (NIL) -8 NIL NIL NIL) (-472 1078081 1078188 1078302 "INFINITY" NIL INFINITY (NIL) -7 NIL NIL NIL) (-471 1077237 1077882 1077983 "INETCLTS" NIL INETCLTS (NIL) -8 NIL NIL NIL) (-470 1076087 1076355 1076676 "INEP" NIL INEP (NIL T T T) -7 NIL NIL NIL) (-469 1075109 1076017 1076082 "INDE" NIL INDE (NIL T) -8 NIL NIL NIL) (-468 1074734 1074814 1074931 "INCRMAPS" NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-467 1073648 1074193 1074397 "INBFILE" NIL INBFILE (NIL) -8 NIL NIL NIL) (-466 1069743 1070798 1071741 "INBFF" NIL INBFF (NIL T) -7 NIL NIL NIL) (-465 1068597 1068920 1068948 "INBCON" 1069461 INBCON (NIL) -9 NIL 1069727 NIL) (-464 1068051 1068316 1068592 "INBCON-" NIL INBCON- (NIL T) -7 NIL NIL NIL) (-463 1067545 1067847 1067937 "INAST" NIL INAST (NIL) -8 NIL NIL NIL) (-462 1067002 1067311 1067416 "IMPTAST" NIL IMPTAST (NIL) -8 NIL NIL NIL) (-461 1063102 1066894 1066997 "IMATRIX" NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-460 1061942 1062081 1062396 "IMATQF" NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-459 1060366 1060633 1060970 "IMATLIN" NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-458 1058182 1060248 1060361 "IIARRAY2" NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-457 1053089 1058113 1058177 "IFF" NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-456 1052469 1052803 1052918 "IFAST" NIL IFAST (NIL) -8 NIL NIL NIL) (-455 1047276 1051907 1052093 "IFARRAY" NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-454 1046338 1047198 1047271 "IFAMON" NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-453 1045910 1045987 1046041 "IEVALAB" 1046248 IEVALAB (NIL T T) -9 NIL NIL NIL) (-452 1045665 1045745 1045905 "IEVALAB-" NIL IEVALAB- (NIL T T T) -7 NIL NIL NIL) (-451 1045050 1045277 1045434 "IDPT" NIL IDPT (NIL T T) -8 NIL NIL NIL) (-450 1044075 1044970 1045045 "IDPOAMS" NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-449 1043169 1043995 1044070 "IDPOAM" NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-448 1042251 1042898 1043035 "IDPO" NIL IDPO (NIL T T) -8 NIL NIL NIL) (-447 1040614 1041185 1041236 "IDPC" 1041742 IDPC (NIL T T) -9 NIL 1042055 NIL) (-446 1039933 1040536 1040609 "IDPAM" NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-445 1039135 1039855 1039928 "IDPAG" NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-444 1038828 1039041 1039101 "IDENT" NIL IDENT (NIL) -8 NIL NIL NIL) (-443 1038532 1038572 1038611 "IDEMOPC" 1038616 IDEMOPC (NIL T) -9 NIL 1038753 NIL) (-442 1035603 1036484 1037376 "IDECOMP" NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-441 1029229 1030506 1031545 "IDEAL" NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-440 1028491 1028621 1028820 "ICDEN" NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-439 1027664 1028163 1028301 "ICARD" NIL ICARD (NIL) -8 NIL NIL NIL) (-438 1026053 1026384 1026775 "IBPTOOLS" NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-437 1021822 1026009 1026048 "IBITS" NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-436 1019080 1019704 1020399 "IBATOOL" NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-435 1017306 1017786 1018319 "IBACHIN" NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-434 1015070 1017198 1017301 "IARRAY2" NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-433 1010939 1015008 1015065 "IARRAY1" NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-432 1004582 1009903 1010371 "IAN" NIL IAN (NIL) -8 NIL NIL NIL) (-431 1004150 1004213 1004386 "IALGFACT" NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-430 1003642 1003791 1003819 "HYPCAT" 1004026 HYPCAT (NIL) -9 NIL NIL NIL) (-429 1003298 1003451 1003637 "HYPCAT-" NIL HYPCAT- (NIL T) -7 NIL NIL NIL) (-428 1002911 1003156 1003239 "HOSTNAME" NIL HOSTNAME (NIL) -8 NIL NIL NIL) (-427 1002744 1002793 1002834 "HOMOTOP" 1002839 HOMOTOP (NIL T) -9 NIL 1002872 NIL) (-426 999312 1000686 1000727 "HOAGG" 1001702 HOAGG (NIL T) -9 NIL 1002423 NIL) (-425 998318 998788 999307 "HOAGG-" NIL HOAGG- (NIL T T) -7 NIL NIL NIL) (-424 991582 998043 998191 "HEXADEC" NIL HEXADEC (NIL) -8 NIL NIL NIL) (-423 990517 990775 991038 "HEUGCD" NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-422 989484 990382 990512 "HELLFDIV" NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-421 987678 989317 989405 "HEAP" NIL HEAP (NIL T) -8 NIL NIL NIL) (-420 986993 987345 987478 "HEADAST" NIL HEADAST (NIL) -8 NIL NIL NIL) (-419 980546 986926 986988 "HDP" NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-418 973749 980282 980433 "HDMP" NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-417 973202 973359 973522 "HB" NIL HB (NIL) -7 NIL NIL NIL) (-416 966285 973093 973197 "HASHTBL" NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-415 965776 966079 966170 "HASAST" NIL HASAST (NIL) -8 NIL NIL NIL) (-414 963390 965563 965742 "HACKPI" NIL HACKPI (NIL) -8 NIL NIL NIL) (-413 958783 963273 963385 "GTSET" NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-412 951869 958680 958778 "GSTBL" NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-411 943870 951238 951493 "GSERIES" NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-410 942894 943403 943431 "GROUP" 943634 GROUP (NIL) -9 NIL 943768 NIL) (-409 942437 942638 942889 "GROUP-" NIL GROUP- (NIL T) -7 NIL NIL NIL) (-408 941109 941448 941835 "GROEBSOL" NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-407 939931 940288 940339 "GRMOD" 940868 GRMOD (NIL T T) -9 NIL 941034 NIL) (-406 939750 939798 939926 "GRMOD-" NIL GRMOD- (NIL T T T) -7 NIL NIL NIL) (-405 935873 937084 938084 "GRIMAGE" NIL GRIMAGE (NIL) -8 NIL NIL NIL) (-404 934595 934919 935234 "GRDEF" NIL GRDEF (NIL) -7 NIL NIL NIL) (-403 934148 934276 934417 "GRAY" NIL GRAY (NIL) -7 NIL NIL NIL) (-402 933221 933720 933771 "GRALG" 933924 GRALG (NIL T T) -9 NIL 934014 NIL) (-401 932940 933041 933216 "GRALG-" NIL GRALG- (NIL T T T) -7 NIL NIL NIL) (-400 929657 932622 932798 "GPOLSET" NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-399 929070 929133 929390 "GOSPER" NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-398 924956 925820 926345 "GMODPOL" NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-397 924131 924333 924571 "GHENSEL" NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-396 919134 920061 921080 "GENUPS" NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-395 918882 918939 919028 "GENUFACT" NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-394 918364 918453 918618 "GENPGCD" NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-393 917873 917914 918127 "GENMFACT" NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-392 916674 916957 917261 "GENEEZ" NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-391 910013 916364 916525 "GDMP" NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-390 899828 904803 905907 "GCNAALG" NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-389 897942 898983 899011 "GCDDOM" 899266 GCDDOM (NIL) -9 NIL 899423 NIL) (-388 897565 897722 897937 "GCDDOM-" NIL GCDDOM- (NIL T) -7 NIL NIL NIL) (-387 888358 890828 893216 "GBINTERN" NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-386 886493 886818 887236 "GBF" NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-385 885434 885623 885890 "GBEUCLID" NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-384 884305 884512 884816 "GB" NIL GB (NIL T T T T) -7 NIL NIL NIL) (-383 883768 883910 884058 "GAUSSFAC" NIL GAUSSFAC (NIL) -7 NIL NIL NIL) (-382 882380 882728 883041 "GALUTIL" NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-381 880925 881246 881568 "GALPOLYU" NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-380 878551 878907 879312 "GALFACTU" NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-379 871803 873464 875042 "GALFACT" NIL GALFACT (NIL T) -7 NIL NIL NIL) (-378 871455 871676 871744 "FUNDESC" NIL FUNDESC (NIL) -8 NIL NIL NIL) (-377 871079 871300 871381 "FUNCTION" NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-376 869176 869859 870319 "FT" NIL FT (NIL) -8 NIL NIL NIL) (-375 867769 868076 868468 "FSUPFACT" NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-374 866424 866783 867107 "FST" NIL FST (NIL) -8 NIL NIL NIL) (-373 865727 865851 866038 "FSRED" NIL FSRED (NIL T T) -7 NIL NIL NIL) (-372 864701 864967 865314 "FSPRMELT" NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-371 862359 862889 863371 "FSPECF" NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-370 861942 862002 862171 "FSINT" NIL FSINT (NIL T T) -7 NIL NIL NIL) (-369 860306 861156 861459 "FSERIES" NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-368 859454 859588 859811 "FSCINT" NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-367 858625 858786 859013 "FSAGG2" NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-366 854608 857559 857600 "FSAGG" 857970 FSAGG (NIL T) -9 NIL 858229 NIL) (-365 852962 853721 854513 "FSAGG-" NIL FSAGG- (NIL T T) -7 NIL NIL NIL) (-364 850918 851214 851758 "FS2UPS" NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-363 849965 850147 850447 "FS2EXPXP" NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-362 849646 849695 849822 "FS2" NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-361 829901 839303 839344 "FS" 843214 FS (NIL T) -9 NIL 845492 NIL) (-360 822132 825625 829604 "FS-" NIL FS- (NIL T T) -7 NIL NIL NIL) (-359 821666 821793 821945 "FRUTIL" NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-358 816220 819347 819387 "FRNAALG" 820707 FRNAALG (NIL T) -9 NIL 821305 NIL) (-357 812961 814212 815470 "FRNAALG-" NIL FRNAALG- (NIL T T) -7 NIL NIL NIL) (-356 812642 812691 812818 "FRNAAF2" NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-355 811129 811686 811980 "FRMOD" NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-354 810415 810508 810795 "FRIDEAL2" NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-353 808249 809015 809331 "FRIDEAL" NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-352 807358 807801 807842 "FRETRCT" 807847 FRETRCT (NIL T) -9 NIL 808018 NIL) (-351 806731 807009 807353 "FRETRCT-" NIL FRETRCT- (NIL T T) -7 NIL NIL NIL) (-350 803537 804995 805054 "FRAMALG" 805936 FRAMALG (NIL T T) -9 NIL 806228 NIL) (-349 802133 802684 803314 "FRAMALG-" NIL FRAMALG- (NIL T T T) -7 NIL NIL NIL) (-348 801826 801889 801996 "FRAC2" NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-347 795531 801631 801821 "FRAC" NIL FRAC (NIL T) -8 NIL NIL NIL) (-346 795224 795287 795394 "FR2" NIL FR2 (NIL T T) -7 NIL NIL NIL) (-345 787596 792103 793431 "FR" NIL FR (NIL T) -8 NIL NIL NIL) (-344 781436 784877 784905 "FPS" 786024 FPS (NIL) -9 NIL 786580 NIL) (-343 780993 781126 781290 "FPS-" NIL FPS- (NIL T) -7 NIL NIL NIL) (-342 777866 779846 779874 "FPC" 780099 FPC (NIL) -9 NIL 780241 NIL) (-341 777712 777764 777861 "FPC-" NIL FPC- (NIL T) -7 NIL NIL NIL) (-340 776489 777198 777239 "FPATMAB" 777244 FPATMAB (NIL T) -9 NIL 777396 NIL) (-339 774919 775515 775862 "FPARFRAC" NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-338 774494 774552 774725 "FORDER" NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-337 773029 773892 774066 "FNLA" NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-336 771644 772149 772177 "FNCAT" 772634 FNCAT (NIL) -9 NIL 772891 NIL) (-335 771101 771611 771639 "FNAME" NIL FNAME (NIL) -8 NIL NIL NIL) (-334 769688 771050 771096 "FMONOID" NIL FMONOID (NIL T) -8 NIL NIL NIL) (-333 766276 767634 767675 "FMONCAT" 768892 FMONCAT (NIL T) -9 NIL 769496 NIL) (-332 763165 764212 764265 "FMCAT" 765446 FMCAT (NIL T T) -9 NIL 765938 NIL) (-331 761897 762988 763087 "FM1" NIL FM1 (NIL T T) -8 NIL NIL NIL) (-330 760977 761745 761892 "FM" NIL FM (NIL T T) -8 NIL NIL NIL) (-329 759164 759616 760110 "FLOATRP" NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-328 757099 757635 758213 "FLOATCP" NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-327 750549 755436 756050 "FLOAT" NIL FLOAT (NIL) -8 NIL NIL NIL) (-326 749061 750131 750171 "FLINEXP" 750176 FLINEXP (NIL T) -9 NIL 750269 NIL) (-325 748470 748729 749056 "FLINEXP-" NIL FLINEXP- (NIL T T) -7 NIL NIL NIL) (-324 747685 747844 748065 "FLASORT" NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-323 744599 745647 745699 "FLALG" 746926 FLALG (NIL T T) -9 NIL 747393 NIL) (-322 743770 743931 744158 "FLAGG2" NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-321 737179 741189 741230 "FLAGG" 742485 FLAGG (NIL T) -9 NIL 743130 NIL) (-320 736287 736691 737174 "FLAGG-" NIL FLAGG- (NIL T T) -7 NIL NIL NIL) (-319 732910 734112 734171 "FINRALG" 735299 FINRALG (NIL T T) -9 NIL 735807 NIL) (-318 732301 732566 732905 "FINRALG-" NIL FINRALG- (NIL T T T) -7 NIL NIL NIL) (-317 731599 731895 731923 "FINITE" 732119 FINITE (NIL) -9 NIL 732226 NIL) (-316 731507 731533 731594 "FINITE-" NIL FINITE- (NIL T) -7 NIL NIL NIL) (-315 723499 726059 726099 "FINAALG" 729751 FINAALG (NIL T) -9 NIL 731189 NIL) (-314 719766 721011 722134 "FINAALG-" NIL FINAALG- (NIL T T) -7 NIL NIL NIL) (-313 718318 718737 718791 "FILECAT" 719475 FILECAT (NIL T T) -9 NIL 719691 NIL) (-312 717669 718143 718246 "FILE" NIL FILE (NIL T) -8 NIL NIL NIL) (-311 714979 716795 716823 "FIELD" 716863 FIELD (NIL) -9 NIL 716943 NIL) (-310 714004 714465 714974 "FIELD-" NIL FIELD- (NIL T) -7 NIL NIL NIL) (-309 712008 712954 713300 "FGROUP" NIL FGROUP (NIL T) -8 NIL NIL NIL) (-308 711251 711432 711651 "FGLMICPK" NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-307 706585 711189 711246 "FFX" NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-306 706247 706314 706449 "FFSLPE" NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-305 705787 705829 706038 "FFPOLY2" NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-304 702467 703344 704121 "FFPOLY" NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-303 697815 702399 702462 "FFP" NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-302 692558 697304 697494 "FFNBX" NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-301 687103 691839 692097 "FFNBP" NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-300 681374 686554 686765 "FFNB" NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-299 680397 680607 680922 "FFINTBAS" NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-298 675900 678542 678570 "FFIELDC" 679189 FFIELDC (NIL) -9 NIL 679564 NIL) (-297 674969 675409 675895 "FFIELDC-" NIL FFIELDC- (NIL T) -7 NIL NIL NIL) (-296 674584 674642 674766 "FFHOM" NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-295 672728 673251 673768 "FFF" NIL FFF (NIL T) -7 NIL NIL NIL) (-294 667886 672527 672628 "FFCGX" NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-293 663050 667675 667782 "FFCGP" NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-292 657780 662841 662949 "FFCG" NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-291 657234 657283 657518 "FFCAT2" NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-290 635871 646843 646929 "FFCAT" 652079 FFCAT (NIL T T T) -9 NIL 653515 NIL) (-289 632111 633337 634643 "FFCAT-" NIL FFCAT- (NIL T T T T) -7 NIL NIL NIL) (-288 627018 632042 632106 "FF" NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-287 625910 626379 626420 "FEVALAB" 626504 FEVALAB (NIL T) -9 NIL 626765 NIL) (-286 625315 625567 625905 "FEVALAB-" NIL FEVALAB- (NIL T T) -7 NIL NIL NIL) (-285 622173 623053 623168 "FDIVCAT" 624735 FDIVCAT (NIL T T T T) -9 NIL 625171 NIL) (-284 621967 621999 622168 "FDIVCAT-" NIL FDIVCAT- (NIL T T T T T) -7 NIL NIL NIL) (-283 621274 621367 621644 "FDIV2" NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-282 619792 620758 620961 "FDIV" NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-281 618885 619269 619471 "FCTRDATA" NIL FCTRDATA (NIL) -8 NIL NIL NIL) (-280 618007 618496 618636 "FCOMP" NIL FCOMP (NIL T) -8 NIL NIL NIL) (-279 609656 614237 614277 "FAXF" 616078 FAXF (NIL T) -9 NIL 616768 NIL) (-278 607572 608376 609191 "FAXF-" NIL FAXF- (NIL T T) -7 NIL NIL NIL) (-277 602436 607094 607268 "FARRAY" NIL FARRAY (NIL T) -8 NIL NIL NIL) (-276 596958 599317 599369 "FAMR" 600380 FAMR (NIL T T) -9 NIL 600839 NIL) (-275 596157 596522 596953 "FAMR-" NIL FAMR- (NIL T T T) -7 NIL NIL NIL) (-274 595210 596099 596152 "FAMONOID" NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-273 592835 593683 593736 "FAMONC" 594677 FAMONC (NIL T T) -9 NIL 595062 NIL) (-272 591423 592693 592830 "FAGROUP" NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-271 589503 589864 590266 "FACUTIL" NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-270 588780 588977 589199 "FACTFUNC" NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-269 580704 588227 588426 "EXPUPXS" NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-268 578723 579293 579879 "EXPRTUBE" NIL EXPRTUBE (NIL) -7 NIL NIL NIL) (-267 575625 576267 576987 "EXPRODE" NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-266 570782 571489 572294 "EXPR2UPS" NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-265 570471 570534 570643 "EXPR2" NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-264 555421 569520 569946 "EXPR" NIL EXPR (NIL T) -8 NIL NIL NIL) (-263 546012 554741 555029 "EXPEXPAN" NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-262 545506 545808 545898 "EXITAST" NIL EXITAST (NIL) -8 NIL NIL NIL) (-261 545282 545472 545501 "EXIT" NIL EXIT (NIL) -8 NIL NIL NIL) (-260 544971 545039 545152 "EVALCYC" NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-259 544488 544630 544671 "EVALAB" 544841 EVALAB (NIL T) -9 NIL 544945 NIL) (-258 544116 544262 544483 "EVALAB-" NIL EVALAB- (NIL T T) -7 NIL NIL NIL) (-257 541221 542754 542782 "EUCDOM" 543336 EUCDOM (NIL) -9 NIL 543685 NIL) (-256 540148 540641 541216 "EUCDOM-" NIL EUCDOM- (NIL T) -7 NIL NIL NIL) (-255 539873 539929 540029 "ES2" NIL ES2 (NIL T T) -7 NIL NIL NIL) (-254 539561 539625 539734 "ES1" NIL ES1 (NIL T T) -7 NIL NIL NIL) (-253 533332 535232 535260 "ES" 538002 ES (NIL) -9 NIL 539386 NIL) (-252 529847 531379 533171 "ES-" NIL ES- (NIL T) -7 NIL NIL NIL) (-251 529195 529348 529524 "ERROR" NIL ERROR (NIL) -7 NIL NIL NIL) (-250 522284 529099 529190 "EQTBL" NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-249 521973 522036 522145 "EQ2" NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-248 515699 518725 520158 "EQ" NIL EQ (NIL T) -8 NIL NIL NIL) (-247 512002 513098 514191 "EP" NIL EP (NIL T) -7 NIL NIL NIL) (-246 510831 511181 511486 "ENV" NIL ENV (NIL) -8 NIL NIL NIL) (-245 509778 510447 510475 "ENTIRER" 510480 ENTIRER (NIL) -9 NIL 510524 NIL) (-244 506475 508208 508557 "EMR" NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-243 505567 505778 505832 "ELTAGG" 506212 ELTAGG (NIL T T) -9 NIL 506423 NIL) (-242 505347 505421 505562 "ELTAGG-" NIL ELTAGG- (NIL T T T) -7 NIL NIL NIL) (-241 505093 505128 505182 "ELTAB" 505266 ELTAB (NIL T T) -9 NIL 505318 NIL) (-240 504344 504514 504713 "ELFUTS" NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-239 504068 504142 504170 "ELEMFUN" 504275 ELEMFUN (NIL) -9 NIL NIL NIL) (-238 503968 503995 504063 "ELEMFUN-" NIL ELEMFUN- (NIL T) -7 NIL NIL NIL) (-237 498514 502009 502050 "ELAGG" 502987 ELAGG (NIL T) -9 NIL 503447 NIL) (-236 497312 497850 498509 "ELAGG-" NIL ELAGG- (NIL T T) -7 NIL NIL NIL) (-235 496730 496897 497053 "ELABOR" NIL ELABOR (NIL) -8 NIL NIL NIL) (-234 495643 495962 496241 "ELABEXPR" NIL ELABEXPR (NIL) -8 NIL NIL NIL) (-233 489036 491034 491861 "EFUPXS" NIL EFUPXS (NIL T T T T) -7 NIL NIL NIL) (-232 483015 485011 485821 "EFULS" NIL EFULS (NIL T T T) -7 NIL NIL NIL) (-231 480829 481235 481706 "EFSTRUC" NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-230 471829 473742 475283 "EF" NIL EF (NIL T T) -7 NIL NIL NIL) (-229 470942 471443 471592 "EAB" NIL EAB (NIL) -8 NIL NIL NIL) (-228 469640 470314 470354 "DVARCAT" 470637 DVARCAT (NIL T) -9 NIL 470777 NIL) (-227 469059 469323 469635 "DVARCAT-" NIL DVARCAT- (NIL T T) -7 NIL NIL NIL) (-226 461190 468927 469054 "DSMP" NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-225 459528 460319 460360 "DSEXT" 460723 DSEXT (NIL T) -9 NIL 461017 NIL) (-224 458333 458857 459523 "DSEXT-" NIL DSEXT- (NIL T T) -7 NIL NIL NIL) (-223 458057 458122 458220 "DROPT1" NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-222 454208 455424 456555 "DROPT0" NIL DROPT0 (NIL) -7 NIL NIL NIL) (-221 449854 451209 452273 "DROPT" NIL DROPT (NIL) -8 NIL NIL NIL) (-220 448529 448890 449276 "DRAWPT" NIL DRAWPT (NIL) -7 NIL NIL NIL) (-219 448215 448274 448392 "DRAWHACK" NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-218 447190 447488 447778 "DRAWCX" NIL DRAWCX (NIL) -7 NIL NIL NIL) (-217 446775 446850 447000 "DRAWCURV" NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-216 439188 441300 443415 "DRAWCFUN" NIL DRAWCFUN (NIL) -7 NIL NIL NIL) (-215 434705 435724 436803 "DRAW" NIL DRAW (NIL T) -7 NIL NIL NIL) (-214 431300 433369 433410 "DQAGG" 434039 DQAGG (NIL T) -9 NIL 434312 NIL) (-213 417907 425483 425565 "DPOLCAT" 427402 DPOLCAT (NIL T T T T) -9 NIL 427945 NIL) (-212 414315 415963 417902 "DPOLCAT-" NIL DPOLCAT- (NIL T T T T T) -7 NIL NIL NIL) (-211 407402 414213 414310 "DPMO" NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-210 400398 407231 407397 "DPMM" NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-209 399991 400251 400340 "DOMTMPLT" NIL DOMTMPLT (NIL) -8 NIL NIL NIL) (-208 399405 399853 399933 "DOMCTOR" NIL DOMCTOR (NIL) -8 NIL NIL NIL) (-207 398691 399016 399167 "DOMAIN" NIL DOMAIN (NIL) -8 NIL NIL NIL) (-206 391894 398427 398578 "DMP" NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-205 389674 390960 391000 "DMEXT" 391005 DMEXT (NIL T) -9 NIL 391180 NIL) (-204 389330 389392 389536 "DLP" NIL DLP (NIL T) -7 NIL NIL NIL) (-203 382655 388815 389005 "DLIST" NIL DLIST (NIL T) -8 NIL NIL NIL) (-202 379321 381478 381519 "DLAGG" 382069 DLAGG (NIL T) -9 NIL 382298 NIL) (-201 377734 378543 378571 "DIVRING" 378663 DIVRING (NIL) -9 NIL 378746 NIL) (-200 377185 377429 377729 "DIVRING-" NIL DIVRING- (NIL T) -7 NIL NIL NIL) (-199 375613 376030 376436 "DISPLAY" NIL DISPLAY (NIL) -7 NIL NIL NIL) (-198 374650 374871 375136 "DIRPROD2" NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-197 368223 374582 374645 "DIRPROD" NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-196 356642 363003 363056 "DIRPCAT" 363312 DIRPCAT (NIL NIL T) -9 NIL 364185 NIL) (-195 354648 355418 356305 "DIRPCAT-" NIL DIRPCAT- (NIL T NIL T) -7 NIL NIL NIL) (-194 354095 354261 354447 "DIOSP" NIL DIOSP (NIL) -7 NIL NIL NIL) (-193 350641 352981 353022 "DIOPS" 353454 DIOPS (NIL T) -9 NIL 353680 NIL) (-192 350301 350445 350636 "DIOPS-" NIL DIOPS- (NIL T T) -7 NIL NIL NIL) (-191 349339 350054 350082 "DIOID" 350087 DIOID (NIL) -9 NIL 350109 NIL) (-190 348229 348996 349024 "DIFRING" 349029 DIFRING (NIL) -9 NIL 349050 NIL) (-189 347865 347963 347991 "DIFFSPC" 348110 DIFFSPC (NIL) -9 NIL 348185 NIL) (-188 347606 347708 347860 "DIFFSPC-" NIL DIFFSPC- (NIL T) -7 NIL NIL NIL) (-187 346540 347134 347174 "DIFFMOD" 347179 DIFFMOD (NIL T) -9 NIL 347276 NIL) (-186 346224 346281 346322 "DIFFDOM" 346443 DIFFDOM (NIL T) -9 NIL 346511 NIL) (-185 346105 346135 346219 "DIFFDOM-" NIL DIFFDOM- (NIL T T) -7 NIL NIL NIL) (-184 343840 345299 345339 "DIFEXT" 345344 DIFEXT (NIL T) -9 NIL 345496 NIL) (-183 341001 343341 343382 "DIAGG" 343387 DIAGG (NIL T) -9 NIL 343407 NIL) (-182 340557 340747 340996 "DIAGG-" NIL DIAGG- (NIL T T) -7 NIL NIL NIL) (-181 335769 339747 340024 "DHMATRIX" NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-180 332227 333280 334290 "DFSFUN" NIL DFSFUN (NIL) -7 NIL NIL NIL) (-179 326841 331381 331708 "DFLOAT" NIL DFLOAT (NIL) -8 NIL NIL NIL) (-178 325407 325699 326074 "DFINTTLS" NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-177 322591 323779 324175 "DERHAM" NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-176 320311 322422 322511 "DEQUEUE" NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-175 319694 319839 320021 "DEGRED" NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-174 317012 317736 318536 "DEFINTRF" NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-173 315121 315579 316141 "DEFINTEF" NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-172 314504 314837 314951 "DEFAST" NIL DEFAST (NIL) -8 NIL NIL NIL) (-171 307768 314229 314377 "DECIMAL" NIL DECIMAL (NIL) -8 NIL NIL NIL) (-170 305688 306198 306702 "DDFACT" NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-169 305327 305376 305527 "DBLRESP" NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-168 304586 305148 305239 "DBASIS" NIL DBASIS (NIL NIL) -8 NIL NIL NIL) (-167 302610 303052 303412 "DBASE" NIL DBASE (NIL T) -8 NIL NIL NIL) (-166 301902 302191 302337 "DATAARY" NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-165 301353 301499 301651 "CYCLOTOM" NIL CYCLOTOM (NIL) -7 NIL NIL NIL) (-164 298715 299508 300235 "CYCLES" NIL CYCLES (NIL) -7 NIL NIL NIL) (-163 298154 298300 298471 "CVMP" NIL CVMP (NIL T) -7 NIL NIL NIL) (-162 296226 296537 296904 "CTRIGMNP" NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-161 295783 296038 296139 "CTORKIND" NIL CTORKIND (NIL) -8 NIL NIL NIL) (-160 294984 295367 295395 "CTORCAT" 295576 CTORCAT (NIL) -9 NIL 295688 NIL) (-159 294687 294821 294979 "CTORCAT-" NIL CTORCAT- (NIL T) -7 NIL NIL NIL) (-158 294180 294437 294545 "CTORCALL" NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-157 293596 294027 294100 "CTOR" NIL CTOR (NIL) -8 NIL NIL NIL) (-156 293055 293172 293325 "CSTTOOLS" NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-155 289449 290205 290960 "CRFP" NIL CRFP (NIL T T) -7 NIL NIL NIL) (-154 288940 289243 289334 "CRCEAST" NIL CRCEAST (NIL) -8 NIL NIL NIL) (-153 288159 288368 288596 "CRAPACK" NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-152 287663 287768 287972 "CPMATCH" NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-151 287416 287450 287556 "CPIMA" NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-150 284355 285117 285835 "COORDSYS" NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-149 283874 284016 284155 "CONTOUR" NIL CONTOUR (NIL) -8 NIL NIL NIL) (-148 279831 282337 282829 "CONTFRAC" NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-147 279705 279732 279760 "CONDUIT" 279797 CONDUIT (NIL) -9 NIL NIL NIL) (-146 278646 279315 279343 "COMRING" 279348 COMRING (NIL) -9 NIL 279398 NIL) (-145 277811 278178 278356 "COMPPROP" NIL COMPPROP (NIL) -8 NIL NIL NIL) (-144 277507 277548 277676 "COMPLPAT" NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-143 277200 277263 277370 "COMPLEX2" NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-142 266106 277150 277195 "COMPLEX" NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-141 265567 265706 265866 "COMPILER" NIL COMPILER (NIL) -7 NIL NIL NIL) (-140 265320 265361 265459 "COMPFACT" NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-139 246813 259001 259041 "COMPCAT" 260042 COMPCAT (NIL T) -9 NIL 261384 NIL) (-138 239351 242864 246457 "COMPCAT-" NIL COMPCAT- (NIL T T) -7 NIL NIL NIL) (-137 239110 239144 239246 "COMMUPC" NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-136 238940 238979 239037 "COMMONOP" NIL COMMONOP (NIL) -7 NIL NIL NIL) (-135 238521 238800 238874 "COMMAAST" NIL COMMAAST (NIL) -8 NIL NIL NIL) (-134 238098 238339 238426 "COMM" NIL COMM (NIL) -8 NIL NIL NIL) (-133 237293 237541 237569 "COMBOPC" 237907 COMBOPC (NIL) -9 NIL 238082 NIL) (-132 236357 236609 236851 "COMBINAT" NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-131 233289 233973 234596 "COMBF" NIL COMBF (NIL T T) -7 NIL NIL NIL) (-130 232169 232620 232855 "COLOR" NIL COLOR (NIL) -8 NIL NIL NIL) (-129 231660 231963 232054 "COLONAST" NIL COLONAST (NIL) -8 NIL NIL NIL) (-128 231347 231400 231525 "CMPLXRT" NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-127 230817 231127 231225 "CLLCTAST" NIL CLLCTAST (NIL) -8 NIL NIL NIL) (-126 227337 228407 229487 "CLIP" NIL CLIP (NIL) -7 NIL NIL NIL) (-125 225696 226617 226855 "CLIF" NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-124 221808 223816 223857 "CLAGG" 224783 CLAGG (NIL T) -9 NIL 225316 NIL) (-123 220701 221228 221803 "CLAGG-" NIL CLAGG- (NIL T T) -7 NIL NIL NIL) (-122 220330 220421 220561 "CINTSLPE" NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-121 218267 218774 219322 "CHVAR" NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-120 217290 217959 217987 "CHARZ" 217992 CHARZ (NIL) -9 NIL 218006 NIL) (-119 217084 217130 217208 "CHARPOL" NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-118 215985 216686 216714 "CHARNZ" 216775 CHARNZ (NIL) -9 NIL 216823 NIL) (-117 213463 214560 215083 "CHAR" NIL CHAR (NIL) -8 NIL NIL NIL) (-116 213171 213250 213278 "CFCAT" 213389 CFCAT (NIL) -9 NIL NIL NIL) (-115 212514 212643 212825 "CDEN" NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-114 208503 211927 212207 "CCLASS" NIL CCLASS (NIL) -8 NIL NIL NIL) (-113 207881 208068 208245 "CATEGORY" NIL -10 (NIL) -8 NIL NIL NIL) (-112 207409 207828 207876 "CATCTOR" NIL CATCTOR (NIL) -8 NIL NIL NIL) (-111 206882 207191 207288 "CATAST" NIL CATAST (NIL) -8 NIL NIL NIL) (-110 206373 206676 206767 "CASEAST" NIL CASEAST (NIL) -8 NIL NIL NIL) (-109 205622 205782 206003 "CARTEN2" NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-108 201722 202979 203687 "CARTEN" NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-107 200120 201119 201370 "CARD" NIL CARD (NIL) -8 NIL NIL NIL) (-106 199701 199980 200054 "CAPSLAST" NIL CAPSLAST (NIL) -8 NIL NIL NIL) (-105 199135 199388 199416 "CACHSET" 199548 CACHSET (NIL) -9 NIL 199626 NIL) (-104 198518 198902 198930 "CABMON" 198980 CABMON (NIL) -9 NIL 199036 NIL) (-103 198048 198312 198422 "BYTEORD" NIL BYTEORD (NIL) -8 NIL NIL NIL) (-102 193271 197705 197877 "BYTEBUF" NIL BYTEBUF (NIL) -8 NIL NIL NIL) (-101 192241 192945 193080 "BYTE" NIL BYTE (NIL) -8 NIL NIL 193243) (-100 189712 192008 192114 "BTREE" NIL BTREE (NIL T) -8 NIL NIL NIL) (-99 187143 189455 189574 "BTOURN" NIL BTOURN (NIL T) -8 NIL NIL NIL) (-98 184383 186587 186626 "BTCAT" 186693 BTCAT (NIL T) -9 NIL 186769 NIL) (-97 184134 184232 184378 "BTCAT-" NIL BTCAT- (NIL T T) -7 NIL NIL NIL) (-96 179244 183365 183391 "BTAGG" 183502 BTAGG (NIL) -9 NIL 183610 NIL) (-95 178875 179036 179239 "BTAGG-" NIL BTAGG- (NIL T) -7 NIL NIL NIL) (-94 175937 178345 178557 "BSTREE" NIL BSTREE (NIL T) -8 NIL NIL NIL) (-93 175207 175359 175537 "BRILL" NIL BRILL (NIL T) -7 NIL NIL NIL) (-92 171740 173913 173952 "BRAGG" 174593 BRAGG (NIL T) -9 NIL 174850 NIL) (-91 170695 171190 171735 "BRAGG-" NIL BRAGG- (NIL T T) -7 NIL NIL NIL) (-90 163293 170200 170381 "BPADICRT" NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-89 161349 163245 163288 "BPADIC" NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-88 161082 161118 161229 "BOUNDZRO" NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-87 159321 159754 160202 "BOP1" NIL BOP1 (NIL T) -7 NIL NIL NIL) (-86 155287 156703 157593 "BOP" NIL BOP (NIL) -8 NIL NIL NIL) (-85 154163 155054 155176 "BOOLEAN" NIL BOOLEAN (NIL) -8 NIL NIL NIL) (-84 153749 153906 153932 "BOOLE" 154040 BOOLE (NIL) -9 NIL 154121 NIL) (-83 153542 153623 153744 "BOOLE-" NIL BOOLE- (NIL T) -7 NIL NIL NIL) (-82 152711 153207 153257 "BMODULE" 153262 BMODULE (NIL T T) -9 NIL 153326 NIL) (-81 148328 152568 152637 "BITS" NIL BITS (NIL) -8 NIL NIL NIL) (-80 148141 148181 148220 "BINOPC" 148225 BINOPC (NIL T) -9 NIL 148270 NIL) (-79 147683 147956 148058 "BINOP" NIL BINOP (NIL T) -8 NIL NIL NIL) (-78 147204 147348 147486 "BINDING" NIL BINDING (NIL) -8 NIL NIL NIL) (-77 140474 146934 147079 "BINARY" NIL BINARY (NIL) -8 NIL NIL NIL) (-76 138208 139703 139742 "BGAGG" 139998 BGAGG (NIL T) -9 NIL 140135 NIL) (-75 138077 138115 138203 "BGAGG-" NIL BGAGG- (NIL T T) -7 NIL NIL NIL) (-74 136928 137129 137414 "BEZOUT" NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-73 133566 136086 136413 "BBTREE" NIL 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T) ((-592 |#2|) |has| |#1| (-312)) ((-592 $) . T) ((-584 (-348 (-485))) OR (|has| |#1| (-312)) (|has| |#1| (-38 (-348 (-485))))) ((-584 |#1|) |has| |#1| (-146)) ((-584 |#2|) |has| |#1| (-312)) ((-584 $) OR (|has| |#1| (-496)) (|has| |#1| (-312))) ((-582 (-485)) -12 (|has| |#1| (-312)) (|has| |#2| (-582 (-485)))) ((-582 |#2|) |has| |#1| (-312)) ((-656 (-348 (-485))) OR (|has| |#1| (-312)) (|has| |#1| (-38 (-348 (-485))))) ((-656 |#1|) |has| |#1| (-146)) ((-656 |#2|) |has| |#1| (-312)) ((-656 $) OR (|has| |#1| (-496)) (|has| |#1| (-312))) ((-665) . 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(NIL T T) -8 NIL NIL NIL) (-1200 2789015 2790648 2790702 "XFALG" 2792847 XFALG (NIL T T) -9 NIL 2793631 NIL) (-1199 2784171 2786904 2786946 "XF" 2787564 XF (NIL T) -9 NIL 2787960 NIL) (-1198 2783889 2783999 2784166 "XF-" NIL XF- (NIL T T) -7 NIL NIL NIL) (-1197 2783116 2783238 2783442 "XEXPPKG" NIL XEXPPKG (NIL T T T) -7 NIL NIL NIL) (-1196 2780858 2783016 2783111 "XDPOLY" NIL XDPOLY (NIL T T) -8 NIL NIL NIL) (-1195 2779439 2780234 2780276 "XALG" 2780281 XALG (NIL T) -9 NIL 2780390 NIL) (-1194 2772996 2777849 2778327 "WUTSET" NIL WUTSET (NIL T T T T) -8 NIL NIL NIL) (-1193 2771239 2772241 2772562 "WP" NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL NIL) (-1192 2770838 2771110 2771179 "WHILEAST" NIL WHILEAST (NIL) -8 NIL NIL NIL) (-1191 2770325 2770628 2770721 "WHEREAST" NIL WHEREAST (NIL) -8 NIL NIL NIL) (-1190 2769402 2769612 2769907 "WFFINTBS" NIL WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1189 2767698 2768161 2768623 "WEIER" NIL WEIER (NIL T) -7 NIL NIL NIL) (-1188 2766587 2767172 2767214 "VSPACE" 2767350 VSPACE (NIL T) -9 NIL 2767424 NIL) (-1187 2766458 2766491 2766582 "VSPACE-" NIL VSPACE- (NIL T T) -7 NIL NIL NIL) (-1186 2766301 2766355 2766423 "VOID" NIL VOID (NIL) -8 NIL NIL NIL) (-1185 2763284 2764079 2764816 "VIEWDEF" NIL VIEWDEF (NIL) -7 NIL NIL NIL) (-1184 2754382 2756983 2759156 "VIEW3D" NIL VIEW3D (NIL) -8 NIL NIL NIL) (-1183 2747959 2749850 2751429 "VIEW2D" NIL VIEW2D (NIL) -8 NIL NIL NIL) (-1182 2746443 2746838 2747244 "VIEW" NIL VIEW (NIL) -7 NIL NIL NIL) (-1181 2745270 2745551 2745867 "VECTOR2" NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1180 2740384 2745097 2745189 "VECTOR" NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1179 2733486 2738094 2738137 "VECTCAT" 2739125 VECTCAT (NIL T) -9 NIL 2739709 NIL) (-1178 2732765 2733091 2733481 "VECTCAT-" NIL VECTCAT- (NIL T T) -7 NIL NIL NIL) (-1177 2732259 2732501 2732621 "VARIABLE" NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1176 2732192 2732197 2732227 "UTYPE" 2732232 UTYPE (NIL) -9 NIL NIL NIL) (-1175 2731179 2731355 2731616 "UTSODETL" NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1174 2729030 2729538 2730062 "UTSODE" NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1173 2718912 2724882 2724924 "UTSCAT" 2726022 UTSCAT (NIL T) -9 NIL 2726779 NIL) (-1172 2716977 2717920 2718907 "UTSCAT-" NIL UTSCAT- (NIL T T) -7 NIL NIL NIL) (-1171 2716651 2716700 2716831 "UTS2" NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1170 2708362 2714847 2715326 "UTS" NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1169 2702357 2705170 2705213 "URAGG" 2707283 URAGG (NIL T) -9 NIL 2708005 NIL) (-1168 2700372 2701334 2702352 "URAGG-" NIL URAGG- (NIL T T) -7 NIL NIL NIL) (-1167 2696079 2699348 2699810 "UPXSSING" NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1166 2688508 2696003 2696074 "UPXSCONS" NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1165 2677159 2684646 2684707 "UPXSCCA" 2685275 UPXSCCA (NIL T T) -9 NIL 2685507 NIL) (-1164 2676880 2676982 2677154 "UPXSCCA-" NIL UPXSCCA- (NIL T T T) -7 NIL NIL NIL) (-1163 2665432 2672644 2672686 "UPXSCAT" 2673326 UPXSCAT (NIL T) -9 NIL 2673934 NIL) (-1162 2664945 2665030 2665207 "UPXS2" NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1161 2656631 2664536 2664798 "UPXS" NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1160 2655526 2655796 2656146 "UPSQFREE" NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1159 2648229 2651714 2651768 "UPSCAT" 2652837 UPSCAT (NIL T T) -9 NIL 2653601 NIL) (-1158 2647649 2647901 2648224 "UPSCAT-" NIL UPSCAT- (NIL T T T) -7 NIL NIL NIL) (-1157 2647323 2647372 2647503 "UPOLYC2" NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1156 2631453 2640407 2640449 "UPOLYC" 2642527 UPOLYC (NIL T) -9 NIL 2643747 NIL) (-1155 2625508 2628356 2631448 "UPOLYC-" NIL UPOLYC- (NIL T T) -7 NIL NIL NIL) (-1154 2624944 2625069 2625232 "UPMP" NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1153 2624578 2624665 2624804 "UPDIVP" NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1152 2623391 2623658 2623962 "UPDECOMP" NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1151 2622724 2622854 2623039 "UPCDEN" NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1150 2622316 2622391 2622538 "UP2" NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1149 2613080 2622082 2622210 "UP" NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1148 2612442 2612579 2612784 "UNISEG2" NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1147 2611043 2611890 2612166 "UNISEG" NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1146 2610272 2610469 2610694 "UNIFACT" NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1145 2597082 2610196 2610267 "ULSCONS" NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1144 2576934 2590169 2590230 "ULSCCAT" 2590861 ULSCCAT (NIL T T) -9 NIL 2591148 NIL) (-1143 2576269 2576555 2576929 "ULSCCAT-" NIL ULSCCAT- (NIL T T T) -7 NIL NIL NIL) (-1142 2564641 2571775 2571817 "ULSCAT" 2572670 ULSCAT (NIL T) -9 NIL 2573400 NIL) (-1141 2564154 2564239 2564416 "ULS2" NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1140 2546271 2563653 2563894 "ULS" NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1139 2545305 2545998 2546112 "UINT8" NIL UINT8 (NIL) -8 NIL NIL 2546223) (-1138 2544338 2545031 2545145 "UINT64" NIL UINT64 (NIL) -8 NIL NIL 2545256) (-1137 2543371 2544064 2544178 "UINT32" NIL UINT32 (NIL) -8 NIL NIL 2544289) (-1136 2542404 2543097 2543211 "UINT16" NIL UINT16 (NIL) -8 NIL NIL 2543322) (-1135 2540411 2541632 2541662 "UFD" 2541873 UFD (NIL) -9 NIL 2541986 NIL) (-1134 2540255 2540312 2540406 "UFD-" NIL UFD- (NIL T) -7 NIL NIL NIL) (-1133 2539507 2539714 2539930 "UDVO" NIL UDVO (NIL) -7 NIL NIL NIL) (-1132 2537727 2538180 2538645 "UDPO" NIL UDPO (NIL T) -7 NIL NIL NIL) (-1131 2537452 2537692 2537722 "TYPEAST" NIL TYPEAST (NIL) -8 NIL NIL NIL) (-1130 2537390 2537395 2537425 "TYPE" 2537430 TYPE (NIL) -9 NIL 2537437 NIL) (-1129 2536549 2536769 2537009 "TWOFACT" NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1128 2535727 2536158 2536393 "TUPLE" NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1127 2533881 2534454 2534993 "TUBETOOL" NIL TUBETOOL (NIL) -7 NIL NIL NIL) (-1126 2532915 2533151 2533387 "TUBE" NIL TUBE (NIL T) -8 NIL NIL NIL) (-1125 2521269 2525737 2525833 "TSETCAT" 2531048 TSETCAT (NIL T T T T) -9 NIL 2532560 NIL) (-1124 2517606 2519422 2521264 "TSETCAT-" NIL TSETCAT- (NIL T T T T T) -7 NIL NIL NIL) (-1123 2511998 2516832 2517114 "TS" NIL TS (NIL T) -8 NIL NIL NIL) (-1122 2507335 2508348 2509277 "TRMANIP" NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1121 2506832 2506907 2507070 "TRIMAT" NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1120 2504908 2505198 2505553 "TRIGMNIP" NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1119 2504392 2504541 2504571 "TRIGCAT" 2504784 TRIGCAT (NIL) -9 NIL NIL NIL) (-1118 2504143 2504246 2504387 "TRIGCAT-" NIL TRIGCAT- (NIL T) -7 NIL NIL NIL) (-1117 2501139 2503252 2503530 "TREE" NIL TREE (NIL T) -8 NIL NIL NIL) (-1116 2500245 2500941 2500971 "TRANFUN" 2501006 TRANFUN (NIL) -9 NIL 2501072 NIL) (-1115 2499709 2499960 2500240 "TRANFUN-" NIL TRANFUN- (NIL T) -7 NIL NIL NIL) (-1114 2499546 2499584 2499645 "TOPSP" NIL TOPSP (NIL) -7 NIL NIL NIL) (-1113 2499003 2499134 2499285 "TOOLSIGN" NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1112 2497744 2498401 2498637 "TEXTFILE" NIL TEXTFILE (NIL) -8 NIL NIL NIL) (-1111 2497556 2497593 2497665 "TEX1" NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1110 2495770 2496416 2496845 "TEX" NIL TEX (NIL) -8 NIL NIL NIL) (-1109 2494150 2494487 2494809 "TBCMPPK" NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1108 2485208 2491951 2492007 "TBAGG" 2492409 TBAGG (NIL T T) -9 NIL 2492622 NIL) (-1107 2481739 2483431 2485203 "TBAGG-" NIL TBAGG- (NIL T T T) -7 NIL NIL NIL) (-1106 2481216 2481341 2481486 "TANEXP" NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1105 2480726 2481046 2481136 "TALGOP" NIL TALGOP (NIL T) -8 NIL NIL NIL) (-1104 2480223 2480340 2480478 "TABLEAU" NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1103 2473310 2480125 2480218 "TABLE" NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1102 2469063 2470358 2471603 "TABLBUMP" NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1101 2468432 2468591 2468772 "SYSTEM" NIL SYSTEM (NIL) -7 NIL NIL NIL) (-1100 2465586 2466339 2467122 "SYSSOLP" NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1099 2465360 2465550 2465581 "SYSPTR" NIL SYSPTR (NIL) -8 NIL NIL NIL) (-1098 2464314 2464999 2465125 "SYSNNI" NIL SYSNNI (NIL NIL) -8 NIL NIL 2465311) (-1097 2463578 2464126 2464205 "SYSINT" NIL SYSINT (NIL NIL) -8 NIL NIL 2464265) (-1096 2460401 2461560 2462260 "SYNTAX" NIL SYNTAX (NIL) -8 NIL NIL NIL) (-1095 2458084 2458767 2459401 "SYMTAB" NIL SYMTAB (NIL) -8 NIL NIL NIL) (-1094 2454162 2455208 2456185 "SYMS" NIL SYMS (NIL) -8 NIL NIL NIL) (-1093 2451261 2453817 2454046 "SYMPOLY" NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1092 2450857 2450944 2451066 "SYMFUNC" NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1091 2447481 2448955 2449774 "SYMBOL" NIL SYMBOL (NIL) -8 NIL NIL NIL) (-1090 2440441 2446678 2446971 "SUTS" NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1089 2432127 2440032 2440294 "SUPXS" NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1088 2431406 2431545 2431762 "SUPFRACF" NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1087 2431090 2431155 2431266 "SUP2" NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1086 2421813 2430802 2430927 "SUP" NIL SUP (NIL T) -8 NIL NIL NIL) (-1085 2420543 2420841 2421196 "SUMRF" NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1084 2419948 2420026 2420217 "SUMFS" NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1083 2402100 2419447 2419688 "SULS" NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1082 2401699 2401971 2402040 "SUCHTAST" NIL SUCHTAST (NIL) -8 NIL NIL NIL) (-1081 2401035 2401316 2401456 "SUCH" NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1080 2395637 2396896 2397849 "SUBSPACE" NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1079 2395169 2395269 2395433 "SUBRESP" NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1078 2390280 2391562 2392709 "STTFNC" NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1077 2384738 2386209 2387520 "STTF" NIL STTF (NIL T) -7 NIL NIL NIL) (-1076 2377653 2379717 2381508 "STTAYLOR" NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1075 2370483 2377565 2377648 "STRTBL" NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1074 2365177 2370197 2370312 "STRING" NIL STRING (NIL) -8 NIL NIL NIL) (-1073 2364764 2364847 2364991 "STREAM3" NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1072 2363915 2364116 2364351 "STREAM2" NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1071 2363655 2363713 2363806 "STREAM1" NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1070 2356393 2361860 2362466 "STREAM" NIL STREAM (NIL T) -8 NIL NIL NIL) (-1069 2355569 2355774 2356005 "STINPROD" NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1068 2354814 2355185 2355332 "STEPAST" NIL STEPAST (NIL) -8 NIL NIL NIL) (-1067 2354302 2354544 2354574 "STEP" 2354668 STEP (NIL) -9 NIL 2354739 NIL) (-1066 2347405 2354220 2354297 "STBL" NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1065 2341620 2346203 2346246 "STAGG" 2346673 STAGG (NIL T) -9 NIL 2346847 NIL) (-1064 2339999 2340747 2341615 "STAGG-" NIL STAGG- (NIL T T) -7 NIL NIL NIL) (-1063 2338156 2339826 2339918 "STACK" NIL STACK (NIL T) -8 NIL NIL NIL) (-1062 2337436 2337975 2338005 "SRING" 2338010 SRING (NIL) -9 NIL 2338030 NIL) (-1061 2330058 2335974 2336413 "SREGSET" NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1060 2323832 2325271 2326775 "SRDCMPK" NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1059 2316257 2321168 2321198 "SRAGG" 2322497 SRAGG (NIL) -9 NIL 2323101 NIL) (-1058 2315554 2315874 2316252 "SRAGG-" NIL SRAGG- (NIL T) -7 NIL NIL NIL) (-1057 2309609 2314876 2315299 "SQMATRIX" NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1056 2303822 2306991 2307713 "SPLTREE" NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1055 2300251 2301070 2301707 "SPLNODE" NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1054 2299226 2299531 2299561 "SPFCAT" 2300005 SPFCAT (NIL) -9 NIL NIL NIL) (-1053 2298163 2298415 2298679 "SPECOUT" NIL SPECOUT (NIL) -7 NIL NIL NIL) (-1052 2288921 2291195 2291225 "SPADXPT" 2295862 SPADXPT (NIL) -9 NIL 2297986 NIL) (-1051 2288723 2288769 2288838 "SPADPRSR" NIL SPADPRSR (NIL) -7 NIL NIL NIL) (-1050 2286379 2288687 2288718 "SPADAST" NIL SPADAST (NIL) -8 NIL NIL NIL) (-1049 2278053 2280142 2280184 "SPACEC" 2284499 SPACEC (NIL T) -9 NIL 2286304 NIL) (-1048 2275882 2278000 2278048 "SPACE3" NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1047 2274815 2275004 2275293 "SORTPAK" NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1046 2273219 2273552 2273963 "SOLVETRA" NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1045 2272484 2272718 2272979 "SOLVESER" NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1044 2268664 2269624 2270619 "SOLVERAD" NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1043 2265022 2265721 2266450 "SOLVEFOR" NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1042 2258808 2264362 2264458 "SNTSCAT" 2264463 SNTSCAT (NIL T T T T) -9 NIL 2264533 NIL) (-1041 2252629 2257449 2257839 "SMTS" NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1040 2246401 2252548 2252624 "SMP" NIL SMP (NIL T T) -8 NIL NIL NIL) (-1039 2244833 2245164 2245562 "SMITH" NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1038 2236438 2241417 2241519 "SMATCAT" 2242862 SMATCAT (NIL NIL T T T) -9 NIL 2243410 NIL) (-1037 2234279 2235263 2236433 "SMATCAT-" NIL SMATCAT- (NIL T NIL T T T) -7 NIL NIL NIL) (-1036 2231871 2233485 2233528 "SKAGG" 2233789 SKAGG (NIL T) -9 NIL 2233923 NIL) (-1035 2227917 2231691 2231802 "SINT" NIL SINT (NIL) -8 NIL NIL 2231843) (-1034 2227727 2227771 2227837 "SIMPAN" NIL SIMPAN (NIL) -7 NIL NIL NIL) (-1033 2226802 2227034 2227302 "SIGNRF" NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1032 2225806 2225968 2226244 "SIGNEF" NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1031 2225152 2225492 2225615 "SIGAST" NIL SIGAST (NIL) -8 NIL NIL NIL) (-1030 2224498 2224805 2224945 "SIG" NIL SIG (NIL) -8 NIL NIL NIL) (-1029 2222609 2223101 2223607 "SHP" NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1028 2216049 2222528 2222604 "SHDP" NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1027 2215552 2215789 2215819 "SGROUP" 2215912 SGROUP (NIL) -9 NIL 2215974 NIL) (-1026 2215442 2215474 2215547 "SGROUP-" NIL SGROUP- (NIL T) -7 NIL NIL NIL) (-1025 2215080 2215120 2215161 "SGPOPC" 2215166 SGPOPC (NIL T) -9 NIL 2215367 NIL) (-1024 2214614 2214891 2214997 "SGPOP" NIL SGPOP (NIL T) -8 NIL NIL NIL) (-1023 2212037 2212806 2213528 "SGCF" NIL SGCF (NIL) -7 NIL NIL NIL) (-1022 2205922 2211476 2211572 "SFRTCAT" 2211577 SFRTCAT (NIL T T T T) -9 NIL 2211615 NIL) (-1021 2200314 2201427 2202554 "SFRGCD" NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1020 2194490 2195651 2196815 "SFQCMPK" NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1019 2193462 2194364 2194485 "SEXOF" NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1018 2189070 2189965 2190060 "SEXCAT" 2192673 SEXCAT (NIL T T T T T) -9 NIL 2193224 NIL) (-1017 2188043 2188997 2189065 "SEX" NIL SEX (NIL) -8 NIL NIL NIL) (-1016 2186434 2187019 2187321 "SETMN" NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1015 2185957 2186142 2186172 "SETCAT" 2186289 SETCAT (NIL) -9 NIL 2186373 NIL) (-1014 2185789 2185853 2185952 "SETCAT-" NIL SETCAT- (NIL T) -7 NIL NIL NIL) (-1013 2182012 2184243 2184286 "SETAGG" 2185154 SETAGG (NIL T) -9 NIL 2185492 NIL) (-1012 2181618 2181770 2182007 "SETAGG-" NIL SETAGG- (NIL T T) -7 NIL NIL NIL) (-1011 2178572 2181565 2181613 "SET" NIL SET (NIL T) -8 NIL NIL NIL) (-1010 2178038 2178348 2178448 "SEQAST" NIL SEQAST (NIL) -8 NIL NIL NIL) (-1009 2177165 2177531 2177592 "SEGXCAT" 2177878 SEGXCAT (NIL T T) -9 NIL 2177998 NIL) (-1008 2176090 2176358 2176401 "SEGCAT" 2176923 SEGCAT (NIL T) -9 NIL 2177144 NIL) (-1007 2175770 2175835 2175948 "SEGBIND2" NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1006 2174836 2175306 2175514 "SEGBIND" NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1005 2174414 2174693 2174769 "SEGAST" NIL SEGAST (NIL) -8 NIL NIL NIL) (-1004 2173779 2173915 2174119 "SEG2" NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1003 2172845 2173592 2173774 "SEG" NIL SEG (NIL T) -8 NIL NIL NIL) (-1002 2172098 2172793 2172840 "SDVAR" NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1001 2163583 2171965 2172093 "SDPOL" NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1000 2162437 2162727 2163046 "SCPKG" NIL SCPKG (NIL T) -7 NIL NIL NIL) (-999 2161743 2161955 2162143 "SCOPE" NIL SCOPE (NIL) -8 NIL NIL NIL) (-998 2161093 2161250 2161426 "SCACHE" NIL SCACHE (NIL T) -7 NIL NIL NIL) (-997 2160666 2160897 2160925 "SASTCAT" 2160930 SASTCAT (NIL) -9 NIL 2160943 NIL) (-996 2160133 2160558 2160632 "SAOS" NIL SAOS (NIL) -8 NIL NIL NIL) (-995 2159736 2159777 2159948 "SAERFFC" NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-994 2159367 2159408 2159565 "SAEFACT" NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-993 2152448 2159284 2159362 "SAE" NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-992 2151098 2151427 2151823 "RURPK" NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-991 2149859 2150220 2150520 "RULESET" NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-990 2149483 2149704 2149785 "RULECOLD" NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-989 2146943 2147577 2148030 "RULE" NIL RULE (NIL T T T) -8 NIL NIL NIL) (-988 2146782 2146815 2146883 "RTVALUE" NIL RTVALUE (NIL) -8 NIL NIL NIL) (-987 2146273 2146576 2146667 "RSTRCAST" NIL RSTRCAST (NIL) -8 NIL NIL NIL) (-986 2141901 2142769 2143680 "RSETGCD" NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-985 2130720 2136274 2136368 "RSETCAT" 2140424 RSETCAT (NIL T T T T) -9 NIL 2141512 NIL) (-984 2129258 2129900 2130715 "RSETCAT-" NIL RSETCAT- (NIL T T T T T) -7 NIL NIL NIL) (-983 2123032 2124477 2125984 "RSDCMPK" NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-982 2120914 2121471 2121543 "RRCC" 2122616 RRCC (NIL T T) -9 NIL 2122957 NIL) (-981 2120439 2120638 2120909 "RRCC-" NIL RRCC- (NIL T T T) -7 NIL NIL NIL) (-980 2119909 2120219 2120317 "RPTAST" NIL RPTAST (NIL) -8 NIL NIL NIL) (-979 2092461 2103174 2103238 "RPOLCAT" 2113712 RPOLCAT (NIL T T T) -9 NIL 2116857 NIL) (-978 2086560 2089383 2092456 "RPOLCAT-" NIL RPOLCAT- (NIL T T T T) -7 NIL NIL NIL) (-977 2082727 2086308 2086446 "ROMAN" NIL ROMAN (NIL) -8 NIL NIL NIL) (-976 2081055 2081794 2082050 "ROIRC" NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-975 2076698 2079510 2079538 "RNS" 2079800 RNS (NIL) -9 NIL 2080052 NIL) (-974 2075601 2076088 2076625 "RNS-" NIL RNS- (NIL T) -7 NIL NIL NIL) (-973 2074719 2075120 2075320 "RNGBIND" NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-972 2073857 2074419 2074447 "RNG" 2074507 RNG (NIL) -9 NIL 2074561 NIL) (-971 2073746 2073780 2073852 "RNG-" NIL RNG- (NIL T) -7 NIL NIL NIL) (-970 2073008 2073513 2073553 "RMODULE" 2073558 RMODULE (NIL T) -9 NIL 2073584 NIL) (-969 2071947 2072053 2072383 "RMCAT2" NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-968 2068793 2071537 2071830 "RMATRIX" NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-967 2061442 2063934 2064046 "RMATCAT" 2067351 RMATCAT (NIL NIL NIL T T T) -9 NIL 2068328 NIL) (-966 2060959 2061138 2061437 "RMATCAT-" NIL RMATCAT- (NIL T NIL NIL T T T) -7 NIL NIL NIL) (-965 2060527 2060738 2060779 "RLINSET" 2060840 RLINSET (NIL T) -9 NIL 2060884 NIL) (-964 2060172 2060253 2060379 "RINTERP" NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-963 2059018 2059749 2059777 "RING" 2059832 RING (NIL) -9 NIL 2059924 NIL) (-962 2058863 2058919 2059013 "RING-" NIL RING- (NIL T) -7 NIL NIL NIL) (-961 2057917 2058184 2058440 "RIDIST" NIL RIDIST (NIL) -7 NIL NIL NIL) (-960 2048904 2057545 2057746 "RGCHAIN" NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-959 2048129 2048640 2048679 "RGBCSPC" 2048736 RGBCSPC (NIL T) -9 NIL 2048787 NIL) (-958 2047163 2047649 2047688 "RGBCMDL" 2047916 RGBCMDL (NIL T) -9 NIL 2048030 NIL) (-957 2046875 2046944 2047045 "RFFACTOR" NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-956 2046638 2046679 2046774 "RFFACT" NIL RFFACT (NIL T) -7 NIL NIL NIL) (-955 2045062 2045492 2045872 "RFDIST" NIL RFDIST (NIL) -7 NIL NIL NIL) (-954 2042649 2043317 2043985 "RF" NIL RF (NIL T) -7 NIL NIL NIL) (-953 2042199 2042297 2042457 "RETSOL" NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-952 2041821 2041919 2041960 "RETRACT" 2042091 RETRACT (NIL T) -9 NIL 2042178 NIL) (-951 2041701 2041732 2041816 "RETRACT-" NIL RETRACT- (NIL T T) -7 NIL NIL NIL) (-950 2041303 2041575 2041642 "RETAST" NIL RETAST (NIL) -8 NIL NIL NIL) (-949 2039783 2040674 2040871 "RESRING" NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-948 2039474 2039535 2039631 "RESLATC" NIL RESLATC (NIL T) -7 NIL NIL NIL) (-947 2039217 2039258 2039363 "REPSQ" NIL REPSQ (NIL T) -7 NIL NIL NIL) (-946 2038952 2038993 2039102 "REPDB" NIL REPDB (NIL T) -7 NIL NIL NIL) (-945 2034023 2035474 2036689 "REP2" NIL REP2 (NIL T) -7 NIL NIL NIL) (-944 2031122 2031880 2032688 "REP1" NIL REP1 (NIL T) -7 NIL NIL NIL) (-943 2029091 2029713 2030313 "REP" NIL REP (NIL) -7 NIL NIL NIL) (-942 2021726 2027642 2028078 "REGSET" NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-941 2021038 2021318 2021467 "REF" NIL REF (NIL T) -8 NIL NIL NIL) (-940 2020523 2020638 2020803 "REDORDER" NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-939 2016116 2019926 2020147 "RECLOS" NIL RECLOS (NIL T) -8 NIL NIL NIL) (-938 2015348 2015547 2015760 "REALSOLV" NIL REALSOLV (NIL) -7 NIL NIL NIL) (-937 2012638 2013476 2014358 "REAL0Q" NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-936 2009220 2010256 2011315 "REAL0" NIL REAL0 (NIL T) -7 NIL NIL NIL) (-935 2009056 2009109 2009137 "REAL" 2009142 REAL (NIL) -9 NIL 2009177 NIL) (-934 2008546 2008850 2008941 "RDUCEAST" NIL RDUCEAST (NIL) -8 NIL NIL NIL) (-933 2008026 2008104 2008309 "RDIV" NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-932 2007259 2007451 2007662 "RDIST" NIL RDIST (NIL T) -7 NIL NIL NIL) (-931 2006147 2006444 2006811 "RDETRS" NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-930 2004414 2004884 2005417 "RDETR" NIL RDETR (NIL T T) -7 NIL NIL NIL) (-929 2003336 2003613 2004000 "RDEEFS" NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-928 2002163 2002472 2002891 "RDEEF" NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-927 1995511 1999023 1999051 "RCFIELD" 2000328 RCFIELD (NIL) -9 NIL 2001058 NIL) (-926 1994129 1994741 1995438 "RCFIELD-" NIL RCFIELD- (NIL T) -7 NIL NIL NIL) (-925 1990329 1992221 1992262 "RCAGG" 1993329 RCAGG (NIL T) -9 NIL 1993790 NIL) (-924 1990056 1990166 1990324 "RCAGG-" NIL RCAGG- (NIL T T) -7 NIL NIL NIL) (-923 1989501 1989630 1989791 "RATRET" NIL RATRET (NIL T) -7 NIL NIL NIL) (-922 1989118 1989197 1989316 "RATFACT" NIL RATFACT (NIL T) -7 NIL NIL NIL) (-921 1988533 1988683 1988833 "RANDSRC" NIL RANDSRC (NIL) -7 NIL NIL NIL) (-920 1988315 1988365 1988436 "RADUTIL" NIL RADUTIL (NIL) -7 NIL NIL NIL) (-919 1980757 1987433 1987741 "RADIX" NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-918 1970459 1980624 1980752 "RADFF" NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-917 1970093 1970186 1970214 "RADCAT" 1970371 RADCAT (NIL) -9 NIL NIL NIL) (-916 1969931 1969991 1970088 "RADCAT-" NIL RADCAT- (NIL T) -7 NIL NIL NIL) (-915 1968031 1969762 1969851 "QUEUE" NIL QUEUE (NIL T) -8 NIL NIL NIL) (-914 1967712 1967761 1967888 "QUATCT2" NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-913 1959999 1964083 1964123 "QUATCAT" 1964901 QUATCAT (NIL T) -9 NIL 1965665 NIL) (-912 1957249 1958529 1959905 "QUATCAT-" NIL QUATCAT- (NIL T T) -7 NIL NIL NIL) (-911 1953089 1957199 1957244 "QUAT" NIL QUAT (NIL T) -8 NIL NIL NIL) (-910 1950476 1952143 1952184 "QUAGG" 1952559 QUAGG (NIL T) -9 NIL 1952733 NIL) (-909 1950078 1950350 1950417 "QQUTAST" NIL QQUTAST (NIL) -8 NIL NIL NIL) (-908 1949084 1949714 1949877 "QFORM" NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-907 1948765 1948814 1948941 "QFCAT2" NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-906 1938390 1944559 1944599 "QFCAT" 1945257 QFCAT (NIL T) -9 NIL 1946250 NIL) (-905 1935274 1936713 1938296 "QFCAT-" NIL QFCAT- (NIL T T) -7 NIL NIL NIL) (-904 1934820 1934954 1935084 "QEQUAT" NIL QEQUAT (NIL) -8 NIL NIL NIL) (-903 1929016 1930177 1931339 "QCMPACK" NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-902 1928435 1928615 1928847 "QALGSET2" NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-901 1926257 1926785 1927208 "QALGSET" NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-900 1925156 1925398 1925715 "PWFFINTB" NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-899 1923517 1923715 1924068 "PUSHVAR" NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-898 1919273 1920489 1920530 "PTRANFN" 1922414 PTRANFN (NIL T) -9 NIL NIL NIL) (-897 1917920 1918265 1918586 "PTPACK" NIL PTPACK (NIL T) -7 NIL NIL NIL) (-896 1917613 1917676 1917783 "PTFUNC2" NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-895 1911686 1916409 1916449 "PTCAT" 1916741 PTCAT (NIL T) -9 NIL 1916894 NIL) (-894 1911379 1911420 1911544 "PSQFR" NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-893 1910258 1910574 1910908 "PSEUDLIN" NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-892 1899137 1901698 1904007 "PSETPK" NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-891 1892044 1894940 1895034 "PSETCAT" 1898008 PSETCAT (NIL T T T T) -9 NIL 1898815 NIL) (-890 1890494 1891228 1892039 "PSETCAT-" NIL PSETCAT- (NIL T T T T T) -7 NIL NIL NIL) (-889 1889813 1890008 1890036 "PSCURVE" 1890304 PSCURVE (NIL) -9 NIL 1890471 NIL) (-888 1885415 1887235 1887299 "PSCAT" 1888134 PSCAT (NIL T T T) -9 NIL 1888373 NIL) (-887 1884729 1885011 1885410 "PSCAT-" NIL PSCAT- (NIL T T T T) -7 NIL NIL NIL) (-886 1883126 1884041 1884304 "PRTITION" NIL PRTITION (NIL) -8 NIL NIL NIL) (-885 1882617 1882920 1883011 "PRTDAST" NIL PRTDAST (NIL) -8 NIL NIL NIL) (-884 1873637 1876059 1878247 "PRS" NIL PRS (NIL T T) -7 NIL NIL NIL) (-883 1871380 1872957 1872997 "PRQAGG" 1873180 PRQAGG (NIL T) -9 NIL 1873281 NIL) (-882 1870553 1870999 1871027 "PROPLOG" 1871166 PROPLOG (NIL) -9 NIL 1871280 NIL) (-881 1870228 1870291 1870414 "PROPFUN2" NIL PROPFUN2 (NIL T T) -7 NIL NIL NIL) (-880 1869664 1869803 1869975 "PROPFUN1" NIL PROPFUN1 (NIL T) -7 NIL NIL NIL) (-879 1867912 1868675 1868972 "PROPFRML" NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-878 1867464 1867596 1867724 "PROPERTY" NIL PROPERTY (NIL) -8 NIL NIL NIL) (-877 1861905 1866404 1867224 "PRODUCT" NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-876 1861734 1861772 1861831 "PRINT" NIL PRINT (NIL) -7 NIL NIL NIL) (-875 1861173 1861313 1861464 "PRIMES" NIL PRIMES (NIL T) -7 NIL NIL NIL) (-874 1859641 1860060 1860526 "PRIMELT" NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-873 1859358 1859419 1859447 "PRIMCAT" 1859571 PRIMCAT (NIL) -9 NIL NIL NIL) (-872 1858529 1858725 1858953 "PRIMARR2" NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-871 1854407 1858479 1858524 "PRIMARR" NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-870 1854106 1854168 1854279 "PREASSOC" NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-869 1851242 1853755 1853988 "PR" NIL PR (NIL T T) -8 NIL NIL NIL) (-868 1850693 1850850 1850878 "PPCURVE" 1851083 PPCURVE (NIL) -9 NIL 1851219 NIL) (-867 1850306 1850551 1850634 "PORTNUM" NIL PORTNUM (NIL) -8 NIL NIL NIL) (-866 1848062 1848483 1849075 "POLYROOT" NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-865 1847505 1847569 1847802 "POLYLIFT" NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-864 1844225 1844711 1845322 "POLYCATQ" NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-863 1829816 1835945 1836009 "POLYCAT" 1839494 POLYCAT (NIL T T T) -9 NIL 1841371 NIL) (-862 1825326 1827473 1829811 "POLYCAT-" NIL POLYCAT- (NIL T T T T) -7 NIL NIL NIL) (-861 1824983 1825057 1825176 "POLY2UP" NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-860 1824676 1824739 1824846 "POLY2" NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-859 1818039 1824409 1824568 "POLY" NIL POLY (NIL T) -8 NIL NIL NIL) (-858 1816926 1817189 1817465 "POLUTIL" NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-857 1815530 1815843 1816173 "POLTOPOL" NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-856 1810692 1815480 1815525 "POINT" NIL POINT (NIL T) -8 NIL NIL NIL) (-855 1809180 1809591 1809966 "PNTHEORY" NIL PNTHEORY (NIL) -7 NIL NIL NIL) (-854 1807937 1808246 1808642 "PMTOOLS" NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-853 1807608 1807692 1807809 "PMSYM" NIL PMSYM (NIL T) -7 NIL NIL NIL) (-852 1807187 1807262 1807436 "PMQFCAT" NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-851 1806673 1806769 1806929 "PMPREDFS" NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-850 1806145 1806265 1806419 "PMPRED" NIL PMPRED (NIL T) -7 NIL NIL NIL) (-849 1805040 1805258 1805635 "PMPLCAT" NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-848 1804651 1804736 1804888 "PMLSAGG" NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-847 1804202 1804284 1804465 "PMKERNEL" NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-846 1803894 1803975 1804088 "PMINS" NIL PMINS (NIL T) -7 NIL NIL NIL) (-845 1803407 1803482 1803690 "PMFS" NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-844 1802755 1802883 1803085 "PMDOWN" NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-843 1802117 1802251 1802414 "PMASSFS" NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-842 1801421 1801603 1801784 "PMASS" NIL PMASS (NIL) -7 NIL NIL NIL) (-841 1801144 1801218 1801312 "PLOTTOOL" NIL PLOTTOOL (NIL) -7 NIL NIL NIL) (-840 1797712 1798901 1799817 "PLOT3D" NIL PLOT3D (NIL) -8 NIL NIL NIL) (-839 1796796 1796997 1797232 "PLOT1" NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-838 1792361 1793745 1794887 "PLOT" NIL PLOT (NIL) -8 NIL NIL NIL) (-837 1772282 1777169 1782016 "PLEQN" NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-836 1772022 1772075 1772178 "PINTERPA" NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-835 1771463 1771597 1771777 "PINTERP" NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-834 1769472 1770693 1770721 "PID" 1770918 PID (NIL) -9 NIL 1771045 NIL) (-833 1769260 1769303 1769378 "PICOERCE" NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-832 1768447 1769107 1769194 "PI" NIL PI (NIL) -8 NIL NIL 1769234) (-831 1767899 1768050 1768226 "PGROEB" NIL PGROEB (NIL T) -7 NIL NIL NIL) (-830 1764227 1765185 1766090 "PGE" NIL PGE (NIL) -7 NIL NIL NIL) (-829 1762591 1762880 1763246 "PGCD" NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-828 1762033 1762148 1762309 "PFRPAC" NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-827 1758574 1760902 1761255 "PFR" NIL PFR (NIL T) -8 NIL NIL NIL) (-826 1757180 1757460 1757785 "PFOTOOLS" NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-825 1755945 1756199 1756547 "PFOQ" NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-824 1754655 1754882 1755234 "PFO" NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-823 1751665 1753225 1753253 "PFECAT" 1753846 PFECAT (NIL) -9 NIL 1754223 NIL) (-822 1751288 1751453 1751660 "PFECAT-" NIL PFECAT- (NIL T) -7 NIL NIL NIL) (-821 1750112 1750394 1750695 "PFBRU" NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-820 1748294 1748681 1749111 "PFBR" NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-819 1744264 1748220 1748289 "PF" NIL PF (NIL NIL) -8 NIL NIL NIL) (-818 1740167 1741314 1742181 "PERMGRP" NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-817 1738099 1739188 1739229 "PERMCAT" 1739628 PERMCAT (NIL T) -9 NIL 1739925 NIL) (-816 1737795 1737842 1737965 "PERMAN" NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-815 1734244 1735925 1736570 "PERM" NIL PERM (NIL T) -8 NIL NIL NIL) (-814 1731709 1733999 1734120 "PENDTREE" NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-813 1730578 1730841 1730882 "PDSPC" 1731415 PDSPC (NIL T) -9 NIL 1731660 NIL) (-812 1729945 1730211 1730573 "PDSPC-" NIL PDSPC- (NIL T T) -7 NIL NIL NIL) (-811 1728580 1729573 1729614 "PDRING" 1729619 PDRING (NIL T) -9 NIL 1729646 NIL) (-810 1727290 1728079 1728132 "PDMOD" 1728137 PDMOD (NIL T T) -9 NIL 1728240 NIL) (-809 1726383 1726595 1726844 "PDECOMP" NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-808 1725988 1726055 1726109 "PDDOM" 1726274 PDDOM (NIL T T) -9 NIL 1726354 NIL) (-807 1725840 1725876 1725983 "PDDOM-" NIL PDDOM- (NIL T T T) -7 NIL NIL NIL) (-806 1725626 1725665 1725754 "PCOMP" NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-805 1723943 1724697 1724996 "PBWLB" NIL PBWLB (NIL T) -8 NIL NIL NIL) (-804 1723632 1723695 1723804 "PATTERN2" NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-803 1721770 1722200 1722651 "PATTERN1" NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-802 1715390 1717219 1718511 "PATTERN" NIL PATTERN (NIL T) -8 NIL NIL NIL) (-801 1715021 1715094 1715226 "PATRES2" NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-800 1712723 1713403 1713884 "PATRES" NIL PATRES (NIL T T) -8 NIL NIL NIL) (-799 1710927 1711355 1711758 "PATMATCH" NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-798 1710373 1710621 1710662 "PATMAB" 1710769 PATMAB (NIL T) -9 NIL 1710852 NIL) (-797 1709020 1709424 1709681 "PATLRES" NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-796 1708558 1708689 1708730 "PATAB" 1708735 PATAB (NIL T) -9 NIL 1708907 NIL) (-795 1707101 1707538 1707961 "PARTPERM" NIL PARTPERM (NIL) -7 NIL NIL NIL) (-794 1706779 1706854 1706956 "PARSURF" NIL PARSURF (NIL T) -8 NIL NIL NIL) (-793 1706468 1706531 1706640 "PARSU2" NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-792 1706273 1706319 1706386 "PARSER" NIL PARSER (NIL) -7 NIL NIL NIL) (-791 1705951 1706026 1706128 "PARSCURV" NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-790 1705640 1705703 1705812 "PARSC2" NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-789 1705331 1705401 1705498 "PARPCURV" NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-788 1705020 1705083 1705192 "PARPC2" NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-787 1704181 1704560 1704739 "PARAMAST" NIL PARAMAST (NIL) -8 NIL NIL NIL) (-786 1703788 1703886 1704005 "PAN2EXPR" NIL PAN2EXPR (NIL) -7 NIL NIL NIL) (-785 1702756 1703181 1703400 "PALETTE" NIL PALETTE (NIL) -8 NIL NIL NIL) (-784 1701421 1702075 1702435 "PAIR" NIL PAIR (NIL T T) -8 NIL NIL NIL) (-783 1694511 1700825 1701019 "PADICRC" NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-782 1686932 1694009 1694193 "PADICRAT" NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-781 1683657 1685572 1685612 "PADICCT" 1686193 PADICCT (NIL NIL) -9 NIL 1686475 NIL) (-780 1681647 1683607 1683652 "PADIC" NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-779 1680809 1681019 1681285 "PADEPAC" NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-778 1680151 1680294 1680498 "PADE" NIL PADE (NIL T T T) -7 NIL NIL NIL) (-777 1678532 1679559 1679837 "OWP" NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-776 1678056 1678315 1678412 "OVERSET" NIL OVERSET (NIL) -8 NIL NIL NIL) (-775 1677115 1677793 1677965 "OVAR" NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-774 1667537 1670406 1672605 "OUTFORM" NIL OUTFORM (NIL) -8 NIL NIL NIL) (-773 1666929 1667243 1667369 "OUTBFILE" NIL OUTBFILE (NIL) -8 NIL NIL NIL) (-772 1666206 1666401 1666429 "OUTBCON" 1666747 OUTBCON (NIL) -9 NIL 1666913 NIL) (-771 1665914 1666044 1666201 "OUTBCON-" NIL OUTBCON- (NIL T) -7 NIL NIL NIL) (-770 1665295 1665440 1665601 "OUT" NIL OUT (NIL) -7 NIL NIL NIL) (-769 1664666 1665093 1665182 "OSI" NIL OSI (NIL) -8 NIL NIL NIL) (-768 1664081 1664496 1664524 "OSGROUP" 1664529 OSGROUP (NIL) -9 NIL 1664551 NIL) (-767 1663045 1663306 1663591 "ORTHPOL" NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-766 1660314 1662920 1663040 "OREUP" NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-765 1657455 1660065 1660191 "ORESUP" NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-764 1655473 1656001 1656561 "OREPCTO" NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-763 1648815 1651355 1651395 "OREPCAT" 1653716 OREPCAT (NIL T) -9 NIL 1654818 NIL) (-762 1646841 1647775 1648810 "OREPCAT-" NIL OREPCAT- (NIL T T) -7 NIL NIL NIL) (-761 1646038 1646309 1646337 "ORDTYPE" 1646642 ORDTYPE (NIL) -9 NIL 1646800 NIL) (-760 1645572 1645783 1646033 "ORDTYPE-" NIL ORDTYPE- (NIL T) -7 NIL NIL NIL) (-759 1645034 1645410 1645567 "ORDSTRCT" NIL ORDSTRCT (NIL T NIL) -8 NIL NIL NIL) (-758 1644528 1644891 1644919 "ORDSET" 1644924 ORDSET (NIL) -9 NIL 1644946 NIL) (-757 1643106 1644128 1644156 "ORDRING" 1644161 ORDRING (NIL) -9 NIL 1644189 NIL) (-756 1642354 1642911 1642939 "ORDMON" 1642944 ORDMON (NIL) -9 NIL 1642965 NIL) (-755 1641658 1641820 1642012 "ORDFUNS" NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-754 1640869 1641377 1641405 "ORDFIN" 1641470 ORDFIN (NIL) -9 NIL 1641544 NIL) (-753 1640263 1640402 1640588 "ORDCOMP2" NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-752 1636938 1639231 1639637 "ORDCOMP" NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-751 1636345 1636700 1636805 "OPSIG" NIL OPSIG (NIL) -8 NIL NIL NIL) (-750 1636153 1636198 1636264 "OPQUERY" NIL OPQUERY (NIL) -7 NIL NIL NIL) (-749 1635454 1635730 1635771 "OPERCAT" 1635982 OPERCAT (NIL T) -9 NIL 1636078 NIL) (-748 1635266 1635333 1635449 "OPERCAT-" NIL OPERCAT- (NIL T T) -7 NIL NIL NIL) (-747 1632632 1634068 1634564 "OP" NIL OP (NIL T) -8 NIL NIL NIL) (-746 1632053 1632180 1632354 "ONECOMP2" NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-745 1628954 1631192 1631558 "ONECOMP" NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-744 1625585 1628384 1628424 "OMSAGG" 1628485 OMSAGG (NIL T) -9 NIL 1628549 NIL) (-743 1623997 1625256 1625424 "OMLO" NIL OMLO (NIL T T) -8 NIL NIL NIL) (-742 1622206 1623447 1623475 "OINTDOM" 1623480 OINTDOM (NIL) -9 NIL 1623501 NIL) (-741 1619636 1621208 1621537 "OFMONOID" NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-740 1618890 1619586 1619631 "ODVAR" NIL ODVAR (NIL T) -8 NIL NIL NIL) (-739 1616092 1618731 1618885 "ODR" NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-738 1607629 1615963 1616087 "ODPOL" NIL ODPOL (NIL T) -8 NIL NIL NIL) (-737 1601040 1607520 1607624 "ODP" NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-736 1600012 1600249 1600522 "ODETOOLS" NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-735 1597646 1598316 1599020 "ODESYS" NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-734 1593423 1594383 1595406 "ODERTRIC" NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-733 1592931 1593019 1593213 "ODERED" NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-732 1590380 1590962 1591635 "ODERAT" NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-731 1587775 1588283 1588879 "ODEPRRIC" NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-730 1584772 1585311 1585957 "ODEPRIM" NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-729 1584127 1584235 1584493 "ODEPAL" NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-728 1583285 1583410 1583631 "ODEINT" NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-727 1579569 1580365 1581278 "ODEEF" NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-726 1579009 1579104 1579326 "ODECONST" NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-725 1578690 1578739 1578866 "OCTCT2" NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-724 1575293 1578489 1578608 "OCT" NIL OCT (NIL T) -8 NIL NIL NIL) (-723 1574453 1575075 1575103 "OCAMON" 1575108 OCAMON (NIL) -9 NIL 1575129 NIL) (-722 1568665 1571479 1571519 "OC" 1572614 OC (NIL T) -9 NIL 1573470 NIL) (-721 1566665 1567591 1568571 "OC-" NIL OC- (NIL T T) -7 NIL NIL NIL) (-720 1566081 1566499 1566527 "OASGP" 1566532 OASGP (NIL) -9 NIL 1566552 NIL) (-719 1565144 1565793 1565821 "OAMONS" 1565861 OAMONS (NIL) -9 NIL 1565904 NIL) (-718 1564289 1564870 1564898 "OAMON" 1564955 OAMON (NIL) -9 NIL 1565006 NIL) (-717 1564185 1564217 1564284 "OAMON-" NIL OAMON- (NIL T) -7 NIL NIL NIL) (-716 1562936 1563710 1563738 "OAGROUP" 1563884 OAGROUP (NIL) -9 NIL 1563976 NIL) (-715 1562666 1562784 1562931 "OAGROUP-" NIL OAGROUP- (NIL T) -7 NIL NIL NIL) (-714 1562406 1562462 1562550 "NUMTUBE" NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-713 1557468 1559031 1560558 "NUMQUAD" NIL NUMQUAD (NIL) -7 NIL NIL NIL) (-712 1554163 1555197 1556232 "NUMODE" NIL NUMODE (NIL) -7 NIL NIL NIL) (-711 1553273 1553506 1553724 "NUMFMT" NIL NUMFMT (NIL) -7 NIL NIL NIL) (-710 1542134 1545162 1547610 "NUMERIC" NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-709 1536021 1541575 1541669 "NTSCAT" 1541674 NTSCAT (NIL T T T T) -9 NIL 1541712 NIL) (-708 1535362 1535541 1535734 "NTPOLFN" NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-707 1535055 1535118 1535225 "NSUP2" NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-706 1522722 1532675 1533485 "NSUP" NIL NSUP (NIL T) -8 NIL NIL NIL) (-705 1511731 1522587 1522717 "NSMP" NIL NSMP (NIL T T) -8 NIL NIL NIL) (-704 1510451 1510776 1511133 "NREP" NIL NREP (NIL T) -7 NIL NIL NIL) (-703 1509287 1509551 1509909 "NPCOEF" NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-702 1508454 1508587 1508803 "NORMRETR" NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-701 1506772 1507091 1507497 "NORMPK" NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-700 1506485 1506519 1506643 "NORMMA" NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-699 1506304 1506339 1506408 "NONE1" NIL NONE1 (NIL T) -7 NIL NIL NIL) (-698 1506080 1506270 1506299 "NONE" NIL NONE (NIL) -8 NIL NIL NIL) (-697 1505644 1505711 1505888 "NODE1" NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-696 1503930 1505007 1505262 "NNI" NIL NNI (NIL) -8 NIL NIL 1505609) (-695 1502658 1502995 1503359 "NLINSOL" NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-694 1501635 1501887 1502189 "NFINTBAS" NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-693 1500722 1501287 1501328 "NETCLT" 1501499 NETCLT (NIL T) -9 NIL 1501580 NIL) (-692 1499626 1499893 1500174 "NCODIV" NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-691 1499425 1499468 1499543 "NCNTFRAC" NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-690 1497956 1498344 1498764 "NCEP" NIL NCEP (NIL T) -7 NIL NIL NIL) (-689 1496589 1497555 1497583 "NASRING" 1497693 NASRING (NIL) -9 NIL 1497773 NIL) (-688 1496434 1496490 1496584 "NASRING-" NIL NASRING- (NIL T) -7 NIL NIL NIL) (-687 1495363 1496041 1496069 "NARNG" 1496186 NARNG (NIL) -9 NIL 1496277 NIL) (-686 1495139 1495224 1495358 "NARNG-" NIL NARNG- (NIL T) -7 NIL NIL NIL) (-685 1493905 1494659 1494699 "NAALG" 1494778 NAALG (NIL T) -9 NIL 1494839 NIL) (-684 1493775 1493810 1493900 "NAALG-" NIL NAALG- (NIL T T) -7 NIL NIL NIL) (-683 1488754 1489939 1491125 "MULTSQFR" NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-682 1488149 1488236 1488420 "MULTFACT" NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-681 1480159 1484653 1484705 "MTSCAT" 1485765 MTSCAT (NIL T T) -9 NIL 1486279 NIL) (-680 1479925 1479985 1480077 "MTHING" NIL MTHING (NIL T) -7 NIL NIL NIL) (-679 1479751 1479790 1479850 "MSYSCMD" NIL MSYSCMD (NIL) -7 NIL NIL NIL) (-678 1476613 1479302 1479343 "MSETAGG" 1479348 MSETAGG (NIL T) -9 NIL 1479382 NIL) (-677 1472750 1475659 1475977 "MSET" NIL MSET (NIL T) -8 NIL NIL NIL) (-676 1469024 1470847 1471587 "MRING" NIL MRING (NIL T T) -8 NIL NIL NIL) (-675 1468661 1468734 1468863 "MRF2" NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-674 1468314 1468355 1468499 "MRATFAC" NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-673 1466179 1466516 1466947 "MPRFF" NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-672 1459577 1466078 1466174 "MPOLY" NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-671 1459102 1459143 1459351 "MPCPF" NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-670 1458661 1458710 1458893 "MPC3" NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-669 1457935 1458028 1458247 "MPC2" NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-668 1456552 1456913 1457303 "MONOTOOL" NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-667 1456073 1456140 1456179 "MONOPC" 1456239 MONOPC (NIL T) -9 NIL 1456458 NIL) (-666 1455524 1455860 1455988 "MONOP" NIL MONOP (NIL T) -8 NIL NIL NIL) (-665 1454666 1455045 1455073 "MONOID" 1455291 MONOID (NIL) -9 NIL 1455435 NIL) (-664 1454325 1454475 1454661 "MONOID-" NIL MONOID- (NIL T) -7 NIL NIL NIL) (-663 1443263 1450133 1450192 "MONOGEN" 1450866 MONOGEN (NIL T T) -9 NIL 1451322 NIL) (-662 1441275 1442161 1443144 "MONOGEN-" NIL MONOGEN- (NIL T T T) -7 NIL NIL NIL) (-661 1439989 1440533 1440561 "MONADWU" 1440952 MONADWU (NIL) -9 NIL 1441187 NIL) (-660 1439537 1439737 1439984 "MONADWU-" NIL MONADWU- (NIL T) -7 NIL NIL NIL) (-659 1438814 1439115 1439143 "MONAD" 1439350 MONAD (NIL) -9 NIL 1439462 NIL) (-658 1438581 1438677 1438809 "MONAD-" NIL MONAD- (NIL T) -7 NIL NIL NIL) (-657 1436971 1437741 1438020 "MOEBIUS" NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-656 1436105 1436632 1436672 "MODULE" 1436677 MODULE (NIL T) -9 NIL 1436715 NIL) (-655 1435784 1435910 1436100 "MODULE-" NIL MODULE- (NIL T T) -7 NIL NIL NIL) (-654 1433495 1434381 1434695 "MODRING" NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-653 1430674 1432091 1432604 "MODOP" NIL MODOP (NIL T T) -8 NIL NIL NIL) (-652 1429308 1429882 1430158 "MODMONOM" NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-651 1418527 1427973 1428386 "MODMON" NIL MODMON (NIL T T) -8 NIL NIL NIL) (-650 1415483 1417527 1417796 "MODFIELD" NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-649 1414567 1414934 1415124 "MMLFORM" NIL MMLFORM (NIL) -8 NIL NIL NIL) (-648 1414136 1414185 1414364 "MMAP" NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-647 1411961 1412957 1412997 "MLO" 1413414 MLO (NIL T) -9 NIL 1413654 NIL) (-646 1409842 1410369 1410964 "MLIFT" NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-645 1409310 1409406 1409560 "MKUCFUNC" NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-644 1408980 1409056 1409179 "MKRECORD" NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-643 1408192 1408378 1408606 "MKFUNC" NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-642 1407685 1407801 1407957 "MKFLCFN" NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-641 1407057 1407171 1407356 "MKBCFUNC" NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-640 1406084 1406357 1406634 "MHROWRED" NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-639 1405517 1405605 1405776 "MFINFACT" NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-638 1402675 1403554 1404433 "MESH" NIL MESH (NIL) -7 NIL NIL NIL) (-637 1401342 1401690 1402043 "MDDFACT" NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-636 1397999 1400466 1400507 "MDAGG" 1400764 MDAGG (NIL T) -9 NIL 1400909 NIL) (-635 1397273 1397437 1397637 "MCDEN" NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-634 1396351 1396637 1396867 "MAYBE" NIL MAYBE (NIL T) -8 NIL NIL NIL) (-633 1394448 1395025 1395586 "MATSTOR" NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-632 1390219 1394038 1394285 "MATRIX" NIL MATRIX (NIL T) -8 NIL NIL NIL) (-631 1386568 1387337 1388071 "MATLIN" NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-630 1385321 1385490 1385819 "MATCAT2" NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-629 1374834 1378423 1378499 "MATCAT" 1383487 MATCAT (NIL T T T) -9 NIL 1384955 NIL) (-628 1372115 1373421 1374829 "MATCAT-" NIL MATCAT- (NIL T T T T) -7 NIL NIL NIL) (-627 1370516 1370876 1371260 "MAPPKG3" NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-626 1369649 1369846 1370068 "MAPPKG2" NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-625 1368400 1368726 1369053 "MAPPKG1" NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-624 1367562 1367964 1368140 "MAPPAST" NIL MAPPAST (NIL) -8 NIL NIL NIL) (-623 1367231 1367295 1367418 "MAPHACK3" NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-622 1366879 1366952 1367066 "MAPHACK2" NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-621 1366414 1366529 1366671 "MAPHACK1" NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-620 1364623 1365391 1365692 "MAGMA" NIL MAGMA (NIL T) -8 NIL NIL NIL) (-619 1364117 1364419 1364509 "MACROAST" NIL MACROAST (NIL) -8 NIL NIL NIL) (-618 1357626 1362432 1362473 "LZSTAGG" 1363250 LZSTAGG (NIL T) -9 NIL 1363540 NIL) (-617 1354745 1356179 1357621 "LZSTAGG-" NIL LZSTAGG- (NIL T T) -7 NIL NIL NIL) (-616 1352132 1353098 1353581 "LWORD" NIL LWORD (NIL T) -8 NIL NIL NIL) (-615 1351713 1351992 1352066 "LSTAST" NIL LSTAST (NIL) -8 NIL NIL NIL) (-614 1343877 1351574 1351708 "LSQM" NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-613 1343240 1343385 1343613 "LSPP" NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-612 1340724 1341422 1342134 "LSMP1" NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-611 1338836 1339159 1339607 "LSMP" NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-610 1332005 1337923 1337964 "LSAGG" 1338026 LSAGG (NIL T) -9 NIL 1338104 NIL) (-609 1329699 1330798 1332000 "LSAGG-" NIL LSAGG- (NIL T T) -7 NIL NIL NIL) (-608 1327179 1329048 1329297 "LPOLY" NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-607 1326846 1326937 1327060 "LPEFRAC" NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-606 1326517 1326596 1326624 "LOGIC" 1326735 LOGIC (NIL) -9 NIL 1326817 NIL) (-605 1326412 1326441 1326512 "LOGIC-" NIL LOGIC- (NIL T) -7 NIL NIL NIL) (-604 1325731 1325889 1326082 "LODOOPS" NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-603 1324516 1324765 1325116 "LODOF" NIL LODOF (NIL T T) -7 NIL NIL NIL) (-602 1320338 1323137 1323177 "LODOCAT" 1323609 LODOCAT (NIL T) -9 NIL 1323820 NIL) (-601 1320131 1320207 1320333 "LODOCAT-" NIL LODOCAT- (NIL T T) -7 NIL NIL NIL) (-600 1317131 1320008 1320126 "LODO2" NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-599 1314229 1317081 1317126 "LODO1" NIL LODO1 (NIL T) -8 NIL NIL NIL) (-598 1311316 1314159 1314224 "LODO" NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-597 1310369 1310544 1310846 "LODEEF" NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-596 1308501 1309631 1309884 "LO" NIL LO (NIL T T T) -8 NIL NIL NIL) (-595 1303596 1306660 1306701 "LNAGG" 1307563 LNAGG (NIL T) -9 NIL 1307998 NIL) (-594 1302983 1303250 1303591 "LNAGG-" NIL LNAGG- (NIL T T) -7 NIL NIL NIL) (-593 1299555 1300496 1301133 "LMOPS" NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-592 1298817 1299322 1299362 "LMODULE" 1299367 LMODULE (NIL T) -9 NIL 1299393 NIL) (-591 1295996 1298554 1298676 "LMDICT" NIL LMDICT (NIL T) -8 NIL NIL NIL) (-590 1295564 1295775 1295816 "LLINSET" 1295877 LLINSET (NIL T) -9 NIL 1295921 NIL) (-589 1295240 1295500 1295559 "LITERAL" NIL LITERAL (NIL T) -8 NIL NIL NIL) (-588 1294839 1294919 1295058 "LIST3" NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-587 1293290 1293638 1294037 "LIST2MAP" NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-586 1292461 1292657 1292885 "LIST2" NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-585 1285507 1291717 1291971 "LIST" NIL LIST (NIL T) -8 NIL NIL NIL) (-584 1285084 1285317 1285358 "LINSET" 1285363 LINSET (NIL T) -9 NIL 1285396 NIL) (-583 1283985 1284707 1284874 "LINFORM" NIL LINFORM (NIL T NIL) -8 NIL NIL NIL) (-582 1282251 1283006 1283046 "LINEXP" 1283532 LINEXP (NIL T) -9 NIL 1283805 NIL) (-581 1280873 1281860 1282041 "LINELT" NIL LINELT (NIL T NIL) -8 NIL NIL NIL) (-580 1279700 1279972 1280274 "LINDEP" NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-579 1278913 1279502 1279612 "LINBASIS" NIL LINBASIS (NIL NIL) -8 NIL NIL NIL) (-578 1276463 1277185 1277935 "LIMITRF" NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-577 1275093 1275390 1275781 "LIMITPS" NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-576 1273886 1274488 1274528 "LIECAT" 1274668 LIECAT (NIL T) -9 NIL 1274819 NIL) (-575 1273760 1273793 1273881 "LIECAT-" NIL LIECAT- (NIL T T) -7 NIL NIL NIL) (-574 1268016 1273450 1273678 "LIE" NIL LIE (NIL T T) -8 NIL NIL NIL) (-573 1260365 1267692 1267848 "LIB" NIL LIB (NIL) -8 NIL NIL NIL) (-572 1256817 1257766 1258701 "LGROBP" NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-571 1255441 1256349 1256377 "LFCAT" 1256584 LFCAT (NIL) -9 NIL 1256723 NIL) (-570 1253680 1254010 1254355 "LF" NIL LF (NIL T T) -7 NIL NIL NIL) (-569 1251197 1251862 1252543 "LEXTRIPK" NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-568 1248209 1249187 1249690 "LEXP" NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-567 1247700 1248003 1248094 "LETAST" NIL LETAST (NIL) -8 NIL NIL NIL) (-566 1246407 1246731 1247131 "LEADCDET" NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-565 1245673 1245758 1245984 "LAZM3PK" NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-564 1240676 1244241 1244777 "LAUPOL" NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-563 1240301 1240351 1240511 "LAPLACE" NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-562 1239072 1239845 1239885 "LALG" 1239946 LALG (NIL T) -9 NIL 1240004 NIL) (-561 1238855 1238932 1239067 "LALG-" NIL LALG- (NIL T T) -7 NIL NIL NIL) (-560 1236708 1238123 1238374 "LA" NIL LA (NIL T T T) -8 NIL NIL NIL) (-559 1236537 1236567 1236608 "KVTFROM" 1236670 KVTFROM (NIL T) -9 NIL NIL NIL) (-558 1235353 1236068 1236257 "KTVLOGIC" NIL KTVLOGIC (NIL) -8 NIL NIL NIL) (-557 1235182 1235212 1235253 "KRCFROM" 1235315 KRCFROM (NIL T) -9 NIL NIL NIL) (-556 1234284 1234481 1234776 "KOVACIC" NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-555 1234113 1234143 1234184 "KONVERT" 1234246 KONVERT (NIL T) -9 NIL NIL NIL) (-554 1233942 1233972 1234013 "KOERCE" 1234075 KOERCE (NIL T) -9 NIL NIL NIL) (-553 1233512 1233605 1233737 "KERNEL2" NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-552 1231565 1232459 1232831 "KERNEL" NIL KERNEL (NIL T) -8 NIL NIL NIL) (-551 1224742 1229757 1229811 "KDAGG" 1230187 KDAGG (NIL T T) -9 NIL 1230394 NIL) (-550 1224390 1224532 1224737 "KDAGG-" NIL KDAGG- (NIL T T T) -7 NIL NIL NIL) (-549 1217220 1224171 1224328 "KAFILE" NIL KAFILE (NIL T) -8 NIL NIL NIL) (-548 1216870 1217152 1217215 "JVMOP" NIL JVMOP (NIL) -8 NIL NIL NIL) (-547 1215840 1216339 1216588 "JVMMDACC" NIL JVMMDACC (NIL) -8 NIL NIL NIL) (-546 1214966 1215415 1215620 "JVMFDACC" NIL JVMFDACC (NIL) -8 NIL NIL NIL) (-545 1213830 1214322 1214622 "JVMCSTTG" NIL JVMCSTTG (NIL) -8 NIL NIL NIL) (-544 1213112 1213511 1213672 "JVMCFACC" NIL JVMCFACC (NIL) -8 NIL NIL NIL) (-543 1212822 1213058 1213107 "JVMBCODE" NIL JVMBCODE (NIL) -8 NIL NIL NIL) (-542 1207077 1212512 1212740 "JORDAN" NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-541 1206495 1206828 1206948 "JOINAST" NIL JOINAST (NIL) -8 NIL NIL NIL) (-540 1202657 1204672 1204726 "IXAGG" 1205653 IXAGG (NIL T T) -9 NIL 1206110 NIL) (-539 1201863 1202234 1202652 "IXAGG-" NIL IXAGG- (NIL T T T) -7 NIL NIL NIL) (-538 1197117 1201799 1201858 "IVECTOR" NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-537 1196084 1196359 1196622 "ITUPLE" NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-536 1194746 1194953 1195246 "ITRIGMNP" NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-535 1193697 1193919 1194202 "ITFUN3" NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-534 1193372 1193435 1193558 "ITFUN2" NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-533 1192634 1193006 1193180 "ITFORM" NIL ITFORM (NIL) -8 NIL NIL NIL) (-532 1190610 1191910 1192184 "ITAYLOR" NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-531 1180158 1185927 1187084 "ISUPS" NIL ISUPS (NIL T) -8 NIL NIL NIL) (-530 1179403 1179555 1179791 "ISUMP" NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-529 1178894 1179197 1179288 "ISAST" NIL ISAST (NIL) -8 NIL NIL NIL) (-528 1178187 1178278 1178491 "IRURPK" NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-527 1177319 1177544 1177784 "IRSN" NIL IRSN (NIL) -7 NIL NIL NIL) (-526 1175732 1176113 1176541 "IRRF2F" NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-525 1175517 1175561 1175637 "IRREDFFX" NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-524 1174367 1174664 1174959 "IROOT" NIL IROOT (NIL T) -7 NIL NIL NIL) (-523 1173640 1173991 1174142 "IRFORM" NIL IRFORM (NIL) -8 NIL NIL NIL) (-522 1172843 1172974 1173187 "IR2F" NIL IR2F (NIL T T) -7 NIL NIL NIL) (-521 1170998 1171495 1172039 "IR2" NIL IR2 (NIL T T) -7 NIL NIL NIL) (-520 1168079 1169347 1170036 "IR" NIL IR (NIL T) -8 NIL NIL NIL) (-519 1167904 1167944 1168004 "IPRNTPK" NIL IPRNTPK (NIL) -7 NIL NIL NIL) (-518 1163902 1167830 1167899 "IPF" NIL IPF (NIL NIL) -8 NIL NIL NIL) (-517 1161905 1163841 1163897 "IPADIC" NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-516 1161276 1161575 1161705 "IP4ADDR" NIL IP4ADDR (NIL) -8 NIL NIL NIL) (-515 1160729 1161017 1161149 "IOMODE" NIL IOMODE (NIL) -8 NIL NIL NIL) (-514 1159810 1160435 1160561 "IOBFILE" NIL IOBFILE (NIL) -8 NIL NIL NIL) (-513 1159220 1159714 1159742 "IOBCON" 1159747 IOBCON (NIL) -9 NIL 1159768 NIL) (-512 1158791 1158855 1159037 "INVLAPLA" NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-511 1150835 1153206 1155531 "INTTR" NIL INTTR (NIL T T) -7 NIL NIL NIL) (-510 1147946 1148729 1149593 "INTTOOLS" NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-509 1147623 1147720 1147837 "INTSLPE" NIL INTSLPE (NIL) -7 NIL NIL NIL) (-508 1145065 1147559 1147618 "INTRVL" NIL INTRVL (NIL T) -8 NIL NIL NIL) (-507 1143177 1143706 1144273 "INTRF" NIL INTRF (NIL T) -7 NIL NIL NIL) (-506 1142679 1142793 1142933 "INTRET" NIL INTRET (NIL T) -7 NIL NIL NIL) (-505 1141063 1141469 1141931 "INTRAT" NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-504 1138842 1139436 1140047 "INTPM" NIL INTPM (NIL T T) -7 NIL NIL NIL) (-503 1136215 1136825 1137545 "INTPAF" NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-502 1135619 1135777 1135985 "INTHERTR" NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-501 1135138 1135224 1135412 "INTHERAL" NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-500 1133343 1133864 1134321 "INTHEORY" NIL INTHEORY (NIL) -7 NIL NIL NIL) (-499 1126425 1128078 1129807 "INTG0" NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-498 1125791 1125953 1126126 "INTFACT" NIL INTFACT (NIL T) -7 NIL NIL NIL) (-497 1123664 1124128 1124672 "INTEF" NIL INTEF (NIL T T) -7 NIL NIL NIL) (-496 1121790 1122740 1122768 "INTDOM" 1123067 INTDOM (NIL) -9 NIL 1123272 NIL) (-495 1121343 1121545 1121785 "INTDOM-" NIL INTDOM- (NIL T) -7 NIL NIL NIL) (-494 1117150 1119622 1119676 "INTCAT" 1120472 INTCAT (NIL T) -9 NIL 1120788 NIL) (-493 1116715 1116835 1116962 "INTBIT" NIL INTBIT (NIL) -7 NIL NIL NIL) (-492 1115555 1115727 1116033 "INTALG" NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-491 1115128 1115224 1115381 "INTAF" NIL INTAF (NIL T T) -7 NIL NIL NIL) (-490 1108168 1114983 1115123 "INTABL" NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-489 1107466 1108021 1108086 "INT8" NIL INT8 (NIL) -8 NIL NIL 1108120) (-488 1106763 1107318 1107383 "INT64" NIL INT64 (NIL) -8 NIL NIL 1107417) (-487 1106060 1106615 1106680 "INT32" NIL INT32 (NIL) -8 NIL NIL 1106714) (-486 1105357 1105912 1105977 "INT16" NIL INT16 (NIL) -8 NIL NIL 1106011) (-485 1101820 1105276 1105352 "INT" NIL INT (NIL) -8 NIL NIL NIL) (-484 1095877 1099360 1099388 "INS" 1100318 INS (NIL) -9 NIL 1100977 NIL) (-483 1093939 1094857 1095804 "INS-" NIL INS- (NIL T) -7 NIL NIL NIL) (-482 1092998 1093221 1093496 "INPSIGN" NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-481 1092212 1092353 1092550 "INPRODPF" NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-480 1091202 1091343 1091580 "INPRODFF" NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-479 1090354 1090518 1090778 "INNMFACT" NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-478 1089634 1089749 1089937 "INMODGCD" NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-477 1088373 1088642 1088966 "INFSP" NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-476 1087653 1087794 1087977 "INFPROD0" NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-475 1087316 1087388 1087486 "INFORM1" NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-474 1084394 1085880 1086403 "INFORM" NIL INFORM (NIL) -8 NIL NIL NIL) (-473 1083993 1084100 1084214 "INFINITY" NIL INFINITY (NIL) -7 NIL NIL NIL) (-472 1083149 1083794 1083895 "INETCLTS" NIL INETCLTS (NIL) -8 NIL NIL NIL) (-471 1081999 1082267 1082588 "INEP" NIL INEP (NIL T T T) -7 NIL NIL NIL) (-470 1080989 1081929 1081994 "INDE" NIL INDE (NIL T) -8 NIL NIL NIL) (-469 1080614 1080694 1080811 "INCRMAPS" NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-468 1079528 1080073 1080277 "INBFILE" NIL INBFILE (NIL) -8 NIL NIL NIL) (-467 1075623 1076678 1077621 "INBFF" NIL INBFF (NIL T) -7 NIL NIL NIL) (-466 1074477 1074800 1074828 "INBCON" 1075341 INBCON (NIL) -9 NIL 1075607 NIL) (-465 1073931 1074196 1074472 "INBCON-" NIL INBCON- (NIL T) -7 NIL NIL NIL) (-464 1073425 1073727 1073817 "INAST" NIL INAST (NIL) -8 NIL NIL NIL) (-463 1072882 1073191 1073296 "IMPTAST" NIL IMPTAST (NIL) -8 NIL NIL NIL) (-462 1068982 1072774 1072877 "IMATRIX" NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-461 1067822 1067961 1068276 "IMATQF" NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-460 1066246 1066513 1066850 "IMATLIN" NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-459 1064062 1066128 1066241 "IIARRAY2" NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-458 1058905 1063993 1064057 "IFF" NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-457 1058285 1058619 1058734 "IFAST" NIL IFAST (NIL) -8 NIL NIL NIL) (-456 1053092 1057723 1057909 "IFARRAY" NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-455 1052122 1053014 1053087 "IFAMON" NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-454 1051694 1051771 1051825 "IEVALAB" 1052032 IEVALAB (NIL T T) -9 NIL NIL NIL) (-453 1051449 1051529 1051689 "IEVALAB-" NIL IEVALAB- (NIL T T T) -7 NIL NIL NIL) (-452 1050834 1051061 1051218 "IDPT" NIL IDPT (NIL T T) -8 NIL NIL NIL) (-451 1049827 1050754 1050829 "IDPOAMS" NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-450 1048889 1049747 1049822 "IDPOAM" NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-449 1047971 1048618 1048755 "IDPO" NIL IDPO (NIL T T) -8 NIL NIL NIL) (-448 1046334 1046905 1046956 "IDPC" 1047462 IDPC (NIL T T) -9 NIL 1047775 NIL) (-447 1045621 1046256 1046329 "IDPAM" NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-446 1044791 1045543 1045616 "IDPAG" NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-445 1044484 1044697 1044757 "IDENT" NIL IDENT (NIL) -8 NIL NIL NIL) (-444 1044188 1044228 1044267 "IDEMOPC" 1044272 IDEMOPC (NIL T) -9 NIL 1044409 NIL) (-443 1041259 1042140 1043032 "IDECOMP" NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-442 1034885 1036162 1037201 "IDEAL" NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-441 1034147 1034277 1034476 "ICDEN" NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-440 1033320 1033819 1033957 "ICARD" NIL ICARD (NIL) -8 NIL NIL NIL) (-439 1031709 1032040 1032431 "IBPTOOLS" NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-438 1027478 1031665 1031704 "IBITS" NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-437 1024736 1025360 1026055 "IBATOOL" NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-436 1022962 1023442 1023975 "IBACHIN" NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-435 1020726 1022854 1022957 "IARRAY2" NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-434 1016595 1020664 1020721 "IARRAY1" NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-433 1010174 1015559 1016027 "IAN" NIL IAN (NIL) -8 NIL NIL NIL) (-432 1009742 1009805 1009978 "IALGFACT" NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-431 1009234 1009383 1009411 "HYPCAT" 1009618 HYPCAT (NIL) -9 NIL NIL NIL) (-430 1008890 1009043 1009229 "HYPCAT-" NIL HYPCAT- (NIL T) -7 NIL NIL NIL) (-429 1008503 1008748 1008831 "HOSTNAME" NIL HOSTNAME (NIL) -8 NIL NIL NIL) (-428 1008336 1008385 1008426 "HOMOTOP" 1008431 HOMOTOP (NIL T) -9 NIL 1008464 NIL) (-427 1004904 1006278 1006319 "HOAGG" 1007294 HOAGG (NIL T) -9 NIL 1008015 NIL) (-426 1003910 1004380 1004899 "HOAGG-" NIL HOAGG- (NIL T T) -7 NIL NIL NIL) (-425 997110 1003635 1003783 "HEXADEC" NIL HEXADEC (NIL) -8 NIL NIL NIL) (-424 996045 996303 996566 "HEUGCD" NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-423 994980 995910 996040 "HELLFDIV" NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-422 993174 994813 994901 "HEAP" NIL HEAP (NIL T) -8 NIL NIL NIL) (-421 992489 992841 992974 "HEADAST" NIL HEADAST (NIL) -8 NIL NIL NIL) (-420 985943 992422 992484 "HDP" NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-419 979082 985679 985830 "HDMP" NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-418 978535 978692 978855 "HB" NIL HB (NIL) -7 NIL NIL NIL) (-417 971618 978426 978530 "HASHTBL" NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-416 971109 971412 971503 "HASAST" NIL HASAST (NIL) -8 NIL NIL NIL) (-415 968659 970896 971075 "HACKPI" NIL HACKPI (NIL) -8 NIL NIL NIL) (-414 964052 968542 968654 "GTSET" NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-413 957138 963949 964047 "GSTBL" NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-412 949075 956507 956762 "GSERIES" NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-411 948099 948608 948636 "GROUP" 948839 GROUP (NIL) -9 NIL 948973 NIL) (-410 947642 947843 948094 "GROUP-" NIL GROUP- (NIL T) -7 NIL NIL NIL) (-409 946314 946653 947040 "GROEBSOL" NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-408 945136 945493 945544 "GRMOD" 946073 GRMOD (NIL T T) -9 NIL 946239 NIL) (-407 944955 945003 945131 "GRMOD-" NIL GRMOD- (NIL T T T) -7 NIL NIL NIL) (-406 941078 942289 943289 "GRIMAGE" NIL GRIMAGE (NIL) -8 NIL NIL NIL) (-405 939800 940124 940439 "GRDEF" NIL GRDEF (NIL) -7 NIL NIL NIL) (-404 939353 939481 939622 "GRAY" NIL GRAY (NIL) -7 NIL NIL NIL) (-403 938426 938925 938976 "GRALG" 939129 GRALG (NIL T T) -9 NIL 939219 NIL) (-402 938145 938246 938421 "GRALG-" NIL GRALG- (NIL T T T) -7 NIL NIL NIL) (-401 934862 937827 938003 "GPOLSET" NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-400 934275 934338 934595 "GOSPER" NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-399 930129 931025 931550 "GMODPOL" NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-398 929304 929506 929744 "GHENSEL" NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-397 924307 925234 926253 "GENUPS" NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-396 924055 924112 924201 "GENUFACT" NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-395 923537 923626 923791 "GENPGCD" NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-394 923046 923087 923300 "GENMFACT" NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-393 921847 922130 922434 "GENEEZ" NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-392 915122 921537 921698 "GDMP" NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-391 904905 909912 911016 "GCNAALG" NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-390 902957 904060 904088 "GCDDOM" 904343 GCDDOM (NIL) -9 NIL 904500 NIL) (-389 902580 902737 902952 "GCDDOM-" NIL GCDDOM- (NIL T) -7 NIL NIL NIL) (-388 893373 895843 898231 "GBINTERN" NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-387 891508 891833 892251 "GBF" NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-386 890449 890638 890905 "GBEUCLID" NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-385 889320 889527 889831 "GB" NIL GB (NIL T T T T) -7 NIL NIL NIL) (-384 888783 888925 889073 "GAUSSFAC" NIL GAUSSFAC (NIL) -7 NIL NIL NIL) (-383 887395 887743 888056 "GALUTIL" NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-382 885940 886261 886583 "GALPOLYU" NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-381 883566 883922 884327 "GALFACTU" NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-380 876818 878479 880057 "GALFACT" NIL GALFACT (NIL T) -7 NIL NIL NIL) (-379 876470 876691 876759 "FUNDESC" NIL FUNDESC (NIL) -8 NIL NIL NIL) (-378 876094 876315 876396 "FUNCTION" NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-377 874191 874874 875334 "FT" NIL FT (NIL) -8 NIL NIL NIL) (-376 872784 873091 873483 "FSUPFACT" NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-375 871439 871798 872122 "FST" NIL FST (NIL) -8 NIL NIL NIL) (-374 870742 870866 871053 "FSRED" NIL FSRED (NIL T T) -7 NIL NIL NIL) (-373 869716 869982 870329 "FSPRMELT" NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-372 867374 867904 868386 "FSPECF" NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-371 866957 867017 867186 "FSINT" NIL FSINT (NIL T T) -7 NIL NIL NIL) (-370 865257 866171 866474 "FSERIES" NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-369 864405 864539 864762 "FSCINT" NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-368 863576 863737 863964 "FSAGG2" NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-367 859559 862510 862551 "FSAGG" 862921 FSAGG (NIL T) -9 NIL 863180 NIL) (-366 857913 858672 859464 "FSAGG-" NIL FSAGG- (NIL T T) -7 NIL NIL NIL) (-365 855869 856165 856709 "FS2UPS" NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-364 854916 855098 855398 "FS2EXPXP" NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-363 854597 854646 854773 "FS2" NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-362 834753 844254 844295 "FS" 848165 FS (NIL T) -9 NIL 850443 NIL) (-361 826984 830477 834456 "FS-" NIL FS- (NIL T T) -7 NIL NIL NIL) (-360 826518 826645 826797 "FRUTIL" NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-359 821041 824199 824239 "FRNAALG" 825559 FRNAALG (NIL T) -9 NIL 826157 NIL) (-358 817782 819033 820291 "FRNAALG-" NIL FRNAALG- (NIL T T) -7 NIL NIL NIL) (-357 817463 817512 817639 "FRNAAF2" NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-356 815950 816507 816801 "FRMOD" NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-355 815236 815329 815616 "FRIDEAL2" NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-354 813070 813836 814152 "FRIDEAL" NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-353 812179 812622 812663 "FRETRCT" 812668 FRETRCT (NIL T) -9 NIL 812839 NIL) (-352 811552 811830 812174 "FRETRCT-" NIL FRETRCT- (NIL T T) -7 NIL NIL NIL) (-351 808296 809816 809875 "FRAMALG" 810757 FRAMALG (NIL T T) -9 NIL 811049 NIL) (-350 806892 807443 808073 "FRAMALG-" NIL FRAMALG- (NIL T T T) -7 NIL NIL NIL) (-349 806585 806648 806755 "FRAC2" NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-348 800226 806390 806580 "FRAC" NIL FRAC (NIL T) -8 NIL NIL NIL) (-347 799919 799982 800089 "FR2" NIL FR2 (NIL T T) -7 NIL NIL NIL) (-346 792227 796798 798126 "FR" NIL FR (NIL T) -8 NIL NIL NIL) (-345 786005 789508 789536 "FPS" 790655 FPS (NIL) -9 NIL 791211 NIL) (-344 785562 785695 785859 "FPS-" NIL FPS- (NIL T) -7 NIL NIL NIL) (-343 782372 784415 784443 "FPC" 784668 FPC (NIL) -9 NIL 784810 NIL) (-342 782218 782270 782367 "FPC-" NIL FPC- (NIL T) -7 NIL NIL NIL) (-341 780995 781704 781745 "FPATMAB" 781750 FPATMAB (NIL T) -9 NIL 781902 NIL) (-340 779425 780021 780368 "FPARFRAC" NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-339 779000 779058 779231 "FORDER" NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-338 777503 778398 778572 "FNLA" NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-337 776118 776623 776651 "FNCAT" 777108 FNCAT (NIL) -9 NIL 777365 NIL) (-336 775575 776085 776113 "FNAME" NIL FNAME (NIL) -8 NIL NIL NIL) (-335 774162 775524 775570 "FMONOID" NIL FMONOID (NIL T) -8 NIL NIL NIL) (-334 770750 772108 772149 "FMONCAT" 773366 FMONCAT (NIL T) -9 NIL 773970 NIL) (-333 767608 768686 768739 "FMCAT" 769920 FMCAT (NIL T T) -9 NIL 770412 NIL) (-332 766308 767431 767530 "FM1" NIL FM1 (NIL T T) -8 NIL NIL NIL) (-331 765356 766156 766303 "FM" NIL FM (NIL T T) -8 NIL NIL NIL) (-330 763543 763995 764489 "FLOATRP" NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-329 761478 762014 762592 "FLOATCP" NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-328 754864 759815 760429 "FLOAT" NIL FLOAT (NIL) -8 NIL NIL NIL) (-327 753345 754446 754486 "FLINEXP" 754491 FLINEXP (NIL T) -9 NIL 754584 NIL) (-326 752754 753013 753340 "FLINEXP-" NIL FLINEXP- (NIL T T) -7 NIL NIL NIL) (-325 751969 752128 752349 "FLASORT" NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-324 748852 749931 749983 "FLALG" 751210 FLALG (NIL T T) -9 NIL 751677 NIL) (-323 748023 748184 748411 "FLAGG2" NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-322 741432 745442 745483 "FLAGG" 746738 FLAGG (NIL T) -9 NIL 747383 NIL) (-321 740540 740944 741427 "FLAGG-" NIL FLAGG- (NIL T T) -7 NIL NIL NIL) (-320 737101 738365 738424 "FINRALG" 739552 FINRALG (NIL T T) -9 NIL 740060 NIL) (-319 736492 736757 737096 "FINRALG-" NIL FINRALG- (NIL T T T) -7 NIL NIL NIL) (-318 735790 736086 736114 "FINITE" 736310 FINITE (NIL) -9 NIL 736417 NIL) (-317 735698 735724 735785 "FINITE-" NIL FINITE- (NIL T) -7 NIL NIL NIL) (-316 727659 730250 730290 "FINAALG" 733942 FINAALG (NIL T) -9 NIL 735380 NIL) (-315 723926 725171 726294 "FINAALG-" NIL FINAALG- (NIL T T) -7 NIL NIL NIL) (-314 722478 722897 722951 "FILECAT" 723635 FILECAT (NIL T T) -9 NIL 723851 NIL) (-313 721829 722303 722406 "FILE" NIL FILE (NIL T) -8 NIL NIL NIL) (-312 719077 720955 720983 "FIELD" 721023 FIELD (NIL) -9 NIL 721103 NIL) (-311 718102 718563 719072 "FIELD-" NIL FIELD- (NIL T) -7 NIL NIL NIL) (-310 716106 717052 717398 "FGROUP" NIL FGROUP (NIL T) -8 NIL NIL NIL) (-309 715349 715530 715749 "FGLMICPK" NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-308 710619 715287 715344 "FFX" NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-307 710281 710348 710483 "FFSLPE" NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-306 709821 709863 710072 "FFPOLY2" NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-305 706501 707378 708155 "FFPOLY" NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-304 701785 706433 706496 "FFP" NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-303 696464 701274 701464 "FFNBX" NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-302 690945 695745 696003 "FFNBP" NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-301 685152 690396 690607 "FFNB" NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-300 684175 684385 684700 "FFINTBAS" NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-299 679615 682320 682348 "FFIELDC" 682967 FFIELDC (NIL) -9 NIL 683342 NIL) (-298 678684 679124 679610 "FFIELDC-" NIL FFIELDC- (NIL T) -7 NIL NIL NIL) (-297 678299 678357 678481 "FFHOM" NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-296 676443 676966 677483 "FFF" NIL FFF (NIL T) -7 NIL NIL NIL) (-295 671537 676242 676343 "FFCGX" NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-294 666637 671326 671433 "FFCGP" NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-293 661303 666428 666536 "FFCG" NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-292 660757 660806 661041 "FFCAT2" NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-291 639332 650366 650452 "FFCAT" 655602 FFCAT (NIL T T T) -9 NIL 657038 NIL) (-290 635572 636798 638104 "FFCAT-" NIL FFCAT- (NIL T T T T) -7 NIL NIL NIL) (-289 630415 635503 635567 "FF" NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-288 629307 629776 629817 "FEVALAB" 629901 FEVALAB (NIL T) -9 NIL 630162 NIL) (-287 628712 628964 629302 "FEVALAB-" NIL FEVALAB- (NIL T T) -7 NIL NIL NIL) (-286 625539 626450 626565 "FDIVCAT" 628132 FDIVCAT (NIL T T T T) -9 NIL 628568 NIL) (-285 625333 625365 625534 "FDIVCAT-" NIL FDIVCAT- (NIL T T T T T) -7 NIL NIL NIL) (-284 624640 624733 625010 "FDIV2" NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-283 623126 624124 624327 "FDIV" NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-282 622219 622603 622805 "FCTRDATA" NIL FCTRDATA (NIL) -8 NIL NIL NIL) (-281 621341 621830 621970 "FCOMP" NIL FCOMP (NIL T) -8 NIL NIL NIL) (-280 612928 617571 617611 "FAXF" 619412 FAXF (NIL T) -9 NIL 620102 NIL) (-279 610844 611648 612463 "FAXF-" NIL FAXF- (NIL T T) -7 NIL NIL NIL) (-278 605708 610366 610540 "FARRAY" NIL FARRAY (NIL T) -8 NIL NIL NIL) (-277 600166 602589 602641 "FAMR" 603652 FAMR (NIL T T) -9 NIL 604111 NIL) (-276 599365 599730 600161 "FAMR-" NIL FAMR- (NIL T T T) -7 NIL NIL NIL) (-275 598386 599307 599360 "FAMONOID" NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-274 595980 596859 596912 "FAMONC" 597853 FAMONC (NIL T T) -9 NIL 598238 NIL) (-273 594536 595838 595975 "FAGROUP" NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-272 592616 592977 593379 "FACUTIL" NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-271 591893 592090 592312 "FACTFUNC" NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-270 583753 591340 591539 "EXPUPXS" NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-269 581772 582342 582928 "EXPRTUBE" NIL EXPRTUBE (NIL) -7 NIL NIL NIL) (-268 578674 579316 580036 "EXPRODE" NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-267 573831 574538 575343 "EXPR2UPS" NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-266 573520 573583 573692 "EXPR2" NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-265 558313 572569 572995 "EXPR" NIL EXPR (NIL T) -8 NIL NIL NIL) (-264 548840 557633 557921 "EXPEXPAN" NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-263 548334 548636 548726 "EXITAST" NIL EXITAST (NIL) -8 NIL NIL NIL) (-262 548110 548300 548329 "EXIT" NIL EXIT (NIL) -8 NIL NIL NIL) (-261 547799 547867 547980 "EVALCYC" NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-260 547316 547458 547499 "EVALAB" 547669 EVALAB (NIL T) -9 NIL 547773 NIL) (-259 546944 547090 547311 "EVALAB-" NIL EVALAB- (NIL T T) -7 NIL NIL NIL) (-258 543987 545582 545610 "EUCDOM" 546164 EUCDOM (NIL) -9 NIL 546513 NIL) (-257 542914 543407 543982 "EUCDOM-" NIL EUCDOM- (NIL T) -7 NIL NIL NIL) (-256 542639 542695 542795 "ES2" NIL ES2 (NIL T T) -7 NIL NIL NIL) (-255 542327 542391 542500 "ES1" NIL ES1 (NIL T T) -7 NIL NIL NIL) (-254 536098 537998 538026 "ES" 540768 ES (NIL) -9 NIL 542152 NIL) (-253 532613 534145 535937 "ES-" NIL ES- (NIL T) -7 NIL NIL NIL) (-252 531961 532114 532290 "ERROR" NIL ERROR (NIL) -7 NIL NIL NIL) (-251 525050 531865 531956 "EQTBL" NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-250 524739 524802 524911 "EQ2" NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-249 518366 521491 522924 "EQ" NIL EQ (NIL T) -8 NIL NIL NIL) (-248 514669 515765 516858 "EP" NIL EP (NIL T) -7 NIL NIL NIL) (-247 513498 513848 514153 "ENV" NIL ENV (NIL) -8 NIL NIL NIL) (-246 512383 513114 513142 "ENTIRER" 513147 ENTIRER (NIL) -9 NIL 513191 NIL) (-245 512272 512306 512378 "ENTIRER-" NIL ENTIRER- (NIL T) -7 NIL NIL NIL) (-244 508905 510702 511051 "EMR" NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-243 507997 508208 508262 "ELTAGG" 508642 ELTAGG (NIL T T) -9 NIL 508853 NIL) (-242 507777 507851 507992 "ELTAGG-" NIL ELTAGG- (NIL T T T) -7 NIL NIL NIL) (-241 507523 507558 507612 "ELTAB" 507696 ELTAB (NIL T T) -9 NIL 507748 NIL) (-240 506774 506944 507143 "ELFUTS" NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-239 506498 506572 506600 "ELEMFUN" 506705 ELEMFUN (NIL) -9 NIL NIL NIL) (-238 506398 506425 506493 "ELEMFUN-" NIL ELEMFUN- (NIL T) -7 NIL NIL NIL) (-237 500944 504439 504480 "ELAGG" 505417 ELAGG (NIL T) -9 NIL 505877 NIL) (-236 499742 500280 500939 "ELAGG-" NIL ELAGG- (NIL T T) -7 NIL NIL NIL) (-235 499160 499327 499483 "ELABOR" NIL ELABOR (NIL) -8 NIL NIL NIL) (-234 498073 498392 498671 "ELABEXPR" NIL ELABEXPR (NIL) -8 NIL NIL NIL) (-233 491466 493464 494291 "EFUPXS" NIL EFUPXS (NIL T T T T) -7 NIL NIL NIL) (-232 485445 487441 488251 "EFULS" NIL EFULS (NIL T T T) -7 NIL NIL NIL) (-231 483259 483665 484136 "EFSTRUC" NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-230 474259 476172 477713 "EF" NIL EF (NIL T T) -7 NIL NIL NIL) (-229 473372 473873 474022 "EAB" NIL EAB (NIL) -8 NIL NIL NIL) (-228 472070 472744 472784 "DVARCAT" 473067 DVARCAT (NIL T) -9 NIL 473207 NIL) (-227 471489 471753 472065 "DVARCAT-" NIL DVARCAT- (NIL T T) -7 NIL NIL NIL) (-226 463556 471357 471484 "DSMP" NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-225 461894 462685 462726 "DSEXT" 463089 DSEXT (NIL T) -9 NIL 463383 NIL) (-224 460699 461223 461889 "DSEXT-" NIL DSEXT- (NIL T T) -7 NIL NIL NIL) (-223 460423 460488 460586 "DROPT1" NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-222 456574 457790 458921 "DROPT0" NIL DROPT0 (NIL) -7 NIL NIL NIL) (-221 452220 453575 454639 "DROPT" NIL DROPT (NIL) -8 NIL NIL NIL) (-220 450895 451256 451642 "DRAWPT" NIL DRAWPT (NIL) -7 NIL NIL NIL) (-219 450581 450640 450758 "DRAWHACK" NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-218 449556 449854 450144 "DRAWCX" NIL DRAWCX (NIL) -7 NIL NIL NIL) (-217 449141 449216 449366 "DRAWCURV" NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-216 441554 443666 445781 "DRAWCFUN" NIL DRAWCFUN (NIL) -7 NIL NIL NIL) (-215 437071 438090 439169 "DRAW" NIL DRAW (NIL T) -7 NIL NIL NIL) (-214 433666 435735 435776 "DQAGG" 436405 DQAGG (NIL T) -9 NIL 436678 NIL) (-213 420209 427849 427931 "DPOLCAT" 429768 DPOLCAT (NIL T T T T) -9 NIL 430311 NIL) (-212 416617 418265 420204 "DPOLCAT-" NIL DPOLCAT- (NIL T T T T T) -7 NIL NIL NIL) (-211 409622 416515 416612 "DPMO" NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-210 402536 409451 409617 "DPMM" NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-209 402129 402389 402478 "DOMTMPLT" NIL DOMTMPLT (NIL) -8 NIL NIL NIL) (-208 401543 401991 402071 "DOMCTOR" NIL DOMCTOR (NIL) -8 NIL NIL NIL) (-207 400829 401154 401305 "DOMAIN" NIL DOMAIN (NIL) -8 NIL NIL NIL) (-206 393968 400565 400716 "DMP" NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-205 391717 393034 393074 "DMEXT" 393079 DMEXT (NIL T) -9 NIL 393254 NIL) (-204 391373 391435 391579 "DLP" NIL DLP (NIL T) -7 NIL NIL NIL) (-203 384698 390858 391048 "DLIST" NIL DLIST (NIL T) -8 NIL NIL NIL) (-202 381364 383521 383562 "DLAGG" 384112 DLAGG (NIL T) -9 NIL 384341 NIL) (-201 379715 380586 380614 "DIVRING" 380706 DIVRING (NIL) -9 NIL 380789 NIL) (-200 379166 379410 379710 "DIVRING-" NIL DIVRING- (NIL T) -7 NIL NIL NIL) (-199 377594 378011 378417 "DISPLAY" NIL DISPLAY (NIL) -7 NIL NIL NIL) (-198 376631 376852 377117 "DIRPROD2" NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-197 370105 376563 376626 "DIRPROD" NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-196 358425 364885 364938 "DIRPCAT" 365194 DIRPCAT (NIL NIL T) -9 NIL 366067 NIL) (-195 356431 357201 358088 "DIRPCAT-" NIL DIRPCAT- (NIL T NIL T) -7 NIL NIL NIL) (-194 355878 356044 356230 "DIOSP" NIL DIOSP (NIL) -7 NIL NIL NIL) (-193 352424 354764 354805 "DIOPS" 355237 DIOPS (NIL T) -9 NIL 355463 NIL) (-192 352084 352228 352419 "DIOPS-" NIL DIOPS- (NIL T T) -7 NIL NIL NIL) (-191 351091 351837 351865 "DIOID" 351870 DIOID (NIL) -9 NIL 351892 NIL) (-190 349919 350748 350776 "DIFRING" 350781 DIFRING (NIL) -9 NIL 350802 NIL) (-189 349555 349653 349681 "DIFFSPC" 349800 DIFFSPC (NIL) -9 NIL 349875 NIL) (-188 349296 349398 349550 "DIFFSPC-" NIL DIFFSPC- (NIL T) -7 NIL NIL NIL) (-187 348199 348824 348864 "DIFFMOD" 348869 DIFFMOD (NIL T) -9 NIL 348966 NIL) (-186 347883 347940 347981 "DIFFDOM" 348102 DIFFDOM (NIL T) -9 NIL 348170 NIL) (-185 347764 347794 347878 "DIFFDOM-" NIL DIFFDOM- (NIL T T) -7 NIL NIL NIL) (-184 345437 346958 346998 "DIFEXT" 347003 DIFEXT (NIL T) -9 NIL 347155 NIL) (-183 342598 344938 344979 "DIAGG" 344984 DIAGG (NIL T) -9 NIL 345004 NIL) (-182 342154 342344 342593 "DIAGG-" NIL DIAGG- (NIL T T) -7 NIL NIL NIL) (-181 337366 341344 341621 "DHMATRIX" NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-180 333824 334877 335887 "DFSFUN" NIL DFSFUN (NIL) -7 NIL NIL NIL) (-179 328374 332978 333305 "DFLOAT" NIL DFLOAT (NIL) -8 NIL NIL NIL) (-178 326940 327232 327607 "DFINTTLS" NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-177 324060 325312 325708 "DERHAM" NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-176 321780 323891 323980 "DEQUEUE" NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-175 321163 321308 321490 "DEGRED" NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-174 318481 319205 320005 "DEFINTRF" NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-173 316590 317048 317610 "DEFINTEF" NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-172 315973 316306 316420 "DEFAST" NIL DEFAST (NIL) -8 NIL NIL NIL) (-171 309173 315698 315846 "DECIMAL" NIL DECIMAL (NIL) -8 NIL NIL NIL) (-170 307093 307603 308107 "DDFACT" NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-169 306732 306781 306932 "DBLRESP" NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-168 305991 306553 306644 "DBASIS" NIL DBASIS (NIL NIL) -8 NIL NIL NIL) (-167 304015 304457 304817 "DBASE" NIL DBASE (NIL T) -8 NIL NIL NIL) (-166 303307 303596 303742 "DATAARY" NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-165 302758 302904 303056 "CYCLOTOM" NIL CYCLOTOM (NIL) -7 NIL NIL NIL) (-164 300120 300913 301640 "CYCLES" NIL CYCLES (NIL) -7 NIL NIL NIL) (-163 299559 299705 299876 "CVMP" NIL CVMP (NIL T) -7 NIL NIL NIL) (-162 297631 297942 298309 "CTRIGMNP" NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-161 297188 297443 297544 "CTORKIND" NIL CTORKIND (NIL) -8 NIL NIL NIL) (-160 296389 296772 296800 "CTORCAT" 296981 CTORCAT (NIL) -9 NIL 297093 NIL) (-159 296092 296226 296384 "CTORCAT-" NIL CTORCAT- (NIL T) -7 NIL NIL NIL) (-158 295585 295842 295950 "CTORCALL" NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-157 295001 295432 295505 "CTOR" NIL CTOR (NIL) -8 NIL NIL NIL) (-156 294460 294577 294730 "CSTTOOLS" NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-155 290854 291610 292365 "CRFP" NIL CRFP (NIL T T) -7 NIL NIL NIL) (-154 290345 290648 290739 "CRCEAST" NIL CRCEAST (NIL) -8 NIL NIL NIL) (-153 289564 289773 290001 "CRAPACK" NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-152 289068 289173 289377 "CPMATCH" NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-151 288821 288855 288961 "CPIMA" NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-150 285760 286522 287240 "COORDSYS" NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-149 285279 285421 285560 "CONTOUR" NIL CONTOUR (NIL) -8 NIL NIL NIL) (-148 281172 283742 284234 "CONTFRAC" NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-147 281046 281073 281101 "CONDUIT" 281138 CONDUIT (NIL) -9 NIL NIL NIL) (-146 279925 280656 280684 "COMRING" 280689 COMRING (NIL) -9 NIL 280739 NIL) (-145 279090 279457 279635 "COMPPROP" NIL COMPPROP (NIL) -8 NIL NIL NIL) (-144 278786 278827 278955 "COMPLPAT" NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-143 278479 278542 278649 "COMPLEX2" NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-142 267321 278429 278474 "COMPLEX" NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-141 266782 266921 267081 "COMPILER" NIL COMPILER (NIL) -7 NIL NIL NIL) (-140 266535 266576 266674 "COMPFACT" NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-139 247966 260216 260256 "COMPCAT" 261257 COMPCAT (NIL T) -9 NIL 262599 NIL) (-138 240504 244017 247610 "COMPCAT-" NIL COMPCAT- (NIL T T) -7 NIL NIL NIL) (-137 240263 240297 240399 "COMMUPC" NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-136 240093 240132 240190 "COMMONOP" NIL COMMONOP (NIL) -7 NIL NIL NIL) (-135 239674 239953 240027 "COMMAAST" NIL COMMAAST (NIL) -8 NIL NIL NIL) (-134 239251 239492 239579 "COMM" NIL COMM (NIL) -8 NIL NIL NIL) (-133 238446 238694 238722 "COMBOPC" 239060 COMBOPC (NIL) -9 NIL 239235 NIL) (-132 237510 237762 238004 "COMBINAT" NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-131 234442 235126 235749 "COMBF" NIL COMBF (NIL T T) -7 NIL NIL NIL) (-130 233322 233773 234008 "COLOR" NIL COLOR (NIL) -8 NIL NIL NIL) (-129 232813 233116 233207 "COLONAST" NIL COLONAST (NIL) -8 NIL NIL NIL) (-128 232500 232553 232678 "CMPLXRT" NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-127 231970 232280 232378 "CLLCTAST" NIL CLLCTAST (NIL) -8 NIL NIL NIL) (-126 228490 229560 230640 "CLIP" NIL CLIP (NIL) -7 NIL NIL NIL) (-125 226785 227770 228008 "CLIF" NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-124 222897 224905 224946 "CLAGG" 225872 CLAGG (NIL T) -9 NIL 226405 NIL) (-123 221790 222317 222892 "CLAGG-" NIL CLAGG- (NIL T T) -7 NIL NIL NIL) (-122 221419 221510 221650 "CINTSLPE" NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-121 219356 219863 220411 "CHVAR" NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-120 218317 219048 219076 "CHARZ" 219081 CHARZ (NIL) -9 NIL 219095 NIL) (-119 218111 218157 218235 "CHARPOL" NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-118 216950 217713 217741 "CHARNZ" 217802 CHARNZ (NIL) -9 NIL 217850 NIL) (-117 214428 215525 216048 "CHAR" NIL CHAR (NIL) -8 NIL NIL NIL) (-116 214136 214215 214243 "CFCAT" 214354 CFCAT (NIL) -9 NIL NIL NIL) (-115 213479 213608 213790 "CDEN" NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-114 209468 212892 213172 "CCLASS" NIL CCLASS (NIL) -8 NIL NIL NIL) (-113 208846 209033 209210 "CATEGORY" NIL -10 (NIL) -8 NIL NIL NIL) (-112 208374 208793 208841 "CATCTOR" NIL CATCTOR (NIL) -8 NIL NIL NIL) (-111 207847 208156 208253 "CATAST" NIL CATAST (NIL) -8 NIL NIL NIL) (-110 207338 207641 207732 "CASEAST" NIL CASEAST (NIL) -8 NIL NIL NIL) (-109 206587 206747 206968 "CARTEN2" NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-108 202687 203944 204652 "CARTEN" NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-107 201053 202084 202335 "CARD" NIL CARD (NIL) -8 NIL NIL NIL) (-106 200634 200913 200987 "CAPSLAST" NIL CAPSLAST (NIL) -8 NIL NIL NIL) (-105 200068 200321 200349 "CACHSET" 200481 CACHSET (NIL) -9 NIL 200559 NIL) (-104 199420 199835 199863 "CABMON" 199913 CABMON (NIL) -9 NIL 199969 NIL) (-103 198950 199214 199324 "BYTEORD" NIL BYTEORD (NIL) -8 NIL NIL NIL) (-102 194173 198607 198779 "BYTEBUF" NIL BYTEBUF (NIL) -8 NIL NIL NIL) (-101 193143 193847 193982 "BYTE" NIL BYTE (NIL) -8 NIL NIL 194145) (-100 190614 192910 193016 "BTREE" NIL BTREE (NIL T) -8 NIL NIL NIL) (-99 188045 190357 190476 "BTOURN" NIL BTOURN (NIL T) -8 NIL NIL NIL) (-98 185285 187489 187528 "BTCAT" 187595 BTCAT (NIL T) -9 NIL 187671 NIL) (-97 185036 185134 185280 "BTCAT-" NIL BTCAT- (NIL T T) -7 NIL NIL NIL) (-96 180146 184267 184293 "BTAGG" 184404 BTAGG (NIL) -9 NIL 184512 NIL) (-95 179777 179938 180141 "BTAGG-" NIL BTAGG- (NIL T) -7 NIL NIL NIL) (-94 176839 179247 179459 "BSTREE" NIL BSTREE (NIL T) -8 NIL NIL NIL) (-93 176109 176261 176439 "BRILL" NIL BRILL (NIL T) -7 NIL NIL NIL) (-92 172642 174815 174854 "BRAGG" 175495 BRAGG (NIL T) -9 NIL 175752 NIL) (-91 171597 172092 172637 "BRAGG-" NIL BRAGG- (NIL T T) -7 NIL NIL NIL) (-90 164131 171102 171283 "BPADICRT" NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-89 162123 164083 164126 "BPADIC" NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-88 161856 161892 162003 "BOUNDZRO" NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-87 160095 160528 160976 "BOP1" NIL BOP1 (NIL T) -7 NIL NIL NIL) (-86 156061 157477 158367 "BOP" NIL BOP (NIL) -8 NIL NIL NIL) (-85 154937 155828 155950 "BOOLEAN" NIL BOOLEAN (NIL) -8 NIL NIL NIL) (-84 154523 154680 154706 "BOOLE" 154814 BOOLE (NIL) -9 NIL 154895 NIL) (-83 154316 154397 154518 "BOOLE-" NIL BOOLE- (NIL T) -7 NIL NIL NIL) (-82 153454 153981 154031 "BMODULE" 154036 BMODULE (NIL T T) -9 NIL 154100 NIL) (-81 149071 153311 153380 "BITS" NIL BITS (NIL) -8 NIL NIL NIL) (-80 148884 148924 148963 "BINOPC" 148968 BINOPC (NIL T) -9 NIL 149013 NIL) (-79 148426 148699 148801 "BINOP" NIL BINOP (NIL T) -8 NIL NIL NIL) (-78 147947 148091 148229 "BINDING" NIL BINDING (NIL) -8 NIL NIL NIL) (-77 141153 147677 147822 "BINARY" NIL BINARY (NIL) -8 NIL NIL NIL) (-76 138887 140382 140421 "BGAGG" 140677 BGAGG (NIL T) -9 NIL 140814 NIL) (-75 138756 138794 138882 "BGAGG-" NIL BGAGG- (NIL T T) -7 NIL NIL NIL) (-74 137607 137808 138093 "BEZOUT" NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-73 134245 136765 137092 "BBTREE" NIL BBTREE (NIL T) -8 NIL NIL NIL) (-72 133830 133923 133949 "BASTYPE" 134120 BASTYPE (NIL) -9 NIL 134216 NIL) (-71 133600 133696 133825 "BASTYPE-" NIL BASTYPE- (NIL T) -7 NIL NIL NIL) (-70 133115 133203 133353 "BALFACT" NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-69 132014 132689 132874 "AUTOMOR" NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-68 131740 131745 131771 "ATTREG" 131776 ATTREG (NIL) -9 NIL NIL NIL) (-67 131345 131617 131682 "ATTRAST" NIL ATTRAST (NIL) -8 NIL NIL NIL) (-66 130845 130994 131020 "ATRIG" 131221 ATRIG (NIL) -9 NIL NIL NIL) (-65 130700 130753 130840 "ATRIG-" NIL ATRIG- (NIL T) -7 NIL NIL NIL) (-64 130270 130501 130527 "ASTCAT" 130532 ASTCAT (NIL) -9 NIL 130562 NIL) (-63 130069 130146 130265 "ASTCAT-" NIL ASTCAT- (NIL T) -7 NIL NIL NIL) (-62 128228 129902 129990 "ASTACK" NIL ASTACK (NIL T) -8 NIL NIL NIL) (-61 127035 127348 127713 "ASSOCEQ" NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-60 124835 126939 127030 "ARRAY2" NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 124026 124217 124438 "ARRAY12" NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-58 119613 123757 123871 "ARRAY1" NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-57 113779 115811 115886 "ARR2CAT" 118516 ARR2CAT (NIL T T T) -9 NIL 119274 NIL) (-56 112156 112926 113774 "ARR2CAT-" NIL ARR2CAT- (NIL T T T T) -7 NIL NIL NIL) (-55 111524 111895 112017 "ARITY" NIL ARITY (NIL) -8 NIL NIL NIL) (-54 110456 110624 110920 "APPRULE" NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 110157 110211 110329 "APPLYORE" NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 109540 109686 109842 "ANY1" NIL ANY1 (NIL T) -7 NIL NIL NIL) (-51 108945 109235 109355 "ANY" NIL ANY (NIL) -8 NIL NIL NIL) (-50 106513 107674 107997 "ANTISYM" NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 106038 106298 106394 "ANON" NIL ANON (NIL) -8 NIL NIL NIL) (-48 99733 105100 105542 "AN" NIL AN (NIL) -8 NIL NIL NIL) (-47 95267 96930 96980 "AMR" 97718 AMR (NIL T T) -9 NIL 98315 NIL) (-46 94621 94901 95262 "AMR-" NIL AMR- (NIL T T T) -7 NIL NIL NIL) (-45 77801 94555 94616 "ALIST" NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 74204 77477 77646 "ALGSC" NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 71214 71874 72481 "ALGPKG" NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 70593 70706 70890 "ALGMFACT" NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 67005 67630 68222 "ALGMANIP" NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 56494 66698 66848 "ALGFF" NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 55811 55965 56143 "ALGFACT" NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 54524 55319 55357 "ALGEBRA" 55362 ALGEBRA (NIL T) -9 NIL 55402 NIL) (-37 54310 54387 54519 "ALGEBRA-" NIL ALGEBRA- (NIL T T) -7 NIL NIL NIL) (-36 34307 51516 51568 "ALAGG" 51706 ALAGG (NIL T T) -9 NIL 51871 NIL) (-35 33807 33956 33982 "AHYP" 34183 AHYP (NIL) -9 NIL NIL NIL) (-34 33103 33284 33310 "AGG" 33591 AGG (NIL) -9 NIL 33778 NIL) (-33 32892 32979 33098 "AGG-" NIL AGG- (NIL T) -7 NIL NIL NIL) (-32 31031 31491 31891 "AF" NIL AF (NIL T T) -7 NIL NIL NIL) (-31 30526 30829 30918 "ADDAST" NIL ADDAST (NIL) -8 NIL NIL NIL) (-30 29896 30191 30347 "ACPLOT" NIL ACPLOT (NIL) -8 NIL NIL NIL) (-29 17454 26733 26771 "ACFS" 27378 ACFS (NIL T) -9 NIL 27617 NIL) (-28 16077 16687 17449 "ACFS-" NIL ACFS- (NIL T T) -7 NIL NIL NIL) (-27 11629 14008 14034 "ACF" 14913 ACF (NIL) -9 NIL 15325 NIL) (-26 10725 11131 11624 "ACF-" NIL ACF- (NIL T) -7 NIL NIL NIL) (-25 10227 10467 10493 "ABELSG" 10585 ABELSG (NIL) -9 NIL 10650 NIL) (-24 10125 10156 10222 "ABELSG-" NIL ABELSG- (NIL T) -7 NIL NIL NIL) (-23 9280 9654 9680 "ABELMON" 9905 ABELMON (NIL) -9 NIL 10038 NIL) (-22 8962 9102 9275 "ABELMON-" NIL ABELMON- (NIL T) -7 NIL NIL NIL) (-21 8174 8657 8683 "ABELGRP" 8755 ABELGRP (NIL) -9 NIL 8830 NIL) (-20 7788 7953 8169 "ABELGRP-" NIL ABELGRP- (NIL T) -7 NIL NIL NIL) (-19 3036 7046 7085 "A1AGG" 7090 A1AGG (NIL T) -9 NIL 7130 NIL) (-18 30 1483 3031 "A1AGG-" NIL A1AGG- (NIL T T) -7 NIL NIL NIL)) \ No newline at end of file
diff --git a/src/share/algebra/operation.daase b/src/share/algebra/operation.daase
index 26687276..710ed06e 100644
--- a/src/share/algebra/operation.daase
+++ b/src/share/algebra/operation.daase
@@ -1,13161 +1,13162 @@
-(630951 . 3577105536)
+(631062 . 3577141753)
(((*1 *2 *3 *4)
- (|partial| -12 (-5 *3 (-1178 *4)) (-4 *4 (-13 (-962) (-581 (-484))))
- (-5 *2 (-1178 (-347 (-484)))) (-5 *1 (-1207 *4)))))
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((*1 *1 *1 *2)
(OR
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((*1 *1 *1)
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((*1 *1 *1 *2)
(OR
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((*1 *1 *1)
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((*1 *1 *1 *2)
(OR
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- (-12 (-4 *3 (-29 (-484))) (-4 *3 (-872)) (-4 *3 (-1114))
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((*1 *1 *1)
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((*1 *2 *1 *3)
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((*1 *1 *1)
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((*1 *1 *1)
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((*1 *1 *1)
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((*1 *1 *1)
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(((*1 *2 *2 *3 *3)
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((*1 *1 *1 *2 *2)
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((*1 *1 *1)
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((*1 *2 *1 *3 *3)
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((*1 *2 *1 *3)
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((*1 *2 *1 *3 *3 *3 *3)
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((*1 *2 *1 *3 *3 *3)
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((*1 *2 *1 *3 *3)
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((*1 *2 *1 *3)
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(-4 *4
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((*1 *1 *1 *2)
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(-4 *3
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((*1 *2 *1 *3)
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((*1 *2 *3 *4)
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- (-4 *7 (-718))
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+ (-4 *7 (-719))
(-5 *2
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- (-2 (|:| |eqzro| (-584 *8)) (|:| |neqzro| (-584 *8))
- (|:| |wcond| (-584 (-858 *5)))
+ (-585
+ (-2 (|:| |eqzro| (-585 *8)) (|:| |neqzro| (-585 *8))
+ (|:| |wcond| (-585 (-859 *5)))
(|:| |bsoln|
- (-2 (|:| |partsol| (-1178 (-347 (-858 *5))))
- (|:| -2011 (-584 (-1178 (-347 (-858 *5))))))))))
- (-5 *1 (-836 *5 *6 *7 *8))))
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((*1 *2 *3)
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(-5 *2
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+ (-585
+ (-2 (|:| |eqzro| (-585 *7)) (|:| |neqzro| (-585 *7))
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(|:| |bsoln|
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- (-5 *1 (-836 *4 *5 *6 *7))))
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((*1 *2 *3 *4 *5)
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(-5 *2
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+ (-585
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(|:| |bsoln|
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- (-5 *1 (-836 *6 *7 *8 *9)) (-5 *4 (-584 *9))))
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((*1 *2 *3 *4 *5)
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(-5 *2
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(|:| |bsoln|
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((*1 *2 *3 *4)
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(-5 *2
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(|:| |bsoln|
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((*1 *2 *3 *4 *5)
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((*1 *2 *3 *4 *5 *6)
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((*1 *2 *3 *4 *5 *6)
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((*1 *2 *3 *4 *5)
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(((*1 *2 *3 *3)
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(((*1 *2 *3)
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(((*1 *2 *3 *1)
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(((*1 *2 *2 *3)
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(((*1 *2 *2 *3)
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(|:| |a0| *7)))
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(|:| |answer|
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(|:| |a0| *7)))
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+ (-3833 . 76511) (-3834 . 75846) (-3835 . 75654) (-3836 . 75559)
+ (-3837 . 75251) (-3838 . 74079) (-3839 . 73873) (-3840 . 72698)
+ (-3841 . 72623) (-3842 . 71442) (-3843 . 67861) (-3844 . 67497)
+ (-3845 . 67220) (-3846 . 67128) (-3847 . 67035) (-3848 . 66758)
+ (-3849 . 66665) (-3850 . 66572) (-3851 . 66479) (-3852 . 66095)
+ (-3853 . 66024) (-3854 . 65932) (-3855 . 65774) (-3856 . 65420)
+ (-3857 . 65262) (-3858 . 65154) (-3859 . 65125) (-3860 . 65058)
+ (-3861 . 64904) (-3862 . 64746) (-3863 . 64352) (-3864 . 64277)
+ (-3865 . 64171) (-3866 . 64099) (-3867 . 64021) (-3868 . 63948)
+ (-3869 . 63875) (-3870 . 63802) (-3871 . 63730) (-3872 . 63658)
+ (-3873 . 63585) (-3874 . 63344) (-3875 . 63004) (-3876 . 62856)
+ (-3877 . 62783) (-3878 . 62710) (-3879 . 62637) (-3880 . 62383)
+ (-3881 . 62239) (-3882 . 60903) (-3883 . 60709) (-3884 . 60438)
+ (-3885 . 60290) (-3886 . 60142) (-3887 . 59902) (-3888 . 59708)
+ (-3889 . 59440) (-3890 . 59244) (-3891 . 59215) (-3892 . 59114)
+ (-3893 . 59013) (-3894 . 58912) (-3895 . 58811) (-3896 . 58710)
+ (-3897 . 58609) (-3898 . 58508) (-3899 . 58407) (-3900 . 58306)
+ (-3901 . 58205) (-3902 . 58090) (-3903 . 57975) (-3904 . 57924)
+ (-3905 . 57807) (-3906 . 57749) (-3907 . 57648) (-3908 . 57547)
+ (-3909 . 57446) (-3910 . 57330) (-3911 . 57301) (-3912 . 56570)
+ (-3913 . 56445) (-3914 . 56320) (-3915 . 56180) (-3916 . 56062)
+ (-3917 . 55937) (-3918 . 55782) (-3919 . 54799) (-3920 . 53940)
+ (-3921 . 53886) (-3922 . 53832) (-3923 . 53624) (-3924 . 53252)
+ (-3925 . 52841) (-3926 . 52483) (-3927 . 52125) (-3928 . 51973)
+ (-3929 . 51671) (-3930 . 51515) (-3931 . 51189) (-3932 . 51119)
+ (-3933 . 51049) (-3934 . 50840) (-3935 . 50231) (-3936 . 50027)
+ (-3937 . 49654) (-3938 . 49145) (-3939 . 48880) (-3940 . 48399)
+ (-3941 . 47918) (-3942 . 47793) (-3943 . 46693) (-3944 . 45617)
+ (-3945 . 45044) (-3946 . 44826) (-3947 . 36500) (-3948 . 36315)
+ (-3949 . 34232) (-3950 . 32064) (-3951 . 31918) (-3952 . 31740)
+ (-3953 . 31333) (-3954 . 31038) (-3955 . 30690) (-3956 . 30524)
+ (-3957 . 30358) (-3958 . 29945) (-3959 . 16071) (-3960 . 14964) (* . 10917)
+ (-3962 . 10663) (-3963 . 10479) (-3964 . 9522) (-3965 . 9469) (-3966 . 9409)
+ (-3967 . 9140) (-3968 . 8513) (-3969 . 7240) (-3970 . 5996) (-3971 . 5127)
+ (-3972 . 3864) (-3973 . 420) (-3974 . 306) (-3975 . 173) (-3976 . 30)) \ No newline at end of file