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authordos-reis <gdr@axiomatics.org>2013-05-09 16:40:30 +0000
committerdos-reis <gdr@axiomatics.org>2013-05-09 16:40:30 +0000
commit4233705a72aa0f223e5567ba21ea7e0aaaa49280 (patch)
tree2a875936a349bab87bf40a7e1d0f317c1b03872b
parent78a10a3795011b28c3f143512a9b935edbb4e9c9 (diff)
downloadopen-axiom-4233705a72aa0f223e5567ba21ea7e0aaaa49280.tar.gz
* algebra/indexedp.spad.pamphlet (IndexedDirectProductObject)
[combineWithIf]: New.
-rw-r--r--src/ChangeLog5
-rw-r--r--src/algebra/indexedp.spad.pamphlet39
-rw-r--r--src/share/algebra/browse.daase1062
-rw-r--r--src/share/algebra/category.daase190
-rw-r--r--src/share/algebra/compress.daase8
-rw-r--r--src/share/algebra/interp.daase6134
-rw-r--r--src/share/algebra/operation.daase2483
7 files changed, 4983 insertions, 4938 deletions
diff --git a/src/ChangeLog b/src/ChangeLog
index 73058d5e..163d64a1 100644
--- a/src/ChangeLog
+++ b/src/ChangeLog
@@ -1,5 +1,10 @@
2013-05-09 Gabriel Dos Reis <gdr@integrable-solutions.net>
+ * algebra/indexedp.spad.pamphlet (IndexedDirectProductObject)
+ [combineWithIf]: New.
+
+2013-05-09 Gabriel Dos Reis <gdr@integrable-solutions.net>
+
* interp/i-special.boot (evalIF): Generate OIL intermediate
instruction %otherwise, not Lisp expression T.
* interp/slam.boot (isRecurrenceRelation): Likewise.
diff --git a/src/algebra/indexedp.spad.pamphlet b/src/algebra/indexedp.spad.pamphlet
index bbb78cd0..c296f271 100644
--- a/src/algebra/indexedp.spad.pamphlet
+++ b/src/algebra/indexedp.spad.pamphlet
@@ -93,7 +93,12 @@ IndexedProductTerm(A,S): Public == Private where
IndexedDirectProductObject(A,S): Public == Private where
A: BasicType
S: OrderedType
- Public == IndexedDirectProductCategory(A,S)
+ Public == IndexedDirectProductCategory(A,S) with
+ combineWithIf: (%,%, (A,A) -> A, (A,A) -> Boolean) -> %
+ ++ \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.
Private == List IndexedProductTerm(A,S) add
if A has CoercibleTo OutputForm and S has CoercibleTo OutputForm then
coerce(x:%):OutputForm ==
@@ -113,6 +118,38 @@ IndexedDirectProductObject(A,S): Public == Private where
index first rep x
terms x == rep x
convert l == per l
+ combineWithIf(u, v, f, p) ==
+ x := rep u
+ y := rep v
+ empty? x => v
+ empty? y => u
+ z: Rep := nil
+ prev: Rep := nil
+ while not empty? x and not empty? y repeat
+ xt := first x
+ yt := first y
+ index xt > index yt =>
+ t := [xt]
+ if empty? z then z := t
+ else setrest!(prev,t)
+ prev := t
+ x := rest x
+ index xt < index yt =>
+ t := [yt]
+ if empty? z then z := t
+ else setrest!(prev,t)
+ prev := t
+ y := rest y
+ not p(coefficient xt, coefficient yt) => iterate
+ t := [term(index xt, f(coefficient xt, coefficient yt))]
+ if empty? z then z := t
+ else setrest!(prev,t)
+ prev := t
+ x := rest x
+ y := rest y
+ if empty? x then setrest!(prev,y)
+ else if empty? y then setrest!(prev,x)
+ per z
@
\section{domain IDPAM IndexedDirectProductAbelianMonoid}
diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase
index 8d714c85..c0908d72 100644
--- a/src/share/algebra/browse.daase
+++ b/src/share/algebra/browse.daase
@@ -1,12 +1,12 @@
-(1961818 . 3576910161)
+(1962139 . 3577105535)
(-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.")))
-((-3992 . T) (-3991 . T))
+((-3993 . T) (-3992 . T))
NIL
(-20 S)
((|constructor| (NIL "The class of abelian groups,{} \\spadignore{i.e.} additive monoids where each element has an additive inverse. \\blankline")) (- (($ $ $) "\\spad{x-y} is the difference of \\spad{x} and \\spad{y} \\spadignore{i.e.} \\spad{x + (-y)}.") (($ $) "\\spad{-x} is the additive inverse of \\spad{x}")))
@@ -38,7 +38,7 @@ NIL
NIL
(-27)
((|constructor| (NIL "Model for algebraically closed fields.")) (|zerosOf| (((|List| $) (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{zerosOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}'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}.")))
-((-3983 . T) (-3989 . T) (-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . T))
+((-3984 . T) (-3990 . T) (-3985 . T) ((-3994 "*") . T) (-3986 . T) (-3987 . T) (-3989 . 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}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}.")))
-((-3988 . T) (-3986 . T) (-3985 . T) ((-3993 "*") . T) (-3984 . T) (-3989 . T) (-3983 . T))
+((-3989 . T) (-3987 . T) (-3986 . T) ((-3994 "*") . T) (-3985 . T) (-3990 . T) (-3984 . T))
NIL
(-30)
((|refine| (($ $ (|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 -3090)
+(-32 R -3091)
((|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)))))
(-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 -3991)))
+((|HasAttribute| |#1| (QUOTE -3992)))
(-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}.")))
-((-3991 . T) (-3992 . T))
+((-3992 . T) (-3993 . T))
NIL
(-37 S R)
((|constructor| (NIL "The category of associative algebras (modules which are themselves rings). \\blankline")))
@@ -82,17 +82,17 @@ NIL
NIL
(-38 R)
((|constructor| (NIL "The category of associative algebras (modules which are themselves rings). \\blankline")))
-((-3985 . T) (-3986 . T) (-3988 . T))
+((-3986 . T) (-3987 . T) (-3989 . 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 -3090 UP UPUP -2612)
+(-40 -3091 UP UPUP -2613)
((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}")))
-((-3984 |has| (-347 |#2|) (-311)) (-3989 |has| (-347 |#2|) (-311)) (-3983 |has| (-347 |#2|) (-311)) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . T))
+((-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 -3090)
+(-41 R -3091)
((|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| $)) $) "\\spad{numer(x)} \\undocumented")))
NIL
((-12 (|HasCategory| |#1| (QUOTE (-389))) (|HasCategory| |#1| (QUOTE (-951 (-484)))) (|HasCategory| |#2| (|%list| (QUOTE -361) (|devaluate| |#1|)))))
@@ -106,23 +106,23 @@ NIL
((|HasCategory| |#1| (QUOTE (-257))))
(-44 R |n| |ls| |gamma|)
((|constructor| (NIL "AlgebraGivenByStructuralConstants implements finite rank algebras over a commutative ring,{} given by the structural constants \\spad{gamma} with respect to a fixed basis \\spad{[a1,..,an]},{} where \\spad{gamma} is an \\spad{n}-vector of \\spad{n} by \\spad{n} matrices \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{ai * aj = gammaij1 * a1 + ... + gammaijn * an}. The symbols for the fixed basis have to be given as a list of symbols.")) (|coerce| (($ (|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.")))
-((-3988 |has| |#1| (-495)) (-3986 . T) (-3985 . T))
+((-3989 |has| |#1| (-495)) (-3987 . T) (-3986 . T))
((|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-495))))
(-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.")))
-((-3991 . T) (-3992 . T))
-((OR (-12 (|HasCategory| (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -259) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3856) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)) (QUOTE (-757)))) (-12 (|HasCategory| (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -259) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3856) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013))))) (OR (|HasCategory| (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-553 (-773))))) (|HasCategory| (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-473)))) (-12 (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (|%list| (QUOTE -259) (|devaluate| |#2|)))) (OR (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)) (QUOTE (-757))) (|HasCategory| (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (|HasCategory| (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)) (QUOTE (-757))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)) (QUOTE (-757))) (|HasCategory| (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| (-484) (QUOTE (-757))) (|HasCategory| (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013))) (OR (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (-12 (|HasCategory| (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -259) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3856) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))))
+((-3992 . T) (-3993 . T))
+((OR (-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 (-757)))) (-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 (|:| -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|)))) (OR (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3857 |#1|) (|:| |entry| |#2|)) (QUOTE (-757))) (|HasCategory| (-2 (|:| -3857 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (|HasCategory| (-2 (|:| -3857 |#1|) (|:| |entry| |#2|)) (QUOTE (-757))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3857 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3857 |#1|) (|:| |entry| |#2|)) (QUOTE (-757))) (|HasCategory| (-2 (|:| -3857 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| (-484) (QUOTE (-757))) (|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 (|:| -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))) (-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)))))
(-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| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}.")))
NIL
((|HasCategory| |#2| (QUOTE (-38 (-347 (-484))))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-311))))
(-47 R E)
((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#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| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}.")))
-(((-3993 "*") |has| |#1| (-146)) (-3984 |has| |#1| (-495)) (-3985 . T) (-3986 . T) (-3988 . T))
+(((-3994 "*") |has| |#1| (-146)) (-3985 |has| |#1| (-495)) (-3986 . T) (-3987 . T) (-3989 . T))
NIL
(-48)
((|constructor| (NIL "Algebraic closure of the rational numbers,{} with mathematical =")) (|norm| (($ $ (|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}.")))
-((-3983 . T) (-3989 . T) (-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . T))
+((-3984 . T) (-3990 . T) (-3985 . T) ((-3994 "*") . T) (-3986 . T) (-3987 . T) (-3989 . T))
((|HasCategory| $ (QUOTE (-962))) (|HasCategory| $ (QUOTE (-951 (-484)))))
(-49)
((|constructor| (NIL "This domain implements anonymous functions")) (|body| (((|Syntax|) $) "\\spad{body(f)} returns the body of the unnamed function `f'.")) (|parameters| (((|List| (|Identifier|)) $) "\\spad{parameters(f)} returns the list of parameters bound by `f'.")))
@@ -130,7 +130,7 @@ NIL
NIL
(-50 R |lVar|)
((|constructor| (NIL "The domain of antisymmetric polynomials.")) (|map| (($ (|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}.")))
-((-3988 . T))
+((-3989 . 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 -3090)
+(-54 |Base| R -3091)
((|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
@@ -158,11 +158,11 @@ 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")))
-((-3991 . T) (-3992 . T))
+((-3992 . T) (-3993 . 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}")))
-((-3992 . T) (-3991 . T))
+((-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|)))))
(-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),...]}.")))
@@ -170,7 +170,7 @@ 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.")))
-((-3991 . T) (-3992 . T))
+((-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))))
(-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}.")))
@@ -178,7 +178,7 @@ NIL
((|HasCategory| |#1| (QUOTE (-311))))
(-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}.")))
-((-3991 . T) (-3992 . T))
+((-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))))
(-63 S)
((|constructor| (NIL "This is the category of Spad abstract syntax trees.")))
@@ -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.")))
-((-3991 . T) ((-3993 "*") . T) (-3992 . T) (-3988 . T) (-3986 . T) (-3985 . T) (-3984 . T) (-3989 . T) (-3983 . T) (-3982 . T) (-3981 . T) (-3980 . T) (-3979 . T) (-3987 . T) (-3990 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-3978 . T))
+((-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))
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}.")))
-((-3988 . T))
+((-3989 . 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}.")))
@@ -222,23 +222,23 @@ 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}.")))
-((-3991 . T) (-3992 . T))
+((-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))))
(-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 (-3993 "*"))))
+((|HasAttribute| |#1| (QUOTE (-3994 "*"))))
(-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.")))
-((-3992 . T))
+((-3993 . 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.")))
-((-3983 . T) (-3989 . T) (-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . T))
+((-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)))))
(-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|) $) "\\spad{name(b)} returns the name of binding \\spad{b}")))
@@ -254,11 +254,11 @@ NIL
NIL
(-81)
((|constructor| (NIL "\\spadtype{Bits} provides logical functions for Indexed Bits.")) (|bits| (($ (|NonNegativeInteger|) (|Boolean|)) "\\spad{bits(n,b)} creates bits with \\spad{n} values of \\spad{b}")))
-((-3992 . T) (-3991 . T))
+((-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))))
(-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}")))
-((-3986 . T) (-3985 . T))
+((-3987 . T) (-3986 . 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 -3090 UP)
+(-88 -3091 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}.")))
-((-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . T))
+((-3985 . T) ((-3994 "*") . T) (-3986 . T) (-3987 . T) (-3989 . 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}.")))
-((-3983 . T) (-3989 . T) (-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . T))
+((-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)))))
(-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| (($ $) "\\spad{left(u)} returns the left child.")))
NIL
-((|HasAttribute| |#1| (QUOTE -3992)))
+((|HasAttribute| |#1| (QUOTE -3993)))
(-92 S)
((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "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
@@ -306,7 +306,7 @@ 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")))
-((-3991 . T) (-3992 . T))
+((-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))))
(-95 S)
((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")))
@@ -314,7 +314,7 @@ NIL
NIL
(-96)
((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")))
-((-3992 . T) (-3991 . T))
+((-3993 . T) (-3992 . T))
NIL
(-97 A S)
((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#2| $) "\\spad{node(left,v,right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components")))
@@ -322,15 +322,15 @@ NIL
NIL
(-98 S)
((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#1| $) "\\spad{node(left,v,right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components")))
-((-3991 . T) (-3992 . T))
+((-3992 . T) (-3993 . T))
NIL
(-99 S)
((|constructor| (NIL "\\spadtype{BinaryTournament(S)} is the domain of binary trees where elements are ordered down the tree. A binary search tree is either empty or is a node containing a \\spadfun{value} of type \\spad{S},{} and a \\spadfun{right} and a \\spadfun{left} which are both \\spadtype{BinaryTree(S)}")) (|insert!| (($ |#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.")))
-((-3991 . T) (-3992 . T))
+((-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))))
(-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.")))
-((-3991 . T) (-3992 . T))
+((-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))))
(-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.")))
@@ -338,7 +338,7 @@ 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.")))
-((-3992 . T) (-3991 . T))
+((-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)))))
(-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")))
@@ -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") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,D) -> D} which is commutative.")))
-(((-3993 "*") . T))
+(((-3994 "*") . T))
NIL
-(-108 |minix| -2619 R)
+(-108 |minix| -2620 R)
((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\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|) $) "\\spad{rank(t)} returns the tensorial rank of \\spad{t} (that is,{} the number of indices). This is the same as the graded module degree.")))
NIL
NIL
-(-109 |minix| -2619 S T$)
+(-109 |minix| -2620 S T$)
((|constructor| (NIL "This package provides functions to enable conversion of tensors given conversion of the components.")) (|map| (((|CartesianTensor| |#1| |#2| |#4|) (|Mapping| |#4| |#3|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{map(f,ts)} does a componentwise conversion of the tensor \\spad{ts} to a tensor with components of type \\spad{T}.")) (|reshape| (((|CartesianTensor| |#1| |#2| |#4|) (|List| |#4|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{reshape(lt,ts)} organizes the list of components \\spad{lt} into a tensor with the same shape as \\spad{ts}.")))
NIL
NIL
@@ -386,7 +386,7 @@ NIL
NIL
(-114)
((|constructor| (NIL "This domain allows classes of characters to be defined and manipulated efficiently.")) (|alphanumeric| (($) "\\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}.")))
-((-3991 . T) (-3981 . T) (-3992 . T))
+((-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)))))
(-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.")))
@@ -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.")))
-((-3988 . T))
+((-3989 . 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.")))
-((-3988 . T))
+((-3989 . T))
NIL
-(-121 -3090 UP UPUP)
+(-121 -3091 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 -3991)))
+((|HasCategory| |#2| (QUOTE (-554 (-473)))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasAttribute| |#1| (QUOTE -3992)))
(-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.")))
-((-3986 . T) (-3985 . T) (-3988 . T))
+((-3987 . T) (-3986 . T) (-3989 . 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 -3090)
+(-131 R -3091)
((|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 -3987)) (|HasAttribute| |#2| (QUOTE -3990)) (|HasCategory| |#2| (QUOTE (-257))) (|HasCategory| |#2| (QUOTE (-495))))
+((|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))))
(-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})")))
-((-3984 OR (|has| |#1| (-495)) (-12 (|has| |#1| (-257)) (|has| |#1| (-822)))) (-3989 |has| |#1| (-311)) (-3983 |has| |#1| (-311)) (-3987 |has| |#1| (-6 -3987)) (-3990 |has| |#1| (-6 -3990)) (-1374 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . T))
+((-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))
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}.")))
-((-3984 OR (|has| |#1| (-495)) (-12 (|has| |#1| (-257)) (|has| |#1| (-822)))) (-3989 |has| |#1| (-311)) (-3983 |has| |#1| (-311)) (-3987 |has| |#1| (-6 -3987)) (-3990 |has| |#1| (-6 -3990)) (-1374 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . T))
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+((-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))
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(-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.")))
-(((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . T))
+(((-3994 "*") . T) (-3986 . T) (-3987 . T) (-3989 . 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}.")))
-(((-3993 "*") . T) (-3984 . T) (-3989 . T) (-3983 . T) (-3985 . T) (-3986 . T) (-3988 . T))
+(((-3994 "*") . T) (-3985 . T) (-3990 . T) (-3984 . T) (-3986 . T) (-3987 . T) (-3989 . 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|)) $) "\\spad{bindings(c)} returns the list of bindings in countour \\spad{c}.")))
@@ -576,7 +576,7 @@ NIL
((|constructor| (NIL "This domain enumerates the three kinds of constructors available in OpenAxiom: category constructors,{} domain constructors,{} and package constructors.")) (|package| (($) "`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 -3090)
+(-162 R -3091)
((|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 -3090 UP UPUP R)
+(-169 -3091 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 -3090 FP)
+(-170 -3091 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.")))
-((-3983 . T) (-3989 . T) (-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . T))
+((-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)))))
(-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|) $) "\\spad{head(d)} returns the head of the definition `d'. This is a list of identifiers starting with the name of the operation followed by the name of the parameters,{} if any.")))
NIL
NIL
-(-173 R -3090)
+(-173 R -3091)
((|constructor| (NIL "\\spadtype{ElementaryFunctionDefiniteIntegration} provides functions to compute definite integrals of elementary functions.")) (|innerint| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| #1="failed") (|:| |pole| #2="potentialPole")) |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{innerint(f, x, a, b, ignore?)} should be local but conditional")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| #1#) (|:| |pole| #2#)) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|)) (|String|)) "\\spad{integrate(f, x = a..b, \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| #1#) (|:| |pole| #2#)) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|))) "\\spad{integrate(f, x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}.")))
NIL
NIL
@@ -634,19 +634,19 @@ NIL
NIL
(-176 S)
((|constructor| (NIL "Linked list implementation of a Dequeue")) (|dequeue| (($ (|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}.")))
-((-3991 . T) (-3992 . T))
+((-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))))
(-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}.")))
-((-3988 . T))
+((-3989 . T))
NIL
-(-178 R -3090)
+(-178 R -3091)
((|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}.")))
-((-3766 . T) (-3983 . T) (-3989 . T) (-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . T))
+((-3767 . T) (-3984 . T) (-3990 . T) (-3985 . T) ((-3994 "*") . T) (-3986 . T) (-3987 . T) (-3989 . 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}")))
-((-3991 . 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 (-257))) (|HasCategory| |#1| (QUOTE (-495))) (|HasAttribute| |#1| (QUOTE (-3993 "*"))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-72))))
+((-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))))
(-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.")))
-((-3992 . T))
+((-3993 . 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 \\%.")))
-((-3988 . T))
+((-3989 . 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| $) "\\spad{differentiate x} compute the derivative of \\spad{x}.")))
@@ -678,7 +678,7 @@ NIL
NIL
(-187 R)
((|constructor| (NIL "An \\spad{R}-module equipped with a distinguised differential operator. If \\spad{R} is a differential ring,{} then differentiation on the module should extend differentiation on the differential ring \\spad{R}. The latter can be the null operator. In that case,{} the differentiation operator on the module is just an \\spad{R}-linear operator. For that reason,{} we do not require that the ring \\spad{R} be a DifferentialRing; \\blankline")))
-((-3986 . T) (-3985 . T))
+((-3987 . T) (-3986 . T))
NIL
(-188 S)
((|constructor| (NIL "This category is like \\spadtype{DifferentialDomain} where the target of the differentiation operator is the same as its source.")) (D (($ $ (|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")))
-((-3988 . T))
+((-3989 . 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 -3991)))
+((|HasAttribute| |#1| (QUOTE -3992)))
(-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}.")))
-((-3992 . 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
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((|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
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((|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")))
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NIL
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((|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 -2620 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}.")))
-((-3984 . T) (-3985 . T) (-3986 . T) (-3988 . T))
+((-3985 . T) (-3986 . T) (-3987 . T) (-3989 . T))
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.")))
@@ -742,7 +742,7 @@ 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}")))
-((-3992 . T) (-3991 . T))
+((-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|)))))
(-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}")))
@@ -750,12 +750,12 @@ NIL
NIL
(-205 R)
((|constructor| (NIL "Category of modules that extend differential rings. \\blankline")))
-((-3986 . T) (-3985 . T))
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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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(-211 |n| R S)
((|constructor| (NIL "This constructor provides a direct product of \\spad{R}-modules with an \\spad{R}-module view.")))
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+((-3989 OR (-2561 (|has| |#3| (-962)) (|has| |#3| (-190))) (|has| |#3| (-6 -3989)) (-2561 (|has| |#3| (-962)) (|has| |#3| (-810 (-1089))))) (-3986 |has| |#3| (-962)) (-3987 |has| |#3| (-962)) (-3992 . T))
+((OR (-12 (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (|%list| (QUOTE -259) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (|%list| (QUOTE -259) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-190))) (|HasCategory| |#3| (|%list| (QUOTE -259) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-311))) (|HasCategory| |#3| (|%list| (QUOTE -259) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-317))) (|HasCategory| |#3| (|%list| (QUOTE -259) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-664))) (|HasCategory| |#3| (|%list| (QUOTE -259) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-718))) (|HasCategory| |#3| (|%list| (QUOTE -259) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-757))) (|HasCategory| |#3| (|%list| (QUOTE -259) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-810 (-1089)))) (|HasCategory| |#3| (|%list| (QUOTE -259) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-962))) (|HasCategory| |#3| (|%list| (QUOTE -259) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1013))) (|HasCategory| |#3| (|%list| (QUOTE -259) (|devaluate| |#3|))))) (|HasCategory| |#3| (QUOTE (-311))) (OR (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-311))) (|HasCategory| |#3| (QUOTE (-962)))) (OR (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-311)))) (|HasCategory| |#3| (QUOTE (-962))) (|HasCategory| |#3| (QUOTE (-664))) (|HasCategory| |#3| (QUOTE (-718))) (OR (|HasCategory| |#3| (QUOTE (-718))) (|HasCategory| |#3| (QUOTE (-757)))) (|HasCategory| |#3| (QUOTE (-757))) (|HasCategory| |#3| (QUOTE (-317))) (OR (-12 (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-581 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-190))) (|HasCategory| |#3| (QUOTE (-581 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-311))) (|HasCategory| |#3| (QUOTE (-581 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-581 (-484)))) (|HasCategory| |#3| (QUOTE (-810 (-1089))))) (-12 (|HasCategory| |#3| (QUOTE (-581 (-484)))) (|HasCategory| |#3| (QUOTE (-962))))) (|HasCategory| |#3| (QUOTE (-810 (-1089)))) (OR (|HasCategory| |#3| (QUOTE (-190))) (|HasCategory| |#3| (QUOTE (-810 (-1089)))) (|HasCategory| |#3| (QUOTE (-962)))) (|HasCategory| |#3| (QUOTE (-190))) (OR (|HasCategory| |#3| (QUOTE (-190))) (-12 (|HasCategory| |#3| (QUOTE (-189))) (|HasCategory| |#3| (QUOTE (-962))))) (OR (-12 (|HasCategory| |#3| (QUOTE (-812 (-1089)))) (|HasCategory| |#3| (QUOTE (-962)))) (|HasCategory| |#3| (QUOTE (-810 (-1089))))) (|HasCategory| |#3| (QUOTE (-1013))) (OR (-12 (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-951 (-347 (-484)))))) (-12 (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-951 (-347 (-484)))))) (-12 (|HasCategory| |#3| (QUOTE (-190))) (|HasCategory| |#3| (QUOTE (-951 (-347 (-484)))))) (-12 (|HasCategory| |#3| (QUOTE (-311))) (|HasCategory| |#3| (QUOTE (-951 (-347 (-484)))))) (-12 (|HasCategory| |#3| (QUOTE (-317))) (|HasCategory| |#3| (QUOTE (-951 (-347 (-484)))))) (-12 (|HasCategory| |#3| (QUOTE (-664))) (|HasCategory| |#3| (QUOTE (-951 (-347 (-484)))))) (-12 (|HasCategory| |#3| (QUOTE (-718))) (|HasCategory| |#3| (QUOTE (-951 (-347 (-484)))))) (-12 (|HasCategory| |#3| (QUOTE (-757))) (|HasCategory| |#3| (QUOTE (-951 (-347 (-484)))))) (-12 (|HasCategory| |#3| (QUOTE (-810 (-1089)))) (|HasCategory| |#3| (QUOTE (-951 (-347 (-484)))))) (-12 (|HasCategory| |#3| (QUOTE (-951 (-347 (-484))))) (|HasCategory| |#3| (QUOTE (-962)))) (-12 (|HasCategory| |#3| (QUOTE (-951 (-347 (-484))))) (|HasCategory| |#3| (QUOTE (-1013))))) (OR (-12 (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-190))) (|HasCategory| |#3| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-718))) (|HasCategory| |#3| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-757))) (|HasCategory| |#3| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-810 (-1089)))) (|HasCategory| |#3| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-951 (-484)))) (|HasCategory| |#3| (QUOTE (-1013)))) (-12 (|HasCategory| |#3| (QUOTE (-311))) (|HasCategory| |#3| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-317))) (|HasCategory| |#3| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-664))) (|HasCategory| |#3| (QUOTE (-951 (-484))))) (|HasCategory| |#3| (QUOTE (-962)))) (OR (-12 (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-190))) (|HasCategory| |#3| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-718))) (|HasCategory| |#3| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-757))) (|HasCategory| |#3| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-810 (-1089)))) (|HasCategory| |#3| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-951 (-484)))) (|HasCategory| |#3| (QUOTE (-1013)))) (-12 (|HasCategory| |#3| (QUOTE (-311))) (|HasCategory| |#3| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-317))) (|HasCategory| |#3| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-664))) (|HasCategory| |#3| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-951 (-484)))) (|HasCategory| |#3| (QUOTE (-962))))) (|HasCategory| (-484) (QUOTE (-757))) (-12 (|HasCategory| |#3| (QUOTE (-581 (-484)))) (|HasCategory| |#3| (QUOTE (-962)))) (OR (-12 (|HasCategory| |#3| (QUOTE (-810 (-1089)))) (|HasCategory| |#3| (QUOTE (-962)))) (-12 (|HasCategory| |#3| (QUOTE (-812 (-1089)))) (|HasCategory| |#3| (QUOTE (-962))))) (OR (-12 (|HasCategory| |#3| (QUOTE (-190))) (|HasCategory| |#3| (QUOTE (-962)))) (-12 (|HasCategory| |#3| (QUOTE (-189))) (|HasCategory| |#3| (QUOTE (-962))))) (-12 (|HasCategory| |#3| (QUOTE (-951 (-484)))) (|HasCategory| |#3| (QUOTE (-1013)))) (OR (-12 (|HasCategory| |#3| (QUOTE (-951 (-484)))) (|HasCategory| |#3| (QUOTE (-1013)))) (|HasCategory| |#3| (QUOTE (-962)))) (-12 (|HasCategory| |#3| (QUOTE (-951 (-347 (-484))))) (|HasCategory| |#3| (QUOTE (-1013)))) (OR (-12 (|HasCategory| |#3| (QUOTE (-810 (-1089)))) (|HasCategory| |#3| (QUOTE (-962)))) (|HasAttribute| |#3| (QUOTE -3989)) (-12 (|HasCategory| |#3| (QUOTE (-190))) (|HasCategory| |#3| (QUOTE (-962))))) (-12 (|HasCategory| |#3| (QUOTE (-189))) (|HasCategory| |#3| (QUOTE (-962)))) (-12 (|HasCategory| |#3| (QUOTE (-812 (-1089)))) (|HasCategory| |#3| (QUOTE (-962)))) (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-104))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-553 (-773)))) (|HasCategory| |#3| (QUOTE (-72))) (-12 (|HasCategory| |#3| (QUOTE (-1013))) (|HasCategory| |#3| (|%list| (QUOTE -259) (|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.")))
-(((-3993 "*") |has| |#1| (-146)) (-3984 |has| |#1| (-495)) (-3989 |has| |#1| (-6 -3989)) (-3986 . T) (-3985 . T) (-3988 . T))
+(((-3994 "*") |has| |#1| (-146)) (-3985 |has| |#1| (-495)) (-3990 |has| |#1| (-6 -3990)) (-3987 . T) (-3986 . T) (-3989 . 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}.")))
-((-3991 . T) (-3992 . T))
+((-3992 . T) (-3993 . 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.")))
@@ -834,8 +834,8 @@ 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")))
-(((-3993 "*") |has| |#1| (-146)) (-3984 |has| |#1| (-495)) (-3989 |has| |#1| (-6 -3989)) (-3986 . T) (-3985 . T) (-3988 . 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| |#3| (QUOTE (-797 (-327))))) (-12 (|HasCategory| |#1| (QUOTE (-797 (-484)))) (|HasCategory| |#3| (QUOTE (-797 (-484))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-327))))) (|HasCategory| |#3| (QUOTE (-554 (-801 (-327)))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-484))))) (|HasCategory| |#3| (QUOTE (-554 (-801 (-484)))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-473)))) (|HasCategory| |#3| (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 -3989)) (|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)))))
+(((-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| |#3| (QUOTE (-797 (-327))))) (-12 (|HasCategory| |#1| (QUOTE (-797 (-484)))) (|HasCategory| |#3| (QUOTE (-797 (-484))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-327))))) (|HasCategory| |#3| (QUOTE (-554 (-801 (-327)))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-484))))) (|HasCategory| |#3| (QUOTE (-554 (-801 (-484)))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-473)))) (|HasCategory| |#3| (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)))))
(-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
@@ -848,11 +848,11 @@ NIL
((|constructor| (NIL "A domain used in the construction of the exterior algebra on a set \\spad{X} over a ring \\spad{R}. This domain represents the set of all ordered subsets of the set \\spad{X},{} assumed to be in correspondance with {1,{}2,{}3,{} ...}. The ordered subsets are themselves ordered lexicographically and are in bijective correspondance with an ordered basis of the exterior algebra. In this domain we are dealing strictly with the exponents of basis elements which can only be 0 or 1. \\blankline The multiplicative identity element of the exterior algebra corresponds to the empty subset of \\spad{X}. A coerce from List Integer to an ordered basis element is provided to allow the convenient input of expressions. Another exported function forgets the ordered structure and simply returns the list corresponding to an ordered subset.")) (|Nul| (($ (|NonNegativeInteger|)) "\\spad{Nul()} gives the basis element 1 for the algebra generated by \\spad{n} generators.")) (|exponents| (((|List| (|Integer|)) $) "\\spad{exponents(x)} converts a domain element into a list of zeros and ones corresponding to the exponents in the basis element that \\spad{x} represents.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(x)} gives the numbers of 1's in \\spad{x},{} \\spadignore{i.e.} the number of non-zero exponents in the basis element that \\spad{x} represents.")) (|coerce| (($ (|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 -3090)
+(-230 R -3091)
((|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 -3090)
+(-231 R -3091)
((|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
@@ -878,7 +878,7 @@ NIL
((|HasCategory| |#2| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-1013))))
(-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}.")))
-((-3992 . T))
+((-3993 . 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}.")))
@@ -899,18 +899,18 @@ 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 -3992)))
+((|HasAttribute| |#1| (QUOTE -3993)))
(-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| -2035 -3514 |exactQuo|)
+(-244 S R |Mod| -2036 -3515 |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| $) "\\spad{modulus(x)} \\undocumented")))
-((-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . T))
+((-3985 . T) ((-3994 "*") . T) (-3986 . T) (-3987 . T) (-3989 . T))
NIL
(-245)
((|constructor| (NIL "Entire Rings (non-commutative Integral Domains),{} \\spadignore{i.e.} a ring not necessarily commutative which has no zero divisors. \\blankline")) (|noZeroDivisors| ((|attribute|) "if a product is zero then one of the factors must be zero.")))
-((-3984 . T) (-3985 . T) (-3986 . T) (-3988 . T))
+((-3985 . T) (-3986 . T) (-3987 . T) (-3989 . T))
NIL
(-246)
((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: March 18,{} 2010. An `Environment' is a stack of scope.")) (|categoryFrame| (($) "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")))
@@ -922,7 +922,7 @@ NIL
NIL
(-248 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.")))
-((-3988 OR (|has| |#1| (-962)) (|has| |#1| (-410))) (-3985 |has| |#1| (-962)) (-3986 |has| |#1| (-962)))
+((-3989 OR (|has| |#1| (-962)) (|has| |#1| (-410))) (-3986 |has| |#1| (-962)) (-3987 |has| |#1| (-962)))
((|HasCategory| |#1| (QUOTE (-311))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-962)))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-311)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-962))) (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-810 (-1089)))) (OR (|HasCategory| |#1| (QUOTE (-810 (-1089)))) (|HasCategory| |#1| (QUOTE (-962)))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-810 (-1089)))) (|HasCategory| |#1| (QUOTE (-962)))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-810 (-1089)))) (|HasCategory| |#1| (QUOTE (-962)))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-962)))) (OR (|HasCategory| |#1| (QUOTE (-410))) (|HasCategory| |#1| (QUOTE (-664)))) (|HasCategory| |#1| (QUOTE (-410))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-410))) (|HasCategory| |#1| (QUOTE (-664))) (|HasCategory| |#1| (QUOTE (-810 (-1089)))) (|HasCategory| |#1| (QUOTE (-962))) (|HasCategory| |#1| (QUOTE (-1025))) (|HasCategory| |#1| (QUOTE (-1013)))) (OR (|HasCategory| |#1| (QUOTE (-410))) (|HasCategory| |#1| (QUOTE (-664))) (|HasCategory| |#1| (QUOTE (-1025)))) (|HasCategory| |#1| (|%list| (QUOTE -453) (QUOTE (-1089)) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-253))) (OR (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-410)))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-664)))) (OR (|HasCategory| |#1| (QUOTE (-410))) (|HasCategory| |#1| (QUOTE (-962)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1025))) (|HasCategory| |#1| (QUOTE (-664))))
(-249 S R)
((|constructor| (NIL "This package provides operations for mapping the sides of equations.")) (|map| (((|Equation| |#2|) (|Mapping| |#2| |#1|) (|Equation| |#1|)) "\\spad{map(f,eq)} returns an equation where \\spad{f} is applied to the sides of \\spad{eq}")))
@@ -930,8 +930,8 @@ NIL
NIL
(-250 |Key| |Entry|)
((|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.")))
-((-3991 . T) (-3992 . T))
-((-12 (|HasCategory| (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -259) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3856) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-553 (-773))))) (|HasCategory| (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-473)))) (-12 (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (|%list| (QUOTE -259) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-1013))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))))
+((-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))))
(-251)
((|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
@@ -944,11 +944,11 @@ NIL
((|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 -3090 S)
+(-254 -3091 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 -3090)
+(-255 E -3091)
((|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
@@ -958,7 +958,7 @@ NIL
NIL
(-257)
((|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|) $ $) "\\spad{sizeLess?(x,y)} tests whether \\spad{x} is strictly smaller than \\spad{y} with respect to the \\spadfunFrom{euclideanSize}{EuclideanDomain}.")))
-((-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . T))
+((-3985 . T) ((-3994 "*") . T) (-3986 . T) (-3987 . T) (-3989 . T))
NIL
(-258 S R)
((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation'' substitutions.")) (|eval| (($ $ (|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}.")))
@@ -968,7 +968,7 @@ NIL
((|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 -3090)
+(-260 -3091)
((|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
@@ -982,11 +982,11 @@ NIL
NIL
(-263 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))}.")))
-((-3983 . T) (-3989 . T) (-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . T))
+((-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)
((|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.")))
-((-3988 OR (-12 (|has| |#1| (-495)) (OR (|has| |#1| (-962)) (|has| |#1| (-410)))) (|has| |#1| (-962)) (|has| |#1| (-410))) (-3986 |has| |#1| (-146)) (-3985 |has| |#1| (-146)) ((-3993 "*") |has| |#1| (-495)) (-3984 |has| |#1| (-495)) (-3989 |has| |#1| (-495)) (-3983 |has| |#1| (-495)))
+((-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)
((|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}.")))
@@ -996,7 +996,7 @@ NIL
((|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 -3090)
+(-267 R -3091)
((|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
@@ -1006,8 +1006,8 @@ NIL
NIL
(-269 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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+(((-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|)))))))
(-270 M)
((|constructor| (NIL "computes various functions on factored arguments.")) (|log| (((|List| (|Record| (|:| |coef| (|NonNegativeInteger|)) (|:| |logand| |#1|))) (|Factored| |#1|)) "\\spad{log(f)} returns \\spad{[(a1,b1),...,(am,bm)]} such that the logarithm of \\spad{f} is equal to \\spad{a1*log(b1) + ... + am*log(bm)}.")) (|nthRoot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#1|) (|:| |radicand| (|List| |#1|))) (|Factored| |#1|) (|NonNegativeInteger|)) "\\spad{nthRoot(f, n)} returns \\spad{(p, r, [r1,...,rm])} such that the \\spad{n}th-root of \\spad{f} is equal to \\spad{r * \\spad{p}th-root(r1 * ... * rm)},{} where \\spad{r1},{}...,{}rm are distinct factors of \\spad{f},{} each of which has an exponent smaller than \\spad{p} in \\spad{f}.")))
NIL
@@ -1018,7 +1018,7 @@ NIL
NIL
(-272 S)
((|constructor| (NIL "The free abelian group on a set \\spad{S} is the monoid of finite sums of the form \\spad{reduce(+,[ni * si])} where the \\spad{si}'s are in \\spad{S},{} and the \\spad{ni}'s are integers. The operation is commutative.")))
-((-3986 . T) (-3985 . T))
+((-3987 . T) (-3986 . T))
((|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| (-484) (QUOTE (-717))))
(-273 S E)
((|constructor| (NIL "A free abelian monoid on a set \\spad{S} is the monoid of finite sums of the form \\spad{reduce(+,[ni * si])} where the \\spad{si}'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| $) "\\spad{s + x} returns the sum of \\spad{s} and \\spad{x}.")))
@@ -1034,19 +1034,19 @@ NIL
((|HasCategory| |#2| (QUOTE (-389))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-146))))
(-276 R E)
((|constructor| (NIL "This category is similar to AbelianMonoidRing,{} except that the sum is assumed to be finite. It is a useful model for polynomials,{} but is somewhat more general.")) (|primitivePart| (($ $) "\\spad{primitivePart(p)} returns the unit normalized form of polynomial \\spad{p} divided by the content of \\spad{p}.")) (|content| ((|#1| $) "\\spad{content(p)} gives the 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.")))
-(((-3993 "*") |has| |#1| (-146)) (-3984 |has| |#1| (-495)) (-3985 . T) (-3986 . T) (-3988 . T))
+(((-3994 "*") |has| |#1| (-146)) (-3985 |has| |#1| (-495)) (-3986 . T) (-3987 . T) (-3989 . T))
NIL
(-277 S)
((|constructor| (NIL "\\indented{1}{A FlexibleArray is the notion of an array intended to allow for growth} at the end only. Hence the following efficient operations \\indented{2}{\\spad{append(x,a)} meaning append item \\spad{x} at the end of the array \\spad{a}} \\indented{2}{\\spad{delete(a,n)} meaning delete the last item from the array \\spad{a}} Flexible arrays support the other operations inherited from \\spadtype{ExtensibleLinearAggregate}. However,{} these are not efficient. Flexible arrays combine the \\spad{O(1)} access time property of arrays with growing and shrinking at the end in \\spad{O(1)} (average) time. This is done by using an ordinary array which may have zero or more empty slots at the end. When the array becomes full it is copied into a new larger (50\\% larger) array. Conversely,{} when the array becomes less than 1/2 full,{} it is copied into a smaller array. Flexible arrays provide for an efficient implementation of many data structures in particular heaps,{} stacks and sets.")))
-((-3992 . T) (-3991 . T))
+((-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|)))))
-(-278 S -3090)
+(-278 S -3091)
((|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
((|HasCategory| |#2| (QUOTE (-317))))
-(-279 -3090)
+(-279 -3091)
((|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.")))
-((-3983 . T) (-3989 . T) (-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . T))
+((-3984 . T) (-3990 . T) (-3985 . T) ((-3994 "*") . T) (-3986 . T) (-3987 . T) (-3989 . T))
NIL
(-280 E)
((|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")))
@@ -1056,7 +1056,7 @@ NIL
((|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
NIL
-(-282 -3090 UP UPUP R)
+(-282 -3091 UP UPUP R)
((|constructor| (NIL "This domains implements finite rational divisors on a curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}'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
@@ -1064,11 +1064,11 @@ NIL
((|constructor| (NIL "\\indented{1}{Lift a map to finite divisors.} Author: Manuel Bronstein Date Created: 1988 Date Last Updated: 19 May 1993")) (|map| (((|FiniteDivisor| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FiniteDivisor| |#1| |#2| |#3| |#4|)) "\\spad{map(f,d)} \\undocumented{}")))
NIL
NIL
-(-284 S -3090 UP UPUP R)
+(-284 S -3091 UP UPUP R)
((|constructor| (NIL "This category describes finite rational divisors on a curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}'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
NIL
-(-285 -3090 UP UPUP R)
+(-285 -3091 UP UPUP R)
((|constructor| (NIL "This category describes finite rational divisors on a curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}'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
NIL
@@ -1082,15 +1082,15 @@ NIL
NIL
(-288 |p| |n|)
((|constructor| (NIL "FiniteField(\\spad{p},{}\\spad{n}) implements finite fields with p**n elements. This packages checks that \\spad{p} is prime. For a non-checking version,{} see \\spadtype{InnerFiniteField}.")))
-((-3983 . T) (-3989 . T) (-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . T))
+((-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))))
-(-289 S -3090 UP UPUP)
+(-289 S -3091 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 -3090 UP UPUP)
+(-290 -3091 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.")))
-((-3984 |has| (-347 |#2|) (-311)) (-3989 |has| (-347 |#2|) (-311)) (-3983 |has| (-347 |#2|) (-311)) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . T))
+((-3985 |has| (-347 |#2|) (-311)) (-3990 |has| (-347 |#2|) (-311)) (-3984 |has| (-347 |#2|) (-311)) ((-3994 "*") . T) (-3986 . T) (-3987 . T) (-3989 . T))
NIL
(-291 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}.")))
@@ -1098,15 +1098,15 @@ NIL
NIL
(-292 |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.")))
-((-3983 . T) (-3989 . T) (-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . T))
+((-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|)
((|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.")))
-((-3983 . T) (-3989 . T) (-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . T))
+((-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|)
((|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.")))
-((-3983 . T) (-3989 . T) (-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . T))
+((-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)
((|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}.")))
@@ -1122,43 +1122,43 @@ NIL
NIL
(-298)
((|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.")))
-((-3983 . T) (-3989 . T) (-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . T))
+((-3984 . T) (-3990 . T) (-3985 . T) ((-3994 "*") . T) (-3986 . T) (-3987 . T) (-3989 . T))
NIL
-(-299 R UP -3090)
+(-299 R UP -3091)
((|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|)
((|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.")))
-((-3983 . T) (-3989 . T) (-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . T))
+((-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|)
((|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.")))
-((-3983 . T) (-3989 . T) (-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . T))
+((-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|)
((|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.")))
-((-3983 . T) (-3989 . T) (-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . T))
+((-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|)
((|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.")))
-((-3983 . T) (-3989 . T) (-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . T))
+((-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)
((|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 -3090 GF)
+(-305 -3091 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 -3090 FP FPP)
+(-306 -3091 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|)
((|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}.")))
-((-3983 . T) (-3989 . T) (-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . T))
+((-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|)
((|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}.")))
@@ -1166,7 +1166,7 @@ NIL
NIL
(-309 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| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left.")))
-((-3988 . T))
+((-3989 . T))
NIL
(-310 S)
((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0.")))
@@ -1174,7 +1174,7 @@ NIL
NIL
(-311)
((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0.")))
-((-3983 . T) (-3989 . T) (-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . T))
+((-3984 . T) (-3990 . T) (-3985 . T) ((-3994 "*") . T) (-3986 . T) (-3987 . T) (-3989 . T))
NIL
(-312 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.")))
@@ -1190,7 +1190,7 @@ NIL
((|HasCategory| |#2| (QUOTE (-495))))
(-315 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| $)) "\\spad{someBasis()} returns some \\spad{R}-module basis.")))
-((-3988 |has| |#1| (-495)) (-3986 . T) (-3985 . T))
+((-3989 |has| |#1| (-495)) (-3987 . T) (-3986 . T))
NIL
(-316 S)
((|constructor| (NIL "The category of domains composed of a finite set of elements. We include the functions \\spadfun{lookup} and \\spadfun{index} to give a bijection between the finite set and an initial segment of positive integers. \\blankline")) (|random| (($) "\\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.")))
@@ -1206,15 +1206,15 @@ NIL
((|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-311))))
(-319 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| $)) "\\spad{regularRepresentation(a,basis)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra.")))
-((-3985 . T) (-3986 . T) (-3988 . T))
+((-3986 . T) (-3987 . T) (-3989 . T))
NIL
(-320 A S)
((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|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|) $ $) "\\spad{merge(p,a,b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}.")))
NIL
-((|HasAttribute| |#1| (QUOTE -3992)) (|HasCategory| |#2| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-1013))))
+((|HasAttribute| |#1| (QUOTE -3993)) (|HasCategory| |#2| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-1013))))
(-321 S)
((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|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|) $ $) "\\spad{merge(p,a,b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}.")))
-((-3991 . T))
+((-3992 . T))
NIL
(-322 S A R B)
((|constructor| (NIL "\\spad{FiniteLinearAggregateFunctions2} provides functions involving two FiniteLinearAggregates where the underlying domains might be different. An example of this might be creating a list of rational numbers by mapping a function across a list of integers where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-aggregates \\spad{x} of aggregrate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad{[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$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.")))
@@ -1222,7 +1222,7 @@ NIL
NIL
(-323 |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) (-3986 . T) (-3985 . T))
+((|JacobiIdentity| . T) (|NullSquare| . T) (-3987 . T) (-3986 . T))
NIL
(-324 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.")))
@@ -1238,7 +1238,7 @@ NIL
NIL
(-327)
((|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}.")))
-((-3974 . T) (-3982 . T) (-3766 . T) (-3983 . T) (-3989 . T) (-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . T))
+((-3975 . T) (-3983 . T) (-3767 . T) (-3984 . T) (-3990 . T) (-3985 . T) ((-3994 "*") . T) (-3986 . T) (-3987 . T) (-3989 . T))
NIL
(-328 |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}.")))
@@ -1250,15 +1250,15 @@ 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.")))
-((-3986 . T) (-3985 . T))
+((-3987 . T) (-3986 . T))
((|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-1013)))))
(-331 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}")))
-((-3986 . T) (-3985 . T))
+((-3987 . T) (-3986 . T))
((|HasCategory| |#1| (QUOTE (-146))))
(-332 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}.")))
-((-3986 . T) (-3985 . T))
+((-3987 . T) (-3986 . T))
NIL
(-333 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| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left.")))
@@ -1278,13 +1278,13 @@ NIL
NIL
(-337 |n| |class| R)
((|constructor| (NIL "Generate the Free Lie Algebra over a ring \\spad{R} with identity; A \\spad{P}. Hall basis is generated by a package call to HallBasis.")) (|generator| (($ (|NonNegativeInteger|)) "\\spad{generator(i)} is the \\spad{i}th Hall Basis element")) (|shallowExpand| (((|OutputForm|) $) "\\spad{shallowExpand(x)} \\undocumented{}")) (|deepExpand| (((|OutputForm|) $) "\\spad{deepExpand(x)} \\undocumented{}")) (|dimension| (((|NonNegativeInteger|)) "\\spad{dimension()} is the rank of this Lie algebra")))
-((-3986 . T) (-3985 . T))
+((-3987 . T) (-3986 . T))
NIL
-(-338 -3090 UP UPUP R)
+(-338 -3091 UP UPUP R)
((|constructor| (NIL "\\indented{1}{Finds the order of a divisor over a finite field} Author: Manuel Bronstein Date Created: 1988 Date Last Updated: 11 Jul 1990")) (|order| (((|NonNegativeInteger|) (|FiniteDivisor| |#1| |#2| |#3| |#4|)) "\\spad{order(x)} \\undocumented")))
NIL
NIL
-(-339 -3090 UP)
+(-339 -3091 UP)
((|constructor| (NIL "\\indented{1}{Full partial fraction expansion of rational functions} Author: Manuel Bronstein Date Created: 9 December 1992 Date Last Updated: June 18,{} 2010 References: \\spad{M}.Bronstein & \\spad{B}.Salvy,{} \\indented{12}{Full Partial Fraction Decomposition of Rational Functions,{}} \\indented{12}{in Proceedings of \\spad{ISSAC'93},{} Kiev,{} ACM Press.}")) (|construct| (($ (|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| $) "\\spad{p + x} returns the sum of \\spad{p} and \\spad{x}")))
NIL
NIL
@@ -1298,19 +1298,19 @@ NIL
NIL
(-342)
((|constructor| (NIL "FieldOfPrimeCharacteristic is the category of fields of prime characteristic,{} \\spadignore{e.g.} finite fields,{} algebraic closures of fields of prime characteristic,{} transcendental extensions of of fields of prime characteristic.")) (|primeFrobenius| (($ $ (|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|)) $) "\\spad{order(a)} computes the order of an element in the multiplicative group of the field. Error: if \\spad{a} is 0.")))
-((-3983 . T) (-3989 . T) (-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . T))
+((-3984 . T) (-3990 . T) (-3985 . T) ((-3994 "*") . T) (-3986 . T) (-3987 . T) (-3989 . T))
NIL
(-343 S)
((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\"+\") does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\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 -3974)) (|HasAttribute| |#1| (QUOTE -3982)))
+((|HasAttribute| |#1| (QUOTE -3975)) (|HasAttribute| |#1| (QUOTE -3983)))
(-344)
((|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\".")))
-((-3766 . T) (-3983 . T) (-3989 . T) (-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . T))
+((-3767 . T) (-3984 . T) (-3990 . T) (-3985 . T) ((-3994 "*") . T) (-3986 . T) (-3987 . T) (-3989 . T))
NIL
(-345 R)
((|constructor| (NIL "\\spadtype{Factored} creates a domain whose objects are kept in factored form as long as possible. Thus certain operations like multiplication and 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.")))
-((-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . T))
+((-3985 . T) ((-3994 "*") . T) (-3986 . T) (-3987 . T) (-3989 . T))
((|HasCategory| |#1| (QUOTE (-453 (-1089) $))) (|HasCategory| |#1| (QUOTE (-259 $))) (|HasCategory| |#1| (QUOTE (-241 $ $))) (|HasCategory| |#1| (QUOTE (-554 (-473)))) (|HasCategory| |#1| (QUOTE (-1133))) (OR (|HasCategory| |#1| (QUOTE (-389))) (|HasCategory| |#1| (QUOTE (-1133)))) (|HasCategory| |#1| (QUOTE (-934))) (|HasCategory| |#1| (QUOTE (-951 (-347 (-484))))) (|HasCategory| |#1| (QUOTE (-951 (-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)))) (|HasCategory| |#1| (QUOTE (-483))) (|HasCategory| |#1| (QUOTE (-389))))
(-346 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.")))
@@ -1318,8 +1318,8 @@ NIL
NIL
(-347 S)
((|constructor| (NIL "Fraction takes an IntegralDomain \\spad{S} and produces the domain of Fractions with numerators and denominators from \\spad{S}. If \\spad{S} is also a GcdDomain,{} then gcd's between numerator and denominator will be cancelled during all operations.")) (|canonical| ((|attribute|) "\\spad{canonical} means that equal elements are in fact identical.")))
-((-3978 -12 (|has| |#1| (-6 -3989)) (|has| |#1| (-389)) (|has| |#1| (-6 -3978))) (-3983 . T) (-3989 . T) (-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . T))
-((|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| |#1| (QUOTE (-951 (-1089)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-554 (-473)))) (|HasCategory| |#1| (QUOTE (-934))) (|HasCategory| |#1| (QUOTE (-741))) (|HasCategory| |#1| (QUOTE (-757))) (OR (|HasCategory| |#1| (QUOTE (-741))) (|HasCategory| |#1| (QUOTE (-757)))) (|HasCategory| |#1| (QUOTE (-951 (-484)))) (|HasCategory| |#1| (QUOTE (-1065))) (|HasCategory| |#1| (QUOTE (-797 (-327)))) (|HasCategory| |#1| (QUOTE (-797 (-484)))) (|HasCategory| |#1| (QUOTE (-554 (-801 (-327))))) (|HasCategory| |#1| (QUOTE (-554 (-801 (-484))))) (|HasCategory| |#1| (QUOTE (-581 (-484)))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-812 (-1089)))) (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-810 (-1089)))) (|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 (-257))) (|HasCategory| |#1| (QUOTE (-483))) (-12 (|HasAttribute| |#1| (QUOTE -3978)) (|HasAttribute| |#1| (QUOTE -3989)) (|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)))))
+((-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))
+((|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| |#1| (QUOTE (-951 (-1089)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-554 (-473)))) (|HasCategory| |#1| (QUOTE (-934))) (|HasCategory| |#1| (QUOTE (-741))) (|HasCategory| |#1| (QUOTE (-757))) (OR (|HasCategory| |#1| (QUOTE (-741))) (|HasCategory| |#1| (QUOTE (-757)))) (|HasCategory| |#1| (QUOTE (-951 (-484)))) (|HasCategory| |#1| (QUOTE (-1065))) (|HasCategory| |#1| (QUOTE (-797 (-327)))) (|HasCategory| |#1| (QUOTE (-797 (-484)))) (|HasCategory| |#1| (QUOTE (-554 (-801 (-327))))) (|HasCategory| |#1| (QUOTE (-554 (-801 (-484))))) (|HasCategory| |#1| (QUOTE (-581 (-484)))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-812 (-1089)))) (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-810 (-1089)))) (|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 (-257))) (|HasCategory| |#1| (QUOTE (-483))) (-12 (|HasAttribute| |#1| (QUOTE -3979)) (|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)))))
(-348 A B)
((|constructor| (NIL "This package extends a map between integral domains to a map between Fractions over those domains by applying the map to the numerators and denominators.")) (|map| (((|Fraction| |#2|) (|Mapping| |#2| |#1|) (|Fraction| |#1|)) "\\spad{map(func,frac)} applies the function \\spad{func} to the numerator and denominator of the fraction \\spad{frac}.")))
NIL
@@ -1330,7 +1330,7 @@ NIL
NIL
(-350 R UP)
((|constructor| (NIL "A \\spadtype{FramedAlgebra} is a \\spadtype{FiniteRankAlgebra} together with a fixed \\spad{R}-module basis.")) (|regularRepresentation| (((|Matrix| |#1|) $) "\\spad{regularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed basis.")) (|discriminant| ((|#1|) "\\spad{discriminant()} = determinant(traceMatrix()).")) (|traceMatrix| (((|Matrix| |#1|)) "\\spad{traceMatrix()} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr(vi * vj)} ),{} where \\spad{v1},{} ...,{} vn are the elements of the fixed basis.")) (|convert| (($ (|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| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis.")))
-((-3985 . T) (-3986 . T) (-3988 . T))
+((-3986 . T) (-3987 . T) (-3989 . T))
NIL
(-351 A S)
((|constructor| (NIL "\\indented{2}{A is fully retractable to \\spad{B} means that A is retractable to \\spad{B},{} and,{}} \\indented{2}{in addition,{} if \\spad{B} is retractable to the integers or rational} \\indented{2}{numbers then so is A.} \\indented{2}{In particular,{} what we are asserting is that there are no integers} \\indented{2}{(rationals) in A which don't retract into \\spad{B}.} Date Created: March 1990 Date Last Updated: 9 April 1991")))
@@ -1340,15 +1340,15 @@ NIL
((|constructor| (NIL "\\indented{2}{A is fully retractable to \\spad{B} means that A is retractable to \\spad{B},{} and,{}} \\indented{2}{in addition,{} if \\spad{B} is retractable to the integers or rational} \\indented{2}{numbers then so is A.} \\indented{2}{In particular,{} what we are asserting is that there are no integers} \\indented{2}{(rationals) in A which don't retract into \\spad{B}.} Date Created: March 1990 Date Last Updated: 9 April 1991")))
NIL
NIL
-(-353 R -3090 UP A)
+(-353 R -3091 UP A)
((|constructor| (NIL "Fractional ideals in a framed algebra.")) (|randomLC| ((|#4| (|NonNegativeInteger|) (|Vector| |#4|)) "\\spad{randomLC(n,x)} should be local but conditional.")) (|minimize| (($ $) "\\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)}.")))
-((-3988 . T))
+((-3989 . T))
NIL
(-354 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 -3090 UP A |ibasis|)
+(-355 R -3091 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|) $) "\\spad{basis((f1,...,fn))} = the vector \\spad{[f1,...,fn]}.")))
NIL
((|HasCategory| |#4| (|%list| (QUOTE -951) (|devaluate| |#2|))))
@@ -1362,7 +1362,7 @@ NIL
((|HasCategory| |#2| (QUOTE (-311))))
(-358 R)
((|constructor| (NIL "FramedNonAssociativeAlgebra(\\spad{R}) is a \\spadtype{FiniteRankNonAssociativeAlgebra} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank) over a commutative ring \\spad{R} together with a fixed \\spad{R}-module basis.")) (|apply| (($ (|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.")))
-((-3988 |has| |#1| (-495)) (-3986 . T) (-3985 . T))
+((-3989 |has| |#1| (-495)) (-3987 . T) (-3986 . T))
NIL
(-359 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)}.")))
@@ -1374,7 +1374,7 @@ 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)
((|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}.")))
-((-3988 OR (|has| |#1| (-962)) (|has| |#1| (-410))) (-3986 |has| |#1| (-146)) (-3985 |has| |#1| (-146)) ((-3993 "*") |has| |#1| (-495)) (-3984 |has| |#1| (-495)) (-3989 |has| |#1| (-495)) (-3983 |has| |#1| (-495)))
+((-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)))
NIL
(-362 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}.")))
@@ -1394,33 +1394,33 @@ NIL
((|HasCategory| |#2| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-317))))
(-366 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|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}.")))
-((-3991 . T) (-3981 . T) (-3992 . T))
+((-3992 . T) (-3982 . T) (-3993 . T))
NIL
(-367 S A R B)
((|constructor| (NIL "\\spad{FiniteSetAggregateFunctions2} provides functions involving two finite set aggregates where the underlying domains might be different. An example of this is to create a set of rational numbers by mapping a function across a set of integers,{} where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-aggregates \\spad{x} of aggregate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad {[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialised to \\spad{r}. For example,{} \\spad{reduce(_+\\$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 -3090)
+(-368 R -3091)
((|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)
((|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")))
-((-3978 -12 (|has| |#1| (-6 -3978)) (|has| |#2| (-6 -3978))) (-3985 . T) (-3986 . T) (-3988 . T))
-((-12 (|HasAttribute| |#1| (QUOTE -3978)) (|HasAttribute| |#2| (QUOTE -3978))))
-(-370 R -3090)
+((-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)
((|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 -3090)
+(-371 R -3091)
((|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 -3090)
+(-372 R -3091)
((|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 -3090)
+(-373 R -3091)
((|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
@@ -1428,7 +1428,7 @@ NIL
((|constructor| (NIL "Creates and manipulates objects which correspond to the basic FORTRAN data types: REAL,{} INTEGER,{} COMPLEX,{} LOGICAL and CHARACTER")) (= (((|Boolean|) $ $) "\\spad{x=y} tests for equality")) (|logical?| (((|Boolean|) $) "\\spad{logical?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type LOGICAL.")) (|character?| (((|Boolean|) $) "\\spad{character?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type CHARACTER.")) (|doubleComplex?| (((|Boolean|) $) "\\spad{doubleComplex?(t)} tests whether \\spad{t} is equivalent to the (non-standard) FORTRAN type DOUBLE COMPLEX.")) (|complex?| (((|Boolean|) $) "\\spad{complex?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type COMPLEX.")) (|integer?| (((|Boolean|) $) "\\spad{integer?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type INTEGER.")) (|double?| (((|Boolean|) $) "\\spad{double?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type DOUBLE PRECISION")) (|real?| (((|Boolean|) $) "\\spad{real?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type REAL.")) (|coerce| (((|SExpression|) $) "\\spad{coerce(x)} returns the \\spad{s}-expression associated with \\spad{x}") (((|Symbol|) $) "\\spad{coerce(x)} returns the symbol associated with \\spad{x}") (($ (|Symbol|)) "\\spad{coerce(s)} transforms the symbol \\spad{s} into an element of FortranScalarType provided \\spad{s} is one of real,{} complex,{}double precision,{} logical,{} integer,{} character,{} REAL,{} COMPLEX,{} LOGICAL,{} INTEGER,{} CHARACTER,{} DOUBLE PRECISION") (($ (|String|)) "\\spad{coerce(s)} transforms the string \\spad{s} into an element of FortranScalarType provided \\spad{s} is one of \"real\",{} \"double precision\",{} \"complex\",{} \"logical\",{} \"integer\",{} \"character\",{} \"REAL\",{} \"COMPLEX\",{} \"LOGICAL\",{} \"INTEGER\",{} \"CHARACTER\",{} \"DOUBLE PRECISION\"")))
NIL
NIL
-(-375 R -3090 UP)
+(-375 R -3091 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)))))
@@ -1448,7 +1448,7 @@ NIL
((|constructor| (NIL "\\spadtype{GaloisGroupFactorizer} provides functions to factor resolvents.")) (|btwFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|) (|Set| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{btwFact(p,sqf,pd,r)} returns the factorization of \\spad{p},{} the result is a Record such that \\spad{contp=}content \\spad{p},{} \\spad{factors=}List of irreducible factors of \\spad{p} with exponent. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors). \\spad{pd} is the \\spadtype{Set} of possible degrees. \\spad{r} is a lower bound for the number of factors of \\spad{p}. Please do not use this function in your code because its design may change.")) (|henselFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|)) "\\spad{henselFact(p,sqf)} returns the factorization of \\spad{p},{} the result is a Record such that \\spad{contp=}content \\spad{p},{} \\spad{factors=}List of irreducible factors of \\spad{p} with exponent. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors).")) (|factorOfDegree| (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|) (|Boolean|)) "\\spad{factorOfDegree(d,p,listOfDegrees,r,sqf)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees},{} and that \\spad{p} has at least \\spad{r} factors. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors).") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factorOfDegree(d,p,listOfDegrees,r)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees},{} and that \\spad{p} has at least \\spad{r} factors.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factorOfDegree(d,p,listOfDegrees)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|NonNegativeInteger|)) "\\spad{factorOfDegree(d,p,r)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has at least \\spad{r} factors.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1|) "\\spad{factorOfDegree(d,p)} returns a factor of \\spad{p} of degree \\spad{d}.")) (|factorSquareFree| (((|Factored| |#1|) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,d,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{d} divides the degree of all factors of \\spad{p} and that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,listOfDegrees,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees} and that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factorSquareFree(p,listOfDegrees)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(p)} returns the factorization of \\spad{p} which is supposed not having any repeated factor (this is not checked).")) (|factor| (((|Factored| |#1|) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factor(p,d,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{d} divides the degree of all factors of \\spad{p} and that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factor(p,listOfDegrees,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees} and that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factor(p,listOfDegrees)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}.") (((|Factored| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{factor(p,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns the factorization of \\spad{p} over the integers.")) (|tryFunctionalDecomposition| (((|Boolean|) (|Boolean|)) "\\spad{tryFunctionalDecomposition(b)} chooses whether factorizers have to look for functional decomposition of polynomials (\\spad{true}) or not (\\spad{false}). Returns the previous value.")) (|tryFunctionalDecomposition?| (((|Boolean|)) "\\spad{tryFunctionalDecomposition?()} returns \\spad{true} if factorizers try functional decomposition of polynomials before factoring them.")) (|eisensteinIrreducible?| (((|Boolean|) |#1|) "\\spad{eisensteinIrreducible?(p)} returns \\spad{true} if \\spad{p} can be shown to be irreducible by Eisenstein'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 -3090)
+(-380 R UP -3091)
((|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
@@ -1486,16 +1486,16 @@ NIL
NIL
(-389)
((|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}.")))
-((-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . T))
+((-3985 . T) ((-3994 "*") . T) (-3986 . T) (-3987 . T) (-3989 . T))
NIL
(-390 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")))
-((-3988 |has| (-347 (-858 |#1|)) (-495)) (-3986 . T) (-3985 . T))
+((-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)
((|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")))
-(((-3993 "*") |has| |#2| (-146)) (-3984 |has| |#2| (-495)) (-3989 |has| |#2| (-6 -3989)) (-3986 . T) (-3985 . T) (-3988 . 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 -3989)) (|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)))))
+(((-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)
((|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
@@ -1522,7 +1522,7 @@ NIL
NIL
(-398 |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| $) "\\spad{leadingCoefficient(x)} \\undocumented")))
-((-3986 . T) (-3985 . T))
+((-3987 . T) (-3986 . T))
NIL
(-399 E V R P Q)
((|constructor| (NIL "Gosper's summation algorithm.")) (|GospersMethod| (((|Union| |#5| "failed") |#5| |#2| (|Mapping| |#2|)) "\\spad{GospersMethod(b, n, new)} returns a rational function \\spad{rf(n)} such that \\spad{a(n) * rf(n)} is the indefinite sum of \\spad{a(n)} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{a(n+1) * rf(n+1) - a(n) * rf(n) = a(n)},{} where \\spad{b(n) = a(n)/a(n-1)} is a rational function. Returns \"failed\" if no such rational function \\spad{rf(n)} exists. Note: \\spad{new} is a nullary function returning a new \\spad{V} every time. The condition on \\spad{a(n)} is that \\spad{a(n)/a(n-1)} is a rational function of \\spad{n}.")))
@@ -1530,7 +1530,7 @@ NIL
NIL
(-400 R E |VarSet| P)
((|constructor| (NIL "A domain for polynomial sets.")) (|convert| (($ (|List| |#4|)) "\\axiom{convert(lp)} returns the polynomial set whose members are the polynomials of \\axiom{lp}.")))
-((-3992 . T) (-3991 . T))
+((-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)
((|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}.")))
@@ -1560,7 +1560,7 @@ NIL
((|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| $) "\\spad{degree(g)} names the degree of \\spad{g}. The set of all elements of a given degree form an \\spad{R}-module.")))
NIL
NIL
-(-408 |lv| -3090 R)
+(-408 |lv| -3091 R)
((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni,{} Summer \\spad{'88},{} revised November \\spad{'89}} Solve systems of polynomial equations using Groebner bases Total order Groebner bases are computed and then converted to lex ones This package is mostly intended for internal use.")) (|genericPosition| (((|Record| (|:| |dpolys| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |coords| (|List| (|Integer|)))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{genericPosition(lp,lv)} puts a radical zero dimensional ideal in general position,{} for system \\spad{lp} in variables \\spad{lv}.")) (|testDim| (((|Union| (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "failed") (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{testDim(lp,lv)} tests if the polynomial system \\spad{lp} in variables \\spad{lv} is zero dimensional.")) (|groebSolve| (((|List| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{groebSolve(lp,lv)} reduces the polynomial system \\spad{lp} in variables \\spad{lv} to triangular form. Algorithm based on groebner bases algorithm with linear algebra for change of ordering. Preprocessing for the general solver. The polynomials in input are of type \\spadtype{DMP}.")))
NIL
NIL
@@ -1570,23 +1570,23 @@ NIL
NIL
(-410)
((|constructor| (NIL "The class of multiplicative groups,{} \\spadignore{i.e.} monoids with multiplicative inverses. \\blankline")) (|commutator| (($ $ $) "\\spad{commutator(p,q)} computes \\spad{inv(p) * inv(q) * p * q}.")) (|conjugate| (($ $ $) "\\spad{conjugate(p,q)} computes \\spad{inv(q) * p * q}; this is 'right action by conjugation'.")) (|unitsKnown| ((|attribute|) "unitsKnown asserts that recip only returns \"failed\" for non-units.")) (** (($ $ (|Integer|)) "\\spad{x**n} returns \\spad{x} raised to the integer power \\spad{n}.")) (/ (($ $ $) "\\spad{x/y} is the same as \\spad{x} times the inverse of \\spad{y}.")) (|inv| (($ $) "\\spad{inv(x)} returns the inverse of \\spad{x}.")))
-((-3988 . T))
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NIL
(-411 |Coef| |var| |cen|)
((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x\\^r)}.")) (|integrate| (($ $ (|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.")))
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-((|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 -3942) (|%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 -3808) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1089))))) (|HasSignature| |#1| (|%list| (QUOTE -3079) (|%list| (|%list| (QUOTE -584) (QUOTE (-1089))) (|devaluate| |#1|)))))))
+(((-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|)
((|constructor| (NIL "A sparse table has a default entry,{} which is returned if no other value has been explicitly stored for a key.")))
-((-3992 . T))
-((-12 (|HasCategory| (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -259) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3856) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-553 (-773))))) (|HasCategory| (-2 (|:| -3856 |#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 (|:| -3856 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013))))
+((-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)
((|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)}")))
-((-3992 . T) (-3991 . T))
+((-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)
((|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}.")))
-((-3983 . T) (-3989 . T) (-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . T))
+((-3984 . T) (-3990 . T) (-3985 . T) ((-3994 "*") . T) (-3986 . T) (-3987 . T) (-3989 . T))
NIL
(-415)
((|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'.")))
@@ -1594,29 +1594,29 @@ NIL
NIL
(-416 |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.")))
-((-3991 . T) (-3992 . T))
-((-12 (|HasCategory| (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -259) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3856) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-553 (-773))))) (|HasCategory| (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-473)))) (-12 (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (|%list| (QUOTE -259) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-1013))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))))
+((-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))))
(-417)
((|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
(-418 |vl| R)
((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is total degree ordering refined by reverse lexicographic ordering with respect to the position that the variables appear in the list of variables parameter.")) (|reorder| (($ $ (|List| (|Integer|))) "\\spad{reorder(p, perm)} applies the permutation perm to the variables in a polynomial and returns the new correctly ordered polynomial")))
-(((-3993 "*") |has| |#2| (-146)) (-3984 |has| |#2| (-495)) (-3989 |has| |#2| (-6 -3989)) (-3986 . T) (-3985 . T) (-3988 . 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 -3989)) (|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)))))
-(-419 -2619 S)
+(((-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)))))
+(-419 -2620 S)
((|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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(-189))) (|HasCategory| |#2| (QUOTE (-962)))) (-12 (|HasCategory| |#2| (QUOTE (-812 (-1089)))) (|HasCategory| |#2| (QUOTE (-962)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-951 (-484)))) (|HasCategory| |#2| (QUOTE (-1013)))) (|HasCategory| |#2| (QUOTE (-962)))) (-12 (|HasCategory| |#2| (QUOTE (-951 (-484)))) (|HasCategory| |#2| (QUOTE (-1013)))) (-12 (|HasCategory| |#2| (QUOTE (-951 (-347 (-484))))) (|HasCategory| |#2| (QUOTE (-1013)))) (|HasAttribute| |#2| (QUOTE -3989)) (-12 (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-962)))) (-12 (|HasCategory| |#2| (QUOTE (-810 (-1089)))) (|HasCategory| |#2| (QUOTE (-962)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-72))) (-12 (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (|%list| (QUOTE -259) (|devaluate| |#2|)))))
(-420)
((|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)
((|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}.")))
-((-3991 . T) (-3992 . T))
+((-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 -3090 UP UPUP R)
+(-422 -3091 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
@@ -1626,12 +1626,12 @@ NIL
NIL
(-424)
((|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.")))
-((-3983 . T) (-3989 . T) (-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . T))
+((-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)))))
(-425 A S)
((|constructor| (NIL "A homogeneous aggregate is an aggregate of elements all of the same type. In the current system,{} all aggregates are homogeneous. Two attributes characterize classes of aggregates. Aggregates from domains with attribute \\spadatt{finiteAggregate} have a finite number of members. Those with attribute \\spadatt{shallowlyMutable} allow an element to be modified or updated without changing its overall value.")) (|member?| (((|Boolean|) |#2| $) "\\spad{member?(x,u)} tests if \\spad{x} is a member of \\spad{u}. For collections,{} \\axiom{member?(\\spad{x},{}\\spad{u}) = reduce(or,{}[x=y for \\spad{y} in \\spad{u}],{}\\spad{false})}.")) (|members| (((|List| |#2|) $) "\\spad{members(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|parts| (((|List| |#2|) $) "\\spad{parts(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|count| (((|NonNegativeInteger|) |#2| $) "\\spad{count(x,u)} returns the number of occurrences of \\spad{x} in \\spad{u}. For collections,{} \\axiom{count(\\spad{x},{}\\spad{u}) = reduce(+,{}[x=y for \\spad{y} in \\spad{u}],{}0)}.") (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{count(p,u)} returns the number of elements \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. For collections,{} \\axiom{count(\\spad{p},{}\\spad{u}) = reduce(+,{}[1 for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})],{}0)}.")) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{every?(f,u)} tests if \\spad{p}(\\spad{x}) is \\spad{true} for all elements \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{every?(\\spad{p},{}\\spad{u}) = reduce(and,{}map(\\spad{f},{}\\spad{u}),{}\\spad{true},{}\\spad{false})}.")) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{any?(p,u)} tests if \\axiom{\\spad{p}(\\spad{x})} is \\spad{true} for any element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{any?(\\spad{p},{}\\spad{u}) = reduce(or,{}map(\\spad{f},{}\\spad{u}),{}\\spad{false},{}\\spad{true})}.")) (|map!| (($ (|Mapping| |#2| |#2|) $) "\\spad{map!(f,u)} destructively replaces each element \\spad{x} of \\spad{u} by \\axiom{\\spad{f}(\\spad{x})}.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(f,u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}.")))
NIL
-((|HasAttribute| |#1| (QUOTE -3991)) (|HasAttribute| |#1| (QUOTE -3992)) (|HasCategory| |#2| (|%list| (QUOTE -259) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-553 (-773)))))
+((|HasAttribute| |#1| (QUOTE -3992)) (|HasAttribute| |#1| (QUOTE -3993)) (|HasCategory| |#2| (|%list| (QUOTE -259) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-553 (-773)))))
(-426 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|) $) "\\spad{map(f,u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}.")))
NIL
@@ -1652,33 +1652,33 @@ NIL
((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}.")))
NIL
NIL
-(-431 -3090 UP |AlExt| |AlPol|)
+(-431 -3091 UP |AlExt| |AlPol|)
((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of a field over which we can factor UP's.")) (|factor| (((|Factored| |#4|) |#4| (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{factor(p, f)} returns a prime factorisation of \\spad{p}; \\spad{f} is a factorisation map for elements of UP.")))
NIL
NIL
(-432)
((|constructor| (NIL "Algebraic closure of the rational numbers.")) (|norm| (($ $ (|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}.")))
-((-3983 . T) (-3989 . T) (-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . T))
+((-3984 . T) (-3990 . T) (-3985 . T) ((-3994 "*") . T) (-3986 . T) (-3987 . T) (-3989 . T))
((|HasCategory| $ (QUOTE (-962))) (|HasCategory| $ (QUOTE (-951 (-484)))))
(-433 S |mn|)
((|constructor| (NIL "\\indented{1}{Author Micheal Monagan \\spad{Aug/87}} This is the basic one dimensional array data type.")))
-((-3992 . T) (-3991 . T))
+((-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|)
((|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.")))
-((-3991 . T) (-3992 . T))
+((-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)
((|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 -3090)
+(-436 R UP -3091)
((|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|)
((|constructor| (NIL "\\spadtype{IndexedBits} is a domain to compactly represent large quantities of Boolean data.")))
-((-3992 . T) (-3991 . T))
+((-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)
((|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)}.")))
@@ -1692,7 +1692,7 @@ NIL
((|constructor| (NIL "InnerCommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#4|) "\\spad{splitDenominator([q1,...,qn])} returns \\spad{[[p1,...,pn], d]} such that \\spad{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 -3090 |Expon| |VarSet| |DPoly|)
+(-441 -3091 |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}.")) (* (($ $ $) "\\spad{I*J} computes the product of the ideal \\spad{I} and \\spad{J}.")))
NIL
((|HasCategory| |#3| (QUOTE (-554 (-1089)))))
@@ -1702,7 +1702,7 @@ NIL
NIL
(-443 T$)
((|constructor| (NIL "This is the category of all domains that implement idempotent operations.")))
-(((|%Rule| |idempotence| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|)) (-3054 (|f| |x| |x|) |x|))) . T))
+(((|%Rule| |idempotence| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|)) (-3055 (|f| |x| |x|) |x|))) . T))
NIL
(-444)
((|constructor| (NIL "This domain provides representation for plain identifiers. It differs from Symbol in that it does not support any form of scripting. It is a plain basic data structure. \\blankline")) (|gensym| (($) "\\spad{gensym()} returns a new identifier,{} different from any other identifier in the running system")))
@@ -1721,7 +1721,7 @@ NIL
NIL
NIL
(-448 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.")))
+((|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)
@@ -1750,7 +1750,7 @@ NIL
((|HasCategory| |#2| (QUOTE (-717))))
(-455 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}")))
-((-3992 . T) (-3991 . T))
+((-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)
((|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'.")))
@@ -1758,24 +1758,24 @@ NIL
NIL
(-457 |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}.")))
-((-3983 . T) (-3989 . T) (-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . T))
+((-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|)
((|constructor| (NIL "\\indented{1}{This is an internal type which provides an implementation of} 2-dimensional arrays as PrimitiveArray's of PrimitiveArray's.")))
-((-3991 . T) (-3992 . T))
+((-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)
((|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 -3992)))
+((|HasAttribute| |#3| (QUOTE -3993)))
(-460 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 -3992)))
+((|HasAttribute| |#7| (QUOTE -3993)))
(-461 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.")))
-((-3991 . 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 (-257))) (|HasCategory| |#1| (QUOTE (-495))) (|HasAttribute| |#1| (QUOTE (-3993 "*"))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-72))))
+((-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)
((|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
@@ -1808,7 +1808,7 @@ NIL
((|constructor| (NIL "\\indented{2}{IndexedExponents of an ordered set of variables gives a representation} for the degree of polynomials in commuting variables. It gives an ordered pairing of non negative integer exponents with variables")))
NIL
((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| (-695) (QUOTE (-1013)))))
-(-470 K -3090 |Par|)
+(-470 K -3091 |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
@@ -1832,7 +1832,7 @@ NIL
((|constructor| (NIL "This package computes infinite products of univariate Taylor series over an integral domain of characteristic 0.")) (|generalInfiniteProduct| ((|#2| |#2| (|Integer|) (|Integer|)) "\\spad{generalInfiniteProduct(f(x),a,d)} computes \\spad{product(n=a,a+d,a+2*d,...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|oddInfiniteProduct| ((|#2| |#2|) "\\spad{oddInfiniteProduct(f(x))} computes \\spad{product(n=1,3,5...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|evenInfiniteProduct| ((|#2| |#2|) "\\spad{evenInfiniteProduct(f(x))} computes \\spad{product(n=2,4,6...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|infiniteProduct| ((|#2| |#2|) "\\spad{infiniteProduct(f(x))} computes \\spad{product(n=1,2,3...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")))
NIL
NIL
-(-476 K -3090 |Par|)
+(-476 K -3091 |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
@@ -1862,11 +1862,11 @@ NIL
NIL
(-483)
((|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.")))
-((-3989 . T) (-3990 . T) (-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . T))
+((-3990 . T) (-3991 . T) (-3985 . T) ((-3994 "*") . T) (-3986 . T) (-3987 . T) (-3989 . T))
NIL
(-484)
((|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.")))
-((-3979 . T) (-3983 . T) (-3978 . T) (-3989 . T) (-3990 . T) (-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . T))
+((-3980 . T) (-3984 . T) (-3979 . T) (-3990 . T) (-3991 . T) (-3985 . T) ((-3994 "*") . T) (-3986 . T) (-3987 . T) (-3989 . T))
NIL
(-485)
((|constructor| (NIL "This domain is a datatype for (signed) integer values of precision 16 bits.")))
@@ -1886,13 +1886,13 @@ NIL
NIL
(-489 |Key| |Entry| |addDom|)
((|constructor| (NIL "This domain is used to provide a conditional \"add\" domain for the implementation of \\spadtype{Table}.")))
-((-3991 . T) (-3992 . T))
-((-12 (|HasCategory| (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -259) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3856) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-553 (-773))))) (|HasCategory| (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-473)))) (-12 (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (|%list| (QUOTE -259) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-1013))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))))
-(-490 R -3090)
+((-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)
((|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 -3090 UP UPUP R)
+(-491 R0 -3091 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
@@ -1902,7 +1902,7 @@ NIL
NIL
(-493 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.")))
-((-3766 . T) (-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . T))
+((-3767 . T) (-3985 . T) ((-3994 "*") . T) (-3986 . T) (-3987 . T) (-3989 . T))
NIL
(-494 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.")))
@@ -1910,9 +1910,9 @@ NIL
NIL
(-495)
((|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.")))
-((-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . T))
+((-3985 . T) ((-3994 "*") . T) (-3986 . T) (-3987 . T) (-3989 . T))
NIL
-(-496 R -3090)
+(-496 R -3091)
((|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
@@ -1920,7 +1920,7 @@ NIL
((|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 -3090 L)
+(-498 R -3091 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|))))
@@ -1928,23 +1928,23 @@ NIL
((|constructor| (NIL "This package provides various number theoretic functions on the integers.")) (|sumOfKthPowerDivisors| (((|Integer|) (|Integer|) (|NonNegativeInteger|)) "\\spad{sumOfKthPowerDivisors(n,k)} returns the sum of the \\spad{k}th powers of the integers between 1 and \\spad{n} (inclusive) which divide \\spad{n}. the sum of the \\spad{k}th powers of the divisors of \\spad{n} is often denoted by \\spad{sigma_k(n)}.")) (|sumOfDivisors| (((|Integer|) (|Integer|)) "\\spad{sumOfDivisors(n)} returns the sum of the integers between 1 and \\spad{n} (inclusive) which divide \\spad{n}. The sum of the divisors of \\spad{n} is often denoted by \\spad{sigma(n)}.")) (|numberOfDivisors| (((|Integer|) (|Integer|)) "\\spad{numberOfDivisors(n)} returns the number of integers between 1 and \\spad{n} (inclusive) which divide \\spad{n}. The number of divisors of \\spad{n} is often denoted by \\spad{tau(n)}.")) (|moebiusMu| (((|Integer|) (|Integer|)) "\\spad{moebiusMu(n)} returns the Moebius function \\spad{mu(n)}. \\spad{mu(n)} is either \\spad{-1},{}0 or 1 as follows: \\spad{mu(n) = 0} if \\spad{n} is divisible by a square > 1,{} \\spad{mu(n) = (-1)^k} if \\spad{n} is square-free and has \\spad{k} distinct prime divisors.")) (|legendre| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{legendre(a,p)} returns the Legendre symbol \\spad{L(a/p)}. \\spad{L(a/p) = (-1)**((p-1)/2) mod p} (\\spad{p} prime),{} which is 0 if \\spad{a} is 0,{} 1 if \\spad{a} is a quadratic residue \\spad{mod p} and \\spad{-1} otherwise. Note: because the primality test is expensive,{} if it is known that \\spad{p} is prime then use \\spad{jacobi(a,p)}.")) (|jacobi| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{jacobi(a,b)} returns the Jacobi symbol \\spad{J(a/b)}. When \\spad{b} is odd,{} \\spad{J(a/b) = product(L(a/p) for p in factor b )}. Note: by convention,{} 0 is returned if \\spad{gcd(a,b) ~= 1}. Iterative \\spad{O(log(b)^2)} version coded by Michael Monagan June 1987.")) (|harmonic| (((|Fraction| (|Integer|)) (|Integer|)) "\\spad{harmonic(n)} returns the \\spad{n}th harmonic number. This is \\spad{H[n] = sum(1/k,k=1..n)}.")) (|fibonacci| (((|Integer|) (|Integer|)) "\\spad{fibonacci(n)} returns the \\spad{n}th Fibonacci number. the Fibonacci numbers \\spad{F[n]} are defined by \\spad{F[0] = F[1] = 1} and \\spad{F[n] = F[n-1] + F[n-2]}. The algorithm has running time \\spad{O(log(n)^3)}. Reference: Knuth,{} The Art of Computer Programming Vol 2,{} Semi-Numerical Algorithms.")) (|eulerPhi| (((|Integer|) (|Integer|)) "\\spad{eulerPhi(n)} returns the number of integers between 1 and \\spad{n} (including 1) which are relatively prime to \\spad{n}. This is the Euler phi function \\spad{\\phi(n)} is also called the totient function.")) (|euler| (((|Integer|) (|Integer|)) "\\spad{euler(n)} returns the \\spad{n}th Euler number. This is \\spad{2^n E(n,1/2)},{} where \\spad{E(n,x)} is the \\spad{n}th Euler polynomial.")) (|divisors| (((|List| (|Integer|)) (|Integer|)) "\\spad{divisors(n)} returns a list of the divisors of \\spad{n}.")) (|chineseRemainder| (((|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{chineseRemainder(x1,m1,x2,m2)} returns \\spad{w},{} where \\spad{w} is such that \\spad{w = x1 mod m1} and \\spad{w = x2 mod m2}. Note: \\spad{m1} and \\spad{m2} must be relatively prime.")) (|bernoulli| (((|Fraction| (|Integer|)) (|Integer|)) "\\spad{bernoulli(n)} returns the \\spad{n}th Bernoulli number. this is \\spad{B(n,0)},{} where \\spad{B(n,x)} is the \\spad{n}th Bernoulli polynomial.")))
NIL
NIL
-(-500 -3090 UP UPUP R)
+(-500 -3091 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 -3090 UP)
+(-501 -3091 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 -3090 L)
+(-502 R -3091 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 -3090)
+(-503 R -3091)
((|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 -3090 UP)
+(-504 -3091 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
@@ -1952,27 +1952,27 @@ NIL
((|constructor| (NIL "Provides integer testing and retraction functions. Date Created: March 1990 Date Last Updated: 9 April 1991")) (|integerIfCan| (((|Union| (|Integer|) "failed") |#1|) "\\spad{integerIfCan(x)} returns \\spad{x} as an integer,{} \"failed\" if \\spad{x} is not an integer.")) (|integer?| (((|Boolean|) |#1|) "\\spad{integer?(x)} is \\spad{true} if \\spad{x} is an integer,{} \\spad{false} otherwise.")) (|integer| (((|Integer|) |#1|) "\\spad{integer(x)} returns \\spad{x} as an integer; error if \\spad{x} is not an integer.")))
NIL
NIL
-(-506 -3090)
+(-506 -3091)
((|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)
((|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.")))
-((-3766 . T) (-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . T))
+((-3767 . T) (-3985 . T) ((-3994 "*") . T) (-3986 . T) (-3987 . T) (-3989 . T))
NIL
(-508)
((|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 -3090)
+(-509 R -3091)
((|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 -3090 UP)
+(-510 -3091 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 -3090)
+(-511 R -3091)
((|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
@@ -1994,25 +1994,25 @@ NIL
NIL
(-516 |p| |unBalanced?|)
((|constructor| (NIL "This domain implements Zp,{} the \\spad{p}-adic completion of the integers. This is an internal domain.")))
-((-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . T))
+((-3985 . T) ((-3994 "*") . T) (-3986 . T) (-3987 . T) (-3989 . T))
NIL
(-517 |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.")))
-((-3983 . T) (-3989 . T) (-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . T))
+((-3984 . T) (-3990 . T) (-3985 . T) ((-3994 "*") . T) (-3986 . T) (-3987 . T) (-3989 . T))
((|HasCategory| $ (QUOTE (-120))) (|HasCategory| $ (QUOTE (-118))) (|HasCategory| $ (QUOTE (-317))))
(-518)
((|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 -3090)
+(-519 -3091)
((|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}.")))
-((-3986 . T) (-3985 . T))
+((-3987 . T) (-3986 . T))
((|HasCategory| |#1| (QUOTE (-810 (-1089)))) (|HasCategory| |#1| (QUOTE (-951 (-1089)))))
-(-520 E -3090)
+(-520 E -3091)
((|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 -3090)
+(-521 R -3091)
((|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
@@ -2050,11 +2050,11 @@ 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}.")))
-(((-3993 "*") |has| |#1| (-146)) (-3984 |has| |#1| (-495)) (-3985 . T) (-3986 . T) (-3988 . 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 -3942) (|%list| (|devaluate| |#1|) (QUOTE (-1089)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-484))))))
+(((-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 "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|) $) "\\spad{coefficients(x)} returns a stream of ring elements. \\indented{1}{When \\spad{x} is a univariate series,{} this is a stream of Taylor} \\indented{1}{coefficients. When \\spad{x} is a multivariate series,{} the} \\indented{1}{\\spad{n}th element of the stream is a form of} \\indented{1}{degree \\spad{n} in the power series variables.}")))
-(((-3993 "*") |has| |#1| (-495)) (-3984 |has| |#1| (-495)) (-3985 . T) (-3986 . T) (-3988 . T))
+(((-3994 "*") |has| |#1| (-495)) (-3985 |has| |#1| (-495)) (-3986 . T) (-3987 . T) (-3989 . T))
((|HasCategory| |#1| (QUOTE (-495))))
(-532)
((|constructor| (NIL "This domain provides representations for internal type form.")) (|mappingMode| (($ $ (|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")))
@@ -2068,7 +2068,7 @@ NIL
((|constructor| (NIL "Functions defined on streams with entries in two sets.")) (|map| (((|Stream| |#3|) (|Mapping| |#3| |#1| |#2|) (|InfiniteTuple| |#1|) (|Stream| |#2|)) "\\spad{map(f,a,b)} \\undocumented") (((|Stream| |#3|) (|Mapping| |#3| |#1| |#2|) (|Stream| |#1|) (|InfiniteTuple| |#2|)) "\\spad{map(f,a,b)} \\undocumented") (((|InfiniteTuple| |#3|) (|Mapping| |#3| |#1| |#2|) (|InfiniteTuple| |#1|) (|InfiniteTuple| |#2|)) "\\spad{map(f,a,b)} \\undocumented")))
NIL
NIL
-(-535 R -3090 FG)
+(-535 R -3091 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
@@ -2078,12 +2078,12 @@ NIL
NIL
(-537 R |mn|)
((|constructor| (NIL "\\indented{2}{This type represents vector like objects with varying lengths} and a user-specified initial index.")))
-((-3992 . T) (-3991 . T))
+((-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|)
((|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 -3992)) (|HasCategory| |#2| (QUOTE (-757))) (|HasAttribute| |#1| (QUOTE -3991)) (|HasCategory| |#3| (QUOTE (-1013))))
+((|HasAttribute| |#1| (QUOTE -3993)) (|HasCategory| |#2| (QUOTE (-757))) (|HasAttribute| |#1| (QUOTE -3992)) (|HasCategory| |#3| (QUOTE (-1013))))
(-539 |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|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order.")))
NIL
@@ -2094,7 +2094,7 @@ NIL
NIL
(-541 R A)
((|constructor| (NIL "\\indented{1}{AssociatedJordanAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$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).")))
-((-3988 OR (-2560 (|has| |#2| (-315 |#1|)) (|has| |#1| (-495))) (-12 (|has| |#2| (-358 |#1|)) (|has| |#1| (-495)))) (-3986 . T) (-3985 . T))
+((-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)
((|constructor| (NIL "This is the datatype for the JVM bytecodes.")))
@@ -2122,15 +2122,15 @@ NIL
NIL
(-548 |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.")))
-((-3991 . T) (-3992 . T))
-((-12 (|HasCategory| (-2 (|:| -3856 (-1072)) (|:| |entry| |#1|)) (|%list| (QUOTE -259) (|%list| (QUOTE -2) (QUOTE (|:| -3856 (-1072))) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -3856 (-1072)) (|:| |entry| |#1|)) (QUOTE (-1013)))) (|HasCategory| (-2 (|:| -3856 (-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 (|:| -3856 (-1072)) (|:| |entry| |#1|)) (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3856 (-1072)) (|:| |entry| |#1|)) (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3856 (-1072)) (|:| |entry| |#1|)) (QUOTE (-72))))
+((-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|)
((|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|)
((|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}.")))
-((-3992 . T))
+((-3993 . T))
NIL
(-551 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.")))
@@ -2148,7 +2148,7 @@ NIL
((|constructor| (NIL "A is convertible to \\spad{B} means any element of A can be converted into an element of \\spad{B},{} but not automatically by the interpreter.")) (|convert| ((|#1| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}.")))
NIL
NIL
-(-555 -3090 UP)
+(-555 -3091 UP)
((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic's algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,a_1,a_2,ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$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
@@ -2166,7 +2166,7 @@ NIL
NIL
(-559 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}.")))
-((-3985 . T) (-3986 . T) (-3988 . T))
+((-3986 . T) (-3987 . T) (-3989 . T))
((|HasCategory| |#1| (QUOTE (-756))))
(-560 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.")))
@@ -2174,15 +2174,15 @@ NIL
NIL
(-561 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.")))
-((-3988 . T))
+((-3989 . T))
NIL
-(-562 R -3090)
+(-562 R -3091)
((|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)
((|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")))
-((-3986 . T) (-3985 . T) ((-3993 "*") . T) (-3984 . T) (-3988 . T))
+((-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)
((|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.")))
@@ -2198,13 +2198,13 @@ NIL
NIL
(-567 |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}}.")))
-((-3988 . T))
+((-3989 . T))
NIL
(-568 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 -3090)
+(-569 R -3091)
((|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
@@ -2212,17 +2212,17 @@ NIL
((|constructor| (NIL "Category for the transcendental Liouvillian functions.")) (|erf| (($ $) "\\spad{erf(x)} returns the error function of \\spad{x},{} \\spadignore{i.e.} \\spad{2 / sqrt(\\%pi)} times the integral of \\spad{exp(-x**2) dx}.")) (|dilog| (($ $) "\\spad{dilog(x)} returns the dilogarithm of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{log(x) / (1 - x) dx}.")) (|li| (($ $) "\\spad{li(x)} returns the logarithmic integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{dx / log(x)}.")) (|Ci| (($ $) "\\spad{Ci(x)} returns the cosine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{cos(x) / x dx}.")) (|Si| (($ $) "\\spad{Si(x)} returns the sine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{sin(x) / x dx}.")) (|Ei| (($ $) "\\spad{Ei(x)} returns the exponential integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{exp(x)/x dx}.")))
NIL
NIL
-(-571 |lv| -3090)
+(-571 |lv| -3091)
((|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)
((|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.")))
-((-3992 . T))
-((-12 (|HasCategory| (-2 (|:| -3856 (-1072)) (|:| |entry| (-51))) (QUOTE (-259 (-2 (|:| -3856 (-1072)) (|:| |entry| (-51)))))) (|HasCategory| (-2 (|:| -3856 (-1072)) (|:| |entry| (-51))) (QUOTE (-1013)))) (OR (|HasCategory| (-51) (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3856 (-1072)) (|:| |entry| (-51))) (QUOTE (-1013)))) (OR (|HasCategory| (-51) (QUOTE (-72))) (|HasCategory| (-51) (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3856 (-1072)) (|:| |entry| (-51))) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3856 (-1072)) (|:| |entry| (-51))) (QUOTE (-1013)))) (OR (|HasCategory| (-2 (|:| -3856 (-1072)) (|:| |entry| (-51))) (QUOTE (-553 (-773)))) (|HasCategory| (-51) (QUOTE (-553 (-773))))) (|HasCategory| (-2 (|:| -3856 (-1072)) (|:| |entry| (-51))) (QUOTE (-554 (-473)))) (-12 (|HasCategory| (-51) (QUOTE (-259 (-51)))) (|HasCategory| (-51) (QUOTE (-1013)))) (|HasCategory| (-1072) (QUOTE (-757))) (OR (|HasCategory| (-51) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3856 (-1072)) (|:| |entry| (-51))) (QUOTE (-72)))) (|HasCategory| (-51) (QUOTE (-1013))) (|HasCategory| (-51) (QUOTE (-72))) (|HasCategory| (-51) (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3856 (-1072)) (|:| |entry| (-51))) (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3856 (-1072)) (|:| |entry| (-51))) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3856 (-1072)) (|:| |entry| (-51))) (QUOTE (-1013))))
+((-3993 . T))
+((-12 (|HasCategory| (-2 (|:| -3857 (-1072)) (|:| |entry| (-51))) (QUOTE (-259 (-2 (|:| -3857 (-1072)) (|:| |entry| (-51)))))) (|HasCategory| (-2 (|:| -3857 (-1072)) (|:| |entry| (-51))) (QUOTE (-1013)))) (OR (|HasCategory| (-51) (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3857 (-1072)) (|:| |entry| (-51))) (QUOTE (-1013)))) (OR (|HasCategory| (-51) (QUOTE (-72))) (|HasCategory| (-51) (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3857 (-1072)) (|:| |entry| (-51))) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3857 (-1072)) (|:| |entry| (-51))) (QUOTE (-1013)))) (OR (|HasCategory| (-2 (|:| -3857 (-1072)) (|:| |entry| (-51))) (QUOTE (-553 (-773)))) (|HasCategory| (-51) (QUOTE (-553 (-773))))) (|HasCategory| (-2 (|:| -3857 (-1072)) (|:| |entry| (-51))) (QUOTE (-554 (-473)))) (-12 (|HasCategory| (-51) (QUOTE (-259 (-51)))) (|HasCategory| (-51) (QUOTE (-1013)))) (|HasCategory| (-1072) (QUOTE (-757))) (OR (|HasCategory| (-51) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3857 (-1072)) (|:| |entry| (-51))) (QUOTE (-72)))) (|HasCategory| (-51) (QUOTE (-1013))) (|HasCategory| (-51) (QUOTE (-72))) (|HasCategory| (-51) (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3857 (-1072)) (|:| |entry| (-51))) (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3857 (-1072)) (|:| |entry| (-51))) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3857 (-1072)) (|:| |entry| (-51))) (QUOTE (-1013))))
(-573 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).")))
-((-3988 OR (-2560 (|has| |#2| (-315 |#1|)) (|has| |#1| (-495))) (-12 (|has| |#2| (-358 |#1|)) (|has| |#1| (-495)))) (-3986 . T) (-3985 . T))
+((-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|))))
(-574 S R)
((|constructor| (NIL "\\axiom{JacobiIdentity} means that \\axiom{[\\spad{x},{}[\\spad{y},{}\\spad{z}]]+[\\spad{y},{}[\\spad{z},{}\\spad{x}]]+[\\spad{z},{}[\\spad{x},{}\\spad{y}]] = 0} holds.")) (/ (($ $ |#2|) "\\axiom{x/r} returns the division of \\axiom{\\spad{x}} by \\axiom{\\spad{r}}.")) (|construct| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}.")))
@@ -2230,7 +2230,7 @@ NIL
((|HasCategory| |#2| (QUOTE (-311))))
(-575 R)
((|constructor| (NIL "\\axiom{JacobiIdentity} means that \\axiom{[\\spad{x},{}[\\spad{y},{}\\spad{z}]]+[\\spad{y},{}[\\spad{z},{}\\spad{x}]]+[\\spad{z},{}[\\spad{x},{}\\spad{y}]] = 0} holds.")) (/ (($ $ |#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) (-3986 . T) (-3985 . T))
+((|JacobiIdentity| . T) (|NullSquare| . T) (-3987 . T) (-3986 . T))
NIL
(-576 R FE)
((|constructor| (NIL "PowerSeriesLimitPackage implements limits of expressions in one or more variables as one of the variables approaches a limiting value. Included are two-sided limits,{} left- and right- hand limits,{} and limits at plus or minus infinity.")) (|complexLimit| (((|Union| (|OnePointCompletion| |#2|) "failed") |#2| (|Equation| (|OnePointCompletion| |#2|))) "\\spad{complexLimit(f(x),x = a)} computes the complex limit \\spad{lim(x -> a,f(x))}.")) (|limit| (((|Union| (|OrderedCompletion| |#2|) #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))}.")))
@@ -2247,10 +2247,10 @@ NIL
(-579 S R)
((|constructor| (NIL "Test for linear dependence.")) (|solveLinear| (((|Union| (|Vector| (|Fraction| |#1|)) "failed") (|Vector| |#2|) |#2|) "\\spad{solveLinear([v1,...,vn], u)} returns \\spad{[c1,...,cn]} such that \\spad{c1*v1 + ... + cn*vn = u},{} \"failed\" if no such \\spad{ci}'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
-((-2558 (|HasCategory| |#1| (QUOTE (-311)))) (|HasCategory| |#1| (QUOTE (-311))))
+((-2559 (|HasCategory| |#1| (QUOTE (-311)))) (|HasCategory| |#1| (QUOTE (-311))))
(-580 K B)
((|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}.")))
-((-3986 . T) (-3985 . T))
+((-3987 . T) (-3986 . T))
((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| (-578 |#2|) (QUOTE (-1013)))))
(-581 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]}.")))
@@ -2258,7 +2258,7 @@ NIL
NIL
(-582 K B)
((|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}.")))
-((-3986 . T) (-3985 . T))
+((-3987 . T) (-3986 . T))
NIL
(-583 S)
((|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.")))
@@ -2266,7 +2266,7 @@ NIL
NIL
(-584 S)
((|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.")))
-((-3992 . T) (-3991 . T))
+((-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|)))))
(-585 A B)
((|constructor| (NIL "\\spadtype{ListFunctions2} implements utility functions that operate on two kinds of lists,{} each with a possibly different type of element.")) (|map| (((|List| |#2|) (|Mapping| |#2| |#1|) (|List| |#1|)) "\\spad{map(fn,u)} applies \\spad{fn} to each element of list \\spad{u} and returns a new list with the results. For example \\spad{map(square,[1,2,3]) = [1,4,9]}.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|List| |#1|) |#2|) "\\spad{reduce(fn,u,ident)} successively uses the binary function \\spad{fn} on the elements of list \\spad{u} and the result of previous applications. \\spad{ident} is returned if the \\spad{u} is empty. Note the order of application in the following examples: \\spad{reduce(fn,[1,2,3],0) = fn(3,fn(2,fn(1,0)))} and \\spad{reduce(*,[2,3],1) = 3 * (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)]}.")))
@@ -2290,7 +2290,7 @@ NIL
NIL
(-590 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.")))
-((-3991 . T) (-3992 . T))
+((-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)
((|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")))
@@ -2303,30 +2303,30 @@ NIL
(-593 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 -3992)))
+((|HasAttribute| |#1| (QUOTE -3993)))
(-594 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)
((|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}.")))
-((-3986 . T) (-3985 . T))
+((-3987 . T) (-3986 . T))
((|HasCategory| |#1| (QUOTE (-715))))
-(-596 R -3090 L)
+(-596 R -3091 L)
((|constructor| (NIL "\\spad{ElementaryFunctionLODESolver} provides the top-level functions for finding closed form solutions of linear ordinary differential equations and initial value problems.")) (|solve| (((|Union| |#2| "failed") |#3| |#2| (|Symbol|) |#2| (|List| |#2|)) "\\spad{solve(op, g, x, a, [y0,...,ym])} returns either the solution of the initial value problem \\spad{op y = g, y(a) = y0, y'(a) = y1,...} or \"failed\" if the solution cannot be found; \\spad{x} is the dependent variable.") (((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) "failed") |#3| |#2| (|Symbol|)) "\\spad{solve(op, g, x)} returns either a solution of the ordinary differential equation \\spad{op y = g} or \"failed\" if no non-trivial solution can be found; When found,{} the solution is returned in the form \\spad{[h, [b1,...,bm]]} where \\spad{h} is a particular solution and and \\spad{[b1,...bm]} are linearly independent solutions of the associated homogenuous equation \\spad{op y = 0}. A full basis for the solutions of the homogenuous equation is not always returned,{} only the solutions which were found; \\spad{x} is the dependent variable.")))
NIL
NIL
-(-597 A -2490)
+(-597 A -2491)
((|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}}")))
-((-3985 . T) (-3986 . T) (-3988 . T))
+((-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))))
(-598 A)
((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperator1} defines a ring of differential operators with coefficients in a differential ring A. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")))
-((-3985 . T) (-3986 . T) (-3988 . T))
+((-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))))
(-599 A M)
((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperator2} defines a ring of differential operators with coefficients in a differential ring A and acting on an A-module \\spad{M}. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|differentiate| (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}")))
-((-3985 . T) (-3986 . T) (-3988 . T))
+((-3986 . T) (-3987 . T) (-3989 . T))
((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-951 (-347 (-484))))) (|HasCategory| |#1| (QUOTE (-951 (-484)))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-389))) (|HasCategory| |#1| (QUOTE (-311))))
(-600 S A)
((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorCategory} is the category of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|directSum| (($ $ $) "\\spad{directSum(a,b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}.")) (|symmetricSquare| (($ $) "\\spad{symmetricSquare(a)} computes \\spad{symmetricProduct(a,a)} using a more efficient method.")) (|symmetricPower| (($ $ (|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}.")))
@@ -2334,9 +2334,9 @@ NIL
((|HasCategory| |#2| (QUOTE (-311))))
(-601 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}.")))
-((-3985 . T) (-3986 . T) (-3988 . T))
+((-3986 . T) (-3987 . T) (-3989 . T))
NIL
-(-602 -3090 UP)
+(-602 -3091 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))))
@@ -2358,7 +2358,7 @@ NIL
NIL
(-607 |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) (-3986 . T) (-3985 . T))
+((|JacobiIdentity| . T) (|NullSquare| . T) (-3987 . T) (-3986 . T))
((|HasCategory| |#2| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-146))))
(-608 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}.")))
@@ -2366,13 +2366,13 @@ NIL
NIL
(-609 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}.")))
-((-3992 . T) (-3991 . T))
+((-3993 . T) (-3992 . T))
NIL
-(-610 -3090 |Row| |Col| M)
+(-610 -3091 |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 -3090)
+(-611 -3091)
((|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
@@ -2382,8 +2382,8 @@ NIL
NIL
(-613 |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.")))
-((-3988 . T) (-3991 . T) (-3985 . T) (-3986 . T))
-((|HasCategory| |#2| (QUOTE (-810 (-1089)))) (|HasCategory| |#2| (QUOTE (-812 (-1089)))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-189))) (|HasAttribute| |#2| (QUOTE (-3993 #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 (-3993 #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))))
+((-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)
((|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
@@ -2439,10 +2439,10 @@ NIL
(-627 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 (-3993 "*"))) (|HasCategory| |#2| (QUOTE (-257))) (|HasCategory| |#2| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-495))))
+((|HasAttribute| |#2| (QUOTE (-3994 "*"))) (|HasCategory| |#2| (QUOTE (-257))) (|HasCategory| |#2| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-495))))
(-628 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")))
-((-3991 . T) (-3992 . T))
+((-3992 . T) (-3993 . T))
NIL
(-629 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}.")))
@@ -2454,8 +2454,8 @@ 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.")))
-((-3991 . T) (-3992 . 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 (-3993 "*"))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))))
+((-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|)))))
(-632 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
@@ -2470,7 +2470,7 @@ NIL
NIL
(-635 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}.")))
-((-3992 . T))
+((-3993 . T))
NIL
(-636 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}.")))
@@ -2480,7 +2480,7 @@ NIL
((|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 -3090 PG)
+(-638 OV E -3091 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
@@ -2504,7 +2504,7 @@ NIL
((|constructor| (NIL "MakeRecord is used internally by the interpreter to create record types which are used for doing parallel iterations on streams.")) (|makeRecord| (((|Record| (|:| |part1| |#1|) (|:| |part2| |#2|)) |#1| |#2|) "\\spad{makeRecord(a,b)} creates a record object with type Record(part1:S,{} part2:R),{} where \\spad{part1} is \\spad{a} and \\spad{part2} is \\spad{b}.")))
NIL
NIL
-(-644 S -2667 I)
+(-644 S -2668 I)
((|constructor| (NIL "transforms top-level objects into compiled functions.")) (|compiledFunction| (((|Mapping| |#3| |#2|) |#1| (|Symbol|)) "\\spad{compiledFunction(expr, x)} returns a function \\spad{f: D -> I} defined by \\spad{f(x) == expr}. Function \\spad{f} is compiled and directly applicable to objects of type \\spad{D}.")) (|unaryFunction| (((|Mapping| |#3| |#2|) (|Symbol|)) "\\spad{unaryFunction(a)} is a local function")))
NIL
NIL
@@ -2514,7 +2514,7 @@ NIL
NIL
(-646 R)
((|constructor| (NIL "This is the category of linear operator rings with one generator. The generator is not named by the category but can always be constructed as \\spad{monomial(1,1)}. \\blankline For convenience,{} call the generator \\spad{G}. Then each value is equal to \\indented{4}{\\spad{sum(a(i)*G**i, i = 0..n)}} for some unique \\spad{n} and \\spad{a(i)} in \\spad{R}. \\blankline Note that multiplication is not necessarily commutative. In fact,{} if \\spad{a} is in \\spad{R},{} it is quite normal to have \\spad{a*G \\~= G*a}.")) (|monomial| (($ |#1| (|NonNegativeInteger|)) "\\spad{monomial(c,k)} produces \\spad{c} times the \\spad{k}-th power of the generating operator,{} \\spad{monomial(1,1)}.")) (|coefficient| ((|#1| $ (|NonNegativeInteger|)) "\\spad{coefficient(l,k)} is \\spad{a(k)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|reductum| (($ $) "\\spad{reductum(l)} is \\spad{l - monomial(a(n),n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(l)} is \\spad{a(n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|minimumDegree| (((|NonNegativeInteger|) $) "\\spad{minimumDegree(l)} is the smallest \\spad{k} such that \\spad{a(k) \\~= 0} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(l)} is \\spad{n} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")))
-((-3985 . T) (-3986 . T) (-3988 . T))
+((-3986 . T) (-3987 . T) (-3989 . T))
NIL
(-647 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}.")))
@@ -2524,25 +2524,25 @@ NIL
((|constructor| (NIL "\\spadtype{MathMLFormat} provides a coercion from \\spadtype{OutputForm} to MathML format.")) (|display| (((|Void|) (|String|)) "prints the string returned by coerce,{} adding <math ...> tags.")) (|exprex| (((|String|) (|OutputForm|)) "coverts \\spadtype{OutputForm} to \\spadtype{String} with the structure preserved with braces. Actually this is not quite accurate. The function \\spadfun{precondition} is first applied to the \\spadtype{OutputForm} expression before \\spadfun{exprex}. The raw \\spadtype{OutputForm} and the nature of the \\spadfun{precondition} function is still obscure to me at the time of this writing (2007-02-14).")) (|coerceL| (((|String|) (|OutputForm|)) "coerceS(\\spad{o}) changes \\spad{o} in the standard output format to MathML format and displays result as one long string.")) (|coerceS| (((|String|) (|OutputForm|)) "\\spad{coerceS(o)} changes \\spad{o} in the standard output format to MathML format and displays formatted result.")) (|coerce| (((|String|) (|OutputForm|)) "coerceS(\\spad{o}) changes \\spad{o} in the standard output format to MathML format.")))
NIL
NIL
-(-649 R |Mod| -2035 -3514 |exactQuo|)
+(-649 R |Mod| -2036 -3515 |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| $) "\\spad{modulus(x)} \\undocumented")))
-((-3983 . T) (-3989 . T) (-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . T))
+((-3984 . T) (-3990 . T) (-3985 . T) ((-3994 "*") . T) (-3986 . T) (-3987 . T) (-3989 . T))
NIL
(-650 R P)
((|constructor| (NIL "This package \\undocumented")) (|frobenius| (($ $) "\\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")))
-(((-3993 "*") |has| |#1| (-146)) (-3984 |has| |#1| (-495)) (-3987 |has| |#1| (-311)) (-3989 |has| |#1| (-6 -3989)) (-3986 . T) (-3985 . T) (-3988 . 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 -3989)) (|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)))))
+(((-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|)
((|constructor| (NIL "This package \\undocumented")) (|construct| (($ |#1| |#2|) "\\spad{construct(i,e)} \\undocumented")) (|index| ((|#1| $) "\\spad{index(x)} \\undocumented")) (|exponent| ((|#2| $) "\\spad{exponent(x)} \\undocumented")))
NIL
NIL
(-652 R M)
((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#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| (($ $ $) "\\spad{adjoint(op1, op2)} sets the adjoint of \\spad{op1} to be \\spad{op2}. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}.")))
-((-3986 |has| |#1| (-146)) (-3985 |has| |#1| (-146)) (-3988 . T))
+((-3987 |has| |#1| (-146)) (-3986 |has| |#1| (-146)) (-3989 . T))
((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))))
-(-653 R |Mod| -2035 -3514 |exactQuo|)
+(-653 R |Mod| -2036 -3515 |exactQuo|)
((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\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")))
-((-3988 . T))
+((-3989 . T))
NIL
(-654 S R)
((|constructor| (NIL "The category of modules over a commutative ring. \\blankline")))
@@ -2550,11 +2550,11 @@ NIL
NIL
(-655 R)
((|constructor| (NIL "The category of modules over a commutative ring. \\blankline")))
-((-3986 . T) (-3985 . T))
+((-3987 . T) (-3986 . T))
NIL
-(-656 -3090)
+(-656 -3091)
((|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]]}.")))
-((-3988 . T))
+((-3989 . T))
NIL
(-657 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.")))
@@ -2578,7 +2578,7 @@ NIL
((|HasCategory| |#2| (QUOTE (-298))) (|HasCategory| |#2| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-317))))
(-662 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.")))
-((-3984 |has| |#1| (-311)) (-3989 |has| |#1| (-311)) (-3983 |has| |#1| (-311)) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . T))
+((-3985 |has| |#1| (-311)) (-3990 |has| |#1| (-311)) (-3984 |has| |#1| (-311)) ((-3994 "*") . T) (-3986 . T) (-3987 . T) (-3989 . T))
NIL
(-663 S)
((|constructor| (NIL "The class of multiplicative monoids,{} \\spadignore{i.e.} semigroups with a multiplicative identity element. \\blankline")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} tries to compute the multiplicative inverse for \\spad{x} or \"failed\" if it cannot find the inverse (see unitsKnown).")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (|one?| (((|Boolean|) $) "\\spad{one?(x)} tests if \\spad{x} is equal to 1.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) (|One| (($) "1 is the multiplicative identity.")))
@@ -2590,13 +2590,13 @@ NIL
NIL
(-665 T$)
((|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}.")))
-(((|%Rule| |neutrality| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|)) (SEQ (-3054 (|f| |x| (-2410 |f|)) |x|) (|exit| 1 (-3054 (|f| (-2410 |f|) |x|) |x|))))) . T) ((|%Rule| |associativity| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|) (|:| |y| |#1|) (|:| |z| |#1|)) (-3054 (|f| (|f| |x| |y|) |z|) (|f| |x| (|f| |y| |z|))))) . T))
+(((|%Rule| |neutrality| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|)) (SEQ (-3055 (|f| |x| (-2411 |f|)) |x|) (|exit| 1 (-3055 (|f| (-2411 |f|) |x|) |x|))))) . T) ((|%Rule| |associativity| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|) (|:| |y| |#1|) (|:| |z| |#1|)) (-3055 (|f| (|f| |x| |y|) |z|) (|f| |x| (|f| |y| |z|))))) . T))
NIL
(-666 T$)
((|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}.")))
-(((|%Rule| |neutrality| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|)) (SEQ (-3054 (|f| |x| (-2410 |f|)) |x|) (|exit| 1 (-3054 (|f| (-2410 |f|) |x|) |x|))))) . T) ((|%Rule| |associativity| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|) (|:| |y| |#1|) (|:| |z| |#1|)) (-3054 (|f| (|f| |x| |y|) |z|) (|f| |x| (|f| |y| |z|))))) . T))
+(((|%Rule| |neutrality| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|)) (SEQ (-3055 (|f| |x| (-2411 |f|)) |x|) (|exit| 1 (-3055 (|f| (-2411 |f|) |x|) |x|))))) . T) ((|%Rule| |associativity| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|) (|:| |y| |#1|) (|:| |z| |#1|)) (-3055 (|f| (|f| |x| |y|) |z|) (|f| |x| (|f| |y| |z|))))) . T))
NIL
-(-667 -3090 UP)
+(-667 -3091 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
@@ -2614,8 +2614,8 @@ NIL
NIL
(-671 |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.")))
-(((-3993 "*") |has| |#2| (-146)) (-3984 |has| |#2| (-495)) (-3989 |has| |#2| (-6 -3989)) (-3986 . T) (-3985 . T) (-3988 . 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 -3989)) (|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)))))
+(((-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)
((|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|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol")))
NIL
@@ -2630,15 +2630,15 @@ NIL
NIL
(-675 R M)
((|constructor| (NIL "\\spadtype{MonoidRing}(\\spad{R},{}\\spad{M}),{} implements the algebra of all maps from the monoid \\spad{M} to the commutative ring \\spad{R} with finite support. Multiplication of two maps \\spad{f} and \\spad{g} is defined to map an element \\spad{c} of \\spad{M} to the (convolution) sum over {\\em f(a)g(b)} such that {\\em ab = c}. Thus \\spad{M} can be identified with a canonical basis and the maps can also be considered as formal linear combinations of the elements in \\spad{M}. Scalar multiples of a basis element are called monomials. A prominent example is the class of polynomials where the monoid is a direct product of the natural numbers with pointwise addition. When \\spad{M} is \\spadtype{FreeMonoid Symbol},{} one gets polynomials in infinitely many non-commuting variables. Another application area is representation theory of finite groups \\spad{G},{} where modules over \\spadtype{MonoidRing}(\\spad{R},{}\\spad{G}) are studied.")) (|reductum| (($ $) "\\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}.")))
-((-3986 |has| |#1| (-146)) (-3985 |has| |#1| (-146)) (-3988 . T))
+((-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}.")))
-((-3991 . T) (-3981 . T) (-3992 . T))
+((-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))))
(-677 S)
((|constructor| (NIL "A multi-set aggregate is a set which keeps track of the multiplicity of its elements.")))
-((-3981 . T) (-3992 . T))
+((-3982 . T) (-3993 . T))
NIL
(-678)
((|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.")))
@@ -2650,7 +2650,7 @@ NIL
NIL
(-680 |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}.")))
-(((-3993 "*") |has| |#1| (-146)) (-3984 |has| |#1| (-495)) (-3986 . T) (-3985 . T) (-3988 . T))
+(((-3994 "*") |has| |#1| (-146)) (-3985 |has| |#1| (-495)) (-3987 . T) (-3986 . T) (-3989 . T))
NIL
(-681 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")))
@@ -2666,7 +2666,7 @@ NIL
NIL
(-684 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}.")))
-((-3986 . T) (-3985 . T))
+((-3987 . T) (-3986 . T))
NIL
(-685 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)}.")))
@@ -2688,11 +2688,11 @@ NIL
((|constructor| (NIL "This package computes explicitly eigenvalues and eigenvectors of matrices with entries over the complex rational numbers. The results are expressed either as complex floating numbers or as complex rational numbers depending on the type of the precision parameter.")) (|complexEigenvectors| (((|List| (|Record| (|:| |outval| (|Complex| |#1|)) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| (|Complex| |#1|)))))) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) |#1|) "\\spad{complexEigenvectors(m,eps)} returns a list of records each one containing a complex eigenvalue,{} its algebraic multiplicity,{} and a list of associated eigenvectors. All these results are computed to precision \\spad{eps} and are expressed as complex floats or complex rational numbers depending on the type of \\spad{eps} (float or rational).")) (|complexEigenvalues| (((|List| (|Complex| |#1|)) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) |#1|) "\\spad{complexEigenvalues(m,eps)} computes the eigenvalues of the matrix \\spad{m} to precision \\spad{eps}. The eigenvalues are expressed as complex floats or complex rational numbers depending on the type of \\spad{eps} (float or rational).")) (|characteristicPolynomial| (((|Polynomial| (|Complex| (|Fraction| (|Integer|)))) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) (|Symbol|)) "\\spad{characteristicPolynomial(m,x)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over Complex Rationals with variable \\spad{x}.") (((|Polynomial| (|Complex| (|Fraction| (|Integer|)))) (|Matrix| (|Complex| (|Fraction| (|Integer|))))) "\\spad{characteristicPolynomial(m)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over complex rationals with a new symbol as variable.")))
NIL
NIL
-(-690 -3090)
+(-690 -3091)
((|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 -3090)
+(-691 P -3091)
((|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
@@ -2700,7 +2700,7 @@ NIL
NIL
NIL
NIL
-(-693 UP -3090)
+(-693 UP -3091)
((|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
@@ -2710,9 +2710,9 @@ NIL
NIL
(-695)
((|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.")))
-(((-3993 "*") . T))
+(((-3994 "*") . T))
NIL
-(-696 R -3090)
+(-696 R -3091)
((|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
@@ -2732,7 +2732,7 @@ NIL
((|constructor| (NIL "A package for computing normalized assocites of univariate polynomials with coefficients in a tower of simple extensions of a field.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. MORENO MAZA and \\spad{R}. RIOBOO \"Computations of 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 -3090 |ExtF| |SUEx| |ExtP| |n|)
+(-701 -3091 |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
@@ -2746,12 +2746,12 @@ NIL
NIL
(-704 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.")))
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(-705 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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+((|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 (-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)))))
(-706 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
@@ -2762,7 +2762,7 @@ NIL
((|HasCategory| |#1| (QUOTE (-38 (-347 (-484))))))
(-708 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.}")))
-((-3992 . T) (-3991 . T))
+((-3993 . T) (-3992 . T))
NIL
(-709 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}.")))
@@ -2814,7 +2814,7 @@ 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)
((|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| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}.")))
-((-3985 . T) (-3986 . T) (-3988 . T))
+((-3986 . T) (-3987 . T) (-3989 . T))
NIL
(-722)
((|constructor| (NIL "Ordered sets which are also abelian cancellation monoids,{} such that the addition preserves the ordering.")))
@@ -2822,67 +2822,67 @@ NIL
NIL
(-723 R)
((|constructor| (NIL "Octonion implements octonions (Cayley-Dixon algebra) over a commutative ring,{} an eight-dimensional non-associative algebra,{} doubling the quaternions in the same way as doubling the complex numbers to get the quaternions the main constructor function is {\\em octon} which takes 8 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j} imaginary part,{} the \\spad{k} imaginary part,{} (as with quaternions) and in addition the imaginary parts \\spad{E},{} \\spad{I},{} \\spad{J},{} \\spad{K}.")) (|octon| (($ (|Quaternion| |#1|) (|Quaternion| |#1|)) "\\spad{octon(qe,qE)} constructs an octonion from two quaternions using the relation {\\em O = Q + QE}.")))
-((-3985 . T) (-3986 . T) (-3988 . T))
+((-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)
((|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 -3090 L)
+(-725 R -3091 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 -3090)
+(-726 R -3091)
((|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 -3090)
+(-727 R -3091)
((|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 -3090 UP UPUP R)
+(-728 -3091 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 -3090 UP L LQ)
+(-729 -3091 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 -3090 UP L LQ)
+(-730 -3091 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 -3090 UP)
+(-731 -3091 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 -3090 L UP A LO)
+(-732 -3091 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 -3090 UP)
+(-733 -3091 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 -3090 LO)
+(-734 -3091 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 -3090 LODO)
+(-735 -3091 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
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((|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}.")))
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(|HasCategory| |#2| (QUOTE (-718))) (|HasCategory| |#2| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-810 (-1089)))) (|HasCategory| |#2| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-951 (-484)))) (|HasCategory| |#2| (QUOTE (-1013)))) (-12 (|HasCategory| |#2| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-317))) (|HasCategory| |#2| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-664))) (|HasCategory| |#2| (QUOTE (-951 (-484))))) (|HasCategory| |#2| (QUOTE (-962)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-718))) (|HasCategory| |#2| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-810 (-1089)))) (|HasCategory| |#2| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-951 (-484)))) (|HasCategory| |#2| (QUOTE (-1013)))) (-12 (|HasCategory| |#2| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-317))) (|HasCategory| |#2| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-664))) (|HasCategory| |#2| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-951 (-484)))) (|HasCategory| |#2| (QUOTE (-962))))) (|HasCategory| (-484) (QUOTE (-757))) (-12 (|HasCategory| |#2| (QUOTE (-581 (-484)))) (|HasCategory| |#2| (QUOTE (-962)))) (-12 (|HasCategory| |#2| (QUOTE (-189))) (|HasCategory| |#2| (QUOTE (-962)))) (-12 (|HasCategory| |#2| (QUOTE (-812 (-1089)))) (|HasCategory| |#2| (QUOTE (-962)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-951 (-484)))) (|HasCategory| |#2| (QUOTE (-1013)))) (|HasCategory| |#2| (QUOTE (-962)))) (-12 (|HasCategory| |#2| (QUOTE (-951 (-484)))) (|HasCategory| |#2| (QUOTE (-1013)))) (-12 (|HasCategory| |#2| (QUOTE (-951 (-347 (-484))))) (|HasCategory| |#2| (QUOTE (-1013)))) (|HasAttribute| |#2| (QUOTE -3989)) (-12 (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-962)))) (-12 (|HasCategory| |#2| (QUOTE (-810 (-1089)))) (|HasCategory| |#2| (QUOTE (-962)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-72))) (-12 (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (|%list| (QUOTE -259) (|devaluate| |#2|)))))
(-737 R)
((|constructor| (NIL "\\spadtype{OrderlyDifferentialPolynomial} implements an ordinary differential polynomial ring in arbitrary number of differential indeterminates,{} with coefficients in a ring. The ranking on the differential indeterminate is orderly. This is analogous to the domain \\spadtype{Polynomial}. \\blankline")))
-(((-3993 "*") |has| |#1| (-146)) (-3984 |has| |#1| (-495)) (-3989 |has| |#1| (-6 -3989)) (-3986 . T) (-3985 . T) (-3988 . 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| (-739 (-1089)) (QUOTE (-797 (-327))))) (-12 (|HasCategory| |#1| (QUOTE (-797 (-484)))) (|HasCategory| (-739 (-1089)) (QUOTE (-797 (-484))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-327))))) (|HasCategory| (-739 (-1089)) (QUOTE (-554 (-801 (-327)))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-484))))) (|HasCategory| (-739 (-1089)) (QUOTE (-554 (-801 (-484)))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-473)))) (|HasCategory| (-739 (-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 -3989)) (|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)))))
+(((-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| (-739 (-1089)) (QUOTE (-797 (-327))))) (-12 (|HasCategory| |#1| (QUOTE (-797 (-484)))) (|HasCategory| (-739 (-1089)) (QUOTE (-797 (-484))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-327))))) (|HasCategory| (-739 (-1089)) (QUOTE (-554 (-801 (-327)))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-484))))) (|HasCategory| (-739 (-1089)) (QUOTE (-554 (-801 (-484)))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-473)))) (|HasCategory| (-739 (-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)))))
(-738 |Kernels| R |var|)
((|constructor| (NIL "This constructor produces an ordinary differential ring from a partial differential ring by specifying a variable.")))
-(((-3993 "*") |has| |#2| (-311)) (-3984 |has| |#2| (-311)) (-3989 |has| |#2| (-311)) (-3983 |has| |#2| (-311)) (-3988 . T) (-3986 . T) (-3985 . T))
+(((-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)
((|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})).")))
@@ -2894,19 +2894,19 @@ NIL
((|HasCategory| |#1| (QUOTE (-757))))
(-741)
((|constructor| (NIL "The category of ordered commutative integral domains,{} where ordering and the arithmetic operations are compatible \\blankline")))
-((-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . T))
+((-3985 . T) ((-3994 "*") . T) (-3986 . T) (-3987 . T) (-3989 . T))
NIL
(-742 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}.")))
-((-3985 . T) (-3986 . T) (-3988 . T))
+((-3986 . T) (-3987 . T) (-3989 . T))
((|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-190))))
(-743 S)
((|constructor| (NIL "to become an in order iterator")) (|min| ((|#1| $) "\\spad{min(u)} returns the smallest entry in the multiset aggregate \\spad{u}.")))
-((-3991 . T) (-3981 . T) (-3992 . T))
+((-3992 . T) (-3982 . T) (-3993 . T))
NIL
(-744 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.")))
-((-3988 |has| |#1| (-756)))
+((-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)
((|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.")))
@@ -2914,7 +2914,7 @@ NIL
NIL
(-746 R)
((|constructor| (NIL "Algebra of ADDITIVE operators over a ring.")))
-((-3986 |has| |#1| (-146)) (-3985 |has| |#1| (-146)) (-3988 . T))
+((-3987 |has| |#1| (-146)) (-3986 |has| |#1| (-146)) (-3989 . T))
((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))))
(-747 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}.")))
@@ -2934,7 +2934,7 @@ NIL
NIL
(-751 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| (($) "\\spad{plusInfinity()} returns +infinity.")))
-((-3988 |has| |#1| (-756)))
+((-3989 |has| |#1| (-756)))
((|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-21))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-756)))) (|HasCategory| |#1| (QUOTE (-951 (-347 (-484))))) (OR (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-951 (-484))))) (|HasCategory| |#1| (QUOTE (-951 (-484)))) (|HasCategory| |#1| (QUOTE (-483))))
(-752 R S)
((|constructor| (NIL "Lifting of maps to ordered completions. Date Created: 4 Oct 1989 Date Last Updated: 4 Oct 1989")) (|map| (((|OrderedCompletion| |#2|) (|Mapping| |#2| |#1|) (|OrderedCompletion| |#1|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|)) "\\spad{map(f, r, p, m)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(plusInfinity) = \\spad{p} and that \\spad{f}(minusInfinity) = \\spad{m}.") (((|OrderedCompletion| |#2|) (|Mapping| |#2| |#1|) (|OrderedCompletion| |#1|)) "\\spad{map(f, r)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(plusInfinity) = plusInfinity and that \\spad{f}(minusInfinity) = minusInfinity.")))
@@ -2944,7 +2944,7 @@ NIL
((|constructor| (NIL "Ordered finite sets.")) (|max| (($) "\\spad{max} is the maximum value of \\%.")) (|min| (($) "\\spad{min} is the minimum value of \\%.")))
NIL
NIL
-(-754 -2619 S)
+(-754 -2620 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
@@ -2954,7 +2954,7 @@ NIL
NIL
(-756)
((|constructor| (NIL "Ordered sets which are also rings,{} that is,{} domains where the ring operations are compatible with the ordering. \\blankline")))
-((-3988 . T))
+((-3989 . T))
NIL
(-757)
((|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}.")))
@@ -2978,19 +2978,19 @@ NIL
((|HasCategory| |#2| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-389))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-146))))
(-762 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)}.}")))
-((-3985 . T) (-3986 . T) (-3988 . T))
+((-3986 . T) (-3987 . T) (-3989 . T))
NIL
(-763 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| -3241)
+(-764 R |sigma| -3242)
((|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.")))
-((-3985 . T) (-3986 . T) (-3988 . T))
+((-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| -3241)
+(-765 |x| R |sigma| -3242)
((|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}.")))
-((-3985 . T) (-3986 . T) (-3988 . T))
+((-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)
((|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..)}.")))
@@ -3034,7 +3034,7 @@ NIL
NIL
(-776 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)")))
-((-3986 |has| |#1| (-146)) (-3985 |has| |#1| (-146)) (-3988 . T))
+((-3987 |has| |#1| (-146)) (-3986 |has| |#1| (-146)) (-3989 . T))
((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-311))))
(-777 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).")))
@@ -3046,19 +3046,19 @@ NIL
NIL
(-779 |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).")))
-((-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . T))
+((-3985 . T) ((-3994 "*") . T) (-3986 . T) (-3987 . T) (-3989 . T))
NIL
(-780 |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}.")))
-((-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . T))
+((-3985 . T) ((-3994 "*") . T) (-3986 . T) (-3987 . T) (-3989 . T))
NIL
(-781 |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).")))
-((-3983 . T) (-3989 . T) (-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . T))
+((-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)
((|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)}.")))
-((-3983 . T) (-3989 . T) (-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . T))
+((-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$)
((|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'.")))
@@ -3123,7 +3123,7 @@ NIL
(-798 |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 (-2558 (|HasCategory| |#2| (QUOTE (-951 (-1089))))) (-2558 (|HasCategory| |#2| (QUOTE (-962))))) (-12 (|HasCategory| |#2| (QUOTE (-962))) (-2558 (|HasCategory| |#2| (QUOTE (-951 (-1089)))))) (|HasCategory| |#2| (QUOTE (-951 (-1089)))))
+((-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)
((|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
@@ -3136,7 +3136,7 @@ NIL
((|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 -2667)
+(-802 R -2668)
((|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
@@ -3160,17 +3160,17 @@ NIL
((|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 -3090)
+(-808 UP -3091)
((|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)
((|constructor| (NIL "A partial differential \\spad{R}-module with differentiations indexed by a parameter type \\spad{S}. \\blankline")))
-((-3986 . T) (-3985 . T))
+((-3987 . T) (-3986 . T))
NIL
(-810 S)
((|constructor| (NIL "A partial differential ring with differentiations indexed by a parameter type \\spad{S}. \\blankline")))
-((-3988 . T))
+((-3989 . T))
NIL
(-811 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)}.")))
@@ -3186,7 +3186,7 @@ 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)
((|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|))) $) "\\spad{listRepresentation(p)} produces a representation {\\em rep} of the permutation \\spad{p} as a list of preimages and images,{} \\spad{i}.\\spad{e} \\spad{p} maps {\\em (rep.preimage).k} to {\\em (rep.image).k} for all indices \\spad{k}. Elements of \\spad{S} not in {\\em (rep.preimage).k} are fixed points,{} and these are the only fixed points of the permutation.")))
-((-3988 . T))
+((-3989 . T))
((OR (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-757)))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-757))))
(-815 |n| R)
((|constructor| (NIL "Permanent implements the functions {\\em permanent},{} the permanent for square matrices.")) (|permanent| ((|#2| (|SquareMatrix| |#1| |#2|)) "\\spad{permanent(x)} computes the permanent of a square matrix \\spad{x}. The {\\em permanent} is equivalent to the \\spadfun{determinant} except that coefficients have no change of sign. This function is much more difficult to compute than the {\\em determinant}. The formula used is by \\spad{H}.\\spad{J}. Ryser,{} improved by [Nijenhuis and Wilf,{} Ch. 19]. Note: permanent(\\spad{x}) choose one of three algorithms,{} depending on the underlying ring \\spad{R} and on \\spad{n},{} the number of rows (and columns) of x:\\begin{items} \\item 1. if 2 has an inverse in \\spad{R} we can use the algorithm of \\indented{3}{[Nijenhuis and Wilf,{} ch.19,{}\\spad{p}.158]; if 2 has no inverse,{}} \\indented{3}{some modifications are necessary:} \\item 2. if {\\em n > 6} and \\spad{R} is an integral domain with characteristic \\indented{3}{different from 2 (the algorithm works if and only 2 is not a} \\indented{3}{zero-divisor of \\spad{R} and {\\em characteristic()\\$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}")))
@@ -3194,7 +3194,7 @@ NIL
NIL
(-816 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.")))
-((-3988 . T))
+((-3989 . T))
NIL
(-817 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}.")))
@@ -3202,7 +3202,7 @@ NIL
NIL
(-818 |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.")))
-((-3983 . T) (-3989 . T) (-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . T))
+((-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)
((|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.")))
@@ -3218,9 +3218,9 @@ NIL
((|HasCategory| |#1| (QUOTE (-118))))
(-822)
((|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}.")))
-((-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . T))
+((-3985 . T) ((-3994 "*") . T) (-3986 . T) (-3987 . T) (-3989 . T))
NIL
-(-823 R0 -3090 UP UPUP R)
+(-823 R0 -3091 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
@@ -3234,7 +3234,7 @@ NIL
NIL
(-826 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.")))
-((-3983 . T) (-3989 . T) (-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . T))
+((-3984 . T) (-3990 . T) (-3985 . T) ((-3994 "*") . T) (-3986 . T) (-3987 . T) (-3989 . T))
NIL
(-827 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.")))
@@ -3248,13 +3248,13 @@ NIL
((|constructor| (NIL "PermutationGroupExamples provides permutation groups for some classes of groups: symmetric,{} alternating,{} dihedral,{} cyclic,{} direct products of cyclic,{} which are in fact the finite abelian groups of symmetric groups called Young subgroups. Furthermore,{} Rubik'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 -3090)
+(-830 -3091)
((|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)
((|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}.")))
-(((-3993 "*") . T))
+(((-3994 "*") . T))
NIL
(-832 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}).")))
@@ -3262,13 +3262,13 @@ NIL
NIL
(-833)
((|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)}")))
-((-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . T))
+((-3985 . T) ((-3994 "*") . T) (-3986 . T) (-3987 . T) (-3989 . T))
NIL
-(-834 |xx| -3090)
+(-834 |xx| -3091)
((|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 -3090 P)
+(-835 -3091 P)
((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,l2)} \\undocumented")))
NIL
NIL
@@ -3296,7 +3296,7 @@ NIL
((|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 -3090)
+(-842 R -3091)
((|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
@@ -3304,7 +3304,7 @@ NIL
((|constructor| (NIL "This packages provides tools for matching recursively in type towers.")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#2| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(expr, pat, res)} matches the pattern \\spad{pat} to the expression \\spad{expr}; res contains the variables of \\spad{pat} which are already matched and their matches. Note: this function handles type towers by changing the predicates and calling the matching function provided by \\spad{A}.")) (|fixPredicate| (((|Mapping| (|Boolean|) |#2|) (|Mapping| (|Boolean|) |#3|)) "\\spad{fixPredicate(f)} returns \\spad{g} defined by \\spad{g}(a) = \\spad{f}(a::B).")))
NIL
NIL
-(-844 S R -3090)
+(-844 S R -3091)
((|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
@@ -3324,11 +3324,11 @@ NIL
((|constructor| (NIL "This package provides pattern matching functions on polynomials.")) (|patternMatch| (((|PatternMatchResult| |#1| |#5|) |#5| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|)) "\\spad{patternMatch(p, pat, res)} matches the pattern \\spad{pat} to the polynomial \\spad{p}; res contains the variables of \\spad{pat} which are already matched and their matches.") (((|PatternMatchResult| |#1| |#5|) |#5| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|) (|Mapping| (|PatternMatchResult| |#1| |#5|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|))) "\\spad{patternMatch(p, pat, res, vmatch)} matches the pattern \\spad{pat} to the polynomial \\spad{p}. \\spad{res} contains the variables of \\spad{pat} which are already matched and their matches; vmatch is the matching function to use on the variables.")))
NIL
((|HasCategory| |#3| (|%list| (QUOTE -797) (|devaluate| |#1|))))
-(-849 -2667)
+(-849 -2668)
((|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 -3090 -2667)
+(-850 R -3091 -2668)
((|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
@@ -3350,7 +3350,7 @@ NIL
NIL
(-855 R)
((|constructor| (NIL "This domain implements points in coordinate space")))
-((-3992 . T) (-3991 . T))
+((-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|)))))
(-856 |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}.")))
@@ -3362,8 +3362,8 @@ NIL
((|HasCategory| |#1| (QUOTE (-756))))
(-858 R)
((|constructor| (NIL "\\indented{2}{This type is the basic representation of sparse recursive multivariate} polynomials whose variables are arbitrary symbols. The ordering is alphabetic determined by the Symbol type. The coefficient ring may be non commutative,{} but the variables are assumed to commute.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(p,x)} computes the integral of \\spad{p*dx},{} \\spadignore{i.e.} integrates the polynomial \\spad{p} with respect to the variable \\spad{x}.")))
-(((-3993 "*") |has| |#1| (-146)) (-3984 |has| |#1| (-495)) (-3989 |has| |#1| (-6 -3989)) (-3986 . T) (-3985 . T) (-3988 . T))
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+(((-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| (-1089) (QUOTE (-797 (-327))))) (-12 (|HasCategory| |#1| (QUOTE (-797 (-484)))) (|HasCategory| (-1089) (QUOTE (-797 (-484))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-327))))) (|HasCategory| (-1089) (QUOTE (-554 (-801 (-327)))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-484))))) (|HasCategory| (-1089) (QUOTE (-554 (-801 (-484)))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-473)))) (|HasCategory| (-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 (-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)))))
(-859 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
@@ -3375,12 +3375,12 @@ NIL
(-861 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
-((|HasCategory| |#2| (QUOTE (-822))) (|HasAttribute| |#2| (QUOTE -3989)) (|HasCategory| |#2| (QUOTE (-389))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#4| (QUOTE (-797 (-327)))) (|HasCategory| |#2| (QUOTE (-797 (-327)))) (|HasCategory| |#4| (QUOTE (-797 (-484)))) (|HasCategory| |#2| (QUOTE (-797 (-484)))) (|HasCategory| |#4| (QUOTE (-554 (-801 (-327))))) (|HasCategory| |#2| (QUOTE (-554 (-801 (-327))))) (|HasCategory| |#4| (QUOTE (-554 (-801 (-484))))) (|HasCategory| |#2| (QUOTE (-554 (-801 (-484))))) (|HasCategory| |#4| (QUOTE (-554 (-473)))) (|HasCategory| |#2| (QUOTE (-554 (-473)))))
+((|HasCategory| |#2| (QUOTE (-822))) (|HasAttribute| |#2| (QUOTE -3990)) (|HasCategory| |#2| (QUOTE (-389))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#4| (QUOTE (-797 (-327)))) (|HasCategory| |#2| (QUOTE (-797 (-327)))) (|HasCategory| |#4| (QUOTE (-797 (-484)))) (|HasCategory| |#2| (QUOTE (-797 (-484)))) (|HasCategory| |#4| (QUOTE (-554 (-801 (-327))))) (|HasCategory| |#2| (QUOTE (-554 (-801 (-327))))) (|HasCategory| |#4| (QUOTE (-554 (-801 (-484))))) (|HasCategory| |#2| (QUOTE (-554 (-801 (-484))))) (|HasCategory| |#4| (QUOTE (-554 (-473)))) (|HasCategory| |#2| (QUOTE (-554 (-473)))))
(-862 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}.")))
-(((-3993 "*") |has| |#1| (-146)) (-3984 |has| |#1| (-495)) (-3989 |has| |#1| (-6 -3989)) (-3986 . T) (-3985 . T) (-3988 . T))
+(((-3994 "*") |has| |#1| (-146)) (-3985 |has| |#1| (-495)) (-3990 |has| |#1| (-6 -3990)) (-3987 . T) (-3986 . T) (-3989 . T))
NIL
-(-863 E V R P -3090)
+(-863 E V R P -3091)
((|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
@@ -3388,7 +3388,7 @@ NIL
((|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 -3090)
+(-865 E V R P -3091)
((|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| $) "\\spad{numer(x)} \\undocumented")))
NIL
((|HasCategory| |#3| (QUOTE (-389))))
@@ -3402,15 +3402,15 @@ NIL
NIL
(-868 R E)
((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and terms indexed by their exponents (from an arbitrary ordered abelian monoid). This type is used,{} for example,{} by the \\spadtype{DistributedMultivariatePolynomial} domain where the exponent domain is a direct product of non negative integers.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (|fmecg| (($ $ |#2| |#1| $) "\\spad{fmecg(p1,e,r,p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}")))
-(((-3993 "*") |has| |#1| (-146)) (-3984 |has| |#1| (-495)) (-3989 |has| |#1| (-6 -3989)) (-3985 . T) (-3986 . T) (-3988 . 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 -3989)))
+(((-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)
((|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)
((|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")))
-((-3992 . T) (-3991 . T))
+((-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)
((|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),...]}.")))
@@ -3420,7 +3420,7 @@ NIL
((|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 -3090)
+(-873 -3091)
((|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
@@ -3434,7 +3434,7 @@ NIL
NIL
(-876 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")))
-((-3988 -12 (|has| |#2| (-410)) (|has| |#1| (-410))))
+((-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)
((|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|) $) "\\spad{name(p)} returns the name of property \\spad{p}")))
@@ -3458,7 +3458,7 @@ NIL
NIL
(-882 S)
((|constructor| (NIL "A priority queue is a bag of items from an ordered set where the item extracted is always the maximum element.")) (|merge!| (($ $ $) "\\spad{merge!(q,q1)} destructively changes priority queue \\spad{q} to include the values from priority queue \\spad{q1}.")) (|merge| (($ $ $) "\\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}.")))
-((-3991 . T) (-3992 . T))
+((-3992 . T) (-3993 . T))
NIL
(-883 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}}")))
@@ -3478,7 +3478,7 @@ NIL
NIL
(-887 |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}.")))
-(((-3993 "*") |has| |#1| (-146)) (-3984 |has| |#1| (-495)) (-3985 . T) (-3986 . T) (-3988 . T))
+(((-3994 "*") |has| |#1| (-146)) (-3985 |has| |#1| (-495)) (-3986 . T) (-3987 . T) (-3989 . T))
NIL
(-888)
((|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}.")))
@@ -3490,7 +3490,7 @@ NIL
((|HasCategory| |#2| (QUOTE (-495))))
(-890 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.")))
-((-3991 . T))
+((-3992 . T))
NIL
(-891 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.")))
@@ -3506,7 +3506,7 @@ NIL
NIL
(-894 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}.")))
-((-3992 . T) (-3991 . T))
+((-3993 . T) (-3992 . T))
NIL
(-895 R1 R2)
((|constructor| (NIL "This package \\undocumented")) (|map| (((|Point| |#2|) (|Mapping| |#2| |#1|) (|Point| |#1|)) "\\spad{map(f,p)} \\undocumented")))
@@ -3524,7 +3524,7 @@ NIL
((|constructor| (NIL "This package \\undocumented{}")) (|map| ((|#4| (|Mapping| |#4| (|Polynomial| |#1|)) |#4|) "\\spad{map(f,p)} \\undocumented{}")) (|pushup| ((|#4| |#4| (|List| |#3|)) "\\spad{pushup(p,lv)} \\undocumented{}") ((|#4| |#4| |#3|) "\\spad{pushup(p,v)} \\undocumented{}")) (|pushdown| ((|#4| |#4| (|List| |#3|)) "\\spad{pushdown(p,lv)} \\undocumented{}") ((|#4| |#4| |#3|) "\\spad{pushdown(p,v)} \\undocumented{}")) (|variable| (((|Union| $ "failed") (|Symbol|)) "\\spad{variable(s)} makes an element from symbol \\spad{s} or fails")) (|convert| (((|Symbol|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol")))
NIL
NIL
-(-899 K R UP -3090)
+(-899 K R UP -3091)
((|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
@@ -3550,7 +3550,7 @@ 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)
((|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}.")))
-((-3983 . T) (-3989 . T) (-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . T))
+((-3984 . T) (-3990 . T) (-3985 . T) ((-3994 "*") . T) (-3986 . T) (-3987 . T) (-3989 . T))
NIL
(-906 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}.")))
@@ -3566,11 +3566,11 @@ NIL
NIL
(-909 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.")))
-((-3991 . T) (-3992 . T))
+((-3992 . T) (-3993 . T))
NIL
(-910 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.}")))
-((-3984 |has| |#1| (-245)) (-3985 . T) (-3986 . T) (-3988 . T))
+((-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)
((|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}.")))
@@ -3578,7 +3578,7 @@ 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)
((|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| $) "\\spad{imagI(q)} extracts the imaginary \\spad{i} part of quaternion \\spad{q}.")) (|conjugate| (($ $) "\\spad{conjugate(q)} negates the imaginary parts of quaternion \\spad{q}.")))
-((-3984 |has| |#1| (-245)) (-3985 . T) (-3986 . T) (-3988 . T))
+((-3985 |has| |#1| (-245)) (-3986 . T) (-3987 . T) (-3989 . T))
NIL
(-913 QR R QS S)
((|constructor| (NIL "\\spadtype{QuaternionCategoryFunctions2} implements functions between two quaternion domains. The function \\spadfun{map} is used by the system interpreter to coerce between quaternion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,u)} maps \\spad{f} onto the component parts of the quaternion \\spad{u}.")))
@@ -3586,7 +3586,7 @@ NIL
NIL
(-914 S)
((|constructor| (NIL "Linked List implementation of a Queue")) (|queue| (($ (|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}.")))
-((-3991 . T) (-3992 . T))
+((-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 "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| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}.")))
@@ -3596,13 +3596,13 @@ NIL
((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|Fraction| (|Integer|))) "\\spad{x ** y} is the rational exponentiation of \\spad{x} by the power \\spad{y}.")) (|nthRoot| (($ $ (|Integer|)) "\\spad{nthRoot(x,n)} returns the \\spad{n}th root of \\spad{x}.")) (|sqrt| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}.")))
NIL
NIL
-(-917 -3090 UP UPUP |radicnd| |n|)
+(-917 -3091 UP UPUP |radicnd| |n|)
((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x}).")))
-((-3984 |has| (-347 |#2|) (-311)) (-3989 |has| (-347 |#2|) (-311)) (-3983 |has| (-347 |#2|) (-311)) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . T))
+((-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))))))
(-918 |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.")))
-((-3983 . T) (-3989 . T) (-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . T))
+((-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)
((|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}.")))
@@ -3623,7 +3623,7 @@ NIL
(-923 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 -3992)) (|HasCategory| |#2| (QUOTE (-1013))))
+((|HasAttribute| |#1| (QUOTE -3993)) (|HasCategory| |#2| (QUOTE (-1013))))
(-924 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
@@ -3634,21 +3634,21 @@ NIL
NIL
(-926)
((|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}}")))
-((-3984 . T) (-3989 . T) (-3983 . T) (-3986 . T) (-3985 . T) ((-3993 "*") . T) (-3988 . T))
+((-3985 . T) (-3990 . T) (-3984 . T) (-3987 . T) (-3986 . T) ((-3994 "*") . T) (-3989 . T))
NIL
-(-927 R -3090)
+(-927 R -3091)
((|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 -3090)
+(-928 R -3091)
((|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 -3090 UP)
+(-929 -3091 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 -3090 UP)
+(-930 -3091 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
@@ -3682,9 +3682,9 @@ NIL
NIL
(-938 |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")))
-((-3984 . T) (-3989 . T) (-3983 . T) (-3986 . T) (-3985 . T) ((-3993 "*") . T) (-3988 . T))
+((-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 -3090 L)
+(-939 -3091 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
@@ -3694,7 +3694,7 @@ NIL
NIL
(-941 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.")))
-((-3992 . T) (-3991 . T))
+((-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)
((|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.")))
@@ -3703,7 +3703,7 @@ NIL
(-943 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 (-3993 "*"))))
+((|HasAttribute| |#1| (QUOTE (-3994 "*"))))
(-944 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
@@ -3720,9 +3720,9 @@ NIL
((|constructor| (NIL "This package provides coercions for the special types \\spadtype{Exit} and \\spadtype{Void}.")) (|coerce| ((|#1| (|Exit|)) "\\spad{coerce(e)} is never really evaluated. This coercion is used for formal type correctness when a function will not return directly to its caller.") (((|Void|) |#1|) "\\spad{coerce(s)} throws all information about \\spad{s} away. This coercion allows values of any type to appear in contexts where they will not be used. For example,{} it allows the resolution of different types in the \\spad{then} and \\spad{else} branches when an \\spad{if} is in a context where the resulting value is not used.")))
NIL
NIL
-(-948 -3090 |Expon| |VarSet| |FPol| |LFPol|)
+(-948 -3091 |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")))
-(((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . T))
+(((-3994 "*") . T) (-3986 . T) (-3987 . T) (-3989 . T))
NIL
(-949)
((|constructor| (NIL "This domain represents `return' expressions.")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression returned by `e'.")))
@@ -3766,7 +3766,7 @@ NIL
NIL
(-959 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}.")))
-((-3992 . T) (-3991 . T))
+((-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)
((|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")))
@@ -3778,9 +3778,9 @@ NIL
NIL
(-962)
((|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.")))
-((-3988 . T))
+((-3989 . T))
NIL
-(-963 |xx| -3090)
+(-963 |xx| -3091)
((|constructor| (NIL "This package exports rational interpolation algorithms")))
NIL
NIL
@@ -3794,11 +3794,11 @@ NIL
((|HasCategory| |#4| (QUOTE (-257))) (|HasCategory| |#4| (QUOTE (-311))) (|HasCategory| |#4| (QUOTE (-495))) (|HasCategory| |#4| (QUOTE (-146))))
(-966 |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")))
-((-3991 . T) (-3986 . T) (-3985 . T))
+((-3992 . T) (-3987 . T) (-3986 . T))
NIL
(-967 |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}.")))
-((-3991 . T) (-3986 . T) (-3985 . T))
+((-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)
((|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}.")))
@@ -3822,7 +3822,7 @@ NIL
NIL
(-973)
((|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.")))
-((-3983 . T) (-3989 . T) (-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . T))
+((-3984 . T) (-3990 . T) (-3985 . T) ((-3994 "*") . T) (-3986 . T) (-3987 . T) (-3989 . T))
NIL
(-974 |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| $) "\\axiom{left(rootChar)} is the left bound of the isolating interval")))
@@ -3830,7 +3830,7 @@ NIL
NIL
(-975)
((|constructor| (NIL "\\spadtype{RomanNumeral} provides functions for converting \\indented{1}{integers to roman numerals.}")) (|roman| (($ (|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.")))
-((-3979 . T) (-3983 . T) (-3978 . T) (-3989 . T) (-3990 . T) (-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . T))
+((-3980 . T) (-3984 . T) (-3979 . T) (-3990 . T) (-3991 . T) (-3985 . T) ((-3994 "*") . T) (-3986 . T) (-3987 . T) (-3989 . T))
NIL
(-976 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| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}.")))
@@ -3838,7 +3838,7 @@ NIL
((|HasCategory| |#2| (QUOTE (-389))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-951 (-484)))) (|HasCategory| |#2| (QUOTE (-483))) (|HasCategory| |#2| (QUOTE (-38 (-484)))) (|HasCategory| |#2| (QUOTE (-905 (-484)))) (|HasCategory| |#2| (QUOTE (-38 (-347 (-484))))) (|HasCategory| |#4| (QUOTE (-554 (-1089)))))
(-977 R E V)
((|constructor| (NIL "A category for general multi-variate polynomials with coefficients in a ring,{} variables in an ordered set,{} and exponents from an ordered abelian monoid,{} with a \\axiomOp{sup} operation. When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\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}}.")))
-(((-3993 "*") |has| |#1| (-146)) (-3984 |has| |#1| (-495)) (-3989 |has| |#1| (-6 -3989)) (-3986 . T) (-3985 . T) (-3988 . T))
+(((-3994 "*") |has| |#1| (-146)) (-3985 |has| |#1| (-495)) (-3990 |has| |#1| (-6 -3990)) (-3987 . T) (-3986 . T) (-3989 . T))
NIL
(-978)
((|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'.")))
@@ -3862,7 +3862,7 @@ NIL
NIL
(-983 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}.")))
-((-3992 . T) (-3991 . T))
+((-3993 . T) (-3992 . T))
NIL
(-984 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.")))
@@ -3876,7 +3876,7 @@ NIL
((|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 -3090)
+(-987 |Base| R -3091)
((|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
@@ -3884,7 +3884,7 @@ NIL
((|constructor| (NIL "This domain implements named rules")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol")))
NIL
NIL
-(-989 |Base| R -3090)
+(-989 |Base| R -3091)
((|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
@@ -3894,7 +3894,7 @@ NIL
NIL
(-991 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.")))
-((-3984 |has| |#1| (-311)) (-3989 |has| |#1| (-311)) (-3983 |has| |#1| (-311)) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . T))
+((-3985 |has| |#1| (-311)) (-3990 |has| |#1| (-311)) (-3984 |has| |#1| (-311)) ((-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 (-311))) (|HasCategory| |#1| (QUOTE (-317))) (OR (-12 (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-311)))) (|HasCategory| |#1| (QUOTE (-298)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-311)))) (-12 (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-311)))) (|HasCategory| |#1| (QUOTE (-298)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-810 (-1089))))) (-12 (|HasCategory| |#1| (QUOTE (-298))) (|HasCategory| |#1| (QUOTE (-810 (-1089)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-810 (-1089))))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|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 (-189))) (|HasCategory| |#1| (QUOTE (-311)))) (|HasCategory| |#1| (QUOTE (-298)))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-812 (-1089))))) (-12 (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-311)))) (-12 (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-311)))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-810 (-1089))))))
(-992 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}.")))
@@ -3926,8 +3926,8 @@ NIL
NIL
(-999 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")))
-(((-3993 "*") |has| |#1| (-146)) (-3984 |has| |#1| (-495)) (-3989 |has| |#1| (-6 -3989)) (-3986 . T) (-3985 . T) (-3988 . 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 -3989)) (|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)))))
+(((-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)
((|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
@@ -3966,7 +3966,7 @@ NIL
NIL
(-1009 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)}}")))
-((-3991 . T) (-3981 . T) (-3992 . T))
+((-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)
((|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|) $ $) "\\spad{s} < \\spad{t} returns \\spad{true} if all elements of set aggregate \\spad{s} are also elements of set aggregate \\spad{t}.")))
@@ -3974,7 +3974,7 @@ NIL
NIL
(-1011 S)
((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#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}.")))
-((-3981 . T))
+((-3982 . T))
NIL
(-1012 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}.")))
@@ -4010,7 +4010,7 @@ NIL
NIL
(-1020 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.}")))
-((-3992 . T) (-3991 . T))
+((-3993 . T) (-3992 . T))
NIL
(-1021)
((|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.")))
@@ -4018,11 +4018,11 @@ NIL
NIL
(-1022 T$)
((|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.")))
-(((|%Rule| |associativity| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|) (|:| |y| |#1|) (|:| |z| |#1|)) (-3054 (|f| (|f| |x| |y|) |z|) (|f| |x| (|f| |y| |z|))))) . T))
+(((|%Rule| |associativity| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|) (|:| |y| |#1|) (|:| |z| |#1|)) (-3055 (|f| (|f| |x| |y|) |z|) (|f| |x| (|f| |y| |z|))))) . T))
NIL
(-1023 T$)
((|constructor| (NIL "This is the category of all domains that implement semigroup operations")))
-(((|%Rule| |associativity| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|) (|:| |y| |#1|) (|:| |z| |#1|)) (-3054 (|f| (|f| |x| |y|) |z|) (|f| |x| (|f| |y| |z|))))) . T))
+(((|%Rule| |associativity| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|) (|:| |y| |#1|) (|:| |z| |#1|)) (-3055 (|f| (|f| |x| |y|) |z|) (|f| |x| (|f| |y| |z|))))) . T))
NIL
(-1024 S)
((|constructor| (NIL "the class of all multiplicative semigroups,{} \\spadignore{i.e.} a set with an associative operation \\spadop{*}. \\blankline")) (** (($ $ (|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}.")))
@@ -4034,8 +4034,8 @@ NIL
NIL
(-1026 |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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(|HasCategory| |#3| (QUOTE (-718))) (|HasCategory| |#3| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-757))) (|HasCategory| |#3| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-810 (-1089)))) (|HasCategory| |#3| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-951 (-484)))) (|HasCategory| |#3| (QUOTE (-1013)))) (-12 (|HasCategory| |#3| (QUOTE (-311))) (|HasCategory| |#3| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-317))) (|HasCategory| |#3| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-664))) (|HasCategory| |#3| (QUOTE (-951 (-484))))) (|HasCategory| |#3| (QUOTE (-962)))) (OR (-12 (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-104))) (|HasCategory| |#3| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-190))) (|HasCategory| |#3| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-718))) (|HasCategory| |#3| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-757))) (|HasCategory| |#3| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-810 (-1089)))) (|HasCategory| |#3| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-951 (-484)))) (|HasCategory| |#3| (QUOTE (-1013)))) (-12 (|HasCategory| |#3| (QUOTE (-311))) (|HasCategory| |#3| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-317))) (|HasCategory| |#3| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-664))) (|HasCategory| |#3| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-951 (-484)))) (|HasCategory| |#3| (QUOTE (-962))))) (|HasCategory| (-484) (QUOTE (-757))) (-12 (|HasCategory| |#3| (QUOTE (-581 (-484)))) (|HasCategory| |#3| (QUOTE (-962)))) (-12 (|HasCategory| |#3| (QUOTE (-189))) (|HasCategory| |#3| (QUOTE (-962)))) (-12 (|HasCategory| |#3| (QUOTE (-812 (-1089)))) (|HasCategory| |#3| (QUOTE (-962)))) (OR (-12 (|HasCategory| |#3| (QUOTE (-951 (-484)))) (|HasCategory| |#3| (QUOTE (-1013)))) (|HasCategory| |#3| (QUOTE (-962)))) (-12 (|HasCategory| |#3| (QUOTE (-951 (-484)))) (|HasCategory| |#3| (QUOTE (-1013)))) (-12 (|HasCategory| |#3| (QUOTE (-951 (-347 (-484))))) (|HasCategory| |#3| (QUOTE (-1013)))) (|HasAttribute| |#3| (QUOTE -3989)) (-12 (|HasCategory| |#3| (QUOTE (-190))) (|HasCategory| |#3| (QUOTE (-962)))) (-12 (|HasCategory| |#3| (QUOTE (-810 (-1089)))) (|HasCategory| |#3| (QUOTE (-962)))) (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-104))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-72))) (-12 (|HasCategory| |#3| (QUOTE (-1013))) (|HasCategory| |#3| (|%list| (QUOTE -259) (|devaluate| |#3|)))))
(-1027 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
@@ -4048,7 +4048,7 @@ NIL
((|constructor| (NIL "This domain represents a signature AST. A signature AST \\indented{2}{is a description of an exported operation,{} \\spadignore{e.g.} its name,{} result} \\indented{2}{type,{} and the list of its argument types.}")) (|signature| (((|Signature|) $) "\\spad{signature(s)} returns AST of the declared signature for `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 -3090)
+(-1030 R -3091)
((|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
@@ -4062,19 +4062,19 @@ NIL
NIL
(-1033)
((|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.")))
-((-3979 . T) (-3983 . T) (-3978 . T) (-3989 . T) (-3990 . T) (-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . T))
+((-3980 . T) (-3984 . T) (-3979 . T) (-3990 . T) (-3991 . T) (-3985 . T) ((-3994 "*") . T) (-3986 . T) (-3987 . T) (-3989 . T))
NIL
(-1034 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| $) "\\spad{push!(x,s)} pushes \\spad{x} onto stack \\spad{s},{} \\spadignore{i.e.} destructively changing \\spad{s} so as to have a new first (top) element \\spad{x}. Afterwards,{} pop!(\\spad{s}) produces \\spad{x} and pop!(\\spad{s}) produces the original \\spad{s}.")))
-((-3991 . T) (-3992 . T))
+((-3992 . T) (-3993 . T))
NIL
(-1035 S |ndim| R |Row| |Col|)
((|constructor| (NIL "\\spadtype{SquareMatrixCategory} is a general square matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col.")) (** (($ $ (|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 (-3993 "*"))) (|HasCategory| |#3| (QUOTE (-146))))
+((|HasCategory| |#3| (QUOTE (-311))) (|HasAttribute| |#3| (QUOTE (-3994 "*"))) (|HasCategory| |#3| (QUOTE (-146))))
(-1036 |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.")))
-((-3991 . T) (-3985 . T) (-3986 . T) (-3988 . T))
+((-3992 . T) (-3986 . T) (-3987 . T) (-3989 . T))
NIL
(-1037 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}.")))
@@ -4082,17 +4082,17 @@ NIL
NIL
(-1038 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.")))
-(((-3993 "*") |has| |#1| (-146)) (-3984 |has| |#1| (-495)) (-3989 |has| |#1| (-6 -3989)) (-3986 . T) (-3985 . T) (-3988 . 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 -3989)) (|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)))))
+(((-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)
((|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}.")))
-(((-3993 "*") |has| |#1| (-146)) (-3984 |has| |#1| (-495)) (-3986 . T) (-3985 . T) (-3988 . T))
+(((-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)
((|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}")))
-((-3992 . T) (-3991 . T))
+((-3993 . T) (-3992 . T))
NIL
-(-1041 UP -3090)
+(-1041 UP -3091)
((|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
@@ -4146,19 +4146,19 @@ NIL
NIL
(-1054 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") $) "\\axiom{extractSplittingLeaf(a)} returns the left most leaf (as a tree) whose status is \\spad{false} if any,{} else \"failed\" is returned.")))
-((-3991 . T) (-3992 . T))
+((-3992 . T) (-3993 . T))
((-12 (|HasCategory| (-1053 |#1| |#2|) (|%list| (QUOTE -259) (|%list| (QUOTE -1053) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1053 |#1| |#2|) (QUOTE (-1013)))) (|HasCategory| (-1053 |#1| |#2|) (QUOTE (-1013))) (OR (|HasCategory| (-1053 |#1| |#2|) (QUOTE (-72))) (|HasCategory| (-1053 |#1| |#2|) (QUOTE (-1013)))) (|HasCategory| (-1053 |#1| |#2|) (QUOTE (-553 (-773)))) (|HasCategory| (-1053 |#1| |#2|) (QUOTE (-72))))
(-1055 |ndim| R)
((|constructor| (NIL "\\spadtype{SquareMatrix} is a matrix domain of square matrices,{} where the number of rows (= number of columns) is a parameter of the type.")) (|unitsKnown| ((|attribute|) "the invertible matrices are simply the matrices whose determinants are units in the Ring \\spad{R}.")) (|central| ((|attribute|) "the elements of the Ring \\spad{R},{} viewed as diagonal matrices,{} commute with all matrices and,{} indeed,{} are the only matrices which commute with all matrices.")) (|squareMatrix| (($ (|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}.")))
-((-3988 . T) (-3980 |has| |#2| (-6 (-3993 "*"))) (-3991 . T) (-3985 . T) (-3986 . T))
-((|HasCategory| |#2| (QUOTE (-810 (-1089)))) (|HasCategory| |#2| (QUOTE (-812 (-1089)))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-189))) (|HasAttribute| |#2| (QUOTE (-3993 #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 (-554 (-473)))) (|HasCategory| |#2| (QUOTE (-257))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-311))) (OR (|HasAttribute| |#2| (QUOTE (-3993 #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))))
+((-3989 . T) (-3981 |has| |#2| (-6 (-3994 "*"))) (-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 (-554 (-473)))) (|HasCategory| |#2| (QUOTE (-257))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-311))) (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))))
(-1056 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|) $ $) "\\spad{prefix?(s,t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) == reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case.")))
NIL
NIL
(-1057)
((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|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.")))
-((-3992 . T) (-3991 . T))
+((-3993 . T) (-3992 . T))
NIL
(-1058 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.}")))
@@ -4166,7 +4166,7 @@ NIL
NIL
(-1059 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.")))
-((-3992 . T) (-3991 . T))
+((-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)
((|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:")))
@@ -4174,7 +4174,7 @@ NIL
NIL
(-1061 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}.")))
-((-3991 . T) (-3992 . T))
+((-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)
((|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})}.")))
@@ -4186,8 +4186,8 @@ NIL
NIL
(-1064 |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.")))
-((-3992 . T))
-((-12 (|HasCategory| (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -259) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3856) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-553 (-773))))) (|HasCategory| (-2 (|:| -3856 |#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 (|:| -3856 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013))))
+((-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)
((|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
@@ -4202,7 +4202,7 @@ NIL
NIL
(-1068 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.")))
-((-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| (-484) (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-72))))
(-1069 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)}.")))
@@ -4218,12 +4218,12 @@ NIL
NIL
(-1072)
((|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")))
-((-3992 . T) (-3991 . T))
+((-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|)
((|constructor| (NIL "This domain provides tables where the keys are strings. A specialized hash function for strings is used.")))
-((-3991 . T) (-3992 . T))
-((-12 (|HasCategory| (-2 (|:| -3856 (-1072)) (|:| |entry| |#1|)) (|%list| (QUOTE -259) (|%list| (QUOTE -2) (QUOTE (|:| -3856 (-1072))) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -3856 (-1072)) (|:| |entry| |#1|)) (QUOTE (-1013)))) (OR (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3856 (-1072)) (|:| |entry| |#1|)) (QUOTE (-1013)))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3856 (-1072)) (|:| |entry| |#1|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3856 (-1072)) (|:| |entry| |#1|)) (QUOTE (-1013)))) (OR (|HasCategory| (-2 (|:| -3856 (-1072)) (|:| |entry| |#1|)) (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-553 (-773))))) (|HasCategory| (-2 (|:| -3856 (-1072)) (|:| |entry| |#1|)) (QUOTE (-554 (-473)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -3856 (-1072)) (|:| |entry| |#1|)) (QUOTE (-1013))) (|HasCategory| (-1072) (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1013))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3856 (-1072)) (|:| |entry| |#1|)) (QUOTE (-72)))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3856 (-1072)) (|:| |entry| |#1|)) (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3856 (-1072)) (|:| |entry| |#1|)) (QUOTE (-72))))
+((-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)
((|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
@@ -4254,9 +4254,9 @@ NIL
NIL
(-1081 |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)
((|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
@@ -4266,8 +4266,8 @@ NIL
NIL
(-1084 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)
((|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
@@ -4278,12 +4278,12 @@ NIL
NIL
(-1087 |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|)
((|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}.")))
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-((|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 -3942) (|%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 -3808) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1089))))) (|HasSignature| |#1| (|%list| (QUOTE -3079) (|%list| (|%list| (QUOTE -584) (QUOTE (-1089))) (|devaluate| |#1|)))))))
+(((-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)
((|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
@@ -4294,8 +4294,8 @@ NIL
NIL
(-1091 R)
((|constructor| (NIL "This domain implements symmetric polynomial")))
-(((-3993 "*") |has| |#1| (-146)) (-3984 |has| |#1| (-495)) (-3989 |has| |#1| (-6 -3989)) (-3985 . T) (-3986 . T) (-3988 . 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 -3989)))
+(((-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)
((|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
@@ -4334,8 +4334,8 @@ NIL
NIL
(-1101 |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}")))
-((-3991 . T) (-3992 . T))
-((-12 (|HasCategory| (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -259) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3856) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-553 (-773))))) (|HasCategory| (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-473)))) (-12 (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (|%list| (QUOTE -259) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-1013))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))))
+((-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)
((|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
@@ -4354,7 +4354,7 @@ NIL
NIL
(-1106 |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})}.")))
-((-3992 . T))
+((-3993 . T))
NIL
(-1107 |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.")))
@@ -4390,7 +4390,7 @@ NIL
NIL
(-1115 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| $)) "\\spad{tree(nd,ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}.")))
-((-3992 . T) (-3991 . T))
+((-3993 . T) (-3992 . T))
((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1013))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-72))))
(-1116 S)
((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}.")))
@@ -4400,7 +4400,7 @@ NIL
((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}.")))
NIL
NIL
-(-1118 R -3090)
+(-1118 R -3091)
((|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
@@ -4408,13 +4408,13 @@ NIL
((|constructor| (NIL "This package provides functions that compute \"fraction-free\" inverses of upper and lower triangular matrices over a integral domain. By \"fraction-free inverses\" we mean the following: given a matrix \\spad{B} with entries in \\spad{R} and an element \\spad{d} of \\spad{R} such that \\spad{d} * inv(\\spad{B}) also has entries in \\spad{R},{} we return \\spad{d} * inv(\\spad{B}). Thus,{} it is not necessary to pass to the quotient field in any of our computations.")) (|LowTriBddDenomInv| ((|#4| |#4| |#1|) "\\spad{LowTriBddDenomInv(B,d)} returns \\spad{M},{} where \\spad{B} is a non-singular lower triangular matrix and \\spad{d} is an element of \\spad{R} such that \\spad{M = d * inv(B)} has entries in \\spad{R}.")) (|UpTriBddDenomInv| ((|#4| |#4| |#1|) "\\spad{UpTriBddDenomInv(B,d)} returns \\spad{M},{} where \\spad{B} is a non-singular upper triangular matrix and \\spad{d} is an element of \\spad{R} such that \\spad{M = d * inv(B)} has entries in \\spad{R}.")))
NIL
NIL
-(-1120 R -3090)
+(-1120 R -3091)
((|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|)
((|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}.")))
-(((-3993 "*") |has| |#1| (-146)) (-3984 |has| |#1| (-495)) (-3986 . T) (-3985 . T) (-3988 . T))
+(((-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)
((|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.")))
@@ -4422,7 +4422,7 @@ NIL
((|HasCategory| |#4| (QUOTE (-317))))
(-1123 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|) $ $) "\\axiom{infRittWu?(\\spad{ts1},{}\\spad{ts2})} returns \\spad{true} iff \\axiom{\\spad{ts2}} has higher rank than \\axiom{\\spad{ts1}} in Wu Wen Tsun sense.")))
-((-3992 . T) (-3991 . T))
+((-3993 . T) (-3992 . T))
NIL
(-1124 |Curve|)
((|constructor| (NIL "\\indented{2}{Package for constructing tubes around 3-dimensional parametric curves.} Domain of tubes around 3-dimensional parametric curves.")) (|tube| (($ |#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}.")))
@@ -4436,7 +4436,7 @@ NIL
((|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 -3090)
+(-1127 -3091)
((|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
@@ -4462,7 +4462,7 @@ NIL
NIL
(-1133)
((|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|) $) "\\spad{prime?(x)} tests if \\spad{x} can never be written as the product of two non-units of the ring,{} \\spadignore{i.e.} \\spad{x} is an irreducible element.")))
-((-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . T))
+((-3985 . T) ((-3994 "*") . T) (-3986 . T) (-3987 . T) (-3989 . T))
NIL
(-1134)
((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 16 bits.")))
@@ -4482,15 +4482,15 @@ NIL
NIL
(-1138 |Coef| |var| |cen|)
((|constructor| (NIL "Dense Laurent series in one variable \\indented{2}{\\spadtype{UnivariateLaurentSeries} is a domain representing Laurent} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{UnivariateLaurentSeries(Integer,x,3)} represents Laurent series in} \\indented{2}{\\spad{(x - 3)} with integer coefficients.}")) (|integrate| (($ $ (|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.")))
-(((-3993 "*") OR (-2560 (|has| |#1| (-311)) (|has| (-1168 |#1| |#2| |#3|) (-741))) (|has| |#1| (-146)) (-2560 (|has| |#1| (-311)) (|has| (-1168 |#1| |#2| |#3|) (-822)))) (-3984 OR (-2560 (|has| |#1| (-311)) (|has| (-1168 |#1| |#2| |#3|) (-741))) (|has| |#1| (-495)) (-2560 (|has| |#1| (-311)) (|has| (-1168 |#1| |#2| |#3|) (-822)))) (-3989 |has| |#1| (-311)) (-3983 |has| |#1| (-311)) (-3985 . T) (-3986 . T) (-3988 . T))
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|#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|)
((|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|)
((|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.")))
-(((-3993 "*") |has| |#1| (-146)) (-3984 |has| |#1| (-495)) (-3989 |has| |#1| (-311)) (-3983 |has| |#1| (-311)) (-3985 . T) (-3986 . T) (-3988 . T))
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NIL
(-1141 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)}.")))
@@ -4498,12 +4498,12 @@ NIL
((|HasCategory| |#2| (QUOTE (-311))))
(-1142 |Coef| UTS)
((|constructor| (NIL "This is a category of univariate Laurent series constructed from univariate Taylor series. A Laurent series is represented by a pair \\spad{[n,f(x)]},{} where \\spad{n} is an arbitrary integer and \\spad{f(x)} is a Taylor series. This pair represents the Laurent series \\spad{x**n * f(x)}.")) (|taylorIfCan| (((|Union| |#2| "failed") $) "\\spad{taylorIfCan(f(x))} converts the Laurent series \\spad{f(x)} to a Taylor series,{} if possible. If this is not possible,{} \"failed\" is returned.")) (|taylor| ((|#2| $) "\\spad{taylor(f(x))} converts the Laurent series \\spad{f}(\\spad{x}) to a Taylor series,{} if possible. Error: if this is not possible.")) (|removeZeroes| (($ (|Integer|) $) "\\spad{removeZeroes(n,f(x))} removes up to \\spad{n} leading zeroes from the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable.") (($ $) "\\spad{removeZeroes(f(x))} removes leading zeroes from the representation of the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable. Note: \\spad{removeZeroes(f)} removes all leading zeroes from \\spad{f}")) (|taylorRep| ((|#2| $) "\\spad{taylorRep(f(x))} returns \\spad{g(x)},{} where \\spad{f = x**n * g(x)} is represented by \\spad{[n,g(x)]}.")) (|degree| (((|Integer|) $) "\\spad{degree(f(x))} returns the degree of the lowest order term of \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurent| (($ (|Integer|) |#2|) "\\spad{laurent(n,f(x))} returns \\spad{x**n * f(x)}.")))
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NIL
(-1143 |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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(|HasCategory| |#2| (QUOTE (-812 (-1089))))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-189)))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-118))))))
(-1144 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
@@ -4518,8 +4518,8 @@ NIL
((|HasCategory| |#1| (QUOTE (-756))))
(-1147 |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| $) "\\spad{fmecg(p1,e,r,p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}")))
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(-1148 |x| R |y| S)
((|constructor| (NIL "This package lifts a mapping from coefficient rings \\spad{R} to \\spad{S} to a mapping from \\spadtype{UnivariatePolynomial}(\\spad{x},{}\\spad{R}) to \\spadtype{UnivariatePolynomial}(\\spad{y},{}\\spad{S}). Note that the mapping is assumed to send zero to zero,{} since it will only be applied to the non-zero coefficients of the polynomial.")) (|map| (((|UnivariatePolynomial| |#3| |#4|) (|Mapping| |#4| |#2|) (|UnivariatePolynomial| |#1| |#2|)) "\\spad{map(func, poly)} creates a new polynomial by applying \\spad{func} to every non-zero coefficient of the polynomial poly.")))
NIL
@@ -4546,7 +4546,7 @@ NIL
((|HasCategory| |#2| (QUOTE (-38 (-347 (-484))))) (|HasCategory| |#2| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-389))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-1065))))
(-1154 R)
((|constructor| (NIL "The category of univariate polynomials over a ring \\spad{R}. No particular model is assumed - implementations can be either sparse or dense.")) (|integrate| (($ $) "\\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}.")))
-(((-3993 "*") |has| |#1| (-146)) (-3984 |has| |#1| (-495)) (-3987 |has| |#1| (-311)) (-3989 |has| |#1| (-6 -3989)) (-3986 . T) (-3985 . T) (-3988 . T))
+(((-3994 "*") |has| |#1| (-146)) (-3985 |has| |#1| (-495)) (-3988 |has| |#1| (-311)) (-3990 |has| |#1| (-6 -3990)) (-3987 . T) (-3986 . T) (-3989 . T))
NIL
(-1155 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.")))
@@ -4555,10 +4555,10 @@ NIL
(-1156 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 -3942) (|%list| (|devaluate| |#2|) (QUOTE (-1089))))))
+((|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|)
((|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|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents.")))
-(((-3993 "*") |has| |#1| (-146)) (-3984 |has| |#1| (-495)) (-3985 . T) (-3986 . T) (-3988 . T))
+(((-3994 "*") |has| |#1| (-146)) (-3985 |has| |#1| (-495)) (-3986 . T) (-3987 . T) (-3989 . T))
NIL
(-1158 RC P)
((|constructor| (NIL "This package provides for square-free decomposition of univariate polynomials over arbitrary rings,{} \\spadignore{i.e.} a partial factorization such that each factor is a product of irreducibles with multiplicity one and the factors are pairwise relatively prime. If the ring has characteristic zero,{} the result is guaranteed to satisfy this condition. If the ring is an infinite ring of finite characteristic,{} then it may not be possible to decide when polynomials contain factors which are \\spad{p}th powers. In this case,{} the flag associated with that polynomial is set to \"nil\" (meaning that that polynomials are not guaranteed to be square-free).")) (|BumInSepFFE| (((|Record| (|:| |flg| (|Union| #1="nil" #2="sqfr" #3="irred" #4="prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|))) (|Record| (|:| |flg| (|Union| #1# #2# #3# #4#)) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|)))) "\\spad{BumInSepFFE(f)} is a local function,{} exported only because it has multiple conditional definitions.")) (|squareFreePart| ((|#2| |#2|) "\\spad{squareFreePart(p)} returns a polynomial which has the same irreducible factors as the univariate polynomial \\spad{p},{} but each factor has multiplicity one.")) (|squareFree| (((|Factored| |#2|) |#2|) "\\spad{squareFree(p)} computes the square-free factorization of the univariate polynomial \\spad{p}. Each factor has no repeated roots,{} and the factors are pairwise relatively prime.")) (|gcd| (($ $ $) "\\spad{gcd(p,q)} computes the greatest-common-divisor of \\spad{p} and \\spad{q}.")))
@@ -4566,15 +4566,15 @@ NIL
NIL
(-1159 |Coef| |var| |cen|)
((|constructor| (NIL "Dense Puiseux series in one variable \\indented{2}{\\spadtype{UnivariatePuiseuxSeries} is a domain representing Puiseux} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{UnivariatePuiseuxSeries(Integer,x,3)} represents Puiseux series in} \\indented{2}{\\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|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.")))
-(((-3993 "*") |has| |#1| (-146)) (-3984 |has| |#1| (-495)) (-3989 |has| |#1| (-311)) (-3983 |has| |#1| (-311)) (-3985 . T) (-3986 . T) (-3988 . 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 -3942) (|%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 -3808) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1089))))) (|HasSignature| |#1| (|%list| (QUOTE -3079) (|%list| (|%list| (QUOTE -584) (QUOTE (-1089))) (|devaluate| |#1|)))))))
+(((-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|)
((|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|)
((|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.")))
-(((-3993 "*") |has| |#1| (-146)) (-3984 |has| |#1| (-495)) (-3989 |has| |#1| (-311)) (-3983 |has| |#1| (-311)) (-3985 . T) (-3986 . T) (-3988 . T))
+(((-3994 "*") |has| |#1| (-146)) (-3985 |has| |#1| (-495)) (-3990 |has| |#1| (-311)) (-3984 |has| |#1| (-311)) (-3986 . T) (-3987 . T) (-3989 . T))
NIL
(-1162 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)}.")))
@@ -4582,28 +4582,28 @@ NIL
NIL
(-1163 |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)}.")))
-(((-3993 "*") |has| |#1| (-146)) (-3984 |has| |#1| (-495)) (-3989 |has| |#1| (-311)) (-3983 |has| |#1| (-311)) (-3985 . T) (-3986 . T) (-3988 . T))
+(((-3994 "*") |has| |#1| (-146)) (-3985 |has| |#1| (-495)) (-3990 |has| |#1| (-311)) (-3984 |has| |#1| (-311)) (-3986 . T) (-3987 . T) (-3989 . T))
NIL
(-1164 |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)}.")))
-(((-3993 "*") |has| |#1| (-146)) (-3984 |has| |#1| (-495)) (-3989 |has| |#1| (-311)) (-3983 |has| |#1| (-311)) (-3985 . T) (-3986 . T) (-3988 . T))
-((|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 -3942) (|%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 -3808) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1089))))) (|HasSignature| |#1| (|%list| (QUOTE -3079) (|%list| (|%list| (QUOTE -584) (QUOTE (-1089))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (QUOTE (-38 (-347 (-484))))))
+(((-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 (-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|)))))) (|HasCategory| |#1| (QUOTE (-38 (-347 (-484))))))
(-1165 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") $) "\\spad{limitPlus(f(var))} returns \\spad{limit(var -> cen+,f(var))}.")))
-(((-3993 "*") |has| (-1159 |#2| |#3| |#4|) (-146)) (-3984 |has| (-1159 |#2| |#3| |#4|) (-495)) (-3985 . T) (-3986 . T) (-3988 . T))
+(((-3994 "*") |has| (-1159 |#2| |#3| |#4|) (-146)) (-3985 |has| (-1159 |#2| |#3| |#4|) (-495)) (-3986 . T) (-3987 . T) (-3989 . T))
((|HasCategory| (-1159 |#2| |#3| |#4|) (QUOTE (-38 (-347 (-484))))) (|HasCategory| (-1159 |#2| |#3| |#4|) (QUOTE (-118))) (|HasCategory| (-1159 |#2| |#3| |#4|) (QUOTE (-120))) (|HasCategory| (-1159 |#2| |#3| |#4|) (QUOTE (-146))) (OR (|HasCategory| (-1159 |#2| |#3| |#4|) (QUOTE (-38 (-347 (-484))))) (|HasCategory| (-1159 |#2| |#3| |#4|) (QUOTE (-951 (-347 (-484)))))) (|HasCategory| (-1159 |#2| |#3| |#4|) (QUOTE (-951 (-347 (-484))))) (|HasCategory| (-1159 |#2| |#3| |#4|) (QUOTE (-951 (-484)))) (|HasCategory| (-1159 |#2| |#3| |#4|) (QUOTE (-311))) (|HasCategory| (-1159 |#2| |#3| |#4|) (QUOTE (-389))) (|HasCategory| (-1159 |#2| |#3| |#4|) (QUOTE (-495))))
(-1166 A S)
((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|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| $) "\\spad{concat(x,u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}.")))
NIL
-((|HasAttribute| |#1| (QUOTE -3992)))
+((|HasAttribute| |#1| (QUOTE -3993)))
(-1167 S)
((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|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| $) "\\spad{concat(x,u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}.")))
NIL
NIL
(-1168 |Coef| |var| |cen|)
((|constructor| (NIL "Dense Taylor series in one variable \\spadtype{UnivariateTaylorSeries} is a domain representing Taylor series in one variable with coefficients in an arbitrary ring. The parameters of the type specify the coefficient ring,{} the power series variable,{} and the center of the power series expansion. For example,{} \\spadtype{UnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.")) (|integrate| (($ $ (|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}.")))
-(((-3993 "*") |has| |#1| (-146)) (-3984 |has| |#1| (-495)) (-3985 . T) (-3986 . T) (-3988 . 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 -3942) (|%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 -3808) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1089))))) (|HasSignature| |#1| (|%list| (QUOTE -3079) (|%list| (|%list| (QUOTE -584) (QUOTE (-1089))) (|devaluate| |#1|)))))))
+(((-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)
((|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
@@ -4611,16 +4611,16 @@ NIL
(-1170 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 -3079) (|%list| (|%list| (QUOTE -584) (QUOTE (-1089))) (|devaluate| |#2|)))) (|HasSignature| |#2| (|%list| (QUOTE -3808) (|%list| (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1089))))) (|HasCategory| |#2| (QUOTE (-38 (-347 (-484))))) (|HasCategory| |#2| (QUOTE (-311))))
+((|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|)
((|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.")))
-(((-3993 "*") |has| |#1| (-146)) (-3984 |has| |#1| (-495)) (-3985 . T) (-3986 . T) (-3988 . T))
+(((-3994 "*") |has| |#1| (-146)) (-3985 |has| |#1| (-495)) (-3986 . T) (-3987 . T) (-3989 . T))
NIL
(-1172 |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 -3090 UP L UTS)
+(-1173 -3091 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))))
@@ -4638,11 +4638,11 @@ 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)
((|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}.")) (+ (($ $ $) "\\spad{x + y} returns the component-wise sum of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.")))
-((-3992 . T) (-3991 . T))
+((-3993 . T) (-3992 . T))
NIL
(-1178 R)
((|constructor| (NIL "This type represents vector like objects with varying lengths and indexed by a finite segment of integers starting at 1.")) (|vector| (($ (|List| |#1|)) "\\spad{vector(l)} converts the list \\spad{l} to a vector.")))
-((-3992 . T) (-3991 . T))
+((-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)
((|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}.")))
@@ -4674,13 +4674,13 @@ NIL
NIL
(-1186 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}.")))
-((-3986 . T) (-3985 . T))
+((-3987 . T) (-3986 . T))
NIL
(-1187 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 -3090)
+(-1188 K R UP -3091)
((|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
@@ -4694,56 +4694,56 @@ NIL
NIL
(-1191 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)")))
-((-3986 |has| |#1| (-146)) (-3985 |has| |#1| (-146)) (-3988 . T))
+((-3987 |has| |#1| (-146)) (-3986 |has| |#1| (-146)) (-3989 . T))
((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-311))))
(-1192 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}.")))
-((-3992 . T) (-3991 . T))
+((-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)
((|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)")))
-((-3985 . T) (-3986 . T) (-3988 . T))
+((-3986 . T) (-3987 . T) (-3989 . T))
NIL
(-1194 |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.")))
-((-3988 . T) (-3984 |has| |#2| (-6 -3984)) (-3986 . T) (-3985 . T))
-((|HasCategory| |#2| (QUOTE (-146))) (|HasAttribute| |#2| (QUOTE -3984)))
+((-3989 . T) (-3985 |has| |#2| (-6 -3985)) (-3987 . T) (-3986 . T))
+((|HasCategory| |#2| (QUOTE (-146))) (|HasAttribute| |#2| (QUOTE -3985)))
(-1195 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 -3090)
+(-1196 S -3091)
((|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}.")))
NIL
((|HasCategory| |#2| (QUOTE (-317))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))))
-(-1197 -3090)
+(-1197 -3091)
((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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}.")))
-((-3983 . T) (-3989 . T) (-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . T))
+((-3984 . T) (-3990 . T) (-3985 . T) ((-3994 "*") . T) (-3986 . T) (-3987 . T) (-3989 . T))
NIL
(-1198 |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| $) "\\spad{v * x} returns the product of a variable \\spad{x} by \\spad{x}.")))
-((-3984 |has| |#2| (-6 -3984)) (-3986 . T) (-3985 . T) (-3988 . T))
+((-3985 |has| |#2| (-6 -3985)) (-3987 . T) (-3986 . T) (-3989 . T))
NIL
(-1199 |VarSet| R)
((|constructor| (NIL "This domain constructor implements polynomials in non-commutative variables written in the Poincare-Birkhoff-Witt basis from the Lyndon basis. These polynomials can be used to compute Baker-Campbell-Hausdorff relations. \\newline Author: Michel Petitot (petitot@lifl.fr).")) (|log| (($ $ (|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}}.")))
-((-3984 |has| |#2| (-6 -3984)) (-3986 . T) (-3985 . T) (-3988 . T))
-((|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-655 (-347 (-484))))) (|HasAttribute| |#2| (QUOTE -3984)))
+((-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)
((|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.")))
-((-3984 |has| |#1| (-6 -3984)) (-3986 . T) (-3985 . T) (-3988 . T))
-((|HasCategory| |#1| (QUOTE (-146))) (|HasAttribute| |#1| (QUOTE -3984)))
+((-3985 |has| |#1| (-6 -3985)) (-3987 . T) (-3986 . T) (-3989 . T))
+((|HasCategory| |#1| (QUOTE (-146))) (|HasAttribute| |#1| (QUOTE -3985)))
(-1201 |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|) $) "\\spad{maxdeg(p)} returns the greatest leading word in the support of \\spad{p}.")))
-((-3984 |has| |#2| (-6 -3984)) (-3986 . T) (-3985 . T) (-3988 . T))
+((-3985 |has| |#2| (-6 -3985)) (-3987 . T) (-3986 . T) (-3989 . T))
NIL
(-1202 R E)
((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and words belonging to an arbitrary \\spadtype{OrderedMonoid}. This type is used,{} for instance,{} by the \\spadtype{XDistributedPolynomial} domain constructor where the Monoid is free.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (/ (($ $ |#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}.")))
-((-3988 . T) (-3989 |has| |#1| (-6 -3989)) (-3984 |has| |#1| (-6 -3984)) (-3986 . T) (-3985 . T))
-((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-311))) (|HasAttribute| |#1| (QUOTE -3988)) (|HasAttribute| |#1| (QUOTE -3989)) (|HasAttribute| |#1| (QUOTE -3984)))
+((-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)
((|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.")))
-((-3984 |has| |#2| (-6 -3984)) (-3986 . T) (-3985 . T) (-3988 . T))
-((|HasCategory| |#2| (QUOTE (-146))) (|HasAttribute| |#2| (QUOTE -3984)))
+((-3985 |has| |#2| (-6 -3985)) (-3987 . T) (-3986 . T) (-3989 . T))
+((|HasCategory| |#2| (QUOTE (-146))) (|HasAttribute| |#2| (QUOTE -3985)))
(-1204)
((|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
@@ -4762,7 +4762,7 @@ NIL
NIL
(-1208 |p|)
((|constructor| (NIL "IntegerMod(\\spad{n}) creates the ring of integers reduced modulo the integer \\spad{n}.")))
-(((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . T))
+(((-3994 "*") . T) (-3986 . T) (-3987 . T) (-3989 . T))
NIL
NIL
NIL
@@ -4780,4 +4780,4 @@ NIL
NIL
NIL
NIL
-((-3 NIL 1961798 1961803 1961808 1961813) (-2 NIL 1961778 1961783 1961788 1961793) (-1 NIL 1961758 1961763 1961768 1961773) (0 NIL 1961738 1961743 1961748 1961753) (-1208 "ZMOD.spad" 1961547 1961560 1961676 1961733) (-1207 "ZLINDEP.spad" 1960645 1960656 1961537 1961542) (-1206 "ZDSOLVE.spad" 1950606 1950628 1960635 1960640) (-1205 "YSTREAM.spad" 1950101 1950112 1950596 1950601) (-1204 "YDIAGRAM.spad" 1949735 1949744 1950091 1950096) (-1203 "XRPOLY.spad" 1948955 1948975 1949591 1949660) (-1202 "XPR.spad" 1946750 1946763 1948673 1948772) (-1201 "XPOLYC.spad" 1946069 1946085 1946676 1946745) (-1200 "XPOLY.spad" 1945624 1945635 1945925 1945994) (-1199 "XPBWPOLY.spad" 1944095 1944115 1945430 1945499) (-1198 "XFALG.spad" 1941143 1941159 1944021 1944090) (-1197 "XF.spad" 1939606 1939621 1941045 1941138) (-1196 "XF.spad" 1938049 1938066 1939490 1939495) (-1195 "XEXPPKG.spad" 1937308 1937334 1938039 1938044) (-1194 "XDPOLY.spad" 1936922 1936938 1937164 1937233) (-1193 "XALG.spad" 1936590 1936601 1936878 1936917) (-1192 "WUTSET.spad" 1932593 1932610 1936224 1936251) (-1191 "WP.spad" 1931800 1931844 1932451 1932518) (-1190 "WHILEAST.spad" 1931598 1931607 1931790 1931795) (-1189 "WHEREAST.spad" 1931269 1931278 1931588 1931593) (-1188 "WFFINTBS.spad" 1928932 1928954 1931259 1931264) (-1187 "WEIER.spad" 1927154 1927165 1928922 1928927) (-1186 "VSPACE.spad" 1926827 1926838 1927122 1927149) (-1185 "VSPACE.spad" 1926520 1926533 1926817 1926822) (-1184 "VOID.spad" 1926197 1926206 1926510 1926515) (-1183 "VIEWDEF.spad" 1921398 1921407 1926187 1926192) (-1182 "VIEW3D.spad" 1905359 1905368 1921388 1921393) (-1181 "VIEW2D.spad" 1893258 1893267 1905349 1905354) (-1180 "VIEW.spad" 1890978 1890987 1893248 1893253) (-1179 "VECTOR2.spad" 1889617 1889630 1890968 1890973) (-1178 "VECTOR.spad" 1888336 1888347 1888587 1888614) (-1177 "VECTCAT.spad" 1886248 1886259 1888304 1888331) (-1176 "VECTCAT.spad" 1883969 1883982 1886027 1886032) (-1175 "VARIABLE.spad" 1883749 1883764 1883959 1883964) (-1174 "UTYPE.spad" 1883393 1883402 1883739 1883744) (-1173 "UTSODETL.spad" 1882688 1882712 1883349 1883354) (-1172 "UTSODE.spad" 1880904 1880924 1882678 1882683) (-1171 "UTSCAT.spad" 1878383 1878399 1880802 1880899) (-1170 "UTSCAT.spad" 1875530 1875548 1877951 1877956) (-1169 "UTS2.spad" 1875125 1875160 1875520 1875525) (-1168 "UTS.spad" 1870137 1870165 1873657 1873754) (-1167 "URAGG.spad" 1864858 1864869 1870127 1870132) (-1166 "URAGG.spad" 1859543 1859556 1864814 1864819) (-1165 "UPXSSING.spad" 1857311 1857337 1858747 1858880) (-1164 "UPXSCONS.spad" 1855129 1855149 1855502 1855651) (-1163 "UPXSCCA.spad" 1853700 1853720 1854975 1855124) (-1162 "UPXSCCA.spad" 1852413 1852435 1853690 1853695) (-1161 "UPXSCAT.spad" 1851002 1851018 1852259 1852408) (-1160 "UPXS2.spad" 1850545 1850598 1850992 1850997) (-1159 "UPXS.spad" 1847900 1847928 1848736 1848885) (-1158 "UPSQFREE.spad" 1846315 1846329 1847890 1847895) (-1157 "UPSCAT.spad" 1844110 1844134 1846213 1846310) (-1156 "UPSCAT.spad" 1841606 1841632 1843711 1843716) (-1155 "UPOLYC2.spad" 1841077 1841096 1841596 1841601) (-1154 "UPOLYC.spad" 1836157 1836168 1840919 1841072) (-1153 "UPOLYC.spad" 1831155 1831168 1835919 1835924) (-1152 "UPMP.spad" 1830087 1830100 1831145 1831150) (-1151 "UPDIVP.spad" 1829652 1829666 1830077 1830082) (-1150 "UPDECOMP.spad" 1827913 1827927 1829642 1829647) (-1149 "UPCDEN.spad" 1827130 1827146 1827903 1827908) (-1148 "UP2.spad" 1826494 1826515 1827120 1827125) (-1147 "UP.spad" 1823964 1823979 1824351 1824504) (-1146 "UNISEG2.spad" 1823461 1823474 1823920 1823925) (-1145 "UNISEG.spad" 1822814 1822825 1823380 1823385) (-1144 "UNIFACT.spad" 1821917 1821929 1822804 1822809) (-1143 "ULSCONS.spad" 1815960 1815980 1816330 1816479) (-1142 "ULSCCAT.spad" 1813697 1813717 1815806 1815955) (-1141 "ULSCCAT.spad" 1811542 1811564 1813653 1813658) (-1140 "ULSCAT.spad" 1809782 1809798 1811388 1811537) (-1139 "ULS2.spad" 1809296 1809349 1809772 1809777) (-1138 "ULS.spad" 1801562 1801590 1802507 1802930) (-1137 "UINT8.spad" 1801439 1801448 1801552 1801557) (-1136 "UINT64.spad" 1801315 1801324 1801429 1801434) (-1135 "UINT32.spad" 1801191 1801200 1801305 1801310) (-1134 "UINT16.spad" 1801067 1801076 1801181 1801186) (-1133 "UFD.spad" 1800132 1800141 1800993 1801062) (-1132 "UFD.spad" 1799259 1799270 1800122 1800127) (-1131 "UDVO.spad" 1798140 1798149 1799249 1799254) (-1130 "UDPO.spad" 1795721 1795732 1798096 1798101) (-1129 "TYPEAST.spad" 1795640 1795649 1795711 1795716) (-1128 "TYPE.spad" 1795572 1795581 1795630 1795635) (-1127 "TWOFACT.spad" 1794224 1794239 1795562 1795567) (-1126 "TUPLE.spad" 1793731 1793742 1794136 1794141) (-1125 "TUBETOOL.spad" 1790598 1790607 1793721 1793726) (-1124 "TUBE.spad" 1789245 1789262 1790588 1790593) (-1123 "TSETCAT.spad" 1777316 1777333 1789213 1789240) (-1122 "TSETCAT.spad" 1765373 1765392 1777272 1777277) (-1121 "TS.spad" 1764001 1764017 1764967 1765064) (-1120 "TRMANIP.spad" 1758365 1758382 1763689 1763694) (-1119 "TRIMAT.spad" 1757328 1757353 1758355 1758360) (-1118 "TRIGMNIP.spad" 1755855 1755872 1757318 1757323) (-1117 "TRIGCAT.spad" 1755367 1755376 1755845 1755850) (-1116 "TRIGCAT.spad" 1754877 1754888 1755357 1755362) (-1115 "TREE.spad" 1753517 1753528 1754549 1754576) (-1114 "TRANFUN.spad" 1753356 1753365 1753507 1753512) (-1113 "TRANFUN.spad" 1753193 1753204 1753346 1753351) (-1112 "TOPSP.spad" 1752867 1752876 1753183 1753188) (-1111 "TOOLSIGN.spad" 1752530 1752541 1752857 1752862) (-1110 "TEXTFILE.spad" 1751091 1751100 1752520 1752525) (-1109 "TEX1.spad" 1750647 1750658 1751081 1751086) (-1108 "TEX.spad" 1747841 1747850 1750637 1750642) (-1107 "TBCMPPK.spad" 1745942 1745965 1747831 1747836) (-1106 "TBAGG.spad" 1745000 1745023 1745922 1745937) (-1105 "TBAGG.spad" 1744066 1744091 1744990 1744995) (-1104 "TANEXP.spad" 1743474 1743485 1744056 1744061) (-1103 "TALGOP.spad" 1743198 1743209 1743464 1743469) (-1102 "TABLEAU.spad" 1742679 1742690 1743188 1743193) (-1101 "TABLE.spad" 1740954 1740977 1741224 1741251) (-1100 "TABLBUMP.spad" 1737733 1737744 1740944 1740949) (-1099 "SYSTEM.spad" 1736961 1736970 1737723 1737728) (-1098 "SYSSOLP.spad" 1734444 1734455 1736951 1736956) (-1097 "SYSPTR.spad" 1734343 1734352 1734434 1734439) (-1096 "SYSNNI.spad" 1733566 1733577 1734333 1734338) (-1095 "SYSINT.spad" 1732970 1732981 1733556 1733561) (-1094 "SYNTAX.spad" 1729304 1729313 1732960 1732965) (-1093 "SYMTAB.spad" 1727372 1727381 1729294 1729299) (-1092 "SYMS.spad" 1723401 1723410 1727362 1727367) (-1091 "SYMPOLY.spad" 1722534 1722545 1722616 1722743) (-1090 "SYMFUNC.spad" 1722035 1722046 1722524 1722529) (-1089 "SYMBOL.spad" 1719530 1719539 1722025 1722030) (-1088 "SUTS.spad" 1716643 1716671 1718062 1718159) (-1087 "SUPXS.spad" 1713985 1714013 1714834 1714983) (-1086 "SUPFRACF.spad" 1713090 1713108 1713975 1713980) (-1085 "SUP2.spad" 1712482 1712495 1713080 1713085) (-1084 "SUP.spad" 1709566 1709577 1710339 1710492) (-1083 "SUMRF.spad" 1708540 1708551 1709556 1709561) (-1082 "SUMFS.spad" 1708169 1708186 1708530 1708535) (-1081 "SULS.spad" 1700422 1700450 1701380 1701803) (-1080 "syntax.spad" 1700191 1700200 1700412 1700417) (-1079 "SUCH.spad" 1699881 1699896 1700181 1700186) (-1078 "SUBSPACE.spad" 1692012 1692027 1699871 1699876) (-1077 "SUBRESP.spad" 1691182 1691196 1691968 1691973) (-1076 "STTFNC.spad" 1687650 1687666 1691172 1691177) (-1075 "STTF.spad" 1683749 1683765 1687640 1687645) (-1074 "STTAYLOR.spad" 1676426 1676437 1683656 1683661) (-1073 "STRTBL.spad" 1674813 1674830 1674962 1674989) (-1072 "STRING.spad" 1673681 1673690 1674066 1674093) (-1071 "STREAM3.spad" 1673254 1673269 1673671 1673676) (-1070 "STREAM2.spad" 1672382 1672395 1673244 1673249) (-1069 "STREAM1.spad" 1672088 1672099 1672372 1672377) (-1068 "STREAM.spad" 1669084 1669095 1671691 1671706) (-1067 "STINPROD.spad" 1668020 1668036 1669074 1669079) (-1066 "STEPAST.spad" 1667254 1667263 1668010 1668015) (-1065 "STEP.spad" 1666571 1666580 1667244 1667249) (-1064 "STBL.spad" 1664961 1664989 1665128 1665143) (-1063 "STAGG.spad" 1663660 1663671 1664951 1664956) (-1062 "STAGG.spad" 1662357 1662370 1663650 1663655) (-1061 "STACK.spad" 1661779 1661790 1662029 1662056) (-1060 "SRING.spad" 1661539 1661548 1661769 1661774) (-1059 "SREGSET.spad" 1659271 1659288 1661173 1661200) (-1058 "SRDCMPK.spad" 1657848 1657868 1659261 1659266) (-1057 "SRAGG.spad" 1653031 1653040 1657816 1657843) (-1056 "SRAGG.spad" 1648234 1648245 1653021 1653026) (-1055 "SQMATRIX.spad" 1645911 1645929 1646827 1646914) (-1054 "SPLTREE.spad" 1640653 1640666 1645449 1645476) (-1053 "SPLNODE.spad" 1637273 1637286 1640643 1640648) (-1052 "SPFCAT.spad" 1636082 1636091 1637263 1637268) (-1051 "SPECOUT.spad" 1634634 1634643 1636072 1636077) (-1050 "SPADXPT.spad" 1626725 1626734 1634624 1634629) (-1049 "spad-parser.spad" 1626190 1626199 1626715 1626720) (-1048 "SPADAST.spad" 1625891 1625900 1626180 1626185) (-1047 "SPACEC.spad" 1610106 1610117 1625881 1625886) (-1046 "SPACE3.spad" 1609882 1609893 1610096 1610101) (-1045 "SORTPAK.spad" 1609431 1609444 1609838 1609843) (-1044 "SOLVETRA.spad" 1607194 1607205 1609421 1609426) (-1043 "SOLVESER.spad" 1605650 1605661 1607184 1607189) (-1042 "SOLVERAD.spad" 1601676 1601687 1605640 1605645) (-1041 "SOLVEFOR.spad" 1600138 1600156 1601666 1601671) (-1040 "SNTSCAT.spad" 1599738 1599755 1600106 1600133) (-1039 "SMTS.spad" 1598055 1598081 1599332 1599429) (-1038 "SMP.spad" 1595863 1595883 1596253 1596380) (-1037 "SMITH.spad" 1594708 1594733 1595853 1595858) (-1036 "SMATCAT.spad" 1592826 1592856 1594652 1594703) (-1035 "SMATCAT.spad" 1590876 1590908 1592704 1592709) (-1034 "SKAGG.spad" 1589845 1589856 1590844 1590871) (-1033 "SINT.spad" 1589144 1589153 1589711 1589840) (-1032 "SIMPAN.spad" 1588872 1588881 1589134 1589139) (-1031 "SIGNRF.spad" 1587997 1588008 1588862 1588867) (-1030 "SIGNEF.spad" 1587283 1587300 1587987 1587992) (-1029 "syntax.spad" 1586700 1586709 1587273 1587278) (-1028 "SIG.spad" 1586062 1586071 1586690 1586695) (-1027 "SHP.spad" 1584006 1584021 1586018 1586023) (-1026 "SHDP.spad" 1573499 1573526 1574016 1574113) (-1025 "SGROUP.spad" 1573107 1573116 1573489 1573494) (-1024 "SGROUP.spad" 1572713 1572724 1573097 1573102) (-1023 "catdef.spad" 1572423 1572435 1572534 1572708) (-1022 "catdef.spad" 1571979 1571991 1572244 1572418) (-1021 "SGCF.spad" 1565118 1565127 1571969 1571974) (-1020 "SFRTCAT.spad" 1564064 1564081 1565086 1565113) (-1019 "SFRGCD.spad" 1563127 1563147 1564054 1564059) (-1018 "SFQCMPK.spad" 1557940 1557960 1563117 1563122) (-1017 "SEXOF.spad" 1557783 1557823 1557930 1557935) (-1016 "SEXCAT.spad" 1555611 1555651 1557773 1557778) (-1015 "SEX.spad" 1555503 1555512 1555601 1555606) (-1014 "SETMN.spad" 1553963 1553980 1555493 1555498) (-1013 "SETCAT.spad" 1553448 1553457 1553953 1553958) (-1012 "SETCAT.spad" 1552931 1552942 1553438 1553443) (-1011 "SETAGG.spad" 1549480 1549491 1552911 1552926) (-1010 "SETAGG.spad" 1546037 1546050 1549470 1549475) (-1009 "SET.spad" 1544346 1544357 1545443 1545482) (-1008 "syntax.spad" 1544049 1544058 1544336 1544341) (-1007 "SEGXCAT.spad" 1543205 1543218 1544039 1544044) (-1006 "SEGCAT.spad" 1542130 1542141 1543195 1543200) (-1005 "SEGBIND2.spad" 1541828 1541841 1542120 1542125) (-1004 "SEGBIND.spad" 1541586 1541597 1541775 1541780) (-1003 "SEGAST.spad" 1541316 1541325 1541576 1541581) (-1002 "SEG2.spad" 1540751 1540764 1541272 1541277) (-1001 "SEG.spad" 1540564 1540575 1540670 1540675) (-1000 "SDVAR.spad" 1539840 1539851 1540554 1540559) (-999 "SDPOL.spad" 1537533 1537543 1537823 1537950) (-998 "SCPKG.spad" 1535623 1535633 1537523 1537528) (-997 "SCOPE.spad" 1534801 1534809 1535613 1535618) (-996 "SCACHE.spad" 1533498 1533508 1534791 1534796) (-995 "SASTCAT.spad" 1533408 1533416 1533488 1533493) (-994 "SAOS.spad" 1533281 1533289 1533398 1533403) (-993 "SAERFFC.spad" 1532995 1533014 1533271 1533276) (-992 "SAEFACT.spad" 1532697 1532716 1532985 1532990) (-991 "SAE.spad" 1530348 1530363 1530958 1531093) (-990 "RURPK.spad" 1528008 1528023 1530338 1530343) (-989 "RULESET.spad" 1527462 1527485 1527998 1528003) (-988 "RULECOLD.spad" 1527315 1527327 1527452 1527457) (-987 "RULE.spad" 1525564 1525587 1527305 1527310) (-986 "RTVALUE.spad" 1525300 1525308 1525554 1525559) (-985 "syntax.spad" 1525018 1525026 1525290 1525295) (-984 "RSETGCD.spad" 1521461 1521480 1525008 1525013) (-983 "RSETCAT.spad" 1511430 1511446 1521429 1521456) (-982 "RSETCAT.spad" 1501419 1501437 1511420 1511425) (-981 "RSDCMPK.spad" 1499920 1499939 1501409 1501414) (-980 "RRCC.spad" 1498305 1498334 1499910 1499915) (-979 "RRCC.spad" 1496688 1496719 1498295 1498300) (-978 "RPTAST.spad" 1496391 1496399 1496678 1496683) (-977 "RPOLCAT.spad" 1475896 1475910 1496259 1496386) (-976 "RPOLCAT.spad" 1455194 1455210 1475559 1475564) (-975 "ROMAN.spad" 1454523 1454531 1455060 1455189) (-974 "ROIRC.spad" 1453604 1453635 1454513 1454518) (-973 "RNS.spad" 1452581 1452589 1453506 1453599) (-972 "RNS.spad" 1451644 1451654 1452571 1452576) (-971 "RNGBIND.spad" 1450805 1450818 1451599 1451604) (-970 "RNG.spad" 1450541 1450549 1450795 1450800) (-969 "RMODULE.spad" 1450323 1450333 1450531 1450536) (-968 "RMCAT2.spad" 1449744 1449800 1450313 1450318) (-967 "RMATRIX.spad" 1448554 1448572 1448896 1448935) (-966 "RMATCAT.spad" 1444134 1444164 1448510 1448549) (-965 "RMATCAT.spad" 1439604 1439636 1443982 1443987) (-964 "RLINSET.spad" 1439309 1439319 1439594 1439599) (-963 "RINTERP.spad" 1439198 1439217 1439299 1439304) (-962 "RING.spad" 1438669 1438677 1439178 1439193) (-961 "RING.spad" 1438148 1438158 1438659 1438664) (-960 "RIDIST.spad" 1437541 1437549 1438138 1438143) (-959 "RGCHAIN.spad" 1436096 1436111 1436989 1437016) (-958 "RGBCSPC.spad" 1435886 1435897 1436086 1436091) (-957 "RGBCMDL.spad" 1435449 1435460 1435876 1435881) (-956 "RFFACTOR.spad" 1434912 1434922 1435439 1435444) (-955 "RFFACT.spad" 1434648 1434659 1434902 1434907) (-954 "RFDIST.spad" 1433645 1433653 1434638 1434643) (-953 "RF.spad" 1431320 1431330 1433635 1433640) (-952 "RETSOL.spad" 1430740 1430752 1431310 1431315) (-951 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"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 "DFINTTLS.spad" 191459 191475 193218 193223) (-177 "DERHAM.spad" 189373 189405 191439 191454) (-176 "DEQUEUE.spad" 188762 188772 189045 189072) (-175 "DEGRED.spad" 188379 188393 188752 188757) (-174 "DEFINTRF.spad" 185961 185971 188369 188374) (-173 "DEFINTEF.spad" 184499 184515 185951 185956) (-172 "DEFAST.spad" 183883 183891 184489 184494) (-171 "DECIMAL.spad" 182112 182120 182473 182566) (-170 "DDFACT.spad" 179933 179950 182102 182107) (-169 "DBLRESP.spad" 179533 179557 179923 179928) (-168 "DBASIS.spad" 179159 179174 179523 179528) (-167 "DBASE.spad" 177823 177833 179149 179154) (-166 "DATAARY.spad" 177309 177322 177813 177818) (-165 "CYCLOTOM.spad" 176815 176823 177299 177304) (-164 "CYCLES.spad" 173607 173615 176805 176810) (-163 "CVMP.spad" 173024 173034 173597 173602) (-162 "CTRIGMNP.spad" 171524 171540 173014 173019) (-161 "CTORKIND.spad" 171127 171135 171514 171519) (-160 "CTORCAT.spad" 170368 170376 171117 171122) (-159 "CTORCAT.spad" 169607 169617 170358 170363) (-158 "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 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 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(-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 "DFINTTLS.spad" 191459 191475 193218 193223) (-177 "DERHAM.spad" 189373 189405 191439 191454) (-176 "DEQUEUE.spad" 188762 188772 189045 189072) (-175 "DEGRED.spad" 188379 188393 188752 188757) (-174 "DEFINTRF.spad" 185961 185971 188369 188374) (-173 "DEFINTEF.spad" 184499 184515 185951 185956) (-172 "DEFAST.spad" 183883 183891 184489 184494) (-171 "DECIMAL.spad" 182112 182120 182473 182566) (-170 "DDFACT.spad" 179933 179950 182102 182107) (-169 "DBLRESP.spad" 179533 179557 179923 179928) (-168 "DBASIS.spad" 179159 179174 179523 179528) (-167 "DBASE.spad" 177823 177833 179149 179154) (-166 "DATAARY.spad" 177309 177322 177813 177818) (-165 "CYCLOTOM.spad" 176815 176823 177299 177304) (-164 "CYCLES.spad" 173607 173615 176805 176810) (-163 "CVMP.spad" 173024 173034 173597 173602) (-162 "CTRIGMNP.spad" 171524 171540 173014 173019) (-161 "CTORKIND.spad" 171127 171135 171514 171519) (-160 "CTORCAT.spad" 170368 170376 171117 171122) (-159 "CTORCAT.spad" 169607 169617 170358 170363) (-158 "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
diff --git a/src/share/algebra/category.daase b/src/share/algebra/category.daase
index 8586ca8f..c54e7356 100644
--- a/src/share/algebra/category.daase
+++ b/src/share/algebra/category.daase
@@ -1,5 +1,5 @@
-(199610 . 3576910165)
+(199610 . 3577105538)
((((-773)) . T))
((((-773)) . T))
((((-773)) . T))
@@ -49,26 +49,26 @@
(((|#1| |#1|) . T))
(((|#1|) . T))
(((|#1|) . T))
-((((-2 (|:| -3856 |#1|) (|:| |entry| |#2|))) . T))
-((((-2 (|:| -3856 |#1|) (|:| |entry| |#2|))) . T))
-((((-2 (|:| -3856 |#1|) (|:| |entry| |#2|))) . T))
-((((-2 (|:| -3856 |#1|) (|:| |entry| |#2|))) . T))
-((((-2 (|:| -3856 |#1|) (|:| |entry| |#2|))) . T))
-((((-2 (|:| -3856 |#1|) (|:| |entry| |#2|))) . T))
+((((-2 (|:| -3857 |#1|) (|:| |entry| |#2|))) . T))
+((((-2 (|:| -3857 |#1|) (|:| |entry| |#2|))) . T))
+((((-2 (|:| -3857 |#1|) (|:| |entry| |#2|))) . T))
+((((-2 (|:| -3857 |#1|) (|:| |entry| |#2|))) . T))
+((((-2 (|:| -3857 |#1|) (|:| |entry| |#2|))) . T))
+((((-2 (|:| -3857 |#1|) (|:| |entry| |#2|))) . T))
((((-773)) . T))
-((((-2 (|:| -3856 |#1|) (|:| |entry| |#2|))) . T))
-((((-2 (|:| -3856 |#1|) (|:| |entry| |#2|))) . T))
+((((-2 (|:| -3857 |#1|) (|:| |entry| |#2|))) . T))
+((((-2 (|:| -3857 |#1|) (|:| |entry| |#2|))) . T))
(((|#1| |#2|) . T))
-((((-2 (|:| -3856 |#1|) (|:| |entry| |#2|))) . T))
-((((-2 (|:| -3856 |#1|) (|:| |entry| |#2|))) . T))
-((((-2 (|:| -3856 |#1|) (|:| |entry| |#2|))) . T))
+((((-2 (|:| -3857 |#1|) (|:| |entry| |#2|))) . T))
+((((-2 (|:| -3857 |#1|) (|:| |entry| |#2|))) . T))
+((((-2 (|:| -3857 |#1|) (|:| |entry| |#2|))) . T))
(((|#1| |#2|) . T))
-((((-484) (-2 (|:| -3856 |#1|) (|:| |entry| |#2|))) . T) ((|#1| |#2|) . T))
-((((-484) (-2 (|:| -3856 |#1|) (|:| |entry| |#2|))) . T) (((-1145 (-484)) $) . T) ((|#1| |#2|) . T))
-((((-2 (|:| -3856 |#1|) (|:| |entry| |#2|))) . T) ((|#2|) . T))
-((((-2 (|:| -3856 |#1|) (|:| |entry| |#2|)) (-2 (|:| -3856 |#1|) (|:| |entry| |#2|))) |has| (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)) (-259 (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-259 |#2|)) (|has| |#2| (-1013))))
-((((-2 (|:| -3856 |#1|) (|:| |entry| |#2|))) |has| (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)) (-259 (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)))) ((|#2|) -12 (|has| |#2| (-259 |#2|)) (|has| |#2| (-1013))))
-((((-484) (-2 (|:| -3856 |#1|) (|:| |entry| |#2|))) . T) ((|#1| |#2|) . T))
+((((-484) (-2 (|:| -3857 |#1|) (|:| |entry| |#2|))) . T) ((|#1| |#2|) . T))
+((((-484) (-2 (|:| -3857 |#1|) (|:| |entry| |#2|))) . T) (((-1145 (-484)) $) . T) ((|#1| |#2|) . T))
+((((-2 (|:| -3857 |#1|) (|:| |entry| |#2|))) . T) ((|#2|) . T))
+((((-2 (|:| -3857 |#1|) (|:| |entry| |#2|)) (-2 (|:| -3857 |#1|) (|:| |entry| |#2|))) |has| (-2 (|:| -3857 |#1|) (|:| |entry| |#2|)) (-259 (-2 (|:| -3857 |#1|) (|:| |entry| |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-259 |#2|)) (|has| |#2| (-1013))))
+((((-2 (|:| -3857 |#1|) (|:| |entry| |#2|))) |has| (-2 (|:| -3857 |#1|) (|:| |entry| |#2|)) (-259 (-2 (|:| -3857 |#1|) (|:| |entry| |#2|)))) ((|#2|) -12 (|has| |#2| (-259 |#2|)) (|has| |#2| (-1013))))
+((((-484) (-2 (|:| -3857 |#1|) (|:| |entry| |#2|))) . T) ((|#1| |#2|) . T))
(((|#1| |#2|) . T))
((($) . T))
((((-142 (-327))) . T) (((-179)) . T) (((-327)) . T))
@@ -519,7 +519,7 @@
(((|#1|) . T))
((((-473)) |has| |#2| (-554 (-473))) (((-801 (-327))) |has| |#2| (-554 (-801 (-327)))) (((-801 (-484))) |has| |#2| (-554 (-801 (-484)))))
((($) . T))
-(((|#2| (-197 (-3953 |#1|) (-695))) . T))
+(((|#2| (-197 (-3954 |#1|) (-695))) . T))
(((|#2|) . T))
((((-773)) . T))
((($) . T) (((-484)) . T) (((-347 (-484))) |has| |#2| (-38 (-347 (-484)))) ((|#2|) . T))
@@ -534,7 +534,7 @@
((((-347 (-484))) |has| |#2| (-38 (-347 (-484)))) ((|#2|) |has| |#2| (-146)) (($) OR (|has| |#2| (-389)) (|has| |#2| (-495)) (|has| |#2| (-822))))
((((-347 (-484))) |has| |#2| (-38 (-347 (-484)))) ((|#2|) |has| |#2| (-146)) (($) OR (|has| |#2| (-389)) (|has| |#2| (-495)) (|has| |#2| (-822))))
((((-347 (-484))) |has| |#2| (-38 (-347 (-484)))) ((|#2|) |has| |#2| (-146)) (($) OR (|has| |#2| (-389)) (|has| |#2| (-495)) (|has| |#2| (-822))))
-(((|#2| (-197 (-3953 |#1|) (-695))) . T))
+(((|#2| (-197 (-3954 |#1|) (-695))) . T))
(((|#2|) . T))
((($) . T) (((-347 (-484))) |has| |#2| (-38 (-347 (-484)))) ((|#2|) . T) (((-484)) |has| |#2| (-581 (-484))))
(((|#2|) . T) (((-484)) |has| |#2| (-581 (-484))))
@@ -547,7 +547,7 @@
(|has| |#2| (-822))
((((-347 (-484))) |has| |#2| (-951 (-347 (-484)))) (((-484)) |has| |#2| (-951 (-484))) ((|#2|) . T) (((-774 |#1|)) . T))
((((-484)) . T) (((-347 (-484))) OR (|has| |#2| (-38 (-347 (-484)))) (|has| |#2| (-951 (-347 (-484))))) ((|#2|) . T) (($) OR (|has| |#2| (-389)) (|has| |#2| (-495)) (|has| |#2| (-822))) (((-774 |#1|)) . T))
-(((|#2| (-197 (-3953 |#1|) (-695)) (-774 |#1|)) . T))
+(((|#2| (-197 (-3954 |#1|) (-695)) (-774 |#1|)) . T))
((((-773)) . T))
((((-444)) . T))
((((-157)) . T) (((-773)) . T))
@@ -720,13 +720,13 @@
(((|#1| |#2|) . T))
(((|#1| |#2|) . T))
(((|#1| |#2|) . T))
-((((-2 (|:| -3856 |#1|) (|:| |entry| |#2|))) . T))
-((((-2 (|:| -3856 |#1|) (|:| |entry| |#2|))) . T))
-(((|#2|) . T) (((-2 (|:| -3856 |#1|) (|:| |entry| |#2|))) . T))
-(((|#2| |#2|) -12 (|has| |#2| (-259 |#2|)) (|has| |#2| (-1013))) (((-2 (|:| -3856 |#1|) (|:| |entry| |#2|)) (-2 (|:| -3856 |#1|) (|:| |entry| |#2|))) |has| (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)) (-259 (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)))))
-(((|#2|) -12 (|has| |#2| (-259 |#2|)) (|has| |#2| (-1013))) (((-2 (|:| -3856 |#1|) (|:| |entry| |#2|))) |has| (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)) (-259 (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)))))
-((((-2 (|:| -3856 |#1|) (|:| |entry| |#2|))) . T))
-((((-2 (|:| -3856 |#1|) (|:| |entry| |#2|))) . T))
+((((-2 (|:| -3857 |#1|) (|:| |entry| |#2|))) . T))
+((((-2 (|:| -3857 |#1|) (|:| |entry| |#2|))) . T))
+(((|#2|) . T) (((-2 (|:| -3857 |#1|) (|:| |entry| |#2|))) . T))
+(((|#2| |#2|) -12 (|has| |#2| (-259 |#2|)) (|has| |#2| (-1013))) (((-2 (|:| -3857 |#1|) (|:| |entry| |#2|)) (-2 (|:| -3857 |#1|) (|:| |entry| |#2|))) |has| (-2 (|:| -3857 |#1|) (|:| |entry| |#2|)) (-259 (-2 (|:| -3857 |#1|) (|:| |entry| |#2|)))))
+(((|#2|) -12 (|has| |#2| (-259 |#2|)) (|has| |#2| (-1013))) (((-2 (|:| -3857 |#1|) (|:| |entry| |#2|))) |has| (-2 (|:| -3857 |#1|) (|:| |entry| |#2|)) (-259 (-2 (|:| -3857 |#1|) (|:| |entry| |#2|)))))
+((((-2 (|:| -3857 |#1|) (|:| |entry| |#2|))) . T))
+((((-2 (|:| -3857 |#1|) (|:| |entry| |#2|))) . T))
(((|#1| |#2|) . T))
((((-773)) . T))
((((-1094)) . T))
@@ -1331,13 +1331,13 @@
(((|#1| |#2|) . T))
(((|#1| |#2|) . T))
(((|#1| |#2|) . T))
-((((-2 (|:| -3856 |#1|) (|:| |entry| |#2|))) . T))
-((((-2 (|:| -3856 |#1|) (|:| |entry| |#2|))) . T))
-(((|#2|) . T) (((-2 (|:| -3856 |#1|) (|:| |entry| |#2|))) . T))
-(((|#2| |#2|) -12 (|has| |#2| (-259 |#2|)) (|has| |#2| (-1013))) (((-2 (|:| -3856 |#1|) (|:| |entry| |#2|)) (-2 (|:| -3856 |#1|) (|:| |entry| |#2|))) |has| (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)) (-259 (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)))))
-(((|#2|) -12 (|has| |#2| (-259 |#2|)) (|has| |#2| (-1013))) (((-2 (|:| -3856 |#1|) (|:| |entry| |#2|))) |has| (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)) (-259 (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)))))
-((((-2 (|:| -3856 |#1|) (|:| |entry| |#2|))) . T))
-((((-2 (|:| -3856 |#1|) (|:| |entry| |#2|))) . T))
+((((-2 (|:| -3857 |#1|) (|:| |entry| |#2|))) . T))
+((((-2 (|:| -3857 |#1|) (|:| |entry| |#2|))) . T))
+(((|#2|) . T) (((-2 (|:| -3857 |#1|) (|:| |entry| |#2|))) . T))
+(((|#2| |#2|) -12 (|has| |#2| (-259 |#2|)) (|has| |#2| (-1013))) (((-2 (|:| -3857 |#1|) (|:| |entry| |#2|)) (-2 (|:| -3857 |#1|) (|:| |entry| |#2|))) |has| (-2 (|:| -3857 |#1|) (|:| |entry| |#2|)) (-259 (-2 (|:| -3857 |#1|) (|:| |entry| |#2|)))))
+(((|#2|) -12 (|has| |#2| (-259 |#2|)) (|has| |#2| (-1013))) (((-2 (|:| -3857 |#1|) (|:| |entry| |#2|))) |has| (-2 (|:| -3857 |#1|) (|:| |entry| |#2|)) (-259 (-2 (|:| -3857 |#1|) (|:| |entry| |#2|)))))
+((((-2 (|:| -3857 |#1|) (|:| |entry| |#2|))) . T))
+((((-2 (|:| -3857 |#1|) (|:| |entry| |#2|))) . T))
(((|#1| |#2|) . T))
(((|#1| |#2| |#3| |#4|) . T))
((((-473)) |has| |#4| (-554 (-473))))
@@ -1367,17 +1367,17 @@
(((|#1| |#2|) . T))
(((|#1| |#2|) . T))
(((|#1| |#2|) . T))
-((((-2 (|:| -3856 |#1|) (|:| |entry| |#2|))) . T))
-((((-2 (|:| -3856 |#1|) (|:| |entry| |#2|))) . T))
-(((|#2|) . T) (((-2 (|:| -3856 |#1|) (|:| |entry| |#2|))) . T))
-(((|#2| |#2|) -12 (|has| |#2| (-259 |#2|)) (|has| |#2| (-1013))) (((-2 (|:| -3856 |#1|) (|:| |entry| |#2|)) (-2 (|:| -3856 |#1|) (|:| |entry| |#2|))) |has| (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)) (-259 (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)))))
-(((|#2|) -12 (|has| |#2| (-259 |#2|)) (|has| |#2| (-1013))) (((-2 (|:| -3856 |#1|) (|:| |entry| |#2|))) |has| (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)) (-259 (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)))))
-((((-2 (|:| -3856 |#1|) (|:| |entry| |#2|))) . T))
-((((-2 (|:| -3856 |#1|) (|:| |entry| |#2|))) . T))
+((((-2 (|:| -3857 |#1|) (|:| |entry| |#2|))) . T))
+((((-2 (|:| -3857 |#1|) (|:| |entry| |#2|))) . T))
+(((|#2|) . T) (((-2 (|:| -3857 |#1|) (|:| |entry| |#2|))) . T))
+(((|#2| |#2|) -12 (|has| |#2| (-259 |#2|)) (|has| |#2| (-1013))) (((-2 (|:| -3857 |#1|) (|:| |entry| |#2|)) (-2 (|:| -3857 |#1|) (|:| |entry| |#2|))) |has| (-2 (|:| -3857 |#1|) (|:| |entry| |#2|)) (-259 (-2 (|:| -3857 |#1|) (|:| |entry| |#2|)))))
+(((|#2|) -12 (|has| |#2| (-259 |#2|)) (|has| |#2| (-1013))) (((-2 (|:| -3857 |#1|) (|:| |entry| |#2|))) |has| (-2 (|:| -3857 |#1|) (|:| |entry| |#2|)) (-259 (-2 (|:| -3857 |#1|) (|:| |entry| |#2|)))))
+((((-2 (|:| -3857 |#1|) (|:| |entry| |#2|))) . T))
+((((-2 (|:| -3857 |#1|) (|:| |entry| |#2|))) . T))
(((|#1| |#2|) . T))
((((-473)) |has| |#2| (-554 (-473))) (((-801 (-327))) |has| |#2| (-554 (-801 (-327)))) (((-801 (-484))) |has| |#2| (-554 (-801 (-484)))))
((($) . T))
-(((|#2| (-419 (-3953 |#1|) (-695))) . T))
+(((|#2| (-419 (-3954 |#1|) (-695))) . T))
(((|#2|) . T))
((((-773)) . T))
((($) . T) (((-484)) . T) (((-347 (-484))) |has| |#2| (-38 (-347 (-484)))) ((|#2|) . T))
@@ -1392,7 +1392,7 @@
((((-347 (-484))) |has| |#2| (-38 (-347 (-484)))) ((|#2|) |has| |#2| (-146)) (($) OR (|has| |#2| (-389)) (|has| |#2| (-495)) (|has| |#2| (-822))))
((((-347 (-484))) |has| |#2| (-38 (-347 (-484)))) ((|#2|) |has| |#2| (-146)) (($) OR (|has| |#2| (-389)) (|has| |#2| (-495)) (|has| |#2| (-822))))
((((-347 (-484))) |has| |#2| (-38 (-347 (-484)))) ((|#2|) |has| |#2| (-146)) (($) OR (|has| |#2| (-389)) (|has| |#2| (-495)) (|has| |#2| (-822))))
-(((|#2| (-419 (-3953 |#1|) (-695))) . T))
+(((|#2| (-419 (-3954 |#1|) (-695))) . T))
(((|#2|) . T))
((($) . T) (((-347 (-484))) |has| |#2| (-38 (-347 (-484)))) ((|#2|) . T) (((-484)) |has| |#2| (-581 (-484))))
(((|#2|) . T) (((-484)) |has| |#2| (-581 (-484))))
@@ -1405,7 +1405,7 @@
(|has| |#2| (-822))
((((-347 (-484))) |has| |#2| (-951 (-347 (-484)))) (((-484)) |has| |#2| (-951 (-484))) ((|#2|) . T) (((-774 |#1|)) . T))
((((-484)) . T) (((-347 (-484))) OR (|has| |#2| (-38 (-347 (-484)))) (|has| |#2| (-951 (-347 (-484))))) ((|#2|) . T) (($) OR (|has| |#2| (-389)) (|has| |#2| (-495)) (|has| |#2| (-822))) (((-774 |#1|)) . T))
-(((|#2| (-419 (-3953 |#1|) (-695)) (-774 |#1|)) . T))
+(((|#2| (-419 (-3954 |#1|) (-695)) (-774 |#1|)) . T))
(OR (|has| |#2| (-21)) (|has| |#2| (-146)) (|has| |#2| (-311)) (|has| |#2| (-962)))
(OR (|has| |#2| (-21)) (|has| |#2| (-23)) (|has| |#2| (-104)) (|has| |#2| (-146)) (|has| |#2| (-311)) (|has| |#2| (-718)) (|has| |#2| (-962)))
(OR (|has| |#2| (-21)) (|has| |#2| (-23)) (|has| |#2| (-25)) (|has| |#2| (-104)) (|has| |#2| (-146)) (|has| |#2| (-311)) (|has| |#2| (-317)) (|has| |#2| (-664)) (|has| |#2| (-718)) (|has| |#2| (-757)) (|has| |#2| (-962)) (|has| |#2| (-1013)))
@@ -1657,13 +1657,13 @@
(((|#1| |#2|) . T))
(((|#1| |#2|) . T))
(((|#1| |#2|) . T))
-((((-2 (|:| -3856 |#1|) (|:| |entry| |#2|))) . T))
-((((-2 (|:| -3856 |#1|) (|:| |entry| |#2|))) . T))
-(((|#2|) . T) (((-2 (|:| -3856 |#1|) (|:| |entry| |#2|))) . T))
-(((|#2| |#2|) -12 (|has| |#2| (-259 |#2|)) (|has| |#2| (-1013))) (((-2 (|:| -3856 |#1|) (|:| |entry| |#2|)) (-2 (|:| -3856 |#1|) (|:| |entry| |#2|))) |has| (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)) (-259 (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)))))
-(((|#2|) -12 (|has| |#2| (-259 |#2|)) (|has| |#2| (-1013))) (((-2 (|:| -3856 |#1|) (|:| |entry| |#2|))) |has| (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)) (-259 (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)))))
-((((-2 (|:| -3856 |#1|) (|:| |entry| |#2|))) . T))
-((((-2 (|:| -3856 |#1|) (|:| |entry| |#2|))) . T))
+((((-2 (|:| -3857 |#1|) (|:| |entry| |#2|))) . T))
+((((-2 (|:| -3857 |#1|) (|:| |entry| |#2|))) . T))
+(((|#2|) . T) (((-2 (|:| -3857 |#1|) (|:| |entry| |#2|))) . T))
+(((|#2| |#2|) -12 (|has| |#2| (-259 |#2|)) (|has| |#2| (-1013))) (((-2 (|:| -3857 |#1|) (|:| |entry| |#2|)) (-2 (|:| -3857 |#1|) (|:| |entry| |#2|))) |has| (-2 (|:| -3857 |#1|) (|:| |entry| |#2|)) (-259 (-2 (|:| -3857 |#1|) (|:| |entry| |#2|)))))
+(((|#2|) -12 (|has| |#2| (-259 |#2|)) (|has| |#2| (-1013))) (((-2 (|:| -3857 |#1|) (|:| |entry| |#2|))) |has| (-2 (|:| -3857 |#1|) (|:| |entry| |#2|)) (-259 (-2 (|:| -3857 |#1|) (|:| |entry| |#2|)))))
+((((-2 (|:| -3857 |#1|) (|:| |entry| |#2|))) . T))
+((((-2 (|:| -3857 |#1|) (|:| |entry| |#2|))) . T))
(((|#1| |#2|) . T))
((($) . T))
((($ $) . T))
@@ -1812,16 +1812,16 @@
((((-1072) |#1|) . T))
((((-1072) |#1|) . T))
((((-1072) |#1|) . T))
-((((-2 (|:| -3856 (-1072)) (|:| |entry| |#1|))) . T))
-((((-2 (|:| -3856 (-1072)) (|:| |entry| |#1|))) . T))
-(((|#1|) . T) (((-2 (|:| -3856 (-1072)) (|:| |entry| |#1|))) . T))
-(((|#1| |#1|) -12 (|has| |#1| (-259 |#1|)) (|has| |#1| (-1013))) (((-2 (|:| -3856 (-1072)) (|:| |entry| |#1|)) (-2 (|:| -3856 (-1072)) (|:| |entry| |#1|))) |has| (-2 (|:| -3856 (-1072)) (|:| |entry| |#1|)) (-259 (-2 (|:| -3856 (-1072)) (|:| |entry| |#1|)))))
-(((|#1|) -12 (|has| |#1| (-259 |#1|)) (|has| |#1| (-1013))) (((-2 (|:| -3856 (-1072)) (|:| |entry| |#1|))) |has| (-2 (|:| -3856 (-1072)) (|:| |entry| |#1|)) (-259 (-2 (|:| -3856 (-1072)) (|:| |entry| |#1|)))))
-((((-2 (|:| -3856 (-1072)) (|:| |entry| |#1|))) . T))
-((((-2 (|:| -3856 (-1072)) (|:| |entry| |#1|))) . T))
+((((-2 (|:| -3857 (-1072)) (|:| |entry| |#1|))) . T))
+((((-2 (|:| -3857 (-1072)) (|:| |entry| |#1|))) . T))
+(((|#1|) . T) (((-2 (|:| -3857 (-1072)) (|:| |entry| |#1|))) . T))
+(((|#1| |#1|) -12 (|has| |#1| (-259 |#1|)) (|has| |#1| (-1013))) (((-2 (|:| -3857 (-1072)) (|:| |entry| |#1|)) (-2 (|:| -3857 (-1072)) (|:| |entry| |#1|))) |has| (-2 (|:| -3857 (-1072)) (|:| |entry| |#1|)) (-259 (-2 (|:| -3857 (-1072)) (|:| |entry| |#1|)))))
+(((|#1|) -12 (|has| |#1| (-259 |#1|)) (|has| |#1| (-1013))) (((-2 (|:| -3857 (-1072)) (|:| |entry| |#1|))) |has| (-2 (|:| -3857 (-1072)) (|:| |entry| |#1|)) (-259 (-2 (|:| -3857 (-1072)) (|:| |entry| |#1|)))))
+((((-2 (|:| -3857 (-1072)) (|:| |entry| |#1|))) . T))
+((((-2 (|:| -3857 (-1072)) (|:| |entry| |#1|))) . T))
((((-1072) |#1|) . T))
((((-773)) . T))
-((((-335) (-2 (|:| -3856 (-1072)) (|:| |entry| |#1|))) . T))
+((((-335) (-2 (|:| -3857 (-1072)) (|:| |entry| |#1|))) . T))
((((-473)) |has| |#1| (-554 (-473))) (((-801 (-327))) |has| |#1| (-554 (-801 (-327)))) (((-801 (-484))) |has| |#1| (-554 (-801 (-484)))))
(((|#1|) . T))
((((-773)) . T))
@@ -1878,13 +1878,13 @@
((((-1089) (-51)) . T) (((-1072) (-51)) . T))
((((-1072) (-51)) . T))
((((-1072) (-51)) . T))
-((((-2 (|:| -3856 (-1072)) (|:| |entry| (-51)))) . T))
-((((-2 (|:| -3856 (-1072)) (|:| |entry| (-51)))) . T))
-((((-51)) . T) (((-2 (|:| -3856 (-1072)) (|:| |entry| (-51)))) . T))
-((((-2 (|:| -3856 (-1072)) (|:| |entry| (-51))) (-2 (|:| -3856 (-1072)) (|:| |entry| (-51)))) |has| (-2 (|:| -3856 (-1072)) (|:| |entry| (-51))) (-259 (-2 (|:| -3856 (-1072)) (|:| |entry| (-51))))))
-((((-2 (|:| -3856 (-1072)) (|:| |entry| (-51)))) |has| (-2 (|:| -3856 (-1072)) (|:| |entry| (-51))) (-259 (-2 (|:| -3856 (-1072)) (|:| |entry| (-51))))))
-((((-2 (|:| -3856 (-1072)) (|:| |entry| (-51)))) . T))
-((((-2 (|:| -3856 (-1072)) (|:| |entry| (-51)))) . T))
+((((-2 (|:| -3857 (-1072)) (|:| |entry| (-51)))) . T))
+((((-2 (|:| -3857 (-1072)) (|:| |entry| (-51)))) . T))
+((((-51)) . T) (((-2 (|:| -3857 (-1072)) (|:| |entry| (-51)))) . T))
+((((-2 (|:| -3857 (-1072)) (|:| |entry| (-51))) (-2 (|:| -3857 (-1072)) (|:| |entry| (-51)))) |has| (-2 (|:| -3857 (-1072)) (|:| |entry| (-51))) (-259 (-2 (|:| -3857 (-1072)) (|:| |entry| (-51))))))
+((((-2 (|:| -3857 (-1072)) (|:| |entry| (-51)))) |has| (-2 (|:| -3857 (-1072)) (|:| |entry| (-51))) (-259 (-2 (|:| -3857 (-1072)) (|:| |entry| (-51))))))
+((((-2 (|:| -3857 (-1072)) (|:| |entry| (-51)))) . T))
+((((-2 (|:| -3857 (-1072)) (|:| |entry| (-51)))) . T))
((((-1072) (-51)) . T))
((((-484) |#1|) |has| |#2| (-358 |#1|)))
(((|#1|) OR (|has| |#2| (-315 |#1|)) (|has| |#2| (-358 |#1|))))
@@ -2035,7 +2035,7 @@
(((|#2|) . T))
(((|#2|) . T))
(((|#2|) . T))
-(((|#2|) |has| |#2| (-6 (-3993 "*"))))
+(((|#2|) |has| |#2| (-6 (-3994 "*"))))
(((|#2| |#2|) . T))
(((|#2|) . T))
(((|#2|) . T))
@@ -2139,9 +2139,9 @@
((($) . T))
(|has| |#1| (-1065))
(((|#1|) . T))
-((((-2 (|:| -2398 |#1|) (|:| -2399 |#2|))) . T))
-((((-2 (|:| -2398 |#1|) (|:| -2399 |#2|))) . T))
-((((-2 (|:| -2398 |#1|) (|:| -2399 |#2|))) . T) (((-773)) . T))
+((((-2 (|:| -2399 |#1|) (|:| -2400 |#2|))) . T))
+((((-2 (|:| -2399 |#1|) (|:| -2400 |#2|))) . T))
+((((-2 (|:| -2399 |#1|) (|:| -2400 |#2|))) . T) (((-773)) . T))
(((|#1|) |has| |#1| (-146)))
(((|#1|) |has| |#1| (-146)))
(((|#1|) |has| |#1| (-146)))
@@ -3259,14 +3259,14 @@
((((-773)) . T))
((((-1053 |#1| |#2|)) . T))
((((-473)) |has| |#2| (-554 (-473))))
-(((|#2|) |has| |#2| (-6 (-3993 "*"))))
+(((|#2|) |has| |#2| (-6 (-3994 "*"))))
(((|#2| |#2|) . T))
(((|#2|) . T))
(((|#2|) . T))
((((-631 |#2|)) . T) (((-773)) . T))
((($) . T) (((-484)) . T) ((|#2|) . T))
-(((|#2|) OR (|has| |#2| (-6 (-3993 "*"))) (|has| |#2| (-146))))
-(((|#2|) OR (|has| |#2| (-6 (-3993 "*"))) (|has| |#2| (-146))))
+(((|#2|) OR (|has| |#2| (-6 (-3994 "*"))) (|has| |#2| (-146))))
+(((|#2|) OR (|has| |#2| (-6 (-3994 "*"))) (|has| |#2| (-146))))
(((|#2|) . T))
((((-1089)) |has| |#2| (-810 (-1089))))
((((-1089)) OR (|has| |#2| (-810 (-1089))) (|has| |#2| (-812 (-1089)))))
@@ -3309,13 +3309,13 @@
(((|#1| |#2|) . T))
(((|#1| |#2|) . T))
(((|#1| |#2|) . T))
-((((-2 (|:| -3856 |#1|) (|:| |entry| |#2|))) . T))
-((((-2 (|:| -3856 |#1|) (|:| |entry| |#2|))) . T))
-(((|#2|) . T) (((-2 (|:| -3856 |#1|) (|:| |entry| |#2|))) . T))
-(((|#2| |#2|) -12 (|has| |#2| (-259 |#2|)) (|has| |#2| (-1013))) (((-2 (|:| -3856 |#1|) (|:| |entry| |#2|)) (-2 (|:| -3856 |#1|) (|:| |entry| |#2|))) |has| (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)) (-259 (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)))))
-(((|#2|) -12 (|has| |#2| (-259 |#2|)) (|has| |#2| (-1013))) (((-2 (|:| -3856 |#1|) (|:| |entry| |#2|))) |has| (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)) (-259 (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)))))
-((((-2 (|:| -3856 |#1|) (|:| |entry| |#2|))) . T))
-((((-2 (|:| -3856 |#1|) (|:| |entry| |#2|))) . T))
+((((-2 (|:| -3857 |#1|) (|:| |entry| |#2|))) . T))
+((((-2 (|:| -3857 |#1|) (|:| |entry| |#2|))) . T))
+(((|#2|) . T) (((-2 (|:| -3857 |#1|) (|:| |entry| |#2|))) . T))
+(((|#2| |#2|) -12 (|has| |#2| (-259 |#2|)) (|has| |#2| (-1013))) (((-2 (|:| -3857 |#1|) (|:| |entry| |#2|)) (-2 (|:| -3857 |#1|) (|:| |entry| |#2|))) |has| (-2 (|:| -3857 |#1|) (|:| |entry| |#2|)) (-259 (-2 (|:| -3857 |#1|) (|:| |entry| |#2|)))))
+(((|#2|) -12 (|has| |#2| (-259 |#2|)) (|has| |#2| (-1013))) (((-2 (|:| -3857 |#1|) (|:| |entry| |#2|))) |has| (-2 (|:| -3857 |#1|) (|:| |entry| |#2|)) (-259 (-2 (|:| -3857 |#1|) (|:| |entry| |#2|)))))
+((((-2 (|:| -3857 |#1|) (|:| |entry| |#2|))) . T))
+((((-2 (|:| -3857 |#1|) (|:| |entry| |#2|))) . T))
(((|#1| |#2|) . T))
((((-1094)) . T))
((((-773)) . T) (((-1094)) . T))
@@ -3351,13 +3351,13 @@
((((-1072) |#1|) . T))
((((-1072) |#1|) . T))
((((-1072) |#1|) . T))
-((((-2 (|:| -3856 (-1072)) (|:| |entry| |#1|))) . T))
-((((-2 (|:| -3856 (-1072)) (|:| |entry| |#1|))) . T))
-(((|#1|) . T) (((-2 (|:| -3856 (-1072)) (|:| |entry| |#1|))) . T))
-(((|#1| |#1|) -12 (|has| |#1| (-259 |#1|)) (|has| |#1| (-1013))) (((-2 (|:| -3856 (-1072)) (|:| |entry| |#1|)) (-2 (|:| -3856 (-1072)) (|:| |entry| |#1|))) |has| (-2 (|:| -3856 (-1072)) (|:| |entry| |#1|)) (-259 (-2 (|:| -3856 (-1072)) (|:| |entry| |#1|)))))
-(((|#1|) -12 (|has| |#1| (-259 |#1|)) (|has| |#1| (-1013))) (((-2 (|:| -3856 (-1072)) (|:| |entry| |#1|))) |has| (-2 (|:| -3856 (-1072)) (|:| |entry| |#1|)) (-259 (-2 (|:| -3856 (-1072)) (|:| |entry| |#1|)))))
-((((-2 (|:| -3856 (-1072)) (|:| |entry| |#1|))) . T))
-((((-2 (|:| -3856 (-1072)) (|:| |entry| |#1|))) . T))
+((((-2 (|:| -3857 (-1072)) (|:| |entry| |#1|))) . T))
+((((-2 (|:| -3857 (-1072)) (|:| |entry| |#1|))) . T))
+(((|#1|) . T) (((-2 (|:| -3857 (-1072)) (|:| |entry| |#1|))) . T))
+(((|#1| |#1|) -12 (|has| |#1| (-259 |#1|)) (|has| |#1| (-1013))) (((-2 (|:| -3857 (-1072)) (|:| |entry| |#1|)) (-2 (|:| -3857 (-1072)) (|:| |entry| |#1|))) |has| (-2 (|:| -3857 (-1072)) (|:| |entry| |#1|)) (-259 (-2 (|:| -3857 (-1072)) (|:| |entry| |#1|)))))
+(((|#1|) -12 (|has| |#1| (-259 |#1|)) (|has| |#1| (-1013))) (((-2 (|:| -3857 (-1072)) (|:| |entry| |#1|))) |has| (-2 (|:| -3857 (-1072)) (|:| |entry| |#1|)) (-259 (-2 (|:| -3857 (-1072)) (|:| |entry| |#1|)))))
+((((-2 (|:| -3857 (-1072)) (|:| |entry| |#1|))) . T))
+((((-2 (|:| -3857 (-1072)) (|:| |entry| |#1|))) . T))
((((-1072) |#1|) . T))
((((-773)) . T))
((((-773)) . T))
@@ -3564,13 +3564,13 @@
(((|#1| |#2|) . T))
(((|#1| |#2|) . T))
(((|#1| |#2|) . T))
-((((-2 (|:| -3856 |#1|) (|:| |entry| |#2|))) . T))
-((((-2 (|:| -3856 |#1|) (|:| |entry| |#2|))) . T))
-(((|#2|) . T) (((-2 (|:| -3856 |#1|) (|:| |entry| |#2|))) . T))
-(((|#2| |#2|) -12 (|has| |#2| (-259 |#2|)) (|has| |#2| (-1013))) (((-2 (|:| -3856 |#1|) (|:| |entry| |#2|)) (-2 (|:| -3856 |#1|) (|:| |entry| |#2|))) |has| (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)) (-259 (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)))))
-(((|#2|) -12 (|has| |#2| (-259 |#2|)) (|has| |#2| (-1013))) (((-2 (|:| -3856 |#1|) (|:| |entry| |#2|))) |has| (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)) (-259 (-2 (|:| -3856 |#1|) (|:| |entry| |#2|)))))
-((((-2 (|:| -3856 |#1|) (|:| |entry| |#2|))) . T))
-((((-2 (|:| -3856 |#1|) (|:| |entry| |#2|))) . T))
+((((-2 (|:| -3857 |#1|) (|:| |entry| |#2|))) . T))
+((((-2 (|:| -3857 |#1|) (|:| |entry| |#2|))) . T))
+(((|#2|) . T) (((-2 (|:| -3857 |#1|) (|:| |entry| |#2|))) . T))
+(((|#2| |#2|) -12 (|has| |#2| (-259 |#2|)) (|has| |#2| (-1013))) (((-2 (|:| -3857 |#1|) (|:| |entry| |#2|)) (-2 (|:| -3857 |#1|) (|:| |entry| |#2|))) |has| (-2 (|:| -3857 |#1|) (|:| |entry| |#2|)) (-259 (-2 (|:| -3857 |#1|) (|:| |entry| |#2|)))))
+(((|#2|) -12 (|has| |#2| (-259 |#2|)) (|has| |#2| (-1013))) (((-2 (|:| -3857 |#1|) (|:| |entry| |#2|))) |has| (-2 (|:| -3857 |#1|) (|:| |entry| |#2|)) (-259 (-2 (|:| -3857 |#1|) (|:| |entry| |#2|)))))
+((((-2 (|:| -3857 |#1|) (|:| |entry| |#2|))) . T))
+((((-2 (|:| -3857 |#1|) (|:| |entry| |#2|))) . T))
(((|#1| |#2|) . T))
((((-773)) . T))
(((|#1|) . T))
diff --git a/src/share/algebra/compress.daase b/src/share/algebra/compress.daase
index a1618df5..269f49ab 100644
--- a/src/share/algebra/compress.daase
+++ b/src/share/algebra/compress.daase
@@ -1,6 +1,6 @@
-(30 . 3576910160)
-(3994 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain|
+(30 . 3577105534)
+(3995 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain|
ATTRIBUTE |package| |domain| |category| CATEGORY |nobranch| AND |Join|
|ofType| SIGNATURE "failed" "algebra" |OneDimensionalArrayAggregate&|
|OneDimensionalArrayAggregate| |AbelianGroup&| |AbelianGroup| |AbelianMonoid&|
@@ -552,8 +552,8 @@
|relationsIdeal| |saturate| |groebner?| |groebnerIdeal| |ideal| |leadingIdeal|
|backOldPos| |generalPosition| |quotient| |zeroDim?| |inRadical?| |in?|
|element?| |zeroDimPrime?| |zeroDimPrimary?| |radical| |primaryDecomp|
- |contract| |gensym| |leadingSupport| |term| |shrinkable| |physicalLength!|
- |physicalLength| |flexibleArray| |elseBranch| |thenBranch|
+ |contract| |gensym| |leadingSupport| |combineWithIf| |term| |shrinkable|
+ |physicalLength!| |physicalLength| |flexibleArray| |elseBranch| |thenBranch|
|generalizedInverse| |imports| |sequence| |readBytes!| |readUInt32!|
|readInt32!| |readUInt16!| |readInt16!| |readUInt8!| |readInt8!| |readByte!|
|setFieldInfo| |pol| |xn| |dAndcExp| |repSq| |expPot| |qPot| |lookup|
diff --git a/src/share/algebra/interp.daase b/src/share/algebra/interp.daase
index 0d908030..4417a140 100644
--- a/src/share/algebra/interp.daase
+++ b/src/share/algebra/interp.daase
@@ -1,687 +1,687 @@
-(2806036 . 3576910170)
-((-1730 (((-85) (-1 (-85) |#2| |#2|) $) 86 T ELT) (((-85) $) NIL T ELT)) (-1728 (($ (-1 (-85) |#2| |#2|) $) 18 T ELT) (($ $) NIL T ELT)) (-3784 ((|#2| $ (-484) |#2|) NIL T ELT) ((|#2| $ (-1145 (-484)) |#2|) 44 T ELT)) (-2295 (($ $) 80 T ELT)) (-3838 ((|#2| (-1 |#2| |#2| |#2|) $ |#2| |#2|) 52 T ELT) ((|#2| (-1 |#2| |#2| |#2|) $ |#2|) 50 T ELT) ((|#2| (-1 |#2| |#2| |#2|) $) 49 T ELT)) (-3415 (((-484) (-1 (-85) |#2|) $) 27 T ELT) (((-484) |#2| $) NIL T ELT) (((-484) |#2| $ (-484)) 96 T ELT)) (-2887 (((-584 |#2|) $) 13 T ELT)) (-3514 (($ (-1 (-85) |#2| |#2|) $ $) 64 T ELT) (($ $ $) NIL T ELT)) (-1947 (($ (-1 |#2| |#2|) $) 37 T ELT)) (-3954 (($ (-1 |#2| |#2|) $) NIL T ELT) (($ (-1 |#2| |#2| |#2|) $ $) 60 T ELT)) (-2302 (($ |#2| $ (-484)) NIL T ELT) (($ $ $ (-484)) 67 T ELT)) (-1352 (((-3 |#2| "failed") (-1 (-85) |#2|) $) 29 T ELT)) (-1945 (((-85) (-1 (-85) |#2|) $) 23 T ELT)) (-3796 ((|#2| $ (-484) |#2|) NIL T ELT) ((|#2| $ (-484)) NIL T ELT) (($ $ (-1145 (-484))) 66 T ELT)) (-2303 (($ $ (-484)) 76 T ELT) (($ $ (-1145 (-484))) 75 T ELT)) (-1944 (((-695) (-1 (-85) |#2|) $) 34 T ELT) (((-695) |#2| $) NIL T ELT)) (-1729 (($ $ $ (-484)) 69 T ELT)) (-3396 (($ $) 68 T ELT)) (-3526 (($ (-584 |#2|)) 73 T ELT)) (-3798 (($ $ |#2|) NIL T ELT) (($ |#2| $) NIL T ELT) (($ $ $) 87 T ELT) (($ (-584 $)) 85 T ELT)) (-3942 (((-773) $) 92 T ELT)) (-1946 (((-85) (-1 (-85) |#2|) $) 22 T ELT)) (-3054 (((-85) $ $) 95 T ELT)) (-2683 (((-85) $ $) 99 T ELT)))
-(((-18 |#1| |#2|) (-10 -7 (-15 -3054 ((-85) |#1| |#1|)) (-15 -3942 ((-773) |#1|)) (-15 -2683 ((-85) |#1| |#1|)) (-15 -1728 (|#1| |#1|)) (-15 -1728 (|#1| (-1 (-85) |#2| |#2|) |#1|)) (-15 -2295 (|#1| |#1|)) (-15 -1729 (|#1| |#1| |#1| (-484))) (-15 -1730 ((-85) |#1|)) (-15 -3514 (|#1| |#1| |#1|)) (-15 -3415 ((-484) |#2| |#1| (-484))) (-15 -3415 ((-484) |#2| |#1|)) (-15 -3415 ((-484) (-1 (-85) |#2|) |#1|)) (-15 -1730 ((-85) (-1 (-85) |#2| |#2|) |#1|)) (-15 -3514 (|#1| (-1 (-85) |#2| |#2|) |#1| |#1|)) (-15 -3784 (|#2| |#1| (-1145 (-484)) |#2|)) (-15 -2302 (|#1| |#1| |#1| (-484))) (-15 -2302 (|#1| |#2| |#1| (-484))) (-15 -2303 (|#1| |#1| (-1145 (-484)))) (-15 -2303 (|#1| |#1| (-484))) (-15 -3954 (|#1| (-1 |#2| |#2| |#2|) |#1| |#1|)) (-15 -3798 (|#1| (-584 |#1|))) (-15 -3798 (|#1| |#1| |#1|)) (-15 -3798 (|#1| |#2| |#1|)) (-15 -3798 (|#1| |#1| |#2|)) (-15 -3796 (|#1| |#1| (-1145 (-484)))) (-15 -3526 (|#1| (-584 |#2|))) (-15 -1352 ((-3 |#2| "failed") (-1 (-85) |#2|) |#1|)) (-15 -3838 (|#2| (-1 |#2| |#2| |#2|) |#1|)) (-15 -3838 (|#2| (-1 |#2| |#2| |#2|) |#1| |#2|)) (-15 -3838 (|#2| (-1 |#2| |#2| |#2|) |#1| |#2| |#2|)) (-15 -3796 (|#2| |#1| (-484))) (-15 -3796 (|#2| |#1| (-484) |#2|)) (-15 -3784 (|#2| |#1| (-484) |#2|)) (-15 -1944 ((-695) |#2| |#1|)) (-15 -2887 ((-584 |#2|) |#1|)) (-15 -1944 ((-695) (-1 (-85) |#2|) |#1|)) (-15 -1945 ((-85) (-1 (-85) |#2|) |#1|)) (-15 -1946 ((-85) (-1 (-85) |#2|) |#1|)) (-15 -1947 (|#1| (-1 |#2| |#2|) |#1|)) (-15 -3954 (|#1| (-1 |#2| |#2|) |#1|)) (-15 -3396 (|#1| |#1|))) (-19 |#2|) (-1128)) (T -18))
+(2806310 . 3577105543)
+((-1730 (((-85) (-1 (-85) |#2| |#2|) $) 86 T ELT) (((-85) $) NIL T ELT)) (-1728 (($ (-1 (-85) |#2| |#2|) $) 18 T ELT) (($ $) NIL T ELT)) (-3785 ((|#2| $ (-484) |#2|) NIL T ELT) ((|#2| $ (-1145 (-484)) |#2|) 44 T ELT)) (-2296 (($ $) 80 T ELT)) (-3839 ((|#2| (-1 |#2| |#2| |#2|) $ |#2| |#2|) 52 T ELT) ((|#2| (-1 |#2| |#2| |#2|) $ |#2|) 50 T ELT) ((|#2| (-1 |#2| |#2| |#2|) $) 49 T ELT)) (-3416 (((-484) (-1 (-85) |#2|) $) 27 T ELT) (((-484) |#2| $) NIL T ELT) (((-484) |#2| $ (-484)) 96 T ELT)) (-2888 (((-584 |#2|) $) 13 T ELT)) (-3515 (($ (-1 (-85) |#2| |#2|) $ $) 64 T ELT) (($ $ $) NIL T ELT)) (-1947 (($ (-1 |#2| |#2|) $) 37 T ELT)) (-3955 (($ (-1 |#2| |#2|) $) NIL T ELT) (($ (-1 |#2| |#2| |#2|) $ $) 60 T ELT)) (-2303 (($ |#2| $ (-484)) NIL T ELT) (($ $ $ (-484)) 67 T ELT)) (-1352 (((-3 |#2| "failed") (-1 (-85) |#2|) $) 29 T ELT)) (-1945 (((-85) (-1 (-85) |#2|) $) 23 T ELT)) (-3797 ((|#2| $ (-484) |#2|) NIL T ELT) ((|#2| $ (-484)) NIL T ELT) (($ $ (-1145 (-484))) 66 T ELT)) (-2304 (($ $ (-484)) 76 T ELT) (($ $ (-1145 (-484))) 75 T ELT)) (-1944 (((-695) (-1 (-85) |#2|) $) 34 T ELT) (((-695) |#2| $) NIL T ELT)) (-1729 (($ $ $ (-484)) 69 T ELT)) (-3397 (($ $) 68 T ELT)) (-3527 (($ (-584 |#2|)) 73 T ELT)) (-3799 (($ $ |#2|) NIL T ELT) (($ |#2| $) NIL T ELT) (($ $ $) 87 T ELT) (($ (-584 $)) 85 T ELT)) (-3943 (((-773) $) 92 T ELT)) (-1946 (((-85) (-1 (-85) |#2|) $) 22 T ELT)) (-3055 (((-85) $ $) 95 T ELT)) (-2684 (((-85) $ $) 99 T ELT)))
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NIL
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(((-19 |#1|) (-113) (-1128)) (T -19))
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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(((-21) . T) ((-23) . T) ((-25) . T) ((-72) . T) ((-82 |#1| |#1|) . T) ((-104) . T) ((-556 (-484)) . T) ((-556 |#1|) . T) ((-553 (-773)) . T) ((-13) . T) ((-589 (-484)) . T) ((-589 |#1|) . T) ((-589 $) . T) ((-591 |#1|) . T) ((-591 $) . T) ((-583 |#1|) . T) ((-655 |#1|) . T) ((-664) . T) ((-964 |#1|) . T) ((-969 |#1|) . T) ((-962) . T) ((-970) . T) ((-1025) . T) ((-1060) . T) ((-1013) . T) ((-1128) . T))
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NIL
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NIL
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(((-64) (-113)) (T -64))
NIL
(-13 (-1013) (-427 (-1094)))
(((-72) . T) ((-556 (-1094)) . T) ((-553 (-773)) . T) ((-553 (-1094)) . T) ((-427 (-1094)) . T) ((-13) . T) ((-1013) . T) ((-1128) . T))
-((-3484 (($ $) 10 T ELT)) (-3485 (($ $) 12 T ELT)))
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NIL
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(((-66) (-113)) (T -66))
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NIL
(((-68) (-113)) (T -68))
NIL
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(((-69 |#1|) (-13 (-410) (-241 |#1| |#1|) (-10 -8 (-15 -1261 ($ (-1 |#1| |#1|))) (-15 -1261 ($ (-1 |#1| |#1|) (-1 |#1| |#1|))) (-15 -1261 ($ (-1 |#1| |#1| (-484)))))) (-962)) (T -69))
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((-1262 (((-345 |#2|) |#2| (-584 |#2|)) 10 T ELT) (((-345 |#2|) |#2| |#2|) 11 T ELT)))
(((-70 |#1| |#2|) (-10 -7 (-15 -1262 ((-345 |#2|) |#2| |#2|)) (-15 -1262 ((-345 |#2|) |#2| (-584 |#2|)))) (-13 (-389) (-120)) (-1154 |#1|)) (T -70))
((-1262 (*1 *2 *3 *4) (-12 (-5 *4 (-584 *3)) (-4 *3 (-1154 *5)) (-4 *5 (-13 (-389) (-120))) (-5 *2 (-345 *3)) (-5 *1 (-70 *5 *3)))) (-1262 (*1 *2 *3 *3) (-12 (-4 *4 (-13 (-389) (-120))) (-5 *2 (-345 *3)) (-5 *1 (-70 *4 *3)) (-4 *3 (-1154 *4)))))
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NIL
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(((-72) (-113)) (T -72))
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NIL
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NIL
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(((-34) . T) ((-72) OR (|has| |#1| (-1013)) (|has| |#1| (-72))) ((-553 (-773)) OR (|has| |#1| (-1013)) (|has| |#1| (-553 (-773)))) ((-259 |#1|) -12 (|has| |#1| (-259 |#1|)) (|has| |#1| (-1013))) ((-426 |#1|) . T) ((-453 |#1| |#1|) -12 (|has| |#1| (-259 |#1|)) (|has| |#1| (-1013))) ((-13) . T) ((-924 |#1|) . T) ((-1013) |has| |#1| (-1013)) ((-1128) . T))
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NIL
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NIL
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NIL
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(((-120) (-113)) (T -120))
NIL
(-13 (-962))
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-NIL
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+NIL
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(((-124 |#1|) (-113) (-1128)) (T -124))
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NIL
(-13 (-193 |t#1|))
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NIL
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(((-21) . T) ((-23) . T) ((-25) . T) ((-72) . T) ((-104) . T) ((-556 (-484)) . T) ((-553 (-773)) . T) ((-186 $) OR (|has| |#1| (-189)) (|has| |#1| (-190))) ((-190) |has| |#1| (-190)) ((-189) OR (|has| |#1| (-189)) (|has| |#1| (-190))) ((-225 |#1|) . T) ((-13) . T) ((-589 (-484)) . T) ((-589 $) . T) ((-591 $) . T) ((-664) . T) ((-807 $ (-1089)) OR (|has| |#1| (-812 (-1089))) (|has| |#1| (-810 (-1089)))) ((-810 (-1089)) |has| |#1| (-810 (-1089))) ((-812 (-1089)) OR (|has| |#1| (-812 (-1089))) (|has| |#1| (-810 (-1089)))) ((-962) . T) ((-970) . T) ((-1025) . T) ((-1060) . T) ((-1013) . T) ((-1128) . T))
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NIL
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(((-13) . T) ((-1128) . T))
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NIL
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NIL
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NIL
(-13 (-962) (-189))
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NIL
(-13 (-717) (-1060))
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NIL
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NIL
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@@ -695,425 +695,425 @@ NIL
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(((-34) . T) ((-72) OR (|has| |#1| (-1013)) (|has| |#1| (-72))) ((-553 (-773)) OR (|has| |#1| (-1013)) (|has| |#1| (-553 (-773)))) ((-124 |#1|) . T) ((-554 (-473)) |has| |#1| (-554 (-473))) ((-241 (-484) |#1|) . T) ((-241 (-1145 (-484)) $) . T) ((-243 (-484) |#1|) . T) ((-259 |#1|) -12 (|has| |#1| (-259 |#1|)) (|has| |#1| (-1013))) ((-426 |#1|) . T) ((-539 (-484) |#1|) . T) ((-453 |#1| |#1|) -12 (|has| |#1| (-259 |#1|)) (|has| |#1| (-1013))) ((-13) . T) ((-594 |#1|) . T) ((-1013) |has| |#1| (-1013)) ((-1128) . T))
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NIL
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(((-13) . T) ((-1128) . T))
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NIL
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(((-241 |#1| |#2|) . T) ((-13) . T) ((-1128) . T))
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(((-245) (-113)) (T -245))
NIL
-(-13 (-962) (-82 $ $) (-10 -7 (-6 -3984)))
+(-13 (-962) (-82 $ $) (-10 -7 (-6 -3985)))
(((-21) . T) ((-23) . T) ((-25) . T) ((-72) . T) ((-82 $ $) . T) ((-104) . T) ((-556 (-484)) . T) ((-553 (-773)) . T) ((-13) . T) ((-589 (-484)) . T) ((-589 $) . T) ((-591 $) . T) ((-664) . T) ((-964 $) . T) ((-969 $) . T) ((-962) . T) ((-970) . T) ((-1025) . T) ((-1060) . T) ((-1013) . T) ((-1128) . T))
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(((-21) . T) ((-23) . T) ((-25) . T) ((-38 $) . T) ((-72) . T) ((-82 $ $) . T) ((-104) . T) ((-556 (-484)) . T) ((-556 $) . T) ((-553 (-773)) . T) ((-146) . T) ((-245) . T) ((-389) . T) ((-495) . T) ((-13) . T) ((-589 (-484)) . T) ((-589 $) . T) ((-591 $) . T) ((-583 $) . T) ((-655 $) . T) ((-664) . T) ((-833) . T) ((-964 $) . T) ((-969 $) . T) ((-962) . T) ((-970) . T) ((-1025) . T) ((-1060) . T) ((-1013) . T) ((-1128) . T))
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NIL
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(((-259 |#1|) (-113) (-1013)) (T -259))
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(((-453 |#1| |#1|) . T))
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(((-261) (-1013)) (T -261))
NIL
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-((-3203 (*1 *2 *1) (-12 (-5 *2 (-1048)) (-5 *1 (-262)))) (-3502 (*1 *2 *1) (-12 (-5 *2 (-484)) (-5 *1 (-262)))))
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(((-23) . T) ((-25) . T) ((-72) . T) ((-104) . T) ((-556 |#1|) . T) ((-553 (-773)) . T) ((-13) . T) ((-951 |#1|) . T) ((-1013) . T) ((-1128) . T))
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NIL
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NIL
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(((-21) . T) ((-23) . T) ((-25) . T) ((-72) . T) ((-104) . T) ((-553 (-773)) . T) ((-13) . T) ((-589 (-484)) . T) ((-1013) . T) ((-1128) . T))
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NIL
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(((-287 |#1|) (-113) (-1013)) (T -287))
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(((-241 |#1| $) |has| |#1| (-241 |#1| |#1|)) ((-259 |#1|) |has| |#1| (-259 |#1|)) ((-453 (-1089) |#1|) |has| |#1| (-453 (-1089) |#1|)) ((-453 |#1| |#1|) |has| |#1| (-259 |#1|)) ((-13) |has| |#1| (-241 |#1| |#1|)) ((-1128) |has| |#1| (-241 |#1| |#1|)))
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NIL
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NIL
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NIL
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(((-319 |#1| |#2|) (-113) (-146) (-1154 |t#1|)) (T -319))
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(((-21) . T) ((-23) . T) ((-25) . T) ((-38 |#1|) . T) ((-72) . T) ((-82 |#1| |#1|) . T) ((-104) . T) ((-118) |has| |#1| (-118)) ((-120) |has| |#1| (-120)) ((-556 (-484)) . T) ((-556 |#1|) . T) ((-553 (-773)) . T) ((-13) . T) ((-589 (-484)) . T) ((-589 |#1|) . T) ((-589 $) . T) ((-591 |#1|) . T) ((-591 $) . T) ((-583 |#1|) . T) ((-655 |#1|) . T) ((-664) . T) ((-964 |#1|) . T) ((-969 |#1|) . T) ((-962) . T) ((-970) . T) ((-1025) . T) ((-1060) . T) ((-1013) . T) ((-1128) . T))
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NIL
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(((-21) . T) ((-23) . T) ((-25) . T) ((-72) . T) ((-82 |#1| |#1|) . T) ((-104) . T) ((-556 |#2|) . T) ((-553 (-773)) . T) ((-13) . T) ((-589 (-484)) . T) ((-589 |#1|) . T) ((-591 |#1|) . T) ((-583 |#1|) |has| |#1| (-146)) ((-655 |#1|) |has| |#1| (-146)) ((-951 |#2|) . T) ((-964 |#1|) . T) ((-969 |#1|) . T) ((-1013) . T) ((-1128) . T))
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(((-340 |#1|) (-113) (-1128)) (T -340))
NIL
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@@ -1121,2910 +1121,2910 @@ NIL
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(((-341 |#1|) (-10 -7 (-15 -1762 (|#1| |#1| (-695))) (-15 -1762 (|#1| |#1|))) (-342)) (T -341))
NIL
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NIL
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NIL
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NIL
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(((-389) (-113)) (T -389))
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(((-412 |#1| |#2| |#3| |#4|) (-1106 |#1| |#2|) (-1013) (-1013) (-1106 |#1| |#2|) |#2|) (T -412))
NIL
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NIL
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NIL
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(((-450 |#1| |#2|) (-13 (-718) (-447 |#1| |#2|)) (-718) (-757)) (T -450))
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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(((-537 |#1| |#2|) (-1177 |#1|) (-1128) (-484)) (T -537))
NIL
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NIL
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NIL
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(((-597 |#1| |#2|) (-601 |#1|) (-962) (-1 |#1| |#1|)) (T -597))
NIL
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(((-598 |#1|) (-601 |#1|) (-190)) (T -598))
NIL
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NIL
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NIL
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(((-21) . T) ((-23) . T) ((-25) . T) ((-38 |#1|) |has| |#1| (-146)) ((-72) . T) ((-82 |#1| |#1|) . T) ((-104) . T) ((-556 (-347 (-484))) |has| |#1| (-951 (-347 (-484)))) ((-556 (-484)) . T) ((-556 |#1|) . T) ((-553 (-773)) . T) ((-241 |#1| |#1|) . T) ((-352 |#1|) . T) ((-13) . T) ((-589 (-484)) . T) ((-589 |#1|) . T) ((-589 $) . T) ((-591 |#1|) . T) ((-591 $) . T) ((-583 |#1|) |has| |#1| (-146)) ((-655 |#1|) |has| |#1| (-146)) ((-664) . T) ((-951 (-347 (-484))) |has| |#1| (-951 (-347 (-484)))) ((-951 (-484)) |has| |#1| (-951 (-484))) ((-951 |#1|) . T) ((-964 |#1|) . T) ((-969 |#1|) . T) ((-962) . T) ((-970) . T) ((-1025) . T) ((-1060) . T) ((-1013) . T) ((-1128) . T) ((-762 |#1|) . T))
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NIL
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NIL
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NIL
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(((-147) . T) ((-465) . T) ((-512) . T) ((-771) . T))
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NIL
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NIL
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(((-21) . T) ((-23) . T) ((-25) . T) ((-38 |#1|) . T) ((-72) . T) ((-82 |#1| |#1|) . T) ((-104) . T) ((-118) |has| |#1| (-118)) ((-120) |has| |#1| (-120)) ((-556 (-347 (-484))) |has| |#1| (-951 (-347 (-484)))) ((-556 (-484)) . T) ((-556 |#1|) . T) ((-553 (-773)) . T) ((-554 (-473)) |has| |#1| (-554 (-473))) ((-241 |#1| $) |has| |#1| (-241 |#1| |#1|)) ((-259 |#1|) |has| |#1| (-259 |#1|)) ((-317) |has| |#1| (-317)) ((-287 |#1|) . T) ((-352 |#1|) . T) ((-453 (-1089) |#1|) |has| |#1| (-453 (-1089) |#1|)) ((-453 |#1| |#1|) |has| |#1| (-259 |#1|)) ((-13) . T) ((-589 (-484)) . T) ((-589 |#1|) . T) ((-589 $) . T) ((-591 |#1|) . T) ((-591 $) . T) ((-583 |#1|) . T) ((-655 |#1|) . T) ((-664) . T) ((-757) |has| |#1| (-757)) ((-760) |has| |#1| (-757)) ((-951 (-347 (-484))) |has| |#1| (-951 (-347 (-484)))) ((-951 (-484)) |has| |#1| (-951 (-484))) ((-951 |#1|) . T) ((-964 |#1|) . T) ((-969 |#1|) . T) ((-962) . T) ((-970) . T) ((-1025) . T) ((-1060) . T) ((-1013) . T) ((-1128) . T))
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(((-722) (-113)) (T -722))
NIL
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NIL
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NIL
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(((-738 |#1| |#2| |#3|) (-13 (-82 $ $) (-190) (-427 |#2|) (-10 -7 (IF (|has| |#2| (-311)) (-6 (-311)) |%noBranch|))) (-1013) (-810 |#1|) |#1|) (T -738))
NIL
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(((-739 |#1|) (-228 |#1|) (-757)) (T -739))
NIL
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(((-741) (-113)) (T -741))
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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(((-767) (-113)) (T -767))
NIL
(-13 (-757) (-1025))
(((-72) . T) ((-553 (-773)) . T) ((-13) . T) ((-757) . T) ((-760) . T) ((-1025) . T) ((-1013) . T) ((-1128) . T))
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-NIL
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+NIL
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(((-771) (-113)) (T -771))
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(((-147) . T))
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NIL
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NIL
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(((-822) (-113)) (T -822))
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NIL
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+NIL
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(((-887 |#1| |#2| |#3|) (-113) (-962) (-717) (-757)) (T -887))
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(((-21) . T) ((-23) . T) ((-47 |#1| |#2|) . T) ((-25) . T) ((-38 (-347 (-484))) |has| |#1| (-38 (-347 (-484)))) ((-38 |#1|) |has| |#1| (-146)) ((-38 $) |has| |#1| (-495)) ((-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))) ((-245) |has| |#1| (-495)) ((-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) ((-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) ((-1128) . T))
-((-2893 (((-1001 (-179)) $) 8 T ELT)) (-2894 (((-1001 (-179)) $) 9 T ELT)) (-2895 (((-1001 (-179)) $) 10 T ELT)) (-2896 (((-584 (-584 (-855 (-179)))) $) 11 T ELT)) (-3942 (((-773) $) 6 T ELT)))
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(((-888) (-113)) (T -888))
-((-2896 (*1 *2 *1) (-12 (-4 *1 (-888)) (-5 *2 (-584 (-584 (-855 (-179))))))) (-2895 (*1 *2 *1) (-12 (-4 *1 (-888)) (-5 *2 (-1001 (-179))))) (-2894 (*1 *2 *1) (-12 (-4 *1 (-888)) (-5 *2 (-1001 (-179))))) (-2893 (*1 *2 *1) (-12 (-4 *1 (-888)) (-5 *2 (-1001 (-179))))))
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(((-553 (-773)) . T))
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-(((-889 |#1| |#2| |#3| |#4| |#5|) (-10 -7 (-15 -2897 ((-85) |#1|)) (-15 -2898 ((-584 |#5|) (-584 |#5|) |#1|)) (-15 -2899 ((-584 |#5|) (-584 |#5|) |#1|)) (-15 -2900 ((-2 (|:| |rnum| |#2|) (|:| |polnum| |#5|) (|:| |den| |#2|)) |#5| |#1|)) (-15 -2901 ((-2 (|:| |num| |#5|) (|:| |den| |#2|)) |#5| |#1|)) (-15 -2902 ((-85) |#1|)) (-15 -2903 ((-85) |#1| |#1|)) (-15 -2904 ((-85) |#1| |#1|)) (-15 -2905 ((-85) |#1|)) (-15 -2906 ((-85) |#1|)) (-15 -2907 ((-2 (|:| |under| |#1|) (|:| -3127 |#1|) (|:| |upper| |#1|)) |#1| |#4|)) (-15 -2908 (|#1| |#1| |#4|)) (-15 -2909 (|#1| |#1| |#4|)) (-15 -2910 (|#1| |#1| |#4|)) (-15 -2911 ((-85) |#4| |#1|)) (-15 -2912 ((-584 |#4|) |#1|)) (-15 -3079 ((-584 |#4|) |#1|)) (-15 -3054 ((-85) |#1| |#1|))) (-890 |#2| |#3| |#4| |#5|) (-962) (-718) (-757) (-977 |#2| |#3| |#4|)) (T -889))
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NIL
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NIL
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(((-554 (-179)) . T) ((-554 (-327)) . T))
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-((-3098 (((-1 (-484)) (-1001 (-484))) 32 T ELT)) (-3102 (((-484) (-484) (-484) (-484) (-484)) 29 T ELT)) (-3100 (((-1 (-484)) |RationalNumber|) NIL T ELT)) (-3101 (((-1 (-484)) |RationalNumber|) NIL T ELT)) (-3099 (((-1 (-484)) (-484) |RationalNumber|) NIL T ELT)))
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-((-3102 (*1 *2 *2 *2 *2 *2) (-12 (-5 *2 (-484)) (-5 *1 (-960)))) (-3101 (*1 *2 *3) (-12 (-5 *3 |RationalNumber|) (-5 *2 (-1 (-484))) (-5 *1 (-960)))) (-3100 (*1 *2 *3) (-12 (-5 *3 |RationalNumber|) (-5 *2 (-1 (-484))) (-5 *1 (-960)))) (-3099 (*1 *2 *3 *4) (-12 (-5 *4 |RationalNumber|) (-5 *2 (-1 (-484))) (-5 *1 (-960)) (-5 *3 (-484)))) (-3098 (*1 *2 *3) (-12 (-5 *3 (-1001 (-484))) (-5 *2 (-1 (-484))) (-5 *1 (-960)))))
-((-3942 (((-773) $) NIL T ELT) (($ (-484)) 10 T ELT)))
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-NIL
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ELT) (($ (-584 (-704 |#1| (-774 |#2|))) $) NIL T ELT)) (-3694 (((-584 (-704 |#1| (-774 |#2|))) $) NIL T ELT)) (-3688 (((-85) (-704 |#1| (-774 |#2|)) $) NIL T ELT) (((-85) $) NIL T ELT)) (-3683 (((-704 |#1| (-774 |#2|)) (-704 |#1| (-774 |#2|)) $) NIL T ELT)) (-3696 (((-85) $ $) NIL T ELT)) (-2902 (((-2 (|:| |num| (-704 |#1| (-774 |#2|))) (|:| |den| |#1|)) (-704 |#1| (-774 |#2|)) $) NIL (|has| |#1| (-495)) ELT)) (-3689 (((-85) (-704 |#1| (-774 |#2|)) $) NIL T ELT) (((-85) $) NIL T ELT)) (-3684 (((-704 |#1| (-774 |#2|)) (-704 |#1| (-774 |#2|)) $) NIL T ELT)) (-3241 (((-1033) $) NIL T ELT)) (-3798 (((-3 (-704 |#1| (-774 |#2|)) #1#) $) NIL T ELT)) (-1352 (((-3 (-704 |#1| (-774 |#2|)) #1#) (-1 (-85) (-704 |#1| (-774 |#2|))) $) NIL T ELT)) (-3676 (((-3 $ #1#) $ (-704 |#1| (-774 |#2|))) NIL T ELT)) (-3766 (($ $ (-704 |#1| (-774 |#2|))) NIL T ELT) (((-584 $) (-704 |#1| (-774 |#2|)) $) NIL T ELT) (((-584 $) (-704 |#1| (-774 |#2|)) (-584 $)) NIL T ELT) (((-584 $) (-584 (-704 |#1| (-774 |#2|))) $) 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|#2|)))) NIL T ELT)) (-3687 (((-85) $ (-1 (-85) (-704 |#1| (-774 |#2|)) (-584 (-704 |#1| (-774 |#2|))))) NIL T ELT)) (-3187 (((-584 $) (-704 |#1| (-774 |#2|)) $) NIL T ELT) (((-584 $) (-704 |#1| (-774 |#2|)) (-584 $)) NIL T ELT) (((-584 $) (-584 (-704 |#1| (-774 |#2|))) $) NIL T ELT) (((-584 $) (-584 (-704 |#1| (-774 |#2|))) (-584 $)) NIL T ELT)) (-1946 (((-85) (-1 (-85) (-704 |#1| (-774 |#2|))) $) NIL (|has| $ (-6 -3992)) ELT)) (-3677 (((-584 (-774 |#2|)) $) NIL T ELT)) (-3194 (((-85) (-704 |#1| (-774 |#2|)) $) NIL T ELT)) (-3930 (((-85) (-774 |#2|) $) NIL T ELT)) (-3055 (((-85) $ $) NIL T ELT)) (-3954 (((-695) $) NIL (|has| $ (-6 -3992)) ELT)))
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+NIL
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(((-962) (-113)) (T -962))
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(((-21) . T) ((-23) . T) ((-25) . T) ((-72) . T) ((-104) . T) ((-556 (-484)) . T) ((-553 (-773)) . T) ((-13) . T) ((-589 (-484)) . T) ((-589 $) . T) ((-591 $) . T) ((-664) . T) ((-970) . T) ((-1025) . T) ((-1060) . T) ((-1013) . T) ((-1128) . T))
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(((-964 |#1|) (-113) (-1025)) (T -964))
((* (*1 *1 *1 *2) (-12 (-4 *1 (-964 *2)) (-4 *2 (-1025)))))
(-13 (-1013) (-10 -8 (-15 * ($ $ |t#1|))))
(((-72) . T) ((-553 (-773)) . T) ((-13) . T) ((-1013) . T) ((-1128) . T))
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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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(((-72) . T) ((-553 (-773)) . T) ((-558 (-584 $)) . T) ((-558 |#1|) . T) ((-558 |#2|) . T) ((-558 |#3|) . T) ((-558 |#4|) . T) ((-558 |#5|) . T) ((-241 (-484) $) . T) ((-241 (-584 (-484)) $) . T) ((-13) . T) ((-1013) . T) ((-1128) . T))
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NIL
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NIL
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(-13 (-23) (-664))
(((-23) . T) ((-25) . T) ((-72) . T) ((-553 (-773)) . T) ((-13) . T) ((-664) . T) ((-1025) . T) ((-1013) . T) ((-1128) . T))
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(((-35) . T) ((-66) . T) ((-239) . T) ((-430) . T) ((-1117) . T))
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NIL
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(((-1117) (-113)) (T -1117))
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-NIL
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NIL
(-13)
(((-13) . 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|) . T) ((-556 $) OR (|has| |#1| (-495)) (|has| |#1| (-311))) ((-553 (-773)) . T) ((-146) OR (|has| |#1| (-495)) (|has| |#1| (-311)) (|has| |#1| (-146))) ((-554 (-179)) -12 (|has| |#1| (-311)) (|has| |#2| (-934))) ((-554 (-327)) -12 (|has| |#1| (-311)) (|has| |#2| (-934))) ((-554 (-473)) -12 (|has| |#1| (-311)) (|has| |#2| (-554 (-473)))) ((-554 (-801 (-327))) -12 (|has| |#1| (-311)) (|has| |#2| (-554 (-801 (-327))))) ((-554 (-801 (-484))) -12 (|has| |#1| (-311)) (|has| |#2| (-554 (-801 (-484))))) ((-186 $) OR (|has| |#1| (-15 * (|#1| (-484) |#1|))) (-12 (|has| |#1| (-311)) (|has| |#2| (-189))) (-12 (|has| |#1| (-311)) (|has| |#2| (-190)))) ((-184 |#2|) |has| |#1| (-311)) ((-190) OR (|has| |#1| (-15 * (|#1| (-484) |#1|))) (-12 (|has| |#1| (-311)) (|has| |#2| (-190)))) ((-189) OR (|has| |#1| (-15 * (|#1| (-484) |#1|))) (-12 (|has| |#1| (-311)) (|has| |#2| (-189))) (-12 (|has| |#1| (-311)) (|has| |#2| (-190)))) ((-225 |#2|) |has| |#1| (-311)) ((-201) |has| |#1| (-311)) ((-239) |has| |#1| (-38 (-347 (-484)))) ((-241 (-484) |#1|) . 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) . T) ((-715) -12 (|has| |#1| (-311)) (|has| |#2| (-741))) ((-717) -12 (|has| |#1| (-311)) (|has| |#2| (-741))) ((-719) -12 (|has| |#1| (-311)) (|has| |#2| (-741))) ((-722) -12 (|has| |#1| (-311)) (|has| |#2| (-741))) ((-741) -12 (|has| |#1| (-311)) (|has| |#2| (-741))) ((-756) -12 (|has| |#1| (-311)) (|has| |#2| (-741))) ((-757) OR (-12 (|has| |#1| (-311)) (|has| |#2| (-757))) (-12 (|has| |#1| (-311)) (|has| |#2| (-741)))) ((-760) OR (-12 (|has| |#1| (-311)) (|has| |#2| (-757))) (-12 (|has| |#1| (-311)) (|has| |#2| (-741)))) ((-807 $ (-1089)) OR (-12 (|has| |#1| (-810 (-1089))) (|has| |#1| (-15 * (|#1| (-484) |#1|)))) (-12 (|has| |#1| (-311)) (|has| |#2| (-812 (-1089)))) (-12 (|has| |#1| (-311)) (|has| |#2| (-810 (-1089))))) ((-810 (-1089)) OR (-12 (|has| |#1| (-810 (-1089))) (|has| |#1| (-15 * (|#1| (-484) |#1|)))) (-12 (|has| |#1| (-311)) (|has| |#2| (-810 (-1089))))) ((-812 (-1089)) OR (-12 (|has| |#1| (-810 (-1089))) (|has| |#1| (-15 * (|#1| (-484) |#1|)))) (-12 (|has| |#1| (-311)) (|has| |#2| (-812 (-1089)))) (-12 (|has| |#1| (-311)) (|has| |#2| (-810 (-1089))))) ((-797 (-327)) -12 (|has| |#1| (-311)) (|has| |#2| (-797 (-327)))) ((-797 (-484)) -12 (|has| |#1| (-311)) (|has| |#2| (-797 (-484)))) ((-795 |#2|) |has| |#1| (-311)) ((-822) -12 (|has| |#1| (-311)) (|has| |#2| (-822))) ((-887 |#1| (-484) (-994)) . T) ((-833) |has| |#1| (-311)) ((-905 |#2|) |has| |#1| (-311)) ((-916) |has| |#1| (-38 (-347 (-484)))) ((-934) -12 (|has| |#1| (-311)) (|has| |#2| (-934))) ((-951 (-347 (-484))) -12 (|has| |#1| (-311)) (|has| |#2| (-951 (-484)))) ((-951 (-484)) -12 (|has| |#1| (-311)) (|has| |#2| (-951 (-484)))) ((-951 (-1089)) -12 (|has| |#1| (-311)) (|has| |#2| (-951 (-1089)))) ((-951 |#2|) . T) ((-964 (-347 (-484))) OR (|has| |#1| (-311)) (|has| |#1| (-38 (-347 (-484))))) ((-964 |#1|) . T) ((-964 |#2|) |has| |#1| (-311)) ((-964 $) OR (|has| |#1| (-495)) (|has| |#1| (-311)) (|has| |#1| (-146))) ((-969 (-347 (-484))) OR (|has| |#1| (-311)) (|has| |#1| (-38 (-347 (-484))))) ((-969 |#1|) . T) ((-969 |#2|) |has| |#1| (-311)) ((-969 $) OR (|has| |#1| (-495)) (|has| |#1| (-311)) (|has| |#1| (-146))) ((-962) . T) ((-970) . T) ((-1025) . T) ((-1060) . T) ((-1013) . 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 $) OR (|has| |#1| (-822)) (|has| |#1| (-495)) (|has| |#1| (-389)) (|has| |#1| (-311))) ((-72) . T) ((-82 (-347 (-484)) (-347 (-484))) |has| |#1| (-38 (-347 (-484)))) ((-82 |#1| |#1|) . T) ((-82 $ $) OR (|has| |#1| (-822)) (|has| |#1| (-495)) (|has| |#1| (-389)) (|has| |#1| (-311)) (|has| |#1| (-146))) ((-104) . T) ((-118) |has| |#1| (-118)) ((-120) |has| |#1| (-120)) ((-556 (-347 (-484))) OR (|has| |#1| (-951 (-347 (-484)))) (|has| |#1| (-38 (-347 (-484))))) ((-556 (-484)) . T) ((-556 (-994)) . T) ((-556 |#1|) . T) ((-556 $) OR (|has| |#1| (-822)) (|has| |#1| (-495)) (|has| |#1| (-389)) (|has| |#1| (-311))) ((-553 (-773)) . T) ((-146) OR (|has| |#1| (-822)) (|has| |#1| (-495)) (|has| |#1| (-389)) (|has| |#1| (-311)) (|has| |#1| (-146))) ((-554 (-473)) -12 (|has| |#1| (-554 (-473))) (|has| (-994) (-554 (-473)))) ((-554 (-801 (-327))) -12 (|has| |#1| (-554 (-801 (-327)))) (|has| (-994) (-554 (-801 (-327))))) ((-554 (-801 (-484))) -12 (|has| |#1| (-554 (-801 (-484)))) (|has| (-994) (-554 (-801 (-484))))) ((-186 $) . T) ((-184 |#1|) . T) ((-190) . T) ((-189) . T) ((-225 |#1|) . T) ((-241 (-347 $) (-347 $)) |has| |#1| (-495)) ((-241 |#1| |#1|) . T) ((-241 $ $) . T) ((-245) OR (|has| |#1| (-822)) (|has| |#1| (-495)) (|has| |#1| (-389)) (|has| |#1| (-311))) ((-257) |has| |#1| (-311)) ((-259 $) . T) ((-276 |#1| (-695)) . T) ((-326 |#1|) . T) ((-352 |#1|) . T) ((-389) OR (|has| |#1| (-822)) (|has| |#1| (-389)) (|has| |#1| (-311))) ((-453 (-994) |#1|) . T) ((-453 (-994) $) . T) ((-453 $ $) . T) ((-495) OR (|has| |#1| (-822)) (|has| |#1| (-495)) (|has| |#1| (-389)) (|has| |#1| (-311))) ((-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 (-484)) |has| |#1| (-581 (-484))) ((-591 |#1|) . T) ((-591 $) . T) ((-583 (-347 (-484))) |has| |#1| (-38 (-347 (-484)))) ((-583 |#1|) |has| |#1| (-146)) ((-583 $) OR (|has| |#1| (-822)) (|has| |#1| (-495)) (|has| |#1| (-389)) (|has| |#1| (-311))) ((-581 (-484)) |has| |#1| (-581 (-484))) ((-581 |#1|) . T) ((-655 (-347 (-484))) |has| |#1| (-38 (-347 (-484)))) ((-655 |#1|) |has| |#1| (-146)) ((-655 $) OR (|has| |#1| (-822)) (|has| |#1| (-495)) (|has| |#1| (-389)) (|has| |#1| (-311))) ((-664) . T) ((-807 $ (-994)) . T) ((-807 $ (-1089)) OR (|has| |#1| (-812 (-1089))) (|has| |#1| (-810 (-1089)))) ((-810 (-994)) . T) ((-810 (-1089)) |has| |#1| (-810 (-1089))) ((-812 (-994)) . T) ((-812 (-1089)) OR (|has| |#1| (-812 (-1089))) (|has| |#1| (-810 (-1089)))) ((-797 (-327)) -12 (|has| |#1| (-797 (-327))) (|has| (-994) (-797 (-327)))) ((-797 (-484)) -12 (|has| |#1| (-797 (-484))) (|has| (-994) (-797 (-484)))) ((-862 |#1| (-695) (-994)) . T) ((-822) |has| |#1| (-822)) ((-833) |has| |#1| (-311)) ((-951 (-347 (-484))) |has| |#1| (-951 (-347 (-484)))) ((-951 (-484)) |has| |#1| (-951 (-484))) ((-951 (-994)) . T) ((-951 |#1|) . T) ((-964 (-347 (-484))) |has| |#1| (-38 (-347 (-484)))) ((-964 |#1|) . T) ((-964 $) OR (|has| |#1| (-822)) (|has| |#1| (-495)) (|has| |#1| (-389)) (|has| |#1| (-311)) (|has| |#1| (-146))) ((-969 (-347 (-484))) |has| |#1| (-38 (-347 (-484)))) ((-969 |#1|) . T) ((-969 $) OR (|has| |#1| (-822)) (|has| |#1| (-495)) (|has| |#1| (-389)) (|has| |#1| (-311)) (|has| |#1| (-146))) ((-962) . T) ((-970) . T) ((-1025) . T) ((-1060) . T) ((-1013) . T) ((-1065) |has| |#1| (-1065)) ((-1128) . T) ((-1133) |has| |#1| (-822)))
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NIL
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(((-21) . T) ((-23) . T) ((-47 |#1| |#2|) . T) ((-25) . T) ((-38 (-347 (-484))) |has| |#1| (-38 (-347 (-484)))) ((-38 |#1|) |has| |#1| (-146)) ((-38 $) |has| |#1| (-495)) ((-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| |#2| |#1|))) ((-190) |has| |#1| (-15 * (|#1| |#2| |#1|))) ((-189) |has| |#1| (-15 * (|#1| |#2| |#1|))) ((-241 |#2| |#1|) . T) ((-241 $ $) |has| |#2| (-1025)) ((-245) |has| |#1| (-495)) ((-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| |#2| |#1|)))) ((-810 (-1089)) -12 (|has| |#1| (-810 (-1089))) (|has| |#1| (-15 * (|#1| |#2| |#1|)))) ((-812 (-1089)) -12 (|has| |#1| (-810 (-1089))) (|has| |#1| (-15 * (|#1| |#2| |#1|)))) ((-887 |#1| |#2| (-994)) . T) ((-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) ((-1128) . T))
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NIL
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NIL
(((-1174) (-113)) (T -1174))
NIL
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NIL
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NIL
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NIL
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(((-1197 |#1|) (-113) (-311)) (T -1197))
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(((-1208 |#1|) (-13 (-146) (-317) (-554 (-484)) (-1065)) (-831)) (T -1208))
NIL
NIL
@@ -4039,4 +4039,4 @@ NIL
NIL
NIL
NIL
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UPXSCAT (NIL T) -9 NIL 2660336 NIL) (-1160 2651409 2651494 2651671 "UPXS2" NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1159 2643159 2651000 2651262 "UPXS" NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1158 2642054 2642324 2642674 "UPSQFREE" NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1157 2634819 2638242 2638296 "UPSCAT" 2639365 UPSCAT (NIL T T) -9 NIL 2640129 NIL) (-1156 2634239 2634491 2634814 "UPSCAT-" NIL UPSCAT- (NIL T T T) -7 NIL NIL NIL) (-1155 2633913 2633962 2634093 "UPOLYC2" NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1154 2618107 2626997 2627039 "UPOLYC" 2629117 UPOLYC (NIL T) -9 NIL 2630337 NIL) (-1153 2612162 2615010 2618102 "UPOLYC-" NIL UPOLYC- (NIL T T) -7 NIL NIL NIL) (-1152 2611598 2611723 2611886 "UPMP" NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1151 2611232 2611319 2611458 "UPDIVP" NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1150 2610045 2610312 2610616 "UPDECOMP" NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1149 2609378 2609508 2609693 "UPCDEN" NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1148 2608970 2609045 2609192 "UP2" NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1147 2599798 2608736 2608864 "UP" NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1146 2599160 2599297 2599502 "UNISEG2" NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1145 2597761 2598608 2598884 "UNISEG" NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1144 2596990 2597187 2597412 "UNIFACT" NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1143 2583864 2596914 2596985 "ULSCONS" NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1142 2563778 2576951 2577012 "ULSCCAT" 2577643 ULSCCAT (NIL T T) -9 NIL 2577930 NIL) (-1141 2563113 2563399 2563773 "ULSCCAT-" NIL ULSCCAT- (NIL T T T) -7 NIL NIL NIL) (-1140 2551547 2558619 2558661 "ULSCAT" 2559514 ULSCAT (NIL T) -9 NIL 2560244 NIL) (-1139 2551060 2551145 2551322 "ULS2" NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1138 2533241 2550559 2550800 "ULS" NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1137 2532275 2532968 2533082 "UINT8" NIL UINT8 (NIL) -8 NIL NIL 2533193) (-1136 2531308 2532001 2532115 "UINT64" NIL UINT64 (NIL) -8 NIL NIL 2532226) (-1135 2530341 2531034 2531148 "UINT32" NIL UINT32 (NIL) -8 NIL NIL 2531259) (-1134 2529374 2530067 2530181 "UINT16" NIL UINT16 (NIL) -8 NIL NIL 2530292) (-1133 2527443 2528602 2528632 "UFD" 2528843 UFD (NIL) -9 NIL 2528956 NIL) (-1132 2527287 2527344 2527438 "UFD-" NIL UFD- (NIL T) -7 NIL NIL NIL) (-1131 2526539 2526746 2526962 "UDVO" NIL UDVO (NIL) -7 NIL NIL NIL) (-1130 2524759 2525212 2525677 "UDPO" NIL UDPO (NIL T) -7 NIL NIL NIL) (-1129 2524484 2524724 2524754 "TYPEAST" NIL TYPEAST (NIL) -8 NIL NIL NIL) (-1128 2524422 2524427 2524457 "TYPE" 2524462 TYPE (NIL) -9 NIL 2524469 NIL) (-1127 2523581 2523801 2524041 "TWOFACT" NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1126 2522759 2523190 2523425 "TUPLE" NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1125 2520913 2521486 2522025 "TUBETOOL" NIL TUBETOOL (NIL) -7 NIL NIL NIL) (-1124 2519947 2520183 2520419 "TUBE" NIL TUBE (NIL T) -8 NIL NIL NIL) (-1123 2508301 2512769 2512865 "TSETCAT" 2518080 TSETCAT (NIL T T T T) -9 NIL 2519592 NIL) (-1122 2504638 2506454 2508296 "TSETCAT-" NIL TSETCAT- (NIL T T T T T) -7 NIL NIL NIL) (-1121 2499094 2503864 2504146 "TS" NIL TS (NIL T) -8 NIL NIL NIL) (-1120 2494431 2495444 2496373 "TRMANIP" NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1119 2493928 2494003 2494166 "TRIMAT" NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1118 2492004 2492294 2492649 "TRIGMNIP" NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1117 2491488 2491637 2491667 "TRIGCAT" 2491880 TRIGCAT (NIL) -9 NIL NIL NIL) (-1116 2491239 2491342 2491483 "TRIGCAT-" NIL TRIGCAT- (NIL T) -7 NIL NIL NIL) (-1115 2488235 2490348 2490626 "TREE" NIL TREE (NIL T) -8 NIL NIL NIL) (-1114 2487341 2488037 2488067 "TRANFUN" 2488102 TRANFUN (NIL) -9 NIL 2488168 NIL) (-1113 2486805 2487056 2487336 "TRANFUN-" NIL TRANFUN- (NIL T) -7 NIL NIL NIL) (-1112 2486642 2486680 2486741 "TOPSP" NIL TOPSP (NIL) -7 NIL NIL NIL) (-1111 2486099 2486230 2486381 "TOOLSIGN" NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1110 2484840 2485497 2485733 "TEXTFILE" NIL TEXTFILE (NIL) -8 NIL NIL NIL) (-1109 2484652 2484689 2484761 "TEX1" NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1108 2482866 2483512 2483941 "TEX" NIL TEX (NIL) -8 NIL NIL NIL) (-1107 2481246 2481583 2481905 "TBCMPPK" NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1106 2472304 2479047 2479103 "TBAGG" 2479505 TBAGG (NIL T T) -9 NIL 2479718 NIL) (-1105 2468835 2470527 2472299 "TBAGG-" NIL TBAGG- (NIL T T T) -7 NIL NIL NIL) (-1104 2468312 2468437 2468582 "TANEXP" NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1103 2467822 2468142 2468232 "TALGOP" NIL TALGOP (NIL T) -8 NIL NIL NIL) (-1102 2467319 2467436 2467574 "TABLEAU" NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1101 2460406 2467221 2467314 "TABLE" NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1100 2456159 2457454 2458699 "TABLBUMP" NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1099 2455528 2455687 2455868 "SYSTEM" NIL SYSTEM (NIL) -7 NIL NIL NIL) (-1098 2452682 2453435 2454218 "SYSSOLP" NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1097 2452456 2452646 2452677 "SYSPTR" NIL SYSPTR (NIL) -8 NIL NIL NIL) (-1096 2451410 2452095 2452221 "SYSNNI" NIL SYSNNI (NIL NIL) -8 NIL NIL 2452407) (-1095 2450674 2451222 2451301 "SYSINT" NIL SYSINT (NIL NIL) -8 NIL NIL 2451361) (-1094 2447497 2448656 2449356 "SYNTAX" NIL SYNTAX (NIL) -8 NIL NIL NIL) (-1093 2445180 2445863 2446497 "SYMTAB" NIL SYMTAB (NIL) -8 NIL NIL NIL) (-1092 2441258 2442304 2443281 "SYMS" NIL SYMS (NIL) -8 NIL NIL NIL) (-1091 2438421 2440913 2441142 "SYMPOLY" NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1090 2438017 2438104 2438226 "SYMFUNC" NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1089 2434641 2436115 2436934 "SYMBOL" NIL SYMBOL (NIL) -8 NIL NIL NIL) (-1088 2427665 2433838 2434131 "SUTS" NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1087 2419415 2427256 2427518 "SUPXS" NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1086 2418694 2418833 2419050 "SUPFRACF" NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1085 2418378 2418443 2418554 "SUP2" NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1084 2409165 2418090 2418215 "SUP" NIL SUP (NIL T) -8 NIL NIL NIL) (-1083 2407895 2408193 2408548 "SUMRF" NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1082 2407300 2407378 2407569 "SUMFS" NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1081 2389516 2406799 2407040 "SULS" NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1080 2389115 2389387 2389456 "SUCHTAST" NIL SUCHTAST (NIL) -8 NIL NIL NIL) (-1079 2388451 2388732 2388872 "SUCH" NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1078 2383053 2384312 2385265 "SUBSPACE" NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1077 2382585 2382685 2382849 "SUBRESP" NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1076 2377696 2378978 2380125 "STTFNC" NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1075 2372154 2373625 2374936 "STTF" NIL STTF (NIL T) -7 NIL NIL NIL) (-1074 2365069 2367133 2368924 "STTAYLOR" NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1073 2357899 2364981 2365064 "STRTBL" NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1072 2352593 2357613 2357728 "STRING" NIL STRING (NIL) -8 NIL NIL NIL) (-1071 2352180 2352263 2352407 "STREAM3" NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1070 2351331 2351532 2351767 "STREAM2" NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1069 2351071 2351129 2351222 "STREAM1" NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1068 2343809 2349276 2349882 "STREAM" NIL STREAM (NIL T) -8 NIL NIL NIL) (-1067 2342985 2343190 2343421 "STINPROD" NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1066 2342230 2342601 2342748 "STEPAST" NIL STEPAST (NIL) -8 NIL NIL NIL) (-1065 2341718 2341960 2341990 "STEP" 2342084 STEP (NIL) -9 NIL 2342155 NIL) (-1064 2334821 2341636 2341713 "STBL" NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1063 2329036 2333619 2333662 "STAGG" 2334089 STAGG (NIL T) -9 NIL 2334263 NIL) (-1062 2327415 2328163 2329031 "STAGG-" NIL STAGG- (NIL T T) -7 NIL NIL NIL) (-1061 2325572 2327242 2327334 "STACK" NIL STACK (NIL T) -8 NIL NIL NIL) (-1060 2324883 2325391 2325421 "SRING" 2325426 SRING (NIL) -9 NIL 2325446 NIL) (-1059 2317505 2323421 2323860 "SREGSET" NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1058 2311279 2312718 2314222 "SRDCMPK" NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1057 2303704 2308615 2308645 "SRAGG" 2309944 SRAGG (NIL) -9 NIL 2310548 NIL) (-1056 2303001 2303321 2303699 "SRAGG-" NIL SRAGG- (NIL T) -7 NIL NIL NIL) (-1055 2297120 2302323 2302746 "SQMATRIX" NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1054 2291333 2294502 2295224 "SPLTREE" NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1053 2287762 2288581 2289218 "SPLNODE" NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1052 2286737 2287042 2287072 "SPFCAT" 2287516 SPFCAT (NIL) -9 NIL NIL NIL) (-1051 2285674 2285926 2286190 "SPECOUT" NIL SPECOUT (NIL) -7 NIL NIL NIL) (-1050 2276432 2278706 2278736 "SPADXPT" 2283373 SPADXPT (NIL) -9 NIL 2285497 NIL) (-1049 2276234 2276280 2276349 "SPADPRSR" NIL SPADPRSR (NIL) -7 NIL NIL NIL) (-1048 2273890 2276198 2276229 "SPADAST" NIL SPADAST (NIL) -8 NIL NIL NIL) (-1047 2265564 2267653 2267695 "SPACEC" 2272010 SPACEC (NIL T) -9 NIL 2273815 NIL) (-1046 2263393 2265511 2265559 "SPACE3" NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1045 2262326 2262515 2262804 "SORTPAK" NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1044 2260730 2261063 2261474 "SOLVETRA" NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1043 2259995 2260229 2260490 "SOLVESER" NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1042 2256175 2257135 2258130 "SOLVERAD" NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1041 2252533 2253232 2253961 "SOLVEFOR" NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1040 2246319 2251873 2251969 "SNTSCAT" 2251974 SNTSCAT (NIL T T T T) -9 NIL 2252044 NIL) (-1039 2240204 2244960 2245350 "SMTS" NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1038 2234040 2240123 2240199 "SMP" NIL SMP (NIL T T) -8 NIL NIL NIL) (-1037 2232472 2232803 2233201 "SMITH" NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1036 2224141 2229056 2229158 "SMATCAT" 2230501 SMATCAT (NIL NIL T T T) -9 NIL 2231049 NIL) (-1035 2221982 2222966 2224136 "SMATCAT-" NIL SMATCAT- (NIL T NIL T T T) -7 NIL NIL NIL) (-1034 2219574 2221188 2221231 "SKAGG" 2221492 SKAGG (NIL T) -9 NIL 2221626 NIL) (-1033 2215684 2219394 2219505 "SINT" NIL SINT (NIL) -8 NIL NIL 2219546) (-1032 2215494 2215538 2215604 "SIMPAN" NIL SIMPAN (NIL) -7 NIL NIL NIL) (-1031 2214569 2214801 2215069 "SIGNRF" NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1030 2213573 2213735 2214011 "SIGNEF" NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1029 2212919 2213259 2213382 "SIGAST" NIL SIGAST (NIL) -8 NIL NIL NIL) (-1028 2212265 2212572 2212712 "SIG" NIL SIG (NIL) -8 NIL NIL NIL) (-1027 2210376 2210868 2211374 "SHP" NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1026 2203915 2210295 2210371 "SHDP" NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1025 2203418 2203655 2203685 "SGROUP" 2203778 SGROUP (NIL) -9 NIL 2203840 NIL) (-1024 2203308 2203340 2203413 "SGROUP-" NIL SGROUP- (NIL T) -7 NIL NIL NIL) (-1023 2202946 2202986 2203027 "SGPOPC" 2203032 SGPOPC (NIL T) -9 NIL 2203233 NIL) (-1022 2202480 2202757 2202863 "SGPOP" NIL SGPOP (NIL T) -8 NIL NIL NIL) (-1021 2199903 2200672 2201394 "SGCF" NIL SGCF (NIL) -7 NIL NIL NIL) (-1020 2193788 2199342 2199438 "SFRTCAT" 2199443 SFRTCAT (NIL T T T T) -9 NIL 2199481 NIL) (-1019 2188180 2189293 2190420 "SFRGCD" NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1018 2182356 2183517 2184681 "SFQCMPK" NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1017 2181328 2182230 2182351 "SEXOF" NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1016 2176936 2177831 2177926 "SEXCAT" 2180539 SEXCAT (NIL T T T T T) -9 NIL 2181090 NIL) (-1015 2175909 2176863 2176931 "SEX" NIL SEX (NIL) -8 NIL NIL NIL) (-1014 2174300 2174885 2175187 "SETMN" NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1013 2173823 2174008 2174038 "SETCAT" 2174155 SETCAT (NIL) -9 NIL 2174239 NIL) (-1012 2173655 2173719 2173818 "SETCAT-" NIL SETCAT- (NIL T) -7 NIL NIL NIL) (-1011 2169878 2172109 2172152 "SETAGG" 2173020 SETAGG (NIL T) -9 NIL 2173358 NIL) (-1010 2169484 2169636 2169873 "SETAGG-" NIL SETAGG- (NIL T T) -7 NIL NIL NIL) (-1009 2166438 2169431 2169479 "SET" NIL SET (NIL T) -8 NIL NIL NIL) (-1008 2165904 2166214 2166314 "SEQAST" NIL SEQAST (NIL) -8 NIL NIL NIL) (-1007 2165031 2165397 2165458 "SEGXCAT" 2165744 SEGXCAT (NIL T T) -9 NIL 2165864 NIL) (-1006 2163956 2164224 2164267 "SEGCAT" 2164789 SEGCAT (NIL T) -9 NIL 2165010 NIL) (-1005 2163636 2163701 2163814 "SEGBIND2" NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1004 2162702 2163172 2163380 "SEGBIND" NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1003 2162280 2162559 2162635 "SEGAST" NIL SEGAST (NIL) -8 NIL NIL NIL) (-1002 2161645 2161781 2161985 "SEG2" NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1001 2160711 2161458 2161640 "SEG" NIL SEG (NIL T) -8 NIL NIL NIL) (-1000 2159964 2160659 2160706 "SDVAR" NIL SDVAR (NIL T) -8 NIL NIL NIL) (-999 2151515 2159833 2159959 "SDPOL" NIL SDPOL (NIL T) -8 NIL NIL NIL) (-998 2150375 2150665 2150982 "SCPKG" NIL SCPKG (NIL T) -7 NIL NIL NIL) (-997 2149681 2149893 2150081 "SCOPE" NIL SCOPE (NIL) -8 NIL NIL NIL) (-996 2149031 2149188 2149364 "SCACHE" NIL SCACHE (NIL T) -7 NIL NIL NIL) (-995 2148604 2148835 2148863 "SASTCAT" 2148868 SASTCAT (NIL) -9 NIL 2148881 NIL) (-994 2148071 2148496 2148570 "SAOS" NIL SAOS (NIL) -8 NIL NIL NIL) (-993 2147674 2147715 2147886 "SAERFFC" NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-992 2147305 2147346 2147503 "SAEFACT" NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-991 2140450 2147222 2147300 "SAE" NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-990 2139100 2139429 2139825 "RURPK" NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-989 2137861 2138222 2138522 "RULESET" NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-988 2137485 2137706 2137787 "RULECOLD" NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-987 2134945 2135579 2136032 "RULE" NIL RULE (NIL T T T) -8 NIL NIL NIL) (-986 2134784 2134817 2134885 "RTVALUE" NIL RTVALUE (NIL) -8 NIL NIL NIL) (-985 2134275 2134578 2134669 "RSTRCAST" NIL RSTRCAST (NIL) -8 NIL NIL NIL) (-984 2129903 2130771 2131682 "RSETGCD" NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-983 2118722 2124276 2124370 "RSETCAT" 2128426 RSETCAT (NIL T T T T) -9 NIL 2129514 NIL) (-982 2117260 2117902 2118717 "RSETCAT-" NIL RSETCAT- (NIL T T T T T) -7 NIL NIL NIL) (-981 2111034 2112479 2113986 "RSDCMPK" NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-980 2108916 2109473 2109545 "RRCC" 2110618 RRCC (NIL T T) -9 NIL 2110959 NIL) (-979 2108441 2108640 2108911 "RRCC-" NIL RRCC- (NIL T T T) -7 NIL NIL NIL) (-978 2107911 2108221 2108319 "RPTAST" NIL RPTAST (NIL) -8 NIL NIL NIL) (-977 2080527 2091176 2091240 "RPOLCAT" 2101714 RPOLCAT (NIL T T T) -9 NIL 2104859 NIL) (-976 2074626 2077449 2080522 "RPOLCAT-" NIL RPOLCAT- (NIL T T T T) -7 NIL NIL NIL) (-975 2070857 2074374 2074512 "ROMAN" NIL ROMAN (NIL) -8 NIL NIL NIL) (-974 2069185 2069924 2070180 "ROIRC" NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-973 2064890 2067640 2067668 "RNS" 2067930 RNS (NIL) -9 NIL 2068182 NIL) (-972 2063793 2064280 2064817 "RNS-" NIL RNS- (NIL T) -7 NIL NIL NIL) (-971 2062911 2063312 2063512 "RNGBIND" NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-970 2062199 2062699 2062727 "RNG" 2062732 RNG (NIL) -9 NIL 2062753 NIL) (-969 2061492 2061966 2062006 "RMODULE" 2062011 RMODULE (NIL T) -9 NIL 2062037 NIL) (-968 2060431 2060537 2060867 "RMCAT2" NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-967 2057309 2060021 2060314 "RMATRIX" NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-966 2049989 2052450 2052562 "RMATCAT" 2055867 RMATCAT (NIL NIL NIL T T T) -9 NIL 2056844 NIL) (-965 2049506 2049685 2049984 "RMATCAT-" NIL RMATCAT- (NIL T NIL NIL T T T) -7 NIL NIL NIL) (-964 2049074 2049285 2049326 "RLINSET" 2049387 RLINSET (NIL T) -9 NIL 2049431 NIL) (-963 2048719 2048800 2048926 "RINTERP" NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-962 2047627 2048296 2048324 "RING" 2048379 RING (NIL) -9 NIL 2048471 NIL) (-961 2047472 2047528 2047622 "RING-" NIL RING- (NIL T) -7 NIL NIL NIL) (-960 2046526 2046793 2047049 "RIDIST" NIL RIDIST (NIL) -7 NIL NIL NIL) (-959 2037513 2046154 2046355 "RGCHAIN" NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-958 2036769 2037249 2037288 "RGBCSPC" 2037345 RGBCSPC (NIL T) -9 NIL 2037396 NIL) (-957 2035834 2036289 2036328 "RGBCMDL" 2036556 RGBCMDL (NIL T) -9 NIL 2036670 NIL) (-956 2035546 2035615 2035716 "RFFACTOR" NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-955 2035309 2035350 2035445 "RFFACT" NIL RFFACT (NIL T) -7 NIL NIL NIL) (-954 2033733 2034163 2034543 "RFDIST" NIL RFDIST (NIL) -7 NIL NIL NIL) (-953 2031320 2031988 2032656 "RF" NIL RF (NIL T) -7 NIL NIL NIL) (-952 2030870 2030968 2031128 "RETSOL" NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-951 2030492 2030590 2030631 "RETRACT" 2030762 RETRACT (NIL T) -9 NIL 2030849 NIL) (-950 2030372 2030403 2030487 "RETRACT-" NIL RETRACT- (NIL T T) -7 NIL NIL NIL) (-949 2029974 2030246 2030313 "RETAST" NIL RETAST (NIL) -8 NIL NIL NIL) (-948 2028518 2029345 2029542 "RESRING" NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-947 2028209 2028270 2028366 "RESLATC" NIL RESLATC (NIL T) -7 NIL NIL NIL) (-946 2027952 2027993 2028098 "REPSQ" NIL REPSQ (NIL T) -7 NIL NIL NIL) (-945 2027687 2027728 2027837 "REPDB" NIL REPDB (NIL T) -7 NIL NIL NIL) (-944 2022758 2024209 2025424 "REP2" NIL REP2 (NIL T) -7 NIL NIL NIL) (-943 2019857 2020615 2021423 "REP1" NIL REP1 (NIL T) -7 NIL NIL NIL) (-942 2017826 2018448 2019048 "REP" NIL REP (NIL) -7 NIL NIL NIL) (-941 2010461 2016377 2016813 "REGSET" NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-940 2009773 2010053 2010202 "REF" NIL REF (NIL T) -8 NIL NIL NIL) (-939 2009258 2009373 2009538 "REDORDER" NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-938 2004915 2008661 2008882 "RECLOS" NIL RECLOS (NIL T) -8 NIL NIL NIL) (-937 2004147 2004346 2004559 "REALSOLV" NIL REALSOLV (NIL) -7 NIL NIL NIL) (-936 2001437 2002275 2003157 "REAL0Q" NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-935 1998019 1999055 2000114 "REAL0" NIL REAL0 (NIL T) -7 NIL NIL NIL) (-934 1997855 1997908 1997936 "REAL" 1997941 REAL (NIL) -9 NIL 1997976 NIL) (-933 1997345 1997649 1997740 "RDUCEAST" NIL RDUCEAST (NIL) -8 NIL NIL NIL) (-932 1996825 1996903 1997108 "RDIV" NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-931 1996058 1996250 1996461 "RDIST" NIL RDIST (NIL T) -7 NIL NIL NIL) (-930 1994946 1995243 1995610 "RDETRS" NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-929 1993213 1993683 1994216 "RDETR" NIL RDETR (NIL T T) -7 NIL NIL NIL) (-928 1992135 1992412 1992799 "RDEEFS" NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-927 1990962 1991271 1991690 "RDEEF" NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-926 1984374 1987822 1987850 "RCFIELD" 1989127 RCFIELD (NIL) -9 NIL 1989857 NIL) (-925 1982992 1983604 1984301 "RCFIELD-" NIL RCFIELD- (NIL T) -7 NIL NIL NIL) (-924 1979192 1981084 1981125 "RCAGG" 1982192 RCAGG (NIL T) -9 NIL 1982653 NIL) (-923 1978919 1979029 1979187 "RCAGG-" NIL RCAGG- (NIL T T) -7 NIL NIL NIL) (-922 1978364 1978493 1978654 "RATRET" NIL RATRET (NIL T) -7 NIL NIL NIL) (-921 1977981 1978060 1978179 "RATFACT" NIL RATFACT (NIL T) -7 NIL NIL NIL) (-920 1977396 1977546 1977696 "RANDSRC" NIL RANDSRC (NIL) -7 NIL NIL NIL) (-919 1977178 1977228 1977299 "RADUTIL" NIL RADUTIL (NIL) -7 NIL NIL NIL) (-918 1969684 1976296 1976604 "RADIX" NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-917 1959450 1969551 1969679 "RADFF" NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-916 1959084 1959177 1959205 "RADCAT" 1959362 RADCAT (NIL) -9 NIL NIL NIL) (-915 1958922 1958982 1959079 "RADCAT-" NIL RADCAT- (NIL T) -7 NIL NIL NIL) (-914 1957022 1958753 1958842 "QUEUE" NIL QUEUE (NIL T) -8 NIL NIL NIL) (-913 1956703 1956752 1956879 "QUATCT2" NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-912 1949054 1953074 1953114 "QUATCAT" 1953892 QUATCAT (NIL T) -9 NIL 1954656 NIL) (-911 1946304 1947584 1948960 "QUATCAT-" NIL QUATCAT- (NIL T T) -7 NIL NIL NIL) (-910 1942208 1946254 1946299 "QUAT" NIL QUAT (NIL T) -8 NIL NIL NIL) (-909 1939595 1941262 1941303 "QUAGG" 1941678 QUAGG (NIL T) -9 NIL 1941852 NIL) (-908 1939197 1939469 1939536 "QQUTAST" NIL QQUTAST (NIL) -8 NIL NIL NIL) (-907 1938235 1938833 1938996 "QFORM" NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-906 1937916 1937965 1938092 "QFCAT2" NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-905 1927603 1933710 1933750 "QFCAT" 1934408 QFCAT (NIL T) -9 NIL 1935401 NIL) (-904 1924487 1925926 1927509 "QFCAT-" NIL QFCAT- (NIL T T) -7 NIL NIL NIL) (-903 1924033 1924167 1924297 "QEQUAT" NIL QEQUAT (NIL) -8 NIL NIL NIL) (-902 1918229 1919390 1920552 "QCMPACK" NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-901 1917648 1917828 1918060 "QALGSET2" NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-900 1915470 1915998 1916421 "QALGSET" NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-899 1914369 1914611 1914928 "PWFFINTB" NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-898 1912730 1912928 1913281 "PUSHVAR" NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-897 1908486 1909702 1909743 "PTRANFN" 1911627 PTRANFN (NIL T) -9 NIL NIL NIL) (-896 1907133 1907478 1907799 "PTPACK" NIL PTPACK (NIL T) -7 NIL NIL NIL) (-895 1906826 1906889 1906996 "PTFUNC2" NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-894 1900899 1905622 1905662 "PTCAT" 1905954 PTCAT (NIL T) -9 NIL 1906107 NIL) (-893 1900592 1900633 1900757 "PSQFR" NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-892 1899471 1899787 1900121 "PSEUDLIN" NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-891 1888350 1890911 1893220 "PSETPK" NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-890 1881257 1884153 1884247 "PSETCAT" 1887221 PSETCAT (NIL T T T T) -9 NIL 1888028 NIL) (-889 1879707 1880441 1881252 "PSETCAT-" NIL PSETCAT- (NIL T T T T T) -7 NIL NIL NIL) (-888 1879026 1879221 1879249 "PSCURVE" 1879517 PSCURVE (NIL) -9 NIL 1879684 NIL) (-887 1874690 1876448 1876512 "PSCAT" 1877347 PSCAT (NIL T T T) -9 NIL 1877586 NIL) (-886 1874004 1874286 1874685 "PSCAT-" NIL PSCAT- (NIL T T T T) -7 NIL NIL NIL) (-885 1872433 1873316 1873579 "PRTITION" NIL PRTITION (NIL) -8 NIL NIL NIL) (-884 1871924 1872227 1872318 "PRTDAST" NIL PRTDAST (NIL) -8 NIL NIL NIL) (-883 1862944 1865366 1867554 "PRS" NIL PRS (NIL T T) -7 NIL NIL NIL) (-882 1860687 1862264 1862304 "PRQAGG" 1862487 PRQAGG (NIL T) -9 NIL 1862588 NIL) (-881 1859860 1860306 1860334 "PROPLOG" 1860473 PROPLOG (NIL) -9 NIL 1860587 NIL) (-880 1859535 1859598 1859721 "PROPFUN2" NIL PROPFUN2 (NIL T T) -7 NIL NIL NIL) (-879 1858971 1859110 1859282 "PROPFUN1" NIL PROPFUN1 (NIL T) -7 NIL NIL NIL) (-878 1857219 1857982 1858279 "PROPFRML" NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-877 1856771 1856903 1857031 "PROPERTY" NIL PROPERTY (NIL) -8 NIL NIL NIL) (-876 1851427 1855711 1856531 "PRODUCT" NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-875 1851256 1851294 1851353 "PRINT" NIL PRINT (NIL) -7 NIL NIL NIL) (-874 1850695 1850835 1850986 "PRIMES" NIL PRIMES (NIL T) -7 NIL NIL NIL) (-873 1849163 1849582 1850048 "PRIMELT" NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-872 1848880 1848941 1848969 "PRIMCAT" 1849093 PRIMCAT (NIL) -9 NIL NIL NIL) (-871 1848051 1848247 1848475 "PRIMARR2" NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-870 1843929 1848001 1848046 "PRIMARR" NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-869 1843628 1843690 1843801 "PREASSOC" NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-868 1840828 1843277 1843510 "PR" NIL PR (NIL T T) -8 NIL NIL NIL) (-867 1840279 1840436 1840464 "PPCURVE" 1840669 PPCURVE (NIL) -9 NIL 1840805 NIL) (-866 1839892 1840137 1840220 "PORTNUM" NIL PORTNUM (NIL) -8 NIL NIL NIL) (-865 1837648 1838069 1838661 "POLYROOT" NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-864 1837091 1837155 1837388 "POLYLIFT" NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-863 1833811 1834297 1834908 "POLYCATQ" NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-862 1819466 1825531 1825595 "POLYCAT" 1829080 POLYCAT (NIL T T T) -9 NIL 1830957 NIL) (-861 1814976 1817123 1819461 "POLYCAT-" NIL POLYCAT- (NIL T T T T) -7 NIL NIL NIL) (-860 1814633 1814707 1814826 "POLY2UP" NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-859 1814326 1814389 1814496 "POLY2" NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-858 1807753 1814059 1814218 "POLY" NIL POLY (NIL T) -8 NIL NIL NIL) (-857 1806640 1806903 1807179 "POLUTIL" NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-856 1805244 1805557 1805887 "POLTOPOL" NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-855 1800406 1805194 1805239 "POINT" NIL POINT (NIL T) -8 NIL NIL NIL) (-854 1798894 1799305 1799680 "PNTHEORY" NIL PNTHEORY (NIL) -7 NIL NIL NIL) (-853 1797651 1797960 1798356 "PMTOOLS" NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-852 1797322 1797406 1797523 "PMSYM" NIL PMSYM (NIL T) -7 NIL NIL NIL) (-851 1796901 1796976 1797150 "PMQFCAT" NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-850 1796387 1796483 1796643 "PMPREDFS" NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-849 1795859 1795979 1796133 "PMPRED" NIL PMPRED (NIL T) -7 NIL NIL NIL) (-848 1794754 1794972 1795349 "PMPLCAT" NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-847 1794365 1794450 1794602 "PMLSAGG" NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-846 1793916 1793998 1794179 "PMKERNEL" NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-845 1793608 1793689 1793802 "PMINS" NIL PMINS (NIL T) -7 NIL NIL NIL) (-844 1793121 1793196 1793404 "PMFS" NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-843 1792469 1792597 1792799 "PMDOWN" NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-842 1791831 1791965 1792128 "PMASSFS" NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-841 1791135 1791317 1791498 "PMASS" NIL PMASS (NIL) -7 NIL NIL NIL) (-840 1790858 1790932 1791026 "PLOTTOOL" NIL PLOTTOOL (NIL) -7 NIL NIL NIL) (-839 1787426 1788615 1789531 "PLOT3D" NIL PLOT3D (NIL) -8 NIL NIL NIL) (-838 1786510 1786711 1786946 "PLOT1" NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-837 1782075 1783459 1784601 "PLOT" NIL PLOT (NIL) -8 NIL NIL NIL) (-836 1761996 1766883 1771730 "PLEQN" NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-835 1761736 1761789 1761892 "PINTERPA" NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-834 1761177 1761311 1761491 "PINTERP" NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-833 1759248 1760407 1760435 "PID" 1760632 PID (NIL) -9 NIL 1760759 NIL) (-832 1759036 1759079 1759154 "PICOERCE" NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-831 1758223 1758883 1758970 "PI" NIL PI (NIL) -8 NIL NIL 1759010) (-830 1757675 1757826 1758002 "PGROEB" NIL PGROEB (NIL T) -7 NIL NIL NIL) (-829 1754003 1754961 1755866 "PGE" NIL PGE (NIL) -7 NIL NIL NIL) (-828 1752367 1752656 1753022 "PGCD" NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-827 1751809 1751924 1752085 "PFRPAC" NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-826 1748414 1750678 1751031 "PFR" NIL PFR (NIL T) -8 NIL NIL NIL) (-825 1747020 1747300 1747625 "PFOTOOLS" NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-824 1745785 1746039 1746387 "PFOQ" NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-823 1744495 1744722 1745074 "PFO" NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-822 1741567 1743065 1743093 "PFECAT" 1743686 PFECAT (NIL) -9 NIL 1744063 NIL) (-821 1741190 1741355 1741562 "PFECAT-" NIL PFECAT- (NIL T) -7 NIL NIL NIL) (-820 1740014 1740296 1740597 "PFBRU" NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-819 1738196 1738583 1739013 "PFBR" NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-818 1734230 1738122 1738191 "PF" NIL PF (NIL NIL) -8 NIL NIL NIL) (-817 1730133 1731280 1732147 "PERMGRP" NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-816 1728065 1729154 1729195 "PERMCAT" 1729594 PERMCAT (NIL T) -9 NIL 1729891 NIL) (-815 1727761 1727808 1727931 "PERMAN" NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-814 1724210 1725891 1726536 "PERM" NIL PERM (NIL T) -8 NIL NIL NIL) (-813 1721675 1723965 1724086 "PENDTREE" NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-812 1720544 1720807 1720848 "PDSPC" 1721381 PDSPC (NIL T) -9 NIL 1721626 NIL) (-811 1719911 1720177 1720539 "PDSPC-" NIL PDSPC- (NIL T T) -7 NIL NIL NIL) (-810 1718608 1719539 1719580 "PDRING" 1719585 PDRING (NIL T) -9 NIL 1719612 NIL) (-809 1717349 1718107 1718160 "PDMOD" 1718165 PDMOD (NIL T T) -9 NIL 1718268 NIL) (-808 1716442 1716654 1716903 "PDECOMP" NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-807 1716047 1716114 1716168 "PDDOM" 1716333 PDDOM (NIL T T) -9 NIL 1716413 NIL) (-806 1715899 1715935 1716042 "PDDOM-" NIL PDDOM- (NIL T T T) -7 NIL NIL NIL) (-805 1715685 1715724 1715813 "PCOMP" NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-804 1714002 1714756 1715055 "PBWLB" NIL PBWLB (NIL T) -8 NIL NIL NIL) (-803 1713691 1713754 1713863 "PATTERN2" NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-802 1711829 1712259 1712710 "PATTERN1" NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-801 1705449 1707278 1708570 "PATTERN" NIL PATTERN (NIL T) -8 NIL NIL NIL) (-800 1705080 1705153 1705285 "PATRES2" NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-799 1702782 1703462 1703943 "PATRES" NIL PATRES (NIL T T) -8 NIL NIL NIL) (-798 1700986 1701414 1701817 "PATMATCH" NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-797 1700432 1700680 1700721 "PATMAB" 1700828 PATMAB (NIL T) -9 NIL 1700911 NIL) (-796 1699079 1699483 1699740 "PATLRES" NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-795 1698617 1698748 1698789 "PATAB" 1698794 PATAB (NIL T) -9 NIL 1698966 NIL) (-794 1697160 1697597 1698020 "PARTPERM" NIL PARTPERM (NIL) -7 NIL NIL NIL) (-793 1696838 1696913 1697015 "PARSURF" NIL PARSURF (NIL T) -8 NIL NIL NIL) (-792 1696527 1696590 1696699 "PARSU2" NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-791 1696332 1696378 1696445 "PARSER" NIL PARSER (NIL) -7 NIL NIL NIL) (-790 1696010 1696085 1696187 "PARSCURV" NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-789 1695699 1695762 1695871 "PARSC2" NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-788 1695390 1695460 1695557 "PARPCURV" NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-787 1695079 1695142 1695251 "PARPC2" NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-786 1694240 1694619 1694798 "PARAMAST" NIL PARAMAST (NIL) -8 NIL NIL NIL) (-785 1693847 1693945 1694064 "PAN2EXPR" NIL PAN2EXPR (NIL) -7 NIL NIL NIL) (-784 1692815 1693240 1693459 "PALETTE" NIL PALETTE (NIL) -8 NIL NIL NIL) (-783 1691480 1692134 1692494 "PAIR" NIL PAIR (NIL T T) -8 NIL NIL NIL) (-782 1684634 1690884 1691078 "PADICRC" NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-781 1677119 1684132 1684316 "PADICRAT" NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-780 1673906 1675759 1675799 "PADICCT" 1676380 PADICCT (NIL NIL) -9 NIL 1676662 NIL) (-779 1671960 1673856 1673901 "PADIC" NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-778 1671122 1671332 1671598 "PADEPAC" NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-777 1670464 1670607 1670811 "PADE" NIL PADE (NIL T T T) -7 NIL NIL NIL) (-776 1668909 1669872 1670150 "OWP" NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-775 1668433 1668692 1668789 "OVERSET" NIL OVERSET (NIL) -8 NIL NIL NIL) (-774 1667492 1668170 1668342 "OVAR" NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-773 1657914 1660783 1662982 "OUTFORM" NIL OUTFORM (NIL) -8 NIL NIL NIL) (-772 1657306 1657620 1657746 "OUTBFILE" NIL OUTBFILE (NIL) -8 NIL NIL NIL) (-771 1656583 1656778 1656806 "OUTBCON" 1657124 OUTBCON (NIL) -9 NIL 1657290 NIL) (-770 1656291 1656421 1656578 "OUTBCON-" NIL OUTBCON- (NIL T) -7 NIL NIL NIL) (-769 1655672 1655817 1655978 "OUT" NIL OUT (NIL) -7 NIL NIL NIL) (-768 1655043 1655470 1655559 "OSI" NIL OSI (NIL) -8 NIL NIL NIL) (-767 1654458 1654873 1654901 "OSGROUP" 1654906 OSGROUP (NIL) -9 NIL 1654928 NIL) (-766 1653422 1653683 1653968 "ORTHPOL" NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-765 1650755 1653297 1653417 "OREUP" NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-764 1647960 1650506 1650632 "ORESUP" NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-763 1645978 1646506 1647066 "OREPCTO" NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-762 1639382 1641860 1641900 "OREPCAT" 1644221 OREPCAT (NIL T) -9 NIL 1645323 NIL) (-761 1637408 1638342 1639377 "OREPCAT-" NIL OREPCAT- (NIL T T) -7 NIL NIL NIL) (-760 1636605 1636876 1636904 "ORDTYPE" 1637209 ORDTYPE (NIL) -9 NIL 1637367 NIL) (-759 1636139 1636350 1636600 "ORDTYPE-" NIL ORDTYPE- (NIL T) -7 NIL NIL NIL) (-758 1635601 1635977 1636134 "ORDSTRCT" NIL ORDSTRCT (NIL T NIL) -8 NIL NIL NIL) (-757 1635095 1635458 1635486 "ORDSET" 1635491 ORDSET (NIL) -9 NIL 1635513 NIL) (-756 1633735 1634695 1634723 "ORDRING" 1634728 ORDRING (NIL) -9 NIL 1634756 NIL) (-755 1632983 1633540 1633568 "ORDMON" 1633573 ORDMON (NIL) -9 NIL 1633594 NIL) (-754 1632287 1632449 1632641 "ORDFUNS" NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-753 1631498 1632006 1632034 "ORDFIN" 1632099 ORDFIN (NIL) -9 NIL 1632173 NIL) (-752 1630892 1631031 1631217 "ORDCOMP2" NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-751 1627666 1629860 1630266 "ORDCOMP" NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-750 1627073 1627428 1627533 "OPSIG" NIL OPSIG (NIL) -8 NIL NIL NIL) (-749 1626881 1626926 1626992 "OPQUERY" NIL OPQUERY (NIL) -7 NIL NIL NIL) (-748 1626182 1626458 1626499 "OPERCAT" 1626710 OPERCAT (NIL T) -9 NIL 1626806 NIL) (-747 1625994 1626061 1626177 "OPERCAT-" NIL OPERCAT- (NIL T T) -7 NIL NIL NIL) (-746 1623424 1624796 1625292 "OP" NIL OP (NIL T) -8 NIL NIL NIL) (-745 1622845 1622972 1623146 "ONECOMP2" NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-744 1619845 1621984 1622350 "ONECOMP" NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-743 1616476 1619275 1619315 "OMSAGG" 1619376 OMSAGG (NIL T) -9 NIL 1619440 NIL) (-742 1614952 1616147 1616315 "OMLO" NIL OMLO (NIL T T) -8 NIL NIL NIL) (-741 1613223 1614402 1614430 "OINTDOM" 1614435 OINTDOM (NIL) -9 NIL 1614456 NIL) (-740 1610653 1612225 1612554 "OFMONOID" NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-739 1609907 1610603 1610648 "ODVAR" NIL ODVAR (NIL T) -8 NIL NIL NIL) (-738 1607173 1609748 1609902 "ODR" NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-737 1598774 1607044 1607168 "ODPOL" NIL ODPOL (NIL T) -8 NIL NIL NIL) (-736 1592284 1598665 1598769 "ODP" NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-735 1591256 1591493 1591766 "ODETOOLS" NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-734 1588890 1589560 1590264 "ODESYS" NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-733 1584667 1585627 1586650 "ODERTRIC" NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-732 1584175 1584263 1584457 "ODERED" NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-731 1581624 1582206 1582879 "ODERAT" NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-730 1579019 1579527 1580123 "ODEPRRIC" NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-729 1576016 1576555 1577201 "ODEPRIM" NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-728 1575371 1575479 1575737 "ODEPAL" NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-727 1574529 1574654 1574875 "ODEINT" NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-726 1570813 1571609 1572522 "ODEEF" NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-725 1570253 1570348 1570570 "ODECONST" NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-724 1569934 1569983 1570110 "OCTCT2" NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-723 1566601 1569733 1569852 "OCT" NIL OCT (NIL T) -8 NIL NIL NIL) (-722 1565792 1566383 1566411 "OCAMON" 1566416 OCAMON (NIL) -9 NIL 1566437 NIL) (-721 1560068 1562818 1562858 "OC" 1563953 OC (NIL T) -9 NIL 1564809 NIL) (-720 1558068 1558994 1559974 "OC-" NIL OC- (NIL T T) -7 NIL NIL NIL) (-719 1557484 1557902 1557930 "OASGP" 1557935 OASGP (NIL) -9 NIL 1557955 NIL) (-718 1556578 1557196 1557224 "OAMONS" 1557264 OAMONS (NIL) -9 NIL 1557307 NIL) (-717 1555754 1556304 1556332 "OAMON" 1556389 OAMON (NIL) -9 NIL 1556440 NIL) (-716 1555650 1555682 1555749 "OAMON-" NIL OAMON- (NIL T) -7 NIL NIL NIL) (-715 1554432 1555175 1555203 "OAGROUP" 1555349 OAGROUP (NIL) -9 NIL 1555441 NIL) (-714 1554223 1554310 1554427 "OAGROUP-" NIL OAGROUP- (NIL T) -7 NIL NIL NIL) (-713 1553963 1554019 1554107 "NUMTUBE" NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-712 1549025 1550588 1552115 "NUMQUAD" NIL NUMQUAD (NIL) -7 NIL NIL NIL) (-711 1545720 1546754 1547789 "NUMODE" NIL NUMODE (NIL) -7 NIL NIL NIL) (-710 1544830 1545063 1545281 "NUMFMT" NIL NUMFMT (NIL) -7 NIL NIL NIL) (-709 1533691 1536719 1539167 "NUMERIC" NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-708 1527578 1533132 1533226 "NTSCAT" 1533231 NTSCAT (NIL T T T T) -9 NIL 1533269 NIL) (-707 1526919 1527098 1527291 "NTPOLFN" NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-706 1526612 1526675 1526782 "NSUP2" NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-705 1514343 1524232 1525042 "NSUP" NIL NSUP (NIL T) -8 NIL NIL NIL) (-704 1503416 1514208 1514338 "NSMP" NIL NSMP (NIL T T) -8 NIL NIL NIL) (-703 1502136 1502461 1502818 "NREP" NIL NREP (NIL T) -7 NIL NIL NIL) (-702 1500972 1501236 1501594 "NPCOEF" NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-701 1500139 1500272 1500488 "NORMRETR" NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-700 1498457 1498776 1499182 "NORMPK" NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-699 1498170 1498204 1498328 "NORMMA" NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-698 1497989 1498024 1498093 "NONE1" NIL NONE1 (NIL T) -7 NIL NIL NIL) (-697 1497765 1497955 1497984 "NONE" NIL NONE (NIL) -8 NIL NIL NIL) (-696 1497329 1497396 1497573 "NODE1" NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-695 1495647 1496692 1496947 "NNI" NIL NNI (NIL) -8 NIL NIL 1497294) (-694 1494375 1494712 1495076 "NLINSOL" NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-693 1493352 1493604 1493906 "NFINTBAS" NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-692 1492439 1493004 1493045 "NETCLT" 1493216 NETCLT (NIL T) -9 NIL 1493297 NIL) (-691 1491343 1491610 1491891 "NCODIV" NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-690 1491142 1491185 1491260 "NCNTFRAC" NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-689 1489673 1490061 1490481 "NCEP" NIL NCEP (NIL T) -7 NIL NIL NIL) (-688 1488337 1489272 1489300 "NASRING" 1489410 NASRING (NIL) -9 NIL 1489490 NIL) (-687 1488182 1488238 1488332 "NASRING-" NIL NASRING- (NIL T) -7 NIL NIL NIL) (-686 1487142 1487789 1487817 "NARNG" 1487934 NARNG (NIL) -9 NIL 1488025 NIL) (-685 1486918 1487003 1487137 "NARNG-" NIL NARNG- (NIL T) -7 NIL NIL NIL) (-684 1485715 1486438 1486478 "NAALG" 1486557 NAALG (NIL T) -9 NIL 1486618 NIL) (-683 1485585 1485620 1485710 "NAALG-" NIL NAALG- (NIL T T) -7 NIL NIL NIL) (-682 1480564 1481749 1482935 "MULTSQFR" NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-681 1479959 1480046 1480230 "MULTFACT" NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-680 1472033 1476463 1476515 "MTSCAT" 1477575 MTSCAT (NIL T T) -9 NIL 1478089 NIL) (-679 1471799 1471859 1471951 "MTHING" NIL MTHING (NIL T) -7 NIL NIL NIL) (-678 1471625 1471664 1471724 "MSYSCMD" NIL MSYSCMD (NIL) -7 NIL NIL NIL) (-677 1468487 1471176 1471217 "MSETAGG" 1471222 MSETAGG (NIL T) -9 NIL 1471256 NIL) (-676 1464624 1467533 1467851 "MSET" NIL MSET (NIL T) -8 NIL NIL NIL) (-675 1460962 1462721 1463461 "MRING" NIL MRING (NIL T T) -8 NIL NIL NIL) (-674 1460599 1460672 1460801 "MRF2" NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-673 1460252 1460293 1460437 "MRATFAC" NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-672 1458117 1458454 1458885 "MPRFF" NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-671 1451579 1458016 1458112 "MPOLY" NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-670 1451104 1451145 1451353 "MPCPF" NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-669 1450663 1450712 1450895 "MPC3" NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-668 1449937 1450030 1450249 "MPC2" NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-667 1448554 1448915 1449305 "MONOTOOL" NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-666 1448075 1448142 1448181 "MONOPC" 1448241 MONOPC (NIL T) -9 NIL 1448460 NIL) (-665 1447526 1447862 1447990 "MONOP" NIL MONOP (NIL T) -8 NIL NIL NIL) (-664 1446668 1447047 1447075 "MONOID" 1447293 MONOID (NIL) -9 NIL 1447437 NIL) (-663 1446327 1446477 1446663 "MONOID-" NIL MONOID- (NIL T) -7 NIL NIL NIL) (-662 1435327 1442135 1442194 "MONOGEN" 1442868 MONOGEN (NIL T T) -9 NIL 1443324 NIL) (-661 1433339 1434225 1435208 "MONOGEN-" NIL MONOGEN- (NIL T T T) -7 NIL NIL NIL) (-660 1432053 1432597 1432625 "MONADWU" 1433016 MONADWU (NIL) -9 NIL 1433251 NIL) (-659 1431601 1431801 1432048 "MONADWU-" NIL MONADWU- (NIL T) -7 NIL NIL NIL) (-658 1430878 1431179 1431207 "MONAD" 1431414 MONAD (NIL) -9 NIL 1431526 NIL) (-657 1430645 1430741 1430873 "MONAD-" NIL MONAD- (NIL T) -7 NIL NIL NIL) (-656 1429035 1429805 1430084 "MOEBIUS" NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-655 1428200 1428696 1428736 "MODULE" 1428741 MODULE (NIL T) -9 NIL 1428779 NIL) (-654 1427879 1428005 1428195 "MODULE-" NIL MODULE- (NIL T T) -7 NIL NIL NIL) (-653 1425654 1426476 1426790 "MODRING" NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-652 1422897 1424250 1424763 "MODOP" NIL MODOP (NIL T T) -8 NIL NIL NIL) (-651 1421531 1422105 1422381 "MODMONOM" NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-650 1410814 1420196 1420609 "MODMON" NIL MODMON (NIL T T) -8 NIL NIL NIL) (-649 1407834 1409814 1410083 "MODFIELD" NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-648 1406918 1407285 1407475 "MMLFORM" NIL MMLFORM (NIL) -8 NIL NIL NIL) (-647 1406487 1406536 1406715 "MMAP" NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-646 1404374 1405308 1405348 "MLO" 1405765 MLO (NIL T) -9 NIL 1406005 NIL) (-645 1402255 1402782 1403377 "MLIFT" NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-644 1401723 1401819 1401973 "MKUCFUNC" NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-643 1401393 1401469 1401592 "MKRECORD" NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-642 1400605 1400791 1401019 "MKFUNC" NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-641 1400098 1400214 1400370 "MKFLCFN" NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-640 1399470 1399584 1399769 "MKBCFUNC" NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-639 1398497 1398770 1399047 "MHROWRED" NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-638 1397930 1398018 1398189 "MFINFACT" NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-637 1395088 1395967 1396846 "MESH" NIL MESH (NIL) -7 NIL NIL NIL) (-636 1393755 1394103 1394456 "MDDFACT" NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-635 1390412 1392879 1392920 "MDAGG" 1393177 MDAGG (NIL T) -9 NIL 1393322 NIL) (-634 1389686 1389850 1390050 "MCDEN" NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-633 1388764 1389050 1389280 "MAYBE" NIL MAYBE (NIL T) -8 NIL NIL NIL) (-632 1386861 1387438 1387999 "MATSTOR" NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-631 1382632 1386451 1386698 "MATRIX" NIL MATRIX (NIL T) -8 NIL NIL NIL) (-630 1378981 1379750 1380484 "MATLIN" NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-629 1377734 1377903 1378232 "MATCAT2" NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-628 1367247 1370836 1370912 "MATCAT" 1375900 MATCAT (NIL T T T) -9 NIL 1377368 NIL) (-627 1364528 1365834 1367242 "MATCAT-" NIL MATCAT- (NIL T T T T) -7 NIL NIL NIL) (-626 1362929 1363289 1363673 "MAPPKG3" NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-625 1362062 1362259 1362481 "MAPPKG2" NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-624 1360813 1361139 1361466 "MAPPKG1" NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-623 1359975 1360377 1360553 "MAPPAST" NIL MAPPAST (NIL) -8 NIL NIL NIL) (-622 1359644 1359708 1359831 "MAPHACK3" NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-621 1359292 1359365 1359479 "MAPHACK2" NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-620 1358827 1358942 1359084 "MAPHACK1" NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-619 1357036 1357804 1358105 "MAGMA" NIL MAGMA (NIL T) -8 NIL NIL NIL) (-618 1356530 1356832 1356922 "MACROAST" NIL MACROAST (NIL) -8 NIL NIL NIL) (-617 1350039 1354845 1354886 "LZSTAGG" 1355663 LZSTAGG (NIL T) -9 NIL 1355953 NIL) (-616 1347158 1348592 1350034 "LZSTAGG-" NIL LZSTAGG- (NIL T T) -7 NIL NIL NIL) (-615 1344545 1345511 1345994 "LWORD" NIL LWORD (NIL T) -8 NIL NIL NIL) (-614 1344126 1344405 1344479 "LSTAST" NIL LSTAST (NIL) -8 NIL NIL NIL) (-613 1336354 1343987 1344121 "LSQM" NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-612 1335717 1335862 1336090 "LSPP" NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-611 1333201 1333899 1334611 "LSMP1" NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-610 1331313 1331636 1332084 "LSMP" NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-609 1324482 1330400 1330441 "LSAGG" 1330503 LSAGG (NIL T) -9 NIL 1330581 NIL) (-608 1322176 1323275 1324477 "LSAGG-" NIL LSAGG- (NIL T T) -7 NIL NIL NIL) (-607 1319688 1321525 1321774 "LPOLY" NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-606 1319355 1319446 1319569 "LPEFRAC" NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-605 1319026 1319105 1319133 "LOGIC" 1319244 LOGIC (NIL) -9 NIL 1319326 NIL) (-604 1318921 1318950 1319021 "LOGIC-" NIL LOGIC- (NIL T) -7 NIL NIL NIL) (-603 1318240 1318398 1318591 "LODOOPS" NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-602 1317025 1317274 1317625 "LODOF" NIL LODOF (NIL T T) -7 NIL NIL NIL) (-601 1312911 1315646 1315686 "LODOCAT" 1316118 LODOCAT (NIL T) -9 NIL 1316329 NIL) (-600 1312704 1312780 1312906 "LODOCAT-" NIL LODOCAT- (NIL T T) -7 NIL NIL NIL) (-599 1309768 1312581 1312699 "LODO2" NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-598 1306930 1309718 1309763 "LODO1" NIL LODO1 (NIL T) -8 NIL NIL NIL) (-597 1304081 1306860 1306925 "LODO" NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-596 1303134 1303309 1303611 "LODEEF" NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-595 1301298 1302396 1302649 "LO" NIL LO (NIL T T T) -8 NIL NIL NIL) (-594 1296393 1299457 1299498 "LNAGG" 1300360 LNAGG (NIL T) -9 NIL 1300795 NIL) (-593 1295780 1296047 1296388 "LNAGG-" NIL LNAGG- (NIL T T) -7 NIL NIL NIL) (-592 1292352 1293293 1293930 "LMOPS" NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-591 1291645 1292119 1292159 "LMODULE" 1292164 LMODULE (NIL T) -9 NIL 1292190 NIL) (-590 1288824 1291382 1291504 "LMDICT" NIL LMDICT (NIL T) -8 NIL NIL NIL) (-589 1288392 1288603 1288644 "LLINSET" 1288705 LLINSET (NIL T) -9 NIL 1288749 NIL) (-588 1288068 1288328 1288387 "LITERAL" NIL LITERAL (NIL T) -8 NIL NIL NIL) (-587 1287667 1287747 1287886 "LIST3" NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-586 1286118 1286466 1286865 "LIST2MAP" NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-585 1285289 1285485 1285713 "LIST2" NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-584 1278336 1284545 1284799 "LIST" NIL LIST (NIL T) -8 NIL NIL NIL) (-583 1277913 1278146 1278187 "LINSET" 1278192 LINSET (NIL T) -9 NIL 1278225 NIL) (-582 1276846 1277536 1277703 "LINFORM" NIL LINFORM (NIL T NIL) -8 NIL NIL NIL) (-581 1275143 1275867 1275907 "LINEXP" 1276393 LINEXP (NIL T) -9 NIL 1276666 NIL) (-580 1273797 1274752 1274933 "LINELT" NIL LINELT (NIL T NIL) -8 NIL NIL NIL) (-579 1272624 1272896 1273198 "LINDEP" NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-578 1271837 1272426 1272536 "LINBASIS" NIL LINBASIS (NIL NIL) -8 NIL NIL NIL) (-577 1269387 1270109 1270859 "LIMITRF" NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-576 1268017 1268314 1268705 "LIMITPS" NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-575 1266841 1267412 1267452 "LIECAT" 1267592 LIECAT (NIL T) -9 NIL 1267743 NIL) (-574 1266715 1266748 1266836 "LIECAT-" NIL LIECAT- (NIL T T) -7 NIL NIL NIL) (-573 1261003 1266405 1266633 "LIE" NIL LIE (NIL T T) -8 NIL NIL NIL) (-572 1253352 1260679 1260835 "LIB" NIL LIB (NIL) -8 NIL NIL NIL) (-571 1249804 1250753 1251688 "LGROBP" NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-570 1248428 1249336 1249364 "LFCAT" 1249571 LFCAT (NIL) -9 NIL 1249710 NIL) (-569 1246667 1246997 1247342 "LF" NIL LF (NIL T T) -7 NIL NIL NIL) (-568 1244184 1244849 1245530 "LEXTRIPK" NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-567 1241196 1242174 1242677 "LEXP" NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-566 1240687 1240990 1241081 "LETAST" NIL LETAST (NIL) -8 NIL NIL NIL) (-565 1239394 1239718 1240118 "LEADCDET" NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-564 1238660 1238745 1238971 "LAZM3PK" NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-563 1233727 1237228 1237764 "LAUPOL" NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-562 1233352 1233402 1233562 "LAPLACE" NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-561 1232185 1232896 1232936 "LALG" 1232997 LALG (NIL T) -9 NIL 1233055 NIL) (-560 1231968 1232045 1232180 "LALG-" NIL LALG- (NIL T T) -7 NIL NIL NIL) (-559 1229885 1231236 1231487 "LA" NIL LA (NIL T T T) -8 NIL NIL NIL) (-558 1229714 1229744 1229785 "KVTFROM" 1229847 KVTFROM (NIL T) -9 NIL NIL NIL) (-557 1228530 1229245 1229434 "KTVLOGIC" NIL KTVLOGIC (NIL) -8 NIL NIL NIL) (-556 1228359 1228389 1228430 "KRCFROM" 1228492 KRCFROM (NIL T) -9 NIL NIL NIL) (-555 1227461 1227658 1227953 "KOVACIC" NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-554 1227290 1227320 1227361 "KONVERT" 1227423 KONVERT (NIL T) -9 NIL NIL NIL) (-553 1227119 1227149 1227190 "KOERCE" 1227252 KOERCE (NIL T) -9 NIL NIL NIL) (-552 1226689 1226782 1226914 "KERNEL2" NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-551 1224742 1225636 1226008 "KERNEL" NIL KERNEL (NIL T) -8 NIL NIL NIL) (-550 1217919 1222934 1222988 "KDAGG" 1223364 KDAGG (NIL T T) -9 NIL 1223571 NIL) (-549 1217567 1217709 1217914 "KDAGG-" NIL KDAGG- (NIL T T T) -7 NIL NIL NIL) (-548 1210397 1217348 1217505 "KAFILE" NIL KAFILE (NIL T) -8 NIL NIL NIL) (-547 1210047 1210329 1210392 "JVMOP" NIL JVMOP (NIL) -8 NIL NIL NIL) (-546 1209017 1209516 1209765 "JVMMDACC" NIL JVMMDACC (NIL) -8 NIL NIL NIL) (-545 1208143 1208592 1208797 "JVMFDACC" NIL JVMFDACC (NIL) -8 NIL NIL NIL) (-544 1207007 1207499 1207799 "JVMCSTTG" NIL JVMCSTTG (NIL) -8 NIL NIL NIL) (-543 1206289 1206688 1206849 "JVMCFACC" NIL JVMCFACC (NIL) -8 NIL NIL NIL) (-542 1205999 1206235 1206284 "JVMBCODE" NIL JVMBCODE (NIL) -8 NIL NIL NIL) (-541 1200286 1205689 1205917 "JORDAN" NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-540 1199704 1200037 1200157 "JOINAST" NIL JOINAST (NIL) -8 NIL NIL NIL) (-539 1195866 1197881 1197935 "IXAGG" 1198862 IXAGG (NIL T T) -9 NIL 1199319 NIL) (-538 1195072 1195443 1195861 "IXAGG-" NIL IXAGG- (NIL T T T) -7 NIL NIL NIL) (-537 1190326 1195008 1195067 "IVECTOR" NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-536 1189293 1189568 1189831 "ITUPLE" NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-535 1187955 1188162 1188455 "ITRIGMNP" NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-534 1186906 1187128 1187411 "ITFUN3" NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-533 1186581 1186644 1186767 "ITFUN2" NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-532 1185843 1186215 1186389 "ITFORM" NIL ITFORM (NIL) -8 NIL NIL NIL) (-531 1183883 1185119 1185393 "ITAYLOR" NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-530 1173495 1179200 1180357 "ISUPS" NIL ISUPS (NIL T) -8 NIL NIL NIL) (-529 1172740 1172892 1173128 "ISUMP" NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-528 1172231 1172534 1172625 "ISAST" NIL ISAST (NIL) -8 NIL NIL NIL) (-527 1171524 1171615 1171828 "IRURPK" NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-526 1170656 1170881 1171121 "IRSN" NIL IRSN (NIL) -7 NIL NIL NIL) (-525 1169069 1169450 1169878 "IRRF2F" NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-524 1168854 1168898 1168974 "IRREDFFX" NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-523 1167704 1168001 1168296 "IROOT" NIL IROOT (NIL T) -7 NIL NIL NIL) (-522 1166977 1167328 1167479 "IRFORM" NIL IRFORM (NIL) -8 NIL NIL NIL) (-521 1166180 1166311 1166524 "IR2F" NIL IR2F (NIL T T) -7 NIL NIL NIL) (-520 1164335 1164832 1165376 "IR2" NIL IR2 (NIL T T) -7 NIL NIL NIL) (-519 1161448 1162684 1163373 "IR" NIL IR (NIL T) -8 NIL NIL NIL) (-518 1161273 1161313 1161373 "IPRNTPK" NIL IPRNTPK (NIL) -7 NIL NIL NIL) (-517 1157335 1161199 1161268 "IPF" NIL IPF (NIL NIL) -8 NIL NIL NIL) (-516 1155402 1157274 1157330 "IPADIC" NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-515 1154773 1155072 1155202 "IP4ADDR" NIL IP4ADDR (NIL) -8 NIL NIL NIL) (-514 1154226 1154514 1154646 "IOMODE" NIL IOMODE (NIL) -8 NIL NIL NIL) (-513 1153307 1153932 1154058 "IOBFILE" NIL IOBFILE (NIL) -8 NIL NIL NIL) (-512 1152717 1153211 1153239 "IOBCON" 1153244 IOBCON (NIL) -9 NIL 1153265 NIL) (-511 1152288 1152352 1152534 "INVLAPLA" NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-510 1144332 1146703 1149028 "INTTR" NIL INTTR (NIL T T) -7 NIL NIL NIL) (-509 1141443 1142226 1143090 "INTTOOLS" NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-508 1141120 1141217 1141334 "INTSLPE" NIL INTSLPE (NIL) -7 NIL NIL NIL) (-507 1138626 1141056 1141115 "INTRVL" NIL INTRVL (NIL T) -8 NIL NIL NIL) (-506 1136738 1137267 1137834 "INTRF" NIL INTRF (NIL T) -7 NIL NIL NIL) (-505 1136240 1136354 1136494 "INTRET" NIL INTRET (NIL T) -7 NIL NIL NIL) (-504 1134624 1135030 1135492 "INTRAT" NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-503 1132403 1132997 1133608 "INTPM" NIL INTPM (NIL T T) -7 NIL NIL NIL) (-502 1129776 1130386 1131106 "INTPAF" NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-501 1129180 1129338 1129546 "INTHERTR" NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-500 1128699 1128785 1128973 "INTHERAL" NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-499 1126904 1127425 1127882 "INTHEORY" NIL INTHEORY (NIL) -7 NIL NIL NIL) (-498 1119986 1121639 1123368 "INTG0" NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-497 1119352 1119514 1119687 "INTFACT" NIL INTFACT (NIL T) -7 NIL NIL NIL) (-496 1117225 1117689 1118233 "INTEF" NIL INTEF (NIL T T) -7 NIL NIL NIL) (-495 1115413 1116301 1116329 "INTDOM" 1116628 INTDOM (NIL) -9 NIL 1116833 NIL) (-494 1114966 1115168 1115408 "INTDOM-" NIL INTDOM- (NIL T) -7 NIL NIL NIL) (-493 1110837 1113245 1113299 "INTCAT" 1114095 INTCAT (NIL T) -9 NIL 1114411 NIL) (-492 1110402 1110522 1110649 "INTBIT" NIL INTBIT (NIL) -7 NIL NIL NIL) (-491 1109242 1109414 1109720 "INTALG" NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-490 1108815 1108911 1109068 "INTAF" NIL INTAF (NIL T T) -7 NIL NIL NIL) (-489 1101855 1108670 1108810 "INTABL" NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-488 1101153 1101708 1101773 "INT8" NIL INT8 (NIL) -8 NIL NIL 1101807) (-487 1100450 1101005 1101070 "INT64" NIL INT64 (NIL) -8 NIL NIL 1101104) (-486 1099747 1100302 1100367 "INT32" NIL INT32 (NIL) -8 NIL NIL 1100401) (-485 1099044 1099599 1099664 "INT16" NIL INT16 (NIL) -8 NIL NIL 1099698) (-484 1095571 1098963 1099039 "INT" NIL INT (NIL) -8 NIL NIL NIL) (-483 1089692 1093111 1093139 "INS" 1094069 INS (NIL) -9 NIL 1094728 NIL) (-482 1087754 1088672 1089619 "INS-" NIL INS- (NIL T) -7 NIL NIL NIL) (-481 1086813 1087036 1087311 "INPSIGN" NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-480 1086027 1086168 1086365 "INPRODPF" NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-479 1085017 1085158 1085395 "INPRODFF" NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-478 1084169 1084333 1084593 "INNMFACT" NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-477 1083449 1083564 1083752 "INMODGCD" NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-476 1082188 1082457 1082781 "INFSP" NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-475 1081468 1081609 1081792 "INFPROD0" NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-474 1081131 1081203 1081301 "INFORM1" NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-473 1078209 1079695 1080218 "INFORM" NIL INFORM (NIL) -8 NIL NIL NIL) (-472 1077808 1077915 1078029 "INFINITY" NIL INFINITY (NIL) -7 NIL NIL NIL) (-471 1076964 1077609 1077710 "INETCLTS" NIL INETCLTS (NIL) -8 NIL NIL NIL) (-470 1075814 1076082 1076403 "INEP" NIL INEP (NIL T T T) -7 NIL NIL NIL) (-469 1074836 1075744 1075809 "INDE" NIL INDE (NIL T) -8 NIL NIL NIL) (-468 1074461 1074541 1074658 "INCRMAPS" NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-467 1073375 1073920 1074124 "INBFILE" NIL INBFILE (NIL) -8 NIL NIL NIL) (-466 1069470 1070525 1071468 "INBFF" NIL INBFF (NIL T) -7 NIL NIL NIL) (-465 1068324 1068647 1068675 "INBCON" 1069188 INBCON (NIL) -9 NIL 1069454 NIL) (-464 1067778 1068043 1068319 "INBCON-" NIL INBCON- (NIL T) -7 NIL NIL NIL) (-463 1067272 1067574 1067664 "INAST" NIL INAST (NIL) -8 NIL NIL NIL) (-462 1066729 1067038 1067143 "IMPTAST" NIL IMPTAST (NIL) -8 NIL NIL NIL) (-461 1062829 1066621 1066724 "IMATRIX" NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-460 1061669 1061808 1062123 "IMATQF" NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-459 1060093 1060360 1060697 "IMATLIN" NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-458 1057909 1059975 1060088 "IIARRAY2" NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-457 1052816 1057840 1057904 "IFF" NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-456 1052196 1052530 1052645 "IFAST" NIL IFAST (NIL) -8 NIL NIL NIL) (-455 1047003 1051634 1051820 "IFARRAY" NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-454 1046065 1046925 1046998 "IFAMON" NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-453 1045637 1045714 1045768 "IEVALAB" 1045975 IEVALAB (NIL T T) -9 NIL NIL NIL) (-452 1045392 1045472 1045632 "IEVALAB-" NIL IEVALAB- (NIL T T T) -7 NIL NIL NIL) (-451 1044777 1045004 1045161 "IDPT" NIL IDPT (NIL T T) -8 NIL NIL NIL) (-450 1043802 1044697 1044772 "IDPOAMS" NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-449 1042896 1043722 1043797 "IDPOAM" NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-448 1042251 1042830 1042891 "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 BBTREE (NIL T) -8 NIL NIL NIL) (-72 133151 133244 133270 "BASTYPE" 133441 BASTYPE (NIL) -9 NIL 133537 NIL) (-71 132921 133017 133146 "BASTYPE-" NIL BASTYPE- (NIL T) -7 NIL NIL NIL) (-70 132436 132524 132674 "BALFACT" NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-69 131335 132010 132195 "AUTOMOR" NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-68 131061 131066 131092 "ATTREG" 131097 ATTREG (NIL) -9 NIL NIL NIL) (-67 130666 130938 131003 "ATTRAST" NIL ATTRAST (NIL) -8 NIL NIL NIL) (-66 130166 130315 130341 "ATRIG" 130542 ATRIG (NIL) -9 NIL NIL NIL) (-65 130021 130074 130161 "ATRIG-" NIL ATRIG- (NIL T) -7 NIL NIL NIL) (-64 129591 129822 129848 "ASTCAT" 129853 ASTCAT (NIL) -9 NIL 129883 NIL) (-63 129390 129467 129586 "ASTCAT-" NIL ASTCAT- (NIL T) -7 NIL NIL NIL) (-62 127549 129223 129311 "ASTACK" NIL ASTACK (NIL T) -8 NIL NIL NIL) (-61 126356 126669 127034 "ASSOCEQ" NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-60 124156 126260 126351 "ARRAY2" NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 123347 123538 123759 "ARRAY12" NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-58 118934 123078 123192 "ARRAY1" NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-57 113100 115132 115207 "ARR2CAT" 117837 ARR2CAT (NIL T T T) -9 NIL 118595 NIL) (-56 111477 112247 113095 "ARR2CAT-" NIL ARR2CAT- (NIL T T T T) -7 NIL NIL NIL) (-55 110845 111216 111338 "ARITY" NIL ARITY (NIL) -8 NIL NIL NIL) (-54 109777 109945 110241 "APPRULE" NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 109478 109532 109650 "APPLYORE" NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 108861 109007 109163 "ANY1" NIL ANY1 (NIL T) -7 NIL NIL NIL) (-51 108266 108556 108676 "ANY" NIL ANY (NIL) -8 NIL NIL NIL) (-50 105898 106995 107318 "ANTISYM" NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 105423 105683 105779 "ANON" NIL ANON (NIL) -8 NIL NIL NIL) (-48 99182 104485 104927 "AN" NIL AN (NIL) -8 NIL NIL NIL) (-47 94778 96379 96429 "AMR" 97167 AMR (NIL T T) -9 NIL 97764 NIL) (-46 94132 94412 94773 "AMR-" NIL AMR- (NIL T T T) -7 NIL NIL NIL) (-45 77312 94066 94127 "ALIST" NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 73747 76988 77157 "ALGSC" NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 70757 71417 72024 "ALGPKG" NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 70136 70249 70433 "ALGMFACT" NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 66548 67173 67765 "ALGMANIP" NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 56101 66241 66391 "ALGFF" NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 55418 55572 55750 "ALGFACT" NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 54193 54926 54964 "ALGEBRA" 54969 ALGEBRA (NIL T) -9 NIL 55009 NIL) (-37 53979 54056 54188 "ALGEBRA-" NIL ALGEBRA- (NIL T T) -7 NIL NIL NIL) (-36 33976 51185 51237 "ALAGG" 51375 ALAGG (NIL T T) -9 NIL 51540 NIL) (-35 33476 33625 33651 "AHYP" 33852 AHYP (NIL) -9 NIL NIL NIL) (-34 32772 32953 32979 "AGG" 33260 AGG (NIL) -9 NIL 33447 NIL) (-33 32561 32648 32767 "AGG-" NIL AGG- (NIL T) -7 NIL NIL NIL) (-32 30700 31160 31560 "AF" NIL AF (NIL T T) -7 NIL NIL NIL) (-31 30195 30498 30587 "ADDAST" NIL ADDAST (NIL) -8 NIL NIL NIL) (-30 29565 29860 30016 "ACPLOT" NIL ACPLOT (NIL) -8 NIL NIL NIL) (-29 17187 26402 26440 "ACFS" 27047 ACFS (NIL T) -9 NIL 27286 NIL) (-28 15810 16420 17182 "ACFS-" NIL ACFS- (NIL T T) -7 NIL NIL NIL) (-27 11426 13741 13767 "ACF" 14646 ACF (NIL) -9 NIL 15058 NIL) (-26 10522 10928 11421 "ACF-" NIL ACF- (NIL T) -7 NIL NIL NIL) (-25 10024 10264 10290 "ABELSG" 10382 ABELSG (NIL) -9 NIL 10447 NIL) (-24 9922 9953 10019 "ABELSG-" NIL ABELSG- (NIL T) -7 NIL NIL NIL) (-23 9188 9531 9557 "ABELMON" 9726 ABELMON (NIL) -9 NIL 9835 NIL) (-22 8931 9040 9183 "ABELMON-" NIL ABELMON- (NIL T) -7 NIL NIL NIL) (-21 8174 8626 8652 "ABELGRP" 8724 ABELGRP (NIL) -9 NIL 8799 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
+((-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 BBTREE (NIL T) -8 NIL NIL NIL) (-72 133151 133244 133270 "BASTYPE" 133441 BASTYPE (NIL) -9 NIL 133537 NIL) (-71 132921 133017 133146 "BASTYPE-" NIL BASTYPE- (NIL T) -7 NIL NIL NIL) (-70 132436 132524 132674 "BALFACT" NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-69 131335 132010 132195 "AUTOMOR" NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-68 131061 131066 131092 "ATTREG" 131097 ATTREG (NIL) -9 NIL NIL NIL) (-67 130666 130938 131003 "ATTRAST" NIL ATTRAST (NIL) -8 NIL NIL NIL) (-66 130166 130315 130341 "ATRIG" 130542 ATRIG (NIL) -9 NIL NIL NIL) (-65 130021 130074 130161 "ATRIG-" NIL ATRIG- (NIL T) -7 NIL NIL NIL) (-64 129591 129822 129848 "ASTCAT" 129853 ASTCAT (NIL) -9 NIL 129883 NIL) (-63 129390 129467 129586 "ASTCAT-" NIL ASTCAT- (NIL T) -7 NIL NIL NIL) (-62 127549 129223 129311 "ASTACK" NIL ASTACK (NIL T) -8 NIL NIL NIL) (-61 126356 126669 127034 "ASSOCEQ" NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-60 124156 126260 126351 "ARRAY2" NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 123347 123538 123759 "ARRAY12" NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-58 118934 123078 123192 "ARRAY1" NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-57 113100 115132 115207 "ARR2CAT" 117837 ARR2CAT (NIL T T T) -9 NIL 118595 NIL) (-56 111477 112247 113095 "ARR2CAT-" NIL ARR2CAT- (NIL T T T T) -7 NIL NIL NIL) (-55 110845 111216 111338 "ARITY" NIL ARITY (NIL) -8 NIL NIL NIL) (-54 109777 109945 110241 "APPRULE" NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 109478 109532 109650 "APPLYORE" NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 108861 109007 109163 "ANY1" NIL ANY1 (NIL T) -7 NIL NIL NIL) (-51 108266 108556 108676 "ANY" NIL ANY (NIL) -8 NIL NIL NIL) (-50 105898 106995 107318 "ANTISYM" NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 105423 105683 105779 "ANON" NIL ANON (NIL) -8 NIL NIL NIL) (-48 99182 104485 104927 "AN" NIL AN (NIL) -8 NIL NIL NIL) (-47 94778 96379 96429 "AMR" 97167 AMR (NIL T T) -9 NIL 97764 NIL) (-46 94132 94412 94773 "AMR-" NIL AMR- (NIL T T T) -7 NIL NIL NIL) (-45 77312 94066 94127 "ALIST" NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 73747 76988 77157 "ALGSC" NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 70757 71417 72024 "ALGPKG" NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 70136 70249 70433 "ALGMFACT" NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 66548 67173 67765 "ALGMANIP" NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 56101 66241 66391 "ALGFF" NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 55418 55572 55750 "ALGFACT" NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 54193 54926 54964 "ALGEBRA" 54969 ALGEBRA (NIL T) -9 NIL 55009 NIL) (-37 53979 54056 54188 "ALGEBRA-" NIL ALGEBRA- (NIL T T) -7 NIL NIL NIL) (-36 33976 51185 51237 "ALAGG" 51375 ALAGG (NIL T T) -9 NIL 51540 NIL) (-35 33476 33625 33651 "AHYP" 33852 AHYP (NIL) -9 NIL NIL NIL) (-34 32772 32953 32979 "AGG" 33260 AGG (NIL) -9 NIL 33447 NIL) (-33 32561 32648 32767 "AGG-" NIL AGG- (NIL T) -7 NIL NIL NIL) (-32 30700 31160 31560 "AF" NIL AF (NIL T T) -7 NIL NIL NIL) (-31 30195 30498 30587 "ADDAST" NIL ADDAST (NIL) -8 NIL NIL NIL) (-30 29565 29860 30016 "ACPLOT" NIL ACPLOT (NIL) -8 NIL NIL NIL) (-29 17187 26402 26440 "ACFS" 27047 ACFS (NIL T) -9 NIL 27286 NIL) (-28 15810 16420 17182 "ACFS-" NIL ACFS- (NIL T T) -7 NIL NIL NIL) (-27 11426 13741 13767 "ACF" 14646 ACF (NIL) -9 NIL 15058 NIL) (-26 10522 10928 11421 "ACF-" NIL ACF- (NIL T) -7 NIL NIL NIL) (-25 10024 10264 10290 "ABELSG" 10382 ABELSG (NIL) -9 NIL 10447 NIL) (-24 9922 9953 10019 "ABELSG-" NIL ABELSG- (NIL T) -7 NIL NIL NIL) (-23 9188 9531 9557 "ABELMON" 9726 ABELMON (NIL) -9 NIL 9835 NIL) (-22 8931 9040 9183 "ABELMON-" NIL ABELMON- (NIL T) -7 NIL NIL NIL) (-21 8174 8626 8652 "ABELGRP" 8724 ABELGRP (NIL) -9 NIL 8799 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 db9897e9..26687276 100644
--- a/src/share/algebra/operation.daase
+++ b/src/share/algebra/operation.daase
@@ -1,5 +1,5 @@
-(630818 . 3576910162)
+(630951 . 3577105536)
(((*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)))))
@@ -36,7 +36,7 @@
((*1 *1 *2)
(OR
(-12 (-5 *2 (-858 (-484))) (-4 *1 (-977 *3 *4 *5))
- (-12 (-2558 (-4 *3 (-38 (-347 (-484))))) (-4 *3 (-38 (-484)))
+ (-12 (-2559 (-4 *3 (-38 (-347 (-484))))) (-4 *3 (-38 (-484)))
(-4 *5 (-554 (-1089))))
(-4 *3 (-962)) (-4 *4 (-718)) (-4 *5 (-757)))
(-12 (-5 *2 (-858 (-484))) (-4 *1 (-977 *3 *4 *5))
@@ -101,7 +101,7 @@
((*1 *2 *1) (-12 (-5 *2 (-345 *1)) (-4 *1 (-1133))))
((*1 *2 *3)
(-12 (-4 *4 (-495)) (-5 *2 (-345 *3)) (-5 *1 (-1158 *4 *3))
- (-4 *3 (-13 (-1154 *4) (-495) (-10 -8 (-15 -3141 ($ $ $)))))))
+ (-4 *3 (-13 (-1154 *4) (-495) (-10 -8 (-15 -3142 ($ $ $)))))))
((*1 *2 *3)
(-12 (-5 *3 (-959 *4 *5)) (-4 *4 (-13 (-756) (-257) (-120) (-934)))
(-14 *5 (-584 (-1089)))
@@ -154,26 +154,26 @@
(((*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)) (|:| -3221 (-584 (-858 *4))))))
+ (-5 *2 (-584 (-2 (|:| -1745 (-1084 *4)) (|:| -3222 (-584 (-858 *4))))))
(-5 *1 (-1206 *4 *5 *6)) (-14 *6 (-584 (-1089)))))
((*1 *2 *3 *4 *4 *4)
(-12 (-5 *4 (-85)) (-4 *5 (-13 (-756) (-257) (-120) (-934)))
- (-5 *2 (-584 (-2 (|:| -1745 (-1084 *5)) (|:| -3221 (-584 (-858 *5))))))
+ (-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)))))
((*1 *2 *3 *4 *4)
(-12 (-5 *4 (-85)) (-4 *5 (-13 (-756) (-257) (-120) (-934)))
- (-5 *2 (-584 (-2 (|:| -1745 (-1084 *5)) (|:| -3221 (-584 (-858 *5))))))
+ (-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)))))
((*1 *2 *3 *4)
(-12 (-5 *4 (-85)) (-4 *5 (-13 (-756) (-257) (-120) (-934)))
- (-5 *2 (-584 (-2 (|:| -1745 (-1084 *5)) (|:| -3221 (-584 (-858 *5))))))
+ (-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)))))
((*1 *2 *3)
(-12 (-4 *4 (-13 (-756) (-257) (-120) (-934)))
- (-5 *2 (-584 (-2 (|:| -1745 (-1084 *4)) (|:| -3221 (-584 (-858 *4))))))
+ (-5 *2 (-584 (-2 (|:| -1745 (-1084 *4)) (|:| -3222 (-584 (-858 *4))))))
(-5 *1 (-1206 *4 *5 *6)) (-5 *3 (-584 (-858 *4))) (-14 *5 (-584 (-1089)))
(-14 *6 (-584 (-1089))))))
(((*1 *2 *3 *4 *4)
@@ -248,10 +248,10 @@
((*1 *1 *1 *2) (-12 (-4 *1 (-333 *2)) (-4 *2 (-1013))))
((*1 *1 *2 *1) (-12 (-4 *1 (-333 *2)) (-4 *2 (-1013))))
((*1 *1 *2 *1)
- (-12 (-14 *3 (-584 (-1089))) (-4 *4 (-146)) (-4 *6 (-196 (-3953 *3) (-695)))
+ (-12 (-14 *3 (-584 (-1089))) (-4 *4 (-146)) (-4 *6 (-196 (-3954 *3) (-695)))
(-14 *7
- (-1 (-85) (-2 (|:| -2398 *5) (|:| -2399 *6))
- (-2 (|:| -2398 *5) (|:| -2399 *6))))
+ (-1 (-85) (-2 (|:| -2399 *5) (|:| -2400 *6))
+ (-2 (|:| -2399 *5) (|:| -2400 *6))))
(-5 *1 (-398 *3 *4 *5 *6 *7 *2)) (-4 *5 (-757))
(-4 *2 (-862 *4 *6 (-774 *3)))))
((*1 *1 *1 *2) (-12 (-4 *1 (-407 *2 *3)) (-4 *2 (-146)) (-4 *3 (-23))))
@@ -319,10 +319,10 @@
(-14 *3 (-584 (-1089)))))
((*1 *1 *1) (-12 (-4 *1 (-332 *2 *3)) (-4 *2 (-962)) (-4 *3 (-1013))))
((*1 *1 *1)
- (-12 (-14 *2 (-584 (-1089))) (-4 *3 (-146)) (-4 *5 (-196 (-3953 *2) (-695)))
+ (-12 (-14 *2 (-584 (-1089))) (-4 *3 (-146)) (-4 *5 (-196 (-3954 *2) (-695)))
(-14 *6
- (-1 (-85) (-2 (|:| -2398 *4) (|:| -2399 *5))
- (-2 (|:| -2398 *4) (|:| -2399 *5))))
+ (-1 (-85) (-2 (|:| -2399 *4) (|:| -2400 *5))
+ (-2 (|:| -2399 *4) (|:| -2400 *5))))
(-5 *1 (-398 *2 *3 *4 *5 *6 *7)) (-4 *4 (-757))
(-4 *7 (-862 *3 *5 (-774 *2)))))
((*1 *1 *1) (-12 (-4 *1 (-447 *2 *3)) (-4 *2 (-72)) (-4 *3 (-760))))
@@ -425,8 +425,8 @@
(-5 *2 (-519 *6)) (-5 *1 (-520 *5 *6))))
((*1 *2 *3 *4)
(|partial| -12 (-5 *3 (-1 *6 *5))
- (-5 *4 (-3 (-2 (|:| -2134 *5) (|:| |coeff| *5)) "failed")) (-4 *5 (-311))
- (-4 *6 (-311)) (-5 *2 (-2 (|:| -2134 *6) (|:| |coeff| *6)))
+ (-5 *4 (-3 (-2 (|:| -2135 *5) (|:| |coeff| *5)) "failed")) (-4 *5 (-311))
+ (-4 *6 (-311)) (-5 *2 (-2 (|:| -2135 *6) (|:| |coeff| *6)))
(-5 *1 (-520 *5 *6))))
((*1 *2 *3 *4)
(|partial| -12 (-5 *3 (-1 *2 *5)) (-5 *4 (-3 *5 "failed")) (-4 *5 (-311))
@@ -536,7 +536,7 @@
(-4 *6 (-718))
(-4 *2
(-13 (-1013)
- (-10 -8 (-15 -3835 ($ $ $)) (-15 * ($ $ $)) (-15 ** ($ $ (-695))))))
+ (-10 -8 (-15 -3836 ($ $ $)) (-15 * ($ $ $)) (-15 ** ($ $ (-695))))))
(-5 *1 (-864 *6 *7 *8 *5 *2)) (-4 *5 (-862 *8 *6 *7))))
((*1 *2 *3 *4)
(-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-870 *5)) (-4 *5 (-1128)) (-4 *6 (-1128))
@@ -552,7 +552,7 @@
(-4 *5 (-718))
(-4 *6
(-13 (-757)
- (-10 -8 (-15 -3968 ((-1089) $)) (-15 -3827 ((-3 $ "failed") (-1089))))))
+ (-10 -8 (-15 -3969 ((-1089) $)) (-15 -3828 ((-3 $ "failed") (-1089))))))
(-5 *1 (-898 *4 *5 *6 *2))))
((*1 *2 *3 *4)
(-12 (-5 *3 (-1 *6 *5)) (-4 *5 (-495)) (-4 *6 (-495)) (-4 *2 (-905 *6))
@@ -634,7 +634,7 @@
(-12 (-5 *2 (-1 *4 *4)) (-4 *1 (-1198 *3 *4)) (-4 *3 (-757)) (-4 *4 (-962))))
((*1 *1 *2 *1)
(-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-962)) (-5 *1 (-1202 *3 *4)) (-4 *4 (-755)))))
-(((*1 *2 *1) (-12 (|has| *1 (-6 -3991)) (-4 *1 (-34)) (-5 *2 (-695))))
+(((*1 *2 *1) (-12 (|has| *1 (-6 -3992)) (-4 *1 (-34)) (-5 *2 (-695))))
((*1 *2 *1) (-12 (-5 *2 (-695)) (-5 *1 (-209))))
((*1 *2 *1) (-12 (-5 *2 (-695)) (-5 *1 (-885))))
((*1 *2 *1)
@@ -870,7 +870,7 @@
(-14 *4 (-1 *2 *2 *3)) (-14 *5 (-1 (-3 *3 "failed") *3 *3))
(-14 *6 (-1 (-3 *2 "failed") *2 *2 *3))))
((*1 *1 *2)
- (-12 (-5 *2 (-584 (-2 (|:| -3950 *3) (|:| -3934 *4)))) (-4 *3 (-962))
+ (-12 (-5 *2 (-584 (-2 (|:| -3951 *3) (|:| -3935 *4)))) (-4 *3 (-962))
(-4 *4 (-664)) (-5 *1 (-675 *3 *4))))
((*1 *1 *2) (-12 (-5 *2 (-484)) (-4 *1 (-688))))
((*1 *2 *3) (-12 (-5 *2 (-697)) (-5 *1 (-698 *3)) (-4 *3 (-1128))))
@@ -999,7 +999,7 @@
((*1 *1 *1) (-4 *1 (-239)))
((*1 *2 *3)
(-12 (-5 *3 (-345 *4)) (-4 *4 (-495))
- (-5 *2 (-584 (-2 (|:| -3950 (-695)) (|:| |logand| *4)))) (-5 *1 (-270 *4))))
+ (-5 *2 (-584 (-2 (|:| -3951 (-695)) (|:| |logand| *4)))) (-5 *1 (-270 *4))))
((*1 *2 *1)
(-12 (-5 *2 (-607 *3 *4)) (-5 *1 (-567 *3 *4 *5)) (-4 *3 (-757))
(-4 *4 (-13 (-146) (-655 (-347 (-484))))) (-14 *5 (-831))))
@@ -1135,50 +1135,50 @@
(((*1 *2 *1) (-12 (-5 *2 (-1048)) (-5 *1 (-1189)))))
(((*1 *2 *1) (-12 (-5 *2 (-1048)) (-5 *1 (-1189)))))
(((*1 *2 *3)
- (-12 (-4 *3 (-13 (-257) (-10 -8 (-15 -3967 ((-345 $) $)))))
+ (-12 (-4 *3 (-13 (-257) (-10 -8 (-15 -3968 ((-345 $) $)))))
(-4 *4 (-1154 *3))
(-5 *2
- (-2 (|:| -2010 (-631 *3)) (|:| |basisDen| *3) (|:| |basisInv| (-631 *3))))
+ (-2 (|:| -2011 (-631 *3)) (|:| |basisDen| *3) (|:| |basisInv| (-631 *3))))
(-5 *1 (-299 *3 *4 *5)) (-4 *5 (-350 *3 *4))))
((*1 *2 *3)
(-12 (-5 *3 (-484)) (-4 *4 (-1154 *3))
(-5 *2
- (-2 (|:| -2010 (-631 *3)) (|:| |basisDen| *3) (|:| |basisInv| (-631 *3))))
+ (-2 (|:| -2011 (-631 *3)) (|:| |basisDen| *3) (|:| |basisInv| (-631 *3))))
(-5 *1 (-693 *4 *5)) (-4 *5 (-350 *3 *4))))
((*1 *2 *3)
(-12 (-4 *4 (-298)) (-4 *3 (-1154 *4)) (-4 *5 (-1154 *3))
(-5 *2
- (-2 (|:| -2010 (-631 *3)) (|:| |basisDen| *3) (|:| |basisInv| (-631 *3))))
+ (-2 (|:| -2011 (-631 *3)) (|:| |basisDen| *3) (|:| |basisInv| (-631 *3))))
(-5 *1 (-899 *4 *3 *5 *6)) (-4 *6 (-662 *3 *5))))
((*1 *2 *3)
(-12 (-4 *4 (-298)) (-4 *3 (-1154 *4)) (-4 *5 (-1154 *3))
(-5 *2
- (-2 (|:| -2010 (-631 *3)) (|:| |basisDen| *3) (|:| |basisInv| (-631 *3))))
+ (-2 (|:| -2011 (-631 *3)) (|:| |basisDen| *3) (|:| |basisInv| (-631 *3))))
(-5 *1 (-1188 *4 *3 *5 *6)) (-4 *6 (-350 *3 *5)))))
(((*1 *2)
(-12 (-4 *3 (-1133)) (-4 *4 (-1154 *3)) (-4 *5 (-1154 (-347 *4)))
(-5 *2 (-1178 *1)) (-4 *1 (-290 *3 *4 *5))))
((*1 *2)
- (-12 (-4 *3 (-13 (-257) (-10 -8 (-15 -3967 ((-345 $) $)))))
+ (-12 (-4 *3 (-13 (-257) (-10 -8 (-15 -3968 ((-345 $) $)))))
(-4 *4 (-1154 *3))
(-5 *2
- (-2 (|:| -2010 (-631 *3)) (|:| |basisDen| *3) (|:| |basisInv| (-631 *3))))
+ (-2 (|:| -2011 (-631 *3)) (|:| |basisDen| *3) (|:| |basisInv| (-631 *3))))
(-5 *1 (-299 *3 *4 *5)) (-4 *5 (-350 *3 *4))))
((*1 *2)
(-12 (-4 *3 (-1154 (-484)))
(-5 *2
- (-2 (|:| -2010 (-631 (-484))) (|:| |basisDen| (-484))
+ (-2 (|:| -2011 (-631 (-484))) (|:| |basisDen| (-484))
(|:| |basisInv| (-631 (-484)))))
(-5 *1 (-693 *3 *4)) (-4 *4 (-350 (-484) *3))))
((*1 *2)
(-12 (-4 *3 (-298)) (-4 *4 (-1154 *3)) (-4 *5 (-1154 *4))
(-5 *2
- (-2 (|:| -2010 (-631 *4)) (|:| |basisDen| *4) (|:| |basisInv| (-631 *4))))
+ (-2 (|:| -2011 (-631 *4)) (|:| |basisDen| *4) (|:| |basisInv| (-631 *4))))
(-5 *1 (-899 *3 *4 *5 *6)) (-4 *6 (-662 *4 *5))))
((*1 *2)
(-12 (-4 *3 (-298)) (-4 *4 (-1154 *3)) (-4 *5 (-1154 *4))
(-5 *2
- (-2 (|:| -2010 (-631 *4)) (|:| |basisDen| *4) (|:| |basisInv| (-631 *4))))
+ (-2 (|:| -2011 (-631 *4)) (|:| |basisDen| *4) (|:| |basisInv| (-631 *4))))
(-5 *1 (-1188 *3 *4 *5 *6)) (-4 *6 (-350 *4 *5)))))
(((*1 *2 *3 *4 *5)
(-12 (-5 *3 (-695)) (-4 *6 (-311)) (-5 *4 (-1121 *6))
@@ -1283,14 +1283,14 @@
(((*1 *1 *2)
(-12
(-5 *2
- (-2 (|:| |theta| (-179)) (|:| |phi| (-179)) (|:| -3843 (-179))
+ (-2 (|:| |theta| (-179)) (|:| |phi| (-179)) (|:| -3844 (-179))
(|:| |scaleX| (-179)) (|:| |scaleY| (-179)) (|:| |scaleZ| (-179))
(|:| |deltaX| (-179)) (|:| |deltaY| (-179))))
(-5 *1 (-221))))
((*1 *2 *3 *2)
(-12
(-5 *2
- (-2 (|:| |theta| (-179)) (|:| |phi| (-179)) (|:| -3843 (-179))
+ (-2 (|:| |theta| (-179)) (|:| |phi| (-179)) (|:| -3844 (-179))
(|:| |scaleX| (-179)) (|:| |scaleY| (-179)) (|:| |scaleZ| (-179))
(|:| |deltaX| (-179)) (|:| |deltaY| (-179))))
(-5 *3 (-584 (-221))) (-5 *1 (-222))))
@@ -1301,14 +1301,14 @@
((*1 *2 *1 *3)
(-12
(-5 *3
- (-2 (|:| |theta| (-179)) (|:| |phi| (-179)) (|:| -3843 (-179))
+ (-2 (|:| |theta| (-179)) (|:| |phi| (-179)) (|:| -3844 (-179))
(|:| |scaleX| (-179)) (|:| |scaleY| (-179)) (|:| |scaleZ| (-179))
(|:| |deltaX| (-179)) (|:| |deltaY| (-179))))
(-5 *2 (-1184)) (-5 *1 (-1182))))
((*1 *2 *1)
(-12
(-5 *2
- (-2 (|:| |theta| (-179)) (|:| |phi| (-179)) (|:| -3843 (-179))
+ (-2 (|:| |theta| (-179)) (|:| |phi| (-179)) (|:| -3844 (-179))
(|:| |scaleX| (-179)) (|:| |scaleY| (-179)) (|:| |scaleZ| (-179))
(|:| |deltaX| (-179)) (|:| |deltaY| (-179))))
(-5 *1 (-1182))))
@@ -1372,9 +1372,9 @@
(-5 *2
(-1178
(-2 (|:| |scaleX| (-179)) (|:| |scaleY| (-179)) (|:| |deltaX| (-179))
- (|:| |deltaY| (-179)) (|:| -3846 (-484)) (|:| -3844 (-484))
- (|:| |spline| (-484)) (|:| -3875 (-484)) (|:| |axesColor| (-784))
- (|:| -3847 (-484)) (|:| |unitsColor| (-784)) (|:| |showing| (-484)))))
+ (|:| |deltaY| (-179)) (|:| -3847 (-484)) (|:| -3845 (-484))
+ (|:| |spline| (-484)) (|:| -3876 (-484)) (|:| |axesColor| (-784))
+ (|:| -3848 (-484)) (|:| |unitsColor| (-784)) (|:| |showing| (-484)))))
(-5 *1 (-1181)))))
(((*1 *2 *3) (-12 (-5 *3 (-831)) (-5 *2 (-1091 (-347 (-484)))) (-5 *1 (-164))))
((*1 *2 *1) (-12 (-5 *2 (-1178 (-3 (-405) "undefined"))) (-5 *1 (-1181)))))
@@ -1423,16 +1423,16 @@
(-12 (-5 *3 (-1 *2 *5 *2)) (-5 *4 (-58 *5)) (-4 *5 (-1128)) (-4 *2 (-1128))
(-5 *1 (-59 *5 *2))))
((*1 *2 *3 *1 *2 *2)
- (-12 (-5 *3 (-1 *2 *2 *2)) (-4 *2 (-1013)) (|has| *1 (-6 -3991))
+ (-12 (-5 *3 (-1 *2 *2 *2)) (-4 *2 (-1013)) (|has| *1 (-6 -3992))
(-4 *1 (-124 *2)) (-4 *2 (-1128))))
((*1 *2 *3 *1 *2)
- (-12 (-5 *3 (-1 *2 *2 *2)) (|has| *1 (-6 -3991)) (-4 *1 (-124 *2))
+ (-12 (-5 *3 (-1 *2 *2 *2)) (|has| *1 (-6 -3992)) (-4 *1 (-124 *2))
(-4 *2 (-1128))))
((*1 *2 *3 *1)
- (-12 (-5 *3 (-1 *2 *2 *2)) (|has| *1 (-6 -3991)) (-4 *1 (-124 *2))
+ (-12 (-5 *3 (-1 *2 *2 *2)) (|has| *1 (-6 -3992)) (-4 *1 (-124 *2))
(-4 *2 (-1128))))
((*1 *2 *3)
- (-12 (-4 *4 (-962)) (-5 *2 (-2 (|:| -2002 (-1084 *4)) (|:| |deg| (-831))))
+ (-12 (-4 *4 (-962)) (-5 *2 (-2 (|:| -2003 (-1084 *4)) (|:| |deg| (-831))))
(-5 *1 (-175 *4 *5)) (-5 *3 (-1084 *4)) (-4 *5 (-495))))
((*1 *2 *3 *4 *2)
(-12 (-5 *3 (-1 *2 *6 *2)) (-5 *4 (-197 *5 *6)) (-14 *5 (-695))
@@ -1526,7 +1526,7 @@
(-12 (-5 *1 (-167 *2))
(-4 *2
(-13 (-757)
- (-10 -8 (-15 -3796 ((-1072) $ (-1089))) (-15 -3613 ((-1184) $))
+ (-10 -8 (-15 -3797 ((-1072) $ (-1089))) (-15 -3614 ((-1184) $))
(-15 -1962 ((-1184) $)))))))
((*1 *1 *1 *2) (-12 (-5 *1 (-248 *2)) (-4 *2 (-25)) (-4 *2 (-1128))))
((*1 *1 *2 *1) (-12 (-5 *1 (-248 *2)) (-4 *2 (-25)) (-4 *2 (-1128))))
@@ -1557,7 +1557,7 @@
(-12 (-5 *1 (-167 *2))
(-4 *2
(-13 (-757)
- (-10 -8 (-15 -3796 ((-1072) $ (-1089))) (-15 -3613 ((-1184) $))
+ (-10 -8 (-15 -3797 ((-1072) $ (-1089))) (-15 -3614 ((-1184) $))
(-15 -1962 ((-1184) $)))))))
((*1 *1 *1 *2) (-12 (-5 *1 (-248 *2)) (-4 *2 (-21)) (-4 *2 (-1128))))
((*1 *1 *2 *1) (-12 (-5 *1 (-248 *2)) (-4 *2 (-21)) (-4 *2 (-1128))))
@@ -1885,8 +1885,8 @@
(-12 (-4 *3 (-29 (-484))) (-4 *3 (-872)) (-4 *3 (-1114))
(-4 *3 (-38 (-347 (-484))))))
(-12 (-5 *2 (-1089)) (-4 *1 (-1140 *3)) (-4 *3 (-962))
- (-12 (|has| *3 (-15 -3079 ((-584 *2) *3)))
- (|has| *3 (-15 -3808 (*3 *3 *2))) (-4 *3 (-38 (-347 (-484))))))))
+ (-12 (|has| *3 (-15 -3080 ((-584 *2) *3)))
+ (|has| *3 (-15 -3809 (*3 *3 *2))) (-4 *3 (-38 (-347 (-484))))))))
((*1 *1 *1)
(-12 (-4 *1 (-1140 *2)) (-4 *2 (-962)) (-4 *2 (-38 (-347 (-484))))))
((*1 *1 *1)
@@ -1900,8 +1900,8 @@
(-12 (-4 *3 (-29 (-484))) (-4 *3 (-872)) (-4 *3 (-1114))
(-4 *3 (-38 (-347 (-484))))))
(-12 (-5 *2 (-1089)) (-4 *1 (-1161 *3)) (-4 *3 (-962))
- (-12 (|has| *3 (-15 -3079 ((-584 *2) *3)))
- (|has| *3 (-15 -3808 (*3 *3 *2))) (-4 *3 (-38 (-347 (-484))))))))
+ (-12 (|has| *3 (-15 -3080 ((-584 *2) *3)))
+ (|has| *3 (-15 -3809 (*3 *3 *2))) (-4 *3 (-38 (-347 (-484))))))))
((*1 *1 *1)
(-12 (-4 *1 (-1161 *2)) (-4 *2 (-962)) (-4 *2 (-38 (-347 (-484))))))
((*1 *1 *1 *2)
@@ -1913,8 +1913,8 @@
(-12 (-4 *3 (-29 (-484))) (-4 *3 (-872)) (-4 *3 (-1114))
(-4 *3 (-38 (-347 (-484))))))
(-12 (-5 *2 (-1089)) (-4 *1 (-1171 *3)) (-4 *3 (-962))
- (-12 (|has| *3 (-15 -3079 ((-584 *2) *3)))
- (|has| *3 (-15 -3808 (*3 *3 *2))) (-4 *3 (-38 (-347 (-484))))))))
+ (-12 (|has| *3 (-15 -3080 ((-584 *2) *3)))
+ (|has| *3 (-15 -3809 (*3 *3 *2))) (-4 *3 (-38 (-347 (-484))))))))
((*1 *1 *1)
(-12 (-4 *1 (-1171 *2)) (-4 *2 (-962)) (-4 *2 (-38 (-347 (-484)))))))
(((*1 *2 *1 *3)
@@ -1999,13 +1999,13 @@
(-12 (-5 *3 (-1089)) (-5 *2 (-203 (-1072))) (-5 *1 (-167 *4))
(-4 *4
(-13 (-757)
- (-10 -8 (-15 -3796 ((-1072) $ *3)) (-15 -3613 ((-1184) $))
+ (-10 -8 (-15 -3797 ((-1072) $ *3)) (-15 -3614 ((-1184) $))
(-15 -1962 ((-1184) $)))))))
((*1 *1 *1 *2)
(-12 (-5 *2 (-903)) (-5 *1 (-167 *3))
(-4 *3
(-13 (-757)
- (-10 -8 (-15 -3796 ((-1072) $ (-1089))) (-15 -3613 ((-1184) $))
+ (-10 -8 (-15 -3797 ((-1072) $ (-1089))) (-15 -3614 ((-1184) $))
(-15 -1962 ((-1184) $)))))))
((*1 *2 *1 *3)
(-12 (-5 *3 "count") (-5 *2 (-695)) (-5 *1 (-203 *4)) (-4 *4 (-757))))
@@ -2080,48 +2080,48 @@
(((*1 *1 *1) (-12 (-4 *1 (-1167 *2)) (-4 *2 (-1128)))))
(((*1 *2 *1) (-12 (-4 *1 (-1167 *3)) (-4 *3 (-1128)) (-5 *2 (-695)))))
(((*1 *1 *1) (-12 (-4 *1 (-1167 *2)) (-4 *2 (-1128)))))
-(((*1 *1 *1 *1) (-12 (|has| *1 (-6 -3992)) (-4 *1 (-202 *2)) (-4 *2 (-1128))))
+(((*1 *1 *1 *1) (-12 (|has| *1 (-6 -3993)) (-4 *1 (-202 *2)) (-4 *2 (-1128))))
((*1 *1 *1 *1) (-12 (-4 *1 (-237 *2)) (-4 *2 (-1128))))
((*1 *1 *1 *2) (-12 (-4 *1 (-237 *2)) (-4 *2 (-1128))))
- ((*1 *1 *1 *2) (-12 (|has| *1 (-6 -3992)) (-4 *1 (-1167 *2)) (-4 *2 (-1128))))
- ((*1 *1 *1 *1) (-12 (|has| *1 (-6 -3992)) (-4 *1 (-1167 *2)) (-4 *2 (-1128)))))
-(((*1 *1 *1) (-12 (|has| *1 (-6 -3992)) (-4 *1 (-1167 *2)) (-4 *2 (-1128)))))
-(((*1 *2 *1 *2) (-12 (|has| *1 (-6 -3992)) (-4 *1 (-1167 *2)) (-4 *2 (-1128)))))
+ ((*1 *1 *1 *2) (-12 (|has| *1 (-6 -3993)) (-4 *1 (-1167 *2)) (-4 *2 (-1128))))
+ ((*1 *1 *1 *1) (-12 (|has| *1 (-6 -3993)) (-4 *1 (-1167 *2)) (-4 *2 (-1128)))))
+(((*1 *1 *1) (-12 (|has| *1 (-6 -3993)) (-4 *1 (-1167 *2)) (-4 *2 (-1128)))))
+(((*1 *2 *1 *2) (-12 (|has| *1 (-6 -3993)) (-4 *1 (-1167 *2)) (-4 *2 (-1128)))))
(((*1 *2 *1 *3 *3 *2)
(-12 (-5 *3 (-484)) (-4 *1 (-57 *2 *4 *5)) (-4 *2 (-1128)) (-4 *4 (-321 *2))
(-4 *5 (-321 *2))))
((*1 *1 *1 *2 *1)
- (-12 (-5 *2 "right") (|has| *1 (-6 -3992)) (-4 *1 (-92 *3)) (-4 *3 (-1128))))
+ (-12 (-5 *2 "right") (|has| *1 (-6 -3993)) (-4 *1 (-92 *3)) (-4 *3 (-1128))))
((*1 *1 *1 *2 *1)
- (-12 (-5 *2 "left") (|has| *1 (-6 -3992)) (-4 *1 (-92 *3)) (-4 *3 (-1128))))
+ (-12 (-5 *2 "left") (|has| *1 (-6 -3993)) (-4 *1 (-92 *3)) (-4 *3 (-1128))))
((*1 *2 *1 *3 *2)
- (-12 (|has| *1 (-6 -3992)) (-4 *1 (-243 *3 *2)) (-4 *3 (-1013))
+ (-12 (|has| *1 (-6 -3993)) (-4 *1 (-243 *3 *2)) (-4 *3 (-1013))
(-4 *2 (-1128))))
((*1 *2 *1 *3 *2) (-12 (-5 *2 (-51)) (-5 *3 (-1089)) (-5 *1 (-572))))
((*1 *2 *1 *3 *2)
- (-12 (-5 *3 (-1145 (-484))) (|has| *1 (-6 -3992)) (-4 *1 (-594 *2))
+ (-12 (-5 *3 (-1145 (-484))) (|has| *1 (-6 -3993)) (-4 *1 (-594 *2))
(-4 *2 (-1128))))
((*1 *1 *1 *2 *2 *1)
(-12 (-5 *2 (-584 (-484))) (-4 *1 (-628 *3 *4 *5)) (-4 *3 (-962))
(-4 *4 (-321 *3)) (-4 *5 (-321 *3))))
((*1 *2 *1 *3 *2)
- (-12 (-5 *3 "value") (|has| *1 (-6 -3992)) (-4 *1 (-924 *2))
+ (-12 (-5 *3 "value") (|has| *1 (-6 -3993)) (-4 *1 (-924 *2))
(-4 *2 (-1128))))
((*1 *2 *1 *3 *2) (-12 (-4 *1 (-1106 *3 *2)) (-4 *3 (-1013)) (-4 *2 (-1013))))
((*1 *2 *1 *3 *2)
- (-12 (-5 *3 "last") (|has| *1 (-6 -3992)) (-4 *1 (-1167 *2))
+ (-12 (-5 *3 "last") (|has| *1 (-6 -3993)) (-4 *1 (-1167 *2))
(-4 *2 (-1128))))
((*1 *1 *1 *2 *1)
- (-12 (-5 *2 "rest") (|has| *1 (-6 -3992)) (-4 *1 (-1167 *3))
+ (-12 (-5 *2 "rest") (|has| *1 (-6 -3993)) (-4 *1 (-1167 *3))
(-4 *3 (-1128))))
((*1 *2 *1 *3 *2)
- (-12 (-5 *3 "first") (|has| *1 (-6 -3992)) (-4 *1 (-1167 *2))
+ (-12 (-5 *3 "first") (|has| *1 (-6 -3993)) (-4 *1 (-1167 *2))
(-4 *2 (-1128)))))
(((*1 *1 *1 *2 *1) (-12 (-5 *2 (-484)) (-5 *1 (-1068 *3)) (-4 *3 (-1128))))
- ((*1 *1 *1 *1) (-12 (|has| *1 (-6 -3992)) (-4 *1 (-1167 *2)) (-4 *2 (-1128)))))
-(((*1 *2 *1 *2) (-12 (|has| *1 (-6 -3992)) (-4 *1 (-1167 *2)) (-4 *2 (-1128)))))
+ ((*1 *1 *1 *1) (-12 (|has| *1 (-6 -3993)) (-4 *1 (-1167 *2)) (-4 *2 (-1128)))))
+(((*1 *2 *1 *2) (-12 (|has| *1 (-6 -3993)) (-4 *1 (-1167 *2)) (-4 *2 (-1128)))))
(((*1 *1 *1 *2)
- (-12 (-5 *2 (-484)) (|has| *1 (-6 -3992)) (-4 *1 (-1167 *3))
+ (-12 (-5 *2 (-484)) (|has| *1 (-6 -3993)) (-4 *1 (-1167 *3))
(-4 *3 (-1128)))))
(((*1 *2 *1)
(|partial| -12 (-4 *3 (-13 (-951 (-484)) (-581 (-484)) (-389)))
@@ -2218,7 +2218,7 @@
(-5 *2
(-2 (|:| |flg| (-3 "nil" "sqfr" "irred" "prime")) (|:| |fctr| *4)
(|:| |xpnt| (-484))))
- (-4 *4 (-13 (-1154 *3) (-495) (-10 -8 (-15 -3141 ($ $ $))))) (-4 *3 (-495))
+ (-4 *4 (-13 (-1154 *3) (-495) (-10 -8 (-15 -3142 ($ $ $))))) (-4 *3 (-495))
(-5 *1 (-1158 *3 *4)))))
(((*1 *1 *1)
(-12 (-4 *1 (-862 *2 *3 *4)) (-4 *2 (-962)) (-4 *3 (-718)) (-4 *4 (-757))
@@ -2230,15 +2230,15 @@
((*1 *1 *1) (-4 *1 (-1133)))
((*1 *2 *2)
(-12 (-4 *3 (-495)) (-5 *1 (-1158 *3 *2))
- (-4 *2 (-13 (-1154 *3) (-495) (-10 -8 (-15 -3141 ($ $ $))))))))
+ (-4 *2 (-13 (-1154 *3) (-495) (-10 -8 (-15 -3142 ($ $ $))))))))
(((*1 *2 *1)
(-12 (-4 *1 (-273 *3 *4)) (-4 *3 (-1013)) (-4 *4 (-104))
- (-5 *2 (-584 (-2 (|:| |gen| *3) (|:| -3939 *4))))))
+ (-5 *2 (-584 (-2 (|:| |gen| *3) (|:| -3940 *4))))))
((*1 *2 *1)
(-12 (-4 *1 (-447 *3 *4)) (-4 *3 (-72)) (-4 *4 (-760))
(-5 *2 (-584 (-451 *3 *4)))))
((*1 *2 *1)
- (-12 (-5 *2 (-584 (-2 (|:| -3950 *3) (|:| -3934 *4)))) (-5 *1 (-675 *3 *4))
+ (-12 (-5 *2 (-584 (-2 (|:| -3951 *3) (|:| -3935 *4)))) (-5 *1 (-675 *3 *4))
(-4 *3 (-962)) (-4 *4 (-664))))
((*1 *2 *1)
(-12 (-4 *1 (-1157 *3 *4)) (-4 *3 (-962)) (-4 *4 (-717))
@@ -2307,7 +2307,7 @@
(-12 (-4 *1 (-980 *2 *3)) (-4 *2 (-13 (-756) (-311))) (-4 *3 (-1154 *2))))
((*1 *2 *1 *3)
(-12 (-4 *1 (-1157 *2 *3)) (-4 *3 (-717)) (|has| *2 (-15 ** (*2 *2 *3)))
- (|has| *2 (-15 -3942 (*2 (-1089)))) (-4 *2 (-962)))))
+ (|has| *2 (-15 -3943 (*2 (-1089)))) (-4 *2 (-962)))))
(((*1 *1 *1 *2) (-12 (-5 *2 (-484)) (-5 *1 (-148 *3)) (-4 *3 (-257))))
((*1 *1 *1 *2) (-12 (-5 *2 (-484)) (-4 *1 (-617 *3)) (-4 *3 (-1128))))
((*1 *1 *1 *2)
@@ -2420,12 +2420,12 @@
(|partial| -12 (-5 *2 (-695)) (-4 *1 (-1154 *3)) (-4 *3 (-962)))))
(((*1 *2 *1 *1 *3)
(-12 (-4 *4 (-962)) (-4 *5 (-718)) (-4 *3 (-757))
- (-5 *2 (-2 (|:| -1971 *1) (|:| -2900 *1))) (-4 *1 (-862 *4 *5 *3))))
+ (-5 *2 (-2 (|:| -1971 *1) (|:| -2901 *1))) (-4 *1 (-862 *4 *5 *3))))
((*1 *2 *1 *1)
- (-12 (-4 *3 (-962)) (-5 *2 (-2 (|:| -1971 *1) (|:| -2900 *1)))
+ (-12 (-4 *3 (-962)) (-5 *2 (-2 (|:| -1971 *1) (|:| -2901 *1)))
(-4 *1 (-1154 *3)))))
(((*1 *2 *1 *3)
- (-12 (-5 *3 (-695)) (-4 *4 (-962)) (-5 *2 (-2 (|:| -1971 *1) (|:| -2900 *1)))
+ (-12 (-5 *3 (-695)) (-4 *4 (-962)) (-5 *2 (-2 (|:| -1971 *1) (|:| -2901 *1)))
(-4 *1 (-1154 *4)))))
(((*1 *1 *1 *2) (-12 (-5 *2 (-695)) (-4 *1 (-1154 *3)) (-4 *3 (-962)))))
(((*1 *1 *1 *2) (-12 (-5 *2 (-695)) (-4 *1 (-1154 *3)) (-4 *3 (-962)))))
@@ -2486,14 +2486,14 @@
(|partial| -12 (-4 *1 (-1154 *2)) (-4 *2 (-962)) (-4 *2 (-495)))))
(((*1 *1 *1 *1) (-12 (-4 *1 (-1154 *2)) (-4 *2 (-962)) (-4 *2 (-495)))))
(((*1 *2 *3 *3)
- (-12 (-4 *4 (-495)) (-5 *2 (-2 (|:| -3950 *4) (|:| -1971 *3) (|:| -2900 *3)))
+ (-12 (-4 *4 (-495)) (-5 *2 (-2 (|:| -3951 *4) (|:| -1971 *3) (|:| -2901 *3)))
(-5 *1 (-883 *4 *3)) (-4 *3 (-1154 *4))))
((*1 *2 *1 *1)
(-12 (-4 *3 (-962)) (-4 *4 (-718)) (-4 *5 (-757))
- (-5 *2 (-2 (|:| -1971 *1) (|:| -2900 *1))) (-4 *1 (-977 *3 *4 *5))))
+ (-5 *2 (-2 (|:| -1971 *1) (|:| -2901 *1))) (-4 *1 (-977 *3 *4 *5))))
((*1 *2 *1 *1)
(-12 (-4 *3 (-495)) (-4 *3 (-962))
- (-5 *2 (-2 (|:| -3950 *3) (|:| -1971 *1) (|:| -2900 *1)))
+ (-5 *2 (-2 (|:| -3951 *3) (|:| -1971 *1) (|:| -2901 *1)))
(-4 *1 (-1154 *3)))))
(((*1 *2 *3)
(-12 (-4 *4 (-311)) (-4 *4 (-495)) (-4 *5 (-1154 *4))
@@ -2510,14 +2510,14 @@
(((*1 *2 *2 *2) (-12 (-4 *3 (-962)) (-5 *1 (-1152 *3 *2)) (-4 *2 (-1154 *3)))))
(((*1 *2 *2 *2) (-12 (-4 *3 (-962)) (-5 *1 (-1152 *3 *2)) (-4 *2 (-1154 *3)))))
(((*1 *2 *3 *3)
- (|partial| -12 (-4 *4 (-495)) (-5 *2 (-2 (|:| -1971 *3) (|:| -2900 *3)))
+ (|partial| -12 (-4 *4 (-495)) (-5 *2 (-2 (|:| -1971 *3) (|:| -2901 *3)))
(-5 *1 (-1151 *4 *3)) (-4 *3 (-1154 *4)))))
(((*1 *2 *3)
(-12 (-4 *4 (-13 (-495) (-120))) (-5 *2 (-584 *3)) (-5 *1 (-1150 *4 *3))
(-4 *3 (-1154 *4)))))
(((*1 *2 *3)
(|partial| -12 (-4 *4 (-13 (-495) (-120)))
- (-5 *2 (-2 (|:| -3135 *3) (|:| -3134 *3))) (-5 *1 (-1150 *4 *3))
+ (-5 *2 (-2 (|:| -3136 *3) (|:| -3135 *3))) (-5 *1 (-1150 *4 *3))
(-4 *3 (-1154 *4)))))
(((*1 *2 *2 *2)
(|partial| -12 (-4 *3 (-13 (-495) (-120))) (-5 *1 (-1150 *3 *2))
@@ -2541,7 +2541,7 @@
(-5 *2 (-2 (|:| |num| (-631 *4)) (|:| |den| *4))) (-5 *1 (-634 *4 *5))))
((*1 *2 *3 *4)
(-12 (-4 *5 (-13 (-311) (-120) (-951 (-347 (-484))))) (-4 *6 (-1154 *5))
- (-5 *2 (-2 (|:| -3263 *7) (|:| |rh| (-584 (-347 *6)))))
+ (-5 *2 (-2 (|:| -3264 *7) (|:| |rh| (-584 (-347 *6)))))
(-5 *1 (-729 *5 *6 *7 *3)) (-5 *4 (-584 (-347 *6))) (-4 *7 (-601 *6))
(-4 *3 (-601 (-347 *6)))))
((*1 *2 *3)
@@ -2594,13 +2594,13 @@
(-12 (-5 *4 (-85))
(-5 *2
(-2 (|:| |contp| (-484))
- (|:| -1777 (-584 (-2 (|:| |irr| *3) (|:| -2393 (-484)))))))
+ (|:| -1777 (-584 (-2 (|:| |irr| *3) (|:| -2394 (-484)))))))
(-5 *1 (-379 *3)) (-4 *3 (-1154 (-484)))))
((*1 *2 *3 *4)
(-12 (-5 *4 (-85))
(-5 *2
(-2 (|:| |contp| (-484))
- (|:| -1777 (-584 (-2 (|:| |irr| *3) (|:| -2393 (-484)))))))
+ (|:| -1777 (-584 (-2 (|:| |irr| *3) (|:| -2394 (-484)))))))
(-5 *1 (-1144 *3)) (-4 *3 (-1154 (-484))))))
(((*1 *2 *3)
(-12 (-4 *4 (-298)) (-5 *2 (-345 *3)) (-5 *1 (-170 *4 *3))
@@ -2666,7 +2666,7 @@
(-12
(-4 *4
(-13 (-757)
- (-10 -8 (-15 -3968 ((-1089) $)) (-15 -3827 ((-3 $ "failed") (-1089))))))
+ (-10 -8 (-15 -3969 ((-1089) $)) (-15 -3828 ((-3 $ "failed") (-1089))))))
(-4 *5 (-718)) (-4 *7 (-495)) (-5 *2 (-345 *3))
(-5 *1 (-393 *4 *5 *6 *7 *3)) (-4 *6 (-495)) (-4 *3 (-862 *7 *5 *4))))
((*1 *2 *3)
@@ -2710,11 +2710,11 @@
(-12 (-4 *4 (-718))
(-4 *5
(-13 (-757)
- (-10 -8 (-15 -3968 ((-1089) $)) (-15 -3827 ((-3 $ "failed") (-1089))))))
+ (-10 -8 (-15 -3969 ((-1089) $)) (-15 -3828 ((-3 $ "failed") (-1089))))))
(-4 *6 (-257)) (-5 *2 (-345 *3)) (-5 *1 (-670 *4 *5 *6 *3))
(-4 *3 (-862 (-858 *6) *4 *5))))
((*1 *2 *3)
- (-12 (-4 *4 (-718)) (-4 *5 (-13 (-757) (-10 -8 (-15 -3968 ((-1089) $)))))
+ (-12 (-4 *4 (-718)) (-4 *5 (-13 (-757) (-10 -8 (-15 -3969 ((-1089) $)))))
(-4 *6 (-495)) (-5 *2 (-345 *3)) (-5 *1 (-672 *4 *5 *6 *3))
(-4 *3 (-862 (-347 (-858 *6)) *4 *5))))
((*1 *2 *3)
@@ -2829,7 +2829,7 @@
((*1 *2 *1) (-12 (-4 *1 (-1133)) (-5 *2 (-85)))))
(((*1 *2) (-12 (-5 *2 (-1184)) (-5 *1 (-1131)))))
(((*1 *2)
- (-12 (-5 *2 (-2 (|:| -3225 (-584 (-1089))) (|:| -3226 (-584 (-1089)))))
+ (-12 (-5 *2 (-2 (|:| -3226 (-584 (-1089))) (|:| -3227 (-584 (-1089)))))
(-5 *1 (-1131)))))
(((*1 *2 *3) (-12 (-5 *3 (-584 (-1089))) (-5 *2 (-1184)) (-5 *1 (-1131))))
((*1 *2 *3 *3) (-12 (-5 *3 (-584 (-1089))) (-5 *2 (-1184)) (-5 *1 (-1131)))))
@@ -2851,7 +2851,7 @@
(-12 (-5 *4 (-1 (-85) *3 *3)) (-4 *3 (-1013)) (-5 *2 (-85))
(-5 *1 (-1130 *3)))))
(((*1 *2)
- (-12 (-5 *2 (-2 (|:| -3226 (-584 *3)) (|:| -3225 (-584 *3))))
+ (-12 (-5 *2 (-2 (|:| -3227 (-584 *3)) (|:| -3226 (-584 *3))))
(-5 *1 (-1130 *3)) (-4 *3 (-1013)))))
(((*1 *2 *3)
(-12 (-5 *3 (-584 *4)) (-4 *4 (-1013)) (-5 *2 (-1184)) (-5 *1 (-1130 *4))))
@@ -2867,7 +2867,7 @@
(-12 (-4 *4 (-298)) (-5 *2 (-345 (-1084 (-1084 *4)))) (-5 *1 (-1127 *4))
(-5 *3 (-1084 (-1084 *4))))))
(((*1 *1 *2 *1)
- (-12 (-5 *2 (-1 (-85) *3)) (|has| *1 (-6 -3991)) (-4 *1 (-124 *3))
+ (-12 (-5 *2 (-1 (-85) *3)) (|has| *1 (-6 -3992)) (-4 *1 (-124 *3))
(-4 *3 (-1128))))
((*1 *1 *2 *1) (-12 (-5 *2 (-1 (-85) *3)) (-4 *3 (-1128)) (-5 *1 (-536 *3))))
((*1 *1 *2 *1) (-12 (-5 *2 (-1 (-85) *3)) (-4 *1 (-617 *3)) (-4 *3 (-1128))))
@@ -2882,10 +2882,10 @@
(((*1 *1 *2)
(-12 (-5 *2 (-831)) (-4 *1 (-196 *3 *4)) (-4 *4 (-962)) (-4 *4 (-1128))))
((*1 *1 *2)
- (-12 (-14 *3 (-584 (-1089))) (-4 *4 (-146)) (-4 *5 (-196 (-3953 *3) (-695)))
+ (-12 (-14 *3 (-584 (-1089))) (-4 *4 (-146)) (-4 *5 (-196 (-3954 *3) (-695)))
(-14 *6
- (-1 (-85) (-2 (|:| -2398 *2) (|:| -2399 *5))
- (-2 (|:| -2398 *2) (|:| -2399 *5))))
+ (-1 (-85) (-2 (|:| -2399 *2) (|:| -2400 *5))
+ (-2 (|:| -2399 *2) (|:| -2400 *5))))
(-5 *1 (-398 *3 *4 *2 *5 *6 *7)) (-4 *2 (-757))
(-4 *7 (-862 *4 *5 (-774 *3)))))
((*1 *2 *2) (-12 (-5 *2 (-855 (-179))) (-5 *1 (-1125)))))
@@ -2929,12 +2929,12 @@
(((*1 *2 *3 *4 *5)
(|partial| -12 (-5 *4 (-1 (-85) *9)) (-5 *5 (-1 (-85) *9 *9))
(-4 *9 (-977 *6 *7 *8)) (-4 *6 (-495)) (-4 *7 (-718)) (-4 *8 (-757))
- (-5 *2 (-2 (|:| |bas| *1) (|:| -3320 (-584 *9)))) (-5 *3 (-584 *9))
+ (-5 *2 (-2 (|:| |bas| *1) (|:| -3321 (-584 *9)))) (-5 *3 (-584 *9))
(-4 *1 (-1123 *6 *7 *8 *9))))
((*1 *2 *3 *4)
(|partial| -12 (-5 *4 (-1 (-85) *8 *8)) (-4 *8 (-977 *5 *6 *7))
(-4 *5 (-495)) (-4 *6 (-718)) (-4 *7 (-757))
- (-5 *2 (-2 (|:| |bas| *1) (|:| -3320 (-584 *8)))) (-5 *3 (-584 *8))
+ (-5 *2 (-2 (|:| |bas| *1) (|:| -3321 (-584 *8)))) (-5 *3 (-584 *8))
(-4 *1 (-1123 *5 *6 *7 *8)))))
(((*1 *2 *1)
(-12 (-4 *1 (-1123 *3 *4 *5 *6)) (-4 *3 (-495)) (-4 *4 (-718)) (-4 *5 (-757))
@@ -2942,7 +2942,7 @@
(((*1 *2 *1)
(-12 (-4 *1 (-1123 *3 *4 *5 *6)) (-4 *3 (-495)) (-4 *4 (-718)) (-4 *5 (-757))
(-4 *6 (-977 *3 *4 *5))
- (-5 *2 (-2 (|:| -3857 (-584 *6)) (|:| -1700 (-584 *6)))))))
+ (-5 *2 (-2 (|:| -3858 (-584 *6)) (|:| -1700 (-584 *6)))))))
(((*1 *2 *1 *3)
(-12 (-5 *3 (-584 *1)) (-4 *1 (-977 *4 *5 *6)) (-4 *4 (-962)) (-4 *5 (-718))
(-4 *6 (-757)) (-5 *2 (-85))))
@@ -3064,7 +3064,7 @@
(-4 *6 (-757)) (-5 *2 (-584 *1)) (-4 *1 (-1123 *4 *5 *6 *7)))))
(((*1 *2 *3)
(-12 (-4 *4 (-495)) (-4 *5 (-718)) (-4 *6 (-757)) (-4 *7 (-977 *4 *5 *6))
- (-5 *2 (-584 (-2 (|:| -3857 *1) (|:| -1700 (-584 *7))))) (-5 *3 (-584 *7))
+ (-5 *2 (-584 (-2 (|:| -3858 *1) (|:| -1700 (-584 *7))))) (-5 *3 (-584 *7))
(-4 *1 (-1123 *4 *5 *6 *7)))))
(((*1 *2 *1)
(-12 (-4 *1 (-1123 *3 *4 *5 *6)) (-4 *3 (-495)) (-4 *4 (-718)) (-4 *5 (-757))
@@ -3380,7 +3380,7 @@
(-12 (-5 *2 (-1184)) (-5 *1 (-167 *3))
(-4 *3
(-13 (-757)
- (-10 -8 (-15 -3796 ((-1072) $ (-1089))) (-15 -3613 (*2 $))
+ (-10 -8 (-15 -3797 ((-1072) $ (-1089))) (-15 -3614 (*2 $))
(-15 -1962 (*2 $)))))))
((*1 *2 *1) (-12 (-5 *2 (-1184)) (-5 *1 (-439))))
((*1 *2 *3) (-12 (-5 *3 (-1072)) (-5 *2 (-1184)) (-5 *1 (-648))))
@@ -3436,7 +3436,7 @@
(((*1 *2)
(-12 (-5 *2 (-1184)) (-5 *1 (-1107 *3 *4)) (-4 *3 (-1013)) (-4 *4 (-1013)))))
(((*1 *1 *2)
- (-12 (-5 *2 (-584 (-2 (|:| -3856 *3) (|:| |entry| *4)))) (-4 *3 (-1013))
+ (-12 (-5 *2 (-584 (-2 (|:| -3857 *3) (|:| |entry| *4)))) (-4 *3 (-1013))
(-4 *4 (-1013)) (-4 *1 (-1106 *3 *4))))
((*1 *1) (-12 (-4 *1 (-1106 *2 *3)) (-4 *2 (-1013)) (-4 *3 (-1013)))))
(((*1 *2 *2 *3) (-12 (-5 *3 (-484)) (-5 *1 (-1104 *2)) (-4 *2 (-311)))))
@@ -3559,7 +3559,7 @@
(|partial| -12 (-5 *5 (-1089))
(-4 *6 (-13 (-257) (-951 (-484)) (-581 (-484)) (-120)))
(-4 *4 (-13 (-29 *6) (-1114) (-872)))
- (-5 *2 (-2 (|:| |particular| *4) (|:| -2010 (-584 *4))))
+ (-5 *2 (-2 (|:| |particular| *4) (|:| -2011 (-584 *4))))
(-5 *1 (-596 *6 *4 *3)) (-4 *3 (-601 *4))))
((*1 *2 *3 *2 *4 *2 *5)
(|partial| -12 (-5 *4 (-1089)) (-5 *5 (-584 *2))
@@ -3567,39 +3567,39 @@
(-4 *6 (-13 (-257) (-951 (-484)) (-581 (-484)) (-120)))
(-5 *1 (-596 *6 *2 *3)) (-4 *3 (-601 *2))))
((*1 *2 *3 *4)
- (-12 (-4 *5 (-311)) (-4 *6 (-13 (-321 *5) (-10 -7 (-6 -3992))))
- (-4 *4 (-13 (-321 *5) (-10 -7 (-6 -3992))))
- (-5 *2 (-2 (|:| |particular| (-3 *4 #1="failed")) (|:| -2010 (-584 *4))))
+ (-12 (-4 *5 (-311)) (-4 *6 (-13 (-321 *5) (-10 -7 (-6 -3993))))
+ (-4 *4 (-13 (-321 *5) (-10 -7 (-6 -3993))))
+ (-5 *2 (-2 (|:| |particular| (-3 *4 #1="failed")) (|:| -2011 (-584 *4))))
(-5 *1 (-610 *5 *6 *4 *3)) (-4 *3 (-628 *5 *6 *4))))
((*1 *2 *3 *4)
- (-12 (-4 *5 (-311)) (-4 *6 (-13 (-321 *5) (-10 -7 (-6 -3992))))
- (-4 *7 (-13 (-321 *5) (-10 -7 (-6 -3992))))
- (-5 *2 (-584 (-2 (|:| |particular| (-3 *7 #1#)) (|:| -2010 (-584 *7)))))
+ (-12 (-4 *5 (-311)) (-4 *6 (-13 (-321 *5) (-10 -7 (-6 -3993))))
+ (-4 *7 (-13 (-321 *5) (-10 -7 (-6 -3993))))
+ (-5 *2 (-584 (-2 (|:| |particular| (-3 *7 #1#)) (|:| -2011 (-584 *7)))))
(-5 *1 (-610 *5 *6 *7 *3)) (-5 *4 (-584 *7)) (-4 *3 (-628 *5 *6 *7))))
((*1 *2 *3 *4)
(-12 (-5 *3 (-631 *5)) (-4 *5 (-311))
(-5 *2
(-2 (|:| |particular| (-3 (-1178 *5) #2="failed"))
- (|:| -2010 (-584 (-1178 *5)))))
+ (|:| -2011 (-584 (-1178 *5)))))
(-5 *1 (-611 *5)) (-5 *4 (-1178 *5))))
((*1 *2 *3 *4)
(-12 (-5 *3 (-584 (-584 *5))) (-4 *5 (-311))
(-5 *2
- (-2 (|:| |particular| (-3 (-1178 *5) #2#)) (|:| -2010 (-584 (-1178 *5)))))
+ (-2 (|:| |particular| (-3 (-1178 *5) #2#)) (|:| -2011 (-584 (-1178 *5)))))
(-5 *1 (-611 *5)) (-5 *4 (-1178 *5))))
((*1 *2 *3 *4)
(-12 (-5 *3 (-631 *5)) (-4 *5 (-311))
(-5 *2
(-584
(-2 (|:| |particular| (-3 (-1178 *5) #2#))
- (|:| -2010 (-584 (-1178 *5))))))
+ (|:| -2011 (-584 (-1178 *5))))))
(-5 *1 (-611 *5)) (-5 *4 (-584 (-1178 *5)))))
((*1 *2 *3 *4)
(-12 (-5 *3 (-584 (-584 *5))) (-4 *5 (-311))
(-5 *2
(-584
(-2 (|:| |particular| (-3 (-1178 *5) #2#))
- (|:| -2010 (-584 (-1178 *5))))))
+ (|:| -2011 (-584 (-1178 *5))))))
(-5 *1 (-611 *5)) (-5 *4 (-584 (-1178 *5)))))
((*1 *2 *3 *4)
(-12 (-5 *3 (-584 (-858 *5))) (-5 *4 (-584 (-1089))) (-4 *5 (-495))
@@ -3615,7 +3615,7 @@
(|partial| -12 (-5 *3 (-631 *7)) (-5 *5 (-1089))
(-4 *7 (-13 (-29 *6) (-1114) (-872)))
(-4 *6 (-13 (-257) (-951 (-484)) (-581 (-484)) (-120)))
- (-5 *2 (-2 (|:| |particular| (-1178 *7)) (|:| -2010 (-584 (-1178 *7)))))
+ (-5 *2 (-2 (|:| |particular| (-1178 *7)) (|:| -2011 (-584 (-1178 *7)))))
(-5 *1 (-726 *6 *7)) (-5 *4 (-1178 *7))))
((*1 *2 *3 *4)
(|partial| -12 (-5 *3 (-631 *6)) (-5 *4 (-1089))
@@ -3626,24 +3626,24 @@
(|partial| -12 (-5 *3 (-584 (-248 *7))) (-5 *4 (-584 (-86))) (-5 *5 (-1089))
(-4 *7 (-13 (-29 *6) (-1114) (-872)))
(-4 *6 (-13 (-257) (-951 (-484)) (-581 (-484)) (-120)))
- (-5 *2 (-2 (|:| |particular| (-1178 *7)) (|:| -2010 (-584 (-1178 *7)))))
+ (-5 *2 (-2 (|:| |particular| (-1178 *7)) (|:| -2011 (-584 (-1178 *7)))))
(-5 *1 (-726 *6 *7))))
((*1 *2 *3 *4 *5)
(|partial| -12 (-5 *3 (-584 *7)) (-5 *4 (-584 (-86))) (-5 *5 (-1089))
(-4 *7 (-13 (-29 *6) (-1114) (-872)))
(-4 *6 (-13 (-257) (-951 (-484)) (-581 (-484)) (-120)))
- (-5 *2 (-2 (|:| |particular| (-1178 *7)) (|:| -2010 (-584 (-1178 *7)))))
+ (-5 *2 (-2 (|:| |particular| (-1178 *7)) (|:| -2011 (-584 (-1178 *7)))))
(-5 *1 (-726 *6 *7))))
((*1 *2 *3 *4 *5)
(-12 (-5 *3 (-248 *7)) (-5 *4 (-86)) (-5 *5 (-1089))
(-4 *7 (-13 (-29 *6) (-1114) (-872)))
(-4 *6 (-13 (-257) (-951 (-484)) (-581 (-484)) (-120)))
- (-5 *2 (-3 (-2 (|:| |particular| *7) (|:| -2010 (-584 *7))) *7 #3="failed"))
+ (-5 *2 (-3 (-2 (|:| |particular| *7) (|:| -2011 (-584 *7))) *7 #3="failed"))
(-5 *1 (-726 *6 *7))))
((*1 *2 *3 *4 *5)
(-12 (-5 *4 (-86)) (-5 *5 (-1089))
(-4 *6 (-13 (-257) (-951 (-484)) (-581 (-484)) (-120)))
- (-5 *2 (-3 (-2 (|:| |particular| *3) (|:| -2010 (-584 *3))) *3 #3#))
+ (-5 *2 (-3 (-2 (|:| |particular| *3) (|:| -2011 (-584 *3))) *3 #3#))
(-5 *1 (-726 *6 *3)) (-4 *3 (-13 (-29 *6) (-1114) (-872)))))
((*1 *2 *3 *4 *3 *5)
(|partial| -12 (-5 *3 (-248 *2)) (-5 *4 (-86)) (-5 *5 (-584 *2))
@@ -3657,9 +3657,9 @@
((*1 *2 *3 *4 *5)
(|partial| -12
(-5 *5
- (-1 (-3 (-2 (|:| |particular| *6) (|:| -2010 (-584 *6))) "failed") *7 *6))
+ (-1 (-3 (-2 (|:| |particular| *6) (|:| -2011 (-584 *6))) "failed") *7 *6))
(-4 *6 (-311)) (-4 *7 (-601 *6))
- (-5 *2 (-2 (|:| |particular| (-1178 *6)) (|:| -2010 (-631 *6))))
+ (-5 *2 (-2 (|:| |particular| (-1178 *6)) (|:| -2011 (-631 *6))))
(-5 *1 (-734 *6 *7)) (-5 *3 (-631 *6)) (-5 *4 (-1178 *6))))
((*1 *2 *3 *4)
(-12 (-5 *3 (-858 (-347 (-484)))) (-5 *2 (-584 (-327))) (-5 *1 (-937))
@@ -3763,11 +3763,11 @@
(((*1 *2 *1) (|partial| -12 (-5 *2 (-584 (-234))) (-5 *1 (-234))))
((*1 *2 *1) (-12 (-5 *2 (-584 (-1094))) (-5 *1 (-1094)))))
(((*1 *2 *1) (-12 (-5 *2 (-85)) (-5 *1 (-1094)))))
-(((*1 *2 *1 *3) (-12 (-5 *3 (|[\|\|]| -2853)) (-5 *2 (-85)) (-5 *1 (-557))))
- ((*1 *2 *1 *3) (-12 (-5 *3 (|[\|\|]| -2238)) (-5 *2 (-85)) (-5 *1 (-557))))
- ((*1 *2 *1 *3) (-12 (-5 *3 (|[\|\|]| -2852)) (-5 *2 (-85)) (-5 *1 (-557))))
+(((*1 *2 *1 *3) (-12 (-5 *3 (|[\|\|]| -2854)) (-5 *2 (-85)) (-5 *1 (-557))))
+ ((*1 *2 *1 *3) (-12 (-5 *3 (|[\|\|]| -2239)) (-5 *2 (-85)) (-5 *1 (-557))))
+ ((*1 *2 *1 *3) (-12 (-5 *3 (|[\|\|]| -2853)) (-5 *2 (-85)) (-5 *1 (-557))))
((*1 *2 *1 *3)
- (-12 (-5 *3 (|[\|\|]| -2363)) (-5 *2 (-85)) (-5 *1 (-633 *4))
+ (-12 (-5 *3 (|[\|\|]| -2364)) (-5 *2 (-85)) (-5 *1 (-633 *4))
(-4 *4 (-553 (-773)))))
((*1 *2 *1 *3)
(-12 (-5 *3 (|[\|\|]| *4)) (-4 *4 (-553 (-773))) (-5 *2 (-85))
@@ -3833,8 +3833,8 @@
(-12 (-5 *3 (-374))
(-5 *2
(-584
- (-3 (|:| -3538 (-1089))
- (|:| -3222 (-584 (-3 (|:| S (-1089)) (|:| P (-858 (-484)))))))))
+ (-3 (|:| -3539 (-1089))
+ (|:| -3223 (-584 (-3 (|:| S (-1089)) (|:| P (-858 (-484)))))))))
(-5 *1 (-1093)))))
(((*1 *2 *1) (-12 (-5 *2 (-584 (-1089))) (-5 *1 (-1093)))))
(((*1 *2 *1)
@@ -3842,14 +3842,14 @@
(-5 *2
(-584
(-584
- (-3 (|:| -3538 (-1089))
- (|:| -3222 (-584 (-3 (|:| S (-1089)) (|:| P (-858 (-484))))))))))
+ (-3 (|:| -3539 (-1089))
+ (|:| -3223 (-584 (-3 (|:| S (-1089)) (|:| P (-858 (-484))))))))))
(-5 *1 (-1093)))))
(((*1 *2 *1) (-12 (-5 *2 (-1015)) (-5 *1 (-1093)))))
(((*1 *2 *3) (-12 (-5 *3 (-1089)) (-5 *2 (-1184)) (-5 *1 (-1092))))
((*1 *2 *1) (-12 (-5 *2 (-1184)) (-5 *1 (-1093)))))
(((*1 *1 *2)
- (-12 (-5 *2 (-584 (-2 (|:| -3856 (-1089)) (|:| |entry| (-376)))))
+ (-12 (-5 *2 (-584 (-2 (|:| -3857 (-1089)) (|:| |entry| (-376)))))
(-5 *1 (-1093)))))
(((*1 *1) (-5 *1 (-1092))))
(((*1 *2 *3) (-12 (-5 *3 (-1089)) (-5 *2 (-1184)) (-5 *1 (-1092))))
@@ -3863,19 +3863,19 @@
((*1 *2 *3 *4 *1)
(-12 (-5 *4 (-584 (-1089))) (-5 *3 (-1089)) (-5 *2 (-1184)) (-5 *1 (-1092)))))
(((*1 *2 *3)
- (-12 (-5 *3 (-3 (|:| |fst| (-374)) (|:| -3906 #1="void"))) (-5 *2 (-1184))
+ (-12 (-5 *3 (-3 (|:| |fst| (-374)) (|:| -3907 #1="void"))) (-5 *2 (-1184))
(-5 *1 (-1092))))
((*1 *2 *3 *4)
- (-12 (-5 *3 (-1089)) (-5 *4 (-3 (|:| |fst| (-374)) (|:| -3906 #1#)))
+ (-12 (-5 *3 (-1089)) (-5 *4 (-3 (|:| |fst| (-374)) (|:| -3907 #1#)))
(-5 *2 (-1184)) (-5 *1 (-1092))))
((*1 *2 *3 *4 *1)
- (-12 (-5 *3 (-1089)) (-5 *4 (-3 (|:| |fst| (-374)) (|:| -3906 #1#)))
+ (-12 (-5 *3 (-1089)) (-5 *4 (-3 (|:| |fst| (-374)) (|:| -3907 #1#)))
(-5 *2 (-1184)) (-5 *1 (-1092)))))
(((*1 *2) (-12 (-5 *2 (-1184)) (-5 *1 (-1092))))
((*1 *2 *3) (-12 (-5 *3 (-1089)) (-5 *2 (-1184)) (-5 *1 (-1092))))
((*1 *2 *3 *1) (-12 (-5 *3 (-1089)) (-5 *2 (-1184)) (-5 *1 (-1092)))))
(((*1 *2 *3 *1)
- (-12 (-5 *3 (-1089)) (-5 *2 (-3 (|:| |fst| (-374)) (|:| -3906 "void")))
+ (-12 (-5 *3 (-1089)) (-5 *2 (-3 (|:| |fst| (-374)) (|:| -3907 "void")))
(-5 *1 (-1092)))))
(((*1 *2 *3 *1) (-12 (-5 *2 (-584 (-1089))) (-5 *1 (-1092)) (-5 *3 (-1089)))))
(((*1 *2 *3 *1) (-12 (-5 *3 (-1089)) (-5 *2 (-1093)) (-5 *1 (-1092)))))
@@ -3900,15 +3900,15 @@
((*1 *2 *1)
(-12
(-5 *2
- (-2 (|:| -2582 (-584 (-773))) (|:| -2481 (-584 (-773)))
- (|:| |presup| (-584 (-773))) (|:| -2580 (-584 (-773)))
+ (-2 (|:| -2583 (-584 (-773))) (|:| -2482 (-584 (-773)))
+ (|:| |presup| (-584 (-773))) (|:| -2581 (-584 (-773)))
(|:| |args| (-584 (-773)))))
(-5 *1 (-1089)))))
(((*1 *1 *1 *2)
(-12
(-5 *2
- (-2 (|:| -2582 (-584 (-773))) (|:| -2481 (-584 (-773)))
- (|:| |presup| (-584 (-773))) (|:| -2580 (-584 (-773)))
+ (-2 (|:| -2583 (-584 (-773))) (|:| -2482 (-584 (-773)))
+ (|:| |presup| (-584 (-773))) (|:| -2581 (-584 (-773)))
(|:| |args| (-584 (-773)))))
(-5 *1 (-1089))))
((*1 *1 *1 *2) (-12 (-5 *2 (-584 (-584 (-773)))) (-5 *1 (-1089)))))
@@ -3972,13 +3972,13 @@
((*1 *2 *1) (-12 (-5 *2 (-1048)) (-5 *1 (-1080)))))
(((*1 *1 *2) (-12 (-5 *2 (-584 *3)) (-4 *3 (-1128)) (-4 *1 (-124 *3))))
((*1 *1 *2)
- (-12 (-5 *2 (-584 (-2 (|:| -2399 (-695)) (|:| -3769 *4) (|:| |num| *4))))
+ (-12 (-5 *2 (-584 (-2 (|:| -2400 (-695)) (|:| -3770 *4) (|:| |num| *4))))
(-4 *4 (-1154 *3)) (-4 *3 (-13 (-311) (-120))) (-5 *1 (-339 *3 *4))))
((*1 *1 *2 *3 *4)
- (-12 (-5 *2 (-3 (|:| |fst| (-374)) (|:| -3906 #1="void")))
+ (-12 (-5 *2 (-3 (|:| |fst| (-374)) (|:| -3907 #1="void")))
(-5 *3 (-584 (-858 (-484)))) (-5 *4 (-85)) (-5 *1 (-376))))
((*1 *1 *2 *3 *4)
- (-12 (-5 *2 (-3 (|:| |fst| (-374)) (|:| -3906 #1#))) (-5 *3 (-584 (-1089)))
+ (-12 (-5 *2 (-3 (|:| |fst| (-374)) (|:| -3907 #1#))) (-5 *3 (-584 (-1089)))
(-5 *4 (-85)) (-5 *1 (-376))))
((*1 *2 *1) (-12 (-5 *2 (-1068 *3)) (-5 *1 (-536 *3)) (-4 *3 (-1128))))
((*1 *1 *1 *1) (-12 (-4 *1 (-575 *2)) (-4 *2 (-146))))
@@ -3991,12 +3991,12 @@
((*1 *1 *2 *3)
(-12 (-5 *1 (-651 *2 *3 *4)) (-4 *2 (-757)) (-4 *3 (-1013))
(-14 *4
- (-1 (-85) (-2 (|:| -2398 *2) (|:| -2399 *3))
- (-2 (|:| -2398 *2) (|:| -2399 *3))))))
+ (-1 (-85) (-2 (|:| -2399 *2) (|:| -2400 *3))
+ (-2 (|:| -2399 *2) (|:| -2400 *3))))))
((*1 *1 *2 *3) (-12 (-5 *2 (-444)) (-5 *3 (-1028)) (-5 *1 (-750))))
((*1 *1 *2 *3) (-12 (-5 *1 (-783 *2 *3)) (-4 *2 (-1128)) (-4 *3 (-1128))))
((*1 *1 *2)
- (-12 (-5 *2 (-584 (-2 (|:| -3856 (-1089)) (|:| |entry| *4)))) (-4 *4 (-1013))
+ (-12 (-5 *2 (-584 (-2 (|:| -3857 (-1089)) (|:| |entry| *4)))) (-4 *4 (-1013))
(-5 *1 (-799 *3 *4)) (-4 *3 (-1013))))
((*1 *2 *3 *4)
(-12 (-5 *4 (-584 *5)) (-4 *5 (-13 (-1013) (-34)))
@@ -4377,11 +4377,11 @@
(-12 (-5 *2 (-1068 *3)) (-4 *3 (-38 (-347 (-484)))) (-5 *1 (-1076 *3)))))
(((*1 *2 *3)
(-12 (-4 *4 (-38 (-347 (-484))))
- (-5 *2 (-2 (|:| -3486 (-1068 *4)) (|:| -3487 (-1068 *4))))
+ (-5 *2 (-2 (|:| -3487 (-1068 *4)) (|:| -3488 (-1068 *4))))
(-5 *1 (-1075 *4)) (-5 *3 (-1068 *4)))))
(((*1 *2 *3)
(-12 (-4 *4 (-38 (-347 (-484))))
- (-5 *2 (-2 (|:| -3634 (-1068 *4)) (|:| -3630 (-1068 *4))))
+ (-5 *2 (-2 (|:| -3635 (-1068 *4)) (|:| -3631 (-1068 *4))))
(-5 *1 (-1075 *4)) (-5 *3 (-1068 *4)))))
(((*1 *2 *3 *2)
(-12 (-5 *2 (-1068 *3)) (-4 *3 (-311)) (-4 *3 (-962)) (-5 *1 (-1074 *3)))))
@@ -4473,7 +4473,7 @@
(-5 *1 (-1068 *4)))))
(((*1 *2 *3 *1)
(-12
- (-5 *2 (-2 (|:| |cycle?| (-85)) (|:| -2593 (-695)) (|:| |period| (-695))))
+ (-5 *2 (-2 (|:| |cycle?| (-85)) (|:| -2594 (-695)) (|:| |period| (-695))))
(-5 *1 (-1068 *4)) (-4 *4 (-1128)) (-5 *3 (-695)))))
(((*1 *1 *2) (-12 (-5 *2 (-1 (-1068 *3))) (-5 *1 (-1068 *3)) (-4 *3 (-1128)))))
(((*1 *1 *2 *1) (-12 (-5 *1 (-584 *2)) (-4 *2 (-1128))))
@@ -4619,17 +4619,17 @@
(-12 (-4 *1 (-285 *3 *4 *5 *6)) (-4 *3 (-311)) (-4 *4 (-1154 *3))
(-4 *5 (-1154 (-347 *4))) (-4 *6 (-290 *3 *4 *5))
(-5 *2
- (-2 (|:| -2334 (-353 *4 (-347 *4) *5 *6)) (|:| |principalPart| *6)))))
+ (-2 (|:| -2335 (-353 *4 (-347 *4) *5 *6)) (|:| |principalPart| *6)))))
((*1 *2 *3 *4)
(-12 (-5 *4 (-1 *6 *6)) (-4 *6 (-1154 *5)) (-4 *5 (-311))
- (-5 *2 (-2 (|:| |poly| *6) (|:| -3087 (-347 *6)) (|:| |special| (-347 *6))))
+ (-5 *2 (-2 (|:| |poly| *6) (|:| -3088 (-347 *6)) (|:| |special| (-347 *6))))
(-5 *1 (-667 *5 *6)) (-5 *3 (-347 *6))))
((*1 *2 *3)
(-12 (-4 *4 (-311)) (-5 *2 (-584 *3)) (-5 *1 (-808 *3 *4))
(-4 *3 (-1154 *4))))
((*1 *2 *3 *4 *4)
(|partial| -12 (-5 *4 (-695)) (-4 *5 (-311))
- (-5 *2 (-2 (|:| -3135 *3) (|:| -3134 *3))) (-5 *1 (-808 *3 *5))
+ (-5 *2 (-2 (|:| -3136 *3) (|:| -3135 *3))) (-5 *1 (-808 *3 *5))
(-4 *3 (-1154 *5))))
((*1 *2 *3 *2 *4 *4)
(-12 (-5 *2 (-584 *9)) (-5 *3 (-584 *8)) (-5 *4 (-85))
@@ -4794,7 +4794,7 @@
(-4 *3 (-13 (-389) (-951 (-484)) (-581 (-484)))) (-5 *1 (-525 *3))))
((*1 *2 *3 *4)
(-12 (-5 *4 (-1 *3 *3)) (-4 *3 (-1154 *5)) (-4 *5 (-311))
- (-5 *2 (-2 (|:| -3087 *3) (|:| |special| *3))) (-5 *1 (-667 *5 *3))))
+ (-5 *2 (-2 (|:| -3088 *3) (|:| |special| *3))) (-5 *1 (-667 *5 *3))))
((*1 *2 *3 *4)
(-12 (-5 *4 (-1178 *5)) (-4 *5 (-311)) (-4 *5 (-962))
(-5 *2 (-584 (-584 (-631 *5)))) (-5 *1 (-944 *5)) (-5 *3 (-584 (-631 *5)))))
@@ -4843,10 +4843,10 @@
(-4 *5 (-13 (-1013) (-34))) (-4 *6 (-13 (-1013) (-34))) (-5 *2 (-85))
(-5 *1 (-1054 *5 *6)))))
(((*1 *1 *2 *1)
- (-12 (|has| *1 (-6 -3991)) (-4 *1 (-124 *2)) (-4 *2 (-1128))
+ (-12 (|has| *1 (-6 -3992)) (-4 *1 (-124 *2)) (-4 *2 (-1128))
(-4 *2 (-1013))))
((*1 *1 *2 *1)
- (-12 (-5 *2 (-1 (-85) *3)) (|has| *1 (-6 -3991)) (-4 *1 (-124 *3))
+ (-12 (-5 *2 (-1 (-85) *3)) (|has| *1 (-6 -3992)) (-4 *1 (-124 *3))
(-4 *3 (-1128))))
((*1 *1 *2 *1) (-12 (-5 *2 (-1 (-85) *3)) (-4 *1 (-617 *3)) (-4 *3 (-1128))))
((*1 *1 *2 *1 *3)
@@ -4856,9 +4856,9 @@
(-12 (-5 *2 (-1053 *3 *4)) (-4 *3 (-13 (-1013) (-34)))
(-4 *4 (-13 (-1013) (-34))) (-5 *1 (-1054 *3 *4)))))
(((*1 *1 *2 *1)
- (-12 (-5 *2 (-1 (-85) *3)) (|has| *1 (-6 -3991)) (-4 *1 (-193 *3))
+ (-12 (-5 *2 (-1 (-85) *3)) (|has| *1 (-6 -3992)) (-4 *1 (-193 *3))
(-4 *3 (-1013))))
- ((*1 *1 *2 *1) (-12 (|has| *1 (-6 -3991)) (-4 *1 (-193 *2)) (-4 *2 (-1013))))
+ ((*1 *1 *2 *1) (-12 (|has| *1 (-6 -3992)) (-4 *1 (-193 *2)) (-4 *2 (-1013))))
((*1 *1 *2 *1) (-12 (-4 *1 (-237 *2)) (-4 *2 (-1128)) (-4 *2 (-1013))))
((*1 *1 *2 *1) (-12 (-5 *2 (-1 (-85) *3)) (-4 *1 (-237 *3)) (-4 *3 (-1128))))
((*1 *2 *3 *1)
@@ -5051,25 +5051,25 @@
(((*1 *2 *1)
(-12 (-4 *1 (-1047 *3)) (-4 *3 (-962))
(-5 *2
- (-2 (|:| -3846 (-695)) (|:| |curves| (-695)) (|:| |polygons| (-695))
+ (-2 (|:| -3847 (-695)) (|:| |curves| (-695)) (|:| |polygons| (-695))
(|:| |constructs| (-695)))))))
(((*1 *2 *3 *3)
- (-12 (-5 *3 (-584 (-2 (|:| -3728 (-1084 *6)) (|:| -2399 (-484)))))
+ (-12 (-5 *3 (-584 (-2 (|:| -3729 (-1084 *6)) (|:| -2400 (-484)))))
(-4 *6 (-257)) (-4 *4 (-718)) (-4 *5 (-757)) (-5 *2 (-85))
(-5 *1 (-682 *4 *5 *6 *7)) (-4 *7 (-862 *6 *4 *5))))
((*1 *1 *1) (-12 (-4 *1 (-1047 *2)) (-4 *2 (-962)))))
(((*1 *2 *2 *3)
(-12 (-5 *3 (-1 (-85) *4 *4)) (-4 *4 (-1128)) (-5 *1 (-1045 *4 *2))
- (-4 *2 (-13 (-539 (-484) *4) (-10 -7 (-6 -3991) (-6 -3992))))))
+ (-4 *2 (-13 (-539 (-484) *4) (-10 -7 (-6 -3992) (-6 -3993))))))
((*1 *2 *2)
(-12 (-4 *3 (-757)) (-4 *3 (-1128)) (-5 *1 (-1045 *3 *2))
- (-4 *2 (-13 (-539 (-484) *3) (-10 -7 (-6 -3991) (-6 -3992)))))))
+ (-4 *2 (-13 (-539 (-484) *3) (-10 -7 (-6 -3992) (-6 -3993)))))))
(((*1 *2 *2 *3)
(-12 (-5 *3 (-1 (-85) *4 *4)) (-4 *4 (-1128)) (-5 *1 (-1045 *4 *2))
- (-4 *2 (-13 (-539 (-484) *4) (-10 -7 (-6 -3991) (-6 -3992))))))
+ (-4 *2 (-13 (-539 (-484) *4) (-10 -7 (-6 -3992) (-6 -3993))))))
((*1 *2 *2)
(-12 (-4 *3 (-757)) (-4 *3 (-1128)) (-5 *1 (-1045 *3 *2))
- (-4 *2 (-13 (-539 (-484) *3) (-10 -7 (-6 -3991) (-6 -3992)))))))
+ (-4 *2 (-13 (-539 (-484) *3) (-10 -7 (-6 -3992) (-6 -3993)))))))
(((*1 *2 *3)
(-12 (-5 *3 (-1178 *4)) (-4 *4 (-962)) (-4 *2 (-1154 *4))
(-5 *1 (-381 *4 *2))))
@@ -5165,8 +5165,8 @@
(|:| |maps| (-584 (-2 (|:| |arg| *5) (|:| |res| *5))))))
(-5 *1 (-1041 *3 *5)) (-4 *3 (-1154 *5)))))
(((*1 *2 *3 *2)
- (|partial| -12 (-4 *4 (-311)) (-4 *5 (-13 (-321 *4) (-10 -7 (-6 -3992))))
- (-4 *2 (-13 (-321 *4) (-10 -7 (-6 -3992)))) (-5 *1 (-610 *4 *5 *2 *3))
+ (|partial| -12 (-4 *4 (-311)) (-4 *5 (-13 (-321 *4) (-10 -7 (-6 -3993))))
+ (-4 *2 (-13 (-321 *4) (-10 -7 (-6 -3993)))) (-5 *1 (-610 *4 *5 *2 *3))
(-4 *3 (-628 *4 *5 *2))))
((*1 *2 *3 *2)
(|partial| -12 (-5 *2 (-1178 *4)) (-5 *3 (-631 *4)) (-4 *4 (-311))
@@ -5183,7 +5183,7 @@
(-5 *1 (-1039 *5 *6 *7)))))
(((*1 *2 *3 *4)
(-12 (-4 *5 (-257)) (-4 *6 (-321 *5)) (-4 *4 (-321 *5))
- (-5 *2 (-2 (|:| |particular| (-3 *4 "failed")) (|:| -2010 (-584 *4))))
+ (-5 *2 (-2 (|:| |particular| (-3 *4 "failed")) (|:| -2011 (-584 *4))))
(-5 *1 (-1037 *5 *6 *4 *3)) (-4 *3 (-628 *5 *6 *4)))))
(((*1 *2 *3)
(-12 (-4 *4 (-257)) (-4 *5 (-321 *4)) (-4 *6 (-321 *4))
@@ -5230,7 +5230,7 @@
(-4 *2 (-962)))))
(((*1 *2 *3)
(-12 (-5 *3 (-631 *2)) (-4 *4 (-1154 *2))
- (-4 *2 (-13 (-257) (-10 -8 (-15 -3967 ((-345 $) $)))))
+ (-4 *2 (-13 (-257) (-10 -8 (-15 -3968 ((-345 $) $)))))
(-5 *1 (-436 *2 *4 *5)) (-4 *5 (-350 *2 *4))))
((*1 *2 *1)
(-12 (-4 *1 (-1036 *3 *2 *4 *5)) (-4 *4 (-196 *3 *2)) (-4 *5 (-196 *3 *2))
@@ -5240,22 +5240,22 @@
(-5 *1 (-459 *2 *4 *5 *3)) (-4 *3 (-628 *2 *4 *5))))
((*1 *2 *1)
(-12 (-4 *1 (-628 *2 *3 *4)) (-4 *3 (-321 *2)) (-4 *4 (-321 *2))
- (|has| *2 (-6 (-3993 "*"))) (-4 *2 (-962))))
+ (|has| *2 (-6 (-3994 "*"))) (-4 *2 (-962))))
((*1 *2 *3)
(-12 (-4 *4 (-321 *2)) (-4 *5 (-321 *2)) (-4 *2 (-146))
(-5 *1 (-630 *2 *4 *5 *3)) (-4 *3 (-628 *2 *4 *5))))
((*1 *2 *1)
(-12 (-4 *1 (-1036 *3 *2 *4 *5)) (-4 *4 (-196 *3 *2)) (-4 *5 (-196 *3 *2))
- (|has| *2 (-6 (-3993 "*"))) (-4 *2 (-962)))))
+ (|has| *2 (-6 (-3994 "*"))) (-4 *2 (-962)))))
(((*1 *2 *1)
(-12 (-4 *1 (-628 *2 *3 *4)) (-4 *3 (-321 *2)) (-4 *4 (-321 *2))
- (|has| *2 (-6 (-3993 "*"))) (-4 *2 (-962))))
+ (|has| *2 (-6 (-3994 "*"))) (-4 *2 (-962))))
((*1 *2 *3)
(-12 (-4 *4 (-321 *2)) (-4 *5 (-321 *2)) (-4 *2 (-146))
(-5 *1 (-630 *2 *4 *5 *3)) (-4 *3 (-628 *2 *4 *5))))
((*1 *2 *1)
(-12 (-4 *1 (-1036 *3 *2 *4 *5)) (-4 *4 (-196 *3 *2)) (-4 *5 (-196 *3 *2))
- (|has| *2 (-6 (-3993 "*"))) (-4 *2 (-962)))))
+ (|has| *2 (-6 (-3994 "*"))) (-4 *2 (-962)))))
(((*1 *2 *2 *1) (-12 (-4 *1 (-1034 *2)) (-4 *2 (-1128)))))
(((*1 *2 *1) (-12 (-4 *1 (-1034 *2)) (-4 *2 (-1128)))))
(((*1 *2 *1) (-12 (-4 *1 (-1034 *2)) (-4 *2 (-1128)))))
@@ -5404,25 +5404,25 @@
(((*1 *2 *3 *4 *3 *5 *5 *5 *5 *5)
(|partial| -12 (-5 *5 (-85)) (-4 *6 (-389)) (-4 *7 (-718)) (-4 *8 (-757))
(-4 *9 (-977 *6 *7 *8))
- (-5 *2 (-2 (|:| -3263 (-584 *9)) (|:| -1598 *4) (|:| |ineq| (-584 *9))))
+ (-5 *2 (-2 (|:| -3264 (-584 *9)) (|:| -1598 *4) (|:| |ineq| (-584 *9))))
(-5 *1 (-902 *6 *7 *8 *9 *4)) (-5 *3 (-584 *9)) (-4 *4 (-983 *6 *7 *8 *9))))
((*1 *2 *3 *4 *3 *5 *5 *5 *5 *5)
(|partial| -12 (-5 *5 (-85)) (-4 *6 (-389)) (-4 *7 (-718)) (-4 *8 (-757))
(-4 *9 (-977 *6 *7 *8))
- (-5 *2 (-2 (|:| -3263 (-584 *9)) (|:| -1598 *4) (|:| |ineq| (-584 *9))))
+ (-5 *2 (-2 (|:| -3264 (-584 *9)) (|:| -1598 *4) (|:| |ineq| (-584 *9))))
(-5 *1 (-1018 *6 *7 *8 *9 *4)) (-5 *3 (-584 *9))
(-4 *4 (-983 *6 *7 *8 *9)))))
(((*1 *2 *3 *4 *5 *5)
(-12 (-5 *4 (-584 *10)) (-5 *5 (-85)) (-4 *10 (-983 *6 *7 *8 *9))
(-4 *6 (-389)) (-4 *7 (-718)) (-4 *8 (-757)) (-4 *9 (-977 *6 *7 *8))
(-5 *2
- (-584 (-2 (|:| -3263 (-584 *9)) (|:| -1598 *10) (|:| |ineq| (-584 *9)))))
+ (-584 (-2 (|:| -3264 (-584 *9)) (|:| -1598 *10) (|:| |ineq| (-584 *9)))))
(-5 *1 (-902 *6 *7 *8 *9 *10)) (-5 *3 (-584 *9))))
((*1 *2 *3 *4 *5 *5)
(-12 (-5 *4 (-584 *10)) (-5 *5 (-85)) (-4 *10 (-983 *6 *7 *8 *9))
(-4 *6 (-389)) (-4 *7 (-718)) (-4 *8 (-757)) (-4 *9 (-977 *6 *7 *8))
(-5 *2
- (-584 (-2 (|:| -3263 (-584 *9)) (|:| -1598 *10) (|:| |ineq| (-584 *9)))))
+ (-584 (-2 (|:| -3264 (-584 *9)) (|:| -1598 *10) (|:| |ineq| (-584 *9)))))
(-5 *1 (-1018 *6 *7 *8 *9 *10)) (-5 *3 (-584 *9)))))
(((*1 *2 *2)
(-12 (-5 *2 (-584 (-2 (|:| |val| (-584 *6)) (|:| -1598 *7))))
@@ -5566,7 +5566,7 @@
(-12 (-4 *1 (-1016 *3 *4 *5 *6 *7)) (-4 *3 (-1013)) (-4 *4 (-1013))
(-4 *5 (-1013)) (-4 *6 (-1013)) (-4 *7 (-1013)) (-5 *2 (-85)))))
(((*1 *2 *1)
- (-12 (-5 *2 (-584 (-2 (|:| -3856 (-1089)) (|:| |entry| *4))))
+ (-12 (-5 *2 (-584 (-2 (|:| -3857 (-1089)) (|:| |entry| *4))))
(-5 *1 (-799 *3 *4)) (-4 *3 (-1013)) (-4 *4 (-1013))))
((*1 *2 *1)
(-12 (-4 *3 (-1013)) (-4 *4 (-1013)) (-4 *5 (-1013)) (-4 *6 (-1013))
@@ -5607,7 +5607,7 @@
(-12 (-5 *2 (-1178 (-1014 *3 *4))) (-5 *1 (-1014 *3 *4)) (-14 *3 (-831))
(-14 *4 (-831)))))
(((*1 *2 *3 *1)
- (-12 (|has| *1 (-6 -3991)) (-4 *1 (-426 *3)) (-4 *3 (-1128)) (-4 *3 (-1013))
+ (-12 (|has| *1 (-6 -3992)) (-4 *1 (-426 *3)) (-4 *3 (-1128)) (-4 *3 (-1013))
(-5 *2 (-85))))
((*1 *2 *3 *1)
(-12 (-5 *3 (-814 *4)) (-4 *4 (-1013)) (-5 *2 (-85)) (-5 *1 (-817 *4))))
@@ -5748,15 +5748,15 @@
(-4 *3 (-1020 *5 *6 *7 *8))))
((*1 *2 *3 *4)
(-12 (-5 *4 (-85)) (-4 *5 (-13 (-257) (-120)))
- (-5 *2 (-584 (-2 (|:| -1745 (-1084 *5)) (|:| -3221 (-584 (-858 *5))))))
+ (-5 *2 (-584 (-2 (|:| -1745 (-1084 *5)) (|:| -3222 (-584 (-858 *5))))))
(-5 *1 (-990 *5 *6)) (-5 *3 (-584 (-858 *5))) (-14 *6 (-584 (-1089)))))
((*1 *2 *3)
(-12 (-4 *4 (-13 (-257) (-120)))
- (-5 *2 (-584 (-2 (|:| -1745 (-1084 *4)) (|:| -3221 (-584 (-858 *4))))))
+ (-5 *2 (-584 (-2 (|:| -1745 (-1084 *4)) (|:| -3222 (-584 (-858 *4))))))
(-5 *1 (-990 *4 *5)) (-5 *3 (-584 (-858 *4))) (-14 *5 (-584 (-1089)))))
((*1 *2 *3 *4 *4)
(-12 (-5 *4 (-85)) (-4 *5 (-13 (-257) (-120)))
- (-5 *2 (-584 (-2 (|:| -1745 (-1084 *5)) (|:| -3221 (-584 (-858 *5))))))
+ (-5 *2 (-584 (-2 (|:| -1745 (-1084 *5)) (|:| -3222 (-584 (-858 *5))))))
(-5 *1 (-990 *5 *6)) (-5 *3 (-584 (-858 *5))) (-14 *6 (-584 (-1089))))))
(((*1 *1 *2)
(-12 (-5 *2 (-584 (-987 *3 *4 *5))) (-4 *3 (-1013))
@@ -5994,10 +5994,10 @@
(-14 *4 (-584 (-1089)))))
((*1 *2 *1) (-12 (-4 *1 (-332 *2 *3)) (-4 *3 (-1013)) (-4 *2 (-962))))
((*1 *2 *1)
- (-12 (-14 *3 (-584 (-1089))) (-4 *5 (-196 (-3953 *3) (-695)))
+ (-12 (-14 *3 (-584 (-1089))) (-4 *5 (-196 (-3954 *3) (-695)))
(-14 *6
- (-1 (-85) (-2 (|:| -2398 *4) (|:| -2399 *5))
- (-2 (|:| -2398 *4) (|:| -2399 *5))))
+ (-1 (-85) (-2 (|:| -2399 *4) (|:| -2400 *5))
+ (-2 (|:| -2399 *4) (|:| -2400 *5))))
(-4 *2 (-146)) (-5 *1 (-398 *3 *2 *4 *5 *6 *7)) (-4 *4 (-757))
(-4 *7 (-862 *2 *5 (-774 *3)))))
((*1 *2 *1) (-12 (-4 *1 (-447 *2 *3)) (-4 *3 (-760)) (-4 *2 (-72))))
@@ -6052,36 +6052,36 @@
(-12 (-4 *1 (-977 *2 *3 *4)) (-4 *2 (-962)) (-4 *3 (-718)) (-4 *4 (-757)))))
(((*1 *2 *1 *1 *3)
(-12 (-4 *4 (-962)) (-4 *5 (-718)) (-4 *3 (-757))
- (-5 *2 (-2 (|:| -3950 *1) (|:| |gap| (-695)) (|:| -2900 *1)))
+ (-5 *2 (-2 (|:| -3951 *1) (|:| |gap| (-695)) (|:| -2901 *1)))
(-4 *1 (-977 *4 *5 *3))))
((*1 *2 *1 *1)
(-12 (-4 *3 (-962)) (-4 *4 (-718)) (-4 *5 (-757))
- (-5 *2 (-2 (|:| -3950 *1) (|:| |gap| (-695)) (|:| -2900 *1)))
+ (-5 *2 (-2 (|:| -3951 *1) (|:| |gap| (-695)) (|:| -2901 *1)))
(-4 *1 (-977 *3 *4 *5)))))
(((*1 *2 *1 *1)
(-12
(-5 *2
- (-2 (|:| -3950 *3) (|:| |gap| (-695)) (|:| -1971 (-705 *3))
- (|:| -2900 (-705 *3))))
+ (-2 (|:| -3951 *3) (|:| |gap| (-695)) (|:| -1971 (-705 *3))
+ (|:| -2901 (-705 *3))))
(-5 *1 (-705 *3)) (-4 *3 (-962))))
((*1 *2 *1 *1 *3)
(-12 (-4 *4 (-962)) (-4 *5 (-718)) (-4 *3 (-757))
- (-5 *2 (-2 (|:| -3950 *1) (|:| |gap| (-695)) (|:| -1971 *1) (|:| -2900 *1)))
+ (-5 *2 (-2 (|:| -3951 *1) (|:| |gap| (-695)) (|:| -1971 *1) (|:| -2901 *1)))
(-4 *1 (-977 *4 *5 *3))))
((*1 *2 *1 *1)
(-12 (-4 *3 (-962)) (-4 *4 (-718)) (-4 *5 (-757))
- (-5 *2 (-2 (|:| -3950 *1) (|:| |gap| (-695)) (|:| -1971 *1) (|:| -2900 *1)))
+ (-5 *2 (-2 (|:| -3951 *1) (|:| |gap| (-695)) (|:| -1971 *1) (|:| -2901 *1)))
(-4 *1 (-977 *3 *4 *5)))))
(((*1 *1 *1 *1) (-12 (-5 *1 (-705 *2)) (-4 *2 (-962))))
((*1 *1 *1 *1)
(-12 (-4 *1 (-977 *2 *3 *4)) (-4 *2 (-962)) (-4 *3 (-718)) (-4 *4 (-757)))))
(((*1 *2 *1 *1)
(-12
- (-5 *2 (-2 (|:| |polnum| (-705 *3)) (|:| |polden| *3) (|:| -3477 (-695))))
+ (-5 *2 (-2 (|:| |polnum| (-705 *3)) (|:| |polden| *3) (|:| -3478 (-695))))
(-5 *1 (-705 *3)) (-4 *3 (-962))))
((*1 *2 *1 *1)
(-12 (-4 *3 (-962)) (-4 *4 (-718)) (-4 *5 (-757))
- (-5 *2 (-2 (|:| |polnum| *1) (|:| |polden| *1) (|:| -3477 (-695))))
+ (-5 *2 (-2 (|:| |polnum| *1) (|:| |polden| *1) (|:| -3478 (-695))))
(-4 *1 (-977 *3 *4 *5)))))
(((*1 *2 *3) (|partial| -12 (-5 *3 (-51)) (-5 *1 (-52 *2)) (-4 *2 (-1128))))
((*1 *2 *3)
@@ -6095,21 +6095,21 @@
((*1 *1 *2)
(|partial| OR
(-12 (-5 *2 (-858 *3))
- (-12 (-2558 (-4 *3 (-38 (-347 (-484))))) (-2558 (-4 *3 (-38 (-484))))
+ (-12 (-2559 (-4 *3 (-38 (-347 (-484))))) (-2559 (-4 *3 (-38 (-484))))
(-4 *5 (-554 (-1089))))
(-4 *3 (-962)) (-4 *1 (-977 *3 *4 *5)) (-4 *4 (-718)) (-4 *5 (-757)))
(-12 (-5 *2 (-858 *3))
- (-12 (-2558 (-4 *3 (-483))) (-2558 (-4 *3 (-38 (-347 (-484)))))
+ (-12 (-2559 (-4 *3 (-483))) (-2559 (-4 *3 (-38 (-347 (-484)))))
(-4 *3 (-38 (-484))) (-4 *5 (-554 (-1089))))
(-4 *3 (-962)) (-4 *1 (-977 *3 *4 *5)) (-4 *4 (-718)) (-4 *5 (-757)))
(-12 (-5 *2 (-858 *3))
- (-12 (-2558 (-4 *3 (-905 (-484)))) (-4 *3 (-38 (-347 (-484))))
+ (-12 (-2559 (-4 *3 (-905 (-484)))) (-4 *3 (-38 (-347 (-484))))
(-4 *5 (-554 (-1089))))
(-4 *3 (-962)) (-4 *1 (-977 *3 *4 *5)) (-4 *4 (-718)) (-4 *5 (-757)))))
((*1 *1 *2)
(|partial| OR
(-12 (-5 *2 (-858 (-484))) (-4 *1 (-977 *3 *4 *5))
- (-12 (-2558 (-4 *3 (-38 (-347 (-484))))) (-4 *3 (-38 (-484)))
+ (-12 (-2559 (-4 *3 (-38 (-347 (-484))))) (-4 *3 (-38 (-484)))
(-4 *5 (-554 (-1089))))
(-4 *3 (-962)) (-4 *4 (-718)) (-4 *5 (-757)))
(-12 (-5 *2 (-858 (-484))) (-4 *1 (-977 *3 *4 *5))
@@ -6127,21 +6127,21 @@
((*1 *1 *2)
(OR
(-12 (-5 *2 (-858 *3))
- (-12 (-2558 (-4 *3 (-38 (-347 (-484))))) (-2558 (-4 *3 (-38 (-484))))
+ (-12 (-2559 (-4 *3 (-38 (-347 (-484))))) (-2559 (-4 *3 (-38 (-484))))
(-4 *5 (-554 (-1089))))
(-4 *3 (-962)) (-4 *1 (-977 *3 *4 *5)) (-4 *4 (-718)) (-4 *5 (-757)))
(-12 (-5 *2 (-858 *3))
- (-12 (-2558 (-4 *3 (-483))) (-2558 (-4 *3 (-38 (-347 (-484)))))
+ (-12 (-2559 (-4 *3 (-483))) (-2559 (-4 *3 (-38 (-347 (-484)))))
(-4 *3 (-38 (-484))) (-4 *5 (-554 (-1089))))
(-4 *3 (-962)) (-4 *1 (-977 *3 *4 *5)) (-4 *4 (-718)) (-4 *5 (-757)))
(-12 (-5 *2 (-858 *3))
- (-12 (-2558 (-4 *3 (-905 (-484)))) (-4 *3 (-38 (-347 (-484))))
+ (-12 (-2559 (-4 *3 (-905 (-484)))) (-4 *3 (-38 (-347 (-484))))
(-4 *5 (-554 (-1089))))
(-4 *3 (-962)) (-4 *1 (-977 *3 *4 *5)) (-4 *4 (-718)) (-4 *5 (-757)))))
((*1 *1 *2)
(OR
(-12 (-5 *2 (-858 (-484))) (-4 *1 (-977 *3 *4 *5))
- (-12 (-2558 (-4 *3 (-38 (-347 (-484))))) (-4 *3 (-38 (-484)))
+ (-12 (-2559 (-4 *3 (-38 (-347 (-484))))) (-4 *3 (-38 (-484)))
(-4 *5 (-554 (-1089))))
(-4 *3 (-962)) (-4 *4 (-718)) (-4 *5 (-757)))
(-12 (-5 *2 (-858 (-484))) (-4 *1 (-977 *3 *4 *5))
@@ -6172,24 +6172,24 @@
(((*1 *2 *1 *1)
(-12
(-5 *2
- (-2 (|:| -3141 (-705 *3)) (|:| |coef1| (-705 *3)) (|:| |coef2| (-705 *3))))
+ (-2 (|:| -3142 (-705 *3)) (|:| |coef1| (-705 *3)) (|:| |coef2| (-705 *3))))
(-5 *1 (-705 *3)) (-4 *3 (-495)) (-4 *3 (-962))))
((*1 *2 *1 *1)
(-12 (-4 *3 (-495)) (-4 *3 (-962)) (-4 *4 (-718)) (-4 *5 (-757))
- (-5 *2 (-2 (|:| -3141 *1) (|:| |coef1| *1) (|:| |coef2| *1)))
+ (-5 *2 (-2 (|:| -3142 *1) (|:| |coef1| *1) (|:| |coef2| *1)))
(-4 *1 (-977 *3 *4 *5)))))
(((*1 *2 *1 *1)
- (-12 (-5 *2 (-2 (|:| -3141 (-705 *3)) (|:| |coef1| (-705 *3))))
+ (-12 (-5 *2 (-2 (|:| -3142 (-705 *3)) (|:| |coef1| (-705 *3))))
(-5 *1 (-705 *3)) (-4 *3 (-495)) (-4 *3 (-962))))
((*1 *2 *1 *1)
(-12 (-4 *3 (-495)) (-4 *3 (-962)) (-4 *4 (-718)) (-4 *5 (-757))
- (-5 *2 (-2 (|:| -3141 *1) (|:| |coef1| *1))) (-4 *1 (-977 *3 *4 *5)))))
+ (-5 *2 (-2 (|:| -3142 *1) (|:| |coef1| *1))) (-4 *1 (-977 *3 *4 *5)))))
(((*1 *2 *1 *1)
- (-12 (-5 *2 (-2 (|:| -3141 (-705 *3)) (|:| |coef2| (-705 *3))))
+ (-12 (-5 *2 (-2 (|:| -3142 (-705 *3)) (|:| |coef2| (-705 *3))))
(-5 *1 (-705 *3)) (-4 *3 (-495)) (-4 *3 (-962))))
((*1 *2 *1 *1)
(-12 (-4 *3 (-495)) (-4 *3 (-962)) (-4 *4 (-718)) (-4 *5 (-757))
- (-5 *2 (-2 (|:| -3141 *1) (|:| |coef2| *1))) (-4 *1 (-977 *3 *4 *5)))))
+ (-5 *2 (-2 (|:| -3142 *1) (|:| |coef2| *1))) (-4 *1 (-977 *3 *4 *5)))))
(((*1 *2 *1 *1)
(-12 (-4 *3 (-495)) (-4 *3 (-962)) (-4 *4 (-718)) (-4 *5 (-757))
(-5 *2 (-584 *1)) (-4 *1 (-977 *3 *4 *5)))))
@@ -6285,18 +6285,18 @@
((*1 *1 *1) (-5 *1 (-839)))
((*1 *1 *1 *2) (-12 (-5 *2 (-1001 (-179))) (-5 *1 (-839))))
((*1 *2 *3 *2 *4)
- (-12 (-5 *2 (-2 (|:| -3135 (-347 (-484))) (|:| -3134 (-347 (-484)))))
+ (-12 (-5 *2 (-2 (|:| -3136 (-347 (-484))) (|:| -3135 (-347 (-484)))))
(-5 *4 (-347 (-484))) (-5 *1 (-935 *3)) (-4 *3 (-1154 (-484)))))
((*1 *2 *3 *2 *2)
(|partial| -12
- (-5 *2 (-2 (|:| -3135 (-347 (-484))) (|:| -3134 (-347 (-484)))))
+ (-5 *2 (-2 (|:| -3136 (-347 (-484))) (|:| -3135 (-347 (-484)))))
(-5 *1 (-935 *3)) (-4 *3 (-1154 (-484)))))
((*1 *2 *3 *2 *4)
- (-12 (-5 *2 (-2 (|:| -3135 (-347 (-484))) (|:| -3134 (-347 (-484)))))
+ (-12 (-5 *2 (-2 (|:| -3136 (-347 (-484))) (|:| -3135 (-347 (-484)))))
(-5 *4 (-347 (-484))) (-5 *1 (-936 *3)) (-4 *3 (-1154 *4))))
((*1 *2 *3 *2 *2)
(|partial| -12
- (-5 *2 (-2 (|:| -3135 (-347 (-484))) (|:| -3134 (-347 (-484)))))
+ (-5 *2 (-2 (|:| -3136 (-347 (-484))) (|:| -3135 (-347 (-484)))))
(-5 *1 (-936 *3)) (-4 *3 (-1154 (-347 (-484))))))
((*1 *1 *1)
(-12 (-4 *2 (-13 (-756) (-311))) (-5 *1 (-974 *2 *3)) (-4 *3 (-1154 *2)))))
@@ -6499,8 +6499,8 @@
(-12 (-4 *4 (-311)) (-4 *5 (-321 *4)) (-4 *6 (-321 *4)) (-5 *2 (-695))
(-5 *1 (-459 *4 *5 *6 *3)) (-4 *3 (-628 *4 *5 *6))))
((*1 *2 *3 *4)
- (-12 (-4 *5 (-311)) (-4 *6 (-13 (-321 *5) (-10 -7 (-6 -3992))))
- (-4 *4 (-13 (-321 *5) (-10 -7 (-6 -3992)))) (-5 *2 (-695))
+ (-12 (-4 *5 (-311)) (-4 *6 (-13 (-321 *5) (-10 -7 (-6 -3993))))
+ (-4 *4 (-13 (-321 *5) (-10 -7 (-6 -3993)))) (-5 *2 (-695))
(-5 *1 (-610 *5 *6 *4 *3)) (-4 *3 (-628 *5 *6 *4))))
((*1 *2 *3 *4)
(-12 (-5 *3 (-631 *5)) (-5 *4 (-1178 *5)) (-4 *5 (-311)) (-5 *2 (-695))
@@ -6527,10 +6527,10 @@
(-12 (-4 *1 (-966 *3 *4 *5 *6 *7)) (-4 *5 (-962)) (-4 *6 (-196 *4 *5))
(-4 *7 (-196 *3 *5)) (-4 *5 (-495)) (-5 *2 (-695)))))
(((*1 *2 *3)
- (-12 (|has| *6 (-6 -3992)) (-4 *4 (-311)) (-4 *5 (-321 *4)) (-4 *6 (-321 *4))
+ (-12 (|has| *6 (-6 -3993)) (-4 *4 (-311)) (-4 *5 (-321 *4)) (-4 *6 (-321 *4))
(-5 *2 (-584 *6)) (-5 *1 (-459 *4 *5 *6 *3)) (-4 *3 (-628 *4 *5 *6))))
((*1 *2 *3)
- (-12 (|has| *9 (-6 -3992)) (-4 *4 (-495)) (-4 *5 (-321 *4)) (-4 *6 (-321 *4))
+ (-12 (|has| *9 (-6 -3993)) (-4 *4 (-495)) (-4 *5 (-321 *4)) (-4 *6 (-321 *4))
(-4 *7 (-905 *4)) (-4 *8 (-321 *7)) (-4 *9 (-321 *7)) (-5 *2 (-584 *6))
(-5 *1 (-460 *4 *5 *6 *3 *7 *8 *9 *10)) (-4 *3 (-628 *4 *5 *6))
(-4 *10 (-628 *7 *8 *9))))
@@ -6601,7 +6601,7 @@
(-12 (-5 *3 (-347 (-1084 *2))) (-4 *5 (-718)) (-4 *4 (-757)) (-4 *6 (-962))
(-4 *2
(-13 (-311)
- (-10 -8 (-15 -3942 ($ *7)) (-15 -2996 (*7 $)) (-15 -2995 (*7 $)))))
+ (-10 -8 (-15 -3943 ($ *7)) (-15 -2997 (*7 $)) (-15 -2996 (*7 $)))))
(-5 *1 (-863 *5 *4 *6 *7 *2)) (-4 *7 (-862 *6 *5 *4))))
((*1 *2 *3 *4)
(-12 (-5 *3 (-347 (-1084 (-347 (-858 *5))))) (-5 *4 (-1089))
@@ -6628,12 +6628,12 @@
(-5 *2 (-347 (-1084 *3))) (-5 *1 (-863 *5 *4 *6 *7 *3))
(-4 *3
(-13 (-311)
- (-10 -8 (-15 -3942 ($ *7)) (-15 -2996 (*7 $)) (-15 -2995 (*7 $)))))))
+ (-10 -8 (-15 -3943 ($ *7)) (-15 -2997 (*7 $)) (-15 -2996 (*7 $)))))))
((*1 *2 *3 *4 *2)
(-12 (-5 *2 (-1084 *3))
(-4 *3
(-13 (-311)
- (-10 -8 (-15 -3942 ($ *7)) (-15 -2996 (*7 $)) (-15 -2995 (*7 $)))))
+ (-10 -8 (-15 -3943 ($ *7)) (-15 -2997 (*7 $)) (-15 -2996 (*7 $)))))
(-4 *7 (-862 *6 *5 *4)) (-4 *5 (-718)) (-4 *4 (-757)) (-4 *6 (-962))
(-5 *1 (-863 *5 *4 *6 *7 *3))))
((*1 *2 *3 *4)
@@ -6647,7 +6647,7 @@
(-4 *2 (-757)) (-5 *1 (-863 *4 *2 *5 *6 *3))
(-4 *3
(-13 (-311)
- (-10 -8 (-15 -3942 ($ *6)) (-15 -2996 (*6 $)) (-15 -2995 (*6 $)))))))
+ (-10 -8 (-15 -3943 ($ *6)) (-15 -2997 (*6 $)) (-15 -2996 (*6 $)))))))
((*1 *2 *3)
(|partial| -12 (-5 *3 (-347 (-858 *4))) (-4 *4 (-495)) (-5 *2 (-1089))
(-5 *1 (-953 *4)))))
@@ -6664,7 +6664,7 @@
(-5 *2 (-584 *5)) (-5 *1 (-863 *4 *5 *6 *7 *3))
(-4 *3
(-13 (-311)
- (-10 -8 (-15 -3942 ($ *7)) (-15 -2996 (*7 $)) (-15 -2995 (*7 $)))))))
+ (-10 -8 (-15 -3943 ($ *7)) (-15 -2997 (*7 $)) (-15 -2996 (*7 $)))))))
((*1 *2 *1)
(-12 (-4 *1 (-887 *3 *4 *5)) (-4 *3 (-962)) (-4 *4 (-717)) (-4 *5 (-757))
(-5 *2 (-584 *5))))
@@ -6698,7 +6698,7 @@
(-4 *2 (-13 (-1013) (-10 -8 (-15 * ($ $ $))))))))
(((*1 *2 *3 *2)
(-12 (-5 *3 (-831)) (-5 *1 (-945 *2))
- (-4 *2 (-13 (-1013) (-10 -8 (-15 -3835 ($ $ $))))))))
+ (-4 *2 (-13 (-1013) (-10 -8 (-15 -3836 ($ $ $))))))))
(((*1 *2 *3 *4)
(-12 (-5 *3 (-584 (-1178 *5))) (-5 *4 (-484)) (-5 *2 (-1178 *5))
(-5 *1 (-944 *5)) (-4 *5 (-311)) (-4 *5 (-317)) (-4 *5 (-962)))))
@@ -6768,10 +6768,10 @@
(-12 (-5 *3 (-695)) (-5 *2 (-631 (-858 *4))) (-5 *1 (-943 *4))
(-4 *4 (-962)))))
(((*1 *2 *2 *3)
- (-12 (-5 *2 (-631 *4)) (-5 *3 (-831)) (|has| *4 (-6 (-3993 "*")))
+ (-12 (-5 *2 (-631 *4)) (-5 *3 (-831)) (|has| *4 (-6 (-3994 "*")))
(-4 *4 (-962)) (-5 *1 (-943 *4))))
((*1 *2 *2 *3)
- (-12 (-5 *2 (-584 (-631 *4))) (-5 *3 (-831)) (|has| *4 (-6 (-3993 "*")))
+ (-12 (-5 *2 (-584 (-631 *4))) (-5 *3 (-831)) (|has| *4 (-6 (-3994 "*")))
(-4 *4 (-962)) (-5 *1 (-943 *4)))))
(((*1 *2 *3)
(-12 (-5 *3 (-631 (-347 (-858 (-484))))) (-5 *2 (-584 (-631 (-264 (-484)))))
@@ -6804,7 +6804,7 @@
(((*1 *2 *1 *2) (-12 (-5 *1 (-940 *2)) (-4 *2 (-1128)))))
(((*1 *2 *2 *3) (-12 (-4 *3 (-311)) (-5 *1 (-939 *3 *2)) (-4 *2 (-601 *3))))
((*1 *2 *3 *4)
- (-12 (-4 *5 (-311)) (-5 *2 (-2 (|:| -3263 *3) (|:| -2511 (-584 *5))))
+ (-12 (-4 *5 (-311)) (-5 *2 (-2 (|:| -3264 *3) (|:| -2512 (-584 *5))))
(-5 *1 (-939 *5 *3)) (-5 *4 (-584 *5)) (-4 *3 (-601 *5)))))
(((*1 *1 *2 *3)
(-12 (-5 *2 (-974 (-938 *4) (-1084 (-938 *4)))) (-5 *3 (-773))
@@ -6813,44 +6813,44 @@
(|partial| -12 (-5 *2 (-974 (-938 *3) (-1084 (-938 *3)))) (-5 *1 (-938 *3))
(-4 *3 (-13 (-756) (-311) (-934))))))
(((*1 *2 *3)
- (-12 (-5 *2 (-584 (-2 (|:| -3135 (-347 (-484))) (|:| -3134 (-347 (-484))))))
+ (-12 (-5 *2 (-584 (-2 (|:| -3136 (-347 (-484))) (|:| -3135 (-347 (-484))))))
(-5 *1 (-935 *3)) (-4 *3 (-1154 (-484)))))
((*1 *2 *3 *4)
- (-12 (-5 *2 (-584 (-2 (|:| -3135 (-347 (-484))) (|:| -3134 (-347 (-484))))))
+ (-12 (-5 *2 (-584 (-2 (|:| -3136 (-347 (-484))) (|:| -3135 (-347 (-484))))))
(-5 *1 (-935 *3)) (-4 *3 (-1154 (-484)))
- (-5 *4 (-2 (|:| -3135 (-347 (-484))) (|:| -3134 (-347 (-484)))))))
+ (-5 *4 (-2 (|:| -3136 (-347 (-484))) (|:| -3135 (-347 (-484)))))))
((*1 *2 *3 *4)
- (-12 (-5 *2 (-584 (-2 (|:| -3135 (-347 (-484))) (|:| -3134 (-347 (-484))))))
+ (-12 (-5 *2 (-584 (-2 (|:| -3136 (-347 (-484))) (|:| -3135 (-347 (-484))))))
(-5 *1 (-935 *3)) (-4 *3 (-1154 (-484))) (-5 *4 (-347 (-484)))))
((*1 *2 *3 *4 *5)
- (-12 (-5 *5 (-347 (-484))) (-5 *2 (-584 (-2 (|:| -3135 *5) (|:| -3134 *5))))
+ (-12 (-5 *5 (-347 (-484))) (-5 *2 (-584 (-2 (|:| -3136 *5) (|:| -3135 *5))))
(-5 *1 (-935 *3)) (-4 *3 (-1154 (-484)))
- (-5 *4 (-2 (|:| -3135 *5) (|:| -3134 *5)))))
+ (-5 *4 (-2 (|:| -3136 *5) (|:| -3135 *5)))))
((*1 *2 *3)
- (-12 (-5 *2 (-584 (-2 (|:| -3135 (-347 (-484))) (|:| -3134 (-347 (-484))))))
+ (-12 (-5 *2 (-584 (-2 (|:| -3136 (-347 (-484))) (|:| -3135 (-347 (-484))))))
(-5 *1 (-936 *3)) (-4 *3 (-1154 (-347 (-484))))))
((*1 *2 *3 *4)
- (-12 (-5 *2 (-584 (-2 (|:| -3135 (-347 (-484))) (|:| -3134 (-347 (-484))))))
+ (-12 (-5 *2 (-584 (-2 (|:| -3136 (-347 (-484))) (|:| -3135 (-347 (-484))))))
(-5 *1 (-936 *3)) (-4 *3 (-1154 (-347 (-484))))
- (-5 *4 (-2 (|:| -3135 (-347 (-484))) (|:| -3134 (-347 (-484)))))))
+ (-5 *4 (-2 (|:| -3136 (-347 (-484))) (|:| -3135 (-347 (-484)))))))
((*1 *2 *3 *4)
- (-12 (-5 *4 (-347 (-484))) (-5 *2 (-584 (-2 (|:| -3135 *4) (|:| -3134 *4))))
+ (-12 (-5 *4 (-347 (-484))) (-5 *2 (-584 (-2 (|:| -3136 *4) (|:| -3135 *4))))
(-5 *1 (-936 *3)) (-4 *3 (-1154 *4))))
((*1 *2 *3 *4 *5)
- (-12 (-5 *5 (-347 (-484))) (-5 *2 (-584 (-2 (|:| -3135 *5) (|:| -3134 *5))))
+ (-12 (-5 *5 (-347 (-484))) (-5 *2 (-584 (-2 (|:| -3136 *5) (|:| -3135 *5))))
(-5 *1 (-936 *3)) (-4 *3 (-1154 *5))
- (-5 *4 (-2 (|:| -3135 *5) (|:| -3134 *5))))))
+ (-5 *4 (-2 (|:| -3136 *5) (|:| -3135 *5))))))
(((*1 *2 *3)
- (-12 (-5 *3 (-584 (-2 (|:| -3135 (-347 (-484))) (|:| -3134 (-347 (-484))))))
+ (-12 (-5 *3 (-584 (-2 (|:| -3136 (-347 (-484))) (|:| -3135 (-347 (-484))))))
(-5 *2 (-584 (-347 (-484)))) (-5 *1 (-935 *4)) (-4 *4 (-1154 (-484))))))
(((*1 *2 *3)
- (-12 (-5 *3 (-2 (|:| -3135 (-347 (-484))) (|:| -3134 (-347 (-484)))))
+ (-12 (-5 *3 (-2 (|:| -3136 (-347 (-484))) (|:| -3135 (-347 (-484)))))
(-5 *2 (-347 (-484))) (-5 *1 (-935 *4)) (-4 *4 (-1154 (-484))))))
(((*1 *2 *3 *4 *5)
(-12 (-5 *3 (-1178 *6)) (-5 *4 (-1178 (-484))) (-5 *5 (-484)) (-4 *6 (-1013))
(-5 *2 (-1 *6)) (-5 *1 (-931 *6)))))
(((*1 *2 *3)
- (-12 (-5 *3 (-584 (-2 (|:| -3398 *4) (|:| -1520 (-484))))) (-4 *4 (-1013))
+ (-12 (-5 *3 (-584 (-2 (|:| -3399 *4) (|:| -1520 (-484))))) (-4 *4 (-1013))
(-5 *2 (-1 *4)) (-5 *1 (-931 *4)))))
(((*1 *2 *3 *3 *3)
(|partial| -12 (-4 *4 (-13 (-311) (-120) (-951 (-484)))) (-4 *5 (-1154 *4))
@@ -6860,14 +6860,14 @@
(-4 *5 (-13 (-311) (-120) (-951 (-484))))
(-5 *2
(-2 (|:| |a| *6) (|:| |b| (-347 *6)) (|:| |h| *6) (|:| |c1| (-347 *6))
- (|:| |c2| (-347 *6)) (|:| -3091 *6)))
+ (|:| |c2| (-347 *6)) (|:| -3092 *6)))
(-5 *1 (-930 *5 *6)) (-5 *3 (-347 *6)))))
(((*1 *2 *3 *3 *3 *4 *5)
(-12 (-5 *5 (-1 *3 *3)) (-4 *3 (-1154 *6))
(-4 *6 (-13 (-311) (-120) (-951 *4))) (-5 *4 (-484))
(-5 *2
(-3 (|:| |ans| (-2 (|:| |ans| *3) (|:| |nosol| (-85))))
- (|:| -3263
+ (|:| -3264
(-2 (|:| |b| *3) (|:| |c| *3) (|:| |m| *4) (|:| |alpha| *3)
(|:| |beta| *3)))))
(-5 *1 (-929 *6 *3)))))
@@ -6879,7 +6879,7 @@
(|partial| -12 (-5 *4 (-1 *6 *6)) (-4 *6 (-1154 *5))
(-4 *5 (-13 (-311) (-120) (-951 (-484))))
(-5 *2
- (-2 (|:| |a| *6) (|:| |b| (-347 *6)) (|:| |c| (-347 *6)) (|:| -3091 *6)))
+ (-2 (|:| |a| *6) (|:| |b| (-347 *6)) (|:| |c| (-347 *6)) (|:| -3092 *6)))
(-5 *1 (-929 *5 *6)) (-5 *3 (-347 *6)))))
(((*1 *2 *3 *4 *4 *4 *5 *6 *7)
(|partial| -12 (-5 *5 (-1089))
@@ -6890,7 +6890,7 @@
(|:| |limitedlogs| (-584 (-2 (|:| |coeff| *4) (|:| |logand| *4)))))
"failed")
*4 (-584 *4)))
- (-5 *7 (-1 (-3 (-2 (|:| -2134 *4) (|:| |coeff| *4)) "failed") *4 *4))
+ (-5 *7 (-1 (-3 (-2 (|:| -2135 *4) (|:| |coeff| *4)) "failed") *4 *4))
(-4 *4 (-13 (-1114) (-27) (-361 *8)))
(-4 *8 (-13 (-389) (-120) (-951 *3) (-581 *3))) (-5 *3 (-484))
(-5 *2 (-584 *4)) (-5 *1 (-928 *8 *4)))))
@@ -6903,10 +6903,10 @@
(|:| |limitedlogs| (-584 (-2 (|:| |coeff| *4) (|:| |logand| *4)))))
"failed")
*4 (-584 *4)))
- (-5 *7 (-1 (-3 (-2 (|:| -2134 *4) (|:| |coeff| *4)) "failed") *4 *4))
+ (-5 *7 (-1 (-3 (-2 (|:| -2135 *4) (|:| |coeff| *4)) "failed") *4 *4))
(-4 *4 (-13 (-1114) (-27) (-361 *8)))
(-4 *8 (-13 (-389) (-120) (-951 *3) (-581 *3))) (-5 *3 (-484))
- (-5 *2 (-2 (|:| |ans| *4) (|:| -3134 *4) (|:| |sol?| (-85))))
+ (-5 *2 (-2 (|:| |ans| *4) (|:| -3135 *4) (|:| |sol?| (-85))))
(-5 *1 (-927 *8 *4)))))
(((*1 *1 *1 *2) (-12 (-4 *1 (-780 *3)) (-5 *2 (-484))))
((*1 *1 *1) (-4 *1 (-916))) ((*1 *1 *2) (-12 (-5 *2 (-484)) (-4 *1 (-926))))
@@ -6926,9 +6926,9 @@
(((*1 *2 *1 *1)
(-12 (-4 *1 (-924 *3)) (-4 *3 (-1128)) (-4 *3 (-1013)) (-5 *2 (-85)))))
(((*1 *1 *1 *2)
- (-12 (-5 *2 (-584 *1)) (|has| *1 (-6 -3992)) (-4 *1 (-924 *3))
+ (-12 (-5 *2 (-584 *1)) (|has| *1 (-6 -3993)) (-4 *1 (-924 *3))
(-4 *3 (-1128)))))
-(((*1 *2 *1 *2) (-12 (|has| *1 (-6 -3992)) (-4 *1 (-924 *2)) (-4 *2 (-1128)))))
+(((*1 *2 *1 *2) (-12 (|has| *1 (-6 -3993)) (-4 *1 (-924 *2)) (-4 *2 (-1128)))))
(((*1 *2 *1)
(|partial| -12 (-4 *1 (-139 *3)) (-4 *3 (-146)) (-4 *3 (-483))
(-5 *2 (-347 (-484)))))
@@ -6993,7 +6993,7 @@
(((*1 *1 *2 *2) (-12 (-5 *2 (-584 (-484))) (-5 *1 (-918 *3)) (-14 *3 (-484)))))
(((*1 *2 *3 *4)
(-12 (-5 *3 (-345 *5)) (-4 *5 (-495))
- (-5 *2 (-2 (|:| -2399 (-695)) (|:| -3950 *5) (|:| |radicand| (-584 *5))))
+ (-5 *2 (-2 (|:| -2400 (-695)) (|:| -3951 *5) (|:| |radicand| (-584 *5))))
(-5 *1 (-270 *5)) (-5 *4 (-695))))
((*1 *1 *1 *2) (-12 (-4 *1 (-916)) (-5 *2 (-484)))))
(((*1 *1 *2) (-12 (-5 *2 (-584 *3)) (-4 *3 (-1013)) (-5 *1 (-914 *3)))))
@@ -7089,39 +7089,39 @@
(-12 (-4 *3 (-1154 *2)) (-4 *2 (-1154 *4)) (-5 *1 (-899 *4 *2 *3 *5))
(-4 *4 (-298)) (-4 *5 (-662 *2 *3)))))
(((*1 *2 *2 *3)
- (-12 (-4 *4 (-718)) (-4 *3 (-13 (-757) (-10 -8 (-15 -3968 ((-1089) $)))))
+ (-12 (-4 *4 (-718)) (-4 *3 (-13 (-757) (-10 -8 (-15 -3969 ((-1089) $)))))
(-4 *5 (-495)) (-5 *1 (-672 *4 *3 *5 *2))
(-4 *2 (-862 (-347 (-858 *5)) *4 *3))))
((*1 *2 *2 *3)
(-12 (-4 *4 (-962)) (-4 *5 (-718))
(-4 *3
(-13 (-757)
- (-10 -8 (-15 -3968 ((-1089) $))
- (-15 -3827 ((-3 $ #1="failed") (-1089))))))
+ (-10 -8 (-15 -3969 ((-1089) $))
+ (-15 -3828 ((-3 $ #1="failed") (-1089))))))
(-5 *1 (-898 *4 *5 *3 *2)) (-4 *2 (-862 (-858 *4) *5 *3))))
((*1 *2 *2 *3)
(-12 (-5 *3 (-584 *6))
(-4 *6
(-13 (-757)
- (-10 -8 (-15 -3968 ((-1089) $)) (-15 -3827 ((-3 $ #1#) (-1089))))))
+ (-10 -8 (-15 -3969 ((-1089) $)) (-15 -3828 ((-3 $ #1#) (-1089))))))
(-4 *4 (-962)) (-4 *5 (-718)) (-5 *1 (-898 *4 *5 *6 *2))
(-4 *2 (-862 (-858 *4) *5 *6)))))
(((*1 *2 *2 *3)
- (-12 (-4 *4 (-718)) (-4 *3 (-13 (-757) (-10 -8 (-15 -3968 ((-1089) $)))))
+ (-12 (-4 *4 (-718)) (-4 *3 (-13 (-757) (-10 -8 (-15 -3969 ((-1089) $)))))
(-4 *5 (-495)) (-5 *1 (-672 *4 *3 *5 *2))
(-4 *2 (-862 (-347 (-858 *5)) *4 *3))))
((*1 *2 *2 *3)
(-12 (-4 *4 (-962)) (-4 *5 (-718))
(-4 *3
(-13 (-757)
- (-10 -8 (-15 -3968 ((-1089) $))
- (-15 -3827 ((-3 $ #1="failed") (-1089))))))
+ (-10 -8 (-15 -3969 ((-1089) $))
+ (-15 -3828 ((-3 $ #1="failed") (-1089))))))
(-5 *1 (-898 *4 *5 *3 *2)) (-4 *2 (-862 (-858 *4) *5 *3))))
((*1 *2 *2 *3)
(-12 (-5 *3 (-584 *6))
(-4 *6
(-13 (-757)
- (-10 -8 (-15 -3968 ((-1089) $)) (-15 -3827 ((-3 $ #1#) (-1089))))))
+ (-10 -8 (-15 -3969 ((-1089) $)) (-15 -3828 ((-3 $ #1#) (-1089))))))
(-4 *4 (-962)) (-4 *5 (-718)) (-5 *1 (-898 *4 *5 *6 *2))
(-4 *2 (-862 (-858 *4) *5 *6)))))
(((*1 *2 *2) (|partial| -12 (-4 *1 (-897 *2)) (-4 *2 (-1114)))))
@@ -7220,7 +7220,7 @@
(((*1 *2 *3)
(|partial| -12 (-4 *4 (-495)) (-4 *5 (-718)) (-4 *6 (-757))
(-4 *7 (-977 *4 *5 *6))
- (-5 *2 (-2 (|:| |bas| (-413 *4 *5 *6 *7)) (|:| -3320 (-584 *7))))
+ (-5 *2 (-2 (|:| |bas| (-413 *4 *5 *6 *7)) (|:| -3321 (-584 *7))))
(-5 *1 (-891 *4 *5 *6 *7)) (-5 *3 (-584 *7)))))
(((*1 *2 *2)
(-12 (-5 *2 (-584 *6)) (-4 *6 (-977 *3 *4 *5)) (-4 *3 (-495)) (-4 *4 (-718))
@@ -7327,7 +7327,7 @@
((*1 *2 *2) (-12 (-5 *2 (-584 (-814 *3))) (-5 *1 (-814 *3)) (-4 *3 (-1013))))
((*1 *2 *1 *3)
(-12 (-4 *4 (-962)) (-4 *5 (-718)) (-4 *3 (-757)) (-4 *6 (-977 *4 *5 *3))
- (-5 *2 (-2 (|:| |under| *1) (|:| -3127 *1) (|:| |upper| *1)))
+ (-5 *2 (-2 (|:| |under| *1) (|:| -3128 *1) (|:| |upper| *1)))
(-4 *1 (-890 *4 *5 *3 *6)))))
(((*1 *2 *1)
(-12 (-4 *1 (-890 *3 *4 *5 *6)) (-4 *3 (-962)) (-4 *4 (-718)) (-4 *5 (-757))
@@ -7371,10 +7371,10 @@
(((*1 *1 *1) (-12 (-4 *1 (-47 *2 *3)) (-4 *2 (-962)) (-4 *3 (-717))))
((*1 *2 *1) (-12 (-4 *1 (-332 *3 *2)) (-4 *3 (-962)) (-4 *2 (-1013))))
((*1 *2 *1)
- (-12 (-14 *3 (-584 (-1089))) (-4 *4 (-146)) (-4 *6 (-196 (-3953 *3) (-695)))
+ (-12 (-14 *3 (-584 (-1089))) (-4 *4 (-146)) (-4 *6 (-196 (-3954 *3) (-695)))
(-14 *7
- (-1 (-85) (-2 (|:| -2398 *5) (|:| -2399 *6))
- (-2 (|:| -2398 *5) (|:| -2399 *6))))
+ (-1 (-85) (-2 (|:| -2399 *5) (|:| -2400 *6))
+ (-2 (|:| -2399 *5) (|:| -2400 *6))))
(-5 *2 (-651 *5 *6 *7)) (-5 *1 (-398 *3 *4 *5 *6 *7 *8)) (-4 *5 (-757))
(-4 *8 (-862 *4 *6 (-774 *3)))))
((*1 *2 *1)
@@ -7386,10 +7386,10 @@
(-12 (-5 *3 (-584 (-831))) (-5 *1 (-125 *4 *2 *5)) (-14 *4 (-831))
(-4 *2 (-311)) (-14 *5 (-907 *4 *2))))
((*1 *1 *2 *3)
- (-12 (-5 *3 (-651 *5 *6 *7)) (-4 *5 (-757)) (-4 *6 (-196 (-3953 *4) (-695)))
+ (-12 (-5 *3 (-651 *5 *6 *7)) (-4 *5 (-757)) (-4 *6 (-196 (-3954 *4) (-695)))
(-14 *7
- (-1 (-85) (-2 (|:| -2398 *5) (|:| -2399 *6))
- (-2 (|:| -2398 *5) (|:| -2399 *6))))
+ (-1 (-85) (-2 (|:| -2399 *5) (|:| -2400 *6))
+ (-2 (|:| -2399 *5) (|:| -2400 *6))))
(-14 *4 (-584 (-1089))) (-4 *2 (-146)) (-5 *1 (-398 *4 *2 *5 *6 *7 *8))
(-4 *8 (-862 *2 *6 (-774 *4)))))
((*1 *1 *2 *3) (-12 (-4 *1 (-447 *2 *3)) (-4 *2 (-72)) (-4 *3 (-760))))
@@ -7430,18 +7430,18 @@
(-12 (-4 *1 (-57 *3 *4 *5)) (-4 *3 (-1128)) (-4 *4 (-321 *3))
(-4 *5 (-321 *3)) (-5 *2 (-584 *3))))
((*1 *2 *1)
- (-12 (|has| *1 (-6 -3991)) (-4 *1 (-426 *3)) (-4 *3 (-1128))
+ (-12 (|has| *1 (-6 -3992)) (-4 *1 (-426 *3)) (-4 *3 (-1128))
(-5 *2 (-584 *3))))
((*1 *2 *1) (-12 (-5 *2 (-584 (-831))) (-5 *1 (-885)))))
(((*1 *2 *3) (-12 (-5 *3 (-695)) (-5 *2 (-1068 (-885))) (-5 *1 (-885)))))
(((*1 *2 *1) (-12 (-5 *2 (-584 (-783 (-831) (-831)))) (-5 *1 (-885)))))
(((*1 *2 *1) (-12 (-5 *2 (-831)) (-5 *1 (-885)))))
(((*1 *2 *3 *3)
- (-12 (-4 *4 (-495)) (-5 *2 (-2 (|:| |coef2| *3) (|:| -3752 *4)))
+ (-12 (-4 *4 (-495)) (-5 *2 (-2 (|:| |coef2| *3) (|:| -3753 *4)))
(-5 *1 (-883 *4 *3)) (-4 *3 (-1154 *4)))))
(((*1 *2 *3 *3)
(-12 (-4 *4 (-495))
- (-5 *2 (-2 (|:| |coef1| *3) (|:| |coef2| *3) (|:| -3752 *4)))
+ (-5 *2 (-2 (|:| |coef1| *3) (|:| |coef2| *3) (|:| -3753 *4)))
(-5 *1 (-883 *4 *3)) (-4 *3 (-1154 *4)))))
(((*1 *2 *3 *3) (-12 (-4 *2 (-495)) (-5 *1 (-883 *2 *3)) (-4 *3 (-1154 *2)))))
(((*1 *2 *2 *2 *2 *3)
@@ -7451,22 +7451,22 @@
(((*1 *2 *2 *2 *3)
(-12 (-5 *3 (-695)) (-4 *2 (-495)) (-5 *1 (-883 *2 *4)) (-4 *4 (-1154 *2)))))
(((*1 *2 *1 *1)
- (-12 (-5 *2 (-2 (|:| -1971 *1) (|:| -2900 *1))) (-4 *1 (-257))))
+ (-12 (-5 *2 (-2 (|:| -1971 *1) (|:| -2901 *1))) (-4 *1 (-257))))
((*1 *2 *1 *1)
(|partial| -12 (-4 *3 (-1013)) (-5 *2 (-2 (|:| |lm| *1) (|:| |rm| *1)))
(-4 *1 (-333 *3))))
((*1 *2 *1 *1)
- (-12 (-5 *2 (-2 (|:| -1971 (-695)) (|:| -2900 (-695)))) (-5 *1 (-695))))
+ (-12 (-5 *2 (-2 (|:| -1971 (-695)) (|:| -2901 (-695)))) (-5 *1 (-695))))
((*1 *2 *3 *3)
- (-12 (-4 *4 (-495)) (-5 *2 (-2 (|:| -1971 *3) (|:| -2900 *3)))
+ (-12 (-4 *4 (-495)) (-5 *2 (-2 (|:| -1971 *3) (|:| -2901 *3)))
(-5 *1 (-883 *4 *3)) (-4 *3 (-1154 *4)))))
(((*1 *2 *3 *3)
(-12 (-4 *4 (-389)) (-4 *4 (-495))
- (-5 *2 (-2 (|:| |coef2| *3) (|:| -2874 *4))) (-5 *1 (-883 *4 *3))
+ (-5 *2 (-2 (|:| |coef2| *3) (|:| -2875 *4))) (-5 *1 (-883 *4 *3))
(-4 *3 (-1154 *4)))))
(((*1 *2 *3 *3)
(-12 (-4 *4 (-389)) (-4 *4 (-495))
- (-5 *2 (-2 (|:| |coef1| *3) (|:| |coef2| *3) (|:| -2874 *4)))
+ (-5 *2 (-2 (|:| |coef1| *3) (|:| |coef2| *3) (|:| -2875 *4)))
(-5 *1 (-883 *4 *3)) (-4 *3 (-1154 *4)))))
(((*1 *2 *3 *3)
(-12 (-4 *2 (-495)) (-4 *2 (-389)) (-5 *1 (-883 *2 *3)) (-4 *3 (-1154 *2)))))
@@ -7477,21 +7477,21 @@
(-12 (-4 *4 (-495)) (-5 *2 (-584 *3)) (-5 *1 (-883 *4 *3))
(-4 *3 (-1154 *4)))))
(((*1 *2 *3)
- (-12 (-4 *4 (-495)) (-5 *2 (-2 (|:| |coef2| *3) (|:| -3753 *4)))
+ (-12 (-4 *4 (-495)) (-5 *2 (-2 (|:| |coef2| *3) (|:| -3754 *4)))
(-5 *1 (-883 *4 *3)) (-4 *3 (-1154 *4)))))
(((*1 *2 *3)
(-12 (-4 *4 (-495))
- (-5 *2 (-2 (|:| |coef1| *3) (|:| |coef2| *3) (|:| -3753 *4)))
+ (-5 *2 (-2 (|:| |coef1| *3) (|:| |coef2| *3) (|:| -3754 *4)))
(-5 *1 (-883 *4 *3)) (-4 *3 (-1154 *4)))))
(((*1 *2 *3 *3)
- (-12 (-4 *4 (-495)) (-5 *2 (-2 (|:| |coef1| *3) (|:| -3141 *3)))
+ (-12 (-4 *4 (-495)) (-5 *2 (-2 (|:| |coef1| *3) (|:| -3142 *3)))
(-5 *1 (-883 *4 *3)) (-4 *3 (-1154 *4)))))
(((*1 *2 *3 *3)
- (-12 (-4 *4 (-495)) (-5 *2 (-2 (|:| |coef2| *3) (|:| -3141 *3)))
+ (-12 (-4 *4 (-495)) (-5 *2 (-2 (|:| |coef2| *3) (|:| -3142 *3)))
(-5 *1 (-883 *4 *3)) (-4 *3 (-1154 *4)))))
(((*1 *2 *3 *3)
(-12 (-4 *4 (-495))
- (-5 *2 (-2 (|:| |coef1| *3) (|:| |coef2| *3) (|:| -3141 *3)))
+ (-5 *2 (-2 (|:| |coef1| *3) (|:| |coef2| *3) (|:| -3142 *3)))
(-5 *1 (-883 *4 *3)) (-4 *3 (-1154 *4)))))
(((*1 *2 *3 *3)
(-12 (-4 *4 (-495)) (-5 *2 (-2 (|:| |coef2| *3) (|:| |subResultant| *3)))
@@ -7521,18 +7521,18 @@
(((*1 *2 *2 *2 *3)
(-12 (-5 *3 (-695)) (-4 *4 (-495)) (-5 *1 (-883 *4 *2)) (-4 *2 (-1154 *4)))))
(((*1 *2 *3 *3)
- (-12 (-4 *4 (-495)) (-5 *2 (-2 (|:| |coef1| *3) (|:| -3752 *4)))
+ (-12 (-4 *4 (-495)) (-5 *2 (-2 (|:| |coef1| *3) (|:| -3753 *4)))
(-5 *1 (-883 *4 *3)) (-4 *3 (-1154 *4)))))
(((*1 *2 *3 *3)
- (-12 (-4 *4 (-495)) (-5 *2 (-2 (|:| |coef2| *3) (|:| -3752 *4)))
+ (-12 (-4 *4 (-495)) (-5 *2 (-2 (|:| |coef2| *3) (|:| -3753 *4)))
(-5 *1 (-883 *4 *3)) (-4 *3 (-1154 *4)))))
(((*1 *2 *3 *3)
(-12 (-4 *4 (-495))
- (-5 *2 (-2 (|:| |coef1| *3) (|:| |coef2| *3) (|:| -3752 *4)))
+ (-5 *2 (-2 (|:| |coef1| *3) (|:| |coef2| *3) (|:| -3753 *4)))
(-5 *1 (-883 *4 *3)) (-4 *3 (-1154 *4)))))
(((*1 *1)
- (-12 (-4 *1 (-344)) (-2558 (|has| *1 (-6 -3982)))
- (-2558 (|has| *1 (-6 -3974)))))
+ (-12 (-4 *1 (-344)) (-2559 (|has| *1 (-6 -3983)))
+ (-2559 (|has| *1 (-6 -3975)))))
((*1 *2 *1) (-12 (-4 *1 (-366 *2)) (-4 *2 (-1013)) (-4 *2 (-757))))
((*1 *1) (-4 *1 (-753))) ((*1 *1 *1 *1) (-4 *1 (-760)))
((*1 *2 *1) (-12 (-4 *1 (-882 *2)) (-4 *2 (-757)))))
@@ -7601,14 +7601,14 @@
(-12 (-5 *3 (-584 (-858 *5))) (-5 *4 (-584 (-1089)))
(-4 *5 (-13 (-311) (-120)))
(-5 *2
- (-2 (|:| -3950 (-584 (-484))) (|:| |poly| (-584 (-1084 *5)))
+ (-2 (|:| -3951 (-584 (-484))) (|:| |poly| (-584 (-1084 *5)))
(|:| |prim| (-1084 *5))))
(-5 *1 (-873 *5))))
((*1 *2 *3 *4 *5)
(-12 (-5 *3 (-584 (-858 *6))) (-5 *4 (-584 (-1089))) (-5 *5 (-1089))
(-4 *6 (-13 (-311) (-120)))
(-5 *2
- (-2 (|:| -3950 (-584 (-484))) (|:| |poly| (-584 (-1084 *6)))
+ (-2 (|:| -3951 (-584 (-484))) (|:| |poly| (-584 (-1084 *6)))
(|:| |prim| (-1084 *6))))
(-5 *1 (-873 *6)))))
(((*1 *1 *2 *3)
@@ -7628,69 +7628,69 @@
(((*1 *1 *2) (-12 (-5 *2 (-1033)) (-5 *1 (-866)))))
(((*1 *2 *3 *4)
(-12 (-4 *5 (-718)) (-4 *6 (-757)) (-4 *7 (-495)) (-4 *3 (-862 *7 *5 *6))
- (-5 *2 (-2 (|:| -2399 (-695)) (|:| -3950 *3) (|:| |radicand| (-584 *3))))
+ (-5 *2 (-2 (|:| -2400 (-695)) (|:| -3951 *3) (|:| |radicand| (-584 *3))))
(-5 *1 (-865 *5 *6 *7 *3 *8)) (-5 *4 (-695))
(-4 *8
(-13 (-311)
- (-10 -8 (-15 -3942 ($ *3)) (-15 -2996 (*3 $)) (-15 -2995 (*3 $))))))))
+ (-10 -8 (-15 -3943 ($ *3)) (-15 -2997 (*3 $)) (-15 -2996 (*3 $))))))))
(((*1 *2 *3 *4)
(-12 (-4 *7 (-389)) (-4 *5 (-718)) (-4 *6 (-757)) (-4 *7 (-495))
(-4 *8 (-862 *7 *5 *6))
- (-5 *2 (-2 (|:| -2399 (-695)) (|:| -3950 *3) (|:| |radicand| *3)))
+ (-5 *2 (-2 (|:| -2400 (-695)) (|:| -3951 *3) (|:| |radicand| *3)))
(-5 *1 (-865 *5 *6 *7 *8 *3)) (-5 *4 (-695))
(-4 *3
(-13 (-311)
- (-10 -8 (-15 -3942 ($ *8)) (-15 -2996 (*8 $)) (-15 -2995 (*8 $))))))))
+ (-10 -8 (-15 -3943 ($ *8)) (-15 -2997 (*8 $)) (-15 -2996 (*8 $))))))))
(((*1 *2 *3 *4)
(-12 (-5 *3 (-347 (-484))) (-4 *5 (-718)) (-4 *6 (-757)) (-4 *7 (-495))
(-4 *8 (-862 *7 *5 *6))
- (-5 *2 (-2 (|:| -2399 (-695)) (|:| -3950 *9) (|:| |radicand| *9)))
+ (-5 *2 (-2 (|:| -2400 (-695)) (|:| -3951 *9) (|:| |radicand| *9)))
(-5 *1 (-865 *5 *6 *7 *8 *9)) (-5 *4 (-695))
(-4 *9
(-13 (-311)
- (-10 -8 (-15 -3942 ($ *8)) (-15 -2996 (*8 $)) (-15 -2995 (*8 $))))))))
+ (-10 -8 (-15 -3943 ($ *8)) (-15 -2997 (*8 $)) (-15 -2996 (*8 $))))))))
(((*1 *2 *3 *4)
(-12 (-4 *5 (-718)) (-4 *6 (-757)) (-4 *3 (-495)) (-4 *7 (-862 *3 *5 *6))
- (-5 *2 (-2 (|:| -2399 (-695)) (|:| -3950 *8) (|:| |radicand| *8)))
+ (-5 *2 (-2 (|:| -2400 (-695)) (|:| -3951 *8) (|:| |radicand| *8)))
(-5 *1 (-865 *5 *6 *3 *7 *8)) (-5 *4 (-695))
(-4 *8
(-13 (-311)
- (-10 -8 (-15 -3942 ($ *7)) (-15 -2996 (*7 $)) (-15 -2995 (*7 $))))))))
+ (-10 -8 (-15 -3943 ($ *7)) (-15 -2997 (*7 $)) (-15 -2996 (*7 $))))))))
(((*1 *2 *1)
(|partial| -12 (-4 *3 (-962)) (-4 *3 (-1013))
- (-5 *2 (-2 (|:| |val| *1) (|:| -2399 (-484)))) (-4 *1 (-361 *3))))
+ (-5 *2 (-2 (|:| |val| *1) (|:| -2400 (-484)))) (-4 *1 (-361 *3))))
((*1 *2 *1)
- (|partial| -12 (-5 *2 (-2 (|:| |val| (-801 *3)) (|:| -2399 (-801 *3))))
+ (|partial| -12 (-5 *2 (-2 (|:| |val| (-801 *3)) (|:| -2400 (-801 *3))))
(-5 *1 (-801 *3)) (-4 *3 (-1013))))
((*1 *2 *3)
(|partial| -12 (-4 *4 (-718)) (-4 *5 (-757)) (-4 *6 (-962))
- (-4 *7 (-862 *6 *4 *5)) (-5 *2 (-2 (|:| |val| *3) (|:| -2399 (-484))))
+ (-4 *7 (-862 *6 *4 *5)) (-5 *2 (-2 (|:| |val| *3) (|:| -2400 (-484))))
(-5 *1 (-863 *4 *5 *6 *7 *3))
(-4 *3
(-13 (-311)
- (-10 -8 (-15 -3942 ($ *7)) (-15 -2996 (*7 $)) (-15 -2995 (*7 $))))))))
+ (-10 -8 (-15 -3943 ($ *7)) (-15 -2997 (*7 $)) (-15 -2996 (*7 $))))))))
(((*1 *2 *1 *3)
(|partial| -12 (-5 *3 (-1089)) (-4 *4 (-962)) (-4 *4 (-1013))
- (-5 *2 (-2 (|:| |var| (-551 *1)) (|:| -2399 (-484)))) (-4 *1 (-361 *4))))
+ (-5 *2 (-2 (|:| |var| (-551 *1)) (|:| -2400 (-484)))) (-4 *1 (-361 *4))))
((*1 *2 *1 *3)
(|partial| -12 (-5 *3 (-86)) (-4 *4 (-962)) (-4 *4 (-1013))
- (-5 *2 (-2 (|:| |var| (-551 *1)) (|:| -2399 (-484)))) (-4 *1 (-361 *4))))
+ (-5 *2 (-2 (|:| |var| (-551 *1)) (|:| -2400 (-484)))) (-4 *1 (-361 *4))))
((*1 *2 *1)
(|partial| -12 (-4 *3 (-1025)) (-4 *3 (-1013))
- (-5 *2 (-2 (|:| |var| (-551 *1)) (|:| -2399 (-484)))) (-4 *1 (-361 *3))))
+ (-5 *2 (-2 (|:| |var| (-551 *1)) (|:| -2400 (-484)))) (-4 *1 (-361 *3))))
((*1 *2 *1)
- (|partial| -12 (-5 *2 (-2 (|:| |val| (-801 *3)) (|:| -2399 (-695))))
+ (|partial| -12 (-5 *2 (-2 (|:| |val| (-801 *3)) (|:| -2400 (-695))))
(-5 *1 (-801 *3)) (-4 *3 (-1013))))
((*1 *2 *1)
(|partial| -12 (-4 *1 (-862 *3 *4 *5)) (-4 *3 (-962)) (-4 *4 (-718))
- (-4 *5 (-757)) (-5 *2 (-2 (|:| |var| *5) (|:| -2399 (-695))))))
+ (-4 *5 (-757)) (-5 *2 (-2 (|:| |var| *5) (|:| -2400 (-695))))))
((*1 *2 *3)
(|partial| -12 (-4 *4 (-718)) (-4 *5 (-757)) (-4 *6 (-962))
- (-4 *7 (-862 *6 *4 *5)) (-5 *2 (-2 (|:| |var| *5) (|:| -2399 (-484))))
+ (-4 *7 (-862 *6 *4 *5)) (-5 *2 (-2 (|:| |var| *5) (|:| -2400 (-484))))
(-5 *1 (-863 *4 *5 *6 *7 *3))
(-4 *3
(-13 (-311)
- (-10 -8 (-15 -3942 ($ *7)) (-15 -2996 (*7 $)) (-15 -2995 (*7 $))))))))
+ (-10 -8 (-15 -3943 ($ *7)) (-15 -2997 (*7 $)) (-15 -2996 (*7 $))))))))
(((*1 *2 *1)
(|partial| -12 (-4 *3 (-1025)) (-4 *3 (-1013)) (-5 *2 (-584 *1))
(-4 *1 (-361 *3))))
@@ -7704,7 +7704,7 @@
(-4 *7 (-862 *6 *4 *5)) (-5 *2 (-584 *3)) (-5 *1 (-863 *4 *5 *6 *7 *3))
(-4 *3
(-13 (-311)
- (-10 -8 (-15 -3942 ($ *7)) (-15 -2996 (*7 $)) (-15 -2995 (*7 $))))))))
+ (-10 -8 (-15 -3943 ($ *7)) (-15 -2997 (*7 $)) (-15 -2996 (*7 $))))))))
(((*1 *2 *1)
(|partial| -12 (-4 *3 (-25)) (-4 *3 (-1013)) (-5 *2 (-584 *1))
(-4 *1 (-361 *3))))
@@ -7718,7 +7718,7 @@
(-4 *7 (-862 *6 *4 *5)) (-5 *2 (-584 *3)) (-5 *1 (-863 *4 *5 *6 *7 *3))
(-4 *3
(-13 (-311)
- (-10 -8 (-15 -3942 ($ *7)) (-15 -2996 (*7 $)) (-15 -2995 (*7 $))))))))
+ (-10 -8 (-15 -3943 ($ *7)) (-15 -2997 (*7 $)) (-15 -2996 (*7 $))))))))
(((*1 *2 *1)
(-12 (-4 *3 (-962)) (-4 *4 (-1013)) (-5 *2 (-584 *1)) (-4 *1 (-332 *3 *4))))
((*1 *2 *1)
@@ -7967,7 +7967,7 @@
(|:| |wcond| (-584 (-858 *9)))
(|:| |bsoln|
(-2 (|:| |partsol| (-1178 (-347 (-858 *9))))
- (|:| -2010 (-584 (-1178 (-347 (-858 *9)))))))))
+ (|:| -2011 (-584 (-1178 (-347 (-858 *9)))))))))
(-5 *1 (-836 *9 *10 *11 *12)))))
(((*1 *2 *2 *3)
(-12 (-5 *2 (-631 *7)) (-5 *3 (-584 *7)) (-4 *7 (-862 *4 *6 *5))
@@ -7998,7 +7998,7 @@
(-12
(-5 *3
(-584
- (-2 (|:| -3106 (-695))
+ (-2 (|:| -3107 (-695))
(|:| |eqns|
(-584
(-2 (|:| |det| *7) (|:| |rows| (-584 (-484)))
@@ -8011,7 +8011,7 @@
(-12
(-5 *3
(-584
- (-2 (|:| -3106 (-695))
+ (-2 (|:| -3107 (-695))
(|:| |eqns|
(-584
(-2 (|:| |det| *7) (|:| |rows| (-584 (-484)))
@@ -8028,18 +8028,18 @@
(-12
(-5 *3
(-2 (|:| |mat| (-631 (-347 (-858 *4)))) (|:| |vec| (-584 (-347 (-858 *4))))
- (|:| -3106 (-695)) (|:| |rows| (-584 (-484))) (|:| |cols| (-584 (-484)))))
+ (|:| -3107 (-695)) (|:| |rows| (-584 (-484))) (|:| |cols| (-584 (-484)))))
(-4 *4 (-13 (-257) (-120))) (-4 *5 (-13 (-757) (-554 (-1089))))
(-4 *6 (-718))
(-5 *2
(-2 (|:| |partsol| (-1178 (-347 (-858 *4))))
- (|:| -2010 (-584 (-1178 (-347 (-858 *4)))))))
+ (|:| -2011 (-584 (-1178 (-347 (-858 *4)))))))
(-5 *1 (-836 *4 *5 *6 *7)) (-4 *7 (-862 *4 *6 *5)))))
(((*1 *2 *2 *3)
(-12
(-5 *2
(-2 (|:| |partsol| (-1178 (-347 (-858 *4))))
- (|:| -2010 (-584 (-1178 (-347 (-858 *4)))))))
+ (|:| -2011 (-584 (-1178 (-347 (-858 *4)))))))
(-5 *3 (-584 *7)) (-4 *4 (-13 (-257) (-120))) (-4 *7 (-862 *4 *6 *5))
(-4 *5 (-13 (-757) (-554 (-1089)))) (-4 *6 (-718))
(-5 *1 (-836 *4 *5 *6 *7)))))
@@ -8048,7 +8048,7 @@
(-4 *6 (-13 (-757) (-554 (-1089)))) (-4 *7 (-718))
(-5 *2
(-584
- (-2 (|:| -3106 (-695))
+ (-2 (|:| -3107 (-695))
(|:| |eqns|
(-584
(-2 (|:| |det| *8) (|:| |rows| (-584 (-484)))
@@ -8093,7 +8093,7 @@
(|:| |wcond| (-584 (-858 *8)))
(|:| |bsoln|
(-2 (|:| |partsol| (-1178 (-347 (-858 *8))))
- (|:| -2010 (-584 (-1178 (-347 (-858 *8))))))))))
+ (|:| -2011 (-584 (-1178 (-347 (-858 *8))))))))))
(|:| |rgsz| (-484))))
(-5 *1 (-836 *8 *9 *10 *11)) (-5 *7 (-484)))))
(((*1 *2 *3)
@@ -8105,7 +8105,7 @@
(|:| |wcond| (-584 (-858 *4)))
(|:| |bsoln|
(-2 (|:| |partsol| (-1178 (-347 (-858 *4))))
- (|:| -2010 (-584 (-1178 (-347 (-858 *4))))))))))
+ (|:| -2011 (-584 (-1178 (-347 (-858 *4))))))))))
(-5 *1 (-836 *4 *5 *6 *7)) (-4 *7 (-862 *4 *6 *5)))))
(((*1 *2 *3 *4)
(-12
@@ -8115,7 +8115,7 @@
(|:| |wcond| (-584 (-858 *5)))
(|:| |bsoln|
(-2 (|:| |partsol| (-1178 (-347 (-858 *5))))
- (|:| -2010 (-584 (-1178 (-347 (-858 *5))))))))))
+ (|:| -2011 (-584 (-1178 (-347 (-858 *5))))))))))
(-5 *4 (-1072)) (-4 *5 (-13 (-257) (-120))) (-4 *8 (-862 *5 *7 *6))
(-4 *6 (-13 (-757) (-554 (-1089)))) (-4 *7 (-718)) (-5 *2 (-484))
(-5 *1 (-836 *5 *6 *7 *8)))))
@@ -8128,7 +8128,7 @@
(|:| |wcond| (-584 (-858 *5)))
(|:| |bsoln|
(-2 (|:| |partsol| (-1178 (-347 (-858 *5))))
- (|:| -2010 (-584 (-1178 (-347 (-858 *5))))))))))
+ (|:| -2011 (-584 (-1178 (-347 (-858 *5))))))))))
(-5 *1 (-836 *5 *6 *7 *8)) (-5 *4 (-584 *8))))
((*1 *2 *3 *4)
(-12 (-5 *3 (-631 *8)) (-5 *4 (-584 (-1089))) (-4 *8 (-862 *5 *7 *6))
@@ -8140,7 +8140,7 @@
(|:| |wcond| (-584 (-858 *5)))
(|:| |bsoln|
(-2 (|:| |partsol| (-1178 (-347 (-858 *5))))
- (|:| -2010 (-584 (-1178 (-347 (-858 *5))))))))))
+ (|:| -2011 (-584 (-1178 (-347 (-858 *5))))))))))
(-5 *1 (-836 *5 *6 *7 *8))))
((*1 *2 *3)
(-12 (-5 *3 (-631 *7)) (-4 *7 (-862 *4 *6 *5)) (-4 *4 (-13 (-257) (-120)))
@@ -8151,7 +8151,7 @@
(|:| |wcond| (-584 (-858 *4)))
(|:| |bsoln|
(-2 (|:| |partsol| (-1178 (-347 (-858 *4))))
- (|:| -2010 (-584 (-1178 (-347 (-858 *4))))))))))
+ (|:| -2011 (-584 (-1178 (-347 (-858 *4))))))))))
(-5 *1 (-836 *4 *5 *6 *7))))
((*1 *2 *3 *4 *5)
(-12 (-5 *3 (-631 *9)) (-5 *5 (-831)) (-4 *9 (-862 *6 *8 *7))
@@ -8163,7 +8163,7 @@
(|:| |wcond| (-584 (-858 *6)))
(|:| |bsoln|
(-2 (|:| |partsol| (-1178 (-347 (-858 *6))))
- (|:| -2010 (-584 (-1178 (-347 (-858 *6))))))))))
+ (|:| -2011 (-584 (-1178 (-347 (-858 *6))))))))))
(-5 *1 (-836 *6 *7 *8 *9)) (-5 *4 (-584 *9))))
((*1 *2 *3 *4 *5)
(-12 (-5 *3 (-631 *9)) (-5 *4 (-584 (-1089))) (-5 *5 (-831))
@@ -8175,7 +8175,7 @@
(|:| |wcond| (-584 (-858 *6)))
(|:| |bsoln|
(-2 (|:| |partsol| (-1178 (-347 (-858 *6))))
- (|:| -2010 (-584 (-1178 (-347 (-858 *6))))))))))
+ (|:| -2011 (-584 (-1178 (-347 (-858 *6))))))))))
(-5 *1 (-836 *6 *7 *8 *9))))
((*1 *2 *3 *4)
(-12 (-5 *3 (-631 *8)) (-5 *4 (-831)) (-4 *8 (-862 *5 *7 *6))
@@ -8187,7 +8187,7 @@
(|:| |wcond| (-584 (-858 *5)))
(|:| |bsoln|
(-2 (|:| |partsol| (-1178 (-347 (-858 *5))))
- (|:| -2010 (-584 (-1178 (-347 (-858 *5))))))))))
+ (|:| -2011 (-584 (-1178 (-347 (-858 *5))))))))))
(-5 *1 (-836 *5 *6 *7 *8))))
((*1 *2 *3 *4 *5)
(-12 (-5 *3 (-631 *9)) (-5 *4 (-584 *9)) (-5 *5 (-1072))
@@ -8221,7 +8221,7 @@
(-12 (-5 *3 (-584 *4)) (-4 *4 (-311)) (-4 *2 (-1154 *4))
(-5 *1 (-835 *4 *2)))))
(((*1 *2 *3)
- (-12 (-4 *1 (-833)) (-5 *2 (-2 (|:| -3950 (-584 *1)) (|:| -2407 *1)))
+ (-12 (-4 *1 (-833)) (-5 *2 (-2 (|:| -3951 (-584 *1)) (|:| -2408 *1)))
(-5 *3 (-584 *1)))))
(((*1 *2 *3 *1)
(-12 (-4 *1 (-833)) (-5 *2 (-633 (-584 *1))) (-5 *3 (-584 *1)))))
@@ -8302,13 +8302,13 @@
(|partial| -12 (-5 *3 (-282 *5 *6 *7 *8)) (-4 *5 (-361 *4))
(-4 *6 (-1154 *5)) (-4 *7 (-1154 (-347 *6))) (-4 *8 (-290 *5 *6 *7))
(-4 *4 (-13 (-495) (-951 (-484))))
- (-5 *2 (-2 (|:| -3768 (-695)) (|:| -2381 *8)))
+ (-5 *2 (-2 (|:| -3769 (-695)) (|:| -2382 *8)))
(-5 *1 (-823 *4 *5 *6 *7 *8))))
((*1 *2 *3)
(|partial| -12 (-5 *3 (-282 (-347 (-484)) *4 *5 *6))
(-4 *4 (-1154 (-347 (-484)))) (-4 *5 (-1154 (-347 *4)))
(-4 *6 (-290 (-347 (-484)) *4 *5))
- (-5 *2 (-2 (|:| -3768 (-695)) (|:| -2381 *6))) (-5 *1 (-824 *4 *5 *6)))))
+ (-5 *2 (-2 (|:| -3769 (-695)) (|:| -2382 *6))) (-5 *1 (-824 *4 *5 *6)))))
(((*1 *2 *3)
(-12 (-5 *3 (-282 *5 *6 *7 *8)) (-4 *5 (-361 *4)) (-4 *6 (-1154 *5))
(-4 *7 (-1154 (-347 *6))) (-4 *8 (-290 *5 *6 *7))
@@ -8431,7 +8431,7 @@
(((*1 *1 *2) (-12 (-5 *2 (-584 (-584 *3))) (-4 *3 (-1013)) (-4 *1 (-816 *3)))))
(((*1 *2 *3)
(-12 (-5 *3 (-1055 *4 *2)) (-14 *4 (-831))
- (-4 *2 (-13 (-962) (-10 -7 (-6 (-3993 "*"))))) (-5 *1 (-815 *4 *2)))))
+ (-4 *2 (-13 (-962) (-10 -7 (-6 (-3994 "*"))))) (-5 *1 (-815 *4 *2)))))
(((*1 *2 *1)
(-12 (-5 *2 (-2 (|:| |preimage| (-584 *3)) (|:| |image| (-584 *3))))
(-5 *1 (-814 *3)) (-4 *3 (-1013)))))
@@ -8508,7 +8508,7 @@
((*1 *1) (-12 (-4 *1 (-407 *2 *3)) (-4 *2 (-146)) (-4 *3 (-23))))
((*1 *1) (-5 *1 (-473))) ((*1 *1) (-12 (-5 *1 (-801 *2)) (-4 *2 (-1013)))))
(((*1 *2 *1)
- (|partial| -12 (-5 *2 (-2 (|:| -2511 (-86)) (|:| |arg| (-584 (-801 *3)))))
+ (|partial| -12 (-5 *2 (-2 (|:| -2512 (-86)) (|:| |arg| (-584 (-801 *3)))))
(-5 *1 (-801 *3)) (-4 *3 (-1013))))
((*1 *2 *1 *3)
(|partial| -12 (-5 *3 (-86)) (-5 *2 (-584 (-801 *4))) (-5 *1 (-801 *4))
@@ -8565,11 +8565,11 @@
(-4 *3 (-951 (-1089))) (-4 *3 (-797 *5)) (-4 *4 (-554 (-801 *5)))))
((*1 *2 *3 *4)
(-12 (-4 *5 (-1013)) (-5 *2 (-584 (-248 (-858 *3)))) (-5 *1 (-798 *5 *3 *4))
- (-4 *3 (-962)) (-2558 (-4 *3 (-951 (-1089)))) (-4 *3 (-797 *5))
+ (-4 *3 (-962)) (-2559 (-4 *3 (-951 (-1089)))) (-4 *3 (-797 *5))
(-4 *4 (-554 (-801 *5)))))
((*1 *2 *3 *4)
(-12 (-4 *5 (-1013)) (-5 *2 (-799 *5 *3)) (-5 *1 (-798 *5 *3 *4))
- (-2558 (-4 *3 (-951 (-1089)))) (-2558 (-4 *3 (-962))) (-4 *3 (-797 *5))
+ (-2559 (-4 *3 (-951 (-1089)))) (-2559 (-4 *3 (-962))) (-4 *3 (-797 *5))
(-4 *4 (-554 (-801 *5))))))
(((*1 *2 *1 *3) (-12 (-4 *1 (-253)) (-5 *3 (-1089)) (-5 *2 (-85))))
((*1 *2 *1 *3) (-12 (-4 *1 (-253)) (-5 *3 (-86)) (-5 *2 (-85))))
@@ -8625,7 +8625,7 @@
(-4 *4 (-780 *3)))))
(((*1 *2 *2) (-12 (-5 *2 (-831)) (-5 *1 (-343 *3)) (-4 *3 (-344))))
((*1 *2) (-12 (-5 *2 (-831)) (-5 *1 (-343 *3)) (-4 *3 (-344))))
- ((*1 *2 *2) (-12 (-5 *2 (-831)) (|has| *1 (-6 -3982)) (-4 *1 (-344))))
+ ((*1 *2 *2) (-12 (-5 *2 (-831)) (|has| *1 (-6 -3983)) (-4 *1 (-344))))
((*1 *2) (-12 (-4 *1 (-344)) (-5 *2 (-831))))
((*1 *2 *1) (-12 (-4 *1 (-780 *3)) (-5 *2 (-1068 (-484))))))
(((*1 *2 *1)
@@ -8662,7 +8662,7 @@
(|partial| -12 (-5 *3 (-695)) (-4 *5 (-311)) (-5 *2 (-148 *6))
(-5 *1 (-777 *5 *4 *6)) (-4 *4 (-1171 *5)) (-4 *6 (-1154 *5)))))
(((*1 *2 *1)
- (-12 (|has| *1 (-6 -3991)) (-4 *1 (-426 *3)) (-4 *3 (-1128))
+ (-12 (|has| *1 (-6 -3992)) (-4 *1 (-426 *3)) (-4 *3 (-1128))
(-5 *2 (-584 *3))))
((*1 *2 *1) (-12 (-5 *2 (-584 *3)) (-5 *1 (-676 *3)) (-4 *3 (-1013))))
((*1 *2 *1) (-12 (-5 *2 (-584 (-378))) (-5 *1 (-775)))))
@@ -8758,35 +8758,35 @@
((*1 *2 *3 *3 *2) (-12 (-5 *3 (-695)) (-5 *1 (-766 *2)) (-4 *2 (-146)))))
(((*1 *2 *3 *2) (-12 (-5 *3 (-695)) (-5 *1 (-766 *2)) (-4 *2 (-146)))))
(((*1 *2 *1 *1)
- (-12 (-4 *3 (-311)) (-4 *3 (-962)) (-5 *2 (-2 (|:| -1971 *1) (|:| -2900 *1)))
+ (-12 (-4 *3 (-311)) (-4 *3 (-962)) (-5 *2 (-2 (|:| -1971 *1) (|:| -2901 *1)))
(-4 *1 (-762 *3))))
((*1 *2 *3 *3 *4)
(-12 (-5 *4 (-69 *5)) (-4 *5 (-311)) (-4 *5 (-962))
- (-5 *2 (-2 (|:| -1971 *3) (|:| -2900 *3))) (-5 *1 (-763 *5 *3))
+ (-5 *2 (-2 (|:| -1971 *3) (|:| -2901 *3))) (-5 *1 (-763 *5 *3))
(-4 *3 (-762 *5)))))
(((*1 *2 *3 *3)
- (-12 (-4 *4 (-311)) (-5 *2 (-2 (|:| -1971 *3) (|:| -2900 *3)))
+ (-12 (-4 *4 (-311)) (-5 *2 (-2 (|:| -1971 *3) (|:| -2901 *3)))
(-5 *1 (-691 *3 *4)) (-4 *3 (-646 *4))))
((*1 *2 *1 *1)
- (-12 (-4 *3 (-311)) (-4 *3 (-962)) (-5 *2 (-2 (|:| -1971 *1) (|:| -2900 *1)))
+ (-12 (-4 *3 (-311)) (-4 *3 (-962)) (-5 *2 (-2 (|:| -1971 *1) (|:| -2901 *1)))
(-4 *1 (-762 *3))))
((*1 *2 *3 *3 *4)
(-12 (-5 *4 (-69 *5)) (-4 *5 (-311)) (-4 *5 (-962))
- (-5 *2 (-2 (|:| -1971 *3) (|:| -2900 *3))) (-5 *1 (-763 *5 *3))
+ (-5 *2 (-2 (|:| -1971 *3) (|:| -2901 *3))) (-5 *1 (-763 *5 *3))
(-4 *3 (-762 *5)))))
(((*1 *2 *1 *1)
- (-12 (-4 *3 (-495)) (-4 *3 (-962)) (-5 *2 (-2 (|:| -1971 *1) (|:| -2900 *1)))
+ (-12 (-4 *3 (-495)) (-4 *3 (-962)) (-5 *2 (-2 (|:| -1971 *1) (|:| -2901 *1)))
(-4 *1 (-762 *3))))
((*1 *2 *3 *3 *4)
(-12 (-5 *4 (-69 *5)) (-4 *5 (-495)) (-4 *5 (-962))
- (-5 *2 (-2 (|:| -1971 *3) (|:| -2900 *3))) (-5 *1 (-763 *5 *3))
+ (-5 *2 (-2 (|:| -1971 *3) (|:| -2901 *3))) (-5 *1 (-763 *5 *3))
(-4 *3 (-762 *5)))))
(((*1 *2 *1 *1)
- (-12 (-4 *3 (-495)) (-4 *3 (-962)) (-5 *2 (-2 (|:| -1971 *1) (|:| -2900 *1)))
+ (-12 (-4 *3 (-495)) (-4 *3 (-962)) (-5 *2 (-2 (|:| -1971 *1) (|:| -2901 *1)))
(-4 *1 (-762 *3))))
((*1 *2 *3 *3 *4)
(-12 (-5 *4 (-69 *5)) (-4 *5 (-495)) (-4 *5 (-962))
- (-5 *2 (-2 (|:| -1971 *3) (|:| -2900 *3))) (-5 *1 (-763 *5 *3))
+ (-5 *2 (-2 (|:| -1971 *3) (|:| -2901 *3))) (-5 *1 (-763 *5 *3))
(-4 *3 (-762 *5)))))
(((*1 *2 *3 *4 *2)
(-12 (-5 *4 (-1 *2 *2)) (-4 *2 (-591 *5)) (-4 *5 (-962))
@@ -8811,7 +8811,7 @@
((*1 *1 *1 *1) (-12 (-4 *1 (-762 *2)) (-4 *2 (-962)) (-4 *2 (-311)))))
(((*1 *2 *1 *1)
(-12 (-4 *3 (-311)) (-4 *3 (-962))
- (-5 *2 (-2 (|:| |coef1| *1) (|:| |coef2| *1) (|:| -2407 *1)))
+ (-5 *2 (-2 (|:| |coef1| *1) (|:| |coef2| *1) (|:| -2408 *1)))
(-4 *1 (-762 *3)))))
(((*1 *1 *1 *1) (-12 (-4 *1 (-762 *2)) (-4 *2 (-962)) (-4 *2 (-311)))))
(((*1 *1 *1 *1) (-12 (-4 *1 (-762 *2)) (-4 *2 (-962)) (-4 *2 (-311)))))
@@ -8821,13 +8821,13 @@
(((*1 *1 *1 *1) (-12 (-4 *1 (-762 *2)) (-4 *2 (-962)) (-4 *2 (-311)))))
(((*1 *2 *1 *1)
(-12 (-4 *3 (-311)) (-4 *3 (-962))
- (-5 *2 (-2 (|:| |coef1| *1) (|:| |coef2| *1) (|:| -2407 *1)))
+ (-5 *2 (-2 (|:| |coef1| *1) (|:| |coef2| *1) (|:| -2408 *1)))
(-4 *1 (-762 *3)))))
(((*1 *2 *2 *2) (-12 (-4 *3 (-311)) (-5 *1 (-691 *2 *3)) (-4 *2 (-646 *3))))
((*1 *1 *1 *1) (-12 (-4 *1 (-762 *2)) (-4 *2 (-962)) (-4 *2 (-311)))))
(((*1 *1)
- (-12 (-4 *1 (-344)) (-2558 (|has| *1 (-6 -3982)))
- (-2558 (|has| *1 (-6 -3974)))))
+ (-12 (-4 *1 (-344)) (-2559 (|has| *1 (-6 -3983)))
+ (-2559 (|has| *1 (-6 -3975)))))
((*1 *2 *1) (-12 (-4 *1 (-366 *2)) (-4 *2 (-1013)) (-4 *2 (-757))))
((*1 *2 *1) (-12 (-4 *1 (-743 *2)) (-4 *2 (-757)))) ((*1 *1) (-4 *1 (-753)))
((*1 *1 *1 *1) (-4 *1 (-760))))
@@ -8917,11 +8917,11 @@
((*1 *2 *3 *4 *5)
(-12 (-5 *3 (-631 *7))
(-5 *5
- (-1 (-2 (|:| |particular| (-3 *6 "failed")) (|:| -2010 (-584 *6))) *7 *6))
+ (-1 (-2 (|:| |particular| (-3 *6 "failed")) (|:| -2011 (-584 *6))) *7 *6))
(-4 *6 (-311)) (-4 *7 (-601 *6))
(-5 *2
(-2 (|:| |particular| (-3 (-1178 *6) "failed"))
- (|:| -2010 (-584 (-1178 *6)))))
+ (|:| -2011 (-584 (-1178 *6)))))
(-5 *1 (-734 *6 *7)) (-5 *4 (-1178 *6)))))
(((*1 *2 *3 *4)
(-12 (-4 *5 (-311))
@@ -8929,7 +8929,7 @@
(-2 (|:| A (-631 *5))
(|:| |eqs|
(-584
- (-2 (|:| C (-631 *5)) (|:| |g| (-1178 *5)) (|:| -3263 *6)
+ (-2 (|:| C (-631 *5)) (|:| |g| (-1178 *5)) (|:| -3264 *6)
(|:| |rh| *5))))))
(-5 *1 (-734 *5 *6)) (-5 *3 (-631 *5)) (-5 *4 (-1178 *5))
(-4 *6 (-601 *5))))
@@ -8974,23 +8974,23 @@
(((*1 *2 *3 *4)
(-12 (-5 *4 (-1 (-584 *5) *6))
(-4 *5 (-13 (-311) (-120) (-951 (-347 (-484))))) (-4 *6 (-1154 *5))
- (-5 *2 (-584 (-2 (|:| |poly| *6) (|:| -3263 *3))))
+ (-5 *2 (-584 (-2 (|:| |poly| *6) (|:| -3264 *3))))
(-5 *1 (-730 *5 *6 *3 *7)) (-4 *3 (-601 *6)) (-4 *7 (-601 (-347 *6)))))
((*1 *2 *3 *4)
(-12 (-5 *4 (-1 (-584 *5) *6))
(-4 *5 (-13 (-311) (-120) (-951 (-484)) (-951 (-347 (-484)))))
(-4 *6 (-1154 *5))
- (-5 *2 (-584 (-2 (|:| |poly| *6) (|:| -3263 (-599 *6 (-347 *6))))))
+ (-5 *2 (-584 (-2 (|:| |poly| *6) (|:| -3264 (-599 *6 (-347 *6))))))
(-5 *1 (-733 *5 *6)) (-5 *3 (-599 *6 (-347 *6))))))
(((*1 *2 *3 *4 *5)
(-12 (-5 *4 (-1 (-584 *7) *7 (-1084 *7))) (-5 *5 (-1 (-345 *7) *7))
(-4 *7 (-1154 *6)) (-4 *6 (-13 (-311) (-120) (-951 (-347 (-484)))))
- (-5 *2 (-584 (-2 (|:| |frac| (-347 *7)) (|:| -3263 *3))))
+ (-5 *2 (-584 (-2 (|:| |frac| (-347 *7)) (|:| -3264 *3))))
(-5 *1 (-730 *6 *7 *3 *8)) (-4 *3 (-601 *7)) (-4 *8 (-601 (-347 *7)))))
((*1 *2 *3 *4)
(-12 (-5 *4 (-1 (-345 *6) *6)) (-4 *6 (-1154 *5))
(-4 *5 (-13 (-311) (-120) (-951 (-484)) (-951 (-347 (-484)))))
- (-5 *2 (-584 (-2 (|:| |frac| (-347 *6)) (|:| -3263 (-599 *6 (-347 *6))))))
+ (-5 *2 (-584 (-2 (|:| |frac| (-347 *6)) (|:| -3264 (-599 *6 (-347 *6))))))
(-5 *1 (-733 *5 *6)) (-5 *3 (-599 *6 (-347 *6))))))
(((*1 *2 *3 *4)
(-12 (-4 *5 (-311)) (-4 *7 (-1154 *5)) (-4 *4 (-662 *5 *7))
@@ -9005,22 +9005,22 @@
(((*1 *2 *3 *4)
(-12 (-5 *3 (-598 (-347 *6))) (-5 *4 (-347 *6)) (-4 *6 (-1154 *5))
(-4 *5 (-13 (-311) (-120) (-951 (-484)) (-951 (-347 (-484)))))
- (-5 *2 (-2 (|:| |particular| (-3 *4 #1="failed")) (|:| -2010 (-584 *4))))
+ (-5 *2 (-2 (|:| |particular| (-3 *4 #1="failed")) (|:| -2011 (-584 *4))))
(-5 *1 (-731 *5 *6))))
((*1 *2 *3 *4)
(-12 (-5 *3 (-598 (-347 *6))) (-4 *6 (-1154 *5))
(-4 *5 (-13 (-311) (-120) (-951 (-484)) (-951 (-347 (-484)))))
- (-5 *2 (-2 (|:| -2010 (-584 (-347 *6))) (|:| |mat| (-631 *5))))
+ (-5 *2 (-2 (|:| -2011 (-584 (-347 *6))) (|:| |mat| (-631 *5))))
(-5 *1 (-731 *5 *6)) (-5 *4 (-584 (-347 *6)))))
((*1 *2 *3 *4)
(-12 (-5 *3 (-599 *6 (-347 *6))) (-5 *4 (-347 *6)) (-4 *6 (-1154 *5))
(-4 *5 (-13 (-311) (-120) (-951 (-484)) (-951 (-347 (-484)))))
- (-5 *2 (-2 (|:| |particular| (-3 *4 #1#)) (|:| -2010 (-584 *4))))
+ (-5 *2 (-2 (|:| |particular| (-3 *4 #1#)) (|:| -2011 (-584 *4))))
(-5 *1 (-731 *5 *6))))
((*1 *2 *3 *4)
(-12 (-5 *3 (-599 *6 (-347 *6))) (-4 *6 (-1154 *5))
(-4 *5 (-13 (-311) (-120) (-951 (-484)) (-951 (-347 (-484)))))
- (-5 *2 (-2 (|:| -2010 (-584 (-347 *6))) (|:| |mat| (-631 *5))))
+ (-5 *2 (-2 (|:| -2011 (-584 (-347 *6))) (|:| |mat| (-631 *5))))
(-5 *1 (-731 *5 *6)) (-5 *4 (-584 (-347 *6))))))
(((*1 *2 *2 *3)
(-12 (-4 *4 (-13 (-311) (-120) (-951 (-347 (-484))))) (-4 *3 (-1154 *4))
@@ -9032,11 +9032,11 @@
(((*1 *2 *3 *4)
(-12 (-5 *4 (-1 (-584 *5) *6))
(-4 *5 (-13 (-311) (-120) (-951 (-347 (-484))))) (-4 *6 (-1154 *5))
- (-5 *2 (-584 (-2 (|:| -3948 *5) (|:| -3263 *3)))) (-5 *1 (-730 *5 *6 *3 *7))
+ (-5 *2 (-584 (-2 (|:| -3949 *5) (|:| -3264 *3)))) (-5 *1 (-730 *5 *6 *3 *7))
(-4 *3 (-601 *6)) (-4 *7 (-601 (-347 *6))))))
(((*1 *2 *3)
(-12 (-4 *4 (-13 (-311) (-120) (-951 (-347 (-484))))) (-4 *5 (-1154 *4))
- (-5 *2 (-584 (-2 (|:| |deg| (-695)) (|:| -3263 *5))))
+ (-5 *2 (-584 (-2 (|:| |deg| (-695)) (|:| -3264 *5))))
(-5 *1 (-730 *4 *5 *3 *6)) (-4 *3 (-601 *5)) (-4 *6 (-601 (-347 *5))))))
(((*1 *2 *3)
(-12 (-4 *2 (-1154 *4)) (-5 *1 (-730 *4 *2 *3 *5))
@@ -9052,19 +9052,19 @@
(-4 *3 (-601 (-347 *2))))))
(((*1 *2 *3)
(-12 (-4 *4 (-13 (-311) (-120) (-951 (-347 (-484))))) (-4 *5 (-1154 *4))
- (-5 *2 (-584 (-2 (|:| -3769 *5) (|:| -3223 *5)))) (-5 *1 (-729 *4 *5 *3 *6))
+ (-5 *2 (-584 (-2 (|:| -3770 *5) (|:| -3224 *5)))) (-5 *1 (-729 *4 *5 *3 *6))
(-4 *3 (-601 *5)) (-4 *6 (-601 (-347 *5)))))
((*1 *2 *3 *4)
(-12 (-4 *5 (-13 (-311) (-120) (-951 (-347 (-484))))) (-4 *4 (-1154 *5))
- (-5 *2 (-584 (-2 (|:| -3769 *4) (|:| -3223 *4)))) (-5 *1 (-729 *5 *4 *3 *6))
+ (-5 *2 (-584 (-2 (|:| -3770 *4) (|:| -3224 *4)))) (-5 *1 (-729 *5 *4 *3 *6))
(-4 *3 (-601 *4)) (-4 *6 (-601 (-347 *4)))))
((*1 *2 *3)
(-12 (-4 *4 (-13 (-311) (-120) (-951 (-347 (-484))))) (-4 *5 (-1154 *4))
- (-5 *2 (-584 (-2 (|:| -3769 *5) (|:| -3223 *5)))) (-5 *1 (-729 *4 *5 *6 *3))
+ (-5 *2 (-584 (-2 (|:| -3770 *5) (|:| -3224 *5)))) (-5 *1 (-729 *4 *5 *6 *3))
(-4 *6 (-601 *5)) (-4 *3 (-601 (-347 *5)))))
((*1 *2 *3 *4)
(-12 (-4 *5 (-13 (-311) (-120) (-951 (-347 (-484))))) (-4 *4 (-1154 *5))
- (-5 *2 (-584 (-2 (|:| -3769 *4) (|:| -3223 *4)))) (-5 *1 (-729 *5 *4 *6 *3))
+ (-5 *2 (-584 (-2 (|:| -3770 *4) (|:| -3224 *4)))) (-5 *1 (-729 *5 *4 *6 *3))
(-4 *6 (-601 *4)) (-4 *3 (-601 (-347 *4))))))
(((*1 *2 *3 *4)
(|partial| -12 (-5 *4 (-347 *2)) (-4 *2 (-1154 *5))
@@ -9078,7 +9078,7 @@
(-12 (-5 *3 (-598 *4)) (-4 *4 (-290 *5 *6 *7))
(-4 *5 (-13 (-311) (-120) (-951 (-484)) (-951 (-347 (-484)))))
(-4 *6 (-1154 *5)) (-4 *7 (-1154 (-347 *6)))
- (-5 *2 (-2 (|:| |particular| (-3 *4 "failed")) (|:| -2010 (-584 *4))))
+ (-5 *2 (-2 (|:| |particular| (-3 *4 "failed")) (|:| -2011 (-584 *4))))
(-5 *1 (-728 *5 *6 *7 *4)))))
(((*1 *2 *3)
(-12 (-5 *3 (-1089)) (-4 *4 (-13 (-257) (-951 (-484)) (-581 (-484)) (-120)))
@@ -9090,7 +9090,7 @@
(((*1 *2 *3 *4 *5)
(-12 (-5 *5 (-1089)) (-4 *6 (-13 (-257) (-951 (-484)) (-581 (-484)) (-120)))
(-4 *4 (-13 (-29 *6) (-1114) (-872)))
- (-5 *2 (-2 (|:| |particular| *4) (|:| -2010 (-584 *4))))
+ (-5 *2 (-2 (|:| |particular| *4) (|:| -2011 (-584 *4))))
(-5 *1 (-725 *6 *4 *3)) (-4 *3 (-601 *4)))))
(((*1 *1 *2 *2 *2 *2 *2 *2 *2 *2) (-12 (-4 *1 (-721 *2)) (-4 *2 (-146))))
((*1 *1 *2 *2) (-12 (-5 *2 (-910 *3)) (-4 *3 (-146)) (-5 *1 (-723 *3)))))
@@ -9118,55 +9118,55 @@
(((*1 *2 *3 *4 *4 *4 *4 *5 *5)
(-12 (-5 *3 (-1 (-327) (-327))) (-5 *4 (-327))
(-5 *2
- (-2 (|:| -3398 *4) (|:| -1594 *4) (|:| |totalpts| (-484))
+ (-2 (|:| -3399 *4) (|:| -1594 *4) (|:| |totalpts| (-484))
(|:| |success| (-85))))
(-5 *1 (-712)) (-5 *5 (-484)))))
(((*1 *2 *3 *4 *4 *4 *4 *5 *5)
(-12 (-5 *3 (-1 (-327) (-327))) (-5 *4 (-327))
(-5 *2
- (-2 (|:| -3398 *4) (|:| -1594 *4) (|:| |totalpts| (-484))
+ (-2 (|:| -3399 *4) (|:| -1594 *4) (|:| |totalpts| (-484))
(|:| |success| (-85))))
(-5 *1 (-712)) (-5 *5 (-484)))))
(((*1 *2 *3 *4 *4 *4 *4 *5 *5)
(-12 (-5 *3 (-1 (-327) (-327))) (-5 *4 (-327))
(-5 *2
- (-2 (|:| -3398 *4) (|:| -1594 *4) (|:| |totalpts| (-484))
+ (-2 (|:| -3399 *4) (|:| -1594 *4) (|:| |totalpts| (-484))
(|:| |success| (-85))))
(-5 *1 (-712)) (-5 *5 (-484)))))
(((*1 *2 *3 *4 *4 *4 *4 *5 *5)
(-12 (-5 *3 (-1 (-327) (-327))) (-5 *4 (-327))
(-5 *2
- (-2 (|:| -3398 *4) (|:| -1594 *4) (|:| |totalpts| (-484))
+ (-2 (|:| -3399 *4) (|:| -1594 *4) (|:| |totalpts| (-484))
(|:| |success| (-85))))
(-5 *1 (-712)) (-5 *5 (-484)))))
(((*1 *2 *3 *4 *4 *4 *4 *5 *5)
(-12 (-5 *3 (-1 (-327) (-327))) (-5 *4 (-327))
(-5 *2
- (-2 (|:| -3398 *4) (|:| -1594 *4) (|:| |totalpts| (-484))
+ (-2 (|:| -3399 *4) (|:| -1594 *4) (|:| |totalpts| (-484))
(|:| |success| (-85))))
(-5 *1 (-712)) (-5 *5 (-484)))))
(((*1 *2 *3 *4 *4 *4 *4 *5 *5)
(-12 (-5 *3 (-1 (-327) (-327))) (-5 *4 (-327))
(-5 *2
- (-2 (|:| -3398 *4) (|:| -1594 *4) (|:| |totalpts| (-484))
+ (-2 (|:| -3399 *4) (|:| -1594 *4) (|:| |totalpts| (-484))
(|:| |success| (-85))))
(-5 *1 (-712)) (-5 *5 (-484)))))
(((*1 *2 *3 *4 *4 *4 *4 *5 *5 *5)
(-12 (-5 *3 (-1 (-327) (-327))) (-5 *4 (-327))
(-5 *2
- (-2 (|:| -3398 *4) (|:| -1594 *4) (|:| |totalpts| (-484))
+ (-2 (|:| -3399 *4) (|:| -1594 *4) (|:| |totalpts| (-484))
(|:| |success| (-85))))
(-5 *1 (-712)) (-5 *5 (-484)))))
(((*1 *2 *3 *4 *4 *4 *4 *5 *5 *5)
(-12 (-5 *3 (-1 (-327) (-327))) (-5 *4 (-327))
(-5 *2
- (-2 (|:| -3398 *4) (|:| -1594 *4) (|:| |totalpts| (-484))
+ (-2 (|:| -3399 *4) (|:| -1594 *4) (|:| |totalpts| (-484))
(|:| |success| (-85))))
(-5 *1 (-712)) (-5 *5 (-484)))))
(((*1 *2 *3 *4 *4 *4 *4 *5 *5 *5)
(-12 (-5 *3 (-1 (-327) (-327))) (-5 *4 (-327))
(-5 *2
- (-2 (|:| -3398 *4) (|:| -1594 *4) (|:| |totalpts| (-484))
+ (-2 (|:| -3399 *4) (|:| -1594 *4) (|:| |totalpts| (-484))
(|:| |success| (-85))))
(-5 *1 (-712)) (-5 *5 (-484)))))
(((*1 *2 *3 *4 *5 *5 *4 *6)
@@ -9333,13 +9333,13 @@
(-4 *3 (-962)))))
(((*1 *2 *1 *1)
(-12
- (-5 *2 (-2 (|:| -3752 *3) (|:| |coef1| (-705 *3)) (|:| |coef2| (-705 *3))))
+ (-5 *2 (-2 (|:| -3753 *3) (|:| |coef1| (-705 *3)) (|:| |coef2| (-705 *3))))
(-5 *1 (-705 *3)) (-4 *3 (-495)) (-4 *3 (-962)))))
(((*1 *2 *1 *1)
- (-12 (-5 *2 (-2 (|:| -3752 *3) (|:| |coef1| (-705 *3)))) (-5 *1 (-705 *3))
+ (-12 (-5 *2 (-2 (|:| -3753 *3) (|:| |coef1| (-705 *3)))) (-5 *1 (-705 *3))
(-4 *3 (-495)) (-4 *3 (-962)))))
(((*1 *2 *1 *1)
- (-12 (-5 *2 (-2 (|:| -3752 *3) (|:| |coef2| (-705 *3)))) (-5 *1 (-705 *3))
+ (-12 (-5 *2 (-2 (|:| -3753 *3) (|:| |coef2| (-705 *3)))) (-5 *1 (-705 *3))
(-4 *3 (-495)) (-4 *3 (-962)))))
(((*1 *2 *3 *4)
(-12 (-5 *3 (-631 (-347 (-484))))
@@ -9383,7 +9383,7 @@
(-4 *10 (-862 *9 *7 *8))
(-5 *2
(-2 (|:| |deter| (-584 (-1084 *10)))
- (|:| |dterm| (-584 (-584 (-2 (|:| -3076 (-695)) (|:| |pcoef| *10)))))
+ (|:| |dterm| (-584 (-584 (-2 (|:| -3077 (-695)) (|:| |pcoef| *10)))))
(|:| |nfacts| (-584 *6)) (|:| |nlead| (-584 *10))))
(-5 *1 (-702 *6 *7 *8 *9 *10)) (-5 *3 (-1084 *10)) (-5 *4 (-584 *6))
(-5 *5 (-584 *10)))))
@@ -9451,7 +9451,7 @@
(-4 *7 (-757)) (-4 *8 (-257)) (-4 *9 (-862 *8 *6 *7)) (-4 *6 (-718))
(-5 *2
(-2 (|:| |upol| (-1084 *8)) (|:| |Lval| (-584 *8))
- (|:| |Lfact| (-584 (-2 (|:| -3728 (-1084 *8)) (|:| -2399 (-484)))))
+ (|:| |Lfact| (-584 (-2 (|:| -3729 (-1084 *8)) (|:| -2400 (-484)))))
(|:| |ctpol| *8)))
(-5 *1 (-682 *6 *7 *8 *9)))))
(((*1 *2 *3 *4 *5)
@@ -9459,18 +9459,18 @@
(-4 *6 (-718)) (-4 *9 (-862 *8 *6 *7))
(-5 *2
(-2 (|:| |unitPart| *9)
- (|:| |suPart| (-584 (-2 (|:| -3728 (-1084 *9)) (|:| -2399 (-484)))))))
+ (|:| |suPart| (-584 (-2 (|:| -3729 (-1084 *9)) (|:| -2400 (-484)))))))
(-5 *1 (-682 *6 *7 *8 *9)) (-5 *3 (-1084 *9)))))
(((*1 *2 *3 *4 *5)
(-12 (-5 *5 (-484)) (-4 *6 (-718)) (-4 *7 (-757)) (-4 *8 (-257))
(-4 *9 (-862 *8 *6 *7))
- (-5 *2 (-2 (|:| -2002 (-1084 *9)) (|:| |polval| (-1084 *8))))
+ (-5 *2 (-2 (|:| -2003 (-1084 *9)) (|:| |polval| (-1084 *8))))
(-5 *1 (-682 *6 *7 *8 *9)) (-5 *3 (-1084 *9)) (-5 *4 (-1084 *8)))))
(((*1 *2 *3 *4)
(-12 (-4 *5 (-718)) (-4 *4 (-757)) (-4 *6 (-257)) (-5 *2 (-345 *3))
(-5 *1 (-682 *5 *4 *6 *3)) (-4 *3 (-862 *6 *5 *4)))))
(((*1 *2 *3)
- (-12 (-5 *3 (-584 (-2 (|:| -3728 (-1084 *6)) (|:| -2399 (-484)))))
+ (-12 (-5 *3 (-584 (-2 (|:| -3729 (-1084 *6)) (|:| -2400 (-484)))))
(-4 *6 (-257)) (-4 *4 (-718)) (-4 *5 (-757)) (-5 *2 (-484))
(-5 *1 (-682 *4 *5 *6 *7)) (-4 *7 (-862 *6 *4 *5)))))
(((*1 *2 *3)
@@ -9490,18 +9490,18 @@
(((*1 *2 *3 *4)
(-12 (-4 *6 (-495)) (-4 *2 (-862 *3 *5 *4)) (-5 *1 (-672 *5 *4 *6 *2))
(-5 *3 (-347 (-858 *6))) (-4 *5 (-718))
- (-4 *4 (-13 (-757) (-10 -8 (-15 -3968 ((-1089) $))))))))
+ (-4 *4 (-13 (-757) (-10 -8 (-15 -3969 ((-1089) $))))))))
(((*1 *2 *3 *4)
(-12 (-5 *3 (-1084 (-858 *6))) (-4 *6 (-495))
(-4 *2 (-862 (-347 (-858 *6)) *5 *4)) (-5 *1 (-672 *5 *4 *6 *2))
- (-4 *5 (-718)) (-4 *4 (-13 (-757) (-10 -8 (-15 -3968 ((-1089) $))))))))
+ (-4 *5 (-718)) (-4 *4 (-13 (-757) (-10 -8 (-15 -3969 ((-1089) $))))))))
(((*1 *2 *3 *4)
(-12 (-5 *3 (-1084 *2)) (-4 *2 (-862 (-347 (-858 *6)) *5 *4))
(-5 *1 (-672 *5 *4 *6 *2)) (-4 *5 (-718))
- (-4 *4 (-13 (-757) (-10 -8 (-15 -3968 ((-1089) $))))) (-4 *6 (-495)))))
+ (-4 *4 (-13 (-757) (-10 -8 (-15 -3969 ((-1089) $))))) (-4 *6 (-495)))))
(((*1 *2 *3)
- (-12 (-4 *4 (-718)) (-4 *5 (-13 (-757) (-10 -8 (-15 -3968 ((-1089) $)))))
- (-4 *6 (-495)) (-5 *2 (-2 (|:| -2481 (-858 *6)) (|:| -2056 (-858 *6))))
+ (-12 (-4 *4 (-718)) (-4 *5 (-13 (-757) (-10 -8 (-15 -3969 ((-1089) $)))))
+ (-4 *6 (-495)) (-5 *2 (-2 (|:| -2482 (-858 *6)) (|:| -2057 (-858 *6))))
(-5 *1 (-672 *4 *5 *6 *3)) (-4 *3 (-862 (-347 (-858 *6)) *4 *5)))))
(((*1 *2 *3 *4)
(-12 (-5 *3 (-584 *8)) (-5 *4 (-108 *5 *6 *7)) (-14 *5 (-484))
@@ -9516,7 +9516,7 @@
(-5 *1 (-667 *5 *2)) (-4 *5 (-311)))))
(((*1 *2 *3 *4)
(-12 (-5 *4 (-1 *3 *3)) (-4 *3 (-1154 *5)) (-4 *5 (-311))
- (-5 *2 (-2 (|:| -3087 (-345 *3)) (|:| |special| (-345 *3))))
+ (-5 *2 (-2 (|:| -3088 (-345 *3)) (|:| |special| (-345 *3))))
(-5 *1 (-667 *5 *3)))))
(((*1 *2 *1) (-12 (-4 *1 (-666 *2)) (-4 *2 (-72)))))
(((*1 *1 *2 *3) (-12 (-5 *2 (-1 *3 *3 *3)) (-4 *3 (-72)) (-5 *1 (-665 *3)))))
@@ -9573,8 +9573,8 @@
((*1 *2 *1)
(-12 (-4 *2 (-1013)) (-5 *1 (-651 *3 *2 *4)) (-4 *3 (-757))
(-14 *4
- (-1 (-85) (-2 (|:| -2398 *3) (|:| -2399 *2))
- (-2 (|:| -2398 *3) (|:| -2399 *2)))))))
+ (-1 (-85) (-2 (|:| -2399 *3) (|:| -2400 *2))
+ (-2 (|:| -2399 *3) (|:| -2400 *2)))))))
(((*1 *1 *2) (-12 (-5 *2 (-831)) (-4 *1 (-317))))
((*1 *2 *1) (-12 (-4 *2 (-760)) (-5 *1 (-451 *3 *2)) (-4 *3 (-72))))
((*1 *2 *3 *3)
@@ -9582,8 +9582,8 @@
((*1 *2 *1)
(-12 (-4 *2 (-757)) (-5 *1 (-651 *2 *3 *4)) (-4 *3 (-1013))
(-14 *4
- (-1 (-85) (-2 (|:| -2398 *2) (|:| -2399 *3))
- (-2 (|:| -2398 *2) (|:| -2399 *3)))))))
+ (-1 (-85) (-2 (|:| -2399 *2) (|:| -2400 *3))
+ (-2 (|:| -2399 *2) (|:| -2400 *3)))))))
(((*1 *2 *2) (-12 (-4 *3 (-962)) (-5 *1 (-650 *3 *2)) (-4 *2 (-1154 *3)))))
(((*1 *2 *1)
(-12 (-4 *3 (-962)) (-5 *2 (-1178 *3)) (-5 *1 (-650 *3 *4))
@@ -9608,7 +9608,7 @@
(((*1 *2 *3 *4 *2 *5 *6 *7 *8 *9 *10)
(|partial| -12 (-5 *2 (-584 (-1084 *13))) (-5 *3 (-1084 *13))
(-5 *4 (-584 *12)) (-5 *5 (-584 *10)) (-5 *6 (-584 *13))
- (-5 *7 (-584 (-584 (-2 (|:| -3076 (-695)) (|:| |pcoef| *13)))))
+ (-5 *7 (-584 (-584 (-2 (|:| -3077 (-695)) (|:| |pcoef| *13)))))
(-5 *8 (-584 (-695))) (-5 *9 (-1178 (-584 (-1084 *10)))) (-4 *12 (-757))
(-4 *10 (-257)) (-4 *13 (-862 *10 *11 *12)) (-4 *11 (-718))
(-5 *1 (-645 *11 *12 *10 *13)))))
@@ -9654,10 +9654,10 @@
(-4 *4 (-554 (-473))) (-4 *5 (-1128)) (-4 *6 (-1128)) (-4 *7 (-1128)))))
(((*1 *2 *3 *3)
(-12 (-4 *3 (-257)) (-4 *3 (-146)) (-4 *4 (-321 *3)) (-4 *5 (-321 *3))
- (-5 *2 (-2 (|:| -1971 *3) (|:| -2900 *3))) (-5 *1 (-630 *3 *4 *5 *6))
+ (-5 *2 (-2 (|:| -1971 *3) (|:| -2901 *3))) (-5 *1 (-630 *3 *4 *5 *6))
(-4 *6 (-628 *3 *4 *5))))
((*1 *2 *3 *3)
- (-12 (-5 *2 (-2 (|:| -1971 *3) (|:| -2900 *3))) (-5 *1 (-639 *3))
+ (-12 (-5 *2 (-2 (|:| -1971 *3) (|:| -2901 *3))) (-5 *1 (-639 *3))
(-4 *3 (-257)))))
(((*1 *2 *2 *3 *3) (-12 (-5 *2 (-631 *3)) (-4 *3 (-257)) (-5 *1 (-639 *3)))))
(((*1 *2 *2 *3) (-12 (-5 *2 (-631 *3)) (-4 *3 (-257)) (-5 *1 (-639 *3)))))
@@ -9690,13 +9690,13 @@
((*1 *2 *2 *3 *2 *3)
(-12 (-5 *3 (-484)) (-5 *1 (-636 *2)) (-4 *2 (-1154 *3)))))
(((*1 *2 *3)
- (-12 (-5 *3 (-584 (-2 (|:| |deg| (-695)) (|:| -2573 *5)))) (-4 *5 (-1154 *4))
+ (-12 (-5 *3 (-584 (-2 (|:| |deg| (-695)) (|:| -2574 *5)))) (-4 *5 (-1154 *4))
(-4 *4 (-298)) (-5 *2 (-584 *5)) (-5 *1 (-170 *4 *5))))
((*1 *2 *3 *4)
- (-12 (-5 *3 (-584 (-2 (|:| -3728 *5) (|:| -3944 (-484))))) (-5 *4 (-484))
+ (-12 (-5 *3 (-584 (-2 (|:| -3729 *5) (|:| -3945 (-484))))) (-5 *4 (-484))
(-4 *5 (-1154 *4)) (-5 *2 (-584 *5)) (-5 *1 (-636 *5)))))
(((*1 *2 *3 *4)
- (-12 (-5 *4 (-484)) (-5 *2 (-584 (-2 (|:| -3728 *3) (|:| -3944 *4))))
+ (-12 (-5 *4 (-484)) (-5 *2 (-584 (-2 (|:| -3729 *3) (|:| -3945 *4))))
(-5 *1 (-636 *3)) (-4 *3 (-1154 *4)))))
(((*1 *2 *2 *3) (-12 (-5 *3 (-484)) (-5 *1 (-636 *2)) (-4 *2 (-1154 *3)))))
(((*1 *1 *1) (-12 (-4 *1 (-237 *2)) (-4 *2 (-1128)) (-4 *2 (-1013))))
@@ -9816,11 +9816,11 @@
(-4 *8 (-862 *5 *6 *7)) (-4 *5 (-495)) (-4 *6 (-718))
(-5 *2
(-2 (|:| |particular| (-3 (-1178 (-347 *8)) "failed"))
- (|:| -2010 (-584 (-1178 (-347 *8))))))
+ (|:| -2011 (-584 (-1178 (-347 *8))))))
(-5 *1 (-612 *5 *6 *7 *8)))))
(((*1 *2 *3 *4)
- (-12 (-4 *5 (-311)) (-4 *6 (-13 (-321 *5) (-10 -7 (-6 -3992))))
- (-4 *4 (-13 (-321 *5) (-10 -7 (-6 -3992)))) (-5 *2 (-85))
+ (-12 (-4 *5 (-311)) (-4 *6 (-13 (-321 *5) (-10 -7 (-6 -3993))))
+ (-4 *4 (-13 (-321 *5) (-10 -7 (-6 -3993)))) (-5 *2 (-85))
(-5 *1 (-610 *5 *6 *4 *3)) (-4 *3 (-628 *5 *6 *4))))
((*1 *2 *3 *4)
(-12 (-5 *3 (-631 *5)) (-5 *4 (-1178 *5)) (-4 *5 (-311)) (-5 *2 (-85))
@@ -9855,12 +9855,12 @@
(((*1 *1 *1 *1 *2) (-12 (-5 *2 (-484)) (-4 *1 (-594 *3)) (-4 *3 (-1128))))
((*1 *1 *2 *1 *3) (-12 (-5 *3 (-484)) (-4 *1 (-594 *2)) (-4 *2 (-1128)))))
(((*1 *2 *1)
- (-12 (-5 *2 (-584 (-2 (|:| |gen| *3) (|:| -3939 *4))))
+ (-12 (-5 *2 (-584 (-2 (|:| |gen| *3) (|:| -3940 *4))))
(-5 *1 (-592 *3 *4 *5)) (-4 *3 (-1013)) (-4 *4 (-23)) (-14 *5 *4))))
(((*1 *1 *2 *3)
(-12 (-5 *1 (-592 *2 *3 *4)) (-4 *2 (-1013)) (-4 *3 (-23)) (-14 *4 *3))))
(((*1 *1 *2)
- (-12 (-5 *2 (-584 (-2 (|:| |gen| *3) (|:| -3939 *4)))) (-4 *3 (-1013))
+ (-12 (-5 *2 (-584 (-2 (|:| |gen| *3) (|:| -3940 *4)))) (-4 *3 (-1013))
(-4 *4 (-23)) (-14 *5 *4) (-5 *1 (-592 *3 *4 *5)))))
(((*1 *2 *1 *2) (-12 (-5 *2 (-484)) (-5 *1 (-309 *3)) (-4 *3 (-1013))))
((*1 *2 *1 *3)
@@ -9881,7 +9881,7 @@
((*1 *1 *1)
(-12 (-5 *1 (-592 *2 *3 *4)) (-4 *2 (-1013)) (-4 *3 (-23)) (-14 *4 *3))))
(((*1 *1 *1) (-12 (-4 *1 (-214 *2)) (-4 *2 (-1128))))
- ((*1 *1 *1) (-12 (|has| *1 (-6 -3992)) (-4 *1 (-321 *2)) (-4 *2 (-1128))))
+ ((*1 *1 *1) (-12 (|has| *1 (-6 -3993)) (-4 *1 (-321 *2)) (-4 *2 (-1128))))
((*1 *1 *1)
(-12 (-5 *1 (-592 *2 *3 *4)) (-4 *2 (-1013)) (-4 *3 (-23)) (-14 *4 *3))))
(((*1 *1)
@@ -9940,7 +9940,7 @@
(-4 *5 (-311)) (-4 *5 (-495)) (-5 *2 (-1178 *5)) (-5 *1 (-579 *5 *4))))
((*1 *2 *3 *4)
(|partial| -12 (-5 *3 (-1178 *4)) (-4 *4 (-13 (-962) (-581 *5)))
- (-2558 (-4 *5 (-311))) (-4 *5 (-495)) (-5 *2 (-1178 (-347 *5)))
+ (-2559 (-4 *5 (-311))) (-4 *5 (-495)) (-5 *2 (-1178 (-347 *5)))
(-5 *1 (-579 *5 *4)))))
(((*1 *2 *3)
(|partial| -12 (-5 *3 (-1178 *5)) (-4 *5 (-13 (-962) (-581 *4)))
@@ -10132,7 +10132,7 @@
(|partial| -12
(-5 *5
(-2 (|:| |contp| *3)
- (|:| -1777 (-584 (-2 (|:| |irr| *10) (|:| -2393 (-484)))))))
+ (|:| -1777 (-584 (-2 (|:| |irr| *10) (|:| -2394 (-484)))))))
(-5 *6 (-584 *3)) (-5 *7 (-584 *8)) (-4 *8 (-757)) (-4 *3 (-257))
(-4 *10 (-862 *3 *9 *8)) (-4 *9 (-718))
(-5 *2
@@ -10214,7 +10214,7 @@
(((*1 *2 *1)
(-12 (-4 *1 (-539 *3 *4)) (-4 *3 (-1013)) (-4 *4 (-1128)) (-5 *2 (-584 *3)))))
(((*1 *2 *3 *1)
- (-12 (|has| *1 (-6 -3991)) (-4 *1 (-539 *4 *3)) (-4 *4 (-1013))
+ (-12 (|has| *1 (-6 -3992)) (-4 *1 (-539 *4 *3)) (-4 *4 (-1013))
(-4 *3 (-1128)) (-4 *3 (-1013)) (-5 *2 (-85)))))
(((*1 *2 *1)
(-12 (-4 *1 (-539 *2 *3)) (-4 *3 (-1128)) (-4 *2 (-1013)) (-4 *2 (-757)))))
@@ -10224,10 +10224,10 @@
(-12 (-4 *1 (-57 *2 *3 *4)) (-4 *2 (-1128)) (-4 *3 (-321 *2))
(-4 *4 (-321 *2))))
((*1 *1 *1 *2)
- (-12 (|has| *1 (-6 -3992)) (-4 *1 (-539 *3 *2)) (-4 *3 (-1013))
+ (-12 (|has| *1 (-6 -3993)) (-4 *1 (-539 *3 *2)) (-4 *3 (-1013))
(-4 *2 (-1128)))))
(((*1 *2 *1 *3 *3)
- (-12 (|has| *1 (-6 -3992)) (-4 *1 (-539 *3 *4)) (-4 *3 (-1013))
+ (-12 (|has| *1 (-6 -3993)) (-4 *1 (-539 *3 *4)) (-4 *3 (-1013))
(-4 *4 (-1128)) (-5 *2 (-1184)))))
(((*1 *2 *2 *3 *4)
(-12 (-5 *3 (-584 (-551 *2))) (-5 *4 (-584 (-1089)))
@@ -10361,7 +10361,7 @@
(((*1 *2 *2 *3)
(|partial| -12 (-5 *3 (-695)) (-5 *1 (-523 *2)) (-4 *2 (-483))))
((*1 *2 *3)
- (-12 (-5 *2 (-2 (|:| -2692 *3) (|:| -2399 (-695)))) (-5 *1 (-523 *3))
+ (-12 (-5 *2 (-2 (|:| -2693 *3) (|:| -2400 (-695)))) (-5 *1 (-523 *3))
(-4 *3 (-483)))))
(((*1 *2 *3 *4)
(-12 (-5 *4 (-695)) (-5 *2 (-85)) (-5 *1 (-523 *3)) (-4 *3 (-483)))))
@@ -10414,11 +10414,11 @@
(-5 *1 (-510 *5 *6)) (-5 *3 (-347 *6)))))
(((*1 *2 *2 *3)
(|partial| -12 (-5 *2 (-563 *4 *5))
- (-5 *3 (-1 (-2 (|:| |ans| *4) (|:| -3134 *4) (|:| |sol?| (-85))) (-484) *4))
+ (-5 *3 (-1 (-2 (|:| |ans| *4) (|:| -3135 *4) (|:| |sol?| (-85))) (-484) *4))
(-4 *4 (-311)) (-4 *5 (-1154 *4)) (-5 *1 (-510 *4 *5)))))
(((*1 *2 *2 *3 *4)
(|partial| -12
- (-5 *3 (-1 (-3 (-2 (|:| -2134 *4) (|:| |coeff| *4)) "failed") *4))
+ (-5 *3 (-1 (-3 (-2 (|:| -2135 *4) (|:| |coeff| *4)) "failed") *4))
(-4 *4 (-311)) (-5 *1 (-510 *4 *2)) (-4 *2 (-1154 *4)))))
(((*1 *2 *3 *4 *5)
(|partial| -12 (-5 *4 (-1 *7 *7)) (-5 *5 (-584 (-347 *7))) (-4 *7 (-1154 *6))
@@ -10429,11 +10429,11 @@
(-5 *1 (-510 *6 *7)))))
(((*1 *2 *3 *4 *3)
(|partial| -12 (-5 *4 (-1 *6 *6)) (-4 *6 (-1154 *5)) (-4 *5 (-311))
- (-5 *2 (-2 (|:| -2134 (-347 *6)) (|:| |coeff| (-347 *6))))
+ (-5 *2 (-2 (|:| -2135 (-347 *6)) (|:| |coeff| (-347 *6))))
(-5 *1 (-510 *5 *6)) (-5 *3 (-347 *6)))))
(((*1 *2 *3 *4 *5 *6)
(|partial| -12 (-5 *4 (-1 *8 *8))
- (-5 *5 (-1 (-2 (|:| |ans| *7) (|:| -3134 *7) (|:| |sol?| (-85))) (-484) *7))
+ (-5 *5 (-1 (-2 (|:| |ans| *7) (|:| -3135 *7) (|:| |sol?| (-85))) (-484) *7))
(-5 *6 (-584 (-347 *8))) (-4 *7 (-311)) (-4 *8 (-1154 *7)) (-5 *3 (-347 *8))
(-5 *2
(-2
@@ -10444,7 +10444,7 @@
(-5 *1 (-510 *7 *8)))))
(((*1 *2 *3 *4 *5 *6)
(|partial| -12 (-5 *4 (-1 *8 *8))
- (-5 *5 (-1 (-3 (-2 (|:| -2134 *7) (|:| |coeff| *7)) "failed") *7))
+ (-5 *5 (-1 (-3 (-2 (|:| -2135 *7) (|:| |coeff| *7)) "failed") *7))
(-5 *6 (-584 (-347 *8))) (-4 *7 (-311)) (-4 *8 (-1154 *7)) (-5 *3 (-347 *8))
(-5 *2
(-2
@@ -10455,19 +10455,19 @@
(-5 *1 (-510 *7 *8)))))
(((*1 *2 *3 *4 *5 *3)
(-12 (-5 *4 (-1 *7 *7))
- (-5 *5 (-1 (-2 (|:| |ans| *6) (|:| -3134 *6) (|:| |sol?| (-85))) (-484) *6))
+ (-5 *5 (-1 (-2 (|:| |ans| *6) (|:| -3135 *6) (|:| |sol?| (-85))) (-484) *6))
(-4 *6 (-311)) (-4 *7 (-1154 *6))
(-5 *2
(-3 (-2 (|:| |answer| (-347 *7)) (|:| |a0| *6))
- (-2 (|:| -2134 (-347 *7)) (|:| |coeff| (-347 *7))) "failed"))
+ (-2 (|:| -2135 (-347 *7)) (|:| |coeff| (-347 *7))) "failed"))
(-5 *1 (-510 *6 *7)) (-5 *3 (-347 *7)))))
(((*1 *2 *3 *4 *5 *3)
(-12 (-5 *4 (-1 *7 *7))
- (-5 *5 (-1 (-3 (-2 (|:| -2134 *6) (|:| |coeff| *6)) "failed") *6))
+ (-5 *5 (-1 (-3 (-2 (|:| -2135 *6) (|:| |coeff| *6)) "failed") *6))
(-4 *6 (-311)) (-4 *7 (-1154 *6))
(-5 *2
(-3 (-2 (|:| |answer| (-347 *7)) (|:| |a0| *6))
- (-2 (|:| -2134 (-347 *7)) (|:| |coeff| (-347 *7))) "failed"))
+ (-2 (|:| -2135 (-347 *7)) (|:| |coeff| (-347 *7))) "failed"))
(-5 *1 (-510 *6 *7)) (-5 *3 (-347 *7)))))
(((*1 *2 *3 *4 *5)
(-12 (-5 *4 (-1 *7 *7)) (-5 *5 (-1 (-3 (-584 *6) "failed") (-484) *6 *6))
@@ -10476,13 +10476,13 @@
(-5 *1 (-510 *6 *7)) (-5 *3 (-347 *7)))))
(((*1 *2 *3 *4 *5)
(-12 (-5 *4 (-1 *7 *7))
- (-5 *5 (-1 (-2 (|:| |ans| *6) (|:| -3134 *6) (|:| |sol?| (-85))) (-484) *6))
+ (-5 *5 (-1 (-2 (|:| |ans| *6) (|:| -3135 *6) (|:| |sol?| (-85))) (-484) *6))
(-4 *6 (-311)) (-4 *7 (-1154 *6))
(-5 *2 (-2 (|:| |answer| (-519 (-347 *7))) (|:| |a0| *6)))
(-5 *1 (-510 *6 *7)) (-5 *3 (-347 *7)))))
(((*1 *2 *3 *4 *5)
(-12 (-5 *4 (-1 *7 *7))
- (-5 *5 (-1 (-3 (-2 (|:| -2134 *6) (|:| |coeff| *6)) "failed") *6))
+ (-5 *5 (-1 (-3 (-2 (|:| -2135 *6) (|:| |coeff| *6)) "failed") *6))
(-4 *6 (-311)) (-4 *7 (-1154 *6))
(-5 *2 (-2 (|:| |answer| (-519 (-347 *7))) (|:| |a0| *6)))
(-5 *1 (-510 *6 *7)) (-5 *3 (-347 *7)))))
@@ -10514,7 +10514,7 @@
(-4 *4 (-1013)) (-5 *1 (-509 *4 *5)))))
(((*1 *2 *3 *4 *3)
(|partial| -12 (-5 *4 (-1089)) (-4 *5 (-13 (-495) (-951 (-484)) (-120)))
- (-5 *2 (-2 (|:| -2134 (-347 (-858 *5))) (|:| |coeff| (-347 (-858 *5)))))
+ (-5 *2 (-2 (|:| -2135 (-347 (-858 *5))) (|:| |coeff| (-347 (-858 *5)))))
(-5 *1 (-506 *5)) (-5 *3 (-347 (-858 *5))))))
(((*1 *2 *3 *4 *5)
(|partial| -12 (-5 *4 (-1089)) (-5 *5 (-584 (-347 (-858 *6))))
@@ -10543,7 +10543,7 @@
(-5 *1 (-504 *5 *6)))))
(((*1 *2 *3 *3)
(|partial| -12 (-4 *4 (-13 (-311) (-120) (-951 (-484)))) (-4 *5 (-1154 *4))
- (-5 *2 (-2 (|:| -2134 (-347 *5)) (|:| |coeff| (-347 *5))))
+ (-5 *2 (-2 (|:| -2135 (-347 *5)) (|:| |coeff| (-347 *5))))
(-5 *1 (-504 *4 *5)) (-5 *3 (-347 *5)))))
(((*1 *2 *2)
(|partial| -12 (-5 *2 (-347 *4)) (-4 *4 (-1154 *3))
@@ -10565,12 +10565,12 @@
(-4 *3 (-570)) (-4 *3 (-13 (-27) (-1114) (-361 *5))))))
(((*1 *2 *3 *4)
(-12 (-5 *4 (-1089)) (-4 *5 (-13 (-951 (-484)) (-389) (-581 (-484))))
- (-5 *2 (-2 (|:| -2336 *3) (|:| |nconst| *3))) (-5 *1 (-503 *5 *3))
+ (-5 *2 (-2 (|:| -2337 *3) (|:| |nconst| *3))) (-5 *1 (-503 *5 *3))
(-4 *3 (-13 (-27) (-1114) (-361 *5))))))
(((*1 *2 *3 *4 *5 *5 *6)
(-12 (-5 *5 (-551 *4)) (-5 *6 (-1089)) (-4 *4 (-13 (-361 *7) (-27) (-1114)))
(-4 *7 (-13 (-389) (-951 (-484)) (-120) (-581 (-484))))
- (-5 *2 (-2 (|:| |particular| (-3 *4 "failed")) (|:| -2010 (-584 *4))))
+ (-5 *2 (-2 (|:| |particular| (-3 *4 "failed")) (|:| -2011 (-584 *4))))
(-5 *1 (-502 *7 *4 *3)) (-4 *3 (-601 *4)) (-4 *3 (-1013)))))
(((*1 *2 *2 *2 *2 *3 *3 *4)
(|partial| -12 (-5 *3 (-551 *2)) (-5 *4 (-1 (-3 *2 "failed") *2 *2 (-1089)))
@@ -10588,7 +10588,7 @@
(((*1 *2 *3 *4 *4 *3)
(|partial| -12 (-5 *4 (-551 *3)) (-4 *3 (-13 (-361 *5) (-27) (-1114)))
(-4 *5 (-13 (-389) (-951 (-484)) (-120) (-581 (-484))))
- (-5 *2 (-2 (|:| -2134 *3) (|:| |coeff| *3))) (-5 *1 (-502 *5 *3 *6))
+ (-5 *2 (-2 (|:| -2135 *3) (|:| |coeff| *3))) (-5 *1 (-502 *5 *3 *6))
(-4 *6 (-1013)))))
(((*1 *2 *3 *4 *4)
(-12 (-5 *4 (-551 *3)) (-4 *3 (-13 (-361 *5) (-27) (-1114)))
@@ -10596,12 +10596,12 @@
(-5 *1 (-502 *5 *3 *6)) (-4 *6 (-1013)))))
(((*1 *2 *3 *4)
(-12 (-5 *4 (-1 *6 *6)) (-4 *6 (-1154 *5)) (-4 *5 (-311))
- (-4 *7 (-1154 (-347 *6))) (-5 *2 (-2 (|:| |answer| *3) (|:| -2133 *3)))
+ (-4 *7 (-1154 (-347 *6))) (-5 *2 (-2 (|:| |answer| *3) (|:| -2134 *3)))
(-5 *1 (-500 *5 *6 *7 *3)) (-4 *3 (-290 *5 *6 *7))))
((*1 *2 *3 *4)
(-12 (-5 *4 (-1 *6 *6)) (-4 *6 (-1154 *5)) (-4 *5 (-311))
(-5 *2
- (-2 (|:| |answer| (-347 *6)) (|:| -2133 (-347 *6))
+ (-2 (|:| |answer| (-347 *6)) (|:| -2134 (-347 *6))
(|:| |specpart| (-347 *6)) (|:| |polypart| *6)))
(-5 *1 (-501 *5 *6)) (-5 *3 (-347 *6)))))
(((*1 *2 *2 *3) (-12 (-5 *2 (-484)) (-5 *3 (-695)) (-5 *1 (-499)))))
@@ -10621,24 +10621,24 @@
(-12 (-5 *3 (-584 *8))
(-5 *4
(-584
- (-2 (|:| -2010 (-631 *7)) (|:| |basisDen| *7)
+ (-2 (|:| -2011 (-631 *7)) (|:| |basisDen| *7)
(|:| |basisInv| (-631 *7)))))
(-5 *5 (-695)) (-4 *8 (-1154 *7)) (-4 *7 (-1154 *6)) (-4 *6 (-298))
(-5 *2
- (-2 (|:| -2010 (-631 *7)) (|:| |basisDen| *7) (|:| |basisInv| (-631 *7))))
+ (-2 (|:| -2011 (-631 *7)) (|:| |basisDen| *7) (|:| |basisInv| (-631 *7))))
(-5 *1 (-435 *6 *7 *8))))
((*1 *2 *2 *2 *2 *2) (-12 (-5 *2 (-484)) (-5 *1 (-499)))))
(((*1 *2 *3 *4 *5 *5 *4 *6)
(-12 (-5 *5 (-551 *4)) (-5 *6 (-1084 *4))
(-4 *4 (-13 (-361 *7) (-27) (-1114)))
(-4 *7 (-13 (-389) (-951 (-484)) (-120) (-581 (-484))))
- (-5 *2 (-2 (|:| |particular| (-3 *4 #1="failed")) (|:| -2010 (-584 *4))))
+ (-5 *2 (-2 (|:| |particular| (-3 *4 #1="failed")) (|:| -2011 (-584 *4))))
(-5 *1 (-498 *7 *4 *3)) (-4 *3 (-601 *4)) (-4 *3 (-1013))))
((*1 *2 *3 *4 *5 *5 *5 *4 *6)
(-12 (-5 *5 (-551 *4)) (-5 *6 (-347 (-1084 *4)))
(-4 *4 (-13 (-361 *7) (-27) (-1114)))
(-4 *7 (-13 (-389) (-951 (-484)) (-120) (-581 (-484))))
- (-5 *2 (-2 (|:| |particular| (-3 *4 #1#)) (|:| -2010 (-584 *4))))
+ (-5 *2 (-2 (|:| |particular| (-3 *4 #1#)) (|:| -2011 (-584 *4))))
(-5 *1 (-498 *7 *4 *3)) (-4 *3 (-601 *4)) (-4 *3 (-1013)))))
(((*1 *2 *2 *2 *3 *3 *4 *2 *5)
(|partial| -12 (-5 *3 (-551 *2))
@@ -10671,13 +10671,13 @@
(|partial| -12 (-5 *4 (-551 *3)) (-5 *5 (-1084 *3))
(-4 *3 (-13 (-361 *6) (-27) (-1114)))
(-4 *6 (-13 (-389) (-951 (-484)) (-120) (-581 (-484))))
- (-5 *2 (-2 (|:| -2134 *3) (|:| |coeff| *3))) (-5 *1 (-498 *6 *3 *7))
+ (-5 *2 (-2 (|:| -2135 *3) (|:| |coeff| *3))) (-5 *1 (-498 *6 *3 *7))
(-4 *7 (-1013))))
((*1 *2 *3 *4 *4 *3 *4 *3 *5)
(|partial| -12 (-5 *4 (-551 *3)) (-5 *5 (-347 (-1084 *3)))
(-4 *3 (-13 (-361 *6) (-27) (-1114)))
(-4 *6 (-13 (-389) (-951 (-484)) (-120) (-581 (-484))))
- (-5 *2 (-2 (|:| -2134 *3) (|:| |coeff| *3))) (-5 *1 (-498 *6 *3 *7))
+ (-5 *2 (-2 (|:| -2135 *3) (|:| |coeff| *3))) (-5 *1 (-498 *6 *3 *7))
(-4 *7 (-1013)))))
(((*1 *2 *3 *4 *4 *3 *5)
(-12 (-5 *4 (-551 *3)) (-5 *5 (-1084 *3))
@@ -10695,7 +10695,7 @@
(|partial| -12 (-5 *4 (-1089)) (-5 *6 (-584 (-551 *3))) (-5 *5 (-551 *3))
(-4 *3 (-13 (-27) (-1114) (-361 *7)))
(-4 *7 (-13 (-389) (-120) (-951 (-484)) (-581 (-484))))
- (-5 *2 (-2 (|:| -2134 *3) (|:| |coeff| *3))) (-5 *1 (-496 *7 *3)))))
+ (-5 *2 (-2 (|:| -2135 *3) (|:| |coeff| *3))) (-5 *1 (-496 *7 *3)))))
(((*1 *2 *3 *4)
(-12 (-5 *4 (-1089)) (-4 *5 (-13 (-389) (-120) (-951 (-484)) (-581 (-484))))
(-5 *2 (-519 *3)) (-5 *1 (-496 *5 *3))
@@ -10715,10 +10715,10 @@
(((*1 *2 *3 *4 *3)
(|partial| -12 (-5 *4 (-1089))
(-4 *5 (-13 (-389) (-120) (-951 (-484)) (-581 (-484))))
- (-5 *2 (-2 (|:| -2134 *3) (|:| |coeff| *3))) (-5 *1 (-496 *5 *3))
+ (-5 *2 (-2 (|:| -2135 *3) (|:| |coeff| *3))) (-5 *1 (-496 *5 *3))
(-4 *3 (-13 (-27) (-1114) (-361 *5))))))
(((*1 *2 *1)
- (-12 (-5 *2 (-2 (|:| -1770 *1) (|:| -3978 *1) (|:| |associate| *1)))
+ (-12 (-5 *2 (-2 (|:| -1770 *1) (|:| -3979 *1) (|:| |associate| *1)))
(-4 *1 (-495)))))
(((*1 *1 *1) (-4 *1 (-495))))
(((*1 *2 *1 *1) (-12 (-4 *1 (-495)) (-5 *2 (-85)))))
@@ -10883,7 +10883,7 @@
(((*1 *2 *3)
(-12 (-5 *3 (-1178 *4)) (-4 *4 (-298)) (-5 *2 (-1084 *4)) (-5 *1 (-466 *4)))))
(((*1 *2 *3 *4)
- (-12 (-5 *3 (-1178 (-584 (-2 (|:| -3398 *4) (|:| -2398 (-1033))))))
+ (-12 (-5 *3 (-1178 (-584 (-2 (|:| -3399 *4) (|:| -2399 (-1033))))))
(-4 *4 (-298)) (-5 *2 (-1184)) (-5 *1 (-466 *4)))))
(((*1 *2 *1) (-12 (-4 *1 (-465)) (-5 *2 (-633 (-101))))))
(((*1 *2 *1) (-12 (-4 *1 (-465)) (-5 *2 (-633 (-488))))))
@@ -10913,6 +10913,9 @@
((*1 *2 *2)
(-12 (-5 *2 (-85)) (-5 *1 (-455 *3 *4)) (-4 *3 (-1128)) (-14 *4 (-484)))))
(((*1 *1 *2 *3) (-12 (-5 *1 (-451 *3 *2)) (-4 *3 (-72)) (-4 *2 (-760)))))
+(((*1 *1 *1 *1 *2 *3)
+ (-12 (-5 *2 (-1 *4 *4 *4)) (-5 *3 (-1 (-85) *4 *4)) (-4 *4 (-72))
+ (-5 *1 (-448 *4 *5)) (-4 *5 (-760)))))
(((*1 *2 *1) (-12 (-4 *1 (-447 *3 *2)) (-4 *3 (-72)) (-4 *2 (-760)))))
(((*1 *1) (-5 *1 (-444))))
(((*1 *1 *1 *2 *2)
@@ -11019,13 +11022,13 @@
(-12 (-5 *3 (-831)) (-5 *2 (-1184)) (-5 *1 (-167 *4))
(-4 *4
(-13 (-757)
- (-10 -8 (-15 -3796 ((-1072) $ (-1089))) (-15 -3613 (*2 $))
+ (-10 -8 (-15 -3797 ((-1072) $ (-1089))) (-15 -3614 (*2 $))
(-15 -1962 (*2 $)))))))
((*1 *2 *1)
(-12 (-5 *2 (-1184)) (-5 *1 (-167 *3))
(-4 *3
(-13 (-757)
- (-10 -8 (-15 -3796 ((-1072) $ (-1089))) (-15 -3613 (*2 $))
+ (-10 -8 (-15 -3797 ((-1072) $ (-1089))) (-15 -3614 (*2 $))
(-15 -1962 (*2 $)))))))
((*1 *2 *1) (-12 (-5 *2 (-1184)) (-5 *1 (-439)))))
(((*1 *2 *3 *4)
@@ -11048,38 +11051,38 @@
(((*1 *2 *2 *2)
(-12
(-5 *2
- (-2 (|:| -2010 (-631 *3)) (|:| |basisDen| *3) (|:| |basisInv| (-631 *3))))
- (-4 *3 (-13 (-257) (-10 -8 (-15 -3967 ((-345 $) $))))) (-4 *4 (-1154 *3))
+ (-2 (|:| -2011 (-631 *3)) (|:| |basisDen| *3) (|:| |basisInv| (-631 *3))))
+ (-4 *3 (-13 (-257) (-10 -8 (-15 -3968 ((-345 $) $))))) (-4 *4 (-1154 *3))
(-5 *1 (-436 *3 *4 *5)) (-4 *5 (-350 *3 *4)))))
(((*1 *2 *2 *2)
- (-12 (-5 *2 (-631 *3)) (-4 *3 (-13 (-257) (-10 -8 (-15 -3967 ((-345 $) $)))))
+ (-12 (-5 *2 (-631 *3)) (-4 *3 (-13 (-257) (-10 -8 (-15 -3968 ((-345 $) $)))))
(-4 *4 (-1154 *3)) (-5 *1 (-436 *3 *4 *5)) (-4 *5 (-350 *3 *4)))))
(((*1 *2 *2 *2)
- (-12 (-5 *2 (-631 *3)) (-4 *3 (-13 (-257) (-10 -8 (-15 -3967 ((-345 $) $)))))
+ (-12 (-5 *2 (-631 *3)) (-4 *3 (-13 (-257) (-10 -8 (-15 -3968 ((-345 $) $)))))
(-4 *4 (-1154 *3)) (-5 *1 (-436 *3 *4 *5)) (-4 *5 (-350 *3 *4))))
((*1 *2 *2 *2 *3)
- (-12 (-5 *2 (-631 *3)) (-4 *3 (-13 (-257) (-10 -8 (-15 -3967 ((-345 $) $)))))
+ (-12 (-5 *2 (-631 *3)) (-4 *3 (-13 (-257) (-10 -8 (-15 -3968 ((-345 $) $)))))
(-4 *4 (-1154 *3)) (-5 *1 (-436 *3 *4 *5)) (-4 *5 (-350 *3 *4)))))
(((*1 *2 *2 *2)
- (-12 (-5 *2 (-695)) (-4 *3 (-13 (-257) (-10 -8 (-15 -3967 ((-345 $) $)))))
+ (-12 (-5 *2 (-695)) (-4 *3 (-13 (-257) (-10 -8 (-15 -3968 ((-345 $) $)))))
(-4 *4 (-1154 *3)) (-5 *1 (-436 *3 *4 *5)) (-4 *5 (-350 *3 *4)))))
(((*1 *2 *3 *3 *2 *4)
(-12 (-5 *3 (-631 *2)) (-5 *4 (-484))
- (-4 *2 (-13 (-257) (-10 -8 (-15 -3967 ((-345 $) $))))) (-4 *5 (-1154 *2))
+ (-4 *2 (-13 (-257) (-10 -8 (-15 -3968 ((-345 $) $))))) (-4 *5 (-1154 *2))
(-5 *1 (-436 *2 *5 *6)) (-4 *6 (-350 *2 *5)))))
(((*1 *2 *3 *2 *4)
(-12 (-5 *3 (-631 *2)) (-5 *4 (-695))
- (-4 *2 (-13 (-257) (-10 -8 (-15 -3967 ((-345 $) $))))) (-4 *5 (-1154 *2))
+ (-4 *2 (-13 (-257) (-10 -8 (-15 -3968 ((-345 $) $))))) (-4 *5 (-1154 *2))
(-5 *1 (-436 *2 *5 *6)) (-4 *6 (-350 *2 *5)))))
(((*1 *2 *3 *4 *4)
(-12 (-5 *4 (-695)) (-4 *5 (-298)) (-4 *6 (-1154 *5))
(-5 *2
(-584
- (-2 (|:| -2010 (-631 *6)) (|:| |basisDen| *6)
+ (-2 (|:| -2011 (-631 *6)) (|:| |basisDen| *6)
(|:| |basisInv| (-631 *6)))))
(-5 *1 (-435 *5 *6 *7))
(-5 *3
- (-2 (|:| -2010 (-631 *6)) (|:| |basisDen| *6) (|:| |basisInv| (-631 *6))))
+ (-2 (|:| -2011 (-631 *6)) (|:| |basisDen| *6) (|:| |basisInv| (-631 *6))))
(-4 *7 (-1154 *6)))))
(((*1 *2 *1)
(-12
@@ -11097,19 +11100,19 @@
(-12 (-5 *2 (-1 *3 *3)) (-4 *1 (-57 *3 *4 *5)) (-4 *3 (-1128))
(-4 *4 (-321 *3)) (-4 *5 (-321 *3))))
((*1 *1 *2 *1)
- (-12 (-5 *2 (-1 *3 *3)) (|has| *1 (-6 -3992)) (-4 *1 (-426 *3))
+ (-12 (-5 *2 (-1 *3 *3)) (|has| *1 (-6 -3993)) (-4 *1 (-426 *3))
(-4 *3 (-1128)))))
(((*1 *2 *3 *1)
- (-12 (-5 *3 (-1 (-85) *4)) (|has| *1 (-6 -3991)) (-4 *1 (-426 *4))
+ (-12 (-5 *3 (-1 (-85) *4)) (|has| *1 (-6 -3992)) (-4 *1 (-426 *4))
(-4 *4 (-1128)) (-5 *2 (-85)))))
(((*1 *2 *3 *1)
- (-12 (-5 *3 (-1 (-85) *4)) (|has| *1 (-6 -3991)) (-4 *1 (-426 *4))
+ (-12 (-5 *3 (-1 (-85) *4)) (|has| *1 (-6 -3992)) (-4 *1 (-426 *4))
(-4 *4 (-1128)) (-5 *2 (-85)))))
(((*1 *2 *3 *1)
- (-12 (|has| *1 (-6 -3991)) (-4 *1 (-426 *3)) (-4 *3 (-1128)) (-4 *3 (-1013))
+ (-12 (|has| *1 (-6 -3992)) (-4 *1 (-426 *3)) (-4 *3 (-1128)) (-4 *3 (-1013))
(-5 *2 (-695))))
((*1 *2 *3 *1)
- (-12 (-5 *3 (-1 (-85) *4)) (|has| *1 (-6 -3991)) (-4 *1 (-426 *4))
+ (-12 (-5 *3 (-1 (-85) *4)) (|has| *1 (-6 -3992)) (-4 *1 (-426 *4))
(-4 *4 (-1128)) (-5 *2 (-695)))))
(((*1 *1 *2) (-12 (-5 *2 (-347 (-484))) (-5 *1 (-424)))))
(((*1 *2 *3)
@@ -11127,7 +11130,7 @@
(-4 *4 (-962))))
((*1 *1 *1 *2)
(-12 (-5 *2 (-584 (-484))) (-14 *3 (-584 (-1089))) (-5 *1 (-391 *3 *4 *5))
- (-4 *4 (-962)) (-4 *5 (-196 (-3953 *3) (-695)))))
+ (-4 *4 (-962)) (-4 *5 (-196 (-3954 *3) (-695)))))
((*1 *1 *1 *2)
(-12 (-5 *2 (-584 (-484))) (-5 *1 (-418 *3 *4)) (-14 *3 (-584 (-1089)))
(-4 *4 (-962)))))
@@ -11191,33 +11194,33 @@
(-4 *7 (-862 *6 *5 *3)) (-5 *1 (-399 *5 *3 *6 *7 *2))
(-4 *2
(-13 (-951 (-347 (-484))) (-311)
- (-10 -8 (-15 -3942 ($ *7)) (-15 -2996 (*7 $)) (-15 -2995 (*7 $))))))))
+ (-10 -8 (-15 -3943 ($ *7)) (-15 -2997 (*7 $)) (-15 -2996 (*7 $))))))))
(((*1 *2 *1)
(-12 (-14 *3 (-584 (-1089))) (-4 *4 (-146))
(-14 *6
- (-1 (-85) (-2 (|:| -2398 *5) (|:| -2399 *2))
- (-2 (|:| -2398 *5) (|:| -2399 *2))))
- (-4 *2 (-196 (-3953 *3) (-695))) (-5 *1 (-398 *3 *4 *5 *2 *6 *7))
+ (-1 (-85) (-2 (|:| -2399 *5) (|:| -2400 *2))
+ (-2 (|:| -2399 *5) (|:| -2400 *2))))
+ (-4 *2 (-196 (-3954 *3) (-695))) (-5 *1 (-398 *3 *4 *5 *2 *6 *7))
(-4 *5 (-757)) (-4 *7 (-862 *4 *2 (-774 *3))))))
(((*1 *2 *1)
- (-12 (-14 *3 (-584 (-1089))) (-4 *4 (-146)) (-4 *5 (-196 (-3953 *3) (-695)))
+ (-12 (-14 *3 (-584 (-1089))) (-4 *4 (-146)) (-4 *5 (-196 (-3954 *3) (-695)))
(-14 *6
- (-1 (-85) (-2 (|:| -2398 *2) (|:| -2399 *5))
- (-2 (|:| -2398 *2) (|:| -2399 *5))))
+ (-1 (-85) (-2 (|:| -2399 *2) (|:| -2400 *5))
+ (-2 (|:| -2399 *2) (|:| -2400 *5))))
(-4 *2 (-757)) (-5 *1 (-398 *3 *4 *2 *5 *6 *7))
(-4 *7 (-862 *4 *5 (-774 *3))))))
(((*1 *1 *2 *3 *4)
- (-12 (-14 *5 (-584 (-1089))) (-4 *2 (-146)) (-4 *4 (-196 (-3953 *5) (-695)))
+ (-12 (-14 *5 (-584 (-1089))) (-4 *2 (-146)) (-4 *4 (-196 (-3954 *5) (-695)))
(-14 *6
- (-1 (-85) (-2 (|:| -2398 *3) (|:| -2399 *4))
- (-2 (|:| -2398 *3) (|:| -2399 *4))))
+ (-1 (-85) (-2 (|:| -2399 *3) (|:| -2400 *4))
+ (-2 (|:| -2399 *3) (|:| -2400 *4))))
(-5 *1 (-398 *5 *2 *3 *4 *6 *7)) (-4 *3 (-757))
(-4 *7 (-862 *2 *4 (-774 *5))))))
(((*1 *1 *2 *3 *1)
- (-12 (-14 *4 (-584 (-1089))) (-4 *2 (-146)) (-4 *3 (-196 (-3953 *4) (-695)))
+ (-12 (-14 *4 (-584 (-1089))) (-4 *2 (-146)) (-4 *3 (-196 (-3954 *4) (-695)))
(-14 *6
- (-1 (-85) (-2 (|:| -2398 *5) (|:| -2399 *3))
- (-2 (|:| -2398 *5) (|:| -2399 *3))))
+ (-1 (-85) (-2 (|:| -2399 *5) (|:| -2400 *3))
+ (-2 (|:| -2399 *5) (|:| -2400 *3))))
(-5 *1 (-398 *4 *2 *5 *3 *6 *7)) (-4 *5 (-757))
(-4 *7 (-862 *2 *3 (-774 *4))))))
(((*1 *2 *3 *2 *4 *5)
@@ -11241,22 +11244,22 @@
(-5 *1 (-392 *5 *3)))))
(((*1 *2)
(|partial| -12 (-4 *3 (-495)) (-4 *3 (-146))
- (-5 *2 (-2 (|:| |particular| *1) (|:| -2010 (-584 *1)))) (-4 *1 (-315 *3))))
+ (-5 *2 (-2 (|:| |particular| *1) (|:| -2011 (-584 *1)))) (-4 *1 (-315 *3))))
((*1 *2)
(|partial| -12
(-5 *2
(-2 (|:| |particular| (-390 *3 *4 *5 *6))
- (|:| -2010 (-584 (-390 *3 *4 *5 *6)))))
+ (|:| -2011 (-584 (-390 *3 *4 *5 *6)))))
(-5 *1 (-390 *3 *4 *5 *6)) (-4 *3 (-146)) (-14 *4 (-831))
(-14 *5 (-584 (-1089))) (-14 *6 (-1178 (-631 *3))))))
(((*1 *2)
(|partial| -12 (-4 *3 (-495)) (-4 *3 (-146))
- (-5 *2 (-2 (|:| |particular| *1) (|:| -2010 (-584 *1)))) (-4 *1 (-315 *3))))
+ (-5 *2 (-2 (|:| |particular| *1) (|:| -2011 (-584 *1)))) (-4 *1 (-315 *3))))
((*1 *2)
(|partial| -12
(-5 *2
(-2 (|:| |particular| (-390 *3 *4 *5 *6))
- (|:| -2010 (-584 (-390 *3 *4 *5 *6)))))
+ (|:| -2011 (-584 (-390 *3 *4 *5 *6)))))
(-5 *1 (-390 *3 *4 *5 *6)) (-4 *3 (-146)) (-14 *4 (-831))
(-14 *5 (-584 (-1089))) (-14 *6 (-1178 (-631 *3))))))
(((*1 *1 *2 *3)
@@ -11361,7 +11364,7 @@
(-12 (-4 *4 (-389)) (-4 *5 (-718)) (-4 *6 (-757)) (-5 *2 (-695))
(-5 *1 (-387 *4 *5 *6 *3)) (-4 *3 (-862 *4 *5 *6)))))
(((*1 *2 *3 *4 *5)
- (-12 (-5 *3 (-2 (|:| |totdeg| (-695)) (|:| -2002 *4))) (-5 *5 (-695))
+ (-12 (-5 *3 (-2 (|:| |totdeg| (-695)) (|:| -2003 *4))) (-5 *5 (-695))
(-4 *4 (-862 *6 *7 *8)) (-4 *6 (-389)) (-4 *7 (-718)) (-4 *8 (-757))
(-5 *2
(-2 (|:| |lcmfij| *7) (|:| |totdeg| *5) (|:| |poli| *4) (|:| |polj| *4)))
@@ -11418,7 +11421,7 @@
(-4 *5 (-718)) (-4 *2 (-862 *4 *5 *6)) (-5 *1 (-387 *4 *5 *6 *2))
(-4 *4 (-389)) (-4 *6 (-757)))))
(((*1 *2 *3 *4 *2)
- (-12 (-5 *2 (-584 (-2 (|:| |totdeg| (-695)) (|:| -2002 *3)))) (-5 *4 (-695))
+ (-12 (-5 *2 (-584 (-2 (|:| |totdeg| (-695)) (|:| -2003 *3)))) (-5 *4 (-695))
(-4 *3 (-862 *5 *6 *7)) (-4 *5 (-389)) (-4 *6 (-718)) (-4 *7 (-757))
(-5 *1 (-387 *5 *6 *7 *3)))))
(((*1 *2 *2)
@@ -11545,7 +11548,7 @@
(-12 (-5 *3 (-831)) (-5 *4 (-345 *2)) (-4 *2 (-1154 *5)) (-5 *1 (-381 *5 *2))
(-4 *5 (-962)))))
(((*1 *2 *3)
- (-12 (-5 *3 (-584 (-2 (|:| -3728 *4) (|:| -3944 (-484)))))
+ (-12 (-5 *3 (-584 (-2 (|:| -3729 *4) (|:| -3945 (-484)))))
(-4 *4 (-1154 (-484))) (-5 *2 (-676 (-695))) (-5 *1 (-379 *4))))
((*1 *2 *3)
(-12 (-5 *3 (-345 *5)) (-4 *5 (-1154 *4)) (-4 *4 (-962))
@@ -11581,7 +11584,7 @@
(-12 (-5 *4 (-85)) (-5 *5 (-1009 (-695))) (-5 *6 (-695))
(-5 *2
(-2 (|:| |contp| (-484))
- (|:| -1777 (-584 (-2 (|:| |irr| *3) (|:| -2393 (-484)))))))
+ (|:| -1777 (-584 (-2 (|:| |irr| *3) (|:| -2394 (-484)))))))
(-5 *1 (-379 *3)) (-4 *3 (-1154 (-484))))))
(((*1 *2 *2) (-12 (-5 *2 (-85)) (-5 *1 (-379 *3)) (-4 *3 (-1154 (-484))))))
(((*1 *2) (-12 (-5 *2 (-85)) (-5 *1 (-379 *3)) (-4 *3 (-1154 (-484))))))
@@ -11591,11 +11594,11 @@
(((*1 *2 *2) (-12 (-5 *2 (-85)) (-5 *1 (-379 *3)) (-4 *3 (-1154 (-484))))))
(((*1 *2) (-12 (-5 *2 (-85)) (-5 *1 (-379 *3)) (-4 *3 (-1154 (-484))))))
(((*1 *2 *3)
- (-12 (-5 *2 (-2 (|:| -2576 (-484)) (|:| -1777 (-584 *3)))) (-5 *1 (-379 *3))
+ (-12 (-5 *2 (-2 (|:| -2577 (-484)) (|:| -1777 (-584 *3)))) (-5 *1 (-379 *3))
(-4 *3 (-1154 (-484))))))
(((*1 *2 *1) (-12 (-5 *2 (-695)) (-5 *1 (-345 *3)) (-4 *3 (-495))))
((*1 *2 *3)
- (-12 (-5 *3 (-584 (-2 (|:| -3728 *4) (|:| -3944 (-484)))))
+ (-12 (-5 *3 (-584 (-2 (|:| -3729 *4) (|:| -3945 (-484)))))
(-4 *4 (-1154 (-484))) (-5 *2 (-695)) (-5 *1 (-379 *4)))))
(((*1 *2) (-12 (-5 *2 (-831)) (-5 *1 (-379 *3)) (-4 *3 (-1154 (-484)))))
((*1 *2 *2) (-12 (-5 *2 (-831)) (-5 *1 (-379 *3)) (-4 *3 (-1154 (-484))))))
@@ -11612,10 +11615,10 @@
(-12
(-5 *3
(-2 (|:| |contp| (-484))
- (|:| -1777 (-584 (-2 (|:| |irr| *4) (|:| -2393 (-484)))))))
+ (|:| -1777 (-584 (-2 (|:| |irr| *4) (|:| -2394 (-484)))))))
(-4 *4 (-1154 (-484))) (-5 *2 (-345 *4)) (-5 *1 (-379 *4)))))
(((*1 *2 *1)
- (-12 (-5 *2 (-3 (|:| |fst| (-374)) (|:| -3906 "void"))) (-5 *1 (-376)))))
+ (-12 (-5 *2 (-3 (|:| |fst| (-374)) (|:| -3907 "void"))) (-5 *1 (-376)))))
(((*1 *2 *1) (-12 (-5 *2 (-584 (-858 (-484)))) (-5 *1 (-376)))))
(((*1 *2 *1) (-12 (-5 *2 (-85)) (-5 *1 (-376)))))
(((*1 *1) (-5 *1 (-376))))
@@ -11633,7 +11636,7 @@
(-12 (-4 *4 (-13 (-495) (-951 (-484)))) (-4 *5 (-361 *4))
(-5 *2
(-3 (|:| |overq| (-1084 (-347 (-484)))) (|:| |overan| (-1084 (-48)))
- (|:| -2637 (-85))))
+ (|:| -2638 (-85))))
(-5 *1 (-375 *4 *5 *3)) (-4 *3 (-1154 *5)))))
(((*1 *2 *3)
(|partial| -12 (-4 *4 (-13 (-495) (-951 (-484)))) (-4 *5 (-361 *4))
@@ -11676,19 +11679,19 @@
(-14 *4 (-1089)) (-14 *5 *2)))
((*1 *2 *2)
(-12 (-4 *3 (-13 (-389) (-951 (-484)) (-581 (-484))))
- (-4 *2 (-13 (-27) (-1114) (-361 *3) (-10 -8 (-15 -3942 ($ *4)))))
+ (-4 *2 (-13 (-27) (-1114) (-361 *3) (-10 -8 (-15 -3943 ($ *4)))))
(-4 *4 (-756))
(-4 *5
(-13 (-1157 *2 *4) (-311) (-1114)
- (-10 -8 (-15 -3754 ($ $)) (-15 -3808 ($ $)))))
+ (-10 -8 (-15 -3755 ($ $)) (-15 -3809 ($ $)))))
(-5 *1 (-364 *3 *2 *4 *5 *6 *7)) (-4 *6 (-897 *5)) (-14 *7 (-1089)))))
(((*1 *2 *3 *4 *5)
(-12 (-5 *4 (-85)) (-4 *6 (-13 (-389) (-951 (-484)) (-581 (-484))))
- (-4 *3 (-13 (-27) (-1114) (-361 *6) (-10 -8 (-15 -3942 ($ *7)))))
+ (-4 *3 (-13 (-27) (-1114) (-361 *6) (-10 -8 (-15 -3943 ($ *7)))))
(-4 *7 (-756))
(-4 *8
(-13 (-1157 *3 *7) (-311) (-1114)
- (-10 -8 (-15 -3754 ($ $)) (-15 -3808 ($ $)))))
+ (-10 -8 (-15 -3755 ($ $)) (-15 -3809 ($ $)))))
(-5 *2
(-3 (|:| |%series| *8)
(|:| |%problem| (-2 (|:| |func| (-1072)) (|:| |prob| (-1072))))))
@@ -11696,11 +11699,11 @@
(-14 *10 (-1089)))))
(((*1 *2 *3 *4 *5)
(-12 (-5 *4 (-85)) (-4 *6 (-13 (-389) (-951 (-484)) (-581 (-484))))
- (-4 *3 (-13 (-27) (-1114) (-361 *6) (-10 -8 (-15 -3942 ($ *7)))))
+ (-4 *3 (-13 (-27) (-1114) (-361 *6) (-10 -8 (-15 -3943 ($ *7)))))
(-4 *7 (-756))
(-4 *8
(-13 (-1157 *3 *7) (-311) (-1114)
- (-10 -8 (-15 -3754 ($ $)) (-15 -3808 ($ $)))))
+ (-10 -8 (-15 -3755 ($ $)) (-15 -3809 ($ $)))))
(-5 *2
(-3 (|:| |%series| *8)
(|:| |%problem| (-2 (|:| |func| (-1072)) (|:| |prob| (-1072))))))
@@ -11727,7 +11730,7 @@
((*1 *1 *2 *1) (-12 (-5 *2 (-1089)) (-4 *1 (-361 *3)) (-4 *3 (-1013)))))
(((*1 *2 *1)
(|partial| -12 (-4 *3 (-25)) (-4 *3 (-1013))
- (-5 *2 (-2 (|:| -3950 (-484)) (|:| |var| (-551 *1)))) (-4 *1 (-361 *3)))))
+ (-5 *2 (-2 (|:| -3951 (-484)) (|:| |var| (-551 *1)))) (-4 *1 (-361 *3)))))
(((*1 *2 *2 *2) (-12 (-5 *2 (-345 *3)) (-4 *3 (-495)) (-5 *1 (-359 *3)))))
(((*1 *1 *2) (-12 (-5 *2 (-1178 *3)) (-4 *3 (-311)) (-4 *1 (-279 *3))))
((*1 *1 *2 *3)
@@ -11798,13 +11801,13 @@
(-5 *2 (-631 *3)))))
(((*1 *1 *2 *3) (-12 (-5 *3 (-484)) (-5 *1 (-345 *2)) (-4 *2 (-495)))))
(((*1 *2 *1)
- (-12 (-5 *2 (-584 (-2 (|:| |gen| *3) (|:| -3939 (-484))))) (-5 *1 (-309 *3))
+ (-12 (-5 *2 (-584 (-2 (|:| |gen| *3) (|:| -3940 (-484))))) (-5 *1 (-309 *3))
(-4 *3 (-1013))))
((*1 *2 *1)
(-12 (-4 *1 (-333 *3)) (-4 *3 (-1013))
- (-5 *2 (-584 (-2 (|:| |gen| *3) (|:| -3939 (-695)))))))
+ (-5 *2 (-584 (-2 (|:| |gen| *3) (|:| -3940 (-695)))))))
((*1 *2 *1)
- (-12 (-5 *2 (-584 (-2 (|:| -3728 *3) (|:| -2399 (-484))))) (-5 *1 (-345 *3))
+ (-12 (-5 *2 (-584 (-2 (|:| -3729 *3) (|:| -2400 (-484))))) (-5 *1 (-345 *3))
(-4 *3 (-495)))))
(((*1 *1 *2 *3) (-12 (-5 *3 (-484)) (-5 *1 (-345 *2)) (-4 *2 (-495)))))
(((*1 *2 *1 *2) (-12 (-5 *2 (-484)) (-5 *1 (-345 *3)) (-4 *3 (-495)))))
@@ -11822,14 +11825,14 @@
(((*1 *1 *1) (-12 (-5 *1 (-345 *2)) (-4 *2 (-495)))))
(((*1 *2 *1) (-12 (-4 *1 (-344)) (-5 *2 (-484)))))
(((*1 *1 *2 *3) (-12 (-5 *2 (-695)) (-5 *3 (-85)) (-5 *1 (-81))))
- ((*1 *2 *2) (-12 (-5 *2 (-831)) (|has| *1 (-6 -3982)) (-4 *1 (-344))))
+ ((*1 *2 *2) (-12 (-5 *2 (-831)) (|has| *1 (-6 -3983)) (-4 *1 (-344))))
((*1 *2) (-12 (-4 *1 (-344)) (-5 *2 (-831)))))
-(((*1 *2 *2) (-12 (-5 *2 (-831)) (|has| *1 (-6 -3982)) (-4 *1 (-344))))
+(((*1 *2 *2) (-12 (-5 *2 (-831)) (|has| *1 (-6 -3983)) (-4 *1 (-344))))
((*1 *2) (-12 (-4 *1 (-344)) (-5 *2 (-831)))))
(((*1 *2 *3)
- (-12 (-5 *3 (-484)) (|has| *1 (-6 -3982)) (-4 *1 (-344)) (-5 *2 (-831)))))
+ (-12 (-5 *3 (-484)) (|has| *1 (-6 -3983)) (-4 *1 (-344)) (-5 *2 (-831)))))
(((*1 *2 *3)
- (-12 (-5 *3 (-484)) (|has| *1 (-6 -3982)) (-4 *1 (-344)) (-5 *2 (-831)))))
+ (-12 (-5 *3 (-484)) (|has| *1 (-6 -3983)) (-4 *1 (-344)) (-5 *2 (-831)))))
(((*1 *2 *1) (-12 (-4 *1 (-298)) (-5 *2 (-695))))
((*1 *2 *1 *1) (|partial| -12 (-4 *1 (-342)) (-5 *2 (-695)))))
(((*1 *1 *1 *2) (-12 (-4 *1 (-342)) (-5 *2 (-695))))
@@ -11841,7 +11844,7 @@
(-12 (-4 *2 (-1154 *3)) (-5 *1 (-339 *3 *2)) (-4 *3 (-13 (-311) (-120))))))
(((*1 *2 *1)
(-12 (-4 *3 (-13 (-311) (-120)))
- (-5 *2 (-584 (-2 (|:| -2399 (-695)) (|:| -3769 *4) (|:| |num| *4))))
+ (-5 *2 (-584 (-2 (|:| -2400 (-695)) (|:| -3770 *4) (|:| |num| *4))))
(-5 *1 (-339 *3 *4)) (-4 *4 (-1154 *3)))))
(((*1 *2 *1)
(-12 (-5 *2 (-773)) (-5 *1 (-337 *3 *4 *5)) (-14 *3 (-695)) (-14 *4 (-695))
@@ -11911,13 +11914,13 @@
(((*1 *2 *3) (-12 (-5 *3 (-695)) (-5 *2 (-1184)) (-5 *1 (-327)))))
(((*1 *2 *3 *2)
(-12 (-5 *3 (-1 (-85) *4 *4)) (-4 *4 (-1128)) (-5 *1 (-324 *4 *2))
- (-4 *2 (-13 (-321 *4) (-10 -7 (-6 -3992)))))))
+ (-4 *2 (-13 (-321 *4) (-10 -7 (-6 -3993)))))))
(((*1 *2 *3 *2)
(-12 (-5 *3 (-1 (-85) *4 *4)) (-4 *4 (-1128)) (-5 *1 (-324 *4 *2))
- (-4 *2 (-13 (-321 *4) (-10 -7 (-6 -3992)))))))
+ (-4 *2 (-13 (-321 *4) (-10 -7 (-6 -3993)))))))
(((*1 *2 *3 *2)
(-12 (-5 *3 (-1 (-85) *4 *4)) (-4 *4 (-1128)) (-5 *1 (-324 *4 *2))
- (-4 *2 (-13 (-321 *4) (-10 -7 (-6 -3992)))))))
+ (-4 *2 (-13 (-321 *4) (-10 -7 (-6 -3993)))))))
(((*1 *1 *2)
(-12 (-5 *2 (-615 *3)) (-4 *3 (-757)) (-4 *1 (-323 *3 *4)) (-4 *4 (-146)))))
(((*1 *2 *1)
@@ -11926,11 +11929,11 @@
(-12 (-5 *3 (-1 (-85) *4 *4)) (-4 *1 (-321 *4)) (-4 *4 (-1128))
(-5 *2 (-85)))))
(((*1 *1 *1 *1 *2)
- (-12 (-5 *2 (-484)) (|has| *1 (-6 -3992)) (-4 *1 (-321 *3)) (-4 *3 (-1128)))))
+ (-12 (-5 *2 (-484)) (|has| *1 (-6 -3993)) (-4 *1 (-321 *3)) (-4 *3 (-1128)))))
(((*1 *1 *1)
- (-12 (|has| *1 (-6 -3992)) (-4 *1 (-321 *2)) (-4 *2 (-1128)) (-4 *2 (-757))))
+ (-12 (|has| *1 (-6 -3993)) (-4 *1 (-321 *2)) (-4 *2 (-1128)) (-4 *2 (-757))))
((*1 *1 *2 *1)
- (-12 (-5 *2 (-1 (-85) *3 *3)) (|has| *1 (-6 -3992)) (-4 *1 (-321 *3))
+ (-12 (-5 *2 (-1 (-85) *3 *3)) (|has| *1 (-6 -3993)) (-4 *1 (-321 *3))
(-4 *3 (-1128)))))
(((*1 *2) (-12 (-4 *3 (-146)) (-5 *2 (-1178 *1)) (-4 *1 (-315 *3)))))
(((*1 *2 *1) (-12 (-4 *1 (-315 *2)) (-4 *2 (-146)))))
@@ -12009,8 +12012,8 @@
(-12 (-5 *3 (-1084 *4)) (-4 *4 (-298))
(-4 *2
(-13 (-342)
- (-10 -7 (-15 -3942 (*2 *4)) (-15 -2008 ((-831) *2))
- (-15 -2010 ((-1178 *2) (-831))) (-15 -3924 (*2 *2)))))
+ (-10 -7 (-15 -3943 (*2 *4)) (-15 -2009 ((-831) *2))
+ (-15 -2011 ((-1178 *2) (-831))) (-15 -3925 (*2 *2)))))
(-5 *1 (-305 *2 *4)))))
(((*1 *2 *3)
(-12 (-4 *4 (-298)) (-5 *2 (-870 (-1084 *4))) (-5 *1 (-304 *4))
@@ -12043,13 +12046,13 @@
((*1 *2 *3)
(-12 (-5 *3 (-1084 *4)) (-4 *4 (-298)) (-5 *2 (-85)) (-5 *1 (-304 *4)))))
(((*1 *2)
- (-12 (-5 *2 (-1178 (-584 (-2 (|:| -3398 (-818 *3)) (|:| -2398 (-1033))))))
+ (-12 (-5 *2 (-1178 (-584 (-2 (|:| -3399 (-818 *3)) (|:| -2399 (-1033))))))
(-5 *1 (-300 *3 *4)) (-14 *3 (-831)) (-14 *4 (-831))))
((*1 *2)
- (-12 (-5 *2 (-1178 (-584 (-2 (|:| -3398 *3) (|:| -2398 (-1033))))))
+ (-12 (-5 *2 (-1178 (-584 (-2 (|:| -3399 *3) (|:| -2399 (-1033))))))
(-5 *1 (-301 *3 *4)) (-4 *3 (-298)) (-14 *4 (-3 (-1084 *3) *2))))
((*1 *2)
- (-12 (-5 *2 (-1178 (-584 (-2 (|:| -3398 *3) (|:| -2398 (-1033))))))
+ (-12 (-5 *2 (-1178 (-584 (-2 (|:| -3399 *3) (|:| -2399 (-1033))))))
(-5 *1 (-302 *3 *4)) (-4 *3 (-298)) (-14 *4 (-831)))))
(((*1 *2)
(-12 (-5 *2 (-631 (-818 *3))) (-5 *1 (-300 *3 *4)) (-14 *3 (-831))
@@ -12057,23 +12060,23 @@
((*1 *2)
(-12 (-5 *2 (-631 *3)) (-5 *1 (-301 *3 *4)) (-4 *3 (-298))
(-14 *4
- (-3 (-1084 *3) (-1178 (-584 (-2 (|:| -3398 *3) (|:| -2398 (-1033)))))))))
+ (-3 (-1084 *3) (-1178 (-584 (-2 (|:| -3399 *3) (|:| -2399 (-1033)))))))))
((*1 *2)
(-12 (-5 *2 (-631 *3)) (-5 *1 (-302 *3 *4)) (-4 *3 (-298)) (-14 *4 (-831)))))
(((*1 *2 *3)
- (-12 (-5 *3 (-1178 (-584 (-2 (|:| -3398 *4) (|:| -2398 (-1033))))))
+ (-12 (-5 *3 (-1178 (-584 (-2 (|:| -3399 *4) (|:| -2399 (-1033))))))
(-4 *4 (-298)) (-5 *2 (-695)) (-5 *1 (-295 *4))))
((*1 *2)
(-12 (-5 *2 (-695)) (-5 *1 (-300 *3 *4)) (-14 *3 (-831)) (-14 *4 (-831))))
((*1 *2)
(-12 (-5 *2 (-695)) (-5 *1 (-301 *3 *4)) (-4 *3 (-298))
(-14 *4
- (-3 (-1084 *3) (-1178 (-584 (-2 (|:| -3398 *3) (|:| -2398 (-1033)))))))))
+ (-3 (-1084 *3) (-1178 (-584 (-2 (|:| -3399 *3) (|:| -2399 (-1033)))))))))
((*1 *2)
(-12 (-5 *2 (-695)) (-5 *1 (-302 *3 *4)) (-4 *3 (-298)) (-14 *4 (-831)))))
(((*1 *2)
(-12 (-4 *1 (-298))
- (-5 *2 (-584 (-2 (|:| -3728 (-484)) (|:| -2399 (-484))))))))
+ (-5 *2 (-584 (-2 (|:| -3729 (-484)) (|:| -2400 (-484))))))))
(((*1 *2 *3) (-12 (-4 *1 (-298)) (-5 *3 (-484)) (-5 *2 (-1101 (-831) (-695))))))
(((*1 *1) (-4 *1 (-298))))
(((*1 *2)
@@ -12081,18 +12084,18 @@
(((*1 *2 *3)
(-12 (-5 *3 (-831))
(-5 *2
- (-3 (-1084 *4) (-1178 (-584 (-2 (|:| -3398 *4) (|:| -2398 (-1033)))))))
+ (-3 (-1084 *4) (-1178 (-584 (-2 (|:| -3399 *4) (|:| -2399 (-1033)))))))
(-5 *1 (-295 *4)) (-4 *4 (-298)))))
(((*1 *2 *3)
(|partial| -12 (-5 *3 (-831))
- (-5 *2 (-1178 (-584 (-2 (|:| -3398 *4) (|:| -2398 (-1033))))))
+ (-5 *2 (-1178 (-584 (-2 (|:| -3399 *4) (|:| -2399 (-1033))))))
(-5 *1 (-295 *4)) (-4 *4 (-298)))))
(((*1 *2 *3)
- (-12 (-5 *3 (-1178 (-584 (-2 (|:| -3398 *4) (|:| -2398 (-1033))))))
+ (-12 (-5 *3 (-1178 (-584 (-2 (|:| -3399 *4) (|:| -2399 (-1033))))))
(-4 *4 (-298)) (-5 *2 (-631 *4)) (-5 *1 (-295 *4)))))
(((*1 *2 *3)
(-12 (-5 *3 (-1084 *4)) (-4 *4 (-298))
- (-5 *2 (-1178 (-584 (-2 (|:| -3398 *4) (|:| -2398 (-1033))))))
+ (-5 *2 (-1178 (-584 (-2 (|:| -3399 *4) (|:| -2399 (-1033))))))
(-5 *1 (-295 *4)))))
(((*1 *2 *3)
(-12 (-5 *3 (-1084 *4)) (-4 *4 (-298)) (-5 *2 (-870 (-1033)))
@@ -12367,7 +12370,7 @@
(|partial| -12 (-5 *2 (-2 (|:| |coef1| *1) (|:| |coef2| *1)))
(-4 *1 (-257))))
((*1 *2 *1 *1)
- (-12 (-5 *2 (-2 (|:| |coef1| *1) (|:| |coef2| *1) (|:| -2407 *1)))
+ (-12 (-5 *2 (-2 (|:| |coef1| *1) (|:| |coef2| *1) (|:| -2408 *1)))
(-4 *1 (-257)))))
(((*1 *2 *2 *1) (|partial| -12 (-5 *2 (-584 *1)) (-4 *1 (-257)))))
(((*1 *1 *1 *1) (-12 (-5 *1 (-248 *2)) (-4 *2 (-253)) (-4 *2 (-1128))))
@@ -12448,7 +12451,7 @@
(-12 (-5 *3 (-484)) (-4 *1 (-57 *2 *4 *5)) (-4 *2 (-1128)) (-4 *4 (-321 *2))
(-4 *5 (-321 *2))))
((*1 *2 *1 *3 *2)
- (-12 (|has| *1 (-6 -3992)) (-4 *1 (-243 *3 *2)) (-4 *3 (-1013))
+ (-12 (|has| *1 (-6 -3993)) (-4 *1 (-243 *3 *2)) (-4 *3 (-1013))
(-4 *2 (-1128)))))
(((*1 *2 *3 *4)
(-12 (-4 *4 (-311)) (-5 *2 (-584 (-1068 *4))) (-5 *1 (-240 *4 *5))
@@ -12459,7 +12462,7 @@
(((*1 *1 *1 *2) (-12 (-5 *2 (-1145 (-484))) (-4 *1 (-237 *3)) (-4 *3 (-1128))))
((*1 *1 *1 *2) (-12 (-5 *2 (-484)) (-4 *1 (-237 *3)) (-4 *3 (-1128)))))
(((*1 *1 *2 *1)
- (-12 (-5 *2 (-1 (-85) *3)) (|has| *1 (-6 -3991)) (-4 *1 (-193 *3))
+ (-12 (-5 *2 (-1 (-85) *3)) (|has| *1 (-6 -3992)) (-4 *1 (-193 *3))
(-4 *3 (-1013))))
((*1 *1 *2 *1) (-12 (-5 *2 (-1 (-85) *3)) (-4 *1 (-237 *3)) (-4 *3 (-1128)))))
(((*1 *1 *2 *3 *4)
@@ -12830,8 +12833,8 @@
(((*1 *1 *2) (-12 (-5 *2 (-584 *3)) (-4 *3 (-757)) (-5 *1 (-203 *3)))))
(((*1 *1 *1) (-12 (-4 *1 (-202 *2)) (-4 *2 (-1128)))))
(((*1 *1 *1) (-12 (-4 *1 (-202 *2)) (-4 *2 (-1128)))))
-(((*1 *1 *1 *1) (-12 (|has| *1 (-6 -3992)) (-4 *1 (-202 *2)) (-4 *2 (-1128)))))
-(((*1 *1 *1 *1) (-12 (|has| *1 (-6 -3992)) (-4 *1 (-202 *2)) (-4 *2 (-1128)))))
+(((*1 *1 *1 *1) (-12 (|has| *1 (-6 -3993)) (-4 *1 (-202 *2)) (-4 *2 (-1128)))))
+(((*1 *1 *1 *1) (-12 (|has| *1 (-6 -3993)) (-4 *1 (-202 *2)) (-4 *2 (-1128)))))
(((*1 *2 *3) (-12 (-5 *3 (-1072)) (-5 *2 (-484)) (-5 *1 (-199))))
((*1 *2 *3) (-12 (-5 *3 (-584 (-1072))) (-5 *2 (-484)) (-5 *1 (-199)))))
(((*1 *2 *3) (-12 (-5 *3 (-1072)) (-5 *2 (-1184)) (-5 *1 (-199))))
@@ -12904,13 +12907,13 @@
(((*1 *2 *2 *3 *2)
(-12 (-5 *3 (-695)) (-4 *4 (-298)) (-5 *1 (-170 *4 *2)) (-4 *2 (-1154 *4)))))
(((*1 *2 *3)
- (-12 (-4 *4 (-298)) (-5 *2 (-584 (-2 (|:| |deg| (-695)) (|:| -2573 *3))))
+ (-12 (-4 *4 (-298)) (-5 *2 (-584 (-2 (|:| |deg| (-695)) (|:| -2574 *3))))
(-5 *1 (-170 *4 *3)) (-4 *3 (-1154 *4)))))
(((*1 *2 *3 *4)
(-12 (-5 *4 (-85)) (-4 *5 (-298))
(-5 *2
(-2 (|:| |cont| *5)
- (|:| -1777 (-584 (-2 (|:| |irr| *3) (|:| -2393 (-484)))))))
+ (|:| -1777 (-584 (-2 (|:| |irr| *3) (|:| -2394 (-484)))))))
(-5 *1 (-170 *5 *3)) (-4 *3 (-1154 *5)))))
(((*1 *2 *3 *4)
(-12 (-5 *4 (-1 *2 *2)) (-4 *5 (-311)) (-4 *6 (-1154 (-347 *2)))
@@ -13127,7 +13130,7 @@
(((*1 *2 *3 *1)
(|partial| -12 (-5 *3 (-1 (-85) *2)) (-4 *1 (-124 *2)) (-4 *2 (-1128)))))
(((*1 *1 *1)
- (-12 (|has| *1 (-6 -3991)) (-4 *1 (-124 *2)) (-4 *2 (-1128))
+ (-12 (|has| *1 (-6 -3992)) (-4 *1 (-124 *2)) (-4 *2 (-1128))
(-4 *2 (-1013)))))
(((*1 *2 *3 *3)
(-12 (-4 *4 (-1133)) (-4 *5 (-1154 *4))
@@ -13140,7 +13143,7 @@
(-4 *3 (-1154 (-347 *4))))))
(((*1 *2 *3 *4)
(-12 (-5 *3 (-347 *6)) (-4 *5 (-1133)) (-4 *6 (-1154 *5))
- (-5 *2 (-2 (|:| -2399 (-695)) (|:| -3950 *3) (|:| |radicand| *6)))
+ (-5 *2 (-2 (|:| -2400 (-695)) (|:| -3951 *3) (|:| |radicand| *6)))
(-5 *1 (-121 *5 *6 *7)) (-5 *4 (-695)) (-4 *7 (-1154 *3)))))
(((*1 *2 *3)
(|partial| -12 (-4 *4 (-1133)) (-4 *5 (-1154 *4))
@@ -13148,7 +13151,7 @@
(-5 *1 (-121 *4 *5 *3)) (-4 *3 (-1154 (-347 *5))))))
(((*1 *2 *3)
(-12 (-4 *4 (-1133)) (-4 *5 (-1154 *4))
- (-5 *2 (-2 (|:| -3950 (-347 *5)) (|:| |poly| *3))) (-5 *1 (-121 *4 *5 *3))
+ (-5 *2 (-2 (|:| -3951 (-347 *5)) (|:| |poly| *3))) (-5 *1 (-121 *4 *5 *3))
(-4 *3 (-1154 (-347 *5))))))
(((*1 *2 *1) (-12 (-5 *2 (-695)) (-5 *1 (-117)))))
(((*1 *1 *2) (-12 (-5 *2 (-1072)) (-5 *1 (-117))))
@@ -13216,8 +13219,8 @@
((*1 *2 *2) (-12 (-5 *2 (-695)) (-5 *1 (-93 *3)) (-4 *3 (-1154 (-484))))))
(((*1 *2 *3) (-12 (-5 *2 (-85)) (-5 *1 (-93 *3)) (-4 *3 (-1154 (-484)))))
((*1 *2 *3 *2) (-12 (-5 *2 (-85)) (-5 *1 (-93 *3)) (-4 *3 (-1154 (-484))))))
-(((*1 *1 *1 *1) (-12 (|has| *1 (-6 -3992)) (-4 *1 (-92 *2)) (-4 *2 (-1128)))))
-(((*1 *1 *1 *1) (-12 (|has| *1 (-6 -3992)) (-4 *1 (-92 *2)) (-4 *2 (-1128)))))
+(((*1 *1 *1 *1) (-12 (|has| *1 (-6 -3993)) (-4 *1 (-92 *2)) (-4 *2 (-1128)))))
+(((*1 *1 *1 *1) (-12 (|has| *1 (-6 -3993)) (-4 *1 (-92 *2)) (-4 *2 (-1128)))))
(((*1 *2 *3)
(-12 (-4 *4 (-13 (-311) (-951 (-347 *2)))) (-5 *2 (-484)) (-5 *1 (-88 *4 *3))
(-4 *3 (-1154 *4)))))
@@ -13250,11 +13253,11 @@
(((*1 *2 *1) (-12 (-4 *1 (-76 *2)) (-4 *2 (-1128)))))
(((*1 *2 *1) (-12 (-4 *1 (-76 *2)) (-4 *2 (-1128)))))
(((*1 *2 *3)
- (-12 (|has| *2 (-6 (-3993 "*"))) (-4 *5 (-321 *2)) (-4 *6 (-321 *2))
+ (-12 (|has| *2 (-6 (-3994 "*"))) (-4 *5 (-321 *2)) (-4 *6 (-321 *2))
(-4 *2 (-962)) (-5 *1 (-74 *2 *3 *4 *5 *6)) (-4 *3 (-1154 *2))
(-4 *4 (-628 *2 *5 *6)))))
(((*1 *2 *3 *3)
- (-12 (|has| *2 (-6 (-3993 "*"))) (-4 *5 (-321 *2)) (-4 *6 (-321 *2))
+ (-12 (|has| *2 (-6 (-3994 "*"))) (-4 *5 (-321 *2)) (-4 *6 (-321 *2))
(-4 *2 (-962)) (-5 *1 (-74 *2 *3 *4 *5 *6)) (-4 *3 (-1154 *2))
(-4 *4 (-628 *2 *5 *6)))))
(((*1 *2 *3 *3)
@@ -13286,7 +13289,7 @@
(((*1 *2 *3 *4)
(-12 (-4 *5 (-311)) (-4 *5 (-495))
(-5 *2
- (-2 (|:| |minor| (-584 (-831))) (|:| -3263 *3)
+ (-2 (|:| |minor| (-584 (-831))) (|:| -3264 *3)
(|:| |minors| (-584 (-584 (-831)))) (|:| |ops| (-584 *3))))
(-5 *1 (-61 *5 *3)) (-5 *4 (-831)) (-4 *3 (-601 *5)))))
(((*1 *2 *3)
@@ -13362,84 +13365,84 @@
(-4 *5 (-495)) (-5 *1 (-41 *5 *2)) (-4 *2 (-361 *5))
(-4 *2
(-13 (-311) (-253)
- (-10 -8 (-15 -2996 ((-1038 *5 (-551 $)) $))
- (-15 -2995 ((-1038 *5 (-551 $)) $))
- (-15 -3942 ($ (-1038 *5 (-551 $))))))))))
+ (-10 -8 (-15 -2997 ((-1038 *5 (-551 $)) $))
+ (-15 -2996 ((-1038 *5 (-551 $)) $))
+ (-15 -3943 ($ (-1038 *5 (-551 $))))))))))
(((*1 *2 *2)
(-12 (-4 *3 (-13 (-389) (-951 (-484)))) (-4 *3 (-495)) (-5 *1 (-41 *3 *2))
(-4 *2 (-361 *3))
(-4 *2
(-13 (-311) (-253)
- (-10 -8 (-15 -2996 ((-1038 *3 (-551 $)) $))
- (-15 -2995 ((-1038 *3 (-551 $)) $))
- (-15 -3942 ($ (-1038 *3 (-551 $))))))))))
+ (-10 -8 (-15 -2997 ((-1038 *3 (-551 $)) $))
+ (-15 -2996 ((-1038 *3 (-551 $)) $))
+ (-15 -3943 ($ (-1038 *3 (-551 $))))))))))
(((*1 *2 *2)
(-12 (-4 *3 (-13 (-389) (-951 (-484)))) (-4 *3 (-495)) (-5 *1 (-41 *3 *2))
(-4 *2 (-361 *3))
(-4 *2
(-13 (-311) (-253)
- (-10 -8 (-15 -2996 ((-1038 *3 (-551 $)) $))
- (-15 -2995 ((-1038 *3 (-551 $)) $))
- (-15 -3942 ($ (-1038 *3 (-551 $))))))))))
+ (-10 -8 (-15 -2997 ((-1038 *3 (-551 $)) $))
+ (-15 -2996 ((-1038 *3 (-551 $)) $))
+ (-15 -3943 ($ (-1038 *3 (-551 $))))))))))
(((*1 *2 *2)
(-12 (-4 *3 (-13 (-389) (-951 (-484)))) (-4 *3 (-495)) (-5 *1 (-41 *3 *2))
(-4 *2 (-361 *3))
(-4 *2
(-13 (-311) (-253)
- (-10 -8 (-15 -2996 ((-1038 *3 (-551 $)) $))
- (-15 -2995 ((-1038 *3 (-551 $)) $))
- (-15 -3942 ($ (-1038 *3 (-551 $))))))))))
+ (-10 -8 (-15 -2997 ((-1038 *3 (-551 $)) $))
+ (-15 -2996 ((-1038 *3 (-551 $)) $))
+ (-15 -3943 ($ (-1038 *3 (-551 $))))))))))
(((*1 *2 *3)
(-12 (-4 *4 (-495)) (-5 *2 (-1084 *3)) (-5 *1 (-41 *4 *3))
(-4 *3
(-13 (-311) (-253)
- (-10 -8 (-15 -2996 ((-1038 *4 (-551 $)) $))
- (-15 -2995 ((-1038 *4 (-551 $)) $))
- (-15 -3942 ($ (-1038 *4 (-551 $))))))))))
+ (-10 -8 (-15 -2997 ((-1038 *4 (-551 $)) $))
+ (-15 -2996 ((-1038 *4 (-551 $)) $))
+ (-15 -3943 ($ (-1038 *4 (-551 $))))))))))
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