* algebra/indexedp.spad.pamphlet (IndexedProductTerm): New domain.

5 files changed, 18090 insertions, 18077 deletions

diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase
index 52405adb..887a25f4 100644
--- a/src/share/algebra/browse.daase
+++ b/src/share/algebra/browse.daase
@@ -1,12 +1,12 @@
 
-(1965419 . 3539125283)       
+(1961804 . 3576902405)       
 (-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."))) 
-((-3990 . T) (-3989 . T)) 
+((-3992 . T) (-3991 . 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}."))) 
-((-3981 . T) (-3987 . T) (-3982 . T) ((-3991 "*") . T) (-3983 . T) (-3984 . T) (-3986 . T)) 
+((-3983 . T) (-3989 . T) (-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . 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}."))) 
@@ -46,24 +46,24 @@ 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}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) 
-((-3986 . T) (-3984 . T) (-3983 . T) ((-3991 "*") . T) (-3982 . T) (-3987 . T) (-3981 . T)) 
+((-3988 . T) (-3986 . T) (-3985 . T) ((-3993 "*") . T) (-3984 . T) (-3989 . T) (-3983 . T)) 
 NIL 
 (-30) 
-((|constructor| (NIL "\\indented{1}{Plot a NON-SINGULAR plane algebraic curve \\spad{p}(\\spad{x},{}\\spad{y}) = 0.} Author: Clifton \\spad{J}. Williamson Date Created: Fall 1988 Date Last Updated: 27 April 1990 Keywords: algebraic curve,{} non-singular,{} plot Examples: References:")) (|refine| (($ $ (|DoubleFloat|)) "\\spad{refine(p,x)} \\undocumented{}")) (|makeSketch| (($ (|Polynomial| (|Integer|)) (|Symbol|) (|Symbol|) (|Segment| (|Fraction| (|Integer|))) (|Segment| (|Fraction| (|Integer|)))) "\\spad{makeSketch(p,x,y,a..b,c..d)} creates an ACPLOT of the curve \\spad{p = 0} in the region {\\em a <= x <= b, c <= y <= d}. More specifically,{} 'makeSketch' plots a non-singular algebraic curve \\spad{p = 0} in an rectangular region {\\em xMin <= x <= xMax},{} {\\em yMin <= y <= yMax}. The user inputs \\spad{makeSketch(p,x,y,xMin..xMax,yMin..yMax)}. Here \\spad{p} is a polynomial in the variables \\spad{x} and \\spad{y} with integer coefficients (\\spad{p} belongs to the domain \\spad{Polynomial Integer}). The case where \\spad{p} is a polynomial in only one of the variables is allowed. The variables \\spad{x} and \\spad{y} are input to specify the the coordinate axes. The horizontal axis is the \\spad{x}-axis and the vertical axis is the \\spad{y}-axis. The rational numbers xMin,{}...,{}yMax specify the boundaries of the region in which the curve is to be plotted."))) 
+((|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."))) 
 NIL 
 NIL 
 (-31) 
 ((|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 -3088) 
+(-32 R -3090) 
 ((|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 (-950 (-483))))) 
+((|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 -3989))) 
+((|HasAttribute| |#1| (QUOTE -3991))) 
 (-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}."))) 
-((-3989 . T) (-3990 . T)) 
+((-3991 . T) (-3992 . T)) 
 NIL 
 (-37 S R) 
 ((|constructor| (NIL "The category of associative algebras (modules which are themselves rings). \\blankline"))) 
@@ -82,20 +82,20 @@ NIL
 NIL 
 (-38 R) 
 ((|constructor| (NIL "The category of associative algebras (modules which are themselves rings). \\blankline"))) 
-((-3983 . T) (-3984 . T) (-3986 . T)) 
+((-3985 . T) (-3986 . T) (-3988 . 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 -3088 UP UPUP -2610) 
+(-40 -3090 UP UPUP -2612) 
 ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) 
-((-3982 |has| (-347 |#2|) (-311)) (-3987 |has| (-347 |#2|) (-311)) (-3981 |has| (-347 |#2|) (-311)) ((-3991 "*") . T) (-3983 . T) (-3984 . T) (-3986 . 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 (-809 (-1088))))) (-12 (|HasCategory| (-347 |#2|) (QUOTE (-298))) (|HasCategory| (-347 |#2|) (QUOTE (-809 (-1088)))))) (OR (-12 (|HasCategory| (-347 |#2|) (QUOTE (-311))) (|HasCategory| (-347 |#2|) (QUOTE (-809 (-1088))))) (-12 (|HasCategory| (-347 |#2|) (QUOTE (-311))) (|HasCategory| (-347 |#2|) (QUOTE (-811 (-1088)))))) (|HasCategory| (-347 |#2|) (QUOTE (-580 (-483)))) (OR (|HasCategory| (-347 |#2|) (QUOTE (-311))) (|HasCategory| (-347 |#2|) (QUOTE (-950 (-347 (-483)))))) (|HasCategory| (-347 |#2|) (QUOTE (-950 (-347 (-483))))) (|HasCategory| (-347 |#2|) (QUOTE (-950 (-483)))) (|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 (-811 (-1088))))) (-12 (|HasCategory| (-347 |#2|) (QUOTE (-190))) (|HasCategory| (-347 |#2|) (QUOTE (-311)))) (-12 (|HasCategory| (-347 |#2|) (QUOTE (-311))) (|HasCategory| (-347 |#2|) (QUOTE (-809 (-1088)))))) 
-(-41 R -3088) 
+((-3984 |has| (-347 |#2|) (-311)) (-3989 |has| (-347 |#2|) (-311)) (-3983 |has| (-347 |#2|) (-311)) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . 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) 
 ((|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| $)) $) "\\spad{numer(x)} \\undocumented"))) 
 NIL 
-((-12 (|HasCategory| |#1| (QUOTE (-389))) (|HasCategory| |#1| (QUOTE (-950 (-483)))) (|HasCategory| |#2| (|%list| (QUOTE -361) (|devaluate| |#1|))))) 
+((-12 (|HasCategory| |#1| (QUOTE (-389))) (|HasCategory| |#1| (QUOTE (-951 (-484)))) (|HasCategory| |#2| (|%list| (QUOTE -361) (|devaluate| |#1|))))) 
 (-42 OV E P) 
 ((|constructor| (NIL "This package factors multivariate polynomials over the domain of \\spadtype{AlgebraicNumber} by allowing the user to specify a list of algebraic numbers generating the particular extension to factor over.")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| |#3|)) (|SparseUnivariatePolynomial| |#3|) (|List| (|AlgebraicNumber|))) "\\spad{factor(p,lan)} factors the polynomial \\spad{p} over the extension generated by the algebraic numbers given by the list \\spad{lan}. \\spad{p} is presented as a univariate polynomial with multivariate coefficients.") (((|Factored| |#3|) |#3| (|List| (|AlgebraicNumber|))) "\\spad{factor(p,lan)} factors the polynomial \\spad{p} over the extension generated by the algebraic numbers given by the list \\spad{lan}."))) 
 NIL 
@@ -106,31 +106,31 @@ NIL
 ((|HasCategory| |#1| (QUOTE (-257)))) 
 (-44 R |n| |ls| |gamma|) 
 ((|constructor| (NIL "AlgebraGivenByStructuralConstants implements finite rank algebras over a commutative ring,{} given by the structural constants \\spad{gamma} with respect to a fixed basis \\spad{[a1,..,an]},{} where \\spad{gamma} is an \\spad{n}-vector of \\spad{n} by \\spad{n} matrices \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{ai * aj = gammaij1 * a1 + ... + gammaijn * an}. The symbols for the fixed basis have to be given as a list of symbols.")) (|coerce| (($ (|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."))) 
-((-3986 |has| |#1| (-494)) (-3984 . T) (-3983 . T)) 
-((|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-494)))) 
+((-3988 |has| |#1| (-495)) (-3986 . T) (-3985 . 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."))) 
-((-3989 . T) (-3990 . T)) 
-((OR (-12 (|HasCategory| (-2 (|:| -3854 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -259) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3854) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3854 |#1|) (|:| |entry| |#2|)) (QUOTE (-756)))) (-12 (|HasCategory| (-2 (|:| -3854 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -259) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3854) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3854 |#1|) (|:| |entry| |#2|)) (QUOTE (-1012))))) (OR (|HasCategory| (-2 (|:| -3854 |#1|) (|:| |entry| |#2|)) (QUOTE (-552 (-772)))) (|HasCategory| |#2| (QUOTE (-552 (-772))))) (|HasCategory| (-2 (|:| -3854 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-472)))) (-12 (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| |#2| (|%list| (QUOTE -259) (|devaluate| |#2|)))) (OR (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| (-2 (|:| -3854 |#1|) (|:| |entry| |#2|)) (QUOTE (-756))) (|HasCategory| (-2 (|:| -3854 |#1|) (|:| |entry| |#2|)) (QUOTE (-1012)))) (|HasCategory| (-2 (|:| -3854 |#1|) (|:| |entry| |#2|)) (QUOTE (-756))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| (-2 (|:| -3854 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3854 |#1|) (|:| |entry| |#2|)) (QUOTE (-756))) (|HasCategory| (-2 (|:| -3854 |#1|) (|:| |entry| |#2|)) (QUOTE (-1012)))) (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| (-483) (QUOTE (-756))) (|HasCategory| (-2 (|:| -3854 |#1|) (|:| |entry| |#2|)) (QUOTE (-1012))) (OR (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| (-2 (|:| -3854 |#1|) (|:| |entry| |#2|)) (QUOTE (-1012)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3854 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3854 |#1|) (|:| |entry| |#2|)) (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3854 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (-12 (|HasCategory| (-2 (|:| -3854 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -259) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3854) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3854 |#1|) (|:| |entry| |#2|)) (QUOTE (-1012))))) 
+((-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))))) 
 (-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| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-38 (-347 (-483))))) (|HasCategory| |#2| (QUOTE (-494))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-311)))) 
+((|HasCategory| |#2| (QUOTE (-38 (-347 (-484))))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-311)))) 
 (-47 R E) 
 ((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#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| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) 
-(((-3991 "*") |has| |#1| (-146)) (-3982 |has| |#1| (-494)) (-3983 . T) (-3984 . T) (-3986 . T)) 
+(((-3993 "*") |has| |#1| (-146)) (-3984 |has| |#1| (-495)) (-3985 . T) (-3986 . T) (-3988 . T)) 
 NIL 
 (-48) 
 ((|constructor| (NIL "Algebraic closure of the rational numbers,{} with mathematical =")) (|norm| (($ $ (|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}."))) 
-((-3981 . T) (-3987 . T) (-3982 . T) ((-3991 "*") . T) (-3983 . T) (-3984 . T) (-3986 . T)) 
-((|HasCategory| $ (QUOTE (-961))) (|HasCategory| $ (QUOTE (-950 (-483))))) 
+((-3983 . T) (-3989 . T) (-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . 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|)) $) "\\spad{parameters(f)} returns the list of parameters bound by `f'."))) 
 NIL 
 NIL 
 (-50 R |lVar|) 
 ((|constructor| (NIL "The domain of antisymmetric polynomials.")) (|map| (($ (|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}."))) 
-((-3986 . T)) 
+((-3988 . 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 -3088) 
+(-54 |Base| R -3090) 
 ((|constructor| (NIL "This package apply rewrite rules to expressions,{} calling the pattern matcher.")) (|localUnquote| ((|#3| |#3| (|List| (|Symbol|))) "\\spad{localUnquote(f,ls)} is a local function.")) (|applyRules| ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3| (|PositiveInteger|)) "\\spad{applyRules([r1,...,rn], expr, n)} applies the rules \\spad{r1},{}...,{}rn to \\spad{f} a most \\spad{n} times.") ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3|) "\\spad{applyRules([r1,...,rn], expr)} applies the rules \\spad{r1},{}...,{}rn to \\spad{f} an unlimited number of times,{} \\spadignore{i.e.} until none of \\spad{r1},{}...,{}rn is applicable to the expression."))) 
 NIL 
 NIL 
@@ -158,28 +158,28 @@ NIL
 NIL 
 (-57 R |Row| |Col|) 
 ((|constructor| (NIL "\\indented{1}{TwoDimensionalArrayCategory is a general array category which} allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and columns returned as objects of type Col. The index of the 'first' row may be obtained by calling the function 'minRowIndex'. The index of the 'first' column may be obtained by calling the function 'minColIndex'. The index of the first element of a 'Row' is the same as the index of the first column in an array and vice versa.")) (|map!| (($ (|Mapping| |#1| |#1|) $) "\\spad{map!(f,a)} assign \\spad{a(i,j)} to \\spad{f(a(i,j))} for all \\spad{i, j}")) (|map| (($ (|Mapping| |#1| |#1| |#1|) $ $ |#1|) "\\spad{map(f,a,b,r)} returns \\spad{c},{} where \\spad{c(i,j) = f(a(i,j),b(i,j))} when both \\spad{a(i,j)} and \\spad{b(i,j)} exist; else \\spad{c(i,j) = f(r, b(i,j))} when \\spad{a(i,j)} does not exist; else \\spad{c(i,j) = f(a(i,j),r)} when \\spad{b(i,j)} does not exist; otherwise \\spad{c(i,j) = f(r,r)}.") (($ (|Mapping| |#1| |#1| |#1|) $ $) "\\spad{map(f,a,b)} returns \\spad{c},{} where \\spad{c(i,j) = f(a(i,j),b(i,j))} for all \\spad{i, j}") (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,a)} returns \\spad{b},{} where \\spad{b(i,j) = f(a(i,j))} for all \\spad{i, j}")) (|setColumn!| (($ $ (|Integer|) |#3|) "\\spad{setColumn!(m,j,v)} sets to \\spad{j}th column of \\spad{m} to \\spad{v}")) (|setRow!| (($ $ (|Integer|) |#2|) "\\spad{setRow!(m,i,v)} sets to \\spad{i}th row of \\spad{m} to \\spad{v}")) (|qsetelt!| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\spad{qsetelt!(m,i,j,r)} sets the element in the \\spad{i}th row and \\spad{j}th column of \\spad{m} to \\spad{r} NO error check to determine if indices are in proper ranges")) (|setelt| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\spad{setelt(m,i,j,r)} sets the element in the \\spad{i}th row and \\spad{j}th column of \\spad{m} to \\spad{r} error check to determine if indices are in proper ranges")) (|parts| (((|List| |#1|) $) "\\spad{parts(m)} returns a list of the elements of \\spad{m} in row major order")) (|column| ((|#3| $ (|Integer|)) "\\spad{column(m,j)} returns the \\spad{j}th column of \\spad{m} error check to determine if index is in proper ranges")) (|row| ((|#2| $ (|Integer|)) "\\spad{row(m,i)} returns the \\spad{i}th row of \\spad{m} error check to determine if index is in proper ranges")) (|qelt| ((|#1| $ (|Integer|) (|Integer|)) "\\spad{qelt(m,i,j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the array \\spad{m} NO error check to determine if indices are in proper ranges")) (|elt| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\spad{elt(m,i,j,r)} returns the element in the \\spad{i}th row and \\spad{j}th column of the array \\spad{m},{} if \\spad{m} has an \\spad{i}th row and a \\spad{j}th column,{} and returns \\spad{r} otherwise") ((|#1| $ (|Integer|) (|Integer|)) "\\spad{elt(m,i,j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the array \\spad{m} error check to determine if indices are in proper ranges")) (|ncols| (((|NonNegativeInteger|) $) "\\spad{ncols(m)} returns the number of columns in the array \\spad{m}")) (|nrows| (((|NonNegativeInteger|) $) "\\spad{nrows(m)} returns the number of rows in the array \\spad{m}")) (|maxColIndex| (((|Integer|) $) "\\spad{maxColIndex(m)} returns the index of the 'last' column of the array \\spad{m}")) (|minColIndex| (((|Integer|) $) "\\spad{minColIndex(m)} returns the index of the 'first' column of the array \\spad{m}")) (|maxRowIndex| (((|Integer|) $) "\\spad{maxRowIndex(m)} returns the index of the 'last' row of the array \\spad{m}")) (|minRowIndex| (((|Integer|) $) "\\spad{minRowIndex(m)} returns the index of the 'first' row of the array \\spad{m}")) (|fill!| (($ $ |#1|) "\\spad{fill!(m,r)} fills \\spad{m} with \\spad{r}'s")) (|new| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|) "\\spad{new(m,n,r)} is an \\spad{m}-by-\\spad{n} array all of whose entries are \\spad{r}")) (|finiteAggregate| ((|attribute|) "two-dimensional arrays are finite")) (|shallowlyMutable| ((|attribute|) "one may destructively alter arrays"))) 
-((-3989 . T) (-3990 . T)) 
+((-3991 . T) (-3992 . 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}"))) 
-((-3990 . T) (-3989 . T)) 
-((OR (-12 (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-553 (-472)))) (OR (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| |#1| (QUOTE (-756))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| (-483) (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|))))) 
+((-3992 . T) (-3991 . 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),...]}."))) 
 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."))) 
-((-3989 . T) (-3990 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1012))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-72)))) 
+((-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 (-72)))) 
 (-61 R L) 
 ((|constructor| (NIL "\\spadtype{AssociatedEquations} provides functions to compute the associated equations needed for factoring operators")) (|associatedEquations| (((|Record| (|:| |minor| (|List| (|PositiveInteger|))) (|:| |eq| |#2|) (|:| |minors| (|List| (|List| (|PositiveInteger|)))) (|:| |ops| (|List| |#2|))) |#2| (|PositiveInteger|)) "\\spad{associatedEquations(op, m)} returns \\spad{[w, eq, lw, lop]} such that \\spad{eq(w) = 0} where \\spad{w} is the given minor,{} and \\spad{lw_i = lop_i(w)} for all the other minors.")) (|uncouplingMatrices| (((|Vector| (|Matrix| |#1|)) (|Matrix| |#1|)) "\\spad{uncouplingMatrices(M)} returns \\spad{[A_1,...,A_n]} such that if \\spad{y = [y_1,...,y_n]} is a solution of \\spad{y' = M y},{} then \\spad{[\\$y_j',y_j'',...,y_j^{(n)}\\$] = \\$A_j y\\$} for all \\spad{j}'s.")) (|associatedSystem| (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| (|List| (|PositiveInteger|))))) |#2| (|PositiveInteger|)) "\\spad{associatedSystem(op, m)} returns \\spad{[M,w]} such that the \\spad{m}-th associated equation system to \\spad{L} is \\spad{w' = M w}."))) 
 NIL 
 ((|HasCategory| |#1| (QUOTE (-311)))) 
 (-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}."))) 
-((-3989 . T) (-3990 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1012))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-72)))) 
+((-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 (-72)))) 
 (-63 S) 
 ((|constructor| (NIL "This is the category of Spad abstract syntax trees."))) 
 NIL 
@@ -202,11 +202,11 @@ NIL
 NIL 
 (-68) 
 ((|constructor| (NIL "This category exports the attributes in the AXIOM Library")) (|canonical| ((|attribute|) "\\spad{canonical} is \\spad{true} if and only if distinct elements have distinct data structures. For example,{} a domain of mathematical objects which has the \\spad{canonical} attribute means that two objects are mathematically equal if and only if their data structures are equal.")) (|multiplicativeValuation| ((|attribute|) "\\spad{multiplicativeValuation} implies \\spad{euclideanSize(a*b)=euclideanSize(a)*euclideanSize(b)}.")) (|additiveValuation| ((|attribute|) "\\spad{additiveValuation} implies \\spad{euclideanSize(a*b)=euclideanSize(a)+euclideanSize(b)}.")) (|noetherian| ((|attribute|) "\\spad{noetherian} is \\spad{true} if all of its ideals are finitely generated.")) (|central| ((|attribute|) "\\spad{central} is \\spad{true} if,{} given an algebra over a ring \\spad{R},{} the image of \\spad{R} is the center of the algebra,{} \\spadignore{i.e.} the set of members of the algebra which commute with all others is precisely the image of \\spad{R} in the algebra.")) (|partiallyOrderedSet| ((|attribute|) "\\spad{partiallyOrderedSet} is \\spad{true} if a set with \\spadop{<} which is transitive,{} but \\spad{not(a < b or a = b)} does not necessarily imply \\spad{b<a}.")) (|arbitraryPrecision| ((|attribute|) "\\spad{arbitraryPrecision} means the user can set the precision for subsequent calculations.")) (|canonicalsClosed| ((|attribute|) "\\spad{canonicalsClosed} is \\spad{true} if \\spad{unitCanonical(a)*unitCanonical(b) = unitCanonical(a*b)}.")) (|canonicalUnitNormal| ((|attribute|) "\\spad{canonicalUnitNormal} is \\spad{true} if we can choose a canonical representative for each class of associate elements,{} that is \\spad{associates?(a,b)} returns \\spad{true} if and only if \\spad{unitCanonical(a) = unitCanonical(b)}.")) (|noZeroDivisors| ((|attribute|) "\\spad{noZeroDivisors} is \\spad{true} if \\spad{x * y \\~~= 0} implies both \\spad{x} and \\spad{y} are non-zero.")) (|rightUnitary| ((|attribute|) "\\spad{rightUnitary} is \\spad{true} if \\spad{x * 1 = x} for all \\spad{x}.")) (|leftUnitary| ((|attribute|) "\\spad{leftUnitary} is \\spad{true} if \\spad{1 * x = x} for all \\spad{x}.")) (|unitsKnown| ((|attribute|) "\\spad{unitsKnown} is \\spad{true} if a monoid (a multiplicative semigroup with a 1) has \\spad{unitsKnown} means that the operation \\spadfun{recip} can only return \"failed\" if its argument is not a unit.")) (|shallowlyMutable| ((|attribute|) "\\spad{shallowlyMutable} is \\spad{true} if its values have immediate components that are updateable (mutable). Note: the properties of any component domain are irrevelant to the \\spad{shallowlyMutable} proper.")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} is \\spad{true} if it has an operation \\spad{\"*\": (D,D) -> D} which is commutative.")) (|finiteAggregate| ((|attribute|) "\\spad{finiteAggregate} is \\spad{true} if it is an aggregate with a finite number of elements."))) 
-((-3989 . T) ((-3991 "*") . T) (-3990 . T) (-3986 . T) (-3984 . T) (-3983 . T) (-3982 . T) (-3987 . T) (-3981 . T) (-3980 . T) (-3979 . T) (-3978 . T) (-3977 . T) (-3985 . T) (-3988 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-3976 . T)) 
+((-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)) 
 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}."))) 
-((-3986 . T)) 
+((-3988 . T)) 
 NIL 
 (-70 R UP) 
 ((|constructor| (NIL "This package provides balanced factorisations of polynomials.")) (|balancedFactorisation| (((|Factored| |#2|) |#2| (|List| |#2|)) "\\spad{balancedFactorisation(a, [b1,...,bn])} returns a factorisation \\spad{a = p1^e1 ... pm^em} such that each \\spad{pi} is balanced with respect to \\spad{[b1,...,bm]}.") (((|Factored| |#2|) |#2| |#2|) "\\spad{balancedFactorisation(a, b)} returns a factorisation \\spad{a = p1^e1 ... pm^em} such that each \\spad{pi} is balanced with respect to \\spad{b}."))) 
@@ -222,24 +222,24 @@ NIL
 NIL 
 (-73 S) 
 ((|constructor| (NIL "\\spadtype{BalancedBinaryTree(S)} is the domain of balanced binary trees (bbtree). A balanced binary tree of \\spad{2**k} leaves,{} for some \\spad{k > 0},{} is symmetric,{} that is,{} the left and right subtree of each interior node have identical shape. In general,{} the left and right subtree of a given node can differ by at most leaf node.")) (|mapDown!| (($ $ |#1| (|Mapping| (|List| |#1|) |#1| |#1| |#1|)) "\\spad{mapDown!(t,p,f)} returns \\spad{t} after traversing \\spad{t} in \"preorder\" (node then left then right) fashion replacing the successive interior nodes as follows. Let \\spad{l} and \\spad{r} denote the left and right subtrees of \\spad{t}. The root value \\spad{x} of \\spad{t} is replaced by \\spad{p}. Then \\spad{f}(value \\spad{l},{} value \\spad{r},{} \\spad{p}),{} where \\spad{l} and \\spad{r} denote the left and right subtrees of \\spad{t},{} is evaluated producing two values pl and pr. Then \\spad{mapDown!(l,pl,f)} and \\spad{mapDown!(l,pr,f)} are evaluated.") (($ $ |#1| (|Mapping| |#1| |#1| |#1|)) "\\spad{mapDown!(t,p,f)} returns \\spad{t} after traversing \\spad{t} in \"preorder\" (node then left then right) fashion replacing the successive interior nodes as follows. The root value \\spad{x} is replaced by \\spad{q} := \\spad{f}(\\spad{p},{}\\spad{x}). The mapDown!(\\spad{l},{}\\spad{q},{}\\spad{f}) and mapDown!(\\spad{r},{}\\spad{q},{}\\spad{f}) are evaluated for the left and right subtrees \\spad{l} and \\spad{r} of \\spad{t}.")) (|mapUp!| (($ $ $ (|Mapping| |#1| |#1| |#1| |#1| |#1|)) "\\spad{mapUp!(t,t1,f)} traverses \\spad{t} in an \"endorder\" (left then right then node) fashion returning \\spad{t} with the value at each successive interior node of \\spad{t} replaced by \\spad{f}(\\spad{l},{}\\spad{r},{}\\spad{l1},{}\\spad{r1}) where \\spad{l} and \\spad{r} are the values at the immediate left and right nodes. Values \\spad{l1} and \\spad{r1} are values at the corresponding nodes of a balanced binary tree \\spad{t1},{} of identical shape at \\spad{t}.") ((|#1| $ (|Mapping| |#1| |#1| |#1|)) "\\spad{mapUp!(t,f)} traverses balanced binary tree \\spad{t} in an \"endorder\" (left then right then node) fashion returning \\spad{t} with the value at each successive interior node of \\spad{t} replaced by \\spad{f}(\\spad{l},{}\\spad{r}) where \\spad{l} and \\spad{r} are the values at the immediate left and right nodes.")) (|setleaves!| (($ $ (|List| |#1|)) "\\spad{setleaves!(t, ls)} sets the leaves of \\spad{t} in left-to-right order to the elements of ls.")) (|balancedBinaryTree| (($ (|NonNegativeInteger|) |#1|) "\\spad{balancedBinaryTree(n, s)} creates a balanced binary tree with \\spad{n} nodes each with value \\spad{s}."))) 
-((-3989 . T) (-3990 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1012))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-72)))) 
+((-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 (-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 (-3991 "*")))) 
+((|HasAttribute| |#1| (QUOTE (-3993 "*")))) 
 (-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."))) 
-((-3990 . T)) 
+((-3992 . 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."))) 
-((-3981 . T) (-3987 . T) (-3982 . T) ((-3991 "*") . T) (-3983 . T) (-3984 . T) (-3986 . T)) 
-((|HasCategory| (-483) (QUOTE (-821))) (|HasCategory| (-483) (QUOTE (-950 (-1088)))) (|HasCategory| (-483) (QUOTE (-118))) (|HasCategory| (-483) (QUOTE (-120))) (|HasCategory| (-483) (QUOTE (-553 (-472)))) (|HasCategory| (-483) (QUOTE (-933))) (|HasCategory| (-483) (QUOTE (-740))) (|HasCategory| (-483) (QUOTE (-756))) (OR (|HasCategory| (-483) (QUOTE (-740))) (|HasCategory| (-483) (QUOTE (-756)))) (|HasCategory| (-483) (QUOTE (-950 (-483)))) (|HasCategory| (-483) (QUOTE (-1064))) (|HasCategory| (-483) (QUOTE (-796 (-327)))) (|HasCategory| (-483) (QUOTE (-796 (-483)))) (|HasCategory| (-483) (QUOTE (-553 (-800 (-327))))) (|HasCategory| (-483) (QUOTE (-553 (-800 (-483))))) (|HasCategory| (-483) (QUOTE (-189))) (|HasCategory| (-483) (QUOTE (-811 (-1088)))) (|HasCategory| (-483) (QUOTE (-190))) (|HasCategory| (-483) (QUOTE (-809 (-1088)))) (|HasCategory| (-483) (QUOTE (-452 (-1088) (-483)))) (|HasCategory| (-483) (QUOTE (-259 (-483)))) (|HasCategory| (-483) (QUOTE (-241 (-483) (-483)))) (|HasCategory| (-483) (QUOTE (-257))) (|HasCategory| (-483) (QUOTE (-482))) (|HasCategory| (-483) (QUOTE (-580 (-483)))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-483) (QUOTE (-821)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-483) (QUOTE (-821)))) (|HasCategory| (-483) (QUOTE (-118))))) 
+((-3983 . T) (-3989 . T) (-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . 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|) $) "\\spad{name(b)} returns the name of binding \\spad{b}"))) 
 NIL 
@@ -254,11 +254,11 @@ NIL
 NIL 
 (-81) 
 ((|constructor| (NIL "\\spadtype{Bits} provides logical functions for Indexed Bits.")) (|bits| (($ (|NonNegativeInteger|) (|Boolean|)) "\\spad{bits(n,b)} creates bits with \\spad{n} values of \\spad{b}"))) 
-((-3990 . T) (-3989 . T)) 
-((-12 (|HasCategory| (-85) (QUOTE (-259 (-85)))) (|HasCategory| (-85) (QUOTE (-1012)))) (|HasCategory| (-85) (QUOTE (-553 (-472)))) (|HasCategory| (-85) (QUOTE (-756))) (|HasCategory| (-483) (QUOTE (-756))) (|HasCategory| (-85) (QUOTE (-1012))) (|HasCategory| (-85) (QUOTE (-552 (-772)))) (|HasCategory| (-85) (QUOTE (-72)))) 
+((-3992 . T) (-3991 . 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}"))) 
-((-3984 . T) (-3983 . T)) 
+((-3986 . T) (-3985 . 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 -3088 UP) 
+(-88 -3090 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}."))) 
-((-3982 . T) ((-3991 "*") . T) (-3983 . T) (-3984 . T) (-3986 . T)) 
+((-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . 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}."))) 
-((-3981 . T) (-3987 . T) (-3982 . T) ((-3991 "*") . T) (-3983 . T) (-3984 . T) (-3986 . T)) 
-((|HasCategory| (-89 |#1|) (QUOTE (-821))) (|HasCategory| (-89 |#1|) (QUOTE (-950 (-1088)))) (|HasCategory| (-89 |#1|) (QUOTE (-118))) (|HasCategory| (-89 |#1|) (QUOTE (-120))) (|HasCategory| (-89 |#1|) (QUOTE (-553 (-472)))) (|HasCategory| (-89 |#1|) (QUOTE (-933))) (|HasCategory| (-89 |#1|) (QUOTE (-740))) (|HasCategory| (-89 |#1|) (QUOTE (-756))) (OR (|HasCategory| (-89 |#1|) (QUOTE (-740))) (|HasCategory| (-89 |#1|) (QUOTE (-756)))) (|HasCategory| (-89 |#1|) (QUOTE (-950 (-483)))) (|HasCategory| (-89 |#1|) (QUOTE (-1064))) (|HasCategory| (-89 |#1|) (QUOTE (-796 (-327)))) (|HasCategory| (-89 |#1|) (QUOTE (-796 (-483)))) (|HasCategory| (-89 |#1|) (QUOTE (-553 (-800 (-327))))) (|HasCategory| (-89 |#1|) (QUOTE (-553 (-800 (-483))))) (|HasCategory| (-89 |#1|) (QUOTE (-580 (-483)))) (|HasCategory| (-89 |#1|) (QUOTE (-189))) (|HasCategory| (-89 |#1|) (QUOTE (-811 (-1088)))) (|HasCategory| (-89 |#1|) (QUOTE (-190))) (|HasCategory| (-89 |#1|) (QUOTE (-809 (-1088)))) (|HasCategory| (-89 |#1|) (|%list| (QUOTE -452) (QUOTE (-1088)) (|%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 (-482))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-89 |#1|) (QUOTE (-821)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-89 |#1|) (QUOTE (-821)))) (|HasCategory| (-89 |#1|) (QUOTE (-118))))) 
+((-3983 . T) (-3989 . T) (-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . 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| (($ $) "\\spad{left(u)} returns the left child."))) 
 NIL 
-((|HasAttribute| |#1| (QUOTE -3990))) 
+((|HasAttribute| |#1| (QUOTE -3992))) 
 (-92 S) 
 ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "right" $) "\\spad{setelt(a,\"right\",b)} (also written \\axiom{\\spad{b} . right := \\spad{b}}) is equivalent to \\axiom{setright!(a,{}\\spad{b})}.") (($ $ "left" $) "\\spad{setelt(a,\"left\",b)} (also written \\axiom{a . left := \\spad{b}}) is equivalent to \\axiom{setleft!(a,{}\\spad{b})}.")) (|right| (($ $) "\\spad{right(a)} returns the right child.")) (|elt| (($ $ "right") "\\spad{elt(a,\"right\")} (also written: \\axiom{a . right}) is equivalent to \\axiom{right(a)}.") (($ $ "left") "\\spad{elt(u,\"left\")} (also written: \\axiom{a . left}) is equivalent to \\axiom{left(a)}.")) (|left| (($ $) "\\spad{left(u)} returns the left child."))) 
 NIL 
@@ -306,15 +306,15 @@ NIL
 NIL 
 (-94 S) 
 ((|constructor| (NIL "BinarySearchTree(\\spad{S}) is the domain of a binary trees where elements are ordered across the tree. A binary search tree is either empty or has a value which is an \\spad{S},{} and a right and left which are both BinaryTree(\\spad{S}) Elements are ordered across the tree.")) (|split| (((|Record| (|:| |less| $) (|:| |greater| $)) |#1| $) "\\spad{split(x,b)} splits binary tree \\spad{b} into two trees,{} one with elements greater than \\spad{x},{} the other with elements less than \\spad{x}.")) (|insertRoot!| (($ |#1| $) "\\spad{insertRoot!(x,b)} inserts element \\spad{x} as a root of binary search tree \\spad{b}.")) (|insert!| (($ |#1| $) "\\spad{insert!(x,b)} inserts element \\spad{x} as leaves into binary search tree \\spad{b}.")) (|binarySearchTree| (($ (|List| |#1|)) "\\spad{binarySearchTree(l)} \\undocumented"))) 
-((-3989 . T) (-3990 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1012))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-72)))) 
+((-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 (-72)))) 
 (-95 S) 
 ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}."))) 
 NIL 
 NIL 
 (-96) 
 ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}."))) 
-((-3990 . T) (-3989 . T)) 
+((-3992 . T) (-3991 . T)) 
 NIL 
 (-97 A S) 
 ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#2| $) "\\spad{node(left,v,right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) 
@@ -322,24 +322,24 @@ NIL
 NIL 
 (-98 S) 
 ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#1| $) "\\spad{node(left,v,right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) 
-((-3989 . T) (-3990 . T)) 
+((-3991 . T) (-3992 . T)) 
 NIL 
 (-99 S) 
 ((|constructor| (NIL "\\spadtype{BinaryTournament(S)} is the domain of binary trees where elements are ordered down the tree. A binary search tree is either empty or is a node containing a \\spadfun{value} of type \\spad{S},{} and a \\spadfun{right} and a \\spadfun{left} which are both \\spadtype{BinaryTree(S)}")) (|insert!| (($ |#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."))) 
-((-3989 . T) (-3990 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1012))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-72)))) 
+((-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 (-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."))) 
-((-3989 . T) (-3990 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1012))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-72)))) 
+((-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 (-72)))) 
 (-101) 
 ((|constructor| (NIL "Byte is the datatype of 8-bit sized unsigned integer values.")) (|sample| (($) "\\spad{sample} gives a sample datum of type Byte.")) (|bitior| (($ $ $) "bitor(\\spad{x},{}\\spad{y}) returns the bitwise `inclusive or' of `x' and `y'.")) (|bitand| (($ $ $) "\\spad{bitand(x,y)} returns the bitwise `and' of `x' and `y'.")) (|byte| (($ (|NonNegativeInteger|)) "\\spad{byte(x)} injects the unsigned integer value `v' into the Byte algebra. `v' must be non-negative and less than 256."))) 
 NIL 
 NIL 
 (-102) 
 ((|constructor| (NIL "ByteBuffer provides datatype for buffers of bytes. This domain differs from PrimitiveArray Byte in that it is not as rigid as PrimitiveArray Byte. That is,{} the typical use of ByteBuffer is to pre-allocate a vector of Byte of some capacity `n'. The array can then store up to `n' bytes. The actual interesting bytes count (the length of the buffer) is therefore different from the capacity. The length is no more than the capacity,{} but it can be set dynamically as needed. This functionality is used for example when reading bytes from input/output devices where we use buffers to transfer data in and out of the system. Note: a value of type ByteBuffer is 0-based indexed,{} as opposed \\indented{6}{Vector,{} but not unlike PrimitiveArray Byte.}")) (|finiteAggregate| ((|attribute|) "A ByteBuffer object is a finite aggregate")) (|setLength!| (((|NonNegativeInteger|) $ (|NonNegativeInteger|)) "\\spad{setLength!(buf,n)} sets the number of active bytes in the `buf'. Error if `n' is more than the capacity.")) (|capacity| (((|NonNegativeInteger|) $) "\\spad{capacity(buf)} returns the pre-allocated maximum size of `buf'.")) (|byteBuffer| (($ (|NonNegativeInteger|)) "\\spad{byteBuffer(n)} creates a buffer of capacity \\spad{n},{} and length 0."))) 
-((-3990 . T) (-3989 . T)) 
-((OR (-12 (|HasCategory| (-101) (QUOTE (-259 (-101)))) (|HasCategory| (-101) (QUOTE (-756)))) (-12 (|HasCategory| (-101) (QUOTE (-259 (-101)))) (|HasCategory| (-101) (QUOTE (-1012))))) (|HasCategory| (-101) (QUOTE (-552 (-772)))) (|HasCategory| (-101) (QUOTE (-553 (-472)))) (OR (|HasCategory| (-101) (QUOTE (-756))) (|HasCategory| (-101) (QUOTE (-1012)))) (|HasCategory| (-101) (QUOTE (-756))) (OR (|HasCategory| (-101) (QUOTE (-72))) (|HasCategory| (-101) (QUOTE (-756))) (|HasCategory| (-101) (QUOTE (-1012)))) (|HasCategory| (-483) (QUOTE (-756))) (|HasCategory| (-101) (QUOTE (-1012))) (|HasCategory| (-101) (QUOTE (-72))) (-12 (|HasCategory| (-101) (QUOTE (-259 (-101)))) (|HasCategory| (-101) (QUOTE (-1012))))) 
+((-3992 . T) (-3991 . 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"))) 
 NIL 
@@ -358,13 +358,13 @@ NIL
 NIL 
 (-107) 
 ((|constructor| (NIL "Members of the domain CardinalNumber are values indicating the cardinality of sets,{} both finite and infinite. Arithmetic operations are defined on cardinal numbers as follows. \\blankline If \\spad{x = \\#X} and \\spad{y = \\#Y} then \\indented{2}{\\spad{x+y\\space{2}= \\#(X+Y)}\\space{3}\\tab{30}disjoint union} \\indented{2}{\\spad{x-y\\space{2}= \\#(X-Y)}\\space{3}\\tab{30}relative complement} \\indented{2}{\\spad{x*y\\space{2}= \\#(X*Y)}\\space{3}\\tab{30}cartesian product} \\indented{2}{\\spad{x**y = \\#(X**Y)}\\space{2}\\tab{30}\\spad{X**Y = \\{g| g:Y->X\\}}} \\blankline The non-negative integers have a natural construction as cardinals \\indented{2}{\\spad{0 = \\#\\{\\}},{} \\spad{1 = \\{0\\}},{} \\spad{2 = \\{0, 1\\}},{} ...,{} \\spad{n = \\{i| 0 <= i < n\\}}.} \\blankline That \\spad{0} acts as a zero for the multiplication of cardinals is equivalent to the axiom of choice. \\blankline The generalized continuum hypothesis asserts \\center{\\spad{2**Aleph i = Aleph(i+1)}} and is independent of the axioms of set theory [Goedel 1940]. \\blankline Three commonly encountered cardinal numbers are \\indented{3}{\\spad{a = \\#Z}\\space{7}\\tab{30}countable infinity} \\indented{3}{\\spad{c = \\#R}\\space{7}\\tab{30}the continuum} \\indented{3}{\\spad{f = \\#\\{g| g:[0,1]->R\\}}} \\blankline In this domain,{} these values are obtained using \\indented{3}{\\spad{a := Aleph 0},{} \\spad{c := 2**a},{} \\spad{f := 2**c}.} \\blankline")) (|generalizedContinuumHypothesisAssumed| (((|Boolean|) (|Boolean|)) "\\spad{generalizedContinuumHypothesisAssumed(bool)} is used to dictate whether the hypothesis is to be assumed.")) (|generalizedContinuumHypothesisAssumed?| (((|Boolean|)) "\\spad{generalizedContinuumHypothesisAssumed?()} tests if the hypothesis is currently assumed.")) (|countable?| (((|Boolean|) $) "\\spad{countable?(\\spad{a})} determines whether \\spad{a} is a countable cardinal,{} \\spadignore{i.e.} an integer or \\spad{Aleph 0}.")) (|finite?| (((|Boolean|) $) "\\spad{finite?(\\spad{a})} determines whether \\spad{a} is a finite cardinal,{} \\spadignore{i.e.} an integer.")) (|Aleph| (($ (|NonNegativeInteger|)) "\\spad{Aleph(n)} provides the named (infinite) cardinal number.")) (** (($ $ $) "\\spad{x**y} returns \\spad{\\#(X**Y)} where \\spad{X**Y} is defined \\indented{1}{as \\spad{\\{g| g:Y->X\\}}.}")) (- (((|Union| $ "failed") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,D) -> D} which is commutative."))) 
-(((-3991 "*") . T)) 
+(((-3993 "*") . T)) 
 NIL 
-(-108 |minix| -2617 R) 
+(-108 |minix| -2619 R) 
 ((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\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|) $) "\\spad{rank(t)} returns the tensorial rank of \\spad{t} (that is,{} the number of indices). This is the same as the graded module degree."))) 
 NIL 
 NIL 
-(-109 |minix| -2617 S T$) 
+(-109 |minix| -2619 S T$) 
 ((|constructor| (NIL "This package provides functions to enable conversion of tensors given conversion of the components.")) (|map| (((|CartesianTensor| |#1| |#2| |#4|) (|Mapping| |#4| |#3|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{map(f,ts)} does a componentwise conversion of the tensor \\spad{ts} to a tensor with components of type \\spad{T}.")) (|reshape| (((|CartesianTensor| |#1| |#2| |#4|) (|List| |#4|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{reshape(lt,ts)} organizes the list of components \\spad{lt} into a tensor with the same shape as \\spad{ts}."))) 
 NIL 
 NIL 
@@ -386,8 +386,8 @@ NIL
 NIL 
 (-114) 
 ((|constructor| (NIL "This domain allows classes of characters to be defined and manipulated efficiently.")) (|alphanumeric| (($) "\\spad{alphanumeric()} returns the class of all characters for which \\spadfunFrom{alphanumeric?}{Character} is \\spad{true}.")) (|alphabetic| (($) "\\spad{alphabetic()} returns the class of all characters for which \\spadfunFrom{alphabetic?}{Character} is \\spad{true}.")) (|lowerCase| (($) "\\spad{lowerCase()} returns the class of all characters for which \\spadfunFrom{lowerCase?}{Character} is \\spad{true}.")) (|upperCase| (($) "\\spad{upperCase()} returns the class of all characters for which \\spadfunFrom{upperCase?}{Character} is \\spad{true}.")) (|hexDigit| (($) "\\spad{hexDigit()} returns the class of all characters for which \\spadfunFrom{hexDigit?}{Character} is \\spad{true}.")) (|digit| (($) "\\spad{digit()} returns the class of all characters for which \\spadfunFrom{digit?}{Character} is \\spad{true}.")) (|charClass| (($ (|List| (|Character|))) "\\spad{charClass(l)} creates a character class which contains exactly the characters given in the list \\spad{l}.") (($ (|String|)) "\\spad{charClass(s)} creates a character class which contains exactly the characters given in the string \\spad{s}."))) 
-((-3989 . T) (-3979 . T) (-3990 . T)) 
-((OR (-12 (|HasCategory| (-117) (QUOTE (-259 (-117)))) (|HasCategory| (-117) (QUOTE (-317)))) (-12 (|HasCategory| (-117) (QUOTE (-259 (-117)))) (|HasCategory| (-117) (QUOTE (-1012))))) (|HasCategory| (-117) (QUOTE (-553 (-472)))) (|HasCategory| (-117) (QUOTE (-317))) (|HasCategory| (-117) (QUOTE (-756))) (|HasCategory| (-117) (QUOTE (-1012))) (|HasCategory| (-117) (QUOTE (-552 (-772)))) (|HasCategory| (-117) (QUOTE (-72))) (-12 (|HasCategory| (-117) (QUOTE (-259 (-117)))) (|HasCategory| (-117) (QUOTE (-1012))))) 
+((-3991 . T) (-3981 . T) (-3992 . 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."))) 
 NIL 
@@ -402,7 +402,7 @@ NIL
 NIL 
 (-118) 
 ((|constructor| (NIL "Rings of Characteristic Non Zero")) (|charthRoot| (((|Maybe| $) $) "\\spad{charthRoot(x)} returns the \\spad{p}th root of \\spad{x} where \\spad{p} is the characteristic of the ring."))) 
-((-3986 . T)) 
+((-3988 . 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."))) 
-((-3986 . T)) 
+((-3988 . T)) 
 NIL 
-(-121 -3088 UP UPUP) 
+(-121 -3090 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 (-553 (-472)))) (|HasCategory| |#2| (QUOTE (-1012))) (|HasAttribute| |#1| (QUOTE -3989))) 
+((|HasCategory| |#2| (QUOTE (-554 (-473)))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasAttribute| |#1| (QUOTE -3991))) 
 (-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."))) 
-((-3984 . T) (-3983 . T) (-3986 . T)) 
+((-3986 . T) (-3985 . T) (-3988 . 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 -3088) 
+(-131 R -3090) 
 ((|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 (-821))) (|HasCategory| |#2| (QUOTE (-482))) (|HasCategory| |#2| (QUOTE (-915))) (|HasCategory| |#2| (QUOTE (-1113))) (|HasCategory| |#2| (QUOTE (-972))) (|HasCategory| |#2| (QUOTE (-933))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-553 (-472)))) (|HasCategory| |#2| (QUOTE (-311))) (|HasAttribute| |#2| (QUOTE -3985)) (|HasAttribute| |#2| (QUOTE -3988)) (|HasCategory| |#2| (QUOTE (-257))) (|HasCategory| |#2| (QUOTE (-494)))) 
+((|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)))) 
 (-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})"))) 
-((-3982 OR (|has| |#1| (-494)) (-12 (|has| |#1| (-257)) (|has| |#1| (-821)))) (-3987 |has| |#1| (-311)) (-3981 |has| |#1| (-311)) (-3985 |has| |#1| (-6 -3985)) (-3988 |has| |#1| (-6 -3988)) (-1373 . T) ((-3991 "*") . T) (-3983 . T) (-3984 . T) (-3986 . T)) 
+((-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)) 
 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}."))) 
-((-3982 OR (|has| |#1| (-494)) (-12 (|has| |#1| (-257)) (|has| |#1| (-821)))) (-3987 |has| |#1| (-311)) (-3981 |has| |#1| (-311)) (-3985 |has| |#1| (-6 -3985)) (-3988 |has| |#1| (-6 -3988)) (-1373 . T) ((-3991 "*") . T) (-3983 . T) (-3984 . T) (-3986 . T)) 
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+((-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)) 
+((|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-298))) (OR (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-298)))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-317))) (OR (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-298)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-311)))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-298)))) (|HasCategory| |#1| (QUOTE (-810 (-1089)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-810 (-1089))))) (|HasCategory| |#1| (QUOTE (-812 (-1089))))) (|HasCategory| |#1| (QUOTE (-581 (-484)))) (OR (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-951 (-347 (-484)))))) (|HasCategory| |#1| (QUOTE (-951 (-347 (-484))))) (|HasCategory| |#1| (QUOTE (-951 (-484)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-257))) (|HasCategory| |#1| (QUOTE (-822)))) (-12 (|HasCategory| |#1| (QUOTE (-298))) (|HasCategory| |#1| (QUOTE (-822)))) (|HasCategory| |#1| (QUOTE (-311)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-257))) (|HasCategory| |#1| (QUOTE (-822)))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-822)))) (-12 (|HasCategory| |#1| (QUOTE (-298))) (|HasCategory| |#1| (QUOTE (-822))))) (OR (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-495)))) (-12 (|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| |#1| (QUOTE (-1114)))) (|HasCategory| |#1| (QUOTE (-1114))) (|HasCategory| |#1| (QUOTE (-934))) (|HasCategory| |#1| (QUOTE (-554 (-473)))) (OR (|HasCategory| |#1| (QUOTE (-257))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-298))) (|HasCategory| |#1| (QUOTE (-495)))) (OR (|HasCategory| |#1| (QUOTE (-257))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-298)))) (|HasCategory| |#1| (QUOTE (-554 (-801 (-327))))) (|HasCategory| |#1| (QUOTE (-554 (-801 (-484))))) (|HasCategory| |#1| (QUOTE (-797 (-327)))) (|HasCategory| |#1| (QUOTE (-797 (-484)))) (|HasCategory| |#1| (|%list| (QUOTE -453) (QUOTE (-1089)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -241) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-973))) (-12 (|HasCategory| |#1| (QUOTE (-973))) (|HasCategory| |#1| (QUOTE (-1114)))) (|HasCategory| |#1| (QUOTE (-483))) (|HasCategory| |#1| (QUOTE (-257))) (|HasCategory| |#1| (QUOTE (-822))) (OR (-12 (|HasCategory| |#1| (QUOTE (-257))) (|HasCategory| |#1| (QUOTE (-822)))) (|HasCategory| |#1| (QUOTE (-311)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-257))) (|HasCategory| |#1| (QUOTE (-822)))) (|HasCategory| |#1| (QUOTE (-495)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-311)))) (|HasCategory| |#1| (QUOTE (-189)))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-812 (-1089)))) (|HasCategory| |#1| (QUOTE (-190))) (-12 (|HasCategory| |#1| (QUOTE (-257))) (|HasCategory| |#1| (QUOTE (-822)))) (|HasAttribute| |#1| (QUOTE -3987)) (|HasAttribute| |#1| (QUOTE -3990)) (-12 (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-311)))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-812 (-1089))))) (-12 (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-311)))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-810 (-1089))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-257))) (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-298)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-257))) (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) 
 (-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."))) 
-(((-3991 "*") . T) (-3983 . T) (-3984 . T) (-3986 . T)) 
+(((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . 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}."))) 
-(((-3991 "*") . T) (-3982 . T) (-3987 . T) (-3981 . T) (-3983 . T) (-3984 . T) (-3986 . T)) 
+(((-3993 "*") . T) (-3984 . T) (-3989 . T) (-3983 . T) (-3985 . T) (-3986 . T) (-3988 . T)) 
 NIL 
 (-149) 
 ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. A `Contour' a list of bindings making up a `virtual scope'.")) (|findBinding| (((|Maybe| (|Binding|)) (|Identifier|) $) "\\spad{findBinding(c,n)} returns the first binding associated with `n'. Otherwise `nothing.")) (|push| (($ (|Binding|) $) "\\spad{push(c,b)} augments the contour with binding `b'.")) (|bindings| (((|List| (|Binding|)) $) "\\spad{bindings(c)} returns the list of bindings in countour \\spad{c}."))) 
@@ -539,7 +539,7 @@ NIL
 (-152 R S CS) 
 ((|constructor| (NIL "This package supports matching patterns involving complex expressions")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(cexpr, pat, res)} matches the pattern \\spad{pat} to the complex expression \\spad{cexpr}. res contains the variables of \\spad{pat} which are already matched and their matches."))) 
 NIL 
-((|HasCategory| (-857 |#2|) (|%list| (QUOTE -796) (|devaluate| |#1|)))) 
+((|HasCategory| (-858 |#2|) (|%list| (QUOTE -797) (|devaluate| |#1|)))) 
 (-153 R) 
 ((|constructor| (NIL "This package \\undocumented{}")) (|multiEuclideanTree| (((|List| |#1|) (|List| |#1|) |#1|) "\\spad{multiEuclideanTree(l,r)} \\undocumented{}")) (|chineseRemainder| (((|List| |#1|) (|List| (|List| |#1|)) (|List| |#1|)) "\\spad{chineseRemainder(llv,lm)} returns a list of values,{} each of which corresponds to the Chinese remainder of the associated element of \\axiom{\\spad{llv}} and axiom{\\spad{lm}}. This is more efficient than applying chineseRemainder several times.") ((|#1| (|List| |#1|) (|List| |#1|)) "\\spad{chineseRemainder(lv,lm)} returns a value \\axiom{\\spad{v}} such that,{} if \\spad{x} is \\axiom{\\spad{lv}.\\spad{i}} modulo \\axiom{\\spad{lm}.\\spad{i}} for all \\axiom{\\spad{i}},{} then \\spad{x} is \\axiom{\\spad{v}} modulo \\axiom{\\spad{lm}(1)*lm(2)*...*lm(\\spad{n})}.")) (|modTree| (((|List| |#1|) |#1| (|List| |#1|)) "\\spad{modTree(r,l)} \\undocumented{}"))) 
 NIL 
@@ -576,7 +576,7 @@ NIL
 ((|constructor| (NIL "This domain enumerates the three kinds of constructors available in OpenAxiom: category constructors,{} domain constructors,{} and package constructors.")) (|package| (($) "`package' is the kind of package constructors.")) (|domain| (($) "`domain' is the kind of domain constructors")) (|category| (($) "`category' is the kind of category constructors"))) 
 NIL 
 NIL 
-(-162 R -3088) 
+(-162 R -3090) 
 ((|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 -3088 UP UPUP R) 
+(-169 -3090 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 -3088 FP) 
+(-170 -3090 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."))) 
-((-3981 . T) (-3987 . T) (-3982 . T) ((-3991 "*") . T) (-3983 . T) (-3984 . T) (-3986 . T)) 
-((|HasCategory| (-483) (QUOTE (-821))) (|HasCategory| (-483) (QUOTE (-950 (-1088)))) (|HasCategory| (-483) (QUOTE (-118))) (|HasCategory| (-483) (QUOTE (-120))) (|HasCategory| (-483) (QUOTE (-553 (-472)))) (|HasCategory| (-483) (QUOTE (-933))) (|HasCategory| (-483) (QUOTE (-740))) (|HasCategory| (-483) (QUOTE (-756))) (OR (|HasCategory| (-483) (QUOTE (-740))) (|HasCategory| (-483) (QUOTE (-756)))) (|HasCategory| (-483) (QUOTE (-950 (-483)))) (|HasCategory| (-483) (QUOTE (-1064))) (|HasCategory| (-483) (QUOTE (-796 (-327)))) (|HasCategory| (-483) (QUOTE (-796 (-483)))) (|HasCategory| (-483) (QUOTE (-553 (-800 (-327))))) (|HasCategory| (-483) (QUOTE (-553 (-800 (-483))))) (|HasCategory| (-483) (QUOTE (-189))) (|HasCategory| (-483) (QUOTE (-811 (-1088)))) (|HasCategory| (-483) (QUOTE (-190))) (|HasCategory| (-483) (QUOTE (-809 (-1088)))) (|HasCategory| (-483) (QUOTE (-452 (-1088) (-483)))) (|HasCategory| (-483) (QUOTE (-259 (-483)))) (|HasCategory| (-483) (QUOTE (-241 (-483) (-483)))) (|HasCategory| (-483) (QUOTE (-257))) (|HasCategory| (-483) (QUOTE (-482))) (|HasCategory| (-483) (QUOTE (-580 (-483)))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-483) (QUOTE (-821)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-483) (QUOTE (-821)))) (|HasCategory| (-483) (QUOTE (-118))))) 
+((-3983 . T) (-3989 . T) (-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . 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|) $) "\\spad{head(d)} returns the head of the definition `d'. This is a list of identifiers starting with the name of the operation followed by the name of the parameters,{} if any."))) 
 NIL 
 NIL 
-(-173 R -3088) 
+(-173 R -3090) 
 ((|constructor| (NIL "\\spadtype{ElementaryFunctionDefiniteIntegration} provides functions to compute definite integrals of elementary functions.")) (|innerint| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| #1="failed") (|:| |pole| #2="potentialPole")) |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{innerint(f, x, a, b, ignore?)} should be local but conditional")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| #1#) (|:| |pole| #2#)) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|)) (|String|)) "\\spad{integrate(f, x = a..b, \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| #1#) (|:| |pole| #2#)) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|))) "\\spad{integrate(f, x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}."))) 
 NIL 
 NIL 
@@ -634,19 +634,19 @@ NIL
 NIL 
 (-176 S) 
 ((|constructor| (NIL "Linked list implementation of a Dequeue")) (|dequeue| (($ (|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}."))) 
-((-3989 . T) (-3990 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1012))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-72)))) 
+((-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 (-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}."))) 
-((-3986 . T)) 
+((-3988 . T)) 
 NIL 
-(-178 R -3088) 
+(-178 R -3090) 
 ((|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}."))) 
-((-3764 . T) (-3981 . T) (-3987 . T) (-3982 . T) ((-3991 "*") . T) (-3983 . T) (-3984 . T) (-3986 . T)) 
+((-3766 . T) (-3983 . T) (-3989 . T) (-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . 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}"))) 
-((-3989 . T) (-3990 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1012))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-257))) (|HasCategory| |#1| (QUOTE (-494))) (|HasAttribute| |#1| (QUOTE (-3991 "*"))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-72)))) 
+((-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)))) 
 (-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."))) 
-((-3990 . T)) 
+((-3992 . 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 \\%."))) 
-((-3986 . T)) 
+((-3988 . 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| $) "\\spad{differentiate x} compute the derivative of \\spad{x}."))) 
@@ -678,7 +678,7 @@ NIL
 NIL 
 (-187 R) 
 ((|constructor| (NIL "An \\spad{R}-module equipped with a distinguised differential operator. If \\spad{R} is a differential ring,{} then differentiation on the module should extend differentiation on the differential ring \\spad{R}. The latter can be the null operator. In that case,{} the differentiation operator on the module is just an \\spad{R}-linear operator. For that reason,{} we do not require that the ring \\spad{R} be a DifferentialRing; \\blankline"))) 
-((-3984 . T) (-3983 . T)) 
+((-3986 . T) (-3985 . T)) 
 NIL 
 (-188 S) 
 ((|constructor| (NIL "This category is like \\spadtype{DifferentialDomain} where the target of the differentiation operator is the same as its source.")) (D (($ $ (|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"))) 
-((-3986 . T)) 
+((-3988 . 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 -3989))) 
+((|HasAttribute| |#1| (QUOTE -3991))) 
 (-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}."))) 
-((-3990 . T)) 
+((-3992 . T)) 
 NIL 
 (-194) 
 ((|constructor| (NIL "any solution of a homogeneous linear Diophantine equation can be represented as a sum of minimal solutions,{} which form a \"basis\" (a minimal solution cannot be represented as a nontrivial sum of solutions) in the case of an inhomogeneous linear Diophantine equation,{} each solution is the sum of a inhomogeneous solution and any number of homogeneous solutions therefore,{} it suffices to compute two sets: \\indented{3}{1. all minimal inhomogeneous solutions} \\indented{3}{2. all minimal homogeneous solutions} the algorithm implemented is a completion procedure,{} which enumerates all solutions in a recursive depth-first-search it can be seen as finding monotone paths in a graph for more details see Reference")) (|dioSolve| (((|Record| (|:| |varOrder| (|List| (|Symbol|))) (|:| |inhom| (|Union| (|List| (|Vector| (|NonNegativeInteger|))) "failed")) (|:| |hom| (|List| (|Vector| (|NonNegativeInteger|))))) (|Equation| (|Polynomial| (|Integer|)))) "\\spad{dioSolve(u)} computes a basis of all minimal solutions for linear homogeneous Diophantine equation \\spad{u},{} then all minimal solutions of inhomogeneous equation"))) 
 NIL 
 NIL 
-(-195 S -2617 R) 
+(-195 S -2619 R) 
 ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (|dot| ((|#3| $ $) "\\spad{dot(x,y)} computes the inner product of the vectors \\spad{x} and \\spad{y}.")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#3|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim.")) (|finiteAggregate| ((|attribute|) "attribute to indicate an aggregate of finite size"))) 
 NIL 
-((|HasCategory| |#3| (QUOTE (-311))) (|HasCategory| |#3| (QUOTE (-717))) (|HasCategory| |#3| (QUOTE (-756))) (|HasAttribute| |#3| (QUOTE -3986)) (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-317))) (|HasCategory| |#3| (QUOTE (-663))) (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-104))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-961))) (|HasCategory| |#3| (QUOTE (-1012)))) 
-(-196 -2617 R) 
+((|HasCategory| |#3| (QUOTE (-311))) (|HasCategory| |#3| (QUOTE (-718))) (|HasCategory| |#3| (QUOTE (-757))) (|HasAttribute| |#3| (QUOTE -3988)) (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-317))) (|HasCategory| |#3| (QUOTE (-664))) (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-104))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-962))) (|HasCategory| |#3| (QUOTE (-1013)))) 
+(-196 -2619 R) 
 ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (|dot| ((|#2| $ $) "\\spad{dot(x,y)} computes the inner product of the vectors \\spad{x} and \\spad{y}.")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#2|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim.")) (|finiteAggregate| ((|attribute|) "attribute to indicate an aggregate of finite size"))) 
-((-3983 |has| |#2| (-961)) (-3984 |has| |#2| (-961)) (-3986 |has| |#2| (-6 -3986)) (-3989 . T)) 
+((-3985 |has| |#2| (-962)) (-3986 |has| |#2| (-962)) (-3988 |has| |#2| (-6 -3988)) (-3991 . T)) 
 NIL 
-(-197 -2617 R) 
+(-197 -2619 R) 
 ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying component type. This contrasts with simple vectors in that the members can be viewed as having constant length. Thus many categorical properties can by lifted from the underlying component type. Component extraction operations are provided but no updating operations. Thus new direct product elements can either be created by converting vector elements using the \\spadfun{directProduct} function or by taking appropriate linear combinations of basis vectors provided by the \\spad{unitVector} operation."))) 
-((-3983 |has| |#2| (-961)) (-3984 |has| |#2| (-961)) (-3986 |has| |#2| (-6 -3986)) (-3989 . T)) 
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+(-198 -2619 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}."))) 
-((-3982 . T) (-3983 . T) (-3984 . T) (-3986 . T)) 
+((-3984 . T) (-3985 . T) (-3986 . T) (-3988 . 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."))) 
@@ -742,20 +742,20 @@ NIL
 NIL 
 (-203 S) 
 ((|constructor| (NIL "This domain provides some nice functions on lists")) (|elt| (((|NonNegativeInteger|) $ "count") "\\axiom{\\spad{l}.\"count\"} returns the number of elements in \\axiom{\\spad{l}}.") (($ $ "sort") "\\axiom{\\spad{l}.sort} returns \\axiom{\\spad{l}} with elements sorted. Note: \\axiom{\\spad{l}.sort = sort(\\spad{l})}") (($ $ "unique") "\\axiom{\\spad{l}.unique} returns \\axiom{\\spad{l}} with duplicates removed. Note: \\axiom{\\spad{l}.unique = removeDuplicates(\\spad{l})}.")) (|datalist| (($ (|List| |#1|)) "\\spad{datalist(l)} creates a datalist from \\spad{l}"))) 
-((-3990 . T) (-3989 . T)) 
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+((-3992 . T) (-3991 . T)) 
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 (-204 M) 
 ((|constructor| (NIL "DiscreteLogarithmPackage implements help functions for discrete logarithms in monoids using small cyclic groups.")) (|shanksDiscLogAlgorithm| (((|Union| (|NonNegativeInteger|) "failed") |#1| |#1| (|NonNegativeInteger|)) "\\spad{shanksDiscLogAlgorithm(b,a,p)} computes \\spad{s} with \\spad{b**s = a} for assuming that \\spad{a} and \\spad{b} are elements in a 'small' cyclic group of order \\spad{p} by Shank's algorithm. Note: this is a subroutine of the function \\spadfun{discreteLog}.")) (** ((|#1| |#1| (|Integer|)) "\\spad{x ** n} returns \\spad{x} raised to the integer power \\spad{n}"))) 
 NIL 
 NIL 
 (-205 R) 
 ((|constructor| (NIL "Category of modules that extend differential rings. \\blankline"))) 
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 NIL 
 (-206 |vl| R) 
 ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is lexicographic specified by the variable list parameter with the most significant variable first in the list.")) (|reorder| (($ $ (|List| (|Integer|))) "\\spad{reorder(p, perm)} applies the permutation perm to the variables in a polynomial and returns the new correctly ordered polynomial"))) 
-(((-3991 "*") |has| |#2| (-146)) (-3982 |has| |#2| (-494)) (-3987 |has| |#2| (-6 -3987)) (-3984 . T) (-3983 . T) (-3986 . T)) 
-((|HasCategory| |#2| (QUOTE (-821))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-389))) (|HasCategory| |#2| (QUOTE (-494))) (|HasCategory| |#2| (QUOTE (-821)))) (OR (|HasCategory| |#2| (QUOTE (-389))) (|HasCategory| |#2| (QUOTE (-494))) (|HasCategory| |#2| (QUOTE (-821)))) (OR (|HasCategory| |#2| (QUOTE (-389))) (|HasCategory| |#2| (QUOTE (-821)))) (|HasCategory| |#2| (QUOTE (-494))) (|HasCategory| |#2| (QUOTE (-146))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-494)))) (-12 (|HasCategory| |#2| (QUOTE (-796 (-327)))) (|HasCategory| (-773 |#1|) (QUOTE (-796 (-327))))) (-12 (|HasCategory| |#2| (QUOTE (-796 (-483)))) (|HasCategory| (-773 |#1|) (QUOTE (-796 (-483))))) (-12 (|HasCategory| |#2| (QUOTE (-553 (-800 (-327))))) (|HasCategory| (-773 |#1|) (QUOTE (-553 (-800 (-327)))))) (-12 (|HasCategory| |#2| (QUOTE (-553 (-800 (-483))))) (|HasCategory| (-773 |#1|) (QUOTE (-553 (-800 (-483)))))) (-12 (|HasCategory| |#2| (QUOTE (-553 (-472)))) (|HasCategory| (-773 |#1|) (QUOTE (-553 (-472))))) (|HasCategory| |#2| (QUOTE (-580 (-483)))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-38 (-347 (-483))))) (|HasCategory| |#2| (QUOTE (-950 (-483)))) (OR (|HasCategory| |#2| (QUOTE (-38 (-347 (-483))))) (|HasCategory| |#2| (QUOTE (-950 (-347 (-483)))))) (|HasCategory| |#2| (QUOTE (-950 (-347 (-483))))) (|HasCategory| |#2| (QUOTE (-311))) (|HasAttribute| |#2| (QUOTE -3987)) (|HasCategory| |#2| (QUOTE (-389))) (-12 (|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#2| (QUOTE (-118))))) 
+(((-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))))) 
 (-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."))) 
-((-3986 OR (-2558 (|has| |#4| (-961)) (|has| |#4| (-190))) (|has| |#4| (-6 -3986)) (-2558 (|has| |#4| (-961)) (|has| |#4| (-809 (-1088))))) (-3983 |has| |#4| (-961)) (-3984 |has| |#4| (-961)) (-3989 . T)) 
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(|HasCategory| |#4| (|%list| (QUOTE -259) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-1012))) (|HasCategory| |#4| (|%list| (QUOTE -259) (|devaluate| |#4|))))) (|HasCategory| |#4| (QUOTE (-311))) (OR (|HasCategory| |#4| (QUOTE (-146))) (|HasCategory| |#4| (QUOTE (-311))) (|HasCategory| |#4| (QUOTE (-961)))) (OR (|HasCategory| |#4| (QUOTE (-146))) (|HasCategory| |#4| (QUOTE (-311)))) (|HasCategory| |#4| (QUOTE (-961))) (|HasCategory| |#4| (QUOTE (-663))) (|HasCategory| |#4| (QUOTE (-717))) (OR (|HasCategory| |#4| (QUOTE (-717))) (|HasCategory| |#4| (QUOTE (-756)))) (|HasCategory| |#4| (QUOTE (-756))) (|HasCategory| |#4| (QUOTE (-317))) (OR (-12 (|HasCategory| |#4| (QUOTE (-146))) (|HasCategory| |#4| (QUOTE (-580 (-483))))) (-12 (|HasCategory| |#4| (QUOTE (-190))) (|HasCategory| |#4| (QUOTE (-580 (-483))))) (-12 (|HasCategory| |#4| (QUOTE (-311))) (|HasCategory| |#4| (QUOTE (-580 (-483))))) (-12 (|HasCategory| |#4| (QUOTE (-580 (-483)))) (|HasCategory| |#4| (QUOTE (-809 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(-317))) (|HasCategory| |#4| (QUOTE (-950 (-347 (-483)))))) (-12 (|HasCategory| |#4| (QUOTE (-663))) (|HasCategory| |#4| (QUOTE (-950 (-347 (-483)))))) (-12 (|HasCategory| |#4| (QUOTE (-717))) (|HasCategory| |#4| (QUOTE (-950 (-347 (-483)))))) (-12 (|HasCategory| |#4| (QUOTE (-756))) (|HasCategory| |#4| (QUOTE (-950 (-347 (-483)))))) (-12 (|HasCategory| |#4| (QUOTE (-809 (-1088)))) (|HasCategory| |#4| (QUOTE (-950 (-347 (-483)))))) (-12 (|HasCategory| |#4| (QUOTE (-950 (-347 (-483))))) (|HasCategory| |#4| (QUOTE (-961)))) (-12 (|HasCategory| |#4| (QUOTE (-950 (-347 (-483))))) (|HasCategory| |#4| (QUOTE (-1012))))) (OR (-12 (|HasCategory| |#4| (QUOTE (-21))) (|HasCategory| |#4| (QUOTE (-950 (-483))))) (-12 (|HasCategory| |#4| (QUOTE (-146))) (|HasCategory| |#4| (QUOTE (-950 (-483))))) (-12 (|HasCategory| |#4| (QUOTE (-190))) (|HasCategory| |#4| (QUOTE (-950 (-483))))) (-12 (|HasCategory| |#4| (QUOTE (-717))) (|HasCategory| |#4| (QUOTE (-950 (-483))))) (-12 (|HasCategory| |#4| (QUOTE (-756))) (|HasCategory| |#4| (QUOTE (-950 (-483))))) (-12 (|HasCategory| |#4| (QUOTE (-809 (-1088)))) (|HasCategory| |#4| (QUOTE (-950 (-483))))) (-12 (|HasCategory| |#4| (QUOTE (-950 (-483)))) (|HasCategory| |#4| (QUOTE (-1012)))) (-12 (|HasCategory| |#4| (QUOTE (-311))) (|HasCategory| |#4| (QUOTE (-950 (-483))))) (-12 (|HasCategory| |#4| (QUOTE (-317))) (|HasCategory| |#4| (QUOTE (-950 (-483))))) (-12 (|HasCategory| |#4| (QUOTE (-663))) (|HasCategory| |#4| (QUOTE (-950 (-483))))) (|HasCategory| |#4| (QUOTE (-961)))) (OR (-12 (|HasCategory| |#4| (QUOTE (-21))) (|HasCategory| |#4| (QUOTE (-950 (-483))))) (-12 (|HasCategory| |#4| (QUOTE (-146))) (|HasCategory| |#4| (QUOTE (-950 (-483))))) (-12 (|HasCategory| |#4| (QUOTE (-190))) (|HasCategory| |#4| (QUOTE (-950 (-483))))) (-12 (|HasCategory| |#4| (QUOTE (-717))) (|HasCategory| |#4| (QUOTE (-950 (-483))))) (-12 (|HasCategory| |#4| (QUOTE (-756))) (|HasCategory| |#4| (QUOTE (-950 (-483))))) (-12 (|HasCategory| |#4| (QUOTE (-809 (-1088)))) 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(QUOTE (-1012)))) (OR (-12 (|HasCategory| |#4| (QUOTE (-950 (-483)))) (|HasCategory| |#4| (QUOTE (-1012)))) (|HasCategory| |#4| (QUOTE (-961)))) (-12 (|HasCategory| |#4| (QUOTE (-950 (-347 (-483))))) (|HasCategory| |#4| (QUOTE (-1012)))) (OR (-12 (|HasCategory| |#4| (QUOTE (-809 (-1088)))) (|HasCategory| |#4| (QUOTE (-961)))) (|HasAttribute| |#4| (QUOTE -3986)) (-12 (|HasCategory| |#4| (QUOTE (-190))) (|HasCategory| |#4| (QUOTE (-961))))) (-12 (|HasCategory| |#4| (QUOTE (-189))) (|HasCategory| |#4| (QUOTE (-961)))) (-12 (|HasCategory| |#4| (QUOTE (-811 (-1088)))) (|HasCategory| |#4| (QUOTE (-961)))) (|HasCategory| |#4| (QUOTE (-146))) (|HasCategory| |#4| (QUOTE (-21))) (|HasCategory| |#4| (QUOTE (-23))) (|HasCategory| |#4| (QUOTE (-104))) (|HasCategory| |#4| (QUOTE (-25))) (|HasCategory| |#4| (QUOTE (-552 (-772)))) (|HasCategory| |#4| (QUOTE (-72))) (-12 (|HasCategory| |#4| (QUOTE (-1012))) (|HasCategory| |#4| (|%list| (QUOTE -259) (|devaluate| |#4|))))) 
+((-3988 OR (-2560 (|has| |#4| (-962)) (|has| |#4| (-190))) (|has| |#4| (-6 -3988)) (-2560 (|has| |#4| (-962)) (|has| |#4| (-810 (-1089))))) (-3985 |has| |#4| (-962)) (-3986 |has| |#4| (-962)) (-3991 . T)) 
+((OR (-12 (|HasCategory| |#4| (QUOTE (-21))) (|HasCategory| |#4| (|%list| (QUOTE -259) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-146))) (|HasCategory| |#4| (|%list| (QUOTE -259) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-190))) (|HasCategory| |#4| (|%list| (QUOTE -259) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-311))) (|HasCategory| |#4| (|%list| (QUOTE -259) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-317))) (|HasCategory| |#4| (|%list| (QUOTE -259) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-664))) (|HasCategory| |#4| (|%list| (QUOTE -259) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-718))) (|HasCategory| |#4| (|%list| (QUOTE -259) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-757))) (|HasCategory| |#4| (|%list| (QUOTE -259) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-810 (-1089)))) (|HasCategory| |#4| (|%list| (QUOTE -259) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-962))) (|HasCategory| |#4| (|%list| (QUOTE -259) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-1013))) (|HasCategory| |#4| (|%list| (QUOTE -259) (|devaluate| |#4|))))) (|HasCategory| |#4| (QUOTE (-311))) (OR (|HasCategory| |#4| (QUOTE (-146))) (|HasCategory| |#4| (QUOTE (-311))) (|HasCategory| |#4| (QUOTE (-962)))) (OR (|HasCategory| |#4| (QUOTE (-146))) (|HasCategory| |#4| (QUOTE (-311)))) (|HasCategory| |#4| (QUOTE (-962))) (|HasCategory| |#4| (QUOTE (-664))) (|HasCategory| |#4| (QUOTE (-718))) (OR (|HasCategory| |#4| (QUOTE (-718))) (|HasCategory| |#4| (QUOTE (-757)))) (|HasCategory| |#4| (QUOTE (-757))) (|HasCategory| |#4| (QUOTE (-317))) (OR (-12 (|HasCategory| |#4| (QUOTE (-146))) (|HasCategory| |#4| (QUOTE (-581 (-484))))) (-12 (|HasCategory| |#4| (QUOTE (-190))) (|HasCategory| |#4| (QUOTE (-581 (-484))))) (-12 (|HasCategory| |#4| (QUOTE (-311))) (|HasCategory| |#4| (QUOTE (-581 (-484))))) (-12 (|HasCategory| |#4| (QUOTE (-581 (-484)))) (|HasCategory| |#4| (QUOTE (-810 (-1089))))) (-12 (|HasCategory| |#4| (QUOTE (-581 (-484)))) (|HasCategory| |#4| (QUOTE (-962))))) (|HasCategory| |#4| (QUOTE (-810 (-1089)))) (OR (|HasCategory| |#4| (QUOTE (-190))) (|HasCategory| |#4| (QUOTE (-810 (-1089)))) (|HasCategory| |#4| (QUOTE (-962)))) (|HasCategory| |#4| (QUOTE (-190))) (OR (|HasCategory| |#4| (QUOTE (-190))) (-12 (|HasCategory| |#4| (QUOTE (-189))) (|HasCategory| |#4| (QUOTE (-962))))) (OR (-12 (|HasCategory| |#4| (QUOTE (-812 (-1089)))) (|HasCategory| |#4| (QUOTE (-962)))) (|HasCategory| |#4| (QUOTE (-810 (-1089))))) (|HasCategory| |#4| (QUOTE (-1013))) (OR (-12 (|HasCategory| |#4| (QUOTE (-21))) (|HasCategory| |#4| (QUOTE (-951 (-347 (-484)))))) (-12 (|HasCategory| |#4| (QUOTE (-146))) (|HasCategory| |#4| (QUOTE (-951 (-347 (-484)))))) (-12 (|HasCategory| |#4| (QUOTE (-190))) (|HasCategory| |#4| (QUOTE (-951 (-347 (-484)))))) (-12 (|HasCategory| |#4| (QUOTE (-311))) (|HasCategory| |#4| (QUOTE (-951 (-347 (-484)))))) (-12 (|HasCategory| |#4| (QUOTE (-317))) (|HasCategory| |#4| (QUOTE (-951 (-347 (-484)))))) (-12 (|HasCategory| |#4| (QUOTE (-664))) (|HasCategory| |#4| (QUOTE (-951 (-347 (-484)))))) (-12 (|HasCategory| |#4| (QUOTE (-718))) (|HasCategory| |#4| (QUOTE (-951 (-347 (-484)))))) (-12 (|HasCategory| |#4| (QUOTE (-757))) (|HasCategory| |#4| (QUOTE (-951 (-347 (-484)))))) (-12 (|HasCategory| |#4| (QUOTE (-810 (-1089)))) (|HasCategory| |#4| (QUOTE (-951 (-347 (-484)))))) (-12 (|HasCategory| |#4| (QUOTE (-951 (-347 (-484))))) (|HasCategory| |#4| (QUOTE (-962)))) (-12 (|HasCategory| |#4| (QUOTE (-951 (-347 (-484))))) (|HasCategory| |#4| (QUOTE (-1013))))) (OR (-12 (|HasCategory| |#4| (QUOTE (-21))) (|HasCategory| |#4| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#4| (QUOTE (-146))) (|HasCategory| |#4| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#4| (QUOTE (-190))) (|HasCategory| |#4| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#4| (QUOTE (-718))) (|HasCategory| |#4| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#4| (QUOTE (-757))) (|HasCategory| |#4| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#4| (QUOTE (-810 (-1089)))) (|HasCategory| |#4| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#4| (QUOTE (-951 (-484)))) (|HasCategory| |#4| (QUOTE (-1013)))) (-12 (|HasCategory| |#4| (QUOTE (-311))) (|HasCategory| |#4| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#4| (QUOTE (-317))) (|HasCategory| |#4| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#4| (QUOTE (-664))) (|HasCategory| |#4| (QUOTE (-951 (-484))))) (|HasCategory| |#4| (QUOTE (-962)))) (OR (-12 (|HasCategory| |#4| (QUOTE (-21))) (|HasCategory| |#4| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#4| (QUOTE (-146))) (|HasCategory| |#4| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#4| (QUOTE (-190))) (|HasCategory| |#4| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#4| (QUOTE (-718))) (|HasCategory| |#4| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#4| (QUOTE (-757))) (|HasCategory| |#4| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#4| (QUOTE (-810 (-1089)))) (|HasCategory| |#4| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#4| (QUOTE (-951 (-484)))) (|HasCategory| |#4| (QUOTE (-1013)))) (-12 (|HasCategory| |#4| (QUOTE (-311))) (|HasCategory| |#4| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#4| (QUOTE (-317))) (|HasCategory| |#4| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#4| (QUOTE (-664))) (|HasCategory| |#4| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#4| (QUOTE (-951 (-484)))) (|HasCategory| |#4| (QUOTE (-962))))) (|HasCategory| (-484) (QUOTE (-757))) (-12 (|HasCategory| |#4| (QUOTE (-581 (-484)))) (|HasCategory| |#4| (QUOTE (-962)))) (OR (-12 (|HasCategory| |#4| (QUOTE (-810 (-1089)))) (|HasCategory| |#4| (QUOTE (-962)))) (-12 (|HasCategory| |#4| (QUOTE (-812 (-1089)))) (|HasCategory| |#4| (QUOTE (-962))))) (OR (-12 (|HasCategory| |#4| (QUOTE (-190))) (|HasCategory| |#4| (QUOTE (-962)))) (-12 (|HasCategory| |#4| (QUOTE (-189))) (|HasCategory| |#4| (QUOTE (-962))))) (-12 (|HasCategory| |#4| (QUOTE (-951 (-484)))) (|HasCategory| |#4| (QUOTE (-1013)))) (OR (-12 (|HasCategory| |#4| (QUOTE (-951 (-484)))) (|HasCategory| |#4| (QUOTE (-1013)))) (|HasCategory| |#4| (QUOTE (-962)))) (-12 (|HasCategory| |#4| (QUOTE (-951 (-347 (-484))))) (|HasCategory| |#4| (QUOTE (-1013)))) (OR (-12 (|HasCategory| |#4| (QUOTE (-810 (-1089)))) (|HasCategory| |#4| (QUOTE (-962)))) (|HasAttribute| |#4| (QUOTE -3988)) (-12 (|HasCategory| |#4| (QUOTE (-190))) (|HasCategory| |#4| (QUOTE (-962))))) (-12 (|HasCategory| |#4| (QUOTE (-189))) (|HasCategory| |#4| (QUOTE (-962)))) (-12 (|HasCategory| |#4| (QUOTE (-812 (-1089)))) (|HasCategory| |#4| (QUOTE (-962)))) (|HasCategory| |#4| (QUOTE (-146))) (|HasCategory| |#4| (QUOTE (-21))) (|HasCategory| |#4| (QUOTE (-23))) (|HasCategory| |#4| (QUOTE (-104))) (|HasCategory| |#4| (QUOTE (-25))) (|HasCategory| |#4| (QUOTE (-553 (-773)))) (|HasCategory| |#4| (QUOTE (-72))) (-12 (|HasCategory| |#4| (QUOTE (-1013))) (|HasCategory| |#4| (|%list| (QUOTE -259) (|devaluate| |#4|))))) 
 (-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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 (-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."))) 
-(((-3991 "*") |has| |#1| (-146)) (-3982 |has| |#1| (-494)) (-3987 |has| |#1| (-6 -3987)) (-3984 . T) (-3983 . T) (-3986 . T)) 
+(((-3993 "*") |has| |#1| (-146)) (-3984 |has| |#1| (-495)) (-3989 |has| |#1| (-6 -3989)) (-3986 . T) (-3985 . T) (-3988 . 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}."))) 
-((-3989 . T) (-3990 . T)) 
+((-3991 . T) (-3992 . T)) 
 NIL 
 (-215 |Ex|) 
 ((|constructor| (NIL "TopLevelDrawFunctions provides top level functions for drawing graphics of expressions.")) (|makeObject| (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSurface| |#1|) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|))) "\\spad{makeObject(surface(f(u,v),g(u,v),h(u,v)),u = a..b,v = c..d)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{x = f(u,v)},{} \\spad{y = g(u,v)},{} \\spad{z = h(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{h(t)} is the default title.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSurface| |#1|) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(surface(f(u,v),g(u,v),h(u,v)),u = a..b,v = c..d,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{x = f(u,v)},{} \\spad{y = g(u,v)},{} \\spad{z = h(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{h(t)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) |#1| (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|))) "\\spad{makeObject(f(x,y),x = a..b,y = c..d)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of \\spad{z = f(x,y)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{y} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{f(x,y)} appears as the default title.") (((|ThreeSpace| (|DoubleFloat|)) |#1| (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(f(x,y),x = a..b,y = c..d,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of \\spad{z = f(x,y)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{y} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{f(x,y)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSpaceCurve| |#1|) (|SegmentBinding| (|Float|))) "\\spad{makeObject(curve(f(t),g(t),h(t)),t = a..b)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{h(t)} is the default title.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSpaceCurve| |#1|) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(curve(f(t),g(t),h(t)),t = a..b,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{h(t)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.")) (|draw| (((|ThreeDimensionalViewport|) (|ParametricSurface| |#1|) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|))) "\\spad{draw(surface(f(u,v),g(u,v),h(u,v)),u = a..b,v = c..d)} draws the graph of the parametric surface \\spad{x = f(u,v)},{} \\spad{y = g(u,v)},{} \\spad{z = h(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{h(t)} is the default title.") (((|ThreeDimensionalViewport|) (|ParametricSurface| |#1|) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(surface(f(u,v),g(u,v),h(u,v)),u = a..b,v = c..d,l)} draws the graph of the parametric surface \\spad{x = f(u,v)},{} \\spad{y = g(u,v)},{} \\spad{z = h(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{h(t)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) |#1| (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|))) "\\spad{draw(f(x,y),x = a..b,y = c..d)} draws the graph of \\spad{z = f(x,y)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{y} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{f(x,y)} appears in the title bar.") (((|ThreeDimensionalViewport|) |#1| (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f(x,y),x = a..b,y = c..d,l)} draws the graph of \\spad{z = f(x,y)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{y} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{f(x,y)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|ParametricSpaceCurve| |#1|) (|SegmentBinding| (|Float|))) "\\spad{draw(curve(f(t),g(t),h(t)),t = a..b)} draws the graph of the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{h(t)} is the default title.") (((|ThreeDimensionalViewport|) (|ParametricSpaceCurve| |#1|) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(curve(f(t),g(t),h(t)),t = a..b,l)} draws the graph of the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{h(t)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) (|ParametricPlaneCurve| |#1|) (|SegmentBinding| (|Float|))) "\\spad{draw(curve(f(t),g(t)),t = a..b)} draws the graph of the parametric curve \\spad{x = f(t), y = g(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{(f(t),g(t))} appears in the title bar.") (((|TwoDimensionalViewport|) (|ParametricPlaneCurve| |#1|) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(curve(f(t),g(t)),t = a..b,l)} draws the graph of the parametric curve \\spad{x = f(t), y = g(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{(f(t),g(t))} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) |#1| (|SegmentBinding| (|Float|))) "\\spad{draw(f(x),x = a..b)} draws the graph of \\spad{y = f(x)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{f(x)} appears in the title bar.") (((|TwoDimensionalViewport|) |#1| (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f(x),x = a..b,l)} draws the graph of \\spad{y = f(x)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{f(x)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied."))) 
@@ -827,15 +827,15 @@ NIL
 (-224 S R) 
 ((|constructor| (NIL "Extension of a base differential space with a derivation. \\blankline")) (D (($ $ (|Mapping| |#2| |#2|) (|NonNegativeInteger|)) "\\spad{D(x,d,n)} is a shorthand for \\spad{differentiate(x,d,n)}.") (($ $ (|Mapping| |#2| |#2|)) "\\spad{D(x,d)} is a shorthand for \\spad{differentiate(x,d)}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|) (|NonNegativeInteger|)) "\\spad{differentiate(x,d,n)} computes the \\spad{n}\\spad{-}th derivative of \\spad{x} using a derivation extending \\spad{d} on \\spad{R}.") (($ $ (|Mapping| |#2| |#2|)) "\\spad{differentiate(x,d)} computes the derivative of \\spad{x},{} extending differentiation \\spad{d} on \\spad{R}."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-811 (-1088)))) (|HasCategory| |#2| (QUOTE (-189)))) 
+((|HasCategory| |#2| (QUOTE (-812 (-1089)))) (|HasCategory| |#2| (QUOTE (-189)))) 
 (-225 R) 
 ((|constructor| (NIL "Extension of a base differential space with a derivation. \\blankline")) (D (($ $ (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) "\\spad{D(x,d,n)} is a shorthand for \\spad{differentiate(x,d,n)}.") (($ $ (|Mapping| |#1| |#1|)) "\\spad{D(x,d)} is a shorthand for \\spad{differentiate(x,d)}.")) (|differentiate| (($ $ (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) "\\spad{differentiate(x,d,n)} computes the \\spad{n}\\spad{-}th derivative of \\spad{x} using a derivation extending \\spad{d} on \\spad{R}.") (($ $ (|Mapping| |#1| |#1|)) "\\spad{differentiate(x,d)} computes the derivative of \\spad{x},{} extending differentiation \\spad{d} on \\spad{R}."))) 
 NIL 
 NIL 
 (-226 R S V) 
 ((|constructor| (NIL "\\spadtype{DifferentialSparseMultivariatePolynomial} implements an ordinary differential polynomial ring by combining a domain belonging to the category \\spadtype{DifferentialVariableCategory} with the domain \\spadtype{SparseMultivariatePolynomial}. \\blankline"))) 
-(((-3991 "*") |has| |#1| (-146)) (-3982 |has| |#1| (-494)) (-3987 |has| |#1| (-6 -3987)) (-3984 . T) (-3983 . T) (-3986 . T)) 
-((|HasCategory| |#1| (QUOTE (-821))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-389))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-821)))) (OR (|HasCategory| |#1| (QUOTE (-389))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-821)))) (OR (|HasCategory| |#1| (QUOTE (-389))) (|HasCategory| |#1| (QUOTE (-821)))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-494)))) (-12 (|HasCategory| |#1| (QUOTE (-796 (-327)))) (|HasCategory| |#3| (QUOTE (-796 (-327))))) (-12 (|HasCategory| |#1| (QUOTE (-796 (-483)))) (|HasCategory| |#3| (QUOTE (-796 (-483))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-800 (-327))))) (|HasCategory| |#3| (QUOTE (-553 (-800 (-327)))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-800 (-483))))) (|HasCategory| |#3| (QUOTE (-553 (-800 (-483)))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-472)))) (|HasCategory| |#3| (QUOTE (-553 (-472))))) (|HasCategory| |#1| (QUOTE (-580 (-483)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-347 (-483))))) (|HasCategory| |#1| (QUOTE (-950 (-483)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-347 (-483))))) (|HasCategory| |#1| (QUOTE (-950 (-347 (-483)))))) (|HasCategory| |#1| (QUOTE (-950 (-347 (-483))))) (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-811 (-1088)))) (|HasCategory| |#1| (QUOTE (-809 (-1088)))) (|HasCategory| |#1| (QUOTE (-311))) (|HasAttribute| |#1| (QUOTE -3987)) (|HasCategory| |#1| (QUOTE (-389))) (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) 
+(((-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))))) 
 (-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 -3088) 
+(-230 R -3090) 
 ((|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 -3088) 
+(-231 R -3090) 
 ((|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 
@@ -875,10 +875,10 @@ NIL
 (-236 A S) 
 ((|constructor| (NIL "An extensible aggregate is one which allows insertion and deletion of entries. These aggregates are models of lists and streams which are represented by linked structures so as to make insertion,{} deletion,{} and concatenation efficient. However,{} access to elements of these extensible aggregates is generally slow since access is made from the end. See \\spadtype{FlexibleArray} for an exception.")) (|removeDuplicates!| (($ $) "\\spad{removeDuplicates!(u)} destructively removes duplicates from \\spad{u}.")) (|select!| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{select!(p,u)} destructively changes \\spad{u} by keeping only values \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})}.")) (|merge!| (($ $ $) "\\spad{merge!(u,v)} destructively merges \\spad{u} and \\spad{v} in ascending order.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $ $) "\\spad{merge!(p,u,v)} destructively merges \\spad{u} and \\spad{v} using predicate \\spad{p}.")) (|insert!| (($ $ $ (|Integer|)) "\\spad{insert!(v,u,i)} destructively inserts aggregate \\spad{v} into \\spad{u} at position \\spad{i}.") (($ |#2| $ (|Integer|)) "\\spad{insert!(x,u,i)} destructively inserts \\spad{x} into \\spad{u} at position \\spad{i}.")) (|remove!| (($ |#2| $) "\\spad{remove!(x,u)} destructively removes all values \\spad{x} from \\spad{u}.") (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{remove!(p,u)} destructively removes all elements \\spad{x} of \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}.")) (|delete!| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete!(u,i..j)} destructively deletes elements \\spad{u}.\\spad{i} through \\spad{u}.\\spad{j}.") (($ $ (|Integer|)) "\\spad{delete!(u,i)} destructively deletes the \\axiom{\\spad{i}}th element of \\spad{u}.")) (|concat!| (($ $ $) "\\spad{concat!(u,v)} destructively appends \\spad{v} to the end of \\spad{u}. \\spad{v} is unchanged") (($ $ |#2|) "\\spad{concat!(u,x)} destructively adds element \\spad{x} to the end of \\spad{u}."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-756))) (|HasCategory| |#2| (QUOTE (-1012)))) 
+((|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}."))) 
-((-3990 . T)) 
+((-3992 . 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 -3990))) 
+((|HasAttribute| |#1| (QUOTE -3992))) 
 (-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| -2033 -3512 |exactQuo|) 
+(-244 S R |Mod| -2035 -3514 |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| $) "\\spad{modulus(x)} \\undocumented"))) 
-((-3982 . T) ((-3991 "*") . T) (-3983 . T) (-3984 . T) (-3986 . T)) 
+((-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . T)) 
 NIL 
 (-245) 
 ((|constructor| (NIL "Entire Rings (non-commutative Integral Domains),{} \\spadignore{i.e.} a ring not necessarily commutative which has no zero divisors. \\blankline")) (|noZeroDivisors| ((|attribute|) "if a product is zero then one of the factors must be zero."))) 
-((-3982 . T) (-3983 . T) (-3984 . T) (-3986 . T)) 
+((-3984 . T) (-3985 . T) (-3986 . T) (-3988 . T)) 
 NIL 
 (-246) 
 ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: March 18,{} 2010. An `Environment' is a stack of scope.")) (|categoryFrame| (($) "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"))) 
@@ -922,16 +922,16 @@ 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."))) 
-((-3986 OR (|has| |#1| (-961)) (|has| |#1| (-410))) (-3983 |has| |#1| (-961)) (-3984 |has| |#1| (-961))) 
-((|HasCategory| |#1| (QUOTE (-311))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-961)))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-311)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-961))) (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-809 (-1088)))) (OR (|HasCategory| |#1| (QUOTE (-809 (-1088)))) (|HasCategory| |#1| (QUOTE (-961)))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-809 (-1088)))) (|HasCategory| |#1| (QUOTE (-961)))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-809 (-1088)))) (|HasCategory| |#1| (QUOTE (-961)))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-961)))) (OR (|HasCategory| |#1| (QUOTE (-410))) (|HasCategory| |#1| (QUOTE (-663)))) (|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 (-663))) (|HasCategory| |#1| (QUOTE (-809 (-1088)))) (|HasCategory| |#1| (QUOTE (-961))) (|HasCategory| |#1| (QUOTE (-1024))) (|HasCategory| |#1| (QUOTE (-1012)))) (OR (|HasCategory| |#1| (QUOTE (-410))) (|HasCategory| |#1| (QUOTE (-663))) (|HasCategory| |#1| (QUOTE (-1024)))) (|HasCategory| |#1| (|%list| (QUOTE -452) (QUOTE (-1088)) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-253))) (OR (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-410)))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-663)))) (OR (|HasCategory| |#1| (QUOTE (-410))) (|HasCategory| |#1| (QUOTE (-961)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1024))) (|HasCategory| |#1| (QUOTE (-663)))) 
+((-3988 OR (|has| |#1| (-962)) (|has| |#1| (-410))) (-3985 |has| |#1| (-962)) (-3986 |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}"))) 
 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."))) 
-((-3989 . T) (-3990 . T)) 
-((-12 (|HasCategory| (-2 (|:| -3854 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -259) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3854) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3854 |#1|) (|:| |entry| |#2|)) (QUOTE (-1012)))) (OR (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| (-2 (|:| -3854 |#1|) (|:| |entry| |#2|)) (QUOTE (-1012)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| (-2 (|:| -3854 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3854 |#1|) (|:| |entry| |#2|)) (QUOTE (-1012)))) (OR (|HasCategory| (-2 (|:| -3854 |#1|) (|:| |entry| |#2|)) (QUOTE (-552 (-772)))) (|HasCategory| |#2| (QUOTE (-552 (-772))))) (|HasCategory| (-2 (|:| -3854 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-472)))) (-12 (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| |#2| (|%list| (QUOTE -259) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3854 |#1|) (|:| |entry| |#2|)) (QUOTE (-1012))) (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#2| (QUOTE (-1012))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3854 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3854 |#1|) (|:| |entry| |#2|)) (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3854 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) 
+((-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)))) 
 (-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 
@@ -939,16 +939,16 @@ NIL
 (-252 S) 
 ((|constructor| (NIL "An expression space is a set which is closed under certain operators.")) (|odd?| (((|Boolean|) $) "\\spad{odd? x} is \\spad{true} if \\spad{x} is an odd integer.")) (|even?| (((|Boolean|) $) "\\spad{even? x} is \\spad{true} if \\spad{x} is an even integer.")) (|definingPolynomial| (($ $) "\\spad{definingPolynomial(x)} returns an expression \\spad{p} such that \\spad{p(x) = 0}.")) (|minPoly| (((|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{minPoly(k)} returns \\spad{p} such that \\spad{p(k) = 0}.")) (|eval| (($ $ (|BasicOperator|) (|Mapping| $ $)) "\\spad{eval(x, s, f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|BasicOperator|) (|Mapping| $ (|List| $))) "\\spad{eval(x, s, f)} replaces every \\spad{s(a1,..,am)} in \\spad{x} by \\spad{f(a1,..,am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ $)) "\\spad{eval(x, s, f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ (|List| $))) "\\spad{eval(x, s, f)} replaces every \\spad{s(a1,..,am)} in \\spad{x} by \\spad{f(a1,..,am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.")) (|freeOf?| (((|Boolean|) $ (|Symbol|)) "\\spad{freeOf?(x, s)} tests if \\spad{x} does not contain any operator whose name is \\spad{s}.") (((|Boolean|) $ $) "\\spad{freeOf?(x, y)} tests if \\spad{x} does not contain any occurrence of \\spad{y},{} where \\spad{y} is a single kernel.")) (|map| (($ (|Mapping| $ $) (|Kernel| $)) "\\spad{map(f, k)} returns \\spad{op(f(x1),...,f(xn))} where \\spad{k = op(x1,...,xn)}.")) (|kernel| (($ (|BasicOperator|) (|List| $)) "\\spad{kernel(op, [f1,...,fn])} constructs \\spad{op(f1,...,fn)} without evaluating it.") (($ (|BasicOperator|) $) "\\spad{kernel(op, x)} constructs \\spad{op}(\\spad{x}) without evaluating it.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(x, s)} tests if \\spad{x} is a kernel and is the name of its operator is \\spad{s}.") (((|Boolean|) $ (|BasicOperator|)) "\\spad{is?(x, op)} tests if \\spad{x} is a kernel and is its operator is op.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} tests if \\% accepts \\spad{op} as applicable to its elements.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\%.")) (|operators| (((|List| (|BasicOperator|)) $) "\\spad{operators(f)} returns all the basic operators appearing in \\spad{f},{} no matter what their levels are.")) (|tower| (((|List| (|Kernel| $)) $) "\\spad{tower(f)} returns all the kernels appearing in \\spad{f},{} no matter what their levels are.")) (|kernels| (((|List| (|Kernel| $)) $) "\\spad{kernels(f)} returns the list of all the top-level kernels appearing in \\spad{f},{} but not the ones appearing in the arguments of the top-level kernels.")) (|mainKernel| (((|Union| (|Kernel| $) "failed") $) "\\spad{mainKernel(f)} returns a kernel of \\spad{f} with maximum nesting level,{} or if \\spad{f} has no kernels (\\spadignore{i.e.} \\spad{f} is a constant).")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(f)} returns the highest nesting level appearing in \\spad{f}. Constants have height 0. Symbols have height 1. For any operator op and expressions \\spad{f1},{}...,{}fn,{} \\spad{op(f1,...,fn)} has height equal to \\spad{1 + max(height(f1),...,height(fn))}.")) (|distribute| (($ $ $) "\\spad{distribute(f, g)} expands all the kernels in \\spad{f} that contain \\spad{g} in their arguments and that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or a \\spadfunFrom{paren}{ExpressionSpace} expression.") (($ $) "\\spad{distribute(f)} expands all the kernels in \\spad{f} that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or \\spadfunFrom{paren}{ExpressionSpace} expression.")) (|paren| (($ (|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 
-((|HasCategory| |#1| (QUOTE (-950 (-483)))) (|HasCategory| |#1| (QUOTE (-961)))) 
+((|HasCategory| |#1| (QUOTE (-951 (-484)))) (|HasCategory| |#1| (QUOTE (-962)))) 
 (-253) 
 ((|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 -3088 S) 
+(-254 -3090 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 -3088) 
+(-255 E -3090) 
 ((|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|) $ $) "\\spad{sizeLess?(x,y)} tests whether \\spad{x} is strictly smaller than \\spad{y} with respect to the \\spadfunFrom{euclideanSize}{EuclideanDomain}."))) 
-((-3982 . T) ((-3991 "*") . T) (-3983 . T) (-3984 . T) (-3986 . T)) 
+((-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . T)) 
 NIL 
 (-258 S R) 
 ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation'' substitutions.")) (|eval| (($ $ (|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 -3088) 
+(-260 -3090) 
 ((|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 
@@ -982,12 +982,12 @@ 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))}."))) 
-((-3981 . T) (-3987 . T) (-3982 . T) ((-3991 "*") . T) (-3983 . T) (-3984 . T) (-3986 . T)) 
-((|HasCategory| (-1164 |#1| |#2| |#3| |#4|) (QUOTE (-821))) (|HasCategory| (-1164 |#1| |#2| |#3| |#4|) (QUOTE (-950 (-1088)))) (|HasCategory| (-1164 |#1| |#2| |#3| |#4|) (QUOTE (-118))) (|HasCategory| (-1164 |#1| |#2| |#3| |#4|) (QUOTE (-120))) (|HasCategory| (-1164 |#1| |#2| |#3| |#4|) (QUOTE (-553 (-472)))) (|HasCategory| (-1164 |#1| |#2| |#3| |#4|) (QUOTE (-933))) (|HasCategory| (-1164 |#1| |#2| |#3| |#4|) (QUOTE (-740))) (|HasCategory| (-1164 |#1| |#2| |#3| |#4|) (QUOTE (-756))) (OR (|HasCategory| (-1164 |#1| |#2| |#3| |#4|) (QUOTE (-740))) (|HasCategory| (-1164 |#1| |#2| |#3| |#4|) (QUOTE (-756)))) (|HasCategory| (-1164 |#1| |#2| |#3| |#4|) (QUOTE (-950 (-483)))) (|HasCategory| (-1164 |#1| |#2| |#3| |#4|) (QUOTE (-1064))) (|HasCategory| (-1164 |#1| |#2| |#3| |#4|) (QUOTE (-796 (-327)))) (|HasCategory| (-1164 |#1| |#2| |#3| |#4|) (QUOTE (-796 (-483)))) (|HasCategory| (-1164 |#1| |#2| |#3| |#4|) (QUOTE (-553 (-800 (-327))))) (|HasCategory| (-1164 |#1| |#2| |#3| |#4|) (QUOTE (-553 (-800 (-483))))) (|HasCategory| (-1164 |#1| |#2| |#3| |#4|) (QUOTE (-580 (-483)))) (|HasCategory| (-1164 |#1| |#2| |#3| |#4|) (QUOTE (-189))) (|HasCategory| (-1164 |#1| |#2| |#3| |#4|) (QUOTE (-811 (-1088)))) (|HasCategory| (-1164 |#1| |#2| |#3| |#4|) (QUOTE (-190))) (|HasCategory| (-1164 |#1| |#2| |#3| |#4|) (QUOTE (-809 (-1088)))) (|HasCategory| (-1164 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -452) (QUOTE (-1088)) (|%list| (QUOTE -1164) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1164 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -259) (|%list| (QUOTE -1164) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1164 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -241) (|%list| (QUOTE -1164) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (|%list| (QUOTE -1164) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1164 |#1| |#2| |#3| |#4|) (QUOTE (-257))) (|HasCategory| (-1164 |#1| |#2| |#3| |#4|) (QUOTE (-482))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-1164 |#1| |#2| |#3| |#4|) (QUOTE (-821)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-1164 |#1| |#2| |#3| |#4|) (QUOTE (-821)))) (|HasCategory| (-1164 |#1| |#2| |#3| |#4|) (QUOTE (-118))))) 
+((-3983 . T) (-3989 . T) (-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . 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."))) 
-((-3986 OR (-12 (|has| |#1| (-494)) (OR (|has| |#1| (-961)) (|has| |#1| (-410)))) (|has| |#1| (-961)) (|has| |#1| (-410))) (-3984 |has| |#1| (-146)) (-3983 |has| |#1| (-146)) ((-3991 "*") |has| |#1| (-494)) (-3982 |has| |#1| (-494)) (-3987 |has| |#1| (-494)) (-3981 |has| |#1| (-494))) 
-((OR (-12 (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-950 (-483))))) (|HasCategory| |#1| (QUOTE (-950 (-347 (-483)))))) (|HasCategory| |#1| (QUOTE (-494))) (OR (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-961)))) (|HasCategory| |#1| (QUOTE (-961))) (|HasCategory| |#1| (QUOTE (-21))) (OR (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-950 (-347 (-483)))))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-961)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-580 (-483))))) (-12 (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-580 (-483))))) (-12 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-580 (-483))))) (-12 (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-580 (-483))))) (-12 (|HasCategory| |#1| (QUOTE (-580 (-483)))) (|HasCategory| |#1| (QUOTE (-961))))) (OR (|HasCategory| |#1| (QUOTE (-410))) (|HasCategory| |#1| (QUOTE (-1024)))) (|HasCategory| |#1| (QUOTE (-410))) (|HasCategory| |#1| (QUOTE (-553 (-472)))) (OR (|HasCategory| |#1| (QUOTE (-950 (-483)))) (|HasCategory| |#1| (QUOTE (-961)))) (|HasCategory| |#1| (QUOTE (-950 (-483)))) (|HasCategory| |#1| (QUOTE (-796 (-327)))) (|HasCategory| |#1| (QUOTE (-796 (-483)))) (|HasCategory| |#1| (QUOTE (-553 (-800 (-327))))) (|HasCategory| |#1| (QUOTE (-553 (-800 (-483))))) (-12 (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-950 (-483))))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-961)))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-961)))) (OR (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-961)))) (-12 (|HasCategory| |#1| (QUOTE (-389))) (|HasCategory| |#1| (QUOTE (-494)))) (OR (|HasCategory| |#1| (QUOTE (-410))) (|HasCategory| |#1| (QUOTE (-494)))) (-12 (|HasCategory| |#1| (QUOTE (-580 (-483)))) (|HasCategory| |#1| (QUOTE (-961)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-580 (-483)))) (|HasCategory| |#1| (QUOTE (-961)))) (|HasCategory| |#1| (QUOTE (-21)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-580 (-483)))) (|HasCategory| |#1| (QUOTE (-961)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1024)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-580 (-483)))) (|HasCategory| |#1| (QUOTE (-961)))) (|HasCategory| |#1| (QUOTE (-25)))) (OR (|HasCategory| |#1| (QUOTE (-410))) (|HasCategory| |#1| (QUOTE (-961)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-950 (-347 (-483)))))) (-12 (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-950 (-483)))))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1024))) (|HasCategory| |#1| (QUOTE (-950 (-347 (-483))))) (|HasCategory| $ (QUOTE (-961))) (|HasCategory| $ (QUOTE (-950 (-483))))) 
+((-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))) 
+((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}."))) 
 NIL 
@@ -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 -3088) 
+(-267 R -3090) 
 ((|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."))) 
-(((-3991 "*") |has| |#1| (-146)) (-3982 |has| |#1| (-494)) (-3987 |has| |#1| (-311)) (-3981 |has| |#1| (-311)) (-3983 . T) (-3984 . T) (-3986 . T)) 
-((|HasCategory| |#1| (QUOTE (-38 (-347 (-483))))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-494)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-809 (-1088)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -347) (QUOTE (-483))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -347) (QUOTE (-483))) (|devaluate| |#1|)))) (|HasCategory| (-347 (-483)) (QUOTE (-1024))) (|HasCategory| |#1| (QUOTE (-311))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-494)))) (OR (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-494)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -347) (QUOTE (-483)))))) (|HasSignature| |#1| (|%list| (QUOTE -3940) (|%list| (|devaluate| |#1|) (QUOTE (-1088)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -347) (QUOTE (-483)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-347 (-483))))) (|HasCategory| |#1| (QUOTE (-29 (-483)))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1113)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-347 (-483))))) (|HasSignature| |#1| (|%list| (QUOTE -3806) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1088))))) (|HasSignature| |#1| (|%list| (QUOTE -3077) (|%list| (|%list| (QUOTE -583) (QUOTE (-1088))) (|devaluate| |#1|))))))) 
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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|))))))) 
 (-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 
@@ -1018,8 +1018,8 @@ 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."))) 
-((-3984 . T) (-3983 . T)) 
-((|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| (-483) (QUOTE (-716)))) 
+((-3986 . T) (-3985 . 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| $) "\\spad{s + x} returns the sum of \\spad{s} and \\spad{x}."))) 
 NIL 
@@ -1027,26 +1027,26 @@ NIL
 (-274 S) 
 ((|constructor| (NIL "The free abelian monoid on a set \\spad{S} is the monoid of finite sums of the form \\spad{reduce(+,[ni * si])} where the \\spad{si}'s are in \\spad{S},{} and the \\spad{ni}'s are non-negative integers. The operation is commutative."))) 
 NIL 
-((|HasCategory| (-694) (QUOTE (-716)))) 
+((|HasCategory| (-695) (QUOTE (-717)))) 
 (-275 S R E) 
 ((|constructor| (NIL "This category is similar to AbelianMonoidRing,{} except that the sum is assumed to be finite. It is a useful model for polynomials,{} but is somewhat more general.")) (|primitivePart| (($ $) "\\spad{primitivePart(p)} returns the unit normalized form of polynomial \\spad{p} divided by the content of \\spad{p}.")) (|content| ((|#2| $) "\\spad{content(p)} gives the gcd of the coefficients of polynomial \\spad{p}.")) (|exquo| (((|Union| $ "failed") $ |#2|) "\\spad{exquo(p,r)} returns the exact quotient of polynomial \\spad{p} by \\spad{r},{} or \"failed\" if none exists.")) (|binomThmExpt| (($ $ $ (|NonNegativeInteger|)) "\\spad{binomThmExpt(p,q,n)} returns \\spad{(x+y)^n} by means of the binomial theorem trick.")) (|pomopo!| (($ $ |#2| |#3| $) "\\spad{pomopo!(p1,r,e,p2)} returns \\spad{p1 + monomial(e,r) * p2} and may use \\spad{p1} as workspace. The constaant \\spad{r} is assumed to be nonzero.")) (|mapExponents| (($ (|Mapping| |#3| |#3|) $) "\\spad{mapExponents(fn,u)} maps function \\spad{fn} onto the exponents of the non-zero monomials of polynomial \\spad{u}.")) (|minimumDegree| ((|#3| $) "\\spad{minimumDegree(p)} gives the least exponent of a non-zero term of polynomial \\spad{p}. Error: if applied to 0.")) (|numberOfMonomials| (((|NonNegativeInteger|) $) "\\spad{numberOfMonomials(p)} gives the number of non-zero monomials in polynomial \\spad{p}.")) (|coefficients| (((|List| |#2|) $) "\\spad{coefficients(p)} gives the list of non-zero coefficients of polynomial \\spad{p}.")) (|ground| ((|#2| $) "\\spad{ground(p)} retracts polynomial \\spad{p} to the coefficient ring.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(p)} tests if polynomial \\spad{p} is a member of the coefficient ring."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-389))) (|HasCategory| |#2| (QUOTE (-494))) (|HasCategory| |#2| (QUOTE (-146)))) 
+((|HasCategory| |#2| (QUOTE (-389))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-146)))) 
 (-276 R E) 
 ((|constructor| (NIL "This category is similar to AbelianMonoidRing,{} except that the sum is assumed to be finite. It is a useful model for polynomials,{} but is somewhat more general.")) (|primitivePart| (($ $) "\\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."))) 
-(((-3991 "*") |has| |#1| (-146)) (-3982 |has| |#1| (-494)) (-3983 . T) (-3984 . T) (-3986 . T)) 
+(((-3993 "*") |has| |#1| (-146)) (-3984 |has| |#1| (-495)) (-3985 . T) (-3986 . T) (-3988 . 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."))) 
-((-3990 . T) (-3989 . T)) 
-((OR (-12 (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-553 (-472)))) (OR (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| |#1| (QUOTE (-756))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| (-483) (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|))))) 
-(-278 S -3088) 
+((-3992 . T) (-3991 . 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) 
 ((|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 -3088) 
+(-279 -3090) 
 ((|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."))) 
-((-3981 . T) (-3987 . T) (-3982 . T) ((-3991 "*") . T) (-3983 . T) (-3984 . T) (-3986 . T)) 
+((-3983 . T) (-3989 . T) (-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . 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 -3088 UP UPUP R) 
+(-282 -3090 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 
@@ -1064,33 +1064,33 @@ 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 -3088 UP UPUP R) 
+(-284 S -3090 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 -3088 UP UPUP R) 
+(-285 -3090 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|) $) "\\spad{ideal(D)} returns the ideal corresponding to a divisor \\spad{D}."))) 
 NIL 
 NIL 
 (-286 S R) 
 ((|constructor| (NIL "This category provides a selection of evaluation operations depending on what the argument type \\spad{R} provides.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(f, ex)} evaluates ex,{} applying \\spad{f} to values of type \\spad{R} in ex."))) 
 NIL 
-((|HasCategory| |#2| (|%list| (QUOTE -452) (QUOTE (-1088)) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -259) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -241) (|devaluate| |#2|) (|devaluate| |#2|)))) 
+((|HasCategory| |#2| (|%list| (QUOTE -453) (QUOTE (-1089)) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -259) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -241) (|devaluate| |#2|) (|devaluate| |#2|)))) 
 (-287 R) 
 ((|constructor| (NIL "This category provides a selection of evaluation operations depending on what the argument type \\spad{R} provides.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f, ex)} evaluates ex,{} applying \\spad{f} to values of type \\spad{R} in ex."))) 
 NIL 
 NIL 
 (-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}."))) 
-((-3981 . T) (-3987 . T) (-3982 . T) ((-3991 "*") . T) (-3983 . T) (-3984 . T) (-3986 . T)) 
-((OR (|HasCategory| (-817 |#1|) (QUOTE (-118))) (|HasCategory| (-817 |#1|) (QUOTE (-317)))) (|HasCategory| (-817 |#1|) (QUOTE (-120))) (|HasCategory| (-817 |#1|) (QUOTE (-317))) (|HasCategory| (-817 |#1|) (QUOTE (-118)))) 
-(-289 S -3088 UP UPUP) 
+((-3983 . T) (-3989 . T) (-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . 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) 
 ((|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 -3088 UP UPUP) 
+(-290 -3090 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."))) 
-((-3982 |has| (-347 |#2|) (-311)) (-3987 |has| (-347 |#2|) (-311)) (-3981 |has| (-347 |#2|) (-311)) ((-3991 "*") . T) (-3983 . T) (-3984 . T) (-3986 . T)) 
+((-3984 |has| (-347 |#2|) (-311)) (-3989 |has| (-347 |#2|) (-311)) (-3983 |has| (-347 |#2|) (-311)) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . 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."))) 
-((-3981 . T) (-3987 . T) (-3982 . T) ((-3991 "*") . T) (-3983 . T) (-3984 . T) (-3986 . T)) 
-((OR (|HasCategory| (-817 |#1|) (QUOTE (-118))) (|HasCategory| (-817 |#1|) (QUOTE (-317)))) (|HasCategory| (-817 |#1|) (QUOTE (-120))) (|HasCategory| (-817 |#1|) (QUOTE (-317))) (|HasCategory| (-817 |#1|) (QUOTE (-118)))) 
+((-3983 . T) (-3989 . T) (-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . 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."))) 
-((-3981 . T) (-3987 . T) (-3982 . T) ((-3991 "*") . T) (-3983 . T) (-3984 . T) (-3986 . T)) 
+((-3983 . T) (-3989 . T) (-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . 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."))) 
-((-3981 . T) (-3987 . T) (-3982 . T) ((-3991 "*") . T) (-3983 . T) (-3984 . T) (-3986 . T)) 
+((-3983 . T) (-3989 . T) (-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . 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."))) 
-((-3981 . T) (-3987 . T) (-3982 . T) ((-3991 "*") . T) (-3983 . T) (-3984 . T) (-3986 . T)) 
+((-3983 . T) (-3989 . T) (-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . T)) 
 NIL 
-(-299 R UP -3088) 
+(-299 R UP -3090) 
 ((|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."))) 
-((-3981 . T) (-3987 . T) (-3982 . T) ((-3991 "*") . T) (-3983 . T) (-3984 . T) (-3986 . T)) 
-((OR (|HasCategory| (-817 |#1|) (QUOTE (-118))) (|HasCategory| (-817 |#1|) (QUOTE (-317)))) (|HasCategory| (-817 |#1|) (QUOTE (-120))) (|HasCategory| (-817 |#1|) (QUOTE (-317))) (|HasCategory| (-817 |#1|) (QUOTE (-118)))) 
+((-3983 . T) (-3989 . T) (-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . 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."))) 
-((-3981 . T) (-3987 . T) (-3982 . T) ((-3991 "*") . T) (-3983 . T) (-3984 . T) (-3986 . T)) 
+((-3983 . T) (-3989 . T) (-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . 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."))) 
-((-3981 . T) (-3987 . T) (-3982 . T) ((-3991 "*") . T) (-3983 . T) (-3984 . T) (-3986 . T)) 
+((-3983 . T) (-3989 . T) (-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . 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."))) 
-((-3981 . T) (-3987 . T) (-3982 . T) ((-3991 "*") . T) (-3983 . T) (-3984 . T) (-3986 . T)) 
+((-3983 . T) (-3989 . T) (-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . 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 -3088 GF) 
+(-305 -3090 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 -3088 FP FPP) 
+(-306 -3090 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}."))) 
-((-3981 . T) (-3987 . T) (-3982 . T) ((-3991 "*") . T) (-3983 . T) (-3984 . T) (-3986 . T)) 
+((-3983 . T) (-3989 . T) (-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . 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| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) 
-((-3986 . T)) 
+((-3988 . T)) 
 NIL 
 (-310 S) 
 ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) 
@@ -1174,7 +1174,7 @@ NIL
 NIL 
 (-311) 
 ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) 
-((-3981 . T) (-3987 . T) (-3982 . T) ((-3991 "*") . T) (-3983 . T) (-3984 . T) (-3986 . T)) 
+((-3983 . T) (-3989 . T) (-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . 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."))) 
@@ -1187,10 +1187,10 @@ NIL
 (-314 S R) 
 ((|constructor| (NIL "A FiniteRankNonAssociativeAlgebra is a non associative algebra over a commutative ring \\spad{R} which is a free \\spad{R}-module of finite rank.")) (|unitsKnown| ((|attribute|) "unitsKnown means that \\spadfun{recip} truly yields reciprocal or \\spad{\"failed\"} if not a unit,{} similarly for \\spadfun{leftRecip} and \\spadfun{rightRecip}. The reason is that we use left,{} respectively right,{} minimal polynomials to decide this question.")) (|unit| (((|Union| $ "failed")) "\\spad{unit()} returns a unit of the algebra (necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnit| (((|Union| $ "failed")) "\\spad{rightUnit()} returns a right unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|leftUnit| (((|Union| $ "failed")) "\\spad{leftUnit()} returns a left unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{rightUnits()} returns the affine space of all right units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|leftUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{leftUnits()} returns the affine space of all left units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|rightMinimalPolynomial| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{rightMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of right powers of \\spad{a}. Note: the polynomial never has a constant term as in general the algebra has no unit.")) (|leftMinimalPolynomial| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{leftMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of left powers of \\spad{a}. Note: the polynomial never has a constant term as in general the algebra has no unit.")) (|associatorDependence| (((|List| (|Vector| |#2|))) "\\spad{associatorDependence()} looks for the associator identities,{} \\spadignore{i.e.} finds a basis of the solutions of the linear combinations of the six permutations of \\spad{associator(a,b,c)} which yield 0,{} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra. The order of the permutations is \\spad{123 231 312 132 321 213}.")) (|rightRecip| (((|Union| $ "failed") $) "\\spad{rightRecip(a)} returns an element,{} which is a right inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (|leftRecip| (((|Union| $ "failed") $) "\\spad{leftRecip(a)} returns an element,{} which is a left inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(a)} returns an element,{} which is both a left and a right inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (|lieAlgebra?| (((|Boolean|)) "\\spad{lieAlgebra?()} tests if the algebra is anticommutative and \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra (Jacobi identity). Example: for every associative algebra \\spad{(A,+,@)} we can construct a Lie algebra \\spad{(A,+,*)},{} where \\spad{a*b := a@b-b@a}.")) (|jordanAlgebra?| (((|Boolean|)) "\\spad{jordanAlgebra?()} tests if the algebra is commutative,{} characteristic is not 2,{} and \\spad{(a*b)*a**2 - a*(b*a**2) = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra (Jordan identity). Example: for every associative algebra \\spad{(A,+,@)} we can construct a Jordan algebra \\spad{(A,+,*)},{} where \\spad{a*b := (a@b+b@a)/2}.")) (|noncommutativeJordanAlgebra?| (((|Boolean|)) "\\spad{noncommutativeJordanAlgebra?()} tests if the algebra is flexible and Jordan admissible.")) (|jordanAdmissible?| (((|Boolean|)) "\\spad{jordanAdmissible?()} tests if 2 is invertible in the coefficient domain and the multiplication defined by \\spad{(1/2)(a*b+b*a)} determines a Jordan algebra,{} \\spadignore{i.e.} satisfies the Jordan identity. The property of \\spadatt{commutative(\"*\")} follows from by definition.")) (|lieAdmissible?| (((|Boolean|)) "\\spad{lieAdmissible?()} tests if the algebra defined by the commutators is a Lie algebra,{} \\spadignore{i.e.} satisfies the Jacobi identity. The property of anticommutativity follows from definition.")) (|jacobiIdentity?| (((|Boolean|)) "\\spad{jacobiIdentity?()} tests if \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra. For example,{} this holds for crossed products of 3-dimensional vectors.")) (|powerAssociative?| (((|Boolean|)) "\\spad{powerAssociative?()} tests if all subalgebras generated by a single element are associative.")) (|alternative?| (((|Boolean|)) "\\spad{alternative?()} tests if \\spad{2*associator(a,a,b) = 0 = 2*associator(a,b,b)} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don't know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|flexible?| (((|Boolean|)) "\\spad{flexible?()} tests if \\spad{2*associator(a,b,a) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don't know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|rightAlternative?| (((|Boolean|)) "\\spad{rightAlternative?()} tests if \\spad{2*associator(a,b,b) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don't know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|leftAlternative?| (((|Boolean|)) "\\spad{leftAlternative?()} tests if \\spad{2*associator(a,a,b) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don't know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|antiAssociative?| (((|Boolean|)) "\\spad{antiAssociative?()} tests if multiplication in algebra is anti-associative,{} \\spadignore{i.e.} \\spad{(a*b)*c + a*(b*c) = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra.")) (|associative?| (((|Boolean|)) "\\spad{associative?()} tests if multiplication in algebra is associative.")) (|antiCommutative?| (((|Boolean|)) "\\spad{antiCommutative?()} tests if \\spad{a*a = 0} for all \\spad{a} in the algebra. Note: this implies \\spad{a*b + b*a = 0} for all \\spad{a} and \\spad{b}.")) (|commutative?| (((|Boolean|)) "\\spad{commutative?()} tests if multiplication in the algebra is commutative.")) (|rightCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{rightCharacteristicPolynomial(a)} returns the characteristic polynomial of the right regular representation of \\spad{a} with respect to any basis.")) (|leftCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{leftCharacteristicPolynomial(a)} returns the characteristic polynomial of the left regular representation of \\spad{a} with respect to any basis.")) (|rightTraceMatrix| (((|Matrix| |#2|) (|Vector| $)) "\\spad{rightTraceMatrix([v1,...,vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj}.")) (|leftTraceMatrix| (((|Matrix| |#2|) (|Vector| $)) "\\spad{leftTraceMatrix([v1,...,vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj}.")) (|rightDiscriminant| ((|#2| (|Vector| $)) "\\spad{rightDiscriminant([v1,...,vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj}. Note: the same as \\spad{determinant(rightTraceMatrix([v1,...,vn]))}.")) (|leftDiscriminant| ((|#2| (|Vector| $)) "\\spad{leftDiscriminant([v1,...,vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj}. Note: the same as \\spad{determinant(leftTraceMatrix([v1,...,vn]))}.")) (|represents| (($ (|Vector| |#2|) (|Vector| $)) "\\spad{represents([a1,...,am],[v1,...,vm])} returns the linear combination \\spad{a1*vm + ... + an*vm}.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $) (|Vector| $)) "\\spad{coordinates([a1,...,am],[v1,...,vn])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{ai} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.") (((|Vector| |#2|) $ (|Vector| $)) "\\spad{coordinates(a,[v1,...,vn])} returns the coordinates of \\spad{a} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rightNorm| ((|#2| $) "\\spad{rightNorm(a)} returns the determinant of the right regular representation of \\spad{a}.")) (|leftNorm| ((|#2| $) "\\spad{leftNorm(a)} returns the determinant of the left regular representation of \\spad{a}.")) (|rightTrace| ((|#2| $) "\\spad{rightTrace(a)} returns the trace of the right regular representation of \\spad{a}.")) (|leftTrace| ((|#2| $) "\\spad{leftTrace(a)} returns the trace of the left regular representation of \\spad{a}.")) (|rightRegularRepresentation| (((|Matrix| |#2|) $ (|Vector| $)) "\\spad{rightRegularRepresentation(a,[v1,...,vn])} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,...,vn]}.")) (|leftRegularRepresentation| (((|Matrix| |#2|) $ (|Vector| $)) "\\spad{leftRegularRepresentation(a,[v1,...,vn])} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,...,vn]}.")) (|structuralConstants| (((|Vector| (|Matrix| |#2|)) (|Vector| $)) "\\spad{structuralConstants([v1,v2,...,vm])} calculates the structural constants \\spad{[(gammaijk) for k in 1..m]} defined by \\spad{vi * vj = gammaij1 * v1 + ... + gammaijm * vm},{} where \\spad{[v1,...,vm]} is an \\spad{R}-module basis of a subalgebra.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#2|)) (|Vector| $)) "\\spad{conditionsForIdempotents([v1,...,vn])} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra as \\spad{R}-module.")) (|someBasis| (((|Vector| $)) "\\spad{someBasis()} returns some \\spad{R}-module basis."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-494)))) 
+((|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| $)) "\\spad{someBasis()} returns some \\spad{R}-module basis."))) 
-((-3986 |has| |#1| (-494)) (-3984 . T) (-3983 . T)) 
+((-3988 |has| |#1| (-495)) (-3986 . T) (-3985 . T)) 
 NIL 
 (-316 S) 
 ((|constructor| (NIL "The category of domains composed of a finite set of elements. We include the functions \\spadfun{lookup} and \\spadfun{index} to give a bijection between the finite set and an initial segment of positive integers. \\blankline")) (|random| (($) "\\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| $)) "\\spad{regularRepresentation(a,basis)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra."))) 
-((-3983 . T) (-3984 . T) (-3986 . T)) 
+((-3985 . T) (-3986 . T) (-3988 . T)) 
 NIL 
 (-320 A S) 
 ((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|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|) $ $) "\\spad{merge(p,a,b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) 
 NIL 
-((|HasAttribute| |#1| (QUOTE -3990)) (|HasCategory| |#2| (QUOTE (-756))) (|HasCategory| |#2| (QUOTE (-1012)))) 
+((|HasAttribute| |#1| (QUOTE -3992)) (|HasCategory| |#2| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-1013)))) 
 (-321 S) 
 ((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|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|) $ $) "\\spad{merge(p,a,b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) 
-((-3989 . T)) 
+((-3991 . T)) 
 NIL 
 (-322 S A R B) 
 ((|constructor| (NIL "\\spad{FiniteLinearAggregateFunctions2} provides functions involving two FiniteLinearAggregates where the underlying domains might be different. An example of this might be creating a list of rational numbers by mapping a function across a list of integers where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-aggregates \\spad{x} of aggregrate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad{[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$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) (-3984 . T) (-3983 . T)) 
+((|JacobiIdentity| . T) (|NullSquare| . T) (-3986 . T) (-3985 . 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."))) 
@@ -1231,14 +1231,14 @@ NIL
 (-325 S R) 
 ((|constructor| (NIL "\\spad{S} is \\spadtype{FullyLinearlyExplicitRingOver R} means that \\spad{S} is a \\spadtype{LinearlyExplicitRingOver R} and,{} in addition,{} if \\spad{R} is a \\spadtype{LinearlyExplicitRingOver Integer},{} then so is \\spad{S}"))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-580 (-483))))) 
+((|HasCategory| |#2| (QUOTE (-581 (-484))))) 
 (-326 R) 
 ((|constructor| (NIL "\\spad{S} is \\spadtype{FullyLinearlyExplicitRingOver R} means that \\spad{S} is a \\spadtype{LinearlyExplicitRingOver R} and,{} in addition,{} if \\spad{R} is a \\spadtype{LinearlyExplicitRingOver Integer},{} then so is \\spad{S}"))) 
 NIL 
 NIL 
 (-327) 
-((|constructor| (NIL "\\spadtype{Float} implements arbitrary precision floating point arithmetic. The number of significant digits of each operation can be set to an arbitrary value (the default is 20 decimal digits). The operation \\spad{float(mantissa,exponent,\\spadfunFrom{base}{FloatingPointSystem})} for integer \\spad{mantissa},{} \\spad{exponent} specifies the number \\spad{mantissa * \\spadfunFrom{base}{FloatingPointSystem} ** exponent} The underlying representation for floats is binary not decimal. The implications of this are described below. \\blankline The model adopted is that arithmetic operations are rounded to to nearest unit in the last place,{} that is,{} accurate to within \\spad{2**(-\\spadfunFrom{bits}{FloatingPointSystem})}. Also,{} the elementary functions and constants are accurate to one unit in the last place. A float is represented as a record of two integers,{} the mantissa and the exponent. The \\spadfunFrom{base}{FloatingPointSystem} of the representation is binary,{} hence a \\spad{Record(m:mantissa,e:exponent)} represents the number \\spad{m * 2 ** e}. Though it is not assumed that the underlying integers are represented with a binary \\spadfunFrom{base}{FloatingPointSystem},{} the code will be most efficient when this is the the case (this is \\spad{true} in most implementations of Lisp). The decision to choose the \\spadfunFrom{base}{FloatingPointSystem} to be binary has some unfortunate consequences. First,{} decimal numbers like 0.3 cannot be represented exactly. Second,{} there is a further loss of accuracy during conversion to decimal for output. To compensate for this,{} if \\spad{d} digits of precision are specified,{} \\spad{1 + ceiling(log2 d)} bits are used. Two numbers that are displayed identically may therefore be not equal. On the other hand,{} a significant efficiency loss would be incurred if we chose to use a decimal \\spadfunFrom{base}{FloatingPointSystem} when the underlying integer base is binary. \\blankline Algorithms used: For the elementary functions,{} the general approach is to apply identities so that the taylor series can be used,{} and,{} so that it will converge within \\spad{O( sqrt n )} steps. For example,{} using the identity \\spad{exp(x) = exp(x/2)**2},{} we can compute \\spad{exp(1/3)} to \\spad{n} digits of precision as follows. We have \\spad{exp(1/3) = exp(2 ** (-sqrt s) / 3) ** (2 ** sqrt s)}. The taylor series will converge in less than sqrt \\spad{n} steps and the exponentiation requires sqrt \\spad{n} multiplications for a total of \\spad{2 sqrt n} multiplications. Assuming integer multiplication costs \\spad{O( n**2 )} the overall running time is \\spad{O( sqrt(n) n**2 )}. This approach is the best known approach for precisions up to about 10,{}000 digits at which point the methods of Brent which are \\spad{O( log(n) n**2 )} become competitive. Note also that summing the terms of the taylor series for the elementary functions is done using integer operations. This avoids the overhead of floating point operations and results in efficient code at low precisions. This implementation makes no attempt to reuse storage,{} relying on the underlying system to do \\spadgloss{garbage collection}. \\spad{I} estimate that the efficiency of this package at low precisions could be improved by a factor of 2 if in-place operations were available. \\blankline Running times: in the following,{} \\spad{n} is the number of bits of precision \\indented{5}{\\spad{*},{} \\spad{/},{} \\spad{sqrt},{} \\spad{pi},{} \\spad{exp1},{} \\spad{log2},{} \\spad{log10}: \\spad{ O( n**2 )}} \\indented{5}{\\spad{exp},{} \\spad{log},{} \\spad{sin},{} \\spad{atan}:\\space{2}\\spad{ O( sqrt(n) n**2 )}} The other elementary functions are coded in terms of the ones above.")) (|outputSpacing| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputSpacing(n)} inserts a space after \\spad{n} (default 10) digits on output; outputSpacing(0) means no spaces are inserted.")) (|outputGeneral| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputGeneral(n)} sets the output mode to general notation with \\spad{n} significant digits displayed.") (((|Void|)) "\\spad{outputGeneral()} sets the output mode (default mode) to general notation; numbers will be displayed in either fixed or floating (scientific) notation depending on the magnitude.")) (|outputFixed| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFixed(n)} sets the output mode to fixed point notation,{} with \\spad{n} digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFixed()} sets the output mode to fixed point notation; the output will contain a decimal point.")) (|outputFloating| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFloating(n)} sets the output mode to floating (scientific) notation with \\spad{n} significant digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFloating()} sets the output mode to floating (scientific) notation,{} \\spadignore{i.e.} \\spad{mantissa * 10 exponent} is displayed as \\spad{0.mantissa E exponent}.")) (|atan| (($ $ $) "\\spad{atan(x,y)} computes the arc tangent from \\spad{x} with phase \\spad{y}.")) (|exp1| (($) "\\spad{exp1()} returns exp 1: \\spad{2.7182818284...}.")) (|log10| (($ $) "\\spad{log10(x)} computes the logarithm for \\spad{x} to base 10.") (($) "\\spad{log10()} returns \\spad{ln 10}: \\spad{2.3025809299...}.")) (|log2| (($ $) "\\spad{log2(x)} computes the logarithm for \\spad{x} to base 2.") (($) "\\spad{log2()} returns \\spad{ln 2},{} \\spadignore{i.e.} \\spad{0.6931471805...}.")) (|rationalApproximation| (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rationalApproximation(f, n, b)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< b**(-n)},{} that is \\spad{|(r-f)/f| < b**(-n)}.") (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|)) "\\spad{rationalApproximation(f, n)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< 10**(-n)}.")) (|shift| (($ $ (|Integer|)) "\\spad{shift(x,n)} adds \\spad{n} to the exponent of float \\spad{x}.")) (|relerror| (((|Integer|) $ $) "\\spad{relerror(x,y)} computes the absolute value of \\spad{x - y} divided by \\spad{y},{} when \\spad{y \\~= 0}.")) (|normalize| (($ $) "\\spad{normalize(x)} normalizes \\spad{x} at current precision.")) (** (($ $ $) "\\spad{x ** y} computes \\spad{exp(y log x)} where \\spad{x >= 0}.")) (/ (($ $ (|Integer|)) "\\spad{x / i} computes the division from \\spad{x} by an integer \\spad{i}."))) 
-((-3972 . T) (-3980 . T) (-3764 . T) (-3981 . T) (-3987 . T) (-3982 . T) ((-3991 "*") . T) (-3983 . T) (-3984 . T) (-3986 . T)) 
+((|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)) 
 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."))) 
-((-3984 . T) (-3983 . T)) 
-((|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#2| (QUOTE (-1012))))) 
+((-3986 . T) (-3985 . 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}"))) 
-((-3984 . T) (-3983 . T)) 
+((-3986 . T) (-3985 . 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}."))) 
-((-3984 . T) (-3983 . T)) 
+((-3986 . T) (-3985 . 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| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) 
@@ -1267,7 +1267,7 @@ NIL
 (-334 S) 
 ((|constructor| (NIL "The free monoid on a set \\spad{S} is the monoid of finite products of the form \\spad{reduce(*,[si ** ni])} where the \\spad{si}'s are in \\spad{S},{} and the \\spad{ni}'s are nonnegative integers. The multiplication is not commutative."))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-756)))) 
+((|HasCategory| |#1| (QUOTE (-757)))) 
 (-335) 
 ((|constructor| (NIL "This domain provides an interface to names in the file system."))) 
 NIL 
@@ -1278,13 +1278,13 @@ NIL
 NIL 
 (-337 |n| |class| R) 
 ((|constructor| (NIL "Generate the Free Lie Algebra over a ring \\spad{R} with identity; A \\spad{P}. Hall basis is generated by a package call to HallBasis.")) (|generator| (($ (|NonNegativeInteger|)) "\\spad{generator(i)} is the \\spad{i}th Hall Basis element")) (|shallowExpand| (((|OutputForm|) $) "\\spad{shallowExpand(x)} \\undocumented{}")) (|deepExpand| (((|OutputForm|) $) "\\spad{deepExpand(x)} \\undocumented{}")) (|dimension| (((|NonNegativeInteger|)) "\\spad{dimension()} is the rank of this Lie algebra"))) 
-((-3984 . T) (-3983 . T)) 
+((-3986 . T) (-3985 . T)) 
 NIL 
-(-338 -3088 UP UPUP R) 
+(-338 -3090 UP UPUP R) 
 ((|constructor| (NIL "\\indented{1}{Finds the order of a divisor over a finite field} Author: Manuel Bronstein Date Created: 1988 Date Last Updated: 11 Jul 1990")) (|order| (((|NonNegativeInteger|) (|FiniteDivisor| |#1| |#2| |#3| |#4|)) "\\spad{order(x)} \\undocumented"))) 
 NIL 
 NIL 
-(-339 -3088 UP) 
+(-339 -3090 UP) 
 ((|constructor| (NIL "\\indented{1}{Full partial fraction expansion of rational functions} Author: Manuel Bronstein Date Created: 9 December 1992 Date Last Updated: June 18,{} 2010 References: \\spad{M}.Bronstein & \\spad{B}.Salvy,{} \\indented{12}{Full Partial Fraction Decomposition of Rational Functions,{}} \\indented{12}{in Proceedings of \\spad{ISSAC'93},{} Kiev,{} ACM Press.}")) (|construct| (($ (|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| $) "\\spad{p + x} returns the sum of \\spad{p} and \\spad{x}"))) 
 NIL 
 NIL 
@@ -1298,28 +1298,28 @@ NIL
 NIL 
 (-342) 
 ((|constructor| (NIL "FieldOfPrimeCharacteristic is the category of fields of prime characteristic,{} \\spadignore{e.g.} finite fields,{} algebraic closures of fields of prime characteristic,{} transcendental extensions of of fields of prime characteristic.")) (|primeFrobenius| (($ $ (|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|)) $) "\\spad{order(a)} computes the order of an element in the multiplicative group of the field. Error: if \\spad{a} is 0."))) 
-((-3981 . T) (-3987 . T) (-3982 . T) ((-3991 "*") . T) (-3983 . T) (-3984 . T) (-3986 . T)) 
+((-3983 . T) (-3989 . T) (-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . T)) 
 NIL 
 (-343 S) 
 ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\"+\") does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\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 -3972)) (|HasAttribute| |#1| (QUOTE -3980))) 
+((|HasAttribute| |#1| (QUOTE -3974)) (|HasAttribute| |#1| (QUOTE -3982))) 
 (-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\"."))) 
-((-3764 . T) (-3981 . T) (-3987 . T) (-3982 . T) ((-3991 "*") . T) (-3983 . T) (-3984 . T) (-3986 . T)) 
+((-3766 . T) (-3983 . T) (-3989 . T) (-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . 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."))) 
-((-3982 . T) ((-3991 "*") . T) (-3983 . T) (-3984 . T) (-3986 . T)) 
-((|HasCategory| |#1| (QUOTE (-452 (-1088) $))) (|HasCategory| |#1| (QUOTE (-259 $))) (|HasCategory| |#1| (QUOTE (-241 $ $))) (|HasCategory| |#1| (QUOTE (-553 (-472)))) (|HasCategory| |#1| (QUOTE (-1132))) (OR (|HasCategory| |#1| (QUOTE (-389))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-933))) (|HasCategory| |#1| (QUOTE (-950 (-347 (-483))))) (|HasCategory| |#1| (QUOTE (-950 (-483)))) (|HasCategory| |#1| (|%list| (QUOTE -452) (QUOTE (-1088)) (|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 (-811 (-1088)))) (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-809 (-1088)))) (|HasCategory| |#1| (QUOTE (-482))) (|HasCategory| |#1| (QUOTE (-389)))) 
+((-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . 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."))) 
 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."))) 
-((-3976 -12 (|has| |#1| (-6 -3987)) (|has| |#1| (-389)) (|has| |#1| (-6 -3976))) (-3981 . T) (-3987 . T) (-3982 . T) ((-3991 "*") . T) (-3983 . T) (-3984 . T) (-3986 . T)) 
-((|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-950 (-1088)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-553 (-472)))) (|HasCategory| |#1| (QUOTE (-933))) (|HasCategory| |#1| (QUOTE (-740))) (|HasCategory| |#1| (QUOTE (-756))) (OR (|HasCategory| |#1| (QUOTE (-740))) (|HasCategory| |#1| (QUOTE (-756)))) (|HasCategory| |#1| (QUOTE (-950 (-483)))) (|HasCategory| |#1| (QUOTE (-1064))) (|HasCategory| |#1| (QUOTE (-796 (-327)))) (|HasCategory| |#1| (QUOTE (-796 (-483)))) (|HasCategory| |#1| (QUOTE (-553 (-800 (-327))))) (|HasCategory| |#1| (QUOTE (-553 (-800 (-483))))) (|HasCategory| |#1| (QUOTE (-580 (-483)))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-811 (-1088)))) (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-809 (-1088)))) (|HasCategory| |#1| (|%list| (QUOTE -452) (QUOTE (-1088)) (|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 (-482))) (-12 (|HasAttribute| |#1| (QUOTE -3976)) (|HasAttribute| |#1| (QUOTE -3987)) (|HasCategory| |#1| (QUOTE (-389)))) (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) 
+((-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))))) 
 (-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 
@@ -1330,28 +1330,28 @@ 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| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) 
-((-3983 . T) (-3984 . T) (-3986 . T)) 
+((-3985 . T) (-3986 . T) (-3988 . T)) 
 NIL 
 (-351 A S) 
 ((|constructor| (NIL "\\indented{2}{A is fully retractable to \\spad{B} means that A is retractable to \\spad{B},{} and,{}} \\indented{2}{in addition,{} if \\spad{B} is retractable to the integers or rational} \\indented{2}{numbers then so is A.} \\indented{2}{In particular,{} what we are asserting is that there are no integers} \\indented{2}{(rationals) in A which don't retract into \\spad{B}.} Date Created: March 1990 Date Last Updated: 9 April 1991"))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-950 (-347 (-483))))) (|HasCategory| |#2| (QUOTE (-950 (-483))))) 
+((|HasCategory| |#2| (QUOTE (-951 (-347 (-484))))) (|HasCategory| |#2| (QUOTE (-951 (-484))))) 
 (-352 S) 
 ((|constructor| (NIL "\\indented{2}{A is fully retractable to \\spad{B} means that A is retractable to \\spad{B},{} and,{}} \\indented{2}{in addition,{} if \\spad{B} is retractable to the integers or rational} \\indented{2}{numbers then so is A.} \\indented{2}{In particular,{} what we are asserting is that there are no integers} \\indented{2}{(rationals) in A which don't retract into \\spad{B}.} Date Created: March 1990 Date Last Updated: 9 April 1991"))) 
 NIL 
 NIL 
-(-353 R -3088 UP A) 
+(-353 R -3090 UP A) 
 ((|constructor| (NIL "Fractional ideals in a framed algebra.")) (|randomLC| ((|#4| (|NonNegativeInteger|) (|Vector| |#4|)) "\\spad{randomLC(n,x)} should be local but conditional.")) (|minimize| (($ $) "\\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)}."))) 
-((-3986 . T)) 
+((-3988 . 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 -3088 UP A |ibasis|) 
+(-355 R -3090 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|) $) "\\spad{basis((f1,...,fn))} = the vector \\spad{[f1,...,fn]}."))) 
 NIL 
-((|HasCategory| |#4| (|%list| (QUOTE -950) (|devaluate| |#2|)))) 
+((|HasCategory| |#4| (|%list| (QUOTE -951) (|devaluate| |#2|)))) 
 (-356 AR R AS S) 
 ((|constructor| (NIL "\\spad{FramedNonAssociativeAlgebraFunctions2} implements functions between two framed non associative algebra domains defined over different rings. The function map is used to coerce between algebras over different domains having the same structural constants.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,u)} maps \\spad{f} onto the coordinates of \\spad{u} to get an element in \\spad{AS} via identification of the basis of \\spad{AR} as beginning part of the basis of \\spad{AS}."))) 
 NIL 
@@ -1362,7 +1362,7 @@ NIL
 ((|HasCategory| |#2| (QUOTE (-311)))) 
 (-358 R) 
 ((|constructor| (NIL "FramedNonAssociativeAlgebra(\\spad{R}) is a \\spadtype{FiniteRankNonAssociativeAlgebra} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank) over a commutative ring \\spad{R} together with a fixed \\spad{R}-module basis.")) (|apply| (($ (|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."))) 
-((-3986 |has| |#1| (-494)) (-3984 . T) (-3983 . T)) 
+((-3988 |has| |#1| (-495)) (-3986 . T) (-3985 . 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)}."))) 
@@ -1371,10 +1371,10 @@ NIL
 (-360 S R) 
 ((|constructor| (NIL "A space of formal functions with arguments in an arbitrary ordered set.")) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| $)) $ (|Kernel| $)) "\\spad{univariate(f, k)} returns \\spad{f} viewed as a univariate fraction in \\spad{k}.")) (/ (($ (|SparseMultivariatePolynomial| |#2| (|Kernel| $)) (|SparseMultivariatePolynomial| |#2| (|Kernel| $))) "\\spad{p1/p2} returns the quotient of \\spad{p1} and \\spad{p2} as an element of \\%.")) (|denominator| (($ $) "\\spad{denominator(f)} returns the denominator of \\spad{f} converted to \\%.")) (|denom| (((|SparseMultivariatePolynomial| |#2| (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|convert| (($ (|Factored| $)) "\\spad{convert(f1\\^e1 ... fm\\^em)} returns \\spad{(f1)\\^e1 ... (fm)\\^em} as an element of \\%,{} using formal kernels created using a \\spadfunFrom{paren}{ExpressionSpace}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isPower(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|numerator| (($ $) "\\spad{numerator(f)} returns the numerator of \\spad{f} converted to \\%.")) (|numer| (((|SparseMultivariatePolynomial| |#2| (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R} if \\spad{R} is an integral domain. If not,{} then numer(\\spad{f}) = \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|coerce| (($ (|Fraction| (|Polynomial| (|Fraction| |#2|)))) "\\spad{coerce(f)} returns \\spad{f} as an element of \\%.") (($ (|Polynomial| (|Fraction| |#2|))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.") (($ (|Fraction| |#2|)) "\\spad{coerce(q)} returns \\spad{q} as an element of \\%.") (($ (|SparseMultivariatePolynomial| |#2| (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.")) (|isMult| (((|Union| (|Record| (|:| |coef| (|Integer|)) (|:| |var| (|Kernel| $))) "failed") $) "\\spad{isMult(p)} returns \\spad{[n, x]} if \\spad{p = n * x} and \\spad{n <> 0}.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,...,mn]} if \\spad{p = m1 +...+ mn} and \\spad{n > 1}.")) (|isExpt| (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|Symbol|)) "\\spad{isExpt(p,f)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = f(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|BasicOperator|)) "\\spad{isExpt(p,op)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = op(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if \\spad{p = a1*...*an} and \\spad{n > 1}.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns \\spad{x} * \\spad{x} * \\spad{x} * ... * \\spad{x} (\\spad{n} times).")) (|eval| (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ $)) "\\spad{eval(x, s, n, f)} replaces every \\spad{s(a)**n} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ (|List| $))) "\\spad{eval(x, s, n, f)} replaces every \\spad{s(a1,...,am)**n} in \\spad{x} by \\spad{f(a1,...,am)} for any \\spad{a1},{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [n1,...,nm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)**ni} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [n1,...,nm], [f1,...,fm])} replaces every \\spad{si(a)**ni} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.") (($ $ (|List| (|BasicOperator|)) (|List| $) (|Symbol|)) "\\spad{eval(x, [s1,...,sm], [f1,...,fm], y)} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $ (|BasicOperator|) $ (|Symbol|)) "\\spad{eval(x, s, f, y)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $) "\\spad{eval(f)} unquotes all the quoted operators in \\spad{f}.") (($ $ (|List| (|Symbol|))) "\\spad{eval(f, [foo1,...,foon])} unquotes all the \\spad{fooi}'s in \\spad{f}.") (($ $ (|Symbol|)) "\\spad{eval(f, foo)} unquotes all the foo's in \\spad{f}.")) (|applyQuote| (($ (|Symbol|) (|List| $)) "\\spad{applyQuote(foo, [x1,...,xn])} returns \\spad{'foo(x1,...,xn)}.") (($ (|Symbol|) $ $ $ $) "\\spad{applyQuote(foo, x, y, z, t)} returns \\spad{'foo(x,y,z,t)}.") (($ (|Symbol|) $ $ $) "\\spad{applyQuote(foo, x, y, z)} returns \\spad{'foo(x,y,z)}.") (($ (|Symbol|) $ $) "\\spad{applyQuote(foo, x, y)} returns \\spad{'foo(x,y)}.") (($ (|Symbol|) $) "\\spad{applyQuote(foo, x)} returns \\spad{'foo(x)}.")) (|variables| (((|List| (|Symbol|)) $) "\\spad{variables(f)} returns the list of all the variables of \\spad{f}.")) (|ground| ((|#2| $) "\\spad{ground(f)} returns \\spad{f} as an element of \\spad{R}. An error occurs if \\spad{f} is not an element of \\spad{R}.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(f)} tests if \\spad{f} is an element of \\spad{R}."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-950 (-483)))) (|HasCategory| |#2| (QUOTE (-494))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-961))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-410))) (|HasCategory| |#2| (QUOTE (-1024))) (|HasCategory| |#2| (QUOTE (-553 (-472))))) 
+((|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}."))) 
-((-3986 OR (|has| |#1| (-961)) (|has| |#1| (-410))) (-3984 |has| |#1| (-146)) (-3983 |has| |#1| (-146)) ((-3991 "*") |has| |#1| (-494)) (-3982 |has| |#1| (-494)) (-3987 |has| |#1| (-494)) (-3981 |has| |#1| (-494))) 
+((-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))) 
 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}."))) 
@@ -1391,36 +1391,36 @@ NIL
 (-365 A S) 
 ((|constructor| (NIL "A finite-set aggregate models the notion of a finite set,{} that is,{} a collection of elements characterized by membership,{} but not by order or multiplicity. See \\spadtype{Set} for an example.")) (|min| ((|#2| $) "\\spad{min(u)} returns the smallest element of aggregate \\spad{u}.")) (|max| ((|#2| $) "\\spad{max(u)} returns the largest element of aggregate \\spad{u}.")) (|universe| (($) "\\spad{universe()}\\$\\spad{D} returns the universal set for finite set aggregate \\spad{D}.")) (|complement| (($ $) "\\spad{complement(u)} returns the complement of the set \\spad{u},{} \\spadignore{i.e.} the set of all values not in \\spad{u}.")) (|cardinality| (((|NonNegativeInteger|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-756))) (|HasCategory| |#2| (QUOTE (-317)))) 
+((|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|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) 
-((-3989 . T) (-3979 . T) (-3990 . T)) 
+((-3991 . T) (-3981 . T) (-3992 . T)) 
 NIL 
 (-367 S A R B) 
 ((|constructor| (NIL "\\spad{FiniteSetAggregateFunctions2} provides functions involving two finite set aggregates where the underlying domains might be different. An example of this is to create a set of rational numbers by mapping a function across a set of integers,{} where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-aggregates \\spad{x} of aggregate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad {[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialised to \\spad{r}. For example,{} \\spad{reduce(_+\\$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 -3088) 
+(-368 R -3090) 
 ((|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"))) 
-((-3976 -12 (|has| |#1| (-6 -3976)) (|has| |#2| (-6 -3976))) (-3983 . T) (-3984 . T) (-3986 . T)) 
-((-12 (|HasAttribute| |#1| (QUOTE -3976)) (|HasAttribute| |#2| (QUOTE -3976)))) 
-(-370 R -3088) 
+((-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) 
 ((|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 -3088) 
+(-371 R -3090) 
 ((|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 -3088) 
+(-372 R -3090) 
 ((|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 -3088) 
+(-373 R -3090) 
 ((|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 
@@ -1428,10 +1428,10 @@ NIL
 ((|constructor| (NIL "Creates and manipulates objects which correspond to the basic FORTRAN data types: REAL,{} INTEGER,{} COMPLEX,{} LOGICAL and CHARACTER")) (= (((|Boolean|) $ $) "\\spad{x=y} tests for equality")) (|logical?| (((|Boolean|) $) "\\spad{logical?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type LOGICAL.")) (|character?| (((|Boolean|) $) "\\spad{character?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type CHARACTER.")) (|doubleComplex?| (((|Boolean|) $) "\\spad{doubleComplex?(t)} tests whether \\spad{t} is equivalent to the (non-standard) FORTRAN type DOUBLE COMPLEX.")) (|complex?| (((|Boolean|) $) "\\spad{complex?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type COMPLEX.")) (|integer?| (((|Boolean|) $) "\\spad{integer?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type INTEGER.")) (|double?| (((|Boolean|) $) "\\spad{double?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type DOUBLE PRECISION")) (|real?| (((|Boolean|) $) "\\spad{real?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type REAL.")) (|coerce| (((|SExpression|) $) "\\spad{coerce(x)} returns the \\spad{s}-expression associated with \\spad{x}") (((|Symbol|) $) "\\spad{coerce(x)} returns the symbol associated with \\spad{x}") (($ (|Symbol|)) "\\spad{coerce(s)} transforms the symbol \\spad{s} into an element of FortranScalarType provided \\spad{s} is one of real,{} complex,{}double precision,{} logical,{} integer,{} character,{} REAL,{} COMPLEX,{} LOGICAL,{} INTEGER,{} CHARACTER,{} DOUBLE PRECISION") (($ (|String|)) "\\spad{coerce(s)} transforms the string \\spad{s} into an element of FortranScalarType provided \\spad{s} is one of \"real\",{} \"double precision\",{} \"complex\",{} \"logical\",{} \"integer\",{} \"character\",{} \"REAL\",{} \"COMPLEX\",{} \"LOGICAL\",{} \"INTEGER\",{} \"CHARACTER\",{} \"DOUBLE PRECISION\""))) 
 NIL 
 NIL 
-(-375 R -3088 UP) 
+(-375 R -3090 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 (-950 (-48))))) 
+((|HasCategory| |#2| (QUOTE (-951 (-48))))) 
 (-376) 
 ((|constructor| (NIL "Creates and manipulates objects which correspond to FORTRAN data types,{} including array dimensions.")) (|fortranCharacter| (($) "\\spad{fortranCharacter()} returns CHARACTER,{} an element of FortranType")) (|fortranDoubleComplex| (($) "\\spad{fortranDoubleComplex()} returns DOUBLE COMPLEX,{} an element of FortranType")) (|fortranComplex| (($) "\\spad{fortranComplex()} returns COMPLEX,{} an element of FortranType")) (|fortranLogical| (($) "\\spad{fortranLogical()} returns LOGICAL,{} an element of FortranType")) (|fortranInteger| (($) "\\spad{fortranInteger()} returns INTEGER,{} an element of FortranType")) (|fortranDouble| (($) "\\spad{fortranDouble()} returns DOUBLE PRECISION,{} an element of FortranType")) (|fortranReal| (($) "\\spad{fortranReal()} returns REAL,{} an element of FortranType")) (|construct| (($ (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| #1="void")) (|List| (|Polynomial| (|Integer|))) (|Boolean|)) "\\spad{construct(type,dims)} creates an element of FortranType") (($ (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| #1#)) (|List| (|Symbol|)) (|Boolean|)) "\\spad{construct(type,dims)} creates an element of FortranType")) (|external?| (((|Boolean|) $) "\\spad{external?(u)} returns \\spad{true} if \\spad{u} is declared to be EXTERNAL")) (|dimensionsOf| (((|List| (|Polynomial| (|Integer|))) $) "\\spad{dimensionsOf(t)} returns the dimensions of \\spad{t}")) (|scalarTypeOf| (((|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| #1#)) $) "\\spad{scalarTypeOf(t)} returns the FORTRAN data type of \\spad{t}")) (|coerce| (($ (|FortranScalarType|)) "\\spad{coerce(t)} creates an element from a scalar type"))) 
 NIL 
@@ -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 -3088) 
+(-380 R UP -3090) 
 ((|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}."))) 
-((-3982 . T) ((-3991 "*") . T) (-3983 . T) (-3984 . T) (-3986 . T)) 
+((-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . 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"))) 
-((-3986 |has| (-347 (-857 |#1|)) (-494)) (-3984 . T) (-3983 . T)) 
-((|HasCategory| (-347 (-857 |#1|)) (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| (-347 (-857 |#1|)) (QUOTE (-494)))) 
+((-3988 |has| (-347 (-858 |#1|)) (-495)) (-3986 . T) (-3985 . 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"))) 
-(((-3991 "*") |has| |#2| (-146)) (-3982 |has| |#2| (-494)) (-3987 |has| |#2| (-6 -3987)) (-3984 . T) (-3983 . T) (-3986 . T)) 
-((|HasCategory| |#2| (QUOTE (-821))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-389))) (|HasCategory| |#2| (QUOTE (-494))) (|HasCategory| |#2| (QUOTE (-821)))) (OR (|HasCategory| |#2| (QUOTE (-389))) (|HasCategory| |#2| (QUOTE (-494))) (|HasCategory| |#2| (QUOTE (-821)))) (OR (|HasCategory| |#2| (QUOTE (-389))) (|HasCategory| |#2| (QUOTE (-821)))) (|HasCategory| |#2| (QUOTE (-494))) (|HasCategory| |#2| (QUOTE (-146))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-494)))) (-12 (|HasCategory| |#2| (QUOTE (-796 (-327)))) (|HasCategory| (-773 |#1|) (QUOTE (-796 (-327))))) (-12 (|HasCategory| |#2| (QUOTE (-796 (-483)))) (|HasCategory| (-773 |#1|) (QUOTE (-796 (-483))))) (-12 (|HasCategory| |#2| (QUOTE (-553 (-800 (-327))))) (|HasCategory| (-773 |#1|) (QUOTE (-553 (-800 (-327)))))) (-12 (|HasCategory| |#2| (QUOTE (-553 (-800 (-483))))) (|HasCategory| (-773 |#1|) (QUOTE (-553 (-800 (-483)))))) (-12 (|HasCategory| |#2| (QUOTE (-553 (-472)))) (|HasCategory| (-773 |#1|) (QUOTE (-553 (-472))))) (|HasCategory| |#2| (QUOTE (-580 (-483)))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-38 (-347 (-483))))) (|HasCategory| |#2| (QUOTE (-950 (-483)))) (OR (|HasCategory| |#2| (QUOTE (-38 (-347 (-483))))) (|HasCategory| |#2| (QUOTE (-950 (-347 (-483)))))) (|HasCategory| |#2| (QUOTE (-950 (-347 (-483))))) (|HasCategory| |#2| (QUOTE (-311))) (|HasAttribute| |#2| (QUOTE -3987)) (|HasCategory| |#2| (QUOTE (-389))) (-12 (|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#2| (QUOTE (-118))))) 
+(((-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))))) 
 (-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| $) "\\spad{leadingCoefficient(x)} \\undocumented"))) 
-((-3984 . T) (-3983 . T)) 
+((-3986 . T) (-3985 . T)) 
 NIL 
 (-399 E V R P Q) 
 ((|constructor| (NIL "Gosper's summation algorithm.")) (|GospersMethod| (((|Union| |#5| "failed") |#5| |#2| (|Mapping| |#2|)) "\\spad{GospersMethod(b, n, new)} returns a rational function \\spad{rf(n)} such that \\spad{a(n) * rf(n)} is the indefinite sum of \\spad{a(n)} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{a(n+1) * rf(n+1) - a(n) * rf(n) = a(n)},{} where \\spad{b(n) = a(n)/a(n-1)} is a rational function. Returns \"failed\" if no such rational function \\spad{rf(n)} exists. Note: \\spad{new} is a nullary function returning a new \\spad{V} every time. The condition on \\spad{a(n)} is that \\spad{a(n)/a(n-1)} is a rational function of \\spad{n}."))) 
@@ -1530,8 +1530,8 @@ NIL
 NIL 
 (-400 R E |VarSet| P) 
 ((|constructor| (NIL "A domain for polynomial sets.")) (|convert| (($ (|List| |#4|)) "\\axiom{convert(lp)} returns the polynomial set whose members are the polynomials of \\axiom{lp}."))) 
-((-3990 . T) (-3989 . T)) 
-((-12 (|HasCategory| |#4| (QUOTE (-1012))) (|HasCategory| |#4| (|%list| (QUOTE -259) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-553 (-472)))) (|HasCategory| |#4| (QUOTE (-1012))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#4| (QUOTE (-552 (-772)))) (|HasCategory| |#4| (QUOTE (-72)))) 
+((-3992 . T) (-3991 . 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}."))) 
 NIL 
@@ -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| $) "\\spad{degree(g)} names the degree of \\spad{g}. The set of all elements of a given degree form an \\spad{R}-module."))) 
 NIL 
 NIL 
-(-408 |lv| -3088 R) 
+(-408 |lv| -3090 R) 
 ((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni,{} Summer \\spad{'88},{} revised November \\spad{'89}} Solve systems of polynomial equations using Groebner bases Total order Groebner bases are computed and then converted to lex ones This package is mostly intended for internal use.")) (|genericPosition| (((|Record| (|:| |dpolys| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |coords| (|List| (|Integer|)))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{genericPosition(lp,lv)} puts a radical zero dimensional ideal in general position,{} for system \\spad{lp} in variables \\spad{lv}.")) (|testDim| (((|Union| (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "failed") (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{testDim(lp,lv)} tests if the polynomial system \\spad{lp} in variables \\spad{lv} is zero dimensional.")) (|groebSolve| (((|List| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{groebSolve(lp,lv)} reduces the polynomial system \\spad{lp} in variables \\spad{lv} to triangular form. Algorithm based on groebner bases algorithm with linear algebra for change of ordering. Preprocessing for the general solver. The polynomials in input are of type \\spadtype{DMP}."))) 
 NIL 
 NIL 
@@ -1570,23 +1570,23 @@ NIL
 NIL 
 (-410) 
 ((|constructor| (NIL "The class of multiplicative groups,{} \\spadignore{i.e.} monoids with multiplicative inverses. \\blankline")) (|commutator| (($ $ $) "\\spad{commutator(p,q)} computes \\spad{inv(p) * inv(q) * p * q}.")) (|conjugate| (($ $ $) "\\spad{conjugate(p,q)} computes \\spad{inv(q) * p * q}; this is 'right action by conjugation'.")) (|unitsKnown| ((|attribute|) "unitsKnown asserts that recip only returns \"failed\" for non-units.")) (** (($ $ (|Integer|)) "\\spad{x**n} returns \\spad{x} raised to the integer power \\spad{n}.")) (/ (($ $ $) "\\spad{x/y} is the same as \\spad{x} times the inverse of \\spad{y}.")) (|inv| (($ $) "\\spad{inv(x)} returns the inverse of \\spad{x}."))) 
-((-3986 . T)) 
+((-3988 . T)) 
 NIL 
 (-411 |Coef| |var| |cen|) 
 ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x\\^r)}.")) (|integrate| (($ $ (|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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+(((-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|))))))) 
 (-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."))) 
-((-3990 . T)) 
-((-12 (|HasCategory| (-2 (|:| -3854 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -259) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3854) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3854 |#1|) (|:| |entry| |#2|)) (QUOTE (-1012)))) (OR (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| (-2 (|:| -3854 |#1|) (|:| |entry| |#2|)) (QUOTE (-1012)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| (-2 (|:| -3854 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3854 |#1|) (|:| |entry| |#2|)) (QUOTE (-1012)))) (OR (|HasCategory| (-2 (|:| -3854 |#1|) (|:| |entry| |#2|)) (QUOTE (-552 (-772)))) (|HasCategory| |#2| (QUOTE (-552 (-772))))) (|HasCategory| (-2 (|:| -3854 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-472)))) (-12 (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| |#2| (|%list| (QUOTE -259) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-756))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3854 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3854 |#1|) (|:| |entry| |#2|)) (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3854 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3854 |#1|) (|:| |entry| |#2|)) (QUOTE (-1012)))) 
+((-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)))) 
 (-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)}"))) 
-((-3990 . T) (-3989 . T)) 
-((-12 (|HasCategory| |#4| (QUOTE (-1012))) (|HasCategory| |#4| (|%list| (QUOTE -259) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-553 (-472)))) (|HasCategory| |#4| (QUOTE (-1012))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#3| (QUOTE (-317))) (|HasCategory| |#4| (QUOTE (-552 (-772)))) (|HasCategory| |#4| (QUOTE (-72)))) 
+((-3992 . T) (-3991 . 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}."))) 
-((-3981 . T) (-3987 . T) (-3982 . T) ((-3991 "*") . T) (-3983 . T) (-3984 . T) (-3986 . T)) 
+((-3983 . T) (-3989 . T) (-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . 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."))) 
-((-3989 . T) (-3990 . T)) 
-((-12 (|HasCategory| (-2 (|:| -3854 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -259) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3854) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3854 |#1|) (|:| |entry| |#2|)) (QUOTE (-1012)))) (OR (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| (-2 (|:| -3854 |#1|) (|:| |entry| |#2|)) (QUOTE (-1012)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| (-2 (|:| -3854 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3854 |#1|) (|:| |entry| |#2|)) (QUOTE (-1012)))) (OR (|HasCategory| (-2 (|:| -3854 |#1|) (|:| |entry| |#2|)) (QUOTE (-552 (-772)))) (|HasCategory| |#2| (QUOTE (-552 (-772))))) (|HasCategory| (-2 (|:| -3854 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-472)))) (-12 (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| |#2| (|%list| (QUOTE -259) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3854 |#1|) (|:| |entry| |#2|)) (QUOTE (-1012))) (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#2| (QUOTE (-1012))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3854 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3854 |#1|) (|:| |entry| |#2|)) (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3854 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) 
+((-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)))) 
 (-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"))) 
-(((-3991 "*") |has| |#2| (-146)) (-3982 |has| |#2| (-494)) (-3987 |has| |#2| (-6 -3987)) (-3984 . T) (-3983 . T) (-3986 . T)) 
-((|HasCategory| |#2| (QUOTE (-821))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-389))) (|HasCategory| |#2| (QUOTE (-494))) (|HasCategory| |#2| (QUOTE (-821)))) (OR (|HasCategory| |#2| (QUOTE (-389))) (|HasCategory| |#2| (QUOTE (-494))) (|HasCategory| |#2| (QUOTE (-821)))) (OR (|HasCategory| |#2| (QUOTE (-389))) (|HasCategory| |#2| (QUOTE (-821)))) (|HasCategory| |#2| (QUOTE (-494))) (|HasCategory| |#2| (QUOTE (-146))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-494)))) (-12 (|HasCategory| |#2| (QUOTE (-796 (-327)))) (|HasCategory| (-773 |#1|) (QUOTE (-796 (-327))))) (-12 (|HasCategory| |#2| (QUOTE (-796 (-483)))) (|HasCategory| (-773 |#1|) (QUOTE (-796 (-483))))) (-12 (|HasCategory| |#2| (QUOTE (-553 (-800 (-327))))) (|HasCategory| (-773 |#1|) (QUOTE (-553 (-800 (-327)))))) (-12 (|HasCategory| |#2| (QUOTE (-553 (-800 (-483))))) (|HasCategory| (-773 |#1|) (QUOTE (-553 (-800 (-483)))))) (-12 (|HasCategory| |#2| (QUOTE (-553 (-472)))) (|HasCategory| (-773 |#1|) (QUOTE (-553 (-472))))) (|HasCategory| |#2| (QUOTE (-580 (-483)))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-38 (-347 (-483))))) (|HasCategory| |#2| (QUOTE (-950 (-483)))) (OR (|HasCategory| |#2| (QUOTE (-38 (-347 (-483))))) (|HasCategory| |#2| (QUOTE (-950 (-347 (-483)))))) (|HasCategory| |#2| (QUOTE (-950 (-347 (-483))))) (|HasCategory| |#2| (QUOTE (-311))) (|HasAttribute| |#2| (QUOTE -3987)) (|HasCategory| |#2| (QUOTE (-389))) (-12 (|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#2| (QUOTE (-118))))) 
-(-419 -2617 S) 
+(((-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) 
 ((|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}."))) 
-((-3983 |has| |#2| (-961)) (-3984 |has| |#2| (-961)) (-3986 |has| |#2| (-6 -3986)) (-3989 . T)) 
-((OR (-12 (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (|%list| (QUOTE -259) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (|%list| (QUOTE -259) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (|%list| (QUOTE -259) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-104))) (|HasCategory| |#2| (|%list| (QUOTE -259) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (|%list| (QUOTE -259) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (|%list| (QUOTE -259) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-311))) (|HasCategory| |#2| (|%list| (QUOTE -259) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-317))) (|HasCategory| |#2| (|%list| (QUOTE -259) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-663))) (|HasCategory| |#2| (|%list| (QUOTE -259) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-717))) (|HasCategory| |#2| (|%list| (QUOTE -259) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-756))) (|HasCategory| |#2| (|%list| (QUOTE -259) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-809 (-1088)))) (|HasCategory| |#2| (|%list| (QUOTE -259) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-961))) (|HasCategory| |#2| (|%list| (QUOTE -259) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| |#2| (|%list| (QUOTE -259) (|devaluate| |#2|))))) (|HasCategory| |#2| (QUOTE (-552 (-772)))) (|HasCategory| |#2| (QUOTE (-311))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-961)))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-311)))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-961))) (|HasCategory| |#2| (QUOTE (-663))) (|HasCategory| |#2| (QUOTE (-717))) (OR (|HasCategory| |#2| (QUOTE (-717))) (|HasCategory| |#2| (QUOTE (-756)))) (|HasCategory| 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+(-422 -3090 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."))) 
-((-3981 . T) (-3987 . T) (-3982 . T) ((-3991 "*") . T) (-3983 . T) (-3984 . T) (-3986 . T)) 
-((|HasCategory| (-483) (QUOTE (-821))) (|HasCategory| (-483) (QUOTE (-950 (-1088)))) (|HasCategory| (-483) (QUOTE (-118))) (|HasCategory| (-483) (QUOTE (-120))) (|HasCategory| (-483) (QUOTE (-553 (-472)))) (|HasCategory| (-483) (QUOTE (-933))) (|HasCategory| (-483) (QUOTE (-740))) (|HasCategory| (-483) (QUOTE (-756))) (OR (|HasCategory| (-483) (QUOTE (-740))) (|HasCategory| (-483) (QUOTE (-756)))) (|HasCategory| (-483) (QUOTE (-950 (-483)))) (|HasCategory| (-483) (QUOTE (-1064))) (|HasCategory| (-483) (QUOTE (-796 (-327)))) (|HasCategory| (-483) (QUOTE (-796 (-483)))) (|HasCategory| (-483) (QUOTE (-553 (-800 (-327))))) (|HasCategory| (-483) (QUOTE (-553 (-800 (-483))))) (|HasCategory| (-483) (QUOTE (-189))) (|HasCategory| (-483) (QUOTE (-811 (-1088)))) (|HasCategory| (-483) (QUOTE (-190))) (|HasCategory| (-483) (QUOTE (-809 (-1088)))) (|HasCategory| (-483) (QUOTE (-452 (-1088) (-483)))) (|HasCategory| (-483) (QUOTE (-259 (-483)))) (|HasCategory| (-483) (QUOTE (-241 (-483) (-483)))) (|HasCategory| (-483) (QUOTE (-257))) (|HasCategory| (-483) (QUOTE (-482))) (|HasCategory| (-483) (QUOTE (-580 (-483)))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-483) (QUOTE (-821)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-483) (QUOTE (-821)))) (|HasCategory| (-483) (QUOTE (-118))))) 
+((-3983 . T) (-3989 . T) (-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . 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 -3989)) (|HasAttribute| |#1| (QUOTE -3990)) (|HasCategory| |#2| (|%list| (QUOTE -259) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-552 (-772))))) 
+((|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))))) 
 (-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|) $) "\\spad{map(f,u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) 
 NIL 
@@ -1652,34 +1652,34 @@ NIL
 ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) 
 NIL 
 NIL 
-(-431 -3088 UP |AlExt| |AlPol|) 
+(-431 -3090 UP |AlExt| |AlPol|) 
 ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of a field over which we can factor UP's.")) (|factor| (((|Factored| |#4|) |#4| (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{factor(p, f)} returns a prime factorisation of \\spad{p}; \\spad{f} is a factorisation map for elements of UP."))) 
 NIL 
 NIL 
 (-432) 
 ((|constructor| (NIL "Algebraic closure of the rational numbers.")) (|norm| (($ $ (|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}."))) 
-((-3981 . T) (-3987 . T) (-3982 . T) ((-3991 "*") . T) (-3983 . T) (-3984 . T) (-3986 . T)) 
-((|HasCategory| $ (QUOTE (-961))) (|HasCategory| $ (QUOTE (-950 (-483))))) 
+((-3983 . T) (-3989 . T) (-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . 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."))) 
-((-3990 . T) (-3989 . T)) 
-((OR (-12 (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-553 (-472)))) (OR (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| |#1| (QUOTE (-756))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| (-483) (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|))))) 
+((-3992 . T) (-3991 . 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."))) 
-((-3989 . T) (-3990 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1012))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-72)))) 
+((-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 (-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 -3088) 
+(-436 R UP -3090) 
 ((|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."))) 
-((-3990 . T) (-3989 . T)) 
-((-12 (|HasCategory| (-85) (QUOTE (-259 (-85)))) (|HasCategory| (-85) (QUOTE (-1012)))) (|HasCategory| (-85) (QUOTE (-553 (-472)))) (|HasCategory| (-85) (QUOTE (-756))) (|HasCategory| (-483) (QUOTE (-756))) (|HasCategory| (-85) (QUOTE (-1012))) (|HasCategory| (-85) (QUOTE (-552 (-772)))) (|HasCategory| (-85) (QUOTE (-72)))) 
+((-3992 . T) (-3991 . 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)}."))) 
 NIL 
@@ -1692,17 +1692,17 @@ 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 -3088 |Expon| |VarSet| |DPoly|) 
+(-441 -3090 |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 (-553 (-1088))))) 
+((|HasCategory| |#3| (QUOTE (-554 (-1089))))) 
 (-442 |vl| |nv|) 
 ((|constructor| (NIL "\\indented{2}{This package provides functions for the primary decomposition of} polynomial ideals over the rational numbers. The ideals are members of the \\spadtype{PolynomialIdeals} domain,{} and the polynomial generators are required to be from the \\spadtype{DistributedMultivariatePolynomial} domain.")) (|contract| (((|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|)))) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|)))) (|List| (|OrderedVariableList| |#1|))) "\\spad{contract(I,lvar)} contracts the ideal \\spad{I} to the polynomial ring \\spad{F[lvar]}.")) (|primaryDecomp| (((|List| (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{primaryDecomp(I)} returns a list of primary ideals such that their intersection is the ideal \\spad{I}.")) (|radical| (((|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|)))) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{radical(I)} returns the radical of the ideal \\spad{I}.")) (|prime?| (((|Boolean|) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{prime?(I)} tests if the ideal \\spad{I} is prime.")) (|zeroDimPrimary?| (((|Boolean|) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{zeroDimPrimary?(I)} tests if the ideal \\spad{I} is 0-dimensional primary.")) (|zeroDimPrime?| (((|Boolean|) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{zeroDimPrime?(I)} tests if the ideal \\spad{I} is a 0-dimensional prime."))) 
 NIL 
 NIL 
 (-443 T$) 
 ((|constructor| (NIL "This is the category of all domains that implement idempotent operations."))) 
-(((|%Rule| |idempotence| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|)) (-3052 (|f| |x| |x|) |x|))) . T)) 
+(((|%Rule| |idempotence| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|)) (-3054 (|f| |x| |x|) |x|))) . T)) 
 NIL 
 (-444) 
 ((|constructor| (NIL "This domain provides representation for plain identifiers. It differs from Symbol in that it does not support any form of scripting. It is a plain basic data structure. \\blankline")) (|gensym| (($) "\\spad{gensym()} returns a new identifier,{} different from any other identifier in the running system"))) 
@@ -1711,11 +1711,11 @@ NIL
 (-445 A S) 
 ((|constructor| (NIL "\\indented{1}{Indexed direct products of abelian groups over an abelian group \\spad{A} of} generators indexed by the ordered set \\spad{S}. All items have finite support: only non-zero terms are stored."))) 
 NIL 
-((-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#2| (QUOTE (-1012))))) 
+((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-1013))))) 
 (-446 A S) 
 ((|constructor| (NIL "\\indented{1}{Indexed direct products of abelian monoids over an abelian monoid \\spad{A} of} generators indexed by the ordered set \\spad{S}. All items have finite support. Only non-zero terms are stored."))) 
 NIL 
-((-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#2| (QUOTE (-1012))))) 
+((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-1013))))) 
 (-447 A S) 
 ((|constructor| (NIL "This category represents the direct product of some set with respect to an ordered indexing set.")) (|terms| (((|List| (|Pair| |#2| |#1|)) $) "\\spad{terms x} returns the list of terms in \\spad{x}. Each term is a pair of a support (the first component) and the corresponding value (the second component).")) (|reductum| (($ $) "\\spad{reductum(z)} returns a new element created by removing the leading coefficient/support pair from the element \\spad{z}. Error: if \\spad{z} has no support.")) (|leadingSupport| ((|#2| $) "\\spad{leadingSupport(z)} returns the index of leading (with respect to the ordering on the indexing set) monomial of \\spad{z}. Error: if \\spad{z} has no support.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(z)} returns the coefficient of the leading (with respect to the ordering on the indexing set) monomial of \\spad{z}. Error: if \\spad{z} has no support.")) (|monomial| (($ |#1| |#2|) "\\spad{monomial(a,s)} constructs a direct product element with the \\spad{s} component set to \\spad{a}")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,z)} returns the new element created by applying the function \\spad{f} to each component of the direct product element \\spad{z}."))) 
 NIL 
@@ -1723,3042 +1723,3046 @@ 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."))) 
 NIL 
-((-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#2| (QUOTE (-1012))))) 
+((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-1013))))) 
 (-449 A S) 
 ((|constructor| (NIL "\\indented{1}{Indexed direct products of ordered abelian monoids \\spad{A} of} generators indexed by the ordered set \\spad{S}. The inherited order is lexicographical. All items have finite support: only non-zero terms are stored."))) 
 NIL 
-((-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#2| (QUOTE (-1012))))) 
+((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-1013))))) 
 (-450 A S) 
 ((|constructor| (NIL "\\indented{1}{Indexed direct products of ordered abelian monoid sups \\spad{A},{}} generators indexed by the ordered set \\spad{S}. All items have finite support: only non-zero terms are stored."))) 
 NIL 
-((-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#2| (QUOTE (-1012))))) 
-(-451 S A B) 
+((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-1013))))) 
+(-451 A S) 
+((|constructor| (NIL "An indexed product term is a utility domain used in the representation of indexed direct product objects.")) (|coefficient| ((|#1| $) "\\spad{coefficient t} returns the coefficient of the tern \\spad{t}.")) (|index| ((|#2| $) "\\spad{index t} returns the index of the term \\spad{t}.")) (|term| (($ |#2| |#1|) "\\spad{term(s,a)} constructs a term with index \\spad{s} and coefficient \\spad{a}."))) 
+NIL 
+NIL 
+(-452 S A B) 
 ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation'' substitutions. The difference between this and \\spadtype{Evalable} is that the operations in this category specify the substitution as a pair of arguments rather than as an equation.")) (|eval| (($ $ (|List| |#2|) (|List| |#3|)) "\\spad{eval(f, [x1,...,xn], [v1,...,vn])} replaces \\spad{xi} by \\spad{vi} in \\spad{f}.") (($ $ |#2| |#3|) "\\spad{eval(f, x, v)} replaces \\spad{x} by \\spad{v} in \\spad{f}."))) 
 NIL 
 NIL 
-(-452 A B) 
+(-453 A B) 
 ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation'' substitutions. The difference between this and \\spadtype{Evalable} is that the operations in this category specify the substitution as a pair of arguments rather than as an equation.")) (|eval| (($ $ (|List| |#1|) (|List| |#2|)) "\\spad{eval(f, [x1,...,xn], [v1,...,vn])} replaces \\spad{xi} by \\spad{vi} in \\spad{f}.") (($ $ |#1| |#2|) "\\spad{eval(f, x, v)} replaces \\spad{x} by \\spad{v} in \\spad{f}."))) 
 NIL 
 NIL 
-(-453 S E |un|) 
+(-454 S E |un|) 
 ((|constructor| (NIL "Internal implementation of a free abelian monoid."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-716)))) 
-(-454 S |mn|) 
+((|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}"))) 
-((-3990 . T) (-3989 . T)) 
-((OR (-12 (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-553 (-472)))) (OR (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| |#1| (QUOTE (-756))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| (-483) (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|))))) 
-(-455) 
+((-3992 . T) (-3991 . 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'."))) 
 NIL 
 NIL 
-(-456 |p| |n|) 
+(-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}."))) 
-((-3981 . T) (-3987 . T) (-3982 . T) ((-3991 "*") . T) (-3983 . T) (-3984 . T) (-3986 . T)) 
-((OR (|HasCategory| (-516 |#1|) (QUOTE (-118))) (|HasCategory| (-516 |#1|) (QUOTE (-317)))) (|HasCategory| (-516 |#1|) (QUOTE (-120))) (|HasCategory| (-516 |#1|) (QUOTE (-317))) (|HasCategory| (-516 |#1|) (QUOTE (-118)))) 
-(-457 R |mnRow| |mnCol| |Row| |Col|) 
+((-3983 . T) (-3989 . T) (-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . 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."))) 
-((-3989 . T) (-3990 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1012))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-72)))) 
-(-458 R |Row| |Col| M) 
+((-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 (-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 -3990))) 
-(-459 R |Row| |Col| M QF |Row2| |Col2| M2) 
+((|HasAttribute| |#3| (QUOTE -3992))) 
+(-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 -3990))) 
-(-460 R |mnRow| |mnCol|) 
+((|HasAttribute| |#7| (QUOTE -3992))) 
+(-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."))) 
-((-3989 . T) (-3990 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1012))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-257))) (|HasCategory| |#1| (QUOTE (-494))) (|HasAttribute| |#1| (QUOTE (-3991 "*"))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-72)))) 
-(-461) 
+((-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)))) 
+(-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 
 NIL 
-(-462) 
+(-463) 
 ((|constructor| (NIL "This domain represents the `in' iterator syntax.")) (|sequence| (((|SpadAst|) $) "\\spad{sequence(i)} returns the sequence expression being iterated over by `i'.")) (|iterationVar| (((|Identifier|) $) "\\spad{iterationVar(i)} returns the name of the iterating variable of the `in' iterator 'i'"))) 
 NIL 
 NIL 
-(-463 S) 
+(-464 S) 
 ((|constructor| (NIL "This category describes input byte stream conduits.")) (|readBytes!| (((|NonNegativeInteger|) $ (|ByteBuffer|)) "\\spad{readBytes!(c,b)} reads byte sequences from conduit `c' into the byte buffer `b'. The actual number of bytes written is returned,{} and the length of `b' is set to that amount.")) (|readUInt32!| (((|Maybe| (|UInt32|)) $) "\\spad{readUInt32!(cond)} attempts to read a \\spad{UInt32} value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readInt32!| (((|Maybe| (|Int32|)) $) "\\spad{readInt32!(cond)} attempts to read an \\spad{Int32} value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readUInt16!| (((|Maybe| (|UInt16|)) $) "\\spad{readUInt16!(cond)} attempts to read a \\spad{UInt16} value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readInt16!| (((|Maybe| (|Int16|)) $) "\\spad{readInt16!(cond)} attempts to read an \\spad{Int16} value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readUInt8!| (((|Maybe| (|UInt8|)) $) "\\spad{readUInt8!(cond)} attempts to read a \\spad{UInt8} value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readInt8!| (((|Maybe| (|Int8|)) $) "\\spad{readInt8!(cond)} attempts to read an \\spad{Int8} value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readByte!| (((|Maybe| (|Byte|)) $) "\\spad{readByte!(cond)} attempts to read a byte from the input conduit `cond'. Returns the read byte if successful,{} otherwise \\spad{nothing}."))) 
 NIL 
 NIL 
-(-464) 
+(-465) 
 ((|constructor| (NIL "This category describes input byte stream conduits.")) (|readBytes!| (((|NonNegativeInteger|) $ (|ByteBuffer|)) "\\spad{readBytes!(c,b)} reads byte sequences from conduit `c' into the byte buffer `b'. The actual number of bytes written is returned,{} and the length of `b' is set to that amount.")) (|readUInt32!| (((|Maybe| (|UInt32|)) $) "\\spad{readUInt32!(cond)} attempts to read a \\spad{UInt32} value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readInt32!| (((|Maybe| (|Int32|)) $) "\\spad{readInt32!(cond)} attempts to read an \\spad{Int32} value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readUInt16!| (((|Maybe| (|UInt16|)) $) "\\spad{readUInt16!(cond)} attempts to read a \\spad{UInt16} value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readInt16!| (((|Maybe| (|Int16|)) $) "\\spad{readInt16!(cond)} attempts to read an \\spad{Int16} value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readUInt8!| (((|Maybe| (|UInt8|)) $) "\\spad{readUInt8!(cond)} attempts to read a \\spad{UInt8} value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readInt8!| (((|Maybe| (|Int8|)) $) "\\spad{readInt8!(cond)} attempts to read an \\spad{Int8} value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readByte!| (((|Maybe| (|Byte|)) $) "\\spad{readByte!(cond)} attempts to read a byte from the input conduit `cond'. Returns the read byte if successful,{} otherwise \\spad{nothing}."))) 
 NIL 
 NIL 
-(-465 GF) 
+(-466 GF) 
 ((|constructor| (NIL "InnerNormalBasisFieldFunctions(GF) (unexposed): This package has functions used by every normal basis finite field extension domain.")) (|minimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) (|Vector| |#1|)) "\\spad{minimalPolynomial(x)} \\undocumented{} See \\axiomFunFrom{minimalPolynomial}{FiniteAlgebraicExtensionField}")) (|normalElement| (((|Vector| |#1|) (|PositiveInteger|)) "\\spad{normalElement(n)} \\undocumented{} See \\axiomFunFrom{normalElement}{FiniteAlgebraicExtensionField}")) (|basis| (((|Vector| (|Vector| |#1|)) (|PositiveInteger|)) "\\spad{basis(n)} \\undocumented{} See \\axiomFunFrom{basis}{FiniteAlgebraicExtensionField}")) (|normal?| (((|Boolean|) (|Vector| |#1|)) "\\spad{normal?(x)} \\undocumented{} See \\axiomFunFrom{normal?}{FiniteAlgebraicExtensionField}")) (|lookup| (((|PositiveInteger|) (|Vector| |#1|)) "\\spad{lookup(x)} \\undocumented{} See \\axiomFunFrom{lookup}{Finite}")) (|inv| (((|Vector| |#1|) (|Vector| |#1|)) "\\spad{inv x} \\undocumented{} See \\axiomFunFrom{inv}{DivisionRing}")) (|trace| (((|Vector| |#1|) (|Vector| |#1|) (|PositiveInteger|)) "\\spad{trace(x,n)} \\undocumented{} See \\axiomFunFrom{trace}{FiniteAlgebraicExtensionField}")) (|norm| (((|Vector| |#1|) (|Vector| |#1|) (|PositiveInteger|)) "\\spad{norm(x,n)} \\undocumented{} See \\axiomFunFrom{norm}{FiniteAlgebraicExtensionField}")) (/ (((|Vector| |#1|) (|Vector| |#1|) (|Vector| |#1|)) "\\spad{x/y} \\undocumented{} See \\axiomFunFrom{/}{Field}")) (* (((|Vector| |#1|) (|Vector| |#1|) (|Vector| |#1|)) "\\spad{x*y} \\undocumented{} See \\axiomFunFrom{*}{SemiGroup}")) (** (((|Vector| |#1|) (|Vector| |#1|) (|Integer|)) "\\spad{x**n} \\undocumented{} See \\axiomFunFrom{**}{DivisionRing}")) (|qPot| (((|Vector| |#1|) (|Vector| |#1|) (|Integer|)) "\\spad{qPot(v,e)} computes \\spad{v**(q**e)},{} interpreting \\spad{v} as an element of normal basis field,{} \\spad{q} the size of the ground field. This is done by a cyclic \\spad{e}-shift of the vector \\spad{v}.")) (|expPot| (((|Vector| |#1|) (|Vector| |#1|) (|SingleInteger|) (|SingleInteger|)) "\\spad{expPot(v,e,d)} returns the sum from \\spad{i = 0} to \\spad{e - 1} of \\spad{v**(q**i*d)},{} interpreting \\spad{v} as an element of a normal basis field and where \\spad{q} is the size of the ground field. Note: for a description of the algorithm,{} see \\spad{T}.Itoh and \\spad{S}.Tsujii,{} \"A fast algorithm for computing multiplicative inverses in GF(2^m) using normal bases\",{} Information and Computation 78,{} pp.171-177,{} 1988.")) (|repSq| (((|Vector| |#1|) (|Vector| |#1|) (|NonNegativeInteger|)) "\\spad{repSq(v,e)} computes \\spad{v**e} by repeated squaring,{} interpreting \\spad{v} as an element of a normal basis field.")) (|dAndcExp| (((|Vector| |#1|) (|Vector| |#1|) (|NonNegativeInteger|) (|SingleInteger|)) "\\spad{dAndcExp(v,n,k)} computes \\spad{v**e} interpreting \\spad{v} as an element of normal basis field. A divide and conquer algorithm similar to the one from \\spad{D}.\\spad{R}.Stinson,{} \"Some observations on parallel Algorithms for fast exponentiation in GF(2^n)\",{} Siam \\spad{J}. Computation,{} Vol.19,{} No.4,{} pp.711-717,{} August 1990 is used. Argument \\spad{k} is a parameter of this algorithm.")) (|xn| (((|SparseUnivariatePolynomial| |#1|) (|NonNegativeInteger|)) "\\spad{xn(n)} returns the polynomial \\spad{x**n-1}.")) (|pol| (((|SparseUnivariatePolynomial| |#1|) (|Vector| |#1|)) "\\spad{pol(v)} turns the vector \\spad{[v0,...,vn]} into the polynomial \\spad{v0+v1*x+ ... + vn*x**n}.")) (|index| (((|Vector| |#1|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{index(n,m)} is a index function for vectors of length \\spad{n} over the ground field.")) (|random| (((|Vector| |#1|) (|PositiveInteger|)) "\\spad{random(n)} creates a vector over the ground field with random entries.")) (|setFieldInfo| (((|Void|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) |#1|) "\\spad{setFieldInfo(m,p)} initializes the field arithmetic,{} where \\spad{m} is the multiplication table and \\spad{p} is the respective normal element of the ground field GF."))) 
 NIL 
 NIL 
-(-466) 
+(-467) 
 ((|constructor| (NIL "This domain provides representation for binary files open for input operations. `Binary' here means that the conduits do not interpret their contents.")) (|position!| (((|SingleInteger|) $ (|SingleInteger|)) "position(\\spad{f},{}\\spad{p}) sets the current byte-position to `i'.")) (|position| (((|SingleInteger|) $) "\\spad{position(f)} returns the current byte-position in the file `f'.")) (|isOpen?| (((|Boolean|) $) "\\spad{isOpen?(ifile)} holds if `ifile' is in open state.")) (|eof?| (((|Boolean|) $) "\\spad{eof?(ifile)} holds when the last read reached end of file.")) (|inputBinaryFile| (($ (|String|)) "\\spad{inputBinaryFile(f)} returns an input conduit obtained by opening the file named by `f' as a binary file.") (($ (|FileName|)) "\\spad{inputBinaryFile(f)} returns an input conduit obtained by opening the file named by `f' as a binary file."))) 
 NIL 
 NIL 
-(-467 R) 
+(-468 R) 
 ((|constructor| (NIL "This package provides operations to create incrementing functions.")) (|incrementBy| (((|Mapping| |#1| |#1|) |#1|) "\\spad{incrementBy(n)} produces a function which adds \\spad{n} to whatever argument it is given. For example,{} if {\\spad{f} := increment(\\spad{n})} then \\spad{f x} is \\spad{x+n}.")) (|increment| (((|Mapping| |#1| |#1|)) "\\spad{increment()} produces a function which adds \\spad{1} to whatever argument it is given. For example,{} if {\\spad{f} := increment()} then \\spad{f x} is \\spad{x+1}."))) 
 NIL 
 NIL 
-(-468 |Varset|) 
+(-469 |Varset|) 
 ((|constructor| (NIL "\\indented{2}{IndexedExponents of an ordered set of variables gives a representation} for the degree of polynomials in commuting variables. It gives an ordered pairing of non negative integer exponents with variables"))) 
 NIL 
-((-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| (-694) (QUOTE (-1012))))) 
-(-469 K -3088 |Par|) 
+((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| (-695) (QUOTE (-1013))))) 
+(-470 K -3090 |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 
-(-470) 
+(-471) 
 NIL 
 NIL 
 NIL 
-(-471) 
+(-472) 
 ((|constructor| (NIL "Default infinity signatures for the interpreter; Date Created: 4 Oct 1989 Date Last Updated: 4 Oct 1989")) (|minusInfinity| (((|OrderedCompletion| (|Integer|))) "\\spad{minusInfinity()} returns minusInfinity.")) (|plusInfinity| (((|OrderedCompletion| (|Integer|))) "\\spad{plusInfinity()} returns plusIinfinity.")) (|infinity| (((|OnePointCompletion| (|Integer|))) "\\spad{infinity()} returns infinity."))) 
 NIL 
 NIL 
-(-472) 
+(-473) 
 ((|constructor| (NIL "Domain of parsed forms which can be passed to the interpreter. This is also the interface between algebra code and facilities in the interpreter.")) (|compile| (((|Symbol|) (|Symbol|) (|List| $)) "\\spad{compile(f, [t1,...,tn])} forces the interpreter to compile the function \\spad{f} with signature \\spad{(t1,...,tn) -> ?}. returns the symbol \\spad{f} if successful. Error: if \\spad{f} was not defined beforehand in the interpreter,{} or if the \\spad{ti}'s are not valid types,{} or if the compiler fails.")) (|declare| (((|Symbol|) (|List| $)) "\\spad{declare(t)} returns a name \\spad{f} such that \\spad{f} has been declared to the interpreter to be of type \\spad{t},{} but has not been assigned a value yet. Note: \\spad{t} should be created as \\spad{devaluate(T)\\$Lisp} where \\spad{T} is the actual type of \\spad{f} (this hack is required for the case where \\spad{T} is a mapping type).")) (|parseString| (($ (|String|)) "parseString is the inverse of unparse. It parses a string to InputForm.")) (|unparse| (((|String|) $) "\\spad{unparse(f)} returns a string \\spad{s} such that the parser would transform \\spad{s} to \\spad{f}. Error: if \\spad{f} is not the parsed form of a string.")) (|flatten| (($ $) "\\spad{flatten(s)} returns an input form corresponding to \\spad{s} with all the nested operations flattened to triples using new local variables. If \\spad{s} is a piece of code,{} this speeds up the compilation tremendously later on.")) (|One| (($) "\\spad{1} returns the input form corresponding to 1.")) (|Zero| (($) "\\spad{0} returns the input form corresponding to 0.")) (** (($ $ (|Integer|)) "\\spad{a ** b} returns the input form corresponding to \\spad{a ** b}.") (($ $ (|NonNegativeInteger|)) "\\spad{a ** b} returns the input form corresponding to \\spad{a ** b}.")) (/ (($ $ $) "\\spad{a / b} returns the input form corresponding to \\spad{a / b}.")) (* (($ $ $) "\\spad{a * b} returns the input form corresponding to \\spad{a * b}.")) (+ (($ $ $) "\\spad{a + b} returns the input form corresponding to \\spad{a + b}.")) (|lambda| (($ $ (|List| (|Symbol|))) "\\spad{lambda(code, [x1,...,xn])} returns the input form corresponding to \\spad{(x1,...,xn) +-> code} if \\spad{n > 1},{} or to \\spad{x1 +-> code} if \\spad{n = 1}.")) (|function| (($ $ (|List| (|Symbol|)) (|Symbol|)) "\\spad{function(code, [x1,...,xn], f)} returns the input form corresponding to \\spad{f(x1,...,xn) == code}.")) (|binary| (($ $ (|List| $)) "\\spad{binary(op, [a1,...,an])} returns the input form corresponding to \\spad{a1 op a2 op ... op an}.")) (|convert| (($ (|SExpression|)) "\\spad{convert(s)} makes \\spad{s} into an input form.")) (|interpret| (((|Any|) $) "\\spad{interpret(f)} passes \\spad{f} to the interpreter."))) 
 NIL 
 NIL 
-(-473 R) 
+(-474 R) 
 ((|constructor| (NIL "Tools for manipulating input forms.")) (|interpret| ((|#1| (|InputForm|)) "\\spad{interpret(f)} passes \\spad{f} to the interpreter,{} and transforms the result into an object of type \\spad{R}.")) (|packageCall| (((|InputForm|) (|Symbol|)) "\\spad{packageCall(f)} returns the input form corresponding to \\spad{f}\\$\\spad{R}."))) 
 NIL 
 NIL 
-(-474 |Coef| UTS) 
+(-475 |Coef| UTS) 
 ((|constructor| (NIL "This package computes infinite products of univariate Taylor series over an integral domain of characteristic 0.")) (|generalInfiniteProduct| ((|#2| |#2| (|Integer|) (|Integer|)) "\\spad{generalInfiniteProduct(f(x),a,d)} computes \\spad{product(n=a,a+d,a+2*d,...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|oddInfiniteProduct| ((|#2| |#2|) "\\spad{oddInfiniteProduct(f(x))} computes \\spad{product(n=1,3,5...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|evenInfiniteProduct| ((|#2| |#2|) "\\spad{evenInfiniteProduct(f(x))} computes \\spad{product(n=2,4,6...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|infiniteProduct| ((|#2| |#2|) "\\spad{infiniteProduct(f(x))} computes \\spad{product(n=1,2,3...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1."))) 
 NIL 
 NIL 
-(-475 K -3088 |Par|) 
+(-476 K -3090 |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 
-(-476 R BP |pMod| |nextMod|) 
+(-477 R BP |pMod| |nextMod|) 
 ((|reduction| ((|#2| |#2| |#1|) "\\spad{reduction(f,p)} reduces the coefficients of the polynomial \\spad{f} modulo the prime \\spad{p}.")) (|modularGcd| ((|#2| (|List| |#2|)) "\\spad{modularGcd(listf)} computes the gcd of the list of polynomials \\spad{listf} by modular methods.")) (|modularGcdPrimitive| ((|#2| (|List| |#2|)) "\\spad{modularGcdPrimitive(f1,f2)} computes the gcd of the two polynomials \\spad{f1} and \\spad{f2} by modular methods."))) 
 NIL 
 NIL 
-(-477 OV E R P) 
+(-478 OV E R P) 
 ((|constructor| (NIL "\\indented{2}{This is an inner package for factoring multivariate polynomials} over various coefficient domains in characteristic 0. The univariate factor operation is passed as a parameter. Multivariate hensel lifting is used to lift the univariate factorization")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|) (|Mapping| (|Factored| (|SparseUnivariatePolynomial| |#3|)) (|SparseUnivariatePolynomial| |#3|))) "\\spad{factor(p,ufact)} factors the multivariate polynomial \\spad{p} by specializing variables and calling the univariate factorizer \\spad{ufact}. \\spad{p} is represented as a univariate polynomial with multivariate coefficients.") (((|Factored| |#4|) |#4| (|Mapping| (|Factored| (|SparseUnivariatePolynomial| |#3|)) (|SparseUnivariatePolynomial| |#3|))) "\\spad{factor(p,ufact)} factors the multivariate polynomial \\spad{p} by specializing variables and calling the univariate factorizer \\spad{ufact}."))) 
 NIL 
 NIL 
-(-478 K UP |Coef| UTS) 
+(-479 K UP |Coef| UTS) 
 ((|constructor| (NIL "This package computes infinite products of univariate Taylor series over an arbitrary finite field.")) (|generalInfiniteProduct| ((|#4| |#4| (|Integer|) (|Integer|)) "\\spad{generalInfiniteProduct(f(x),a,d)} computes \\spad{product(n=a,a+d,a+2*d,...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|oddInfiniteProduct| ((|#4| |#4|) "\\spad{oddInfiniteProduct(f(x))} computes \\spad{product(n=1,3,5...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|evenInfiniteProduct| ((|#4| |#4|) "\\spad{evenInfiniteProduct(f(x))} computes \\spad{product(n=2,4,6...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|infiniteProduct| ((|#4| |#4|) "\\spad{infiniteProduct(f(x))} computes \\spad{product(n=1,2,3...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1."))) 
 NIL 
 NIL 
-(-479 |Coef| UTS) 
+(-480 |Coef| UTS) 
 ((|constructor| (NIL "This package computes infinite products of univariate Taylor series over a field of prime order.")) (|generalInfiniteProduct| ((|#2| |#2| (|Integer|) (|Integer|)) "\\spad{generalInfiniteProduct(f(x),a,d)} computes \\spad{product(n=a,a+d,a+2*d,...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|oddInfiniteProduct| ((|#2| |#2|) "\\spad{oddInfiniteProduct(f(x))} computes \\spad{product(n=1,3,5...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|evenInfiniteProduct| ((|#2| |#2|) "\\spad{evenInfiniteProduct(f(x))} computes \\spad{product(n=2,4,6...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|infiniteProduct| ((|#2| |#2|) "\\spad{infiniteProduct(f(x))} computes \\spad{product(n=1,2,3...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1."))) 
 NIL 
 NIL 
-(-480 R UP) 
+(-481 R UP) 
 ((|constructor| (NIL "Find the sign of a polynomial around a point or infinity.")) (|signAround| (((|Union| (|Integer|) #1="failed") |#2| |#1| (|Mapping| (|Union| (|Integer|) #1#) |#1|)) "\\spad{signAround(u,r,f)} \\undocumented") (((|Union| (|Integer|) #1#) |#2| |#1| (|Integer|) (|Mapping| (|Union| (|Integer|) #1#) |#1|)) "\\spad{signAround(u,r,i,f)} \\undocumented") (((|Union| (|Integer|) #1#) |#2| (|Integer|) (|Mapping| (|Union| (|Integer|) #1#) |#1|)) "\\spad{signAround(u,i,f)} \\undocumented"))) 
 NIL 
 NIL 
-(-481 S) 
+(-482 S) 
 ((|constructor| (NIL "An \\spad{IntegerNumberSystem} is a model for the integers.")) (|invmod| (($ $ $) "\\spad{invmod(a,b)},{} \\spad{0<=a<b>1},{} \\spad{(a,b)=1} means \\spad{1/a mod b}.")) (|powmod| (($ $ $ $) "\\spad{powmod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a**b mod p}.")) (|mulmod| (($ $ $ $) "\\spad{mulmod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a*b mod p}.")) (|submod| (($ $ $ $) "\\spad{submod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a-b mod p}.")) (|addmod| (($ $ $ $) "\\spad{addmod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a+b mod p}.")) (|mask| (($ $) "\\spad{mask(n)} returns \\spad{2**n-1} (an \\spad{n} bit mask).")) (|dec| (($ $) "\\spad{dec(x)} returns \\spad{x - 1}.")) (|inc| (($ $) "\\spad{inc(x)} returns \\spad{x + 1}.")) (|copy| (($ $) "\\spad{copy(n)} gives a copy of \\spad{n}.")) (|random| (($ $) "\\spad{random(a)} creates a random element from 0 to \\spad{a-1}.") (($) "\\spad{random()} creates a random element.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(n)} creates a rational number,{} or returns \"failed\" if this is not possible.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(n)} creates a rational number (see \\spadtype{Fraction Integer})..")) (|rational?| (((|Boolean|) $) "\\spad{rational?(n)} tests if \\spad{n} is a rational number (see \\spadtype{Fraction Integer}).")) (|symmetricRemainder| (($ $ $) "\\spad{symmetricRemainder(a,b)} (where \\spad{b > 1}) yields \\spad{r} where \\spad{ -b/2 <= r < b/2 }.")) (|positiveRemainder| (($ $ $) "\\spad{positiveRemainder(a,b)} (where \\spad{b > 1}) yields \\spad{r} where \\spad{0 <= r < b} and \\spad{r == a rem b}.")) (|bit?| (((|Boolean|) $ $) "\\spad{bit?(n,i)} returns \\spad{true} if and only if \\spad{i}-th bit of \\spad{n} is a 1.")) (|shift| (($ $ $) "\\spad{shift(a,i)} shift \\spad{a} by \\spad{i} digits.")) (|length| (($ $) "\\spad{length(a)} length of \\spad{a} in digits.")) (|base| (($) "\\spad{base()} returns the base for the operations of \\spad{IntegerNumberSystem}.")) (|multiplicativeValuation| ((|attribute|) "euclideanSize(a*b) returns \\spad{euclideanSize(a)*euclideanSize(b)}.")) (|even?| (((|Boolean|) $) "\\spad{even?(n)} returns \\spad{true} if and only if \\spad{n} is even.")) (|odd?| (((|Boolean|) $) "\\spad{odd?(n)} returns \\spad{true} if and only if \\spad{n} is odd."))) 
 NIL 
 NIL 
-(-482) 
+(-483) 
 ((|constructor| (NIL "An \\spad{IntegerNumberSystem} is a model for the integers.")) (|invmod| (($ $ $) "\\spad{invmod(a,b)},{} \\spad{0<=a<b>1},{} \\spad{(a,b)=1} means \\spad{1/a mod b}.")) (|powmod| (($ $ $ $) "\\spad{powmod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a**b mod p}.")) (|mulmod| (($ $ $ $) "\\spad{mulmod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a*b mod p}.")) (|submod| (($ $ $ $) "\\spad{submod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a-b mod p}.")) (|addmod| (($ $ $ $) "\\spad{addmod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a+b mod p}.")) (|mask| (($ $) "\\spad{mask(n)} returns \\spad{2**n-1} (an \\spad{n} bit mask).")) (|dec| (($ $) "\\spad{dec(x)} returns \\spad{x - 1}.")) (|inc| (($ $) "\\spad{inc(x)} returns \\spad{x + 1}.")) (|copy| (($ $) "\\spad{copy(n)} gives a copy of \\spad{n}.")) (|random| (($ $) "\\spad{random(a)} creates a random element from 0 to \\spad{a-1}.") (($) "\\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."))) 
-((-3987 . T) (-3988 . T) (-3982 . T) ((-3991 "*") . T) (-3983 . T) (-3984 . T) (-3986 . T)) 
+((-3989 . T) (-3990 . T) (-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . T)) 
 NIL 
-(-483) 
+(-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."))) 
-((-3977 . T) (-3981 . T) (-3976 . T) (-3987 . T) (-3988 . T) (-3982 . T) ((-3991 "*") . T) (-3983 . T) (-3984 . T) (-3986 . T)) 
+((-3979 . T) (-3983 . T) (-3978 . T) (-3989 . T) (-3990 . T) (-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . T)) 
 NIL 
-(-484) 
+(-485) 
 ((|constructor| (NIL "This domain is a datatype for (signed) integer values of precision 16 bits."))) 
 NIL 
 NIL 
-(-485) 
+(-486) 
 ((|constructor| (NIL "This domain is a datatype for (signed) integer values of precision 32 bits."))) 
 NIL 
 NIL 
-(-486) 
+(-487) 
 ((|constructor| (NIL "This domain is a datatype for (signed) integer values of precision 64 bits."))) 
 NIL 
 NIL 
-(-487) 
+(-488) 
 ((|constructor| (NIL "This domain is a datatype for (signed) integer values of precision 8 bits."))) 
 NIL 
 NIL 
-(-488 |Key| |Entry| |addDom|) 
+(-489 |Key| |Entry| |addDom|) 
 ((|constructor| (NIL "This domain is used to provide a conditional \"add\" domain for the implementation of \\spadtype{Table}."))) 
-((-3989 . T) (-3990 . T)) 
-((-12 (|HasCategory| (-2 (|:| -3854 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -259) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3854) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3854 |#1|) (|:| |entry| |#2|)) (QUOTE (-1012)))) (OR (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| (-2 (|:| -3854 |#1|) (|:| |entry| |#2|)) (QUOTE (-1012)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| (-2 (|:| -3854 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3854 |#1|) (|:| |entry| |#2|)) (QUOTE (-1012)))) (OR (|HasCategory| (-2 (|:| -3854 |#1|) (|:| |entry| |#2|)) (QUOTE (-552 (-772)))) (|HasCategory| |#2| (QUOTE (-552 (-772))))) (|HasCategory| (-2 (|:| -3854 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-472)))) (-12 (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| |#2| (|%list| (QUOTE -259) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3854 |#1|) (|:| |entry| |#2|)) (QUOTE (-1012))) (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#2| (QUOTE (-1012))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3854 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3854 |#1|) (|:| |entry| |#2|)) (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3854 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) 
-(-489 R -3088) 
+((-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) 
 ((|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 
-(-490 R0 -3088 UP UPUP R) 
+(-491 R0 -3090 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 
-(-491) 
+(-492) 
 ((|constructor| (NIL "This package provides functions to lookup bits in integers")) (|bitTruth| (((|Boolean|) (|Integer|) (|Integer|)) "\\spad{bitTruth(n,m)} returns \\spad{true} if coefficient of 2**m in abs(\\spad{n}) is 1")) (|bitCoef| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{bitCoef(n,m)} returns the coefficient of 2**m in abs(\\spad{n})")) (|bitLength| (((|Integer|) (|Integer|)) "\\spad{bitLength(n)} returns the number of bits to represent abs(\\spad{n})"))) 
 NIL 
 NIL 
-(-492 R) 
+(-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."))) 
-((-3764 . T) (-3982 . T) ((-3991 "*") . T) (-3983 . T) (-3984 . T) (-3986 . T)) 
+((-3766 . T) (-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . T)) 
 NIL 
-(-493 S) 
+(-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."))) 
 NIL 
 NIL 
-(-494) 
+(-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."))) 
-((-3982 . T) ((-3991 "*") . T) (-3983 . T) (-3984 . T) (-3986 . T)) 
+((-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . T)) 
 NIL 
-(-495 R -3088) 
+(-496 R -3090) 
 ((|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 
-(-496 I) 
+(-497 I) 
 ((|constructor| (NIL "\\indented{1}{This Package contains basic methods for integer factorization.} The factor operation employs trial division up to 10,{}000. It then tests to see if \\spad{n} is a perfect power before using Pollards rho method. Because Pollards method may fail,{} the result of factor may contain composite factors. We should also employ Lenstra's eliptic curve method.")) (|PollardSmallFactor| (((|Union| |#1| "failed") |#1|) "\\spad{PollardSmallFactor(n)} returns a factor of \\spad{n} or \"failed\" if no one is found")) (|BasicMethod| (((|Factored| |#1|) |#1|) "\\spad{BasicMethod(n)} returns the factorization of integer \\spad{n} by trial division")) (|squareFree| (((|Factored| |#1|) |#1|) "\\spad{squareFree(n)} returns the square free factorization of integer \\spad{n}")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(n)} returns the full factorization of integer \\spad{n}"))) 
 NIL 
 NIL 
-(-497 R -3088 L) 
+(-498 R -3090 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 -600) (|devaluate| |#2|)))) 
-(-498) 
+((|HasCategory| |#3| (|%list| (QUOTE -601) (|devaluate| |#2|)))) 
+(-499) 
 ((|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 
-(-499 -3088 UP UPUP R) 
+(-500 -3090 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 
-(-500 -3088 UP) 
+(-501 -3090 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 
-(-501 R -3088 L) 
+(-502 R -3090 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 -600) (|devaluate| |#2|)))) 
-(-502 R -3088) 
+((|HasCategory| |#3| (|%list| (QUOTE -601) (|devaluate| |#2|)))) 
+(-503 R -3090) 
 ((|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 (-553 (-800 (-483))))) (|HasCategory| |#1| (QUOTE (-796 (-483)))) (|HasCategory| |#2| (QUOTE (-1051)))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-800 (-483))))) (|HasCategory| |#1| (QUOTE (-796 (-483)))) (|HasCategory| |#2| (QUOTE (-569))))) 
-(-503 -3088 UP) 
+((-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) 
 ((|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 
-(-504 S) 
+(-505 S) 
 ((|constructor| (NIL "Provides integer testing and retraction functions. Date Created: March 1990 Date Last Updated: 9 April 1991")) (|integerIfCan| (((|Union| (|Integer|) "failed") |#1|) "\\spad{integerIfCan(x)} returns \\spad{x} as an integer,{} \"failed\" if \\spad{x} is not an integer.")) (|integer?| (((|Boolean|) |#1|) "\\spad{integer?(x)} is \\spad{true} if \\spad{x} is an integer,{} \\spad{false} otherwise.")) (|integer| (((|Integer|) |#1|) "\\spad{integer(x)} returns \\spad{x} as an integer; error if \\spad{x} is not an integer."))) 
 NIL 
 NIL 
-(-505 -3088) 
+(-506 -3090) 
 ((|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 
-(-506 R) 
+(-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."))) 
-((-3764 . T) (-3982 . T) ((-3991 "*") . T) (-3983 . T) (-3984 . T) (-3986 . T)) 
+((-3766 . T) (-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . T)) 
 NIL 
-(-507) 
+(-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 
-(-508 R -3088) 
+(-509 R -3090) 
 ((|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 (-553 (-800 (-483))))) (|HasCategory| |#1| (QUOTE (-389))) (|HasCategory| |#1| (QUOTE (-796 (-483)))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-950 (-1088))))) (-12 (|HasCategory| |#1| (QUOTE (-389))) (|HasCategory| |#2| (QUOTE (-239)))) (|HasCategory| |#1| (QUOTE (-494)))) 
-(-509 -3088 UP) 
+((-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) 
 ((|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 
-(-510 R -3088) 
+(-511 R -3090) 
 ((|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 
-(-511) 
+(-512) 
 ((|constructor| (NIL "This category describes byte stream conduits supporting both input and output operations."))) 
 NIL 
 NIL 
-(-512) 
+(-513) 
 ((|constructor| (NIL "\\indented{2}{This domain provides representation for binary files open} \\indented{2}{for input and output operations.} See Also: InputBinaryFile,{} OutputBinaryFile")) (|isOpen?| (((|Boolean|) $) "\\spad{isOpen?(f)} holds if `f' is in open state.")) (|inputOutputBinaryFile| (($ (|String|)) "\\spad{inputOutputBinaryFile(f)} returns an input/output conduit obtained by opening the file named by `f' as a binary file.") (($ (|FileName|)) "\\spad{inputOutputBinaryFile(f)} returns an input/output conduit obtained by opening the file designated by `f' as a binary file."))) 
 NIL 
 NIL 
-(-513) 
+(-514) 
 ((|constructor| (NIL "This domain provides constants to describe directions of IO conduits (file,{} etc) mode of operations.")) (|closed| (($) "\\spad{closed} indicates that the IO conduit has been closed.")) (|bothWays| (($) "\\spad{bothWays} indicates that an IO conduit is for both input and output.")) (|output| (($) "\\spad{output} indicates that an IO conduit is for output")) (|input| (($) "\\spad{input} indicates that an IO conduit is for input."))) 
 NIL 
 NIL 
-(-514) 
+(-515) 
 ((|constructor| (NIL "This domain provides representation for ARPA Internet \\spad{IP4} addresses.")) (|resolve| (((|Maybe| $) (|Hostname|)) "\\spad{resolve(h)} returns the \\spad{IP4} address of host `h'.")) (|bytes| (((|DataArray| 4 (|Byte|)) $) "\\spad{bytes(x)} returns the bytes of the numeric address `x'.")) (|ip4Address| (($ (|String|)) "\\spad{ip4Address(a)} builds a numeric address out of the ASCII form `a'."))) 
 NIL 
 NIL 
-(-515 |p| |unBalanced?|) 
+(-516 |p| |unBalanced?|) 
 ((|constructor| (NIL "This domain implements Zp,{} the \\spad{p}-adic completion of the integers. This is an internal domain."))) 
-((-3982 . T) ((-3991 "*") . T) (-3983 . T) (-3984 . T) (-3986 . T)) 
+((-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . T)) 
 NIL 
-(-516 |p|) 
+(-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."))) 
-((-3981 . T) (-3987 . T) (-3982 . T) ((-3991 "*") . T) (-3983 . T) (-3984 . T) (-3986 . T)) 
+((-3983 . T) (-3989 . T) (-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . T)) 
 ((|HasCategory| $ (QUOTE (-120))) (|HasCategory| $ (QUOTE (-118))) (|HasCategory| $ (QUOTE (-317)))) 
-(-517) 
+(-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 
-(-518 -3088) 
+(-519 -3090) 
 ((|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}."))) 
-((-3984 . T) (-3983 . T)) 
-((|HasCategory| |#1| (QUOTE (-809 (-1088)))) (|HasCategory| |#1| (QUOTE (-950 (-1088))))) 
-(-519 E -3088) 
+((-3986 . T) (-3985 . T)) 
+((|HasCategory| |#1| (QUOTE (-810 (-1089)))) (|HasCategory| |#1| (QUOTE (-951 (-1089))))) 
+(-520 E -3090) 
 ((|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 
-(-520 R -3088) 
+(-521 R -3090) 
 ((|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 
-(-521) 
+(-522) 
 ((|constructor| (NIL "This domain provides representations for the intermediate form data structure used by the Spad elaborator.")) (|irDef| (($ (|Identifier|) (|InternalTypeForm|) $) "\\spad{irDef(f,ts,e)} returns an IR representation for a definition of a function named \\spad{f},{} with signature \\spad{ts} and body \\spad{e}.")) (|irCtor| (($ (|Identifier|) (|InternalTypeForm|)) "\\spad{irCtor(n,t)} returns an IR for a constructor reference of type designated by the type form \\spad{t}")) (|irVar| (($ (|Identifier|) (|InternalTypeForm|)) "\\spad{irVar(x,t)} returns an IR for a variable reference of type designated by the type form \\spad{t}"))) 
 NIL 
 NIL 
-(-522 I) 
+(-523 I) 
 ((|constructor| (NIL "The \\spadtype{IntegerRoots} package computes square roots and \\indented{2}{\\spad{n}th roots of integers efficiently.}")) (|approxSqrt| ((|#1| |#1|) "\\spad{approxSqrt(n)} returns an approximation \\spad{x} to \\spad{sqrt(n)} such that \\spad{-1 < x - sqrt(n) < 1}. Compute an approximation \\spad{s} to \\spad{sqrt(n)} such that \\indented{10}{\\spad{-1 < s - sqrt(n) < 1}} A variable precision Newton iteration is used. The running time is \\spad{O( log(n)**2 )}.")) (|perfectSqrt| (((|Union| |#1| "failed") |#1|) "\\spad{perfectSqrt(n)} returns the square root of \\spad{n} if \\spad{n} is a perfect square and returns \"failed\" otherwise")) (|perfectSquare?| (((|Boolean|) |#1|) "\\spad{perfectSquare?(n)} returns \\spad{true} if \\spad{n} is a perfect square and \\spad{false} otherwise")) (|approxNthRoot| ((|#1| |#1| (|NonNegativeInteger|)) "\\spad{approxRoot(n,r)} returns an approximation \\spad{x} to \\spad{n**(1/r)} such that \\spad{-1 < x - n**(1/r) < 1}")) (|perfectNthRoot| (((|Record| (|:| |base| |#1|) (|:| |exponent| (|NonNegativeInteger|))) |#1|) "\\spad{perfectNthRoot(n)} returns \\spad{[x,r]},{} where \\spad{n = x\\^r} and \\spad{r} is the largest integer such that \\spad{n} is a perfect \\spad{r}th power") (((|Union| |#1| "failed") |#1| (|NonNegativeInteger|)) "\\spad{perfectNthRoot(n,r)} returns the \\spad{r}th root of \\spad{n} if \\spad{n} is an \\spad{r}th power and returns \"failed\" otherwise")) (|perfectNthPower?| (((|Boolean|) |#1| (|NonNegativeInteger|)) "\\spad{perfectNthPower?(n,r)} returns \\spad{true} if \\spad{n} is an \\spad{r}th power and \\spad{false} otherwise"))) 
 NIL 
 NIL 
-(-523 GF) 
+(-524 GF) 
 ((|constructor| (NIL "This package exports the function generateIrredPoly that computes a monic irreducible polynomial of degree \\spad{n} over a finite field.")) (|generateIrredPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{generateIrredPoly(n)} generates an irreducible univariate polynomial of the given degree \\spad{n} over the finite field."))) 
 NIL 
 NIL 
-(-524 R) 
+(-525 R) 
 ((|constructor| (NIL "\\indented{2}{This package allows a sum of logs over the roots of a polynomial} \\indented{2}{to be expressed as explicit logarithms and arc tangents,{} provided} \\indented{2}{that the indexing polynomial can be factored into quadratics.} Date Created: 21 August 1988 Date Last Updated: 4 October 1993")) (|complexIntegrate| (((|Expression| |#1|) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{complexIntegrate(f, x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable.")) (|integrate| (((|Union| (|Expression| |#1|) (|List| (|Expression| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{integrate(f, x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a real variable..")) (|complexExpand| (((|Expression| |#1|) (|IntegrationResult| (|Fraction| (|Polynomial| |#1|)))) "\\spad{complexExpand(i)} returns the expanded complex function corresponding to \\spad{i}.")) (|expand| (((|List| (|Expression| |#1|)) (|IntegrationResult| (|Fraction| (|Polynomial| |#1|)))) "\\spad{expand(i)} returns the list of possible real functions corresponding to \\spad{i}.")) (|split| (((|IntegrationResult| (|Fraction| (|Polynomial| |#1|))) (|IntegrationResult| (|Fraction| (|Polynomial| |#1|)))) "\\spad{split(u(x) + sum_{P(a)=0} Q(a,x))} returns \\spad{u(x) + sum_{P1(a)=0} Q(a,x) + ... + sum_{Pn(a)=0} Q(a,x)} where \\spad{P1},{}...,{}Pn are the factors of \\spad{P}."))) 
 NIL 
 ((|HasCategory| |#1| (QUOTE (-120)))) 
-(-525) 
+(-526) 
 ((|constructor| (NIL "IrrRepSymNatPackage contains functions for computing the ordinary irreducible representations of symmetric groups on \\spad{n} letters {\\em {1,2,...,n}} in Young's natural form and their dimensions. These representations can be labelled by number partitions of \\spad{n},{} \\spadignore{i.e.} a weakly decreasing sequence of integers summing up to \\spad{n},{} \\spadignore{e.g.} {\\em [3,3,3,1]} labels an irreducible representation for \\spad{n} equals 10. Note: whenever a \\spadtype{List Integer} appears in a signature,{} a partition required.")) (|irreducibleRepresentation| (((|List| (|Matrix| (|Integer|))) (|List| (|PositiveInteger|)) (|List| (|Permutation| (|Integer|)))) "\\spad{irreducibleRepresentation(lambda,listOfPerm)} is the list of the irreducible representations corresponding to {\\em lambda} in Young's natural form for the list of permutations given by {\\em listOfPerm}.") (((|List| (|Matrix| (|Integer|))) (|List| (|PositiveInteger|))) "\\spad{irreducibleRepresentation(lambda)} is the list of the two irreducible representations corresponding to the partition {\\em lambda} in Young's natural form for the following two generators of the symmetric group,{} whose elements permute {\\em {1,2,...,n}},{} namely {\\em (1 2)} (2-cycle) and {\\em (1 2 ... n)} (\\spad{n}-cycle).") (((|Matrix| (|Integer|)) (|List| (|PositiveInteger|)) (|Permutation| (|Integer|))) "\\spad{irreducibleRepresentation(lambda,pi)} is the irreducible representation corresponding to partition {\\em lambda} in Young's natural form of the permutation {\\em pi} in the symmetric group,{} whose elements permute {\\em {1,2,...,n}}.")) (|dimensionOfIrreducibleRepresentation| (((|NonNegativeInteger|) (|List| (|PositiveInteger|))) "\\spad{dimensionOfIrreducibleRepresentation(lambda)} is the dimension of the ordinary irreducible representation of the symmetric group corresponding to {\\em lambda}. Note: the Robinson-Thrall hook formula is implemented."))) 
 NIL 
 NIL 
-(-526 R E V P TS) 
+(-527 R E V P TS) 
 ((|constructor| (NIL "\\indented{1}{An internal package for computing the rational univariate representation} \\indented{1}{of a zero-dimensional algebraic variety given by a square-free} \\indented{1}{triangular set.} \\indented{1}{The main operation is \\axiomOpFrom{rur}{InternalRationalUnivariateRepresentationPackage}.} \\indented{1}{It is based on the {\\em generic} algorithm description in [1]. \\newline References:} [1] \\spad{D}. LAZARD \"Solving Zero-dimensional Algebraic Systems\" \\indented{4}{Journal of Symbolic Computation,{} 1992,{} 13,{} 117-131}")) (|checkRur| (((|Boolean|) |#5| (|List| |#5|)) "\\spad{checkRur(ts,lus)} returns \\spad{true} if \\spad{lus} is a rational univariate representation of \\spad{ts}.")) (|rur| (((|List| |#5|) |#5| (|Boolean|)) "\\spad{rur(ts,univ?)} returns a rational univariate representation of \\spad{ts}. This assumes that the lowest polynomial in \\spad{ts} is a variable \\spad{v} which does not occur in the other polynomials of \\spad{ts}. This variable will be used to define the simple algebraic extension over which these other polynomials will be rewritten as univariate polynomials with degree one. If \\spad{univ?} is \\spad{true} then these polynomials will have a constant initial."))) 
 NIL 
 NIL 
-(-527) 
+(-528) 
 ((|constructor| (NIL "This domain represents a `has' expression.")) (|rhs| (((|SpadAst|) $) "\\spad{rhs(e)} returns the right hand side of the is expression `e'.")) (|lhs| (((|SpadAst|) $) "\\spad{lhs(e)} returns the left hand side of the is expression `e'."))) 
 NIL 
 NIL 
-(-528 E V R P) 
+(-529 E V R P) 
 ((|constructor| (NIL "tools for the summation packages.")) (|sum| (((|Record| (|:| |num| |#4|) (|:| |den| (|Integer|))) |#4| |#2|) "\\spad{sum(p(n), n)} returns \\spad{P(n)},{} the indefinite sum of \\spad{p(n)} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{P(n+1) - P(n) = a(n)}.") (((|Record| (|:| |num| |#4|) (|:| |den| (|Integer|))) |#4| |#2| (|Segment| |#4|)) "\\spad{sum(p(n), n = a..b)} returns \\spad{p(a) + p(a+1) + ... + p(b)}."))) 
 NIL 
 NIL 
-(-529 |Coef|) 
-((|constructor| (NIL "InnerSparseUnivariatePowerSeries is an internal domain \\indented{2}{used for creating sparse Taylor and Laurent series.}")) (|cAcsch| (($ $) "\\spad{cAcsch(f)} computes the inverse hyperbolic cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsech| (($ $) "\\spad{cAsech(f)} computes the inverse hyperbolic secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcoth| (($ $) "\\spad{cAcoth(f)} computes the inverse hyperbolic cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAtanh| (($ $) "\\spad{cAtanh(f)} computes the inverse hyperbolic tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcosh| (($ $) "\\spad{cAcosh(f)} computes the inverse hyperbolic cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsinh| (($ $) "\\spad{cAsinh(f)} computes the inverse hyperbolic sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCsch| (($ $) "\\spad{cCsch(f)} computes the hyperbolic cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSech| (($ $) "\\spad{cSech(f)} computes the hyperbolic secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCoth| (($ $) "\\spad{cCoth(f)} computes the hyperbolic cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cTanh| (($ $) "\\spad{cTanh(f)} computes the hyperbolic tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCosh| (($ $) "\\spad{cCosh(f)} computes the hyperbolic cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSinh| (($ $) "\\spad{cSinh(f)} computes the hyperbolic sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcsc| (($ $) "\\spad{cAcsc(f)} computes the arccosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsec| (($ $) "\\spad{cAsec(f)} computes the arcsecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcot| (($ $) "\\spad{cAcot(f)} computes the arccotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAtan| (($ $) "\\spad{cAtan(f)} computes the arctangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcos| (($ $) "\\spad{cAcos(f)} computes the arccosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsin| (($ $) "\\spad{cAsin(f)} computes the arcsine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCsc| (($ $) "\\spad{cCsc(f)} computes the cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSec| (($ $) "\\spad{cSec(f)} computes the secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCot| (($ $) "\\spad{cCot(f)} computes the cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cTan| (($ $) "\\spad{cTan(f)} computes the tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCos| (($ $) "\\spad{cCos(f)} computes the cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSin| (($ $) "\\spad{cSin(f)} computes the sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cLog| (($ $) "\\spad{cLog(f)} computes the logarithm of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cExp| (($ $) "\\spad{cExp(f)} computes the exponential of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cRationalPower| (($ $ (|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}."))) 
-(((-3991 "*") |has| |#1| (-146)) (-3982 |has| |#1| (-494)) (-3983 . T) (-3984 . T) (-3986 . T)) 
-((|HasCategory| |#1| (QUOTE (-38 (-347 (-483))))) (|HasCategory| |#1| (QUOTE (-494))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-494)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-809 (-1088)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-483)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-483)) (|devaluate| |#1|)))) (|HasCategory| (-483) (QUOTE (-1024))) (|HasCategory| |#1| (QUOTE (-311))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-483))))) (|HasSignature| |#1| (|%list| (QUOTE -3940) (|%list| (|devaluate| |#1|) (QUOTE (-1088)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-483)))))) 
 (-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)))))) 
+(-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|) $) "\\spad{coefficients(x)} returns a stream of ring elements. \\indented{1}{When \\spad{x} is a univariate series,{} this is a stream of Taylor} \\indented{1}{coefficients. When \\spad{x} is a multivariate series,{} the} \\indented{1}{\\spad{n}th element of the stream is a form of} \\indented{1}{degree \\spad{n} in the power series variables.}"))) 
-(((-3991 "*") |has| |#1| (-494)) (-3982 |has| |#1| (-494)) (-3983 . T) (-3984 . T) (-3986 . T)) 
-((|HasCategory| |#1| (QUOTE (-494)))) 
-(-531) 
+(((-3993 "*") |has| |#1| (-495)) (-3984 |has| |#1| (-495)) (-3985 . T) (-3986 . T) (-3988 . T)) 
+((|HasCategory| |#1| (QUOTE (-495)))) 
+(-532) 
 ((|constructor| (NIL "This domain provides representations for internal type form.")) (|mappingMode| (($ $ (|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"))) 
 NIL 
 NIL 
-(-532 A B) 
+(-533 A B) 
 ((|constructor| (NIL "Functions defined on streams with entries in two sets.")) (|map| (((|InfiniteTuple| |#2|) (|Mapping| |#2| |#1|) (|InfiniteTuple| |#1|)) "\\spad{map(f,[x0,x1,x2,...])} returns \\spad{[f(x0),f(x1),f(x2),..]}."))) 
 NIL 
 NIL 
-(-533 A B C) 
+(-534 A B C) 
 ((|constructor| (NIL "Functions defined on streams with entries in two sets.")) (|map| (((|Stream| |#3|) (|Mapping| |#3| |#1| |#2|) (|InfiniteTuple| |#1|) (|Stream| |#2|)) "\\spad{map(f,a,b)} \\undocumented") (((|Stream| |#3|) (|Mapping| |#3| |#1| |#2|) (|Stream| |#1|) (|InfiniteTuple| |#2|)) "\\spad{map(f,a,b)} \\undocumented") (((|InfiniteTuple| |#3|) (|Mapping| |#3| |#1| |#2|) (|InfiniteTuple| |#1|) (|InfiniteTuple| |#2|)) "\\spad{map(f,a,b)} \\undocumented"))) 
 NIL 
 NIL 
-(-534 R -3088 FG) 
+(-535 R -3090 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 
-(-535 S) 
+(-536 S) 
 ((|constructor| (NIL "This package implements 'infinite tuples' for the interpreter. The representation is a stream.")) (|construct| (((|Stream| |#1|) $) "\\spad{construct(t)} converts an infinite tuple to a stream.")) (|generate| (($ (|Mapping| |#1| |#1|) |#1|) "\\spad{generate(f,s)} returns \\spad{[s,f(s),f(f(s)),...]}.")) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select(p,t)} returns \\spad{[x for x in t | p(x)]}.")) (|filterUntil| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterUntil(p,t)} returns \\spad{[x for x in t while not p(x)]}.")) (|filterWhile| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterWhile(p,t)} returns \\spad{[x for x in t while p(x)]}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,t)} replaces the tuple \\spad{t} by \\spad{[f(x) for x in t]}."))) 
 NIL 
 NIL 
-(-536 R |mn|) 
+(-537 R |mn|) 
 ((|constructor| (NIL "\\indented{2}{This type represents vector like objects with varying lengths} and a user-specified initial index."))) 
-((-3990 . T) (-3989 . T)) 
-((OR (-12 (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-553 (-472)))) (OR (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| |#1| (QUOTE (-756))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| (-483) (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-663))) (|HasCategory| |#1| (QUOTE (-961))) (-12 (|HasCategory| |#1| (QUOTE (-915))) (|HasCategory| |#1| (QUOTE (-961)))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|))))) 
-(-537 S |Index| |Entry|) 
+((-3992 . T) (-3991 . 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 -3990)) (|HasCategory| |#2| (QUOTE (-756))) (|HasAttribute| |#1| (QUOTE -3989)) (|HasCategory| |#3| (QUOTE (-1012)))) 
-(-538 |Index| |Entry|) 
+((|HasAttribute| |#1| (QUOTE -3992)) (|HasCategory| |#2| (QUOTE (-757))) (|HasAttribute| |#1| (QUOTE -3991)) (|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 
 NIL 
-(-539) 
+(-540) 
 ((|constructor| (NIL "This domain represents the join of categories ASTs.")) (|categories| (((|List| (|TypeAst|)) $) "catehories(\\spad{x}) returns the types in the join `x'.")) (|coerce| (($ (|List| (|TypeAst|))) "ts::JoinAst construct the AST for a join of the types `ts'."))) 
 NIL 
 NIL 
-(-540 R A) 
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 ((|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)."))) 
-((-3986 OR (-2558 (|has| |#2| (-315 |#1|)) (|has| |#1| (-494))) (-12 (|has| |#2| (-358 |#1|)) (|has| |#1| (-494)))) (-3984 . T) (-3983 . 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 (-494))) (|HasCategory| |#2| (|%list| (QUOTE -315) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#2| (|%list| (QUOTE -358) (|devaluate| |#1|))))) (|HasCategory| |#2| (|%list| (QUOTE -315) (|devaluate| |#1|)))) 
-(-541) 
+((-3988 OR (-2560 (|has| |#2| (-315 |#1|)) (|has| |#1| (-495))) (-12 (|has| |#2| (-358 |#1|)) (|has| |#1| (-495)))) (-3986 . T) (-3985 . 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."))) 
 NIL 
 NIL 
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+(-543) 
 ((|constructor| (NIL "JVM class file access bitmask and values.")) (|jvmAbstract| (($) "The class was declared abstract; therefore object of this class may not be created.")) (|jvmInterface| (($) "The class file represents an interface,{} not a class.")) (|jvmSuper| (($) "Instruct the JVM to treat base clss method invokation specially.")) (|jvmFinal| (($) "The class was declared final; therefore no derived class allowed.")) (|jvmPublic| (($) "The class was declared public,{} therefore may be accessed from outside its package"))) 
 NIL 
 NIL 
-(-543) 
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 ((|constructor| (NIL "JVM class file constant pool tags.")) (|jvmNameAndTypeConstantTag| (($) "The correspondong constant pool entry represents the name and type of a field or method info.")) (|jvmInterfaceMethodConstantTag| (($) "The correspondong constant pool entry represents an interface method info.")) (|jvmMethodrefConstantTag| (($) "The correspondong constant pool entry represents a class method info.")) (|jvmFieldrefConstantTag| (($) "The corresponding constant pool entry represents a class field info.")) (|jvmStringConstantTag| (($) "The corresponding constant pool entry is a string constant info.")) (|jvmClassConstantTag| (($) "The corresponding constant pool entry represents a class or and interface.")) (|jvmDoubleConstantTag| (($) "The corresponding constant pool entry is a double constant info.")) (|jvmLongConstantTag| (($) "The corresponding constant pool entry is a long constant info.")) (|jvmFloatConstantTag| (($) "The corresponding constant pool entry is a float constant info.")) (|jvmIntegerConstantTag| (($) "The corresponding constant pool entry is an integer constant info.")) (|jvmUTF8ConstantTag| (($) "The corresponding constant pool entry is sequence of bytes representing Java \\spad{UTF8} string constant."))) 
 NIL 
 NIL 
-(-544) 
+(-545) 
 ((|constructor| (NIL "JVM class field access bitmask and values.")) (|jvmTransient| (($) "The field was declared transient.")) (|jvmVolatile| (($) "The field was declared volatile.")) (|jvmFinal| (($) "The field was declared final; therefore may not be modified after initialization.")) (|jvmStatic| (($) "The field was declared static.")) (|jvmProtected| (($) "The field was declared protected; therefore may be accessed withing derived classes.")) (|jvmPrivate| (($) "The field was declared private; threfore can be accessed only within the defining class.")) (|jvmPublic| (($) "The field was declared public; therefore mey accessed from outside its package."))) 
 NIL 
 NIL 
-(-545) 
+(-546) 
 ((|constructor| (NIL "JVM class method access bitmask and values.")) (|jvmStrict| (($) "The method was declared fpstrict; therefore floating-point mode is FP-strict.")) (|jvmAbstract| (($) "The method was declared abstract; therefore no implementation is provided.")) (|jvmNative| (($) "The method was declared native; therefore implemented in a language other than Java.")) (|jvmSynchronized| (($) "The method was declared synchronized.")) (|jvmFinal| (($) "The method was declared final; therefore may not be overriden. in derived classes.")) (|jvmStatic| (($) "The method was declared static.")) (|jvmProtected| (($) "The method was declared protected; therefore may be accessed withing derived classes.")) (|jvmPrivate| (($) "The method was declared private; threfore can be accessed only within the defining class.")) (|jvmPublic| (($) "The method was declared public; therefore mey accessed from outside its package."))) 
 NIL 
 NIL 
-(-546) 
+(-547) 
 ((|constructor| (NIL "This is the datatype for the JVM opcodes."))) 
 NIL 
 NIL 
-(-547 |Entry|) 
+(-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."))) 
-((-3989 . T) (-3990 . T)) 
-((-12 (|HasCategory| (-2 (|:| -3854 (-1071)) (|:| |entry| |#1|)) (|%list| (QUOTE -259) (|%list| (QUOTE -2) (QUOTE (|:| -3854 (-1071))) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -3854 (-1071)) (|:| |entry| |#1|)) (QUOTE (-1012)))) (|HasCategory| (-2 (|:| -3854 (-1071)) (|:| |entry| |#1|)) (QUOTE (-553 (-472)))) (-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| (-1071) (QUOTE (-756))) (|HasCategory| (-2 (|:| -3854 (-1071)) (|:| |entry| |#1|)) (QUOTE (-1012))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3854 (-1071)) (|:| |entry| |#1|)) (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3854 (-1071)) (|:| |entry| |#1|)) (QUOTE (-72)))) 
-(-548 S |Key| |Entry|) 
+((-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)))) 
+(-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 
-(-549 |Key| |Entry|) 
+(-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}."))) 
-((-3990 . T)) 
+((-3992 . T)) 
 NIL 
-(-550 S) 
+(-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."))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-553 (-472)))) (|HasCategory| |#1| (QUOTE (-553 (-800 (-327))))) (|HasCategory| |#1| (QUOTE (-553 (-800 (-483)))))) 
-(-551 R S) 
+((|HasCategory| |#1| (QUOTE (-554 (-473)))) (|HasCategory| |#1| (QUOTE (-554 (-801 (-327))))) (|HasCategory| |#1| (QUOTE (-554 (-801 (-484)))))) 
+(-552 R S) 
 ((|constructor| (NIL "This package exports some auxiliary functions on kernels")) (|constantIfCan| (((|Union| |#1| "failed") (|Kernel| |#2|)) "\\spad{constantIfCan(k)} \\undocumented")) (|constantKernel| (((|Kernel| |#2|) |#1|) "\\spad{constantKernel(r)} \\undocumented"))) 
 NIL 
 NIL 
-(-552 S) 
+(-553 S) 
 ((|constructor| (NIL "A is coercible to \\spad{B} means any element of A can automatically be converted into an element of \\spad{B} by the interpreter.")) (|coerce| ((|#1| $) "\\spad{coerce(a)} transforms a into an element of \\spad{S}."))) 
 NIL 
 NIL 
-(-553 S) 
+(-554 S) 
 ((|constructor| (NIL "A is convertible to \\spad{B} means any element of A can be converted into an element of \\spad{B},{} but not automatically by the interpreter.")) (|convert| ((|#1| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}."))) 
 NIL 
 NIL 
-(-554 -3088 UP) 
+(-555 -3090 UP) 
 ((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic's algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,a_1,a_2,ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$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 
-(-555 S) 
+(-556 S) 
 ((|constructor| (NIL "A is coercible from \\spad{B} iff any element of domain \\spad{B} can be automically converted into an element of domain A.")) (|coerce| (($ |#1|) "\\spad{coerce(s)} transforms `s' into an element of `\\%'."))) 
 NIL 
 NIL 
-(-556) 
+(-557) 
 ((|constructor| (NIL "This domain implements Kleene's 3-valued propositional logic.")) (|case| (((|Boolean|) $ (|[\|\|]| |true|)) "\\spad{s case true} holds if the value of `x' is `true'.") (((|Boolean|) $ (|[\|\|]| |unknown|)) "\\spad{x case unknown} holds if the value of `x' is `unknown'") (((|Boolean|) $ (|[\|\|]| |false|)) "\\spad{x case false} holds if the value of `x' is `false'")) (|unknown| (($) "the indefinite `unknown'"))) 
 NIL 
 NIL 
-(-557 S) 
+(-558 S) 
 ((|constructor| (NIL "A is convertible from \\spad{B} iff any element of domain \\spad{B} can be explicitly converted into an element of domain A.")) (|convert| (($ |#1|) "\\spad{convert(s)} transforms `s' into an element of `\\%'."))) 
 NIL 
 NIL 
-(-558 A R S) 
+(-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}."))) 
-((-3983 . T) (-3984 . T) (-3986 . T)) 
-((|HasCategory| |#1| (QUOTE (-755)))) 
-(-559 S R) 
+((-3985 . T) (-3986 . T) (-3988 . 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."))) 
 NIL 
 NIL 
-(-560 R) 
+(-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."))) 
-((-3986 . T)) 
+((-3988 . T)) 
 NIL 
-(-561 R -3088) 
+(-562 R -3090) 
 ((|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 
-(-562 R UP) 
+(-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"))) 
-((-3984 . T) (-3983 . T) ((-3991 "*") . T) (-3982 . T) (-3986 . T)) 
-((|HasCategory| |#2| (QUOTE (-809 (-1088)))) (|HasCategory| |#2| (QUOTE (-811 (-1088)))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-950 (-347 (-483))))) (|HasCategory| |#1| (QUOTE (-950 (-483))))) 
-(-563 R E V P TS ST) 
+((-3986 . T) (-3985 . T) ((-3993 "*") . T) (-3984 . T) (-3988 . 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."))) 
 NIL 
 NIL 
-(-564 OV E Z P) 
+(-565 OV E Z P) 
 ((|constructor| (NIL "Package for leading coefficient determination in the lifting step. Package working for every \\spad{R} euclidean with property \"F\".")) (|distFact| (((|Union| (|Record| (|:| |polfac| (|List| |#4|)) (|:| |correct| |#3|) (|:| |corrfact| (|List| (|SparseUnivariatePolynomial| |#3|)))) "failed") |#3| (|List| (|SparseUnivariatePolynomial| |#3|)) (|Record| (|:| |contp| |#3|) (|:| |factors| (|List| (|Record| (|:| |irr| |#4|) (|:| |pow| (|Integer|)))))) (|List| |#3|) (|List| |#1|) (|List| |#3|)) "\\spad{distFact(contm,unilist,plead,vl,lvar,lval)},{} where \\spad{contm} is the content of the evaluated polynomial,{} \\spad{unilist} is the list of factors of the evaluated polynomial,{} \\spad{plead} is the complete factorization of the leading coefficient,{} \\spad{vl} is the list of factors of the leading coefficient evaluated,{} \\spad{lvar} is the list of variables,{} \\spad{lval} is the list of values,{} returns a record giving the list of leading coefficients to impose on the univariate factors,{}")) (|polCase| (((|Boolean|) |#3| (|NonNegativeInteger|) (|List| |#3|)) "\\spad{polCase(contprod, numFacts, evallcs)},{} where \\spad{contprod} is the product of the content of the leading coefficient of the polynomial to be factored with the content of the evaluated polynomial,{} \\spad{numFacts} is the number of factors of the leadingCoefficient,{} and evallcs is the list of the evaluated factors of the leadingCoefficient,{} returns \\spad{true} if the factors of the leading Coefficient can be distributed with this valuation."))) 
 NIL 
 NIL 
-(-565) 
+(-566) 
 ((|constructor| (NIL "This domain represents assignment expressions.")) (|rhs| (((|SpadAst|) $) "\\spad{rhs(e)} returns the right hand side of the assignment expression `e'.")) (|lhs| (((|SpadAst|) $) "\\spad{lhs(e)} returns the left hand side of the assignment expression `e'."))) 
 NIL 
 NIL 
-(-566 |VarSet| R |Order|) 
+(-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}}."))) 
-((-3986 . T)) 
+((-3988 . T)) 
 NIL 
-(-567 R |ls|) 
+(-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 
-(-568 R -3088) 
+(-569 R -3090) 
 ((|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 
-(-569) 
+(-570) 
 ((|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 
-(-570 |lv| -3088) 
+(-571 |lv| -3090) 
 ((|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 
-(-571) 
+(-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."))) 
-((-3990 . T)) 
-((-12 (|HasCategory| (-2 (|:| -3854 (-1071)) (|:| |entry| (-51))) (QUOTE (-259 (-2 (|:| -3854 (-1071)) (|:| |entry| (-51)))))) (|HasCategory| (-2 (|:| -3854 (-1071)) (|:| |entry| (-51))) (QUOTE (-1012)))) (OR (|HasCategory| (-51) (QUOTE (-1012))) (|HasCategory| (-2 (|:| -3854 (-1071)) (|:| |entry| (-51))) (QUOTE (-1012)))) (OR (|HasCategory| (-51) (QUOTE (-72))) (|HasCategory| (-51) (QUOTE (-1012))) (|HasCategory| (-2 (|:| -3854 (-1071)) (|:| |entry| (-51))) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3854 (-1071)) (|:| |entry| (-51))) (QUOTE (-1012)))) (OR (|HasCategory| (-2 (|:| -3854 (-1071)) (|:| |entry| (-51))) (QUOTE (-552 (-772)))) (|HasCategory| (-51) (QUOTE (-552 (-772))))) (|HasCategory| (-2 (|:| -3854 (-1071)) (|:| |entry| (-51))) (QUOTE (-553 (-472)))) (-12 (|HasCategory| (-51) (QUOTE (-259 (-51)))) (|HasCategory| (-51) (QUOTE (-1012)))) (|HasCategory| (-1071) (QUOTE (-756))) (OR (|HasCategory| (-51) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3854 (-1071)) (|:| |entry| (-51))) (QUOTE (-72)))) (|HasCategory| (-51) (QUOTE (-1012))) (|HasCategory| (-51) (QUOTE (-72))) (|HasCategory| (-51) (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3854 (-1071)) (|:| |entry| (-51))) (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3854 (-1071)) (|:| |entry| (-51))) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3854 (-1071)) (|:| |entry| (-51))) (QUOTE (-1012)))) 
-(-572 R A) 
+((-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)))) 
+(-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)."))) 
-((-3986 OR (-2558 (|has| |#2| (-315 |#1|)) (|has| |#1| (-494))) (-12 (|has| |#2| (-358 |#1|)) (|has| |#1| (-494)))) (-3984 . T) (-3983 . 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 (-494))) (|HasCategory| |#2| (|%list| (QUOTE -315) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#2| (|%list| (QUOTE -358) (|devaluate| |#1|))))) (|HasCategory| |#2| (|%list| (QUOTE -315) (|devaluate| |#1|)))) 
-(-573 S R) 
+((-3988 OR (-2560 (|has| |#2| (-315 |#1|)) (|has| |#1| (-495))) (-12 (|has| |#2| (-358 |#1|)) (|has| |#1| (-495)))) (-3986 . T) (-3985 . 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| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) 
 NIL 
 ((|HasCategory| |#2| (QUOTE (-311)))) 
-(-574 R) 
+(-575 R) 
 ((|constructor| (NIL "\\axiom{JacobiIdentity} means that \\axiom{[\\spad{x},{}[\\spad{y},{}\\spad{z}]]+[\\spad{y},{}[\\spad{z},{}\\spad{x}]]+[\\spad{z},{}[\\spad{x},{}\\spad{y}]] = 0} holds.")) (/ (($ $ |#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) (-3984 . T) (-3983 . T)) 
+((|JacobiIdentity| . T) (|NullSquare| . T) (-3986 . T) (-3985 . T)) 
 NIL 
-(-575 R FE) 
+(-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))}."))) 
 NIL 
 NIL 
-(-576 R) 
+(-577 R) 
 ((|constructor| (NIL "Computation of limits for rational functions.")) (|complexLimit| (((|OnePointCompletion| (|Fraction| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|)))) "\\spad{complexLimit(f(x),x = a)} computes the complex limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a}.") (((|OnePointCompletion| (|Fraction| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Equation| (|OnePointCompletion| (|Polynomial| |#1|)))) "\\spad{complexLimit(f(x),x = a)} computes the complex limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a}.")) (|limit| (((|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) #1="failed") (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|))) (|String|)) "\\spad{limit(f(x),x,a,\"left\")} computes the real limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a} from the left; limit(\\spad{f}(\\spad{x}),{}\\spad{x},{}a,{}\"right\") computes the corresponding limit as \\spad{x} approaches \\spad{a} from the right.") (((|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) (|Record| (|:| |leftHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) #1#)) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) #1#))) #2="failed") (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|)))) "\\spad{limit(f(x),x = a)} computes the real two-sided limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a}.") (((|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) (|Record| (|:| |leftHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) #1#)) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) #1#))) #2#) (|Fraction| (|Polynomial| |#1|)) (|Equation| (|OrderedCompletion| (|Polynomial| |#1|)))) "\\spad{limit(f(x),x = a)} computes the real two-sided limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a}."))) 
 NIL 
 NIL 
-(-577 |vars|) 
+(-578 |vars|) 
 ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: July 2,{} 2010 Date Last Modified: July 2,{} 2010 Descrption: \\indented{2}{Representation of a vector space basis,{} given by symbols.}")) (|dual| (($ (|DualBasis| |#1|)) "\\spad{dual f} constructs the dual vector of a linear form which is part of a basis."))) 
 NIL 
 NIL 
-(-578 S R) 
+(-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 
-((-2556 (|HasCategory| |#1| (QUOTE (-311)))) (|HasCategory| |#1| (QUOTE (-311)))) 
-(-579 K B) 
+((-2558 (|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}."))) 
-((-3984 . T) (-3983 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| (-577 |#2|) (QUOTE (-1012))))) 
-(-580 R) 
+((-3986 . T) (-3985 . 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]}."))) 
 NIL 
 NIL 
-(-581 K B) 
+(-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}."))) 
-((-3984 . T) (-3983 . T)) 
+((-3986 . T) (-3985 . T)) 
 NIL 
-(-582 S) 
+(-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."))) 
 NIL 
 NIL 
-(-583 S) 
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 ((|constructor| (NIL "\\spadtype{List} implements singly-linked lists that are addressable by indices; the index of the first element is 1. this constructor provides some LISP-like functions such as \\spadfun{null} and \\spadfun{cons}.")) (|setDifference| (($ $ $) "\\spad{setDifference(u1,u2)} returns a list of the elements of \\spad{u1} that are not also in \\spad{u2}. The order of elements in the resulting list is unspecified.")) (|setIntersection| (($ $ $) "\\spad{setIntersection(u1,u2)} returns a list of the elements that lists \\spad{u1} and \\spad{u2} have in common. The order of elements in the resulting list is unspecified.")) (|setUnion| (($ $ $) "\\spad{setUnion(u1,u2)} appends the two lists \\spad{u1} and \\spad{u2},{} then removes all duplicates. The order of elements in the resulting list is unspecified.")) (|append| (($ $ $) "\\spad{append(u1,u2)} appends the elements of list \\spad{u1} onto the front of list \\spad{u2}. This new list and \\spad{u2} will share some structure.")) (|cons| (($ |#1| $) "\\spad{cons(element,u)} appends \\spad{element} onto the front of list \\spad{u} and returns the new list. This new list and the old one will share some structure.")) (|null| (((|Boolean|) $) "\\spad{null(u)} tests if list \\spad{u} is the empty list.")) (|nil| (($) "\\spad{nil} is the empty list."))) 
-((-3990 . T) (-3989 . T)) 
-((OR (-12 (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-553 (-472)))) (OR (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| |#1| (QUOTE (-756))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| (-483) (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|))))) 
-(-584 A B) 
+((-3992 . T) (-3991 . 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)]}."))) 
 NIL 
 NIL 
-(-585 A B) 
+(-586 A B) 
 ((|constructor| (NIL "\\spadtype{ListToMap} allows mappings to be described by a pair of lists of equal lengths. The image of an element \\spad{x},{} which appears in position \\spad{n} in the first list,{} is then the \\spad{n}th element of the second list. A default value or default function can be specified to be used when \\spad{x} does not appear in the first list. In the absence of defaults,{} an error will occur in that case.")) (|match| ((|#2| (|List| |#1|) (|List| |#2|) |#1| (|Mapping| |#2| |#1|)) "\\spad{match(la, lb, a, f)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length. and applies this map to a. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Argument \\spad{f} is a default function to call if a is not in \\spad{la}. The value returned is then obtained by applying \\spad{f} to argument a.") (((|Mapping| |#2| |#1|) (|List| |#1|) (|List| |#2|) (|Mapping| |#2| |#1|)) "\\spad{match(la, lb, f)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Argument \\spad{f} is used as the function to call when the given function argument is not in \\spad{la}. The value returned is \\spad{f} applied to that argument.") ((|#2| (|List| |#1|) (|List| |#2|) |#1| |#2|) "\\spad{match(la, lb, a, b)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length. and applies this map to a. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Argument \\spad{b} is the default target value if a is not in \\spad{la}. Error: if \\spad{la} and \\spad{lb} are not of equal length.") (((|Mapping| |#2| |#1|) (|List| |#1|) (|List| |#2|) |#2|) "\\spad{match(la, lb, b)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length,{} where \\spad{b} is used as the default target value if the given function argument is not in \\spad{la}. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Error: if \\spad{la} and \\spad{lb} are not of equal length.") ((|#2| (|List| |#1|) (|List| |#2|) |#1|) "\\spad{match(la, lb, a)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length,{} where \\spad{a} is used as the default source value if the given one is not in \\spad{la}. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Error: if \\spad{la} and \\spad{lb} are not of equal length.") (((|Mapping| |#2| |#1|) (|List| |#1|) (|List| |#2|)) "\\spad{match(la, lb)} creates a map with no default source or target values defined by lists \\spad{la} and lb of equal length. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index lb. Error: if \\spad{la} and lb are not of equal length. Note: when this map is applied,{} an error occurs when applied to a value missing from \\spad{la}."))) 
 NIL 
 NIL 
-(-586 A B C) 
+(-587 A B C) 
 ((|constructor| (NIL "\\spadtype{ListFunctions3} implements utility functions that operate on three kinds of lists,{} each with a possibly different type of element.")) (|map| (((|List| |#3|) (|Mapping| |#3| |#1| |#2|) (|List| |#1|) (|List| |#2|)) "\\spad{map(fn,list1, u2)} applies the binary function \\spad{fn} to corresponding elements of lists \\spad{u1} and \\spad{u2} and returns a list of the results (in the same order). Thus \\spad{map(/,[1,2,3],[4,5,6]) = [1/4,2/4,1/2]}. The computation terminates when the end of either list is reached. That is,{} the length of the result list is equal to the minimum of the lengths of \\spad{u1} and \\spad{u2}."))) 
 NIL 
 NIL 
-(-587 T$) 
+(-588 T$) 
 ((|constructor| (NIL "This domain represents AST for Spad literals."))) 
 NIL 
 NIL 
-(-588 S) 
+(-589 S) 
 ((|constructor| (NIL "\\indented{2}{A set is an \\spad{S}-left linear set if it is stable by left-dilation} \\indented{2}{by elements in the semigroup \\spad{S}.} See Also: RightLinearSet.")) (* (($ |#1| $) "\\spad{s*x} is the left-dilation of \\spad{x} by \\spad{s}."))) 
 NIL 
 NIL 
-(-589 S) 
+(-590 S) 
 ((|substitute| (($ |#1| |#1| $) "\\spad{substitute(x,y,d)} replace \\spad{x}'s with \\spad{y}'s in dictionary \\spad{d}.")) (|duplicates?| (((|Boolean|) $) "\\spad{duplicates?(d)} tests if dictionary \\spad{d} has duplicate entries."))) 
-((-3989 . T) (-3990 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1012))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-553 (-472)))) (|HasCategory| |#1| (QUOTE (-72)))) 
-(-590 R) 
+((-3991 . T) (-3992 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1013))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-554 (-473)))) (|HasCategory| |#1| (QUOTE (-72)))) 
+(-591 R) 
 ((|constructor| (NIL "The category of left modules over an rng (ring not necessarily with unit). This is an abelian group which supports left multiplation by elements of the rng. \\blankline"))) 
 NIL 
 NIL 
-(-591 S E |un|) 
+(-592 S E |un|) 
 ((|constructor| (NIL "This internal package represents monoid (abelian or not,{} with or without inverses) as lists and provides some common operations to the various flavors of monoids.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f, a1\\^e1 ... an\\^en)} returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (|mapExpon| (($ (|Mapping| |#2| |#2|) $) "\\spad{mapExpon(f, a1\\^e1 ... an\\^en)} returns \\spad{a1\\^f(e1) ... an\\^f(en)}.")) (|commutativeEquality| (((|Boolean|) $ $) "\\spad{commutativeEquality(x,y)} returns \\spad{true} if \\spad{x} and \\spad{y} are equal assuming commutativity")) (|plus| (($ $ $) "\\spad{plus(x, y)} returns \\spad{x + y} where \\spad{+} is the monoid operation,{} which is assumed commutative.") (($ |#1| |#2| $) "\\spad{plus(s, e, x)} returns \\spad{e * s + x} where \\spad{+} is the monoid operation,{} which is assumed commutative.")) (|leftMult| (($ |#1| $) "\\spad{leftMult(s, a)} returns \\spad{s * a} where \\spad{*} is the monoid operation,{} which is assumed non-commutative.")) (|rightMult| (($ $ |#1|) "\\spad{rightMult(a, s)} returns \\spad{a * s} where \\spad{*} is the monoid operation,{} which is assumed non-commutative.")) (|makeUnit| (($) "\\spad{makeUnit()} returns the unit element of the monomial.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(l)} returns the number of monomials forming \\spad{l}.")) (|reverse!| (($ $) "\\spad{reverse!(l)} reverses the list of monomials forming \\spad{l},{} destroying the element \\spad{l}.")) (|reverse| (($ $) "\\spad{reverse(l)} reverses the list of monomials forming \\spad{l}. This has some effect if the monoid is non-abelian,{} \\spadignore{i.e.} \\spad{reverse(a1\\^e1 ... an\\^en) = an\\^en ... a1\\^e1} which is different.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(l, n)} returns the factor of the n^th monomial of \\spad{l}.")) (|nthExpon| ((|#2| $ (|Integer|)) "\\spad{nthExpon(l, n)} returns the exponent of the n^th monomial of \\spad{l}.")) (|makeMulti| (($ (|List| (|Record| (|:| |gen| |#1|) (|:| |exp| |#2|)))) "\\spad{makeMulti(l)} returns the element whose list of monomials is \\spad{l}.")) (|makeTerm| (($ |#1| |#2|) "\\spad{makeTerm(s, e)} returns the monomial \\spad{s} exponentiated by \\spad{e} (\\spadignore{e.g.} s^e or \\spad{e} * \\spad{s}).")) (|listOfMonoms| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| |#2|))) $) "\\spad{listOfMonoms(l)} returns the list of the monomials forming \\spad{l}.")) (|outputForm| (((|OutputForm|) $ (|Mapping| (|OutputForm|) (|OutputForm|) (|OutputForm|)) (|Mapping| (|OutputForm|) (|OutputForm|) (|OutputForm|)) (|Integer|)) "\\spad{outputForm(l, fop, fexp, unit)} converts the monoid element represented by \\spad{l} to an \\spadtype{OutputForm}. Argument unit is the output form for the \\spadignore{unit} of the monoid (\\spadignore{e.g.} 0 or 1),{} \\spad{fop(a, b)} is the output form for the monoid operation applied to \\spad{a} and \\spad{b} (\\spadignore{e.g.} \\spad{a + b},{} \\spad{a * b},{} \\spad{ab}),{} and \\spad{fexp(a, n)} is the output form for the exponentiation operation applied to \\spad{a} and \\spad{n} (\\spadignore{e.g.} \\spad{n a},{} \\spad{n * a},{} \\spad{a ** n},{} \\spad{a\\^n})."))) 
 NIL 
 NIL 
-(-592 A S) 
+(-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 -3990))) 
-(-593 S) 
+((|HasAttribute| |#1| (QUOTE -3992))) 
+(-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 
-(-594 M R S) 
+(-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}."))) 
-((-3984 . T) (-3983 . T)) 
-((|HasCategory| |#1| (QUOTE (-714)))) 
-(-595 R -3088 L) 
+((-3986 . T) (-3985 . T)) 
+((|HasCategory| |#1| (QUOTE (-715)))) 
+(-596 R -3090 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 
-(-596 A -2488) 
+(-597 A -2490) 
 ((|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}}"))) 
-((-3983 . T) (-3984 . T) (-3986 . T)) 
-((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-950 (-347 (-483))))) (|HasCategory| |#1| (QUOTE (-950 (-483)))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-389))) (|HasCategory| |#1| (QUOTE (-311)))) 
-(-597 A) 
+((-3985 . T) (-3986 . T) (-3988 . 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}}"))) 
-((-3983 . T) (-3984 . T) (-3986 . T)) 
-((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-950 (-347 (-483))))) (|HasCategory| |#1| (QUOTE (-950 (-483)))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-389))) (|HasCategory| |#1| (QUOTE (-311)))) 
-(-598 A M) 
+((-3985 . T) (-3986 . T) (-3988 . 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| (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}"))) 
-((-3983 . T) (-3984 . T) (-3986 . T)) 
-((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-950 (-347 (-483))))) (|HasCategory| |#1| (QUOTE (-950 (-483)))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-389))) (|HasCategory| |#1| (QUOTE (-311)))) 
-(-599 S A) 
+((-3985 . T) (-3986 . T) (-3988 . T)) 
+((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-951 (-347 (-484))))) (|HasCategory| |#1| (QUOTE (-951 (-484)))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-389))) (|HasCategory| |#1| (QUOTE (-311)))) 
+(-600 S A) 
 ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorCategory} is the category of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|directSum| (($ $ $) "\\spad{directSum(a,b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}.")) (|symmetricSquare| (($ $) "\\spad{symmetricSquare(a)} computes \\spad{symmetricProduct(a,a)} using a more efficient method.")) (|symmetricPower| (($ $ (|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}."))) 
 NIL 
 ((|HasCategory| |#2| (QUOTE (-311)))) 
-(-600 A) 
+(-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}."))) 
-((-3983 . T) (-3984 . T) (-3986 . T)) 
+((-3985 . T) (-3986 . T) (-3988 . T)) 
 NIL 
-(-601 -3088 UP) 
+(-602 -3090 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)))) 
-(-602 A L) 
+(-603 A L) 
 ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorsOps} provides symmetric products and sums for linear ordinary differential operators.")) (|directSum| ((|#2| |#2| |#2| (|Mapping| |#1| |#1|)) "\\spad{directSum(a,b,D)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}. \\spad{D} is the derivation to use.")) (|symmetricPower| ((|#2| |#2| (|NonNegativeInteger|) (|Mapping| |#1| |#1|)) "\\spad{symmetricPower(a,n,D)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of \\spad{n} solutions of \\spad{a}. \\spad{D} is the derivation to use.")) (|symmetricProduct| ((|#2| |#2| |#2| (|Mapping| |#1| |#1|)) "\\spad{symmetricProduct(a,b,D)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of a solution of \\spad{a} by a solution of \\spad{b}. \\spad{D} is the derivation to use."))) 
 NIL 
 NIL 
-(-603 S) 
+(-604 S) 
 ((|constructor| (NIL "`Logic' provides the basic operations for lattices,{} \\spadignore{e.g.} boolean algebra.")) (|\\/| (($ $ $) "\\spadignore{ \\/ } returns the logical `join',{} \\spadignore{e.g.} `or'.")) (|/\\| (($ $ $) "\\spadignore { /\\ }returns the logical `meet',{} \\spadignore{e.g.} `and'.")) (~ (($ $) "\\spad{~(x)} returns the logical complement of \\spad{x}."))) 
 NIL 
 NIL 
-(-604) 
+(-605) 
 ((|constructor| (NIL "`Logic' provides the basic operations for lattices,{} \\spadignore{e.g.} boolean algebra.")) (|\\/| (($ $ $) "\\spadignore{ \\/ } returns the logical `join',{} \\spadignore{e.g.} `or'.")) (|/\\| (($ $ $) "\\spadignore { /\\ }returns the logical `meet',{} \\spadignore{e.g.} `and'.")) (~ (($ $) "\\spad{~(x)} returns the logical complement of \\spad{x}."))) 
 NIL 
 NIL 
-(-605 R) 
+(-606 R) 
 ((|constructor| (NIL "Given a PolynomialFactorizationExplicit ring,{} this package provides a defaulting rule for the \\spad{solveLinearPolynomialEquation} operation,{} by moving into the field of fractions,{} and solving it there via the \\spad{multiEuclidean} operation.")) (|solveLinearPolynomialEquationByFractions| (((|Union| (|List| (|SparseUnivariatePolynomial| |#1|)) "failed") (|List| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{solveLinearPolynomialEquationByFractions([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such exists."))) 
 NIL 
 NIL 
-(-606 |VarSet| R) 
+(-607 |VarSet| R) 
 ((|constructor| (NIL "This type supports Lie polynomials in Lyndon basis see Free Lie Algebras by \\spad{C}. Reutenauer (Oxford science publications). \\newline Author: Michel Petitot (petitot@lifl.fr).")) (|construct| (($ $ (|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) (-3984 . T) (-3983 . T)) 
+((|JacobiIdentity| . T) (|NullSquare| . T) (-3986 . T) (-3985 . T)) 
 ((|HasCategory| |#2| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-146)))) 
-(-607 A S) 
+(-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}."))) 
 NIL 
 NIL 
-(-608 S) 
+(-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}."))) 
-((-3990 . T) (-3989 . T)) 
+((-3992 . T) (-3991 . T)) 
 NIL 
-(-609 -3088 |Row| |Col| M) 
+(-610 -3090 |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 
-(-610 -3088) 
+(-611 -3090) 
 ((|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 
-(-611 R E OV P) 
+(-612 R E OV P) 
 ((|constructor| (NIL "this package finds the solutions of linear systems presented as a list of polynomials.")) (|linSolve| (((|Record| (|:| |particular| (|Union| (|Vector| (|Fraction| |#4|)) "failed")) (|:| |basis| (|List| (|Vector| (|Fraction| |#4|))))) (|List| |#4|) (|List| |#3|)) "\\spad{linSolve(lp,lvar)} finds the solutions of the linear system of polynomials \\spad{lp} = 0 with respect to the list of symbols \\spad{lvar}."))) 
 NIL 
 NIL 
-(-612 |n| R) 
+(-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."))) 
-((-3986 . T) (-3989 . T) (-3983 . T) (-3984 . T)) 
-((|HasCategory| |#2| (QUOTE (-809 (-1088)))) (|HasCategory| |#2| (QUOTE (-811 (-1088)))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-189))) (|HasAttribute| |#2| (QUOTE (-3991 #1="*"))) (|HasCategory| |#2| (QUOTE (-580 (-483)))) (|HasCategory| |#2| (QUOTE (-950 (-347 (-483))))) (|HasCategory| |#2| (QUOTE (-950 (-483)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (|%list| (QUOTE -259) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-580 (-483)))) (|HasCategory| |#2| (|%list| (QUOTE -259) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-809 (-1088)))) (|HasCategory| |#2| (|%list| (QUOTE -259) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| |#2| (|%list| (QUOTE -259) (|devaluate| |#2|))))) (|HasCategory| |#2| (QUOTE (-257))) (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| |#2| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-494))) (OR (|HasAttribute| |#2| (QUOTE (-3991 #1#))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-809 (-1088))))) (|HasCategory| |#2| (QUOTE (-552 (-772)))) (|HasCategory| |#2| (QUOTE (-72))) (-12 (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| |#2| (|%list| (QUOTE -259) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-146)))) 
-(-613) 
+((-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)))) 
+(-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 
 NIL 
-(-614 |VarSet|) 
+(-615 |VarSet|) 
 ((|constructor| (NIL "Lyndon words over arbitrary (ordered) symbols: see Free Lie Algebras by \\spad{C}. Reutenauer (Oxford science publications). A Lyndon word is a word which is smaller than any of its right factors \\spad{w}.\\spad{r}.\\spad{t}. the pure lexicographical ordering. If \\axiom{a} and \\axiom{\\spad{b}} are two Lyndon words such that \\axiom{a < \\spad{b}} holds \\spad{w}.\\spad{r}.\\spad{t} lexicographical ordering then \\axiom{a*b} is a Lyndon word. Parenthesized Lyndon words can be generated from symbols by using the following rule: \\axiom{[[a,{}\\spad{b}],{}\\spad{c}]} is a Lyndon word iff \\axiom{a*b < \\spad{c} <= \\spad{b}} holds. Lyndon words are internally represented by binary trees using the \\spadtype{Magma} domain constructor. Two ordering are provided: lexicographic and length-lexicographic. \\newline Author : Michel Petitot (petitot@lifl.fr).")) (|LyndonWordsList| (((|List| $) (|List| |#1|) (|PositiveInteger|)) "\\axiom{LyndonWordsList(vl,{} \\spad{n})} returns the list of Lyndon words over the alphabet \\axiom{vl},{} up to order \\axiom{\\spad{n}}.")) (|LyndonWordsList1| (((|OneDimensionalArray| (|List| $)) (|List| |#1|) (|PositiveInteger|)) "\\axiom{\\spad{LyndonWordsList1}(vl,{} \\spad{n})} returns an array of lists of Lyndon words over the alphabet \\axiom{vl},{} up to order \\axiom{\\spad{n}}.")) (|varList| (((|List| |#1|) $) "\\axiom{varList(\\spad{x})} returns the list of distinct entries of \\axiom{\\spad{x}}.")) (|lyndonIfCan| (((|Union| $ "failed") (|OrderedFreeMonoid| |#1|)) "\\axiom{lyndonIfCan(\\spad{w})} convert \\axiom{\\spad{w}} into a Lyndon word.")) (|lyndon| (($ (|OrderedFreeMonoid| |#1|)) "\\axiom{lyndon(\\spad{w})} convert \\axiom{\\spad{w}} into a Lyndon word,{} error if \\axiom{\\spad{w}} is not a Lyndon word.")) (|lyndon?| (((|Boolean|) (|OrderedFreeMonoid| |#1|)) "\\axiom{lyndon?(\\spad{w})} test if \\axiom{\\spad{w}} is a Lyndon word.")) (|factor| (((|List| $) (|OrderedFreeMonoid| |#1|)) "\\axiom{factor(\\spad{x})} returns the decreasing factorization into Lyndon words.")) (|coerce| (((|Magma| |#1|) $) "\\axiom{coerce(\\spad{x})} returns the element of \\axiomType{Magma}(VarSet) corresponding to \\axiom{\\spad{x}}.") (((|OrderedFreeMonoid| |#1|) $) "\\axiom{coerce(\\spad{x})} returns the element of \\axiomType{OrderedFreeMonoid}(VarSet) corresponding to \\axiom{\\spad{x}}.")) (|lexico| (((|Boolean|) $ $) "\\axiom{lexico(\\spad{x},{}\\spad{y})} returns \\axiom{\\spad{true}} iff \\axiom{\\spad{x}} is smaller than \\axiom{\\spad{y}} \\spad{w}.\\spad{r}.\\spad{t}. the lexicographical ordering induced by \\axiom{VarSet}.")) (|length| (((|PositiveInteger|) $) "\\axiom{length(\\spad{x})} returns the number of entries in \\axiom{\\spad{x}}.")) (|right| (($ $) "\\axiom{right(\\spad{x})} returns right subtree of \\axiom{\\spad{x}} or error if \\axiomOpFrom{retractable?}{LyndonWord}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|left| (($ $) "\\axiom{left(\\spad{x})} returns left subtree of \\axiom{\\spad{x}} or error if \\axiomOpFrom{retractable?}{LyndonWord}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|retractable?| (((|Boolean|) $) "\\axiom{retractable?(\\spad{x})} tests if \\axiom{\\spad{x}} is a tree with only one entry."))) 
 NIL 
 NIL 
-(-615 A S) 
+(-616 A S) 
 ((|constructor| (NIL "LazyStreamAggregate is the category of streams with lazy evaluation. It is understood that the function 'empty?' will cause lazy evaluation if necessary to determine if there are entries. Functions which call 'empty?',{} \\spadignore{e.g.} 'first' and 'rest',{} will also cause lazy evaluation if necessary.")) (|complete| (($ $) "\\spad{complete(st)} causes all entries of 'st' to be computed. this function should only be called on streams which are known to be finite.")) (|extend| (($ $ (|Integer|)) "\\spad{extend(st,n)} causes entries to be computed,{} if necessary,{} so that 'st' will have at least 'n' explicit entries or so that all entries of 'st' will be computed if 'st' is finite with length <= \\spad{n}.")) (|numberOfComputedEntries| (((|NonNegativeInteger|) $) "\\spad{numberOfComputedEntries(st)} returns the number of explicitly computed entries of stream \\spad{st} which exist immediately prior to the time this function is called.")) (|rst| (($ $) "\\spad{rst(s)} returns a pointer to the next node of stream \\spad{s}. Caution: this function should only be called after a \\spad{empty?} test has been made since there no error check.")) (|frst| ((|#2| $) "\\spad{frst(s)} returns the first element of stream \\spad{s}. Caution: this function should only be called after a \\spad{empty?} test has been made since there no error check.")) (|lazyEvaluate| (($ $) "\\spad{lazyEvaluate(s)} causes one lazy evaluation of stream \\spad{s}. Caution: the first node must be a lazy evaluation mechanism (satisfies \\spad{lazy?(s) = true}) as there is no error check. Note: a call to this function may or may not produce an explicit first entry")) (|lazy?| (((|Boolean|) $) "\\spad{lazy?(s)} returns \\spad{true} if the first node of the stream \\spad{s} is a lazy evaluation mechanism which could produce an additional entry to \\spad{s}.")) (|explicitlyEmpty?| (((|Boolean|) $) "\\spad{explicitlyEmpty?(s)} returns \\spad{true} if the stream is an (explicitly) empty stream. Note: this is a null test which will not cause lazy evaluation.")) (|explicitEntries?| (((|Boolean|) $) "\\spad{explicitEntries?(s)} returns \\spad{true} if the stream \\spad{s} has explicitly computed entries,{} and \\spad{false} otherwise.")) (|select| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{select(f,st)} returns a stream consisting of those elements of stream \\spad{st} satisfying the predicate \\spad{f}. Note: \\spad{select(f,st) = [x for x in st | f(x)]}.")) (|remove| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{remove(f,st)} returns a stream consisting of those elements of stream \\spad{st} which do not satisfy the predicate \\spad{f}. Note: \\spad{remove(f,st) = [x for x in st | not f(x)]}."))) 
 NIL 
 NIL 
-(-616 S) 
+(-617 S) 
 ((|constructor| (NIL "LazyStreamAggregate is the category of streams with lazy evaluation. It is understood that the function 'empty?' will cause lazy evaluation if necessary to determine if there are entries. Functions which call 'empty?',{} \\spadignore{e.g.} 'first' and 'rest',{} will also cause lazy evaluation if necessary.")) (|complete| (($ $) "\\spad{complete(st)} causes all entries of 'st' to be computed. this function should only be called on streams which are known to be finite.")) (|extend| (($ $ (|Integer|)) "\\spad{extend(st,n)} causes entries to be computed,{} if necessary,{} so that 'st' will have at least 'n' explicit entries or so that all entries of 'st' will be computed if 'st' is finite with length <= \\spad{n}.")) (|numberOfComputedEntries| (((|NonNegativeInteger|) $) "\\spad{numberOfComputedEntries(st)} returns the number of explicitly computed entries of stream \\spad{st} which exist immediately prior to the time this function is called.")) (|rst| (($ $) "\\spad{rst(s)} returns a pointer to the next node of stream \\spad{s}. Caution: this function should only be called after a \\spad{empty?} test has been made since there no error check.")) (|frst| ((|#1| $) "\\spad{frst(s)} returns the first element of stream \\spad{s}. Caution: this function should only be called after a \\spad{empty?} test has been made since there no error check.")) (|lazyEvaluate| (($ $) "\\spad{lazyEvaluate(s)} causes one lazy evaluation of stream \\spad{s}. Caution: the first node must be a lazy evaluation mechanism (satisfies \\spad{lazy?(s) = true}) as there is no error check. Note: a call to this function may or may not produce an explicit first entry")) (|lazy?| (((|Boolean|) $) "\\spad{lazy?(s)} returns \\spad{true} if the first node of the stream \\spad{s} is a lazy evaluation mechanism which could produce an additional entry to \\spad{s}.")) (|explicitlyEmpty?| (((|Boolean|) $) "\\spad{explicitlyEmpty?(s)} returns \\spad{true} if the stream is an (explicitly) empty stream. Note: this is a null test which will not cause lazy evaluation.")) (|explicitEntries?| (((|Boolean|) $) "\\spad{explicitEntries?(s)} returns \\spad{true} if the stream \\spad{s} has explicitly computed entries,{} and \\spad{false} otherwise.")) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select(f,st)} returns a stream consisting of those elements of stream \\spad{st} satisfying the predicate \\spad{f}. Note: \\spad{select(f,st) = [x for x in st | f(x)]}.")) (|remove| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove(f,st)} returns a stream consisting of those elements of stream \\spad{st} which do not satisfy the predicate \\spad{f}. Note: \\spad{remove(f,st) = [x for x in st | not f(x)]}."))) 
 NIL 
 NIL 
-(-617) 
+(-618) 
 ((|constructor| (NIL "This domain represents the syntax of a macro definition.")) (|body| (((|SpadAst|) $) "\\spad{body(m)} returns the right hand side of the definition `m'.")) (|head| (((|HeadAst|) $) "\\spad{head(m)} returns the head of the macro definition `m'. This is a list of identifiers starting with the name of the macro followed by the name of the parameters,{} if any."))) 
 NIL 
 NIL 
-(-618 |VarSet|) 
+(-619 |VarSet|) 
 ((|constructor| (NIL "This type is the basic representation of parenthesized words (binary trees over arbitrary symbols) useful in \\spadtype{LiePolynomial}. \\newline Author: Michel Petitot (petitot@lifl.fr).")) (|varList| (((|List| |#1|) $) "\\axiom{varList(\\spad{x})} returns the list of distinct entries of \\axiom{\\spad{x}}.")) (|right| (($ $) "\\axiom{right(\\spad{x})} returns right subtree of \\axiom{\\spad{x}} or error if \\axiomOpFrom{retractable?}{Magma}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|retractable?| (((|Boolean|) $) "\\axiom{retractable?(\\spad{x})} tests if \\axiom{\\spad{x}} is a tree with only one entry.")) (|rest| (($ $) "\\axiom{rest(\\spad{x})} return \\axiom{\\spad{x}} without the first entry or error if \\axiomOpFrom{retractable?}{Magma}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|mirror| (($ $) "\\axiom{mirror(\\spad{x})} returns the reversed word of \\axiom{\\spad{x}}. That is \\axiom{\\spad{x}} itself if \\axiomOpFrom{retractable?}{Magma}(\\axiom{\\spad{x}}) is \\spad{true} and \\axiom{mirror(\\spad{z}) * mirror(\\spad{y})} if \\axiom{\\spad{x}} is \\axiom{y*z}.")) (|lexico| (((|Boolean|) $ $) "\\axiom{lexico(\\spad{x},{}\\spad{y})} returns \\axiom{\\spad{true}} iff \\axiom{\\spad{x}} is smaller than \\axiom{\\spad{y}} \\spad{w}.\\spad{r}.\\spad{t}. the lexicographical ordering induced by \\axiom{VarSet}. \\spad{N}.\\spad{B}. This operation does not take into account the tree structure of its arguments. Thus this is not a total ordering.")) (|length| (((|PositiveInteger|) $) "\\axiom{length(\\spad{x})} returns the number of entries in \\axiom{\\spad{x}}.")) (|left| (($ $) "\\axiom{left(\\spad{x})} returns left subtree of \\axiom{\\spad{x}} or error if \\axiomOpFrom{retractable?}{Magma}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|first| ((|#1| $) "\\axiom{first(\\spad{x})} returns the first entry of the tree \\axiom{\\spad{x}}.")) (|coerce| (((|OrderedFreeMonoid| |#1|) $) "\\axiom{coerce(\\spad{x})} returns the element of \\axiomType{OrderedFreeMonoid}(VarSet) corresponding to \\axiom{\\spad{x}} by removing parentheses.")) (* (($ $ $) "\\axiom{x*y} returns the tree \\axiom{[\\spad{x},{}\\spad{y}]}."))) 
 NIL 
 NIL 
-(-619 A) 
+(-620 A) 
 ((|constructor| (NIL "various Currying operations.")) (|recur| ((|#1| (|Mapping| |#1| (|NonNegativeInteger|) |#1|) (|NonNegativeInteger|) |#1|) "\\spad{recur(n,g,x)} is \\spad{g(n,g(n-1,..g(1,x)..))}.")) (|iter| ((|#1| (|Mapping| |#1| |#1|) (|NonNegativeInteger|) |#1|) "\\spad{iter(f,n,x)} applies \\spad{f n} times to \\spad{x}."))) 
 NIL 
 NIL 
-(-620 A C) 
+(-621 A C) 
 ((|constructor| (NIL "various Currying operations.")) (|arg2| ((|#2| |#1| |#2|) "\\spad{arg2(a,c)} selects its second argument.")) (|arg1| ((|#1| |#1| |#2|) "\\spad{arg1(a,c)} selects its first argument."))) 
 NIL 
 NIL 
-(-621 A B C) 
+(-622 A B C) 
 ((|constructor| (NIL "various Currying operations.")) (|comp| ((|#3| (|Mapping| |#3| |#2|) (|Mapping| |#2| |#1|) |#1|) "\\spad{comp(f,g,x)} is \\spad{f(g x)}."))) 
 NIL 
 NIL 
-(-622) 
+(-623) 
 ((|constructor| (NIL "This domain represents a mapping type AST. A mapping AST \\indented{2}{is a syntactic description of a function type,{} \\spadignore{e.g.} its result} \\indented{2}{type and the list of its argument types.}")) (|target| (((|TypeAst|) $) "\\spad{target(s)} returns the result type AST for `s'.")) (|source| (((|List| (|TypeAst|)) $) "\\spad{source(s)} returns the parameter type AST list of `s'.")) (|mappingAst| (($ (|List| (|TypeAst|)) (|TypeAst|)) "\\spad{mappingAst(s,t)} builds the mapping AST \\spad{s} -> \\spad{t}")) (|coerce| (($ (|Signature|)) "sig::MappingAst builds a MappingAst from the Signature `sig'."))) 
 NIL 
 NIL 
-(-623 A) 
+(-624 A) 
 ((|constructor| (NIL "various Currying operations.")) (|recur| (((|Mapping| |#1| (|NonNegativeInteger|) |#1|) (|Mapping| |#1| (|NonNegativeInteger|) |#1|)) "\\spad{recur(g)} is the function \\spad{h} such that \\indented{1}{\\spad{h(n,x)= g(n,g(n-1,..g(1,x)..))}.}")) (** (((|Mapping| |#1| |#1|) (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) "\\spad{f**n} is the function which is the \\spad{n}-fold application \\indented{1}{of \\spad{f}.}")) (|id| ((|#1| |#1|) "\\spad{id x} is \\spad{x}.")) (|fixedPoint| (((|List| |#1|) (|Mapping| (|List| |#1|) (|List| |#1|)) (|Integer|)) "\\spad{fixedPoint(f,n)} is the fixed point of function \\indented{1}{\\spad{f} which is assumed to transform a list of length} \\indented{1}{\\spad{n}.}") ((|#1| (|Mapping| |#1| |#1|)) "\\spad{fixedPoint f} is the fixed point of function \\spad{f}. \\indented{1}{\\spadignore{i.e.} such that \\spad{fixedPoint f = f(fixedPoint f)}.}")) (|coerce| (((|Mapping| |#1|) |#1|) "\\spad{coerce A} changes its argument into a \\indented{1}{nullary function.}")) (|nullary| (((|Mapping| |#1|) |#1|) "\\spad{nullary A} changes its argument into a \\indented{1}{nullary function.}"))) 
 NIL 
 NIL 
-(-624 A C) 
+(-625 A C) 
 ((|constructor| (NIL "various Currying operations.")) (|diag| (((|Mapping| |#2| |#1|) (|Mapping| |#2| |#1| |#1|)) "\\spad{diag(f)} is the function \\spad{g} \\indented{1}{such that \\spad{g a = f(a,a)}.}")) (|constant| (((|Mapping| |#2| |#1|) (|Mapping| |#2|)) "\\spad{vu(f)} is the function \\spad{g} \\indented{1}{such that \\spad{g a= f ()}.}")) (|curry| (((|Mapping| |#2|) (|Mapping| |#2| |#1|) |#1|) "\\spad{cu(f,a)} is the function \\spad{g} \\indented{1}{such that \\spad{g ()= f a}.}")) (|const| (((|Mapping| |#2| |#1|) |#2|) "\\spad{const c} is a function which produces \\spad{c} when \\indented{1}{applied to its argument.}"))) 
 NIL 
 NIL 
-(-625 A B C) 
+(-626 A B C) 
 ((|constructor| (NIL "various Currying operations.")) (* (((|Mapping| |#3| |#1|) (|Mapping| |#3| |#2|) (|Mapping| |#2| |#1|)) "\\spad{f*g} is the function \\spad{h} \\indented{1}{such that \\spad{h x= f(g x)}.}")) (|twist| (((|Mapping| |#3| |#2| |#1|) (|Mapping| |#3| |#1| |#2|)) "\\spad{twist(f)} is the function \\spad{g} \\indented{1}{such that \\spad{g (a,b)= f(b,a)}.}")) (|constantLeft| (((|Mapping| |#3| |#1| |#2|) (|Mapping| |#3| |#2|)) "\\spad{constantLeft(f)} is the function \\spad{g} \\indented{1}{such that \\spad{g (a,b)= f b}.}")) (|constantRight| (((|Mapping| |#3| |#1| |#2|) (|Mapping| |#3| |#1|)) "\\spad{constantRight(f)} is the function \\spad{g} \\indented{1}{such that \\spad{g (a,b)= f a}.}")) (|curryLeft| (((|Mapping| |#3| |#2|) (|Mapping| |#3| |#1| |#2|) |#1|) "\\spad{curryLeft(f,a)} is the function \\spad{g} \\indented{1}{such that \\spad{g b = f(a,b)}.}")) (|curryRight| (((|Mapping| |#3| |#1|) (|Mapping| |#3| |#1| |#2|) |#2|) "\\spad{curryRight(f,b)} is the function \\spad{g} such that \\indented{1}{\\spad{g a = f(a,b)}.}"))) 
 NIL 
 NIL 
-(-626 S R |Row| |Col|) 
+(-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 (-3991 "*"))) (|HasCategory| |#2| (QUOTE (-257))) (|HasCategory| |#2| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-494)))) 
-(-627 R |Row| |Col|) 
+((|HasAttribute| |#2| (QUOTE (-3993 "*"))) (|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"))) 
-((-3989 . T) (-3990 . T)) 
+((-3991 . T) (-3992 . T)) 
 NIL 
-(-628 R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2) 
+(-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}."))) 
 NIL 
 NIL 
-(-629 R |Row| |Col| M) 
+(-630 R |Row| |Col| M) 
 ((|constructor| (NIL "\\spadtype{MatrixLinearAlgebraFunctions} provides functions to compute inverses and canonical forms.")) (|inverse| (((|Union| |#4| "failed") |#4|) "\\spad{inverse(m)} returns the inverse of the matrix. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|normalizedDivide| (((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|) "\\spad{normalizedDivide(n,d)} returns a normalized quotient and remainder such that consistently unique representatives for the residue class are chosen,{} \\spadignore{e.g.} positive remainders")) (|rowEchelon| ((|#4| |#4|) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (|adjoint| (((|Record| (|:| |adjMat| |#4|) (|:| |detMat| |#1|)) |#4|) "\\spad{adjoint(m)} returns the ajoint matrix of \\spad{m} (\\spadignore{i.e.} the matrix \\spad{n} such that m*n = determinant(\\spad{m})*id) and the detrminant of \\spad{m}.")) (|invertIfCan| (((|Union| |#4| "failed") |#4|) "\\spad{invertIfCan(m)} returns the inverse of \\spad{m} over \\spad{R}")) (|fractionFreeGauss!| ((|#4| |#4|) "\\spad{fractionFreeGauss(m)} performs the fraction free gaussian elimination on the matrix \\spad{m}.")) (|nullSpace| (((|List| |#3|) |#4|) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) |#4|) "\\spad{nullity(m)} returns the mullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) |#4|) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|elColumn2!| ((|#4| |#4| |#1| (|Integer|) (|Integer|)) "\\spad{elColumn2!(m,a,i,j)} adds to column \\spad{i} a*column(\\spad{m},{}\\spad{j}) : elementary operation of second kind. (\\spad{i} ~=j)")) (|elRow2!| ((|#4| |#4| |#1| (|Integer|) (|Integer|)) "\\spad{elRow2!(m,a,i,j)} adds to row \\spad{i} a*row(\\spad{m},{}\\spad{j}) : elementary operation of second kind. (\\spad{i} ~=j)")) (|elRow1!| ((|#4| |#4| (|Integer|) (|Integer|)) "\\spad{elRow1!(m,i,j)} swaps rows \\spad{i} and \\spad{j} of matrix \\spad{m} : elementary operation of first kind")) (|minordet| ((|#1| |#4|) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors. Error: if the matrix is not square.")) (|determinant| ((|#1| |#4|) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. an error message is returned if the matrix is not square."))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-257))) (|HasCategory| |#1| (QUOTE (-494)))) 
-(-630 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."))) 
-((-3989 . T) (-3990 . T)) 
-((OR (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1012))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-553 (-472)))) (|HasCategory| |#1| (QUOTE (-257))) (|HasCategory| |#1| (QUOTE (-494))) (|HasAttribute| |#1| (QUOTE (-3991 "*"))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|))))) 
+((|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|))))) 
+(-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 
 NIL 
-(-632 T$) 
+(-633 T$) 
 ((|constructor| (NIL "This domain implements the notion of optional value,{} where a computation may fail to produce expected value.")) (|nothing| (($) "\\spad{nothing} represents failure or absence of value.")) (|autoCoerce| ((|#1| $) "\\spad{autoCoerce} is a courtesy coercion function used by the compiler in case it knows that `x' really is a \\spadtype{T}.")) (|case| (((|Boolean|) $ (|[\|\|]| |nothing|)) "\\spad{x case nothing} holds if the value for \\spad{x} is missing.") (((|Boolean|) $ (|[\|\|]| |#1|)) "\\spad{x case T} returns \\spad{true} if \\spad{x} is actually a data of type \\spad{T}.")) (|just| (($ |#1|) "\\spad{just x} injects the value `x' into \\%."))) 
 NIL 
 NIL 
-(-633 R Q) 
+(-634 R Q) 
 ((|constructor| (NIL "MatrixCommonDenominator provides functions to compute the common denominator of a matrix of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| (|Matrix| |#1|)) (|:| |den| |#1|)) (|Matrix| |#2|)) "\\spad{splitDenominator(q)} returns \\spad{[p, d]} such that \\spad{q = p/d} and \\spad{d} is a common denominator for the elements of \\spad{q}.")) (|clearDenominator| (((|Matrix| |#1|) (|Matrix| |#2|)) "\\spad{clearDenominator(q)} returns \\spad{p} such that \\spad{q = p/d} where \\spad{d} is a common denominator for the elements of \\spad{q}.")) (|commonDenominator| ((|#1| (|Matrix| |#2|)) "\\spad{commonDenominator(q)} returns a common denominator \\spad{d} for the elements of \\spad{q}."))) 
 NIL 
 NIL 
-(-634 S) 
+(-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}."))) 
-((-3990 . T)) 
+((-3992 . T)) 
 NIL 
-(-635 U) 
+(-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}."))) 
 NIL 
 NIL 
-(-636) 
+(-637) 
 ((|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 
-(-637 OV E -3088 PG) 
+(-638 OV E -3090 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 
-(-638 R) 
+(-639 R) 
 ((|constructor| (NIL "\\indented{1}{Modular hermitian row reduction.} Author: Manuel Bronstein Date Created: 22 February 1989 Date Last Updated: 24 November 1993 Keywords: matrix,{} reduction.")) (|normalizedDivide| (((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|) "\\spad{normalizedDivide(n,d)} returns a normalized quotient and remainder such that consistently unique representatives for the residue class are chosen,{} \\spadignore{e.g.} positive remainders")) (|rowEchelonLocal| (((|Matrix| |#1|) (|Matrix| |#1|) |#1| |#1|) "\\spad{rowEchelonLocal(m, d, p)} computes the row-echelon form of \\spad{m} concatenated with \\spad{d} times the identity matrix over a local ring where \\spad{p} is the only prime.")) (|rowEchLocal| (((|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{rowEchLocal(m,p)} computes a modular row-echelon form of \\spad{m},{} finding an appropriate modulus over a local ring where \\spad{p} is the only prime.")) (|rowEchelon| (((|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{rowEchelon(m, d)} computes a modular row-echelon form mod \\spad{d} of \\indented{3}{[\\spad{d}\\space{5}]} \\indented{3}{[\\space{2}\\spad{d}\\space{3}]} \\indented{3}{[\\space{4}. ]} \\indented{3}{[\\space{5}\\spad{d}]} \\indented{3}{[\\space{3}\\spad{M}\\space{2}]} where \\spad{M = m mod d}.")) (|rowEch| (((|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{rowEch(m)} computes a modular row-echelon form of \\spad{m},{} finding an appropriate modulus."))) 
 NIL 
 NIL 
-(-639 S D1 D2 I) 
+(-640 S D1 D2 I) 
 ((|constructor| (NIL "transforms top-level objects into compiled functions.")) (|compiledFunction| (((|Mapping| |#4| |#2| |#3|) |#1| (|Symbol|) (|Symbol|)) "\\spad{compiledFunction(expr,x,y)} returns a function \\spad{f: (D1, D2) -> I} defined by \\spad{f(x, y) == expr}. Function \\spad{f} is compiled and directly applicable to objects of type \\spad{(D1, D2)}")) (|binaryFunction| (((|Mapping| |#4| |#2| |#3|) (|Symbol|)) "\\spad{binaryFunction(s)} is a local function"))) 
 NIL 
 NIL 
-(-640 S) 
+(-641 S) 
 ((|constructor| (NIL "MakeFloatCompiledFunction transforms top-level objects into compiled Lisp functions whose arguments are Lisp floats. This by-passes the \\Language{} compiler and interpreter,{} thereby gaining several orders of magnitude.")) (|makeFloatFunction| (((|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) |#1| (|Symbol|) (|Symbol|)) "\\spad{makeFloatFunction(expr, x, y)} returns a Lisp function \\spad{f: (\\axiomType{DoubleFloat}, \\axiomType{DoubleFloat}) -> \\axiomType{DoubleFloat}} defined by \\spad{f(x, y) == expr}. Function \\spad{f} is compiled and directly applicable to objects of type \\spad{(\\axiomType{DoubleFloat}, \\axiomType{DoubleFloat})}.") (((|Mapping| (|DoubleFloat|) (|DoubleFloat|)) |#1| (|Symbol|)) "\\spad{makeFloatFunction(expr, x)} returns a Lisp function \\spad{f: \\axiomType{DoubleFloat} -> \\axiomType{DoubleFloat}} defined by \\spad{f(x) == expr}. Function \\spad{f} is compiled and directly applicable to objects of type \\axiomType{DoubleFloat}."))) 
 NIL 
 NIL 
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 ((|constructor| (NIL "transforms top-level objects into interpreter functions.")) (|function| (((|Symbol|) |#1| (|Symbol|) (|List| (|Symbol|))) "\\spad{function(e, foo, [x1,...,xn])} creates a function \\spad{foo(x1,...,xn) == e}.") (((|Symbol|) |#1| (|Symbol|) (|Symbol|) (|Symbol|)) "\\spad{function(e, foo, x, y)} creates a function \\spad{foo(x, y) = e}.") (((|Symbol|) |#1| (|Symbol|) (|Symbol|)) "\\spad{function(e, foo, x)} creates a function \\spad{foo(x) == e}.") (((|Symbol|) |#1| (|Symbol|)) "\\spad{function(e, foo)} creates a function \\spad{foo() == e}."))) 
 NIL 
 NIL 
-(-642 S T$) 
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 ((|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 
-(-643 S -2665 I) 
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 ((|constructor| (NIL "transforms top-level objects into compiled functions.")) (|compiledFunction| (((|Mapping| |#3| |#2|) |#1| (|Symbol|)) "\\spad{compiledFunction(expr, x)} returns a function \\spad{f: D -> I} defined by \\spad{f(x) == expr}. Function \\spad{f} is compiled and directly applicable to objects of type \\spad{D}.")) (|unaryFunction| (((|Mapping| |#3| |#2|) (|Symbol|)) "\\spad{unaryFunction(a)} is a local function"))) 
 NIL 
 NIL 
-(-644 E OV R P) 
+(-645 E OV R P) 
 ((|constructor| (NIL "This package provides the functions for the multivariate \"lifting\",{} using an algorithm of Paul Wang. This package will work for every euclidean domain \\spad{R} which has property \\spad{F},{} \\spadignore{i.e.} there exists a factor operation in \\spad{R[x]}.")) (|lifting1| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|List| (|SparseUnivariatePolynomial| |#4|)) (|List| |#3|) (|List| |#4|) (|List| (|List| (|Record| (|:| |expt| (|NonNegativeInteger|)) (|:| |pcoef| |#4|)))) (|List| (|NonNegativeInteger|)) (|Vector| (|List| (|SparseUnivariatePolynomial| |#3|))) |#3|) "\\spad{lifting1(u,lv,lu,lr,lp,lt,ln,t,r)} \\undocumented")) (|lifting| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|List| (|SparseUnivariatePolynomial| |#3|)) (|List| |#3|) (|List| |#4|) (|List| (|NonNegativeInteger|)) |#3|) "\\spad{lifting(u,lv,lu,lr,lp,ln,r)} \\undocumented")) (|corrPoly| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|List| |#3|) (|List| (|NonNegativeInteger|)) (|List| (|SparseUnivariatePolynomial| |#4|)) (|Vector| (|List| (|SparseUnivariatePolynomial| |#3|))) |#3|) "\\spad{corrPoly(u,lv,lr,ln,lu,t,r)} \\undocumented"))) 
 NIL 
 NIL 
-(-645 R) 
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 ((|constructor| (NIL "This is the category of linear operator rings with one generator. The generator is not named by the category but can always be constructed as \\spad{monomial(1,1)}. \\blankline For convenience,{} call the generator \\spad{G}. Then each value is equal to \\indented{4}{\\spad{sum(a(i)*G**i, i = 0..n)}} for some unique \\spad{n} and \\spad{a(i)} in \\spad{R}. \\blankline Note that multiplication is not necessarily commutative. In fact,{} if \\spad{a} is in \\spad{R},{} it is quite normal to have \\spad{a*G \\~= G*a}.")) (|monomial| (($ |#1| (|NonNegativeInteger|)) "\\spad{monomial(c,k)} produces \\spad{c} times the \\spad{k}-th power of the generating operator,{} \\spad{monomial(1,1)}.")) (|coefficient| ((|#1| $ (|NonNegativeInteger|)) "\\spad{coefficient(l,k)} is \\spad{a(k)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|reductum| (($ $) "\\spad{reductum(l)} is \\spad{l - monomial(a(n),n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(l)} is \\spad{a(n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|minimumDegree| (((|NonNegativeInteger|) $) "\\spad{minimumDegree(l)} is the smallest \\spad{k} such that \\spad{a(k) \\~= 0} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(l)} is \\spad{n} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}"))) 
-((-3983 . T) (-3984 . T) (-3986 . T)) 
+((-3985 . T) (-3986 . T) (-3988 . T)) 
 NIL 
-(-646 R1 UP1 UPUP1 R2 UP2 UPUP2) 
+(-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}."))) 
 NIL 
 NIL 
-(-647) 
+(-648) 
 ((|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 
-(-648 R |Mod| -2033 -3512 |exactQuo|) 
+(-649 R |Mod| -2035 -3514 |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| $) "\\spad{modulus(x)} \\undocumented"))) 
-((-3981 . T) (-3987 . T) (-3982 . T) ((-3991 "*") . T) (-3983 . T) (-3984 . T) (-3986 . T)) 
+((-3983 . T) (-3989 . T) (-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . T)) 
 NIL 
-(-649 R P) 
+(-650 R P) 
 ((|constructor| (NIL "This package \\undocumented")) (|frobenius| (($ $) "\\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"))) 
-(((-3991 "*") |has| |#1| (-146)) (-3982 |has| |#1| (-494)) (-3985 |has| |#1| (-311)) (-3987 |has| |#1| (-6 -3987)) (-3984 . T) (-3983 . T) (-3986 . T)) 
-((|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-494)))) (-12 (|HasCategory| |#1| (QUOTE (-796 (-327)))) (|HasCategory| (-993) (QUOTE (-796 (-327))))) (-12 (|HasCategory| |#1| (QUOTE (-796 (-483)))) (|HasCategory| (-993) (QUOTE (-796 (-483))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-800 (-327))))) (|HasCategory| (-993) (QUOTE (-553 (-800 (-327)))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-800 (-483))))) (|HasCategory| (-993) (QUOTE (-553 (-800 (-483)))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-472)))) (|HasCategory| (-993) (QUOTE (-553 (-472))))) (|HasCategory| |#1| (QUOTE (-580 (-483)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-347 (-483))))) (|HasCategory| |#1| (QUOTE (-950 (-483)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-347 (-483))))) (|HasCategory| |#1| (QUOTE (-950 (-347 (-483)))))) (|HasCategory| |#1| (QUOTE (-950 (-347 (-483))))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-389))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-821)))) (OR (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-389))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-821)))) (OR (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-389))) (|HasCategory| |#1| (QUOTE (-821)))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-1064))) (|HasCategory| |#1| (QUOTE (-811 (-1088)))) (|HasCategory| |#1| (QUOTE (-809 (-1088)))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-298))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-190))) (|HasAttribute| |#1| (QUOTE -3987)) (|HasCategory| |#1| (QUOTE (-389))) (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) 
-(-650 IS E |ff|) 
+(((-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))))) 
+(-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| $) "\\spad{exponent(x)} \\undocumented"))) 
 NIL 
 NIL 
-(-651 R M) 
+(-652 R M) 
 ((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#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| (($ $ $) "\\spad{adjoint(op1, op2)} sets the adjoint of \\spad{op1} to be \\spad{op2}. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) 
-((-3984 |has| |#1| (-146)) (-3983 |has| |#1| (-146)) (-3986 . T)) 
+((-3986 |has| |#1| (-146)) (-3985 |has| |#1| (-146)) (-3988 . T)) 
 ((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120)))) 
-(-652 R |Mod| -2033 -3512 |exactQuo|) 
+(-653 R |Mod| -2035 -3514 |exactQuo|) 
 ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\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"))) 
-((-3986 . T)) 
+((-3988 . T)) 
 NIL 
-(-653 S R) 
+(-654 S R) 
 ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) 
 NIL 
 NIL 
-(-654 R) 
+(-655 R) 
 ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) 
-((-3984 . T) (-3983 . T)) 
+((-3986 . T) (-3985 . T)) 
 NIL 
-(-655 -3088) 
+(-656 -3090) 
 ((|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]]}."))) 
-((-3986 . T)) 
+((-3988 . T)) 
 NIL 
-(-656 S) 
+(-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}.")) (* (($ $ $) "\\spad{a*b} is the product of \\spad{a} and \\spad{b} in a set with a binary operation."))) 
 NIL 
 NIL 
-(-657) 
+(-658) 
 ((|constructor| (NIL "Monad is the class of all multiplicative monads,{} \\spadignore{i.e.} sets with a binary operation.")) (** (($ $ (|PositiveInteger|)) "\\spad{a**n} returns the \\spad{n}\\spad{-}th power of \\spad{a},{} defined by repeated squaring.")) (|leftPower| (($ $ (|PositiveInteger|)) "\\spad{leftPower(a,n)} returns the \\spad{n}\\spad{-}th left power of \\spad{a},{} \\spadignore{i.e.} \\spad{leftPower(a,n) := a * leftPower(a,n-1)} and \\spad{leftPower(a,1) := a}.")) (|rightPower| (($ $ (|PositiveInteger|)) "\\spad{rightPower(a,n)} returns the \\spad{n}\\spad{-}th right power of \\spad{a},{} \\spadignore{i.e.} \\spad{rightPower(a,n) := rightPower(a,n-1) * a} and \\spad{rightPower(a,1) := a}.")) (* (($ $ $) "\\spad{a*b} is the product of \\spad{a} and \\spad{b} in a set with a binary operation."))) 
 NIL 
 NIL 
-(-658 S) 
+(-659 S) 
 ((|constructor| (NIL "\\indented{1}{MonadWithUnit is the class of multiplicative monads with unit,{}} \\indented{1}{\\spadignore{i.e.} sets with a binary operation and a unit element.} Axioms \\indented{3}{leftIdentity(\"*\":(\\%,{}\\%)->\\%,{}1)\\space{3}\\tab{30} 1*x=x} \\indented{3}{rightIdentity(\"*\":(\\%,{}\\%)->\\%,{}1)\\space{2}\\tab{30} x*1=x} Common Additional Axioms \\indented{3}{unitsKnown---if \"recip\" says \"failed\",{} that PROVES input wasn't a unit}")) (|rightRecip| (((|Union| $ "failed") $) "\\spad{rightRecip(a)} returns an element,{} which is a right inverse of \\spad{a},{} or \\spad{\"failed\"} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (|leftRecip| (((|Union| $ "failed") $) "\\spad{leftRecip(a)} returns an element,{} which is a left inverse of \\spad{a},{} or \\spad{\"failed\"} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(a)} returns an element,{} which is both a left and a right inverse of \\spad{a},{} or \\spad{\"failed\"} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (** (($ $ (|NonNegativeInteger|)) "\\spad{a**n} returns the \\spad{n}\\spad{-}th power of \\spad{a},{} defined by repeated squaring.")) (|leftPower| (($ $ (|NonNegativeInteger|)) "\\spad{leftPower(a,n)} returns the \\spad{n}\\spad{-}th left power of \\spad{a},{} \\spadignore{i.e.} \\spad{leftPower(a,n) := a * leftPower(a,n-1)} and \\spad{leftPower(a,0) := 1}.")) (|rightPower| (($ $ (|NonNegativeInteger|)) "\\spad{rightPower(a,n)} returns the \\spad{n}\\spad{-}th right power of \\spad{a},{} \\spadignore{i.e.} \\spad{rightPower(a,n) := rightPower(a,n-1) * a} and \\spad{rightPower(a,0) := 1}.")) (|one?| (((|Boolean|) $) "\\spad{one?(a)} tests whether \\spad{a} is the unit 1.")) (|One| (($) "1 returns the unit element,{} denoted by 1."))) 
 NIL 
 NIL 
-(-659) 
+(-660) 
 ((|constructor| (NIL "\\indented{1}{MonadWithUnit is the class of multiplicative monads with unit,{}} \\indented{1}{\\spadignore{i.e.} sets with a binary operation and a unit element.} Axioms \\indented{3}{leftIdentity(\"*\":(\\%,{}\\%)->\\%,{}1)\\space{3}\\tab{30} 1*x=x} \\indented{3}{rightIdentity(\"*\":(\\%,{}\\%)->\\%,{}1)\\space{2}\\tab{30} x*1=x} Common Additional Axioms \\indented{3}{unitsKnown---if \"recip\" says \"failed\",{} that PROVES input wasn't a unit}")) (|rightRecip| (((|Union| $ "failed") $) "\\spad{rightRecip(a)} returns an element,{} which is a right inverse of \\spad{a},{} or \\spad{\"failed\"} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (|leftRecip| (((|Union| $ "failed") $) "\\spad{leftRecip(a)} returns an element,{} which is a left inverse of \\spad{a},{} or \\spad{\"failed\"} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(a)} returns an element,{} which is both a left and a right inverse of \\spad{a},{} or \\spad{\"failed\"} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (** (($ $ (|NonNegativeInteger|)) "\\spad{a**n} returns the \\spad{n}\\spad{-}th power of \\spad{a},{} defined by repeated squaring.")) (|leftPower| (($ $ (|NonNegativeInteger|)) "\\spad{leftPower(a,n)} returns the \\spad{n}\\spad{-}th left power of \\spad{a},{} \\spadignore{i.e.} \\spad{leftPower(a,n) := a * leftPower(a,n-1)} and \\spad{leftPower(a,0) := 1}.")) (|rightPower| (($ $ (|NonNegativeInteger|)) "\\spad{rightPower(a,n)} returns the \\spad{n}\\spad{-}th right power of \\spad{a},{} \\spadignore{i.e.} \\spad{rightPower(a,n) := rightPower(a,n-1) * a} and \\spad{rightPower(a,0) := 1}.")) (|one?| (((|Boolean|) $) "\\spad{one?(a)} tests whether \\spad{a} is the unit 1.")) (|One| (($) "1 returns the unit element,{} denoted by 1."))) 
 NIL 
 NIL 
-(-660 S R UP) 
+(-661 S R UP) 
 ((|constructor| (NIL "A \\spadtype{MonogenicAlgebra} is an algebra of finite rank which can be generated by a single element.")) (|derivationCoordinates| (((|Matrix| |#2|) (|Vector| $) (|Mapping| |#2| |#2|)) "\\spad{derivationCoordinates(b, ')} returns \\spad{M} such that \\spad{b' = M b}.")) (|lift| ((|#3| $) "\\spad{lift(z)} returns a minimal degree univariate polynomial up such that \\spad{z=reduce up}.")) (|convert| (($ |#3|) "\\spad{convert(up)} converts the univariate polynomial \\spad{up} to an algebra element,{} reducing by the \\spad{definingPolynomial()} if necessary.")) (|reduce| (((|Union| $ "failed") (|Fraction| |#3|)) "\\spad{reduce(frac)} converts the fraction \\spad{frac} to an algebra element.") (($ |#3|) "\\spad{reduce(up)} converts the univariate polynomial \\spad{up} to an algebra element,{} reducing by the \\spad{definingPolynomial()} if necessary.")) (|definingPolynomial| ((|#3|) "\\spad{definingPolynomial()} returns the minimal polynomial which \\spad{generator()} satisfies.")) (|generator| (($) "\\spad{generator()} returns the generator for this domain."))) 
 NIL 
 ((|HasCategory| |#2| (QUOTE (-298))) (|HasCategory| |#2| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-317)))) 
-(-661 R UP) 
+(-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."))) 
-((-3982 |has| |#1| (-311)) (-3987 |has| |#1| (-311)) (-3981 |has| |#1| (-311)) ((-3991 "*") . T) (-3983 . T) (-3984 . T) (-3986 . T)) 
+((-3984 |has| |#1| (-311)) (-3989 |has| |#1| (-311)) (-3983 |has| |#1| (-311)) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . T)) 
 NIL 
-(-662 S) 
+(-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."))) 
 NIL 
 NIL 
-(-663) 
+(-664) 
 ((|constructor| (NIL "The class of multiplicative monoids,{} \\spadignore{i.e.} semigroups with a multiplicative identity element. \\blankline")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} tries to compute the multiplicative inverse for \\spad{x} or \"failed\" if it cannot find the inverse (see unitsKnown).")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (|one?| (((|Boolean|) $) "\\spad{one?(x)} tests if \\spad{x} is equal to 1.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) (|One| (($) "1 is the multiplicative identity."))) 
 NIL 
 NIL 
-(-664 T$) 
+(-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 (-3052 (|f| |x| (-2408 |f|)) |x|) (|exit| 1 (-3052 (|f| (-2408 |f|) |x|) |x|))))) . T) ((|%Rule| |associativity| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|) (|:| |y| |#1|) (|:| |z| |#1|)) (-3052 (|f| (|f| |x| |y|) |z|) (|f| |x| (|f| |y| |z|))))) . T)) 
+(((|%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| $) (|:| |x| |#1|) (|:| |y| |#1|) (|:| |z| |#1|)) (-3054 (|f| (|f| |x| |y|) |z|) (|f| |x| (|f| |y| |z|))))) . T)) 
 NIL 
-(-665 T$) 
+(-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 (-3052 (|f| |x| (-2408 |f|)) |x|) (|exit| 1 (-3052 (|f| (-2408 |f|) |x|) |x|))))) . T) ((|%Rule| |associativity| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|) (|:| |y| |#1|) (|:| |z| |#1|)) (-3052 (|f| (|f| |x| |y|) |z|) (|f| |x| (|f| |y| |z|))))) . T)) 
+(((|%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)) 
 NIL 
-(-666 -3088 UP) 
+(-667 -3090 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 
-(-667 |VarSet| E1 E2 R S PR PS) 
-((|constructor| (NIL "\\indented{1}{Utilities for MPolyCat} Author: Manuel Bronstein Date Created: 1987 Date Last Updated: 28 March 1990 (PG)")) (|reshape| ((|#7| (|List| |#5|) |#6|) "\\spad{reshape(l,p)} \\undocumented")) (|map| ((|#7| (|Mapping| |#5| |#4|) |#6|) "\\spad{map(f,p)} \\undocumented	"))) 
+(-668 |VarSet| E1 E2 R S PR PS) 
+((|constructor| (NIL "\\indented{1}{Utilities for MPolyCat} Author: Manuel Bronstein Date Created: 1987 Date Last Updated: 28 March 1990 (PG)")) (|reshape| ((|#7| (|List| |#5|) |#6|) "\\spad{reshape(l,p)} \\undocumented")) (|map| ((|#7| (|Mapping| |#5| |#4|) |#6|) "\\spad{map(f,p)} \\undocumented"))) 
 NIL 
 NIL 
-(-668 |Vars1| |Vars2| E1 E2 R PR1 PR2) 
+(-669 |Vars1| |Vars2| E1 E2 R PR1 PR2) 
 ((|constructor| (NIL "This package \\undocumented")) (|map| ((|#7| (|Mapping| |#2| |#1|) |#6|) "\\spad{map(f,x)} \\undocumented"))) 
 NIL 
 NIL 
-(-669 E OV R PPR) 
+(-670 E OV R PPR) 
 ((|constructor| (NIL "\\indented{3}{This package exports a factor operation for multivariate polynomials} with coefficients which are polynomials over some ring \\spad{R} over which we can factor. It is used internally by packages such as the solve package which need to work with polynomials in a specific set of variables with coefficients which are polynomials in all the other variables.")) (|factor| (((|Factored| |#4|) |#4|) "\\spad{factor(p)} factors a polynomial with polynomial coefficients.")) (|variable| (((|Union| $ "failed") (|Symbol|)) "\\spad{variable(s)} makes an element from symbol \\spad{s} or fails.")) (|convert| (((|Symbol|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) 
 NIL 
 NIL 
-(-670 |vl| R) 
+(-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."))) 
-(((-3991 "*") |has| |#2| (-146)) (-3982 |has| |#2| (-494)) (-3987 |has| |#2| (-6 -3987)) (-3984 . T) (-3983 . T) (-3986 . T)) 
-((|HasCategory| |#2| (QUOTE (-821))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-389))) (|HasCategory| |#2| (QUOTE (-494))) (|HasCategory| |#2| (QUOTE (-821)))) (OR (|HasCategory| |#2| (QUOTE (-389))) (|HasCategory| |#2| (QUOTE (-494))) (|HasCategory| |#2| (QUOTE (-821)))) (OR (|HasCategory| |#2| (QUOTE (-389))) (|HasCategory| |#2| (QUOTE (-821)))) (|HasCategory| |#2| (QUOTE (-494))) (|HasCategory| |#2| (QUOTE (-146))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-494)))) (-12 (|HasCategory| |#2| (QUOTE (-796 (-327)))) (|HasCategory| (-773 |#1|) (QUOTE (-796 (-327))))) (-12 (|HasCategory| |#2| (QUOTE (-796 (-483)))) (|HasCategory| (-773 |#1|) (QUOTE (-796 (-483))))) (-12 (|HasCategory| |#2| (QUOTE (-553 (-800 (-327))))) (|HasCategory| (-773 |#1|) (QUOTE (-553 (-800 (-327)))))) (-12 (|HasCategory| |#2| (QUOTE (-553 (-800 (-483))))) (|HasCategory| (-773 |#1|) (QUOTE (-553 (-800 (-483)))))) (-12 (|HasCategory| |#2| (QUOTE (-553 (-472)))) (|HasCategory| (-773 |#1|) (QUOTE (-553 (-472))))) (|HasCategory| |#2| (QUOTE (-580 (-483)))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-38 (-347 (-483))))) (|HasCategory| |#2| (QUOTE (-950 (-483)))) (OR (|HasCategory| |#2| (QUOTE (-38 (-347 (-483))))) (|HasCategory| |#2| (QUOTE (-950 (-347 (-483)))))) (|HasCategory| |#2| (QUOTE (-950 (-347 (-483))))) (|HasCategory| |#2| (QUOTE (-311))) (|HasAttribute| |#2| (QUOTE -3987)) (|HasCategory| |#2| (QUOTE (-389))) (-12 (|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#2| (QUOTE (-118))))) 
-(-671 E OV R PRF) 
+(((-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))))) 
+(-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 
 NIL 
-(-672 E OV R P) 
+(-673 E OV R P) 
 ((|constructor| (NIL "\\indented{1}{MRationalFactorize contains the factor function for multivariate} polynomials over the quotient field of a ring \\spad{R} such that the package MultivariateFactorize can factor multivariate polynomials over \\spad{R}.")) (|factor| (((|Factored| |#4|) |#4|) "\\spad{factor(p)} factors the multivariate polynomial \\spad{p} with coefficients which are fractions of elements of \\spad{R}."))) 
 NIL 
 NIL 
-(-673 R S M) 
+(-674 R S M) 
 ((|constructor| (NIL "\\spad{MonoidRingFunctions2} implements functions between two monoid rings defined with the same monoid over different rings.")) (|map| (((|MonoidRing| |#2| |#3|) (|Mapping| |#2| |#1|) (|MonoidRing| |#1| |#3|)) "\\spad{map(f,u)} maps \\spad{f} onto the coefficients \\spad{f} the element \\spad{u} of the monoid ring to create an element of a monoid ring with the same monoid \\spad{b}."))) 
 NIL 
 NIL 
-(-674 R M) 
+(-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}."))) 
-((-3984 |has| |#1| (-146)) (-3983 |has| |#1| (-146)) (-3986 . 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 (-756)))) 
-(-675 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}."))) 
-((-3989 . T) (-3979 . T) (-3990 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-553 (-472)))) (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-72)))) 
+((-3986 |has| |#1| (-146)) (-3985 |has| |#1| (-146)) (-3988 . 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)) 
+((-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."))) 
-((-3979 . T) (-3990 . T)) 
+((-3981 . T) (-3992 . T)) 
 NIL 
-(-677) 
+(-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."))) 
 NIL 
 NIL 
-(-678 S) 
+(-679 S) 
 ((|constructor| (NIL "This package exports tools for merging lists")) (|mergeDifference| (((|List| |#1|) (|List| |#1|) (|List| |#1|)) "\\spad{mergeDifference(l1,l2)} returns a list of elements in \\spad{l1} not present in \\spad{l2}. Assumes lists are ordered and all \\spad{x} in \\spad{l2} are also in \\spad{l1}."))) 
 NIL 
 NIL 
-(-679 |Coef| |Var|) 
+(-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}."))) 
-(((-3991 "*") |has| |#1| (-146)) (-3982 |has| |#1| (-494)) (-3984 . T) (-3983 . T) (-3986 . T)) 
+(((-3993 "*") |has| |#1| (-146)) (-3984 |has| |#1| (-495)) (-3986 . T) (-3985 . T) (-3988 . T)) 
 NIL 
-(-680 OV E R P) 
+(-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"))) 
 NIL 
 NIL 
-(-681 E OV R P) 
+(-682 E OV R P) 
 ((|constructor| (NIL "Author : \\spad{P}.Gianni This package provides the functions for the computation of the square free decomposition of a multivariate polynomial. It uses the package GenExEuclid for the resolution of the equation \\spad{Af + Bg = h} and its generalization to \\spad{n} polynomials over an integral domain and the package \\spad{MultivariateLifting} for the \"multivariate\" lifting.")) (|normDeriv2| (((|SparseUnivariatePolynomial| |#3|) (|SparseUnivariatePolynomial| |#3|) (|Integer|)) "\\spad{normDeriv2 should} be local")) (|myDegree| (((|List| (|NonNegativeInteger|)) (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|NonNegativeInteger|)) "\\spad{myDegree should} be local")) (|lift| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#3|) (|SparseUnivariatePolynomial| |#3|) |#4| (|List| |#2|) (|List| (|NonNegativeInteger|)) (|List| |#3|)) "\\spad{lift should} be local")) (|check| (((|Boolean|) (|List| (|Record| (|:| |factor| (|SparseUnivariatePolynomial| |#3|)) (|:| |exponent| (|Integer|)))) (|List| (|Record| (|:| |factor| (|SparseUnivariatePolynomial| |#3|)) (|:| |exponent| (|Integer|))))) "\\spad{check should} be local")) (|coefChoose| ((|#4| (|Integer|) (|Factored| |#4|)) "\\spad{coefChoose should} be local")) (|intChoose| (((|Record| (|:| |upol| (|SparseUnivariatePolynomial| |#3|)) (|:| |Lval| (|List| |#3|)) (|:| |Lfact| (|List| (|Record| (|:| |factor| (|SparseUnivariatePolynomial| |#3|)) (|:| |exponent| (|Integer|))))) (|:| |ctpol| |#3|)) (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|List| (|List| |#3|))) "\\spad{intChoose should} be local")) (|nsqfree| (((|Record| (|:| |unitPart| |#4|) (|:| |suPart| (|List| (|Record| (|:| |factor| (|SparseUnivariatePolynomial| |#4|)) (|:| |exponent| (|Integer|)))))) (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|List| (|List| |#3|))) "\\spad{nsqfree should} be local")) (|consnewpol| (((|Record| (|:| |pol| (|SparseUnivariatePolynomial| |#4|)) (|:| |polval| (|SparseUnivariatePolynomial| |#3|))) (|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#3|) (|Integer|)) "\\spad{consnewpol should} be local")) (|univcase| (((|Factored| |#4|) |#4| |#2|) "\\spad{univcase should} be local")) (|compdegd| (((|Integer|) (|List| (|Record| (|:| |factor| (|SparseUnivariatePolynomial| |#3|)) (|:| |exponent| (|Integer|))))) "\\spad{compdegd should} be local")) (|squareFreePrim| (((|Factored| |#4|) |#4|) "\\spad{squareFreePrim(p)} compute the square free decomposition of a primitive multivariate polynomial \\spad{p}.")) (|squareFree| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{squareFree(p)} computes the square free decomposition of a multivariate polynomial \\spad{p} presented as a univariate polynomial with multivariate coefficients.") (((|Factored| |#4|) |#4|) "\\spad{squareFree(p)} computes the square free decomposition of a multivariate polynomial \\spad{p}."))) 
 NIL 
 NIL 
-(-682 S R) 
+(-683 S R) 
 ((|constructor| (NIL "NonAssociativeAlgebra is the category of non associative algebras (modules which are themselves non associative rngs). Axioms \\indented{3}{r*(a*b) = (r*a)*b = a*(r*b)}")) (|plenaryPower| (($ $ (|PositiveInteger|)) "\\spad{plenaryPower(a,n)} is recursively defined to be \\spad{plenaryPower(a,n-1)*plenaryPower(a,n-1)} for \\spad{n>1} and \\spad{a} for \\spad{n=1}."))) 
 NIL 
 NIL 
-(-683 R) 
+(-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}."))) 
-((-3984 . T) (-3983 . T)) 
+((-3986 . T) (-3985 . T)) 
 NIL 
-(-684 S) 
+(-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| (($ $ $) "\\spad{antiCommutator(a,b)} returns \\spad{a*b+b*a}.")) (|commutator| (($ $ $) "\\spad{commutator(a,b)} returns \\spad{a*b-b*a}.")) (|associator| (($ $ $ $) "\\spad{associator(a,b,c)} returns \\spad{(a*b)*c-a*(b*c)}."))) 
 NIL 
 NIL 
-(-685) 
+(-686) 
 ((|constructor| (NIL "NonAssociativeRng is a basic ring-type structure,{} not necessarily commutative or associative,{} and not necessarily with unit. Axioms \\indented{2}{x*(y+z) = x*y + x*z} \\indented{2}{(x+y)*z = x*z + y*z} Common Additional Axioms \\indented{2}{noZeroDivisors\\space{2}ab = 0 => \\spad{a=0} or \\spad{b=0}}")) (|antiCommutator| (($ $ $) "\\spad{antiCommutator(a,b)} returns \\spad{a*b+b*a}.")) (|commutator| (($ $ $) "\\spad{commutator(a,b)} returns \\spad{a*b-b*a}.")) (|associator| (($ $ $ $) "\\spad{associator(a,b,c)} returns \\spad{(a*b)*c-a*(b*c)}."))) 
 NIL 
 NIL 
-(-686 S) 
+(-687 S) 
 ((|constructor| (NIL "A NonAssociativeRing is a non associative rng which has a unit,{} the multiplication is not necessarily commutative or associative.")) (|coerce| (($ (|Integer|)) "\\spad{coerce(n)} coerces the integer \\spad{n} to an element of the ring.")) (|characteristic| (((|NonNegativeInteger|)) "\\spad{characteristic()} returns the characteristic of the ring."))) 
 NIL 
 NIL 
-(-687) 
+(-688) 
 ((|constructor| (NIL "A NonAssociativeRing is a non associative rng which has a unit,{} the multiplication is not necessarily commutative or associative.")) (|coerce| (($ (|Integer|)) "\\spad{coerce(n)} coerces the integer \\spad{n} to an element of the ring.")) (|characteristic| (((|NonNegativeInteger|)) "\\spad{characteristic()} returns the characteristic of the ring."))) 
 NIL 
 NIL 
-(-688 |Par|) 
+(-689 |Par|) 
 ((|constructor| (NIL "This package computes explicitly eigenvalues and eigenvectors of matrices with entries over the complex rational numbers. The results are expressed either as complex floating numbers or as complex rational numbers depending on the type of the precision parameter.")) (|complexEigenvectors| (((|List| (|Record| (|:| |outval| (|Complex| |#1|)) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| (|Complex| |#1|)))))) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) |#1|) "\\spad{complexEigenvectors(m,eps)} returns a list of records each one containing a complex eigenvalue,{} its algebraic multiplicity,{} and a list of associated eigenvectors. All these results are computed to precision \\spad{eps} and are expressed as complex floats or complex rational numbers depending on the type of \\spad{eps} (float or rational).")) (|complexEigenvalues| (((|List| (|Complex| |#1|)) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) |#1|) "\\spad{complexEigenvalues(m,eps)} computes the eigenvalues of the matrix \\spad{m} to precision \\spad{eps}. The eigenvalues are expressed as complex floats or complex rational numbers depending on the type of \\spad{eps} (float or rational).")) (|characteristicPolynomial| (((|Polynomial| (|Complex| (|Fraction| (|Integer|)))) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) (|Symbol|)) "\\spad{characteristicPolynomial(m,x)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over Complex Rationals with variable \\spad{x}.") (((|Polynomial| (|Complex| (|Fraction| (|Integer|)))) (|Matrix| (|Complex| (|Fraction| (|Integer|))))) "\\spad{characteristicPolynomial(m)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over complex rationals with a new symbol as variable."))) 
 NIL 
 NIL 
-(-689 -3088) 
+(-690 -3090) 
 ((|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 
-(-690 P -3088) 
+(-691 P -3090) 
 ((|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 
-(-691 T$) 
+(-692 T$) 
 NIL 
 NIL 
 NIL 
-(-692 UP -3088) 
+(-693 UP -3090) 
 ((|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 
-(-693 R) 
+(-694 R) 
 ((|constructor| (NIL "NonLinearSolvePackage is an interface to \\spadtype{SystemSolvePackage} that attempts to retract the coefficients of the equations before solving. The solutions are given in the algebraic closure of \\spad{R} whenever possible.")) (|solve| (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|))) "\\spad{solve(lp)} finds the solution in the algebraic closure of \\spad{R} of the list \\spad{lp} of rational functions with respect to all the symbols appearing in \\spad{lp}.") (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{solve(lp,lv)} finds the solutions in the algebraic closure of \\spad{R} of the list \\spad{lp} of rational functions with respect to the list of symbols \\spad{lv}.")) (|solveInField| (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|))) "\\spad{solveInField(lp)} finds the solution of the list \\spad{lp} of rational functions with respect to all the symbols appearing in \\spad{lp}.") (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{solveInField(lp,lv)} finds the solutions of the list \\spad{lp} of rational functions with respect to the list of symbols \\spad{lv}."))) 
 NIL 
 NIL 
-(-694) 
+(-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."))) 
-(((-3991 "*") . T)) 
+(((-3993 "*") . T)) 
 NIL 
-(-695 R -3088) 
+(-696 R -3090) 
 ((|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 
-(-696) 
+(-697) 
 ((|constructor| (NIL "\\spadtype{None} implements a type with no objects. It is mainly used in technical situations where such a thing is needed (\\spadignore{e.g.} the interpreter and some of the internal \\spadtype{Expression} code)."))) 
 NIL 
 NIL 
-(-697 S) 
+(-698 S) 
 ((|constructor| (NIL "\\spadtype{NoneFunctions1} implements functions on \\spadtype{None}. It particular it includes a particulary dangerous coercion from any other type to \\spadtype{None}.")) (|coerce| (((|None|) |#1|) "\\spad{coerce(x)} changes \\spad{x} into an object of type \\spadtype{None}."))) 
 NIL 
 NIL 
-(-698 R |PolR| E |PolE|) 
+(-699 R |PolR| E |PolE|) 
 ((|constructor| (NIL "This package implements the norm of a polynomial with coefficients in a monogenic algebra (using resultants)")) (|norm| ((|#2| |#4|) "\\spad{norm q} returns the norm of \\spad{q},{} \\spadignore{i.e.} the product of all the conjugates of \\spad{q}."))) 
 NIL 
 NIL 
-(-699 R E V P TS) 
+(-700 R E V P TS) 
 ((|constructor| (NIL "A package for computing normalized assocites of univariate polynomials with coefficients in a tower of simple extensions of a field.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. MORENO MAZA and \\spad{R}. RIOBOO \"Computations of gcd over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of \\spad{AAECC11}} \\indented{5}{Paris,{} 1995.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.}")) (|normInvertible?| (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{normInvertible?(\\spad{p},{}ts)} is an internal subroutine,{} exported only for developement.")) (|outputArgs| (((|Void|) (|String|) (|String|) |#4| |#5|) "\\axiom{outputArgs(\\spad{s1},{}\\spad{s2},{}\\spad{p},{}ts)} is an internal subroutine,{} exported only for developement.")) (|normalize| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{normalize(\\spad{p},{}ts)} normalizes \\axiom{\\spad{p}} \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}.")) (|normalizedAssociate| ((|#4| |#4| |#5|) "\\axiom{normalizedAssociate(\\spad{p},{}ts)} returns a normalized polynomial \\axiom{\\spad{n}} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts} such that \\axiom{\\spad{n}} and \\axiom{\\spad{p}} are associates \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts} and assuming that \\axiom{\\spad{p}} is invertible \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}.")) (|recip| (((|Record| (|:| |num| |#4|) (|:| |den| |#4|)) |#4| |#5|) "\\axiom{recip(\\spad{p},{}ts)} returns the inverse of \\axiom{\\spad{p}} \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts} assuming that \\axiom{\\spad{p}} is invertible \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}."))) 
 NIL 
 NIL 
-(-700 -3088 |ExtF| |SUEx| |ExtP| |n|) 
+(-701 -3090 |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 
-(-701 BP E OV R P) 
+(-702 BP E OV R P) 
 ((|constructor| (NIL "Package for the determination of the coefficients in the lifting process. Used by \\spadtype{MultivariateLifting}. This package will work for every euclidean domain \\spad{R} which has property \\spad{F},{} \\spadignore{i.e.} there exists a factor operation in \\spad{R[x]}.")) (|listexp| (((|List| (|NonNegativeInteger|)) |#1|) "\\spad{listexp }\\undocumented")) (|npcoef| (((|Record| (|:| |deter| (|List| (|SparseUnivariatePolynomial| |#5|))) (|:| |dterm| (|List| (|List| (|Record| (|:| |expt| (|NonNegativeInteger|)) (|:| |pcoef| |#5|))))) (|:| |nfacts| (|List| |#1|)) (|:| |nlead| (|List| |#5|))) (|SparseUnivariatePolynomial| |#5|) (|List| |#1|) (|List| |#5|)) "\\spad{npcoef }\\undocumented"))) 
 NIL 
 NIL 
-(-702 |Par|) 
+(-703 |Par|) 
 ((|constructor| (NIL "This package computes explicitly eigenvalues and eigenvectors of matrices with entries over the Rational Numbers. The results are expressed as floating numbers or as rational numbers depending on the type of the parameter Par.")) (|realEigenvectors| (((|List| (|Record| (|:| |outval| |#1|) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| |#1|))))) (|Matrix| (|Fraction| (|Integer|))) |#1|) "\\spad{realEigenvectors(m,eps)} returns a list of records each one containing a real eigenvalue,{} its algebraic multiplicity,{} and a list of associated eigenvectors. All these results are computed to precision \\spad{eps} as floats or rational numbers depending on the type of \\spad{eps} .")) (|realEigenvalues| (((|List| |#1|) (|Matrix| (|Fraction| (|Integer|))) |#1|) "\\spad{realEigenvalues(m,eps)} computes the eigenvalues of the matrix \\spad{m} to precision \\spad{eps}. The eigenvalues are expressed as floats or rational numbers depending on the type of \\spad{eps} (float or rational).")) (|characteristicPolynomial| (((|Polynomial| (|Fraction| (|Integer|))) (|Matrix| (|Fraction| (|Integer|))) (|Symbol|)) "\\spad{characteristicPolynomial(m,x)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over RN with variable \\spad{x}. Fraction \\spad{P} RN.") (((|Polynomial| (|Fraction| (|Integer|))) (|Matrix| (|Fraction| (|Integer|)))) "\\spad{characteristicPolynomial(m)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over RN with a new symbol as variable."))) 
 NIL 
 NIL 
-(-703 R |VarSet|) 
+(-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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-(-704 R) 
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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 (-821))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-494)))) (-12 (|HasCategory| |#1| (QUOTE (-796 (-327)))) (|HasCategory| (-993) (QUOTE (-796 (-327))))) (-12 (|HasCategory| |#1| (QUOTE (-796 (-483)))) (|HasCategory| (-993) (QUOTE (-796 (-483))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-800 (-327))))) (|HasCategory| (-993) (QUOTE (-553 (-800 (-327)))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-800 (-483))))) (|HasCategory| (-993) (QUOTE (-553 (-800 (-483)))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-472)))) (|HasCategory| (-993) (QUOTE (-553 (-472))))) (|HasCategory| |#1| (QUOTE (-580 (-483)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-347 (-483))))) (|HasCategory| |#1| (QUOTE (-950 (-483)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-347 (-483))))) (|HasCategory| |#1| (QUOTE (-950 (-347 (-483)))))) (|HasCategory| |#1| (QUOTE (-950 (-347 (-483))))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-389))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-821)))) (OR (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-389))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-821)))) (OR (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-389))) (|HasCategory| |#1| (QUOTE (-821)))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-1064))) (|HasCategory| |#1| (QUOTE (-811 (-1088)))) (|HasCategory| |#1| (QUOTE (-809 (-1088)))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-190))) (|HasAttribute| |#1| (QUOTE -3987)) (|HasCategory| |#1| (QUOTE (-389))) (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) 
-(-705 R S) 
+(((-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 (-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))))) 
+(-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 
 NIL 
-(-706 R) 
+(-707 R) 
 ((|constructor| (NIL "This package provides polynomials as functions on a ring.")) (|eulerE| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{eulerE(n,r)} \\undocumented")) (|bernoulliB| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{bernoulliB(n,r)} \\undocumented")) (|cyclotomic| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{cyclotomic(n,r)} \\undocumented"))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-38 (-347 (-483)))))) 
-(-707 R E V P) 
+((|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.}"))) 
-((-3990 . T) (-3989 . T)) 
+((-3992 . T) (-3991 . T)) 
 NIL 
-(-708 S) 
+(-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}."))) 
 NIL 
-((-12 (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-756)))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-961))) (|HasCategory| |#1| (QUOTE (-146)))) 
-(-709) 
+((-12 (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-757)))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-962))) (|HasCategory| |#1| (QUOTE (-146)))) 
+(-710) 
 ((|constructor| (NIL "NumberFormats provides function to format and read arabic and roman numbers,{} to convert numbers to strings and to read floating-point numbers.")) (|ScanFloatIgnoreSpacesIfCan| (((|Union| (|Float|) "failed") (|String|)) "\\spad{ScanFloatIgnoreSpacesIfCan(s)} tries to form a floating point number from the string \\spad{s} ignoring any spaces.")) (|ScanFloatIgnoreSpaces| (((|Float|) (|String|)) "\\spad{ScanFloatIgnoreSpaces(s)} forms a floating point number from the string \\spad{s} ignoring any spaces. Error is generated if the string is not recognised as a floating point number.")) (|ScanRoman| (((|PositiveInteger|) (|String|)) "\\spad{ScanRoman(s)} forms an integer from a Roman numeral string \\spad{s}.")) (|FormatRoman| (((|String|) (|PositiveInteger|)) "\\spad{FormatRoman(n)} forms a Roman numeral string from an integer \\spad{n}.")) (|ScanArabic| (((|PositiveInteger|) (|String|)) "\\spad{ScanArabic(s)} forms an integer from an Arabic numeral string \\spad{s}.")) (|FormatArabic| (((|String|) (|PositiveInteger|)) "\\spad{FormatArabic(n)} forms an Arabic numeral string from an integer \\spad{n}."))) 
 NIL 
 NIL 
-(-710) 
+(-711) 
 ((|constructor| (NIL "This package is a suite of functions for the numerical integration of an ordinary differential equation of \\spad{n} variables: \\blankline \\indented{8}{\\center{dy/dx = \\spad{f}(\\spad{y},{}\\spad{x})\\space{5}\\spad{y} is an \\spad{n}-vector}} \\blankline \\par All the routines are based on a 4-th order Runge-Kutta kernel. These routines generally have as arguments: \\spad{n},{} the number of dependent variables; \\spad{x1},{} the initial point; \\spad{h},{} the step size; \\spad{y},{} a vector of initial conditions of length \\spad{n} which upon exit contains the solution at \\spad{x1 + h}; \\spad{derivs},{} a function which computes the right hand side of the ordinary differential equation: \\spad{derivs(dydx,y,x)} computes \\spad{dydx},{} a vector which contains the derivative information. \\blankline \\par In order of increasing complexity:\\begin{items} \\blankline \\item \\spad{rk4(y,n,x1,h,derivs)} advances the solution vector to \\spad{x1 + h} and return the values in \\spad{y}. \\blankline \\item \\spad{rk4(y,n,x1,h,derivs,t1,t2,t3,t4)} is the same as \\spad{rk4(y,n,x1,h,derivs)} except that you must provide 4 scratch arrays \\spad{t1}-\\spad{t4} of size \\spad{n}. \\blankline \\item Starting with \\spad{y} at \\spad{x1},{} \\spad{rk4f(y,n,x1,x2,ns,derivs)} uses \\spad{ns} fixed steps of a 4-th order Runge-Kutta integrator to advance the solution vector to \\spad{x2} and return the values in \\spad{y}. Argument \\spad{x2},{} is the final point,{} and \\spad{ns},{} the number of steps to take. \\blankline \\item \\spad{rk4qc(y,n,x1,step,eps,yscal,derivs)} takes a 5-th order Runge-Kutta step with monitoring of local truncation to ensure accuracy and adjust stepsize. The function takes two half steps and one full step and scales the difference in solutions at the final point. If the error is within \\spad{eps},{} the step is taken and the result is returned. If the error is not within \\spad{eps},{} the stepsize if decreased and the procedure is tried again until the desired accuracy is reached. Upon input,{} an trial step size must be given and upon return,{} an estimate of the next step size to use is returned as well as the step size which produced the desired accuracy. The scaled error is computed as \\center{\\spad{error = MAX(ABS((y2steps(i) - y1step(i))/yscal(i)))}} and this is compared against \\spad{eps}. If this is greater than \\spad{eps},{} the step size is reduced accordingly to \\center{\\spad{hnew = 0.9 * hdid * (error/eps)**(-1/4)}} If the error criterion is satisfied,{} then we check if the step size was too fine and return a more efficient one. If \\spad{error > \\spad{eps} * (6.0E-04)} then the next step size should be \\center{\\spad{hnext = 0.9 * hdid * (error/\\spad{eps})**(\\spad{-1/5})}} Otherwise \\spad{hnext = 4.0 * hdid} is returned. A more detailed discussion of this and related topics can be found in the book \"Numerical Recipies\" by \\spad{W}.Press,{} \\spad{B}.\\spad{P}. Flannery,{} \\spad{S}.A. Teukolsky,{} \\spad{W}.\\spad{T}. Vetterling published by Cambridge University Press. Argument \\spad{step} is a record of 3 floating point numbers \\spad{(try , did , next)},{} \\spad{eps} is the required accuracy,{} \\spad{yscal} is the scaling vector for the difference in solutions. On input,{} \\spad{step.try} should be the guess at a step size to achieve the accuracy. On output,{} \\spad{step.did} contains the step size which achieved the accuracy and \\spad{step.next} is the next step size to use. \\blankline \\item \\spad{rk4qc(y,n,x1,step,eps,yscal,derivs,t1,t2,t3,t4,t5,t6,t7)} is the same as \\spad{rk4qc(y,n,x1,step,eps,yscal,derivs)} except that the user must provide the 7 scratch arrays \\spad{t1-t7} of size \\spad{n}. \\blankline \\item \\spad{rk4a(y,n,x1,x2,eps,h,ns,derivs)} is a driver program which uses \\spad{rk4qc} to integrate \\spad{n} ordinary differential equations starting at \\spad{x1} to \\spad{x2},{} keeping the local truncation error to within \\spad{eps} by changing the local step size. The scaling vector is defined as \\center{\\spad{yscal(i) = abs(y(i)) + abs(h*dydx(i)) + tiny}} where \\spad{y(i)} is the solution at location \\spad{x},{} \\spad{dydx} is the ordinary differential equation's right hand side,{} \\spad{h} is the current step size and \\spad{tiny} is 10 times the smallest positive number representable. The user must supply an estimate for a trial step size and the maximum number of calls to \\spad{rk4qc} to use. Argument \\spad{x2} is the final point,{} \\spad{eps} is local truncation,{} \\spad{ns} is the maximum number of call to \\spad{rk4qc} to use. \\end{items}")) (|rk4f| (((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Float|) (|Integer|) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|))) "\\spad{rk4f(y,n,x1,x2,ns,derivs)} uses a 4-th order Runge-Kutta method to numerically integrate the ordinary differential equation {\\em dy/dx = f(y,x)} of \\spad{n} variables,{} where \\spad{y} is an \\spad{n}-vector. Starting with \\spad{y} at \\spad{x1},{} this function uses \\spad{ns} fixed steps of a 4-th order Runge-Kutta integrator to advance the solution vector to \\spad{x2} and return the values in \\spad{y}. For details,{} see \\con{NumericalOrdinaryDifferentialEquations}.")) (|rk4qc| (((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Record| (|:| |tryValue| (|Float|)) (|:| |did| (|Float|)) (|:| |next| (|Float|))) (|Float|) (|Vector| (|Float|)) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|))) "\\spad{rk4qc(y,n,x1,step,eps,yscal,derivs,t1,t2,t3,t4,t5,t6,t7)} is a subfunction for the numerical integration of an ordinary differential equation {\\em dy/dx = f(y,x)} of \\spad{n} variables,{} where \\spad{y} is an \\spad{n}-vector using a 4-th order Runge-Kutta method. This function takes a 5-th order Runge-Kutta \\spad{step} with monitoring of local truncation to ensure accuracy and adjust stepsize. For details,{} see \\con{NumericalOrdinaryDifferentialEquations}.") (((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Record| (|:| |tryValue| (|Float|)) (|:| |did| (|Float|)) (|:| |next| (|Float|))) (|Float|) (|Vector| (|Float|)) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|))) "\\spad{rk4qc(y,n,x1,step,eps,yscal,derivs)} is a subfunction for the numerical integration of an ordinary differential equation {\\em dy/dx = f(y,x)} of \\spad{n} variables,{} where \\spad{y} is an \\spad{n}-vector using a 4-th order Runge-Kutta method. This function takes a 5-th order Runge-Kutta \\spad{step} with monitoring of local truncation to ensure accuracy and adjust stepsize. For details,{} see \\con{NumericalOrdinaryDifferentialEquations}.")) (|rk4a| (((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|))) "\\spad{rk4a(y,n,x1,x2,eps,h,ns,derivs)} is a driver function for the numerical integration of an ordinary differential equation {\\em dy/dx = f(y,x)} of \\spad{n} variables,{} where \\spad{y} is an \\spad{n}-vector using a 4-th order Runge-Kutta method. For details,{} see \\con{NumericalOrdinaryDifferentialEquations}.")) (|rk4| (((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Float|) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|))) "\\spad{rk4(y,n,x1,h,derivs,t1,t2,t3,t4)} is the same as \\spad{rk4(y,n,x1,h,derivs)} except that you must provide 4 scratch arrays \\spad{t1}-\\spad{t4} of size \\spad{n}. For details,{} see \\con{NumericalOrdinaryDifferentialEquations}.") (((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Float|) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|))) "\\spad{rk4(y,n,x1,h,derivs)} uses a 4-th order Runge-Kutta method to numerically integrate the ordinary differential equation {\\em dy/dx = f(y,x)} of \\spad{n} variables,{} where \\spad{y} is an \\spad{n}-vector. Argument \\spad{y} is a vector of initial conditions of length \\spad{n} which upon exit contains the solution at \\spad{x1 + h},{} \\spad{n} is the number of dependent variables,{} \\spad{x1} is the initial point,{} \\spad{h} is the step size,{} and \\spad{derivs} is a function which computes the right hand side of the ordinary differential equation. For details,{} see \\spadtype{NumericalOrdinaryDifferentialEquations}."))) 
 NIL 
 NIL 
-(-711) 
+(-712) 
 ((|constructor| (NIL "This suite of routines performs numerical quadrature using algorithms derived from the basic trapezoidal rule. Because the error term of this rule contains only even powers of the step size (for open and closed versions),{} fast convergence can be obtained if the integrand is sufficiently smooth. \\blankline Each routine returns a Record of type TrapAns,{} which contains\\indent{3} \\newline value (\\spadtype{Float}):\\tab{20} estimate of the integral \\newline error (\\spadtype{Float}):\\tab{20} estimate of the error in the computation \\newline totalpts (\\spadtype{Integer}):\\tab{20} total number of function evaluations \\newline success (\\spadtype{Boolean}):\\tab{20} if the integral was computed within the user specified error criterion \\indent{0}\\indent{0} To produce this estimate,{} each routine generates an internal sequence of sub-estimates,{} denoted by {\\em S(i)},{} depending on the routine,{} to which the various convergence criteria are applied. The user must supply a relative accuracy,{} \\spad{eps_r},{} and an absolute accuracy,{} \\spad{eps_a}. Convergence is obtained when either \\center{\\spad{ABS(S(i) - S(i-1)) < eps_r * ABS(S(i-1))}} \\center{or \\spad{ABS(S(i) - S(i-1)) < eps_a}} are \\spad{true} statements. \\blankline The routines come in three families and three flavors: \\newline\\tab{3} closed:\\tab{20}romberg,{}\\tab{30}simpson,{}\\tab{42}trapezoidal \\newline\\tab{3} open: \\tab{20}rombergo,{}\\tab{30}simpsono,{}\\tab{42}trapezoidalo \\newline\\tab{3} adaptive closed:\\tab{20}aromberg,{}\\tab{30}asimpson,{}\\tab{42}atrapezoidal \\par The {\\em S(i)} for the trapezoidal family is the value of the integral using an equally spaced absicca trapezoidal rule for that level of refinement. \\par The {\\em S(i)} for the simpson family is the value of the integral using an equally spaced absicca simpson rule for that level of refinement. \\par The {\\em S(i)} for the romberg family is the estimate of the integral using an equally spaced absicca romberg method. For the \\spad{i}\\spad{-}th level,{} this is an appropriate combination of all the previous trapezodial estimates so that the error term starts with the \\spad{2*(i+1)} power only. \\par The three families come in a closed version,{} where the formulas include the endpoints,{} an open version where the formulas do not include the endpoints and an adaptive version,{} where the user is required to input the number of subintervals over which the appropriate closed family integrator will apply with the usual convergence parmeters for each subinterval. This is useful where a large number of points are needed only in a small fraction of the entire domain. \\par Each routine takes as arguments: \\newline \\spad{f}\\tab{10} integrand \\newline a\\tab{10} starting point \\newline \\spad{b}\\tab{10} ending point \\newline \\spad{eps_r}\\tab{10} relative error \\newline \\spad{eps_a}\\tab{10} absolute error \\newline \\spad{nmin} \\tab{10} refinement level when to start checking for convergence (> 1) \\newline \\spad{nmax} \\tab{10} maximum level of refinement \\par The adaptive routines take as an additional parameter \\newline \\spad{nint}\\tab{10} the number of independent intervals to apply a closed \\indented{1}{family integrator of the same name.} \\par Notes: \\newline Closed family level \\spad{i} uses \\spad{1 + 2**i} points. \\newline Open family level \\spad{i} uses \\spad{1 + 3**i} points.")) (|trapezoidalo| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|)) "\\spad{trapezoidalo(fn,a,b,epsrel,epsabs,nmin,nmax)} uses the trapezoidal method to numerically integrate function \\spad{fn} over the open interval from \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax}. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|simpsono| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|)) "\\spad{simpsono(fn,a,b,epsrel,epsabs,nmin,nmax)} uses the simpson method to numerically integrate function \\spad{fn} over the open interval from \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax}. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|rombergo| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|)) "\\spad{rombergo(fn,a,b,epsrel,epsabs,nmin,nmax)} uses the romberg method to numerically integrate function \\spad{fn} over the open interval from \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax}. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|trapezoidal| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|)) "\\spad{trapezoidal(fn,a,b,epsrel,epsabs,nmin,nmax)} uses the trapezoidal method to numerically integrate function \\spadvar{\\spad{fn}} over the closed interval \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax}. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|simpson| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|)) "\\spad{simpson(fn,a,b,epsrel,epsabs,nmin,nmax)} uses the simpson method to numerically integrate function \\spad{fn} over the closed interval \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax}. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|romberg| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|)) "\\spad{romberg(fn,a,b,epsrel,epsabs,nmin,nmax)} uses the romberg method to numerically integrate function \\spadvar{\\spad{fn}} over the closed interval \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax}. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|atrapezoidal| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{atrapezoidal(fn,a,b,epsrel,epsabs,nmin,nmax,nint)} uses the adaptive trapezoidal method to numerically integrate function \\spad{fn} over the closed interval from \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax},{} and where \\spad{nint} is the number of independent intervals to apply the integrator. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|asimpson| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{asimpson(fn,a,b,epsrel,epsabs,nmin,nmax,nint)} uses the adaptive simpson method to numerically integrate function \\spad{fn} over the closed interval from \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax},{} and where \\spad{nint} is the number of independent intervals to apply the integrator. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|aromberg| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{aromberg(fn,a,b,epsrel,epsabs,nmin,nmax,nint)} uses the adaptive romberg method to numerically integrate function \\spad{fn} over the closed interval from \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax},{} and where \\spad{nint} is the number of independent intervals to apply the integrator. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details."))) 
 NIL 
 NIL 
-(-712 |Curve|) 
+(-713 |Curve|) 
 ((|constructor| (NIL "\\indented{1}{Author: Clifton \\spad{J}. Williamson} Date Created: Bastille Day 1989 Date Last Updated: 5 June 1990 Keywords: Examples: Package for constructing tubes around 3-dimensional parametric curves.")) (|tube| (((|TubePlot| |#1|) |#1| (|DoubleFloat|) (|Integer|)) "\\spad{tube(c,r,n)} creates a tube of radius \\spad{r} around the curve \\spad{c}."))) 
 NIL 
 NIL 
-(-713 S) 
+(-714 S) 
 ((|constructor| (NIL "Ordered sets which are also abelian groups,{} such that the addition preserves the ordering.")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x}.")) (|sign| (((|Integer|) $) "\\spad{sign(x)} is \\spad{1} if \\spad{x} is positive,{} \\spad{-1} if \\spad{x} is negative,{} and \\spad{0} otherwise.")) (|negative?| (((|Boolean|) $) "\\spad{negative?(x)} holds when \\spad{x} is less than \\spad{0}."))) 
 NIL 
 NIL 
-(-714) 
+(-715) 
 ((|constructor| (NIL "Ordered sets which are also abelian groups,{} such that the addition preserves the ordering.")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x}.")) (|sign| (((|Integer|) $) "\\spad{sign(x)} is \\spad{1} if \\spad{x} is positive,{} \\spad{-1} if \\spad{x} is negative,{} and \\spad{0} otherwise.")) (|negative?| (((|Boolean|) $) "\\spad{negative?(x)} holds when \\spad{x} is less than \\spad{0}."))) 
 NIL 
 NIL 
-(-715 S) 
+(-716 S) 
 ((|constructor| (NIL "Ordered sets which are also abelian monoids,{} such that the addition preserves the ordering.")) (|positive?| (((|Boolean|) $) "\\spad{positive?(x)} holds when \\spad{x} is greater than \\spad{0}."))) 
 NIL 
 NIL 
-(-716) 
+(-717) 
 ((|constructor| (NIL "Ordered sets which are also abelian monoids,{} such that the addition preserves the ordering.")) (|positive?| (((|Boolean|) $) "\\spad{positive?(x)} holds when \\spad{x} is greater than \\spad{0}."))) 
 NIL 
 NIL 
-(-717) 
+(-718) 
 ((|constructor| (NIL "This domain is an OrderedAbelianMonoid with a \\spadfun{sup} operation added. The purpose of the \\spadfun{sup} operator in this domain is to act as a supremum with respect to the partial order imposed by \\spadop{-},{} rather than with respect to the total \\spad{>} order (since that is \"max\"). \\blankline")) (|sup| (($ $ $) "\\spad{sup(x,y)} returns the least element from which both \\spad{x} and \\spad{y} can be subtracted."))) 
 NIL 
 NIL 
-(-718) 
+(-719) 
 ((|constructor| (NIL "Ordered sets which are also abelian semigroups,{} such that the addition preserves the ordering. \\indented{2}{\\spad{ x < y => x+z < y+z}}"))) 
 NIL 
 NIL 
-(-719 S R) 
+(-720 S R) 
 ((|constructor| (NIL "OctonionCategory gives the categorial frame for the octonions,{} and eight-dimensional non-associative algebra,{} doubling the the quaternions in the same way as doubling the Complex numbers to get the quaternions.")) (|inv| (($ $) "\\spad{inv(o)} returns the inverse of \\spad{o} if it exists.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(o)} returns the real part if all seven imaginary parts are 0,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(o)} returns the real part if all seven imaginary parts are 0. Error: if \\spad{o} is not rational.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(o)} tests if \\spad{o} is rational,{} \\spadignore{i.e.} that all seven imaginary parts are 0.")) (|abs| ((|#2| $) "\\spad{abs(o)} computes the absolute value of an octonion,{} equal to the square root of the \\spadfunFrom{norm}{Octonion}.")) (|octon| (($ |#2| |#2| |#2| |#2| |#2| |#2| |#2| |#2|) "\\spad{octon(re,ri,rj,rk,rE,rI,rJ,rK)} constructs an octonion from scalars.")) (|norm| ((|#2| $) "\\spad{norm(o)} returns the norm of an octonion,{} equal to the sum of the squares of its coefficients.")) (|imagK| ((|#2| $) "\\spad{imagK(o)} extracts the imaginary \\spad{K} part of octonion \\spad{o}.")) (|imagJ| ((|#2| $) "\\spad{imagJ(o)} extracts the imaginary \\spad{J} part of octonion \\spad{o}.")) (|imagI| ((|#2| $) "\\spad{imagI(o)} extracts the imaginary \\spad{I} part of octonion \\spad{o}.")) (|imagE| ((|#2| $) "\\spad{imagE(o)} extracts the imaginary \\spad{E} part of octonion \\spad{o}.")) (|imagk| ((|#2| $) "\\spad{imagk(o)} extracts the \\spad{k} part of octonion \\spad{o}.")) (|imagj| ((|#2| $) "\\spad{imagj(o)} extracts the \\spad{j} part of octonion \\spad{o}.")) (|imagi| ((|#2| $) "\\spad{imagi(o)} extracts the \\spad{i} part of octonion \\spad{o}.")) (|real| ((|#2| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-482))) (|HasCategory| |#2| (QUOTE (-972))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-553 (-472)))) (|HasCategory| |#2| (QUOTE (-756))) (|HasCategory| |#2| (QUOTE (-317)))) 
-(-720 R) 
+((|HasCategory| |#2| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-483))) (|HasCategory| |#2| (QUOTE (-973))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-554 (-473)))) (|HasCategory| |#2| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-317)))) 
+(-721 R) 
 ((|constructor| (NIL "OctonionCategory gives the categorial frame for the octonions,{} and eight-dimensional non-associative algebra,{} doubling the the quaternions in the same way as doubling the Complex numbers to get the quaternions.")) (|inv| (($ $) "\\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| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) 
-((-3983 . T) (-3984 . T) (-3986 . T)) 
+((-3985 . T) (-3986 . T) (-3988 . T)) 
 NIL 
-(-721) 
+(-722) 
 ((|constructor| (NIL "Ordered sets which are also abelian cancellation monoids,{} such that the addition preserves the ordering."))) 
 NIL 
 NIL 
-(-722 R) 
+(-723 R) 
 ((|constructor| (NIL "Octonion implements octonions (Cayley-Dixon algebra) over a commutative ring,{} an eight-dimensional non-associative algebra,{} doubling the quaternions in the same way as doubling the complex numbers to get the quaternions the main constructor function is {\\em octon} which takes 8 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j} imaginary part,{} the \\spad{k} imaginary part,{} (as with quaternions) and in addition the imaginary parts \\spad{E},{} \\spad{I},{} \\spad{J},{} \\spad{K}.")) (|octon| (($ (|Quaternion| |#1|) (|Quaternion| |#1|)) "\\spad{octon(qe,qE)} constructs an octonion from two quaternions using the relation {\\em O = Q + QE}."))) 
-((-3983 . T) (-3984 . T) (-3986 . T)) 
-((|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-553 (-472)))) (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (|%list| (QUOTE -452) (QUOTE (-1088)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -241) (|devaluate| |#1|) (|devaluate| |#1|))) (OR (|HasCategory| |#1| (QUOTE (-950 (-347 (-483))))) (|HasCategory| (-909 |#1|) (QUOTE (-950 (-347 (-483)))))) (OR (|HasCategory| |#1| (QUOTE (-950 (-483)))) (|HasCategory| (-909 |#1|) (QUOTE (-950 (-483))))) (|HasCategory| |#1| (QUOTE (-972))) (|HasCategory| |#1| (QUOTE (-482))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| (-909 |#1|) (QUOTE (-950 (-347 (-483))))) (|HasCategory| (-909 |#1|) (QUOTE (-950 (-483)))) (|HasCategory| |#1| (QUOTE (-950 (-347 (-483))))) (|HasCategory| |#1| (QUOTE (-950 (-483))))) 
-(-723 OR R OS S) 
+((-3985 . T) (-3986 . T) (-3988 . 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 
-(-724 R -3088 L) 
+(-725 R -3090 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 
-(-725 R -3088) 
+(-726 R -3090) 
 ((|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 
-(-726 R -3088) 
+(-727 R -3090) 
 ((|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 
-(-727 -3088 UP UPUP R) 
+(-728 -3090 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 
-(-728 -3088 UP L LQ) 
+(-729 -3090 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 
-(-729 -3088 UP L LQ) 
+(-730 -3090 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 
-(-730 -3088 UP) 
+(-731 -3090 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 
-(-731 -3088 L UP A LO) 
+(-732 -3090 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 
-(-732 -3088 UP) 
+(-733 -3090 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)))) 
-(-733 -3088 LO) 
+(-734 -3090 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 
-(-734 -3088 LODO) 
+(-735 -3090 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 
-(-735 -2617 S |f|) 
+(-736 -2619 S |f|) 
 ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying ordered component type. The ordering on the type is determined by its third argument which represents the less than function on vectors. This type is a suitable third argument for \\spadtype{GeneralDistributedMultivariatePolynomial}."))) 
-((-3983 |has| |#2| (-961)) (-3984 |has| |#2| (-961)) (-3986 |has| |#2| (-6 -3986)) (-3989 . T)) 
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-(-737 |Kernels| R |var|) 
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+((|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))))) 
+(-738 |Kernels| R |var|) 
 ((|constructor| (NIL "This constructor produces an ordinary differential ring from a partial differential ring by specifying a variable."))) 
-(((-3991 "*") |has| |#2| (-311)) (-3982 |has| |#2| (-311)) (-3987 |has| |#2| (-311)) (-3981 |has| |#2| (-311)) (-3986 . T) (-3984 . T) (-3983 . T)) 
+(((-3993 "*") |has| |#2| (-311)) (-3984 |has| |#2| (-311)) (-3989 |has| |#2| (-311)) (-3983 |has| |#2| (-311)) (-3988 . T) (-3986 . T) (-3985 . T)) 
 ((|HasCategory| |#2| (QUOTE (-311)))) 
-(-738 S) 
+(-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}))."))) 
 NIL 
 NIL 
-(-739 S) 
+(-740 S) 
 ((|constructor| (NIL "\\indented{3}{The free monoid on a set \\spad{S} is the monoid of finite products of} the form \\spad{reduce(*,[si ** ni])} where the \\spad{si}'s are in \\spad{S},{} and the \\spad{ni}'s are non-negative integers. The multiplication is not commutative. For two elements \\spad{x} and \\spad{y} the relation \\spad{x < y} holds if either \\spad{length(x) < length(y)} holds or if these lengths are equal and if \\spad{x} is smaller than \\spad{y} \\spad{w}.\\spad{r}.\\spad{t}. the lexicographical ordering induced by \\spad{S}. This domain inherits implementation from \\spadtype{FreeMonoid}.")) (|varList| (((|List| |#1|) $) "\\spad{varList(x)} returns the list of variables of \\spad{x}.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length(x)} returns the length of \\spad{x}.")) (|div| (((|Union| (|Record| (|:| |lm| $) (|:| |rm| $)) "failed") $ $) "\\spad{x div y} returns the left and right exact quotients of \\spad{x} by \\spad{y},{} that is \\spad{[l, r]} such that \\spad{x = l * y * r}. \"failed\" is returned iff \\spad{x} is not of the form \\spad{l * y * r}. monomial of \\spad{x}.")) (|rquo| (((|Union| $ "failed") $ |#1|) "\\spad{rquo(x, s)} returns the exact right quotient of \\spad{x} by \\spad{s}.")) (|lquo| (((|Union| $ "failed") $ |#1|) "\\spad{lquo(x, s)} returns the exact left quotient of \\spad{x} by \\spad{s}.")) (|lexico| (((|Boolean|) $ $) "\\spad{lexico(x,y)} returns \\spad{true} iff \\spad{x} is smaller than \\spad{y} \\spad{w}.\\spad{r}.\\spad{t}. the pure lexicographical ordering induced by \\spad{S}.")) (|mirror| (($ $) "\\spad{mirror(x)} returns the reversed word of \\spad{x}.")) (|rest| (($ $) "\\spad{rest(x)} returns \\spad{x} except the first letter.")) (|first| ((|#1| $) "\\spad{first(x)} returns the first letter of \\spad{x}."))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-756)))) 
-(-740) 
+((|HasCategory| |#1| (QUOTE (-757)))) 
+(-741) 
 ((|constructor| (NIL "The category of ordered commutative integral domains,{} where ordering and the arithmetic operations are compatible \\blankline"))) 
-((-3982 . T) ((-3991 "*") . T) (-3983 . T) (-3984 . T) (-3986 . T)) 
+((-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . T)) 
 NIL 
-(-741 P R) 
+(-742 P R) 
 ((|constructor| (NIL "This constructor creates the \\spadtype{MonogenicLinearOperator} domain which is ``opposite'' in the ring sense to \\spad{P}. That is,{} as sets \\spad{P = \\$} 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}."))) 
-((-3983 . T) (-3984 . T) (-3986 . T)) 
+((-3985 . T) (-3986 . T) (-3988 . T)) 
 ((|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-190)))) 
-(-742 S) 
+(-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}."))) 
-((-3989 . T) (-3979 . T) (-3990 . T)) 
+((-3991 . T) (-3981 . T) (-3992 . T)) 
 NIL 
-(-743 R) 
+(-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."))) 
-((-3986 |has| |#1| (-755))) 
-((|HasCategory| |#1| (QUOTE (-755))) (|HasCategory| |#1| (QUOTE (-21))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-755)))) (|HasCategory| |#1| (QUOTE (-950 (-347 (-483))))) (OR (|HasCategory| |#1| (QUOTE (-755))) (|HasCategory| |#1| (QUOTE (-950 (-483))))) (|HasCategory| |#1| (QUOTE (-950 (-483)))) (|HasCategory| |#1| (QUOTE (-482)))) 
-(-744 R S) 
+((-3988 |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."))) 
 NIL 
 NIL 
-(-745 R) 
+(-746 R) 
 ((|constructor| (NIL "Algebra of ADDITIVE operators over a ring."))) 
-((-3984 |has| |#1| (-146)) (-3983 |has| |#1| (-146)) (-3986 . T)) 
+((-3986 |has| |#1| (-146)) (-3985 |has| |#1| (-146)) (-3988 . T)) 
 ((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120)))) 
-(-746 A S) 
+(-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}."))) 
 NIL 
 NIL 
-(-747 S) 
+(-748 S) 
 ((|constructor| (NIL "This category specifies the interface for operators used to build terms,{} in the sense of Universal Algebra. The domain parameter \\spad{S} provides representation for the `external name' of an operator.")) (|is?| (((|Boolean|) $ |#1|) "\\spad{is?(op,n)} holds if the name of the operator \\spad{op} is \\spad{n}.")) (|arity| (((|Arity|) $) "\\spad{arity(op)} returns the arity of the operator \\spad{op}.")) (|name| ((|#1| $) "\\spad{name(op)} returns the externam name of \\spad{op}."))) 
 NIL 
 NIL 
-(-748) 
+(-749) 
 ((|constructor| (NIL "This package exports tools to create AXIOM Library information databases.")) (|getDatabase| (((|Database| (|IndexCard|)) (|String|)) "\\spad{getDatabase(\"char\")} returns a list of appropriate entries in the browser database. The legal values for \\spad{\"char\"} are \"o\" (operations),{} \"k\" (constructors),{} \"d\" (domains),{} \"c\" (categories) or \"p\" (packages)."))) 
 NIL 
 NIL 
-(-749) 
+(-750) 
 ((|constructor| (NIL "This the datatype for an operator-signature pair.")) (|construct| (($ (|Identifier|) (|Signature|)) "\\spad{construct(op,sig)} construct a signature-operator with operator name `op',{} and signature `sig'.")) (|signature| (((|Signature|) $) "\\spad{signature(x)} returns the signature of `x'."))) 
 NIL 
 NIL 
-(-750 R) 
+(-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| (($) "\\spad{plusInfinity()} returns +infinity."))) 
-((-3986 |has| |#1| (-755))) 
-((|HasCategory| |#1| (QUOTE (-755))) (|HasCategory| |#1| (QUOTE (-21))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-755)))) (|HasCategory| |#1| (QUOTE (-950 (-347 (-483))))) (OR (|HasCategory| |#1| (QUOTE (-755))) (|HasCategory| |#1| (QUOTE (-950 (-483))))) (|HasCategory| |#1| (QUOTE (-950 (-483)))) (|HasCategory| |#1| (QUOTE (-482)))) 
-(-751 R S) 
+((-3988 |has| |#1| (-756))) 
+((|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-21))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-756)))) (|HasCategory| |#1| (QUOTE (-951 (-347 (-484))))) (OR (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-951 (-484))))) (|HasCategory| |#1| (QUOTE (-951 (-484)))) (|HasCategory| |#1| (QUOTE (-483)))) 
+(-752 R S) 
 ((|constructor| (NIL "Lifting of maps to ordered completions. Date Created: 4 Oct 1989 Date Last Updated: 4 Oct 1989")) (|map| (((|OrderedCompletion| |#2|) (|Mapping| |#2| |#1|) (|OrderedCompletion| |#1|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|)) "\\spad{map(f, r, p, m)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(plusInfinity) = \\spad{p} and that \\spad{f}(minusInfinity) = \\spad{m}.") (((|OrderedCompletion| |#2|) (|Mapping| |#2| |#1|) (|OrderedCompletion| |#1|)) "\\spad{map(f, r)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(plusInfinity) = plusInfinity and that \\spad{f}(minusInfinity) = minusInfinity."))) 
 NIL 
 NIL 
-(-752) 
+(-753) 
 ((|constructor| (NIL "Ordered finite sets.")) (|max| (($) "\\spad{max} is the maximum value of \\%.")) (|min| (($) "\\spad{min} is the minimum value of \\%."))) 
 NIL 
 NIL 
-(-753 -2617 S) 
+(-754 -2619 S) 
 ((|constructor| (NIL "\\indented{3}{This package provides ordering functions on vectors which} are suitable parameters for OrderedDirectProduct.")) (|reverseLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{reverseLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by the reverse lexicographic ordering.")) (|totalLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{totalLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by lexicographic ordering.")) (|pureLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{pureLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the lexicographic ordering."))) 
 NIL 
 NIL 
-(-754) 
+(-755) 
 ((|constructor| (NIL "Ordered sets which are also monoids,{} such that multiplication preserves the ordering. \\blankline"))) 
 NIL 
 NIL 
-(-755) 
+(-756) 
 ((|constructor| (NIL "Ordered sets which are also rings,{} that is,{} domains where the ring operations are compatible with the ordering. \\blankline"))) 
-((-3986 . T)) 
+((-3988 . T)) 
 NIL 
-(-756) 
+(-757) 
 ((|constructor| (NIL "The class of totally ordered sets,{} that is,{} sets such that for each pair of elements \\spad{(a,b)} exactly one of the following relations holds \\spad{a<b or a=b or b<a} and the relation is transitive,{} \\spadignore{i.e.} \\spad{a<b and b<c => a<c}."))) 
 NIL 
 NIL 
-(-757 T$ |f|) 
+(-758 T$ |f|) 
 ((|constructor| (NIL "This domain turns any total ordering \\spad{f} on a type \\spad{T} into a model of the category \\spadtype{OrderedType}."))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-552 (-772))))) 
-(-758 S) 
+((|HasCategory| |#1| (QUOTE (-553 (-773))))) 
+(-759 S) 
 ((|constructor| (NIL "Category of types equipped with a total ordering.")) (|min| (($ $ $) "\\spad{min(x,y)} returns the minimum of \\spad{x} and \\spad{y} relative to the ordering.")) (|max| (($ $ $) "\\spad{max(x,y)} returns the maximum of \\spad{x} and \\spad{y} relative to the ordering.")) (>= (((|Boolean|) $ $) "\\spad{x <= y} holds if \\spad{x} is greater or equal than \\spad{y} in the current domain.")) (<= (((|Boolean|) $ $) "\\spad{x <= y} holds if \\spad{x} is less or equal than \\spad{y} in the current domain.")) (> (((|Boolean|) $ $) "\\spad{x > y} holds if \\spad{x} is greater than \\spad{y} in the current domain.")) (< (((|Boolean|) $ $) "\\spad{x < y} holds if \\spad{x} is less than \\spad{y} in the current domain."))) 
 NIL 
 NIL 
-(-759) 
+(-760) 
 ((|constructor| (NIL "Category of types equipped with a total ordering.")) (|min| (($ $ $) "\\spad{min(x,y)} returns the minimum of \\spad{x} and \\spad{y} relative to the ordering.")) (|max| (($ $ $) "\\spad{max(x,y)} returns the maximum of \\spad{x} and \\spad{y} relative to the ordering.")) (>= (((|Boolean|) $ $) "\\spad{x <= y} holds if \\spad{x} is greater or equal than \\spad{y} in the current domain.")) (<= (((|Boolean|) $ $) "\\spad{x <= y} holds if \\spad{x} is less or equal than \\spad{y} in the current domain.")) (> (((|Boolean|) $ $) "\\spad{x > y} holds if \\spad{x} is greater than \\spad{y} in the current domain.")) (< (((|Boolean|) $ $) "\\spad{x < y} holds if \\spad{x} is less than \\spad{y} in the current domain."))) 
 NIL 
 NIL 
-(-760 S R) 
+(-761 S R) 
 ((|constructor| (NIL "This is the category of univariate skew polynomials over an Ore coefficient ring. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}. This category is an evolution of the types \\indented{2}{MonogenicLinearOperator,{} OppositeMonogenicLinearOperator,{} and} \\indented{2}{NonCommutativeOperatorDivision} developped by Jean Della Dora and Stephen \\spad{M}. Watt.")) (|leftLcm| (($ $ $) "\\spad{leftLcm(a,b)} computes the value \\spad{m} of lowest degree such that \\spad{m = aa*a = bb*b} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using right-division.")) (|rightExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{rightExtendedGcd(a,b)} returns \\spad{[c,d]} such that \\spad{g = c * a + d * b = rightGcd(a, b)}.")) (|rightGcd| (($ $ $) "\\spad{rightGcd(a,b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = aa*g}} \\indented{3}{\\spad{b = bb*g}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using right-division.")) (|rightExactQuotient| (((|Union| $ "failed") $ $) "\\spad{rightExactQuotient(a,b)} computes the value \\spad{q},{} if it exists such that \\spad{a = q*b}.")) (|rightRemainder| (($ $ $) "\\spad{rightRemainder(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|rightQuotient| (($ $ $) "\\spad{rightQuotient(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|rightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{rightDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``right division''.")) (|rightLcm| (($ $ $) "\\spad{rightLcm(a,b)} computes the value \\spad{m} of lowest degree such that \\spad{m = a*aa = b*bb} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using left-division.")) (|leftExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{leftExtendedGcd(a,b)} returns \\spad{[c,d]} such that \\spad{g = a * c + b * d = leftGcd(a, b)}.")) (|leftGcd| (($ $ $) "\\spad{leftGcd(a,b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = g*aa}} \\indented{3}{\\spad{b = g*bb}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using left-division.")) (|leftExactQuotient| (((|Union| $ "failed") $ $) "\\spad{leftExactQuotient(a,b)} computes the value \\spad{q},{} if it exists,{} \\indented{1}{such that \\spad{a = b*q}.}")) (|leftRemainder| (($ $ $) "\\spad{leftRemainder(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|leftQuotient| (($ $ $) "\\spad{leftQuotient(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|leftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{leftDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division''.")) (|primitivePart| (($ $) "\\spad{primitivePart(l)} returns \\spad{l0} such that \\spad{l = a * l0} for some a in \\spad{R},{} and \\spad{content(l0) = 1}.")) (|content| ((|#2| $) "\\spad{content(l)} returns the gcd of all the coefficients of \\spad{l}.")) (|monicRightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicRightDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``right division''.")) (|monicLeftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicLeftDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``left division''.")) (|exquo| (((|Union| $ "failed") $ |#2|) "\\spad{exquo(l, a)} returns the exact quotient of \\spad{l} by a,{} returning \\axiom{\"failed\"} if this is not possible.")) (|apply| ((|#2| $ |#2| |#2|) "\\spad{apply(p, c, m)} returns \\spad{p(m)} where the action is given by \\spad{x m = c sigma(m) + delta(m)}.")) (|coefficients| (((|List| |#2|) $) "\\spad{coefficients(l)} returns the list of all the nonzero coefficients of \\spad{l}.")) (|monomial| (($ |#2| (|NonNegativeInteger|)) "\\spad{monomial(c,k)} produces \\spad{c} times the \\spad{k}-th power of the generating operator,{} \\spad{monomial(1,1)}.")) (|coefficient| ((|#2| $ (|NonNegativeInteger|)) "\\spad{coefficient(l,k)} is \\spad{a(k)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|reductum| (($ $) "\\spad{reductum(l)} is \\spad{l - monomial(a(n),n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(l)} is \\spad{a(n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|minimumDegree| (((|NonNegativeInteger|) $) "\\spad{minimumDegree(l)} is the smallest \\spad{k} such that \\spad{a(k) ~= 0} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(l)} is \\spad{n} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}"))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-389))) (|HasCategory| |#2| (QUOTE (-494))) (|HasCategory| |#2| (QUOTE (-146)))) 
-(-761 R) 
+((|HasCategory| |#2| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-389))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-146)))) 
+(-762 R) 
 ((|constructor| (NIL "This is the category of univariate skew polynomials over an Ore coefficient ring. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}. This category is an evolution of the types \\indented{2}{MonogenicLinearOperator,{} OppositeMonogenicLinearOperator,{} and} \\indented{2}{NonCommutativeOperatorDivision} developped by Jean Della Dora and Stephen \\spad{M}. Watt.")) (|leftLcm| (($ $ $) "\\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)}.}"))) 
-((-3983 . T) (-3984 . T) (-3986 . T)) 
+((-3985 . T) (-3986 . T) (-3988 . T)) 
 NIL 
-(-762 R C) 
+(-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 (-494)))) 
-(-763 R |sigma| -3239) 
+((|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-495)))) 
+(-764 R |sigma| -3241) 
 ((|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."))) 
-((-3983 . T) (-3984 . T) (-3986 . T)) 
-((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-950 (-347 (-483))))) (|HasCategory| |#1| (QUOTE (-950 (-483)))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-389))) (|HasCategory| |#1| (QUOTE (-311)))) 
-(-764 |x| R |sigma| -3239) 
+((-3985 . T) (-3986 . T) (-3988 . 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) 
 ((|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}."))) 
-((-3983 . T) (-3984 . T) (-3986 . T)) 
-((|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-950 (-347 (-483))))) (|HasCategory| |#2| (QUOTE (-950 (-483)))) (|HasCategory| |#2| (QUOTE (-494))) (|HasCategory| |#2| (QUOTE (-389))) (|HasCategory| |#2| (QUOTE (-311)))) 
-(-765 R) 
+((-3985 . T) (-3986 . T) (-3988 . 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..)}."))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-38 (-347 (-483)))))) 
-(-766) 
+((|HasCategory| |#1| (QUOTE (-38 (-347 (-484)))))) 
+(-767) 
 ((|constructor| (NIL "Semigroups with compatible ordering."))) 
 NIL 
 NIL 
-(-767) 
+(-768) 
 ((|constructor| (NIL "\\indented{1}{Author : Larry Lambe} Date created : 14 August 1988 Date Last Updated : 11 March 1991 Description : A domain used in order to take the free \\spad{R}-module on the Integers \\spad{I}. This is actually the forgetful functor from OrderedRings to OrderedSets applied to \\spad{I}")) (|value| (((|Integer|) $) "\\spad{value(x)} returns the integer associated with \\spad{x}")) (|coerce| (($ (|Integer|)) "\\spad{coerce(i)} returns the element corresponding to \\spad{i}"))) 
 NIL 
 NIL 
-(-768) 
+(-769) 
 ((|constructor| (NIL "OutPackage allows pretty-printing from programs.")) (|outputList| (((|Void|) (|List| (|Any|))) "\\spad{outputList(l)} displays the concatenated components of the list \\spad{l} on the ``algebra output'' stream,{} as defined by \\spadsyscom{set output algebra}; quotes are stripped from strings.")) (|output| (((|Void|) (|String|) (|OutputForm|)) "\\spad{output(s,x)} displays the string \\spad{s} followed by the form \\spad{x} on the ``algebra output'' stream,{} as defined by \\spadsyscom{set output algebra}.") (((|Void|) (|OutputForm|)) "\\spad{output(x)} displays the output form \\spad{x} on the ``algebra output'' stream,{} as defined by \\spadsyscom{set output algebra}.") (((|Void|) (|String|)) "\\spad{output(s)} displays the string \\spad{s} on the ``algebra output'' stream,{} as defined by \\spadsyscom{set output algebra}."))) 
 NIL 
 NIL 
-(-769 S) 
+(-770 S) 
 ((|constructor| (NIL "This category describes output byte stream conduits.")) (|writeBytes!| (((|NonNegativeInteger|) $ (|ByteBuffer|)) "\\spad{writeBytes!(c,b)} write bytes from buffer `b' onto the conduit `c'. The actual number of written bytes is returned.")) (|writeUInt8!| (((|Maybe| (|UInt8|)) $ (|UInt8|)) "\\spad{writeUInt8!(c,b)} attempts to write the unsigned 8-bit value `v' on the conduit `c'. Returns the written value if successful,{} otherwise,{} returns \\spad{nothing}.")) (|writeInt8!| (((|Maybe| (|Int8|)) $ (|Int8|)) "\\spad{writeInt8!(c,b)} attempts to write the 8-bit value `v' on the conduit `c'. Returns the written value if successful,{} otherwise,{} returns \\spad{nothing}.")) (|writeByte!| (((|Maybe| (|Byte|)) $ (|Byte|)) "\\spad{writeByte!(c,b)} attempts to write the byte `b' on the conduit `c'. Returns the written byte if successful,{} otherwise,{} returns \\spad{nothing}."))) 
 NIL 
 NIL 
-(-770) 
+(-771) 
 ((|constructor| (NIL "This category describes output byte stream conduits.")) (|writeBytes!| (((|NonNegativeInteger|) $ (|ByteBuffer|)) "\\spad{writeBytes!(c,b)} write bytes from buffer `b' onto the conduit `c'. The actual number of written bytes is returned.")) (|writeUInt8!| (((|Maybe| (|UInt8|)) $ (|UInt8|)) "\\spad{writeUInt8!(c,b)} attempts to write the unsigned 8-bit value `v' on the conduit `c'. Returns the written value if successful,{} otherwise,{} returns \\spad{nothing}.")) (|writeInt8!| (((|Maybe| (|Int8|)) $ (|Int8|)) "\\spad{writeInt8!(c,b)} attempts to write the 8-bit value `v' on the conduit `c'. Returns the written value if successful,{} otherwise,{} returns \\spad{nothing}.")) (|writeByte!| (((|Maybe| (|Byte|)) $ (|Byte|)) "\\spad{writeByte!(c,b)} attempts to write the byte `b' on the conduit `c'. Returns the written byte if successful,{} otherwise,{} returns \\spad{nothing}."))) 
 NIL 
 NIL 
-(-771) 
+(-772) 
 ((|constructor| (NIL "This domain provides representation for binary files open for output operations. `Binary' here means that the conduits do not interpret their contents.")) (|isOpen?| (((|Boolean|) $) "open?(ifile) holds if `ifile' is in open state.")) (|outputBinaryFile| (($ (|String|)) "\\spad{outputBinaryFile(f)} returns an output conduit obtained by opening the file named by `f' as a binary file.") (($ (|FileName|)) "\\spad{outputBinaryFile(f)} returns an output conduit obtained by opening the file named by `f' as a binary file."))) 
 NIL 
 NIL 
-(-772) 
+(-773) 
 ((|constructor| (NIL "This domain is used to create and manipulate mathematical expressions for output. It is intended to provide an insulating layer between the expression rendering software (\\spadignore{e.g.} TeX,{} or Script) and the output coercions in the various domains.")) (SEGMENT (($ $) "\\spad{SEGMENT(x)} creates the prefix form: \\spad{x..}.") (($ $ $) "\\spad{SEGMENT(x,y)} creates the infix form: \\spad{x..y}.")) (|not| (($ $) "\\spad{not f} creates the equivalent prefix form.")) (|or| (($ $ $) "\\spad{f or g} creates the equivalent infix form.")) (|and| (($ $ $) "\\spad{f and g} creates the equivalent infix form.")) (|exquo| (($ $ $) "\\spad{exquo(f,g)} creates the equivalent infix form.")) (|quo| (($ $ $) "\\spad{f quo g} creates the equivalent infix form.")) (|rem| (($ $ $) "\\spad{f rem g} creates the equivalent infix form.")) (|div| (($ $ $) "\\spad{f div g} creates the equivalent infix form.")) (** (($ $ $) "\\spad{f ** g} creates the equivalent infix form.")) (/ (($ $ $) "\\spad{f / g} creates the equivalent infix form.")) (* (($ $ $) "\\spad{f * g} creates the equivalent infix form.")) (- (($ $) "\\spad{- f} creates the equivalent prefix form.") (($ $ $) "\\spad{f - g} creates the equivalent infix form.")) (+ (($ $ $) "\\spad{f + g} creates the equivalent infix form.")) (>= (($ $ $) "\\spad{f >= g} creates the equivalent infix form.")) (<= (($ $ $) "\\spad{f <= g} creates the equivalent infix form.")) (> (($ $ $) "\\spad{f > g} creates the equivalent infix form.")) (< (($ $ $) "\\spad{f < g} creates the equivalent infix form.")) (~= (($ $ $) "\\spad{f ~= g} creates the equivalent infix form.")) (= (($ $ $) "\\spad{f = g} creates the equivalent infix form.")) (|blankSeparate| (($ (|List| $)) "\\spad{blankSeparate(l)} creates the form separating the elements of \\spad{l} by blanks.")) (|semicolonSeparate| (($ (|List| $)) "\\spad{semicolonSeparate(l)} creates the form separating the elements of \\spad{l} by semicolons.")) (|commaSeparate| (($ (|List| $)) "\\spad{commaSeparate(l)} creates the form separating the elements of \\spad{l} by commas.")) (|pile| (($ (|List| $)) "\\spad{pile(l)} creates the form consisting of the elements of \\spad{l} which displays as a pile,{} \\spadignore{i.e.} the elements begin on a new line and are indented right to the same margin.")) (|paren| (($ (|List| $)) "\\spad{paren(lf)} creates the form separating the elements of \\spad{lf} by commas and encloses the result in parentheses.") (($ $) "\\spad{paren(f)} creates the form enclosing \\spad{f} in parentheses.")) (|bracket| (($ (|List| $)) "\\spad{bracket(lf)} creates the form separating the elements of \\spad{lf} by commas and encloses the result in square brackets.") (($ $) "\\spad{bracket(f)} creates the form enclosing \\spad{f} in square brackets.")) (|brace| (($ (|List| $)) "\\spad{brace(lf)} creates the form separating the elements of \\spad{lf} by commas and encloses the result in curly brackets.") (($ $) "\\spad{brace(f)} creates the form enclosing \\spad{f} in braces (curly brackets).")) (|int| (($ $ $ $) "\\spad{int(expr,lowerlimit,upperlimit)} creates the form prefixing \\spad{expr} by an integral sign with both a \\spad{lowerlimit} and \\spad{upperlimit}.") (($ $ $) "\\spad{int(expr,lowerlimit)} creates the form prefixing \\spad{expr} by an integral sign with a \\spad{lowerlimit}.") (($ $) "\\spad{int(expr)} creates the form prefixing \\spad{expr} with an integral sign.")) (|prod| (($ $ $ $) "\\spad{prod(expr,lowerlimit,upperlimit)} creates the form prefixing \\spad{expr} by a capital \\spad{pi} with both a \\spad{lowerlimit} and \\spad{upperlimit}.") (($ $ $) "\\spad{prod(expr,lowerlimit)} creates the form prefixing \\spad{expr} by a capital \\spad{pi} with a \\spad{lowerlimit}.") (($ $) "\\spad{prod(expr)} creates the form prefixing \\spad{expr} by a capital \\spad{pi}.")) (|sum| (($ $ $ $) "\\spad{sum(expr,lowerlimit,upperlimit)} creates the form prefixing \\spad{expr} by a capital sigma with both a \\spad{lowerlimit} and \\spad{upperlimit}.") (($ $ $) "\\spad{sum(expr,lowerlimit)} creates the form prefixing \\spad{expr} by a capital sigma with a \\spad{lowerlimit}.") (($ $) "\\spad{sum(expr)} creates the form prefixing \\spad{expr} by a capital sigma.")) (|overlabel| (($ $ $) "\\spad{overlabel(x,f)} creates the form \\spad{f} with \"x overbar\" over the top.")) (|overbar| (($ $) "\\spad{overbar(f)} creates the form \\spad{f} with an overbar.")) (|prime| (($ $ (|NonNegativeInteger|)) "\\spad{prime(f,n)} creates the form \\spad{f} followed by \\spad{n} primes.") (($ $) "\\spad{prime(f)} creates the form \\spad{f} followed by a suffix prime (single quote).")) (|dot| (($ $ (|NonNegativeInteger|)) "\\spad{dot(f,n)} creates the form \\spad{f} with \\spad{n} dots overhead.") (($ $) "\\spad{dot(f)} creates the form with a one dot overhead.")) (|quote| (($ $) "\\spad{quote(f)} creates the form \\spad{f} with a prefix quote.")) (|supersub| (($ $ (|List| $)) "\\spad{supersub(a,[sub1,super1,sub2,super2,...])} creates a form with each subscript aligned under each superscript.")) (|scripts| (($ $ (|List| $)) "\\spad{scripts(f, [sub, super, presuper, presub])} \\indented{1}{creates a form for \\spad{f} with scripts on all 4 corners.}")) (|presuper| (($ $ $) "\\spad{presuper(f,n)} creates a form for \\spad{f} presuperscripted by \\spad{n}.")) (|presub| (($ $ $) "\\spad{presub(f,n)} creates a form for \\spad{f} presubscripted by \\spad{n}.")) (|super| (($ $ $) "\\spad{super(f,n)} creates a form for \\spad{f} superscripted by \\spad{n}.")) (|sub| (($ $ $) "\\spad{sub(f,n)} creates a form for \\spad{f} subscripted by \\spad{n}.")) (|binomial| (($ $ $) "\\spad{binomial(n,m)} creates a form for the binomial coefficient of \\spad{n} and \\spad{m}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(f,n)} creates a form for the \\spad{n}th derivative of \\spad{f},{} \\spadignore{e.g.} \\spad{f'},{} \\spad{f''},{} \\spad{f'''},{} \"f super \\spad{iv}\".")) (|rarrow| (($ $ $) "\\spad{rarrow(f,g)} creates a form for the mapping \\spad{f -> g}.")) (|assign| (($ $ $) "\\spad{assign(f,g)} creates a form for the assignment \\spad{f := g}.")) (|slash| (($ $ $) "\\spad{slash(f,g)} creates a form for the horizontal fraction of \\spad{f} over \\spad{g}.")) (|over| (($ $ $) "\\spad{over(f,g)} creates a form for the vertical fraction of \\spad{f} over \\spad{g}.")) (|root| (($ $ $) "\\spad{root(f,n)} creates a form for the \\spad{n}th root of form \\spad{f}.") (($ $) "\\spad{root(f)} creates a form for the square root of form \\spad{f}.")) (|zag| (($ $ $) "\\spad{zag(f,g)} creates a form for the continued fraction form for \\spad{f} over \\spad{g}.")) (|matrix| (($ (|List| (|List| $))) "\\spad{matrix(llf)} makes \\spad{llf} (a list of lists of forms) into a form which displays as a matrix.")) (|box| (($ $) "\\spad{box(f)} encloses \\spad{f} in a box.")) (|label| (($ $ $) "\\spad{label(n,f)} gives form \\spad{f} an equation label \\spad{n}.")) (|string| (($ $) "\\spad{string(f)} creates \\spad{f} with string quotes.")) (|elt| (($ $ (|List| $)) "\\spad{elt(op,l)} creates a form for application of \\spad{op} to list of arguments \\spad{l}.")) (|infix?| (((|Boolean|) $) "\\spad{infix?(op)} returns \\spad{true} if \\spad{op} is an infix operator,{} and \\spad{false} otherwise.")) (|postfix| (($ $ $) "\\spad{postfix(op, a)} creates a form which prints as: a \\spad{op}.")) (|infix| (($ $ $ $) "\\spad{infix(op, a, b)} creates a form which prints as: a \\spad{op} \\spad{b}.") (($ $ (|List| $)) "\\spad{infix(f,l)} creates a form depicting the \\spad{n}-ary application of infix operation \\spad{f} to a tuple of arguments \\spad{l}.")) (|prefix| (($ $ (|List| $)) "\\spad{prefix(f,l)} creates a form depicting the \\spad{n}-ary prefix application of \\spad{f} to a tuple of arguments given by list \\spad{l}.")) (|vconcat| (($ (|List| $)) "\\spad{vconcat(u)} vertically concatenates all forms in list \\spad{u}.") (($ $ $) "\\spad{vconcat(f,g)} vertically concatenates forms \\spad{f} and \\spad{g}.")) (|hconcat| (($ (|List| $)) "\\spad{hconcat(u)} horizontally concatenates all forms in list \\spad{u}.") (($ $ $) "\\spad{hconcat(f,g)} horizontally concatenate forms \\spad{f} and \\spad{g}.")) (|center| (($ $) "\\spad{center(f)} centers form \\spad{f} in total space.") (($ $ (|Integer|)) "\\spad{center(f,n)} centers form \\spad{f} within space of width \\spad{n}.")) (|right| (($ $) "\\spad{right(f)} right-justifies form \\spad{f} in total space.") (($ $ (|Integer|)) "\\spad{right(f,n)} right-justifies form \\spad{f} within space of width \\spad{n}.")) (|left| (($ $) "\\spad{left(f)} left-justifies form \\spad{f} in total space.") (($ $ (|Integer|)) "\\spad{left(f,n)} left-justifies form \\spad{f} within space of width \\spad{n}.")) (|rspace| (($ (|Integer|) (|Integer|)) "\\spad{rspace(n,m)} creates rectangular white space,{} \\spad{n} wide by \\spad{m} high.")) (|vspace| (($ (|Integer|)) "\\spad{vspace(n)} creates white space of height \\spad{n}.")) (|hspace| (($ (|Integer|)) "\\spad{hspace(n)} creates white space of width \\spad{n}.")) (|superHeight| (((|Integer|) $) "\\spad{superHeight(f)} returns the height of form \\spad{f} above the base line.")) (|subHeight| (((|Integer|) $) "\\spad{subHeight(f)} returns the height of form \\spad{f} below the base line.")) (|height| (((|Integer|)) "\\spad{height()} returns the height of the display area (an integer).") (((|Integer|) $) "\\spad{height(f)} returns the height of form \\spad{f} (an integer).")) (|width| (((|Integer|)) "\\spad{width()} returns the width of the display area (an integer).") (((|Integer|) $) "\\spad{width(f)} returns the width of form \\spad{f} (an integer).")) (|doubleFloatFormat| (((|String|) (|String|)) "change the output format for doublefloats using lisp format strings")) (|empty| (($) "\\spad{empty()} creates an empty form.")) (|outputForm| (($ (|DoubleFloat|)) "\\spad{outputForm(sf)} creates an form for small float \\spad{sf}.") (($ (|String|)) "\\spad{outputForm(s)} creates an form for string \\spad{s}.") (($ (|Symbol|)) "\\spad{outputForm(s)} creates an form for symbol \\spad{s}.") (($ (|Integer|)) "\\spad{outputForm(n)} creates an form for integer \\spad{n}.")) (|messagePrint| (((|Void|) (|String|)) "\\spad{messagePrint(s)} prints \\spad{s} without string quotes. Note: \\spad{messagePrint(s)} is equivalent to \\spad{print message(s)}.")) (|message| (($ (|String|)) "\\spad{message(s)} creates an form with no string quotes from string \\spad{s}.")) (|print| (((|Void|) $) "\\spad{print(u)} prints the form \\spad{u}."))) 
 NIL 
 NIL 
-(-773 |VariableList|) 
+(-774 |VariableList|) 
 ((|constructor| (NIL "This domain implements ordered variables")) (|variable| (((|Union| $ "failed") (|Symbol|)) "\\spad{variable(s)} returns a member of the variable set or failed"))) 
 NIL 
 NIL 
-(-774) 
+(-775) 
 ((|constructor| (NIL "This domain represents set of overloaded operators (in fact operator descriptors).")) (|members| (((|List| (|FunctionDescriptor|)) $) "\\spad{members(x)} returns the list of operator descriptors,{} \\spadignore{e.g.} signature and implementation slots,{} of the overload set \\spad{x}.")) (|name| (((|Identifier|) $) "\\spad{name(x)} returns the name of the overload set \\spad{x}."))) 
 NIL 
 NIL 
-(-775 R |vl| |wl| |wtlevel|) 
+(-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)"))) 
-((-3984 |has| |#1| (-146)) (-3983 |has| |#1| (-146)) (-3986 . T)) 
+((-3986 |has| |#1| (-146)) (-3985 |has| |#1| (-146)) (-3988 . T)) 
 ((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-311)))) 
-(-776 R PS UP) 
+(-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)."))) 
 NIL 
 NIL 
-(-777 R |x| |pt|) 
+(-778 R |x| |pt|) 
 ((|constructor| (NIL "\\indented{1}{This package computes reliable Pad&ea. approximants using} a generalized Viskovatov continued fraction algorithm. Authors: Trager,{}Burge,{} Hassner & Watt. Date Created: April 1987 Date Last Updated: 12 April 1990 Keywords: Pade,{} series Examples: References: \\indented{2}{\"Pade Approximants,{} Part I: Basic Theory\",{} Baker & Graves-Morris.}")) (|pade| (((|Union| (|Fraction| (|UnivariatePolynomial| |#2| |#1|)) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) (|UnivariateTaylorSeries| |#1| |#2| |#3|)) "\\spad{pade(nd,dd,s)} computes the quotient of polynomials (if it exists) with numerator degree at most \\spad{nd} and denominator degree at most \\spad{dd} which matches the series \\spad{s} to order \\spad{nd + dd}.") (((|Union| (|Fraction| (|UnivariatePolynomial| |#2| |#1|)) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) (|UnivariateTaylorSeries| |#1| |#2| |#3|) (|UnivariateTaylorSeries| |#1| |#2| |#3|)) "\\spad{pade(nd,dd,ns,ds)} computes the approximant as a quotient of polynomials (if it exists) for arguments \\spad{nd} (numerator degree of approximant),{} \\spad{dd} (denominator degree of approximant),{} \\spad{ns} (numerator series of function),{} and \\spad{ds} (denominator series of function)."))) 
 NIL 
 NIL 
-(-778 |p|) 
+(-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)."))) 
-((-3982 . T) ((-3991 "*") . T) (-3983 . T) (-3984 . T) (-3986 . T)) 
+((-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . T)) 
 NIL 
-(-779 |p|) 
+(-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}."))) 
-((-3982 . T) ((-3991 "*") . T) (-3983 . T) (-3984 . T) (-3986 . T)) 
+((-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . T)) 
 NIL 
-(-780 |p|) 
+(-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)."))) 
-((-3981 . T) (-3987 . T) (-3982 . T) ((-3991 "*") . T) (-3983 . T) (-3984 . T) (-3986 . T)) 
-((|HasCategory| (-778 |#1|) (QUOTE (-821))) (|HasCategory| (-778 |#1|) (QUOTE (-950 (-1088)))) (|HasCategory| (-778 |#1|) (QUOTE (-118))) (|HasCategory| (-778 |#1|) (QUOTE (-120))) (|HasCategory| (-778 |#1|) (QUOTE (-553 (-472)))) (|HasCategory| (-778 |#1|) (QUOTE (-933))) (|HasCategory| (-778 |#1|) (QUOTE (-740))) (|HasCategory| (-778 |#1|) (QUOTE (-756))) (OR (|HasCategory| (-778 |#1|) (QUOTE (-740))) (|HasCategory| (-778 |#1|) (QUOTE (-756)))) (|HasCategory| (-778 |#1|) (QUOTE (-950 (-483)))) (|HasCategory| (-778 |#1|) (QUOTE (-1064))) (|HasCategory| (-778 |#1|) (QUOTE (-796 (-327)))) (|HasCategory| (-778 |#1|) (QUOTE (-796 (-483)))) (|HasCategory| (-778 |#1|) (QUOTE (-553 (-800 (-327))))) (|HasCategory| (-778 |#1|) (QUOTE (-553 (-800 (-483))))) (|HasCategory| (-778 |#1|) (QUOTE (-580 (-483)))) (|HasCategory| (-778 |#1|) (QUOTE (-189))) (|HasCategory| (-778 |#1|) (QUOTE (-811 (-1088)))) (|HasCategory| (-778 |#1|) (QUOTE (-190))) (|HasCategory| (-778 |#1|) (QUOTE (-809 (-1088)))) (|HasCategory| (-778 |#1|) (|%list| (QUOTE -452) (QUOTE (-1088)) (|%list| (QUOTE -778) (|devaluate| |#1|)))) (|HasCategory| (-778 |#1|) (|%list| (QUOTE -259) (|%list| (QUOTE -778) (|devaluate| |#1|)))) (|HasCategory| (-778 |#1|) (|%list| (QUOTE -241) (|%list| (QUOTE -778) (|devaluate| |#1|)) (|%list| (QUOTE -778) (|devaluate| |#1|)))) (|HasCategory| (-778 |#1|) (QUOTE (-257))) (|HasCategory| (-778 |#1|) (QUOTE (-482))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-778 |#1|) (QUOTE (-821)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-778 |#1|) (QUOTE (-821)))) (|HasCategory| (-778 |#1|) (QUOTE (-118))))) 
-(-781 |p| PADIC) 
+((-3983 . T) (-3989 . T) (-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . 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)}."))) 
-((-3981 . T) (-3987 . T) (-3982 . T) ((-3991 "*") . T) (-3983 . T) (-3984 . T) (-3986 . T)) 
-((|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| |#2| (QUOTE (-950 (-1088)))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-553 (-472)))) (|HasCategory| |#2| (QUOTE (-933))) (|HasCategory| |#2| (QUOTE (-740))) (|HasCategory| |#2| (QUOTE (-756))) (OR (|HasCategory| |#2| (QUOTE (-740))) (|HasCategory| |#2| (QUOTE (-756)))) (|HasCategory| |#2| (QUOTE (-950 (-483)))) (|HasCategory| |#2| (QUOTE (-1064))) (|HasCategory| |#2| (QUOTE (-796 (-327)))) (|HasCategory| |#2| (QUOTE (-796 (-483)))) (|HasCategory| |#2| (QUOTE (-553 (-800 (-327))))) (|HasCategory| |#2| (QUOTE (-553 (-800 (-483))))) (|HasCategory| |#2| (QUOTE (-580 (-483)))) (|HasCategory| |#2| (QUOTE (-189))) (|HasCategory| |#2| (QUOTE (-811 (-1088)))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-809 (-1088)))) (|HasCategory| |#2| (|%list| (QUOTE -452) (QUOTE (-1088)) (|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 (-482))) (-12 (|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#2| (QUOTE (-118))))) 
-(-782 S T$) 
+((-3983 . T) (-3989 . T) (-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . 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'."))) 
 NIL 
-((-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#2| (QUOTE (-1012)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#2| (QUOTE (-552 (-772))))) (-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#2| (QUOTE (-1012))))) (-12 (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#2| (QUOTE (-552 (-772)))))) 
-(-783) 
+((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-1013)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-553 (-773))))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-1013))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-553 (-773)))))) 
+(-784) 
 ((|constructor| (NIL "This domain describes four groups of color shades (palettes).")) (|shade| (((|Integer|) $) "\\spad{shade(p)} returns the shade index of the indicated palette \\spad{p}.")) (|hue| (((|Color|) $) "\\spad{hue(p)} returns the hue field of the indicated palette \\spad{p}.")) (|light| (($ (|Color|)) "\\spad{light(c)} sets the shade of a hue,{} \\spad{c},{} to it's highest value.")) (|pastel| (($ (|Color|)) "\\spad{pastel(c)} sets the shade of a hue,{} \\spad{c},{} above bright,{} but below light.")) (|bright| (($ (|Color|)) "\\spad{bright(c)} sets the shade of a hue,{} \\spad{c},{} above dim,{} but below pastel.")) (|dim| (($ (|Color|)) "\\spad{dim(c)} sets the shade of a hue,{} \\spad{c},{} above dark,{} but below bright.")) (|dark| (($ (|Color|)) "\\spad{dark(c)} sets the shade of the indicated hue of \\spad{c} to it's lowest value."))) 
 NIL 
 NIL 
-(-784) 
+(-785) 
 ((|constructor| (NIL "This package provides a coerce from polynomials over algebraic numbers to \\spadtype{Expression AlgebraicNumber}.")) (|coerce| (((|Expression| (|Integer|)) (|Fraction| (|Polynomial| (|AlgebraicNumber|)))) "\\spad{coerce(rf)} converts \\spad{rf},{} a fraction of polynomial \\spad{p} with algebraic number coefficients to \\spadtype{Expression Integer}.") (((|Expression| (|Integer|)) (|Polynomial| (|AlgebraicNumber|))) "\\spad{coerce(p)} converts the polynomial \\spad{p} with algebraic number coefficients to \\spadtype{Expression Integer}."))) 
 NIL 
 NIL 
-(-785) 
+(-786) 
 ((|constructor| (NIL "Representation of parameters to functions or constructors. For the most part,{} they are Identifiers. However,{} in very cases,{} they are \"flags\",{} \\spadignore{e.g.} string literals.")) (|autoCoerce| (((|String|) $) "\\spad{autoCoerce(x)@String} implicitly coerce the object \\spad{x} to \\spadtype{String}. This function is left at the discretion of the compiler.") (((|Identifier|) $) "\\spad{autoCoerce(x)@Identifier} implicitly coerce the object \\spad{x} to \\spadtype{Identifier}. This function is left at the discretion of the compiler.")) (|case| (((|Boolean|) $ (|[\|\|]| (|String|))) "\\spad{x case String} if the parameter AST object \\spad{x} designates a flag.") (((|Boolean|) $ (|[\|\|]| (|Identifier|))) "\\spad{x case Identifier} if the parameter AST object \\spad{x} designates an \\spadtype{Identifier}."))) 
 NIL 
 NIL 
-(-786 CF1 CF2) 
+(-787 CF1 CF2) 
 ((|constructor| (NIL "This package \\undocumented")) (|map| (((|ParametricPlaneCurve| |#2|) (|Mapping| |#2| |#1|) (|ParametricPlaneCurve| |#1|)) "\\spad{map(f,x)} \\undocumented"))) 
 NIL 
 NIL 
-(-787 |ComponentFunction|) 
+(-788 |ComponentFunction|) 
 ((|constructor| (NIL "ParametricPlaneCurve is used for plotting parametric plane curves in the affine plane.")) (|coordinate| ((|#1| $ (|NonNegativeInteger|)) "\\spad{coordinate(c,i)} returns a coordinate function for \\spad{c} using 1-based indexing according to \\spad{i}. This indicates what the function for the coordinate component \\spad{i} of the plane curve is.")) (|curve| (($ |#1| |#1|) "\\spad{curve(c1,c2)} creates a plane curve from 2 component functions \\spad{c1} and \\spad{c2}."))) 
 NIL 
 NIL 
-(-788 CF1 CF2) 
+(-789 CF1 CF2) 
 ((|constructor| (NIL "This package \\undocumented")) (|map| (((|ParametricSpaceCurve| |#2|) (|Mapping| |#2| |#1|) (|ParametricSpaceCurve| |#1|)) "\\spad{map(f,x)} \\undocumented"))) 
 NIL 
 NIL 
-(-789 |ComponentFunction|) 
+(-790 |ComponentFunction|) 
 ((|constructor| (NIL "ParametricSpaceCurve is used for plotting parametric space curves in affine 3-space.")) (|coordinate| ((|#1| $ (|NonNegativeInteger|)) "\\spad{coordinate(c,i)} returns a coordinate function of \\spad{c} using 1-based indexing according to \\spad{i}. This indicates what the function for the coordinate component,{} \\spad{i},{} of the space curve is.")) (|curve| (($ |#1| |#1| |#1|) "\\spad{curve(c1,c2,c3)} creates a space curve from 3 component functions \\spad{c1},{} \\spad{c2},{} and \\spad{c3}."))) 
 NIL 
 NIL 
-(-790) 
+(-791) 
 ((|constructor| (NIL "\\indented{1}{This package provides a simple Spad script parser.} Related Constructors: Syntax. See Also: Syntax.")) (|getSyntaxFormsFromFile| (((|List| (|Syntax|)) (|String|)) "\\spad{getSyntaxFormsFromFile(f)} parses the source file \\spad{f} (supposedly containing Spad scripts) and returns a List Syntax. The filename \\spad{f} is supposed to have the proper extension. Note that source location information is not part of result."))) 
 NIL 
 NIL 
-(-791 CF1 CF2) 
+(-792 CF1 CF2) 
 ((|constructor| (NIL "This package \\undocumented")) (|map| (((|ParametricSurface| |#2|) (|Mapping| |#2| |#1|) (|ParametricSurface| |#1|)) "\\spad{map(f,x)} \\undocumented"))) 
 NIL 
 NIL 
-(-792 |ComponentFunction|) 
+(-793 |ComponentFunction|) 
 ((|constructor| (NIL "ParametricSurface is used for plotting parametric surfaces in affine 3-space.")) (|coordinate| ((|#1| $ (|NonNegativeInteger|)) "\\spad{coordinate(s,i)} returns a coordinate function of \\spad{s} using 1-based indexing according to \\spad{i}. This indicates what the function for the coordinate component,{} \\spad{i},{} of the surface is.")) (|surface| (($ |#1| |#1| |#1|) "\\spad{surface(c1,c2,c3)} creates a surface from 3 parametric component functions \\spad{c1},{} \\spad{c2},{} and \\spad{c3}."))) 
 NIL 
 NIL 
-(-793) 
+(-794) 
 ((|constructor| (NIL "PartitionsAndPermutations contains functions for generating streams of integer partitions,{} and streams of sequences of integers composed from a multi-set.")) (|permutations| (((|Stream| (|List| (|Integer|))) (|Integer|)) "\\spad{permutations(n)} is the stream of permutations \\indented{1}{formed from \\spad{1,2,3,...,n}.}")) (|sequences| (((|Stream| (|List| (|Integer|))) (|List| (|Integer|))) "\\spad{sequences([l0,l1,l2,..,ln])} is the set of \\indented{1}{all sequences formed from} \\spad{l0} 0's,{}\\spad{l1} 1's,{}\\spad{l2} 2's,{}...,{}\\spad{ln} \\spad{n}'s.") (((|Stream| (|List| (|Integer|))) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{sequences(l1,l2)} is the stream of all sequences that \\indented{1}{can be composed from the multiset defined from} \\indented{1}{two lists of integers \\spad{l1} and \\spad{l2}.} \\indented{1}{For example,{}the pair \\spad{([1,2,4],[2,3,5])} represents} \\indented{1}{multi-set with 1 \\spad{2},{} 2 \\spad{3}'s,{} and 4 \\spad{5}'s.}")) (|shufflein| (((|Stream| (|List| (|Integer|))) (|List| (|Integer|)) (|Stream| (|List| (|Integer|)))) "\\spad{shufflein(l,st)} maps shuffle(\\spad{l},{}\\spad{u}) on to all \\indented{1}{members \\spad{u} of \\spad{st},{} concatenating the results.}")) (|shuffle| (((|Stream| (|List| (|Integer|))) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{shuffle(l1,l2)} forms the stream of all shuffles of \\spad{l1} \\indented{1}{and \\spad{l2},{} \\spadignore{i.e.} all sequences that can be formed from} \\indented{1}{merging \\spad{l1} and \\spad{l2}.}")) (|conjugates| (((|Stream| (|List| (|PositiveInteger|))) (|Stream| (|List| (|PositiveInteger|)))) "\\spad{conjugates(lp)} is the stream of conjugates of a stream \\indented{1}{of partitions \\spad{lp}.}")) (|conjugate| (((|List| (|PositiveInteger|)) (|List| (|PositiveInteger|))) "\\spad{conjugate(pt)} is the conjugate of the partition \\spad{pt}."))) 
 NIL 
 NIL 
-(-794 R) 
+(-795 R) 
 ((|constructor| (NIL "An object \\spad{S} is Patternable over an object \\spad{R} if \\spad{S} can lift the conversions from \\spad{R} into \\spadtype{Pattern(Integer)} and \\spadtype{Pattern(Float)} to itself."))) 
 NIL 
 NIL 
-(-795 R S L) 
+(-796 R S L) 
 ((|constructor| (NIL "A PatternMatchListResult is an object internally returned by the pattern matcher when matching on lists. It is either a failed match,{} or a pair of PatternMatchResult,{} one for atoms (elements of the list),{} and one for lists.")) (|lists| (((|PatternMatchResult| |#1| |#3|) $) "\\spad{lists(r)} returns the list of matches that match lists.")) (|atoms| (((|PatternMatchResult| |#1| |#2|) $) "\\spad{atoms(r)} returns the list of matches that match atoms (elements of the lists).")) (|makeResult| (($ (|PatternMatchResult| |#1| |#2|) (|PatternMatchResult| |#1| |#3|)) "\\spad{makeResult(r1,r2)} makes the combined result [\\spad{r1},{}\\spad{r2}].")) (|new| (($) "\\spad{new()} returns a new empty match result.")) (|failed| (($) "\\spad{failed()} returns a failed match.")) (|failed?| (((|Boolean|) $) "\\spad{failed?(r)} tests if \\spad{r} is a failed match."))) 
 NIL 
 NIL 
-(-796 S) 
+(-797 S) 
 ((|constructor| (NIL "A set \\spad{R} is PatternMatchable over \\spad{S} if elements of \\spad{R} can be matched to patterns over \\spad{S}.")) (|patternMatch| (((|PatternMatchResult| |#1| $) $ (|Pattern| |#1|) (|PatternMatchResult| |#1| $)) "\\spad{patternMatch(expr, pat, res)} matches the pattern \\spad{pat} to the expression \\spad{expr}. res contains the variables of \\spad{pat} which are already matched and their matches (necessary for recursion). Initially,{} res is just the result of \\spadfun{new} which is an empty list of matches."))) 
 NIL 
 NIL 
-(-797 |Base| |Subject| |Pat|) 
+(-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 (-2556 (|HasCategory| |#2| (QUOTE (-950 (-1088))))) (-2556 (|HasCategory| |#2| (QUOTE (-961))))) (-12 (|HasCategory| |#2| (QUOTE (-961))) (-2556 (|HasCategory| |#2| (QUOTE (-950 (-1088)))))) (|HasCategory| |#2| (QUOTE (-950 (-1088))))) 
-(-798 R S) 
+((-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))))) 
+(-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 
 NIL 
-(-799 R A B) 
+(-800 R A B) 
 ((|constructor| (NIL "Lifts maps to pattern matching results.")) (|map| (((|PatternMatchResult| |#1| |#3|) (|Mapping| |#3| |#2|) (|PatternMatchResult| |#1| |#2|)) "\\spad{map(f, [(v1,a1),...,(vn,an)])} returns the matching result [(\\spad{v1},{}\\spad{f}(\\spad{a1})),{}...,{}(vn,{}\\spad{f}(an))]."))) 
 NIL 
 NIL 
-(-800 R) 
+(-801 R) 
 ((|constructor| (NIL "Patterns for use by the pattern matcher.")) (|optpair| (((|Union| (|List| $) "failed") (|List| $)) "\\spad{optpair(l)} returns \\spad{l} has the form \\spad{[a, b]} and a is optional,{} and \"failed\" otherwise.")) (|variables| (((|List| $) $) "\\spad{variables(p)} returns the list of matching variables appearing in \\spad{p}.")) (|getBadValues| (((|List| (|Any|)) $) "\\spad{getBadValues(p)} returns the list of \"bad values\" for \\spad{p}. Note: \\spad{p} is not allowed to match any of its \"bad values\".")) (|addBadValue| (($ $ (|Any|)) "\\spad{addBadValue(p, v)} adds \\spad{v} to the list of \"bad values\" for \\spad{p}. Note: \\spad{p} is not allowed to match any of its \"bad values\".")) (|resetBadValues| (($ $) "\\spad{resetBadValues(p)} initializes the list of \"bad values\" for \\spad{p} to \\spad{[]}. Note: \\spad{p} is not allowed to match any of its \"bad values\".")) (|hasTopPredicate?| (((|Boolean|) $) "\\spad{hasTopPredicate?(p)} tests if \\spad{p} has a top-level predicate.")) (|topPredicate| (((|Record| (|:| |var| (|List| (|Symbol|))) (|:| |pred| (|Any|))) $) "\\spad{topPredicate(x)} returns \\spad{[[a1,...,an], f]} where the top-level predicate of \\spad{x} is \\spad{f(a1,...,an)}. Note: \\spad{n} is 0 if \\spad{x} has no top-level predicate.")) (|setTopPredicate| (($ $ (|List| (|Symbol|)) (|Any|)) "\\spad{setTopPredicate(x, [a1,...,an], f)} returns \\spad{x} with the top-level predicate set to \\spad{f(a1,...,an)}.")) (|patternVariable| (($ (|Symbol|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\spad{patternVariable(x, c?, o?, m?)} creates a pattern variable \\spad{x},{} which is constant if \\spad{c? = true},{} optional if \\spad{o? = true},{} and multiple if \\spad{m? = true}.")) (|withPredicates| (($ $ (|List| (|Any|))) "\\spad{withPredicates(p, [p1,...,pn])} makes a copy of \\spad{p} and attaches the predicate \\spad{p1} and ... and pn to the copy,{} which is returned.")) (|setPredicates| (($ $ (|List| (|Any|))) "\\spad{setPredicates(p, [p1,...,pn])} attaches the predicate \\spad{p1} and ... and pn to \\spad{p}.")) (|predicates| (((|List| (|Any|)) $) "\\spad{predicates(p)} returns \\spad{[p1,...,pn]} such that the predicate attached to \\spad{p} is \\spad{p1} and ... and pn.")) (|hasPredicate?| (((|Boolean|) $) "\\spad{hasPredicate?(p)} tests if \\spad{p} has predicates attached to it.")) (|optional?| (((|Boolean|) $) "\\spad{optional?(p)} tests if \\spad{p} is a single matching variable which can match an identity.")) (|multiple?| (((|Boolean|) $) "\\spad{multiple?(p)} tests if \\spad{p} is a single matching variable allowing list matching or multiple term matching in a sum or product.")) (|generic?| (((|Boolean|) $) "\\spad{generic?(p)} tests if \\spad{p} is a single matching variable.")) (|constant?| (((|Boolean|) $) "\\spad{constant?(p)} tests if \\spad{p} contains no matching variables.")) (|symbol?| (((|Boolean|) $) "\\spad{symbol?(p)} tests if \\spad{p} is a symbol.")) (|quoted?| (((|Boolean|) $) "\\spad{quoted?(p)} tests if \\spad{p} is of the form 's for a symbol \\spad{s}.")) (|inR?| (((|Boolean|) $) "\\spad{inR?(p)} tests if \\spad{p} is an atom (\\spadignore{i.e.} an element of \\spad{R}).")) (|copy| (($ $) "\\spad{copy(p)} returns a recursive copy of \\spad{p}.")) (|convert| (($ (|List| $)) "\\spad{convert([a1,...,an])} returns the pattern \\spad{[a1,...,an]}.")) (|depth| (((|NonNegativeInteger|) $) "\\spad{depth(p)} returns the nesting level of \\spad{p}.")) (/ (($ $ $) "\\spad{a / b} returns the pattern \\spad{a / b}.")) (** (($ $ $) "\\spad{a ** b} returns the pattern \\spad{a ** b}.") (($ $ (|NonNegativeInteger|)) "\\spad{a ** n} returns the pattern \\spad{a ** n}.")) (* (($ $ $) "\\spad{a * b} returns the pattern \\spad{a * b}.")) (+ (($ $ $) "\\spad{a + b} returns the pattern \\spad{a + b}.")) (|elt| (($ (|BasicOperator|) (|List| $)) "\\spad{elt(op, [a1,...,an])} returns \\spad{op(a1,...,an)}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| $)) "failed") $) "\\spad{isPower(p)} returns \\spad{[a, b]} if \\spad{p = a ** b},{} and \"failed\" otherwise.")) (|isList| (((|Union| (|List| $) "failed") $) "\\spad{isList(p)} returns \\spad{[a1,...,an]} if \\spad{p = [a1,...,an]},{} \"failed\" otherwise.")) (|isQuotient| (((|Union| (|Record| (|:| |num| $) (|:| |den| $)) "failed") $) "\\spad{isQuotient(p)} returns \\spad{[a, b]} if \\spad{p = a / b},{} and \"failed\" otherwise.")) (|isExpt| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|NonNegativeInteger|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[q, n]} if \\spad{n > 0} and \\spad{p = q ** n},{} and \"failed\" otherwise.")) (|isOp| (((|Union| (|Record| (|:| |op| (|BasicOperator|)) (|:| |arg| (|List| $))) "failed") $) "\\spad{isOp(p)} returns \\spad{[op, [a1,...,an]]} if \\spad{p = op(a1,...,an)},{} and \"failed\" otherwise.") (((|Union| (|List| $) "failed") $ (|BasicOperator|)) "\\spad{isOp(p, op)} returns \\spad{[a1,...,an]} if \\spad{p = op(a1,...,an)},{} and \"failed\" otherwise.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if \\spad{n > 1} and \\spad{p = a1 * ... * an},{} and \"failed\" otherwise.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[a1,...,an]} if \\spad{n > 1} \\indented{1}{and \\spad{p = a1 + ... + an},{}} and \"failed\" otherwise.")) (|One| (($) "1")) (|Zero| (($) "0"))) 
 NIL 
 NIL 
-(-801 R -2665) 
+(-802 R -2667) 
 ((|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 
-(-802 R S) 
+(-803 R S) 
 ((|constructor| (NIL "Lifts maps to patterns.")) (|map| (((|Pattern| |#2|) (|Mapping| |#2| |#1|) (|Pattern| |#1|)) "\\spad{map(f, p)} applies \\spad{f} to all the leaves of \\spad{p} and returns the result as a pattern over \\spad{S}."))) 
 NIL 
 NIL 
-(-803 |VarSet|) 
+(-804 |VarSet|) 
 ((|constructor| (NIL "This domain provides the internal representation of polynomials in non-commutative variables written over the Poincare-Birkhoff-Witt basis. See the \\spadtype{XPBWPolynomial} domain constructor. See Free Lie Algebras by \\spad{C}. Reutenauer (Oxford science publications). \\newline Author: Michel Petitot (petitot@lifl.fr).")) (|varList| (((|List| |#1|) $) "\\spad{varList([l1]*[l2]*...[ln])} returns the list of variables in the word \\spad{l1*l2*...*ln}.")) (|retractable?| (((|Boolean|) $) "\\spad{retractable?([l1]*[l2]*...[ln])} returns \\spad{true} iff \\spad{n} equals \\spad{1}.")) (|rest| (($ $) "\\spad{rest([l1]*[l2]*...[ln])} returns the list \\spad{l2, .... ln}.")) (|ListOfTerms| (((|List| (|LyndonWord| |#1|)) $) "\\spad{ListOfTerms([l1]*[l2]*...[ln])} returns the list of words \\spad{l1, l2, .... ln}.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length([l1]*[l2]*...[ln])} returns the length of the word \\spad{l1*l2*...*ln}.")) (|first| (((|LyndonWord| |#1|) $) "\\spad{first([l1]*[l2]*...[ln])} returns the Lyndon word \\spad{l1}.")) (|coerce| (($ |#1|) "\\spad{coerce(v)} return \\spad{v}") (((|OrderedFreeMonoid| |#1|) $) "\\spad{coerce([l1]*[l2]*...[ln])} returns the word \\spad{l1*l2*...*ln},{} where \\spad{[l_i]} is the backeted form of the Lyndon word \\spad{l_i}.")) (|One| (($) "\\spad{1} returns the empty list."))) 
 NIL 
 NIL 
-(-804 UP R) 
+(-805 UP R) 
 ((|constructor| (NIL "This package \\undocumented")) (|compose| ((|#1| |#1| |#1|) "\\spad{compose(p,q)} \\undocumented"))) 
 NIL 
 NIL 
-(-805 A T$ S) 
+(-806 A T$ S) 
 ((|constructor| (NIL "\\indented{2}{This category captures the interface of domains with a distinguished} \\indented{2}{operation named \\spad{differentiate} for partial differentiation with} \\indented{2}{respect to some domain of variables.} See Also: \\indented{2}{DifferentialDomain,{} PartialDifferentialSpace}")) (D ((|#2| $ |#3|) "\\spad{D(x,v)} is a shorthand for \\spad{differentiate(x,v)}")) (|differentiate| ((|#2| $ |#3|) "\\spad{differentiate(x,v)} computes the partial derivative of \\spad{x} with respect to \\spad{v}."))) 
 NIL 
 NIL 
-(-806 T$ S) 
+(-807 T$ S) 
 ((|constructor| (NIL "\\indented{2}{This category captures the interface of domains with a distinguished} \\indented{2}{operation named \\spad{differentiate} for partial differentiation with} \\indented{2}{respect to some domain of variables.} See Also: \\indented{2}{DifferentialDomain,{} PartialDifferentialSpace}")) (D ((|#1| $ |#2|) "\\spad{D(x,v)} is a shorthand for \\spad{differentiate(x,v)}")) (|differentiate| ((|#1| $ |#2|) "\\spad{differentiate(x,v)} computes the partial derivative of \\spad{x} with respect to \\spad{v}."))) 
 NIL 
 NIL 
-(-807 UP -3088) 
+(-808 UP -3090) 
 ((|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 
-(-808 R S) 
+(-809 R S) 
 ((|constructor| (NIL "A partial differential \\spad{R}-module with differentiations indexed by a parameter type \\spad{S}. \\blankline"))) 
-((-3984 . T) (-3983 . T)) 
+((-3986 . T) (-3985 . T)) 
 NIL 
-(-809 S) 
+(-810 S) 
 ((|constructor| (NIL "A partial differential ring with differentiations indexed by a parameter type \\spad{S}. \\blankline"))) 
-((-3986 . T)) 
+((-3988 . T)) 
 NIL 
-(-810 A S) 
+(-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)}."))) 
 NIL 
 NIL 
-(-811 S) 
+(-812 S) 
 ((|constructor| (NIL "\\indented{2}{This category captures the interface of domains stable by partial} \\indented{2}{differentiation with respect to variables from some domain.} See Also: \\indented{2}{PartialDifferentialDomain}")) (D (($ $ (|List| |#1|) (|List| (|NonNegativeInteger|))) "\\spad{D(x,[s1,...,sn],[n1,...,nn])} is a shorthand for \\spad{differentiate(x,[s1,...,sn],[n1,...,nn])}.") (($ $ |#1| (|NonNegativeInteger|)) "\\spad{D(x,s,n)} is a shorthand for \\spad{differentiate(x,s,n)}.") (($ $ (|List| |#1|)) "\\spad{D(x,[s1,...sn])} is a shorthand for \\spad{differentiate(x,[s1,...sn])}.")) (|differentiate| (($ $ (|List| |#1|) (|List| (|NonNegativeInteger|))) "\\spad{differentiate(x,[s1,...,sn],[n1,...,nn])} computes multiple partial derivatives,{} \\spadignore{i.e.}") (($ $ |#1| (|NonNegativeInteger|)) "\\spad{differentiate(x,s,n)} computes multiple partial derivatives,{} \\spadignore{i.e.} \\spad{n}\\spad{-}th derivative of \\spad{x} with respect to \\spad{s}.") (($ $ (|List| |#1|)) "\\spad{differentiate(x,[s1,...sn])} computes successive partial derivatives,{} \\spadignore{i.e.} \\spad{differentiate(...differentiate(x, s1)..., sn)}."))) 
 NIL 
 NIL 
-(-812 S) 
+(-813 S) 
 ((|constructor| (NIL "\\indented{1}{A PendantTree(\\spad{S})is either a leaf? and is an \\spad{S} or has} a left and a right both PendantTree(\\spad{S})'s")) (|ptree| (($ $ $) "\\spad{ptree(x,y)} \\undocumented") (($ |#1|) "\\spad{ptree(s)} is a leaf? pendant tree"))) 
 NIL 
-((-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1012))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-72)))) 
-(-813 S) 
+((-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|))) $) "\\spad{listRepresentation(p)} produces a representation {\\em rep} of the permutation \\spad{p} as a list of preimages and images,{} \\spad{i}.\\spad{e} \\spad{p} maps {\\em (rep.preimage).k} to {\\em (rep.image).k} for all indices \\spad{k}. Elements of \\spad{S} not in {\\em (rep.preimage).k} are fixed points,{} and these are the only fixed points of the permutation."))) 
-((-3986 . T)) 
-((OR (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-756)))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-756)))) 
-(-814 |n| R) 
+((-3988 . T)) 
+((OR (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-757)))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-757)))) 
+(-815 |n| R) 
 ((|constructor| (NIL "Permanent implements the functions {\\em permanent},{} the permanent for square matrices.")) (|permanent| ((|#2| (|SquareMatrix| |#1| |#2|)) "\\spad{permanent(x)} computes the permanent of a square matrix \\spad{x}. The {\\em permanent} is equivalent to the \\spadfun{determinant} except that coefficients have no change of sign. This function is much more difficult to compute than the {\\em determinant}. The formula used is by \\spad{H}.\\spad{J}. Ryser,{} improved by [Nijenhuis and Wilf,{} Ch. 19]. Note: permanent(\\spad{x}) choose one of three algorithms,{} depending on the underlying ring \\spad{R} and on \\spad{n},{} the number of rows (and columns) of x:\\begin{items} \\item 1. if 2 has an inverse in \\spad{R} we can use the algorithm of \\indented{3}{[Nijenhuis and Wilf,{} ch.19,{}\\spad{p}.158]; if 2 has no inverse,{}} \\indented{3}{some modifications are necessary:} \\item 2. if {\\em n > 6} and \\spad{R} is an integral domain with characteristic \\indented{3}{different from 2 (the algorithm works if and only 2 is not a} \\indented{3}{zero-divisor of \\spad{R} and {\\em characteristic()\\$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}"))) 
 NIL 
 NIL 
-(-815 S) 
+(-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."))) 
-((-3986 . T)) 
+((-3988 . T)) 
 NIL 
-(-816 S) 
+(-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}."))) 
 NIL 
 NIL 
-(-817 |p|) 
+(-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."))) 
-((-3981 . T) (-3987 . T) (-3982 . T) ((-3991 "*") . T) (-3983 . T) (-3984 . T) (-3986 . T)) 
+((-3983 . T) (-3989 . T) (-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . T)) 
 ((|HasCategory| $ (QUOTE (-120))) (|HasCategory| $ (QUOTE (-118))) (|HasCategory| $ (QUOTE (-317)))) 
-(-818 R E |VarSet| S) 
+(-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."))) 
 NIL 
 NIL 
-(-819 R S) 
+(-820 R S) 
 ((|constructor| (NIL "\\indented{1}{PolynomialFactorizationByRecursionUnivariate} \\spad{R} is a \\spadfun{PolynomialFactorizationExplicit} domain,{} \\spad{S} is univariate polynomials over \\spad{R} We are interested in handling SparseUnivariatePolynomials over \\spad{S},{} is a variable we shall call \\spad{z}")) (|factorSFBRlcUnit| (((|Factored| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|)) "\\spad{factorSFBRlcUnit(p)} returns the square free factorization of polynomial \\spad{p} (see \\spadfun{factorSquareFreeByRecursion}{PolynomialFactorizationByRecursionUnivariate}) in the case where the leading coefficient of \\spad{p} is a unit.")) (|randomR| ((|#1|) "\\spad{randomR()} produces a random element of \\spad{R}")) (|factorSquareFreeByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|)) "\\spad{factorSquareFreeByRecursion(p)} returns the square free factorization of \\spad{p}. This functions performs the recursion step for factorSquareFreePolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorSquareFreePolynomial}).")) (|factorByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|)) "\\spad{factorByRecursion(p)} factors polynomial \\spad{p}. This function performs the recursion step for factorPolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorPolynomial})")) (|solveLinearPolynomialEquationByRecursion| (((|Union| (|List| (|SparseUnivariatePolynomial| |#2|)) "failed") (|List| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|)) "\\spad{solveLinearPolynomialEquationByRecursion([p1,...,pn],p)} returns the list of polynomials \\spad{[q1,...,qn]} such that \\spad{sum qi/pi = p / prod pi},{} a recursion step for solveLinearPolynomialEquation as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{solveLinearPolynomialEquation}). If no such list of \\spad{qi} exists,{} then \"failed\" is returned."))) 
 NIL 
 NIL 
-(-820 S) 
+(-821 S) 
 ((|constructor| (NIL "This is the category of domains that know \"enough\" about themselves in order to factor univariate polynomials over themselves. This will be used in future releases for supporting factorization over finitely generated coefficient fields,{} it is not yet available in the current release of axiom.")) (|charthRoot| (((|Maybe| $) $) "\\spad{charthRoot(r)} returns the \\spad{p}\\spad{-}th root of \\spad{r},{} or \\spad{nothing} if none exists in the domain.")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(m)} returns a vector of elements,{} not all zero,{} whose \\spad{p}\\spad{-}th powers (\\spad{p} is the characteristic of the domain) are a solution of the homogenous linear system represented by \\spad{m},{} or \"failed\" is there is no such vector.")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| $)) "failed") (|List| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{solveLinearPolynomialEquation([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}'s exists.")) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) "\\spad{gcdPolynomial(p,q)} returns the gcd of the univariate polynomials \\spad{p} qnd \\spad{q}.")) (|factorSquareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorSquareFreePolynomial(p)} factors the univariate polynomial \\spad{p} into irreducibles where \\spad{p} is known to be square free and primitive with respect to its main variable.")) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorPolynomial(p)} returns the factorization into irreducibles of the univariate polynomial \\spad{p}.")) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{squareFreePolynomial(p)} returns the square-free factorization of the univariate polynomial \\spad{p}."))) 
 NIL 
 ((|HasCategory| |#1| (QUOTE (-118)))) 
-(-821) 
+(-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}."))) 
-((-3982 . T) ((-3991 "*") . T) (-3983 . T) (-3984 . T) (-3986 . T)) 
+((-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . T)) 
 NIL 
-(-822 R0 -3088 UP UPUP R) 
+(-823 R0 -3090 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 
-(-823 UP UPUP R) 
+(-824 UP UPUP R) 
 ((|constructor| (NIL "This package provides function for testing whether a divisor on a curve is a torsion divisor.")) (|torsionIfCan| (((|Union| (|Record| (|:| |order| (|NonNegativeInteger|)) (|:| |function| |#3|)) "failed") (|FiniteDivisor| (|Fraction| (|Integer|)) |#1| |#2| |#3|)) "\\spad{torsionIfCan(f)} \\undocumented")) (|torsion?| (((|Boolean|) (|FiniteDivisor| (|Fraction| (|Integer|)) |#1| |#2| |#3|)) "\\spad{torsion?(f)} \\undocumented")) (|order| (((|Union| (|NonNegativeInteger|) "failed") (|FiniteDivisor| (|Fraction| (|Integer|)) |#1| |#2| |#3|)) "\\spad{order(f)} \\undocumented"))) 
 NIL 
 NIL 
-(-824 UP UPUP) 
+(-825 UP UPUP) 
 ((|constructor| (NIL "\\indented{1}{Utilities for PFOQ and PFO} Author: Manuel Bronstein Date Created: 25 Aug 1988 Date Last Updated: 11 Jul 1990")) (|polyred| ((|#2| |#2|) "\\spad{polyred(u)} \\undocumented")) (|doubleDisc| (((|Integer|) |#2|) "\\spad{doubleDisc(u)} \\undocumented")) (|mix| (((|Integer|) (|List| (|Record| (|:| |den| (|Integer|)) (|:| |gcdnum| (|Integer|))))) "\\spad{mix(l)} \\undocumented")) (|badNum| (((|Integer|) |#2|) "\\spad{badNum(u)} \\undocumented") (((|Record| (|:| |den| (|Integer|)) (|:| |gcdnum| (|Integer|))) |#1|) "\\spad{badNum(p)} \\undocumented")) (|getGoodPrime| (((|PositiveInteger|) (|Integer|)) "\\spad{getGoodPrime n} returns the smallest prime not dividing \\spad{n}"))) 
 NIL 
 NIL 
-(-825 R) 
+(-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."))) 
-((-3981 . T) (-3987 . T) (-3982 . T) ((-3991 "*") . T) (-3983 . T) (-3984 . T) (-3986 . T)) 
+((-3983 . T) (-3989 . T) (-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . T)) 
 NIL 
-(-826 R) 
+(-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."))) 
 NIL 
 NIL 
-(-827 E OV R P) 
+(-828 E OV R P) 
 ((|gcdPrimitive| ((|#4| (|List| |#4|)) "\\spad{gcdPrimitive lp} computes the gcd of the list of primitive polynomials lp.") (((|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{gcdPrimitive(p,q)} computes the gcd of the primitive polynomials \\spad{p} and \\spad{q}.") ((|#4| |#4| |#4|) "\\spad{gcdPrimitive(p,q)} computes the gcd of the primitive polynomials \\spad{p} and \\spad{q}.")) (|gcd| (((|SparseUnivariatePolynomial| |#4|) (|List| (|SparseUnivariatePolynomial| |#4|))) "\\spad{gcd(lp)} computes the gcd of the list of polynomials \\spad{lp}.") (((|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{gcd(p,q)} computes the gcd of the two polynomials \\spad{p} and \\spad{q}.") ((|#4| (|List| |#4|)) "\\spad{gcd(lp)} computes the gcd of the list of polynomials \\spad{lp}.") ((|#4| |#4| |#4|) "\\spad{gcd(p,q)} computes the gcd of the two polynomials \\spad{p} and \\spad{q}."))) 
 NIL 
 NIL 
-(-828) 
+(-829) 
 ((|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 
-(-829 -3088) 
+(-830 -3090) 
 ((|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 
-(-830) 
+(-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}."))) 
-(((-3991 "*") . T)) 
+(((-3993 "*") . T)) 
 NIL 
-(-831 R) 
+(-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})."))) 
 NIL 
 NIL 
-(-832) 
+(-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)}"))) 
-((-3982 . T) ((-3991 "*") . T) (-3983 . T) (-3984 . T) (-3986 . T)) 
+((-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . T)) 
 NIL 
-(-833 |xx| -3088) 
+(-834 |xx| -3090) 
 ((|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 
-(-834 -3088 P) 
+(-835 -3090 P) 
 ((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,l2)} \\undocumented"))) 
 NIL 
 NIL 
-(-835 R |Var| |Expon| GR) 
+(-836 R |Var| |Expon| GR) 
 ((|constructor| (NIL "Author: William Sit,{} spring 89")) (|inconsistent?| (((|Boolean|) (|List| (|Polynomial| |#1|))) "inconsistant?(pl) returns \\spad{true} if the system of equations \\spad{p} = 0 for \\spad{p} in pl is inconsistent. It is assumed that pl is a groebner basis.") (((|Boolean|) (|List| |#4|)) "inconsistant?(pl) returns \\spad{true} if the system of equations \\spad{p} = 0 for \\spad{p} in pl is inconsistent. It is assumed that pl is a groebner basis.")) (|sqfree| ((|#4| |#4|) "\\spad{sqfree(p)} returns the product of square free factors of \\spad{p}")) (|regime| (((|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))))) (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))) (|Matrix| |#4|) (|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|List| |#4|)) (|NonNegativeInteger|) (|NonNegativeInteger|) (|Integer|)) "\\spad{regime(y,c, w, p, r, rm, m)} returns a regime,{} a list of polynomials specifying the consistency conditions,{} a particular solution and basis representing the general solution of the parametric linear system \\spad{c} \\spad{z} = \\spad{w} on that regime. The regime returned depends on the subdeterminant \\spad{y}.det and the row and column indices. The solutions are simplified using the assumption that the system has rank \\spad{r} and maximum rank \\spad{rm}. The list \\spad{p} represents a list of list of factors of polynomials in a groebner basis of the ideal generated by higher order subdeterminants,{} and ius used for the simplification. The mode \\spad{m} distinguishes the cases when the system is homogeneous,{} or the right hand side is arbitrary,{} or when there is no new right hand side variables.")) (|redmat| (((|Matrix| |#4|) (|Matrix| |#4|) (|List| |#4|)) "\\spad{redmat(m,g)} returns a matrix whose entries are those of \\spad{m} modulo the ideal generated by the groebner basis \\spad{g}")) (|ParCond| (((|List| (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|))))) (|Matrix| |#4|) (|NonNegativeInteger|)) "\\spad{ParCond(m,k)} returns the list of all \\spad{k} by \\spad{k} subdeterminants in the matrix \\spad{m}")) (|overset?| (((|Boolean|) (|List| |#4|) (|List| (|List| |#4|))) "\\spad{overset?(s,sl)} returns \\spad{true} if \\spad{s} properly a sublist of a member of \\spad{sl}; otherwise it returns \\spad{false}")) (|nextSublist| (((|List| (|List| (|Integer|))) (|Integer|) (|Integer|)) "\\spad{nextSublist(n,k)} returns a list of \\spad{k}-subsets of {1,{} ...,{} \\spad{n}}.")) (|minset| (((|List| (|List| |#4|)) (|List| (|List| |#4|))) "\\spad{minset(sl)} returns the sublist of \\spad{sl} consisting of the minimal lists (with respect to inclusion) in the list \\spad{sl} of lists")) (|minrank| (((|NonNegativeInteger|) (|List| (|Record| (|:| |rank| (|NonNegativeInteger|)) (|:| |eqns| (|List| (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))))) (|:| |fgb| (|List| |#4|))))) "\\spad{minrank(r)} returns the minimum rank in the list \\spad{r} of regimes")) (|maxrank| (((|NonNegativeInteger|) (|List| (|Record| (|:| |rank| (|NonNegativeInteger|)) (|:| |eqns| (|List| (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))))) (|:| |fgb| (|List| |#4|))))) "\\spad{maxrank(r)} returns the maximum rank in the list \\spad{r} of regimes")) (|factorset| (((|List| |#4|) |#4|) "\\spad{factorset(p)} returns the set of irreducible factors of \\spad{p}.")) (|B1solve| (((|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))) (|Record| (|:| |mat| (|Matrix| (|Fraction| (|Polynomial| |#1|)))) (|:| |vec| (|List| (|Fraction| (|Polynomial| |#1|)))) (|:| |rank| (|NonNegativeInteger|)) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|))))) "\\spad{B1solve(s)} solves the system (\\spad{s}.mat) \\spad{z} = \\spad{s}.vec for the variables given by the column indices of \\spad{s}.cols in terms of the other variables and the right hand side \\spad{s}.vec by assuming that the rank is \\spad{s}.rank,{} that the system is consistent,{} with the linearly independent equations indexed by the given row indices \\spad{s}.rows; the coefficients in \\spad{s}.mat involving parameters are treated as polynomials. B1solve(\\spad{s}) returns a particular solution to the system and a basis of the homogeneous system (\\spad{s}.mat) \\spad{z} = 0.")) (|redpps| (((|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))) (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))) (|List| |#4|)) "\\spad{redpps(s,g)} returns the simplified form of \\spad{s} after reducing modulo a groebner basis \\spad{g}")) (|ParCondList| (((|List| (|Record| (|:| |rank| (|NonNegativeInteger|)) (|:| |eqns| (|List| (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))))) (|:| |fgb| (|List| |#4|)))) (|Matrix| |#4|) (|NonNegativeInteger|)) "\\spad{ParCondList(c,r)} computes a list of subdeterminants of each rank >= \\spad{r} of the matrix \\spad{c} and returns a groebner basis for the ideal they generate")) (|hasoln| (((|Record| (|:| |sysok| (|Boolean|)) (|:| |z0| (|List| |#4|)) (|:| |n0| (|List| |#4|))) (|List| |#4|) (|List| |#4|)) "\\spad{hasoln(g, l)} tests whether the quasi-algebraic set defined by \\spad{p} = 0 for \\spad{p} in \\spad{g} and \\spad{q} ~= 0 for \\spad{q} in \\spad{l} is empty or not and returns a simplified definition of the quasi-algebraic set")) (|pr2dmp| ((|#4| (|Polynomial| |#1|)) "\\spad{pr2dmp(p)} converts \\spad{p} to target domain")) (|se2rfi| (((|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|Symbol|))) "\\spad{se2rfi(l)} converts \\spad{l} to target domain")) (|dmp2rfi| (((|List| (|Fraction| (|Polynomial| |#1|))) (|List| |#4|)) "\\spad{dmp2rfi(l)} converts \\spad{l} to target domain") (((|Matrix| (|Fraction| (|Polynomial| |#1|))) (|Matrix| |#4|)) "\\spad{dmp2rfi(m)} converts \\spad{m} to target domain") (((|Fraction| (|Polynomial| |#1|)) |#4|) "\\spad{dmp2rfi(p)} converts \\spad{p} to target domain")) (|bsolve| (((|Record| (|:| |rgl| (|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))))))) (|:| |rgsz| (|Integer|))) (|Matrix| |#4|) (|List| (|Fraction| (|Polynomial| |#1|))) (|NonNegativeInteger|) (|String|) (|Integer|)) "\\spad{bsolve(c, w, r, s, m)} returns a list of regimes and solutions of the system \\spad{c} \\spad{z} = \\spad{w} for ranks at least \\spad{r}; depending on the mode \\spad{m} chosen,{} it writes the output to a file given by the string \\spad{s}.")) (|rdregime| (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|String|)) "\\spad{rdregime(s)} reads in a list from a file with name \\spad{s}")) (|wrregime| (((|Integer|) (|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|String|)) "\\spad{wrregime(l,s)} writes a list of regimes to a file named \\spad{s} and returns the number of regimes written")) (|psolve| (((|Integer|) (|Matrix| |#4|) (|PositiveInteger|) (|String|)) "\\spad{psolve(c,k,s)} solves \\spad{c} \\spad{z} = 0 for all possible ranks >= \\spad{k} of the matrix \\spad{c},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|List| (|Symbol|)) (|PositiveInteger|) (|String|)) "\\spad{psolve(c,w,k,s)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks >= \\spad{k} of the matrix \\spad{c} and indeterminate right hand side \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|List| |#4|) (|PositiveInteger|) (|String|)) "\\spad{psolve(c,w,k,s)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks >= \\spad{k} of the matrix \\spad{c} and given right hand side \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|String|)) "\\spad{psolve(c,s)} solves \\spad{c} \\spad{z} = 0 for all possible ranks of the matrix \\spad{c} and given right hand side vector \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|List| (|Symbol|)) (|String|)) "\\spad{psolve(c,w,s)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks of the matrix \\spad{c} and indeterminate right hand side \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|List| |#4|) (|String|)) "\\spad{psolve(c,w,s)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks of the matrix \\spad{c} and given right hand side vector \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|PositiveInteger|)) "\\spad{psolve(c)} solves the homogeneous linear system \\spad{c} \\spad{z} = 0 for all possible ranks >= \\spad{k} of the matrix \\spad{c}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|List| (|Symbol|)) (|PositiveInteger|)) "\\spad{psolve(c,w,k)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks >= \\spad{k} of the matrix \\spad{c} and indeterminate right hand side \\spad{w}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|List| |#4|) (|PositiveInteger|)) "\\spad{psolve(c,w,k)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks >= \\spad{k} of the matrix \\spad{c} and given right hand side vector \\spad{w}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|)) "\\spad{psolve(c)} solves the homogeneous linear system \\spad{c} \\spad{z} = 0 for all possible ranks of the matrix \\spad{c}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|List| (|Symbol|))) "\\spad{psolve(c,w)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks of the matrix \\spad{c} and indeterminate right hand side \\spad{w}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|List| |#4|)) "\\spad{psolve(c,w)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks of the matrix \\spad{c} and given right hand side vector \\spad{w}"))) 
 NIL 
 NIL 
-(-836) 
+(-837) 
 ((|constructor| (NIL "The Plot domain supports plotting of functions defined over a real number system. A real number system is a model for the real numbers and as such may be an approximation. For example floating point numbers and infinite continued fractions. The facilities at this point are limited to 2-dimensional plots or either a single function or a parametric function.")) (|debug| (((|Boolean|) (|Boolean|)) "\\spad{debug(true)} turns debug mode on \\spad{debug(false)} turns debug mode off")) (|numFunEvals| (((|Integer|)) "\\spad{numFunEvals()} returns the number of points computed")) (|setAdaptive| (((|Boolean|) (|Boolean|)) "\\spad{setAdaptive(true)} turns adaptive plotting on \\spad{setAdaptive(false)} turns adaptive plotting off")) (|adaptive?| (((|Boolean|)) "\\spad{adaptive?()} determines whether plotting be done adaptively")) (|setScreenResolution| (((|Integer|) (|Integer|)) "\\spad{setScreenResolution(i)} sets the screen resolution to \\spad{i}")) (|screenResolution| (((|Integer|)) "\\spad{screenResolution()} returns the screen resolution")) (|setMaxPoints| (((|Integer|) (|Integer|)) "\\spad{setMaxPoints(i)} sets the maximum number of points in a plot to \\spad{i}")) (|maxPoints| (((|Integer|)) "\\spad{maxPoints()} returns the maximum number of points in a plot")) (|setMinPoints| (((|Integer|) (|Integer|)) "\\spad{setMinPoints(i)} sets the minimum number of points in a plot to \\spad{i}")) (|minPoints| (((|Integer|)) "\\spad{minPoints()} returns the minimum number of points in a plot")) (|tRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{tRange(p)} returns the range of the parameter in a parametric plot \\spad{p}")) (|refine| (($ $) "\\spad{refine(p)} performs a refinement on the plot \\spad{p}") (($ $ (|Segment| (|DoubleFloat|))) "\\spad{refine(x,r)} \\undocumented")) (|zoom| (($ $ (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{zoom(x,r,s)} \\undocumented") (($ $ (|Segment| (|DoubleFloat|))) "\\spad{zoom(x,r)} \\undocumented")) (|parametric?| (((|Boolean|) $) "\\spad{parametric? determines} whether it is a parametric plot?")) (|plotPolar| (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) "\\spad{plotPolar(f)} plots the polar curve \\spad{r = f(theta)} as theta ranges over the interval \\spad{[0,2*\\%pi]}; this is the same as the parametric curve \\spad{x = f(t) * cos(t)},{} \\spad{y = f(t) * sin(t)}.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plotPolar(f,a..b)} plots the polar curve \\spad{r = f(theta)} as theta ranges over the interval \\spad{[a,b]}; this is the same as the parametric curve \\spad{x = f(t) * cos(t)},{} \\spad{y = f(t) * sin(t)}.")) (|pointPlot| (($ (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{pointPlot(t +-> (f(t),g(t)),a..b,c..d,e..f)} plots the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over the interval \\spad{[a,b]}; \\spad{x}-range of \\spad{[c,d]} and \\spad{y}-range of \\spad{[e,f]} are noted in Plot object.") (($ (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{pointPlot(t +-> (f(t),g(t)),a..b)} plots the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over the interval \\spad{[a,b]}.")) (|plot| (($ $ (|Segment| (|DoubleFloat|))) "\\spad{plot(x,r)} \\undocumented") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,g,a..b,c..d,e..f)} plots the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over the interval \\spad{[a,b]}; \\spad{x}-range of \\spad{[c,d]} and \\spad{y}-range of \\spad{[e,f]} are noted in Plot object.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,g,a..b)} plots the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over the interval \\spad{[a,b]}.") (($ (|List| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot([f1,...,fm],a..b,c..d)} plots the functions \\spad{y = f1(x)},{}...,{} \\spad{y = fm(x)} on the interval \\spad{a..b}; \\spad{y}-range of \\spad{[c,d]} is noted in Plot object.") (($ (|List| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|DoubleFloat|))) "\\spad{plot([f1,...,fm],a..b)} plots the functions \\spad{y = f1(x)},{}...,{} \\spad{y = fm(x)} on the interval \\spad{a..b}.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,a..b,c..d)} plots the function \\spad{f(x)} on the interval \\spad{[a,b]}; \\spad{y}-range of \\spad{[c,d]} is noted in Plot object.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,a..b)} plots the function \\spad{f(x)} on the interval \\spad{[a,b]}."))) 
 NIL 
 NIL 
-(-837 S) 
+(-838 S) 
 ((|constructor| (NIL "\\spad{PlotFunctions1} provides facilities for plotting curves where functions SF -> SF are specified by giving an expression")) (|plotPolar| (((|Plot|) |#1| (|Symbol|)) "\\spad{plotPolar(f,theta)} plots the graph of \\spad{r = f(theta)} as \\spad{theta} ranges from 0 to 2 \\spad{pi}") (((|Plot|) |#1| (|Symbol|) (|Segment| (|DoubleFloat|))) "\\spad{plotPolar(f,theta,seg)} plots the graph of \\spad{r = f(theta)} as \\spad{theta} ranges over an interval")) (|plot| (((|Plot|) |#1| |#1| (|Symbol|) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,g,t,seg)} plots the graph of \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over an interval.") (((|Plot|) |#1| (|Symbol|) (|Segment| (|DoubleFloat|))) "\\spad{plot(fcn,x,seg)} plots the graph of \\spad{y = f(x)} on a interval"))) 
 NIL 
 NIL 
-(-838) 
+(-839) 
 ((|constructor| (NIL "Plot3D supports parametric plots defined over a real number system. A real number system is a model for the real numbers and as such may be an approximation. For example,{} floating point numbers and infinite continued fractions are real number systems. The facilities at this point are limited to 3-dimensional parametric plots.")) (|debug3D| (((|Boolean|) (|Boolean|)) "\\spad{debug3D(true)} turns debug mode on; debug3D(\\spad{false}) turns debug mode off.")) (|numFunEvals3D| (((|Integer|)) "\\spad{numFunEvals3D()} returns the number of points computed.")) (|setAdaptive3D| (((|Boolean|) (|Boolean|)) "\\spad{setAdaptive3D(true)} turns adaptive plotting on; setAdaptive3D(\\spad{false}) turns adaptive plotting off.")) (|adaptive3D?| (((|Boolean|)) "\\spad{adaptive3D?()} determines whether plotting be done adaptively.")) (|setScreenResolution3D| (((|Integer|) (|Integer|)) "\\spad{setScreenResolution3D(i)} sets the screen resolution for a 3d graph to \\spad{i}.")) (|screenResolution3D| (((|Integer|)) "\\spad{screenResolution3D()} returns the screen resolution for a 3d graph.")) (|setMaxPoints3D| (((|Integer|) (|Integer|)) "\\spad{setMaxPoints3D(i)} sets the maximum number of points in a plot to \\spad{i}.")) (|maxPoints3D| (((|Integer|)) "\\spad{maxPoints3D()} returns the maximum number of points in a plot.")) (|setMinPoints3D| (((|Integer|) (|Integer|)) "\\spad{setMinPoints3D(i)} sets the minimum number of points in a plot to \\spad{i}.")) (|minPoints3D| (((|Integer|)) "\\spad{minPoints3D()} returns the minimum number of points in a plot.")) (|tValues| (((|List| (|List| (|DoubleFloat|))) $) "\\spad{tValues(p)} returns a list of lists of the values of the parameter for which a point is computed,{} one list for each curve in the plot \\spad{p}.")) (|tRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{tRange(p)} returns the range of the parameter in a parametric plot \\spad{p}.")) (|refine| (($ $) "\\spad{refine(x)} \\undocumented") (($ $ (|Segment| (|DoubleFloat|))) "\\spad{refine(x,r)} \\undocumented")) (|zoom| (($ $ (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{zoom(x,r,s,t)} \\undocumented")) (|plot| (($ $ (|Segment| (|DoubleFloat|))) "\\spad{plot(x,r)} \\undocumented") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f1,f2,f3,f4,x,y,z,w)} \\undocumented") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,g,h,a..b)} plots {/emx = \\spad{f}(\\spad{t}),{} \\spad{y} = \\spad{g}(\\spad{t}),{} \\spad{z} = \\spad{h}(\\spad{t})} as \\spad{t} ranges over {/em[a,{}\\spad{b}]}.")) (|pointPlot| (($ (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{pointPlot(f,x,y,z,w)} \\undocumented") (($ (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{pointPlot(f,g,h,a..b)} plots {/emx = \\spad{f}(\\spad{t}),{} \\spad{y} = \\spad{g}(\\spad{t}),{} \\spad{z} = \\spad{h}(\\spad{t})} as \\spad{t} ranges over {/em[a,{}\\spad{b}]}."))) 
 NIL 
 NIL 
-(-839) 
+(-840) 
 ((|constructor| (NIL "This package exports plotting tools")) (|calcRanges| (((|List| (|Segment| (|DoubleFloat|))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{calcRanges(l)} \\undocumented"))) 
 NIL 
 NIL 
-(-840) 
+(-841) 
 ((|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 
-(-841 R -3088) 
+(-842 R -3090) 
 ((|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 
-(-842 S A B) 
+(-843 S A B) 
 ((|constructor| (NIL "This packages provides tools for matching recursively in type towers.")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#2| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(expr, pat, res)} matches the pattern \\spad{pat} to the expression \\spad{expr}; res contains the variables of \\spad{pat} which are already matched and their matches. Note: this function handles type towers by changing the predicates and calling the matching function provided by \\spad{A}.")) (|fixPredicate| (((|Mapping| (|Boolean|) |#2|) (|Mapping| (|Boolean|) |#3|)) "\\spad{fixPredicate(f)} returns \\spad{g} defined by \\spad{g}(a) = \\spad{f}(a::B)."))) 
 NIL 
 NIL 
-(-843 S R -3088) 
+(-844 S R -3090) 
 ((|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 
-(-844 I) 
+(-845 I) 
 ((|constructor| (NIL "This package provides pattern matching functions on integers.")) (|patternMatch| (((|PatternMatchResult| (|Integer|) |#1|) |#1| (|Pattern| (|Integer|)) (|PatternMatchResult| (|Integer|) |#1|)) "\\spad{patternMatch(n, pat, res)} matches the pattern \\spad{pat} to the integer \\spad{n}; res contains the variables of \\spad{pat} which are already matched and their matches."))) 
 NIL 
 NIL 
-(-845 S E) 
+(-846 S E) 
 ((|constructor| (NIL "This package provides pattern matching functions on kernels.")) (|patternMatch| (((|PatternMatchResult| |#1| |#2|) (|Kernel| |#2|) (|Pattern| |#1|) (|PatternMatchResult| |#1| |#2|)) "\\spad{patternMatch(f(e1,...,en), pat, res)} matches the pattern \\spad{pat} to \\spad{f(e1,...,en)}; res contains the variables of \\spad{pat} which are already matched and their matches."))) 
 NIL 
 NIL 
-(-846 S R L) 
+(-847 S R L) 
 ((|constructor| (NIL "This package provides pattern matching functions on lists.")) (|patternMatch| (((|PatternMatchListResult| |#1| |#2| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchListResult| |#1| |#2| |#3|)) "\\spad{patternMatch(l, pat, res)} matches the pattern \\spad{pat} to the list \\spad{l}; res contains the variables of \\spad{pat} which are already matched and their matches."))) 
 NIL 
 NIL 
-(-847 S E V R P) 
+(-848 S E V R P) 
 ((|constructor| (NIL "This package provides pattern matching functions on polynomials.")) (|patternMatch| (((|PatternMatchResult| |#1| |#5|) |#5| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|)) "\\spad{patternMatch(p, pat, res)} matches the pattern \\spad{pat} to the polynomial \\spad{p}; res contains the variables of \\spad{pat} which are already matched and their matches.") (((|PatternMatchResult| |#1| |#5|) |#5| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|) (|Mapping| (|PatternMatchResult| |#1| |#5|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|))) "\\spad{patternMatch(p, pat, res, vmatch)} matches the pattern \\spad{pat} to the polynomial \\spad{p}. \\spad{res} contains the variables of \\spad{pat} which are already matched and their matches; vmatch is the matching function to use on the variables."))) 
 NIL 
-((|HasCategory| |#3| (|%list| (QUOTE -796) (|devaluate| |#1|)))) 
-(-848 -2665) 
+((|HasCategory| |#3| (|%list| (QUOTE -797) (|devaluate| |#1|)))) 
+(-849 -2667) 
 ((|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 
-(-849 R -3088 -2665) 
+(-850 R -3090 -2667) 
 ((|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 
-(-850 S R Q) 
+(-851 S R Q) 
 ((|constructor| (NIL "This package provides pattern matching functions on quotients.")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(a/b, pat, res)} matches the pattern \\spad{pat} to the quotient \\spad{a/b}; res contains the variables of \\spad{pat} which are already matched and their matches."))) 
 NIL 
 NIL 
-(-851 S) 
+(-852 S) 
 ((|constructor| (NIL "This package provides pattern matching functions on symbols.")) (|patternMatch| (((|PatternMatchResult| |#1| (|Symbol|)) (|Symbol|) (|Pattern| |#1|) (|PatternMatchResult| |#1| (|Symbol|))) "\\spad{patternMatch(expr, pat, res)} matches the pattern \\spad{pat} to the expression \\spad{expr}; res contains the variables of \\spad{pat} which are already matched and their matches (necessary for recursion)."))) 
 NIL 
 NIL 
-(-852 S R P) 
+(-853 S R P) 
 ((|constructor| (NIL "This package provides tools for the pattern matcher.")) (|patternMatchTimes| (((|PatternMatchResult| |#1| |#3|) (|List| |#3|) (|List| (|Pattern| |#1|)) (|PatternMatchResult| |#1| |#3|) (|Mapping| (|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|))) "\\spad{patternMatchTimes(lsubj, lpat, res, match)} matches the product of patterns \\spad{reduce(*,lpat)} to the product of subjects \\spad{reduce(*,lsubj)}; \\spad{r} contains the previous matches and match is a pattern-matching function on \\spad{P}.")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) (|List| |#3|) (|List| (|Pattern| |#1|)) (|Mapping| |#3| (|List| |#3|)) (|PatternMatchResult| |#1| |#3|) (|Mapping| (|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|))) "\\spad{patternMatch(lsubj, lpat, op, res, match)} matches the list of patterns \\spad{lpat} to the list of subjects \\spad{lsubj},{} allowing for commutativity; \\spad{op} is the operator such that \\spad{op}(\\spad{lpat}) should match \\spad{op}(\\spad{lsubj}) at the end,{} \\spad{r} contains the previous matches,{} and match is a pattern-matching function on \\spad{P}."))) 
 NIL 
 NIL 
-(-853) 
+(-854) 
 ((|constructor| (NIL "This package provides various polynomial number theoretic functions over the integers.")) (|legendre| (((|SparseUnivariatePolynomial| (|Fraction| (|Integer|))) (|Integer|)) "\\spad{legendre(n)} returns the \\spad{n}th Legendre polynomial \\spad{P[n](x)}. Note: Legendre polynomials,{} denoted \\spad{P[n](x)},{} are computed from the two term recurrence. The generating function is: \\spad{1/sqrt(1-2*t*x+t**2) = sum(P[n](x)*t**n, n=0..infinity)}.")) (|laguerre| (((|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{laguerre(n)} returns the \\spad{n}th Laguerre polynomial \\spad{L[n](x)}. Note: Laguerre polynomials,{} denoted \\spad{L[n](x)},{} are computed from the two term recurrence. The generating function is: \\spad{exp(x*t/(t-1))/(1-t) = sum(L[n](x)*t**n/n!, n=0..infinity)}.")) (|hermite| (((|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{hermite(n)} returns the \\spad{n}th Hermite polynomial \\spad{H[n](x)}. Note: Hermite polynomials,{} denoted \\spad{H[n](x)},{} are computed from the two term recurrence. The generating function is: \\spad{exp(2*t*x-t**2) = sum(H[n](x)*t**n/n!, n=0..infinity)}.")) (|fixedDivisor| (((|Integer|) (|SparseUnivariatePolynomial| (|Integer|))) "\\spad{fixedDivisor(a)} for \\spad{a(x)} in \\spad{Z[x]} is the largest integer \\spad{f} such that \\spad{f} divides \\spad{a(x=k)} for all integers \\spad{k}. Note: fixed divisor of \\spad{a} is \\spad{reduce(gcd,[a(x=k) for k in 0..degree(a)])}.")) (|euler| (((|SparseUnivariatePolynomial| (|Fraction| (|Integer|))) (|Integer|)) "\\spad{euler(n)} returns the \\spad{n}th Euler polynomial \\spad{E[n](x)}. Note: Euler polynomials denoted \\spad{E(n,x)} computed by solving the differential equation \\spad{differentiate(E(n,x),x) = n E(n-1,x)} where \\spad{E(0,x) = 1} and initial condition comes from \\spad{E(n) = 2**n E(n,1/2)}.")) (|cyclotomic| (((|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{cyclotomic(n)} returns the \\spad{n}th cyclotomic polynomial \\spad{phi[n](x)}. Note: \\spad{phi[n](x)} is the factor of \\spad{x**n - 1} whose roots are the primitive \\spad{n}th roots of unity.")) (|chebyshevU| (((|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{chebyshevU(n)} returns the \\spad{n}th Chebyshev polynomial \\spad{U[n](x)}. Note: Chebyshev polynomials of the second kind,{} denoted \\spad{U[n](x)},{} computed from the two term recurrence. The generating function \\spad{1/(1-2*t*x+t**2) = sum(T[n](x)*t**n, n=0..infinity)}.")) (|chebyshevT| (((|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{chebyshevT(n)} returns the \\spad{n}th Chebyshev polynomial \\spad{T[n](x)}. Note: Chebyshev polynomials of the first kind,{} denoted \\spad{T[n](x)},{} computed from the two term recurrence. The generating function \\spad{(1-t*x)/(1-2*t*x+t**2) = sum(T[n](x)*t**n, n=0..infinity)}.")) (|bernoulli| (((|SparseUnivariatePolynomial| (|Fraction| (|Integer|))) (|Integer|)) "\\spad{bernoulli(n)} returns the \\spad{n}th Bernoulli polynomial \\spad{B[n](x)}. Note: Bernoulli polynomials denoted \\spad{B(n,x)} computed by solving the differential equation \\spad{differentiate(B(n,x),x) = n B(n-1,x)} where \\spad{B(0,x) = 1} and initial condition comes from \\spad{B(n) = B(n,0)}."))) 
 NIL 
 NIL 
-(-854 R) 
+(-855 R) 
 ((|constructor| (NIL "This domain implements points in coordinate space"))) 
-((-3990 . T) (-3989 . T)) 
-((OR (-12 (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-553 (-472)))) (OR (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| |#1| (QUOTE (-756))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| (-483) (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-663))) (|HasCategory| |#1| (QUOTE (-961))) (-12 (|HasCategory| |#1| (QUOTE (-915))) (|HasCategory| |#1| (QUOTE (-961)))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|))))) 
-(-855 |lv| R) 
+((-3992 . T) (-3991 . 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}."))) 
 NIL 
 NIL 
-(-856 |TheField| |ThePols|) 
+(-857 |TheField| |ThePols|) 
 ((|constructor| (NIL "\\axiomType{RealPolynomialUtilitiesPackage} provides common functions used by interval coding.")) (|lazyVariations| (((|NonNegativeInteger|) (|List| |#1|) (|Integer|) (|Integer|)) "\\axiom{lazyVariations(\\spad{l},{}\\spad{s1},{}sn)} is the number of sign variations in the list of non null numbers [s1::l]@sn,{}")) (|sturmVariationsOf| (((|NonNegativeInteger|) (|List| |#1|)) "\\axiom{sturmVariationsOf(\\spad{l})} is the number of sign variations in the list of numbers \\spad{l},{} note that the first term counts as a sign")) (|boundOfCauchy| ((|#1| |#2|) "\\axiom{boundOfCauchy(\\spad{p})} bounds the roots of \\spad{p}")) (|sturmSequence| (((|List| |#2|) |#2|) "\\axiom{sturmSequence(\\spad{p}) = sylvesterSequence(\\spad{p},{}p')}")) (|sylvesterSequence| (((|List| |#2|) |#2| |#2|) "\\axiom{sylvesterSequence(\\spad{p},{}\\spad{q})} is the negated remainder sequence of \\spad{p} and \\spad{q} divided by the last computed term"))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-755)))) 
-(-857 R) 
+((|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}."))) 
-(((-3991 "*") |has| |#1| (-146)) (-3982 |has| |#1| (-494)) (-3987 |has| |#1| (-6 -3987)) (-3984 . T) (-3983 . T) (-3986 . T)) 
-((|HasCategory| |#1| (QUOTE (-821))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-389))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-821)))) (OR (|HasCategory| |#1| (QUOTE (-389))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-821)))) (OR (|HasCategory| |#1| (QUOTE (-389))) (|HasCategory| |#1| (QUOTE (-821)))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-494)))) (-12 (|HasCategory| |#1| (QUOTE (-796 (-327)))) (|HasCategory| (-1088) (QUOTE (-796 (-327))))) (-12 (|HasCategory| |#1| (QUOTE (-796 (-483)))) (|HasCategory| (-1088) (QUOTE (-796 (-483))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-800 (-327))))) (|HasCategory| (-1088) (QUOTE (-553 (-800 (-327)))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-800 (-483))))) (|HasCategory| (-1088) (QUOTE (-553 (-800 (-483)))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-472)))) (|HasCategory| (-1088) (QUOTE (-553 (-472))))) (|HasCategory| |#1| (QUOTE (-580 (-483)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-347 (-483))))) (|HasCategory| |#1| (QUOTE (-950 (-483)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-347 (-483))))) (|HasCategory| |#1| (QUOTE (-950 (-347 (-483)))))) (|HasCategory| |#1| (QUOTE (-950 (-347 (-483))))) (|HasCategory| |#1| (QUOTE (-311))) (|HasAttribute| |#1| (QUOTE -3987)) (|HasCategory| |#1| (QUOTE (-389))) (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) 
-(-858 R S) 
+(((-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| (-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 -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))))) 
+(-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 
 NIL 
-(-859 |x| R) 
+(-860 |x| R) 
 ((|constructor| (NIL "This package is primarily to help the interpreter do coercions. It allows you to view a polynomial as a univariate polynomial in one of its variables with coefficients which are again a polynomial in all the other variables.")) (|univariate| (((|UnivariatePolynomial| |#1| (|Polynomial| |#2|)) (|Polynomial| |#2|) (|Variable| |#1|)) "\\spad{univariate(p, x)} converts the polynomial \\spad{p} to a one of type \\spad{UnivariatePolynomial(x,Polynomial(R))},{} ie. as a member of \\spad{R[...][x]}."))) 
 NIL 
 NIL 
-(-860 S R E |VarSet|) 
+(-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 (-821))) (|HasAttribute| |#2| (QUOTE -3987)) (|HasCategory| |#2| (QUOTE (-389))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#4| (QUOTE (-796 (-327)))) (|HasCategory| |#2| (QUOTE (-796 (-327)))) (|HasCategory| |#4| (QUOTE (-796 (-483)))) (|HasCategory| |#2| (QUOTE (-796 (-483)))) (|HasCategory| |#4| (QUOTE (-553 (-800 (-327))))) (|HasCategory| |#2| (QUOTE (-553 (-800 (-327))))) (|HasCategory| |#4| (QUOTE (-553 (-800 (-483))))) (|HasCategory| |#2| (QUOTE (-553 (-800 (-483))))) (|HasCategory| |#4| (QUOTE (-553 (-472)))) (|HasCategory| |#2| (QUOTE (-553 (-472))))) 
-(-861 R E |VarSet|) 
+((|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))))) 
+(-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}."))) 
-(((-3991 "*") |has| |#1| (-146)) (-3982 |has| |#1| (-494)) (-3987 |has| |#1| (-6 -3987)) (-3984 . T) (-3983 . T) (-3986 . T)) 
+(((-3993 "*") |has| |#1| (-146)) (-3984 |has| |#1| (-495)) (-3989 |has| |#1| (-6 -3989)) (-3986 . T) (-3985 . T) (-3988 . T)) 
 NIL 
-(-862 E V R P -3088) 
+(-863 E V R P -3090) 
 ((|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 
-(-863 E |Vars| R P S) 
+(-864 E |Vars| R P S) 
 ((|constructor| (NIL "This package provides a very general map function,{} which given a set \\spad{S} and polynomials over \\spad{R} with maps from the variables into \\spad{S} and the coefficients into \\spad{S},{} maps polynomials into \\spad{S}. \\spad{S} is assumed to support \\spad{+},{} \\spad{*} and \\spad{**}.")) (|map| ((|#5| (|Mapping| |#5| |#2|) (|Mapping| |#5| |#3|) |#4|) "\\spad{map(varmap, coefmap, p)} takes a \\spad{varmap},{} a mapping from the variables of polynomial \\spad{p} into \\spad{S},{} \\spad{coefmap},{} a mapping from coefficients of \\spad{p} into \\spad{S},{} and \\spad{p},{} and produces a member of \\spad{S} using the corresponding arithmetic. in \\spad{S}"))) 
 NIL 
 NIL 
-(-864 E V R P -3088) 
+(-865 E V R P -3090) 
 ((|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| $) "\\spad{numer(x)} \\undocumented"))) 
 NIL 
 ((|HasCategory| |#3| (QUOTE (-389)))) 
-(-865) 
+(-866) 
 ((|constructor| (NIL "This domain represents network port numbers (notable TCP and UDP).")) (|port| (($ (|SingleInteger|)) "\\spad{port(n)} constructs a PortNumber from the integer `n'."))) 
 NIL 
 NIL 
-(-866) 
+(-867) 
 ((|constructor| (NIL "PlottablePlaneCurveCategory is the category of curves in the plane which may be plotted via the graphics facilities. Functions are provided for obtaining lists of lists of points,{} representing the branches of the curve,{} and for determining the ranges of the \\spad{x}-coordinates and \\spad{y}-coordinates of the points on the curve.")) (|yRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{yRange(c)} returns the range of the \\spad{y}-coordinates of the points on the curve \\spad{c}.")) (|xRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{xRange(c)} returns the range of the \\spad{x}-coordinates of the points on the curve \\spad{c}.")) (|listBranches| (((|List| (|List| (|Point| (|DoubleFloat|)))) $) "\\spad{listBranches(c)} returns a list of lists of points,{} representing the branches of the curve \\spad{c}."))) 
 NIL 
 NIL 
-(-867 R E) 
+(-868 R E) 
 ((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and terms indexed by their exponents (from an arbitrary ordered abelian monoid). This type is used,{} for example,{} by the \\spadtype{DistributedMultivariatePolynomial} domain where the exponent domain is a direct product of non negative integers.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (|fmecg| (($ $ |#2| |#1| $) "\\spad{fmecg(p1,e,r,p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}"))) 
-(((-3991 "*") |has| |#1| (-146)) (-3982 |has| |#1| (-494)) (-3987 |has| |#1| (-6 -3987)) (-3983 . T) (-3984 . T) (-3986 . T)) 
-((|HasCategory| |#1| (QUOTE (-38 (-347 (-483))))) (|HasCategory| |#1| (QUOTE (-494))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-494)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (OR (|HasCategory| |#1| (QUOTE (-38 (-347 (-483))))) (|HasCategory| |#1| (QUOTE (-950 (-347 (-483)))))) (|HasCategory| |#1| (QUOTE (-950 (-347 (-483))))) (|HasCategory| |#1| (QUOTE (-950 (-483)))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-389))) (-12 (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#2| (QUOTE (-104)))) (|HasAttribute| |#1| (QUOTE -3987))) 
-(-868 R L) 
+(((-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))) 
+(-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 
-(-869 S) 
+(-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"))) 
-((-3990 . T) (-3989 . T)) 
-((OR (-12 (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-553 (-472)))) (OR (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| |#1| (QUOTE (-756))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| (-483) (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|))))) 
-(-870 A B) 
+((-3992 . T) (-3991 . 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),...]}."))) 
 NIL 
 NIL 
-(-871) 
+(-872) 
 ((|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 
-(-872 -3088) 
+(-873 -3090) 
 ((|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 
-(-873 I) 
+(-874 I) 
 ((|constructor| (NIL "The \\spadtype{IntegerPrimesPackage} implements a modification of Rabin's probabilistic primality test and the utility functions \\spadfun{nextPrime},{} \\spadfun{prevPrime} and \\spadfun{primes}.")) (|primes| (((|List| |#1|) |#1| |#1|) "\\spad{primes(a,b)} returns a list of all primes \\spad{p} with \\spad{a <= p <= b}")) (|prevPrime| ((|#1| |#1|) "\\spad{prevPrime(n)} returns the largest prime strictly smaller than \\spad{n}")) (|nextPrime| ((|#1| |#1|) "\\spad{nextPrime(n)} returns the smallest prime strictly larger than \\spad{n}")) (|prime?| (((|Boolean|) |#1|) "\\spad{prime?(n)} returns \\spad{true} if \\spad{n} is prime and \\spad{false} if not. The algorithm used is Rabin's probabilistic primality test (reference: Knuth Volume 2 Semi Numerical Algorithms). If \\spad{prime? n} returns \\spad{false},{} \\spad{n} is proven composite. If \\spad{prime? n} returns \\spad{true},{} prime? may be in error however,{} the probability of error is very low. and is zero below 25*10**9 (due to a result of Pomerance et al),{} below 10**12 and 10**13 due to results of Pinch,{} and below 341550071728321 due to a result of Jaeschke. Specifically,{} this implementation does at least 10 pseudo prime tests and so the probability of error is \\spad{< 4**(-10)}. The running time of this method is cubic in the length of the input \\spad{n},{} that is \\spad{O( (log n)**3 )},{} for \\spad{n<10**20}. beyond that,{} the algorithm is quartic,{} \\spad{O( (log n)**4 )}. Two improvements due to Davenport have been incorporated which catches some trivial strong pseudo-primes,{} such as [Jaeschke,{} 1991] 1377161253229053 * 413148375987157,{} which the original algorithm regards as prime"))) 
 NIL 
 NIL 
-(-874) 
+(-875) 
 ((|constructor| (NIL "PrintPackage provides a print function for output forms.")) (|print| (((|Void|) (|OutputForm|)) "\\spad{print(o)} writes the output form \\spad{o} on standard output using the two-dimensional formatter."))) 
 NIL 
 NIL 
-(-875 A B) 
+(-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"))) 
-((-3986 -12 (|has| |#2| (-410)) (|has| |#1| (-410)))) 
-((OR (-12 (|HasCategory| |#1| (QUOTE (-717))) (|HasCategory| |#2| (QUOTE (-717)))) (-12 (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#2| (QUOTE (-756))))) (-12 (|HasCategory| |#1| (QUOTE (-717))) (|HasCategory| |#2| (QUOTE (-717)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-104)))) (-12 (|HasCategory| |#1| (QUOTE (-717))) (|HasCategory| |#2| (QUOTE (-717)))) (-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 (-717))) (|HasCategory| |#2| (QUOTE (-717)))) (-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 (-663))) (|HasCategory| |#2| (QUOTE (-663))))) (-12 (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#2| (QUOTE (-317)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-104)))) (-12 (|HasCategory| |#1| (QUOTE (-717))) (|HasCategory| |#2| (QUOTE (-717)))) (-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 (-663))) (|HasCategory| |#2| (QUOTE (-663))))) (-12 (|HasCategory| |#1| (QUOTE (-663))) (|HasCategory| |#2| (QUOTE (-663)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-104)))) (-12 (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#2| (QUOTE (-756))))) 
-(-876) 
+((-3988 -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|) $) "\\spad{name(p)} returns the name of property \\spad{p}"))) 
 NIL 
 NIL 
-(-877 T$) 
+(-878 T$) 
 ((|constructor| (NIL "This domain implements propositional formula build over a term domain,{} that itself belongs to PropositionalLogic")) (|disjunction| (($ $ $) "\\spad{disjunction(p,q)} returns a formula denoting the disjunction of \\spad{p} and \\spad{q}.")) (|conjunction| (($ $ $) "\\spad{conjunction(p,q)} returns a formula denoting the conjunction of \\spad{p} and \\spad{q}.")) (|isEquiv| (((|Maybe| (|Pair| $ $)) $) "\\spad{isEquiv f} returns a value \\spad{v} such that \\spad{v case Pair(\\%,\\%)} holds if the formula \\spad{f} is an equivalence formula.")) (|isImplies| (((|Maybe| (|Pair| $ $)) $) "\\spad{isImplies f} returns a value \\spad{v} such that \\spad{v case Pair(\\%,\\%)} holds if the formula \\spad{f} is an implication formula.")) (|isOr| (((|Maybe| (|Pair| $ $)) $) "\\spad{isOr f} returns a value \\spad{v} such that \\spad{v case Pair(\\%,\\%)} holds if the formula \\spad{f} is a disjunction formula.")) (|isAnd| (((|Maybe| (|Pair| $ $)) $) "\\spad{isAnd f} returns a value \\spad{v} such that \\spad{v case Pair(\\%,\\%)} holds if the formula \\spad{f} is a conjunction formula.")) (|isNot| (((|Maybe| $) $) "\\spad{isNot f} returns a value \\spad{v} such that \\spad{v case \\%} holds if the formula \\spad{f} is a negation.")) (|isAtom| (((|Maybe| |#1|) $) "\\spad{isAtom f} returns a value \\spad{v} such that \\spad{v case T} holds if the formula \\spad{f} is a term."))) 
 NIL 
 NIL 
-(-878 T$) 
+(-879 T$) 
 ((|constructor| (NIL "This package collects unary functions operating on propositional formulae.")) (|simplify| (((|PropositionalFormula| |#1|) (|PropositionalFormula| |#1|)) "\\spad{simplify f} returns a formula logically equivalent to \\spad{f} where obvious tautologies have been removed.")) (|atoms| (((|Set| |#1|) (|PropositionalFormula| |#1|)) "\\spad{atoms f} ++ returns the set of atoms appearing in the formula \\spad{f}.")) (|dual| (((|PropositionalFormula| |#1|) (|PropositionalFormula| |#1|)) "\\spad{dual f} returns the dual of the proposition \\spad{f}."))) 
 NIL 
 NIL 
-(-879 S T$) 
+(-880 S T$) 
 ((|constructor| (NIL "This package collects binary functions operating on propositional formulae.")) (|map| (((|PropositionalFormula| |#2|) (|Mapping| |#2| |#1|) (|PropositionalFormula| |#1|)) "\\spad{map(f,x)} returns a propositional formula where all atoms in \\spad{x} have been replaced by the result of applying the function \\spad{f} to them."))) 
 NIL 
 NIL 
-(-880) 
+(-881) 
 ((|constructor| (NIL "This category declares the connectives of Propositional Logic.")) (|equiv| (($ $ $) "\\spad{equiv(p,q)} returns the logical equivalence of `p',{} `q'.")) (|implies| (($ $ $) "\\spad{implies(p,q)} returns the logical implication of `q' by `p'.")) (|false| (($) "\\spad{false} is a logical constant.")) (|true| (($) "\\spad{true} is a logical constant."))) 
 NIL 
 NIL 
-(-881 S) 
+(-882 S) 
 ((|constructor| (NIL "A priority queue is a bag of items from an ordered set where the item extracted is always the maximum element.")) (|merge!| (($ $ $) "\\spad{merge!(q,q1)} destructively changes priority queue \\spad{q} to include the values from priority queue \\spad{q1}.")) (|merge| (($ $ $) "\\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}."))) 
-((-3989 . T) (-3990 . T)) 
+((-3991 . T) (-3992 . T)) 
 NIL 
-(-882 R |polR|) 
+(-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}}"))) 
 NIL 
 ((|HasCategory| |#1| (QUOTE (-389)))) 
-(-883) 
+(-884) 
 ((|constructor| (NIL "This domain represents `pretend' expressions.")) (|target| (((|TypeAst|) $) "\\spad{target(e)} returns the target type of the conversion..")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression being converted."))) 
 NIL 
 NIL 
-(-884) 
+(-885) 
 ((|constructor| (NIL "Partition is an OrderedCancellationAbelianMonoid which is used as the basis for symmetric polynomial representation of the sums of powers in SymmetricPolynomial. Thus,{} \\spad{(5 2 2 1)} will represent \\spad{s5 * s2**2 * s1}.")) (|conjugate| (($ $) "\\spad{conjugate(p)} returns the conjugate partition of a partition \\spad{p}")) (|pdct| (((|PositiveInteger|) $) "\\spad{pdct(a1**n1 a2**n2 ...)} returns \\spad{n1! * a1**n1 * n2! * a2**n2 * ...}. This function is used in the package \\spadtype{CycleIndicators}.")) (|powers| (((|List| (|Pair| (|PositiveInteger|) (|PositiveInteger|))) $) "\\spad{powers(x)} returns a list of pairs. The second component of each pair is the multiplicity with which the first component occurs in \\spad{li}.")) (|partitions| (((|Stream| $) (|NonNegativeInteger|)) "\\spad{partitions n} returns the stream of all partitions of size \\spad{n}.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\#x} returns the sum of all parts of the partition \\spad{x}.")) (|parts| (((|List| (|PositiveInteger|)) $) "\\spad{parts x} returns the list of decreasing integer sequence making up the partition \\spad{x}.")) (|partition| (($ (|List| (|PositiveInteger|))) "\\spad{partition(li)} converts a list of integers \\spad{li} to a partition"))) 
 NIL 
 NIL 
-(-885 S |Coef| |Expon| |Var|) 
+(-886 S |Coef| |Expon| |Var|) 
 ((|constructor| (NIL "\\spadtype{PowerSeriesCategory} is the most general power series category with exponents in an ordered abelian monoid.")) (|complete| (($ $) "\\spad{complete(f)} causes all terms of \\spad{f} to be computed. Note: this results in an infinite loop if \\spad{f} has infinitely many terms.")) (|pole?| (((|Boolean|) $) "\\spad{pole?(f)} determines if the power series \\spad{f} has a pole.")) (|variables| (((|List| |#4|) $) "\\spad{variables(f)} returns a list of the variables occuring in the power series \\spad{f}.")) (|degree| ((|#3| $) "\\spad{degree(f)} returns the exponent of the lowest order term of \\spad{f}.")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(f)} returns the coefficient of the lowest order term of \\spad{f}")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(f)} returns the monomial of \\spad{f} of lowest order.")) (|monomial| (($ $ (|List| |#4|) (|List| |#3|)) "\\spad{monomial(a,[x1,..,xk],[n1,..,nk])} computes \\spad{a * x1**n1 * .. * xk**nk}.") (($ $ |#4| |#3|) "\\spad{monomial(a,x,n)} computes \\spad{a*x**n}."))) 
 NIL 
 NIL 
-(-886 |Coef| |Expon| |Var|) 
+(-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}."))) 
-(((-3991 "*") |has| |#1| (-146)) (-3982 |has| |#1| (-494)) (-3983 . T) (-3984 . T) (-3986 . T)) 
+(((-3993 "*") |has| |#1| (-146)) (-3984 |has| |#1| (-495)) (-3985 . T) (-3986 . T) (-3988 . T)) 
 NIL 
-(-887) 
+(-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}."))) 
 NIL 
 NIL 
-(-888 S R E |VarSet| P) 
+(-889 S R E |VarSet| P) 
 ((|constructor| (NIL "A category for finite subsets of a polynomial ring. Such a set is only regarded as a set of polynomials and not identified to the ideal it generates. So two distinct sets may generate the same the ideal. Furthermore,{} for \\spad{R} being an integral domain,{} a set of polynomials may be viewed as a representation of the ideal it generates in the polynomial ring \\spad{(R)^(-1) P},{} or the set of its zeros (described for instance by the radical of the previous ideal,{} or a split of the associated affine variety) and so on. So this category provides operations about those different notions.")) (|triangular?| (((|Boolean|) $) "\\axiom{triangular?(ps)} returns \\spad{true} iff \\axiom{ps} is a triangular set,{} \\spadignore{i.e.} two distinct polynomials have distinct main variables and no constant lies in \\axiom{ps}.")) (|rewriteIdealWithRemainder| (((|List| |#5|) (|List| |#5|) $) "\\axiom{rewriteIdealWithRemainder(lp,{}cs)} returns \\axiom{lr} such that every polynomial in \\axiom{lr} is fully reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{cs} and \\axiom{(lp,{}cs)} and \\axiom{(lr,{}cs)} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}.")) (|rewriteIdealWithHeadRemainder| (((|List| |#5|) (|List| |#5|) $) "\\axiom{rewriteIdealWithHeadRemainder(lp,{}cs)} returns \\axiom{lr} such that the leading monomial of every polynomial in \\axiom{lr} is reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{cs} and \\axiom{(lp,{}cs)} and \\axiom{(lr,{}cs)} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}.")) (|remainder| (((|Record| (|:| |rnum| |#2|) (|:| |polnum| |#5|) (|:| |den| |#2|)) |#5| $) "\\axiom{remainder(a,{}ps)} returns \\axiom{[\\spad{c},{}\\spad{b},{}\\spad{r}]} such that \\axiom{\\spad{b}} is fully reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ps},{} \\axiom{r*a - c*b} lies in the ideal generated by \\axiom{ps}. Furthermore,{} if \\axiom{\\spad{R}} is a gcd-domain,{} \\axiom{\\spad{b}} is primitive.")) (|headRemainder| (((|Record| (|:| |num| |#5|) (|:| |den| |#2|)) |#5| $) "\\axiom{headRemainder(a,{}ps)} returns \\axiom{[\\spad{b},{}\\spad{r}]} such that the leading monomial of \\axiom{\\spad{b}} is reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ps} and \\axiom{r*a - \\spad{b}} lies in the ideal generated by \\axiom{ps}.")) (|roughUnitIdeal?| (((|Boolean|) $) "\\axiom{roughUnitIdeal?(ps)} returns \\spad{true} iff \\axiom{ps} contains some non null element lying in the base ring \\axiom{\\spad{R}}.")) (|roughEqualIdeals?| (((|Boolean|) $ $) "\\axiom{roughEqualIdeals?(\\spad{ps1},{}\\spad{ps2})} returns \\spad{true} iff it can proved that \\axiom{\\spad{ps1}} and \\axiom{\\spad{ps2}} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}} without computing Groebner bases.")) (|roughSubIdeal?| (((|Boolean|) $ $) "\\axiom{roughSubIdeal?(\\spad{ps1},{}\\spad{ps2})} returns \\spad{true} iff it can proved that all polynomials in \\axiom{\\spad{ps1}} lie in the ideal generated by \\axiom{\\spad{ps2}} in \\axiom{\\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}} without computing Groebner bases.")) (|roughBase?| (((|Boolean|) $) "\\axiom{roughBase?(ps)} returns \\spad{true} iff for every pair \\axiom{{\\spad{p},{}\\spad{q}}} of polynomials in \\axiom{ps} their leading monomials are relatively prime.")) (|trivialIdeal?| (((|Boolean|) $) "\\axiom{trivialIdeal?(ps)} returns \\spad{true} iff \\axiom{ps} does not contain non-zero elements.")) (|sort| (((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |#4|) "\\axiom{sort(\\spad{v},{}ps)} returns \\axiom{us,{}vs,{}ws} such that \\axiom{us} is \\axiom{collectUnder(ps,{}\\spad{v})},{} \\axiom{vs} is \\axiom{collect(ps,{}\\spad{v})} and \\axiom{ws} is \\axiom{collectUpper(ps,{}\\spad{v})}.")) (|collectUpper| (($ $ |#4|) "\\axiom{collectUpper(ps,{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{ps} with main variable greater than \\axiom{\\spad{v}}.")) (|collect| (($ $ |#4|) "\\axiom{collect(ps,{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{ps} with \\axiom{\\spad{v}} as main variable.")) (|collectUnder| (($ $ |#4|) "\\axiom{collectUnder(ps,{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{ps} with main variable less than \\axiom{\\spad{v}}.")) (|mainVariable?| (((|Boolean|) |#4| $) "\\axiom{mainVariable?(\\spad{v},{}ps)} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{ps}.")) (|mainVariables| (((|List| |#4|) $) "\\axiom{mainVariables(ps)} returns the decreasingly sorted list of the variables which are main variables of some polynomial in \\axiom{ps}.")) (|variables| (((|List| |#4|) $) "\\axiom{variables(ps)} returns the decreasingly sorted list of the variables which are variables of some polynomial in \\axiom{ps}.")) (|mvar| ((|#4| $) "\\axiom{mvar(ps)} returns the main variable of the non constant polynomial with the greatest main variable,{} if any,{} else an error is returned.")) (|retract| (($ (|List| |#5|)) "\\axiom{retract(lp)} returns an element of the domain whose elements are the members of \\axiom{lp} if such an element exists,{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|List| |#5|)) "\\axiom{retractIfCan(lp)} returns an element of the domain whose elements are the members of \\axiom{lp} if such an element exists,{} otherwise \\axiom{\"failed\"} is returned."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-494)))) 
-(-889 R E |VarSet| P) 
+((|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."))) 
-((-3989 . T)) 
+((-3991 . T)) 
 NIL 
-(-890 R E V P) 
+(-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."))) 
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 ((-12 (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-257)))) (|HasCategory| |#1| (QUOTE (-389)))) 
-(-891 K) 
+(-892 K) 
 ((|constructor| (NIL "PseudoLinearNormalForm provides a function for computing a block-companion form for pseudo-linear operators.")) (|companionBlocks| (((|List| (|Record| (|:| C (|Matrix| |#1|)) (|:| |g| (|Vector| |#1|)))) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{companionBlocks(m, v)} returns \\spad{[[C_1, g_1],...,[C_k, g_k]]} such that each \\spad{C_i} is a companion block and \\spad{m = diagonal(C_1,...,C_k)}.")) (|changeBase| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{changeBase(M, A, sig, der)}: computes the new matrix of a pseudo-linear transform given by the matrix \\spad{M} under the change of base A")) (|normalForm| (((|Record| (|:| R (|Matrix| |#1|)) (|:| A (|Matrix| |#1|)) (|:| |Ainv| (|Matrix| |#1|))) (|Matrix| |#1|) (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{normalForm(M, sig, der)} returns \\spad{[R, A, A^{-1}]} such that the pseudo-linear operator whose matrix in the basis \\spad{y} is \\spad{M} had matrix \\spad{R} in the basis \\spad{z = A y}. \\spad{der} is a \\spad{sig}-derivation."))) 
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-(-892 |VarSet| E RC P) 
+(-893 |VarSet| E RC P) 
 ((|constructor| (NIL "This package computes square-free decomposition of multivariate polynomials over a coefficient ring which is an arbitrary gcd domain. The requirement on the coefficient domain guarantees that the \\spadfun{content} can be removed so that factors will be primitive as well as square-free. Over an infinite ring of finite characteristic,{}it may not be possible to guarantee that the factors are square-free.")) (|squareFree| (((|Factored| |#4|) |#4|) "\\spad{squareFree(p)} returns the square-free factorization of the polynomial \\spad{p}. Each factor has no repeated roots,{} and the factors are pairwise relatively prime."))) 
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-(-893 R) 
+(-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}."))) 
-((-3990 . T) (-3989 . T)) 
+((-3992 . T) (-3991 . T)) 
 NIL 
-(-894 R1 R2) 
+(-895 R1 R2) 
 ((|constructor| (NIL "This package \\undocumented")) (|map| (((|Point| |#2|) (|Mapping| |#2| |#1|) (|Point| |#1|)) "\\spad{map(f,p)} \\undocumented"))) 
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-(-895 R) 
+(-896 R) 
 ((|constructor| (NIL "This package \\undocumented")) (|shade| ((|#1| (|Point| |#1|)) "\\spad{shade(pt)} returns the fourth element of the two dimensional point,{} \\spad{pt},{} although no assumptions are made with regards as to how the components of higher dimensional points are interpreted. This function is defined for the convenience of the user using specifically,{} shade to express a fourth dimension.")) (|hue| ((|#1| (|Point| |#1|)) "\\spad{hue(pt)} returns the third element of the two dimensional point,{} \\spad{pt},{} although no assumptions are made with regards as to how the components of higher dimensional points are interpreted. This function is defined for the convenience of the user using specifically,{} hue to express a third dimension.")) (|color| ((|#1| (|Point| |#1|)) "\\spad{color(pt)} returns the fourth element of the point,{} \\spad{pt},{} although no assumptions are made with regards as to how the components of higher dimensional points are interpreted. This function is defined for the convenience of the user using specifically,{} color to express a fourth dimension.")) (|phiCoord| ((|#1| (|Point| |#1|)) "\\spad{phiCoord(pt)} returns the third element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a spherical coordinate system.")) (|thetaCoord| ((|#1| (|Point| |#1|)) "\\spad{thetaCoord(pt)} returns the second element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a spherical or a cylindrical coordinate system.")) (|rCoord| ((|#1| (|Point| |#1|)) "\\spad{rCoord(pt)} returns the first element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a spherical or a cylindrical coordinate system.")) (|zCoord| ((|#1| (|Point| |#1|)) "\\spad{zCoord(pt)} returns the third element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a Cartesian or a cylindrical coordinate system.")) (|yCoord| ((|#1| (|Point| |#1|)) "\\spad{yCoord(pt)} returns the second element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a Cartesian coordinate system.")) (|xCoord| ((|#1| (|Point| |#1|)) "\\spad{xCoord(pt)} returns the first element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a Cartesian coordinate system."))) 
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-(-896 K) 
+(-897 K) 
 ((|constructor| (NIL "This is the description of any package which provides partial functions on a domain belonging to TranscendentalFunctionCategory.")) (|acschIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acschIfCan(z)} returns acsch(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|asechIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{asechIfCan(z)} returns asech(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|acothIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acothIfCan(z)} returns acoth(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|atanhIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{atanhIfCan(z)} returns atanh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|acoshIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acoshIfCan(z)} returns acosh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|asinhIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{asinhIfCan(z)} returns asinh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|cschIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cschIfCan(z)} returns csch(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|sechIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{sechIfCan(z)} returns sech(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|cothIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cothIfCan(z)} returns coth(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|tanhIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{tanhIfCan(z)} returns tanh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|coshIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{coshIfCan(z)} returns cosh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|sinhIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{sinhIfCan(z)} returns sinh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|acscIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acscIfCan(z)} returns acsc(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|asecIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{asecIfCan(z)} returns asec(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|acotIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acotIfCan(z)} returns acot(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|atanIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{atanIfCan(z)} returns atan(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|acosIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acosIfCan(z)} returns acos(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|asinIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{asinIfCan(z)} returns asin(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|cscIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cscIfCan(z)} returns csc(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|secIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{secIfCan(z)} returns sec(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|cotIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cotIfCan(z)} returns cot(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|tanIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{tanIfCan(z)} returns tan(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|cosIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cosIfCan(z)} returns cos(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|sinIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{sinIfCan(z)} returns sin(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|logIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{logIfCan(z)} returns log(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|expIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{expIfCan(z)} returns exp(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|nthRootIfCan| (((|Union| |#1| "failed") |#1| (|NonNegativeInteger|)) "\\spad{nthRootIfCan(z,n)} returns the \\spad{n}th root of \\spad{z} if possible,{} and \"failed\" otherwise."))) 
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-(-897 R E OV PPR) 
+(-898 R E OV PPR) 
 ((|constructor| (NIL "This package \\undocumented{}")) (|map| ((|#4| (|Mapping| |#4| (|Polynomial| |#1|)) |#4|) "\\spad{map(f,p)} \\undocumented{}")) (|pushup| ((|#4| |#4| (|List| |#3|)) "\\spad{pushup(p,lv)} \\undocumented{}") ((|#4| |#4| |#3|) "\\spad{pushup(p,v)} \\undocumented{}")) (|pushdown| ((|#4| |#4| (|List| |#3|)) "\\spad{pushdown(p,lv)} \\undocumented{}") ((|#4| |#4| |#3|) "\\spad{pushdown(p,v)} \\undocumented{}")) (|variable| (((|Union| $ "failed") (|Symbol|)) "\\spad{variable(s)} makes an element from symbol \\spad{s} or fails")) (|convert| (((|Symbol|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) 
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-(-898 K R UP -3088) 
+(-899 K R UP -3090) 
 ((|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)}."))) 
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-(-899 R |Var| |Expon| |Dpoly|) 
+(-900 R |Var| |Expon| |Dpoly|) 
 ((|constructor| (NIL "\\spadtype{QuasiAlgebraicSet} constructs a domain representing quasi-algebraic sets,{} which is the intersection of a Zariski closed set,{} defined as the common zeros of a given list of polynomials (the defining polynomials for equations),{} and a principal Zariski open set,{} defined as the complement of the common zeros of a polynomial \\spad{f} (the defining polynomial for the inequation). This domain provides simplification of a user-given representation using groebner basis computations. There are two simplification routines: the first function \\spadfun{idealSimplify} uses groebner basis of ideals alone,{} while the second,{} \\spadfun{simplify} uses both groebner basis and factorization. The resulting defining equations \\spad{L} always form a groebner basis,{} and the resulting defining inequation \\spad{f} is always reduced. The function \\spadfun{simplify} may be applied several times if desired. A third simplification routine \\spadfun{radicalSimplify} is provided in \\spadtype{QuasiAlgebraicSet2} for comparison study only,{} as it is inefficient compared to the other two,{} as well as is restricted to only certain coefficient domains. For detail analysis and a comparison of the three methods,{} please consult the reference cited. \\blankline A polynomial function \\spad{q} defined on the quasi-algebraic set is equivalent to its reduced form with respect to \\spad{L}. While this may be obtained using the usual normal form algorithm,{} there is no canonical form for \\spad{q}. \\blankline The ordering in groebner basis computation is determined by the data type of the input polynomials. If it is possible we suggest to use refinements of total degree orderings.")) (|simplify| (($ $) "\\spad{simplify(s)} returns a different and presumably simpler representation of \\spad{s} with the defining polynomials for the equations forming a groebner basis,{} and the defining polynomial for the inequation reduced with respect to the basis,{} using a heuristic algorithm based on factoring.")) (|idealSimplify| (($ $) "\\spad{idealSimplify(s)} returns a different and presumably simpler representation of \\spad{s} with the defining polynomials for the equations forming a groebner basis,{} and the defining polynomial for the inequation reduced with respect to the basis,{} using Buchberger's algorithm.")) (|definingInequation| ((|#4| $) "\\spad{definingInequation(s)} returns a single defining polynomial for the inequation,{} that is,{} the Zariski open part of \\spad{s}.")) (|definingEquations| (((|List| |#4|) $) "\\spad{definingEquations(s)} returns a list of defining polynomials for equations,{} that is,{} for the Zariski closed part of \\spad{s}.")) (|empty?| (((|Boolean|) $) "\\spad{empty?(s)} returns \\spad{true} if the quasialgebraic set \\spad{s} has no points,{} and \\spad{false} otherwise.")) (|setStatus| (($ $ (|Union| (|Boolean|) #1="failed")) "\\spad{setStatus(s,t)} returns the same representation for \\spad{s},{} but asserts the following: if \\spad{t} is \\spad{true},{} then \\spad{s} is empty,{} if \\spad{t} is \\spad{false},{} then \\spad{s} is non-empty,{} and if \\spad{t} = \"failed\",{} then no assertion is made (that is,{} \"don't know\"). Note: for internal use only,{} with care.")) (|status| (((|Union| (|Boolean|) #1#) $) "\\spad{status(s)} returns \\spad{true} if the quasi-algebraic set is empty,{} \\spad{false} if it is not,{} and \"failed\" if not yet known")) (|quasiAlgebraicSet| (($ (|List| |#4|) |#4|) "\\spad{quasiAlgebraicSet(pl,q)} returns the quasi-algebraic set with defining equations \\spad{p} = 0 for \\spad{p} belonging to the list \\spad{pl},{} and defining inequation \\spad{q} ~= 0.")) (|empty| (($) "\\spad{empty()} returns the empty quasi-algebraic set"))) 
 NIL 
 ((-12 (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-257))))) 
-(-900 |vl| |nv|) 
+(-901 |vl| |nv|) 
 ((|constructor| (NIL "\\spadtype{QuasiAlgebraicSet2} adds a function \\spadfun{radicalSimplify} which uses \\spadtype{IdealDecompositionPackage} to simplify the representation of a quasi-algebraic set. A quasi-algebraic set is the intersection of a Zariski closed set,{} defined as the common zeros of a given list of polynomials (the defining polynomials for equations),{} and a principal Zariski open set,{} defined as the complement of the common zeros of a polynomial \\spad{f} (the defining polynomial for the inequation). Quasi-algebraic sets are implemented in the domain \\spadtype{QuasiAlgebraicSet},{} where two simplification routines are provided: \\spadfun{idealSimplify} and \\spadfun{simplify}. The function \\spadfun{radicalSimplify} is added for comparison study only. Because the domain \\spadtype{IdealDecompositionPackage} provides facilities for computing with radical ideals,{} it is necessary to restrict the ground ring to the domain \\spadtype{Fraction Integer},{} and the polynomial ring to be of type \\spadtype{DistributedMultivariatePolynomial}. The routine \\spadfun{radicalSimplify} uses these to compute groebner basis of radical ideals and is inefficient and restricted when compared to the two in \\spadtype{QuasiAlgebraicSet}.")) (|radicalSimplify| (((|QuasiAlgebraicSet| (|Fraction| (|Integer|)) (|OrderedVariableList| |#1|) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|)))) (|QuasiAlgebraicSet| (|Fraction| (|Integer|)) (|OrderedVariableList| |#1|) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{radicalSimplify(s)} returns a different and presumably simpler representation of \\spad{s} with the defining polynomials for the equations forming a groebner basis,{} and the defining polynomial for the inequation reduced with respect to the basis,{} using using groebner basis of radical ideals"))) 
 NIL 
 NIL 
-(-901 R E V P TS) 
+(-902 R E V P TS) 
 ((|constructor| (NIL "A package for removing redundant quasi-components and redundant branches when decomposing a variety by means of quasi-components of regular triangular sets. \\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|branchIfCan| (((|Union| (|Record| (|:| |eq| (|List| |#4|)) (|:| |tower| |#5|) (|:| |ineq| (|List| |#4|))) "failed") (|List| |#4|) |#5| (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{branchIfCan(leq,{}ts,{}lineq,{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement.")) (|prepareDecompose| (((|List| (|Record| (|:| |eq| (|List| |#4|)) (|:| |tower| |#5|) (|:| |ineq| (|List| |#4|)))) (|List| |#4|) (|List| |#5|) (|Boolean|) (|Boolean|)) "\\axiom{prepareDecompose(lp,{}lts,{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|removeSuperfluousCases| (((|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|)))) "\\axiom{removeSuperfluousCases(llpwt)} is an internal subroutine,{} exported only for developement.")) (|subCase?| (((|Boolean|) (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|)) (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) "\\axiom{subCase?(\\spad{lpwt1},{}\\spad{lpwt2})} is an internal subroutine,{} exported only for developement.")) (|removeSuperfluousQuasiComponents| (((|List| |#5|) (|List| |#5|)) "\\axiom{removeSuperfluousQuasiComponents(lts)} removes from \\axiom{lts} any \\spad{ts} such that \\axiom{subQuasiComponent?(ts,{}us)} holds for another \\spad{us} in \\axiom{lts}.")) (|subQuasiComponent?| (((|Boolean|) |#5| (|List| |#5|)) "\\axiom{subQuasiComponent?(ts,{}lus)} returns \\spad{true} iff \\axiom{subQuasiComponent?(ts,{}us)} holds for one \\spad{us} in \\spad{lus}.") (((|Boolean|) |#5| |#5|) "\\axiom{subQuasiComponent?(ts,{}us)} returns \\spad{true} iff \\axiomOpFrom{internalSubQuasiComponent?}{QuasiComponentPackage} returs \\spad{true}.")) (|internalSubQuasiComponent?| (((|Union| (|Boolean|) "failed") |#5| |#5|) "\\axiom{internalSubQuasiComponent?(ts,{}us)} returns a boolean \\spad{b} value if the fact that the regular zero set of \\axiom{us} contains that of \\axiom{ts} can be decided (and in that case \\axiom{\\spad{b}} gives this inclusion) otherwise returns \\axiom{\"failed\"}.")) (|infRittWu?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{infRittWu?(\\spad{lp1},{}\\spad{lp2})} is an internal subroutine,{} exported only for developement.")) (|internalInfRittWu?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{internalInfRittWu?(\\spad{lp1},{}\\spad{lp2})} is an internal subroutine,{} exported only for developement.")) (|internalSubPolSet?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{internalSubPolSet?(\\spad{lp1},{}\\spad{lp2})} returns \\spad{true} iff \\axiom{\\spad{lp1}} is a sub-set of \\axiom{\\spad{lp2}} assuming that these lists are sorted increasingly \\spad{w}.\\spad{r}.\\spad{t}. \\axiomOpFrom{infRittWu?}{RecursivePolynomialCategory}.")) (|subPolSet?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{subPolSet?(\\spad{lp1},{}\\spad{lp2})} returns \\spad{true} iff \\axiom{\\spad{lp1}} is a sub-set of \\axiom{\\spad{lp2}}.")) (|subTriSet?| (((|Boolean|) |#5| |#5|) "\\axiom{subTriSet?(ts,{}us)} returns \\spad{true} iff \\axiom{ts} is a sub-set of \\axiom{us}.")) (|moreAlgebraic?| (((|Boolean|) |#5| |#5|) "\\axiom{moreAlgebraic?(ts,{}us)} returns \\spad{false} iff \\axiom{ts} and \\axiom{us} are both empty,{} or \\axiom{ts} has less elements than \\axiom{us},{} or some variable is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{us} and is not \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ts}.")) (|algebraicSort| (((|List| |#5|) (|List| |#5|)) "\\axiom{algebraicSort(lts)} sorts \\axiom{lts} \\spad{w}.\\spad{r}.\\spad{t} \\axiomOpFrom{supDimElseRittWu?}{QuasiComponentPackage}.")) (|supDimElseRittWu?| (((|Boolean|) |#5| |#5|) "\\axiom{supDimElseRittWu(ts,{}us)} returns \\spad{true} iff \\axiom{ts} has less elements than \\axiom{us} otherwise if \\axiom{ts} has higher rank than \\axiom{us} \\spad{w}.\\spad{r}.\\spad{t}. Riit and Wu ordering.")) (|stopTable!| (((|Void|)) "\\axiom{stopTableGcd!()} is an internal subroutine,{} exported only for developement.")) (|startTable!| (((|Void|) (|String|) (|String|) (|String|)) "\\axiom{startTableGcd!(\\spad{s1},{}\\spad{s2},{}\\spad{s3})} is an internal subroutine,{} exported only for developement."))) 
 NIL 
 NIL 
-(-902) 
+(-903) 
 ((|constructor| (NIL "This domain implements simple database queries")) (|value| (((|String|) $) "\\spad{value(q)} returns the value (\\spadignore{i.e.} right hand side) of \\axiom{\\spad{q}}.")) (|variable| (((|Symbol|) $) "\\spad{variable(q)} returns the variable (\\spadignore{i.e.} left hand side) of \\axiom{\\spad{q}}.")) (|equation| (($ (|Symbol|) (|String|)) "\\spad{equation(s,\"a\")} creates a new equation."))) 
 NIL 
 NIL 
-(-903 A S) 
+(-904 A S) 
 ((|constructor| (NIL "QuotientField(\\spad{S}) is the category of fractions of an Integral Domain \\spad{S}.")) (|floor| ((|#2| $) "\\spad{floor(x)} returns the largest integral element below \\spad{x}.")) (|ceiling| ((|#2| $) "\\spad{ceiling(x)} returns the smallest integral element above \\spad{x}.")) (|random| (($) "\\spad{random()} returns a random fraction.")) (|fractionPart| (($ $) "\\spad{fractionPart(x)} returns the fractional part of \\spad{x}. \\spad{x} = wholePart(\\spad{x}) + fractionPart(\\spad{x})")) (|wholePart| ((|#2| $) "\\spad{wholePart(x)} returns the whole part of the fraction \\spad{x} \\spadignore{i.e.} the truncated quotient of the numerator by the denominator.")) (|denominator| (($ $) "\\spad{denominator(x)} is the denominator of the fraction \\spad{x} converted to \\%.")) (|numerator| (($ $) "\\spad{numerator(x)} is the numerator of the fraction \\spad{x} converted to \\%.")) (|denom| ((|#2| $) "\\spad{denom(x)} returns the denominator of the fraction \\spad{x}.")) (|numer| ((|#2| $) "\\spad{numer(x)} returns the numerator of the fraction \\spad{x}.")) (/ (($ |#2| |#2|) "\\spad{d1 / d2} returns the fraction \\spad{d1} divided by \\spad{d2}."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| |#2| (QUOTE (-482))) (|HasCategory| |#2| (QUOTE (-257))) (|HasCategory| |#2| (QUOTE (-950 (-1088)))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-553 (-472)))) (|HasCategory| |#2| (QUOTE (-933))) (|HasCategory| |#2| (QUOTE (-740))) (|HasCategory| |#2| (QUOTE (-756))) (|HasCategory| |#2| (QUOTE (-950 (-483)))) (|HasCategory| |#2| (QUOTE (-1064)))) 
-(-904 S) 
+((|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}."))) 
-((-3981 . T) (-3987 . T) (-3982 . T) ((-3991 "*") . T) (-3983 . T) (-3984 . T) (-3986 . T)) 
+((-3983 . T) (-3989 . T) (-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . T)) 
 NIL 
-(-905 A B R S) 
+(-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}."))) 
 NIL 
 NIL 
-(-906 |n| K) 
+(-907 |n| K) 
 ((|constructor| (NIL "This domain provides modest support for quadratic forms.")) (|matrix| (((|SquareMatrix| |#1| |#2|) $) "\\spad{matrix(qf)} creates a square matrix from the quadratic form \\spad{qf}.")) (|quadraticForm| (($ (|SquareMatrix| |#1| |#2|)) "\\spad{quadraticForm(m)} creates a quadratic form from a symmetric,{} square matrix \\spad{m}."))) 
 NIL 
 NIL 
-(-907) 
+(-908) 
 ((|constructor| (NIL "This domain represents the syntax of a quasiquote \\indented{2}{expression.}")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the syntax for the expression being quoted."))) 
 NIL 
 NIL 
-(-908 S) 
+(-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."))) 
-((-3989 . T) (-3990 . T)) 
+((-3991 . T) (-3992 . T)) 
 NIL 
-(-909 R) 
+(-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.}"))) 
-((-3982 |has| |#1| (-245)) (-3983 . T) (-3984 . T) (-3986 . T)) 
-((|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-553 (-472)))) (|HasCategory| |#1| (QUOTE (-311))) (OR (|HasCategory| |#1| (QUOTE (-245))) (|HasCategory| |#1| (QUOTE (-311)))) (|HasCategory| |#1| (QUOTE (-245))) (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-580 (-483)))) (|HasCategory| |#1| (|%list| (QUOTE -452) (QUOTE (-1088)) (|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 (-811 (-1088)))) (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-809 (-1088)))) (OR (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-950 (-347 (-483)))))) (|HasCategory| |#1| (QUOTE (-950 (-347 (-483))))) (|HasCategory| |#1| (QUOTE (-950 (-483)))) (|HasCategory| |#1| (QUOTE (-972))) (|HasCategory| |#1| (QUOTE (-482)))) 
-(-910 S R) 
+((-3984 |has| |#1| (-245)) (-3985 . T) (-3986 . T) (-3988 . 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}."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-482))) (|HasCategory| |#2| (QUOTE (-972))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-553 (-472)))) (|HasCategory| |#2| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-756))) (|HasCategory| |#2| (QUOTE (-245)))) 
-(-911 R) 
+((|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| $) "\\spad{imagI(q)} extracts the imaginary \\spad{i} part of quaternion \\spad{q}.")) (|conjugate| (($ $) "\\spad{conjugate(q)} negates the imaginary parts of quaternion \\spad{q}."))) 
-((-3982 |has| |#1| (-245)) (-3983 . T) (-3984 . T) (-3986 . T)) 
+((-3984 |has| |#1| (-245)) (-3985 . T) (-3986 . T) (-3988 . T)) 
 NIL 
-(-912 QR R QS S) 
+(-913 QR R QS S) 
 ((|constructor| (NIL "\\spadtype{QuaternionCategoryFunctions2} implements functions between two quaternion domains. The function \\spadfun{map} is used by the system interpreter to coerce between quaternion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,u)} maps \\spad{f} onto the component parts of the quaternion \\spad{u}."))) 
 NIL 
 NIL 
-(-913 S) 
-((|constructor| (NIL "Linked List implementation of a Queue")) (|queue| (($ (|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}."))) 
-((-3989 . T) (-3990 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1012))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-72)))) 
 (-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)) 
+((-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| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) 
 NIL 
 NIL 
-(-915) 
+(-916) 
 ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|Fraction| (|Integer|))) "\\spad{x ** y} is the rational exponentiation of \\spad{x} by the power \\spad{y}.")) (|nthRoot| (($ $ (|Integer|)) "\\spad{nthRoot(x,n)} returns the \\spad{n}th root of \\spad{x}.")) (|sqrt| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) 
 NIL 
 NIL 
-(-916 -3088 UP UPUP |radicnd| |n|) 
+(-917 -3090 UP UPUP |radicnd| |n|) 
 ((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x})."))) 
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-((|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 (-809 (-1088))))) (-12 (|HasCategory| (-347 |#2|) (QUOTE (-298))) (|HasCategory| (-347 |#2|) (QUOTE (-809 (-1088)))))) (OR (-12 (|HasCategory| (-347 |#2|) (QUOTE (-311))) (|HasCategory| (-347 |#2|) (QUOTE (-809 (-1088))))) (-12 (|HasCategory| (-347 |#2|) (QUOTE (-311))) (|HasCategory| (-347 |#2|) (QUOTE (-811 (-1088)))))) (|HasCategory| (-347 |#2|) (QUOTE (-580 (-483)))) (OR (|HasCategory| (-347 |#2|) (QUOTE (-311))) (|HasCategory| (-347 |#2|) (QUOTE (-950 (-347 (-483)))))) (|HasCategory| (-347 |#2|) (QUOTE (-950 (-347 (-483))))) (|HasCategory| (-347 |#2|) (QUOTE (-950 (-483)))) (|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 (-811 (-1088))))) (-12 (|HasCategory| (-347 |#2|) (QUOTE (-190))) (|HasCategory| (-347 |#2|) (QUOTE (-311)))) (-12 (|HasCategory| (-347 |#2|) (QUOTE (-311))) (|HasCategory| (-347 |#2|) (QUOTE (-809 (-1088)))))) 
-(-917 |bb|) 
+((-3984 |has| (-347 |#2|) (-311)) (-3989 |has| (-347 |#2|) (-311)) (-3983 |has| (-347 |#2|) (-311)) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . 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."))) 
-((-3981 . T) (-3987 . T) (-3982 . T) ((-3991 "*") . T) (-3983 . T) (-3984 . T) (-3986 . T)) 
-((|HasCategory| (-483) (QUOTE (-821))) (|HasCategory| (-483) (QUOTE (-950 (-1088)))) (|HasCategory| (-483) (QUOTE (-118))) (|HasCategory| (-483) (QUOTE (-120))) (|HasCategory| (-483) (QUOTE (-553 (-472)))) (|HasCategory| (-483) (QUOTE (-933))) (|HasCategory| (-483) (QUOTE (-740))) (|HasCategory| (-483) (QUOTE (-756))) (OR (|HasCategory| (-483) (QUOTE (-740))) (|HasCategory| (-483) (QUOTE (-756)))) (|HasCategory| (-483) (QUOTE (-950 (-483)))) (|HasCategory| (-483) (QUOTE (-1064))) (|HasCategory| (-483) (QUOTE (-796 (-327)))) (|HasCategory| (-483) (QUOTE (-796 (-483)))) (|HasCategory| (-483) (QUOTE (-553 (-800 (-327))))) (|HasCategory| (-483) (QUOTE (-553 (-800 (-483))))) (|HasCategory| (-483) (QUOTE (-189))) (|HasCategory| (-483) (QUOTE (-811 (-1088)))) (|HasCategory| (-483) (QUOTE (-190))) (|HasCategory| (-483) (QUOTE (-809 (-1088)))) (|HasCategory| (-483) (QUOTE (-452 (-1088) (-483)))) (|HasCategory| (-483) (QUOTE (-259 (-483)))) (|HasCategory| (-483) (QUOTE (-241 (-483) (-483)))) (|HasCategory| (-483) (QUOTE (-257))) (|HasCategory| (-483) (QUOTE (-482))) (|HasCategory| (-483) (QUOTE (-580 (-483)))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-483) (QUOTE (-821)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-483) (QUOTE (-821)))) (|HasCategory| (-483) (QUOTE (-118))))) 
-(-918) 
+((-3983 . T) (-3989 . T) (-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . 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}."))) 
 NIL 
 NIL 
-(-919) 
+(-920) 
 ((|constructor| (NIL "Random number generators \\indented{2}{All random numbers used in the system should originate from} \\indented{2}{the same generator.\\space{2}This package is intended to be the source.}")) (|seed| (((|Integer|)) "\\spad{seed()} returns the current seed value.")) (|reseed| (((|Void|) (|Integer|)) "\\spad{reseed(n)} restarts the random number generator at \\spad{n}.")) (|size| (((|Integer|)) "\\spad{size()} is the base of the random number generator")) (|randnum| (((|Integer|) (|Integer|)) "\\spad{randnum(n)} is a random number between 0 and \\spad{n}.") (((|Integer|)) "\\spad{randnum()} is a random number between 0 and size()."))) 
 NIL 
 NIL 
-(-920 RP) 
+(-921 RP) 
 ((|factorSquareFree| (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(p)} factors an extended squareFree polynomial \\spad{p} over the rational numbers.")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(p)} factors an extended polynomial \\spad{p} over the rational numbers."))) 
 NIL 
 NIL 
-(-921 S) 
+(-922 S) 
 ((|constructor| (NIL "rational number testing and retraction functions. Date Created: March 1990 Date Last Updated: 9 April 1991")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") |#1|) "\\spad{rationalIfCan(x)} returns \\spad{x} as a rational number,{} \"failed\" if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) |#1|) "\\spad{rational?(x)} returns \\spad{true} if \\spad{x} is a rational number,{} \\spad{false} otherwise.")) (|rational| (((|Fraction| (|Integer|)) |#1|) "\\spad{rational(x)} returns \\spad{x} as a rational number; error if \\spad{x} is not a rational number."))) 
 NIL 
 NIL 
-(-922 A S) 
+(-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 -3990)) (|HasCategory| |#2| (QUOTE (-1012)))) 
-(-923 S) 
+((|HasAttribute| |#1| (QUOTE -3992)) (|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 
 NIL 
-(-924 S) 
+(-925 S) 
 ((|constructor| (NIL "\\axiomType{RealClosedField} provides common acces functions for all real closed fields.")) (|approximate| (((|Fraction| (|Integer|)) $ $) "\\axiom{approximate(\\spad{n},{}\\spad{p})} gives an approximation of \\axiom{\\spad{n}} that has precision \\axiom{\\spad{p}}")) (|rename| (($ $ (|OutputForm|)) "\\axiom{rename(\\spad{x},{}name)} gives a new number that prints as name")) (|rename!| (($ $ (|OutputForm|)) "\\axiom{rename!(\\spad{x},{}name)} changes the way \\axiom{\\spad{x}} is printed")) (|sqrt| (($ (|Integer|)) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} ** (1/2)}") (($ (|Fraction| (|Integer|))) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} ** (1/2)}") (($ $) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} ** (1/2)}") (($ $ (|PositiveInteger|)) "\\axiom{sqrt(\\spad{x},{}\\spad{n})} is \\axiom{\\spad{x} ** (1/n)}")) (|allRootsOf| (((|List| $) (|Polynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely")) (|rootOf| (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|)) "\\axiom{rootOf(pol,{}\\spad{n})} creates the \\spad{n}th root for the order of \\axiom{pol} and gives it unique name") (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|) (|OutputForm|)) "\\axiom{rootOf(pol,{}\\spad{n},{}name)} creates the \\spad{n}th root for the order of \\axiom{pol} and names it \\axiom{name}")) (|mainValue| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainValue(\\spad{x})} is the expression of \\axiom{\\spad{x}} in terms of \\axiom{SparseUnivariatePolynomial(\\$)}")) (|mainDefiningPolynomial| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainDefiningPolynomial(\\spad{x})} is the defining polynomial for the main algebraic quantity of \\axiom{\\spad{x}}")) (|mainForm| (((|Union| (|OutputForm|) "failed") $) "\\axiom{mainForm(\\spad{x})} is the main algebraic quantity name of \\axiom{\\spad{x}}"))) 
 NIL 
 NIL 
-(-925) 
+(-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}}"))) 
-((-3982 . T) (-3987 . T) (-3981 . T) (-3984 . T) (-3983 . T) ((-3991 "*") . T) (-3986 . T)) 
+((-3984 . T) (-3989 . T) (-3983 . T) (-3986 . T) (-3985 . T) ((-3993 "*") . T) (-3988 . T)) 
 NIL 
-(-926 R -3088) 
+(-927 R -3090) 
 ((|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 
-(-927 R -3088) 
+(-928 R -3090) 
 ((|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 
-(-928 -3088 UP) 
+(-929 -3090 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 
-(-929 -3088 UP) 
+(-930 -3090 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 
-(-930 S) 
+(-931 S) 
 ((|constructor| (NIL "This package exports random distributions")) (|rdHack1| (((|Mapping| |#1|) (|Vector| |#1|) (|Vector| (|Integer|)) (|Integer|)) "\\spad{rdHack1(v,u,n)} \\undocumented")) (|weighted| (((|Mapping| |#1|) (|List| (|Record| (|:| |value| |#1|) (|:| |weight| (|Integer|))))) "\\spad{weighted(l)} \\undocumented")) (|uniform| (((|Mapping| |#1|) (|Set| |#1|)) "\\spad{uniform(s)} \\undocumented"))) 
 NIL 
 NIL 
-(-931 F1 UP UPUP R F2) 
+(-932 F1 UP UPUP R F2) 
 ((|constructor| (NIL "\\indented{1}{Finds the order of a divisor over a finite field} Author: Manuel Bronstein Date Created: 1988 Date Last Updated: 8 November 1994")) (|order| (((|NonNegativeInteger|) (|FiniteDivisor| |#1| |#2| |#3| |#4|) |#3| (|Mapping| |#5| |#1|)) "\\spad{order(f,u,g)} \\undocumented"))) 
 NIL 
 NIL 
-(-932) 
+(-933) 
 ((|constructor| (NIL "This domain represents list reduction syntax.")) (|body| (((|SpadAst|) $) "\\spad{body(e)} return the list of expressions being redcued.")) (|operator| (((|SpadAst|) $) "\\spad{operator(e)} returns the magma operation being applied."))) 
 NIL 
 NIL 
-(-933) 
+(-934) 
 ((|constructor| (NIL "The category of real numeric domains,{} \\spadignore{i.e.} convertible to floats."))) 
 NIL 
 NIL 
-(-934 |Pol|) 
+(-935 |Pol|) 
 ((|constructor| (NIL "\\indented{2}{This package provides functions for finding the real zeros} of univariate polynomials over the integers to arbitrary user-specified precision. The results are returned as a list of isolating intervals which are expressed as records with \"left\" and \"right\" rational number components.")) (|midpoints| (((|List| (|Fraction| (|Integer|))) (|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))))) "\\spad{midpoints(isolist)} returns the list of midpoints for the list of intervals \\spad{isolist}.")) (|midpoint| (((|Fraction| (|Integer|)) (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{midpoint(int)} returns the midpoint of the interval \\spad{int}.")) (|refine| (((|Union| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) "failed") |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{refine(pol, int, range)} takes a univariate polynomial \\spad{pol} and and isolating interval \\spad{int} containing exactly one real root of \\spad{pol}; the operation returns an isolating interval which is contained within range,{} or \"failed\" if no such isolating interval exists.") (((|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|))) "\\spad{refine(pol, int, eps)} refines the interval \\spad{int} containing exactly one root of the univariate polynomial \\spad{pol} to size less than the rational number eps.")) (|realZeros| (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|))) "\\spad{realZeros(pol, int, eps)} returns a list of intervals of length less than the rational number eps for all the real roots of the polynomial \\spad{pol} which lie in the interval expressed by the record \\spad{int}.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Fraction| (|Integer|))) "\\spad{realZeros(pol, eps)} returns a list of intervals of length less than the rational number eps for all the real roots of the polynomial \\spad{pol}.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{realZeros(pol, range)} returns a list of isolating intervals for all the real zeros of the univariate polynomial \\spad{pol} which lie in the interval expressed by the record range.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1|) "\\spad{realZeros(pol)} returns a list of isolating intervals for all the real zeros of the univariate polynomial \\spad{pol}."))) 
 NIL 
 NIL 
-(-935 |Pol|) 
+(-936 |Pol|) 
 ((|constructor| (NIL "\\indented{2}{This package provides functions for finding the real zeros} of univariate polynomials over the rational numbers to arbitrary user-specified precision. The results are returned as a list of isolating intervals,{} expressed as records with \"left\" and \"right\" rational number components.")) (|refine| (((|Union| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) "failed") |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{refine(pol, int, range)} takes a univariate polynomial \\spad{pol} and and isolating interval \\spad{int} which must contain exactly one real root of \\spad{pol},{} and returns an isolating interval which is contained within range,{} or \"failed\" if no such isolating interval exists.") (((|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|))) "\\spad{refine(pol, int, eps)} refines the interval \\spad{int} containing exactly one root of the univariate polynomial \\spad{pol} to size less than the rational number eps.")) (|realZeros| (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|))) "\\spad{realZeros(pol, int, eps)} returns a list of intervals of length less than the rational number eps for all the real roots of the polynomial \\spad{pol} which lie in the interval expressed by the record \\spad{int}.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Fraction| (|Integer|))) "\\spad{realZeros(pol, eps)} returns a list of intervals of length less than the rational number eps for all the real roots of the polynomial \\spad{pol}.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{realZeros(pol, range)} returns a list of isolating intervals for all the real zeros of the univariate polynomial \\spad{pol} which lie in the interval expressed by the record range.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1|) "\\spad{realZeros(pol)} returns a list of isolating intervals for all the real zeros of the univariate polynomial \\spad{pol}."))) 
 NIL 
 NIL 
-(-936) 
+(-937) 
 ((|constructor| (NIL "\\indented{1}{This package provides numerical solutions of systems of polynomial} equations for use in ACPLOT.")) (|realSolve| (((|List| (|List| (|Float|))) (|List| (|Polynomial| (|Integer|))) (|List| (|Symbol|)) (|Float|)) "\\spad{realSolve(lp,lv,eps)} = compute the list of the real solutions of the list \\spad{lp} of polynomials with integer coefficients with respect to the variables in \\spad{lv},{} with precision \\spad{eps}.")) (|solve| (((|List| (|Float|)) (|Polynomial| (|Integer|)) (|Float|)) "\\spad{solve(p,eps)} finds the real zeroes of a univariate integer polynomial \\spad{p} with precision \\spad{eps}.") (((|List| (|Float|)) (|Polynomial| (|Fraction| (|Integer|))) (|Float|)) "\\spad{solve(p,eps)} finds the real zeroes of a univariate rational polynomial \\spad{p} with precision \\spad{eps}."))) 
 NIL 
 NIL 
-(-937 |TheField|) 
+(-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"))) 
-((-3982 . T) (-3987 . T) (-3981 . T) (-3984 . T) (-3983 . T) ((-3991 "*") . T) (-3986 . T)) 
-((OR (|HasCategory| |#1| (QUOTE (-950 (-483)))) (|HasCategory| (-347 (-483)) (QUOTE (-950 (-483))))) (|HasCategory| |#1| (QUOTE (-950 (-347 (-483))))) (|HasCategory| |#1| (QUOTE (-950 (-483)))) (|HasCategory| (-347 (-483)) (QUOTE (-950 (-347 (-483))))) (|HasCategory| (-347 (-483)) (QUOTE (-950 (-483))))) 
-(-938 -3088 L) 
+((-3984 . T) (-3989 . T) (-3983 . T) (-3986 . T) (-3985 . T) ((-3993 "*") . T) (-3988 . 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) 
 ((|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 
-(-939 S) 
+(-940 S) 
 ((|constructor| (NIL "\\indented{1}{\\spadtype{Reference} is for making a changeable instance} of something.")) (= (((|Boolean|) $ $) "\\spad{a=b} tests if \\spad{a} and \\spad{b} are equal.")) (|setref| ((|#1| $ |#1|) "\\spad{setref(r,s)} reset the reference \\spad{r} to refer to \\spad{s}")) (|deref| ((|#1| $) "\\spad{deref(r)} returns the object referenced by \\spad{r}")) (|ref| (($ |#1|) "\\spad{ref(s)} creates a reference to the object \\spad{s}."))) 
 NIL 
 NIL 
-(-940 R E V P) 
+(-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."))) 
-((-3990 . T) (-3989 . T)) 
-((-12 (|HasCategory| |#4| (QUOTE (-1012))) (|HasCategory| |#4| (|%list| (QUOTE -259) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-553 (-472)))) (|HasCategory| |#4| (QUOTE (-1012))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#3| (QUOTE (-317))) (|HasCategory| |#4| (QUOTE (-552 (-772)))) (|HasCategory| |#4| (QUOTE (-72)))) 
-(-941) 
+((-3992 . T) (-3991 . 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."))) 
 NIL 
 NIL 
-(-942 R) 
+(-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 (-3991 "*")))) 
-(-943 R) 
+((|HasAttribute| |#1| (QUOTE (-3993 "*")))) 
+(-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 
 ((-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-317)))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-257)))) 
-(-944 S) 
+(-945 S) 
 ((|constructor| (NIL "Implements multiplication by repeated addition")) (|double| ((|#1| (|PositiveInteger|) |#1|) "\\spad{double(i, r)} multiplies \\spad{r} by \\spad{i} using repeated doubling.")) (+ (($ $ $) "\\spad{x+y} returns the sum of \\spad{x} and \\spad{y}"))) 
 NIL 
 NIL 
-(-945 S) 
+(-946 S) 
 ((|constructor| (NIL "Implements exponentiation by repeated squaring")) (|expt| ((|#1| |#1| (|PositiveInteger|)) "\\spad{expt(r, i)} computes r**i by repeated squaring")) (* (($ $ $) "\\spad{x*y} returns the product of \\spad{x} and \\spad{y}"))) 
 NIL 
 NIL 
-(-946 S) 
+(-947 S) 
 ((|constructor| (NIL "This package provides coercions for the special types \\spadtype{Exit} and \\spadtype{Void}.")) (|coerce| ((|#1| (|Exit|)) "\\spad{coerce(e)} is never really evaluated. This coercion is used for formal type correctness when a function will not return directly to its caller.") (((|Void|) |#1|) "\\spad{coerce(s)} throws all information about \\spad{s} away. This coercion allows values of any type to appear in contexts where they will not be used. For example,{} it allows the resolution of different types in the \\spad{then} and \\spad{else} branches when an \\spad{if} is in a context where the resulting value is not used."))) 
 NIL 
 NIL 
-(-947 -3088 |Expon| |VarSet| |FPol| |LFPol|) 
+(-948 -3090 |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"))) 
-(((-3991 "*") . T) (-3983 . T) (-3984 . T) (-3986 . T)) 
+(((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . T)) 
 NIL 
-(-948) 
+(-949) 
 ((|constructor| (NIL "This domain represents `return' expressions.")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression returned by `e'."))) 
 NIL 
 NIL 
-(-949 A S) 
+(-950 A S) 
 ((|constructor| (NIL "A is retractable to \\spad{B} means that some elementsif A can be converted into elements of \\spad{B} and any element of \\spad{B} can be converted into an element of A.")) (|retract| ((|#2| $) "\\spad{retract(a)} transforms a into an element of \\spad{S} if possible. Error: if a cannot be made into an element of \\spad{S}.")) (|retractIfCan| (((|Union| |#2| "failed") $) "\\spad{retractIfCan(a)} transforms a into an element of \\spad{S} if possible. Returns \"failed\" if a cannot be made into an element of \\spad{S}."))) 
 NIL 
 NIL 
-(-950 S) 
+(-951 S) 
 ((|constructor| (NIL "A is retractable to \\spad{B} means that some elementsif A can be converted into elements of \\spad{B} and any element of \\spad{B} can be converted into an element of A.")) (|retract| ((|#1| $) "\\spad{retract(a)} transforms a into an element of \\spad{S} if possible. Error: if a cannot be made into an element of \\spad{S}.")) (|retractIfCan| (((|Union| |#1| "failed") $) "\\spad{retractIfCan(a)} transforms a into an element of \\spad{S} if possible. Returns \"failed\" if a cannot be made into an element of \\spad{S}."))) 
 NIL 
 NIL 
-(-951 Q R) 
+(-952 Q R) 
 ((|constructor| (NIL "RetractSolvePackage is an interface to \\spadtype{SystemSolvePackage} that attempts to retract the coefficients of the equations before solving.")) (|solveRetract| (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#2|))))) (|List| (|Polynomial| |#2|)) (|List| (|Symbol|))) "\\spad{solveRetract(lp,lv)} finds the solutions of the list \\spad{lp} of rational functions with respect to the list of symbols \\spad{lv}. The function tries to retract all the coefficients of the equations to \\spad{Q} before solving if possible."))) 
 NIL 
 NIL 
-(-952 R) 
+(-953 R) 
 ((|constructor| (NIL "Utilities that provide the same top-level manipulations on fractions than on polynomials.")) (|coerce| (((|Fraction| (|Polynomial| |#1|)) |#1|) "\\spad{coerce(r)} returns \\spad{r} viewed as a rational function over \\spad{R}.")) (|eval| (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) "\\spad{eval(f, [v1 = g1,...,vn = gn])} returns \\spad{f} with each \\spad{vi} replaced by \\spad{gi} in parallel,{} \\spadignore{i.e.} \\spad{vi}'s appearing inside the \\spad{gi}'s are not replaced. Error: if any \\spad{vi} is not a symbol.") (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|)))) "\\spad{eval(f, v = g)} returns \\spad{f} with \\spad{v} replaced by \\spad{g}. Error: if \\spad{v} is not a symbol.") (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|List| (|Symbol|)) (|List| (|Fraction| (|Polynomial| |#1|)))) "\\spad{eval(f, [v1,...,vn], [g1,...,gn])} returns \\spad{f} with each \\spad{vi} replaced by \\spad{gi} in parallel,{} \\spadignore{i.e.} \\spad{vi}'s appearing inside the \\spad{gi}'s are not replaced.") (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|))) "\\spad{eval(f, v, g)} returns \\spad{f} with \\spad{v} replaced by \\spad{g}.")) (|multivariate| (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|)))) (|Symbol|)) "\\spad{multivariate(f, v)} applies both the numerator and denominator of \\spad{f} to \\spad{v}.")) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|)))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{univariate(f, v)} returns \\spad{f} viewed as a univariate rational function in \\spad{v}.")) (|mainVariable| (((|Union| (|Symbol|) "failed") (|Fraction| (|Polynomial| |#1|))) "\\spad{mainVariable(f)} returns the highest variable appearing in the numerator or the denominator of \\spad{f},{} \"failed\" if \\spad{f} has no variables.")) (|variables| (((|List| (|Symbol|)) (|Fraction| (|Polynomial| |#1|))) "\\spad{variables(f)} returns the list of variables appearing in the numerator or the denominator of \\spad{f}."))) 
 NIL 
 NIL 
-(-953) 
+(-954) 
 ((|t| (((|Mapping| (|Float|)) (|NonNegativeInteger|)) "\\spad{t(n)} \\undocumented")) (F (((|Mapping| (|Float|)) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{F(n,m)} \\undocumented")) (|Beta| (((|Mapping| (|Float|)) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{Beta(n,m)} \\undocumented")) (|chiSquare| (((|Mapping| (|Float|)) (|NonNegativeInteger|)) "\\spad{chiSquare(n)} \\undocumented")) (|exponential| (((|Mapping| (|Float|)) (|Float|)) "\\spad{exponential(f)} \\undocumented")) (|normal| (((|Mapping| (|Float|)) (|Float|) (|Float|)) "\\spad{normal(f,g)} \\undocumented")) (|uniform| (((|Mapping| (|Float|)) (|Float|) (|Float|)) "\\spad{uniform(f,g)} \\undocumented")) (|chiSquare1| (((|Float|) (|NonNegativeInteger|)) "\\spad{chiSquare1(n)} \\undocumented")) (|exponential1| (((|Float|)) "\\spad{exponential1()} \\undocumented")) (|normal01| (((|Float|)) "\\spad{normal01()} \\undocumented")) (|uniform01| (((|Float|)) "\\spad{uniform01()} \\undocumented"))) 
 NIL 
 NIL 
-(-954 UP) 
+(-955 UP) 
 ((|constructor| (NIL "Factorization of univariate polynomials with coefficients which are rational functions with integer coefficients.")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p}."))) 
 NIL 
 NIL 
-(-955 R) 
+(-956 R) 
 ((|constructor| (NIL "\\spadtype{RationalFunctionFactorizer} contains the factor function (called factorFraction) which factors fractions of polynomials by factoring the numerator and denominator. Since any non zero fraction is a unit the usual factor operation will just return the original fraction.")) (|factorFraction| (((|Fraction| (|Factored| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|))) "\\spad{factorFraction(r)} factors the numerator and the denominator of the polynomial fraction \\spad{r}."))) 
 NIL 
 NIL 
-(-956 T$) 
+(-957 T$) 
 ((|constructor| (NIL "This category defines the common interface for RGB color models.")) (|componentUpperBound| ((|#1|) "componentUpperBound is an upper bound for all component values.")) (|blue| ((|#1| $) "\\spad{blue(c)} returns the `blue' component of `c'.")) (|green| ((|#1| $) "\\spad{green(c)} returns the `green' component of `c'.")) (|red| ((|#1| $) "\\spad{red(c)} returns the `red' component of `c'."))) 
 NIL 
 NIL 
-(-957 T$) 
+(-958 T$) 
 ((|constructor| (NIL "This category defines the common interface for RGB color spaces.")) (|whitePoint| (($) "whitePoint is the contant indicating the white point of this color space."))) 
 NIL 
 NIL 
-(-958 R |ls|) 
+(-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}."))) 
-((-3990 . T) (-3989 . T)) 
-((-12 (|HasCategory| (-703 |#1| (-773 |#2|)) (QUOTE (-1012))) (|HasCategory| (-703 |#1| (-773 |#2|)) (|%list| (QUOTE -259) (|%list| (QUOTE -703) (|devaluate| |#1|) (|%list| (QUOTE -773) (|devaluate| |#2|)))))) (|HasCategory| (-703 |#1| (-773 |#2|)) (QUOTE (-553 (-472)))) (|HasCategory| (-703 |#1| (-773 |#2|)) (QUOTE (-1012))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| (-773 |#2|) (QUOTE (-317))) (|HasCategory| (-703 |#1| (-773 |#2|)) (QUOTE (-552 (-772)))) (|HasCategory| (-703 |#1| (-773 |#2|)) (QUOTE (-72)))) 
-(-959) 
+((-3992 . T) (-3991 . 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"))) 
 NIL 
 NIL 
-(-960 S) 
+(-961 S) 
 ((|constructor| (NIL "The category of rings with unity,{} always associative,{} but not necessarily commutative.")) (|unitsKnown| ((|attribute|) "recip truly yields reciprocal or \"failed\" if not a unit. Note: \\spad{recip(0) = \"failed\"}.")) (|characteristic| (((|NonNegativeInteger|)) "\\spad{characteristic()} returns the characteristic of the ring this is the smallest positive integer \\spad{n} such that \\spad{n*x=0} for all \\spad{x} in the ring,{} or zero if no such \\spad{n} exists."))) 
 NIL 
 NIL 
-(-961) 
+(-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."))) 
-((-3986 . T)) 
+((-3988 . T)) 
 NIL 
-(-962 |xx| -3088) 
+(-963 |xx| -3090) 
 ((|constructor| (NIL "This package exports rational interpolation algorithms"))) 
 NIL 
 NIL 
-(-963 S) 
+(-964 S) 
 ((|constructor| (NIL "\\indented{2}{A set is an \\spad{S}-right linear set if it is stable by right-dilation} \\indented{2}{by elements in the semigroup \\spad{S}.} See Also: LeftLinearSet.")) (* (($ $ |#1|) "\\spad{x*s} is the right-dilation of \\spad{x} by \\spad{s}."))) 
 NIL 
 NIL 
-(-964 S |m| |n| R |Row| |Col|) 
+(-965 S |m| |n| R |Row| |Col|) 
 ((|constructor| (NIL "\\spadtype{RectangularMatrixCategory} is a category of matrices of fixed dimensions. The dimensions of the matrix will be parameters of the domain. Domains in this category will be \\spad{R}-modules and will be non-mutable.")) (|nullSpace| (((|List| |#6|) $) "\\spad{nullSpace(m)}+ returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#4|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#4|) "\\spad{exquo(m,r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (|map| (($ (|Mapping| |#4| |#4| |#4|) $ $) "\\spad{map(f,a,b)} returns \\spad{c},{} where \\spad{c} is such that \\spad{c(i,j) = f(a(i,j),b(i,j))} for all \\spad{i},{} \\spad{j}.") (($ (|Mapping| |#4| |#4|) $) "\\spad{map(f,a)} returns \\spad{b},{} where \\spad{b(i,j) = a(i,j)} for all \\spad{i},{} \\spad{j}.")) (|column| ((|#6| $ (|Integer|)) "\\spad{column(m,j)} returns the \\spad{j}th column of the matrix \\spad{m}. Error: if the index outside the proper range.")) (|row| ((|#5| $ (|Integer|)) "\\spad{row(m,i)} returns the \\spad{i}th row of the matrix \\spad{m}. Error: if the index is outside the proper range.")) (|qelt| ((|#4| $ (|Integer|) (|Integer|)) "\\spad{qelt(m,i,j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m}. Note: there is NO error check to determine if indices are in the proper ranges.")) (|elt| ((|#4| $ (|Integer|) (|Integer|) |#4|) "\\spad{elt(m,i,j,r)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m},{} if \\spad{m} has an \\spad{i}th row and a \\spad{j}th column,{} and returns \\spad{r} otherwise.") ((|#4| $ (|Integer|) (|Integer|)) "\\spad{elt(m,i,j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m}. Error: if indices are outside the proper ranges.")) (|listOfLists| (((|List| (|List| |#4|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|ncols| (((|NonNegativeInteger|) $) "\\spad{ncols(m)} returns the number of columns in the matrix \\spad{m}.")) (|nrows| (((|NonNegativeInteger|) $) "\\spad{nrows(m)} returns the number of rows in the matrix \\spad{m}.")) (|maxColIndex| (((|Integer|) $) "\\spad{maxColIndex(m)} returns the index of the 'last' column of the matrix \\spad{m}.")) (|minColIndex| (((|Integer|) $) "\\spad{minColIndex(m)} returns the index of the 'first' column of the matrix \\spad{m}.")) (|maxRowIndex| (((|Integer|) $) "\\spad{maxRowIndex(m)} returns the index of the 'last' row of the matrix \\spad{m}.")) (|minRowIndex| (((|Integer|) $) "\\spad{minRowIndex(m)} returns the index of the 'first' row of the matrix \\spad{m}.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,j] = -m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,j] = m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.")) (|matrix| (($ (|List| (|List| |#4|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix.")) (|finiteAggregate| ((|attribute|) "matrices are finite"))) 
 NIL 
-((|HasCategory| |#4| (QUOTE (-257))) (|HasCategory| |#4| (QUOTE (-311))) (|HasCategory| |#4| (QUOTE (-494))) (|HasCategory| |#4| (QUOTE (-146)))) 
-(-965 |m| |n| R |Row| |Col|) 
+((|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"))) 
-((-3989 . T) (-3984 . T) (-3983 . T)) 
+((-3991 . T) (-3986 . T) (-3985 . T)) 
 NIL 
-(-966 |m| |n| R) 
+(-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}."))) 
-((-3989 . T) (-3984 . T) (-3983 . 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 (-1012))) (|HasCategory| |#3| (|%list| (QUOTE -259) (|devaluate| |#3|))))) (|HasCategory| |#3| (QUOTE (-553 (-472)))) (OR (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-311)))) (|HasCategory| |#3| (QUOTE (-311))) (|HasCategory| |#3| (QUOTE (-1012))) (|HasCategory| |#3| (QUOTE (-257))) (|HasCategory| |#3| (QUOTE (-494))) (-12 (|HasCategory| |#3| (QUOTE (-1012))) (|HasCategory| |#3| (|%list| (QUOTE -259) (|devaluate| |#3|)))) (|HasCategory| |#3| (QUOTE (-72))) (|HasCategory| |#3| (QUOTE (-552 (-772))))) 
-(-967 |m| |n| R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2) 
+((-3991 . T) (-3986 . T) (-3985 . 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}."))) 
 NIL 
 NIL 
-(-968 R) 
+(-969 R) 
 ((|constructor| (NIL "The category of right modules over an rng (ring not necessarily with unit). This is an abelian group which supports right multiplation by elements of the rng. \\blankline"))) 
 NIL 
 NIL 
-(-969) 
+(-970) 
 ((|constructor| (NIL "The category of associative rings,{} not necessarily commutative,{} and not necessarily with a 1. This is a combination of an abelian group and a semigroup,{} with multiplication distributing over addition. \\blankline"))) 
 NIL 
 NIL 
-(-970 S T$) 
+(-971 S T$) 
 ((|constructor| (NIL "This domain represents the notion of binding a variable to range over a specific segment (either bounded,{} or half bounded).")) (|segment| ((|#1| $) "\\spad{segment(x)} returns the segment from the right hand side of the \\spadtype{RangeBinding}. For example,{} if \\spad{x} is \\spad{v=s},{} then \\spad{segment(x)} returns \\spad{s}.")) (|variable| (((|Symbol|) $) "\\spad{variable(x)} returns the variable from the left hand side of the \\spadtype{RangeBinding}. For example,{} if \\spad{x} is \\spad{v=s},{} then \\spad{variable(x)} returns \\spad{v}.")) (|equation| (($ (|Symbol|) |#1|) "\\spad{equation(v,s)} creates a segment binding value with variable \\spad{v} and segment \\spad{s}. Note that the interpreter parses \\spad{v=s} to this form."))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-1012)))) 
-(-971 S) 
+((|HasCategory| |#1| (QUOTE (-1013)))) 
+(-972 S) 
 ((|constructor| (NIL "The real number system category is intended as a model for the real numbers. The real numbers form an ordered normed field. Note that we have purposely not included \\spadtype{DifferentialRing} or the elementary functions (see \\spadtype{TranscendentalFunctionCategory}) in the definition.")) (|round| (($ $) "\\spad{round x} computes the integer closest to \\spad{x}.")) (|truncate| (($ $) "\\spad{truncate x} returns the integer between \\spad{x} and 0 closest to \\spad{x}.")) (|fractionPart| (($ $) "\\spad{fractionPart x} returns the fractional part of \\spad{x}.")) (|wholePart| (((|Integer|) $) "\\spad{wholePart x} returns the integer part of \\spad{x}.")) (|floor| (($ $) "\\spad{floor x} returns the largest integer \\spad{<= x}.")) (|ceiling| (($ $) "\\spad{ceiling x} returns the small integer \\spad{>= x}.")) (|norm| (($ $) "\\spad{norm x} returns the same as absolute value."))) 
 NIL 
 NIL 
-(-972) 
+(-973) 
 ((|constructor| (NIL "The real number system category is intended as a model for the real numbers. The real numbers form an ordered normed field. Note that we have purposely not included \\spadtype{DifferentialRing} or the elementary functions (see \\spadtype{TranscendentalFunctionCategory}) in the definition.")) (|round| (($ $) "\\spad{round x} computes the integer closest to \\spad{x}.")) (|truncate| (($ $) "\\spad{truncate x} returns the integer between \\spad{x} and 0 closest to \\spad{x}.")) (|fractionPart| (($ $) "\\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."))) 
-((-3981 . T) (-3987 . T) (-3982 . T) ((-3991 "*") . T) (-3983 . T) (-3984 . T) (-3986 . T)) 
+((-3983 . T) (-3989 . T) (-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . T)) 
 NIL 
-(-973 |TheField| |ThePolDom|) 
+(-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| $) "\\axiom{left(rootChar)} is the left bound of the isolating interval"))) 
 NIL 
 NIL 
-(-974) 
+(-975) 
 ((|constructor| (NIL "\\spadtype{RomanNumeral} provides functions for converting \\indented{1}{integers to roman numerals.}")) (|roman| (($ (|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."))) 
-((-3977 . T) (-3981 . T) (-3976 . T) (-3987 . T) (-3988 . T) (-3982 . T) ((-3991 "*") . T) (-3983 . T) (-3984 . T) (-3986 . T)) 
+((-3979 . T) (-3983 . T) (-3978 . T) (-3989 . T) (-3990 . T) (-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . T)) 
 NIL 
-(-975 S R E V) 
+(-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| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-389))) (|HasCategory| |#2| (QUOTE (-494))) (|HasCategory| |#2| (QUOTE (-950 (-483)))) (|HasCategory| |#2| (QUOTE (-482))) (|HasCategory| |#2| (QUOTE (-38 (-483)))) (|HasCategory| |#2| (QUOTE (-904 (-483)))) (|HasCategory| |#2| (QUOTE (-38 (-347 (-483))))) (|HasCategory| |#4| (QUOTE (-553 (-1088))))) 
-(-976 R E V) 
+((|HasCategory| |#2| (QUOTE (-389))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-951 (-484)))) (|HasCategory| |#2| (QUOTE (-483))) (|HasCategory| |#2| (QUOTE (-38 (-484)))) (|HasCategory| |#2| (QUOTE (-905 (-484)))) (|HasCategory| |#2| (QUOTE (-38 (-347 (-484))))) (|HasCategory| |#4| (QUOTE (-554 (-1089))))) 
+(-977 R E V) 
 ((|constructor| (NIL "A category for general multi-variate polynomials with coefficients in a ring,{} variables in an ordered set,{} and exponents from an ordered abelian monoid,{} with a \\axiomOp{sup} operation. When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\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}}."))) 
-(((-3991 "*") |has| |#1| (-146)) (-3982 |has| |#1| (-494)) (-3987 |has| |#1| (-6 -3987)) (-3984 . T) (-3983 . T) (-3986 . T)) 
+(((-3993 "*") |has| |#1| (-146)) (-3984 |has| |#1| (-495)) (-3989 |has| |#1| (-6 -3989)) (-3986 . T) (-3985 . T) (-3988 . T)) 
 NIL 
-(-977) 
+(-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'."))) 
 NIL 
 NIL 
-(-978 S |TheField| |ThePols|) 
+(-979 S |TheField| |ThePols|) 
 ((|constructor| (NIL "\\axiomType{RealRootCharacterizationCategory} provides common acces functions for all real root codings.")) (|relativeApprox| ((|#2| |#3| $ |#2|) "\\axiom{approximate(term,{}root,{}prec)} gives an approximation of \\axiom{term} over \\axiom{root} with precision \\axiom{prec}")) (|approximate| ((|#2| |#3| $ |#2|) "\\axiom{approximate(term,{}root,{}prec)} gives an approximation of \\axiom{term} over \\axiom{root} with precision \\axiom{prec}")) (|rootOf| (((|Union| $ "failed") |#3| (|PositiveInteger|)) "\\axiom{rootOf(pol,{}\\spad{n})} gives the \\spad{n}th root for the order of the Real Closure")) (|allRootsOf| (((|List| $) |#3|) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} in the Real Closure,{} assumed in order.")) (|definingPolynomial| ((|#3| $) "\\axiom{definingPolynomial(aRoot)} gives a polynomial such that \\axiom{definingPolynomial(aRoot).aRoot = 0}")) (|recip| (((|Union| |#3| "failed") |#3| $) "\\axiom{recip(pol,{}aRoot)} tries to inverse \\axiom{pol} interpreted as \\axiom{aRoot}")) (|positive?| (((|Boolean|) |#3| $) "\\axiom{positive?(pol,{}aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is positive")) (|negative?| (((|Boolean|) |#3| $) "\\axiom{negative?(pol,{}aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is negative")) (|zero?| (((|Boolean|) |#3| $) "\\axiom{zero?(pol,{}aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is \\axiom{0}")) (|sign| (((|Integer|) |#3| $) "\\axiom{sign(pol,{}aRoot)} gives the sign of \\axiom{pol} interpreted as \\axiom{aRoot}"))) 
 NIL 
 NIL 
-(-979 |TheField| |ThePols|) 
+(-980 |TheField| |ThePols|) 
 ((|constructor| (NIL "\\axiomType{RealRootCharacterizationCategory} provides common acces functions for all real root codings.")) (|relativeApprox| ((|#1| |#2| $ |#1|) "\\axiom{approximate(term,{}root,{}prec)} gives an approximation of \\axiom{term} over \\axiom{root} with precision \\axiom{prec}")) (|approximate| ((|#1| |#2| $ |#1|) "\\axiom{approximate(term,{}root,{}prec)} gives an approximation of \\axiom{term} over \\axiom{root} with precision \\axiom{prec}")) (|rootOf| (((|Union| $ "failed") |#2| (|PositiveInteger|)) "\\axiom{rootOf(pol,{}\\spad{n})} gives the \\spad{n}th root for the order of the Real Closure")) (|allRootsOf| (((|List| $) |#2|) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} in the Real Closure,{} assumed in order.")) (|definingPolynomial| ((|#2| $) "\\axiom{definingPolynomial(aRoot)} gives a polynomial such that \\axiom{definingPolynomial(aRoot).aRoot = 0}")) (|recip| (((|Union| |#2| "failed") |#2| $) "\\axiom{recip(pol,{}aRoot)} tries to inverse \\axiom{pol} interpreted as \\axiom{aRoot}")) (|positive?| (((|Boolean|) |#2| $) "\\axiom{positive?(pol,{}aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is positive")) (|negative?| (((|Boolean|) |#2| $) "\\axiom{negative?(pol,{}aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is negative")) (|zero?| (((|Boolean|) |#2| $) "\\axiom{zero?(pol,{}aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is \\axiom{0}")) (|sign| (((|Integer|) |#2| $) "\\axiom{sign(pol,{}aRoot)} gives the sign of \\axiom{pol} interpreted as \\axiom{aRoot}"))) 
 NIL 
 NIL 
-(-980 R E V P TS) 
+(-981 R E V P TS) 
 ((|constructor| (NIL "A package providing a new algorithm for solving polynomial systems by means of regular chains. Two ways of solving are proposed: in the sense of Zariski closure (like in Kalkbrener's algorithm) or in the sense of the regular zeros (like in Wu,{} Wang or Lazard methods). This algorithm is valid for nay type of regular set. It does not care about the way a polynomial is added in an regular set,{} or how two quasi-components are compared (by an inclusion-test),{} or how the invertibility test is made in the tower of simple extensions associated with a regular set. These operations are realized respectively by the domain \\spad{TS} and the packages \\axiomType{QCMPACK}(\\spad{R},{}\\spad{E},{}\\spad{V},{}\\spad{P},{}TS) and \\axiomType{RSETGCD}(\\spad{R},{}\\spad{E},{}\\spad{V},{}\\spad{P},{}TS). The same way it does not care about the way univariate polynomial gcd (with coefficients in the tower of simple extensions associated with a regular set) are computed. The only requirement is that these gcd need to have invertible initials (normalized or not). WARNING. There is no need for a user to call diectly any operation of this package since they can be accessed by the domain \\axiom{TS}. Thus,{} the operations of this package are not documented.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}"))) 
 NIL 
 NIL 
-(-981 S R E V P) 
+(-982 S R E V P) 
 ((|constructor| (NIL "The category of regular triangular sets,{} introduced under the name regular chains in [1] (and other papers). In [3] it is proved that regular triangular sets and towers of simple extensions of a field are equivalent notions. In the following definitions,{} all polynomials and ideals are taken from the polynomial ring \\spad{k[x1,...,xn]} where \\spad{k} is the fraction field of \\spad{R}. The triangular set \\spad{[t1,...,tm]} is regular iff for every \\spad{i} the initial of \\spad{ti+1} is invertible in the tower of simple extensions associated with \\spad{[t1,...,ti]}. A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Kalkbrener of a given ideal \\spad{I} iff the radical of \\spad{I} is equal to the intersection of the radical ideals generated by the saturated ideals of the \\spad{[T1,...,Ti]}. A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Kalkbrener of a given triangular set \\spad{T} iff it is a split of Kalkbrener of the saturated ideal of \\spad{T}. Let \\spad{K} be an algebraic closure of \\spad{k}. Assume that \\spad{V} is finite with cardinality \\spad{n} and let \\spad{A} be the affine space \\spad{K^n}. For a regular triangular set \\spad{T} let denote by \\spad{W(T)} the set of regular zeros of \\spad{T}. A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Lazard of a given subset \\spad{S} of \\spad{A} iff the union of the \\spad{W(Ti)} contains \\spad{S} and is contained in the closure of \\spad{S} (\\spad{w}.\\spad{r}.\\spad{t}. Zariski topology). A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Lazard of a given triangular set \\spad{T} if it is a split of Lazard of \\spad{W(T)}. Note that if \\spad{[T1,...,Ts]} is a split of Lazard of \\spad{T} then it is also a split of Kalkbrener of \\spad{T}. The converse is \\spad{false}. This category provides operations related to both kinds of splits,{} the former being related to ideals decomposition whereas the latter deals with varieties decomposition. See the example illustrating the \\spadtype{RegularTriangularSet} constructor for more explanations about decompositions by means of regular triangular sets. \\newline References : \\indented{1}{[1] \\spad{M}. KALKBRENER \"Three contributions to elimination theory\"} \\indented{5}{Phd Thesis,{} University of Linz,{} Austria,{} 1991.} \\indented{1}{[2] \\spad{M}. KALKBRENER \"Algorithmic properties of polynomial rings\"} \\indented{5}{Journal of Symbol. Comp. 1998} \\indented{1}{[3] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)} \\indented{1}{[4] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|zeroSetSplit| (((|List| $) (|List| |#5|) (|Boolean|)) "\\spad{zeroSetSplit(lp,clos?)} returns \\spad{lts} a split of Kalkbrener of the radical ideal associated with \\spad{lp}. If \\spad{clos?} is \\spad{false},{} it is also a decomposition of the variety associated with \\spad{lp} into the regular zero set of the \\spad{ts} in \\spad{lts} (or,{} in other words,{} a split of Lazard of this variety). See the example illustrating the \\spadtype{RegularTriangularSet} constructor for more explanations about decompositions by means of regular triangular sets.")) (|extend| (((|List| $) (|List| |#5|) (|List| $)) "\\spad{extend(lp,lts)} returns the same as \\spad{concat([extend(lp,ts) for ts in lts])|}") (((|List| $) (|List| |#5|) $) "\\spad{extend(lp,ts)} returns \\spad{ts} if \\spad{empty? lp} \\spad{extend(p,ts)} if \\spad{lp = [p]} else \\spad{extend(first lp, extend(rest lp, ts))}") (((|List| $) |#5| (|List| $)) "\\spad{extend(p,lts)} returns the same as \\spad{concat([extend(p,ts) for ts in lts])|}") (((|List| $) |#5| $) "\\spad{extend(p,ts)} assumes that \\spad{p} is a non-constant polynomial whose main variable is greater than any variable of \\spad{ts}. Then it returns a split of Kalkbrener of \\spad{ts+p}. This may not be \\spad{ts+p} itself,{} if for instance \\spad{ts+p} is not a regular triangular set.")) (|internalAugment| (($ (|List| |#5|) $) "\\spad{internalAugment(lp,ts)} returns \\spad{ts} if \\spad{lp} is empty otherwise returns \\spad{internalAugment(rest lp, internalAugment(first lp, ts))}") (($ |#5| $) "\\spad{internalAugment(p,ts)} assumes that \\spad{augment(p,ts)} returns a singleton and returns it.")) (|augment| (((|List| $) (|List| |#5|) (|List| $)) "\\spad{augment(lp,lts)} returns the same as \\spad{concat([augment(lp,ts) for ts in lts])}") (((|List| $) (|List| |#5|) $) "\\spad{augment(lp,ts)} returns \\spad{ts} if \\spad{empty? lp},{} \\spad{augment(p,ts)} if \\spad{lp = [p]},{} otherwise \\spad{augment(first lp, augment(rest lp, ts))}") (((|List| $) |#5| (|List| $)) "\\spad{augment(p,lts)} returns the same as \\spad{concat([augment(p,ts) for ts in lts])}") (((|List| $) |#5| $) "\\spad{augment(p,ts)} assumes that \\spad{p} is a non-constant polynomial whose main variable is greater than any variable of \\spad{ts}. This operation assumes also that if \\spad{p} is added to \\spad{ts} the resulting set,{} say \\spad{ts+p},{} is a regular triangular set. Then it returns a split of Kalkbrener of \\spad{ts+p}. This may not be \\spad{ts+p} itself,{} if for instance \\spad{ts+p} is required to be square-free.")) (|intersect| (((|List| $) |#5| (|List| $)) "\\spad{intersect(p,lts)} returns the same as \\spad{intersect([p],lts)}") (((|List| $) (|List| |#5|) (|List| $)) "\\spad{intersect(lp,lts)} returns the same as \\spad{concat([intersect(lp,ts) for ts in lts])|}") (((|List| $) (|List| |#5|) $) "\\spad{intersect(lp,ts)} returns \\spad{lts} a split of Lazard of the intersection of the affine variety associated with \\spad{lp} and the regular zero set of \\spad{ts}.") (((|List| $) |#5| $) "\\spad{intersect(p,ts)} returns the same as \\spad{intersect([p],ts)}")) (|squareFreePart| (((|List| (|Record| (|:| |val| |#5|) (|:| |tower| $))) |#5| $) "\\spad{squareFreePart(p,ts)} returns \\spad{lpwt} such that \\spad{lpwt.i.val} is a square-free polynomial \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower},{} this polynomial being associated with \\spad{p} modulo \\spad{lpwt.i.tower},{} for every \\spad{i}. Moreover,{} the list of the \\spad{lpwt.i.tower} is a split of Kalkbrener of \\spad{ts}. WARNING: This assumes that \\spad{p} is a non-constant polynomial such that if \\spad{p} is added to \\spad{ts},{} then the resulting set is a regular triangular set.")) (|lastSubResultant| (((|List| (|Record| (|:| |val| |#5|) (|:| |tower| $))) |#5| |#5| $) "\\spad{lastSubResultant(p1,p2,ts)} returns \\spad{lpwt} such that \\spad{lpwt.i.val} is a quasi-monic gcd of \\spad{p1} and \\spad{p2} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower},{} for every \\spad{i},{} and such that the list of the \\spad{lpwt.i.tower} is a split of Kalkbrener of \\spad{ts}. Moreover,{} if \\spad{p1} and \\spad{p2} do not have a non-trivial gcd \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower} then \\spad{lpwt.i.val} is the resultant of these polynomials \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower}. This assumes that \\spad{p1} and \\spad{p2} have the same maim variable and that this variable is greater that any variable occurring in \\spad{ts}.")) (|lastSubResultantElseSplit| (((|Union| |#5| (|List| $)) |#5| |#5| $) "\\spad{lastSubResultantElseSplit(p1,p2,ts)} returns either \\spad{g} a quasi-monic gcd of \\spad{p1} and \\spad{p2} \\spad{w}.\\spad{r}.\\spad{t}. the \\spad{ts} or a split of Kalkbrener of \\spad{ts}. This assumes that \\spad{p1} and \\spad{p2} have the same maim variable and that this variable is greater that any variable occurring in \\spad{ts}.")) (|invertibleSet| (((|List| $) |#5| $) "\\spad{invertibleSet(p,ts)} returns a split of Kalkbrener of the quotient ideal of the ideal \\axiom{\\spad{I}} by \\spad{p} where \\spad{I} is the radical of saturated of \\spad{ts}.")) (|invertible?| (((|Boolean|) |#5| $) "\\spad{invertible?(p,ts)} returns \\spad{true} iff \\spad{p} is invertible in the tower associated with \\spad{ts}.") (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| $))) |#5| $) "\\spad{invertible?(p,ts)} returns \\spad{lbwt} where \\spad{lbwt.i} is the result of \\spad{invertibleElseSplit?(p,lbwt.i.tower)} and the list of the \\spad{(lqrwt.i).tower} is a split of Kalkbrener of \\spad{ts}.")) (|invertibleElseSplit?| (((|Union| (|Boolean|) (|List| $)) |#5| $) "\\spad{invertibleElseSplit?(p,ts)} returns \\spad{true} (resp. \\spad{false}) if \\spad{p} is invertible in the tower associated with \\spad{ts} or returns a split of Kalkbrener of \\spad{ts}.")) (|purelyAlgebraicLeadingMonomial?| (((|Boolean|) |#5| $) "\\spad{purelyAlgebraicLeadingMonomial?(p,ts)} returns \\spad{true} iff the main variable of any non-constant iterarted initial of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}.")) (|algebraicCoefficients?| (((|Boolean|) |#5| $) "\\spad{algebraicCoefficients?(p,ts)} returns \\spad{true} iff every variable of \\spad{p} which is not the main one of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}.")) (|purelyTranscendental?| (((|Boolean|) |#5| $) "\\spad{purelyTranscendental?(p,ts)} returns \\spad{true} iff every variable of \\spad{p} is not algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}")) (|purelyAlgebraic?| (((|Boolean|) $) "\\spad{purelyAlgebraic?(ts)} returns \\spad{true} iff for every algebraic variable \\spad{v} of \\spad{ts} we have \\spad{algebraicCoefficients?(t_v,ts_v_-)} where \\spad{ts_v} is \\axiomOpFrom{select}{TriangularSetCategory}(\\spad{ts},{}\\spad{v}) and \\spad{ts_v_-} is \\axiomOpFrom{collectUnder}{TriangularSetCategory}(\\spad{ts},{}\\spad{v}).") (((|Boolean|) |#5| $) "\\spad{purelyAlgebraic?(p,ts)} returns \\spad{true} iff every variable of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}."))) 
 NIL 
 NIL 
-(-982 R E V P) 
+(-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}."))) 
-((-3990 . T) (-3989 . T)) 
+((-3992 . T) (-3991 . T)) 
 NIL 
-(-983 R E V P TS) 
+(-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."))) 
 NIL 
 NIL 
-(-984) 
+(-985) 
 ((|constructor| (NIL "This domain represents `restrict' expressions.")) (|target| (((|TypeAst|) $) "\\spad{target(e)} returns the target type of the conversion..")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression being converted."))) 
 NIL 
 NIL 
-(-985) 
+(-986) 
 ((|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 
-(-986 |Base| R -3088) 
+(-987 |Base| R -3090) 
 ((|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 
-(-987 |f|) 
+(-988 |f|) 
 ((|constructor| (NIL "This domain implements named rules")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) 
 NIL 
 NIL 
-(-988 |Base| R -3088) 
+(-989 |Base| R -3090) 
 ((|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 
-(-989 R |ls|) 
+(-990 R |ls|) 
 ((|constructor| (NIL "\\indented{1}{A package for computing the rational univariate representation} \\indented{1}{of a zero-dimensional algebraic variety given by a regular} \\indented{1}{triangular set. This package is essentially an interface for the} \\spadtype{InternalRationalUnivariateRepresentationPackage} constructor. It is used in the \\spadtype{ZeroDimensionalSolvePackage} for solving polynomial systems with finitely many solutions.")) (|rur| (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{rur(lp,univ?,check?)} returns the same as \\spad{rur(lp,true)}. Moreover,{} if \\spad{check?} is \\spad{true} then the result is checked.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|))) "\\spad{rur(lp)} returns the same as \\spad{rur(lp,true)}") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{rur(lp,univ?)} returns a rational univariate representation of \\spad{lp}. This assumes that \\spad{lp} defines a regular triangular \\spad{ts} whose associated variety is zero-dimensional over \\spad{R}. \\spad{rur(lp,univ?)} returns a list of items \\spad{[u,lc]} where \\spad{u} is an irreducible univariate polynomial and each \\spad{c} in \\spad{lc} involves two variables: one from \\spad{ls},{} called the coordinate of \\spad{c},{} and an extra variable which represents any root of \\spad{u}. Every root of \\spad{u} leads to a tuple of values for the coordinates of \\spad{lc}. Moreover,{} a point \\spad{x} belongs to the variety associated with \\spad{lp} iff there exists an item \\spad{[u,lc]} in \\spad{rur(lp,univ?)} and a root \\spad{r} of \\spad{u} such that \\spad{x} is given by the tuple of values for the coordinates of \\spad{lc} evaluated at \\spad{r}. If \\spad{univ?} is \\spad{true} then each polynomial \\spad{c} will have a constant leading coefficient \\spad{w}.\\spad{r}.\\spad{t}. its coordinate. See the example which illustrates the \\spadtype{ZeroDimensionalSolvePackage} package constructor."))) 
 NIL 
 NIL 
-(-990 R UP M) 
+(-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."))) 
-((-3982 |has| |#1| (-311)) (-3987 |has| |#1| (-311)) (-3981 |has| |#1| (-311)) ((-3991 "*") . T) (-3983 . T) (-3984 . T) (-3986 . 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 (-809 (-1088))))) (-12 (|HasCategory| |#1| (QUOTE (-298))) (|HasCategory| |#1| (QUOTE (-809 (-1088)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-809 (-1088))))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-811 (-1088)))))) (|HasCategory| |#1| (QUOTE (-580 (-483)))) (OR (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-950 (-347 (-483)))))) (|HasCategory| |#1| (QUOTE (-950 (-347 (-483))))) (|HasCategory| |#1| (QUOTE (-950 (-483)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-311)))) (|HasCategory| |#1| (QUOTE (-298)))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-811 (-1088))))) (-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 (-809 (-1088)))))) 
-(-991 UP SAE UPA) 
+((-3984 |has| |#1| (-311)) (-3989 |has| |#1| (-311)) (-3983 |has| |#1| (-311)) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . 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}."))) 
 NIL 
 NIL 
-(-992 UP SAE UPA) 
+(-993 UP SAE UPA) 
 ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of \\spadtype{Fraction Polynomial Integer}.")) (|factor| (((|Factored| |#3|) |#3|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p}."))) 
 NIL 
 NIL 
-(-993) 
+(-994) 
 ((|constructor| (NIL "This trivial domain lets us build Univariate Polynomials in an anonymous variable"))) 
 NIL 
 NIL 
-(-994) 
+(-995) 
 ((|constructor| (NIL "This is the category of Spad syntax objects."))) 
 NIL 
 NIL 
-(-995 S) 
+(-996 S) 
 ((|constructor| (NIL "\\indented{1}{Cache of elements in a set} Author: Manuel Bronstein Date Created: 31 Oct 1988 Date Last Updated: 14 May 1991 \\indented{2}{A sorted cache of a cachable set \\spad{S} is a dynamic structure that} \\indented{2}{keeps the elements of \\spad{S} sorted and assigns an integer to each} \\indented{2}{element of \\spad{S} once it is in the cache. This way,{} equality and ordering} \\indented{2}{on \\spad{S} are tested directly on the integers associated with the elements} \\indented{2}{of \\spad{S},{} once they have been entered in the cache.}")) (|enterInCache| ((|#1| |#1| (|Mapping| (|Integer|) |#1| |#1|)) "\\spad{enterInCache(x, f)} enters \\spad{x} in the cache,{} calling \\spad{f(x, y)} to determine whether \\spad{x < y (f(x,y) < 0), x = y (f(x,y) = 0)},{} or \\spad{x > y (f(x,y) > 0)}. It returns \\spad{x} with an integer associated with it.") ((|#1| |#1| (|Mapping| (|Boolean|) |#1|)) "\\spad{enterInCache(x, f)} enters \\spad{x} in the cache,{} calling \\spad{f(y)} to determine whether \\spad{x} is equal to \\spad{y}. It returns \\spad{x} with an integer associated with it.")) (|cache| (((|List| |#1|)) "\\spad{cache()} returns the current cache as a list.")) (|clearCache| (((|Void|)) "\\spad{clearCache()} empties the cache."))) 
 NIL 
 NIL 
-(-996) 
+(-997) 
 ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. A `Scope' is a sequence of contours.")) (|currentCategoryFrame| (($) "\\spad{currentCategoryFrame()} returns the category frame currently in effect.")) (|currentScope| (($) "\\spad{currentScope()} returns the scope currently in effect")) (|pushNewContour| (($ (|Binding|) $) "\\spad{pushNewContour(b,s)} pushs a new contour with sole binding `b'.")) (|findBinding| (((|Maybe| (|Binding|)) (|Identifier|) $) "\\spad{findBinding(n,s)} returns the first binding of `n' in `s'; otherwise `nothing'.")) (|contours| (((|List| (|Contour|)) $) "\\spad{contours(s)} returns the list of contours in scope \\spad{s}.")) (|empty| (($) "\\spad{empty()} returns an empty scope."))) 
 NIL 
 NIL 
-(-997 R) 
+(-998 R) 
 ((|constructor| (NIL "StructuralConstantsPackage provides functions creating structural constants from a multiplication tables or a basis of a matrix algebra and other useful functions in this context.")) (|coordinates| (((|Vector| |#1|) (|Matrix| |#1|) (|List| (|Matrix| |#1|))) "\\spad{coordinates(a,[v1,...,vn])} returns the coordinates of \\spad{a} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|structuralConstants| (((|Vector| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{structuralConstants(basis)} takes the \\spad{basis} of a matrix algebra,{} \\spadignore{e.g.} the result of \\spadfun{basisOfCentroid} and calculates the structural constants. Note,{} that the it is not checked,{} whether \\spad{basis} really is a \\spad{basis} of a matrix algebra.") (((|Vector| (|Matrix| (|Polynomial| |#1|))) (|List| (|Symbol|)) (|Matrix| (|Polynomial| |#1|))) "\\spad{structuralConstants(ls,mt)} determines the structural constants of an algebra with generators \\spad{ls} and multiplication table \\spad{mt},{} the entries of which must be given as linear polynomials in the indeterminates given by \\spad{ls}. The result is in particular useful \\indented{1}{as fourth argument for \\spadtype{AlgebraGivenByStructuralConstants}} \\indented{1}{and \\spadtype{GenericNonAssociativeAlgebra}.}") (((|Vector| (|Matrix| (|Fraction| (|Polynomial| |#1|)))) (|List| (|Symbol|)) (|Matrix| (|Fraction| (|Polynomial| |#1|)))) "\\spad{structuralConstants(ls,mt)} determines the structural constants of an algebra with generators \\spad{ls} and multiplication table \\spad{mt},{} the entries of which must be given as linear polynomials in the indeterminates given by \\spad{ls}. The result is in particular useful \\indented{1}{as fourth argument for \\spadtype{AlgebraGivenByStructuralConstants}} \\indented{1}{and \\spadtype{GenericNonAssociativeAlgebra}.}"))) 
 NIL 
 NIL 
-(-998 R) 
+(-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"))) 
-(((-3991 "*") |has| |#1| (-146)) (-3982 |has| |#1| (-494)) (-3987 |has| |#1| (-6 -3987)) (-3984 . T) (-3983 . T) (-3986 . T)) 
-((|HasCategory| |#1| (QUOTE (-821))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-389))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-821)))) (OR (|HasCategory| |#1| (QUOTE (-389))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-821)))) (OR (|HasCategory| |#1| (QUOTE (-389))) (|HasCategory| |#1| (QUOTE (-821)))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-494)))) (-12 (|HasCategory| |#1| (QUOTE (-796 (-327)))) (|HasCategory| (-999 (-1088)) (QUOTE (-796 (-327))))) (-12 (|HasCategory| |#1| (QUOTE (-796 (-483)))) (|HasCategory| (-999 (-1088)) (QUOTE (-796 (-483))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-800 (-327))))) (|HasCategory| (-999 (-1088)) (QUOTE (-553 (-800 (-327)))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-800 (-483))))) (|HasCategory| (-999 (-1088)) (QUOTE (-553 (-800 (-483)))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-472)))) (|HasCategory| (-999 (-1088)) (QUOTE (-553 (-472))))) (|HasCategory| |#1| (QUOTE (-580 (-483)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-347 (-483))))) (|HasCategory| |#1| (QUOTE (-950 (-483)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-347 (-483))))) (|HasCategory| |#1| (QUOTE (-950 (-347 (-483)))))) (|HasCategory| |#1| (QUOTE (-950 (-347 (-483))))) (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-811 (-1088)))) (|HasCategory| |#1| (QUOTE (-809 (-1088)))) (|HasCategory| |#1| (QUOTE (-311))) (|HasAttribute| |#1| (QUOTE -3987)) (|HasCategory| |#1| (QUOTE (-389))) (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) 
-(-999 S) 
+(((-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))))) 
+(-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 
 NIL 
-(-1000 S) 
+(-1001 S) 
 ((|constructor| (NIL "This type is used to specify a range of values from type \\spad{S}."))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-755))) (|HasCategory| |#1| (QUOTE (-1012)))) 
-(-1001 R S) 
+((|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1013)))) 
+(-1002 R S) 
 ((|constructor| (NIL "This package provides operations for mapping functions onto segments.")) (|map| (((|List| |#2|) (|Mapping| |#2| |#1|) (|Segment| |#1|)) "\\spad{map(f,s)} expands the segment \\spad{s},{} applying \\spad{f} to each value. For example,{} if \\spad{s = l..h by k},{} then the list \\spad{[f(l), f(l+k),..., f(lN)]} is computed,{} where \\spad{lN <= h < lN+k}.") (((|Segment| |#2|) (|Mapping| |#2| |#1|) (|Segment| |#1|)) "\\spad{map(f,l..h)} returns a new segment \\spad{f(l)..f(h)}."))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-755)))) 
-(-1002) 
+((|HasCategory| |#1| (QUOTE (-756)))) 
+(-1003) 
 ((|constructor| (NIL "This domain represents segement expressions.")) (|bounds| (((|List| (|SpadAst|)) $) "\\spad{bounds(s)} returns the bounds of the segment `s'. If `s' designates an infinite interval,{} then the returns list a singleton list."))) 
 NIL 
 NIL 
-(-1003 S) 
+(-1004 S) 
 ((|constructor| (NIL "This domain is used to provide the function argument syntax \\spad{v=a..b}. This is used,{} for example,{} by the top-level \\spadfun{draw} functions."))) 
 NIL 
-((|HasCategory| (-1000 |#1|) (QUOTE (-1012)))) 
-(-1004 R S) 
+((|HasCategory| (-1001 |#1|) (QUOTE (-1013)))) 
+(-1005 R S) 
 ((|constructor| (NIL "This package provides operations for mapping functions onto \\spadtype{SegmentBinding}\\spad{s}.")) (|map| (((|SegmentBinding| |#2|) (|Mapping| |#2| |#1|) (|SegmentBinding| |#1|)) "\\spad{map(f,v=a..b)} returns the value given by \\spad{v=f(a)..f(b)}."))) 
 NIL 
 NIL 
-(-1005 S) 
+(-1006 S) 
 ((|constructor| (NIL "This category provides operations on ranges,{} or {\\em segments} as they are called.")) (|segment| (($ |#1| |#1|) "\\spad{segment(i,j)} is an alternate way to create the segment \\spad{i..j}.")) (|incr| (((|Integer|) $) "\\spad{incr(s)} returns \\spad{n},{} where \\spad{s} is a segment in which every \\spad{n}\\spad{-}th element is used. Note: \\spad{incr(l..h by n) = n}.")) (|high| ((|#1| $) "\\spad{high(s)} returns the second endpoint of \\spad{s}. Note: \\spad{high(l..h) = h}.")) (|low| ((|#1| $) "\\spad{low(s)} returns the first endpoint of \\spad{s}. Note: \\spad{low(l..h) = l}.")) (|hi| ((|#1| $) "\\spad{hi(s)} returns the second endpoint of \\spad{s}. Note: \\spad{hi(l..h) = h}.")) (|lo| ((|#1| $) "\\spad{lo(s)} returns the first endpoint of \\spad{s}. Note: \\spad{lo(l..h) = l}.")) (BY (($ $ (|Integer|)) "\\spad{s by n} creates a new segment in which only every \\spad{n}\\spad{-}th element is used.")) (SEGMENT (($ |#1| |#1|) "\\spad{l..h} creates a segment with \\spad{l} and \\spad{h} as the endpoints."))) 
 NIL 
 NIL 
-(-1006 S L) 
+(-1007 S L) 
 ((|constructor| (NIL "This category provides an interface for expanding segments to a stream of elements.")) (|map| ((|#2| (|Mapping| |#1| |#1|) $) "\\spad{map(f,l..h by k)} produces a value of type \\spad{L} by applying \\spad{f} to each of the succesive elements of the segment,{} that is,{} \\spad{[f(l), f(l+k), ..., f(lN)]},{} where \\spad{lN <= h < lN+k}.")) (|expand| ((|#2| $) "\\spad{expand(l..h by k)} creates value of type \\spad{L} with elements \\spad{l, l+k, ... lN} where \\spad{lN <= h < lN+k}. For example,{} \\spad{expand(1..5 by 2) = [1,3,5]}.") ((|#2| (|List| $)) "\\spad{expand(l)} creates a new value of type \\spad{L} in which each segment \\spad{l..h by k} is replaced with \\spad{l, l+k, ... lN},{} where \\spad{lN <= h < lN+k}. For example,{} \\spad{expand [1..4, 7..9] = [1,2,3,4,7,8,9]}."))) 
 NIL 
 NIL 
-(-1007) 
+(-1008) 
 ((|constructor| (NIL "This domain represents a block of expressions.")) (|last| (((|SpadAst|) $) "\\spad{last(e)} returns the last instruction in `e'.")) (|body| (((|List| (|SpadAst|)) $) "\\spad{body(e)} returns the list of expressions in the sequence of instruction `e'."))) 
 NIL 
 NIL 
-(-1008 S) 
+(-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)}}"))) 
-((-3989 . T) (-3979 . T) (-3990 . T)) 
-((OR (-12 (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-553 (-472)))) (|HasCategory| |#1| (QUOTE (-317))) (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|))))) 
-(-1009 A S) 
+((-3991 . T) (-3981 . T) (-3992 . 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|) $ $) "\\spad{s} < \\spad{t} returns \\spad{true} if all elements of set aggregate \\spad{s} are also elements of set aggregate \\spad{t}."))) 
 NIL 
 NIL 
-(-1010 S) 
+(-1011 S) 
 ((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#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}."))) 
-((-3979 . T)) 
+((-3981 . T)) 
 NIL 
-(-1011 S) 
+(-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}."))) 
 NIL 
 NIL 
-(-1012) 
+(-1013) 
 ((|constructor| (NIL "\\spadtype{SetCategory} is the basic category for describing a collection of elements with \\spadop{=} (equality) and \\spadfun{coerce} to output form. \\blankline Conditional Attributes: \\indented{3}{canonical\\tab{15}data structure equality is the same as \\spadop{=}}")) (|latex| (((|String|) $) "\\spad{latex(s)} returns a LaTeX-printable output representation of \\spad{s}.")) (|hash| (((|SingleInteger|) $) "\\spad{hash(s)} calculates a hash code for \\spad{s}."))) 
 NIL 
 NIL 
-(-1013 |m| |n|) 
+(-1014 |m| |n|) 
 ((|constructor| (NIL "\\spadtype{SetOfMIntegersInOneToN} implements the subsets of \\spad{M} integers in the interval \\spad{[1..n]}")) (|delta| (((|NonNegativeInteger|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{delta(S,k,p)} returns the number of elements of \\spad{S} which are strictly between \\spad{p} and the k^{th} element of \\spad{S}.")) (|member?| (((|Boolean|) (|PositiveInteger|) $) "\\spad{member?(p, s)} returns \\spad{true} is \\spad{p} is in \\spad{s},{} \\spad{false} otherwise.")) (|enumerate| (((|Vector| $)) "\\spad{enumerate()} returns a vector of all the sets of \\spad{M} integers in \\spad{1..n}.")) (|setOfMinN| (($ (|List| (|PositiveInteger|))) "\\spad{setOfMinN([a_1,...,a_m])} returns the set {\\spad{a_1},{}...,{}a_m}. Error if {\\spad{a_1},{}...,{}a_m} is not a set of \\spad{M} integers in \\spad{1..n}.")) (|elements| (((|List| (|PositiveInteger|)) $) "\\spad{elements(S)} returns the list of the elements of \\spad{S} in increasing order.")) (|replaceKthElement| (((|Union| $ #1="failed") $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{replaceKthElement(S,k,p)} replaces the k^{th} element of \\spad{S} by \\spad{p},{} and returns \"failed\" if the result is not a set of \\spad{M} integers in \\spad{1..n} any more.")) (|incrementKthElement| (((|Union| $ #1#) $ (|PositiveInteger|)) "\\spad{incrementKthElement(S,k)} increments the k^{th} element of \\spad{S},{} and returns \"failed\" if the result is not a set of \\spad{M} integers in \\spad{1..n} any more."))) 
 NIL 
 NIL 
-(-1014) 
+(-1015) 
 ((|constructor| (NIL "This domain allows the manipulation of the usual Lisp values."))) 
 NIL 
 NIL 
-(-1015 |Str| |Sym| |Int| |Flt| |Expr|) 
+(-1016 |Str| |Sym| |Int| |Flt| |Expr|) 
 ((|constructor| (NIL "This category allows the manipulation of Lisp values while keeping the grunge fairly localized.")) (|#| (((|Integer|) $) "\\spad{\\#((a1,...,an))} returns \\spad{n}.")) (|cdr| (($ $) "\\spad{cdr((a1,...,an))} returns \\spad{(a2,...,an)}.")) (|car| (($ $) "\\spad{car((a1,...,an))} returns \\spad{a1}.")) (|expr| ((|#5| $) "\\spad{expr(s)} returns \\spad{s} as an element of Expr; Error: if \\spad{s} is not an atom that also belongs to Expr.")) (|float| ((|#4| $) "\\spad{float(s)} returns \\spad{s} as an element of Flt; Error: if \\spad{s} is not an atom that also belongs to Flt.")) (|integer| ((|#3| $) "\\spad{integer(s)} returns \\spad{s} as an element of Int. Error: if \\spad{s} is not an atom that also belongs to Int.")) (|symbol| ((|#2| $) "\\spad{symbol(s)} returns \\spad{s} as an element of Sym. Error: if \\spad{s} is not an atom that also belongs to Sym.")) (|string| ((|#1| $) "\\spad{string(s)} returns \\spad{s} as an element of Str. Error: if \\spad{s} is not an atom that also belongs to Str.")) (|destruct| (((|List| $) $) "\\spad{destruct((a1,...,an))} returns the list [\\spad{a1},{}...,{}an].")) (|float?| (((|Boolean|) $) "\\spad{float?(s)} is \\spad{true} if \\spad{s} is an atom and belong to Flt.")) (|integer?| (((|Boolean|) $) "\\spad{integer?(s)} is \\spad{true} if \\spad{s} is an atom and belong to Int.")) (|symbol?| (((|Boolean|) $) "\\spad{symbol?(s)} is \\spad{true} if \\spad{s} is an atom and belong to Sym.")) (|string?| (((|Boolean|) $) "\\spad{string?(s)} is \\spad{true} if \\spad{s} is an atom and belong to Str.")) (|list?| (((|Boolean|) $) "\\spad{list?(s)} is \\spad{true} if \\spad{s} is a Lisp list,{} possibly ().")) (|pair?| (((|Boolean|) $) "\\spad{pair?(s)} is \\spad{true} if \\spad{s} has is a non-null Lisp list.")) (|atom?| (((|Boolean|) $) "\\spad{atom?(s)} is \\spad{true} if \\spad{s} is a Lisp atom.")) (|null?| (((|Boolean|) $) "\\spad{null?(s)} is \\spad{true} if \\spad{s} is the \\spad{S}-expression ().")) (|eq| (((|Boolean|) $ $) "\\spad{eq(s, t)} is \\spad{true} if \\%peq(\\spad{s},{}\\spad{t}) is \\spad{true} for pointers."))) 
 NIL 
 NIL 
-(-1016 |Str| |Sym| |Int| |Flt| |Expr|) 
+(-1017 |Str| |Sym| |Int| |Flt| |Expr|) 
 ((|constructor| (NIL "This domain allows the manipulation of Lisp values over arbitrary atomic types."))) 
 NIL 
 NIL 
-(-1017 R E V P TS) 
+(-1018 R E V P TS) 
 ((|constructor| (NIL "\\indented{2}{A internal package for removing redundant quasi-components and redundant} \\indented{2}{branches when decomposing a variety by means of quasi-components} \\indented{2}{of regular triangular sets. \\newline} References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{5}{Tech. Report (PoSSo project)} \\indented{1}{[2] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|branchIfCan| (((|Union| (|Record| (|:| |eq| (|List| |#4|)) (|:| |tower| |#5|) (|:| |ineq| (|List| |#4|))) "failed") (|List| |#4|) |#5| (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{branchIfCan(leq,{}ts,{}lineq,{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement.")) (|prepareDecompose| (((|List| (|Record| (|:| |eq| (|List| |#4|)) (|:| |tower| |#5|) (|:| |ineq| (|List| |#4|)))) (|List| |#4|) (|List| |#5|) (|Boolean|) (|Boolean|)) "\\axiom{prepareDecompose(lp,{}lts,{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|removeSuperfluousCases| (((|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|)))) "\\axiom{removeSuperfluousCases(llpwt)} is an internal subroutine,{} exported only for developement.")) (|subCase?| (((|Boolean|) (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|)) (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) "\\axiom{subCase?(\\spad{lpwt1},{}\\spad{lpwt2})} is an internal subroutine,{} exported only for developement.")) (|removeSuperfluousQuasiComponents| (((|List| |#5|) (|List| |#5|)) "\\axiom{removeSuperfluousQuasiComponents(lts)} removes from \\axiom{lts} any \\spad{ts} such that \\axiom{subQuasiComponent?(ts,{}us)} holds for another \\spad{us} in \\axiom{lts}.")) (|subQuasiComponent?| (((|Boolean|) |#5| (|List| |#5|)) "\\axiom{subQuasiComponent?(ts,{}lus)} returns \\spad{true} iff \\axiom{subQuasiComponent?(ts,{}us)} holds for one \\spad{us} in \\spad{lus}.") (((|Boolean|) |#5| |#5|) "\\axiom{subQuasiComponent?(ts,{}us)} returns \\spad{true} iff \\axiomOpFrom{internalSubQuasiComponent?(ts,{}us)}{QuasiComponentPackage} returs \\spad{true}.")) (|internalSubQuasiComponent?| (((|Union| (|Boolean|) "failed") |#5| |#5|) "\\axiom{internalSubQuasiComponent?(ts,{}us)} returns a boolean \\spad{b} value if the fact the regular zero set of \\axiom{us} contains that of \\axiom{ts} can be decided (and in that case \\axiom{\\spad{b}} gives this inclusion) otherwise returns \\axiom{\"failed\"}.")) (|infRittWu?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{infRittWu?(\\spad{lp1},{}\\spad{lp2})} is an internal subroutine,{} exported only for developement.")) (|internalInfRittWu?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{internalInfRittWu?(\\spad{lp1},{}\\spad{lp2})} is an internal subroutine,{} exported only for developement.")) (|internalSubPolSet?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{internalSubPolSet?(\\spad{lp1},{}\\spad{lp2})} returns \\spad{true} iff \\axiom{\\spad{lp1}} is a sub-set of \\axiom{\\spad{lp2}} assuming that these lists are sorted increasingly \\spad{w}.\\spad{r}.\\spad{t}. \\axiomOpFrom{infRittWu?}{RecursivePolynomialCategory}.")) (|subPolSet?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{subPolSet?(\\spad{lp1},{}\\spad{lp2})} returns \\spad{true} iff \\axiom{\\spad{lp1}} is a sub-set of \\axiom{\\spad{lp2}}.")) (|subTriSet?| (((|Boolean|) |#5| |#5|) "\\axiom{subTriSet?(ts,{}us)} returns \\spad{true} iff \\axiom{ts} is a sub-set of \\axiom{us}.")) (|moreAlgebraic?| (((|Boolean|) |#5| |#5|) "\\axiom{moreAlgebraic?(ts,{}us)} returns \\spad{false} iff \\axiom{ts} and \\axiom{us} are both empty,{} or \\axiom{ts} has less elements than \\axiom{us},{} or some variable is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{us} and is not \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ts}.")) (|algebraicSort| (((|List| |#5|) (|List| |#5|)) "\\axiom{algebraicSort(lts)} sorts \\axiom{lts} \\spad{w}.\\spad{r}.\\spad{t} \\axiomOpFrom{supDimElseRittWu}{QuasiComponentPackage}.")) (|supDimElseRittWu?| (((|Boolean|) |#5| |#5|) "\\axiom{supDimElseRittWu(ts,{}us)} returns \\spad{true} iff \\axiom{ts} has less elements than \\axiom{us} otherwise if \\axiom{ts} has higher rank than \\axiom{us} \\spad{w}.\\spad{r}.\\spad{t}. Riit and Wu ordering.")) (|stopTable!| (((|Void|)) "\\axiom{stopTableGcd!()} is an internal subroutine,{} exported only for developement.")) (|startTable!| (((|Void|) (|String|) (|String|) (|String|)) "\\axiom{startTableGcd!(\\spad{s1},{}\\spad{s2},{}\\spad{s3})} is an internal subroutine,{} exported only for developement."))) 
 NIL 
 NIL 
-(-1018 R E V P TS) 
+(-1019 R E V P TS) 
 ((|constructor| (NIL "A internal package for computing gcds and resultants of univariate polynomials with coefficients in a tower of simple extensions of a field. There is no need to use directly this package since its main operations are available from \\spad{TS}. \\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA and \\spad{R}. RIOBOO \"Computations of gcd over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of \\spad{AAECC11}} \\indented{5}{Paris,{} 1995.} \\indented{1}{[2] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}"))) 
 NIL 
 NIL 
-(-1019 R E V P) 
+(-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.}"))) 
-((-3990 . T) (-3989 . T)) 
+((-3992 . T) (-3991 . T)) 
 NIL 
-(-1020) 
+(-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."))) 
 NIL 
 NIL 
-(-1021 T$) 
+(-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."))) 
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+(((|%Rule| |associativity| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|) (|:| |y| |#1|) (|:| |z| |#1|)) (-3054 (|f| (|f| |x| |y|) |z|) (|f| |x| (|f| |y| |z|))))) . T)) 
 NIL 
-(-1022 T$) 
+(-1023 T$) 
 ((|constructor| (NIL "This is the category of all domains that implement semigroup operations"))) 
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+(((|%Rule| |associativity| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|) (|:| |y| |#1|) (|:| |z| |#1|)) (-3054 (|f| (|f| |x| |y|) |z|) (|f| |x| (|f| |y| |z|))))) . T)) 
 NIL 
-(-1023 S) 
+(-1024 S) 
 ((|constructor| (NIL "the class of all multiplicative semigroups,{} \\spadignore{i.e.} a set with an associative operation \\spadop{*}. \\blankline")) (** (($ $ (|PositiveInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (* (($ $ $) "\\spad{x*y} returns the product of \\spad{x} and \\spad{y}."))) 
 NIL 
 NIL 
-(-1024) 
+(-1025) 
 ((|constructor| (NIL "the class of all multiplicative semigroups,{} \\spadignore{i.e.} a set with an associative operation \\spadop{*}. \\blankline")) (** (($ $ (|PositiveInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (* (($ $ $) "\\spad{x*y} returns the product of \\spad{x} and \\spad{y}."))) 
 NIL 
 NIL 
-(-1025 |dimtot| |dim1| S) 
+(-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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-(-1026 R |x|) 
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(-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 (-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))))) (|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 -3988)) (-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 
 ((|HasCategory| |#1| (QUOTE (-389)))) 
-(-1027) 
+(-1028) 
 ((|constructor| (NIL "This is the datatype for operation signatures as \\indented{2}{used by the compiler and the interpreter.\\space{2}Note that this domain} \\indented{2}{differs from SignatureAst.} See also: ConstructorCall,{} Domain.")) (|source| (((|List| (|Syntax|)) $) "\\spad{source(s)} returns the list of parameter types of `s'.")) (|target| (((|Syntax|) $) "\\spad{target(s)} returns the target type of the signature `s'.")) (|signature| (($ (|List| (|Syntax|)) (|Syntax|)) "\\spad{signature(s,t)} constructs a Signature object with parameter types indicaded by `s',{} and return type indicated by `t'."))) 
 NIL 
 NIL 
-(-1028) 
+(-1029) 
 ((|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 
-(-1029 R -3088) 
+(-1030 R -3090) 
 ((|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 
-(-1030 R) 
+(-1031 R) 
 ((|constructor| (NIL "Find the sign of a rational function around a point or infinity.")) (|sign| (((|Union| (|Integer|) #1="failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|)) (|String|)) "\\spad{sign(f, x, a, s)} returns the sign of \\spad{f} as \\spad{x} nears \\spad{a} from the left (below) if \\spad{s} is the string \\spad{\"left\"},{} or from the right (above) if \\spad{s} is the string \\spad{\"right\"}.") (((|Union| (|Integer|) #1#) (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|)))) "\\spad{sign(f, x, a)} returns the sign of \\spad{f} as \\spad{x} approaches \\spad{a},{} from both sides if \\spad{a} is finite.") (((|Union| (|Integer|) #1#) (|Fraction| (|Polynomial| |#1|))) "\\spad{sign f} returns the sign of \\spad{f} if it is constant everywhere."))) 
 NIL 
 NIL 
-(-1031) 
+(-1032) 
 ((|constructor| (NIL "\\indented{1}{Package to allow simplify to be called on AlgebraicNumbers} by converting to EXPR(INT)")) (|simplify| (((|Expression| (|Integer|)) (|AlgebraicNumber|)) "\\spad{simplify(an)} applies simplifications to \\spad{an}"))) 
 NIL 
 NIL 
-(-1032) 
+(-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."))) 
-((-3977 . T) (-3981 . T) (-3976 . T) (-3987 . T) (-3988 . T) (-3982 . T) ((-3991 "*") . T) (-3983 . T) (-3984 . T) (-3986 . T)) 
+((-3979 . T) (-3983 . T) (-3978 . T) (-3989 . T) (-3990 . T) (-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . T)) 
 NIL 
-(-1033 S) 
+(-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| $) "\\spad{push!(x,s)} pushes \\spad{x} onto stack \\spad{s},{} \\spadignore{i.e.} destructively changing \\spad{s} so as to have a new first (top) element \\spad{x}. Afterwards,{} pop!(\\spad{s}) produces \\spad{x} and pop!(\\spad{s}) produces the original \\spad{s}."))) 
-((-3989 . T) (-3990 . T)) 
+((-3991 . T) (-3992 . T)) 
 NIL 
-(-1034 S |ndim| R |Row| |Col|) 
+(-1035 S |ndim| R |Row| |Col|) 
 ((|constructor| (NIL "\\spadtype{SquareMatrixCategory} is a general square matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col.")) (** (($ $ (|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 (-3991 "*"))) (|HasCategory| |#3| (QUOTE (-146)))) 
-(-1035 |ndim| R |Row| |Col|) 
+((|HasCategory| |#3| (QUOTE (-311))) (|HasAttribute| |#3| (QUOTE (-3993 "*"))) (|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."))) 
-((-3989 . T) (-3983 . T) (-3984 . T) (-3986 . T)) 
+((-3991 . T) (-3985 . T) (-3986 . T) (-3988 . T)) 
 NIL 
-(-1036 R |Row| |Col| M) 
+(-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}."))) 
 NIL 
 NIL 
-(-1037 R |VarSet|) 
+(-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."))) 
-(((-3991 "*") |has| |#1| (-146)) (-3982 |has| |#1| (-494)) (-3987 |has| |#1| (-6 -3987)) (-3984 . T) (-3983 . T) (-3986 . T)) 
-((|HasCategory| |#1| (QUOTE (-821))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-389))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-821)))) (OR (|HasCategory| |#1| (QUOTE (-389))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-821)))) (OR (|HasCategory| |#1| (QUOTE (-389))) (|HasCategory| |#1| (QUOTE (-821)))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-494)))) (-12 (|HasCategory| |#1| (QUOTE (-796 (-327)))) (|HasCategory| |#2| (QUOTE (-796 (-327))))) (-12 (|HasCategory| |#1| (QUOTE (-796 (-483)))) (|HasCategory| |#2| (QUOTE (-796 (-483))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-800 (-327))))) (|HasCategory| |#2| (QUOTE (-553 (-800 (-327)))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-800 (-483))))) (|HasCategory| |#2| (QUOTE (-553 (-800 (-483)))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-472)))) (|HasCategory| |#2| (QUOTE (-553 (-472))))) (|HasCategory| |#1| (QUOTE (-580 (-483)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-347 (-483))))) (|HasCategory| |#1| (QUOTE (-950 (-483)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-347 (-483))))) (|HasCategory| |#1| (QUOTE (-950 (-347 (-483)))))) (|HasCategory| |#1| (QUOTE (-950 (-347 (-483))))) (|HasCategory| |#1| (QUOTE (-311))) (|HasAttribute| |#1| (QUOTE -3987)) (|HasCategory| |#1| (QUOTE (-389))) (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) 
-(-1038 |Coef| |Var| SMP) 
+(((-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))))) 
+(-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}."))) 
-(((-3991 "*") |has| |#1| (-146)) (-3982 |has| |#1| (-494)) (-3984 . T) (-3983 . T) (-3986 . T)) 
-((|HasCategory| |#1| (QUOTE (-38 (-347 (-483))))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-494)))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-311)))) 
-(-1039 R E V P) 
+(((-3993 "*") |has| |#1| (-146)) (-3984 |has| |#1| (-495)) (-3986 . T) (-3985 . T) (-3988 . 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}"))) 
-((-3990 . T) (-3989 . T)) 
+((-3992 . T) (-3991 . T)) 
 NIL 
-(-1040 UP -3088) 
+(-1041 UP -3090) 
 ((|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 
-(-1041 R) 
+(-1042 R) 
 ((|constructor| (NIL "This package tries to find solutions expressed in terms of radicals for systems of equations of rational functions with coefficients in an integral domain \\spad{R}.")) (|contractSolve| (((|SuchThat| (|List| (|Expression| |#1|)) (|List| (|Equation| (|Expression| |#1|)))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{contractSolve(rf,x)} finds the solutions expressed in terms of radicals of the equation \\spad{rf} = 0 with respect to the symbol \\spad{x},{} where \\spad{rf} is a rational function. The result contains new symbols for common subexpressions in order to reduce the size of the output.") (((|SuchThat| (|List| (|Expression| |#1|)) (|List| (|Equation| (|Expression| |#1|)))) (|Equation| (|Fraction| (|Polynomial| |#1|))) (|Symbol|)) "\\spad{contractSolve(eq,x)} finds the solutions expressed in terms of radicals of the equation of rational functions \\spad{eq} with respect to the symbol \\spad{x}. The result contains new symbols for common subexpressions in order to reduce the size of the output.")) (|radicalRoots| (((|List| (|List| (|Expression| |#1|))) (|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|Symbol|))) "\\spad{radicalRoots(lrf,lvar)} finds the roots expressed in terms of radicals of the list of rational functions \\spad{lrf} with respect to the list of symbols \\spad{lvar}.") (((|List| (|Expression| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{radicalRoots(rf,x)} finds the roots expressed in terms of radicals of the rational function \\spad{rf} with respect to the symbol \\spad{x}.")) (|radicalSolve| (((|List| (|List| (|Equation| (|Expression| |#1|)))) (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) "\\spad{radicalSolve(leq)} finds the solutions expressed in terms of radicals of the system of equations of rational functions \\spad{leq} with respect to the unique symbol \\spad{x} appearing in \\spad{leq}.") (((|List| (|List| (|Equation| (|Expression| |#1|)))) (|List| (|Equation| (|Fraction| (|Polynomial| |#1|)))) (|List| (|Symbol|))) "\\spad{radicalSolve(leq,lvar)} finds the solutions expressed in terms of radicals of the system of equations of rational functions \\spad{leq} with respect to the list of symbols \\spad{lvar}.") (((|List| (|List| (|Equation| (|Expression| |#1|)))) (|List| (|Fraction| (|Polynomial| |#1|)))) "\\spad{radicalSolve(lrf)} finds the solutions expressed in terms of radicals of the system of equations \\spad{lrf} = 0,{} where \\spad{lrf} is a system of univariate rational functions.") (((|List| (|List| (|Equation| (|Expression| |#1|)))) (|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|Symbol|))) "\\spad{radicalSolve(lrf,lvar)} finds the solutions expressed in terms of radicals of the system of equations \\spad{lrf} = 0 with respect to the list of symbols \\spad{lvar},{} where \\spad{lrf} is a list of rational functions.") (((|List| (|Equation| (|Expression| |#1|))) (|Equation| (|Fraction| (|Polynomial| |#1|)))) "\\spad{radicalSolve(eq)} finds the solutions expressed in terms of radicals of the equation of rational functions \\spad{eq} with respect to the unique symbol \\spad{x} appearing in \\spad{eq}.") (((|List| (|Equation| (|Expression| |#1|))) (|Equation| (|Fraction| (|Polynomial| |#1|))) (|Symbol|)) "\\spad{radicalSolve(eq,x)} finds the solutions expressed in terms of radicals of the equation of rational functions \\spad{eq} with respect to the symbol \\spad{x}.") (((|List| (|Equation| (|Expression| |#1|))) (|Fraction| (|Polynomial| |#1|))) "\\spad{radicalSolve(rf)} finds the solutions expressed in terms of radicals of the equation \\spad{rf} = 0,{} where \\spad{rf} is a univariate rational function.") (((|List| (|Equation| (|Expression| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{radicalSolve(rf,x)} finds the solutions expressed in terms of radicals of the equation \\spad{rf} = 0 with respect to the symbol \\spad{x},{} where \\spad{rf} is a rational function."))) 
 NIL 
 NIL 
-(-1042 R) 
+(-1043 R) 
 ((|constructor| (NIL "This package finds the function \\spad{func3} where \\spad{func1} and \\spad{func2} \\indented{1}{are given and\\space{2}\\spad{func1} = \\spad{func3}(\\spad{func2}) .\\space{2}If there is no solution then} \\indented{1}{function \\spad{func1} will be returned.} \\indented{1}{An example would be\\space{2}\\spad{func1:= 8*X**3+32*X**2-14*X ::EXPR INT} and} \\indented{1}{\\spad{func2:=2*X ::EXPR INT} convert them via univariate} \\indented{1}{to FRAC SUP EXPR INT and then the solution is \\spad{func3:=X**3+X**2-X}} \\indented{1}{of type FRAC SUP EXPR INT}")) (|unvectorise| (((|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Vector| (|Expression| |#1|)) (|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Integer|)) "\\spad{unvectorise(vect, var, n)} returns \\spad{vect(1) + vect(2)*var + ... + vect(n+1)*var**(n)} where \\spad{vect} is the vector of the coefficients of the polynomail ,{} \\spad{var} the new variable and \\spad{n} the degree.")) (|decomposeFunc| (((|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|)))) "\\spad{decomposeFunc(func1, func2, newvar)} returns a function \\spad{func3} where \\spad{func1} = \\spad{func3}(\\spad{func2}) and expresses it in the new variable newvar. If there is no solution then \\spad{func1} will be returned."))) 
 NIL 
 NIL 
-(-1043 R) 
+(-1044 R) 
 ((|constructor| (NIL "This package tries to find solutions of equations of type Expression(\\spad{R}). This means expressions involving transcendental,{} exponential,{} logarithmic and nthRoot functions. After trying to transform different kernels to one kernel by applying several rules,{} it calls zerosOf for the SparseUnivariatePolynomial in the remaining kernel. For example the expression \\spad{sin(x)*cos(x)-2} will be transformed to \\indented{3}{\\spad{-2 tan(x/2)**4 -2 tan(x/2)**3 -4 tan(x/2)**2 +2 tan(x/2) -2}} by using the function normalize and then to \\indented{3}{\\spad{-2 tan(x)**2 + tan(x) -2}} with help of subsTan. This function tries to express the given function in terms of \\spad{tan(x/2)} to express in terms of \\spad{tan(x)} . Other examples are the expressions \\spad{sqrt(x+1)+sqrt(x+7)+1} or \\indented{1}{\\spad{sqrt(sin(x))+1} .}")) (|solve| (((|List| (|List| (|Equation| (|Expression| |#1|)))) (|List| (|Equation| (|Expression| |#1|))) (|List| (|Symbol|))) "\\spad{solve(leqs, lvar)} returns a list of solutions to the list of equations \\spad{leqs} with respect to the list of symbols lvar.") (((|List| (|Equation| (|Expression| |#1|))) (|Expression| |#1|) (|Symbol|)) "\\spad{solve(expr,x)} finds the solutions of the equation \\spad{expr} = 0 with respect to the symbol \\spad{x} where \\spad{expr} is a function of type Expression(\\spad{R}).") (((|List| (|Equation| (|Expression| |#1|))) (|Equation| (|Expression| |#1|)) (|Symbol|)) "\\spad{solve(eq,x)} finds the solutions of the equation \\spad{eq} where \\spad{eq} is an equation of functions of type Expression(\\spad{R}) with respect to the symbol \\spad{x}.") (((|List| (|Equation| (|Expression| |#1|))) (|Equation| (|Expression| |#1|))) "\\spad{solve(eq)} finds the solutions of the equation \\spad{eq} where \\spad{eq} is an equation of functions of type Expression(\\spad{R}) with respect to the unique symbol \\spad{x} appearing in \\spad{eq}.") (((|List| (|Equation| (|Expression| |#1|))) (|Expression| |#1|)) "\\spad{solve(expr)} finds the solutions of the equation \\spad{expr} = 0 where \\spad{expr} is a function of type Expression(\\spad{R}) with respect to the unique symbol \\spad{x} appearing in eq."))) 
 NIL 
 NIL 
-(-1044 S A) 
+(-1045 S A) 
 ((|constructor| (NIL "This package exports sorting algorithnms")) (|insertionSort!| ((|#2| |#2|) "\\spad{insertionSort! }\\undocumented") ((|#2| |#2| (|Mapping| (|Boolean|) |#1| |#1|)) "\\spad{insertionSort!(a,f)} \\undocumented")) (|bubbleSort!| ((|#2| |#2|) "\\spad{bubbleSort!(a)} \\undocumented") ((|#2| |#2| (|Mapping| (|Boolean|) |#1| |#1|)) "\\spad{bubbleSort!(a,f)} \\undocumented"))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-756)))) 
-(-1045 R) 
+((|HasCategory| |#1| (QUOTE (-757)))) 
+(-1046 R) 
 ((|constructor| (NIL "The domain ThreeSpace is used for creating three dimensional objects using functions for defining points,{} curves,{} polygons,{} constructs and the subspaces containing them."))) 
 NIL 
 NIL 
-(-1046 R) 
+(-1047 R) 
 ((|constructor| (NIL "The category ThreeSpaceCategory is used for creating three dimensional objects using functions for defining points,{} curves,{} polygons,{} constructs and the subspaces containing them.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(s)} returns the \\spadtype{ThreeSpace} \\spad{s} to Output format.")) (|subspace| (((|SubSpace| 3 |#1|) $) "\\spad{subspace(s)} returns the \\spadtype{SubSpace} which holds all the point information in the \\spadtype{ThreeSpace},{} \\spad{s}.")) (|check| (($ $) "\\spad{check(s)} returns lllpt,{} list of lists of lists of point information about the \\spadtype{ThreeSpace} \\spad{s}.")) (|objects| (((|Record| (|:| |points| (|NonNegativeInteger|)) (|:| |curves| (|NonNegativeInteger|)) (|:| |polygons| (|NonNegativeInteger|)) (|:| |constructs| (|NonNegativeInteger|))) $) "\\spad{objects(s)} returns the \\spadtype{ThreeSpace},{} \\spad{s},{} in the form of a 3D object record containing information on the number of points,{} curves,{} polygons and constructs comprising the \\spadtype{ThreeSpace}..")) (|lprop| (((|List| (|SubSpaceComponentProperty|)) $) "\\spad{lprop(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a list of subspace component properties,{} and if so,{} returns the list; An error is signaled otherwise.")) (|llprop| (((|List| (|List| (|SubSpaceComponentProperty|))) $) "\\spad{llprop(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a list of curves which are lists of the subspace component properties of the curves,{} and if so,{} returns the list of lists; An error is signaled otherwise.")) (|lllp| (((|List| (|List| (|List| (|Point| |#1|)))) $) "\\spad{lllp(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a list of components,{} which are lists of curves,{} which are lists of points,{} and if so,{} returns the list of lists of lists; An error is signaled otherwise.")) (|lllip| (((|List| (|List| (|List| (|NonNegativeInteger|)))) $) "\\spad{lllip(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a list of components,{} which are lists of curves,{} which are lists of indices to points,{} and if so,{} returns the list of lists of lists; An error is signaled otherwise.")) (|lp| (((|List| (|Point| |#1|)) $) "\\spad{lp(s)} returns the list of points component which the \\spadtype{ThreeSpace},{} \\spad{s},{} contains; these points are used by reference,{} \\spadignore{i.e.} the component holds indices referring to the points rather than the points themselves. This allows for sharing of the points.")) (|mesh?| (((|Boolean|) $) "\\spad{mesh?(s)} returns \\spad{true} if the \\spadtype{ThreeSpace} \\spad{s} is composed of one component,{} a mesh comprising a list of curves which are lists of points,{} or returns \\spad{false} if otherwise")) (|mesh| (((|List| (|List| (|Point| |#1|))) $) "\\spad{mesh(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single surface component defined by a list curves which contain lists of points,{} and if so,{} returns the list of lists of points; An error is signaled otherwise.") (($ (|List| (|List| (|Point| |#1|))) (|Boolean|) (|Boolean|)) "\\spad{mesh([[p0],[p1],...,[pn]], close1, close2)} creates a surface defined over a list of curves,{} \\spad{p0} through pn,{} which are lists of points; the booleans \\spad{close1} and \\spad{close2} indicate how the surface is to be closed: \\spad{close1} set to \\spad{true} means that each individual list (a curve) is to be closed (that is,{} the last point of the list is to be connected to the first point); \\spad{close2} set to \\spad{true} means that the boundary at one end of the surface is to be connected to the boundary at the other end (the boundaries are defined as the first list of points (curve) and the last list of points (curve)); the \\spadtype{ThreeSpace} containing this surface is returned.") (($ (|List| (|List| (|Point| |#1|)))) "\\spad{mesh([[p0],[p1],...,[pn]])} creates a surface defined by a list of curves which are lists,{} \\spad{p0} through pn,{} of points,{} and returns a \\spadtype{ThreeSpace} whose component is the surface.") (($ $ (|List| (|List| (|List| |#1|))) (|Boolean|) (|Boolean|)) "\\spad{mesh(s,[ [[r10]...,[r1m]], [[r20]...,[r2m]],..., [[rn0]...,[rnm]] ], close1, close2)} adds a surface component to the \\spadtype{ThreeSpace} \\spad{s},{} which is defined over a rectangular domain of size WxH where \\spad{W} is the number of lists of points from the domain \\spad{PointDomain(R)} and \\spad{H} is the number of elements in each of those lists; the booleans \\spad{close1} and \\spad{close2} indicate how the surface is to be closed: if \\spad{close1} is \\spad{true} this means that each individual list (a curve) is to be closed (\\spadignore{i.e.} the last point of the list is to be connected to the first point); if \\spad{close2} is \\spad{true},{} this means that the boundary at one end of the surface is to be connected to the boundary at the other end (the boundaries are defined as the first list of points (curve) and the last list of points (curve)).") (($ $ (|List| (|List| (|Point| |#1|))) (|Boolean|) (|Boolean|)) "\\spad{mesh(s,[[p0],[p1],...,[pn]], close1, close2)} adds a surface component to the \\spadtype{ThreeSpace},{} which is defined over a list of curves,{} in which each of these curves is a list of points. The boolean arguments \\spad{close1} and \\spad{close2} indicate how the surface is to be closed. Argument \\spad{close1} equal \\spad{true} means that each individual list (a curve) is to be closed,{} \\spadignore{i.e.} the last point of the list is to be connected to the first point. Argument \\spad{close2} equal \\spad{true} means that the boundary at one end of the surface is to be connected to the boundary at the other end,{} \\spadignore{i.e.} the boundaries are defined as the first list of points (curve) and the last list of points (curve).") (($ $ (|List| (|List| (|List| |#1|))) (|List| (|SubSpaceComponentProperty|)) (|SubSpaceComponentProperty|)) "\\spad{mesh(s,[ [[r10]...,[r1m]], [[r20]...,[r2m]],..., [[rn0]...,[rnm]] ], [props], prop)} adds a surface component to the \\spadtype{ThreeSpace} \\spad{s},{} which is defined over a rectangular domain of size WxH where \\spad{W} is the number of lists of points from the domain \\spad{PointDomain(R)} and \\spad{H} is the number of elements in each of those lists; lprops is the list of the subspace component properties for each curve list,{} and prop is the subspace component property by which the points are defined.") (($ $ (|List| (|List| (|Point| |#1|))) (|List| (|SubSpaceComponentProperty|)) (|SubSpaceComponentProperty|)) "\\spad{mesh(s,[[p0],[p1],...,[pn]],[props],prop)} adds a surface component,{} defined over a list curves which contains lists of points,{} to the \\spadtype{ThreeSpace} \\spad{s}; props is a list which contains the subspace component properties for each surface parameter,{} and \\spad{prop} is the subspace component property by which the points are defined.")) (|polygon?| (((|Boolean|) $) "\\spad{polygon?(s)} returns \\spad{true} if the \\spadtype{ThreeSpace} \\spad{s} contains a single polygon component,{} or \\spad{false} otherwise.")) (|polygon| (((|List| (|Point| |#1|)) $) "\\spad{polygon(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single polygon component defined by a list of points,{} and if so,{} returns the list of points; An error is signaled otherwise.") (($ (|List| (|Point| |#1|))) "\\spad{polygon([p0,p1,...,pn])} creates a polygon defined by a list of points,{} \\spad{p0} through pn,{} and returns a \\spadtype{ThreeSpace} whose component is the polygon.") (($ $ (|List| (|List| |#1|))) "\\spad{polygon(s,[[r0],[r1],...,[rn]])} adds a polygon component defined by a list of points \\spad{r0} through \\spad{rn},{} which are lists of elements from the domain \\spad{PointDomain(m,R)} to the \\spadtype{ThreeSpace} \\spad{s},{} where \\spad{m} is the dimension of the points and \\spad{R} is the \\spadtype{Ring} over which the points are defined.") (($ $ (|List| (|Point| |#1|))) "\\spad{polygon(s,[p0,p1,...,pn])} adds a polygon component defined by a list of points,{} \\spad{p0} throught pn,{} to the \\spadtype{ThreeSpace} \\spad{s}.")) (|closedCurve?| (((|Boolean|) $) "\\spad{closedCurve?(s)} returns \\spad{true} if the \\spadtype{ThreeSpace} \\spad{s} contains a single closed curve component,{} \\spadignore{i.e.} the first element of the curve is also the last element,{} or \\spad{false} otherwise.")) (|closedCurve| (((|List| (|Point| |#1|)) $) "\\spad{closedCurve(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single closed curve component defined by a list of points in which the first point is also the last point,{} all of which are from the domain \\spad{PointDomain(m,R)} and if so,{} returns the list of points. An error is signaled otherwise.") (($ (|List| (|Point| |#1|))) "\\spad{closedCurve(lp)} sets a list of points defined by the first element of \\spad{lp} through the last element of \\spad{lp} and back to the first elelment again and returns a \\spadtype{ThreeSpace} whose component is the closed curve defined by \\spad{lp}.") (($ $ (|List| (|List| |#1|))) "\\spad{closedCurve(s,[[lr0],[lr1],...,[lrn],[lr0]])} adds a closed curve component defined by a list of points \\spad{lr0} through \\spad{lrn},{} which are lists of elements from the domain \\spad{PointDomain(m,R)},{} where \\spad{R} is the \\spadtype{Ring} over which the point elements are defined and \\spad{m} is the dimension of the points,{} in which the last element of the list of points contains a copy of the first element list,{} \\spad{lr0}. The closed curve is added to the \\spadtype{ThreeSpace},{} \\spad{s}.") (($ $ (|List| (|Point| |#1|))) "\\spad{closedCurve(s,[p0,p1,...,pn,p0])} adds a closed curve component which is a list of points defined by the first element \\spad{p0} through the last element \\spad{pn} and back to the first element \\spad{p0} again,{} to the \\spadtype{ThreeSpace} \\spad{s}.")) (|curve?| (((|Boolean|) $) "\\spad{curve?(s)} queries whether the \\spadtype{ThreeSpace},{} \\spad{s},{} is a curve,{} \\spadignore{i.e.} has one component,{} a list of list of points,{} and returns \\spad{true} if it is,{} or \\spad{false} otherwise.")) (|curve| (((|List| (|Point| |#1|)) $) "\\spad{curve(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single curve defined by a list of points and if so,{} returns the curve,{} \\spadignore{i.e.} list of points. An error is signaled otherwise.") (($ (|List| (|Point| |#1|))) "\\spad{curve([p0,p1,p2,...,pn])} creates a space curve defined by the list of points \\spad{p0} through \\spad{pn},{} and returns the \\spadtype{ThreeSpace} whose component is the curve.") (($ $ (|List| (|List| |#1|))) "\\spad{curve(s,[[p0],[p1],...,[pn]])} adds a space curve which is a list of points \\spad{p0} through pn defined by lists of elements from the domain \\spad{PointDomain(m,R)},{} where \\spad{R} is the \\spadtype{Ring} over which the point elements are defined and \\spad{m} is the dimension of the points,{} to the \\spadtype{ThreeSpace} \\spad{s}.") (($ $ (|List| (|Point| |#1|))) "\\spad{curve(s,[p0,p1,...,pn])} adds a space curve component defined by a list of points \\spad{p0} through \\spad{pn},{} to the \\spadtype{ThreeSpace} \\spad{s}.")) (|point?| (((|Boolean|) $) "\\spad{point?(s)} queries whether the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single component which is a point and returns the boolean result.")) (|point| (((|Point| |#1|) $) "\\spad{point(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of only a single point and if so,{} returns the point. An error is signaled otherwise.") (($ (|Point| |#1|)) "\\spad{point(p)} returns a \\spadtype{ThreeSpace} object which is composed of one component,{} the point \\spad{p}.") (($ $ (|NonNegativeInteger|)) "\\spad{point(s,i)} adds a point component which is placed into a component list of the \\spadtype{ThreeSpace},{} \\spad{s},{} at the index given by \\spad{i}.") (($ $ (|List| |#1|)) "\\spad{point(s,[x,y,z])} adds a point component defined by a list of elements which are from the \\spad{PointDomain(R)} to the \\spadtype{ThreeSpace},{} \\spad{s},{} where \\spad{R} is the \\spadtype{Ring} over which the point elements are defined.") (($ $ (|Point| |#1|)) "\\spad{point(s,p)} adds a point component defined by the point,{} \\spad{p},{} specified as a list from \\spad{List(R)},{} to the \\spadtype{ThreeSpace},{} \\spad{s},{} where \\spad{R} is the \\spadtype{Ring} over which the point is defined.")) (|modifyPointData| (($ $ (|NonNegativeInteger|) (|Point| |#1|)) "\\spad{modifyPointData(s,i,p)} changes the point at the indexed location \\spad{i} in the \\spadtype{ThreeSpace},{} \\spad{s},{} to that of point \\spad{p}. This is useful for making changes to a point which has been transformed.")) (|enterPointData| (((|NonNegativeInteger|) $ (|List| (|Point| |#1|))) "\\spad{enterPointData(s,[p0,p1,...,pn])} adds a list of points from \\spad{p0} through pn to the \\spadtype{ThreeSpace},{} \\spad{s},{} and returns the index,{} to the starting point of the list.")) (|copy| (($ $) "\\spad{copy(s)} returns a new \\spadtype{ThreeSpace} that is an exact copy of \\spad{s}.")) (|composites| (((|List| $) $) "\\spad{composites(s)} takes the \\spadtype{ThreeSpace} \\spad{s},{} and creates a list containing a unique \\spadtype{ThreeSpace} for each single composite of \\spad{s}. If \\spad{s} has no composites defined (composites need to be explicitly created),{} the list returned is empty. Note that not all the components need to be part of a composite.")) (|components| (((|List| $) $) "\\spad{components(s)} takes the \\spadtype{ThreeSpace} \\spad{s},{} and creates a list containing a unique \\spadtype{ThreeSpace} for each single component of \\spad{s}. If \\spad{s} has no components defined,{} the list returned is empty.")) (|composite| (($ (|List| $)) "\\spad{composite([s1,s2,...,sn])} will create a new \\spadtype{ThreeSpace} that is a union of all the components from each \\spadtype{ThreeSpace} in the parameter list,{} grouped as a composite.")) (|merge| (($ $ $) "\\spad{merge(s1,s2)} will create a new \\spadtype{ThreeSpace} that has the components of \\spad{s1} and \\spad{s2}; Groupings of components into composites are maintained.") (($ (|List| $)) "\\spad{merge([s1,s2,...,sn])} will create a new \\spadtype{ThreeSpace} that has the components of all the ones in the list; Groupings of components into composites are maintained.")) (|numberOfComposites| (((|NonNegativeInteger|) $) "\\spad{numberOfComposites(s)} returns the number of supercomponents,{} or composites,{} in the \\spadtype{ThreeSpace},{} \\spad{s}; Composites are arbitrary groupings of otherwise distinct and unrelated components; A \\spadtype{ThreeSpace} need not have any composites defined at all and,{} outside of the requirement that no component can belong to more than one composite at a time,{} the definition and interpretation of composites are unrestricted.")) (|numberOfComponents| (((|NonNegativeInteger|) $) "\\spad{numberOfComponents(s)} returns the number of distinct object components in the indicated \\spadtype{ThreeSpace},{} \\spad{s},{} such as points,{} curves,{} polygons,{} and constructs.")) (|create3Space| (($ (|SubSpace| 3 |#1|)) "\\spad{create3Space(s)} creates a \\spadtype{ThreeSpace} object containing objects pre-defined within some \\spadtype{SubSpace} \\spad{s}.") (($) "\\spad{create3Space()} creates a \\spadtype{ThreeSpace} object capable of holding point,{} curve,{} mesh components and any combination."))) 
 NIL 
 NIL 
-(-1047) 
+(-1048) 
 ((|constructor| (NIL "This domain represents a kind of base domain \\indented{2}{for Spad syntax domain.\\space{2}It merely exists as a kind of} \\indented{2}{of abstract base in object-oriented programming language.} \\indented{2}{However,{} this is not an abstract class.}"))) 
 NIL 
 NIL 
-(-1048) 
+(-1049) 
 ((|constructor| (NIL "\\indented{1}{This package provides a simple Spad algebra parser.} Related Constructors: Syntax. See Also: Syntax.")) (|parse| (((|List| (|Syntax|)) (|String|)) "\\spad{parse(f)} parses the source file \\spad{f} (supposedly containing Spad algebras) and returns a List Syntax. The filename \\spad{f} is supposed to have the proper extension. Note that this function has the side effect of executing any system command contained in the file \\spad{f},{} even if it might not be meaningful."))) 
 NIL 
 NIL 
-(-1049) 
+(-1050) 
 ((|constructor| (NIL "This category describes the exported \\indented{2}{signatures of the SpadAst domain.}")) (|autoCoerce| (((|Integer|) $) "\\spad{autoCoerce(s)} returns the Integer view of `s'. Left at the discretion of the compiler.") (((|String|) $) "\\spad{autoCoerce(s)} returns the String view of `s'. Left at the discretion of the compiler.") (((|Identifier|) $) "\\spad{autoCoerce(s)} returns the Identifier view of `s'. Left at the discretion of the compiler.") (((|IsAst|) $) "\\spad{autoCoerce(s)} returns the IsAst view of `s'. Left at the discretion of the compiler.") (((|HasAst|) $) "\\spad{autoCoerce(s)} returns the HasAst view of `s'. Left at the discretion of the compiler.") (((|CaseAst|) $) "\\spad{autoCoerce(s)} returns the CaseAst view of `s'. Left at the discretion of the compiler.") (((|ColonAst|) $) "\\spad{autoCoerce(s)} returns the ColoonAst view of `s'. Left at the discretion of the compiler.") (((|SuchThatAst|) $) "\\spad{autoCoerce(s)} returns the SuchThatAst view of `s'. Left at the discretion of the compiler.") (((|LetAst|) $) "\\spad{autoCoerce(s)} returns the LetAst view of `s'. Left at the discretion of the compiler.") (((|SequenceAst|) $) "\\spad{autoCoerce(s)} returns the SequenceAst view of `s'. Left at the discretion of the compiler.") (((|SegmentAst|) $) "\\spad{autoCoerce(s)} returns the SegmentAst view of `s'. Left at the discretion of the compiler.") (((|RestrictAst|) $) "\\spad{autoCoerce(s)} returns the RestrictAst view of `s'. Left at the discretion of the compiler.") (((|PretendAst|) $) "\\spad{autoCoerce(s)} returns the PretendAst view of `s'. Left at the discretion of the compiler.") (((|CoerceAst|) $) "\\spad{autoCoerce(s)} returns the CoerceAst view of `s'. Left at the discretion of the compiler.") (((|ReturnAst|) $) "\\spad{autoCoerce(s)} returns the ReturnAst view of `s'. Left at the discretion of the compiler.") (((|ExitAst|) $) "\\spad{autoCoerce(s)} returns the ExitAst view of `s'. Left at the discretion of the compiler.") (((|ConstructAst|) $) "\\spad{autoCoerce(s)} returns the ConstructAst view of `s'. Left at the discretion of the compiler.") (((|CollectAst|) $) "\\spad{autoCoerce(s)} returns the CollectAst view of `s'. Left at the discretion of the compiler.") (((|StepAst|) $) "\\spad{autoCoerce(s)} returns the InAst view of \\spad{s}. Left at the discretion of the compiler.") (((|InAst|) $) "\\spad{autoCoerce(s)} returns the InAst view of `s'. Left at the discretion of the compiler.") (((|WhileAst|) $) "\\spad{autoCoerce(s)} returns the WhileAst view of `s'. Left at the discretion of the compiler.") (((|RepeatAst|) $) "\\spad{autoCoerce(s)} returns the RepeatAst view of `s'. Left at the discretion of the compiler.") (((|IfAst|) $) "\\spad{autoCoerce(s)} returns the IfAst view of `s'. Left at the discretion of the compiler.") (((|MappingAst|) $) "\\spad{autoCoerce(s)} returns the MappingAst view of `s'. Left at the discretion of the compiler.") (((|AttributeAst|) $) "\\spad{autoCoerce(s)} returns the AttributeAst view of `s'. Left at the discretion of the compiler.") (((|SignatureAst|) $) "\\spad{autoCoerce(s)} returns the SignatureAst view of `s'. Left at the discretion of the compiler.") (((|CapsuleAst|) $) "\\spad{autoCoerce(s)} returns the CapsuleAst view of `s'. Left at the discretion of the compiler.") (((|JoinAst|) $) "\\spad{autoCoerce(s)} returns the \\spadype{JoinAst} view of of the AST object \\spad{s}. Left at the discretion of the compiler.") (((|CategoryAst|) $) "\\spad{autoCoerce(s)} returns the CategoryAst view of `s'. Left at the discretion of the compiler.") (((|WhereAst|) $) "\\spad{autoCoerce(s)} returns the WhereAst view of `s'. Left at the discretion of the compiler.") (((|MacroAst|) $) "\\spad{autoCoerce(s)} returns the MacroAst view of `s'. Left at the discretion of the compiler.") (((|DefinitionAst|) $) "\\spad{autoCoerce(s)} returns the DefinitionAst view of `s'. Left at the discretion of the compiler.") (((|ImportAst|) $) "\\spad{autoCoerce(s)} returns the ImportAst view of `s'. Left at the discretion of the compiler.")) (|case| (((|Boolean|) $ (|[\|\|]| (|Integer|))) "\\spad{s case Integer} holds if `s' represents an integer literal.") (((|Boolean|) $ (|[\|\|]| (|String|))) "\\spad{s case String} holds if `s' represents a string literal.") (((|Boolean|) $ (|[\|\|]| (|Identifier|))) "\\spad{s case Identifier} holds if `s' represents an identifier.") (((|Boolean|) $ (|[\|\|]| (|IsAst|))) "\\spad{s case IsAst} holds if `s' represents an is-expression.") (((|Boolean|) $ (|[\|\|]| (|HasAst|))) "\\spad{s case HasAst} holds if `s' represents a has-expression.") (((|Boolean|) $ (|[\|\|]| (|CaseAst|))) "\\spad{s case CaseAst} holds if `s' represents a case-expression.") (((|Boolean|) $ (|[\|\|]| (|ColonAst|))) "\\spad{s case ColonAst} holds if `s' represents a colon-expression.") (((|Boolean|) $ (|[\|\|]| (|SuchThatAst|))) "\\spad{s case SuchThatAst} holds if `s' represents a qualified-expression.") (((|Boolean|) $ (|[\|\|]| (|LetAst|))) "\\spad{s case LetAst} holds if `s' represents an assignment-expression.") (((|Boolean|) $ (|[\|\|]| (|SequenceAst|))) "\\spad{s case SequenceAst} holds if `s' represents a sequence-of-statements.") (((|Boolean|) $ (|[\|\|]| (|SegmentAst|))) "\\spad{s case SegmentAst} holds if `s' represents a segment-expression.") (((|Boolean|) $ (|[\|\|]| (|RestrictAst|))) "\\spad{s case RestrictAst} holds if `s' represents a restrict-expression.") (((|Boolean|) $ (|[\|\|]| (|PretendAst|))) "\\spad{s case PretendAst} holds if `s' represents a pretend-expression.") (((|Boolean|) $ (|[\|\|]| (|CoerceAst|))) "\\spad{s case ReturnAst} holds if `s' represents a coerce-expression.") (((|Boolean|) $ (|[\|\|]| (|ReturnAst|))) "\\spad{s case ReturnAst} holds if `s' represents a return-statement.") (((|Boolean|) $ (|[\|\|]| (|ExitAst|))) "\\spad{s case ExitAst} holds if `s' represents an exit-expression.") (((|Boolean|) $ (|[\|\|]| (|ConstructAst|))) "\\spad{s case ConstructAst} holds if `s' represents a list-expression.") (((|Boolean|) $ (|[\|\|]| (|CollectAst|))) "\\spad{s case CollectAst} holds if `s' represents a list-comprehension.") (((|Boolean|) $ (|[\|\|]| (|StepAst|))) "\\spad{s case StepAst} holds if \\spad{s} represents an arithmetic progression iterator.") (((|Boolean|) $ (|[\|\|]| (|InAst|))) "\\spad{s case InAst} holds if `s' represents a in-iterator") (((|Boolean|) $ (|[\|\|]| (|WhileAst|))) "\\spad{s case WhileAst} holds if `s' represents a while-iterator") (((|Boolean|) $ (|[\|\|]| (|RepeatAst|))) "\\spad{s case RepeatAst} holds if `s' represents an repeat-loop.") (((|Boolean|) $ (|[\|\|]| (|IfAst|))) "\\spad{s case IfAst} holds if `s' represents an if-statement.") (((|Boolean|) $ (|[\|\|]| (|MappingAst|))) "\\spad{s case MappingAst} holds if `s' represents a mapping type.") (((|Boolean|) $ (|[\|\|]| (|AttributeAst|))) "\\spad{s case AttributeAst} holds if `s' represents an attribute.") (((|Boolean|) $ (|[\|\|]| (|SignatureAst|))) "\\spad{s case SignatureAst} holds if `s' represents a signature export.") (((|Boolean|) $ (|[\|\|]| (|CapsuleAst|))) "\\spad{s case CapsuleAst} holds if `s' represents a domain capsule.") (((|Boolean|) $ (|[\|\|]| (|JoinAst|))) "\\spad{s case JoinAst} holds is the syntax object \\spad{s} denotes the join of several categories.") (((|Boolean|) $ (|[\|\|]| (|CategoryAst|))) "\\spad{s case CategoryAst} holds if `s' represents an unnamed category.") (((|Boolean|) $ (|[\|\|]| (|WhereAst|))) "\\spad{s case WhereAst} holds if `s' represents an expression with local definitions.") (((|Boolean|) $ (|[\|\|]| (|MacroAst|))) "\\spad{s case MacroAst} holds if `s' represents a macro definition.") (((|Boolean|) $ (|[\|\|]| (|DefinitionAst|))) "\\spad{s case DefinitionAst} holds if `s' represents a definition.") (((|Boolean|) $ (|[\|\|]| (|ImportAst|))) "\\spad{s case ImportAst} holds if `s' represents an `import' statement."))) 
 NIL 
 NIL 
-(-1050) 
+(-1051) 
 ((|constructor| (NIL "SpecialOutputPackage allows FORTRAN,{} Tex and \\indented{2}{Script Formula Formatter output from programs.}")) (|outputAsTex| (((|Void|) (|List| (|OutputForm|))) "\\spad{outputAsTex(l)} sends (for each expression in the list \\spad{l}) output in Tex format to the destination as defined by \\spadsyscom{set output tex}.") (((|Void|) (|OutputForm|)) "\\spad{outputAsTex(o)} sends output \\spad{o} in Tex format to the destination defined by \\spadsyscom{set output tex}.")) (|outputAsScript| (((|Void|) (|List| (|OutputForm|))) "\\spad{outputAsScript(l)} sends (for each expression in the list \\spad{l}) output in Script Formula Formatter format to the destination defined. by \\spadsyscom{set output forumula}.") (((|Void|) (|OutputForm|)) "\\spad{outputAsScript(o)} sends output \\spad{o} in Script Formula Formatter format to the destination defined by \\spadsyscom{set output formula}.")) (|outputAsFortran| (((|Void|) (|List| (|OutputForm|))) "\\spad{outputAsFortran(l)} sends (for each expression in the list \\spad{l}) output in FORTRAN format to the destination defined by \\spadsyscom{set output fortran}.") (((|Void|) (|OutputForm|)) "\\spad{outputAsFortran(o)} sends output \\spad{o} in FORTRAN format.") (((|Void|) (|String|) (|OutputForm|)) "\\spad{outputAsFortran(v,o)} sends output \\spad{v} = \\spad{o} in FORTRAN format to the destination defined by \\spadsyscom{set output fortran}."))) 
 NIL 
 NIL 
-(-1051) 
+(-1052) 
 ((|constructor| (NIL "Category for the other special functions.")) (|airyBi| (($ $) "\\spad{airyBi(x)} is the Airy function \\spad{Bi(x)}.")) (|airyAi| (($ $) "\\spad{airyAi(x)} is the Airy function \\spad{Ai(x)}.")) (|besselK| (($ $ $) "\\spad{besselK(v,z)} is the modified Bessel function of the second kind.")) (|besselI| (($ $ $) "\\spad{besselI(v,z)} is the modified Bessel function of the first kind.")) (|besselY| (($ $ $) "\\spad{besselY(v,z)} is the Bessel function of the second kind.")) (|besselJ| (($ $ $) "\\spad{besselJ(v,z)} is the Bessel function of the first kind.")) (|polygamma| (($ $ $) "\\spad{polygamma(k,x)} is the \\spad{k-th} derivative of \\spad{digamma(x)},{} (often written \\spad{psi(k,x)} in the literature).")) (|digamma| (($ $) "\\spad{digamma(x)} is the logarithmic derivative of \\spad{Gamma(x)} (often written \\spad{psi(x)} in the literature).")) (|Beta| (($ $ $) "\\spad{Beta(x,y)} is \\spad{Gamma(x) * Gamma(y)/Gamma(x+y)}.")) (|Gamma| (($ $ $) "\\spad{Gamma(a,x)} is the incomplete Gamma function.") (($ $) "\\spad{Gamma(x)} is the Euler Gamma function.")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x}."))) 
 NIL 
 NIL 
-(-1052 V C) 
+(-1053 V C) 
 ((|constructor| (NIL "This domain exports a modest implementation for the vertices of splitting trees. These vertices are called here splitting nodes. Every of these nodes store 3 informations. The first one is its value,{} that is the current expression to evaluate. The second one is its condition,{} that is the hypothesis under which the value has to be evaluated. The last one is its status,{} that is a boolean flag which is \\spad{true} iff the value is the result of its evaluation under its condition. Two splitting vertices are equal iff they have the sane values and the same conditions (so their status do not matter).")) (|subNode?| (((|Boolean|) $ $ (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{subNode?(\\spad{n1},{}\\spad{n2},{}\\spad{o2})} returns \\spad{true} iff \\axiom{value(\\spad{n1}) = value(\\spad{n2})} and \\axiom{\\spad{o2}(condition(\\spad{n1}),{}condition(\\spad{n2}))}")) (|infLex?| (((|Boolean|) $ $ (|Mapping| (|Boolean|) |#1| |#1|) (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{infLex?(\\spad{n1},{}\\spad{n2},{}\\spad{o1},{}\\spad{o2})} returns \\spad{true} iff \\axiom{\\spad{o1}(value(\\spad{n1}),{}value(\\spad{n2}))} or \\axiom{value(\\spad{n1}) = value(\\spad{n2})} and \\axiom{\\spad{o2}(condition(\\spad{n1}),{}condition(\\spad{n2}))}.")) (|setEmpty!| (($ $) "\\axiom{setEmpty!(\\spad{n})} replaces \\spad{n} by \\axiom{empty()\\$\\%}.")) (|setStatus!| (($ $ (|Boolean|)) "\\axiom{setStatus!(\\spad{n},{}\\spad{b})} returns \\spad{n} whose status has been replaced by \\spad{b} if it is not empty,{} else an error is produced.")) (|setCondition!| (($ $ |#2|) "\\axiom{setCondition!(\\spad{n},{}\\spad{t})} returns \\spad{n} whose condition has been replaced by \\spad{t} if it is not empty,{} else an error is produced.")) (|setValue!| (($ $ |#1|) "\\axiom{setValue!(\\spad{n},{}\\spad{v})} returns \\spad{n} whose value has been replaced by \\spad{v} if it is not empty,{} else an error is produced.")) (|copy| (($ $) "\\axiom{copy(\\spad{n})} returns a copy of \\spad{n}.")) (|construct| (((|List| $) |#1| (|List| |#2|)) "\\axiom{construct(\\spad{v},{}lt)} returns the same as \\axiom{[construct(\\spad{v},{}\\spad{t}) for \\spad{t} in lt]}") (((|List| $) (|List| (|Record| (|:| |val| |#1|) (|:| |tower| |#2|)))) "\\axiom{construct(lvt)} returns the same as \\axiom{[construct(vt.val,{}vt.tower) for vt in lvt]}") (($ (|Record| (|:| |val| |#1|) (|:| |tower| |#2|))) "\\axiom{construct(vt)} returns the same as \\axiom{construct(vt.val,{}vt.tower)}") (($ |#1| |#2|) "\\axiom{construct(\\spad{v},{}\\spad{t})} returns the same as \\axiom{construct(\\spad{v},{}\\spad{t},{}\\spad{false})}") (($ |#1| |#2| (|Boolean|)) "\\axiom{construct(\\spad{v},{}\\spad{t},{}\\spad{b})} returns the non-empty node with value \\spad{v},{} condition \\spad{t} and flag \\spad{b}")) (|status| (((|Boolean|) $) "\\axiom{status(\\spad{n})} returns the status of the node \\spad{n}.")) (|condition| ((|#2| $) "\\axiom{condition(\\spad{n})} returns the condition of the node \\spad{n}.")) (|value| ((|#1| $) "\\axiom{value(\\spad{n})} returns the value of the node \\spad{n}.")) (|empty?| (((|Boolean|) $) "\\axiom{empty?(\\spad{n})} returns \\spad{true} iff the node \\spad{n} is \\axiom{empty()\\$\\%}.")) (|empty| (($) "\\axiom{empty()} returns the same as \\axiom{[empty()\\$\\spad{V},{}empty()\\$\\spad{C},{}\\spad{false}]\\$\\%}"))) 
 NIL 
 NIL 
-(-1053 V C) 
+(-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") $) "\\axiom{extractSplittingLeaf(a)} returns the left most leaf (as a tree) whose status is \\spad{false} if any,{} else \"failed\" is returned."))) 
-((-3989 . T) (-3990 . T)) 
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-(-1054 |ndim| R) 
+((-3991 . T) (-3992 . T)) 
+((-12 (|HasCategory| (-1053 |#1| |#2|) (|%list| (QUOTE -259) (|%list| (QUOTE -1053) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1053 |#1| |#2|) (QUOTE (-1013)))) (|HasCategory| (-1053 |#1| |#2|) (QUOTE (-1013))) (OR (|HasCategory| (-1053 |#1| |#2|) (QUOTE (-72))) (|HasCategory| (-1053 |#1| |#2|) (QUOTE (-1013)))) (|HasCategory| (-1053 |#1| |#2|) (QUOTE (-553 (-773)))) (|HasCategory| (-1053 |#1| |#2|) (QUOTE (-72)))) 
+(-1055 |ndim| R) 
 ((|constructor| (NIL "\\spadtype{SquareMatrix} is a matrix domain of square matrices,{} where the number of rows (= number of columns) is a parameter of the type.")) (|unitsKnown| ((|attribute|) "the invertible matrices are simply the matrices whose determinants are units in the Ring \\spad{R}.")) (|central| ((|attribute|) "the elements of the Ring \\spad{R},{} viewed as diagonal matrices,{} commute with all matrices and,{} indeed,{} are the only matrices which commute with all matrices.")) (|squareMatrix| (($ (|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}."))) 
-((-3986 . T) (-3978 |has| |#2| (-6 (-3991 "*"))) (-3989 . T) (-3983 . T) (-3984 . T)) 
-((|HasCategory| |#2| (QUOTE (-809 (-1088)))) (|HasCategory| |#2| (QUOTE (-811 (-1088)))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-189))) (|HasAttribute| |#2| (QUOTE (-3991 #1="*"))) (|HasCategory| |#2| (QUOTE (-580 (-483)))) (|HasCategory| |#2| (QUOTE (-950 (-347 (-483))))) (|HasCategory| |#2| (QUOTE (-950 (-483)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (|%list| (QUOTE -259) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-580 (-483)))) (|HasCategory| |#2| (|%list| (QUOTE -259) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-809 (-1088)))) (|HasCategory| |#2| (|%list| (QUOTE -259) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| |#2| (|%list| (QUOTE -259) (|devaluate| |#2|))))) (|HasCategory| |#2| (QUOTE (-553 (-472)))) (|HasCategory| |#2| (QUOTE (-257))) (|HasCategory| |#2| (QUOTE (-494))) (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| |#2| (QUOTE (-311))) (OR (|HasAttribute| |#2| (QUOTE (-3991 #1#))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-809 (-1088))))) (|HasCategory| |#2| (QUOTE (-552 (-772)))) (|HasCategory| |#2| (QUOTE (-72))) (-12 (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| |#2| (|%list| (QUOTE -259) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-146)))) 
-(-1055 S) 
+((-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)))) 
+(-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|) $ $) "\\spad{prefix?(s,t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) == reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) 
 NIL 
 NIL 
-(-1056) 
+(-1057) 
 ((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|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."))) 
-((-3990 . T) (-3989 . T)) 
+((-3992 . T) (-3991 . T)) 
 NIL 
-(-1057 R E V P TS) 
+(-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.}"))) 
 NIL 
 NIL 
-(-1058 R E V P) 
+(-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."))) 
-((-3990 . T) (-3989 . T)) 
-((-12 (|HasCategory| |#4| (QUOTE (-1012))) (|HasCategory| |#4| (|%list| (QUOTE -259) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-553 (-472)))) (|HasCategory| |#4| (QUOTE (-1012))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#3| (QUOTE (-317))) (|HasCategory| |#4| (QUOTE (-552 (-772)))) (|HasCategory| |#4| (QUOTE (-72)))) 
-(-1059) 
+((-3992 . T) (-3991 . 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:"))) 
 NIL 
 NIL 
-(-1060 S) 
+(-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}."))) 
-((-3989 . T) (-3990 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1012))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-72)))) 
-(-1061 A S) 
+((-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 (-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})}."))) 
 NIL 
 NIL 
-(-1062 S) 
+(-1063 S) 
 ((|constructor| (NIL "A stream aggregate is a linear aggregate which possibly has an infinite number of elements. A basic domain constructor which builds stream aggregates is \\spadtype{Stream}. From streams,{} a number of infinite structures such power series can be built. A stream aggregate may also be infinite since it may be cyclic. For example,{} see \\spadtype{DecimalExpansion}.")) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{size?(u,n)} tests if \\spad{u} has exactly \\spad{n} elements.")) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{more?(u,n)} tests if \\spad{u} has greater than \\spad{n} elements.")) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{less?(u,n)} tests if \\spad{u} has less than \\spad{n} elements.")) (|possiblyInfinite?| (((|Boolean|) $) "\\spad{possiblyInfinite?(s)} tests if the stream \\spad{s} could possibly have an infinite number of elements. Note: for many datatypes,{} \\axiom{possiblyInfinite?(\\spad{s}) = not explictlyFinite?(\\spad{s})}.")) (|explicitlyFinite?| (((|Boolean|) $) "\\spad{explicitlyFinite?(s)} tests if the stream has a finite number of elements,{} and \\spad{false} otherwise. Note: for many datatypes,{} \\axiom{explicitlyFinite?(\\spad{s}) = not possiblyInfinite?(\\spad{s})}."))) 
 NIL 
 NIL 
-(-1063 |Key| |Ent| |dent|) 
+(-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."))) 
-((-3990 . T)) 
-((-12 (|HasCategory| (-2 (|:| -3854 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -259) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3854) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3854 |#1|) (|:| |entry| |#2|)) (QUOTE (-1012)))) (OR (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| (-2 (|:| -3854 |#1|) (|:| |entry| |#2|)) (QUOTE (-1012)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| (-2 (|:| -3854 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3854 |#1|) (|:| |entry| |#2|)) (QUOTE (-1012)))) (OR (|HasCategory| (-2 (|:| -3854 |#1|) (|:| |entry| |#2|)) (QUOTE (-552 (-772)))) (|HasCategory| |#2| (QUOTE (-552 (-772))))) (|HasCategory| (-2 (|:| -3854 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-472)))) (-12 (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| |#2| (|%list| (QUOTE -259) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-756))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3854 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3854 |#1|) (|:| |entry| |#2|)) (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3854 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3854 |#1|) (|:| |entry| |#2|)) (QUOTE (-1012)))) 
-(-1064) 
+((-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)))) 
+(-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 
 NIL 
-(-1065) 
+(-1066) 
 ((|constructor| (NIL "This domain represents an arithmetic progression iterator syntax.")) (|step| (((|SpadAst|) $) "\\spad{step(i)} returns the Spad AST denoting the step of the arithmetic progression represented by the iterator \\spad{i}.")) (|upperBound| (((|Maybe| (|SpadAst|)) $) "If the set of values assumed by the iteration variable is bounded from above,{} \\spad{upperBound(i)} returns the upper bound. Otherwise,{} its returns \\spad{nothing}.")) (|lowerBound| (((|SpadAst|) $) "\\spad{lowerBound(i)} returns the lower bound on the values assumed by the iteration variable.")) (|iterationVar| (((|Identifier|) $) "\\spad{iterationVar(i)} returns the name of the iterating variable of the arithmetic progression iterator \\spad{i}."))) 
 NIL 
 NIL 
-(-1066 |Coef|) 
+(-1067 |Coef|) 
 ((|constructor| (NIL "This package computes infinite products of Taylor series over an integral domain of characteristic 0. Here Taylor series are represented by streams of Taylor coefficients.")) (|generalInfiniteProduct| (((|Stream| |#1|) (|Stream| |#1|) (|Integer|) (|Integer|)) "\\spad{generalInfiniteProduct(f(x),a,d)} computes \\spad{product(n=a,a+d,a+2*d,...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|oddInfiniteProduct| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{oddInfiniteProduct(f(x))} computes \\spad{product(n=1,3,5...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|evenInfiniteProduct| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{evenInfiniteProduct(f(x))} computes \\spad{product(n=2,4,6...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|infiniteProduct| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{infiniteProduct(f(x))} computes \\spad{product(n=1,2,3...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1."))) 
 NIL 
 NIL 
-(-1067 S) 
-((|constructor| (NIL "A stream is an implementation of an infinite sequence using a list of terms that have been computed and a function closure to compute additional terms when needed.")) (|filterUntil| (($ (|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."))) 
-((-3990 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1012))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-553 (-472)))) (|HasCategory| (-483) (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-72)))) 
 (-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)) 
+((-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)}."))) 
 NIL 
 NIL 
-(-1069 A B) 
+(-1070 A B) 
 ((|constructor| (NIL "Functions defined on streams with entries in two sets.")) (|reduce| ((|#2| |#2| (|Mapping| |#2| |#1| |#2|) (|Stream| |#1|)) "\\spad{reduce(b,f,u)},{} where \\spad{u} is a finite stream \\spad{[x0,x1,...,xn]},{} returns the value \\spad{r(n)} computed as follows: \\spad{r0 = f(x0,b), r1 = f(x1,r0),..., r(n) = f(xn,r(n-1))}.")) (|scan| (((|Stream| |#2|) |#2| (|Mapping| |#2| |#1| |#2|) (|Stream| |#1|)) "\\spad{scan(b,h,[x0,x1,x2,...])} returns \\spad{[y0,y1,y2,...]},{} where \\spad{y0 = h(x0,b)},{} \\spad{y1 = h(x1,y0)},{}\\spad{...} \\spad{yn = h(xn,y(n-1))}.")) (|map| (((|Stream| |#2|) (|Mapping| |#2| |#1|) (|Stream| |#1|)) "\\spad{map(f,s)} returns a stream whose elements are the function \\spad{f} applied to the corresponding elements of \\spad{s}. Note: \\spad{map(f,[x0,x1,x2,...]) = [f(x0),f(x1),f(x2),..]}."))) 
 NIL 
 NIL 
-(-1070 A B C) 
+(-1071 A B C) 
 ((|constructor| (NIL "Functions defined on streams with entries in three sets.")) (|map| (((|Stream| |#3|) (|Mapping| |#3| |#1| |#2|) (|Stream| |#1|) (|Stream| |#2|)) "\\spad{map(f,st1,st2)} returns the stream whose elements are the function \\spad{f} applied to the corresponding elements of \\spad{st1} and \\spad{st2}. Note: \\spad{map(f,[x0,x1,x2,..],[y0,y1,y2,..]) = [f(x0,y0),f(x1,y1),..]}."))) 
 NIL 
 NIL 
-(-1071) 
+(-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"))) 
-((-3990 . T) (-3989 . T)) 
-((OR (-12 (|HasCategory| (-117) (QUOTE (-259 (-117)))) (|HasCategory| (-117) (QUOTE (-756)))) (-12 (|HasCategory| (-117) (QUOTE (-259 (-117)))) (|HasCategory| (-117) (QUOTE (-1012))))) (|HasCategory| (-117) (QUOTE (-552 (-772)))) (|HasCategory| (-117) (QUOTE (-553 (-472)))) (OR (|HasCategory| (-117) (QUOTE (-756))) (|HasCategory| (-117) (QUOTE (-1012)))) (|HasCategory| (-117) (QUOTE (-756))) (OR (|HasCategory| (-117) (QUOTE (-72))) (|HasCategory| (-117) (QUOTE (-756))) (|HasCategory| (-117) (QUOTE (-1012)))) (|HasCategory| (-483) (QUOTE (-756))) (|HasCategory| (-117) (QUOTE (-1012))) (|HasCategory| (-117) (QUOTE (-72))) (-12 (|HasCategory| (-117) (QUOTE (-259 (-117)))) (|HasCategory| (-117) (QUOTE (-1012))))) 
-(-1072 |Entry|) 
+((-3992 . T) (-3991 . 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."))) 
-((-3989 . T) (-3990 . T)) 
-((-12 (|HasCategory| (-2 (|:| -3854 (-1071)) (|:| |entry| |#1|)) (|%list| (QUOTE -259) (|%list| (QUOTE -2) (QUOTE (|:| -3854 (-1071))) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -3854 (-1071)) (|:| |entry| |#1|)) (QUOTE (-1012)))) (OR (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| (-2 (|:| -3854 (-1071)) (|:| |entry| |#1|)) (QUOTE (-1012)))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| (-2 (|:| -3854 (-1071)) (|:| |entry| |#1|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3854 (-1071)) (|:| |entry| |#1|)) (QUOTE (-1012)))) (OR (|HasCategory| (-2 (|:| -3854 (-1071)) (|:| |entry| |#1|)) (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-552 (-772))))) (|HasCategory| (-2 (|:| -3854 (-1071)) (|:| |entry| |#1|)) (QUOTE (-553 (-472)))) (-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -3854 (-1071)) (|:| |entry| |#1|)) (QUOTE (-1012))) (|HasCategory| (-1071) (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1012))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3854 (-1071)) (|:| |entry| |#1|)) (QUOTE (-72)))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3854 (-1071)) (|:| |entry| |#1|)) (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3854 (-1071)) (|:| |entry| |#1|)) (QUOTE (-72)))) 
-(-1073 A) 
+((-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)))) 
+(-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 
-((|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-38 (-347 (-483)))))) 
-(-1074 |Coef|) 
+((|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-38 (-347 (-484)))))) 
+(-1075 |Coef|) 
 ((|constructor| (NIL "StreamTranscendentalFunctions implements transcendental functions on Taylor series,{} where a Taylor series is represented by a stream of its coefficients.")) (|acsch| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acsch(st)} computes the inverse hyperbolic cosecant of a power series \\spad{st}.")) (|asech| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asech(st)} computes the inverse hyperbolic secant of a power series \\spad{st}.")) (|acoth| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acoth(st)} computes the inverse hyperbolic cotangent of a power series \\spad{st}.")) (|atanh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{atanh(st)} computes the inverse hyperbolic tangent of a power series \\spad{st}.")) (|acosh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acosh(st)} computes the inverse hyperbolic cosine of a power series \\spad{st}.")) (|asinh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asinh(st)} computes the inverse hyperbolic sine of a power series \\spad{st}.")) (|csch| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{csch(st)} computes the hyperbolic cosecant of a power series \\spad{st}.")) (|sech| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sech(st)} computes the hyperbolic secant of a power series \\spad{st}.")) (|coth| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{coth(st)} computes the hyperbolic cotangent of a power series \\spad{st}.")) (|tanh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{tanh(st)} computes the hyperbolic tangent of a power series \\spad{st}.")) (|cosh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cosh(st)} computes the hyperbolic cosine of a power series \\spad{st}.")) (|sinh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sinh(st)} computes the hyperbolic sine of a power series \\spad{st}.")) (|sinhcosh| (((|Record| (|:| |sinh| (|Stream| |#1|)) (|:| |cosh| (|Stream| |#1|))) (|Stream| |#1|)) "\\spad{sinhcosh(st)} returns a record containing the hyperbolic sine and cosine of a power series \\spad{st}.")) (|acsc| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acsc(st)} computes arccosecant of a power series \\spad{st}.")) (|asec| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asec(st)} computes arcsecant of a power series \\spad{st}.")) (|acot| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acot(st)} computes arccotangent of a power series \\spad{st}.")) (|atan| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{atan(st)} computes arctangent of a power series \\spad{st}.")) (|acos| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acos(st)} computes arccosine of a power series \\spad{st}.")) (|asin| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asin(st)} computes arcsine of a power series \\spad{st}.")) (|csc| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{csc(st)} computes cosecant of a power series \\spad{st}.")) (|sec| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sec(st)} computes secant of a power series \\spad{st}.")) (|cot| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cot(st)} computes cotangent of a power series \\spad{st}.")) (|tan| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{tan(st)} computes tangent of a power series \\spad{st}.")) (|cos| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cos(st)} computes cosine of a power series \\spad{st}.")) (|sin| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sin(st)} computes sine of a power series \\spad{st}.")) (|sincos| (((|Record| (|:| |sin| (|Stream| |#1|)) (|:| |cos| (|Stream| |#1|))) (|Stream| |#1|)) "\\spad{sincos(st)} returns a record containing the sine and cosine of a power series \\spad{st}.")) (** (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{st1 ** st2} computes the power of a power series \\spad{st1} by another power series \\spad{st2}.")) (|log| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{log(st)} computes the log of a power series.")) (|exp| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{exp(st)} computes the exponential of a power series \\spad{st}."))) 
 NIL 
 NIL 
-(-1075 |Coef|) 
+(-1076 |Coef|) 
 ((|constructor| (NIL "StreamTranscendentalFunctionsNonCommutative implements transcendental functions on Taylor series over a non-commutative ring,{} where a Taylor series is represented by a stream of its coefficients.")) (|acsch| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acsch(st)} computes the inverse hyperbolic cosecant of a power series \\spad{st}.")) (|asech| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asech(st)} computes the inverse hyperbolic secant of a power series \\spad{st}.")) (|acoth| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acoth(st)} computes the inverse hyperbolic cotangent of a power series \\spad{st}.")) (|atanh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{atanh(st)} computes the inverse hyperbolic tangent of a power series \\spad{st}.")) (|acosh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acosh(st)} computes the inverse hyperbolic cosine of a power series \\spad{st}.")) (|asinh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asinh(st)} computes the inverse hyperbolic sine of a power series \\spad{st}.")) (|csch| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{csch(st)} computes the hyperbolic cosecant of a power series \\spad{st}.")) (|sech| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sech(st)} computes the hyperbolic secant of a power series \\spad{st}.")) (|coth| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{coth(st)} computes the hyperbolic cotangent of a power series \\spad{st}.")) (|tanh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{tanh(st)} computes the hyperbolic tangent of a power series \\spad{st}.")) (|cosh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cosh(st)} computes the hyperbolic cosine of a power series \\spad{st}.")) (|sinh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sinh(st)} computes the hyperbolic sine of a power series \\spad{st}.")) (|acsc| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acsc(st)} computes arccosecant of a power series \\spad{st}.")) (|asec| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asec(st)} computes arcsecant of a power series \\spad{st}.")) (|acot| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acot(st)} computes arccotangent of a power series \\spad{st}.")) (|atan| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{atan(st)} computes arctangent of a power series \\spad{st}.")) (|acos| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acos(st)} computes arccosine of a power series \\spad{st}.")) (|asin| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asin(st)} computes arcsine of a power series \\spad{st}.")) (|csc| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{csc(st)} computes cosecant of a power series \\spad{st}.")) (|sec| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sec(st)} computes secant of a power series \\spad{st}.")) (|cot| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cot(st)} computes cotangent of a power series \\spad{st}.")) (|tan| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{tan(st)} computes tangent of a power series \\spad{st}.")) (|cos| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cos(st)} computes cosine of a power series \\spad{st}.")) (|sin| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sin(st)} computes sine of a power series \\spad{st}.")) (** (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{st1 ** st2} computes the power of a power series \\spad{st1} by another power series \\spad{st2}.")) (|log| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{log(st)} computes the log of a power series.")) (|exp| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{exp(st)} computes the exponential of a power series \\spad{st}."))) 
 NIL 
 NIL 
-(-1076 R UP) 
+(-1077 R UP) 
 ((|constructor| (NIL "This package computes the subresultants of two polynomials which is needed for the `Lazard Rioboo' enhancement to Tragers integrations formula For efficiency reasons this has been rewritten to call Lionel Ducos package which is currently the best one. \\blankline")) (|primitivePart| ((|#2| |#2| |#1|) "\\spad{primitivePart(p, q)} reduces the coefficient of \\spad{p} modulo \\spad{q},{} takes the primitive part of the result,{} and ensures that the leading coefficient of that result is monic.")) (|subresultantVector| (((|PrimitiveArray| |#2|) |#2| |#2|) "\\spad{subresultantVector(p, q)} returns \\spad{[p0,...,pn]} where \\spad{pi} is the \\spad{i}-th subresultant of \\spad{p} and \\spad{q}. In particular,{} \\spad{p0 = resultant(p, q)}."))) 
 NIL 
 ((|HasCategory| |#1| (QUOTE (-257)))) 
-(-1077 |n| R) 
+(-1078 |n| R) 
 ((|constructor| (NIL "This domain \\undocumented")) (|pointData| (((|List| (|Point| |#2|)) $) "\\spad{pointData(s)} returns the list of points from the point data field of the 3 dimensional subspace \\spad{s}.")) (|parent| (($ $) "\\spad{parent(s)} returns the subspace which is the parent of the indicated 3 dimensional subspace \\spad{s}. If \\spad{s} is the top level subspace an error message is returned.")) (|level| (((|NonNegativeInteger|) $) "\\spad{level(s)} returns a non negative integer which is the current level field of the indicated 3 dimensional subspace \\spad{s}.")) (|extractProperty| (((|SubSpaceComponentProperty|) $) "\\spad{extractProperty(s)} returns the property of domain \\spadtype{SubSpaceComponentProperty} of the indicated 3 dimensional subspace \\spad{s}.")) (|extractClosed| (((|Boolean|) $) "\\spad{extractClosed(s)} returns the \\spadtype{Boolean} value of the closed property for the indicated 3 dimensional subspace \\spad{s}. If the property is closed,{} \\spad{True} is returned,{} otherwise \\spad{False} is returned.")) (|extractIndex| (((|NonNegativeInteger|) $) "\\spad{extractIndex(s)} returns a non negative integer which is the current index of the 3 dimensional subspace \\spad{s}.")) (|extractPoint| (((|Point| |#2|) $) "\\spad{extractPoint(s)} returns the point which is given by the current index location into the point data field of the 3 dimensional subspace \\spad{s}.")) (|traverse| (($ $ (|List| (|NonNegativeInteger|))) "\\spad{traverse(s,li)} follows the branch list of the 3 dimensional subspace,{} \\spad{s},{} along the path dictated by the list of non negative integers,{} \\spad{li},{} which points to the component which has been traversed to. The subspace,{} \\spad{s},{} is returned,{} where \\spad{s} is now the subspace pointed to by \\spad{li}.")) (|defineProperty| (($ $ (|List| (|NonNegativeInteger|)) (|SubSpaceComponentProperty|)) "\\spad{defineProperty(s,li,p)} defines the component property in the 3 dimensional subspace,{} \\spad{s},{} to be that of \\spad{p},{} where \\spad{p} is of the domain \\spadtype{SubSpaceComponentProperty}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component whose property is being defined. The subspace,{} \\spad{s},{} is returned with the component property definition.")) (|closeComponent| (($ $ (|List| (|NonNegativeInteger|)) (|Boolean|)) "\\spad{closeComponent(s,li,b)} sets the property of the component in the 3 dimensional subspace,{} \\spad{s},{} to be closed if \\spad{b} is \\spad{true},{} or open if \\spad{b} is \\spad{false}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component whose closed property is to be set. The subspace,{} \\spad{s},{} is returned with the component property modification.")) (|modifyPoint| (($ $ (|NonNegativeInteger|) (|Point| |#2|)) "\\spad{modifyPoint(s,ind,p)} modifies the point referenced by the index location,{} \\spad{ind},{} by replacing it with the point,{} \\spad{p} in the 3 dimensional subspace,{} \\spad{s}. An error message occurs if \\spad{s} is empty,{} otherwise the subspace \\spad{s} is returned with the point modification.") (($ $ (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{modifyPoint(s,li,i)} replaces an existing point in the 3 dimensional subspace,{} \\spad{s},{} with the 4 dimensional point indicated by the index location,{} \\spad{i}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component in which the existing point is to be modified. An error message occurs if \\spad{s} is empty,{} otherwise the subspace \\spad{s} is returned with the point modification.") (($ $ (|List| (|NonNegativeInteger|)) (|Point| |#2|)) "\\spad{modifyPoint(s,li,p)} replaces an existing point in the 3 dimensional subspace,{} \\spad{s},{} with the 4 dimensional point,{} \\spad{p}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component in which the existing point is to be modified. An error message occurs if \\spad{s} is empty,{} otherwise the subspace \\spad{s} is returned with the point modification.")) (|addPointLast| (($ $ $ (|Point| |#2|) (|NonNegativeInteger|)) "\\spad{addPointLast(s,s2,li,p)} adds the 4 dimensional point,{} \\spad{p},{} to the 3 dimensional subspace,{} \\spad{s}. \\spad{s2} point to the end of the subspace \\spad{s}. \\spad{n} is the path in the \\spad{s2} component. The subspace \\spad{s} is returned with the additional point.")) (|addPoint2| (($ $ (|Point| |#2|)) "\\spad{addPoint2(s,p)} adds the 4 dimensional point,{} \\spad{p},{} to the 3 dimensional subspace,{} \\spad{s}. The subspace \\spad{s} is returned with the additional point.")) (|addPoint| (((|NonNegativeInteger|) $ (|Point| |#2|)) "\\spad{addPoint(s,p)} adds the point,{} \\spad{p},{} to the 3 dimensional subspace,{} \\spad{s},{} and returns the new total number of points in \\spad{s}.") (($ $ (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{addPoint(s,li,i)} adds the 4 dimensional point indicated by the index location,{} \\spad{i},{} to the 3 dimensional subspace,{} \\spad{s}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component in which the point is to be added. It's length should range from 0 to \\spad{n - 1} where \\spad{n} is the dimension of the subspace. If the length is \\spad{n - 1},{} then a specific lowest level component is being referenced. If it is less than \\spad{n - 1},{} then some higher level component (0 indicates top level component) is being referenced and a component of that level with the desired point is created. The subspace \\spad{s} is returned with the additional point.") (($ $ (|List| (|NonNegativeInteger|)) (|Point| |#2|)) "\\spad{addPoint(s,li,p)} adds the 4 dimensional point,{} \\spad{p},{} to the 3 dimensional subspace,{} \\spad{s}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component in which the point is to be added. It's length should range from 0 to \\spad{n - 1} where \\spad{n} is the dimension of the subspace. If the length is \\spad{n - 1},{} then a specific lowest level component is being referenced. If it is less than \\spad{n - 1},{} then some higher level component (0 indicates top level component) is being referenced and a component of that level with the desired point is created. The subspace \\spad{s} is returned with the additional point.")) (|separate| (((|List| $) $) "\\spad{separate(s)} makes each of the components of the \\spadtype{SubSpace},{} \\spad{s},{} into a list of separate and distinct subspaces and returns the list.")) (|merge| (($ (|List| $)) "\\spad{merge(ls)} a list of subspaces,{} \\spad{ls},{} into one subspace.") (($ $ $) "\\spad{merge(s1,s2)} the subspaces \\spad{s1} and \\spad{s2} into a single subspace.")) (|deepCopy| (($ $) "\\spad{deepCopy(x)} \\undocumented")) (|shallowCopy| (($ $) "\\spad{shallowCopy(x)} \\undocumented")) (|numberOfChildren| (((|NonNegativeInteger|) $) "\\spad{numberOfChildren(x)} \\undocumented")) (|children| (((|List| $) $) "\\spad{children(x)} \\undocumented")) (|child| (($ $ (|NonNegativeInteger|)) "\\spad{child(x,n)} \\undocumented")) (|birth| (($ $) "\\spad{birth(x)} \\undocumented")) (|subspace| (($) "\\spad{subspace()} \\undocumented")) (|new| (($) "\\spad{new()} \\undocumented")) (|internal?| (((|Boolean|) $) "\\spad{internal?(x)} \\undocumented")) (|root?| (((|Boolean|) $) "\\spad{root?(x)} \\undocumented")) (|leaf?| (((|Boolean|) $) "\\spad{leaf?(x)} \\undocumented"))) 
 NIL 
 NIL 
-(-1078 S1 S2) 
+(-1079 S1 S2) 
 ((|constructor| (NIL "This domain implements \"such that\" forms")) (|rhs| ((|#2| $) "\\spad{rhs(f)} returns the right side of \\spad{f}")) (|lhs| ((|#1| $) "\\spad{lhs(f)} returns the left side of \\spad{f}")) (|construct| (($ |#1| |#2|) "\\spad{construct(s,t)} makes a form s:t"))) 
 NIL 
 NIL 
-(-1079) 
+(-1080) 
 ((|constructor| (NIL "This domain represents the filter iterator syntax.")) (|predicate| (((|SpadAst|) $) "\\spad{predicate(e)} returns the syntax object for the predicate in the filter iterator syntax `e'."))) 
 NIL 
 NIL 
-(-1080 |Coef| |var| |cen|) 
+(-1081 |Coef| |var| |cen|) 
 ((|constructor| (NIL "Sparse Laurent series in one variable \\indented{2}{\\spadtype{SparseUnivariateLaurentSeries} is a domain representing Laurent} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{SparseUnivariateLaurentSeries(Integer,x,3)} represents Laurent} \\indented{2}{series in \\spad{(x - 3)} with integer coefficients.}")) (|integrate| (($ $ (|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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-(-1081 R -3088) 
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|#2| |#3|) (|%list| (QUOTE -241) (|%list| (QUOTE -1088) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|)) (|%list| (QUOTE -1088) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|))))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| (-1088 |#1| |#2| |#3|) (|%list| (QUOTE -259) (|%list| (QUOTE -1088) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|))))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| (-1088 |#1| |#2| |#3|) (|%list| (QUOTE -453) (QUOTE (-1089)) (|%list| (QUOTE -1088) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|))))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| (-1088 |#1| |#2| |#3|) (QUOTE (-581 (-484))))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| (-1088 |#1| |#2| |#3|) (QUOTE (-554 (-801 (-484)))))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| (-1088 |#1| |#2| |#3|) (QUOTE (-554 (-801 (-327)))))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| (-1088 |#1| |#2| |#3|) (QUOTE (-797 (-484))))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| (-1088 |#1| |#2| |#3|) (QUOTE (-797 (-327))))) (-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))))) (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|)))))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| (-1088 |#1| |#2| |#3|) (QUOTE (-483)))) (-12 (|HasCategory| |#1| (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 -3090) 
 ((|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 
-(-1082 R) 
+(-1083 R) 
 ((|constructor| (NIL "Computes sums of rational functions.")) (|sum| (((|Union| (|Fraction| (|Polynomial| |#1|)) (|Expression| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|Fraction| (|Polynomial| |#1|)))) "\\spad{sum(f(n), n = a..b)} returns \\spad{f(a) + f(a+1) + ... f(b)}.") (((|Fraction| (|Polynomial| |#1|)) (|Polynomial| |#1|) (|SegmentBinding| (|Polynomial| |#1|))) "\\spad{sum(f(n), n = a..b)} returns \\spad{f(a) + f(a+1) + ... f(b)}.") (((|Union| (|Fraction| (|Polynomial| |#1|)) (|Expression| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{sum(a(n), n)} returns \\spad{A} which is the indefinite sum of \\spad{a} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{A(n+1) - A(n) = a(n)}.") (((|Fraction| (|Polynomial| |#1|)) (|Polynomial| |#1|) (|Symbol|)) "\\spad{sum(a(n), n)} returns \\spad{A} which is the indefinite sum of \\spad{a} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{A(n+1) - A(n) = a(n)}."))) 
 NIL 
 NIL 
-(-1083 R) 
+(-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."))) 
-(((-3991 "*") |has| |#1| (-146)) (-3982 |has| |#1| (-494)) (-3985 |has| |#1| (-311)) (-3987 |has| |#1| (-6 -3987)) (-3984 . T) (-3983 . T) (-3986 . T)) 
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-(-1084 R S) 
+(((-3993 "*") |has| |#1| (-146)) (-3984 |has| |#1| (-495)) (-3987 |has| |#1| (-311)) (-3989 |has| |#1| (-6 -3989)) (-3986 . T) (-3985 . T) (-3988 . T)) 
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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 
 NIL 
-(-1085 E OV R P) 
+(-1086 E OV R P) 
 ((|constructor| (NIL "\\indented{1}{SupFractionFactorize} contains the factor function for univariate polynomials over the quotient field of a ring \\spad{S} such that the package MultivariateFactorize works for \\spad{S}")) (|squareFree| (((|Factored| (|SparseUnivariatePolynomial| (|Fraction| |#4|))) (|SparseUnivariatePolynomial| (|Fraction| |#4|))) "\\spad{squareFree(p)} returns the square-free factorization of the univariate polynomial \\spad{p} with coefficients which are fractions of polynomials over \\spad{R}. Each factor has no repeated roots and the factors are pairwise relatively prime.")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| (|Fraction| |#4|))) (|SparseUnivariatePolynomial| (|Fraction| |#4|))) "\\spad{factor(p)} factors the univariate polynomial \\spad{p} with coefficients which are fractions of polynomials over \\spad{R}."))) 
 NIL 
 NIL 
-(-1086 |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."))) 
-(((-3991 "*") |has| |#1| (-146)) (-3982 |has| |#1| (-494)) (-3987 |has| |#1| (-311)) (-3981 |has| |#1| (-311)) (-3983 . T) (-3984 . T) (-3986 . T)) 
-((|HasCategory| |#1| (QUOTE (-38 (-347 (-483))))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-494)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-809 (-1088)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -347) (QUOTE (-483))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -347) (QUOTE (-483))) (|devaluate| |#1|)))) (|HasCategory| (-347 (-483)) (QUOTE (-1024))) (|HasCategory| |#1| (QUOTE (-311))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-494)))) (OR (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-494)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -347) (QUOTE (-483)))))) (|HasSignature| |#1| (|%list| (QUOTE -3940) (|%list| (|devaluate| |#1|) (QUOTE (-1088)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -347) (QUOTE (-483)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-347 (-483))))) (|HasCategory| |#1| (QUOTE (-29 (-483)))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1113)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-347 (-483))))) (|HasSignature| |#1| (|%list| (QUOTE -3806) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1088))))) (|HasSignature| |#1| (|%list| (QUOTE -3077) (|%list| (|%list| (QUOTE -583) (QUOTE (-1088))) (|devaluate| |#1|))))))) 
 (-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."))) 
+(((-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|))))))) 
+(-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}."))) 
-(((-3991 "*") |has| |#1| (-146)) (-3982 |has| |#1| (-494)) (-3983 . T) (-3984 . T) (-3986 . T)) 
-((|HasCategory| |#1| (QUOTE (-38 (-347 (-483))))) (|HasCategory| |#1| (QUOTE (-494))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-494)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-809 (-1088)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-694)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-694)) (|devaluate| |#1|)))) (|HasCategory| (-694) (QUOTE (-1024))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-694))))) (|HasSignature| |#1| (|%list| (QUOTE -3940) (|%list| (|devaluate| |#1|) (QUOTE (-1088)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-694))))) (|HasCategory| |#1| (QUOTE (-311))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-347 (-483))))) (|HasCategory| |#1| (QUOTE (-29 (-483)))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1113)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-347 (-483))))) (|HasSignature| |#1| (|%list| (QUOTE -3806) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1088))))) (|HasSignature| |#1| (|%list| (QUOTE -3077) (|%list| (|%list| (QUOTE -583) (QUOTE (-1088))) (|devaluate| |#1|))))))) 
-(-1088) 
+(((-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|))))))) 
+(-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 
 NIL 
-(-1089 R) 
+(-1090 R) 
 ((|constructor| (NIL "Computes all the symmetric functions in \\spad{n} variables.")) (|symFunc| (((|Vector| |#1|) |#1| (|PositiveInteger|)) "\\spad{symFunc(r, n)} returns the vector of the elementary symmetric functions in \\spad{[r,r,...,r]} \\spad{n} times.") (((|Vector| |#1|) (|List| |#1|)) "\\spad{symFunc([r1,...,rn])} returns the vector of the elementary symmetric functions in the \\spad{ri's}: \\spad{[r1 + ... + rn, r1 r2 + ... + r(n-1) rn, ..., r1 r2 ... rn]}."))) 
 NIL 
 NIL 
-(-1090 R) 
+(-1091 R) 
 ((|constructor| (NIL "This domain implements symmetric polynomial"))) 
-(((-3991 "*") |has| |#1| (-146)) (-3982 |has| |#1| (-494)) (-3987 |has| |#1| (-6 -3987)) (-3983 . T) (-3984 . T) (-3986 . T)) 
-((|HasCategory| |#1| (QUOTE (-38 (-347 (-483))))) (|HasCategory| |#1| (QUOTE (-494))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-494)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (OR (|HasCategory| |#1| (QUOTE (-38 (-347 (-483))))) (|HasCategory| |#1| (QUOTE (-950 (-347 (-483)))))) (|HasCategory| |#1| (QUOTE (-950 (-347 (-483))))) (|HasCategory| |#1| (QUOTE (-950 (-483)))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-389))) (-12 (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| (-884) (QUOTE (-104)))) (|HasAttribute| |#1| (QUOTE -3987))) 
-(-1091) 
+(((-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))) 
+(-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 
 NIL 
-(-1092) 
+(-1093) 
 ((|constructor| (NIL "Create and manipulate a symbol table for generated FORTRAN code")) (|symbolTable| (($ (|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| (|FortranType|))))) "\\spad{symbolTable(l)} creates a symbol table from the elements of \\spad{l}.")) (|printTypes| (((|Void|) $) "\\spad{printTypes(tab)} produces FORTRAN type declarations from \\spad{tab},{} on the current FORTRAN output stream")) (|newTypeLists| (((|SExpression|) $) "\\spad{newTypeLists(x)} \\undocumented")) (|typeLists| (((|List| (|List| (|Union| (|:| |name| (|Symbol|)) (|:| |bounds| (|List| (|Union| (|:| S (|Symbol|)) (|:| P (|Polynomial| (|Integer|))))))))) $) "\\spad{typeLists(tab)} returns a list of lists of types of objects in \\spad{tab}")) (|externalList| (((|List| (|Symbol|)) $) "\\spad{externalList(tab)} returns a list of all the external symbols in \\spad{tab}")) (|typeList| (((|List| (|Union| (|:| |name| (|Symbol|)) (|:| |bounds| (|List| (|Union| (|:| S (|Symbol|)) (|:| P (|Polynomial| (|Integer|)))))))) (|FortranScalarType|) $) "\\spad{typeList(t,tab)} returns a list of all the objects of type \\spad{t} in \\spad{tab}")) (|parametersOf| (((|List| (|Symbol|)) $) "\\spad{parametersOf(tab)} returns a list of all the symbols declared in \\spad{tab}")) (|fortranTypeOf| (((|FortranType|) (|Symbol|) $) "\\spad{fortranTypeOf(u,tab)} returns the type of \\spad{u} in \\spad{tab}")) (|declare!| (((|FortranType|) (|Symbol|) (|FortranType|) $) "\\spad{declare!(u,t,tab)} creates a new entry in \\spad{tab},{} declaring \\spad{u} to be of type \\spad{t}") (((|FortranType|) (|List| (|Symbol|)) (|FortranType|) $) "\\spad{declare!(l,t,tab)} creates new entrys in \\spad{tab},{} declaring each of \\spad{l} to be of type \\spad{t}")) (|empty| (($) "\\spad{empty()} returns a new,{} empty symbol table")) (|coerce| (((|Table| (|Symbol|) (|FortranType|)) $) "\\spad{coerce(x)} returns a table view of \\spad{x}"))) 
 NIL 
 NIL 
-(-1093) 
+(-1094) 
 ((|constructor| (NIL "\\indented{1}{This domain provides a simple domain,{} general enough for} \\indented{2}{building complete representation of Spad programs as objects} \\indented{2}{of a term algebra built from ground terms of type integers,{} foats,{}} \\indented{2}{identifiers,{} and strings.} \\indented{2}{This domain differs from InputForm in that it represents} \\indented{2}{any entity in a Spad program,{} not just expressions.\\space{2}Furthermore,{}} \\indented{2}{while InputForm may contain atoms like vectors and other Lisp} \\indented{2}{objects,{} the Syntax domain is supposed to contain only that} \\indented{2}{initial algebra build from the primitives listed above.} Related Constructors: \\indented{2}{Integer,{} DoubleFloat,{} Identifier,{} String,{} SExpression.} See Also: SExpression,{} InputForm. The equality supported by this domain is structural.")) (|case| (((|Boolean|) $ (|[\|\|]| (|String|))) "\\spad{x case String} is \\spad{true} if `x' really is a String") (((|Boolean|) $ (|[\|\|]| (|Identifier|))) "\\spad{x case Identifier} is \\spad{true} if `x' really is an Identifier") (((|Boolean|) $ (|[\|\|]| (|DoubleFloat|))) "\\spad{x case DoubleFloat} is \\spad{true} if `x' really is a DoubleFloat") (((|Boolean|) $ (|[\|\|]| (|Integer|))) "\\spad{x case Integer} is \\spad{true} if `x' really is an Integer")) (|compound?| (((|Boolean|) $) "\\spad{compound? x} is \\spad{true} when `x' is not an atomic syntax.")) (|getOperands| (((|List| $) $) "\\spad{getOperands(x)} returns the list of operands to the operator in `x'.")) (|getOperator| (((|Union| (|Integer|) (|DoubleFloat|) (|Identifier|) (|String|) $) $) "\\spad{getOperator(x)} returns the operator,{} or tag,{} of the syntax `x'. The value returned is itself a syntax if `x' really is an application of a function symbol as opposed to being an atomic ground term.")) (|nil?| (((|Boolean|) $) "\\spad{nil?(s)} is \\spad{true} when `s' is a syntax for the constant nil.")) (|buildSyntax| (($ $ (|List| $)) "\\spad{buildSyntax(op, [a1, ..., an])} builds a syntax object for \\spad{op}(\\spad{a1},{}...,{}an).") (($ (|Identifier|) (|List| $)) "\\spad{buildSyntax(op, [a1, ..., an])} builds a syntax object for \\spad{op}(\\spad{a1},{}...,{}an).")) (|autoCoerce| (((|String|) $) "\\spad{autoCoerce(s)} forcibly extracts a string value from the syntax `s'; no check performed. To be called only at the discretion of the compiler.") (((|Identifier|) $) "\\spad{autoCoerce(s)} forcibly extracts an identifier from the Syntax domain `s'; no check performed. To be called only at at the discretion of the compiler.") (((|DoubleFloat|) $) "\\spad{autoCoerce(s)} forcibly extracts a float value from the syntax `s'; no check performed. To be called only at the discretion of the compiler") (((|Integer|) $) "\\spad{autoCoerce(s)} forcibly extracts an integer value from the syntax `s'; no check performed. To be called only at the discretion of the compiler.")) (|coerce| (((|String|) $) "\\spad{coerce(s)} extracts a string value from the syntax `s'.") (((|Identifier|) $) "\\spad{coerce(s)} extracts an identifier from the syntax `s'.") (((|DoubleFloat|) $) "\\spad{coerce(s)} extracts a float value from the syntax `s'.") (((|Integer|) $) "\\spad{coerce(s)} extracts and integer value from the syntax `s'")) (|convert| (($ (|SExpression|)) "\\spad{convert(s)} converts an \\spad{s}-expression to Syntax. Note,{} when `s' is not an atom,{} it is expected that it designates a proper list,{} \\spadignore{e.g.} a sequence of cons cells ending with nil.") (((|SExpression|) $) "\\spad{convert(s)} returns the \\spad{s}-expression representation of a syntax."))) 
 NIL 
 NIL 
-(-1094 N) 
+(-1095 N) 
 ((|constructor| (NIL "This domain implements sized (signed) integer datatypes parameterized by the precision (or width) of the underlying representation. The intent is that they map directly to the hosting hardware natural integer datatypes. Consequently,{} natural values for \\spad{N} are: 8,{} 16,{} 32,{} 64,{} etc. These datatypes are mostly useful for system programming tasks,{} \\spadignore{i.e.} interfacting with the hosting operating system,{} reading/writing external binary format files.")) (|sample| (($) "\\spad{sample} gives a sample datum of this type."))) 
 NIL 
 NIL 
-(-1095 N) 
+(-1096 N) 
 ((|constructor| (NIL "This domain implements sized (unsigned) integer datatypes parameterized by the precision (or width) of the underlying representation. The intent is that they map directly to the hosting hardware natural integer datatypes. Consequently,{} natural values for \\spad{N} are: 8,{} 16,{} 32,{} 64,{} etc. These datatypes are mostly useful for system programming tasks,{} \\spadignore{i.e.} interfacting with the hosting operating system,{} reading/writing external binary format files.")) (|sample| (($) "\\spad{sample} gives a sample datum of type Byte.")) (|bitior| (($ $ $) "\\spad{bitior(x,y)} returns the bitwise `inclusive or' of `x' and `y'.")) (|bitand| (($ $ $) "\\spad{bitand(x,y)} returns the bitwise `and' of `x' and `y'."))) 
 NIL 
 NIL 
-(-1096) 
+(-1097) 
 ((|constructor| (NIL "This domain is a datatype system-level pointer values."))) 
 NIL 
 NIL 
-(-1097 R) 
+(-1098 R) 
 ((|triangularSystems| (((|List| (|List| (|Polynomial| |#1|))) (|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|Symbol|))) "\\spad{triangularSystems(lf,lv)} solves the system of equations defined by \\spad{lf} with respect to the list of symbols \\spad{lv}; the system of equations is obtaining by equating to zero the list of rational functions \\spad{lf}. The output is a list of solutions where each solution is expressed as a \"reduced\" triangular system of polynomials.")) (|solve| (((|List| (|Equation| (|Fraction| (|Polynomial| |#1|)))) (|Equation| (|Fraction| (|Polynomial| |#1|)))) "\\spad{solve(eq)} finds the solutions of the equation \\spad{eq} with respect to the unique variable appearing in \\spad{eq}.") (((|List| (|Equation| (|Fraction| (|Polynomial| |#1|)))) (|Fraction| (|Polynomial| |#1|))) "\\spad{solve(p)} finds the solution of a rational function \\spad{p} = 0 with respect to the unique variable appearing in \\spad{p}.") (((|List| (|Equation| (|Fraction| (|Polynomial| |#1|)))) (|Equation| (|Fraction| (|Polynomial| |#1|))) (|Symbol|)) "\\spad{solve(eq,v)} finds the solutions of the equation \\spad{eq} with respect to the variable \\spad{v}.") (((|List| (|Equation| (|Fraction| (|Polynomial| |#1|)))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{solve(p,v)} solves the equation \\spad{p=0},{} where \\spad{p} is a rational function with respect to the variable \\spad{v}.") (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) "\\spad{solve(le)} finds the solutions of the list \\spad{le} of equations of rational functions with respect to all symbols appearing in \\spad{le}.") (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Fraction| (|Polynomial| |#1|)))) "\\spad{solve(lp)} finds the solutions of the list \\spad{lp} of rational functions with respect to all symbols appearing in \\spad{lp}.") (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Equation| (|Fraction| (|Polynomial| |#1|)))) (|List| (|Symbol|))) "\\spad{solve(le,lv)} finds the solutions of the list \\spad{le} of equations of rational functions with respect to the list of symbols \\spad{lv}.") (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|Symbol|))) "\\spad{solve(lp,lv)} finds the solutions of the list \\spad{lp} of rational functions with respect to the list of symbols \\spad{lv}."))) 
 NIL 
 NIL 
-(-1098) 
+(-1099) 
 ((|constructor| (NIL "The package \\spadtype{System} provides information about the runtime system and its characteristics.")) (|loadNativeModule| (((|Void|) (|String|)) "\\spad{loadNativeModule(path)} loads the native modile designated by \\spadvar{\\spad{path}}.")) (|nativeModuleExtension| (((|String|)) "\\spad{nativeModuleExtension} is a string representation of a filename extension for native modules.")) (|hostByteOrder| (((|ByteOrder|)) "\\sapd{hostByteOrder}")) (|hostPlatform| (((|String|)) "\\spad{hostPlatform} is a string `triplet' description of the platform hosting the running OpenAxiom system.")) (|rootDirectory| (((|String|)) "\\spad{rootDirectory()} returns the pathname of the root directory for the running OpenAxiom system."))) 
 NIL 
 NIL 
-(-1099 S) 
+(-1100 S) 
 ((|constructor| (NIL "TableauBumpers implements the Schenstead-Knuth correspondence between sequences and pairs of Young tableaux. The 2 Young tableaux are represented as a single tableau with pairs as components.")) (|mr| (((|Record| (|:| |f1| (|List| |#1|)) (|:| |f2| (|List| (|List| (|List| |#1|)))) (|:| |f3| (|List| (|List| |#1|))) (|:| |f4| (|List| (|List| (|List| |#1|))))) (|List| (|List| (|List| |#1|)))) "\\spad{mr(t)} is an auxiliary function which finds the position of the maximum element of a tableau \\spad{t} which is in the lowest row,{} producing a record of results")) (|maxrow| (((|Record| (|:| |f1| (|List| |#1|)) (|:| |f2| (|List| (|List| (|List| |#1|)))) (|:| |f3| (|List| (|List| |#1|))) (|:| |f4| (|List| (|List| (|List| |#1|))))) (|List| |#1|) (|List| (|List| (|List| |#1|))) (|List| (|List| |#1|)) (|List| (|List| (|List| |#1|))) (|List| (|List| (|List| |#1|))) (|List| (|List| (|List| |#1|)))) "\\spad{maxrow(a,b,c,d,e)} is an auxiliary function for mr")) (|inverse| (((|List| |#1|) (|List| |#1|)) "\\spad{inverse(ls)} forms the inverse of a sequence \\spad{ls}")) (|slex| (((|List| (|List| |#1|)) (|List| |#1|)) "\\spad{slex(ls)} sorts the argument sequence \\spad{ls},{} then zips (see \\spadfunFrom{map}{\\spad{ListFunctions3}}) the original argument sequence with the sorted result to a list of pairs")) (|lex| (((|List| (|List| |#1|)) (|List| (|List| |#1|))) "\\spad{lex(ls)} sorts a list of pairs to lexicographic order")) (|tab| (((|Tableau| (|List| |#1|)) (|List| |#1|)) "\\spad{tab(ls)} creates a tableau from \\spad{ls} by first creating a list of pairs using \\spadfunFrom{slex}{TableauBumpers},{} then creating a tableau using \\spadfunFrom{\\spad{tab1}}{TableauBumpers}.")) (|tab1| (((|List| (|List| (|List| |#1|))) (|List| (|List| |#1|))) "\\spad{tab1(lp)} creates a tableau from a list of pairs \\spad{lp}")) (|bat| (((|List| (|List| |#1|)) (|Tableau| (|List| |#1|))) "\\spad{bat(ls)} unbumps a tableau \\spad{ls}")) (|bat1| (((|List| (|List| |#1|)) (|List| (|List| (|List| |#1|)))) "\\spad{bat1(llp)} unbumps a tableau \\spad{llp}. Operation \\spad{bat1} is the inverse of \\spad{tab1}.")) (|untab| (((|List| (|List| |#1|)) (|List| (|List| |#1|)) (|List| (|List| (|List| |#1|)))) "\\spad{untab(lp,llp)} is an auxiliary function which unbumps a tableau \\spad{llp},{} using \\spad{lp} to accumulate pairs")) (|bumptab1| (((|List| (|List| (|List| |#1|))) (|List| |#1|) (|List| (|List| (|List| |#1|)))) "\\spad{bumptab1(pr,t)} bumps a tableau \\spad{t} with a pair \\spad{pr} using comparison function \\spadfun{<},{} returning a new tableau")) (|bumptab| (((|List| (|List| (|List| |#1|))) (|Mapping| (|Boolean|) |#1| |#1|) (|List| |#1|) (|List| (|List| (|List| |#1|)))) "\\spad{bumptab(cf,pr,t)} bumps a tableau \\spad{t} with a pair \\spad{pr} using comparison function \\spad{cf},{} returning a new tableau")) (|bumprow| (((|Record| (|:| |fs| (|Boolean|)) (|:| |sd| (|List| |#1|)) (|:| |td| (|List| (|List| |#1|)))) (|Mapping| (|Boolean|) |#1| |#1|) (|List| |#1|) (|List| (|List| |#1|))) "\\spad{bumprow(cf,pr,r)} is an auxiliary function which bumps a row \\spad{r} with a pair \\spad{pr} using comparison function \\spad{cf},{} and returns a record"))) 
 NIL 
 NIL 
-(-1100 |Key| |Entry|) 
+(-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}"))) 
-((-3989 . T) (-3990 . T)) 
-((-12 (|HasCategory| (-2 (|:| -3854 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -259) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3854) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3854 |#1|) (|:| |entry| |#2|)) (QUOTE (-1012)))) (OR (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| (-2 (|:| -3854 |#1|) (|:| |entry| |#2|)) (QUOTE (-1012)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| (-2 (|:| -3854 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3854 |#1|) (|:| |entry| |#2|)) (QUOTE (-1012)))) (OR (|HasCategory| (-2 (|:| -3854 |#1|) (|:| |entry| |#2|)) (QUOTE (-552 (-772)))) (|HasCategory| |#2| (QUOTE (-552 (-772))))) (|HasCategory| (-2 (|:| -3854 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-472)))) (-12 (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| |#2| (|%list| (QUOTE -259) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3854 |#1|) (|:| |entry| |#2|)) (QUOTE (-1012))) (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#2| (QUOTE (-1012))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3854 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3854 |#1|) (|:| |entry| |#2|)) (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3854 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) 
-(-1101 S) 
+((-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)))) 
+(-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 
 NIL 
-(-1102 S) 
+(-1103 S) 
 ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: April 17,{} 2010 Date Last Modified: April 17,{} 2010")) (|operator| (($ |#1| (|Arity|)) "\\spad{operator(n,a)} returns an operator named \\spad{n} and with arity \\spad{a}."))) 
 NIL 
 NIL 
-(-1103 R) 
+(-1104 R) 
 ((|constructor| (NIL "Expands tangents of sums and scalar products.")) (|tanNa| ((|#1| |#1| (|Integer|)) "\\spad{tanNa(a, n)} returns \\spad{f(a)} such that if \\spad{a = tan(u)} then \\spad{f(a) = tan(n * u)}.")) (|tanAn| (((|SparseUnivariatePolynomial| |#1|) |#1| (|PositiveInteger|)) "\\spad{tanAn(a, n)} returns \\spad{P(x)} such that if \\spad{a = tan(u)} then \\spad{P(tan(u/n)) = 0}.")) (|tanSum| ((|#1| (|List| |#1|)) "\\spad{tanSum([a1,...,an])} returns \\spad{f(a1,...,an)} such that if \\spad{ai = tan(ui)} then \\spad{f(a1,...,an) = tan(u1 + ... + un)}."))) 
 NIL 
 NIL 
-(-1104 S |Key| |Entry|) 
+(-1105 S |Key| |Entry|) 
 ((|constructor| (NIL "A table aggregate is a model of a table,{} \\spadignore{i.e.} a discrete many-to-one mapping from keys to entries.")) (|map| (($ (|Mapping| |#3| |#3| |#3|) $ $) "\\spad{map(fn,t1,t2)} creates a new table \\spad{t} from given tables \\spad{t1} and \\spad{t2} with elements \\spad{fn}(\\spad{x},{}\\spad{y}) where \\spad{x} and \\spad{y} are corresponding elements from \\spad{t1} and \\spad{t2} respectively.")) (|table| (($ (|List| (|Record| (|:| |key| |#2|) (|:| |entry| |#3|)))) "\\spad{table([x,y,...,z])} creates a table consisting of entries \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}}.") (($) "\\spad{table()}\\$\\spad{T} creates an empty table of type \\spad{T}.")) (|setelt| ((|#3| $ |#2| |#3|) "\\spad{setelt(t,k,e)} (also written \\axiom{\\spad{t}.\\spad{k} := \\spad{e}}) is equivalent to \\axiom{(insert([\\spad{k},{}\\spad{e}],{}\\spad{t}); \\spad{e})}."))) 
 NIL 
 NIL 
-(-1105 |Key| |Entry|) 
+(-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})}."))) 
-((-3990 . T)) 
+((-3992 . T)) 
 NIL 
-(-1106 |Key| |Entry|) 
+(-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."))) 
 NIL 
 NIL 
-(-1107) 
+(-1108) 
 ((|constructor| (NIL "\\spadtype{TexFormat} provides a coercion from \\spadtype{OutputForm} to \\TeX{} format. The particular dialect of \\TeX{} used is \\LaTeX{}. The basic object consists of three parts: a prologue,{} a tex part and an epilogue. The functions \\spadfun{prologue},{} \\spadfun{tex} and \\spadfun{epilogue} extract these parts,{} respectively. The main guts of the expression go into the tex part. The other parts can be set (\\spadfun{setPrologue!},{} \\spadfun{setEpilogue!}) so that contain the appropriate tags for printing. For example,{} the prologue and epilogue might simply contain ``\\verb+\\[+'' and ``\\verb+\\]+'',{} respectively,{} so that the TeX section will be printed in LaTeX display math mode.")) (|setPrologue!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setPrologue!(t,strings)} sets the prologue section of a TeX form \\spad{t} to \\spad{strings}.")) (|setTex!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setTex!(t,strings)} sets the TeX section of a TeX form \\spad{t} to \\spad{strings}.")) (|setEpilogue!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setEpilogue!(t,strings)} sets the epilogue section of a TeX form \\spad{t} to \\spad{strings}.")) (|prologue| (((|List| (|String|)) $) "\\spad{prologue(t)} extracts the prologue section of a TeX form \\spad{t}.")) (|new| (($) "\\spad{new()} create a new,{} empty object. Use \\spadfun{setPrologue!},{} \\spadfun{setTex!} and \\spadfun{setEpilogue!} to set the various components of this object.")) (|tex| (((|List| (|String|)) $) "\\spad{tex(t)} extracts the TeX section of a TeX form \\spad{t}.")) (|epilogue| (((|List| (|String|)) $) "\\spad{epilogue(t)} extracts the epilogue section of a TeX form \\spad{t}.")) (|display| (((|Void|) $) "\\spad{display(t)} outputs the TeX formatted code \\spad{t} so that each line has length less than or equal to the value set by the system command \\spadsyscom{set output length}.") (((|Void|) $ (|Integer|)) "\\spad{display(t,width)} outputs the TeX formatted code \\spad{t} so that each line has length less than or equal to \\spadvar{\\spad{width}}.")) (|convert| (($ (|OutputForm|) (|Integer|) (|OutputForm|)) "\\spad{convert(o,step,type)} changes \\spad{o} in standard output format to TeX format and also adds the given \\spad{step} number and \\spad{type}. This is useful if you want to create equations with given numbers or have the equation numbers correspond to the interpreter \\spad{step} numbers.") (($ (|OutputForm|) (|Integer|)) "\\spad{convert(o,step)} changes \\spad{o} in standard output format to TeX format and also adds the given \\spad{step} number. This is useful if you want to create equations with given numbers or have the equation numbers correspond to the interpreter \\spad{step} numbers."))) 
 NIL 
 NIL 
-(-1108 S) 
+(-1109 S) 
 ((|constructor| (NIL "\\spadtype{TexFormat1} provides a utility coercion for changing to TeX format anything that has a coercion to the standard output format.")) (|coerce| (((|TexFormat|) |#1|) "\\spad{coerce(s)} provides a direct coercion from a domain \\spad{S} to TeX format. This allows the user to skip the step of first manually coercing the object to standard output format before it is coerced to TeX format."))) 
 NIL 
 NIL 
-(-1109) 
+(-1110) 
 ((|constructor| (NIL "This domain provides an implementation of text files. Text is stored in these files using the native character set of the computer.")) (|endOfFile?| (((|Boolean|) $) "\\spad{endOfFile?(f)} tests whether the file \\spad{f} is positioned after the end of all text. If the file is open for output,{} then this test is always \\spad{true}.")) (|readIfCan!| (((|Union| (|String|) "failed") $) "\\spad{readIfCan!(f)} returns a string of the contents of a line from file \\spad{f},{} if possible. If \\spad{f} is not readable or if it is positioned at the end of file,{} then \\spad{\"failed\"} is returned.")) (|readLineIfCan!| (((|Union| (|String|) "failed") $) "\\spad{readLineIfCan!(f)} returns a string of the contents of a line from file \\spad{f},{} if possible. If \\spad{f} is not readable or if it is positioned at the end of file,{} then \\spad{\"failed\"} is returned.")) (|readLine!| (((|String|) $) "\\spad{readLine!(f)} returns a string of the contents of a line from the file \\spad{f}.")) (|writeLine!| (((|String|) $) "\\spad{writeLine!(f)} finishes the current line in the file \\spad{f}. An empty string is returned. The call \\spad{writeLine!(f)} is equivalent to \\spad{writeLine!(f,\"\")}.") (((|String|) $ (|String|)) "\\spad{writeLine!(f,s)} writes the contents of the string \\spad{s} and finishes the current line in the file \\spad{f}. The value of \\spad{s} is returned."))) 
 NIL 
 NIL 
-(-1110 R) 
+(-1111 R) 
 ((|constructor| (NIL "Tools for the sign finding utilities.")) (|direction| (((|Integer|) (|String|)) "\\spad{direction(s)} \\undocumented")) (|nonQsign| (((|Union| (|Integer|) "failed") |#1|) "\\spad{nonQsign(r)} \\undocumented")) (|sign| (((|Union| (|Integer|) "failed") |#1|) "\\spad{sign(r)} \\undocumented"))) 
 NIL 
 NIL 
-(-1111) 
+(-1112) 
 ((|constructor| (NIL "This package exports a function for making a \\spadtype{ThreeSpace}")) (|createThreeSpace| (((|ThreeSpace| (|DoubleFloat|))) "\\spad{createThreeSpace()} creates a \\spadtype{ThreeSpace(DoubleFloat)} object capable of holding point,{} curve,{} mesh components and any combination."))) 
 NIL 
 NIL 
-(-1112 S) 
+(-1113 S) 
 ((|constructor| (NIL "Category for the transcendental elementary functions.")) (|pi| (($) "\\spad{pi()} returns the constant \\spad{pi}."))) 
 NIL 
 NIL 
-(-1113) 
+(-1114) 
 ((|constructor| (NIL "Category for the transcendental elementary functions.")) (|pi| (($) "\\spad{pi()} returns the constant \\spad{pi}."))) 
 NIL 
 NIL 
-(-1114 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}."))) 
-((-3990 . T) (-3989 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1012))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-72)))) 
 (-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| $)) "\\spad{tree(nd,ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}."))) 
+((-3992 . T) (-3991 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1013))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-72)))) 
+(-1116 S) 
 ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) 
 NIL 
 NIL 
-(-1116) 
+(-1117) 
 ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) 
 NIL 
 NIL 
-(-1117 R -3088) 
+(-1118 R -3090) 
 ((|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 
-(-1118 R |Row| |Col| M) 
+(-1119 R |Row| |Col| M) 
 ((|constructor| (NIL "This package provides functions that compute \"fraction-free\" inverses of upper and lower triangular matrices over a integral domain. By \"fraction-free inverses\" we mean the following: given a matrix \\spad{B} with entries in \\spad{R} and an element \\spad{d} of \\spad{R} such that \\spad{d} * inv(\\spad{B}) also has entries in \\spad{R},{} we return \\spad{d} * inv(\\spad{B}). Thus,{} it is not necessary to pass to the quotient field in any of our computations.")) (|LowTriBddDenomInv| ((|#4| |#4| |#1|) "\\spad{LowTriBddDenomInv(B,d)} returns \\spad{M},{} where \\spad{B} is a non-singular lower triangular matrix and \\spad{d} is an element of \\spad{R} such that \\spad{M = d * inv(B)} has entries in \\spad{R}.")) (|UpTriBddDenomInv| ((|#4| |#4| |#1|) "\\spad{UpTriBddDenomInv(B,d)} returns \\spad{M},{} where \\spad{B} is a non-singular upper triangular matrix and \\spad{d} is an element of \\spad{R} such that \\spad{M = d * inv(B)} has entries in \\spad{R}."))) 
 NIL 
 NIL 
-(-1119 R -3088) 
+(-1120 R -3090) 
 ((|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 -553) (|%list| (QUOTE -800) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -796) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -553) (|%list| (QUOTE -800) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -796) (|devaluate| |#1|))))) 
-(-1120 |Coef|) 
+((-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}."))) 
-(((-3991 "*") |has| |#1| (-146)) (-3982 |has| |#1| (-494)) (-3984 . T) (-3983 . T) (-3986 . T)) 
-((|HasCategory| |#1| (QUOTE (-38 (-347 (-483))))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-494)))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-311)))) 
-(-1121 S R E V P) 
+(((-3993 "*") |has| |#1| (-146)) (-3984 |has| |#1| (-495)) (-3986 . T) (-3985 . T) (-3988 . 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."))) 
 NIL 
 ((|HasCategory| |#4| (QUOTE (-317)))) 
-(-1122 R E V P) 
+(-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|) $ $) "\\axiom{infRittWu?(\\spad{ts1},{}\\spad{ts2})} returns \\spad{true} iff \\axiom{\\spad{ts2}} has higher rank than \\axiom{\\spad{ts1}} in Wu Wen Tsun sense."))) 
-((-3990 . T) (-3989 . T)) 
+((-3992 . T) (-3991 . T)) 
 NIL 
-(-1123 |Curve|) 
+(-1124 |Curve|) 
 ((|constructor| (NIL "\\indented{2}{Package for constructing tubes around 3-dimensional parametric curves.} Domain of tubes around 3-dimensional parametric curves.")) (|tube| (($ |#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}."))) 
 NIL 
 NIL 
-(-1124) 
+(-1125) 
 ((|constructor| (NIL "Tools for constructing tubes around 3-dimensional parametric curves.")) (|loopPoints| (((|List| (|Point| (|DoubleFloat|))) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|List| (|List| (|DoubleFloat|)))) "\\spad{loopPoints(p,n,b,r,lls)} creates and returns a list of points which form the loop with radius \\spad{r},{} around the center point indicated by the point \\spad{p},{} with the principal normal vector of the space curve at point \\spad{p} given by the point(vector) \\spad{n},{} and the binormal vector given by the point(vector) \\spad{b},{} and a list of lists,{} \\spad{lls},{} which is the \\spadfun{cosSinInfo} of the number of points defining the loop.")) (|cosSinInfo| (((|List| (|List| (|DoubleFloat|))) (|Integer|)) "\\spad{cosSinInfo(n)} returns the list of lists of values for \\spad{n},{} in the form: \\spad{[[cos(n - 1) a,sin(n - 1) a],...,[cos 2 a,sin 2 a],[cos a,sin a]]} where \\spad{a = 2 pi/n}. Note: \\spad{n} should be greater than 2.")) (|unitVector| (((|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))) "\\spad{unitVector(p)} creates the unit vector of the point \\spad{p} and returns the result as a point. Note: \\spad{unitVector(p) = p/|p|}.")) (|cross| (((|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))) "\\spad{cross(p,q)} computes the cross product of the two points \\spad{p} and \\spad{q} using only the first three coordinates,{} and keeping the color of the first point \\spad{p}. The result is returned as a point.")) (|dot| (((|DoubleFloat|) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))) "\\spad{dot(p,q)} computes the dot product of the two points \\spad{p} and \\spad{q} using only the first three coordinates,{} and returns the resulting \\spadtype{DoubleFloat}.")) (- (((|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))) "\\spad{p - q} computes and returns a point whose coordinates are the differences of the coordinates of two points \\spad{p} and \\spad{q},{} using the color,{} or fourth coordinate,{} of the first point \\spad{p} as the color also of the point \\spad{q}.")) (+ (((|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))) "\\spad{p + q} computes and returns a point whose coordinates are the sums of the coordinates of the two points \\spad{p} and \\spad{q},{} using the color,{} or fourth coordinate,{} of the first point \\spad{p} as the color also of the point \\spad{q}.")) (* (((|Point| (|DoubleFloat|)) (|DoubleFloat|) (|Point| (|DoubleFloat|))) "\\spad{s * p} returns a point whose coordinates are the scalar multiple of the point \\spad{p} by the scalar \\spad{s},{} preserving the color,{} or fourth coordinate,{} of \\spad{p}.")) (|point| (((|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{point(x1,x2,x3,c)} creates and returns a point from the three specified coordinates \\spad{x1},{} \\spad{x2},{} \\spad{x3},{} and also a fourth coordinate,{} \\spad{c},{} which is generally used to specify the color of the point."))) 
 NIL 
 NIL 
-(-1125 S) 
+(-1126 S) 
 ((|constructor| (NIL "\\indented{1}{This domain is used to interface with the interpreter's notion} of comma-delimited sequences of values.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length(x)} returns the number of elements in tuple \\spad{x}")) (|select| ((|#1| $ (|NonNegativeInteger|)) "\\spad{select(x,n)} returns the \\spad{n}-th element of tuple \\spad{x}. tuples are 0-based"))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (QUOTE (-552 (-772))))) 
-(-1126 -3088) 
+((|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-553 (-773))))) 
+(-1127 -3090) 
 ((|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 
-(-1127) 
+(-1128) 
 ((|constructor| (NIL "The fundamental Type."))) 
 NIL 
 NIL 
-(-1128) 
+(-1129) 
 ((|constructor| (NIL "This domain represents a type AST."))) 
 NIL 
 NIL 
-(-1129 S) 
+(-1130 S) 
 ((|constructor| (NIL "Provides functions to force a partial ordering on any set.")) (|more?| (((|Boolean|) |#1| |#1|) "\\spad{more?(a, b)} compares \\spad{a} and \\spad{b} in the partial ordering induced by setOrder,{} and uses the ordering on \\spad{S} if \\spad{a} and \\spad{b} are not comparable in the partial ordering.")) (|userOrdered?| (((|Boolean|)) "\\spad{userOrdered?()} tests if the partial ordering induced by \\spadfunFrom{setOrder}{UserDefinedPartialOrdering} is not empty.")) (|largest| ((|#1| (|List| |#1|)) "\\spad{largest l} returns the largest element of \\spad{l} where the partial ordering induced by setOrder is completed into a total one by the ordering on \\spad{S}.") ((|#1| (|List| |#1|) (|Mapping| (|Boolean|) |#1| |#1|)) "\\spad{largest(l, fn)} returns the largest element of \\spad{l} where the partial ordering induced by setOrder is completed into a total one by fn.")) (|less?| (((|Boolean|) |#1| |#1| (|Mapping| (|Boolean|) |#1| |#1|)) "\\spad{less?(a, b, fn)} compares \\spad{a} and \\spad{b} in the partial ordering induced by setOrder,{} and returns \\spad{fn(a, b)} if \\spad{a} and \\spad{b} are not comparable in that ordering.") (((|Union| (|Boolean|) "failed") |#1| |#1|) "\\spad{less?(a, b)} compares \\spad{a} and \\spad{b} in the partial ordering induced by setOrder.")) (|getOrder| (((|Record| (|:| |low| (|List| |#1|)) (|:| |high| (|List| |#1|)))) "\\spad{getOrder()} returns \\spad{[[b1,...,bm], [a1,...,an]]} such that the partial ordering on \\spad{S} was given by \\spad{setOrder([b1,...,bm],[a1,...,an])}.")) (|setOrder| (((|Void|) (|List| |#1|) (|List| |#1|)) "\\spad{setOrder([b1,...,bm], [a1,...,an])} defines a partial ordering on \\spad{S} given by: \\indented{3}{(1)\\space{2}\\spad{b1 < b2 < ... < bm < a1 < a2 < ... < an}.} \\indented{3}{(2)\\space{2}\\spad{bj < c < ai}\\space{2}for \\spad{c} not among the \\spad{ai}'s and bj's.} \\indented{3}{(3)\\space{2}undefined on \\spad{(c,d)} if neither is among the \\spad{ai}'s,{}bj's.}") (((|Void|) (|List| |#1|)) "\\spad{setOrder([a1,...,an])} defines a partial ordering on \\spad{S} given by: \\indented{3}{(1)\\space{2}\\spad{a1 < a2 < ... < an}.} \\indented{3}{(2)\\space{2}\\spad{b < ai\\space{3}for i = 1..n} and \\spad{b} not among the \\spad{ai}'s.} \\indented{3}{(3)\\space{2}undefined on \\spad{(b, c)} if neither is among the \\spad{ai}'s.}"))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-756)))) 
-(-1130) 
+((|HasCategory| |#1| (QUOTE (-757)))) 
+(-1131) 
 ((|constructor| (NIL "This packages provides functions to allow the user to select the ordering on the variables and operators for displaying polynomials,{} fractions and expressions. The ordering affects the display only and not the computations.")) (|resetVariableOrder| (((|Void|)) "\\spad{resetVariableOrder()} cancels any previous use of setVariableOrder and returns to the default system ordering.")) (|getVariableOrder| (((|Record| (|:| |high| (|List| (|Symbol|))) (|:| |low| (|List| (|Symbol|))))) "\\spad{getVariableOrder()} returns \\spad{[[b1,...,bm], [a1,...,an]]} such that the ordering on the variables was given by \\spad{setVariableOrder([b1,...,bm], [a1,...,an])}.")) (|setVariableOrder| (((|Void|) (|List| (|Symbol|)) (|List| (|Symbol|))) "\\spad{setVariableOrder([b1,...,bm], [a1,...,an])} defines an ordering on the variables given by \\spad{b1 > b2 > ... > bm >} other variables \\spad{> a1 > a2 > ... > an}.") (((|Void|) (|List| (|Symbol|))) "\\spad{setVariableOrder([a1,...,an])} defines an ordering on the variables given by \\spad{a1 > a2 > ... > an > other variables}."))) 
 NIL 
 NIL 
-(-1131 S) 
+(-1132 S) 
 ((|constructor| (NIL "A constructive unique factorization domain,{} \\spadignore{i.e.} where we can constructively factor members into a product of a finite number of irreducible elements.")) (|factor| (((|Factored| $) $) "\\spad{factor(x)} returns the factorization of \\spad{x} into irreducibles.")) (|squareFreePart| (($ $) "\\spad{squareFreePart(x)} returns a product of prime factors of \\spad{x} each taken with multiplicity one.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns the square-free factorization of \\spad{x} \\spadignore{i.e.} such that the factors are pairwise relatively prime and each has multiple prime factors.")) (|prime?| (((|Boolean|) $) "\\spad{prime?(x)} tests if \\spad{x} can never be written as the product of two non-units of the ring,{} \\spadignore{i.e.} \\spad{x} is an irreducible element."))) 
 NIL 
 NIL 
-(-1132) 
+(-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|) $) "\\spad{prime?(x)} tests if \\spad{x} can never be written as the product of two non-units of the ring,{} \\spadignore{i.e.} \\spad{x} is an irreducible element."))) 
-((-3982 . T) ((-3991 "*") . T) (-3983 . T) (-3984 . T) (-3986 . T)) 
+((-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . T)) 
 NIL 
-(-1133) 
+(-1134) 
 ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 16 bits."))) 
 NIL 
 NIL 
-(-1134) 
+(-1135) 
 ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 32 bits."))) 
 NIL 
 NIL 
-(-1135) 
+(-1136) 
 ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 64 bits."))) 
 NIL 
 NIL 
-(-1136) 
+(-1137) 
 ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 8 bits."))) 
 NIL 
 NIL 
-(-1137 |Coef| |var| |cen|) 
+(-1138 |Coef| |var| |cen|) 
 ((|constructor| (NIL "Dense Laurent series in one variable \\indented{2}{\\spadtype{UnivariateLaurentSeries} is a domain representing Laurent} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{UnivariateLaurentSeries(Integer,x,3)} represents Laurent series in} \\indented{2}{\\spad{(x - 3)} with integer coefficients.}")) (|integrate| (($ $ (|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."))) 
-(((-3991 "*") OR (-2558 (|has| |#1| (-311)) (|has| (-1167 |#1| |#2| |#3|) (-740))) (|has| |#1| (-146)) (-2558 (|has| |#1| (-311)) (|has| (-1167 |#1| |#2| |#3|) (-821)))) (-3982 OR (-2558 (|has| |#1| (-311)) (|has| (-1167 |#1| |#2| |#3|) (-740))) (|has| |#1| (-494)) (-2558 (|has| |#1| (-311)) (|has| (-1167 |#1| |#2| |#3|) (-821)))) (-3987 |has| |#1| (-311)) (-3981 |has| |#1| (-311)) (-3983 . T) (-3984 . T) (-3986 . T)) 
-((|HasCategory| |#1| (QUOTE (-38 (-347 (-483))))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-494)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| (-1167 |#1| |#2| |#3|) (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| (-1167 |#1| |#2| |#3|) (QUOTE (-120)))) (|HasCategory| |#1| (QUOTE (-120)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| (-1167 |#1| |#2| |#3|) (QUOTE (-809 (-1088))))) (-12 (|HasCategory| |#1| (QUOTE (-809 (-1088)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-483)) (|devaluate| |#1|)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| (-1167 |#1| |#2| |#3|) (QUOTE (-809 (-1088))))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| (-1167 |#1| |#2| |#3|) (QUOTE (-811 (-1088))))) (-12 (|HasCategory| |#1| (QUOTE (-809 (-1088)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-483)) (|devaluate| |#1|)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| (-1167 |#1| |#2| |#3|) (QUOTE (-190)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-483)) (|devaluate| |#1|))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| (-1167 |#1| |#2| |#3|) (QUOTE (-190)))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| (-1167 |#1| |#2| |#3|) (QUOTE (-189)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-483)) (|devaluate| |#1|))))) (|HasCategory| (-483) (QUOTE (-1024))) (OR (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-494)))) (|HasCategory| |#1| (QUOTE (-311))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| (-1167 |#1| |#2| |#3|) (QUOTE (-821)))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| (-1167 |#1| |#2| |#3|) (QUOTE (-950 (-1088))))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| (-1167 |#1| |#2| |#3|) (QUOTE (-553 (-472))))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| (-1167 |#1| |#2| |#3|) (QUOTE (-933)))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-494)))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| (-1167 |#1| |#2| |#3|) (QUOTE (-740)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| (-1167 |#1| |#2| |#3|) (QUOTE (-740)))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| (-1167 |#1| |#2| |#3|) (QUOTE (-756))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| (-1167 |#1| |#2| |#3|) (QUOTE (-950 (-483))))) (|HasCategory| |#1| (QUOTE (-38 (-347 (-483)))))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| (-1167 |#1| |#2| |#3|) (QUOTE (-950 (-483))))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| (-1167 |#1| |#2| |#3|) (QUOTE (-1064)))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| (-1167 |#1| |#2| |#3|) (|%list| (QUOTE -241) (|%list| (QUOTE -1167) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|)) (|%list| (QUOTE -1167) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|))))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| (-1167 |#1| |#2| |#3|) (|%list| (QUOTE -259) (|%list| (QUOTE -1167) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|))))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| (-1167 |#1| |#2| |#3|) (|%list| (QUOTE -452) (QUOTE (-1088)) (|%list| (QUOTE -1167) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|))))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| (-1167 |#1| |#2| |#3|) (QUOTE (-580 (-483))))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| (-1167 |#1| |#2| |#3|) (QUOTE (-553 (-800 (-483)))))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| (-1167 |#1| |#2| |#3|) (QUOTE (-553 (-800 (-327)))))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| (-1167 |#1| |#2| |#3|) (QUOTE (-796 (-483))))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| (-1167 |#1| |#2| |#3|) (QUOTE (-796 (-327))))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-483))))) (|HasSignature| |#1| (|%list| (QUOTE -3940) (|%list| (|devaluate| |#1|) (QUOTE (-1088)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-483))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-347 (-483))))) (|HasCategory| |#1| (QUOTE (-29 (-483)))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1113)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-347 (-483))))) (|HasSignature| |#1| (|%list| (QUOTE -3806) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1088))))) (|HasSignature| |#1| (|%list| (QUOTE -3077) (|%list| (|%list| (QUOTE -583) (QUOTE (-1088))) (|devaluate| |#1|)))))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| (-1167 |#1| |#2| |#3|) (QUOTE (-482)))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| (-1167 |#1| |#2| |#3|) (QUOTE (-257)))) (|HasCategory| (-1167 |#1| |#2| |#3|) (QUOTE (-821))) (|HasCategory| (-1167 |#1| |#2| |#3|) (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-118))) (OR (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| (-1167 |#1| |#2| |#3|) (QUOTE (-821)))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| (-1167 |#1| |#2| |#3|) (QUOTE (-740)))) (|HasCategory| |#1| (QUOTE (-494)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| (-1167 |#1| |#2| |#3|) (QUOTE (-821)))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| (-1167 |#1| |#2| |#3|) (QUOTE (-740)))) (|HasCategory| |#1| (QUOTE (-146)))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| (-1167 |#1| |#2| |#3|) (QUOTE (-811 (-1088))))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| (-1167 |#1| |#2| |#3|) (QUOTE (-189)))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| (-1167 |#1| |#2| |#3|) (QUOTE (-756)))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-1167 |#1| |#2| |#3|) (QUOTE (-821)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| (-1167 |#1| |#2| |#3|) (QUOTE (-118)))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-1167 |#1| |#2| |#3|) (QUOTE (-821)))) (|HasCategory| |#1| (QUOTE (-118))))) 
-(-1138 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) 
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(QUOTE (-311))) (|HasCategory| (-1168 |#1| |#2| |#3|) (QUOTE (-257)))) (|HasCategory| (-1168 |#1| |#2| |#3|) (QUOTE (-822))) (|HasCategory| (-1168 |#1| |#2| |#3|) (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-118))) (OR (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| (-1168 |#1| |#2| |#3|) (QUOTE (-822)))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| (-1168 |#1| |#2| |#3|) (QUOTE (-741)))) (|HasCategory| |#1| (QUOTE (-495)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| (-1168 |#1| |#2| |#3|) (QUOTE (-822)))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| (-1168 |#1| |#2| |#3|) (QUOTE (-741)))) (|HasCategory| |#1| (QUOTE (-146)))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| (-1168 |#1| |#2| |#3|) (QUOTE (-812 (-1089))))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| (-1168 |#1| |#2| |#3|) (QUOTE (-189)))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| (-1168 |#1| |#2| |#3|) (QUOTE (-757)))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-1168 |#1| |#2| |#3|) (QUOTE (-822)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| (-1168 |#1| |#2| |#3|) (QUOTE (-118)))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-1168 |#1| |#2| |#3|) (QUOTE (-822)))) (|HasCategory| |#1| (QUOTE (-118))))) 
+(-1139 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) 
 ((|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 
-(-1139 |Coef|) 
+(-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."))) 
-(((-3991 "*") |has| |#1| (-146)) (-3982 |has| |#1| (-494)) (-3987 |has| |#1| (-311)) (-3981 |has| |#1| (-311)) (-3983 . T) (-3984 . T) (-3986 . T)) 
+(((-3993 "*") |has| |#1| (-146)) (-3984 |has| |#1| (-495)) (-3989 |has| |#1| (-311)) (-3983 |has| |#1| (-311)) (-3985 . T) (-3986 . T) (-3988 . T)) 
 NIL 
-(-1140 S |Coef| UTS) 
+(-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)}."))) 
 NIL 
 ((|HasCategory| |#2| (QUOTE (-311)))) 
-(-1141 |Coef| UTS) 
+(-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)}."))) 
-(((-3991 "*") |has| |#1| (-146)) (-3982 |has| |#1| (-494)) (-3987 |has| |#1| (-311)) (-3981 |has| |#1| (-311)) (-3983 . T) (-3984 . T) (-3986 . T)) 
+(((-3993 "*") |has| |#1| (-146)) (-3984 |has| |#1| (-495)) (-3989 |has| |#1| (-311)) (-3983 |has| |#1| (-311)) (-3985 . T) (-3986 . T) (-3988 . T)) 
 NIL 
-(-1142 |Coef| UTS) 
+(-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 (-811 (-1088))))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-189)))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-118)))))) 
-(-1143 ZP) 
+(((-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)))) (OR (|HasCategory| |#1| (QUOTE (-118))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-118))))) (OR (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-120))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-810 (-1089))))) (-12 (|HasCategory| |#1| (QUOTE (-810 (-1089)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-484)) (|devaluate| |#1|)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-810 (-1089))))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-812 (-1089))))) (-12 (|HasCategory| |#1| (QUOTE (-810 (-1089)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-484)) (|devaluate| |#1|)))))) (OR (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-484)) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-190))))) (OR (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-484)) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-190)))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-189))))) (|HasCategory| (-484) (QUOTE (-1025))) (OR (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-495)))) (|HasCategory| |#1| (QUOTE (-311))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-822)))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-951 (-1089))))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-554 (-473))))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-934)))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-495)))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-741)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-741)))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-757))))) (OR (|HasCategory| |#1| (QUOTE (-38 (-347 (-484))))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-951 (-484)))))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-951 (-484))))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-1065)))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#2| (|%list| (QUOTE -241) (|devaluate| |#2|) (|devaluate| |#2|)))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#2| (|%list| (QUOTE -259) (|devaluate| |#2|)))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#2| (|%list| (QUOTE -453) (QUOTE (-1089)) (|devaluate| |#2|)))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-581 (-484))))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-554 (-801 (-484)))))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-554 (-801 (-327)))))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-797 (-484))))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-797 (-327))))) (-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))))) (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|)))))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-757)))) (|HasCategory| |#2| (QUOTE (-822))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-483)))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-257)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-118))) (OR (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-484)) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-189))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-812 (-1089))))) (-12 (|HasCategory| |#1| (QUOTE (-810 (-1089)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-484)) (|devaluate| |#1|)))))) (-12 (|HasCategory| |#1| (QUOTE (-311))) (|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 
 NIL 
-(-1144 S) 
+(-1145 S) 
 ((|constructor| (NIL "This domain provides segments which may be half open. That is,{} ranges of the form \\spad{a..} or \\spad{a..b}.")) (|hasHi| (((|Boolean|) $) "\\spad{hasHi(s)} tests whether the segment \\spad{s} has an upper bound.")) (|coerce| (($ (|Segment| |#1|)) "\\spad{coerce(x)} allows \\spadtype{Segment} values to be used as \\%.")) (|segment| (($ |#1|) "\\spad{segment(l)} is an alternate way to construct the segment \\spad{l..}.")) (SEGMENT (($ |#1|) "\\spad{l..} produces a half open segment,{} that is,{} one with no upper bound."))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-755))) (|HasCategory| |#1| (QUOTE (-1012)))) 
-(-1145 R S) 
+((|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1013)))) 
+(-1146 R S) 
 ((|constructor| (NIL "This package provides operations for mapping functions onto segments.")) (|map| (((|Stream| |#2|) (|Mapping| |#2| |#1|) (|UniversalSegment| |#1|)) "\\spad{map(f,s)} expands the segment \\spad{s},{} applying \\spad{f} to each value.") (((|UniversalSegment| |#2|) (|Mapping| |#2| |#1|) (|UniversalSegment| |#1|)) "\\spad{map(f,seg)} returns the new segment obtained by applying \\spad{f} to the endpoints of \\spad{seg}."))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-755)))) 
-(-1146 |x| R) 
+((|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}"))) 
-(((-3991 "*") |has| |#2| (-146)) (-3982 |has| |#2| (-494)) (-3985 |has| |#2| (-311)) (-3987 |has| |#2| (-6 -3987)) (-3984 . T) (-3983 . T) (-3986 . T)) 
-((|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| |#2| (QUOTE (-494))) (|HasCategory| |#2| (QUOTE (-146))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-494)))) (-12 (|HasCategory| |#2| (QUOTE (-796 (-327)))) (|HasCategory| (-993) (QUOTE (-796 (-327))))) (-12 (|HasCategory| |#2| (QUOTE (-796 (-483)))) (|HasCategory| (-993) (QUOTE (-796 (-483))))) (-12 (|HasCategory| |#2| (QUOTE (-553 (-800 (-327))))) (|HasCategory| (-993) (QUOTE (-553 (-800 (-327)))))) (-12 (|HasCategory| |#2| (QUOTE (-553 (-800 (-483))))) (|HasCategory| (-993) (QUOTE (-553 (-800 (-483)))))) (-12 (|HasCategory| |#2| (QUOTE (-553 (-472)))) (|HasCategory| (-993) (QUOTE (-553 (-472))))) (|HasCategory| |#2| (QUOTE (-580 (-483)))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-38 (-347 (-483))))) (|HasCategory| |#2| (QUOTE (-950 (-483)))) (OR (|HasCategory| |#2| (QUOTE (-38 (-347 (-483))))) (|HasCategory| |#2| (QUOTE (-950 (-347 (-483)))))) (|HasCategory| |#2| (QUOTE (-950 (-347 (-483))))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-389))) (|HasCategory| |#2| (QUOTE (-494))) (|HasCategory| |#2| (QUOTE (-821)))) (OR (|HasCategory| |#2| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-389))) (|HasCategory| |#2| (QUOTE (-494))) (|HasCategory| |#2| (QUOTE (-821)))) (OR (|HasCategory| |#2| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-389))) (|HasCategory| |#2| (QUOTE (-821)))) (|HasCategory| |#2| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-1064))) (|HasCategory| |#2| (QUOTE (-811 (-1088)))) (|HasCategory| |#2| (QUOTE (-809 (-1088)))) (|HasCategory| |#2| (QUOTE (-189))) (|HasCategory| |#2| (QUOTE (-190))) (|HasAttribute| |#2| (QUOTE -3987)) (|HasCategory| |#2| (QUOTE (-389))) (-12 (|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#2| (QUOTE (-118))))) 
-(-1147 |x| R |y| S) 
+(((-3993 "*") |has| |#2| (-146)) (-3984 |has| |#2| (-495)) (-3987 |has| |#2| (-311)) (-3989 |has| |#2| (-6 -3989)) (-3986 . T) (-3985 . T) (-3988 . T)) 
+((|HasCategory| |#2| (QUOTE (-822))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-146))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-495)))) (-12 (|HasCategory| |#2| (QUOTE (-797 (-327)))) (|HasCategory| (-994) (QUOTE (-797 (-327))))) (-12 (|HasCategory| |#2| (QUOTE (-797 (-484)))) (|HasCategory| (-994) (QUOTE (-797 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-554 (-801 (-327))))) (|HasCategory| (-994) (QUOTE (-554 (-801 (-327)))))) (-12 (|HasCategory| |#2| (QUOTE (-554 (-801 (-484))))) (|HasCategory| (-994) (QUOTE (-554 (-801 (-484)))))) (-12 (|HasCategory| |#2| (QUOTE (-554 (-473)))) (|HasCategory| (-994) (QUOTE (-554 (-473))))) (|HasCategory| |#2| (QUOTE (-581 (-484)))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-38 (-347 (-484))))) (|HasCategory| |#2| (QUOTE (-951 (-484)))) (OR (|HasCategory| |#2| (QUOTE (-38 (-347 (-484))))) (|HasCategory| |#2| (QUOTE (-951 (-347 (-484)))))) (|HasCategory| |#2| (QUOTE (-951 (-347 (-484))))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-389))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-822)))) (OR (|HasCategory| |#2| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-389))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-822)))) (OR (|HasCategory| |#2| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-389))) (|HasCategory| |#2| (QUOTE (-822)))) (|HasCategory| |#2| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-1065))) (|HasCategory| |#2| (QUOTE (-812 (-1089)))) (|HasCategory| |#2| (QUOTE (-810 (-1089)))) (|HasCategory| |#2| (QUOTE (-189))) (|HasCategory| |#2| (QUOTE (-190))) (|HasAttribute| |#2| (QUOTE -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))))) 
+(-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 
 NIL 
-(-1148 R Q UP) 
+(-1149 R Q UP) 
 ((|constructor| (NIL "UnivariatePolynomialCommonDenominator provides functions to compute the common denominator of the coefficients of univariate polynomials over the quotient field of a gcd domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#3|) "\\spad{splitDenominator(q)} returns \\spad{[p, d]} such that \\spad{q = p/d} and \\spad{d} is a common denominator for the coefficients of \\spad{q}.")) (|clearDenominator| ((|#3| |#3|) "\\spad{clearDenominator(q)} returns \\spad{p} such that \\spad{q = p/d} where \\spad{d} is a common denominator for the coefficients of \\spad{q}.")) (|commonDenominator| ((|#1| |#3|) "\\spad{commonDenominator(q)} returns a common denominator \\spad{d} for the coefficients of \\spad{q}."))) 
 NIL 
 NIL 
-(-1149 R UP) 
+(-1150 R UP) 
 ((|constructor| (NIL "UnivariatePolynomialDecompositionPackage implements functional decomposition of univariate polynomial with coefficients in an \\spad{IntegralDomain} of \\spad{CharacteristicZero}.")) (|monicCompleteDecompose| (((|List| |#2|) |#2|) "\\spad{monicCompleteDecompose(f)} returns a list of factors of \\spad{f} for the functional decomposition ([ \\spad{f1},{} ...,{} fn ] means \\spad{f} = \\spad{f1} \\spad{o} ... \\spad{o} fn).")) (|monicDecomposeIfCan| (((|Union| (|Record| (|:| |left| |#2|) (|:| |right| |#2|)) "failed") |#2|) "\\spad{monicDecomposeIfCan(f)} returns a functional decomposition of the monic polynomial \\spad{f} of \"failed\" if it has not found any.")) (|leftFactorIfCan| (((|Union| |#2| "failed") |#2| |#2|) "\\spad{leftFactorIfCan(f,h)} returns the left factor (\\spad{g} in \\spad{f} = \\spad{g} \\spad{o} \\spad{h}) of the functional decomposition of the polynomial \\spad{f} with given \\spad{h} or \\spad{\"failed\"} if \\spad{g} does not exist.")) (|rightFactorIfCan| (((|Union| |#2| "failed") |#2| (|NonNegativeInteger|) |#1|) "\\spad{rightFactorIfCan(f,d,c)} returns a candidate to be the right factor (\\spad{h} in \\spad{f} = \\spad{g} \\spad{o} \\spad{h}) of degree \\spad{d} with leading coefficient \\spad{c} of a functional decomposition of the polynomial \\spad{f} or \\spad{\"failed\"} if no such candidate.")) (|monicRightFactorIfCan| (((|Union| |#2| "failed") |#2| (|NonNegativeInteger|)) "\\spad{monicRightFactorIfCan(f,d)} returns a candidate to be the monic right factor (\\spad{h} in \\spad{f} = \\spad{g} \\spad{o} \\spad{h}) of degree \\spad{d} of a functional decomposition of the polynomial \\spad{f} or \\spad{\"failed\"} if no such candidate."))) 
 NIL 
 NIL 
-(-1150 R UP) 
+(-1151 R UP) 
 ((|constructor| (NIL "UnivariatePolynomialDivisionPackage provides a division for non monic univarite polynomials with coefficients in an \\spad{IntegralDomain}.")) (|divideIfCan| (((|Union| (|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) "failed") |#2| |#2|) "\\spad{divideIfCan(f,g)} returns quotient and remainder of the division of \\spad{f} by \\spad{g} or \"failed\" if it has not succeeded."))) 
 NIL 
 NIL 
-(-1151 R U) 
+(-1152 R U) 
 ((|constructor| (NIL "This package implements Karatsuba's trick for multiplying (large) univariate polynomials. It could be improved with a version doing the work on place and also with a special case for squares. We've done this in Basicmath,{} but we believe that this out of the scope of AXIOM.")) (|karatsuba| ((|#2| |#2| |#2| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{karatsuba(a,b,l,k)} returns \\spad{a*b} by applying Karatsuba's trick provided that both \\spad{a} and \\spad{b} have at least \\spad{l} terms and \\spad{k > 0} holds and by calling \\spad{noKaratsuba} otherwise. The other multiplications are performed by recursive calls with the same third argument and \\spad{k-1} as fourth argument.")) (|karatsubaOnce| ((|#2| |#2| |#2|) "\\spad{karatsuba(a,b)} returns \\spad{a*b} by applying Karatsuba's trick once. The other multiplications are performed by calling \\spad{*} from \\spad{U}.")) (|noKaratsuba| ((|#2| |#2| |#2|) "\\spad{noKaratsuba(a,b)} returns \\spad{a*b} without using Karatsuba's trick at all."))) 
 NIL 
 NIL 
-(-1152 S R) 
+(-1153 S R) 
 ((|constructor| (NIL "The category of univariate polynomials over a ring \\spad{R}. No particular model is assumed - implementations can be either sparse or dense.")) (|integrate| (($ $) "\\spad{integrate(p)} integrates the univariate polynomial \\spad{p} with respect to its distinguished variable.")) (|additiveValuation| ((|attribute|) "euclideanSize(a*b) = euclideanSize(a) + euclideanSize(\\spad{b})")) (|separate| (((|Record| (|:| |primePart| $) (|:| |commonPart| $)) $ $) "\\spad{separate(p, q)} returns \\spad{[a, b]} such that polynomial \\spad{p = a b} and \\spad{a} is relatively prime to \\spad{q}.")) (|pseudoDivide| (((|Record| (|:| |coef| |#2|) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{pseudoDivide(p,q)} returns \\spad{[c, q, r]},{} when \\spad{p' := p*lc(q)**(deg p - deg q + 1) = c * p} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|pseudoQuotient| (($ $ $) "\\spad{pseudoQuotient(p,q)} returns \\spad{r},{} the quotient when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|composite| (((|Union| (|Fraction| $) "failed") (|Fraction| $) $) "\\spad{composite(f, q)} returns \\spad{h} if \\spad{f} = \\spad{h}(\\spad{q}),{} and \"failed\" is no such \\spad{h} exists.") (((|Union| $ "failed") $ $) "\\spad{composite(p, q)} returns \\spad{h} if \\spad{p = h(q)},{} and \"failed\" no such \\spad{h} exists.")) (|subResultantGcd| (($ $ $) "\\spad{subResultantGcd(p,q)} computes the gcd of the polynomials \\spad{p} and \\spad{q} using the SubResultant GCD algorithm.")) (|order| (((|NonNegativeInteger|) $ $) "\\spad{order(p, q)} returns the largest \\spad{n} such that \\spad{q**n} divides polynomial \\spad{p} \\spadignore{i.e.} the order of \\spad{p(x)} at \\spad{q(x)=0}.")) (|elt| ((|#2| (|Fraction| $) |#2|) "\\spad{elt(a,r)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by the constant \\spad{r}.") (((|Fraction| $) (|Fraction| $) (|Fraction| $)) "\\spad{elt(a,b)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by \\spad{b}.")) (|resultant| ((|#2| $ $) "\\spad{resultant(p,q)} returns the resultant of the polynomials \\spad{p} and \\spad{q}.")) (|discriminant| ((|#2| $) "\\spad{discriminant(p)} returns the discriminant of the polynomial \\spad{p}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|) $) "\\spad{differentiate(p, d, x')} extends the \\spad{R}-derivation \\spad{d} to an extension \\spad{D} in \\spad{R[x]} where Dx is given by x',{} and returns \\spad{Dp}.")) (|pseudoRemainder| (($ $ $) "\\spad{pseudoRemainder(p,q)} = \\spad{r},{} for polynomials \\spad{p} and \\spad{q},{} returns the remainder when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|shiftLeft| (($ $ (|NonNegativeInteger|)) "\\spad{shiftLeft(p,n)} returns \\spad{p * monomial(1,n)}")) (|shiftRight| (($ $ (|NonNegativeInteger|)) "\\spad{shiftRight(p,n)} returns \\spad{monicDivide(p,monomial(1,n)).quotient}")) (|karatsubaDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ (|NonNegativeInteger|)) "\\spad{karatsubaDivide(p,n)} returns the same as \\spad{monicDivide(p,monomial(1,n))}")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicDivide(p,q)} divide the polynomial \\spad{p} by the monic polynomial \\spad{q},{} returning the pair \\spad{[quotient, remainder]}. Error: if \\spad{q} isn't monic.")) (|divideExponents| (((|Union| $ "failed") $ (|NonNegativeInteger|)) "\\spad{divideExponents(p,n)} returns a new polynomial resulting from dividing all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n},{} or \"failed\" if some exponent is not exactly divisible by \\spad{n}.")) (|multiplyExponents| (($ $ (|NonNegativeInteger|)) "\\spad{multiplyExponents(p,n)} returns a new polynomial resulting from multiplying all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n}.")) (|unmakeSUP| (($ (|SparseUnivariatePolynomial| |#2|)) "\\spad{unmakeSUP(sup)} converts \\spad{sup} of type \\spadtype{SparseUnivariatePolynomial(R)} to be a member of the given type. Note: converse of makeSUP.")) (|makeSUP| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{makeSUP(p)} converts the polynomial \\spad{p} to be of type SparseUnivariatePolynomial over the same coefficients.")) (|vectorise| (((|Vector| |#2|) $ (|NonNegativeInteger|)) "\\spad{vectorise(p, n)} returns \\spad{[a0,...,a(n-1)]} where \\spad{p = a0 + a1*x + ... + a(n-1)*x**(n-1)} + higher order terms. The degree of polynomial \\spad{p} can be different from \\spad{n-1}."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-38 (-347 (-483))))) (|HasCategory| |#2| (QUOTE (-311))) (|HasCategory| |#2| (QUOTE (-389))) (|HasCategory| |#2| (QUOTE (-494))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-1064)))) 
-(-1153 R) 
+((|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}."))) 
-(((-3991 "*") |has| |#1| (-146)) (-3982 |has| |#1| (-494)) (-3985 |has| |#1| (-311)) (-3987 |has| |#1| (-6 -3987)) (-3984 . T) (-3983 . T) (-3986 . T)) 
+(((-3993 "*") |has| |#1| (-146)) (-3984 |has| |#1| (-495)) (-3987 |has| |#1| (-311)) (-3989 |has| |#1| (-6 -3989)) (-3986 . T) (-3985 . T) (-3988 . T)) 
 NIL 
-(-1154 R PR S PS) 
+(-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."))) 
 NIL 
 NIL 
-(-1155 S |Coef| |Expon|) 
+(-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 (-809 (-1088)))) (|HasSignature| |#2| (|%list| (QUOTE *) (|%list| (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1024))) (|HasSignature| |#2| (|%list| (QUOTE **) (|%list| (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (|%list| (QUOTE -3940) (|%list| (|devaluate| |#2|) (QUOTE (-1088)))))) 
-(-1156 |Coef| |Expon|) 
+((|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)))))) 
+(-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|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) 
-(((-3991 "*") |has| |#1| (-146)) (-3982 |has| |#1| (-494)) (-3983 . T) (-3984 . T) (-3986 . T)) 
+(((-3993 "*") |has| |#1| (-146)) (-3984 |has| |#1| (-495)) (-3985 . T) (-3986 . T) (-3988 . T)) 
 NIL 
-(-1157 RC P) 
+(-1158 RC P) 
 ((|constructor| (NIL "This package provides for square-free decomposition of univariate polynomials over arbitrary rings,{} \\spadignore{i.e.} a partial factorization such that each factor is a product of irreducibles with multiplicity one and the factors are pairwise relatively prime. If the ring has characteristic zero,{} the result is guaranteed to satisfy this condition. If the ring is an infinite ring of finite characteristic,{} then it may not be possible to decide when polynomials contain factors which are \\spad{p}th powers. In this case,{} the flag associated with that polynomial is set to \"nil\" (meaning that that polynomials are not guaranteed to be square-free).")) (|BumInSepFFE| (((|Record| (|:| |flg| (|Union| #1="nil" #2="sqfr" #3="irred" #4="prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|))) (|Record| (|:| |flg| (|Union| #1# #2# #3# #4#)) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|)))) "\\spad{BumInSepFFE(f)} is a local function,{} exported only because it has multiple conditional definitions.")) (|squareFreePart| ((|#2| |#2|) "\\spad{squareFreePart(p)} returns a polynomial which has the same irreducible factors as the univariate polynomial \\spad{p},{} but each factor has multiplicity one.")) (|squareFree| (((|Factored| |#2|) |#2|) "\\spad{squareFree(p)} computes the square-free factorization of the univariate polynomial \\spad{p}. Each factor has no repeated roots,{} and the factors are pairwise relatively prime.")) (|gcd| (($ $ $) "\\spad{gcd(p,q)} computes the greatest-common-divisor of \\spad{p} and \\spad{q}."))) 
 NIL 
 NIL 
-(-1158 |Coef| |var| |cen|) 
+(-1159 |Coef| |var| |cen|) 
 ((|constructor| (NIL "Dense Puiseux series in one variable \\indented{2}{\\spadtype{UnivariatePuiseuxSeries} is a domain representing Puiseux} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{UnivariatePuiseuxSeries(Integer,x,3)} represents Puiseux series in} \\indented{2}{\\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|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."))) 
-(((-3991 "*") |has| |#1| (-146)) (-3982 |has| |#1| (-494)) (-3987 |has| |#1| (-311)) (-3981 |has| |#1| (-311)) (-3983 . T) (-3984 . T) (-3986 . T)) 
-((|HasCategory| |#1| (QUOTE (-38 (-347 (-483))))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-494)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-809 (-1088)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -347) (QUOTE (-483))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -347) (QUOTE (-483))) (|devaluate| |#1|)))) (|HasCategory| (-347 (-483)) (QUOTE (-1024))) (|HasCategory| |#1| (QUOTE (-311))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-494)))) (OR (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-494)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -347) (QUOTE (-483)))))) (|HasSignature| |#1| (|%list| (QUOTE -3940) (|%list| (|devaluate| |#1|) (QUOTE (-1088)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -347) (QUOTE (-483)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-347 (-483))))) (|HasCategory| |#1| (QUOTE (-29 (-483)))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1113)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-347 (-483))))) (|HasSignature| |#1| (|%list| (QUOTE -3806) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1088))))) (|HasSignature| |#1| (|%list| (QUOTE -3077) (|%list| (|%list| (QUOTE -583) (QUOTE (-1088))) (|devaluate| |#1|))))))) 
-(-1159 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) 
+(((-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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+(-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 
-(-1160 |Coef|) 
+(-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."))) 
-(((-3991 "*") |has| |#1| (-146)) (-3982 |has| |#1| (-494)) (-3987 |has| |#1| (-311)) (-3981 |has| |#1| (-311)) (-3983 . T) (-3984 . T) (-3986 . T)) 
+(((-3993 "*") |has| |#1| (-146)) (-3984 |has| |#1| (-495)) (-3989 |has| |#1| (-311)) (-3983 |has| |#1| (-311)) (-3985 . T) (-3986 . T) (-3988 . T)) 
 NIL 
-(-1161 S |Coef| ULS) 
+(-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)}."))) 
 NIL 
 NIL 
-(-1162 |Coef| ULS) 
+(-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)}."))) 
-(((-3991 "*") |has| |#1| (-146)) (-3982 |has| |#1| (-494)) (-3987 |has| |#1| (-311)) (-3981 |has| |#1| (-311)) (-3983 . T) (-3984 . T) (-3986 . T)) 
+(((-3993 "*") |has| |#1| (-146)) (-3984 |has| |#1| (-495)) (-3989 |has| |#1| (-311)) (-3983 |has| |#1| (-311)) (-3985 . T) (-3986 . T) (-3988 . T)) 
 NIL 
-(-1163 |Coef| ULS) 
+(-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)}."))) 
-(((-3991 "*") |has| |#1| (-146)) (-3982 |has| |#1| (-494)) (-3987 |has| |#1| (-311)) (-3981 |has| |#1| (-311)) (-3983 . T) (-3984 . T) (-3986 . T)) 
-((|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-494)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-809 (-1088)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -347) (QUOTE (-483))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -347) (QUOTE (-483))) (|devaluate| |#1|)))) (|HasCategory| (-347 (-483)) (QUOTE (-1024))) (|HasCategory| |#1| (QUOTE (-311))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-494)))) (OR (|HasCategory| |#1| (QUOTE (-311))) (|HasCategory| |#1| (QUOTE (-494)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -347) (QUOTE (-483)))))) (|HasSignature| |#1| (|%list| (QUOTE -3940) (|%list| (|devaluate| |#1|) (QUOTE (-1088)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -347) (QUOTE (-483)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-347 (-483))))) (|HasCategory| |#1| (QUOTE (-29 (-483)))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1113)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-347 (-483))))) (|HasSignature| |#1| (|%list| (QUOTE -3806) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1088))))) (|HasSignature| |#1| (|%list| (QUOTE -3077) (|%list| (|%list| (QUOTE -583) (QUOTE (-1088))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (QUOTE (-38 (-347 (-483)))))) 
-(-1164 R FE |var| |cen|) 
+(((-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)))))) 
+(-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))}."))) 
-(((-3991 "*") |has| (-1158 |#2| |#3| |#4|) (-146)) (-3982 |has| (-1158 |#2| |#3| |#4|) (-494)) (-3983 . T) (-3984 . T) (-3986 . T)) 
-((|HasCategory| (-1158 |#2| |#3| |#4|) (QUOTE (-38 (-347 (-483))))) (|HasCategory| (-1158 |#2| |#3| |#4|) (QUOTE (-118))) (|HasCategory| (-1158 |#2| |#3| |#4|) (QUOTE (-120))) (|HasCategory| (-1158 |#2| |#3| |#4|) (QUOTE (-146))) (OR (|HasCategory| (-1158 |#2| |#3| |#4|) (QUOTE (-38 (-347 (-483))))) (|HasCategory| (-1158 |#2| |#3| |#4|) (QUOTE (-950 (-347 (-483)))))) (|HasCategory| (-1158 |#2| |#3| |#4|) (QUOTE (-950 (-347 (-483))))) (|HasCategory| (-1158 |#2| |#3| |#4|) (QUOTE (-950 (-483)))) (|HasCategory| (-1158 |#2| |#3| |#4|) (QUOTE (-311))) (|HasCategory| (-1158 |#2| |#3| |#4|) (QUOTE (-389))) (|HasCategory| (-1158 |#2| |#3| |#4|) (QUOTE (-494)))) 
-(-1165 A S) 
+(((-3993 "*") |has| (-1159 |#2| |#3| |#4|) (-146)) (-3984 |has| (-1159 |#2| |#3| |#4|) (-495)) (-3985 . T) (-3986 . T) (-3988 . 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| $) "\\spad{concat(x,u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) 
 NIL 
-((|HasAttribute| |#1| (QUOTE -3990))) 
-(-1166 S) 
+((|HasAttribute| |#1| (QUOTE -3992))) 
+(-1167 S) 
 ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|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| $) "\\spad{concat(x,u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) 
 NIL 
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-(-1167 |Coef| |var| |cen|) 
+(-1168 |Coef| |var| |cen|) 
 ((|constructor| (NIL "Dense Taylor series in one variable \\spadtype{UnivariateTaylorSeries} is a domain representing Taylor series in one variable with coefficients in an arbitrary ring. The parameters of the type specify the coefficient ring,{} the power series variable,{} and the center of the power series expansion. For example,{} \\spadtype{UnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.")) (|integrate| (($ $ (|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}."))) 
-(((-3991 "*") |has| |#1| (-146)) (-3982 |has| |#1| (-494)) (-3983 . T) (-3984 . T) (-3986 . T)) 
-((|HasCategory| |#1| (QUOTE (-38 (-347 (-483))))) (|HasCategory| |#1| (QUOTE (-494))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-494)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-809 (-1088)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-694)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-694)) (|devaluate| |#1|)))) (|HasCategory| (-694) (QUOTE (-1024))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-694))))) (|HasSignature| |#1| (|%list| (QUOTE -3940) (|%list| (|devaluate| |#1|) (QUOTE (-1088)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-694))))) (|HasCategory| |#1| (QUOTE (-311))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-347 (-483))))) (|HasCategory| |#1| (QUOTE (-29 (-483)))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1113)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-347 (-483))))) (|HasSignature| |#1| (|%list| (QUOTE -3806) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1088))))) (|HasSignature| |#1| (|%list| (QUOTE -3077) (|%list| (|%list| (QUOTE -583) (QUOTE (-1088))) (|devaluate| |#1|))))))) 
-(-1168 |Coef1| |Coef2| UTS1 UTS2) 
+(((-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|))))))) 
+(-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 
 NIL 
-(-1169 S |Coef|) 
+(-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 (-483)))) (|HasCategory| |#2| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-1113))) (|HasSignature| |#2| (|%list| (QUOTE -3077) (|%list| (|%list| (QUOTE -583) (QUOTE (-1088))) (|devaluate| |#2|)))) (|HasSignature| |#2| (|%list| (QUOTE -3806) (|%list| (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1088))))) (|HasCategory| |#2| (QUOTE (-38 (-347 (-483))))) (|HasCategory| |#2| (QUOTE (-311)))) 
-(-1170 |Coef|) 
+((|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)))) 
+(-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."))) 
-(((-3991 "*") |has| |#1| (-146)) (-3982 |has| |#1| (-494)) (-3983 . T) (-3984 . T) (-3986 . T)) 
+(((-3993 "*") |has| |#1| (-146)) (-3984 |has| |#1| (-495)) (-3985 . T) (-3986 . T) (-3988 . T)) 
 NIL 
-(-1171 |Coef| UTS) 
+(-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 
-(-1172 -3088 UP L UTS) 
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 ((|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 
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-(-1173) 
+((|HasCategory| |#1| (QUOTE (-495)))) 
+(-1174) 
 ((|constructor| (NIL "The category of domains that act like unions. UnionType,{} like Type or Category,{} acts mostly as a take that communicates `union-like' intended semantics to the compiler. A domain \\spad{D} that satifies UnionType should provide definitions for `case' operators,{} with corresponding `autoCoerce' operators."))) 
 NIL 
 NIL 
-(-1174 |sym|) 
+(-1175 |sym|) 
 ((|constructor| (NIL "This domain implements variables")) (|variable| (((|Symbol|)) "\\spad{variable()} returns the symbol")) (|coerce| (((|Symbol|) $) "\\spad{coerce(x)} returns the symbol"))) 
 NIL 
 NIL 
-(-1175 S R) 
+(-1176 S R) 
 ((|constructor| (NIL "\\spadtype{VectorCategory} represents the type of vector like objects,{} \\spadignore{i.e.} finite sequences indexed by some finite segment of the integers. The operations available on vectors depend on the structure of the underlying components. Many operations from the component domain are defined for vectors componentwise. It can by assumed that extraction or updating components can be done in constant time.")) (|magnitude| ((|#2| $) "\\spad{magnitude(v)} computes the sqrt(dot(\\spad{v},{}\\spad{v})),{} \\spadignore{i.e.} the length")) (|length| ((|#2| $) "\\spad{length(v)} computes the sqrt(dot(\\spad{v},{}\\spad{v})),{} \\spadignore{i.e.} the magnitude")) (|cross| (($ $ $) "vectorProduct(\\spad{u},{}\\spad{v}) constructs the cross product of \\spad{u} and \\spad{v}. Error: if \\spad{u} and \\spad{v} are not of length 3.")) (|outerProduct| (((|Matrix| |#2|) $ $) "\\spad{outerProduct(u,v)} constructs the matrix whose (\\spad{i},{}\\spad{j})\\spad{'}th element is \\spad{u}(\\spad{i})*v(\\spad{j}).")) (|dot| ((|#2| $ $) "\\spad{dot(x,y)} computes the inner product of the two vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.")) (* (($ $ |#2|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#2| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.") (($ (|Integer|) $) "\\spad{n * y} multiplies each component of the vector \\spad{y} by the integer \\spad{n}.")) (- (($ $ $) "\\spad{x - y} returns the component-wise difference of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.") (($ $) "\\spad{-x} negates all components of the vector \\spad{x}.")) (|zero| (($ (|NonNegativeInteger|)) "\\spad{zero(n)} creates a zero vector of length \\spad{n}.")) (+ (($ $ $) "\\spad{x + y} returns the component-wise sum of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-915))) (|HasCategory| |#2| (QUOTE (-961))) (|HasCategory| |#2| (QUOTE (-663))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25)))) 
-(-1176 R) 
+((|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}.")) (+ (($ $ $) "\\spad{x + y} returns the component-wise sum of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length."))) 
-((-3990 . T) (-3989 . T)) 
+((-3992 . T) (-3991 . T)) 
 NIL 
-(-1177 R) 
+(-1178 R) 
 ((|constructor| (NIL "This type represents vector like objects with varying lengths and indexed by a finite segment of integers starting at 1.")) (|vector| (($ (|List| |#1|)) "\\spad{vector(l)} converts the list \\spad{l} to a vector."))) 
-((-3990 . T) (-3989 . T)) 
-((OR (-12 (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-553 (-472)))) (OR (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| |#1| (QUOTE (-756))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1012)))) (|HasCategory| (-483) (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-663))) (|HasCategory| |#1| (QUOTE (-961))) (-12 (|HasCategory| |#1| (QUOTE (-915))) (|HasCategory| |#1| (QUOTE (-961)))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (|%list| (QUOTE -259) (|devaluate| |#1|))))) 
-(-1178 A B) 
+((-3992 . T) (-3991 . 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}."))) 
 NIL 
 NIL 
-(-1179) 
+(-1180) 
 ((|constructor| (NIL "ViewportPackage provides functions for creating GraphImages and TwoDimensionalViewports from lists of lists of points.")) (|coerce| (((|TwoDimensionalViewport|) (|GraphImage|)) "\\spad{coerce(gi)} converts the indicated \\spadtype{GraphImage},{} \\spad{gi},{} into the \\spadtype{TwoDimensionalViewport} form.")) (|drawCurves| (((|TwoDimensionalViewport|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|DrawOption|))) "\\spad{drawCurves([[p0],[p1],...,[pn]],[options])} creates a \\spadtype{TwoDimensionalViewport} from the list of lists of points,{} \\spad{p0} throught pn,{} using the options specified in the list \\spad{options}.") (((|TwoDimensionalViewport|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|Palette|) (|Palette|) (|PositiveInteger|) (|List| (|DrawOption|))) "\\spad{drawCurves([[p0],[p1],...,[pn]],ptColor,lineColor,ptSize,[options])} creates a \\spadtype{TwoDimensionalViewport} from the list of lists of points,{} \\spad{p0} throught pn,{} using the options specified in the list \\spad{options}. The point color is specified by \\spad{ptColor},{} the line color is specified by \\spad{lineColor},{} and the point size is specified by \\spad{ptSize}.")) (|graphCurves| (((|GraphImage|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|DrawOption|))) "\\spad{graphCurves([[p0],[p1],...,[pn]],[options])} creates a \\spadtype{GraphImage} from the list of lists of points,{} \\spad{p0} throught pn,{} using the options specified in the list \\spad{options}.") (((|GraphImage|) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{graphCurves([[p0],[p1],...,[pn]])} creates a \\spadtype{GraphImage} from the list of lists of points indicated by \\spad{p0} through pn.") (((|GraphImage|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|Palette|) (|Palette|) (|PositiveInteger|) (|List| (|DrawOption|))) "\\spad{graphCurves([[p0],[p1],...,[pn]],ptColor,lineColor,ptSize,[options])} creates a \\spadtype{GraphImage} from the list of lists of points,{} \\spad{p0} throught pn,{} using the options specified in the list \\spad{options}. The graph point color is specified by \\spad{ptColor},{} the graph line color is specified by \\spad{lineColor},{} and the size of the points is specified by \\spad{ptSize}."))) 
 NIL 
 NIL 
-(-1180) 
+(-1181) 
 ((|constructor| (NIL "TwoDimensionalViewport creates viewports to display graphs.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(v)} returns the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport} as output of the domain \\spadtype{OutputForm}.")) (|key| (((|Integer|) $) "\\spad{key(v)} returns the process ID number of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport}.")) (|reset| (((|Void|) $) "\\spad{reset(v)} sets the current state of the graph characteristics of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} back to their initial settings.")) (|write| (((|String|) $ (|String|) (|List| (|String|))) "\\spad{write(v,s,lf)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v} and the optional file types indicated by the list \\spad{lf}.") (((|String|) $ (|String|) (|String|)) "\\spad{write(v,s,f)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v} and an optional file type \\spad{f}.") (((|String|) $ (|String|)) "\\spad{write(v,s)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v}.")) (|resize| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{resize(v,w,h)} displays the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with a width of \\spad{w} and a height of \\spad{h},{} keeping the upper left-hand corner position unchanged.")) (|update| (((|Void|) $ (|GraphImage|) (|PositiveInteger|)) "\\spad{update(v,gr,n)} drops the graph \\spad{gr} in slot \\spad{n} of viewport \\spad{v}. The graph \\spad{gr} must have been transmitted already and acquired an integer key.")) (|move| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{move(v,x,y)} displays the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the upper left-hand corner of the viewport window at the screen coordinate position \\spad{x},{} \\spad{y}.")) (|show| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{show(v,n,s)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the graph if \\spad{s} is \"off\".")) (|translate| (((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|)) "\\spad{translate(v,n,dx,dy)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} translated by \\spad{dx} in the \\spad{x}-coordinate direction from the center of the viewport,{} and by \\spad{dy} in the \\spad{y}-coordinate direction from the center. Setting \\spad{dx} and \\spad{dy} to \\spad{0} places the center of the graph at the center of the viewport.")) (|scale| (((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|)) "\\spad{scale(v,n,sx,sy)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} scaled by the factor \\spad{sx} in the \\spad{x}-coordinate direction and by the factor \\spad{sy} in the \\spad{y}-coordinate direction.")) (|dimensions| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{dimensions(v,x,y,width,height)} sets the position of the upper left-hand corner of the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} to the window coordinate \\spad{x},{} \\spad{y},{} and sets the dimensions of the window to that of \\spad{width},{} \\spad{height}. The new dimensions are not displayed until the function \\spadfun{makeViewport2D} is executed again for \\spad{v}.")) (|close| (((|Void|) $) "\\spad{close(v)} closes the viewport window of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and terminates the corresponding process ID.")) (|controlPanel| (((|Void|) $ (|String|)) "\\spad{controlPanel(v,s)} displays the control panel of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or hides the control panel if \\spad{s} is \"off\".")) (|connect| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{connect(v,n,s)} displays the lines connecting the graph points in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the lines if \\spad{s} is \"off\".")) (|region| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{region(v,n,s)} displays the bounding box of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the bounding box if \\spad{s} is \"off\".")) (|points| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{points(v,n,s)} displays the points of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the points if \\spad{s} is \"off\".")) (|units| (((|Void|) $ (|PositiveInteger|) (|Palette|)) "\\spad{units(v,n,c)} displays the units of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the units color set to the given palette color \\spad{c}.") (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{units(v,n,s)} displays the units of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the units if \\spad{s} is \"off\".")) (|axes| (((|Void|) $ (|PositiveInteger|) (|Palette|)) "\\spad{axes(v,n,c)} displays the axes of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the axes color set to the given palette color \\spad{c}.") (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{axes(v,n,s)} displays the axes of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the axes if \\spad{s} is \"off\".")) (|getGraph| (((|GraphImage|) $ (|PositiveInteger|)) "\\spad{getGraph(v,n)} returns the graph which is of the domain \\spadtype{GraphImage} which is located in graph field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of the domain \\spadtype{TwoDimensionalViewport}.")) (|putGraph| (((|Void|) $ (|GraphImage|) (|PositiveInteger|)) "\\spad{putGraph(v,gi,n)} sets the graph field indicated by \\spad{n},{} of the indicated two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} to be the graph,{} \\spad{gi} of domain \\spadtype{GraphImage}. The contents of viewport,{} \\spad{v},{} will contain \\spad{gi} when the function \\spadfun{makeViewport2D} is called to create the an updated viewport \\spad{v}.")) (|title| (((|Void|) $ (|String|)) "\\spad{title(v,s)} changes the title which is shown in the two-dimensional viewport window,{} \\spad{v} of domain \\spadtype{TwoDimensionalViewport}.")) (|graphs| (((|Vector| (|Union| (|GraphImage|) "undefined")) $) "\\spad{graphs(v)} returns a vector,{} or list,{} which is a union of all the graphs,{} of the domain \\spadtype{GraphImage},{} which are allocated for the two-dimensional viewport,{} \\spad{v},{} of domain \\spadtype{TwoDimensionalViewport}. Those graphs which have no data are labeled \"undefined\",{} otherwise their contents are shown.")) (|graphStates| (((|Vector| (|Record| (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)) (|:| |points| (|Integer|)) (|:| |connect| (|Integer|)) (|:| |spline| (|Integer|)) (|:| |axes| (|Integer|)) (|:| |axesColor| (|Palette|)) (|:| |units| (|Integer|)) (|:| |unitsColor| (|Palette|)) (|:| |showing| (|Integer|)))) $) "\\spad{graphStates(v)} returns and shows a listing of a record containing the current state of the characteristics of each of the ten graph records in the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport}.")) (|graphState| (((|Void|) $ (|PositiveInteger|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Palette|) (|Integer|) (|Palette|) (|Integer|)) "\\spad{graphState(v,num,sX,sY,dX,dY,pts,lns,box,axes,axesC,un,unC,cP)} sets the state of the characteristics for the graph indicated by \\spad{num} in the given two-dimensional viewport \\spad{v},{} of domain \\spadtype{TwoDimensionalViewport},{} to the values given as parameters. The scaling of the graph in the \\spad{x} and \\spad{y} component directions is set to be \\spad{sX} and \\spad{sY}; the window translation in the \\spad{x} and \\spad{y} component directions is set to be \\spad{dX} and \\spad{dY}; The graph points,{} lines,{} bounding \\spad{box},{} \\spad{axes},{} or units will be shown in the viewport if their given parameters \\spad{pts},{} \\spad{lns},{} \\spad{box},{} \\spad{axes} or \\spad{un} are set to be \\spad{1},{} but will not be shown if they are set to \\spad{0}. The color of the \\spad{axes} and the color of the units are indicated by the palette colors \\spad{axesC} and \\spad{unC} respectively. To display the control panel when the viewport window is displayed,{} set \\spad{cP} to \\spad{1},{} otherwise set it to \\spad{0}.")) (|options| (($ $ (|List| (|DrawOption|))) "\\spad{options(v,lopt)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and returns \\spad{v} with it's draw options modified to be those which are indicated in the given list,{} \\spad{lopt} of domain \\spadtype{DrawOption}.") (((|List| (|DrawOption|)) $) "\\spad{options(v)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and returns a list containing the draw options from the domain \\spadtype{DrawOption} for \\spad{v}.")) (|makeViewport2D| (($ (|GraphImage|) (|List| (|DrawOption|))) "\\spad{makeViewport2D(gi,lopt)} creates and displays a viewport window of the domain \\spadtype{TwoDimensionalViewport} whose graph field is assigned to be the given graph,{} \\spad{gi},{} of domain \\spadtype{GraphImage},{} and whose options field is set to be the list of options,{} \\spad{lopt} of domain \\spadtype{DrawOption}.") (($ $) "\\spad{makeViewport2D(v)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and displays a viewport window on the screen which contains the contents of \\spad{v}.")) (|viewport2D| (($) "\\spad{viewport2D()} returns an undefined two-dimensional viewport of the domain \\spadtype{TwoDimensionalViewport} whose contents are empty.")) (|getPickedPoints| (((|List| (|Point| (|DoubleFloat|))) $) "\\spad{getPickedPoints(x)} returns a list of small floats for the points the user interactively picked on the viewport for full integration into the system,{} some design issues need to be addressed: \\spadignore{e.g.} how to go through the GraphImage interface,{} how to default to graphs,{} etc."))) 
 NIL 
 NIL 
-(-1181) 
+(-1182) 
 ((|key| (((|Integer|) $) "\\spad{key(v)} returns the process ID number of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|close| (((|Void|) $) "\\spad{close(v)} closes the viewport window of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} and terminates the corresponding process ID.")) (|write| (((|String|) $ (|String|) (|List| (|String|))) "\\spad{write(v,s,lf)} takes the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data file for \\spad{v} and the optional file types indicated by the list \\spad{lf}.") (((|String|) $ (|String|) (|String|)) "\\spad{write(v,s,f)} takes the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data file for \\spad{v} and an optional file type \\spad{f}.") (((|String|) $ (|String|)) "\\spad{write(v,s)} takes the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data file for \\spad{v}.")) (|colorDef| (((|Void|) $ (|Color|) (|Color|)) "\\spad{colorDef(v,c1,c2)} sets the range of colors along the colormap so that the lower end of the colormap is defined by \\spad{c1} and the top end of the colormap is defined by \\spad{c2},{} for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|reset| (((|Void|) $) "\\spad{reset(v)} sets the current state of the graph characteristics of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} back to their initial settings.")) (|intensity| (((|Void|) $ (|Float|)) "\\spad{intensity(v,i)} sets the intensity of the light source to \\spad{i},{} for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|lighting| (((|Void|) $ (|Float|) (|Float|) (|Float|)) "\\spad{lighting(v,x,y,z)} sets the position of the light source to the coordinates \\spad{x},{} \\spad{y},{} and \\spad{z} and displays the graph for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|clipSurface| (((|Void|) $ (|String|)) "\\spad{clipSurface(v,s)} displays the graph with the specified clipping region removed if \\spad{s} is \"on\",{} or displays the graph without clipping implemented if \\spad{s} is \"off\",{} for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|showClipRegion| (((|Void|) $ (|String|)) "\\spad{showClipRegion(v,s)} displays the clipping region of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the region if \\spad{s} is \"off\".")) (|showRegion| (((|Void|) $ (|String|)) "\\spad{showRegion(v,s)} displays the bounding box of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the box if \\spad{s} is \"off\".")) (|hitherPlane| (((|Void|) $ (|Float|)) "\\spad{hitherPlane(v,h)} sets the hither clipping plane of the graph to \\spad{h},{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|eyeDistance| (((|Void|) $ (|Float|)) "\\spad{eyeDistance(v,d)} sets the distance of the observer from the center of the graph to \\spad{d},{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|perspective| (((|Void|) $ (|String|)) "\\spad{perspective(v,s)} displays the graph in perspective if \\spad{s} is \"on\",{} or does not display perspective if \\spad{s} is \"off\" for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|translate| (((|Void|) $ (|Float|) (|Float|)) "\\spad{translate(v,dx,dy)} sets the horizontal viewport offset to \\spad{dx} and the vertical viewport offset to \\spad{dy},{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|zoom| (((|Void|) $ (|Float|) (|Float|) (|Float|)) "\\spad{zoom(v,sx,sy,sz)} sets the graph scaling factors for the \\spad{x}-coordinate axis to \\spad{sx},{} the \\spad{y}-coordinate axis to \\spad{sy} and the \\spad{z}-coordinate axis to \\spad{sz} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.") (((|Void|) $ (|Float|)) "\\spad{zoom(v,s)} sets the graph scaling factor to \\spad{s},{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|rotate| (((|Void|) $ (|Integer|) (|Integer|)) "\\spad{rotate(v,th,phi)} rotates the graph to the longitudinal view angle \\spad{th} degrees and the latitudinal view angle \\spad{phi} degrees for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}. The new rotation position is not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.") (((|Void|) $ (|Float|) (|Float|)) "\\spad{rotate(v,th,phi)} rotates the graph to the longitudinal view angle \\spad{th} radians and the latitudinal view angle \\spad{phi} radians for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|drawStyle| (((|Void|) $ (|String|)) "\\spad{drawStyle(v,s)} displays the surface for the given three-dimensional viewport \\spad{v} which is of domain \\spadtype{ThreeDimensionalViewport} in the style of drawing indicated by \\spad{s}. If \\spad{s} is not a valid drawing style the style is wireframe by default. Possible styles are \\spad{\"shade\"},{} \\spad{\"solid\"} or \\spad{\"opaque\"},{} \\spad{\"smooth\"},{} and \\spad{\"wireMesh\"}.")) (|outlineRender| (((|Void|) $ (|String|)) "\\spad{outlineRender(v,s)} displays the polygon outline showing either triangularized surface or a quadrilateral surface outline depending on the whether the \\spadfun{diagonals} function has been set,{} for the given three-dimensional viewport \\spad{v} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the polygon outline if \\spad{s} is \"off\".")) (|diagonals| (((|Void|) $ (|String|)) "\\spad{diagonals(v,s)} displays the diagonals of the polygon outline showing a triangularized surface instead of a quadrilateral surface outline,{} for the given three-dimensional viewport \\spad{v} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the diagonals if \\spad{s} is \"off\".")) (|axes| (((|Void|) $ (|String|)) "\\spad{axes(v,s)} displays the axes of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the axes if \\spad{s} is \"off\".")) (|controlPanel| (((|Void|) $ (|String|)) "\\spad{controlPanel(v,s)} displays the control panel of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or hides the control panel if \\spad{s} is \"off\".")) (|viewpoint| (((|Void|) $ (|Float|) (|Float|) (|Float|)) "\\spad{viewpoint(v,rotx,roty,rotz)} sets the rotation about the \\spad{x}-axis to be \\spad{rotx} radians,{} sets the rotation about the \\spad{y}-axis to be \\spad{roty} radians,{} and sets the rotation about the \\spad{z}-axis to be \\spad{rotz} radians,{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport} and displays \\spad{v} with the new view position.") (((|Void|) $ (|Float|) (|Float|)) "\\spad{viewpoint(v,th,phi)} sets the longitudinal view angle to \\spad{th} radians and the latitudinal view angle to \\spad{phi} radians for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}. The new viewpoint position is not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.") (((|Void|) $ (|Integer|) (|Integer|) (|Float|) (|Float|) (|Float|)) "\\spad{viewpoint(v,th,phi,s,dx,dy)} sets the longitudinal view angle to \\spad{th} degrees,{} the latitudinal view angle to \\spad{phi} degrees,{} the scale factor to \\spad{s},{} the horizontal viewport offset to \\spad{dx},{} and the vertical viewport offset to \\spad{dy} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}. The new viewpoint position is not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.") (((|Void|) $ (|Record| (|:| |theta| (|DoubleFloat|)) (|:| |phi| (|DoubleFloat|)) (|:| |scale| (|DoubleFloat|)) (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |scaleZ| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)))) "\\spad{viewpoint(v,viewpt)} sets the viewpoint for the viewport. The viewport record consists of the latitudal and longitudal angles,{} the zoom factor,{} the \\spad{X},{} \\spad{Y},{} and \\spad{Z} scales,{} and the \\spad{X} and \\spad{Y} displacements.") (((|Record| (|:| |theta| (|DoubleFloat|)) (|:| |phi| (|DoubleFloat|)) (|:| |scale| (|DoubleFloat|)) (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |scaleZ| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|))) $) "\\spad{viewpoint(v)} returns the current viewpoint setting of the given viewport,{} \\spad{v}. This function is useful in the situation where the user has created a viewport,{} proceeded to interact with it via the control panel and desires to save the values of the viewpoint as the default settings for another viewport to be created using the system.") (((|Void|) $ (|Float|) (|Float|) (|Float|) (|Float|) (|Float|)) "\\spad{viewpoint(v,th,phi,s,dx,dy)} sets the longitudinal view angle to \\spad{th} radians,{} the latitudinal view angle to \\spad{phi} radians,{} the scale factor to \\spad{s},{} the horizontal viewport offset to \\spad{dx},{} and the vertical viewport offset to \\spad{dy} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}. The new viewpoint position is not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.")) (|dimensions| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{dimensions(v,x,y,width,height)} sets the position of the upper left-hand corner of the three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} to the window coordinate \\spad{x},{} \\spad{y},{} and sets the dimensions of the window to that of \\spad{width},{} \\spad{height}. The new dimensions are not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.")) (|title| (((|Void|) $ (|String|)) "\\spad{title(v,s)} changes the title which is shown in the three-dimensional viewport window,{} \\spad{v} of domain \\spadtype{ThreeDimensionalViewport}.")) (|resize| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{resize(v,w,h)} displays the three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} with a width of \\spad{w} and a height of \\spad{h},{} keeping the upper left-hand corner position unchanged.")) (|move| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{move(v,x,y)} displays the three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} with the upper left-hand corner of the viewport window at the screen coordinate position \\spad{x},{} \\spad{y}.")) (|options| (($ $ (|List| (|DrawOption|))) "\\spad{options(v,lopt)} takes the viewport,{} \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport} and sets the draw options being used by \\spad{v} to those indicated in the list,{} \\spad{lopt},{} which is a list of options from the domain \\spad{DrawOption}.") (((|List| (|DrawOption|)) $) "\\spad{options(v)} takes the viewport,{} \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport} and returns a list of all the draw options from the domain \\spad{DrawOption} which are being used by \\spad{v}.")) (|modifyPointData| (((|Void|) $ (|NonNegativeInteger|) (|Point| (|DoubleFloat|))) "\\spad{modifyPointData(v,ind,pt)} takes the viewport,{} \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport},{} and places the data point,{} \\spad{pt} into the list of points database of \\spad{v} at the index location given by \\spad{ind}.")) (|subspace| (($ $ (|ThreeSpace| (|DoubleFloat|))) "\\spad{subspace(v,sp)} places the contents of the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport},{} in the subspace \\spad{sp},{} which is of the domain \\spad{ThreeSpace}.") (((|ThreeSpace| (|DoubleFloat|)) $) "\\spad{subspace(v)} returns the contents of the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport},{} as a subspace of the domain \\spad{ThreeSpace}.")) (|makeViewport3D| (($ (|ThreeSpace| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{makeViewport3D(sp,lopt)} takes the given space,{} \\spad{sp} which is of the domain \\spadtype{ThreeSpace} and displays a viewport window on the screen which contains the contents of \\spad{sp},{} and whose draw options are indicated by the list \\spad{lopt},{} which is a list of options from the domain \\spad{DrawOption}.") (($ (|ThreeSpace| (|DoubleFloat|)) (|String|)) "\\spad{makeViewport3D(sp,s)} takes the given space,{} \\spad{sp} which is of the domain \\spadtype{ThreeSpace} and displays a viewport window on the screen which contains the contents of \\spad{sp},{} and whose title is given by \\spad{s}.") (($ $) "\\spad{makeViewport3D(v)} takes the given three-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{ThreeDimensionalViewport} and displays a viewport window on the screen which contains the contents of \\spad{v}.")) (|viewport3D| (($) "\\spad{viewport3D()} returns an undefined three-dimensional viewport of the domain \\spadtype{ThreeDimensionalViewport} whose contents are empty.")) (|viewDeltaYDefault| (((|Float|) (|Float|)) "\\spad{viewDeltaYDefault(dy)} sets the current default vertical offset from the center of the viewport window to be \\spad{dy} and returns \\spad{dy}.") (((|Float|)) "\\spad{viewDeltaYDefault()} returns the current default vertical offset from the center of the viewport window.")) (|viewDeltaXDefault| (((|Float|) (|Float|)) "\\spad{viewDeltaXDefault(dx)} sets the current default horizontal offset from the center of the viewport window to be \\spad{dx} and returns \\spad{dx}.") (((|Float|)) "\\spad{viewDeltaXDefault()} returns the current default horizontal offset from the center of the viewport window.")) (|viewZoomDefault| (((|Float|) (|Float|)) "\\spad{viewZoomDefault(s)} sets the current default graph scaling value to \\spad{s} and returns \\spad{s}.") (((|Float|)) "\\spad{viewZoomDefault()} returns the current default graph scaling value.")) (|viewPhiDefault| (((|Float|) (|Float|)) "\\spad{viewPhiDefault(p)} sets the current default latitudinal view angle in radians to the value \\spad{p} and returns \\spad{p}.") (((|Float|)) "\\spad{viewPhiDefault()} returns the current default latitudinal view angle in radians.")) (|viewThetaDefault| (((|Float|) (|Float|)) "\\spad{viewThetaDefault(t)} sets the current default longitudinal view angle in radians to the value \\spad{t} and returns \\spad{t}.") (((|Float|)) "\\spad{viewThetaDefault()} returns the current default longitudinal view angle in radians."))) 
 NIL 
 NIL 
-(-1182) 
+(-1183) 
 ((|constructor| (NIL "ViewportDefaultsPackage describes default and user definable values for graphics")) (|tubeRadiusDefault| (((|DoubleFloat|)) "\\spad{tubeRadiusDefault()} returns the radius used for a 3D tube plot.") (((|DoubleFloat|) (|Float|)) "\\spad{tubeRadiusDefault(r)} sets the default radius for a 3D tube plot to \\spad{r}.")) (|tubePointsDefault| (((|PositiveInteger|)) "\\spad{tubePointsDefault()} returns the number of points to be used when creating the circle to be used in creating a 3D tube plot.") (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{tubePointsDefault(i)} sets the number of points to use when creating the circle to be used in creating a 3D tube plot to \\spad{i}.")) (|var2StepsDefault| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{var2StepsDefault(i)} sets the number of steps to take when creating a 3D mesh in the direction of the first defined free variable to \\spad{i} (a free variable is considered defined when its range is specified (\\spadignore{e.g.} \\spad{x=0}..10)).") (((|PositiveInteger|)) "\\spad{var2StepsDefault()} is the current setting for the number of steps to take when creating a 3D mesh in the direction of the first defined free variable (a free variable is considered defined when its range is specified (\\spadignore{e.g.} \\spad{x=0}..10)).")) (|var1StepsDefault| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{var1StepsDefault(i)} sets the number of steps to take when creating a 3D mesh in the direction of the first defined free variable to \\spad{i} (a free variable is considered defined when its range is specified (\\spadignore{e.g.} \\spad{x=0}..10)).") (((|PositiveInteger|)) "\\spad{var1StepsDefault()} is the current setting for the number of steps to take when creating a 3D mesh in the direction of the first defined free variable (a free variable is considered defined when its range is specified (\\spadignore{e.g.} \\spad{x=0}..10)).")) (|viewWriteAvailable| (((|List| (|String|))) "\\spad{viewWriteAvailable()} returns a list of available methods for writing,{} such as BITMAP,{} POSTSCRIPT,{} etc.")) (|viewWriteDefault| (((|List| (|String|)) (|List| (|String|))) "\\spad{viewWriteDefault(l)} sets the default list of things to write in a viewport data file to the strings in \\spad{l}; a viewAlone file is always genereated.") (((|List| (|String|))) "\\spad{viewWriteDefault()} returns the list of things to write in a viewport data file; a viewAlone file is always generated.")) (|viewDefaults| (((|Void|)) "\\spad{viewDefaults()} resets all the default graphics settings.")) (|viewSizeDefault| (((|List| (|PositiveInteger|)) (|List| (|PositiveInteger|))) "\\spad{viewSizeDefault([w,h])} sets the default viewport width to \\spad{w} and height to \\spad{h}.") (((|List| (|PositiveInteger|))) "\\spad{viewSizeDefault()} returns the default viewport width and height.")) (|viewPosDefault| (((|List| (|NonNegativeInteger|)) (|List| (|NonNegativeInteger|))) "\\spad{viewPosDefault([x,y])} sets the default \\spad{X} and \\spad{Y} position of a viewport window unless overriden explicityly,{} newly created viewports will have th \\spad{X} and \\spad{Y} coordinates \\spad{x},{} \\spad{y}.") (((|List| (|NonNegativeInteger|))) "\\spad{viewPosDefault()} returns the default \\spad{X} and \\spad{Y} position of a viewport window unless overriden explicityly,{} newly created viewports will have this \\spad{X} and \\spad{Y} coordinate.")) (|pointSizeDefault| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{pointSizeDefault(i)} sets the default size of the points in a 2D viewport to \\spad{i}.") (((|PositiveInteger|)) "\\spad{pointSizeDefault()} returns the default size of the points in a 2D viewport.")) (|unitsColorDefault| (((|Palette|) (|Palette|)) "\\spad{unitsColorDefault(p)} sets the default color of the unit ticks in a 2D viewport to the palette \\spad{p}.") (((|Palette|)) "\\spad{unitsColorDefault()} returns the default color of the unit ticks in a 2D viewport.")) (|axesColorDefault| (((|Palette|) (|Palette|)) "\\spad{axesColorDefault(p)} sets the default color of the axes in a 2D viewport to the palette \\spad{p}.") (((|Palette|)) "\\spad{axesColorDefault()} returns the default color of the axes in a 2D viewport.")) (|lineColorDefault| (((|Palette|) (|Palette|)) "\\spad{lineColorDefault(p)} sets the default color of lines connecting points in a 2D viewport to the palette \\spad{p}.") (((|Palette|)) "\\spad{lineColorDefault()} returns the default color of lines connecting points in a 2D viewport.")) (|pointColorDefault| (((|Palette|) (|Palette|)) "\\spad{pointColorDefault(p)} sets the default color of points in a 2D viewport to the palette \\spad{p}.") (((|Palette|)) "\\spad{pointColorDefault()} returns the default color of points in a 2D viewport."))) 
 NIL 
 NIL 
-(-1183) 
+(-1184) 
 ((|constructor| (NIL "This type is used when no value is needed,{} \\spadignore{e.g.} in the \\spad{then} part of a one armed \\spad{if}. All values can be coerced to type Void. Once a value has been coerced to Void,{} it cannot be recovered.")) (|void| (($) "\\spad{void()} produces a void object."))) 
 NIL 
 NIL 
-(-1184 A S) 
+(-1185 A S) 
 ((|constructor| (NIL "Vector Spaces (not necessarily finite dimensional) over a field.")) (|dimension| (((|CardinalNumber|)) "\\spad{dimension()} returns the dimensionality of the vector space.")) (/ (($ $ |#2|) "\\spad{x/y} divides the vector \\spad{x} by the scalar \\spad{y}."))) 
 NIL 
 NIL 
-(-1185 S) 
+(-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}."))) 
-((-3984 . T) (-3983 . T)) 
+((-3986 . T) (-3985 . T)) 
 NIL 
-(-1186 R) 
+(-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 
-(-1187 K R UP -3088) 
+(-1188 K R UP -3090) 
 ((|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 
-(-1188) 
+(-1189) 
 ((|constructor| (NIL "This domain represents the syntax of a `where' expression.")) (|qualifier| (((|SpadAst|) $) "\\spad{qualifier(e)} returns the qualifier of the expression `e'.")) (|mainExpression| (((|SpadAst|) $) "\\spad{mainExpression(e)} returns the main expression of the `where' expression `e'."))) 
 NIL 
 NIL 
-(-1189) 
+(-1190) 
 ((|constructor| (NIL "This domain represents the `while' iterator syntax.")) (|condition| (((|SpadAst|) $) "\\spad{condition(i)} returns the condition of the while iterator `i'."))) 
 NIL 
 NIL 
-(-1190 R |VarSet| E P |vl| |wl| |wtlevel|) 
+(-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)"))) 
-((-3984 |has| |#1| (-146)) (-3983 |has| |#1| (-146)) (-3986 . T)) 
+((-3986 |has| |#1| (-146)) (-3985 |has| |#1| (-146)) (-3988 . T)) 
 ((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-311)))) 
-(-1191 R E V P) 
+(-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}."))) 
-((-3990 . T) (-3989 . T)) 
-((-12 (|HasCategory| |#4| (QUOTE (-1012))) (|HasCategory| |#4| (|%list| (QUOTE -259) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-553 (-472)))) (|HasCategory| |#4| (QUOTE (-1012))) (|HasCategory| |#1| (QUOTE (-494))) (|HasCategory| |#3| (QUOTE (-317))) (|HasCategory| |#4| (QUOTE (-552 (-772)))) (|HasCategory| |#4| (QUOTE (-72)))) 
-(-1192 R) 
+((-3992 . T) (-3991 . 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)"))) 
-((-3983 . T) (-3984 . T) (-3986 . T)) 
+((-3985 . T) (-3986 . T) (-3988 . T)) 
 NIL 
-(-1193 |vl| R) 
+(-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."))) 
-((-3986 . T) (-3982 |has| |#2| (-6 -3982)) (-3984 . T) (-3983 . T)) 
-((|HasCategory| |#2| (QUOTE (-146))) (|HasAttribute| |#2| (QUOTE -3982))) 
-(-1194 R |VarSet| XPOLY) 
+((-3988 . T) (-3984 |has| |#2| (-6 -3984)) (-3986 . T) (-3985 . T)) 
+((|HasCategory| |#2| (QUOTE (-146))) (|HasAttribute| |#2| (QUOTE -3984))) 
+(-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 
-(-1195 S -3088) 
+(-1196 S -3090) 
 ((|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) 
 NIL 
 ((|HasCategory| |#2| (QUOTE (-317))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120)))) 
-(-1196 -3088) 
+(-1197 -3090) 
 ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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}."))) 
-((-3981 . T) (-3987 . T) (-3982 . T) ((-3991 "*") . T) (-3983 . T) (-3984 . T) (-3986 . T)) 
+((-3983 . T) (-3989 . T) (-3984 . T) ((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . T)) 
 NIL 
-(-1197 |vl| R) 
+(-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| $) "\\spad{v * x} returns the product of a variable \\spad{x} by \\spad{x}."))) 
-((-3982 |has| |#2| (-6 -3982)) (-3984 . T) (-3983 . T) (-3986 . T)) 
+((-3984 |has| |#2| (-6 -3984)) (-3986 . T) (-3985 . T) (-3988 . T)) 
 NIL 
-(-1198 |VarSet| R) 
+(-1199 |VarSet| R) 
 ((|constructor| (NIL "This domain constructor implements polynomials in non-commutative variables written in the Poincare-Birkhoff-Witt basis from the Lyndon basis. These polynomials can be used to compute Baker-Campbell-Hausdorff relations. \\newline Author: Michel Petitot (petitot@lifl.fr).")) (|log| (($ $ (|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}}."))) 
-((-3982 |has| |#2| (-6 -3982)) (-3984 . T) (-3983 . T) (-3986 . T)) 
-((|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-654 (-347 (-483))))) (|HasAttribute| |#2| (QUOTE -3982))) 
-(-1199 R) 
+((-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))) 
+(-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."))) 
-((-3982 |has| |#1| (-6 -3982)) (-3984 . T) (-3983 . T) (-3986 . T)) 
-((|HasCategory| |#1| (QUOTE (-146))) (|HasAttribute| |#1| (QUOTE -3982))) 
-(-1200 |vl| R) 
+((-3984 |has| |#1| (-6 -3984)) (-3986 . T) (-3985 . T) (-3988 . T)) 
+((|HasCategory| |#1| (QUOTE (-146))) (|HasAttribute| |#1| (QUOTE -3984))) 
+(-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|) $) "\\spad{maxdeg(p)} returns the greatest leading word in the support of \\spad{p}."))) 
-((-3982 |has| |#2| (-6 -3982)) (-3984 . T) (-3983 . T) (-3986 . T)) 
+((-3984 |has| |#2| (-6 -3984)) (-3986 . T) (-3985 . T) (-3988 . T)) 
 NIL 
-(-1201 R E) 
+(-1202 R E) 
 ((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and words belonging to an arbitrary \\spadtype{OrderedMonoid}. This type is used,{} for instance,{} by the \\spadtype{XDistributedPolynomial} domain constructor where the Monoid is free.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (/ (($ $ |#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}."))) 
-((-3986 . T) (-3987 |has| |#1| (-6 -3987)) (-3982 |has| |#1| (-6 -3982)) (-3984 . T) (-3983 . T)) 
-((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-311))) (|HasAttribute| |#1| (QUOTE -3986)) (|HasAttribute| |#1| (QUOTE -3987)) (|HasAttribute| |#1| (QUOTE -3982))) 
-(-1202 |VarSet| 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))) 
+(-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."))) 
-((-3982 |has| |#2| (-6 -3982)) (-3984 . T) (-3983 . T) (-3986 . T)) 
-((|HasCategory| |#2| (QUOTE (-146))) (|HasAttribute| |#2| (QUOTE -3982))) 
-(-1203) 
+((-3984 |has| |#2| (-6 -3984)) (-3986 . T) (-3985 . T) (-3988 . T)) 
+((|HasCategory| |#2| (QUOTE (-146))) (|HasAttribute| |#2| (QUOTE -3984))) 
+(-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 
 NIL 
-(-1204 A) 
+(-1205 A) 
 ((|constructor| (NIL "This package implements fixed-point computations on streams.")) (Y (((|List| (|Stream| |#1|)) (|Mapping| (|List| (|Stream| |#1|)) (|List| (|Stream| |#1|))) (|Integer|)) "\\spad{Y(g,n)} computes a fixed point of the function \\spad{g},{} where \\spad{g} takes a list of \\spad{n} streams and returns a list of \\spad{n} streams.") (((|Stream| |#1|) (|Mapping| (|Stream| |#1|) (|Stream| |#1|))) "\\spad{Y(f)} computes a fixed point of the function \\spad{f}."))) 
 NIL 
 NIL 
-(-1205 R |ls| |ls2|) 
-((|constructor| (NIL "A package for computing symbolically the complex and real roots of zero-dimensional algebraic systems over the integer or rational numbers. Complex roots are given by means of univariate representations of irreducible regular chains. Real roots are given by means of tuples of coordinates lying in the \\spadtype{RealClosure} of the coefficient ring. This constructor takes three arguments. The first one \\spad{R} is the coefficient ring. The second one \\spad{ls} is the list of variables involved in the systems to solve. The third one must be \\spad{concat(ls,s)} where \\spad{s} is an additional symbol used for the univariate representations. WARNING: The third argument is not checked. All operations are based on triangular decompositions. The default is to compute these decompositions directly from the input system by using the \\spadtype{RegularChain} domain constructor. The lexTriangular algorithm can also be used for computing these decompositions (see the \\spadtype{LexTriangularPackage} package constructor). For that purpose,{} the operations \\axiomOpFrom{univariateSolve}{ZeroDimensionalSolvePackage},{} \\axiomOpFrom{realSolve}{ZeroDimensionalSolvePackage} and \\axiomOpFrom{positiveSolve}{ZeroDimensionalSolvePackage} admit an optional argument. \\newline Author: Marc Moreno Maza.")) (|convert| (((|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|))) (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#3|)) (|OrderedVariableList| |#3|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|)))) "\\spad{convert(st)} returns the members of \\spad{st}.	") (((|SparseUnivariatePolynomial| (|RealClosure| (|Fraction| |#1|))) (|SparseUnivariatePolynomial| |#1|)) "\\spad{convert(u)} converts \\spad{u}.") (((|Polynomial| (|RealClosure| (|Fraction| |#1|))) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|))) "\\spad{convert(q)} converts \\spad{q}.") (((|Polynomial| (|RealClosure| (|Fraction| |#1|))) (|Polynomial| |#1|)) "\\spad{convert(p)} converts \\spad{p}.") (((|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|)) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) "\\spad{convert(q)} converts \\spad{q}.")) (|squareFree| (((|List| (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#3|)) (|OrderedVariableList| |#3|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|)))) (|RegularChain| |#1| |#2|)) "\\spad{squareFree(ts)} returns the square-free factorization of \\spad{ts}. Moreover,{} each factor is a Lazard triangular set and the decomposition is a Kalkbrener split of \\spad{ts},{} which is enough here for the matter of solving zero-dimensional algebraic systems. WARNING: \\spad{ts} is not checked to be zero-dimensional.")) (|positiveSolve| (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|))) "\\spad{positiveSolve(lp)} returns the same as \\spad{positiveSolve(lp,false,false)}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{positiveSolve(lp)} returns the same as \\spad{positiveSolve(lp,info?,false)}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{positiveSolve(lp,info?,lextri?)} returns the set of the points in the variety associated with \\spad{lp} whose coordinates are (real) strictly positive. Moreover,{} if \\spad{info?} is \\spad{true} then some information is displayed during decomposition into regular chains. If \\spad{lextri?} is \\spad{true} then the lexTriangular algorithm is called from the \\spadtype{LexTriangularPackage} constructor (see \\axiomOpFrom{zeroSetSplit}{LexTriangularPackage}(\\spad{lp},{}\\spad{false})). Otherwise,{} the triangular decomposition is computed directly from the input system by using the \\axiomOpFrom{zeroSetSplit}{RegularChain} from \\spadtype{RegularChain}. WARNING: For each set of coordinates given by \\spad{positiveSolve(lp,info?,lextri?)} the ordering of the indeterminates is reversed \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ls}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|RegularChain| |#1| |#2|)) "\\spad{positiveSolve(ts)} returns the points of the regular set of \\spad{ts} with (real) strictly positive coordinates.")) (|realSolve| (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|))) "\\spad{realSolve(lp)} returns the same as \\spad{realSolve(ts,false,false,false)}") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{realSolve(ts,info?)} returns the same as \\spad{realSolve(ts,info?,false,false)}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{realSolve(ts,info?,check?)} returns the same as \\spad{realSolve(ts,info?,check?,false)}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|) (|Boolean|)) "\\spad{realSolve(ts,info?,check?,lextri?)} returns the set of the points in the variety associated with \\spad{lp} whose coordinates are all real. Moreover,{} if \\spad{info?} is \\spad{true} then some information is displayed during decomposition into regular chains. If \\spad{check?} is \\spad{true} then the result is checked. If \\spad{lextri?} is \\spad{true} then the lexTriangular algorithm is called from the \\spadtype{LexTriangularPackage} constructor (see \\axiomOpFrom{zeroSetSplit}{LexTriangularPackage}(lp,{}\\spad{false})). Otherwise,{} the triangular decomposition is computed directly from the input system by using the \\axiomOpFrom{zeroSetSplit}{RegularChain} from \\spadtype{RegularChain}. WARNING: For each set of coordinates given by \\spad{realSolve(ts,info?,check?,lextri?)} the ordering of the indeterminates is reversed \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ls}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|RegularChain| |#1| |#2|)) "\\spad{realSolve(ts)} returns the set of the points in the regular zero set of \\spad{ts} whose coordinates are all real. WARNING: For each set of coordinates given by \\spad{realSolve(ts)} the ordering of the indeterminates is reversed \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ls}.")) (|univariateSolve| (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|))) "\\spad{univariateSolve(lp)} returns the same as \\spad{univariateSolve(lp,false,false,false)}.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{univariateSolve(lp,info?)} returns the same as \\spad{univariateSolve(lp,info?,false,false)}.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{univariateSolve(lp,info?,check?)} returns the same as \\spad{univariateSolve(lp,info?,check?,false)}.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|) (|Boolean|)) "\\spad{univariateSolve(lp,info?,check?,lextri?)} returns a univariate representation of the variety associated with \\spad{lp}. Moreover,{} if \\spad{info?} is \\spad{true} then some information is displayed during the decomposition into regular chains. If \\spad{check?} is \\spad{true} then the result is checked. See \\axiomOpFrom{rur}{RationalUnivariateRepresentationPackage}(\\spad{lp},{}\\spad{true}). If \\spad{lextri?} is \\spad{true} then the lexTriangular algorithm is called from the \\spadtype{LexTriangularPackage} constructor (see \\axiomOpFrom{zeroSetSplit}{LexTriangularPackage}(\\spad{lp},{}\\spad{false})). Otherwise,{} the triangular decomposition is computed directly from the input system by using the \\axiomOpFrom{zeroSetSplit}{RegularChain} from \\spadtype{RegularChain}.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|RegularChain| |#1| |#2|)) "\\spad{univariateSolve(ts)} returns a univariate representation of \\spad{ts}. See \\axiomOpFrom{rur}{RationalUnivariateRepresentationPackage}(lp,{}\\spad{true}).")) (|triangSolve| (((|List| (|RegularChain| |#1| |#2|)) (|List| (|Polynomial| |#1|))) "\\spad{triangSolve(lp)} returns the same as \\spad{triangSolve(lp,false,false)}") (((|List| (|RegularChain| |#1| |#2|)) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{triangSolve(lp,info?)} returns the same as \\spad{triangSolve(lp,false)}") (((|List| (|RegularChain| |#1| |#2|)) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{triangSolve(lp,info?,lextri?)} decomposes the variety associated with \\axiom{\\spad{lp}} into regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{\\spad{lp}} needs to generate a zero-dimensional ideal. If \\axiom{\\spad{lp}} is not zero-dimensional then the result is only a decomposition of its zero-set in the sense of the closure (\\spad{w}.\\spad{r}.\\spad{t}. Zarisky topology). Moreover,{} if \\spad{info?} is \\spad{true} then some information is displayed during the computations. See \\axiomOpFrom{zeroSetSplit}{RegularTriangularSetCategory}(\\spad{lp},{}\\spad{true},{}\\spad{info?}). If \\spad{lextri?} is \\spad{true} then the lexTriangular algorithm is called from the \\spadtype{LexTriangularPackage} constructor (see \\axiomOpFrom{zeroSetSplit}{LexTriangularPackage}(\\spad{lp},{}\\spad{false})). Otherwise,{} the triangular decomposition is computed directly from the input system by using the \\axiomOpFrom{zeroSetSplit}{RegularChain} from \\spadtype{RegularChain}."))) 
+(-1206 R |ls| |ls2|) 
+((|constructor| (NIL "A package for computing symbolically the complex and real roots of zero-dimensional algebraic systems over the integer or rational numbers. Complex roots are given by means of univariate representations of irreducible regular chains. Real roots are given by means of tuples of coordinates lying in the \\spadtype{RealClosure} of the coefficient ring. This constructor takes three arguments. The first one \\spad{R} is the coefficient ring. The second one \\spad{ls} is the list of variables involved in the systems to solve. The third one must be \\spad{concat(ls,s)} where \\spad{s} is an additional symbol used for the univariate representations. WARNING: The third argument is not checked. All operations are based on triangular decompositions. The default is to compute these decompositions directly from the input system by using the \\spadtype{RegularChain} domain constructor. The lexTriangular algorithm can also be used for computing these decompositions (see the \\spadtype{LexTriangularPackage} package constructor). For that purpose,{} the operations \\axiomOpFrom{univariateSolve}{ZeroDimensionalSolvePackage},{} \\axiomOpFrom{realSolve}{ZeroDimensionalSolvePackage} and \\axiomOpFrom{positiveSolve}{ZeroDimensionalSolvePackage} admit an optional argument. \\newline Author: Marc Moreno Maza.")) (|convert| (((|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|))) (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#3|)) (|OrderedVariableList| |#3|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|)))) "\\spad{convert(st)} returns the members of \\spad{st}.") (((|SparseUnivariatePolynomial| (|RealClosure| (|Fraction| |#1|))) (|SparseUnivariatePolynomial| |#1|)) "\\spad{convert(u)} converts \\spad{u}.") (((|Polynomial| (|RealClosure| (|Fraction| |#1|))) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|))) "\\spad{convert(q)} converts \\spad{q}.") (((|Polynomial| (|RealClosure| (|Fraction| |#1|))) (|Polynomial| |#1|)) "\\spad{convert(p)} converts \\spad{p}.") (((|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|)) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) "\\spad{convert(q)} converts \\spad{q}.")) (|squareFree| (((|List| (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#3|)) (|OrderedVariableList| |#3|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|)))) (|RegularChain| |#1| |#2|)) "\\spad{squareFree(ts)} returns the square-free factorization of \\spad{ts}. Moreover,{} each factor is a Lazard triangular set and the decomposition is a Kalkbrener split of \\spad{ts},{} which is enough here for the matter of solving zero-dimensional algebraic systems. WARNING: \\spad{ts} is not checked to be zero-dimensional.")) (|positiveSolve| (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|))) "\\spad{positiveSolve(lp)} returns the same as \\spad{positiveSolve(lp,false,false)}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{positiveSolve(lp)} returns the same as \\spad{positiveSolve(lp,info?,false)}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{positiveSolve(lp,info?,lextri?)} returns the set of the points in the variety associated with \\spad{lp} whose coordinates are (real) strictly positive. Moreover,{} if \\spad{info?} is \\spad{true} then some information is displayed during decomposition into regular chains. If \\spad{lextri?} is \\spad{true} then the lexTriangular algorithm is called from the \\spadtype{LexTriangularPackage} constructor (see \\axiomOpFrom{zeroSetSplit}{LexTriangularPackage}(\\spad{lp},{}\\spad{false})). Otherwise,{} the triangular decomposition is computed directly from the input system by using the \\axiomOpFrom{zeroSetSplit}{RegularChain} from \\spadtype{RegularChain}. WARNING: For each set of coordinates given by \\spad{positiveSolve(lp,info?,lextri?)} the ordering of the indeterminates is reversed \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ls}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|RegularChain| |#1| |#2|)) "\\spad{positiveSolve(ts)} returns the points of the regular set of \\spad{ts} with (real) strictly positive coordinates.")) (|realSolve| (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|))) "\\spad{realSolve(lp)} returns the same as \\spad{realSolve(ts,false,false,false)}") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{realSolve(ts,info?)} returns the same as \\spad{realSolve(ts,info?,false,false)}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{realSolve(ts,info?,check?)} returns the same as \\spad{realSolve(ts,info?,check?,false)}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|) (|Boolean|)) "\\spad{realSolve(ts,info?,check?,lextri?)} returns the set of the points in the variety associated with \\spad{lp} whose coordinates are all real. Moreover,{} if \\spad{info?} is \\spad{true} then some information is displayed during decomposition into regular chains. If \\spad{check?} is \\spad{true} then the result is checked. If \\spad{lextri?} is \\spad{true} then the lexTriangular algorithm is called from the \\spadtype{LexTriangularPackage} constructor (see \\axiomOpFrom{zeroSetSplit}{LexTriangularPackage}(lp,{}\\spad{false})). Otherwise,{} the triangular decomposition is computed directly from the input system by using the \\axiomOpFrom{zeroSetSplit}{RegularChain} from \\spadtype{RegularChain}. WARNING: For each set of coordinates given by \\spad{realSolve(ts,info?,check?,lextri?)} the ordering of the indeterminates is reversed \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ls}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|RegularChain| |#1| |#2|)) "\\spad{realSolve(ts)} returns the set of the points in the regular zero set of \\spad{ts} whose coordinates are all real. WARNING: For each set of coordinates given by \\spad{realSolve(ts)} the ordering of the indeterminates is reversed \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ls}.")) (|univariateSolve| (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|))) "\\spad{univariateSolve(lp)} returns the same as \\spad{univariateSolve(lp,false,false,false)}.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{univariateSolve(lp,info?)} returns the same as \\spad{univariateSolve(lp,info?,false,false)}.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{univariateSolve(lp,info?,check?)} returns the same as \\spad{univariateSolve(lp,info?,check?,false)}.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|) (|Boolean|)) "\\spad{univariateSolve(lp,info?,check?,lextri?)} returns a univariate representation of the variety associated with \\spad{lp}. Moreover,{} if \\spad{info?} is \\spad{true} then some information is displayed during the decomposition into regular chains. If \\spad{check?} is \\spad{true} then the result is checked. See \\axiomOpFrom{rur}{RationalUnivariateRepresentationPackage}(\\spad{lp},{}\\spad{true}). If \\spad{lextri?} is \\spad{true} then the lexTriangular algorithm is called from the \\spadtype{LexTriangularPackage} constructor (see \\axiomOpFrom{zeroSetSplit}{LexTriangularPackage}(\\spad{lp},{}\\spad{false})). Otherwise,{} the triangular decomposition is computed directly from the input system by using the \\axiomOpFrom{zeroSetSplit}{RegularChain} from \\spadtype{RegularChain}.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|RegularChain| |#1| |#2|)) "\\spad{univariateSolve(ts)} returns a univariate representation of \\spad{ts}. See \\axiomOpFrom{rur}{RationalUnivariateRepresentationPackage}(lp,{}\\spad{true}).")) (|triangSolve| (((|List| (|RegularChain| |#1| |#2|)) (|List| (|Polynomial| |#1|))) "\\spad{triangSolve(lp)} returns the same as \\spad{triangSolve(lp,false,false)}") (((|List| (|RegularChain| |#1| |#2|)) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{triangSolve(lp,info?)} returns the same as \\spad{triangSolve(lp,false)}") (((|List| (|RegularChain| |#1| |#2|)) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{triangSolve(lp,info?,lextri?)} decomposes the variety associated with \\axiom{\\spad{lp}} into regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{\\spad{lp}} needs to generate a zero-dimensional ideal. If \\axiom{\\spad{lp}} is not zero-dimensional then the result is only a decomposition of its zero-set in the sense of the closure (\\spad{w}.\\spad{r}.\\spad{t}. Zarisky topology). Moreover,{} if \\spad{info?} is \\spad{true} then some information is displayed during the computations. See \\axiomOpFrom{zeroSetSplit}{RegularTriangularSetCategory}(\\spad{lp},{}\\spad{true},{}\\spad{info?}). If \\spad{lextri?} is \\spad{true} then the lexTriangular algorithm is called from the \\spadtype{LexTriangularPackage} constructor (see \\axiomOpFrom{zeroSetSplit}{LexTriangularPackage}(\\spad{lp},{}\\spad{false})). Otherwise,{} the triangular decomposition is computed directly from the input system by using the \\axiomOpFrom{zeroSetSplit}{RegularChain} from \\spadtype{RegularChain}."))) 
 NIL 
 NIL 
-(-1206 R) 
+(-1207 R) 
 ((|constructor| (NIL "Test for linear dependence over the integers.")) (|solveLinearlyOverQ| (((|Union| (|Vector| (|Fraction| (|Integer|))) "failed") (|Vector| |#1|) |#1|) "\\spad{solveLinearlyOverQ([v1,...,vn], u)} returns \\spad{[c1,...,cn]} such that \\spad{c1*v1 + ... + cn*vn = u},{} \"failed\" if no such rational numbers \\spad{ci}'s exist.")) (|linearDependenceOverZ| (((|Union| (|Vector| (|Integer|)) "failed") (|Vector| |#1|)) "\\spad{linearlyDependenceOverZ([v1,...,vn])} returns \\spad{[c1,...,cn]} if \\spad{c1*v1 + ... + cn*vn = 0} and not all the \\spad{ci}'s are 0,{} \"failed\" if the \\spad{vi}'s are linearly independent over the integers.")) (|linearlyDependentOverZ?| (((|Boolean|) (|Vector| |#1|)) "\\spad{linearlyDependentOverZ?([v1,...,vn])} returns \\spad{true} if the \\spad{vi}'s are linearly dependent over the integers,{} \\spad{false} otherwise."))) 
 NIL 
 NIL 
-(-1207 |p|) 
+(-1208 |p|) 
 ((|constructor| (NIL "IntegerMod(\\spad{n}) creates the ring of integers reduced modulo the integer \\spad{n}."))) 
-(((-3991 "*") . T) (-3983 . T) (-3984 . T) (-3986 . T)) 
+(((-3993 "*") . T) (-3985 . T) (-3986 . T) (-3988 . T)) 
 NIL 
 NIL 
 NIL 
@@ -4776,4 +4780,4 @@ NIL
 NIL 
 NIL 
 NIL 
-((-3 NIL 1965399 1965404 1965409 1965414) (-2 NIL 1965379 1965384 1965389 1965394) (-1 NIL 1965359 1965364 1965369 1965374) (0 NIL 1965339 1965344 1965349 1965354) (-1207 "ZMOD.spad" 1965148 1965161 1965277 1965334) (-1206 "ZLINDEP.spad" 1964246 1964257 1965138 1965143) (-1205 "ZDSOLVE.spad" 1954206 1954228 1964236 1964241) (-1204 "YSTREAM.spad" 1953701 1953712 1954196 1954201) (-1203 "YDIAGRAM.spad" 1953335 1953344 1953691 1953696) (-1202 "XRPOLY.spad" 1952555 1952575 1953191 1953260) (-1201 "XPR.spad" 1950350 1950363 1952273 1952372) (-1200 "XPOLYC.spad" 1949669 1949685 1950276 1950345) (-1199 "XPOLY.spad" 1949224 1949235 1949525 1949594) (-1198 "XPBWPOLY.spad" 1947695 1947715 1949030 1949099) (-1197 "XFALG.spad" 1944743 1944759 1947621 1947690) (-1196 "XF.spad" 1943206 1943221 1944645 1944738) (-1195 "XF.spad" 1941649 1941666 1943090 1943095) (-1194 "XEXPPKG.spad" 1940908 1940934 1941639 1941644) (-1193 "XDPOLY.spad" 1940522 1940538 1940764 1940833) (-1192 "XALG.spad" 1940190 1940201 1940478 1940517) (-1191 "WUTSET.spad" 1936193 1936210 1939824 1939851) (-1190 "WP.spad" 1935400 1935444 1936051 1936118) (-1189 "WHILEAST.spad" 1935198 1935207 1935390 1935395) (-1188 "WHEREAST.spad" 1934869 1934878 1935188 1935193) (-1187 "WFFINTBS.spad" 1932532 1932554 1934859 1934864) (-1186 "WEIER.spad" 1930754 1930765 1932522 1932527) (-1185 "VSPACE.spad" 1930427 1930438 1930722 1930749) (-1184 "VSPACE.spad" 1930120 1930133 1930417 1930422) (-1183 "VOID.spad" 1929797 1929806 1930110 1930115) (-1182 "VIEWDEF.spad" 1924998 1925007 1929787 1929792) (-1181 "VIEW3D.spad" 1908959 1908968 1924988 1924993) (-1180 "VIEW2D.spad" 1896858 1896867 1908949 1908954) (-1179 "VIEW.spad" 1894578 1894587 1896848 1896853) (-1178 "VECTOR2.spad" 1893217 1893230 1894568 1894573) (-1177 "VECTOR.spad" 1891936 1891947 1892187 1892214) (-1176 "VECTCAT.spad" 1889848 1889859 1891904 1891931) (-1175 "VECTCAT.spad" 1887569 1887582 1889627 1889632) (-1174 "VARIABLE.spad" 1887349 1887364 1887559 1887564) (-1173 "UTYPE.spad" 1886993 1887002 1887339 1887344) (-1172 "UTSODETL.spad" 1886288 1886312 1886949 1886954) (-1171 "UTSODE.spad" 1884504 1884524 1886278 1886283) (-1170 "UTSCAT.spad" 1881983 1881999 1884402 1884499) (-1169 "UTSCAT.spad" 1879130 1879148 1881551 1881556) (-1168 "UTS2.spad" 1878725 1878760 1879120 1879125) (-1167 "UTS.spad" 1873737 1873765 1877257 1877354) (-1166 "URAGG.spad" 1868458 1868469 1873727 1873732) (-1165 "URAGG.spad" 1863143 1863156 1868414 1868419) (-1164 "UPXSSING.spad" 1860911 1860937 1862347 1862480) (-1163 "UPXSCONS.spad" 1858729 1858749 1859102 1859251) (-1162 "UPXSCCA.spad" 1857300 1857320 1858575 1858724) (-1161 "UPXSCCA.spad" 1856013 1856035 1857290 1857295) (-1160 "UPXSCAT.spad" 1854602 1854618 1855859 1856008) (-1159 "UPXS2.spad" 1854145 1854198 1854592 1854597) (-1158 "UPXS.spad" 1851500 1851528 1852336 1852485) (-1157 "UPSQFREE.spad" 1849915 1849929 1851490 1851495) (-1156 "UPSCAT.spad" 1847710 1847734 1849813 1849910) (-1155 "UPSCAT.spad" 1845206 1845232 1847311 1847316) (-1154 "UPOLYC2.spad" 1844677 1844696 1845196 1845201) (-1153 "UPOLYC.spad" 1839757 1839768 1844519 1844672) (-1152 "UPOLYC.spad" 1834755 1834768 1839519 1839524) (-1151 "UPMP.spad" 1833687 1833700 1834745 1834750) (-1150 "UPDIVP.spad" 1833252 1833266 1833677 1833682) (-1149 "UPDECOMP.spad" 1831513 1831527 1833242 1833247) (-1148 "UPCDEN.spad" 1830730 1830746 1831503 1831508) (-1147 "UP2.spad" 1830094 1830115 1830720 1830725) (-1146 "UP.spad" 1827564 1827579 1827951 1828104) (-1145 "UNISEG2.spad" 1827061 1827074 1827520 1827525) (-1144 "UNISEG.spad" 1826414 1826425 1826980 1826985) (-1143 "UNIFACT.spad" 1825517 1825529 1826404 1826409) (-1142 "ULSCONS.spad" 1819560 1819580 1819930 1820079) (-1141 "ULSCCAT.spad" 1817297 1817317 1819406 1819555) (-1140 "ULSCCAT.spad" 1815142 1815164 1817253 1817258) (-1139 "ULSCAT.spad" 1813382 1813398 1814988 1815137) (-1138 "ULS2.spad" 1812896 1812949 1813372 1813377) (-1137 "ULS.spad" 1805162 1805190 1806107 1806530) (-1136 "UINT8.spad" 1805039 1805048 1805152 1805157) (-1135 "UINT64.spad" 1804915 1804924 1805029 1805034) (-1134 "UINT32.spad" 1804791 1804800 1804905 1804910) (-1133 "UINT16.spad" 1804667 1804676 1804781 1804786) (-1132 "UFD.spad" 1803732 1803741 1804593 1804662) (-1131 "UFD.spad" 1802859 1802870 1803722 1803727) (-1130 "UDVO.spad" 1801740 1801749 1802849 1802854) (-1129 "UDPO.spad" 1799321 1799332 1801696 1801701) (-1128 "TYPEAST.spad" 1799240 1799249 1799311 1799316) (-1127 "TYPE.spad" 1799172 1799181 1799230 1799235) (-1126 "TWOFACT.spad" 1797824 1797839 1799162 1799167) (-1125 "TUPLE.spad" 1797331 1797342 1797736 1797741) (-1124 "TUBETOOL.spad" 1794198 1794207 1797321 1797326) (-1123 "TUBE.spad" 1792845 1792862 1794188 1794193) (-1122 "TSETCAT.spad" 1780916 1780933 1792813 1792840) (-1121 "TSETCAT.spad" 1768973 1768992 1780872 1780877) (-1120 "TS.spad" 1767601 1767617 1768567 1768664) (-1119 "TRMANIP.spad" 1761965 1761982 1767289 1767294) (-1118 "TRIMAT.spad" 1760928 1760953 1761955 1761960) (-1117 "TRIGMNIP.spad" 1759455 1759472 1760918 1760923) (-1116 "TRIGCAT.spad" 1758967 1758976 1759445 1759450) (-1115 "TRIGCAT.spad" 1758477 1758488 1758957 1758962) (-1114 "TREE.spad" 1757117 1757128 1758149 1758176) (-1113 "TRANFUN.spad" 1756956 1756965 1757107 1757112) (-1112 "TRANFUN.spad" 1756793 1756804 1756946 1756951) (-1111 "TOPSP.spad" 1756467 1756476 1756783 1756788) (-1110 "TOOLSIGN.spad" 1756130 1756141 1756457 1756462) (-1109 "TEXTFILE.spad" 1754691 1754700 1756120 1756125) (-1108 "TEX1.spad" 1754247 1754258 1754681 1754686) (-1107 "TEX.spad" 1751441 1751450 1754237 1754242) (-1106 "TBCMPPK.spad" 1749542 1749565 1751431 1751436) (-1105 "TBAGG.spad" 1748600 1748623 1749522 1749537) (-1104 "TBAGG.spad" 1747666 1747691 1748590 1748595) (-1103 "TANEXP.spad" 1747074 1747085 1747656 1747661) (-1102 "TALGOP.spad" 1746798 1746809 1747064 1747069) (-1101 "TABLEAU.spad" 1746279 1746290 1746788 1746793) (-1100 "TABLE.spad" 1744554 1744577 1744824 1744851) (-1099 "TABLBUMP.spad" 1741333 1741344 1744544 1744549) (-1098 "SYSTEM.spad" 1740561 1740570 1741323 1741328) (-1097 "SYSSOLP.spad" 1738044 1738055 1740551 1740556) (-1096 "SYSPTR.spad" 1737943 1737952 1738034 1738039) (-1095 "SYSNNI.spad" 1737166 1737177 1737933 1737938) (-1094 "SYSINT.spad" 1736570 1736581 1737156 1737161) (-1093 "SYNTAX.spad" 1732904 1732913 1736560 1736565) (-1092 "SYMTAB.spad" 1730972 1730981 1732894 1732899) (-1091 "SYMS.spad" 1727001 1727010 1730962 1730967) (-1090 "SYMPOLY.spad" 1726134 1726145 1726216 1726343) (-1089 "SYMFUNC.spad" 1725635 1725646 1726124 1726129) (-1088 "SYMBOL.spad" 1723130 1723139 1725625 1725630) (-1087 "SUTS.spad" 1720243 1720271 1721662 1721759) (-1086 "SUPXS.spad" 1717585 1717613 1718434 1718583) (-1085 "SUPFRACF.spad" 1716690 1716708 1717575 1717580) (-1084 "SUP2.spad" 1716082 1716095 1716680 1716685) (-1083 "SUP.spad" 1713166 1713177 1713939 1714092) (-1082 "SUMRF.spad" 1712140 1712151 1713156 1713161) (-1081 "SUMFS.spad" 1711769 1711786 1712130 1712135) (-1080 "SULS.spad" 1704022 1704050 1704980 1705403) (-1079 "syntax.spad" 1703791 1703800 1704012 1704017) (-1078 "SUCH.spad" 1703481 1703496 1703781 1703786) (-1077 "SUBSPACE.spad" 1695612 1695627 1703471 1703476) (-1076 "SUBRESP.spad" 1694782 1694796 1695568 1695573) (-1075 "STTFNC.spad" 1691250 1691266 1694772 1694777) (-1074 "STTF.spad" 1687349 1687365 1691240 1691245) (-1073 "STTAYLOR.spad" 1680026 1680037 1687256 1687261) (-1072 "STRTBL.spad" 1678413 1678430 1678562 1678589) (-1071 "STRING.spad" 1677281 1677290 1677666 1677693) (-1070 "STREAM3.spad" 1676854 1676869 1677271 1677276) (-1069 "STREAM2.spad" 1675982 1675995 1676844 1676849) (-1068 "STREAM1.spad" 1675688 1675699 1675972 1675977) (-1067 "STREAM.spad" 1672684 1672695 1675291 1675306) (-1066 "STINPROD.spad" 1671620 1671636 1672674 1672679) (-1065 "STEPAST.spad" 1670854 1670863 1671610 1671615) (-1064 "STEP.spad" 1670171 1670180 1670844 1670849) (-1063 "STBL.spad" 1668561 1668589 1668728 1668743) (-1062 "STAGG.spad" 1667260 1667271 1668551 1668556) (-1061 "STAGG.spad" 1665957 1665970 1667250 1667255) (-1060 "STACK.spad" 1665379 1665390 1665629 1665656) (-1059 "SRING.spad" 1665139 1665148 1665369 1665374) (-1058 "SREGSET.spad" 1662871 1662888 1664773 1664800) (-1057 "SRDCMPK.spad" 1661448 1661468 1662861 1662866) (-1056 "SRAGG.spad" 1656631 1656640 1661416 1661443) (-1055 "SRAGG.spad" 1651834 1651845 1656621 1656626) (-1054 "SQMATRIX.spad" 1649511 1649529 1650427 1650514) (-1053 "SPLTREE.spad" 1644253 1644266 1649049 1649076) (-1052 "SPLNODE.spad" 1640873 1640886 1644243 1644248) (-1051 "SPFCAT.spad" 1639682 1639691 1640863 1640868) (-1050 "SPECOUT.spad" 1638234 1638243 1639672 1639677) (-1049 "SPADXPT.spad" 1630325 1630334 1638224 1638229) (-1048 "spad-parser.spad" 1629790 1629799 1630315 1630320) (-1047 "SPADAST.spad" 1629491 1629500 1629780 1629785) (-1046 "SPACEC.spad" 1613706 1613717 1629481 1629486) (-1045 "SPACE3.spad" 1613482 1613493 1613696 1613701) (-1044 "SORTPAK.spad" 1613031 1613044 1613438 1613443) (-1043 "SOLVETRA.spad" 1610794 1610805 1613021 1613026) (-1042 "SOLVESER.spad" 1609250 1609261 1610784 1610789) (-1041 "SOLVERAD.spad" 1605276 1605287 1609240 1609245) (-1040 "SOLVEFOR.spad" 1603738 1603756 1605266 1605271) (-1039 "SNTSCAT.spad" 1603338 1603355 1603706 1603733) (-1038 "SMTS.spad" 1601655 1601681 1602932 1603029) (-1037 "SMP.spad" 1599463 1599483 1599853 1599980) (-1036 "SMITH.spad" 1598308 1598333 1599453 1599458) (-1035 "SMATCAT.spad" 1596426 1596456 1598252 1598303) (-1034 "SMATCAT.spad" 1594476 1594508 1596304 1596309) (-1033 "SKAGG.spad" 1593445 1593456 1594444 1594471) (-1032 "SINT.spad" 1592744 1592753 1593311 1593440) (-1031 "SIMPAN.spad" 1592472 1592481 1592734 1592739) (-1030 "SIGNRF.spad" 1591597 1591608 1592462 1592467) (-1029 "SIGNEF.spad" 1590883 1590900 1591587 1591592) (-1028 "syntax.spad" 1590300 1590309 1590873 1590878) (-1027 "SIG.spad" 1589662 1589671 1590290 1590295) (-1026 "SHP.spad" 1587606 1587621 1589618 1589623) (-1025 "SHDP.spad" 1577099 1577126 1577616 1577713) (-1024 "SGROUP.spad" 1576707 1576716 1577089 1577094) (-1023 "SGROUP.spad" 1576313 1576324 1576697 1576702) (-1022 "catdef.spad" 1576023 1576035 1576134 1576308) (-1021 "catdef.spad" 1575579 1575591 1575844 1576018) (-1020 "SGCF.spad" 1568718 1568727 1575569 1575574) (-1019 "SFRTCAT.spad" 1567664 1567681 1568686 1568713) (-1018 "SFRGCD.spad" 1566727 1566747 1567654 1567659) (-1017 "SFQCMPK.spad" 1561540 1561560 1566717 1566722) (-1016 "SEXOF.spad" 1561383 1561423 1561530 1561535) (-1015 "SEXCAT.spad" 1559211 1559251 1561373 1561378) (-1014 "SEX.spad" 1559103 1559112 1559201 1559206) (-1013 "SETMN.spad" 1557563 1557580 1559093 1559098) (-1012 "SETCAT.spad" 1557048 1557057 1557553 1557558) (-1011 "SETCAT.spad" 1556531 1556542 1557038 1557043) (-1010 "SETAGG.spad" 1553080 1553091 1556511 1556526) (-1009 "SETAGG.spad" 1549637 1549650 1553070 1553075) (-1008 "SET.spad" 1547946 1547957 1549043 1549082) (-1007 "syntax.spad" 1547649 1547658 1547936 1547941) (-1006 "SEGXCAT.spad" 1546805 1546818 1547639 1547644) (-1005 "SEGCAT.spad" 1545730 1545741 1546795 1546800) (-1004 "SEGBIND2.spad" 1545428 1545441 1545720 1545725) (-1003 "SEGBIND.spad" 1545186 1545197 1545375 1545380) (-1002 "SEGAST.spad" 1544916 1544925 1545176 1545181) (-1001 "SEG2.spad" 1544351 1544364 1544872 1544877) (-1000 "SEG.spad" 1544164 1544175 1544270 1544275) (-999 "SDVAR.spad" 1543441 1543451 1544154 1544159) (-998 "SDPOL.spad" 1541139 1541149 1541429 1541556) (-997 "SCPKG.spad" 1539229 1539239 1541129 1541134) (-996 "SCOPE.spad" 1538407 1538415 1539219 1539224) (-995 "SCACHE.spad" 1537104 1537114 1538397 1538402) (-994 "SASTCAT.spad" 1537014 1537022 1537094 1537099) (-993 "SAOS.spad" 1536887 1536895 1537004 1537009) (-992 "SAERFFC.spad" 1536601 1536620 1536877 1536882) (-991 "SAEFACT.spad" 1536303 1536322 1536591 1536596) (-990 "SAE.spad" 1533954 1533969 1534564 1534699) (-989 "RURPK.spad" 1531614 1531629 1533944 1533949) (-988 "RULESET.spad" 1531068 1531091 1531604 1531609) (-987 "RULECOLD.spad" 1530921 1530933 1531058 1531063) (-986 "RULE.spad" 1529170 1529193 1530911 1530916) (-985 "RTVALUE.spad" 1528906 1528914 1529160 1529165) (-984 "syntax.spad" 1528624 1528632 1528896 1528901) (-983 "RSETGCD.spad" 1525067 1525086 1528614 1528619) (-982 "RSETCAT.spad" 1515036 1515052 1525035 1525062) (-981 "RSETCAT.spad" 1505025 1505043 1515026 1515031) (-980 "RSDCMPK.spad" 1503526 1503545 1505015 1505020) (-979 "RRCC.spad" 1501911 1501940 1503516 1503521) (-978 "RRCC.spad" 1500294 1500325 1501901 1501906) (-977 "RPTAST.spad" 1499997 1500005 1500284 1500289) (-976 "RPOLCAT.spad" 1479502 1479516 1499865 1499992) (-975 "RPOLCAT.spad" 1458800 1458816 1479165 1479170) (-974 "ROMAN.spad" 1458129 1458137 1458666 1458795) (-973 "ROIRC.spad" 1457210 1457241 1458119 1458124) (-972 "RNS.spad" 1456187 1456195 1457112 1457205) (-971 "RNS.spad" 1455250 1455260 1456177 1456182) (-970 "RNGBIND.spad" 1454411 1454424 1455205 1455210) (-969 "RNG.spad" 1454147 1454155 1454401 1454406) (-968 "RMODULE.spad" 1453929 1453939 1454137 1454142) (-967 "RMCAT2.spad" 1453350 1453406 1453919 1453924) (-966 "RMATRIX.spad" 1452160 1452178 1452502 1452541) (-965 "RMATCAT.spad" 1447740 1447770 1452116 1452155) (-964 "RMATCAT.spad" 1443210 1443242 1447588 1447593) (-963 "RLINSET.spad" 1442915 1442925 1443200 1443205) (-962 "RINTERP.spad" 1442804 1442823 1442905 1442910) (-961 "RING.spad" 1442275 1442283 1442784 1442799) (-960 "RING.spad" 1441754 1441764 1442265 1442270) (-959 "RIDIST.spad" 1441147 1441155 1441744 1441749) (-958 "RGCHAIN.spad" 1439702 1439717 1440595 1440622) (-957 "RGBCSPC.spad" 1439492 1439503 1439692 1439697) (-956 "RGBCMDL.spad" 1439055 1439066 1439482 1439487) (-955 "RFFACTOR.spad" 1438518 1438528 1439045 1439050) (-954 "RFFACT.spad" 1438254 1438265 1438508 1438513) (-953 "RFDIST.spad" 1437251 1437259 1438244 1438249) (-952 "RF.spad" 1434926 1434936 1437241 1437246) (-951 "RETSOL.spad" 1434346 1434358 1434916 1434921) (-950 "RETRACT.spad" 1433775 1433785 1434336 1434341) (-949 "RETRACT.spad" 1433202 1433214 1433765 1433770) (-948 "RETAST.spad" 1433015 1433023 1433192 1433197) (-947 "RESRING.spad" 1432363 1432409 1432953 1433010) (-946 "RESLATC.spad" 1431688 1431698 1432353 1432358) (-945 "REPSQ.spad" 1431420 1431430 1431678 1431683) (-944 "REPDB.spad" 1431128 1431138 1431410 1431415) (-943 "REP2.spad" 1420843 1420853 1430970 1430975) (-942 "REP1.spad" 1415064 1415074 1420793 1420798) (-941 "REP.spad" 1412619 1412627 1415054 1415059) (-940 "REGSET.spad" 1410445 1410461 1412253 1412280) (-939 "REF.spad" 1409964 1409974 1410435 1410440) (-938 "REDORDER.spad" 1409171 1409187 1409954 1409959) (-937 "RECLOS.spad" 1408068 1408087 1408771 1408864) (-936 "REALSOLV.spad" 1407209 1407217 1408058 1408063) (-935 "REAL0Q.spad" 1404508 1404522 1407199 1407204) (-934 "REAL0.spad" 1401353 1401367 1404498 1404503) (-933 "REAL.spad" 1401226 1401234 1401343 1401348) (-932 "RDUCEAST.spad" 1400948 1400956 1401216 1401221) (-931 "RDIV.spad" 1400604 1400628 1400938 1400943) (-930 "RDIST.spad" 1400172 1400182 1400594 1400599) (-929 "RDETRS.spad" 1399037 1399054 1400162 1400167) (-928 "RDETR.spad" 1397177 1397194 1399027 1399032) (-927 "RDEEFS.spad" 1396277 1396293 1397167 1397172) (-926 "RDEEF.spad" 1395288 1395304 1396267 1396272) (-925 "RCFIELD.spad" 1392507 1392515 1395190 1395283) (-924 "RCFIELD.spad" 1389812 1389822 1392497 1392502) (-923 "RCAGG.spad" 1387749 1387759 1389802 1389807) (-922 "RCAGG.spad" 1385613 1385625 1387668 1387673) (-921 "RATRET.spad" 1384974 1384984 1385603 1385608) (-920 "RATFACT.spad" 1384667 1384678 1384964 1384969) (-919 "RANDSRC.spad" 1383987 1383995 1384657 1384662) (-918 "RADUTIL.spad" 1383744 1383752 1383977 1383982) (-917 "RADIX.spad" 1380789 1380802 1382334 1382427) (-916 "RADFF.spad" 1378706 1378742 1378824 1378980) (-915 "RADCAT.spad" 1378302 1378310 1378696 1378701) (-914 "RADCAT.spad" 1377896 1377906 1378292 1378297) (-913 "QUEUE.spad" 1377310 1377320 1377568 1377595) (-912 "QUATCT2.spad" 1376931 1376949 1377300 1377305) (-911 "QUATCAT.spad" 1375102 1375112 1376861 1376926) (-910 "QUATCAT.spad" 1373038 1373050 1374799 1374804) (-909 "QUAT.spad" 1371645 1371655 1371987 1372052) (-908 "QUAGG.spad" 1370479 1370489 1371613 1371640) (-907 "QQUTAST.spad" 1370248 1370256 1370469 1370474) (-906 "QFORM.spad" 1369867 1369881 1370238 1370243) (-905 "QFCAT2.spad" 1369560 1369576 1369857 1369862) (-904 "QFCAT.spad" 1368263 1368273 1369462 1369555) (-903 "QFCAT.spad" 1366599 1366611 1367800 1367805) (-902 "QEQUAT.spad" 1366158 1366166 1366589 1366594) (-901 "QCMPACK.spad" 1361073 1361092 1366148 1366153) (-900 "QALGSET2.spad" 1359069 1359087 1361063 1361068) (-899 "QALGSET.spad" 1355174 1355206 1358983 1358988) (-898 "PWFFINTB.spad" 1352590 1352611 1355164 1355169) (-897 "PUSHVAR.spad" 1351929 1351948 1352580 1352585) (-896 "PTRANFN.spad" 1348065 1348075 1351919 1351924) (-895 "PTPACK.spad" 1345153 1345163 1348055 1348060) (-894 "PTFUNC2.spad" 1344976 1344990 1345143 1345148) (-893 "PTCAT.spad" 1344231 1344241 1344944 1344971) (-892 "PSQFR.spad" 1343546 1343570 1344221 1344226) (-891 "PSEUDLIN.spad" 1342432 1342442 1343536 1343541) (-890 "PSETPK.spad" 1329137 1329153 1342310 1342315) (-889 "PSETCAT.spad" 1323537 1323560 1329117 1329132) (-888 "PSETCAT.spad" 1317911 1317936 1323493 1323498) (-887 "PSCURVE.spad" 1316910 1316918 1317901 1317906) (-886 "PSCAT.spad" 1315693 1315722 1316808 1316905) (-885 "PSCAT.spad" 1314566 1314597 1315683 1315688) (-884 "PRTITION.spad" 1313264 1313272 1314556 1314561) (-883 "PRTDAST.spad" 1312983 1312991 1313254 1313259) (-882 "PRS.spad" 1302601 1302618 1312939 1312944) (-881 "PRQAGG.spad" 1302036 1302046 1302569 1302596) (-880 "PROPLOG.spad" 1301640 1301648 1302026 1302031) (-879 "PROPFUN2.spad" 1301263 1301276 1301630 1301635) (-878 "PROPFUN1.spad" 1300669 1300680 1301253 1301258) (-877 "PROPFRML.spad" 1299237 1299248 1300659 1300664) (-876 "PROPERTY.spad" 1298733 1298741 1299227 1299232) (-875 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414972 414982 415583 415588) (-279 "FAXF.spad" 408007 408021 414874 414967) (-278 "FAXF.spad" 401094 401110 407963 407968) (-277 "FARRAY.spad" 399286 399296 400319 400346) (-276 "FAMR.spad" 397430 397442 399184 399281) (-275 "FAMR.spad" 395558 395572 397314 397319) (-274 "FAMONOID.spad" 395242 395252 395512 395517) (-273 "FAMONC.spad" 393562 393574 395232 395237) (-272 "FAGROUP.spad" 393202 393212 393458 393485) (-271 "FACUTIL.spad" 391414 391431 393192 393197) (-270 "FACTFUNC.spad" 390616 390626 391404 391409) (-269 "EXPUPXS.spad" 387508 387531 388807 388956) (-268 "EXPRTUBE.spad" 384796 384804 387498 387503) (-267 "EXPRODE.spad" 381964 381980 384786 384791) (-266 "EXPR2UPS.spad" 378086 378099 381954 381959) (-265 "EXPR2.spad" 377791 377803 378076 378081) (-264 "EXPR.spad" 373436 373446 374150 374437) (-263 "EXPEXPAN.spad" 370381 370406 371013 371106) (-262 "EXITAST.spad" 370117 370125 370371 370376) (-261 "EXIT.spad" 369788 369796 370107 370112) (-260 "EVALCYC.spad" 369248 369262 369778 369783) (-259 "EVALAB.spad" 368828 368838 369238 369243) (-258 "EVALAB.spad" 368406 368418 368818 368823) (-257 "EUCDOM.spad" 365996 366004 368332 368401) (-256 "EUCDOM.spad" 363648 363658 365986 365991) (-255 "ES2.spad" 363161 363177 363638 363643) (-254 "ES1.spad" 362731 362747 363151 363156) (-253 "ES.spad" 355602 355610 362721 362726) (-252 "ES.spad" 348394 348404 355515 355520) (-251 "ERROR.spad" 345721 345729 348384 348389) (-250 "EQTBL.spad" 344057 344079 344266 344293) (-249 "EQ2.spad" 343775 343787 344047 344052) (-248 "EQ.spad" 338681 338691 341476 341582) (-247 "EP.spad" 335007 335017 338671 338676) (-246 "ENV.spad" 333685 333693 334997 335002) (-245 "ENTIRER.spad" 333353 333361 333629 333680) (-244 "EMR.spad" 332641 332682 333279 333348) (-243 "ELTAGG.spad" 330895 330914 332631 332636) (-242 "ELTAGG.spad" 329113 329134 330851 330856) (-241 "ELTAB.spad" 328588 328601 329103 329108) (-240 "ELFUTS.spad" 328023 328042 328578 328583) (-239 "ELEMFUN.spad" 327712 327720 328013 328018) (-238 "ELEMFUN.spad" 327399 327409 327702 327707) (-237 "ELAGG.spad" 325370 325380 327379 327394) (-236 "ELAGG.spad" 323278 323290 325289 325294) (-235 "ELABOR.spad" 322624 322632 323268 323273) (-234 "ELABEXPR.spad" 321556 321564 322614 322619) (-233 "EFUPXS.spad" 318332 318362 321512 321517) (-232 "EFULS.spad" 315168 315191 318288 318293) (-231 "EFSTRUC.spad" 313183 313199 315158 315163) (-230 "EF.spad" 307959 307975 313173 313178) (-229 "EAB.spad" 306259 306267 307949 307954) (-228 "DVARCAT.spad" 303265 303275 306249 306254) (-227 "DVARCAT.spad" 300269 300281 303255 303260) (-226 "DSMP.spad" 298002 298016 298307 298434) (-225 "DSEXT.spad" 297304 297314 297992 297997) (-224 "DSEXT.spad" 296526 296538 297216 297221) (-223 "DROPT1.spad" 296191 296201 296516 296521) (-222 "DROPT0.spad" 291056 291064 296181 296186) (-221 "DROPT.spad" 285015 285023 291046 291051) (-220 "DRAWPT.spad" 283188 283196 285005 285010) (-219 "DRAWHACK.spad" 282496 282506 283178 283183) (-218 "DRAWCX.spad" 279974 279982 282486 282491) (-217 "DRAWCURV.spad" 279521 279536 279964 279969) (-216 "DRAWCFUN.spad" 269053 269061 279511 279516) (-215 "DRAW.spad" 261929 261942 269043 269048) (-214 "DQAGG.spad" 260107 260117 261897 261924) (-213 "DPOLCAT.spad" 255464 255480 259975 260102) (-212 "DPOLCAT.spad" 250907 250925 255420 255425) (-211 "DPMO.spad" 243610 243626 243748 243954) (-210 "DPMM.spad" 236326 236344 236451 236657) (-209 "DOMTMPLT.spad" 236097 236105 236316 236321) (-208 "DOMCTOR.spad" 235852 235860 236087 236092) (-207 "DOMAIN.spad" 234963 234971 235842 235847) (-206 "DMP.spad" 232556 232571 233126 233253) (-205 "DMEXT.spad" 232423 232433 232524 232551) (-204 "DLP.spad" 231783 231793 232413 232418) (-203 "DLIST.spad" 230404 230414 231008 231035) (-202 "DLAGG.spad" 228821 228831 230394 230399) (-201 "DIVRING.spad" 228363 228371 228765 228816) (-200 "DIVRING.spad" 227949 227959 228353 228358) (-199 "DISPLAY.spad" 226139 226147 227939 227944) (-198 "DIRPROD2.spad" 224957 224975 226129 226134) (-197 "DIRPROD.spad" 214327 214343 214967 215064) (-196 "DIRPCAT.spad" 213522 213538 214225 214322) (-195 "DIRPCAT.spad" 212343 212361 213048 213053) (-194 "DIOSP.spad" 211168 211176 212333 212338) (-193 "DIOPS.spad" 210164 210174 211148 211163) (-192 "DIOPS.spad" 209134 209146 210120 210125) (-191 "catdef.spad" 208992 209000 209124 209129) (-190 "DIFRING.spad" 208830 208838 208972 208987) (-189 "DIFFSPC.spad" 208409 208417 208820 208825) (-188 "DIFFSPC.spad" 207986 207996 208399 208404) (-187 "DIFFMOD.spad" 207475 207485 207954 207981) (-186 "DIFFDOM.spad" 206640 206651 207465 207470) (-185 "DIFFDOM.spad" 205803 205816 206630 206635) (-184 "DIFEXT.spad" 205622 205632 205783 205798) (-183 "DIAGG.spad" 205252 205262 205602 205617) (-182 "DIAGG.spad" 204890 204902 205242 205247) (-181 "DHMATRIX.spad" 203267 203277 204412 204439) (-180 "DFSFUN.spad" 196907 196915 203257 203262) (-179 "DFLOAT.spad" 193514 193522 196797 196902) (-178 "DFINTTLS.spad" 191745 191761 193504 193509) (-177 "DERHAM.spad" 189659 189691 191725 191740) (-176 "DEQUEUE.spad" 189048 189058 189331 189358) (-175 "DEGRED.spad" 188665 188679 189038 189043) (-174 "DEFINTRF.spad" 186247 186257 188655 188660) (-173 "DEFINTEF.spad" 184785 184801 186237 186242) (-172 "DEFAST.spad" 184169 184177 184775 184780) (-171 "DECIMAL.spad" 182398 182406 182759 182852) (-170 "DDFACT.spad" 180219 180236 182388 182393) (-169 "DBLRESP.spad" 179819 179843 180209 180214) (-168 "DBASIS.spad" 179445 179460 179809 179814) (-167 "DBASE.spad" 178109 178119 179435 179440) (-166 "DATAARY.spad" 177595 177608 178099 178104) (-165 "CYCLOTOM.spad" 177101 177109 177585 177590) (-164 "CYCLES.spad" 173893 173901 177091 177096) (-163 "CVMP.spad" 173310 173320 173883 173888) (-162 "CTRIGMNP.spad" 171810 171826 173300 173305) (-161 "CTORKIND.spad" 171413 171421 171800 171805) (-160 "CTORCAT.spad" 170654 170662 171403 171408) (-159 "CTORCAT.spad" 169893 169903 170644 170649) (-158 "CTORCALL.spad" 169482 169492 169883 169888) (-157 "CTOR.spad" 169173 169181 169472 169477) (-156 "CSTTOOLS.spad" 168418 168431 169163 169168) (-155 "CRFP.spad" 162190 162203 168408 168413) (-154 "CRCEAST.spad" 161910 161918 162180 162185) (-153 "CRAPACK.spad" 160977 160987 161900 161905) (-152 "CPMATCH.spad" 160478 160493 160899 160904) (-151 "CPIMA.spad" 160183 160202 160468 160473) (-150 "COORDSYS.spad" 155192 155202 160173 160178) (-149 "CONTOUR.spad" 154619 154627 155182 155187) (-148 "CONTFRAC.spad" 150369 150379 154521 154614) (-147 "CONDUIT.spad" 150127 150135 150359 150364) (-146 "COMRING.spad" 149801 149809 150065 150122) (-145 "COMPPROP.spad" 149319 149327 149791 149796) (-144 "COMPLPAT.spad" 149086 149101 149309 149314) (-143 "COMPLEX2.spad" 148801 148813 149076 149081) (-142 "COMPLEX.spad" 144507 144517 144751 145009) (-141 "COMPILER.spad" 144056 144064 144497 144502) (-140 "COMPFACT.spad" 143658 143672 144046 144051) (-139 "COMPCAT.spad" 141733 141743 143395 143653) (-138 "COMPCAT.spad" 139549 139561 141213 141218) (-137 "COMMUPC.spad" 139297 139315 139539 139544) (-136 "COMMONOP.spad" 138830 138838 139287 139292) (-135 "COMMAAST.spad" 138593 138601 138820 138825) (-134 "COMM.spad" 138404 138412 138583 138588) (-133 "COMBOPC.spad" 137327 137335 138394 138399) (-132 "COMBINAT.spad" 136094 136104 137317 137322) (-131 "COMBF.spad" 133516 133532 136084 136089) (-130 "COLOR.spad" 132353 132361 133506 133511) (-129 "COLONAST.spad" 132019 132027 132343 132348) (-128 "CMPLXRT.spad" 131730 131747 132009 132014) (-127 "CLLCTAST.spad" 131392 131400 131720 131725) (-126 "CLIP.spad" 127500 127508 131382 131387) (-125 "CLIF.spad" 126155 126171 127456 127495) (-124 "CLAGG.spad" 122692 122702 126145 126150) (-123 "CLAGG.spad" 119113 119125 122568 122573) (-122 "CINTSLPE.spad" 118468 118481 119103 119108) (-121 "CHVAR.spad" 116606 116628 118458 118463) (-120 "CHARZ.spad" 116521 116529 116586 116601) (-119 "CHARPOL.spad" 116047 116057 116511 116516) (-118 "CHARNZ.spad" 115809 115817 116027 116042) (-117 "CHAR.spad" 113177 113185 115799 115804) (-116 "CFCAT.spad" 112505 112513 113167 113172) (-115 "CDEN.spad" 111725 111739 112495 112500) (-114 "CCLASS.spad" 109905 109913 111167 111206) (-113 "CATEGORY.spad" 108979 108987 109895 109900) (-112 "CATCTOR.spad" 108870 108878 108969 108974) (-111 "CATAST.spad" 108496 108504 108860 108865) (-110 "CASEAST.spad" 108210 108218 108486 108491) (-109 "CARTEN2.spad" 107600 107627 108200 108205) (-108 "CARTEN.spad" 103352 103376 107590 107595) (-107 "CARD.spad" 100647 100655 103326 103347) (-106 "CAPSLAST.spad" 100429 100437 100637 100642) (-105 "CACHSET.spad" 100053 100061 100419 100424) (-104 "CABMON.spad" 99608 99616 100043 100048) (-103 "BYTEORD.spad" 99283 99291 99598 99603) (-102 "BYTEBUF.spad" 97250 97258 98536 98563) (-101 "BYTE.spad" 96725 96733 97240 97245) (-100 "BTREE.spad" 95863 95873 96397 96424) (-99 "BTOURN.spad" 94934 94943 95535 95562) (-98 "BTCAT.spad" 94327 94336 94902 94929) (-97 "BTCAT.spad" 93740 93751 94317 94322) (-96 "BTAGG.spad" 93207 93214 93708 93735) (-95 "BTAGG.spad" 92694 92703 93197 93202) (-94 "BSTREE.spad" 91501 91510 92366 92393) (-93 "BRILL.spad" 89707 89717 91491 91496) (-92 "BRAGG.spad" 88664 88673 89697 89702) (-91 "BRAGG.spad" 87585 87596 88620 88625) (-90 "BPADICRT.spad" 85645 85656 85891 85984) (-89 "BPADIC.spad" 85318 85329 85571 85640) (-88 "BOUNDZRO.spad" 84975 84991 85308 85313) (-87 "BOP1.spad" 82434 82443 84965 84970) (-86 "BOP.spad" 77577 77584 82424 82429) (-85 "BOOLEAN.spad" 77126 77133 77567 77572) (-84 "BOOLE.spad" 76777 76784 77116 77121) (-83 "BOOLE.spad" 76426 76435 76767 76772) (-82 "BMODULE.spad" 76139 76150 76394 76421) (-81 "BITS.spad" 75571 75578 75785 75812) (-80 "catdef.spad" 75454 75464 75561 75566) (-79 "catdef.spad" 75205 75215 75444 75449) (-78 "BINDING.spad" 74627 74634 75195 75200) (-77 "BINARY.spad" 72862 72869 73217 73310) (-76 "BGAGG.spad" 72068 72077 72842 72857) (-75 "BGAGG.spad" 71282 71293 72058 72063) (-74 "BEZOUT.spad" 70423 70449 71232 71237) (-73 "BBTREE.spad" 67366 67375 70095 70122) (-72 "BASTYPE.spad" 66866 66873 67356 67361) (-71 "BASTYPE.spad" 66364 66373 66856 66861) (-70 "BALFACT.spad" 65824 65836 66354 66359) (-69 "AUTOMOR.spad" 65275 65284 65804 65819) (-68 "ATTREG.spad" 61998 62005 65027 65270) (-67 "ATTRAST.spad" 61715 61722 61988 61993) (-66 "ATRIG.spad" 61185 61192 61705 61710) (-65 "ATRIG.spad" 60653 60662 61175 61180) (-64 "ASTCAT.spad" 60557 60564 60643 60648) (-63 "ASTCAT.spad" 60459 60468 60547 60552) (-62 "ASTACK.spad" 59863 59872 60131 60158) (-61 "ASSOCEQ.spad" 58697 58708 59819 59824) (-60 "ARRAY2.spad" 58130 58139 58369 58396) (-59 "ARRAY12.spad" 56843 56854 58120 58125) (-58 "ARRAY1.spad" 55722 55731 56068 56095) (-57 "ARR2CAT.spad" 51504 51525 55690 55717) (-56 "ARR2CAT.spad" 47306 47329 51494 51499) (-55 "ARITY.spad" 46678 46685 47296 47301) (-54 "APPRULE.spad" 45962 45984 46668 46673) (-53 "APPLYORE.spad" 45581 45594 45952 45957) (-52 "ANY1.spad" 44652 44661 45571 45576) (-51 "ANY.spad" 43503 43510 44642 44647) (-50 "ANTISYM.spad" 41948 41964 43483 43498) (-49 "ANON.spad" 41657 41664 41938 41943) (-48 "AN.spad" 40125 40132 41488 41581) (-47 "AMR.spad" 38310 38321 40023 40120) (-46 "AMR.spad" 36358 36371 38073 38078) (-45 "ALIST.spad" 33596 33617 33946 33973) (-44 "ALGSC.spad" 32731 32757 33468 33521) (-43 "ALGPKG.spad" 28514 28525 32687 32692) (-42 "ALGMFACT.spad" 27707 27721 28504 28509) (-41 "ALGMANIP.spad" 25208 25223 27551 27556) (-40 "ALGFF.spad" 23026 23053 23243 23399) (-39 "ALGFACT.spad" 22145 22155 23016 23021) (-38 "ALGEBRA.spad" 21978 21987 22101 22140) (-37 "ALGEBRA.spad" 21843 21854 21968 21973) (-36 "ALAGG.spad" 21355 21376 21811 21838) (-35 "AHYP.spad" 20736 20743 21345 21350) (-34 "AGG.spad" 19445 19452 20726 20731) (-33 "AGG.spad" 18118 18127 19401 19406) (-32 "AF.spad" 16563 16578 18067 18072) (-31 "ADDAST.spad" 16249 16256 16553 16558) (-30 "ACPLOT.spad" 14840 14847 16239 16244) (-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 1961784 1961789 1961794 1961799) (-2 NIL 1961764 1961769 1961774 1961779) (-1 NIL 1961744 1961749 1961754 1961759) (0 NIL 1961724 1961729 1961734 1961739) (-1208 "ZMOD.spad" 1961533 1961546 1961662 1961719) (-1207 "ZLINDEP.spad" 1960631 1960642 1961523 1961528) (-1206 "ZDSOLVE.spad" 1950592 1950614 1960621 1960626) (-1205 "YSTREAM.spad" 1950087 1950098 1950582 1950587) (-1204 "YDIAGRAM.spad" 1949721 1949730 1950077 1950082) (-1203 "XRPOLY.spad" 1948941 1948961 1949577 1949646) (-1202 "XPR.spad" 1946736 1946749 1948659 1948758) (-1201 "XPOLYC.spad" 1946055 1946071 1946662 1946731) (-1200 "XPOLY.spad" 1945610 1945621 1945911 1945980) (-1199 "XPBWPOLY.spad" 1944081 1944101 1945416 1945485) (-1198 "XFALG.spad" 1941129 1941145 1944007 1944076) (-1197 "XF.spad" 1939592 1939607 1941031 1941124) (-1196 "XF.spad" 1938035 1938052 1939476 1939481) (-1195 "XEXPPKG.spad" 1937294 1937320 1938025 1938030) (-1194 "XDPOLY.spad" 1936908 1936924 1937150 1937219) (-1193 "XALG.spad" 1936576 1936587 1936864 1936903) (-1192 "WUTSET.spad" 1932579 1932596 1936210 1936237) (-1191 "WP.spad" 1931786 1931830 1932437 1932504) (-1190 "WHILEAST.spad" 1931584 1931593 1931776 1931781) (-1189 "WHEREAST.spad" 1931255 1931264 1931574 1931579) (-1188 "WFFINTBS.spad" 1928918 1928940 1931245 1931250) (-1187 "WEIER.spad" 1927140 1927151 1928908 1928913) (-1186 "VSPACE.spad" 1926813 1926824 1927108 1927135) (-1185 "VSPACE.spad" 1926506 1926519 1926803 1926808) (-1184 "VOID.spad" 1926183 1926192 1926496 1926501) (-1183 "VIEWDEF.spad" 1921384 1921393 1926173 1926178) (-1182 "VIEW3D.spad" 1905345 1905354 1921374 1921379) (-1181 "VIEW2D.spad" 1893244 1893253 1905335 1905340) (-1180 "VIEW.spad" 1890964 1890973 1893234 1893239) (-1179 "VECTOR2.spad" 1889603 1889616 1890954 1890959) (-1178 "VECTOR.spad" 1888322 1888333 1888573 1888600) (-1177 "VECTCAT.spad" 1886234 1886245 1888290 1888317) (-1176 "VECTCAT.spad" 1883955 1883968 1886013 1886018) (-1175 "VARIABLE.spad" 1883735 1883750 1883945 1883950) (-1174 "UTYPE.spad" 1883379 1883388 1883725 1883730) (-1173 "UTSODETL.spad" 1882674 1882698 1883335 1883340) (-1172 "UTSODE.spad" 1880890 1880910 1882664 1882669) (-1171 "UTSCAT.spad" 1878369 1878385 1880788 1880885) (-1170 "UTSCAT.spad" 1875516 1875534 1877937 1877942) (-1169 "UTS2.spad" 1875111 1875146 1875506 1875511) (-1168 "UTS.spad" 1870123 1870151 1873643 1873740) (-1167 "URAGG.spad" 1864844 1864855 1870113 1870118) (-1166 "URAGG.spad" 1859529 1859542 1864800 1864805) (-1165 "UPXSSING.spad" 1857297 1857323 1858733 1858866) (-1164 "UPXSCONS.spad" 1855115 1855135 1855488 1855637) (-1163 "UPXSCCA.spad" 1853686 1853706 1854961 1855110) (-1162 "UPXSCCA.spad" 1852399 1852421 1853676 1853681) (-1161 "UPXSCAT.spad" 1850988 1851004 1852245 1852394) (-1160 "UPXS2.spad" 1850531 1850584 1850978 1850983) (-1159 "UPXS.spad" 1847886 1847914 1848722 1848871) (-1158 "UPSQFREE.spad" 1846301 1846315 1847876 1847881) (-1157 "UPSCAT.spad" 1844096 1844120 1846199 1846296) (-1156 "UPSCAT.spad" 1841592 1841618 1843697 1843702) (-1155 "UPOLYC2.spad" 1841063 1841082 1841582 1841587) (-1154 "UPOLYC.spad" 1836143 1836154 1840905 1841058) (-1153 "UPOLYC.spad" 1831141 1831154 1835905 1835910) (-1152 "UPMP.spad" 1830073 1830086 1831131 1831136) (-1151 "UPDIVP.spad" 1829638 1829652 1830063 1830068) (-1150 "UPDECOMP.spad" 1827899 1827913 1829628 1829633) (-1149 "UPCDEN.spad" 1827116 1827132 1827889 1827894) (-1148 "UP2.spad" 1826480 1826501 1827106 1827111) (-1147 "UP.spad" 1823950 1823965 1824337 1824490) (-1146 "UNISEG2.spad" 1823447 1823460 1823906 1823911) (-1145 "UNISEG.spad" 1822800 1822811 1823366 1823371) (-1144 "UNIFACT.spad" 1821903 1821915 1822790 1822795) (-1143 "ULSCONS.spad" 1815946 1815966 1816316 1816465) (-1142 "ULSCCAT.spad" 1813683 1813703 1815792 1815941) (-1141 "ULSCCAT.spad" 1811528 1811550 1813639 1813644) (-1140 "ULSCAT.spad" 1809768 1809784 1811374 1811523) (-1139 "ULS2.spad" 1809282 1809335 1809758 1809763) (-1138 "ULS.spad" 1801548 1801576 1802493 1802916) (-1137 "UINT8.spad" 1801425 1801434 1801538 1801543) (-1136 "UINT64.spad" 1801301 1801310 1801415 1801420) (-1135 "UINT32.spad" 1801177 1801186 1801291 1801296) (-1134 "UINT16.spad" 1801053 1801062 1801167 1801172) (-1133 "UFD.spad" 1800118 1800127 1800979 1801048) (-1132 "UFD.spad" 1799245 1799256 1800108 1800113) (-1131 "UDVO.spad" 1798126 1798135 1799235 1799240) (-1130 "UDPO.spad" 1795707 1795718 1798082 1798087) (-1129 "TYPEAST.spad" 1795626 1795635 1795697 1795702) (-1128 "TYPE.spad" 1795558 1795567 1795616 1795621) (-1127 "TWOFACT.spad" 1794210 1794225 1795548 1795553) (-1126 "TUPLE.spad" 1793717 1793728 1794122 1794127) (-1125 "TUBETOOL.spad" 1790584 1790593 1793707 1793712) (-1124 "TUBE.spad" 1789231 1789248 1790574 1790579) (-1123 "TSETCAT.spad" 1777302 1777319 1789199 1789226) (-1122 "TSETCAT.spad" 1765359 1765378 1777258 1777263) (-1121 "TS.spad" 1763987 1764003 1764953 1765050) (-1120 "TRMANIP.spad" 1758351 1758368 1763675 1763680) (-1119 "TRIMAT.spad" 1757314 1757339 1758341 1758346) (-1118 "TRIGMNIP.spad" 1755841 1755858 1757304 1757309) (-1117 "TRIGCAT.spad" 1755353 1755362 1755831 1755836) (-1116 "TRIGCAT.spad" 1754863 1754874 1755343 1755348) (-1115 "TREE.spad" 1753503 1753514 1754535 1754562) (-1114 "TRANFUN.spad" 1753342 1753351 1753493 1753498) (-1113 "TRANFUN.spad" 1753179 1753190 1753332 1753337) (-1112 "TOPSP.spad" 1752853 1752862 1753169 1753174) (-1111 "TOOLSIGN.spad" 1752516 1752527 1752843 1752848) (-1110 "TEXTFILE.spad" 1751077 1751086 1752506 1752511) (-1109 "TEX1.spad" 1750633 1750644 1751067 1751072) (-1108 "TEX.spad" 1747827 1747836 1750623 1750628) (-1107 "TBCMPPK.spad" 1745928 1745951 1747817 1747822) (-1106 "TBAGG.spad" 1744986 1745009 1745908 1745923) (-1105 "TBAGG.spad" 1744052 1744077 1744976 1744981) (-1104 "TANEXP.spad" 1743460 1743471 1744042 1744047) (-1103 "TALGOP.spad" 1743184 1743195 1743450 1743455) (-1102 "TABLEAU.spad" 1742665 1742676 1743174 1743179) (-1101 "TABLE.spad" 1740940 1740963 1741210 1741237) (-1100 "TABLBUMP.spad" 1737719 1737730 1740930 1740935) (-1099 "SYSTEM.spad" 1736947 1736956 1737709 1737714) (-1098 "SYSSOLP.spad" 1734430 1734441 1736937 1736942) (-1097 "SYSPTR.spad" 1734329 1734338 1734420 1734425) (-1096 "SYSNNI.spad" 1733552 1733563 1734319 1734324) (-1095 "SYSINT.spad" 1732956 1732967 1733542 1733547) (-1094 "SYNTAX.spad" 1729290 1729299 1732946 1732951) (-1093 "SYMTAB.spad" 1727358 1727367 1729280 1729285) (-1092 "SYMS.spad" 1723387 1723396 1727348 1727353) (-1091 "SYMPOLY.spad" 1722520 1722531 1722602 1722729) (-1090 "SYMFUNC.spad" 1722021 1722032 1722510 1722515) (-1089 "SYMBOL.spad" 1719516 1719525 1722011 1722016) (-1088 "SUTS.spad" 1716629 1716657 1718048 1718145) (-1087 "SUPXS.spad" 1713971 1713999 1714820 1714969) (-1086 "SUPFRACF.spad" 1713076 1713094 1713961 1713966) (-1085 "SUP2.spad" 1712468 1712481 1713066 1713071) (-1084 "SUP.spad" 1709552 1709563 1710325 1710478) (-1083 "SUMRF.spad" 1708526 1708537 1709542 1709547) (-1082 "SUMFS.spad" 1708155 1708172 1708516 1708521) (-1081 "SULS.spad" 1700408 1700436 1701366 1701789) (-1080 "syntax.spad" 1700177 1700186 1700398 1700403) (-1079 "SUCH.spad" 1699867 1699882 1700167 1700172) (-1078 "SUBSPACE.spad" 1691998 1692013 1699857 1699862) (-1077 "SUBRESP.spad" 1691168 1691182 1691954 1691959) (-1076 "STTFNC.spad" 1687636 1687652 1691158 1691163) (-1075 "STTF.spad" 1683735 1683751 1687626 1687631) (-1074 "STTAYLOR.spad" 1676412 1676423 1683642 1683647) (-1073 "STRTBL.spad" 1674799 1674816 1674948 1674975) (-1072 "STRING.spad" 1673667 1673676 1674052 1674079) (-1071 "STREAM3.spad" 1673240 1673255 1673657 1673662) (-1070 "STREAM2.spad" 1672368 1672381 1673230 1673235) (-1069 "STREAM1.spad" 1672074 1672085 1672358 1672363) (-1068 "STREAM.spad" 1669070 1669081 1671677 1671692) (-1067 "STINPROD.spad" 1668006 1668022 1669060 1669065) (-1066 "STEPAST.spad" 1667240 1667249 1667996 1668001) (-1065 "STEP.spad" 1666557 1666566 1667230 1667235) (-1064 "STBL.spad" 1664947 1664975 1665114 1665129) (-1063 "STAGG.spad" 1663646 1663657 1664937 1664942) (-1062 "STAGG.spad" 1662343 1662356 1663636 1663641) (-1061 "STACK.spad" 1661765 1661776 1662015 1662042) (-1060 "SRING.spad" 1661525 1661534 1661755 1661760) (-1059 "SREGSET.spad" 1659257 1659274 1661159 1661186) (-1058 "SRDCMPK.spad" 1657834 1657854 1659247 1659252) (-1057 "SRAGG.spad" 1653017 1653026 1657802 1657829) (-1056 "SRAGG.spad" 1648220 1648231 1653007 1653012) (-1055 "SQMATRIX.spad" 1645897 1645915 1646813 1646900) (-1054 "SPLTREE.spad" 1640639 1640652 1645435 1645462) (-1053 "SPLNODE.spad" 1637259 1637272 1640629 1640634) (-1052 "SPFCAT.spad" 1636068 1636077 1637249 1637254) (-1051 "SPECOUT.spad" 1634620 1634629 1636058 1636063) (-1050 "SPADXPT.spad" 1626711 1626720 1634610 1634615) (-1049 "spad-parser.spad" 1626176 1626185 1626701 1626706) (-1048 "SPADAST.spad" 1625877 1625886 1626166 1626171) (-1047 "SPACEC.spad" 1610092 1610103 1625867 1625872) (-1046 "SPACE3.spad" 1609868 1609879 1610082 1610087) (-1045 "SORTPAK.spad" 1609417 1609430 1609824 1609829) (-1044 "SOLVETRA.spad" 1607180 1607191 1609407 1609412) (-1043 "SOLVESER.spad" 1605636 1605647 1607170 1607175) (-1042 "SOLVERAD.spad" 1601662 1601673 1605626 1605631) (-1041 "SOLVEFOR.spad" 1600124 1600142 1601652 1601657) (-1040 "SNTSCAT.spad" 1599724 1599741 1600092 1600119) (-1039 "SMTS.spad" 1598041 1598067 1599318 1599415) (-1038 "SMP.spad" 1595849 1595869 1596239 1596366) (-1037 "SMITH.spad" 1594694 1594719 1595839 1595844) (-1036 "SMATCAT.spad" 1592812 1592842 1594638 1594689) (-1035 "SMATCAT.spad" 1590862 1590894 1592690 1592695) (-1034 "SKAGG.spad" 1589831 1589842 1590830 1590857) (-1033 "SINT.spad" 1589130 1589139 1589697 1589826) (-1032 "SIMPAN.spad" 1588858 1588867 1589120 1589125) (-1031 "SIGNRF.spad" 1587983 1587994 1588848 1588853) (-1030 "SIGNEF.spad" 1587269 1587286 1587973 1587978) (-1029 "syntax.spad" 1586686 1586695 1587259 1587264) (-1028 "SIG.spad" 1586048 1586057 1586676 1586681) (-1027 "SHP.spad" 1583992 1584007 1586004 1586009) (-1026 "SHDP.spad" 1573485 1573512 1574002 1574099) (-1025 "SGROUP.spad" 1573093 1573102 1573475 1573480) (-1024 "SGROUP.spad" 1572699 1572710 1573083 1573088) (-1023 "catdef.spad" 1572409 1572421 1572520 1572694) (-1022 "catdef.spad" 1571965 1571977 1572230 1572404) (-1021 "SGCF.spad" 1565104 1565113 1571955 1571960) (-1020 "SFRTCAT.spad" 1564050 1564067 1565072 1565099) (-1019 "SFRGCD.spad" 1563113 1563133 1564040 1564045) (-1018 "SFQCMPK.spad" 1557926 1557946 1563103 1563108) (-1017 "SEXOF.spad" 1557769 1557809 1557916 1557921) (-1016 "SEXCAT.spad" 1555597 1555637 1557759 1557764) (-1015 "SEX.spad" 1555489 1555498 1555587 1555592) (-1014 "SETMN.spad" 1553949 1553966 1555479 1555484) (-1013 "SETCAT.spad" 1553434 1553443 1553939 1553944) (-1012 "SETCAT.spad" 1552917 1552928 1553424 1553429) (-1011 "SETAGG.spad" 1549466 1549477 1552897 1552912) (-1010 "SETAGG.spad" 1546023 1546036 1549456 1549461) (-1009 "SET.spad" 1544332 1544343 1545429 1545468) (-1008 "syntax.spad" 1544035 1544044 1544322 1544327) (-1007 "SEGXCAT.spad" 1543191 1543204 1544025 1544030) (-1006 "SEGCAT.spad" 1542116 1542127 1543181 1543186) (-1005 "SEGBIND2.spad" 1541814 1541827 1542106 1542111) (-1004 "SEGBIND.spad" 1541572 1541583 1541761 1541766) (-1003 "SEGAST.spad" 1541302 1541311 1541562 1541567) (-1002 "SEG2.spad" 1540737 1540750 1541258 1541263) (-1001 "SEG.spad" 1540550 1540561 1540656 1540661) (-1000 "SDVAR.spad" 1539826 1539837 1540540 1540545) (-999 "SDPOL.spad" 1537519 1537529 1537809 1537936) (-998 "SCPKG.spad" 1535609 1535619 1537509 1537514) (-997 "SCOPE.spad" 1534787 1534795 1535599 1535604) (-996 "SCACHE.spad" 1533484 1533494 1534777 1534782) (-995 "SASTCAT.spad" 1533394 1533402 1533474 1533479) (-994 "SAOS.spad" 1533267 1533275 1533384 1533389) (-993 "SAERFFC.spad" 1532981 1533000 1533257 1533262) (-992 "SAEFACT.spad" 1532683 1532702 1532971 1532976) (-991 "SAE.spad" 1530334 1530349 1530944 1531079) (-990 "RURPK.spad" 1527994 1528009 1530324 1530329) (-989 "RULESET.spad" 1527448 1527471 1527984 1527989) (-988 "RULECOLD.spad" 1527301 1527313 1527438 1527443) (-987 "RULE.spad" 1525550 1525573 1527291 1527296) (-986 "RTVALUE.spad" 1525286 1525294 1525540 1525545) (-985 "syntax.spad" 1525004 1525012 1525276 1525281) (-984 "RSETGCD.spad" 1521447 1521466 1524994 1524999) (-983 "RSETCAT.spad" 1511416 1511432 1521415 1521442) (-982 "RSETCAT.spad" 1501405 1501423 1511406 1511411) (-981 "RSDCMPK.spad" 1499906 1499925 1501395 1501400) (-980 "RRCC.spad" 1498291 1498320 1499896 1499901) (-979 "RRCC.spad" 1496674 1496705 1498281 1498286) (-978 "RPTAST.spad" 1496377 1496385 1496664 1496669) (-977 "RPOLCAT.spad" 1475882 1475896 1496245 1496372) (-976 "RPOLCAT.spad" 1455180 1455196 1475545 1475550) (-975 "ROMAN.spad" 1454509 1454517 1455046 1455175) (-974 "ROIRC.spad" 1453590 1453621 1454499 1454504) (-973 "RNS.spad" 1452567 1452575 1453492 1453585) (-972 "RNS.spad" 1451630 1451640 1452557 1452562) (-971 "RNGBIND.spad" 1450791 1450804 1451585 1451590) (-970 "RNG.spad" 1450527 1450535 1450781 1450786) (-969 "RMODULE.spad" 1450309 1450319 1450517 1450522) (-968 "RMCAT2.spad" 1449730 1449786 1450299 1450304) (-967 "RMATRIX.spad" 1448540 1448558 1448882 1448921) (-966 "RMATCAT.spad" 1444120 1444150 1448496 1448535) (-965 "RMATCAT.spad" 1439590 1439622 1443968 1443973) (-964 "RLINSET.spad" 1439295 1439305 1439580 1439585) (-963 "RINTERP.spad" 1439184 1439203 1439285 1439290) (-962 "RING.spad" 1438655 1438663 1439164 1439179) (-961 "RING.spad" 1438134 1438144 1438645 1438650) (-960 "RIDIST.spad" 1437527 1437535 1438124 1438129) (-959 "RGCHAIN.spad" 1436082 1436097 1436975 1437002) (-958 "RGBCSPC.spad" 1435872 1435883 1436072 1436077) (-957 "RGBCMDL.spad" 1435435 1435446 1435862 1435867) (-956 "RFFACTOR.spad" 1434898 1434908 1435425 1435430) (-955 "RFFACT.spad" 1434634 1434645 1434888 1434893) (-954 "RFDIST.spad" 1433631 1433639 1434624 1434629) (-953 "RF.spad" 1431306 1431316 1433621 1433626) (-952 "RETSOL.spad" 1430726 1430738 1431296 1431301) (-951 "RETRACT.spad" 1430155 1430165 1430716 1430721) (-950 "RETRACT.spad" 1429582 1429594 1430145 1430150) (-949 "RETAST.spad" 1429395 1429403 1429572 1429577) (-948 "RESRING.spad" 1428743 1428789 1429333 1429390) (-947 "RESLATC.spad" 1428068 1428078 1428733 1428738) (-946 "REPSQ.spad" 1427800 1427810 1428058 1428063) (-945 "REPDB.spad" 1427508 1427518 1427790 1427795) (-944 "REP2.spad" 1417223 1417233 1427350 1427355) (-943 "REP1.spad" 1411444 1411454 1417173 1417178) (-942 "REP.spad" 1408999 1409007 1411434 1411439) (-941 "REGSET.spad" 1406825 1406841 1408633 1408660) (-940 "REF.spad" 1406344 1406354 1406815 1406820) (-939 "REDORDER.spad" 1405551 1405567 1406334 1406339) (-938 "RECLOS.spad" 1404448 1404467 1405151 1405244) (-937 "REALSOLV.spad" 1403589 1403597 1404438 1404443) (-936 "REAL0Q.spad" 1400888 1400902 1403579 1403584) (-935 "REAL0.spad" 1397733 1397747 1400878 1400883) (-934 "REAL.spad" 1397606 1397614 1397723 1397728) (-933 "RDUCEAST.spad" 1397328 1397336 1397596 1397601) (-932 "RDIV.spad" 1396984 1397008 1397318 1397323) (-931 "RDIST.spad" 1396552 1396562 1396974 1396979) (-930 "RDETRS.spad" 1395417 1395434 1396542 1396547) (-929 "RDETR.spad" 1393557 1393574 1395407 1395412) (-928 "RDEEFS.spad" 1392657 1392673 1393547 1393552) (-927 "RDEEF.spad" 1391668 1391684 1392647 1392652) (-926 "RCFIELD.spad" 1388887 1388895 1391570 1391663) (-925 "RCFIELD.spad" 1386192 1386202 1388877 1388882) (-924 "RCAGG.spad" 1384129 1384139 1386182 1386187) (-923 "RCAGG.spad" 1381993 1382005 1384048 1384053) (-922 "RATRET.spad" 1381354 1381364 1381983 1381988) (-921 "RATFACT.spad" 1381047 1381058 1381344 1381349) (-920 "RANDSRC.spad" 1380367 1380375 1381037 1381042) (-919 "RADUTIL.spad" 1380124 1380132 1380357 1380362) (-918 "RADIX.spad" 1377169 1377182 1378714 1378807) (-917 "RADFF.spad" 1375086 1375122 1375204 1375360) (-916 "RADCAT.spad" 1374682 1374690 1375076 1375081) (-915 "RADCAT.spad" 1374276 1374286 1374672 1374677) (-914 "QUEUE.spad" 1373690 1373700 1373948 1373975) (-913 "QUATCT2.spad" 1373311 1373329 1373680 1373685) (-912 "QUATCAT.spad" 1371482 1371492 1373241 1373306) (-911 "QUATCAT.spad" 1369418 1369430 1371179 1371184) (-910 "QUAT.spad" 1368025 1368035 1368367 1368432) (-909 "QUAGG.spad" 1366859 1366869 1367993 1368020) (-908 "QQUTAST.spad" 1366628 1366636 1366849 1366854) (-907 "QFORM.spad" 1366247 1366261 1366618 1366623) (-906 "QFCAT2.spad" 1365940 1365956 1366237 1366242) (-905 "QFCAT.spad" 1364643 1364653 1365842 1365935) (-904 "QFCAT.spad" 1362979 1362991 1364180 1364185) (-903 "QEQUAT.spad" 1362538 1362546 1362969 1362974) (-902 "QCMPACK.spad" 1357453 1357472 1362528 1362533) (-901 "QALGSET2.spad" 1355449 1355467 1357443 1357448) (-900 "QALGSET.spad" 1351554 1351586 1355363 1355368) (-899 "PWFFINTB.spad" 1348970 1348991 1351544 1351549) (-898 "PUSHVAR.spad" 1348309 1348328 1348960 1348965) (-897 "PTRANFN.spad" 1344445 1344455 1348299 1348304) (-896 "PTPACK.spad" 1341533 1341543 1344435 1344440) (-895 "PTFUNC2.spad" 1341356 1341370 1341523 1341528) (-894 "PTCAT.spad" 1340611 1340621 1341324 1341351) (-893 "PSQFR.spad" 1339926 1339950 1340601 1340606) (-892 "PSEUDLIN.spad" 1338812 1338822 1339916 1339921) (-891 "PSETPK.spad" 1325517 1325533 1338690 1338695) (-890 "PSETCAT.spad" 1319917 1319940 1325497 1325512) (-889 "PSETCAT.spad" 1314291 1314316 1319873 1319878) (-888 "PSCURVE.spad" 1313290 1313298 1314281 1314286) (-887 "PSCAT.spad" 1312073 1312102 1313188 1313285) (-886 "PSCAT.spad" 1310946 1310977 1312063 1312068) (-885 "PRTITION.spad" 1309644 1309652 1310936 1310941) (-884 "PRTDAST.spad" 1309363 1309371 1309634 1309639) (-883 "PRS.spad" 1298981 1298998 1309319 1309324) (-882 "PRQAGG.spad" 1298416 1298426 1298949 1298976) (-881 "PROPLOG.spad" 1298020 1298028 1298406 1298411) (-880 "PROPFUN2.spad" 1297643 1297656 1298010 1298015) (-879 "PROPFUN1.spad" 1297049 1297060 1297633 1297638) (-878 "PROPFRML.spad" 1295617 1295628 1297039 1297044) (-877 "PROPERTY.spad" 1295113 1295121 1295607 1295612) (-876 "PRODUCT.spad" 1292810 1292822 1293094 1293149) (-875 "PRINT.spad" 1292562 1292570 1292800 1292805) (-874 "PRIMES.spad" 1290823 1290833 1292552 1292557) (-873 "PRIMELT.spad" 1288944 1288958 1290813 1290818) (-872 "PRIMCAT.spad" 1288587 1288595 1288934 1288939) (-871 "PRIMARR2.spad" 1287354 1287366 1288577 1288582) (-870 "PRIMARR.spad" 1286409 1286419 1286579 1286606) (-869 "PREASSOC.spad" 1285791 1285803 1286399 1286404) (-868 "PR.spad" 1284309 1284321 1285008 1285135) (-867 "PPCURVE.spad" 1283446 1283454 1284299 1284304) (-866 "PORTNUM.spad" 1283237 1283245 1283436 1283441) (-865 "POLYROOT.spad" 1282086 1282108 1283193 1283198) (-864 "POLYLIFT.spad" 1281351 1281374 1282076 1282081) (-863 "POLYCATQ.spad" 1279477 1279499 1281341 1281346) (-862 "POLYCAT.spad" 1272979 1273000 1279345 1279472) (-861 "POLYCAT.spad" 1266001 1266024 1272369 1272374) (-860 "POLY2UP.spad" 1265453 1265467 1265991 1265996) (-859 "POLY2.spad" 1265050 1265062 1265443 1265448) (-858 "POLY.spad" 1262718 1262728 1263233 1263360) (-857 "POLUTIL.spad" 1261683 1261712 1262674 1262679) (-856 "POLTOPOL.spad" 1260431 1260446 1261673 1261678) (-855 "POINT.spad" 1259314 1259324 1259401 1259428) (-854 "PNTHEORY.spad" 1256016 1256024 1259304 1259309) (-853 "PMTOOLS.spad" 1254791 1254805 1256006 1256011) (-852 "PMSYM.spad" 1254340 1254350 1254781 1254786) (-851 "PMQFCAT.spad" 1253931 1253945 1254330 1254335) (-850 "PMPREDFS.spad" 1253393 1253415 1253921 1253926) (-849 "PMPRED.spad" 1252880 1252894 1253383 1253388) (-848 "PMPLCAT.spad" 1251957 1251975 1252809 1252814) (-847 "PMLSAGG.spad" 1251542 1251556 1251947 1251952) (-846 "PMKERNEL.spad" 1251121 1251133 1251532 1251537) (-845 "PMINS.spad" 1250701 1250711 1251111 1251116) (-844 "PMFS.spad" 1250278 1250296 1250691 1250696) (-843 "PMDOWN.spad" 1249568 1249582 1250268 1250273) (-842 "PMASSFS.spad" 1248543 1248559 1249558 1249563) (-841 "PMASS.spad" 1247561 1247569 1248533 1248538) (-840 "PLOTTOOL.spad" 1247341 1247349 1247551 1247556) (-839 "PLOT3D.spad" 1243805 1243813 1247331 1247336) (-838 "PLOT1.spad" 1242978 1242988 1243795 1243800) (-837 "PLOT.spad" 1237901 1237909 1242968 1242973) (-836 "PLEQN.spad" 1225303 1225330 1237891 1237896) (-835 "PINTERPA.spad" 1225087 1225103 1225293 1225298) (-834 "PINTERP.spad" 1224709 1224728 1225077 1225082) (-833 "PID.spad" 1223683 1223691 1224635 1224704) (-832 "PICOERCE.spad" 1223340 1223350 1223673 1223678) (-831 "PI.spad" 1222957 1222965 1223314 1223335) (-830 "PGROEB.spad" 1221566 1221580 1222947 1222952) (-829 "PGE.spad" 1213239 1213247 1221556 1221561) (-828 "PGCD.spad" 1212193 1212210 1213229 1213234) (-827 "PFRPAC.spad" 1211342 1211352 1212183 1212188) (-826 "PFR.spad" 1208045 1208055 1211244 1211337) (-825 "PFOTOOLS.spad" 1207303 1207319 1208035 1208040) (-824 "PFOQ.spad" 1206673 1206691 1207293 1207298) (-823 "PFO.spad" 1206092 1206119 1206663 1206668) (-822 "PFECAT.spad" 1203802 1203810 1206018 1206087) (-821 "PFECAT.spad" 1201540 1201550 1203758 1203763) (-820 "PFBRU.spad" 1199428 1199440 1201530 1201535) (-819 "PFBR.spad" 1196988 1197011 1199418 1199423) (-818 "PF.spad" 1196562 1196574 1196793 1196886) (-817 "PERMGRP.spad" 1191332 1191342 1196552 1196557) (-816 "PERMCAT.spad" 1189993 1190003 1191312 1191327) (-815 "PERMAN.spad" 1188549 1188563 1189983 1189988) (-814 "PERM.spad" 1184359 1184369 1188382 1188397) (-813 "PENDTREE.spad" 1183773 1183783 1184053 1184058) (-812 "PDSPC.spad" 1182586 1182596 1183763 1183768) (-811 "PDSPC.spad" 1181397 1181409 1182576 1182581) (-810 "PDRING.spad" 1181239 1181249 1181377 1181392) (-809 "PDMOD.spad" 1181055 1181067 1181207 1181234) (-808 "PDECOMP.spad" 1180525 1180542 1181045 1181050) (-807 "PDDOM.spad" 1179963 1179976 1180515 1180520) (-806 "PDDOM.spad" 1179399 1179414 1179953 1179958) (-805 "PCOMP.spad" 1179252 1179265 1179389 1179394) (-804 "PBWLB.spad" 1177850 1177867 1179242 1179247) (-803 "PATTERN2.spad" 1177588 1177600 1177840 1177845) (-802 "PATTERN1.spad" 1175932 1175948 1177578 1177583) (-801 "PATTERN.spad" 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"INT16.spad" 753621 753629 753732 753737) (-484 "INT.spad" 753147 753155 753487 753616) (-483 "INS.spad" 750650 750658 753049 753142) (-482 "INS.spad" 748239 748249 750640 750645) (-481 "INPSIGN.spad" 747709 747722 748229 748234) (-480 "INPRODPF.spad" 746805 746824 747699 747704) (-479 "INPRODFF.spad" 745893 745917 746795 746800) (-478 "INNMFACT.spad" 744868 744885 745883 745888) (-477 "INMODGCD.spad" 744372 744402 744858 744863) (-476 "INFSP.spad" 742669 742691 744362 744367) (-475 "INFPROD0.spad" 741749 741768 742659 742664) (-474 "INFORM1.spad" 741374 741384 741739 741744) (-473 "INFORM.spad" 738585 738593 741364 741369) (-472 "INFINITY.spad" 738137 738145 738575 738580) (-471 "INETCLTS.spad" 738114 738122 738127 738132) (-470 "INEP.spad" 736660 736682 738104 738109) (-469 "INDE.spad" 736309 736326 736570 736575) (-468 "INCRMAPS.spad" 735746 735756 736299 736304) (-467 "INBFILE.spad" 734842 734850 735736 735741) (-466 "INBFF.spad" 730692 730703 734832 734837) (-465 "INBCON.spad" 728958 728966 730682 730687) (-464 "INBCON.spad" 727222 727232 728948 728953) (-463 "INAST.spad" 726883 726891 727212 727217) (-462 "IMPTAST.spad" 726591 726599 726873 726878) (-461 "IMATRIX.spad" 725601 725627 726113 726140) (-460 "IMATQF.spad" 724695 724739 725557 725562) (-459 "IMATLIN.spad" 723316 723340 724651 724656) (-458 "IIARRAY2.spad" 722785 722823 722988 723015) (-457 "IFF.spad" 722198 722214 722469 722562) (-456 "IFAST.spad" 721812 721820 722188 722193) (-455 "IFARRAY.spad" 719339 719354 721037 721064) (-454 "IFAMON.spad" 719201 719218 719295 719300) (-453 "IEVALAB.spad" 718614 718626 719191 719196) (-452 "IEVALAB.spad" 718025 718039 718604 718609) (-451 "indexedp.spad" 717581 717593 718015 718020) (-450 "IDPOAMS.spad" 717259 717271 717493 717498) (-449 "IDPOAM.spad" 716901 716913 717171 717176) (-448 "IDPO.spad" 716636 716648 716813 716818) (-447 "IDPC.spad" 715365 715377 716626 716631) (-446 "IDPAM.spad" 715032 715044 715277 715282) (-445 "IDPAG.spad" 714701 714713 714944 714949) (-444 "IDENT.spad" 714353 714361 714691 714696) (-443 "catdef.spad" 714124 714135 714236 714348) (-442 "IDECOMP.spad" 711363 711381 714114 714119) (-441 "IDEAL.spad" 706325 706364 711311 711316) (-440 "ICDEN.spad" 705538 705554 706315 706320) (-439 "ICARD.spad" 704931 704939 705528 705533) (-438 "IBPTOOLS.spad" 703538 703555 704921 704926) (-437 "IBITS.spad" 703051 703064 703184 703211) (-436 "IBATOOL.spad" 700036 700055 703041 703046) (-435 "IBACHIN.spad" 698543 698558 700026 700031) (-434 "IARRAY2.spad" 697604 697630 698215 698242) (-433 "IARRAY1.spad" 696683 696698 696829 696856) (-432 "IAN.spad" 695065 695073 696514 696607) (-431 "IALGFACT.spad" 694676 694709 695055 695060) (-430 "HYPCAT.spad" 694100 694108 694666 694671) (-429 "HYPCAT.spad" 693522 693532 694090 694095) (-428 "HOSTNAME.spad" 693338 693346 693512 693517) (-427 "HOMOTOP.spad" 693081 693091 693328 693333) (-426 "HOAGG.spad" 690363 690373 693071 693076) (-425 "HOAGG.spad" 687395 687407 690105 690110) (-424 "HEXADEC.spad" 685620 685628 685985 686078) (-423 "HEUGCD.spad" 684711 684722 685610 685615) (-422 "HELLFDIV.spad" 684317 684341 684701 684706) (-421 "HEAP.spad" 683774 683784 683989 684016) (-420 "HEADAST.spad" 683315 683323 683764 683769) (-419 "HDP.spad" 672948 672964 673325 673422) (-418 "HDMP.spad" 670495 670510 671111 671238) (-417 "HB.spad" 668770 668778 670485 670490) (-416 "HASHTBL.spad" 667104 667135 667315 667342) (-415 "HASAST.spad" 666820 666828 667094 667099) (-414 "HACKPI.spad" 666311 666319 666722 666815) (-413 "GTSET.spad" 665238 665254 665945 665972) (-412 "GSTBL.spad" 663621 663656 663795 663810) (-411 "GSERIES.spad" 660993 661020 661812 661961) (-410 "GROUP.spad" 660266 660274 660973 660988) (-409 "GROUP.spad" 659547 659557 660256 660261) (-408 "GROEBSOL.spad" 658041 658062 659537 659542) (-407 "GRMOD.spad" 656622 656634 658031 658036) (-406 "GRMOD.spad" 655201 655215 656612 656617) (-405 "GRIMAGE.spad" 648114 648122 655191 655196) (-404 "GRDEF.spad" 646493 646501 648104 648109) (-403 "GRAY.spad" 644964 644972 646483 646488) (-402 "GRALG.spad" 644059 644071 644954 644959) (-401 "GRALG.spad" 643152 643166 644049 644054) (-400 "GPOLSET.spad" 642610 642633 642822 642849) (-399 "GOSPER.spad" 641887 641905 642600 642605) (-398 "GMODPOL.spad" 641035 641062 641855 641882) (-397 "GHENSEL.spad" 640118 640132 641025 641030) (-396 "GENUPS.spad" 636411 636424 640108 640113) (-395 "GENUFACT.spad" 635988 635998 636401 636406) (-394 "GENPGCD.spad" 635590 635607 635978 635983) (-393 "GENMFACT.spad" 635042 635061 635580 635585) (-392 "GENEEZ.spad" 633001 633014 635032 635037) (-391 "GDMP.spad" 630390 630407 631164 631291) (-390 "GCNAALG.spad" 624313 624340 630184 630251) (-389 "GCDDOM.spad" 623505 623513 624239 624308) (-388 "GCDDOM.spad" 622759 622769 623495 623500) (-387 "GBINTERN.spad" 618779 618817 622749 622754) (-386 "GBF.spad" 614562 614600 618769 618774) (-385 "GBEUCLID.spad" 612444 612482 614552 614557) (-384 "GB.spad" 609970 610008 612400 612405) (-383 "GAUSSFAC.spad" 609283 609291 609960 609965) (-382 "GALUTIL.spad" 607609 607619 609239 609244) (-381 "GALPOLYU.spad" 606063 606076 607599 607604) (-380 "GALFACTU.spad" 604276 604295 606053 606058) (-379 "GALFACT.spad" 594489 594500 604266 604271) (-378 "FUNDESC.spad" 594167 594175 594479 594484) (-377 "FUNCTION.spad" 594016 594028 594157 594162) (-376 "FT.spad" 592316 592324 594006 594011) (-375 "FSUPFACT.spad" 591230 591249 592266 592271) (-374 "FST.spad" 589316 589324 591220 591225) (-373 "FSRED.spad" 588796 588812 589306 589311) (-372 "FSPRMELT.spad" 587662 587678 588753 588758) (-371 "FSPECF.spad" 585753 585769 587652 587657) (-370 "FSINT.spad" 585413 585429 585743 585748) (-369 "FSERIES.spad" 584604 584616 585233 585332) (-368 "FSCINT.spad" 583921 583937 584594 584599) (-367 "FSAGG2.spad" 582656 582672 583911 583916) (-366 "FSAGG.spad" 581773 581783 582612 582651) (-365 "FSAGG.spad" 580852 580864 581693 581698) (-364 "FS2UPS.spad" 575367 575401 580842 580847) (-363 "FS2EXPXP.spad" 574508 574531 575357 575362) (-362 "FS2.spad" 574163 574179 574498 574503) (-361 "FS.spad" 568435 568445 573942 574158) (-360 "FS.spad" 562509 562521 568018 568023) (-359 "FRUTIL.spad" 561463 561473 562499 562504) (-358 "FRNAALG.spad" 556740 556750 561405 561458) (-357 "FRNAALG.spad" 552029 552041 556696 556701) (-356 "FRNAAF2.spad" 551477 551495 552019 552024) (-355 "FRMOD.spad" 550885 550915 551406 551411) (-354 "FRIDEAL2.spad" 550489 550521 550875 550880) (-353 "FRIDEAL.spad" 549714 549735 550469 550484) (-352 "FRETRCT.spad" 549233 549243 549704 549709) (-351 "FRETRCT.spad" 548659 548671 549132 549137) (-350 "FRAMALG.spad" 547039 547052 548615 548654) (-349 "FRAMALG.spad" 545451 545466 547029 547034) (-348 "FRAC2.spad" 545056 545068 545441 545446) (-347 "FRAC.spad" 543043 543053 543430 543603) (-346 "FR2.spad" 542379 542391 543033 543038) (-345 "FR.spad" 536167 536177 541440 541509) (-344 "FPS.spad" 533006 533014 536057 536162) (-343 "FPS.spad" 529873 529883 532926 532931) (-342 "FPC.spad" 528919 528927 529775 529868) (-341 "FPC.spad" 528051 528061 528909 528914) (-340 "FPATMAB.spad" 527813 527823 528041 528046) (-339 "FPARFRAC.spad" 526655 526672 527803 527808) (-338 "FORDER.spad" 526346 526370 526645 526650) (-337 "FNLA.spad" 525770 525792 526314 526341) (-336 "FNCAT.spad" 524365 524373 525760 525765) (-335 "FNAME.spad" 524257 524265 524355 524360) (-334 "FMONOID.spad" 523938 523948 524213 524218) (-333 "FMONCAT.spad" 521107 521117 523928 523933) (-332 "FMCAT.spad" 518783 518801 521075 521102) (-331 "FM1.spad" 518148 518160 518717 518744) (-330 "FM.spad" 517763 517775 518002 518029) (-329 "FLOATRP.spad" 515506 515520 517753 517758) (-328 "FLOATCP.spad" 512945 512959 515496 515501) (-327 "FLOAT.spad" 510036 510044 512811 512940) (-326 "FLINEXP.spad" 509758 509768 510026 510031) (-325 "FLINEXP.spad" 509437 509449 509707 509712) (-324 "FLASORT.spad" 508763 508775 509427 509432) (-323 "FLALG.spad" 506433 506452 508689 508758) (-322 "FLAGG2.spad" 505150 505166 506423 506428) (-321 "FLAGG.spad" 502216 502226 505130 505145) (-320 "FLAGG.spad" 499183 499195 502099 502104) (-319 "FINRALG.spad" 497268 497281 499139 499178) (-318 "FINRALG.spad" 495279 495294 497152 497157) (-317 "FINITE.spad" 494431 494439 495269 495274) (-316 "FINITE.spad" 493581 493591 494421 494426) (-315 "FINAALG.spad" 482766 482776 493523 493576) (-314 "FINAALG.spad" 471963 471975 482722 482727) (-313 "FILECAT.spad" 470497 470514 471953 471958) (-312 "FILE.spad" 470080 470090 470487 470492) (-311 "FIELD.spad" 469486 469494 469982 470075) (-310 "FIELD.spad" 468978 468988 469476 469481) (-309 "FGROUP.spad" 467641 467651 468958 468973) (-308 "FGLMICPK.spad" 466436 466451 467631 467636) (-307 "FFX.spad" 465822 465837 466155 466248) (-306 "FFSLPE.spad" 465333 465354 465812 465817) (-305 "FFPOLY2.spad" 464393 464410 465323 465328) (-304 "FFPOLY.spad" 455735 455746 464383 464388) (-303 "FFP.spad" 455143 455163 455454 455547) (-302 "FFNBX.spad" 453666 453686 454862 454955) (-301 "FFNBP.spad" 452190 452207 453385 453478) (-300 "FFNB.spad" 450658 450679 451874 451967) (-299 "FFINTBAS.spad" 448172 448191 450648 450653) (-298 "FFIELDC.spad" 445757 445765 448074 448167) (-297 "FFIELDC.spad" 443428 443438 445747 445752) (-296 "FFHOM.spad" 442200 442217 443418 443423) (-295 "FFF.spad" 439643 439654 442190 442195) (-294 "FFCGX.spad" 438501 438521 439362 439455) (-293 "FFCGP.spad" 437401 437421 438220 438313) (-292 "FFCG.spad" 436196 436217 437085 437178) (-291 "FFCAT2.spad" 435943 435983 436186 436191) (-290 "FFCAT.spad" 429108 429130 435782 435938) (-289 "FFCAT.spad" 422352 422376 429028 429033) (-288 "FF.spad" 421803 421819 422036 422129) (-287 "FEVALAB.spad" 421511 421521 421793 421798) (-286 "FEVALAB.spad" 420995 421007 421279 421284) (-285 "FDIVCAT.spad" 419091 419115 420985 420990) (-284 "FDIVCAT.spad" 417185 417211 419081 419086) (-283 "FDIV2.spad" 416841 416881 417175 417180) (-282 "FDIV.spad" 416299 416323 416831 416836) (-281 "FCTRDATA.spad" 415307 415315 416289 416294) (-280 "FCOMP.spad" 414686 414696 415297 415302) (-279 "FAXF.spad" 407721 407735 414588 414681) (-278 "FAXF.spad" 400808 400824 407677 407682) (-277 "FARRAY.spad" 399000 399010 400033 400060) (-276 "FAMR.spad" 397144 397156 398898 398995) (-275 "FAMR.spad" 395272 395286 397028 397033) (-274 "FAMONOID.spad" 394956 394966 395226 395231) (-273 "FAMONC.spad" 393276 393288 394946 394951) (-272 "FAGROUP.spad" 392916 392926 393172 393199) (-271 "FACUTIL.spad" 391128 391145 392906 392911) (-270 "FACTFUNC.spad" 390330 390340 391118 391123) (-269 "EXPUPXS.spad" 387222 387245 388521 388670) (-268 "EXPRTUBE.spad" 384510 384518 387212 387217) (-267 "EXPRODE.spad" 381678 381694 384500 384505) (-266 "EXPR2UPS.spad" 377800 377813 381668 381673) (-265 "EXPR2.spad" 377505 377517 377790 377795) (-264 "EXPR.spad" 373150 373160 373864 374151) (-263 "EXPEXPAN.spad" 370095 370120 370727 370820) (-262 "EXITAST.spad" 369831 369839 370085 370090) (-261 "EXIT.spad" 369502 369510 369821 369826) (-260 "EVALCYC.spad" 368962 368976 369492 369497) (-259 "EVALAB.spad" 368542 368552 368952 368957) (-258 "EVALAB.spad" 368120 368132 368532 368537) (-257 "EUCDOM.spad" 365710 365718 368046 368115) (-256 "EUCDOM.spad" 363362 363372 365700 365705) (-255 "ES2.spad" 362875 362891 363352 363357) (-254 "ES1.spad" 362445 362461 362865 362870) (-253 "ES.spad" 355316 355324 362435 362440) (-252 "ES.spad" 348108 348118 355229 355234) (-251 "ERROR.spad" 345435 345443 348098 348103) (-250 "EQTBL.spad" 343771 343793 343980 344007) (-249 "EQ2.spad" 343489 343501 343761 343766) (-248 "EQ.spad" 338395 338405 341190 341296) (-247 "EP.spad" 334721 334731 338385 338390) (-246 "ENV.spad" 333399 333407 334711 334716) (-245 "ENTIRER.spad" 333067 333075 333343 333394) (-244 "EMR.spad" 332355 332396 332993 333062) (-243 "ELTAGG.spad" 330609 330628 332345 332350) (-242 "ELTAGG.spad" 328827 328848 330565 330570) (-241 "ELTAB.spad" 328302 328315 328817 328822) (-240 "ELFUTS.spad" 327737 327756 328292 328297) (-239 "ELEMFUN.spad" 327426 327434 327727 327732) (-238 "ELEMFUN.spad" 327113 327123 327416 327421) (-237 "ELAGG.spad" 325084 325094 327093 327108) (-236 "ELAGG.spad" 322992 323004 325003 325008) (-235 "ELABOR.spad" 322338 322346 322982 322987) (-234 "ELABEXPR.spad" 321270 321278 322328 322333) (-233 "EFUPXS.spad" 318046 318076 321226 321231) (-232 "EFULS.spad" 314882 314905 318002 318007) (-231 "EFSTRUC.spad" 312897 312913 314872 314877) (-230 "EF.spad" 307673 307689 312887 312892) (-229 "EAB.spad" 305973 305981 307663 307668) (-228 "DVARCAT.spad" 302979 302989 305963 305968) (-227 "DVARCAT.spad" 299983 299995 302969 302974) (-226 "DSMP.spad" 297716 297730 298021 298148) (-225 "DSEXT.spad" 297018 297028 297706 297711) (-224 "DSEXT.spad" 296240 296252 296930 296935) (-223 "DROPT1.spad" 295905 295915 296230 296235) (-222 "DROPT0.spad" 290770 290778 295895 295900) (-221 "DROPT.spad" 284729 284737 290760 290765) (-220 "DRAWPT.spad" 282902 282910 284719 284724) (-219 "DRAWHACK.spad" 282210 282220 282892 282897) (-218 "DRAWCX.spad" 279688 279696 282200 282205) (-217 "DRAWCURV.spad" 279235 279250 279678 279683) (-216 "DRAWCFUN.spad" 268767 268775 279225 279230) (-215 "DRAW.spad" 261643 261656 268757 268762) (-214 "DQAGG.spad" 259821 259831 261611 261638) (-213 "DPOLCAT.spad" 255178 255194 259689 259816) (-212 "DPOLCAT.spad" 250621 250639 255134 255139) (-211 "DPMO.spad" 243324 243340 243462 243668) (-210 "DPMM.spad" 236040 236058 236165 236371) (-209 "DOMTMPLT.spad" 235811 235819 236030 236035) (-208 "DOMCTOR.spad" 235566 235574 235801 235806) (-207 "DOMAIN.spad" 234677 234685 235556 235561) (-206 "DMP.spad" 232270 232285 232840 232967) (-205 "DMEXT.spad" 232137 232147 232238 232265) (-204 "DLP.spad" 231497 231507 232127 232132) (-203 "DLIST.spad" 230118 230128 230722 230749) (-202 "DLAGG.spad" 228535 228545 230108 230113) (-201 "DIVRING.spad" 228077 228085 228479 228530) (-200 "DIVRING.spad" 227663 227673 228067 228072) (-199 "DISPLAY.spad" 225853 225861 227653 227658) 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\ No newline at end of file
diff --git a/src/share/algebra/category.daase b/src/share/algebra/category.daase
index 6163ed50..e42ee62d 100644
--- a/src/share/algebra/category.daase
+++ b/src/share/algebra/category.daase
@@ -1,279 +1,279 @@
 
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 (((|#1| |#2|) . T)) 
 (((|#2|) |has| |#2| (-146))) 
 (((|#2| |#2|) . T)) 
@@ -4024,20 +4025,20 @@
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-((((-739 |#1|)) . T)) 
+((((-773)) . T)) 
+(((|#2|) . T) (($) . T) (((-484)) . T)) 
+(((|#2|) . T) (((-484)) . T) (((-740 |#1|)) . T)) 
+((((-740 |#1|)) . T)) 
 (((|#1| |#2|) . T)) 
-((((-884)) . T)) 
-((((-884)) . T)) 
-((((-884)) . T) (((-772)) . T)) 
-((((-483)) . T)) 
+((((-885)) . T)) 
+((((-885)) . T)) 
+((((-885)) . T) (((-773)) . T)) 
+((((-484)) . T)) 
 ((($ $) . T)) 
 ((($) . T)) 
 ((($) . T)) 
-((((-772)) . T)) 
-((((-483)) . T) (($) . T)) 
+((((-773)) . T)) 
+((((-484)) . T) (($) . T)) 
 ((($) . T)) 
-((((-483)) . T)) 
-(((-1207 . -146) T) ((-1207 . -555) 199241) ((-1207 . -969) T) ((-1207 . -1024) T) ((-1207 . -1059) T) ((-1207 . -663) T) ((-1207 . -961) T) ((-1207 . -590) 199228) ((-1207 . -588) 199200) ((-1207 . -104) T) ((-1207 . -25) T) ((-1207 . -72) T) ((-1207 . -13) T) ((-1207 . -1127) T) ((-1207 . -552) 199182) ((-1207 . -1012) T) ((-1207 . -23) T) ((-1207 . -21) T) ((-1207 . -968) 199169) ((-1207 . -963) 199156) ((-1207 . -82) 199141) ((-1207 . -317) T) ((-1207 . -553) 199123) ((-1207 . -1064) T) ((-1203 . -1012) T) ((-1203 . -552) 199090) ((-1203 . -1127) T) ((-1203 . -13) T) ((-1203 . -72) T) ((-1203 . -427) 199072) ((-1203 . -555) 199054) ((-1202 . -1200) 199033) ((-1202 . -950) 199010) ((-1202 . -555) 198959) ((-1202 . -961) T) ((-1202 . -663) T) ((-1202 . -1059) T) ((-1202 . -1024) T) ((-1202 . -969) T) ((-1202 . -21) T) ((-1202 . -588) 198918) ((-1202 . -23) T) ((-1202 . -1012) T) ((-1202 . -552) 198900) ((-1202 . -1127) T) ((-1202 . -13) T) ((-1202 . -72) T) ((-1202 . -25) T) ((-1202 . -104) T) ((-1202 . -590) 198874) ((-1202 . -1192) 198858) ((-1202 . -654) 198828) ((-1202 . -582) 198798) ((-1202 . -968) 198782) ((-1202 . -963) 198766) ((-1202 . -82) 198745) ((-1202 . -38) 198715) ((-1202 . -1197) 198694) ((-1201 . -961) T) ((-1201 . -663) T) ((-1201 . -1059) T) ((-1201 . -1024) T) ((-1201 . -969) T) ((-1201 . -21) T) ((-1201 . -588) 198653) ((-1201 . -23) T) ((-1201 . -1012) T) ((-1201 . -552) 198635) ((-1201 . -1127) T) ((-1201 . -13) T) ((-1201 . -72) T) ((-1201 . -25) T) ((-1201 . -104) T) ((-1201 . -590) 198609) ((-1201 . -555) 198565) ((-1201 . -1192) 198549) ((-1201 . -654) 198519) ((-1201 . -582) 198489) ((-1201 . -968) 198473) ((-1201 . -963) 198457) ((-1201 . -82) 198436) ((-1201 . -38) 198406) ((-1201 . -332) 198385) ((-1201 . -950) 198369) ((-1199 . -1200) 198345) ((-1199 . -950) 198319) ((-1199 . -555) 198265) ((-1199 . -961) T) ((-1199 . -663) T) ((-1199 . -1059) T) ((-1199 . -1024) T) ((-1199 . -969) T) ((-1199 . -21) T) ((-1199 . -588) 198224) ((-1199 . -23) T) ((-1199 . -1012) T) ((-1199 . -552) 198206) ((-1199 . -1127) T) ((-1199 . -13) T) ((-1199 . -72) T) ((-1199 . -25) T) ((-1199 . -104) T) ((-1199 . -590) 198180) ((-1199 . -1192) 198164) ((-1199 . -654) 198134) ((-1199 . -582) 198104) ((-1199 . -968) 198088) ((-1199 . -963) 198072) ((-1199 . -82) 198051) ((-1199 . -38) 198021) ((-1199 . -1197) 197997) ((-1198 . -1200) 197976) ((-1198 . -950) 197933) ((-1198 . -555) 197862) ((-1198 . -961) T) ((-1198 . -663) T) ((-1198 . -1059) T) ((-1198 . -1024) T) ((-1198 . -969) T) ((-1198 . -21) T) ((-1198 . -588) 197821) ((-1198 . -23) T) ((-1198 . -1012) T) ((-1198 . -552) 197803) ((-1198 . -1127) T) ((-1198 . -13) T) ((-1198 . -72) T) ((-1198 . -25) T) ((-1198 . -104) T) ((-1198 . -590) 197777) ((-1198 . -1192) 197761) ((-1198 . -654) 197731) ((-1198 . -582) 197701) ((-1198 . -968) 197685) ((-1198 . -963) 197669) ((-1198 . -82) 197648) ((-1198 . -38) 197618) ((-1198 . -1197) 197597) ((-1198 . -332) 197569) ((-1193 . -332) 197541) ((-1193 . -555) 197490) ((-1193 . -950) 197467) ((-1193 . -582) 197437) ((-1193 . -654) 197407) ((-1193 . -590) 197381) ((-1193 . -588) 197340) ((-1193 . -104) T) ((-1193 . -25) T) ((-1193 . -72) T) ((-1193 . -13) T) ((-1193 . -1127) T) ((-1193 . -552) 197322) ((-1193 . -1012) T) ((-1193 . -23) T) ((-1193 . -21) T) ((-1193 . -968) 197306) ((-1193 . -963) 197290) ((-1193 . -82) 197269) ((-1193 . -1200) 197248) ((-1193 . -961) T) ((-1193 . -663) T) ((-1193 . -1059) T) ((-1193 . -1024) T) ((-1193 . -969) T) ((-1193 . -1192) 197232) ((-1193 . -38) 197202) ((-1193 . -1197) 197181) ((-1191 . -1122) 197150) ((-1191 . -552) 197112) ((-1191 . -124) 197096) ((-1191 . -34) T) ((-1191 . -13) T) ((-1191 . -1127) T) ((-1191 . -72) T) ((-1191 . -259) 197034) ((-1191 . -452) 196967) ((-1191 . -1012) T) ((-1191 . -426) 196951) ((-1191 . -553) 196912) ((-1191 . -889) 196881) ((-1190 . -961) T) ((-1190 . -663) T) ((-1190 . -1059) T) ((-1190 . -1024) T) ((-1190 . -969) T) ((-1190 . -21) T) ((-1190 . -588) 196826) ((-1190 . -23) T) ((-1190 . -1012) T) ((-1190 . -552) 196795) ((-1190 . -1127) T) ((-1190 . -13) T) ((-1190 . -72) T) ((-1190 . -25) T) ((-1190 . -104) T) ((-1190 . -590) 196755) ((-1190 . -555) 196697) ((-1190 . -427) 196681) ((-1190 . -38) 196651) ((-1190 . -82) 196616) ((-1190 . -963) 196586) ((-1190 . -968) 196556) ((-1190 . -582) 196526) ((-1190 . -654) 196496) ((-1189 . -994) T) ((-1189 . -427) 196477) ((-1189 . -552) 196443) ((-1189 . -555) 196424) ((-1189 . -1012) T) ((-1189 . -1127) T) ((-1189 . -13) T) ((-1189 . -72) T) ((-1189 . -64) T) ((-1188 . -994) T) ((-1188 . -427) 196405) ((-1188 . -552) 196371) ((-1188 . -555) 196352) ((-1188 . -1012) T) ((-1188 . -1127) T) ((-1188 . -13) T) ((-1188 . -72) T) ((-1188 . -64) T) ((-1183 . -552) 196334) ((-1181 . -1012) T) ((-1181 . -552) 196316) ((-1181 . -1127) T) ((-1181 . -13) T) ((-1181 . -72) T) ((-1180 . -1012) T) ((-1180 . -552) 196298) ((-1180 . -1127) T) ((-1180 . -13) T) ((-1180 . -72) T) ((-1177 . -1176) 196282) ((-1177 . -321) 196266) ((-1177 . -759) 196245) ((-1177 . -756) 196224) ((-1177 . -124) 196208) ((-1177 . -34) T) ((-1177 . -13) T) ((-1177 . -1127) T) ((-1177 . -72) 196142) ((-1177 . -552) 196057) ((-1177 . -259) 195995) ((-1177 . -452) 195928) ((-1177 . -1012) 195881) ((-1177 . -426) 195865) ((-1177 . -553) 195826) ((-1177 . -241) 195778) ((-1177 . -538) 195755) ((-1177 . -243) 195732) ((-1177 . -593) 195716) ((-1177 . -19) 195700) ((-1174 . -1012) T) ((-1174 . -552) 195666) ((-1174 . -1127) T) ((-1174 . -13) T) ((-1174 . -72) T) ((-1167 . -1170) 195650) ((-1167 . -190) 195609) ((-1167 . -555) 195491) ((-1167 . -590) 195416) ((-1167 . -588) 195326) ((-1167 . -104) T) ((-1167 . -25) T) ((-1167 . -72) T) ((-1167 . -552) 195308) ((-1167 . -1012) T) ((-1167 . -23) T) ((-1167 . -21) T) ((-1167 . -969) T) ((-1167 . -1024) T) ((-1167 . -1059) T) ((-1167 . -663) T) ((-1167 . -961) T) ((-1167 . -186) 195261) ((-1167 . -13) T) ((-1167 . -1127) T) ((-1167 . -189) 195220) ((-1167 . -241) 195185) ((-1167 . -809) 195098) ((-1167 . -806) 194986) ((-1167 . -811) 194899) ((-1167 . -886) 194869) ((-1167 . -38) 194766) ((-1167 . -82) 194631) ((-1167 . -963) 194517) ((-1167 . -968) 194403) ((-1167 . -582) 194300) ((-1167 . -654) 194197) ((-1167 . -118) 194176) ((-1167 . -120) 194155) ((-1167 . -146) 194109) ((-1167 . -494) 194088) ((-1167 . -245) 194067) ((-1167 . -47) 194044) ((-1167 . -1156) 194021) ((-1167 . -35) 193987) ((-1167 . -66) 193953) ((-1167 . -239) 193919) ((-1167 . -430) 193885) ((-1167 . -1116) 193851) ((-1167 . -1113) 193817) ((-1167 . -915) 193783) ((-1164 . -276) 193727) ((-1164 . -950) 193693) ((-1164 . -352) 193659) ((-1164 . -38) 193516) ((-1164 . -555) 193390) ((-1164 . -590) 193279) ((-1164 . -588) 193153) ((-1164 . -969) T) ((-1164 . -1024) T) ((-1164 . -1059) T) ((-1164 . -663) T) ((-1164 . -961) T) ((-1164 . -82) 193003) ((-1164 . -963) 192892) ((-1164 . -968) 192781) ((-1164 . -21) T) ((-1164 . -23) T) ((-1164 . -1012) T) ((-1164 . -552) 192763) ((-1164 . -1127) T) ((-1164 . -13) T) ((-1164 . -72) T) ((-1164 . -25) T) ((-1164 . -104) T) ((-1164 . -582) 192620) ((-1164 . -654) 192477) ((-1164 . -118) 192438) ((-1164 . -120) 192399) ((-1164 . -146) T) ((-1164 . -494) T) ((-1164 . -245) T) ((-1164 . -47) 192343) ((-1163 . -1162) 192322) ((-1163 . -311) 192301) ((-1163 . -1132) 192280) ((-1163 . -832) 192259) ((-1163 . -494) 192213) ((-1163 . -146) 192147) ((-1163 . -555) 191966) ((-1163 . -654) 191813) ((-1163 . -582) 191660) ((-1163 . -38) 191507) ((-1163 . -389) 191486) ((-1163 . -257) 191465) ((-1163 . -590) 191365) ((-1163 . -588) 191250) ((-1163 . -969) T) ((-1163 . -1024) T) ((-1163 . -1059) T) ((-1163 . -663) T) ((-1163 . -961) T) ((-1163 . -82) 191070) ((-1163 . -963) 190911) ((-1163 . -968) 190752) ((-1163 . -21) T) ((-1163 . -23) T) ((-1163 . -1012) T) ((-1163 . -552) 190734) ((-1163 . -1127) T) ((-1163 . -13) T) ((-1163 . -72) T) ((-1163 . -25) T) ((-1163 . -104) T) ((-1163 . -245) 190688) ((-1163 . -201) 190667) ((-1163 . -915) 190633) ((-1163 . -1113) 190599) ((-1163 . -1116) 190565) ((-1163 . -430) 190531) ((-1163 . -239) 190497) ((-1163 . -66) 190463) ((-1163 . -35) 190429) ((-1163 . -1156) 190399) ((-1163 . -47) 190369) ((-1163 . -120) 190348) ((-1163 . -118) 190327) ((-1163 . -886) 190290) ((-1163 . -811) 190196) ((-1163 . -806) 190100) ((-1163 . -809) 190006) ((-1163 . -241) 189964) ((-1163 . -189) 189916) ((-1163 . -186) 189862) ((-1163 . -190) 189814) ((-1163 . -1160) 189798) ((-1163 . -950) 189782) ((-1158 . -1162) 189743) ((-1158 . -311) 189722) ((-1158 . -1132) 189701) ((-1158 . -832) 189680) ((-1158 . -494) 189634) ((-1158 . -146) 189568) ((-1158 . -555) 189317) ((-1158 . -654) 189164) ((-1158 . -582) 189011) ((-1158 . -38) 188858) ((-1158 . -389) 188837) ((-1158 . -257) 188816) ((-1158 . -590) 188716) ((-1158 . -588) 188601) ((-1158 . -969) T) ((-1158 . -1024) T) ((-1158 . -1059) T) ((-1158 . -663) T) ((-1158 . -961) T) ((-1158 . -82) 188421) ((-1158 . -963) 188262) ((-1158 . -968) 188103) ((-1158 . -21) T) ((-1158 . -23) T) ((-1158 . -1012) T) ((-1158 . -552) 188085) ((-1158 . -1127) T) ((-1158 . -13) T) ((-1158 . -72) T) ((-1158 . -25) T) ((-1158 . -104) T) ((-1158 . -245) 188039) ((-1158 . -201) 188018) ((-1158 . -915) 187984) ((-1158 . -1113) 187950) ((-1158 . -1116) 187916) ((-1158 . -430) 187882) ((-1158 . -239) 187848) ((-1158 . -66) 187814) ((-1158 . -35) 187780) ((-1158 . -1156) 187750) ((-1158 . -47) 187720) ((-1158 . -120) 187699) ((-1158 . -118) 187678) ((-1158 . -886) 187641) ((-1158 . -811) 187547) ((-1158 . -806) 187428) ((-1158 . -809) 187334) ((-1158 . -241) 187292) ((-1158 . -189) 187244) ((-1158 . -186) 187190) ((-1158 . -190) 187142) ((-1158 . -1160) 187126) ((-1158 . -950) 187061) ((-1146 . -1153) 187045) ((-1146 . -1064) 187023) ((-1146 . -553) NIL) ((-1146 . -259) 187010) ((-1146 . -452) 186958) ((-1146 . -276) 186935) ((-1146 . -950) 186818) ((-1146 . -352) 186802) ((-1146 . -38) 186634) ((-1146 . -82) 186439) ((-1146 . -963) 186265) ((-1146 . -968) 186091) ((-1146 . -588) 186001) ((-1146 . -590) 185890) ((-1146 . -582) 185722) ((-1146 . -654) 185554) ((-1146 . -555) 185310) ((-1146 . -118) 185289) ((-1146 . -120) 185268) ((-1146 . -47) 185245) ((-1146 . -326) 185229) ((-1146 . -580) 185177) ((-1146 . -809) 185121) ((-1146 . -806) 185028) ((-1146 . -811) 184939) ((-1146 . -796) NIL) ((-1146 . -821) 184918) ((-1146 . -1132) 184897) ((-1146 . -861) 184867) ((-1146 . -832) 184846) ((-1146 . -494) 184760) ((-1146 . -245) 184674) ((-1146 . -146) 184568) ((-1146 . -389) 184502) ((-1146 . -257) 184481) ((-1146 . -241) 184408) ((-1146 . -190) T) ((-1146 . -104) T) ((-1146 . -25) T) ((-1146 . -72) T) ((-1146 . -552) 184390) ((-1146 . -1012) T) ((-1146 . -23) T) ((-1146 . -21) T) ((-1146 . -969) T) ((-1146 . -1024) T) ((-1146 . -1059) T) ((-1146 . -663) T) ((-1146 . -961) T) ((-1146 . -186) 184377) ((-1146 . -13) T) ((-1146 . -1127) T) ((-1146 . -189) T) ((-1146 . -225) 184361) ((-1146 . -184) 184345) ((-1144 . -1005) 184329) ((-1144 . -557) 184313) ((-1144 . -1012) 184291) ((-1144 . -552) 184258) ((-1144 . -1127) 184236) ((-1144 . -13) 184214) ((-1144 . -72) 184192) ((-1144 . -1006) 184149) ((-1142 . -1141) 184128) ((-1142 . -915) 184094) ((-1142 . -1113) 184060) ((-1142 . -1116) 184026) ((-1142 . -430) 183992) ((-1142 . -239) 183958) ((-1142 . -66) 183924) ((-1142 . -35) 183890) ((-1142 . -1156) 183867) ((-1142 . -47) 183844) ((-1142 . -555) 183599) ((-1142 . -654) 183419) ((-1142 . -582) 183239) ((-1142 . -590) 183050) ((-1142 . -588) 182908) ((-1142 . -968) 182722) ((-1142 . -963) 182536) ((-1142 . -82) 182324) ((-1142 . -38) 182144) ((-1142 . -886) 182114) ((-1142 . -241) 182014) ((-1142 . -1139) 181998) ((-1142 . -969) T) ((-1142 . -1024) T) ((-1142 . -1059) T) ((-1142 . -663) T) ((-1142 . -961) T) ((-1142 . -21) T) ((-1142 . -23) T) ((-1142 . -1012) T) ((-1142 . -552) 181980) ((-1142 . -1127) T) ((-1142 . -13) T) ((-1142 . -72) T) ((-1142 . -25) T) ((-1142 . -104) T) ((-1142 . -118) 181908) ((-1142 . -120) 181836) ((-1142 . -553) 181509) ((-1142 . -184) 181479) ((-1142 . -809) 181333) ((-1142 . -811) 181133) ((-1142 . -806) 180931) ((-1142 . -225) 180901) ((-1142 . -189) 180763) ((-1142 . -186) 180619) ((-1142 . -190) 180527) ((-1142 . -311) 180506) ((-1142 . -1132) 180485) ((-1142 . -832) 180464) ((-1142 . -494) 180418) ((-1142 . -146) 180352) ((-1142 . -389) 180331) ((-1142 . -257) 180310) ((-1142 . -245) 180264) ((-1142 . -201) 180243) ((-1142 . -287) 180213) ((-1142 . -452) 180073) ((-1142 . -259) 180012) ((-1142 . -326) 179982) ((-1142 . -580) 179890) ((-1142 . -340) 179860) ((-1142 . -796) 179733) ((-1142 . -740) 179686) ((-1142 . -714) 179639) ((-1142 . -716) 179592) ((-1142 . -756) 179494) ((-1142 . -759) 179396) ((-1142 . -718) 179349) ((-1142 . -721) 179302) ((-1142 . -755) 179255) ((-1142 . -794) 179225) ((-1142 . -821) 179178) ((-1142 . -933) 179131) ((-1142 . -950) 178920) ((-1142 . -1064) 178872) ((-1142 . -904) 178842) ((-1137 . -1141) 178803) ((-1137 . -915) 178769) ((-1137 . -1113) 178735) ((-1137 . -1116) 178701) ((-1137 . -430) 178667) ((-1137 . -239) 178633) ((-1137 . -66) 178599) ((-1137 . -35) 178565) ((-1137 . -1156) 178542) ((-1137 . -47) 178519) ((-1137 . -555) 178320) ((-1137 . -654) 178122) ((-1137 . -582) 177924) ((-1137 . -590) 177779) ((-1137 . -588) 177619) ((-1137 . -968) 177415) ((-1137 . -963) 177211) ((-1137 . -82) 176963) ((-1137 . -38) 176765) ((-1137 . -886) 176735) ((-1137 . -241) 176563) ((-1137 . -1139) 176547) ((-1137 . -969) T) ((-1137 . -1024) T) ((-1137 . -1059) T) ((-1137 . -663) T) ((-1137 . -961) T) ((-1137 . -21) T) ((-1137 . -23) T) ((-1137 . -1012) T) ((-1137 . -552) 176529) ((-1137 . -1127) T) ((-1137 . -13) T) ((-1137 . -72) T) ((-1137 . -25) T) ((-1137 . -104) T) ((-1137 . -118) 176439) ((-1137 . -120) 176349) ((-1137 . -553) NIL) ((-1137 . -184) 176301) ((-1137 . -809) 176137) ((-1137 . -811) 175901) ((-1137 . -806) 175640) ((-1137 . -225) 175592) ((-1137 . -189) 175418) ((-1137 . -186) 175238) ((-1137 . -190) 175128) ((-1137 . -311) 175107) ((-1137 . -1132) 175086) ((-1137 . -832) 175065) ((-1137 . -494) 175019) ((-1137 . -146) 174953) ((-1137 . -389) 174932) ((-1137 . -257) 174911) ((-1137 . -245) 174865) ((-1137 . -201) 174844) ((-1137 . -287) 174796) ((-1137 . -452) 174530) ((-1137 . -259) 174415) ((-1137 . -326) 174367) ((-1137 . -580) 174319) ((-1137 . -340) 174271) ((-1137 . -796) NIL) ((-1137 . -740) NIL) ((-1137 . -714) NIL) ((-1137 . -716) NIL) ((-1137 . -756) NIL) ((-1137 . -759) NIL) ((-1137 . -718) NIL) ((-1137 . -721) NIL) ((-1137 . -755) NIL) ((-1137 . -794) 174223) ((-1137 . -821) NIL) ((-1137 . -933) NIL) ((-1137 . -950) 174189) ((-1137 . -1064) NIL) ((-1137 . -904) 174141) ((-1136 . -752) T) ((-1136 . -759) T) ((-1136 . -756) T) ((-1136 . -1012) T) ((-1136 . -552) 174123) ((-1136 . -1127) T) ((-1136 . -13) T) ((-1136 . -72) T) ((-1136 . -317) T) ((-1136 . -604) T) ((-1135 . -752) T) ((-1135 . -759) T) ((-1135 . -756) T) ((-1135 . -1012) T) ((-1135 . -552) 174105) ((-1135 . -1127) T) ((-1135 . -13) T) ((-1135 . -72) T) ((-1135 . -317) T) ((-1135 . -604) T) ((-1134 . -752) T) ((-1134 . -759) T) ((-1134 . -756) T) ((-1134 . -1012) T) ((-1134 . -552) 174087) ((-1134 . -1127) T) ((-1134 . -13) T) ((-1134 . -72) T) ((-1134 . -317) T) ((-1134 . -604) T) ((-1133 . -752) T) ((-1133 . -759) T) ((-1133 . -756) T) ((-1133 . -1012) T) ((-1133 . -552) 174069) ((-1133 . -1127) T) ((-1133 . -13) T) ((-1133 . -72) T) ((-1133 . -317) T) ((-1133 . -604) T) ((-1128 . -994) T) ((-1128 . -427) 174050) ((-1128 . -552) 174016) ((-1128 . -555) 173997) ((-1128 . -1012) T) ((-1128 . -1127) T) ((-1128 . -13) T) ((-1128 . -72) T) ((-1128 . -64) T) ((-1125 . -427) 173974) ((-1125 . -552) 173915) ((-1125 . -555) 173892) ((-1125 . -1012) 173870) ((-1125 . -1127) 173848) ((-1125 . -13) 173826) ((-1125 . -72) 173804) ((-1120 . -679) 173780) ((-1120 . -35) 173746) ((-1120 . -66) 173712) ((-1120 . -239) 173678) ((-1120 . -430) 173644) ((-1120 . -1116) 173610) ((-1120 . -1113) 173576) ((-1120 . -915) 173542) ((-1120 . -47) 173511) ((-1120 . -38) 173408) ((-1120 . -582) 173305) ((-1120 . -654) 173202) ((-1120 . -555) 173084) ((-1120 . -245) 173063) ((-1120 . -494) 173042) ((-1120 . -82) 172907) ((-1120 . -963) 172793) ((-1120 . -968) 172679) ((-1120 . -146) 172633) ((-1120 . -120) 172612) ((-1120 . -118) 172591) ((-1120 . -590) 172516) ((-1120 . -588) 172426) ((-1120 . -886) 172387) ((-1120 . -811) 172368) ((-1120 . -1127) T) ((-1120 . -13) T) ((-1120 . -806) 172347) ((-1120 . -961) T) ((-1120 . -663) T) ((-1120 . -1059) T) ((-1120 . -1024) T) ((-1120 . -969) T) ((-1120 . -21) T) ((-1120 . -23) T) ((-1120 . -1012) T) ((-1120 . -552) 172329) ((-1120 . -72) T) ((-1120 . -25) T) ((-1120 . -104) T) ((-1120 . -809) 172310) ((-1120 . -452) 172277) ((-1120 . -259) 172264) ((-1114 . -923) 172248) ((-1114 . -34) T) ((-1114 . -13) T) ((-1114 . -1127) T) ((-1114 . -72) 172202) ((-1114 . -552) 172137) ((-1114 . -259) 172075) ((-1114 . -452) 172008) ((-1114 . -1012) 171986) ((-1114 . -426) 171970) ((-1109 . -313) 171944) ((-1109 . -72) T) ((-1109 . -13) T) ((-1109 . -1127) T) ((-1109 . -552) 171926) ((-1109 . -1012) T) ((-1107 . -1012) T) ((-1107 . -552) 171908) ((-1107 . -1127) T) ((-1107 . -13) T) ((-1107 . -72) T) ((-1107 . -555) 171890) ((-1102 . -747) 171874) ((-1102 . -72) T) ((-1102 . -13) T) ((-1102 . -1127) T) ((-1102 . -552) 171856) ((-1102 . -1012) T) ((-1100 . -1105) 171835) ((-1100 . -183) 171783) ((-1100 . -76) 171731) ((-1100 . -259) 171529) ((-1100 . -452) 171281) ((-1100 . -426) 171216) ((-1100 . -124) 171164) ((-1100 . -553) NIL) ((-1100 . -193) 171112) ((-1100 . -549) 171091) ((-1100 . -243) 171070) ((-1100 . -1127) T) ((-1100 . -13) T) ((-1100 . -241) 171049) ((-1100 . -1012) T) ((-1100 . -552) 171031) ((-1100 . -72) T) ((-1100 . -34) T) ((-1100 . -538) 171010) ((-1096 . -1012) T) ((-1096 . -552) 170992) ((-1096 . -1127) T) ((-1096 . -13) T) ((-1096 . -72) T) ((-1095 . -752) T) ((-1095 . -759) T) ((-1095 . -756) T) ((-1095 . -1012) T) ((-1095 . -552) 170974) ((-1095 . -1127) T) ((-1095 . -13) T) ((-1095 . -72) T) ((-1095 . -317) T) ((-1095 . -604) T) ((-1094 . -752) T) ((-1094 . -759) T) ((-1094 . -756) T) ((-1094 . -1012) T) ((-1094 . -552) 170956) ((-1094 . -1127) T) ((-1094 . -13) T) ((-1094 . -72) T) ((-1094 . -317) T) ((-1093 . -1173) T) ((-1093 . -1012) T) ((-1093 . -552) 170923) ((-1093 . -1127) T) ((-1093 . -13) T) ((-1093 . -72) T) ((-1093 . -950) 170859) ((-1093 . -555) 170795) ((-1092 . -552) 170777) ((-1091 . -552) 170759) ((-1090 . -276) 170736) ((-1090 . -950) 170634) ((-1090 . -352) 170618) ((-1090 . -38) 170515) ((-1090 . -555) 170372) ((-1090 . -590) 170297) ((-1090 . -588) 170207) ((-1090 . -969) T) ((-1090 . -1024) T) ((-1090 . -1059) T) ((-1090 . -663) T) ((-1090 . -961) T) ((-1090 . -82) 170072) ((-1090 . -963) 169958) ((-1090 . -968) 169844) ((-1090 . -21) T) ((-1090 . -23) T) ((-1090 . -1012) T) ((-1090 . -552) 169826) ((-1090 . -1127) T) ((-1090 . -13) T) ((-1090 . -72) T) ((-1090 . -25) T) ((-1090 . -104) T) ((-1090 . -582) 169723) ((-1090 . -654) 169620) ((-1090 . -118) 169599) ((-1090 . -120) 169578) ((-1090 . -146) 169532) ((-1090 . -494) 169511) ((-1090 . -245) 169490) ((-1090 . -47) 169467) ((-1088 . -756) T) ((-1088 . -552) 169449) ((-1088 . -1012) T) ((-1088 . -72) T) ((-1088 . -13) T) ((-1088 . -1127) T) ((-1088 . -759) T) ((-1088 . -553) 169371) ((-1088 . -555) 169337) ((-1088 . -950) 169319) ((-1088 . -796) 169286) ((-1087 . -1170) 169270) ((-1087 . -190) 169229) ((-1087 . -555) 169111) ((-1087 . -590) 169036) ((-1087 . -588) 168946) ((-1087 . -104) T) ((-1087 . -25) T) ((-1087 . -72) T) ((-1087 . -552) 168928) ((-1087 . -1012) T) ((-1087 . -23) T) ((-1087 . -21) T) ((-1087 . -969) T) ((-1087 . -1024) T) ((-1087 . -1059) T) ((-1087 . -663) T) ((-1087 . -961) T) ((-1087 . -186) 168881) ((-1087 . -13) T) ((-1087 . -1127) T) ((-1087 . -189) 168840) ((-1087 . -241) 168805) ((-1087 . -809) 168718) ((-1087 . -806) 168606) ((-1087 . -811) 168519) ((-1087 . -886) 168489) ((-1087 . -38) 168386) ((-1087 . -82) 168251) ((-1087 . -963) 168137) ((-1087 . -968) 168023) ((-1087 . -582) 167920) ((-1087 . -654) 167817) ((-1087 . -118) 167796) ((-1087 . -120) 167775) ((-1087 . -146) 167729) ((-1087 . -494) 167708) ((-1087 . -245) 167687) ((-1087 . -47) 167664) ((-1087 . -1156) 167641) ((-1087 . -35) 167607) ((-1087 . -66) 167573) ((-1087 . -239) 167539) ((-1087 . -430) 167505) ((-1087 . -1116) 167471) ((-1087 . -1113) 167437) ((-1087 . -915) 167403) ((-1086 . -1162) 167364) ((-1086 . -311) 167343) ((-1086 . -1132) 167322) ((-1086 . -832) 167301) ((-1086 . -494) 167255) ((-1086 . -146) 167189) ((-1086 . -555) 166938) ((-1086 . -654) 166785) ((-1086 . -582) 166632) ((-1086 . -38) 166479) ((-1086 . -389) 166458) ((-1086 . -257) 166437) ((-1086 . -590) 166337) ((-1086 . -588) 166222) ((-1086 . -969) T) ((-1086 . -1024) T) ((-1086 . -1059) T) ((-1086 . -663) T) ((-1086 . -961) T) ((-1086 . -82) 166042) ((-1086 . -963) 165883) ((-1086 . -968) 165724) ((-1086 . -21) T) ((-1086 . -23) T) ((-1086 . -1012) T) ((-1086 . -552) 165706) ((-1086 . -1127) T) ((-1086 . -13) T) ((-1086 . -72) T) ((-1086 . -25) T) ((-1086 . -104) T) ((-1086 . -245) 165660) ((-1086 . -201) 165639) ((-1086 . -915) 165605) ((-1086 . -1113) 165571) ((-1086 . -1116) 165537) ((-1086 . -430) 165503) ((-1086 . -239) 165469) ((-1086 . -66) 165435) ((-1086 . -35) 165401) ((-1086 . -1156) 165371) ((-1086 . -47) 165341) ((-1086 . -120) 165320) ((-1086 . -118) 165299) ((-1086 . -886) 165262) ((-1086 . -811) 165168) ((-1086 . -806) 165049) ((-1086 . -809) 164955) ((-1086 . -241) 164913) ((-1086 . -189) 164865) ((-1086 . -186) 164811) ((-1086 . -190) 164763) ((-1086 . -1160) 164747) ((-1086 . -950) 164682) ((-1083 . -1153) 164666) ((-1083 . -1064) 164644) ((-1083 . -553) NIL) ((-1083 . -259) 164631) ((-1083 . -452) 164579) ((-1083 . -276) 164556) ((-1083 . -950) 164439) ((-1083 . -352) 164423) ((-1083 . -38) 164255) ((-1083 . -82) 164060) ((-1083 . -963) 163886) ((-1083 . -968) 163712) ((-1083 . -588) 163622) ((-1083 . -590) 163511) ((-1083 . -582) 163343) ((-1083 . -654) 163175) ((-1083 . -555) 162952) ((-1083 . -118) 162931) ((-1083 . -120) 162910) ((-1083 . -47) 162887) ((-1083 . -326) 162871) ((-1083 . -580) 162819) ((-1083 . -809) 162763) ((-1083 . -806) 162670) ((-1083 . -811) 162581) ((-1083 . -796) NIL) ((-1083 . -821) 162560) ((-1083 . -1132) 162539) ((-1083 . -861) 162509) ((-1083 . -832) 162488) ((-1083 . -494) 162402) ((-1083 . -245) 162316) ((-1083 . -146) 162210) ((-1083 . -389) 162144) ((-1083 . -257) 162123) ((-1083 . -241) 162050) ((-1083 . -190) T) ((-1083 . -104) T) ((-1083 . -25) T) ((-1083 . -72) T) ((-1083 . -552) 162032) ((-1083 . -1012) T) ((-1083 . -23) T) ((-1083 . -21) T) ((-1083 . -969) T) ((-1083 . -1024) T) ((-1083 . -1059) T) ((-1083 . -663) T) ((-1083 . -961) T) ((-1083 . -186) 162019) ((-1083 . -13) T) ((-1083 . -1127) T) ((-1083 . -189) T) ((-1083 . -225) 162003) ((-1083 . -184) 161987) ((-1080 . -1141) 161948) ((-1080 . -915) 161914) ((-1080 . -1113) 161880) ((-1080 . -1116) 161846) ((-1080 . -430) 161812) ((-1080 . -239) 161778) ((-1080 . -66) 161744) ((-1080 . -35) 161710) ((-1080 . -1156) 161687) ((-1080 . -47) 161664) ((-1080 . -555) 161465) ((-1080 . -654) 161267) ((-1080 . -582) 161069) ((-1080 . -590) 160924) ((-1080 . -588) 160764) ((-1080 . -968) 160560) ((-1080 . -963) 160356) ((-1080 . -82) 160108) ((-1080 . -38) 159910) ((-1080 . -886) 159880) ((-1080 . -241) 159708) ((-1080 . -1139) 159692) ((-1080 . -969) T) ((-1080 . -1024) T) ((-1080 . -1059) T) ((-1080 . -663) T) ((-1080 . -961) T) ((-1080 . -21) T) ((-1080 . -23) T) ((-1080 . -1012) T) ((-1080 . -552) 159674) ((-1080 . -1127) T) ((-1080 . -13) T) ((-1080 . -72) T) ((-1080 . -25) T) ((-1080 . -104) T) ((-1080 . -118) 159584) ((-1080 . -120) 159494) ((-1080 . -553) NIL) ((-1080 . -184) 159446) ((-1080 . -809) 159282) ((-1080 . -811) 159046) ((-1080 . -806) 158785) ((-1080 . -225) 158737) ((-1080 . -189) 158563) ((-1080 . -186) 158383) ((-1080 . -190) 158273) ((-1080 . -311) 158252) ((-1080 . -1132) 158231) ((-1080 . -832) 158210) ((-1080 . -494) 158164) ((-1080 . -146) 158098) ((-1080 . -389) 158077) ((-1080 . -257) 158056) ((-1080 . -245) 158010) ((-1080 . -201) 157989) ((-1080 . -287) 157941) ((-1080 . -452) 157675) ((-1080 . -259) 157560) ((-1080 . -326) 157512) ((-1080 . -580) 157464) ((-1080 . -340) 157416) ((-1080 . -796) NIL) ((-1080 . -740) NIL) ((-1080 . -714) NIL) ((-1080 . -716) NIL) ((-1080 . -756) NIL) ((-1080 . -759) NIL) ((-1080 . -718) NIL) ((-1080 . -721) NIL) ((-1080 . -755) NIL) ((-1080 . -794) 157368) ((-1080 . -821) NIL) ((-1080 . -933) NIL) ((-1080 . -950) 157334) ((-1080 . -1064) NIL) ((-1080 . -904) 157286) ((-1079 . -994) T) ((-1079 . -427) 157267) ((-1079 . -552) 157233) ((-1079 . -555) 157214) ((-1079 . -1012) T) ((-1079 . -1127) T) ((-1079 . -13) T) ((-1079 . -72) T) ((-1079 . -64) T) ((-1078 . -1012) T) ((-1078 . -552) 157196) ((-1078 . -1127) T) ((-1078 . -13) T) ((-1078 . -72) T) ((-1077 . -1012) T) ((-1077 . -552) 157178) ((-1077 . -1127) T) ((-1077 . -13) T) ((-1077 . -72) T) ((-1072 . -1105) 157154) ((-1072 . -183) 157099) ((-1072 . -76) 157044) ((-1072 . -259) 156833) ((-1072 . -452) 156573) ((-1072 . -426) 156505) ((-1072 . -124) 156450) ((-1072 . -553) NIL) ((-1072 . -193) 156395) ((-1072 . -549) 156371) ((-1072 . -243) 156347) ((-1072 . -1127) T) ((-1072 . -13) T) ((-1072 . -241) 156323) ((-1072 . -1012) T) ((-1072 . -552) 156305) ((-1072 . -72) T) ((-1072 . -34) T) ((-1072 . -538) 156281) ((-1071 . -1056) T) ((-1071 . -321) 156263) ((-1071 . -759) T) ((-1071 . -756) T) ((-1071 . -124) 156245) ((-1071 . -34) T) ((-1071 . -13) T) ((-1071 . -1127) T) ((-1071 . -72) T) ((-1071 . -552) 156227) ((-1071 . -259) NIL) ((-1071 . -452) NIL) ((-1071 . -1012) T) ((-1071 . -426) 156209) ((-1071 . -553) NIL) ((-1071 . -241) 156159) ((-1071 . -538) 156134) ((-1071 . -243) 156109) ((-1071 . -593) 156091) ((-1071 . -19) 156073) ((-1067 . -616) 156057) ((-1067 . -593) 156041) ((-1067 . -243) 156018) ((-1067 . -241) 155970) ((-1067 . -538) 155947) ((-1067 . -553) 155908) ((-1067 . -426) 155892) ((-1067 . -1012) 155870) ((-1067 . -452) 155803) ((-1067 . -259) 155741) ((-1067 . -552) 155676) ((-1067 . -72) 155630) ((-1067 . -1127) T) ((-1067 . -13) T) ((-1067 . -34) T) ((-1067 . -124) 155614) ((-1067 . -1166) 155598) ((-1067 . -923) 155582) ((-1067 . -1062) 155566) ((-1067 . -555) 155543) ((-1065 . -994) T) ((-1065 . -427) 155524) ((-1065 . -552) 155490) ((-1065 . -555) 155471) ((-1065 . -1012) T) ((-1065 . -1127) T) ((-1065 . -13) T) ((-1065 . -72) T) ((-1065 . -64) T) ((-1063 . -1105) 155450) ((-1063 . -183) 155398) ((-1063 . -76) 155346) ((-1063 . -259) 155144) ((-1063 . -452) 154896) ((-1063 . -426) 154831) ((-1063 . -124) 154779) ((-1063 . -553) NIL) ((-1063 . -193) 154727) ((-1063 . -549) 154706) ((-1063 . -243) 154685) ((-1063 . -1127) T) ((-1063 . -13) T) ((-1063 . -241) 154664) ((-1063 . -1012) T) ((-1063 . -552) 154646) ((-1063 . -72) T) ((-1063 . -34) T) ((-1063 . -538) 154625) ((-1060 . -1033) 154609) ((-1060 . -426) 154593) ((-1060 . -1012) 154571) ((-1060 . -452) 154504) ((-1060 . -259) 154442) ((-1060 . -552) 154377) ((-1060 . -72) 154331) ((-1060 . -1127) T) ((-1060 . -13) T) ((-1060 . -34) T) ((-1060 . -76) 154315) ((-1058 . -1019) 154284) ((-1058 . -1122) 154253) ((-1058 . -552) 154215) ((-1058 . -124) 154199) ((-1058 . -34) T) ((-1058 . -13) T) ((-1058 . -1127) T) ((-1058 . -72) T) ((-1058 . -259) 154137) ((-1058 . -452) 154070) ((-1058 . -1012) T) ((-1058 . -426) 154054) ((-1058 . -553) 154015) ((-1058 . -889) 153984) ((-1058 . -982) 153953) ((-1054 . -1035) 153898) ((-1054 . -426) 153882) ((-1054 . -452) 153815) ((-1054 . -259) 153753) ((-1054 . -34) T) ((-1054 . -965) 153693) ((-1054 . -950) 153591) ((-1054 . -555) 153510) ((-1054 . -352) 153494) ((-1054 . -580) 153442) ((-1054 . -590) 153380) ((-1054 . -326) 153364) ((-1054 . -190) 153343) ((-1054 . -186) 153291) ((-1054 . -189) 153245) ((-1054 . -225) 153229) ((-1054 . -806) 153153) ((-1054 . -811) 153079) ((-1054 . -809) 153038) ((-1054 . -184) 153022) ((-1054 . -654) 152957) ((-1054 . -582) 152892) ((-1054 . -588) 152851) ((-1054 . -104) T) ((-1054 . -25) T) ((-1054 . -72) T) ((-1054 . -13) T) ((-1054 . -1127) T) ((-1054 . -552) 152813) ((-1054 . -1012) T) ((-1054 . -23) T) ((-1054 . -21) T) ((-1054 . -968) 152797) ((-1054 . -963) 152781) ((-1054 . -82) 152760) ((-1054 . -961) T) ((-1054 . -663) T) ((-1054 . -1059) T) ((-1054 . -1024) T) ((-1054 . -969) T) ((-1054 . -38) 152720) ((-1054 . -553) 152681) ((-1053 . -923) 152652) ((-1053 . -34) T) ((-1053 . -13) T) ((-1053 . -1127) T) ((-1053 . -72) T) ((-1053 . -552) 152634) ((-1053 . -259) 152560) ((-1053 . -452) 152468) ((-1053 . -1012) T) ((-1053 . -426) 152439) ((-1052 . -1012) T) ((-1052 . -552) 152421) ((-1052 . -1127) T) ((-1052 . -13) T) ((-1052 . -72) T) ((-1047 . -1049) T) ((-1047 . -1173) T) ((-1047 . -64) T) ((-1047 . -72) T) ((-1047 . -13) T) ((-1047 . -1127) T) ((-1047 . -552) 152387) ((-1047 . -1012) T) ((-1047 . -555) 152368) ((-1047 . -427) 152349) ((-1047 . -994) T) ((-1045 . -1046) 152333) ((-1045 . -72) T) ((-1045 . -13) T) ((-1045 . -1127) T) ((-1045 . -552) 152315) ((-1045 . -1012) T) ((-1038 . -679) 152294) ((-1038 . -35) 152260) ((-1038 . -66) 152226) ((-1038 . -239) 152192) ((-1038 . -430) 152158) ((-1038 . -1116) 152124) ((-1038 . -1113) 152090) ((-1038 . -915) 152056) ((-1038 . -47) 152028) ((-1038 . -38) 151925) ((-1038 . -582) 151822) ((-1038 . -654) 151719) ((-1038 . -555) 151601) ((-1038 . -245) 151580) ((-1038 . -494) 151559) ((-1038 . -82) 151424) ((-1038 . -963) 151310) ((-1038 . -968) 151196) ((-1038 . -146) 151150) ((-1038 . -120) 151129) ((-1038 . -118) 151108) ((-1038 . -590) 151033) ((-1038 . -588) 150943) ((-1038 . -886) 150910) ((-1038 . -811) 150894) ((-1038 . -1127) T) ((-1038 . -13) T) ((-1038 . -806) 150876) ((-1038 . -961) T) ((-1038 . -663) T) ((-1038 . -1059) T) ((-1038 . -1024) T) 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136717) ((-973 . -72) T) ((-973 . -13) T) ((-973 . -1127) T) ((-973 . -552) 136699) ((-973 . -1012) T) ((-970 . -1127) T) ((-970 . -13) T) ((-970 . -1012) 136677) ((-970 . -552) 136644) ((-970 . -72) 136622) ((-966 . -965) 136562) ((-966 . -582) 136507) ((-966 . -654) 136452) ((-966 . -34) T) ((-966 . -259) 136390) ((-966 . -452) 136323) ((-966 . -426) 136307) ((-966 . -590) 136291) ((-966 . -588) 136260) ((-966 . -104) T) ((-966 . -25) T) ((-966 . -72) T) ((-966 . -13) T) ((-966 . -1127) T) ((-966 . -552) 136222) ((-966 . -1012) T) ((-966 . -23) T) ((-966 . -21) T) ((-966 . -968) 136206) ((-966 . -963) 136190) ((-966 . -82) 136169) ((-966 . -1185) 136139) ((-966 . -553) 136100) ((-958 . -982) 136029) ((-958 . -889) 135958) ((-958 . -553) 135900) ((-958 . -426) 135865) ((-958 . -1012) T) ((-958 . -452) 135749) ((-958 . -259) 135657) ((-958 . -552) 135600) ((-958 . -72) T) ((-958 . -1127) T) ((-958 . -13) T) ((-958 . -34) T) ((-958 . -124) 135565) ((-958 . -1122) 135494) ((-948 . -994) T) ((-948 . -427) 135475) ((-948 . -552) 135441) ((-948 . -555) 135422) ((-948 . -1012) T) ((-948 . -1127) T) ((-948 . -13) T) ((-948 . -72) T) ((-948 . -64) T) ((-947 . -146) T) ((-947 . -555) 135391) ((-947 . -969) T) ((-947 . -1024) T) ((-947 . -1059) T) ((-947 . -663) T) ((-947 . -961) T) ((-947 . -590) 135365) ((-947 . -588) 135324) ((-947 . -104) T) ((-947 . -25) T) ((-947 . -72) T) ((-947 . -13) T) ((-947 . -1127) T) ((-947 . -552) 135306) ((-947 . -1012) T) ((-947 . -23) T) ((-947 . -21) T) ((-947 . -968) 135280) ((-947 . -963) 135254) ((-947 . -82) 135221) ((-947 . -38) 135205) ((-947 . -582) 135189) ((-947 . -654) 135173) ((-940 . -982) 135142) ((-940 . -889) 135111) ((-940 . -553) 135072) ((-940 . -426) 135056) ((-940 . -1012) T) ((-940 . -452) 134989) ((-940 . -259) 134927) ((-940 . -552) 134889) ((-940 . -72) T) ((-940 . -1127) T) ((-940 . -13) T) ((-940 . -34) T) ((-940 . -124) 134873) ((-940 . -1122) 134842) ((-939 . -1012) T) ((-939 . -552) 134824) ((-939 . -1127) T) ((-939 . -13) T) ((-939 . -72) T) ((-937 . -925) T) ((-937 . -915) T) ((-937 . -714) T) ((-937 . -716) T) ((-937 . -756) T) ((-937 . -759) T) ((-937 . -718) T) ((-937 . -721) T) ((-937 . -755) T) ((-937 . -950) 134709) ((-937 . -352) 134671) ((-937 . -201) T) ((-937 . -245) T) ((-937 . -257) T) ((-937 . -389) T) ((-937 . -38) 134608) ((-937 . -582) 134545) ((-937 . -654) 134482) ((-937 . -555) 134419) ((-937 . -494) T) ((-937 . -832) T) ((-937 . -1132) T) ((-937 . -311) T) ((-937 . -82) 134328) ((-937 . -963) 134265) ((-937 . -968) 134202) ((-937 . -146) T) ((-937 . -120) T) ((-937 . -590) 134139) ((-937 . -588) 134076) ((-937 . -104) T) ((-937 . -25) T) ((-937 . -72) T) ((-937 . -13) T) ((-937 . -1127) T) ((-937 . -552) 134058) ((-937 . -1012) T) ((-937 . -23) T) ((-937 . -21) T) ((-937 . -961) T) ((-937 . -663) T) ((-937 . -1059) T) ((-937 . -1024) T) ((-937 . -969) T) ((-932 . -994) T) ((-932 . -427) 134039) ((-932 . -552) 134005) ((-932 . -555) 133986) ((-932 . -1012) T) ((-932 . -1127) T) ((-932 . -13) T) ((-932 . -72) T) ((-932 . -64) T) ((-917 . -904) 133968) ((-917 . -1064) T) ((-917 . -555) 133918) ((-917 . -950) 133878) ((-917 . -553) 133808) ((-917 . -933) T) ((-917 . -821) NIL) ((-917 . -794) 133790) ((-917 . -755) T) ((-917 . -721) T) ((-917 . -718) T) ((-917 . -759) T) ((-917 . -756) T) ((-917 . -716) T) ((-917 . -714) T) ((-917 . -740) T) ((-917 . -796) 133772) ((-917 . -340) 133754) ((-917 . -580) 133736) ((-917 . -326) 133718) ((-917 . -241) NIL) ((-917 . -259) NIL) ((-917 . -452) NIL) ((-917 . -287) 133700) ((-917 . -201) T) ((-917 . -82) 133627) ((-917 . -963) 133577) ((-917 . -968) 133527) ((-917 . -245) T) ((-917 . -654) 133477) ((-917 . -582) 133427) ((-917 . -590) 133377) ((-917 . -588) 133327) ((-917 . -38) 133277) ((-917 . -257) T) ((-917 . -389) T) ((-917 . -146) T) ((-917 . -494) T) ((-917 . -832) T) ((-917 . -1132) T) ((-917 . -311) T) ((-917 . -190) T) ((-917 . -186) 133264) ((-917 . -189) T) ((-917 . -225) 133246) ((-917 . -806) NIL) 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. -963) 114107) ((-741 . -82) 114086) ((-741 . -961) T) ((-741 . -663) T) ((-741 . -1059) T) ((-741 . -1024) T) ((-741 . -969) T) ((-741 . -38) 114056) ((-741 . -190) 114035) ((-741 . -186) 114008) ((-741 . -189) 113987) ((-739 . -333) 113971) ((-739 . -555) 113955) ((-739 . -950) 113939) ((-739 . -759) T) ((-739 . -756) T) ((-739 . -1024) T) ((-739 . -72) T) ((-739 . -13) T) ((-739 . -1127) T) ((-739 . -552) 113921) ((-739 . -1012) T) ((-739 . -663) T) ((-739 . -754) T) ((-739 . -766) T) ((-738 . -228) 113905) ((-738 . -555) 113889) ((-738 . -950) 113873) ((-738 . -759) T) ((-738 . -72) T) ((-738 . -1012) T) ((-738 . -552) 113855) ((-738 . -756) T) ((-738 . -186) 113842) ((-738 . -13) T) ((-738 . -1127) T) ((-738 . -189) T) ((-737 . -82) 113777) ((-737 . -963) 113728) ((-737 . -968) 113679) ((-737 . -21) T) ((-737 . -588) 113615) ((-737 . -23) T) ((-737 . -1012) T) ((-737 . -552) 113584) ((-737 . -1127) T) ((-737 . -13) T) ((-737 . -72) T) ((-737 . -25) T) ((-737 . -104) T) ((-737 . 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. -186) 73192) ((-432 . -189) T) ((-428 . -1012) T) ((-428 . -552) 73158) ((-428 . -1127) T) ((-428 . -13) T) ((-428 . -72) T) ((-424 . -904) 73140) ((-424 . -1064) T) ((-424 . -555) 73090) ((-424 . -950) 73050) ((-424 . -553) 72980) ((-424 . -933) T) ((-424 . -821) NIL) ((-424 . -794) 72962) ((-424 . -755) T) ((-424 . -721) T) ((-424 . -718) T) ((-424 . -759) T) ((-424 . -756) T) ((-424 . -716) T) ((-424 . -714) T) ((-424 . -740) T) ((-424 . -796) 72944) ((-424 . -340) 72926) ((-424 . -580) 72908) ((-424 . -326) 72890) ((-424 . -241) NIL) ((-424 . -259) NIL) ((-424 . -452) NIL) ((-424 . -287) 72872) ((-424 . -201) T) ((-424 . -82) 72799) ((-424 . -963) 72749) ((-424 . -968) 72699) ((-424 . -245) T) ((-424 . -654) 72649) ((-424 . -582) 72599) ((-424 . -590) 72549) ((-424 . -588) 72499) ((-424 . -38) 72449) ((-424 . -257) T) ((-424 . -389) T) ((-424 . -146) T) ((-424 . -494) T) ((-424 . -832) T) ((-424 . -1132) T) ((-424 . -311) T) ((-424 . -190) T) ((-424 . -186) 72436) ((-424 . -189) 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. -13) T) ((-419 . -1127) T) ((-419 . -1012) 68325) ((-419 . -23) 68181) ((-419 . -21) 68096) ((-418 . -861) 68041) ((-418 . -555) 67833) ((-418 . -950) 67711) ((-418 . -1132) 67690) ((-418 . -821) 67669) ((-418 . -796) NIL) ((-418 . -811) 67646) ((-418 . -806) 67621) ((-418 . -809) 67598) ((-418 . -452) 67536) ((-418 . -389) 67490) ((-418 . -580) 67438) ((-418 . -590) 67327) ((-418 . -326) 67311) ((-418 . -47) 67268) ((-418 . -38) 67120) ((-418 . -582) 66972) ((-418 . -654) 66824) ((-418 . -245) 66758) ((-418 . -494) 66692) ((-418 . -82) 66517) ((-418 . -963) 66363) ((-418 . -968) 66209) ((-418 . -146) 66123) ((-418 . -120) 66102) ((-418 . -118) 66081) ((-418 . -588) 65991) ((-418 . -104) T) ((-418 . -25) T) ((-418 . -72) T) ((-418 . -13) T) ((-418 . -1127) T) ((-418 . -552) 65973) ((-418 . -1012) T) ((-418 . -23) T) ((-418 . -21) T) ((-418 . -961) T) ((-418 . -663) T) ((-418 . -1059) T) ((-418 . -1024) T) ((-418 . -969) T) ((-418 . -352) 65957) ((-418 . -276) 65914) ((-418 . -259) 65901) ((-418 . -553) 65762) ((-416 . -1105) 65741) ((-416 . -183) 65689) ((-416 . -76) 65637) ((-416 . -259) 65435) ((-416 . -452) 65187) ((-416 . -426) 65122) ((-416 . -124) 65070) ((-416 . -553) NIL) ((-416 . -193) 65018) ((-416 . -549) 64997) ((-416 . -243) 64976) ((-416 . -1127) T) ((-416 . -13) T) ((-416 . -241) 64955) ((-416 . -1012) T) ((-416 . -552) 64937) ((-416 . -72) T) ((-416 . -34) T) ((-416 . -538) 64916) ((-415 . -994) T) ((-415 . -427) 64897) ((-415 . -552) 64863) ((-415 . -555) 64844) ((-415 . -1012) T) ((-415 . -1127) T) ((-415 . -13) T) ((-415 . -72) T) ((-415 . -64) T) ((-414 . -311) T) ((-414 . -1132) T) ((-414 . -832) T) ((-414 . -494) T) ((-414 . -146) T) ((-414 . -555) 64794) ((-414 . -654) 64759) ((-414 . -582) 64724) ((-414 . -38) 64689) ((-414 . -389) T) ((-414 . -257) T) ((-414 . -590) 64654) ((-414 . -588) 64604) ((-414 . -969) T) ((-414 . -1024) T) ((-414 . -1059) T) ((-414 . -663) T) ((-414 . -961) T) ((-414 . -82) 64553) ((-414 . -963) 64518) ((-414 . 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\ No newline at end of file
+((((-484)) . T)) 
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. -104) T) ((-1203 . -591) 198936) ((-1203 . -1193) 198920) ((-1203 . -655) 198890) ((-1203 . -583) 198860) ((-1203 . -969) 198844) ((-1203 . -964) 198828) ((-1203 . -82) 198807) ((-1203 . -38) 198777) ((-1203 . -1198) 198756) ((-1202 . -962) T) ((-1202 . -664) T) ((-1202 . -1060) T) ((-1202 . -1025) T) ((-1202 . -970) T) ((-1202 . -21) T) ((-1202 . -589) 198715) ((-1202 . -23) T) ((-1202 . -1013) T) ((-1202 . -553) 198697) ((-1202 . -1128) T) ((-1202 . -13) T) ((-1202 . -72) T) ((-1202 . -25) T) ((-1202 . -104) T) ((-1202 . -591) 198671) ((-1202 . -556) 198627) ((-1202 . -1193) 198611) ((-1202 . -655) 198581) ((-1202 . -583) 198551) ((-1202 . -969) 198535) ((-1202 . -964) 198519) ((-1202 . -82) 198498) ((-1202 . -38) 198468) ((-1202 . -332) 198447) ((-1202 . -951) 198431) ((-1200 . -1201) 198407) ((-1200 . -951) 198381) ((-1200 . -556) 198327) ((-1200 . -962) T) ((-1200 . -664) T) ((-1200 . -1060) T) ((-1200 . -1025) T) ((-1200 . -970) T) ((-1200 . -21) T) ((-1200 . -589) 198286) ((-1200 . -23) T) ((-1200 . -1013) T) ((-1200 . -553) 198268) ((-1200 . -1128) T) ((-1200 . -13) T) ((-1200 . -72) T) ((-1200 . -25) T) ((-1200 . -104) T) ((-1200 . -591) 198242) ((-1200 . -1193) 198226) ((-1200 . -655) 198196) ((-1200 . -583) 198166) ((-1200 . -969) 198150) ((-1200 . -964) 198134) ((-1200 . -82) 198113) ((-1200 . -38) 198083) ((-1200 . -1198) 198059) ((-1199 . -1201) 198038) ((-1199 . -951) 197995) ((-1199 . -556) 197924) ((-1199 . -962) T) ((-1199 . -664) T) ((-1199 . -1060) T) ((-1199 . -1025) T) ((-1199 . -970) T) ((-1199 . -21) T) ((-1199 . -589) 197883) ((-1199 . -23) T) ((-1199 . -1013) T) ((-1199 . -553) 197865) ((-1199 . -1128) T) ((-1199 . -13) T) ((-1199 . -72) T) ((-1199 . -25) T) ((-1199 . -104) T) ((-1199 . -591) 197839) ((-1199 . -1193) 197823) ((-1199 . -655) 197793) ((-1199 . -583) 197763) ((-1199 . -969) 197747) ((-1199 . -964) 197731) ((-1199 . -82) 197710) ((-1199 . -38) 197680) ((-1199 . -1198) 197659) ((-1199 . -332) 197631) ((-1194 . -332) 197603) ((-1194 . -556) 197552) ((-1194 . -951) 197529) ((-1194 . -583) 197499) ((-1194 . -655) 197469) ((-1194 . -591) 197443) ((-1194 . -589) 197402) ((-1194 . -104) T) ((-1194 . -25) T) ((-1194 . -72) T) ((-1194 . -13) T) ((-1194 . -1128) T) ((-1194 . -553) 197384) ((-1194 . -1013) T) ((-1194 . -23) T) ((-1194 . -21) T) ((-1194 . -969) 197368) ((-1194 . -964) 197352) ((-1194 . -82) 197331) ((-1194 . -1201) 197310) ((-1194 . -962) T) ((-1194 . -664) T) ((-1194 . -1060) T) ((-1194 . -1025) T) ((-1194 . -970) T) ((-1194 . -1193) 197294) ((-1194 . -38) 197264) ((-1194 . -1198) 197243) ((-1192 . -1123) 197212) ((-1192 . -553) 197174) ((-1192 . -124) 197158) ((-1192 . -34) T) ((-1192 . -13) T) ((-1192 . -1128) T) ((-1192 . -72) T) ((-1192 . -259) 197096) ((-1192 . -453) 197029) ((-1192 . -1013) T) ((-1192 . -426) 197013) ((-1192 . -554) 196974) ((-1192 . -890) 196943) ((-1191 . -962) T) ((-1191 . -664) T) ((-1191 . -1060) T) ((-1191 . -1025) T) ((-1191 . -970) T) ((-1191 . -21) T) ((-1191 . -589) 196888) ((-1191 . -23) T) ((-1191 . -1013) T) ((-1191 . -553) 196857) ((-1191 . -1128) T) ((-1191 . -13) T) ((-1191 . -72) T) ((-1191 . -25) T) ((-1191 . -104) T) ((-1191 . -591) 196817) ((-1191 . -556) 196759) ((-1191 . -427) 196743) ((-1191 . -38) 196713) ((-1191 . -82) 196678) ((-1191 . -964) 196648) ((-1191 . -969) 196618) ((-1191 . -583) 196588) ((-1191 . -655) 196558) ((-1190 . -995) T) ((-1190 . -427) 196539) ((-1190 . -553) 196505) ((-1190 . -556) 196486) ((-1190 . -1013) T) ((-1190 . -1128) T) ((-1190 . -13) T) ((-1190 . -72) T) ((-1190 . -64) T) ((-1189 . -995) T) ((-1189 . -427) 196467) ((-1189 . -553) 196433) ((-1189 . -556) 196414) ((-1189 . -1013) T) ((-1189 . -1128) T) ((-1189 . -13) T) ((-1189 . -72) T) ((-1189 . -64) T) ((-1184 . -553) 196396) ((-1182 . -1013) T) ((-1182 . -553) 196378) ((-1182 . -1128) T) ((-1182 . -13) T) ((-1182 . -72) T) ((-1181 . -1013) T) ((-1181 . -553) 196360) ((-1181 . -1128) T) ((-1181 . -13) T) ((-1181 . -72) T) ((-1178 . -1177) 196344) ((-1178 . -321) 196328) ((-1178 . -760) 196307) ((-1178 . -757) 196286) ((-1178 . -124) 196270) ((-1178 . -34) T) ((-1178 . -13) T) ((-1178 . -1128) T) ((-1178 . -72) 196204) ((-1178 . -553) 196119) ((-1178 . -259) 196057) ((-1178 . -453) 195990) ((-1178 . -1013) 195943) ((-1178 . -426) 195927) ((-1178 . -554) 195888) ((-1178 . -241) 195840) ((-1178 . -539) 195817) ((-1178 . -243) 195794) ((-1178 . -594) 195778) ((-1178 . -19) 195762) ((-1175 . -1013) T) ((-1175 . -553) 195728) ((-1175 . -1128) T) ((-1175 . -13) T) ((-1175 . -72) T) ((-1168 . -1171) 195712) ((-1168 . -190) 195671) ((-1168 . -556) 195553) ((-1168 . -591) 195478) ((-1168 . -589) 195388) ((-1168 . -104) T) ((-1168 . -25) T) ((-1168 . -72) T) ((-1168 . -553) 195370) ((-1168 . -1013) T) ((-1168 . -23) T) ((-1168 . -21) T) ((-1168 . -970) T) ((-1168 . -1025) T) ((-1168 . -1060) T) ((-1168 . -664) T) ((-1168 . -962) T) ((-1168 . -186) 195323) ((-1168 . -13) T) ((-1168 . -1128) T) ((-1168 . -189) 195282) ((-1168 . -241) 195247) ((-1168 . -810) 195160) ((-1168 . -807) 195048) ((-1168 . -812) 194961) ((-1168 . -887) 194931) ((-1168 . -38) 194828) ((-1168 . -82) 194693) ((-1168 . -964) 194579) ((-1168 . -969) 194465) ((-1168 . -583) 194362) ((-1168 . -655) 194259) ((-1168 . -118) 194238) ((-1168 . -120) 194217) ((-1168 . -146) 194171) ((-1168 . -495) 194150) ((-1168 . -245) 194129) ((-1168 . -47) 194106) ((-1168 . -1157) 194083) ((-1168 . -35) 194049) ((-1168 . -66) 194015) ((-1168 . -239) 193981) ((-1168 . -430) 193947) ((-1168 . -1117) 193913) ((-1168 . -1114) 193879) ((-1168 . -916) 193845) ((-1165 . -276) 193789) ((-1165 . -951) 193755) ((-1165 . -352) 193721) ((-1165 . -38) 193578) ((-1165 . -556) 193452) ((-1165 . -591) 193341) ((-1165 . -589) 193215) ((-1165 . -970) T) ((-1165 . -1025) T) ((-1165 . -1060) T) ((-1165 . -664) T) ((-1165 . -962) T) ((-1165 . -82) 193065) ((-1165 . -964) 192954) ((-1165 . -969) 192843) ((-1165 . -21) T) ((-1165 . -23) T) ((-1165 . -1013) T) ((-1165 . -553) 192825) ((-1165 . -1128) T) ((-1165 . -13) T) ((-1165 . -72) T) ((-1165 . -25) T) ((-1165 . -104) T) ((-1165 . -583) 192682) ((-1165 . -655) 192539) ((-1165 . -118) 192500) ((-1165 . -120) 192461) ((-1165 . -146) T) ((-1165 . -495) T) ((-1165 . -245) T) ((-1165 . -47) 192405) ((-1164 . -1163) 192384) ((-1164 . -311) 192363) ((-1164 . -1133) 192342) ((-1164 . -833) 192321) ((-1164 . -495) 192275) ((-1164 . -146) 192209) ((-1164 . -556) 192028) ((-1164 . -655) 191875) ((-1164 . -583) 191722) ((-1164 . -38) 191569) ((-1164 . -389) 191548) ((-1164 . -257) 191527) ((-1164 . -591) 191427) ((-1164 . -589) 191312) ((-1164 . -970) T) ((-1164 . -1025) T) ((-1164 . -1060) T) ((-1164 . -664) T) ((-1164 . -962) T) ((-1164 . -82) 191132) ((-1164 . -964) 190973) ((-1164 . -969) 190814) ((-1164 . -21) T) ((-1164 . -23) T) ((-1164 . -1013) T) ((-1164 . -553) 190796) ((-1164 . -1128) T) ((-1164 . -13) T) ((-1164 . -72) T) ((-1164 . -25) T) ((-1164 . -104) T) ((-1164 . -245) 190750) ((-1164 . -201) 190729) ((-1164 . -916) 190695) ((-1164 . -1114) 190661) ((-1164 . -1117) 190627) ((-1164 . -430) 190593) ((-1164 . -239) 190559) ((-1164 . -66) 190525) ((-1164 . -35) 190491) ((-1164 . -1157) 190461) ((-1164 . -47) 190431) ((-1164 . -120) 190410) ((-1164 . -118) 190389) ((-1164 . -887) 190352) ((-1164 . -812) 190258) ((-1164 . -807) 190162) ((-1164 . -810) 190068) ((-1164 . -241) 190026) ((-1164 . -189) 189978) ((-1164 . -186) 189924) ((-1164 . -190) 189876) ((-1164 . -1161) 189860) ((-1164 . -951) 189844) ((-1159 . -1163) 189805) ((-1159 . -311) 189784) ((-1159 . -1133) 189763) ((-1159 . -833) 189742) ((-1159 . -495) 189696) ((-1159 . -146) 189630) ((-1159 . -556) 189379) ((-1159 . -655) 189226) ((-1159 . -583) 189073) ((-1159 . -38) 188920) ((-1159 . -389) 188899) ((-1159 . -257) 188878) ((-1159 . -591) 188778) ((-1159 . -589) 188663) ((-1159 . -970) T) ((-1159 . -1025) T) ((-1159 . -1060) T) ((-1159 . -664) T) ((-1159 . -962) T) ((-1159 . -82) 188483) ((-1159 . -964) 188324) 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-1006) 184391) ((-1145 . -558) 184375) ((-1145 . -1013) 184353) ((-1145 . -553) 184320) ((-1145 . -1128) 184298) ((-1145 . -13) 184276) ((-1145 . -72) 184254) ((-1145 . -1007) 184211) ((-1143 . -1142) 184190) ((-1143 . -916) 184156) ((-1143 . -1114) 184122) ((-1143 . -1117) 184088) ((-1143 . -430) 184054) ((-1143 . -239) 184020) ((-1143 . -66) 183986) ((-1143 . -35) 183952) ((-1143 . -1157) 183929) ((-1143 . -47) 183906) ((-1143 . -556) 183661) ((-1143 . -655) 183481) ((-1143 . -583) 183301) ((-1143 . -591) 183112) ((-1143 . -589) 182970) ((-1143 . -969) 182784) ((-1143 . -964) 182598) ((-1143 . -82) 182386) ((-1143 . -38) 182206) ((-1143 . -887) 182176) ((-1143 . -241) 182076) ((-1143 . -1140) 182060) ((-1143 . -970) T) ((-1143 . -1025) T) ((-1143 . -1060) T) ((-1143 . -664) T) ((-1143 . -962) T) ((-1143 . -21) T) ((-1143 . -23) T) ((-1143 . -1013) T) ((-1143 . -553) 182042) ((-1143 . -1128) T) ((-1143 . -13) T) ((-1143 . -72) T) ((-1143 . -25) T) ((-1143 . -104) T) ((-1143 . -118) 181970) ((-1143 . -120) 181898) ((-1143 . -554) 181571) ((-1143 . -184) 181541) ((-1143 . -810) 181395) ((-1143 . -812) 181195) ((-1143 . -807) 180993) ((-1143 . -225) 180963) ((-1143 . -189) 180825) ((-1143 . -186) 180681) ((-1143 . -190) 180589) ((-1143 . -311) 180568) ((-1143 . -1133) 180547) ((-1143 . -833) 180526) ((-1143 . -495) 180480) ((-1143 . -146) 180414) ((-1143 . -389) 180393) ((-1143 . -257) 180372) ((-1143 . -245) 180326) ((-1143 . -201) 180305) ((-1143 . -287) 180275) ((-1143 . -453) 180135) ((-1143 . -259) 180074) ((-1143 . -326) 180044) ((-1143 . -581) 179952) ((-1143 . -340) 179922) ((-1143 . -797) 179795) ((-1143 . -741) 179748) ((-1143 . -715) 179701) ((-1143 . -717) 179654) ((-1143 . -757) 179556) ((-1143 . -760) 179458) ((-1143 . -719) 179411) ((-1143 . -722) 179364) ((-1143 . -756) 179317) ((-1143 . -795) 179287) ((-1143 . -822) 179240) ((-1143 . -934) 179193) ((-1143 . -951) 178982) ((-1143 . -1065) 178934) ((-1143 . -905) 178904) ((-1138 . -1142) 178865) 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-186) 175300) ((-1138 . -190) 175190) ((-1138 . -311) 175169) ((-1138 . -1133) 175148) ((-1138 . -833) 175127) ((-1138 . -495) 175081) ((-1138 . -146) 175015) ((-1138 . -389) 174994) ((-1138 . -257) 174973) ((-1138 . -245) 174927) ((-1138 . -201) 174906) ((-1138 . -287) 174858) ((-1138 . -453) 174592) ((-1138 . -259) 174477) ((-1138 . -326) 174429) ((-1138 . -581) 174381) ((-1138 . -340) 174333) ((-1138 . -797) NIL) ((-1138 . -741) NIL) ((-1138 . -715) NIL) ((-1138 . -717) NIL) ((-1138 . -757) NIL) ((-1138 . -760) NIL) ((-1138 . -719) NIL) ((-1138 . -722) NIL) ((-1138 . -756) NIL) ((-1138 . -795) 174285) ((-1138 . -822) NIL) ((-1138 . -934) NIL) ((-1138 . -951) 174251) ((-1138 . -1065) NIL) ((-1138 . -905) 174203) ((-1137 . -753) T) ((-1137 . -760) T) ((-1137 . -757) T) ((-1137 . -1013) T) ((-1137 . -553) 174185) ((-1137 . -1128) T) ((-1137 . -13) T) ((-1137 . -72) T) ((-1137 . -317) T) ((-1137 . -605) T) ((-1136 . -753) T) ((-1136 . -760) T) ((-1136 . -757) T) ((-1136 . -1013) T) ((-1136 . -553) 174167) ((-1136 . -1128) T) ((-1136 . -13) T) ((-1136 . -72) T) ((-1136 . -317) T) ((-1136 . -605) T) ((-1135 . -753) T) ((-1135 . -760) T) ((-1135 . -757) T) ((-1135 . -1013) T) ((-1135 . -553) 174149) ((-1135 . -1128) T) ((-1135 . -13) T) ((-1135 . -72) T) ((-1135 . -317) T) ((-1135 . -605) T) ((-1134 . -753) T) ((-1134 . -760) T) ((-1134 . -757) T) ((-1134 . -1013) T) ((-1134 . -553) 174131) ((-1134 . -1128) T) ((-1134 . -13) T) ((-1134 . -72) T) ((-1134 . -317) T) ((-1134 . -605) T) ((-1129 . -995) T) ((-1129 . -427) 174112) ((-1129 . -553) 174078) ((-1129 . -556) 174059) ((-1129 . -1013) T) ((-1129 . -1128) T) ((-1129 . -13) T) ((-1129 . -72) T) ((-1129 . -64) T) ((-1126 . -427) 174036) ((-1126 . -553) 173977) ((-1126 . -556) 173954) ((-1126 . -1013) 173932) ((-1126 . -1128) 173910) ((-1126 . -13) 173888) ((-1126 . -72) 173866) ((-1121 . -680) 173842) ((-1121 . -35) 173808) ((-1121 . -66) 173774) ((-1121 . -239) 173740) ((-1121 . -430) 173706) ((-1121 . -1117) 173672) ((-1121 . -1114) 173638) ((-1121 . -916) 173604) ((-1121 . -47) 173573) ((-1121 . -38) 173470) ((-1121 . -583) 173367) ((-1121 . -655) 173264) ((-1121 . -556) 173146) ((-1121 . -245) 173125) ((-1121 . -495) 173104) ((-1121 . -82) 172969) ((-1121 . -964) 172855) ((-1121 . -969) 172741) ((-1121 . -146) 172695) ((-1121 . -120) 172674) ((-1121 . -118) 172653) ((-1121 . -591) 172578) ((-1121 . -589) 172488) ((-1121 . -887) 172449) ((-1121 . -812) 172430) ((-1121 . -1128) T) ((-1121 . -13) T) ((-1121 . -807) 172409) ((-1121 . -962) T) ((-1121 . -664) T) ((-1121 . -1060) T) ((-1121 . -1025) T) ((-1121 . -970) T) ((-1121 . -21) T) ((-1121 . -23) T) ((-1121 . -1013) T) ((-1121 . -553) 172391) ((-1121 . -72) T) ((-1121 . -25) T) ((-1121 . -104) T) ((-1121 . -810) 172372) ((-1121 . -453) 172339) ((-1121 . -259) 172326) ((-1115 . -924) 172310) ((-1115 . -34) T) ((-1115 . -13) T) ((-1115 . -1128) T) ((-1115 . -72) 172264) ((-1115 . -553) 172199) ((-1115 . -259) 172137) ((-1115 . -453) 172070) ((-1115 . -1013) 172048) ((-1115 . -426) 172032) ((-1110 . -313) 172006) ((-1110 . -72) T) ((-1110 . -13) T) ((-1110 . -1128) T) ((-1110 . -553) 171988) ((-1110 . -1013) T) ((-1108 . -1013) T) ((-1108 . -553) 171970) ((-1108 . -1128) T) ((-1108 . -13) T) ((-1108 . -72) T) ((-1108 . -556) 171952) ((-1103 . -748) 171936) ((-1103 . -72) T) ((-1103 . -13) T) ((-1103 . -1128) T) ((-1103 . -553) 171918) ((-1103 . -1013) T) ((-1101 . -1106) 171897) ((-1101 . -183) 171845) ((-1101 . -76) 171793) ((-1101 . -259) 171591) ((-1101 . -453) 171343) ((-1101 . -426) 171278) ((-1101 . -124) 171226) ((-1101 . -554) NIL) ((-1101 . -193) 171174) ((-1101 . -550) 171153) ((-1101 . -243) 171132) ((-1101 . -1128) T) ((-1101 . -13) T) ((-1101 . -241) 171111) ((-1101 . -1013) T) ((-1101 . -553) 171093) ((-1101 . -72) T) ((-1101 . -34) T) ((-1101 . -539) 171072) ((-1097 . -1013) T) ((-1097 . -553) 171054) ((-1097 . -1128) T) ((-1097 . -13) T) ((-1097 . -72) T) ((-1096 . -753) T) ((-1096 . -760) T) ((-1096 . -757) T) ((-1096 . -1013) T) ((-1096 . -553) 171036) ((-1096 . -1128) T) ((-1096 . -13) T) ((-1096 . -72) T) ((-1096 . -317) T) ((-1096 . -605) T) ((-1095 . -753) T) ((-1095 . -760) T) ((-1095 . -757) T) ((-1095 . -1013) T) ((-1095 . -553) 171018) ((-1095 . -1128) T) ((-1095 . -13) T) ((-1095 . -72) T) ((-1095 . -317) T) ((-1094 . -1174) T) ((-1094 . -1013) T) ((-1094 . -553) 170985) ((-1094 . -1128) T) ((-1094 . -13) T) ((-1094 . -72) T) ((-1094 . -951) 170921) ((-1094 . -556) 170857) ((-1093 . -553) 170839) ((-1092 . -553) 170821) ((-1091 . -276) 170798) ((-1091 . -951) 170696) ((-1091 . -352) 170680) ((-1091 . -38) 170577) ((-1091 . -556) 170434) ((-1091 . -591) 170359) ((-1091 . -589) 170269) ((-1091 . -970) T) ((-1091 . -1025) T) ((-1091 . -1060) T) ((-1091 . -664) T) ((-1091 . -962) T) ((-1091 . -82) 170134) ((-1091 . -964) 170020) ((-1091 . -969) 169906) ((-1091 . -21) T) ((-1091 . -23) T) ((-1091 . -1013) T) ((-1091 . -553) 169888) ((-1091 . -1128) T) ((-1091 . -13) T) ((-1091 . -72) T) ((-1091 . -25) T) ((-1091 . -104) T) ((-1091 . -583) 169785) ((-1091 . -655) 169682) ((-1091 . -118) 169661) ((-1091 . -120) 169640) ((-1091 . -146) 169594) ((-1091 . -495) 169573) ((-1091 . -245) 169552) ((-1091 . -47) 169529) ((-1089 . -757) T) ((-1089 . -553) 169511) ((-1089 . -1013) T) ((-1089 . -72) T) ((-1089 . -13) T) ((-1089 . -1128) T) ((-1089 . -760) T) ((-1089 . -554) 169433) ((-1089 . -556) 169399) ((-1089 . -951) 169381) ((-1089 . -797) 169348) ((-1088 . -1171) 169332) ((-1088 . -190) 169291) ((-1088 . -556) 169173) ((-1088 . -591) 169098) ((-1088 . -589) 169008) ((-1088 . -104) T) ((-1088 . -25) T) ((-1088 . -72) T) ((-1088 . -553) 168990) ((-1088 . -1013) T) ((-1088 . -23) T) ((-1088 . -21) T) ((-1088 . -970) T) ((-1088 . -1025) T) ((-1088 . -1060) T) ((-1088 . -664) T) ((-1088 . -962) T) ((-1088 . -186) 168943) ((-1088 . -13) T) ((-1088 . -1128) T) ((-1088 . -189) 168902) ((-1088 . -241) 168867) ((-1088 . -810) 168780) ((-1088 . -807) 168668) ((-1088 . -812) 168581) ((-1088 . -887) 168551) ((-1088 . -38) 168448) ((-1088 . -82) 168313) ((-1088 . -964) 168199) ((-1088 . -969) 168085) ((-1088 . -583) 167982) ((-1088 . -655) 167879) ((-1088 . -118) 167858) ((-1088 . -120) 167837) ((-1088 . -146) 167791) ((-1088 . -495) 167770) ((-1088 . -245) 167749) ((-1088 . -47) 167726) ((-1088 . -1157) 167703) ((-1088 . -35) 167669) ((-1088 . -66) 167635) ((-1088 . -239) 167601) ((-1088 . -430) 167567) ((-1088 . -1117) 167533) ((-1088 . -1114) 167499) ((-1088 . -916) 167465) ((-1087 . -1163) 167426) ((-1087 . -311) 167405) ((-1087 . -1133) 167384) ((-1087 . -833) 167363) ((-1087 . -495) 167317) ((-1087 . -146) 167251) ((-1087 . -556) 167000) ((-1087 . -655) 166847) ((-1087 . -583) 166694) ((-1087 . -38) 166541) ((-1087 . -389) 166520) ((-1087 . -257) 166499) ((-1087 . -591) 166399) ((-1087 . -589) 166284) ((-1087 . -970) T) ((-1087 . -1025) T) ((-1087 . -1060) T) ((-1087 . -664) T) ((-1087 . -962) T) ((-1087 . -82) 166104) ((-1087 . -964) 165945) ((-1087 . -969) 165786) ((-1087 . -21) T) ((-1087 . -23) T) ((-1087 . -1013) T) ((-1087 . -553) 165768) ((-1087 . -1128) T) ((-1087 . -13) T) ((-1087 . -72) T) ((-1087 . -25) T) ((-1087 . -104) T) ((-1087 . -245) 165722) ((-1087 . -201) 165701) ((-1087 . -916) 165667) ((-1087 . -1114) 165633) ((-1087 . -1117) 165599) ((-1087 . -430) 165565) ((-1087 . -239) 165531) ((-1087 . -66) 165497) ((-1087 . -35) 165463) ((-1087 . -1157) 165433) ((-1087 . -47) 165403) ((-1087 . -120) 165382) ((-1087 . -118) 165361) ((-1087 . -887) 165324) ((-1087 . -812) 165230) ((-1087 . -807) 165111) ((-1087 . -810) 165017) ((-1087 . -241) 164975) ((-1087 . -189) 164927) ((-1087 . -186) 164873) ((-1087 . -190) 164825) ((-1087 . -1161) 164809) ((-1087 . -951) 164744) ((-1084 . -1154) 164728) ((-1084 . -1065) 164706) ((-1084 . -554) NIL) ((-1084 . -259) 164693) ((-1084 . -453) 164641) ((-1084 . -276) 164618) ((-1084 . -951) 164501) ((-1084 . -352) 164485) ((-1084 . -38) 164317) ((-1084 . -82) 164122) ((-1084 . -964) 163948) ((-1084 . -969) 163774) ((-1084 . -589) 163684) ((-1084 . -591) 163573) ((-1084 . -583) 163405) ((-1084 . -655) 163237) ((-1084 . -556) 163014) ((-1084 . -118) 162993) ((-1084 . -120) 162972) ((-1084 . -47) 162949) ((-1084 . -326) 162933) ((-1084 . -581) 162881) ((-1084 . -810) 162825) ((-1084 . -807) 162732) ((-1084 . -812) 162643) ((-1084 . -797) NIL) ((-1084 . -822) 162622) ((-1084 . -1133) 162601) ((-1084 . -862) 162571) ((-1084 . -833) 162550) ((-1084 . -495) 162464) ((-1084 . -245) 162378) ((-1084 . -146) 162272) ((-1084 . -389) 162206) ((-1084 . -257) 162185) ((-1084 . -241) 162112) ((-1084 . -190) T) ((-1084 . -104) T) ((-1084 . -25) T) ((-1084 . -72) T) ((-1084 . -553) 162094) ((-1084 . -1013) T) ((-1084 . -23) T) ((-1084 . -21) T) ((-1084 . -970) T) ((-1084 . -1025) T) ((-1084 . -1060) T) ((-1084 . -664) T) ((-1084 . -962) T) ((-1084 . -186) 162081) ((-1084 . -13) T) ((-1084 . -1128) T) ((-1084 . -189) T) ((-1084 . -225) 162065) ((-1084 . -184) 162049) 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-189) 158625) ((-1081 . -186) 158445) ((-1081 . -190) 158335) ((-1081 . -311) 158314) ((-1081 . -1133) 158293) ((-1081 . -833) 158272) ((-1081 . -495) 158226) ((-1081 . -146) 158160) ((-1081 . -389) 158139) ((-1081 . -257) 158118) ((-1081 . -245) 158072) ((-1081 . -201) 158051) ((-1081 . -287) 158003) ((-1081 . -453) 157737) ((-1081 . -259) 157622) ((-1081 . -326) 157574) ((-1081 . -581) 157526) ((-1081 . -340) 157478) ((-1081 . -797) NIL) ((-1081 . -741) NIL) ((-1081 . -715) NIL) ((-1081 . -717) NIL) ((-1081 . -757) NIL) ((-1081 . -760) NIL) ((-1081 . -719) NIL) ((-1081 . -722) NIL) ((-1081 . -756) NIL) ((-1081 . -795) 157430) ((-1081 . -822) NIL) ((-1081 . -934) NIL) ((-1081 . -951) 157396) ((-1081 . -1065) NIL) ((-1081 . -905) 157348) ((-1080 . -995) T) ((-1080 . -427) 157329) ((-1080 . -553) 157295) ((-1080 . -556) 157276) ((-1080 . -1013) T) ((-1080 . -1128) T) ((-1080 . -13) T) ((-1080 . -72) T) ((-1080 . -64) T) ((-1079 . -1013) T) ((-1079 . -553) 157258) ((-1079 . -1128) T) ((-1079 . -13) T) ((-1079 . -72) T) ((-1078 . -1013) T) ((-1078 . -553) 157240) ((-1078 . -1128) T) ((-1078 . -13) T) ((-1078 . -72) T) ((-1073 . -1106) 157216) ((-1073 . -183) 157161) ((-1073 . -76) 157106) ((-1073 . -259) 156895) ((-1073 . -453) 156635) ((-1073 . -426) 156567) ((-1073 . -124) 156512) ((-1073 . -554) NIL) ((-1073 . -193) 156457) ((-1073 . -550) 156433) ((-1073 . -243) 156409) ((-1073 . -1128) T) ((-1073 . -13) T) ((-1073 . -241) 156385) ((-1073 . -1013) T) ((-1073 . -553) 156367) ((-1073 . -72) T) ((-1073 . -34) T) ((-1073 . -539) 156343) ((-1072 . -1057) T) ((-1072 . -321) 156325) ((-1072 . -760) T) ((-1072 . -757) T) ((-1072 . -124) 156307) ((-1072 . -34) T) ((-1072 . -13) T) ((-1072 . -1128) T) ((-1072 . -72) T) ((-1072 . -553) 156289) ((-1072 . -259) NIL) ((-1072 . -453) NIL) ((-1072 . -1013) T) ((-1072 . -426) 156271) ((-1072 . -554) NIL) ((-1072 . -241) 156221) ((-1072 . -539) 156196) ((-1072 . -243) 156171) ((-1072 . -594) 156153) ((-1072 . -19) 156135) ((-1068 . -617) 156119) ((-1068 . -594) 156103) ((-1068 . -243) 156080) ((-1068 . -241) 156032) ((-1068 . -539) 156009) ((-1068 . -554) 155970) ((-1068 . -426) 155954) ((-1068 . -1013) 155932) ((-1068 . -453) 155865) ((-1068 . -259) 155803) ((-1068 . -553) 155738) ((-1068 . -72) 155692) ((-1068 . -1128) T) ((-1068 . -13) T) ((-1068 . -34) T) ((-1068 . -124) 155676) ((-1068 . -1167) 155660) ((-1068 . -924) 155644) ((-1068 . -1063) 155628) ((-1068 . -556) 155605) ((-1066 . -995) T) ((-1066 . -427) 155586) ((-1066 . -553) 155552) ((-1066 . -556) 155533) ((-1066 . -1013) T) ((-1066 . -1128) T) ((-1066 . -13) T) ((-1066 . -72) T) ((-1066 . -64) T) ((-1064 . -1106) 155512) ((-1064 . -183) 155460) ((-1064 . -76) 155408) ((-1064 . -259) 155206) ((-1064 . -453) 154958) ((-1064 . -426) 154893) ((-1064 . -124) 154841) ((-1064 . -554) NIL) ((-1064 . -193) 154789) ((-1064 . -550) 154768) ((-1064 . -243) 154747) ((-1064 . -1128) T) ((-1064 . -13) T) ((-1064 . -241) 154726) ((-1064 . -1013) T) ((-1064 . -553) 154708) ((-1064 . -72) T) ((-1064 . -34) T) ((-1064 . -539) 154687) ((-1061 . -1034) 154671) ((-1061 . -426) 154655) ((-1061 . -1013) 154633) ((-1061 . -453) 154566) ((-1061 . -259) 154504) ((-1061 . -553) 154439) ((-1061 . -72) 154393) ((-1061 . -1128) T) ((-1061 . -13) T) ((-1061 . -34) T) ((-1061 . -76) 154377) ((-1059 . -1020) 154346) ((-1059 . -1123) 154315) ((-1059 . -553) 154277) ((-1059 . -124) 154261) ((-1059 . -34) T) ((-1059 . -13) T) ((-1059 . -1128) T) ((-1059 . -72) T) ((-1059 . -259) 154199) ((-1059 . -453) 154132) ((-1059 . -1013) T) ((-1059 . -426) 154116) ((-1059 . -554) 154077) ((-1059 . -890) 154046) ((-1059 . -983) 154015) ((-1055 . -1036) 153960) ((-1055 . -426) 153944) ((-1055 . -453) 153877) ((-1055 . -259) 153815) ((-1055 . -34) T) ((-1055 . -966) 153755) ((-1055 . -951) 153653) ((-1055 . -556) 153572) ((-1055 . -352) 153556) ((-1055 . -581) 153504) ((-1055 . -591) 153442) ((-1055 . -326) 153426) ((-1055 . -190) 153405) ((-1055 . -186) 153353) ((-1055 . -189) 153307) ((-1055 . -225) 153291) ((-1055 . -807) 153215) ((-1055 . -812) 153141) ((-1055 . -810) 153100) ((-1055 . -184) 153084) ((-1055 . -655) 153019) ((-1055 . -583) 152954) ((-1055 . -589) 152913) ((-1055 . -104) T) ((-1055 . -25) T) ((-1055 . -72) T) ((-1055 . -13) T) ((-1055 . -1128) T) ((-1055 . -553) 152875) ((-1055 . -1013) T) ((-1055 . -23) T) ((-1055 . -21) T) ((-1055 . -969) 152859) ((-1055 . -964) 152843) ((-1055 . -82) 152822) ((-1055 . -962) T) ((-1055 . -664) T) ((-1055 . -1060) T) ((-1055 . -1025) T) ((-1055 . -970) T) ((-1055 . -38) 152782) ((-1055 . -554) 152743) ((-1054 . -924) 152714) ((-1054 . -34) T) ((-1054 . -13) T) ((-1054 . -1128) T) ((-1054 . -72) T) ((-1054 . -553) 152696) ((-1054 . -259) 152622) ((-1054 . -453) 152530) ((-1054 . -1013) T) ((-1054 . -426) 152501) ((-1053 . -1013) T) ((-1053 . -553) 152483) ((-1053 . -1128) T) ((-1053 . -13) T) ((-1053 . -72) T) ((-1048 . -1050) T) ((-1048 . -1174) T) ((-1048 . -64) T) ((-1048 . -72) T) ((-1048 . -13) T) ((-1048 . -1128) T) ((-1048 . -553) 152449) ((-1048 . -1013) T) ((-1048 . -556) 152430) ((-1048 . -427) 152411) ((-1048 . -995) T) ((-1046 . -1047) 152395) ((-1046 . -72) T) ((-1046 . -13) T) ((-1046 . -1128) T) ((-1046 . -553) 152377) ((-1046 . -1013) T) ((-1039 . -680) 152356) ((-1039 . -35) 152322) ((-1039 . -66) 152288) ((-1039 . -239) 152254) ((-1039 . -430) 152220) ((-1039 . -1117) 152186) ((-1039 . -1114) 152152) ((-1039 . -916) 152118) ((-1039 . -47) 152090) ((-1039 . -38) 151987) ((-1039 . -583) 151884) ((-1039 . -655) 151781) ((-1039 . -556) 151663) ((-1039 . -245) 151642) ((-1039 . -495) 151621) ((-1039 . -82) 151486) ((-1039 . -964) 151372) ((-1039 . -969) 151258) ((-1039 . -146) 151212) ((-1039 . -120) 151191) ((-1039 . -118) 151170) ((-1039 . -591) 151095) ((-1039 . -589) 151005) ((-1039 . -887) 150972) ((-1039 . -812) 150956) ((-1039 . -1128) T) ((-1039 . -13) T) ((-1039 . -807) 150938) ((-1039 . -962) T) ((-1039 . -664) T) ((-1039 . -1060) T) ((-1039 . -1025) T) 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. -1016) 144041) ((-1017 . -72) T) ((-1017 . -553) 144023) ((-1017 . -1013) T) ((-1017 . -241) 143979) ((-1017 . -1128) T) ((-1017 . -13) T) ((-1017 . -558) 143894) ((-1015 . -1016) 143846) ((-1015 . -72) T) ((-1015 . -553) 143828) ((-1015 . -1013) T) ((-1015 . -241) 143784) ((-1015 . -1128) T) ((-1015 . -13) T) ((-1015 . -558) 143687) ((-1014 . -317) T) ((-1014 . -72) T) ((-1014 . -13) T) ((-1014 . -1128) T) ((-1014 . -553) 143669) ((-1014 . -1013) T) ((-1009 . -366) 143653) ((-1009 . -1011) 143637) ((-1009 . -317) 143616) ((-1009 . -193) 143600) ((-1009 . -554) 143561) ((-1009 . -124) 143545) ((-1009 . -426) 143529) ((-1009 . -1013) T) ((-1009 . -453) 143462) ((-1009 . -259) 143400) ((-1009 . -553) 143382) ((-1009 . -72) T) ((-1009 . -1128) T) ((-1009 . -13) T) ((-1009 . -34) T) ((-1009 . -76) 143366) ((-1009 . -183) 143350) ((-1008 . -995) T) ((-1008 . -427) 143331) ((-1008 . -553) 143297) ((-1008 . -556) 143278) ((-1008 . -1013) T) ((-1008 . -1128) T) ((-1008 . -13) T) ((-1008 . -72) T) ((-1008 . -64) T) ((-1004 . -1128) T) ((-1004 . -13) T) ((-1004 . -1013) 143248) ((-1004 . -553) 143207) ((-1004 . -72) 143177) ((-1003 . -995) T) ((-1003 . -427) 143158) ((-1003 . -553) 143124) ((-1003 . -556) 143105) ((-1003 . -1013) T) ((-1003 . -1128) T) ((-1003 . -13) T) ((-1003 . -72) T) ((-1003 . -64) T) ((-1001 . -1006) 143089) ((-1001 . -558) 143073) ((-1001 . -1013) 143051) ((-1001 . -553) 143018) ((-1001 . -1128) 142996) ((-1001 . -13) 142974) ((-1001 . -72) 142952) ((-1001 . -1007) 142910) ((-1000 . -228) 142894) ((-1000 . -556) 142878) ((-1000 . -951) 142862) ((-1000 . -760) T) ((-1000 . -72) T) ((-1000 . -1013) T) ((-1000 . -553) 142844) ((-1000 . -757) T) ((-1000 . -186) 142831) ((-1000 . -13) T) ((-1000 . -1128) T) ((-1000 . -189) T) ((-999 . -213) 142768) ((-999 . -556) 142511) ((-999 . -951) 142340) ((-999 . -554) NIL) ((-999 . -276) 142301) ((-999 . -352) 142285) ((-999 . -38) 142137) ((-999 . -82) 141962) ((-999 . -964) 141808) ((-999 . -969) 141654) ((-999 . -589) 141564) ((-999 . -591) 141453) ((-999 . -583) 141305) ((-999 . -655) 141157) ((-999 . -118) 141136) ((-999 . -120) 141115) ((-999 . -146) 141029) ((-999 . -495) 140963) ((-999 . -245) 140897) ((-999 . -47) 140858) ((-999 . -326) 140842) ((-999 . -581) 140790) ((-999 . -389) 140744) ((-999 . -453) 140607) ((-999 . -810) 140542) ((-999 . -807) 140440) ((-999 . -812) 140342) ((-999 . -797) NIL) ((-999 . -822) 140321) ((-999 . -1133) 140300) ((-999 . -862) 140245) ((-999 . -259) 140232) ((-999 . -190) 140211) ((-999 . -104) T) ((-999 . -25) T) ((-999 . -72) T) ((-999 . -553) 140193) ((-999 . -1013) T) ((-999 . -23) T) ((-999 . -21) T) ((-999 . -970) T) ((-999 . -1025) T) ((-999 . -1060) T) ((-999 . -664) T) ((-999 . -962) T) ((-999 . -186) 140141) ((-999 . -13) T) ((-999 . -1128) T) ((-999 . -189) 140095) ((-999 . -225) 140079) ((-999 . -184) 140063) ((-997 . -553) 140045) ((-994 . -757) T) ((-994 . -553) 140027) ((-994 . -1013) T) ((-994 . -72) T) ((-994 . -13) T) ((-994 . -1128) T) ((-994 . -760) T) ((-994 . -554) 140008) ((-991 . -662) 139987) ((-991 . -951) 139885) ((-991 . -352) 139869) ((-991 . -581) 139817) ((-991 . -591) 139694) ((-991 . -326) 139678) ((-991 . -319) 139657) ((-991 . -120) 139636) ((-991 . -556) 139461) ((-991 . -655) 139335) ((-991 . -583) 139209) ((-991 . -589) 139107) ((-991 . -969) 139020) ((-991 . -964) 138933) ((-991 . -82) 138825) ((-991 . -38) 138699) ((-991 . -350) 138678) ((-991 . -342) 138657) ((-991 . -118) 138611) ((-991 . -1065) 138590) ((-991 . -298) 138569) ((-991 . -317) 138523) ((-991 . -201) 138477) ((-991 . -245) 138431) ((-991 . -257) 138385) ((-991 . -389) 138339) ((-991 . -495) 138293) ((-991 . -833) 138247) ((-991 . -1133) 138201) ((-991 . -311) 138155) ((-991 . -190) 138083) ((-991 . -186) 137959) ((-991 . -189) 137841) ((-991 . -225) 137811) ((-991 . -807) 137683) ((-991 . -812) 137557) ((-991 . -810) 137490) ((-991 . -184) 137460) ((-991 . -554) 137444) ((-991 . -21) T) ((-991 . -23) T) ((-991 . -1013) T) ((-991 . -553) 137426) ((-991 . -1128) T) ((-991 . -13) T) ((-991 . -72) T) ((-991 . -25) T) ((-991 . -104) T) ((-991 . -962) T) ((-991 . -664) T) ((-991 . -1060) T) ((-991 . -1025) T) ((-991 . -970) T) ((-991 . -146) T) ((-989 . -1013) T) ((-989 . -553) 137408) ((-989 . -1128) T) ((-989 . -13) T) ((-989 . -72) T) ((-989 . -241) 137387) ((-988 . -1013) T) ((-988 . -553) 137369) ((-988 . -1128) T) ((-988 . -13) T) ((-988 . -72) T) ((-987 . -1013) T) ((-987 . -553) 137351) ((-987 . -1128) T) ((-987 . -13) T) ((-987 . -72) T) ((-987 . -241) 137330) ((-987 . -951) 137307) ((-987 . -556) 137284) ((-986 . -1128) T) ((-986 . -13) T) ((-985 . -995) T) ((-985 . -427) 137265) ((-985 . -553) 137231) ((-985 . -556) 137212) ((-985 . -1013) T) ((-985 . -1128) T) ((-985 . -13) T) ((-985 . -72) T) ((-985 . -64) T) ((-978 . -995) T) ((-978 . -427) 137193) ((-978 . -553) 137159) ((-978 . -556) 137140) ((-978 . -1013) T) ((-978 . -1128) T) ((-978 . -13) T) ((-978 . -72) T) ((-978 . -64) T) ((-975 . -483) T) 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136766) ((-974 . -72) T) ((-974 . -13) T) ((-974 . -1128) T) ((-974 . -553) 136748) ((-974 . -1013) T) ((-971 . -1128) T) ((-971 . -13) T) ((-971 . -1013) 136726) ((-971 . -553) 136693) ((-971 . -72) 136671) ((-967 . -966) 136611) ((-967 . -583) 136556) ((-967 . -655) 136501) ((-967 . -34) T) ((-967 . -259) 136439) ((-967 . -453) 136372) ((-967 . -426) 136356) ((-967 . -591) 136340) ((-967 . -589) 136309) ((-967 . -104) T) ((-967 . -25) T) ((-967 . -72) T) ((-967 . -13) T) ((-967 . -1128) T) ((-967 . -553) 136271) ((-967 . -1013) T) ((-967 . -23) T) ((-967 . -21) T) ((-967 . -969) 136255) ((-967 . -964) 136239) ((-967 . -82) 136218) ((-967 . -1186) 136188) ((-967 . -554) 136149) ((-959 . -983) 136078) ((-959 . -890) 136007) ((-959 . -554) 135949) ((-959 . -426) 135914) ((-959 . -1013) T) ((-959 . -453) 135798) ((-959 . -259) 135706) ((-959 . -553) 135649) ((-959 . -72) T) ((-959 . -1128) T) ((-959 . -13) T) ((-959 . -34) T) ((-959 . -124) 135614) ((-959 . -1123) 135543) ((-949 . -995) T) ((-949 . -427) 135524) ((-949 . -553) 135490) ((-949 . -556) 135471) ((-949 . -1013) T) ((-949 . -1128) T) ((-949 . -13) T) ((-949 . -72) T) ((-949 . -64) T) ((-948 . -146) T) ((-948 . -556) 135440) ((-948 . -970) T) ((-948 . -1025) T) ((-948 . -1060) T) ((-948 . -664) T) ((-948 . -962) T) ((-948 . -591) 135414) ((-948 . -589) 135373) ((-948 . -104) T) ((-948 . -25) T) ((-948 . -72) T) ((-948 . -13) T) ((-948 . -1128) T) ((-948 . -553) 135355) ((-948 . -1013) T) ((-948 . -23) T) ((-948 . -21) T) ((-948 . -969) 135329) ((-948 . -964) 135303) ((-948 . -82) 135270) ((-948 . -38) 135254) ((-948 . -583) 135238) ((-948 . -655) 135222) ((-941 . -983) 135191) ((-941 . -890) 135160) ((-941 . -554) 135121) ((-941 . -426) 135105) ((-941 . -1013) T) ((-941 . -453) 135038) ((-941 . -259) 134976) ((-941 . -553) 134938) ((-941 . -72) T) ((-941 . -1128) T) ((-941 . -13) T) ((-941 . -34) T) ((-941 . -124) 134922) ((-941 . -1123) 134891) ((-940 . -1013) T) ((-940 . -553) 134873) ((-940 . -1128) T) ((-940 . -13) T) ((-940 . -72) T) ((-938 . -926) T) ((-938 . -916) T) ((-938 . -715) T) ((-938 . -717) T) ((-938 . -757) T) ((-938 . -760) T) ((-938 . -719) T) ((-938 . -722) T) ((-938 . -756) T) ((-938 . -951) 134758) ((-938 . -352) 134720) ((-938 . -201) T) ((-938 . -245) T) ((-938 . -257) T) ((-938 . -389) T) ((-938 . -38) 134657) ((-938 . -583) 134594) ((-938 . -655) 134531) ((-938 . -556) 134468) ((-938 . -495) T) ((-938 . -833) T) ((-938 . -1133) T) ((-938 . -311) T) ((-938 . -82) 134377) ((-938 . -964) 134314) ((-938 . -969) 134251) ((-938 . -146) T) ((-938 . -120) T) ((-938 . -591) 134188) ((-938 . -589) 134125) ((-938 . -104) T) ((-938 . -25) T) ((-938 . -72) T) ((-938 . -13) T) ((-938 . -1128) T) ((-938 . -553) 134107) ((-938 . -1013) T) ((-938 . -23) T) ((-938 . -21) T) ((-938 . -962) T) ((-938 . -664) T) ((-938 . -1060) T) ((-938 . -1025) T) ((-938 . -970) T) ((-933 . -995) T) ((-933 . -427) 134088) ((-933 . -553) 134054) ((-933 . -556) 134035) ((-933 . -1013) T) ((-933 . -1128) T) ((-933 . -13) T) ((-933 . -72) T) ((-933 . -64) T) ((-918 . -905) 134017) ((-918 . -1065) T) ((-918 . -556) 133967) ((-918 . -951) 133927) ((-918 . -554) 133857) ((-918 . -934) T) ((-918 . -822) NIL) ((-918 . -795) 133839) ((-918 . -756) T) ((-918 . -722) T) ((-918 . -719) T) ((-918 . -760) T) ((-918 . -757) T) ((-918 . -717) T) ((-918 . -715) T) ((-918 . -741) T) ((-918 . -797) 133821) ((-918 . -340) 133803) ((-918 . -581) 133785) ((-918 . -326) 133767) ((-918 . -241) NIL) ((-918 . -259) NIL) ((-918 . -453) NIL) ((-918 . -287) 133749) ((-918 . -201) T) ((-918 . -82) 133676) ((-918 . -964) 133626) ((-918 . -969) 133576) ((-918 . -245) T) ((-918 . -655) 133526) ((-918 . -583) 133476) ((-918 . -591) 133426) ((-918 . -589) 133376) ((-918 . -38) 133326) ((-918 . -257) T) ((-918 . -389) T) ((-918 . -146) T) ((-918 . -495) T) ((-918 . -833) T) ((-918 . -1133) T) ((-918 . -311) T) ((-918 . -190) T) ((-918 . -186) 133313) ((-918 . -189) T) ((-918 . -225) 133295) ((-918 . -807) NIL) ((-918 . -812) NIL) ((-918 . -810) NIL) ((-918 . -184) 133277) ((-918 . -120) T) ((-918 . -118) NIL) ((-918 . -104) T) ((-918 . -25) T) ((-918 . -72) T) ((-918 . -13) T) ((-918 . -1128) T) ((-918 . -553) 133237) ((-918 . -1013) T) ((-918 . -23) T) ((-918 . -21) T) ((-918 . -962) T) ((-918 . -664) T) ((-918 . -1060) T) ((-918 . -1025) T) ((-918 . -970) T) ((-917 . -290) 133211) ((-917 . -146) T) ((-917 . -556) 133141) ((-917 . -970) T) ((-917 . -1025) T) ((-917 . -1060) T) ((-917 . -664) T) ((-917 . -962) T) ((-917 . -591) 133043) ((-917 . -589) 132973) ((-917 . -104) T) ((-917 . -25) T) ((-917 . -72) T) ((-917 . -13) T) ((-917 . -1128) T) ((-917 . -553) 132955) ((-917 . -1013) T) ((-917 . -23) T) ((-917 . -21) T) ((-917 . -969) 132900) ((-917 . -964) 132845) ((-917 . -82) 132762) ((-917 . -554) 132746) ((-917 . -184) 132723) ((-917 . -810) 132675) ((-917 . -812) 132587) ((-917 . -807) 132497) ((-917 . -225) 132474) ((-917 . -189) 132414) ((-917 . -186) 132348) ((-917 . -190) 132320) 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. -589) 119709) ((-782 . -38) 119661) ((-782 . -257) T) ((-782 . -389) T) ((-782 . -146) T) ((-782 . -495) T) ((-782 . -833) T) ((-782 . -1133) T) ((-782 . -311) T) ((-782 . -190) 119640) ((-782 . -186) 119588) ((-782 . -189) 119542) ((-782 . -225) 119526) ((-782 . -807) 119450) ((-782 . -812) 119376) ((-782 . -810) 119335) ((-782 . -184) 119319) ((-782 . -120) 119298) ((-782 . -118) 119277) ((-782 . -104) T) ((-782 . -25) T) ((-782 . -72) T) ((-782 . -13) T) ((-782 . -1128) T) ((-782 . -553) 119259) ((-782 . -1013) T) ((-782 . -23) T) ((-782 . -21) T) ((-782 . -962) T) ((-782 . -664) T) ((-782 . -1060) T) ((-782 . -1025) T) ((-782 . -970) T) ((-781 . -905) 119236) ((-781 . -1065) NIL) ((-781 . -951) 119213) ((-781 . -556) 119143) ((-781 . -554) NIL) ((-781 . -934) NIL) ((-781 . -822) NIL) ((-781 . -795) 119120) ((-781 . -756) NIL) ((-781 . -722) NIL) ((-781 . -719) NIL) ((-781 . -760) NIL) ((-781 . -757) NIL) ((-781 . -717) NIL) ((-781 . -715) NIL) ((-781 . -741) NIL) ((-781 . -797) 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. -833) T) ((-779 . -495) T) ((-779 . -245) T) ((-779 . -146) T) ((-779 . -556) 118174) ((-779 . -655) 118161) ((-779 . -583) 118148) ((-779 . -969) 118135) ((-779 . -964) 118122) ((-779 . -82) 118107) ((-779 . -38) 118094) ((-779 . -389) T) ((-779 . -257) T) ((-779 . -962) T) ((-779 . -664) T) ((-779 . -1060) T) ((-779 . -1025) T) ((-779 . -970) T) ((-779 . -21) T) ((-779 . -589) 118066) ((-779 . -23) T) ((-779 . -1013) T) ((-779 . -553) 118048) ((-779 . -1128) T) ((-779 . -13) T) ((-779 . -72) T) ((-779 . -25) T) ((-779 . -104) T) ((-779 . -591) 118035) ((-779 . -120) T) ((-776 . -962) T) ((-776 . -664) T) ((-776 . -1060) T) ((-776 . -1025) T) ((-776 . -970) T) ((-776 . -21) T) ((-776 . -589) 117980) ((-776 . -23) T) ((-776 . -1013) T) ((-776 . -553) 117942) ((-776 . -1128) T) ((-776 . -13) T) ((-776 . -72) T) ((-776 . -25) T) ((-776 . -104) T) ((-776 . -591) 117902) ((-776 . -556) 117837) ((-776 . -427) 117814) ((-776 . -38) 117784) ((-776 . -82) 117749) ((-776 . -964) 117719) 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. -964) 114156) ((-742 . -82) 114135) ((-742 . -962) T) ((-742 . -664) T) ((-742 . -1060) T) ((-742 . -1025) T) ((-742 . -970) T) ((-742 . -38) 114105) ((-742 . -190) 114084) ((-742 . -186) 114057) ((-742 . -189) 114036) ((-740 . -333) 114020) ((-740 . -556) 114004) ((-740 . -951) 113988) ((-740 . -760) T) ((-740 . -757) T) ((-740 . -1025) T) ((-740 . -72) T) ((-740 . -13) T) ((-740 . -1128) T) ((-740 . -553) 113970) ((-740 . -1013) T) ((-740 . -664) T) ((-740 . -755) T) ((-740 . -767) T) ((-739 . -228) 113954) ((-739 . -556) 113938) ((-739 . -951) 113922) ((-739 . -760) T) ((-739 . -72) T) ((-739 . -1013) T) ((-739 . -553) 113904) ((-739 . -757) T) ((-739 . -186) 113891) ((-739 . -13) T) ((-739 . -1128) T) ((-739 . -189) T) ((-738 . -82) 113826) ((-738 . -964) 113777) ((-738 . -969) 113728) ((-738 . -21) T) ((-738 . -589) 113664) ((-738 . -23) T) ((-738 . -1013) T) ((-738 . -553) 113633) ((-738 . -1128) T) ((-738 . -13) T) ((-738 . -72) T) ((-738 . -25) T) ((-738 . -104) T) ((-738 . -591) 113584) ((-738 . -190) T) ((-738 . -556) 113493) ((-738 . -970) T) ((-738 . -1025) T) ((-738 . -1060) T) ((-738 . -664) T) ((-738 . -962) T) ((-738 . -186) 113480) ((-738 . -189) T) ((-738 . -427) 113464) ((-738 . -311) 113443) ((-738 . -1133) 113422) ((-738 . -833) 113401) ((-738 . -495) 113380) ((-738 . -146) 113359) ((-738 . -655) 113296) ((-738 . -583) 113233) ((-738 . -38) 113170) ((-738 . -389) 113149) ((-738 . -257) 113128) ((-738 . -245) 113107) ((-738 . -201) 113086) ((-737 . -213) 113025) ((-737 . -556) 112769) ((-737 . -951) 112599) ((-737 . -554) NIL) ((-737 . -276) 112561) ((-737 . -352) 112545) ((-737 . -38) 112397) ((-737 . -82) 112222) ((-737 . -964) 112068) ((-737 . -969) 111914) ((-737 . -589) 111824) ((-737 . -591) 111713) ((-737 . -583) 111565) ((-737 . -655) 111417) ((-737 . -118) 111396) ((-737 . -120) 111375) ((-737 . -146) 111289) ((-737 . -495) 111223) ((-737 . -245) 111157) ((-737 . -47) 111119) ((-737 . -326) 111103) ((-737 . -581) 111051) ((-737 . 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103656) ((-705 . -807) 103563) ((-705 . -812) 103474) ((-705 . -797) NIL) ((-705 . -822) 103453) ((-705 . -1133) 103432) ((-705 . -862) 103402) ((-705 . -833) 103381) ((-705 . -495) 103295) ((-705 . -245) 103209) ((-705 . -146) 103103) ((-705 . -389) 103037) ((-705 . -257) 103016) ((-705 . -241) 102943) ((-705 . -190) T) ((-705 . -104) T) ((-705 . -25) T) ((-705 . -72) T) ((-705 . -553) 102904) ((-705 . -1013) T) ((-705 . -23) T) ((-705 . -21) T) ((-705 . -970) T) ((-705 . -1025) T) ((-705 . -1060) T) ((-705 . -664) T) ((-705 . -962) T) ((-705 . -186) 102891) ((-705 . -13) T) ((-705 . -1128) T) ((-705 . -189) T) ((-705 . -225) 102875) ((-705 . -184) 102859) ((-704 . -977) 102826) ((-704 . -554) 102461) ((-704 . -259) 102448) ((-704 . -453) 102400) ((-704 . -276) 102372) ((-704 . -951) 102231) ((-704 . -352) 102215) ((-704 . -38) 102067) ((-704 . -556) 101840) ((-704 . -591) 101729) ((-704 . -589) 101639) ((-704 . -970) T) ((-704 . -1025) T) ((-704 . -1060) T) ((-704 . -664) T) ((-704 . 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-722) T) ((-695 . -664) T) ((-695 . -1025) T) ((-676 . -677) 100054) ((-676 . -1011) 100038) ((-676 . -193) 100022) ((-676 . -554) 99983) ((-676 . -124) 99967) ((-676 . -426) 99951) ((-676 . -1013) T) ((-676 . -453) 99884) ((-676 . -259) 99822) ((-676 . -553) 99804) ((-676 . -72) T) ((-676 . -1128) T) ((-676 . -13) T) ((-676 . -34) T) ((-676 . -76) 99788) ((-676 . -635) 99772) ((-675 . -962) T) ((-675 . -664) T) ((-675 . -1060) T) ((-675 . -1025) T) ((-675 . -970) T) ((-675 . -21) T) ((-675 . -589) 99717) ((-675 . -23) T) ((-675 . -1013) T) ((-675 . -553) 99699) ((-675 . -1128) T) ((-675 . -13) T) ((-675 . -72) T) ((-675 . -25) T) ((-675 . -104) T) ((-675 . -591) 99659) ((-675 . -556) 99615) ((-675 . -951) 99586) ((-675 . -120) 99565) ((-675 . -118) 99544) ((-675 . -38) 99514) ((-675 . -82) 99479) ((-675 . -964) 99449) ((-675 . -969) 99419) ((-675 . -583) 99389) ((-675 . -655) 99359) ((-675 . -317) 99312) ((-671 . -862) 99265) ((-671 . -556) 99057) ((-671 . -951) 98935) ((-671 . -1133) 98914) ((-671 . -822) 98893) ((-671 . -797) NIL) ((-671 . -812) 98870) ((-671 . -807) 98845) ((-671 . -810) 98822) ((-671 . -453) 98760) ((-671 . -389) 98714) ((-671 . -581) 98662) ((-671 . -591) 98551) ((-671 . -326) 98535) ((-671 . -47) 98500) ((-671 . -38) 98352) ((-671 . -583) 98204) ((-671 . -655) 98056) ((-671 . -245) 97990) ((-671 . -495) 97924) ((-671 . -82) 97749) ((-671 . -964) 97595) ((-671 . -969) 97441) ((-671 . -146) 97355) ((-671 . -120) 97334) ((-671 . -118) 97313) ((-671 . -589) 97223) ((-671 . -104) T) ((-671 . -25) T) ((-671 . -72) T) ((-671 . -13) T) ((-671 . -1128) T) ((-671 . -553) 97205) ((-671 . -1013) T) ((-671 . -23) T) ((-671 . -21) T) ((-671 . -962) T) ((-671 . -664) T) ((-671 . -1060) T) ((-671 . -1025) T) ((-671 . -970) T) ((-671 . -352) 97189) ((-671 . -276) 97154) ((-671 . -259) 97141) ((-671 . -554) 97002) ((-665 . -666) 96986) ((-665 . -80) 96970) ((-665 . -1128) T) ((-665 . |MappingCategory|) 96944) ((-665 . -1023) 96928) ((-665 . -1013) T) ((-665 . -553) 96889) ((-665 . -13) T) ((-665 . -72) T) ((-656 . -410) T) ((-656 . -1025) T) ((-656 . -72) T) ((-656 . -13) T) ((-656 . -1128) T) ((-656 . -553) 96871) ((-656 . -1013) T) ((-656 . -664) T) ((-653 . -962) T) ((-653 . -664) T) ((-653 . -1060) T) ((-653 . -1025) T) ((-653 . -970) T) ((-653 . -21) T) ((-653 . -589) 96843) ((-653 . -23) T) ((-653 . -1013) T) ((-653 . -553) 96825) ((-653 . -1128) T) ((-653 . -13) T) ((-653 . -72) T) ((-653 . -25) T) ((-653 . -104) T) ((-653 . -591) 96812) ((-653 . -556) 96794) ((-652 . -962) T) ((-652 . -664) T) ((-652 . -1060) T) ((-652 . -1025) T) ((-652 . -970) T) ((-652 . -21) T) ((-652 . -589) 96739) ((-652 . -23) T) ((-652 . -1013) T) ((-652 . -553) 96721) ((-652 . -1128) T) ((-652 . -13) T) ((-652 . -72) T) ((-652 . -25) T) ((-652 . -104) T) ((-652 . -591) 96681) ((-652 . -556) 96636) ((-652 . -951) 96606) ((-652 . -241) 96585) ((-652 . -120) 96564) ((-652 . -118) 96543) ((-652 . -38) 96513) ((-652 . -82) 96478) ((-652 . -964) 96448) ((-652 . -969) 96418) ((-652 . -583) 96388) ((-652 . -655) 96358) ((-651 . -757) T) ((-651 . -553) 96293) ((-651 . -1013) T) ((-651 . -72) T) ((-651 . -13) T) ((-651 . -1128) T) ((-651 . -760) T) ((-651 . -427) 96243) ((-651 . -556) 96193) ((-650 . -1154) 96177) ((-650 . -1065) 96155) ((-650 . -554) NIL) ((-650 . -259) 96142) ((-650 . -453) 96090) ((-650 . -276) 96067) ((-650 . -951) 95950) ((-650 . -352) 95934) ((-650 . -38) 95766) ((-650 . -82) 95571) ((-650 . -964) 95397) ((-650 . -969) 95223) ((-650 . -589) 95133) ((-650 . -591) 95022) ((-650 . -583) 94854) ((-650 . -655) 94686) ((-650 . -556) 94450) ((-650 . -118) 94429) ((-650 . -120) 94408) ((-650 . -47) 94385) ((-650 . -326) 94369) ((-650 . -581) 94317) ((-650 . -810) 94261) ((-650 . -807) 94168) ((-650 . -812) 94079) ((-650 . -797) NIL) ((-650 . -822) 94058) ((-650 . -1133) 94037) ((-650 . -862) 94007) ((-650 . -833) 93986) ((-650 . -495) 93900) ((-650 . -245) 93814) ((-650 . -146) 93708) ((-650 . -389) 93642) ((-650 . -257) 93621) 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92388) ((-615 . -1013) T) ((-615 . -72) T) ((-615 . -13) T) ((-615 . -1128) T) ((-615 . -760) T) ((-615 . -951) 92372) ((-615 . -556) 92356) ((-614 . -995) T) ((-614 . -427) 92337) ((-614 . -553) 92303) ((-614 . -556) 92284) ((-614 . -1013) T) ((-614 . -1128) T) ((-614 . -13) T) ((-614 . -72) T) ((-614 . -64) T) ((-613 . -1036) 92229) ((-613 . -426) 92213) ((-613 . -453) 92146) ((-613 . -259) 92084) ((-613 . -34) T) ((-613 . -966) 92024) ((-613 . -951) 91922) ((-613 . -556) 91841) ((-613 . -352) 91825) ((-613 . -581) 91773) ((-613 . -591) 91711) ((-613 . -326) 91695) ((-613 . -190) 91674) ((-613 . -186) 91622) ((-613 . -189) 91576) ((-613 . -225) 91560) ((-613 . -807) 91484) ((-613 . -812) 91410) ((-613 . -810) 91369) ((-613 . -184) 91353) ((-613 . -655) 91337) ((-613 . -583) 91321) ((-613 . -589) 91280) ((-613 . -104) T) ((-613 . -25) T) ((-613 . -72) T) ((-613 . -13) T) ((-613 . -1128) T) ((-613 . -553) 91242) ((-613 . -1013) T) ((-613 . -23) T) ((-613 . -21) T) ((-613 . -969) 91226) 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. -553) 76962) ((-458 . -259) 76900) ((-458 . -453) 76833) ((-458 . -1013) 76811) ((-458 . -426) 76795) ((-457 . -279) 76772) ((-457 . -190) T) ((-457 . -186) 76759) ((-457 . -189) T) ((-457 . -317) T) ((-457 . -1065) T) ((-457 . -298) T) ((-457 . -120) 76741) ((-457 . -556) 76671) ((-457 . -591) 76616) ((-457 . -589) 76546) ((-457 . -104) T) ((-457 . -25) T) ((-457 . -72) T) ((-457 . -13) T) ((-457 . -1128) T) ((-457 . -553) 76528) ((-457 . -1013) T) ((-457 . -23) T) ((-457 . -21) T) ((-457 . -970) T) ((-457 . -1025) T) ((-457 . -1060) T) ((-457 . -664) T) ((-457 . -962) T) ((-457 . -311) T) ((-457 . -1133) T) ((-457 . -833) T) ((-457 . -495) T) ((-457 . -146) T) ((-457 . -655) 76473) ((-457 . -583) 76418) ((-457 . -38) 76383) ((-457 . -389) T) ((-457 . -257) T) ((-457 . -82) 76300) ((-457 . -964) 76245) ((-457 . -969) 76190) ((-457 . -245) T) ((-457 . -201) T) ((-457 . -342) T) ((-457 . -118) T) ((-457 . -951) 76167) ((-457 . -1186) 76144) ((-457 . -1197) 76121) ((-456 . -995) T) 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60812) ((-411 . -146) 60746) ((-411 . -495) 60700) ((-411 . -833) 60679) ((-411 . -1133) 60658) ((-411 . -311) 60637) ((-405 . -1013) T) ((-405 . -553) 60619) ((-405 . -1128) T) ((-405 . -13) T) ((-405 . -72) T) ((-400 . -890) 60588) ((-400 . -554) 60549) ((-400 . -426) 60533) ((-400 . -1013) T) ((-400 . -453) 60466) ((-400 . -259) 60404) ((-400 . -553) 60366) ((-400 . -72) T) ((-400 . -1128) T) ((-400 . -13) T) ((-400 . -34) T) ((-400 . -124) 60350) ((-398 . -655) 60321) ((-398 . -583) 60292) ((-398 . -591) 60263) ((-398 . -589) 60219) ((-398 . -104) T) ((-398 . -25) T) ((-398 . -72) T) ((-398 . -13) T) ((-398 . -1128) T) ((-398 . -553) 60201) ((-398 . -1013) T) ((-398 . -23) T) ((-398 . -21) T) ((-398 . -969) 60172) ((-398 . -964) 60143) ((-398 . -82) 60104) ((-391 . -862) 60071) ((-391 . -556) 59863) ((-391 . -951) 59741) ((-391 . -1133) 59720) ((-391 . -822) 59699) ((-391 . -797) NIL) ((-391 . -812) 59676) ((-391 . -807) 59651) ((-391 . -810) 59628) ((-391 . -453) 59566) ((-391 . 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. -25) 18167) ((-197 . -72) 17904) ((-197 . -13) T) ((-197 . -1128) T) ((-197 . -1013) 17660) ((-197 . -23) 17516) ((-197 . -21) 17431) ((-181 . -628) 17389) ((-181 . -426) 17373) ((-181 . -1013) 17351) ((-181 . -453) 17284) ((-181 . -259) 17222) ((-181 . -553) 17157) ((-181 . -72) 17111) ((-181 . -1128) T) ((-181 . -13) T) ((-181 . -34) T) ((-181 . -57) 17069) ((-179 . -344) T) ((-179 . -120) T) ((-179 . -556) 17019) ((-179 . -591) 16984) ((-179 . -589) 16934) ((-179 . -104) T) ((-179 . -25) T) ((-179 . -72) T) ((-179 . -13) T) ((-179 . -1128) T) ((-179 . -553) 16916) ((-179 . -1013) T) ((-179 . -23) T) ((-179 . -21) T) ((-179 . -970) T) ((-179 . -1025) T) ((-179 . -1060) T) ((-179 . -664) T) ((-179 . -962) T) ((-179 . -554) 16846) ((-179 . -311) T) ((-179 . -1133) T) ((-179 . -833) T) ((-179 . -495) T) ((-179 . -146) T) ((-179 . -655) 16811) ((-179 . -583) 16776) ((-179 . -38) 16741) ((-179 . -389) T) ((-179 . -257) T) ((-179 . -82) 16690) ((-179 . -964) 16655) ((-179 . -969) 16620) 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((-81 . -34) T) ((-81 . -72) T) ((-81 . -553) 6943) ((-81 . -259) NIL) ((-81 . -453) NIL) ((-81 . -1013) T) ((-81 . -426) 6926) ((-81 . -554) 6908) ((-81 . -241) 6859) ((-81 . -539) 6835) ((-81 . -243) 6811) ((-81 . -594) 6794) ((-81 . -19) 6777) ((-81 . -605) T) ((-81 . -13) T) ((-81 . -1128) T) ((-81 . -84) T) ((-79 . -80) 6761) ((-79 . -1128) T) ((-79 . |MappingCategory|) 6735) ((-79 . -1013) T) ((-79 . -553) 6717) ((-79 . -13) T) ((-79 . -72) T) ((-78 . -553) 6699) ((-77 . -905) 6681) ((-77 . -1065) T) ((-77 . -556) 6631) ((-77 . -951) 6591) ((-77 . -554) 6521) ((-77 . -934) T) ((-77 . -822) NIL) ((-77 . -795) 6503) ((-77 . -756) T) ((-77 . -722) T) ((-77 . -719) T) ((-77 . -760) T) ((-77 . -757) T) ((-77 . -717) T) ((-77 . -715) T) ((-77 . -741) T) ((-77 . -797) 6485) ((-77 . -340) 6467) ((-77 . -581) 6449) ((-77 . -326) 6431) ((-77 . -241) NIL) ((-77 . -259) NIL) ((-77 . -453) NIL) ((-77 . -287) 6413) ((-77 . -201) T) ((-77 . -82) 6340) ((-77 . -964) 6290) ((-77 . -969) 6240) ((-77 . -245) T) ((-77 . -655) 6190) ((-77 . -583) 6140) ((-77 . -591) 6090) ((-77 . -589) 6040) ((-77 . -38) 5990) ((-77 . -257) T) ((-77 . -389) T) ((-77 . -146) T) ((-77 . -495) T) ((-77 . -833) T) ((-77 . -1133) T) ((-77 . -311) T) ((-77 . -190) T) ((-77 . -186) 5977) ((-77 . -189) T) ((-77 . -225) 5959) ((-77 . -807) NIL) ((-77 . -812) NIL) ((-77 . -810) NIL) ((-77 . -184) 5941) ((-77 . -120) T) ((-77 . -118) NIL) ((-77 . -104) T) ((-77 . -25) T) ((-77 . -72) T) ((-77 . -13) T) ((-77 . -1128) T) ((-77 . -553) 5884) ((-77 . -1013) T) ((-77 . -23) T) ((-77 . -21) T) ((-77 . -962) T) ((-77 . -664) T) ((-77 . -1060) T) ((-77 . -1025) T) ((-77 . -970) T) ((-73 . -98) 5868) ((-73 . -924) 5852) ((-73 . -34) T) ((-73 . -13) T) ((-73 . -1128) T) ((-73 . -72) 5806) ((-73 . -553) 5741) ((-73 . -259) 5679) ((-73 . -453) 5612) ((-73 . -1013) 5590) ((-73 . -426) 5574) ((-73 . -92) 5558) ((-69 . -410) T) ((-69 . -1025) T) ((-69 . -72) T) ((-69 . -13) T) ((-69 . -1128) T) ((-69 . -553) 5540) ((-69 . -1013) T) ((-69 . -664) T) ((-69 . -241) 5519) ((-67 . -995) T) ((-67 . -427) 5500) ((-67 . -553) 5466) ((-67 . -556) 5447) ((-67 . -1013) T) ((-67 . -1128) T) ((-67 . -13) T) ((-67 . -72) T) ((-67 . -64) T) ((-62 . -1034) 5431) ((-62 . -426) 5415) ((-62 . -1013) 5393) ((-62 . -453) 5326) ((-62 . -259) 5264) ((-62 . -553) 5199) ((-62 . -72) 5153) ((-62 . -1128) T) ((-62 . -13) T) ((-62 . -34) T) ((-62 . -76) 5137) ((-60 . -57) 5099) ((-60 . -34) T) ((-60 . -13) T) ((-60 . -1128) T) ((-60 . -72) 5053) ((-60 . -553) 4988) ((-60 . -259) 4926) ((-60 . -453) 4859) ((-60 . -1013) 4837) ((-60 . -426) 4821) ((-58 . -19) 4805) ((-58 . -594) 4789) ((-58 . -243) 4766) ((-58 . -241) 4718) ((-58 . -539) 4695) ((-58 . -554) 4656) ((-58 . -426) 4640) ((-58 . -1013) 4593) ((-58 . -453) 4526) ((-58 . -259) 4464) ((-58 . -553) 4379) ((-58 . -72) 4313) ((-58 . -1128) T) ((-58 . -13) T) ((-58 . -34) T) ((-58 . -124) 4297) ((-58 . -757) 4276) ((-58 . -760) 4255) ((-58 . -321) 4239) ((-55 . -1013) T) ((-55 . -553) 4221) ((-55 . -1128) T) ((-55 . -13) T) ((-55 . -72) T) ((-55 . -951) 4203) ((-55 . -556) 4185) ((-51 . -1013) T) ((-51 . -553) 4167) ((-51 . -1128) T) ((-51 . -13) T) ((-51 . -72) T) ((-50 . -561) 4151) ((-50 . -556) 4120) ((-50 . -591) 4094) ((-50 . -589) 4053) ((-50 . -970) T) ((-50 . -1025) T) ((-50 . -1060) T) ((-50 . -664) T) ((-50 . -962) T) ((-50 . -21) T) ((-50 . -23) T) ((-50 . -1013) T) ((-50 . -553) 4035) ((-50 . -1128) T) ((-50 . -13) T) ((-50 . -72) T) ((-50 . -25) T) ((-50 . -104) T) ((-50 . -951) 4019) ((-49 . -1013) T) ((-49 . -553) 4001) ((-49 . -1128) T) ((-49 . -13) T) ((-49 . -72) T) ((-48 . -253) T) ((-48 . -72) T) ((-48 . -13) T) ((-48 . -1128) T) ((-48 . -553) 3983) ((-48 . -1013) T) ((-48 . -556) 3884) ((-48 . -951) 3827) ((-48 . -453) 3793) ((-48 . -259) 3780) ((-48 . -27) T) ((-48 . -916) T) ((-48 . -201) T) ((-48 . -82) 3729) ((-48 . -964) 3694) ((-48 . -969) 3659) ((-48 . -245) T) ((-48 . -655) 3624) ((-48 . -583) 3589) ((-48 . -591) 3539) ((-48 . -589) 3489) ((-48 . -104) T) ((-48 . -25) T) ((-48 . -23) T) ((-48 . -21) T) ((-48 . -962) T) ((-48 . -664) T) ((-48 . -1060) T) ((-48 . -1025) T) ((-48 . -970) T) ((-48 . -38) 3454) ((-48 . -257) T) ((-48 . -389) T) ((-48 . -146) T) ((-48 . -495) T) ((-48 . -833) T) ((-48 . -1133) T) ((-48 . -311) T) ((-48 . -581) 3414) ((-48 . -934) T) ((-48 . -554) 3359) ((-48 . -120) T) ((-48 . -190) T) ((-48 . -186) 3346) ((-48 . -189) T) ((-45 . -36) 3325) ((-45 . -539) 3248) ((-45 . -259) 3046) ((-45 . -453) 2798) ((-45 . -426) 2733) ((-45 . -241) 2631) ((-45 . -243) 2554) ((-45 . -550) 2533) ((-45 . -193) 2481) ((-45 . -76) 2429) ((-45 . -183) 2377) ((-45 . -1106) 2356) ((-45 . -237) 2304) ((-45 . -124) 2252) ((-45 . -34) T) ((-45 . -13) T) ((-45 . -1128) T) ((-45 . -72) T) ((-45 . -553) 2234) ((-45 . -1013) T) ((-45 . -554) NIL) ((-45 . -594) 2182) ((-45 . -321) 2130) ((-45 . -760) NIL) ((-45 . -757) NIL) ((-45 . -1063) 2078) ((-45 . -924) 2026) ((-45 . -1167) 1974) ((-45 . -609) 1922) ((-44 . -358) 1906) ((-44 . -684) 1890) ((-44 . -658) T) ((-44 . -686) T) ((-44 . -82) 1869) ((-44 . -964) 1853) ((-44 . -969) 1837) ((-44 . -21) T) ((-44 . -589) 1780) ((-44 . -23) T) ((-44 . -1013) T) ((-44 . -553) 1762) ((-44 . -72) T) ((-44 . -25) T) ((-44 . -104) T) ((-44 . -591) 1720) ((-44 . -583) 1704) ((-44 . -655) 1688) ((-44 . -315) 1672) ((-44 . -1128) T) ((-44 . -13) T) ((-44 . -241) 1649) ((-40 . -290) 1623) ((-40 . -146) T) ((-40 . -556) 1553) ((-40 . -970) T) ((-40 . -1025) T) ((-40 . -1060) T) ((-40 . -664) T) ((-40 . -962) T) ((-40 . -591) 1455) ((-40 . -589) 1385) ((-40 . -104) T) ((-40 . -25) T) ((-40 . -72) T) ((-40 . -13) T) ((-40 . -1128) T) ((-40 . -553) 1367) ((-40 . -1013) T) ((-40 . -23) T) ((-40 . -21) T) ((-40 . -969) 1312) ((-40 . -964) 1257) ((-40 . -82) 1174) ((-40 . -554) 1158) ((-40 . -184) 1135) ((-40 . -810) 1087) ((-40 . -812) 999) ((-40 . -807) 909) ((-40 . -225) 886) ((-40 . -189) 826) ((-40 . -186) 760) ((-40 . -190) 732) ((-40 . -311) T) ((-40 . -1133) T) ((-40 . -833) T) ((-40 . -495) T) ((-40 . -655) 677) ((-40 . -583) 622) ((-40 . -38) 567) ((-40 . -389) T) ((-40 . -257) T) ((-40 . -245) T) ((-40 . -201) T) ((-40 . -317) NIL) ((-40 . -298) NIL) ((-40 . -1065) NIL) ((-40 . -118) 539) ((-40 . -342) NIL) ((-40 . -350) 511) ((-40 . -120) 483) ((-40 . -319) 455) ((-40 . -326) 432) ((-40 . -581) 366) ((-40 . -352) 343) ((-40 . -951) 220) ((-40 . -662) 192) ((-31 . -995) T) ((-31 . -427) 173) ((-31 . -553) 139) ((-31 . -556) 120) ((-31 . -1013) T) ((-31 . -1128) T) ((-31 . -13) T) ((-31 . -72) T) ((-31 . -64) T) ((-30 . -867) T) ((-30 . -553) 102) ((0 . |EnumerationCategory|) T) ((0 . -553) 84) ((0 . -1013) T) ((0 . -72) T) ((0 . -1128) T) ((-2 . |RecordCategory|) T) ((-2 . -553) 66) ((-2 . -1013) T) ((-2 . -72) T) ((-2 . -1128) T) ((-3 . |UnionCategory|) T) ((-3 . -553) 48) ((-3 . -1013) T) ((-3 . -72) T) ((-3 . -1128) T) ((-1 . -1013) T) ((-1 . -553) 30) ((-1 . -1128) T) ((-1 . -13) T) ((-1 . -72) T)) 
\ No newline at end of file
diff --git a/src/share/algebra/compress.daase b/src/share/algebra/compress.daase
index 45e17117..a6e9ceb1 100644
--- a/src/share/algebra/compress.daase
+++ b/src/share/algebra/compress.daase
@@ -1,6 +1,6 @@
 
-(30 . 3539125282)            
-(3992 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain|
+(30 . 3576902404)            
+(3994 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain|
  ATTRIBUTE |package| |domain| |category| CATEGORY |nobranch| AND |Join|
  |ofType| SIGNATURE "failed" "algebra" |OneDimensionalArrayAggregate&|
  |OneDimensionalArrayAggregate| |AbelianGroup&| |AbelianGroup| |AbelianMonoid&|
@@ -144,8 +144,9 @@
  |IdempotentOperatorCategory| |Identifier| |IndexedDirectProductAbelianGroup|
  |IndexedDirectProductAbelianMonoid| |IndexedDirectProductCategory|
  |IndexedDirectProductObject| |IndexedDirectProductOrderedAbelianMonoid|
- |IndexedDirectProductOrderedAbelianMonoidSup| |InnerEvalable&| |InnerEvalable|
- |InnerFreeAbelianMonoid| |IndexedFlexibleArray| |IfAst| |InnerFiniteField|
+ |IndexedDirectProductOrderedAbelianMonoidSup| |IndexedProductTerm|
+ |InnerEvalable&| |InnerEvalable| |InnerFreeAbelianMonoid|
+ |IndexedFlexibleArray| |IfAst| |InnerFiniteField|
  |InnerIndexedTwoDimensionalArray| |InnerMatrixLinearAlgebraFunctions|
  |InnerMatrixQuotientFieldFunctions| |IndexedMatrix| |ImportAst| |InAst|
  |InputByteConduit&| |InputByteConduit| |InnerNormalBasisFieldFunctions|
@@ -551,7 +552,7 @@
  |relationsIdeal| |saturate| |groebner?| |groebnerIdeal| |ideal| |leadingIdeal|
  |backOldPos| |generalPosition| |quotient| |zeroDim?| |inRadical?| |in?|
  |element?| |zeroDimPrime?| |zeroDimPrimary?| |radical| |primaryDecomp|
- |contract| |gensym| |leadingSupport| |shrinkable| |physicalLength!|
+ |contract| |gensym| |leadingSupport| |term| |shrinkable| |physicalLength!|
  |physicalLength| |flexibleArray| |elseBranch| |thenBranch|
  |generalizedInverse| |imports| |sequence| |readBytes!| |readUInt32!|
  |readInt32!| |readUInt16!| |readInt16!| |readUInt8!| |readInt8!| |readByte!|
diff --git a/src/share/algebra/interp.daase b/src/share/algebra/interp.daase
index 02d7945e..29132c62 100644
--- a/src/share/algebra/interp.daase
+++ b/src/share/algebra/interp.daase
@@ -1,4039 +1,4042 @@
 
-(2804812 . 3539125292)       
-((-1729 (((-85) (-1 (-85) |#2| |#2|) $) 86 T ELT) (((-85) $) NIL T ELT)) (-1727 (($ (-1 (-85) |#2| |#2|) $) 18 T ELT) (($ $) NIL T ELT)) (-3782 ((|#2| $ (-483) |#2|) NIL T ELT) ((|#2| $ (-1144 (-483)) |#2|) 44 T ELT)) (-2293 (($ $) 80 T ELT)) (-3836 ((|#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)) (-3413 (((-483) (-1 (-85) |#2|) $) 27 T ELT) (((-483) |#2| $) NIL T ELT) (((-483) |#2| $ (-483)) 96 T ELT)) (-2885 (((-583 |#2|) $) 13 T ELT)) (-3512 (($ (-1 (-85) |#2| |#2|) $ $) 64 T ELT) (($ $ $) NIL T ELT)) (-1946 (($ (-1 |#2| |#2|) $) 37 T ELT)) (-3952 (($ (-1 |#2| |#2|) $) NIL T ELT) (($ (-1 |#2| |#2| |#2|) $ $) 60 T ELT)) (-2300 (($ |#2| $ (-483)) NIL T ELT) (($ $ $ (-483)) 67 T ELT)) (-1351 (((-3 |#2| "failed") (-1 (-85) |#2|) $) 29 T ELT)) (-1944 (((-85) (-1 (-85) |#2|) $) 23 T ELT)) (-3794 ((|#2| $ (-483) |#2|) NIL T ELT) ((|#2| $ (-483)) NIL T ELT) (($ $ (-1144 (-483))) 66 T ELT)) (-2301 (($ $ (-483)) 76 T ELT) (($ $ (-1144 (-483))) 75 T ELT)) (-1943 (((-694) (-1 (-85) |#2|) $) 34 T ELT) (((-694) |#2| $) NIL T ELT)) (-1728 (($ $ $ (-483)) 69 T ELT)) (-3394 (($ $) 68 T ELT)) (-3524 (($ (-583 |#2|)) 73 T ELT)) (-3796 (($ $ |#2|) NIL T ELT) (($ |#2| $) NIL T ELT) (($ $ $) 87 T ELT) (($ (-583 $)) 85 T ELT)) (-3940 (((-772) $) 92 T ELT)) (-1945 (((-85) (-1 (-85) |#2|) $) 22 T ELT)) (-3052 (((-85) $ $) 95 T ELT)) (-2681 (((-85) $ $) 99 T ELT))) 
-(((-18 |#1| |#2|) (-10 -7 (-15 -3052 ((-85) |#1| |#1|)) (-15 -3940 ((-772) |#1|)) (-15 -2681 ((-85) |#1| |#1|)) (-15 -1727 (|#1| |#1|)) (-15 -1727 (|#1| (-1 (-85) |#2| |#2|) |#1|)) (-15 -2293 (|#1| |#1|)) (-15 -1728 (|#1| |#1| |#1| (-483))) (-15 -1729 ((-85) |#1|)) (-15 -3512 (|#1| |#1| |#1|)) (-15 -3413 ((-483) |#2| |#1| (-483))) (-15 -3413 ((-483) |#2| |#1|)) (-15 -3413 ((-483) (-1 (-85) |#2|) |#1|)) (-15 -1729 ((-85) (-1 (-85) |#2| |#2|) |#1|)) (-15 -3512 (|#1| (-1 (-85) |#2| |#2|) |#1| |#1|)) (-15 -3782 (|#2| |#1| (-1144 (-483)) |#2|)) (-15 -2300 (|#1| |#1| |#1| (-483))) (-15 -2300 (|#1| |#2| |#1| (-483))) (-15 -2301 (|#1| |#1| (-1144 (-483)))) (-15 -2301 (|#1| |#1| (-483))) (-15 -3952 (|#1| (-1 |#2| |#2| |#2|) |#1| |#1|)) (-15 -3796 (|#1| (-583 |#1|))) (-15 -3796 (|#1| |#1| |#1|)) (-15 -3796 (|#1| |#2| |#1|)) (-15 -3796 (|#1| |#1| |#2|)) (-15 -3794 (|#1| |#1| (-1144 (-483)))) (-15 -3524 (|#1| (-583 |#2|))) (-15 -1351 ((-3 |#2| "failed") (-1 (-85) |#2|) |#1|)) (-15 -3836 (|#2| (-1 |#2| |#2| |#2|) |#1|)) (-15 -3836 (|#2| (-1 |#2| |#2| |#2|) |#1| |#2|)) (-15 -3836 (|#2| (-1 |#2| |#2| |#2|) |#1| |#2| |#2|)) (-15 -3794 (|#2| |#1| (-483))) (-15 -3794 (|#2| |#1| (-483) |#2|)) (-15 -3782 (|#2| |#1| (-483) |#2|)) (-15 -1943 ((-694) |#2| |#1|)) (-15 -2885 ((-583 |#2|) |#1|)) (-15 -1943 ((-694) (-1 (-85) |#2|) |#1|)) (-15 -1944 ((-85) (-1 (-85) |#2|) |#1|)) (-15 -1945 ((-85) (-1 (-85) |#2|) |#1|)) (-15 -1946 (|#1| (-1 |#2| |#2|) |#1|)) (-15 -3952 (|#1| (-1 |#2| |#2|) |#1|)) (-15 -3394 (|#1| |#1|))) (-19 |#2|) (-1127)) (T -18)) 
+(2805528 . 3576902413)       
+((-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)) 
 NIL 
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-(((-19 |#1|) (-113) (-1127)) (T -19)) 
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 NIL 
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 NIL 
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-(((-21) . T) ((-23) . T) ((-25) . T) ((-38 (-347 (-483))) . T) ((-38 |#1|) |has| |#1| (-146)) ((-38 $) . T) ((-27) . T) ((-72) . T) ((-82 (-347 (-483)) (-347 (-483))) . T) ((-82 |#1| |#1|) |has| |#1| (-146)) ((-82 $ $) . T) ((-104) . T) ((-118) |has| |#1| (-118)) ((-120) |has| |#1| (-120)) ((-555 (-347 (-483))) . T) ((-555 (-347 (-857 |#1|))) |has| |#1| (-494)) ((-555 (-483)) . T) ((-555 (-550 $)) . T) ((-555 (-857 |#1|)) |has| |#1| (-961)) ((-555 (-1088)) . T) ((-555 |#1|) . T) ((-555 $) . T) ((-552 (-772)) . T) ((-146) . T) ((-553 (-472)) |has| |#1| (-553 (-472))) ((-553 (-800 (-327))) |has| |#1| (-553 (-800 (-327)))) ((-553 (-800 (-483))) |has| |#1| (-553 (-800 (-483)))) ((-201) . T) ((-245) . T) ((-257) . T) ((-259 $) . T) ((-253) . T) ((-311) . T) ((-326 |#1|) |has| |#1| (-961)) ((-340 |#1|) . T) ((-352 |#1|) . T) ((-361 |#1|) . T) ((-389) . T) ((-410) |has| |#1| (-410)) ((-452 (-550 $) $) . T) ((-452 $ $) . T) ((-494) . T) ((-13) . T) ((-588 (-347 (-483))) . T) ((-588 (-483)) . T) ((-588 |#1|) OR (|has| |#1| (-961)) (|has| |#1| (-146))) ((-588 $) . T) ((-590 (-347 (-483))) . T) ((-590 (-483)) -12 (|has| |#1| (-580 (-483))) (|has| |#1| (-961))) ((-590 |#1|) OR (|has| |#1| (-961)) (|has| |#1| (-146))) ((-590 $) . T) ((-582 (-347 (-483))) . T) ((-582 |#1|) |has| |#1| (-146)) ((-582 $) . T) ((-580 (-483)) -12 (|has| |#1| (-580 (-483))) (|has| |#1| (-961))) ((-580 |#1|) |has| |#1| (-961)) ((-654 (-347 (-483))) . T) ((-654 |#1|) |has| |#1| (-146)) ((-654 $) . T) ((-663) . T) ((-806 $ (-1088)) |has| |#1| (-961)) ((-809 (-1088)) |has| |#1| (-961)) ((-811 (-1088)) |has| |#1| (-961)) ((-796 (-327)) |has| |#1| (-796 (-327))) ((-796 (-483)) |has| |#1| (-796 (-483))) ((-794 |#1|) . T) ((-832) . T) ((-915) . T) ((-950 (-347 (-483))) OR (|has| |#1| (-950 (-347 (-483)))) (-12 (|has| |#1| (-494)) (|has| |#1| (-950 (-483))))) ((-950 (-347 (-857 |#1|))) |has| |#1| (-494)) ((-950 (-483)) |has| |#1| (-950 (-483))) ((-950 (-550 $)) . T) ((-950 (-857 |#1|)) |has| |#1| (-961)) ((-950 (-1088)) . T) ((-950 |#1|) . T) ((-963 (-347 (-483))) . T) ((-963 |#1|) |has| |#1| (-146)) ((-963 $) . T) ((-968 (-347 (-483))) . T) ((-968 |#1|) |has| |#1| (-146)) ((-968 $) . T) ((-961) . T) ((-969) . T) ((-1024) . T) ((-1059) . T) ((-1012) . T) ((-1127) . T) ((-1132) . T)) 
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-NIL 
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+(((-21) . T) ((-23) . T) ((-25) . T) ((-38 (-347 (-484))) . T) ((-38 $) . T) ((-72) . T) ((-82 (-347 (-484)) (-347 (-484))) . T) ((-82 $ $) . T) ((-104) . T) ((-556 (-347 (-484))) . T) ((-556 (-484)) . T) ((-556 $) . T) ((-553 (-773)) . T) ((-146) . T) ((-201) . T) ((-245) . T) ((-257) . T) ((-311) . T) ((-389) . T) ((-495) . T) ((-13) . T) ((-589 (-347 (-484))) . T) ((-589 (-484)) . T) ((-589 $) . T) ((-591 (-347 (-484))) . T) ((-591 $) . T) ((-583 (-347 (-484))) . T) ((-583 $) . T) ((-655 (-347 (-484))) . T) ((-655 $) . T) ((-664) . T) ((-833) . T) ((-916) . T) ((-964 (-347 (-484))) . T) ((-964 $) . T) ((-969 (-347 (-484))) . T) ((-969 $) . T) ((-962) . T) ((-970) . T) ((-1025) . T) ((-1060) . T) ((-1013) . T) ((-1128) . T) ((-1133) . T)) 
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+NIL 
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+NIL 
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 (((-38 |#1|) (-113) (-146)) (T -38)) 
 NIL 
-(-13 (-961) (-654 |t#1|) (-555 |t#1|)) 
-(((-21) . T) ((-23) . T) ((-25) . T) ((-72) . T) ((-82 |#1| |#1|) . T) ((-104) . T) ((-555 (-483)) . T) ((-555 |#1|) . T) ((-552 (-772)) . T) ((-13) . T) ((-588 (-483)) . T) ((-588 |#1|) . T) ((-588 $) . T) ((-590 |#1|) . T) ((-590 $) . T) ((-582 |#1|) . T) ((-654 |#1|) . T) ((-663) . T) ((-963 |#1|) . T) ((-968 |#1|) . T) ((-961) . T) ((-969) . T) ((-1024) . T) ((-1059) . T) ((-1012) . T) ((-1127) . 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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 (((-64) (-113)) (T -64)) 
 NIL 
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-(((-72) . T) ((-555 (-1093)) . T) ((-552 (-772)) . T) ((-552 (-1093)) . T) ((-427 (-1093)) . T) ((-13) . T) ((-1012) . T) ((-1127) . T)) 
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+(((-72) . T) ((-556 (-1094)) . T) ((-553 (-773)) . T) ((-553 (-1094)) . T) ((-427 (-1094)) . T) ((-13) . T) ((-1013) . T) ((-1128) . T)) 
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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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-NIL 
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-NIL 
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-NIL 
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+NIL 
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 NIL 
 (-13 (-193 |t#1|)) 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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+NIL 
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+NIL 
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 (((-190) (-113)) (T -190)) 
 NIL 
-(-13 (-961) (-189)) 
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 (((-191) (-113)) (T -191)) 
 NIL 
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-NIL 
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(|:| |mat| (-631 (-484))) (|:| |vec| (-1178 (-484)))) (-631 $) (-1178 $)) NIL (-12 (|has| |#2| (-581 (-484))) (|has| |#2| (-962))) ELT) (((-2 (|:| |mat| (-631 |#2|)) (|:| |vec| (-1178 |#2|))) (-631 $) (-1178 $)) NIL (|has| |#2| (-962)) ELT) (((-631 |#2|) (-631 $)) NIL (|has| |#2| (-962)) ELT)) (-3463 (((-3 $ #1#) $) 59 (|has| |#2| (-962)) ELT)) (-2992 (($) NIL (|has| |#2| (-317)) ELT)) (-1574 ((|#2| $ (-484) |#2|) NIL (|has| $ (-6 -3992)) ELT)) (-3110 ((|#2| $ (-484)) 57 T ELT)) (-3183 (((-85) $) NIL (|has| |#2| (-718)) ELT)) (-2887 (((-584 |#2|) $) 14 (|has| $ (-6 -3991)) ELT)) (-2408 (((-85) $) NIL (|has| |#2| (-962)) ELT)) (-2198 (((-484) $) 20 (|has| (-484) (-757)) ELT)) (-2529 (($ $ $) NIL (|has| |#2| (-757)) ELT)) (-2606 (((-584 |#2|) $) NIL (|has| $ (-6 -3991)) ELT)) (-3242 (((-85) |#2| $) NIL (-12 (|has| $ (-6 -3991)) (|has| |#2| (-1013))) ELT)) (-2199 (((-484) $) NIL (|has| (-484) (-757)) ELT)) (-2855 (($ $ $) NIL (|has| |#2| (-757)) ELT)) (-1947 (($ (-1 |#2| |#2|) $) NIL 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|#2|)) NIL (-12 (|has| |#2| (-259 |#2|)) (|has| |#2| (-1013))) ELT) (($ $ |#2| |#2|) NIL (-12 (|has| |#2| (-259 |#2|)) (|has| |#2| (-1013))) ELT) (($ $ (-584 |#2|) (-584 |#2|)) NIL (-12 (|has| |#2| (-259 |#2|)) (|has| |#2| (-1013))) ELT)) (-1220 (((-85) $ $) NIL T ELT)) (-2200 (((-85) |#2| $) NIL (-12 (|has| $ (-6 -3991)) (|has| |#2| (-1013))) ELT)) (-2203 (((-584 |#2|) $) NIL T ELT)) (-3399 (((-85) $) NIL T ELT)) (-3561 (($) NIL T ELT)) (-3796 ((|#2| $ (-484) |#2|) NIL T ELT) ((|#2| $ (-484)) 21 T ELT)) (-3832 ((|#2| $ $) NIL (|has| |#2| (-962)) ELT)) (-1466 (($ (-1178 |#2|)) 18 T ELT)) (-3907 (((-107)) NIL (|has| |#2| (-311)) ELT)) (-3754 (($ $ (-695)) NIL (-12 (|has| |#2| (-189)) (|has| |#2| (-962))) ELT) (($ $) NIL (-12 (|has| |#2| (-189)) (|has| |#2| (-962))) ELT) (($ $ (-584 (-1089)) (-584 (-695))) NIL (-12 (|has| |#2| (-812 (-1089))) (|has| |#2| (-962))) ELT) (($ $ (-1089) (-695)) NIL (-12 (|has| |#2| (-812 (-1089))) (|has| |#2| (-962))) ELT) (($ $ (-584 (-1089))) NIL (-12 (|has| |#2| (-812 (-1089))) (|has| |#2| (-962))) ELT) (($ $ (-1089)) NIL (-12 (|has| |#2| (-812 (-1089))) (|has| |#2| (-962))) ELT) (($ $ (-1 |#2| |#2|)) NIL (|has| |#2| (-962)) ELT) (($ $ (-1 |#2| |#2|) (-695)) NIL (|has| |#2| (-962)) ELT)) (-1944 (((-695) (-1 (-85) |#2|) $) NIL (|has| $ (-6 -3991)) ELT) (((-695) |#2| $) NIL (-12 (|has| $ (-6 -3991)) (|has| |#2| (-1013))) ELT)) (-3396 (($ $) NIL T ELT)) (-3942 (((-1178 |#2|) $) 9 T ELT) (($ (-484)) NIL (OR (-12 (|has| |#2| (-951 (-484))) (|has| |#2| (-1013))) (|has| |#2| (-962))) ELT) (($ (-347 (-484))) NIL (-12 (|has| |#2| (-951 (-347 (-484)))) (|has| |#2| (-1013))) ELT) (($ |#2|) 12 (|has| |#2| (-1013)) ELT) (((-773) $) NIL (|has| |#2| (-553 (-773))) ELT)) (-3123 (((-695)) NIL (|has| |#2| (-962)) CONST)) (-1263 (((-85) $ $) NIL (|has| |#2| (-72)) ELT)) (-1946 (((-85) (-1 (-85) |#2|) $) NIL (|has| $ (-6 -3991)) ELT)) (-2658 (($) 37 (|has| |#2| (-23)) CONST)) (-2664 (($) 41 (|has| |#2| (-962)) CONST)) (-2667 (($ $ (-695)) NIL (-12 (|has| |#2| (-189)) (|has| |#2| (-962))) ELT) (($ $) NIL (-12 (|has| |#2| (-189)) (|has| |#2| (-962))) ELT) (($ $ (-584 (-1089)) (-584 (-695))) NIL (-12 (|has| |#2| (-812 (-1089))) (|has| |#2| (-962))) ELT) (($ $ (-1089) (-695)) NIL (-12 (|has| |#2| (-812 (-1089))) (|has| |#2| (-962))) ELT) (($ $ (-584 (-1089))) NIL (-12 (|has| |#2| (-812 (-1089))) (|has| |#2| (-962))) ELT) (($ $ (-1089)) NIL (-12 (|has| |#2| (-812 (-1089))) (|has| |#2| (-962))) ELT) (($ $ (-1 |#2| |#2|)) NIL (|has| |#2| (-962)) ELT) (($ $ (-1 |#2| |#2|) (-695)) NIL (|has| |#2| (-962)) ELT)) (-2564 (((-85) $ $) NIL (|has| |#2| (-757)) ELT)) (-2565 (((-85) $ $) NIL (|has| |#2| (-757)) ELT)) (-3054 (((-85) $ $) 28 (|has| |#2| (-72)) ELT)) (-2682 (((-85) $ $) NIL (|has| |#2| (-757)) ELT)) (-2683 (((-85) $ $) 67 (|has| |#2| (-757)) ELT)) (-3945 (($ $ |#2|) NIL (|has| |#2| (-311)) ELT)) (-3833 (($ $ $) NIL (|has| |#2| (-21)) ELT) (($ $) NIL (|has| |#2| (-21)) ELT)) (-3835 (($ $ $) 35 (|has| |#2| (-25)) ELT)) (** (($ $ (-695)) NIL (|has| |#2| (-962)) ELT) (($ $ (-831)) NIL (|has| |#2| (-962)) ELT)) (* (($ $ $) 47 (|has| |#2| (-962)) ELT) (($ $ |#2|) 45 (|has| |#2| (-664)) ELT) (($ |#2| $) 46 (|has| |#2| (-664)) ELT) (($ (-484) $) NIL (|has| |#2| (-21)) ELT) (($ (-695) $) NIL (|has| |#2| (-23)) ELT) (($ (-831) $) NIL (|has| |#2| (-25)) ELT)) (-3953 (((-695) $) NIL (|has| $ (-6 -3991)) ELT))) 
+(((-197 |#1| |#2|) (-196 |#1| |#2|) (-695) (-1128)) (T -197)) 
+NIL 
+((-3837 (((-197 |#1| |#3|) (-1 |#3| |#2| |#3|) (-197 |#1| |#2|) |#3|) 21 T ELT)) (-3838 ((|#3| (-1 |#3| |#2| |#3|) (-197 |#1| |#2|) |#3|) 23 T ELT)) (-3954 (((-197 |#1| |#3|) (-1 |#3| |#2|) (-197 |#1| |#2|)) 18 T ELT))) 
+(((-198 |#1| |#2| |#3|) (-10 -7 (-15 -3837 ((-197 |#1| |#3|) (-1 |#3| |#2| |#3|) (-197 |#1| |#2|) |#3|)) (-15 -3838 (|#3| (-1 |#3| |#2| |#3|) (-197 |#1| |#2|) |#3|)) (-15 -3954 ((-197 |#1| |#3|) (-1 |#3| |#2|) (-197 |#1| |#2|)))) (-695) (-1128) (-1128)) (T -198)) 
+((-3954 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-197 *5 *6)) (-14 *5 (-695)) (-4 *6 (-1128)) (-4 *7 (-1128)) (-5 *2 (-197 *5 *7)) (-5 *1 (-198 *5 *6 *7)))) (-3838 (*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *6 *2)) (-5 *4 (-197 *5 *6)) (-14 *5 (-695)) (-4 *6 (-1128)) (-4 *2 (-1128)) (-5 *1 (-198 *5 *6 *2)))) (-3837 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *5 *7 *5)) (-5 *4 (-197 *6 *7)) (-14 *6 (-695)) (-4 *7 (-1128)) (-4 *5 (-1128)) (-5 *2 (-197 *6 *5)) (-5 *1 (-198 *6 *7 *5))))) 
+((-1470 (((-484) (-584 (-1072))) 36 T ELT) (((-484) (-1072)) 29 T ELT)) (-1469 (((-1184) (-584 (-1072))) 40 T ELT) (((-1184) (-1072)) 39 T ELT)) (-1467 (((-1072)) 16 T ELT)) (-1468 (((-1072) (-484) (-1072)) 23 T ELT)) (-3769 (((-584 (-1072)) (-584 (-1072)) (-484) (-1072)) 37 T ELT) (((-1072) (-1072) (-484) (-1072)) 35 T ELT)) (-2618 (((-584 (-1072)) (-584 (-1072))) 15 T ELT) (((-584 (-1072)) (-1072)) 11 T ELT))) 
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+((-1470 (*1 *2 *3) (-12 (-5 *3 (-584 (-1072))) (-5 *2 (-484)) (-5 *1 (-199)))) (-1470 (*1 *2 *3) (-12 (-5 *3 (-1072)) (-5 *2 (-484)) (-5 *1 (-199)))) (-1469 (*1 *2 *3) (-12 (-5 *3 (-584 (-1072))) (-5 *2 (-1184)) (-5 *1 (-199)))) (-1469 (*1 *2 *3) (-12 (-5 *3 (-1072)) (-5 *2 (-1184)) (-5 *1 (-199)))) (-3769 (*1 *2 *2 *3 *4) (-12 (-5 *2 (-584 (-1072))) (-5 *3 (-484)) (-5 *4 (-1072)) (-5 *1 (-199)))) (-3769 (*1 *2 *2 *3 *2) (-12 (-5 *2 (-1072)) (-5 *3 (-484)) (-5 *1 (-199)))) (-1468 (*1 *2 *3 *2) (-12 (-5 *2 (-1072)) (-5 *3 (-484)) (-5 *1 (-199)))) (-1467 (*1 *2) (-12 (-5 *2 (-1072)) (-5 *1 (-199)))) (-2618 (*1 *2 *2) (-12 (-5 *2 (-584 (-1072))) (-5 *1 (-199)))) (-2618 (*1 *2 *3) (-12 (-5 *2 (-584 (-1072))) (-5 *1 (-199)) (-5 *3 (-1072))))) 
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+(((-200 |#1|) (-10 -7 (-15 ** (|#1| |#1| (-484))) (-15 * (|#1| |#1| (-347 (-484)))) (-15 * (|#1| (-347 (-484)) |#1|)) (-15 ** (|#1| |#1| (-695))) (-15 * (|#1| |#1| |#1|)) (-15 ** (|#1| |#1| (-831))) (-15 * (|#1| (-484) |#1|)) (-15 * (|#1| (-695) |#1|)) (-15 * (|#1| (-831) |#1|))) (-201)) (T -200)) 
+NIL 
+((-2566 (((-85) $ $) 7 T ELT)) (-3185 (((-85) $) 21 T ELT)) (-1310 (((-3 $ "failed") $ $) 25 T ELT)) (-3720 (($) 22 T CONST)) (-3463 (((-3 $ "failed") $) 40 T ELT)) (-2408 (((-85) $) 42 T ELT)) (-3239 (((-1072) $) 11 T ELT)) (-2482 (($ $) 53 T ELT)) (-3240 (((-1033) $) 12 T ELT)) (-3942 (((-773) $) 13 T ELT) (($ (-484)) 39 T ELT) (($ (-347 (-484))) 57 T ELT)) (-3123 (((-695)) 38 T CONST)) (-1263 (((-85) $ $) 6 T ELT)) (-2658 (($) 23 T CONST)) (-2664 (($) 43 T CONST)) (-3054 (((-85) $ $) 8 T ELT)) (-3833 (($ $) 28 T ELT) (($ $ $) 27 T ELT)) (-3835 (($ $ $) 18 T ELT)) (** (($ $ (-831)) 33 T ELT) (($ $ (-695)) 41 T ELT) (($ $ (-484)) 54 T ELT)) (* (($ (-831) $) 17 T ELT) (($ (-695) $) 20 T ELT) (($ (-484) $) 29 T ELT) (($ $ $) 32 T ELT) (($ (-347 (-484)) $) 56 T ELT) (($ $ (-347 (-484))) 55 T ELT))) 
 (((-201) (-113)) (T -201)) 
-((** (*1 *1 *1 *2) (-12 (-4 *1 (-201)) (-5 *2 (-483)))) (-2480 (*1 *1 *1) (-4 *1 (-201)))) 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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+NIL 
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$) NIL T ELT) (($ (-484)) NIL T ELT) (($ |#1|) 26 T ELT) (($ |#3|) 25 T ELT) (($ |#2|) NIL T ELT) (($ (-1038 |#1| |#2|)) 32 T ELT) (($ (-347 (-484))) NIL (OR (|has| |#1| (-38 (-347 (-484)))) (|has| |#1| (-951 (-347 (-484))))) ELT) (($ $) NIL (|has| |#1| (-495)) ELT)) (-3813 (((-584 |#1|) $) NIL T ELT)) (-3673 ((|#1| $ (-469 |#3|)) NIL T ELT) (($ $ |#3| (-695)) NIL T ELT) (($ $ (-584 |#3|) (-584 (-695))) NIL T ELT)) (-2700 (((-633 $) $) NIL (OR (-12 (|has| $ (-118)) (|has| |#1| (-822))) (|has| |#1| (-118))) ELT)) (-3123 (((-695)) NIL T CONST)) (-1621 (($ $ $ (-695)) NIL (|has| |#1| (-146)) ELT)) (-1263 (((-85) $ $) NIL T ELT)) (-2060 (((-85) $ $) NIL (|has| |#1| (-495)) ELT)) (-2658 (($) NIL T CONST)) (-2664 (($) NIL T CONST)) (-2667 (($ $ (-584 |#3|) (-584 (-695))) NIL T ELT) (($ $ |#3| (-695)) NIL T ELT) (($ $ (-584 |#3|)) NIL T ELT) (($ $ |#3|) NIL T ELT) (($ $ (-1 |#1| |#1|)) NIL T ELT) (($ $ (-1 |#1| |#1|) (-695)) NIL T ELT) (($ $ (-1089)) NIL (|has| |#1| (-812 (-1089))) ELT) (($ $ 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+NIL 
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+NIL 
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 ((** (($ $ $) 10 T ELT))) 
 (((-238 |#1|) (-10 -7 (-15 ** (|#1| |#1| |#1|))) (-239)) (T -238)) 
 NIL 
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+NIL 
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 (((-245) (-113)) (T -245)) 
 NIL 
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+NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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(-818 |#1|) $) NIL T ELT))) 
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+NIL 
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-NIL 
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-(((-307 |#1| |#2|) (-279 |#1|) (-298) (-830)) (T -307)) 
-NIL 
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-(((-309 |#1|) (-13 (-410) (-950 |#1|) (-10 -8 (-15 * ($ |#1| $)) (-15 * ($ $ |#1|)) (-15 ** ($ |#1| (-483))) (-15 -3131 ((-694) $)) (-15 -2296 ((-483) $ (-483))) (-15 -2295 (|#1| $ (-483))) (-15 -2287 ($ (-1 (-483) (-483)) $)) (-15 -2286 ($ (-1 |#1| |#1|) $)) (-15 -1776 ((-583 (-2 (|:| |gen| |#1|) (|:| -3937 (-483)))) $)))) (-1012)) (T -309)) 
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-NIL 
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-NIL 
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-NIL 
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-(((-334 |#1|) (-333 |#1|) (-1012)) (T -334)) 
-NIL 
-((-2564 (((-85) $ $) NIL T ELT)) (-1750 (((-85) $) 25 T ELT)) (-1751 (((-85) $) 22 T ELT)) (-3608 (($ (-1071) (-1071) (-1071)) 26 T ELT)) (-3536 (((-1071) $) 16 T ELT)) (-3237 (((-1071) $) NIL T ELT)) (-3238 (((-1032) $) NIL T ELT)) (-1755 (($ (-1071) (-1071) (-1071)) 14 T ELT)) (-1753 (((-1071) $) 17 T ELT)) (-1752 (((-85) $) 18 T ELT)) (-1754 (((-1071) $) 15 T ELT)) (-3940 (((-772) $) 12 T ELT) (($ (-1071)) 13 T ELT) (((-1071) $) 9 T ELT)) (-1262 (((-85) $ $) NIL T ELT)) (-3052 (((-85) $ $) 7 T ELT))) 
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+(((-72) . T) ((-553 (-773)) . T) ((-13) . T) ((-1013) . T) ((-1128) . T)) 
+((-1780 (((-631 |#2|) (-1178 $)) 45 T ELT)) (-1790 (($ (-1178 |#2|) (-1178 $)) 39 T ELT)) (-1779 (((-631 |#2|) $ (-1178 $)) 47 T ELT)) (-3753 ((|#2| (-1178 $)) 13 T ELT)) (-3221 (((-1178 |#2|) $ (-1178 $)) NIL T ELT) (((-631 |#2|) (-1178 $) (-1178 $)) 27 T ELT))) 
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+NIL 
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+(((-319 |#1| |#2|) (-113) (-146) (-1154 |t#1|)) (T -319)) 
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+(-13 (-38 |t#1|) (-10 -8 (-15 -3106 ((-831))) (-15 -1779 ((-631 |t#1|) $ (-1178 $))) (-15 -3326 (|t#1| $)) (-15 -3129 (|t#1| $)) (-15 -3221 ((-1178 |t#1|) $ (-1178 $))) (-15 -3221 ((-631 |t#1|) (-1178 $) (-1178 $))) (-15 -1790 ($ (-1178 |t#1|) (-1178 $))) (-15 -3753 (|t#1| (-1178 $))) (-15 -1780 ((-631 |t#1|) (-1178 $))) (-15 -2447 (|t#2| $)) (IF (|has| |t#1| (-311)) (-15 -2012 (|t#2| $)) |%noBranch|) (IF (|has| |t#1| (-120)) (-6 (-120)) |%noBranch|) (IF (|has| |t#1| (-118)) (-6 (-118)) |%noBranch|))) 
+(((-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)) 
+((-1730 (((-85) (-1 (-85) |#2| |#2|) $) NIL T ELT) (((-85) $) 18 T ELT)) (-1728 (($ (-1 (-85) |#2| |#2|) $) NIL T ELT) (($ $) 28 T ELT)) (-2907 (($ (-1 (-85) |#2| |#2|) $) 27 T ELT) (($ $) 22 T ELT)) (-2296 (($ $) 25 T ELT)) (-3415 (((-484) (-1 (-85) |#2|) $) NIL T ELT) (((-484) |#2| $) 11 T ELT) (((-484) |#2| $ (-484)) NIL T ELT)) (-3514 (($ (-1 (-85) |#2| |#2|) $ $) NIL T ELT) (($ $ $) 20 T ELT))) 
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+NIL 
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+NIL 
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+NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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+NIL 
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+(((-352 |#1|) (-113) (-1128)) (T -352)) 
+NIL 
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-((-1887 (((-694) |#4|) 12 T ELT)) (-1875 (((-583 (-2 (|:| |totdeg| (-694)) (|:| -2000 |#4|))) |#4| (-694) (-583 (-2 (|:| |totdeg| (-694)) (|:| -2000 |#4|)))) 39 T ELT)) (-1877 (((-583 (-2 (|:| |lcmfij| |#2|) (|:| |totdeg| (-694)) (|:| |poli| |#4|) (|:| |polj| |#4|))) (-583 (-2 (|:| |lcmfij| |#2|) (|:| |totdeg| (-694)) (|:| |poli| |#4|) (|:| |polj| |#4|))) (-583 (-2 (|:| |lcmfij| |#2|) (|:| |totdeg| (-694)) (|:| |poli| |#4|) (|:| |polj| |#4|)))) 49 T ELT)) (-1876 ((|#4| (-2 (|:| |lcmfij| |#2|) (|:| |totdeg| (-694)) (|:| |poli| |#4|) (|:| |polj| |#4|))) 52 T ELT)) (-1865 ((|#4| |#4| (-583 |#4|)) 54 T ELT)) (-1873 (((-2 (|:| |poly| |#4|) (|:| |mult| |#1|)) |#4| (-583 |#4|)) 96 T ELT)) (-1880 (((-1183) |#4|) 59 T ELT)) (-1883 (((-1183) (-583 |#4|)) 69 T ELT)) (-1881 (((-483) (-2 (|:| |lcmfij| |#2|) (|:| |totdeg| (-694)) (|:| |poli| |#4|) (|:| |polj| |#4|)) |#4| |#4| (-483) (-483) (-483)) 66 T ELT)) (-1884 (((-1183) (-483)) 110 T ELT)) (-1878 (((-583 |#4|) (-583 |#4|)) 104 T ELT)) (-1886 (((-2 (|:| |lcmfij| |#2|) (|:| |totdeg| (-694)) (|:| |poli| |#4|) (|:| |polj| |#4|)) (-2 (|:| |totdeg| (-694)) (|:| -2000 |#4|)) |#4| (-694)) 31 T ELT)) (-1879 (((-483) |#4|) 109 T ELT)) (-1874 ((|#4| |#4|) 37 T ELT)) (-1866 (((-583 |#4|) (-583 |#4|) (-483) (-483)) 74 T ELT)) (-1882 (((-483) (-2 (|:| |lcmfij| |#2|) (|:| |totdeg| (-694)) (|:| |poli| |#4|) (|:| |polj| |#4|)) |#4| |#4| (-483) (-483) (-483) (-483)) 123 T ELT)) (-1885 (((-85) (-2 (|:| |lcmfij| |#2|) (|:| |totdeg| (-694)) (|:| |poli| |#4|) (|:| |polj| |#4|)) (-2 (|:| |lcmfij| |#2|) (|:| |totdeg| (-694)) (|:| |poli| |#4|) (|:| |polj| |#4|))) 20 T ELT)) (-1867 (((-85) (-2 (|:| |lcmfij| |#2|) (|:| |totdeg| (-694)) (|:| |poli| |#4|) (|:| |polj| |#4|))) 78 T ELT)) (-1872 (((-583 (-2 (|:| |lcmfij| |#2|) (|:| |totdeg| (-694)) (|:| |poli| |#4|) (|:| |polj| |#4|))) |#2| (-583 (-2 (|:| |lcmfij| |#2|) (|:| |totdeg| (-694)) (|:| |poli| |#4|) (|:| |polj| |#4|)))) 76 T ELT)) (-1871 (((-583 (-2 (|:| |lcmfij| |#2|) (|:| |totdeg| (-694)) (|:| |poli| |#4|) (|:| |polj| |#4|))) (-583 (-2 (|:| |lcmfij| |#2|) (|:| |totdeg| (-694)) (|:| |poli| |#4|) (|:| |polj| |#4|)))) 47 T ELT)) (-1868 (((-85) |#2| |#2|) 75 T ELT)) (-1870 (((-583 (-2 (|:| |lcmfij| |#2|) (|:| |totdeg| (-694)) (|:| |poli| |#4|) (|:| |polj| |#4|))) |#4| (-583 (-2 (|:| |lcmfij| |#2|) (|:| |totdeg| (-694)) (|:| |poli| |#4|) (|:| |polj| |#4|)))) 48 T ELT)) (-1869 (((-85) |#2| |#2| |#2| |#2|) 80 T ELT)) (-1864 ((|#4| |#4| (-583 |#4|)) 97 T ELT))) 
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-((-1887 (*1 *2 *3) (-12 (-4 *4 (-389)) (-4 *5 (-717)) (-4 *6 (-756)) (-5 *2 (-694)) (-5 *1 (-387 *4 *5 *6 *3)) (-4 *3 (-861 *4 *5 *6)))) (-1886 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-2 (|:| |totdeg| (-694)) (|:| -2000 *4))) (-5 *5 (-694)) (-4 *4 (-861 *6 *7 *8)) (-4 *6 (-389)) (-4 *7 (-717)) (-4 *8 (-756)) (-5 *2 (-2 (|:| |lcmfij| *7) (|:| |totdeg| *5) (|:| |poli| *4) (|:| |polj| *4))) (-5 *1 (-387 *6 *7 *8 *4)))) (-1885 (*1 *2 *3 *3) (-12 (-5 *3 (-2 (|:| |lcmfij| *5) (|:| |totdeg| (-694)) (|:| |poli| *7) (|:| |polj| *7))) (-4 *5 (-717)) (-4 *7 (-861 *4 *5 *6)) (-4 *4 (-389)) (-4 *6 (-756)) (-5 *2 (-85)) (-5 *1 (-387 *4 *5 *6 *7)))) (-1884 (*1 *2 *3) (-12 (-5 *3 (-483)) (-4 *4 (-389)) (-4 *5 (-717)) (-4 *6 (-756)) (-5 *2 (-1183)) (-5 *1 (-387 *4 *5 *6 *7)) (-4 *7 (-861 *4 *5 *6)))) (-1883 (*1 *2 *3) (-12 (-5 *3 (-583 *7)) (-4 *7 (-861 *4 *5 *6)) (-4 *4 (-389)) (-4 *5 (-717)) (-4 *6 (-756)) (-5 *2 (-1183)) (-5 *1 (-387 *4 *5 *6 *7)))) (-1882 (*1 *2 *3 *4 *4 *2 *2 *2 *2) (-12 (-5 *2 (-483)) (-5 *3 (-2 (|:| |lcmfij| *6) (|:| |totdeg| (-694)) (|:| |poli| *4) (|:| |polj| *4))) (-4 *6 (-717)) (-4 *4 (-861 *5 *6 *7)) (-4 *5 (-389)) (-4 *7 (-756)) (-5 *1 (-387 *5 *6 *7 *4)))) (-1881 (*1 *2 *3 *4 *4 *2 *2 *2) (-12 (-5 *2 (-483)) (-5 *3 (-2 (|:| |lcmfij| *6) (|:| |totdeg| (-694)) (|:| |poli| *4) (|:| |polj| *4))) (-4 *6 (-717)) (-4 *4 (-861 *5 *6 *7)) (-4 *5 (-389)) (-4 *7 (-756)) (-5 *1 (-387 *5 *6 *7 *4)))) (-1880 (*1 *2 *3) (-12 (-4 *4 (-389)) (-4 *5 (-717)) (-4 *6 (-756)) (-5 *2 (-1183)) (-5 *1 (-387 *4 *5 *6 *3)) (-4 *3 (-861 *4 *5 *6)))) (-1879 (*1 *2 *3) (-12 (-4 *4 (-389)) (-4 *5 (-717)) (-4 *6 (-756)) (-5 *2 (-483)) (-5 *1 (-387 *4 *5 *6 *3)) (-4 *3 (-861 *4 *5 *6)))) (-1878 (*1 *2 *2) (-12 (-5 *2 (-583 *6)) (-4 *6 (-861 *3 *4 *5)) (-4 *3 (-389)) (-4 *4 (-717)) (-4 *5 (-756)) (-5 *1 (-387 *3 *4 *5 *6)))) (-1877 (*1 *2 *2 *2) (-12 (-5 *2 (-583 (-2 (|:| |lcmfij| *4) (|:| |totdeg| (-694)) (|:| |poli| *6) (|:| |polj| *6)))) (-4 *4 (-717)) (-4 *6 (-861 *3 *4 *5)) (-4 *3 (-389)) (-4 *5 (-756)) (-5 *1 (-387 *3 *4 *5 *6)))) (-1876 (*1 *2 *3) (-12 (-5 *3 (-2 (|:| |lcmfij| *5) (|:| |totdeg| (-694)) (|:| |poli| *2) (|:| |polj| *2))) (-4 *5 (-717)) (-4 *2 (-861 *4 *5 *6)) (-5 *1 (-387 *4 *5 *6 *2)) (-4 *4 (-389)) (-4 *6 (-756)))) (-1875 (*1 *2 *3 *4 *2) (-12 (-5 *2 (-583 (-2 (|:| |totdeg| (-694)) (|:| -2000 *3)))) (-5 *4 (-694)) (-4 *3 (-861 *5 *6 *7)) (-4 *5 (-389)) (-4 *6 (-717)) (-4 *7 (-756)) (-5 *1 (-387 *5 *6 *7 *3)))) (-1874 (*1 *2 *2) (-12 (-4 *3 (-389)) (-4 *4 (-717)) (-4 *5 (-756)) (-5 *1 (-387 *3 *4 *5 *2)) (-4 *2 (-861 *3 *4 *5)))) (-1873 (*1 *2 *3 *4) (-12 (-5 *4 (-583 *3)) (-4 *3 (-861 *5 *6 *7)) (-4 *5 (-389)) (-4 *6 (-717)) (-4 *7 (-756)) (-5 *2 (-2 (|:| |poly| *3) (|:| |mult| *5))) (-5 *1 (-387 *5 *6 *7 *3)))) (-1872 (*1 *2 *3 *2) (-12 (-5 *2 (-583 (-2 (|:| |lcmfij| *3) (|:| |totdeg| (-694)) (|:| |poli| *6) (|:| |polj| *6)))) (-4 *3 (-717)) (-4 *6 (-861 *4 *3 *5)) (-4 *4 (-389)) (-4 *5 (-756)) (-5 *1 (-387 *4 *3 *5 *6)))) (-1871 (*1 *2 *2) (-12 (-5 *2 (-583 (-2 (|:| |lcmfij| *4) (|:| |totdeg| (-694)) (|:| |poli| *6) (|:| |polj| *6)))) (-4 *4 (-717)) (-4 *6 (-861 *3 *4 *5)) (-4 *3 (-389)) (-4 *5 (-756)) (-5 *1 (-387 *3 *4 *5 *6)))) (-1870 (*1 *2 *3 *2) (-12 (-5 *2 (-583 (-2 (|:| |lcmfij| *5) (|:| |totdeg| (-694)) (|:| |poli| *3) (|:| |polj| *3)))) (-4 *5 (-717)) (-4 *3 (-861 *4 *5 *6)) (-4 *4 (-389)) (-4 *6 (-756)) (-5 *1 (-387 *4 *5 *6 *3)))) (-1869 (*1 *2 *3 *3 *3 *3) (-12 (-4 *4 (-389)) (-4 *3 (-717)) (-4 *5 (-756)) (-5 *2 (-85)) (-5 *1 (-387 *4 *3 *5 *6)) (-4 *6 (-861 *4 *3 *5)))) (-1868 (*1 *2 *3 *3) (-12 (-4 *4 (-389)) (-4 *3 (-717)) (-4 *5 (-756)) (-5 *2 (-85)) (-5 *1 (-387 *4 *3 *5 *6)) (-4 *6 (-861 *4 *3 *5)))) (-1867 (*1 *2 *3) (-12 (-5 *3 (-2 (|:| |lcmfij| *5) (|:| |totdeg| (-694)) (|:| |poli| *7) (|:| |polj| *7))) (-4 *5 (-717)) (-4 *7 (-861 *4 *5 *6)) (-4 *4 (-389)) (-4 *6 (-756)) (-5 *2 (-85)) (-5 *1 (-387 *4 *5 *6 *7)))) (-1866 (*1 *2 *2 *3 *3) (-12 (-5 *2 (-583 *7)) (-5 *3 (-483)) (-4 *7 (-861 *4 *5 *6)) (-4 *4 (-389)) (-4 *5 (-717)) (-4 *6 (-756)) (-5 *1 (-387 *4 *5 *6 *7)))) (-1865 (*1 *2 *2 *3) (-12 (-5 *3 (-583 *2)) (-4 *2 (-861 *4 *5 *6)) (-4 *4 (-389)) (-4 *5 (-717)) (-4 *6 (-756)) (-5 *1 (-387 *4 *5 *6 *2)))) (-1864 (*1 *2 *2 *3) (-12 (-5 *3 (-583 *2)) (-4 *2 (-861 *4 *5 *6)) (-4 *4 (-389)) (-4 *5 (-717)) (-4 *6 (-756)) (-5 *1 (-387 *4 *5 *6 *2))))) 
-((-1888 (($ $ $) 14 T ELT) (($ (-583 $)) 21 T ELT)) (-2704 (((-1083 $) (-1083 $) (-1083 $)) 45 T ELT)) (-3139 (($ $ $) NIL T ELT) (($ (-583 $)) 22 T ELT))) 
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-NIL 
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+((-1889 (($ $ $) 14 T ELT) (($ (-584 $)) 21 T ELT)) (-2706 (((-1084 $) (-1084 $) (-1084 $)) 45 T ELT)) (-3141 (($ $ $) NIL T ELT) (($ (-584 $)) 22 T ELT))) 
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+NIL 
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-NIL 
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-NIL 
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-((-3621 (*1 *1) (-5 *1 (-414)))) 
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-((-3523 (*1 *2 *1) (-12 (-5 *2 (-1047)) (-5 *1 (-415)))) (-3522 (*1 *2 *1) (-12 (-5 *2 (-1047)) (-5 *1 (-415))))) 
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-NIL 
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-NIL 
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-NIL 
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 (((-443 |#1|) (-113) (-72)) (T -443)) 
 NIL 
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-NIL 
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-NIL 
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-NIL 
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-((-1985 (*1 *1 *2) (-12 (-5 *2 (-583 *3)) (-4 *3 (-1127)) (-5 *1 (-454 *3 *4)) (-14 *4 (-483)))) (-1984 (*1 *2 *1) (-12 (-5 *2 (-694)) (-5 *1 (-454 *3 *4)) (-4 *3 (-1127)) (-14 *4 (-483)))) (-1983 (*1 *1 *1 *2) (-12 (-5 *2 (-483)) (-5 *1 (-454 *3 *4)) (-4 *3 (-1127)) (-14 *4 *2))) (-1982 (*1 *2 *2) (-12 (-5 *2 (-85)) (-5 *1 (-454 *3 *4)) (-4 *3 (-1127)) (-14 *4 (-483))))) 
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-(((-455) (-13 (-994) (-10 -8 (-15 -3916 ((-1047) $)) (-15 -1987 ((-1047) $)) (-15 -1986 ((-1047) $))))) (T -455)) 
-((-3916 (*1 *2 *1) (-12 (-5 *2 (-1047)) (-5 *1 (-455)))) (-1987 (*1 *2 *1) (-12 (-5 *2 (-1047)) (-5 *1 (-455)))) (-1986 (*1 *2 *1) (-12 (-5 *2 (-1047)) (-5 *1 (-455))))) 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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+NIL 
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+NIL 
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+NIL 
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+(((-461 |#1| |#2| |#3|) (-628 |#1| (-537 |#1| |#3|) (-537 |#1| |#2|)) (-962) (-484) (-484)) (T -461)) 
+NIL 
+((-2566 (((-85) $ $) NIL T ELT)) (-3239 (((-1072) $) NIL T ELT)) (-1991 (((-584 (-1129)) $) 14 T ELT)) (-3240 (((-1033) $) NIL T ELT)) (-3942 (((-773) $) 20 T ELT) (($ (-1094)) NIL T ELT) (((-1094) $) NIL T ELT) (($ (-584 (-1129))) 12 T ELT)) (-1263 (((-85) $ $) NIL T ELT)) (-3054 (((-85) $ $) NIL T ELT))) 
+(((-462) (-13 (-995) (-10 -8 (-15 -3942 ($ (-584 (-1129)))) (-15 -1991 ((-584 (-1129)) $))))) (T -462)) 
+((-3942 (*1 *1 *2) (-12 (-5 *2 (-584 (-1129))) (-5 *1 (-462)))) (-1991 (*1 *2 *1) (-12 (-5 *2 (-584 (-1129))) (-5 *1 (-462))))) 
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+(((-463) (-13 (-995) (-10 -8 (-15 -3446 ((-444) $)) (-15 -1992 ((-1048) $))))) (T -463)) 
+((-3446 (*1 *2 *1) (-12 (-5 *2 (-444)) (-5 *1 (-463)))) (-1992 (*1 *2 *1) (-12 (-5 *2 (-1048)) (-5 *1 (-463))))) 
+((-1998 (((-633 (-1137)) $) 15 T ELT)) (-1994 (((-633 (-1135)) $) 38 T ELT)) (-1996 (((-633 (-1134)) $) 29 T ELT)) (-1999 (((-633 (-488)) $) 12 T ELT)) (-1995 (((-633 (-486)) $) 42 T ELT)) (-1997 (((-633 (-485)) $) 33 T ELT)) (-1993 (((-695) $ (-102)) 54 T ELT))) 
+(((-464 |#1|) (-10 -7 (-15 -1993 ((-695) |#1| (-102))) (-15 -1994 ((-633 (-1135)) |#1|)) (-15 -1995 ((-633 (-486)) |#1|)) (-15 -1996 ((-633 (-1134)) |#1|)) (-15 -1997 ((-633 (-485)) |#1|)) (-15 -1998 ((-633 (-1137)) |#1|)) (-15 -1999 ((-633 (-488)) |#1|))) (-465)) (T -464)) 
+NIL 
+((-1998 (((-633 (-1137)) $) 12 T ELT)) (-1994 (((-633 (-1135)) $) 8 T ELT)) (-1996 (((-633 (-1134)) $) 10 T ELT)) (-1999 (((-633 (-488)) $) 13 T ELT)) (-1995 (((-633 (-486)) $) 9 T ELT)) (-1997 (((-633 (-485)) $) 11 T ELT)) (-1993 (((-695) $ (-102)) 7 T ELT)) (-2000 (((-633 (-101)) $) 14 T ELT)) (-1698 (($ $) 6 T ELT))) 
+(((-465) (-113)) (T -465)) 
+((-2000 (*1 *2 *1) (-12 (-4 *1 (-465)) (-5 *2 (-633 (-101))))) (-1999 (*1 *2 *1) (-12 (-4 *1 (-465)) (-5 *2 (-633 (-488))))) (-1998 (*1 *2 *1) (-12 (-4 *1 (-465)) (-5 *2 (-633 (-1137))))) (-1997 (*1 *2 *1) (-12 (-4 *1 (-465)) (-5 *2 (-633 (-485))))) (-1996 (*1 *2 *1) (-12 (-4 *1 (-465)) (-5 *2 (-633 (-1134))))) (-1995 (*1 *2 *1) (-12 (-4 *1 (-465)) (-5 *2 (-633 (-486))))) (-1994 (*1 *2 *1) (-12 (-4 *1 (-465)) (-5 *2 (-633 (-1135))))) (-1993 (*1 *2 *1 *3) (-12 (-4 *1 (-465)) (-5 *3 (-102)) (-5 *2 (-695))))) 
+(-13 (-147) (-10 -8 (-15 -2000 ((-633 (-101)) $)) (-15 -1999 ((-633 (-488)) $)) (-15 -1998 ((-633 (-1137)) $)) (-15 -1997 ((-633 (-485)) $)) (-15 -1996 ((-633 (-1134)) $)) (-15 -1995 ((-633 (-486)) $)) (-15 -1994 ((-633 (-1135)) $)) (-15 -1993 ((-695) $ (-102))))) 
 (((-147) . T)) 
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-(((-466) (-13 (-464) (-552 (-772)) (-10 -8 (-15 -2013 ($ (-335))) (-15 -2013 ($ (-1071))) (-15 -2012 ((-85) $)) (-15 -2554 ((-85) $)) (-15 -3413 ((-1032) $)) (-15 -2011 ((-1032) $ (-1032)))))) (T -466)) 
-((-2013 (*1 *1 *2) (-12 (-5 *2 (-335)) (-5 *1 (-466)))) (-2013 (*1 *1 *2) (-12 (-5 *2 (-1071)) (-5 *1 (-466)))) (-2012 (*1 *2 *1) (-12 (-5 *2 (-85)) (-5 *1 (-466)))) (-2554 (*1 *2 *1) (-12 (-5 *2 (-85)) (-5 *1 (-466)))) (-3413 (*1 *2 *1) (-12 (-5 *2 (-1032)) (-5 *1 (-466)))) (-2011 (*1 *2 *1 *2) (-12 (-5 *2 (-1032)) (-5 *1 (-466))))) 
-((-2015 (((-1 |#1| |#1|) |#1|) 11 T ELT)) (-2014 (((-1 |#1| |#1|)) 10 T ELT))) 
-(((-467 |#1|) (-10 -7 (-15 -2014 ((-1 |#1| |#1|))) (-15 -2015 ((-1 |#1| |#1|) |#1|))) (-13 (-663) (-25))) (T -467)) 
-((-2015 (*1 *2 *3) (-12 (-5 *2 (-1 *3 *3)) (-5 *1 (-467 *3)) (-4 *3 (-13 (-663) (-25))))) (-2014 (*1 *2) (-12 (-5 *2 (-1 *3 *3)) (-5 *1 (-467 *3)) (-4 *3 (-13 (-663) (-25)))))) 
-((-2564 (((-85) $ $) NIL T ELT)) (-3183 (((-85) $) NIL T ELT)) (-3768 (((-583 (-782 |#1| (-694))) $) NIL T ELT)) (-2479 (($ $ $) NIL T ELT)) (-1309 (((-3 $ "failed") $ $) NIL T ELT)) (-3718 (($) NIL T CONST)) (-3953 (($ $) NIL T ELT)) (-3181 (((-85) $) NIL T ELT)) (-2889 (($ (-694) |#1|) NIL T ELT)) (-2527 (($ $ $) NIL T ELT)) (-2853 (($ $ $) NIL T ELT)) (-3952 (($ (-1 (-694) (-694)) $) NIL T ELT)) (-1981 ((|#1| $) NIL T ELT)) (-3169 (((-694) $) NIL T ELT)) (-3237 (((-1071) $) NIL T ELT)) (-3238 (((-1032) $) NIL T ELT)) (-3940 (((-772) $) 28 T ELT)) (-1262 (((-85) $ $) NIL T ELT)) (-2656 (($) NIL T CONST)) (-2562 (((-85) $ $) NIL T ELT)) (-2563 (((-85) $ $) NIL T ELT)) (-3052 (((-85) $ $) NIL T ELT)) (-2680 (((-85) $ $) NIL T ELT)) (-2681 (((-85) $ $) NIL T ELT)) (-3833 (($ $ $) NIL T ELT)) (* (($ (-830) $) NIL T ELT) (($ (-694) $) NIL T ELT))) 
-(((-468 |#1|) (-13 (-717) (-447 (-694) |#1|)) (-756)) (T -468)) 
-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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+NIL 
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+NIL 
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+(((-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 $) . T) ((-583 |#1|) |has| |#1| (-146)) ((-655 |#1|) |has| |#1| (-146)) ((-664) . T) ((-951 (-347 (-484))) |has| |#1| (-951 (-347 (-484)))) ((-951 (-484)) |has| |#1| (-951 (-484))) ((-951 |#1|) . T) ((-964 |#1|) . T) ((-969 |#1|) . T) ((-962) . T) ((-970) . T) ((-1025) . T) ((-1060) . T) ((-1013) . T) ((-1128) . T) ((-762 |#1|) . T)) 
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+NIL 
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|#2| (-812 (-1089))) ELT) (($ $ (-584 (-1089)) (-584 (-695))) NIL (|has| |#2| (-812 (-1089))) ELT)) (-3054 (((-85) $ $) NIL T ELT)) (-3945 (($ $ |#2|) NIL (|has| |#2| (-311)) ELT)) (-3833 (($ $) NIL T ELT) (($ $ $) NIL T ELT)) (-3835 (($ $ $) NIL T ELT)) (** (($ $ (-831)) NIL T ELT) (($ $ (-695)) NIL T ELT) (($ $ (-484)) NIL (|has| |#2| (-311)) ELT)) (* (($ (-831) $) NIL T ELT) (($ (-695) $) NIL T ELT) (($ (-484) $) NIL T ELT) (($ $ $) NIL T ELT) (($ $ |#2|) NIL T ELT) (($ |#2| $) NIL T ELT) (((-197 |#1| |#2|) $ (-197 |#1| |#2|)) NIL T ELT) (((-197 |#1| |#2|) (-197 |#1| |#2|) $) NIL T ELT)) (-3953 (((-695) $) NIL (|has| $ (-6 -3991)) ELT))) 
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+NIL 
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+((-3245 (*1 *2 *1) (-12 (-5 *2 (-584 (-1048))) (-5 *1 (-614))))) 
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+NIL 
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+NIL 
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+(((-655 |#1|) (-113) (-146)) (T -655)) 
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+NIL 
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+NIL 
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+NIL 
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-NIL 
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-NIL 
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-NIL 
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-((-2525 (((-85) (-1177 |#2|) (-1177 |#2|)) 19 T ELT)) (-2526 (((-85) (-1177 |#2|) (-1177 |#2|)) 20 T ELT)) (-2524 (((-85) (-1177 |#2|) (-1177 |#2|)) 16 T ELT))) 
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-((-2526 (*1 *2 *3 *3) (-12 (-5 *3 (-1177 *5)) (-4 *5 (-716)) (-5 *2 (-85)) (-5 *1 (-753 *4 *5)) (-14 *4 (-694)))) (-2525 (*1 *2 *3 *3) (-12 (-5 *3 (-1177 *5)) (-4 *5 (-716)) (-5 *2 (-85)) (-5 *1 (-753 *4 *5)) (-14 *4 (-694)))) (-2524 (*1 *2 *3 *3) (-12 (-5 *3 (-1177 *5)) (-4 *5 (-716)) (-5 *2 (-85)) (-5 *1 (-753 *4 *5)) (-14 *4 (-694))))) 
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-(((-754) (-113)) (T -754)) 
-NIL 
-(-13 (-766) (-663)) 
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+((-2481 (*1 *1 *1 *1) (-4 *1 (-718)))) 
+(-13 (-722) (-10 -8 (-15 -2481 ($ $ $)))) 
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+((-2566 (((-85) $ $) 7 T ELT)) (-2529 (($ $ $) 23 T ELT)) (-2855 (($ $ $) 22 T ELT)) (-3239 (((-1072) $) 11 T ELT)) (-3240 (((-1033) $) 12 T ELT)) (-3942 (((-773) $) 13 T ELT)) (-1263 (((-85) $ $) 6 T ELT)) (-2564 (((-85) $ $) 21 T ELT)) (-2565 (((-85) $ $) 19 T ELT)) (-3054 (((-85) $ $) 8 T ELT)) (-2682 (((-85) $ $) 20 T ELT)) (-2683 (((-85) $ $) 18 T ELT)) (-3835 (($ $ $) 25 T ELT)) (* (($ (-831) $) 26 T ELT))) 
+(((-719) (-113)) (T -719)) 
+NIL 
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+(((-25) . T) ((-72) . T) ((-553 (-773)) . T) ((-13) . T) ((-757) . T) ((-760) . T) ((-1013) . T) ((-1128) . T)) 
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+((-3123 (*1 *2) (-12 (-4 *4 (-146)) (-5 *2 (-695)) (-5 *1 (-720 *3 *4)) (-4 *3 (-721 *4))))) 
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+(((-721 |#1|) (-113) (-146)) (T -721)) 
+((-3007 (*1 *1 *1) (-12 (-4 *1 (-721 *2)) (-4 *2 (-146)))) (-3639 (*1 *2 *1) (-12 (-4 *1 (-721 *2)) (-4 *2 (-146)))) (-2486 (*1 *2 *1) (-12 (-4 *1 (-721 *2)) (-4 *2 (-146)))) (-2485 (*1 *2 *1) (-12 (-4 *1 (-721 *2)) (-4 *2 (-146)))) (-2484 (*1 *2 *1) (-12 (-4 *1 (-721 *2)) (-4 *2 (-146)))) (-2483 (*1 *2 *1) (-12 (-4 *1 (-721 *2)) (-4 *2 (-146)))) (-3006 (*1 *2 *1) (-12 (-4 *1 (-721 *2)) (-4 *2 (-146)))) (-3005 (*1 *2 *1) (-12 (-4 *1 (-721 *2)) (-4 *2 (-146)))) (-3004 (*1 *2 *1) (-12 (-4 *1 (-721 *2)) (-4 *2 (-146)))) (-3129 (*1 *2 *1) (-12 (-4 *1 (-721 *2)) (-4 *2 (-146)))) (-2487 (*1 *1 *2 *2 *2 *2 *2 *2 *2 *2) (-12 (-4 *1 (-721 *2)) (-4 *2 (-146)))) (-3379 (*1 *2 *1) (-12 (-4 *1 (-721 *2)) (-4 *2 (-146)) (-4 *2 (-973)))) (-3021 (*1 *2 *1) (-12 (-4 *1 (-721 *3)) (-4 *3 (-146)) (-4 *3 (-483)) (-5 *2 (-85)))) (-3020 (*1 *2 *1) (-12 (-4 *1 (-721 *3)) (-4 *3 (-146)) (-4 *3 (-483)) (-5 *2 (-347 (-484))))) (-3022 (*1 *2 *1) (|partial| -12 (-4 *1 (-721 *3)) (-4 *3 (-146)) (-4 *3 (-483)) (-5 *2 (-347 (-484))))) (-2482 (*1 *1 *1) (-12 (-4 *1 (-721 *2)) (-4 *2 (-146)) (-4 *2 (-311))))) 
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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)) 
+((-2566 (((-85) $ $) 7 T ELT)) (-3185 (((-85) $) 31 T ELT)) (-1310 (((-3 $ "failed") $ $) 34 T ELT)) (-3720 (($) 30 T CONST)) (-3183 (((-85) $) 28 T ELT)) (-2529 (($ $ $) 23 T ELT)) (-2855 (($ $ $) 22 T ELT)) (-3239 (((-1072) $) 11 T ELT)) (-3240 (((-1033) $) 12 T ELT)) (-3942 (((-773) $) 13 T ELT)) (-1263 (((-85) $ $) 6 T ELT)) (-2658 (($) 29 T CONST)) (-2564 (((-85) $ $) 21 T ELT)) (-2565 (((-85) $ $) 19 T ELT)) (-3054 (((-85) $ $) 8 T ELT)) (-2682 (((-85) $ $) 20 T ELT)) (-2683 (((-85) $ $) 18 T ELT)) (-3835 (($ $ $) 25 T ELT)) (* (($ (-831) $) 26 T ELT) (($ (-695) $) 32 T ELT))) 
+(((-722) (-113)) (T -722)) 
+NIL 
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 (((-755) (-113)) (T -755)) 
 NIL 
-(-13 (-714) (-961) (-663)) 
-(((-21) . T) ((-23) . T) ((-25) . T) ((-72) . T) ((-104) . T) ((-555 (-483)) . T) ((-552 (-772)) . T) ((-13) . T) ((-588 (-483)) . T) ((-588 $) . T) ((-590 $) . T) ((-663) . T) ((-714) . T) ((-716) . T) ((-718) . T) ((-721) . T) ((-756) . T) ((-759) . T) ((-961) . T) ((-969) . T) ((-1024) . T) ((-1059) . T) ((-1012) . T) ((-1127) . T)) 
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 (((-756) (-113)) (T -756)) 
 NIL 
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-NIL 
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-NIL 
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-NIL 
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-(((-766) (-113)) (T -766)) 
-NIL 
-(-13 (-756) (-1024)) 
-(((-72) . T) ((-552 (-772)) . T) ((-13) . T) ((-756) . T) ((-759) . T) ((-1024) . T) ((-1012) . T) ((-1127) . T)) 
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-(((-767) (-13 (-756) (-10 -8 (-15 -3940 ($ (-483))) (-15 -3396 ((-483) $))))) (T -767)) 
-((-3940 (*1 *1 *2) (-12 (-5 *2 (-483)) (-5 *1 (-767)))) (-3396 (*1 *2 *1) (-12 (-5 *2 (-483)) (-5 *1 (-767))))) 
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-((-2551 (((-632 (-1136)) $ (-1136)) 15 T ELT)) (-2552 (((-632 (-487)) $ (-487)) 12 T ELT)) (-2550 (((-694) $ (-102)) 30 T ELT))) 
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-NIL 
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+(-13 (-715) (-962) (-664)) 
+(((-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) ((-715) . T) ((-717) . T) ((-719) . T) ((-722) . T) ((-757) . T) ((-760) . T) ((-962) . T) ((-970) . T) ((-1025) . T) ((-1060) . T) ((-1013) . T) ((-1128) . T)) 
+((-2566 (((-85) $ $) 7 T ELT)) (-2529 (($ $ $) 23 T ELT)) (-2855 (($ $ $) 22 T ELT)) (-3239 (((-1072) $) 11 T ELT)) (-3240 (((-1033) $) 12 T ELT)) (-3942 (((-773) $) 13 T ELT)) (-1263 (((-85) $ $) 6 T ELT)) (-2564 (((-85) $ $) 21 T ELT)) (-2565 (((-85) $ $) 19 T ELT)) (-3054 (((-85) $ $) 8 T ELT)) (-2682 (((-85) $ $) 20 T ELT)) (-2683 (((-85) $ $) 18 T ELT))) 
+(((-757) (-113)) (T -757)) 
+NIL 
+(-13 (-1013) (-760)) 
+(((-72) . T) ((-553 (-773)) . T) ((-13) . T) ((-760) . T) ((-1013) . T) ((-1128) . T)) 
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+NIL 
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+NIL 
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+(((-760) (-113)) (T -760)) 
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+(((-72) . T) ((-13) . T) ((-1128) . T)) 
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+NIL 
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+NIL 
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+NIL 
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 (((-147) . T)) 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-(((-552 (-772)) . 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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-NIL 
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-NIL 
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-NIL 
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-NIL 
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+NIL 
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+NIL 
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+NIL 
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+NIL 
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+NIL 
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+NIL 
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+(((-21) . T) ((-23) . T) ((-25) . T) ((-34) . T) ((-38 |#2|) |has| |#2| (-6 (-3993 #1="*"))) ((-72) . T) ((-82 |#2| |#2|) . T) ((-104) . T) ((-556 (-347 (-484))) |has| |#2| (-951 (-347 (-484)))) ((-556 (-484)) . T) ((-556 |#2|) . T) ((-553 (-773)) . T) ((-186 $) OR (|has| |#2| (-189)) (|has| |#2| (-190))) ((-184 |#2|) . T) ((-190) |has| |#2| (-190)) ((-189) OR (|has| |#2| (-189)) (|has| |#2| (-190))) ((-225 |#2|) . T) ((-259 |#2|) -12 (|has| |#2| (-259 |#2|)) (|has| |#2| (-1013))) ((-326 |#2|) . T) ((-352 |#2|) . T) ((-426 |#2|) . T) ((-453 |#2| |#2|) -12 (|has| |#2| (-259 |#2|)) (|has| |#2| (-1013))) ((-13) . T) ((-589 (-484)) . T) ((-589 |#2|) . T) ((-589 $) . T) ((-591 (-484)) |has| |#2| (-581 (-484))) ((-591 |#2|) . T) ((-591 $) . T) ((-583 |#2|) OR (|has| |#2| (-146)) (|has| |#2| (-6 (-3993 #1#)))) ((-581 (-484)) |has| |#2| (-581 (-484))) ((-581 |#2|) . T) ((-655 |#2|) OR (|has| |#2| (-146)) (|has| |#2| (-6 (-3993 #1#)))) ((-664) . T) ((-807 $ (-1089)) OR (|has| |#2| (-812 (-1089))) (|has| |#2| (-810 (-1089)))) ((-810 (-1089)) |has| |#2| (-810 (-1089))) ((-812 (-1089)) OR (|has| |#2| (-812 (-1089))) (|has| |#2| (-810 (-1089)))) ((-966 |#1| |#1| |#2| |#3| |#4|) . T) ((-951 (-347 (-484))) |has| |#2| (-951 (-347 (-484)))) ((-951 (-484)) |has| |#2| (-951 (-484))) ((-951 |#2|) . T) ((-964 |#2|) . T) ((-969 |#2|) . T) ((-962) . T) ((-970) . T) ((-1025) . T) ((-1060) . T) ((-1013) . T) ((-1128) . T)) 
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(|has| |#1| (-38 (-347 (-484)))) ELT) (($ |#1| $) 99 T ELT) (($ $ |#1|) NIL T ELT))) 
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+NIL 
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+NIL 
+(-13 (-1020 |t#1| |t#2| |t#3| |t#4|) (-708 |t#1| |t#2| |t#3| |t#4|)) 
+(((-34) . T) ((-72) . T) ((-553 (-584 |#4|)) . T) ((-553 (-773)) . T) ((-124 |#4|) . T) ((-554 (-473)) |has| |#4| (-554 (-473))) ((-259 |#4|) -12 (|has| |#4| (-259 |#4|)) (|has| |#4| (-1013))) ((-426 |#4|) . T) ((-453 |#4| |#4|) -12 (|has| |#4| (-259 |#4|)) (|has| |#4| (-1013))) ((-13) . T) ((-708 |#1| |#2| |#3| |#4|) . T) ((-890 |#1| |#2| |#3| |#4|) . T) ((-983 |#1| |#2| |#3| |#4|) . T) ((-1013) . T) ((-1020 |#1| |#2| |#3| |#4|) . T) ((-1123 |#1| |#2| |#3| |#4|) . T) ((-1128) . T)) 
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$) NIL T ELT) (($ $ |#2|) NIL T ELT) (($ |#2| $) NIL T ELT) (((-197 |#1| |#2|) $ (-197 |#1| |#2|)) 58 T ELT) (((-197 |#1| |#2|) (-197 |#1| |#2|) $) 60 T ELT)) (-3953 (((-695) $) NIL (|has| $ (-6 -3991)) ELT))) 
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+NIL 
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+NIL 
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 NIL 
 (-13) 
 (((-13) . T)) 
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-(((-21) . T) ((-23) . T) ((-47 |#1| (-483)) . T) ((-25) . T) ((-38 (-347 (-483))) OR (|has| |#1| (-311)) (|has| |#1| (-38 (-347 (-483))))) ((-38 |#1|) |has| |#1| (-146)) ((-38 |#2|) |has| |#1| (-311)) ((-38 $) OR (|has| |#1| (-494)) (|has| |#1| (-311))) ((-35) |has| |#1| (-38 (-347 (-483)))) ((-66) |has| |#1| (-38 (-347 (-483)))) ((-72) . T) ((-82 (-347 (-483)) (-347 (-483))) OR (|has| |#1| (-311)) (|has| |#1| (-38 (-347 (-483))))) ((-82 |#1| |#1|) . T) ((-82 |#2| |#2|) |has| |#1| (-311)) ((-82 $ $) OR (|has| |#1| (-494)) (|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))) ((-555 (-347 (-483))) OR (|has| |#1| (-311)) (|has| |#1| (-38 (-347 (-483))))) ((-555 (-483)) . T) ((-555 (-1088)) -12 (|has| |#1| (-311)) (|has| |#2| (-950 (-1088)))) ((-555 |#1|) |has| |#1| (-146)) ((-555 |#2|) . 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T) ((-241 |#2| $) -12 (|has| |#1| (-311)) (|has| |#2| (-241 |#2| |#2|))) ((-241 $ $) |has| (-483) (-1024)) ((-245) OR (|has| |#1| (-494)) (|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 (-483)))) ((-452 (-1088) |#2|) -12 (|has| |#1| (-311)) (|has| |#2| (-452 (-1088) |#2|))) ((-452 |#2| |#2|) -12 (|has| |#1| (-311)) (|has| |#2| (-259 |#2|))) ((-494) OR (|has| |#1| (-494)) (|has| |#1| (-311))) ((-13) . T) ((-588 (-347 (-483))) OR (|has| |#1| (-311)) (|has| |#1| (-38 (-347 (-483))))) ((-588 (-483)) . T) ((-588 |#1|) . T) ((-588 |#2|) |has| |#1| (-311)) ((-588 $) . T) ((-590 (-347 (-483))) OR (|has| |#1| (-311)) (|has| |#1| (-38 (-347 (-483))))) ((-590 (-483)) -12 (|has| |#1| (-311)) (|has| |#2| (-580 (-483)))) ((-590 |#1|) . T) ((-590 |#2|) |has| |#1| (-311)) ((-590 $) . T) ((-582 (-347 (-483))) OR (|has| |#1| (-311)) (|has| |#1| (-38 (-347 (-483))))) ((-582 |#1|) |has| |#1| (-146)) ((-582 |#2|) |has| |#1| (-311)) ((-582 $) OR (|has| |#1| (-494)) (|has| |#1| (-311))) ((-580 (-483)) -12 (|has| |#1| (-311)) (|has| |#2| (-580 (-483)))) ((-580 |#2|) |has| |#1| (-311)) ((-654 (-347 (-483))) OR (|has| |#1| (-311)) (|has| |#1| (-38 (-347 (-483))))) ((-654 |#1|) |has| |#1| (-146)) ((-654 |#2|) |has| |#1| (-311)) ((-654 $) OR (|has| |#1| (-494)) (|has| |#1| (-311))) ((-663) . 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T) ((-832) |has| |#1| (-311)) ((-904 |#2|) |has| |#1| (-311)) ((-915) |has| |#1| (-38 (-347 (-483)))) ((-933) -12 (|has| |#1| (-311)) (|has| |#2| (-933))) ((-950 (-347 (-483))) -12 (|has| |#1| (-311)) (|has| |#2| (-950 (-483)))) ((-950 (-483)) -12 (|has| |#1| (-311)) (|has| |#2| (-950 (-483)))) ((-950 (-1088)) -12 (|has| |#1| (-311)) (|has| |#2| (-950 (-1088)))) ((-950 |#2|) . T) ((-963 (-347 (-483))) OR (|has| |#1| (-311)) (|has| |#1| (-38 (-347 (-483))))) ((-963 |#1|) . T) ((-963 |#2|) |has| |#1| (-311)) ((-963 $) OR (|has| |#1| (-494)) (|has| |#1| (-311)) (|has| |#1| (-146))) ((-968 (-347 (-483))) OR (|has| |#1| (-311)) (|has| |#1| (-38 (-347 (-483))))) ((-968 |#1|) . T) ((-968 |#2|) |has| |#1| (-311)) ((-968 $) OR (|has| |#1| (-494)) (|has| |#1| (-311)) (|has| |#1| (-146))) ((-961) . T) ((-969) . T) ((-1024) . T) ((-1059) . T) ((-1012) . 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-NIL 
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-((-3812 (*1 *1 *2) (-12 (-5 *2 (-1067 (-2 (|:| |k| (-694)) (|:| |c| *3)))) (-4 *3 (-961)) (-4 *1 (-1170 *3)))) (-3811 (*1 *2 *1) (-12 (-4 *1 (-1170 *3)) (-4 *3 (-961)) (-5 *2 (-1067 *3)))) (-3812 (*1 *1 *2) (-12 (-5 *2 (-1067 *3)) (-4 *3 (-961)) (-4 *1 (-1170 *3)))) (-3810 (*1 *1 *1) (-12 (-4 *1 (-1170 *2)) (-4 *2 (-961)))) (-3809 (*1 *1 *2 *1) (-12 (-5 *2 (-1 *3 (-483))) (-4 *1 (-1170 *3)) (-4 *3 (-961)))) (-3808 (*1 *2 *1 *3) (-12 (-5 *3 (-694)) (-4 *1 (-1170 *4)) (-4 *4 (-961)) (-5 *2 (-857 *4)))) (-3808 (*1 *2 *1 *3 *3) (-12 (-5 *3 (-694)) (-4 *1 (-1170 *4)) (-4 *4 (-961)) (-5 *2 (-857 *4)))) (** (*1 *1 *1 *2) (-12 (-4 *1 (-1170 *2)) (-4 *2 (-961)) (-4 *2 (-311)))) (-3806 (*1 *1 *1) (-12 (-4 *1 (-1170 *2)) (-4 *2 (-961)) (-4 *2 (-38 (-347 (-483)))))) (-3806 (*1 *1 *1 *2) (OR (-12 (-5 *2 (-1088)) (-4 *1 (-1170 *3)) (-4 *3 (-961)) (-12 (-4 *3 (-29 (-483))) (-4 *3 (-871)) (-4 *3 (-1113)) (-4 *3 (-38 (-347 (-483)))))) (-12 (-5 *2 (-1088)) (-4 *1 (-1170 *3)) (-4 *3 (-961)) (-12 (|has| *3 (-15 -3077 ((-583 *2) *3))) (|has| *3 (-15 -3806 (*3 *3 *2))) (-4 *3 (-38 (-347 (-483))))))))) 
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-(((-21) . T) ((-23) . T) ((-47 |#1| (-694)) . T) ((-25) . T) ((-38 (-347 (-483))) |has| |#1| (-38 (-347 (-483)))) ((-38 |#1|) |has| |#1| (-146)) ((-38 $) |has| |#1| (-494)) ((-35) |has| |#1| (-38 (-347 (-483)))) ((-66) |has| |#1| (-38 (-347 (-483)))) ((-72) . T) ((-82 (-347 (-483)) (-347 (-483))) |has| |#1| (-38 (-347 (-483)))) ((-82 |#1| |#1|) . T) ((-82 $ $) OR (|has| |#1| (-494)) (|has| |#1| (-146))) ((-104) . T) ((-118) |has| |#1| (-118)) ((-120) |has| |#1| (-120)) ((-555 (-347 (-483))) |has| |#1| (-38 (-347 (-483)))) ((-555 (-483)) . T) ((-555 |#1|) |has| |#1| (-146)) ((-555 $) |has| |#1| (-494)) ((-552 (-772)) . T) ((-146) OR (|has| |#1| (-494)) (|has| |#1| (-146))) ((-186 $) |has| |#1| (-15 * (|#1| (-694) |#1|))) ((-190) |has| |#1| (-15 * (|#1| (-694) |#1|))) ((-189) |has| |#1| (-15 * (|#1| (-694) |#1|))) ((-239) |has| |#1| (-38 (-347 (-483)))) ((-241 (-694) |#1|) . T) ((-241 $ $) |has| (-694) (-1024)) ((-245) |has| |#1| (-494)) ((-430) |has| |#1| (-38 (-347 (-483)))) ((-494) |has| |#1| (-494)) ((-13) . T) ((-588 (-347 (-483))) |has| |#1| (-38 (-347 (-483)))) ((-588 (-483)) . T) ((-588 |#1|) . T) ((-588 $) . T) ((-590 (-347 (-483))) |has| |#1| (-38 (-347 (-483)))) ((-590 |#1|) . T) ((-590 $) . T) ((-582 (-347 (-483))) |has| |#1| (-38 (-347 (-483)))) ((-582 |#1|) |has| |#1| (-146)) ((-582 $) |has| |#1| (-494)) ((-654 (-347 (-483))) |has| |#1| (-38 (-347 (-483)))) ((-654 |#1|) |has| |#1| (-146)) ((-654 $) |has| |#1| (-494)) ((-663) . T) ((-806 $ (-1088)) -12 (|has| |#1| (-809 (-1088))) (|has| |#1| (-15 * (|#1| (-694) |#1|)))) ((-809 (-1088)) -12 (|has| |#1| (-809 (-1088))) (|has| |#1| (-15 * (|#1| (-694) |#1|)))) ((-811 (-1088)) -12 (|has| |#1| (-809 (-1088))) (|has| |#1| (-15 * (|#1| (-694) |#1|)))) ((-886 |#1| (-694) (-993)) . T) ((-915) |has| |#1| (-38 (-347 (-483)))) ((-963 (-347 (-483))) |has| |#1| (-38 (-347 (-483)))) ((-963 |#1|) . T) ((-963 $) OR (|has| |#1| (-494)) (|has| |#1| (-146))) ((-968 (-347 (-483))) |has| |#1| (-38 (-347 (-483)))) ((-968 |#1|) . T) ((-968 $) OR (|has| |#1| (-494)) (|has| |#1| (-146))) ((-961) . T) ((-969) . T) ((-1024) . T) ((-1059) . T) ((-1012) . T) ((-1113) |has| |#1| (-38 (-347 (-483)))) ((-1116) |has| |#1| (-38 (-347 (-483)))) ((-1127) . T) ((-1156 |#1| (-694)) . T)) 
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-((-3822 ((|#2| |#4| (-694)) 31 T ELT)) (-3821 ((|#4| |#2|) 26 T ELT)) (-3824 ((|#4| (-347 |#2|)) 49 (|has| |#1| (-494)) ELT)) (-3823 (((-1 |#4| (-583 |#4|)) |#3|) 43 T ELT))) 
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-((-3824 (*1 *2 *3) (-12 (-5 *3 (-347 *5)) (-4 *5 (-1153 *4)) (-4 *4 (-494)) (-4 *4 (-961)) (-4 *2 (-1170 *4)) (-5 *1 (-1172 *4 *5 *6 *2)) (-4 *6 (-600 *5)))) (-3823 (*1 *2 *3) (-12 (-4 *4 (-961)) (-4 *5 (-1153 *4)) (-5 *2 (-1 *6 (-583 *6))) (-5 *1 (-1172 *4 *5 *3 *6)) (-4 *3 (-600 *5)) (-4 *6 (-1170 *4)))) (-3822 (*1 *2 *3 *4) (-12 (-5 *4 (-694)) (-4 *5 (-961)) (-4 *2 (-1153 *5)) (-5 *1 (-1172 *5 *2 *6 *3)) (-4 *6 (-600 *2)) (-4 *3 (-1170 *5)))) (-3821 (*1 *2 *3) (-12 (-4 *4 (-961)) (-4 *3 (-1153 *4)) (-4 *2 (-1170 *4)) (-5 *1 (-1172 *4 *3 *5 *2)) (-4 *5 (-600 *3))))) 
-NIL 
-(((-1173) (-113)) (T -1173)) 
-NIL 
-(-13 (-10 -7 (-6 -2283))) 
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-((-3940 (*1 *2 *1) (-12 (-5 *2 (-1088)) (-5 *1 (-1174 *3)) (-14 *3 *2))) (-3825 (*1 *2) (-12 (-5 *2 (-1088)) (-5 *1 (-1174 *3)) (-14 *3 *2)))) 
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-NIL 
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-NIL 
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-NIL 
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-NIL 
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-((-3959 (*1 *1 *2) (-12 (-5 *2 (-583 (-830))) (-5 *1 (-1203)))) (-3958 (*1 *2 *1) (-12 (-5 *2 (-884)) (-5 *1 (-1203))))) 
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-((-3960 (*1 *2 *3 *4) (-12 (-5 *3 (-1 (-583 (-1067 *5)) (-583 (-1067 *5)))) (-5 *4 (-483)) (-5 *2 (-583 (-1067 *5))) (-5 *1 (-1204 *5)) (-4 *5 (-1127)))) (-3960 (*1 *2 *3) (-12 (-5 *3 (-1 (-1067 *4) (-1067 *4))) (-5 *2 (-1067 *4)) (-5 *1 (-1204 *4)) (-4 *4 (-1127))))) 
-((-3962 (((-583 (-2 (|:| -1744 (-1083 |#1|)) (|:| -3219 (-583 (-857 |#1|))))) (-583 (-857 |#1|))) 174 T ELT) (((-583 (-2 (|:| -1744 (-1083 |#1|)) (|:| -3219 (-583 (-857 |#1|))))) (-583 (-857 |#1|)) (-85)) 173 T ELT) (((-583 (-2 (|:| -1744 (-1083 |#1|)) (|:| -3219 (-583 (-857 |#1|))))) (-583 (-857 |#1|)) (-85) (-85)) 172 T ELT) (((-583 (-2 (|:| -1744 (-1083 |#1|)) (|:| -3219 (-583 (-857 |#1|))))) (-583 (-857 |#1|)) (-85) (-85) (-85)) 171 T ELT) (((-583 (-2 (|:| -1744 (-1083 |#1|)) (|:| -3219 (-583 (-857 |#1|))))) (-958 |#1| |#2|)) 156 T ELT)) (-3961 (((-583 (-958 |#1| |#2|)) (-583 (-857 |#1|))) 85 T ELT) (((-583 (-958 |#1| |#2|)) (-583 (-857 |#1|)) (-85)) 84 T ELT) (((-583 (-958 |#1| |#2|)) (-583 (-857 |#1|)) (-85) (-85)) 83 T ELT)) (-3965 (((-583 (-1058 |#1| (-468 (-773 |#3|)) (-773 |#3|) (-703 |#1| (-773 |#3|)))) (-958 |#1| |#2|)) 73 T ELT)) (-3963 (((-583 (-583 (-937 (-347 |#1|)))) (-583 (-857 |#1|))) 140 T ELT) (((-583 (-583 (-937 (-347 |#1|)))) (-583 (-857 |#1|)) (-85)) 139 T ELT) (((-583 (-583 (-937 (-347 |#1|)))) (-583 (-857 |#1|)) (-85) (-85)) 138 T ELT) (((-583 (-583 (-937 (-347 |#1|)))) (-583 (-857 |#1|)) (-85) (-85) (-85)) 137 T ELT) (((-583 (-583 (-937 (-347 |#1|)))) (-958 |#1| |#2|)) 132 T ELT)) (-3964 (((-583 (-583 (-937 (-347 |#1|)))) (-583 (-857 |#1|))) 145 T ELT) (((-583 (-583 (-937 (-347 |#1|)))) (-583 (-857 |#1|)) (-85)) 144 T ELT) (((-583 (-583 (-937 (-347 |#1|)))) (-583 (-857 |#1|)) (-85) (-85)) 143 T ELT) (((-583 (-583 (-937 (-347 |#1|)))) (-958 |#1| |#2|)) 142 T ELT)) (-3966 (((-583 (-703 |#1| (-773 |#3|))) (-1058 |#1| (-468 (-773 |#3|)) (-773 |#3|) (-703 |#1| (-773 |#3|)))) 111 T ELT) (((-1083 (-937 (-347 |#1|))) (-1083 |#1|)) 102 T ELT) (((-857 (-937 (-347 |#1|))) (-703 |#1| (-773 |#3|))) 109 T ELT) (((-857 (-937 (-347 |#1|))) (-857 |#1|)) 107 T ELT) (((-703 |#1| (-773 |#3|)) (-703 |#1| (-773 |#2|))) 33 T ELT))) 
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-((-3966 (*1 *2 *3) (-12 (-5 *3 (-1058 *4 (-468 (-773 *6)) (-773 *6) (-703 *4 (-773 *6)))) (-4 *4 (-13 (-755) (-257) (-120) (-933))) (-14 *6 (-583 (-1088))) (-5 *2 (-583 (-703 *4 (-773 *6)))) (-5 *1 (-1205 *4 *5 *6)) (-14 *5 (-583 (-1088))))) (-3966 (*1 *2 *3) (-12 (-5 *3 (-1083 *4)) (-4 *4 (-13 (-755) (-257) (-120) (-933))) (-5 *2 (-1083 (-937 (-347 *4)))) (-5 *1 (-1205 *4 *5 *6)) (-14 *5 (-583 (-1088))) (-14 *6 (-583 (-1088))))) (-3966 (*1 *2 *3) (-12 (-5 *3 (-703 *4 (-773 *6))) (-4 *4 (-13 (-755) (-257) (-120) (-933))) (-14 *6 (-583 (-1088))) (-5 *2 (-857 (-937 (-347 *4)))) (-5 *1 (-1205 *4 *5 *6)) (-14 *5 (-583 (-1088))))) (-3966 (*1 *2 *3) (-12 (-5 *3 (-857 *4)) (-4 *4 (-13 (-755) (-257) (-120) (-933))) (-5 *2 (-857 (-937 (-347 *4)))) (-5 *1 (-1205 *4 *5 *6)) (-14 *5 (-583 (-1088))) (-14 *6 (-583 (-1088))))) (-3966 (*1 *2 *3) (-12 (-5 *3 (-703 *4 (-773 *5))) (-4 *4 (-13 (-755) (-257) (-120) (-933))) (-14 *5 (-583 (-1088))) (-5 *2 (-703 *4 (-773 *6))) (-5 *1 (-1205 *4 *5 *6)) (-14 *6 (-583 (-1088))))) (-3965 (*1 *2 *3) (-12 (-5 *3 (-958 *4 *5)) (-4 *4 (-13 (-755) (-257) (-120) (-933))) (-14 *5 (-583 (-1088))) (-5 *2 (-583 (-1058 *4 (-468 (-773 *6)) (-773 *6) (-703 *4 (-773 *6))))) (-5 *1 (-1205 *4 *5 *6)) (-14 *6 (-583 (-1088))))) (-3964 (*1 *2 *3) (-12 (-5 *3 (-583 (-857 *4))) (-4 *4 (-13 (-755) (-257) (-120) (-933))) (-5 *2 (-583 (-583 (-937 (-347 *4))))) (-5 *1 (-1205 *4 *5 *6)) (-14 *5 (-583 (-1088))) (-14 *6 (-583 (-1088))))) (-3964 (*1 *2 *3 *4) (-12 (-5 *3 (-583 (-857 *5))) (-5 *4 (-85)) (-4 *5 (-13 (-755) (-257) (-120) (-933))) (-5 *2 (-583 (-583 (-937 (-347 *5))))) (-5 *1 (-1205 *5 *6 *7)) (-14 *6 (-583 (-1088))) (-14 *7 (-583 (-1088))))) (-3964 (*1 *2 *3 *4 *4) (-12 (-5 *3 (-583 (-857 *5))) (-5 *4 (-85)) (-4 *5 (-13 (-755) (-257) (-120) (-933))) (-5 *2 (-583 (-583 (-937 (-347 *5))))) (-5 *1 (-1205 *5 *6 *7)) (-14 *6 (-583 (-1088))) (-14 *7 (-583 (-1088))))) (-3964 (*1 *2 *3) (-12 (-5 *3 (-958 *4 *5)) (-4 *4 (-13 (-755) (-257) (-120) (-933))) (-14 *5 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(-12 (-5 *3 (-958 *4 *5)) (-4 *4 (-13 (-755) (-257) (-120) (-933))) (-14 *5 (-583 (-1088))) (-5 *2 (-583 (-583 (-937 (-347 *4))))) (-5 *1 (-1205 *4 *5 *6)) (-14 *6 (-583 (-1088))))) (-3962 (*1 *2 *3) (-12 (-4 *4 (-13 (-755) (-257) (-120) (-933))) (-5 *2 (-583 (-2 (|:| -1744 (-1083 *4)) (|:| -3219 (-583 (-857 *4)))))) (-5 *1 (-1205 *4 *5 *6)) (-5 *3 (-583 (-857 *4))) (-14 *5 (-583 (-1088))) (-14 *6 (-583 (-1088))))) (-3962 (*1 *2 *3 *4) (-12 (-5 *4 (-85)) (-4 *5 (-13 (-755) (-257) (-120) (-933))) (-5 *2 (-583 (-2 (|:| -1744 (-1083 *5)) (|:| -3219 (-583 (-857 *5)))))) (-5 *1 (-1205 *5 *6 *7)) (-5 *3 (-583 (-857 *5))) (-14 *6 (-583 (-1088))) (-14 *7 (-583 (-1088))))) (-3962 (*1 *2 *3 *4 *4) (-12 (-5 *4 (-85)) (-4 *5 (-13 (-755) (-257) (-120) (-933))) (-5 *2 (-583 (-2 (|:| -1744 (-1083 *5)) (|:| -3219 (-583 (-857 *5)))))) (-5 *1 (-1205 *5 *6 *7)) (-5 *3 (-583 (-857 *5))) (-14 *6 (-583 (-1088))) (-14 *7 (-583 (-1088))))) (-3962 (*1 *2 *3 *4 *4 *4) (-12 (-5 *4 (-85)) (-4 *5 (-13 (-755) (-257) (-120) (-933))) (-5 *2 (-583 (-2 (|:| -1744 (-1083 *5)) (|:| -3219 (-583 (-857 *5)))))) (-5 *1 (-1205 *5 *6 *7)) (-5 *3 (-583 (-857 *5))) (-14 *6 (-583 (-1088))) (-14 *7 (-583 (-1088))))) (-3962 (*1 *2 *3) (-12 (-5 *3 (-958 *4 *5)) (-4 *4 (-13 (-755) (-257) (-120) (-933))) (-14 *5 (-583 (-1088))) (-5 *2 (-583 (-2 (|:| -1744 (-1083 *4)) (|:| -3219 (-583 (-857 *4)))))) (-5 *1 (-1205 *4 *5 *6)) (-14 *6 (-583 (-1088))))) (-3961 (*1 *2 *3) (-12 (-5 *3 (-583 (-857 *4))) (-4 *4 (-13 (-755) (-257) (-120) (-933))) (-5 *2 (-583 (-958 *4 *5))) (-5 *1 (-1205 *4 *5 *6)) (-14 *5 (-583 (-1088))) (-14 *6 (-583 (-1088))))) (-3961 (*1 *2 *3 *4) (-12 (-5 *3 (-583 (-857 *5))) (-5 *4 (-85)) (-4 *5 (-13 (-755) (-257) (-120) (-933))) (-5 *2 (-583 (-958 *5 *6))) (-5 *1 (-1205 *5 *6 *7)) (-14 *6 (-583 (-1088))) (-14 *7 (-583 (-1088))))) (-3961 (*1 *2 *3 *4 *4) (-12 (-5 *3 (-583 (-857 *5))) (-5 *4 (-85)) (-4 *5 (-13 (-755) (-257) (-120) (-933))) (-5 *2 (-583 (-958 *5 *6))) (-5 *1 (-1205 *5 *6 *7)) (-14 *6 (-583 (-1088))) (-14 *7 (-583 (-1088)))))) 
-((-3969 (((-3 (-1177 (-347 (-483))) #1="failed") (-1177 |#1|) |#1|) 21 T ELT)) (-3967 (((-85) (-1177 |#1|)) 12 T ELT)) (-3968 (((-3 (-1177 (-483)) #1#) (-1177 |#1|)) 16 T ELT))) 
-(((-1206 |#1|) (-10 -7 (-15 -3967 ((-85) (-1177 |#1|))) (-15 -3968 ((-3 (-1177 (-483)) #1="failed") (-1177 |#1|))) (-15 -3969 ((-3 (-1177 (-347 (-483))) #1#) (-1177 |#1|) |#1|))) (-13 (-961) (-580 (-483)))) (T -1206)) 
-((-3969 (*1 *2 *3 *4) (|partial| -12 (-5 *3 (-1177 *4)) (-4 *4 (-13 (-961) (-580 (-483)))) (-5 *2 (-1177 (-347 (-483)))) (-5 *1 (-1206 *4)))) (-3968 (*1 *2 *3) (|partial| -12 (-5 *3 (-1177 *4)) (-4 *4 (-13 (-961) (-580 (-483)))) (-5 *2 (-1177 (-483))) (-5 *1 (-1206 *4)))) (-3967 (*1 *2 *3) (-12 (-5 *3 (-1177 *4)) (-4 *4 (-13 (-961) (-580 (-483)))) (-5 *2 (-85)) (-5 *1 (-1206 *4))))) 
-((-2564 (((-85) $ $) NIL T ELT)) (-3183 (((-85) $) 12 T ELT)) (-1309 (((-3 $ #1="failed") $ $) NIL T ELT)) (-3131 (((-694)) 9 T ELT)) (-3718 (($) NIL T CONST)) (-3461 (((-3 $ #1#) $) 57 T ELT)) (-2990 (($) 46 T ELT)) (-2406 (((-85) $) 38 T ELT)) (-3439 (((-632 $) $) 36 T ELT)) (-2006 (((-830) $) 14 T ELT)) (-3237 (((-1071) $) NIL T ELT)) (-3440 (($) 26 T CONST)) (-2396 (($ (-830)) 47 T ELT)) (-3238 (((-1032) $) NIL T ELT)) (-3966 (((-483) $) 16 T ELT)) (-3940 (((-772) $) 21 T ELT) (($ (-483)) 18 T ELT)) (-3121 (((-694)) 10 T CONST)) (-1262 (((-85) $ $) 59 T ELT)) (-2656 (($) 23 T CONST)) (-2662 (($) 25 T CONST)) (-3052 (((-85) $ $) 31 T ELT)) (-3831 (($ $) 50 T ELT) (($ $ $) 44 T ELT)) (-3833 (($ $ $) 29 T ELT)) (** (($ $ (-830)) NIL T ELT) (($ $ (-694)) 52 T ELT)) (* (($ (-830) $) NIL T ELT) (($ (-694) $) NIL T ELT) (($ (-483) $) 41 T ELT) (($ $ $) 40 T ELT))) 
-(((-1207 |#1|) (-13 (-146) (-317) (-553 (-483)) (-1064)) (-830)) (T -1207)) 
-NIL 
-NIL 
-NIL 
-NIL 
-NIL 
-NIL 
-NIL 
-NIL 
-NIL 
-NIL 
-NIL 
-NIL 
-NIL 
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(NIL T T) -8 NIL NIL NIL) (-1197 2773594 2775165 2775219 "XFALG" 2777364 XFALG (NIL T T) -9 NIL 2778148 NIL) (-1196 2768812 2771483 2771525 "XF" 2772143 XF (NIL T) -9 NIL 2772539 NIL) (-1195 2768530 2768640 2768807 "XF-" NIL XF- (NIL T T) -7 NIL NIL NIL) (-1194 2767757 2767879 2768083 "XEXPPKG" NIL XEXPPKG (NIL T T T) -7 NIL NIL NIL) (-1193 2765563 2767657 2767752 "XDPOLY" NIL XDPOLY (NIL T T) -8 NIL NIL NIL) (-1192 2764206 2764939 2764981 "XALG" 2764986 XALG (NIL T) -9 NIL 2765095 NIL) (-1191 2757763 2762616 2763094 "WUTSET" NIL WUTSET (NIL T T T T) -8 NIL NIL NIL) (-1190 2756070 2757008 2757329 "WP" NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL NIL) (-1189 2755669 2755941 2756010 "WHILEAST" NIL WHILEAST (NIL) -8 NIL NIL NIL) (-1188 2755156 2755459 2755552 "WHEREAST" NIL WHEREAST (NIL) -8 NIL NIL NIL) (-1187 2754233 2754443 2754738 "WFFINTBS" NIL WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1186 2752529 2752992 2753454 "WEIER" NIL WEIER (NIL T) -7 NIL NIL NIL) (-1185 2751449 2752003 2752045 "VSPACE" 2752181 VSPACE (NIL T) -9 NIL 2752255 NIL) (-1184 2751320 2751353 2751444 "VSPACE-" NIL VSPACE- (NIL T T) -7 NIL NIL NIL) (-1183 2751163 2751217 2751285 "VOID" NIL VOID (NIL) -8 NIL NIL NIL) (-1182 2748146 2748941 2749678 "VIEWDEF" NIL VIEWDEF (NIL) -7 NIL NIL NIL) (-1181 2739244 2741845 2744018 "VIEW3D" NIL VIEW3D (NIL) -8 NIL NIL NIL) (-1180 2732821 2734712 2736291 "VIEW2D" NIL VIEW2D (NIL) -8 NIL NIL NIL) (-1179 2731305 2731700 2732106 "VIEW" NIL VIEW (NIL) -7 NIL NIL NIL) (-1178 2730132 2730413 2730729 "VECTOR2" NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1177 2725246 2729959 2730051 "VECTOR" NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1176 2718348 2722956 2722999 "VECTCAT" 2723987 VECTCAT (NIL T) -9 NIL 2724571 NIL) (-1175 2717627 2717953 2718343 "VECTCAT-" NIL VECTCAT- (NIL T T) -7 NIL NIL NIL) (-1174 2717121 2717363 2717483 "VARIABLE" NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1173 2717054 2717059 2717089 "UTYPE" 2717094 UTYPE (NIL) -9 NIL NIL NIL) (-1172 2716041 2716217 2716478 "UTSODETL" NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1171 2713892 2714400 2714924 "UTSODE" NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1170 2703836 2709744 2709786 "UTSCAT" 2710884 UTSCAT (NIL T) -9 NIL 2711641 NIL) (-1169 2701901 2702844 2703831 "UTSCAT-" NIL UTSCAT- (NIL T T) -7 NIL NIL NIL) (-1168 2701575 2701624 2701755 "UTS2" NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1167 2693350 2699771 2700250 "UTS" NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1166 2687345 2690158 2690201 "URAGG" 2692271 URAGG (NIL T) -9 NIL 2692993 NIL) (-1165 2685360 2686322 2687340 "URAGG-" NIL URAGG- (NIL T T) -7 NIL NIL NIL) (-1164 2681131 2684336 2684798 "UPXSSING" NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1163 2673624 2681055 2681126 "UPXSCONS" NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1162 2662337 2669762 2669823 "UPXSCCA" 2670391 UPXSCCA (NIL T T) -9 NIL 2670623 NIL) (-1161 2662058 2662160 2662332 "UPXSCCA-" NIL UPXSCCA- (NIL T T T) -7 NIL NIL NIL) (-1160 2650672 2657822 2657864 "UPXSCAT" 2658504 UPXSCAT (NIL T) -9 NIL 2659112 NIL) (-1159 2650185 2650270 2650447 "UPXS2" NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1158 2641935 2649776 2650038 "UPXS" NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1157 2640830 2641100 2641450 "UPSQFREE" NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1156 2633595 2637018 2637072 "UPSCAT" 2638141 UPSCAT (NIL T T) -9 NIL 2638905 NIL) (-1155 2633015 2633267 2633590 "UPSCAT-" NIL UPSCAT- (NIL T T T) -7 NIL NIL NIL) (-1154 2632689 2632738 2632869 "UPOLYC2" NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1153 2616883 2625773 2625815 "UPOLYC" 2627893 UPOLYC (NIL T) -9 NIL 2629113 NIL) (-1152 2610938 2613786 2616878 "UPOLYC-" NIL UPOLYC- (NIL T T) -7 NIL NIL NIL) (-1151 2610374 2610499 2610662 "UPMP" NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1150 2610008 2610095 2610234 "UPDIVP" NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1149 2608821 2609088 2609392 "UPDECOMP" NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1148 2608154 2608284 2608469 "UPCDEN" NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1147 2607746 2607821 2607968 "UP2" NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1146 2598574 2607512 2607640 "UP" NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1145 2597936 2598073 2598278 "UNISEG2" NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1144 2596537 2597384 2597660 "UNISEG" NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1143 2595766 2595963 2596188 "UNIFACT" NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1142 2582640 2595690 2595761 "ULSCONS" NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1141 2562554 2575727 2575788 "ULSCCAT" 2576419 ULSCCAT (NIL T T) -9 NIL 2576706 NIL) (-1140 2561889 2562175 2562549 "ULSCCAT-" NIL ULSCCAT- (NIL T T T) -7 NIL NIL NIL) (-1139 2550323 2557395 2557437 "ULSCAT" 2558290 ULSCAT (NIL T) -9 NIL 2559020 NIL) (-1138 2549836 2549921 2550098 "ULS2" NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1137 2532017 2549335 2549576 "ULS" NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1136 2531051 2531744 2531858 "UINT8" NIL UINT8 (NIL) -8 NIL NIL 2531969) (-1135 2530084 2530777 2530891 "UINT64" NIL UINT64 (NIL) -8 NIL NIL 2531002) (-1134 2529117 2529810 2529924 "UINT32" NIL UINT32 (NIL) -8 NIL NIL 2530035) (-1133 2528150 2528843 2528957 "UINT16" NIL UINT16 (NIL) -8 NIL NIL 2529068) (-1132 2526219 2527378 2527408 "UFD" 2527619 UFD (NIL) -9 NIL 2527732 NIL) (-1131 2526063 2526120 2526214 "UFD-" NIL UFD- (NIL T) -7 NIL NIL NIL) (-1130 2525315 2525522 2525738 "UDVO" NIL UDVO (NIL) -7 NIL NIL NIL) (-1129 2523535 2523988 2524453 "UDPO" NIL UDPO (NIL T) -7 NIL NIL NIL) (-1128 2523260 2523500 2523530 "TYPEAST" NIL TYPEAST (NIL) -8 NIL NIL NIL) (-1127 2523198 2523203 2523233 "TYPE" 2523238 TYPE (NIL) -9 NIL 2523245 NIL) (-1126 2522357 2522577 2522817 "TWOFACT" NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1125 2521535 2521966 2522201 "TUPLE" NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1124 2519689 2520262 2520801 "TUBETOOL" NIL TUBETOOL (NIL) -7 NIL NIL NIL) (-1123 2518723 2518959 2519195 "TUBE" NIL TUBE (NIL T) -8 NIL NIL NIL) (-1122 2507077 2511545 2511641 "TSETCAT" 2516856 TSETCAT (NIL T T T T) -9 NIL 2518368 NIL) (-1121 2503414 2505230 2507072 "TSETCAT-" NIL TSETCAT- (NIL T T T T T) -7 NIL NIL NIL) (-1120 2497870 2502640 2502922 "TS" NIL TS (NIL T) -8 NIL NIL NIL) (-1119 2493207 2494220 2495149 "TRMANIP" NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1118 2492704 2492779 2492942 "TRIMAT" NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1117 2490780 2491070 2491425 "TRIGMNIP" NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1116 2490264 2490413 2490443 "TRIGCAT" 2490656 TRIGCAT (NIL) -9 NIL NIL NIL) (-1115 2490015 2490118 2490259 "TRIGCAT-" NIL TRIGCAT- (NIL T) -7 NIL NIL NIL) (-1114 2487011 2489124 2489402 "TREE" NIL TREE (NIL T) -8 NIL NIL NIL) (-1113 2486117 2486813 2486843 "TRANFUN" 2486878 TRANFUN (NIL) -9 NIL 2486944 NIL) (-1112 2485581 2485832 2486112 "TRANFUN-" NIL TRANFUN- (NIL T) -7 NIL NIL NIL) (-1111 2485418 2485456 2485517 "TOPSP" NIL TOPSP (NIL) -7 NIL NIL NIL) (-1110 2484875 2485006 2485157 "TOOLSIGN" NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1109 2483616 2484273 2484509 "TEXTFILE" NIL TEXTFILE (NIL) -8 NIL NIL NIL) (-1108 2483428 2483465 2483537 "TEX1" NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1107 2481642 2482288 2482717 "TEX" NIL TEX (NIL) -8 NIL NIL NIL) (-1106 2480022 2480359 2480681 "TBCMPPK" NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1105 2471080 2477823 2477879 "TBAGG" 2478281 TBAGG (NIL T T) -9 NIL 2478494 NIL) (-1104 2467611 2469303 2471075 "TBAGG-" NIL TBAGG- (NIL T T T) -7 NIL NIL NIL) (-1103 2467088 2467213 2467358 "TANEXP" NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1102 2466598 2466918 2467008 "TALGOP" NIL TALGOP (NIL T) -8 NIL NIL NIL) (-1101 2466095 2466212 2466350 "TABLEAU" NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1100 2459182 2465997 2466090 "TABLE" NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1099 2454935 2456230 2457475 "TABLBUMP" NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1098 2454304 2454463 2454644 "SYSTEM" NIL SYSTEM (NIL) -7 NIL NIL NIL) (-1097 2451458 2452211 2452994 "SYSSOLP" NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1096 2451232 2451422 2451453 "SYSPTR" NIL SYSPTR (NIL) -8 NIL NIL NIL) (-1095 2450186 2450871 2450997 "SYSNNI" NIL SYSNNI (NIL NIL) -8 NIL NIL 2451183) (-1094 2449450 2449998 2450077 "SYSINT" NIL SYSINT (NIL NIL) -8 NIL NIL 2450137) (-1093 2446273 2447432 2448132 "SYNTAX" NIL SYNTAX (NIL) -8 NIL NIL NIL) (-1092 2443956 2444639 2445273 "SYMTAB" NIL SYMTAB (NIL) -8 NIL NIL NIL) (-1091 2440034 2441080 2442057 "SYMS" NIL SYMS (NIL) -8 NIL NIL NIL) (-1090 2437197 2439689 2439918 "SYMPOLY" NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1089 2436793 2436880 2437002 "SYMFUNC" NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1088 2433417 2434891 2435710 "SYMBOL" NIL SYMBOL (NIL) -8 NIL NIL NIL) (-1087 2426441 2432614 2432907 "SUTS" NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1086 2418191 2426032 2426294 "SUPXS" NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1085 2417470 2417609 2417826 "SUPFRACF" NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1084 2417154 2417219 2417330 "SUP2" NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1083 2407941 2416866 2416991 "SUP" NIL SUP (NIL T) -8 NIL NIL NIL) (-1082 2406671 2406969 2407324 "SUMRF" NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1081 2406076 2406154 2406345 "SUMFS" NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1080 2388292 2405575 2405816 "SULS" NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1079 2387891 2388163 2388232 "SUCHTAST" NIL SUCHTAST (NIL) -8 NIL NIL NIL) (-1078 2387227 2387508 2387648 "SUCH" NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1077 2381829 2383088 2384041 "SUBSPACE" NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1076 2381361 2381461 2381625 "SUBRESP" NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1075 2376472 2377754 2378901 "STTFNC" NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1074 2370930 2372401 2373712 "STTF" NIL STTF (NIL T) -7 NIL NIL NIL) (-1073 2363845 2365909 2367700 "STTAYLOR" NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1072 2356675 2363757 2363840 "STRTBL" NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1071 2351369 2356389 2356504 "STRING" NIL STRING (NIL) -8 NIL NIL NIL) (-1070 2350956 2351039 2351183 "STREAM3" NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1069 2350107 2350308 2350543 "STREAM2" NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1068 2349847 2349905 2349998 "STREAM1" NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1067 2342585 2348052 2348658 "STREAM" NIL STREAM (NIL T) -8 NIL NIL NIL) (-1066 2341761 2341966 2342197 "STINPROD" NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1065 2341006 2341377 2341524 "STEPAST" NIL STEPAST (NIL) -8 NIL NIL NIL) (-1064 2340494 2340736 2340766 "STEP" 2340860 STEP (NIL) -9 NIL 2340931 NIL) (-1063 2333597 2340412 2340489 "STBL" NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1062 2327812 2332395 2332438 "STAGG" 2332865 STAGG (NIL T) -9 NIL 2333039 NIL) (-1061 2326191 2326939 2327807 "STAGG-" NIL STAGG- (NIL T T) -7 NIL NIL NIL) (-1060 2324348 2326018 2326110 "STACK" NIL STACK (NIL T) -8 NIL NIL NIL) (-1059 2323659 2324167 2324197 "SRING" 2324202 SRING (NIL) -9 NIL 2324222 NIL) (-1058 2316281 2322197 2322636 "SREGSET" NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1057 2310055 2311494 2312998 "SRDCMPK" NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1056 2302480 2307391 2307421 "SRAGG" 2308720 SRAGG (NIL) -9 NIL 2309324 NIL) (-1055 2301777 2302097 2302475 "SRAGG-" NIL SRAGG- (NIL T) -7 NIL NIL NIL) (-1054 2295896 2301099 2301522 "SQMATRIX" NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1053 2290109 2293278 2294000 "SPLTREE" NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1052 2286538 2287357 2287994 "SPLNODE" NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1051 2285513 2285818 2285848 "SPFCAT" 2286292 SPFCAT (NIL) -9 NIL NIL NIL) (-1050 2284450 2284702 2284966 "SPECOUT" NIL SPECOUT (NIL) -7 NIL NIL NIL) (-1049 2275208 2277482 2277512 "SPADXPT" 2282149 SPADXPT (NIL) -9 NIL 2284273 NIL) (-1048 2275010 2275056 2275125 "SPADPRSR" NIL SPADPRSR (NIL) -7 NIL NIL NIL) (-1047 2272666 2274974 2275005 "SPADAST" NIL SPADAST (NIL) -8 NIL NIL NIL) (-1046 2264340 2266429 2266471 "SPACEC" 2270786 SPACEC (NIL T) -9 NIL 2272591 NIL) (-1045 2262169 2264287 2264335 "SPACE3" NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1044 2261102 2261291 2261580 "SORTPAK" NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1043 2259506 2259839 2260250 "SOLVETRA" NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1042 2258771 2259005 2259266 "SOLVESER" NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1041 2254951 2255911 2256906 "SOLVERAD" NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1040 2251309 2252008 2252737 "SOLVEFOR" NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1039 2245095 2250649 2250745 "SNTSCAT" 2250750 SNTSCAT (NIL T T T T) -9 NIL 2250820 NIL) (-1038 2238980 2243736 2244126 "SMTS" NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1037 2232816 2238899 2238975 "SMP" NIL SMP (NIL T T) -8 NIL NIL NIL) (-1036 2231248 2231579 2231977 "SMITH" NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1035 2222917 2227832 2227934 "SMATCAT" 2229277 SMATCAT (NIL NIL T T T) -9 NIL 2229825 NIL) (-1034 2220758 2221742 2222912 "SMATCAT-" NIL SMATCAT- (NIL T NIL T T T) -7 NIL NIL NIL) (-1033 2218350 2219964 2220007 "SKAGG" 2220268 SKAGG (NIL T) -9 NIL 2220402 NIL) (-1032 2214460 2218170 2218281 "SINT" NIL SINT (NIL) -8 NIL NIL 2218322) (-1031 2214270 2214314 2214380 "SIMPAN" NIL SIMPAN (NIL) -7 NIL NIL NIL) (-1030 2213345 2213577 2213845 "SIGNRF" NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1029 2212349 2212511 2212787 "SIGNEF" NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1028 2211695 2212035 2212158 "SIGAST" NIL SIGAST (NIL) -8 NIL NIL NIL) (-1027 2211041 2211348 2211488 "SIG" NIL SIG (NIL) -8 NIL NIL NIL) (-1026 2209152 2209644 2210150 "SHP" NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1025 2202691 2209071 2209147 "SHDP" NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1024 2202194 2202431 2202461 "SGROUP" 2202554 SGROUP (NIL) -9 NIL 2202616 NIL) (-1023 2202084 2202116 2202189 "SGROUP-" NIL SGROUP- (NIL T) -7 NIL NIL NIL) (-1022 2201722 2201762 2201803 "SGPOPC" 2201808 SGPOPC (NIL T) -9 NIL 2202009 NIL) (-1021 2201256 2201533 2201639 "SGPOP" NIL SGPOP (NIL T) -8 NIL NIL NIL) (-1020 2198679 2199448 2200170 "SGCF" NIL SGCF (NIL) -7 NIL NIL NIL) (-1019 2192564 2198118 2198214 "SFRTCAT" 2198219 SFRTCAT (NIL T T T T) -9 NIL 2198257 NIL) (-1018 2186956 2188069 2189196 "SFRGCD" NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1017 2181132 2182293 2183457 "SFQCMPK" NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1016 2180104 2181006 2181127 "SEXOF" NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1015 2175712 2176607 2176702 "SEXCAT" 2179315 SEXCAT (NIL T T T T T) -9 NIL 2179866 NIL) (-1014 2174685 2175639 2175707 "SEX" NIL SEX (NIL) -8 NIL NIL NIL) (-1013 2173076 2173661 2173963 "SETMN" NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1012 2172599 2172784 2172814 "SETCAT" 2172931 SETCAT (NIL) -9 NIL 2173015 NIL) (-1011 2172431 2172495 2172594 "SETCAT-" NIL SETCAT- (NIL T) -7 NIL NIL NIL) (-1010 2168654 2170885 2170928 "SETAGG" 2171796 SETAGG (NIL T) -9 NIL 2172134 NIL) (-1009 2168260 2168412 2168649 "SETAGG-" NIL SETAGG- (NIL T T) -7 NIL NIL NIL) (-1008 2165214 2168207 2168255 "SET" NIL SET (NIL T) -8 NIL NIL NIL) (-1007 2164680 2164990 2165090 "SEQAST" NIL SEQAST (NIL) -8 NIL NIL NIL) (-1006 2163807 2164173 2164234 "SEGXCAT" 2164520 SEGXCAT (NIL T T) -9 NIL 2164640 NIL) (-1005 2162732 2163000 2163043 "SEGCAT" 2163565 SEGCAT (NIL T) -9 NIL 2163786 NIL) (-1004 2162412 2162477 2162590 "SEGBIND2" NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1003 2161478 2161948 2162156 "SEGBIND" NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1002 2161056 2161335 2161411 "SEGAST" NIL SEGAST (NIL) -8 NIL NIL NIL) (-1001 2160421 2160557 2160761 "SEG2" NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1000 2159487 2160234 2160416 "SEG" NIL SEG (NIL T) -8 NIL NIL NIL) (-999 2158742 2159437 2159482 "SDVAR" NIL SDVAR (NIL T) -8 NIL NIL NIL) (-998 2150343 2158613 2158737 "SDPOL" NIL SDPOL (NIL T) -8 NIL NIL NIL) (-997 2149203 2149493 2149810 "SCPKG" NIL SCPKG (NIL T) -7 NIL NIL NIL) (-996 2148509 2148721 2148909 "SCOPE" NIL SCOPE (NIL) -8 NIL NIL NIL) (-995 2147859 2148016 2148192 "SCACHE" NIL SCACHE (NIL T) -7 NIL NIL NIL) (-994 2147432 2147663 2147691 "SASTCAT" 2147696 SASTCAT (NIL) -9 NIL 2147709 NIL) (-993 2146899 2147324 2147398 "SAOS" NIL SAOS (NIL) -8 NIL NIL NIL) (-992 2146502 2146543 2146714 "SAERFFC" NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-991 2146133 2146174 2146331 "SAEFACT" NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-990 2139278 2146050 2146128 "SAE" NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-989 2137928 2138257 2138653 "RURPK" NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-988 2136689 2137050 2137350 "RULESET" NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-987 2136313 2136534 2136615 "RULECOLD" NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-986 2133773 2134407 2134860 "RULE" NIL RULE (NIL T T T) -8 NIL NIL NIL) (-985 2133612 2133645 2133713 "RTVALUE" NIL RTVALUE (NIL) -8 NIL NIL NIL) (-984 2133103 2133406 2133497 "RSTRCAST" NIL RSTRCAST (NIL) -8 NIL NIL NIL) (-983 2128731 2129599 2130510 "RSETGCD" NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-982 2117550 2123104 2123198 "RSETCAT" 2127254 RSETCAT (NIL T T T T) -9 NIL 2128342 NIL) (-981 2116088 2116730 2117545 "RSETCAT-" NIL RSETCAT- (NIL T T T T T) -7 NIL NIL NIL) (-980 2109862 2111307 2112814 "RSDCMPK" NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-979 2107744 2108301 2108373 "RRCC" 2109446 RRCC (NIL T T) -9 NIL 2109787 NIL) (-978 2107269 2107468 2107739 "RRCC-" NIL RRCC- (NIL T T T) -7 NIL NIL NIL) (-977 2106739 2107049 2107147 "RPTAST" NIL RPTAST (NIL) -8 NIL NIL NIL) (-976 2079355 2090004 2090068 "RPOLCAT" 2100542 RPOLCAT (NIL T T T) -9 NIL 2103687 NIL) (-975 2073454 2076277 2079350 "RPOLCAT-" NIL RPOLCAT- (NIL T T T T) -7 NIL NIL NIL) (-974 2069685 2073202 2073340 "ROMAN" NIL ROMAN (NIL) -8 NIL NIL NIL) (-973 2068013 2068752 2069008 "ROIRC" NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-972 2063718 2066468 2066496 "RNS" 2066758 RNS (NIL) -9 NIL 2067010 NIL) (-971 2062621 2063108 2063645 "RNS-" NIL RNS- (NIL T) -7 NIL NIL NIL) (-970 2061739 2062140 2062340 "RNGBIND" NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-969 2061027 2061527 2061555 "RNG" 2061560 RNG (NIL) -9 NIL 2061581 NIL) (-968 2060320 2060794 2060834 "RMODULE" 2060839 RMODULE (NIL T) -9 NIL 2060865 NIL) (-967 2059259 2059365 2059695 "RMCAT2" NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-966 2056137 2058849 2059142 "RMATRIX" NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-965 2048817 2051278 2051390 "RMATCAT" 2054695 RMATCAT (NIL NIL NIL T T T) -9 NIL 2055672 NIL) (-964 2048334 2048513 2048812 "RMATCAT-" NIL RMATCAT- (NIL T NIL NIL T T T) -7 NIL NIL NIL) (-963 2047902 2048113 2048154 "RLINSET" 2048215 RLINSET (NIL T) -9 NIL 2048259 NIL) (-962 2047547 2047628 2047754 "RINTERP" NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-961 2046455 2047124 2047152 "RING" 2047207 RING (NIL) -9 NIL 2047299 NIL) (-960 2046300 2046356 2046450 "RING-" NIL RING- (NIL T) -7 NIL NIL NIL) (-959 2045354 2045621 2045877 "RIDIST" NIL RIDIST (NIL) -7 NIL NIL NIL) (-958 2036341 2044982 2045183 "RGCHAIN" NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-957 2035597 2036077 2036116 "RGBCSPC" 2036173 RGBCSPC (NIL T) -9 NIL 2036224 NIL) (-956 2034662 2035117 2035156 "RGBCMDL" 2035384 RGBCMDL (NIL T) -9 NIL 2035498 NIL) (-955 2034374 2034443 2034544 "RFFACTOR" NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-954 2034137 2034178 2034273 "RFFACT" NIL RFFACT (NIL T) -7 NIL NIL NIL) (-953 2032561 2032991 2033371 "RFDIST" NIL RFDIST (NIL) -7 NIL NIL NIL) (-952 2030148 2030816 2031484 "RF" NIL RF (NIL T) -7 NIL NIL NIL) (-951 2029698 2029796 2029956 "RETSOL" NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-950 2029320 2029418 2029459 "RETRACT" 2029590 RETRACT (NIL T) -9 NIL 2029677 NIL) (-949 2029200 2029231 2029315 "RETRACT-" NIL RETRACT- (NIL T T) -7 NIL NIL NIL) (-948 2028802 2029074 2029141 "RETAST" NIL RETAST (NIL) -8 NIL NIL NIL) (-947 2027346 2028173 2028370 "RESRING" NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-946 2027037 2027098 2027194 "RESLATC" NIL RESLATC (NIL T) -7 NIL NIL NIL) (-945 2026780 2026821 2026926 "REPSQ" NIL REPSQ (NIL T) -7 NIL NIL NIL) (-944 2026515 2026556 2026665 "REPDB" NIL REPDB (NIL T) -7 NIL NIL NIL) (-943 2021586 2023037 2024252 "REP2" NIL REP2 (NIL T) -7 NIL NIL NIL) (-942 2018685 2019443 2020251 "REP1" NIL REP1 (NIL T) -7 NIL NIL NIL) (-941 2016654 2017276 2017876 "REP" NIL REP (NIL) -7 NIL NIL NIL) (-940 2009289 2015205 2015641 "REGSET" NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-939 2008601 2008881 2009030 "REF" NIL REF (NIL T) -8 NIL NIL NIL) (-938 2008086 2008201 2008366 "REDORDER" NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-937 2003743 2007489 2007710 "RECLOS" NIL RECLOS (NIL T) -8 NIL NIL NIL) (-936 2002975 2003174 2003387 "REALSOLV" NIL REALSOLV (NIL) -7 NIL NIL NIL) (-935 2000265 2001103 2001985 "REAL0Q" NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-934 1996847 1997883 1998942 "REAL0" NIL REAL0 (NIL T) -7 NIL NIL NIL) (-933 1996683 1996736 1996764 "REAL" 1996769 REAL (NIL) -9 NIL 1996804 NIL) (-932 1996173 1996477 1996568 "RDUCEAST" NIL RDUCEAST (NIL) -8 NIL NIL NIL) (-931 1995653 1995731 1995936 "RDIV" NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-930 1994886 1995078 1995289 "RDIST" NIL RDIST (NIL T) -7 NIL NIL NIL) (-929 1993774 1994071 1994438 "RDETRS" NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-928 1992041 1992511 1993044 "RDETR" NIL RDETR (NIL T T) -7 NIL NIL NIL) (-927 1990963 1991240 1991627 "RDEEFS" NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-926 1989790 1990099 1990518 "RDEEF" NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-925 1983202 1986650 1986678 "RCFIELD" 1987955 RCFIELD (NIL) -9 NIL 1988685 NIL) (-924 1981820 1982432 1983129 "RCFIELD-" NIL RCFIELD- (NIL T) -7 NIL NIL NIL) (-923 1978020 1979912 1979953 "RCAGG" 1981020 RCAGG (NIL T) -9 NIL 1981481 NIL) (-922 1977747 1977857 1978015 "RCAGG-" NIL RCAGG- (NIL T T) -7 NIL NIL NIL) (-921 1977192 1977321 1977482 "RATRET" NIL RATRET (NIL T) -7 NIL NIL NIL) (-920 1976809 1976888 1977007 "RATFACT" NIL RATFACT (NIL T) -7 NIL NIL NIL) (-919 1976224 1976374 1976524 "RANDSRC" NIL RANDSRC (NIL) -7 NIL NIL NIL) (-918 1976006 1976056 1976127 "RADUTIL" NIL RADUTIL (NIL) -7 NIL NIL NIL) (-917 1968512 1975124 1975432 "RADIX" NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-916 1958278 1968379 1968507 "RADFF" NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-915 1957912 1958005 1958033 "RADCAT" 1958190 RADCAT (NIL) -9 NIL NIL NIL) (-914 1957750 1957810 1957907 "RADCAT-" NIL RADCAT- (NIL T) -7 NIL NIL NIL) (-913 1955850 1957581 1957670 "QUEUE" NIL QUEUE (NIL T) -8 NIL NIL NIL) (-912 1955531 1955580 1955707 "QUATCT2" NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-911 1947882 1951902 1951942 "QUATCAT" 1952720 QUATCAT (NIL T) -9 NIL 1953484 NIL) (-910 1945132 1946412 1947788 "QUATCAT-" NIL QUATCAT- (NIL T T) -7 NIL NIL NIL) (-909 1941036 1945082 1945127 "QUAT" NIL QUAT (NIL T) -8 NIL NIL NIL) (-908 1938423 1940090 1940131 "QUAGG" 1940506 QUAGG (NIL T) -9 NIL 1940680 NIL) (-907 1938025 1938297 1938364 "QQUTAST" NIL QQUTAST (NIL) -8 NIL NIL NIL) (-906 1937063 1937661 1937824 "QFORM" NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-905 1936744 1936793 1936920 "QFCAT2" NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-904 1926431 1932538 1932578 "QFCAT" 1933236 QFCAT (NIL T) -9 NIL 1934229 NIL) (-903 1923315 1924754 1926337 "QFCAT-" NIL QFCAT- (NIL T T) -7 NIL NIL NIL) (-902 1922861 1922995 1923125 "QEQUAT" NIL QEQUAT (NIL) -8 NIL NIL NIL) (-901 1917057 1918218 1919380 "QCMPACK" NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-900 1916476 1916656 1916888 "QALGSET2" NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-899 1914298 1914826 1915249 "QALGSET" NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-898 1913197 1913439 1913756 "PWFFINTB" NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-897 1911558 1911756 1912109 "PUSHVAR" NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-896 1907314 1908530 1908571 "PTRANFN" 1910455 PTRANFN (NIL T) -9 NIL NIL NIL) (-895 1905961 1906306 1906627 "PTPACK" NIL PTPACK (NIL T) -7 NIL NIL NIL) (-894 1905654 1905717 1905824 "PTFUNC2" NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-893 1899727 1904450 1904490 "PTCAT" 1904782 PTCAT (NIL T) -9 NIL 1904935 NIL) (-892 1899420 1899461 1899585 "PSQFR" NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-891 1898299 1898615 1898949 "PSEUDLIN" NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-890 1887178 1889739 1892048 "PSETPK" NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-889 1880085 1882981 1883075 "PSETCAT" 1886049 PSETCAT (NIL T T T T) -9 NIL 1886856 NIL) (-888 1878535 1879269 1880080 "PSETCAT-" NIL PSETCAT- (NIL T T T T T) -7 NIL NIL NIL) (-887 1877854 1878049 1878077 "PSCURVE" 1878345 PSCURVE (NIL) -9 NIL 1878512 NIL) (-886 1873518 1875276 1875340 "PSCAT" 1876175 PSCAT (NIL T T T) -9 NIL 1876414 NIL) (-885 1872832 1873114 1873513 "PSCAT-" NIL PSCAT- (NIL T T T T) -7 NIL NIL NIL) (-884 1871261 1872144 1872407 "PRTITION" NIL PRTITION (NIL) -8 NIL NIL NIL) (-883 1870752 1871055 1871146 "PRTDAST" NIL PRTDAST (NIL) -8 NIL NIL NIL) (-882 1861772 1864194 1866382 "PRS" NIL PRS (NIL T T) -7 NIL NIL NIL) (-881 1859515 1861092 1861132 "PRQAGG" 1861315 PRQAGG (NIL T) -9 NIL 1861416 NIL) (-880 1858688 1859134 1859162 "PROPLOG" 1859301 PROPLOG (NIL) -9 NIL 1859415 NIL) (-879 1858363 1858426 1858549 "PROPFUN2" NIL PROPFUN2 (NIL T T) -7 NIL NIL NIL) (-878 1857799 1857938 1858110 "PROPFUN1" NIL PROPFUN1 (NIL T) -7 NIL NIL NIL) (-877 1856047 1856810 1857107 "PROPFRML" NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-876 1855599 1855731 1855859 "PROPERTY" NIL PROPERTY (NIL) -8 NIL NIL NIL) (-875 1850255 1854539 1855359 "PRODUCT" NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-874 1850084 1850122 1850181 "PRINT" NIL PRINT (NIL) -7 NIL NIL NIL) (-873 1849523 1849663 1849814 "PRIMES" NIL PRIMES (NIL T) -7 NIL NIL NIL) (-872 1847991 1848410 1848876 "PRIMELT" NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-871 1847708 1847769 1847797 "PRIMCAT" 1847921 PRIMCAT (NIL) -9 NIL NIL NIL) (-870 1846879 1847075 1847303 "PRIMARR2" NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-869 1842757 1846829 1846874 "PRIMARR" NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-868 1842456 1842518 1842629 "PREASSOC" NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-867 1839656 1842105 1842338 "PR" NIL PR (NIL T T) -8 NIL NIL NIL) (-866 1839107 1839264 1839292 "PPCURVE" 1839497 PPCURVE (NIL) -9 NIL 1839633 NIL) (-865 1838720 1838965 1839048 "PORTNUM" NIL PORTNUM (NIL) -8 NIL NIL NIL) (-864 1836476 1836897 1837489 "POLYROOT" NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-863 1835919 1835983 1836216 "POLYLIFT" NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-862 1832639 1833125 1833736 "POLYCATQ" NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-861 1818294 1824359 1824423 "POLYCAT" 1827908 POLYCAT (NIL T T T) -9 NIL 1829785 NIL) (-860 1813804 1815951 1818289 "POLYCAT-" NIL POLYCAT- (NIL T T T T) -7 NIL NIL NIL) (-859 1813461 1813535 1813654 "POLY2UP" NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-858 1813154 1813217 1813324 "POLY2" NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-857 1806581 1812887 1813046 "POLY" NIL POLY (NIL T) -8 NIL NIL NIL) (-856 1805468 1805731 1806007 "POLUTIL" NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-855 1804072 1804385 1804715 "POLTOPOL" NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-854 1799234 1804022 1804067 "POINT" NIL POINT (NIL T) -8 NIL NIL NIL) (-853 1797722 1798133 1798508 "PNTHEORY" NIL PNTHEORY (NIL) -7 NIL NIL NIL) (-852 1796479 1796788 1797184 "PMTOOLS" NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-851 1796150 1796234 1796351 "PMSYM" NIL PMSYM (NIL T) -7 NIL NIL NIL) (-850 1795729 1795804 1795978 "PMQFCAT" NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-849 1795215 1795311 1795471 "PMPREDFS" NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-848 1794687 1794807 1794961 "PMPRED" NIL PMPRED (NIL T) -7 NIL NIL NIL) (-847 1793582 1793800 1794177 "PMPLCAT" NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-846 1793193 1793278 1793430 "PMLSAGG" NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-845 1792744 1792826 1793007 "PMKERNEL" NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-844 1792436 1792517 1792630 "PMINS" NIL PMINS (NIL T) -7 NIL NIL NIL) (-843 1791949 1792024 1792232 "PMFS" NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-842 1791297 1791425 1791627 "PMDOWN" NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-841 1790659 1790793 1790956 "PMASSFS" NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-840 1789963 1790145 1790326 "PMASS" NIL PMASS (NIL) -7 NIL NIL NIL) (-839 1789686 1789760 1789854 "PLOTTOOL" NIL PLOTTOOL (NIL) -7 NIL NIL NIL) (-838 1786254 1787443 1788359 "PLOT3D" NIL PLOT3D (NIL) -8 NIL NIL NIL) (-837 1785338 1785539 1785774 "PLOT1" NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-836 1780903 1782287 1783429 "PLOT" NIL PLOT (NIL) -8 NIL NIL NIL) (-835 1760824 1765711 1770558 "PLEQN" NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-834 1760564 1760617 1760720 "PINTERPA" NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-833 1760005 1760139 1760319 "PINTERP" NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-832 1758076 1759235 1759263 "PID" 1759460 PID (NIL) -9 NIL 1759587 NIL) (-831 1757864 1757907 1757982 "PICOERCE" NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-830 1757051 1757711 1757798 "PI" NIL PI (NIL) -8 NIL NIL 1757838) (-829 1756503 1756654 1756830 "PGROEB" NIL PGROEB (NIL T) -7 NIL NIL NIL) (-828 1752831 1753789 1754694 "PGE" NIL PGE (NIL) -7 NIL NIL NIL) (-827 1751195 1751484 1751850 "PGCD" NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-826 1750637 1750752 1750913 "PFRPAC" NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-825 1747242 1749506 1749859 "PFR" NIL PFR (NIL T) -8 NIL NIL NIL) (-824 1745848 1746128 1746453 "PFOTOOLS" NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-823 1744613 1744867 1745215 "PFOQ" NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-822 1743323 1743550 1743902 "PFO" NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-821 1740395 1741893 1741921 "PFECAT" 1742514 PFECAT (NIL) -9 NIL 1742891 NIL) (-820 1740018 1740183 1740390 "PFECAT-" NIL PFECAT- (NIL T) -7 NIL NIL NIL) (-819 1738842 1739124 1739425 "PFBRU" NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-818 1737024 1737411 1737841 "PFBR" NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-817 1733058 1736950 1737019 "PF" NIL PF (NIL NIL) -8 NIL NIL NIL) (-816 1728961 1730108 1730975 "PERMGRP" NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-815 1726893 1727982 1728023 "PERMCAT" 1728422 PERMCAT (NIL T) -9 NIL 1728719 NIL) (-814 1726589 1726636 1726759 "PERMAN" NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-813 1723038 1724719 1725364 "PERM" NIL PERM (NIL T) -8 NIL NIL NIL) (-812 1720503 1722793 1722914 "PENDTREE" NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-811 1719372 1719635 1719676 "PDSPC" 1720209 PDSPC (NIL T) -9 NIL 1720454 NIL) (-810 1718739 1719005 1719367 "PDSPC-" NIL PDSPC- (NIL T T) -7 NIL NIL NIL) (-809 1717436 1718367 1718408 "PDRING" 1718413 PDRING (NIL T) -9 NIL 1718440 NIL) (-808 1716177 1716935 1716988 "PDMOD" 1716993 PDMOD (NIL T T) -9 NIL 1717096 NIL) (-807 1715270 1715482 1715731 "PDECOMP" NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-806 1714875 1714942 1714996 "PDDOM" 1715161 PDDOM (NIL T T) -9 NIL 1715241 NIL) (-805 1714727 1714763 1714870 "PDDOM-" NIL PDDOM- (NIL T T T) -7 NIL NIL NIL) (-804 1714513 1714552 1714641 "PCOMP" NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-803 1712830 1713584 1713883 "PBWLB" NIL PBWLB (NIL T) -8 NIL NIL NIL) (-802 1712519 1712582 1712691 "PATTERN2" NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-801 1710657 1711087 1711538 "PATTERN1" NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-800 1704277 1706106 1707398 "PATTERN" NIL PATTERN (NIL T) -8 NIL NIL NIL) (-799 1703908 1703981 1704113 "PATRES2" NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-798 1701610 1702290 1702771 "PATRES" NIL PATRES (NIL T T) -8 NIL NIL NIL) (-797 1699814 1700242 1700645 "PATMATCH" NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-796 1699260 1699508 1699549 "PATMAB" 1699656 PATMAB (NIL T) -9 NIL 1699739 NIL) (-795 1697907 1698311 1698568 "PATLRES" NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-794 1697445 1697576 1697617 "PATAB" 1697622 PATAB (NIL T) -9 NIL 1697794 NIL) (-793 1695988 1696425 1696848 "PARTPERM" NIL PARTPERM (NIL) -7 NIL NIL NIL) (-792 1695666 1695741 1695843 "PARSURF" NIL PARSURF (NIL T) -8 NIL NIL NIL) (-791 1695355 1695418 1695527 "PARSU2" NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-790 1695160 1695206 1695273 "PARSER" NIL PARSER (NIL) -7 NIL NIL NIL) (-789 1694838 1694913 1695015 "PARSCURV" NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-788 1694527 1694590 1694699 "PARSC2" NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-787 1694218 1694288 1694385 "PARPCURV" NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-786 1693907 1693970 1694079 "PARPC2" NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-785 1693068 1693447 1693626 "PARAMAST" NIL PARAMAST (NIL) -8 NIL NIL NIL) (-784 1692675 1692773 1692892 "PAN2EXPR" NIL PAN2EXPR (NIL) -7 NIL NIL NIL) (-783 1691643 1692068 1692287 "PALETTE" NIL PALETTE (NIL) -8 NIL NIL NIL) (-782 1690308 1690962 1691322 "PAIR" NIL PAIR (NIL T T) -8 NIL NIL NIL) (-781 1683462 1689712 1689906 "PADICRC" NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-780 1675947 1682960 1683144 "PADICRAT" NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-779 1672734 1674587 1674627 "PADICCT" 1675208 PADICCT (NIL NIL) -9 NIL 1675490 NIL) (-778 1670788 1672684 1672729 "PADIC" NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-777 1669950 1670160 1670426 "PADEPAC" NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-776 1669292 1669435 1669639 "PADE" NIL PADE (NIL T T T) -7 NIL NIL NIL) (-775 1667737 1668700 1668978 "OWP" NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-774 1667261 1667520 1667617 "OVERSET" NIL OVERSET (NIL) -8 NIL NIL NIL) (-773 1666320 1666998 1667170 "OVAR" NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-772 1656742 1659611 1661810 "OUTFORM" NIL OUTFORM (NIL) -8 NIL NIL NIL) (-771 1656134 1656448 1656574 "OUTBFILE" NIL OUTBFILE (NIL) -8 NIL NIL NIL) (-770 1655411 1655606 1655634 "OUTBCON" 1655952 OUTBCON (NIL) -9 NIL 1656118 NIL) (-769 1655119 1655249 1655406 "OUTBCON-" NIL OUTBCON- (NIL T) -7 NIL NIL NIL) (-768 1654500 1654645 1654806 "OUT" NIL OUT (NIL) -7 NIL NIL NIL) (-767 1653871 1654298 1654387 "OSI" NIL OSI (NIL) -8 NIL NIL NIL) (-766 1653286 1653701 1653729 "OSGROUP" 1653734 OSGROUP (NIL) -9 NIL 1653756 NIL) (-765 1652250 1652511 1652796 "ORTHPOL" NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-764 1649583 1652125 1652245 "OREUP" NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-763 1646788 1649334 1649460 "ORESUP" NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-762 1644806 1645334 1645894 "OREPCTO" NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-761 1638210 1640688 1640728 "OREPCAT" 1643049 OREPCAT (NIL T) -9 NIL 1644151 NIL) (-760 1636236 1637170 1638205 "OREPCAT-" NIL OREPCAT- (NIL T T) -7 NIL NIL NIL) (-759 1635433 1635704 1635732 "ORDTYPE" 1636037 ORDTYPE (NIL) -9 NIL 1636195 NIL) (-758 1634967 1635178 1635428 "ORDTYPE-" NIL ORDTYPE- (NIL T) -7 NIL NIL NIL) (-757 1634429 1634805 1634962 "ORDSTRCT" NIL ORDSTRCT (NIL T NIL) -8 NIL NIL NIL) (-756 1633923 1634286 1634314 "ORDSET" 1634319 ORDSET (NIL) -9 NIL 1634341 NIL) (-755 1632563 1633523 1633551 "ORDRING" 1633556 ORDRING (NIL) -9 NIL 1633584 NIL) (-754 1631811 1632368 1632396 "ORDMON" 1632401 ORDMON (NIL) -9 NIL 1632422 NIL) (-753 1631115 1631277 1631469 "ORDFUNS" NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-752 1630326 1630834 1630862 "ORDFIN" 1630927 ORDFIN (NIL) -9 NIL 1631001 NIL) (-751 1629720 1629859 1630045 "ORDCOMP2" NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-750 1626494 1628688 1629094 "ORDCOMP" NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-749 1625901 1626256 1626361 "OPSIG" NIL OPSIG (NIL) -8 NIL NIL NIL) (-748 1625709 1625754 1625820 "OPQUERY" NIL OPQUERY (NIL) -7 NIL NIL NIL) (-747 1625010 1625286 1625327 "OPERCAT" 1625538 OPERCAT (NIL T) -9 NIL 1625634 NIL) (-746 1624822 1624889 1625005 "OPERCAT-" NIL OPERCAT- (NIL T T) -7 NIL NIL NIL) (-745 1622252 1623624 1624120 "OP" NIL OP (NIL T) -8 NIL NIL NIL) (-744 1621673 1621800 1621974 "ONECOMP2" NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-743 1618673 1620812 1621178 "ONECOMP" NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-742 1615304 1618103 1618143 "OMSAGG" 1618204 OMSAGG (NIL T) -9 NIL 1618268 NIL) (-741 1613780 1614975 1615143 "OMLO" NIL OMLO (NIL T T) -8 NIL NIL NIL) (-740 1612051 1613230 1613258 "OINTDOM" 1613263 OINTDOM (NIL) -9 NIL 1613284 NIL) (-739 1609481 1611053 1611382 "OFMONOID" NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-738 1608735 1609431 1609476 "ODVAR" NIL ODVAR (NIL T) -8 NIL NIL NIL) (-737 1606001 1608576 1608730 "ODR" NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-736 1597602 1605872 1605996 "ODPOL" NIL ODPOL (NIL T) -8 NIL NIL NIL) (-735 1591112 1597493 1597597 "ODP" NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-734 1590084 1590321 1590594 "ODETOOLS" NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-733 1587718 1588388 1589092 "ODESYS" NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-732 1583495 1584455 1585478 "ODERTRIC" NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-731 1583003 1583091 1583285 "ODERED" NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-730 1580452 1581034 1581707 "ODERAT" NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-729 1577847 1578355 1578951 "ODEPRRIC" NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-728 1574844 1575383 1576029 "ODEPRIM" NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-727 1574199 1574307 1574565 "ODEPAL" NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-726 1573357 1573482 1573703 "ODEINT" NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-725 1569641 1570437 1571350 "ODEEF" NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-724 1569081 1569176 1569398 "ODECONST" NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-723 1568762 1568811 1568938 "OCTCT2" NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-722 1565429 1568561 1568680 "OCT" NIL OCT (NIL T) -8 NIL NIL NIL) (-721 1564620 1565211 1565239 "OCAMON" 1565244 OCAMON (NIL) -9 NIL 1565265 NIL) (-720 1558896 1561646 1561686 "OC" 1562781 OC (NIL T) -9 NIL 1563637 NIL) (-719 1556896 1557822 1558802 "OC-" NIL OC- (NIL T T) -7 NIL NIL NIL) (-718 1556312 1556730 1556758 "OASGP" 1556763 OASGP (NIL) -9 NIL 1556783 NIL) (-717 1555406 1556024 1556052 "OAMONS" 1556092 OAMONS (NIL) -9 NIL 1556135 NIL) (-716 1554582 1555132 1555160 "OAMON" 1555217 OAMON (NIL) -9 NIL 1555268 NIL) (-715 1554478 1554510 1554577 "OAMON-" NIL OAMON- (NIL T) -7 NIL NIL NIL) (-714 1553260 1554003 1554031 "OAGROUP" 1554177 OAGROUP (NIL) -9 NIL 1554269 NIL) (-713 1553051 1553138 1553255 "OAGROUP-" NIL OAGROUP- (NIL T) -7 NIL NIL NIL) (-712 1552791 1552847 1552935 "NUMTUBE" NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-711 1547853 1549416 1550943 "NUMQUAD" NIL NUMQUAD (NIL) -7 NIL NIL NIL) (-710 1544548 1545582 1546617 "NUMODE" NIL NUMODE (NIL) -7 NIL NIL NIL) (-709 1543658 1543891 1544109 "NUMFMT" NIL NUMFMT (NIL) -7 NIL NIL NIL) (-708 1532519 1535547 1537995 "NUMERIC" NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-707 1526406 1531960 1532054 "NTSCAT" 1532059 NTSCAT (NIL T T T T) -9 NIL 1532097 NIL) (-706 1525747 1525926 1526119 "NTPOLFN" NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-705 1525440 1525503 1525610 "NSUP2" NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-704 1513171 1523060 1523870 "NSUP" NIL NSUP (NIL T) -8 NIL NIL NIL) (-703 1502244 1513036 1513166 "NSMP" NIL NSMP (NIL T T) -8 NIL NIL NIL) (-702 1500964 1501289 1501646 "NREP" NIL NREP (NIL T) -7 NIL NIL NIL) (-701 1499800 1500064 1500422 "NPCOEF" NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-700 1498967 1499100 1499316 "NORMRETR" NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-699 1497285 1497604 1498010 "NORMPK" NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-698 1496998 1497032 1497156 "NORMMA" NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-697 1496817 1496852 1496921 "NONE1" NIL NONE1 (NIL T) -7 NIL NIL NIL) (-696 1496593 1496783 1496812 "NONE" NIL NONE (NIL) -8 NIL NIL NIL) (-695 1496157 1496224 1496401 "NODE1" NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-694 1494475 1495520 1495775 "NNI" NIL NNI (NIL) -8 NIL NIL 1496122) (-693 1493203 1493540 1493904 "NLINSOL" NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-692 1492180 1492432 1492734 "NFINTBAS" NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-691 1491267 1491832 1491873 "NETCLT" 1492044 NETCLT (NIL T) -9 NIL 1492125 NIL) (-690 1490171 1490438 1490719 "NCODIV" NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-689 1489970 1490013 1490088 "NCNTFRAC" NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-688 1488501 1488889 1489309 "NCEP" NIL NCEP (NIL T) -7 NIL NIL NIL) (-687 1487165 1488100 1488128 "NASRING" 1488238 NASRING (NIL) -9 NIL 1488318 NIL) (-686 1487010 1487066 1487160 "NASRING-" NIL NASRING- (NIL T) -7 NIL NIL NIL) (-685 1485970 1486617 1486645 "NARNG" 1486762 NARNG (NIL) -9 NIL 1486853 NIL) (-684 1485746 1485831 1485965 "NARNG-" NIL NARNG- (NIL T) -7 NIL NIL NIL) (-683 1484543 1485266 1485306 "NAALG" 1485385 NAALG (NIL T) -9 NIL 1485446 NIL) (-682 1484413 1484448 1484538 "NAALG-" NIL NAALG- (NIL T T) -7 NIL NIL NIL) (-681 1479392 1480577 1481763 "MULTSQFR" NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-680 1478787 1478874 1479058 "MULTFACT" NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-679 1470861 1475291 1475343 "MTSCAT" 1476403 MTSCAT (NIL T T) -9 NIL 1476917 NIL) (-678 1470627 1470687 1470779 "MTHING" NIL MTHING (NIL T) -7 NIL NIL NIL) (-677 1470453 1470492 1470552 "MSYSCMD" NIL MSYSCMD (NIL) -7 NIL NIL NIL) (-676 1467315 1470004 1470045 "MSETAGG" 1470050 MSETAGG (NIL T) -9 NIL 1470084 NIL) (-675 1463452 1466361 1466679 "MSET" NIL MSET (NIL T) -8 NIL NIL NIL) (-674 1459790 1461549 1462289 "MRING" NIL MRING (NIL T T) -8 NIL NIL NIL) (-673 1459427 1459500 1459629 "MRF2" NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-672 1459080 1459121 1459265 "MRATFAC" NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-671 1456945 1457282 1457713 "MPRFF" NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-670 1450407 1456844 1456940 "MPOLY" NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-669 1449932 1449973 1450181 "MPCPF" NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-668 1449491 1449540 1449723 "MPC3" NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-667 1448765 1448858 1449077 "MPC2" NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-666 1447382 1447743 1448133 "MONOTOOL" NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-665 1446903 1446970 1447009 "MONOPC" 1447069 MONOPC (NIL T) -9 NIL 1447288 NIL) (-664 1446403 1446710 1446818 "MONOP" NIL MONOP (NIL T) -8 NIL NIL NIL) (-663 1445545 1445924 1445952 "MONOID" 1446170 MONOID (NIL) -9 NIL 1446314 NIL) (-662 1445204 1445354 1445540 "MONOID-" NIL MONOID- (NIL T) -7 NIL NIL NIL) (-661 1434204 1441012 1441071 "MONOGEN" 1441745 MONOGEN (NIL T T) -9 NIL 1442201 NIL) (-660 1432216 1433102 1434085 "MONOGEN-" NIL MONOGEN- (NIL T T T) -7 NIL NIL NIL) (-659 1430930 1431474 1431502 "MONADWU" 1431893 MONADWU (NIL) -9 NIL 1432128 NIL) (-658 1430478 1430678 1430925 "MONADWU-" NIL MONADWU- (NIL T) -7 NIL NIL NIL) (-657 1429755 1430056 1430084 "MONAD" 1430291 MONAD (NIL) -9 NIL 1430403 NIL) (-656 1429522 1429618 1429750 "MONAD-" NIL MONAD- (NIL T) -7 NIL NIL NIL) (-655 1427912 1428682 1428961 "MOEBIUS" NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-654 1427077 1427573 1427613 "MODULE" 1427618 MODULE (NIL T) -9 NIL 1427656 NIL) (-653 1426756 1426882 1427072 "MODULE-" NIL MODULE- (NIL T T) -7 NIL NIL NIL) (-652 1424531 1425353 1425667 "MODRING" NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-651 1421774 1423127 1423640 "MODOP" NIL MODOP (NIL T T) -8 NIL NIL NIL) (-650 1420408 1420982 1421258 "MODMONOM" NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-649 1409691 1419073 1419486 "MODMON" NIL MODMON (NIL T T) -8 NIL NIL NIL) (-648 1406711 1408691 1408960 "MODFIELD" NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-647 1405795 1406162 1406352 "MMLFORM" NIL MMLFORM (NIL) -8 NIL NIL NIL) (-646 1405364 1405413 1405592 "MMAP" NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-645 1403251 1404185 1404225 "MLO" 1404642 MLO (NIL T) -9 NIL 1404882 NIL) (-644 1401132 1401659 1402254 "MLIFT" NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-643 1400600 1400696 1400850 "MKUCFUNC" NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-642 1400270 1400346 1400469 "MKRECORD" NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-641 1399482 1399668 1399896 "MKFUNC" NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-640 1398975 1399091 1399247 "MKFLCFN" NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-639 1398347 1398461 1398646 "MKBCFUNC" NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-638 1397374 1397647 1397924 "MHROWRED" NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-637 1396807 1396895 1397066 "MFINFACT" NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-636 1393965 1394844 1395723 "MESH" NIL MESH (NIL) -7 NIL NIL NIL) (-635 1392632 1392980 1393333 "MDDFACT" NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-634 1389289 1391756 1391797 "MDAGG" 1392054 MDAGG (NIL T) -9 NIL 1392199 NIL) (-633 1388563 1388727 1388927 "MCDEN" NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-632 1387641 1387927 1388157 "MAYBE" NIL MAYBE (NIL T) -8 NIL NIL NIL) (-631 1385738 1386315 1386876 "MATSTOR" NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-630 1381509 1385328 1385575 "MATRIX" NIL MATRIX (NIL T) -8 NIL NIL NIL) (-629 1377858 1378627 1379361 "MATLIN" NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-628 1376611 1376780 1377109 "MATCAT2" NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-627 1366124 1369713 1369789 "MATCAT" 1374777 MATCAT (NIL T T T) -9 NIL 1376245 NIL) (-626 1363405 1364711 1366119 "MATCAT-" NIL MATCAT- (NIL T T T T) -7 NIL NIL NIL) (-625 1361806 1362166 1362550 "MAPPKG3" NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-624 1360939 1361136 1361358 "MAPPKG2" NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-623 1359690 1360016 1360343 "MAPPKG1" NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-622 1358852 1359254 1359430 "MAPPAST" NIL MAPPAST (NIL) -8 NIL NIL NIL) (-621 1358521 1358585 1358708 "MAPHACK3" NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-620 1358169 1358242 1358356 "MAPHACK2" NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-619 1357704 1357819 1357961 "MAPHACK1" NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-618 1355913 1356681 1356982 "MAGMA" NIL MAGMA (NIL T) -8 NIL NIL NIL) (-617 1355407 1355709 1355799 "MACROAST" NIL MACROAST (NIL) -8 NIL NIL NIL) (-616 1348916 1353722 1353763 "LZSTAGG" 1354540 LZSTAGG (NIL T) -9 NIL 1354830 NIL) (-615 1346035 1347469 1348911 "LZSTAGG-" NIL LZSTAGG- (NIL T T) -7 NIL NIL NIL) (-614 1343422 1344388 1344871 "LWORD" NIL LWORD (NIL T) -8 NIL NIL NIL) (-613 1343003 1343282 1343356 "LSTAST" NIL LSTAST (NIL) -8 NIL NIL NIL) (-612 1335231 1342864 1342998 "LSQM" NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-611 1334594 1334739 1334967 "LSPP" NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-610 1332078 1332776 1333488 "LSMP1" NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-609 1330190 1330513 1330961 "LSMP" NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-608 1323359 1329277 1329318 "LSAGG" 1329380 LSAGG (NIL T) -9 NIL 1329458 NIL) (-607 1321053 1322152 1323354 "LSAGG-" NIL LSAGG- (NIL T T) -7 NIL NIL NIL) (-606 1318565 1320402 1320651 "LPOLY" NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-605 1318232 1318323 1318446 "LPEFRAC" NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-604 1317903 1317982 1318010 "LOGIC" 1318121 LOGIC (NIL) -9 NIL 1318203 NIL) (-603 1317798 1317827 1317898 "LOGIC-" NIL LOGIC- (NIL T) -7 NIL NIL NIL) (-602 1317117 1317275 1317468 "LODOOPS" NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-601 1315902 1316151 1316502 "LODOF" NIL LODOF (NIL T T) -7 NIL NIL NIL) (-600 1311788 1314523 1314563 "LODOCAT" 1314995 LODOCAT (NIL T) -9 NIL 1315206 NIL) (-599 1311581 1311657 1311783 "LODOCAT-" NIL LODOCAT- (NIL T T) -7 NIL NIL NIL) (-598 1308645 1311458 1311576 "LODO2" NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-597 1305807 1308595 1308640 "LODO1" NIL LODO1 (NIL T) -8 NIL NIL NIL) (-596 1302958 1305737 1305802 "LODO" NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-595 1302011 1302186 1302488 "LODEEF" NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-594 1300175 1301273 1301526 "LO" NIL LO (NIL T T T) -8 NIL NIL NIL) (-593 1295270 1298334 1298375 "LNAGG" 1299237 LNAGG (NIL T) -9 NIL 1299672 NIL) (-592 1294657 1294924 1295265 "LNAGG-" NIL LNAGG- (NIL T T) -7 NIL NIL NIL) (-591 1291229 1292170 1292807 "LMOPS" NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-590 1290522 1290996 1291036 "LMODULE" 1291041 LMODULE (NIL T) -9 NIL 1291067 NIL) (-589 1287701 1290259 1290381 "LMDICT" NIL LMDICT (NIL T) -8 NIL NIL NIL) (-588 1287269 1287480 1287521 "LLINSET" 1287582 LLINSET (NIL T) -9 NIL 1287626 NIL) (-587 1286945 1287205 1287264 "LITERAL" NIL LITERAL (NIL T) -8 NIL NIL NIL) (-586 1286544 1286624 1286763 "LIST3" NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-585 1284995 1285343 1285742 "LIST2MAP" NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-584 1284166 1284362 1284590 "LIST2" NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-583 1277213 1283422 1283676 "LIST" NIL LIST (NIL T) -8 NIL NIL NIL) (-582 1276790 1277023 1277064 "LINSET" 1277069 LINSET (NIL T) -9 NIL 1277102 NIL) (-581 1275723 1276413 1276580 "LINFORM" NIL LINFORM (NIL T NIL) -8 NIL NIL NIL) (-580 1274020 1274744 1274784 "LINEXP" 1275270 LINEXP (NIL T) -9 NIL 1275543 NIL) (-579 1272729 1273629 1273810 "LINELT" NIL LINELT (NIL T NIL) -8 NIL NIL NIL) (-578 1271556 1271828 1272130 "LINDEP" NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-577 1270769 1271358 1271468 "LINBASIS" NIL LINBASIS (NIL NIL) -8 NIL NIL NIL) (-576 1268319 1269041 1269791 "LIMITRF" NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-575 1266949 1267246 1267637 "LIMITPS" NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-574 1265773 1266344 1266384 "LIECAT" 1266524 LIECAT (NIL T) -9 NIL 1266675 NIL) (-573 1265647 1265680 1265768 "LIECAT-" NIL LIECAT- (NIL T T) -7 NIL NIL NIL) (-572 1259935 1265337 1265565 "LIE" NIL LIE (NIL T T) -8 NIL NIL NIL) (-571 1252284 1259611 1259767 "LIB" NIL LIB (NIL) -8 NIL NIL NIL) (-570 1248736 1249685 1250620 "LGROBP" NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-569 1247360 1248268 1248296 "LFCAT" 1248503 LFCAT (NIL) -9 NIL 1248642 NIL) (-568 1245599 1245929 1246274 "LF" NIL LF (NIL T T) -7 NIL NIL NIL) (-567 1243116 1243781 1244462 "LEXTRIPK" NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-566 1240128 1241106 1241609 "LEXP" NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-565 1239619 1239922 1240013 "LETAST" NIL LETAST (NIL) -8 NIL NIL NIL) (-564 1238326 1238650 1239050 "LEADCDET" NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-563 1237592 1237677 1237903 "LAZM3PK" NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-562 1232659 1236160 1236696 "LAUPOL" NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-561 1232284 1232334 1232494 "LAPLACE" NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-560 1231117 1231828 1231868 "LALG" 1231929 LALG (NIL T) -9 NIL 1231987 NIL) (-559 1230900 1230977 1231112 "LALG-" NIL LALG- (NIL T T) -7 NIL NIL NIL) (-558 1228817 1230168 1230419 "LA" NIL LA (NIL T T T) -8 NIL NIL NIL) (-557 1228646 1228676 1228717 "KVTFROM" 1228779 KVTFROM (NIL T) -9 NIL NIL NIL) (-556 1227462 1228177 1228366 "KTVLOGIC" NIL KTVLOGIC (NIL) -8 NIL NIL NIL) (-555 1227291 1227321 1227362 "KRCFROM" 1227424 KRCFROM (NIL T) -9 NIL NIL NIL) (-554 1226393 1226590 1226885 "KOVACIC" NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-553 1226222 1226252 1226293 "KONVERT" 1226355 KONVERT (NIL T) -9 NIL NIL NIL) (-552 1226051 1226081 1226122 "KOERCE" 1226184 KOERCE (NIL T) -9 NIL NIL NIL) (-551 1225621 1225714 1225846 "KERNEL2" NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-550 1223674 1224568 1224940 "KERNEL" NIL KERNEL (NIL T) -8 NIL NIL NIL) (-549 1216851 1221866 1221920 "KDAGG" 1222296 KDAGG (NIL T T) -9 NIL 1222503 NIL) (-548 1216499 1216641 1216846 "KDAGG-" NIL KDAGG- (NIL T T T) -7 NIL NIL NIL) (-547 1209329 1216280 1216437 "KAFILE" NIL KAFILE (NIL T) -8 NIL NIL NIL) (-546 1208979 1209261 1209324 "JVMOP" NIL JVMOP (NIL) -8 NIL NIL NIL) (-545 1207949 1208448 1208697 "JVMMDACC" NIL JVMMDACC (NIL) -8 NIL NIL NIL) (-544 1207075 1207524 1207729 "JVMFDACC" NIL JVMFDACC (NIL) -8 NIL NIL NIL) (-543 1205939 1206431 1206731 "JVMCSTTG" NIL JVMCSTTG (NIL) -8 NIL NIL NIL) (-542 1205221 1205620 1205781 "JVMCFACC" NIL JVMCFACC (NIL) -8 NIL NIL NIL) (-541 1204931 1205167 1205216 "JVMBCODE" NIL JVMBCODE (NIL) -8 NIL NIL NIL) (-540 1199218 1204621 1204849 "JORDAN" NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-539 1198636 1198969 1199089 "JOINAST" NIL JOINAST (NIL) -8 NIL NIL NIL) (-538 1194798 1196813 1196867 "IXAGG" 1197794 IXAGG (NIL T T) -9 NIL 1198251 NIL) (-537 1194004 1194375 1194793 "IXAGG-" NIL IXAGG- (NIL T T T) -7 NIL NIL NIL) (-536 1189258 1193940 1193999 "IVECTOR" NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-535 1188225 1188500 1188763 "ITUPLE" NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-534 1186887 1187094 1187387 "ITRIGMNP" NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-533 1185838 1186060 1186343 "ITFUN3" NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-532 1185513 1185576 1185699 "ITFUN2" NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-531 1184775 1185147 1185321 "ITFORM" NIL ITFORM (NIL) -8 NIL NIL NIL) (-530 1182815 1184051 1184325 "ITAYLOR" NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-529 1172427 1178132 1179289 "ISUPS" NIL ISUPS (NIL T) -8 NIL NIL NIL) (-528 1171672 1171824 1172060 "ISUMP" NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-527 1171163 1171466 1171557 "ISAST" NIL ISAST (NIL) -8 NIL NIL NIL) (-526 1170456 1170547 1170760 "IRURPK" NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-525 1169588 1169813 1170053 "IRSN" NIL IRSN (NIL) -7 NIL NIL NIL) (-524 1168001 1168382 1168810 "IRRF2F" NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-523 1167786 1167830 1167906 "IRREDFFX" NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-522 1166636 1166933 1167228 "IROOT" NIL IROOT (NIL T) -7 NIL NIL NIL) (-521 1165909 1166260 1166411 "IRFORM" NIL IRFORM (NIL) -8 NIL NIL NIL) (-520 1165112 1165243 1165456 "IR2F" NIL IR2F (NIL T T) -7 NIL NIL NIL) (-519 1163267 1163764 1164308 "IR2" NIL IR2 (NIL T T) -7 NIL NIL NIL) (-518 1160380 1161616 1162305 "IR" NIL IR (NIL T) -8 NIL NIL NIL) (-517 1160205 1160245 1160305 "IPRNTPK" NIL IPRNTPK (NIL) -7 NIL NIL NIL) (-516 1156267 1160131 1160200 "IPF" NIL IPF (NIL NIL) -8 NIL NIL NIL) (-515 1154334 1156206 1156262 "IPADIC" NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-514 1153705 1154004 1154134 "IP4ADDR" NIL IP4ADDR (NIL) -8 NIL NIL NIL) (-513 1153158 1153446 1153578 "IOMODE" NIL IOMODE (NIL) -8 NIL NIL NIL) (-512 1152239 1152864 1152990 "IOBFILE" NIL IOBFILE (NIL) -8 NIL NIL NIL) (-511 1151649 1152143 1152171 "IOBCON" 1152176 IOBCON (NIL) -9 NIL 1152197 NIL) (-510 1151220 1151284 1151466 "INVLAPLA" NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-509 1143264 1145635 1147960 "INTTR" NIL INTTR (NIL T T) -7 NIL NIL NIL) (-508 1140375 1141158 1142022 "INTTOOLS" NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-507 1140052 1140149 1140266 "INTSLPE" NIL INTSLPE (NIL) -7 NIL NIL NIL) (-506 1137558 1139988 1140047 "INTRVL" NIL INTRVL (NIL T) -8 NIL NIL NIL) (-505 1135670 1136199 1136766 "INTRF" NIL INTRF (NIL T) -7 NIL NIL NIL) (-504 1135172 1135286 1135426 "INTRET" NIL INTRET (NIL T) -7 NIL NIL NIL) (-503 1133556 1133962 1134424 "INTRAT" NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-502 1131335 1131929 1132540 "INTPM" NIL INTPM (NIL T T) -7 NIL NIL NIL) (-501 1128708 1129318 1130038 "INTPAF" NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-500 1128112 1128270 1128478 "INTHERTR" NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-499 1127631 1127717 1127905 "INTHERAL" NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-498 1125836 1126357 1126814 "INTHEORY" NIL INTHEORY (NIL) -7 NIL NIL NIL) (-497 1118918 1120571 1122300 "INTG0" NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-496 1118284 1118446 1118619 "INTFACT" NIL INTFACT (NIL T) -7 NIL NIL NIL) (-495 1116157 1116621 1117165 "INTEF" NIL INTEF (NIL T T) -7 NIL NIL NIL) (-494 1114345 1115233 1115261 "INTDOM" 1115560 INTDOM (NIL) -9 NIL 1115765 NIL) (-493 1113898 1114100 1114340 "INTDOM-" NIL INTDOM- (NIL T) -7 NIL NIL NIL) (-492 1109769 1112177 1112231 "INTCAT" 1113027 INTCAT (NIL T) -9 NIL 1113343 NIL) (-491 1109334 1109454 1109581 "INTBIT" NIL INTBIT (NIL) -7 NIL NIL NIL) (-490 1108174 1108346 1108652 "INTALG" NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-489 1107747 1107843 1108000 "INTAF" NIL INTAF (NIL T T) -7 NIL NIL NIL) (-488 1100787 1107602 1107742 "INTABL" NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-487 1100085 1100640 1100705 "INT8" NIL INT8 (NIL) -8 NIL NIL 1100739) (-486 1099382 1099937 1100002 "INT64" NIL INT64 (NIL) -8 NIL NIL 1100036) (-485 1098679 1099234 1099299 "INT32" NIL INT32 (NIL) -8 NIL NIL 1099333) (-484 1097976 1098531 1098596 "INT16" NIL INT16 (NIL) -8 NIL NIL 1098630) (-483 1094503 1097895 1097971 "INT" NIL INT (NIL) -8 NIL NIL NIL) (-482 1088624 1092043 1092071 "INS" 1093001 INS (NIL) -9 NIL 1093660 NIL) (-481 1086686 1087604 1088551 "INS-" NIL INS- (NIL T) -7 NIL NIL NIL) (-480 1085745 1085968 1086243 "INPSIGN" NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-479 1084959 1085100 1085297 "INPRODPF" NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-478 1083949 1084090 1084327 "INPRODFF" NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-477 1083101 1083265 1083525 "INNMFACT" NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-476 1082381 1082496 1082684 "INMODGCD" NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-475 1081120 1081389 1081713 "INFSP" NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-474 1080400 1080541 1080724 "INFPROD0" NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-473 1080063 1080135 1080233 "INFORM1" NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-472 1077141 1078627 1079150 "INFORM" NIL INFORM (NIL) -8 NIL NIL NIL) (-471 1076740 1076847 1076961 "INFINITY" NIL INFINITY (NIL) -7 NIL NIL NIL) (-470 1075896 1076541 1076642 "INETCLTS" NIL INETCLTS (NIL) -8 NIL NIL NIL) (-469 1074746 1075014 1075335 "INEP" NIL INEP (NIL T T T) -7 NIL NIL NIL) (-468 1073818 1074676 1074741 "INDE" NIL INDE (NIL T) -8 NIL NIL NIL) (-467 1073443 1073523 1073640 "INCRMAPS" NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-466 1072357 1072902 1073106 "INBFILE" NIL INBFILE (NIL) -8 NIL NIL NIL) (-465 1068452 1069507 1070450 "INBFF" NIL INBFF (NIL T) -7 NIL NIL NIL) (-464 1067306 1067629 1067657 "INBCON" 1068170 INBCON (NIL) -9 NIL 1068436 NIL) (-463 1066760 1067025 1067301 "INBCON-" NIL INBCON- (NIL T) -7 NIL NIL NIL) (-462 1066254 1066556 1066646 "INAST" NIL INAST (NIL) -8 NIL NIL NIL) (-461 1065711 1066020 1066125 "IMPTAST" NIL IMPTAST (NIL) -8 NIL NIL NIL) (-460 1061811 1065603 1065706 "IMATRIX" NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-459 1060651 1060790 1061105 "IMATQF" NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-458 1059075 1059342 1059679 "IMATLIN" NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-457 1056891 1058957 1059070 "IIARRAY2" NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-456 1051798 1056822 1056886 "IFF" NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-455 1051178 1051512 1051627 "IFAST" NIL IFAST (NIL) -8 NIL NIL NIL) (-454 1045985 1050616 1050802 "IFARRAY" NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-453 1045047 1045907 1045980 "IFAMON" NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-452 1044619 1044696 1044750 "IEVALAB" 1044957 IEVALAB (NIL T T) -9 NIL NIL NIL) (-451 1044374 1044454 1044614 "IEVALAB-" NIL IEVALAB- (NIL T T T) -7 NIL NIL NIL) (-450 1043447 1044294 1044369 "IDPOAMS" NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-449 1042589 1043367 1043442 "IDPOAM" NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-448 1041992 1042523 1042584 "IDPO" NIL IDPO (NIL T T) -8 NIL NIL NIL) (-447 1040472 1040996 1041047 "IDPC" 1041553 IDPC (NIL T T) -9 NIL 1041833 NIL) (-446 1039838 1040394 1040467 "IDPAM" NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-445 1039087 1039760 1039833 "IDPAG" NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-444 1038780 1038993 1039053 "IDENT" NIL IDENT (NIL) -8 NIL NIL NIL) (-443 1038484 1038524 1038563 "IDEMOPC" 1038568 IDEMOPC (NIL T) -9 NIL 1038705 NIL) (-442 1035555 1036436 1037328 "IDECOMP" NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-441 1029181 1030458 1031497 "IDEAL" NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-440 1028443 1028573 1028772 "ICDEN" NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-439 1027616 1028115 1028253 "ICARD" NIL ICARD (NIL) -8 NIL NIL NIL) (-438 1026005 1026336 1026727 "IBPTOOLS" NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-437 1021774 1025961 1026000 "IBITS" NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-436 1019032 1019656 1020351 "IBATOOL" NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-435 1017258 1017738 1018271 "IBACHIN" NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-434 1015022 1017150 1017253 "IARRAY2" NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-433 1010891 1014960 1015017 "IARRAY1" NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-432 1004534 1009855 1010323 "IAN" NIL IAN (NIL) -8 NIL NIL NIL) (-431 1004102 1004165 1004338 "IALGFACT" NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-430 1003594 1003743 1003771 "HYPCAT" 1003978 HYPCAT (NIL) -9 NIL NIL NIL) (-429 1003250 1003403 1003589 "HYPCAT-" NIL HYPCAT- (NIL T) -7 NIL NIL NIL) (-428 1002863 1003108 1003191 "HOSTNAME" NIL HOSTNAME (NIL) -8 NIL NIL NIL) (-427 1002696 1002745 1002786 "HOMOTOP" 1002791 HOMOTOP (NIL T) -9 NIL 1002824 NIL) (-426 999264 1000638 1000679 "HOAGG" 1001654 HOAGG (NIL T) -9 NIL 1002375 NIL) (-425 998270 998740 999259 "HOAGG-" NIL HOAGG- (NIL T T) -7 NIL NIL NIL) (-424 991534 997995 998143 "HEXADEC" NIL HEXADEC (NIL) -8 NIL NIL NIL) (-423 990469 990727 990990 "HEUGCD" NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-422 989436 990334 990464 "HELLFDIV" NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-421 987630 989269 989357 "HEAP" NIL HEAP (NIL T) -8 NIL NIL NIL) (-420 986945 987297 987430 "HEADAST" NIL HEADAST (NIL) -8 NIL NIL NIL) (-419 980498 986878 986940 "HDP" NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-418 973701 980234 980385 "HDMP" NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-417 973154 973311 973474 "HB" NIL HB (NIL) -7 NIL NIL NIL) (-416 966237 973045 973149 "HASHTBL" NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-415 965728 966031 966122 "HASAST" NIL HASAST (NIL) -8 NIL NIL NIL) (-414 963342 965515 965694 "HACKPI" NIL HACKPI (NIL) -8 NIL NIL NIL) (-413 958735 963225 963337 "GTSET" NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-412 951821 958632 958730 "GSTBL" NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-411 943822 951190 951445 "GSERIES" NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-410 942846 943355 943383 "GROUP" 943586 GROUP (NIL) -9 NIL 943720 NIL) (-409 942389 942590 942841 "GROUP-" NIL GROUP- (NIL T) -7 NIL NIL NIL) (-408 941061 941400 941787 "GROEBSOL" NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-407 939883 940240 940291 "GRMOD" 940820 GRMOD (NIL T T) -9 NIL 940986 NIL) (-406 939702 939750 939878 "GRMOD-" NIL GRMOD- (NIL T T T) -7 NIL NIL NIL) (-405 935825 937036 938036 "GRIMAGE" NIL GRIMAGE (NIL) -8 NIL NIL NIL) (-404 934547 934871 935186 "GRDEF" NIL GRDEF (NIL) -7 NIL NIL NIL) (-403 934100 934228 934369 "GRAY" NIL GRAY (NIL) -7 NIL NIL NIL) (-402 933173 933672 933723 "GRALG" 933876 GRALG (NIL T T) -9 NIL 933966 NIL) (-401 932892 932993 933168 "GRALG-" NIL GRALG- (NIL T T T) -7 NIL NIL NIL) (-400 929609 932574 932750 "GPOLSET" NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-399 929022 929085 929342 "GOSPER" NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-398 924908 925772 926297 "GMODPOL" NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-397 924083 924285 924523 "GHENSEL" NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-396 919086 920013 921032 "GENUPS" NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-395 918834 918891 918980 "GENUFACT" NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-394 918316 918405 918570 "GENPGCD" NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-393 917825 917866 918079 "GENMFACT" NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-392 916626 916909 917213 "GENEEZ" NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-391 909965 916316 916477 "GDMP" NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-390 899780 904755 905859 "GCNAALG" NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-389 897894 898935 898963 "GCDDOM" 899218 GCDDOM (NIL) -9 NIL 899375 NIL) (-388 897517 897674 897889 "GCDDOM-" NIL GCDDOM- (NIL T) -7 NIL NIL NIL) (-387 888310 890780 893168 "GBINTERN" NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-386 886445 886770 887188 "GBF" NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-385 885386 885575 885842 "GBEUCLID" NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-384 884257 884464 884768 "GB" NIL GB (NIL T T T T) -7 NIL NIL NIL) (-383 883720 883862 884010 "GAUSSFAC" NIL GAUSSFAC (NIL) -7 NIL NIL NIL) (-382 882332 882680 882993 "GALUTIL" NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-381 880877 881198 881520 "GALPOLYU" NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-380 878503 878859 879264 "GALFACTU" NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-379 871755 873416 874994 "GALFACT" NIL GALFACT (NIL T) -7 NIL NIL NIL) (-378 871407 871628 871696 "FUNDESC" NIL FUNDESC (NIL) -8 NIL NIL NIL) (-377 871031 871252 871333 "FUNCTION" NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-376 869128 869811 870271 "FT" NIL FT (NIL) -8 NIL NIL NIL) (-375 867721 868028 868420 "FSUPFACT" NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-374 866376 866735 867059 "FST" NIL FST (NIL) -8 NIL NIL NIL) (-373 865679 865803 865990 "FSRED" NIL FSRED (NIL T T) -7 NIL NIL NIL) (-372 864653 864919 865266 "FSPRMELT" NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-371 862311 862841 863323 "FSPECF" NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-370 861894 861954 862123 "FSINT" NIL FSINT (NIL T T) -7 NIL NIL NIL) (-369 860258 861108 861411 "FSERIES" NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-368 859406 859540 859763 "FSCINT" NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-367 858577 858738 858965 "FSAGG2" NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-366 854560 857511 857552 "FSAGG" 857922 FSAGG (NIL T) -9 NIL 858181 NIL) (-365 852914 853673 854465 "FSAGG-" NIL FSAGG- (NIL T T) -7 NIL NIL NIL) (-364 850870 851166 851710 "FS2UPS" NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-363 849917 850099 850399 "FS2EXPXP" NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-362 849598 849647 849774 "FS2" NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-361 829853 839255 839296 "FS" 843166 FS (NIL T) -9 NIL 845444 NIL) (-360 822084 825577 829556 "FS-" NIL FS- (NIL T T) -7 NIL NIL NIL) (-359 821618 821745 821897 "FRUTIL" NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-358 816172 819299 819339 "FRNAALG" 820659 FRNAALG (NIL T) -9 NIL 821257 NIL) (-357 812913 814164 815422 "FRNAALG-" NIL FRNAALG- (NIL T T) -7 NIL NIL NIL) (-356 812594 812643 812770 "FRNAAF2" NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-355 811081 811638 811932 "FRMOD" NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-354 810367 810460 810747 "FRIDEAL2" NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-353 808201 808967 809283 "FRIDEAL" NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-352 807310 807753 807794 "FRETRCT" 807799 FRETRCT (NIL T) -9 NIL 807970 NIL) (-351 806683 806961 807305 "FRETRCT-" NIL FRETRCT- (NIL T T) -7 NIL NIL NIL) (-350 803489 804947 805006 "FRAMALG" 805888 FRAMALG (NIL T T) -9 NIL 806180 NIL) (-349 802085 802636 803266 "FRAMALG-" NIL FRAMALG- (NIL T T T) -7 NIL NIL NIL) (-348 801778 801841 801948 "FRAC2" NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-347 795483 801583 801773 "FRAC" NIL FRAC (NIL T) -8 NIL NIL NIL) (-346 795176 795239 795346 "FR2" NIL FR2 (NIL T T) -7 NIL NIL NIL) (-345 787548 792055 793383 "FR" NIL FR (NIL T) -8 NIL NIL NIL) (-344 781388 784829 784857 "FPS" 785976 FPS (NIL) -9 NIL 786532 NIL) (-343 780945 781078 781242 "FPS-" NIL FPS- (NIL T) -7 NIL NIL NIL) (-342 777818 779798 779826 "FPC" 780051 FPC (NIL) -9 NIL 780193 NIL) (-341 777664 777716 777813 "FPC-" NIL FPC- (NIL T) -7 NIL NIL NIL) (-340 776441 777150 777191 "FPATMAB" 777196 FPATMAB (NIL T) -9 NIL 777348 NIL) (-339 774871 775467 775814 "FPARFRAC" NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-338 774446 774504 774677 "FORDER" NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-337 772981 773844 774018 "FNLA" NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-336 771596 772101 772129 "FNCAT" 772586 FNCAT (NIL) -9 NIL 772843 NIL) (-335 771053 771563 771591 "FNAME" NIL FNAME (NIL) -8 NIL NIL NIL) (-334 769640 771002 771048 "FMONOID" NIL FMONOID (NIL T) -8 NIL NIL NIL) (-333 766228 767586 767627 "FMONCAT" 768844 FMONCAT (NIL T) -9 NIL 769448 NIL) (-332 763117 764164 764217 "FMCAT" 765398 FMCAT (NIL T T) -9 NIL 765890 NIL) (-331 761849 762940 763039 "FM1" NIL FM1 (NIL T T) -8 NIL NIL NIL) (-330 760977 761697 761844 "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
+((-2566 (((-85) $ $) NIL T ELT)) (-3239 (((-1072) $) NIL T ELT)) (-3240 (((-1033) $) NIL T ELT)) (-3942 (((-773) $) 9 T ELT) (($ (-1094)) NIL T ELT) (((-1094) $) NIL T ELT)) (-1263 (((-85) $ $) NIL T ELT)) (-3054 (((-85) $ $) NIL T ELT))) 
+(((-1129) (-995)) (T -1129)) 
+NIL 
+((-3713 (((-85)) 18 T ELT)) (-3710 (((-1184) (-584 |#1|) (-584 |#1|)) 22 T ELT) (((-1184) (-584 |#1|)) 23 T ELT)) (-3715 (((-85) |#1| |#1|) 37 (|has| |#1| (-757)) ELT)) (-3712 (((-85) |#1| |#1| (-1 (-85) |#1| |#1|)) 29 T ELT) (((-3 (-85) "failed") |#1| |#1|) 27 T ELT)) (-3714 ((|#1| (-584 |#1|)) 38 (|has| |#1| (-757)) ELT) ((|#1| (-584 |#1|) (-1 (-85) |#1| |#1|)) 32 T ELT)) (-3711 (((-2 (|:| -3226 (-584 |#1|)) (|:| -3225 (-584 |#1|)))) 20 T ELT))) 
+(((-1130 |#1|) (-10 -7 (-15 -3710 ((-1184) (-584 |#1|))) (-15 -3710 ((-1184) (-584 |#1|) (-584 |#1|))) (-15 -3711 ((-2 (|:| -3226 (-584 |#1|)) (|:| -3225 (-584 |#1|))))) (-15 -3712 ((-3 (-85) "failed") |#1| |#1|)) (-15 -3712 ((-85) |#1| |#1| (-1 (-85) |#1| |#1|))) (-15 -3714 (|#1| (-584 |#1|) (-1 (-85) |#1| |#1|))) (-15 -3713 ((-85))) (IF (|has| |#1| (-757)) (PROGN (-15 -3714 (|#1| (-584 |#1|))) (-15 -3715 ((-85) |#1| |#1|))) |%noBranch|)) (-1013)) (T -1130)) 
+((-3715 (*1 *2 *3 *3) (-12 (-5 *2 (-85)) (-5 *1 (-1130 *3)) (-4 *3 (-757)) (-4 *3 (-1013)))) (-3714 (*1 *2 *3) (-12 (-5 *3 (-584 *2)) (-4 *2 (-1013)) (-4 *2 (-757)) (-5 *1 (-1130 *2)))) (-3713 (*1 *2) (-12 (-5 *2 (-85)) (-5 *1 (-1130 *3)) (-4 *3 (-1013)))) (-3714 (*1 *2 *3 *4) (-12 (-5 *3 (-584 *2)) (-5 *4 (-1 (-85) *2 *2)) (-5 *1 (-1130 *2)) (-4 *2 (-1013)))) (-3712 (*1 *2 *3 *3 *4) (-12 (-5 *4 (-1 (-85) *3 *3)) (-4 *3 (-1013)) (-5 *2 (-85)) (-5 *1 (-1130 *3)))) (-3712 (*1 *2 *3 *3) (|partial| -12 (-5 *2 (-85)) (-5 *1 (-1130 *3)) (-4 *3 (-1013)))) (-3711 (*1 *2) (-12 (-5 *2 (-2 (|:| -3226 (-584 *3)) (|:| -3225 (-584 *3)))) (-5 *1 (-1130 *3)) (-4 *3 (-1013)))) (-3710 (*1 *2 *3 *3) (-12 (-5 *3 (-584 *4)) (-4 *4 (-1013)) (-5 *2 (-1184)) (-5 *1 (-1130 *4)))) (-3710 (*1 *2 *3) (-12 (-5 *3 (-584 *4)) (-4 *4 (-1013)) (-5 *2 (-1184)) (-5 *1 (-1130 *4))))) 
+((-3716 (((-1184) (-584 (-1089)) (-584 (-1089))) 14 T ELT) (((-1184) (-584 (-1089))) 12 T ELT)) (-3718 (((-1184)) 16 T ELT)) (-3717 (((-2 (|:| -3225 (-584 (-1089))) (|:| -3226 (-584 (-1089))))) 20 T ELT))) 
+(((-1131) (-10 -7 (-15 -3716 ((-1184) (-584 (-1089)))) (-15 -3716 ((-1184) (-584 (-1089)) (-584 (-1089)))) (-15 -3717 ((-2 (|:| -3225 (-584 (-1089))) (|:| -3226 (-584 (-1089)))))) (-15 -3718 ((-1184))))) (T -1131)) 
+((-3718 (*1 *2) (-12 (-5 *2 (-1184)) (-5 *1 (-1131)))) (-3717 (*1 *2) (-12 (-5 *2 (-2 (|:| -3225 (-584 (-1089))) (|:| -3226 (-584 (-1089))))) (-5 *1 (-1131)))) (-3716 (*1 *2 *3 *3) (-12 (-5 *3 (-584 (-1089))) (-5 *2 (-1184)) (-5 *1 (-1131)))) (-3716 (*1 *2 *3) (-12 (-5 *3 (-584 (-1089))) (-5 *2 (-1184)) (-5 *1 (-1131))))) 
+((-3771 (($ $) 17 T ELT)) (-3719 (((-85) $) 27 T ELT))) 
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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 $) OR (|has| |#1| (-495)) (|has| |#1| (-311)) (|has| |#1| (-146))) ((-962) . T) ((-970) . T) ((-1025) . T) ((-1060) . T) ((-1013) . T) ((-1065) -12 (|has| |#1| (-311)) (|has| |#2| (-1065))) ((-1114) |has| |#1| (-38 (-347 (-484)))) ((-1117) |has| |#1| (-38 (-347 (-484)))) ((-1128) . T) ((-1133) |has| |#1| (-311)) ((-1140 |#1|) . T) ((-1157 |#1| (-484)) . T)) 
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+NIL 
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+((-3814 (*1 *1 *2) (-12 (-5 *2 (-1068 (-2 (|:| |k| (-695)) (|:| |c| *3)))) (-4 *3 (-962)) (-4 *1 (-1171 *3)))) (-3813 (*1 *2 *1) (-12 (-4 *1 (-1171 *3)) (-4 *3 (-962)) (-5 *2 (-1068 *3)))) (-3814 (*1 *1 *2) (-12 (-5 *2 (-1068 *3)) (-4 *3 (-962)) (-4 *1 (-1171 *3)))) (-3812 (*1 *1 *1) (-12 (-4 *1 (-1171 *2)) (-4 *2 (-962)))) (-3811 (*1 *1 *2 *1) (-12 (-5 *2 (-1 *3 (-484))) (-4 *1 (-1171 *3)) (-4 *3 (-962)))) (-3810 (*1 *2 *1 *3) (-12 (-5 *3 (-695)) (-4 *1 (-1171 *4)) (-4 *4 (-962)) (-5 *2 (-858 *4)))) (-3810 (*1 *2 *1 *3 *3) (-12 (-5 *3 (-695)) (-4 *1 (-1171 *4)) (-4 *4 (-962)) (-5 *2 (-858 *4)))) (** (*1 *1 *1 *2) (-12 (-4 *1 (-1171 *2)) (-4 *2 (-962)) (-4 *2 (-311)))) (-3808 (*1 *1 *1) (-12 (-4 *1 (-1171 *2)) (-4 *2 (-962)) (-4 *2 (-38 (-347 (-484)))))) (-3808 (*1 *1 *1 *2) (OR (-12 (-5 *2 (-1089)) (-4 *1 (-1171 *3)) (-4 *3 (-962)) (-12 (-4 *3 (-29 (-484))) (-4 *3 (-872)) (-4 *3 (-1114)) (-4 *3 (-38 (-347 (-484)))))) (-12 (-5 *2 (-1089)) (-4 *1 (-1171 *3)) (-4 *3 (-962)) (-12 (|has| *3 (-15 -3079 ((-584 *2) *3))) (|has| *3 (-15 -3808 (*3 *3 *2))) (-4 *3 (-38 (-347 (-484))))))))) 
+(-13 (-1157 |t#1| (-695)) (-10 -8 (-15 -3814 ($ (-1068 (-2 (|:| |k| (-695)) (|:| |c| |t#1|))))) (-15 -3813 ((-1068 |t#1|) $)) (-15 -3814 ($ (-1068 |t#1|))) (-15 -3812 ($ $)) (-15 -3811 ($ (-1 |t#1| (-484)) $)) (-15 -3810 ((-858 |t#1|) $ (-695))) (-15 -3810 ((-858 |t#1|) $ (-695) (-695))) (IF (|has| |t#1| (-311)) (-15 ** ($ $ |t#1|)) |%noBranch|) (IF (|has| |t#1| (-38 (-347 (-484)))) (PROGN (-15 -3808 ($ $)) (IF (|has| |t#1| (-15 -3808 (|t#1| |t#1| (-1089)))) (IF (|has| |t#1| (-15 -3079 ((-584 (-1089)) |t#1|))) (-15 -3808 ($ $ (-1089))) |%noBranch|) |%noBranch|) (IF (|has| |t#1| (-1114)) (IF (|has| |t#1| (-872)) (IF (|has| |t#1| (-29 (-484))) (-15 -3808 ($ $ (-1089))) |%noBranch|) |%noBranch|) |%noBranch|) (-6 (-916)) (-6 (-1114))) |%noBranch|))) 
+(((-21) . T) ((-23) . T) ((-47 |#1| (-695)) . T) ((-25) . T) ((-38 (-347 (-484))) |has| |#1| (-38 (-347 (-484)))) ((-38 |#1|) |has| |#1| (-146)) ((-38 $) |has| |#1| (-495)) ((-35) |has| |#1| (-38 (-347 (-484)))) ((-66) |has| |#1| (-38 (-347 (-484)))) ((-72) . T) ((-82 (-347 (-484)) (-347 (-484))) |has| |#1| (-38 (-347 (-484)))) ((-82 |#1| |#1|) . T) ((-82 $ $) OR (|has| |#1| (-495)) (|has| |#1| (-146))) ((-104) . T) ((-118) |has| |#1| (-118)) ((-120) |has| |#1| (-120)) ((-556 (-347 (-484))) |has| |#1| (-38 (-347 (-484)))) ((-556 (-484)) . T) ((-556 |#1|) |has| |#1| (-146)) ((-556 $) |has| |#1| (-495)) ((-553 (-773)) . T) ((-146) OR (|has| |#1| (-495)) (|has| |#1| (-146))) ((-186 $) |has| |#1| (-15 * (|#1| (-695) |#1|))) ((-190) |has| |#1| (-15 * (|#1| (-695) |#1|))) ((-189) |has| |#1| (-15 * (|#1| (-695) |#1|))) ((-239) |has| |#1| (-38 (-347 (-484)))) ((-241 (-695) |#1|) . T) ((-241 $ $) |has| (-695) (-1025)) ((-245) |has| |#1| (-495)) ((-430) |has| |#1| (-38 (-347 (-484)))) ((-495) |has| |#1| (-495)) ((-13) . T) ((-589 (-347 (-484))) |has| |#1| (-38 (-347 (-484)))) ((-589 (-484)) . T) ((-589 |#1|) . T) ((-589 $) . T) ((-591 (-347 (-484))) |has| |#1| (-38 (-347 (-484)))) ((-591 |#1|) . T) ((-591 $) . T) ((-583 (-347 (-484))) |has| |#1| (-38 (-347 (-484)))) ((-583 |#1|) |has| |#1| (-146)) ((-583 $) |has| |#1| (-495)) ((-655 (-347 (-484))) |has| |#1| (-38 (-347 (-484)))) ((-655 |#1|) |has| |#1| (-146)) ((-655 $) |has| |#1| (-495)) ((-664) . T) ((-807 $ (-1089)) -12 (|has| |#1| (-810 (-1089))) (|has| |#1| (-15 * (|#1| (-695) |#1|)))) ((-810 (-1089)) -12 (|has| |#1| (-810 (-1089))) (|has| |#1| (-15 * (|#1| (-695) |#1|)))) ((-812 (-1089)) -12 (|has| |#1| (-810 (-1089))) (|has| |#1| (-15 * (|#1| (-695) |#1|)))) ((-887 |#1| (-695) (-994)) . T) ((-916) |has| |#1| (-38 (-347 (-484)))) ((-964 (-347 (-484))) |has| |#1| (-38 (-347 (-484)))) ((-964 |#1|) . T) ((-964 $) OR (|has| |#1| (-495)) (|has| |#1| (-146))) ((-969 (-347 (-484))) |has| |#1| (-38 (-347 (-484)))) ((-969 |#1|) . T) ((-969 $) OR (|has| |#1| (-495)) (|has| |#1| (-146))) ((-962) . T) ((-970) . T) ((-1025) . T) ((-1060) . T) ((-1013) . T) ((-1114) |has| |#1| (-38 (-347 (-484)))) ((-1117) |has| |#1| (-38 (-347 (-484)))) ((-1128) . T) ((-1157 |#1| (-695)) . T)) 
+((-3817 (((-1 (-1068 |#1|) (-584 (-1068 |#1|))) (-1 |#2| (-584 |#2|))) 24 T ELT)) (-3816 (((-1 (-1068 |#1|) (-1068 |#1|) (-1068 |#1|)) (-1 |#2| |#2| |#2|)) 16 T ELT)) (-3815 (((-1 (-1068 |#1|) (-1068 |#1|)) (-1 |#2| |#2|)) 13 T ELT)) (-3820 ((|#2| (-1 |#2| |#2| |#2|) |#1| |#1|) 48 T ELT)) (-3819 ((|#2| (-1 |#2| |#2|) |#1|) 46 T ELT)) (-3821 ((|#2| (-1 |#2| (-584 |#2|)) (-584 |#1|)) 60 T ELT)) (-3822 (((-584 |#2|) (-584 |#1|) (-584 (-1 |#2| (-584 |#2|)))) 66 T ELT)) (-3818 ((|#2| |#2| |#2|) 43 T ELT))) 
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+((-3824 ((|#2| |#4| (-695)) 31 T ELT)) (-3823 ((|#4| |#2|) 26 T ELT)) (-3826 ((|#4| (-347 |#2|)) 49 (|has| |#1| (-495)) ELT)) (-3825 (((-1 |#4| (-584 |#4|)) |#3|) 43 T ELT))) 
+(((-1173 |#1| |#2| |#3| |#4|) (-10 -7 (-15 -3823 (|#4| |#2|)) (-15 -3824 (|#2| |#4| (-695))) (-15 -3825 ((-1 |#4| (-584 |#4|)) |#3|)) (IF (|has| |#1| (-495)) (-15 -3826 (|#4| (-347 |#2|))) |%noBranch|)) (-962) (-1154 |#1|) (-601 |#2|) (-1171 |#1|)) (T -1173)) 
+((-3826 (*1 *2 *3) (-12 (-5 *3 (-347 *5)) (-4 *5 (-1154 *4)) (-4 *4 (-495)) (-4 *4 (-962)) (-4 *2 (-1171 *4)) (-5 *1 (-1173 *4 *5 *6 *2)) (-4 *6 (-601 *5)))) (-3825 (*1 *2 *3) (-12 (-4 *4 (-962)) (-4 *5 (-1154 *4)) (-5 *2 (-1 *6 (-584 *6))) (-5 *1 (-1173 *4 *5 *3 *6)) (-4 *3 (-601 *5)) (-4 *6 (-1171 *4)))) (-3824 (*1 *2 *3 *4) (-12 (-5 *4 (-695)) (-4 *5 (-962)) (-4 *2 (-1154 *5)) (-5 *1 (-1173 *5 *2 *6 *3)) (-4 *6 (-601 *2)) (-4 *3 (-1171 *5)))) (-3823 (*1 *2 *3) (-12 (-4 *4 (-962)) (-4 *3 (-1154 *4)) (-4 *2 (-1171 *4)) (-5 *1 (-1173 *4 *3 *5 *2)) (-4 *5 (-601 *3))))) 
+NIL 
+(((-1174) (-113)) (T -1174)) 
+NIL 
+(-13 (-10 -7 (-6 -2285))) 
+((-2566 (((-85) $ $) NIL T ELT)) (-3827 (((-1089)) 12 T ELT)) (-3239 (((-1072) $) 18 T ELT)) (-3240 (((-1033) $) NIL T ELT)) (-3942 (((-773) $) 11 T ELT) (((-1089) $) 8 T ELT)) (-1263 (((-85) $ $) NIL T ELT)) (-3054 (((-85) $ $) 15 T ELT))) 
+(((-1175 |#1|) (-13 (-1013) (-553 (-1089)) (-10 -8 (-15 -3942 ((-1089) $)) (-15 -3827 ((-1089))))) (-1089)) (T -1175)) 
+((-3942 (*1 *2 *1) (-12 (-5 *2 (-1089)) (-5 *1 (-1175 *3)) (-14 *3 *2))) (-3827 (*1 *2) (-12 (-5 *2 (-1089)) (-5 *1 (-1175 *3)) (-14 *3 *2)))) 
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+(((-1176 |#1| |#2|) (-10 -7 (-15 -3828 (|#2| |#1|)) (-15 -3829 (|#2| |#1|)) (-15 -3830 (|#1| |#1| |#1|)) (-15 -3831 ((-631 |#2|) |#1| |#1|)) (-15 -3832 (|#2| |#1| |#1|)) (-15 * (|#1| |#1| |#2|)) (-15 * (|#1| |#2| |#1|)) (-15 * (|#1| (-484) |#1|)) (-15 -3833 (|#1| |#1| |#1|)) (-15 -3833 (|#1| |#1|)) (-15 -3834 (|#1| (-695))) (-15 -3835 (|#1| |#1| |#1|))) (-1177 |#2|) (-1128)) (T -1176)) 
+NIL 
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(-257) (-120) (-934))) (-5 *2 (-584 (-2 (|:| -1745 (-1084 *5)) (|:| -3221 (-584 (-858 *5)))))) (-5 *1 (-1206 *5 *6 *7)) (-5 *3 (-584 (-858 *5))) (-14 *6 (-584 (-1089))) (-14 *7 (-584 (-1089))))) (-3964 (*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 *1 (-1206 *4 *5 *6)) (-14 *6 (-584 (-1089))))) (-3963 (*1 *2 *3) (-12 (-5 *3 (-584 (-858 *4))) (-4 *4 (-13 (-756) (-257) (-120) (-934))) (-5 *2 (-584 (-959 *4 *5))) (-5 *1 (-1206 *4 *5 *6)) (-14 *5 (-584 (-1089))) (-14 *6 (-584 (-1089))))) (-3963 (*1 *2 *3 *4) (-12 (-5 *3 (-584 (-858 *5))) (-5 *4 (-85)) (-4 *5 (-13 (-756) (-257) (-120) (-934))) (-5 *2 (-584 (-959 *5 *6))) (-5 *1 (-1206 *5 *6 *7)) (-14 *6 (-584 (-1089))) (-14 *7 (-584 (-1089))))) (-3963 (*1 *2 *3 *4 *4) (-12 (-5 *3 (-584 (-858 *5))) (-5 *4 (-85)) (-4 *5 (-13 (-756) (-257) (-120) (-934))) (-5 *2 (-584 (-959 *5 *6))) (-5 *1 (-1206 *5 *6 *7)) (-14 *6 (-584 (-1089))) (-14 *7 (-584 (-1089)))))) 
+((-3971 (((-3 (-1178 (-347 (-484))) #1="failed") (-1178 |#1|) |#1|) 21 T ELT)) (-3969 (((-85) (-1178 |#1|)) 12 T ELT)) (-3970 (((-3 (-1178 (-484)) #1#) (-1178 |#1|)) 16 T ELT))) 
+(((-1207 |#1|) (-10 -7 (-15 -3969 ((-85) (-1178 |#1|))) (-15 -3970 ((-3 (-1178 (-484)) #1="failed") (-1178 |#1|))) (-15 -3971 ((-3 (-1178 (-347 (-484))) #1#) (-1178 |#1|) |#1|))) (-13 (-962) (-581 (-484)))) (T -1207)) 
+((-3971 (*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)))) (-3970 (*1 *2 *3) (|partial| -12 (-5 *3 (-1178 *4)) (-4 *4 (-13 (-962) (-581 (-484)))) (-5 *2 (-1178 (-484))) (-5 *1 (-1207 *4)))) (-3969 (*1 *2 *3) (-12 (-5 *3 (-1178 *4)) (-4 *4 (-13 (-962) (-581 (-484)))) (-5 *2 (-85)) (-5 *1 (-1207 *4))))) 
+((-2566 (((-85) $ $) NIL T ELT)) (-3185 (((-85) $) 12 T ELT)) (-1310 (((-3 $ #1="failed") $ $) NIL T ELT)) (-3133 (((-695)) 9 T ELT)) (-3720 (($) NIL T CONST)) (-3463 (((-3 $ #1#) $) 57 T ELT)) (-2992 (($) 46 T ELT)) (-2408 (((-85) $) 38 T ELT)) (-3441 (((-633 $) $) 36 T ELT)) (-2008 (((-831) $) 14 T ELT)) (-3239 (((-1072) $) NIL T ELT)) (-3442 (($) 26 T CONST)) (-2398 (($ (-831)) 47 T ELT)) (-3240 (((-1033) $) NIL T ELT)) (-3968 (((-484) $) 16 T ELT)) (-3942 (((-773) $) 21 T ELT) (($ (-484)) 18 T ELT)) (-3123 (((-695)) 10 T CONST)) (-1263 (((-85) $ $) 59 T ELT)) (-2658 (($) 23 T CONST)) (-2664 (($) 25 T CONST)) (-3054 (((-85) $ $) 31 T ELT)) (-3833 (($ $) 50 T ELT) (($ $ $) 44 T ELT)) (-3835 (($ $ $) 29 T ELT)) (** (($ $ (-831)) NIL T ELT) (($ $ (-695)) 52 T ELT)) (* (($ (-831) $) NIL T ELT) (($ (-695) $) NIL T ELT) (($ (-484) $) 41 T ELT) (($ $ $) 40 T ELT))) 
+(((-1208 |#1|) (-13 (-146) (-317) (-554 (-484)) (-1065)) (-831)) (T -1208)) 
+NIL 
+NIL 
+NIL 
+NIL 
+NIL 
+NIL 
+NIL 
+NIL 
+NIL 
+NIL 
+NIL 
+NIL 
+NIL 
+((-3 2805513 2805518 2805523 NIL NIL NIL (NIL) -8 NIL NIL NIL) (-2 2805498 2805503 2805508 NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1 2805483 2805488 2805493 NIL NIL NIL (NIL) -8 NIL NIL NIL) (0 2805468 2805473 2805478 NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1208 2804511 2805386 2805463 "ZMOD" NIL ZMOD (NIL NIL) -8 NIL NIL NIL) (-1207 2803726 2803905 2804124 "ZLINDEP" NIL ZLINDEP (NIL T) -7 NIL NIL NIL) (-1206 2794885 2796754 2798688 "ZDSOLVE" NIL ZDSOLVE (NIL T NIL NIL) -7 NIL NIL NIL) (-1205 2794273 2794426 2794615 "YSTREAM" NIL YSTREAM (NIL T) -7 NIL NIL NIL) (-1204 2793735 2794038 2794151 "YDIAGRAM" NIL YDIAGRAM (NIL) -8 NIL NIL NIL) (-1203 2791359 2793197 2793400 "XRPOLY" NIL XRPOLY (NIL T T) -8 NIL NIL NIL) (-1202 2788187 2789776 2790347 "XPR" NIL XPR (NIL T T) -8 NIL NIL NIL) (-1201 2785506 2787174 2787228 "XPOLYC" 2787513 XPOLYC (NIL T T) -9 NIL 2787626 NIL) (-1200 2783089 2785010 2785213 "XPOLY" NIL XPOLY (NIL T) -8 NIL NIL NIL) (-1199 2779401 2781948 2782336 "XPBWPOLY" NIL XPBWPOLY (NIL T T) -8 NIL NIL NIL) (-1198 2774310 2775881 2775935 "XFALG" 2778080 XFALG (NIL T T) -9 NIL 2778864 NIL) (-1197 2769528 2772199 2772241 "XF" 2772859 XF (NIL T) -9 NIL 2773255 NIL) (-1196 2769246 2769356 2769523 "XF-" NIL XF- (NIL T T) -7 NIL NIL NIL) (-1195 2768473 2768595 2768799 "XEXPPKG" NIL XEXPPKG (NIL T T T) -7 NIL NIL NIL) (-1194 2766279 2768373 2768468 "XDPOLY" NIL XDPOLY (NIL T T) -8 NIL NIL NIL) (-1193 2764922 2765655 2765697 "XALG" 2765702 XALG (NIL T) -9 NIL 2765811 NIL) (-1192 2758479 2763332 2763810 "WUTSET" NIL WUTSET (NIL T T T T) -8 NIL NIL NIL) (-1191 2756786 2757724 2758045 "WP" NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL NIL) (-1190 2756385 2756657 2756726 "WHILEAST" NIL WHILEAST (NIL) -8 NIL NIL NIL) (-1189 2755872 2756175 2756268 "WHEREAST" NIL WHEREAST (NIL) -8 NIL NIL NIL) (-1188 2754949 2755159 2755454 "WFFINTBS" NIL WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1187 2753245 2753708 2754170 "WEIER" NIL WEIER (NIL T) -7 NIL NIL NIL) (-1186 2752165 2752719 2752761 "VSPACE" 2752897 VSPACE (NIL T) -9 NIL 2752971 NIL) (-1185 2752036 2752069 2752160 "VSPACE-" NIL VSPACE- (NIL T T) -7 NIL NIL NIL) (-1184 2751879 2751933 2752001 "VOID" NIL VOID (NIL) -8 NIL NIL NIL) (-1183 2748862 2749657 2750394 "VIEWDEF" NIL VIEWDEF (NIL) -7 NIL NIL NIL) (-1182 2739960 2742561 2744734 "VIEW3D" NIL VIEW3D (NIL) -8 NIL NIL NIL) (-1181 2733537 2735428 2737007 "VIEW2D" NIL VIEW2D (NIL) -8 NIL NIL NIL) (-1180 2732021 2732416 2732822 "VIEW" NIL VIEW (NIL) -7 NIL NIL NIL) (-1179 2730848 2731129 2731445 "VECTOR2" NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1178 2725962 2730675 2730767 "VECTOR" NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1177 2719064 2723672 2723715 "VECTCAT" 2724703 VECTCAT (NIL T) -9 NIL 2725287 NIL) (-1176 2718343 2718669 2719059 "VECTCAT-" NIL VECTCAT- (NIL T T) -7 NIL NIL NIL) (-1175 2717837 2718079 2718199 "VARIABLE" NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1174 2717770 2717775 2717805 "UTYPE" 2717810 UTYPE (NIL) -9 NIL NIL NIL) (-1173 2716757 2716933 2717194 "UTSODETL" NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1172 2714608 2715116 2715640 "UTSODE" NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1171 2704552 2710460 2710502 "UTSCAT" 2711600 UTSCAT (NIL T) -9 NIL 2712357 NIL) (-1170 2702617 2703560 2704547 "UTSCAT-" NIL UTSCAT- (NIL T T) -7 NIL NIL NIL) (-1169 2702291 2702340 2702471 "UTS2" NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1168 2694066 2700487 2700966 "UTS" NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1167 2688061 2690874 2690917 "URAGG" 2692987 URAGG (NIL T) -9 NIL 2693709 NIL) (-1166 2686076 2687038 2688056 "URAGG-" NIL URAGG- (NIL T T) -7 NIL NIL NIL) (-1165 2681847 2685052 2685514 "UPXSSING" NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1164 2674340 2681771 2681842 "UPXSCONS" NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1163 2663053 2670478 2670539 "UPXSCCA" 2671107 UPXSCCA (NIL T T) -9 NIL 2671339 NIL) (-1162 2662774 2662876 2663048 "UPXSCCA-" NIL UPXSCCA- (NIL T T T) -7 NIL NIL NIL) (-1161 2651388 2658538 2658580 "UPXSCAT" 2659220 UPXSCAT (NIL T) -9 NIL 2659828 NIL) (-1160 2650901 2650986 2651163 "UPXS2" NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1159 2642651 2650492 2650754 "UPXS" NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1158 2641546 2641816 2642166 "UPSQFREE" NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1157 2634311 2637734 2637788 "UPSCAT" 2638857 UPSCAT (NIL T T) -9 NIL 2639621 NIL) (-1156 2633731 2633983 2634306 "UPSCAT-" NIL UPSCAT- (NIL T T T) -7 NIL NIL NIL) (-1155 2633405 2633454 2633585 "UPOLYC2" NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1154 2617599 2626489 2626531 "UPOLYC" 2628609 UPOLYC (NIL T) -9 NIL 2629829 NIL) (-1153 2611654 2614502 2617594 "UPOLYC-" NIL UPOLYC- (NIL T T) -7 NIL NIL NIL) (-1152 2611090 2611215 2611378 "UPMP" NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1151 2610724 2610811 2610950 "UPDIVP" NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1150 2609537 2609804 2610108 "UPDECOMP" NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1149 2608870 2609000 2609185 "UPCDEN" NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1148 2608462 2608537 2608684 "UP2" NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1147 2599290 2608228 2608356 "UP" NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1146 2598652 2598789 2598994 "UNISEG2" NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1145 2597253 2598100 2598376 "UNISEG" NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1144 2596482 2596679 2596904 "UNIFACT" NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1143 2583356 2596406 2596477 "ULSCONS" NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1142 2563270 2576443 2576504 "ULSCCAT" 2577135 ULSCCAT (NIL T T) -9 NIL 2577422 NIL) (-1141 2562605 2562891 2563265 "ULSCCAT-" NIL ULSCCAT- (NIL T T T) -7 NIL NIL NIL) (-1140 2551039 2558111 2558153 "ULSCAT" 2559006 ULSCAT (NIL T) -9 NIL 2559736 NIL) (-1139 2550552 2550637 2550814 "ULS2" NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1138 2532733 2550051 2550292 "ULS" NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1137 2531767 2532460 2532574 "UINT8" NIL UINT8 (NIL) -8 NIL NIL 2532685) (-1136 2530800 2531493 2531607 "UINT64" NIL UINT64 (NIL) -8 NIL NIL 2531718) (-1135 2529833 2530526 2530640 "UINT32" NIL UINT32 (NIL) -8 NIL NIL 2530751) (-1134 2528866 2529559 2529673 "UINT16" NIL UINT16 (NIL) -8 NIL NIL 2529784) (-1133 2526935 2528094 2528124 "UFD" 2528335 UFD (NIL) -9 NIL 2528448 NIL) (-1132 2526779 2526836 2526930 "UFD-" NIL UFD- (NIL T) -7 NIL NIL NIL) (-1131 2526031 2526238 2526454 "UDVO" NIL UDVO (NIL) -7 NIL NIL NIL) (-1130 2524251 2524704 2525169 "UDPO" NIL UDPO (NIL T) -7 NIL NIL NIL) (-1129 2523976 2524216 2524246 "TYPEAST" NIL TYPEAST (NIL) -8 NIL NIL NIL) (-1128 2523914 2523919 2523949 "TYPE" 2523954 TYPE (NIL) -9 NIL 2523961 NIL) (-1127 2523073 2523293 2523533 "TWOFACT" NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1126 2522251 2522682 2522917 "TUPLE" NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1125 2520405 2520978 2521517 "TUBETOOL" NIL TUBETOOL (NIL) -7 NIL NIL NIL) (-1124 2519439 2519675 2519911 "TUBE" NIL TUBE (NIL T) -8 NIL NIL NIL) (-1123 2507793 2512261 2512357 "TSETCAT" 2517572 TSETCAT (NIL T T T T) -9 NIL 2519084 NIL) (-1122 2504130 2505946 2507788 "TSETCAT-" NIL TSETCAT- (NIL T T T T T) -7 NIL NIL NIL) (-1121 2498586 2503356 2503638 "TS" NIL TS (NIL T) -8 NIL NIL NIL) (-1120 2493923 2494936 2495865 "TRMANIP" NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1119 2493420 2493495 2493658 "TRIMAT" NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1118 2491496 2491786 2492141 "TRIGMNIP" NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1117 2490980 2491129 2491159 "TRIGCAT" 2491372 TRIGCAT (NIL) -9 NIL NIL NIL) (-1116 2490731 2490834 2490975 "TRIGCAT-" NIL TRIGCAT- (NIL T) -7 NIL NIL NIL) (-1115 2487727 2489840 2490118 "TREE" NIL TREE (NIL T) -8 NIL NIL NIL) (-1114 2486833 2487529 2487559 "TRANFUN" 2487594 TRANFUN (NIL) -9 NIL 2487660 NIL) (-1113 2486297 2486548 2486828 "TRANFUN-" NIL TRANFUN- (NIL T) -7 NIL NIL NIL) (-1112 2486134 2486172 2486233 "TOPSP" NIL TOPSP (NIL) -7 NIL NIL NIL) (-1111 2485591 2485722 2485873 "TOOLSIGN" NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1110 2484332 2484989 2485225 "TEXTFILE" NIL TEXTFILE (NIL) -8 NIL NIL NIL) (-1109 2484144 2484181 2484253 "TEX1" NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1108 2482358 2483004 2483433 "TEX" NIL TEX (NIL) -8 NIL NIL NIL) (-1107 2480738 2481075 2481397 "TBCMPPK" NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1106 2471796 2478539 2478595 "TBAGG" 2478997 TBAGG (NIL T T) -9 NIL 2479210 NIL) (-1105 2468327 2470019 2471791 "TBAGG-" NIL TBAGG- (NIL T T T) -7 NIL NIL NIL) (-1104 2467804 2467929 2468074 "TANEXP" NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1103 2467314 2467634 2467724 "TALGOP" NIL TALGOP (NIL T) -8 NIL NIL NIL) (-1102 2466811 2466928 2467066 "TABLEAU" NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1101 2459898 2466713 2466806 "TABLE" NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1100 2455651 2456946 2458191 "TABLBUMP" NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1099 2455020 2455179 2455360 "SYSTEM" NIL SYSTEM (NIL) -7 NIL NIL NIL) (-1098 2452174 2452927 2453710 "SYSSOLP" NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1097 2451948 2452138 2452169 "SYSPTR" NIL SYSPTR (NIL) -8 NIL NIL NIL) (-1096 2450902 2451587 2451713 "SYSNNI" NIL SYSNNI (NIL NIL) -8 NIL NIL 2451899) (-1095 2450166 2450714 2450793 "SYSINT" NIL SYSINT (NIL NIL) -8 NIL NIL 2450853) (-1094 2446989 2448148 2448848 "SYNTAX" NIL SYNTAX (NIL) -8 NIL NIL NIL) (-1093 2444672 2445355 2445989 "SYMTAB" NIL SYMTAB (NIL) -8 NIL NIL NIL) (-1092 2440750 2441796 2442773 "SYMS" NIL SYMS (NIL) -8 NIL NIL NIL) (-1091 2437913 2440405 2440634 "SYMPOLY" NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1090 2437509 2437596 2437718 "SYMFUNC" NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1089 2434133 2435607 2436426 "SYMBOL" NIL SYMBOL (NIL) -8 NIL NIL NIL) (-1088 2427157 2433330 2433623 "SUTS" NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1087 2418907 2426748 2427010 "SUPXS" NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1086 2418186 2418325 2418542 "SUPFRACF" NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1085 2417870 2417935 2418046 "SUP2" NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1084 2408657 2417582 2417707 "SUP" NIL SUP (NIL T) -8 NIL NIL NIL) (-1083 2407387 2407685 2408040 "SUMRF" NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1082 2406792 2406870 2407061 "SUMFS" NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1081 2389008 2406291 2406532 "SULS" NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1080 2388607 2388879 2388948 "SUCHTAST" NIL SUCHTAST (NIL) -8 NIL NIL NIL) (-1079 2387943 2388224 2388364 "SUCH" NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1078 2382545 2383804 2384757 "SUBSPACE" NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1077 2382077 2382177 2382341 "SUBRESP" NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1076 2377188 2378470 2379617 "STTFNC" NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1075 2371646 2373117 2374428 "STTF" NIL STTF (NIL T) -7 NIL NIL NIL) (-1074 2364561 2366625 2368416 "STTAYLOR" NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1073 2357391 2364473 2364556 "STRTBL" NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1072 2352085 2357105 2357220 "STRING" NIL STRING (NIL) -8 NIL NIL NIL) (-1071 2351672 2351755 2351899 "STREAM3" NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1070 2350823 2351024 2351259 "STREAM2" NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1069 2350563 2350621 2350714 "STREAM1" NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1068 2343301 2348768 2349374 "STREAM" NIL STREAM (NIL T) -8 NIL NIL NIL) (-1067 2342477 2342682 2342913 "STINPROD" NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1066 2341722 2342093 2342240 "STEPAST" NIL STEPAST (NIL) -8 NIL NIL NIL) (-1065 2341210 2341452 2341482 "STEP" 2341576 STEP (NIL) -9 NIL 2341647 NIL) (-1064 2334313 2341128 2341205 "STBL" NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1063 2328528 2333111 2333154 "STAGG" 2333581 STAGG (NIL T) -9 NIL 2333755 NIL) (-1062 2326907 2327655 2328523 "STAGG-" NIL STAGG- (NIL T T) -7 NIL NIL NIL) (-1061 2325064 2326734 2326826 "STACK" NIL STACK (NIL T) -8 NIL NIL NIL) (-1060 2324375 2324883 2324913 "SRING" 2324918 SRING (NIL) -9 NIL 2324938 NIL) (-1059 2316997 2322913 2323352 "SREGSET" NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1058 2310771 2312210 2313714 "SRDCMPK" NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1057 2303196 2308107 2308137 "SRAGG" 2309436 SRAGG (NIL) -9 NIL 2310040 NIL) (-1056 2302493 2302813 2303191 "SRAGG-" NIL SRAGG- (NIL T) -7 NIL NIL NIL) (-1055 2296612 2301815 2302238 "SQMATRIX" NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1054 2290825 2293994 2294716 "SPLTREE" NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1053 2287254 2288073 2288710 "SPLNODE" NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1052 2286229 2286534 2286564 "SPFCAT" 2287008 SPFCAT (NIL) -9 NIL NIL NIL) (-1051 2285166 2285418 2285682 "SPECOUT" NIL SPECOUT (NIL) -7 NIL NIL NIL) (-1050 2275924 2278198 2278228 "SPADXPT" 2282865 SPADXPT (NIL) -9 NIL 2284989 NIL) (-1049 2275726 2275772 2275841 "SPADPRSR" NIL SPADPRSR (NIL) -7 NIL NIL NIL) (-1048 2273382 2275690 2275721 "SPADAST" NIL SPADAST (NIL) -8 NIL NIL NIL) (-1047 2265056 2267145 2267187 "SPACEC" 2271502 SPACEC (NIL T) -9 NIL 2273307 NIL) (-1046 2262885 2265003 2265051 "SPACE3" NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1045 2261818 2262007 2262296 "SORTPAK" NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1044 2260222 2260555 2260966 "SOLVETRA" NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1043 2259487 2259721 2259982 "SOLVESER" NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1042 2255667 2256627 2257622 "SOLVERAD" NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1041 2252025 2252724 2253453 "SOLVEFOR" NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1040 2245811 2251365 2251461 "SNTSCAT" 2251466 SNTSCAT (NIL T T T T) -9 NIL 2251536 NIL) (-1039 2239696 2244452 2244842 "SMTS" NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1038 2233532 2239615 2239691 "SMP" NIL SMP (NIL T T) -8 NIL NIL NIL) (-1037 2231964 2232295 2232693 "SMITH" NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1036 2223633 2228548 2228650 "SMATCAT" 2229993 SMATCAT (NIL NIL T T T) -9 NIL 2230541 NIL) (-1035 2221474 2222458 2223628 "SMATCAT-" NIL SMATCAT- (NIL T NIL T T T) -7 NIL NIL NIL) (-1034 2219066 2220680 2220723 "SKAGG" 2220984 SKAGG (NIL T) -9 NIL 2221118 NIL) (-1033 2215176 2218886 2218997 "SINT" NIL SINT (NIL) -8 NIL NIL 2219038) (-1032 2214986 2215030 2215096 "SIMPAN" NIL SIMPAN (NIL) -7 NIL NIL NIL) (-1031 2214061 2214293 2214561 "SIGNRF" NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1030 2213065 2213227 2213503 "SIGNEF" NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1029 2212411 2212751 2212874 "SIGAST" NIL SIGAST (NIL) -8 NIL NIL NIL) (-1028 2211757 2212064 2212204 "SIG" NIL SIG (NIL) -8 NIL NIL NIL) (-1027 2209868 2210360 2210866 "SHP" NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1026 2203407 2209787 2209863 "SHDP" NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1025 2202910 2203147 2203177 "SGROUP" 2203270 SGROUP (NIL) -9 NIL 2203332 NIL) (-1024 2202800 2202832 2202905 "SGROUP-" NIL SGROUP- (NIL T) -7 NIL NIL NIL) (-1023 2202438 2202478 2202519 "SGPOPC" 2202524 SGPOPC (NIL T) -9 NIL 2202725 NIL) (-1022 2201972 2202249 2202355 "SGPOP" NIL SGPOP (NIL T) -8 NIL NIL NIL) (-1021 2199395 2200164 2200886 "SGCF" NIL SGCF (NIL) -7 NIL NIL NIL) (-1020 2193280 2198834 2198930 "SFRTCAT" 2198935 SFRTCAT (NIL T T T T) -9 NIL 2198973 NIL) (-1019 2187672 2188785 2189912 "SFRGCD" NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1018 2181848 2183009 2184173 "SFQCMPK" NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1017 2180820 2181722 2181843 "SEXOF" NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1016 2176428 2177323 2177418 "SEXCAT" 2180031 SEXCAT (NIL T T T T T) -9 NIL 2180582 NIL) (-1015 2175401 2176355 2176423 "SEX" NIL SEX (NIL) -8 NIL NIL NIL) (-1014 2173792 2174377 2174679 "SETMN" NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1013 2173315 2173500 2173530 "SETCAT" 2173647 SETCAT (NIL) -9 NIL 2173731 NIL) (-1012 2173147 2173211 2173310 "SETCAT-" NIL SETCAT- (NIL T) -7 NIL NIL NIL) (-1011 2169370 2171601 2171644 "SETAGG" 2172512 SETAGG (NIL T) -9 NIL 2172850 NIL) (-1010 2168976 2169128 2169365 "SETAGG-" NIL SETAGG- (NIL T T) -7 NIL NIL NIL) (-1009 2165930 2168923 2168971 "SET" NIL SET (NIL T) -8 NIL NIL NIL) (-1008 2165396 2165706 2165806 "SEQAST" NIL SEQAST (NIL) -8 NIL NIL NIL) (-1007 2164523 2164889 2164950 "SEGXCAT" 2165236 SEGXCAT (NIL T T) -9 NIL 2165356 NIL) (-1006 2163448 2163716 2163759 "SEGCAT" 2164281 SEGCAT (NIL T) -9 NIL 2164502 NIL) (-1005 2163128 2163193 2163306 "SEGBIND2" NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1004 2162194 2162664 2162872 "SEGBIND" NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1003 2161772 2162051 2162127 "SEGAST" NIL SEGAST (NIL) -8 NIL NIL NIL) (-1002 2161137 2161273 2161477 "SEG2" NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1001 2160203 2160950 2161132 "SEG" NIL SEG (NIL T) -8 NIL NIL NIL) (-1000 2159456 2160151 2160198 "SDVAR" NIL SDVAR (NIL T) -8 NIL NIL NIL) (-999 2151007 2159325 2159451 "SDPOL" NIL SDPOL (NIL T) -8 NIL NIL NIL) (-998 2149867 2150157 2150474 "SCPKG" NIL SCPKG (NIL T) -7 NIL NIL NIL) (-997 2149173 2149385 2149573 "SCOPE" NIL SCOPE (NIL) -8 NIL NIL NIL) (-996 2148523 2148680 2148856 "SCACHE" NIL SCACHE (NIL T) -7 NIL NIL NIL) (-995 2148096 2148327 2148355 "SASTCAT" 2148360 SASTCAT (NIL) -9 NIL 2148373 NIL) (-994 2147563 2147988 2148062 "SAOS" NIL SAOS (NIL) -8 NIL NIL NIL) (-993 2147166 2147207 2147378 "SAERFFC" NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-992 2146797 2146838 2146995 "SAEFACT" NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-991 2139942 2146714 2146792 "SAE" NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-990 2138592 2138921 2139317 "RURPK" NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-989 2137353 2137714 2138014 "RULESET" NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-988 2136977 2137198 2137279 "RULECOLD" NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-987 2134437 2135071 2135524 "RULE" NIL RULE (NIL T T T) -8 NIL NIL NIL) (-986 2134276 2134309 2134377 "RTVALUE" NIL RTVALUE (NIL) -8 NIL NIL NIL) (-985 2133767 2134070 2134161 "RSTRCAST" NIL RSTRCAST (NIL) -8 NIL NIL NIL) (-984 2129395 2130263 2131174 "RSETGCD" NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-983 2118214 2123768 2123862 "RSETCAT" 2127918 RSETCAT (NIL T T T T) -9 NIL 2129006 NIL) (-982 2116752 2117394 2118209 "RSETCAT-" NIL RSETCAT- (NIL T T T T T) -7 NIL NIL NIL) (-981 2110526 2111971 2113478 "RSDCMPK" NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-980 2108408 2108965 2109037 "RRCC" 2110110 RRCC (NIL T T) -9 NIL 2110451 NIL) (-979 2107933 2108132 2108403 "RRCC-" NIL RRCC- (NIL T T T) -7 NIL NIL NIL) (-978 2107403 2107713 2107811 "RPTAST" NIL RPTAST (NIL) -8 NIL NIL NIL) (-977 2080019 2090668 2090732 "RPOLCAT" 2101206 RPOLCAT (NIL T T T) -9 NIL 2104351 NIL) (-976 2074118 2076941 2080014 "RPOLCAT-" NIL RPOLCAT- (NIL T T T T) -7 NIL NIL NIL) (-975 2070349 2073866 2074004 "ROMAN" NIL ROMAN (NIL) -8 NIL NIL NIL) (-974 2068677 2069416 2069672 "ROIRC" NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-973 2064382 2067132 2067160 "RNS" 2067422 RNS (NIL) -9 NIL 2067674 NIL) (-972 2063285 2063772 2064309 "RNS-" NIL RNS- (NIL T) -7 NIL NIL NIL) (-971 2062403 2062804 2063004 "RNGBIND" NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-970 2061691 2062191 2062219 "RNG" 2062224 RNG (NIL) -9 NIL 2062245 NIL) (-969 2060984 2061458 2061498 "RMODULE" 2061503 RMODULE (NIL T) -9 NIL 2061529 NIL) (-968 2059923 2060029 2060359 "RMCAT2" NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-967 2056801 2059513 2059806 "RMATRIX" NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-966 2049481 2051942 2052054 "RMATCAT" 2055359 RMATCAT (NIL NIL NIL T T T) -9 NIL 2056336 NIL) (-965 2048998 2049177 2049476 "RMATCAT-" NIL RMATCAT- (NIL T NIL NIL T T T) -7 NIL NIL NIL) (-964 2048566 2048777 2048818 "RLINSET" 2048879 RLINSET (NIL T) -9 NIL 2048923 NIL) (-963 2048211 2048292 2048418 "RINTERP" NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-962 2047119 2047788 2047816 "RING" 2047871 RING (NIL) -9 NIL 2047963 NIL) (-961 2046964 2047020 2047114 "RING-" NIL RING- (NIL T) -7 NIL NIL NIL) (-960 2046018 2046285 2046541 "RIDIST" NIL RIDIST (NIL) -7 NIL NIL NIL) (-959 2037005 2045646 2045847 "RGCHAIN" NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-958 2036261 2036741 2036780 "RGBCSPC" 2036837 RGBCSPC (NIL T) -9 NIL 2036888 NIL) (-957 2035326 2035781 2035820 "RGBCMDL" 2036048 RGBCMDL (NIL T) -9 NIL 2036162 NIL) (-956 2035038 2035107 2035208 "RFFACTOR" NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-955 2034801 2034842 2034937 "RFFACT" NIL RFFACT (NIL T) -7 NIL NIL NIL) (-954 2033225 2033655 2034035 "RFDIST" NIL RFDIST (NIL) -7 NIL NIL NIL) (-953 2030812 2031480 2032148 "RF" NIL RF (NIL T) -7 NIL NIL NIL) (-952 2030362 2030460 2030620 "RETSOL" NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-951 2029984 2030082 2030123 "RETRACT" 2030254 RETRACT (NIL T) -9 NIL 2030341 NIL) (-950 2029864 2029895 2029979 "RETRACT-" NIL RETRACT- (NIL T T) -7 NIL NIL NIL) (-949 2029466 2029738 2029805 "RETAST" NIL RETAST (NIL) -8 NIL NIL NIL) (-948 2028010 2028837 2029034 "RESRING" NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-947 2027701 2027762 2027858 "RESLATC" NIL RESLATC (NIL T) -7 NIL NIL NIL) (-946 2027444 2027485 2027590 "REPSQ" NIL REPSQ (NIL T) -7 NIL NIL NIL) (-945 2027179 2027220 2027329 "REPDB" NIL REPDB (NIL T) -7 NIL NIL NIL) (-944 2022250 2023701 2024916 "REP2" NIL REP2 (NIL T) -7 NIL NIL NIL) (-943 2019349 2020107 2020915 "REP1" NIL REP1 (NIL T) -7 NIL NIL NIL) (-942 2017318 2017940 2018540 "REP" NIL REP (NIL) -7 NIL NIL NIL) (-941 2009953 2015869 2016305 "REGSET" NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-940 2009265 2009545 2009694 "REF" NIL REF (NIL T) -8 NIL NIL NIL) (-939 2008750 2008865 2009030 "REDORDER" NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-938 2004407 2008153 2008374 "RECLOS" NIL RECLOS (NIL T) -8 NIL NIL NIL) (-937 2003639 2003838 2004051 "REALSOLV" NIL REALSOLV (NIL) -7 NIL NIL NIL) (-936 2000929 2001767 2002649 "REAL0Q" NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-935 1997511 1998547 1999606 "REAL0" NIL REAL0 (NIL T) -7 NIL NIL NIL) (-934 1997347 1997400 1997428 "REAL" 1997433 REAL (NIL) -9 NIL 1997468 NIL) (-933 1996837 1997141 1997232 "RDUCEAST" NIL RDUCEAST (NIL) -8 NIL NIL NIL) (-932 1996317 1996395 1996600 "RDIV" NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-931 1995550 1995742 1995953 "RDIST" NIL RDIST (NIL T) -7 NIL NIL NIL) (-930 1994438 1994735 1995102 "RDETRS" NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-929 1992705 1993175 1993708 "RDETR" NIL RDETR (NIL T T) -7 NIL NIL NIL) (-928 1991627 1991904 1992291 "RDEEFS" NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-927 1990454 1990763 1991182 "RDEEF" NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-926 1983866 1987314 1987342 "RCFIELD" 1988619 RCFIELD (NIL) -9 NIL 1989349 NIL) (-925 1982484 1983096 1983793 "RCFIELD-" NIL RCFIELD- (NIL T) -7 NIL NIL NIL) (-924 1978684 1980576 1980617 "RCAGG" 1981684 RCAGG (NIL T) -9 NIL 1982145 NIL) (-923 1978411 1978521 1978679 "RCAGG-" NIL RCAGG- (NIL T T) -7 NIL NIL NIL) (-922 1977856 1977985 1978146 "RATRET" NIL RATRET (NIL T) -7 NIL NIL NIL) (-921 1977473 1977552 1977671 "RATFACT" NIL RATFACT (NIL T) -7 NIL NIL NIL) (-920 1976888 1977038 1977188 "RANDSRC" NIL RANDSRC (NIL) -7 NIL NIL NIL) (-919 1976670 1976720 1976791 "RADUTIL" NIL RADUTIL (NIL) -7 NIL NIL NIL) (-918 1969176 1975788 1976096 "RADIX" NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-917 1958942 1969043 1969171 "RADFF" NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-916 1958576 1958669 1958697 "RADCAT" 1958854 RADCAT (NIL) -9 NIL NIL NIL) (-915 1958414 1958474 1958571 "RADCAT-" NIL RADCAT- (NIL T) -7 NIL NIL NIL) (-914 1956514 1958245 1958334 "QUEUE" NIL QUEUE (NIL T) -8 NIL NIL NIL) (-913 1956195 1956244 1956371 "QUATCT2" NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-912 1948546 1952566 1952606 "QUATCAT" 1953384 QUATCAT (NIL T) -9 NIL 1954148 NIL) (-911 1945796 1947076 1948452 "QUATCAT-" NIL QUATCAT- (NIL T T) -7 NIL NIL NIL) (-910 1941700 1945746 1945791 "QUAT" NIL QUAT (NIL T) -8 NIL NIL NIL) (-909 1939087 1940754 1940795 "QUAGG" 1941170 QUAGG (NIL T) -9 NIL 1941344 NIL) (-908 1938689 1938961 1939028 "QQUTAST" NIL QQUTAST (NIL) -8 NIL NIL NIL) (-907 1937727 1938325 1938488 "QFORM" NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-906 1937408 1937457 1937584 "QFCAT2" NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-905 1927095 1933202 1933242 "QFCAT" 1933900 QFCAT (NIL T) -9 NIL 1934893 NIL) (-904 1923979 1925418 1927001 "QFCAT-" NIL QFCAT- (NIL T T) -7 NIL NIL NIL) (-903 1923525 1923659 1923789 "QEQUAT" NIL QEQUAT (NIL) -8 NIL NIL NIL) (-902 1917721 1918882 1920044 "QCMPACK" NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-901 1917140 1917320 1917552 "QALGSET2" NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-900 1914962 1915490 1915913 "QALGSET" NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-899 1913861 1914103 1914420 "PWFFINTB" NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-898 1912222 1912420 1912773 "PUSHVAR" NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-897 1907978 1909194 1909235 "PTRANFN" 1911119 PTRANFN (NIL T) -9 NIL NIL NIL) (-896 1906625 1906970 1907291 "PTPACK" NIL PTPACK (NIL T) -7 NIL NIL NIL) (-895 1906318 1906381 1906488 "PTFUNC2" NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-894 1900391 1905114 1905154 "PTCAT" 1905446 PTCAT (NIL T) -9 NIL 1905599 NIL) (-893 1900084 1900125 1900249 "PSQFR" NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-892 1898963 1899279 1899613 "PSEUDLIN" NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-891 1887842 1890403 1892712 "PSETPK" NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-890 1880749 1883645 1883739 "PSETCAT" 1886713 PSETCAT (NIL T T T T) -9 NIL 1887520 NIL) (-889 1879199 1879933 1880744 "PSETCAT-" NIL PSETCAT- (NIL T T T T T) -7 NIL NIL NIL) (-888 1878518 1878713 1878741 "PSCURVE" 1879009 PSCURVE (NIL) -9 NIL 1879176 NIL) (-887 1874182 1875940 1876004 "PSCAT" 1876839 PSCAT (NIL T T T) -9 NIL 1877078 NIL) (-886 1873496 1873778 1874177 "PSCAT-" NIL PSCAT- (NIL T T T T) -7 NIL NIL NIL) (-885 1871925 1872808 1873071 "PRTITION" NIL PRTITION (NIL) -8 NIL NIL NIL) (-884 1871416 1871719 1871810 "PRTDAST" NIL PRTDAST (NIL) -8 NIL NIL NIL) (-883 1862436 1864858 1867046 "PRS" NIL PRS (NIL T T) -7 NIL NIL NIL) (-882 1860179 1861756 1861796 "PRQAGG" 1861979 PRQAGG (NIL T) -9 NIL 1862080 NIL) (-881 1859352 1859798 1859826 "PROPLOG" 1859965 PROPLOG (NIL) -9 NIL 1860079 NIL) (-880 1859027 1859090 1859213 "PROPFUN2" NIL PROPFUN2 (NIL T T) -7 NIL NIL NIL) (-879 1858463 1858602 1858774 "PROPFUN1" NIL PROPFUN1 (NIL T) -7 NIL NIL NIL) (-878 1856711 1857474 1857771 "PROPFRML" NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-877 1856263 1856395 1856523 "PROPERTY" NIL PROPERTY (NIL) -8 NIL NIL NIL) (-876 1850919 1855203 1856023 "PRODUCT" NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-875 1850748 1850786 1850845 "PRINT" NIL PRINT (NIL) -7 NIL NIL NIL) (-874 1850187 1850327 1850478 "PRIMES" NIL PRIMES (NIL T) -7 NIL NIL NIL) (-873 1848655 1849074 1849540 "PRIMELT" NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-872 1848372 1848433 1848461 "PRIMCAT" 1848585 PRIMCAT (NIL) -9 NIL NIL NIL) (-871 1847543 1847739 1847967 "PRIMARR2" NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-870 1843421 1847493 1847538 "PRIMARR" NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-869 1843120 1843182 1843293 "PREASSOC" NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-868 1840320 1842769 1843002 "PR" NIL PR (NIL T T) -8 NIL NIL NIL) (-867 1839771 1839928 1839956 "PPCURVE" 1840161 PPCURVE (NIL) -9 NIL 1840297 NIL) (-866 1839384 1839629 1839712 "PORTNUM" NIL PORTNUM (NIL) -8 NIL NIL NIL) (-865 1837140 1837561 1838153 "POLYROOT" NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-864 1836583 1836647 1836880 "POLYLIFT" NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-863 1833303 1833789 1834400 "POLYCATQ" NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-862 1818958 1825023 1825087 "POLYCAT" 1828572 POLYCAT (NIL T T T) -9 NIL 1830449 NIL) (-861 1814468 1816615 1818953 "POLYCAT-" NIL POLYCAT- (NIL T T T T) -7 NIL NIL NIL) (-860 1814125 1814199 1814318 "POLY2UP" NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-859 1813818 1813881 1813988 "POLY2" NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-858 1807245 1813551 1813710 "POLY" NIL POLY (NIL T) -8 NIL NIL NIL) (-857 1806132 1806395 1806671 "POLUTIL" NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-856 1804736 1805049 1805379 "POLTOPOL" NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-855 1799898 1804686 1804731 "POINT" NIL POINT (NIL T) -8 NIL NIL NIL) (-854 1798386 1798797 1799172 "PNTHEORY" NIL PNTHEORY (NIL) -7 NIL NIL NIL) (-853 1797143 1797452 1797848 "PMTOOLS" NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-852 1796814 1796898 1797015 "PMSYM" NIL PMSYM (NIL T) -7 NIL NIL NIL) (-851 1796393 1796468 1796642 "PMQFCAT" NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-850 1795879 1795975 1796135 "PMPREDFS" NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-849 1795351 1795471 1795625 "PMPRED" NIL PMPRED (NIL T) -7 NIL NIL NIL) (-848 1794246 1794464 1794841 "PMPLCAT" NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-847 1793857 1793942 1794094 "PMLSAGG" NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-846 1793408 1793490 1793671 "PMKERNEL" NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-845 1793100 1793181 1793294 "PMINS" NIL PMINS (NIL T) -7 NIL NIL NIL) (-844 1792613 1792688 1792896 "PMFS" NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-843 1791961 1792089 1792291 "PMDOWN" NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-842 1791323 1791457 1791620 "PMASSFS" NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-841 1790627 1790809 1790990 "PMASS" NIL PMASS (NIL) -7 NIL NIL NIL) (-840 1790350 1790424 1790518 "PLOTTOOL" NIL PLOTTOOL (NIL) -7 NIL NIL NIL) (-839 1786918 1788107 1789023 "PLOT3D" NIL PLOT3D (NIL) -8 NIL NIL NIL) (-838 1786002 1786203 1786438 "PLOT1" NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-837 1781567 1782951 1784093 "PLOT" NIL PLOT (NIL) -8 NIL NIL NIL) (-836 1761488 1766375 1771222 "PLEQN" NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-835 1761228 1761281 1761384 "PINTERPA" NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-834 1760669 1760803 1760983 "PINTERP" NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-833 1758740 1759899 1759927 "PID" 1760124 PID (NIL) -9 NIL 1760251 NIL) (-832 1758528 1758571 1758646 "PICOERCE" NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-831 1757715 1758375 1758462 "PI" NIL PI (NIL) -8 NIL NIL 1758502) (-830 1757167 1757318 1757494 "PGROEB" NIL PGROEB (NIL T) -7 NIL NIL NIL) (-829 1753495 1754453 1755358 "PGE" NIL PGE (NIL) -7 NIL NIL NIL) (-828 1751859 1752148 1752514 "PGCD" NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-827 1751301 1751416 1751577 "PFRPAC" NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-826 1747906 1750170 1750523 "PFR" NIL PFR (NIL T) -8 NIL NIL NIL) (-825 1746512 1746792 1747117 "PFOTOOLS" NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-824 1745277 1745531 1745879 "PFOQ" NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-823 1743987 1744214 1744566 "PFO" NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-822 1741059 1742557 1742585 "PFECAT" 1743178 PFECAT (NIL) -9 NIL 1743555 NIL) (-821 1740682 1740847 1741054 "PFECAT-" NIL PFECAT- (NIL T) -7 NIL NIL NIL) (-820 1739506 1739788 1740089 "PFBRU" NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-819 1737688 1738075 1738505 "PFBR" NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-818 1733722 1737614 1737683 "PF" NIL PF (NIL NIL) -8 NIL NIL NIL) (-817 1729625 1730772 1731639 "PERMGRP" NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-816 1727557 1728646 1728687 "PERMCAT" 1729086 PERMCAT (NIL T) -9 NIL 1729383 NIL) (-815 1727253 1727300 1727423 "PERMAN" NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-814 1723702 1725383 1726028 "PERM" NIL PERM (NIL T) -8 NIL NIL NIL) (-813 1721167 1723457 1723578 "PENDTREE" NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-812 1720036 1720299 1720340 "PDSPC" 1720873 PDSPC (NIL T) -9 NIL 1721118 NIL) (-811 1719403 1719669 1720031 "PDSPC-" NIL PDSPC- (NIL T T) -7 NIL NIL NIL) (-810 1718100 1719031 1719072 "PDRING" 1719077 PDRING (NIL T) -9 NIL 1719104 NIL) (-809 1716841 1717599 1717652 "PDMOD" 1717657 PDMOD (NIL T T) -9 NIL 1717760 NIL) (-808 1715934 1716146 1716395 "PDECOMP" NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-807 1715539 1715606 1715660 "PDDOM" 1715825 PDDOM (NIL T T) -9 NIL 1715905 NIL) (-806 1715391 1715427 1715534 "PDDOM-" NIL PDDOM- (NIL T T T) -7 NIL NIL NIL) (-805 1715177 1715216 1715305 "PCOMP" NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-804 1713494 1714248 1714547 "PBWLB" NIL PBWLB (NIL T) -8 NIL NIL NIL) (-803 1713183 1713246 1713355 "PATTERN2" NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-802 1711321 1711751 1712202 "PATTERN1" NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-801 1704941 1706770 1708062 "PATTERN" NIL PATTERN (NIL T) -8 NIL NIL NIL) (-800 1704572 1704645 1704777 "PATRES2" NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-799 1702274 1702954 1703435 "PATRES" NIL PATRES (NIL T T) -8 NIL NIL NIL) (-798 1700478 1700906 1701309 "PATMATCH" NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-797 1699924 1700172 1700213 "PATMAB" 1700320 PATMAB (NIL T) -9 NIL 1700403 NIL) (-796 1698571 1698975 1699232 "PATLRES" NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-795 1698109 1698240 1698281 "PATAB" 1698286 PATAB (NIL T) -9 NIL 1698458 NIL) (-794 1696652 1697089 1697512 "PARTPERM" NIL PARTPERM (NIL) -7 NIL NIL NIL) (-793 1696330 1696405 1696507 "PARSURF" NIL PARSURF (NIL T) -8 NIL NIL NIL) (-792 1696019 1696082 1696191 "PARSU2" NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-791 1695824 1695870 1695937 "PARSER" NIL PARSER (NIL) -7 NIL NIL NIL) (-790 1695502 1695577 1695679 "PARSCURV" NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-789 1695191 1695254 1695363 "PARSC2" NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-788 1694882 1694952 1695049 "PARPCURV" NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-787 1694571 1694634 1694743 "PARPC2" NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-786 1693732 1694111 1694290 "PARAMAST" NIL PARAMAST (NIL) -8 NIL NIL NIL) (-785 1693339 1693437 1693556 "PAN2EXPR" NIL PAN2EXPR (NIL) -7 NIL NIL NIL) (-784 1692307 1692732 1692951 "PALETTE" NIL PALETTE (NIL) -8 NIL NIL NIL) (-783 1690972 1691626 1691986 "PAIR" NIL PAIR (NIL T T) -8 NIL NIL NIL) (-782 1684126 1690376 1690570 "PADICRC" NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-781 1676611 1683624 1683808 "PADICRAT" NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-780 1673398 1675251 1675291 "PADICCT" 1675872 PADICCT (NIL NIL) -9 NIL 1676154 NIL) (-779 1671452 1673348 1673393 "PADIC" NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-778 1670614 1670824 1671090 "PADEPAC" NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-777 1669956 1670099 1670303 "PADE" NIL PADE (NIL T T T) -7 NIL NIL NIL) (-776 1668401 1669364 1669642 "OWP" NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-775 1667925 1668184 1668281 "OVERSET" NIL OVERSET (NIL) -8 NIL NIL NIL) (-774 1666984 1667662 1667834 "OVAR" NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-773 1657406 1660275 1662474 "OUTFORM" NIL OUTFORM (NIL) -8 NIL NIL NIL) (-772 1656798 1657112 1657238 "OUTBFILE" NIL OUTBFILE (NIL) -8 NIL NIL NIL) (-771 1656075 1656270 1656298 "OUTBCON" 1656616 OUTBCON (NIL) -9 NIL 1656782 NIL) (-770 1655783 1655913 1656070 "OUTBCON-" NIL OUTBCON- (NIL T) -7 NIL NIL NIL) (-769 1655164 1655309 1655470 "OUT" NIL OUT (NIL) -7 NIL NIL NIL) (-768 1654535 1654962 1655051 "OSI" NIL OSI (NIL) -8 NIL NIL NIL) (-767 1653950 1654365 1654393 "OSGROUP" 1654398 OSGROUP (NIL) -9 NIL 1654420 NIL) (-766 1652914 1653175 1653460 "ORTHPOL" NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-765 1650247 1652789 1652909 "OREUP" NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-764 1647452 1649998 1650124 "ORESUP" NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-763 1645470 1645998 1646558 "OREPCTO" NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-762 1638874 1641352 1641392 "OREPCAT" 1643713 OREPCAT (NIL T) -9 NIL 1644815 NIL) (-761 1636900 1637834 1638869 "OREPCAT-" NIL OREPCAT- (NIL T T) -7 NIL NIL NIL) (-760 1636097 1636368 1636396 "ORDTYPE" 1636701 ORDTYPE (NIL) -9 NIL 1636859 NIL) (-759 1635631 1635842 1636092 "ORDTYPE-" NIL ORDTYPE- (NIL T) -7 NIL NIL NIL) (-758 1635093 1635469 1635626 "ORDSTRCT" NIL ORDSTRCT (NIL T NIL) -8 NIL NIL NIL) (-757 1634587 1634950 1634978 "ORDSET" 1634983 ORDSET (NIL) -9 NIL 1635005 NIL) (-756 1633227 1634187 1634215 "ORDRING" 1634220 ORDRING (NIL) -9 NIL 1634248 NIL) (-755 1632475 1633032 1633060 "ORDMON" 1633065 ORDMON (NIL) -9 NIL 1633086 NIL) (-754 1631779 1631941 1632133 "ORDFUNS" NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-753 1630990 1631498 1631526 "ORDFIN" 1631591 ORDFIN (NIL) -9 NIL 1631665 NIL) (-752 1630384 1630523 1630709 "ORDCOMP2" NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-751 1627158 1629352 1629758 "ORDCOMP" NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-750 1626565 1626920 1627025 "OPSIG" NIL OPSIG (NIL) -8 NIL NIL NIL) (-749 1626373 1626418 1626484 "OPQUERY" NIL OPQUERY (NIL) -7 NIL NIL NIL) (-748 1625674 1625950 1625991 "OPERCAT" 1626202 OPERCAT (NIL T) -9 NIL 1626298 NIL) (-747 1625486 1625553 1625669 "OPERCAT-" NIL OPERCAT- (NIL T T) -7 NIL NIL NIL) (-746 1622916 1624288 1624784 "OP" NIL OP (NIL T) -8 NIL NIL NIL) (-745 1622337 1622464 1622638 "ONECOMP2" NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-744 1619337 1621476 1621842 "ONECOMP" NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-743 1615968 1618767 1618807 "OMSAGG" 1618868 OMSAGG (NIL T) -9 NIL 1618932 NIL) (-742 1614444 1615639 1615807 "OMLO" NIL OMLO (NIL T T) -8 NIL NIL NIL) (-741 1612715 1613894 1613922 "OINTDOM" 1613927 OINTDOM (NIL) -9 NIL 1613948 NIL) (-740 1610145 1611717 1612046 "OFMONOID" NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-739 1609399 1610095 1610140 "ODVAR" NIL ODVAR (NIL T) -8 NIL NIL NIL) (-738 1606665 1609240 1609394 "ODR" NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-737 1598266 1606536 1606660 "ODPOL" NIL ODPOL (NIL T) -8 NIL NIL NIL) (-736 1591776 1598157 1598261 "ODP" NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-735 1590748 1590985 1591258 "ODETOOLS" NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-734 1588382 1589052 1589756 "ODESYS" NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-733 1584159 1585119 1586142 "ODERTRIC" NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-732 1583667 1583755 1583949 "ODERED" NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-731 1581116 1581698 1582371 "ODERAT" NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-730 1578511 1579019 1579615 "ODEPRRIC" NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-729 1575508 1576047 1576693 "ODEPRIM" NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-728 1574863 1574971 1575229 "ODEPAL" NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-727 1574021 1574146 1574367 "ODEINT" NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-726 1570305 1571101 1572014 "ODEEF" NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-725 1569745 1569840 1570062 "ODECONST" NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-724 1569426 1569475 1569602 "OCTCT2" NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-723 1566093 1569225 1569344 "OCT" NIL OCT (NIL T) -8 NIL NIL NIL) (-722 1565284 1565875 1565903 "OCAMON" 1565908 OCAMON (NIL) -9 NIL 1565929 NIL) (-721 1559560 1562310 1562350 "OC" 1563445 OC (NIL T) -9 NIL 1564301 NIL) (-720 1557560 1558486 1559466 "OC-" NIL OC- (NIL T T) -7 NIL NIL NIL) (-719 1556976 1557394 1557422 "OASGP" 1557427 OASGP (NIL) -9 NIL 1557447 NIL) (-718 1556070 1556688 1556716 "OAMONS" 1556756 OAMONS (NIL) -9 NIL 1556799 NIL) (-717 1555246 1555796 1555824 "OAMON" 1555881 OAMON (NIL) -9 NIL 1555932 NIL) (-716 1555142 1555174 1555241 "OAMON-" NIL OAMON- (NIL T) -7 NIL NIL NIL) (-715 1553924 1554667 1554695 "OAGROUP" 1554841 OAGROUP (NIL) -9 NIL 1554933 NIL) (-714 1553715 1553802 1553919 "OAGROUP-" NIL OAGROUP- (NIL T) -7 NIL NIL NIL) (-713 1553455 1553511 1553599 "NUMTUBE" NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-712 1548517 1550080 1551607 "NUMQUAD" NIL NUMQUAD (NIL) -7 NIL NIL NIL) (-711 1545212 1546246 1547281 "NUMODE" NIL NUMODE (NIL) -7 NIL NIL NIL) (-710 1544322 1544555 1544773 "NUMFMT" NIL NUMFMT (NIL) -7 NIL NIL NIL) (-709 1533183 1536211 1538659 "NUMERIC" NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-708 1527070 1532624 1532718 "NTSCAT" 1532723 NTSCAT (NIL T T T T) -9 NIL 1532761 NIL) (-707 1526411 1526590 1526783 "NTPOLFN" NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-706 1526104 1526167 1526274 "NSUP2" NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-705 1513835 1523724 1524534 "NSUP" NIL NSUP (NIL T) -8 NIL NIL NIL) (-704 1502908 1513700 1513830 "NSMP" NIL NSMP (NIL T T) -8 NIL NIL NIL) (-703 1501628 1501953 1502310 "NREP" NIL NREP (NIL T) -7 NIL NIL NIL) (-702 1500464 1500728 1501086 "NPCOEF" NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-701 1499631 1499764 1499980 "NORMRETR" NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-700 1497949 1498268 1498674 "NORMPK" NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-699 1497662 1497696 1497820 "NORMMA" NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-698 1497481 1497516 1497585 "NONE1" NIL NONE1 (NIL T) -7 NIL NIL NIL) (-697 1497257 1497447 1497476 "NONE" NIL NONE (NIL) -8 NIL NIL NIL) (-696 1496821 1496888 1497065 "NODE1" NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-695 1495139 1496184 1496439 "NNI" NIL NNI (NIL) -8 NIL NIL 1496786) (-694 1493867 1494204 1494568 "NLINSOL" NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-693 1492844 1493096 1493398 "NFINTBAS" NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-692 1491931 1492496 1492537 "NETCLT" 1492708 NETCLT (NIL T) -9 NIL 1492789 NIL) (-691 1490835 1491102 1491383 "NCODIV" NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-690 1490634 1490677 1490752 "NCNTFRAC" NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-689 1489165 1489553 1489973 "NCEP" NIL NCEP (NIL T) -7 NIL NIL NIL) (-688 1487829 1488764 1488792 "NASRING" 1488902 NASRING (NIL) -9 NIL 1488982 NIL) (-687 1487674 1487730 1487824 "NASRING-" NIL NASRING- (NIL T) -7 NIL NIL NIL) (-686 1486634 1487281 1487309 "NARNG" 1487426 NARNG (NIL) -9 NIL 1487517 NIL) (-685 1486410 1486495 1486629 "NARNG-" NIL NARNG- (NIL T) -7 NIL NIL NIL) (-684 1485207 1485930 1485970 "NAALG" 1486049 NAALG (NIL T) -9 NIL 1486110 NIL) (-683 1485077 1485112 1485202 "NAALG-" NIL NAALG- (NIL T T) -7 NIL NIL NIL) (-682 1480056 1481241 1482427 "MULTSQFR" NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-681 1479451 1479538 1479722 "MULTFACT" NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-680 1471525 1475955 1476007 "MTSCAT" 1477067 MTSCAT (NIL T T) -9 NIL 1477581 NIL) (-679 1471291 1471351 1471443 "MTHING" NIL MTHING (NIL T) -7 NIL NIL NIL) (-678 1471117 1471156 1471216 "MSYSCMD" NIL MSYSCMD (NIL) -7 NIL NIL NIL) (-677 1467979 1470668 1470709 "MSETAGG" 1470714 MSETAGG (NIL T) -9 NIL 1470748 NIL) (-676 1464116 1467025 1467343 "MSET" NIL MSET (NIL T) -8 NIL NIL NIL) (-675 1460454 1462213 1462953 "MRING" NIL MRING (NIL T T) -8 NIL NIL NIL) (-674 1460091 1460164 1460293 "MRF2" NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-673 1459744 1459785 1459929 "MRATFAC" NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-672 1457609 1457946 1458377 "MPRFF" NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-671 1451071 1457508 1457604 "MPOLY" NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-670 1450596 1450637 1450845 "MPCPF" NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-669 1450155 1450204 1450387 "MPC3" NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-668 1449429 1449522 1449741 "MPC2" NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-667 1448046 1448407 1448797 "MONOTOOL" NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-666 1447567 1447634 1447673 "MONOPC" 1447733 MONOPC (NIL T) -9 NIL 1447952 NIL) (-665 1447018 1447354 1447482 "MONOP" NIL MONOP (NIL T) -8 NIL NIL NIL) (-664 1446160 1446539 1446567 "MONOID" 1446785 MONOID (NIL) -9 NIL 1446929 NIL) (-663 1445819 1445969 1446155 "MONOID-" NIL MONOID- (NIL T) -7 NIL NIL NIL) (-662 1434819 1441627 1441686 "MONOGEN" 1442360 MONOGEN (NIL T T) -9 NIL 1442816 NIL) (-661 1432831 1433717 1434700 "MONOGEN-" NIL MONOGEN- (NIL T T T) -7 NIL NIL NIL) (-660 1431545 1432089 1432117 "MONADWU" 1432508 MONADWU (NIL) -9 NIL 1432743 NIL) (-659 1431093 1431293 1431540 "MONADWU-" NIL MONADWU- (NIL T) -7 NIL NIL NIL) (-658 1430370 1430671 1430699 "MONAD" 1430906 MONAD (NIL) -9 NIL 1431018 NIL) (-657 1430137 1430233 1430365 "MONAD-" NIL MONAD- (NIL T) -7 NIL NIL NIL) (-656 1428527 1429297 1429576 "MOEBIUS" NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-655 1427692 1428188 1428228 "MODULE" 1428233 MODULE (NIL T) -9 NIL 1428271 NIL) (-654 1427371 1427497 1427687 "MODULE-" NIL MODULE- (NIL T T) -7 NIL NIL NIL) (-653 1425146 1425968 1426282 "MODRING" NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-652 1422389 1423742 1424255 "MODOP" NIL MODOP (NIL T T) -8 NIL NIL NIL) (-651 1421023 1421597 1421873 "MODMONOM" NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-650 1410306 1419688 1420101 "MODMON" NIL MODMON (NIL T T) -8 NIL NIL NIL) (-649 1407326 1409306 1409575 "MODFIELD" NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-648 1406410 1406777 1406967 "MMLFORM" NIL MMLFORM (NIL) -8 NIL NIL NIL) (-647 1405979 1406028 1406207 "MMAP" NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-646 1403866 1404800 1404840 "MLO" 1405257 MLO (NIL T) -9 NIL 1405497 NIL) (-645 1401747 1402274 1402869 "MLIFT" NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-644 1401215 1401311 1401465 "MKUCFUNC" NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-643 1400885 1400961 1401084 "MKRECORD" NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-642 1400097 1400283 1400511 "MKFUNC" NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-641 1399590 1399706 1399862 "MKFLCFN" NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-640 1398962 1399076 1399261 "MKBCFUNC" NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-639 1397989 1398262 1398539 "MHROWRED" NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-638 1397422 1397510 1397681 "MFINFACT" NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-637 1394580 1395459 1396338 "MESH" NIL MESH (NIL) -7 NIL NIL NIL) (-636 1393247 1393595 1393948 "MDDFACT" NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-635 1389904 1392371 1392412 "MDAGG" 1392669 MDAGG (NIL T) -9 NIL 1392814 NIL) (-634 1389178 1389342 1389542 "MCDEN" NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-633 1388256 1388542 1388772 "MAYBE" NIL MAYBE (NIL T) -8 NIL NIL NIL) (-632 1386353 1386930 1387491 "MATSTOR" NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-631 1382124 1385943 1386190 "MATRIX" NIL MATRIX (NIL T) -8 NIL NIL NIL) (-630 1378473 1379242 1379976 "MATLIN" NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-629 1377226 1377395 1377724 "MATCAT2" NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-628 1366739 1370328 1370404 "MATCAT" 1375392 MATCAT (NIL T T T) -9 NIL 1376860 NIL) (-627 1364020 1365326 1366734 "MATCAT-" NIL MATCAT- (NIL T T T T) -7 NIL NIL NIL) (-626 1362421 1362781 1363165 "MAPPKG3" NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-625 1361554 1361751 1361973 "MAPPKG2" NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-624 1360305 1360631 1360958 "MAPPKG1" NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-623 1359467 1359869 1360045 "MAPPAST" NIL MAPPAST (NIL) -8 NIL NIL NIL) (-622 1359136 1359200 1359323 "MAPHACK3" NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-621 1358784 1358857 1358971 "MAPHACK2" NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-620 1358319 1358434 1358576 "MAPHACK1" NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-619 1356528 1357296 1357597 "MAGMA" NIL MAGMA (NIL T) -8 NIL NIL NIL) (-618 1356022 1356324 1356414 "MACROAST" NIL MACROAST (NIL) -8 NIL NIL NIL) (-617 1349531 1354337 1354378 "LZSTAGG" 1355155 LZSTAGG (NIL T) -9 NIL 1355445 NIL) (-616 1346650 1348084 1349526 "LZSTAGG-" NIL LZSTAGG- (NIL T T) -7 NIL NIL NIL) (-615 1344037 1345003 1345486 "LWORD" NIL LWORD (NIL T) -8 NIL NIL NIL) (-614 1343618 1343897 1343971 "LSTAST" NIL LSTAST (NIL) -8 NIL NIL NIL) (-613 1335846 1343479 1343613 "LSQM" NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-612 1335209 1335354 1335582 "LSPP" NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-611 1332693 1333391 1334103 "LSMP1" NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-610 1330805 1331128 1331576 "LSMP" NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-609 1323974 1329892 1329933 "LSAGG" 1329995 LSAGG (NIL T) -9 NIL 1330073 NIL) (-608 1321668 1322767 1323969 "LSAGG-" NIL LSAGG- (NIL T T) -7 NIL NIL NIL) (-607 1319180 1321017 1321266 "LPOLY" NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-606 1318847 1318938 1319061 "LPEFRAC" NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-605 1318518 1318597 1318625 "LOGIC" 1318736 LOGIC (NIL) -9 NIL 1318818 NIL) (-604 1318413 1318442 1318513 "LOGIC-" NIL LOGIC- (NIL T) -7 NIL NIL NIL) (-603 1317732 1317890 1318083 "LODOOPS" NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-602 1316517 1316766 1317117 "LODOF" NIL LODOF (NIL T T) -7 NIL NIL NIL) (-601 1312403 1315138 1315178 "LODOCAT" 1315610 LODOCAT (NIL T) -9 NIL 1315821 NIL) (-600 1312196 1312272 1312398 "LODOCAT-" NIL LODOCAT- (NIL T T) -7 NIL NIL NIL) (-599 1309260 1312073 1312191 "LODO2" NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-598 1306422 1309210 1309255 "LODO1" NIL LODO1 (NIL T) -8 NIL NIL NIL) (-597 1303573 1306352 1306417 "LODO" NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-596 1302626 1302801 1303103 "LODEEF" NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-595 1300790 1301888 1302141 "LO" NIL LO (NIL T T T) -8 NIL NIL NIL) (-594 1295885 1298949 1298990 "LNAGG" 1299852 LNAGG (NIL T) -9 NIL 1300287 NIL) (-593 1295272 1295539 1295880 "LNAGG-" NIL LNAGG- (NIL T T) -7 NIL NIL NIL) (-592 1291844 1292785 1293422 "LMOPS" NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-591 1291137 1291611 1291651 "LMODULE" 1291656 LMODULE (NIL T) -9 NIL 1291682 NIL) (-590 1288316 1290874 1290996 "LMDICT" NIL LMDICT (NIL T) -8 NIL NIL NIL) (-589 1287884 1288095 1288136 "LLINSET" 1288197 LLINSET (NIL T) -9 NIL 1288241 NIL) (-588 1287560 1287820 1287879 "LITERAL" NIL LITERAL (NIL T) -8 NIL NIL NIL) (-587 1287159 1287239 1287378 "LIST3" NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-586 1285610 1285958 1286357 "LIST2MAP" NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-585 1284781 1284977 1285205 "LIST2" NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-584 1277828 1284037 1284291 "LIST" NIL LIST (NIL T) -8 NIL NIL NIL) (-583 1277405 1277638 1277679 "LINSET" 1277684 LINSET (NIL T) -9 NIL 1277717 NIL) (-582 1276338 1277028 1277195 "LINFORM" NIL LINFORM (NIL T NIL) -8 NIL NIL NIL) (-581 1274635 1275359 1275399 "LINEXP" 1275885 LINEXP (NIL T) -9 NIL 1276158 NIL) (-580 1273344 1274244 1274425 "LINELT" NIL LINELT (NIL T NIL) -8 NIL NIL NIL) (-579 1272171 1272443 1272745 "LINDEP" NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-578 1271384 1271973 1272083 "LINBASIS" NIL LINBASIS (NIL NIL) -8 NIL NIL NIL) (-577 1268934 1269656 1270406 "LIMITRF" NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-576 1267564 1267861 1268252 "LIMITPS" NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-575 1266388 1266959 1266999 "LIECAT" 1267139 LIECAT (NIL T) -9 NIL 1267290 NIL) (-574 1266262 1266295 1266383 "LIECAT-" NIL LIECAT- (NIL T T) -7 NIL NIL NIL) (-573 1260550 1265952 1266180 "LIE" NIL LIE (NIL T T) -8 NIL NIL NIL) (-572 1252899 1260226 1260382 "LIB" NIL LIB (NIL) -8 NIL NIL NIL) (-571 1249351 1250300 1251235 "LGROBP" NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-570 1247975 1248883 1248911 "LFCAT" 1249118 LFCAT (NIL) -9 NIL 1249257 NIL) (-569 1246214 1246544 1246889 "LF" NIL LF (NIL T T) -7 NIL NIL NIL) (-568 1243731 1244396 1245077 "LEXTRIPK" NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-567 1240743 1241721 1242224 "LEXP" NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-566 1240234 1240537 1240628 "LETAST" NIL LETAST (NIL) -8 NIL NIL NIL) (-565 1238941 1239265 1239665 "LEADCDET" NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-564 1238207 1238292 1238518 "LAZM3PK" NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-563 1233274 1236775 1237311 "LAUPOL" NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-562 1232899 1232949 1233109 "LAPLACE" NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-561 1231732 1232443 1232483 "LALG" 1232544 LALG (NIL T) -9 NIL 1232602 NIL) (-560 1231515 1231592 1231727 "LALG-" NIL LALG- (NIL T T) -7 NIL NIL NIL) (-559 1229432 1230783 1231034 "LA" NIL LA (NIL T T T) -8 NIL NIL NIL) (-558 1229261 1229291 1229332 "KVTFROM" 1229394 KVTFROM (NIL T) -9 NIL NIL NIL) (-557 1228077 1228792 1228981 "KTVLOGIC" NIL KTVLOGIC (NIL) -8 NIL NIL NIL) (-556 1227906 1227936 1227977 "KRCFROM" 1228039 KRCFROM (NIL T) -9 NIL NIL NIL) (-555 1227008 1227205 1227500 "KOVACIC" NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-554 1226837 1226867 1226908 "KONVERT" 1226970 KONVERT (NIL T) -9 NIL NIL NIL) (-553 1226666 1226696 1226737 "KOERCE" 1226799 KOERCE (NIL T) -9 NIL NIL NIL) (-552 1226236 1226329 1226461 "KERNEL2" NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-551 1224289 1225183 1225555 "KERNEL" NIL KERNEL (NIL T) -8 NIL NIL NIL) (-550 1217466 1222481 1222535 "KDAGG" 1222911 KDAGG (NIL T T) -9 NIL 1223118 NIL) (-549 1217114 1217256 1217461 "KDAGG-" NIL KDAGG- (NIL T T T) -7 NIL NIL NIL) (-548 1209944 1216895 1217052 "KAFILE" NIL KAFILE (NIL T) -8 NIL NIL NIL) (-547 1209594 1209876 1209939 "JVMOP" NIL JVMOP (NIL) -8 NIL NIL NIL) (-546 1208564 1209063 1209312 "JVMMDACC" NIL JVMMDACC (NIL) -8 NIL NIL NIL) (-545 1207690 1208139 1208344 "JVMFDACC" NIL JVMFDACC (NIL) -8 NIL NIL NIL) (-544 1206554 1207046 1207346 "JVMCSTTG" NIL JVMCSTTG (NIL) -8 NIL NIL NIL) (-543 1205836 1206235 1206396 "JVMCFACC" NIL JVMCFACC (NIL) -8 NIL NIL NIL) (-542 1205546 1205782 1205831 "JVMBCODE" NIL JVMBCODE (NIL) -8 NIL NIL NIL) (-541 1199833 1205236 1205464 "JORDAN" NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-540 1199251 1199584 1199704 "JOINAST" NIL JOINAST (NIL) -8 NIL NIL NIL) (-539 1195413 1197428 1197482 "IXAGG" 1198409 IXAGG (NIL T T) -9 NIL 1198866 NIL) (-538 1194619 1194990 1195408 "IXAGG-" NIL IXAGG- (NIL T T T) -7 NIL NIL NIL) (-537 1189873 1194555 1194614 "IVECTOR" NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-536 1188840 1189115 1189378 "ITUPLE" NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-535 1187502 1187709 1188002 "ITRIGMNP" NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-534 1186453 1186675 1186958 "ITFUN3" NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-533 1186128 1186191 1186314 "ITFUN2" NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-532 1185390 1185762 1185936 "ITFORM" NIL ITFORM (NIL) -8 NIL NIL NIL) (-531 1183430 1184666 1184940 "ITAYLOR" NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-530 1173042 1178747 1179904 "ISUPS" NIL ISUPS (NIL T) -8 NIL NIL NIL) (-529 1172287 1172439 1172675 "ISUMP" NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-528 1171778 1172081 1172172 "ISAST" NIL ISAST (NIL) -8 NIL NIL NIL) (-527 1171071 1171162 1171375 "IRURPK" NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-526 1170203 1170428 1170668 "IRSN" NIL IRSN (NIL) -7 NIL NIL NIL) (-525 1168616 1168997 1169425 "IRRF2F" NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-524 1168401 1168445 1168521 "IRREDFFX" NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-523 1167251 1167548 1167843 "IROOT" NIL IROOT (NIL T) -7 NIL NIL NIL) (-522 1166524 1166875 1167026 "IRFORM" NIL IRFORM (NIL) -8 NIL NIL NIL) (-521 1165727 1165858 1166071 "IR2F" NIL IR2F (NIL T T) -7 NIL NIL NIL) (-520 1163882 1164379 1164923 "IR2" NIL IR2 (NIL T T) -7 NIL NIL NIL) (-519 1160995 1162231 1162920 "IR" NIL IR (NIL T) -8 NIL NIL NIL) (-518 1160820 1160860 1160920 "IPRNTPK" NIL IPRNTPK (NIL) -7 NIL NIL NIL) (-517 1156882 1160746 1160815 "IPF" NIL IPF (NIL NIL) -8 NIL NIL NIL) (-516 1154949 1156821 1156877 "IPADIC" NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-515 1154320 1154619 1154749 "IP4ADDR" NIL IP4ADDR (NIL) -8 NIL NIL NIL) (-514 1153773 1154061 1154193 "IOMODE" NIL IOMODE (NIL) -8 NIL NIL NIL) (-513 1152854 1153479 1153605 "IOBFILE" NIL IOBFILE (NIL) -8 NIL NIL NIL) (-512 1152264 1152758 1152786 "IOBCON" 1152791 IOBCON (NIL) -9 NIL 1152812 NIL) (-511 1151835 1151899 1152081 "INVLAPLA" NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-510 1143879 1146250 1148575 "INTTR" NIL INTTR (NIL T T) -7 NIL NIL NIL) (-509 1140990 1141773 1142637 "INTTOOLS" NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-508 1140667 1140764 1140881 "INTSLPE" NIL INTSLPE (NIL) -7 NIL NIL NIL) (-507 1138173 1140603 1140662 "INTRVL" NIL INTRVL (NIL T) -8 NIL NIL NIL) (-506 1136285 1136814 1137381 "INTRF" NIL INTRF (NIL T) -7 NIL NIL NIL) (-505 1135787 1135901 1136041 "INTRET" NIL INTRET (NIL T) -7 NIL NIL NIL) (-504 1134171 1134577 1135039 "INTRAT" NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-503 1131950 1132544 1133155 "INTPM" NIL INTPM (NIL T T) -7 NIL NIL NIL) (-502 1129323 1129933 1130653 "INTPAF" NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-501 1128727 1128885 1129093 "INTHERTR" NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-500 1128246 1128332 1128520 "INTHERAL" NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-499 1126451 1126972 1127429 "INTHEORY" NIL INTHEORY (NIL) -7 NIL NIL NIL) (-498 1119533 1121186 1122915 "INTG0" NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-497 1118899 1119061 1119234 "INTFACT" NIL INTFACT (NIL T) -7 NIL NIL NIL) (-496 1116772 1117236 1117780 "INTEF" NIL INTEF (NIL T T) -7 NIL NIL NIL) (-495 1114960 1115848 1115876 "INTDOM" 1116175 INTDOM (NIL) -9 NIL 1116380 NIL) (-494 1114513 1114715 1114955 "INTDOM-" NIL INTDOM- (NIL T) -7 NIL NIL NIL) (-493 1110384 1112792 1112846 "INTCAT" 1113642 INTCAT (NIL T) -9 NIL 1113958 NIL) (-492 1109949 1110069 1110196 "INTBIT" NIL INTBIT (NIL) -7 NIL NIL NIL) (-491 1108789 1108961 1109267 "INTALG" NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-490 1108362 1108458 1108615 "INTAF" NIL INTAF (NIL T T) -7 NIL NIL NIL) (-489 1101402 1108217 1108357 "INTABL" NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-488 1100700 1101255 1101320 "INT8" NIL INT8 (NIL) -8 NIL NIL 1101354) (-487 1099997 1100552 1100617 "INT64" NIL INT64 (NIL) -8 NIL NIL 1100651) (-486 1099294 1099849 1099914 "INT32" NIL INT32 (NIL) -8 NIL NIL 1099948) (-485 1098591 1099146 1099211 "INT16" NIL INT16 (NIL) -8 NIL NIL 1099245) (-484 1095118 1098510 1098586 "INT" NIL INT (NIL) -8 NIL NIL NIL) (-483 1089239 1092658 1092686 "INS" 1093616 INS (NIL) -9 NIL 1094275 NIL) (-482 1087301 1088219 1089166 "INS-" NIL INS- (NIL T) -7 NIL NIL NIL) (-481 1086360 1086583 1086858 "INPSIGN" NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-480 1085574 1085715 1085912 "INPRODPF" NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-479 1084564 1084705 1084942 "INPRODFF" NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-478 1083716 1083880 1084140 "INNMFACT" NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-477 1082996 1083111 1083299 "INMODGCD" NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-476 1081735 1082004 1082328 "INFSP" NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-475 1081015 1081156 1081339 "INFPROD0" NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-474 1080678 1080750 1080848 "INFORM1" NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-473 1077756 1079242 1079765 "INFORM" NIL INFORM (NIL) -8 NIL NIL NIL) (-472 1077355 1077462 1077576 "INFINITY" NIL INFINITY (NIL) -7 NIL NIL NIL) (-471 1076511 1077156 1077257 "INETCLTS" NIL INETCLTS (NIL) -8 NIL NIL NIL) (-470 1075361 1075629 1075950 "INEP" NIL INEP (NIL T T T) -7 NIL NIL NIL) (-469 1074433 1075291 1075356 "INDE" NIL INDE (NIL T) -8 NIL NIL NIL) (-468 1074058 1074138 1074255 "INCRMAPS" NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-467 1072972 1073517 1073721 "INBFILE" NIL INBFILE (NIL) -8 NIL NIL NIL) (-466 1069067 1070122 1071065 "INBFF" NIL INBFF (NIL T) -7 NIL NIL NIL) (-465 1067921 1068244 1068272 "INBCON" 1068785 INBCON (NIL) -9 NIL 1069051 NIL) (-464 1067375 1067640 1067916 "INBCON-" NIL INBCON- (NIL T) -7 NIL NIL NIL) (-463 1066869 1067171 1067261 "INAST" NIL INAST (NIL) -8 NIL NIL NIL) (-462 1066326 1066635 1066740 "IMPTAST" NIL IMPTAST (NIL) -8 NIL NIL NIL) (-461 1062426 1066218 1066321 "IMATRIX" NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-460 1061266 1061405 1061720 "IMATQF" NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-459 1059690 1059957 1060294 "IMATLIN" NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-458 1057506 1059572 1059685 "IIARRAY2" NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-457 1052413 1057437 1057501 "IFF" NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-456 1051793 1052127 1052242 "IFAST" NIL IFAST (NIL) -8 NIL NIL NIL) (-455 1046600 1051231 1051417 "IFARRAY" NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-454 1045662 1046522 1046595 "IFAMON" NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-453 1045234 1045311 1045365 "IEVALAB" 1045572 IEVALAB (NIL T T) -9 NIL NIL NIL) (-452 1044989 1045069 1045229 "IEVALAB-" NIL IEVALAB- (NIL T T T) -7 NIL NIL NIL) (-451 1044374 1044601 1044758 "IDPT" NIL IDPT (NIL T T) -8 NIL NIL NIL) (-450 1043447 1044294 1044369 "IDPOAMS" NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-449 1042589 1043367 1043442 "IDPOAM" NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-448 1041992 1042523 1042584 "IDPO" NIL IDPO (NIL T T) -8 NIL NIL NIL) (-447 1040472 1040996 1041047 "IDPC" 1041553 IDPC (NIL T T) -9 NIL 1041833 NIL) (-446 1039838 1040394 1040467 "IDPAM" NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-445 1039087 1039760 1039833 "IDPAG" NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-444 1038780 1038993 1039053 "IDENT" NIL IDENT (NIL) -8 NIL NIL NIL) (-443 1038484 1038524 1038563 "IDEMOPC" 1038568 IDEMOPC (NIL T) -9 NIL 1038705 NIL) (-442 1035555 1036436 1037328 "IDECOMP" NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-441 1029181 1030458 1031497 "IDEAL" NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-440 1028443 1028573 1028772 "ICDEN" NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-439 1027616 1028115 1028253 "ICARD" NIL ICARD (NIL) -8 NIL NIL NIL) (-438 1026005 1026336 1026727 "IBPTOOLS" NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-437 1021774 1025961 1026000 "IBITS" NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-436 1019032 1019656 1020351 "IBATOOL" NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-435 1017258 1017738 1018271 "IBACHIN" NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-434 1015022 1017150 1017253 "IARRAY2" NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-433 1010891 1014960 1015017 "IARRAY1" NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-432 1004534 1009855 1010323 "IAN" NIL IAN (NIL) -8 NIL NIL NIL) (-431 1004102 1004165 1004338 "IALGFACT" NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-430 1003594 1003743 1003771 "HYPCAT" 1003978 HYPCAT (NIL) -9 NIL NIL NIL) (-429 1003250 1003403 1003589 "HYPCAT-" NIL HYPCAT- (NIL T) -7 NIL NIL NIL) (-428 1002863 1003108 1003191 "HOSTNAME" NIL HOSTNAME (NIL) -8 NIL NIL NIL) (-427 1002696 1002745 1002786 "HOMOTOP" 1002791 HOMOTOP (NIL T) -9 NIL 1002824 NIL) (-426 999264 1000638 1000679 "HOAGG" 1001654 HOAGG (NIL T) -9 NIL 1002375 NIL) (-425 998270 998740 999259 "HOAGG-" NIL HOAGG- (NIL T T) -7 NIL NIL NIL) (-424 991534 997995 998143 "HEXADEC" NIL HEXADEC (NIL) -8 NIL NIL NIL) (-423 990469 990727 990990 "HEUGCD" NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-422 989436 990334 990464 "HELLFDIV" NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-421 987630 989269 989357 "HEAP" NIL HEAP (NIL T) -8 NIL NIL NIL) (-420 986945 987297 987430 "HEADAST" NIL HEADAST (NIL) -8 NIL NIL NIL) (-419 980498 986878 986940 "HDP" NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-418 973701 980234 980385 "HDMP" NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-417 973154 973311 973474 "HB" NIL HB (NIL) -7 NIL NIL NIL) (-416 966237 973045 973149 "HASHTBL" NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-415 965728 966031 966122 "HASAST" NIL HASAST (NIL) -8 NIL NIL NIL) (-414 963342 965515 965694 "HACKPI" NIL HACKPI (NIL) -8 NIL NIL NIL) (-413 958735 963225 963337 "GTSET" NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-412 951821 958632 958730 "GSTBL" NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-411 943822 951190 951445 "GSERIES" NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-410 942846 943355 943383 "GROUP" 943586 GROUP (NIL) -9 NIL 943720 NIL) (-409 942389 942590 942841 "GROUP-" NIL GROUP- (NIL T) -7 NIL NIL NIL) (-408 941061 941400 941787 "GROEBSOL" NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-407 939883 940240 940291 "GRMOD" 940820 GRMOD (NIL T T) -9 NIL 940986 NIL) (-406 939702 939750 939878 "GRMOD-" NIL GRMOD- (NIL T T T) -7 NIL NIL NIL) (-405 935825 937036 938036 "GRIMAGE" NIL GRIMAGE (NIL) -8 NIL NIL NIL) (-404 934547 934871 935186 "GRDEF" NIL GRDEF (NIL) -7 NIL NIL NIL) (-403 934100 934228 934369 "GRAY" NIL GRAY (NIL) -7 NIL NIL NIL) (-402 933173 933672 933723 "GRALG" 933876 GRALG (NIL T T) -9 NIL 933966 NIL) (-401 932892 932993 933168 "GRALG-" NIL GRALG- (NIL T T T) -7 NIL NIL NIL) (-400 929609 932574 932750 "GPOLSET" NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-399 929022 929085 929342 "GOSPER" NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-398 924908 925772 926297 "GMODPOL" NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-397 924083 924285 924523 "GHENSEL" NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-396 919086 920013 921032 "GENUPS" NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-395 918834 918891 918980 "GENUFACT" NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-394 918316 918405 918570 "GENPGCD" NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-393 917825 917866 918079 "GENMFACT" NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-392 916626 916909 917213 "GENEEZ" NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-391 909965 916316 916477 "GDMP" NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-390 899780 904755 905859 "GCNAALG" NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-389 897894 898935 898963 "GCDDOM" 899218 GCDDOM (NIL) -9 NIL 899375 NIL) (-388 897517 897674 897889 "GCDDOM-" NIL GCDDOM- (NIL T) -7 NIL NIL NIL) (-387 888310 890780 893168 "GBINTERN" NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-386 886445 886770 887188 "GBF" NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-385 885386 885575 885842 "GBEUCLID" NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-384 884257 884464 884768 "GB" NIL GB (NIL T T T T) -7 NIL NIL NIL) (-383 883720 883862 884010 "GAUSSFAC" NIL GAUSSFAC (NIL) -7 NIL NIL NIL) (-382 882332 882680 882993 "GALUTIL" NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-381 880877 881198 881520 "GALPOLYU" NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-380 878503 878859 879264 "GALFACTU" NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-379 871755 873416 874994 "GALFACT" NIL GALFACT (NIL T) -7 NIL NIL NIL) (-378 871407 871628 871696 "FUNDESC" NIL FUNDESC (NIL) -8 NIL NIL NIL) (-377 871031 871252 871333 "FUNCTION" NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-376 869128 869811 870271 "FT" NIL FT (NIL) -8 NIL NIL NIL) (-375 867721 868028 868420 "FSUPFACT" NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-374 866376 866735 867059 "FST" NIL FST (NIL) -8 NIL NIL NIL) (-373 865679 865803 865990 "FSRED" NIL FSRED (NIL T T) -7 NIL NIL NIL) (-372 864653 864919 865266 "FSPRMELT" NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-371 862311 862841 863323 "FSPECF" NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-370 861894 861954 862123 "FSINT" NIL FSINT (NIL T T) -7 NIL NIL NIL) (-369 860258 861108 861411 "FSERIES" NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-368 859406 859540 859763 "FSCINT" NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-367 858577 858738 858965 "FSAGG2" NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-366 854560 857511 857552 "FSAGG" 857922 FSAGG (NIL T) -9 NIL 858181 NIL) (-365 852914 853673 854465 "FSAGG-" NIL FSAGG- (NIL T T) -7 NIL NIL NIL) (-364 850870 851166 851710 "FS2UPS" NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-363 849917 850099 850399 "FS2EXPXP" NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-362 849598 849647 849774 "FS2" NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-361 829853 839255 839296 "FS" 843166 FS (NIL T) -9 NIL 845444 NIL) (-360 822084 825577 829556 "FS-" NIL FS- (NIL T T) -7 NIL NIL NIL) (-359 821618 821745 821897 "FRUTIL" NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-358 816172 819299 819339 "FRNAALG" 820659 FRNAALG (NIL T) -9 NIL 821257 NIL) (-357 812913 814164 815422 "FRNAALG-" NIL FRNAALG- (NIL T T) -7 NIL NIL NIL) (-356 812594 812643 812770 "FRNAAF2" NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-355 811081 811638 811932 "FRMOD" NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-354 810367 810460 810747 "FRIDEAL2" NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-353 808201 808967 809283 "FRIDEAL" NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-352 807310 807753 807794 "FRETRCT" 807799 FRETRCT (NIL T) -9 NIL 807970 NIL) (-351 806683 806961 807305 "FRETRCT-" NIL FRETRCT- (NIL T T) -7 NIL NIL NIL) (-350 803489 804947 805006 "FRAMALG" 805888 FRAMALG (NIL T T) -9 NIL 806180 NIL) (-349 802085 802636 803266 "FRAMALG-" NIL FRAMALG- (NIL T T T) -7 NIL NIL NIL) (-348 801778 801841 801948 "FRAC2" NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-347 795483 801583 801773 "FRAC" NIL FRAC (NIL T) -8 NIL NIL NIL) (-346 795176 795239 795346 "FR2" NIL FR2 (NIL T T) -7 NIL NIL NIL) (-345 787548 792055 793383 "FR" NIL FR (NIL T) -8 NIL NIL NIL) (-344 781388 784829 784857 "FPS" 785976 FPS (NIL) -9 NIL 786532 NIL) (-343 780945 781078 781242 "FPS-" NIL FPS- (NIL T) -7 NIL NIL NIL) (-342 777818 779798 779826 "FPC" 780051 FPC (NIL) -9 NIL 780193 NIL) (-341 777664 777716 777813 "FPC-" NIL FPC- (NIL T) -7 NIL NIL NIL) (-340 776441 777150 777191 "FPATMAB" 777196 FPATMAB (NIL T) -9 NIL 777348 NIL) (-339 774871 775467 775814 "FPARFRAC" NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-338 774446 774504 774677 "FORDER" NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-337 772981 773844 774018 "FNLA" NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-336 771596 772101 772129 "FNCAT" 772586 FNCAT (NIL) -9 NIL 772843 NIL) (-335 771053 771563 771591 "FNAME" NIL FNAME (NIL) -8 NIL NIL NIL) (-334 769640 771002 771048 "FMONOID" NIL FMONOID (NIL T) -8 NIL NIL NIL) (-333 766228 767586 767627 "FMONCAT" 768844 FMONCAT (NIL T) -9 NIL 769448 NIL) (-332 763117 764164 764217 "FMCAT" 765398 FMCAT (NIL T T) -9 NIL 765890 NIL) (-331 761849 762940 763039 "FM1" NIL FM1 (NIL T T) -8 NIL NIL NIL) (-330 760977 761697 761844 "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 e1142baa..8f555e93 100644
--- a/src/share/algebra/operation.daase
+++ b/src/share/algebra/operation.daase
@@ -1,793 +1,793 @@
 
-(630603 . 3539125284)        
+(630818 . 3576902406)        
 (((*1 *2 *3 *4)
-  (|partial| -12 (-5 *3 (-1177 *4)) (-4 *4 (-13 (-961) (-580 (-483))))
-   (-5 *2 (-1177 (-347 (-483)))) (-5 *1 (-1206 *4))))) 
+  (|partial| -12 (-5 *3 (-1178 *4)) (-4 *4 (-13 (-962) (-581 (-484))))
+   (-5 *2 (-1178 (-347 (-484)))) (-5 *1 (-1207 *4))))) 
 (((*1 *2 *3)
-  (|partial| -12 (-5 *3 (-1177 *4)) (-4 *4 (-13 (-961) (-580 (-483))))
-   (-5 *2 (-1177 (-483))) (-5 *1 (-1206 *4))))) 
+  (|partial| -12 (-5 *3 (-1178 *4)) (-4 *4 (-13 (-962) (-581 (-484))))
+   (-5 *2 (-1178 (-484))) (-5 *1 (-1207 *4))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-1177 *4)) (-4 *4 (-13 (-961) (-580 (-483)))) (-5 *2 (-85))
-   (-5 *1 (-1206 *4))))) 
+  (-12 (-5 *3 (-1178 *4)) (-4 *4 (-13 (-962) (-581 (-484)))) (-5 *2 (-85))
+   (-5 *1 (-1207 *4))))) 
 (((*1 *2 *3)
-  (-12 (-4 *5 (-13 (-553 *2) (-146))) (-5 *2 (-800 *4)) (-5 *1 (-144 *4 *5 *3))
-   (-4 *4 (-1012)) (-4 *3 (-139 *5))))
+  (-12 (-4 *5 (-13 (-554 *2) (-146))) (-5 *2 (-801 *4)) (-5 *1 (-144 *4 *5 *3))
+   (-4 *4 (-1013)) (-4 *3 (-139 *5))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-1177 *3)) (-4 *3 (-146)) (-4 *1 (-350 *3 *4))
-   (-4 *4 (-1153 *3))))
+  (-12 (-5 *2 (-1178 *3)) (-4 *3 (-146)) (-4 *1 (-350 *3 *4))
+   (-4 *4 (-1154 *3))))
  ((*1 *2 *1)
-  (-12 (-4 *1 (-350 *3 *4)) (-4 *3 (-146)) (-4 *4 (-1153 *3))
-   (-5 *2 (-1177 *3))))
- ((*1 *1 *2) (-12 (-5 *2 (-1177 *3)) (-4 *3 (-146)) (-4 *1 (-358 *3))))
- ((*1 *2 *1) (-12 (-4 *1 (-358 *3)) (-4 *3 (-146)) (-5 *2 (-1177 *3))))
+  (-12 (-4 *1 (-350 *3 *4)) (-4 *3 (-146)) (-4 *4 (-1154 *3))
+   (-5 *2 (-1178 *3))))
+ ((*1 *1 *2) (-12 (-5 *2 (-1178 *3)) (-4 *3 (-146)) (-4 *1 (-358 *3))))
+ ((*1 *2 *1) (-12 (-4 *1 (-358 *3)) (-4 *3 (-146)) (-5 *2 (-1178 *3))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-345 *1)) (-4 *1 (-361 *3)) (-4 *3 (-494)) (-4 *3 (-1012))))
+  (-12 (-5 *2 (-345 *1)) (-4 *1 (-361 *3)) (-4 *3 (-495)) (-4 *3 (-1013))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-583 *6)) (-4 *6 (-976 *3 *4 *5)) (-4 *3 (-961)) (-4 *4 (-717))
-   (-4 *5 (-756)) (-5 *1 (-400 *3 *4 *5 *6))))
- ((*1 *1 *2) (-12 (-5 *2 (-1014)) (-5 *1 (-472))))
- ((*1 *2 *1) (-12 (-4 *1 (-553 *2)) (-4 *2 (-1127))))
- ((*1 *1 *2) (-12 (-4 *1 (-557 *2)) (-4 *2 (-1127))))
- ((*1 *1 *2) (-12 (-4 *3 (-146)) (-4 *1 (-661 *3 *2)) (-4 *2 (-1153 *3))))
- ((*1 *1 *2) (-12 (-5 *2 (-583 (-800 *3))) (-5 *1 (-800 *3)) (-4 *3 (-1012))))
+  (-12 (-5 *2 (-584 *6)) (-4 *6 (-977 *3 *4 *5)) (-4 *3 (-962)) (-4 *4 (-718))
+   (-4 *5 (-757)) (-5 *1 (-400 *3 *4 *5 *6))))
+ ((*1 *1 *2) (-12 (-5 *2 (-1015)) (-5 *1 (-473))))
+ ((*1 *2 *1) (-12 (-4 *1 (-554 *2)) (-4 *2 (-1128))))
+ ((*1 *1 *2) (-12 (-4 *1 (-558 *2)) (-4 *2 (-1128))))
+ ((*1 *1 *2) (-12 (-4 *3 (-146)) (-4 *1 (-662 *3 *2)) (-4 *2 (-1154 *3))))
+ ((*1 *1 *2) (-12 (-5 *2 (-584 (-801 *3))) (-5 *1 (-801 *3)) (-4 *3 (-1013))))
  ((*1 *1 *2)
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-   (-4 *5 (-553 (-1088))) (-4 *4 (-717)) (-4 *5 (-756))))
+  (-12 (-5 *2 (-858 *3)) (-4 *3 (-962)) (-4 *1 (-977 *3 *4 *5))
+   (-4 *5 (-554 (-1089))) (-4 *4 (-718)) (-4 *5 (-757))))
  ((*1 *1 *2)
   (OR
-   (-12 (-5 *2 (-857 (-483))) (-4 *1 (-976 *3 *4 *5))
-    (-12 (-2556 (-4 *3 (-38 (-347 (-483))))) (-4 *3 (-38 (-483)))
-     (-4 *5 (-553 (-1088))))
-    (-4 *3 (-961)) (-4 *4 (-717)) (-4 *5 (-756)))
-   (-12 (-5 *2 (-857 (-483))) (-4 *1 (-976 *3 *4 *5))
-    (-12 (-4 *3 (-38 (-347 (-483)))) (-4 *5 (-553 (-1088)))) (-4 *3 (-961))
-    (-4 *4 (-717)) (-4 *5 (-756)))))
+   (-12 (-5 *2 (-858 (-484))) (-4 *1 (-977 *3 *4 *5))
+    (-12 (-2558 (-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))
+    (-12 (-4 *3 (-38 (-347 (-484)))) (-4 *5 (-554 (-1089)))) (-4 *3 (-962))
+    (-4 *4 (-718)) (-4 *5 (-757)))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-857 (-347 (-483)))) (-4 *1 (-976 *3 *4 *5))
-   (-4 *3 (-38 (-347 (-483)))) (-4 *5 (-553 (-1088))) (-4 *3 (-961))
-   (-4 *4 (-717)) (-4 *5 (-756))))
- ((*1 *2 *3)
-  (-12 (-5 *3 (-2 (|:| |val| (-583 *7)) (|:| -1597 *8)))
-   (-4 *7 (-976 *4 *5 *6)) (-4 *8 (-982 *4 *5 *6 *7)) (-4 *4 (-389))
-   (-4 *5 (-717)) (-4 *6 (-756)) (-5 *2 (-1071))
-   (-5 *1 (-980 *4 *5 *6 *7 *8))))
- ((*1 *2 *3)
-  (-12 (-5 *3 (-2 (|:| |val| (-583 *7)) (|:| -1597 *8)))
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-   (-4 *5 (-717)) (-4 *6 (-756)) (-5 *2 (-1071))
-   (-5 *1 (-1057 *4 *5 *6 *7 *8))))
- ((*1 *1 *2) (-12 (-5 *2 (-1014)) (-5 *1 (-1093))))
- ((*1 *2 *1) (-12 (-5 *2 (-1014)) (-5 *1 (-1093))))
- ((*1 *1 *2 *3 *2) (-12 (-5 *2 (-772)) (-5 *3 (-483)) (-5 *1 (-1107))))
- ((*1 *1 *2 *3) (-12 (-5 *2 (-772)) (-5 *3 (-483)) (-5 *1 (-1107))))
- ((*1 *2 *3)
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-   (-14 *5 (-583 (-1088))) (-5 *2 (-703 *4 (-773 *6))) (-5 *1 (-1205 *4 *5 *6))
-   (-14 *6 (-583 (-1088)))))
- ((*1 *2 *3)
-  (-12 (-5 *3 (-857 *4)) (-4 *4 (-13 (-755) (-257) (-120) (-933)))
-   (-5 *2 (-857 (-937 (-347 *4)))) (-5 *1 (-1205 *4 *5 *6))
-   (-14 *5 (-583 (-1088))) (-14 *6 (-583 (-1088)))))
- ((*1 *2 *3)
-  (-12 (-5 *3 (-703 *4 (-773 *6))) (-4 *4 (-13 (-755) (-257) (-120) (-933)))
-   (-14 *6 (-583 (-1088))) (-5 *2 (-857 (-937 (-347 *4))))
-   (-5 *1 (-1205 *4 *5 *6)) (-14 *5 (-583 (-1088)))))
- ((*1 *2 *3)
-  (-12 (-5 *3 (-1083 *4)) (-4 *4 (-13 (-755) (-257) (-120) (-933)))
-   (-5 *2 (-1083 (-937 (-347 *4)))) (-5 *1 (-1205 *4 *5 *6))
-   (-14 *5 (-583 (-1088))) (-14 *6 (-583 (-1088)))))
- ((*1 *2 *3)
-  (-12 (-5 *3 (-1058 *4 (-468 (-773 *6)) (-773 *6) (-703 *4 (-773 *6))))
-   (-4 *4 (-13 (-755) (-257) (-120) (-933))) (-14 *6 (-583 (-1088)))
-   (-5 *2 (-583 (-703 *4 (-773 *6)))) (-5 *1 (-1205 *4 *5 *6))
-   (-14 *5 (-583 (-1088)))))) 
-(((*1 *2 *3) (-12 (-5 *2 (-345 *3)) (-5 *1 (-496 *3)) (-4 *3 (-482))))
- ((*1 *2 *3)
-  (-12 (-4 *4 (-717)) (-4 *5 (-756)) (-4 *6 (-257)) (-5 *2 (-345 *3))
-   (-5 *1 (-681 *4 *5 *6 *3)) (-4 *3 (-861 *6 *4 *5))))
- ((*1 *2 *3)
-  (-12 (-4 *4 (-717)) (-4 *5 (-756)) (-4 *6 (-257)) (-4 *7 (-861 *6 *4 *5))
-   (-5 *2 (-345 (-1083 *7))) (-5 *1 (-681 *4 *5 *6 *7)) (-5 *3 (-1083 *7))))
- ((*1 *2 *1)
-  (-12 (-4 *3 (-389)) (-4 *3 (-961)) (-4 *4 (-717)) (-4 *5 (-756))
-   (-5 *2 (-345 *1)) (-4 *1 (-861 *3 *4 *5))))
- ((*1 *2 *3)
-  (-12 (-4 *4 (-756)) (-4 *5 (-717)) (-4 *6 (-389)) (-5 *2 (-345 *3))
-   (-5 *1 (-892 *4 *5 *6 *3)) (-4 *3 (-861 *6 *5 *4))))
- ((*1 *2 *3)
-  (-12 (-4 *4 (-717)) (-4 *5 (-756)) (-4 *6 (-389)) (-4 *7 (-861 *6 *4 *5))
-   (-5 *2 (-345 (-1083 (-347 *7)))) (-5 *1 (-1085 *4 *5 *6 *7))
-   (-5 *3 (-1083 (-347 *7)))))
- ((*1 *2 *1) (-12 (-5 *2 (-345 *1)) (-4 *1 (-1132))))
- ((*1 *2 *3)
-  (-12 (-4 *4 (-494)) (-5 *2 (-345 *3)) (-5 *1 (-1157 *4 *3))
-   (-4 *3 (-13 (-1153 *4) (-494) (-10 -8 (-15 -3139 ($ $ $)))))))
- ((*1 *2 *3)
-  (-12 (-5 *3 (-958 *4 *5)) (-4 *4 (-13 (-755) (-257) (-120) (-933)))
-   (-14 *5 (-583 (-1088)))
-   (-5 *2 (-583 (-1058 *4 (-468 (-773 *6)) (-773 *6) (-703 *4 (-773 *6)))))
-   (-5 *1 (-1205 *4 *5 *6)) (-14 *6 (-583 (-1088)))))) 
-(((*1 *2 *3)
-  (-12 (-5 *3 (-958 *4 *5)) (-4 *4 (-13 (-755) (-257) (-120) (-933)))
-   (-14 *5 (-583 (-1088))) (-5 *2 (-583 (-583 (-937 (-347 *4)))))
-   (-5 *1 (-1205 *4 *5 *6)) (-14 *6 (-583 (-1088)))))
+  (-12 (-5 *2 (-858 (-347 (-484)))) (-4 *1 (-977 *3 *4 *5))
+   (-4 *3 (-38 (-347 (-484)))) (-4 *5 (-554 (-1089))) (-4 *3 (-962))
+   (-4 *4 (-718)) (-4 *5 (-757))))
+ ((*1 *2 *3)
+  (-12 (-5 *3 (-2 (|:| |val| (-584 *7)) (|:| -1598 *8)))
+   (-4 *7 (-977 *4 *5 *6)) (-4 *8 (-983 *4 *5 *6 *7)) (-4 *4 (-389))
+   (-4 *5 (-718)) (-4 *6 (-757)) (-5 *2 (-1072))
+   (-5 *1 (-981 *4 *5 *6 *7 *8))))
+ ((*1 *2 *3)
+  (-12 (-5 *3 (-2 (|:| |val| (-584 *7)) (|:| -1598 *8)))
+   (-4 *7 (-977 *4 *5 *6)) (-4 *8 (-1020 *4 *5 *6 *7)) (-4 *4 (-389))
+   (-4 *5 (-718)) (-4 *6 (-757)) (-5 *2 (-1072))
+   (-5 *1 (-1058 *4 *5 *6 *7 *8))))
+ ((*1 *1 *2) (-12 (-5 *2 (-1015)) (-5 *1 (-1094))))
+ ((*1 *2 *1) (-12 (-5 *2 (-1015)) (-5 *1 (-1094))))
+ ((*1 *1 *2 *3 *2) (-12 (-5 *2 (-773)) (-5 *3 (-484)) (-5 *1 (-1108))))
+ ((*1 *1 *2 *3) (-12 (-5 *2 (-773)) (-5 *3 (-484)) (-5 *1 (-1108))))
+ ((*1 *2 *3)
+  (-12 (-5 *3 (-704 *4 (-774 *5))) (-4 *4 (-13 (-756) (-257) (-120) (-934)))
+   (-14 *5 (-584 (-1089))) (-5 *2 (-704 *4 (-774 *6))) (-5 *1 (-1206 *4 *5 *6))
+   (-14 *6 (-584 (-1089)))))
+ ((*1 *2 *3)
+  (-12 (-5 *3 (-858 *4)) (-4 *4 (-13 (-756) (-257) (-120) (-934)))
+   (-5 *2 (-858 (-938 (-347 *4)))) (-5 *1 (-1206 *4 *5 *6))
+   (-14 *5 (-584 (-1089))) (-14 *6 (-584 (-1089)))))
+ ((*1 *2 *3)
+  (-12 (-5 *3 (-704 *4 (-774 *6))) (-4 *4 (-13 (-756) (-257) (-120) (-934)))
+   (-14 *6 (-584 (-1089))) (-5 *2 (-858 (-938 (-347 *4))))
+   (-5 *1 (-1206 *4 *5 *6)) (-14 *5 (-584 (-1089)))))
+ ((*1 *2 *3)
+  (-12 (-5 *3 (-1084 *4)) (-4 *4 (-13 (-756) (-257) (-120) (-934)))
+   (-5 *2 (-1084 (-938 (-347 *4)))) (-5 *1 (-1206 *4 *5 *6))
+   (-14 *5 (-584 (-1089))) (-14 *6 (-584 (-1089)))))
+ ((*1 *2 *3)
+  (-12 (-5 *3 (-1059 *4 (-469 (-774 *6)) (-774 *6) (-704 *4 (-774 *6))))
+   (-4 *4 (-13 (-756) (-257) (-120) (-934))) (-14 *6 (-584 (-1089)))
+   (-5 *2 (-584 (-704 *4 (-774 *6)))) (-5 *1 (-1206 *4 *5 *6))
+   (-14 *5 (-584 (-1089)))))) 
+(((*1 *2 *3) (-12 (-5 *2 (-345 *3)) (-5 *1 (-497 *3)) (-4 *3 (-483))))
+ ((*1 *2 *3)
+  (-12 (-4 *4 (-718)) (-4 *5 (-757)) (-4 *6 (-257)) (-5 *2 (-345 *3))
+   (-5 *1 (-682 *4 *5 *6 *3)) (-4 *3 (-862 *6 *4 *5))))
+ ((*1 *2 *3)
+  (-12 (-4 *4 (-718)) (-4 *5 (-757)) (-4 *6 (-257)) (-4 *7 (-862 *6 *4 *5))
+   (-5 *2 (-345 (-1084 *7))) (-5 *1 (-682 *4 *5 *6 *7)) (-5 *3 (-1084 *7))))
+ ((*1 *2 *1)
+  (-12 (-4 *3 (-389)) (-4 *3 (-962)) (-4 *4 (-718)) (-4 *5 (-757))
+   (-5 *2 (-345 *1)) (-4 *1 (-862 *3 *4 *5))))
+ ((*1 *2 *3)
+  (-12 (-4 *4 (-757)) (-4 *5 (-718)) (-4 *6 (-389)) (-5 *2 (-345 *3))
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@@ -796,10383 +796,10386 @@
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-(((*1 *2 *1 *3 *3) (-12 (-5 *3 (-830)) (-5 *2 (-1183)) (-5 *1 (-1180))))
- ((*1 *2 *1 *3 *3) (-12 (-5 *3 (-830)) (-5 *2 (-1183)) (-5 *1 (-1181))))) 
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- ((*1 *2 *3 *2) (-12 (-5 *2 (-1071)) (-5 *3 (-583 (-221))) (-5 *1 (-222))))
- ((*1 *2 *1 *3) (-12 (-5 *3 (-1071)) (-5 *2 (-1183)) (-5 *1 (-1180))))
- ((*1 *2 *1 *3) (-12 (-5 *3 (-1071)) (-5 *2 (-1183)) (-5 *1 (-1181))))) 
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+ ((*1 *2 *1) (-12 (-5 *2 (-584 (-221))) (-5 *1 (-1181))))
+ ((*1 *1 *1 *2) (-12 (-5 *2 (-584 (-221))) (-5 *1 (-1182))))
+ ((*1 *2 *1) (-12 (-5 *2 (-584 (-221))) (-5 *1 (-1182))))) 
+(((*1 *2 *1 *3 *3) (-12 (-5 *3 (-695)) (-5 *2 (-1184)) (-5 *1 (-1181))))
+ ((*1 *2 *1 *3 *3) (-12 (-5 *3 (-695)) (-5 *2 (-1184)) (-5 *1 (-1182))))) 
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+ ((*1 *2 *3 *2) (-12 (-5 *2 (-1072)) (-5 *3 (-584 (-221))) (-5 *1 (-222))))
+ ((*1 *2 *1 *3) (-12 (-5 *3 (-1072)) (-5 *2 (-1184)) (-5 *1 (-1181))))
+ ((*1 *2 *1 *3) (-12 (-5 *3 (-1072)) (-5 *2 (-1184)) (-5 *1 (-1182))))) 
 (((*1 *2 *1 *3 *3 *4 *4)
-  (-12 (-5 *3 (-694)) (-5 *4 (-830)) (-5 *2 (-1183)) (-5 *1 (-1180))))
+  (-12 (-5 *3 (-695)) (-5 *4 (-831)) (-5 *2 (-1184)) (-5 *1 (-1181))))
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-  (-12 (-5 *3 (-694)) (-5 *4 (-830)) (-5 *2 (-1183)) (-5 *1 (-1181))))) 
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   (-12
    (-5 *2
-    (-2 (|:| |theta| (-179)) (|:| |phi| (-179)) (|:| -3841 (-179))
+    (-2 (|:| |theta| (-179)) (|:| |phi| (-179)) (|:| -3843 (-179))
      (|:| |scaleX| (-179)) (|:| |scaleY| (-179)) (|:| |scaleZ| (-179))
      (|:| |deltaX| (-179)) (|:| |deltaY| (-179))))
    (-5 *1 (-221))))
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   (-12
    (-5 *2
-    (-2 (|:| |theta| (-179)) (|:| |phi| (-179)) (|:| -3841 (-179))
+    (-2 (|:| |theta| (-179)) (|:| |phi| (-179)) (|:| -3843 (-179))
      (|:| |scaleX| (-179)) (|:| |scaleY| (-179)) (|:| |scaleZ| (-179))
      (|:| |deltaX| (-179)) (|:| |deltaY| (-179))))
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- ((*1 *2 *1 *3 *3 *3) (-12 (-5 *3 (-327)) (-5 *2 (-1183)) (-5 *1 (-1181))))
- ((*1 *2 *1 *3 *3) (-12 (-5 *3 (-327)) (-5 *2 (-1183)) (-5 *1 (-1181))))
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+ ((*1 *2 *1 *3 *3 *3) (-12 (-5 *3 (-327)) (-5 *2 (-1184)) (-5 *1 (-1182))))
+ ((*1 *2 *1 *3 *3) (-12 (-5 *3 (-327)) (-5 *2 (-1184)) (-5 *1 (-1182))))
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-  (-12 (-5 *3 (-483)) (-5 *4 (-327)) (-5 *2 (-1183)) (-5 *1 (-1181))))
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  ((*1 *2 *1 *3)
   (-12
    (-5 *3
-    (-2 (|:| |theta| (-179)) (|:| |phi| (-179)) (|:| -3841 (-179))
+    (-2 (|:| |theta| (-179)) (|:| |phi| (-179)) (|:| -3843 (-179))
      (|:| |scaleX| (-179)) (|:| |scaleY| (-179)) (|:| |scaleZ| (-179))
      (|:| |deltaX| (-179)) (|:| |deltaY| (-179))))
-   (-5 *2 (-1183)) (-5 *1 (-1181))))
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  ((*1 *2 *1)
   (-12
    (-5 *2
-    (-2 (|:| |theta| (-179)) (|:| |phi| (-179)) (|:| -3841 (-179))
+    (-2 (|:| |theta| (-179)) (|:| |phi| (-179)) (|:| -3843 (-179))
      (|:| |scaleX| (-179)) (|:| |scaleY| (-179)) (|:| |scaleZ| (-179))
      (|:| |deltaX| (-179)) (|:| |deltaY| (-179))))
-   (-5 *1 (-1181))))
+   (-5 *1 (-1182))))
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-  (-12 (-5 *3 (-327)) (-5 *2 (-1183)) (-5 *1 (-1181))))) 
-(((*1 *2 *1 *3) (-12 (-5 *3 (-1071)) (-5 *2 (-1183)) (-5 *1 (-1180))))
- ((*1 *2 *1 *3) (-12 (-5 *3 (-1071)) (-5 *2 (-1183)) (-5 *1 (-1181))))) 
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+ ((*1 *2 *1 *3) (-12 (-5 *3 (-1072)) (-5 *2 (-1184)) (-5 *1 (-1182))))) 
 (((*1 *2 *1 *3 *4)
-  (-12 (-5 *3 (-830)) (-5 *4 (-783)) (-5 *2 (-1183)) (-5 *1 (-1180))))
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-(((*1 *2 *1 *3) (-12 (-5 *3 (-1071)) (-5 *2 (-1183)) (-5 *1 (-1181))))) 
-(((*1 *2 *1 *3) (-12 (-5 *3 (-1071)) (-5 *2 (-1183)) (-5 *1 (-1181))))) 
-(((*1 *2 *1 *3) (-12 (-5 *3 (-1071)) (-5 *2 (-1183)) (-5 *1 (-1181))))) 
-(((*1 *2 *1 *3 *3) (-12 (-5 *3 (-483)) (-5 *2 (-1183)) (-5 *1 (-1181))))
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+ ((*1 *2 *1 *3 *3 *3) (-12 (-5 *3 (-327)) (-5 *2 (-1184)) (-5 *1 (-1182))))
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-(((*1 *2 *1 *3) (-12 (-5 *3 (-1071)) (-5 *2 (-1183)) (-5 *1 (-1181))))) 
-(((*1 *2 *1 *3 *3 *3) (-12 (-5 *3 (-327)) (-5 *2 (-1183)) (-5 *1 (-1181))))) 
-(((*1 *2 *1 *3) (-12 (-5 *3 (-327)) (-5 *2 (-1183)) (-5 *1 (-1181))))) 
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-(((*1 *2 *1 *3 *3) (-12 (-5 *3 (-130)) (-5 *2 (-1183)) (-5 *1 (-1181))))) 
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 (((*1 *2 *1 *2 *3)
-  (-12 (-5 *3 (-583 (-1071))) (-5 *2 (-1071)) (-5 *1 (-1180))))
- ((*1 *2 *1 *2 *2) (-12 (-5 *2 (-1071)) (-5 *1 (-1180))))
- ((*1 *2 *1 *2) (-12 (-5 *2 (-1071)) (-5 *1 (-1180))))
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+ ((*1 *2 *1 *2 *2) (-12 (-5 *2 (-1072)) (-5 *1 (-1181))))
+ ((*1 *2 *1 *2) (-12 (-5 *2 (-1072)) (-5 *1 (-1181))))
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- ((*1 *2 *1 *2 *2) (-12 (-5 *2 (-1071)) (-5 *1 (-1181))))
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+ ((*1 *2 *1 *2 *2) (-12 (-5 *2 (-1072)) (-5 *1 (-1182))))
+ ((*1 *2 *1 *2) (-12 (-5 *2 (-1072)) (-5 *1 (-1182))))) 
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-(((*1 *1 *2 *3) (-12 (-5 *2 (-405)) (-5 *3 (-583 (-221))) (-5 *1 (-1180))))
- ((*1 *1 *1) (-5 *1 (-1180)))) 
+ ((*1 *2 *1) (-12 (-5 *2 (-1184)) (-5 *1 (-1181))))
+ ((*1 *2 *1) (-12 (-5 *2 (-1184)) (-5 *1 (-1182))))) 
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+ ((*1 *1 *1) (-5 *1 (-1181)))) 
 (((*1 *2 *1 *3 *4 *4 *4 *4 *5 *5 *5 *5 *6 *5 *6 *5)
-  (-12 (-5 *3 (-830)) (-5 *4 (-179)) (-5 *5 (-483)) (-5 *6 (-783))
-   (-5 *2 (-1183)) (-5 *1 (-1180))))) 
+  (-12 (-5 *3 (-831)) (-5 *4 (-179)) (-5 *5 (-484)) (-5 *6 (-784))
+   (-5 *2 (-1184)) (-5 *1 (-1181))))) 
 (((*1 *2 *1)
   (-12
    (-5 *2
-    (-1177
+    (-1178
      (-2 (|:| |scaleX| (-179)) (|:| |scaleY| (-179)) (|:| |deltaX| (-179))
-      (|:| |deltaY| (-179)) (|:| -3844 (-483)) (|:| -3842 (-483))
-      (|:| |spline| (-483)) (|:| -3873 (-483)) (|:| |axesColor| (-783))
-      (|:| -3845 (-483)) (|:| |unitsColor| (-783)) (|:| |showing| (-483)))))
-   (-5 *1 (-1180))))) 
-(((*1 *2 *3) (-12 (-5 *3 (-830)) (-5 *2 (-1090 (-347 (-483)))) (-5 *1 (-164))))
- ((*1 *2 *1) (-12 (-5 *2 (-1177 (-3 (-405) "undefined"))) (-5 *1 (-1180))))) 
+      (|:| |deltaY| (-179)) (|:| -3846 (-484)) (|:| -3844 (-484))
+      (|:| |spline| (-484)) (|:| -3875 (-484)) (|:| |axesColor| (-784))
+      (|:| -3847 (-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))))) 
 (((*1 *2 *1 *3 *4)
-  (-12 (-5 *3 (-405)) (-5 *4 (-830)) (-5 *2 (-1183)) (-5 *1 (-1180))))) 
-(((*1 *2 *1 *3) (-12 (-5 *3 (-830)) (-5 *2 (-405)) (-5 *1 (-1180))))) 
+  (-12 (-5 *3 (-405)) (-5 *4 (-831)) (-5 *2 (-1184)) (-5 *1 (-1181))))) 
+(((*1 *2 *1 *3) (-12 (-5 *3 (-831)) (-5 *2 (-405)) (-5 *1 (-1181))))) 
 (((*1 *2 *3 *2)
-  (-12 (-5 *2 (-583 (-327))) (-5 *3 (-583 (-221))) (-5 *1 (-222))))
- ((*1 *2 *1 *2) (-12 (-5 *2 (-583 (-327))) (-5 *1 (-405))))
- ((*1 *2 *1) (-12 (-5 *2 (-583 (-327))) (-5 *1 (-405))))
+  (-12 (-5 *2 (-584 (-327))) (-5 *3 (-584 (-221))) (-5 *1 (-222))))
+ ((*1 *2 *1 *2) (-12 (-5 *2 (-584 (-327))) (-5 *1 (-405))))
+ ((*1 *2 *1) (-12 (-5 *2 (-584 (-327))) (-5 *1 (-405))))
  ((*1 *2 *1 *3 *4)
-  (-12 (-5 *3 (-830)) (-5 *4 (-783)) (-5 *2 (-1183)) (-5 *1 (-1180))))
+  (-12 (-5 *3 (-831)) (-5 *4 (-784)) (-5 *2 (-1184)) (-5 *1 (-1181))))
  ((*1 *2 *1 *3 *4)
-  (-12 (-5 *3 (-830)) (-5 *4 (-1071)) (-5 *2 (-1183)) (-5 *1 (-1180))))) 
+  (-12 (-5 *3 (-831)) (-5 *4 (-1072)) (-5 *2 (-1184)) (-5 *1 (-1181))))) 
 (((*1 *2 *1 *3 *4)
-  (-12 (-5 *3 (-830)) (-5 *4 (-1071)) (-5 *2 (-1183)) (-5 *1 (-1180))))) 
+  (-12 (-5 *3 (-831)) (-5 *4 (-1072)) (-5 *2 (-1184)) (-5 *1 (-1181))))) 
 (((*1 *2 *1 *3 *4)
-  (-12 (-5 *3 (-830)) (-5 *4 (-1071)) (-5 *2 (-1183)) (-5 *1 (-1180))))) 
+  (-12 (-5 *3 (-831)) (-5 *4 (-1072)) (-5 *2 (-1184)) (-5 *1 (-1181))))) 
 (((*1 *2 *1 *3 *4)
-  (-12 (-5 *3 (-830)) (-5 *4 (-1071)) (-5 *2 (-1183)) (-5 *1 (-1180))))) 
-(((*1 *1 *2 *2 *2) (-12 (-5 *1 (-181 *2)) (-4 *2 (-13 (-311) (-1113)))))
- ((*1 *1 *1 *2) (-12 (-5 *1 (-655 *2)) (-4 *2 (-311))))
- ((*1 *1 *2) (-12 (-5 *1 (-655 *2)) (-4 *2 (-311))))
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+ ((*1 *1 *1 *2) (-12 (-5 *1 (-656 *2)) (-4 *2 (-311))))
+ ((*1 *1 *2) (-12 (-5 *1 (-656 *2)) (-4 *2 (-311))))
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-  (-12 (-5 *3 (-830)) (-5 *4 (-327)) (-5 *2 (-1183)) (-5 *1 (-1180))))) 
+  (-12 (-5 *3 (-831)) (-5 *4 (-327)) (-5 *2 (-1184)) (-5 *1 (-1181))))) 
 (((*1 *2 *1 *3 *4)
-  (-12 (-5 *3 (-830)) (-5 *4 (-1071)) (-5 *2 (-1183)) (-5 *1 (-1180))))) 
+  (-12 (-5 *3 (-831)) (-5 *4 (-1072)) (-5 *2 (-1184)) (-5 *1 (-1181))))) 
 (((*1 *2 *1 *3 *4)
-  (-12 (-5 *3 (-405)) (-5 *4 (-830)) (-5 *2 (-1183)) (-5 *1 (-1180))))) 
+  (-12 (-5 *3 (-405)) (-5 *4 (-831)) (-5 *2 (-1184)) (-5 *1 (-1181))))) 
 (((*1 *2 *3 *4 *4 *5 *6)
-  (-12 (-5 *3 (-583 (-583 (-854 (-179))))) (-5 *4 (-783)) (-5 *5 (-830))
-   (-5 *6 (-583 (-221))) (-5 *2 (-1180)) (-5 *1 (-1179))))
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-  (-12 (-5 *3 (-583 (-583 (-854 (-179))))) (-5 *4 (-583 (-221)))
-   (-5 *2 (-1180)) (-5 *1 (-1179))))) 
+  (-12 (-5 *3 (-584 (-584 (-855 (-179))))) (-5 *4 (-584 (-221)))
+   (-5 *2 (-1181)) (-5 *1 (-1180))))) 
 (((*1 *2 *3 *4 *4 *5 *6)
-  (-12 (-5 *3 (-583 (-583 (-854 (-179))))) (-5 *4 (-783)) (-5 *5 (-830))
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+   (-5 *6 (-584 (-221))) (-5 *2 (-405)) (-5 *1 (-1180))))
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+  (-12 (-5 *3 (-584 (-584 (-855 (-179))))) (-5 *2 (-405)) (-5 *1 (-1180))))
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-  (-12 (-5 *3 (-583 (-583 (-854 (-179))))) (-5 *4 (-583 (-221))) (-5 *2 (-405))
-   (-5 *1 (-1179))))) 
+  (-12 (-5 *3 (-584 (-584 (-855 (-179))))) (-5 *4 (-584 (-221))) (-5 *2 (-405))
+   (-5 *1 (-1180))))) 
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-  (-12 (-5 *3 (-1 *2 *5 *2)) (-5 *4 (-58 *5)) (-4 *5 (-1127)) (-4 *2 (-1127))
+  (-12 (-5 *3 (-1 *2 *5 *2)) (-5 *4 (-58 *5)) (-4 *5 (-1128)) (-4 *2 (-1128))
    (-5 *1 (-59 *5 *2))))
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-  (-12 (-5 *3 (-1 *2 *2 *2)) (-4 *2 (-1012)) (|has| *1 (-6 -3989))
-   (-4 *1 (-124 *2)) (-4 *2 (-1127))))
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+   (-4 *1 (-124 *2)) (-4 *2 (-1128))))
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-  (-12 (-5 *3 (-1 *2 *2 *2)) (|has| *1 (-6 -3989)) (-4 *1 (-124 *2))
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-  (|partial| -12 (-4 *1 (-1141 *3 *2)) (-4 *3 (-961)) (-4 *2 (-1170 *3))))) 
+  (|partial| -12 (-4 *1 (-1142 *3 *2)) (-4 *3 (-962)) (-4 *2 (-1171 *3))))) 
 (((*1 *2 *1 *3 *3)
-  (-12 (-5 *3 (-483)) (-4 *1 (-1139 *4)) (-4 *4 (-961)) (-4 *4 (-494))
-   (-5 *2 (-347 (-857 *4)))))
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+   (-5 *2 (-347 (-858 *4)))))
  ((*1 *2 *1 *3)
-  (-12 (-5 *3 (-483)) (-4 *1 (-1139 *4)) (-4 *4 (-961)) (-4 *4 (-494))
-   (-5 *2 (-347 (-857 *4)))))) 
+  (-12 (-5 *3 (-484)) (-4 *1 (-1140 *4)) (-4 *4 (-962)) (-4 *4 (-495))
+   (-5 *2 (-347 (-858 *4)))))) 
 (((*1 *1 *1 *1) (-5 *1 (-101)))
- ((*1 *1 *1 *1) (-12 (-5 *1 (-1095 *2)) (-14 *2 (-830))))
- ((*1 *1 *1 *1) (-5 *1 (-1133))) ((*1 *1 *1 *1) (-5 *1 (-1134)))
- ((*1 *1 *1 *1) (-5 *1 (-1135))) ((*1 *1 *1 *1) (-5 *1 (-1136)))) 
+ ((*1 *1 *1 *1) (-12 (-5 *1 (-1096 *2)) (-14 *2 (-831))))
+ ((*1 *1 *1 *1) (-5 *1 (-1134))) ((*1 *1 *1 *1) (-5 *1 (-1135)))
+ ((*1 *1 *1 *1) (-5 *1 (-1136))) ((*1 *1 *1 *1) (-5 *1 (-1137)))) 
 (((*1 *1 *1 *1) (-5 *1 (-101)))
- ((*1 *1 *1 *1) (-12 (-5 *1 (-1095 *2)) (-14 *2 (-830))))
- ((*1 *1 *1 *1) (-5 *1 (-1133))) ((*1 *1 *1 *1) (-5 *1 (-1134)))
- ((*1 *1 *1 *1) (-5 *1 (-1135))) ((*1 *1 *1 *1) (-5 *1 (-1136)))) 
+ ((*1 *1 *1 *1) (-12 (-5 *1 (-1096 *2)) (-14 *2 (-831))))
+ ((*1 *1 *1 *1) (-5 *1 (-1134))) ((*1 *1 *1 *1) (-5 *1 (-1135)))
+ ((*1 *1 *1 *1) (-5 *1 (-1136))) ((*1 *1 *1 *1) (-5 *1 (-1137)))) 
 (((*1 *1) (-4 *1 (-23))) ((*1 *1) (-4 *1 (-34))) ((*1 *1) (-5 *1 (-101)))
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- ((*1 *1) (-5 *1 (-484))) ((*1 *1) (-5 *1 (-485))) ((*1 *1) (-5 *1 (-486)))
- ((*1 *1) (-5 *1 (-487))) ((*1 *1) (-4 *1 (-663))) ((*1 *1) (-5 *1 (-1088)))
- ((*1 *1) (-12 (-5 *1 (-1094 *2)) (-14 *2 (-830))))
- ((*1 *1) (-12 (-5 *1 (-1095 *2)) (-14 *2 (-830)))) ((*1 *1) (-5 *1 (-1133)))
- ((*1 *1) (-5 *1 (-1134))) ((*1 *1) (-5 *1 (-1135))) ((*1 *1) (-5 *1 (-1136)))) 
-(((*1 *2 *3) (-12 (-5 *3 (-142 (-483))) (-5 *2 (-85)) (-5 *1 (-383))))
+  (-12 (-5 *1 (-108 *2 *3 *4)) (-14 *2 (-484)) (-14 *3 (-695)) (-4 *4 (-146))))
+ ((*1 *1) (-5 *1 (-485))) ((*1 *1) (-5 *1 (-486))) ((*1 *1) (-5 *1 (-487)))
+ ((*1 *1) (-5 *1 (-488))) ((*1 *1) (-4 *1 (-664))) ((*1 *1) (-5 *1 (-1089)))
+ ((*1 *1) (-12 (-5 *1 (-1095 *2)) (-14 *2 (-831))))
+ ((*1 *1) (-12 (-5 *1 (-1096 *2)) (-14 *2 (-831)))) ((*1 *1) (-5 *1 (-1134)))
+ ((*1 *1) (-5 *1 (-1135))) ((*1 *1) (-5 *1 (-1136))) ((*1 *1) (-5 *1 (-1137)))) 
+(((*1 *2 *3) (-12 (-5 *3 (-142 (-484))) (-5 *2 (-85)) (-5 *1 (-383))))
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   (-12
    (-5 *3
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-   (-14 *4 (-583 (-1088))) (-14 *5 (-694)) (-5 *2 (-85)) (-5 *1 (-442 *4 *5))))
- ((*1 *2 *3) (-12 (-5 *2 (-85)) (-5 *1 (-873 *3)) (-4 *3 (-482))))
- ((*1 *2 *1) (-12 (-4 *1 (-1132)) (-5 *2 (-85))))) 
-(((*1 *2) (-12 (-5 *2 (-1183)) (-5 *1 (-1130))))) 
+    (-441 (-347 (-484)) (-197 *5 (-695)) (-774 *4) (-206 *4 (-347 (-484)))))
+   (-14 *4 (-584 (-1089))) (-14 *5 (-695)) (-5 *2 (-85)) (-5 *1 (-442 *4 *5))))
+ ((*1 *2 *3) (-12 (-5 *2 (-85)) (-5 *1 (-874 *3)) (-4 *3 (-483))))
+ ((*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 (|:| -3223 (-583 (-1088))) (|:| -3224 (-583 (-1088)))))
-   (-5 *1 (-1130))))) 
-(((*1 *2 *3) (-12 (-5 *3 (-583 (-1088))) (-5 *2 (-1183)) (-5 *1 (-1130))))
- ((*1 *2 *3 *3) (-12 (-5 *3 (-583 (-1088))) (-5 *2 (-1183)) (-5 *1 (-1130))))) 
+  (-12 (-5 *2 (-2 (|:| -3225 (-584 (-1089))) (|:| -3226 (-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))))) 
 (((*1 *2 *1 *3)
-  (-12 (-5 *3 (-694)) (-4 *1 (-1062 *4)) (-4 *4 (-1127)) (-5 *2 (-85))))
+  (-12 (-5 *3 (-695)) (-4 *1 (-1063 *4)) (-4 *4 (-1128)) (-5 *2 (-85))))
  ((*1 *2 *3 *3)
-  (-12 (-5 *2 (-85)) (-5 *1 (-1129 *3)) (-4 *3 (-756)) (-4 *3 (-1012))))) 
+  (-12 (-5 *2 (-85)) (-5 *1 (-1130 *3)) (-4 *3 (-757)) (-4 *3 (-1013))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *3 (-583 *2)) (-5 *4 (-1 (-85) *2 *2)) (-5 *1 (-1129 *2))
-   (-4 *2 (-1012))))
+  (-12 (-5 *3 (-584 *2)) (-5 *4 (-1 (-85) *2 *2)) (-5 *1 (-1130 *2))
+   (-4 *2 (-1013))))
  ((*1 *2 *3)
-  (-12 (-5 *3 (-583 *2)) (-4 *2 (-1012)) (-4 *2 (-756)) (-5 *1 (-1129 *2))))) 
-(((*1 *2) (-12 (-5 *2 (-85)) (-5 *1 (-1129 *3)) (-4 *3 (-1012))))) 
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+(((*1 *2) (-12 (-5 *2 (-85)) (-5 *1 (-1130 *3)) (-4 *3 (-1013))))) 
 (((*1 *2 *1 *3)
-  (-12 (-5 *3 (-694)) (-4 *1 (-1062 *4)) (-4 *4 (-1127)) (-5 *2 (-85))))
+  (-12 (-5 *3 (-695)) (-4 *1 (-1063 *4)) (-4 *4 (-1128)) (-5 *2 (-85))))
  ((*1 *2 *3 *3)
-  (|partial| -12 (-5 *2 (-85)) (-5 *1 (-1129 *3)) (-4 *3 (-1012))))
+  (|partial| -12 (-5 *2 (-85)) (-5 *1 (-1130 *3)) (-4 *3 (-1013))))
  ((*1 *2 *3 *3 *4)
-  (-12 (-5 *4 (-1 (-85) *3 *3)) (-4 *3 (-1012)) (-5 *2 (-85))
-   (-5 *1 (-1129 *3))))) 
+  (-12 (-5 *4 (-1 (-85) *3 *3)) (-4 *3 (-1013)) (-5 *2 (-85))
+   (-5 *1 (-1130 *3))))) 
 (((*1 *2)
-  (-12 (-5 *2 (-2 (|:| -3224 (-583 *3)) (|:| -3223 (-583 *3))))
-   (-5 *1 (-1129 *3)) (-4 *3 (-1012))))) 
+  (-12 (-5 *2 (-2 (|:| -3226 (-584 *3)) (|:| -3225 (-584 *3))))
+   (-5 *1 (-1130 *3)) (-4 *3 (-1013))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-583 *4)) (-4 *4 (-1012)) (-5 *2 (-1183)) (-5 *1 (-1129 *4))))
+  (-12 (-5 *3 (-584 *4)) (-4 *4 (-1013)) (-5 *2 (-1184)) (-5 *1 (-1130 *4))))
  ((*1 *2 *3 *3)
-  (-12 (-5 *3 (-583 *4)) (-4 *4 (-1012)) (-5 *2 (-1183)) (-5 *1 (-1129 *4))))) 
+  (-12 (-5 *3 (-584 *4)) (-4 *4 (-1013)) (-5 *2 (-1184)) (-5 *1 (-1130 *4))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *4 (-483)) (-4 *5 (-298)) (-5 *2 (-345 (-1083 (-1083 *5))))
-   (-5 *1 (-1126 *5)) (-5 *3 (-1083 (-1083 *5)))))) 
+  (-12 (-5 *4 (-484)) (-4 *5 (-298)) (-5 *2 (-345 (-1084 (-1084 *5))))
+   (-5 *1 (-1127 *5)) (-5 *3 (-1084 (-1084 *5)))))) 
 (((*1 *2 *3)
-  (-12 (-4 *4 (-298)) (-5 *2 (-345 (-1083 (-1083 *4)))) (-5 *1 (-1126 *4))
-   (-5 *3 (-1083 (-1083 *4)))))) 
+  (-12 (-4 *4 (-298)) (-5 *2 (-345 (-1084 (-1084 *4)))) (-5 *1 (-1127 *4))
+   (-5 *3 (-1084 (-1084 *4)))))) 
 (((*1 *2 *3)
-  (-12 (-4 *4 (-298)) (-5 *2 (-345 (-1083 (-1083 *4)))) (-5 *1 (-1126 *4))
-   (-5 *3 (-1083 (-1083 *4)))))) 
+  (-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 -3989)) (-4 *1 (-124 *3))
-   (-4 *3 (-1127))))
- ((*1 *1 *2 *1) (-12 (-5 *2 (-1 (-85) *3)) (-4 *3 (-1127)) (-5 *1 (-535 *3))))
- ((*1 *1 *2 *1) (-12 (-5 *2 (-1 (-85) *3)) (-4 *1 (-616 *3)) (-4 *3 (-1127))))
+  (-12 (-5 *2 (-1 (-85) *3)) (|has| *1 (-6 -3991)) (-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))))
  ((*1 *2 *1 *3)
-  (|partial| -12 (-4 *1 (-1122 *4 *5 *3 *2)) (-4 *4 (-494)) (-4 *5 (-717))
-   (-4 *3 (-756)) (-4 *2 (-976 *4 *5 *3))))
- ((*1 *2 *1 *3) (-12 (-5 *3 (-694)) (-5 *1 (-1125 *2)) (-4 *2 (-1127))))) 
+  (|partial| -12 (-4 *1 (-1123 *4 *5 *3 *2)) (-4 *4 (-495)) (-4 *5 (-718))
+   (-4 *3 (-757)) (-4 *2 (-977 *4 *5 *3))))
+ ((*1 *2 *1 *3) (-12 (-5 *3 (-695)) (-5 *1 (-1126 *2)) (-4 *2 (-1128))))) 
 (((*1 *2 *3 *3 *3 *4 *5)
-  (-12 (-5 *5 (-583 (-583 (-179)))) (-5 *4 (-179)) (-5 *2 (-583 (-854 *4)))
-   (-5 *1 (-1124)) (-5 *3 (-854 *4))))) 
-(((*1 *2 *3) (-12 (-5 *3 (-483)) (-5 *2 (-583 (-583 (-179)))) (-5 *1 (-1124))))) 
+  (-12 (-5 *5 (-584 (-584 (-179)))) (-5 *4 (-179)) (-5 *2 (-584 (-855 *4)))
+   (-5 *1 (-1125)) (-5 *3 (-855 *4))))) 
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 (((*1 *1 *2)
-  (-12 (-5 *2 (-830)) (-4 *1 (-196 *3 *4)) (-4 *4 (-961)) (-4 *4 (-1127))))
+  (-12 (-5 *2 (-831)) (-4 *1 (-196 *3 *4)) (-4 *4 (-962)) (-4 *4 (-1128))))
  ((*1 *1 *2)
-  (-12 (-14 *3 (-583 (-1088))) (-4 *4 (-146)) (-4 *5 (-196 (-3951 *3) (-694)))
+  (-12 (-14 *3 (-584 (-1089))) (-4 *4 (-146)) (-4 *5 (-196 (-3953 *3) (-695)))
    (-14 *6
-    (-1 (-85) (-2 (|:| -2396 *2) (|:| -2397 *5))
-     (-2 (|:| -2396 *2) (|:| -2397 *5))))
-   (-5 *1 (-398 *3 *4 *2 *5 *6 *7)) (-4 *2 (-756))
-   (-4 *7 (-861 *4 *5 (-773 *3)))))
- ((*1 *2 *2) (-12 (-5 *2 (-854 (-179))) (-5 *1 (-1124))))) 
+    (-1 (-85) (-2 (|:| -2398 *2) (|:| -2399 *5))
+     (-2 (|:| -2398 *2) (|:| -2399 *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))))) 
 (((*1 *2 *1 *3 *4)
-  (-12 (-5 *3 (-854 (-179))) (-5 *4 (-783)) (-5 *2 (-1183)) (-5 *1 (-405))))
- ((*1 *1 *2) (-12 (-5 *2 (-583 *3)) (-4 *3 (-961)) (-4 *1 (-893 *3))))
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- ((*1 *1 *1 *2) (-12 (-5 *2 (-694)) (-4 *1 (-1046 *3)) (-4 *3 (-961))))
- ((*1 *1 *1 *2) (-12 (-5 *2 (-583 *3)) (-4 *1 (-1046 *3)) (-4 *3 (-961))))
- ((*1 *1 *1 *2) (-12 (-5 *2 (-854 *3)) (-4 *1 (-1046 *3)) (-4 *3 (-961))))
+  (-12 (-5 *3 (-855 (-179))) (-5 *4 (-784)) (-5 *2 (-1184)) (-5 *1 (-405))))
+ ((*1 *1 *2) (-12 (-5 *2 (-584 *3)) (-4 *3 (-962)) (-4 *1 (-894 *3))))
+ ((*1 *2 *1) (-12 (-4 *1 (-1047 *3)) (-4 *3 (-962)) (-5 *2 (-855 *3))))
+ ((*1 *1 *2) (-12 (-5 *2 (-855 *3)) (-4 *3 (-962)) (-4 *1 (-1047 *3))))
+ ((*1 *1 *1 *2) (-12 (-5 *2 (-695)) (-4 *1 (-1047 *3)) (-4 *3 (-962))))
+ ((*1 *1 *1 *2) (-12 (-5 *2 (-584 *3)) (-4 *1 (-1047 *3)) (-4 *3 (-962))))
+ ((*1 *1 *1 *2) (-12 (-5 *2 (-855 *3)) (-4 *1 (-1047 *3)) (-4 *3 (-962))))
  ((*1 *2 *3 *3 *3 *3)
-  (-12 (-5 *2 (-854 (-179))) (-5 *1 (-1124)) (-5 *3 (-179))))) 
+  (-12 (-5 *2 (-855 (-179))) (-5 *1 (-1125)) (-5 *3 (-179))))) 
 (((*1 *2 *3 *4 *5)
-  (-12 (-5 *4 (-179)) (-5 *5 (-483)) (-5 *2 (-1123 *3)) (-5 *1 (-712 *3))
-   (-4 *3 (-887))))
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+   (-4 *3 (-888))))
  ((*1 *1 *2 *3 *4)
-  (-12 (-5 *3 (-583 (-583 (-854 (-179))))) (-5 *4 (-85)) (-5 *1 (-1123 *2))
-   (-4 *2 (-887))))) 
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-(((*1 *2 *1) (-12 (-5 *2 (-85)) (-5 *1 (-1123 *3)) (-4 *3 (-887))))) 
+  (-12 (-5 *3 (-584 (-584 (-855 (-179))))) (-5 *4 (-85)) (-5 *1 (-1124 *2))
+   (-4 *2 (-888))))) 
+(((*1 *2 *1 *2) (-12 (-5 *2 (-85)) (-5 *1 (-1124 *3)) (-4 *3 (-888))))) 
+(((*1 *2 *1) (-12 (-5 *2 (-85)) (-5 *1 (-1124 *3)) (-4 *3 (-888))))) 
 (((*1 *2 *1) (-12 (-5 *2 (-85)) (-5 *1 (-145))))
- ((*1 *2 *1) (-12 (-5 *2 (-85)) (-5 *1 (-1123 *3)) (-4 *3 (-887))))) 
+ ((*1 *2 *1) (-12 (-5 *2 (-85)) (-5 *1 (-1124 *3)) (-4 *3 (-888))))) 
 (((*1 *2 *1)
-  (-12 (-5 *2 (-583 (-583 (-854 (-179))))) (-5 *1 (-1123 *3)) (-4 *3 (-887))))) 
-(((*1 *2 *1) (-12 (-5 *1 (-1123 *2)) (-4 *2 (-887))))) 
+  (-12 (-5 *2 (-584 (-584 (-855 (-179))))) (-5 *1 (-1124 *3)) (-4 *3 (-888))))) 
+(((*1 *2 *1) (-12 (-5 *1 (-1124 *2)) (-4 *2 (-888))))) 
 (((*1 *2 *3 *3)
-  (-12 (-5 *3 (-583 *7)) (-4 *7 (-976 *4 *5 *6)) (-4 *4 (-389)) (-4 *5 (-717))
-   (-4 *6 (-756)) (-5 *2 (-85)) (-5 *1 (-901 *4 *5 *6 *7 *8))
-   (-4 *8 (-982 *4 *5 *6 *7))))
+  (-12 (-5 *3 (-584 *7)) (-4 *7 (-977 *4 *5 *6)) (-4 *4 (-389)) (-4 *5 (-718))
+   (-4 *6 (-757)) (-5 *2 (-85)) (-5 *1 (-902 *4 *5 *6 *7 *8))
+   (-4 *8 (-983 *4 *5 *6 *7))))
  ((*1 *2 *1 *1)
-  (-12 (-4 *1 (-976 *3 *4 *5)) (-4 *3 (-961)) (-4 *4 (-717)) (-4 *5 (-756))
+  (-12 (-4 *1 (-977 *3 *4 *5)) (-4 *3 (-962)) (-4 *4 (-718)) (-4 *5 (-757))
    (-5 *2 (-85))))
  ((*1 *2 *3 *3)
-  (-12 (-5 *3 (-583 *7)) (-4 *7 (-976 *4 *5 *6)) (-4 *4 (-389)) (-4 *5 (-717))
-   (-4 *6 (-756)) (-5 *2 (-85)) (-5 *1 (-1017 *4 *5 *6 *7 *8))
-   (-4 *8 (-982 *4 *5 *6 *7))))
+  (-12 (-5 *3 (-584 *7)) (-4 *7 (-977 *4 *5 *6)) (-4 *4 (-389)) (-4 *5 (-718))
+   (-4 *6 (-757)) (-5 *2 (-85)) (-5 *1 (-1018 *4 *5 *6 *7 *8))
+   (-4 *8 (-983 *4 *5 *6 *7))))
  ((*1 *2 *1 *1)
-  (-12 (-4 *1 (-1122 *3 *4 *5 *6)) (-4 *3 (-494)) (-4 *4 (-717)) (-4 *5 (-756))
-   (-4 *6 (-976 *3 *4 *5)) (-5 *2 (-85))))) 
+  (-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 (-85))))) 
 (((*1 *2 *3 *4 *5)
   (|partial| -12 (-5 *4 (-1 (-85) *9)) (-5 *5 (-1 (-85) *9 *9))
-   (-4 *9 (-976 *6 *7 *8)) (-4 *6 (-494)) (-4 *7 (-717)) (-4 *8 (-756))
-   (-5 *2 (-2 (|:| |bas| *1) (|:| -3318 (-583 *9)))) (-5 *3 (-583 *9))
-   (-4 *1 (-1122 *6 *7 *8 *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))
+   (-4 *1 (-1123 *6 *7 *8 *9))))
  ((*1 *2 *3 *4)
-  (|partial| -12 (-5 *4 (-1 (-85) *8 *8)) (-4 *8 (-976 *5 *6 *7))
-   (-4 *5 (-494)) (-4 *6 (-717)) (-4 *7 (-756))
-   (-5 *2 (-2 (|:| |bas| *1) (|:| -3318 (-583 *8)))) (-5 *3 (-583 *8))
-   (-4 *1 (-1122 *5 *6 *7 *8))))) 
+  (|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))
+   (-4 *1 (-1123 *5 *6 *7 *8))))) 
 (((*1 *2 *1)
-  (-12 (-4 *1 (-1122 *3 *4 *5 *6)) (-4 *3 (-494)) (-4 *4 (-717)) (-4 *5 (-756))
-   (-4 *6 (-976 *3 *4 *5)) (-5 *2 (-583 *6))))) 
+  (-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 (-584 *6))))) 
 (((*1 *2 *1)
-  (-12 (-4 *1 (-1122 *3 *4 *5 *6)) (-4 *3 (-494)) (-4 *4 (-717)) (-4 *5 (-756))
-   (-4 *6 (-976 *3 *4 *5))
-   (-5 *2 (-2 (|:| -3855 (-583 *6)) (|:| -1699 (-583 *6))))))) 
+  (-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))))))) 
 (((*1 *2 *1 *3)
-  (-12 (-5 *3 (-583 *1)) (-4 *1 (-976 *4 *5 *6)) (-4 *4 (-961)) (-4 *5 (-717))
-   (-4 *6 (-756)) (-5 *2 (-85))))
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+   (-4 *6 (-757)) (-5 *2 (-85))))
  ((*1 *2 *1 *1)
-  (-12 (-4 *1 (-976 *3 *4 *5)) (-4 *3 (-961)) (-4 *4 (-717)) (-4 *5 (-756))
+  (-12 (-4 *1 (-977 *3 *4 *5)) (-4 *3 (-962)) (-4 *4 (-718)) (-4 *5 (-757))
    (-5 *2 (-85))))
  ((*1 *2 *1)
-  (-12 (-4 *1 (-1122 *3 *4 *5 *6)) (-4 *3 (-494)) (-4 *4 (-717)) (-4 *5 (-756))
-   (-4 *6 (-976 *3 *4 *5)) (-5 *2 (-85))))
+  (-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 (-85))))
  ((*1 *2 *3 *1)
-  (-12 (-4 *1 (-1122 *4 *5 *6 *3)) (-4 *4 (-494)) (-4 *5 (-717)) (-4 *6 (-756))
-   (-4 *3 (-976 *4 *5 *6)) (-5 *2 (-85))))) 
+  (-12 (-4 *1 (-1123 *4 *5 *6 *3)) (-4 *4 (-495)) (-4 *5 (-718)) (-4 *6 (-757))
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 (((*1 *2 *1 *3)
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 (((*1 *2 *3 *1)
   (-12
-   (-5 *2 (-2 (|:| |cycle?| (-85)) (|:| -2591 (-694)) (|:| |period| (-694))))
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 (((*1 *2 *2)
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 (((*1 *2 *3 *4 *4 *4)
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   (-12
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-  (-12 (-5 *3 (-1146 *5 *4)) (-4 *4 (-740)) (-14 *5 (-1088)) (-5 *2 (-583 *4))
-   (-5 *1 (-1026 *4 *5))))) 
+  (-12 (-5 *3 (-1147 *5 *4)) (-4 *4 (-741)) (-14 *5 (-1089)) (-5 *2 (-584 *4))
+   (-5 *1 (-1027 *4 *5))))) 
 (((*1 *2 *3 *3)
-  (-12 (-4 *4 (-740)) (-14 *5 (-1088)) (-5 *2 (-583 (-1146 *5 *4)))
-   (-5 *1 (-1026 *4 *5)) (-5 *3 (-1146 *5 *4))))) 
+  (-12 (-4 *4 (-741)) (-14 *5 (-1089)) (-5 *2 (-584 (-1147 *5 *4)))
+   (-5 *1 (-1027 *4 *5)) (-5 *3 (-1147 *5 *4))))) 
 (((*1 *2 *3 *3)
-  (-12 (-4 *4 (-740)) (-14 *5 (-1088)) (-5 *2 (-583 (-1146 *5 *4)))
-   (-5 *1 (-1026 *4 *5)) (-5 *3 (-1146 *5 *4))))) 
-(((*1 *1 *2) (-12 (-5 *2 (-1 *3 *3 *3)) (-4 *3 (-72)) (-5 *1 (-1021 *3))))) 
-(((*1 *2 *3 *3 *3) (-12 (-5 *2 (-583 (-483))) (-5 *1 (-1020)) (-5 *3 (-483))))) 
-(((*1 *2 *3 *3 *3) (-12 (-5 *2 (-583 (-483))) (-5 *1 (-1020)) (-5 *3 (-483))))) 
-(((*1 *2 *3 *3 *3) (-12 (-5 *2 (-583 (-483))) (-5 *1 (-1020)) (-5 *3 (-483))))) 
-(((*1 *2 *2 *2) (-12 (-5 *2 (-483)) (-5 *1 (-1020))))) 
-(((*1 *2 *2 *2 *3) (-12 (-5 *2 (-1177 (-483))) (-5 *3 (-483)) (-5 *1 (-1020))))
+  (-12 (-4 *4 (-741)) (-14 *5 (-1089)) (-5 *2 (-584 (-1147 *5 *4)))
+   (-5 *1 (-1027 *4 *5)) (-5 *3 (-1147 *5 *4))))) 
+(((*1 *1 *2) (-12 (-5 *2 (-1 *3 *3 *3)) (-4 *3 (-72)) (-5 *1 (-1022 *3))))) 
+(((*1 *2 *3 *3 *3) (-12 (-5 *2 (-584 (-484))) (-5 *1 (-1021)) (-5 *3 (-484))))) 
+(((*1 *2 *3 *3 *3) (-12 (-5 *2 (-584 (-484))) (-5 *1 (-1021)) (-5 *3 (-484))))) 
+(((*1 *2 *3 *3 *3) (-12 (-5 *2 (-584 (-484))) (-5 *1 (-1021)) (-5 *3 (-484))))) 
+(((*1 *2 *2 *2) (-12 (-5 *2 (-484)) (-5 *1 (-1021))))) 
+(((*1 *2 *2 *2 *3) (-12 (-5 *2 (-1178 (-484))) (-5 *3 (-484)) (-5 *1 (-1021))))
  ((*1 *2 *3 *2 *4)
-  (-12 (-5 *2 (-1177 (-483))) (-5 *3 (-583 (-483))) (-5 *4 (-483))
-   (-5 *1 (-1020))))) 
+  (-12 (-5 *2 (-1178 (-484))) (-5 *3 (-584 (-484))) (-5 *4 (-484))
+   (-5 *1 (-1021))))) 
 (((*1 *2 *3 *2 *4)
-  (-12 (-5 *2 (-583 (-483))) (-5 *3 (-583 (-830))) (-5 *4 (-85))
-   (-5 *1 (-1020))))) 
+  (-12 (-5 *2 (-584 (-484))) (-5 *3 (-584 (-831))) (-5 *4 (-85))
+   (-5 *1 (-1021))))) 
 (((*1 *2 *3 *3 *2)
-  (-12 (-5 *2 (-630 (-483))) (-5 *3 (-583 (-483))) (-5 *1 (-1020))))) 
+  (-12 (-5 *2 (-631 (-484))) (-5 *3 (-584 (-484))) (-5 *1 (-1021))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *3 (-583 (-830))) (-5 *4 (-583 (-483))) (-5 *2 (-630 (-483)))
-   (-5 *1 (-1020))))) 
+  (-12 (-5 *3 (-584 (-831))) (-5 *4 (-584 (-484))) (-5 *2 (-631 (-484)))
+   (-5 *1 (-1021))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-583 (-830))) (-5 *2 (-583 (-630 (-483)))) (-5 *1 (-1020))))) 
+  (-12 (-5 *3 (-584 (-831))) (-5 *2 (-584 (-631 (-484)))) (-5 *1 (-1021))))) 
 (((*1 *2 *2 *2 *3)
-  (-12 (-5 *2 (-583 (-483))) (-5 *3 (-630 (-483))) (-5 *1 (-1020))))) 
+  (-12 (-5 *2 (-584 (-484))) (-5 *3 (-631 (-484))) (-5 *1 (-1021))))) 
 (((*1 *2 *3 *3 *3)
-  (-12 (-5 *3 (-583 (-483))) (-5 *2 (-630 (-483))) (-5 *1 (-1020))))) 
+  (-12 (-5 *3 (-584 (-484))) (-5 *2 (-631 (-484))) (-5 *1 (-1021))))) 
 (((*1 *2 *3 *4)
-  (-12 (-4 *5 (-389)) (-4 *6 (-717)) (-4 *7 (-756)) (-4 *3 (-976 *5 *6 *7))
-   (-5 *2 (-583 (-2 (|:| |val| *3) (|:| -1597 *4))))
-   (-5 *1 (-1018 *5 *6 *7 *3 *4)) (-4 *4 (-982 *5 *6 *7 *3))))) 
+  (-12 (-4 *5 (-389)) (-4 *6 (-718)) (-4 *7 (-757)) (-4 *3 (-977 *5 *6 *7))
+   (-5 *2 (-584 (-2 (|:| |val| *3) (|:| -1598 *4))))
+   (-5 *1 (-1019 *5 *6 *7 *3 *4)) (-4 *4 (-983 *5 *6 *7 *3))))) 
 (((*1 *2 *3 *4)
-  (-12 (-4 *5 (-389)) (-4 *6 (-717)) (-4 *7 (-756)) (-4 *3 (-976 *5 *6 *7))
-   (-5 *2 (-583 *4)) (-5 *1 (-1018 *5 *6 *7 *3 *4))
-   (-4 *4 (-982 *5 *6 *7 *3))))) 
+  (-12 (-4 *5 (-389)) (-4 *6 (-718)) (-4 *7 (-757)) (-4 *3 (-977 *5 *6 *7))
+   (-5 *2 (-584 *4)) (-5 *1 (-1019 *5 *6 *7 *3 *4))
+   (-4 *4 (-983 *5 *6 *7 *3))))) 
 (((*1 *2 *3 *4)
-  (-12 (-4 *5 (-389)) (-4 *6 (-717)) (-4 *7 (-756)) (-4 *3 (-976 *5 *6 *7))
-   (-5 *2 (-85)) (-5 *1 (-1018 *5 *6 *7 *3 *4)) (-4 *4 (-982 *5 *6 *7 *3))))
+  (-12 (-4 *5 (-389)) (-4 *6 (-718)) (-4 *7 (-757)) (-4 *3 (-977 *5 *6 *7))
+   (-5 *2 (-85)) (-5 *1 (-1019 *5 *6 *7 *3 *4)) (-4 *4 (-983 *5 *6 *7 *3))))
  ((*1 *2 *3 *4)
-  (-12 (-4 *5 (-389)) (-4 *6 (-717)) (-4 *7 (-756)) (-4 *3 (-976 *5 *6 *7))
-   (-5 *2 (-583 (-2 (|:| |val| (-85)) (|:| -1597 *4))))
-   (-5 *1 (-1018 *5 *6 *7 *3 *4)) (-4 *4 (-982 *5 *6 *7 *3))))) 
+  (-12 (-4 *5 (-389)) (-4 *6 (-718)) (-4 *7 (-757)) (-4 *3 (-977 *5 *6 *7))
+   (-5 *2 (-584 (-2 (|:| |val| (-85)) (|:| -1598 *4))))
+   (-5 *1 (-1019 *5 *6 *7 *3 *4)) (-4 *4 (-983 *5 *6 *7 *3))))) 
 (((*1 *2 *3 *4)
-  (-12 (-4 *5 (-389)) (-4 *6 (-717)) (-4 *7 (-756)) (-4 *3 (-976 *5 *6 *7))
-   (-5 *2 (-583 *4)) (-5 *1 (-1018 *5 *6 *7 *3 *4))
-   (-4 *4 (-982 *5 *6 *7 *3))))) 
+  (-12 (-4 *5 (-389)) (-4 *6 (-718)) (-4 *7 (-757)) (-4 *3 (-977 *5 *6 *7))
+   (-5 *2 (-584 *4)) (-5 *1 (-1019 *5 *6 *7 *3 *4))
+   (-4 *4 (-983 *5 *6 *7 *3))))) 
 (((*1 *2 *3 *4)
-  (-12 (-4 *5 (-389)) (-4 *6 (-717)) (-4 *7 (-756)) (-4 *3 (-976 *5 *6 *7))
-   (-5 *2 (-583 (-2 (|:| |val| (-85)) (|:| -1597 *4))))
-   (-5 *1 (-1018 *5 *6 *7 *3 *4)) (-4 *4 (-982 *5 *6 *7 *3))))) 
+  (-12 (-4 *5 (-389)) (-4 *6 (-718)) (-4 *7 (-757)) (-4 *3 (-977 *5 *6 *7))
+   (-5 *2 (-584 (-2 (|:| |val| (-85)) (|:| -1598 *4))))
+   (-5 *1 (-1019 *5 *6 *7 *3 *4)) (-4 *4 (-983 *5 *6 *7 *3))))) 
 (((*1 *2 *3 *4)
-  (-12 (-4 *5 (-389)) (-4 *6 (-717)) (-4 *7 (-756)) (-4 *3 (-976 *5 *6 *7))
-   (-5 *2 (-583 *4)) (-5 *1 (-1018 *5 *6 *7 *3 *4))
-   (-4 *4 (-982 *5 *6 *7 *3))))) 
+  (-12 (-4 *5 (-389)) (-4 *6 (-718)) (-4 *7 (-757)) (-4 *3 (-977 *5 *6 *7))
+   (-5 *2 (-584 *4)) (-5 *1 (-1019 *5 *6 *7 *3 *4))
+   (-4 *4 (-983 *5 *6 *7 *3))))) 
 (((*1 *2 *3 *4)
-  (-12 (-4 *5 (-389)) (-4 *6 (-717)) (-4 *7 (-756)) (-4 *3 (-976 *5 *6 *7))
-   (-5 *2 (-583 (-2 (|:| |val| (-85)) (|:| -1597 *4))))
-   (-5 *1 (-1018 *5 *6 *7 *3 *4)) (-4 *4 (-982 *5 *6 *7 *3))))) 
+  (-12 (-4 *5 (-389)) (-4 *6 (-718)) (-4 *7 (-757)) (-4 *3 (-977 *5 *6 *7))
+   (-5 *2 (-584 (-2 (|:| |val| (-85)) (|:| -1598 *4))))
+   (-5 *1 (-1019 *5 *6 *7 *3 *4)) (-4 *4 (-983 *5 *6 *7 *3))))) 
 (((*1 *2 *3 *3 *4)
-  (-12 (-4 *5 (-389)) (-4 *6 (-717)) (-4 *7 (-756)) (-4 *3 (-976 *5 *6 *7))
-   (-5 *2 (-583 (-2 (|:| |val| *3) (|:| -1597 *4))))
-   (-5 *1 (-1018 *5 *6 *7 *3 *4)) (-4 *4 (-982 *5 *6 *7 *3))))) 
+  (-12 (-4 *5 (-389)) (-4 *6 (-718)) (-4 *7 (-757)) (-4 *3 (-977 *5 *6 *7))
+   (-5 *2 (-584 (-2 (|:| |val| *3) (|:| -1598 *4))))
+   (-5 *1 (-1019 *5 *6 *7 *3 *4)) (-4 *4 (-983 *5 *6 *7 *3))))) 
 (((*1 *2 *3 *3 *4)
-  (-12 (-4 *5 (-389)) (-4 *6 (-717)) (-4 *7 (-756)) (-4 *3 (-976 *5 *6 *7))
-   (-5 *2 (-583 (-2 (|:| |val| *3) (|:| -1597 *4))))
-   (-5 *1 (-1018 *5 *6 *7 *3 *4)) (-4 *4 (-982 *5 *6 *7 *3))))) 
+  (-12 (-4 *5 (-389)) (-4 *6 (-718)) (-4 *7 (-757)) (-4 *3 (-977 *5 *6 *7))
+   (-5 *2 (-584 (-2 (|:| |val| *3) (|:| -1598 *4))))
+   (-5 *1 (-1019 *5 *6 *7 *3 *4)) (-4 *4 (-983 *5 *6 *7 *3))))) 
 (((*1 *2 *3 *3 *4 *5 *5)
-  (-12 (-5 *5 (-85)) (-4 *6 (-389)) (-4 *7 (-717)) (-4 *8 (-756))
-   (-4 *3 (-976 *6 *7 *8)) (-5 *2 (-583 (-2 (|:| |val| *3) (|:| -1597 *4))))
-   (-5 *1 (-1018 *6 *7 *8 *3 *4)) (-4 *4 (-982 *6 *7 *8 *3))))
+  (-12 (-5 *5 (-85)) (-4 *6 (-389)) (-4 *7 (-718)) (-4 *8 (-757))
+   (-4 *3 (-977 *6 *7 *8)) (-5 *2 (-584 (-2 (|:| |val| *3) (|:| -1598 *4))))
+   (-5 *1 (-1019 *6 *7 *8 *3 *4)) (-4 *4 (-983 *6 *7 *8 *3))))
  ((*1 *2 *3 *4 *5)
-  (-12 (-5 *3 (-583 (-2 (|:| |val| (-583 *8)) (|:| -1597 *9)))) (-5 *5 (-85))
-   (-4 *8 (-976 *6 *7 *4)) (-4 *9 (-982 *6 *7 *4 *8)) (-4 *6 (-389))
-   (-4 *7 (-717)) (-4 *4 (-756))
-   (-5 *2 (-583 (-2 (|:| |val| *8) (|:| -1597 *9))))
-   (-5 *1 (-1018 *6 *7 *4 *8 *9))))) 
+  (-12 (-5 *3 (-584 (-2 (|:| |val| (-584 *8)) (|:| -1598 *9)))) (-5 *5 (-85))
+   (-4 *8 (-977 *6 *7 *4)) (-4 *9 (-983 *6 *7 *4 *8)) (-4 *6 (-389))
+   (-4 *7 (-718)) (-4 *4 (-757))
+   (-5 *2 (-584 (-2 (|:| |val| *8) (|:| -1598 *9))))
+   (-5 *1 (-1019 *6 *7 *4 *8 *9))))) 
 (((*1 *2 *3 *3 *4)
-  (-12 (-4 *5 (-389)) (-4 *6 (-717)) (-4 *7 (-756)) (-4 *3 (-976 *5 *6 *7))
-   (-5 *2 (-583 (-2 (|:| |val| (-583 *3)) (|:| -1597 *4))))
-   (-5 *1 (-1018 *5 *6 *7 *3 *4)) (-4 *4 (-982 *5 *6 *7 *3))))) 
+  (-12 (-4 *5 (-389)) (-4 *6 (-718)) (-4 *7 (-757)) (-4 *3 (-977 *5 *6 *7))
+   (-5 *2 (-584 (-2 (|:| |val| (-584 *3)) (|:| -1598 *4))))
+   (-5 *1 (-1019 *5 *6 *7 *3 *4)) (-4 *4 (-983 *5 *6 *7 *3))))) 
 (((*1 *2)
-  (-12 (-4 *3 (-389)) (-4 *4 (-717)) (-4 *5 (-756)) (-4 *6 (-976 *3 *4 *5))
-   (-5 *2 (-1183)) (-5 *1 (-983 *3 *4 *5 *6 *7)) (-4 *7 (-982 *3 *4 *5 *6))))
+  (-12 (-4 *3 (-389)) (-4 *4 (-718)) (-4 *5 (-757)) (-4 *6 (-977 *3 *4 *5))
+   (-5 *2 (-1184)) (-5 *1 (-984 *3 *4 *5 *6 *7)) (-4 *7 (-983 *3 *4 *5 *6))))
  ((*1 *2)
-  (-12 (-4 *3 (-389)) (-4 *4 (-717)) (-4 *5 (-756)) (-4 *6 (-976 *3 *4 *5))
-   (-5 *2 (-1183)) (-5 *1 (-1018 *3 *4 *5 *6 *7)) (-4 *7 (-982 *3 *4 *5 *6))))) 
+  (-12 (-4 *3 (-389)) (-4 *4 (-718)) (-4 *5 (-757)) (-4 *6 (-977 *3 *4 *5))
+   (-5 *2 (-1184)) (-5 *1 (-1019 *3 *4 *5 *6 *7)) (-4 *7 (-983 *3 *4 *5 *6))))) 
 (((*1 *2 *3 *3 *3)
-  (-12 (-5 *3 (-1071)) (-4 *4 (-389)) (-4 *5 (-717)) (-4 *6 (-756))
-   (-4 *7 (-976 *4 *5 *6)) (-5 *2 (-1183)) (-5 *1 (-983 *4 *5 *6 *7 *8))
-   (-4 *8 (-982 *4 *5 *6 *7))))
+  (-12 (-5 *3 (-1072)) (-4 *4 (-389)) (-4 *5 (-718)) (-4 *6 (-757))
+   (-4 *7 (-977 *4 *5 *6)) (-5 *2 (-1184)) (-5 *1 (-984 *4 *5 *6 *7 *8))
+   (-4 *8 (-983 *4 *5 *6 *7))))
  ((*1 *2 *3 *3 *3)
-  (-12 (-5 *3 (-1071)) (-4 *4 (-389)) (-4 *5 (-717)) (-4 *6 (-756))
-   (-4 *7 (-976 *4 *5 *6)) (-5 *2 (-1183)) (-5 *1 (-1018 *4 *5 *6 *7 *8))
-   (-4 *8 (-982 *4 *5 *6 *7))))) 
+  (-12 (-5 *3 (-1072)) (-4 *4 (-389)) (-4 *5 (-718)) (-4 *6 (-757))
+   (-4 *7 (-977 *4 *5 *6)) (-5 *2 (-1184)) (-5 *1 (-1019 *4 *5 *6 *7 *8))
+   (-4 *8 (-983 *4 *5 *6 *7))))) 
 (((*1 *2)
-  (-12 (-4 *3 (-389)) (-4 *4 (-717)) (-4 *5 (-756)) (-4 *6 (-976 *3 *4 *5))
-   (-5 *2 (-1183)) (-5 *1 (-983 *3 *4 *5 *6 *7)) (-4 *7 (-982 *3 *4 *5 *6))))
+  (-12 (-4 *3 (-389)) (-4 *4 (-718)) (-4 *5 (-757)) (-4 *6 (-977 *3 *4 *5))
+   (-5 *2 (-1184)) (-5 *1 (-984 *3 *4 *5 *6 *7)) (-4 *7 (-983 *3 *4 *5 *6))))
  ((*1 *2)
-  (-12 (-4 *3 (-389)) (-4 *4 (-717)) (-4 *5 (-756)) (-4 *6 (-976 *3 *4 *5))
-   (-5 *2 (-1183)) (-5 *1 (-1018 *3 *4 *5 *6 *7)) (-4 *7 (-982 *3 *4 *5 *6))))) 
+  (-12 (-4 *3 (-389)) (-4 *4 (-718)) (-4 *5 (-757)) (-4 *6 (-977 *3 *4 *5))
+   (-5 *2 (-1184)) (-5 *1 (-1019 *3 *4 *5 *6 *7)) (-4 *7 (-983 *3 *4 *5 *6))))) 
 (((*1 *2 *3 *3 *3)
-  (-12 (-5 *3 (-1071)) (-4 *4 (-389)) (-4 *5 (-717)) (-4 *6 (-756))
-   (-4 *7 (-976 *4 *5 *6)) (-5 *2 (-1183)) (-5 *1 (-983 *4 *5 *6 *7 *8))
-   (-4 *8 (-982 *4 *5 *6 *7))))
+  (-12 (-5 *3 (-1072)) (-4 *4 (-389)) (-4 *5 (-718)) (-4 *6 (-757))
+   (-4 *7 (-977 *4 *5 *6)) (-5 *2 (-1184)) (-5 *1 (-984 *4 *5 *6 *7 *8))
+   (-4 *8 (-983 *4 *5 *6 *7))))
  ((*1 *2 *3 *3 *3)
-  (-12 (-5 *3 (-1071)) (-4 *4 (-389)) (-4 *5 (-717)) (-4 *6 (-756))
-   (-4 *7 (-976 *4 *5 *6)) (-5 *2 (-1183)) (-5 *1 (-1018 *4 *5 *6 *7 *8))
-   (-4 *8 (-982 *4 *5 *6 *7))))) 
+  (-12 (-5 *3 (-1072)) (-4 *4 (-389)) (-4 *5 (-718)) (-4 *6 (-757))
+   (-4 *7 (-977 *4 *5 *6)) (-5 *2 (-1184)) (-5 *1 (-1019 *4 *5 *6 *7 *8))
+   (-4 *8 (-983 *4 *5 *6 *7))))) 
 (((*1 *2 *3 *4 *3 *5 *5 *5 *5 *5)
-  (|partial| -12 (-5 *5 (-85)) (-4 *6 (-389)) (-4 *7 (-717)) (-4 *8 (-756))
-   (-4 *9 (-976 *6 *7 *8))
-   (-5 *2 (-2 (|:| -3261 (-583 *9)) (|:| -1597 *4) (|:| |ineq| (-583 *9))))
-   (-5 *1 (-901 *6 *7 *8 *9 *4)) (-5 *3 (-583 *9)) (-4 *4 (-982 *6 *7 *8 *9))))
+  (|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 *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 (-717)) (-4 *8 (-756))
-   (-4 *9 (-976 *6 *7 *8))
-   (-5 *2 (-2 (|:| -3261 (-583 *9)) (|:| -1597 *4) (|:| |ineq| (-583 *9))))
-   (-5 *1 (-1017 *6 *7 *8 *9 *4)) (-5 *3 (-583 *9))
-   (-4 *4 (-982 *6 *7 *8 *9))))) 
+  (|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 *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 (-583 *10)) (-5 *5 (-85)) (-4 *10 (-982 *6 *7 *8 *9))
-   (-4 *6 (-389)) (-4 *7 (-717)) (-4 *8 (-756)) (-4 *9 (-976 *6 *7 *8))
+  (-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
-    (-583 (-2 (|:| -3261 (-583 *9)) (|:| -1597 *10) (|:| |ineq| (-583 *9)))))
-   (-5 *1 (-901 *6 *7 *8 *9 *10)) (-5 *3 (-583 *9))))
+    (-584 (-2 (|:| -3263 (-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 (-583 *10)) (-5 *5 (-85)) (-4 *10 (-982 *6 *7 *8 *9))
-   (-4 *6 (-389)) (-4 *7 (-717)) (-4 *8 (-756)) (-4 *9 (-976 *6 *7 *8))
+  (-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
-    (-583 (-2 (|:| -3261 (-583 *9)) (|:| -1597 *10) (|:| |ineq| (-583 *9)))))
-   (-5 *1 (-1017 *6 *7 *8 *9 *10)) (-5 *3 (-583 *9))))) 
+    (-584 (-2 (|:| -3263 (-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 (-583 (-2 (|:| |val| (-583 *6)) (|:| -1597 *7))))
-   (-4 *6 (-976 *3 *4 *5)) (-4 *7 (-982 *3 *4 *5 *6)) (-4 *3 (-389))
-   (-4 *4 (-717)) (-4 *5 (-756)) (-5 *1 (-901 *3 *4 *5 *6 *7))))
+  (-12 (-5 *2 (-584 (-2 (|:| |val| (-584 *6)) (|:| -1598 *7))))
+   (-4 *6 (-977 *3 *4 *5)) (-4 *7 (-983 *3 *4 *5 *6)) (-4 *3 (-389))
+   (-4 *4 (-718)) (-4 *5 (-757)) (-5 *1 (-902 *3 *4 *5 *6 *7))))
  ((*1 *2 *2)
-  (-12 (-5 *2 (-583 (-2 (|:| |val| (-583 *6)) (|:| -1597 *7))))
-   (-4 *6 (-976 *3 *4 *5)) (-4 *7 (-982 *3 *4 *5 *6)) (-4 *3 (-389))
-   (-4 *4 (-717)) (-4 *5 (-756)) (-5 *1 (-1017 *3 *4 *5 *6 *7))))) 
+  (-12 (-5 *2 (-584 (-2 (|:| |val| (-584 *6)) (|:| -1598 *7))))
+   (-4 *6 (-977 *3 *4 *5)) (-4 *7 (-983 *3 *4 *5 *6)) (-4 *3 (-389))
+   (-4 *4 (-718)) (-4 *5 (-757)) (-5 *1 (-1018 *3 *4 *5 *6 *7))))) 
 (((*1 *2 *3 *3)
-  (-12 (-5 *3 (-2 (|:| |val| (-583 *7)) (|:| -1597 *8)))
-   (-4 *7 (-976 *4 *5 *6)) (-4 *8 (-982 *4 *5 *6 *7)) (-4 *4 (-389))
-   (-4 *5 (-717)) (-4 *6 (-756)) (-5 *2 (-85)) (-5 *1 (-901 *4 *5 *6 *7 *8))))
+  (-12 (-5 *3 (-2 (|:| |val| (-584 *7)) (|:| -1598 *8)))
+   (-4 *7 (-977 *4 *5 *6)) (-4 *8 (-983 *4 *5 *6 *7)) (-4 *4 (-389))
+   (-4 *5 (-718)) (-4 *6 (-757)) (-5 *2 (-85)) (-5 *1 (-902 *4 *5 *6 *7 *8))))
  ((*1 *2 *3 *3)
-  (-12 (-5 *3 (-2 (|:| |val| (-583 *7)) (|:| -1597 *8)))
-   (-4 *7 (-976 *4 *5 *6)) (-4 *8 (-982 *4 *5 *6 *7)) (-4 *4 (-389))
-   (-4 *5 (-717)) (-4 *6 (-756)) (-5 *2 (-85)) (-5 *1 (-1017 *4 *5 *6 *7 *8))))) 
+  (-12 (-5 *3 (-2 (|:| |val| (-584 *7)) (|:| -1598 *8)))
+   (-4 *7 (-977 *4 *5 *6)) (-4 *8 (-983 *4 *5 *6 *7)) (-4 *4 (-389))
+   (-4 *5 (-718)) (-4 *6 (-757)) (-5 *2 (-85)) (-5 *1 (-1018 *4 *5 *6 *7 *8))))) 
 (((*1 *2 *2)
-  (-12 (-5 *2 (-583 *7)) (-4 *7 (-982 *3 *4 *5 *6)) (-4 *3 (-389))
-   (-4 *4 (-717)) (-4 *5 (-756)) (-4 *6 (-976 *3 *4 *5))
-   (-5 *1 (-901 *3 *4 *5 *6 *7))))
+  (-12 (-5 *2 (-584 *7)) (-4 *7 (-983 *3 *4 *5 *6)) (-4 *3 (-389))
+   (-4 *4 (-718)) (-4 *5 (-757)) (-4 *6 (-977 *3 *4 *5))
+   (-5 *1 (-902 *3 *4 *5 *6 *7))))
  ((*1 *2 *2)
-  (-12 (-5 *2 (-583 *7)) (-4 *7 (-982 *3 *4 *5 *6)) (-4 *3 (-389))
-   (-4 *4 (-717)) (-4 *5 (-756)) (-4 *6 (-976 *3 *4 *5))
-   (-5 *1 (-1017 *3 *4 *5 *6 *7))))) 
+  (-12 (-5 *2 (-584 *7)) (-4 *7 (-983 *3 *4 *5 *6)) (-4 *3 (-389))
+   (-4 *4 (-718)) (-4 *5 (-757)) (-4 *6 (-977 *3 *4 *5))
+   (-5 *1 (-1018 *3 *4 *5 *6 *7))))) 
 (((*1 *2 *3 *3)
-  (-12 (-4 *4 (-389)) (-4 *5 (-717)) (-4 *6 (-756)) (-4 *7 (-976 *4 *5 *6))
-   (-5 *2 (-85)) (-5 *1 (-901 *4 *5 *6 *7 *3)) (-4 *3 (-982 *4 *5 *6 *7))))
+  (-12 (-4 *4 (-389)) (-4 *5 (-718)) (-4 *6 (-757)) (-4 *7 (-977 *4 *5 *6))
+   (-5 *2 (-85)) (-5 *1 (-902 *4 *5 *6 *7 *3)) (-4 *3 (-983 *4 *5 *6 *7))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *4 (-583 *3)) (-4 *3 (-982 *5 *6 *7 *8)) (-4 *5 (-389))
-   (-4 *6 (-717)) (-4 *7 (-756)) (-4 *8 (-976 *5 *6 *7)) (-5 *2 (-85))
-   (-5 *1 (-901 *5 *6 *7 *8 *3))))
+  (-12 (-5 *4 (-584 *3)) (-4 *3 (-983 *5 *6 *7 *8)) (-4 *5 (-389))
+   (-4 *6 (-718)) (-4 *7 (-757)) (-4 *8 (-977 *5 *6 *7)) (-5 *2 (-85))
+   (-5 *1 (-902 *5 *6 *7 *8 *3))))
  ((*1 *2 *3 *3)
-  (-12 (-4 *4 (-389)) (-4 *5 (-717)) (-4 *6 (-756)) (-4 *7 (-976 *4 *5 *6))
-   (-5 *2 (-85)) (-5 *1 (-1017 *4 *5 *6 *7 *3)) (-4 *3 (-982 *4 *5 *6 *7))))
+  (-12 (-4 *4 (-389)) (-4 *5 (-718)) (-4 *6 (-757)) (-4 *7 (-977 *4 *5 *6))
+   (-5 *2 (-85)) (-5 *1 (-1018 *4 *5 *6 *7 *3)) (-4 *3 (-983 *4 *5 *6 *7))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *4 (-583 *3)) (-4 *3 (-982 *5 *6 *7 *8)) (-4 *5 (-389))
-   (-4 *6 (-717)) (-4 *7 (-756)) (-4 *8 (-976 *5 *6 *7)) (-5 *2 (-85))
-   (-5 *1 (-1017 *5 *6 *7 *8 *3))))) 
+  (-12 (-5 *4 (-584 *3)) (-4 *3 (-983 *5 *6 *7 *8)) (-4 *5 (-389))
+   (-4 *6 (-718)) (-4 *7 (-757)) (-4 *8 (-977 *5 *6 *7)) (-5 *2 (-85))
+   (-5 *1 (-1018 *5 *6 *7 *8 *3))))) 
 (((*1 *2 *3 *3)
-  (|partial| -12 (-4 *4 (-389)) (-4 *5 (-717)) (-4 *6 (-756))
-   (-4 *7 (-976 *4 *5 *6)) (-5 *2 (-85)) (-5 *1 (-901 *4 *5 *6 *7 *3))
-   (-4 *3 (-982 *4 *5 *6 *7))))
+  (|partial| -12 (-4 *4 (-389)) (-4 *5 (-718)) (-4 *6 (-757))
+   (-4 *7 (-977 *4 *5 *6)) (-5 *2 (-85)) (-5 *1 (-902 *4 *5 *6 *7 *3))
+   (-4 *3 (-983 *4 *5 *6 *7))))
  ((*1 *2 *3 *3)
-  (|partial| -12 (-4 *4 (-389)) (-4 *5 (-717)) (-4 *6 (-756))
-   (-4 *7 (-976 *4 *5 *6)) (-5 *2 (-85)) (-5 *1 (-1017 *4 *5 *6 *7 *3))
-   (-4 *3 (-982 *4 *5 *6 *7))))) 
+  (|partial| -12 (-4 *4 (-389)) (-4 *5 (-718)) (-4 *6 (-757))
+   (-4 *7 (-977 *4 *5 *6)) (-5 *2 (-85)) (-5 *1 (-1018 *4 *5 *6 *7 *3))
+   (-4 *3 (-983 *4 *5 *6 *7))))) 
 (((*1 *2 *3 *3)
-  (-12 (-5 *3 (-583 *7)) (-4 *7 (-976 *4 *5 *6)) (-4 *4 (-389)) (-4 *5 (-717))
-   (-4 *6 (-756)) (-5 *2 (-85)) (-5 *1 (-901 *4 *5 *6 *7 *8))
-   (-4 *8 (-982 *4 *5 *6 *7))))
+  (-12 (-5 *3 (-584 *7)) (-4 *7 (-977 *4 *5 *6)) (-4 *4 (-389)) (-4 *5 (-718))
+   (-4 *6 (-757)) (-5 *2 (-85)) (-5 *1 (-902 *4 *5 *6 *7 *8))
+   (-4 *8 (-983 *4 *5 *6 *7))))
  ((*1 *2 *3 *3)
-  (-12 (-5 *3 (-583 *7)) (-4 *7 (-976 *4 *5 *6)) (-4 *4 (-389)) (-4 *5 (-717))
-   (-4 *6 (-756)) (-5 *2 (-85)) (-5 *1 (-1017 *4 *5 *6 *7 *8))
-   (-4 *8 (-982 *4 *5 *6 *7))))) 
+  (-12 (-5 *3 (-584 *7)) (-4 *7 (-977 *4 *5 *6)) (-4 *4 (-389)) (-4 *5 (-718))
+   (-4 *6 (-757)) (-5 *2 (-85)) (-5 *1 (-1018 *4 *5 *6 *7 *8))
+   (-4 *8 (-983 *4 *5 *6 *7))))) 
 (((*1 *2 *3 *3)
-  (-12 (-5 *3 (-583 *7)) (-4 *7 (-976 *4 *5 *6)) (-4 *4 (-389)) (-4 *5 (-717))
-   (-4 *6 (-756)) (-5 *2 (-85)) (-5 *1 (-901 *4 *5 *6 *7 *8))
-   (-4 *8 (-982 *4 *5 *6 *7))))
+  (-12 (-5 *3 (-584 *7)) (-4 *7 (-977 *4 *5 *6)) (-4 *4 (-389)) (-4 *5 (-718))
+   (-4 *6 (-757)) (-5 *2 (-85)) (-5 *1 (-902 *4 *5 *6 *7 *8))
+   (-4 *8 (-983 *4 *5 *6 *7))))
  ((*1 *2 *3 *3)
-  (-12 (-5 *3 (-583 *7)) (-4 *7 (-976 *4 *5 *6)) (-4 *4 (-389)) (-4 *5 (-717))
-   (-4 *6 (-756)) (-5 *2 (-85)) (-5 *1 (-1017 *4 *5 *6 *7 *8))
-   (-4 *8 (-982 *4 *5 *6 *7))))) 
+  (-12 (-5 *3 (-584 *7)) (-4 *7 (-977 *4 *5 *6)) (-4 *4 (-389)) (-4 *5 (-718))
+   (-4 *6 (-757)) (-5 *2 (-85)) (-5 *1 (-1018 *4 *5 *6 *7 *8))
+   (-4 *8 (-983 *4 *5 *6 *7))))) 
 (((*1 *2 *3 *3)
-  (-12 (-5 *3 (-583 *7)) (-4 *7 (-976 *4 *5 *6)) (-4 *4 (-389)) (-4 *5 (-717))
-   (-4 *6 (-756)) (-5 *2 (-85)) (-5 *1 (-901 *4 *5 *6 *7 *8))
-   (-4 *8 (-982 *4 *5 *6 *7))))
+  (-12 (-5 *3 (-584 *7)) (-4 *7 (-977 *4 *5 *6)) (-4 *4 (-389)) (-4 *5 (-718))
+   (-4 *6 (-757)) (-5 *2 (-85)) (-5 *1 (-902 *4 *5 *6 *7 *8))
+   (-4 *8 (-983 *4 *5 *6 *7))))
  ((*1 *2 *3 *3)
-  (-12 (-5 *3 (-583 *7)) (-4 *7 (-976 *4 *5 *6)) (-4 *4 (-389)) (-4 *5 (-717))
-   (-4 *6 (-756)) (-5 *2 (-85)) (-5 *1 (-1017 *4 *5 *6 *7 *8))
-   (-4 *8 (-982 *4 *5 *6 *7))))) 
+  (-12 (-5 *3 (-584 *7)) (-4 *7 (-977 *4 *5 *6)) (-4 *4 (-389)) (-4 *5 (-718))
+   (-4 *6 (-757)) (-5 *2 (-85)) (-5 *1 (-1018 *4 *5 *6 *7 *8))
+   (-4 *8 (-983 *4 *5 *6 *7))))) 
 (((*1 *2 *3 *3)
-  (-12 (-4 *4 (-389)) (-4 *5 (-717)) (-4 *6 (-756)) (-4 *7 (-976 *4 *5 *6))
-   (-5 *2 (-85)) (-5 *1 (-901 *4 *5 *6 *7 *3)) (-4 *3 (-982 *4 *5 *6 *7))))
+  (-12 (-4 *4 (-389)) (-4 *5 (-718)) (-4 *6 (-757)) (-4 *7 (-977 *4 *5 *6))
+   (-5 *2 (-85)) (-5 *1 (-902 *4 *5 *6 *7 *3)) (-4 *3 (-983 *4 *5 *6 *7))))
  ((*1 *2 *3 *3)
-  (-12 (-4 *4 (-389)) (-4 *5 (-717)) (-4 *6 (-756)) (-4 *7 (-976 *4 *5 *6))
-   (-5 *2 (-85)) (-5 *1 (-1017 *4 *5 *6 *7 *3)) (-4 *3 (-982 *4 *5 *6 *7))))) 
+  (-12 (-4 *4 (-389)) (-4 *5 (-718)) (-4 *6 (-757)) (-4 *7 (-977 *4 *5 *6))
+   (-5 *2 (-85)) (-5 *1 (-1018 *4 *5 *6 *7 *3)) (-4 *3 (-983 *4 *5 *6 *7))))) 
 (((*1 *2 *3 *3)
-  (-12 (-4 *4 (-389)) (-4 *5 (-717)) (-4 *6 (-756)) (-4 *7 (-976 *4 *5 *6))
-   (-5 *2 (-85)) (-5 *1 (-901 *4 *5 *6 *7 *3)) (-4 *3 (-982 *4 *5 *6 *7))))
+  (-12 (-4 *4 (-389)) (-4 *5 (-718)) (-4 *6 (-757)) (-4 *7 (-977 *4 *5 *6))
+   (-5 *2 (-85)) (-5 *1 (-902 *4 *5 *6 *7 *3)) (-4 *3 (-983 *4 *5 *6 *7))))
  ((*1 *2 *3 *3)
-  (-12 (-4 *4 (-389)) (-4 *5 (-717)) (-4 *6 (-756)) (-4 *7 (-976 *4 *5 *6))
-   (-5 *2 (-85)) (-5 *1 (-1017 *4 *5 *6 *7 *3)) (-4 *3 (-982 *4 *5 *6 *7))))) 
+  (-12 (-4 *4 (-389)) (-4 *5 (-718)) (-4 *6 (-757)) (-4 *7 (-977 *4 *5 *6))
+   (-5 *2 (-85)) (-5 *1 (-1018 *4 *5 *6 *7 *3)) (-4 *3 (-983 *4 *5 *6 *7))))) 
 (((*1 *2 *2)
-  (-12 (-5 *2 (-583 *7)) (-4 *7 (-982 *3 *4 *5 *6)) (-4 *3 (-389))
-   (-4 *4 (-717)) (-4 *5 (-756)) (-4 *6 (-976 *3 *4 *5))
-   (-5 *1 (-901 *3 *4 *5 *6 *7))))
+  (-12 (-5 *2 (-584 *7)) (-4 *7 (-983 *3 *4 *5 *6)) (-4 *3 (-389))
+   (-4 *4 (-718)) (-4 *5 (-757)) (-4 *6 (-977 *3 *4 *5))
+   (-5 *1 (-902 *3 *4 *5 *6 *7))))
  ((*1 *2 *2)
-  (-12 (-5 *2 (-583 *7)) (-4 *7 (-982 *3 *4 *5 *6)) (-4 *3 (-389))
-   (-4 *4 (-717)) (-4 *5 (-756)) (-4 *6 (-976 *3 *4 *5))
-   (-5 *1 (-1017 *3 *4 *5 *6 *7))))) 
+  (-12 (-5 *2 (-584 *7)) (-4 *7 (-983 *3 *4 *5 *6)) (-4 *3 (-389))
+   (-4 *4 (-718)) (-4 *5 (-757)) (-4 *6 (-977 *3 *4 *5))
+   (-5 *1 (-1018 *3 *4 *5 *6 *7))))) 
 (((*1 *2 *3 *3)
-  (-12 (-4 *4 (-389)) (-4 *5 (-717)) (-4 *6 (-756)) (-4 *7 (-976 *4 *5 *6))
-   (-5 *2 (-85)) (-5 *1 (-901 *4 *5 *6 *7 *3)) (-4 *3 (-982 *4 *5 *6 *7))))
+  (-12 (-4 *4 (-389)) (-4 *5 (-718)) (-4 *6 (-757)) (-4 *7 (-977 *4 *5 *6))
+   (-5 *2 (-85)) (-5 *1 (-902 *4 *5 *6 *7 *3)) (-4 *3 (-983 *4 *5 *6 *7))))
  ((*1 *2 *3 *3)
-  (-12 (-4 *4 (-389)) (-4 *5 (-717)) (-4 *6 (-756)) (-4 *7 (-976 *4 *5 *6))
-   (-5 *2 (-85)) (-5 *1 (-1017 *4 *5 *6 *7 *3)) (-4 *3 (-982 *4 *5 *6 *7))))) 
+  (-12 (-4 *4 (-389)) (-4 *5 (-718)) (-4 *6 (-757)) (-4 *7 (-977 *4 *5 *6))
+   (-5 *2 (-85)) (-5 *1 (-1018 *4 *5 *6 *7 *3)) (-4 *3 (-983 *4 *5 *6 *7))))) 
 (((*1 *2)
-  (-12 (-4 *3 (-389)) (-4 *4 (-717)) (-4 *5 (-756)) (-4 *6 (-976 *3 *4 *5))
-   (-5 *2 (-1183)) (-5 *1 (-901 *3 *4 *5 *6 *7)) (-4 *7 (-982 *3 *4 *5 *6))))
+  (-12 (-4 *3 (-389)) (-4 *4 (-718)) (-4 *5 (-757)) (-4 *6 (-977 *3 *4 *5))
+   (-5 *2 (-1184)) (-5 *1 (-902 *3 *4 *5 *6 *7)) (-4 *7 (-983 *3 *4 *5 *6))))
  ((*1 *2)
-  (-12 (-4 *3 (-389)) (-4 *4 (-717)) (-4 *5 (-756)) (-4 *6 (-976 *3 *4 *5))
-   (-5 *2 (-1183)) (-5 *1 (-1017 *3 *4 *5 *6 *7)) (-4 *7 (-982 *3 *4 *5 *6))))) 
+  (-12 (-4 *3 (-389)) (-4 *4 (-718)) (-4 *5 (-757)) (-4 *6 (-977 *3 *4 *5))
+   (-5 *2 (-1184)) (-5 *1 (-1018 *3 *4 *5 *6 *7)) (-4 *7 (-983 *3 *4 *5 *6))))) 
 (((*1 *2 *3 *3 *3)
-  (-12 (-5 *3 (-1071)) (-4 *4 (-389)) (-4 *5 (-717)) (-4 *6 (-756))
-   (-4 *7 (-976 *4 *5 *6)) (-5 *2 (-1183)) (-5 *1 (-901 *4 *5 *6 *7 *8))
-   (-4 *8 (-982 *4 *5 *6 *7))))
+  (-12 (-5 *3 (-1072)) (-4 *4 (-389)) (-4 *5 (-718)) (-4 *6 (-757))
+   (-4 *7 (-977 *4 *5 *6)) (-5 *2 (-1184)) (-5 *1 (-902 *4 *5 *6 *7 *8))
+   (-4 *8 (-983 *4 *5 *6 *7))))
  ((*1 *2 *3 *3 *3)
-  (-12 (-5 *3 (-1071)) (-4 *4 (-389)) (-4 *5 (-717)) (-4 *6 (-756))
-   (-4 *7 (-976 *4 *5 *6)) (-5 *2 (-1183)) (-5 *1 (-1017 *4 *5 *6 *7 *8))
-   (-4 *8 (-982 *4 *5 *6 *7))))) 
-(((*1 *2 *1 *1) (-12 (-5 *2 (-85)) (-5 *1 (-985))))
+  (-12 (-5 *3 (-1072)) (-4 *4 (-389)) (-4 *5 (-718)) (-4 *6 (-757))
+   (-4 *7 (-977 *4 *5 *6)) (-5 *2 (-1184)) (-5 *1 (-1018 *4 *5 *6 *7 *8))
+   (-4 *8 (-983 *4 *5 *6 *7))))) 
+(((*1 *2 *1 *1) (-12 (-5 *2 (-85)) (-5 *1 (-986))))
  ((*1 *2 *1 *1)
-  (-12 (-4 *1 (-1015 *3 *4 *5 *6 *7)) (-4 *3 (-1012)) (-4 *4 (-1012))
-   (-4 *5 (-1012)) (-4 *6 (-1012)) (-4 *7 (-1012)) (-5 *2 (-85))))) 
+  (-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 (-4 *1 (-1015 *3 *4 *5 *6 *7)) (-4 *3 (-1012)) (-4 *4 (-1012))
-   (-4 *5 (-1012)) (-4 *6 (-1012)) (-4 *7 (-1012)) (-5 *2 (-85))))) 
+  (-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 (-4 *1 (-1015 *3 *4 *5 *6 *7)) (-4 *3 (-1012)) (-4 *4 (-1012))
-   (-4 *5 (-1012)) (-4 *6 (-1012)) (-4 *7 (-1012)) (-5 *2 (-85))))) 
+  (-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 (-4 *1 (-1015 *3 *4 *5 *6 *7)) (-4 *3 (-1012)) (-4 *4 (-1012))
-   (-4 *5 (-1012)) (-4 *6 (-1012)) (-4 *7 (-1012)) (-5 *2 (-85))))) 
+  (-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 (-4 *1 (-1015 *3 *4 *5 *6 *7)) (-4 *3 (-1012)) (-4 *4 (-1012))
-   (-4 *5 (-1012)) (-4 *6 (-1012)) (-4 *7 (-1012)) (-5 *2 (-85))))) 
+  (-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 (-4 *1 (-1015 *3 *4 *5 *6 *7)) (-4 *3 (-1012)) (-4 *4 (-1012))
-   (-4 *5 (-1012)) (-4 *6 (-1012)) (-4 *7 (-1012)) (-5 *2 (-85))))) 
-(((*1 *2 *1) (-12 (-5 *2 (-85)) (-5 *1 (-800 *3)) (-4 *3 (-1012))))
+  (-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 (-85)) (-5 *1 (-801 *3)) (-4 *3 (-1013))))
  ((*1 *2 *1)
-  (-12 (-4 *1 (-1015 *3 *4 *5 *6 *7)) (-4 *3 (-1012)) (-4 *4 (-1012))
-   (-4 *5 (-1012)) (-4 *6 (-1012)) (-4 *7 (-1012)) (-5 *2 (-85))))) 
+  (-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 (-85)) (-5 *1 (-374))))
- ((*1 *2 *3) (-12 (-5 *2 (-85)) (-5 *1 (-504 *3)) (-4 *3 (-950 (-483)))))
+ ((*1 *2 *3) (-12 (-5 *2 (-85)) (-5 *1 (-505 *3)) (-4 *3 (-951 (-484)))))
  ((*1 *2 *1)
-  (-12 (-4 *1 (-1015 *3 *4 *5 *6 *7)) (-4 *3 (-1012)) (-4 *4 (-1012))
-   (-4 *5 (-1012)) (-4 *6 (-1012)) (-4 *7 (-1012)) (-5 *2 (-85))))) 
+  (-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 (-4 *1 (-1015 *3 *4 *5 *6 *7)) (-4 *3 (-1012)) (-4 *4 (-1012))
-   (-4 *5 (-1012)) (-4 *6 (-1012)) (-4 *7 (-1012)) (-5 *2 (-85))))) 
+  (-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 (-583 (-2 (|:| -3854 (-1088)) (|:| |entry| *4))))
-   (-5 *1 (-798 *3 *4)) (-4 *3 (-1012)) (-4 *4 (-1012))))
+  (-12 (-5 *2 (-584 (-2 (|:| -3856 (-1089)) (|:| |entry| *4))))
+   (-5 *1 (-799 *3 *4)) (-4 *3 (-1013)) (-4 *4 (-1013))))
  ((*1 *2 *1)
-  (-12 (-4 *3 (-1012)) (-4 *4 (-1012)) (-4 *5 (-1012)) (-4 *6 (-1012))
-   (-4 *7 (-1012)) (-5 *2 (-583 *1)) (-4 *1 (-1015 *3 *4 *5 *6 *7))))) 
+  (-12 (-4 *3 (-1013)) (-4 *4 (-1013)) (-4 *5 (-1013)) (-4 *6 (-1013))
+   (-4 *7 (-1013)) (-5 *2 (-584 *1)) (-4 *1 (-1016 *3 *4 *5 *6 *7))))) 
 (((*1 *2 *1)
-  (-12 (-4 *1 (-1015 *3 *2 *4 *5 *6)) (-4 *3 (-1012)) (-4 *4 (-1012))
-   (-4 *5 (-1012)) (-4 *6 (-1012)) (-4 *2 (-1012))))) 
-(((*1 *2 *3) (-12 (-5 *2 (-483)) (-5 *1 (-504 *3)) (-4 *3 (-950 *2))))
+  (-12 (-4 *1 (-1016 *3 *2 *4 *5 *6)) (-4 *3 (-1013)) (-4 *4 (-1013))
+   (-4 *5 (-1013)) (-4 *6 (-1013)) (-4 *2 (-1013))))) 
+(((*1 *2 *3) (-12 (-5 *2 (-484)) (-5 *1 (-505 *3)) (-4 *3 (-951 *2))))
  ((*1 *2 *1)
-  (-12 (-4 *1 (-1015 *3 *4 *2 *5 *6)) (-4 *3 (-1012)) (-4 *4 (-1012))
-   (-4 *5 (-1012)) (-4 *6 (-1012)) (-4 *2 (-1012))))) 
-(((*1 *1 *2 *2 *3) (-12 (-5 *2 (-483)) (-5 *3 (-830)) (-4 *1 (-344))))
- ((*1 *1 *2 *2) (-12 (-5 *2 (-483)) (-4 *1 (-344))))
+  (-12 (-4 *1 (-1016 *3 *4 *2 *5 *6)) (-4 *3 (-1013)) (-4 *4 (-1013))
+   (-4 *5 (-1013)) (-4 *6 (-1013)) (-4 *2 (-1013))))) 
+(((*1 *1 *2 *2 *3) (-12 (-5 *2 (-484)) (-5 *3 (-831)) (-4 *1 (-344))))
+ ((*1 *1 *2 *2) (-12 (-5 *2 (-484)) (-4 *1 (-344))))
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-   (-4 *3 (-1019 *5 *6 *7 *8))))
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   (-12 (-5 *4 (-85)) (-4 *5 (-13 (-257) (-120)))
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   (-12 (-4 *4 (-13 (-257) (-120)))
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-   (-5 *1 (-989 *4 *5)) (-5 *3 (-583 (-857 *4))) (-14 *5 (-583 (-1088)))))
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   (-12 (-5 *4 (-85)) (-4 *5 (-13 (-257) (-120)))
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 (((*1 *1 *2)
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 (((*1 *2 *1)
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 (((*1 *1 *2 *2 *3)
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-   (-5 *1 (-801 *4 *5))))
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 (((*1 *2 *3 *3 *4)
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 (((*1 *2 *3 *3 *4)
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 (((*1 *2 *3 *3 *4)
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-   (-4 *3 (-976 *4 *5 *6)) (-5 *2 (-85))))) 
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 (((*1 *2 *3 *1)
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-   (-4 *3 (-976 *4 *5 *6)) (-5 *2 (-85))))) 
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-   (-4 *3 (-976 *4 *5 *6)) (-5 *2 (-85))))) 
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 (((*1 *2 *3 *1)
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 (((*1 *1 *1)
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 (((*1 *1 *1)
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 (((*1 *1 *1 *1)
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+(((*1 *2) (-12 (-5 *2 (-327)) (-5 *1 (-954))))) 
 (((*1 *2 *3 *4 *2)
-  (-12 (-5 *3 (-1083 (-347 (-1083 *2)))) (-5 *4 (-550 *2))
-   (-4 *2 (-13 (-361 *5) (-27) (-1113)))
-   (-4 *5 (-13 (-389) (-950 (-483)) (-120) (-580 (-483))))
-   (-5 *1 (-497 *5 *2 *6)) (-4 *6 (-1012))))
+  (-12 (-5 *3 (-1084 (-347 (-1084 *2)))) (-5 *4 (-551 *2))
+   (-4 *2 (-13 (-361 *5) (-27) (-1114)))
+   (-4 *5 (-13 (-389) (-951 (-484)) (-120) (-581 (-484))))
+   (-5 *1 (-498 *5 *2 *6)) (-4 *6 (-1013))))
  ((*1 *1 *2 *3)
-  (-12 (-5 *2 (-1083 *1)) (-4 *1 (-861 *4 *5 *3)) (-4 *4 (-961)) (-4 *5 (-717))
-   (-4 *3 (-756))))
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+   (-4 *3 (-757))))
  ((*1 *1 *2 *3)
-  (-12 (-5 *2 (-1083 *4)) (-4 *4 (-961)) (-4 *1 (-861 *4 *5 *3)) (-4 *5 (-717))
-   (-4 *3 (-756))))
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+   (-4 *3 (-757))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *3 (-347 (-1083 *2))) (-4 *5 (-717)) (-4 *4 (-756)) (-4 *6 (-961))
+  (-12 (-5 *3 (-347 (-1084 *2))) (-4 *5 (-718)) (-4 *4 (-757)) (-4 *6 (-962))
    (-4 *2
     (-13 (-311)
-     (-10 -8 (-15 -3940 ($ *7)) (-15 -2994 (*7 $)) (-15 -2993 (*7 $)))))
-   (-5 *1 (-862 *5 *4 *6 *7 *2)) (-4 *7 (-861 *6 *5 *4))))
+     (-10 -8 (-15 -3942 ($ *7)) (-15 -2996 (*7 $)) (-15 -2995 (*7 $)))))
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  ((*1 *2 *3 *4)
-  (-12 (-5 *3 (-347 (-1083 (-347 (-857 *5))))) (-5 *4 (-1088))
-   (-5 *2 (-347 (-857 *5))) (-5 *1 (-952 *5)) (-4 *5 (-494))))) 
+  (-12 (-5 *3 (-347 (-1084 (-347 (-858 *5))))) (-5 *4 (-1089))
+   (-5 *2 (-347 (-858 *5))) (-5 *1 (-953 *5)) (-4 *5 (-495))))) 
 (((*1 *2 *1 *3)
-  (-12 (-5 *3 (-550 *1)) (-4 *1 (-361 *4)) (-4 *4 (-1012)) (-4 *4 (-494))
-   (-5 *2 (-347 (-1083 *1)))))
+  (-12 (-5 *3 (-551 *1)) (-4 *1 (-361 *4)) (-4 *4 (-1013)) (-4 *4 (-495))
+   (-5 *2 (-347 (-1084 *1)))))
  ((*1 *2 *3 *4 *4 *5)
-  (-12 (-5 *4 (-550 *3)) (-4 *3 (-13 (-361 *6) (-27) (-1113)))
-   (-4 *6 (-13 (-389) (-950 (-483)) (-120) (-580 (-483))))
-   (-5 *2 (-1083 (-347 (-1083 *3)))) (-5 *1 (-497 *6 *3 *7)) (-5 *5 (-1083 *3))
-   (-4 *7 (-1012))))
+  (-12 (-5 *4 (-551 *3)) (-4 *3 (-13 (-361 *6) (-27) (-1114)))
+   (-4 *6 (-13 (-389) (-951 (-484)) (-120) (-581 (-484))))
+   (-5 *2 (-1084 (-347 (-1084 *3)))) (-5 *1 (-498 *6 *3 *7)) (-5 *5 (-1084 *3))
+   (-4 *7 (-1013))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *4 (-1174 *5)) (-14 *5 (-1088)) (-4 *6 (-961))
-   (-5 *2 (-1146 *5 (-857 *6))) (-5 *1 (-859 *5 *6)) (-5 *3 (-857 *6))))
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  ((*1 *2 *1)
-  (-12 (-4 *1 (-861 *3 *4 *5)) (-4 *3 (-961)) (-4 *4 (-717)) (-4 *5 (-756))
-   (-5 *2 (-1083 *3))))
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+   (-5 *2 (-1084 *3))))
  ((*1 *2 *1 *3)
-  (-12 (-4 *4 (-961)) (-4 *5 (-717)) (-4 *3 (-756)) (-5 *2 (-1083 *1))
-   (-4 *1 (-861 *4 *5 *3))))
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+   (-4 *1 (-862 *4 *5 *3))))
  ((*1 *2 *3 *4)
-  (-12 (-4 *5 (-717)) (-4 *4 (-756)) (-4 *6 (-961)) (-4 *7 (-861 *6 *5 *4))
-   (-5 *2 (-347 (-1083 *3))) (-5 *1 (-862 *5 *4 *6 *7 *3))
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    (-4 *3
     (-13 (-311)
-     (-10 -8 (-15 -3940 ($ *7)) (-15 -2994 (*7 $)) (-15 -2993 (*7 $)))))))
+     (-10 -8 (-15 -3942 ($ *7)) (-15 -2996 (*7 $)) (-15 -2995 (*7 $)))))))
  ((*1 *2 *3 *4 *2)
-  (-12 (-5 *2 (-1083 *3))
+  (-12 (-5 *2 (-1084 *3))
    (-4 *3
     (-13 (-311)
-     (-10 -8 (-15 -3940 ($ *7)) (-15 -2994 (*7 $)) (-15 -2993 (*7 $)))))
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-   (-5 *1 (-862 *5 *4 *6 *7 *3))))
+     (-10 -8 (-15 -3942 ($ *7)) (-15 -2996 (*7 $)) (-15 -2995 (*7 $)))))
+   (-4 *7 (-862 *6 *5 *4)) (-4 *5 (-718)) (-4 *4 (-757)) (-4 *6 (-962))
+   (-5 *1 (-863 *5 *4 *6 *7 *3))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *4 (-1088)) (-4 *5 (-494)) (-5 *2 (-347 (-1083 (-347 (-857 *5)))))
-   (-5 *1 (-952 *5)) (-5 *3 (-347 (-857 *5)))))) 
+  (-12 (-5 *4 (-1089)) (-4 *5 (-495)) (-5 *2 (-347 (-1084 (-347 (-858 *5)))))
+   (-5 *1 (-953 *5)) (-5 *3 (-347 (-858 *5)))))) 
 (((*1 *2 *1)
-  (|partial| -12 (-4 *1 (-861 *3 *4 *2)) (-4 *3 (-961)) (-4 *4 (-717))
-   (-4 *2 (-756))))
+  (|partial| -12 (-4 *1 (-862 *3 *4 *2)) (-4 *3 (-962)) (-4 *4 (-718))
+   (-4 *2 (-757))))
  ((*1 *2 *3)
-  (|partial| -12 (-4 *4 (-717)) (-4 *5 (-961)) (-4 *6 (-861 *5 *4 *2))
-   (-4 *2 (-756)) (-5 *1 (-862 *4 *2 *5 *6 *3))
+  (|partial| -12 (-4 *4 (-718)) (-4 *5 (-962)) (-4 *6 (-862 *5 *4 *2))
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    (-4 *3
     (-13 (-311)
-     (-10 -8 (-15 -3940 ($ *6)) (-15 -2994 (*6 $)) (-15 -2993 (*6 $)))))))
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  ((*1 *2 *3)
-  (|partial| -12 (-5 *3 (-347 (-857 *4))) (-4 *4 (-494)) (-5 *2 (-1088))
-   (-5 *1 (-952 *4))))) 
+  (|partial| -12 (-5 *3 (-347 (-858 *4))) (-4 *4 (-495)) (-5 *2 (-1089))
+   (-5 *1 (-953 *4))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-1083 *7)) (-4 *7 (-861 *6 *4 *5)) (-4 *4 (-717)) (-4 *5 (-756))
-   (-4 *6 (-961)) (-5 *2 (-583 *5)) (-5 *1 (-271 *4 *5 *6 *7))))
- ((*1 *2 *1) (-12 (-4 *1 (-361 *3)) (-4 *3 (-1012)) (-5 *2 (-583 (-1088)))))
- ((*1 *2 *1) (-12 (-5 *2 (-583 (-800 *3))) (-5 *1 (-800 *3)) (-4 *3 (-1012))))
+  (-12 (-5 *3 (-1084 *7)) (-4 *7 (-862 *6 *4 *5)) (-4 *4 (-718)) (-4 *5 (-757))
+   (-4 *6 (-962)) (-5 *2 (-584 *5)) (-5 *1 (-271 *4 *5 *6 *7))))
+ ((*1 *2 *1) (-12 (-4 *1 (-361 *3)) (-4 *3 (-1013)) (-5 *2 (-584 (-1089)))))
+ ((*1 *2 *1) (-12 (-5 *2 (-584 (-801 *3))) (-5 *1 (-801 *3)) (-4 *3 (-1013))))
  ((*1 *2 *1)
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-   (-5 *2 (-583 *5))))
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+   (-5 *2 (-584 *5))))
  ((*1 *2 *3)
-  (-12 (-4 *4 (-717)) (-4 *5 (-756)) (-4 *6 (-961)) (-4 *7 (-861 *6 *4 *5))
-   (-5 *2 (-583 *5)) (-5 *1 (-862 *4 *5 *6 *7 *3))
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+   (-5 *2 (-584 *5)) (-5 *1 (-863 *4 *5 *6 *7 *3))
    (-4 *3
     (-13 (-311)
-     (-10 -8 (-15 -3940 ($ *7)) (-15 -2994 (*7 $)) (-15 -2993 (*7 $)))))))
+     (-10 -8 (-15 -3942 ($ *7)) (-15 -2996 (*7 $)) (-15 -2995 (*7 $)))))))
  ((*1 *2 *1)
-  (-12 (-4 *1 (-886 *3 *4 *5)) (-4 *3 (-961)) (-4 *4 (-716)) (-4 *5 (-756))
-   (-5 *2 (-583 *5))))
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+   (-5 *2 (-584 *5))))
  ((*1 *2 *1)
-  (-12 (-4 *1 (-889 *3 *4 *5 *6)) (-4 *3 (-961)) (-4 *4 (-717)) (-4 *5 (-756))
-   (-4 *6 (-976 *3 *4 *5)) (-5 *2 (-583 *5))))
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+   (-4 *6 (-977 *3 *4 *5)) (-5 *2 (-584 *5))))
  ((*1 *2 *3)
-  (-12 (-5 *3 (-347 (-857 *4))) (-4 *4 (-494)) (-5 *2 (-583 (-1088)))
-   (-5 *1 (-952 *4))))) 
+  (-12 (-5 *3 (-347 (-858 *4))) (-4 *4 (-495)) (-5 *2 (-584 (-1089)))
+   (-5 *1 (-953 *4))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *3 (-583 (-857 *6))) (-5 *4 (-583 (-1088)))
-   (-4 *6 (-13 (-494) (-950 *5))) (-4 *5 (-494))
-   (-5 *2 (-583 (-583 (-248 (-347 (-857 *6)))))) (-5 *1 (-951 *5 *6))))) 
+  (-12 (-5 *3 (-584 (-858 *6))) (-5 *4 (-584 (-1089)))
+   (-4 *6 (-13 (-495) (-951 *5))) (-4 *5 (-495))
+   (-5 *2 (-584 (-584 (-248 (-347 (-858 *6)))))) (-5 *1 (-952 *5 *6))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *4 (-550 *6)) (-4 *6 (-13 (-361 *5) (-27) (-1113)))
-   (-4 *5 (-13 (-389) (-950 (-483)) (-120) (-580 (-483))))
-   (-5 *2 (-1083 (-347 (-1083 *6)))) (-5 *1 (-497 *5 *6 *7)) (-5 *3 (-1083 *6))
-   (-4 *7 (-1012))))
- ((*1 *2 *1) (-12 (-4 *2 (-1153 *3)) (-5 *1 (-649 *3 *2)) (-4 *3 (-961))))
- ((*1 *2 *1) (-12 (-4 *1 (-661 *3 *2)) (-4 *3 (-146)) (-4 *2 (-1153 *3))))
+  (-12 (-5 *4 (-551 *6)) (-4 *6 (-13 (-361 *5) (-27) (-1114)))
+   (-4 *5 (-13 (-389) (-951 (-484)) (-120) (-581 (-484))))
+   (-5 *2 (-1084 (-347 (-1084 *6)))) (-5 *1 (-498 *5 *6 *7)) (-5 *3 (-1084 *6))
+   (-4 *7 (-1013))))
+ ((*1 *2 *1) (-12 (-4 *2 (-1154 *3)) (-5 *1 (-650 *3 *2)) (-4 *3 (-962))))
+ ((*1 *2 *1) (-12 (-4 *1 (-662 *3 *2)) (-4 *3 (-146)) (-4 *2 (-1154 *3))))
  ((*1 *2 *3 *4 *4 *5 *6 *7 *8)
-  (|partial| -12 (-5 *4 (-1083 *11)) (-5 *6 (-583 *10)) (-5 *7 (-583 (-694)))
-   (-5 *8 (-583 *11)) (-4 *10 (-756)) (-4 *11 (-257)) (-4 *9 (-717))
-   (-4 *5 (-861 *11 *9 *10)) (-5 *2 (-583 (-1083 *5)))
-   (-5 *1 (-681 *9 *10 *11 *5)) (-5 *3 (-1083 *5))))
+  (|partial| -12 (-5 *4 (-1084 *11)) (-5 *6 (-584 *10)) (-5 *7 (-584 (-695)))
+   (-5 *8 (-584 *11)) (-4 *10 (-757)) (-4 *11 (-257)) (-4 *9 (-718))
+   (-4 *5 (-862 *11 *9 *10)) (-5 *2 (-584 (-1084 *5)))
+   (-5 *1 (-682 *9 *10 *11 *5)) (-5 *3 (-1084 *5))))
  ((*1 *2 *1)
-  (-12 (-4 *2 (-861 *3 *4 *5)) (-5 *1 (-947 *3 *4 *5 *2 *6)) (-4 *3 (-311))
-   (-4 *4 (-717)) (-4 *5 (-756)) (-14 *6 (-583 *2))))) 
+  (-12 (-4 *2 (-862 *3 *4 *5)) (-5 *1 (-948 *3 *4 *5 *2 *6)) (-4 *3 (-311))
+   (-4 *4 (-718)) (-4 *5 (-757)) (-14 *6 (-584 *2))))) 
 (((*1 *2 *2 *3)
-  (-12 (-5 *3 (-830)) (-5 *1 (-945 *2))
-   (-4 *2 (-13 (-1012) (-10 -8 (-15 * ($ $ $)))))))) 
+  (-12 (-5 *3 (-831)) (-5 *1 (-946 *2))
+   (-4 *2 (-13 (-1013) (-10 -8 (-15 * ($ $ $)))))))) 
 (((*1 *2 *3 *2)
-  (-12 (-5 *3 (-830)) (-5 *1 (-944 *2))
-   (-4 *2 (-13 (-1012) (-10 -8 (-15 -3833 ($ $ $)))))))) 
+  (-12 (-5 *3 (-831)) (-5 *1 (-945 *2))
+   (-4 *2 (-13 (-1013) (-10 -8 (-15 -3835 ($ $ $)))))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *3 (-583 (-1177 *5))) (-5 *4 (-483)) (-5 *2 (-1177 *5))
-   (-5 *1 (-943 *5)) (-4 *5 (-311)) (-4 *5 (-317)) (-4 *5 (-961))))) 
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+   (-5 *1 (-944 *5)) (-4 *5 (-311)) (-4 *5 (-317)) (-4 *5 (-962))))) 
 (((*1 *2 *3 *4 *5 *5)
-  (-12 (-5 *4 (-85)) (-5 *5 (-483)) (-4 *6 (-311)) (-4 *6 (-317))
-   (-4 *6 (-961)) (-5 *2 (-583 (-583 (-630 *6)))) (-5 *1 (-943 *6))
-   (-5 *3 (-583 (-630 *6)))))
+  (-12 (-5 *4 (-85)) (-5 *5 (-484)) (-4 *6 (-311)) (-4 *6 (-317))
+   (-4 *6 (-962)) (-5 *2 (-584 (-584 (-631 *6)))) (-5 *1 (-944 *6))
+   (-5 *3 (-584 (-631 *6)))))
  ((*1 *2 *3)
-  (-12 (-4 *4 (-311)) (-4 *4 (-317)) (-4 *4 (-961))
-   (-5 *2 (-583 (-583 (-630 *4)))) (-5 *1 (-943 *4)) (-5 *3 (-583 (-630 *4)))))
+  (-12 (-4 *4 (-311)) (-4 *4 (-317)) (-4 *4 (-962))
+   (-5 *2 (-584 (-584 (-631 *4)))) (-5 *1 (-944 *4)) (-5 *3 (-584 (-631 *4)))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *4 (-85)) (-4 *5 (-311)) (-4 *5 (-317)) (-4 *5 (-961))
-   (-5 *2 (-583 (-583 (-630 *5)))) (-5 *1 (-943 *5)) (-5 *3 (-583 (-630 *5)))))
+  (-12 (-5 *4 (-85)) (-4 *5 (-311)) (-4 *5 (-317)) (-4 *5 (-962))
+   (-5 *2 (-584 (-584 (-631 *5)))) (-5 *1 (-944 *5)) (-5 *3 (-584 (-631 *5)))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *4 (-830)) (-4 *5 (-311)) (-4 *5 (-317)) (-4 *5 (-961))
-   (-5 *2 (-583 (-583 (-630 *5)))) (-5 *1 (-943 *5)) (-5 *3 (-583 (-630 *5)))))) 
+  (-12 (-5 *4 (-831)) (-4 *5 (-311)) (-4 *5 (-317)) (-4 *5 (-962))
+   (-5 *2 (-584 (-584 (-631 *5)))) (-5 *1 (-944 *5)) (-5 *3 (-584 (-631 *5)))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *3 (-583 (-630 *5))) (-5 *4 (-483)) (-4 *5 (-311)) (-4 *5 (-961))
-   (-5 *2 (-85)) (-5 *1 (-943 *5))))
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+   (-5 *2 (-85)) (-5 *1 (-944 *5))))
  ((*1 *2 *3)
-  (-12 (-5 *3 (-583 (-630 *4))) (-4 *4 (-311)) (-4 *4 (-961)) (-5 *2 (-85))
-   (-5 *1 (-943 *4))))) 
+  (-12 (-5 *3 (-584 (-631 *4))) (-4 *4 (-311)) (-4 *4 (-962)) (-5 *2 (-85))
+   (-5 *1 (-944 *4))))) 
 (((*1 *2 *3 *3 *4 *5)
-  (-12 (-5 *3 (-583 (-630 *6))) (-5 *4 (-85)) (-5 *5 (-483)) (-5 *2 (-630 *6))
-   (-5 *1 (-943 *6)) (-4 *6 (-311)) (-4 *6 (-961))))
+  (-12 (-5 *3 (-584 (-631 *6))) (-5 *4 (-85)) (-5 *5 (-484)) (-5 *2 (-631 *6))
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  ((*1 *2 *3 *3)
-  (-12 (-5 *3 (-583 (-630 *4))) (-5 *2 (-630 *4)) (-5 *1 (-943 *4))
-   (-4 *4 (-311)) (-4 *4 (-961))))
+  (-12 (-5 *3 (-584 (-631 *4))) (-5 *2 (-631 *4)) (-5 *1 (-944 *4))
+   (-4 *4 (-311)) (-4 *4 (-962))))
  ((*1 *2 *3 *3 *4)
-  (-12 (-5 *3 (-583 (-630 *5))) (-5 *4 (-483)) (-5 *2 (-630 *5))
-   (-5 *1 (-943 *5)) (-4 *5 (-311)) (-4 *5 (-961))))) 
+  (-12 (-5 *3 (-584 (-631 *5))) (-5 *4 (-484)) (-5 *2 (-631 *5))
+   (-5 *1 (-944 *5)) (-4 *5 (-311)) (-4 *5 (-962))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *3 (-583 (-630 *5))) (-5 *4 (-1177 *5)) (-4 *5 (-257))
-   (-4 *5 (-961)) (-5 *2 (-630 *5)) (-5 *1 (-943 *5))))) 
+  (-12 (-5 *3 (-584 (-631 *5))) (-5 *4 (-1178 *5)) (-4 *5 (-257))
+   (-4 *5 (-962)) (-5 *2 (-631 *5)) (-5 *1 (-944 *5))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *3 (-583 (-630 *5))) (-4 *5 (-257)) (-4 *5 (-961))
-   (-5 *2 (-1177 (-1177 *5))) (-5 *1 (-943 *5)) (-5 *4 (-1177 *5))))) 
+  (-12 (-5 *3 (-584 (-631 *5))) (-4 *5 (-257)) (-4 *5 (-962))
+   (-5 *2 (-1178 (-1178 *5))) (-5 *1 (-944 *5)) (-5 *4 (-1178 *5))))) 
 (((*1 *2 *3 *2)
-  (-12 (-5 *3 (-583 (-630 *4))) (-5 *2 (-630 *4)) (-4 *4 (-961))
-   (-5 *1 (-943 *4))))) 
+  (-12 (-5 *3 (-584 (-631 *4))) (-5 *2 (-631 *4)) (-4 *4 (-962))
+   (-5 *1 (-944 *4))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-1177 (-1177 *4))) (-4 *4 (-961)) (-5 *2 (-630 *4))
-   (-5 *1 (-943 *4))))) 
+  (-12 (-5 *3 (-1178 (-1178 *4))) (-4 *4 (-962)) (-5 *2 (-631 *4))
+   (-5 *1 (-944 *4))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *3 (-813 (-483))) (-5 *4 (-483)) (-5 *2 (-630 *4)) (-5 *1 (-942 *5))
-   (-4 *5 (-961))))
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+   (-4 *5 (-962))))
  ((*1 *2 *3)
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-   (-4 *4 (-961))))
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+   (-4 *4 (-962))))
  ((*1 *2 *3 *4)
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-   (-5 *1 (-942 *5)) (-4 *5 (-961))))
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+   (-5 *1 (-943 *5)) (-4 *5 (-962))))
  ((*1 *2 *3)
-  (-12 (-5 *3 (-583 (-583 (-483)))) (-5 *2 (-583 (-630 (-483))))
-   (-5 *1 (-942 *4)) (-4 *4 (-961))))) 
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+  (-12 (-5 *3 (-584 (-584 (-484)))) (-5 *2 (-584 (-631 (-484))))
+   (-5 *1 (-943 *4)) (-4 *4 (-962))))) 
+(((*1 *2 *2 *2) (-12 (-5 *2 (-631 *3)) (-4 *3 (-962)) (-5 *1 (-943 *3))))
  ((*1 *2 *2 *2)
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- ((*1 *2 *2) (-12 (-5 *2 (-630 *3)) (-4 *3 (-961)) (-5 *1 (-942 *3))))
- ((*1 *2 *2) (-12 (-5 *2 (-583 (-630 *3))) (-4 *3 (-961)) (-5 *1 (-942 *3))))) 
+  (-12 (-5 *2 (-584 (-631 *3))) (-4 *3 (-962)) (-5 *1 (-943 *3))))
+ ((*1 *2 *2) (-12 (-5 *2 (-631 *3)) (-4 *3 (-962)) (-5 *1 (-943 *3))))
+ ((*1 *2 *2) (-12 (-5 *2 (-584 (-631 *3))) (-4 *3 (-962)) (-5 *1 (-943 *3))))) 
 (((*1 *2 *2 *3)
-  (-12 (-5 *2 (-630 *4)) (-5 *3 (-830)) (-4 *4 (-961)) (-5 *1 (-942 *4))))
+  (-12 (-5 *2 (-631 *4)) (-5 *3 (-831)) (-4 *4 (-962)) (-5 *1 (-943 *4))))
  ((*1 *2 *2 *3)
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 (((*1 *2 *1) (-12 (-5 *2 (-85)) (-5 *1 (-107))))
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 (((*1 *2 *3 *2)
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 (((*1 *1 *2 *3)
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-  (-12 (-4 *3 (-961)) (-5 *2 (-869 (-649 *3 *4))) (-5 *1 (-649 *3 *4))
-   (-4 *4 (-1153 *3))))) 
+  (-12 (-4 *3 (-962)) (-5 *2 (-870 (-650 *3 *4))) (-5 *1 (-650 *3 *4))
+   (-4 *4 (-1154 *3))))) 
 (((*1 *1 *1)
-  (-12 (-4 *2 (-298)) (-4 *2 (-961)) (-5 *1 (-649 *2 *3)) (-4 *3 (-1153 *2))))) 
-(((*1 *2 *3) (-12 (-5 *3 (-772)) (-5 *2 (-1071)) (-5 *1 (-647))))) 
-(((*1 *2 *3) (-12 (-5 *3 (-772)) (-5 *2 (-1071)) (-5 *1 (-647))))) 
-(((*1 *2 *3) (-12 (-5 *3 (-772)) (-5 *2 (-1071)) (-5 *1 (-647))))) 
+  (-12 (-4 *2 (-298)) (-4 *2 (-962)) (-5 *1 (-650 *2 *3)) (-4 *3 (-1154 *2))))) 
+(((*1 *2 *3) (-12 (-5 *3 (-773)) (-5 *2 (-1072)) (-5 *1 (-648))))) 
+(((*1 *2 *3) (-12 (-5 *3 (-773)) (-5 *2 (-1072)) (-5 *1 (-648))))) 
+(((*1 *2 *3) (-12 (-5 *3 (-773)) (-5 *2 (-1072)) (-5 *1 (-648))))) 
 (((*1 *2 *3 *4 *2 *5 *6 *7 *8 *9 *10)
-  (|partial| -12 (-5 *2 (-583 (-1083 *13))) (-5 *3 (-1083 *13))
-   (-5 *4 (-583 *12)) (-5 *5 (-583 *10)) (-5 *6 (-583 *13))
-   (-5 *7 (-583 (-583 (-2 (|:| -3074 (-694)) (|:| |pcoef| *13)))))
-   (-5 *8 (-583 (-694))) (-5 *9 (-1177 (-583 (-1083 *10)))) (-4 *12 (-756))
-   (-4 *10 (-257)) (-4 *13 (-861 *10 *11 *12)) (-4 *11 (-717))
-   (-5 *1 (-644 *11 *12 *10 *13))))) 
+  (|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 *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))))) 
 (((*1 *2 *3 *4 *5 *6 *7 *8 *9)
-  (|partial| -12 (-5 *4 (-583 *11)) (-5 *5 (-583 (-1083 *9))) (-5 *6 (-583 *9))
-   (-5 *7 (-583 *12)) (-5 *8 (-583 (-694))) (-4 *11 (-756)) (-4 *9 (-257))
-   (-4 *12 (-861 *9 *10 *11)) (-4 *10 (-717)) (-5 *2 (-583 (-1083 *12)))
-   (-5 *1 (-644 *10 *11 *9 *12)) (-5 *3 (-1083 *12))))) 
+  (|partial| -12 (-5 *4 (-584 *11)) (-5 *5 (-584 (-1084 *9))) (-5 *6 (-584 *9))
+   (-5 *7 (-584 *12)) (-5 *8 (-584 (-695))) (-4 *11 (-757)) (-4 *9 (-257))
+   (-4 *12 (-862 *9 *10 *11)) (-4 *10 (-718)) (-5 *2 (-584 (-1084 *12)))
+   (-5 *1 (-645 *10 *11 *9 *12)) (-5 *3 (-1084 *12))))) 
 (((*1 *2 *3 *4 *5 *6 *2 *7 *8)
-  (|partial| -12 (-5 *2 (-583 (-1083 *11))) (-5 *3 (-1083 *11))
-   (-5 *4 (-583 *10)) (-5 *5 (-583 *8)) (-5 *6 (-583 (-694)))
-   (-5 *7 (-1177 (-583 (-1083 *8)))) (-4 *10 (-756)) (-4 *8 (-257))
-   (-4 *11 (-861 *8 *9 *10)) (-4 *9 (-717)) (-5 *1 (-644 *9 *10 *8 *11))))) 
+  (|partial| -12 (-5 *2 (-584 (-1084 *11))) (-5 *3 (-1084 *11))
+   (-5 *4 (-584 *10)) (-5 *5 (-584 *8)) (-5 *6 (-584 (-695)))
+   (-5 *7 (-1178 (-584 (-1084 *8)))) (-4 *10 (-757)) (-4 *8 (-257))
+   (-4 *11 (-862 *8 *9 *10)) (-4 *9 (-718)) (-5 *1 (-645 *9 *10 *8 *11))))) 
 (((*1 *2 *3 *4 *4)
-  (-12 (-5 *4 (-1088)) (-5 *2 (-1 *7 *5 *6)) (-5 *1 (-639 *3 *5 *6 *7))
-   (-4 *3 (-553 (-472))) (-4 *5 (-1127)) (-4 *6 (-1127)) (-4 *7 (-1127))))
+  (-12 (-5 *4 (-1089)) (-5 *2 (-1 *7 *5 *6)) (-5 *1 (-640 *3 *5 *6 *7))
+   (-4 *3 (-554 (-473))) (-4 *5 (-1128)) (-4 *6 (-1128)) (-4 *7 (-1128))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *4 (-1088)) (-5 *2 (-1 *6 *5)) (-5 *1 (-643 *3 *5 *6))
-   (-4 *3 (-553 (-472))) (-4 *5 (-1127)) (-4 *6 (-1127))))) 
+  (-12 (-5 *4 (-1089)) (-5 *2 (-1 *6 *5)) (-5 *1 (-644 *3 *5 *6))
+   (-4 *3 (-554 (-473))) (-4 *5 (-1128)) (-4 *6 (-1128))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-1088)) (-5 *2 (-1 *6 *5)) (-5 *1 (-643 *4 *5 *6))
-   (-4 *4 (-553 (-472))) (-4 *5 (-1127)) (-4 *6 (-1127))))) 
+  (-12 (-5 *3 (-1089)) (-5 *2 (-1 *6 *5)) (-5 *1 (-644 *4 *5 *6))
+   (-4 *4 (-554 (-473))) (-4 *5 (-1128)) (-4 *6 (-1128))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *2 (-2 (|:| |part1| *3) (|:| |part2| *4))) (-5 *1 (-642 *3 *4))
-   (-4 *3 (-1127)) (-4 *4 (-1127))))) 
-(((*1 *1 *1 *2 *3) (-12 (-5 *2 (-583 (-1088))) (-5 *3 (-1088)) (-5 *1 (-472))))
- ((*1 *2 *3 *2) (-12 (-5 *2 (-1088)) (-5 *1 (-641 *3)) (-4 *3 (-553 (-472)))))
+  (-12 (-5 *2 (-2 (|:| |part1| *3) (|:| |part2| *4))) (-5 *1 (-643 *3 *4))
+   (-4 *3 (-1128)) (-4 *4 (-1128))))) 
+(((*1 *1 *1 *2 *3) (-12 (-5 *2 (-584 (-1089))) (-5 *3 (-1089)) (-5 *1 (-473))))
+ ((*1 *2 *3 *2) (-12 (-5 *2 (-1089)) (-5 *1 (-642 *3)) (-4 *3 (-554 (-473)))))
  ((*1 *2 *3 *2 *2)
-  (-12 (-5 *2 (-1088)) (-5 *1 (-641 *3)) (-4 *3 (-553 (-472)))))
+  (-12 (-5 *2 (-1089)) (-5 *1 (-642 *3)) (-4 *3 (-554 (-473)))))
  ((*1 *2 *3 *2 *2 *2)
-  (-12 (-5 *2 (-1088)) (-5 *1 (-641 *3)) (-4 *3 (-553 (-472)))))
+  (-12 (-5 *2 (-1089)) (-5 *1 (-642 *3)) (-4 *3 (-554 (-473)))))
  ((*1 *2 *3 *2 *4)
-  (-12 (-5 *4 (-583 (-1088))) (-5 *2 (-1088)) (-5 *1 (-641 *3))
-   (-4 *3 (-553 (-472)))))) 
+  (-12 (-5 *4 (-584 (-1089))) (-5 *2 (-1089)) (-5 *1 (-642 *3))
+   (-4 *3 (-554 (-473)))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *4 (-1088)) (-5 *2 (-1 (-179) (-179))) (-5 *1 (-640 *3))
-   (-4 *3 (-553 (-472)))))
+  (-12 (-5 *4 (-1089)) (-5 *2 (-1 (-179) (-179))) (-5 *1 (-641 *3))
+   (-4 *3 (-554 (-473)))))
  ((*1 *2 *3 *4 *4)
-  (-12 (-5 *4 (-1088)) (-5 *2 (-1 (-179) (-179) (-179))) (-5 *1 (-640 *3))
-   (-4 *3 (-553 (-472)))))) 
+  (-12 (-5 *4 (-1089)) (-5 *2 (-1 (-179) (-179) (-179))) (-5 *1 (-641 *3))
+   (-4 *3 (-554 (-473)))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-1088)) (-5 *2 (-1 *7 *5 *6)) (-5 *1 (-639 *4 *5 *6 *7))
-   (-4 *4 (-553 (-472))) (-4 *5 (-1127)) (-4 *6 (-1127)) (-4 *7 (-1127))))) 
+  (-12 (-5 *3 (-1089)) (-5 *2 (-1 *7 *5 *6)) (-5 *1 (-640 *4 *5 *6 *7))
+   (-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 (|:| -1970 *3) (|:| -2898 *3))) (-5 *1 (-629 *3 *4 *5 *6))
-   (-4 *6 (-627 *3 *4 *5))))
+   (-5 *2 (-2 (|:| -1971 *3) (|:| -2900 *3))) (-5 *1 (-630 *3 *4 *5 *6))
+   (-4 *6 (-628 *3 *4 *5))))
  ((*1 *2 *3 *3)
-  (-12 (-5 *2 (-2 (|:| -1970 *3) (|:| -2898 *3))) (-5 *1 (-638 *3))
+  (-12 (-5 *2 (-2 (|:| -1971 *3) (|:| -2900 *3))) (-5 *1 (-639 *3))
    (-4 *3 (-257))))) 
-(((*1 *2 *2 *3 *3) (-12 (-5 *2 (-630 *3)) (-4 *3 (-257)) (-5 *1 (-638 *3))))) 
-(((*1 *2 *2 *3) (-12 (-5 *2 (-630 *3)) (-4 *3 (-257)) (-5 *1 (-638 *3))))) 
-(((*1 *2 *2) (-12 (-5 *2 (-630 *3)) (-4 *3 (-257)) (-5 *1 (-638 *3))))) 
+(((*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))))) 
+(((*1 *2 *2) (-12 (-5 *2 (-631 *3)) (-4 *3 (-257)) (-5 *1 (-639 *3))))) 
 (((*1 *2 *3 *3 *3 *4)
   (-12 (-5 *3 (-1 (-179) (-179) (-179)))
    (-5 *4 (-1 (-179) (-179) (-179) (-179)))
-   (-5 *2 (-1 (-854 (-179)) (-179) (-179))) (-5 *1 (-636))))) 
+   (-5 *2 (-1 (-855 (-179)) (-179) (-179))) (-5 *1 (-637))))) 
 (((*1 *2 *3 *3 *3 *4 *5 *6)
-  (-12 (-5 *3 (-264 (-483))) (-5 *4 (-1 (-179) (-179))) (-5 *5 (-1000 (-179)))
-   (-5 *6 (-583 (-221))) (-5 *2 (-1045 (-179))) (-5 *1 (-636))))) 
+  (-12 (-5 *3 (-264 (-484))) (-5 *4 (-1 (-179) (-179))) (-5 *5 (-1001 (-179)))
+   (-5 *6 (-584 (-221))) (-5 *2 (-1046 (-179))) (-5 *1 (-637))))) 
 (((*1 *2 *3 *4 *5 *5 *6)
   (-12 (-5 *3 (-1 (-179) (-179) (-179)))
    (-5 *4 (-3 (-1 (-179) (-179) (-179) (-179)) "undefined"))
-   (-5 *5 (-1000 (-179))) (-5 *6 (-583 (-221))) (-5 *2 (-1045 (-179)))
-   (-5 *1 (-636))))) 
+   (-5 *5 (-1001 (-179))) (-5 *6 (-584 (-221))) (-5 *2 (-1046 (-179)))
+   (-5 *1 (-637))))) 
 (((*1 *2 *3 *3 *3 *4 *5 *5 *6)
   (-12 (-5 *3 (-1 (-179) (-179) (-179)))
    (-5 *4 (-3 (-1 (-179) (-179) (-179) (-179)) "undefined"))
-   (-5 *5 (-1000 (-179))) (-5 *6 (-583 (-221))) (-5 *2 (-1045 (-179)))
-   (-5 *1 (-636))))
+   (-5 *5 (-1001 (-179))) (-5 *6 (-584 (-221))) (-5 *2 (-1046 (-179)))
+   (-5 *1 (-637))))
  ((*1 *2 *3 *4 *4 *5)
-  (-12 (-5 *3 (-1 (-854 (-179)) (-179) (-179))) (-5 *4 (-1000 (-179)))
-   (-5 *5 (-583 (-221))) (-5 *2 (-1045 (-179))) (-5 *1 (-636))))
+  (-12 (-5 *3 (-1 (-855 (-179)) (-179) (-179))) (-5 *4 (-1001 (-179)))
+   (-5 *5 (-584 (-221))) (-5 *2 (-1046 (-179))) (-5 *1 (-637))))
  ((*1 *2 *2 *3 *4 *4 *5)
-  (-12 (-5 *2 (-1045 (-179))) (-5 *3 (-1 (-854 (-179)) (-179) (-179)))
-   (-5 *4 (-1000 (-179))) (-5 *5 (-583 (-221))) (-5 *1 (-636))))) 
+  (-12 (-5 *2 (-1046 (-179))) (-5 *3 (-1 (-855 (-179)) (-179) (-179)))
+   (-5 *4 (-1001 (-179))) (-5 *5 (-584 (-221))) (-5 *1 (-637))))) 
 (((*1 *2 *2 *3 *2)
-  (-12 (-5 *3 (-694)) (-4 *4 (-298)) (-5 *1 (-170 *4 *2)) (-4 *2 (-1153 *4))))
+  (-12 (-5 *3 (-695)) (-4 *4 (-298)) (-5 *1 (-170 *4 *2)) (-4 *2 (-1154 *4))))
  ((*1 *2 *2 *3 *2 *3)
-  (-12 (-5 *3 (-483)) (-5 *1 (-635 *2)) (-4 *2 (-1153 *3))))) 
+  (-12 (-5 *3 (-484)) (-5 *1 (-636 *2)) (-4 *2 (-1154 *3))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-583 (-2 (|:| |deg| (-694)) (|:| -2571 *5)))) (-4 *5 (-1153 *4))
-   (-4 *4 (-298)) (-5 *2 (-583 *5)) (-5 *1 (-170 *4 *5))))
+  (-12 (-5 *3 (-584 (-2 (|:| |deg| (-695)) (|:| -2573 *5)))) (-4 *5 (-1154 *4))
+   (-4 *4 (-298)) (-5 *2 (-584 *5)) (-5 *1 (-170 *4 *5))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *3 (-583 (-2 (|:| -3726 *5) (|:| -3942 (-483))))) (-5 *4 (-483))
-   (-4 *5 (-1153 *4)) (-5 *2 (-583 *5)) (-5 *1 (-635 *5))))) 
+  (-12 (-5 *3 (-584 (-2 (|:| -3728 *5) (|:| -3944 (-484))))) (-5 *4 (-484))
+   (-4 *5 (-1154 *4)) (-5 *2 (-584 *5)) (-5 *1 (-636 *5))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *4 (-483)) (-5 *2 (-583 (-2 (|:| -3726 *3) (|:| -3942 *4))))
-   (-5 *1 (-635 *3)) (-4 *3 (-1153 *4))))) 
-(((*1 *2 *2 *3) (-12 (-5 *3 (-483)) (-5 *1 (-635 *2)) (-4 *2 (-1153 *3))))) 
-(((*1 *1 *1) (-12 (-4 *1 (-237 *2)) (-4 *2 (-1127)) (-4 *2 (-1012))))
- ((*1 *1 *1) (-12 (-4 *1 (-634 *2)) (-4 *2 (-1012))))) 
+  (-12 (-5 *4 (-484)) (-5 *2 (-584 (-2 (|:| -3728 *3) (|:| -3944 *4))))
+   (-5 *1 (-636 *3)) (-4 *3 (-1154 *4))))) 
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+(((*1 *1 *1) (-12 (-4 *1 (-237 *2)) (-4 *2 (-1128)) (-4 *2 (-1013))))
+ ((*1 *1 *1) (-12 (-4 *1 (-635 *2)) (-4 *2 (-1013))))) 
 (((*1 *2 *1)
-  (-12 (-4 *1 (-634 *3)) (-4 *3 (-1012))
-   (-5 *2 (-583 (-2 (|:| |entry| *3) (|:| -1943 (-694)))))))) 
-(((*1 *1 *2) (-12 (-5 *1 (-632 *2)) (-4 *2 (-552 (-772)))))) 
-(((*1 *1) (-12 (-5 *1 (-632 *2)) (-4 *2 (-552 (-772)))))) 
+  (-12 (-4 *1 (-635 *3)) (-4 *3 (-1013))
+   (-5 *2 (-584 (-2 (|:| |entry| *3) (|:| -1944 (-695)))))))) 
+(((*1 *1 *2) (-12 (-5 *1 (-633 *2)) (-4 *2 (-553 (-773)))))) 
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 (((*1 *2 *2 *2 *2 *2 *3)
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-(((*1 *2 *2 *2 *2) (-12 (-5 *2 (-630 *3)) (-4 *3 (-961)) (-5 *1 (-631 *3))))) 
-(((*1 *2 *2 *2 *3) (-12 (-5 *2 (-630 *3)) (-4 *3 (-961)) (-5 *1 (-631 *3))))) 
-(((*1 *2 *2 *3 *2) (-12 (-5 *2 (-630 *3)) (-4 *3 (-961)) (-5 *1 (-631 *3))))) 
-(((*1 *2 *2 *2) (-12 (-5 *2 (-630 *3)) (-4 *3 (-961)) (-5 *1 (-631 *3))))
- ((*1 *2 *2 *2 *2) (-12 (-5 *2 (-630 *3)) (-4 *3 (-961)) (-5 *1 (-631 *3))))) 
-(((*1 *2 *2 *2 *2) (-12 (-5 *2 (-630 *3)) (-4 *3 (-961)) (-5 *1 (-631 *3))))) 
-(((*1 *2 *2 *2) (-12 (-5 *2 (-630 *3)) (-4 *3 (-961)) (-5 *1 (-631 *3))))) 
-(((*1 *2 *2)
-  (|partial| -12 (-4 *3 (-494)) (-4 *3 (-146)) (-4 *4 (-321 *3))
-   (-4 *5 (-321 *3)) (-5 *1 (-629 *3 *4 *5 *2)) (-4 *2 (-627 *3 *4 *5))))) 
-(((*1 *2 *2)
-  (-12 (-4 *3 (-494)) (-4 *3 (-146)) (-4 *4 (-321 *3)) (-4 *5 (-321 *3))
-   (-5 *1 (-629 *3 *4 *5 *2)) (-4 *2 (-627 *3 *4 *5))))) 
+  (-12 (-5 *2 (-631 *4)) (-5 *3 (-695)) (-4 *4 (-962)) (-5 *1 (-632 *4))))) 
+(((*1 *2 *2 *2 *2) (-12 (-5 *2 (-631 *3)) (-4 *3 (-962)) (-5 *1 (-632 *3))))) 
+(((*1 *2 *2 *2 *3) (-12 (-5 *2 (-631 *3)) (-4 *3 (-962)) (-5 *1 (-632 *3))))) 
+(((*1 *2 *2 *3 *2) (-12 (-5 *2 (-631 *3)) (-4 *3 (-962)) (-5 *1 (-632 *3))))) 
+(((*1 *2 *2 *2) (-12 (-5 *2 (-631 *3)) (-4 *3 (-962)) (-5 *1 (-632 *3))))
+ ((*1 *2 *2 *2 *2) (-12 (-5 *2 (-631 *3)) (-4 *3 (-962)) (-5 *1 (-632 *3))))) 
+(((*1 *2 *2 *2 *2) (-12 (-5 *2 (-631 *3)) (-4 *3 (-962)) (-5 *1 (-632 *3))))) 
+(((*1 *2 *2 *2) (-12 (-5 *2 (-631 *3)) (-4 *3 (-962)) (-5 *1 (-632 *3))))) 
+(((*1 *2 *2)
+  (|partial| -12 (-4 *3 (-495)) (-4 *3 (-146)) (-4 *4 (-321 *3))
+   (-4 *5 (-321 *3)) (-5 *1 (-630 *3 *4 *5 *2)) (-4 *2 (-628 *3 *4 *5))))) 
+(((*1 *2 *2)
+  (-12 (-4 *3 (-495)) (-4 *3 (-146)) (-4 *4 (-321 *3)) (-4 *5 (-321 *3))
+   (-5 *1 (-630 *3 *4 *5 *2)) (-4 *2 (-628 *3 *4 *5))))) 
 (((*1 *2 *2 *3 *4 *4)
-  (-12 (-5 *4 (-483)) (-4 *3 (-146)) (-4 *5 (-321 *3)) (-4 *6 (-321 *3))
-   (-5 *1 (-629 *3 *5 *6 *2)) (-4 *2 (-627 *3 *5 *6))))) 
+  (-12 (-5 *4 (-484)) (-4 *3 (-146)) (-4 *5 (-321 *3)) (-4 *6 (-321 *3))
+   (-5 *1 (-630 *3 *5 *6 *2)) (-4 *2 (-628 *3 *5 *6))))) 
 (((*1 *2 *2 *3 *4 *4)
-  (-12 (-5 *4 (-483)) (-4 *3 (-146)) (-4 *5 (-321 *3)) (-4 *6 (-321 *3))
-   (-5 *1 (-629 *3 *5 *6 *2)) (-4 *2 (-627 *3 *5 *6))))) 
+  (-12 (-5 *4 (-484)) (-4 *3 (-146)) (-4 *5 (-321 *3)) (-4 *6 (-321 *3))
+   (-5 *1 (-630 *3 *5 *6 *2)) (-4 *2 (-628 *3 *5 *6))))) 
 (((*1 *2 *2 *3 *3)
-  (-12 (-5 *3 (-483)) (-4 *4 (-146)) (-4 *5 (-321 *4)) (-4 *6 (-321 *4))
-   (-5 *1 (-629 *4 *5 *6 *2)) (-4 *2 (-627 *4 *5 *6))))) 
+  (-12 (-5 *3 (-484)) (-4 *4 (-146)) (-4 *5 (-321 *4)) (-4 *6 (-321 *4))
+   (-5 *1 (-630 *4 *5 *6 *2)) (-4 *2 (-628 *4 *5 *6))))) 
 (((*1 *1 *1)
-  (-12 (-4 *1 (-627 *2 *3 *4)) (-4 *2 (-961)) (-4 *3 (-321 *2))
+  (-12 (-4 *1 (-628 *2 *3 *4)) (-4 *2 (-962)) (-4 *3 (-321 *2))
    (-4 *4 (-321 *2))))) 
 (((*1 *1 *1 *1)
-  (-12 (-4 *1 (-627 *2 *3 *4)) (-4 *2 (-961)) (-4 *3 (-321 *2))
+  (-12 (-4 *1 (-628 *2 *3 *4)) (-4 *2 (-962)) (-4 *3 (-321 *2))
    (-4 *4 (-321 *2))))) 
 (((*1 *1 *1 *1)
-  (-12 (-4 *1 (-627 *2 *3 *4)) (-4 *2 (-961)) (-4 *3 (-321 *2))
+  (-12 (-4 *1 (-628 *2 *3 *4)) (-4 *2 (-962)) (-4 *3 (-321 *2))
    (-4 *4 (-321 *2))))) 
 (((*1 *1 *1 *2 *2)
-  (-12 (-5 *2 (-483)) (-4 *1 (-627 *3 *4 *5)) (-4 *3 (-961)) (-4 *4 (-321 *3))
+  (-12 (-5 *2 (-484)) (-4 *1 (-628 *3 *4 *5)) (-4 *3 (-962)) (-4 *4 (-321 *3))
    (-4 *5 (-321 *3))))) 
 (((*1 *1 *1 *2 *2)
-  (-12 (-5 *2 (-483)) (-4 *1 (-627 *3 *4 *5)) (-4 *3 (-961)) (-4 *4 (-321 *3))
+  (-12 (-5 *2 (-484)) (-4 *1 (-628 *3 *4 *5)) (-4 *3 (-962)) (-4 *4 (-321 *3))
    (-4 *5 (-321 *3))))) 
 (((*1 *1 *1 *2 *2 *2 *2)
-  (-12 (-5 *2 (-483)) (-4 *1 (-627 *3 *4 *5)) (-4 *3 (-961)) (-4 *4 (-321 *3))
+  (-12 (-5 *2 (-484)) (-4 *1 (-628 *3 *4 *5)) (-4 *3 (-962)) (-4 *4 (-321 *3))
    (-4 *5 (-321 *3))))) 
 (((*1 *1 *1 *2 *2 *1)
-  (-12 (-5 *2 (-483)) (-4 *1 (-627 *3 *4 *5)) (-4 *3 (-961)) (-4 *4 (-321 *3))
+  (-12 (-5 *2 (-484)) (-4 *1 (-628 *3 *4 *5)) (-4 *3 (-962)) (-4 *4 (-321 *3))
    (-4 *5 (-321 *3))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-1 *6 *4 *5)) (-4 *4 (-1012)) (-4 *5 (-1012)) (-4 *6 (-1012))
-   (-5 *2 (-1 *6 *5 *4)) (-5 *1 (-625 *4 *5 *6))))) 
+  (-12 (-5 *3 (-1 *6 *4 *5)) (-4 *4 (-1013)) (-4 *5 (-1013)) (-4 *6 (-1013))
+   (-5 *2 (-1 *6 *5 *4)) (-5 *1 (-626 *4 *5 *6))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-1 *6 *5)) (-4 *5 (-1012)) (-4 *6 (-1012)) (-5 *2 (-1 *6 *4 *5))
-   (-5 *1 (-625 *4 *5 *6)) (-4 *4 (-1012))))) 
+  (-12 (-5 *3 (-1 *6 *5)) (-4 *5 (-1013)) (-4 *6 (-1013)) (-5 *2 (-1 *6 *4 *5))
+   (-5 *1 (-626 *4 *5 *6)) (-4 *4 (-1013))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-1 *6 *4)) (-4 *4 (-1012)) (-4 *6 (-1012)) (-5 *2 (-1 *6 *4 *5))
-   (-5 *1 (-625 *4 *5 *6)) (-4 *5 (-1012))))) 
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    (-5 *1 (-405))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-583 (-583 (-854 (-179))))) (-5 *2 (-583 (-179)))
+  (-12 (-5 *3 (-584 (-584 (-855 (-179))))) (-5 *2 (-584 (-179)))
    (-5 *1 (-405))))) 
 (((*1 *1 *2) (-12 (-5 *2 (-85)) (-5 *1 (-221))))
- ((*1 *2 *3 *2) (-12 (-5 *2 (-85)) (-5 *3 (-583 (-221))) (-5 *1 (-222))))
+ ((*1 *2 *3 *2) (-12 (-5 *2 (-85)) (-5 *3 (-584 (-221))) (-5 *1 (-222))))
  ((*1 *2) (-12 (-5 *2 (-85)) (-5 *1 (-404))))
  ((*1 *2 *2) (-12 (-5 *2 (-85)) (-5 *1 (-404))))) 
 (((*1 *2) (-12 (-5 *2 (-85)) (-5 *1 (-404))))
@@ -11180,440 +11183,440 @@
 (((*1 *2) (-12 (-5 *2 (-85)) (-5 *1 (-404))))
  ((*1 *2 *2) (-12 (-5 *2 (-85)) (-5 *1 (-404))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-830)) (-5 *2 (-1177 (-1177 (-483)))) (-5 *1 (-403))))) 
+  (-12 (-5 *3 (-831)) (-5 *2 (-1178 (-1178 (-484)))) (-5 *1 (-403))))) 
 (((*1 *2 *2 *3)
-  (-12 (-5 *2 (-1177 (-1177 (-483)))) (-5 *3 (-830)) (-5 *1 (-403))))) 
+  (-12 (-5 *2 (-1178 (-1178 (-484)))) (-5 *3 (-831)) (-5 *1 (-403))))) 
 (((*1 *2 *2 *3 *4)
-  (|partial| -12 (-5 *4 (-1 *3)) (-4 *3 (-756)) (-4 *5 (-717)) (-4 *6 (-494))
-   (-4 *7 (-861 *6 *5 *3)) (-5 *1 (-399 *5 *3 *6 *7 *2))
+  (|partial| -12 (-5 *4 (-1 *3)) (-4 *3 (-757)) (-4 *5 (-718)) (-4 *6 (-495))
+   (-4 *7 (-862 *6 *5 *3)) (-5 *1 (-399 *5 *3 *6 *7 *2))
    (-4 *2
-    (-13 (-950 (-347 (-483))) (-311)
-     (-10 -8 (-15 -3940 ($ *7)) (-15 -2994 (*7 $)) (-15 -2993 (*7 $)))))))) 
+    (-13 (-951 (-347 (-484))) (-311)
+     (-10 -8 (-15 -3942 ($ *7)) (-15 -2996 (*7 $)) (-15 -2995 (*7 $)))))))) 
 (((*1 *2 *1)
-  (-12 (-14 *3 (-583 (-1088))) (-4 *4 (-146))
+  (-12 (-14 *3 (-584 (-1089))) (-4 *4 (-146))
    (-14 *6
-    (-1 (-85) (-2 (|:| -2396 *5) (|:| -2397 *2))
-     (-2 (|:| -2396 *5) (|:| -2397 *2))))
-   (-4 *2 (-196 (-3951 *3) (-694))) (-5 *1 (-398 *3 *4 *5 *2 *6 *7))
-   (-4 *5 (-756)) (-4 *7 (-861 *4 *2 (-773 *3)))))) 
+    (-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))
+   (-4 *5 (-757)) (-4 *7 (-862 *4 *2 (-774 *3)))))) 
 (((*1 *2 *1)
-  (-12 (-14 *3 (-583 (-1088))) (-4 *4 (-146)) (-4 *5 (-196 (-3951 *3) (-694)))
+  (-12 (-14 *3 (-584 (-1089))) (-4 *4 (-146)) (-4 *5 (-196 (-3953 *3) (-695)))
    (-14 *6
-    (-1 (-85) (-2 (|:| -2396 *2) (|:| -2397 *5))
-     (-2 (|:| -2396 *2) (|:| -2397 *5))))
-   (-4 *2 (-756)) (-5 *1 (-398 *3 *4 *2 *5 *6 *7))
-   (-4 *7 (-861 *4 *5 (-773 *3)))))) 
+    (-1 (-85) (-2 (|:| -2398 *2) (|:| -2399 *5))
+     (-2 (|:| -2398 *2) (|:| -2399 *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 (-583 (-1088))) (-4 *2 (-146)) (-4 *4 (-196 (-3951 *5) (-694)))
+  (-12 (-14 *5 (-584 (-1089))) (-4 *2 (-146)) (-4 *4 (-196 (-3953 *5) (-695)))
    (-14 *6
-    (-1 (-85) (-2 (|:| -2396 *3) (|:| -2397 *4))
-     (-2 (|:| -2396 *3) (|:| -2397 *4))))
-   (-5 *1 (-398 *5 *2 *3 *4 *6 *7)) (-4 *3 (-756))
-   (-4 *7 (-861 *2 *4 (-773 *5)))))) 
+    (-1 (-85) (-2 (|:| -2398 *3) (|:| -2399 *4))
+     (-2 (|:| -2398 *3) (|:| -2399 *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 (-583 (-1088))) (-4 *2 (-146)) (-4 *3 (-196 (-3951 *4) (-694)))
+  (-12 (-14 *4 (-584 (-1089))) (-4 *2 (-146)) (-4 *3 (-196 (-3953 *4) (-695)))
    (-14 *6
-    (-1 (-85) (-2 (|:| -2396 *5) (|:| -2397 *3))
-     (-2 (|:| -2396 *5) (|:| -2397 *3))))
-   (-5 *1 (-398 *4 *2 *5 *3 *6 *7)) (-4 *5 (-756))
-   (-4 *7 (-861 *2 *3 (-773 *4)))))) 
+    (-1 (-85) (-2 (|:| -2398 *5) (|:| -2399 *3))
+     (-2 (|:| -2398 *5) (|:| -2399 *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)
-  (-12 (-5 *2 (-583 *3)) (-5 *5 (-830)) (-4 *3 (-1153 *4)) (-4 *4 (-257))
+  (-12 (-5 *2 (-584 *3)) (-5 *5 (-831)) (-4 *3 (-1154 *4)) (-4 *4 (-257))
    (-5 *1 (-397 *4 *3))))) 
 (((*1 *2 *3 *4 *5 *6)
-  (-12 (-5 *6 (-830)) (-4 *5 (-257)) (-4 *3 (-1153 *5))
-   (-5 *2 (-2 (|:| |plist| (-583 *3)) (|:| |modulo| *5))) (-5 *1 (-397 *5 *3))
-   (-5 *4 (-583 *3))))) 
+  (-12 (-5 *6 (-831)) (-4 *5 (-257)) (-4 *3 (-1154 *5))
+   (-5 *2 (-2 (|:| |plist| (-584 *3)) (|:| |modulo| *5))) (-5 *1 (-397 *5 *3))
+   (-5 *4 (-584 *3))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *4 (-583 *5)) (-4 *5 (-1153 *3)) (-4 *3 (-257)) (-5 *2 (-85))
+  (-12 (-5 *4 (-584 *5)) (-4 *5 (-1154 *3)) (-4 *3 (-257)) (-5 *2 (-85))
    (-5 *1 (-392 *3 *5))))) 
 (((*1 *2 *3 *4 *5)
-  (|partial| -12 (-5 *5 (-1177 (-583 *3))) (-4 *4 (-257)) (-5 *2 (-583 *3))
-   (-5 *1 (-392 *4 *3)) (-4 *3 (-1153 *4))))) 
+  (|partial| -12 (-5 *5 (-1178 (-584 *3))) (-4 *4 (-257)) (-5 *2 (-584 *3))
+   (-5 *1 (-392 *4 *3)) (-4 *3 (-1154 *4))))) 
 (((*1 *2 *3 *4 *5)
-  (|partial| -12 (-5 *3 (-694)) (-4 *4 (-257)) (-4 *6 (-1153 *4))
-   (-5 *2 (-1177 (-583 *6))) (-5 *1 (-392 *4 *6)) (-5 *5 (-583 *6))))) 
+  (|partial| -12 (-5 *3 (-695)) (-4 *4 (-257)) (-4 *6 (-1154 *4))
+   (-5 *2 (-1178 (-584 *6))) (-5 *1 (-392 *4 *6)) (-5 *5 (-584 *6))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *4 (-583 *3)) (-4 *3 (-1153 *5)) (-4 *5 (-257)) (-5 *2 (-694))
+  (-12 (-5 *4 (-584 *3)) (-4 *3 (-1154 *5)) (-4 *5 (-257)) (-5 *2 (-695))
    (-5 *1 (-392 *5 *3))))) 
 (((*1 *2)
-  (|partial| -12 (-4 *3 (-494)) (-4 *3 (-146))
-   (-5 *2 (-2 (|:| |particular| *1) (|:| -2008 (-583 *1)))) (-4 *1 (-315 *3))))
+  (|partial| -12 (-4 *3 (-495)) (-4 *3 (-146))
+   (-5 *2 (-2 (|:| |particular| *1) (|:| -2010 (-584 *1)))) (-4 *1 (-315 *3))))
  ((*1 *2)
   (|partial| -12
    (-5 *2
     (-2 (|:| |particular| (-390 *3 *4 *5 *6))
-     (|:| -2008 (-583 (-390 *3 *4 *5 *6)))))
-   (-5 *1 (-390 *3 *4 *5 *6)) (-4 *3 (-146)) (-14 *4 (-830))
-   (-14 *5 (-583 (-1088))) (-14 *6 (-1177 (-630 *3)))))) 
+     (|:| -2010 (-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 (-494)) (-4 *3 (-146))
-   (-5 *2 (-2 (|:| |particular| *1) (|:| -2008 (-583 *1)))) (-4 *1 (-315 *3))))
+  (|partial| -12 (-4 *3 (-495)) (-4 *3 (-146))
+   (-5 *2 (-2 (|:| |particular| *1) (|:| -2010 (-584 *1)))) (-4 *1 (-315 *3))))
  ((*1 *2)
   (|partial| -12
    (-5 *2
     (-2 (|:| |particular| (-390 *3 *4 *5 *6))
-     (|:| -2008 (-583 (-390 *3 *4 *5 *6)))))
-   (-5 *1 (-390 *3 *4 *5 *6)) (-4 *3 (-146)) (-14 *4 (-830))
-   (-14 *5 (-583 (-1088))) (-14 *6 (-1177 (-630 *3)))))) 
+     (|:| -2010 (-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)
-  (-12 (-5 *2 (-1177 (-1088))) (-5 *3 (-1177 (-390 *4 *5 *6 *7)))
-   (-5 *1 (-390 *4 *5 *6 *7)) (-4 *4 (-146)) (-14 *5 (-830))
-   (-14 *6 (-583 (-1088))) (-14 *7 (-1177 (-630 *4)))))
+  (-12 (-5 *2 (-1178 (-1089))) (-5 *3 (-1178 (-390 *4 *5 *6 *7)))
+   (-5 *1 (-390 *4 *5 *6 *7)) (-4 *4 (-146)) (-14 *5 (-831))
+   (-14 *6 (-584 (-1089))) (-14 *7 (-1178 (-631 *4)))))
  ((*1 *1 *2 *3)
-  (-12 (-5 *2 (-1088)) (-5 *3 (-1177 (-390 *4 *5 *6 *7)))
-   (-5 *1 (-390 *4 *5 *6 *7)) (-4 *4 (-146)) (-14 *5 (-830)) (-14 *6 (-583 *2))
-   (-14 *7 (-1177 (-630 *4)))))
+  (-12 (-5 *2 (-1089)) (-5 *3 (-1178 (-390 *4 *5 *6 *7)))
+   (-5 *1 (-390 *4 *5 *6 *7)) (-4 *4 (-146)) (-14 *5 (-831)) (-14 *6 (-584 *2))
+   (-14 *7 (-1178 (-631 *4)))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-1177 (-390 *3 *4 *5 *6))) (-5 *1 (-390 *3 *4 *5 *6))
-   (-4 *3 (-146)) (-14 *4 (-830)) (-14 *5 (-583 (-1088)))
-   (-14 *6 (-1177 (-630 *3)))))
+  (-12 (-5 *2 (-1178 (-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)
-  (-12 (-5 *2 (-1177 (-1088))) (-5 *1 (-390 *3 *4 *5 *6)) (-4 *3 (-146))
-   (-14 *4 (-830)) (-14 *5 (-583 (-1088))) (-14 *6 (-1177 (-630 *3)))))
+  (-12 (-5 *2 (-1178 (-1089))) (-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)
-  (-12 (-5 *2 (-1088)) (-5 *1 (-390 *3 *4 *5 *6)) (-4 *3 (-146))
-   (-14 *4 (-830)) (-14 *5 (-583 *2)) (-14 *6 (-1177 (-630 *3)))))
+  (-12 (-5 *2 (-1089)) (-5 *1 (-390 *3 *4 *5 *6)) (-4 *3 (-146))
+   (-14 *4 (-831)) (-14 *5 (-584 *2)) (-14 *6 (-1178 (-631 *3)))))
  ((*1 *1)
-  (-12 (-5 *1 (-390 *2 *3 *4 *5)) (-4 *2 (-146)) (-14 *3 (-830))
-   (-14 *4 (-583 (-1088))) (-14 *5 (-1177 (-630 *2)))))) 
+  (-12 (-5 *1 (-390 *2 *3 *4 *5)) (-4 *2 (-146)) (-14 *3 (-831))
+   (-14 *4 (-584 (-1089))) (-14 *5 (-1178 (-631 *2)))))) 
 (((*1 *2)
-  (-12 (-4 *4 (-146)) (-5 *2 (-1083 (-857 *4))) (-5 *1 (-357 *3 *4))
+  (-12 (-4 *4 (-146)) (-5 *2 (-1084 (-858 *4))) (-5 *1 (-357 *3 *4))
    (-4 *3 (-358 *4))))
  ((*1 *2)
   (-12 (-4 *1 (-358 *3)) (-4 *3 (-146)) (-4 *3 (-311))
-   (-5 *2 (-1083 (-857 *3)))))
+   (-5 *2 (-1084 (-858 *3)))))
  ((*1 *2)
-  (-12 (-5 *2 (-1083 (-347 (-857 *3)))) (-5 *1 (-390 *3 *4 *5 *6))
-   (-4 *3 (-494)) (-4 *3 (-146)) (-14 *4 (-830)) (-14 *5 (-583 (-1088)))
-   (-14 *6 (-1177 (-630 *3)))))) 
+  (-12 (-5 *2 (-1084 (-347 (-858 *3)))) (-5 *1 (-390 *3 *4 *5 *6))
+   (-4 *3 (-495)) (-4 *3 (-146)) (-14 *4 (-831)) (-14 *5 (-584 (-1089)))
+   (-14 *6 (-1178 (-631 *3)))))) 
 (((*1 *2 *1)
-  (-12 (-5 *2 (-1083 (-347 (-857 *3)))) (-5 *1 (-390 *3 *4 *5 *6))
-   (-4 *3 (-494)) (-4 *3 (-146)) (-14 *4 (-830)) (-14 *5 (-583 (-1088)))
-   (-14 *6 (-1177 (-630 *3)))))) 
+  (-12 (-5 *2 (-1084 (-347 (-858 *3)))) (-5 *1 (-390 *3 *4 *5 *6))
+   (-4 *3 (-495)) (-4 *3 (-146)) (-14 *4 (-831)) (-14 *5 (-584 (-1089)))
+   (-14 *6 (-1178 (-631 *3)))))) 
 (((*1 *2 *1)
-  (-12 (-5 *2 (-347 (-857 *3))) (-5 *1 (-390 *3 *4 *5 *6)) (-4 *3 (-494))
-   (-4 *3 (-146)) (-14 *4 (-830)) (-14 *5 (-583 (-1088)))
-   (-14 *6 (-1177 (-630 *3)))))) 
+  (-12 (-5 *2 (-347 (-858 *3))) (-5 *1 (-390 *3 *4 *5 *6)) (-4 *3 (-495))
+   (-4 *3 (-146)) (-14 *4 (-831)) (-14 *5 (-584 (-1089)))
+   (-14 *6 (-1178 (-631 *3)))))) 
 (((*1 *2 *1)
-  (-12 (-5 *2 (-347 (-857 *3))) (-5 *1 (-390 *3 *4 *5 *6)) (-4 *3 (-494))
-   (-4 *3 (-146)) (-14 *4 (-830)) (-14 *5 (-583 (-1088)))
-   (-14 *6 (-1177 (-630 *3)))))) 
+  (-12 (-5 *2 (-347 (-858 *3))) (-5 *1 (-390 *3 *4 *5 *6)) (-4 *3 (-495))
+   (-4 *3 (-146)) (-14 *4 (-831)) (-14 *5 (-584 (-1089)))
+   (-14 *6 (-1178 (-631 *3)))))) 
 (((*1 *2)
-  (-12 (-4 *4 (-146)) (-5 *2 (-1083 (-857 *4))) (-5 *1 (-357 *3 *4))
+  (-12 (-4 *4 (-146)) (-5 *2 (-1084 (-858 *4))) (-5 *1 (-357 *3 *4))
    (-4 *3 (-358 *4))))
  ((*1 *2)
   (-12 (-4 *1 (-358 *3)) (-4 *3 (-146)) (-4 *3 (-311))
-   (-5 *2 (-1083 (-857 *3)))))
+   (-5 *2 (-1084 (-858 *3)))))
  ((*1 *2)
-  (-12 (-5 *2 (-1083 (-347 (-857 *3)))) (-5 *1 (-390 *3 *4 *5 *6))
-   (-4 *3 (-494)) (-4 *3 (-146)) (-14 *4 (-830)) (-14 *5 (-583 (-1088)))
-   (-14 *6 (-1177 (-630 *3)))))) 
+  (-12 (-5 *2 (-1084 (-347 (-858 *3)))) (-5 *1 (-390 *3 *4 *5 *6))
+   (-4 *3 (-495)) (-4 *3 (-146)) (-14 *4 (-831)) (-14 *5 (-584 (-1089)))
+   (-14 *6 (-1178 (-631 *3)))))) 
 (((*1 *2 *1)
-  (-12 (-5 *2 (-1083 (-347 (-857 *3)))) (-5 *1 (-390 *3 *4 *5 *6))
-   (-4 *3 (-494)) (-4 *3 (-146)) (-14 *4 (-830)) (-14 *5 (-583 (-1088)))
-   (-14 *6 (-1177 (-630 *3)))))) 
+  (-12 (-5 *2 (-1084 (-347 (-858 *3)))) (-5 *1 (-390 *3 *4 *5 *6))
+   (-4 *3 (-495)) (-4 *3 (-146)) (-14 *4 (-831)) (-14 *5 (-584 (-1089)))
+   (-14 *6 (-1178 (-631 *3)))))) 
 (((*1 *2 *1)
-  (-12 (-5 *2 (-347 (-857 *3))) (-5 *1 (-390 *3 *4 *5 *6)) (-4 *3 (-494))
-   (-4 *3 (-146)) (-14 *4 (-830)) (-14 *5 (-583 (-1088)))
-   (-14 *6 (-1177 (-630 *3)))))) 
+  (-12 (-5 *2 (-347 (-858 *3))) (-5 *1 (-390 *3 *4 *5 *6)) (-4 *3 (-495))
+   (-4 *3 (-146)) (-14 *4 (-831)) (-14 *5 (-584 (-1089)))
+   (-14 *6 (-1178 (-631 *3)))))) 
 (((*1 *2 *1)
-  (-12 (-5 *2 (-347 (-857 *3))) (-5 *1 (-390 *3 *4 *5 *6)) (-4 *3 (-494))
-   (-4 *3 (-146)) (-14 *4 (-830)) (-14 *5 (-583 (-1088)))
-   (-14 *6 (-1177 (-630 *3)))))) 
+  (-12 (-5 *2 (-347 (-858 *3))) (-5 *1 (-390 *3 *4 *5 *6)) (-4 *3 (-495))
+   (-4 *3 (-146)) (-14 *4 (-831)) (-14 *5 (-584 (-1089)))
+   (-14 *6 (-1178 (-631 *3)))))) 
 (((*1 *2 *1 *1)
-  (-12 (-5 *2 (-347 (-857 *3))) (-5 *1 (-390 *3 *4 *5 *6)) (-4 *3 (-494))
-   (-4 *3 (-146)) (-14 *4 (-830)) (-14 *5 (-583 (-1088)))
-   (-14 *6 (-1177 (-630 *3)))))) 
+  (-12 (-5 *2 (-347 (-858 *3))) (-5 *1 (-390 *3 *4 *5 *6)) (-4 *3 (-495))
+   (-4 *3 (-146)) (-14 *4 (-831)) (-14 *5 (-584 (-1089)))
+   (-14 *6 (-1178 (-631 *3)))))) 
 (((*1 *2)
-  (-12 (-5 *2 (-347 (-857 *3))) (-5 *1 (-390 *3 *4 *5 *6)) (-4 *3 (-494))
-   (-4 *3 (-146)) (-14 *4 (-830)) (-14 *5 (-583 (-1088)))
-   (-14 *6 (-1177 (-630 *3)))))) 
+  (-12 (-5 *2 (-347 (-858 *3))) (-5 *1 (-390 *3 *4 *5 *6)) (-4 *3 (-495))
+   (-4 *3 (-146)) (-14 *4 (-831)) (-14 *5 (-584 (-1089)))
+   (-14 *6 (-1178 (-631 *3)))))) 
 (((*1 *2 *1 *1)
-  (-12 (-5 *2 (-347 (-857 *3))) (-5 *1 (-390 *3 *4 *5 *6)) (-4 *3 (-494))
-   (-4 *3 (-146)) (-14 *4 (-830)) (-14 *5 (-583 (-1088)))
-   (-14 *6 (-1177 (-630 *3)))))) 
+  (-12 (-5 *2 (-347 (-858 *3))) (-5 *1 (-390 *3 *4 *5 *6)) (-4 *3 (-495))
+   (-4 *3 (-146)) (-14 *4 (-831)) (-14 *5 (-584 (-1089)))
+   (-14 *6 (-1178 (-631 *3)))))) 
 (((*1 *2)
-  (-12 (-5 *2 (-347 (-857 *3))) (-5 *1 (-390 *3 *4 *5 *6)) (-4 *3 (-494))
-   (-4 *3 (-146)) (-14 *4 (-830)) (-14 *5 (-583 (-1088)))
-   (-14 *6 (-1177 (-630 *3)))))) 
+  (-12 (-5 *2 (-347 (-858 *3))) (-5 *1 (-390 *3 *4 *5 *6)) (-4 *3 (-495))
+   (-4 *3 (-146)) (-14 *4 (-831)) (-14 *5 (-584 (-1089)))
+   (-14 *6 (-1178 (-631 *3)))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-1177 *1)) (-4 *1 (-315 *4)) (-4 *4 (-146))
-   (-5 *2 (-583 (-857 *4)))))
+  (-12 (-5 *3 (-1178 *1)) (-4 *1 (-315 *4)) (-4 *4 (-146))
+   (-5 *2 (-584 (-858 *4)))))
  ((*1 *2)
-  (-12 (-4 *4 (-146)) (-5 *2 (-583 (-857 *4))) (-5 *1 (-357 *3 *4))
+  (-12 (-4 *4 (-146)) (-5 *2 (-584 (-858 *4))) (-5 *1 (-357 *3 *4))
    (-4 *3 (-358 *4))))
- ((*1 *2) (-12 (-4 *1 (-358 *3)) (-4 *3 (-146)) (-5 *2 (-583 (-857 *3)))))
+ ((*1 *2) (-12 (-4 *1 (-358 *3)) (-4 *3 (-146)) (-5 *2 (-584 (-858 *3)))))
  ((*1 *2)
-  (-12 (-5 *2 (-583 (-857 *3))) (-5 *1 (-390 *3 *4 *5 *6)) (-4 *3 (-494))
-   (-4 *3 (-146)) (-14 *4 (-830)) (-14 *5 (-583 (-1088)))
-   (-14 *6 (-1177 (-630 *3)))))
- ((*1 *2 *3)
-  (-12 (-5 *3 (-1177 (-390 *4 *5 *6 *7))) (-5 *2 (-583 (-857 *4)))
-   (-5 *1 (-390 *4 *5 *6 *7)) (-4 *4 (-494)) (-4 *4 (-146)) (-14 *5 (-830))
-   (-14 *6 (-583 (-1088))) (-14 *7 (-1177 (-630 *4)))))) 
-(((*1 *1 *2) (-12 (-5 *2 (-583 *1)) (-4 *1 (-389))))
+  (-12 (-5 *2 (-584 (-858 *3))) (-5 *1 (-390 *3 *4 *5 *6)) (-4 *3 (-495))
+   (-4 *3 (-146)) (-14 *4 (-831)) (-14 *5 (-584 (-1089)))
+   (-14 *6 (-1178 (-631 *3)))))
+ ((*1 *2 *3)
+  (-12 (-5 *3 (-1178 (-390 *4 *5 *6 *7))) (-5 *2 (-584 (-858 *4)))
+   (-5 *1 (-390 *4 *5 *6 *7)) (-4 *4 (-495)) (-4 *4 (-146)) (-14 *5 (-831))
+   (-14 *6 (-584 (-1089))) (-14 *7 (-1178 (-631 *4)))))) 
+(((*1 *1 *2) (-12 (-5 *2 (-584 *1)) (-4 *1 (-389))))
  ((*1 *1 *1 *1) (-4 *1 (-389)))) 
 (((*1 *2 *3)
-  (-12 (-4 *4 (-389)) (-4 *5 (-717)) (-4 *6 (-756)) (-5 *2 (-694))
-   (-5 *1 (-387 *4 *5 *6 *3)) (-4 *3 (-861 *4 *5 *6))))) 
+  (-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| (-694)) (|:| -2000 *4))) (-5 *5 (-694))
-   (-4 *4 (-861 *6 *7 *8)) (-4 *6 (-389)) (-4 *7 (-717)) (-4 *8 (-756))
+  (-12 (-5 *3 (-2 (|:| |totdeg| (-695)) (|:| -2002 *4))) (-5 *5 (-695))
+   (-4 *4 (-862 *6 *7 *8)) (-4 *6 (-389)) (-4 *7 (-718)) (-4 *8 (-757))
    (-5 *2
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   (-12
    (-5 *3
-    (-2 (|:| |lcmfij| *5) (|:| |totdeg| (-694)) (|:| |poli| *7)
+    (-2 (|:| |lcmfij| *5) (|:| |totdeg| (-695)) (|:| |poli| *7)
      (|:| |polj| *7)))
-   (-4 *5 (-717)) (-4 *7 (-861 *4 *5 *6)) (-4 *4 (-389)) (-4 *6 (-756))
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 (((*1 *2 *3)
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-   (-5 *2 (-1183)) (-5 *1 (-387 *4 *5 *6 *7)) (-4 *7 (-861 *4 *5 *6))))) 
+  (-12 (-5 *3 (-484)) (-4 *4 (-389)) (-4 *5 (-718)) (-4 *6 (-757))
+   (-5 *2 (-1184)) (-5 *1 (-387 *4 *5 *6 *7)) (-4 *7 (-862 *4 *5 *6))))) 
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+   (-4 *6 (-757)) (-5 *2 (-1184)) (-5 *1 (-387 *4 *5 *6 *7))))) 
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+  (-12 (-5 *2 (-484))
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+    (-2 (|:| |lcmfij| *6) (|:| |totdeg| (-695)) (|:| |poli| *4)
      (|:| |polj| *4)))
-   (-4 *6 (-717)) (-4 *4 (-861 *5 *6 *7)) (-4 *5 (-389)) (-4 *7 (-756))
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    (-5 *1 (-387 *5 *6 *7 *4))))) 
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-  (-12 (-5 *2 (-483))
+  (-12 (-5 *2 (-484))
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+    (-2 (|:| |lcmfij| *6) (|:| |totdeg| (-695)) (|:| |poli| *4)
      (|:| |polj| *4)))
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    (-5 *1 (-387 *5 *6 *7 *4))))) 
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-   (-5 *1 (-387 *4 *5 *6 *3)) (-4 *3 (-861 *4 *5 *6))))) 
+  (-12 (-4 *4 (-389)) (-4 *5 (-718)) (-4 *6 (-757)) (-5 *2 (-1184))
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-   (-5 *1 (-387 *4 *5 *6 *3)) (-4 *3 (-861 *4 *5 *6))))) 
+  (-12 (-4 *4 (-389)) (-4 *5 (-718)) (-4 *6 (-757)) (-5 *2 (-484))
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-   (-4 *5 (-756)) (-5 *1 (-387 *3 *4 *5 *6))))) 
+  (-12 (-5 *2 (-584 *6)) (-4 *6 (-862 *3 *4 *5)) (-4 *3 (-389)) (-4 *4 (-718))
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   (-12
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-    (-583
-     (-2 (|:| |lcmfij| *4) (|:| |totdeg| (-694)) (|:| |poli| *6)
+    (-584
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       (|:| |polj| *6))))
-   (-4 *4 (-717)) (-4 *6 (-861 *3 *4 *5)) (-4 *3 (-389)) (-4 *5 (-756))
+   (-4 *4 (-718)) (-4 *6 (-862 *3 *4 *5)) (-4 *3 (-389)) (-4 *5 (-757))
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 (((*1 *2 *3)
   (-12
    (-5 *3
-    (-2 (|:| |lcmfij| *5) (|:| |totdeg| (-694)) (|:| |poli| *2)
+    (-2 (|:| |lcmfij| *5) (|:| |totdeg| (-695)) (|:| |poli| *2)
      (|:| |polj| *2)))
-   (-4 *5 (-717)) (-4 *2 (-861 *4 *5 *6)) (-5 *1 (-387 *4 *5 *6 *2))
-   (-4 *4 (-389)) (-4 *6 (-756))))) 
+   (-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)
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+  (-12 (-5 *2 (-584 (-2 (|:| |totdeg| (-695)) (|:| -2002 *3)))) (-5 *4 (-695))
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    (-5 *1 (-387 *5 *6 *7 *3))))) 
 (((*1 *2 *2)
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-   (-4 *2 (-861 *3 *4 *5))))) 
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+   (-4 *2 (-862 *3 *4 *5))))) 
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-   (-4 *7 (-756)) (-5 *2 (-2 (|:| |poly| *3) (|:| |mult| *5)))
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+   (-4 *7 (-757)) (-5 *2 (-2 (|:| |poly| *3) (|:| |mult| *5)))
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 (((*1 *2 *3 *2)
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-    (-583
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+    (-584
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       (|:| |polj| *6))))
-   (-4 *3 (-717)) (-4 *6 (-861 *4 *3 *5)) (-4 *4 (-389)) (-4 *5 (-756))
+   (-4 *3 (-718)) (-4 *6 (-862 *4 *3 *5)) (-4 *4 (-389)) (-4 *5 (-757))
    (-5 *1 (-387 *4 *3 *5 *6))))) 
 (((*1 *2 *2)
   (-12
    (-5 *2
-    (-583
-     (-2 (|:| |lcmfij| *4) (|:| |totdeg| (-694)) (|:| |poli| *6)
+    (-584
+     (-2 (|:| |lcmfij| *4) (|:| |totdeg| (-695)) (|:| |poli| *6)
       (|:| |polj| *6))))
-   (-4 *4 (-717)) (-4 *6 (-861 *3 *4 *5)) (-4 *3 (-389)) (-4 *5 (-756))
+   (-4 *4 (-718)) (-4 *6 (-862 *3 *4 *5)) (-4 *3 (-389)) (-4 *5 (-757))
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 (((*1 *2 *3 *2)
   (-12
    (-5 *2
-    (-583
-     (-2 (|:| |lcmfij| *5) (|:| |totdeg| (-694)) (|:| |poli| *3)
+    (-584
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       (|:| |polj| *3))))
-   (-4 *5 (-717)) (-4 *3 (-861 *4 *5 *6)) (-4 *4 (-389)) (-4 *6 (-756))
+   (-4 *5 (-718)) (-4 *3 (-862 *4 *5 *6)) (-4 *4 (-389)) (-4 *6 (-757))
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 (((*1 *2 *3 *3 *3 *3)
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-   (-5 *1 (-387 *4 *3 *5 *6)) (-4 *6 (-861 *4 *3 *5))))) 
+  (-12 (-4 *4 (-389)) (-4 *3 (-718)) (-4 *5 (-757)) (-5 *2 (-85))
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 (((*1 *2 *3 *3)
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-   (-5 *1 (-387 *4 *3 *5 *6)) (-4 *6 (-861 *4 *3 *5))))) 
+  (-12 (-4 *4 (-389)) (-4 *3 (-718)) (-4 *5 (-757)) (-5 *2 (-85))
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 (((*1 *2 *3)
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    (-5 *3
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+    (-2 (|:| |lcmfij| *5) (|:| |totdeg| (-695)) (|:| |poli| *7)
      (|:| |polj| *7)))
-   (-4 *5 (-717)) (-4 *7 (-861 *4 *5 *6)) (-4 *4 (-389)) (-4 *6 (-756))
+   (-4 *5 (-718)) (-4 *7 (-862 *4 *5 *6)) (-4 *4 (-389)) (-4 *6 (-757))
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 (((*1 *2 *2 *3 *3)
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-   (-4 *5 (-717)) (-4 *6 (-756)) (-5 *1 (-387 *4 *5 *6 *7))))) 
+  (-12 (-5 *2 (-584 *7)) (-5 *3 (-484)) (-4 *7 (-862 *4 *5 *6)) (-4 *4 (-389))
+   (-4 *5 (-718)) (-4 *6 (-757)) (-5 *1 (-387 *4 *5 *6 *7))))) 
 (((*1 *2 *2 *3)
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-   (-4 *6 (-756)) (-5 *1 (-387 *4 *5 *6 *2))))) 
+  (-12 (-5 *3 (-584 *2)) (-4 *2 (-862 *4 *5 *6)) (-4 *4 (-389)) (-4 *5 (-718))
+   (-4 *6 (-757)) (-5 *1 (-387 *4 *5 *6 *2))))) 
 (((*1 *2 *2 *3)
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-   (-4 *6 (-756)) (-5 *1 (-387 *4 *5 *6 *2))))) 
+  (-12 (-5 *3 (-584 *2)) (-4 *2 (-862 *4 *5 *6)) (-4 *4 (-389)) (-4 *5 (-718))
+   (-4 *6 (-757)) (-5 *1 (-387 *4 *5 *6 *2))))) 
 (((*1 *2 *3 *3)
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-   (-5 *3 (-583 *7))))
+  (-12 (-4 *4 (-13 (-257) (-120))) (-4 *5 (-718)) (-4 *6 (-757))
+   (-4 *7 (-862 *4 *5 *6)) (-5 *2 (-584 (-584 *7))) (-5 *1 (-386 *4 *5 *6 *7))
+   (-5 *3 (-584 *7))))
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-   (-5 *3 (-583 *8))))
+  (-12 (-5 *4 (-85)) (-4 *5 (-13 (-257) (-120))) (-4 *6 (-718)) (-4 *7 (-757))
+   (-4 *8 (-862 *5 *6 *7)) (-5 *2 (-584 (-584 *8))) (-5 *1 (-386 *5 *6 *7 *8))
+   (-5 *3 (-584 *8))))
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-   (-5 *3 (-583 *7))))
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+   (-5 *3 (-584 *7))))
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-   (-5 *3 (-583 *8))))) 
+  (-12 (-5 *4 (-85)) (-4 *5 (-13 (-257) (-120))) (-4 *6 (-718)) (-4 *7 (-757))
+   (-4 *8 (-862 *5 *6 *7)) (-5 *2 (-584 (-584 *8))) (-5 *1 (-386 *5 *6 *7 *8))
+   (-5 *3 (-584 *8))))) 
 (((*1 *2 *3)
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-   (-5 *3 (-583 *7))))
+  (-12 (-4 *4 (-13 (-257) (-120))) (-4 *5 (-718)) (-4 *6 (-757))
+   (-4 *7 (-862 *4 *5 *6)) (-5 *2 (-584 (-584 *7))) (-5 *1 (-386 *4 *5 *6 *7))
+   (-5 *3 (-584 *7))))
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-   (-5 *3 (-583 *8))))) 
+  (-12 (-5 *4 (-85)) (-4 *5 (-13 (-257) (-120))) (-4 *6 (-718)) (-4 *7 (-757))
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-   (-4 *5 (-756)) (-5 *1 (-385 *3 *4 *5 *6))))
+  (-12 (-5 *2 (-584 *6)) (-4 *6 (-862 *3 *4 *5)) (-4 *3 (-257)) (-4 *4 (-718))
+   (-4 *5 (-757)) (-5 *1 (-385 *3 *4 *5 *6))))
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+  (-12 (-5 *2 (-584 *7)) (-5 *3 (-1072)) (-4 *7 (-862 *4 *5 *6)) (-4 *4 (-257))
+   (-4 *5 (-718)) (-4 *6 (-757)) (-5 *1 (-385 *4 *5 *6 *7))))
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-   (-4 *5 (-717)) (-4 *6 (-756)) (-5 *1 (-385 *4 *5 *6 *7))))) 
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+   (-4 *5 (-718)) (-4 *6 (-757)) (-5 *1 (-385 *4 *5 *6 *7))))) 
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+   (-4 *6 (-757)) (-5 *1 (-385 *4 *5 *6 *2))))) 
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+  (-12 (-5 *2 (-695)) (-5 *1 (-382 *3)) (-4 *3 (-344)) (-4 *3 (-962))))
+ ((*1 *2) (-12 (-5 *2 (-695)) (-5 *1 (-382 *3)) (-4 *3 (-344)) (-4 *3 (-962))))) 
 (((*1 *2 *3)
-  (-12 (-5 *2 (-483)) (-5 *1 (-382 *3)) (-4 *3 (-344)) (-4 *3 (-961))))) 
+  (-12 (-5 *2 (-484)) (-5 *1 (-382 *3)) (-4 *3 (-344)) (-4 *3 (-962))))) 
 (((*1 *2 *3)
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-(((*1 *2 *2) (-12 (-5 *2 (-694)) (-5 *1 (-382 *3)) (-4 *3 (-961))))
- ((*1 *2) (-12 (-5 *2 (-694)) (-5 *1 (-382 *3)) (-4 *3 (-961))))) 
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+ ((*1 *2) (-12 (-5 *2 (-695)) (-5 *1 (-382 *3)) (-4 *3 (-962))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *3 (-694)) (-5 *4 (-483)) (-5 *1 (-382 *2)) (-4 *2 (-961))))) 
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-   (-5 *2 (-583 *6)) (-5 *1 (-381 *5 *6))))) 
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+   (-5 *2 (-584 *6)) (-5 *1 (-381 *5 *6))))) 
 (((*1 *2 *3 *2)
-  (|partial| -12 (-5 *3 (-830)) (-5 *1 (-379 *2)) (-4 *2 (-1153 (-483)))))
+  (|partial| -12 (-5 *3 (-831)) (-5 *1 (-379 *2)) (-4 *2 (-1154 (-484)))))
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-  (|partial| -12 (-5 *3 (-830)) (-5 *4 (-694)) (-5 *1 (-379 *2))
-   (-4 *2 (-1153 (-483)))))
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+   (-4 *2 (-1154 (-484)))))
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-  (|partial| -12 (-5 *3 (-830)) (-5 *4 (-583 (-694))) (-5 *1 (-379 *2))
-   (-4 *2 (-1153 (-483)))))
+  (|partial| -12 (-5 *3 (-831)) (-5 *4 (-584 (-695))) (-5 *1 (-379 *2))
+   (-4 *2 (-1154 (-484)))))
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-  (|partial| -12 (-5 *3 (-830)) (-5 *4 (-583 (-694))) (-5 *5 (-694))
-   (-5 *1 (-379 *2)) (-4 *2 (-1153 (-483)))))
+  (|partial| -12 (-5 *3 (-831)) (-5 *4 (-584 (-695))) (-5 *5 (-695))
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+  (|partial| -12 (-5 *3 (-831)) (-5 *4 (-584 (-695))) (-5 *5 (-695))
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-   (-4 *5 (-961))))) 
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+   (-4 *5 (-962))))) 
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-(((*1 *2 *2 *3) (-12 (-4 *3 (-961)) (-5 *1 (-381 *3 *2)) (-4 *2 (-1153 *3))))) 
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 (((*1 *2 *3)
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-  (-12 (-4 *4 (-961)) (-5 *2 (-483)) (-5 *1 (-380 *4 *3 *5)) (-4 *3 (-1153 *4))
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 (((*1 *2 *3)
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 (((*1 *2 *3)
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 (((*1 *2 *3)
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 (((*1 *2 *3 *4 *5 *6)
-  (-12 (-5 *4 (-85)) (-5 *5 (-1008 (-694))) (-5 *6 (-694))
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+ ((*1 *2 *3)
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+(((*1 *2) (-12 (-5 *2 (-831)) (-5 *1 (-379 *3)) (-4 *3 (-1154 (-484)))))
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 (((*1 *1 *2 *3)
   (-12
    (-5 *3
-    (-583
+    (-584
      (-2 (|:| |flg| (-3 "nil" "sqfr" "irred" "prime")) (|:| |fctr| *2)
-      (|:| |xpnt| (-483)))))
-   (-4 *2 (-494)) (-5 *1 (-345 *2))))
+      (|:| |xpnt| (-484)))))
+   (-4 *2 (-495)) (-5 *1 (-345 *2))))
  ((*1 *2 *3)
   (-12
    (-5 *3
-    (-2 (|:| |contp| (-483))
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 (((*1 *2 *1)
-  (-12 (-5 *2 (-3 (|:| |fst| (-374)) (|:| -3904 "void"))) (-5 *1 (-376))))) 
-(((*1 *2 *1) (-12 (-5 *2 (-583 (-857 (-483)))) (-5 *1 (-376))))) 
+  (-12 (-5 *2 (-3 (|:| |fst| (-374)) (|:| -3906 "void"))) (-5 *1 (-376))))) 
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 (((*1 *2 *1) (-12 (-5 *2 (-85)) (-5 *1 (-376))))) 
 (((*1 *1) (-5 *1 (-376)))) 
 (((*1 *1) (-5 *1 (-376)))) 
@@ -11623,319 +11626,319 @@
 (((*1 *1) (-5 *1 (-376)))) 
 (((*1 *1) (-5 *1 (-376)))) 
 (((*1 *2 *3)
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-   (-4 *3 (-1153 *5))))) 
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 (((*1 *2 *3)
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+  (-12 (-4 *4 (-13 (-495) (-951 (-484)))) (-4 *5 (-361 *4))
    (-5 *2
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-     (|:| -2635 (-85))))
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 (((*1 *2 *3)
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 (((*1 *2 *3)
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 (((*1 *2 *1) (-12 (-5 *2 (-85)) (-5 *1 (-374))))) 
 (((*1 *2 *1) (-12 (-5 *2 (-85)) (-5 *1 (-374))))) 
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 (((*1 *2 *1) (-12 (-5 *2 (-85)) (-5 *1 (-374))))) 
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 (((*1 *2 *3)
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 (((*1 *2 *3 *4 *5)
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+     (|:| |%problem| (-2 (|:| |func| (-1072)) (|:| |prob| (-1072))))))
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 (((*1 *2 *3 *4)
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 (((*1 *2 *1)
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-  (-12 (-5 *3 (-1 (-85) *4 *4)) (-4 *1 (-321 *4)) (-4 *4 (-1127))
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 (((*1 *1 *1 *1 *2)
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 (((*1 *1 *1)
-  (-12 (|has| *1 (-6 -3990)) (-4 *1 (-321 *2)) (-4 *2 (-1127)) (-4 *2 (-756))))
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+  (-12 (-5 *2 (-1 (-85) *3 *3)) (|has| *1 (-6 -3992)) (-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))))) 
 (((*1 *2 *1) (-12 (-4 *1 (-315 *2)) (-4 *2 (-146))))) 
 (((*1 *2 *1) (-12 (-4 *1 (-315 *2)) (-4 *2 (-146))))) 
 (((*1 *2 *1) (-12 (-4 *1 (-315 *2)) (-4 *2 (-146))))) 
-(((*1 *2 *1) (-12 (-4 *1 (-315 *3)) (-4 *3 (-146)) (-5 *2 (-1083 *3))))) 
-(((*1 *2 *1) (-12 (-4 *1 (-315 *3)) (-4 *3 (-146)) (-5 *2 (-1083 *3))))) 
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 (((*1 *2)
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  ((*1 *2) (-12 (-4 *1 (-315 *3)) (-4 *3 (-146)) (-5 *2 (-85))))) 
@@ -11980,1176 +11983,1176 @@
   (-12 (-4 *4 (-146)) (-5 *2 (-85)) (-5 *1 (-314 *3 *4)) (-4 *3 (-315 *4))))
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 (((*1 *2)
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+  (-12 (-4 *4 (-146)) (-5 *2 (-584 (-1178 *4))) (-5 *1 (-314 *3 *4))
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-  (-12 (-4 *1 (-315 *3)) (-4 *3 (-146)) (-4 *3 (-494))
-   (-5 *2 (-583 (-1177 *3)))))) 
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-  (-12 (-4 *1 (-315 *3)) (-4 *3 (-146)) (-4 *3 (-494)) (-5 *2 (-1083 *3))))) 
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 (((*1 *2 *1)
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 (((*1 *1 *1) (-4 *1 (-147)))
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 (((*1 *2 *3)
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 (((*1 *2 *2)
-  (|partial| -12 (-5 *2 (-1083 *3)) (-4 *3 (-298)) (-5 *1 (-304 *3))))) 
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 (((*1 *2 *2)
-  (|partial| -12 (-5 *2 (-1083 *3)) (-4 *3 (-298)) (-5 *1 (-304 *3))))) 
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 (((*1 *2 *2)
-  (|partial| -12 (-5 *2 (-1083 *3)) (-4 *3 (-298)) (-5 *1 (-304 *3))))) 
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 (((*1 *2 *2)
-  (|partial| -12 (-5 *2 (-1083 *3)) (-4 *3 (-298)) (-5 *1 (-304 *3))))) 
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-  (|partial| -12 (-5 *2 (-1083 *3)) (-4 *3 (-298)) (-5 *1 (-304 *3))))) 
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 (((*1 *2 *3)
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 (((*1 *2 *3)
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 (((*1 *2 *3)
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 (((*1 *2 *3)
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   (|partial| -12 (-4 *1 (-279 *3)) (-4 *3 (-311)) (-4 *3 (-317))
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-  (-12 (-5 *3 (-264 (-483))) (-5 *4 (-1 (-179) (-179))) (-5 *5 (-1000 (-179)))
-   (-5 *6 (-483)) (-5 *2 (-1123 (-838))) (-5 *1 (-268))))
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  ((*1 *2 *3 *3 *3 *4 *5 *6 *7)
-  (-12 (-5 *3 (-264 (-483))) (-5 *4 (-1 (-179) (-179))) (-5 *5 (-1000 (-179)))
-   (-5 *6 (-179)) (-5 *7 (-483)) (-5 *2 (-1123 (-838))) (-5 *1 (-268))))
+  (-12 (-5 *3 (-264 (-484))) (-5 *4 (-1 (-179) (-179))) (-5 *5 (-1001 (-179)))
+   (-5 *6 (-179)) (-5 *7 (-484)) (-5 *2 (-1124 (-839))) (-5 *1 (-268))))
  ((*1 *2 *3 *3 *3 *4 *5 *6 *7 *8)
-  (-12 (-5 *3 (-264 (-483))) (-5 *4 (-1 (-179) (-179))) (-5 *5 (-1000 (-179)))
-   (-5 *6 (-179)) (-5 *7 (-483)) (-5 *8 (-1071)) (-5 *2 (-1123 (-838)))
+  (-12 (-5 *3 (-264 (-484))) (-5 *4 (-1 (-179) (-179))) (-5 *5 (-1001 (-179)))
+   (-5 *6 (-179)) (-5 *7 (-484)) (-5 *8 (-1072)) (-5 *2 (-1124 (-839)))
    (-5 *1 (-268))))) 
 (((*1 *2 *3) (-12 (-5 *2 (-1 (-179) (-179))) (-5 *1 (-268)) (-5 *3 (-179))))) 
 (((*1 *2 *3 *4 *3 *3)
   (-12 (-5 *3 (-248 *6)) (-5 *4 (-86)) (-4 *6 (-361 *5))
-   (-4 *5 (-13 (-494) (-553 (-472)))) (-5 *2 (-51)) (-5 *1 (-267 *5 *6))))
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  ((*1 *2 *3 *4 *3 *5)
-  (-12 (-5 *3 (-248 *7)) (-5 *4 (-86)) (-5 *5 (-583 *7)) (-4 *7 (-361 *6))
-   (-4 *6 (-13 (-494) (-553 (-472)))) (-5 *2 (-51)) (-5 *1 (-267 *6 *7))))
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+   (-4 *6 (-13 (-495) (-554 (-473)))) (-5 *2 (-51)) (-5 *1 (-267 *6 *7))))
  ((*1 *2 *3 *4 *5 *3)
-  (-12 (-5 *3 (-583 (-248 *7))) (-5 *4 (-583 (-86))) (-5 *5 (-248 *7))
-   (-4 *7 (-361 *6)) (-4 *6 (-13 (-494) (-553 (-472)))) (-5 *2 (-51))
+  (-12 (-5 *3 (-584 (-248 *7))) (-5 *4 (-584 (-86))) (-5 *5 (-248 *7))
+   (-4 *7 (-361 *6)) (-4 *6 (-13 (-495) (-554 (-473)))) (-5 *2 (-51))
    (-5 *1 (-267 *6 *7))))
  ((*1 *2 *3 *4 *5 *6)
-  (-12 (-5 *3 (-583 (-248 *8))) (-5 *4 (-583 (-86))) (-5 *5 (-248 *8))
-   (-5 *6 (-583 *8)) (-4 *8 (-361 *7)) (-4 *7 (-13 (-494) (-553 (-472))))
+  (-12 (-5 *3 (-584 (-248 *8))) (-5 *4 (-584 (-86))) (-5 *5 (-248 *8))
+   (-5 *6 (-584 *8)) (-4 *8 (-361 *7)) (-4 *7 (-13 (-495) (-554 (-473))))
    (-5 *2 (-51)) (-5 *1 (-267 *7 *8))))
  ((*1 *2 *3 *4 *5 *3)
-  (-12 (-5 *3 (-583 *7)) (-5 *4 (-583 (-86))) (-5 *5 (-248 *7))
-   (-4 *7 (-361 *6)) (-4 *6 (-13 (-494) (-553 (-472)))) (-5 *2 (-51))
+  (-12 (-5 *3 (-584 *7)) (-5 *4 (-584 (-86))) (-5 *5 (-248 *7))
+   (-4 *7 (-361 *6)) (-4 *6 (-13 (-495) (-554 (-473)))) (-5 *2 (-51))
    (-5 *1 (-267 *6 *7))))
  ((*1 *2 *3 *4 *5 *6)
-  (-12 (-5 *3 (-583 *8)) (-5 *4 (-583 (-86))) (-5 *6 (-583 (-248 *8)))
-   (-4 *8 (-361 *7)) (-5 *5 (-248 *8)) (-4 *7 (-13 (-494) (-553 (-472))))
+  (-12 (-5 *3 (-584 *8)) (-5 *4 (-584 (-86))) (-5 *6 (-584 (-248 *8)))
+   (-4 *8 (-361 *7)) (-5 *5 (-248 *8)) (-4 *7 (-13 (-495) (-554 (-473))))
    (-5 *2 (-51)) (-5 *1 (-267 *7 *8))))
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   (-12 (-5 *3 (-248 *5)) (-5 *4 (-86)) (-4 *5 (-361 *6))
-   (-4 *6 (-13 (-494) (-553 (-472)))) (-5 *2 (-51)) (-5 *1 (-267 *6 *5))))
+   (-4 *6 (-13 (-495) (-554 (-473)))) (-5 *2 (-51)) (-5 *1 (-267 *6 *5))))
  ((*1 *2 *3 *4 *5 *3)
   (-12 (-5 *4 (-86)) (-5 *5 (-248 *3)) (-4 *3 (-361 *6))
-   (-4 *6 (-13 (-494) (-553 (-472)))) (-5 *2 (-51)) (-5 *1 (-267 *6 *3))))
+   (-4 *6 (-13 (-495) (-554 (-473)))) (-5 *2 (-51)) (-5 *1 (-267 *6 *3))))
  ((*1 *2 *3 *4 *5 *5)
   (-12 (-5 *4 (-86)) (-5 *5 (-248 *3)) (-4 *3 (-361 *6))
-   (-4 *6 (-13 (-494) (-553 (-472)))) (-5 *2 (-51)) (-5 *1 (-267 *6 *3))))
+   (-4 *6 (-13 (-495) (-554 (-473)))) (-5 *2 (-51)) (-5 *1 (-267 *6 *3))))
  ((*1 *2 *3 *4 *5 *6)
-  (-12 (-5 *4 (-86)) (-5 *5 (-248 *3)) (-5 *6 (-583 *3)) (-4 *3 (-361 *7))
-   (-4 *7 (-13 (-494) (-553 (-472)))) (-5 *2 (-51)) (-5 *1 (-267 *7 *3))))) 
+  (-12 (-5 *4 (-86)) (-5 *5 (-248 *3)) (-5 *6 (-584 *3)) (-4 *3 (-361 *7))
+   (-4 *7 (-13 (-495) (-554 (-473)))) (-5 *2 (-51)) (-5 *1 (-267 *7 *3))))) 
 (((*1 *2 *1)
-  (-12 (-5 *2 (-85)) (-5 *1 (-264 *3)) (-4 *3 (-494)) (-4 *3 (-1012))))) 
+  (-12 (-5 *2 (-85)) (-5 *1 (-264 *3)) (-4 *3 (-495)) (-4 *3 (-1013))))) 
 (((*1 *1 *1 *2)
-  (-12 (-5 *2 (-483)) (-5 *1 (-264 *3)) (-4 *3 (-494)) (-4 *3 (-1012))))) 
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 (((*1 *2 *1 *1) (-12 (-4 *1 (-257)) (-5 *2 (-85))))) 
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 (((*1 *2 *1 *1 *1)
   (|partial| -12 (-5 *2 (-2 (|:| |coef1| *1) (|:| |coef2| *1)))
    (-4 *1 (-257))))
  ((*1 *2 *1 *1)
-  (-12 (-5 *2 (-2 (|:| |coef1| *1) (|:| |coef2| *1) (|:| -2405 *1)))
+  (-12 (-5 *2 (-2 (|:| |coef1| *1) (|:| |coef2| *1) (|:| -2407 *1)))
    (-4 *1 (-257))))) 
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  ((*1 *1 *1 *2 *3)
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+ ((*1 *1 *1 *2) (-12 (-5 *2 (-584 (-248 *1))) (-4 *1 (-253))))
  ((*1 *1 *1 *2) (-12 (-5 *2 (-248 *1)) (-4 *1 (-253))))) 
 (((*1 *1 *1 *1) (-4 *1 (-253))) ((*1 *1 *1) (-4 *1 (-253)))) 
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-(((*1 *2 *1 *3) (-12 (-4 *1 (-253)) (-5 *3 (-1088)) (-5 *2 (-85))))
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 (((*1 *2 *3)
-  (-12 (-5 *3 (-550 *5)) (-4 *5 (-361 *4)) (-4 *4 (-950 (-483))) (-4 *4 (-494))
-   (-5 *2 (-1083 *5)) (-5 *1 (-32 *4 *5))))
+  (-12 (-5 *3 (-551 *5)) (-4 *5 (-361 *4)) (-4 *4 (-951 (-484))) (-4 *4 (-495))
+   (-5 *2 (-1084 *5)) (-5 *1 (-32 *4 *5))))
  ((*1 *2 *3)
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- ((*1 *2 *3 *3) (-12 (-5 *3 (-1071)) (-5 *2 (-261)) (-5 *1 (-251))))
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+ ((*1 *2 *3) (-12 (-5 *3 (-584 (-1072))) (-5 *2 (-261)) (-5 *1 (-251))))
+ ((*1 *2 *3 *3) (-12 (-5 *3 (-1072)) (-5 *2 (-261)) (-5 *1 (-251))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *4 (-583 (-1071))) (-5 *3 (-1071)) (-5 *2 (-261)) (-5 *1 (-251))))) 
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 (((*1 *2 *2)
-  (-12 (-4 *3 (-961)) (-4 *4 (-1153 *3)) (-5 *1 (-137 *3 *4 *2))
-   (-4 *2 (-1153 *4))))
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-(((*1 *1 *1) (|partial| -12 (-5 *1 (-248 *2)) (-4 *2 (-663)) (-4 *2 (-1127))))) 
+  (-12 (-4 *3 (-962)) (-4 *4 (-1154 *3)) (-5 *1 (-137 *3 *4 *2))
+   (-4 *2 (-1154 *4))))
+ ((*1 *1 *1) (-12 (-5 *1 (-248 *2)) (-4 *2 (-1128))))) 
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 (((*1 *2 *1)
-  (-12 (-5 *2 (-583 (-248 *3))) (-5 *1 (-248 *3)) (-4 *3 (-494))
-   (-4 *3 (-1127))))) 
+  (-12 (-5 *2 (-584 (-248 *3))) (-5 *1 (-248 *3)) (-4 *3 (-495))
+   (-4 *3 (-1128))))) 
 (((*1 *2 *3)
   (-12 (-4 *4 (-389))
    (-5 *2
-    (-583
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-      (|:| |eigmult| (-694)) (|:| |eigvec| (-583 (-630 (-347 (-857 *4))))))))
-   (-5 *1 (-247 *4)) (-5 *3 (-630 (-347 (-857 *4))))))) 
+    (-584
+     (-2 (|:| |eigval| (-3 (-347 (-858 *4)) (-1079 (-1089) (-858 *4))))
+      (|:| |eigmult| (-695)) (|:| |eigvec| (-584 (-631 (-347 (-858 *4))))))))
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 (((*1 *2 *3)
   (-12 (-4 *4 (-389))
    (-5 *2
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+      (|:| |geneigvec| (-584 (-631 (-347 (-858 *4))))))))
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 (((*1 *2 *3 *4 *5 *5)
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-   (-5 *4 (-630 (-347 (-857 *6))))))
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+   (-4 *6 (-389)) (-5 *2 (-584 (-631 (-347 (-858 *6))))) (-5 *1 (-247 *6))
+   (-5 *4 (-631 (-347 (-858 *6))))))
  ((*1 *2 *3 *4)
   (-12
    (-5 *3
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-   (-5 *4 (-630 (-347 (-857 *5))))))) 
+    (-2 (|:| |eigval| (-3 (-347 (-858 *5)) (-1079 (-1089) (-858 *5))))
+     (|:| |eigmult| (-695)) (|:| |eigvec| (-584 *4))))
+   (-4 *5 (-389)) (-5 *2 (-584 (-631 (-347 (-858 *5))))) (-5 *1 (-247 *5))
+   (-5 *4 (-631 (-347 (-858 *5))))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *3 (-3 (-347 (-857 *5)) (-1078 (-1088) (-857 *5)))) (-4 *5 (-389))
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-   (-5 *4 (-630 (-347 (-857 *5))))))) 
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+   (-5 *4 (-631 (-347 (-858 *5))))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-630 (-347 (-857 *4)))) (-4 *4 (-389))
-   (-5 *2 (-583 (-3 (-347 (-857 *4)) (-1078 (-1088) (-857 *4)))))
+  (-12 (-5 *3 (-631 (-347 (-858 *4)))) (-4 *4 (-389))
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    (-5 *1 (-247 *4))))) 
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-(((*1 *1 *2 *3 *1) (-12 (-5 *2 (-444)) (-5 *3 (-583 (-876))) (-5 *1 (-246))))) 
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 (((*1 *1) (-5 *1 (-246)))) 
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    (-4 *5 (-321 *2))))
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 (((*1 *1 *2 *3 *4)
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 (((*1 *2 *1) (-12 (-5 *2 (-246)) (-5 *1 (-235))))) 
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 (((*1 *2 *1) (-12 (-5 *2 (-85)) (-5 *1 (-234))))) 
 (((*1 *2 *1) (|partial| -12 (-5 *2 (-444)) (-5 *1 (-234))))) 
 (((*1 *2 *1) (-12 (-5 *2 (-85)) (-5 *1 (-234))))) 
 (((*1 *2 *3 *2)
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+   (-4 *4 (-13 (-495) (-951 (-484)) (-581 (-484)))) (-5 *1 (-231 *4 *2))))) 
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-  (|partial| -12 (-5 *3 (-583 (-550 *2))) (-5 *4 (-1088))
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 (((*1 *1) (-5 *1 (-117)))) 
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@@ -13165,71 +13168,71 @@
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 (((*1 *1) (-5 *1 (-114)))) 
 (((*1 *1) (-5 *1 (-114)))) 
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 (((*1 *1)
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 (((*1 *2 *2 *3)
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    (-5 *1 (-87 *4))))
  ((*1 *2 *2 *3)
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- ((*1 *2 *1) (-12 (-5 *2 (-45 (-1071) (-696))) (-5 *1 (-86))))) 
+  (|partial| -12 (-5 *3 (-86)) (-5 *2 (-584 (-1 *4 (-584 *4))))
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+ ((*1 *2 *1) (-12 (-5 *2 (-45 (-1072) (-697))) (-5 *1 (-86))))) 
 (((*1 *2 *1) (-12 (-5 *2 (-85)) (-5 *1 (-86))))) 
 (((*1 *2 *1) (-12 (-5 *2 (-85)) (-5 *1 (-86))))) 
 (((*1 *2 *1) (-12 (-5 *2 (-85)) (-5 *1 (-86))))) 
@@ -13237,923 +13240,924 @@
 (((*1 *1 *1 *2) (-12 (-5 *2 (-1 (-85) (-86) (-86))) (-5 *1 (-86))))) 
 (((*1 *2 *1 *3) (-12 (-5 *3 (-444)) (-5 *2 (-85)) (-5 *1 (-86))))) 
 (((*1 *1 *1 *2) (-12 (-5 *2 (-444)) (-5 *1 (-86))))
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-   (-4 *4 (-627 *2 *5 *6))))) 
+ ((*1 *1 *1 *2) (-12 (-5 *2 (-1072)) (-5 *1 (-86))))) 
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 (((*1 *2 *3 *3)
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 (((*1 *2 *3 *3)
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 (((*1 *1 *1 *1 *2)
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 (((*1 *1 *1 *2 *3)
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 (((*1 *2 *1 *1) (-12 (-4 *1 (-72)) (-5 *2 (-85))))) 
 (((*1 *2 *3 *3)
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 (((*1 *2 *3 *4)
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 (((*1 *2 *3)
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 (((*1 *1 *1 *2 *3)
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 (((*1 *1 *1 *2 *3)
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 (((*1 *1) (-5 *1 (-55)))) 
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\ No newline at end of file