Eradicate attribute shallowlyMutable.

5 files changed, 18062 insertions, 18081 deletions

diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase
index 8a5e3dbc..587e8e7a 100644
--- a/src/share/algebra/browse.daase
+++ b/src/share/algebra/browse.daase
@@ -1,12 +1,12 @@
 
-(1968719 . 3577992038)       
+(1968178 . 3577996048)       
 (-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 shallowly mutable 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 shallowly mutable 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."))) 
-((-3998 . T)) 
+((-3997 . 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}."))) 
-((-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
 NIL 
 (-28 S R) 
 ((|constructor| (NIL "Model for algebraically closed function spaces.")) (|zerosOf| (((|List| $) $ (|Symbol|)) "\\spad{zerosOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}'s are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{zerosOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}'s are expressed in radicals if possible. The returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable.")) (|zeroOf| (($ $ (|Symbol|)) "\\spad{zeroOf(p, y)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity which displays as \\spad{'y}.") (($ $) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity. Error: if \\spad{p} has more than one variable.")) (|rootsOf| (((|List| $) $ (|Symbol|)) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; The returned roots display as \\spad{'y1},{}...,{}\\spad{'yn}. Note: the returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; Note: the returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ $ (|Symbol|)) "\\spad{rootOf(p,y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) 
@@ -46,7 +46,7 @@ NIL
 NIL 
 (-29 R) 
 ((|constructor| (NIL "Model for algebraically closed function spaces.")) (|zerosOf| (((|List| $) $ (|Symbol|)) "\\spad{zerosOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}'s are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{zerosOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}'s are expressed in radicals if possible. The returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable.")) (|zeroOf| (($ $ (|Symbol|)) "\\spad{zeroOf(p, y)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity which displays as \\spad{'y}.") (($ $) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity. Error: if \\spad{p} has more than one variable.")) (|rootsOf| (((|List| $) $ (|Symbol|)) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; The returned roots display as \\spad{'y1},{}...,{}\\spad{'yn}. Note: the returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; Note: the returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ $ (|Symbol|)) "\\spad{rootOf(p,y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) 
-((-3994 . T) (-3992 . T) (-3991 . T) ((-3999 "*") . T) (-3990 . T) (-3995 . T) (-3989 . T)) 
+((-3993 . T) (-3991 . T) (-3990 . T) ((-3998 "*") . T) (-3989 . T) (-3994 . T) (-3988 . T)) 
 NIL 
 (-30) 
 ((|refine| (($ $ (|DoubleFloat|)) "\\spad{refine(p,x)} \\undocumented{}")) (|makeSketch| (($ (|Polynomial| (|Integer|)) (|Symbol|) (|Symbol|) (|Segment| (|Fraction| (|Integer|))) (|Segment| (|Fraction| (|Integer|)))) "\\spad{makeSketch(p,x,y,a..b,c..d)} creates an ACPLOT of the curve \\spad{p = 0} in the region {\\em a <= x <= b, c <= y <= d}. More specifically,{} 'makeSketch' plots a non-singular algebraic curve \\spad{p = 0} in an rectangular region {\\em xMin <= x <= xMax},{} {\\em yMin <= y <= yMax}. The user inputs \\spad{makeSketch(p,x,y,xMin..xMax,yMin..yMax)}. Here \\spad{p} is a polynomial in the variables \\spad{x} and \\spad{y} with integer coefficients (\\spad{p} belongs to the domain \\spad{Polynomial Integer}). The case where \\spad{p} is a polynomial in only one of the variables is allowed. The variables \\spad{x} and \\spad{y} are input to specify the the coordinate axes. The horizontal axis is the \\spad{x}-axis and the vertical axis is the \\spad{y}-axis. The rational numbers xMin,{}...,{}yMax specify the boundaries of the region in which the curve is to be plotted."))) 
@@ -56,10 +56,10 @@ NIL
 ((|constructor| (NIL "This domain represents the syntax for an add-expression.")) (|body| (((|SpadAst|) $) "base(\\spad{d}) returns the actual body of the add-domain expression `d'.")) (|base| (((|SpadAst|) $) "\\spad{base(d)} returns the base domain(\\spad{s}) of the add-domain expression."))) 
 NIL 
 NIL 
-(-32 R -3094) 
+(-32 R -3093) 
 ((|constructor| (NIL "This package provides algebraic functions over an integral domain.")) (|iroot| ((|#2| |#1| (|Integer|)) "\\spad{iroot(p, n)} should be a non-exported function.")) (|definingPolynomial| ((|#2| |#2|) "\\spad{definingPolynomial(f)} returns the defining polynomial of \\spad{f} as an element of \\spad{F}. Error: if \\spad{f} is not a kernel.")) (|minPoly| (((|SparseUnivariatePolynomial| |#2|) (|Kernel| |#2|)) "\\spad{minPoly(k)} returns the defining polynomial of \\spad{k}.")) (** ((|#2| |#2| (|Fraction| (|Integer|))) "\\spad{x ** q} is \\spad{x} raised to the rational power \\spad{q}.")) (|droot| (((|OutputForm|) (|List| |#2|)) "\\spad{droot(l)} should be a non-exported function.")) (|inrootof| ((|#2| (|SparseUnivariatePolynomial| |#2|) |#2|) "\\spad{inrootof(p, x)} should be a non-exported function.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} is \\spad{true} if \\spad{op} is an algebraic operator,{} that is,{} an \\spad{n}th root or implicit algebraic operator.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\spad{F}. Error: if \\spad{op} is not an algebraic operator,{} that is,{} an \\spad{n}th root or implicit algebraic operator.")) (|rootOf| ((|#2| (|SparseUnivariatePolynomial| |#2|) (|Symbol|)) "\\spad{rootOf(p, y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}."))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-951 (-485))))) 
+((|HasCategory| |#1| (QUOTE (-950 (-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)}\"")) (|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| (((|Maybe| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) |#1| $) "\\spad{assoc(k,u)} returns the element \\spad{x} in association list \\spad{u} stored with key \\spad{k},{} or \\spad{nothing} if \\spad{u} has no key \\spad{k}."))) 
-((-3998 . T)) 
+((-3997 . T)) 
 NIL 
 (-37 S R) 
 ((|constructor| (NIL "The category of associative algebras (modules which are themselves rings). \\blankline"))) 
@@ -82,20 +82,20 @@ NIL
 NIL 
 (-38 R) 
 ((|constructor| (NIL "The category of associative algebras (modules which are themselves rings). \\blankline"))) 
-((-3991 . T) (-3992 . T) (-3994 . T)) 
+((-3990 . T) (-3991 . T) (-3993 . T)) 
 NIL 
 (-39 UP) 
 ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in \\spadtype{AlgebraicNumber}.")) (|doublyTransitive?| (((|Boolean|) |#1|) "\\spad{doublyTransitive?(p)} is \\spad{true} if \\spad{p} is irreducible over over the field \\spad{K} generated by its coefficients,{} and if \\spad{p(X) / (X - a)} is irreducible over \\spad{K(a)} where \\spad{p(a) = 0}.")) (|split| (((|Factored| |#1|) |#1|) "\\spad{split(p)} returns a prime factorisation of \\spad{p} over its splitting field.")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p} over the field generated by its coefficients.") (((|Factored| |#1|) |#1| (|List| (|AlgebraicNumber|))) "\\spad{factor(p, [a1,...,an])} returns a prime factorisation of \\spad{p} over the field generated by its coefficients and \\spad{a1},{}...,{}an."))) 
 NIL 
 NIL 
-(-40 -3094 UP UPUP -2616) 
+(-40 -3093 UP UPUP -2615) 
 ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) 
-((-3990 |has| (-350 |#2|) (-312)) (-3995 |has| (-350 |#2|) (-312)) (-3989 |has| (-350 |#2|) (-312)) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
-((|HasCategory| (-350 |#2|) (QUOTE (-118))) (|HasCategory| (-350 |#2|) (QUOTE (-120))) (|HasCategory| (-350 |#2|) (QUOTE (-299))) (OR (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-299)))) (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-320))) (OR (-12 (|HasCategory| (-350 |#2|) (QUOTE (-190))) (|HasCategory| (-350 |#2|) (QUOTE (-312)))) (|HasCategory| (-350 |#2|) (QUOTE (-299)))) (OR (-12 (|HasCategory| (-350 |#2|) (QUOTE (-190))) (|HasCategory| (-350 |#2|) (QUOTE (-312)))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-189))) (|HasCategory| (-350 |#2|) (QUOTE (-312)))) (|HasCategory| (-350 |#2|) (QUOTE (-299)))) (OR (-12 (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-810 (-1091))))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-299))) (|HasCategory| (-350 |#2|) (QUOTE (-810 (-1091)))))) (OR (-12 (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-810 (-1091))))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-812 (-1091)))))) (|HasCategory| (-350 |#2|) (QUOTE (-581 (-485)))) (OR (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-951 (-350 (-485)))))) (|HasCategory| (-350 |#2|) (QUOTE (-951 (-350 (-485))))) (|HasCategory| (-350 |#2|) (QUOTE (-951 (-485)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-320))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-189))) (|HasCategory| (-350 |#2|) (QUOTE (-312)))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-812 (-1091))))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-190))) (|HasCategory| (-350 |#2|) (QUOTE (-312)))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-810 (-1091)))))) 
-(-41 R -3094) 
+((-3989 |has| (-350 |#2|) (-312)) (-3994 |has| (-350 |#2|) (-312)) (-3988 |has| (-350 |#2|) (-312)) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((|HasCategory| (-350 |#2|) (QUOTE (-118))) (|HasCategory| (-350 |#2|) (QUOTE (-120))) (|HasCategory| (-350 |#2|) (QUOTE (-299))) (OR (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-299)))) (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-320))) (OR (-12 (|HasCategory| (-350 |#2|) (QUOTE (-190))) (|HasCategory| (-350 |#2|) (QUOTE (-312)))) (|HasCategory| (-350 |#2|) (QUOTE (-299)))) (OR (-12 (|HasCategory| (-350 |#2|) (QUOTE (-190))) (|HasCategory| (-350 |#2|) (QUOTE (-312)))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-189))) (|HasCategory| (-350 |#2|) (QUOTE (-312)))) (|HasCategory| (-350 |#2|) (QUOTE (-299)))) (OR (-12 (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-809 (-1090))))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-299))) (|HasCategory| (-350 |#2|) (QUOTE (-809 (-1090)))))) (OR (-12 (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-809 (-1090))))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-811 (-1090)))))) (|HasCategory| (-350 |#2|) (QUOTE (-580 (-484)))) (OR (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-950 (-350 (-484)))))) (|HasCategory| (-350 |#2|) (QUOTE (-950 (-350 (-484))))) (|HasCategory| (-350 |#2|) (QUOTE (-950 (-484)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-320))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-189))) (|HasCategory| (-350 |#2|) (QUOTE (-312)))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-811 (-1090))))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-190))) (|HasCategory| (-350 |#2|) (QUOTE (-312)))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-809 (-1090)))))) 
+(-41 R -3093) 
 ((|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| $)) $) "\\spad{numer(x)} \\undocumented"))) 
 NIL 
-((-12 (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (|HasCategory| |#2| (|%list| (QUOTE -364) (|devaluate| |#1|))))) 
+((-12 (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-950 (-484)))) (|HasCategory| |#2| (|%list| (QUOTE -364) (|devaluate| |#1|))))) 
 (-42 OV E P) 
 ((|constructor| (NIL "This package factors multivariate polynomials over the domain of \\spadtype{AlgebraicNumber} by allowing the user to specify a list of algebraic numbers generating the particular extension to factor over.")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| |#3|)) (|SparseUnivariatePolynomial| |#3|) (|List| (|AlgebraicNumber|))) "\\spad{factor(p,lan)} factors the polynomial \\spad{p} over the extension generated by the algebraic numbers given by the list \\spad{lan}. \\spad{p} is presented as a univariate polynomial with multivariate coefficients.") (((|Factored| |#3|) |#3| (|List| (|AlgebraicNumber|))) "\\spad{factor(p,lan)} factors the polynomial \\spad{p} over the extension generated by the algebraic numbers given by the list \\spad{lan}."))) 
 NIL 
@@ -106,31 +106,31 @@ NIL
 ((|HasCategory| |#1| (QUOTE (-258)))) 
 (-44 R |n| |ls| |gamma|) 
 ((|constructor| (NIL "AlgebraGivenByStructuralConstants implements finite rank algebras over a commutative ring,{} given by the structural constants \\spad{gamma} with respect to a fixed basis \\spad{[a1,..,an]},{} where \\spad{gamma} is an \\spad{n}-vector of \\spad{n} by \\spad{n} matrices \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{ai * aj = gammaij1 * a1 + ... + gammaijn * an}. The symbols for the fixed basis have to be given as a list of symbols.")) (|coerce| (($ (|Vector| |#1|)) "\\spad{coerce(v)} converts a vector to a member of the algebra by forming a linear combination with the basis element. Note: the vector is assumed to have length equal to the dimension of the algebra."))) 
-((-3994 |has| |#1| (-496)) (-3992 . T) (-3991 . T)) 
-((|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-496)))) 
+((-3993 |has| |#1| (-495)) (-3991 . T) (-3990 . T)) 
+((|HasCategory| |#1| (QUOTE (-312))) (|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."))) 
-((-3998 . T)) 
-((OR (-12 (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3862) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-757)))) (-12 (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3862) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014))))) (OR (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-553 (-773))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-474)))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (OR (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-757))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-757))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-757))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (OR (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014))) (-12 (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3862) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (-12 (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#2|)))) (-12 (|HasCategory| $ (|%list| (QUOTE -1036) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3862) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-757)))) (-12 (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3862) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3862) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| $ (|%list| (QUOTE -1036) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3862) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|)))))) 
+((-3997 . T)) 
+((OR (-12 (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3861) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-756)))) (-12 (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3861) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013))))) (OR (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-552 (-772)))) (|HasCategory| |#2| (QUOTE (-552 (-772))))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-473)))) (-12 (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (OR (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-756))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-756))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-756))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-484) (QUOTE (-756))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (OR (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013))) (-12 (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3861) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (|HasCategory| $ (|%list| (QUOTE -1035) (|devaluate| |#2|))) (-12 (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#2|)))) (-12 (|HasCategory| $ (|%list| (QUOTE -1035) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3861) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-756)))) (-12 (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3861) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3861) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| $ (|%list| (QUOTE -1035) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3861) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|)))))) 
 (-46 S R E) 
 ((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#2|) "\\spad{p/c} divides \\spad{p} by the coefficient \\spad{c}.")) (|coefficient| ((|#2| $ |#3|) "\\spad{coefficient(p,e)} extracts the coefficient of the monomial with exponent \\spad{e} from polynomial \\spad{p},{} or returns zero if exponent is not present.")) (|reductum| (($ $) "\\spad{reductum(u)} returns \\spad{u} minus its leading monomial returns zero if handed the zero element.")) (|monomial| (($ |#2| |#3|) "\\spad{monomial(r,e)} makes a term from a coefficient \\spad{r} and an exponent \\spad{e}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(p)} tests if \\spad{p} is a single monomial.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(fn,u)} maps function \\spad{fn} onto the coefficients of the non-zero monomials of \\spad{u}.")) (|degree| ((|#3| $) "\\spad{degree(p)} returns the maximum of the exponents of the terms of \\spad{p}.")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(p)} returns the monomial of \\spad{p} with the highest degree.")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-312)))) 
+((|HasCategory| |#2| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-312)))) 
 (-47 R E) 
 ((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#1|) "\\spad{p/c} divides \\spad{p} by the coefficient \\spad{c}.")) (|coefficient| ((|#1| $ |#2|) "\\spad{coefficient(p,e)} extracts the coefficient of the monomial with exponent \\spad{e} from polynomial \\spad{p},{} or returns zero if exponent is not present.")) (|reductum| (($ $) "\\spad{reductum(u)} returns \\spad{u} minus its leading monomial returns zero if handed the zero element.")) (|monomial| (($ |#1| |#2|) "\\spad{monomial(r,e)} makes a term from a coefficient \\spad{r} and an exponent \\spad{e}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(p)} tests if \\spad{p} is a single monomial.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,u)} maps function \\spad{fn} onto the coefficients of the non-zero monomials of \\spad{u}.")) (|degree| ((|#2| $) "\\spad{degree(p)} returns the maximum of the exponents of the terms of \\spad{p}.")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(p)} returns the monomial of \\spad{p} with the highest degree.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) 
-(((-3999 "*") |has| |#1| (-146)) (-3990 |has| |#1| (-496)) (-3991 . T) (-3992 . T) (-3994 . T)) 
+(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-495)) (-3990 . T) (-3991 . T) (-3993 . T)) 
 NIL 
 (-48) 
 ((|constructor| (NIL "Algebraic closure of the rational numbers,{} with mathematical =")) (|norm| (($ $ (|List| (|Kernel| $))) "\\spad{norm(f,l)} computes the norm of the algebraic number \\spad{f} with respect to the extension generated by kernels \\spad{l}") (($ $ (|Kernel| $)) "\\spad{norm(f,k)} computes the norm of the algebraic number \\spad{f} with respect to the extension generated by kernel \\spad{k}") (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|List| (|Kernel| $))) "\\spad{norm(p,l)} computes the norm of the polynomial \\spad{p} with respect to the extension generated by kernels \\spad{l}") (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{norm(p,k)} computes the norm of the polynomial \\spad{p} with respect to the extension generated by kernel \\spad{k}")) (|reduce| (($ $) "\\spad{reduce(f)} simplifies all the unreduced algebraic numbers present in \\spad{f} by applying their defining relations.")) (|denom| (((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{Z}.")) (|numer| (((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{Z}."))) 
-((-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
-((|HasCategory| $ (QUOTE (-962))) (|HasCategory| $ (QUOTE (-951 (-485))))) 
+((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((|HasCategory| $ (QUOTE (-961))) (|HasCategory| $ (QUOTE (-950 (-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}."))) 
-((-3994 . T)) 
+((-3993 . T)) 
 NIL 
 (-51) 
 ((|constructor| (NIL "\\spadtype{Any} implements a type that packages up objects and their types in objects of \\spadtype{Any}. Roughly speaking that means that if \\spad{s : S} then when converted to \\spadtype{Any},{} the new object will include both the original object and its type. This is a way of converting arbitrary objects into a single type without losing any of the original information. Any object can be converted to one of \\spadtype{Any}. The original object can be recovered by `is-case' pattern matching as exemplified here and \\spad{AnyFunctions1}.")) (|obj| (((|None|) $) "\\spad{obj(a)} essentially returns the original object that was converted to \\spadtype{Any} except that the type is forced to be \\spadtype{None}.")) (|dom| (((|SExpression|) $) "\\spad{dom(a)} returns a \\spadgloss{LISP} form of the type of the original object that was converted to \\spadtype{Any}.")) (|any| (($ (|SExpression|) (|None|)) "\\spad{any(type,object)} is a technical function for creating an \\spad{object} of \\spadtype{Any}. Arugment \\spad{type} is a \\spadgloss{LISP} form for the \\spad{type} of \\spad{object}."))) 
@@ -144,7 +144,7 @@ NIL
 ((|constructor| (NIL "\\spad{ApplyUnivariateSkewPolynomial} (internal) allows univariate skew polynomials to be applied to appropriate modules.")) (|apply| ((|#2| |#3| (|Mapping| |#2| |#2|) |#2|) "\\spad{apply(p, f, m)} returns \\spad{p(m)} where the action is given by \\spad{x m = f(m)}. \\spad{f} must be an \\spad{R}-pseudo linear map on \\spad{M}."))) 
 NIL 
 NIL 
-(-54 |Base| R -3094) 
+(-54 |Base| R -3093) 
 ((|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")) (|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}"))) 
-((-3998 . T)) 
+((-3997 . T)) 
 NIL 
 (-58 S) 
 ((|constructor| (NIL "This is the domain of 1-based one dimensional arrays")) (|oneDimensionalArray| (($ (|NonNegativeInteger|) |#1|) "\\spad{oneDimensionalArray(n,s)} creates an array from \\spad{n} copies of element \\spad{s}") (($ (|List| |#1|)) "\\spad{oneDimensionalArray(l)} creates an array from a list of elements \\spad{l}"))) 
-((-3998 . T)) 
-((OR (-12 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (OR (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-757))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|))) (|HasCategory| $ (|%list| (QUOTE -1036) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| $ (|%list| (QUOTE -1036) (|devaluate| |#1|))))) 
+((-3997 . T)) 
+((OR (-12 (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-553 (-473)))) (OR (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-756))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| (-484) (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|))) (|HasCategory| $ (|%list| (QUOTE -1035) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| $ (|%list| (QUOTE -1035) (|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."))) 
-((-3998 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-72)))) 
+((-3997 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1013))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|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 (-312)))) 
 (-62 S) 
 ((|constructor| (NIL "A stack represented as a flexible array.")) (|arrayStack| (($ (|List| |#1|)) "\\spad{arrayStack([x,y,...,z])} creates an array stack with first (top) element \\spad{x},{} second element \\spad{y},{}...,{}and last element \\spad{z}."))) 
-((-3998 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-72)))) 
+((-3997 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1013))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|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.")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} is \\spad{true} if it has an operation \\spad{\"*\": (D,D) -> D} which is commutative."))) 
-(((-3999 "*") . T) (-3994 . T) (-3992 . T) (-3991 . T) (-3990 . T) (-3995 . T) (-3989 . T) (-3988 . T) (-3987 . T) (-3986 . T) (-3985 . T) (-3993 . T) (-3996 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-3984 . T)) 
+(((-3998 "*") . T) (-3993 . T) (-3991 . T) (-3990 . T) (-3989 . T) (-3994 . T) (-3988 . T) (-3987 . T) (-3986 . T) (-3985 . T) (-3984 . T) (-3992 . T) (-3995 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-3983 . T)) 
 NIL 
 (-69 R) 
 ((|constructor| (NIL "Automorphism \\spad{R} is the multiplicative group of automorphisms of \\spad{R}.")) (|morphism| (($ (|Mapping| |#1| |#1| (|Integer|))) "\\spad{morphism(f)} returns the morphism given by \\spad{f^n(x) = f(x,n)}.") (($ (|Mapping| |#1| |#1|) (|Mapping| |#1| |#1|)) "\\spad{morphism(f, g)} returns the invertible morphism given by \\spad{f},{} where \\spad{g} is the inverse of \\spad{f}..") (($ (|Mapping| |#1| |#1|)) "\\spad{morphism(f)} returns the non-invertible morphism given by \\spad{f}."))) 
-((-3994 . T)) 
+((-3993 . T)) 
 NIL 
 (-70 R UP) 
 ((|constructor| (NIL "This package provides balanced factorisations of polynomials.")) (|balancedFactorisation| (((|Factored| |#2|) |#2| (|List| |#2|)) "\\spad{balancedFactorisation(a, [b1,...,bn])} returns a factorisation \\spad{a = p1^e1 ... pm^em} such that each \\spad{pi} is balanced with respect to \\spad{[b1,...,bm]}.") (((|Factored| |#2|) |#2| |#2|) "\\spad{balancedFactorisation(a, b)} returns a factorisation \\spad{a = p1^e1 ... pm^em} such that each \\spad{pi} is balanced with respect to \\spad{b}."))) 
@@ -222,24 +222,24 @@ NIL
 NIL 
 (-73 S) 
 ((|constructor| (NIL "\\spadtype{BalancedBinaryTree(S)} is the domain of balanced binary trees (bbtree). A balanced binary tree of \\spad{2**k} leaves,{} for some \\spad{k > 0},{} is symmetric,{} that is,{} the left and right subtree of each interior node have identical shape. In general,{} the left and right subtree of a given node can differ by at most leaf node.")) (|mapDown!| (($ $ |#1| (|Mapping| (|List| |#1|) |#1| |#1| |#1|)) "\\spad{mapDown!(t,p,f)} returns \\spad{t} after traversing \\spad{t} in \"preorder\" (node then left then right) fashion replacing the successive interior nodes as follows. Let \\spad{l} and \\spad{r} denote the left and right subtrees of \\spad{t}. The root value \\spad{x} of \\spad{t} is replaced by \\spad{p}. Then \\spad{f}(value \\spad{l},{} value \\spad{r},{} \\spad{p}),{} where \\spad{l} and \\spad{r} denote the left and right subtrees of \\spad{t},{} is evaluated producing two values pl and pr. Then \\spad{mapDown!(l,pl,f)} and \\spad{mapDown!(l,pr,f)} are evaluated.") (($ $ |#1| (|Mapping| |#1| |#1| |#1|)) "\\spad{mapDown!(t,p,f)} returns \\spad{t} after traversing \\spad{t} in \"preorder\" (node then left then right) fashion replacing the successive interior nodes as follows. The root value \\spad{x} is replaced by \\spad{q} := \\spad{f}(\\spad{p},{}\\spad{x}). The mapDown!(\\spad{l},{}\\spad{q},{}\\spad{f}) and mapDown!(\\spad{r},{}\\spad{q},{}\\spad{f}) are evaluated for the left and right subtrees \\spad{l} and \\spad{r} of \\spad{t}.")) (|mapUp!| (($ $ $ (|Mapping| |#1| |#1| |#1| |#1| |#1|)) "\\spad{mapUp!(t,t1,f)} traverses \\spad{t} in an \"endorder\" (left then right then node) fashion returning \\spad{t} with the value at each successive interior node of \\spad{t} replaced by \\spad{f}(\\spad{l},{}\\spad{r},{}\\spad{l1},{}\\spad{r1}) where \\spad{l} and \\spad{r} are the values at the immediate left and right nodes. Values \\spad{l1} and \\spad{r1} are values at the corresponding nodes of a balanced binary tree \\spad{t1},{} of identical shape at \\spad{t}.") ((|#1| $ (|Mapping| |#1| |#1| |#1|)) "\\spad{mapUp!(t,f)} traverses balanced binary tree \\spad{t} in an \"endorder\" (left then right then node) fashion returning \\spad{t} with the value at each successive interior node of \\spad{t} replaced by \\spad{f}(\\spad{l},{}\\spad{r}) where \\spad{l} and \\spad{r} are the values at the immediate left and right nodes.")) (|setleaves!| (($ $ (|List| |#1|)) "\\spad{setleaves!(t, ls)} sets the leaves of \\spad{t} in left-to-right order to the elements of ls.")) (|balancedBinaryTree| (($ (|NonNegativeInteger|) |#1|) "\\spad{balancedBinaryTree(n, s)} creates a balanced binary tree with \\spad{n} nodes each with value \\spad{s}."))) 
-((-3998 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -1036) (|devaluate| |#1|)))) 
+((-3997 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1013))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -1035) (|devaluate| |#1|)))) 
 (-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 (-3999 "*")))) 
+((|HasAttribute| |#1| (QUOTE (-3998 "*")))) 
 (-75 A S) 
 ((|constructor| (NIL "A bag aggregate is an aggregate for which one can insert and extract objects,{} and where the order in which objects are inserted determines the order of extraction. Examples of bags are stacks,{} queues,{} and dequeues.")) (|inspect| ((|#2| $) "\\spad{inspect(u)} returns an (random) element from a bag.")) (|insert!| (($ |#2| $) "\\spad{insert!(x,u)} inserts item \\spad{x} into bag \\spad{u}.")) (|extract!| ((|#2| $) "\\spad{extract!(u)} destructively removes a (random) item from bag \\spad{u}.")) (|bag| (($ (|List| |#2|)) "\\spad{bag([x,y,...,z])} creates a bag with elements \\spad{x},{}\\spad{y},{}...,{}\\spad{z}."))) 
 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}."))) 
-((-3998 . T)) 
+((-3997 . T)) 
 NIL 
 (-77) 
 ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating binary expansions.")) (|binary| (($ (|Fraction| (|Integer|))) "\\spad{binary(r)} converts a rational number to a binary expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(b)} returns the fractional part of a binary expansion."))) 
-((-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
-((|HasCategory| (-485) (QUOTE (-822))) (|HasCategory| (-485) (QUOTE (-951 (-1091)))) (|HasCategory| (-485) (QUOTE (-118))) (|HasCategory| (-485) (QUOTE (-120))) (|HasCategory| (-485) (QUOTE (-554 (-474)))) (|HasCategory| (-485) (QUOTE (-934))) (|HasCategory| (-485) (QUOTE (-741))) (|HasCategory| (-485) (QUOTE (-757))) (OR (|HasCategory| (-485) (QUOTE (-741))) (|HasCategory| (-485) (QUOTE (-757)))) (|HasCategory| (-485) (QUOTE (-951 (-485)))) (|HasCategory| (-485) (QUOTE (-1067))) (|HasCategory| (-485) (QUOTE (-797 (-330)))) (|HasCategory| (-485) (QUOTE (-797 (-485)))) (|HasCategory| (-485) (QUOTE (-554 (-801 (-330))))) (|HasCategory| (-485) (QUOTE (-554 (-801 (-485))))) (|HasCategory| (-485) (QUOTE (-189))) (|HasCategory| (-485) (QUOTE (-812 (-1091)))) (|HasCategory| (-485) (QUOTE (-190))) (|HasCategory| (-485) (QUOTE (-810 (-1091)))) (|HasCategory| (-485) (QUOTE (-456 (-1091) (-485)))) (|HasCategory| (-485) (QUOTE (-260 (-485)))) (|HasCategory| (-485) (QUOTE (-241 (-485) (-485)))) (|HasCategory| (-485) (QUOTE (-258))) (|HasCategory| (-485) (QUOTE (-484))) (|HasCategory| (-485) (QUOTE (-581 (-485)))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-485) (QUOTE (-822)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-485) (QUOTE (-822)))) (|HasCategory| (-485) (QUOTE (-118))))) 
+((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((|HasCategory| (-484) (QUOTE (-821))) (|HasCategory| (-484) (QUOTE (-950 (-1090)))) (|HasCategory| (-484) (QUOTE (-118))) (|HasCategory| (-484) (QUOTE (-120))) (|HasCategory| (-484) (QUOTE (-553 (-473)))) (|HasCategory| (-484) (QUOTE (-933))) (|HasCategory| (-484) (QUOTE (-740))) (|HasCategory| (-484) (QUOTE (-756))) (OR (|HasCategory| (-484) (QUOTE (-740))) (|HasCategory| (-484) (QUOTE (-756)))) (|HasCategory| (-484) (QUOTE (-950 (-484)))) (|HasCategory| (-484) (QUOTE (-1066))) (|HasCategory| (-484) (QUOTE (-796 (-330)))) (|HasCategory| (-484) (QUOTE (-796 (-484)))) (|HasCategory| (-484) (QUOTE (-553 (-800 (-330))))) (|HasCategory| (-484) (QUOTE (-553 (-800 (-484))))) (|HasCategory| (-484) (QUOTE (-189))) (|HasCategory| (-484) (QUOTE (-811 (-1090)))) (|HasCategory| (-484) (QUOTE (-190))) (|HasCategory| (-484) (QUOTE (-809 (-1090)))) (|HasCategory| (-484) (QUOTE (-455 (-1090) (-484)))) (|HasCategory| (-484) (QUOTE (-260 (-484)))) (|HasCategory| (-484) (QUOTE (-241 (-484) (-484)))) (|HasCategory| (-484) (QUOTE (-258))) (|HasCategory| (-484) (QUOTE (-483))) (|HasCategory| (-484) (QUOTE (-580 (-484)))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-484) (QUOTE (-821)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-484) (QUOTE (-821)))) (|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}"))) 
-((-3998 . T)) 
-((-12 (|HasCategory| (-85) (QUOTE (-260 (-85)))) (|HasCategory| (-85) (QUOTE (-1014)))) (|HasCategory| (-85) (QUOTE (-554 (-474)))) (|HasCategory| (-85) (QUOTE (-757))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| (-85) (QUOTE (-72))) (|HasCategory| (-85) (QUOTE (-553 (-773)))) (|HasCategory| (-85) (QUOTE (-1014))) (-12 (|HasCategory| $ (QUOTE (-1036 (-85)))) (|HasCategory| (-85) (QUOTE (-757)))) (|HasCategory| $ (QUOTE (-1036 (-85)))) (|HasCategory| $ (QUOTE (-318 (-85)))) (-12 (|HasCategory| $ (QUOTE (-318 (-85)))) (|HasCategory| (-85) (QUOTE (-72))))) 
+((-3997 . T)) 
+((-12 (|HasCategory| (-85) (QUOTE (-260 (-85)))) (|HasCategory| (-85) (QUOTE (-1013)))) (|HasCategory| (-85) (QUOTE (-553 (-473)))) (|HasCategory| (-85) (QUOTE (-756))) (|HasCategory| (-484) (QUOTE (-756))) (|HasCategory| (-85) (QUOTE (-72))) (|HasCategory| (-85) (QUOTE (-552 (-772)))) (|HasCategory| (-85) (QUOTE (-1013))) (-12 (|HasCategory| $ (QUOTE (-1035 (-85)))) (|HasCategory| (-85) (QUOTE (-756)))) (|HasCategory| $ (QUOTE (-1035 (-85)))) (|HasCategory| $ (QUOTE (-318 (-85)))) (-12 (|HasCategory| $ (QUOTE (-318 (-85)))) (|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}"))) 
-((-3992 . T) (-3991 . T)) 
+((-3991 . T) (-3990 . T)) 
 NIL 
 (-83 S) 
 ((|constructor| (NIL "This is the category of Boolean logic structures.")) (|or| (($ $ $) "\\spad{x or y} returns the disjunction of \\spad{x} and \\spad{y}.")) (|and| (($ $ $) "\\spad{x and y} returns the conjunction of \\spad{x} and \\spad{y}.")) (|not| (($ $) "\\spad{not x} returns the complement or negation of \\spad{x}."))) 
@@ -280,22 +280,22 @@ NIL
 ((|constructor| (NIL "This package exports functions to set some commonly used properties of operators,{} including properties which contain functions.")) (|constantOpIfCan| (((|Union| |#1| "failed") (|BasicOperator|)) "\\spad{constantOpIfCan(op)} returns \\spad{a} if \\spad{op} is the constant nullary operator always returning \\spad{a},{} \"failed\" otherwise.")) (|constantOperator| (((|BasicOperator|) |#1|) "\\spad{constantOperator(a)} returns a nullary operator op such that \\spad{op()} always evaluate to \\spad{a}.")) (|derivative| (((|Union| (|List| (|Mapping| |#1| (|List| |#1|))) "failed") (|BasicOperator|)) "\\spad{derivative(op)} returns the value of the \"\\%diff\" property of \\spad{op} if it has one,{} and \"failed\" otherwise.") (((|BasicOperator|) (|BasicOperator|) (|Mapping| |#1| |#1|)) "\\spad{derivative(op, foo)} attaches foo as the \"\\%diff\" property of \\spad{op}. If \\spad{op} has an \"\\%diff\" property \\spad{f},{} then applying a derivation \\spad{D} to \\spad{op}(a) returns \\spad{f(a) * D(a)}. Argument \\spad{op} must be unary.") (((|BasicOperator|) (|BasicOperator|) (|List| (|Mapping| |#1| (|List| |#1|)))) "\\spad{derivative(op, [foo1,...,foon])} attaches [\\spad{foo1},{}...,{}foon] as the \"\\%diff\" property of \\spad{op}. If \\spad{op} has an \"\\%diff\" property \\spad{[f1,...,fn]} then applying a derivation \\spad{D} to \\spad{op(a1,...,an)} returns \\spad{f1(a1,...,an) * D(a1) + ... + fn(a1,...,an) * D(an)}.")) (|evaluate| (((|Union| (|Mapping| |#1| (|List| |#1|)) "failed") (|BasicOperator|)) "\\spad{evaluate(op)} returns the value of the \"\\%eval\" property of \\spad{op} if it has one,{} and \"failed\" otherwise.") (((|BasicOperator|) (|BasicOperator|) (|Mapping| |#1| |#1|)) "\\spad{evaluate(op, foo)} attaches foo as the \"\\%eval\" property of \\spad{op}. If \\spad{op} has an \"\\%eval\" property \\spad{f},{} then applying \\spad{op} to a returns the result of \\spad{f(a)}. Argument \\spad{op} must be unary.") (((|BasicOperator|) (|BasicOperator|) (|Mapping| |#1| (|List| |#1|))) "\\spad{evaluate(op, foo)} attaches foo as the \"\\%eval\" property of \\spad{op}. If \\spad{op} has an \"\\%eval\" property \\spad{f},{} then applying \\spad{op} to \\spad{(a1,...,an)} returns the result of \\spad{f(a1,...,an)}.") (((|Union| |#1| "failed") (|BasicOperator|) (|List| |#1|)) "\\spad{evaluate(op, [a1,...,an])} checks if \\spad{op} has an \"\\%eval\" property \\spad{f}. If it has,{} then \\spad{f(a1,...,an)} is returned,{} and \"failed\" otherwise."))) 
 NIL 
 NIL 
-(-88 -3094 UP) 
+(-88 -3093 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}."))) 
-((-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
 NIL 
 (-90 |p|) 
 ((|constructor| (NIL "Stream-based implementation of Qp: numbers are represented as sum(\\spad{i} = \\spad{k}..,{} a[\\spad{i}] * p^i),{} where the a[\\spad{i}] lie in -(\\spad{p} - 1)\\spad{/2},{}...,{}(\\spad{p} - 1)\\spad{/2}."))) 
-((-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
-((|HasCategory| (-89 |#1|) (QUOTE (-822))) (|HasCategory| (-89 |#1|) (QUOTE (-951 (-1091)))) (|HasCategory| (-89 |#1|) (QUOTE (-118))) (|HasCategory| (-89 |#1|) (QUOTE (-120))) (|HasCategory| (-89 |#1|) (QUOTE (-554 (-474)))) (|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 (-485)))) (|HasCategory| (-89 |#1|) (QUOTE (-1067))) (|HasCategory| (-89 |#1|) (QUOTE (-797 (-330)))) (|HasCategory| (-89 |#1|) (QUOTE (-797 (-485)))) (|HasCategory| (-89 |#1|) (QUOTE (-554 (-801 (-330))))) (|HasCategory| (-89 |#1|) (QUOTE (-554 (-801 (-485))))) (|HasCategory| (-89 |#1|) (QUOTE (-581 (-485)))) (|HasCategory| (-89 |#1|) (QUOTE (-189))) (|HasCategory| (-89 |#1|) (QUOTE (-812 (-1091)))) (|HasCategory| (-89 |#1|) (QUOTE (-190))) (|HasCategory| (-89 |#1|) (QUOTE (-810 (-1091)))) (|HasCategory| (-89 |#1|) (|%list| (QUOTE -456) (QUOTE (-1091)) (|%list| (QUOTE -89) (|devaluate| |#1|)))) (|HasCategory| (-89 |#1|) (|%list| (QUOTE -260) (|%list| (QUOTE -89) (|devaluate| |#1|)))) (|HasCategory| (-89 |#1|) (|%list| (QUOTE -241) (|%list| (QUOTE -89) (|devaluate| |#1|)) (|%list| (QUOTE -89) (|devaluate| |#1|)))) (|HasCategory| (-89 |#1|) (QUOTE (-258))) (|HasCategory| (-89 |#1|) (QUOTE (-484))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-89 |#1|) (QUOTE (-822)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-89 |#1|) (QUOTE (-822)))) (|HasCategory| (-89 |#1|) (QUOTE (-118))))) 
+((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((|HasCategory| (-89 |#1|) (QUOTE (-821))) (|HasCategory| (-89 |#1|) (QUOTE (-950 (-1090)))) (|HasCategory| (-89 |#1|) (QUOTE (-118))) (|HasCategory| (-89 |#1|) (QUOTE (-120))) (|HasCategory| (-89 |#1|) (QUOTE (-553 (-473)))) (|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 (-484)))) (|HasCategory| (-89 |#1|) (QUOTE (-1066))) (|HasCategory| (-89 |#1|) (QUOTE (-796 (-330)))) (|HasCategory| (-89 |#1|) (QUOTE (-796 (-484)))) (|HasCategory| (-89 |#1|) (QUOTE (-553 (-800 (-330))))) (|HasCategory| (-89 |#1|) (QUOTE (-553 (-800 (-484))))) (|HasCategory| (-89 |#1|) (QUOTE (-580 (-484)))) (|HasCategory| (-89 |#1|) (QUOTE (-189))) (|HasCategory| (-89 |#1|) (QUOTE (-811 (-1090)))) (|HasCategory| (-89 |#1|) (QUOTE (-190))) (|HasCategory| (-89 |#1|) (QUOTE (-809 (-1090)))) (|HasCategory| (-89 |#1|) (|%list| (QUOTE -455) (QUOTE (-1090)) (|%list| (QUOTE -89) (|devaluate| |#1|)))) (|HasCategory| (-89 |#1|) (|%list| (QUOTE -260) (|%list| (QUOTE -89) (|devaluate| |#1|)))) (|HasCategory| (-89 |#1|) (|%list| (QUOTE -241) (|%list| (QUOTE -89) (|devaluate| |#1|)) (|%list| (QUOTE -89) (|devaluate| |#1|)))) (|HasCategory| (-89 |#1|) (QUOTE (-258))) (|HasCategory| (-89 |#1|) (QUOTE (-483))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-89 |#1|) (QUOTE (-821)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-89 |#1|) (QUOTE (-821)))) (|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| (($ $) "\\spad{left(u)} returns the left child."))) 
 NIL 
-((|HasCategory| |#1| (|%list| (QUOTE -1036) (|devaluate| |#2|)))) 
+((|HasCategory| |#1| (|%list| (QUOTE -1035) (|devaluate| |#2|)))) 
 (-92 S) 
 ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "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"))) 
-((-3998 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -1036) (|devaluate| |#1|)))) 
+((-3997 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1013))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -1035) (|devaluate| |#1|)))) 
 (-95 S) 
 ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}."))) 
 NIL 
 NIL 
 (-96) 
 ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}."))) 
-((-3998 . T)) 
+((-3997 . T)) 
 NIL 
 (-97 A S) 
 ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#2| $) "\\spad{node(left,v,right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}."))) 
@@ -322,24 +322,24 @@ NIL
 NIL 
 (-98 S) 
 ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#1| $) "\\spad{node(left,v,right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}."))) 
-((-3998 . T)) 
+((-3997 . T)) 
 NIL 
 (-99 S) 
 ((|constructor| (NIL "\\spadtype{BinaryTournament(S)} is the domain of binary trees where elements are ordered down the tree. A binary search tree is either empty or is a node containing a \\spadfun{value} of type \\spad{S},{} and a \\spadfun{right} and a \\spadfun{left} which are both \\spadtype{BinaryTree(S)}")) (|insert!| (($ |#1| $) "\\spad{insert!(x,b)} inserts element \\spad{x} as leaves into binary tournament \\spad{b}.")) (|binaryTournament| (($ (|List| |#1|)) "\\spad{binaryTournament(ls)} creates a binary tournament with the elements of \\spad{ls} as values at the nodes."))) 
-((-3998 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -1036) (|devaluate| |#1|)))) 
+((-3997 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1013))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -1035) (|devaluate| |#1|)))) 
 (-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."))) 
-((-3998 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -1036) (|devaluate| |#1|)))) 
+((-3997 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1013))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -1035) (|devaluate| |#1|)))) 
 (-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.}")) (|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."))) 
-((-3998 . T)) 
-((OR (-12 (|HasCategory| (-101) (QUOTE (-260 (-101)))) (|HasCategory| (-101) (QUOTE (-757)))) (-12 (|HasCategory| (-101) (QUOTE (-260 (-101)))) (|HasCategory| (-101) (QUOTE (-1014))))) (|HasCategory| (-101) (QUOTE (-553 (-773)))) (|HasCategory| (-101) (QUOTE (-554 (-474)))) (OR (|HasCategory| (-101) (QUOTE (-757))) (|HasCategory| (-101) (QUOTE (-1014)))) (|HasCategory| (-101) (QUOTE (-757))) (OR (|HasCategory| (-101) (QUOTE (-72))) (|HasCategory| (-101) (QUOTE (-757))) (|HasCategory| (-101) (QUOTE (-1014)))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| (-101) (QUOTE (-72))) (|HasCategory| (-101) (QUOTE (-1014))) (-12 (|HasCategory| (-101) (QUOTE (-260 (-101)))) (|HasCategory| (-101) (QUOTE (-1014)))) (-12 (|HasCategory| $ (QUOTE (-318 (-101)))) (|HasCategory| (-101) (QUOTE (-72)))) (|HasCategory| $ (QUOTE (-318 (-101)))) (|HasCategory| $ (QUOTE (-1036 (-101)))) (-12 (|HasCategory| $ (QUOTE (-1036 (-101)))) (|HasCategory| (-101) (QUOTE (-757))))) 
+((-3997 . T)) 
+((OR (-12 (|HasCategory| (-101) (QUOTE (-260 (-101)))) (|HasCategory| (-101) (QUOTE (-756)))) (-12 (|HasCategory| (-101) (QUOTE (-260 (-101)))) (|HasCategory| (-101) (QUOTE (-1013))))) (|HasCategory| (-101) (QUOTE (-552 (-772)))) (|HasCategory| (-101) (QUOTE (-553 (-473)))) (OR (|HasCategory| (-101) (QUOTE (-756))) (|HasCategory| (-101) (QUOTE (-1013)))) (|HasCategory| (-101) (QUOTE (-756))) (OR (|HasCategory| (-101) (QUOTE (-72))) (|HasCategory| (-101) (QUOTE (-756))) (|HasCategory| (-101) (QUOTE (-1013)))) (|HasCategory| (-484) (QUOTE (-756))) (|HasCategory| (-101) (QUOTE (-72))) (|HasCategory| (-101) (QUOTE (-1013))) (-12 (|HasCategory| (-101) (QUOTE (-260 (-101)))) (|HasCategory| (-101) (QUOTE (-1013)))) (-12 (|HasCategory| $ (QUOTE (-318 (-101)))) (|HasCategory| (-101) (QUOTE (-72)))) (|HasCategory| $ (QUOTE (-318 (-101)))) (|HasCategory| $ (QUOTE (-1035 (-101)))) (-12 (|HasCategory| $ (QUOTE (-1035 (-101)))) (|HasCategory| (-101) (QUOTE (-756))))) 
 (-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") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,D) -> D} which is commutative."))) 
-(((-3999 "*") . T)) 
+(((-3998 "*") . T)) 
 NIL 
-(-108 |minix| -2623 R) 
+(-108 |minix| -2622 R) 
 ((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\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|) $) "\\spad{rank(t)} returns the tensorial rank of \\spad{t} (that is,{} the number of indices). This is the same as the graded module degree."))) 
 NIL 
 NIL 
-(-109 |minix| -2623 S T$) 
+(-109 |minix| -2622 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}."))) 
-((-3987 . T) (-3998 . T)) 
-((OR (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-320)))) (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-1014))))) (|HasCategory| (-117) (QUOTE (-554 (-474)))) (|HasCategory| (-117) (QUOTE (-320))) (|HasCategory| (-117) (QUOTE (-757))) (|HasCategory| (-117) (QUOTE (-72))) (|HasCategory| (-117) (QUOTE (-553 (-773)))) (|HasCategory| (-117) (QUOTE (-1014))) (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-1014)))) (|HasCategory| $ (QUOTE (-318 (-117)))) (-12 (|HasCategory| $ (QUOTE (-318 (-117)))) (|HasCategory| (-117) (QUOTE (-72))))) 
+((-3986 . T) (-3997 . T)) 
+((OR (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-320)))) (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-1013))))) (|HasCategory| (-117) (QUOTE (-553 (-473)))) (|HasCategory| (-117) (QUOTE (-320))) (|HasCategory| (-117) (QUOTE (-756))) (|HasCategory| (-117) (QUOTE (-72))) (|HasCategory| (-117) (QUOTE (-552 (-772)))) (|HasCategory| (-117) (QUOTE (-1013))) (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-1013)))) (|HasCategory| $ (QUOTE (-318 (-117)))) (-12 (|HasCategory| $ (QUOTE (-318 (-117)))) (|HasCategory| (-117) (QUOTE (-72))))) 
 (-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."))) 
-((-3994 . T)) 
+((-3993 . T)) 
 NIL 
 (-119 R) 
 ((|constructor| (NIL "This package provides a characteristicPolynomial function for any matrix over a commutative ring.")) (|characteristicPolynomial| ((|#1| (|Matrix| |#1|) |#1|) "\\spad{characteristicPolynomial(m,r)} computes the characteristic polynomial of the matrix \\spad{m} evaluated at the point \\spad{r}. In particular,{} if \\spad{r} is the polynomial 'x,{} then it returns the characteristic polynomial expressed as a polynomial in 'x."))) 
@@ -410,9 +410,9 @@ NIL
 NIL 
 (-120) 
 ((|constructor| (NIL "Rings of Characteristic Zero."))) 
-((-3994 . T)) 
+((-3993 . T)) 
 NIL 
-(-121 -3094 UP UPUP) 
+(-121 -3093 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})]}.")) (|find| (((|Union| |#2| "failed") (|Mapping| (|Boolean|) |#2|) $) "\\spad{find(p,u)} returns the first \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \"failed\" otherwise.")) (|construct| (($ (|List| |#2|)) "\\axiom{construct(\\spad{x},{}\\spad{y},{}...,{}\\spad{z})} returns the collection of elements \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}} ordered as given. Equivalently written as \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]\\$\\spad{D}},{} where \\spad{D} is the domain. \\spad{D} may be omitted for those of type List."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-554 (-474)))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#1| (|%list| (QUOTE -318) (|devaluate| |#2|)))) 
+((|HasCategory| |#2| (QUOTE (-553 (-473)))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#1| (|%list| (QUOTE -318) (|devaluate| |#2|)))) 
 (-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})]}.")) (|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."))) 
-((-3992 . T) (-3991 . T) (-3994 . T)) 
+((-3991 . T) (-3990 . T) (-3993 . T)) 
 NIL 
 (-126) 
 ((|constructor| (NIL "\\indented{1}{The purpose of this package is to provide reasonable plots of} functions with singularities.")) (|clipWithRanges| (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|List| (|List| (|Point| (|DoubleFloat|)))) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{clipWithRanges(pointLists,xMin,xMax,yMin,yMax)} performs clipping on a list of lists of points,{} \\spad{pointLists}. Clipping is done within the specified ranges of \\spad{xMin},{} \\spad{xMax} and \\spad{yMin},{} \\spad{yMax}. This function is used internally by the \\fakeAxiomFun{iClipParametric} subroutine in this package.")) (|clipParametric| (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|Plot|) (|Fraction| (|Integer|)) (|Fraction| (|Integer|))) "\\spad{clipParametric(p,frac,sc)} performs two-dimensional clipping on a plot,{} \\spad{p},{} from the domain \\spadtype{Plot} for the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)}; the fraction parameter is specified by \\spad{frac} and the scale parameter is specified by \\spad{sc} for use in the \\fakeAxiomFun{iClipParametric} subroutine,{} which is called by this function.") (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|Plot|)) "\\spad{clipParametric(p)} performs two-dimensional clipping on a plot,{} \\spad{p},{} from the domain \\spadtype{Plot} for the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)}; the default parameters \\spad{1/2} for the fraction and \\spad{5/1} for the scale are used in the \\fakeAxiomFun{iClipParametric} subroutine,{} which is called by this function.")) (|clip| (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{clip(ll)} performs two-dimensional clipping on a list of lists of points,{} \\spad{ll}; the default parameters \\spad{1/2} for the fraction and \\spad{5/1} for the scale are used in the \\fakeAxiomFun{iClipParametric} subroutine,{} which is called by this function.") (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|List| (|Point| (|DoubleFloat|)))) "\\spad{clip(l)} performs two-dimensional clipping on a curve \\spad{l},{} which is a list of points; the default parameters \\spad{1/2} for the fraction and \\spad{5/1} for the scale are used in the \\fakeAxiomFun{iClipParametric} subroutine,{} which is called by this function.") (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|Plot|) (|Fraction| (|Integer|)) (|Fraction| (|Integer|))) "\\spad{clip(p,frac,sc)} performs two-dimensional clipping on a plot,{} \\spad{p},{} from the domain \\spadtype{Plot} for the graph of one variable \\spad{y = f(x)}; the fraction parameter is specified by \\spad{frac} and the scale parameter is specified by \\spad{sc} for use in the \\spadfun{clip} function.") (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|Plot|)) "\\spad{clip(p)} performs two-dimensional clipping on a plot,{} \\spad{p},{} from the domain \\spadtype{Plot} for the graph of one variable,{} \\spad{y = f(x)}; the default parameters \\spad{1/4} for the fraction and \\spad{5/1} for the scale are used in the \\spadfun{clip} function."))) 
@@ -452,7 +452,7 @@ NIL
 ((|constructor| (NIL "Color() specifies a domain of 27 colors provided in the \\Language{} system (the colors mix additively).")) (|color| (($ (|Integer|)) "\\spad{color(i)} returns a color of the indicated hue \\spad{i}.")) (|numberOfHues| (((|PositiveInteger|)) "\\spad{numberOfHues()} returns the number of total hues,{} set in totalHues.")) (|hue| (((|Integer|) $) "\\spad{hue(c)} returns the hue index of the indicated color \\spad{c}.")) (|blue| (($) "\\spad{blue()} returns the position of the blue hue from total hues.")) (|green| (($) "\\spad{green()} returns the position of the green hue from total hues.")) (|yellow| (($) "\\spad{yellow()} returns the position of the yellow hue from total hues.")) (|red| (($) "\\spad{red()} returns the position of the red hue from total hues.")) (+ (($ $ $) "\\spad{c1 + c2} additively mixes the two colors \\spad{c1} and \\spad{c2}.")) (* (($ (|DoubleFloat|) $) "\\spad{s * c},{} returns the color \\spad{c},{} whose weighted shade has been scaled by \\spad{s}.") (($ (|PositiveInteger|) $) "\\spad{s * c},{} returns the color \\spad{c},{} whose weighted shade has been scaled by \\spad{s}."))) 
 NIL 
 NIL 
-(-131 R -3094) 
+(-131 R -3093) 
 ((|constructor| (NIL "Provides combinatorial functions over an integral domain.")) (|ipow| ((|#2| (|List| |#2|)) "\\spad{ipow(l)} should be local but conditional.")) (|iidprod| ((|#2| (|List| |#2|)) "\\spad{iidprod(l)} should be local but conditional.")) (|iidsum| ((|#2| (|List| |#2|)) "\\spad{iidsum(l)} should be local but conditional.")) (|iipow| ((|#2| (|List| |#2|)) "\\spad{iipow(l)} should be local but conditional.")) (|iiperm| ((|#2| (|List| |#2|)) "\\spad{iiperm(l)} should be local but conditional.")) (|iibinom| ((|#2| (|List| |#2|)) "\\spad{iibinom(l)} should be local but conditional.")) (|iifact| ((|#2| |#2|) "\\spad{iifact(x)} should be local but conditional.")) (|product| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{product(f(n), n = a..b)} returns \\spad{f}(a) * ... * \\spad{f}(\\spad{b}) as a formal product.") ((|#2| |#2| (|Symbol|)) "\\spad{product(f(n), n)} returns the formal product \\spad{P}(\\spad{n}) which verifies \\spad{P}(\\spad{n+1})/P(\\spad{n}) = \\spad{f}(\\spad{n}).")) (|summation| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{summation(f(n), n = a..b)} returns \\spad{f}(a) + ... + \\spad{f}(\\spad{b}) as a formal sum.") ((|#2| |#2| (|Symbol|)) "\\spad{summation(f(n), n)} returns the formal sum \\spad{S}(\\spad{n}) which verifies \\spad{S}(\\spad{n+1}) - \\spad{S}(\\spad{n}) = \\spad{f}(\\spad{n}).")) (|factorials| ((|#2| |#2| (|Symbol|)) "\\spad{factorials(f, x)} rewrites the permutations and binomials in \\spad{f} involving \\spad{x} in terms of factorials.") ((|#2| |#2|) "\\spad{factorials(f)} rewrites the permutations and binomials in \\spad{f} in terms of factorials.")) (|factorial| ((|#2| |#2|) "\\spad{factorial(n)} returns the factorial of \\spad{n},{} \\spadignore{i.e.} n!.")) (|permutation| ((|#2| |#2| |#2|) "\\spad{permutation(n, r)} returns the number of permutations of \\spad{n} objects taken \\spad{r} at a time,{} \\spadignore{i.e.} n!/(\\spad{n}-\\spad{r})!.")) (|binomial| ((|#2| |#2| |#2|) "\\spad{binomial(n, r)} returns the number of subsets of \\spad{r} objects taken among \\spad{n} objects,{} \\spadignore{i.e.} n!/(r! * (\\spad{n}-\\spad{r})!).")) (** ((|#2| |#2| |#2|) "\\spad{a ** b} is the formal exponential a**b.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\spad{F}; error if \\spad{op} is not a combinatorial operator.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} is \\spad{true} if \\spad{op} is a combinatorial operator."))) 
 NIL 
 NIL 
@@ -483,10 +483,10 @@ NIL
 (-138 S R) 
 ((|constructor| (NIL "This category represents the extension of a ring by a square root of \\spad{-1}.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a rational number,{} or \"failed\" if \\spad{x} is not a rational number.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a rational number. Error: if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a rational number.")) (|polarCoordinates| (((|Record| (|:| |r| |#2|) (|:| |phi| |#2|)) $) "\\spad{polarCoordinates(x)} returns (\\spad{r},{} phi) such that \\spad{x} = \\spad{r} * exp(\\%\\spad{i} * phi).")) (|argument| ((|#2| $) "\\spad{argument(x)} returns the angle made by (0,{}1) and (0,{}\\spad{x}).")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x} = sqrt(norm(\\spad{x})).")) (|exquo| (((|Union| $ "failed") $ |#2|) "\\spad{exquo(x, r)} returns the exact quotient of \\spad{x} by \\spad{r},{} or \"failed\" if \\spad{r} does not divide \\spad{x} exactly.")) (|norm| ((|#2| $) "\\spad{norm(x)} returns \\spad{x} * conjugate(\\spad{x})")) (|real| ((|#2| $) "\\spad{real(x)} returns real part of \\spad{x}.")) (|imag| ((|#2| $) "\\spad{imag(x)} returns imaginary part of \\spad{x}.")) (|conjugate| (($ $) "\\spad{conjugate(x + \\%i y)} returns \\spad{x} - \\%\\spad{i} \\spad{y}.")) (|imaginary| (($) "\\spad{imaginary()} = sqrt(\\spad{-1}) = \\%\\spad{i}.")) (|complex| (($ |#2| |#2|) "\\spad{complex(x,y)} constructs \\spad{x} + \\%i*y.") ((|attribute|) "indicates that \\% has sqrt(\\spad{-1})"))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-822))) (|HasCategory| |#2| (QUOTE (-484))) (|HasCategory| |#2| (QUOTE (-916))) (|HasCategory| |#2| (QUOTE (-1116))) (|HasCategory| |#2| (QUOTE (-974))) (|HasCategory| |#2| (QUOTE (-934))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-554 (-474)))) (|HasCategory| |#2| (QUOTE (-312))) (|HasAttribute| |#2| (QUOTE -3993)) (|HasAttribute| |#2| (QUOTE -3996)) (|HasCategory| |#2| (QUOTE (-258))) (|HasCategory| |#2| (QUOTE (-496)))) 
+((|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| |#2| (QUOTE (-483))) (|HasCategory| |#2| (QUOTE (-915))) (|HasCategory| |#2| (QUOTE (-1115))) (|HasCategory| |#2| (QUOTE (-973))) (|HasCategory| |#2| (QUOTE (-933))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-553 (-473)))) (|HasCategory| |#2| (QUOTE (-312))) (|HasAttribute| |#2| (QUOTE -3992)) (|HasAttribute| |#2| (QUOTE -3995)) (|HasCategory| |#2| (QUOTE (-258))) (|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})"))) 
-((-3990 OR (|has| |#1| (-496)) (-12 (|has| |#1| (-258)) (|has| |#1| (-822)))) (-3995 |has| |#1| (-312)) (-3989 |has| |#1| (-312)) (-3993 |has| |#1| (-6 -3993)) (-3996 |has| |#1| (-6 -3996)) (-1377 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((-3989 OR (|has| |#1| (-495)) (-12 (|has| |#1| (-258)) (|has| |#1| (-821)))) (-3994 |has| |#1| (-312)) (-3988 |has| |#1| (-312)) (-3992 |has| |#1| (-6 -3992)) (-3995 |has| |#1| (-6 -3995)) (-1376 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
 NIL 
 (-140 RR PR) 
 ((|constructor| (NIL "\\indented{1}{Author:} Date Created: Date Last Updated: Basic Functions: Related Constructors: Complex,{} UnivariatePolynomial Also See: AMS Classifications: Keywords: complex,{} polynomial factorization,{} factor References:")) (|factor| (((|Factored| |#2|) |#2|) "\\spad{factor(p)} factorizes the polynomial \\spad{p} with complex coefficients."))) 
@@ -498,8 +498,8 @@ NIL
 NIL 
 (-142 R) 
 ((|constructor| (NIL "\\spadtype {Complex(R)} creates the domain of elements of the form \\spad{a + b * i} where \\spad{a} and \\spad{b} come from the ring \\spad{R},{} and \\spad{i} is a new element such that \\spad{i**2 = -1}."))) 
-((-3990 OR (|has| |#1| (-496)) (-12 (|has| |#1| (-258)) (|has| |#1| (-822)))) (-3995 |has| |#1| (-312)) (-3989 |has| |#1| (-312)) (-3993 |has| |#1| (-6 -3993)) (-3996 |has| |#1| (-6 -3996)) (-1377 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
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+((-3989 OR (|has| |#1| (-495)) (-12 (|has| |#1| (-258)) (|has| |#1| (-821)))) (-3994 |has| |#1| (-312)) (-3988 |has| |#1| (-312)) (-3992 |has| |#1| (-6 -3992)) (-3995 |has| |#1| (-6 -3995)) (-1376 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-299))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-299)))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-320))) (OR (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-299)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-312)))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-299)))) (|HasCategory| |#1| (QUOTE (-809 (-1090)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-809 (-1090))))) (|HasCategory| |#1| (QUOTE (-811 (-1090))))) (|HasCategory| |#1| (QUOTE (-580 (-484)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484)))))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-484)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-821)))) (-12 (|HasCategory| |#1| (QUOTE (-299))) (|HasCategory| |#1| (QUOTE (-821)))) (|HasCategory| |#1| (QUOTE (-312)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-821)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-821)))) (-12 (|HasCategory| |#1| (QUOTE (-299))) (|HasCategory| |#1| (QUOTE (-821))))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-495)))) (-12 (|HasCategory| |#1| (QUOTE (-915))) (|HasCategory| |#1| (QUOTE (-1115)))) (|HasCategory| |#1| (QUOTE (-1115))) (|HasCategory| |#1| (QUOTE (-933))) (|HasCategory| |#1| (QUOTE (-553 (-473)))) (OR (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-299))) (|HasCategory| |#1| (QUOTE (-495)))) (OR (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-299)))) (|HasCategory| |#1| (QUOTE (-553 (-800 (-330))))) (|HasCategory| |#1| (QUOTE (-553 (-800 (-484))))) (|HasCategory| |#1| (QUOTE (-796 (-330)))) (|HasCategory| |#1| (QUOTE (-796 (-484)))) (|HasCategory| |#1| (|%list| (QUOTE -455) (QUOTE (-1090)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -241) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-973))) (-12 (|HasCategory| |#1| (QUOTE (-973))) (|HasCategory| |#1| (QUOTE (-1115)))) (|HasCategory| |#1| (QUOTE (-483))) (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-821))) (OR (-12 (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-821)))) (|HasCategory| |#1| (QUOTE (-312)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-821)))) (|HasCategory| |#1| (QUOTE (-495)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-312)))) (|HasCategory| |#1| (QUOTE (-189)))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-811 (-1090)))) (|HasCategory| |#1| (QUOTE (-190))) (-12 (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-821)))) (|HasAttribute| |#1| (QUOTE -3992)) (|HasAttribute| |#1| (QUOTE -3995)) (-12 (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-312)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-811 (-1090))))) (-12 (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-312)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-809 (-1090))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-299)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-821))) (|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."))) 
-(((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
+(((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
 NIL 
 (-147) 
 ((|constructor| (NIL "This category is the root of the I/O conduits.")) (|close!| (($ $) "\\spad{close!(c)} closes the conduit \\spad{c},{} changing its state to one that is invalid for future read or write operations."))) 
@@ -522,7 +522,7 @@ NIL
 NIL 
 (-148 R) 
 ((|constructor| (NIL "\\spadtype{ContinuedFraction} implements general \\indented{1}{continued fractions.\\space{2}This version is not restricted to simple,{}} \\indented{1}{finite fractions and uses the \\spadtype{Stream} as a} \\indented{1}{representation.\\space{2}The arithmetic functions assume that the} \\indented{1}{approximants alternate below/above the convergence point.} \\indented{1}{This is enforced by ensuring the partial numerators and partial} \\indented{1}{denominators are greater than 0 in the Euclidean domain view of \\spad{R}} \\indented{1}{(\\spadignore{i.e.} \\spad{sizeLess?(0, x)}).}")) (|complete| (($ $) "\\spad{complete(x)} causes all entries in \\spadvar{\\spad{x}} to be computed. Normally entries are only computed as needed. If \\spadvar{\\spad{x}} is an infinite continued fraction,{} a user-initiated interrupt is necessary to stop the computation.")) (|extend| (($ $ (|Integer|)) "\\spad{extend(x,n)} causes the first \\spadvar{\\spad{n}} entries in the continued fraction \\spadvar{\\spad{x}} to be computed. Normally entries are only computed as needed.")) (|denominators| (((|Stream| |#1|) $) "\\spad{denominators(x)} returns the stream of denominators of the approximants of the continued fraction \\spadvar{\\spad{x}}. If the continued fraction is finite,{} then the stream will be finite.")) (|numerators| (((|Stream| |#1|) $) "\\spad{numerators(x)} returns the stream of numerators of the approximants of the continued fraction \\spadvar{\\spad{x}}. If the continued fraction is finite,{} then the stream will be finite.")) (|convergents| (((|Stream| (|Fraction| |#1|)) $) "\\spad{convergents(x)} returns the stream of the convergents of the continued fraction \\spadvar{\\spad{x}}. If the continued fraction is finite,{} then the stream will be finite.")) (|approximants| (((|Stream| (|Fraction| |#1|)) $) "\\spad{approximants(x)} returns the stream of approximants of the continued fraction \\spadvar{\\spad{x}}. If the continued fraction is finite,{} then the stream will be infinite and periodic with period 1.")) (|reducedForm| (($ $) "\\spad{reducedForm(x)} puts the continued fraction \\spadvar{\\spad{x}} in reduced form,{} \\spadignore{i.e.} the function returns an equivalent continued fraction of the form \\spad{continuedFraction(b0,[1,1,1,...],[b1,b2,b3,...])}.")) (|wholePart| ((|#1| $) "\\spad{wholePart(x)} extracts the whole part of \\spadvar{\\spad{x}}. That is,{} if \\spad{x = continuedFraction(b0, [a1,a2,a3,...], [b1,b2,b3,...])},{} then \\spad{wholePart(x) = b0}.")) (|partialQuotients| (((|Stream| |#1|) $) "\\spad{partialQuotients(x)} extracts the partial quotients in \\spadvar{\\spad{x}}. That is,{} if \\spad{x = continuedFraction(b0, [a1,a2,a3,...], [b1,b2,b3,...])},{} then \\spad{partialQuotients(x) = [b0,b1,b2,b3,...]}.")) (|partialDenominators| (((|Stream| |#1|) $) "\\spad{partialDenominators(x)} extracts the denominators in \\spadvar{\\spad{x}}. That is,{} if \\spad{x = continuedFraction(b0, [a1,a2,a3,...], [b1,b2,b3,...])},{} then \\spad{partialDenominators(x) = [b1,b2,b3,...]}.")) (|partialNumerators| (((|Stream| |#1|) $) "\\spad{partialNumerators(x)} extracts the numerators in \\spadvar{\\spad{x}}. That is,{} if \\spad{x = continuedFraction(b0, [a1,a2,a3,...], [b1,b2,b3,...])},{} then \\spad{partialNumerators(x) = [a1,a2,a3,...]}.")) (|reducedContinuedFraction| (($ |#1| (|Stream| |#1|)) "\\spad{reducedContinuedFraction(b0,b)} constructs a continued fraction in the following way: if \\spad{b = [b1,b2,...]} then the result is the continued fraction \\spad{b0 + 1/(b1 + 1/(b2 + ...))}. That is,{} the result is the same as \\spad{continuedFraction(b0,[1,1,1,...],[b1,b2,b3,...])}.")) (|continuedFraction| (($ |#1| (|Stream| |#1|) (|Stream| |#1|)) "\\spad{continuedFraction(b0,a,b)} constructs a continued fraction in the following way: if \\spad{a = [a1,a2,...]} and \\spad{b = [b1,b2,...]} then the result is the continued fraction \\spad{b0 + a1/(b1 + a2/(b2 + ...))}.") (($ (|Fraction| |#1|)) "\\spad{continuedFraction(r)} converts the fraction \\spadvar{\\spad{r}} with components of type \\spad{R} to a continued fraction over \\spad{R}."))) 
-(((-3999 "*") . T) (-3990 . T) (-3995 . T) (-3989 . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
+(((-3998 "*") . T) (-3989 . T) (-3994 . T) (-3988 . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
 NIL 
 (-149) 
 ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. A `Contour' a list of bindings making up a `virtual scope'.")) (|findBinding| (((|Maybe| (|Binding|)) (|Identifier|) $) "\\spad{findBinding(c,n)} returns the first binding associated with `n'. Otherwise `nothing.")) (|push| (($ (|Binding|) $) "\\spad{push(c,b)} augments the contour with binding `b'.")) (|bindings| (((|List| (|Binding|)) $) "\\spad{bindings(c)} returns the list of bindings in countour \\spad{c}."))) 
@@ -539,7 +539,7 @@ NIL
 (-152 R S CS) 
 ((|constructor| (NIL "This package supports matching patterns involving complex expressions")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(cexpr, pat, res)} matches the pattern \\spad{pat} to the complex expression \\spad{cexpr}. res contains the variables of \\spad{pat} which are already matched and their matches."))) 
 NIL 
-((|HasCategory| (-858 |#2|) (|%list| (QUOTE -797) (|devaluate| |#1|)))) 
+((|HasCategory| (-857 |#2|) (|%list| (QUOTE -796) (|devaluate| |#1|)))) 
 (-153 R) 
 ((|constructor| (NIL "This package \\undocumented{}")) (|multiEuclideanTree| (((|List| |#1|) (|List| |#1|) |#1|) "\\spad{multiEuclideanTree(l,r)} \\undocumented{}")) (|chineseRemainder| (((|List| |#1|) (|List| (|List| |#1|)) (|List| |#1|)) "\\spad{chineseRemainder(llv,lm)} returns a list of values,{} each of which corresponds to the Chinese remainder of the associated element of \\axiom{\\spad{llv}} and axiom{\\spad{lm}}. This is more efficient than applying chineseRemainder several times.") ((|#1| (|List| |#1|) (|List| |#1|)) "\\spad{chineseRemainder(lv,lm)} returns a value \\axiom{\\spad{v}} such that,{} if \\spad{x} is \\axiom{\\spad{lv}.\\spad{i}} modulo \\axiom{\\spad{lm}.\\spad{i}} for all \\axiom{\\spad{i}},{} then \\spad{x} is \\axiom{\\spad{v}} modulo \\axiom{\\spad{lm}(1)*lm(2)*...*lm(\\spad{n})}.")) (|modTree| (((|List| |#1|) |#1| (|List| |#1|)) "\\spad{modTree(r,l)} \\undocumented{}"))) 
 NIL 
@@ -576,7 +576,7 @@ NIL
 ((|constructor| (NIL "This domain enumerates the three kinds of constructors available in OpenAxiom: category constructors,{} domain constructors,{} and package constructors.")) (|package| (($) "`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 -3094) 
+(-162 R -3093) 
 ((|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 -3094 UP UPUP R) 
+(-169 -3093 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 -3094 FP) 
+(-170 -3093 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."))) 
-((-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
-((|HasCategory| (-485) (QUOTE (-822))) (|HasCategory| (-485) (QUOTE (-951 (-1091)))) (|HasCategory| (-485) (QUOTE (-118))) (|HasCategory| (-485) (QUOTE (-120))) (|HasCategory| (-485) (QUOTE (-554 (-474)))) (|HasCategory| (-485) (QUOTE (-934))) (|HasCategory| (-485) (QUOTE (-741))) (|HasCategory| (-485) (QUOTE (-757))) (OR (|HasCategory| (-485) (QUOTE (-741))) (|HasCategory| (-485) (QUOTE (-757)))) (|HasCategory| (-485) (QUOTE (-951 (-485)))) (|HasCategory| (-485) (QUOTE (-1067))) (|HasCategory| (-485) (QUOTE (-797 (-330)))) (|HasCategory| (-485) (QUOTE (-797 (-485)))) (|HasCategory| (-485) (QUOTE (-554 (-801 (-330))))) (|HasCategory| (-485) (QUOTE (-554 (-801 (-485))))) (|HasCategory| (-485) (QUOTE (-189))) (|HasCategory| (-485) (QUOTE (-812 (-1091)))) (|HasCategory| (-485) (QUOTE (-190))) (|HasCategory| (-485) (QUOTE (-810 (-1091)))) (|HasCategory| (-485) (QUOTE (-456 (-1091) (-485)))) (|HasCategory| (-485) (QUOTE (-260 (-485)))) (|HasCategory| (-485) (QUOTE (-241 (-485) (-485)))) (|HasCategory| (-485) (QUOTE (-258))) (|HasCategory| (-485) (QUOTE (-484))) (|HasCategory| (-485) (QUOTE (-581 (-485)))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-485) (QUOTE (-822)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-485) (QUOTE (-822)))) (|HasCategory| (-485) (QUOTE (-118))))) 
+((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((|HasCategory| (-484) (QUOTE (-821))) (|HasCategory| (-484) (QUOTE (-950 (-1090)))) (|HasCategory| (-484) (QUOTE (-118))) (|HasCategory| (-484) (QUOTE (-120))) (|HasCategory| (-484) (QUOTE (-553 (-473)))) (|HasCategory| (-484) (QUOTE (-933))) (|HasCategory| (-484) (QUOTE (-740))) (|HasCategory| (-484) (QUOTE (-756))) (OR (|HasCategory| (-484) (QUOTE (-740))) (|HasCategory| (-484) (QUOTE (-756)))) (|HasCategory| (-484) (QUOTE (-950 (-484)))) (|HasCategory| (-484) (QUOTE (-1066))) (|HasCategory| (-484) (QUOTE (-796 (-330)))) (|HasCategory| (-484) (QUOTE (-796 (-484)))) (|HasCategory| (-484) (QUOTE (-553 (-800 (-330))))) (|HasCategory| (-484) (QUOTE (-553 (-800 (-484))))) (|HasCategory| (-484) (QUOTE (-189))) (|HasCategory| (-484) (QUOTE (-811 (-1090)))) (|HasCategory| (-484) (QUOTE (-190))) (|HasCategory| (-484) (QUOTE (-809 (-1090)))) (|HasCategory| (-484) (QUOTE (-455 (-1090) (-484)))) (|HasCategory| (-484) (QUOTE (-260 (-484)))) (|HasCategory| (-484) (QUOTE (-241 (-484) (-484)))) (|HasCategory| (-484) (QUOTE (-258))) (|HasCategory| (-484) (QUOTE (-483))) (|HasCategory| (-484) (QUOTE (-580 (-484)))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-484) (QUOTE (-821)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-484) (QUOTE (-821)))) (|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|) $) "\\spad{head(d)} returns the head of the definition `d'. This is a list of identifiers starting with the name of the operation followed by the name of the parameters,{} if any."))) 
 NIL 
 NIL 
-(-173 R -3094) 
+(-173 R -3093) 
 ((|constructor| (NIL "\\spadtype{ElementaryFunctionDefiniteIntegration} provides functions to compute definite integrals of elementary functions.")) (|innerint| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| #1="failed") (|:| |pole| #2="potentialPole")) |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{innerint(f, x, a, b, ignore?)} should be local but conditional")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| #1#) (|:| |pole| #2#)) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|)) (|String|)) "\\spad{integrate(f, x = a..b, \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| #1#) (|:| |pole| #2#)) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|))) "\\spad{integrate(f, x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}."))) 
 NIL 
 NIL 
@@ -634,19 +634,19 @@ NIL
 NIL 
 (-176 S) 
 ((|constructor| (NIL "Linked list implementation of a Dequeue")) (|dequeue| (($ (|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}."))) 
-((-3998 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-72)))) 
+((-3997 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1013))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|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}."))) 
-((-3994 . T)) 
+((-3993 . T)) 
 NIL 
-(-178 R -3094) 
+(-178 R -3093) 
 ((|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}."))) 
-((-3772 . T) (-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((-3771 . T) (-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
 NIL 
 (-180) 
 ((|constructor| (NIL "This package provides special functions for double precision real and complex floating point.")) (|hypergeometric0F1| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{hypergeometric0F1(c,z)} is the hypergeometric function \\spad{0F1(; c; z)}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{hypergeometric0F1(c,z)} is the hypergeometric function \\spad{0F1(; c; z)}.")) (|airyBi| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyBi(x)} is the Airy function \\spad{Bi(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Bi''(x) - x * Bi(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyBi(x)} is the Airy function \\spad{Bi(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Bi''(x) - x * Bi(x) = 0}.}")) (|airyAi| (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyAi(x)} is the Airy function \\spad{Ai(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Ai''(x) - x * Ai(x) = 0}.}") (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyAi(x)} is the Airy function \\spad{Ai(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Ai''(x) - x * Ai(x) = 0}.}")) (|besselK| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselK(v,x)} is the modified Bessel function of the first kind,{} \\spad{K(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{K(v,x) = \\%pi/2*(I(-v,x) - I(v,x))/sin(v*\\%pi)}} so is not valid for integer values of \\spad{v}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselK(v,x)} is the modified Bessel function of the first kind,{} \\spad{K(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{K(v,x) = \\%pi/2*(I(-v,x) - I(v,x))/sin(v*\\%pi)}.} so is not valid for integer values of \\spad{v}.")) (|besselI| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselI(v,x)} is the modified Bessel function of the first kind,{} \\spad{I(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselI(v,x)} is the modified Bessel function of the first kind,{} \\spad{I(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.}")) (|besselY| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselY(v,x)} is the Bessel function of the second kind,{} \\spad{Y(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{Y(v,x) = (J(v,x) cos(v*\\%pi) - J(-v,x))/sin(v*\\%pi)}} so is not valid for integer values of \\spad{v}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselY(v,x)} is the Bessel function of the second kind,{} \\spad{Y(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{Y(v,x) = (J(v,x) cos(v*\\%pi) - J(-v,x))/sin(v*\\%pi)}} so is not valid for integer values of \\spad{v}.")) (|besselJ| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselJ(v,x)} is the Bessel function of the first kind,{} \\spad{J(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselJ(v,x)} is the Bessel function of the first kind,{} \\spad{J(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.}")) (|polygamma| (((|Complex| (|DoubleFloat|)) (|NonNegativeInteger|) (|Complex| (|DoubleFloat|))) "\\spad{polygamma(n, x)} is the \\spad{n}-th derivative of \\spad{digamma(x)}.") (((|DoubleFloat|) (|NonNegativeInteger|) (|DoubleFloat|)) "\\spad{polygamma(n, x)} is the \\spad{n}-th derivative of \\spad{digamma(x)}.")) (|digamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{digamma(x)} is the function,{} \\spad{psi(x)},{} defined by \\indented{2}{\\spad{psi(x) = Gamma'(x)/Gamma(x)}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{digamma(x)} is the function,{} \\spad{psi(x)},{} defined by \\indented{2}{\\spad{psi(x) = Gamma'(x)/Gamma(x)}.}")) (|logGamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{logGamma(x)} is the natural log of \\spad{Gamma(x)}. This can often be computed even if \\spad{Gamma(x)} cannot.") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{logGamma(x)} is the natural log of \\spad{Gamma(x)}. This can often be computed even if \\spad{Gamma(x)} cannot.")) (|Beta| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{Beta(x, y)} is the Euler beta function,{} \\spad{B(x,y)},{} defined by \\indented{2}{\\spad{Beta(x,y) = integrate(t^(x-1)*(1-t)^(y-1), t=0..1)}.} This is related to \\spad{Gamma(x)} by \\indented{2}{\\spad{Beta(x,y) = Gamma(x)*Gamma(y) / Gamma(x + y)}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{Beta(x, y)} is the Euler beta function,{} \\spad{B(x,y)},{} defined by \\indented{2}{\\spad{Beta(x,y) = integrate(t^(x-1)*(1-t)^(y-1), t=0..1)}.} This is related to \\spad{Gamma(x)} by \\indented{2}{\\spad{Beta(x,y) = Gamma(x)*Gamma(y) / Gamma(x + y)}.}")) (|Gamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{Gamma(x)} is the Euler gamma function,{} \\spad{Gamma(x)},{} defined by \\indented{2}{\\spad{Gamma(x) = integrate(t^(x-1)*exp(-t), t=0..\\%infinity)}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{Gamma(x)} is the Euler gamma function,{} \\spad{Gamma(x)},{} defined by \\indented{2}{\\spad{Gamma(x) = integrate(t^(x-1)*exp(-t), t=0..\\%infinity)}.}"))) 
@@ -654,19 +654,19 @@ NIL
 NIL 
 (-181 R) 
 ((|constructor| (NIL "\\indented{1}{A Denavit-Hartenberg Matrix is a 4x4 Matrix of the form:} \\indented{1}{\\spad{nx ox ax px}} \\indented{1}{\\spad{ny oy ay py}} \\indented{1}{\\spad{nz oz az pz}} \\indented{2}{\\spad{0\\space{2}0\\space{2}0\\space{2}1}} (\\spad{n},{} \\spad{o},{} and a are the direction cosines)")) (|translate| (($ |#1| |#1| |#1|) "\\spad{translate(X,Y,Z)} returns a dhmatrix for translation by \\spad{X},{} \\spad{Y},{} and \\spad{Z}")) (|scale| (($ |#1| |#1| |#1|) "\\spad{scale(sx,sy,sz)} returns a dhmatrix for scaling in the \\spad{X},{} \\spad{Y} and \\spad{Z} directions")) (|rotatez| (($ |#1|) "\\spad{rotatez(r)} returns a dhmatrix for rotation about axis \\spad{Z} for \\spad{r} degrees")) (|rotatey| (($ |#1|) "\\spad{rotatey(r)} returns a dhmatrix for rotation about axis \\spad{Y} for \\spad{r} degrees")) (|rotatex| (($ |#1|) "\\spad{rotatex(r)} returns a dhmatrix for rotation about axis \\spad{X} for \\spad{r} degrees")) (|identity| (($) "\\spad{identity()} create the identity dhmatrix")) (* (((|Point| |#1|) $ (|Point| |#1|)) "\\spad{t*p} applies the dhmatrix \\spad{t} to point \\spad{p}"))) 
-((-3998 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-496))) (|HasAttribute| |#1| (QUOTE (-3999 "*"))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-72)))) 
+((-3997 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1013))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-495))) (|HasAttribute| |#1| (QUOTE (-3998 "*"))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-72)))) 
 (-182 A S) 
 ((|constructor| (NIL "A dictionary is an aggregate in which entries can be inserted,{} searched for and removed. Duplicates are thrown away on insertion. This category models the usual notion of dictionary which involves large amounts of data where copying is impractical. Principal operations are thus destructive (non-copying) ones."))) 
 NIL 
 NIL 
 (-183 S) 
 ((|constructor| (NIL "A dictionary is an aggregate in which entries can be inserted,{} searched for and removed. Duplicates are thrown away on insertion. This category models the usual notion of dictionary which involves large amounts of data where copying is impractical. Principal operations are thus destructive (non-copying) ones."))) 
-((-3998 . T)) 
+((-3997 . T)) 
 NIL 
 (-184 R) 
 ((|constructor| (NIL "Differential extensions of a ring \\spad{R}. Given a differentiation on \\spad{R},{} extend it to a differentiation on \\%."))) 
-((-3994 . T)) 
+((-3993 . T)) 
 NIL 
 (-185 S T$) 
 ((|constructor| (NIL "This category captures the interface of domains with a distinguished operation named \\spad{differentiate}. Usually,{} additional properties are wanted. For example,{} that it obeys the usual Leibniz identity of differentiation of product,{} in case of differential rings. One could also want \\spad{differentiate} to obey the chain rule when considering differential manifolds. The lack of specific requirement in this category is an implicit admission that currently \\Language{} is not expressive enough to express the most general notion of differentiation in an adequate manner,{} suitable for computational purposes.")) (D ((|#2| $) "\\spad{D x} is a shorthand for \\spad{differentiate x}")) (|differentiate| ((|#2| $) "\\spad{differentiate x} compute the derivative of \\spad{x}."))) 
@@ -678,7 +678,7 @@ NIL
 NIL 
 (-187 R) 
 ((|constructor| (NIL "An \\spad{R}-module equipped with a distinguised differential operator. If \\spad{R} is a differential ring,{} then differentiation on the module should extend differentiation on the differential ring \\spad{R}. The latter can be the null operator. In that case,{} the differentiation operator on the module is just an \\spad{R}-linear operator. For that reason,{} we do not require that the ring \\spad{R} be a DifferentialRing; \\blankline"))) 
-((-3992 . T) (-3991 . T)) 
+((-3991 . T) (-3990 . T)) 
 NIL 
 (-188 S) 
 ((|constructor| (NIL "This category is like \\spadtype{DifferentialDomain} where the target of the differentiation operator is the same as its source.")) (D (($ $ (|NonNegativeInteger|)) "\\spad{D(x, n)} returns the \\spad{n}\\spad{-}th derivative of \\spad{x}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(x,n)} returns the \\spad{n}\\spad{-}th derivative of \\spad{x}."))) 
@@ -690,7 +690,7 @@ NIL
 NIL 
 (-190) 
 ((|constructor| (NIL "An ordinary differential ring,{} that is,{} a ring with an operation \\spadfun{differentiate}. \\blankline"))) 
-((-3994 . T)) 
+((-3993 . T)) 
 NIL 
 (-191) 
 ((|constructor| (NIL "Dioid is the class of semirings where the addition operation induces a canonical order relation."))) 
@@ -702,25 +702,25 @@ NIL
 ((|HasCategory| |#1| (|%list| (QUOTE -318) (|devaluate| |#2|)))) 
 (-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}."))) 
-((-3998 . T)) 
+((-3997 . 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 -2623 R) 
+(-195 S -2622 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."))) 
 NIL 
-((|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (QUOTE (-718))) (|HasCategory| |#3| (QUOTE (-757))) (|HasAttribute| |#3| (QUOTE -3994)) (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-320))) (|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 (-1014)))) 
-(-196 -2623 R) 
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+(-196 -2622 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."))) 
-((-3991 |has| |#2| (-962)) (-3992 |has| |#2| (-962)) (-3994 |has| |#2| (-6 -3994))) 
+((-3990 |has| |#2| (-961)) (-3991 |has| |#2| (-961)) (-3993 |has| |#2| (-6 -3993))) 
 NIL 
-(-197 -2623 R) 
+(-197 -2622 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."))) 
-((-3991 |has| |#2| (-962)) (-3992 |has| |#2| (-962)) (-3994 |has| |#2| (-6 -3994))) 
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(QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-810 (-1091)))) (|HasCategory| |#2| (QUOTE (-962)))) (OR (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-810 (-1091)))) (|HasCategory| |#2| (QUOTE (-962)))) (OR (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-810 (-1091)))) (|HasCategory| |#2| (QUOTE (-962)))) (OR (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-810 (-1091)))) (|HasCategory| |#2| (QUOTE (-962)))) (|HasCategory| |#2| (QUOTE (-190))) (OR (|HasCategory| |#2| (QUOTE (-190))) (-12 (|HasCategory| |#2| (QUOTE (-189))) (|HasCategory| |#2| (QUOTE 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(|devaluate| |#2|))))) 
-(-198 -2623 A B) 
+((-3990 |has| |#2| (-961)) (-3991 |has| |#2| (-961)) (-3993 |has| |#2| (-6 -3993))) 
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(|devaluate| |#2|))))) 
+(-198 -2622 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}."))) 
-((-3990 . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((-3989 . T) (-3990 . T) (-3991 . T) (-3993 . 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}"))) 
-((-3998 . T)) 
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+((-3997 . T)) 
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 (-204 M) 
 ((|constructor| (NIL "DiscreteLogarithmPackage implements help functions for discrete logarithms in monoids using small cyclic groups.")) (|shanksDiscLogAlgorithm| (((|Union| (|NonNegativeInteger|) "failed") |#1| |#1| (|NonNegativeInteger|)) "\\spad{shanksDiscLogAlgorithm(b,a,p)} computes \\spad{s} with \\spad{b**s = a} for assuming that \\spad{a} and \\spad{b} are elements in a 'small' cyclic group of order \\spad{p} by Shank's algorithm. Note: this is a subroutine of the function \\spadfun{discreteLog}.")) (** ((|#1| |#1| (|Integer|)) "\\spad{x ** n} returns \\spad{x} raised to the integer power \\spad{n}"))) 
 NIL 
 NIL 
 (-205 R) 
 ((|constructor| (NIL "Category of modules that extend differential rings. \\blankline"))) 
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 NIL 
 (-206 |vl| R) 
 ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is lexicographic specified by the variable list parameter with the most significant variable first in the list.")) (|reorder| (($ $ (|List| (|Integer|))) "\\spad{reorder(p, perm)} applies the permutation perm to the variables in a polynomial and returns the new correctly ordered polynomial"))) 
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 (-207) 
 ((|showSummary| (((|Void|) $) "\\spad{showSummary(d)} prints out implementation detail information of domain `d'.")) (|reflect| (($ (|ConstructorCall| (|DomainConstructor|))) "\\spad{reflect cc} returns the domain object designated by the ConstructorCall syntax `cc'. The constructor implied by `cc' must be known to the system since it is instantiated.")) (|reify| (((|ConstructorCall| (|DomainConstructor|)) $) "\\spad{reify(d)} returns the abstract syntax for the domain `x'.")) (|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Create: October 18,{} 2007. Date Last Updated: December 20,{} 2008. Basic Operations: coerce,{} reify Related Constructors: Type,{} Syntax,{} OutputForm Also See: Type,{} ConstructorCall") (((|DomainConstructor|) $) "\\spad{constructor(d)} returns the domain constructor that is instantiated to the domain object `d'."))) 
 NIL 
@@ -770,23 +770,23 @@ NIL
 NIL 
 (-210 |n| R M S) 
 ((|constructor| (NIL "This constructor provides a direct product type with a left matrix-module view."))) 
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(|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-1014))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|))))) (|HasCategory| |#4| (QUOTE (-312))) (OR (|HasCategory| |#4| (QUOTE (-146))) (|HasCategory| |#4| (QUOTE (-312))) (|HasCategory| |#4| (QUOTE (-962)))) (OR (|HasCategory| |#4| (QUOTE (-146))) (|HasCategory| |#4| (QUOTE (-312)))) (|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 (-320))) (OR (-12 (|HasCategory| |#4| (QUOTE (-146))) (|HasCategory| |#4| (QUOTE (-581 (-485))))) (-12 (|HasCategory| |#4| (QUOTE (-190))) (|HasCategory| |#4| (QUOTE (-581 (-485))))) (-12 (|HasCategory| |#4| (QUOTE (-312))) (|HasCategory| |#4| (QUOTE (-581 (-485))))) (-12 (|HasCategory| |#4| (QUOTE (-581 (-485)))) (|HasCategory| |#4| (QUOTE (-810 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(-951 (-485)))) (|HasCategory| |#4| (QUOTE (-1014)))) (OR (-12 (|HasCategory| |#4| (QUOTE (-951 (-485)))) (|HasCategory| |#4| (QUOTE (-1014)))) (|HasCategory| |#4| (QUOTE (-962)))) (-12 (|HasCategory| |#4| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#4| (QUOTE (-1014)))) (OR (-12 (|HasCategory| |#4| (QUOTE (-810 (-1091)))) (|HasCategory| |#4| (QUOTE (-962)))) (|HasAttribute| |#4| (QUOTE -3994)) (-12 (|HasCategory| |#4| (QUOTE (-190))) (|HasCategory| |#4| (QUOTE (-962))))) (-12 (|HasCategory| |#4| (QUOTE (-189))) (|HasCategory| |#4| (QUOTE (-962)))) (-12 (|HasCategory| |#4| (QUOTE (-812 (-1091)))) (|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)))) (-12 (|HasCategory| |#4| (QUOTE (-1014))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#4|))))) 
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(|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-1013))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|))))) (|HasCategory| |#4| (QUOTE (-312))) (OR (|HasCategory| |#4| (QUOTE (-146))) (|HasCategory| |#4| (QUOTE (-312))) (|HasCategory| |#4| (QUOTE (-961)))) (OR (|HasCategory| |#4| (QUOTE (-146))) (|HasCategory| |#4| (QUOTE (-312)))) (|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 (-320))) (OR (-12 (|HasCategory| |#4| (QUOTE (-146))) (|HasCategory| |#4| (QUOTE (-580 (-484))))) (-12 (|HasCategory| |#4| (QUOTE (-190))) (|HasCategory| |#4| (QUOTE (-580 (-484))))) (-12 (|HasCategory| |#4| (QUOTE (-312))) (|HasCategory| |#4| (QUOTE (-580 (-484))))) (-12 (|HasCategory| |#4| (QUOTE (-580 (-484)))) (|HasCategory| |#4| (QUOTE (-809 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(-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#4|))))) 
 (-211 |n| R S) 
 ((|constructor| (NIL "This constructor provides a direct product of \\spad{R}-modules with an \\spad{R}-module view."))) 
-((-3994 OR (-2564 (|has| |#3| (-962)) (|has| |#3| (-190))) (|has| |#3| (-6 -3994)) (-2564 (|has| |#3| (-962)) (|has| |#3| (-810 (-1091))))) (-3991 |has| |#3| (-962)) (-3992 |has| |#3| (-962))) 
-((OR (-12 (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-190))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-320))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-664))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-718))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-757))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-810 (-1091)))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-962))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1014))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|))))) (|HasCategory| |#3| (QUOTE (-312))) (OR (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (QUOTE (-962)))) (OR (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-312)))) (|HasCategory| |#3| (QUOTE (-962))) (|HasCategory| |#3| (QUOTE (-664))) (|HasCategory| |#3| (QUOTE (-718))) (OR (|HasCategory| |#3| (QUOTE (-718))) (|HasCategory| |#3| (QUOTE (-757)))) (|HasCategory| |#3| (QUOTE (-757))) (|HasCategory| |#3| (QUOTE (-320))) (OR (-12 (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-581 (-485))))) (-12 (|HasCategory| |#3| (QUOTE (-190))) (|HasCategory| |#3| (QUOTE (-581 (-485))))) (-12 (|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (QUOTE (-581 (-485))))) (-12 (|HasCategory| |#3| (QUOTE (-581 (-485)))) (|HasCategory| |#3| (QUOTE (-810 (-1091))))) (-12 (|HasCategory| |#3| (QUOTE (-581 (-485)))) (|HasCategory| |#3| (QUOTE (-962))))) (|HasCategory| |#3| (QUOTE (-810 (-1091)))) (OR (|HasCategory| |#3| (QUOTE (-190))) (|HasCategory| |#3| (QUOTE (-810 (-1091)))) (|HasCategory| |#3| (QUOTE (-962)))) (|HasCategory| |#3| (QUOTE (-190))) (OR (|HasCategory| |#3| (QUOTE (-190))) (-12 (|HasCategory| |#3| (QUOTE (-189))) (|HasCategory| |#3| (QUOTE (-962))))) (OR (-12 (|HasCategory| |#3| (QUOTE (-812 (-1091)))) (|HasCategory| |#3| (QUOTE (-962)))) (|HasCategory| |#3| (QUOTE (-810 (-1091))))) (|HasCategory| |#3| (QUOTE (-1014))) (OR (-12 (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-951 (-350 (-485)))))) (-12 (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-951 (-350 (-485)))))) (-12 (|HasCategory| |#3| (QUOTE (-190))) (|HasCategory| |#3| (QUOTE (-951 (-350 (-485)))))) (-12 (|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (QUOTE (-951 (-350 (-485)))))) (-12 (|HasCategory| |#3| (QUOTE (-320))) (|HasCategory| |#3| (QUOTE (-951 (-350 (-485)))))) (-12 (|HasCategory| |#3| (QUOTE (-664))) (|HasCategory| |#3| (QUOTE (-951 (-350 (-485)))))) (-12 (|HasCategory| |#3| (QUOTE (-718))) (|HasCategory| |#3| (QUOTE (-951 (-350 (-485)))))) (-12 (|HasCategory| |#3| (QUOTE (-757))) (|HasCategory| |#3| (QUOTE (-951 (-350 (-485)))))) (-12 (|HasCategory| |#3| (QUOTE (-810 (-1091)))) (|HasCategory| |#3| (QUOTE (-951 (-350 (-485)))))) (-12 (|HasCategory| |#3| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#3| (QUOTE (-962)))) (-12 (|HasCategory| |#3| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#3| (QUOTE (-1014))))) (OR (-12 (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#3| (QUOTE (-190))) (|HasCategory| |#3| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#3| (QUOTE (-718))) (|HasCategory| |#3| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#3| (QUOTE (-757))) (|HasCategory| |#3| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#3| (QUOTE (-810 (-1091)))) (|HasCategory| |#3| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#3| (QUOTE (-951 (-485)))) (|HasCategory| |#3| (QUOTE (-1014)))) (-12 (|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#3| (QUOTE (-320))) (|HasCategory| |#3| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#3| (QUOTE (-664))) (|HasCategory| |#3| (QUOTE (-951 (-485))))) (|HasCategory| |#3| (QUOTE (-962)))) (OR (-12 (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#3| (QUOTE (-190))) (|HasCategory| |#3| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#3| (QUOTE (-718))) (|HasCategory| |#3| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#3| (QUOTE (-757))) (|HasCategory| |#3| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#3| (QUOTE (-810 (-1091)))) (|HasCategory| |#3| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#3| (QUOTE (-951 (-485)))) (|HasCategory| |#3| (QUOTE (-1014)))) (-12 (|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#3| (QUOTE (-320))) (|HasCategory| |#3| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#3| (QUOTE (-664))) (|HasCategory| |#3| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#3| (QUOTE (-951 (-485)))) (|HasCategory| |#3| (QUOTE (-962))))) (|HasCategory| |#3| (QUOTE (-72))) (|HasCategory| (-485) (QUOTE (-757))) (-12 (|HasCategory| |#3| (QUOTE (-581 (-485)))) (|HasCategory| |#3| (QUOTE (-962)))) (OR (-12 (|HasCategory| |#3| (QUOTE (-810 (-1091)))) (|HasCategory| |#3| (QUOTE (-962)))) (-12 (|HasCategory| |#3| (QUOTE (-812 (-1091)))) (|HasCategory| |#3| (QUOTE (-962))))) (OR (-12 (|HasCategory| |#3| (QUOTE (-190))) (|HasCategory| |#3| (QUOTE (-962)))) (-12 (|HasCategory| |#3| (QUOTE (-189))) (|HasCategory| |#3| (QUOTE (-962))))) (-12 (|HasCategory| |#3| (QUOTE (-951 (-485)))) (|HasCategory| |#3| (QUOTE (-1014)))) (OR (-12 (|HasCategory| |#3| (QUOTE (-951 (-485)))) (|HasCategory| |#3| (QUOTE (-1014)))) (|HasCategory| |#3| (QUOTE (-962)))) (-12 (|HasCategory| |#3| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#3| (QUOTE (-1014)))) (OR (-12 (|HasCategory| |#3| (QUOTE (-810 (-1091)))) (|HasCategory| |#3| (QUOTE (-962)))) (|HasAttribute| |#3| (QUOTE -3994)) (-12 (|HasCategory| |#3| (QUOTE (-190))) (|HasCategory| |#3| (QUOTE (-962))))) (-12 (|HasCategory| |#3| (QUOTE (-189))) (|HasCategory| |#3| (QUOTE (-962)))) (-12 (|HasCategory| |#3| (QUOTE (-812 (-1091)))) (|HasCategory| |#3| (QUOTE (-962)))) (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-104))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-553 (-773)))) (-12 (|HasCategory| |#3| (QUOTE (-1014))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#3|))))) 
+((-3993 OR (-2563 (|has| |#3| (-961)) (|has| |#3| (-190))) (|has| |#3| (-6 -3993)) (-2563 (|has| |#3| (-961)) (|has| |#3| (-809 (-1090))))) (-3990 |has| |#3| (-961)) (-3991 |has| |#3| (-961))) 
+((OR (-12 (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-190))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-320))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-663))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-717))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-756))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-809 (-1090)))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-961))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1013))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|))))) (|HasCategory| |#3| (QUOTE (-312))) (OR (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (QUOTE (-961)))) (OR (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-312)))) (|HasCategory| |#3| (QUOTE (-961))) (|HasCategory| |#3| (QUOTE (-663))) (|HasCategory| |#3| (QUOTE (-717))) (OR (|HasCategory| |#3| (QUOTE (-717))) (|HasCategory| |#3| (QUOTE (-756)))) (|HasCategory| |#3| (QUOTE (-756))) (|HasCategory| |#3| (QUOTE (-320))) (OR (-12 (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-580 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-190))) (|HasCategory| |#3| (QUOTE (-580 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (QUOTE (-580 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-580 (-484)))) (|HasCategory| |#3| (QUOTE (-809 (-1090))))) (-12 (|HasCategory| |#3| (QUOTE (-580 (-484)))) (|HasCategory| |#3| (QUOTE (-961))))) (|HasCategory| |#3| (QUOTE (-809 (-1090)))) (OR (|HasCategory| |#3| (QUOTE (-190))) (|HasCategory| |#3| (QUOTE (-809 (-1090)))) (|HasCategory| |#3| (QUOTE (-961)))) (|HasCategory| |#3| (QUOTE (-190))) (OR (|HasCategory| |#3| (QUOTE (-190))) (-12 (|HasCategory| |#3| (QUOTE (-189))) (|HasCategory| |#3| (QUOTE (-961))))) (OR (-12 (|HasCategory| |#3| (QUOTE (-811 (-1090)))) (|HasCategory| |#3| (QUOTE (-961)))) (|HasCategory| |#3| (QUOTE (-809 (-1090))))) (|HasCategory| |#3| (QUOTE (-1013))) (OR (-12 (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-950 (-350 (-484)))))) (-12 (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-950 (-350 (-484)))))) (-12 (|HasCategory| |#3| (QUOTE (-190))) (|HasCategory| |#3| (QUOTE (-950 (-350 (-484)))))) (-12 (|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (QUOTE (-950 (-350 (-484)))))) (-12 (|HasCategory| |#3| (QUOTE (-320))) (|HasCategory| |#3| (QUOTE (-950 (-350 (-484)))))) (-12 (|HasCategory| |#3| (QUOTE (-663))) (|HasCategory| |#3| (QUOTE (-950 (-350 (-484)))))) (-12 (|HasCategory| |#3| (QUOTE (-717))) (|HasCategory| |#3| (QUOTE (-950 (-350 (-484)))))) (-12 (|HasCategory| |#3| (QUOTE (-756))) (|HasCategory| |#3| (QUOTE (-950 (-350 (-484)))))) (-12 (|HasCategory| |#3| (QUOTE (-809 (-1090)))) (|HasCategory| |#3| (QUOTE (-950 (-350 (-484)))))) (-12 (|HasCategory| |#3| (QUOTE (-950 (-350 (-484))))) (|HasCategory| |#3| (QUOTE (-961)))) (-12 (|HasCategory| |#3| (QUOTE (-950 (-350 (-484))))) (|HasCategory| |#3| (QUOTE (-1013))))) (OR (-12 (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-190))) (|HasCategory| |#3| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-717))) (|HasCategory| |#3| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-756))) (|HasCategory| |#3| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-809 (-1090)))) (|HasCategory| |#3| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-950 (-484)))) (|HasCategory| |#3| (QUOTE (-1013)))) (-12 (|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-320))) (|HasCategory| |#3| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-663))) (|HasCategory| |#3| (QUOTE (-950 (-484))))) (|HasCategory| |#3| (QUOTE (-961)))) (OR (-12 (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-190))) (|HasCategory| |#3| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-717))) (|HasCategory| |#3| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-756))) (|HasCategory| |#3| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-809 (-1090)))) (|HasCategory| |#3| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-950 (-484)))) (|HasCategory| |#3| (QUOTE (-1013)))) (-12 (|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-320))) (|HasCategory| |#3| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-663))) (|HasCategory| |#3| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-950 (-484)))) (|HasCategory| |#3| (QUOTE (-961))))) (|HasCategory| |#3| (QUOTE (-72))) (|HasCategory| (-484) (QUOTE (-756))) (-12 (|HasCategory| |#3| (QUOTE (-580 (-484)))) (|HasCategory| |#3| (QUOTE (-961)))) (OR (-12 (|HasCategory| |#3| (QUOTE (-809 (-1090)))) (|HasCategory| |#3| (QUOTE (-961)))) (-12 (|HasCategory| |#3| (QUOTE (-811 (-1090)))) (|HasCategory| |#3| (QUOTE (-961))))) (OR (-12 (|HasCategory| |#3| (QUOTE (-190))) (|HasCategory| |#3| (QUOTE (-961)))) (-12 (|HasCategory| |#3| (QUOTE (-189))) (|HasCategory| |#3| (QUOTE (-961))))) (-12 (|HasCategory| |#3| (QUOTE (-950 (-484)))) (|HasCategory| |#3| (QUOTE (-1013)))) (OR (-12 (|HasCategory| |#3| (QUOTE (-950 (-484)))) (|HasCategory| |#3| (QUOTE (-1013)))) (|HasCategory| |#3| (QUOTE (-961)))) (-12 (|HasCategory| |#3| (QUOTE (-950 (-350 (-484))))) (|HasCategory| |#3| (QUOTE (-1013)))) (OR (-12 (|HasCategory| |#3| (QUOTE (-809 (-1090)))) (|HasCategory| |#3| (QUOTE (-961)))) (|HasAttribute| |#3| (QUOTE -3993)) (-12 (|HasCategory| |#3| (QUOTE (-190))) (|HasCategory| |#3| (QUOTE (-961))))) (-12 (|HasCategory| |#3| (QUOTE (-189))) (|HasCategory| |#3| (QUOTE (-961)))) (-12 (|HasCategory| |#3| (QUOTE (-811 (-1090)))) (|HasCategory| |#3| (QUOTE (-961)))) (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-104))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-552 (-772)))) (-12 (|HasCategory| |#3| (QUOTE (-1013))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#3|))))) 
 (-212 A R S V E) 
 ((|constructor| (NIL "\\spadtype{DifferentialPolynomialCategory} is a category constructor specifying basic functions in an ordinary differential polynomial ring with a given ordered set of differential indeterminates. In addition,{} it implements defaults for the basic functions. The functions \\spadfun{order} and \\spadfun{weight} are extended from the set of derivatives of differential indeterminates to the set of differential polynomials. Other operations provided on differential polynomials are \\spadfun{leader},{} \\spadfun{initial},{} \\spadfun{separant},{} \\spadfun{differentialVariables},{} and \\spadfun{isobaric?}. Furthermore,{} if the ground ring is a differential ring,{} then evaluation (substitution of differential indeterminates by elements of the ground ring or by differential polynomials) is provided by \\spadfun{eval}. A convenient way of referencing derivatives is provided by the functions \\spadfun{makeVariable}. \\blankline To construct a domain using this constructor,{} one needs to provide a ground ring \\spad{R},{} an ordered set \\spad{S} of differential indeterminates,{} a ranking \\spad{V} on the set of derivatives of the differential indeterminates,{} and a set \\spad{E} of exponents in bijection with the set of differential monomials in the given differential indeterminates. \\blankline")) (|separant| (($ $) "\\spad{separant(p)} returns the partial derivative of the differential polynomial \\spad{p} with respect to its leader.")) (|initial| (($ $) "\\spad{initial(p)} returns the leading coefficient when the differential polynomial \\spad{p} is written as a univariate polynomial in its leader.")) (|leader| ((|#4| $) "\\spad{leader(p)} returns the derivative of the highest rank appearing in the differential polynomial \\spad{p} Note: an error occurs if \\spad{p} is in the ground ring.")) (|isobaric?| (((|Boolean|) $) "\\spad{isobaric?(p)} returns \\spad{true} if every differential monomial appearing in the differential polynomial \\spad{p} has same weight,{} and returns \\spad{false} otherwise.")) (|weight| (((|NonNegativeInteger|) $ |#3|) "\\spad{weight(p, s)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|NonNegativeInteger|) $) "\\spad{weight(p)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p}.")) (|weights| (((|List| (|NonNegativeInteger|)) $ |#3|) "\\spad{weights(p, s)} returns a list of weights of differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|List| (|NonNegativeInteger|)) $) "\\spad{weights(p)} returns a list of weights of differential monomials appearing in differential polynomial \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $ |#3|) "\\spad{degree(p, s)} returns the maximum degree of the differential polynomial \\spad{p} viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of the differential polynomial \\spad{p},{} which is the maximum number of differentiations of a differential indeterminate,{} among all those appearing in \\spad{p}.") (((|NonNegativeInteger|) $ |#3|) "\\spad{order(p,s)} returns the order of the differential polynomial \\spad{p} in differential indeterminate \\spad{s}.")) (|differentialVariables| (((|List| |#3|) $) "\\spad{differentialVariables(p)} returns a list of differential indeterminates occurring in a differential polynomial \\spad{p}.")) (|makeVariable| (((|Mapping| $ (|NonNegativeInteger|)) $) "\\spad{makeVariable(p)} views \\spad{p} as an element of a differential ring,{} in such a way that the \\spad{n}-th derivative of \\spad{p} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} := makeVariable(\\spad{p}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored.") (((|Mapping| $ (|NonNegativeInteger|)) |#3|) "\\spad{makeVariable(s)} views \\spad{s} as a differential indeterminate,{} in such a way that the \\spad{n}-th derivative of \\spad{s} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} :=makeVariable(\\spad{s}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored."))) 
 NIL 
 ((|HasCategory| |#2| (QUOTE (-190)))) 
 (-213 R S V E) 
 ((|constructor| (NIL "\\spadtype{DifferentialPolynomialCategory} is a category constructor specifying basic functions in an ordinary differential polynomial ring with a given ordered set of differential indeterminates. In addition,{} it implements defaults for the basic functions. The functions \\spadfun{order} and \\spadfun{weight} are extended from the set of derivatives of differential indeterminates to the set of differential polynomials. Other operations provided on differential polynomials are \\spadfun{leader},{} \\spadfun{initial},{} \\spadfun{separant},{} \\spadfun{differentialVariables},{} and \\spadfun{isobaric?}. Furthermore,{} if the ground ring is a differential ring,{} then evaluation (substitution of differential indeterminates by elements of the ground ring or by differential polynomials) is provided by \\spadfun{eval}. A convenient way of referencing derivatives is provided by the functions \\spadfun{makeVariable}. \\blankline To construct a domain using this constructor,{} one needs to provide a ground ring \\spad{R},{} an ordered set \\spad{S} of differential indeterminates,{} a ranking \\spad{V} on the set of derivatives of the differential indeterminates,{} and a set \\spad{E} of exponents in bijection with the set of differential monomials in the given differential indeterminates. \\blankline")) (|separant| (($ $) "\\spad{separant(p)} returns the partial derivative of the differential polynomial \\spad{p} with respect to its leader.")) (|initial| (($ $) "\\spad{initial(p)} returns the leading coefficient when the differential polynomial \\spad{p} is written as a univariate polynomial in its leader.")) (|leader| ((|#3| $) "\\spad{leader(p)} returns the derivative of the highest rank appearing in the differential polynomial \\spad{p} Note: an error occurs if \\spad{p} is in the ground ring.")) (|isobaric?| (((|Boolean|) $) "\\spad{isobaric?(p)} returns \\spad{true} if every differential monomial appearing in the differential polynomial \\spad{p} has same weight,{} and returns \\spad{false} otherwise.")) (|weight| (((|NonNegativeInteger|) $ |#2|) "\\spad{weight(p, s)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|NonNegativeInteger|) $) "\\spad{weight(p)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p}.")) (|weights| (((|List| (|NonNegativeInteger|)) $ |#2|) "\\spad{weights(p, s)} returns a list of weights of differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|List| (|NonNegativeInteger|)) $) "\\spad{weights(p)} returns a list of weights of differential monomials appearing in differential polynomial \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $ |#2|) "\\spad{degree(p, s)} returns the maximum degree of the differential polynomial \\spad{p} viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of the differential polynomial \\spad{p},{} which is the maximum number of differentiations of a differential indeterminate,{} among all those appearing in \\spad{p}.") (((|NonNegativeInteger|) $ |#2|) "\\spad{order(p,s)} returns the order of the differential polynomial \\spad{p} in differential indeterminate \\spad{s}.")) (|differentialVariables| (((|List| |#2|) $) "\\spad{differentialVariables(p)} returns a list of differential indeterminates occurring in a differential polynomial \\spad{p}.")) (|makeVariable| (((|Mapping| $ (|NonNegativeInteger|)) $) "\\spad{makeVariable(p)} views \\spad{p} as an element of a differential ring,{} in such a way that the \\spad{n}-th derivative of \\spad{p} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} := makeVariable(\\spad{p}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored.") (((|Mapping| $ (|NonNegativeInteger|)) |#2|) "\\spad{makeVariable(s)} views \\spad{s} as a differential indeterminate,{} in such a way that the \\spad{n}-th derivative of \\spad{s} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} :=makeVariable(\\spad{s}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored."))) 
-(((-3999 "*") |has| |#1| (-146)) (-3990 |has| |#1| (-496)) (-3995 |has| |#1| (-6 -3995)) (-3992 . T) (-3991 . T) (-3994 . T)) 
+(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-495)) (-3994 |has| |#1| (-6 -3994)) (-3991 . T) (-3990 . T) (-3993 . T)) 
 NIL 
 (-214 S) 
 ((|constructor| (NIL "A dequeue is a doubly ended stack,{} that is,{} a bag where first items inserted are the first items extracted,{} at either the front or the back end of the data structure.")) (|reverse!| (($ $) "\\spad{reverse!(d)} destructively replaces \\spad{d} by its reverse dequeue,{} \\spadignore{i.e.} the top (front) element is now the bottom (back) element,{} and so on.")) (|extractBottom!| ((|#1| $) "\\spad{extractBottom!(d)} destructively extracts the bottom (back) element from the dequeue \\spad{d}. Error: if \\spad{d} is empty.")) (|extractTop!| ((|#1| $) "\\spad{extractTop!(d)} destructively extracts the top (front) element from the dequeue \\spad{d}. Error: if \\spad{d} is empty.")) (|insertBottom!| ((|#1| |#1| $) "\\spad{insertBottom!(x,d)} destructively inserts \\spad{x} into the dequeue \\spad{d} at the bottom (back) of the dequeue.")) (|insertTop!| ((|#1| |#1| $) "\\spad{insertTop!(x,d)} destructively inserts \\spad{x} into the dequeue \\spad{d},{} that is,{} at the top (front) of the dequeue. The element previously at the top of the dequeue becomes the second in the dequeue,{} and so on.")) (|bottom!| ((|#1| $) "\\spad{bottom!(d)} returns the element at the bottom (back) of the dequeue.")) (|top!| ((|#1| $) "\\spad{top!(d)} returns the element at the top (front) of the dequeue.")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(d)} returns the number of elements in dequeue \\spad{d}. Note: \\axiom{height(\\spad{d}) = \\# \\spad{d}}.")) (|dequeue| (($ (|List| |#1|)) "\\spad{dequeue([x,y,...,z])} creates a dequeue with first (top or front) element \\spad{x},{} second element \\spad{y},{}...,{}and last (bottom or back) element \\spad{z}.") (($) "\\spad{dequeue()}\\$\\spad{D} creates an empty dequeue of type \\spad{D}."))) 
-((-3998 . T)) 
+((-3997 . T)) 
 NIL 
 (-215 |Ex|) 
 ((|constructor| (NIL "TopLevelDrawFunctions provides top level functions for drawing graphics of expressions.")) (|makeObject| (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSurface| |#1|) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|))) "\\spad{makeObject(surface(f(u,v),g(u,v),h(u,v)),u = a..b,v = c..d)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{x = f(u,v)},{} \\spad{y = g(u,v)},{} \\spad{z = h(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{h(t)} is the default title.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSurface| |#1|) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(surface(f(u,v),g(u,v),h(u,v)),u = a..b,v = c..d,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{x = f(u,v)},{} \\spad{y = g(u,v)},{} \\spad{z = h(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{h(t)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) |#1| (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|))) "\\spad{makeObject(f(x,y),x = a..b,y = c..d)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of \\spad{z = f(x,y)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{y} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{f(x,y)} appears as the default title.") (((|ThreeSpace| (|DoubleFloat|)) |#1| (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(f(x,y),x = a..b,y = c..d,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of \\spad{z = f(x,y)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{y} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{f(x,y)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSpaceCurve| |#1|) (|SegmentBinding| (|Float|))) "\\spad{makeObject(curve(f(t),g(t),h(t)),t = a..b)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{h(t)} is the default title.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSpaceCurve| |#1|) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(curve(f(t),g(t),h(t)),t = a..b,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{h(t)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.")) (|draw| (((|ThreeDimensionalViewport|) (|ParametricSurface| |#1|) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|))) "\\spad{draw(surface(f(u,v),g(u,v),h(u,v)),u = a..b,v = c..d)} draws the graph of the parametric surface \\spad{x = f(u,v)},{} \\spad{y = g(u,v)},{} \\spad{z = h(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{h(t)} is the default title.") (((|ThreeDimensionalViewport|) (|ParametricSurface| |#1|) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(surface(f(u,v),g(u,v),h(u,v)),u = a..b,v = c..d,l)} draws the graph of the parametric surface \\spad{x = f(u,v)},{} \\spad{y = g(u,v)},{} \\spad{z = h(u,v)} as \\spad{u} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{v} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{h(t)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) |#1| (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|))) "\\spad{draw(f(x,y),x = a..b,y = c..d)} draws the graph of \\spad{z = f(x,y)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{y} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{f(x,y)} appears in the title bar.") (((|ThreeDimensionalViewport|) |#1| (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f(x,y),x = a..b,y = c..d,l)} draws the graph of \\spad{z = f(x,y)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)} and \\spad{y} ranges from \\spad{min(c,d)} to \\spad{max(c,d)}; \\spad{f(x,y)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|ParametricSpaceCurve| |#1|) (|SegmentBinding| (|Float|))) "\\spad{draw(curve(f(t),g(t),h(t)),t = a..b)} draws the graph of the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{h(t)} is the default title.") (((|ThreeDimensionalViewport|) (|ParametricSpaceCurve| |#1|) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(curve(f(t),g(t),h(t)),t = a..b,l)} draws the graph of the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{h(t)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) (|ParametricPlaneCurve| |#1|) (|SegmentBinding| (|Float|))) "\\spad{draw(curve(f(t),g(t)),t = a..b)} draws the graph of the parametric curve \\spad{x = f(t), y = g(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{(f(t),g(t))} appears in the title bar.") (((|TwoDimensionalViewport|) (|ParametricPlaneCurve| |#1|) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(curve(f(t),g(t)),t = a..b,l)} draws the graph of the parametric curve \\spad{x = f(t), y = g(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{(f(t),g(t))} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) |#1| (|SegmentBinding| (|Float|))) "\\spad{draw(f(x),x = a..b)} draws the graph of \\spad{y = f(x)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{f(x)} appears in the title bar.") (((|TwoDimensionalViewport|) |#1| (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f(x),x = a..b,l)} draws the graph of \\spad{y = f(x)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{f(x)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied."))) 
@@ -827,15 +827,15 @@ NIL
 (-224 S R) 
 ((|constructor| (NIL "Extension of a base differential space with a derivation. \\blankline")) (D (($ $ (|Mapping| |#2| |#2|) (|NonNegativeInteger|)) "\\spad{D(x,d,n)} is a shorthand for \\spad{differentiate(x,d,n)}.") (($ $ (|Mapping| |#2| |#2|)) "\\spad{D(x,d)} is a shorthand for \\spad{differentiate(x,d)}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|) (|NonNegativeInteger|)) "\\spad{differentiate(x,d,n)} computes the \\spad{n}\\spad{-}th derivative of \\spad{x} using a derivation extending \\spad{d} on \\spad{R}.") (($ $ (|Mapping| |#2| |#2|)) "\\spad{differentiate(x,d)} computes the derivative of \\spad{x},{} extending differentiation \\spad{d} on \\spad{R}."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-812 (-1091)))) (|HasCategory| |#2| (QUOTE (-189)))) 
+((|HasCategory| |#2| (QUOTE (-811 (-1090)))) (|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"))) 
-(((-3999 "*") |has| |#1| (-146)) (-3990 |has| |#1| (-496)) (-3995 |has| |#1| (-6 -3995)) (-3992 . T) (-3991 . T) (-3994 . T)) 
-((|HasCategory| |#1| (QUOTE (-822))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-822)))) (OR (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-822)))) (OR (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-822)))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (-12 (|HasCategory| |#1| (QUOTE (-797 (-330)))) (|HasCategory| |#3| (QUOTE (-797 (-330))))) (-12 (|HasCategory| |#1| (QUOTE (-797 (-485)))) (|HasCategory| |#3| (QUOTE (-797 (-485))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-330))))) (|HasCategory| |#3| (QUOTE (-554 (-801 (-330)))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-485))))) (|HasCategory| |#3| (QUOTE (-554 (-801 (-485)))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-474)))) (|HasCategory| |#3| (QUOTE (-554 (-474))))) (|HasCategory| |#1| (QUOTE (-581 (-485)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485)))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-812 (-1091)))) (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasAttribute| |#1| (QUOTE -3995)) (|HasCategory| |#1| (QUOTE (-392))) (-12 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) 
+(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-495)) (-3994 |has| |#1| (-6 -3994)) (-3991 . T) (-3990 . T) (-3993 . T)) 
+((|HasCategory| |#1| (QUOTE (-821))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-821)))) (OR (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-821)))) (OR (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-821)))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-495)))) (-12 (|HasCategory| |#1| (QUOTE (-796 (-330)))) (|HasCategory| |#3| (QUOTE (-796 (-330))))) (-12 (|HasCategory| |#1| (QUOTE (-796 (-484)))) (|HasCategory| |#3| (QUOTE (-796 (-484))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-800 (-330))))) (|HasCategory| |#3| (QUOTE (-553 (-800 (-330)))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-800 (-484))))) (|HasCategory| |#3| (QUOTE (-553 (-800 (-484)))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-473)))) (|HasCategory| |#3| (QUOTE (-553 (-473))))) (|HasCategory| |#1| (QUOTE (-580 (-484)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-484)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484)))))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-811 (-1090)))) (|HasCategory| |#1| (QUOTE (-809 (-1090)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasAttribute| |#1| (QUOTE -3994)) (|HasCategory| |#1| (QUOTE (-392))) (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-821))) (|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 -3094) 
+(-230 R -3093) 
 ((|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 -3094) 
+(-231 R -3093) 
 ((|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 (-757))) (|HasCategory| |#2| (QUOTE (-72)))) 
+((|HasCategory| |#2| (QUOTE (-756))) (|HasCategory| |#2| (QUOTE (-72)))) 
 (-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}."))) 
-((-3998 . T)) 
+((-3997 . T)) 
 NIL 
 (-238 S) 
 ((|constructor| (NIL "Category for the elementary functions.")) (** (($ $ $) "\\spad{x**y} returns \\spad{x} to the power \\spad{y}.")) (|exp| (($ $) "\\spad{exp(x)} returns \\%\\spad{e} to the power \\spad{x}.")) (|log| (($ $) "\\spad{log(x)} returns the natural logarithm of \\spad{x}."))) 
@@ -899,14 +899,14 @@ 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 -3998))) 
+((|HasAttribute| |#1| (QUOTE -3997))) 
 (-243 |Dom| |Im|) 
 ((|constructor| (NIL "An eltable aggregate is one which can be viewed as a function. For example,{} the list \\axiom{[1,{}7,{}4]} can applied to 0,{}1,{} and 2 respectively will return the integers 1,{}7,{} and 4; thus this list may be viewed as mapping 0 to 1,{} 1 to 7 and 2 to 4. In general,{} an aggregate can map members of a domain {\\em Dom} to an image domain {\\em Im}.")) (|qsetelt!| ((|#2| $ |#1| |#2|) "\\spad{qsetelt!(u,x,y)} sets the image of \\axiom{\\spad{x}} to be \\axiom{\\spad{y}} under \\axiom{\\spad{u}},{} without checking that \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If such a check is required use the function \\axiom{setelt}.")) (|setelt| ((|#2| $ |#1| |#2|) "\\spad{setelt(u,x,y)} sets the image of \\spad{x} to be \\spad{y} under \\spad{u},{} assuming \\spad{x} is in the domain of \\spad{u}. Error: if \\spad{x} is not in the domain of \\spad{u}.")) (|qelt| ((|#2| $ |#1|) "\\spad{qelt(u, x)} applies \\axiom{\\spad{u}} to \\axiom{\\spad{x}} without checking whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If \\axiom{\\spad{x}} is not in the domain of \\axiom{\\spad{u}} a memory-access violation may occur. If a check on whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}} is required,{} use the function \\axiom{elt}.")) (|elt| ((|#2| $ |#1| |#2|) "\\spad{elt(u, x, y)} applies \\spad{u} to \\spad{x} if \\spad{x} is in the domain of \\spad{u},{} and returns \\spad{y} otherwise. For example,{} if \\spad{u} is a polynomial in \\axiom{\\spad{x}} over the rationals,{} \\axiom{elt(\\spad{u},{}\\spad{n},{}0)} may define the coefficient of \\axiom{\\spad{x}} to the power \\spad{n},{} returning 0 when \\spad{n} is out of range."))) 
 NIL 
 NIL 
-(-244 S R |Mod| -2038 -3520 |exactQuo|) 
+(-244 S R |Mod| -2037 -3519 |exactQuo|) 
 ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{ModularRing},{} \\spadtype{ModularField}")) (|inv| (($ $) "\\spad{inv(x)} \\undocumented")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} \\undocumented")) (|exQuo| (((|Union| $ "failed") $ $) "\\spad{exQuo(x,y)} \\undocumented")) (|reduce| (($ |#2| |#3|) "\\spad{reduce(r,m)} \\undocumented")) (|coerce| ((|#2| $) "\\spad{coerce(x)} \\undocumented")) (|modulus| ((|#3| $) "\\spad{modulus(x)} \\undocumented"))) 
-((-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
 NIL 
 (-245 S) 
 ((|constructor| (NIL "Entire Rings (non-commutative Integral Domains),{} \\spadignore{i.e.} a ring not necessarily commutative which has no zero divisors. \\blankline")) (|noZeroDivisors| ((|attribute|) "if a product is zero then one of the factors must be zero."))) 
@@ -914,7 +914,7 @@ NIL
 NIL 
 (-246) 
 ((|constructor| (NIL "Entire Rings (non-commutative Integral Domains),{} \\spadignore{i.e.} a ring not necessarily commutative which has no zero divisors. \\blankline")) (|noZeroDivisors| ((|attribute|) "if a product is zero then one of the factors must be zero."))) 
-((-3990 . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((-3989 . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
 NIL 
 (-247) 
 ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: March 18,{} 2010. An `Environment' is a stack of scope.")) (|categoryFrame| (($) "the current category environment in the interpreter.")) (|interactiveEnv| (($) "the current interactive environment in effect.")) (|currentEnv| (($) "the current normal environment in effect.")) (|putProperties| (($ (|Identifier|) (|List| (|Property|)) $) "\\spad{putProperties(n,props,e)} set the list of properties of \\spad{n} to \\spad{props} in \\spad{e}.")) (|getProperties| (((|List| (|Property|)) (|Identifier|) $) "\\spad{getBinding(n,e)} returns the list of properties of \\spad{n} in \\spad{e}.")) (|putProperty| (($ (|Identifier|) (|Identifier|) (|SExpression|) $) "\\spad{putProperty(n,p,v,e)} binds the property \\spad{(p,v)} to \\spad{n} in the topmost scope of \\spad{e}.")) (|getProperty| (((|Maybe| (|SExpression|)) (|Identifier|) (|Identifier|) $) "\\spad{getProperty(n,p,e)} returns the value of property with name \\spad{p} for the symbol \\spad{n} in environment \\spad{e}. Otherwise,{} \\spad{nothing}.")) (|scopes| (((|List| (|Scope|)) $) "\\spad{scopes(e)} returns the stack of scopes in environment \\spad{e}.")) (|empty| (($) "\\spad{empty()} constructs an empty environment"))) 
@@ -926,16 +926,16 @@ NIL
 NIL 
 (-249 S) 
 ((|constructor| (NIL "Equations as mathematical objects. All properties of the basis domain,{} \\spadignore{e.g.} being an abelian group are carried over the equation domain,{} by performing the structural operations on the left and on the right hand side.")) (|subst| (($ $ $) "\\spad{subst(eq1,eq2)} substitutes \\spad{eq2} into both sides of \\spad{eq1} the lhs of \\spad{eq2} should be a kernel")) (|inv| (($ $) "\\spad{inv(x)} returns the multiplicative inverse of \\spad{x}.")) (/ (($ $ $) "\\spad{e1/e2} produces a new equation by dividing the left and right hand sides of equations \\spad{e1} and \\spad{e2}.")) (|factorAndSplit| (((|List| $) $) "\\spad{factorAndSplit(eq)} make the right hand side 0 and factors the new left hand side. Each factor is equated to 0 and put into the resulting list without repetitions.")) (|rightOne| (((|Union| $ "failed") $) "\\spad{rightOne(eq)} divides by the right hand side.") (((|Union| $ "failed") $) "\\spad{rightOne(eq)} divides by the right hand side,{} if possible.")) (|leftOne| (((|Union| $ "failed") $) "\\spad{leftOne(eq)} divides by the left hand side.") (((|Union| $ "failed") $) "\\spad{leftOne(eq)} divides by the left hand side,{} if possible.")) (* (($ $ |#1|) "\\spad{eqn*x} produces a new equation by multiplying both sides of equation eqn by \\spad{x}.") (($ |#1| $) "\\spad{x*eqn} produces a new equation by multiplying both sides of equation eqn by \\spad{x}.")) (- (($ $ |#1|) "\\spad{eqn-x} produces a new equation by subtracting \\spad{x} from both sides of equation eqn.") (($ |#1| $) "\\spad{x-eqn} produces a new equation by subtracting both sides of equation eqn from \\spad{x}.")) (|rightZero| (($ $) "\\spad{rightZero(eq)} subtracts the right hand side.")) (|leftZero| (($ $) "\\spad{leftZero(eq)} subtracts the left hand side.")) (+ (($ $ |#1|) "\\spad{eqn+x} produces a new equation by adding \\spad{x} to both sides of equation eqn.") (($ |#1| $) "\\spad{x+eqn} produces a new equation by adding \\spad{x} to both sides of equation eqn.")) (|eval| (($ $ (|List| $)) "\\spad{eval(eqn, [x1=v1, ... xn=vn])} replaces \\spad{xi} by \\spad{vi} in equation \\spad{eqn}.") (($ $ $) "\\spad{eval(eqn, x=f)} replaces \\spad{x} by \\spad{f} in equation \\spad{eqn}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,eqn)} constructs a new equation by applying \\spad{f} to both sides of \\spad{eqn}.")) (|rhs| ((|#1| $) "\\spad{rhs(eqn)} returns the right hand side of equation \\spad{eqn}.")) (|lhs| ((|#1| $) "\\spad{lhs(eqn)} returns the left hand side of equation \\spad{eqn}.")) (|swap| (($ $) "\\spad{swap(eq)} interchanges left and right hand side of equation \\spad{eq}.")) (|equation| (($ |#1| |#1|) "\\spad{equation(a,b)} creates an equation.")) (= (($ |#1| |#1|) "\\spad{a=b} creates an equation."))) 
-((-3994 OR (|has| |#1| (-962)) (|has| |#1| (-413))) (-3991 |has| |#1| (-962)) (-3992 |has| |#1| (-962))) 
-((|HasCategory| |#1| (QUOTE (-312))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-962)))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-962))) (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (OR (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasCategory| |#1| (QUOTE (-962)))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasCategory| |#1| (QUOTE (-962)))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasCategory| |#1| (QUOTE (-962)))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-962)))) (OR (|HasCategory| |#1| (QUOTE (-413))) (|HasCategory| |#1| (QUOTE (-664)))) (|HasCategory| |#1| (QUOTE (-413))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-413))) (|HasCategory| |#1| (QUOTE (-664))) (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasCategory| |#1| (QUOTE (-962))) (|HasCategory| |#1| (QUOTE (-1026))) (|HasCategory| |#1| (QUOTE (-1014)))) (OR (|HasCategory| |#1| (QUOTE (-413))) (|HasCategory| |#1| (QUOTE (-664))) (|HasCategory| |#1| (QUOTE (-1026)))) (|HasCategory| |#1| (|%list| (QUOTE -456) (QUOTE (-1091)) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-254))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-413)))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-664)))) (OR (|HasCategory| |#1| (QUOTE (-413))) (|HasCategory| |#1| (QUOTE (-962)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1026))) (|HasCategory| |#1| (QUOTE (-664)))) 
+((-3993 OR (|has| |#1| (-961)) (|has| |#1| (-413))) (-3990 |has| |#1| (-961)) (-3991 |has| |#1| (-961))) 
+((|HasCategory| |#1| (QUOTE (-312))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-961)))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-961))) (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-809 (-1090)))) (OR (|HasCategory| |#1| (QUOTE (-809 (-1090)))) (|HasCategory| |#1| (QUOTE (-961)))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-809 (-1090)))) (|HasCategory| |#1| (QUOTE (-961)))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-809 (-1090)))) (|HasCategory| |#1| (QUOTE (-961)))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-961)))) (OR (|HasCategory| |#1| (QUOTE (-413))) (|HasCategory| |#1| (QUOTE (-663)))) (|HasCategory| |#1| (QUOTE (-413))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-413))) (|HasCategory| |#1| (QUOTE (-663))) (|HasCategory| |#1| (QUOTE (-809 (-1090)))) (|HasCategory| |#1| (QUOTE (-961))) (|HasCategory| |#1| (QUOTE (-1025))) (|HasCategory| |#1| (QUOTE (-1013)))) (OR (|HasCategory| |#1| (QUOTE (-413))) (|HasCategory| |#1| (QUOTE (-663))) (|HasCategory| |#1| (QUOTE (-1025)))) (|HasCategory| |#1| (|%list| (QUOTE -455) (QUOTE (-1090)) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-254))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-413)))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-663)))) (OR (|HasCategory| |#1| (QUOTE (-413))) (|HasCategory| |#1| (QUOTE (-961)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1025))) (|HasCategory| |#1| (QUOTE (-663)))) 
 (-250 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 
 (-251 |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."))) 
-((-3998 . T)) 
-((-12 (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3862) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-553 (-773))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-474)))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-72))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014))) (-12 (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3862) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3862) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (-12 (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#2|))))) 
+((-3997 . T)) 
+((-12 (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3861) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-552 (-772)))) (|HasCategory| |#2| (QUOTE (-552 (-772))))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-473)))) (-12 (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#2| (QUOTE (-72))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013))) (-12 (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3861) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3861) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (-12 (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#2|))))) 
 (-252) 
 ((|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 
@@ -943,16 +943,16 @@ NIL
 (-253 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 (-951 (-485)))) (|HasCategory| |#1| (QUOTE (-962)))) 
+((|HasCategory| |#1| (QUOTE (-950 (-484)))) (|HasCategory| |#1| (QUOTE (-961)))) 
 (-254) 
 ((|constructor| (NIL "An expression space is a set which is closed under certain operators.")) (|odd?| (((|Boolean|) $) "\\spad{odd? x} is \\spad{true} if \\spad{x} is an odd integer.")) (|even?| (((|Boolean|) $) "\\spad{even? x} is \\spad{true} if \\spad{x} is an even integer.")) (|definingPolynomial| (($ $) "\\spad{definingPolynomial(x)} returns an expression \\spad{p} such that \\spad{p(x) = 0}.")) (|minPoly| (((|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{minPoly(k)} returns \\spad{p} such that \\spad{p(k) = 0}.")) (|eval| (($ $ (|BasicOperator|) (|Mapping| $ $)) "\\spad{eval(x, s, f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|BasicOperator|) (|Mapping| $ (|List| $))) "\\spad{eval(x, s, f)} replaces every \\spad{s(a1,..,am)} in \\spad{x} by \\spad{f(a1,..,am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ $)) "\\spad{eval(x, s, f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ (|List| $))) "\\spad{eval(x, s, f)} replaces every \\spad{s(a1,..,am)} in \\spad{x} by \\spad{f(a1,..,am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.")) (|freeOf?| (((|Boolean|) $ (|Symbol|)) "\\spad{freeOf?(x, s)} tests if \\spad{x} does not contain any operator whose name is \\spad{s}.") (((|Boolean|) $ $) "\\spad{freeOf?(x, y)} tests if \\spad{x} does not contain any occurrence of \\spad{y},{} where \\spad{y} is a single kernel.")) (|map| (($ (|Mapping| $ $) (|Kernel| $)) "\\spad{map(f, k)} returns \\spad{op(f(x1),...,f(xn))} where \\spad{k = op(x1,...,xn)}.")) (|kernel| (($ (|BasicOperator|) (|List| $)) "\\spad{kernel(op, [f1,...,fn])} constructs \\spad{op(f1,...,fn)} without evaluating it.") (($ (|BasicOperator|) $) "\\spad{kernel(op, x)} constructs \\spad{op}(\\spad{x}) without evaluating it.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(x, s)} tests if \\spad{x} is a kernel and is the name of its operator is \\spad{s}.") (((|Boolean|) $ (|BasicOperator|)) "\\spad{is?(x, op)} tests if \\spad{x} is a kernel and is its operator is op.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} tests if \\% accepts \\spad{op} as applicable to its elements.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\%.")) (|operators| (((|List| (|BasicOperator|)) $) "\\spad{operators(f)} returns all the basic operators appearing in \\spad{f},{} no matter what their levels are.")) (|tower| (((|List| (|Kernel| $)) $) "\\spad{tower(f)} returns all the kernels appearing in \\spad{f},{} no matter what their levels are.")) (|kernels| (((|List| (|Kernel| $)) $) "\\spad{kernels(f)} returns the list of all the top-level kernels appearing in \\spad{f},{} but not the ones appearing in the arguments of the top-level kernels.")) (|mainKernel| (((|Union| (|Kernel| $) "failed") $) "\\spad{mainKernel(f)} returns a kernel of \\spad{f} with maximum nesting level,{} or if \\spad{f} has no kernels (\\spadignore{i.e.} \\spad{f} is a constant).")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(f)} returns the highest nesting level appearing in \\spad{f}. Constants have height 0. Symbols have height 1. For any operator op and expressions \\spad{f1},{}...,{}fn,{} \\spad{op(f1,...,fn)} has height equal to \\spad{1 + max(height(f1),...,height(fn))}.")) (|distribute| (($ $ $) "\\spad{distribute(f, g)} expands all the kernels in \\spad{f} that contain \\spad{g} in their arguments and that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or a \\spadfunFrom{paren}{ExpressionSpace} expression.") (($ $) "\\spad{distribute(f)} expands all the kernels in \\spad{f} that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or \\spadfunFrom{paren}{ExpressionSpace} expression.")) (|paren| (($ (|List| $)) "\\spad{paren([f1,...,fn])} returns \\spad{(f1,...,fn)}. This prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(paren [x, 2])} returns the formal kernel \\spad{atan((x, 2))}.") (($ $) "\\spad{paren(f)} returns (\\spad{f}). This prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(paren 1)} returns the formal kernel log((1)).")) (|box| (($ (|List| $)) "\\spad{box([f1,...,fn])} returns \\spad{(f1,...,fn)} with a 'box' around them that prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(box [x, 2])} returns the formal kernel \\spad{atan(x, 2)}.") (($ $) "\\spad{box(f)} returns \\spad{f} with a 'box' around it that prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(box 1)} returns the formal kernel log(1).")) (|subst| (($ $ (|List| (|Kernel| $)) (|List| $)) "\\spad{subst(f, [k1...,kn], [g1,...,gn])} replaces the kernels \\spad{k1},{}...,{}kn by \\spad{g1},{}...,{}gn formally in \\spad{f}.") (($ $ (|List| (|Equation| $))) "\\spad{subst(f, [k1 = g1,...,kn = gn])} replaces the kernels \\spad{k1},{}...,{}kn by \\spad{g1},{}...,{}gn formally in \\spad{f}.") (($ $ (|Equation| $)) "\\spad{subst(f, k = g)} replaces the kernel \\spad{k} by \\spad{g} formally in \\spad{f}.")) (|elt| (($ (|BasicOperator|) (|List| $)) "\\spad{elt(op,[x1,...,xn])} or \\spad{op}([\\spad{x1},{}...,{}xn]) applies the \\spad{n}-ary operator \\spad{op} to \\spad{x1},{}...,{}xn.") (($ (|BasicOperator|) $ $ $ $) "\\spad{elt(op,x,y,z,t)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z},{} \\spad{t}) applies the 4-ary operator \\spad{op} to \\spad{x},{} \\spad{y},{} \\spad{z} and \\spad{t}.") (($ (|BasicOperator|) $ $ $) "\\spad{elt(op,x,y,z)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z}) applies the ternary operator \\spad{op} to \\spad{x},{} \\spad{y} and \\spad{z}.") (($ (|BasicOperator|) $ $) "\\spad{elt(op,x,y)} or \\spad{op}(\\spad{x},{} \\spad{y}) applies the binary operator \\spad{op} to \\spad{x} and \\spad{y}.") (($ (|BasicOperator|) $) "\\spad{elt(op,x)} or \\spad{op}(\\spad{x}) applies the unary operator \\spad{op} to \\spad{x}."))) 
 NIL 
 NIL 
-(-255 -3094 S) 
+(-255 -3093 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 
-(-256 E -3094) 
+(-256 E -3093) 
 ((|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 
@@ -962,7 +962,7 @@ NIL
 NIL 
 (-258) 
 ((|constructor| (NIL "A constructive euclidean domain,{} \\spadignore{i.e.} one can divide producing a quotient and a remainder where the remainder is either zero or is smaller (\\spadfun{euclideanSize}) than the divisor. \\blankline Conditional attributes: \\indented{2}{multiplicativeValuation\\tab{25}\\spad{Size(a*b)=Size(a)*Size(b)}} \\indented{2}{additiveValuation\\tab{25}\\spad{Size(a*b)=Size(a)+Size(b)}}")) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) "\\spad{multiEuclidean([f1,...,fn],z)} returns a list of coefficients \\spad{[a1, ..., an]} such that \\spad{ z / prod fi = sum aj/fj}. If no such list of coefficients exists,{} \"failed\" is returned.")) (|extendedEuclidean| (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) "\\spad{extendedEuclidean(x,y,z)} either returns a record rec where \\spad{rec.coef1*x+rec.coef2*y=z} or returns \"failed\" if \\spad{z} cannot be expressed as a linear combination of \\spad{x} and \\spad{y}.") (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{extendedEuclidean(x,y)} returns a record rec where \\spad{rec.coef1*x+rec.coef2*y = rec.generator} and rec.generator is a gcd of \\spad{x} and \\spad{y}. The gcd is unique only up to associates if \\spadatt{canonicalUnitNormal} is not asserted. \\spadfun{principalIdeal} provides a version of this operation which accepts an arbitrary length list of arguments.")) (|rem| (($ $ $) "\\spad{x rem y} is the same as \\spad{divide(x,y).remainder}. See \\spadfunFrom{divide}{EuclideanDomain}.")) (|quo| (($ $ $) "\\spad{x quo y} is the same as \\spad{divide(x,y).quotient}. See \\spadfunFrom{divide}{EuclideanDomain}.")) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{divide(x,y)} divides \\spad{x} by \\spad{y} producing a record containing a \\spad{quotient} and \\spad{remainder},{} where the remainder is smaller (see \\spadfunFrom{sizeLess?}{EuclideanDomain}) than the divisor \\spad{y}.")) (|euclideanSize| (((|NonNegativeInteger|) $) "\\spad{euclideanSize(x)} returns the euclidean size of the element \\spad{x}. Error: if \\spad{x} is zero.")) (|sizeLess?| (((|Boolean|) $ $) "\\spad{sizeLess?(x,y)} tests whether \\spad{x} is strictly smaller than \\spad{y} with respect to the \\spadfunFrom{euclideanSize}{EuclideanDomain}."))) 
-((-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
 NIL 
 (-259 S R) 
 ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation'' substitutions.")) (|eval| (($ $ (|List| (|Equation| |#2|))) "\\spad{eval(f, [x1 = v1,...,xn = vn])} replaces \\spad{xi} by \\spad{vi} in \\spad{f}.") (($ $ (|Equation| |#2|)) "\\spad{eval(f,x = v)} replaces \\spad{x} by \\spad{v} in \\spad{f}."))) 
@@ -972,7 +972,7 @@ 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 
-(-261 -3094) 
+(-261 -3093) 
 ((|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 
@@ -986,12 +986,12 @@ NIL
 NIL 
 (-264 R FE |var| |cen|) 
 ((|constructor| (NIL "UnivariatePuiseuxSeriesWithExponentialSingularity is a domain used to represent essential singularities of functions. Objects in this domain are quotients of sums,{} where each term in the sum is a univariate Puiseux series times the exponential of a univariate Puiseux series.")) (|coerce| (($ (|UnivariatePuiseuxSeries| |#2| |#3| |#4|)) "\\spad{coerce(f)} converts a \\spadtype{UnivariatePuiseuxSeries} to an \\spadtype{ExponentialExpansion}.")) (|limitPlus| (((|Union| (|OrderedCompletion| |#2|) "failed") $) "\\spad{limitPlus(f(var))} returns \\spad{limit(var -> a+,f(var))}."))) 
-((-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
-((|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-822))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-951 (-1091)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-118))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-120))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-554 (-474)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-934))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-741))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-757))) (OR (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-741))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-757)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-951 (-485)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-1067))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-797 (-330)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-797 (-485)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-554 (-801 (-330))))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-554 (-801 (-485))))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-581 (-485)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-189))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-812 (-1091)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-190))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-810 (-1091)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -456) (QUOTE (-1091)) (|%list| (QUOTE -1167) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -260) (|%list| (QUOTE -1167) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -241) (|%list| (QUOTE -1167) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (|%list| (QUOTE -1167) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-258))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-484))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-822)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-822)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-118))))) 
+((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (QUOTE (-821))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (QUOTE (-950 (-1090)))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (QUOTE (-118))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (QUOTE (-120))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (QUOTE (-553 (-473)))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (QUOTE (-933))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (QUOTE (-740))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (QUOTE (-756))) (OR (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (QUOTE (-740))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (QUOTE (-756)))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (QUOTE (-950 (-484)))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (QUOTE (-1066))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (QUOTE (-796 (-330)))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (QUOTE (-796 (-484)))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (QUOTE (-553 (-800 (-330))))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (QUOTE (-553 (-800 (-484))))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (QUOTE (-580 (-484)))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (QUOTE (-189))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (QUOTE (-811 (-1090)))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (QUOTE (-190))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (QUOTE (-809 (-1090)))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -455) (QUOTE (-1090)) (|%list| (QUOTE -1166) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -260) (|%list| (QUOTE -1166) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -241) (|%list| (QUOTE -1166) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (|%list| (QUOTE -1166) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (QUOTE (-258))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (QUOTE (-483))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (QUOTE (-821)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (QUOTE (-821)))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (QUOTE (-118))))) 
 (-265 R) 
 ((|constructor| (NIL "Expressions involving symbolic functions.")) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{squareFreePolynomial(p)} \\undocumented{}")) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorPolynomial(p)} \\undocumented{}")) (|simplifyPower| (($ $ (|Integer|)) "simplifyPower?(\\spad{f},{}\\spad{n}) \\undocumented{}")) (|number?| (((|Boolean|) $) "\\spad{number?(f)} tests if \\spad{f} is rational")) (|reduce| (($ $) "\\spad{reduce(f)} simplifies all the unreduced algebraic quantities present in \\spad{f} by applying their defining relations."))) 
-((-3994 OR (-12 (|has| |#1| (-496)) (OR (|has| |#1| (-962)) (|has| |#1| (-413)))) (|has| |#1| (-962)) (|has| |#1| (-413))) (-3992 |has| |#1| (-146)) (-3991 |has| |#1| (-146)) ((-3999 "*") |has| |#1| (-496)) (-3990 |has| |#1| (-496)) (-3995 |has| |#1| (-496)) (-3989 |has| |#1| (-496))) 
-((OR (-12 (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-951 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485)))))) (|HasCategory| |#1| (QUOTE (-496))) (OR (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-962)))) (|HasCategory| |#1| (QUOTE (-962))) (|HasCategory| |#1| (QUOTE (-21))) (OR (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485)))))) (|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 (-485))))) (-12 (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-581 (-485))))) (-12 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-581 (-485))))) (-12 (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-581 (-485))))) (-12 (|HasCategory| |#1| (QUOTE (-581 (-485)))) (|HasCategory| |#1| (QUOTE (-962))))) (OR (|HasCategory| |#1| (QUOTE (-413))) (|HasCategory| |#1| (QUOTE (-1026)))) (|HasCategory| |#1| (QUOTE (-413))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (OR (|HasCategory| |#1| (QUOTE (-951 (-485)))) (|HasCategory| |#1| (QUOTE (-962)))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (|HasCategory| |#1| (QUOTE (-797 (-330)))) (|HasCategory| |#1| (QUOTE (-797 (-485)))) (|HasCategory| |#1| (QUOTE (-554 (-801 (-330))))) (|HasCategory| |#1| (QUOTE (-554 (-801 (-485))))) (-12 (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-951 (-485))))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-962)))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-962)))) (OR (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-962)))) (-12 (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-496)))) (OR (|HasCategory| |#1| (QUOTE (-413))) (|HasCategory| |#1| (QUOTE (-496)))) (-12 (|HasCategory| |#1| (QUOTE (-581 (-485)))) (|HasCategory| |#1| (QUOTE (-962)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-581 (-485)))) (|HasCategory| |#1| (QUOTE (-962)))) (|HasCategory| |#1| (QUOTE (-21)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-581 (-485)))) (|HasCategory| |#1| (QUOTE (-962)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1026)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-581 (-485)))) (|HasCategory| |#1| (QUOTE (-962)))) (|HasCategory| |#1| (QUOTE (-25)))) (OR (|HasCategory| |#1| (QUOTE (-413))) (|HasCategory| |#1| (QUOTE (-962)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485)))))) (-12 (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-951 (-485)))))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1026))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485))))) (|HasCategory| $ (QUOTE (-962))) (|HasCategory| $ (QUOTE (-951 (-485))))) 
+((-3993 OR (-12 (|has| |#1| (-495)) (OR (|has| |#1| (-961)) (|has| |#1| (-413)))) (|has| |#1| (-961)) (|has| |#1| (-413))) (-3991 |has| |#1| (-146)) (-3990 |has| |#1| (-146)) ((-3998 "*") |has| |#1| (-495)) (-3989 |has| |#1| (-495)) (-3994 |has| |#1| (-495)) (-3988 |has| |#1| (-495))) 
+((OR (-12 (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-950 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484)))))) (|HasCategory| |#1| (QUOTE (-495))) (OR (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-961)))) (|HasCategory| |#1| (QUOTE (-961))) (|HasCategory| |#1| (QUOTE (-21))) (OR (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484)))))) (|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 (-484))))) (-12 (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-580 (-484))))) (-12 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-580 (-484))))) (-12 (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-580 (-484))))) (-12 (|HasCategory| |#1| (QUOTE (-580 (-484)))) (|HasCategory| |#1| (QUOTE (-961))))) (OR (|HasCategory| |#1| (QUOTE (-413))) (|HasCategory| |#1| (QUOTE (-1025)))) (|HasCategory| |#1| (QUOTE (-413))) (|HasCategory| |#1| (QUOTE (-553 (-473)))) (OR (|HasCategory| |#1| (QUOTE (-950 (-484)))) (|HasCategory| |#1| (QUOTE (-961)))) (|HasCategory| |#1| (QUOTE (-950 (-484)))) (|HasCategory| |#1| (QUOTE (-796 (-330)))) (|HasCategory| |#1| (QUOTE (-796 (-484)))) (|HasCategory| |#1| (QUOTE (-553 (-800 (-330))))) (|HasCategory| |#1| (QUOTE (-553 (-800 (-484))))) (-12 (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-950 (-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 (-961)))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-961)))) (OR (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-961)))) (-12 (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-495)))) (OR (|HasCategory| |#1| (QUOTE (-413))) (|HasCategory| |#1| (QUOTE (-495)))) (-12 (|HasCategory| |#1| (QUOTE (-580 (-484)))) (|HasCategory| |#1| (QUOTE (-961)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-580 (-484)))) (|HasCategory| |#1| (QUOTE (-961)))) (|HasCategory| |#1| (QUOTE (-21)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-580 (-484)))) (|HasCategory| |#1| (QUOTE (-961)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1025)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-580 (-484)))) (|HasCategory| |#1| (QUOTE (-961)))) (|HasCategory| |#1| (QUOTE (-25)))) (OR (|HasCategory| |#1| (QUOTE (-413))) (|HasCategory| |#1| (QUOTE (-961)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484)))))) (-12 (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-950 (-484)))))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1025))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484))))) (|HasCategory| $ (QUOTE (-961))) (|HasCategory| $ (QUOTE (-950 (-484))))) 
 (-266 R S) 
 ((|constructor| (NIL "Lifting of maps to Expressions. Date Created: 16 Jan 1989 Date Last Updated: 22 Jan 1990")) (|map| (((|Expression| |#2|) (|Mapping| |#2| |#1|) (|Expression| |#1|)) "\\spad{map(f, e)} applies \\spad{f} to all the constants appearing in \\spad{e}."))) 
 NIL 
@@ -1000,7 +1000,7 @@ 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 
-(-268 R -3094) 
+(-268 R -3093) 
 ((|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 
@@ -1010,8 +1010,8 @@ NIL
 NIL 
 (-270 FE |var| |cen|) 
 ((|constructor| (NIL "ExponentialOfUnivariatePuiseuxSeries is a domain used to represent essential singularities of functions. An object in this domain is a function of the form \\spad{exp(f(x))},{} where \\spad{f(x)} is a Puiseux series with no terms of non-negative degree. Objects are ordered according to order of singularity,{} with functions which tend more rapidly to zero or infinity considered to be larger. Thus,{} if \\spad{order(f(x)) < order(g(x))},{} \\spadignore{i.e.} the first non-zero term of \\spad{f(x)} has lower degree than the first non-zero term of \\spad{g(x)},{} then \\spad{exp(f(x)) > exp(g(x))}. If \\spad{order(f(x)) = order(g(x))},{} then the ordering is essentially random. This domain is used in computing limits involving functions with essential singularities.")) (|exponentialOrder| (((|Fraction| (|Integer|)) $) "\\spad{exponentialOrder(exp(c * x **(-n) + ...))} returns \\spad{-n}. exponentialOrder(0) returns \\spad{0}.")) (|exponent| (((|UnivariatePuiseuxSeries| |#1| |#2| |#3|) $) "\\spad{exponent(exp(f(x)))} returns \\spad{f(x)}")) (|exponential| (($ (|UnivariatePuiseuxSeries| |#1| |#2| |#3|)) "\\spad{exponential(f(x))} returns \\spad{exp(f(x))}. Note: the function does NOT check that \\spad{f(x)} has no non-negative terms."))) 
-(((-3999 "*") |has| |#1| (-146)) (-3990 |has| |#1| (-496)) (-3995 |has| |#1| (-312)) (-3989 |has| |#1| (-312)) (-3991 . T) (-3992 . T) (-3994 . T)) 
-((|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-485))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-485))) (|devaluate| |#1|)))) (|HasCategory| (-350 (-485)) (QUOTE (-1026))) (|HasCategory| |#1| (QUOTE (-312))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-496)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-496)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-485)))))) (|HasSignature| |#1| (|%list| (QUOTE -3948) (|%list| (|devaluate| |#1|) (QUOTE (-1091)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-485)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-29 (-485)))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1116)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasSignature| |#1| (|%list| (QUOTE -3814) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1091))))) (|HasSignature| |#1| (|%list| (QUOTE -3083) (|%list| (|%list| (QUOTE -584) (QUOTE (-1091))) (|devaluate| |#1|))))))) 
+(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-495)) (-3994 |has| |#1| (-312)) (-3988 |has| |#1| (-312)) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((|HasCategory| |#1| (QUOTE (-38 (-350 (-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 (-809 (-1090)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-484))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-484))) (|devaluate| |#1|)))) (|HasCategory| (-350 (-484)) (QUOTE (-1025))) (|HasCategory| |#1| (QUOTE (-312))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-495)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-495)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-484)))))) (|HasSignature| |#1| (|%list| (QUOTE -3947) (|%list| (|devaluate| |#1|) (QUOTE (-1090)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-484)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-29 (-484)))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1115)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasSignature| |#1| (|%list| (QUOTE -3813) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1090))))) (|HasSignature| |#1| (|%list| (QUOTE -3082) (|%list| (|%list| (QUOTE -583) (QUOTE (-1090))) (|devaluate| |#1|))))))) 
 (-271 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 
@@ -1022,8 +1022,8 @@ NIL
 NIL 
 (-273 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."))) 
-((-3992 . T) (-3991 . T)) 
-((|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| (-485) (QUOTE (-717)))) 
+((-3991 . T) (-3990 . T)) 
+((|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| (-484) (QUOTE (-716)))) 
 (-274 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| $) "\\spad{s + x} returns the sum of \\spad{s} and \\spad{x}."))) 
 NIL 
@@ -1031,26 +1031,26 @@ NIL
 (-275 S) 
 ((|constructor| (NIL "The free abelian monoid on a set \\spad{S} is the monoid of finite sums of the form \\spad{reduce(+,[ni * si])} where the \\spad{si}'s are in \\spad{S},{} and the \\spad{ni}'s are non-negative integers. The operation is commutative."))) 
 NIL 
-((|HasCategory| (-695) (QUOTE (-717)))) 
+((|HasCategory| (-694) (QUOTE (-716)))) 
 (-276 S R E) 
 ((|constructor| (NIL "This category is similar to AbelianMonoidRing,{} except that the sum is assumed to be finite. It is a useful model for polynomials,{} but is somewhat more general.")) (|primitivePart| (($ $) "\\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|) $) "\\spad{ground?(p)} tests if polynomial \\spad{p} is a member of the coefficient ring."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-146)))) 
+((|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-146)))) 
 (-277 R E) 
 ((|constructor| (NIL "This category is similar to AbelianMonoidRing,{} except that the sum is assumed to be finite. It is a useful model for polynomials,{} but is somewhat more general.")) (|primitivePart| (($ $) "\\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."))) 
-(((-3999 "*") |has| |#1| (-146)) (-3990 |has| |#1| (-496)) (-3991 . T) (-3992 . T) (-3994 . T)) 
+(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-495)) (-3990 . T) (-3991 . T) (-3993 . T)) 
 NIL 
 (-278 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."))) 
-((-3998 . T)) 
-((OR (-12 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (OR (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-757))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|))) (|HasCategory| $ (|%list| (QUOTE -1036) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| $ (|%list| (QUOTE -1036) (|devaluate| |#1|))))) 
-(-279 S -3094) 
+((-3997 . T)) 
+((OR (-12 (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-553 (-473)))) (OR (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-756))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| (-484) (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|))) (|HasCategory| $ (|%list| (QUOTE -1035) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| $ (|%list| (QUOTE -1035) (|devaluate| |#1|))))) 
+(-279 S -3093) 
 ((|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 (-320)))) 
-(-280 -3094) 
+(-280 -3093) 
 ((|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."))) 
-((-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
 NIL 
 (-281 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"))) 
@@ -1060,7 +1060,7 @@ 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 
-(-283 -3094 UP UPUP R) 
+(-283 -3093 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 
@@ -1068,33 +1068,33 @@ 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 
-(-285 S -3094 UP UPUP R) 
+(-285 S -3093 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 
-(-286 -3094 UP UPUP R) 
+(-286 -3093 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|) $) "\\spad{ideal(D)} returns the ideal corresponding to a divisor \\spad{D}."))) 
 NIL 
 NIL 
 (-287 S R) 
 ((|constructor| (NIL "This category provides a selection of evaluation operations depending on what the argument type \\spad{R} provides.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(f, ex)} evaluates ex,{} applying \\spad{f} to values of type \\spad{R} in ex."))) 
 NIL 
-((|HasCategory| |#2| (|%list| (QUOTE -456) (QUOTE (-1091)) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -241) (|devaluate| |#2|) (|devaluate| |#2|)))) 
+((|HasCategory| |#2| (|%list| (QUOTE -455) (QUOTE (-1090)) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -241) (|devaluate| |#2|) (|devaluate| |#2|)))) 
 (-288 R) 
 ((|constructor| (NIL "This category provides a selection of evaluation operations depending on what the argument type \\spad{R} provides.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f, ex)} evaluates ex,{} applying \\spad{f} to values of type \\spad{R} in ex."))) 
 NIL 
 NIL 
 (-289 |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}."))) 
-((-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
-((OR (|HasCategory| (-818 |#1|) (QUOTE (-118))) (|HasCategory| (-818 |#1|) (QUOTE (-320)))) (|HasCategory| (-818 |#1|) (QUOTE (-120))) (|HasCategory| (-818 |#1|) (QUOTE (-320))) (|HasCategory| (-818 |#1|) (QUOTE (-118)))) 
-(-290 S -3094 UP UPUP) 
+((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((OR (|HasCategory| (-817 |#1|) (QUOTE (-118))) (|HasCategory| (-817 |#1|) (QUOTE (-320)))) (|HasCategory| (-817 |#1|) (QUOTE (-120))) (|HasCategory| (-817 |#1|) (QUOTE (-320))) (|HasCategory| (-817 |#1|) (QUOTE (-118)))) 
+(-290 S -3093 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 (-320))) (|HasCategory| |#2| (QUOTE (-312)))) 
-(-291 -3094 UP UPUP) 
+(-291 -3093 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."))) 
-((-3990 |has| (-350 |#2|) (-312)) (-3995 |has| (-350 |#2|) (-312)) (-3989 |has| (-350 |#2|) (-312)) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((-3989 |has| (-350 |#2|) (-312)) (-3994 |has| (-350 |#2|) (-312)) (-3988 |has| (-350 |#2|) (-312)) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
 NIL 
 (-292 R1 UP1 UPUP1 F1 R2 UP2 UPUP2 F2) 
 ((|constructor| (NIL "Lifts a map from rings to function fields over them.")) (|map| ((|#8| (|Mapping| |#5| |#1|) |#4|) "\\spad{map(f, p)} lifts \\spad{f} to \\spad{F1} and applies it to \\spad{p}."))) 
@@ -1102,15 +1102,15 @@ NIL
 NIL 
 (-293 |p| |extdeg|) 
 ((|constructor| (NIL "FiniteFieldCyclicGroup(\\spad{p},{}\\spad{n}) implements a finite field extension of degee \\spad{n} over the prime field with \\spad{p} elements. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial,{} which is created by {\\em createPrimitivePoly} from \\spadtype{FiniteFieldPolynomialPackage}. The Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field. This table is used to perform additions in the field quickly."))) 
-((-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
-((OR (|HasCategory| (-818 |#1|) (QUOTE (-118))) (|HasCategory| (-818 |#1|) (QUOTE (-320)))) (|HasCategory| (-818 |#1|) (QUOTE (-120))) (|HasCategory| (-818 |#1|) (QUOTE (-320))) (|HasCategory| (-818 |#1|) (QUOTE (-118)))) 
+((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((OR (|HasCategory| (-817 |#1|) (QUOTE (-118))) (|HasCategory| (-817 |#1|) (QUOTE (-320)))) (|HasCategory| (-817 |#1|) (QUOTE (-120))) (|HasCategory| (-817 |#1|) (QUOTE (-320))) (|HasCategory| (-817 |#1|) (QUOTE (-118)))) 
 (-294 GF |defpol|) 
 ((|constructor| (NIL "FiniteFieldCyclicGroupExtensionByPolynomial(GF,{}defpol) implements a finite extension field of the ground field {\\em GF}. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial {\\em defpol},{} which MUST be primitive (user responsibility). Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field it is used to perform additions in the field quickly."))) 
-((-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
 ((OR (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-320)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-320))) (|HasCategory| |#1| (QUOTE (-118)))) 
 (-295 GF |extdeg|) 
 ((|constructor| (NIL "FiniteFieldCyclicGroupExtension(GF,{}\\spad{n}) implements a extension of degree \\spad{n} over the ground field {\\em GF}. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial,{} which is created by {\\em createPrimitivePoly} from \\spadtype{FiniteFieldPolynomialPackage}. Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field. This table is used to perform additions in the field quickly."))) 
-((-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
 ((OR (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-320)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-320))) (|HasCategory| |#1| (QUOTE (-118)))) 
 (-296 GF) 
 ((|constructor| (NIL "FiniteFieldFunctions(GF) is a package with functions concerning finite extension fields of the finite ground field {\\em GF},{} \\spadignore{e.g.} Zech logarithms.")) (|createLowComplexityNormalBasis| (((|Union| (|SparseUnivariatePolynomial| |#1|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) (|PositiveInteger|)) "\\spad{createLowComplexityNormalBasis(n)} tries to find a a low complexity normal basis of degree {\\em n} over {\\em GF} and returns its multiplication matrix If no low complexity basis is found it calls \\axiomFunFrom{createNormalPoly}{FiniteFieldPolynomialPackage}(\\spad{n}) to produce a normal polynomial of degree {\\em n} over {\\em GF}")) (|createLowComplexityTable| (((|Union| (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) "failed") (|PositiveInteger|)) "\\spad{createLowComplexityTable(n)} tries to find a low complexity normal basis of degree {\\em n} over {\\em GF} and returns its multiplication matrix Fails,{} if it does not find a low complexity basis")) (|sizeMultiplication| (((|NonNegativeInteger|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{sizeMultiplication(m)} returns the number of entries of the multiplication table {\\em m}.")) (|createMultiplicationMatrix| (((|Matrix| |#1|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{createMultiplicationMatrix(m)} forms the multiplication table {\\em m} into a matrix over the ground field.")) (|createMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) (|SparseUnivariatePolynomial| |#1|)) "\\spad{createMultiplicationTable(f)} generates a multiplication table for the normal basis of the field extension determined by {\\em f}. This is needed to perform multiplications between elements represented as coordinate vectors to this basis. See \\spadtype{FFNBP},{} \\spadtype{FFNBX}.")) (|createZechTable| (((|PrimitiveArray| (|SingleInteger|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{createZechTable(f)} generates a Zech logarithm table for the cyclic group representation of a extension of the ground field by the primitive polynomial {\\em f(x)},{} \\spadignore{i.e.} \\spad{Z(i)},{} defined by {\\em x**Z(i) = 1+x**i} is stored at index \\spad{i}. This is needed in particular to perform addition of field elements in finite fields represented in this way. See \\spadtype{FFCGP},{} \\spadtype{FFCGX}."))) 
@@ -1126,43 +1126,43 @@ NIL
 NIL 
 (-299) 
 ((|constructor| (NIL "FiniteFieldCategory is the category of finite fields")) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) "\\spad{representationType()} returns the type of the representation,{} one of: \\spad{prime},{} \\spad{polynomial},{} \\spad{normal},{} or \\spad{cyclic}.")) (|order| (((|PositiveInteger|) $) "\\spad{order(b)} computes the order of an element \\spad{b} in the multiplicative group of the field. Error: if \\spad{b} equals 0.")) (|discreteLog| (((|NonNegativeInteger|) $) "\\spad{discreteLog(a)} computes the discrete logarithm of \\spad{a} with respect to \\spad{primitiveElement()} of the field.")) (|primitive?| (((|Boolean|) $) "\\spad{primitive?(b)} tests whether the element \\spad{b} is a generator of the (cyclic) multiplicative group of the field,{} \\spadignore{i.e.} is a primitive element. Implementation Note: see ch.IX.1.3,{} th.2 in \\spad{D}. Lipson.")) (|primitiveElement| (($) "\\spad{primitiveElement()} returns a primitive element stored in a global variable in the domain. At first call,{} the primitive element is computed by calling \\spadfun{createPrimitiveElement}.")) (|createPrimitiveElement| (($) "\\spad{createPrimitiveElement()} computes a generator of the (cyclic) multiplicative group of the field.")) (|tableForDiscreteLogarithm| (((|Table| (|PositiveInteger|) (|NonNegativeInteger|)) (|Integer|)) "\\spad{tableForDiscreteLogarithm(a,n)} returns a table of the discrete logarithms of \\spad{a**0} up to \\spad{a**(n-1)} which,{} called with key \\spad{lookup(a**i)} returns \\spad{i} for \\spad{i} in \\spad{0..n-1}. Error: if not called for prime divisors of order of \\indented{7}{multiplicative group.}")) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| (|Integer|)) (|:| |exponent| (|Integer|))))) "\\spad{factorsOfCyclicGroupSize()} returns the factorization of size()\\spad{-1}")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(mat)},{} given a matrix representing a homogeneous system of equations,{} returns a vector whose characteristic'th powers is a non-trivial solution,{} or \"failed\" if no such vector exists.")) (|charthRoot| (($ $) "\\spad{charthRoot(a)} takes the characteristic'th root of {\\em a}. Note: such a root is alway defined in finite fields."))) 
-((-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
 NIL 
-(-300 R UP -3094) 
+(-300 R UP -3093) 
 ((|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 
 (-301 |p| |extdeg|) 
 ((|constructor| (NIL "FiniteFieldNormalBasis(\\spad{p},{}\\spad{n}) implements a finite extension field of degree \\spad{n} over the prime field with \\spad{p} elements. The elements are represented by coordinate vectors with respect to a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element. This is chosen as a root of the extension polynomial created by \\spadfunFrom{createNormalPoly}{FiniteFieldPolynomialPackage}.")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: The time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| (|PrimeField| |#1|))) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| (|PrimeField| |#1|)) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) 
-((-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
-((OR (|HasCategory| (-818 |#1|) (QUOTE (-118))) (|HasCategory| (-818 |#1|) (QUOTE (-320)))) (|HasCategory| (-818 |#1|) (QUOTE (-120))) (|HasCategory| (-818 |#1|) (QUOTE (-320))) (|HasCategory| (-818 |#1|) (QUOTE (-118)))) 
+((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((OR (|HasCategory| (-817 |#1|) (QUOTE (-118))) (|HasCategory| (-817 |#1|) (QUOTE (-320)))) (|HasCategory| (-817 |#1|) (QUOTE (-120))) (|HasCategory| (-817 |#1|) (QUOTE (-320))) (|HasCategory| (-817 |#1|) (QUOTE (-118)))) 
 (-302 GF |uni|) 
 ((|constructor| (NIL "FiniteFieldNormalBasisExtensionByPolynomial(GF,{}uni) implements a finite extension of the ground field {\\em GF}. The elements are represented by coordinate vectors with respect to. a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element,{} where \\spad{q} is the size of {\\em GF}. The normal element is chosen as a root of the extension polynomial,{} which MUST be normal over {\\em GF} (user responsibility)")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: the time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| |#1|)) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) 
-((-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
 ((OR (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-320)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-320))) (|HasCategory| |#1| (QUOTE (-118)))) 
 (-303 GF |extdeg|) 
 ((|constructor| (NIL "FiniteFieldNormalBasisExtensionByPolynomial(GF,{}\\spad{n}) implements a finite extension field of degree \\spad{n} over the ground field {\\em GF}. The elements are represented by coordinate vectors with respect to a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element. This is chosen as a root of the extension polynomial,{} created by {\\em createNormalPoly} from \\spadtype{FiniteFieldPolynomialPackage}")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: the time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| |#1|)) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) 
-((-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
 ((OR (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-320)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-320))) (|HasCategory| |#1| (QUOTE (-118)))) 
 (-304 GF |defpol|) 
 ((|constructor| (NIL "FiniteFieldExtensionByPolynomial(GF,{} defpol) implements the extension of the finite field {\\em GF} generated by the extension polynomial {\\em defpol} which MUST be irreducible. Note: the user has the responsibility to ensure that {\\em defpol} is irreducible."))) 
-((-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
 ((OR (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-320)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-320))) (|HasCategory| |#1| (QUOTE (-118)))) 
 (-305 GF) 
 ((|constructor| (NIL "This package provides a number of functions for generating,{} counting and testing irreducible,{} normal,{} primitive,{} random polynomials over finite fields.")) (|reducedQPowers| (((|PrimitiveArray| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{reducedQPowers(f)} generates \\spad{[x,x**q,x**(q**2),...,x**(q**(n-1))]} reduced modulo \\spad{f} where \\spad{q = size()\\$GF} and \\spad{n = degree f}.")) (|leastAffineMultiple| (((|SparseUnivariatePolynomial| |#1|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{leastAffineMultiple(f)} computes the least affine polynomial which is divisible by the polynomial \\spad{f} over the finite field {\\em GF},{} \\spadignore{i.e.} a polynomial whose exponents are 0 or a power of \\spad{q},{} the size of {\\em GF}.")) (|random| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{random(m,n)}\\$FFPOLY(GF) generates a random monic polynomial of degree \\spad{d} over the finite field {\\em GF},{} \\spad{d} between \\spad{m} and \\spad{n}.") (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{random(n)}\\$FFPOLY(GF) generates a random monic polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|nextPrimitiveNormalPoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextPrimitiveNormalPoly(f)} yields the next primitive normal polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g} or,{} in case these numbers are equal,{} if the {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than this number for \\spad{g}. If these numbers are equals,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than that for \\spad{g},{} or if the lists of exponents for \\spad{f} are lexicographically less than those for \\spad{g}. If these lists are also equal,{} the lists of coefficients are coefficients according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}. This operation is equivalent to nextNormalPrimitivePoly(\\spad{f}).")) (|nextNormalPrimitivePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextNormalPrimitivePoly(f)} yields the next normal primitive polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g} or if {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than this number for \\spad{g}. Otherwise,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than that for \\spad{g} or if the lists of exponents for \\spad{f} are lexicographically less than those for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}. This operation is equivalent to nextPrimitiveNormalPoly(\\spad{f}).")) (|nextNormalPoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextNormalPoly(f)} yields the next normal polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than that for \\spad{g}. In case these numbers are equal,{} \\spad{f < g} if if the number of monomials of \\spad{f} is less that for \\spad{g} or if the list of exponents of \\spad{f} are lexicographically less than the corresponding list for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|nextPrimitivePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextPrimitivePoly(f)} yields the next primitive polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g}. If these values are equal,{} then \\spad{f < g} if if the number of monomials of \\spad{f} is less than that for \\spad{g} or if the lists of exponents of \\spad{f} are lexicographically less than the corresponding list for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|nextIrreduciblePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextIrreduciblePoly(f)} yields the next monic irreducible polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than this number for \\spad{g}. If \\spad{f} and \\spad{g} have the same number of monomials,{} the lists of exponents are compared lexicographically. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|createPrimitiveNormalPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createPrimitiveNormalPoly(n)}\\$FFPOLY(GF) generates a normal and primitive polynomial of degree \\spad{n} over the field {\\em GF}. polynomial of degree \\spad{n} over the field {\\em GF}.")) (|createNormalPrimitivePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createNormalPrimitivePoly(n)}\\$FFPOLY(GF) generates a normal and primitive polynomial of degree \\spad{n} over the field {\\em GF}. Note: this function is equivalent to createPrimitiveNormalPoly(\\spad{n})")) (|createNormalPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createNormalPoly(n)}\\$FFPOLY(GF) generates a normal polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|createPrimitivePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createPrimitivePoly(n)}\\$FFPOLY(GF) generates a primitive polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|createIrreduciblePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createIrreduciblePoly(n)}\\$FFPOLY(GF) generates a monic irreducible univariate polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfNormalPoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfNormalPoly(n)}\\$FFPOLY(GF) yields the number of normal polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfPrimitivePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfPrimitivePoly(n)}\\$FFPOLY(GF) yields the number of primitive polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfIrreduciblePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfIrreduciblePoly(n)}\\$FFPOLY(GF) yields the number of monic irreducible univariate polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|normal?| (((|Boolean|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{normal?(f)} tests whether the polynomial \\spad{f} over a finite field is normal,{} \\spadignore{i.e.} its roots are linearly independent over the field.")) (|primitive?| (((|Boolean|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{primitive?(f)} tests whether the polynomial \\spad{f} over a finite field is primitive,{} \\spadignore{i.e.} all its roots are primitive."))) 
 NIL 
 NIL 
-(-306 -3094 GF) 
+(-306 -3093 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 
-(-307 -3094 FP FPP) 
+(-307 -3093 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 
 (-308 GF |n|) 
 ((|constructor| (NIL "FiniteFieldExtensionByPolynomial(GF,{} \\spad{n}) implements an extension of the finite field {\\em GF} of degree \\spad{n} generated by the extension polynomial constructed by \\spadfunFrom{createIrreduciblePoly}{FiniteFieldPolynomialPackage} from \\spadtype{FiniteFieldPolynomialPackage}."))) 
-((-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
 ((OR (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-320)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-320))) (|HasCategory| |#1| (QUOTE (-118)))) 
 (-309 R |ls|) 
 ((|constructor| (NIL "This is just an interface between several packages and domains. The goal is to compute lexicographical Groebner bases of sets of polynomial with type \\spadtype{Polynomial R} by the {\\em FGLM} algorithm if this is possible (\\spadignore{i.e.} if the input system generates a zero-dimensional ideal).")) (|groebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|))) "\\axiom{groebner(\\spad{lq1})} returns the lexicographical Groebner basis of \\axiom{\\spad{lq1}}. If \\axiom{\\spad{lq1}} generates a zero-dimensional ideal then the {\\em FGLM} strategy is used,{} otherwise the {\\em Sugar} strategy is used.")) (|fglmIfCan| (((|Union| (|List| (|Polynomial| |#1|)) "failed") (|List| (|Polynomial| |#1|))) "\\axiom{fglmIfCan(\\spad{lq1})} returns the lexicographical Groebner basis of \\axiom{\\spad{lq1}} by using the {\\em FGLM} strategy,{} if \\axiom{zeroDimensional?(\\spad{lq1})} holds.")) (|zeroDimensional?| (((|Boolean|) (|List| (|Polynomial| |#1|))) "\\axiom{zeroDimensional?(\\spad{lq1})} returns \\spad{true} iff \\axiom{\\spad{lq1}} generates a zero-dimensional ideal \\spad{w}.\\spad{r}.\\spad{t}. the variables of \\axiom{ls}."))) 
@@ -1170,7 +1170,7 @@ NIL
 NIL 
 (-310 S) 
 ((|constructor| (NIL "The free group on a set \\spad{S} is the group of finite products of the form \\spad{reduce(*,[si ** ni])} where the \\spad{si}'s are in \\spad{S},{} and the \\spad{ni}'s are integers. The multiplication is not commutative.")) (|factors| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| (|Integer|)))) $) "\\spad{factors(a1\\^e1,...,an\\^en)} returns \\spad{[[a1, e1],...,[an, en]]}.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f, a1\\^e1 ... an\\^en)} returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (|mapExpon| (($ (|Mapping| (|Integer|) (|Integer|)) $) "\\spad{mapExpon(f, a1\\^e1 ... an\\^en)} returns \\spad{a1\\^f(e1) ... an\\^f(en)}.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(x, n)} returns the factor of the n^th monomial of \\spad{x}.")) (|nthExpon| (((|Integer|) $ (|Integer|)) "\\spad{nthExpon(x, n)} returns the exponent of the n^th monomial of \\spad{x}.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(x)} returns the number of monomials in \\spad{x}.")) (** (($ |#1| (|Integer|)) "\\spad{s ** n} returns the product of \\spad{s} by itself \\spad{n} times.")) (* (($ $ |#1|) "\\spad{x * s} returns the product of \\spad{x} by \\spad{s} on the right.") (($ |#1| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) 
-((-3994 . T)) 
+((-3993 . T)) 
 NIL 
 (-311 S) 
 ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) 
@@ -1178,7 +1178,7 @@ NIL
 NIL 
 (-312) 
 ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) 
-((-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
 NIL 
 (-313 S) 
 ((|constructor| (NIL "This domain provides a basic model of files to save arbitrary values. The operations provide sequential access to the contents.")) (|readIfCan!| (((|Union| |#1| "failed") $) "\\spad{readIfCan!(f)} returns a value from the file \\spad{f},{} if possible. If \\spad{f} is not open for reading,{} or if \\spad{f} is at the end of file then \\spad{\"failed\"} is the result."))) 
@@ -1191,10 +1191,10 @@ NIL
 (-315 S R) 
 ((|constructor| (NIL "A FiniteRankNonAssociativeAlgebra is a non associative algebra over a commutative ring \\spad{R} which is a free \\spad{R}-module of finite rank.")) (|unitsKnown| ((|attribute|) "unitsKnown means that \\spadfun{recip} truly yields reciprocal or \\spad{\"failed\"} if not a unit,{} similarly for \\spadfun{leftRecip} and \\spadfun{rightRecip}. The reason is that we use left,{} respectively right,{} minimal polynomials to decide this question.")) (|unit| (((|Union| $ "failed")) "\\spad{unit()} returns a unit of the algebra (necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnit| (((|Union| $ "failed")) "\\spad{rightUnit()} returns a right unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|leftUnit| (((|Union| $ "failed")) "\\spad{leftUnit()} returns a left unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{rightUnits()} returns the affine space of all right units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|leftUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{leftUnits()} returns the affine space of all left units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|rightMinimalPolynomial| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{rightMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of right powers of \\spad{a}. Note: the polynomial never has a constant term as in general the algebra has no unit.")) (|leftMinimalPolynomial| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{leftMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of left powers of \\spad{a}. Note: the polynomial never has a constant term as in general the algebra has no unit.")) (|associatorDependence| (((|List| (|Vector| |#2|))) "\\spad{associatorDependence()} looks for the associator identities,{} \\spadignore{i.e.} finds a basis of the solutions of the linear combinations of the six permutations of \\spad{associator(a,b,c)} which yield 0,{} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra. The order of the permutations is \\spad{123 231 312 132 321 213}.")) (|rightRecip| (((|Union| $ "failed") $) "\\spad{rightRecip(a)} returns an element,{} which is a right inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (|leftRecip| (((|Union| $ "failed") $) "\\spad{leftRecip(a)} returns an element,{} which is a left inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(a)} returns an element,{} which is both a left and a right inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (|lieAlgebra?| (((|Boolean|)) "\\spad{lieAlgebra?()} tests if the algebra is anticommutative and \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra (Jacobi identity). Example: for every associative algebra \\spad{(A,+,@)} we can construct a Lie algebra \\spad{(A,+,*)},{} where \\spad{a*b := a@b-b@a}.")) (|jordanAlgebra?| (((|Boolean|)) "\\spad{jordanAlgebra?()} tests if the algebra is commutative,{} characteristic is not 2,{} and \\spad{(a*b)*a**2 - a*(b*a**2) = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra (Jordan identity). Example: for every associative algebra \\spad{(A,+,@)} we can construct a Jordan algebra \\spad{(A,+,*)},{} where \\spad{a*b := (a@b+b@a)/2}.")) (|noncommutativeJordanAlgebra?| (((|Boolean|)) "\\spad{noncommutativeJordanAlgebra?()} tests if the algebra is flexible and Jordan admissible.")) (|jordanAdmissible?| (((|Boolean|)) "\\spad{jordanAdmissible?()} tests if 2 is invertible in the coefficient domain and the multiplication defined by \\spad{(1/2)(a*b+b*a)} determines a Jordan algebra,{} \\spadignore{i.e.} satisfies the Jordan identity. The property of \\spadatt{commutative(\"*\")} follows from by definition.")) (|lieAdmissible?| (((|Boolean|)) "\\spad{lieAdmissible?()} tests if the algebra defined by the commutators is a Lie algebra,{} \\spadignore{i.e.} satisfies the Jacobi identity. The property of anticommutativity follows from definition.")) (|jacobiIdentity?| (((|Boolean|)) "\\spad{jacobiIdentity?()} tests if \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra. For example,{} this holds for crossed products of 3-dimensional vectors.")) (|powerAssociative?| (((|Boolean|)) "\\spad{powerAssociative?()} tests if all subalgebras generated by a single element are associative.")) (|alternative?| (((|Boolean|)) "\\spad{alternative?()} tests if \\spad{2*associator(a,a,b) = 0 = 2*associator(a,b,b)} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don't know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|flexible?| (((|Boolean|)) "\\spad{flexible?()} tests if \\spad{2*associator(a,b,a) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don't know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|rightAlternative?| (((|Boolean|)) "\\spad{rightAlternative?()} tests if \\spad{2*associator(a,b,b) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don't know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|leftAlternative?| (((|Boolean|)) "\\spad{leftAlternative?()} tests if \\spad{2*associator(a,a,b) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don't know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|antiAssociative?| (((|Boolean|)) "\\spad{antiAssociative?()} tests if multiplication in algebra is anti-associative,{} \\spadignore{i.e.} \\spad{(a*b)*c + a*(b*c) = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra.")) (|associative?| (((|Boolean|)) "\\spad{associative?()} tests if multiplication in algebra is associative.")) (|antiCommutative?| (((|Boolean|)) "\\spad{antiCommutative?()} tests if \\spad{a*a = 0} for all \\spad{a} in the algebra. Note: this implies \\spad{a*b + b*a = 0} for all \\spad{a} and \\spad{b}.")) (|commutative?| (((|Boolean|)) "\\spad{commutative?()} tests if multiplication in the algebra is commutative.")) (|rightCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{rightCharacteristicPolynomial(a)} returns the characteristic polynomial of the right regular representation of \\spad{a} with respect to any basis.")) (|leftCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{leftCharacteristicPolynomial(a)} returns the characteristic polynomial of the left regular representation of \\spad{a} with respect to any basis.")) (|rightTraceMatrix| (((|Matrix| |#2|) (|Vector| $)) "\\spad{rightTraceMatrix([v1,...,vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj}.")) (|leftTraceMatrix| (((|Matrix| |#2|) (|Vector| $)) "\\spad{leftTraceMatrix([v1,...,vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj}.")) (|rightDiscriminant| ((|#2| (|Vector| $)) "\\spad{rightDiscriminant([v1,...,vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj}. Note: the same as \\spad{determinant(rightTraceMatrix([v1,...,vn]))}.")) (|leftDiscriminant| ((|#2| (|Vector| $)) "\\spad{leftDiscriminant([v1,...,vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj}. Note: the same as \\spad{determinant(leftTraceMatrix([v1,...,vn]))}.")) (|represents| (($ (|Vector| |#2|) (|Vector| $)) "\\spad{represents([a1,...,am],[v1,...,vm])} returns the linear combination \\spad{a1*vm + ... + an*vm}.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $) (|Vector| $)) "\\spad{coordinates([a1,...,am],[v1,...,vn])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{ai} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.") (((|Vector| |#2|) $ (|Vector| $)) "\\spad{coordinates(a,[v1,...,vn])} returns the coordinates of \\spad{a} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rightNorm| ((|#2| $) "\\spad{rightNorm(a)} returns the determinant of the right regular representation of \\spad{a}.")) (|leftNorm| ((|#2| $) "\\spad{leftNorm(a)} returns the determinant of the left regular representation of \\spad{a}.")) (|rightTrace| ((|#2| $) "\\spad{rightTrace(a)} returns the trace of the right regular representation of \\spad{a}.")) (|leftTrace| ((|#2| $) "\\spad{leftTrace(a)} returns the trace of the left regular representation of \\spad{a}.")) (|rightRegularRepresentation| (((|Matrix| |#2|) $ (|Vector| $)) "\\spad{rightRegularRepresentation(a,[v1,...,vn])} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,...,vn]}.")) (|leftRegularRepresentation| (((|Matrix| |#2|) $ (|Vector| $)) "\\spad{leftRegularRepresentation(a,[v1,...,vn])} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,...,vn]}.")) (|structuralConstants| (((|Vector| (|Matrix| |#2|)) (|Vector| $)) "\\spad{structuralConstants([v1,v2,...,vm])} calculates the structural constants \\spad{[(gammaijk) for k in 1..m]} defined by \\spad{vi * vj = gammaij1 * v1 + ... + gammaijm * vm},{} where \\spad{[v1,...,vm]} is an \\spad{R}-module basis of a subalgebra.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#2|)) (|Vector| $)) "\\spad{conditionsForIdempotents([v1,...,vn])} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra as \\spad{R}-module.")) (|someBasis| (((|Vector| $)) "\\spad{someBasis()} returns some \\spad{R}-module basis."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-496)))) 
+((|HasCategory| |#2| (QUOTE (-495)))) 
 (-316 R) 
 ((|constructor| (NIL "A FiniteRankNonAssociativeAlgebra is a non associative algebra over a commutative ring \\spad{R} which is a free \\spad{R}-module of finite rank.")) (|unitsKnown| ((|attribute|) "unitsKnown means that \\spadfun{recip} truly yields reciprocal or \\spad{\"failed\"} if not a unit,{} similarly for \\spadfun{leftRecip} and \\spadfun{rightRecip}. The reason is that we use left,{} respectively right,{} minimal polynomials to decide this question.")) (|unit| (((|Union| $ "failed")) "\\spad{unit()} returns a unit of the algebra (necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnit| (((|Union| $ "failed")) "\\spad{rightUnit()} returns a right unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|leftUnit| (((|Union| $ "failed")) "\\spad{leftUnit()} returns a left unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{rightUnits()} returns the affine space of all right units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|leftUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{leftUnits()} returns the affine space of all left units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|rightMinimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{rightMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of right powers of \\spad{a}. Note: the polynomial never has a constant term as in general the algebra has no unit.")) (|leftMinimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{leftMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of left powers of \\spad{a}. Note: the polynomial never has a constant term as in general the algebra has no unit.")) (|associatorDependence| (((|List| (|Vector| |#1|))) "\\spad{associatorDependence()} looks for the associator identities,{} \\spadignore{i.e.} finds a basis of the solutions of the linear combinations of the six permutations of \\spad{associator(a,b,c)} which yield 0,{} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra. The order of the permutations is \\spad{123 231 312 132 321 213}.")) (|rightRecip| (((|Union| $ "failed") $) "\\spad{rightRecip(a)} returns an element,{} which is a right inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (|leftRecip| (((|Union| $ "failed") $) "\\spad{leftRecip(a)} returns an element,{} which is a left inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(a)} returns an element,{} which is both a left and a right inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (|lieAlgebra?| (((|Boolean|)) "\\spad{lieAlgebra?()} tests if the algebra is anticommutative and \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra (Jacobi identity). Example: for every associative algebra \\spad{(A,+,@)} we can construct a Lie algebra \\spad{(A,+,*)},{} where \\spad{a*b := a@b-b@a}.")) (|jordanAlgebra?| (((|Boolean|)) "\\spad{jordanAlgebra?()} tests if the algebra is commutative,{} characteristic is not 2,{} and \\spad{(a*b)*a**2 - a*(b*a**2) = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra (Jordan identity). Example: for every associative algebra \\spad{(A,+,@)} we can construct a Jordan algebra \\spad{(A,+,*)},{} where \\spad{a*b := (a@b+b@a)/2}.")) (|noncommutativeJordanAlgebra?| (((|Boolean|)) "\\spad{noncommutativeJordanAlgebra?()} tests if the algebra is flexible and Jordan admissible.")) (|jordanAdmissible?| (((|Boolean|)) "\\spad{jordanAdmissible?()} tests if 2 is invertible in the coefficient domain and the multiplication defined by \\spad{(1/2)(a*b+b*a)} determines a Jordan algebra,{} \\spadignore{i.e.} satisfies the Jordan identity. The property of \\spadatt{commutative(\"*\")} follows from by definition.")) (|lieAdmissible?| (((|Boolean|)) "\\spad{lieAdmissible?()} tests if the algebra defined by the commutators is a Lie algebra,{} \\spadignore{i.e.} satisfies the Jacobi identity. The property of anticommutativity follows from definition.")) (|jacobiIdentity?| (((|Boolean|)) "\\spad{jacobiIdentity?()} tests if \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra. For example,{} this holds for crossed products of 3-dimensional vectors.")) (|powerAssociative?| (((|Boolean|)) "\\spad{powerAssociative?()} tests if all subalgebras generated by a single element are associative.")) (|alternative?| (((|Boolean|)) "\\spad{alternative?()} tests if \\spad{2*associator(a,a,b) = 0 = 2*associator(a,b,b)} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don't know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|flexible?| (((|Boolean|)) "\\spad{flexible?()} tests if \\spad{2*associator(a,b,a) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don't know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|rightAlternative?| (((|Boolean|)) "\\spad{rightAlternative?()} tests if \\spad{2*associator(a,b,b) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don't know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|leftAlternative?| (((|Boolean|)) "\\spad{leftAlternative?()} tests if \\spad{2*associator(a,a,b) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don't know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|antiAssociative?| (((|Boolean|)) "\\spad{antiAssociative?()} tests if multiplication in algebra is anti-associative,{} \\spadignore{i.e.} \\spad{(a*b)*c + a*(b*c) = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra.")) (|associative?| (((|Boolean|)) "\\spad{associative?()} tests if multiplication in algebra is associative.")) (|antiCommutative?| (((|Boolean|)) "\\spad{antiCommutative?()} tests if \\spad{a*a = 0} for all \\spad{a} in the algebra. Note: this implies \\spad{a*b + b*a = 0} for all \\spad{a} and \\spad{b}.")) (|commutative?| (((|Boolean|)) "\\spad{commutative?()} tests if multiplication in the algebra is commutative.")) (|rightCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{rightCharacteristicPolynomial(a)} returns the characteristic polynomial of the right regular representation of \\spad{a} with respect to any basis.")) (|leftCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{leftCharacteristicPolynomial(a)} returns the characteristic polynomial of the left regular representation of \\spad{a} with respect to any basis.")) (|rightTraceMatrix| (((|Matrix| |#1|) (|Vector| $)) "\\spad{rightTraceMatrix([v1,...,vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj}.")) (|leftTraceMatrix| (((|Matrix| |#1|) (|Vector| $)) "\\spad{leftTraceMatrix([v1,...,vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj}.")) (|rightDiscriminant| ((|#1| (|Vector| $)) "\\spad{rightDiscriminant([v1,...,vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj}. Note: the same as \\spad{determinant(rightTraceMatrix([v1,...,vn]))}.")) (|leftDiscriminant| ((|#1| (|Vector| $)) "\\spad{leftDiscriminant([v1,...,vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj}. Note: the same as \\spad{determinant(leftTraceMatrix([v1,...,vn]))}.")) (|represents| (($ (|Vector| |#1|) (|Vector| $)) "\\spad{represents([a1,...,am],[v1,...,vm])} returns the linear combination \\spad{a1*vm + ... + an*vm}.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $) (|Vector| $)) "\\spad{coordinates([a1,...,am],[v1,...,vn])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{ai} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.") (((|Vector| |#1|) $ (|Vector| $)) "\\spad{coordinates(a,[v1,...,vn])} returns the coordinates of \\spad{a} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rightNorm| ((|#1| $) "\\spad{rightNorm(a)} returns the determinant of the right regular representation of \\spad{a}.")) (|leftNorm| ((|#1| $) "\\spad{leftNorm(a)} returns the determinant of the left regular representation of \\spad{a}.")) (|rightTrace| ((|#1| $) "\\spad{rightTrace(a)} returns the trace of the right regular representation of \\spad{a}.")) (|leftTrace| ((|#1| $) "\\spad{leftTrace(a)} returns the trace of the left regular representation of \\spad{a}.")) (|rightRegularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) "\\spad{rightRegularRepresentation(a,[v1,...,vn])} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,...,vn]}.")) (|leftRegularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) "\\spad{leftRegularRepresentation(a,[v1,...,vn])} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,...,vn]}.")) (|structuralConstants| (((|Vector| (|Matrix| |#1|)) (|Vector| $)) "\\spad{structuralConstants([v1,v2,...,vm])} calculates the structural constants \\spad{[(gammaijk) for k in 1..m]} defined by \\spad{vi * vj = gammaij1 * v1 + ... + gammaijm * vm},{} where \\spad{[v1,...,vm]} is an \\spad{R}-module basis of a subalgebra.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|)) (|Vector| $)) "\\spad{conditionsForIdempotents([v1,...,vn])} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra as \\spad{R}-module.")) (|someBasis| (((|Vector| $)) "\\spad{someBasis()} returns some \\spad{R}-module basis."))) 
-((-3994 |has| |#1| (-496)) (-3992 . T) (-3991 . T)) 
+((-3993 |has| |#1| (-495)) (-3991 . T) (-3990 . T)) 
 NIL 
 (-317 A S) 
 ((|constructor| (NIL "A finite aggregate is a homogeneous aggregate with a finite number of elements.")) (|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})}.")) (|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 \\spad{reduce(f,u,x)},{} \\spad{x} is the identity operation of \\spad{f}. Same as \\spad{reduce(f,u,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 starting value,{} usually the identity operation of \\spad{f}. Same as \\spad{reduce(f,u)} if \\spad{u} has 2 or more elements. Returns \\spad{f(x,y)} if \\spad{u} has one element \\spad{y},{} \\spad{x} if \\spad{u} is empty. For example,{} \\spad{reduce(+,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 \\spad{[x,y,...,z]} then \\spad{reduce(f,u)} returns \\spad{f(..f(f(x,y),...),z)}. Note: if \\spad{u} has one element \\spad{x},{} \\spad{reduce(f,u)} returns \\spad{x}. Error: if \\spad{u} is empty.")) (|members| (((|List| |#2|) $) "\\spad{members(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{members([\\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} \\indented{1}{in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} holds. 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}) holds 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 \\spad{p(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})}.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\#u} returns the number of items in \\spad{u}."))) 
@@ -1218,12 +1218,12 @@ NIL
 ((|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-312)))) 
 (-322 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| $)) "\\spad{regularRepresentation(a,basis)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra."))) 
-((-3991 . T) (-3992 . T) (-3994 . T)) 
+((-3990 . T) (-3991 . T) (-3993 . T)) 
 NIL 
 (-323 A S) 
 ((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|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|) $ $) "\\spad{merge(p,a,b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) 
 NIL 
-((|HasCategory| |#1| (|%list| (QUOTE -1036) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-72)))) 
+((|HasCategory| |#1| (|%list| (QUOTE -1035) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-756))) (|HasCategory| |#2| (QUOTE (-72)))) 
 (-324 S) 
 ((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|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|) $ $) "\\spad{merge(p,a,b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) 
 NIL 
@@ -1234,7 +1234,7 @@ NIL
 NIL 
 (-326 |VarSet| R) 
 ((|constructor| (NIL "The category of free Lie algebras. It is used by domains of non-commutative algebra: \\spadtype{LiePolynomial} and \\spadtype{XPBWPolynomial}. \\newline Author: Michel Petitot (petitot@lifl.fr)")) (|eval| (($ $ (|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) (-3992 . T) (-3991 . T)) 
+((|JacobiIdentity| . T) (|NullSquare| . T) (-3991 . T) (-3990 . T)) 
 NIL 
 (-327 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."))) 
@@ -1243,14 +1243,14 @@ NIL
 (-328 S R) 
 ((|constructor| (NIL "\\spad{S} is \\spadtype{FullyLinearlyExplicitRingOver R} means that \\spad{S} is a \\spadtype{LinearlyExplicitRingOver R} and,{} in addition,{} if \\spad{R} is a \\spadtype{LinearlyExplicitRingOver Integer},{} then so is \\spad{S}"))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-581 (-485))))) 
+((|HasCategory| |#2| (QUOTE (-580 (-484))))) 
 (-329 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 
 (-330) 
 ((|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}."))) 
-((-3980 . T) (-3988 . T) (-3772 . T) (-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((-3979 . T) (-3987 . T) (-3771 . T) (-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
 NIL 
 (-331 |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}."))) 
@@ -1262,15 +1262,15 @@ NIL
 NIL 
 (-333 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."))) 
-((-3992 . T) (-3991 . T)) 
-((|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-1014))))) 
+((-3991 . T) (-3990 . T)) 
+((|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-1013))))) 
 (-334 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}"))) 
-((-3992 . T) (-3991 . T)) 
+((-3991 . T) (-3990 . T)) 
 ((|HasCategory| |#1| (QUOTE (-146)))) 
 (-335 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}."))) 
-((-3992 . T) (-3991 . T)) 
+((-3991 . T) (-3990 . T)) 
 NIL 
 (-336 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| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) 
@@ -1279,7 +1279,7 @@ NIL
 (-337 S) 
 ((|constructor| (NIL "The free monoid on a set \\spad{S} is the monoid of finite products of the form \\spad{reduce(*,[si ** ni])} where the \\spad{si}'s are in \\spad{S},{} and the \\spad{ni}'s are nonnegative integers. The multiplication is not commutative."))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-757)))) 
+((|HasCategory| |#1| (QUOTE (-756)))) 
 (-338) 
 ((|constructor| (NIL "This domain provides an interface to names in the file system."))) 
 NIL 
@@ -1290,13 +1290,13 @@ NIL
 NIL 
 (-340 |n| |class| R) 
 ((|constructor| (NIL "Generate the Free Lie Algebra over a ring \\spad{R} with identity; A \\spad{P}. Hall basis is generated by a package call to HallBasis.")) (|generator| (($ (|NonNegativeInteger|)) "\\spad{generator(i)} is the \\spad{i}th Hall Basis element")) (|shallowExpand| (((|OutputForm|) $) "\\spad{shallowExpand(x)} \\undocumented{}")) (|deepExpand| (((|OutputForm|) $) "\\spad{deepExpand(x)} \\undocumented{}")) (|dimension| (((|NonNegativeInteger|)) "\\spad{dimension()} is the rank of this Lie algebra"))) 
-((-3992 . T) (-3991 . T)) 
+((-3991 . T) (-3990 . T)) 
 NIL 
-(-341 -3094 UP UPUP R) 
+(-341 -3093 UP UPUP R) 
 ((|constructor| (NIL "\\indented{1}{Finds the order of a divisor over a finite field} Author: Manuel Bronstein Date Created: 1988 Date Last Updated: 11 Jul 1990")) (|order| (((|NonNegativeInteger|) (|FiniteDivisor| |#1| |#2| |#3| |#4|)) "\\spad{order(x)} \\undocumented"))) 
 NIL 
 NIL 
-(-342 -3094 UP) 
+(-342 -3093 UP) 
 ((|constructor| (NIL "\\indented{1}{Full partial fraction expansion of rational functions} Author: Manuel Bronstein Date Created: 9 December 1992 Date Last Updated: June 18,{} 2010 References: \\spad{M}.Bronstein & \\spad{B}.Salvy,{} \\indented{12}{Full Partial Fraction Decomposition of Rational Functions,{}} \\indented{12}{in Proceedings of \\spad{ISSAC'93},{} Kiev,{} ACM Press.}")) (|construct| (($ (|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| $) "\\spad{p + x} returns the sum of \\spad{p} and \\spad{x}"))) 
 NIL 
 NIL 
@@ -1310,28 +1310,28 @@ NIL
 NIL 
 (-345) 
 ((|constructor| (NIL "FieldOfPrimeCharacteristic is the category of fields of prime characteristic,{} \\spadignore{e.g.} finite fields,{} algebraic closures of fields of prime characteristic,{} transcendental extensions of of fields of prime characteristic.")) (|primeFrobenius| (($ $ (|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|)) $) "\\spad{order(a)} computes the order of an element in the multiplicative group of the field. Error: if \\spad{a} is 0."))) 
-((-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
 NIL 
 (-346 S) 
 ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\"+\") does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\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 -3980)) (|HasAttribute| |#1| (QUOTE -3988))) 
+((|HasAttribute| |#1| (QUOTE -3979)) (|HasAttribute| |#1| (QUOTE -3987))) 
 (-347) 
 ((|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\"."))) 
-((-3772 . T) (-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((-3771 . T) (-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
 NIL 
 (-348 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."))) 
-((-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
-((|HasCategory| |#1| (QUOTE (-456 (-1091) $))) (|HasCategory| |#1| (QUOTE (-260 $))) (|HasCategory| |#1| (QUOTE (-241 $ $))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (|HasCategory| |#1| (QUOTE (-1135))) (OR (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-1135)))) (|HasCategory| |#1| (QUOTE (-934))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (|HasCategory| |#1| (|%list| (QUOTE -456) (QUOTE (-1091)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -241) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-812 (-1091)))) (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasCategory| |#1| (QUOTE (-484))) (|HasCategory| |#1| (QUOTE (-392)))) 
+((-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((|HasCategory| |#1| (QUOTE (-455 (-1090) $))) (|HasCategory| |#1| (QUOTE (-260 $))) (|HasCategory| |#1| (QUOTE (-241 $ $))) (|HasCategory| |#1| (QUOTE (-553 (-473)))) (|HasCategory| |#1| (QUOTE (-1134))) (OR (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-1134)))) (|HasCategory| |#1| (QUOTE (-933))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-484)))) (|HasCategory| |#1| (|%list| (QUOTE -455) (QUOTE (-1090)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -241) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-811 (-1090)))) (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-809 (-1090)))) (|HasCategory| |#1| (QUOTE (-483))) (|HasCategory| |#1| (QUOTE (-392)))) 
 (-349 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 
 (-350 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."))) 
-((-3984 -12 (|has| |#1| (-6 -3995)) (|has| |#1| (-392)) (|has| |#1| (-6 -3984))) (-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
-((|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| |#1| (QUOTE (-951 (-1091)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (|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 (-485)))) (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (QUOTE (-797 (-330)))) (|HasCategory| |#1| (QUOTE (-797 (-485)))) (|HasCategory| |#1| (QUOTE (-554 (-801 (-330))))) (|HasCategory| |#1| (QUOTE (-554 (-801 (-485))))) (|HasCategory| |#1| (QUOTE (-581 (-485)))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-812 (-1091)))) (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasCategory| |#1| (|%list| (QUOTE -456) (QUOTE (-1091)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -241) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-484))) (-12 (|HasAttribute| |#1| (QUOTE -3984)) (|HasAttribute| |#1| (QUOTE -3995)) (|HasCategory| |#1| (QUOTE (-392)))) (-12 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) 
+((-3983 -12 (|has| |#1| (-6 -3994)) (|has| |#1| (-392)) (|has| |#1| (-6 -3983))) (-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-950 (-1090)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-553 (-473)))) (|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 (-484)))) (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (QUOTE (-796 (-330)))) (|HasCategory| |#1| (QUOTE (-796 (-484)))) (|HasCategory| |#1| (QUOTE (-553 (-800 (-330))))) (|HasCategory| |#1| (QUOTE (-553 (-800 (-484))))) (|HasCategory| |#1| (QUOTE (-580 (-484)))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-811 (-1090)))) (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-809 (-1090)))) (|HasCategory| |#1| (|%list| (QUOTE -455) (QUOTE (-1090)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -241) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-483))) (-12 (|HasAttribute| |#1| (QUOTE -3983)) (|HasAttribute| |#1| (QUOTE -3994)) (|HasCategory| |#1| (QUOTE (-392)))) (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) 
 (-351 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 
@@ -1342,28 +1342,28 @@ NIL
 NIL 
 (-353 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| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) 
-((-3991 . T) (-3992 . T) (-3994 . T)) 
+((-3990 . T) (-3991 . T) (-3993 . T)) 
 NIL 
 (-354 A S) 
 ((|constructor| (NIL "\\indented{2}{A is fully retractable to \\spad{B} means that A is retractable to \\spad{B},{} and,{}} \\indented{2}{in addition,{} if \\spad{B} is retractable to the integers or rational} \\indented{2}{numbers then so is A.} \\indented{2}{In particular,{} what we are asserting is that there are no integers} \\indented{2}{(rationals) in A which don't retract into \\spad{B}.} Date Created: March 1990 Date Last Updated: 9 April 1991"))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#2| (QUOTE (-951 (-485))))) 
+((|HasCategory| |#2| (QUOTE (-950 (-350 (-484))))) (|HasCategory| |#2| (QUOTE (-950 (-484))))) 
 (-355 S) 
 ((|constructor| (NIL "\\indented{2}{A is fully retractable to \\spad{B} means that A is retractable to \\spad{B},{} and,{}} \\indented{2}{in addition,{} if \\spad{B} is retractable to the integers or rational} \\indented{2}{numbers then so is A.} \\indented{2}{In particular,{} what we are asserting is that there are no integers} \\indented{2}{(rationals) in A which don't retract into \\spad{B}.} Date Created: March 1990 Date Last Updated: 9 April 1991"))) 
 NIL 
 NIL 
-(-356 R -3094 UP A) 
+(-356 R -3093 UP A) 
 ((|constructor| (NIL "Fractional ideals in a framed algebra.")) (|randomLC| ((|#4| (|NonNegativeInteger|) (|Vector| |#4|)) "\\spad{randomLC(n,x)} should be local but conditional.")) (|minimize| (($ $) "\\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)}."))) 
-((-3994 . T)) 
+((-3993 . T)) 
 NIL 
 (-357 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 
-(-358 R -3094 UP A |ibasis|) 
+(-358 R -3093 UP A |ibasis|) 
 ((|constructor| (NIL "Module representation of fractional ideals.")) (|module| (($ (|FractionalIdeal| |#1| |#2| |#3| |#4|)) "\\spad{module(I)} returns \\spad{I} viewed has a module over \\spad{R}.") (($ (|Vector| |#4|)) "\\spad{module([f1,...,fn])} = the module generated by \\spad{(f1,...,fn)} over \\spad{R}.")) (|norm| ((|#2| $) "\\spad{norm(f)} returns the norm of the module \\spad{f}.")) (|basis| (((|Vector| |#4|) $) "\\spad{basis((f1,...,fn))} = the vector \\spad{[f1,...,fn]}."))) 
 NIL 
-((|HasCategory| |#4| (|%list| (QUOTE -951) (|devaluate| |#2|)))) 
+((|HasCategory| |#4| (|%list| (QUOTE -950) (|devaluate| |#2|)))) 
 (-359 AR R AS S) 
 ((|constructor| (NIL "\\spad{FramedNonAssociativeAlgebraFunctions2} implements functions between two framed non associative algebra domains defined over different rings. The function map is used to coerce between algebras over different domains having the same structural constants.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,u)} maps \\spad{f} onto the coordinates of \\spad{u} to get an element in \\spad{AS} via identification of the basis of \\spad{AR} as beginning part of the basis of \\spad{AS}."))) 
 NIL 
@@ -1374,7 +1374,7 @@ NIL
 ((|HasCategory| |#2| (QUOTE (-312)))) 
 (-361 R) 
 ((|constructor| (NIL "FramedNonAssociativeAlgebra(\\spad{R}) is a \\spadtype{FiniteRankNonAssociativeAlgebra} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank) over a commutative ring \\spad{R} together with a fixed \\spad{R}-module basis.")) (|apply| (($ (|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."))) 
-((-3994 |has| |#1| (-496)) (-3992 . T) (-3991 . T)) 
+((-3993 |has| |#1| (-495)) (-3991 . T) (-3990 . T)) 
 NIL 
 (-362 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)}."))) 
@@ -1383,10 +1383,10 @@ NIL
 (-363 S R) 
 ((|constructor| (NIL "A space of formal functions with arguments in an arbitrary ordered set.")) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| $)) $ (|Kernel| $)) "\\spad{univariate(f, k)} returns \\spad{f} viewed as a univariate fraction in \\spad{k}.")) (/ (($ (|SparseMultivariatePolynomial| |#2| (|Kernel| $)) (|SparseMultivariatePolynomial| |#2| (|Kernel| $))) "\\spad{p1/p2} returns the quotient of \\spad{p1} and \\spad{p2} as an element of \\%.")) (|denominator| (($ $) "\\spad{denominator(f)} returns the denominator of \\spad{f} converted to \\%.")) (|denom| (((|SparseMultivariatePolynomial| |#2| (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|convert| (($ (|Factored| $)) "\\spad{convert(f1\\^e1 ... fm\\^em)} returns \\spad{(f1)\\^e1 ... (fm)\\^em} as an element of \\%,{} using formal kernels created using a \\spadfunFrom{paren}{ExpressionSpace}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isPower(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|numerator| (($ $) "\\spad{numerator(f)} returns the numerator of \\spad{f} converted to \\%.")) (|numer| (((|SparseMultivariatePolynomial| |#2| (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R} if \\spad{R} is an integral domain. If not,{} then numer(\\spad{f}) = \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|coerce| (($ (|Fraction| (|Polynomial| (|Fraction| |#2|)))) "\\spad{coerce(f)} returns \\spad{f} as an element of \\%.") (($ (|Polynomial| (|Fraction| |#2|))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.") (($ (|Fraction| |#2|)) "\\spad{coerce(q)} returns \\spad{q} as an element of \\%.") (($ (|SparseMultivariatePolynomial| |#2| (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.")) (|isMult| (((|Union| (|Record| (|:| |coef| (|Integer|)) (|:| |var| (|Kernel| $))) "failed") $) "\\spad{isMult(p)} returns \\spad{[n, x]} if \\spad{p = n * x} and \\spad{n <> 0}.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,...,mn]} if \\spad{p = m1 +...+ mn} and \\spad{n > 1}.")) (|isExpt| (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|Symbol|)) "\\spad{isExpt(p,f)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = f(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|BasicOperator|)) "\\spad{isExpt(p,op)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = op(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if \\spad{p = a1*...*an} and \\spad{n > 1}.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns \\spad{x} * \\spad{x} * \\spad{x} * ... * \\spad{x} (\\spad{n} times).")) (|eval| (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ $)) "\\spad{eval(x, s, n, f)} replaces every \\spad{s(a)**n} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ (|List| $))) "\\spad{eval(x, s, n, f)} replaces every \\spad{s(a1,...,am)**n} in \\spad{x} by \\spad{f(a1,...,am)} for any \\spad{a1},{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [n1,...,nm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)**ni} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [n1,...,nm], [f1,...,fm])} replaces every \\spad{si(a)**ni} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.") (($ $ (|List| (|BasicOperator|)) (|List| $) (|Symbol|)) "\\spad{eval(x, [s1,...,sm], [f1,...,fm], y)} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $ (|BasicOperator|) $ (|Symbol|)) "\\spad{eval(x, s, f, y)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $) "\\spad{eval(f)} unquotes all the quoted operators in \\spad{f}.") (($ $ (|List| (|Symbol|))) "\\spad{eval(f, [foo1,...,foon])} unquotes all the \\spad{fooi}'s in \\spad{f}.") (($ $ (|Symbol|)) "\\spad{eval(f, foo)} unquotes all the foo's in \\spad{f}.")) (|applyQuote| (($ (|Symbol|) (|List| $)) "\\spad{applyQuote(foo, [x1,...,xn])} returns \\spad{'foo(x1,...,xn)}.") (($ (|Symbol|) $ $ $ $) "\\spad{applyQuote(foo, x, y, z, t)} returns \\spad{'foo(x,y,z,t)}.") (($ (|Symbol|) $ $ $) "\\spad{applyQuote(foo, x, y, z)} returns \\spad{'foo(x,y,z)}.") (($ (|Symbol|) $ $) "\\spad{applyQuote(foo, x, y)} returns \\spad{'foo(x,y)}.") (($ (|Symbol|) $) "\\spad{applyQuote(foo, x)} returns \\spad{'foo(x)}.")) (|variables| (((|List| (|Symbol|)) $) "\\spad{variables(f)} returns the list of all the variables of \\spad{f}.")) (|ground| ((|#2| $) "\\spad{ground(f)} returns \\spad{f} as an element of \\spad{R}. An error occurs if \\spad{f} is not an element of \\spad{R}.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(f)} tests if \\spad{f} is an element of \\spad{R}."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-951 (-485)))) (|HasCategory| |#2| (QUOTE (-496))) (|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 (-413))) (|HasCategory| |#2| (QUOTE (-1026))) (|HasCategory| |#2| (QUOTE (-554 (-474))))) 
+((|HasCategory| |#2| (QUOTE (-950 (-484)))) (|HasCategory| |#2| (QUOTE (-495))) (|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 (-413))) (|HasCategory| |#2| (QUOTE (-1025))) (|HasCategory| |#2| (QUOTE (-553 (-473))))) 
 (-364 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}."))) 
-((-3994 OR (|has| |#1| (-962)) (|has| |#1| (-413))) (-3992 |has| |#1| (-146)) (-3991 |has| |#1| (-146)) ((-3999 "*") |has| |#1| (-496)) (-3990 |has| |#1| (-496)) (-3995 |has| |#1| (-496)) (-3989 |has| |#1| (-496))) 
+((-3993 OR (|has| |#1| (-961)) (|has| |#1| (-413))) (-3991 |has| |#1| (-146)) (-3990 |has| |#1| (-146)) ((-3998 "*") |has| |#1| (-495)) (-3989 |has| |#1| (-495)) (-3994 |has| |#1| (-495)) (-3988 |has| |#1| (-495))) 
 NIL 
 (-365 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}."))) 
@@ -1403,36 +1403,36 @@ NIL
 (-368 A S) 
 ((|constructor| (NIL "A finite-set aggregate models the notion of a finite set,{} that is,{} a collection of elements characterized by membership,{} but not by order or multiplicity. See \\spadtype{Set} for an example.")) (|min| ((|#2| $) "\\spad{min(u)} returns the smallest element of aggregate \\spad{u}.")) (|max| ((|#2| $) "\\spad{max(u)} returns the largest element of aggregate \\spad{u}.")) (|universe| (($) "\\spad{universe()}\\$\\spad{D} returns the universal set for finite set aggregate \\spad{D}.")) (|complement| (($ $) "\\spad{complement(u)} returns the complement of the set \\spad{u},{} \\spadignore{i.e.} the set of all values not in \\spad{u}.")) (|cardinality| (((|NonNegativeInteger|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-320)))) 
+((|HasCategory| |#2| (QUOTE (-756))) (|HasCategory| |#2| (QUOTE (-320)))) 
 (-369 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|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) 
-((-3987 . T) (-3998 . T)) 
+((-3986 . T) (-3997 . T)) 
 NIL 
 (-370 S A R B) 
 ((|constructor| (NIL "\\spad{FiniteSetAggregateFunctions2} provides functions involving two finite set aggregates where the underlying domains might be different. An example of this is to create a set of rational numbers by mapping a function across a set of integers,{} where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-aggregates \\spad{x} of aggregate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad {[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialised to \\spad{r}. For example,{} \\spad{reduce(_+\\$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 
-(-371 R -3094) 
+(-371 R -3093) 
 ((|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 
 (-372 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"))) 
-((-3984 -12 (|has| |#1| (-6 -3984)) (|has| |#2| (-6 -3984))) (-3991 . T) (-3992 . T) (-3994 . T)) 
-((-12 (|HasAttribute| |#1| (QUOTE -3984)) (|HasAttribute| |#2| (QUOTE -3984)))) 
-(-373 R -3094) 
+((-3983 -12 (|has| |#1| (-6 -3983)) (|has| |#2| (-6 -3983))) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((-12 (|HasAttribute| |#1| (QUOTE -3983)) (|HasAttribute| |#2| (QUOTE -3983)))) 
+(-373 R -3093) 
 ((|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 
-(-374 R -3094) 
+(-374 R -3093) 
 ((|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 
-(-375 R -3094) 
+(-375 R -3093) 
 ((|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)))) 
-(-376 R -3094) 
+(-376 R -3093) 
 ((|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 
@@ -1440,10 +1440,10 @@ 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 
-(-378 R -3094 UP) 
+(-378 R -3093 UP) 
 ((|constructor| (NIL "\\indented{1}{Used internally by IR2F} Author: Manuel Bronstein Date Created: 12 May 1988 Date Last Updated: 22 September 1993 Keywords: function,{} space,{} polynomial,{} factoring")) (|anfactor| (((|Union| (|Factored| (|SparseUnivariatePolynomial| (|AlgebraicNumber|))) "failed") |#3|) "\\spad{anfactor(p)} tries to factor \\spad{p} over algebraic numbers,{} returning \"failed\" if it cannot")) (|UP2ifCan| (((|Union| (|:| |overq| (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) (|:| |overan| (|SparseUnivariatePolynomial| (|AlgebraicNumber|))) (|:| |failed| (|Boolean|))) |#3|) "\\spad{UP2ifCan(x)} should be local but conditional.")) (|qfactor| (((|Union| (|Factored| (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) "failed") |#3|) "\\spad{qfactor(p)} tries to factor \\spad{p} over fractions of integers,{} returning \"failed\" if it cannot")) (|ffactor| (((|Factored| |#3|) |#3|) "\\spad{ffactor(p)} tries to factor a univariate polynomial \\spad{p} over \\spad{F}"))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-951 (-48))))) 
+((|HasCategory| |#2| (QUOTE (-950 (-48))))) 
 (-379) 
 ((|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 
@@ -1460,7 +1460,7 @@ 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 
-(-383 R UP -3094) 
+(-383 R UP -3093) 
 ((|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 
@@ -1498,16 +1498,16 @@ NIL
 NIL 
 (-392) 
 ((|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}."))) 
-((-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
 NIL 
 (-393 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"))) 
-((-3994 |has| (-350 (-858 |#1|)) (-496)) (-3992 . T) (-3991 . T)) 
-((|HasCategory| (-350 (-858 |#1|)) (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| (-350 (-858 |#1|)) (QUOTE (-496)))) 
+((-3993 |has| (-350 (-857 |#1|)) (-495)) (-3991 . T) (-3990 . T)) 
+((|HasCategory| (-350 (-857 |#1|)) (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| (-350 (-857 |#1|)) (QUOTE (-495)))) 
 (-394 |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"))) 
-(((-3999 "*") |has| |#2| (-146)) (-3990 |has| |#2| (-496)) (-3995 |has| |#2| (-6 -3995)) (-3992 . T) (-3991 . T) (-3994 . T)) 
-((|HasCategory| |#2| (QUOTE (-822))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-822)))) (OR (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-822)))) (OR (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-822)))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-146))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-496)))) (-12 (|HasCategory| |#2| (QUOTE (-797 (-330)))) (|HasCategory| (-774 |#1|) (QUOTE (-797 (-330))))) (-12 (|HasCategory| |#2| (QUOTE (-797 (-485)))) (|HasCategory| (-774 |#1|) (QUOTE (-797 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-554 (-801 (-330))))) (|HasCategory| (-774 |#1|) (QUOTE (-554 (-801 (-330)))))) (-12 (|HasCategory| |#2| (QUOTE (-554 (-801 (-485))))) (|HasCategory| (-774 |#1|) (QUOTE (-554 (-801 (-485)))))) (-12 (|HasCategory| |#2| (QUOTE (-554 (-474)))) (|HasCategory| (-774 |#1|) (QUOTE (-554 (-474))))) (|HasCategory| |#2| (QUOTE (-581 (-485)))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#2| (QUOTE (-951 (-485)))) (OR (|HasCategory| |#2| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#2| (QUOTE (-951 (-350 (-485)))))) (|HasCategory| |#2| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#2| (QUOTE (-312))) (|HasAttribute| |#2| (QUOTE -3995)) (|HasCategory| |#2| (QUOTE (-392))) (-12 (|HasCategory| |#2| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#2| (QUOTE (-118))))) 
+(((-3998 "*") |has| |#2| (-146)) (-3989 |has| |#2| (-495)) (-3994 |has| |#2| (-6 -3994)) (-3991 . T) (-3990 . T) (-3993 . T)) 
+((|HasCategory| |#2| (QUOTE (-821))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-821)))) (OR (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-821)))) (OR (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-821)))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-146))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-495)))) (-12 (|HasCategory| |#2| (QUOTE (-796 (-330)))) (|HasCategory| (-773 |#1|) (QUOTE (-796 (-330))))) (-12 (|HasCategory| |#2| (QUOTE (-796 (-484)))) (|HasCategory| (-773 |#1|) (QUOTE (-796 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-553 (-800 (-330))))) (|HasCategory| (-773 |#1|) (QUOTE (-553 (-800 (-330)))))) (-12 (|HasCategory| |#2| (QUOTE (-553 (-800 (-484))))) (|HasCategory| (-773 |#1|) (QUOTE (-553 (-800 (-484)))))) (-12 (|HasCategory| |#2| (QUOTE (-553 (-473)))) (|HasCategory| (-773 |#1|) (QUOTE (-553 (-473))))) (|HasCategory| |#2| (QUOTE (-580 (-484)))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#2| (QUOTE (-950 (-484)))) (OR (|HasCategory| |#2| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#2| (QUOTE (-950 (-350 (-484)))))) (|HasCategory| |#2| (QUOTE (-950 (-350 (-484))))) (|HasCategory| |#2| (QUOTE (-312))) (|HasAttribute| |#2| (QUOTE -3994)) (|HasCategory| |#2| (QUOTE (-392))) (-12 (|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#2| (QUOTE (-118))))) 
 (-395 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 
@@ -1534,7 +1534,7 @@ NIL
 NIL 
 (-401 |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| $) "\\spad{leadingCoefficient(x)} \\undocumented"))) 
-((-3992 . T) (-3991 . T)) 
+((-3991 . T) (-3990 . T)) 
 NIL 
 (-402 E V R P Q) 
 ((|constructor| (NIL "Gosper's summation algorithm.")) (|GospersMethod| (((|Union| |#5| "failed") |#5| |#2| (|Mapping| |#2|)) "\\spad{GospersMethod(b, n, new)} returns a rational function \\spad{rf(n)} such that \\spad{a(n) * rf(n)} is the indefinite sum of \\spad{a(n)} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{a(n+1) * rf(n+1) - a(n) * rf(n) = a(n)},{} where \\spad{b(n) = a(n)/a(n-1)} is a rational function. Returns \"failed\" if no such rational function \\spad{rf(n)} exists. Note: \\spad{new} is a nullary function returning a new \\spad{V} every time. The condition on \\spad{a(n)} is that \\spad{a(n)/a(n-1)} is a rational function of \\spad{n}."))) 
@@ -1542,8 +1542,8 @@ NIL
 NIL 
 (-403 R E |VarSet| P) 
 ((|constructor| (NIL "A domain for polynomial sets.")) (|convert| (($ (|List| |#4|)) "\\axiom{convert(lp)} returns the polynomial set whose members are the polynomials of \\axiom{lp}."))) 
-((-3998 . T)) 
-((-12 (|HasCategory| |#4| (QUOTE (-1014))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-554 (-474)))) (|HasCategory| |#4| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#4| (QUOTE (-553 (-773)))) (|HasCategory| |#4| (QUOTE (-1014))) (-12 (|HasCategory| |#4| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#4|)))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#4|)))) 
+((-3997 . T)) 
+((-12 (|HasCategory| |#4| (QUOTE (-1013))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-553 (-473)))) (|HasCategory| |#4| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#4| (QUOTE (-552 (-772)))) (|HasCategory| |#4| (QUOTE (-1013))) (-12 (|HasCategory| |#4| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#4|)))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#4|)))) 
 (-404 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 
@@ -1572,7 +1572,7 @@ 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| $) "\\spad{degree(g)} names the degree of \\spad{g}. The set of all elements of a given degree form an \\spad{R}-module."))) 
 NIL 
 NIL 
-(-411 |lv| -3094 R) 
+(-411 |lv| -3093 R) 
 ((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni,{} Summer \\spad{'88},{} revised November \\spad{'89}} Solve systems of polynomial equations using Groebner bases Total order Groebner bases are computed and then converted to lex ones This package is mostly intended for internal use.")) (|genericPosition| (((|Record| (|:| |dpolys| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |coords| (|List| (|Integer|)))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{genericPosition(lp,lv)} puts a radical zero dimensional ideal in general position,{} for system \\spad{lp} in variables \\spad{lv}.")) (|testDim| (((|Union| (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "failed") (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{testDim(lp,lv)} tests if the polynomial system \\spad{lp} in variables \\spad{lv} is zero dimensional.")) (|groebSolve| (((|List| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{groebSolve(lp,lv)} reduces the polynomial system \\spad{lp} in variables \\spad{lv} to triangular form. Algorithm based on groebner bases algorithm with linear algebra for change of ordering. Preprocessing for the general solver. The polynomials in input are of type \\spadtype{DMP}."))) 
 NIL 
 NIL 
@@ -1582,23 +1582,23 @@ NIL
 NIL 
 (-413) 
 ((|constructor| (NIL "The class of multiplicative groups,{} \\spadignore{i.e.} monoids with multiplicative inverses. \\blankline")) (|commutator| (($ $ $) "\\spad{commutator(p,q)} computes \\spad{inv(p) * inv(q) * p * q}.")) (|conjugate| (($ $ $) "\\spad{conjugate(p,q)} computes \\spad{inv(q) * p * q}; this is 'right action by conjugation'.")) (|unitsKnown| ((|attribute|) "unitsKnown asserts that recip only returns \"failed\" for non-units.")) (** (($ $ (|Integer|)) "\\spad{x**n} returns \\spad{x} raised to the integer power \\spad{n}.")) (/ (($ $ $) "\\spad{x/y} is the same as \\spad{x} times the inverse of \\spad{y}.")) (|inv| (($ $) "\\spad{inv(x)} returns the inverse of \\spad{x}."))) 
-((-3994 . T)) 
+((-3993 . T)) 
 NIL 
 (-414 |Coef| |var| |cen|) 
 ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x\\^r)}.")) (|integrate| (($ $ (|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."))) 
-(((-3999 "*") |has| |#1| (-146)) (-3990 |has| |#1| (-496)) (-3995 |has| |#1| (-312)) (-3989 |has| |#1| (-312)) (-3991 . T) (-3992 . T) (-3994 . T)) 
-((|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-485))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-485))) (|devaluate| |#1|)))) (|HasCategory| (-350 (-485)) (QUOTE (-1026))) (|HasCategory| |#1| (QUOTE (-312))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-496)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-496)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-485)))))) (|HasSignature| |#1| (|%list| (QUOTE -3948) (|%list| (|devaluate| |#1|) (QUOTE (-1091)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-485)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-29 (-485)))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1116)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasSignature| |#1| (|%list| (QUOTE -3814) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1091))))) (|HasSignature| |#1| (|%list| (QUOTE -3083) (|%list| (|%list| (QUOTE -584) (QUOTE (-1091))) (|devaluate| |#1|))))))) 
+(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-495)) (-3994 |has| |#1| (-312)) (-3988 |has| |#1| (-312)) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((|HasCategory| |#1| (QUOTE (-38 (-350 (-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 (-809 (-1090)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-484))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-484))) (|devaluate| |#1|)))) (|HasCategory| (-350 (-484)) (QUOTE (-1025))) (|HasCategory| |#1| (QUOTE (-312))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-495)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-495)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-484)))))) (|HasSignature| |#1| (|%list| (QUOTE -3947) (|%list| (|devaluate| |#1|) (QUOTE (-1090)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-484)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-29 (-484)))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1115)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasSignature| |#1| (|%list| (QUOTE -3813) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1090))))) (|HasSignature| |#1| (|%list| (QUOTE -3082) (|%list| (|%list| (QUOTE -583) (QUOTE (-1090))) (|devaluate| |#1|))))))) 
 (-415 |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."))) 
-((-3998 . T)) 
-((-12 (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3862) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-553 (-773))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-474)))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-72))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014))) (-12 (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3862) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3862) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (-12 (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#2|))))) 
+((-3997 . T)) 
+((-12 (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3861) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-552 (-772)))) (|HasCategory| |#2| (QUOTE (-552 (-772))))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-473)))) (-12 (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#2| (QUOTE (-72))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013))) (-12 (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3861) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3861) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (-12 (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#2|))))) 
 (-416 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)}"))) 
-((-3998 . T)) 
-((-12 (|HasCategory| |#4| (QUOTE (-1014))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-554 (-474)))) (|HasCategory| |#4| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#3| (QUOTE (-320))) (|HasCategory| |#4| (QUOTE (-553 (-773)))) (|HasCategory| |#4| (QUOTE (-1014))) (-12 (|HasCategory| |#4| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#4|)))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#4|)))) 
+((-3997 . T)) 
+((-12 (|HasCategory| |#4| (QUOTE (-1013))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-553 (-473)))) (|HasCategory| |#4| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#3| (QUOTE (-320))) (|HasCategory| |#4| (QUOTE (-552 (-772)))) (|HasCategory| |#4| (QUOTE (-1013))) (-12 (|HasCategory| |#4| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#4|)))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#4|)))) 
 (-417) 
 ((|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}."))) 
-((-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
 NIL 
 (-418) 
 ((|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'."))) 
@@ -1606,29 +1606,29 @@ NIL
 NIL 
 (-419 |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."))) 
-((-3998 . T)) 
-((-12 (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3862) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-553 (-773))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-474)))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-72))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014))) (-12 (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3862) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3862) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (-12 (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#2|))))) 
+((-3997 . T)) 
+((-12 (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3861) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-552 (-772)))) (|HasCategory| |#2| (QUOTE (-552 (-772))))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-473)))) (-12 (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#2| (QUOTE (-72))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013))) (-12 (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3861) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3861) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (-12 (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#2|))))) 
 (-420) 
 ((|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 
 (-421 |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"))) 
-(((-3999 "*") |has| |#2| (-146)) (-3990 |has| |#2| (-496)) (-3995 |has| |#2| (-6 -3995)) (-3992 . T) (-3991 . T) (-3994 . T)) 
-((|HasCategory| |#2| (QUOTE (-822))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-822)))) (OR (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-822)))) (OR (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-822)))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-146))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-496)))) (-12 (|HasCategory| |#2| (QUOTE (-797 (-330)))) (|HasCategory| (-774 |#1|) (QUOTE (-797 (-330))))) (-12 (|HasCategory| |#2| (QUOTE (-797 (-485)))) (|HasCategory| (-774 |#1|) (QUOTE (-797 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-554 (-801 (-330))))) (|HasCategory| (-774 |#1|) (QUOTE (-554 (-801 (-330)))))) (-12 (|HasCategory| |#2| (QUOTE (-554 (-801 (-485))))) (|HasCategory| (-774 |#1|) (QUOTE (-554 (-801 (-485)))))) (-12 (|HasCategory| |#2| (QUOTE (-554 (-474)))) (|HasCategory| (-774 |#1|) (QUOTE (-554 (-474))))) (|HasCategory| |#2| (QUOTE (-581 (-485)))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#2| (QUOTE (-951 (-485)))) (OR (|HasCategory| |#2| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#2| (QUOTE (-951 (-350 (-485)))))) (|HasCategory| |#2| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#2| (QUOTE (-312))) (|HasAttribute| |#2| (QUOTE -3995)) (|HasCategory| |#2| (QUOTE (-392))) (-12 (|HasCategory| |#2| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#2| (QUOTE (-118))))) 
-(-422 -2623 S) 
+(((-3998 "*") |has| |#2| (-146)) (-3989 |has| |#2| (-495)) (-3994 |has| |#2| (-6 -3994)) (-3991 . T) (-3990 . T) (-3993 . T)) 
+((|HasCategory| |#2| (QUOTE (-821))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-821)))) (OR (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-821)))) (OR (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-821)))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-146))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-495)))) (-12 (|HasCategory| |#2| (QUOTE (-796 (-330)))) (|HasCategory| (-773 |#1|) (QUOTE (-796 (-330))))) (-12 (|HasCategory| |#2| (QUOTE (-796 (-484)))) (|HasCategory| (-773 |#1|) (QUOTE (-796 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-553 (-800 (-330))))) (|HasCategory| (-773 |#1|) (QUOTE (-553 (-800 (-330)))))) (-12 (|HasCategory| |#2| (QUOTE (-553 (-800 (-484))))) (|HasCategory| (-773 |#1|) (QUOTE (-553 (-800 (-484)))))) (-12 (|HasCategory| |#2| (QUOTE (-553 (-473)))) (|HasCategory| (-773 |#1|) (QUOTE (-553 (-473))))) (|HasCategory| |#2| (QUOTE (-580 (-484)))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#2| (QUOTE (-950 (-484)))) (OR (|HasCategory| |#2| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#2| (QUOTE (-950 (-350 (-484)))))) (|HasCategory| |#2| (QUOTE (-950 (-350 (-484))))) (|HasCategory| |#2| (QUOTE (-312))) (|HasAttribute| |#2| (QUOTE -3994)) (|HasCategory| |#2| (QUOTE (-392))) (-12 (|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#2| (QUOTE (-118))))) 
+(-422 -2622 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}."))) 
-((-3991 |has| |#2| (-962)) (-3992 |has| |#2| (-962)) (-3994 |has| |#2| (-6 -3994))) 
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(-12 (|HasCategory| |#2| (QUOTE (-189))) (|HasCategory| |#2| (QUOTE (-961)))) (-12 (|HasCategory| |#2| (QUOTE (-811 (-1090)))) (|HasCategory| |#2| (QUOTE (-961)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-950 (-484)))) (|HasCategory| |#2| (QUOTE (-1013)))) (|HasCategory| |#2| (QUOTE (-961)))) (-12 (|HasCategory| |#2| (QUOTE (-950 (-484)))) (|HasCategory| |#2| (QUOTE (-1013)))) (-12 (|HasCategory| |#2| (QUOTE (-950 (-350 (-484))))) (|HasCategory| |#2| (QUOTE (-1013)))) (|HasAttribute| |#2| (QUOTE -3993)) (-12 (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-961)))) (-12 (|HasCategory| |#2| (QUOTE (-809 (-1090)))) (|HasCategory| |#2| (QUOTE (-961)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-25))) (-12 (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#2|))))) 
 (-423) 
 ((|constructor| (NIL "This domain represents the header of a definition.")) (|parameters| (((|List| (|ParameterAst|)) $) "\\spad{parameters(h)} gives the parameters specified in the definition header `h'.")) (|name| (((|Identifier|) $) "\\spad{name(h)} returns the name of the operation defined defined.")) (|headAst| (($ (|Identifier|) (|List| (|ParameterAst|))) "\\spad{headAst(f,[x1,..,xn])} constructs a function definition header."))) 
 NIL 
 NIL 
 (-424 S) 
 ((|constructor| (NIL "Heap implemented in a flexible array to allow for insertions")) (|heap| (($ (|List| |#1|)) "\\spad{heap(ls)} creates a heap of elements consisting of the elements of \\spad{ls}."))) 
-((-3998 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-72)))) 
-(-425 -3094 UP UPUP R) 
+((-3997 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1013))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-72)))) 
+(-425 -3093 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 
@@ -1638,12 +1638,12 @@ NIL
 NIL 
 (-427) 
 ((|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."))) 
-((-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
-((|HasCategory| (-485) (QUOTE (-822))) (|HasCategory| (-485) (QUOTE (-951 (-1091)))) (|HasCategory| (-485) (QUOTE (-118))) (|HasCategory| (-485) (QUOTE (-120))) (|HasCategory| (-485) (QUOTE (-554 (-474)))) (|HasCategory| (-485) (QUOTE (-934))) (|HasCategory| (-485) (QUOTE (-741))) (|HasCategory| (-485) (QUOTE (-757))) (OR (|HasCategory| (-485) (QUOTE (-741))) (|HasCategory| (-485) (QUOTE (-757)))) (|HasCategory| (-485) (QUOTE (-951 (-485)))) (|HasCategory| (-485) (QUOTE (-1067))) (|HasCategory| (-485) (QUOTE (-797 (-330)))) (|HasCategory| (-485) (QUOTE (-797 (-485)))) (|HasCategory| (-485) (QUOTE (-554 (-801 (-330))))) (|HasCategory| (-485) (QUOTE (-554 (-801 (-485))))) (|HasCategory| (-485) (QUOTE (-189))) (|HasCategory| (-485) (QUOTE (-812 (-1091)))) (|HasCategory| (-485) (QUOTE (-190))) (|HasCategory| (-485) (QUOTE (-810 (-1091)))) (|HasCategory| (-485) (QUOTE (-456 (-1091) (-485)))) (|HasCategory| (-485) (QUOTE (-260 (-485)))) (|HasCategory| (-485) (QUOTE (-241 (-485) (-485)))) (|HasCategory| (-485) (QUOTE (-258))) (|HasCategory| (-485) (QUOTE (-484))) (|HasCategory| (-485) (QUOTE (-581 (-485)))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-485) (QUOTE (-822)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-485) (QUOTE (-822)))) (|HasCategory| (-485) (QUOTE (-118))))) 
+((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((|HasCategory| (-484) (QUOTE (-821))) (|HasCategory| (-484) (QUOTE (-950 (-1090)))) (|HasCategory| (-484) (QUOTE (-118))) (|HasCategory| (-484) (QUOTE (-120))) (|HasCategory| (-484) (QUOTE (-553 (-473)))) (|HasCategory| (-484) (QUOTE (-933))) (|HasCategory| (-484) (QUOTE (-740))) (|HasCategory| (-484) (QUOTE (-756))) (OR (|HasCategory| (-484) (QUOTE (-740))) (|HasCategory| (-484) (QUOTE (-756)))) (|HasCategory| (-484) (QUOTE (-950 (-484)))) (|HasCategory| (-484) (QUOTE (-1066))) (|HasCategory| (-484) (QUOTE (-796 (-330)))) (|HasCategory| (-484) (QUOTE (-796 (-484)))) (|HasCategory| (-484) (QUOTE (-553 (-800 (-330))))) (|HasCategory| (-484) (QUOTE (-553 (-800 (-484))))) (|HasCategory| (-484) (QUOTE (-189))) (|HasCategory| (-484) (QUOTE (-811 (-1090)))) (|HasCategory| (-484) (QUOTE (-190))) (|HasCategory| (-484) (QUOTE (-809 (-1090)))) (|HasCategory| (-484) (QUOTE (-455 (-1090) (-484)))) (|HasCategory| (-484) (QUOTE (-260 (-484)))) (|HasCategory| (-484) (QUOTE (-241 (-484) (-484)))) (|HasCategory| (-484) (QUOTE (-258))) (|HasCategory| (-484) (QUOTE (-483))) (|HasCategory| (-484) (QUOTE (-580 (-484)))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-484) (QUOTE (-821)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-484) (QUOTE (-821)))) (|HasCategory| (-484) (QUOTE (-118))))) 
 (-428 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. Those with attribute \\spadatt{shallowlyMutable} allow an element to be modified or updated without changing its overall value.")) (|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|) $) "\\spad{map(f,u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) 
 NIL 
-((|HasAttribute| |#1| (QUOTE -3998)) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-553 (-773))))) 
+((|HasAttribute| |#1| (QUOTE -3997)) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-552 (-772))))) 
 (-429 S) 
 ((|constructor| (NIL "A homogeneous aggregate is an aggregate of elements all of the same type. In the current system,{} all aggregates are homogeneous. Two attributes characterize classes of aggregates. Those with attribute \\spadatt{shallowlyMutable} allow an element to be modified or updated without changing its overall value.")) (|map!| (($ (|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|) $) "\\spad{map(f,u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) 
 NIL 
@@ -1664,3113 +1664,3109 @@ NIL
 ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) 
 NIL 
 NIL 
-(-434 -3094 UP |AlExt| |AlPol|) 
+(-434 -3093 UP |AlExt| |AlPol|) 
 ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of a field over which we can factor UP's.")) (|factor| (((|Factored| |#4|) |#4| (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{factor(p, f)} returns a prime factorisation of \\spad{p}; \\spad{f} is a factorisation map for elements of UP."))) 
 NIL 
 NIL 
 (-435) 
 ((|constructor| (NIL "Algebraic closure of the rational numbers.")) (|norm| (($ $ (|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}."))) 
-((-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
-((|HasCategory| $ (QUOTE (-962))) (|HasCategory| $ (QUOTE (-951 (-485))))) 
+((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((|HasCategory| $ (QUOTE (-961))) (|HasCategory| $ (QUOTE (-950 (-484))))) 
 (-436 S |mn|) 
 ((|constructor| (NIL "\\indented{1}{Author Micheal Monagan \\spad{Aug/87}} This is the basic one dimensional array data type."))) 
-((-3998 . T)) 
-((OR (-12 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (OR (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-757))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|))) (|HasCategory| $ (|%list| (QUOTE -1036) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| $ (|%list| (QUOTE -1036) (|devaluate| |#1|))))) 
+((-3997 . T)) 
+((OR (-12 (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-553 (-473)))) (OR (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-756))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| (-484) (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|))) (|HasCategory| $ (|%list| (QUOTE -1035) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| $ (|%list| (QUOTE -1035) (|devaluate| |#1|))))) 
 (-437 R |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."))) 
-((-3998 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-72)))) 
+((-3997 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1013))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-72)))) 
 (-438 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 
-(-439 R UP -3094) 
+(-439 R UP -3093) 
 ((|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 
-(-440 |mn|) 
-((|constructor| (NIL "\\spadtype{IndexedBits} is a domain to compactly represent large quantities of Boolean data."))) 
-((-3998 . T)) 
-((-12 (|HasCategory| (-85) (QUOTE (-260 (-85)))) (|HasCategory| (-85) (QUOTE (-1014)))) (|HasCategory| (-85) (QUOTE (-554 (-474)))) (|HasCategory| (-85) (QUOTE (-757))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| (-85) (QUOTE (-72))) (|HasCategory| (-85) (QUOTE (-553 (-773)))) (|HasCategory| (-85) (QUOTE (-1014))) (-12 (|HasCategory| $ (QUOTE (-1036 (-85)))) (|HasCategory| (-85) (QUOTE (-757)))) (|HasCategory| $ (QUOTE (-1036 (-85)))) (|HasCategory| $ (QUOTE (-318 (-85)))) (-12 (|HasCategory| $ (QUOTE (-318 (-85)))) (|HasCategory| (-85) (QUOTE (-72))))) 
-(-441 K R UP L) 
+(-440 K R UP L) 
 ((|constructor| (NIL "IntegralBasisPolynomialTools provides functions for \\indented{1}{mapping functions on the coefficients of univariate and bivariate} \\indented{1}{polynomials.}")) (|mapBivariate| (((|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#4|)) (|Mapping| |#4| |#1|) |#3|) "\\spad{mapBivariate(f,p(x,y))} applies the function \\spad{f} to the coefficients of \\spad{p(x,y)}.")) (|mapMatrixIfCan| (((|Union| (|Matrix| |#2|) "failed") (|Mapping| (|Union| |#1| "failed") |#4|) (|Matrix| (|SparseUnivariatePolynomial| |#4|))) "\\spad{mapMatrixIfCan(f,mat)} applies the function \\spad{f} to the coefficients of the entries of \\spad{mat} if possible,{} and returns \\spad{\"failed\"} otherwise.")) (|mapUnivariateIfCan| (((|Union| |#2| "failed") (|Mapping| (|Union| |#1| "failed") |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{mapUnivariateIfCan(f,p(x))} applies the function \\spad{f} to the coefficients of \\spad{p(x)},{} if possible,{} and returns \\spad{\"failed\"} otherwise.")) (|mapUnivariate| (((|SparseUnivariatePolynomial| |#4|) (|Mapping| |#4| |#1|) |#2|) "\\spad{mapUnivariate(f,p(x))} applies the function \\spad{f} to the coefficients of \\spad{p(x)}.") ((|#2| (|Mapping| |#1| |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{mapUnivariate(f,p(x))} applies the function \\spad{f} to the coefficients of \\spad{p(x)}."))) 
 NIL 
 NIL 
-(-442) 
+(-441) 
 ((|constructor| (NIL "\\indented{1}{This domain implements a container of information} about the AXIOM library")) (|fullDisplay| (((|Void|) $) "\\spad{fullDisplay(ic)} prints all of the information contained in \\axiom{\\spad{ic}}.")) (|display| (((|Void|) $) "\\spad{display(ic)} prints a summary of the information contained in \\axiom{\\spad{ic}}.")) (|elt| (((|String|) $ (|Symbol|)) "\\spad{elt(ic,s)} selects a particular field from \\axiom{\\spad{ic}}. Valid fields are \\axiom{name,{} nargs,{} exposed,{} type,{} abbreviation,{} kind,{} origin,{} params,{} condition,{} doc}."))) 
 NIL 
 NIL 
-(-443 R Q A B) 
+(-442 R Q A B) 
 ((|constructor| (NIL "InnerCommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#4|) "\\spad{splitDenominator([q1,...,qn])} returns \\spad{[[p1,...,pn], d]} such that \\spad{qi = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}'s.")) (|clearDenominator| ((|#3| |#4|) "\\spad{clearDenominator([q1,...,qn])} returns \\spad{[p1,...,pn]} such that \\spad{qi = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}'s.")) (|commonDenominator| ((|#1| |#4|) "\\spad{commonDenominator([q1,...,qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}qn."))) 
 NIL 
 NIL 
-(-444 -3094 |Expon| |VarSet| |DPoly|) 
+(-443 -3093 |Expon| |VarSet| |DPoly|) 
 ((|constructor| (NIL "This domain represents polynomial ideals with coefficients in any field and supports the basic ideal operations,{} including intersection sum and quotient. An ideal is represented by a list of polynomials (the generators of the ideal) and a boolean that is \\spad{true} if the generators are a Groebner basis. The algorithms used are based on Groebner basis computations. The ordering is determined by the datatype of the input polynomials. Users may use refinements of total degree orderings.")) (|relationsIdeal| (((|SuchThat| (|List| (|Polynomial| |#1|)) (|List| (|Equation| (|Polynomial| |#1|)))) (|List| |#4|)) "\\spad{relationsIdeal(polyList)} returns the ideal of relations among the polynomials in \\spad{polyList}.")) (|saturate| (($ $ |#4| (|List| |#3|)) "\\spad{saturate(I,f,lvar)} is the saturation with respect to the prime principal ideal which is generated by \\spad{f} in the polynomial ring \\spad{F[lvar]}.") (($ $ |#4|) "\\spad{saturate(I,f)} is the saturation of the ideal \\spad{I} with respect to the multiplicative set generated by the polynomial \\spad{f}.")) (|coerce| (($ (|List| |#4|)) "\\spad{coerce(polyList)} converts the list of polynomials \\spad{polyList} to an ideal.")) (|generators| (((|List| |#4|) $) "\\spad{generators(I)} returns a list of generators for the ideal \\spad{I}.")) (|groebner?| (((|Boolean|) $) "\\spad{groebner?(I)} tests if the generators of the ideal \\spad{I} are a Groebner basis.")) (|groebnerIdeal| (($ (|List| |#4|)) "\\spad{groebnerIdeal(polyList)} constructs the ideal generated by the list of polynomials \\spad{polyList} which are assumed to be a Groebner basis. Note: this operation avoids a Groebner basis computation.")) (|ideal| (($ (|List| |#4|)) "\\spad{ideal(polyList)} constructs the ideal generated by the list of polynomials \\spad{polyList}.")) (|leadingIdeal| (($ $) "\\spad{leadingIdeal(I)} is the ideal generated by the leading terms of the elements of the ideal \\spad{I}.")) (|dimension| (((|Integer|) $) "\\spad{dimension(I)} gives the dimension of the ideal \\spad{I}. in the ring \\spad{F[lvar]},{} where lvar are the variables appearing in \\spad{I}") (((|Integer|) $ (|List| |#3|)) "\\spad{dimension(I,lvar)} gives the dimension of the ideal \\spad{I},{} in the ring \\spad{F[lvar]}")) (|backOldPos| (($ (|Record| (|:| |mval| (|Matrix| |#1|)) (|:| |invmval| (|Matrix| |#1|)) (|:| |genIdeal| $))) "\\spad{backOldPos(genPos)} takes the result produced by \\spadfunFrom{generalPosition}{PolynomialIdeals} and performs the inverse transformation,{} returning the original ideal \\spad{backOldPos(generalPosition(I,listvar))} = \\spad{I}.")) (|generalPosition| (((|Record| (|:| |mval| (|Matrix| |#1|)) (|:| |invmval| (|Matrix| |#1|)) (|:| |genIdeal| $)) $ (|List| |#3|)) "\\spad{generalPosition(I,listvar)} perform a random linear transformation on the variables in \\spad{listvar} and returns the transformed ideal along with the change of basis matrix.")) (|groebner| (($ $) "\\spad{groebner(I)} returns a set of generators of \\spad{I} that are a Groebner basis for \\spad{I}.")) (|quotient| (($ $ |#4|) "\\spad{quotient(I,f)} computes the quotient of the ideal \\spad{I} by the principal ideal generated by the polynomial \\spad{f},{} \\spad{(I:(f))}.") (($ $ $) "\\spad{quotient(I,J)} computes the quotient of the ideals \\spad{I} and \\spad{J},{} \\spad{(I:J)}.")) (|intersect| (($ (|List| $)) "\\spad{intersect(LI)} computes the intersection of the list of ideals \\spad{LI}.") (($ $ $) "\\spad{intersect(I,J)} computes the intersection of the ideals \\spad{I} and \\spad{J}.")) (|zeroDim?| (((|Boolean|) $) "\\spad{zeroDim?(I)} tests if the ideal \\spad{I} is zero dimensional,{} \\spadignore{i.e.} all its associated primes are maximal,{} in the ring \\spad{F[lvar]},{} where lvar are the variables appearing in \\spad{I}") (((|Boolean|) $ (|List| |#3|)) "\\spad{zeroDim?(I,lvar)} tests if the ideal \\spad{I} is zero dimensional,{} \\spadignore{i.e.} all its associated primes are maximal,{} in the ring \\spad{F[lvar]}")) (|inRadical?| (((|Boolean|) |#4| $) "\\spad{inRadical?(f,I)} tests if some power of the polynomial \\spad{f} belongs to the ideal \\spad{I}.")) (|in?| (((|Boolean|) $ $) "\\spad{in?(I,J)} tests if the ideal \\spad{I} is contained in the ideal \\spad{J}.")) (|element?| (((|Boolean|) |#4| $) "\\spad{element?(f,I)} tests whether the polynomial \\spad{f} belongs to the ideal \\spad{I}.")) (|zero?| (((|Boolean|) $) "\\spad{zero?(I)} tests whether the ideal \\spad{I} is the zero ideal")) (|one?| (((|Boolean|) $) "\\spad{one?(I)} tests whether the ideal \\spad{I} is the unit ideal,{} \\spadignore{i.e.} contains 1.")) (+ (($ $ $) "\\spad{I+J} computes the ideal generated by the union of \\spad{I} and \\spad{J}.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{I**n} computes the \\spad{n}th power of the ideal \\spad{I}.")) (* (($ $ $) "\\spad{I*J} computes the product of the ideal \\spad{I} and \\spad{J}."))) 
 NIL 
-((|HasCategory| |#3| (QUOTE (-554 (-1091))))) 
-(-445 |vl| |nv|) 
+((|HasCategory| |#3| (QUOTE (-553 (-1090))))) 
+(-444 |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 
-(-446 T$) 
+(-445 T$) 
 ((|constructor| (NIL "This is the category of all domains that implement idempotent operations."))) 
-(((|%Rule| |idempotence| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|)) (-3058 (|f| |x| |x|) |x|))) . T)) 
+(((|%Rule| |idempotence| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|)) (-3057 (|f| |x| |x|) |x|))) . T)) 
 NIL 
-(-447) 
+(-446) 
 ((|constructor| (NIL "This domain provides representation for plain identifiers. It differs from Symbol in that it does not support any form of scripting. It is a plain basic data structure. \\blankline")) (|gensym| (($) "\\spad{gensym()} returns a new identifier,{} different from any other identifier in the running system"))) 
 NIL 
 NIL 
-(-448 A S) 
+(-447 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 (-1014))) (|HasCategory| |#2| (QUOTE (-1014))))) 
-(-449 A S) 
+((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-1013))))) 
+(-448 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 (-1014))) (|HasCategory| |#2| (QUOTE (-1014))))) 
-(-450 A S) 
+((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-1013))))) 
+(-449 A S) 
 ((|constructor| (NIL "This category represents the direct product of some set with respect to an ordered indexing set.")) (|terms| (((|List| (|IndexedProductTerm| |#1| |#2|)) $) "\\spad{terms x} returns the list of terms in \\spad{x}. Each term is a pair of a support (the first component) and the corresponding value (the second component).")) (|reductum| (($ $) "\\spad{reductum(z)} returns a new element created by removing the leading coefficient/support pair from the element \\spad{z}. Error: if \\spad{z} has no support.")) (|leadingSupport| ((|#2| $) "\\spad{leadingSupport(z)} returns the index of leading (with respect to the ordering on the indexing set) monomial of \\spad{z}. Error: if \\spad{z} has no support.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(z)} returns the coefficient of the leading (with respect to the ordering on the indexing set) monomial of \\spad{z}. Error: if \\spad{z} has no support.")) (|monomial| (($ |#1| |#2|) "\\spad{monomial(a,s)} constructs a direct product element with the \\spad{s} component set to \\spad{a}")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,z)} returns the new element created by applying the function \\spad{f} to each component of the direct product element \\spad{z}."))) 
 NIL 
 NIL 
-(-451 A S) 
+(-450 A S) 
 ((|constructor| (NIL "Indexed direct products of objects over a set \\spad{A} of generators indexed by an ordered set \\spad{S}. All items have finite support.")) (|combineWithIf| (($ $ $ (|Mapping| |#1| |#1| |#1|) (|Mapping| (|Boolean|) |#1| |#1|)) "\\spad{combineWithIf(u,v,f,p)} returns the result of combining index-wise,{} coefficients of \\spad{u} and \\spad{u} if when satisfy the predicate \\spad{p}. Those pairs of coefficients which fail\\spad{p} are implicitly ignored."))) 
 NIL 
-((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-1014))))) 
-(-452 A S) 
+((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-1013))))) 
+(-451 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 (-1014))) (|HasCategory| |#2| (QUOTE (-1014))))) 
-(-453 A S) 
+((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-1013))))) 
+(-452 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 (-1014))) (|HasCategory| |#2| (QUOTE (-1014))))) 
-(-454 A S) 
+((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-1013))))) 
+(-453 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 
-(-455 S A B) 
+(-454 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 
-(-456 A B) 
+(-455 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 
-(-457 S E |un|) 
+(-456 S E |un|) 
 ((|constructor| (NIL "Internal implementation of a free abelian monoid."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-717)))) 
-(-458 S |mn|) 
+((|HasCategory| |#2| (QUOTE (-716)))) 
+(-457 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}"))) 
-((-3998 . T)) 
-((OR (-12 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (OR (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-757))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|))) (|HasCategory| $ (|%list| (QUOTE -1036) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| $ (|%list| (QUOTE -1036) (|devaluate| |#1|))))) 
-(-459) 
+((-3997 . T)) 
+((OR (-12 (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-553 (-473)))) (OR (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-756))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| (-484) (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|))) (|HasCategory| $ (|%list| (QUOTE -1035) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| $ (|%list| (QUOTE -1035) (|devaluate| |#1|))))) 
+(-458) 
 ((|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 
-(-460 |p| |n|) 
+(-459 |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}."))) 
-((-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
-((OR (|HasCategory| (-518 |#1|) (QUOTE (-118))) (|HasCategory| (-518 |#1|) (QUOTE (-320)))) (|HasCategory| (-518 |#1|) (QUOTE (-120))) (|HasCategory| (-518 |#1|) (QUOTE (-320))) (|HasCategory| (-518 |#1|) (QUOTE (-118)))) 
-(-461 R |Row| |Col| M) 
+((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((OR (|HasCategory| (-517 |#1|) (QUOTE (-118))) (|HasCategory| (-517 |#1|) (QUOTE (-320)))) (|HasCategory| (-517 |#1|) (QUOTE (-120))) (|HasCategory| (-517 |#1|) (QUOTE (-320))) (|HasCategory| (-517 |#1|) (QUOTE (-118)))) 
+(-460 R |Row| |Col| M) 
 ((|constructor| (NIL "\\spadtype{InnerMatrixLinearAlgebraFunctions} is an internal package which provides standard linear algebra functions on domains in \\spad{MatrixCategory}")) (|inverse| (((|Union| |#4| "failed") |#4|) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|generalizedInverse| ((|#4| |#4|) "\\spad{generalizedInverse(m)} returns the generalized (Moore--Penrose) inverse of the matrix \\spad{m},{} \\spadignore{i.e.} the matrix \\spad{h} such that m*h*m=h,{} h*m*h=m,{} m*h and h*m are both symmetric matrices.")) (|determinant| ((|#1| |#4|) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. an error message is returned if the matrix is not square.")) (|nullSpace| (((|List| |#3|) |#4|) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) |#4|) "\\spad{nullity(m)} returns the mullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) |#4|) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| ((|#4| |#4|) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}."))) 
 NIL 
-((|HasCategory| |#3| (|%list| (QUOTE -1036) (|devaluate| |#1|)))) 
-(-462 R |Row| |Col| M QF |Row2| |Col2| M2) 
+((|HasCategory| |#3| (|%list| (QUOTE -1035) (|devaluate| |#1|)))) 
+(-461 R |Row| |Col| M QF |Row2| |Col2| M2) 
 ((|constructor| (NIL "\\spadtype{InnerMatrixQuotientFieldFunctions} provides functions on matrices over an integral domain which involve the quotient field of that integral domain. The functions rowEchelon and inverse return matrices with entries in the quotient field.")) (|nullSpace| (((|List| |#3|) |#4|) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|inverse| (((|Union| |#8| "failed") |#4|) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square. Note: the result will have entries in the quotient field.")) (|rowEchelon| ((|#8| |#4|) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}. the result will have entries in the quotient field."))) 
 NIL 
-((|HasCategory| |#7| (|%list| (QUOTE -1036) (|devaluate| |#1|)))) 
-(-463) 
+((|HasCategory| |#7| (|%list| (QUOTE -1035) (|devaluate| |#1|)))) 
+(-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 
-(-464) 
+(-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 
-(-465 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 
-(-466) 
+(-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 
-(-467 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 
-(-468) 
+(-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 
-(-469 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 
-(-470 |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 (-1014))) (|HasCategory| (-695) (QUOTE (-1014))))) 
-(-471 K -3094 |Par|) 
+((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| (-694) (QUOTE (-1013))))) 
+(-470 K -3093 |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 
-(-472) 
+(-471) 
 NIL 
 NIL 
 NIL 
-(-473) 
+(-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 
-(-474) 
+(-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|) $) "\\spad{interpret(f)} passes \\spad{f} to the interpreter."))) 
 NIL 
 NIL 
-(-475 R) 
+(-474 R) 
 ((|constructor| (NIL "Tools for manipulating input forms.")) (|interpret| ((|#1| (|InputForm|)) "\\spad{interpret(f)} passes \\spad{f} to the interpreter,{} and transforms the result into an object of type \\spad{R}.")) (|packageCall| (((|InputForm|) (|Symbol|)) "\\spad{packageCall(f)} returns the input form corresponding to \\spad{f}\\$\\spad{R}."))) 
 NIL 
 NIL 
-(-476 |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 
-(-477 K -3094 |Par|) 
+(-476 K -3093 |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 
-(-478 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 
-(-479 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 
-(-480 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 
-(-481 |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 
-(-482 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 
-(-483 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|) $) "\\spad{odd?(n)} returns \\spad{true} if and only if \\spad{n} is odd."))) 
 NIL 
 NIL 
-(-484) 
+(-483) 
 ((|constructor| (NIL "An \\spad{IntegerNumberSystem} is a model for the integers.")) (|invmod| (($ $ $) "\\spad{invmod(a,b)},{} \\spad{0<=a<b>1},{} \\spad{(a,b)=1} means \\spad{1/a mod b}.")) (|powmod| (($ $ $ $) "\\spad{powmod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a**b mod p}.")) (|mulmod| (($ $ $ $) "\\spad{mulmod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a*b mod p}.")) (|submod| (($ $ $ $) "\\spad{submod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a-b mod p}.")) (|addmod| (($ $ $ $) "\\spad{addmod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a+b mod p}.")) (|mask| (($ $) "\\spad{mask(n)} returns \\spad{2**n-1} (an \\spad{n} bit mask).")) (|dec| (($ $) "\\spad{dec(x)} returns \\spad{x - 1}.")) (|inc| (($ $) "\\spad{inc(x)} returns \\spad{x + 1}.")) (|copy| (($ $) "\\spad{copy(n)} gives a copy of \\spad{n}.")) (|random| (($ $) "\\spad{random(a)} creates a random element from 0 to \\spad{a-1}.") (($) "\\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."))) 
-((-3995 . T) (-3996 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((-3994 . T) (-3995 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
 NIL 
-(-485) 
+(-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."))) 
-((-3985 . T) (-3989 . T) (-3984 . T) (-3995 . T) (-3996 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((-3984 . T) (-3988 . T) (-3983 . T) (-3994 . T) (-3995 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
 NIL 
-(-486) 
+(-485) 
 ((|constructor| (NIL "This domain is a datatype for (signed) integer values of precision 16 bits."))) 
 NIL 
 NIL 
-(-487) 
+(-486) 
 ((|constructor| (NIL "This domain is a datatype for (signed) integer values of precision 32 bits."))) 
 NIL 
 NIL 
-(-488) 
+(-487) 
 ((|constructor| (NIL "This domain is a datatype for (signed) integer values of precision 64 bits."))) 
 NIL 
 NIL 
-(-489) 
+(-488) 
 ((|constructor| (NIL "This domain is a datatype for (signed) integer values of precision 8 bits."))) 
 NIL 
 NIL 
-(-490 |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}."))) 
-((-3998 . T)) 
-((-12 (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3862) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-553 (-773))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-474)))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-72))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014))) (-12 (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3862) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3862) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (-12 (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#2|))))) 
-(-491 R -3094) 
+((-3997 . T)) 
+((-12 (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3861) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-552 (-772)))) (|HasCategory| |#2| (QUOTE (-552 (-772))))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-473)))) (-12 (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#2| (QUOTE (-72))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013))) (-12 (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3861) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3861) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (-12 (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#2|))))) 
+(-490 R -3093) 
 ((|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 
-(-492 R0 -3094 UP UPUP R) 
+(-491 R0 -3093 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 
-(-493) 
+(-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 
-(-494 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."))) 
-((-3772 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((-3771 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
 NIL 
-(-495 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 
-(-496) 
+(-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."))) 
-((-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
 NIL 
-(-497 R -3094) 
+(-496 R -3093) 
 ((|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 
-(-498 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 
-(-499 R -3094 L) 
+(-498 R -3093 L) 
 ((|constructor| (NIL "This internal package rationalises integrands on curves of the form: \\indented{2}{\\spad{y\\^2 = a x\\^2 + b x + c}} \\indented{2}{\\spad{y\\^2 = (a x + b) / (c x + d)}} \\indented{2}{\\spad{f(x, y) = 0} where \\spad{f} has degree 1 in \\spad{x}} The rationalization is done for integration,{} limited integration,{} extended integration and the risch differential equation.")) (|palgLODE0| (((|Record| (|:| |particular| (|Union| |#2| #1="failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgLODE0(op,g,x,y,z,t,c)} returns the solution of \\spad{op f = g} Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}.") (((|Record| (|:| |particular| (|Union| |#2| #1#)) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgLODE0(op, g, x, y, d, p)} returns the solution of \\spad{op f = g}. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}.")) (|lift| (((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|SparseUnivariatePolynomial| |#2|) (|Kernel| |#2|)) "\\spad{lift(u,k)} \\undocumented")) (|multivariate| ((|#2| (|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|Kernel| |#2|) |#2|) "\\spad{multivariate(u,k,f)} \\undocumented")) (|univariate| (((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|SparseUnivariatePolynomial| |#2|)) "\\spad{univariate(f,k,k,p)} \\undocumented")) (|palgRDE0| (((|Union| |#2| #2="failed") |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| #2#) |#2| |#2| (|Symbol|)) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgRDE0(f, g, x, y, foo, t, c)} returns a function \\spad{z(x,y)} such that \\spad{dz/dx + n * df/dx z(x,y) = g(x,y)} if such a \\spad{z} exists,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{foo},{} called by \\spad{foo(a, b, x)},{} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}.") (((|Union| |#2| #2#) |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| #2#) |#2| |#2| (|Symbol|)) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgRDE0(f, g, x, y, foo, d, p)} returns a function \\spad{z(x,y)} such that \\spad{dz/dx + n * df/dx z(x,y) = g(x,y)} if such a \\spad{z} exists,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}. Argument \\spad{foo},{} called by \\spad{foo(a, b, x)},{} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}.")) (|palglimint0| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) #3="failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palglimint0(f, x, y, [u1,...,un], z, t, c)} returns functions \\spad{[h,[[ci, ui]]]} such that the \\spad{ui}'s are among \\spad{[u1,...,un]} and \\spad{d(h + sum(ci log(ui)))/dx = f(x,y)} if such functions exist,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}.") (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) #3#) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palglimint0(f, x, y, [u1,...,un], d, p)} returns functions \\spad{[h,[[ci, ui]]]} such that the \\spad{ui}'s are among \\spad{[u1,...,un]} and \\spad{d(h + sum(ci log(ui)))/dx = f(x,y)} if such functions exist,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}.")) (|palgextint0| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) #4="failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgextint0(f, x, y, g, z, t, c)} returns functions \\spad{[h, d]} such that \\spad{dh/dx = f(x,y) - d g},{} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy},{} and \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{z} is a dummy variable not appearing in \\spad{f(x,y)}. The operation returns \"failed\" if no such functions exist.") (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) #4#) |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgextint0(f, x, y, g, d, p)} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f(x,y) - c g},{} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2 y(x)\\^2 = P(x)},{} or \"failed\" if no such functions exist.")) (|palgint0| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgint0(f, x, y, z, t, c)} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{z} is a dummy variable not appearing in \\spad{f(x,y)}.") (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgint0(f, x, y, d, p)} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2 y(x)\\^2 = P(x)}."))) 
 NIL 
-((|HasCategory| |#3| (|%list| (QUOTE -601) (|devaluate| |#2|)))) 
-(-500) 
+((|HasCategory| |#3| (|%list| (QUOTE -600) (|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 
-(-501 -3094 UP UPUP R) 
+(-500 -3093 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 
-(-502 -3094 UP) 
+(-501 -3093 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 
-(-503 R -3094 L) 
+(-502 R -3093 L) 
 ((|constructor| (NIL "This package provides functions for integration,{} limited integration,{} extended integration and the risch differential equation for pure algebraic integrands.")) (|palgLODE| (((|Record| (|:| |particular| (|Union| |#2| #1="failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Symbol|)) "\\spad{palgLODE(op, g, kx, y, x)} returns the solution of \\spad{op f = g}. \\spad{y} is an algebraic function of \\spad{x}.")) (|palgRDE| (((|Union| |#2| #1#) |#2| |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| #1#) |#2| |#2| (|Symbol|))) "\\spad{palgRDE(nfp, f, g, x, y, foo)} returns a function \\spad{z(x,y)} such that \\spad{dz/dx + n * df/dx z(x,y) = g(x,y)} if such a \\spad{z} exists,{} \"failed\" otherwise; \\spad{y} is an algebraic function of \\spad{x}; \\spad{foo(a, b, x)} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}. \\spad{nfp} is \\spad{n * df/dx}.")) (|palglimint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|)) "\\spad{palglimint(f, x, y, [u1,...,un])} returns functions \\spad{[h,[[ci, ui]]]} such that the \\spad{ui}'s are among \\spad{[u1,...,un]} and \\spad{d(h + sum(ci log(ui)))/dx = f(x,y)} if such functions exist,{} \"failed\" otherwise; \\spad{y} is an algebraic function of \\spad{x}.")) (|palgextint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2|) "\\spad{palgextint(f, x, y, g)} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f(x,y) - c g},{} where \\spad{y} is an algebraic function of \\spad{x}; returns \"failed\" if no such functions exist.")) (|palgint| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|)) "\\spad{palgint(f, x, y)} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x}."))) 
 NIL 
-((|HasCategory| |#3| (|%list| (QUOTE -601) (|devaluate| |#2|)))) 
-(-504 R -3094) 
+((|HasCategory| |#3| (|%list| (QUOTE -600) (|devaluate| |#2|)))) 
+(-503 R -3093) 
 ((|constructor| (NIL "\\spadtype{PatternMatchIntegration} provides functions that use the pattern matcher to find some indefinite and definite integrals involving special functions and found in the litterature.")) (|pmintegrate| (((|Union| |#2| "failed") |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|)) "\\spad{pmintegrate(f, x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b} if it can be found by the built-in pattern matching rules.") (((|Union| (|Record| (|:| |special| |#2|) (|:| |integrand| |#2|)) "failed") |#2| (|Symbol|)) "\\spad{pmintegrate(f, x)} returns either \"failed\" or \\spad{[g,h]} such that \\spad{integrate(f,x) = g + integrate(h,x)}.")) (|pmComplexintegrate| (((|Union| (|Record| (|:| |special| |#2|) (|:| |integrand| |#2|)) "failed") |#2| (|Symbol|)) "\\spad{pmComplexintegrate(f, x)} returns either \"failed\" or \\spad{[g,h]} such that \\spad{integrate(f,x) = g + integrate(h,x)}. It only looks for special complex integrals that pmintegrate does not return.")) (|splitConstant| (((|Record| (|:| |const| |#2|) (|:| |nconst| |#2|)) |#2| (|Symbol|)) "\\spad{splitConstant(f, x)} returns \\spad{[c, g]} such that \\spad{f = c * g} and \\spad{c} does not involve \\spad{t}."))) 
 NIL 
-((-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-485))))) (|HasCategory| |#1| (QUOTE (-797 (-485)))) (|HasCategory| |#2| (QUOTE (-1054)))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-485))))) (|HasCategory| |#1| (QUOTE (-797 (-485)))) (|HasCategory| |#2| (QUOTE (-570))))) 
-(-505 -3094 UP) 
+((-12 (|HasCategory| |#1| (QUOTE (-553 (-800 (-484))))) (|HasCategory| |#1| (QUOTE (-796 (-484)))) (|HasCategory| |#2| (QUOTE (-1053)))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-800 (-484))))) (|HasCategory| |#1| (QUOTE (-796 (-484)))) (|HasCategory| |#2| (QUOTE (-569))))) 
+(-504 -3093 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 
-(-506 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 
-(-507 -3094) 
+(-506 -3093) 
 ((|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 
-(-508 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."))) 
-((-3772 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((-3771 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
 NIL 
-(-509) 
+(-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 
-(-510 R -3094) 
+(-509 R -3093) 
 ((|constructor| (NIL "\\indented{1}{Tools for the integrator} Author: Manuel Bronstein Date Created: 25 April 1990 Date Last Updated: 9 June 1993 Keywords: elementary,{} function,{} integration.")) (|intPatternMatch| (((|IntegrationResult| |#2|) |#2| (|Symbol|) (|Mapping| (|IntegrationResult| |#2|) |#2| (|Symbol|)) (|Mapping| (|Union| (|Record| (|:| |special| |#2|) (|:| |integrand| |#2|)) "failed") |#2| (|Symbol|))) "\\spad{intPatternMatch(f, x, int, pmint)} tries to integrate \\spad{f} first by using the integration function \\spad{int},{} and then by using the pattern match intetgration function \\spad{pmint} on any remaining unintegrable part.")) (|mkPrim| ((|#2| |#2| (|Symbol|)) "\\spad{mkPrim(f, x)} makes the logs in \\spad{f} which are linear in \\spad{x} primitive with respect to \\spad{x}.")) (|removeConstantTerm| ((|#2| |#2| (|Symbol|)) "\\spad{removeConstantTerm(f, x)} returns \\spad{f} minus any additive constant with respect to \\spad{x}.")) (|vark| (((|List| (|Kernel| |#2|)) (|List| |#2|) (|Symbol|)) "\\spad{vark([f1,...,fn],x)} returns the set-theoretic union of \\spad{(varselect(f1,x),...,varselect(fn,x))}.")) (|union| (((|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|))) "\\spad{union(l1, l2)} returns set-theoretic union of \\spad{l1} and \\spad{l2}.")) (|ksec| (((|Kernel| |#2|) (|Kernel| |#2|) (|List| (|Kernel| |#2|)) (|Symbol|)) "\\spad{ksec(k, [k1,...,kn], x)} returns the second top-level \\spad{ki} after \\spad{k} involving \\spad{x}.")) (|kmax| (((|Kernel| |#2|) (|List| (|Kernel| |#2|))) "\\spad{kmax([k1,...,kn])} returns the top-level \\spad{ki} for integration.")) (|varselect| (((|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|)) (|Symbol|)) "\\spad{varselect([k1,...,kn], x)} returns the \\spad{ki} which involve \\spad{x}."))) 
 NIL 
-((-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-485))))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-797 (-485)))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (QUOTE (-570))) (|HasCategory| |#2| (QUOTE (-951 (-1091))))) (-12 (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-239)))) (|HasCategory| |#1| (QUOTE (-496)))) 
-(-511 -3094 UP) 
+((-12 (|HasCategory| |#1| (QUOTE (-553 (-800 (-484))))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-796 (-484)))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-950 (-1090))))) (-12 (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-239)))) (|HasCategory| |#1| (QUOTE (-495)))) 
+(-510 -3093 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 
-(-512 R -3094) 
+(-511 R -3093) 
 ((|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 
-(-513) 
+(-512) 
 ((|constructor| (NIL "This category describes byte stream conduits supporting both input and output operations."))) 
 NIL 
 NIL 
-(-514) 
+(-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 
-(-515) 
+(-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 
-(-516) 
+(-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 
-(-517 |p| |unBalanced?|) 
+(-516 |p| |unBalanced?|) 
 ((|constructor| (NIL "This domain implements Zp,{} the \\spad{p}-adic completion of the integers. This is an internal domain."))) 
-((-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
 NIL 
-(-518 |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."))) 
-((-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
 ((|HasCategory| $ (QUOTE (-120))) (|HasCategory| $ (QUOTE (-118))) (|HasCategory| $ (QUOTE (-320)))) 
-(-519) 
+(-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 
-(-520 -3094) 
+(-519 -3093) 
 ((|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}."))) 
-((-3992 . T) (-3991 . T)) 
-((|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasCategory| |#1| (QUOTE (-951 (-1091))))) 
-(-521 E -3094) 
+((-3991 . T) (-3990 . T)) 
+((|HasCategory| |#1| (QUOTE (-809 (-1090)))) (|HasCategory| |#1| (QUOTE (-950 (-1090))))) 
+(-520 E -3093) 
 ((|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 
-(-522 R -3094) 
+(-521 R -3093) 
 ((|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 
-(-523) 
+(-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 
-(-524 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 
-(-525 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 
-(-526 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)))) 
-(-527) 
+(-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 
-(-528 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 
-(-529) 
+(-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|) $) "\\spad{lhs(e)} returns the left hand side of the is expression `e'."))) 
 NIL 
 NIL 
-(-530 E V R P) 
+(-529 E V R P) 
 ((|constructor| (NIL "tools for the summation packages.")) (|sum| (((|Record| (|:| |num| |#4|) (|:| |den| (|Integer|))) |#4| |#2|) "\\spad{sum(p(n), n)} returns \\spad{P(n)},{} the indefinite sum of \\spad{p(n)} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{P(n+1) - P(n) = a(n)}.") (((|Record| (|:| |num| |#4|) (|:| |den| (|Integer|))) |#4| |#2| (|Segment| |#4|)) "\\spad{sum(p(n), n = a..b)} returns \\spad{p(a) + p(a+1) + ... + p(b)}."))) 
 NIL 
 NIL 
-(-531 |Coef|) 
+(-530 |Coef|) 
 ((|constructor| (NIL "InnerSparseUnivariatePowerSeries is an internal domain \\indented{2}{used for creating sparse Taylor and Laurent series.}")) (|cAcsch| (($ $) "\\spad{cAcsch(f)} computes the inverse hyperbolic cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsech| (($ $) "\\spad{cAsech(f)} computes the inverse hyperbolic secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcoth| (($ $) "\\spad{cAcoth(f)} computes the inverse hyperbolic cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAtanh| (($ $) "\\spad{cAtanh(f)} computes the inverse hyperbolic tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcosh| (($ $) "\\spad{cAcosh(f)} computes the inverse hyperbolic cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsinh| (($ $) "\\spad{cAsinh(f)} computes the inverse hyperbolic sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCsch| (($ $) "\\spad{cCsch(f)} computes the hyperbolic cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSech| (($ $) "\\spad{cSech(f)} computes the hyperbolic secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCoth| (($ $) "\\spad{cCoth(f)} computes the hyperbolic cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cTanh| (($ $) "\\spad{cTanh(f)} computes the hyperbolic tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCosh| (($ $) "\\spad{cCosh(f)} computes the hyperbolic cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSinh| (($ $) "\\spad{cSinh(f)} computes the hyperbolic sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcsc| (($ $) "\\spad{cAcsc(f)} computes the arccosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsec| (($ $) "\\spad{cAsec(f)} computes the arcsecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcot| (($ $) "\\spad{cAcot(f)} computes the arccotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAtan| (($ $) "\\spad{cAtan(f)} computes the arctangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcos| (($ $) "\\spad{cAcos(f)} computes the arccosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsin| (($ $) "\\spad{cAsin(f)} computes the arcsine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCsc| (($ $) "\\spad{cCsc(f)} computes the cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSec| (($ $) "\\spad{cSec(f)} computes the secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCot| (($ $) "\\spad{cCot(f)} computes the cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cTan| (($ $) "\\spad{cTan(f)} computes the tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCos| (($ $) "\\spad{cCos(f)} computes the cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSin| (($ $) "\\spad{cSin(f)} computes the sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cLog| (($ $) "\\spad{cLog(f)} computes the logarithm of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cExp| (($ $) "\\spad{cExp(f)} computes the exponential of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cRationalPower| (($ $ (|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}."))) 
-(((-3999 "*") |has| |#1| (-146)) (-3990 |has| |#1| (-496)) (-3991 . T) (-3992 . T) (-3994 . T)) 
-((|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-496))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-485)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-485)) (|devaluate| |#1|)))) (|HasCategory| (-485) (QUOTE (-1026))) (|HasCategory| |#1| (QUOTE (-312))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-485))))) (|HasSignature| |#1| (|%list| (QUOTE -3948) (|%list| (|devaluate| |#1|) (QUOTE (-1091)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-485)))))) 
-(-532 |Coef|) 
+(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-495)) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((|HasCategory| |#1| (QUOTE (-38 (-350 (-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 (-809 (-1090)))) (|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 (-312))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-484))))) (|HasSignature| |#1| (|%list| (QUOTE -3947) (|%list| (|devaluate| |#1|) (QUOTE (-1090)))))) (|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|) $) "\\spad{coefficients(x)} returns a stream of ring elements. \\indented{1}{When \\spad{x} is a univariate series,{} this is a stream of Taylor} \\indented{1}{coefficients. When \\spad{x} is a multivariate series,{} the} \\indented{1}{\\spad{n}th element of the stream is a form of} \\indented{1}{degree \\spad{n} in the power series variables.}"))) 
-(((-3999 "*") |has| |#1| (-496)) (-3990 |has| |#1| (-496)) (-3991 . T) (-3992 . T) (-3994 . T)) 
-((|HasCategory| |#1| (QUOTE (-496)))) 
-(-533) 
+(((-3998 "*") |has| |#1| (-495)) (-3989 |has| |#1| (-495)) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((|HasCategory| |#1| (QUOTE (-495)))) 
+(-532) 
 ((|constructor| (NIL "This domain provides representations for internal type form.")) (|mappingMode| (($ $ (|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 
-(-534 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 
-(-535 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 
-(-536 R -3094 FG) 
+(-535 R -3093 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 
-(-537 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 
-(-538 S |Index| |Entry|) 
+(-537 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 -3998)) (|HasCategory| |#2| (QUOTE (-757))) (|HasCategory| |#1| (|%list| (QUOTE -318) (|devaluate| |#3|))) (|HasCategory| |#3| (QUOTE (-72)))) 
-(-539 |Index| |Entry|) 
+((|HasCategory| |#1| (|%list| (QUOTE -1035) (|devaluate| |#3|))) (|HasCategory| |#2| (QUOTE (-756))) (|HasCategory| |#1| (|%list| (QUOTE -318) (|devaluate| |#3|))) (|HasCategory| |#3| (QUOTE (-72)))) 
+(-538 |Index| |Entry|) 
 ((|constructor| (NIL "An indexed aggregate is a many-to-one mapping of indices to entries. For example,{} a one-dimensional-array is an indexed aggregate where the index is an integer. Also,{} a table is an indexed aggregate where the indices and entries may have any type.")) (|swap!| (((|Void|) $ |#1| |#1|) "\\spad{swap!(u,i,j)} interchanges elements \\spad{i} and \\spad{j} of aggregate \\spad{u}. No meaningful value is returned.")) (|fill!| (($ $ |#2|) "\\spad{fill!(u,x)} replaces each entry in aggregate \\spad{u} by \\spad{x}. The modified \\spad{u} is returned as value.")) (|first| ((|#2| $) "\\spad{first(u)} returns the first element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{first([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = \\spad{x}}. Error: if \\spad{u} is empty.")) (|minIndex| ((|#1| $) "\\spad{minIndex(u)} returns the minimum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{minIndex(a) = reduce(min,{}[\\spad{i} for \\spad{i} in indices a])}; for lists,{} \\axiom{minIndex(a) = 1}.")) (|maxIndex| ((|#1| $) "\\spad{maxIndex(u)} returns the maximum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{maxIndex(\\spad{u}) = reduce(max,{}[\\spad{i} for \\spad{i} in indices \\spad{u}])}; if \\spad{u} is a list,{} \\axiom{maxIndex(\\spad{u}) = \\#u}.")) (|entry?| (((|Boolean|) |#2| $) "\\spad{entry?(x,u)} tests if \\spad{x} equals \\axiom{\\spad{u} . \\spad{i}} for some index \\spad{i}.")) (|indices| (((|List| |#1|) $) "\\spad{indices(u)} returns a list of indices of aggregate \\spad{u} in no particular order.")) (|index?| (((|Boolean|) |#1| $) "\\spad{index?(i,u)} tests if \\spad{i} is an index of aggregate \\spad{u}.")) (|entries| (((|List| |#2|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) 
 NIL 
 NIL 
-(-540) 
+(-539) 
 ((|constructor| (NIL "This domain represents the join of categories ASTs.")) (|categories| (((|List| (|TypeAst|)) $) "catehories(\\spad{x}) returns the types in the join `x'.")) (|coerce| (($ (|List| (|TypeAst|))) "ts::JoinAst construct the AST for a join of the types `ts'."))) 
 NIL 
 NIL 
-(-541 R A) 
+(-540 R A) 
 ((|constructor| (NIL "\\indented{1}{AssociatedJordanAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$A}} \\indented{1}{to define the new multiplications \\spad{a*b := (a *\\$A b + b *\\$A a)/2}} \\indented{1}{(anticommutator).} \\indented{1}{The usual notation \\spad{{a,b}_+} cannot be used due to} \\indented{1}{restrictions in the current language.} \\indented{1}{This domain only gives a Jordan algebra if the} \\indented{1}{Jordan-identity \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} holds} \\indented{1}{for all \\spad{a},{}\\spad{b},{}\\spad{c} in \\spad{A}.} \\indented{1}{This relation can be checked by} \\indented{1}{\\spadfun{jordanAdmissible?()\\$A}.} \\blankline If the underlying algebra is of type \\spadtype{FramedNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank,{} together with a fixed \\spad{R}-module basis),{} then the same is \\spad{true} for the associated Jordan algebra. Moreover,{} if the underlying algebra is of type \\spadtype{FiniteRankNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank),{} then the same \\spad{true} for the associated Jordan algebra.")) (|coerce| (($ |#2|) "\\spad{coerce(a)} coerces the element \\spad{a} of the algebra \\spad{A} to an element of the Jordan algebra \\spadtype{AssociatedJordanAlgebra}(\\spad{R},{}A)."))) 
-((-3994 OR (-2564 (|has| |#2| (-316 |#1|)) (|has| |#1| (-496))) (-12 (|has| |#2| (-361 |#1|)) (|has| |#1| (-496)))) (-3992 . T) (-3991 . T)) 
-((OR (|HasCategory| |#2| (|%list| (QUOTE -316) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -361) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -361) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (|%list| (QUOTE -361) (|devaluate| |#1|)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#2| (|%list| (QUOTE -316) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#2| (|%list| (QUOTE -361) (|devaluate| |#1|))))) (|HasCategory| |#2| (|%list| (QUOTE -316) (|devaluate| |#1|)))) 
-(-542) 
+((-3993 OR (-2563 (|has| |#2| (-316 |#1|)) (|has| |#1| (-495))) (-12 (|has| |#2| (-361 |#1|)) (|has| |#1| (-495)))) (-3991 . T) (-3990 . T)) 
+((OR (|HasCategory| |#2| (|%list| (QUOTE -316) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -361) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -361) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (|%list| (QUOTE -361) (|devaluate| |#1|)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#2| (|%list| (QUOTE -316) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#2| (|%list| (QUOTE -361) (|devaluate| |#1|))))) (|HasCategory| |#2| (|%list| (QUOTE -316) (|devaluate| |#1|)))) 
+(-541) 
 ((|constructor| (NIL "This is the datatype for the JVM bytecodes."))) 
 NIL 
 NIL 
-(-543) 
+(-542) 
 ((|constructor| (NIL "JVM class file access bitmask and values.")) (|jvmAbstract| (($) "The class was declared abstract; therefore object of this class may not be created.")) (|jvmInterface| (($) "The class file represents an interface,{} not a class.")) (|jvmSuper| (($) "Instruct the JVM to treat base clss method invokation specially.")) (|jvmFinal| (($) "The class was declared final; therefore no derived class allowed.")) (|jvmPublic| (($) "The class was declared public,{} therefore may be accessed from outside its package"))) 
 NIL 
 NIL 
-(-544) 
+(-543) 
 ((|constructor| (NIL "JVM class file constant pool tags.")) (|jvmNameAndTypeConstantTag| (($) "The correspondong constant pool entry represents the name and type of a field or method info.")) (|jvmInterfaceMethodConstantTag| (($) "The correspondong constant pool entry represents an interface method info.")) (|jvmMethodrefConstantTag| (($) "The correspondong constant pool entry represents a class method info.")) (|jvmFieldrefConstantTag| (($) "The corresponding constant pool entry represents a class field info.")) (|jvmStringConstantTag| (($) "The corresponding constant pool entry is a string constant info.")) (|jvmClassConstantTag| (($) "The corresponding constant pool entry represents a class or and interface.")) (|jvmDoubleConstantTag| (($) "The corresponding constant pool entry is a double constant info.")) (|jvmLongConstantTag| (($) "The corresponding constant pool entry is a long constant info.")) (|jvmFloatConstantTag| (($) "The corresponding constant pool entry is a float constant info.")) (|jvmIntegerConstantTag| (($) "The corresponding constant pool entry is an integer constant info.")) (|jvmUTF8ConstantTag| (($) "The corresponding constant pool entry is sequence of bytes representing Java \\spad{UTF8} string constant."))) 
 NIL 
 NIL 
-(-545) 
+(-544) 
 ((|constructor| (NIL "JVM class field access bitmask and values.")) (|jvmTransient| (($) "The field was declared transient.")) (|jvmVolatile| (($) "The field was declared volatile.")) (|jvmFinal| (($) "The field was declared final; therefore may not be modified after initialization.")) (|jvmStatic| (($) "The field was declared static.")) (|jvmProtected| (($) "The field was declared protected; therefore may be accessed withing derived classes.")) (|jvmPrivate| (($) "The field was declared private; threfore can be accessed only within the defining class.")) (|jvmPublic| (($) "The field was declared public; therefore mey accessed from outside its package."))) 
 NIL 
 NIL 
-(-546) 
+(-545) 
 ((|constructor| (NIL "JVM class method access bitmask and values.")) (|jvmStrict| (($) "The method was declared fpstrict; therefore floating-point mode is FP-strict.")) (|jvmAbstract| (($) "The method was declared abstract; therefore no implementation is provided.")) (|jvmNative| (($) "The method was declared native; therefore implemented in a language other than Java.")) (|jvmSynchronized| (($) "The method was declared synchronized.")) (|jvmFinal| (($) "The method was declared final; therefore may not be overriden. in derived classes.")) (|jvmStatic| (($) "The method was declared static.")) (|jvmProtected| (($) "The method was declared protected; therefore may be accessed withing derived classes.")) (|jvmPrivate| (($) "The method was declared private; threfore can be accessed only within the defining class.")) (|jvmPublic| (($) "The method was declared public; therefore mey accessed from outside its package."))) 
 NIL 
 NIL 
-(-547) 
+(-546) 
 ((|constructor| (NIL "This is the datatype for the JVM opcodes."))) 
 NIL 
 NIL 
-(-548 |Entry|) 
+(-547 |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."))) 
-((-3998 . T)) 
-((-12 (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (QUOTE (|:| -3862 (-1074))) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (QUOTE (-1014)))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (QUOTE (-554 (-474)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| (-1074) (QUOTE (-757))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (QUOTE (-1014))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (QUOTE (|:| -3862 (-1074))) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#1|))))) (-12 (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (QUOTE (|:| -3862 (-1074))) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (QUOTE (-72))))) 
-(-549 S |Key| |Entry|) 
+((-3997 . T)) 
+((-12 (|HasCategory| (-2 (|:| -3861 (-1073)) (|:| |entry| |#1|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (QUOTE (|:| -3861 (-1073))) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -3861 (-1073)) (|:| |entry| |#1|)) (QUOTE (-1013)))) (|HasCategory| (-2 (|:| -3861 (-1073)) (|:| |entry| |#1|)) (QUOTE (-553 (-473)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| (-1073) (QUOTE (-756))) (|HasCategory| (-2 (|:| -3861 (-1073)) (|:| |entry| |#1|)) (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3861 (-1073)) (|:| |entry| |#1|)) (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3861 (-1073)) (|:| |entry| |#1|)) (QUOTE (-1013))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (QUOTE (|:| -3861 (-1073))) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#1|))))) (-12 (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (QUOTE (|:| -3861 (-1073))) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -3861 (-1073)) (|:| |entry| |#1|)) (QUOTE (-72))))) 
+(-548 S |Key| |Entry|) 
 ((|constructor| (NIL "A keyed dictionary is a dictionary of key-entry pairs for which there is a unique entry for each key.")) (|search| (((|Union| |#3| "failed") |#2| $) "\\spad{search(k,t)} searches the table \\spad{t} for the key \\spad{k},{} returning the entry stored in \\spad{t} for key \\spad{k}. If \\spad{t} has no such key,{} \\axiom{search(\\spad{k},{}\\spad{t})} returns \"failed\".")) (|remove!| (((|Union| |#3| "failed") |#2| $) "\\spad{remove!(k,t)} searches the table \\spad{t} for the key \\spad{k} removing (and return) the entry if there. If \\spad{t} has no such key,{} \\axiom{remove!(\\spad{k},{}\\spad{t})} returns \"failed\".")) (|keys| (((|List| |#2|) $) "\\spad{keys(t)} returns the list the keys in table \\spad{t}.")) (|key?| (((|Boolean|) |#2| $) "\\spad{key?(k,t)} tests if \\spad{k} is a key in table \\spad{t}."))) 
 NIL 
 NIL 
-(-550 |Key| |Entry|) 
+(-549 |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}."))) 
-((-3998 . T)) 
+((-3997 . T)) 
 NIL 
-(-551 S) 
+(-550 S) 
 ((|constructor| (NIL "A kernel over a set \\spad{S} is an operator applied to a given list of arguments from \\spad{S}.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(op(a1,...,an), s)} tests if the name of op is \\spad{s}.") (((|Boolean|) $ (|BasicOperator|)) "\\spad{is?(op(a1,...,an), f)} tests if op = \\spad{f}.")) (|symbolIfCan| (((|Union| (|Symbol|) "failed") $) "\\spad{symbolIfCan(k)} returns \\spad{k} viewed as a symbol if \\spad{k} is a symbol,{} and \"failed\" otherwise.")) (|kernel| (($ (|Symbol|)) "\\spad{kernel(x)} returns \\spad{x} viewed as a kernel.") (($ (|BasicOperator|) (|List| |#1|) (|NonNegativeInteger|)) "\\spad{kernel(op, [a1,...,an], m)} returns the kernel \\spad{op(a1,...,an)} of nesting level \\spad{m}. Error: if \\spad{op} is \\spad{k}-ary for some \\spad{k} not equal to \\spad{m}.")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(k)} returns the nesting level of \\spad{k}.")) (|argument| (((|List| |#1|) $) "\\spad{argument(op(a1,...,an))} returns \\spad{[a1,...,an]}.")) (|operator| (((|BasicOperator|) $) "\\spad{operator(op(a1,...,an))} returns the operator op."))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-554 (-474)))) (|HasCategory| |#1| (QUOTE (-554 (-801 (-330))))) (|HasCategory| |#1| (QUOTE (-554 (-801 (-485)))))) 
-(-552 R S) 
+((|HasCategory| |#1| (QUOTE (-553 (-473)))) (|HasCategory| |#1| (QUOTE (-553 (-800 (-330))))) (|HasCategory| |#1| (QUOTE (-553 (-800 (-484)))))) 
+(-551 R S) 
 ((|constructor| (NIL "This package exports some auxiliary functions on kernels")) (|constantIfCan| (((|Union| |#1| "failed") (|Kernel| |#2|)) "\\spad{constantIfCan(k)} \\undocumented")) (|constantKernel| (((|Kernel| |#2|) |#1|) "\\spad{constantKernel(r)} \\undocumented"))) 
 NIL 
 NIL 
-(-553 S) 
+(-552 S) 
 ((|constructor| (NIL "A is coercible to \\spad{B} means any element of A can automatically be converted into an element of \\spad{B} by the interpreter.")) (|coerce| ((|#1| $) "\\spad{coerce(a)} transforms a into an element of \\spad{S}."))) 
 NIL 
 NIL 
-(-554 S) 
+(-553 S) 
 ((|constructor| (NIL "A is convertible to \\spad{B} means any element of A can be converted into an element of \\spad{B},{} but not automatically by the interpreter.")) (|convert| ((|#1| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}."))) 
 NIL 
 NIL 
-(-555 -3094 UP) 
+(-554 -3093 UP) 
 ((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic's algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,a_1,a_2,ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$e^{\\int(-a_1/2a_2)} e^{\\int u}\\$} is a solution of \\indented{5}{\\spad{\\$a_2 y'' + a_1 y' + a0 y = 0\\$}} whenever \\spad{u} is a solution of \\spad{P u = 0}. The equation must be already irreducible over the rational functions. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{kovacic(a_0,a_1,a_2)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$e^{\\int(-a_1/2a_2)} e^{\\int u}\\$} is a solution of \\indented{5}{\\spad{a_2 y'' + a_1 y' + a0 y = 0}} whenever \\spad{u} is a solution of \\spad{P u = 0}. The equation must be already irreducible over the rational functions."))) 
 NIL 
 NIL 
-(-556 S) 
+(-555 S) 
 ((|constructor| (NIL "A is coercible from \\spad{B} iff any element of domain \\spad{B} can be automically converted into an element of domain A.")) (|coerce| (($ |#1|) "\\spad{coerce(s)} transforms `s' into an element of `\\%'."))) 
 NIL 
 NIL 
-(-557) 
+(-556) 
 ((|constructor| (NIL "This domain implements Kleene's 3-valued propositional logic.")) (|case| (((|Boolean|) $ (|[\|\|]| |true|)) "\\spad{s case true} holds if the value of `x' is `true'.") (((|Boolean|) $ (|[\|\|]| |unknown|)) "\\spad{x case unknown} holds if the value of `x' is `unknown'") (((|Boolean|) $ (|[\|\|]| |false|)) "\\spad{x case false} holds if the value of `x' is `false'")) (|unknown| (($) "the indefinite `unknown'"))) 
 NIL 
 NIL 
-(-558 S) 
+(-557 S) 
 ((|constructor| (NIL "A is convertible from \\spad{B} iff any element of domain \\spad{B} can be explicitly converted into an element of domain A.")) (|convert| (($ |#1|) "\\spad{convert(s)} transforms `s' into an element of `\\%'."))) 
 NIL 
 NIL 
-(-559 A R S) 
+(-558 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}."))) 
-((-3991 . T) (-3992 . T) (-3994 . T)) 
-((|HasCategory| |#1| (QUOTE (-756)))) 
-(-560 S R) 
+((-3990 . T) (-3991 . T) (-3993 . T)) 
+((|HasCategory| |#1| (QUOTE (-755)))) 
+(-559 S R) 
 ((|constructor| (NIL "The category of all left algebras over an arbitrary ring.")) (|coerce| (($ |#2|) "\\spad{coerce(r)} returns \\spad{r} * 1 where 1 is the identity of the left algebra."))) 
 NIL 
 NIL 
-(-561 R) 
+(-560 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."))) 
-((-3994 . T)) 
+((-3993 . T)) 
 NIL 
-(-562 R -3094) 
+(-561 R -3093) 
 ((|constructor| (NIL "This package computes the forward Laplace Transform.")) (|laplace| ((|#2| |#2| (|Symbol|) (|Symbol|)) "\\spad{laplace(f, t, s)} returns the Laplace transform of \\spad{f(t)} using \\spad{s} as the new variable. This is \\spad{integral(exp(-s*t)*f(t), t = 0..\\%plusInfinity)}. Returns the formal object \\spad{laplace(f, t, s)} if it cannot compute the transform."))) 
 NIL 
 NIL 
-(-563 R UP) 
+(-562 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"))) 
-((-3992 . T) (-3991 . T) ((-3999 "*") . T) (-3990 . T) (-3994 . T)) 
-((|HasCategory| |#2| (QUOTE (-810 (-1091)))) (|HasCategory| |#2| (QUOTE (-812 (-1091)))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485))))) 
-(-564 R E V P TS ST) 
+((-3991 . T) (-3990 . T) ((-3998 "*") . T) (-3989 . T) (-3993 . T)) 
+((|HasCategory| |#2| (QUOTE (-809 (-1090)))) (|HasCategory| |#2| (QUOTE (-811 (-1090)))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-484))))) 
+(-563 R E V P TS ST) 
 ((|constructor| (NIL "A package for solving polynomial systems by means of Lazard triangular sets [1]. This package provides two operations. One for solving in the sense of the regular zeros,{} and the other for solving in the sense of the Zariski closure. Both produce square-free regular sets. Moreover,{} the decompositions do not contain any redundant component. However,{} only zero-dimensional regular sets are normalized,{} since normalization may be time consumming in positive dimension. The decomposition process is that of [2].\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|zeroSetSplit| (((|List| |#6|) (|List| |#4|) (|Boolean|)) "\\axiom{zeroSetSplit(lp,{}clos?)} has the same specifications as \\axiomOpFrom{zeroSetSplit(lp,{}clos?)}{RegularTriangularSetCategory}.")) (|normalizeIfCan| ((|#6| |#6|) "\\axiom{normalizeIfCan(ts)} returns \\axiom{ts} in an normalized shape if \\axiom{ts} is zero-dimensional."))) 
 NIL 
 NIL 
-(-565 OV E Z P) 
+(-564 OV E Z P) 
 ((|constructor| (NIL "Package for leading coefficient determination in the lifting step. Package working for every \\spad{R} euclidean with property \"F\".")) (|distFact| (((|Union| (|Record| (|:| |polfac| (|List| |#4|)) (|:| |correct| |#3|) (|:| |corrfact| (|List| (|SparseUnivariatePolynomial| |#3|)))) "failed") |#3| (|List| (|SparseUnivariatePolynomial| |#3|)) (|Record| (|:| |contp| |#3|) (|:| |factors| (|List| (|Record| (|:| |irr| |#4|) (|:| |pow| (|Integer|)))))) (|List| |#3|) (|List| |#1|) (|List| |#3|)) "\\spad{distFact(contm,unilist,plead,vl,lvar,lval)},{} where \\spad{contm} is the content of the evaluated polynomial,{} \\spad{unilist} is the list of factors of the evaluated polynomial,{} \\spad{plead} is the complete factorization of the leading coefficient,{} \\spad{vl} is the list of factors of the leading coefficient evaluated,{} \\spad{lvar} is the list of variables,{} \\spad{lval} is the list of values,{} returns a record giving the list of leading coefficients to impose on the univariate factors,{}")) (|polCase| (((|Boolean|) |#3| (|NonNegativeInteger|) (|List| |#3|)) "\\spad{polCase(contprod, numFacts, evallcs)},{} where \\spad{contprod} is the product of the content of the leading coefficient of the polynomial to be factored with the content of the evaluated polynomial,{} \\spad{numFacts} is the number of factors of the leadingCoefficient,{} and evallcs is the list of the evaluated factors of the leadingCoefficient,{} returns \\spad{true} if the factors of the leading Coefficient can be distributed with this valuation."))) 
 NIL 
 NIL 
-(-566) 
+(-565) 
 ((|constructor| (NIL "This domain represents assignment expressions.")) (|rhs| (((|SpadAst|) $) "\\spad{rhs(e)} returns the right hand side of the assignment expression `e'.")) (|lhs| (((|SpadAst|) $) "\\spad{lhs(e)} returns the left hand side of the assignment expression `e'."))) 
 NIL 
 NIL 
-(-567 |VarSet| R |Order|) 
+(-566 |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}}."))) 
-((-3994 . T)) 
+((-3993 . T)) 
 NIL 
-(-568 R |ls|) 
+(-567 R |ls|) 
 ((|constructor| (NIL "A package for solving polynomial systems with finitely many solutions. The decompositions are given by means of regular triangular sets. The computations use lexicographical Groebner bases. The main operations are \\axiomOpFrom{lexTriangular}{LexTriangularPackage} and \\axiomOpFrom{squareFreeLexTriangular}{LexTriangularPackage}. The second one provide decompositions by means of square-free regular triangular sets. Both are based on the {\\em lexTriangular} method described in [1]. They differ from the algorithm described in [2] by the fact that multiciplities of the roots are not kept. With the \\axiomOpFrom{squareFreeLexTriangular}{LexTriangularPackage} operation all multiciplities are removed. With the other operation some multiciplities may remain. Both operations admit an optional argument to produce normalized triangular sets. \\newline")) (|zeroSetSplit| (((|List| (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#2|)) (|OrderedVariableList| |#2|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{zeroSetSplit(lp,{} norm?)} decomposes the variety associated with \\axiom{lp} into square-free regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{lp} needs to generate a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.") (((|List| (|RegularChain| |#1| |#2|)) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{zeroSetSplit(lp,{} norm?)} decomposes the variety associated with \\axiom{lp} into regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{lp} needs to generate a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.")) (|squareFreeLexTriangular| (((|List| (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#2|)) (|OrderedVariableList| |#2|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{squareFreeLexTriangular(base,{} norm?)} decomposes the variety associated with \\axiom{base} into square-free regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{base} needs to be a lexicographical Groebner basis of a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.")) (|lexTriangular| (((|List| (|RegularChain| |#1| |#2|)) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{lexTriangular(base,{} norm?)} decomposes the variety associated with \\axiom{base} into regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{base} needs to be a lexicographical Groebner basis of a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.")) (|groebner| (((|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) "\\axiom{groebner(lp)} returns the lexicographical Groebner basis of \\axiom{lp}. If \\axiom{lp} generates a zero-dimensional ideal then the {\\em FGLM} strategy is used,{} otherwise the {\\em Sugar} strategy is used.")) (|fglmIfCan| (((|Union| (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) "failed") (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) "\\axiom{fglmIfCan(lp)} returns the lexicographical Groebner basis of \\axiom{lp} by using the {\\em FGLM} strategy,{} if \\axiom{zeroDimensional?(lp)} holds .")) (|zeroDimensional?| (((|Boolean|) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) "\\axiom{zeroDimensional?(lp)} returns \\spad{true} iff \\axiom{lp} generates a zero-dimensional ideal \\spad{w}.\\spad{r}.\\spad{t}. the variables involved in \\axiom{lp}."))) 
 NIL 
 NIL 
-(-569 R -3094) 
+(-568 R -3093) 
 ((|constructor| (NIL "This package provides liouvillian functions over an integral domain.")) (|integral| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{integral(f,x = a..b)} denotes the definite integral of \\spad{f} with respect to \\spad{x} from \\spad{a} to \\spad{b}.") ((|#2| |#2| (|Symbol|)) "\\spad{integral(f,x)} indefinite integral of \\spad{f} with respect to \\spad{x}.")) (|dilog| ((|#2| |#2|) "\\spad{dilog(f)} denotes the dilogarithm")) (|erf| ((|#2| |#2|) "\\spad{erf(f)} denotes the error function")) (|li| ((|#2| |#2|) "\\spad{li(f)} denotes the logarithmic integral")) (|Ci| ((|#2| |#2|) "\\spad{Ci(f)} denotes the cosine integral")) (|Si| ((|#2| |#2|) "\\spad{Si(f)} denotes the sine integral")) (|Ei| ((|#2| |#2|) "\\spad{Ei(f)} denotes the exponential integral")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns the Liouvillian operator based on \\spad{op}")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} checks if \\spad{op} is Liouvillian"))) 
 NIL 
 NIL 
-(-570) 
+(-569) 
 ((|constructor| (NIL "Category for the transcendental Liouvillian functions.")) (|erf| (($ $) "\\spad{erf(x)} returns the error function of \\spad{x},{} \\spadignore{i.e.} \\spad{2 / sqrt(\\%pi)} times the integral of \\spad{exp(-x**2) dx}.")) (|dilog| (($ $) "\\spad{dilog(x)} returns the dilogarithm of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{log(x) / (1 - x) dx}.")) (|li| (($ $) "\\spad{li(x)} returns the logarithmic integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{dx / log(x)}.")) (|Ci| (($ $) "\\spad{Ci(x)} returns the cosine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{cos(x) / x dx}.")) (|Si| (($ $) "\\spad{Si(x)} returns the sine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{sin(x) / x dx}.")) (|Ei| (($ $) "\\spad{Ei(x)} returns the exponential integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{exp(x)/x dx}."))) 
 NIL 
 NIL 
-(-571 |lv| -3094) 
+(-570 |lv| -3093) 
 ((|constructor| (NIL "\\indented{1}{Given a Groebner basis \\spad{B} with respect to the total degree ordering for} a zero-dimensional ideal \\spad{I},{} compute a Groebner basis with respect to the lexicographical ordering by using linear algebra.")) (|transform| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{transform }\\undocumented")) (|choosemon| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{choosemon }\\undocumented")) (|intcompBasis| (((|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|OrderedVariableList| |#1|) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{intcompBasis }\\undocumented")) (|anticoord| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|List| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{anticoord }\\undocumented")) (|coord| (((|Vector| |#2|) (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{coord }\\undocumented")) (|computeBasis| (((|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{computeBasis }\\undocumented")) (|minPol| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|OrderedVariableList| |#1|)) "\\spad{minPol }\\undocumented") (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|OrderedVariableList| |#1|)) "\\spad{minPol }\\undocumented")) (|totolex| (((|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{totolex }\\undocumented")) (|groebgen| (((|Record| (|:| |glbase| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |glval| (|List| (|Integer|)))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{groebgen }\\undocumented")) (|linGenPos| (((|Record| (|:| |gblist| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |gvlist| (|List| (|Integer|)))) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{linGenPos }\\undocumented"))) 
 NIL 
 NIL 
-(-572) 
+(-571) 
 ((|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."))) 
-((-3998 . T)) 
-((-12 (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| (-51))) (QUOTE (-260 (-2 (|:| -3862 (-1074)) (|:| |entry| (-51)))))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| (-51))) (QUOTE (-1014)))) (OR (|HasCategory| (-51) (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| (-51))) (QUOTE (-1014)))) (OR (|HasCategory| (-51) (QUOTE (-72))) (|HasCategory| (-51) (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| (-51))) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| (-51))) (QUOTE (-1014)))) (OR (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| (-51))) (QUOTE (-553 (-773)))) (|HasCategory| (-51) (QUOTE (-553 (-773))))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| (-51))) (QUOTE (-554 (-474)))) (-12 (|HasCategory| (-51) (QUOTE (-260 (-51)))) (|HasCategory| (-51) (QUOTE (-1014)))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| (-51))) (QUOTE (-72))) (|HasCategory| (-1074) (QUOTE (-757))) (|HasCategory| (-51) (QUOTE (-72))) (OR (|HasCategory| (-51) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| (-51))) (QUOTE (-72)))) (|HasCategory| (-51) (QUOTE (-1014))) (|HasCategory| (-51) (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| (-51))) (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| (-51))) (QUOTE (-1014))) (-12 (|HasCategory| $ (QUOTE (-318 (-2 (|:| -3862 (-1074)) (|:| |entry| (-51)))))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| (-51))) (QUOTE (-72)))) (|HasCategory| $ (QUOTE (-318 (-2 (|:| -3862 (-1074)) (|:| |entry| (-51)))))) (-12 (|HasCategory| $ (QUOTE (-318 (-51)))) (|HasCategory| (-51) (QUOTE (-72))))) 
-(-573 R A) 
+((-3997 . T)) 
+((-12 (|HasCategory| (-2 (|:| -3861 (-1073)) (|:| |entry| (-51))) (QUOTE (-260 (-2 (|:| -3861 (-1073)) (|:| |entry| (-51)))))) (|HasCategory| (-2 (|:| -3861 (-1073)) (|:| |entry| (-51))) (QUOTE (-1013)))) (OR (|HasCategory| (-51) (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3861 (-1073)) (|:| |entry| (-51))) (QUOTE (-1013)))) (OR (|HasCategory| (-51) (QUOTE (-72))) (|HasCategory| (-51) (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3861 (-1073)) (|:| |entry| (-51))) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 (-1073)) (|:| |entry| (-51))) (QUOTE (-1013)))) (OR (|HasCategory| (-2 (|:| -3861 (-1073)) (|:| |entry| (-51))) (QUOTE (-552 (-772)))) (|HasCategory| (-51) (QUOTE (-552 (-772))))) (|HasCategory| (-2 (|:| -3861 (-1073)) (|:| |entry| (-51))) (QUOTE (-553 (-473)))) (-12 (|HasCategory| (-51) (QUOTE (-260 (-51)))) (|HasCategory| (-51) (QUOTE (-1013)))) (|HasCategory| (-2 (|:| -3861 (-1073)) (|:| |entry| (-51))) (QUOTE (-72))) (|HasCategory| (-1073) (QUOTE (-756))) (|HasCategory| (-51) (QUOTE (-72))) (OR (|HasCategory| (-51) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 (-1073)) (|:| |entry| (-51))) (QUOTE (-72)))) (|HasCategory| (-51) (QUOTE (-1013))) (|HasCategory| (-51) (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3861 (-1073)) (|:| |entry| (-51))) (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3861 (-1073)) (|:| |entry| (-51))) (QUOTE (-1013))) (-12 (|HasCategory| $ (QUOTE (-318 (-2 (|:| -3861 (-1073)) (|:| |entry| (-51)))))) (|HasCategory| (-2 (|:| -3861 (-1073)) (|:| |entry| (-51))) (QUOTE (-72)))) (|HasCategory| $ (QUOTE (-318 (-2 (|:| -3861 (-1073)) (|:| |entry| (-51)))))) (-12 (|HasCategory| $ (QUOTE (-318 (-51)))) (|HasCategory| (-51) (QUOTE (-72))))) 
+(-572 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)."))) 
-((-3994 OR (-2564 (|has| |#2| (-316 |#1|)) (|has| |#1| (-496))) (-12 (|has| |#2| (-361 |#1|)) (|has| |#1| (-496)))) (-3992 . T) (-3991 . T)) 
-((OR (|HasCategory| |#2| (|%list| (QUOTE -316) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -361) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -361) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (|%list| (QUOTE -361) (|devaluate| |#1|)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#2| (|%list| (QUOTE -316) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#2| (|%list| (QUOTE -361) (|devaluate| |#1|))))) (|HasCategory| |#2| (|%list| (QUOTE -316) (|devaluate| |#1|)))) 
-(-574 S R) 
+((-3993 OR (-2563 (|has| |#2| (-316 |#1|)) (|has| |#1| (-495))) (-12 (|has| |#2| (-361 |#1|)) (|has| |#1| (-495)))) (-3991 . T) (-3990 . T)) 
+((OR (|HasCategory| |#2| (|%list| (QUOTE -316) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -361) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -361) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (|%list| (QUOTE -361) (|devaluate| |#1|)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#2| (|%list| (QUOTE -316) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#2| (|%list| (QUOTE -361) (|devaluate| |#1|))))) (|HasCategory| |#2| (|%list| (QUOTE -316) (|devaluate| |#1|)))) 
+(-573 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| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) 
 NIL 
 ((|HasCategory| |#2| (QUOTE (-312)))) 
-(-575 R) 
+(-574 R) 
 ((|constructor| (NIL "\\axiom{JacobiIdentity} means that \\axiom{[\\spad{x},{}[\\spad{y},{}\\spad{z}]]+[\\spad{y},{}[\\spad{z},{}\\spad{x}]]+[\\spad{z},{}[\\spad{x},{}\\spad{y}]] = 0} holds.")) (/ (($ $ |#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) (-3992 . T) (-3991 . T)) 
+((|JacobiIdentity| . T) (|NullSquare| . T) (-3991 . T) (-3990 . T)) 
 NIL 
-(-576 R FE) 
+(-575 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 
-(-577 R) 
+(-576 R) 
 ((|constructor| (NIL "Computation of limits for rational functions.")) (|complexLimit| (((|OnePointCompletion| (|Fraction| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|)))) "\\spad{complexLimit(f(x),x = a)} computes the complex limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a}.") (((|OnePointCompletion| (|Fraction| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Equation| (|OnePointCompletion| (|Polynomial| |#1|)))) "\\spad{complexLimit(f(x),x = a)} computes the complex limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a}.")) (|limit| (((|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) #1="failed") (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|))) (|String|)) "\\spad{limit(f(x),x,a,\"left\")} computes the real limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a} from the left; limit(\\spad{f}(\\spad{x}),{}\\spad{x},{}a,{}\"right\") computes the corresponding limit as \\spad{x} approaches \\spad{a} from the right.") (((|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) (|Record| (|:| |leftHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) #1#)) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) #1#))) #2="failed") (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|)))) "\\spad{limit(f(x),x = a)} computes the real two-sided limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a}.") (((|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) (|Record| (|:| |leftHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) #1#)) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) #1#))) #2#) (|Fraction| (|Polynomial| |#1|)) (|Equation| (|OrderedCompletion| (|Polynomial| |#1|)))) "\\spad{limit(f(x),x = a)} computes the real two-sided limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a}."))) 
 NIL 
 NIL 
-(-578 |vars|) 
+(-577 |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 
-(-579 S R) 
+(-578 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 
-((-2562 (|HasCategory| |#1| (QUOTE (-312)))) (|HasCategory| |#1| (QUOTE (-312)))) 
-(-580 K B) 
+((-2561 (|HasCategory| |#1| (QUOTE (-312)))) (|HasCategory| |#1| (QUOTE (-312)))) 
+(-579 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}."))) 
-((-3992 . T) (-3991 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| (-578 |#2|) (QUOTE (-1014))))) 
-(-581 R) 
+((-3991 . T) (-3990 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| (-577 |#2|) (QUOTE (-1013))))) 
+(-580 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 
-(-582 K B) 
+(-581 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}."))) 
-((-3992 . T) (-3991 . T)) 
+((-3991 . T) (-3990 . T)) 
 NIL 
-(-583 S) 
+(-582 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 
-(-584 S) 
+(-583 S) 
 ((|constructor| (NIL "\\spadtype{List} implements singly-linked lists that are addressable by indices; the index of the first element is 1. this constructor provides some LISP-like functions such as \\spadfun{null} and \\spadfun{cons}.")) (|setDifference| (($ $ $) "\\spad{setDifference(u1,u2)} returns a list of the elements of \\spad{u1} that are not also in \\spad{u2}. The order of elements in the resulting list is unspecified.")) (|setIntersection| (($ $ $) "\\spad{setIntersection(u1,u2)} returns a list of the elements that lists \\spad{u1} and \\spad{u2} have in common. The order of elements in the resulting list is unspecified.")) (|setUnion| (($ $ $) "\\spad{setUnion(u1,u2)} appends the two lists \\spad{u1} and \\spad{u2},{} then removes all duplicates. The order of elements in the resulting list is unspecified.")) (|append| (($ $ $) "\\spad{append(u1,u2)} appends the elements of list \\spad{u1} onto the front of list \\spad{u2}. This new list and \\spad{u2} will share some structure.")) (|cons| (($ |#1| $) "\\spad{cons(element,u)} appends \\spad{element} onto the front of list \\spad{u} and returns the new list. This new list and the old one will share some structure.")) (|null| (((|Boolean|) $) "\\spad{null(u)} tests if list \\spad{u} is the empty list.")) (|nil| (($) "\\spad{nil} is the empty list."))) 
-((-3998 . T)) 
-((OR (-12 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (OR (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-757))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| $ (|%list| (QUOTE -1036) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -1036) (|devaluate| |#1|)))) 
-(-585 A B) 
+((-3997 . T)) 
+((OR (-12 (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-553 (-473)))) (OR (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-756))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| (-484) (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| $ (|%list| (QUOTE -1035) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -1035) (|devaluate| |#1|)))) 
+(-584 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 
-(-586 A B) 
+(-585 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 
-(-587 A B C) 
+(-586 A B C) 
 ((|constructor| (NIL "\\spadtype{ListFunctions3} implements utility functions that operate on three kinds of lists,{} each with a possibly different type of element.")) (|map| (((|List| |#3|) (|Mapping| |#3| |#1| |#2|) (|List| |#1|) (|List| |#2|)) "\\spad{map(fn,list1, u2)} applies the binary function \\spad{fn} to corresponding elements of lists \\spad{u1} and \\spad{u2} and returns a list of the results (in the same order). Thus \\spad{map(/,[1,2,3],[4,5,6]) = [1/4,2/4,1/2]}. The computation terminates when the end of either list is reached. That is,{} the length of the result list is equal to the minimum of the lengths of \\spad{u1} and \\spad{u2}."))) 
 NIL 
 NIL 
-(-588 T$) 
+(-587 T$) 
 ((|constructor| (NIL "This domain represents AST for Spad literals."))) 
 NIL 
 NIL 
-(-589 S) 
+(-588 S) 
 ((|constructor| (NIL "\\indented{2}{A set is an \\spad{S}-left linear set if it is stable by left-dilation} \\indented{2}{by elements in the semigroup \\spad{S}.} See Also: RightLinearSet.")) (* (($ |#1| $) "\\spad{s*x} is the left-dilation of \\spad{x} by \\spad{s}."))) 
 NIL 
 NIL 
-(-590 S) 
+(-589 S) 
 ((|substitute| (($ |#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."))) 
-((-3998 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|)))) 
-(-591 R) 
+((-3997 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1013))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-553 (-473)))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|)))) 
+(-590 R) 
 ((|constructor| (NIL "The category of left modules over an rng (ring not necessarily with unit). This is an abelian group which supports left multiplation by elements of the rng. \\blankline"))) 
 NIL 
 NIL 
-(-592 S E |un|) 
+(-591 S E |un|) 
 ((|constructor| (NIL "This internal package represents monoid (abelian or not,{} with or without inverses) as lists and provides some common operations to the various flavors of monoids.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f, a1\\^e1 ... an\\^en)} returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (|mapExpon| (($ (|Mapping| |#2| |#2|) $) "\\spad{mapExpon(f, a1\\^e1 ... an\\^en)} returns \\spad{a1\\^f(e1) ... an\\^f(en)}.")) (|commutativeEquality| (((|Boolean|) $ $) "\\spad{commutativeEquality(x,y)} returns \\spad{true} if \\spad{x} and \\spad{y} are equal assuming commutativity")) (|plus| (($ $ $) "\\spad{plus(x, y)} returns \\spad{x + y} where \\spad{+} is the monoid operation,{} which is assumed commutative.") (($ |#1| |#2| $) "\\spad{plus(s, e, x)} returns \\spad{e * s + x} where \\spad{+} is the monoid operation,{} which is assumed commutative.")) (|leftMult| (($ |#1| $) "\\spad{leftMult(s, a)} returns \\spad{s * a} where \\spad{*} is the monoid operation,{} which is assumed non-commutative.")) (|rightMult| (($ $ |#1|) "\\spad{rightMult(a, s)} returns \\spad{a * s} where \\spad{*} is the monoid operation,{} which is assumed non-commutative.")) (|makeUnit| (($) "\\spad{makeUnit()} returns the unit element of the monomial.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(l)} returns the number of monomials forming \\spad{l}.")) (|reverse!| (($ $) "\\spad{reverse!(l)} reverses the list of monomials forming \\spad{l},{} destroying the element \\spad{l}.")) (|reverse| (($ $) "\\spad{reverse(l)} reverses the list of monomials forming \\spad{l}. This has some effect if the monoid is non-abelian,{} \\spadignore{i.e.} \\spad{reverse(a1\\^e1 ... an\\^en) = an\\^en ... a1\\^e1} which is different.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(l, n)} returns the factor of the n^th monomial of \\spad{l}.")) (|nthExpon| ((|#2| $ (|Integer|)) "\\spad{nthExpon(l, n)} returns the exponent of the n^th monomial of \\spad{l}.")) (|makeMulti| (($ (|List| (|Record| (|:| |gen| |#1|) (|:| |exp| |#2|)))) "\\spad{makeMulti(l)} returns the element whose list of monomials is \\spad{l}.")) (|makeTerm| (($ |#1| |#2|) "\\spad{makeTerm(s, e)} returns the monomial \\spad{s} exponentiated by \\spad{e} (\\spadignore{e.g.} s^e or \\spad{e} * \\spad{s}).")) (|listOfMonoms| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| |#2|))) $) "\\spad{listOfMonoms(l)} returns the list of the monomials forming \\spad{l}.")) (|outputForm| (((|OutputForm|) $ (|Mapping| (|OutputForm|) (|OutputForm|) (|OutputForm|)) (|Mapping| (|OutputForm|) (|OutputForm|) (|OutputForm|)) (|Integer|)) "\\spad{outputForm(l, fop, fexp, unit)} converts the monoid element represented by \\spad{l} to an \\spadtype{OutputForm}. Argument unit is the output form for the \\spadignore{unit} of the monoid (\\spadignore{e.g.} 0 or 1),{} \\spad{fop(a, b)} is the output form for the monoid operation applied to \\spad{a} and \\spad{b} (\\spadignore{e.g.} \\spad{a + b},{} \\spad{a * b},{} \\spad{ab}),{} and \\spad{fexp(a, n)} is the output form for the exponentiation operation applied to \\spad{a} and \\spad{n} (\\spadignore{e.g.} \\spad{n a},{} \\spad{n * a},{} \\spad{a ** n},{} \\spad{a\\^n})."))) 
 NIL 
 NIL 
-(-593 A S) 
+(-592 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 -3998))) 
-(-594 S) 
+((|HasCategory| |#1| (|%list| (QUOTE -1035) (|devaluate| |#2|)))) 
+(-593 S) 
 ((|constructor| (NIL "A linear aggregate is an aggregate whose elements are indexed by integers. Examples of linear aggregates are strings,{} lists,{} and arrays. Most of the exported operations for linear aggregates are non-destructive but are not always efficient for a particular aggregate. For example,{} \\spadfun{concat} of two lists needs only to copy its first argument,{} whereas \\spadfun{concat} of two arrays needs to copy both arguments. Most of the operations exported here apply to infinite objects (\\spadignore{e.g.} streams) as well to finite ones. For finite linear aggregates,{} see \\spadtype{FiniteLinearAggregate}.")) (|setelt| ((|#1| $ (|UniversalSegment| (|Integer|)) |#1|) "\\spad{setelt(u,i..j,x)} (also written: \\axiom{\\spad{u}(\\spad{i}..\\spad{j}) := \\spad{x}}) destructively replaces each element in the segment \\axiom{\\spad{u}(\\spad{i}..\\spad{j})} by \\spad{x}. The value \\spad{x} is returned. Note: \\spad{u} is destructively change so that \\axiom{\\spad{u}.\\spad{k} := \\spad{x} for \\spad{k} in \\spad{i}..\\spad{j}}; its length remains unchanged.")) (|insert| (($ $ $ (|Integer|)) "\\spad{insert(v,u,k)} returns a copy of \\spad{u} having \\spad{v} inserted beginning at the \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{v},{}\\spad{u},{}\\spad{k}) = concat( \\spad{u}(0..\\spad{k}-1),{} \\spad{v},{} \\spad{u}(\\spad{k}..) )}.") (($ |#1| $ (|Integer|)) "\\spad{insert(x,u,i)} returns a copy of \\spad{u} having \\spad{x} as its \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{x},{}a,{}\\spad{k}) = concat(concat(a(0..\\spad{k}-1),{}\\spad{x}),{}a(\\spad{k}..))}.")) (|delete| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete(u,i..j)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th through \\axiom{\\spad{j}}th element deleted. Note: \\axiom{delete(a,{}\\spad{i}..\\spad{j}) = concat(a(0..\\spad{i}-1),{}a(\\spad{j+1}..))}.") (($ $ (|Integer|)) "\\spad{delete(u,i)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th element deleted. Note: for lists,{} \\axiom{delete(a,{}\\spad{i}) == concat(a(0..\\spad{i} - 1),{}a(\\spad{i} + 1,{}..))}.")) (|map| (($ (|Mapping| |#1| |#1| |#1|) $ $) "\\spad{map(f,u,v)} returns a new collection \\spad{w} with elements \\axiom{\\spad{z} = \\spad{f}(\\spad{x},{}\\spad{y})} for corresponding elements \\spad{x} and \\spad{y} from \\spad{u} and \\spad{v}. Note: for linear aggregates,{} \\axiom{\\spad{w}.\\spad{i} = \\spad{f}(\\spad{u}.\\spad{i},{}\\spad{v}.\\spad{i})}.")) (|concat| (($ (|List| $)) "\\spad{concat(u)},{} where \\spad{u} is a lists of aggregates \\axiom{[a,{}\\spad{b},{}...,{}\\spad{c}]},{} returns a single aggregate consisting of the elements of \\axiom{a} followed by those of \\spad{b} followed ... by the elements of \\spad{c}. Note: \\axiom{concat(a,{}\\spad{b},{}...,{}\\spad{c}) = concat(a,{}concat(\\spad{b},{}...,{}\\spad{c}))}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} then \\axiom{\\spad{w}.\\spad{i} = \\spad{u}.\\spad{i} for \\spad{i} in indices \\spad{u}} and \\axiom{\\spad{w}.(\\spad{j} + maxIndex \\spad{u}) = \\spad{v}.\\spad{j} for \\spad{j} in indices \\spad{v}}.") (($ |#1| $) "\\spad{concat(x,u)} returns aggregate \\spad{u} with additional element at the front. Note: for lists: \\axiom{concat(\\spad{x},{}\\spad{u}) == concat([\\spad{x}],{}\\spad{u})}.") (($ $ |#1|) "\\spad{concat(u,x)} returns aggregate \\spad{u} with additional element \\spad{x} at the end. Note: for lists,{} \\axiom{concat(\\spad{u},{}\\spad{x}) == concat(\\spad{u},{}[\\spad{x}])}")) (|new| (($ (|NonNegativeInteger|) |#1|) "\\spad{new(n,x)} returns \\axiom{fill!(new \\spad{n},{}\\spad{x})}."))) 
 NIL 
 NIL 
-(-595 M R S) 
+(-594 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}."))) 
-((-3992 . T) (-3991 . T)) 
-((|HasCategory| |#1| (QUOTE (-715)))) 
-(-596 R -3094 L) 
+((-3991 . T) (-3990 . T)) 
+((|HasCategory| |#1| (QUOTE (-714)))) 
+(-595 R -3093 L) 
 ((|constructor| (NIL "\\spad{ElementaryFunctionLODESolver} provides the top-level functions for finding closed form solutions of linear ordinary differential equations and initial value problems.")) (|solve| (((|Union| |#2| "failed") |#3| |#2| (|Symbol|) |#2| (|List| |#2|)) "\\spad{solve(op, g, x, a, [y0,...,ym])} returns either the solution of the initial value problem \\spad{op y = g, y(a) = y0, y'(a) = y1,...} or \"failed\" if the solution cannot be found; \\spad{x} is the dependent variable.") (((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) "failed") |#3| |#2| (|Symbol|)) "\\spad{solve(op, g, x)} returns either a solution of the ordinary differential equation \\spad{op y = g} or \"failed\" if no non-trivial solution can be found; When found,{} the solution is returned in the form \\spad{[h, [b1,...,bm]]} where \\spad{h} is a particular solution and and \\spad{[b1,...bm]} are linearly independent solutions of the associated homogenuous equation \\spad{op y = 0}. A full basis for the solutions of the homogenuous equation is not always returned,{} only the solutions which were found; \\spad{x} is the dependent variable."))) 
 NIL 
 NIL 
-(-597 A -2494) 
+(-596 A -2493) 
 ((|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}}"))) 
-((-3991 . T) (-3992 . T) (-3994 . T)) 
-((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-312)))) 
-(-598 A) 
+((-3990 . T) (-3991 . T) (-3993 . T)) 
+((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-484)))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-312)))) 
+(-597 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}}"))) 
-((-3991 . T) (-3992 . T) (-3994 . T)) 
-((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-312)))) 
-(-599 A M) 
+((-3990 . T) (-3991 . T) (-3993 . T)) 
+((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-484)))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-312)))) 
+(-598 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| (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}"))) 
-((-3991 . T) (-3992 . T) (-3994 . T)) 
-((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-312)))) 
-(-600 S A) 
+((-3990 . T) (-3991 . T) (-3993 . T)) 
+((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-484)))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-312)))) 
+(-599 S A) 
 ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorCategory} is the category of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|directSum| (($ $ $) "\\spad{directSum(a,b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}.")) (|symmetricSquare| (($ $) "\\spad{symmetricSquare(a)} computes \\spad{symmetricProduct(a,a)} using a more efficient method.")) (|symmetricPower| (($ $ (|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 (-312)))) 
-(-601 A) 
+(-600 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}."))) 
-((-3991 . T) (-3992 . T) (-3994 . T)) 
+((-3990 . T) (-3991 . T) (-3993 . T)) 
 NIL 
-(-602 -3094 UP) 
+(-601 -3093 UP) 
 ((|constructor| (NIL "\\spadtype{LinearOrdinaryDifferentialOperatorFactorizer} provides a factorizer for linear ordinary differential operators whose coefficients are rational functions.")) (|factor1| (((|List| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{factor1(a)} returns the factorisation of a,{} assuming that a has no first-order right factor.")) (|factor| (((|List| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{factor(a)} returns the factorisation of a.") (((|List| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{factor(a, zeros)} returns the factorisation of a. \\spad{zeros} is a zero finder in \\spad{UP}."))) 
 NIL 
 ((|HasCategory| |#1| (QUOTE (-27)))) 
-(-603 A L) 
+(-602 A L) 
 ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorsOps} provides symmetric products and sums for linear ordinary differential operators.")) (|directSum| ((|#2| |#2| |#2| (|Mapping| |#1| |#1|)) "\\spad{directSum(a,b,D)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}. \\spad{D} is the derivation to use.")) (|symmetricPower| ((|#2| |#2| (|NonNegativeInteger|) (|Mapping| |#1| |#1|)) "\\spad{symmetricPower(a,n,D)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of \\spad{n} solutions of \\spad{a}. \\spad{D} is the derivation to use.")) (|symmetricProduct| ((|#2| |#2| |#2| (|Mapping| |#1| |#1|)) "\\spad{symmetricProduct(a,b,D)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of a solution of \\spad{a} by a solution of \\spad{b}. \\spad{D} is the derivation to use."))) 
 NIL 
 NIL 
-(-604 S) 
+(-603 S) 
 ((|constructor| (NIL "`Logic' provides the basic operations for lattices,{} \\spadignore{e.g.} boolean algebra.")) (|\\/| (($ $ $) "\\spadignore{ \\/ } returns the logical `join',{} \\spadignore{e.g.} `or'.")) (|/\\| (($ $ $) "\\spadignore { /\\ }returns the logical `meet',{} \\spadignore{e.g.} `and'.")) (~ (($ $) "\\spad{~(x)} returns the logical complement of \\spad{x}."))) 
 NIL 
 NIL 
-(-605) 
+(-604) 
 ((|constructor| (NIL "`Logic' provides the basic operations for lattices,{} \\spadignore{e.g.} boolean algebra.")) (|\\/| (($ $ $) "\\spadignore{ \\/ } returns the logical `join',{} \\spadignore{e.g.} `or'.")) (|/\\| (($ $ $) "\\spadignore { /\\ }returns the logical `meet',{} \\spadignore{e.g.} `and'.")) (~ (($ $) "\\spad{~(x)} returns the logical complement of \\spad{x}."))) 
 NIL 
 NIL 
-(-606 R) 
+(-605 R) 
 ((|constructor| (NIL "Given a PolynomialFactorizationExplicit ring,{} this package provides a defaulting rule for the \\spad{solveLinearPolynomialEquation} operation,{} by moving into the field of fractions,{} and solving it there via the \\spad{multiEuclidean} operation.")) (|solveLinearPolynomialEquationByFractions| (((|Union| (|List| (|SparseUnivariatePolynomial| |#1|)) "failed") (|List| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{solveLinearPolynomialEquationByFractions([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such exists."))) 
 NIL 
 NIL 
-(-607 |VarSet| R) 
+(-606 |VarSet| R) 
 ((|constructor| (NIL "This type supports Lie polynomials in Lyndon basis see Free Lie Algebras by \\spad{C}. Reutenauer (Oxford science publications). \\newline Author: Michel Petitot (petitot@lifl.fr).")) (|construct| (($ $ (|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) (-3992 . T) (-3991 . T)) 
+((|JacobiIdentity| . T) (|NullSquare| . T) (-3991 . T) (-3990 . T)) 
 ((|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-146)))) 
-(-608 A S) 
+(-607 A S) 
 ((|constructor| (NIL "A list aggregate is a model for a linked list data structure. A linked list is a versatile data structure. Insertion and deletion are efficient and searching is a linear operation.")) (|list| (($ |#2|) "\\spad{list(x)} returns the list of one element \\spad{x}."))) 
 NIL 
 NIL 
-(-609 S) 
+(-608 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}."))) 
-((-3998 . T)) 
+((-3997 . T)) 
 NIL 
-(-610 -3094 |Row| |Col| M) 
+(-609 -3093 |Row| |Col| M) 
 ((|constructor| (NIL "This package solves linear system in the matrix form \\spad{AX = B}.")) (|rank| (((|NonNegativeInteger|) |#4| |#3|) "\\spad{rank(A,B)} computes the rank of the complete matrix \\spad{(A|B)} of the linear system \\spad{AX = B}.")) (|hasSolution?| (((|Boolean|) |#4| |#3|) "\\spad{hasSolution?(A,B)} tests if the linear system \\spad{AX = B} has a solution.")) (|particularSolution| (((|Union| |#3| #1="failed") |#4| |#3|) "\\spad{particularSolution(A,B)} finds a particular solution of the linear system \\spad{AX = B}.")) (|solve| (((|List| (|Record| (|:| |particular| (|Union| |#3| #1#)) (|:| |basis| (|List| |#3|)))) |#4| (|List| |#3|)) "\\spad{solve(A,LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|Record| (|:| |particular| (|Union| |#3| #1#)) (|:| |basis| (|List| |#3|))) |#4| |#3|) "\\spad{solve(A,B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}."))) 
 NIL 
 NIL 
-(-611 -3094) 
+(-610 -3093) 
 ((|constructor| (NIL "This package solves linear system in the matrix form \\spad{AX = B}. It is essentially a particular instantiation of the package \\spadtype{LinearSystemMatrixPackage} for Matrix and Vector. This package's existence makes it easier to use \\spadfun{solve} in the AXIOM interpreter.")) (|rank| (((|NonNegativeInteger|) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{rank(A,B)} computes the rank of the complete matrix \\spad{(A|B)} of the linear system \\spad{AX = B}.")) (|hasSolution?| (((|Boolean|) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{hasSolution?(A,B)} tests if the linear system \\spad{AX = B} has a solution.")) (|particularSolution| (((|Union| (|Vector| |#1|) #1="failed") (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{particularSolution(A,B)} finds a particular solution of the linear system \\spad{AX = B}.")) (|solve| (((|List| (|Record| (|:| |particular| (|Union| (|Vector| |#1|) #1#)) (|:| |basis| (|List| (|Vector| |#1|))))) (|List| (|List| |#1|)) (|List| (|Vector| |#1|))) "\\spad{solve(A,LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|List| (|Record| (|:| |particular| (|Union| (|Vector| |#1|) #1#)) (|:| |basis| (|List| (|Vector| |#1|))))) (|Matrix| |#1|) (|List| (|Vector| |#1|))) "\\spad{solve(A,LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) #1#)) (|:| |basis| (|List| (|Vector| |#1|)))) (|List| (|List| |#1|)) (|Vector| |#1|)) "\\spad{solve(A,B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}.") (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) #1#)) (|:| |basis| (|List| (|Vector| |#1|)))) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{solve(A,B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}."))) 
 NIL 
 NIL 
-(-612 R E OV P) 
+(-611 R E OV P) 
 ((|constructor| (NIL "this package finds the solutions of linear systems presented as a list of polynomials.")) (|linSolve| (((|Record| (|:| |particular| (|Union| (|Vector| (|Fraction| |#4|)) "failed")) (|:| |basis| (|List| (|Vector| (|Fraction| |#4|))))) (|List| |#4|) (|List| |#3|)) "\\spad{linSolve(lp,lvar)} finds the solutions of the linear system of polynomials \\spad{lp} = 0 with respect to the list of symbols \\spad{lvar}."))) 
 NIL 
 NIL 
-(-613 |n| R) 
+(-612 |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."))) 
-((-3994 . T) (-3991 . T) (-3992 . T)) 
-((|HasCategory| |#2| (QUOTE (-810 (-1091)))) (|HasCategory| |#2| (QUOTE (-812 (-1091)))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-189))) (|HasAttribute| |#2| (QUOTE (-3999 #1="*"))) (|HasCategory| |#2| (QUOTE (-581 (-485)))) (|HasCategory| |#2| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#2| (QUOTE (-951 (-485)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-581 (-485)))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-810 (-1091)))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|))))) (|HasCategory| |#2| (QUOTE (-258))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-496))) (OR (|HasAttribute| |#2| (QUOTE (-3999 #1#))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-810 (-1091))))) (|HasCategory| |#2| (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1014))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-146)))) 
-(-614) 
+((-3993 . T) (-3990 . T) (-3991 . T)) 
+((|HasCategory| |#2| (QUOTE (-809 (-1090)))) (|HasCategory| |#2| (QUOTE (-811 (-1090)))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-189))) (|HasAttribute| |#2| (QUOTE (-3998 #1="*"))) (|HasCategory| |#2| (QUOTE (-580 (-484)))) (|HasCategory| |#2| (QUOTE (-950 (-350 (-484))))) (|HasCategory| |#2| (QUOTE (-950 (-484)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-580 (-484)))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-809 (-1090)))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|))))) (|HasCategory| |#2| (QUOTE (-258))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-495))) (OR (|HasAttribute| |#2| (QUOTE (-3998 #1#))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-809 (-1090))))) (|HasCategory| |#2| (QUOTE (-552 (-772)))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1013))) (-12 (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-146)))) 
+(-613) 
 ((|constructor| (NIL "This domain represents `literal sequence' syntax.")) (|elements| (((|List| (|SpadAst|)) $) "\\spad{elements(e)} returns the list of expressions in the `literal' list `e'."))) 
 NIL 
 NIL 
-(-615 |VarSet|) 
+(-614 |VarSet|) 
 ((|constructor| (NIL "Lyndon words over arbitrary (ordered) symbols: see Free Lie Algebras by \\spad{C}. Reutenauer (Oxford science publications). A Lyndon word is a word which is smaller than any of its right factors \\spad{w}.\\spad{r}.\\spad{t}. the pure lexicographical ordering. If \\axiom{a} and \\axiom{\\spad{b}} are two Lyndon words such that \\axiom{a < \\spad{b}} holds \\spad{w}.\\spad{r}.\\spad{t} lexicographical ordering then \\axiom{a*b} is a Lyndon word. Parenthesized Lyndon words can be generated from symbols by using the following rule: \\axiom{[[a,{}\\spad{b}],{}\\spad{c}]} is a Lyndon word iff \\axiom{a*b < \\spad{c} <= \\spad{b}} holds. Lyndon words are internally represented by binary trees using the \\spadtype{Magma} domain constructor. Two ordering are provided: lexicographic and length-lexicographic. \\newline Author : Michel Petitot (petitot@lifl.fr).")) (|LyndonWordsList| (((|List| $) (|List| |#1|) (|PositiveInteger|)) "\\axiom{LyndonWordsList(vl,{} \\spad{n})} returns the list of Lyndon words over the alphabet \\axiom{vl},{} up to order \\axiom{\\spad{n}}.")) (|LyndonWordsList1| (((|OneDimensionalArray| (|List| $)) (|List| |#1|) (|PositiveInteger|)) "\\axiom{\\spad{LyndonWordsList1}(vl,{} \\spad{n})} returns an array of lists of Lyndon words over the alphabet \\axiom{vl},{} up to order \\axiom{\\spad{n}}.")) (|varList| (((|List| |#1|) $) "\\axiom{varList(\\spad{x})} returns the list of distinct entries of \\axiom{\\spad{x}}.")) (|lyndonIfCan| (((|Union| $ "failed") (|OrderedFreeMonoid| |#1|)) "\\axiom{lyndonIfCan(\\spad{w})} convert \\axiom{\\spad{w}} into a Lyndon word.")) (|lyndon| (($ (|OrderedFreeMonoid| |#1|)) "\\axiom{lyndon(\\spad{w})} convert \\axiom{\\spad{w}} into a Lyndon word,{} error if \\axiom{\\spad{w}} is not a Lyndon word.")) (|lyndon?| (((|Boolean|) (|OrderedFreeMonoid| |#1|)) "\\axiom{lyndon?(\\spad{w})} test if \\axiom{\\spad{w}} is a Lyndon word.")) (|factor| (((|List| $) (|OrderedFreeMonoid| |#1|)) "\\axiom{factor(\\spad{x})} returns the decreasing factorization into Lyndon words.")) (|coerce| (((|Magma| |#1|) $) "\\axiom{coerce(\\spad{x})} returns the element of \\axiomType{Magma}(VarSet) corresponding to \\axiom{\\spad{x}}.") (((|OrderedFreeMonoid| |#1|) $) "\\axiom{coerce(\\spad{x})} returns the element of \\axiomType{OrderedFreeMonoid}(VarSet) corresponding to \\axiom{\\spad{x}}.")) (|lexico| (((|Boolean|) $ $) "\\axiom{lexico(\\spad{x},{}\\spad{y})} returns \\axiom{\\spad{true}} iff \\axiom{\\spad{x}} is smaller than \\axiom{\\spad{y}} \\spad{w}.\\spad{r}.\\spad{t}. the lexicographical ordering induced by \\axiom{VarSet}.")) (|length| (((|PositiveInteger|) $) "\\axiom{length(\\spad{x})} returns the number of entries in \\axiom{\\spad{x}}.")) (|right| (($ $) "\\axiom{right(\\spad{x})} returns right subtree of \\axiom{\\spad{x}} or error if \\axiomOpFrom{retractable?}{LyndonWord}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|left| (($ $) "\\axiom{left(\\spad{x})} returns left subtree of \\axiom{\\spad{x}} or error if \\axiomOpFrom{retractable?}{LyndonWord}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|retractable?| (((|Boolean|) $) "\\axiom{retractable?(\\spad{x})} tests if \\axiom{\\spad{x}} is a tree with only one entry."))) 
 NIL 
 NIL 
-(-616 A S) 
+(-615 A S) 
 ((|constructor| (NIL "LazyStreamAggregate is the category of streams with lazy evaluation. It is understood that the function 'empty?' will cause lazy evaluation if necessary to determine if there are entries. Functions which call 'empty?',{} \\spadignore{e.g.} 'first' and 'rest',{} will also cause lazy evaluation if necessary.")) (|complete| (($ $) "\\spad{complete(st)} causes all entries of 'st' to be computed. this function should only be called on streams which are known to be finite.")) (|extend| (($ $ (|Integer|)) "\\spad{extend(st,n)} causes entries to be computed,{} if necessary,{} so that 'st' will have at least 'n' explicit entries or so that all entries of 'st' will be computed if 'st' is finite with length <= \\spad{n}.")) (|numberOfComputedEntries| (((|NonNegativeInteger|) $) "\\spad{numberOfComputedEntries(st)} returns the number of explicitly computed entries of stream \\spad{st} which exist immediately prior to the time this function is called.")) (|rst| (($ $) "\\spad{rst(s)} returns a pointer to the next node of stream \\spad{s}. Caution: this function should only be called after a \\spad{empty?} test has been made since there no error check.")) (|frst| ((|#2| $) "\\spad{frst(s)} returns the first element of stream \\spad{s}. Caution: this function should only be called after a \\spad{empty?} test has been made since there no error check.")) (|lazyEvaluate| (($ $) "\\spad{lazyEvaluate(s)} causes one lazy evaluation of stream \\spad{s}. Caution: the first node must be a lazy evaluation mechanism (satisfies \\spad{lazy?(s) = true}) as there is no error check. Note: a call to this function may or may not produce an explicit first entry")) (|lazy?| (((|Boolean|) $) "\\spad{lazy?(s)} returns \\spad{true} if the first node of the stream \\spad{s} is a lazy evaluation mechanism which could produce an additional entry to \\spad{s}.")) (|explicitlyEmpty?| (((|Boolean|) $) "\\spad{explicitlyEmpty?(s)} returns \\spad{true} if the stream is an (explicitly) empty stream. Note: this is a null test which will not cause lazy evaluation.")) (|explicitEntries?| (((|Boolean|) $) "\\spad{explicitEntries?(s)} returns \\spad{true} if the stream \\spad{s} has explicitly computed entries,{} and \\spad{false} otherwise.")) (|select| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{select(f,st)} returns a stream consisting of those elements of stream \\spad{st} satisfying the predicate \\spad{f}. Note: \\spad{select(f,st) = [x for x in st | f(x)]}.")) (|remove| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{remove(f,st)} returns a stream consisting of those elements of stream \\spad{st} which do not satisfy the predicate \\spad{f}. Note: \\spad{remove(f,st) = [x for x in st | not f(x)]}."))) 
 NIL 
 NIL 
-(-617 S) 
+(-616 S) 
 ((|constructor| (NIL "LazyStreamAggregate is the category of streams with lazy evaluation. It is understood that the function 'empty?' will cause lazy evaluation if necessary to determine if there are entries. Functions which call 'empty?',{} \\spadignore{e.g.} 'first' and 'rest',{} will also cause lazy evaluation if necessary.")) (|complete| (($ $) "\\spad{complete(st)} causes all entries of 'st' to be computed. this function should only be called on streams which are known to be finite.")) (|extend| (($ $ (|Integer|)) "\\spad{extend(st,n)} causes entries to be computed,{} if necessary,{} so that 'st' will have at least 'n' explicit entries or so that all entries of 'st' will be computed if 'st' is finite with length <= \\spad{n}.")) (|numberOfComputedEntries| (((|NonNegativeInteger|) $) "\\spad{numberOfComputedEntries(st)} returns the number of explicitly computed entries of stream \\spad{st} which exist immediately prior to the time this function is called.")) (|rst| (($ $) "\\spad{rst(s)} returns a pointer to the next node of stream \\spad{s}. Caution: this function should only be called after a \\spad{empty?} test has been made since there no error check.")) (|frst| ((|#1| $) "\\spad{frst(s)} returns the first element of stream \\spad{s}. Caution: this function should only be called after a \\spad{empty?} test has been made since there no error check.")) (|lazyEvaluate| (($ $) "\\spad{lazyEvaluate(s)} causes one lazy evaluation of stream \\spad{s}. Caution: the first node must be a lazy evaluation mechanism (satisfies \\spad{lazy?(s) = true}) as there is no error check. Note: a call to this function may or may not produce an explicit first entry")) (|lazy?| (((|Boolean|) $) "\\spad{lazy?(s)} returns \\spad{true} if the first node of the stream \\spad{s} is a lazy evaluation mechanism which could produce an additional entry to \\spad{s}.")) (|explicitlyEmpty?| (((|Boolean|) $) "\\spad{explicitlyEmpty?(s)} returns \\spad{true} if the stream is an (explicitly) empty stream. Note: this is a null test which will not cause lazy evaluation.")) (|explicitEntries?| (((|Boolean|) $) "\\spad{explicitEntries?(s)} returns \\spad{true} if the stream \\spad{s} has explicitly computed entries,{} and \\spad{false} otherwise.")) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select(f,st)} returns a stream consisting of those elements of stream \\spad{st} satisfying the predicate \\spad{f}. Note: \\spad{select(f,st) = [x for x in st | f(x)]}.")) (|remove| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove(f,st)} returns a stream consisting of those elements of stream \\spad{st} which do not satisfy the predicate \\spad{f}. Note: \\spad{remove(f,st) = [x for x in st | not f(x)]}."))) 
 NIL 
 NIL 
-(-618) 
+(-617) 
 ((|constructor| (NIL "This domain represents the syntax of a macro definition.")) (|body| (((|SpadAst|) $) "\\spad{body(m)} returns the right hand side of the definition `m'.")) (|head| (((|HeadAst|) $) "\\spad{head(m)} returns the head of the macro definition `m'. This is a list of identifiers starting with the name of the macro followed by the name of the parameters,{} if any."))) 
 NIL 
 NIL 
-(-619 |VarSet|) 
+(-618 |VarSet|) 
 ((|constructor| (NIL "This type is the basic representation of parenthesized words (binary trees over arbitrary symbols) useful in \\spadtype{LiePolynomial}. \\newline Author: Michel Petitot (petitot@lifl.fr).")) (|varList| (((|List| |#1|) $) "\\axiom{varList(\\spad{x})} returns the list of distinct entries of \\axiom{\\spad{x}}.")) (|right| (($ $) "\\axiom{right(\\spad{x})} returns right subtree of \\axiom{\\spad{x}} or error if \\axiomOpFrom{retractable?}{Magma}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|retractable?| (((|Boolean|) $) "\\axiom{retractable?(\\spad{x})} tests if \\axiom{\\spad{x}} is a tree with only one entry.")) (|rest| (($ $) "\\axiom{rest(\\spad{x})} return \\axiom{\\spad{x}} without the first entry or error if \\axiomOpFrom{retractable?}{Magma}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|mirror| (($ $) "\\axiom{mirror(\\spad{x})} returns the reversed word of \\axiom{\\spad{x}}. That is \\axiom{\\spad{x}} itself if \\axiomOpFrom{retractable?}{Magma}(\\axiom{\\spad{x}}) is \\spad{true} and \\axiom{mirror(\\spad{z}) * mirror(\\spad{y})} if \\axiom{\\spad{x}} is \\axiom{y*z}.")) (|lexico| (((|Boolean|) $ $) "\\axiom{lexico(\\spad{x},{}\\spad{y})} returns \\axiom{\\spad{true}} iff \\axiom{\\spad{x}} is smaller than \\axiom{\\spad{y}} \\spad{w}.\\spad{r}.\\spad{t}. the lexicographical ordering induced by \\axiom{VarSet}. \\spad{N}.\\spad{B}. This operation does not take into account the tree structure of its arguments. Thus this is not a total ordering.")) (|length| (((|PositiveInteger|) $) "\\axiom{length(\\spad{x})} returns the number of entries in \\axiom{\\spad{x}}.")) (|left| (($ $) "\\axiom{left(\\spad{x})} returns left subtree of \\axiom{\\spad{x}} or error if \\axiomOpFrom{retractable?}{Magma}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|first| ((|#1| $) "\\axiom{first(\\spad{x})} returns the first entry of the tree \\axiom{\\spad{x}}.")) (|coerce| (((|OrderedFreeMonoid| |#1|) $) "\\axiom{coerce(\\spad{x})} returns the element of \\axiomType{OrderedFreeMonoid}(VarSet) corresponding to \\axiom{\\spad{x}} by removing parentheses.")) (* (($ $ $) "\\axiom{x*y} returns the tree \\axiom{[\\spad{x},{}\\spad{y}]}."))) 
 NIL 
 NIL 
-(-620 A) 
+(-619 A) 
 ((|constructor| (NIL "various Currying operations.")) (|recur| ((|#1| (|Mapping| |#1| (|NonNegativeInteger|) |#1|) (|NonNegativeInteger|) |#1|) "\\spad{recur(n,g,x)} is \\spad{g(n,g(n-1,..g(1,x)..))}.")) (|iter| ((|#1| (|Mapping| |#1| |#1|) (|NonNegativeInteger|) |#1|) "\\spad{iter(f,n,x)} applies \\spad{f n} times to \\spad{x}."))) 
 NIL 
 NIL 
-(-621 A C) 
+(-620 A C) 
 ((|constructor| (NIL "various Currying operations.")) (|arg2| ((|#2| |#1| |#2|) "\\spad{arg2(a,c)} selects its second argument.")) (|arg1| ((|#1| |#1| |#2|) "\\spad{arg1(a,c)} selects its first argument."))) 
 NIL 
 NIL 
-(-622 A B C) 
+(-621 A B C) 
 ((|constructor| (NIL "various Currying operations.")) (|comp| ((|#3| (|Mapping| |#3| |#2|) (|Mapping| |#2| |#1|) |#1|) "\\spad{comp(f,g,x)} is \\spad{f(g x)}."))) 
 NIL 
 NIL 
-(-623) 
+(-622) 
 ((|constructor| (NIL "This domain represents a mapping type AST. A mapping AST \\indented{2}{is a syntactic description of a function type,{} \\spadignore{e.g.} its result} \\indented{2}{type and the list of its argument types.}")) (|target| (((|TypeAst|) $) "\\spad{target(s)} returns the result type AST for `s'.")) (|source| (((|List| (|TypeAst|)) $) "\\spad{source(s)} returns the parameter type AST list of `s'.")) (|mappingAst| (($ (|List| (|TypeAst|)) (|TypeAst|)) "\\spad{mappingAst(s,t)} builds the mapping AST \\spad{s} -> \\spad{t}")) (|coerce| (($ (|Signature|)) "sig::MappingAst builds a MappingAst from the Signature `sig'."))) 
 NIL 
 NIL 
-(-624 A) 
+(-623 A) 
 ((|constructor| (NIL "various Currying operations.")) (|recur| (((|Mapping| |#1| (|NonNegativeInteger|) |#1|) (|Mapping| |#1| (|NonNegativeInteger|) |#1|)) "\\spad{recur(g)} is the function \\spad{h} such that \\indented{1}{\\spad{h(n,x)= g(n,g(n-1,..g(1,x)..))}.}")) (** (((|Mapping| |#1| |#1|) (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) "\\spad{f**n} is the function which is the \\spad{n}-fold application \\indented{1}{of \\spad{f}.}")) (|id| ((|#1| |#1|) "\\spad{id x} is \\spad{x}.")) (|fixedPoint| (((|List| |#1|) (|Mapping| (|List| |#1|) (|List| |#1|)) (|Integer|)) "\\spad{fixedPoint(f,n)} is the fixed point of function \\indented{1}{\\spad{f} which is assumed to transform a list of length} \\indented{1}{\\spad{n}.}") ((|#1| (|Mapping| |#1| |#1|)) "\\spad{fixedPoint f} is the fixed point of function \\spad{f}. \\indented{1}{\\spadignore{i.e.} such that \\spad{fixedPoint f = f(fixedPoint f)}.}")) (|coerce| (((|Mapping| |#1|) |#1|) "\\spad{coerce A} changes its argument into a \\indented{1}{nullary function.}")) (|nullary| (((|Mapping| |#1|) |#1|) "\\spad{nullary A} changes its argument into a \\indented{1}{nullary function.}"))) 
 NIL 
 NIL 
-(-625 A C) 
+(-624 A C) 
 ((|constructor| (NIL "various Currying operations.")) (|diag| (((|Mapping| |#2| |#1|) (|Mapping| |#2| |#1| |#1|)) "\\spad{diag(f)} is the function \\spad{g} \\indented{1}{such that \\spad{g a = f(a,a)}.}")) (|constant| (((|Mapping| |#2| |#1|) (|Mapping| |#2|)) "\\spad{vu(f)} is the function \\spad{g} \\indented{1}{such that \\spad{g a= f ()}.}")) (|curry| (((|Mapping| |#2|) (|Mapping| |#2| |#1|) |#1|) "\\spad{cu(f,a)} is the function \\spad{g} \\indented{1}{such that \\spad{g ()= f a}.}")) (|const| (((|Mapping| |#2| |#1|) |#2|) "\\spad{const c} is a function which produces \\spad{c} when \\indented{1}{applied to its argument.}"))) 
 NIL 
 NIL 
-(-626 A B C) 
+(-625 A B C) 
 ((|constructor| (NIL "various Currying operations.")) (* (((|Mapping| |#3| |#1|) (|Mapping| |#3| |#2|) (|Mapping| |#2| |#1|)) "\\spad{f*g} is the function \\spad{h} \\indented{1}{such that \\spad{h x= f(g x)}.}")) (|twist| (((|Mapping| |#3| |#2| |#1|) (|Mapping| |#3| |#1| |#2|)) "\\spad{twist(f)} is the function \\spad{g} \\indented{1}{such that \\spad{g (a,b)= f(b,a)}.}")) (|constantLeft| (((|Mapping| |#3| |#1| |#2|) (|Mapping| |#3| |#2|)) "\\spad{constantLeft(f)} is the function \\spad{g} \\indented{1}{such that \\spad{g (a,b)= f b}.}")) (|constantRight| (((|Mapping| |#3| |#1| |#2|) (|Mapping| |#3| |#1|)) "\\spad{constantRight(f)} is the function \\spad{g} \\indented{1}{such that \\spad{g (a,b)= f a}.}")) (|curryLeft| (((|Mapping| |#3| |#2|) (|Mapping| |#3| |#1| |#2|) |#1|) "\\spad{curryLeft(f,a)} is the function \\spad{g} \\indented{1}{such that \\spad{g b = f(a,b)}.}")) (|curryRight| (((|Mapping| |#3| |#1|) (|Mapping| |#3| |#1| |#2|) |#2|) "\\spad{curryRight(f,b)} is the function \\spad{g} such that \\indented{1}{\\spad{g a = f(a,b)}.}"))) 
 NIL 
 NIL 
-(-627 S R |Row| |Col|) 
+(-626 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."))) 
 NIL 
-((|HasAttribute| |#2| (QUOTE (-3999 "*"))) (|HasCategory| |#2| (QUOTE (-258))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-496)))) 
-(-628 R |Row| |Col|) 
+((|HasAttribute| |#2| (QUOTE (-3998 "*"))) (|HasCategory| |#2| (QUOTE (-258))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-495)))) 
+(-627 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."))) 
-((-3998 . T)) 
+((-3997 . T)) 
 NIL 
-(-629 R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2) 
+(-628 R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2) 
 ((|constructor| (NIL "\\spadtype{MatrixCategoryFunctions2} provides functions between two matrix domains. The functions provided are \\spadfun{map} and \\spadfun{reduce}.")) (|reduce| ((|#5| (|Mapping| |#5| |#1| |#5|) |#4| |#5|) "\\spad{reduce(f,m,r)} returns a matrix \\spad{n} where \\spad{n[i,j] = f(m[i,j],r)} for all indices \\spad{i} and \\spad{j}.")) (|map| (((|Union| |#8| "failed") (|Mapping| (|Union| |#5| "failed") |#1|) |#4|) "\\spad{map(f,m)} applies the function \\spad{f} to the elements of the matrix \\spad{m}.") ((|#8| (|Mapping| |#5| |#1|) |#4|) "\\spad{map(f,m)} applies the function \\spad{f} to the elements of the matrix \\spad{m}."))) 
 NIL 
 NIL 
-(-630 R |Row| |Col| M) 
+(-629 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 (-312))) (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-496)))) 
-(-631 R) 
+((|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-495)))) 
+(-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."))) 
-((-3998 . T)) 
-((OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-496))) (|HasAttribute| |#1| (QUOTE (-3999 "*"))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) 
-(-632 R) 
+((-3997 . T)) 
+((OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1013))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-553 (-473)))) (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-495))) (|HasAttribute| |#1| (QUOTE (-3998 "*"))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) 
+(-631 R) 
 ((|constructor| (NIL "This package provides standard arithmetic operations on matrices. The functions in this package store the results of computations in existing matrices,{} rather than creating new matrices. This package works only for matrices of type Matrix and uses the internal representation of this type.")) (** (((|Matrix| |#1|) (|Matrix| |#1|) (|NonNegativeInteger|)) "\\spad{x ** n} computes the \\spad{n}-th power of a square matrix. The power \\spad{n} is assumed greater than 1.")) (|power!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|NonNegativeInteger|)) "\\spad{power!(a,b,c,m,n)} computes \\spad{m} ** \\spad{n} and stores the result in \\spad{a}. The matrices \\spad{b} and \\spad{c} are used to store intermediate results. Error: if \\spad{a},{} \\spad{b},{} \\spad{c},{} and \\spad{m} are not square and of the same dimensions.")) (|times!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{times!(c,a,b)} computes the matrix product \\spad{a * b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have compatible dimensions.")) (|rightScalarTimes!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{rightScalarTimes!(c,a,r)} computes the scalar product \\spad{a * r} and stores the result in the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions.")) (|leftScalarTimes!| (((|Matrix| |#1|) (|Matrix| |#1|) |#1| (|Matrix| |#1|)) "\\spad{leftScalarTimes!(c,r,a)} computes the scalar product \\spad{r * a} and stores the result in the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions.")) (|minus!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{!minus!(c,a,b)} computes the matrix difference \\spad{a - b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have the same dimensions.") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{minus!(c,a)} computes \\spad{-a} and stores the result in the matrix \\spad{c}. Error: if a and \\spad{c} do not have the same dimensions.")) (|plus!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{plus!(c,a,b)} computes the matrix sum \\spad{a + b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have the same dimensions.")) (|copy!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{copy!(c,a)} copies the matrix \\spad{a} into the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions."))) 
 NIL 
 NIL 
-(-633 T$) 
+(-632 T$) 
 ((|constructor| (NIL "This domain implements the notion of optional value,{} where a computation may fail to produce expected value.")) (|nothing| (($) "\\spad{nothing} represents failure or absence of value.")) (|autoCoerce| ((|#1| $) "\\spad{autoCoerce} is a courtesy coercion function used by the compiler in case it knows that `x' really is a \\spadtype{T}.")) (|case| (((|Boolean|) $ (|[\|\|]| |nothing|)) "\\spad{x case nothing} holds if the value for \\spad{x} is missing.") (((|Boolean|) $ (|[\|\|]| |#1|)) "\\spad{x case T} returns \\spad{true} if \\spad{x} is actually a data of type \\spad{T}.")) (|just| (($ |#1|) "\\spad{just x} injects the value `x' into \\%."))) 
 NIL 
 NIL 
-(-634 R Q) 
+(-633 R Q) 
 ((|constructor| (NIL "MatrixCommonDenominator provides functions to compute the common denominator of a matrix of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| (|Matrix| |#1|)) (|:| |den| |#1|)) (|Matrix| |#2|)) "\\spad{splitDenominator(q)} returns \\spad{[p, d]} such that \\spad{q = p/d} and \\spad{d} is a common denominator for the elements of \\spad{q}.")) (|clearDenominator| (((|Matrix| |#1|) (|Matrix| |#2|)) "\\spad{clearDenominator(q)} returns \\spad{p} such that \\spad{q = p/d} where \\spad{d} is a common denominator for the elements of \\spad{q}.")) (|commonDenominator| ((|#1| (|Matrix| |#2|)) "\\spad{commonDenominator(q)} returns a common denominator \\spad{d} for the elements of \\spad{q}."))) 
 NIL 
 NIL 
-(-635 S) 
+(-634 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}."))) 
-((-3998 . T)) 
+((-3997 . T)) 
 NIL 
-(-636 U) 
+(-635 U) 
 ((|constructor| (NIL "This package supports factorization and gcds of univariate polynomials over the integers modulo different primes. The inputs are given as polynomials over the integers with the prime passed explicitly as an extra argument.")) (|exptMod| ((|#1| |#1| (|Integer|) |#1| (|Integer|)) "\\spad{exptMod(f,n,g,p)} raises the univariate polynomial \\spad{f} to the \\spad{n}th power modulo the polynomial \\spad{g} and the prime \\spad{p}.")) (|separateFactors| (((|List| |#1|) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|)))) (|Integer|)) "\\spad{separateFactors(ddl, p)} refines the distinct degree factorization produced by \\spadfunFrom{ddFact}{ModularDistinctDegreeFactorizer} to give a complete list of factors.")) (|ddFact| (((|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|)))) |#1| (|Integer|)) "\\spad{ddFact(f,p)} computes a distinct degree factorization of the polynomial \\spad{f} modulo the prime \\spad{p},{} \\spadignore{i.e.} such that each factor is a product of irreducibles of the same degrees. The input polynomial \\spad{f} is assumed to be square-free modulo \\spad{p}.")) (|factor| (((|List| |#1|) |#1| (|Integer|)) "\\spad{factor(f1,p)} returns the list of factors of the univariate polynomial \\spad{f1} modulo the integer prime \\spad{p}. Error: if \\spad{f1} is not square-free modulo \\spad{p}.")) (|linears| ((|#1| |#1| (|Integer|)) "\\spad{linears(f,p)} returns the product of all the linear factors of \\spad{f} modulo \\spad{p}. Potentially incorrect result if \\spad{f} is not square-free modulo \\spad{p}.")) (|gcd| ((|#1| |#1| |#1| (|Integer|)) "\\spad{gcd(f1,f2,p)} computes the gcd of the univariate polynomials \\spad{f1} and \\spad{f2} modulo the integer prime \\spad{p}."))) 
 NIL 
 NIL 
-(-637) 
+(-636) 
 ((|constructor| (NIL "\\indented{1}{<description of package>} Author: Jim Wen Date Created: ?? Date Last Updated: October 1991 by Jon Steinbach Keywords: Examples: References:")) (|ptFunc| (((|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) "\\spad{ptFunc(a,b,c,d)} is an internal function exported in order to compile packages.")) (|meshPar1Var| (((|ThreeSpace| (|DoubleFloat|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar1Var(s,t,u,f,s1,l)} \\undocumented")) (|meshFun2Var| (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Union| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) #1="undefined") (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshFun2Var(f,g,s1,s2,l)} \\undocumented")) (|meshPar2Var| (((|ThreeSpace| (|DoubleFloat|)) (|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(sp,f,s1,s2,l)} \\undocumented") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(f,s1,s2,l)} \\undocumented") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Union| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) #1#) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(f,g,h,j,s1,s2,l)} \\undocumented"))) 
 NIL 
 NIL 
-(-638 OV E -3094 PG) 
+(-637 OV E -3093 PG) 
 ((|constructor| (NIL "Package for factorization of multivariate polynomials over finite fields.")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factor(p)} produces the complete factorization of the multivariate polynomial \\spad{p} over a finite field. \\spad{p} is represented as a univariate polynomial with multivariate coefficients over a finite field.") (((|Factored| |#4|) |#4|) "\\spad{factor(p)} produces the complete factorization of the multivariate polynomial \\spad{p} over a finite field."))) 
 NIL 
 NIL 
-(-639 R) 
+(-638 R) 
 ((|constructor| (NIL "\\indented{1}{Modular hermitian row reduction.} Author: Manuel Bronstein Date Created: 22 February 1989 Date Last Updated: 24 November 1993 Keywords: matrix,{} reduction.")) (|normalizedDivide| (((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|) "\\spad{normalizedDivide(n,d)} returns a normalized quotient and remainder such that consistently unique representatives for the residue class are chosen,{} \\spadignore{e.g.} positive remainders")) (|rowEchelonLocal| (((|Matrix| |#1|) (|Matrix| |#1|) |#1| |#1|) "\\spad{rowEchelonLocal(m, d, p)} computes the row-echelon form of \\spad{m} concatenated with \\spad{d} times the identity matrix over a local ring where \\spad{p} is the only prime.")) (|rowEchLocal| (((|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{rowEchLocal(m,p)} computes a modular row-echelon form of \\spad{m},{} finding an appropriate modulus over a local ring where \\spad{p} is the only prime.")) (|rowEchelon| (((|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{rowEchelon(m, d)} computes a modular row-echelon form mod \\spad{d} of \\indented{3}{[\\spad{d}\\space{5}]} \\indented{3}{[\\space{2}\\spad{d}\\space{3}]} \\indented{3}{[\\space{4}. ]} \\indented{3}{[\\space{5}\\spad{d}]} \\indented{3}{[\\space{3}\\spad{M}\\space{2}]} where \\spad{M = m mod d}.")) (|rowEch| (((|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{rowEch(m)} computes a modular row-echelon form of \\spad{m},{} finding an appropriate modulus."))) 
 NIL 
 NIL 
-(-640 S D1 D2 I) 
+(-639 S D1 D2 I) 
 ((|constructor| (NIL "transforms top-level objects into compiled functions.")) (|compiledFunction| (((|Mapping| |#4| |#2| |#3|) |#1| (|Symbol|) (|Symbol|)) "\\spad{compiledFunction(expr,x,y)} returns a function \\spad{f: (D1, D2) -> I} defined by \\spad{f(x, y) == expr}. Function \\spad{f} is compiled and directly applicable to objects of type \\spad{(D1, D2)}")) (|binaryFunction| (((|Mapping| |#4| |#2| |#3|) (|Symbol|)) "\\spad{binaryFunction(s)} is a local function"))) 
 NIL 
 NIL 
-(-641 S) 
+(-640 S) 
 ((|constructor| (NIL "MakeFloatCompiledFunction transforms top-level objects into compiled Lisp functions whose arguments are Lisp floats. This by-passes the \\Language{} compiler and interpreter,{} thereby gaining several orders of magnitude.")) (|makeFloatFunction| (((|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) |#1| (|Symbol|) (|Symbol|)) "\\spad{makeFloatFunction(expr, x, y)} returns a Lisp function \\spad{f: (\\axiomType{DoubleFloat}, \\axiomType{DoubleFloat}) -> \\axiomType{DoubleFloat}} defined by \\spad{f(x, y) == expr}. Function \\spad{f} is compiled and directly applicable to objects of type \\spad{(\\axiomType{DoubleFloat}, \\axiomType{DoubleFloat})}.") (((|Mapping| (|DoubleFloat|) (|DoubleFloat|)) |#1| (|Symbol|)) "\\spad{makeFloatFunction(expr, x)} returns a Lisp function \\spad{f: \\axiomType{DoubleFloat} -> \\axiomType{DoubleFloat}} defined by \\spad{f(x) == expr}. Function \\spad{f} is compiled and directly applicable to objects of type \\axiomType{DoubleFloat}."))) 
 NIL 
 NIL 
-(-642 S) 
+(-641 S) 
 ((|constructor| (NIL "transforms top-level objects into interpreter functions.")) (|function| (((|Symbol|) |#1| (|Symbol|) (|List| (|Symbol|))) "\\spad{function(e, foo, [x1,...,xn])} creates a function \\spad{foo(x1,...,xn) == e}.") (((|Symbol|) |#1| (|Symbol|) (|Symbol|) (|Symbol|)) "\\spad{function(e, foo, x, y)} creates a function \\spad{foo(x, y) = e}.") (((|Symbol|) |#1| (|Symbol|) (|Symbol|)) "\\spad{function(e, foo, x)} creates a function \\spad{foo(x) == e}.") (((|Symbol|) |#1| (|Symbol|)) "\\spad{function(e, foo)} creates a function \\spad{foo() == e}."))) 
 NIL 
 NIL 
-(-643 S T$) 
+(-642 S T$) 
 ((|constructor| (NIL "MakeRecord is used internally by the interpreter to create record types which are used for doing parallel iterations on streams.")) (|makeRecord| (((|Record| (|:| |part1| |#1|) (|:| |part2| |#2|)) |#1| |#2|) "\\spad{makeRecord(a,b)} creates a record object with type Record(part1:S,{} part2:R),{} where \\spad{part1} is \\spad{a} and \\spad{part2} is \\spad{b}."))) 
 NIL 
 NIL 
-(-644 S -2671 I) 
+(-643 S -2670 I) 
 ((|constructor| (NIL "transforms top-level objects into compiled functions.")) (|compiledFunction| (((|Mapping| |#3| |#2|) |#1| (|Symbol|)) "\\spad{compiledFunction(expr, x)} returns a function \\spad{f: D -> I} defined by \\spad{f(x) == expr}. Function \\spad{f} is compiled and directly applicable to objects of type \\spad{D}.")) (|unaryFunction| (((|Mapping| |#3| |#2|) (|Symbol|)) "\\spad{unaryFunction(a)} is a local function"))) 
 NIL 
 NIL 
-(-645 E OV R P) 
+(-644 E OV R P) 
 ((|constructor| (NIL "This package provides the functions for the multivariate \"lifting\",{} using an algorithm of Paul Wang. This package will work for every euclidean domain \\spad{R} which has property \\spad{F},{} \\spadignore{i.e.} there exists a factor operation in \\spad{R[x]}.")) (|lifting1| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|List| (|SparseUnivariatePolynomial| |#4|)) (|List| |#3|) (|List| |#4|) (|List| (|List| (|Record| (|:| |expt| (|NonNegativeInteger|)) (|:| |pcoef| |#4|)))) (|List| (|NonNegativeInteger|)) (|Vector| (|List| (|SparseUnivariatePolynomial| |#3|))) |#3|) "\\spad{lifting1(u,lv,lu,lr,lp,lt,ln,t,r)} \\undocumented")) (|lifting| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|List| (|SparseUnivariatePolynomial| |#3|)) (|List| |#3|) (|List| |#4|) (|List| (|NonNegativeInteger|)) |#3|) "\\spad{lifting(u,lv,lu,lr,lp,ln,r)} \\undocumented")) (|corrPoly| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|List| |#3|) (|List| (|NonNegativeInteger|)) (|List| (|SparseUnivariatePolynomial| |#4|)) (|Vector| (|List| (|SparseUnivariatePolynomial| |#3|))) |#3|) "\\spad{corrPoly(u,lv,lr,ln,lu,t,r)} \\undocumented"))) 
 NIL 
 NIL 
-(-646 R) 
+(-645 R) 
 ((|constructor| (NIL "This is the category of linear operator rings with one generator. The generator is not named by the category but can always be constructed as \\spad{monomial(1,1)}. \\blankline For convenience,{} call the generator \\spad{G}. Then each value is equal to \\indented{4}{\\spad{sum(a(i)*G**i, i = 0..n)}} for some unique \\spad{n} and \\spad{a(i)} in \\spad{R}. \\blankline Note that multiplication is not necessarily commutative. In fact,{} if \\spad{a} is in \\spad{R},{} it is quite normal to have \\spad{a*G \\~= G*a}.")) (|monomial| (($ |#1| (|NonNegativeInteger|)) "\\spad{monomial(c,k)} produces \\spad{c} times the \\spad{k}-th power of the generating operator,{} \\spad{monomial(1,1)}.")) (|coefficient| ((|#1| $ (|NonNegativeInteger|)) "\\spad{coefficient(l,k)} is \\spad{a(k)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|reductum| (($ $) "\\spad{reductum(l)} is \\spad{l - monomial(a(n),n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(l)} is \\spad{a(n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|minimumDegree| (((|NonNegativeInteger|) $) "\\spad{minimumDegree(l)} is the smallest \\spad{k} such that \\spad{a(k) \\~= 0} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(l)} is \\spad{n} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}"))) 
-((-3991 . T) (-3992 . T) (-3994 . T)) 
+((-3990 . T) (-3991 . T) (-3993 . T)) 
 NIL 
-(-647 R1 UP1 UPUP1 R2 UP2 UPUP2) 
+(-646 R1 UP1 UPUP1 R2 UP2 UPUP2) 
 ((|constructor| (NIL "Lifting of a map through 2 levels of polynomials.")) (|map| ((|#6| (|Mapping| |#4| |#1|) |#3|) "\\spad{map(f, p)} lifts \\spad{f} to the domain of \\spad{p} then applies it to \\spad{p}."))) 
 NIL 
 NIL 
-(-648) 
+(-647) 
 ((|constructor| (NIL "\\spadtype{MathMLFormat} provides a coercion from \\spadtype{OutputForm} to MathML format.")) (|display| (((|Void|) (|String|)) "prints the string returned by coerce,{} adding <math ...> tags.")) (|exprex| (((|String|) (|OutputForm|)) "coverts \\spadtype{OutputForm} to \\spadtype{String} with the structure preserved with braces. Actually this is not quite accurate. The function \\spadfun{precondition} is first applied to the \\spadtype{OutputForm} expression before \\spadfun{exprex}. The raw \\spadtype{OutputForm} and the nature of the \\spadfun{precondition} function is still obscure to me at the time of this writing (2007-02-14).")) (|coerceL| (((|String|) (|OutputForm|)) "coerceS(\\spad{o}) changes \\spad{o} in the standard output format to MathML format and displays result as one long string.")) (|coerceS| (((|String|) (|OutputForm|)) "\\spad{coerceS(o)} changes \\spad{o} in the standard output format to MathML format and displays formatted result.")) (|coerce| (((|String|) (|OutputForm|)) "coerceS(\\spad{o}) changes \\spad{o} in the standard output format to MathML format."))) 
 NIL 
 NIL 
-(-649 R |Mod| -2038 -3520 |exactQuo|) 
+(-648 R |Mod| -2037 -3519 |exactQuo|) 
 ((|constructor| (NIL "\\indented{1}{These domains are used for the factorization and gcds} of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{ModularRing},{} \\spadtype{EuclideanModularRing}")) (|exQuo| (((|Union| $ "failed") $ $) "\\spad{exQuo(x,y)} \\undocumented")) (|reduce| (($ |#1| |#2|) "\\spad{reduce(r,m)} \\undocumented")) (|coerce| ((|#1| $) "\\spad{coerce(x)} \\undocumented")) (|modulus| ((|#2| $) "\\spad{modulus(x)} \\undocumented"))) 
-((-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
 NIL 
-(-650 R P) 
+(-649 R P) 
 ((|constructor| (NIL "This package \\undocumented")) (|frobenius| (($ $) "\\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"))) 
-(((-3999 "*") |has| |#1| (-146)) (-3990 |has| |#1| (-496)) (-3993 |has| |#1| (-312)) (-3995 |has| |#1| (-6 -3995)) (-3992 . T) (-3991 . T) (-3994 . T)) 
-((|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (-12 (|HasCategory| |#1| (QUOTE (-797 (-330)))) (|HasCategory| (-995) (QUOTE (-797 (-330))))) (-12 (|HasCategory| |#1| (QUOTE (-797 (-485)))) (|HasCategory| (-995) (QUOTE (-797 (-485))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-330))))) (|HasCategory| (-995) (QUOTE (-554 (-801 (-330)))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-485))))) (|HasCategory| (-995) (QUOTE (-554 (-801 (-485)))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-474)))) (|HasCategory| (-995) (QUOTE (-554 (-474))))) (|HasCategory| |#1| (QUOTE (-581 (-485)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485)))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485))))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-822)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-822)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-822)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (QUOTE (-812 (-1091)))) (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasCategory| |#1| (QUOTE (-320))) (|HasCategory| |#1| (QUOTE (-299))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-190))) (|HasAttribute| |#1| (QUOTE -3995)) (|HasCategory| |#1| (QUOTE (-392))) (-12 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) 
-(-651 IS E |ff|) 
+(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-495)) (-3992 |has| |#1| (-312)) (-3994 |has| |#1| (-6 -3994)) (-3991 . T) (-3990 . T) (-3993 . T)) 
+((|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-495)))) (-12 (|HasCategory| |#1| (QUOTE (-796 (-330)))) (|HasCategory| (-994) (QUOTE (-796 (-330))))) (-12 (|HasCategory| |#1| (QUOTE (-796 (-484)))) (|HasCategory| (-994) (QUOTE (-796 (-484))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-800 (-330))))) (|HasCategory| (-994) (QUOTE (-553 (-800 (-330)))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-800 (-484))))) (|HasCategory| (-994) (QUOTE (-553 (-800 (-484)))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-473)))) (|HasCategory| (-994) (QUOTE (-553 (-473))))) (|HasCategory| |#1| (QUOTE (-580 (-484)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-484)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484)))))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484))))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-821)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-821)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-821)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (QUOTE (-811 (-1090)))) (|HasCategory| |#1| (QUOTE (-809 (-1090)))) (|HasCategory| |#1| (QUOTE (-320))) (|HasCategory| |#1| (QUOTE (-299))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-190))) (|HasAttribute| |#1| (QUOTE -3994)) (|HasCategory| |#1| (QUOTE (-392))) (-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|) 
 ((|constructor| (NIL "This package \\undocumented")) (|construct| (($ |#1| |#2|) "\\spad{construct(i,e)} \\undocumented")) (|index| ((|#1| $) "\\spad{index(x)} \\undocumented")) (|exponent| ((|#2| $) "\\spad{exponent(x)} \\undocumented"))) 
 NIL 
 NIL 
-(-652 R M) 
+(-651 R M) 
 ((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#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| (($ $ $) "\\spad{adjoint(op1, op2)} sets the adjoint of \\spad{op1} to be \\spad{op2}. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) 
-((-3992 |has| |#1| (-146)) (-3991 |has| |#1| (-146)) (-3994 . T)) 
+((-3991 |has| |#1| (-146)) (-3990 |has| |#1| (-146)) (-3993 . T)) 
 ((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120)))) 
-(-653 R |Mod| -2038 -3520 |exactQuo|) 
+(-652 R |Mod| -2037 -3519 |exactQuo|) 
 ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\spad{inv(x)} \\undocumented")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} \\undocumented")) (|exQuo| (((|Union| $ "failed") $ $) "\\spad{exQuo(x,y)} \\undocumented")) (|reduce| (($ |#1| |#2|) "\\spad{reduce(r,m)} \\undocumented")) (|coerce| ((|#1| $) "\\spad{coerce(x)} \\undocumented")) (|modulus| ((|#2| $) "\\spad{modulus(x)} \\undocumented"))) 
-((-3994 . T)) 
+((-3993 . T)) 
 NIL 
-(-654 S R) 
+(-653 S R) 
 ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) 
 NIL 
 NIL 
-(-655 R) 
+(-654 R) 
 ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) 
-((-3992 . T) (-3991 . T)) 
+((-3991 . T) (-3990 . T)) 
 NIL 
-(-656 -3094) 
+(-655 -3093) 
 ((|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]]}."))) 
-((-3994 . T)) 
+((-3993 . T)) 
 NIL 
-(-657 S) 
+(-656 S) 
 ((|constructor| (NIL "Monad is the class of all multiplicative monads,{} \\spadignore{i.e.} sets with a binary operation.")) (** (($ $ (|PositiveInteger|)) "\\spad{a**n} returns the \\spad{n}\\spad{-}th power of \\spad{a},{} defined by repeated squaring.")) (|leftPower| (($ $ (|PositiveInteger|)) "\\spad{leftPower(a,n)} returns the \\spad{n}\\spad{-}th left power of \\spad{a},{} \\spadignore{i.e.} \\spad{leftPower(a,n) := a * leftPower(a,n-1)} and \\spad{leftPower(a,1) := a}.")) (|rightPower| (($ $ (|PositiveInteger|)) "\\spad{rightPower(a,n)} returns the \\spad{n}\\spad{-}th right power of \\spad{a},{} \\spadignore{i.e.} \\spad{rightPower(a,n) := rightPower(a,n-1) * a} and \\spad{rightPower(a,1) := a}.")) (* (($ $ $) "\\spad{a*b} is the product of \\spad{a} and \\spad{b} in a set with a binary operation."))) 
 NIL 
 NIL 
-(-658) 
+(-657) 
 ((|constructor| (NIL "Monad is the class of all multiplicative monads,{} \\spadignore{i.e.} sets with a binary operation.")) (** (($ $ (|PositiveInteger|)) "\\spad{a**n} returns the \\spad{n}\\spad{-}th power of \\spad{a},{} defined by repeated squaring.")) (|leftPower| (($ $ (|PositiveInteger|)) "\\spad{leftPower(a,n)} returns the \\spad{n}\\spad{-}th left power of \\spad{a},{} \\spadignore{i.e.} \\spad{leftPower(a,n) := a * leftPower(a,n-1)} and \\spad{leftPower(a,1) := a}.")) (|rightPower| (($ $ (|PositiveInteger|)) "\\spad{rightPower(a,n)} returns the \\spad{n}\\spad{-}th right power of \\spad{a},{} \\spadignore{i.e.} \\spad{rightPower(a,n) := rightPower(a,n-1) * a} and \\spad{rightPower(a,1) := a}.")) (* (($ $ $) "\\spad{a*b} is the product of \\spad{a} and \\spad{b} in a set with a binary operation."))) 
 NIL 
 NIL 
-(-659 S) 
+(-658 S) 
 ((|constructor| (NIL "\\indented{1}{MonadWithUnit is the class of multiplicative monads with unit,{}} \\indented{1}{\\spadignore{i.e.} sets with a binary operation and a unit element.} Axioms \\indented{3}{leftIdentity(\"*\":(\\%,{}\\%)->\\%,{}1)\\space{3}\\tab{30} 1*x=x} \\indented{3}{rightIdentity(\"*\":(\\%,{}\\%)->\\%,{}1)\\space{2}\\tab{30} x*1=x} Common Additional Axioms \\indented{3}{unitsKnown---if \"recip\" says \"failed\",{} that PROVES input wasn't a unit}")) (|rightRecip| (((|Union| $ "failed") $) "\\spad{rightRecip(a)} returns an element,{} which is a right inverse of \\spad{a},{} or \\spad{\"failed\"} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (|leftRecip| (((|Union| $ "failed") $) "\\spad{leftRecip(a)} returns an element,{} which is a left inverse of \\spad{a},{} or \\spad{\"failed\"} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(a)} returns an element,{} which is both a left and a right inverse of \\spad{a},{} or \\spad{\"failed\"} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (** (($ $ (|NonNegativeInteger|)) "\\spad{a**n} returns the \\spad{n}\\spad{-}th power of \\spad{a},{} defined by repeated squaring.")) (|leftPower| (($ $ (|NonNegativeInteger|)) "\\spad{leftPower(a,n)} returns the \\spad{n}\\spad{-}th left power of \\spad{a},{} \\spadignore{i.e.} \\spad{leftPower(a,n) := a * leftPower(a,n-1)} and \\spad{leftPower(a,0) := 1}.")) (|rightPower| (($ $ (|NonNegativeInteger|)) "\\spad{rightPower(a,n)} returns the \\spad{n}\\spad{-}th right power of \\spad{a},{} \\spadignore{i.e.} \\spad{rightPower(a,n) := rightPower(a,n-1) * a} and \\spad{rightPower(a,0) := 1}.")) (|one?| (((|Boolean|) $) "\\spad{one?(a)} tests whether \\spad{a} is the unit 1.")) (|One| (($) "1 returns the unit element,{} denoted by 1."))) 
 NIL 
 NIL 
-(-660) 
+(-659) 
 ((|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 
-(-661 S R UP) 
+(-660 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 (-299))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-320)))) 
-(-662 R UP) 
+(-661 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."))) 
-((-3990 |has| |#1| (-312)) (-3995 |has| |#1| (-312)) (-3989 |has| |#1| (-312)) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((-3989 |has| |#1| (-312)) (-3994 |has| |#1| (-312)) (-3988 |has| |#1| (-312)) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
 NIL 
-(-663 S) 
+(-662 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 
-(-664) 
+(-663) 
 ((|constructor| (NIL "The class of multiplicative monoids,{} \\spadignore{i.e.} semigroups with a multiplicative identity element. \\blankline")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} tries to compute the multiplicative inverse for \\spad{x} or \"failed\" if it cannot find the inverse (see unitsKnown).")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (|one?| (((|Boolean|) $) "\\spad{one?(x)} tests if \\spad{x} is equal to 1.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) (|One| (($) "1 is the multiplicative identity."))) 
 NIL 
 NIL 
-(-665 T$) 
+(-664 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 (-3058 (|f| |x| (-2413 |f|)) |x|) (|exit| 1 (-3058 (|f| (-2413 |f|) |x|) |x|))))) . T) ((|%Rule| |associativity| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|) (|:| |y| |#1|) (|:| |z| |#1|)) (-3058 (|f| (|f| |x| |y|) |z|) (|f| |x| (|f| |y| |z|))))) . T)) 
+(((|%Rule| |neutrality| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|)) (SEQ (-3057 (|f| |x| (-2412 |f|)) |x|) (|exit| 1 (-3057 (|f| (-2412 |f|) |x|) |x|))))) . T) ((|%Rule| |associativity| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|) (|:| |y| |#1|) (|:| |z| |#1|)) (-3057 (|f| (|f| |x| |y|) |z|) (|f| |x| (|f| |y| |z|))))) . T)) 
 NIL 
-(-666 T$) 
+(-665 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 (-3058 (|f| |x| (-2413 |f|)) |x|) (|exit| 1 (-3058 (|f| (-2413 |f|) |x|) |x|))))) . T) ((|%Rule| |associativity| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|) (|:| |y| |#1|) (|:| |z| |#1|)) (-3058 (|f| (|f| |x| |y|) |z|) (|f| |x| (|f| |y| |z|))))) . T)) 
+(((|%Rule| |neutrality| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|)) (SEQ (-3057 (|f| |x| (-2412 |f|)) |x|) (|exit| 1 (-3057 (|f| (-2412 |f|) |x|) |x|))))) . T) ((|%Rule| |associativity| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|) (|:| |y| |#1|) (|:| |z| |#1|)) (-3057 (|f| (|f| |x| |y|) |z|) (|f| |x| (|f| |y| |z|))))) . T)) 
 NIL 
-(-667 -3094 UP) 
+(-666 -3093 UP) 
 ((|constructor| (NIL "Tools for handling monomial extensions.")) (|decompose| (((|Record| (|:| |poly| |#2|) (|:| |normal| (|Fraction| |#2|)) (|:| |special| (|Fraction| |#2|))) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{decompose(f, D)} returns \\spad{[p,n,s]} such that \\spad{f = p+n+s},{} all the squarefree factors of \\spad{denom(n)} are normal \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{denom(s)} is special \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} and \\spad{n} and \\spad{s} are proper fractions (no pole at infinity). \\spad{D} is the derivation to use.")) (|normalDenom| ((|#2| (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{normalDenom(f, D)} returns the product of all the normal factors of \\spad{denom(f)}. \\spad{D} is the derivation to use.")) (|splitSquarefree| (((|Record| (|:| |normal| (|Factored| |#2|)) (|:| |special| (|Factored| |#2|))) |#2| (|Mapping| |#2| |#2|)) "\\spad{splitSquarefree(p, D)} returns \\spad{[n_1 n_2\\^2 ... n_m\\^m, s_1 s_2\\^2 ... s_q\\^q]} such that \\spad{p = n_1 n_2\\^2 ... n_m\\^m s_1 s_2\\^2 ... s_q\\^q},{} each \\spad{n_i} is normal \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D} and each \\spad{s_i} is special \\spad{w}.\\spad{r}.\\spad{t} \\spad{D}. \\spad{D} is the derivation to use.")) (|split| (((|Record| (|:| |normal| |#2|) (|:| |special| |#2|)) |#2| (|Mapping| |#2| |#2|)) "\\spad{split(p, D)} returns \\spad{[n,s]} such that \\spad{p = n s},{} all the squarefree factors of \\spad{n} are normal \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} and \\spad{s} is special \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D}. \\spad{D} is the derivation to use."))) 
 NIL 
 NIL 
-(-668 |VarSet| E1 E2 R S PR PS) 
+(-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"))) 
 NIL 
 NIL 
-(-669 |Vars1| |Vars2| E1 E2 R PR1 PR2) 
+(-668 |Vars1| |Vars2| E1 E2 R PR1 PR2) 
 ((|constructor| (NIL "This package \\undocumented")) (|map| ((|#7| (|Mapping| |#2| |#1|) |#6|) "\\spad{map(f,x)} \\undocumented"))) 
 NIL 
 NIL 
-(-670 E OV R PPR) 
+(-669 E OV R PPR) 
 ((|constructor| (NIL "\\indented{3}{This package exports a factor operation for multivariate polynomials} with coefficients which are polynomials over some ring \\spad{R} over which we can factor. It is used internally by packages such as the solve package which need to work with polynomials in a specific set of variables with coefficients which are polynomials in all the other variables.")) (|factor| (((|Factored| |#4|) |#4|) "\\spad{factor(p)} factors a polynomial with polynomial coefficients.")) (|variable| (((|Union| $ "failed") (|Symbol|)) "\\spad{variable(s)} makes an element from symbol \\spad{s} or fails.")) (|convert| (((|Symbol|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) 
 NIL 
 NIL 
-(-671 |vl| R) 
+(-670 |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."))) 
-(((-3999 "*") |has| |#2| (-146)) (-3990 |has| |#2| (-496)) (-3995 |has| |#2| (-6 -3995)) (-3992 . T) (-3991 . T) (-3994 . T)) 
-((|HasCategory| |#2| (QUOTE (-822))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-822)))) (OR (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-822)))) (OR (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-822)))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-146))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-496)))) (-12 (|HasCategory| |#2| (QUOTE (-797 (-330)))) (|HasCategory| (-774 |#1|) (QUOTE (-797 (-330))))) (-12 (|HasCategory| |#2| (QUOTE (-797 (-485)))) (|HasCategory| (-774 |#1|) (QUOTE (-797 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-554 (-801 (-330))))) (|HasCategory| (-774 |#1|) (QUOTE (-554 (-801 (-330)))))) (-12 (|HasCategory| |#2| (QUOTE (-554 (-801 (-485))))) (|HasCategory| (-774 |#1|) (QUOTE (-554 (-801 (-485)))))) (-12 (|HasCategory| |#2| (QUOTE (-554 (-474)))) (|HasCategory| (-774 |#1|) (QUOTE (-554 (-474))))) (|HasCategory| |#2| (QUOTE (-581 (-485)))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#2| (QUOTE (-951 (-485)))) (OR (|HasCategory| |#2| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#2| (QUOTE (-951 (-350 (-485)))))) (|HasCategory| |#2| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#2| (QUOTE (-312))) (|HasAttribute| |#2| (QUOTE -3995)) (|HasCategory| |#2| (QUOTE (-392))) (-12 (|HasCategory| |#2| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#2| (QUOTE (-118))))) 
-(-672 E OV R PRF) 
+(((-3998 "*") |has| |#2| (-146)) (-3989 |has| |#2| (-495)) (-3994 |has| |#2| (-6 -3994)) (-3991 . T) (-3990 . T) (-3993 . T)) 
+((|HasCategory| |#2| (QUOTE (-821))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-821)))) (OR (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-821)))) (OR (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-821)))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-146))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-495)))) (-12 (|HasCategory| |#2| (QUOTE (-796 (-330)))) (|HasCategory| (-773 |#1|) (QUOTE (-796 (-330))))) (-12 (|HasCategory| |#2| (QUOTE (-796 (-484)))) (|HasCategory| (-773 |#1|) (QUOTE (-796 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-553 (-800 (-330))))) (|HasCategory| (-773 |#1|) (QUOTE (-553 (-800 (-330)))))) (-12 (|HasCategory| |#2| (QUOTE (-553 (-800 (-484))))) (|HasCategory| (-773 |#1|) (QUOTE (-553 (-800 (-484)))))) (-12 (|HasCategory| |#2| (QUOTE (-553 (-473)))) (|HasCategory| (-773 |#1|) (QUOTE (-553 (-473))))) (|HasCategory| |#2| (QUOTE (-580 (-484)))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#2| (QUOTE (-950 (-484)))) (OR (|HasCategory| |#2| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#2| (QUOTE (-950 (-350 (-484)))))) (|HasCategory| |#2| (QUOTE (-950 (-350 (-484))))) (|HasCategory| |#2| (QUOTE (-312))) (|HasAttribute| |#2| (QUOTE -3994)) (|HasCategory| |#2| (QUOTE (-392))) (-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) 
 ((|constructor| (NIL "\\indented{3}{This package exports a factor operation for multivariate polynomials} with coefficients which are rational functions over some ring \\spad{R} over which we can factor. It is used internally by packages such as primary decomposition which need to work with polynomials with rational function coefficients,{} \\spadignore{i.e.} themselves fractions of polynomials.")) (|factor| (((|Factored| |#4|) |#4|) "\\spad{factor(prf)} factors a polynomial with rational function coefficients.")) (|pushuconst| ((|#4| (|Fraction| (|Polynomial| |#3|)) |#2|) "\\spad{pushuconst(r,var)} takes a rational function and raises all occurances of the variable \\spad{var} to the polynomial level.")) (|pushucoef| ((|#4| (|SparseUnivariatePolynomial| (|Polynomial| |#3|)) |#2|) "\\spad{pushucoef(upoly,var)} converts the anonymous univariate polynomial \\spad{upoly} to a polynomial in \\spad{var} over rational functions.")) (|pushup| ((|#4| |#4| |#2|) "\\spad{pushup(prf,var)} raises all occurences of the variable \\spad{var} in the coefficients of the polynomial \\spad{prf} back to the polynomial level.")) (|pushdterm| ((|#4| (|SparseUnivariatePolynomial| |#4|) |#2|) "\\spad{pushdterm(monom,var)} pushes all top level occurences of the variable \\spad{var} into the coefficient domain for the monomial \\spad{monom}.")) (|pushdown| ((|#4| |#4| |#2|) "\\spad{pushdown(prf,var)} pushes all top level occurences of the variable \\spad{var} into the coefficient domain for the polynomial \\spad{prf}.")) (|totalfract| (((|Record| (|:| |sup| (|Polynomial| |#3|)) (|:| |inf| (|Polynomial| |#3|))) |#4|) "\\spad{totalfract(prf)} takes a polynomial whose coefficients are themselves fractions of polynomials and returns a record containing the numerator and denominator resulting from putting \\spad{prf} over a common denominator.")) (|convert| (((|Symbol|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) 
 NIL 
 NIL 
-(-673 E OV R P) 
+(-672 E OV R P) 
 ((|constructor| (NIL "\\indented{1}{MRationalFactorize contains the factor function for multivariate} polynomials over the quotient field of a ring \\spad{R} such that the package MultivariateFactorize can factor multivariate polynomials over \\spad{R}.")) (|factor| (((|Factored| |#4|) |#4|) "\\spad{factor(p)} factors the multivariate polynomial \\spad{p} with coefficients which are fractions of elements of \\spad{R}."))) 
 NIL 
 NIL 
-(-674 R S M) 
+(-673 R S M) 
 ((|constructor| (NIL "\\spad{MonoidRingFunctions2} implements functions between two monoid rings defined with the same monoid over different rings.")) (|map| (((|MonoidRing| |#2| |#3|) (|Mapping| |#2| |#1|) (|MonoidRing| |#1| |#3|)) "\\spad{map(f,u)} maps \\spad{f} onto the coefficients \\spad{f} the element \\spad{u} of the monoid ring to create an element of a monoid ring with the same monoid \\spad{b}."))) 
 NIL 
 NIL 
-(-675 R M) 
+(-674 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}."))) 
-((-3992 |has| |#1| (-146)) (-3991 |has| |#1| (-146)) (-3994 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-320))) (|HasCategory| |#2| (QUOTE (-320)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-757)))) 
-(-676 S) 
+((-3991 |has| |#1| (-146)) (-3990 |has| |#1| (-146)) (-3993 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-320))) (|HasCategory| |#2| (QUOTE (-320)))) (|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.")) (|unique| (((|List| |#1|) $) "\\spad{unique ms} returns a list of the elements of \\spad{ms} {\\em without} their multiplicity. See also \\spadfun{members}.")) (|multiset| (($ (|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}."))) 
-((-3987 . T) (-3998 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-1014))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|)))) 
-(-677 S) 
+((-3986 . T) (-3997 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-553 (-473)))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-1013))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|)))) 
+(-676 S) 
 ((|constructor| (NIL "A multi-set aggregate is a set which keeps track of the multiplicity of its elements."))) 
-((-3987 . T) (-3998 . T)) 
+((-3986 . T) (-3997 . T)) 
 NIL 
-(-678) 
+(-677) 
 ((|constructor| (NIL "\\spadtype{MoreSystemCommands} implements an interface with the system command facility. These are the commands that are issued from source files or the system interpreter and they start with a close parenthesis,{} \\spadignore{e.g.} \\spadsyscom{what} commands.")) (|systemCommand| (((|Void|) (|String|)) "\\spad{systemCommand(cmd)} takes the string \\spadvar{\\spad{cmd}} and passes it to the runtime environment for execution as a system command. Although various things may be printed,{} no usable value is returned."))) 
 NIL 
 NIL 
-(-679 S) 
+(-678 S) 
 ((|constructor| (NIL "This package exports tools for merging lists")) (|mergeDifference| (((|List| |#1|) (|List| |#1|) (|List| |#1|)) "\\spad{mergeDifference(l1,l2)} returns a list of elements in \\spad{l1} not present in \\spad{l2}. Assumes lists are ordered and all \\spad{x} in \\spad{l2} are also in \\spad{l1}."))) 
 NIL 
 NIL 
-(-680 |Coef| |Var|) 
+(-679 |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}."))) 
-(((-3999 "*") |has| |#1| (-146)) (-3990 |has| |#1| (-496)) (-3992 . T) (-3991 . T) (-3994 . T)) 
+(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-495)) (-3991 . T) (-3990 . T) (-3993 . T)) 
 NIL 
-(-681 OV E R P) 
+(-680 OV E R P) 
 ((|constructor| (NIL "\\indented{2}{This is the top level package for doing multivariate factorization} over basic domains like \\spadtype{Integer} or \\spadtype{Fraction Integer}.")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factor(p)} factors the multivariate polynomial \\spad{p} over its coefficient domain where \\spad{p} is represented as a univariate polynomial with multivariate coefficients") (((|Factored| |#4|) |#4|) "\\spad{factor(p)} factors the multivariate polynomial \\spad{p} over its coefficient domain"))) 
 NIL 
 NIL 
-(-682 E OV R P) 
+(-681 E OV R P) 
 ((|constructor| (NIL "Author : \\spad{P}.Gianni This package provides the functions for the computation of the square free decomposition of a multivariate polynomial. It uses the package GenExEuclid for the resolution of the equation \\spad{Af + Bg = h} and its generalization to \\spad{n} polynomials over an integral domain and the package \\spad{MultivariateLifting} for the \"multivariate\" lifting.")) (|normDeriv2| (((|SparseUnivariatePolynomial| |#3|) (|SparseUnivariatePolynomial| |#3|) (|Integer|)) "\\spad{normDeriv2 should} be local")) (|myDegree| (((|List| (|NonNegativeInteger|)) (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|NonNegativeInteger|)) "\\spad{myDegree should} be local")) (|lift| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#3|) (|SparseUnivariatePolynomial| |#3|) |#4| (|List| |#2|) (|List| (|NonNegativeInteger|)) (|List| |#3|)) "\\spad{lift should} be local")) (|check| (((|Boolean|) (|List| (|Record| (|:| |factor| (|SparseUnivariatePolynomial| |#3|)) (|:| |exponent| (|Integer|)))) (|List| (|Record| (|:| |factor| (|SparseUnivariatePolynomial| |#3|)) (|:| |exponent| (|Integer|))))) "\\spad{check should} be local")) (|coefChoose| ((|#4| (|Integer|) (|Factored| |#4|)) "\\spad{coefChoose should} be local")) (|intChoose| (((|Record| (|:| |upol| (|SparseUnivariatePolynomial| |#3|)) (|:| |Lval| (|List| |#3|)) (|:| |Lfact| (|List| (|Record| (|:| |factor| (|SparseUnivariatePolynomial| |#3|)) (|:| |exponent| (|Integer|))))) (|:| |ctpol| |#3|)) (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|List| (|List| |#3|))) "\\spad{intChoose should} be local")) (|nsqfree| (((|Record| (|:| |unitPart| |#4|) (|:| |suPart| (|List| (|Record| (|:| |factor| (|SparseUnivariatePolynomial| |#4|)) (|:| |exponent| (|Integer|)))))) (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|List| (|List| |#3|))) "\\spad{nsqfree should} be local")) (|consnewpol| (((|Record| (|:| |pol| (|SparseUnivariatePolynomial| |#4|)) (|:| |polval| (|SparseUnivariatePolynomial| |#3|))) (|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#3|) (|Integer|)) "\\spad{consnewpol should} be local")) (|univcase| (((|Factored| |#4|) |#4| |#2|) "\\spad{univcase should} be local")) (|compdegd| (((|Integer|) (|List| (|Record| (|:| |factor| (|SparseUnivariatePolynomial| |#3|)) (|:| |exponent| (|Integer|))))) "\\spad{compdegd should} be local")) (|squareFreePrim| (((|Factored| |#4|) |#4|) "\\spad{squareFreePrim(p)} compute the square free decomposition of a primitive multivariate polynomial \\spad{p}.")) (|squareFree| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{squareFree(p)} computes the square free decomposition of a multivariate polynomial \\spad{p} presented as a univariate polynomial with multivariate coefficients.") (((|Factored| |#4|) |#4|) "\\spad{squareFree(p)} computes the square free decomposition of a multivariate polynomial \\spad{p}."))) 
 NIL 
 NIL 
-(-683 S R) 
+(-682 S R) 
 ((|constructor| (NIL "NonAssociativeAlgebra is the category of non associative algebras (modules which are themselves non associative rngs). Axioms \\indented{3}{r*(a*b) = (r*a)*b = a*(r*b)}")) (|plenaryPower| (($ $ (|PositiveInteger|)) "\\spad{plenaryPower(a,n)} is recursively defined to be \\spad{plenaryPower(a,n-1)*plenaryPower(a,n-1)} for \\spad{n>1} and \\spad{a} for \\spad{n=1}."))) 
 NIL 
 NIL 
-(-684 R) 
+(-683 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}."))) 
-((-3992 . T) (-3991 . T)) 
+((-3991 . T) (-3990 . T)) 
 NIL 
-(-685 S) 
+(-684 S) 
 ((|constructor| (NIL "NonAssociativeRng is a basic ring-type structure,{} not necessarily commutative or associative,{} and not necessarily with unit. Axioms \\indented{2}{x*(y+z) = x*y + x*z} \\indented{2}{(x+y)*z = x*z + y*z} Common Additional Axioms \\indented{2}{noZeroDivisors\\space{2}ab = 0 => \\spad{a=0} or \\spad{b=0}}")) (|antiCommutator| (($ $ $) "\\spad{antiCommutator(a,b)} returns \\spad{a*b+b*a}.")) (|commutator| (($ $ $) "\\spad{commutator(a,b)} returns \\spad{a*b-b*a}.")) (|associator| (($ $ $ $) "\\spad{associator(a,b,c)} returns \\spad{(a*b)*c-a*(b*c)}."))) 
 NIL 
 NIL 
-(-686) 
+(-685) 
 ((|constructor| (NIL "NonAssociativeRng is a basic ring-type structure,{} not necessarily commutative or associative,{} and not necessarily with unit. Axioms \\indented{2}{x*(y+z) = x*y + x*z} \\indented{2}{(x+y)*z = x*z + y*z} Common Additional Axioms \\indented{2}{noZeroDivisors\\space{2}ab = 0 => \\spad{a=0} or \\spad{b=0}}")) (|antiCommutator| (($ $ $) "\\spad{antiCommutator(a,b)} returns \\spad{a*b+b*a}.")) (|commutator| (($ $ $) "\\spad{commutator(a,b)} returns \\spad{a*b-b*a}.")) (|associator| (($ $ $ $) "\\spad{associator(a,b,c)} returns \\spad{(a*b)*c-a*(b*c)}."))) 
 NIL 
 NIL 
-(-687 S) 
+(-686 S) 
 ((|constructor| (NIL "A NonAssociativeRing is a non associative rng which has a unit,{} the multiplication is not necessarily commutative or associative.")) (|coerce| (($ (|Integer|)) "\\spad{coerce(n)} coerces the integer \\spad{n} to an element of the ring.")) (|characteristic| (((|NonNegativeInteger|)) "\\spad{characteristic()} returns the characteristic of the ring."))) 
 NIL 
 NIL 
-(-688) 
+(-687) 
 ((|constructor| (NIL "A NonAssociativeRing is a non associative rng which has a unit,{} the multiplication is not necessarily commutative or associative.")) (|coerce| (($ (|Integer|)) "\\spad{coerce(n)} coerces the integer \\spad{n} to an element of the ring.")) (|characteristic| (((|NonNegativeInteger|)) "\\spad{characteristic()} returns the characteristic of the ring."))) 
 NIL 
 NIL 
-(-689 |Par|) 
+(-688 |Par|) 
 ((|constructor| (NIL "This package computes explicitly eigenvalues and eigenvectors of matrices with entries over the complex rational numbers. The results are expressed either as complex floating numbers or as complex rational numbers depending on the type of the precision parameter.")) (|complexEigenvectors| (((|List| (|Record| (|:| |outval| (|Complex| |#1|)) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| (|Complex| |#1|)))))) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) |#1|) "\\spad{complexEigenvectors(m,eps)} returns a list of records each one containing a complex eigenvalue,{} its algebraic multiplicity,{} and a list of associated eigenvectors. All these results are computed to precision \\spad{eps} and are expressed as complex floats or complex rational numbers depending on the type of \\spad{eps} (float or rational).")) (|complexEigenvalues| (((|List| (|Complex| |#1|)) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) |#1|) "\\spad{complexEigenvalues(m,eps)} computes the eigenvalues of the matrix \\spad{m} to precision \\spad{eps}. The eigenvalues are expressed as complex floats or complex rational numbers depending on the type of \\spad{eps} (float or rational).")) (|characteristicPolynomial| (((|Polynomial| (|Complex| (|Fraction| (|Integer|)))) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) (|Symbol|)) "\\spad{characteristicPolynomial(m,x)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over Complex Rationals with variable \\spad{x}.") (((|Polynomial| (|Complex| (|Fraction| (|Integer|)))) (|Matrix| (|Complex| (|Fraction| (|Integer|))))) "\\spad{characteristicPolynomial(m)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over complex rationals with a new symbol as variable."))) 
 NIL 
 NIL 
-(-690 -3094) 
+(-689 -3093) 
 ((|constructor| (NIL "\\spadtype{NumericContinuedFraction} provides functions \\indented{2}{for converting floating point numbers to continued fractions.}")) (|continuedFraction| (((|ContinuedFraction| (|Integer|)) |#1|) "\\spad{continuedFraction(f)} converts the floating point number \\spad{f} to a reduced continued fraction."))) 
 NIL 
 NIL 
-(-691 P -3094) 
+(-690 P -3093) 
 ((|constructor| (NIL "This package provides a division and related operations for \\spadtype{MonogenicLinearOperator}\\spad{s} over a \\spadtype{Field}. Since the multiplication is in general non-commutative,{} these operations all have left- and right-hand versions. This package provides the operations based on left-division.")) (|leftLcm| ((|#1| |#1| |#1|) "\\spad{leftLcm(a,b)} computes the value \\spad{m} of lowest degree such that \\spad{m = a*aa = b*bb} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using left-division.")) (|leftGcd| ((|#1| |#1| |#1|) "\\spad{leftGcd(a,b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = aa*g}} \\indented{3}{\\spad{b = bb*g}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using left-division.")) (|leftExactQuotient| (((|Union| |#1| "failed") |#1| |#1|) "\\spad{leftExactQuotient(a,b)} computes the value \\spad{q},{} if it exists,{} \\indented{1}{such that \\spad{a = b*q}.}")) (|leftRemainder| ((|#1| |#1| |#1|) "\\spad{leftRemainder(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|leftQuotient| ((|#1| |#1| |#1|) "\\spad{leftQuotient(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|leftDivide| (((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|) "\\spad{leftDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division''."))) 
 NIL 
 NIL 
-(-692 T$) 
+(-691 T$) 
 NIL 
 NIL 
 NIL 
-(-693 UP -3094) 
+(-692 UP -3093) 
 ((|constructor| (NIL "In this package \\spad{F} is a framed algebra over the integers (typically \\spad{F = Z[a]} for some algebraic integer a). The package provides functions to compute the integral closure of \\spad{Z} in the quotient quotient field of \\spad{F}.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| (|Integer|))) (|:| |basisDen| (|Integer|)) (|:| |basisInv| (|Matrix| (|Integer|)))) (|Integer|)) "\\spad{integralBasis(p)} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the local integral closure of \\spad{Z} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{Z}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| (|Integer|))) (|:| |basisDen| (|Integer|)) (|:| |basisInv| (|Matrix| (|Integer|))))) "\\spad{integralBasis()} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the integral closure of \\spad{Z} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{Z}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|discriminant| (((|Integer|)) "\\spad{discriminant()} returns the discriminant of the integral closure of \\spad{Z} in the quotient field of the framed algebra \\spad{F}."))) 
 NIL 
 NIL 
-(-694 R) 
+(-693 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 
-(-695) 
+(-694) 
 ((|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."))) 
-(((-3999 "*") . T)) 
+(((-3998 "*") . T)) 
 NIL 
-(-696 R -3094) 
+(-695 R -3093) 
 ((|constructor| (NIL "NonLinearFirstOrderODESolver provides a function for finding closed form first integrals of nonlinear ordinary differential equations of order 1.")) (|solve| (((|Union| |#2| "failed") |#2| |#2| (|BasicOperator|) (|Symbol|)) "\\spad{solve(M(x,y), N(x,y), y, x)} returns \\spad{F(x,y)} such that \\spad{F(x,y) = c} for a constant \\spad{c} is a first integral of the equation \\spad{M(x,y) dx + N(x,y) dy = 0},{} or \"failed\" if no first-integral can be found."))) 
 NIL 
 NIL 
-(-697) 
+(-696) 
 ((|constructor| (NIL "\\spadtype{None} implements a type with no objects. It is mainly used in technical situations where such a thing is needed (\\spadignore{e.g.} the interpreter and some of the internal \\spadtype{Expression} code)."))) 
 NIL 
 NIL 
-(-698 S) 
+(-697 S) 
 ((|constructor| (NIL "\\spadtype{NoneFunctions1} implements functions on \\spadtype{None}. It particular it includes a particulary dangerous coercion from any other type to \\spadtype{None}.")) (|coerce| (((|None|) |#1|) "\\spad{coerce(x)} changes \\spad{x} into an object of type \\spadtype{None}."))) 
 NIL 
 NIL 
-(-699 R |PolR| E |PolE|) 
+(-698 R |PolR| E |PolE|) 
 ((|constructor| (NIL "This package implements the norm of a polynomial with coefficients in a monogenic algebra (using resultants)")) (|norm| ((|#2| |#4|) "\\spad{norm q} returns the norm of \\spad{q},{} \\spadignore{i.e.} the product of all the conjugates of \\spad{q}."))) 
 NIL 
 NIL 
-(-700 R E V P TS) 
+(-699 R E V P TS) 
 ((|constructor| (NIL "A package for computing normalized assocites of univariate polynomials with coefficients in a tower of simple extensions of a field.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. MORENO MAZA and \\spad{R}. RIOBOO \"Computations of gcd over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of \\spad{AAECC11}} \\indented{5}{Paris,{} 1995.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.}")) (|normInvertible?| (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{normInvertible?(\\spad{p},{}ts)} is an internal subroutine,{} exported only for developement.")) (|outputArgs| (((|Void|) (|String|) (|String|) |#4| |#5|) "\\axiom{outputArgs(\\spad{s1},{}\\spad{s2},{}\\spad{p},{}ts)} is an internal subroutine,{} exported only for developement.")) (|normalize| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{normalize(\\spad{p},{}ts)} normalizes \\axiom{\\spad{p}} \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}.")) (|normalizedAssociate| ((|#4| |#4| |#5|) "\\axiom{normalizedAssociate(\\spad{p},{}ts)} returns a normalized polynomial \\axiom{\\spad{n}} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts} such that \\axiom{\\spad{n}} and \\axiom{\\spad{p}} are associates \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts} and assuming that \\axiom{\\spad{p}} is invertible \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}.")) (|recip| (((|Record| (|:| |num| |#4|) (|:| |den| |#4|)) |#4| |#5|) "\\axiom{recip(\\spad{p},{}ts)} returns the inverse of \\axiom{\\spad{p}} \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts} assuming that \\axiom{\\spad{p}} is invertible \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}."))) 
 NIL 
 NIL 
-(-701 -3094 |ExtF| |SUEx| |ExtP| |n|) 
+(-700 -3093 |ExtF| |SUEx| |ExtP| |n|) 
 ((|constructor| (NIL "This package \\undocumented")) (|Frobenius| ((|#4| |#4|) "\\spad{Frobenius(x)} \\undocumented")) (|retractIfCan| (((|Union| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|)) "failed") |#4|) "\\spad{retractIfCan(x)} \\undocumented")) (|normFactors| (((|List| |#4|) |#4|) "\\spad{normFactors(x)} \\undocumented"))) 
 NIL 
 NIL 
-(-702 BP E OV R P) 
+(-701 BP E OV R P) 
 ((|constructor| (NIL "Package for the determination of the coefficients in the lifting process. Used by \\spadtype{MultivariateLifting}. This package will work for every euclidean domain \\spad{R} which has property \\spad{F},{} \\spadignore{i.e.} there exists a factor operation in \\spad{R[x]}.")) (|listexp| (((|List| (|NonNegativeInteger|)) |#1|) "\\spad{listexp }\\undocumented")) (|npcoef| (((|Record| (|:| |deter| (|List| (|SparseUnivariatePolynomial| |#5|))) (|:| |dterm| (|List| (|List| (|Record| (|:| |expt| (|NonNegativeInteger|)) (|:| |pcoef| |#5|))))) (|:| |nfacts| (|List| |#1|)) (|:| |nlead| (|List| |#5|))) (|SparseUnivariatePolynomial| |#5|) (|List| |#1|) (|List| |#5|)) "\\spad{npcoef }\\undocumented"))) 
 NIL 
 NIL 
-(-703 |Par|) 
+(-702 |Par|) 
 ((|constructor| (NIL "This package computes explicitly eigenvalues and eigenvectors of matrices with entries over the Rational Numbers. The results are expressed as floating numbers or as rational numbers depending on the type of the parameter Par.")) (|realEigenvectors| (((|List| (|Record| (|:| |outval| |#1|) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| |#1|))))) (|Matrix| (|Fraction| (|Integer|))) |#1|) "\\spad{realEigenvectors(m,eps)} returns a list of records each one containing a real eigenvalue,{} its algebraic multiplicity,{} and a list of associated eigenvectors. All these results are computed to precision \\spad{eps} as floats or rational numbers depending on the type of \\spad{eps} .")) (|realEigenvalues| (((|List| |#1|) (|Matrix| (|Fraction| (|Integer|))) |#1|) "\\spad{realEigenvalues(m,eps)} computes the eigenvalues of the matrix \\spad{m} to precision \\spad{eps}. The eigenvalues are expressed as floats or rational numbers depending on the type of \\spad{eps} (float or rational).")) (|characteristicPolynomial| (((|Polynomial| (|Fraction| (|Integer|))) (|Matrix| (|Fraction| (|Integer|))) (|Symbol|)) "\\spad{characteristicPolynomial(m,x)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over RN with variable \\spad{x}. Fraction \\spad{P} RN.") (((|Polynomial| (|Fraction| (|Integer|))) (|Matrix| (|Fraction| (|Integer|)))) "\\spad{characteristicPolynomial(m)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over RN with a new symbol as variable."))) 
 NIL 
 NIL 
-(-704 R |VarSet|) 
+(-703 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."))) 
-(((-3999 "*") |has| |#1| (-146)) (-3990 |has| |#1| (-496)) (-3995 |has| |#1| (-6 -3995)) (-3992 . T) (-3991 . T) (-3994 . T)) 
-((|HasCategory| |#1| (QUOTE (-822))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-822)))) (OR (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-822)))) (OR (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-822)))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (-12 (|HasCategory| |#1| (QUOTE (-797 (-330)))) (|HasCategory| |#2| (QUOTE (-797 (-330))))) (-12 (|HasCategory| |#1| (QUOTE (-797 (-485)))) (|HasCategory| |#2| (QUOTE (-797 (-485))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-330))))) (|HasCategory| |#2| (QUOTE (-554 (-801 (-330)))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-485))))) (|HasCategory| |#2| (QUOTE (-554 (-801 (-485)))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-474)))) (|HasCategory| |#2| (QUOTE (-554 (-474))))) (|HasCategory| |#1| (QUOTE (-581 (-485)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485)))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485))))) (-12 (|HasCategory| |#1| (QUOTE (-951 (-485)))) (|HasCategory| |#2| (QUOTE (-554 (-1091))))) (|HasCategory| |#2| (QUOTE (-554 (-1091)))) (|HasCategory| |#1| (QUOTE (-312))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#2| (QUOTE (-554 (-1091))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-485)))) (|HasCategory| |#2| (QUOTE (-554 (-1091)))) (-2562 (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#2| (QUOTE (-554 (-1091)))))) (OR (-12 (|HasCategory| |#2| (QUOTE (-554 (-1091)))) (-2562 (|HasCategory| |#1| (QUOTE (-38 (-350 (-485)))))) (-2562 (|HasCategory| |#1| (QUOTE (-38 (-485)))))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-485)))) (|HasCategory| |#2| (QUOTE (-554 (-1091)))) (-2562 (|HasCategory| |#1| (QUOTE (-38 (-350 (-485)))))) (-2562 (|HasCategory| |#1| (QUOTE (-484))))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#2| (QUOTE (-554 (-1091)))) (-2562 (|HasCategory| |#1| (QUOTE (-905 (-485))))))) (|HasAttribute| |#1| (QUOTE -3995)) (|HasCategory| |#1| (QUOTE (-392))) (-12 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) 
-(-705 R) 
+(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-495)) (-3994 |has| |#1| (-6 -3994)) (-3991 . T) (-3990 . T) (-3993 . T)) 
+((|HasCategory| |#1| (QUOTE (-821))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-821)))) (OR (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-821)))) (OR (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-821)))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-495)))) (-12 (|HasCategory| |#1| (QUOTE (-796 (-330)))) (|HasCategory| |#2| (QUOTE (-796 (-330))))) (-12 (|HasCategory| |#1| (QUOTE (-796 (-484)))) (|HasCategory| |#2| (QUOTE (-796 (-484))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-800 (-330))))) (|HasCategory| |#2| (QUOTE (-553 (-800 (-330)))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-800 (-484))))) (|HasCategory| |#2| (QUOTE (-553 (-800 (-484)))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-473)))) (|HasCategory| |#2| (QUOTE (-553 (-473))))) (|HasCategory| |#1| (QUOTE (-580 (-484)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-484)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484)))))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484))))) (-12 (|HasCategory| |#1| (QUOTE (-950 (-484)))) (|HasCategory| |#2| (QUOTE (-553 (-1090))))) (|HasCategory| |#2| (QUOTE (-553 (-1090)))) (|HasCategory| |#1| (QUOTE (-312))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#2| (QUOTE (-553 (-1090))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-484)))) (|HasCategory| |#2| (QUOTE (-553 (-1090)))) (-2561 (|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#2| (QUOTE (-553 (-1090)))))) (OR (-12 (|HasCategory| |#2| (QUOTE (-553 (-1090)))) (-2561 (|HasCategory| |#1| (QUOTE (-38 (-350 (-484)))))) (-2561 (|HasCategory| |#1| (QUOTE (-38 (-484)))))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-484)))) (|HasCategory| |#2| (QUOTE (-553 (-1090)))) (-2561 (|HasCategory| |#1| (QUOTE (-38 (-350 (-484)))))) (-2561 (|HasCategory| |#1| (QUOTE (-483))))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#2| (QUOTE (-553 (-1090)))) (-2561 (|HasCategory| |#1| (QUOTE (-904 (-484))))))) (|HasAttribute| |#1| (QUOTE -3994)) (|HasCategory| |#1| (QUOTE (-392))) (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) 
+(-704 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)}"))) 
-(((-3999 "*") |has| |#1| (-146)) (-3990 |has| |#1| (-496)) (-3993 |has| |#1| (-312)) (-3995 |has| |#1| (-6 -3995)) (-3992 . T) (-3991 . T) (-3994 . T)) 
-((|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (-12 (|HasCategory| |#1| (QUOTE (-797 (-330)))) (|HasCategory| (-995) (QUOTE (-797 (-330))))) (-12 (|HasCategory| |#1| (QUOTE (-797 (-485)))) (|HasCategory| (-995) (QUOTE (-797 (-485))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-330))))) (|HasCategory| (-995) (QUOTE (-554 (-801 (-330)))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-485))))) (|HasCategory| (-995) (QUOTE (-554 (-801 (-485)))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-474)))) (|HasCategory| (-995) (QUOTE (-554 (-474))))) (|HasCategory| |#1| (QUOTE (-581 (-485)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485)))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485))))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-822)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-822)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-822)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (QUOTE (-812 (-1091)))) (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-190))) (|HasAttribute| |#1| (QUOTE -3995)) (|HasCategory| |#1| (QUOTE (-392))) (-12 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) 
-(-706 R S) 
+(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-495)) (-3992 |has| |#1| (-312)) (-3994 |has| |#1| (-6 -3994)) (-3991 . T) (-3990 . T) (-3993 . T)) 
+((|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-495)))) (-12 (|HasCategory| |#1| (QUOTE (-796 (-330)))) (|HasCategory| (-994) (QUOTE (-796 (-330))))) (-12 (|HasCategory| |#1| (QUOTE (-796 (-484)))) (|HasCategory| (-994) (QUOTE (-796 (-484))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-800 (-330))))) (|HasCategory| (-994) (QUOTE (-553 (-800 (-330)))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-800 (-484))))) (|HasCategory| (-994) (QUOTE (-553 (-800 (-484)))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-473)))) (|HasCategory| (-994) (QUOTE (-553 (-473))))) (|HasCategory| |#1| (QUOTE (-580 (-484)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-484)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484)))))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484))))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-821)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-821)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-821)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (QUOTE (-811 (-1090)))) (|HasCategory| |#1| (QUOTE (-809 (-1090)))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-190))) (|HasAttribute| |#1| (QUOTE -3994)) (|HasCategory| |#1| (QUOTE (-392))) (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) 
+(-705 R S) 
 ((|constructor| (NIL "This package lifts a mapping from coefficient rings \\spad{R} to \\spad{S} to a mapping from sparse univariate polynomial over \\spad{R} to a sparse univariate polynomial over \\spad{S}. Note that the mapping is assumed to send zero to zero,{} since it will only be applied to the non-zero coefficients of the polynomial.")) (|map| (((|NewSparseUnivariatePolynomial| |#2|) (|Mapping| |#2| |#1|) (|NewSparseUnivariatePolynomial| |#1|)) "\\axiom{map(func,{} poly)} creates a new polynomial by applying func to every non-zero coefficient of the polynomial poly."))) 
 NIL 
 NIL 
-(-707 R) 
+(-706 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 (-350 (-485)))))) 
-(-708 R E V P) 
+((|HasCategory| |#1| (QUOTE (-38 (-350 (-484)))))) 
+(-707 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.}"))) 
-((-3998 . T)) 
+((-3997 . T)) 
 NIL 
-(-709 S) 
+(-708 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 (-496))) (|HasCategory| |#1| (QUOTE (-757)))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-962))) (|HasCategory| |#1| (QUOTE (-146)))) 
-(-710) 
+((-12 (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-756)))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-961))) (|HasCategory| |#1| (QUOTE (-146)))) 
+(-709) 
 ((|constructor| (NIL "NumberFormats provides function to format and read arabic and roman numbers,{} to convert numbers to strings and to read floating-point numbers.")) (|ScanFloatIgnoreSpacesIfCan| (((|Union| (|Float|) "failed") (|String|)) "\\spad{ScanFloatIgnoreSpacesIfCan(s)} tries to form a floating point number from the string \\spad{s} ignoring any spaces.")) (|ScanFloatIgnoreSpaces| (((|Float|) (|String|)) "\\spad{ScanFloatIgnoreSpaces(s)} forms a floating point number from the string \\spad{s} ignoring any spaces. Error is generated if the string is not recognised as a floating point number.")) (|ScanRoman| (((|PositiveInteger|) (|String|)) "\\spad{ScanRoman(s)} forms an integer from a Roman numeral string \\spad{s}.")) (|FormatRoman| (((|String|) (|PositiveInteger|)) "\\spad{FormatRoman(n)} forms a Roman numeral string from an integer \\spad{n}.")) (|ScanArabic| (((|PositiveInteger|) (|String|)) "\\spad{ScanArabic(s)} forms an integer from an Arabic numeral string \\spad{s}.")) (|FormatArabic| (((|String|) (|PositiveInteger|)) "\\spad{FormatArabic(n)} forms an Arabic numeral string from an integer \\spad{n}."))) 
 NIL 
 NIL 
-(-711) 
+(-710) 
 ((|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}."))) 
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-(-712) 
+(-711) 
 ((|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."))) 
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-(-713 |Curve|) 
+(-712 |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}."))) 
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-(-714 S) 
+(-713 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|) $) "\\spad{negative?(x)} holds when \\spad{x} is less than \\spad{0}."))) 
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-(-715) 
+(-714) 
 ((|constructor| (NIL "Ordered sets which are also abelian groups,{} such that the addition preserves the ordering.")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x}.")) (|sign| (((|Integer|) $) "\\spad{sign(x)} is \\spad{1} if \\spad{x} is positive,{} \\spad{-1} if \\spad{x} is negative,{} and \\spad{0} otherwise.")) (|negative?| (((|Boolean|) $) "\\spad{negative?(x)} holds when \\spad{x} is less than \\spad{0}."))) 
 NIL 
 NIL 
-(-716 S) 
+(-715 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 
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-(-717) 
+(-716) 
 ((|constructor| (NIL "Ordered sets which are also abelian monoids,{} such that the addition preserves the ordering.")) (|positive?| (((|Boolean|) $) "\\spad{positive?(x)} holds when \\spad{x} is greater than \\spad{0}."))) 
 NIL 
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-(-718) 
+(-717) 
 ((|constructor| (NIL "This domain is an OrderedAbelianMonoid with a \\spadfun{sup} operation added. The purpose of the \\spadfun{sup} operator in this domain is to act as a supremum with respect to the partial order imposed by \\spadop{-},{} rather than with respect to the total \\spad{>} order (since that is \"max\"). \\blankline")) (|sup| (($ $ $) "\\spad{sup(x,y)} returns the least element from which both \\spad{x} and \\spad{y} can be subtracted."))) 
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-(-719) 
+(-718) 
 ((|constructor| (NIL "Ordered sets which are also abelian semigroups,{} such that the addition preserves the ordering. \\indented{2}{\\spad{ x < y => x+z < y+z}}"))) 
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-(-720 S R) 
+(-719 S R) 
 ((|constructor| (NIL "OctonionCategory gives the categorial frame for the octonions,{} and eight-dimensional non-associative algebra,{} doubling the the quaternions in the same way as doubling the Complex numbers to get the quaternions.")) (|inv| (($ $) "\\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| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-484))) (|HasCategory| |#2| (QUOTE (-974))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-554 (-474)))) (|HasCategory| |#2| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-320)))) 
-(-721 R) 
+((|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-483))) (|HasCategory| |#2| (QUOTE (-973))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-553 (-473)))) (|HasCategory| |#2| (QUOTE (-756))) (|HasCategory| |#2| (QUOTE (-320)))) 
+(-720 R) 
 ((|constructor| (NIL "OctonionCategory gives the categorial frame for the octonions,{} and eight-dimensional non-associative algebra,{} doubling the the quaternions in the same way as doubling the Complex numbers to get the quaternions.")) (|inv| (($ $) "\\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| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) 
-((-3991 . T) (-3992 . T) (-3994 . T)) 
+((-3990 . T) (-3991 . T) (-3993 . T)) 
 NIL 
-(-722) 
+(-721) 
 ((|constructor| (NIL "Ordered sets which are also abelian cancellation monoids,{} such that the addition preserves the ordering."))) 
 NIL 
 NIL 
-(-723 R) 
+(-722 R) 
 ((|constructor| (NIL "Octonion implements octonions (Cayley-Dixon algebra) over a commutative ring,{} an eight-dimensional non-associative algebra,{} doubling the quaternions in the same way as doubling the complex numbers to get the quaternions the main constructor function is {\\em octon} which takes 8 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j} imaginary part,{} the \\spad{k} imaginary part,{} (as with quaternions) and in addition the imaginary parts \\spad{E},{} \\spad{I},{} \\spad{J},{} \\spad{K}.")) (|octon| (($ (|Quaternion| |#1|) (|Quaternion| |#1|)) "\\spad{octon(qe,qE)} constructs an octonion from two quaternions using the relation {\\em O = Q + QE}."))) 
-((-3991 . T) (-3992 . T) (-3994 . T)) 
-((|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-320))) (|HasCategory| |#1| (|%list| (QUOTE -456) (QUOTE (-1091)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -241) (|devaluate| |#1|) (|devaluate| |#1|))) (OR (|HasCategory| |#1| (QUOTE (-951 (-350 (-485))))) (|HasCategory| (-910 |#1|) (QUOTE (-951 (-350 (-485)))))) (OR (|HasCategory| |#1| (QUOTE (-951 (-485)))) (|HasCategory| (-910 |#1|) (QUOTE (-951 (-485))))) (|HasCategory| |#1| (QUOTE (-974))) (|HasCategory| |#1| (QUOTE (-484))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-910 |#1|) (QUOTE (-951 (-350 (-485))))) (|HasCategory| (-910 |#1|) (QUOTE (-951 (-485)))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485))))) 
-(-724 OR R OS S) 
+((-3990 . T) (-3991 . T) (-3993 . T)) 
+((|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-553 (-473)))) (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-320))) (|HasCategory| |#1| (|%list| (QUOTE -455) (QUOTE (-1090)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -241) (|devaluate| |#1|) (|devaluate| |#1|))) (OR (|HasCategory| |#1| (QUOTE (-950 (-350 (-484))))) (|HasCategory| (-909 |#1|) (QUOTE (-950 (-350 (-484)))))) (OR (|HasCategory| |#1| (QUOTE (-950 (-484)))) (|HasCategory| (-909 |#1|) (QUOTE (-950 (-484))))) (|HasCategory| |#1| (QUOTE (-973))) (|HasCategory| |#1| (QUOTE (-483))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-909 |#1|) (QUOTE (-950 (-350 (-484))))) (|HasCategory| (-909 |#1|) (QUOTE (-950 (-484)))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-484))))) 
+(-723 OR R OS S) 
 ((|constructor| (NIL "\\spad{OctonionCategoryFunctions2} implements functions between two octonion domains defined over different rings. The function map is used to coerce between octonion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,u)} maps \\spad{f} onto the component parts of the octonion \\spad{u}."))) 
 NIL 
 NIL 
-(-725 R -3094 L) 
+(-724 R -3093 L) 
 ((|constructor| (NIL "Solution of linear ordinary differential equations,{} constant coefficient case.")) (|constDsolve| (((|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Symbol|)) "\\spad{constDsolve(op, g, x)} returns \\spad{[f, [y1,...,ym]]} where \\spad{f} is a particular solution of the equation \\spad{op y = g},{} and the \\spad{yi}'s form a basis for the solutions of \\spad{op y = 0}."))) 
 NIL 
 NIL 
-(-726 R -3094) 
+(-725 R -3093) 
 ((|constructor| (NIL "\\spad{ElementaryFunctionODESolver} provides the top-level functions for finding closed form solutions of ordinary differential equations and initial value problems.")) (|solve| (((|Union| |#2| #1="failed") |#2| (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{solve(eq, y, x = a, [y0,...,ym])} returns either the solution of the initial value problem \\spad{eq, y(a) = y0, y'(a) = y1,...} or \"failed\" if the solution cannot be found; error if the equation is not one linear ordinary or of the form \\spad{dy/dx = f(x,y)}.") (((|Union| |#2| #1#) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{solve(eq, y, x = a, [y0,...,ym])} returns either the solution of the initial value problem \\spad{eq, y(a) = y0, y'(a) = y1,...} or \"failed\" if the solution cannot be found; error if the equation is not one linear ordinary or of the form \\spad{dy/dx = f(x,y)}.") (((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#2| #2="failed") |#2| (|BasicOperator|) (|Symbol|)) "\\spad{solve(eq, y, x)} returns either a solution of the ordinary differential equation \\spad{eq} or \"failed\" if no non-trivial solution can be found; If the equation is linear ordinary,{} a solution is of the form \\spad{[h, [b1,...,bm]]} where \\spad{h} is a particular solution and and \\spad{[b1,...bm]} are linearly independent solutions of the associated homogenuous equation \\spad{f(x,y) = 0}; A full basis for the solutions of the homogenuous equation is not always returned,{} only the solutions which were found; If the equation is of the form {dy/dx = \\spad{f}(\\spad{x},{}\\spad{y})},{} a solution is of the form \\spad{h(x,y)} where \\spad{h(x,y) = c} is a first integral of the equation for any constant \\spad{c}.") (((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#2| #2#) (|Equation| |#2|) (|BasicOperator|) (|Symbol|)) "\\spad{solve(eq, y, x)} returns either a solution of the ordinary differential equation \\spad{eq} or \"failed\" if no non-trivial solution can be found; If the equation is linear ordinary,{} a solution is of the form \\spad{[h, [b1,...,bm]]} where \\spad{h} is a particular solution and \\spad{[b1,...bm]} are linearly independent solutions of the associated homogenuous equation \\spad{f(x,y) = 0}; A full basis for the solutions of the homogenuous equation is not always returned,{} only the solutions which were found; If the equation is of the form {dy/dx = \\spad{f}(\\spad{x},{}\\spad{y})},{} a solution is of the form \\spad{h(x,y)} where \\spad{h(x,y) = c} is a first integral of the equation for any constant \\spad{c}; error if the equation is not one of those 2 forms.") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|List| |#2|) (|List| (|BasicOperator|)) (|Symbol|)) "\\spad{solve([eq_1,...,eq_n], [y_1,...,y_n], x)} returns either \"failed\" or,{} if the equations form a fist order linear system,{} a solution of the form \\spad{[y_p, [b_1,...,b_n]]} where \\spad{h_p} is a particular solution and \\spad{[b_1,...b_m]} are linearly independent solutions of the associated homogenuous system. error if the equations do not form a first order linear system") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Symbol|)) "\\spad{solve([eq_1,...,eq_n], [y_1,...,y_n], x)} returns either \"failed\" or,{} if the equations form a fist order linear system,{} a solution of the form \\spad{[y_p, [b_1,...,b_n]]} where \\spad{h_p} is a particular solution and \\spad{[b_1,...b_m]} are linearly independent solutions of the associated homogenuous system. error if the equations do not form a first order linear system") (((|Union| (|List| (|Vector| |#2|)) "failed") (|Matrix| |#2|) (|Symbol|)) "\\spad{solve(m, x)} returns a basis for the solutions of \\spad{D y = m y}. \\spad{x} is the dependent variable.") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|Matrix| |#2|) (|Vector| |#2|) (|Symbol|)) "\\spad{solve(m, v, x)} returns \\spad{[v_p, [v_1,...,v_m]]} such that the solutions of the system \\spad{D y = m y + v} are \\spad{v_p + c_1 v_1 + ... + c_m v_m} where the \\spad{c_i's} are constants,{} and the \\spad{v_i's} form a basis for the solutions of \\spad{D y = m y}. \\spad{x} is the dependent variable."))) 
 NIL 
 NIL 
-(-727 R -3094) 
+(-726 R -3093) 
 ((|constructor| (NIL "\\spadtype{ODEIntegration} provides an interface to the integrator. This package is intended for use by the differential equations solver but not at top-level.")) (|diff| (((|Mapping| |#2| |#2|) (|Symbol|)) "\\spad{diff(x)} returns the derivation with respect to \\spad{x}.")) (|expint| ((|#2| |#2| (|Symbol|)) "\\spad{expint(f, x)} returns e^{the integral of \\spad{f} with respect to \\spad{x}}.")) (|int| ((|#2| |#2| (|Symbol|)) "\\spad{int(f, x)} returns the integral of \\spad{f} with respect to \\spad{x}."))) 
 NIL 
 NIL 
-(-728 -3094 UP UPUP R) 
+(-727 -3093 UP UPUP R) 
 ((|constructor| (NIL "In-field solution of an linear ordinary differential equation,{} pure algebraic case.")) (|algDsolve| (((|Record| (|:| |particular| (|Union| |#4| "failed")) (|:| |basis| (|List| |#4|))) (|LinearOrdinaryDifferentialOperator1| |#4|) |#4|) "\\spad{algDsolve(op, g)} returns \\spad{[\"failed\", []]} if the equation \\spad{op y = g} has no solution in \\spad{R}. Otherwise,{} it returns \\spad{[f, [y1,...,ym]]} where \\spad{f} is a particular rational solution and the \\spad{y_i's} form a basis for the solutions in \\spad{R} of the homogeneous equation."))) 
 NIL 
 NIL 
-(-729 -3094 UP L LQ) 
+(-728 -3093 UP L LQ) 
 ((|constructor| (NIL "\\spad{PrimitiveRatDE} provides functions for in-field solutions of linear \\indented{1}{ordinary differential equations,{} in the transcendental case.} \\indented{1}{The derivation to use is given by the parameter \\spad{L}.}")) (|splitDenominator| (((|Record| (|:| |eq| |#3|) (|:| |rh| (|List| (|Fraction| |#2|)))) |#4| (|List| (|Fraction| |#2|))) "\\spad{splitDenominator(op, [g1,...,gm])} returns \\spad{op0, [h1,...,hm]} such that the equations \\spad{op y = c1 g1 + ... + cm gm} and \\spad{op0 y = c1 h1 + ... + cm hm} have the same solutions.")) (|indicialEquation| ((|#2| |#4| |#1|) "\\spad{indicialEquation(op, a)} returns the indicial equation of \\spad{op} at \\spad{a}.") ((|#2| |#3| |#1|) "\\spad{indicialEquation(op, a)} returns the indicial equation of \\spad{op} at \\spad{a}.")) (|indicialEquations| (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#4| |#2|) "\\spad{indicialEquations(op, p)} returns \\spad{[[d1,e1],...,[dq,eq]]} where the \\spad{d_i}'s are the affine singularities of \\spad{op} above the roots of \\spad{p},{} and the \\spad{e_i}'s are the indicial equations at each \\spad{d_i}.") (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#4|) "\\spad{indicialEquations op} returns \\spad{[[d1,e1],...,[dq,eq]]} where the \\spad{d_i}'s are the affine singularities of \\spad{op},{} and the \\spad{e_i}'s are the indicial equations at each \\spad{d_i}.") (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#3| |#2|) "\\spad{indicialEquations(op, p)} returns \\spad{[[d1,e1],...,[dq,eq]]} where the \\spad{d_i}'s are the affine singularities of \\spad{op} above the roots of \\spad{p},{} and the \\spad{e_i}'s are the indicial equations at each \\spad{d_i}.") (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#3|) "\\spad{indicialEquations op} returns \\spad{[[d1,e1],...,[dq,eq]]} where the \\spad{d_i}'s are the affine singularities of \\spad{op},{} and the \\spad{e_i}'s are the indicial equations at each \\spad{d_i}.")) (|denomLODE| ((|#2| |#3| (|List| (|Fraction| |#2|))) "\\spad{denomLODE(op, [g1,...,gm])} returns a polynomial \\spad{d} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{p/d} for some polynomial \\spad{p}.") (((|Union| |#2| "failed") |#3| (|Fraction| |#2|)) "\\spad{denomLODE(op, g)} returns a polynomial \\spad{d} such that any rational solution of \\spad{op y = g} is of the form \\spad{p/d} for some polynomial \\spad{p},{} and \"failed\",{} if the equation has no rational solution."))) 
 NIL 
 NIL 
-(-730 -3094 UP L LQ) 
+(-729 -3093 UP L LQ) 
 ((|constructor| (NIL "In-field solution of Riccati equations,{} primitive case.")) (|changeVar| ((|#3| |#3| (|Fraction| |#2|)) "\\spad{changeVar(+/[ai D^i], a)} returns the operator \\spad{+/[ai (D+a)^i]}.") ((|#3| |#3| |#2|) "\\spad{changeVar(+/[ai D^i], a)} returns the operator \\spad{+/[ai (D+a)^i]}.")) (|singRicDE| (((|List| (|Record| (|:| |frac| (|Fraction| |#2|)) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{singRicDE(op, zeros, ezfactor)} returns \\spad{[[f1, L1], [f2, L2], ... , [fk, Lk]]} such that the singular part of any rational solution of the associated Riccati equation of \\spad{op y=0} must be one of the \\spad{fi}'s (up to the constant coefficient),{} in which case the equation for \\spad{z=y e^{-int p}} is \\spad{Li z=0}. \\spad{zeros(C(x),H(x,y))} returns all the \\spad{P_i(x)}'s such that \\spad{H(x,P_i(x)) = 0 modulo C(x)}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.")) (|polyRicDE| (((|List| (|Record| (|:| |poly| |#2|) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#1|) |#2|)) "\\spad{polyRicDE(op, zeros)} returns \\spad{[[p1, L1], [p2, L2], ... , [pk, Lk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y=0} must be one of the \\spad{pi}'s (up to the constant coefficient),{} in which case the equation for \\spad{z=y e^{-int p}} is \\spad{Li z =0}. \\spad{zeros} is a zero finder in \\spad{UP}.")) (|constantCoefficientRicDE| (((|List| (|Record| (|:| |constant| |#1|) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#1|) |#2|)) "\\spad{constantCoefficientRicDE(op, ric)} returns \\spad{[[a1, L1], [a2, L2], ... , [ak, Lk]]} such that any rational solution with no polynomial part of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{ai}'s in which case the equation for \\spad{z = y e^{-int ai}} is \\spad{Li z = 0}. \\spad{ric} is a Riccati equation solver over \\spad{F},{} whose input is the associated linear equation.")) (|leadingCoefficientRicDE| (((|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |eq| |#2|))) |#3|) "\\spad{leadingCoefficientRicDE(op)} returns \\spad{[[m1, p1], [m2, p2], ... , [mk, pk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must have degree mj for some \\spad{j},{} and its leading coefficient is then a zero of pj. In addition,{}\\spad{m1>m2> ... >mk}.")) (|denomRicDE| ((|#2| |#3|) "\\spad{denomRicDE(op)} returns a polynomial \\spad{d} such that any rational solution of the associated Riccati equation of \\spad{op y = 0} is of the form \\spad{p/d + q'/q + r} for some polynomials \\spad{p} and \\spad{q} and a reduced \\spad{r}. Also,{} \\spad{deg(p) < deg(d)} and {gcd(\\spad{d},{}\\spad{q}) = 1}."))) 
 NIL 
 NIL 
-(-731 -3094 UP) 
+(-730 -3093 UP) 
 ((|constructor| (NIL "\\spad{RationalLODE} provides functions for in-field solutions of linear \\indented{1}{ordinary differential equations,{} in the rational case.}")) (|indicialEquationAtInfinity| ((|#2| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))) "\\spad{indicialEquationAtInfinity op} returns the indicial equation of \\spad{op} at infinity.") ((|#2| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{indicialEquationAtInfinity op} returns the indicial equation of \\spad{op} at infinity.")) (|ratDsolve| (((|Record| (|:| |basis| (|List| (|Fraction| |#2|))) (|:| |mat| (|Matrix| |#1|))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|List| (|Fraction| |#2|))) "\\spad{ratDsolve(op, [g1,...,gm])} returns \\spad{[[h1,...,hq], M]} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{d1 h1 + ... + dq hq} where \\spad{M [d1,...,dq,c1,...,cm] = 0}.") (((|Record| (|:| |particular| (|Union| (|Fraction| |#2|) #1="failed")) (|:| |basis| (|List| (|Fraction| |#2|)))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{ratDsolve(op, g)} returns \\spad{[\"failed\", []]} if the equation \\spad{op y = g} has no rational solution. Otherwise,{} it returns \\spad{[f, [y1,...,ym]]} where \\spad{f} is a particular rational solution and the \\spad{yi}'s form a basis for the rational solutions of the homogeneous equation.") (((|Record| (|:| |basis| (|List| (|Fraction| |#2|))) (|:| |mat| (|Matrix| |#1|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|List| (|Fraction| |#2|))) "\\spad{ratDsolve(op, [g1,...,gm])} returns \\spad{[[h1,...,hq], M]} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{d1 h1 + ... + dq hq} where \\spad{M [d1,...,dq,c1,...,cm] = 0}.") (((|Record| (|:| |particular| (|Union| (|Fraction| |#2|) #1#)) (|:| |basis| (|List| (|Fraction| |#2|)))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{ratDsolve(op, g)} returns \\spad{[\"failed\", []]} if the equation \\spad{op y = g} has no rational solution. Otherwise,{} it returns \\spad{[f, [y1,...,ym]]} where \\spad{f} is a particular rational solution and the \\spad{yi}'s form a basis for the rational solutions of the homogeneous equation."))) 
 NIL 
 NIL 
-(-732 -3094 L UP A LO) 
+(-731 -3093 L UP A LO) 
 ((|constructor| (NIL "Elimination of an algebraic from the coefficentss of a linear ordinary differential equation.")) (|reduceLODE| (((|Record| (|:| |mat| (|Matrix| |#2|)) (|:| |vec| (|Vector| |#1|))) |#5| |#4|) "\\spad{reduceLODE(op, g)} returns \\spad{[m, v]} such that any solution in \\spad{A} of \\spad{op z = g} is of the form \\spad{z = (z_1,...,z_m) . (b_1,...,b_m)} where the \\spad{b_i's} are the basis of \\spad{A} over \\spad{F} returned by \\spadfun{basis}() from \\spad{A},{} and the \\spad{z_i's} satisfy the differential system \\spad{M.z = v}."))) 
 NIL 
 NIL 
-(-733 -3094 UP) 
+(-732 -3093 UP) 
 ((|constructor| (NIL "In-field solution of Riccati equations,{} rational case.")) (|polyRicDE| (((|List| (|Record| (|:| |poly| |#2|) (|:| |eq| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{polyRicDE(op, zeros)} returns \\spad{[[p1, L1], [p2, L2], ... , [pk,Lk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{pi}'s (up to the constant coefficient),{} in which case the equation for \\spad{z = y e^{-int p}} is \\spad{Li z = 0}. \\spad{zeros} is a zero finder in \\spad{UP}.")) (|singRicDE| (((|List| (|Record| (|:| |frac| (|Fraction| |#2|)) (|:| |eq| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{singRicDE(op, ezfactor)} returns \\spad{[[f1,L1], [f2,L2],..., [fk,Lk]]} such that the singular ++ part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{fi}'s (up to the constant coefficient),{} in which case the equation for \\spad{z = y e^{-int ai}} is \\spad{Li z = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.")) (|ricDsolve| (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))) "\\spad{ricDsolve(op)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{ricDsolve(op)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, zeros, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{ricDsolve(op, zeros)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, zeros, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{ricDsolve(op, zeros)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}."))) 
 NIL 
 ((|HasCategory| |#1| (QUOTE (-27)))) 
-(-734 -3094 LO) 
+(-733 -3093 LO) 
 ((|constructor| (NIL "SystemODESolver provides tools for triangulating and solving some systems of linear ordinary differential equations.")) (|solveInField| (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|)))) (|Matrix| |#2|) (|Vector| |#1|) (|Mapping| (|Record| (|:| |particular| (|Union| |#1| "failed")) (|:| |basis| (|List| |#1|))) |#2| |#1|)) "\\spad{solveInField(m, v, solve)} returns \\spad{[[v_1,...,v_m], v_p]} such that the solutions in \\spad{F} of the system \\spad{m x = v} are \\spad{v_p + c_1 v_1 + ... + c_m v_m} where the \\spad{c_i's} are constants,{} and the \\spad{v_i's} form a basis for the solutions of \\spad{m x = 0}. Argument \\spad{solve} is a function for solving a single linear ordinary differential equation in \\spad{F}.")) (|solve| (((|Union| (|Record| (|:| |particular| (|Vector| |#1|)) (|:| |basis| (|Matrix| |#1|))) "failed") (|Matrix| |#1|) (|Vector| |#1|) (|Mapping| (|Union| (|Record| (|:| |particular| |#1|) (|:| |basis| (|List| |#1|))) "failed") |#2| |#1|)) "\\spad{solve(m, v, solve)} returns \\spad{[[v_1,...,v_m], v_p]} such that the solutions in \\spad{F} of the system \\spad{D x = m x + v} are \\spad{v_p + c_1 v_1 + ... + c_m v_m} where the \\spad{c_i's} are constants,{} and the \\spad{v_i's} form a basis for the solutions of \\spad{D x = m x}. Argument \\spad{solve} is a function for solving a single linear ordinary differential equation in \\spad{F}.")) (|triangulate| (((|Record| (|:| |mat| (|Matrix| |#2|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| |#2|) (|Vector| |#1|)) "\\spad{triangulate(m, v)} returns \\spad{[m_0, v_0]} such that \\spad{m_0} is upper triangular and the system \\spad{m_0 x = v_0} is equivalent to \\spad{m x = v}.") (((|Record| (|:| A (|Matrix| |#1|)) (|:| |eqs| (|List| (|Record| (|:| C (|Matrix| |#1|)) (|:| |g| (|Vector| |#1|)) (|:| |eq| |#2|) (|:| |rh| |#1|))))) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{triangulate(M,v)} returns \\spad{A,[[C_1,g_1,L_1,h_1],...,[C_k,g_k,L_k,h_k]]} such that under the change of variable \\spad{y = A z},{} the first order linear system \\spad{D y = M y + v} is uncoupled as \\spad{D z_i = C_i z_i + g_i} and each \\spad{C_i} is a companion matrix corresponding to the scalar equation \\spad{L_i z_j = h_i}."))) 
 NIL 
 NIL 
-(-735 -3094 LODO) 
+(-734 -3093 LODO) 
 ((|constructor| (NIL "\\spad{ODETools} provides tools for the linear ODE solver.")) (|particularSolution| (((|Union| |#1| "failed") |#2| |#1| (|List| |#1|) (|Mapping| |#1| |#1|)) "\\spad{particularSolution(op, g, [f1,...,fm], I)} returns a particular solution \\spad{h} of the equation \\spad{op y = g} where \\spad{[f1,...,fm]} are linearly independent and \\spad{op(fi)=0}. The value \"failed\" is returned if no particular solution is found. Note: the method of variations of parameters is used.")) (|variationOfParameters| (((|Union| (|Vector| |#1|) "failed") |#2| |#1| (|List| |#1|)) "\\spad{variationOfParameters(op, g, [f1,...,fm])} returns \\spad{[u1,...,um]} such that a particular solution of the equation \\spad{op y = g} is \\spad{f1 int(u1) + ... + fm int(um)} where \\spad{[f1,...,fm]} are linearly independent and \\spad{op(fi)=0}. The value \"failed\" is returned if \\spad{m < n} and no particular solution is found.")) (|wronskianMatrix| (((|Matrix| |#1|) (|List| |#1|) (|NonNegativeInteger|)) "\\spad{wronskianMatrix([f1,...,fn], q, D)} returns the \\spad{q x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),...,fn^(i-1)]}.") (((|Matrix| |#1|) (|List| |#1|)) "\\spad{wronskianMatrix([f1,...,fn])} returns the \\spad{n x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),...,fn^(i-1)]}."))) 
 NIL 
 NIL 
-(-736 -2623 S |f|) 
+(-735 -2622 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}."))) 
-((-3991 |has| |#2| (-962)) (-3992 |has| |#2| (-962)) (-3994 |has| |#2| (-6 -3994))) 
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(|devaluate| |#2|))))) 
-(-737 R) 
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(-809 (-1090)))) (|HasCategory| |#2| (QUOTE (-961))) (|HasCategory| |#2| (QUOTE (-1013)))) (OR (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-320))) (|HasCategory| |#2| (QUOTE (-663))) (|HasCategory| |#2| (QUOTE (-717))) (|HasCategory| |#2| (QUOTE (-756))) (|HasCategory| |#2| (QUOTE (-809 (-1090)))) (|HasCategory| |#2| (QUOTE (-961))) (|HasCategory| |#2| (QUOTE (-1013)))) (OR (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-809 (-1090)))) (|HasCategory| |#2| (QUOTE (-961)))) (OR (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-809 (-1090)))) (|HasCategory| |#2| (QUOTE (-961)))) (OR (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-809 (-1090)))) (|HasCategory| |#2| (QUOTE (-961)))) (OR (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-809 (-1090)))) (|HasCategory| |#2| (QUOTE (-961)))) (OR (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-809 (-1090)))) (|HasCategory| |#2| (QUOTE (-961)))) (|HasCategory| |#2| (QUOTE (-190))) (OR (|HasCategory| |#2| (QUOTE (-190))) (-12 (|HasCategory| |#2| (QUOTE (-189))) (|HasCategory| |#2| (QUOTE (-961))))) (OR (-12 (|HasCategory| |#2| (QUOTE (-811 (-1090)))) (|HasCategory| |#2| (QUOTE (-961)))) (|HasCategory| |#2| (QUOTE (-809 (-1090))))) (|HasCategory| |#2| (QUOTE (-1013))) (OR (-12 (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-950 (-350 (-484)))))) (-12 (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-950 (-350 (-484)))))) (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-950 (-350 (-484)))))) (-12 (|HasCategory| |#2| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-950 (-350 (-484)))))) (-12 (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-950 (-350 (-484)))))) (-12 (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-950 (-350 (-484)))))) (-12 (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-950 (-350 (-484)))))) (-12 (|HasCategory| |#2| (QUOTE (-320))) (|HasCategory| |#2| (QUOTE (-950 (-350 (-484)))))) (-12 (|HasCategory| |#2| (QUOTE (-663))) (|HasCategory| |#2| (QUOTE (-950 (-350 (-484)))))) (-12 (|HasCategory| |#2| (QUOTE (-717))) (|HasCategory| |#2| (QUOTE (-950 (-350 (-484)))))) (-12 (|HasCategory| |#2| (QUOTE (-756))) (|HasCategory| |#2| (QUOTE (-950 (-350 (-484)))))) (-12 (|HasCategory| |#2| (QUOTE (-809 (-1090)))) (|HasCategory| |#2| (QUOTE (-950 (-350 (-484)))))) (-12 (|HasCategory| |#2| (QUOTE (-950 (-350 (-484))))) (|HasCategory| |#2| (QUOTE (-961)))) (-12 (|HasCategory| |#2| (QUOTE (-950 (-350 (-484))))) (|HasCategory| |#2| (QUOTE (-1013))))) (OR (-12 (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-717))) (|HasCategory| |#2| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-756))) (|HasCategory| |#2| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-809 (-1090)))) (|HasCategory| |#2| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-950 (-484)))) (|HasCategory| |#2| (QUOTE (-1013)))) (-12 (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-320))) (|HasCategory| |#2| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-663))) (|HasCategory| |#2| (QUOTE (-950 (-484))))) (|HasCategory| |#2| (QUOTE (-961)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-717))) (|HasCategory| |#2| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-756))) (|HasCategory| |#2| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-809 (-1090)))) (|HasCategory| |#2| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-950 (-484)))) (|HasCategory| |#2| (QUOTE (-1013)))) (-12 (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-320))) (|HasCategory| |#2| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-663))) (|HasCategory| |#2| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-950 (-484)))) (|HasCategory| |#2| (QUOTE (-961))))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-484) (QUOTE (-756))) (-12 (|HasCategory| |#2| (QUOTE (-580 (-484)))) (|HasCategory| |#2| (QUOTE (-961)))) (-12 (|HasCategory| |#2| (QUOTE (-189))) (|HasCategory| |#2| (QUOTE (-961)))) (-12 (|HasCategory| |#2| (QUOTE (-811 (-1090)))) (|HasCategory| |#2| (QUOTE (-961)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-950 (-484)))) (|HasCategory| |#2| (QUOTE (-1013)))) (|HasCategory| |#2| (QUOTE (-961)))) (-12 (|HasCategory| |#2| (QUOTE (-950 (-484)))) (|HasCategory| |#2| (QUOTE (-1013)))) (-12 (|HasCategory| |#2| (QUOTE (-950 (-350 (-484))))) (|HasCategory| |#2| (QUOTE (-1013)))) (|HasAttribute| |#2| (QUOTE -3993)) (-12 (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-961)))) (-12 (|HasCategory| |#2| (QUOTE (-809 (-1090)))) (|HasCategory| |#2| (QUOTE (-961)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-25))) (-12 (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#2|))))) 
+(-736 R) 
 ((|constructor| (NIL "\\spadtype{OrderlyDifferentialPolynomial} implements an ordinary differential polynomial ring in arbitrary number of differential indeterminates,{} with coefficients in a ring. The ranking on the differential indeterminate is orderly. This is analogous to the domain \\spadtype{Polynomial}. \\blankline"))) 
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-(-738 |Kernels| R |var|) 
+(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-495)) (-3994 |has| |#1| (-6 -3994)) (-3991 . T) (-3990 . T) (-3993 . T)) 
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+(-737 |Kernels| R |var|) 
 ((|constructor| (NIL "This constructor produces an ordinary differential ring from a partial differential ring by specifying a variable."))) 
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+(((-3998 "*") |has| |#2| (-312)) (-3989 |has| |#2| (-312)) (-3994 |has| |#2| (-312)) (-3988 |has| |#2| (-312)) (-3993 . T) (-3991 . T) (-3990 . T)) 
 ((|HasCategory| |#2| (QUOTE (-312)))) 
-(-739 S) 
+(-738 S) 
 ((|constructor| (NIL "\\spadtype{OrderlyDifferentialVariable} adds a commonly used orderly ranking to the set of derivatives of an ordered list of differential indeterminates. An orderly ranking is a ranking \\spadfun{<} of the derivatives with the property that for two derivatives \\spad{u} and \\spad{v},{} \\spad{u} \\spadfun{<} \\spad{v} if the \\spadfun{order} of \\spad{u} is less than that of \\spad{v}. This domain belongs to \\spadtype{DifferentialVariableCategory}. It defines \\spadfun{weight} to be just \\spadfun{order},{} and it defines an orderly ranking \\spadfun{<} on derivatives \\spad{u} via the lexicographic order on the pair (\\spadfun{order}(\\spad{u}),{} \\spadfun{variable}(\\spad{u}))."))) 
 NIL 
 NIL 
-(-740 S) 
+(-739 S) 
 ((|constructor| (NIL "\\indented{3}{The free monoid on a set \\spad{S} is the monoid of finite products of} the form \\spad{reduce(*,[si ** ni])} where the \\spad{si}'s are in \\spad{S},{} and the \\spad{ni}'s are non-negative integers. The multiplication is not commutative. For two elements \\spad{x} and \\spad{y} the relation \\spad{x < y} holds if either \\spad{length(x) < length(y)} holds or if these lengths are equal and if \\spad{x} is smaller than \\spad{y} \\spad{w}.\\spad{r}.\\spad{t}. the lexicographical ordering induced by \\spad{S}. This domain inherits implementation from \\spadtype{FreeMonoid}.")) (|varList| (((|List| |#1|) $) "\\spad{varList(x)} returns the list of variables of \\spad{x}.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length(x)} returns the length of \\spad{x}.")) (|div| (((|Union| (|Record| (|:| |lm| $) (|:| |rm| $)) "failed") $ $) "\\spad{x div y} returns the left and right exact quotients of \\spad{x} by \\spad{y},{} that is \\spad{[l, r]} such that \\spad{x = l * y * r}. \"failed\" is returned iff \\spad{x} is not of the form \\spad{l * y * r}. monomial of \\spad{x}.")) (|rquo| (((|Union| $ "failed") $ |#1|) "\\spad{rquo(x, s)} returns the exact right quotient of \\spad{x} by \\spad{s}.")) (|lquo| (((|Union| $ "failed") $ |#1|) "\\spad{lquo(x, s)} returns the exact left quotient of \\spad{x} by \\spad{s}.")) (|lexico| (((|Boolean|) $ $) "\\spad{lexico(x,y)} returns \\spad{true} iff \\spad{x} is smaller than \\spad{y} \\spad{w}.\\spad{r}.\\spad{t}. the pure lexicographical ordering induced by \\spad{S}.")) (|mirror| (($ $) "\\spad{mirror(x)} returns the reversed word of \\spad{x}.")) (|rest| (($ $) "\\spad{rest(x)} returns \\spad{x} except the first letter.")) (|first| ((|#1| $) "\\spad{first(x)} returns the first letter of \\spad{x}."))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-757)))) 
-(-741) 
+((|HasCategory| |#1| (QUOTE (-756)))) 
+(-740) 
 ((|constructor| (NIL "The category of ordered commutative integral domains,{} where ordering and the arithmetic operations are compatible \\blankline"))) 
-((-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
 NIL 
-(-742 P R) 
+(-741 P R) 
 ((|constructor| (NIL "This constructor creates the \\spadtype{MonogenicLinearOperator} domain which is ``opposite'' in the ring sense to \\spad{P}. That is,{} as sets \\spad{P = \\$} 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}."))) 
-((-3991 . T) (-3992 . T) (-3994 . T)) 
+((-3990 . T) (-3991 . T) (-3993 . T)) 
 ((|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-190)))) 
-(-743 S) 
+(-742 S) 
 ((|constructor| (NIL "to become an in order iterator")) (|min| ((|#1| $) "\\spad{min(u)} returns the smallest entry in the multiset aggregate \\spad{u}."))) 
-((-3987 . T) (-3998 . T)) 
+((-3986 . T) (-3997 . T)) 
 NIL 
-(-744 R) 
+(-743 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."))) 
-((-3994 |has| |#1| (-756))) 
-((|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-21))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-756)))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485))))) (OR (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-951 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (|HasCategory| |#1| (QUOTE (-484)))) 
-(-745 R S) 
+((-3993 |has| |#1| (-755))) 
+((|HasCategory| |#1| (QUOTE (-755))) (|HasCategory| |#1| (QUOTE (-21))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-755)))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484))))) (OR (|HasCategory| |#1| (QUOTE (-755))) (|HasCategory| |#1| (QUOTE (-950 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-484)))) (|HasCategory| |#1| (QUOTE (-483)))) 
+(-744 R S) 
 ((|constructor| (NIL "Lifting of maps to one-point completions. Date Created: 4 Oct 1989 Date Last Updated: 4 Oct 1989")) (|map| (((|OnePointCompletion| |#2|) (|Mapping| |#2| |#1|) (|OnePointCompletion| |#1|) (|OnePointCompletion| |#2|)) "\\spad{map(f, r, i)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(infinity) = \\spad{i}.") (((|OnePointCompletion| |#2|) (|Mapping| |#2| |#1|) (|OnePointCompletion| |#1|)) "\\spad{map(f, r)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(infinity) = infinity."))) 
 NIL 
 NIL 
-(-746 R) 
+(-745 R) 
 ((|constructor| (NIL "Algebra of ADDITIVE operators over a ring."))) 
-((-3992 |has| |#1| (-146)) (-3991 |has| |#1| (-146)) (-3994 . T)) 
+((-3991 |has| |#1| (-146)) (-3990 |has| |#1| (-146)) (-3993 . T)) 
 ((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120)))) 
-(-747 A S) 
+(-746 A S) 
 ((|constructor| (NIL "This category specifies the interface for operators used to build terms,{} in the sense of Universal Algebra. The domain parameter \\spad{S} provides representation for the `external name' of an operator.")) (|is?| (((|Boolean|) $ |#2|) "\\spad{is?(op,n)} holds if the name of the operator \\spad{op} is \\spad{n}.")) (|arity| (((|Arity|) $) "\\spad{arity(op)} returns the arity of the operator \\spad{op}.")) (|name| ((|#2| $) "\\spad{name(op)} returns the externam name of \\spad{op}."))) 
 NIL 
 NIL 
-(-748 S) 
+(-747 S) 
 ((|constructor| (NIL "This category specifies the interface for operators used to build terms,{} in the sense of Universal Algebra. The domain parameter \\spad{S} provides representation for the `external name' of an operator.")) (|is?| (((|Boolean|) $ |#1|) "\\spad{is?(op,n)} holds if the name of the operator \\spad{op} is \\spad{n}.")) (|arity| (((|Arity|) $) "\\spad{arity(op)} returns the arity of the operator \\spad{op}.")) (|name| ((|#1| $) "\\spad{name(op)} returns the externam name of \\spad{op}."))) 
 NIL 
 NIL 
-(-749) 
+(-748) 
 ((|constructor| (NIL "This package exports tools to create AXIOM Library information databases.")) (|getDatabase| (((|Database| (|IndexCard|)) (|String|)) "\\spad{getDatabase(\"char\")} returns a list of appropriate entries in the browser database. The legal values for \\spad{\"char\"} are \"o\" (operations),{} \"k\" (constructors),{} \"d\" (domains),{} \"c\" (categories) or \"p\" (packages)."))) 
 NIL 
 NIL 
-(-750) 
+(-749) 
 ((|constructor| (NIL "This the datatype for an operator-signature pair.")) (|construct| (($ (|Identifier|) (|Signature|)) "\\spad{construct(op,sig)} construct a signature-operator with operator name `op',{} and signature `sig'.")) (|signature| (((|Signature|) $) "\\spad{signature(x)} returns the signature of `x'."))) 
 NIL 
 NIL 
-(-751 R) 
+(-750 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| (($) "\\spad{plusInfinity()} returns +infinity."))) 
-((-3994 |has| |#1| (-756))) 
-((|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-21))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-756)))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485))))) (OR (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-951 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (|HasCategory| |#1| (QUOTE (-484)))) 
-(-752 R S) 
+((-3993 |has| |#1| (-755))) 
+((|HasCategory| |#1| (QUOTE (-755))) (|HasCategory| |#1| (QUOTE (-21))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-755)))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484))))) (OR (|HasCategory| |#1| (QUOTE (-755))) (|HasCategory| |#1| (QUOTE (-950 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-484)))) (|HasCategory| |#1| (QUOTE (-483)))) 
+(-751 R S) 
 ((|constructor| (NIL "Lifting of maps to ordered completions. Date Created: 4 Oct 1989 Date Last Updated: 4 Oct 1989")) (|map| (((|OrderedCompletion| |#2|) (|Mapping| |#2| |#1|) (|OrderedCompletion| |#1|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|)) "\\spad{map(f, r, p, m)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(plusInfinity) = \\spad{p} and that \\spad{f}(minusInfinity) = \\spad{m}.") (((|OrderedCompletion| |#2|) (|Mapping| |#2| |#1|) (|OrderedCompletion| |#1|)) "\\spad{map(f, r)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(plusInfinity) = plusInfinity and that \\spad{f}(minusInfinity) = minusInfinity."))) 
 NIL 
 NIL 
-(-753) 
+(-752) 
 ((|constructor| (NIL "Ordered finite sets.")) (|max| (($) "\\spad{max} is the maximum value of \\%.")) (|min| (($) "\\spad{min} is the minimum value of \\%."))) 
 NIL 
 NIL 
-(-754 -2623 S) 
+(-753 -2622 S) 
 ((|constructor| (NIL "\\indented{3}{This package provides ordering functions on vectors which} are suitable parameters for OrderedDirectProduct.")) (|reverseLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{reverseLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by the reverse lexicographic ordering.")) (|totalLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{totalLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by lexicographic ordering.")) (|pureLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{pureLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the lexicographic ordering."))) 
 NIL 
 NIL 
-(-755) 
+(-754) 
 ((|constructor| (NIL "Ordered sets which are also monoids,{} such that multiplication preserves the ordering. \\blankline"))) 
 NIL 
 NIL 
-(-756) 
+(-755) 
 ((|constructor| (NIL "Ordered sets which are also rings,{} that is,{} domains where the ring operations are compatible with the ordering. \\blankline"))) 
-((-3994 . T)) 
+((-3993 . T)) 
 NIL 
-(-757) 
+(-756) 
 ((|constructor| (NIL "The class of totally ordered sets,{} that is,{} sets such that for each pair of elements \\spad{(a,b)} exactly one of the following relations holds \\spad{a<b or a=b or b<a} and the relation is transitive,{} \\spadignore{i.e.} \\spad{a<b and b<c => a<c}."))) 
 NIL 
 NIL 
-(-758 T$ |f|) 
+(-757 T$ |f|) 
 ((|constructor| (NIL "This domain turns any total ordering \\spad{f} on a type \\spad{T} into a model of the category \\spadtype{OrderedType}."))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-553 (-773))))) 
-(-759 S) 
+((|HasCategory| |#1| (QUOTE (-552 (-772))))) 
+(-758 S) 
 ((|constructor| (NIL "Category of types equipped with a total ordering.")) (|min| (($ $ $) "\\spad{min(x,y)} returns the minimum of \\spad{x} and \\spad{y} relative to the ordering.")) (|max| (($ $ $) "\\spad{max(x,y)} returns the maximum of \\spad{x} and \\spad{y} relative to the ordering.")) (>= (((|Boolean|) $ $) "\\spad{x <= y} holds if \\spad{x} is greater or equal than \\spad{y} in the current domain.")) (<= (((|Boolean|) $ $) "\\spad{x <= y} holds if \\spad{x} is less or equal than \\spad{y} in the current domain.")) (> (((|Boolean|) $ $) "\\spad{x > y} holds if \\spad{x} is greater than \\spad{y} in the current domain.")) (< (((|Boolean|) $ $) "\\spad{x < y} holds if \\spad{x} is less than \\spad{y} in the current domain."))) 
 NIL 
 NIL 
-(-760) 
+(-759) 
 ((|constructor| (NIL "Category of types equipped with a total ordering.")) (|min| (($ $ $) "\\spad{min(x,y)} returns the minimum of \\spad{x} and \\spad{y} relative to the ordering.")) (|max| (($ $ $) "\\spad{max(x,y)} returns the maximum of \\spad{x} and \\spad{y} relative to the ordering.")) (>= (((|Boolean|) $ $) "\\spad{x <= y} holds if \\spad{x} is greater or equal than \\spad{y} in the current domain.")) (<= (((|Boolean|) $ $) "\\spad{x <= y} holds if \\spad{x} is less or equal than \\spad{y} in the current domain.")) (> (((|Boolean|) $ $) "\\spad{x > y} holds if \\spad{x} is greater than \\spad{y} in the current domain.")) (< (((|Boolean|) $ $) "\\spad{x < y} holds if \\spad{x} is less than \\spad{y} in the current domain."))) 
 NIL 
 NIL 
-(-761 S R) 
+(-760 S R) 
 ((|constructor| (NIL "This is the category of univariate skew polynomials over an Ore coefficient ring. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}. This category is an evolution of the types \\indented{2}{MonogenicLinearOperator,{} OppositeMonogenicLinearOperator,{} and} \\indented{2}{NonCommutativeOperatorDivision} developped by Jean Della Dora and Stephen \\spad{M}. Watt.")) (|leftLcm| (($ $ $) "\\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|) $) "\\spad{degree(l)} is \\spad{n} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}"))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-146)))) 
-(-762 R) 
+((|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-146)))) 
+(-761 R) 
 ((|constructor| (NIL "This is the category of univariate skew polynomials over an Ore coefficient ring. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}. This category is an evolution of the types \\indented{2}{MonogenicLinearOperator,{} OppositeMonogenicLinearOperator,{} and} \\indented{2}{NonCommutativeOperatorDivision} developped by Jean Della Dora and Stephen \\spad{M}. Watt.")) (|leftLcm| (($ $ $) "\\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)}.}"))) 
-((-3991 . T) (-3992 . T) (-3994 . T)) 
+((-3990 . T) (-3991 . T) (-3993 . T)) 
 NIL 
-(-763 R C) 
+(-762 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 (-312))) (|HasCategory| |#1| (QUOTE (-496)))) 
-(-764 R |sigma| -3246) 
+((|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-495)))) 
+(-763 R |sigma| -3245) 
 ((|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."))) 
-((-3991 . T) (-3992 . T) (-3994 . T)) 
-((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-312)))) 
-(-765 |x| R |sigma| -3246) 
+((-3990 . T) (-3991 . T) (-3993 . T)) 
+((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-484)))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-312)))) 
+(-764 |x| R |sigma| -3245) 
 ((|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}."))) 
-((-3991 . T) (-3992 . T) (-3994 . T)) 
-((|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#2| (QUOTE (-951 (-485)))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-312)))) 
-(-766 R) 
+((-3990 . T) (-3991 . T) (-3993 . T)) 
+((|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-950 (-350 (-484))))) (|HasCategory| |#2| (QUOTE (-950 (-484)))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-312)))) 
+(-765 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 (-350 (-485)))))) 
-(-767) 
+((|HasCategory| |#1| (QUOTE (-38 (-350 (-484)))))) 
+(-766) 
 ((|constructor| (NIL "Semigroups with compatible ordering."))) 
 NIL 
 NIL 
-(-768) 
+(-767) 
 ((|constructor| (NIL "\\indented{1}{Author : Larry Lambe} Date created : 14 August 1988 Date Last Updated : 11 March 1991 Description : A domain used in order to take the free \\spad{R}-module on the Integers \\spad{I}. This is actually the forgetful functor from OrderedRings to OrderedSets applied to \\spad{I}")) (|value| (((|Integer|) $) "\\spad{value(x)} returns the integer associated with \\spad{x}")) (|coerce| (($ (|Integer|)) "\\spad{coerce(i)} returns the element corresponding to \\spad{i}"))) 
 NIL 
 NIL 
-(-769) 
+(-768) 
 ((|constructor| (NIL "OutPackage allows pretty-printing from programs.")) (|outputList| (((|Void|) (|List| (|Any|))) "\\spad{outputList(l)} displays the concatenated components of the list \\spad{l} on the ``algebra output'' stream,{} as defined by \\spadsyscom{set output algebra}; quotes are stripped from strings.")) (|output| (((|Void|) (|String|) (|OutputForm|)) "\\spad{output(s,x)} displays the string \\spad{s} followed by the form \\spad{x} on the ``algebra output'' stream,{} as defined by \\spadsyscom{set output algebra}.") (((|Void|) (|OutputForm|)) "\\spad{output(x)} displays the output form \\spad{x} on the ``algebra output'' stream,{} as defined by \\spadsyscom{set output algebra}.") (((|Void|) (|String|)) "\\spad{output(s)} displays the string \\spad{s} on the ``algebra output'' stream,{} as defined by \\spadsyscom{set output algebra}."))) 
 NIL 
 NIL 
-(-770 S) 
+(-769 S) 
 ((|constructor| (NIL "This category describes output byte stream conduits.")) (|writeBytes!| (((|NonNegativeInteger|) $ (|ByteBuffer|)) "\\spad{writeBytes!(c,b)} write bytes from buffer `b' onto the conduit `c'. The actual number of written bytes is returned.")) (|writeUInt8!| (((|Maybe| (|UInt8|)) $ (|UInt8|)) "\\spad{writeUInt8!(c,b)} attempts to write the unsigned 8-bit value `v' on the conduit `c'. Returns the written value if successful,{} otherwise,{} returns \\spad{nothing}.")) (|writeInt8!| (((|Maybe| (|Int8|)) $ (|Int8|)) "\\spad{writeInt8!(c,b)} attempts to write the 8-bit value `v' on the conduit `c'. Returns the written value if successful,{} otherwise,{} returns \\spad{nothing}.")) (|writeByte!| (((|Maybe| (|Byte|)) $ (|Byte|)) "\\spad{writeByte!(c,b)} attempts to write the byte `b' on the conduit `c'. Returns the written byte if successful,{} otherwise,{} returns \\spad{nothing}."))) 
 NIL 
 NIL 
-(-771) 
+(-770) 
 ((|constructor| (NIL "This category describes output byte stream conduits.")) (|writeBytes!| (((|NonNegativeInteger|) $ (|ByteBuffer|)) "\\spad{writeBytes!(c,b)} write bytes from buffer `b' onto the conduit `c'. The actual number of written bytes is returned.")) (|writeUInt8!| (((|Maybe| (|UInt8|)) $ (|UInt8|)) "\\spad{writeUInt8!(c,b)} attempts to write the unsigned 8-bit value `v' on the conduit `c'. Returns the written value if successful,{} otherwise,{} returns \\spad{nothing}.")) (|writeInt8!| (((|Maybe| (|Int8|)) $ (|Int8|)) "\\spad{writeInt8!(c,b)} attempts to write the 8-bit value `v' on the conduit `c'. Returns the written value if successful,{} otherwise,{} returns \\spad{nothing}.")) (|writeByte!| (((|Maybe| (|Byte|)) $ (|Byte|)) "\\spad{writeByte!(c,b)} attempts to write the byte `b' on the conduit `c'. Returns the written byte if successful,{} otherwise,{} returns \\spad{nothing}."))) 
 NIL 
 NIL 
-(-772) 
+(-771) 
 ((|constructor| (NIL "This domain provides representation for binary files open for output operations. `Binary' here means that the conduits do not interpret their contents.")) (|isOpen?| (((|Boolean|) $) "open?(ifile) holds if `ifile' is in open state.")) (|outputBinaryFile| (($ (|String|)) "\\spad{outputBinaryFile(f)} returns an output conduit obtained by opening the file named by `f' as a binary file.") (($ (|FileName|)) "\\spad{outputBinaryFile(f)} returns an output conduit obtained by opening the file named by `f' as a binary file."))) 
 NIL 
 NIL 
-(-773) 
+(-772) 
 ((|constructor| (NIL "This domain is used to create and manipulate mathematical expressions for output. It is intended to provide an insulating layer between the expression rendering software (\\spadignore{e.g.} TeX,{} or Script) and the output coercions in the various domains.")) (SEGMENT (($ $) "\\spad{SEGMENT(x)} creates the prefix form: \\spad{x..}.") (($ $ $) "\\spad{SEGMENT(x,y)} creates the infix form: \\spad{x..y}.")) (|not| (($ $) "\\spad{not f} creates the equivalent prefix form.")) (|or| (($ $ $) "\\spad{f or g} creates the equivalent infix form.")) (|and| (($ $ $) "\\spad{f and g} creates the equivalent infix form.")) (|exquo| (($ $ $) "\\spad{exquo(f,g)} creates the equivalent infix form.")) (|quo| (($ $ $) "\\spad{f quo g} creates the equivalent infix form.")) (|rem| (($ $ $) "\\spad{f rem g} creates the equivalent infix form.")) (|div| (($ $ $) "\\spad{f div g} creates the equivalent infix form.")) (** (($ $ $) "\\spad{f ** g} creates the equivalent infix form.")) (/ (($ $ $) "\\spad{f / g} creates the equivalent infix form.")) (* (($ $ $) "\\spad{f * g} creates the equivalent infix form.")) (- (($ $) "\\spad{- f} creates the equivalent prefix form.") (($ $ $) "\\spad{f - g} creates the equivalent infix form.")) (+ (($ $ $) "\\spad{f + g} creates the equivalent infix form.")) (>= (($ $ $) "\\spad{f >= g} creates the equivalent infix form.")) (<= (($ $ $) "\\spad{f <= g} creates the equivalent infix form.")) (> (($ $ $) "\\spad{f > g} creates the equivalent infix form.")) (< (($ $ $) "\\spad{f < g} creates the equivalent infix form.")) (~= (($ $ $) "\\spad{f ~= g} creates the equivalent infix form.")) (= (($ $ $) "\\spad{f = g} creates the equivalent infix form.")) (|blankSeparate| (($ (|List| $)) "\\spad{blankSeparate(l)} creates the form separating the elements of \\spad{l} by blanks.")) (|semicolonSeparate| (($ (|List| $)) "\\spad{semicolonSeparate(l)} creates the form separating the elements of \\spad{l} by semicolons.")) (|commaSeparate| (($ (|List| $)) "\\spad{commaSeparate(l)} creates the form separating the elements of \\spad{l} by commas.")) (|pile| (($ (|List| $)) "\\spad{pile(l)} creates the form consisting of the elements of \\spad{l} which displays as a pile,{} \\spadignore{i.e.} the elements begin on a new line and are indented right to the same margin.")) (|paren| (($ (|List| $)) "\\spad{paren(lf)} creates the form separating the elements of \\spad{lf} by commas and encloses the result in parentheses.") (($ $) "\\spad{paren(f)} creates the form enclosing \\spad{f} in parentheses.")) (|bracket| (($ (|List| $)) "\\spad{bracket(lf)} creates the form separating the elements of \\spad{lf} by commas and encloses the result in square brackets.") (($ $) "\\spad{bracket(f)} creates the form enclosing \\spad{f} in square brackets.")) (|brace| (($ (|List| $)) "\\spad{brace(lf)} creates the form separating the elements of \\spad{lf} by commas and encloses the result in curly brackets.") (($ $) "\\spad{brace(f)} creates the form enclosing \\spad{f} in braces (curly brackets).")) (|int| (($ $ $ $) "\\spad{int(expr,lowerlimit,upperlimit)} creates the form prefixing \\spad{expr} by an integral sign with both a \\spad{lowerlimit} and \\spad{upperlimit}.") (($ $ $) "\\spad{int(expr,lowerlimit)} creates the form prefixing \\spad{expr} by an integral sign with a \\spad{lowerlimit}.") (($ $) "\\spad{int(expr)} creates the form prefixing \\spad{expr} with an integral sign.")) (|prod| (($ $ $ $) "\\spad{prod(expr,lowerlimit,upperlimit)} creates the form prefixing \\spad{expr} by a capital \\spad{pi} with both a \\spad{lowerlimit} and \\spad{upperlimit}.") (($ $ $) "\\spad{prod(expr,lowerlimit)} creates the form prefixing \\spad{expr} by a capital \\spad{pi} with a \\spad{lowerlimit}.") (($ $) "\\spad{prod(expr)} creates the form prefixing \\spad{expr} by a capital \\spad{pi}.")) (|sum| (($ $ $ $) "\\spad{sum(expr,lowerlimit,upperlimit)} creates the form prefixing \\spad{expr} by a capital sigma with both a \\spad{lowerlimit} and \\spad{upperlimit}.") (($ $ $) "\\spad{sum(expr,lowerlimit)} creates the form prefixing \\spad{expr} by a capital sigma with a \\spad{lowerlimit}.") (($ $) "\\spad{sum(expr)} creates the form prefixing \\spad{expr} by a capital sigma.")) (|overlabel| (($ $ $) "\\spad{overlabel(x,f)} creates the form \\spad{f} with \"x overbar\" over the top.")) (|overbar| (($ $) "\\spad{overbar(f)} creates the form \\spad{f} with an overbar.")) (|prime| (($ $ (|NonNegativeInteger|)) "\\spad{prime(f,n)} creates the form \\spad{f} followed by \\spad{n} primes.") (($ $) "\\spad{prime(f)} creates the form \\spad{f} followed by a suffix prime (single quote).")) (|dot| (($ $ (|NonNegativeInteger|)) "\\spad{dot(f,n)} creates the form \\spad{f} with \\spad{n} dots overhead.") (($ $) "\\spad{dot(f)} creates the form with a one dot overhead.")) (|quote| (($ $) "\\spad{quote(f)} creates the form \\spad{f} with a prefix quote.")) (|supersub| (($ $ (|List| $)) "\\spad{supersub(a,[sub1,super1,sub2,super2,...])} creates a form with each subscript aligned under each superscript.")) (|scripts| (($ $ (|List| $)) "\\spad{scripts(f, [sub, super, presuper, presub])} \\indented{1}{creates a form for \\spad{f} with scripts on all 4 corners.}")) (|presuper| (($ $ $) "\\spad{presuper(f,n)} creates a form for \\spad{f} presuperscripted by \\spad{n}.")) (|presub| (($ $ $) "\\spad{presub(f,n)} creates a form for \\spad{f} presubscripted by \\spad{n}.")) (|super| (($ $ $) "\\spad{super(f,n)} creates a form for \\spad{f} superscripted by \\spad{n}.")) (|sub| (($ $ $) "\\spad{sub(f,n)} creates a form for \\spad{f} subscripted by \\spad{n}.")) (|binomial| (($ $ $) "\\spad{binomial(n,m)} creates a form for the binomial coefficient of \\spad{n} and \\spad{m}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(f,n)} creates a form for the \\spad{n}th derivative of \\spad{f},{} \\spadignore{e.g.} \\spad{f'},{} \\spad{f''},{} \\spad{f'''},{} \"f super \\spad{iv}\".")) (|rarrow| (($ $ $) "\\spad{rarrow(f,g)} creates a form for the mapping \\spad{f -> g}.")) (|assign| (($ $ $) "\\spad{assign(f,g)} creates a form for the assignment \\spad{f := g}.")) (|slash| (($ $ $) "\\spad{slash(f,g)} creates a form for the horizontal fraction of \\spad{f} over \\spad{g}.")) (|over| (($ $ $) "\\spad{over(f,g)} creates a form for the vertical fraction of \\spad{f} over \\spad{g}.")) (|root| (($ $ $) "\\spad{root(f,n)} creates a form for the \\spad{n}th root of form \\spad{f}.") (($ $) "\\spad{root(f)} creates a form for the square root of form \\spad{f}.")) (|zag| (($ $ $) "\\spad{zag(f,g)} creates a form for the continued fraction form for \\spad{f} over \\spad{g}.")) (|matrix| (($ (|List| (|List| $))) "\\spad{matrix(llf)} makes \\spad{llf} (a list of lists of forms) into a form which displays as a matrix.")) (|box| (($ $) "\\spad{box(f)} encloses \\spad{f} in a box.")) (|label| (($ $ $) "\\spad{label(n,f)} gives form \\spad{f} an equation label \\spad{n}.")) (|string| (($ $) "\\spad{string(f)} creates \\spad{f} with string quotes.")) (|elt| (($ $ (|List| $)) "\\spad{elt(op,l)} creates a form for application of \\spad{op} to list of arguments \\spad{l}.")) (|infix?| (((|Boolean|) $) "\\spad{infix?(op)} returns \\spad{true} if \\spad{op} is an infix operator,{} and \\spad{false} otherwise.")) (|postfix| (($ $ $) "\\spad{postfix(op, a)} creates a form which prints as: a \\spad{op}.")) (|infix| (($ $ $ $) "\\spad{infix(op, a, b)} creates a form which prints as: a \\spad{op} \\spad{b}.") (($ $ (|List| $)) "\\spad{infix(f,l)} creates a form depicting the \\spad{n}-ary application of infix operation \\spad{f} to a tuple of arguments \\spad{l}.")) (|prefix| (($ $ (|List| $)) "\\spad{prefix(f,l)} creates a form depicting the \\spad{n}-ary prefix application of \\spad{f} to a tuple of arguments given by list \\spad{l}.")) (|vconcat| (($ (|List| $)) "\\spad{vconcat(u)} vertically concatenates all forms in list \\spad{u}.") (($ $ $) "\\spad{vconcat(f,g)} vertically concatenates forms \\spad{f} and \\spad{g}.")) (|hconcat| (($ (|List| $)) "\\spad{hconcat(u)} horizontally concatenates all forms in list \\spad{u}.") (($ $ $) "\\spad{hconcat(f,g)} horizontally concatenate forms \\spad{f} and \\spad{g}.")) (|center| (($ $) "\\spad{center(f)} centers form \\spad{f} in total space.") (($ $ (|Integer|)) "\\spad{center(f,n)} centers form \\spad{f} within space of width \\spad{n}.")) (|right| (($ $) "\\spad{right(f)} right-justifies form \\spad{f} in total space.") (($ $ (|Integer|)) "\\spad{right(f,n)} right-justifies form \\spad{f} within space of width \\spad{n}.")) (|left| (($ $) "\\spad{left(f)} left-justifies form \\spad{f} in total space.") (($ $ (|Integer|)) "\\spad{left(f,n)} left-justifies form \\spad{f} within space of width \\spad{n}.")) (|rspace| (($ (|Integer|) (|Integer|)) "\\spad{rspace(n,m)} creates rectangular white space,{} \\spad{n} wide by \\spad{m} high.")) (|vspace| (($ (|Integer|)) "\\spad{vspace(n)} creates white space of height \\spad{n}.")) (|hspace| (($ (|Integer|)) "\\spad{hspace(n)} creates white space of width \\spad{n}.")) (|superHeight| (((|Integer|) $) "\\spad{superHeight(f)} returns the height of form \\spad{f} above the base line.")) (|subHeight| (((|Integer|) $) "\\spad{subHeight(f)} returns the height of form \\spad{f} below the base line.")) (|height| (((|Integer|)) "\\spad{height()} returns the height of the display area (an integer).") (((|Integer|) $) "\\spad{height(f)} returns the height of form \\spad{f} (an integer).")) (|width| (((|Integer|)) "\\spad{width()} returns the width of the display area (an integer).") (((|Integer|) $) "\\spad{width(f)} returns the width of form \\spad{f} (an integer).")) (|doubleFloatFormat| (((|String|) (|String|)) "change the output format for doublefloats using lisp format strings")) (|empty| (($) "\\spad{empty()} creates an empty form.")) (|outputForm| (($ (|DoubleFloat|)) "\\spad{outputForm(sf)} creates an form for small float \\spad{sf}.") (($ (|String|)) "\\spad{outputForm(s)} creates an form for string \\spad{s}.") (($ (|Symbol|)) "\\spad{outputForm(s)} creates an form for symbol \\spad{s}.") (($ (|Integer|)) "\\spad{outputForm(n)} creates an form for integer \\spad{n}.")) (|messagePrint| (((|Void|) (|String|)) "\\spad{messagePrint(s)} prints \\spad{s} without string quotes. Note: \\spad{messagePrint(s)} is equivalent to \\spad{print message(s)}.")) (|message| (($ (|String|)) "\\spad{message(s)} creates an form with no string quotes from string \\spad{s}.")) (|print| (((|Void|) $) "\\spad{print(u)} prints the form \\spad{u}."))) 
 NIL 
 NIL 
-(-774 |VariableList|) 
+(-773 |VariableList|) 
 ((|constructor| (NIL "This domain implements ordered variables")) (|variable| (((|Union| $ "failed") (|Symbol|)) "\\spad{variable(s)} returns a member of the variable set or failed"))) 
 NIL 
 NIL 
-(-775) 
+(-774) 
 ((|constructor| (NIL "This domain represents set of overloaded operators (in fact operator descriptors).")) (|members| (((|List| (|FunctionDescriptor|)) $) "\\spad{members(x)} returns the list of operator descriptors,{} \\spadignore{e.g.} signature and implementation slots,{} of the overload set \\spad{x}.")) (|name| (((|Identifier|) $) "\\spad{name(x)} returns the name of the overload set \\spad{x}."))) 
 NIL 
 NIL 
-(-776 R |vl| |wl| |wtlevel|) 
+(-775 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)"))) 
-((-3992 |has| |#1| (-146)) (-3991 |has| |#1| (-146)) (-3994 . T)) 
+((-3991 |has| |#1| (-146)) (-3990 |has| |#1| (-146)) (-3993 . T)) 
 ((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312)))) 
-(-777 R PS UP) 
+(-776 R PS UP) 
 ((|constructor| (NIL "\\indented{1}{This package computes reliable Pad&ea. approximants using} a generalized Viskovatov continued fraction algorithm. Authors: Burge,{} Hassner & Watt. Date Created: April 1987 Date Last Updated: 12 April 1990 Keywords: Pade,{} series Examples: References: \\indented{2}{\"Pade Approximants,{} Part I: Basic Theory\",{} Baker & Graves-Morris.}")) (|padecf| (((|Union| (|ContinuedFraction| |#3|) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) |#2| |#2|) "\\spad{padecf(nd,dd,ns,ds)} computes the approximant as a continued fraction of polynomials (if it exists) for arguments \\spad{nd} (numerator degree of approximant),{} \\spad{dd} (denominator degree of approximant),{} \\spad{ns} (numerator series of function),{} and \\spad{ds} (denominator series of function).")) (|pade| (((|Union| (|Fraction| |#3|) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) |#2| |#2|) "\\spad{pade(nd,dd,ns,ds)} computes the approximant as a quotient of polynomials (if it exists) for arguments \\spad{nd} (numerator degree of approximant),{} \\spad{dd} (denominator degree of approximant),{} \\spad{ns} (numerator series of function),{} and \\spad{ds} (denominator series of function)."))) 
 NIL 
 NIL 
-(-778 R |x| |pt|) 
+(-777 R |x| |pt|) 
 ((|constructor| (NIL "\\indented{1}{This package computes reliable Pad&ea. approximants using} a generalized Viskovatov continued fraction algorithm. Authors: Trager,{}Burge,{} Hassner & Watt. Date Created: April 1987 Date Last Updated: 12 April 1990 Keywords: Pade,{} series Examples: References: \\indented{2}{\"Pade Approximants,{} Part I: Basic Theory\",{} Baker & Graves-Morris.}")) (|pade| (((|Union| (|Fraction| (|UnivariatePolynomial| |#2| |#1|)) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) (|UnivariateTaylorSeries| |#1| |#2| |#3|)) "\\spad{pade(nd,dd,s)} computes the quotient of polynomials (if it exists) with numerator degree at most \\spad{nd} and denominator degree at most \\spad{dd} which matches the series \\spad{s} to order \\spad{nd + dd}.") (((|Union| (|Fraction| (|UnivariatePolynomial| |#2| |#1|)) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) (|UnivariateTaylorSeries| |#1| |#2| |#3|) (|UnivariateTaylorSeries| |#1| |#2| |#3|)) "\\spad{pade(nd,dd,ns,ds)} computes the approximant as a quotient of polynomials (if it exists) for arguments \\spad{nd} (numerator degree of approximant),{} \\spad{dd} (denominator degree of approximant),{} \\spad{ns} (numerator series of function),{} and \\spad{ds} (denominator series of function)."))) 
 NIL 
 NIL 
-(-779 |p|) 
+(-778 |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)."))) 
-((-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
 NIL 
-(-780 |p|) 
+(-779 |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}."))) 
-((-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
 NIL 
-(-781 |p|) 
+(-780 |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)."))) 
-((-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
-((|HasCategory| (-779 |#1|) (QUOTE (-822))) (|HasCategory| (-779 |#1|) (QUOTE (-951 (-1091)))) (|HasCategory| (-779 |#1|) (QUOTE (-118))) (|HasCategory| (-779 |#1|) (QUOTE (-120))) (|HasCategory| (-779 |#1|) (QUOTE (-554 (-474)))) (|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 (-485)))) (|HasCategory| (-779 |#1|) (QUOTE (-1067))) (|HasCategory| (-779 |#1|) (QUOTE (-797 (-330)))) (|HasCategory| (-779 |#1|) (QUOTE (-797 (-485)))) (|HasCategory| (-779 |#1|) (QUOTE (-554 (-801 (-330))))) (|HasCategory| (-779 |#1|) (QUOTE (-554 (-801 (-485))))) (|HasCategory| (-779 |#1|) (QUOTE (-581 (-485)))) (|HasCategory| (-779 |#1|) (QUOTE (-189))) (|HasCategory| (-779 |#1|) (QUOTE (-812 (-1091)))) (|HasCategory| (-779 |#1|) (QUOTE (-190))) (|HasCategory| (-779 |#1|) (QUOTE (-810 (-1091)))) (|HasCategory| (-779 |#1|) (|%list| (QUOTE -456) (QUOTE (-1091)) (|%list| (QUOTE -779) (|devaluate| |#1|)))) (|HasCategory| (-779 |#1|) (|%list| (QUOTE -260) (|%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 (-258))) (|HasCategory| (-779 |#1|) (QUOTE (-484))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-779 |#1|) (QUOTE (-822)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-779 |#1|) (QUOTE (-822)))) (|HasCategory| (-779 |#1|) (QUOTE (-118))))) 
-(-782 |p| PADIC) 
+((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((|HasCategory| (-778 |#1|) (QUOTE (-821))) (|HasCategory| (-778 |#1|) (QUOTE (-950 (-1090)))) (|HasCategory| (-778 |#1|) (QUOTE (-118))) (|HasCategory| (-778 |#1|) (QUOTE (-120))) (|HasCategory| (-778 |#1|) (QUOTE (-553 (-473)))) (|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 (-484)))) (|HasCategory| (-778 |#1|) (QUOTE (-1066))) (|HasCategory| (-778 |#1|) (QUOTE (-796 (-330)))) (|HasCategory| (-778 |#1|) (QUOTE (-796 (-484)))) (|HasCategory| (-778 |#1|) (QUOTE (-553 (-800 (-330))))) (|HasCategory| (-778 |#1|) (QUOTE (-553 (-800 (-484))))) (|HasCategory| (-778 |#1|) (QUOTE (-580 (-484)))) (|HasCategory| (-778 |#1|) (QUOTE (-189))) (|HasCategory| (-778 |#1|) (QUOTE (-811 (-1090)))) (|HasCategory| (-778 |#1|) (QUOTE (-190))) (|HasCategory| (-778 |#1|) (QUOTE (-809 (-1090)))) (|HasCategory| (-778 |#1|) (|%list| (QUOTE -455) (QUOTE (-1090)) (|%list| (QUOTE -778) (|devaluate| |#1|)))) (|HasCategory| (-778 |#1|) (|%list| (QUOTE -260) (|%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 (-258))) (|HasCategory| (-778 |#1|) (QUOTE (-483))) (-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) 
 ((|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)}."))) 
-((-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
-((|HasCategory| |#2| (QUOTE (-822))) (|HasCategory| |#2| (QUOTE (-951 (-1091)))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-554 (-474)))) (|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 (-485)))) (|HasCategory| |#2| (QUOTE (-1067))) (|HasCategory| |#2| (QUOTE (-797 (-330)))) (|HasCategory| |#2| (QUOTE (-797 (-485)))) (|HasCategory| |#2| (QUOTE (-554 (-801 (-330))))) (|HasCategory| |#2| (QUOTE (-554 (-801 (-485))))) (|HasCategory| |#2| (QUOTE (-581 (-485)))) (|HasCategory| |#2| (QUOTE (-189))) (|HasCategory| |#2| (QUOTE (-812 (-1091)))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-810 (-1091)))) (|HasCategory| |#2| (|%list| (QUOTE -456) (QUOTE (-1091)) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -241) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-258))) (|HasCategory| |#2| (QUOTE (-484))) (-12 (|HasCategory| |#2| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#2| (QUOTE (-118))))) 
-(-783 S T$) 
+((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| |#2| (QUOTE (-950 (-1090)))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-553 (-473)))) (|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 (-484)))) (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| |#2| (QUOTE (-796 (-330)))) (|HasCategory| |#2| (QUOTE (-796 (-484)))) (|HasCategory| |#2| (QUOTE (-553 (-800 (-330))))) (|HasCategory| |#2| (QUOTE (-553 (-800 (-484))))) (|HasCategory| |#2| (QUOTE (-580 (-484)))) (|HasCategory| |#2| (QUOTE (-189))) (|HasCategory| |#2| (QUOTE (-811 (-1090)))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-809 (-1090)))) (|HasCategory| |#2| (|%list| (QUOTE -455) (QUOTE (-1090)) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -241) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-258))) (|HasCategory| |#2| (QUOTE (-483))) (-12 (|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#2| (QUOTE (-118))))) 
+(-782 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 (-1014))) (|HasCategory| |#2| (QUOTE (-1014)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-553 (-773))))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-1014))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-553 (-773)))))) 
-(-784) 
+((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-1013)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#2| (QUOTE (-552 (-772))))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-1013))))) (-12 (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#2| (QUOTE (-552 (-772)))))) 
+(-783) 
 ((|constructor| (NIL "This domain describes four groups of color shades (palettes).")) (|shade| (((|Integer|) $) "\\spad{shade(p)} returns the shade index of the indicated palette \\spad{p}.")) (|hue| (((|Color|) $) "\\spad{hue(p)} returns the hue field of the indicated palette \\spad{p}.")) (|light| (($ (|Color|)) "\\spad{light(c)} sets the shade of a hue,{} \\spad{c},{} to it's highest value.")) (|pastel| (($ (|Color|)) "\\spad{pastel(c)} sets the shade of a hue,{} \\spad{c},{} above bright,{} but below light.")) (|bright| (($ (|Color|)) "\\spad{bright(c)} sets the shade of a hue,{} \\spad{c},{} above dim,{} but below pastel.")) (|dim| (($ (|Color|)) "\\spad{dim(c)} sets the shade of a hue,{} \\spad{c},{} above dark,{} but below bright.")) (|dark| (($ (|Color|)) "\\spad{dark(c)} sets the shade of the indicated hue of \\spad{c} to it's lowest value."))) 
 NIL 
 NIL 
-(-785) 
+(-784) 
 ((|constructor| (NIL "This package provides a coerce from polynomials over algebraic numbers to \\spadtype{Expression AlgebraicNumber}.")) (|coerce| (((|Expression| (|Integer|)) (|Fraction| (|Polynomial| (|AlgebraicNumber|)))) "\\spad{coerce(rf)} converts \\spad{rf},{} a fraction of polynomial \\spad{p} with algebraic number coefficients to \\spadtype{Expression Integer}.") (((|Expression| (|Integer|)) (|Polynomial| (|AlgebraicNumber|))) "\\spad{coerce(p)} converts the polynomial \\spad{p} with algebraic number coefficients to \\spadtype{Expression Integer}."))) 
 NIL 
 NIL 
-(-786) 
+(-785) 
 ((|constructor| (NIL "Representation of parameters to functions or constructors. For the most part,{} they are Identifiers. However,{} in very cases,{} they are \"flags\",{} \\spadignore{e.g.} string literals.")) (|autoCoerce| (((|String|) $) "\\spad{autoCoerce(x)@String} implicitly coerce the object \\spad{x} to \\spadtype{String}. This function is left at the discretion of the compiler.") (((|Identifier|) $) "\\spad{autoCoerce(x)@Identifier} implicitly coerce the object \\spad{x} to \\spadtype{Identifier}. This function is left at the discretion of the compiler.")) (|case| (((|Boolean|) $ (|[\|\|]| (|String|))) "\\spad{x case String} if the parameter AST object \\spad{x} designates a flag.") (((|Boolean|) $ (|[\|\|]| (|Identifier|))) "\\spad{x case Identifier} if the parameter AST object \\spad{x} designates an \\spadtype{Identifier}."))) 
 NIL 
 NIL 
-(-787 CF1 CF2) 
+(-786 CF1 CF2) 
 ((|constructor| (NIL "This package \\undocumented")) (|map| (((|ParametricPlaneCurve| |#2|) (|Mapping| |#2| |#1|) (|ParametricPlaneCurve| |#1|)) "\\spad{map(f,x)} \\undocumented"))) 
 NIL 
 NIL 
-(-788 |ComponentFunction|) 
+(-787 |ComponentFunction|) 
 ((|constructor| (NIL "ParametricPlaneCurve is used for plotting parametric plane curves in the affine plane.")) (|coordinate| ((|#1| $ (|NonNegativeInteger|)) "\\spad{coordinate(c,i)} returns a coordinate function for \\spad{c} using 1-based indexing according to \\spad{i}. This indicates what the function for the coordinate component \\spad{i} of the plane curve is.")) (|curve| (($ |#1| |#1|) "\\spad{curve(c1,c2)} creates a plane curve from 2 component functions \\spad{c1} and \\spad{c2}."))) 
 NIL 
 NIL 
-(-789 CF1 CF2) 
+(-788 CF1 CF2) 
 ((|constructor| (NIL "This package \\undocumented")) (|map| (((|ParametricSpaceCurve| |#2|) (|Mapping| |#2| |#1|) (|ParametricSpaceCurve| |#1|)) "\\spad{map(f,x)} \\undocumented"))) 
 NIL 
 NIL 
-(-790 |ComponentFunction|) 
+(-789 |ComponentFunction|) 
 ((|constructor| (NIL "ParametricSpaceCurve is used for plotting parametric space curves in affine 3-space.")) (|coordinate| ((|#1| $ (|NonNegativeInteger|)) "\\spad{coordinate(c,i)} returns a coordinate function of \\spad{c} using 1-based indexing according to \\spad{i}. This indicates what the function for the coordinate component,{} \\spad{i},{} of the space curve is.")) (|curve| (($ |#1| |#1| |#1|) "\\spad{curve(c1,c2,c3)} creates a space curve from 3 component functions \\spad{c1},{} \\spad{c2},{} and \\spad{c3}."))) 
 NIL 
 NIL 
-(-791) 
+(-790) 
 ((|constructor| (NIL "\\indented{1}{This package provides a simple Spad script parser.} Related Constructors: Syntax. See Also: Syntax.")) (|getSyntaxFormsFromFile| (((|List| (|Syntax|)) (|String|)) "\\spad{getSyntaxFormsFromFile(f)} parses the source file \\spad{f} (supposedly containing Spad scripts) and returns a List Syntax. The filename \\spad{f} is supposed to have the proper extension. Note that source location information is not part of result."))) 
 NIL 
 NIL 
-(-792 CF1 CF2) 
+(-791 CF1 CF2) 
 ((|constructor| (NIL "This package \\undocumented")) (|map| (((|ParametricSurface| |#2|) (|Mapping| |#2| |#1|) (|ParametricSurface| |#1|)) "\\spad{map(f,x)} \\undocumented"))) 
 NIL 
 NIL 
-(-793 |ComponentFunction|) 
+(-792 |ComponentFunction|) 
 ((|constructor| (NIL "ParametricSurface is used for plotting parametric surfaces in affine 3-space.")) (|coordinate| ((|#1| $ (|NonNegativeInteger|)) "\\spad{coordinate(s,i)} returns a coordinate function of \\spad{s} using 1-based indexing according to \\spad{i}. This indicates what the function for the coordinate component,{} \\spad{i},{} of the surface is.")) (|surface| (($ |#1| |#1| |#1|) "\\spad{surface(c1,c2,c3)} creates a surface from 3 parametric component functions \\spad{c1},{} \\spad{c2},{} and \\spad{c3}."))) 
 NIL 
 NIL 
-(-794) 
+(-793) 
 ((|constructor| (NIL "PartitionsAndPermutations contains functions for generating streams of integer partitions,{} and streams of sequences of integers composed from a multi-set.")) (|permutations| (((|Stream| (|List| (|Integer|))) (|Integer|)) "\\spad{permutations(n)} is the stream of permutations \\indented{1}{formed from \\spad{1,2,3,...,n}.}")) (|sequences| (((|Stream| (|List| (|Integer|))) (|List| (|Integer|))) "\\spad{sequences([l0,l1,l2,..,ln])} is the set of \\indented{1}{all sequences formed from} \\spad{l0} 0's,{}\\spad{l1} 1's,{}\\spad{l2} 2's,{}...,{}\\spad{ln} \\spad{n}'s.") (((|Stream| (|List| (|Integer|))) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{sequences(l1,l2)} is the stream of all sequences that \\indented{1}{can be composed from the multiset defined from} \\indented{1}{two lists of integers \\spad{l1} and \\spad{l2}.} \\indented{1}{For example,{}the pair \\spad{([1,2,4],[2,3,5])} represents} \\indented{1}{multi-set with 1 \\spad{2},{} 2 \\spad{3}'s,{} and 4 \\spad{5}'s.}")) (|shufflein| (((|Stream| (|List| (|Integer|))) (|List| (|Integer|)) (|Stream| (|List| (|Integer|)))) "\\spad{shufflein(l,st)} maps shuffle(\\spad{l},{}\\spad{u}) on to all \\indented{1}{members \\spad{u} of \\spad{st},{} concatenating the results.}")) (|shuffle| (((|Stream| (|List| (|Integer|))) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{shuffle(l1,l2)} forms the stream of all shuffles of \\spad{l1} \\indented{1}{and \\spad{l2},{} \\spadignore{i.e.} all sequences that can be formed from} \\indented{1}{merging \\spad{l1} and \\spad{l2}.}")) (|conjugates| (((|Stream| (|List| (|PositiveInteger|))) (|Stream| (|List| (|PositiveInteger|)))) "\\spad{conjugates(lp)} is the stream of conjugates of a stream \\indented{1}{of partitions \\spad{lp}.}")) (|conjugate| (((|List| (|PositiveInteger|)) (|List| (|PositiveInteger|))) "\\spad{conjugate(pt)} is the conjugate of the partition \\spad{pt}."))) 
 NIL 
 NIL 
-(-795 R) 
+(-794 R) 
 ((|constructor| (NIL "An object \\spad{S} is Patternable over an object \\spad{R} if \\spad{S} can lift the conversions from \\spad{R} into \\spadtype{Pattern(Integer)} and \\spadtype{Pattern(Float)} to itself."))) 
 NIL 
 NIL 
-(-796 R S L) 
+(-795 R S L) 
 ((|constructor| (NIL "A PatternMatchListResult is an object internally returned by the pattern matcher when matching on lists. It is either a failed match,{} or a pair of PatternMatchResult,{} one for atoms (elements of the list),{} and one for lists.")) (|lists| (((|PatternMatchResult| |#1| |#3|) $) "\\spad{lists(r)} returns the list of matches that match lists.")) (|atoms| (((|PatternMatchResult| |#1| |#2|) $) "\\spad{atoms(r)} returns the list of matches that match atoms (elements of the lists).")) (|makeResult| (($ (|PatternMatchResult| |#1| |#2|) (|PatternMatchResult| |#1| |#3|)) "\\spad{makeResult(r1,r2)} makes the combined result [\\spad{r1},{}\\spad{r2}].")) (|new| (($) "\\spad{new()} returns a new empty match result.")) (|failed| (($) "\\spad{failed()} returns a failed match.")) (|failed?| (((|Boolean|) $) "\\spad{failed?(r)} tests if \\spad{r} is a failed match."))) 
 NIL 
 NIL 
-(-797 S) 
+(-796 S) 
 ((|constructor| (NIL "A set \\spad{R} is PatternMatchable over \\spad{S} if elements of \\spad{R} can be matched to patterns over \\spad{S}.")) (|patternMatch| (((|PatternMatchResult| |#1| $) $ (|Pattern| |#1|) (|PatternMatchResult| |#1| $)) "\\spad{patternMatch(expr, pat, res)} matches the pattern \\spad{pat} to the expression \\spad{expr}. res contains the variables of \\spad{pat} which are already matched and their matches (necessary for recursion). Initially,{} res is just the result of \\spadfun{new} which is an empty list of matches."))) 
 NIL 
 NIL 
-(-798 |Base| |Subject| |Pat|) 
+(-797 |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 (-2562 (|HasCategory| |#2| (QUOTE (-951 (-1091))))) (-2562 (|HasCategory| |#2| (QUOTE (-962))))) (-12 (|HasCategory| |#2| (QUOTE (-962))) (-2562 (|HasCategory| |#2| (QUOTE (-951 (-1091)))))) (|HasCategory| |#2| (QUOTE (-951 (-1091))))) 
-(-799 R S) 
+((-12 (-2561 (|HasCategory| |#2| (QUOTE (-950 (-1090))))) (-2561 (|HasCategory| |#2| (QUOTE (-961))))) (-12 (|HasCategory| |#2| (QUOTE (-961))) (-2561 (|HasCategory| |#2| (QUOTE (-950 (-1090)))))) (|HasCategory| |#2| (QUOTE (-950 (-1090))))) 
+(-798 R S) 
 ((|constructor| (NIL "A PatternMatchResult is an object internally returned by the pattern matcher; It is either a failed match,{} or a list of matches of the form (var,{} expr) meaning that the variable var matches the expression expr.")) (|satisfy?| (((|Union| (|Boolean|) "failed") $ (|Pattern| |#1|)) "\\spad{satisfy?(r, p)} returns \\spad{true} if the matches satisfy the top-level predicate of \\spad{p},{} \\spad{false} if they don't,{} and \"failed\" if not enough variables of \\spad{p} are matched in \\spad{r} to decide.")) (|construct| (($ (|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| |#2|)))) "\\spad{construct([v1,e1],...,[vn,en])} returns the match result containing the matches (\\spad{v1},{}\\spad{e1}),{}...,{}(vn,{}en).")) (|destruct| (((|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| |#2|))) $) "\\spad{destruct(r)} returns the list of matches (var,{} expr) in \\spad{r}. Error: if \\spad{r} is a failed match.")) (|addMatchRestricted| (($ (|Pattern| |#1|) |#2| $ |#2|) "\\spad{addMatchRestricted(var, expr, r, val)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} provided that \\spad{expr} satisfies the predicates attached to \\spad{var},{} that \\spad{var} is not matched to another expression already,{} and that either \\spad{var} is an optional pattern variable or that \\spad{expr} is not equal to val (usually an identity).")) (|insertMatch| (($ (|Pattern| |#1|) |#2| $) "\\spad{insertMatch(var, expr, r)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} without checking predicates or previous matches for \\spad{var}.")) (|addMatch| (($ (|Pattern| |#1|) |#2| $) "\\spad{addMatch(var, expr, r)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} provided that \\spad{expr} satisfies the predicates attached to \\spad{var},{} and that \\spad{var} is not matched to another expression already.")) (|getMatch| (((|Union| |#2| "failed") (|Pattern| |#1|) $) "\\spad{getMatch(var, r)} returns the expression that \\spad{var} matches in the result \\spad{r},{} and \"failed\" if \\spad{var} is not matched in \\spad{r}.")) (|union| (($ $ $) "\\spad{union(a, b)} makes the set-union of two match results.")) (|new| (($) "\\spad{new()} returns a new empty match result.")) (|failed| (($) "\\spad{failed()} returns a failed match.")) (|failed?| (((|Boolean|) $) "\\spad{failed?(r)} tests if \\spad{r} is a failed match."))) 
 NIL 
 NIL 
-(-800 R A B) 
+(-799 R A B) 
 ((|constructor| (NIL "Lifts maps to pattern matching results.")) (|map| (((|PatternMatchResult| |#1| |#3|) (|Mapping| |#3| |#2|) (|PatternMatchResult| |#1| |#2|)) "\\spad{map(f, [(v1,a1),...,(vn,an)])} returns the matching result [(\\spad{v1},{}\\spad{f}(\\spad{a1})),{}...,{}(vn,{}\\spad{f}(an))]."))) 
 NIL 
 NIL 
-(-801 R) 
+(-800 R) 
 ((|constructor| (NIL "Patterns for use by the pattern matcher.")) (|optpair| (((|Union| (|List| $) "failed") (|List| $)) "\\spad{optpair(l)} returns \\spad{l} has the form \\spad{[a, b]} and a is optional,{} and \"failed\" otherwise.")) (|variables| (((|List| $) $) "\\spad{variables(p)} returns the list of matching variables appearing in \\spad{p}.")) (|getBadValues| (((|List| (|Any|)) $) "\\spad{getBadValues(p)} returns the list of \"bad values\" for \\spad{p}. Note: \\spad{p} is not allowed to match any of its \"bad values\".")) (|addBadValue| (($ $ (|Any|)) "\\spad{addBadValue(p, v)} adds \\spad{v} to the list of \"bad values\" for \\spad{p}. Note: \\spad{p} is not allowed to match any of its \"bad values\".")) (|resetBadValues| (($ $) "\\spad{resetBadValues(p)} initializes the list of \"bad values\" for \\spad{p} to \\spad{[]}. Note: \\spad{p} is not allowed to match any of its \"bad values\".")) (|hasTopPredicate?| (((|Boolean|) $) "\\spad{hasTopPredicate?(p)} tests if \\spad{p} has a top-level predicate.")) (|topPredicate| (((|Record| (|:| |var| (|List| (|Symbol|))) (|:| |pred| (|Any|))) $) "\\spad{topPredicate(x)} returns \\spad{[[a1,...,an], f]} where the top-level predicate of \\spad{x} is \\spad{f(a1,...,an)}. Note: \\spad{n} is 0 if \\spad{x} has no top-level predicate.")) (|setTopPredicate| (($ $ (|List| (|Symbol|)) (|Any|)) "\\spad{setTopPredicate(x, [a1,...,an], f)} returns \\spad{x} with the top-level predicate set to \\spad{f(a1,...,an)}.")) (|patternVariable| (($ (|Symbol|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\spad{patternVariable(x, c?, o?, m?)} creates a pattern variable \\spad{x},{} which is constant if \\spad{c? = true},{} optional if \\spad{o? = true},{} and multiple if \\spad{m? = true}.")) (|withPredicates| (($ $ (|List| (|Any|))) "\\spad{withPredicates(p, [p1,...,pn])} makes a copy of \\spad{p} and attaches the predicate \\spad{p1} and ... and pn to the copy,{} which is returned.")) (|setPredicates| (($ $ (|List| (|Any|))) "\\spad{setPredicates(p, [p1,...,pn])} attaches the predicate \\spad{p1} and ... and pn to \\spad{p}.")) (|predicates| (((|List| (|Any|)) $) "\\spad{predicates(p)} returns \\spad{[p1,...,pn]} such that the predicate attached to \\spad{p} is \\spad{p1} and ... and pn.")) (|hasPredicate?| (((|Boolean|) $) "\\spad{hasPredicate?(p)} tests if \\spad{p} has predicates attached to it.")) (|optional?| (((|Boolean|) $) "\\spad{optional?(p)} tests if \\spad{p} is a single matching variable which can match an identity.")) (|multiple?| (((|Boolean|) $) "\\spad{multiple?(p)} tests if \\spad{p} is a single matching variable allowing list matching or multiple term matching in a sum or product.")) (|generic?| (((|Boolean|) $) "\\spad{generic?(p)} tests if \\spad{p} is a single matching variable.")) (|constant?| (((|Boolean|) $) "\\spad{constant?(p)} tests if \\spad{p} contains no matching variables.")) (|symbol?| (((|Boolean|) $) "\\spad{symbol?(p)} tests if \\spad{p} is a symbol.")) (|quoted?| (((|Boolean|) $) "\\spad{quoted?(p)} tests if \\spad{p} is of the form 's for a symbol \\spad{s}.")) (|inR?| (((|Boolean|) $) "\\spad{inR?(p)} tests if \\spad{p} is an atom (\\spadignore{i.e.} an element of \\spad{R}).")) (|copy| (($ $) "\\spad{copy(p)} returns a recursive copy of \\spad{p}.")) (|convert| (($ (|List| $)) "\\spad{convert([a1,...,an])} returns the pattern \\spad{[a1,...,an]}.")) (|depth| (((|NonNegativeInteger|) $) "\\spad{depth(p)} returns the nesting level of \\spad{p}.")) (/ (($ $ $) "\\spad{a / b} returns the pattern \\spad{a / b}.")) (** (($ $ $) "\\spad{a ** b} returns the pattern \\spad{a ** b}.") (($ $ (|NonNegativeInteger|)) "\\spad{a ** n} returns the pattern \\spad{a ** n}.")) (* (($ $ $) "\\spad{a * b} returns the pattern \\spad{a * b}.")) (+ (($ $ $) "\\spad{a + b} returns the pattern \\spad{a + b}.")) (|elt| (($ (|BasicOperator|) (|List| $)) "\\spad{elt(op, [a1,...,an])} returns \\spad{op(a1,...,an)}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| $)) "failed") $) "\\spad{isPower(p)} returns \\spad{[a, b]} if \\spad{p = a ** b},{} and \"failed\" otherwise.")) (|isList| (((|Union| (|List| $) "failed") $) "\\spad{isList(p)} returns \\spad{[a1,...,an]} if \\spad{p = [a1,...,an]},{} \"failed\" otherwise.")) (|isQuotient| (((|Union| (|Record| (|:| |num| $) (|:| |den| $)) "failed") $) "\\spad{isQuotient(p)} returns \\spad{[a, b]} if \\spad{p = a / b},{} and \"failed\" otherwise.")) (|isExpt| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|NonNegativeInteger|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[q, n]} if \\spad{n > 0} and \\spad{p = q ** n},{} and \"failed\" otherwise.")) (|isOp| (((|Union| (|Record| (|:| |op| (|BasicOperator|)) (|:| |arg| (|List| $))) "failed") $) "\\spad{isOp(p)} returns \\spad{[op, [a1,...,an]]} if \\spad{p = op(a1,...,an)},{} and \"failed\" otherwise.") (((|Union| (|List| $) "failed") $ (|BasicOperator|)) "\\spad{isOp(p, op)} returns \\spad{[a1,...,an]} if \\spad{p = op(a1,...,an)},{} and \"failed\" otherwise.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if \\spad{n > 1} and \\spad{p = a1 * ... * an},{} and \"failed\" otherwise.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[a1,...,an]} if \\spad{n > 1} \\indented{1}{and \\spad{p = a1 + ... + an},{}} and \"failed\" otherwise.")) (|One| (($) "1")) (|Zero| (($) "0"))) 
 NIL 
 NIL 
-(-802 R -2671) 
+(-801 R -2670) 
 ((|constructor| (NIL "Tools for patterns.")) (|badValues| (((|List| |#2|) (|Pattern| |#1|)) "\\spad{badValues(p)} returns the list of \"bad values\" for \\spad{p}; \\spad{p} is not allowed to match any of its \"bad values\".")) (|addBadValue| (((|Pattern| |#1|) (|Pattern| |#1|) |#2|) "\\spad{addBadValue(p, v)} adds \\spad{v} to the list of \"bad values\" for \\spad{p}; \\spad{p} is not allowed to match any of its \"bad values\".")) (|satisfy?| (((|Boolean|) (|List| |#2|) (|Pattern| |#1|)) "\\spad{satisfy?([v1,...,vn], p)} returns \\spad{f(v1,...,vn)} where \\spad{f} is the top-level predicate attached to \\spad{p}.") (((|Boolean|) |#2| (|Pattern| |#1|)) "\\spad{satisfy?(v, p)} returns \\spad{f}(\\spad{v}) where \\spad{f} is the predicate attached to \\spad{p}.")) (|predicate| (((|Mapping| (|Boolean|) |#2|) (|Pattern| |#1|)) "\\spad{predicate(p)} returns the predicate attached to \\spad{p},{} the constant function \\spad{true} if \\spad{p} has no predicates attached to it.")) (|suchThat| (((|Pattern| |#1|) (|Pattern| |#1|) (|List| (|Symbol|)) (|Mapping| (|Boolean|) (|List| |#2|))) "\\spad{suchThat(p, [a1,...,an], f)} returns a copy of \\spad{p} with the top-level predicate set to \\spad{f(a1,...,an)}.") (((|Pattern| |#1|) (|Pattern| |#1|) (|List| (|Mapping| (|Boolean|) |#2|))) "\\spad{suchThat(p, [f1,...,fn])} makes a copy of \\spad{p} and adds the predicate \\spad{f1} and ... and fn to the copy,{} which is returned.") (((|Pattern| |#1|) (|Pattern| |#1|) (|Mapping| (|Boolean|) |#2|)) "\\spad{suchThat(p, f)} makes a copy of \\spad{p} and adds the predicate \\spad{f} to the copy,{} which is returned."))) 
 NIL 
 NIL 
-(-803 R S) 
+(-802 R S) 
 ((|constructor| (NIL "Lifts maps to patterns.")) (|map| (((|Pattern| |#2|) (|Mapping| |#2| |#1|) (|Pattern| |#1|)) "\\spad{map(f, p)} applies \\spad{f} to all the leaves of \\spad{p} and returns the result as a pattern over \\spad{S}."))) 
 NIL 
 NIL 
-(-804 |VarSet|) 
+(-803 |VarSet|) 
 ((|constructor| (NIL "This domain provides the internal representation of polynomials in non-commutative variables written over the Poincare-Birkhoff-Witt basis. See the \\spadtype{XPBWPolynomial} domain constructor. See Free Lie Algebras by \\spad{C}. Reutenauer (Oxford science publications). \\newline Author: Michel Petitot (petitot@lifl.fr).")) (|varList| (((|List| |#1|) $) "\\spad{varList([l1]*[l2]*...[ln])} returns the list of variables in the word \\spad{l1*l2*...*ln}.")) (|retractable?| (((|Boolean|) $) "\\spad{retractable?([l1]*[l2]*...[ln])} returns \\spad{true} iff \\spad{n} equals \\spad{1}.")) (|rest| (($ $) "\\spad{rest([l1]*[l2]*...[ln])} returns the list \\spad{l2, .... ln}.")) (|ListOfTerms| (((|List| (|LyndonWord| |#1|)) $) "\\spad{ListOfTerms([l1]*[l2]*...[ln])} returns the list of words \\spad{l1, l2, .... ln}.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length([l1]*[l2]*...[ln])} returns the length of the word \\spad{l1*l2*...*ln}.")) (|first| (((|LyndonWord| |#1|) $) "\\spad{first([l1]*[l2]*...[ln])} returns the Lyndon word \\spad{l1}.")) (|coerce| (($ |#1|) "\\spad{coerce(v)} return \\spad{v}") (((|OrderedFreeMonoid| |#1|) $) "\\spad{coerce([l1]*[l2]*...[ln])} returns the word \\spad{l1*l2*...*ln},{} where \\spad{[l_i]} is the backeted form of the Lyndon word \\spad{l_i}.")) (|One| (($) "\\spad{1} returns the empty list."))) 
 NIL 
 NIL 
-(-805 UP R) 
+(-804 UP R) 
 ((|constructor| (NIL "This package \\undocumented")) (|compose| ((|#1| |#1| |#1|) "\\spad{compose(p,q)} \\undocumented"))) 
 NIL 
 NIL 
-(-806 A T$ S) 
+(-805 A T$ S) 
 ((|constructor| (NIL "\\indented{2}{This category captures the interface of domains with a distinguished} \\indented{2}{operation named \\spad{differentiate} for partial differentiation with} \\indented{2}{respect to some domain of variables.} See Also: \\indented{2}{DifferentialDomain,{} PartialDifferentialSpace}")) (D ((|#2| $ |#3|) "\\spad{D(x,v)} is a shorthand for \\spad{differentiate(x,v)}")) (|differentiate| ((|#2| $ |#3|) "\\spad{differentiate(x,v)} computes the partial derivative of \\spad{x} with respect to \\spad{v}."))) 
 NIL 
 NIL 
-(-807 T$ S) 
+(-806 T$ S) 
 ((|constructor| (NIL "\\indented{2}{This category captures the interface of domains with a distinguished} \\indented{2}{operation named \\spad{differentiate} for partial differentiation with} \\indented{2}{respect to some domain of variables.} See Also: \\indented{2}{DifferentialDomain,{} PartialDifferentialSpace}")) (D ((|#1| $ |#2|) "\\spad{D(x,v)} is a shorthand for \\spad{differentiate(x,v)}")) (|differentiate| ((|#1| $ |#2|) "\\spad{differentiate(x,v)} computes the partial derivative of \\spad{x} with respect to \\spad{v}."))) 
 NIL 
 NIL 
-(-808 UP -3094) 
+(-807 UP -3093) 
 ((|constructor| (NIL "This package \\undocumented")) (|rightFactorCandidate| ((|#1| |#1| (|NonNegativeInteger|)) "\\spad{rightFactorCandidate(p,n)} \\undocumented")) (|leftFactor| (((|Union| |#1| "failed") |#1| |#1|) "\\spad{leftFactor(p,q)} \\undocumented")) (|decompose| (((|Union| (|Record| (|:| |left| |#1|) (|:| |right| |#1|)) "failed") |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{decompose(up,m,n)} \\undocumented") (((|List| |#1|) |#1|) "\\spad{decompose(up)} \\undocumented"))) 
 NIL 
 NIL 
-(-809 R S) 
+(-808 R S) 
 ((|constructor| (NIL "A partial differential \\spad{R}-module with differentiations indexed by a parameter type \\spad{S}. \\blankline"))) 
-((-3992 . T) (-3991 . T)) 
+((-3991 . T) (-3990 . T)) 
 NIL 
-(-810 S) 
+(-809 S) 
 ((|constructor| (NIL "A partial differential ring with differentiations indexed by a parameter type \\spad{S}. \\blankline"))) 
-((-3994 . T)) 
+((-3993 . T)) 
 NIL 
-(-811 A S) 
+(-810 A S) 
 ((|constructor| (NIL "\\indented{2}{This category captures the interface of domains stable by partial} \\indented{2}{differentiation with respect to variables from some domain.} See Also: \\indented{2}{PartialDifferentialDomain}")) (D (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) "\\spad{D(x,[s1,...,sn],[n1,...,nn])} is a shorthand for \\spad{differentiate(x,[s1,...,sn],[n1,...,nn])}.") (($ $ |#2| (|NonNegativeInteger|)) "\\spad{D(x,s,n)} is a shorthand for \\spad{differentiate(x,s,n)}.") (($ $ (|List| |#2|)) "\\spad{D(x,[s1,...sn])} is a shorthand for \\spad{differentiate(x,[s1,...sn])}.")) (|differentiate| (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) "\\spad{differentiate(x,[s1,...,sn],[n1,...,nn])} computes multiple partial derivatives,{} \\spadignore{i.e.}") (($ $ |#2| (|NonNegativeInteger|)) "\\spad{differentiate(x,s,n)} computes multiple partial derivatives,{} \\spadignore{i.e.} \\spad{n}\\spad{-}th derivative of \\spad{x} with respect to \\spad{s}.") (($ $ (|List| |#2|)) "\\spad{differentiate(x,[s1,...sn])} computes successive partial derivatives,{} \\spadignore{i.e.} \\spad{differentiate(...differentiate(x, s1)..., sn)}."))) 
 NIL 
 NIL 
-(-812 S) 
+(-811 S) 
 ((|constructor| (NIL "\\indented{2}{This category captures the interface of domains stable by partial} \\indented{2}{differentiation with respect to variables from some domain.} See Also: \\indented{2}{PartialDifferentialDomain}")) (D (($ $ (|List| |#1|) (|List| (|NonNegativeInteger|))) "\\spad{D(x,[s1,...,sn],[n1,...,nn])} is a shorthand for \\spad{differentiate(x,[s1,...,sn],[n1,...,nn])}.") (($ $ |#1| (|NonNegativeInteger|)) "\\spad{D(x,s,n)} is a shorthand for \\spad{differentiate(x,s,n)}.") (($ $ (|List| |#1|)) "\\spad{D(x,[s1,...sn])} is a shorthand for \\spad{differentiate(x,[s1,...sn])}.")) (|differentiate| (($ $ (|List| |#1|) (|List| (|NonNegativeInteger|))) "\\spad{differentiate(x,[s1,...,sn],[n1,...,nn])} computes multiple partial derivatives,{} \\spadignore{i.e.}") (($ $ |#1| (|NonNegativeInteger|)) "\\spad{differentiate(x,s,n)} computes multiple partial derivatives,{} \\spadignore{i.e.} \\spad{n}\\spad{-}th derivative of \\spad{x} with respect to \\spad{s}.") (($ $ (|List| |#1|)) "\\spad{differentiate(x,[s1,...sn])} computes successive partial derivatives,{} \\spadignore{i.e.} \\spad{differentiate(...differentiate(x, s1)..., sn)}."))) 
 NIL 
 NIL 
-(-813 S) 
+(-812 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 (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -1036) (|devaluate| |#1|)))) 
-(-814 S) 
+((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1013))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -1035) (|devaluate| |#1|)))) 
+(-813 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|))) $) "\\spad{listRepresentation(p)} produces a representation {\\em rep} of the permutation \\spad{p} as a list of preimages and images,{} \\spad{i}.\\spad{e} \\spad{p} maps {\\em (rep.preimage).k} to {\\em (rep.image).k} for all indices \\spad{k}. Elements of \\spad{S} not in {\\em (rep.preimage).k} are fixed points,{} and these are the only fixed points of the permutation."))) 
-((-3994 . T)) 
-((OR (|HasCategory| |#1| (QUOTE (-320))) (|HasCategory| |#1| (QUOTE (-757)))) (|HasCategory| |#1| (QUOTE (-320))) (|HasCategory| |#1| (QUOTE (-757)))) 
-(-815 |n| R) 
+((-3993 . T)) 
+((OR (|HasCategory| |#1| (QUOTE (-320))) (|HasCategory| |#1| (QUOTE (-756)))) (|HasCategory| |#1| (QUOTE (-320))) (|HasCategory| |#1| (QUOTE (-756)))) 
+(-814 |n| R) 
 ((|constructor| (NIL "Permanent implements the functions {\\em permanent},{} the permanent for square matrices.")) (|permanent| ((|#2| (|SquareMatrix| |#1| |#2|)) "\\spad{permanent(x)} computes the permanent of a square matrix \\spad{x}. The {\\em permanent} is equivalent to the \\spadfun{determinant} except that coefficients have no change of sign. This function is much more difficult to compute than the {\\em determinant}. The formula used is by \\spad{H}.\\spad{J}. Ryser,{} improved by [Nijenhuis and Wilf,{} Ch. 19]. Note: permanent(\\spad{x}) choose one of three algorithms,{} depending on the underlying ring \\spad{R} and on \\spad{n},{} the number of rows (and columns) of x:\\begin{items} \\item 1. if 2 has an inverse in \\spad{R} we can use the algorithm of \\indented{3}{[Nijenhuis and Wilf,{} ch.19,{}\\spad{p}.158]; if 2 has no inverse,{}} \\indented{3}{some modifications are necessary:} \\item 2. if {\\em n > 6} and \\spad{R} is an integral domain with characteristic \\indented{3}{different from 2 (the algorithm works if and only 2 is not a} \\indented{3}{zero-divisor of \\spad{R} and {\\em characteristic()\\$R ~= 2},{}} \\indented{3}{but how to check that for any given \\spad{R} ?),{}} \\indented{3}{the local function {\\em permanent2} is called;} \\item 3. else,{} the local function {\\em permanent3} is called \\indented{3}{(works for all commutative rings \\spad{R}).} \\end{items}"))) 
 NIL 
 NIL 
-(-816 S) 
+(-815 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."))) 
-((-3994 . T)) 
+((-3993 . T)) 
 NIL 
-(-817 S) 
+(-816 S) 
 ((|constructor| (NIL "PermutationGroup implements permutation groups acting on a set \\spad{S},{} \\spadignore{i.e.} all subgroups of the symmetric group of \\spad{S},{} represented as a list of permutations (generators). Note that therefore the objects are not members of the \\Language category \\spadtype{Group}. Using the idea of base and strong generators by Sims,{} basic routines and algorithms are implemented so that the word problem for permutation groups can be solved.")) (|initializeGroupForWordProblem| (((|Void|) $ (|Integer|) (|Integer|)) "\\spad{initializeGroupForWordProblem(gp,m,n)} initializes the group {\\em gp} for the word problem. Notes: (1) with a small integer you get shorter words,{} but the routine takes longer than the standard routine for longer words. (2) be careful: invoking this routine will destroy the possibly stored information about your group (but will recompute it again). (3) users need not call this function normally for the soultion of the word problem.") (((|Void|) $) "\\spad{initializeGroupForWordProblem(gp)} initializes the group {\\em gp} for the word problem. Notes: it calls the other function of this name with parameters 0 and 1: {\\em initializeGroupForWordProblem(gp,0,1)}. Notes: (1) be careful: invoking this routine will destroy the possibly information about your group (but will recompute it again) (2) users need not call this function normally for the soultion of the word problem.")) (<= (((|Boolean|) $ $) "\\spad{gp1 <= gp2} returns \\spad{true} if and only if {\\em gp1} is a subgroup of {\\em gp2}. Note: because of a bug in the parser you have to call this function explicitly by {\\em gp1 <=\\$(PERMGRP S) gp2}.")) (< (((|Boolean|) $ $) "\\spad{gp1 < gp2} returns \\spad{true} if and only if {\\em gp1} is a proper subgroup of {\\em gp2}.")) (|support| (((|Set| |#1|) $) "\\spad{support(gp)} returns the points moved by the group {\\em gp}.")) (|wordInGenerators| (((|List| (|NonNegativeInteger|)) (|Permutation| |#1|) $) "\\spad{wordInGenerators(p,gp)} returns the word for the permutation \\spad{p} in the original generators of the group {\\em gp},{} represented by the indices of the list,{} given by {\\em generators}.")) (|wordInStrongGenerators| (((|List| (|NonNegativeInteger|)) (|Permutation| |#1|) $) "\\spad{wordInStrongGenerators(p,gp)} returns the word for the permutation \\spad{p} in the strong generators of the group {\\em gp},{} represented by the indices of the list,{} given by {\\em strongGenerators}.")) (|member?| (((|Boolean|) (|Permutation| |#1|) $) "\\spad{member?(pp,gp)} answers the question,{} whether the permutation {\\em pp} is in the group {\\em gp} or not.")) (|orbits| (((|Set| (|Set| |#1|)) $) "\\spad{orbits(gp)} returns the orbits of the group {\\em gp},{} \\spadignore{i.e.} it partitions the (finite) of all moved points.")) (|orbit| (((|Set| (|List| |#1|)) $ (|List| |#1|)) "\\spad{orbit(gp,ls)} returns the orbit of the ordered list {\\em ls} under the group {\\em gp}. Note: return type is \\spad{L} \\spad{L} \\spad{S} temporarily because FSET \\spad{L} \\spad{S} has an error.") (((|Set| (|Set| |#1|)) $ (|Set| |#1|)) "\\spad{orbit(gp,els)} returns the orbit of the unordered set {\\em els} under the group {\\em gp}.") (((|Set| |#1|) $ |#1|) "\\spad{orbit(gp,el)} returns the orbit of the element {\\em el} under the group {\\em gp},{} \\spadignore{i.e.} the set of all points gained by applying each group element to {\\em el}.")) (|permutationGroup| (($ (|List| (|Permutation| |#1|))) "\\spad{permutationGroup(ls)} coerces a list of permutations {\\em ls} to the group generated by this list.")) (|wordsForStrongGenerators| (((|List| (|List| (|NonNegativeInteger|))) $) "\\spad{wordsForStrongGenerators(gp)} returns the words for the strong generators of the group {\\em gp} in the original generators of {\\em gp},{} represented by their indices in the list,{} given by {\\em generators}.")) (|strongGenerators| (((|List| (|Permutation| |#1|)) $) "\\spad{strongGenerators(gp)} returns strong generators for the group {\\em gp}.")) (|base| (((|List| |#1|) $) "\\spad{base(gp)} returns a base for the group {\\em gp}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(gp)} returns the number of points moved by all permutations of the group {\\em gp}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(gp)} returns the order of the group {\\em gp}.")) (|random| (((|Permutation| |#1|) $) "\\spad{random(gp)} returns a random product of maximal 20 generators of the group {\\em gp}. Note: {\\em random(gp)=random(gp,20)}.") (((|Permutation| |#1|) $ (|Integer|)) "\\spad{random(gp,i)} returns a random product of maximal \\spad{i} generators of the group {\\em gp}.")) (|elt| (((|Permutation| |#1|) $ (|NonNegativeInteger|)) "\\spad{elt(gp,i)} returns the \\spad{i}-th generator of the group {\\em gp}.")) (|generators| (((|List| (|Permutation| |#1|)) $) "\\spad{generators(gp)} returns the generators of the group {\\em gp}.")) (|coerce| (($ (|List| (|Permutation| |#1|))) "\\spad{coerce(ls)} coerces a list of permutations {\\em ls} to the group generated by this list.") (((|List| (|Permutation| |#1|)) $) "\\spad{coerce(gp)} returns the generators of the group {\\em gp}."))) 
 NIL 
 NIL 
-(-818 |p|) 
+(-817 |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."))) 
-((-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
 ((|HasCategory| $ (QUOTE (-120))) (|HasCategory| $ (QUOTE (-118))) (|HasCategory| $ (QUOTE (-320)))) 
-(-819 R E |VarSet| S) 
+(-818 R E |VarSet| S) 
 ((|constructor| (NIL "PolynomialFactorizationByRecursion(\\spad{R},{}\\spad{E},{}\\spad{VarSet},{}\\spad{S}) is used for factorization of sparse univariate polynomials over a domain \\spad{S} of multivariate polynomials over \\spad{R}.")) (|factorSFBRlcUnit| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|List| |#3|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorSFBRlcUnit(p)} returns the square free factorization of polynomial \\spad{p} (see \\spadfun{factorSquareFreeByRecursion}{PolynomialFactorizationByRecursionUnivariate}) in the case where the leading coefficient of \\spad{p} is a unit.")) (|bivariateSLPEBR| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|List| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|) |#3|) "\\spad{bivariateSLPEBR(lp,p,v)} implements the bivariate case of \\spadfunFrom{solveLinearPolynomialEquationByRecursion}{PolynomialFactorizationByRecursionUnivariate}; its implementation depends on \\spad{R}")) (|randomR| ((|#1|) "\\spad{randomR produces} a random element of \\spad{R}")) (|factorSquareFreeByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorSquareFreeByRecursion(p)} returns the square free factorization of \\spad{p}. This functions performs the recursion step for factorSquareFreePolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorSquareFreePolynomial}).")) (|factorByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorByRecursion(p)} factors polynomial \\spad{p}. This function performs the recursion step for factorPolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorPolynomial})")) (|solveLinearPolynomialEquationByRecursion| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|List| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{solveLinearPolynomialEquationByRecursion([p1,...,pn],p)} returns the list of polynomials \\spad{[q1,...,qn]} such that \\spad{sum qi/pi = p / prod pi},{} a recursion step for solveLinearPolynomialEquation as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{solveLinearPolynomialEquation}). If no such list of \\spad{qi} exists,{} then \"failed\" is returned."))) 
 NIL 
 NIL 
-(-820 R S) 
+(-819 R S) 
 ((|constructor| (NIL "\\indented{1}{PolynomialFactorizationByRecursionUnivariate} \\spad{R} is a \\spadfun{PolynomialFactorizationExplicit} domain,{} \\spad{S} is univariate polynomials over \\spad{R} We are interested in handling SparseUnivariatePolynomials over \\spad{S},{} is a variable we shall call \\spad{z}")) (|factorSFBRlcUnit| (((|Factored| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|)) "\\spad{factorSFBRlcUnit(p)} returns the square free factorization of polynomial \\spad{p} (see \\spadfun{factorSquareFreeByRecursion}{PolynomialFactorizationByRecursionUnivariate}) in the case where the leading coefficient of \\spad{p} is a unit.")) (|randomR| ((|#1|) "\\spad{randomR()} produces a random element of \\spad{R}")) (|factorSquareFreeByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|)) "\\spad{factorSquareFreeByRecursion(p)} returns the square free factorization of \\spad{p}. This functions performs the recursion step for factorSquareFreePolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorSquareFreePolynomial}).")) (|factorByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|)) "\\spad{factorByRecursion(p)} factors polynomial \\spad{p}. This function performs the recursion step for factorPolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorPolynomial})")) (|solveLinearPolynomialEquationByRecursion| (((|Union| (|List| (|SparseUnivariatePolynomial| |#2|)) "failed") (|List| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|)) "\\spad{solveLinearPolynomialEquationByRecursion([p1,...,pn],p)} returns the list of polynomials \\spad{[q1,...,qn]} such that \\spad{sum qi/pi = p / prod pi},{} a recursion step for solveLinearPolynomialEquation as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{solveLinearPolynomialEquation}). If no such list of \\spad{qi} exists,{} then \"failed\" is returned."))) 
 NIL 
 NIL 
-(-821 S) 
+(-820 S) 
 ((|constructor| (NIL "This is the category of domains that know \"enough\" about themselves in order to factor univariate polynomials over themselves. This will be used in future releases for supporting factorization over finitely generated coefficient fields,{} it is not yet available in the current release of axiom.")) (|charthRoot| (((|Maybe| $) $) "\\spad{charthRoot(r)} returns the \\spad{p}\\spad{-}th root of \\spad{r},{} or \\spad{nothing} if none exists in the domain.")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(m)} returns a vector of elements,{} not all zero,{} whose \\spad{p}\\spad{-}th powers (\\spad{p} is the characteristic of the domain) are a solution of the homogenous linear system represented by \\spad{m},{} or \"failed\" is there is no such vector.")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| $)) "failed") (|List| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{solveLinearPolynomialEquation([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}'s exists.")) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) "\\spad{gcdPolynomial(p,q)} returns the gcd of the univariate polynomials \\spad{p} qnd \\spad{q}.")) (|factorSquareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorSquareFreePolynomial(p)} factors the univariate polynomial \\spad{p} into irreducibles where \\spad{p} is known to be square free and primitive with respect to its main variable.")) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorPolynomial(p)} returns the factorization into irreducibles of the univariate polynomial \\spad{p}.")) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{squareFreePolynomial(p)} returns the square-free factorization of the univariate polynomial \\spad{p}."))) 
 NIL 
 ((|HasCategory| |#1| (QUOTE (-118)))) 
-(-822) 
+(-821) 
 ((|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}."))) 
-((-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
 NIL 
-(-823 R0 -3094 UP UPUP R) 
+(-822 R0 -3093 UP UPUP R) 
 ((|constructor| (NIL "This package provides function for testing whether a divisor on a curve is a torsion divisor.")) (|torsionIfCan| (((|Union| (|Record| (|:| |order| (|NonNegativeInteger|)) (|:| |function| |#5|)) "failed") (|FiniteDivisor| |#2| |#3| |#4| |#5|)) "\\spad{torsionIfCan(f)}\\\\ undocumented")) (|torsion?| (((|Boolean|) (|FiniteDivisor| |#2| |#3| |#4| |#5|)) "\\spad{torsion?(f)} \\undocumented")) (|order| (((|Union| (|NonNegativeInteger|) "failed") (|FiniteDivisor| |#2| |#3| |#4| |#5|)) "\\spad{order(f)} \\undocumented"))) 
 NIL 
 NIL 
-(-824 UP UPUP R) 
+(-823 UP UPUP R) 
 ((|constructor| (NIL "This package provides function for testing whether a divisor on a curve is a torsion divisor.")) (|torsionIfCan| (((|Union| (|Record| (|:| |order| (|NonNegativeInteger|)) (|:| |function| |#3|)) "failed") (|FiniteDivisor| (|Fraction| (|Integer|)) |#1| |#2| |#3|)) "\\spad{torsionIfCan(f)} \\undocumented")) (|torsion?| (((|Boolean|) (|FiniteDivisor| (|Fraction| (|Integer|)) |#1| |#2| |#3|)) "\\spad{torsion?(f)} \\undocumented")) (|order| (((|Union| (|NonNegativeInteger|) "failed") (|FiniteDivisor| (|Fraction| (|Integer|)) |#1| |#2| |#3|)) "\\spad{order(f)} \\undocumented"))) 
 NIL 
 NIL 
-(-825 UP UPUP) 
+(-824 UP UPUP) 
 ((|constructor| (NIL "\\indented{1}{Utilities for PFOQ and PFO} Author: Manuel Bronstein Date Created: 25 Aug 1988 Date Last Updated: 11 Jul 1990")) (|polyred| ((|#2| |#2|) "\\spad{polyred(u)} \\undocumented")) (|doubleDisc| (((|Integer|) |#2|) "\\spad{doubleDisc(u)} \\undocumented")) (|mix| (((|Integer|) (|List| (|Record| (|:| |den| (|Integer|)) (|:| |gcdnum| (|Integer|))))) "\\spad{mix(l)} \\undocumented")) (|badNum| (((|Integer|) |#2|) "\\spad{badNum(u)} \\undocumented") (((|Record| (|:| |den| (|Integer|)) (|:| |gcdnum| (|Integer|))) |#1|) "\\spad{badNum(p)} \\undocumented")) (|getGoodPrime| (((|PositiveInteger|) (|Integer|)) "\\spad{getGoodPrime n} returns the smallest prime not dividing \\spad{n}"))) 
 NIL 
 NIL 
-(-826 R) 
+(-825 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."))) 
-((-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
 NIL 
-(-827 R) 
+(-826 R) 
 ((|constructor| (NIL "The package \\spadtype{PartialFractionPackage} gives an easier to use interfact the domain \\spadtype{PartialFraction}. The user gives a fraction of polynomials,{} and a variable and the package converts it to the proper datatype for the \\spadtype{PartialFraction} domain.")) (|partialFraction| (((|Any|) (|Polynomial| |#1|) (|Factored| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{partialFraction(num, facdenom, var)} returns the partial fraction decomposition of the rational function whose numerator is \\spad{num} and whose factored denominator is \\spad{facdenom} with respect to the variable var.") (((|Any|) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{partialFraction(rf, var)} returns the partial fraction decomposition of the rational function \\spad{rf} with respect to the variable var."))) 
 NIL 
 NIL 
-(-828 E OV R P) 
+(-827 E OV R P) 
 ((|gcdPrimitive| ((|#4| (|List| |#4|)) "\\spad{gcdPrimitive lp} computes the gcd of the list of primitive polynomials lp.") (((|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{gcdPrimitive(p,q)} computes the gcd of the primitive polynomials \\spad{p} and \\spad{q}.") ((|#4| |#4| |#4|) "\\spad{gcdPrimitive(p,q)} computes the gcd of the primitive polynomials \\spad{p} and \\spad{q}.")) (|gcd| (((|SparseUnivariatePolynomial| |#4|) (|List| (|SparseUnivariatePolynomial| |#4|))) "\\spad{gcd(lp)} computes the gcd of the list of polynomials \\spad{lp}.") (((|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{gcd(p,q)} computes the gcd of the two polynomials \\spad{p} and \\spad{q}.") ((|#4| (|List| |#4|)) "\\spad{gcd(lp)} computes the gcd of the list of polynomials \\spad{lp}.") ((|#4| |#4| |#4|) "\\spad{gcd(p,q)} computes the gcd of the two polynomials \\spad{p} and \\spad{q}."))) 
 NIL 
 NIL 
-(-829) 
+(-828) 
 ((|constructor| (NIL "PermutationGroupExamples provides permutation groups for some classes of groups: symmetric,{} alternating,{} dihedral,{} cyclic,{} direct products of cyclic,{} which are in fact the finite abelian groups of symmetric groups called Young subgroups. Furthermore,{} Rubik's group as permutation group of 48 integers and a list of sporadic simple groups derived from the atlas of finite groups.")) (|youngGroup| (((|PermutationGroup| (|Integer|)) (|Partition|)) "\\spad{youngGroup(lambda)} constructs the direct product of the symmetric groups given by the parts of the partition {\\em lambda}.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{youngGroup([n1,...,nk])} constructs the direct product of the symmetric groups {\\em Sn1},{}...,{}{\\em Snk}.")) (|rubiksGroup| (((|PermutationGroup| (|Integer|))) "\\spad{rubiksGroup constructs} the permutation group representing Rubic's Cube acting on integers {\\em 10*i+j} for {\\em 1 <= i <= 6},{} {\\em 1 <= j <= 8}. The faces of Rubik's Cube are labelled in the obvious way Front,{} Right,{} Up,{} Down,{} Left,{} Back and numbered from 1 to 6 in this given ordering,{} the pieces on each face (except the unmoveable center piece) are clockwise numbered from 1 to 8 starting with the piece in the upper left corner. The moves of the cube are represented as permutations on these pieces,{} represented as a two digit integer {\\em ij} where \\spad{i} is the numer of theface (1 to 6) and \\spad{j} is the number of the piece on this face. The remaining ambiguities are resolved by looking at the 6 generators,{} which represent a 90 degree turns of the faces,{} or from the following pictorial description. Permutation group representing Rubic's Cube acting on integers 10*i+j for 1 <= \\spad{i} <= 6,{} 1 <= \\spad{j} \\spad{<=8}. \\blankline\\begin{verbatim}Rubik's Cube:   +-----+ +-- B   where: marks Side # :               / U   /|/              /     / |         F(ront)    <->    1      L -->  +-----+ R|         R(ight)    <->    2             |     |  +         U(p)       <->    3             |  F  | /          D(own)     <->    4             |     |/           L(eft)     <->    5             +-----+            B(ack)     <->    6                ^                |                DThe Cube's surface:                               The pieces on each side            +---+              (except the unmoveable center            |567|              piece) are clockwise numbered            |4U8|              from 1 to 8 starting with the            |321|              piece in the upper left        +---+---+---+          corner (see figure on the        |781|123|345|          left).  The moves of the cube        |6L2|8F4|2R6|          are represented as        |543|765|187|          permutations on these pieces.        +---+---+---+          Each of the pieces is            |123|              represented as a two digit            |8D4|              integer ij where i is the            |765|              # of the side ( 1 to 6 for            +---+              F to B (see table above ))            |567|              and j is the # of the piece.            |4B8|            |321|            +---+\\end{verbatim}")) (|janko2| (((|PermutationGroup| (|Integer|))) "\\spad{janko2 constructs} the janko group acting on the integers 1,{}...,{}100.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{janko2(li)} constructs the janko group acting on the 100 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 100 different entries")) (|mathieu24| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu24 constructs} the mathieu group acting on the integers 1,{}...,{}24.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu24(li)} constructs the mathieu group acting on the 24 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 24 different entries.")) (|mathieu23| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu23 constructs} the mathieu group acting on the integers 1,{}...,{}23.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu23(li)} constructs the mathieu group acting on the 23 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 23 different entries.")) (|mathieu22| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu22 constructs} the mathieu group acting on the integers 1,{}...,{}22.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu22(li)} constructs the mathieu group acting on the 22 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 22 different entries.")) (|mathieu12| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu12 constructs} the mathieu group acting on the integers 1,{}...,{}12.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu12(li)} constructs the mathieu group acting on the 12 integers given in the list {\\em li}. Note: duplicates in the list will be removed Error: if {\\em li} has less or more than 12 different entries.")) (|mathieu11| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu11 constructs} the mathieu group acting on the integers 1,{}...,{}11.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu11(li)} constructs the mathieu group acting on the 11 integers given in the list {\\em li}. Note: duplicates in the list will be removed. error,{} if {\\em li} has less or more than 11 different entries.")) (|dihedralGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{dihedralGroup([i1,...,ik])} constructs the dihedral group of order 2k acting on the integers out of {\\em i1},{}...,{}{\\em ik}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{dihedralGroup(n)} constructs the dihedral group of order 2n acting on integers 1,{}...,{}\\spad{N}.")) (|cyclicGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{cyclicGroup([i1,...,ik])} constructs the cyclic group of order \\spad{k} acting on the integers {\\em i1},{}...,{}{\\em ik}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{cyclicGroup(n)} constructs the cyclic group of order \\spad{n} acting on the integers 1,{}...,{}\\spad{n}.")) (|abelianGroup| (((|PermutationGroup| (|Integer|)) (|List| (|PositiveInteger|))) "\\spad{abelianGroup([n1,...,nk])} constructs the abelian group that is the direct product of cyclic groups with order {\\em ni}.")) (|alternatingGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{alternatingGroup(li)} constructs the alternating group acting on the integers in the list {\\em li},{} generators are in general the {\\em n-2}-cycle {\\em (li.3,...,li.n)} and the 3-cycle {\\em (li.1,li.2,li.3)},{} if \\spad{n} is odd and product of the 2-cycle {\\em (li.1,li.2)} with {\\em n-2}-cycle {\\em (li.3,...,li.n)} and the 3-cycle {\\em (li.1,li.2,li.3)},{} if \\spad{n} is even. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{alternatingGroup(n)} constructs the alternating group {\\em An} acting on the integers 1,{}...,{}\\spad{n},{} generators are in general the {\\em n-2}-cycle {\\em (3,...,n)} and the 3-cycle {\\em (1,2,3)} if \\spad{n} is odd and the product of the 2-cycle {\\em (1,2)} with {\\em n-2}-cycle {\\em (3,...,n)} and the 3-cycle {\\em (1,2,3)} if \\spad{n} is even.")) (|symmetricGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{symmetricGroup(li)} constructs the symmetric group acting on the integers in the list {\\em li},{} generators are the cycle given by {\\em li} and the 2-cycle {\\em (li.1,li.2)}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{symmetricGroup(n)} constructs the symmetric group {\\em Sn} acting on the integers 1,{}...,{}\\spad{n},{} generators are the {\\em n}-cycle {\\em (1,...,n)} and the 2-cycle {\\em (1,2)}."))) 
 NIL 
 NIL 
-(-830 -3094) 
+(-829 -3093) 
 ((|constructor| (NIL "Groebner functions for \\spad{P} \\spad{F} \\indented{2}{This package is an interface package to the groebner basis} package which allows you to compute groebner bases for polynomials in either lexicographic ordering or total degree ordering refined by reverse lex. The input is the ordinary polynomial type which is internally converted to a type with the required ordering. The resulting grobner basis is converted back to ordinary polynomials. The ordering among the variables is controlled by an explicit list of variables which is passed as a second argument. The coefficient domain is allowed to be any gcd domain,{} but the groebner basis is computed as if the polynomials were over a field.")) (|totalGroebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{totalGroebner(lp,lv)} computes Groebner basis for the list of polynomials \\spad{lp} with the terms ordered first by total degree and then refined by reverse lexicographic ordering. The variables are ordered by their position in the list \\spad{lv}.")) (|lexGroebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{lexGroebner(lp,lv)} computes Groebner basis for the list of polynomials \\spad{lp} in lexicographic order. The variables are ordered by their position in the list \\spad{lv}."))) 
 NIL 
 NIL 
-(-831) 
+(-830) 
 ((|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}."))) 
-(((-3999 "*") . T)) 
+(((-3998 "*") . T)) 
 NIL 
-(-832 R) 
+(-831 R) 
 ((|constructor| (NIL "\\indented{1}{Provides a coercion from the symbolic fractions in \\%\\spad{pi} with} integer coefficients to any Expression type. Date Created: 21 Feb 1990 Date Last Updated: 21 Feb 1990")) (|coerce| (((|Expression| |#1|) (|Pi|)) "\\spad{coerce(f)} returns \\spad{f} as an Expression(\\spad{R})."))) 
 NIL 
 NIL 
-(-833) 
+(-832) 
 ((|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)}"))) 
-((-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
 NIL 
-(-834 |xx| -3094) 
+(-833 |xx| -3093) 
 ((|constructor| (NIL "This package exports interpolation algorithms")) (|interpolate| (((|SparseUnivariatePolynomial| |#2|) (|List| |#2|) (|List| |#2|)) "\\spad{interpolate(lf,lg)} \\undocumented") (((|UnivariatePolynomial| |#1| |#2|) (|UnivariatePolynomial| |#1| |#2|) (|List| |#2|) (|List| |#2|)) "\\spad{interpolate(u,lf,lg)} \\undocumented"))) 
 NIL 
 NIL 
-(-835 -3094 P) 
+(-834 -3093 P) 
 ((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,l2)} \\undocumented"))) 
 NIL 
 NIL 
-(-836 R |Var| |Expon| GR) 
+(-835 R |Var| |Expon| GR) 
 ((|constructor| (NIL "Author: William Sit,{} spring 89")) (|inconsistent?| (((|Boolean|) (|List| (|Polynomial| |#1|))) "inconsistant?(pl) returns \\spad{true} if the system of equations \\spad{p} = 0 for \\spad{p} in pl is inconsistent. It is assumed that pl is a groebner basis.") (((|Boolean|) (|List| |#4|)) "inconsistant?(pl) returns \\spad{true} if the system of equations \\spad{p} = 0 for \\spad{p} in pl is inconsistent. It is assumed that pl is a groebner basis.")) (|sqfree| ((|#4| |#4|) "\\spad{sqfree(p)} returns the product of square free factors of \\spad{p}")) (|regime| (((|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))))) (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))) (|Matrix| |#4|) (|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|List| |#4|)) (|NonNegativeInteger|) (|NonNegativeInteger|) (|Integer|)) "\\spad{regime(y,c, w, p, r, rm, m)} returns a regime,{} a list of polynomials specifying the consistency conditions,{} a particular solution and basis representing the general solution of the parametric linear system \\spad{c} \\spad{z} = \\spad{w} on that regime. The regime returned depends on the subdeterminant \\spad{y}.det and the row and column indices. The solutions are simplified using the assumption that the system has rank \\spad{r} and maximum rank \\spad{rm}. The list \\spad{p} represents a list of list of factors of polynomials in a groebner basis of the ideal generated by higher order subdeterminants,{} and ius used for the simplification. The mode \\spad{m} distinguishes the cases when the system is homogeneous,{} or the right hand side is arbitrary,{} or when there is no new right hand side variables.")) (|redmat| (((|Matrix| |#4|) (|Matrix| |#4|) (|List| |#4|)) "\\spad{redmat(m,g)} returns a matrix whose entries are those of \\spad{m} modulo the ideal generated by the groebner basis \\spad{g}")) (|ParCond| (((|List| (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|))))) (|Matrix| |#4|) (|NonNegativeInteger|)) "\\spad{ParCond(m,k)} returns the list of all \\spad{k} by \\spad{k} subdeterminants in the matrix \\spad{m}")) (|overset?| (((|Boolean|) (|List| |#4|) (|List| (|List| |#4|))) "\\spad{overset?(s,sl)} returns \\spad{true} if \\spad{s} properly a sublist of a member of \\spad{sl}; otherwise it returns \\spad{false}")) (|nextSublist| (((|List| (|List| (|Integer|))) (|Integer|) (|Integer|)) "\\spad{nextSublist(n,k)} returns a list of \\spad{k}-subsets of {1,{} ...,{} \\spad{n}}.")) (|minset| (((|List| (|List| |#4|)) (|List| (|List| |#4|))) "\\spad{minset(sl)} returns the sublist of \\spad{sl} consisting of the minimal lists (with respect to inclusion) in the list \\spad{sl} of lists")) (|minrank| (((|NonNegativeInteger|) (|List| (|Record| (|:| |rank| (|NonNegativeInteger|)) (|:| |eqns| (|List| (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))))) (|:| |fgb| (|List| |#4|))))) "\\spad{minrank(r)} returns the minimum rank in the list \\spad{r} of regimes")) (|maxrank| (((|NonNegativeInteger|) (|List| (|Record| (|:| |rank| (|NonNegativeInteger|)) (|:| |eqns| (|List| (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))))) (|:| |fgb| (|List| |#4|))))) "\\spad{maxrank(r)} returns the maximum rank in the list \\spad{r} of regimes")) (|factorset| (((|List| |#4|) |#4|) "\\spad{factorset(p)} returns the set of irreducible factors of \\spad{p}.")) (|B1solve| (((|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))) (|Record| (|:| |mat| (|Matrix| (|Fraction| (|Polynomial| |#1|)))) (|:| |vec| (|List| (|Fraction| (|Polynomial| |#1|)))) (|:| |rank| (|NonNegativeInteger|)) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|))))) "\\spad{B1solve(s)} solves the system (\\spad{s}.mat) \\spad{z} = \\spad{s}.vec for the variables given by the column indices of \\spad{s}.cols in terms of the other variables and the right hand side \\spad{s}.vec by assuming that the rank is \\spad{s}.rank,{} that the system is consistent,{} with the linearly independent equations indexed by the given row indices \\spad{s}.rows; the coefficients in \\spad{s}.mat involving parameters are treated as polynomials. B1solve(\\spad{s}) returns a particular solution to the system and a basis of the homogeneous system (\\spad{s}.mat) \\spad{z} = 0.")) (|redpps| (((|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))) (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))) (|List| |#4|)) "\\spad{redpps(s,g)} returns the simplified form of \\spad{s} after reducing modulo a groebner basis \\spad{g}")) (|ParCondList| (((|List| (|Record| (|:| |rank| (|NonNegativeInteger|)) (|:| |eqns| (|List| (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))))) (|:| |fgb| (|List| |#4|)))) (|Matrix| |#4|) (|NonNegativeInteger|)) "\\spad{ParCondList(c,r)} computes a list of subdeterminants of each rank >= \\spad{r} of the matrix \\spad{c} and returns a groebner basis for the ideal they generate")) (|hasoln| (((|Record| (|:| |sysok| (|Boolean|)) (|:| |z0| (|List| |#4|)) (|:| |n0| (|List| |#4|))) (|List| |#4|) (|List| |#4|)) "\\spad{hasoln(g, l)} tests whether the quasi-algebraic set defined by \\spad{p} = 0 for \\spad{p} in \\spad{g} and \\spad{q} ~= 0 for \\spad{q} in \\spad{l} is empty or not and returns a simplified definition of the quasi-algebraic set")) (|pr2dmp| ((|#4| (|Polynomial| |#1|)) "\\spad{pr2dmp(p)} converts \\spad{p} to target domain")) (|se2rfi| (((|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|Symbol|))) "\\spad{se2rfi(l)} converts \\spad{l} to target domain")) (|dmp2rfi| (((|List| (|Fraction| (|Polynomial| |#1|))) (|List| |#4|)) "\\spad{dmp2rfi(l)} converts \\spad{l} to target domain") (((|Matrix| (|Fraction| (|Polynomial| |#1|))) (|Matrix| |#4|)) "\\spad{dmp2rfi(m)} converts \\spad{m} to target domain") (((|Fraction| (|Polynomial| |#1|)) |#4|) "\\spad{dmp2rfi(p)} converts \\spad{p} to target domain")) (|bsolve| (((|Record| (|:| |rgl| (|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))))))) (|:| |rgsz| (|Integer|))) (|Matrix| |#4|) (|List| (|Fraction| (|Polynomial| |#1|))) (|NonNegativeInteger|) (|String|) (|Integer|)) "\\spad{bsolve(c, w, r, s, m)} returns a list of regimes and solutions of the system \\spad{c} \\spad{z} = \\spad{w} for ranks at least \\spad{r}; depending on the mode \\spad{m} chosen,{} it writes the output to a file given by the string \\spad{s}.")) (|rdregime| (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|String|)) "\\spad{rdregime(s)} reads in a list from a file with name \\spad{s}")) (|wrregime| (((|Integer|) (|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|String|)) "\\spad{wrregime(l,s)} writes a list of regimes to a file named \\spad{s} and returns the number of regimes written")) (|psolve| (((|Integer|) (|Matrix| |#4|) (|PositiveInteger|) (|String|)) "\\spad{psolve(c,k,s)} solves \\spad{c} \\spad{z} = 0 for all possible ranks >= \\spad{k} of the matrix \\spad{c},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|List| (|Symbol|)) (|PositiveInteger|) (|String|)) "\\spad{psolve(c,w,k,s)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks >= \\spad{k} of the matrix \\spad{c} and indeterminate right hand side \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|List| |#4|) (|PositiveInteger|) (|String|)) "\\spad{psolve(c,w,k,s)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks >= \\spad{k} of the matrix \\spad{c} and given right hand side \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|String|)) "\\spad{psolve(c,s)} solves \\spad{c} \\spad{z} = 0 for all possible ranks of the matrix \\spad{c} and given right hand side vector \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|List| (|Symbol|)) (|String|)) "\\spad{psolve(c,w,s)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks of the matrix \\spad{c} and indeterminate right hand side \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|List| |#4|) (|String|)) "\\spad{psolve(c,w,s)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks of the matrix \\spad{c} and given right hand side vector \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|PositiveInteger|)) "\\spad{psolve(c)} solves the homogeneous linear system \\spad{c} \\spad{z} = 0 for all possible ranks >= \\spad{k} of the matrix \\spad{c}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|List| (|Symbol|)) (|PositiveInteger|)) "\\spad{psolve(c,w,k)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks >= \\spad{k} of the matrix \\spad{c} and indeterminate right hand side \\spad{w}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|List| |#4|) (|PositiveInteger|)) "\\spad{psolve(c,w,k)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks >= \\spad{k} of the matrix \\spad{c} and given right hand side vector \\spad{w}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|)) "\\spad{psolve(c)} solves the homogeneous linear system \\spad{c} \\spad{z} = 0 for all possible ranks of the matrix \\spad{c}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|List| (|Symbol|))) "\\spad{psolve(c,w)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks of the matrix \\spad{c} and indeterminate right hand side \\spad{w}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|List| |#4|)) "\\spad{psolve(c,w)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks of the matrix \\spad{c} and given right hand side vector \\spad{w}"))) 
 NIL 
 NIL 
-(-837) 
+(-836) 
 ((|constructor| (NIL "The Plot domain supports plotting of functions defined over a real number system. A real number system is a model for the real numbers and as such may be an approximation. For example floating point numbers and infinite continued fractions. The facilities at this point are limited to 2-dimensional plots or either a single function or a parametric function.")) (|debug| (((|Boolean|) (|Boolean|)) "\\spad{debug(true)} turns debug mode on \\spad{debug(false)} turns debug mode off")) (|numFunEvals| (((|Integer|)) "\\spad{numFunEvals()} returns the number of points computed")) (|setAdaptive| (((|Boolean|) (|Boolean|)) "\\spad{setAdaptive(true)} turns adaptive plotting on \\spad{setAdaptive(false)} turns adaptive plotting off")) (|adaptive?| (((|Boolean|)) "\\spad{adaptive?()} determines whether plotting be done adaptively")) (|setScreenResolution| (((|Integer|) (|Integer|)) "\\spad{setScreenResolution(i)} sets the screen resolution to \\spad{i}")) (|screenResolution| (((|Integer|)) "\\spad{screenResolution()} returns the screen resolution")) (|setMaxPoints| (((|Integer|) (|Integer|)) "\\spad{setMaxPoints(i)} sets the maximum number of points in a plot to \\spad{i}")) (|maxPoints| (((|Integer|)) "\\spad{maxPoints()} returns the maximum number of points in a plot")) (|setMinPoints| (((|Integer|) (|Integer|)) "\\spad{setMinPoints(i)} sets the minimum number of points in a plot to \\spad{i}")) (|minPoints| (((|Integer|)) "\\spad{minPoints()} returns the minimum number of points in a plot")) (|tRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{tRange(p)} returns the range of the parameter in a parametric plot \\spad{p}")) (|refine| (($ $) "\\spad{refine(p)} performs a refinement on the plot \\spad{p}") (($ $ (|Segment| (|DoubleFloat|))) "\\spad{refine(x,r)} \\undocumented")) (|zoom| (($ $ (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{zoom(x,r,s)} \\undocumented") (($ $ (|Segment| (|DoubleFloat|))) "\\spad{zoom(x,r)} \\undocumented")) (|parametric?| (((|Boolean|) $) "\\spad{parametric? determines} whether it is a parametric plot?")) (|plotPolar| (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) "\\spad{plotPolar(f)} plots the polar curve \\spad{r = f(theta)} as theta ranges over the interval \\spad{[0,2*\\%pi]}; this is the same as the parametric curve \\spad{x = f(t) * cos(t)},{} \\spad{y = f(t) * sin(t)}.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plotPolar(f,a..b)} plots the polar curve \\spad{r = f(theta)} as theta ranges over the interval \\spad{[a,b]}; this is the same as the parametric curve \\spad{x = f(t) * cos(t)},{} \\spad{y = f(t) * sin(t)}.")) (|pointPlot| (($ (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{pointPlot(t +-> (f(t),g(t)),a..b,c..d,e..f)} plots the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over the interval \\spad{[a,b]}; \\spad{x}-range of \\spad{[c,d]} and \\spad{y}-range of \\spad{[e,f]} are noted in Plot object.") (($ (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{pointPlot(t +-> (f(t),g(t)),a..b)} plots the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over the interval \\spad{[a,b]}.")) (|plot| (($ $ (|Segment| (|DoubleFloat|))) "\\spad{plot(x,r)} \\undocumented") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,g,a..b,c..d,e..f)} plots the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over the interval \\spad{[a,b]}; \\spad{x}-range of \\spad{[c,d]} and \\spad{y}-range of \\spad{[e,f]} are noted in Plot object.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,g,a..b)} plots the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over the interval \\spad{[a,b]}.") (($ (|List| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot([f1,...,fm],a..b,c..d)} plots the functions \\spad{y = f1(x)},{}...,{} \\spad{y = fm(x)} on the interval \\spad{a..b}; \\spad{y}-range of \\spad{[c,d]} is noted in Plot object.") (($ (|List| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|DoubleFloat|))) "\\spad{plot([f1,...,fm],a..b)} plots the functions \\spad{y = f1(x)},{}...,{} \\spad{y = fm(x)} on the interval \\spad{a..b}.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,a..b,c..d)} plots the function \\spad{f(x)} on the interval \\spad{[a,b]}; \\spad{y}-range of \\spad{[c,d]} is noted in Plot object.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,a..b)} plots the function \\spad{f(x)} on the interval \\spad{[a,b]}."))) 
 NIL 
 NIL 
-(-838 S) 
+(-837 S) 
 ((|constructor| (NIL "\\spad{PlotFunctions1} provides facilities for plotting curves where functions SF -> SF are specified by giving an expression")) (|plotPolar| (((|Plot|) |#1| (|Symbol|)) "\\spad{plotPolar(f,theta)} plots the graph of \\spad{r = f(theta)} as \\spad{theta} ranges from 0 to 2 \\spad{pi}") (((|Plot|) |#1| (|Symbol|) (|Segment| (|DoubleFloat|))) "\\spad{plotPolar(f,theta,seg)} plots the graph of \\spad{r = f(theta)} as \\spad{theta} ranges over an interval")) (|plot| (((|Plot|) |#1| |#1| (|Symbol|) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,g,t,seg)} plots the graph of \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over an interval.") (((|Plot|) |#1| (|Symbol|) (|Segment| (|DoubleFloat|))) "\\spad{plot(fcn,x,seg)} plots the graph of \\spad{y = f(x)} on a interval"))) 
 NIL 
 NIL 
-(-839) 
+(-838) 
 ((|constructor| (NIL "Plot3D supports parametric plots defined over a real number system. A real number system is a model for the real numbers and as such may be an approximation. For example,{} floating point numbers and infinite continued fractions are real number systems. The facilities at this point are limited to 3-dimensional parametric plots.")) (|debug3D| (((|Boolean|) (|Boolean|)) "\\spad{debug3D(true)} turns debug mode on; debug3D(\\spad{false}) turns debug mode off.")) (|numFunEvals3D| (((|Integer|)) "\\spad{numFunEvals3D()} returns the number of points computed.")) (|setAdaptive3D| (((|Boolean|) (|Boolean|)) "\\spad{setAdaptive3D(true)} turns adaptive plotting on; setAdaptive3D(\\spad{false}) turns adaptive plotting off.")) (|adaptive3D?| (((|Boolean|)) "\\spad{adaptive3D?()} determines whether plotting be done adaptively.")) (|setScreenResolution3D| (((|Integer|) (|Integer|)) "\\spad{setScreenResolution3D(i)} sets the screen resolution for a 3d graph to \\spad{i}.")) (|screenResolution3D| (((|Integer|)) "\\spad{screenResolution3D()} returns the screen resolution for a 3d graph.")) (|setMaxPoints3D| (((|Integer|) (|Integer|)) "\\spad{setMaxPoints3D(i)} sets the maximum number of points in a plot to \\spad{i}.")) (|maxPoints3D| (((|Integer|)) "\\spad{maxPoints3D()} returns the maximum number of points in a plot.")) (|setMinPoints3D| (((|Integer|) (|Integer|)) "\\spad{setMinPoints3D(i)} sets the minimum number of points in a plot to \\spad{i}.")) (|minPoints3D| (((|Integer|)) "\\spad{minPoints3D()} returns the minimum number of points in a plot.")) (|tValues| (((|List| (|List| (|DoubleFloat|))) $) "\\spad{tValues(p)} returns a list of lists of the values of the parameter for which a point is computed,{} one list for each curve in the plot \\spad{p}.")) (|tRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{tRange(p)} returns the range of the parameter in a parametric plot \\spad{p}.")) (|refine| (($ $) "\\spad{refine(x)} \\undocumented") (($ $ (|Segment| (|DoubleFloat|))) "\\spad{refine(x,r)} \\undocumented")) (|zoom| (($ $ (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{zoom(x,r,s,t)} \\undocumented")) (|plot| (($ $ (|Segment| (|DoubleFloat|))) "\\spad{plot(x,r)} \\undocumented") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f1,f2,f3,f4,x,y,z,w)} \\undocumented") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,g,h,a..b)} plots {/emx = \\spad{f}(\\spad{t}),{} \\spad{y} = \\spad{g}(\\spad{t}),{} \\spad{z} = \\spad{h}(\\spad{t})} as \\spad{t} ranges over {/em[a,{}\\spad{b}]}.")) (|pointPlot| (($ (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{pointPlot(f,x,y,z,w)} \\undocumented") (($ (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{pointPlot(f,g,h,a..b)} plots {/emx = \\spad{f}(\\spad{t}),{} \\spad{y} = \\spad{g}(\\spad{t}),{} \\spad{z} = \\spad{h}(\\spad{t})} as \\spad{t} ranges over {/em[a,{}\\spad{b}]}."))) 
 NIL 
 NIL 
-(-840) 
+(-839) 
 ((|constructor| (NIL "This package exports plotting tools")) (|calcRanges| (((|List| (|Segment| (|DoubleFloat|))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{calcRanges(l)} \\undocumented"))) 
 NIL 
 NIL 
-(-841) 
+(-840) 
 ((|constructor| (NIL "Attaching assertions to symbols for pattern matching. Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|multiple| (((|Expression| (|Integer|)) (|Symbol|)) "\\spad{multiple(x)} tells the pattern matcher that \\spad{x} should preferably match a multi-term quantity in a sum or product. For matching on lists,{} multiple(\\spad{x}) tells the pattern matcher that \\spad{x} should match a list instead of an element of a list.")) (|optional| (((|Expression| (|Integer|)) (|Symbol|)) "\\spad{optional(x)} tells the pattern matcher that \\spad{x} can match an identity (0 in a sum,{} 1 in a product or exponentiation)..")) (|constant| (((|Expression| (|Integer|)) (|Symbol|)) "\\spad{constant(x)} tells the pattern matcher that \\spad{x} should match only the symbol 'x and no other quantity.")) (|assert| (((|Expression| (|Integer|)) (|Symbol|) (|Identifier|)) "\\spad{assert(x, s)} makes the assertion \\spad{s} about \\spad{x}."))) 
 NIL 
 NIL 
-(-842 R -3094) 
+(-841 R -3093) 
 ((|constructor| (NIL "Attaching assertions to symbols for pattern matching; Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|multiple| ((|#2| |#2|) "\\spad{multiple(x)} tells the pattern matcher that \\spad{x} should preferably match a multi-term quantity in a sum or product. For matching on lists,{} multiple(\\spad{x}) tells the pattern matcher that \\spad{x} should match a list instead of an element of a list. Error: if \\spad{x} is not a symbol.")) (|optional| ((|#2| |#2|) "\\spad{optional(x)} tells the pattern matcher that \\spad{x} can match an identity (0 in a sum,{} 1 in a product or exponentiation). Error: if \\spad{x} is not a symbol.")) (|constant| ((|#2| |#2|) "\\spad{constant(x)} tells the pattern matcher that \\spad{x} should match only the symbol 'x and no other quantity. Error: if \\spad{x} is not a symbol.")) (|assert| ((|#2| |#2| (|Identifier|)) "\\spad{assert(x, s)} makes the assertion \\spad{s} about \\spad{x}. Error: if \\spad{x} is not a symbol."))) 
 NIL 
 NIL 
-(-843 S A B) 
+(-842 S A B) 
 ((|constructor| (NIL "This packages provides tools for matching recursively in type towers.")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#2| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(expr, pat, res)} matches the pattern \\spad{pat} to the expression \\spad{expr}; res contains the variables of \\spad{pat} which are already matched and their matches. Note: this function handles type towers by changing the predicates and calling the matching function provided by \\spad{A}.")) (|fixPredicate| (((|Mapping| (|Boolean|) |#2|) (|Mapping| (|Boolean|) |#3|)) "\\spad{fixPredicate(f)} returns \\spad{g} defined by \\spad{g}(a) = \\spad{f}(a::B)."))) 
 NIL 
 NIL 
-(-844 S R -3094) 
+(-843 S R -3093) 
 ((|constructor| (NIL "This package provides pattern matching functions on function spaces.")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(expr, pat, res)} matches the pattern \\spad{pat} to the expression \\spad{expr}; res contains the variables of \\spad{pat} which are already matched and their matches."))) 
 NIL 
 NIL 
-(-845 I) 
+(-844 I) 
 ((|constructor| (NIL "This package provides pattern matching functions on integers.")) (|patternMatch| (((|PatternMatchResult| (|Integer|) |#1|) |#1| (|Pattern| (|Integer|)) (|PatternMatchResult| (|Integer|) |#1|)) "\\spad{patternMatch(n, pat, res)} matches the pattern \\spad{pat} to the integer \\spad{n}; res contains the variables of \\spad{pat} which are already matched and their matches."))) 
 NIL 
 NIL 
-(-846 S E) 
+(-845 S E) 
 ((|constructor| (NIL "This package provides pattern matching functions on kernels.")) (|patternMatch| (((|PatternMatchResult| |#1| |#2|) (|Kernel| |#2|) (|Pattern| |#1|) (|PatternMatchResult| |#1| |#2|)) "\\spad{patternMatch(f(e1,...,en), pat, res)} matches the pattern \\spad{pat} to \\spad{f(e1,...,en)}; res contains the variables of \\spad{pat} which are already matched and their matches."))) 
 NIL 
 NIL 
-(-847 S R L) 
+(-846 S R L) 
 ((|constructor| (NIL "This package provides pattern matching functions on lists.")) (|patternMatch| (((|PatternMatchListResult| |#1| |#2| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchListResult| |#1| |#2| |#3|)) "\\spad{patternMatch(l, pat, res)} matches the pattern \\spad{pat} to the list \\spad{l}; res contains the variables of \\spad{pat} which are already matched and their matches."))) 
 NIL 
 NIL 
-(-848 S E V R P) 
+(-847 S E V R P) 
 ((|constructor| (NIL "This package provides pattern matching functions on polynomials.")) (|patternMatch| (((|PatternMatchResult| |#1| |#5|) |#5| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|)) "\\spad{patternMatch(p, pat, res)} matches the pattern \\spad{pat} to the polynomial \\spad{p}; res contains the variables of \\spad{pat} which are already matched and their matches.") (((|PatternMatchResult| |#1| |#5|) |#5| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|) (|Mapping| (|PatternMatchResult| |#1| |#5|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|))) "\\spad{patternMatch(p, pat, res, vmatch)} matches the pattern \\spad{pat} to the polynomial \\spad{p}. \\spad{res} contains the variables of \\spad{pat} which are already matched and their matches; vmatch is the matching function to use on the variables."))) 
 NIL 
-((|HasCategory| |#3| (|%list| (QUOTE -797) (|devaluate| |#1|)))) 
-(-849 -2671) 
+((|HasCategory| |#3| (|%list| (QUOTE -796) (|devaluate| |#1|)))) 
+(-848 -2670) 
 ((|constructor| (NIL "Attaching predicates to symbols for pattern matching. Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|suchThat| (((|Expression| (|Integer|)) (|Symbol|) (|List| (|Mapping| (|Boolean|) |#1|))) "\\spad{suchThat(x, [f1, f2, ..., fn])} attaches the predicate \\spad{f1} and \\spad{f2} and ... and fn to \\spad{x}.") (((|Expression| (|Integer|)) (|Symbol|) (|Mapping| (|Boolean|) |#1|)) "\\spad{suchThat(x, foo)} attaches the predicate foo to \\spad{x}."))) 
 NIL 
 NIL 
-(-850 R -3094 -2671) 
+(-849 R -3093 -2670) 
 ((|constructor| (NIL "Attaching predicates to symbols for pattern matching. Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|suchThat| ((|#2| |#2| (|List| (|Mapping| (|Boolean|) |#3|))) "\\spad{suchThat(x, [f1, f2, ..., fn])} attaches the predicate \\spad{f1} and \\spad{f2} and ... and fn to \\spad{x}. Error: if \\spad{x} is not a symbol.") ((|#2| |#2| (|Mapping| (|Boolean|) |#3|)) "\\spad{suchThat(x, foo)} attaches the predicate foo to \\spad{x}; error if \\spad{x} is not a symbol."))) 
 NIL 
 NIL 
-(-851 S R Q) 
+(-850 S R Q) 
 ((|constructor| (NIL "This package provides pattern matching functions on quotients.")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(a/b, pat, res)} matches the pattern \\spad{pat} to the quotient \\spad{a/b}; res contains the variables of \\spad{pat} which are already matched and their matches."))) 
 NIL 
 NIL 
-(-852 S) 
+(-851 S) 
 ((|constructor| (NIL "This package provides pattern matching functions on symbols.")) (|patternMatch| (((|PatternMatchResult| |#1| (|Symbol|)) (|Symbol|) (|Pattern| |#1|) (|PatternMatchResult| |#1| (|Symbol|))) "\\spad{patternMatch(expr, pat, res)} matches the pattern \\spad{pat} to the expression \\spad{expr}; res contains the variables of \\spad{pat} which are already matched and their matches (necessary for recursion)."))) 
 NIL 
 NIL 
-(-853 S R P) 
+(-852 S R P) 
 ((|constructor| (NIL "This package provides tools for the pattern matcher.")) (|patternMatchTimes| (((|PatternMatchResult| |#1| |#3|) (|List| |#3|) (|List| (|Pattern| |#1|)) (|PatternMatchResult| |#1| |#3|) (|Mapping| (|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|))) "\\spad{patternMatchTimes(lsubj, lpat, res, match)} matches the product of patterns \\spad{reduce(*,lpat)} to the product of subjects \\spad{reduce(*,lsubj)}; \\spad{r} contains the previous matches and match is a pattern-matching function on \\spad{P}.")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) (|List| |#3|) (|List| (|Pattern| |#1|)) (|Mapping| |#3| (|List| |#3|)) (|PatternMatchResult| |#1| |#3|) (|Mapping| (|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|))) "\\spad{patternMatch(lsubj, lpat, op, res, match)} matches the list of patterns \\spad{lpat} to the list of subjects \\spad{lsubj},{} allowing for commutativity; \\spad{op} is the operator such that \\spad{op}(\\spad{lpat}) should match \\spad{op}(\\spad{lsubj}) at the end,{} \\spad{r} contains the previous matches,{} and match is a pattern-matching function on \\spad{P}."))) 
 NIL 
 NIL 
-(-854) 
+(-853) 
 ((|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 
-(-855 R) 
+(-854 R) 
 ((|constructor| (NIL "This domain implements points in coordinate space"))) 
-((-3998 . T)) 
-((OR (-12 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (OR (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-757))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-72))) (|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 (-1014))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|))) (|HasCategory| $ (|%list| (QUOTE -1036) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| $ (|%list| (QUOTE -1036) (|devaluate| |#1|))))) 
-(-856 |lv| R) 
+((-3997 . T)) 
+((OR (-12 (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-553 (-473)))) (OR (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-756))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| (-484) (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-72))) (|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 (-1013))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|))) (|HasCategory| $ (|%list| (QUOTE -1035) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| $ (|%list| (QUOTE -1035) (|devaluate| |#1|))))) 
+(-855 |lv| R) 
 ((|constructor| (NIL "Package with the conversion functions among different kind of polynomials")) (|pToDmp| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|Polynomial| |#2|)) "\\spad{pToDmp(p)} converts \\spad{p} from a \\spadtype{POLY} to a \\spadtype{DMP}.")) (|dmpToP| (((|Polynomial| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{dmpToP(p)} converts \\spad{p} from a \\spadtype{DMP} to a \\spadtype{POLY}.")) (|hdmpToP| (((|Polynomial| |#2|) (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{hdmpToP(p)} converts \\spad{p} from a \\spadtype{HDMP} to a \\spadtype{POLY}.")) (|pToHdmp| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|Polynomial| |#2|)) "\\spad{pToHdmp(p)} converts \\spad{p} from a \\spadtype{POLY} to a \\spadtype{HDMP}.")) (|hdmpToDmp| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{hdmpToDmp(p)} converts \\spad{p} from a \\spadtype{HDMP} to a \\spadtype{DMP}.")) (|dmpToHdmp| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{dmpToHdmp(p)} converts \\spad{p} from a \\spadtype{DMP} to a \\spadtype{HDMP}."))) 
 NIL 
 NIL 
-(-857 |TheField| |ThePols|) 
+(-856 |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 (-756)))) 
-(-858 R) 
+((|HasCategory| |#1| (QUOTE (-755)))) 
+(-857 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}."))) 
-(((-3999 "*") |has| |#1| (-146)) (-3990 |has| |#1| (-496)) (-3995 |has| |#1| (-6 -3995)) (-3992 . T) (-3991 . T) (-3994 . T)) 
-((|HasCategory| |#1| (QUOTE (-822))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-822)))) (OR (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-822)))) (OR (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-822)))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (-12 (|HasCategory| |#1| (QUOTE (-797 (-330)))) (|HasCategory| (-1091) (QUOTE (-797 (-330))))) (-12 (|HasCategory| |#1| (QUOTE (-797 (-485)))) (|HasCategory| (-1091) (QUOTE (-797 (-485))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-330))))) (|HasCategory| (-1091) (QUOTE (-554 (-801 (-330)))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-485))))) (|HasCategory| (-1091) (QUOTE (-554 (-801 (-485)))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-474)))) (|HasCategory| (-1091) (QUOTE (-554 (-474))))) (|HasCategory| |#1| (QUOTE (-581 (-485)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485)))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-312))) (|HasAttribute| |#1| (QUOTE -3995)) (|HasCategory| |#1| (QUOTE (-392))) (-12 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) 
-(-859 R S) 
+(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-495)) (-3994 |has| |#1| (-6 -3994)) (-3991 . T) (-3990 . T) (-3993 . T)) 
+((|HasCategory| |#1| (QUOTE (-821))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-821)))) (OR (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-821)))) (OR (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-821)))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-495)))) (-12 (|HasCategory| |#1| (QUOTE (-796 (-330)))) (|HasCategory| (-1090) (QUOTE (-796 (-330))))) (-12 (|HasCategory| |#1| (QUOTE (-796 (-484)))) (|HasCategory| (-1090) (QUOTE (-796 (-484))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-800 (-330))))) (|HasCategory| (-1090) (QUOTE (-553 (-800 (-330)))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-800 (-484))))) (|HasCategory| (-1090) (QUOTE (-553 (-800 (-484)))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-473)))) (|HasCategory| (-1090) (QUOTE (-553 (-473))))) (|HasCategory| |#1| (QUOTE (-580 (-484)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-484)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484)))))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-312))) (|HasAttribute| |#1| (QUOTE -3994)) (|HasCategory| |#1| (QUOTE (-392))) (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) 
+(-858 R S) 
 ((|constructor| (NIL "\\indented{2}{This package takes a mapping between coefficient rings,{} and lifts} it to a mapping between polynomials over those rings.")) (|map| (((|Polynomial| |#2|) (|Mapping| |#2| |#1|) (|Polynomial| |#1|)) "\\spad{map(f, p)} produces a new polynomial as a result of applying the function \\spad{f} to every coefficient of the polynomial \\spad{p}."))) 
 NIL 
 NIL 
-(-860 |x| R) 
+(-859 |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 
-(-861 S R E |VarSet|) 
+(-860 S R E |VarSet|) 
 ((|constructor| (NIL "The category for general multi-variate polynomials over a ring \\spad{R},{} in variables from VarSet,{} with exponents from the \\spadtype{OrderedAbelianMonoidSup}.")) (|canonicalUnitNormal| ((|attribute|) "we can choose a unique representative for each associate class. This normalization is chosen to be normalization of leading coefficient (by default).")) (|squareFreePart| (($ $) "\\spad{squareFreePart(p)} returns product of all the irreducible factors of polynomial \\spad{p} each taken with multiplicity one.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(p)} returns the square free factorization of the polynomial \\spad{p}.")) (|primitivePart| (($ $ |#4|) "\\spad{primitivePart(p,v)} returns the unitCanonical associate of the polynomial \\spad{p} with its content with respect to the variable \\spad{v} divided out.") (($ $) "\\spad{primitivePart(p)} returns the unitCanonical associate of the polynomial \\spad{p} with its content divided out.")) (|content| (($ $ |#4|) "\\spad{content(p,v)} is the gcd of the coefficients of the polynomial \\spad{p} when \\spad{p} is viewed as a univariate polynomial with respect to the variable \\spad{v}. Thus,{} for polynomial 7*x**2*y + 14*x*y**2,{} the gcd of the coefficients with respect to \\spad{x} is 7*y.")) (|discriminant| (($ $ |#4|) "\\spad{discriminant(p,v)} returns the disriminant of the polynomial \\spad{p} with respect to the variable \\spad{v}.")) (|resultant| (($ $ $ |#4|) "\\spad{resultant(p,q,v)} returns the resultant of the polynomials \\spad{p} and \\spad{q} with respect to the variable \\spad{v}.")) (|primitiveMonomials| (((|List| $) $) "\\spad{primitiveMonomials(p)} gives the list of monomials of the polynomial \\spad{p} with their coefficients removed. Note: \\spad{primitiveMonomials(sum(a_(i) X^(i))) = [X^(1),...,X^(n)]}.")) (|variables| (((|List| |#4|) $) "\\spad{variables(p)} returns the list of those variables actually appearing in the polynomial \\spad{p}.")) (|totalDegree| (((|NonNegativeInteger|) $ (|List| |#4|)) "\\spad{totalDegree(p, lv)} returns the maximum sum (over all monomials of polynomial \\spad{p}) of the variables in the list lv.") (((|NonNegativeInteger|) $) "\\spad{totalDegree(p)} returns the largest sum over all monomials of all exponents of a monomial.")) (|isExpt| (((|Union| (|Record| (|:| |var| |#4|) (|:| |exponent| (|NonNegativeInteger|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x, n]} if polynomial \\spad{p} has the form \\spad{x**n} and \\spad{n > 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if polynomial \\spad{p = a1 ... an} and \\spad{n >= 2},{} and,{} for each \\spad{i},{} \\spad{ai} is either a nontrivial constant in \\spad{R} or else of the form \\spad{x**e},{} where \\spad{e > 0} is an integer and \\spad{x} in a member of VarSet.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,...,mn]} if polynomial \\spad{p = m1 + ... + mn} and \\spad{n >= 2} and each \\spad{mi} is a nonzero monomial.")) (|multivariate| (($ (|SparseUnivariatePolynomial| $) |#4|) "\\spad{multivariate(sup,v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.") (($ (|SparseUnivariatePolynomial| |#2|) |#4|) "\\spad{multivariate(sup,v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.")) (|monomial| (($ $ (|List| |#4|) (|List| (|NonNegativeInteger|))) "\\spad{monomial(a,[v1..vn],[e1..en])} returns \\spad{a*prod(vi**ei)}.") (($ $ |#4| (|NonNegativeInteger|)) "\\spad{monomial(a,x,n)} creates the monomial \\spad{a*x**n} where \\spad{a} is a polynomial,{} \\spad{x} is a variable and \\spad{n} is a nonnegative integer.")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $ |#4|) "\\spad{monicDivide(a,b,v)} divides the polynomial a by the polynomial \\spad{b},{} with each viewed as a univariate polynomial in \\spad{v} returning both the quotient and remainder. Error: if \\spad{b} is not monic with respect to \\spad{v}.")) (|minimumDegree| (((|List| (|NonNegativeInteger|)) $ (|List| |#4|)) "\\spad{minimumDegree(p, lv)} gives the list of minimum degrees of the polynomial \\spad{p} with respect to each of the variables in the list lv") (((|NonNegativeInteger|) $ |#4|) "\\spad{minimumDegree(p,v)} gives the minimum degree of polynomial \\spad{p} with respect to \\spad{v},{} \\spadignore{i.e.} viewed a univariate polynomial in \\spad{v}")) (|mainVariable| (((|Union| |#4| "failed") $) "\\spad{mainVariable(p)} returns the biggest variable which actually occurs in the polynomial \\spad{p},{} or \"failed\" if no variables are present. fails precisely if polynomial satisfies ground?")) (|univariate| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{univariate(p)} converts the multivariate polynomial \\spad{p},{} which should actually involve only one variable,{} into a univariate polynomial in that variable,{} whose coefficients are in the ground ring. Error: if polynomial is genuinely multivariate") (((|SparseUnivariatePolynomial| $) $ |#4|) "\\spad{univariate(p,v)} converts the multivariate polynomial \\spad{p} into a univariate polynomial in \\spad{v},{} whose coefficients are still multivariate polynomials (in all the other variables).")) (|monomials| (((|List| $) $) "\\spad{monomials(p)} returns the list of non-zero monomials of polynomial \\spad{p},{} \\spadignore{i.e.} \\spad{monomials(sum(a_(i) X^(i))) = [a_(1) X^(1),...,a_(n) X^(n)]}.")) (|coefficient| (($ $ (|List| |#4|) (|List| (|NonNegativeInteger|))) "\\spad{coefficient(p, lv, ln)} views the polynomial \\spad{p} as a polynomial in the variables of \\spad{lv} and returns the coefficient of the term \\spad{lv**ln},{} \\spadignore{i.e.} \\spad{prod(lv_i ** ln_i)}.") (($ $ |#4| (|NonNegativeInteger|)) "\\spad{coefficient(p,v,n)} views the polynomial \\spad{p} as a univariate polynomial in \\spad{v} and returns the coefficient of the \\spad{v**n} term.")) (|degree| (((|List| (|NonNegativeInteger|)) $ (|List| |#4|)) "\\spad{degree(p,lv)} gives the list of degrees of polynomial \\spad{p} with respect to each of the variables in the list \\spad{lv}.") (((|NonNegativeInteger|) $ |#4|) "\\spad{degree(p,v)} gives the degree of polynomial \\spad{p} with respect to the variable \\spad{v}."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-822))) (|HasAttribute| |#2| (QUOTE -3995)) (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#4| (QUOTE (-797 (-330)))) (|HasCategory| |#2| (QUOTE (-797 (-330)))) (|HasCategory| |#4| (QUOTE (-797 (-485)))) (|HasCategory| |#2| (QUOTE (-797 (-485)))) (|HasCategory| |#4| (QUOTE (-554 (-801 (-330))))) (|HasCategory| |#2| (QUOTE (-554 (-801 (-330))))) (|HasCategory| |#4| (QUOTE (-554 (-801 (-485))))) (|HasCategory| |#2| (QUOTE (-554 (-801 (-485))))) (|HasCategory| |#4| (QUOTE (-554 (-474)))) (|HasCategory| |#2| (QUOTE (-554 (-474))))) 
-(-862 R E |VarSet|) 
+((|HasCategory| |#2| (QUOTE (-821))) (|HasAttribute| |#2| (QUOTE -3994)) (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#4| (QUOTE (-796 (-330)))) (|HasCategory| |#2| (QUOTE (-796 (-330)))) (|HasCategory| |#4| (QUOTE (-796 (-484)))) (|HasCategory| |#2| (QUOTE (-796 (-484)))) (|HasCategory| |#4| (QUOTE (-553 (-800 (-330))))) (|HasCategory| |#2| (QUOTE (-553 (-800 (-330))))) (|HasCategory| |#4| (QUOTE (-553 (-800 (-484))))) (|HasCategory| |#2| (QUOTE (-553 (-800 (-484))))) (|HasCategory| |#4| (QUOTE (-553 (-473)))) (|HasCategory| |#2| (QUOTE (-553 (-473))))) 
+(-861 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}."))) 
-(((-3999 "*") |has| |#1| (-146)) (-3990 |has| |#1| (-496)) (-3995 |has| |#1| (-6 -3995)) (-3992 . T) (-3991 . T) (-3994 . T)) 
+(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-495)) (-3994 |has| |#1| (-6 -3994)) (-3991 . T) (-3990 . T) (-3993 . T)) 
 NIL 
-(-863 E V R P -3094) 
+(-862 E V R P -3093) 
 ((|constructor| (NIL "This package transforms multivariate polynomials or fractions into univariate polynomials or fractions,{} and back.")) (|isPower| (((|Union| (|Record| (|:| |val| |#5|) (|:| |exponent| (|Integer|))) "failed") |#5|) "\\spad{isPower(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0},{} \"failed\" otherwise.")) (|isExpt| (((|Union| (|Record| (|:| |var| |#2|) (|:| |exponent| (|Integer|))) "failed") |#5|) "\\spad{isExpt(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0},{} \"failed\" otherwise.")) (|isTimes| (((|Union| (|List| |#5|) "failed") |#5|) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if \\spad{p = a1 ... an} and \\spad{n > 1},{} \"failed\" otherwise.")) (|isPlus| (((|Union| (|List| |#5|) "failed") |#5|) "\\spad{isPlus(p)} returns [\\spad{m1},{}...,{}mn] if \\spad{p = m1 + ... + mn} and \\spad{n > 1},{} \"failed\" otherwise.")) (|multivariate| ((|#5| (|Fraction| (|SparseUnivariatePolynomial| |#5|)) |#2|) "\\spad{multivariate(f, v)} applies both the numerator and denominator of \\spad{f} to \\spad{v}.")) (|univariate| (((|SparseUnivariatePolynomial| |#5|) |#5| |#2| (|SparseUnivariatePolynomial| |#5|)) "\\spad{univariate(f, x, p)} returns \\spad{f} viewed as a univariate polynomial in \\spad{x},{} using the side-condition \\spad{p(x) = 0}.") (((|Fraction| (|SparseUnivariatePolynomial| |#5|)) |#5| |#2|) "\\spad{univariate(f, v)} returns \\spad{f} viewed as a univariate rational function in \\spad{v}.")) (|mainVariable| (((|Union| |#2| "failed") |#5|) "\\spad{mainVariable(f)} returns the highest variable appearing in the numerator or the denominator of \\spad{f},{} \"failed\" if \\spad{f} has no variables.")) (|variables| (((|List| |#2|) |#5|) "\\spad{variables(f)} returns the list of variables appearing in the numerator or the denominator of \\spad{f}."))) 
 NIL 
 NIL 
-(-864 E |Vars| R P S) 
+(-863 E |Vars| R P S) 
 ((|constructor| (NIL "This package provides a very general map function,{} which given a set \\spad{S} and polynomials over \\spad{R} with maps from the variables into \\spad{S} and the coefficients into \\spad{S},{} maps polynomials into \\spad{S}. \\spad{S} is assumed to support \\spad{+},{} \\spad{*} and \\spad{**}.")) (|map| ((|#5| (|Mapping| |#5| |#2|) (|Mapping| |#5| |#3|) |#4|) "\\spad{map(varmap, coefmap, p)} takes a \\spad{varmap},{} a mapping from the variables of polynomial \\spad{p} into \\spad{S},{} \\spad{coefmap},{} a mapping from coefficients of \\spad{p} into \\spad{S},{} and \\spad{p},{} and produces a member of \\spad{S} using the corresponding arithmetic. in \\spad{S}"))) 
 NIL 
 NIL 
-(-865 E V R P -3094) 
+(-864 E V R P -3093) 
 ((|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| $) "\\spad{numer(x)} \\undocumented"))) 
 NIL 
 ((|HasCategory| |#3| (QUOTE (-392)))) 
-(-866) 
+(-865) 
 ((|constructor| (NIL "This domain represents network port numbers (notable TCP and UDP).")) (|port| (($ (|SingleInteger|)) "\\spad{port(n)} constructs a PortNumber from the integer `n'."))) 
 NIL 
 NIL 
-(-867) 
+(-866) 
 ((|constructor| (NIL "PlottablePlaneCurveCategory is the category of curves in the plane which may be plotted via the graphics facilities. Functions are provided for obtaining lists of lists of points,{} representing the branches of the curve,{} and for determining the ranges of the \\spad{x}-coordinates and \\spad{y}-coordinates of the points on the curve.")) (|yRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{yRange(c)} returns the range of the \\spad{y}-coordinates of the points on the curve \\spad{c}.")) (|xRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{xRange(c)} returns the range of the \\spad{x}-coordinates of the points on the curve \\spad{c}.")) (|listBranches| (((|List| (|List| (|Point| (|DoubleFloat|)))) $) "\\spad{listBranches(c)} returns a list of lists of points,{} representing the branches of the curve \\spad{c}."))) 
 NIL 
 NIL 
-(-868 R E) 
+(-867 R E) 
 ((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and terms indexed by their exponents (from an arbitrary ordered abelian monoid). This type is used,{} for example,{} by the \\spadtype{DistributedMultivariatePolynomial} domain where the exponent domain is a direct product of non negative integers.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (|fmecg| (($ $ |#2| |#1| $) "\\spad{fmecg(p1,e,r,p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}"))) 
-(((-3999 "*") |has| |#1| (-146)) (-3990 |has| |#1| (-496)) (-3995 |has| |#1| (-6 -3995)) (-3991 . T) (-3992 . T) (-3994 . T)) 
-((|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-496))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (OR (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485)))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-392))) (-12 (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-104)))) (|HasAttribute| |#1| (QUOTE -3995))) 
-(-869 R L) 
+(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-495)) (-3994 |has| |#1| (-6 -3994)) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((|HasCategory| |#1| (QUOTE (-38 (-350 (-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 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484)))))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-484)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-392))) (-12 (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-104)))) (|HasAttribute| |#1| (QUOTE -3994))) 
+(-868 R L) 
 ((|constructor| (NIL "\\spadtype{PrecomputedAssociatedEquations} stores some generic precomputations which speed up the computations of the associated equations needed for factoring operators.")) (|firstUncouplingMatrix| (((|Union| (|Matrix| |#1|) "failed") |#2| (|PositiveInteger|)) "\\spad{firstUncouplingMatrix(op, m)} returns the matrix A such that \\spad{A w = (W',W'',...,W^N)} in the corresponding associated equations for right-factors of order \\spad{m} of \\spad{op}. Returns \"failed\" if the matrix A has not been precomputed for the particular combination \\spad{degree(L), m}."))) 
 NIL 
 NIL 
-(-870 S) 
+(-869 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"))) 
-((-3998 . T)) 
-((OR (-12 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (OR (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-757))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|))) (|HasCategory| $ (|%list| (QUOTE -1036) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| $ (|%list| (QUOTE -1036) (|devaluate| |#1|))))) 
-(-871 A B) 
+((-3997 . T)) 
+((OR (-12 (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-553 (-473)))) (OR (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-756))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| (-484) (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|))) (|HasCategory| $ (|%list| (QUOTE -1035) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| $ (|%list| (QUOTE -1035) (|devaluate| |#1|))))) 
+(-870 A B) 
 ((|constructor| (NIL "\\indented{1}{This package provides tools for operating on primitive arrays} with unary and binary functions involving different underlying types")) (|map| (((|PrimitiveArray| |#2|) (|Mapping| |#2| |#1|) (|PrimitiveArray| |#1|)) "\\spad{map(f,a)} applies function \\spad{f} to each member of primitive array \\spad{a} resulting in a new primitive array over a possibly different underlying domain.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|PrimitiveArray| |#1|) |#2|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the primitive array \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,[1,2,3],0)} does \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as the identity element for the function \\spad{f}.")) (|scan| (((|PrimitiveArray| |#2|) (|Mapping| |#2| |#1| |#2|) (|PrimitiveArray| |#1|) |#2|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-arrays \\spad{x} of primitive array \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad{[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}."))) 
 NIL 
 NIL 
-(-872) 
+(-871) 
 ((|constructor| (NIL "Category for the functions defined by integrals.")) (|integral| (($ $ (|SegmentBinding| $)) "\\spad{integral(f, x = a..b)} returns the formal definite integral of \\spad{f} dx for \\spad{x} between \\spad{a} and \\spad{b}.") (($ $ (|Symbol|)) "\\spad{integral(f, x)} returns the formal integral of \\spad{f} dx."))) 
 NIL 
 NIL 
-(-873 -3094) 
+(-872 -3093) 
 ((|constructor| (NIL "PrimitiveElement provides functions to compute primitive elements in algebraic extensions.")) (|primitiveElement| (((|Record| (|:| |coef| (|List| (|Integer|))) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#1|))) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|)) (|Symbol|)) "\\spad{primitiveElement([p1,...,pn], [a1,...,an], a)} returns \\spad{[[c1,...,cn], [q1,...,qn], q]} such that then \\spad{k(a1,...,an) = k(a)},{} where \\spad{a = a1 c1 + ... + an cn},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. The \\spad{pi}'s are the defining polynomials for the \\spad{ai}'s. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}.") (((|Record| (|:| |coef| (|List| (|Integer|))) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#1|))) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{primitiveElement([p1,...,pn], [a1,...,an])} returns \\spad{[[c1,...,cn], [q1,...,qn], q]} such that then \\spad{k(a1,...,an) = k(a)},{} where \\spad{a = a1 c1 + ... + an cn},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. The \\spad{pi}'s are the defining polynomials for the \\spad{ai}'s. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}.") (((|Record| (|:| |coef1| (|Integer|)) (|:| |coef2| (|Integer|)) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|Polynomial| |#1|) (|Symbol|) (|Polynomial| |#1|) (|Symbol|)) "\\spad{primitiveElement(p1, a1, p2, a2)} returns \\spad{[c1, c2, q]} such that \\spad{k(a1, a2) = k(a)} where \\spad{a = c1 a1 + c2 a2, and q(a) = 0}. The \\spad{pi}'s are the defining polynomials for the \\spad{ai}'s. The \\spad{p2} may involve \\spad{a1},{} but \\spad{p1} must not involve \\spad{a2}. This operation uses \\spadfun{resultant}."))) 
 NIL 
 NIL 
-(-874 I) 
+(-873 I) 
 ((|constructor| (NIL "The \\spadtype{IntegerPrimesPackage} implements a modification of Rabin's probabilistic primality test and the utility functions \\spadfun{nextPrime},{} \\spadfun{prevPrime} and \\spadfun{primes}.")) (|primes| (((|List| |#1|) |#1| |#1|) "\\spad{primes(a,b)} returns a list of all primes \\spad{p} with \\spad{a <= p <= b}")) (|prevPrime| ((|#1| |#1|) "\\spad{prevPrime(n)} returns the largest prime strictly smaller than \\spad{n}")) (|nextPrime| ((|#1| |#1|) "\\spad{nextPrime(n)} returns the smallest prime strictly larger than \\spad{n}")) (|prime?| (((|Boolean|) |#1|) "\\spad{prime?(n)} returns \\spad{true} if \\spad{n} is prime and \\spad{false} if not. The algorithm used is Rabin's probabilistic primality test (reference: Knuth Volume 2 Semi Numerical Algorithms). If \\spad{prime? n} returns \\spad{false},{} \\spad{n} is proven composite. If \\spad{prime? n} returns \\spad{true},{} prime? may be in error however,{} the probability of error is very low. and is zero below 25*10**9 (due to a result of Pomerance et al),{} below 10**12 and 10**13 due to results of Pinch,{} and below 341550071728321 due to a result of Jaeschke. Specifically,{} this implementation does at least 10 pseudo prime tests and so the probability of error is \\spad{< 4**(-10)}. The running time of this method is cubic in the length of the input \\spad{n},{} that is \\spad{O( (log n)**3 )},{} for \\spad{n<10**20}. beyond that,{} the algorithm is quartic,{} \\spad{O( (log n)**4 )}. Two improvements due to Davenport have been incorporated which catches some trivial strong pseudo-primes,{} such as [Jaeschke,{} 1991] 1377161253229053 * 413148375987157,{} which the original algorithm regards as prime"))) 
 NIL 
 NIL 
-(-875) 
+(-874) 
 ((|constructor| (NIL "PrintPackage provides a print function for output forms.")) (|print| (((|Void|) (|OutputForm|)) "\\spad{print(o)} writes the output form \\spad{o} on standard output using the two-dimensional formatter."))) 
 NIL 
 NIL 
-(-876 A B) 
+(-875 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"))) 
-((-3994 -12 (|has| |#2| (-413)) (|has| |#1| (-413)))) 
-((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 (-413))) (|HasCategory| |#2| (QUOTE (-413)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-413))) (|HasCategory| |#2| (QUOTE (-413)))) (-12 (|HasCategory| |#1| (QUOTE (-664))) (|HasCategory| |#2| (QUOTE (-664))))) (-12 (|HasCategory| |#1| (QUOTE (-320))) (|HasCategory| |#2| (QUOTE (-320)))) (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 (-413))) (|HasCategory| |#2| (QUOTE (-413)))) (-12 (|HasCategory| |#1| (QUOTE (-664))) (|HasCategory| |#2| (QUOTE (-664))))) (-12 (|HasCategory| |#1| (QUOTE (-664))) (|HasCategory| |#2| (QUOTE (-664)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-104)))) (-12 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-757))))) 
-(-877) 
+((-3993 -12 (|has| |#2| (-413)) (|has| |#1| (-413)))) 
+((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 (-413))) (|HasCategory| |#2| (QUOTE (-413)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-413))) (|HasCategory| |#2| (QUOTE (-413)))) (-12 (|HasCategory| |#1| (QUOTE (-663))) (|HasCategory| |#2| (QUOTE (-663))))) (-12 (|HasCategory| |#1| (QUOTE (-320))) (|HasCategory| |#2| (QUOTE (-320)))) (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 (-413))) (|HasCategory| |#2| (QUOTE (-413)))) (-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) 
 ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. An `Property' is a pair of name and value.")) (|property| (($ (|Identifier|) (|SExpression|)) "\\spad{property(n,val)} constructs a property with name `n' and value `val'.")) (|value| (((|SExpression|) $) "\\spad{value(p)} returns value of property \\spad{p}")) (|name| (((|Identifier|) $) "\\spad{name(p)} returns the name of property \\spad{p}"))) 
 NIL 
 NIL 
-(-878 T$) 
+(-877 T$) 
 ((|constructor| (NIL "This domain implements propositional formula build over a term domain,{} that itself belongs to PropositionalLogic")) (|disjunction| (($ $ $) "\\spad{disjunction(p,q)} returns a formula denoting the disjunction of \\spad{p} and \\spad{q}.")) (|conjunction| (($ $ $) "\\spad{conjunction(p,q)} returns a formula denoting the conjunction of \\spad{p} and \\spad{q}.")) (|isEquiv| (((|Maybe| (|Pair| $ $)) $) "\\spad{isEquiv f} returns a value \\spad{v} such that \\spad{v case Pair(\\%,\\%)} holds if the formula \\spad{f} is an equivalence formula.")) (|isImplies| (((|Maybe| (|Pair| $ $)) $) "\\spad{isImplies f} returns a value \\spad{v} such that \\spad{v case Pair(\\%,\\%)} holds if the formula \\spad{f} is an implication formula.")) (|isOr| (((|Maybe| (|Pair| $ $)) $) "\\spad{isOr f} returns a value \\spad{v} such that \\spad{v case Pair(\\%,\\%)} holds if the formula \\spad{f} is a disjunction formula.")) (|isAnd| (((|Maybe| (|Pair| $ $)) $) "\\spad{isAnd f} returns a value \\spad{v} such that \\spad{v case Pair(\\%,\\%)} holds if the formula \\spad{f} is a conjunction formula.")) (|isNot| (((|Maybe| $) $) "\\spad{isNot f} returns a value \\spad{v} such that \\spad{v case \\%} holds if the formula \\spad{f} is a negation.")) (|isAtom| (((|Maybe| |#1|) $) "\\spad{isAtom f} returns a value \\spad{v} such that \\spad{v case T} holds if the formula \\spad{f} is a term."))) 
 NIL 
 NIL 
-(-879 T$) 
+(-878 T$) 
 ((|constructor| (NIL "This package collects unary functions operating on propositional formulae.")) (|simplify| (((|PropositionalFormula| |#1|) (|PropositionalFormula| |#1|)) "\\spad{simplify f} returns a formula logically equivalent to \\spad{f} where obvious tautologies have been removed.")) (|atoms| (((|Set| |#1|) (|PropositionalFormula| |#1|)) "\\spad{atoms f} ++ returns the set of atoms appearing in the formula \\spad{f}.")) (|dual| (((|PropositionalFormula| |#1|) (|PropositionalFormula| |#1|)) "\\spad{dual f} returns the dual of the proposition \\spad{f}."))) 
 NIL 
 NIL 
-(-880 S T$) 
+(-879 S T$) 
 ((|constructor| (NIL "This package collects binary functions operating on propositional formulae.")) (|map| (((|PropositionalFormula| |#2|) (|Mapping| |#2| |#1|) (|PropositionalFormula| |#1|)) "\\spad{map(f,x)} returns a propositional formula where all atoms in \\spad{x} have been replaced by the result of applying the function \\spad{f} to them."))) 
 NIL 
 NIL 
-(-881) 
+(-880) 
 ((|constructor| (NIL "This category declares the connectives of Propositional Logic.")) (|equiv| (($ $ $) "\\spad{equiv(p,q)} returns the logical equivalence of `p',{} `q'.")) (|implies| (($ $ $) "\\spad{implies(p,q)} returns the logical implication of `q' by `p'.")) (|false| (($) "\\spad{false} is a logical constant.")) (|true| (($) "\\spad{true} is a logical constant."))) 
 NIL 
 NIL 
-(-882 S) 
+(-881 S) 
 ((|constructor| (NIL "A priority queue is a bag of items from an ordered set where the item extracted is always the maximum element.")) (|merge!| (($ $ $) "\\spad{merge!(q,q1)} destructively changes priority queue \\spad{q} to include the values from priority queue \\spad{q1}.")) (|merge| (($ $ $) "\\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}."))) 
-((-3998 . T)) 
+((-3997 . T)) 
 NIL 
-(-883 R |polR|) 
+(-882 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 (-392)))) 
-(-884) 
+(-883) 
 ((|constructor| (NIL "This domain represents `pretend' expressions.")) (|target| (((|TypeAst|) $) "\\spad{target(e)} returns the target type of the conversion..")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression being converted."))) 
 NIL 
 NIL 
-(-885) 
+(-884) 
 ((|constructor| (NIL "Partition is an OrderedCancellationAbelianMonoid which is used as the basis for symmetric polynomial representation of the sums of powers in SymmetricPolynomial. Thus,{} \\spad{(5 2 2 1)} will represent \\spad{s5 * s2**2 * s1}.")) (|conjugate| (($ $) "\\spad{conjugate(p)} returns the conjugate partition of a partition \\spad{p}")) (|pdct| (((|PositiveInteger|) $) "\\spad{pdct(a1**n1 a2**n2 ...)} returns \\spad{n1! * a1**n1 * n2! * a2**n2 * ...}. This function is used in the package \\spadtype{CycleIndicators}.")) (|powers| (((|List| (|Pair| (|PositiveInteger|) (|PositiveInteger|))) $) "\\spad{powers(x)} returns a list of pairs. The second component of each pair is the multiplicity with which the first component occurs in \\spad{li}.")) (|partitions| (((|Stream| $) (|NonNegativeInteger|)) "\\spad{partitions n} returns the stream of all partitions of size \\spad{n}.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\#x} returns the sum of all parts of the partition \\spad{x}.")) (|parts| (((|List| (|PositiveInteger|)) $) "\\spad{parts x} returns the list of decreasing integer sequence making up the partition \\spad{x}.")) (|partition| (($ (|List| (|PositiveInteger|))) "\\spad{partition(li)} converts a list of integers \\spad{li} to a partition"))) 
 NIL 
 NIL 
-(-886 S |Coef| |Expon| |Var|) 
+(-885 S |Coef| |Expon| |Var|) 
 ((|constructor| (NIL "\\spadtype{PowerSeriesCategory} is the most general power series category with exponents in an ordered abelian monoid.")) (|complete| (($ $) "\\spad{complete(f)} causes all terms of \\spad{f} to be computed. Note: this results in an infinite loop if \\spad{f} has infinitely many terms.")) (|pole?| (((|Boolean|) $) "\\spad{pole?(f)} determines if the power series \\spad{f} has a pole.")) (|variables| (((|List| |#4|) $) "\\spad{variables(f)} returns a list of the variables occuring in the power series \\spad{f}.")) (|degree| ((|#3| $) "\\spad{degree(f)} returns the exponent of the lowest order term of \\spad{f}.")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(f)} returns the coefficient of the lowest order term of \\spad{f}")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(f)} returns the monomial of \\spad{f} of lowest order.")) (|monomial| (($ $ (|List| |#4|) (|List| |#3|)) "\\spad{monomial(a,[x1,..,xk],[n1,..,nk])} computes \\spad{a * x1**n1 * .. * xk**nk}.") (($ $ |#4| |#3|) "\\spad{monomial(a,x,n)} computes \\spad{a*x**n}."))) 
 NIL 
 NIL 
-(-887 |Coef| |Expon| |Var|) 
+(-886 |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}."))) 
-(((-3999 "*") |has| |#1| (-146)) (-3990 |has| |#1| (-496)) (-3991 . T) (-3992 . T) (-3994 . T)) 
+(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-495)) (-3990 . T) (-3991 . T) (-3993 . T)) 
 NIL 
-(-888) 
+(-887) 
 ((|constructor| (NIL "PlottableSpaceCurveCategory is the category of curves in 3-space which may be plotted via the graphics facilities. Functions are provided for obtaining lists of lists of points,{} representing the branches of the curve,{} and for determining the ranges of the x-,{} y-,{} and \\spad{z}-coordinates of the points on the curve.")) (|zRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{zRange(c)} returns the range of the \\spad{z}-coordinates of the points on the curve \\spad{c}.")) (|yRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{yRange(c)} returns the range of the \\spad{y}-coordinates of the points on the curve \\spad{c}.")) (|xRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{xRange(c)} returns the range of the \\spad{x}-coordinates of the points on the curve \\spad{c}.")) (|listBranches| (((|List| (|List| (|Point| (|DoubleFloat|)))) $) "\\spad{listBranches(c)} returns a list of lists of points,{} representing the branches of the curve \\spad{c}."))) 
 NIL 
 NIL 
-(-889 S R E |VarSet| P) 
+(-888 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 (-496)))) 
-(-890 R E |VarSet| P) 
+((|HasCategory| |#2| (QUOTE (-495)))) 
+(-889 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."))) 
 NIL 
 NIL 
-(-891 R E V P) 
+(-890 R E V P) 
 ((|constructor| (NIL "This package provides modest routines for polynomial system solving. The aim of many of the operations of this package is to remove certain factors in some polynomials in order to avoid unnecessary computations in algorithms involving splitting techniques by partial factorization.")) (|removeIrreducibleRedundantFactors| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeIrreducibleRedundantFactors(lp,{}lq)} returns the same as \\axiom{irreducibleFactors(concat(lp,{}lq))} assuming that \\axiom{irreducibleFactors(lp)} returns \\axiom{lp} up to replacing some polynomial \\axiom{pj} in \\axiom{lp} by some polynomial \\axiom{qj} associated to \\axiom{pj}.")) (|lazyIrreducibleFactors| (((|List| |#4|) (|List| |#4|)) "\\axiom{lazyIrreducibleFactors(lp)} returns \\axiom{lf} such that if \\axiom{lp = [\\spad{p1},{}...,{}pn]} and \\axiom{lf = [\\spad{f1},{}...,{}fm]} then \\axiom{p1*p2*...\\spad{*pn=0}} means \\axiom{f1*f2*...\\spad{*fm=0}},{} and the \\axiom{\\spad{fi}} are irreducible over \\axiom{\\spad{R}} and are pairwise distinct. The algorithm tries to avoid factorization into irreducible factors as far as possible and makes previously use of gcd techniques over \\axiom{\\spad{R}}.")) (|irreducibleFactors| (((|List| |#4|) (|List| |#4|)) "\\axiom{irreducibleFactors(lp)} returns \\axiom{lf} such that if \\axiom{lp = [\\spad{p1},{}...,{}pn]} and \\axiom{lf = [\\spad{f1},{}...,{}fm]} then \\axiom{p1*p2*...\\spad{*pn=0}} means \\axiom{f1*f2*...\\spad{*fm=0}},{} and the \\axiom{\\spad{fi}} are irreducible over \\axiom{\\spad{R}} and are pairwise distinct.")) (|removeRedundantFactorsInPols| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactorsInPols(lp,{}lf)} returns \\axiom{newlp} where \\axiom{newlp} is obtained from \\axiom{lp} by removing in every polynomial \\axiom{\\spad{p}} of \\axiom{lp} any non trivial factor of any polynomial \\axiom{\\spad{f}} in \\axiom{lf}. Moreover,{} squares over \\axiom{\\spad{R}} are first removed in every polynomial \\axiom{lp}.")) (|removeRedundantFactorsInContents| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactorsInContents(lp,{}lf)} returns \\axiom{newlp} where \\axiom{newlp} is obtained from \\axiom{lp} by removing in the content of every polynomial of \\axiom{lp} any non trivial factor of any polynomial \\axiom{\\spad{f}} in \\axiom{lf}. Moreover,{} squares over \\axiom{\\spad{R}} are first removed in the content of every polynomial of \\axiom{lp}.")) (|removeRoughlyRedundantFactorsInContents| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRoughlyRedundantFactorsInContents(lp,{}lf)} returns \\axiom{newlp}where \\axiom{newlp} is obtained from \\axiom{lp} by removing in the content of every polynomial of \\axiom{lp} any occurence of a polynomial \\axiom{\\spad{f}} in \\axiom{lf}. Moreover,{} squares over \\axiom{\\spad{R}} are first removed in the content of every polynomial of \\axiom{lp}.")) (|univariatePolynomialsGcds| (((|List| |#4|) (|List| |#4|) (|Boolean|)) "\\axiom{univariatePolynomialsGcds(lp,{}opt)} returns the same as \\axiom{univariatePolynomialsGcds(lp)} if \\axiom{opt} is \\axiom{\\spad{false}} and if the previous operation does not return any non null and constant polynomial,{} else return \\axiom{[1]}.") (((|List| |#4|) (|List| |#4|)) "\\axiom{univariatePolynomialsGcds(lp)} returns \\axiom{lg} where \\axiom{lg} is a list of the gcds of every pair in \\axiom{lp} of univariate polynomials in the same main variable.")) (|squareFreeFactors| (((|List| |#4|) |#4|) "\\axiom{squareFreeFactors(\\spad{p})} returns the square-free factors of \\axiom{\\spad{p}} over \\axiom{\\spad{R}}")) (|rewriteIdealWithQuasiMonicGenerators| (((|List| |#4|) (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{rewriteIdealWithQuasiMonicGenerators(lp,{}redOp?,{}redOp)} returns \\axiom{lq} where \\axiom{lq} and \\axiom{lp} generate the same ideal in \\axiom{R^(\\spad{-1}) \\spad{P}} and \\axiom{lq} has rank not higher than the one of \\axiom{lp}. Moreover,{} \\axiom{lq} is computed by reducing \\axiom{lp} \\spad{w}.\\spad{r}.\\spad{t}. some basic set of the ideal generated by the quasi-monic polynomials in \\axiom{lp}.")) (|rewriteSetByReducingWithParticularGenerators| (((|List| |#4|) (|List| |#4|) (|Mapping| (|Boolean|) |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{rewriteSetByReducingWithParticularGenerators(lp,{}pred?,{}redOp?,{}redOp)} returns \\axiom{lq} where \\axiom{lq} is computed by the following algorithm. Chose a basic set \\spad{w}.\\spad{r}.\\spad{t}. the reduction-test \\axiom{redOp?} among the polynomials satisfying property \\axiom{pred?},{} if it is empty then leave,{} else reduce the other polynomials by this basic set \\spad{w}.\\spad{r}.\\spad{t}. the reduction-operation \\axiom{redOp}. Repeat while another basic set with smaller rank can be computed. See code. If \\axiom{pred?} is \\axiom{quasiMonic?} the ideal is unchanged.")) (|crushedSet| (((|List| |#4|) (|List| |#4|)) "\\axiom{crushedSet(lp)} returns \\axiom{lq} such that \\axiom{lp} and and \\axiom{lq} generate the same ideal and no rough basic sets reduce (in the sense of Groebner bases) the other polynomials in \\axiom{lq}.")) (|roughBasicSet| (((|Union| (|Record| (|:| |bas| (|GeneralTriangularSet| |#1| |#2| |#3| |#4|)) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|)) "\\axiom{roughBasicSet(lp)} returns the smallest (with Ritt-Wu ordering) triangular set contained in \\axiom{lp}.")) (|interReduce| (((|List| |#4|) (|List| |#4|)) "\\axiom{interReduce(lp)} returns \\axiom{lq} such that \\axiom{lp} and \\axiom{lq} generate the same ideal and no polynomial in \\axiom{lq} is reducuble by the others in the sense of Groebner bases. Since no assumptions are required the result may depend on the ordering the reductions are performed.")) (|removeRoughlyRedundantFactorsInPol| ((|#4| |#4| (|List| |#4|)) "\\axiom{removeRoughlyRedundantFactorsInPol(\\spad{p},{}lf)} returns the same as removeRoughlyRedundantFactorsInPols([\\spad{p}],{}lf,{}\\spad{true})")) (|removeRoughlyRedundantFactorsInPols| (((|List| |#4|) (|List| |#4|) (|List| |#4|) (|Boolean|)) "\\axiom{removeRoughlyRedundantFactorsInPols(lp,{}lf,{}opt)} returns the same as \\axiom{removeRoughlyRedundantFactorsInPols(lp,{}lf)} if \\axiom{opt} is \\axiom{\\spad{false}} and if the previous operation does not return any non null and constant polynomial,{} else return \\axiom{[1]}.") (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRoughlyRedundantFactorsInPols(lp,{}lf)} returns \\axiom{newlp}where \\axiom{newlp} is obtained from \\axiom{lp} by removing in every polynomial \\axiom{\\spad{p}} of \\axiom{lp} any occurence of a polynomial \\axiom{\\spad{f}} in \\axiom{lf}. This may involve a lot of exact-quotients computations.")) (|bivariatePolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{bivariatePolynomials(lp)} returns \\axiom{bps,{}nbps} where \\axiom{bps} is a list of the bivariate polynomials,{} and \\axiom{nbps} are the other ones.")) (|bivariate?| (((|Boolean|) |#4|) "\\axiom{bivariate?(\\spad{p})} returns \\spad{true} iff \\axiom{\\spad{p}} involves two and only two variables.")) (|linearPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{linearPolynomials(lp)} returns \\axiom{lps,{}nlps} where \\axiom{lps} is a list of the linear polynomials in lp,{} and \\axiom{nlps} are the other ones.")) (|linear?| (((|Boolean|) |#4|) "\\axiom{linear?(\\spad{p})} returns \\spad{true} iff \\axiom{\\spad{p}} does not lie in the base ring \\axiom{\\spad{R}} and has main degree \\axiom{1}.")) (|univariatePolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{univariatePolynomials(lp)} returns \\axiom{ups,{}nups} where \\axiom{ups} is a list of the univariate polynomials,{} and \\axiom{nups} are the other ones.")) (|univariate?| (((|Boolean|) |#4|) "\\axiom{univariate?(\\spad{p})} returns \\spad{true} iff \\axiom{\\spad{p}} involves one and only one variable.")) (|quasiMonicPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{quasiMonicPolynomials(lp)} returns \\axiom{qmps,{}nqmps} where \\axiom{qmps} is a list of the quasi-monic polynomials in \\axiom{lp} and \\axiom{nqmps} are the other ones.")) (|selectAndPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| (|Mapping| (|Boolean|) |#4|)) (|List| |#4|)) "\\axiom{selectAndPolynomials(lpred?,{}ps)} returns \\axiom{gps,{}bps} where \\axiom{gps} is a list of the polynomial \\axiom{\\spad{p}} in \\axiom{ps} such that \\axiom{pred?(\\spad{p})} holds for every \\axiom{pred?} in \\axiom{lpred?} and \\axiom{bps} are the other ones.")) (|selectOrPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| (|Mapping| (|Boolean|) |#4|)) (|List| |#4|)) "\\axiom{selectOrPolynomials(lpred?,{}ps)} returns \\axiom{gps,{}bps} where \\axiom{gps} is a list of the polynomial \\axiom{\\spad{p}} in \\axiom{ps} such that \\axiom{pred?(\\spad{p})} holds for some \\axiom{pred?} in \\axiom{lpred?} and \\axiom{bps} are the other ones.")) (|selectPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|Mapping| (|Boolean|) |#4|) (|List| |#4|)) "\\axiom{selectPolynomials(pred?,{}ps)} returns \\axiom{gps,{}bps} where \\axiom{gps} is a list of the polynomial \\axiom{\\spad{p}} in \\axiom{ps} such that \\axiom{pred?(\\spad{p})} holds and \\axiom{bps} are the other ones.")) (|probablyZeroDim?| (((|Boolean|) (|List| |#4|)) "\\axiom{probablyZeroDim?(lp)} returns \\spad{true} iff the number of polynomials in \\axiom{lp} is not smaller than the number of variables occurring in these polynomials.")) (|possiblyNewVariety?| (((|Boolean|) (|List| |#4|) (|List| (|List| |#4|))) "\\axiom{possiblyNewVariety?(newlp,{}llp)} returns \\spad{true} iff for every \\axiom{lp} in \\axiom{llp} certainlySubVariety?(newlp,{}lp) does not hold.")) (|certainlySubVariety?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{certainlySubVariety?(newlp,{}lp)} returns \\spad{true} iff for every \\axiom{\\spad{p}} in \\axiom{lp} the remainder of \\axiom{\\spad{p}} by \\axiom{newlp} using the division algorithm of Groebner techniques is zero.")) (|unprotectedRemoveRedundantFactors| (((|List| |#4|) |#4| |#4|) "\\axiom{unprotectedRemoveRedundantFactors(\\spad{p},{}\\spad{q})} returns the same as \\axiom{removeRedundantFactors(\\spad{p},{}\\spad{q})} but does assume that neither \\axiom{\\spad{p}} nor \\axiom{\\spad{q}} lie in the base ring \\axiom{\\spad{R}} and assumes that \\axiom{infRittWu?(\\spad{p},{}\\spad{q})} holds. Moreover,{} if \\axiom{\\spad{R}} is gcd-domain,{} then \\axiom{\\spad{p}} and \\axiom{\\spad{q}} are assumed to be square free.")) (|removeSquaresIfCan| (((|List| |#4|) (|List| |#4|)) "\\axiom{removeSquaresIfCan(lp)} returns \\axiom{removeDuplicates [squareFreePart(\\spad{p})\\$\\spad{P} for \\spad{p} in lp]} if \\axiom{\\spad{R}} is gcd-domain else returns \\axiom{lp}.")) (|removeRedundantFactors| (((|List| |#4|) (|List| |#4|) (|List| |#4|) (|Mapping| (|List| |#4|) (|List| |#4|))) "\\axiom{removeRedundantFactors(lp,{}lq,{}remOp)} returns the same as \\axiom{concat(remOp(removeRoughlyRedundantFactorsInPols(lp,{}lq)),{}lq)} assuming that \\axiom{remOp(lq)} returns \\axiom{lq} up to similarity.") (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactors(lp,{}lq)} returns the same as \\axiom{removeRedundantFactors(concat(lp,{}lq))} assuming that \\axiom{removeRedundantFactors(lp)} returns \\axiom{lp} up to replacing some polynomial \\axiom{pj} in \\axiom{lp} by some polynomial \\axiom{qj} associated to \\axiom{pj}.") (((|List| |#4|) (|List| |#4|) |#4|) "\\axiom{removeRedundantFactors(lp,{}\\spad{q})} returns the same as \\axiom{removeRedundantFactors(cons(\\spad{q},{}lp))} assuming that \\axiom{removeRedundantFactors(lp)} returns \\axiom{lp} up to replacing some polynomial \\axiom{pj} in \\axiom{lp} by some some polynomial \\axiom{qj} associated to \\axiom{pj}.") (((|List| |#4|) |#4| |#4|) "\\axiom{removeRedundantFactors(\\spad{p},{}\\spad{q})} returns the same as \\axiom{removeRedundantFactors([\\spad{p},{}\\spad{q}])}") (((|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactors(lp)} returns \\axiom{lq} such that if \\axiom{lp = [\\spad{p1},{}...,{}pn]} and \\axiom{lq = [\\spad{q1},{}...,{}qm]} then the product \\axiom{p1*p2*...*pn} vanishes iff the product \\axiom{q1*q2*...*qm} vanishes,{} and the product of degrees of the \\axiom{\\spad{qi}} is not greater than the one of the \\axiom{pj},{} and no polynomial in \\axiom{lq} divides another polynomial in \\axiom{lq}. In particular,{} polynomials lying in the base ring \\axiom{\\spad{R}} are removed. Moreover,{} \\axiom{lq} is sorted \\spad{w}.\\spad{r}.\\spad{t} \\axiom{infRittWu?}. Furthermore,{} if \\spad{R} is gcd-domain,{} the polynomials in \\axiom{lq} are pairwise without common non trivial factor."))) 
 NIL 
 ((-12 (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-258)))) (|HasCategory| |#1| (QUOTE (-392)))) 
-(-892 K) 
+(-891 K) 
 ((|constructor| (NIL "PseudoLinearNormalForm provides a function for computing a block-companion form for pseudo-linear operators.")) (|companionBlocks| (((|List| (|Record| (|:| C (|Matrix| |#1|)) (|:| |g| (|Vector| |#1|)))) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{companionBlocks(m, v)} returns \\spad{[[C_1, g_1],...,[C_k, g_k]]} such that each \\spad{C_i} is a companion block and \\spad{m = diagonal(C_1,...,C_k)}.")) (|changeBase| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{changeBase(M, A, sig, der)}: computes the new matrix of a pseudo-linear transform given by the matrix \\spad{M} under the change of base A")) (|normalForm| (((|Record| (|:| R (|Matrix| |#1|)) (|:| A (|Matrix| |#1|)) (|:| |Ainv| (|Matrix| |#1|))) (|Matrix| |#1|) (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{normalForm(M, sig, der)} returns \\spad{[R, A, A^{-1}]} such that the pseudo-linear operator whose matrix in the basis \\spad{y} is \\spad{M} had matrix \\spad{R} in the basis \\spad{z = A y}. \\spad{der} is a \\spad{sig}-derivation."))) 
 NIL 
 NIL 
-(-893 |VarSet| E RC P) 
+(-892 |VarSet| E RC P) 
 ((|constructor| (NIL "This package computes square-free decomposition of multivariate polynomials over a coefficient ring which is an arbitrary gcd domain. The requirement on the coefficient domain guarantees that the \\spadfun{content} can be removed so that factors will be primitive as well as square-free. Over an infinite ring of finite characteristic,{}it may not be possible to guarantee that the factors are square-free.")) (|squareFree| (((|Factored| |#4|) |#4|) "\\spad{squareFree(p)} returns the square-free factorization of the polynomial \\spad{p}. Each factor has no repeated roots,{} and the factors are pairwise relatively prime."))) 
 NIL 
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-(-894 R) 
+(-893 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}."))) 
-((-3998 . T)) 
+((-3997 . T)) 
 NIL 
-(-895 R1 R2) 
+(-894 R1 R2) 
 ((|constructor| (NIL "This package \\undocumented")) (|map| (((|Point| |#2|) (|Mapping| |#2| |#1|) (|Point| |#1|)) "\\spad{map(f,p)} \\undocumented"))) 
 NIL 
 NIL 
-(-896 R) 
+(-895 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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-(-897 K) 
+(-896 K) 
 ((|constructor| (NIL "This is the description of any package which provides partial functions on a domain belonging to TranscendentalFunctionCategory.")) (|acschIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acschIfCan(z)} returns acsch(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|asechIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{asechIfCan(z)} returns asech(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|acothIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acothIfCan(z)} returns acoth(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|atanhIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{atanhIfCan(z)} returns atanh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|acoshIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acoshIfCan(z)} returns acosh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|asinhIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{asinhIfCan(z)} returns asinh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|cschIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cschIfCan(z)} returns csch(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|sechIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{sechIfCan(z)} returns sech(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|cothIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cothIfCan(z)} returns coth(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|tanhIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{tanhIfCan(z)} returns tanh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|coshIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{coshIfCan(z)} returns cosh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|sinhIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{sinhIfCan(z)} returns sinh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|acscIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acscIfCan(z)} returns acsc(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|asecIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{asecIfCan(z)} returns asec(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|acotIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acotIfCan(z)} returns acot(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|atanIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{atanIfCan(z)} returns atan(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|acosIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acosIfCan(z)} returns acos(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|asinIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{asinIfCan(z)} returns asin(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|cscIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cscIfCan(z)} returns csc(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|secIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{secIfCan(z)} returns sec(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|cotIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cotIfCan(z)} returns cot(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|tanIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{tanIfCan(z)} returns tan(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|cosIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cosIfCan(z)} returns cos(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|sinIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{sinIfCan(z)} returns sin(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|logIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{logIfCan(z)} returns log(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|expIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{expIfCan(z)} returns exp(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|nthRootIfCan| (((|Union| |#1| "failed") |#1| (|NonNegativeInteger|)) "\\spad{nthRootIfCan(z,n)} returns the \\spad{n}th root of \\spad{z} if possible,{} and \"failed\" otherwise."))) 
 NIL 
 NIL 
-(-898 R E OV PPR) 
+(-897 R E OV PPR) 
 ((|constructor| (NIL "This package \\undocumented{}")) (|map| ((|#4| (|Mapping| |#4| (|Polynomial| |#1|)) |#4|) "\\spad{map(f,p)} \\undocumented{}")) (|pushup| ((|#4| |#4| (|List| |#3|)) "\\spad{pushup(p,lv)} \\undocumented{}") ((|#4| |#4| |#3|) "\\spad{pushup(p,v)} \\undocumented{}")) (|pushdown| ((|#4| |#4| (|List| |#3|)) "\\spad{pushdown(p,lv)} \\undocumented{}") ((|#4| |#4| |#3|) "\\spad{pushdown(p,v)} \\undocumented{}")) (|variable| (((|Union| $ "failed") (|Symbol|)) "\\spad{variable(s)} makes an element from symbol \\spad{s} or fails")) (|convert| (((|Symbol|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) 
 NIL 
 NIL 
-(-899 K R UP -3094) 
+(-898 K R UP -3093) 
 ((|constructor| (NIL "In this package \\spad{K} is a finite field,{} \\spad{R} is a ring of univariate polynomials over \\spad{K},{} and \\spad{F} is a monogenic algebra over \\spad{R}. We require that \\spad{F} is monogenic,{} \\spadignore{i.e.} that \\spad{F = K[x,y]/(f(x,y))},{} because the integral basis algorithm used will factor the polynomial \\spad{f(x,y)}. The package provides a function to compute the integral closure of \\spad{R} in the quotient field of \\spad{F} as well as a function to compute a \"local integral basis\" at a specific prime.")) (|reducedDiscriminant| ((|#2| |#3|) "\\spad{reducedDiscriminant(up)} \\undocumented")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) |#2|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,basisDen,basisInv] } containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of the framed algebra \\spad{F}. \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If 'basis' is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix 'basisInv' contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if 'basisInv' is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,basisDen,basisInv] } containing information regarding the integral closure of \\spad{R} in the quotient field of the framed algebra \\spad{F}. \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If 'basis' is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix 'basisInv' contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if 'basisInv' is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}."))) 
 NIL 
 NIL 
-(-900 R |Var| |Expon| |Dpoly|) 
+(-899 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 (-258))))) 
-(-901 |vl| |nv|) 
+(-900 |vl| |nv|) 
 ((|constructor| (NIL "\\spadtype{QuasiAlgebraicSet2} adds a function \\spadfun{radicalSimplify} which uses \\spadtype{IdealDecompositionPackage} to simplify the representation of a quasi-algebraic set. A quasi-algebraic set is the intersection of a Zariski closed set,{} defined as the common zeros of a given list of polynomials (the defining polynomials for equations),{} and a principal Zariski open set,{} defined as the complement of the common zeros of a polynomial \\spad{f} (the defining polynomial for the inequation). Quasi-algebraic sets are implemented in the domain \\spadtype{QuasiAlgebraicSet},{} where two simplification routines are provided: \\spadfun{idealSimplify} and \\spadfun{simplify}. The function \\spadfun{radicalSimplify} is added for comparison study only. Because the domain \\spadtype{IdealDecompositionPackage} provides facilities for computing with radical ideals,{} it is necessary to restrict the ground ring to the domain \\spadtype{Fraction Integer},{} and the polynomial ring to be of type \\spadtype{DistributedMultivariatePolynomial}. The routine \\spadfun{radicalSimplify} uses these to compute groebner basis of radical ideals and is inefficient and restricted when compared to the two in \\spadtype{QuasiAlgebraicSet}.")) (|radicalSimplify| (((|QuasiAlgebraicSet| (|Fraction| (|Integer|)) (|OrderedVariableList| |#1|) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|)))) (|QuasiAlgebraicSet| (|Fraction| (|Integer|)) (|OrderedVariableList| |#1|) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{radicalSimplify(s)} returns a different and presumably simpler representation of \\spad{s} with the defining polynomials for the equations forming a groebner basis,{} and the defining polynomial for the inequation reduced with respect to the basis,{} using using groebner basis of radical ideals"))) 
 NIL 
 NIL 
-(-902 R E V P TS) 
+(-901 R E V P TS) 
 ((|constructor| (NIL "A package for removing redundant quasi-components and redundant branches when decomposing a variety by means of quasi-components of regular triangular sets. \\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|branchIfCan| (((|Union| (|Record| (|:| |eq| (|List| |#4|)) (|:| |tower| |#5|) (|:| |ineq| (|List| |#4|))) "failed") (|List| |#4|) |#5| (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{branchIfCan(leq,{}ts,{}lineq,{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement.")) (|prepareDecompose| (((|List| (|Record| (|:| |eq| (|List| |#4|)) (|:| |tower| |#5|) (|:| |ineq| (|List| |#4|)))) (|List| |#4|) (|List| |#5|) (|Boolean|) (|Boolean|)) "\\axiom{prepareDecompose(lp,{}lts,{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|removeSuperfluousCases| (((|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|)))) "\\axiom{removeSuperfluousCases(llpwt)} is an internal subroutine,{} exported only for developement.")) (|subCase?| (((|Boolean|) (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|)) (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) "\\axiom{subCase?(\\spad{lpwt1},{}\\spad{lpwt2})} is an internal subroutine,{} exported only for developement.")) (|removeSuperfluousQuasiComponents| (((|List| |#5|) (|List| |#5|)) "\\axiom{removeSuperfluousQuasiComponents(lts)} removes from \\axiom{lts} any \\spad{ts} such that \\axiom{subQuasiComponent?(ts,{}us)} holds for another \\spad{us} in \\axiom{lts}.")) (|subQuasiComponent?| (((|Boolean|) |#5| (|List| |#5|)) "\\axiom{subQuasiComponent?(ts,{}lus)} returns \\spad{true} iff \\axiom{subQuasiComponent?(ts,{}us)} holds for one \\spad{us} in \\spad{lus}.") (((|Boolean|) |#5| |#5|) "\\axiom{subQuasiComponent?(ts,{}us)} returns \\spad{true} iff \\axiomOpFrom{internalSubQuasiComponent?}{QuasiComponentPackage} returs \\spad{true}.")) (|internalSubQuasiComponent?| (((|Union| (|Boolean|) "failed") |#5| |#5|) "\\axiom{internalSubQuasiComponent?(ts,{}us)} returns a boolean \\spad{b} value if the fact that the regular zero set of \\axiom{us} contains that of \\axiom{ts} can be decided (and in that case \\axiom{\\spad{b}} gives this inclusion) otherwise returns \\axiom{\"failed\"}.")) (|infRittWu?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{infRittWu?(\\spad{lp1},{}\\spad{lp2})} is an internal subroutine,{} exported only for developement.")) (|internalInfRittWu?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{internalInfRittWu?(\\spad{lp1},{}\\spad{lp2})} is an internal subroutine,{} exported only for developement.")) (|internalSubPolSet?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{internalSubPolSet?(\\spad{lp1},{}\\spad{lp2})} returns \\spad{true} iff \\axiom{\\spad{lp1}} is a sub-set of \\axiom{\\spad{lp2}} assuming that these lists are sorted increasingly \\spad{w}.\\spad{r}.\\spad{t}. \\axiomOpFrom{infRittWu?}{RecursivePolynomialCategory}.")) (|subPolSet?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{subPolSet?(\\spad{lp1},{}\\spad{lp2})} returns \\spad{true} iff \\axiom{\\spad{lp1}} is a sub-set of \\axiom{\\spad{lp2}}.")) (|subTriSet?| (((|Boolean|) |#5| |#5|) "\\axiom{subTriSet?(ts,{}us)} returns \\spad{true} iff \\axiom{ts} is a sub-set of \\axiom{us}.")) (|moreAlgebraic?| (((|Boolean|) |#5| |#5|) "\\axiom{moreAlgebraic?(ts,{}us)} returns \\spad{false} iff \\axiom{ts} and \\axiom{us} are both empty,{} or \\axiom{ts} has less elements than \\axiom{us},{} or some variable is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{us} and is not \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ts}.")) (|algebraicSort| (((|List| |#5|) (|List| |#5|)) "\\axiom{algebraicSort(lts)} sorts \\axiom{lts} \\spad{w}.\\spad{r}.\\spad{t} \\axiomOpFrom{supDimElseRittWu?}{QuasiComponentPackage}.")) (|supDimElseRittWu?| (((|Boolean|) |#5| |#5|) "\\axiom{supDimElseRittWu(ts,{}us)} returns \\spad{true} iff \\axiom{ts} has less elements than \\axiom{us} otherwise if \\axiom{ts} has higher rank than \\axiom{us} \\spad{w}.\\spad{r}.\\spad{t}. Riit and Wu ordering.")) (|stopTable!| (((|Void|)) "\\axiom{stopTableGcd!()} is an internal subroutine,{} exported only for developement.")) (|startTable!| (((|Void|) (|String|) (|String|) (|String|)) "\\axiom{startTableGcd!(\\spad{s1},{}\\spad{s2},{}\\spad{s3})} is an internal subroutine,{} exported only for developement."))) 
 NIL 
 NIL 
-(-903) 
+(-902) 
 ((|constructor| (NIL "This domain implements simple database queries")) (|value| (((|String|) $) "\\spad{value(q)} returns the value (\\spadignore{i.e.} right hand side) of \\axiom{\\spad{q}}.")) (|variable| (((|Symbol|) $) "\\spad{variable(q)} returns the variable (\\spadignore{i.e.} left hand side) of \\axiom{\\spad{q}}.")) (|equation| (($ (|Symbol|) (|String|)) "\\spad{equation(s,\"a\")} creates a new equation."))) 
 NIL 
 NIL 
-(-904 A S) 
+(-903 A S) 
 ((|constructor| (NIL "QuotientField(\\spad{S}) is the category of fractions of an Integral Domain \\spad{S}.")) (|floor| ((|#2| $) "\\spad{floor(x)} returns the largest integral element below \\spad{x}.")) (|ceiling| ((|#2| $) "\\spad{ceiling(x)} returns the smallest integral element above \\spad{x}.")) (|random| (($) "\\spad{random()} returns a random fraction.")) (|fractionPart| (($ $) "\\spad{fractionPart(x)} returns the fractional part of \\spad{x}. \\spad{x} = wholePart(\\spad{x}) + fractionPart(\\spad{x})")) (|wholePart| ((|#2| $) "\\spad{wholePart(x)} returns the whole part of the fraction \\spad{x} \\spadignore{i.e.} the truncated quotient of the numerator by the denominator.")) (|denominator| (($ $) "\\spad{denominator(x)} is the denominator of the fraction \\spad{x} converted to \\%.")) (|numerator| (($ $) "\\spad{numerator(x)} is the numerator of the fraction \\spad{x} converted to \\%.")) (|denom| ((|#2| $) "\\spad{denom(x)} returns the denominator of the fraction \\spad{x}.")) (|numer| ((|#2| $) "\\spad{numer(x)} returns the numerator of the fraction \\spad{x}.")) (/ (($ |#2| |#2|) "\\spad{d1 / d2} returns the fraction \\spad{d1} divided by \\spad{d2}."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-822))) (|HasCategory| |#2| (QUOTE (-484))) (|HasCategory| |#2| (QUOTE (-258))) (|HasCategory| |#2| (QUOTE (-951 (-1091)))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-554 (-474)))) (|HasCategory| |#2| (QUOTE (-934))) (|HasCategory| |#2| (QUOTE (-741))) (|HasCategory| |#2| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-951 (-485)))) (|HasCategory| |#2| (QUOTE (-1067)))) 
-(-905 S) 
+((|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| |#2| (QUOTE (-483))) (|HasCategory| |#2| (QUOTE (-258))) (|HasCategory| |#2| (QUOTE (-950 (-1090)))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-553 (-473)))) (|HasCategory| |#2| (QUOTE (-933))) (|HasCategory| |#2| (QUOTE (-740))) (|HasCategory| |#2| (QUOTE (-756))) (|HasCategory| |#2| (QUOTE (-950 (-484)))) (|HasCategory| |#2| (QUOTE (-1066)))) 
+(-904 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}."))) 
-((-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
 NIL 
-(-906 A B R S) 
+(-905 A B R S) 
 ((|constructor| (NIL "This package extends a function between integral domains to a mapping between their quotient fields.")) (|map| ((|#4| (|Mapping| |#2| |#1|) |#3|) "\\spad{map(func,frac)} applies the function \\spad{func} to the numerator and denominator of \\spad{frac}."))) 
 NIL 
 NIL 
-(-907 |n| K) 
+(-906 |n| K) 
 ((|constructor| (NIL "This domain provides modest support for quadratic forms.")) (|matrix| (((|SquareMatrix| |#1| |#2|) $) "\\spad{matrix(qf)} creates a square matrix from the quadratic form \\spad{qf}.")) (|quadraticForm| (($ (|SquareMatrix| |#1| |#2|)) "\\spad{quadraticForm(m)} creates a quadratic form from a symmetric,{} square matrix \\spad{m}."))) 
 NIL 
 NIL 
-(-908) 
+(-907) 
 ((|constructor| (NIL "This domain represents the syntax of a quasiquote \\indented{2}{expression.}")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the syntax for the expression being quoted."))) 
 NIL 
 NIL 
-(-909 S) 
+(-908 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."))) 
-((-3998 . T)) 
+((-3997 . T)) 
 NIL 
-(-910 R) 
+(-909 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.}"))) 
-((-3990 |has| |#1| (-246)) (-3991 . T) (-3992 . T) (-3994 . T)) 
-((|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (|HasCategory| |#1| (QUOTE (-312))) (OR (|HasCategory| |#1| (QUOTE (-246))) (|HasCategory| |#1| (QUOTE (-312)))) (|HasCategory| |#1| (QUOTE (-246))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-581 (-485)))) (|HasCategory| |#1| (|%list| (QUOTE -456) (QUOTE (-1091)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -241) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-812 (-1091)))) (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485)))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (|HasCategory| |#1| (QUOTE (-974))) (|HasCategory| |#1| (QUOTE (-484)))) 
-(-911 S R) 
+((-3989 |has| |#1| (-246)) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-553 (-473)))) (|HasCategory| |#1| (QUOTE (-312))) (OR (|HasCategory| |#1| (QUOTE (-246))) (|HasCategory| |#1| (QUOTE (-312)))) (|HasCategory| |#1| (QUOTE (-246))) (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-580 (-484)))) (|HasCategory| |#1| (|%list| (QUOTE -455) (QUOTE (-1090)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -241) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-811 (-1090)))) (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-809 (-1090)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484)))))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-484)))) (|HasCategory| |#1| (QUOTE (-973))) (|HasCategory| |#1| (QUOTE (-483)))) 
+(-910 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 (-484))) (|HasCategory| |#2| (QUOTE (-974))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-554 (-474)))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-246)))) 
-(-912 R) 
+((|HasCategory| |#2| (QUOTE (-483))) (|HasCategory| |#2| (QUOTE (-973))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-553 (-473)))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-756))) (|HasCategory| |#2| (QUOTE (-246)))) 
+(-911 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| $) "\\spad{imagI(q)} extracts the imaginary \\spad{i} part of quaternion \\spad{q}.")) (|conjugate| (($ $) "\\spad{conjugate(q)} negates the imaginary parts of quaternion \\spad{q}."))) 
-((-3990 |has| |#1| (-246)) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((-3989 |has| |#1| (-246)) (-3990 . T) (-3991 . T) (-3993 . T)) 
 NIL 
-(-913 QR R QS S) 
+(-912 QR R QS S) 
 ((|constructor| (NIL "\\spadtype{QuaternionCategoryFunctions2} implements functions between two quaternion domains. The function \\spadfun{map} is used by the system interpreter to coerce between quaternion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,u)} maps \\spad{f} onto the component parts of the quaternion \\spad{u}."))) 
 NIL 
 NIL 
-(-914 S) 
+(-913 S) 
 ((|constructor| (NIL "Linked List implementation of a Queue")) (|queue| (($ (|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}."))) 
-((-3998 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-72)))) 
-(-915 S) 
+((-3997 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1013))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-72)))) 
+(-914 S) 
 ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|Fraction| (|Integer|))) "\\spad{x ** y} is the rational exponentiation of \\spad{x} by the power \\spad{y}.")) (|nthRoot| (($ $ (|Integer|)) "\\spad{nthRoot(x,n)} returns the \\spad{n}th root of \\spad{x}.")) (|sqrt| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) 
 NIL 
 NIL 
-(-916) 
+(-915) 
 ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|Fraction| (|Integer|))) "\\spad{x ** y} is the rational exponentiation of \\spad{x} by the power \\spad{y}.")) (|nthRoot| (($ $ (|Integer|)) "\\spad{nthRoot(x,n)} returns the \\spad{n}th root of \\spad{x}.")) (|sqrt| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) 
 NIL 
 NIL 
-(-917 -3094 UP UPUP |radicnd| |n|) 
+(-916 -3093 UP UPUP |radicnd| |n|) 
 ((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x})."))) 
-((-3990 |has| (-350 |#2|) (-312)) (-3995 |has| (-350 |#2|) (-312)) (-3989 |has| (-350 |#2|) (-312)) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
-((|HasCategory| (-350 |#2|) (QUOTE (-118))) (|HasCategory| (-350 |#2|) (QUOTE (-120))) (|HasCategory| (-350 |#2|) (QUOTE (-299))) (OR (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-299)))) (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-320))) (OR (-12 (|HasCategory| (-350 |#2|) (QUOTE (-190))) (|HasCategory| (-350 |#2|) (QUOTE (-312)))) (|HasCategory| (-350 |#2|) (QUOTE (-299)))) (OR (-12 (|HasCategory| (-350 |#2|) (QUOTE (-190))) (|HasCategory| (-350 |#2|) (QUOTE (-312)))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-189))) (|HasCategory| (-350 |#2|) (QUOTE (-312)))) (|HasCategory| (-350 |#2|) (QUOTE (-299)))) (OR (-12 (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-810 (-1091))))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-299))) (|HasCategory| (-350 |#2|) (QUOTE (-810 (-1091)))))) (OR (-12 (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-810 (-1091))))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-812 (-1091)))))) (|HasCategory| (-350 |#2|) (QUOTE (-581 (-485)))) (OR (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-951 (-350 (-485)))))) (|HasCategory| (-350 |#2|) (QUOTE (-951 (-350 (-485))))) (|HasCategory| (-350 |#2|) (QUOTE (-951 (-485)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-320))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-189))) (|HasCategory| (-350 |#2|) (QUOTE (-312)))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-812 (-1091))))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-190))) (|HasCategory| (-350 |#2|) (QUOTE (-312)))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-810 (-1091)))))) 
-(-918 |bb|) 
+((-3989 |has| (-350 |#2|) (-312)) (-3994 |has| (-350 |#2|) (-312)) (-3988 |has| (-350 |#2|) (-312)) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((|HasCategory| (-350 |#2|) (QUOTE (-118))) (|HasCategory| (-350 |#2|) (QUOTE (-120))) (|HasCategory| (-350 |#2|) (QUOTE (-299))) (OR (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-299)))) (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-320))) (OR (-12 (|HasCategory| (-350 |#2|) (QUOTE (-190))) (|HasCategory| (-350 |#2|) (QUOTE (-312)))) (|HasCategory| (-350 |#2|) (QUOTE (-299)))) (OR (-12 (|HasCategory| (-350 |#2|) (QUOTE (-190))) (|HasCategory| (-350 |#2|) (QUOTE (-312)))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-189))) (|HasCategory| (-350 |#2|) (QUOTE (-312)))) (|HasCategory| (-350 |#2|) (QUOTE (-299)))) (OR (-12 (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-809 (-1090))))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-299))) (|HasCategory| (-350 |#2|) (QUOTE (-809 (-1090)))))) (OR (-12 (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-809 (-1090))))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-811 (-1090)))))) (|HasCategory| (-350 |#2|) (QUOTE (-580 (-484)))) (OR (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-950 (-350 (-484)))))) (|HasCategory| (-350 |#2|) (QUOTE (-950 (-350 (-484))))) (|HasCategory| (-350 |#2|) (QUOTE (-950 (-484)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-320))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-189))) (|HasCategory| (-350 |#2|) (QUOTE (-312)))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-811 (-1090))))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-190))) (|HasCategory| (-350 |#2|) (QUOTE (-312)))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-809 (-1090)))))) 
+(-917 |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."))) 
-((-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
-((|HasCategory| (-485) (QUOTE (-822))) (|HasCategory| (-485) (QUOTE (-951 (-1091)))) (|HasCategory| (-485) (QUOTE (-118))) (|HasCategory| (-485) (QUOTE (-120))) (|HasCategory| (-485) (QUOTE (-554 (-474)))) (|HasCategory| (-485) (QUOTE (-934))) (|HasCategory| (-485) (QUOTE (-741))) (|HasCategory| (-485) (QUOTE (-757))) (OR (|HasCategory| (-485) (QUOTE (-741))) (|HasCategory| (-485) (QUOTE (-757)))) (|HasCategory| (-485) (QUOTE (-951 (-485)))) (|HasCategory| (-485) (QUOTE (-1067))) (|HasCategory| (-485) (QUOTE (-797 (-330)))) (|HasCategory| (-485) (QUOTE (-797 (-485)))) (|HasCategory| (-485) (QUOTE (-554 (-801 (-330))))) (|HasCategory| (-485) (QUOTE (-554 (-801 (-485))))) (|HasCategory| (-485) (QUOTE (-189))) (|HasCategory| (-485) (QUOTE (-812 (-1091)))) (|HasCategory| (-485) (QUOTE (-190))) (|HasCategory| (-485) (QUOTE (-810 (-1091)))) (|HasCategory| (-485) (QUOTE (-456 (-1091) (-485)))) (|HasCategory| (-485) (QUOTE (-260 (-485)))) (|HasCategory| (-485) (QUOTE (-241 (-485) (-485)))) (|HasCategory| (-485) (QUOTE (-258))) (|HasCategory| (-485) (QUOTE (-484))) (|HasCategory| (-485) (QUOTE (-581 (-485)))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-485) (QUOTE (-822)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-485) (QUOTE (-822)))) (|HasCategory| (-485) (QUOTE (-118))))) 
-(-919) 
+((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((|HasCategory| (-484) (QUOTE (-821))) (|HasCategory| (-484) (QUOTE (-950 (-1090)))) (|HasCategory| (-484) (QUOTE (-118))) (|HasCategory| (-484) (QUOTE (-120))) (|HasCategory| (-484) (QUOTE (-553 (-473)))) (|HasCategory| (-484) (QUOTE (-933))) (|HasCategory| (-484) (QUOTE (-740))) (|HasCategory| (-484) (QUOTE (-756))) (OR (|HasCategory| (-484) (QUOTE (-740))) (|HasCategory| (-484) (QUOTE (-756)))) (|HasCategory| (-484) (QUOTE (-950 (-484)))) (|HasCategory| (-484) (QUOTE (-1066))) (|HasCategory| (-484) (QUOTE (-796 (-330)))) (|HasCategory| (-484) (QUOTE (-796 (-484)))) (|HasCategory| (-484) (QUOTE (-553 (-800 (-330))))) (|HasCategory| (-484) (QUOTE (-553 (-800 (-484))))) (|HasCategory| (-484) (QUOTE (-189))) (|HasCategory| (-484) (QUOTE (-811 (-1090)))) (|HasCategory| (-484) (QUOTE (-190))) (|HasCategory| (-484) (QUOTE (-809 (-1090)))) (|HasCategory| (-484) (QUOTE (-455 (-1090) (-484)))) (|HasCategory| (-484) (QUOTE (-260 (-484)))) (|HasCategory| (-484) (QUOTE (-241 (-484) (-484)))) (|HasCategory| (-484) (QUOTE (-258))) (|HasCategory| (-484) (QUOTE (-483))) (|HasCategory| (-484) (QUOTE (-580 (-484)))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-484) (QUOTE (-821)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-484) (QUOTE (-821)))) (|HasCategory| (-484) (QUOTE (-118))))) 
+(-918) 
 ((|constructor| (NIL "This package provides tools for creating radix expansions.")) (|radix| (((|Any|) (|Fraction| (|Integer|)) (|Integer|)) "\\spad{radix(x,b)} converts \\spad{x} to a radix expansion in base \\spad{b}."))) 
 NIL 
 NIL 
-(-920) 
+(-919) 
 ((|constructor| (NIL "Random number generators \\indented{2}{All random numbers used in the system should originate from} \\indented{2}{the same generator.\\space{2}This package is intended to be the source.}")) (|seed| (((|Integer|)) "\\spad{seed()} returns the current seed value.")) (|reseed| (((|Void|) (|Integer|)) "\\spad{reseed(n)} restarts the random number generator at \\spad{n}.")) (|size| (((|Integer|)) "\\spad{size()} is the base of the random number generator")) (|randnum| (((|Integer|) (|Integer|)) "\\spad{randnum(n)} is a random number between 0 and \\spad{n}.") (((|Integer|)) "\\spad{randnum()} is a random number between 0 and size()."))) 
 NIL 
 NIL 
-(-921 RP) 
+(-920 RP) 
 ((|factorSquareFree| (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(p)} factors an extended squareFree polynomial \\spad{p} over the rational numbers.")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(p)} factors an extended polynomial \\spad{p} over the rational numbers."))) 
 NIL 
 NIL 
-(-922 S) 
+(-921 S) 
 ((|constructor| (NIL "rational number testing and retraction functions. Date Created: March 1990 Date Last Updated: 9 April 1991")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") |#1|) "\\spad{rationalIfCan(x)} returns \\spad{x} as a rational number,{} \"failed\" if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) |#1|) "\\spad{rational?(x)} returns \\spad{true} if \\spad{x} is a rational number,{} \\spad{false} otherwise.")) (|rational| (((|Fraction| (|Integer|)) |#1|) "\\spad{rational(x)} returns \\spad{x} as a rational number; error if \\spad{x} is not a rational number."))) 
 NIL 
 NIL 
-(-923 A S) 
+(-922 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 
-((|HasCategory| |#1| (|%list| (QUOTE -1036) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-72)))) 
-(-924 S) 
+((|HasCategory| |#1| (|%list| (QUOTE -1035) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-72)))) 
+(-923 S) 
 ((|constructor| (NIL "A recursive aggregate over a type \\spad{S} is a model for a a directed graph containing values of type \\spad{S}. Recursively,{} a recursive aggregate is a {\\em node} consisting of a \\spadfun{value} from \\spad{S} and 0 or more \\spadfun{children} which are recursive aggregates. A node with no children is called a \\spadfun{leaf} node. A recursive aggregate may be cyclic for which some operations as noted may go into an infinite loop.")) (|setvalue!| ((|#1| $ |#1|) "\\spad{setvalue!(u,x)} sets the value of node \\spad{u} to \\spad{x}.")) (|setelt| ((|#1| $ "value" |#1|) "\\spad{setelt(a,\"value\",x)} (also written \\axiom{a . value := \\spad{x}}) is equivalent to \\axiom{setvalue!(a,{}\\spad{x})}")) (|setchildren!| (($ $ (|List| $)) "\\spad{setchildren!(u,v)} replaces the current children of node \\spad{u} with the members of \\spad{v} in left-to-right order.")) (|node?| (((|Boolean|) $ $) "\\spad{node?(u,v)} tests if node \\spad{u} is contained in node \\spad{v} (either as a child,{} a child of a child,{} etc.).")) (|child?| (((|Boolean|) $ $) "\\spad{child?(u,v)} tests if node \\spad{u} is a child of node \\spad{v}.")) (|distance| (((|Integer|) $ $) "\\spad{distance(u,v)} returns the path length (an integer) from node \\spad{u} to \\spad{v}.")) (|leaves| (((|List| |#1|) $) "\\spad{leaves(t)} returns the list of values in obtained by visiting the nodes of tree \\axiom{\\spad{t}} in left-to-right order.")) (|cyclic?| (((|Boolean|) $) "\\spad{cyclic?(u)} tests if \\spad{u} has a cycle.")) (|elt| ((|#1| $ "value") "\\spad{elt(u,\"value\")} (also written: \\axiom{a. value}) is equivalent to \\axiom{value(a)}.")) (|value| ((|#1| $) "\\spad{value(u)} returns the value of the node \\spad{u}.")) (|leaf?| (((|Boolean|) $) "\\spad{leaf?(u)} tests if \\spad{u} is a terminal node.")) (|nodes| (((|List| $) $) "\\spad{nodes(u)} returns a list of all of the nodes of aggregate \\spad{u}.")) (|children| (((|List| $) $) "\\spad{children(u)} returns a list of the children of aggregate \\spad{u}."))) 
 NIL 
 NIL 
-(-925 S) 
+(-924 S) 
 ((|constructor| (NIL "\\axiomType{RealClosedField} provides common acces functions for all real closed fields.")) (|approximate| (((|Fraction| (|Integer|)) $ $) "\\axiom{approximate(\\spad{n},{}\\spad{p})} gives an approximation of \\axiom{\\spad{n}} that has precision \\axiom{\\spad{p}}")) (|rename| (($ $ (|OutputForm|)) "\\axiom{rename(\\spad{x},{}name)} gives a new number that prints as name")) (|rename!| (($ $ (|OutputForm|)) "\\axiom{rename!(\\spad{x},{}name)} changes the way \\axiom{\\spad{x}} is printed")) (|sqrt| (($ (|Integer|)) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} ** (1/2)}") (($ (|Fraction| (|Integer|))) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} ** (1/2)}") (($ $) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} ** (1/2)}") (($ $ (|PositiveInteger|)) "\\axiom{sqrt(\\spad{x},{}\\spad{n})} is \\axiom{\\spad{x} ** (1/n)}")) (|allRootsOf| (((|List| $) (|Polynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely")) (|rootOf| (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|)) "\\axiom{rootOf(pol,{}\\spad{n})} creates the \\spad{n}th root for the order of \\axiom{pol} and gives it unique name") (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|) (|OutputForm|)) "\\axiom{rootOf(pol,{}\\spad{n},{}name)} creates the \\spad{n}th root for the order of \\axiom{pol} and names it \\axiom{name}")) (|mainValue| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainValue(\\spad{x})} is the expression of \\axiom{\\spad{x}} in terms of \\axiom{SparseUnivariatePolynomial(\\$)}")) (|mainDefiningPolynomial| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainDefiningPolynomial(\\spad{x})} is the defining polynomial for the main algebraic quantity of \\axiom{\\spad{x}}")) (|mainForm| (((|Union| (|OutputForm|) "failed") $) "\\axiom{mainForm(\\spad{x})} is the main algebraic quantity name of \\axiom{\\spad{x}}"))) 
 NIL 
 NIL 
-(-926) 
+(-925) 
 ((|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}}"))) 
-((-3990 . T) (-3995 . T) (-3989 . T) (-3992 . T) (-3991 . T) ((-3999 "*") . T) (-3994 . T)) 
+((-3989 . T) (-3994 . T) (-3988 . T) (-3991 . T) (-3990 . T) ((-3998 "*") . T) (-3993 . T)) 
 NIL 
-(-927 R -3094) 
+(-926 R -3093) 
 ((|constructor| (NIL "\\indented{1}{Risch differential equation,{} elementary case.} Author: Manuel Bronstein Date Created: 1 February 1988 Date Last Updated: 2 November 1995 Keywords: elementary,{} function,{} integration.")) (|rischDE| (((|Record| (|:| |ans| |#2|) (|:| |right| |#2|) (|:| |sol?| (|Boolean|))) (|Integer|) |#2| |#2| (|Symbol|) (|Mapping| (|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|List| |#2|)) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| |#2|)) "\\spad{rischDE(n, f, g, x, lim, ext)} returns \\spad{[y, h, b]} such that \\spad{dy/dx + n df/dx y = h} and \\spad{b := h = g}. The equation \\spad{dy/dx + n df/dx y = g} has no solution if \\spad{h \\~~= g} (\\spad{y} is a partial solution in that case). Notes: \\spad{lim} is a limited integration function,{} and ext is an extended integration function."))) 
 NIL 
 NIL 
-(-928 R -3094) 
+(-927 R -3093) 
 ((|constructor| (NIL "\\indented{1}{Risch differential equation,{} elementary case.} Author: Manuel Bronstein Date Created: 12 August 1992 Date Last Updated: 17 August 1992 Keywords: elementary,{} function,{} integration.")) (|rischDEsys| (((|Union| (|List| |#2|) "failed") (|Integer|) |#2| |#2| |#2| (|Symbol|) (|Mapping| (|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|List| |#2|)) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| |#2|)) "\\spad{rischDEsys(n, f, g_1, g_2, x,lim,ext)} returns \\spad{y_1.y_2} such that \\spad{(dy1/dx,dy2/dx) + ((0, - n df/dx),(n df/dx,0)) (y1,y2) = (g1,g2)} if \\spad{y_1,y_2} exist,{} \"failed\" otherwise. \\spad{lim} is a limited integration function,{} \\spad{ext} is an extended integration function."))) 
 NIL 
 NIL 
-(-929 -3094 UP) 
+(-928 -3093 UP) 
 ((|constructor| (NIL "\\indented{1}{Risch differential equation,{} transcendental case.} Author: Manuel Bronstein Date Created: Jan 1988 Date Last Updated: 2 November 1995")) (|polyRDE| (((|Union| (|:| |ans| (|Record| (|:| |ans| |#2|) (|:| |nosol| (|Boolean|)))) (|:| |eq| (|Record| (|:| |b| |#2|) (|:| |c| |#2|) (|:| |m| (|Integer|)) (|:| |alpha| |#2|) (|:| |beta| |#2|)))) |#2| |#2| |#2| (|Integer|) (|Mapping| |#2| |#2|)) "\\spad{polyRDE(a, B, C, n, D)} returns either: 1. \\spad{[Q, b]} such that \\spad{degree(Q) <= n} and \\indented{3}{\\spad{a Q'+ B Q = C} if \\spad{b = true},{} \\spad{Q} is a partial solution} \\indented{3}{otherwise.} 2. \\spad{[B1, C1, m, \\alpha, \\beta]} such that any polynomial solution \\indented{3}{of degree at most \\spad{n} of \\spad{A Q' + BQ = C} must be of the form} \\indented{3}{\\spad{Q = \\alpha H + \\beta} where \\spad{degree(H) <= m} and} \\indented{3}{\\spad{H} satisfies \\spad{H' + B1 H = C1}.} \\spad{D} is the derivation to use.")) (|baseRDE| (((|Record| (|:| |ans| (|Fraction| |#2|)) (|:| |nosol| (|Boolean|))) (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{baseRDE(f, g)} returns a \\spad{[y, b]} such that \\spad{y' + fy = g} if \\spad{b = true},{} \\spad{y} is a partial solution otherwise (no solution in that case). \\spad{D} is the derivation to use.")) (|monomRDE| (((|Union| (|Record| (|:| |a| |#2|) (|:| |b| (|Fraction| |#2|)) (|:| |c| (|Fraction| |#2|)) (|:| |t| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{monomRDE(f,g,D)} returns \\spad{[A, B, C, T]} such that \\spad{y' + f y = g} has a solution if and only if \\spad{y = Q / T},{} where \\spad{Q} satisfies \\spad{A Q' + B Q = C} and has no normal pole. A and \\spad{T} are polynomials and \\spad{B} and \\spad{C} have no normal poles. \\spad{D} is the derivation to use."))) 
 NIL 
 NIL 
-(-930 -3094 UP) 
+(-929 -3093 UP) 
 ((|constructor| (NIL "\\indented{1}{Risch differential equation system,{} transcendental case.} Author: Manuel Bronstein Date Created: 17 August 1992 Date Last Updated: 3 February 1994")) (|baseRDEsys| (((|Union| (|List| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{baseRDEsys(f, g1, g2)} returns fractions \\spad{y_1.y_2} such that \\spad{(y1', y2') + ((0, -f), (f, 0)) (y1,y2) = (g1,g2)} if \\spad{y_1,y_2} exist,{} \"failed\" otherwise.")) (|monomRDEsys| (((|Union| (|Record| (|:| |a| |#2|) (|:| |b| (|Fraction| |#2|)) (|:| |h| |#2|) (|:| |c1| (|Fraction| |#2|)) (|:| |c2| (|Fraction| |#2|)) (|:| |t| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{monomRDEsys(f,g1,g2,D)} returns \\spad{[A, B, H, C1, C2, T]} such that \\spad{(y1', y2') + ((0, -f), (f, 0)) (y1,y2) = (g1,g2)} has a solution if and only if \\spad{y1 = Q1 / T, y2 = Q2 / T},{} where \\spad{B,C1,C2,Q1,Q2} have no normal poles and satisfy A \\spad{(Q1', Q2') + ((H, -B), (B, H)) (Q1,Q2) = (C1,C2)} \\spad{D} is the derivation to use."))) 
 NIL 
 NIL 
-(-931 S) 
+(-930 S) 
 ((|constructor| (NIL "This package exports random distributions")) (|rdHack1| (((|Mapping| |#1|) (|Vector| |#1|) (|Vector| (|Integer|)) (|Integer|)) "\\spad{rdHack1(v,u,n)} \\undocumented")) (|weighted| (((|Mapping| |#1|) (|List| (|Record| (|:| |value| |#1|) (|:| |weight| (|Integer|))))) "\\spad{weighted(l)} \\undocumented")) (|uniform| (((|Mapping| |#1|) (|Set| |#1|)) "\\spad{uniform(s)} \\undocumented"))) 
 NIL 
 NIL 
-(-932 F1 UP UPUP R F2) 
+(-931 F1 UP UPUP R F2) 
 ((|constructor| (NIL "\\indented{1}{Finds the order of a divisor over a finite field} Author: Manuel Bronstein Date Created: 1988 Date Last Updated: 8 November 1994")) (|order| (((|NonNegativeInteger|) (|FiniteDivisor| |#1| |#2| |#3| |#4|) |#3| (|Mapping| |#5| |#1|)) "\\spad{order(f,u,g)} \\undocumented"))) 
 NIL 
 NIL 
-(-933) 
+(-932) 
 ((|constructor| (NIL "This domain represents list reduction syntax.")) (|body| (((|SpadAst|) $) "\\spad{body(e)} return the list of expressions being redcued.")) (|operator| (((|SpadAst|) $) "\\spad{operator(e)} returns the magma operation being applied."))) 
 NIL 
 NIL 
-(-934) 
+(-933) 
 ((|constructor| (NIL "The category of real numeric domains,{} \\spadignore{i.e.} convertible to floats."))) 
 NIL 
 NIL 
-(-935 |Pol|) 
+(-934 |Pol|) 
 ((|constructor| (NIL "\\indented{2}{This package provides functions for finding the real zeros} of univariate polynomials over the integers to arbitrary user-specified precision. The results are returned as a list of isolating intervals which are expressed as records with \"left\" and \"right\" rational number components.")) (|midpoints| (((|List| (|Fraction| (|Integer|))) (|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))))) "\\spad{midpoints(isolist)} returns the list of midpoints for the list of intervals \\spad{isolist}.")) (|midpoint| (((|Fraction| (|Integer|)) (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{midpoint(int)} returns the midpoint of the interval \\spad{int}.")) (|refine| (((|Union| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) "failed") |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{refine(pol, int, range)} takes a univariate polynomial \\spad{pol} and and isolating interval \\spad{int} containing exactly one real root of \\spad{pol}; the operation returns an isolating interval which is contained within range,{} or \"failed\" if no such isolating interval exists.") (((|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|))) "\\spad{refine(pol, int, eps)} refines the interval \\spad{int} containing exactly one root of the univariate polynomial \\spad{pol} to size less than the rational number eps.")) (|realZeros| (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|))) "\\spad{realZeros(pol, int, eps)} returns a list of intervals of length less than the rational number eps for all the real roots of the polynomial \\spad{pol} which lie in the interval expressed by the record \\spad{int}.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Fraction| (|Integer|))) "\\spad{realZeros(pol, eps)} returns a list of intervals of length less than the rational number eps for all the real roots of the polynomial \\spad{pol}.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{realZeros(pol, range)} returns a list of isolating intervals for all the real zeros of the univariate polynomial \\spad{pol} which lie in the interval expressed by the record range.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1|) "\\spad{realZeros(pol)} returns a list of isolating intervals for all the real zeros of the univariate polynomial \\spad{pol}."))) 
 NIL 
 NIL 
-(-936 |Pol|) 
+(-935 |Pol|) 
 ((|constructor| (NIL "\\indented{2}{This package provides functions for finding the real zeros} of univariate polynomials over the rational numbers to arbitrary user-specified precision. The results are returned as a list of isolating intervals,{} expressed as records with \"left\" and \"right\" rational number components.")) (|refine| (((|Union| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) "failed") |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{refine(pol, int, range)} takes a univariate polynomial \\spad{pol} and and isolating interval \\spad{int} which must contain exactly one real root of \\spad{pol},{} and returns an isolating interval which is contained within range,{} or \"failed\" if no such isolating interval exists.") (((|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|))) "\\spad{refine(pol, int, eps)} refines the interval \\spad{int} containing exactly one root of the univariate polynomial \\spad{pol} to size less than the rational number eps.")) (|realZeros| (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|))) "\\spad{realZeros(pol, int, eps)} returns a list of intervals of length less than the rational number eps for all the real roots of the polynomial \\spad{pol} which lie in the interval expressed by the record \\spad{int}.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Fraction| (|Integer|))) "\\spad{realZeros(pol, eps)} returns a list of intervals of length less than the rational number eps for all the real roots of the polynomial \\spad{pol}.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{realZeros(pol, range)} returns a list of isolating intervals for all the real zeros of the univariate polynomial \\spad{pol} which lie in the interval expressed by the record range.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1|) "\\spad{realZeros(pol)} returns a list of isolating intervals for all the real zeros of the univariate polynomial \\spad{pol}."))) 
 NIL 
 NIL 
-(-937) 
+(-936) 
 ((|constructor| (NIL "\\indented{1}{This package provides numerical solutions of systems of polynomial} equations for use in ACPLOT.")) (|realSolve| (((|List| (|List| (|Float|))) (|List| (|Polynomial| (|Integer|))) (|List| (|Symbol|)) (|Float|)) "\\spad{realSolve(lp,lv,eps)} = compute the list of the real solutions of the list \\spad{lp} of polynomials with integer coefficients with respect to the variables in \\spad{lv},{} with precision \\spad{eps}.")) (|solve| (((|List| (|Float|)) (|Polynomial| (|Integer|)) (|Float|)) "\\spad{solve(p,eps)} finds the real zeroes of a univariate integer polynomial \\spad{p} with precision \\spad{eps}.") (((|List| (|Float|)) (|Polynomial| (|Fraction| (|Integer|))) (|Float|)) "\\spad{solve(p,eps)} finds the real zeroes of a univariate rational polynomial \\spad{p} with precision \\spad{eps}."))) 
 NIL 
 NIL 
-(-938 |TheField|) 
+(-937 |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"))) 
-((-3990 . T) (-3995 . T) (-3989 . T) (-3992 . T) (-3991 . T) ((-3999 "*") . T) (-3994 . T)) 
-((OR (|HasCategory| |#1| (QUOTE (-951 (-485)))) (|HasCategory| (-350 (-485)) (QUOTE (-951 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (|HasCategory| (-350 (-485)) (QUOTE (-951 (-350 (-485))))) (|HasCategory| (-350 (-485)) (QUOTE (-951 (-485))))) 
-(-939 -3094 L) 
+((-3989 . T) (-3994 . T) (-3988 . T) (-3991 . T) (-3990 . T) ((-3998 "*") . T) (-3993 . T)) 
+((OR (|HasCategory| |#1| (QUOTE (-950 (-484)))) (|HasCategory| (-350 (-484)) (QUOTE (-950 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-484)))) (|HasCategory| (-350 (-484)) (QUOTE (-950 (-350 (-484))))) (|HasCategory| (-350 (-484)) (QUOTE (-950 (-484))))) 
+(-938 -3093 L) 
 ((|constructor| (NIL "\\spadtype{ReductionOfOrder} provides functions for reducing the order of linear ordinary differential equations once some solutions are known.")) (|ReduceOrder| (((|Record| (|:| |eq| |#2|) (|:| |op| (|List| |#1|))) |#2| (|List| |#1|)) "\\spad{ReduceOrder(op, [f1,...,fk])} returns \\spad{[op1,[g1,...,gk]]} such that for any solution \\spad{z} of \\spad{op1 z = 0},{} \\spad{y = gk \\int(g_{k-1} \\int(... \\int(g1 \\int z)...)} is a solution of \\spad{op y = 0}. Each \\spad{fi} must satisfy \\spad{op fi = 0}.") ((|#2| |#2| |#1|) "\\spad{ReduceOrder(op, s)} returns \\spad{op1} such that for any solution \\spad{z} of \\spad{op1 z = 0},{} \\spad{y = s \\int z} is a solution of \\spad{op y = 0}. \\spad{s} must satisfy \\spad{op s = 0}."))) 
 NIL 
 NIL 
-(-940 S) 
+(-939 S) 
 ((|constructor| (NIL "\\indented{1}{\\spadtype{Reference} is for making a changeable instance} of something.")) (= (((|Boolean|) $ $) "\\spad{a=b} tests if \\spad{a} and \\spad{b} are equal.")) (|setref| ((|#1| $ |#1|) "\\spad{setref(r,s)} reset the reference \\spad{r} to refer to \\spad{s}")) (|deref| ((|#1| $) "\\spad{deref(r)} returns the object referenced by \\spad{r}")) (|ref| (($ |#1|) "\\spad{ref(s)} creates a reference to the object \\spad{s}."))) 
 NIL 
 NIL 
-(-941 R E V P) 
+(-940 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."))) 
-((-3998 . T)) 
-((-12 (|HasCategory| |#4| (QUOTE (-1014))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-554 (-474)))) (|HasCategory| |#4| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#3| (QUOTE (-320))) (|HasCategory| |#4| (QUOTE (-553 (-773)))) (|HasCategory| |#4| (QUOTE (-1014))) (-12 (|HasCategory| |#4| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#4|)))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#4|)))) 
-(-942) 
+((-3997 . T)) 
+((-12 (|HasCategory| |#4| (QUOTE (-1013))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-553 (-473)))) (|HasCategory| |#4| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#3| (QUOTE (-320))) (|HasCategory| |#4| (QUOTE (-552 (-772)))) (|HasCategory| |#4| (QUOTE (-1013))) (-12 (|HasCategory| |#4| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#4|)))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#4|)))) 
+(-941) 
 ((|constructor| (NIL "Package for the computation of eigenvalues and eigenvectors. This package works for matrices with coefficients which are rational functions over the integers. (see \\spadtype{Fraction Polynomial Integer}). The eigenvalues and eigenvectors are expressed in terms of radicals.")) (|orthonormalBasis| (((|List| (|Matrix| (|Expression| (|Integer|)))) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{orthonormalBasis(m)} returns the orthogonal matrix \\spad{b} such that \\spad{b*m*(inverse b)} is diagonal. Error: if \\spad{m} is not a symmetric matrix.")) (|gramschmidt| (((|List| (|Matrix| (|Expression| (|Integer|)))) (|List| (|Matrix| (|Expression| (|Integer|))))) "\\spad{gramschmidt(lv)} converts the list of column vectors \\spad{lv} into a set of orthogonal column vectors of euclidean length 1 using the Gram-Schmidt algorithm.")) (|normalise| (((|Matrix| (|Expression| (|Integer|))) (|Matrix| (|Expression| (|Integer|)))) "\\spad{normalise(v)} returns the column vector \\spad{v} divided by its euclidean norm; when possible,{} the vector \\spad{v} is expressed in terms of radicals.")) (|eigenMatrix| (((|Union| (|Matrix| (|Expression| (|Integer|))) "failed") (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{eigenMatrix(m)} returns the matrix \\spad{b} such that \\spad{b*m*(inverse b)} is diagonal,{} or \"failed\" if no such \\spad{b} exists.")) (|radicalEigenvalues| (((|List| (|Expression| (|Integer|))) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{radicalEigenvalues(m)} computes the eigenvalues of the matrix \\spad{m}; when possible,{} the eigenvalues are expressed in terms of radicals.")) (|radicalEigenvector| (((|List| (|Matrix| (|Expression| (|Integer|)))) (|Expression| (|Integer|)) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{radicalEigenvector(c,m)} computes the eigenvector(\\spad{s}) of the matrix \\spad{m} corresponding to the eigenvalue \\spad{c}; when possible,{} values are expressed in terms of radicals.")) (|radicalEigenvectors| (((|List| (|Record| (|:| |radval| (|Expression| (|Integer|))) (|:| |radmult| (|Integer|)) (|:| |radvect| (|List| (|Matrix| (|Expression| (|Integer|))))))) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{radicalEigenvectors(m)} computes the eigenvalues and the corresponding eigenvectors of the matrix \\spad{m}; when possible,{} values are expressed in terms of radicals."))) 
 NIL 
 NIL 
-(-943 R) 
+(-942 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 (-3999 "*")))) 
-(-944 R) 
+((|HasAttribute| |#1| (QUOTE (-3998 "*")))) 
+(-943 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 (-312))) (|HasCategory| |#1| (QUOTE (-320)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-258)))) 
-(-945 S) 
+(-944 S) 
 ((|constructor| (NIL "Implements multiplication by repeated addition")) (|double| ((|#1| (|PositiveInteger|) |#1|) "\\spad{double(i, r)} multiplies \\spad{r} by \\spad{i} using repeated doubling.")) (+ (($ $ $) "\\spad{x+y} returns the sum of \\spad{x} and \\spad{y}"))) 
 NIL 
 NIL 
-(-946 S) 
+(-945 S) 
 ((|constructor| (NIL "Implements exponentiation by repeated squaring")) (|expt| ((|#1| |#1| (|PositiveInteger|)) "\\spad{expt(r, i)} computes r**i by repeated squaring")) (* (($ $ $) "\\spad{x*y} returns the product of \\spad{x} and \\spad{y}"))) 
 NIL 
 NIL 
-(-947 S) 
+(-946 S) 
 ((|constructor| (NIL "This package provides coercions for the special types \\spadtype{Exit} and \\spadtype{Void}.")) (|coerce| ((|#1| (|Exit|)) "\\spad{coerce(e)} is never really evaluated. This coercion is used for formal type correctness when a function will not return directly to its caller.") (((|Void|) |#1|) "\\spad{coerce(s)} throws all information about \\spad{s} away. This coercion allows values of any type to appear in contexts where they will not be used. For example,{} it allows the resolution of different types in the \\spad{then} and \\spad{else} branches when an \\spad{if} is in a context where the resulting value is not used."))) 
 NIL 
 NIL 
-(-948 -3094 |Expon| |VarSet| |FPol| |LFPol|) 
+(-947 -3093 |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"))) 
-(((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
+(((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
 NIL 
-(-949) 
+(-948) 
 ((|constructor| (NIL "This domain represents `return' expressions.")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression returned by `e'."))) 
 NIL 
 NIL 
-(-950 A S) 
+(-949 A S) 
 ((|constructor| (NIL "A is retractable to \\spad{B} means that some elementsif A can be converted into elements of \\spad{B} and any element of \\spad{B} can be converted into an element of A.")) (|retract| ((|#2| $) "\\spad{retract(a)} transforms a into an element of \\spad{S} if possible. Error: if a cannot be made into an element of \\spad{S}.")) (|retractIfCan| (((|Union| |#2| "failed") $) "\\spad{retractIfCan(a)} transforms a into an element of \\spad{S} if possible. Returns \"failed\" if a cannot be made into an element of \\spad{S}."))) 
 NIL 
 NIL 
-(-951 S) 
+(-950 S) 
 ((|constructor| (NIL "A is retractable to \\spad{B} means that some elementsif A can be converted into elements of \\spad{B} and any element of \\spad{B} can be converted into an element of A.")) (|retract| ((|#1| $) "\\spad{retract(a)} transforms a into an element of \\spad{S} if possible. Error: if a cannot be made into an element of \\spad{S}.")) (|retractIfCan| (((|Union| |#1| "failed") $) "\\spad{retractIfCan(a)} transforms a into an element of \\spad{S} if possible. Returns \"failed\" if a cannot be made into an element of \\spad{S}."))) 
 NIL 
 NIL 
-(-952 Q R) 
+(-951 Q R) 
 ((|constructor| (NIL "RetractSolvePackage is an interface to \\spadtype{SystemSolvePackage} that attempts to retract the coefficients of the equations before solving.")) (|solveRetract| (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#2|))))) (|List| (|Polynomial| |#2|)) (|List| (|Symbol|))) "\\spad{solveRetract(lp,lv)} finds the solutions of the list \\spad{lp} of rational functions with respect to the list of symbols \\spad{lv}. The function tries to retract all the coefficients of the equations to \\spad{Q} before solving if possible."))) 
 NIL 
 NIL 
-(-953 R) 
+(-952 R) 
 ((|constructor| (NIL "Utilities that provide the same top-level manipulations on fractions than on polynomials.")) (|coerce| (((|Fraction| (|Polynomial| |#1|)) |#1|) "\\spad{coerce(r)} returns \\spad{r} viewed as a rational function over \\spad{R}.")) (|eval| (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) "\\spad{eval(f, [v1 = g1,...,vn = gn])} returns \\spad{f} with each \\spad{vi} replaced by \\spad{gi} in parallel,{} \\spadignore{i.e.} \\spad{vi}'s appearing inside the \\spad{gi}'s are not replaced. Error: if any \\spad{vi} is not a symbol.") (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|)))) "\\spad{eval(f, v = g)} returns \\spad{f} with \\spad{v} replaced by \\spad{g}. Error: if \\spad{v} is not a symbol.") (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|List| (|Symbol|)) (|List| (|Fraction| (|Polynomial| |#1|)))) "\\spad{eval(f, [v1,...,vn], [g1,...,gn])} returns \\spad{f} with each \\spad{vi} replaced by \\spad{gi} in parallel,{} \\spadignore{i.e.} \\spad{vi}'s appearing inside the \\spad{gi}'s are not replaced.") (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|))) "\\spad{eval(f, v, g)} returns \\spad{f} with \\spad{v} replaced by \\spad{g}.")) (|multivariate| (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|)))) (|Symbol|)) "\\spad{multivariate(f, v)} applies both the numerator and denominator of \\spad{f} to \\spad{v}.")) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|)))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{univariate(f, v)} returns \\spad{f} viewed as a univariate rational function in \\spad{v}.")) (|mainVariable| (((|Union| (|Symbol|) "failed") (|Fraction| (|Polynomial| |#1|))) "\\spad{mainVariable(f)} returns the highest variable appearing in the numerator or the denominator of \\spad{f},{} \"failed\" if \\spad{f} has no variables.")) (|variables| (((|List| (|Symbol|)) (|Fraction| (|Polynomial| |#1|))) "\\spad{variables(f)} returns the list of variables appearing in the numerator or the denominator of \\spad{f}."))) 
 NIL 
 NIL 
-(-954) 
+(-953) 
 ((|t| (((|Mapping| (|Float|)) (|NonNegativeInteger|)) "\\spad{t(n)} \\undocumented")) (F (((|Mapping| (|Float|)) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{F(n,m)} \\undocumented")) (|Beta| (((|Mapping| (|Float|)) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{Beta(n,m)} \\undocumented")) (|chiSquare| (((|Mapping| (|Float|)) (|NonNegativeInteger|)) "\\spad{chiSquare(n)} \\undocumented")) (|exponential| (((|Mapping| (|Float|)) (|Float|)) "\\spad{exponential(f)} \\undocumented")) (|normal| (((|Mapping| (|Float|)) (|Float|) (|Float|)) "\\spad{normal(f,g)} \\undocumented")) (|uniform| (((|Mapping| (|Float|)) (|Float|) (|Float|)) "\\spad{uniform(f,g)} \\undocumented")) (|chiSquare1| (((|Float|) (|NonNegativeInteger|)) "\\spad{chiSquare1(n)} \\undocumented")) (|exponential1| (((|Float|)) "\\spad{exponential1()} \\undocumented")) (|normal01| (((|Float|)) "\\spad{normal01()} \\undocumented")) (|uniform01| (((|Float|)) "\\spad{uniform01()} \\undocumented"))) 
 NIL 
 NIL 
-(-955 UP) 
+(-954 UP) 
 ((|constructor| (NIL "Factorization of univariate polynomials with coefficients which are rational functions with integer coefficients.")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p}."))) 
 NIL 
 NIL 
-(-956 R) 
+(-955 R) 
 ((|constructor| (NIL "\\spadtype{RationalFunctionFactorizer} contains the factor function (called factorFraction) which factors fractions of polynomials by factoring the numerator and denominator. Since any non zero fraction is a unit the usual factor operation will just return the original fraction.")) (|factorFraction| (((|Fraction| (|Factored| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|))) "\\spad{factorFraction(r)} factors the numerator and the denominator of the polynomial fraction \\spad{r}."))) 
 NIL 
 NIL 
-(-957 T$) 
+(-956 T$) 
 ((|constructor| (NIL "This category defines the common interface for RGB color models.")) (|componentUpperBound| ((|#1|) "componentUpperBound is an upper bound for all component values.")) (|blue| ((|#1| $) "\\spad{blue(c)} returns the `blue' component of `c'.")) (|green| ((|#1| $) "\\spad{green(c)} returns the `green' component of `c'.")) (|red| ((|#1| $) "\\spad{red(c)} returns the `red' component of `c'."))) 
 NIL 
 NIL 
-(-958 T$) 
+(-957 T$) 
 ((|constructor| (NIL "This category defines the common interface for RGB color spaces.")) (|whitePoint| (($) "whitePoint is the contant indicating the white point of this color space."))) 
 NIL 
 NIL 
-(-959 R |ls|) 
+(-958 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}."))) 
-((-3998 . T)) 
-((-12 (|HasCategory| (-704 |#1| (-774 |#2|)) (QUOTE (-1014))) (|HasCategory| (-704 |#1| (-774 |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -704) (|devaluate| |#1|) (|%list| (QUOTE -774) (|devaluate| |#2|)))))) (|HasCategory| (-704 |#1| (-774 |#2|)) (QUOTE (-554 (-474)))) (|HasCategory| (-704 |#1| (-774 |#2|)) (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| (-774 |#2|) (QUOTE (-320))) (|HasCategory| (-704 |#1| (-774 |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| (-704 |#1| (-774 |#2|)) (QUOTE (-1014))) (-12 (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -704) (|devaluate| |#1|) (|%list| (QUOTE -774) (|devaluate| |#2|))))) (|HasCategory| (-704 |#1| (-774 |#2|)) (QUOTE (-72)))) (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -704) (|devaluate| |#1|) (|%list| (QUOTE -774) (|devaluate| |#2|)))))) 
-(-960) 
+((-3997 . T)) 
+((-12 (|HasCategory| (-703 |#1| (-773 |#2|)) (QUOTE (-1013))) (|HasCategory| (-703 |#1| (-773 |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -703) (|devaluate| |#1|) (|%list| (QUOTE -773) (|devaluate| |#2|)))))) (|HasCategory| (-703 |#1| (-773 |#2|)) (QUOTE (-553 (-473)))) (|HasCategory| (-703 |#1| (-773 |#2|)) (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| (-773 |#2|) (QUOTE (-320))) (|HasCategory| (-703 |#1| (-773 |#2|)) (QUOTE (-552 (-772)))) (|HasCategory| (-703 |#1| (-773 |#2|)) (QUOTE (-1013))) (-12 (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -703) (|devaluate| |#1|) (|%list| (QUOTE -773) (|devaluate| |#2|))))) (|HasCategory| (-703 |#1| (-773 |#2|)) (QUOTE (-72)))) (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -703) (|devaluate| |#1|) (|%list| (QUOTE -773) (|devaluate| |#2|)))))) 
+(-959) 
 ((|constructor| (NIL "This package exports integer distributions")) (|ridHack1| (((|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{ridHack1(i,j,k,l)} \\undocumented")) (|geometric| (((|Mapping| (|Integer|)) |RationalNumber|) "\\spad{geometric(f)} \\undocumented")) (|poisson| (((|Mapping| (|Integer|)) |RationalNumber|) "\\spad{poisson(f)} \\undocumented")) (|binomial| (((|Mapping| (|Integer|)) (|Integer|) |RationalNumber|) "\\spad{binomial(n,f)} \\undocumented")) (|uniform| (((|Mapping| (|Integer|)) (|Segment| (|Integer|))) "\\spad{uniform(s)} \\undocumented"))) 
 NIL 
 NIL 
-(-961 S) 
+(-960 S) 
 ((|constructor| (NIL "The category of rings with unity,{} always associative,{} but not necessarily commutative.")) (|unitsKnown| ((|attribute|) "recip truly yields reciprocal or \"failed\" if not a unit. Note: \\spad{recip(0) = \"failed\"}.")) (|characteristic| (((|NonNegativeInteger|)) "\\spad{characteristic()} returns the characteristic of the ring this is the smallest positive integer \\spad{n} such that \\spad{n*x=0} for all \\spad{x} in the ring,{} or zero if no such \\spad{n} exists."))) 
 NIL 
 NIL 
-(-962) 
+(-961) 
 ((|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."))) 
-((-3994 . T)) 
+((-3993 . T)) 
 NIL 
-(-963 |xx| -3094) 
+(-962 |xx| -3093) 
 ((|constructor| (NIL "This package exports rational interpolation algorithms"))) 
 NIL 
 NIL 
-(-964 S) 
+(-963 S) 
 ((|constructor| (NIL "\\indented{2}{A set is an \\spad{S}-right linear set if it is stable by right-dilation} \\indented{2}{by elements in the semigroup \\spad{S}.} See Also: LeftLinearSet.")) (* (($ $ |#1|) "\\spad{x*s} is the right-dilation of \\spad{x} by \\spad{s}."))) 
 NIL 
 NIL 
-(-965 S |m| |n| R |Row| |Col|) 
+(-964 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."))) 
 NIL 
-((|HasCategory| |#4| (QUOTE (-258))) (|HasCategory| |#4| (QUOTE (-312))) (|HasCategory| |#4| (QUOTE (-496))) (|HasCategory| |#4| (QUOTE (-146)))) 
-(-966 |m| |n| R |Row| |Col|) 
+((|HasCategory| |#4| (QUOTE (-258))) (|HasCategory| |#4| (QUOTE (-312))) (|HasCategory| |#4| (QUOTE (-495))) (|HasCategory| |#4| (QUOTE (-146)))) 
+(-965 |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."))) 
-((-3992 . T) (-3991 . T)) 
+((-3991 . T) (-3990 . T)) 
 NIL 
-(-967 |m| |n| R) 
+(-966 |m| |n| R) 
 ((|constructor| (NIL "\\spadtype{RectangularMatrix} is a matrix domain where the number of rows and the number of columns are parameters of the domain.")) (|rectangularMatrix| (($ (|Matrix| |#3|)) "\\spad{rectangularMatrix(m)} converts a matrix of type \\spadtype{Matrix} to a matrix of type \\spad{RectangularMatrix}."))) 
-((-3992 . T) (-3991 . T)) 
-((|HasCategory| |#3| (QUOTE (-146))) (OR (-12 (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1014))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|))))) (|HasCategory| |#3| (QUOTE (-554 (-474)))) (OR (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-312)))) (|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (QUOTE (-258))) (|HasCategory| |#3| (QUOTE (-496))) (-12 (|HasCategory| |#3| (QUOTE (-1014))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (|HasCategory| |#3| (QUOTE (-1014))) (|HasCategory| |#3| (QUOTE (-72))) (|HasCategory| |#3| (QUOTE (-553 (-773))))) 
-(-968 |m| |n| R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2) 
+((-3991 . T) (-3990 . T)) 
+((|HasCategory| |#3| (QUOTE (-146))) (OR (-12 (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1013))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|))))) (|HasCategory| |#3| (QUOTE (-553 (-473)))) (OR (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-312)))) (|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (QUOTE (-258))) (|HasCategory| |#3| (QUOTE (-495))) (-12 (|HasCategory| |#3| (QUOTE (-1013))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (|HasCategory| |#3| (QUOTE (-1013))) (|HasCategory| |#3| (QUOTE (-72))) (|HasCategory| |#3| (QUOTE (-552 (-772))))) 
+(-967 |m| |n| R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2) 
 ((|constructor| (NIL "\\spadtype{RectangularMatrixCategoryFunctions2} provides functions between two matrix domains. The functions provided are \\spadfun{map} and \\spadfun{reduce}.")) (|reduce| ((|#7| (|Mapping| |#7| |#3| |#7|) |#6| |#7|) "\\spad{reduce(f,m,r)} returns a matrix \\spad{n} where \\spad{n[i,j] = f(m[i,j],r)} for all indices spad{\\spad{i}} and \\spad{j}.")) (|map| ((|#10| (|Mapping| |#7| |#3|) |#6|) "\\spad{map(f,m)} applies the function \\spad{f} to the elements of the matrix \\spad{m}."))) 
 NIL 
 NIL 
-(-969 R) 
+(-968 R) 
 ((|constructor| (NIL "The category of right modules over an rng (ring not necessarily with unit). This is an abelian group which supports right multiplation by elements of the rng. \\blankline"))) 
 NIL 
 NIL 
-(-970 S) 
+(-969 S) 
 ((|constructor| (NIL "The category of associative rings,{} not necessarily commutative,{} and not necessarily with a 1. This is a combination of an abelian group and a semigroup,{} with multiplication distributing over addition. \\blankline")) (|annihilate?| (((|Boolean|) $ $) "\\spad{annihilate?(x,y)} holds when the product of \\spad{x} and \\spad{y} is \\spad{0}."))) 
 NIL 
 NIL 
-(-971) 
+(-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")) (|annihilate?| (((|Boolean|) $ $) "\\spad{annihilate?(x,y)} holds when the product of \\spad{x} and \\spad{y} is \\spad{0}."))) 
 NIL 
 NIL 
-(-972 S T$) 
+(-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 (-1014)))) 
-(-973 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|) $) "\\spad{wholePart x} returns the integer part of \\spad{x}.")) (|floor| (($ $) "\\spad{floor x} returns the largest integer \\spad{<= x}.")) (|ceiling| (($ $) "\\spad{ceiling x} returns the small integer \\spad{>= x}.")) (|norm| (($ $) "\\spad{norm x} returns the same as absolute value."))) 
 NIL 
 NIL 
-(-974) 
+(-973) 
 ((|constructor| (NIL "The real number system category is intended as a model for the real numbers. The real numbers form an ordered normed field. Note that we have purposely not included \\spadtype{DifferentialRing} or the elementary functions (see \\spadtype{TranscendentalFunctionCategory}) in the definition.")) (|round| (($ $) "\\spad{round x} computes the integer closest to \\spad{x}.")) (|truncate| (($ $) "\\spad{truncate x} returns the integer between \\spad{x} and 0 closest to \\spad{x}.")) (|fractionPart| (($ $) "\\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."))) 
-((-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
 NIL 
-(-975 |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| $) "\\axiom{left(rootChar)} is the left bound of the isolating interval"))) 
 NIL 
 NIL 
-(-976) 
+(-975) 
 ((|constructor| (NIL "\\spadtype{RomanNumeral} provides functions for converting \\indented{1}{integers to roman numerals.}")) (|roman| (($ (|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."))) 
-((-3985 . T) (-3989 . T) (-3984 . T) (-3995 . T) (-3996 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((-3984 . T) (-3988 . T) (-3983 . T) (-3994 . T) (-3995 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
 NIL 
-(-977 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| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-951 (-485)))) (|HasCategory| |#2| (QUOTE (-484))) (|HasCategory| |#2| (QUOTE (-38 (-485)))) (|HasCategory| |#2| (QUOTE (-905 (-485)))) (|HasCategory| |#2| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#4| (QUOTE (-554 (-1091))))) 
-(-978 R E V) 
+((|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-950 (-484)))) (|HasCategory| |#2| (QUOTE (-483))) (|HasCategory| |#2| (QUOTE (-38 (-484)))) (|HasCategory| |#2| (QUOTE (-904 (-484)))) (|HasCategory| |#2| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#4| (QUOTE (-553 (-1090))))) 
+(-977 R E V) 
 ((|constructor| (NIL "A category for general multi-variate polynomials with coefficients in a ring,{} variables in an ordered set,{} and exponents from an ordered abelian monoid,{} with a \\axiomOp{sup} operation. When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\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}}."))) 
-(((-3999 "*") |has| |#1| (-146)) (-3990 |has| |#1| (-496)) (-3995 |has| |#1| (-6 -3995)) (-3992 . T) (-3991 . T) (-3994 . T)) 
+(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-495)) (-3994 |has| |#1| (-6 -3994)) (-3991 . T) (-3990 . T) (-3993 . T)) 
 NIL 
-(-979) 
+(-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 
-(-980 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 
-(-981 |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 
-(-982 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 
-(-983 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 
-(-984 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}."))) 
-((-3998 . T)) 
+((-3997 . T)) 
 NIL 
-(-985 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 
-(-986) 
+(-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 
-(-987) 
+(-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 
-(-988 |Base| R -3094) 
+(-987 |Base| R -3093) 
 ((|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 
-(-989 |f|) 
+(-988 |f|) 
 ((|constructor| (NIL "This domain implements named rules")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) 
 NIL 
 NIL 
-(-990 |Base| R -3094) 
+(-989 |Base| R -3093) 
 ((|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 
-(-991 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 
-(-992 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."))) 
-((-3990 |has| |#1| (-312)) (-3995 |has| |#1| (-312)) (-3989 |has| |#1| (-312)) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
-((|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-299))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-299)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-320))) (OR (-12 (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-312)))) (|HasCategory| |#1| (QUOTE (-299)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-312)))) (-12 (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-312)))) (|HasCategory| |#1| (QUOTE (-299)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-810 (-1091))))) (-12 (|HasCategory| |#1| (QUOTE (-299))) (|HasCategory| |#1| (QUOTE (-810 (-1091)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-810 (-1091))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-812 (-1091)))))) (|HasCategory| |#1| (QUOTE (-581 (-485)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485)))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-312)))) (|HasCategory| |#1| (QUOTE (-299)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-812 (-1091))))) (-12 (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-312)))) (-12 (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-312)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-810 (-1091)))))) 
-(-993 UP SAE UPA) 
+((-3989 |has| |#1| (-312)) (-3994 |has| |#1| (-312)) (-3988 |has| |#1| (-312)) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-299))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-299)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-320))) (OR (-12 (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-312)))) (|HasCategory| |#1| (QUOTE (-299)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-312)))) (-12 (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-312)))) (|HasCategory| |#1| (QUOTE (-299)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-809 (-1090))))) (-12 (|HasCategory| |#1| (QUOTE (-299))) (|HasCategory| |#1| (QUOTE (-809 (-1090)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-809 (-1090))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-811 (-1090)))))) (|HasCategory| |#1| (QUOTE (-580 (-484)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484)))))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-484)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-312)))) (|HasCategory| |#1| (QUOTE (-299)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-811 (-1090))))) (-12 (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-312)))) (-12 (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-312)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-809 (-1090)))))) 
+(-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 
-(-994 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 
-(-995) 
+(-994) 
 ((|constructor| (NIL "This trivial domain lets us build Univariate Polynomials in an anonymous variable"))) 
 NIL 
 NIL 
-(-996) 
+(-995) 
 ((|constructor| (NIL "This is the category of Spad syntax objects."))) 
 NIL 
 NIL 
-(-997 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 
-(-998) 
+(-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 
-(-999 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 
-(-1000 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"))) 
-(((-3999 "*") |has| |#1| (-146)) (-3990 |has| |#1| (-496)) (-3995 |has| |#1| (-6 -3995)) (-3992 . T) (-3991 . T) (-3994 . T)) 
-((|HasCategory| |#1| (QUOTE (-822))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-822)))) (OR (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-822)))) (OR (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-822)))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (-12 (|HasCategory| |#1| (QUOTE (-797 (-330)))) (|HasCategory| (-1001 (-1091)) (QUOTE (-797 (-330))))) (-12 (|HasCategory| |#1| (QUOTE (-797 (-485)))) (|HasCategory| (-1001 (-1091)) (QUOTE (-797 (-485))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-330))))) (|HasCategory| (-1001 (-1091)) (QUOTE (-554 (-801 (-330)))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-485))))) (|HasCategory| (-1001 (-1091)) (QUOTE (-554 (-801 (-485)))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-474)))) (|HasCategory| (-1001 (-1091)) (QUOTE (-554 (-474))))) (|HasCategory| |#1| (QUOTE (-581 (-485)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485)))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-812 (-1091)))) (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasAttribute| |#1| (QUOTE -3995)) (|HasCategory| |#1| (QUOTE (-392))) (-12 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) 
-(-1001 S) 
+(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-495)) (-3994 |has| |#1| (-6 -3994)) (-3991 . T) (-3990 . T) (-3993 . T)) 
+((|HasCategory| |#1| (QUOTE (-821))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-821)))) (OR (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-821)))) (OR (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-821)))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-495)))) (-12 (|HasCategory| |#1| (QUOTE (-796 (-330)))) (|HasCategory| (-1000 (-1090)) (QUOTE (-796 (-330))))) (-12 (|HasCategory| |#1| (QUOTE (-796 (-484)))) (|HasCategory| (-1000 (-1090)) (QUOTE (-796 (-484))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-800 (-330))))) (|HasCategory| (-1000 (-1090)) (QUOTE (-553 (-800 (-330)))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-800 (-484))))) (|HasCategory| (-1000 (-1090)) (QUOTE (-553 (-800 (-484)))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-473)))) (|HasCategory| (-1000 (-1090)) (QUOTE (-553 (-473))))) (|HasCategory| |#1| (QUOTE (-580 (-484)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-484)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484)))))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-811 (-1090)))) (|HasCategory| |#1| (QUOTE (-809 (-1090)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasAttribute| |#1| (QUOTE -3994)) (|HasCategory| |#1| (QUOTE (-392))) (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-821))) (|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 
-(-1002 S) 
+(-1001 S) 
 ((|constructor| (NIL "This type is used to specify a range of values from type \\spad{S}."))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1014)))) 
-(-1003 R S) 
+((|HasCategory| |#1| (QUOTE (-755))) (|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 (-756)))) 
-(-1004) 
+((|HasCategory| |#1| (QUOTE (-755)))) 
+(-1003) 
 ((|constructor| (NIL "This domain represents segement expressions.")) (|bounds| (((|List| (|SpadAst|)) $) "\\spad{bounds(s)} returns the bounds of the segment `s'. If `s' designates an infinite interval,{} then the returns list a singleton list."))) 
 NIL 
 NIL 
-(-1005 S) 
+(-1004 S) 
 ((|constructor| (NIL "This domain is used to provide the function argument syntax \\spad{v=a..b}. This is used,{} for example,{} by the top-level \\spadfun{draw} functions."))) 
 NIL 
-((|HasCategory| (-1002 |#1|) (QUOTE (-1014)))) 
-(-1006 R S) 
+((|HasCategory| (-1001 |#1|) (QUOTE (-1013)))) 
+(-1005 R S) 
 ((|constructor| (NIL "This package provides operations for mapping functions onto \\spadtype{SegmentBinding}\\spad{s}.")) (|map| (((|SegmentBinding| |#2|) (|Mapping| |#2| |#1|) (|SegmentBinding| |#1|)) "\\spad{map(f,v=a..b)} returns the value given by \\spad{v=f(a)..f(b)}."))) 
 NIL 
 NIL 
-(-1007 S) 
+(-1006 S) 
 ((|constructor| (NIL "This category provides operations on ranges,{} or {\\em segments} as they are called.")) (|segment| (($ |#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 
-(-1008 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 
-(-1009) 
+(-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 
-(-1010 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 members 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)}}"))) 
-((-3987 . T) (-3998 . T)) 
-((OR (-12 (|HasCategory| |#1| (QUOTE (-320))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (|HasCategory| |#1| (QUOTE (-320))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-1014))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|)))) 
-(-1011 A S) 
+((-3986 . T) (-3997 . T)) 
+((OR (-12 (|HasCategory| |#1| (QUOTE (-320))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-553 (-473)))) (|HasCategory| |#1| (QUOTE (-320))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-1013))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -318) (|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|) $ $) "\\spad{s} < \\spad{t} returns \\spad{true} if all elements of set aggregate \\spad{s} are also elements of set aggregate \\spad{t}."))) 
 NIL 
 NIL 
-(-1012 S) 
+(-1011 S) 
 ((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#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}."))) 
-((-3987 . T)) 
+((-3986 . T)) 
 NIL 
-(-1013 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 
-(-1014) 
+(-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 
-(-1015 |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 
-(-1016) 
+(-1015) 
 ((|constructor| (NIL "This domain allows the manipulation of the usual Lisp values."))) 
 NIL 
 NIL 
-(-1017 |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 
-(-1018 |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 
-(-1019 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 
-(-1020 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 
-(-1021 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.}"))) 
-((-3998 . T)) 
+((-3997 . T)) 
 NIL 
-(-1022) 
+(-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 
-(-1023 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| $) (|:| |x| |#1|) (|:| |y| |#1|) (|:| |z| |#1|)) (-3057 (|f| (|f| |x| |y|) |z|) (|f| |x| (|f| |y| |z|))))) . T)) 
 NIL 
-(-1024 T$) 
+(-1023 T$) 
 ((|constructor| (NIL "This is the category of all domains that implement semigroup operations"))) 
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+(((|%Rule| |associativity| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|) (|:| |y| |#1|) (|:| |z| |#1|)) (-3057 (|f| (|f| |x| |y|) |z|) (|f| |x| (|f| |y| |z|))))) . T)) 
 NIL 
-(-1025 S) 
+(-1024 S) 
 ((|constructor| (NIL "the class of all multiplicative semigroups,{} \\spadignore{i.e.} a set with an associative operation \\spadop{*}. \\blankline")) (** (($ $ (|PositiveInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (* (($ $ $) "\\spad{x*y} returns the product of \\spad{x} and \\spad{y}."))) 
 NIL 
 NIL 
-(-1026) 
+(-1025) 
 ((|constructor| (NIL "the class of all multiplicative semigroups,{} \\spadignore{i.e.} a set with an associative operation \\spadop{*}. \\blankline")) (** (($ $ (|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 
-(-1027 |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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-(-1028 R |x|) 
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|#3| (QUOTE (-756))) (|HasCategory| |#3| (QUOTE (-320))) (OR (-12 (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-580 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-190))) (|HasCategory| |#3| (QUOTE (-580 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (QUOTE (-580 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-580 (-484)))) (|HasCategory| |#3| (QUOTE (-809 (-1090))))) (-12 (|HasCategory| |#3| (QUOTE (-580 (-484)))) (|HasCategory| |#3| (QUOTE (-961))))) (|HasCategory| |#3| (QUOTE (-809 (-1090)))) (OR (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-72))) (|HasCategory| |#3| (QUOTE (-104))) (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-190))) (|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (QUOTE (-320))) (|HasCategory| |#3| (QUOTE (-663))) (|HasCategory| |#3| (QUOTE (-717))) (|HasCategory| |#3| (QUOTE (-756))) (|HasCategory| |#3| (QUOTE (-809 (-1090)))) (|HasCategory| |#3| (QUOTE (-961))) (|HasCategory| |#3| (QUOTE (-1013)))) (OR (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-104))) (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-190))) (|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (QUOTE (-320))) (|HasCategory| |#3| (QUOTE (-663))) (|HasCategory| |#3| (QUOTE (-717))) (|HasCategory| |#3| (QUOTE (-756))) (|HasCategory| |#3| (QUOTE (-809 (-1090)))) (|HasCategory| |#3| (QUOTE (-961))) (|HasCategory| |#3| (QUOTE (-1013)))) (OR (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-104))) (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-190))) (|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (QUOTE (-809 (-1090)))) (|HasCategory| |#3| (QUOTE (-961)))) (OR (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-104))) (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-190))) (|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (QUOTE (-809 (-1090)))) (|HasCategory| |#3| (QUOTE (-961)))) (OR (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-104))) (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-190))) (|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (QUOTE (-809 (-1090)))) (|HasCategory| |#3| (QUOTE (-961)))) (OR (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-190))) (|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (QUOTE (-809 (-1090)))) (|HasCategory| |#3| (QUOTE (-961)))) (OR (|HasCategory| |#3| (QUOTE (-190))) (|HasCategory| |#3| (QUOTE (-809 (-1090)))) (|HasCategory| |#3| (QUOTE (-961)))) (|HasCategory| |#3| (QUOTE (-190))) (OR (|HasCategory| |#3| (QUOTE (-190))) (-12 (|HasCategory| |#3| (QUOTE (-189))) (|HasCategory| |#3| (QUOTE (-961))))) (OR (-12 (|HasCategory| |#3| (QUOTE (-811 (-1090)))) (|HasCategory| |#3| (QUOTE (-961)))) (|HasCategory| |#3| (QUOTE (-809 (-1090))))) (|HasCategory| |#3| (QUOTE (-1013))) (OR (-12 (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-950 (-350 (-484)))))) (-12 (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-950 (-350 (-484)))))) (-12 (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-950 (-350 (-484)))))) (-12 (|HasCategory| |#3| (QUOTE (-104))) (|HasCategory| |#3| (QUOTE (-950 (-350 (-484)))))) (-12 (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-950 (-350 (-484)))))) (-12 (|HasCategory| |#3| (QUOTE (-190))) (|HasCategory| |#3| (QUOTE (-950 (-350 (-484)))))) (-12 (|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (QUOTE (-950 (-350 (-484)))))) (-12 (|HasCategory| |#3| (QUOTE (-320))) (|HasCategory| |#3| (QUOTE (-950 (-350 (-484)))))) (-12 (|HasCategory| |#3| (QUOTE (-663))) (|HasCategory| |#3| (QUOTE (-950 (-350 (-484)))))) (-12 (|HasCategory| |#3| (QUOTE (-717))) (|HasCategory| |#3| (QUOTE (-950 (-350 (-484)))))) (-12 (|HasCategory| |#3| (QUOTE (-756))) (|HasCategory| |#3| (QUOTE (-950 (-350 (-484)))))) (-12 (|HasCategory| |#3| (QUOTE (-809 (-1090)))) (|HasCategory| |#3| (QUOTE (-950 (-350 (-484)))))) (-12 (|HasCategory| |#3| (QUOTE (-950 (-350 (-484))))) (|HasCategory| |#3| (QUOTE (-961)))) (-12 (|HasCategory| |#3| (QUOTE (-950 (-350 (-484))))) (|HasCategory| |#3| (QUOTE (-1013))))) (OR (-12 (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-104))) (|HasCategory| |#3| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-190))) (|HasCategory| |#3| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-717))) (|HasCategory| |#3| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-756))) (|HasCategory| |#3| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-809 (-1090)))) (|HasCategory| |#3| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-950 (-484)))) (|HasCategory| |#3| (QUOTE (-1013)))) (-12 (|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-320))) (|HasCategory| |#3| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-663))) (|HasCategory| |#3| (QUOTE (-950 (-484))))) (|HasCategory| |#3| (QUOTE (-961)))) (OR (-12 (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-104))) (|HasCategory| |#3| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-190))) (|HasCategory| |#3| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-717))) (|HasCategory| |#3| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-756))) (|HasCategory| |#3| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-809 (-1090)))) (|HasCategory| |#3| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-950 (-484)))) (|HasCategory| |#3| (QUOTE (-1013)))) (-12 (|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-320))) (|HasCategory| |#3| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-663))) (|HasCategory| |#3| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#3| (QUOTE (-950 (-484)))) (|HasCategory| |#3| (QUOTE (-961))))) (|HasCategory| |#3| (QUOTE (-72))) (|HasCategory| (-484) (QUOTE (-756))) (-12 (|HasCategory| |#3| (QUOTE (-580 (-484)))) (|HasCategory| |#3| (QUOTE (-961)))) (-12 (|HasCategory| |#3| (QUOTE (-189))) (|HasCategory| |#3| (QUOTE (-961)))) (-12 (|HasCategory| |#3| (QUOTE (-811 (-1090)))) (|HasCategory| |#3| (QUOTE (-961)))) (OR (-12 (|HasCategory| |#3| (QUOTE (-950 (-484)))) (|HasCategory| |#3| (QUOTE (-1013)))) (|HasCategory| |#3| (QUOTE (-961)))) (-12 (|HasCategory| |#3| (QUOTE (-950 (-484)))) (|HasCategory| |#3| (QUOTE (-1013)))) (-12 (|HasCategory| |#3| (QUOTE (-950 (-350 (-484))))) (|HasCategory| |#3| (QUOTE (-1013)))) (|HasAttribute| |#3| (QUOTE -3993)) (-12 (|HasCategory| |#3| (QUOTE (-190))) (|HasCategory| |#3| (QUOTE (-961)))) (-12 (|HasCategory| |#3| (QUOTE (-809 (-1090)))) (|HasCategory| |#3| (QUOTE (-961)))) (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-104))) (|HasCategory| |#3| (QUOTE (-25))) (-12 (|HasCategory| |#3| (QUOTE (-1013))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|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 (-392)))) 
-(-1029) 
+(-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 
-(-1030) 
+(-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 
-(-1031 R -3094) 
+(-1030 R -3093) 
 ((|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 
-(-1032 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 
-(-1033) 
+(-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 
-(-1034) 
+(-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."))) 
-((-3985 . T) (-3989 . T) (-3984 . T) (-3995 . T) (-3996 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((-3984 . T) (-3988 . T) (-3983 . T) (-3994 . T) (-3995 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
 NIL 
-(-1035 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| $) "\\spad{push!(x,s)} pushes \\spad{x} onto stack \\spad{s},{} \\spadignore{i.e.} destructively changing \\spad{s} so as to have a new first (top) element \\spad{x}. Afterwards,{} pop!(\\spad{s}) produces \\spad{x} and pop!(\\spad{s}) produces the original \\spad{s}."))) 
-((-3998 . T)) 
+((-3997 . T)) 
 NIL 
-(-1036 S) 
+(-1035 S) 
 ((|constructor| (NIL "This category describes the class of homogeneous aggregates that support in place mutation that do not change their general shapes.")) (|map!| (($ (|Mapping| |#1| |#1|) $) "\\spad{map!(f,u)} destructively replaces each element \\spad{x} of \\spad{u} by \\spad{f(x)}"))) 
-((-3998 . T)) 
+((-3997 . T)) 
 NIL 
-(-1037 S |ndim| R |Row| |Col|) 
+(-1036 S |ndim| R |Row| |Col|) 
 ((|constructor| (NIL "\\spadtype{SquareMatrixCategory} is a general square matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col.")) (** (($ $ (|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 (-312))) (|HasAttribute| |#3| (QUOTE (-3999 "*"))) (|HasCategory| |#3| (QUOTE (-146)))) 
-(-1038 |ndim| R |Row| |Col|) 
+((|HasCategory| |#3| (QUOTE (-312))) (|HasAttribute| |#3| (QUOTE (-3998 "*"))) (|HasCategory| |#3| (QUOTE (-146)))) 
+(-1037 |ndim| R |Row| |Col|) 
 ((|constructor| (NIL "\\spadtype{SquareMatrixCategory} is a general square matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if the matrix is not invertible.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m},{} if that matrix is invertible and returns \"failed\" otherwise.")) (|minordet| ((|#2| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors.")) (|determinant| ((|#2| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}.")) (* ((|#3| |#3| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#4| $ |#4|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.")) (|diagonalProduct| ((|#2| $) "\\spad{diagonalProduct(m)} returns the product of the elements on the diagonal of the matrix \\spad{m}.")) (|trace| ((|#2| $) "\\spad{trace(m)} returns the trace of the matrix \\spad{m}. this is the sum of the elements on the diagonal of the matrix \\spad{m}.")) (|diagonal| ((|#3| $) "\\spad{diagonal(m)} returns a row consisting of the elements on the diagonal of the matrix \\spad{m}.")) (|diagonalMatrix| (($ (|List| |#2|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ |#2|) "\\spad{scalarMatrix(r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}'s on the diagonal and zeroes elsewhere."))) 
-((-3991 . T) (-3992 . T) (-3994 . T)) 
+((-3990 . T) (-3991 . T) (-3993 . T)) 
 NIL 
-(-1039 R |Row| |Col| M) 
+(-1038 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 
-(-1040 R |VarSet|) 
+(-1039 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."))) 
-(((-3999 "*") |has| |#1| (-146)) (-3990 |has| |#1| (-496)) (-3995 |has| |#1| (-6 -3995)) (-3992 . T) (-3991 . T) (-3994 . T)) 
-((|HasCategory| |#1| (QUOTE (-822))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-822)))) (OR (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-822)))) (OR (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-822)))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (-12 (|HasCategory| |#1| (QUOTE (-797 (-330)))) (|HasCategory| |#2| (QUOTE (-797 (-330))))) (-12 (|HasCategory| |#1| (QUOTE (-797 (-485)))) (|HasCategory| |#2| (QUOTE (-797 (-485))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-330))))) (|HasCategory| |#2| (QUOTE (-554 (-801 (-330)))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-485))))) (|HasCategory| |#2| (QUOTE (-554 (-801 (-485)))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-474)))) (|HasCategory| |#2| (QUOTE (-554 (-474))))) (|HasCategory| |#1| (QUOTE (-581 (-485)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485)))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-312))) (|HasAttribute| |#1| (QUOTE -3995)) (|HasCategory| |#1| (QUOTE (-392))) (-12 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) 
-(-1041 |Coef| |Var| SMP) 
+(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-495)) (-3994 |has| |#1| (-6 -3994)) (-3991 . T) (-3990 . T) (-3993 . T)) 
+((|HasCategory| |#1| (QUOTE (-821))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-821)))) (OR (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-821)))) (OR (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-821)))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-495)))) (-12 (|HasCategory| |#1| (QUOTE (-796 (-330)))) (|HasCategory| |#2| (QUOTE (-796 (-330))))) (-12 (|HasCategory| |#1| (QUOTE (-796 (-484)))) (|HasCategory| |#2| (QUOTE (-796 (-484))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-800 (-330))))) (|HasCategory| |#2| (QUOTE (-553 (-800 (-330)))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-800 (-484))))) (|HasCategory| |#2| (QUOTE (-553 (-800 (-484)))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-473)))) (|HasCategory| |#2| (QUOTE (-553 (-473))))) (|HasCategory| |#1| (QUOTE (-580 (-484)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-484)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484)))))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-312))) (|HasAttribute| |#1| (QUOTE -3994)) (|HasCategory| |#1| (QUOTE (-392))) (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) 
+(-1040 |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}."))) 
-(((-3999 "*") |has| |#1| (-146)) (-3990 |has| |#1| (-496)) (-3992 . T) (-3991 . T) (-3994 . T)) 
-((|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-312)))) 
-(-1042 R E V P) 
+(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-495)) (-3991 . T) (-3990 . T) (-3993 . T)) 
+((|HasCategory| |#1| (QUOTE (-38 (-350 (-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 (-312)))) 
+(-1041 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}"))) 
-((-3998 . T)) 
+((-3997 . T)) 
 NIL 
-(-1043 UP -3094) 
+(-1042 UP -3093) 
 ((|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 
-(-1044 R) 
+(-1043 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 
-(-1045 R) 
+(-1044 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 
-(-1046 R) 
+(-1045 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 
-(-1047 S A) 
+(-1046 S A) 
 ((|constructor| (NIL "This package exports sorting algorithnms")) (|insertionSort!| ((|#2| |#2|) "\\spad{insertionSort! }\\undocumented") ((|#2| |#2| (|Mapping| (|Boolean|) |#1| |#1|)) "\\spad{insertionSort!(a,f)} \\undocumented")) (|bubbleSort!| ((|#2| |#2|) "\\spad{bubbleSort!(a)} \\undocumented") ((|#2| |#2| (|Mapping| (|Boolean|) |#1| |#1|)) "\\spad{bubbleSort!(a,f)} \\undocumented"))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-757)))) 
-(-1048 R) 
+((|HasCategory| |#1| (QUOTE (-756)))) 
+(-1047 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 
-(-1049 R) 
+(-1048 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 
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-(-1050) 
+(-1049) 
 ((|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 
-(-1051) 
+(-1050) 
 ((|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 
-(-1052) 
+(-1051) 
 ((|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 
-(-1053) 
+(-1052) 
 ((|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 
-(-1054) 
+(-1053) 
 ((|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 
-(-1055 V C) 
+(-1054 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 
-(-1056 V C) 
+(-1055 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."))) 
-((-3998 . T)) 
-((-12 (|HasCategory| (-1055 |#1| |#2|) (|%list| (QUOTE -260) (|%list| (QUOTE -1055) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1055 |#1| |#2|) (QUOTE (-1014)))) (|HasCategory| (-1055 |#1| |#2|) (QUOTE (-1014))) (OR (|HasCategory| (-1055 |#1| |#2|) (QUOTE (-72))) (|HasCategory| (-1055 |#1| |#2|) (QUOTE (-1014)))) (|HasCategory| (-1055 |#1| |#2|) (QUOTE (-553 (-773)))) (|HasCategory| (-1055 |#1| |#2|) (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -1036) (|%list| (QUOTE -1055) (|devaluate| |#1|) (|devaluate| |#2|))))) 
-(-1057 |ndim| R) 
+((-3997 . T)) 
+((-12 (|HasCategory| (-1054 |#1| |#2|) (|%list| (QUOTE -260) (|%list| (QUOTE -1054) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1054 |#1| |#2|) (QUOTE (-1013)))) (|HasCategory| (-1054 |#1| |#2|) (QUOTE (-1013))) (OR (|HasCategory| (-1054 |#1| |#2|) (QUOTE (-72))) (|HasCategory| (-1054 |#1| |#2|) (QUOTE (-1013)))) (|HasCategory| (-1054 |#1| |#2|) (QUOTE (-552 (-772)))) (|HasCategory| (-1054 |#1| |#2|) (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -1035) (|%list| (QUOTE -1054) (|devaluate| |#1|) (|devaluate| |#2|))))) 
+(-1056 |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}."))) 
-((-3994 . T) (-3986 |has| |#2| (-6 (-3999 "*"))) (-3991 . T) (-3992 . T)) 
-((|HasCategory| |#2| (QUOTE (-810 (-1091)))) (|HasCategory| |#2| (QUOTE (-812 (-1091)))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-189))) (|HasAttribute| |#2| (QUOTE (-3999 #1="*"))) (|HasCategory| |#2| (QUOTE (-581 (-485)))) (|HasCategory| |#2| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#2| (QUOTE (-951 (-485)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-581 (-485)))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-810 (-1091)))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|))))) (|HasCategory| |#2| (QUOTE (-554 (-474)))) (|HasCategory| |#2| (QUOTE (-258))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-312))) (OR (|HasAttribute| |#2| (QUOTE (-3999 #1#))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-810 (-1091))))) (|HasCategory| |#2| (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1014))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-146)))) 
-(-1058 S) 
+((-3993 . T) (-3985 |has| |#2| (-6 (-3998 "*"))) (-3990 . T) (-3991 . T)) 
+((|HasCategory| |#2| (QUOTE (-809 (-1090)))) (|HasCategory| |#2| (QUOTE (-811 (-1090)))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-189))) (|HasAttribute| |#2| (QUOTE (-3998 #1="*"))) (|HasCategory| |#2| (QUOTE (-580 (-484)))) (|HasCategory| |#2| (QUOTE (-950 (-350 (-484))))) (|HasCategory| |#2| (QUOTE (-950 (-484)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-580 (-484)))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-809 (-1090)))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|))))) (|HasCategory| |#2| (QUOTE (-553 (-473)))) (|HasCategory| |#2| (QUOTE (-258))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-312))) (OR (|HasAttribute| |#2| (QUOTE (-3998 #1#))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-809 (-1090))))) (|HasCategory| |#2| (QUOTE (-552 (-772)))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1013))) (-12 (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-146)))) 
+(-1057 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|) $ $) "\\spad{prefix?(s,t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) == reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) 
 NIL 
 NIL 
-(-1059) 
+(-1058) 
 ((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|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."))) 
-((-3998 . T)) 
+((-3997 . T)) 
 NIL 
-(-1060 R E V P TS) 
+(-1059 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 
-(-1061 R E V P) 
+(-1060 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."))) 
-((-3998 . T)) 
-((-12 (|HasCategory| |#4| (QUOTE (-1014))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-554 (-474)))) (|HasCategory| |#4| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#3| (QUOTE (-320))) (|HasCategory| |#4| (QUOTE (-553 (-773)))) (|HasCategory| |#4| (QUOTE (-1014))) (-12 (|HasCategory| |#4| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#4|)))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#4|)))) 
-(-1062) 
+((-3997 . T)) 
+((-12 (|HasCategory| |#4| (QUOTE (-1013))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-553 (-473)))) (|HasCategory| |#4| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#3| (QUOTE (-320))) (|HasCategory| |#4| (QUOTE (-552 (-772)))) (|HasCategory| |#4| (QUOTE (-1013))) (-12 (|HasCategory| |#4| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#4|)))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#4|)))) 
+(-1061) 
 ((|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 
-(-1063 S) 
+(-1062 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}."))) 
-((-3998 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-72)))) 
-(-1064 A S) 
+((-3997 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1013))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-72)))) 
+(-1063 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 
-(-1065 S) 
+(-1064 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 
-(-1066 |Key| |Ent| |dent|) 
+(-1065 |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."))) 
-((-3998 . T)) 
-((-12 (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3862) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-553 (-773))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-474)))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-72))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014))) (-12 (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3862) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3862) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (-12 (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#2|))))) 
-(-1067) 
+((-3997 . T)) 
+((-12 (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3861) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-552 (-772)))) (|HasCategory| |#2| (QUOTE (-552 (-772))))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-473)))) (-12 (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#2| (QUOTE (-72))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013))) (-12 (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3861) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3861) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (-12 (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#2|))))) 
+(-1066) 
 ((|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 
-(-1068) 
+(-1067) 
 ((|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|) $) "\\spad{iterationVar(i)} returns the name of the iterating variable of the arithmetic progression iterator \\spad{i}."))) 
 NIL 
 NIL 
-(-1069 |Coef|) 
+(-1068 |Coef|) 
 ((|constructor| (NIL "This package computes infinite products of Taylor series over an integral domain of characteristic 0. Here Taylor series are represented by streams of Taylor coefficients.")) (|generalInfiniteProduct| (((|Stream| |#1|) (|Stream| |#1|) (|Integer|) (|Integer|)) "\\spad{generalInfiniteProduct(f(x),a,d)} computes \\spad{product(n=a,a+d,a+2*d,...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|oddInfiniteProduct| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{oddInfiniteProduct(f(x))} computes \\spad{product(n=1,3,5...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|evenInfiniteProduct| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{evenInfiniteProduct(f(x))} computes \\spad{product(n=2,4,6...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|infiniteProduct| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{infiniteProduct(f(x))} computes \\spad{product(n=1,2,3...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1."))) 
 NIL 
 NIL 
-(-1070 S) 
+(-1069 S) 
 ((|constructor| (NIL "A stream is an implementation of an infinite sequence using a list of terms that have been computed and a function closure to compute additional terms when needed.")) (|filterUntil| (($ (|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}."))) 
-((-3998 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -1036) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|))))) 
-(-1071 S) 
+((-3997 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1013))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-553 (-473)))) (|HasCategory| (-484) (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -1035) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|))))) 
+(-1070 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 
-(-1072 A B) 
+(-1071 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 
-(-1073 A B C) 
+(-1072 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 
-(-1074) 
+(-1073) 
 ((|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"))) 
-((-3998 . T)) 
-((OR (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-757)))) (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-1014))))) (|HasCategory| (-117) (QUOTE (-553 (-773)))) (|HasCategory| (-117) (QUOTE (-554 (-474)))) (OR (|HasCategory| (-117) (QUOTE (-757))) (|HasCategory| (-117) (QUOTE (-1014)))) (|HasCategory| (-117) (QUOTE (-757))) (OR (|HasCategory| (-117) (QUOTE (-72))) (|HasCategory| (-117) (QUOTE (-757))) (|HasCategory| (-117) (QUOTE (-1014)))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| (-117) (QUOTE (-72))) (|HasCategory| (-117) (QUOTE (-1014))) (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-1014)))) (-12 (|HasCategory| $ (QUOTE (-318 (-117)))) (|HasCategory| (-117) (QUOTE (-72)))) (|HasCategory| $ (QUOTE (-318 (-117)))) (|HasCategory| $ (QUOTE (-1036 (-117)))) (-12 (|HasCategory| $ (QUOTE (-1036 (-117)))) (|HasCategory| (-117) (QUOTE (-757))))) 
-(-1075 |Entry|) 
+((-3997 . T)) 
+((OR (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-756)))) (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-1013))))) (|HasCategory| (-117) (QUOTE (-552 (-772)))) (|HasCategory| (-117) (QUOTE (-553 (-473)))) (OR (|HasCategory| (-117) (QUOTE (-756))) (|HasCategory| (-117) (QUOTE (-1013)))) (|HasCategory| (-117) (QUOTE (-756))) (OR (|HasCategory| (-117) (QUOTE (-72))) (|HasCategory| (-117) (QUOTE (-756))) (|HasCategory| (-117) (QUOTE (-1013)))) (|HasCategory| (-484) (QUOTE (-756))) (|HasCategory| (-117) (QUOTE (-72))) (|HasCategory| (-117) (QUOTE (-1013))) (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-1013)))) (-12 (|HasCategory| $ (QUOTE (-318 (-117)))) (|HasCategory| (-117) (QUOTE (-72)))) (|HasCategory| $ (QUOTE (-318 (-117)))) (|HasCategory| $ (QUOTE (-1035 (-117)))) (-12 (|HasCategory| $ (QUOTE (-1035 (-117)))) (|HasCategory| (-117) (QUOTE (-756))))) 
+(-1074 |Entry|) 
 ((|constructor| (NIL "This domain provides tables where the keys are strings. A specialized hash function for strings is used."))) 
-((-3998 . T)) 
-((-12 (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (QUOTE (|:| -3862 (-1074))) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (QUOTE (-1014)))) (OR (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (QUOTE (-1014)))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (QUOTE (-1014)))) (OR (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-553 (-773))))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (QUOTE (-554 (-474)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (QUOTE (-72))) (|HasCategory| (-1074) (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-72))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (QUOTE (-72)))) (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (QUOTE (-1014))) (-12 (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (QUOTE (|:| -3862 (-1074))) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (QUOTE (-72)))) (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (QUOTE (|:| -3862 (-1074))) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#1|))))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|))))) 
-(-1076 A) 
+((-3997 . T)) 
+((-12 (|HasCategory| (-2 (|:| -3861 (-1073)) (|:| |entry| |#1|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (QUOTE (|:| -3861 (-1073))) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -3861 (-1073)) (|:| |entry| |#1|)) (QUOTE (-1013)))) (OR (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3861 (-1073)) (|:| |entry| |#1|)) (QUOTE (-1013)))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3861 (-1073)) (|:| |entry| |#1|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 (-1073)) (|:| |entry| |#1|)) (QUOTE (-1013)))) (OR (|HasCategory| (-2 (|:| -3861 (-1073)) (|:| |entry| |#1|)) (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-552 (-772))))) (|HasCategory| (-2 (|:| -3861 (-1073)) (|:| |entry| |#1|)) (QUOTE (-553 (-473)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -3861 (-1073)) (|:| |entry| |#1|)) (QUOTE (-72))) (|HasCategory| (-1073) (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-72))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 (-1073)) (|:| |entry| |#1|)) (QUOTE (-72)))) (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3861 (-1073)) (|:| |entry| |#1|)) (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3861 (-1073)) (|:| |entry| |#1|)) (QUOTE (-1013))) (-12 (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (QUOTE (|:| -3861 (-1073))) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -3861 (-1073)) (|:| |entry| |#1|)) (QUOTE (-72)))) (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (QUOTE (|:| -3861 (-1073))) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#1|))))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|))))) 
+(-1075 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 (-312))) (|HasCategory| |#1| (QUOTE (-38 (-350 (-485)))))) 
-(-1077 |Coef|) 
+((|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-38 (-350 (-484)))))) 
+(-1076 |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 
-(-1078 |Coef|) 
+(-1077 |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 
-(-1079 R UP) 
+(-1078 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 (-258)))) 
-(-1080 |n| R) 
+(-1079 |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 
-(-1081 S1 S2) 
+(-1080 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 
-(-1082) 
+(-1081) 
 ((|constructor| (NIL "This domain represents the filter iterator syntax.")) (|predicate| (((|SpadAst|) $) "\\spad{predicate(e)} returns the syntax object for the predicate in the filter iterator syntax `e'."))) 
 NIL 
 NIL 
-(-1083 |Coef| |var| |cen|) 
+(-1082 |Coef| |var| |cen|) 
 ((|constructor| (NIL "Sparse Laurent series in one variable \\indented{2}{\\spadtype{SparseUnivariateLaurentSeries} is a domain representing Laurent} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{SparseUnivariateLaurentSeries(Integer,x,3)} represents Laurent} \\indented{2}{series in \\spad{(x - 3)} with integer coefficients.}")) (|integrate| (($ $ (|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."))) 
-(((-3999 "*") OR (-2564 (|has| |#1| (-312)) (|has| (-1090 |#1| |#2| |#3|) (-741))) (|has| |#1| (-146)) (-2564 (|has| |#1| (-312)) (|has| (-1090 |#1| |#2| |#3|) (-822)))) (-3990 OR (-2564 (|has| |#1| (-312)) (|has| (-1090 |#1| |#2| |#3|) (-741))) (|has| |#1| (-496)) (-2564 (|has| |#1| (-312)) (|has| (-1090 |#1| |#2| |#3|) (-822)))) (-3995 |has| |#1| (-312)) (-3989 |has| |#1| (-312)) (-3991 . T) (-3992 . T) (-3994 . T)) 
-((|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1090 |#1| |#2| |#3|) (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1090 |#1| |#2| |#3|) (QUOTE (-741)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1090 |#1| |#2| |#3|) (QUOTE (-120)))) (|HasCategory| |#1| (QUOTE (-120)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1090 |#1| |#2| |#3|) (QUOTE (-810 (-1091))))) (-12 (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-485)) (|devaluate| |#1|)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1090 |#1| |#2| |#3|) (QUOTE (-810 (-1091))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| 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(-312))) (|HasCategory| (-1089 |#1| |#2| |#3|) (QUOTE (-483)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1089 |#1| |#2| |#3|) (QUOTE (-258)))) (|HasCategory| (-1089 |#1| |#2| |#3|) (QUOTE (-821))) (|HasCategory| (-1089 |#1| |#2| |#3|) (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-118))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1089 |#1| |#2| |#3|) (QUOTE (-740)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1089 |#1| |#2| |#3|) (QUOTE (-821)))) (|HasCategory| |#1| (QUOTE (-495)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1089 |#1| |#2| |#3|) (QUOTE (-740)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1089 |#1| |#2| |#3|) (QUOTE (-821)))) (|HasCategory| |#1| (QUOTE (-146)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1089 |#1| |#2| |#3|) (QUOTE (-811 (-1090))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1089 |#1| |#2| |#3|) (QUOTE (-189)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1089 |#1| |#2| |#3|) (QUOTE (-756)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1089 |#1| |#2| |#3|) (QUOTE (-120)))) (|HasCategory| |#1| (QUOTE (-120)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-1089 |#1| |#2| |#3|) (QUOTE (-821)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1089 |#1| |#2| |#3|) (QUOTE (-118)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-1089 |#1| |#2| |#3|) (QUOTE (-821)))) (|HasCategory| |#1| (QUOTE (-118))))) 
+(-1083 R -3093) 
 ((|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 
-(-1085 R) 
+(-1084 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 
-(-1086 R) 
+(-1085 R) 
 ((|constructor| (NIL "This domain represents univariate polynomials over arbitrary (not necessarily commutative) coefficient rings. The variable is unspecified so that the variable displays as \\spad{?} on output. If it is necessary to specify the variable name,{} use type \\spadtype{UnivariatePolynomial}. The representation is sparse in the sense that only non-zero terms are represented.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#1| $) "\\spad{fmecg(p1,e,r,p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}")) (|outputForm| (((|OutputForm|) $ (|OutputForm|)) "\\spad{outputForm(p,var)} converts the SparseUnivariatePolynomial \\spad{p} to an output form (see \\spadtype{OutputForm}) printed as a polynomial in the output form variable."))) 
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-(-1087 R S) 
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+((|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-495)))) (-12 (|HasCategory| |#1| (QUOTE (-796 (-330)))) (|HasCategory| (-994) (QUOTE (-796 (-330))))) (-12 (|HasCategory| |#1| (QUOTE (-796 (-484)))) (|HasCategory| (-994) (QUOTE (-796 (-484))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-800 (-330))))) (|HasCategory| (-994) (QUOTE (-553 (-800 (-330)))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-800 (-484))))) (|HasCategory| (-994) (QUOTE (-553 (-800 (-484)))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-473)))) (|HasCategory| (-994) (QUOTE (-553 (-473))))) (|HasCategory| |#1| (QUOTE (-580 (-484)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-484)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484)))))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484))))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-821)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-821)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-821)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (QUOTE (-811 (-1090)))) (|HasCategory| |#1| (QUOTE (-809 (-1090)))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-190))) (|HasAttribute| |#1| (QUOTE -3994)) (|HasCategory| |#1| (QUOTE (-392))) (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) 
+(-1086 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 
-(-1088 E OV R P) 
+(-1087 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 
-(-1089 |Coef| |var| |cen|) 
+(-1088 |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."))) 
-(((-3999 "*") |has| |#1| (-146)) (-3990 |has| |#1| (-496)) (-3995 |has| |#1| (-312)) (-3989 |has| |#1| (-312)) (-3991 . T) (-3992 . T) (-3994 . T)) 
-((|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-485))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-485))) (|devaluate| |#1|)))) (|HasCategory| (-350 (-485)) (QUOTE (-1026))) (|HasCategory| |#1| (QUOTE (-312))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-496)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-496)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-485)))))) (|HasSignature| |#1| (|%list| (QUOTE -3948) (|%list| (|devaluate| |#1|) (QUOTE (-1091)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-485)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-29 (-485)))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1116)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasSignature| |#1| (|%list| (QUOTE -3814) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1091))))) (|HasSignature| |#1| (|%list| (QUOTE -3083) (|%list| (|%list| (QUOTE -584) (QUOTE (-1091))) (|devaluate| |#1|))))))) 
-(-1090 |Coef| |var| |cen|) 
+(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-495)) (-3994 |has| |#1| (-312)) (-3988 |has| |#1| (-312)) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((|HasCategory| |#1| (QUOTE (-38 (-350 (-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 (-809 (-1090)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-484))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-484))) (|devaluate| |#1|)))) (|HasCategory| (-350 (-484)) (QUOTE (-1025))) (|HasCategory| |#1| (QUOTE (-312))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-495)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-495)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-484)))))) (|HasSignature| |#1| (|%list| (QUOTE -3947) (|%list| (|devaluate| |#1|) (QUOTE (-1090)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-484)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-29 (-484)))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1115)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasSignature| |#1| (|%list| (QUOTE -3813) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1090))))) (|HasSignature| |#1| (|%list| (QUOTE -3082) (|%list| (|%list| (QUOTE -583) (QUOTE (-1090))) (|devaluate| |#1|))))))) 
+(-1089 |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}."))) 
-(((-3999 "*") |has| |#1| (-146)) (-3990 |has| |#1| (-496)) (-3991 . T) (-3992 . T) (-3994 . T)) 
-((|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-496))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|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 (-1026))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-695))))) (|HasSignature| |#1| (|%list| (QUOTE -3948) (|%list| (|devaluate| |#1|) (QUOTE (-1091)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-695))))) (|HasCategory| |#1| (QUOTE (-312))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-29 (-485)))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1116)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasSignature| |#1| (|%list| (QUOTE -3814) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1091))))) (|HasSignature| |#1| (|%list| (QUOTE -3083) (|%list| (|%list| (QUOTE -584) (QUOTE (-1091))) (|devaluate| |#1|))))))) 
-(-1091) 
+(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-495)) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((|HasCategory| |#1| (QUOTE (-38 (-350 (-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 (-809 (-1090)))) (|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 (-1025))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-694))))) (|HasSignature| |#1| (|%list| (QUOTE -3947) (|%list| (|devaluate| |#1|) (QUOTE (-1090)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-694))))) (|HasCategory| |#1| (QUOTE (-312))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-29 (-484)))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1115)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasSignature| |#1| (|%list| (QUOTE -3813) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1090))))) (|HasSignature| |#1| (|%list| (QUOTE -3082) (|%list| (|%list| (QUOTE -583) (QUOTE (-1090))) (|devaluate| |#1|))))))) 
+(-1090) 
 ((|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 
-(-1092 R) 
+(-1091 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 
-(-1093 R) 
+(-1092 R) 
 ((|constructor| (NIL "This domain implements symmetric polynomial"))) 
-(((-3999 "*") |has| |#1| (-146)) (-3990 |has| |#1| (-496)) (-3995 |has| |#1| (-6 -3995)) (-3991 . T) (-3992 . T) (-3994 . T)) 
-((|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-496))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (OR (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485)))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-392))) (-12 (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| (-885) (QUOTE (-104)))) (|HasAttribute| |#1| (QUOTE -3995))) 
-(-1094) 
+(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-495)) (-3994 |has| |#1| (-6 -3994)) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((|HasCategory| |#1| (QUOTE (-38 (-350 (-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 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484)))))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-484)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-392))) (-12 (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| (-884) (QUOTE (-104)))) (|HasAttribute| |#1| (QUOTE -3994))) 
+(-1093) 
 ((|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 
-(-1095) 
+(-1094) 
 ((|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 
-(-1096) 
+(-1095) 
 ((|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|) $) "\\spad{convert(s)} returns the \\spad{s}-expression representation of a syntax."))) 
 NIL 
 NIL 
-(-1097 N) 
+(-1096 N) 
 ((|constructor| (NIL "This domain implements sized (signed) integer datatypes parameterized by the precision (or width) of the underlying representation. The intent is that they map directly to the hosting hardware natural integer datatypes. Consequently,{} natural values for \\spad{N} are: 8,{} 16,{} 32,{} 64,{} etc. These datatypes are mostly useful for system programming tasks,{} \\spadignore{i.e.} interfacting with the hosting operating system,{} reading/writing external binary format files.")) (|sample| (($) "\\spad{sample} gives a sample datum of this type."))) 
 NIL 
 NIL 
-(-1098 N) 
+(-1097 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 
-(-1099) 
+(-1098) 
 ((|constructor| (NIL "This domain is a datatype system-level pointer values."))) 
 NIL 
 NIL 
-(-1100 R) 
+(-1099 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 
-(-1101) 
+(-1100) 
 ((|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 
-(-1102 S) 
+(-1101 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 
-(-1103 |Key| |Entry|) 
+(-1102 |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}"))) 
-((-3998 . T)) 
-((-12 (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3862) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-553 (-773))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-474)))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-72))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014))) (-12 (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3862) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3862) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (-12 (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#2|))))) 
-(-1104 S) 
+((-3997 . T)) 
+((-12 (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3861) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-552 (-772)))) (|HasCategory| |#2| (QUOTE (-552 (-772))))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-473)))) (-12 (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#2| (QUOTE (-72))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013))) (-12 (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3861) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| $ (|%list| (QUOTE -318) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3861) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| $ (|%list| (QUOTE -1035) (|devaluate| |#2|))) (-12 (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#2|))))) 
+(-1103 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 
-(-1105 S) 
+(-1104 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 
-(-1106 R) 
+(-1105 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 
-(-1107 S |Key| |Entry|) 
+(-1106 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}."))) 
 NIL 
 NIL 
-(-1108 |Key| |Entry|) 
+(-1107 |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}."))) 
-((-3998 . T)) 
+((-3997 . T)) 
 NIL 
-(-1109 |Key| |Entry|) 
+(-1108 |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 
-(-1110) 
+(-1109) 
 ((|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 
-(-1111 S) 
+(-1110 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 
-(-1112) 
+(-1111) 
 ((|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 
-(-1113 R) 
+(-1112 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 
-(-1114) 
+(-1113) 
 ((|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 
-(-1115 S) 
+(-1114 S) 
 ((|constructor| (NIL "Category for the transcendental elementary functions.")) (|pi| (($) "\\spad{pi()} returns the constant \\spad{pi}."))) 
 NIL 
 NIL 
-(-1116) 
+(-1115) 
 ((|constructor| (NIL "Category for the transcendental elementary functions.")) (|pi| (($) "\\spad{pi()} returns the constant \\spad{pi}."))) 
 NIL 
 NIL 
-(-1117 S) 
+(-1116 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}."))) 
-((-3998 . T)) 
-((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -1036) (|devaluate| |#1|)))) 
-(-1118 S) 
+((-3997 . T)) 
+((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1013))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -1035) (|devaluate| |#1|)))) 
+(-1117 S) 
 ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) 
 NIL 
 NIL 
-(-1119) 
+(-1118) 
 ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) 
 NIL 
 NIL 
-(-1120 R -3094) 
+(-1119 R -3093) 
 ((|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 
-(-1121 R |Row| |Col| M) 
+(-1120 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 
-(-1122 R -3094) 
+(-1121 R -3093) 
 ((|constructor| (NIL "TranscendentalManipulations provides functions to simplify and expand expressions involving transcendental operators.")) (|expandTrigProducts| ((|#2| |#2|) "\\spad{expandTrigProducts(e)} replaces \\axiom{sin(\\spad{x})*sin(\\spad{y})} by \\spad{(cos(x-y)-cos(x+y))/2},{} \\axiom{cos(\\spad{x})*cos(\\spad{y})} by \\spad{(cos(x-y)+cos(x+y))/2},{} and \\axiom{sin(\\spad{x})*cos(\\spad{y})} by \\spad{(sin(x-y)+sin(x+y))/2}. Note that this operation uses the pattern matcher and so is relatively expensive. To avoid getting into an infinite loop the transformations are applied at most ten times.")) (|removeSinhSq| ((|#2| |#2|) "\\spad{removeSinhSq(f)} converts every \\spad{sinh(u)**2} appearing in \\spad{f} into \\spad{1 - cosh(x)**2},{} and also reduces higher powers of \\spad{sinh(u)} with that formula.")) (|removeCoshSq| ((|#2| |#2|) "\\spad{removeCoshSq(f)} converts every \\spad{cosh(u)**2} appearing in \\spad{f} into \\spad{1 - sinh(x)**2},{} and also reduces higher powers of \\spad{cosh(u)} with that formula.")) (|removeSinSq| ((|#2| |#2|) "\\spad{removeSinSq(f)} converts every \\spad{sin(u)**2} appearing in \\spad{f} into \\spad{1 - cos(x)**2},{} and also reduces higher powers of \\spad{sin(u)} with that formula.")) (|removeCosSq| ((|#2| |#2|) "\\spad{removeCosSq(f)} converts every \\spad{cos(u)**2} appearing in \\spad{f} into \\spad{1 - sin(x)**2},{} and also reduces higher powers of \\spad{cos(u)} with that formula.")) (|coth2tanh| ((|#2| |#2|) "\\spad{coth2tanh(f)} converts every \\spad{coth(u)} appearing in \\spad{f} into \\spad{1/tanh(u)}.")) (|cot2tan| ((|#2| |#2|) "\\spad{cot2tan(f)} converts every \\spad{cot(u)} appearing in \\spad{f} into \\spad{1/tan(u)}.")) (|tanh2coth| ((|#2| |#2|) "\\spad{tanh2coth(f)} converts every \\spad{tanh(u)} appearing in \\spad{f} into \\spad{1/coth(u)}.")) (|tan2cot| ((|#2| |#2|) "\\spad{tan2cot(f)} converts every \\spad{tan(u)} appearing in \\spad{f} into \\spad{1/cot(u)}.")) (|tanh2trigh| ((|#2| |#2|) "\\spad{tanh2trigh(f)} converts every \\spad{tanh(u)} appearing in \\spad{f} into \\spad{sinh(u)/cosh(u)}.")) (|tan2trig| ((|#2| |#2|) "\\spad{tan2trig(f)} converts every \\spad{tan(u)} appearing in \\spad{f} into \\spad{sin(u)/cos(u)}.")) (|sinh2csch| ((|#2| |#2|) "\\spad{sinh2csch(f)} converts every \\spad{sinh(u)} appearing in \\spad{f} into \\spad{1/csch(u)}.")) (|sin2csc| ((|#2| |#2|) "\\spad{sin2csc(f)} converts every \\spad{sin(u)} appearing in \\spad{f} into \\spad{1/csc(u)}.")) (|sech2cosh| ((|#2| |#2|) "\\spad{sech2cosh(f)} converts every \\spad{sech(u)} appearing in \\spad{f} into \\spad{1/cosh(u)}.")) (|sec2cos| ((|#2| |#2|) "\\spad{sec2cos(f)} converts every \\spad{sec(u)} appearing in \\spad{f} into \\spad{1/cos(u)}.")) (|csch2sinh| ((|#2| |#2|) "\\spad{csch2sinh(f)} converts every \\spad{csch(u)} appearing in \\spad{f} into \\spad{1/sinh(u)}.")) (|csc2sin| ((|#2| |#2|) "\\spad{csc2sin(f)} converts every \\spad{csc(u)} appearing in \\spad{f} into \\spad{1/sin(u)}.")) (|coth2trigh| ((|#2| |#2|) "\\spad{coth2trigh(f)} converts every \\spad{coth(u)} appearing in \\spad{f} into \\spad{cosh(u)/sinh(u)}.")) (|cot2trig| ((|#2| |#2|) "\\spad{cot2trig(f)} converts every \\spad{cot(u)} appearing in \\spad{f} into \\spad{cos(u)/sin(u)}.")) (|cosh2sech| ((|#2| |#2|) "\\spad{cosh2sech(f)} converts every \\spad{cosh(u)} appearing in \\spad{f} into \\spad{1/sech(u)}.")) (|cos2sec| ((|#2| |#2|) "\\spad{cos2sec(f)} converts every \\spad{cos(u)} appearing in \\spad{f} into \\spad{1/sec(u)}.")) (|expandLog| ((|#2| |#2|) "\\spad{expandLog(f)} converts every \\spad{log(a/b)} appearing in \\spad{f} into \\spad{log(a) - log(b)},{} and every \\spad{log(a*b)} into \\spad{log(a) + log(b)}..")) (|expandPower| ((|#2| |#2|) "\\spad{expandPower(f)} converts every power \\spad{(a/b)**c} appearing in \\spad{f} into \\spad{a**c * b**(-c)}.")) (|simplifyLog| ((|#2| |#2|) "\\spad{simplifyLog(f)} converts every \\spad{log(a) - log(b)} appearing in \\spad{f} into \\spad{log(a/b)},{} every \\spad{log(a) + log(b)} into \\spad{log(a*b)} and every \\spad{n*log(a)} into \\spad{log(a^n)}.")) (|simplifyExp| ((|#2| |#2|) "\\spad{simplifyExp(f)} converts every product \\spad{exp(a)*exp(b)} appearing in \\spad{f} into \\spad{exp(a+b)}.")) (|htrigs| ((|#2| |#2|) "\\spad{htrigs(f)} converts all the exponentials in \\spad{f} into hyperbolic sines and cosines.")) (|simplify| ((|#2| |#2|) "\\spad{simplify(f)} performs the following simplifications on f:\\begin{items} \\item 1. rewrites trigs and hyperbolic trigs in terms of \\spad{sin} ,{}\\spad{cos},{} \\spad{sinh},{} \\spad{cosh}. \\item 2. rewrites \\spad{sin**2} and \\spad{sinh**2} in terms of \\spad{cos} and \\spad{cosh},{} \\item 3. rewrites \\spad{exp(a)*exp(b)} as \\spad{exp(a+b)}. \\item 4. rewrites \\spad{(a**(1/n))**m * (a**(1/s))**t} as a single power of a single radical of \\spad{a}. \\end{items}")) (|expand| ((|#2| |#2|) "\\spad{expand(f)} performs the following expansions on f:\\begin{items} \\item 1. logs of products are expanded into sums of logs,{} \\item 2. trigonometric and hyperbolic trigonometric functions of sums are expanded into sums of products of trigonometric and hyperbolic trigonometric functions. \\item 3. formal powers of the form \\spad{(a/b)**c} are expanded into \\spad{a**c * b**(-c)}. \\end{items}"))) 
 NIL 
-((-12 (|HasCategory| |#1| (|%list| (QUOTE -554) (|%list| (QUOTE -801) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -797) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -554) (|%list| (QUOTE -801) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -797) (|devaluate| |#1|))))) 
-(-1123 |Coef|) 
+((-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|))))) 
+(-1122 |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}."))) 
-(((-3999 "*") |has| |#1| (-146)) (-3990 |has| |#1| (-496)) (-3992 . T) (-3991 . T) (-3994 . T)) 
-((|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-312)))) 
-(-1124 S R E V P) 
+(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-495)) (-3991 . T) (-3990 . T) (-3993 . T)) 
+((|HasCategory| |#1| (QUOTE (-38 (-350 (-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 (-312)))) 
+(-1123 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 (-320)))) 
-(-1125 R E V P) 
+(-1124 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|) $ $) "\\axiom{infRittWu?(\\spad{ts1},{}\\spad{ts2})} returns \\spad{true} iff \\axiom{\\spad{ts2}} has higher rank than \\axiom{\\spad{ts1}} in Wu Wen Tsun sense."))) 
-((-3998 . T)) 
+((-3997 . T)) 
 NIL 
-(-1126 |Curve|) 
+(-1125 |Curve|) 
 ((|constructor| (NIL "\\indented{2}{Package for constructing tubes around 3-dimensional parametric curves.} Domain of tubes around 3-dimensional parametric curves.")) (|tube| (($ |#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 
-(-1127) 
+(-1126) 
 ((|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 
-(-1128 S) 
+(-1127 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 (-1014))) (|HasCategory| |#1| (QUOTE (-553 (-773))))) 
-(-1129 -3094) 
+((|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-552 (-772))))) 
+(-1128 -3093) 
 ((|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 
-(-1130) 
+(-1129) 
 ((|constructor| (NIL "The fundamental Type."))) 
 NIL 
 NIL 
-(-1131) 
+(-1130) 
 ((|constructor| (NIL "This domain represents a type AST."))) 
 NIL 
 NIL 
-(-1132 S) 
+(-1131 S) 
 ((|constructor| (NIL "Provides functions to force a partial ordering on any set.")) (|more?| (((|Boolean|) |#1| |#1|) "\\spad{more?(a, b)} compares \\spad{a} and \\spad{b} in the partial ordering induced by setOrder,{} and uses the ordering on \\spad{S} if \\spad{a} and \\spad{b} are not comparable in the partial ordering.")) (|userOrdered?| (((|Boolean|)) "\\spad{userOrdered?()} tests if the partial ordering induced by \\spadfunFrom{setOrder}{UserDefinedPartialOrdering} is not empty.")) (|largest| ((|#1| (|List| |#1|)) "\\spad{largest l} returns the largest element of \\spad{l} where the partial ordering induced by setOrder is completed into a total one by the ordering on \\spad{S}.") ((|#1| (|List| |#1|) (|Mapping| (|Boolean|) |#1| |#1|)) "\\spad{largest(l, fn)} returns the largest element of \\spad{l} where the partial ordering induced by setOrder is completed into a total one by fn.")) (|less?| (((|Boolean|) |#1| |#1| (|Mapping| (|Boolean|) |#1| |#1|)) "\\spad{less?(a, b, fn)} compares \\spad{a} and \\spad{b} in the partial ordering induced by setOrder,{} and returns \\spad{fn(a, b)} if \\spad{a} and \\spad{b} are not comparable in that ordering.") (((|Union| (|Boolean|) "failed") |#1| |#1|) "\\spad{less?(a, b)} compares \\spad{a} and \\spad{b} in the partial ordering induced by setOrder.")) (|getOrder| (((|Record| (|:| |low| (|List| |#1|)) (|:| |high| (|List| |#1|)))) "\\spad{getOrder()} returns \\spad{[[b1,...,bm], [a1,...,an]]} such that the partial ordering on \\spad{S} was given by \\spad{setOrder([b1,...,bm],[a1,...,an])}.")) (|setOrder| (((|Void|) (|List| |#1|) (|List| |#1|)) "\\spad{setOrder([b1,...,bm], [a1,...,an])} defines a partial ordering on \\spad{S} given by: \\indented{3}{(1)\\space{2}\\spad{b1 < b2 < ... < bm < a1 < a2 < ... < an}.} \\indented{3}{(2)\\space{2}\\spad{bj < c < ai}\\space{2}for \\spad{c} not among the \\spad{ai}'s and bj's.} \\indented{3}{(3)\\space{2}undefined on \\spad{(c,d)} if neither is among the \\spad{ai}'s,{}bj's.}") (((|Void|) (|List| |#1|)) "\\spad{setOrder([a1,...,an])} defines a partial ordering on \\spad{S} given by: \\indented{3}{(1)\\space{2}\\spad{a1 < a2 < ... < an}.} \\indented{3}{(2)\\space{2}\\spad{b < ai\\space{3}for i = 1..n} and \\spad{b} not among the \\spad{ai}'s.} \\indented{3}{(3)\\space{2}undefined on \\spad{(b, c)} if neither is among the \\spad{ai}'s.}"))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-757)))) 
-(-1133) 
+((|HasCategory| |#1| (QUOTE (-756)))) 
+(-1132) 
 ((|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 
-(-1134 S) 
+(-1133 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 
-(-1135) 
+(-1134) 
 ((|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|) $) "\\spad{prime?(x)} tests if \\spad{x} can never be written as the product of two non-units of the ring,{} \\spadignore{i.e.} \\spad{x} is an irreducible element."))) 
-((-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
 NIL 
-(-1136) 
+(-1135) 
 ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 16 bits."))) 
 NIL 
 NIL 
-(-1137) 
+(-1136) 
 ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 32 bits."))) 
 NIL 
 NIL 
-(-1138) 
+(-1137) 
 ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 64 bits."))) 
 NIL 
 NIL 
-(-1139) 
+(-1138) 
 ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 8 bits."))) 
 NIL 
 NIL 
-(-1140 |Coef| |var| |cen|) 
+(-1139 |Coef| |var| |cen|) 
 ((|constructor| (NIL "Dense Laurent series in one variable \\indented{2}{\\spadtype{UnivariateLaurentSeries} is a domain representing Laurent} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{UnivariateLaurentSeries(Integer,x,3)} represents Laurent series in} \\indented{2}{\\spad{(x - 3)} with integer coefficients.}")) (|integrate| (($ $ (|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."))) 
-(((-3999 "*") OR (-2564 (|has| |#1| (-312)) (|has| (-1170 |#1| |#2| |#3|) (-741))) (|has| |#1| (-146)) (-2564 (|has| |#1| (-312)) (|has| (-1170 |#1| |#2| |#3|) (-822)))) (-3990 OR (-2564 (|has| |#1| (-312)) (|has| (-1170 |#1| |#2| |#3|) (-741))) (|has| |#1| (-496)) (-2564 (|has| |#1| (-312)) (|has| (-1170 |#1| |#2| |#3|) (-822)))) (-3995 |has| |#1| (-312)) (-3989 |has| |#1| (-312)) (-3991 . T) (-3992 . T) (-3994 . T)) 
-((|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1170 |#1| |#2| |#3|) (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1170 |#1| |#2| |#3|) (QUOTE (-120)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1170 |#1| |#2| |#3|) (QUOTE (-741)))) (|HasCategory| |#1| (QUOTE (-120)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1170 |#1| |#2| |#3|) (QUOTE (-810 (-1091))))) (-12 (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-485)) (|devaluate| |#1|)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1170 |#1| |#2| |#3|) (QUOTE (-810 (-1091))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1170 |#1| |#2| |#3|) (QUOTE (-812 (-1091))))) (-12 (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-485)) (|devaluate| |#1|)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1170 |#1| |#2| |#3|) (QUOTE (-190)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-485)) (|devaluate| |#1|))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1170 |#1| |#2| |#3|) (QUOTE (-190)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1170 |#1| |#2| |#3|) (QUOTE (-189)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-485)) (|devaluate| |#1|))))) (|HasCategory| (-485) (QUOTE (-1026))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-496)))) (|HasCategory| |#1| (QUOTE (-312))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1170 |#1| |#2| |#3|) (QUOTE (-822)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1170 |#1| |#2| |#3|) (QUOTE (-951 (-1091))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1170 |#1| |#2| |#3|) (QUOTE (-554 (-474))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1170 |#1| |#2| |#3|) (QUOTE (-934)))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-496)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1170 |#1| |#2| |#3|) (QUOTE (-741)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1170 |#1| |#2| |#3|) (QUOTE (-741)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1170 |#1| |#2| |#3|) (QUOTE (-757))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1170 |#1| |#2| |#3|) (QUOTE (-951 (-485))))) (|HasCategory| |#1| (QUOTE (-38 (-350 (-485)))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1170 |#1| |#2| |#3|) (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1170 |#1| |#2| |#3|) (QUOTE (-1067)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1170 |#1| |#2| |#3|) (|%list| (QUOTE -241) (|%list| (QUOTE -1170) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|)) (|%list| (QUOTE -1170) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1170 |#1| |#2| |#3|) (|%list| (QUOTE -260) (|%list| (QUOTE -1170) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1170 |#1| |#2| |#3|) (|%list| (QUOTE -456) (QUOTE (-1091)) (|%list| (QUOTE -1170) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1170 |#1| |#2| |#3|) (QUOTE (-581 (-485))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1170 |#1| |#2| |#3|) (QUOTE (-554 (-801 (-485)))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1170 |#1| |#2| |#3|) (QUOTE (-554 (-801 (-330)))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1170 |#1| |#2| |#3|) (QUOTE (-797 (-485))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1170 |#1| |#2| |#3|) (QUOTE (-797 (-330))))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-485))))) (|HasSignature| |#1| (|%list| (QUOTE -3948) (|%list| (|devaluate| |#1|) (QUOTE (-1091)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-485))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-29 (-485)))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1116)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasSignature| |#1| (|%list| (QUOTE -3814) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1091))))) (|HasSignature| |#1| (|%list| (QUOTE -3083) (|%list| (|%list| (QUOTE -584) (QUOTE (-1091))) (|devaluate| |#1|)))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1170 |#1| |#2| |#3|) (QUOTE (-484)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1170 |#1| |#2| |#3|) (QUOTE (-258)))) (|HasCategory| (-1170 |#1| |#2| |#3|) (QUOTE (-822))) (|HasCategory| (-1170 |#1| |#2| |#3|) (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-118))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1170 |#1| |#2| |#3|) (QUOTE (-822)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1170 |#1| |#2| |#3|) (QUOTE (-741)))) (|HasCategory| |#1| (QUOTE (-496)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1170 |#1| |#2| |#3|) (QUOTE (-822)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1170 |#1| |#2| |#3|) (QUOTE (-741)))) (|HasCategory| |#1| (QUOTE (-146)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1170 |#1| |#2| |#3|) (QUOTE (-812 (-1091))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1170 |#1| |#2| |#3|) (QUOTE (-189)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1170 |#1| |#2| |#3|) (QUOTE (-757)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1170 |#1| |#2| |#3|) (QUOTE (-120)))) (|HasCategory| |#1| (QUOTE (-120)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-1170 |#1| |#2| |#3|) (QUOTE (-822)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1170 |#1| |#2| |#3|) (QUOTE (-118)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-1170 |#1| |#2| |#3|) (QUOTE (-822)))) (|HasCategory| |#1| (QUOTE (-118))))) 
-(-1141 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) 
+(((-3998 "*") OR (-2563 (|has| |#1| (-312)) (|has| (-1169 |#1| |#2| |#3|) (-740))) (|has| |#1| (-146)) (-2563 (|has| |#1| (-312)) (|has| (-1169 |#1| |#2| |#3|) (-821)))) (-3989 OR (-2563 (|has| |#1| (-312)) (|has| (-1169 |#1| |#2| |#3|) (-740))) (|has| |#1| (-495)) (-2563 (|has| |#1| (-312)) (|has| (-1169 |#1| |#2| |#3|) (-821)))) (-3994 |has| |#1| (-312)) (-3988 |has| |#1| (-312)) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-495)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1169 |#1| |#2| |#3|) (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1169 |#1| |#2| |#3|) (QUOTE (-120)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1169 |#1| |#2| |#3|) (QUOTE (-740)))) (|HasCategory| |#1| (QUOTE (-120)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1169 |#1| |#2| |#3|) (QUOTE (-809 (-1090))))) (-12 (|HasCategory| |#1| (QUOTE (-809 (-1090)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-484)) (|devaluate| |#1|)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1169 |#1| |#2| |#3|) (QUOTE (-809 (-1090))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1169 |#1| |#2| |#3|) (QUOTE (-811 (-1090))))) (-12 (|HasCategory| |#1| (QUOTE (-809 (-1090)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-484)) (|devaluate| |#1|)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1169 |#1| |#2| |#3|) (QUOTE (-190)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-484)) (|devaluate| |#1|))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1169 |#1| |#2| |#3|) (QUOTE (-190)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1169 |#1| |#2| |#3|) (QUOTE (-189)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-484)) (|devaluate| |#1|))))) (|HasCategory| (-484) (QUOTE (-1025))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-495)))) (|HasCategory| |#1| (QUOTE (-312))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1169 |#1| |#2| |#3|) (QUOTE (-821)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1169 |#1| |#2| |#3|) (QUOTE (-950 (-1090))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1169 |#1| |#2| |#3|) (QUOTE (-553 (-473))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1169 |#1| |#2| |#3|) (QUOTE (-933)))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-495)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1169 |#1| |#2| |#3|) (QUOTE (-740)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1169 |#1| |#2| |#3|) (QUOTE (-740)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1169 |#1| |#2| |#3|) (QUOTE (-756))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1169 |#1| |#2| |#3|) (QUOTE (-950 (-484))))) (|HasCategory| |#1| (QUOTE (-38 (-350 (-484)))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1169 |#1| |#2| |#3|) (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1169 |#1| |#2| |#3|) (QUOTE (-1066)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1169 |#1| |#2| |#3|) (|%list| (QUOTE -241) (|%list| (QUOTE -1169) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|)) (|%list| (QUOTE -1169) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1169 |#1| |#2| |#3|) (|%list| (QUOTE -260) (|%list| (QUOTE -1169) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1169 |#1| |#2| |#3|) (|%list| (QUOTE -455) (QUOTE (-1090)) (|%list| (QUOTE -1169) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1169 |#1| |#2| |#3|) (QUOTE (-580 (-484))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1169 |#1| |#2| |#3|) (QUOTE (-553 (-800 (-484)))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1169 |#1| |#2| |#3|) (QUOTE (-553 (-800 (-330)))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1169 |#1| |#2| |#3|) (QUOTE (-796 (-484))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1169 |#1| |#2| |#3|) (QUOTE (-796 (-330))))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-484))))) (|HasSignature| |#1| (|%list| (QUOTE -3947) (|%list| (|devaluate| |#1|) (QUOTE (-1090)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-484))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-29 (-484)))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1115)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasSignature| |#1| (|%list| (QUOTE -3813) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1090))))) (|HasSignature| |#1| (|%list| (QUOTE -3082) (|%list| (|%list| (QUOTE -583) (QUOTE (-1090))) (|devaluate| |#1|)))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1169 |#1| |#2| |#3|) (QUOTE (-483)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1169 |#1| |#2| |#3|) (QUOTE (-258)))) (|HasCategory| (-1169 |#1| |#2| |#3|) (QUOTE (-821))) (|HasCategory| (-1169 |#1| |#2| |#3|) (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-118))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1169 |#1| |#2| |#3|) (QUOTE (-821)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1169 |#1| |#2| |#3|) (QUOTE (-740)))) (|HasCategory| |#1| (QUOTE (-495)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1169 |#1| |#2| |#3|) (QUOTE (-821)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1169 |#1| |#2| |#3|) (QUOTE (-740)))) (|HasCategory| |#1| (QUOTE (-146)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1169 |#1| |#2| |#3|) (QUOTE (-811 (-1090))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1169 |#1| |#2| |#3|) (QUOTE (-189)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1169 |#1| |#2| |#3|) (QUOTE (-756)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1169 |#1| |#2| |#3|) (QUOTE (-120)))) (|HasCategory| |#1| (QUOTE (-120)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-1169 |#1| |#2| |#3|) (QUOTE (-821)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-1169 |#1| |#2| |#3|) (QUOTE (-118)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-1169 |#1| |#2| |#3|) (QUOTE (-821)))) (|HasCategory| |#1| (QUOTE (-118))))) 
+(-1140 |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 
-(-1142 |Coef|) 
+(-1141 |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."))) 
-(((-3999 "*") |has| |#1| (-146)) (-3990 |has| |#1| (-496)) (-3995 |has| |#1| (-312)) (-3989 |has| |#1| (-312)) (-3991 . T) (-3992 . T) (-3994 . T)) 
+(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-495)) (-3994 |has| |#1| (-312)) (-3988 |has| |#1| (-312)) (-3990 . T) (-3991 . T) (-3993 . T)) 
 NIL 
-(-1143 S |Coef| UTS) 
+(-1142 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 (-312)))) 
-(-1144 |Coef| UTS) 
+(-1143 |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)}."))) 
-(((-3999 "*") |has| |#1| (-146)) (-3990 |has| |#1| (-496)) (-3995 |has| |#1| (-312)) (-3989 |has| |#1| (-312)) (-3991 . T) (-3992 . T) (-3994 . T)) 
+(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-495)) (-3994 |has| |#1| (-312)) (-3988 |has| |#1| (-312)) (-3990 . T) (-3991 . T) (-3993 . T)) 
 NIL 
-(-1145 |Coef| UTS) 
+(-1144 |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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-(-1146 ZP) 
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+(-1145 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 
-(-1147 S) 
+(-1146 S) 
 ((|constructor| (NIL "This domain provides segments which may be half open. That is,{} ranges of the form \\spad{a..} or \\spad{a..b}.")) (|hasHi| (((|Boolean|) $) "\\spad{hasHi(s)} tests whether the segment \\spad{s} has an upper bound.")) (|coerce| (($ (|Segment| |#1|)) "\\spad{coerce(x)} allows \\spadtype{Segment} values to be used as \\%.")) (|segment| (($ |#1|) "\\spad{segment(l)} is an alternate way to construct the segment \\spad{l..}.")) (SEGMENT (($ |#1|) "\\spad{l..} produces a half open segment,{} that is,{} one with no upper bound."))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1014)))) 
-(-1148 R S) 
+((|HasCategory| |#1| (QUOTE (-755))) (|HasCategory| |#1| (QUOTE (-1013)))) 
+(-1147 R S) 
 ((|constructor| (NIL "This package provides operations for mapping functions onto segments.")) (|map| (((|Stream| |#2|) (|Mapping| |#2| |#1|) (|UniversalSegment| |#1|)) "\\spad{map(f,s)} expands the segment \\spad{s},{} applying \\spad{f} to each value.") (((|UniversalSegment| |#2|) (|Mapping| |#2| |#1|) (|UniversalSegment| |#1|)) "\\spad{map(f,seg)} returns the new segment obtained by applying \\spad{f} to the endpoints of \\spad{seg}."))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-756)))) 
-(-1149 |x| R) 
+((|HasCategory| |#1| (QUOTE (-755)))) 
+(-1148 |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}"))) 
-(((-3999 "*") |has| |#2| (-146)) (-3990 |has| |#2| (-496)) (-3993 |has| |#2| (-312)) (-3995 |has| |#2| (-6 -3995)) (-3992 . T) (-3991 . T) (-3994 . T)) 
-((|HasCategory| |#2| (QUOTE (-822))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-146))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-496)))) (-12 (|HasCategory| |#2| (QUOTE (-797 (-330)))) (|HasCategory| (-995) (QUOTE (-797 (-330))))) (-12 (|HasCategory| |#2| (QUOTE (-797 (-485)))) (|HasCategory| (-995) (QUOTE (-797 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-554 (-801 (-330))))) (|HasCategory| (-995) (QUOTE (-554 (-801 (-330)))))) (-12 (|HasCategory| |#2| (QUOTE (-554 (-801 (-485))))) (|HasCategory| (-995) (QUOTE (-554 (-801 (-485)))))) (-12 (|HasCategory| |#2| (QUOTE (-554 (-474)))) (|HasCategory| (-995) (QUOTE (-554 (-474))))) (|HasCategory| |#2| (QUOTE (-581 (-485)))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#2| (QUOTE (-951 (-485)))) (OR (|HasCategory| |#2| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#2| (QUOTE (-951 (-350 (-485)))))) (|HasCategory| |#2| (QUOTE (-951 (-350 (-485))))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-822)))) (OR (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-822)))) (OR (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-822)))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-1067))) (|HasCategory| |#2| (QUOTE (-812 (-1091)))) (|HasCategory| |#2| (QUOTE (-810 (-1091)))) (|HasCategory| |#2| (QUOTE (-189))) (|HasCategory| |#2| (QUOTE (-190))) (|HasAttribute| |#2| (QUOTE -3995)) (|HasCategory| |#2| (QUOTE (-392))) (-12 (|HasCategory| |#2| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#2| (QUOTE (-118))))) 
-(-1150 |x| R |y| S) 
+(((-3998 "*") |has| |#2| (-146)) (-3989 |has| |#2| (-495)) (-3992 |has| |#2| (-312)) (-3994 |has| |#2| (-6 -3994)) (-3991 . T) (-3990 . T) (-3993 . T)) 
+((|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-146))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-495)))) (-12 (|HasCategory| |#2| (QUOTE (-796 (-330)))) (|HasCategory| (-994) (QUOTE (-796 (-330))))) (-12 (|HasCategory| |#2| (QUOTE (-796 (-484)))) (|HasCategory| (-994) (QUOTE (-796 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-553 (-800 (-330))))) (|HasCategory| (-994) (QUOTE (-553 (-800 (-330)))))) (-12 (|HasCategory| |#2| (QUOTE (-553 (-800 (-484))))) (|HasCategory| (-994) (QUOTE (-553 (-800 (-484)))))) (-12 (|HasCategory| |#2| (QUOTE (-553 (-473)))) (|HasCategory| (-994) (QUOTE (-553 (-473))))) (|HasCategory| |#2| (QUOTE (-580 (-484)))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#2| (QUOTE (-950 (-484)))) (OR (|HasCategory| |#2| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#2| (QUOTE (-950 (-350 (-484)))))) (|HasCategory| |#2| (QUOTE (-950 (-350 (-484))))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-821)))) (OR (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-821)))) (OR (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-821)))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| |#2| (QUOTE (-811 (-1090)))) (|HasCategory| |#2| (QUOTE (-809 (-1090)))) (|HasCategory| |#2| (QUOTE (-189))) (|HasCategory| |#2| (QUOTE (-190))) (|HasAttribute| |#2| (QUOTE -3994)) (|HasCategory| |#2| (QUOTE (-392))) (-12 (|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#2| (QUOTE (-118))))) 
+(-1149 |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 
-(-1151 R Q UP) 
+(-1150 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 
-(-1152 R UP) 
+(-1151 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 
-(-1153 R UP) 
+(-1152 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 
-(-1154 R U) 
+(-1153 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 
-(-1155 S R) 
+(-1154 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 (-350 (-485))))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-1067)))) 
-(-1156 R) 
+((|HasCategory| |#2| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-1066)))) 
+(-1155 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}."))) 
-(((-3999 "*") |has| |#1| (-146)) (-3990 |has| |#1| (-496)) (-3993 |has| |#1| (-312)) (-3995 |has| |#1| (-6 -3995)) (-3992 . T) (-3991 . T) (-3994 . T)) 
+(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-495)) (-3992 |has| |#1| (-312)) (-3994 |has| |#1| (-6 -3994)) (-3991 . T) (-3990 . T) (-3993 . T)) 
 NIL 
-(-1157 R PR S PS) 
+(-1156 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 
-(-1158 S |Coef| |Expon|) 
+(-1157 S |Coef| |Expon|) 
 ((|constructor| (NIL "\\spadtype{UnivariatePowerSeriesCategory} is the most general univariate power series category with exponents in an ordered abelian monoid. Note: this category exports a substitution function if it is possible to multiply exponents. Note: this category exports a derivative operation if it is possible to multiply coefficients by exponents.")) (|eval| (((|Stream| |#2|) $ |#2|) "\\spad{eval(f,a)} evaluates a power series at a value in the ground ring by returning a stream of partial sums.")) (|extend| (($ $ |#3|) "\\spad{extend(f,n)} causes all terms of \\spad{f} of degree <= \\spad{n} to be computed.")) (|approximate| ((|#2| $ |#3|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#3| |#3|) "\\spad{truncate(f,k1,k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#3|) "\\spad{truncate(f,k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#3| $ |#3|) "\\spad{order(f,n) = min(m,n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#3| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#2| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#3|) (|:| |c| |#2|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-810 (-1091)))) (|HasSignature| |#2| (|%list| (QUOTE *) (|%list| (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1026))) (|HasSignature| |#2| (|%list| (QUOTE **) (|%list| (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (|%list| (QUOTE -3948) (|%list| (|devaluate| |#2|) (QUOTE (-1091)))))) 
-(-1159 |Coef| |Expon|) 
+((|HasCategory| |#2| (QUOTE (-809 (-1090)))) (|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 -3947) (|%list| (|devaluate| |#2|) (QUOTE (-1090)))))) 
+(-1158 |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|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) 
-(((-3999 "*") |has| |#1| (-146)) (-3990 |has| |#1| (-496)) (-3991 . T) (-3992 . T) (-3994 . T)) 
+(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-495)) (-3990 . T) (-3991 . T) (-3993 . T)) 
 NIL 
-(-1160 RC P) 
+(-1159 RC P) 
 ((|constructor| (NIL "This package provides for square-free decomposition of univariate polynomials over arbitrary rings,{} \\spadignore{i.e.} a partial factorization such that each factor is a product of irreducibles with multiplicity one and the factors are pairwise relatively prime. If the ring has characteristic zero,{} the result is guaranteed to satisfy this condition. If the ring is an infinite ring of finite characteristic,{} then it may not be possible to decide when polynomials contain factors which are \\spad{p}th powers. In this case,{} the flag associated with that polynomial is set to \"nil\" (meaning that that polynomials are not guaranteed to be square-free).")) (|BumInSepFFE| (((|Record| (|:| |flg| (|Union| #1="nil" #2="sqfr" #3="irred" #4="prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|))) (|Record| (|:| |flg| (|Union| #1# #2# #3# #4#)) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|)))) "\\spad{BumInSepFFE(f)} is a local function,{} exported only because it has multiple conditional definitions.")) (|squareFreePart| ((|#2| |#2|) "\\spad{squareFreePart(p)} returns a polynomial which has the same irreducible factors as the univariate polynomial \\spad{p},{} but each factor has multiplicity one.")) (|squareFree| (((|Factored| |#2|) |#2|) "\\spad{squareFree(p)} computes the square-free factorization of the univariate polynomial \\spad{p}. Each factor has no repeated roots,{} and the factors are pairwise relatively prime.")) (|gcd| (($ $ $) "\\spad{gcd(p,q)} computes the greatest-common-divisor of \\spad{p} and \\spad{q}."))) 
 NIL 
 NIL 
-(-1161 |Coef| |var| |cen|) 
+(-1160 |Coef| |var| |cen|) 
 ((|constructor| (NIL "Dense Puiseux series in one variable \\indented{2}{\\spadtype{UnivariatePuiseuxSeries} is a domain representing Puiseux} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{UnivariatePuiseuxSeries(Integer,x,3)} represents Puiseux series in} \\indented{2}{\\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|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."))) 
-(((-3999 "*") |has| |#1| (-146)) (-3990 |has| |#1| (-496)) (-3995 |has| |#1| (-312)) (-3989 |has| |#1| (-312)) (-3991 . T) (-3992 . T) (-3994 . T)) 
-((|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-485))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-485))) (|devaluate| |#1|)))) (|HasCategory| (-350 (-485)) (QUOTE (-1026))) (|HasCategory| |#1| (QUOTE (-312))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-496)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-496)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-485)))))) (|HasSignature| |#1| (|%list| (QUOTE -3948) (|%list| (|devaluate| |#1|) (QUOTE (-1091)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-485)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-29 (-485)))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1116)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasSignature| |#1| (|%list| (QUOTE -3814) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1091))))) (|HasSignature| |#1| (|%list| (QUOTE -3083) (|%list| (|%list| (QUOTE -584) (QUOTE (-1091))) (|devaluate| |#1|))))))) 
-(-1162 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) 
+(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-495)) (-3994 |has| |#1| (-312)) (-3988 |has| |#1| (-312)) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((|HasCategory| |#1| (QUOTE (-38 (-350 (-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 (-809 (-1090)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-484))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-484))) (|devaluate| |#1|)))) (|HasCategory| (-350 (-484)) (QUOTE (-1025))) (|HasCategory| |#1| (QUOTE (-312))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-495)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-495)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-484)))))) (|HasSignature| |#1| (|%list| (QUOTE -3947) (|%list| (|devaluate| |#1|) (QUOTE (-1090)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-484)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-29 (-484)))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1115)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasSignature| |#1| (|%list| (QUOTE -3813) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1090))))) (|HasSignature| |#1| (|%list| (QUOTE -3082) (|%list| (|%list| (QUOTE -583) (QUOTE (-1090))) (|devaluate| |#1|))))))) 
+(-1161 |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 
-(-1163 |Coef|) 
+(-1162 |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."))) 
-(((-3999 "*") |has| |#1| (-146)) (-3990 |has| |#1| (-496)) (-3995 |has| |#1| (-312)) (-3989 |has| |#1| (-312)) (-3991 . T) (-3992 . T) (-3994 . T)) 
+(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-495)) (-3994 |has| |#1| (-312)) (-3988 |has| |#1| (-312)) (-3990 . T) (-3991 . T) (-3993 . T)) 
 NIL 
-(-1164 S |Coef| ULS) 
+(-1163 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 
-(-1165 |Coef| ULS) 
+(-1164 |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)}."))) 
-(((-3999 "*") |has| |#1| (-146)) (-3990 |has| |#1| (-496)) (-3995 |has| |#1| (-312)) (-3989 |has| |#1| (-312)) (-3991 . T) (-3992 . T) (-3994 . T)) 
+(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-495)) (-3994 |has| |#1| (-312)) (-3988 |has| |#1| (-312)) (-3990 . T) (-3991 . T) (-3993 . T)) 
 NIL 
-(-1166 |Coef| ULS) 
+(-1165 |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)}."))) 
-(((-3999 "*") |has| |#1| (-146)) (-3990 |has| |#1| (-496)) (-3995 |has| |#1| (-312)) (-3989 |has| |#1| (-312)) (-3991 . T) (-3992 . T) (-3994 . T)) 
-((|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-485))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-485))) (|devaluate| |#1|)))) (|HasCategory| (-350 (-485)) (QUOTE (-1026))) (|HasCategory| |#1| (QUOTE (-312))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-496)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-496)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-485)))))) (|HasSignature| |#1| (|%list| (QUOTE -3948) (|%list| (|devaluate| |#1|) (QUOTE (-1091)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-485)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-29 (-485)))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1116)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasSignature| |#1| (|%list| (QUOTE -3814) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1091))))) (|HasSignature| |#1| (|%list| (QUOTE -3083) (|%list| (|%list| (QUOTE -584) (QUOTE (-1091))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (QUOTE (-38 (-350 (-485)))))) 
-(-1167 R FE |var| |cen|) 
+(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-495)) (-3994 |has| |#1| (-312)) (-3988 |has| |#1| (-312)) (-3990 . T) (-3991 . T) (-3993 . 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 (-809 (-1090)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-484))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-484))) (|devaluate| |#1|)))) (|HasCategory| (-350 (-484)) (QUOTE (-1025))) (|HasCategory| |#1| (QUOTE (-312))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-495)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-495)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-484)))))) (|HasSignature| |#1| (|%list| (QUOTE -3947) (|%list| (|devaluate| |#1|) (QUOTE (-1090)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-484)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-29 (-484)))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1115)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasSignature| |#1| (|%list| (QUOTE -3813) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1090))))) (|HasSignature| |#1| (|%list| (QUOTE -3082) (|%list| (|%list| (QUOTE -583) (QUOTE (-1090))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (QUOTE (-38 (-350 (-484)))))) 
+(-1166 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))}."))) 
-(((-3999 "*") |has| (-1161 |#2| |#3| |#4|) (-146)) (-3990 |has| (-1161 |#2| |#3| |#4|) (-496)) (-3991 . T) (-3992 . T) (-3994 . T)) 
-((|HasCategory| (-1161 |#2| |#3| |#4|) (QUOTE (-38 (-350 (-485))))) (|HasCategory| (-1161 |#2| |#3| |#4|) (QUOTE (-118))) (|HasCategory| (-1161 |#2| |#3| |#4|) (QUOTE (-120))) (|HasCategory| (-1161 |#2| |#3| |#4|) (QUOTE (-146))) (OR (|HasCategory| (-1161 |#2| |#3| |#4|) (QUOTE (-38 (-350 (-485))))) (|HasCategory| (-1161 |#2| |#3| |#4|) (QUOTE (-951 (-350 (-485)))))) (|HasCategory| (-1161 |#2| |#3| |#4|) (QUOTE (-951 (-350 (-485))))) (|HasCategory| (-1161 |#2| |#3| |#4|) (QUOTE (-951 (-485)))) (|HasCategory| (-1161 |#2| |#3| |#4|) (QUOTE (-312))) (|HasCategory| (-1161 |#2| |#3| |#4|) (QUOTE (-392))) (|HasCategory| (-1161 |#2| |#3| |#4|) (QUOTE (-496)))) 
-(-1168 A S) 
+(((-3998 "*") |has| (-1160 |#2| |#3| |#4|) (-146)) (-3989 |has| (-1160 |#2| |#3| |#4|) (-495)) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((|HasCategory| (-1160 |#2| |#3| |#4|) (QUOTE (-38 (-350 (-484))))) (|HasCategory| (-1160 |#2| |#3| |#4|) (QUOTE (-118))) (|HasCategory| (-1160 |#2| |#3| |#4|) (QUOTE (-120))) (|HasCategory| (-1160 |#2| |#3| |#4|) (QUOTE (-146))) (OR (|HasCategory| (-1160 |#2| |#3| |#4|) (QUOTE (-38 (-350 (-484))))) (|HasCategory| (-1160 |#2| |#3| |#4|) (QUOTE (-950 (-350 (-484)))))) (|HasCategory| (-1160 |#2| |#3| |#4|) (QUOTE (-950 (-350 (-484))))) (|HasCategory| (-1160 |#2| |#3| |#4|) (QUOTE (-950 (-484)))) (|HasCategory| (-1160 |#2| |#3| |#4|) (QUOTE (-312))) (|HasCategory| (-1160 |#2| |#3| |#4|) (QUOTE (-392))) (|HasCategory| (-1160 |#2| |#3| |#4|) (QUOTE (-495)))) 
+(-1167 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| $) "\\spad{concat(x,u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) 
 NIL 
-((|HasCategory| |#1| (|%list| (QUOTE -1036) (|devaluate| |#2|)))) 
-(-1169 S) 
+((|HasCategory| |#1| (|%list| (QUOTE -1035) (|devaluate| |#2|)))) 
+(-1168 S) 
 ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|Integer|)) "\\spad{split!(u,n)} splits \\spad{u} into two aggregates: \\axiom{\\spad{v} = rest(\\spad{u},{}\\spad{n})} and \\axiom{\\spad{w} = first(\\spad{u},{}\\spad{n})},{} returning \\axiom{\\spad{v}}. Note: afterwards \\axiom{rest(\\spad{u},{}\\spad{n})} returns \\axiom{empty()}.")) (|setlast!| ((|#1| $ |#1|) "\\spad{setlast!(u,x)} destructively changes the last element of \\spad{u} to \\spad{x}.")) (|setrest!| (($ $ $) "\\spad{setrest!(u,v)} destructively changes the rest of \\spad{u} to \\spad{v}.")) (|setelt| ((|#1| $ "last" |#1|) "\\spad{setelt(u,\"last\",x)} (also written: \\axiom{\\spad{u}.last := \\spad{b}}) is equivalent to \\axiom{setlast!(\\spad{u},{}\\spad{v})}.") (($ $ "rest" $) "\\spad{setelt(u,\"rest\",v)} (also written: \\axiom{\\spad{u}.rest := \\spad{v}}) is equivalent to \\axiom{setrest!(\\spad{u},{}\\spad{v})}.") ((|#1| $ "first" |#1|) "\\spad{setelt(u,\"first\",x)} (also written: \\axiom{\\spad{u}.first := \\spad{x}}) is equivalent to \\axiom{setfirst!(\\spad{u},{}\\spad{x})}.")) (|setfirst!| ((|#1| $ |#1|) "\\spad{setfirst!(u,x)} destructively changes the first element of a to \\spad{x}.")) (|cycleSplit!| (($ $) "\\spad{cycleSplit!(u)} splits the aggregate by dropping off the cycle. The value returned is the cycle entry,{} or nil if none exists. For example,{} if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} is the cyclic list where \\spad{v} is the head of the cycle,{} \\axiom{cycleSplit!(\\spad{w})} will drop \\spad{v} off \\spad{w} thus destructively changing \\spad{w} to \\spad{u},{} and returning \\spad{v}.")) (|concat!| (($ $ |#1|) "\\spad{concat!(u,x)} destructively adds element \\spad{x} to the end of \\spad{u}. Note: \\axiom{concat!(a,{}\\spad{x}) = setlast!(a,{}[\\spad{x}])}.") (($ $ $) "\\spad{concat!(u,v)} destructively concatenates \\spad{v} to the end of \\spad{u}. Note: \\axiom{concat!(\\spad{u},{}\\spad{v}) = setlast!(\\spad{u},{}\\spad{v})}.")) (|cycleTail| (($ $) "\\spad{cycleTail(u)} returns the last node in the cycle,{} or empty if none exists.")) (|cycleLength| (((|NonNegativeInteger|) $) "\\spad{cycleLength(u)} returns the length of a top-level cycle contained in aggregate \\spad{u},{} or 0 is \\spad{u} has no such cycle.")) (|cycleEntry| (($ $) "\\spad{cycleEntry(u)} returns the head of a top-level cycle contained in aggregate \\spad{u},{} or \\axiom{empty()} if none exists.")) (|third| ((|#1| $) "\\spad{third(u)} returns the third element of \\spad{u}. Note: \\axiom{third(\\spad{u}) = first(rest(rest(\\spad{u})))}.")) (|second| ((|#1| $) "\\spad{second(u)} returns the second element of \\spad{u}. Note: \\axiom{second(\\spad{u}) = first(rest(\\spad{u}))}.")) (|tail| (($ $) "\\spad{tail(u)} returns the last node of \\spad{u}. Note: if \\spad{u} is \\axiom{shallowlyMutable},{} \\axiom{setrest(tail(\\spad{u}),{}\\spad{v}) = concat(\\spad{u},{}\\spad{v})}.")) (|last| (($ $ (|NonNegativeInteger|)) "\\spad{last(u,n)} returns a copy of the last \\spad{n} (\\axiom{\\spad{n} >= 0}) nodes of \\spad{u}. Note: \\axiom{last(\\spad{u},{}\\spad{n})} is a list of \\spad{n} elements.") ((|#1| $) "\\spad{last(u)} resturn the last element of \\spad{u}. Note: for lists,{} \\axiom{last(\\spad{u}) = \\spad{u} . (maxIndex \\spad{u}) = \\spad{u} . (\\# \\spad{u} - 1)}.")) (|rest| (($ $ (|NonNegativeInteger|)) "\\spad{rest(u,n)} returns the \\axiom{\\spad{n}}th (\\spad{n} >= 0) node of \\spad{u}. Note: \\axiom{rest(\\spad{u},{}0) = \\spad{u}}.") (($ $) "\\spad{rest(u)} returns an aggregate consisting of all but the first element of \\spad{u} (equivalently,{} the next node of \\spad{u}).")) (|elt| ((|#1| $ "last") "\\spad{elt(u,\"last\")} (also written: \\axiom{\\spad{u} . last}) is equivalent to last \\spad{u}.") (($ $ "rest") "\\spad{elt(\\%,\"rest\")} (also written: \\axiom{\\spad{u}.rest}) is equivalent to \\axiom{rest \\spad{u}}.") ((|#1| $ "first") "\\spad{elt(u,\"first\")} (also written: \\axiom{\\spad{u} . first}) is equivalent to first \\spad{u}.")) (|first| (($ $ (|NonNegativeInteger|)) "\\spad{first(u,n)} returns a copy of the first \\spad{n} (\\axiom{\\spad{n} >= 0}) elements of \\spad{u}.") ((|#1| $) "\\spad{first(u)} returns the first element of \\spad{u} (equivalently,{} the value at the current node).")) (|concat| (($ |#1| $) "\\spad{concat(x,u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) 
 NIL 
 NIL 
-(-1170 |Coef| |var| |cen|) 
+(-1169 |Coef| |var| |cen|) 
 ((|constructor| (NIL "Dense Taylor series in one variable \\spadtype{UnivariateTaylorSeries} is a domain representing Taylor series in one variable with coefficients in an arbitrary ring. The parameters of the type specify the coefficient ring,{} the power series variable,{} and the center of the power series expansion. For example,{} \\spadtype{UnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.")) (|integrate| (($ $ (|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}."))) 
-(((-3999 "*") |has| |#1| (-146)) (-3990 |has| |#1| (-496)) (-3991 . T) (-3992 . T) (-3994 . T)) 
-((|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-496))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|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 (-1026))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-695))))) (|HasSignature| |#1| (|%list| (QUOTE -3948) (|%list| (|devaluate| |#1|) (QUOTE (-1091)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-695))))) (|HasCategory| |#1| (QUOTE (-312))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-29 (-485)))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1116)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasSignature| |#1| (|%list| (QUOTE -3814) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1091))))) (|HasSignature| |#1| (|%list| (QUOTE -3083) (|%list| (|%list| (QUOTE -584) (QUOTE (-1091))) (|devaluate| |#1|))))))) 
-(-1171 |Coef1| |Coef2| UTS1 UTS2) 
+(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-495)) (-3990 . T) (-3991 . T) (-3993 . T)) 
+((|HasCategory| |#1| (QUOTE (-38 (-350 (-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 (-809 (-1090)))) (|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 (-1025))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-694))))) (|HasSignature| |#1| (|%list| (QUOTE -3947) (|%list| (|devaluate| |#1|) (QUOTE (-1090)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-694))))) (|HasCategory| |#1| (QUOTE (-312))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-29 (-484)))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1115)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasSignature| |#1| (|%list| (QUOTE -3813) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1090))))) (|HasSignature| |#1| (|%list| (QUOTE -3082) (|%list| (|%list| (QUOTE -583) (QUOTE (-1090))) (|devaluate| |#1|))))))) 
+(-1170 |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 
-(-1172 S |Coef|) 
+(-1171 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 (-485)))) (|HasCategory| |#2| (QUOTE (-872))) (|HasCategory| |#2| (QUOTE (-1116))) (|HasSignature| |#2| (|%list| (QUOTE -3083) (|%list| (|%list| (QUOTE -584) (QUOTE (-1091))) (|devaluate| |#2|)))) (|HasSignature| |#2| (|%list| (QUOTE -3814) (|%list| (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1091))))) (|HasCategory| |#2| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#2| (QUOTE (-312)))) 
-(-1173 |Coef|) 
+((|HasCategory| |#2| (QUOTE (-29 (-484)))) (|HasCategory| |#2| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-1115))) (|HasSignature| |#2| (|%list| (QUOTE -3082) (|%list| (|%list| (QUOTE -583) (QUOTE (-1090))) (|devaluate| |#2|)))) (|HasSignature| |#2| (|%list| (QUOTE -3813) (|%list| (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1090))))) (|HasCategory| |#2| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#2| (QUOTE (-312)))) 
+(-1172 |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."))) 
-(((-3999 "*") |has| |#1| (-146)) (-3990 |has| |#1| (-496)) (-3991 . T) (-3992 . T) (-3994 . T)) 
+(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-495)) (-3990 . T) (-3991 . T) (-3993 . T)) 
 NIL 
-(-1174 |Coef| UTS) 
+(-1173 |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 
-(-1175 -3094 UP L UTS) 
+(-1174 -3093 UP L UTS) 
 ((|constructor| (NIL "\\spad{RUTSodetools} provides tools to interface with the series \\indented{1}{ODE solver when presented with linear ODEs.}")) (RF2UTS ((|#4| (|Fraction| |#2|)) "\\spad{RF2UTS(f)} converts \\spad{f} to a Taylor series.")) (LODO2FUN (((|Mapping| |#4| (|List| |#4|)) |#3|) "\\spad{LODO2FUN(op)} returns the function to pass to the series ODE solver in order to solve \\spad{op y = 0}.")) (UTS2UP ((|#2| |#4| (|NonNegativeInteger|)) "\\spad{UTS2UP(s, n)} converts the first \\spad{n} terms of \\spad{s} to a univariate polynomial.")) (UP2UTS ((|#4| |#2|) "\\spad{UP2UTS(p)} converts \\spad{p} to a Taylor series."))) 
 NIL 
-((|HasCategory| |#1| (QUOTE (-496)))) 
-(-1176) 
+((|HasCategory| |#1| (QUOTE (-495)))) 
+(-1175) 
 ((|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 
-(-1177 |sym|) 
+(-1176 |sym|) 
 ((|constructor| (NIL "This domain implements variables")) (|variable| (((|Symbol|)) "\\spad{variable()} returns the symbol")) (|coerce| (((|Symbol|) $) "\\spad{coerce(x)} returns the symbol"))) 
 NIL 
 NIL 
-(-1178 S R) 
+(-1177 S R) 
 ((|constructor| (NIL "\\spadtype{VectorCategory} represents the type of vector like objects,{} \\spadignore{i.e.} finite sequences indexed by some finite segment of the integers. The operations available on vectors depend on the structure of the underlying components. Many operations from the component domain are defined for vectors componentwise. It can by assumed that extraction or updating components can be done in constant time.")) (|magnitude| ((|#2| $) "\\spad{magnitude(v)} computes the sqrt(dot(\\spad{v},{}\\spad{v})),{} \\spadignore{i.e.} the length")) (|length| ((|#2| $) "\\spad{length(v)} computes the sqrt(dot(\\spad{v},{}\\spad{v})),{} \\spadignore{i.e.} the magnitude")) (|cross| (($ $ $) "vectorProduct(\\spad{u},{}\\spad{v}) constructs the cross product of \\spad{u} and \\spad{v}. Error: if \\spad{u} and \\spad{v} are not of length 3.")) (|outerProduct| (((|Matrix| |#2|) $ $) "\\spad{outerProduct(u,v)} constructs the matrix whose (\\spad{i},{}\\spad{j})\\spad{'}th element is \\spad{u}(\\spad{i})*v(\\spad{j}).")) (|dot| ((|#2| $ $) "\\spad{dot(x,y)} computes the inner product of the two vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.")) (* (($ $ |#2|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#2| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.") (($ (|Integer|) $) "\\spad{n * y} multiplies each component of the vector \\spad{y} by the integer \\spad{n}.")) (- (($ $ $) "\\spad{x - y} returns the component-wise difference of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.") (($ $) "\\spad{-x} negates all components of the vector \\spad{x}.")) (|zero| (($ (|NonNegativeInteger|)) "\\spad{zero(n)} creates a zero vector of length \\spad{n}.")) (+ (($ $ $) "\\spad{x + y} returns the component-wise sum of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length."))) 
 NIL 
-((|HasCategory| |#2| (QUOTE (-916))) (|HasCategory| |#2| (QUOTE (-962))) (|HasCategory| |#2| (QUOTE (-664))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25)))) 
-(-1179 R) 
+((|HasCategory| |#2| (QUOTE (-915))) (|HasCategory| |#2| (QUOTE (-961))) (|HasCategory| |#2| (QUOTE (-663))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25)))) 
+(-1178 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}.")) (+ (($ $ $) "\\spad{x + y} returns the component-wise sum of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length."))) 
-((-3998 . T)) 
+((-3997 . T)) 
 NIL 
-(-1180 R) 
+(-1179 R) 
 ((|constructor| (NIL "This type represents vector like objects with varying lengths and indexed by a finite segment of integers starting at 1.")) (|vector| (($ (|List| |#1|)) "\\spad{vector(l)} converts the list \\spad{l} to a vector."))) 
-((-3998 . T)) 
-((OR (-12 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (OR (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-757))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-72))) (|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 (-1014))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|))) (|HasCategory| $ (|%list| (QUOTE -1036) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| $ (|%list| (QUOTE -1036) (|devaluate| |#1|))))) 
-(-1181 A B) 
+((-3997 . T)) 
+((OR (-12 (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-553 (-473)))) (OR (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-756))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| (-484) (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-72))) (|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 (-1013))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|)))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#1|))) (|HasCategory| $ (|%list| (QUOTE -1035) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| $ (|%list| (QUOTE -1035) (|devaluate| |#1|))))) 
+(-1180 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 
-(-1182) 
+(-1181) 
 ((|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 
-(-1183) 
+(-1182) 
 ((|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 
-(-1184) 
+(-1183) 
 ((|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 
-(-1185) 
+(-1184) 
 ((|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 
-(-1186) 
+(-1185) 
 ((|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| (($) "\\spad{void()} produces a void object."))) 
 NIL 
 NIL 
-(-1187 A S) 
+(-1186 A S) 
 ((|constructor| (NIL "Vector Spaces (not necessarily finite dimensional) over a field.")) (|dimension| (((|CardinalNumber|)) "\\spad{dimension()} returns the dimensionality of the vector space.")) (/ (($ $ |#2|) "\\spad{x/y} divides the vector \\spad{x} by the scalar \\spad{y}."))) 
 NIL 
 NIL 
-(-1188 S) 
+(-1187 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}."))) 
-((-3992 . T) (-3991 . T)) 
+((-3991 . T) (-3990 . T)) 
 NIL 
-(-1189 R) 
+(-1188 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 
-(-1190 K R UP -3094) 
+(-1189 K R UP -3093) 
 ((|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 
-(-1191) 
+(-1190) 
 ((|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 
-(-1192) 
+(-1191) 
 ((|constructor| (NIL "This domain represents the `while' iterator syntax.")) (|condition| (((|SpadAst|) $) "\\spad{condition(i)} returns the condition of the while iterator `i'."))) 
 NIL 
 NIL 
-(-1193 R |VarSet| E P |vl| |wl| |wtlevel|) 
+(-1192 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)"))) 
-((-3992 |has| |#1| (-146)) (-3991 |has| |#1| (-146)) (-3994 . T)) 
+((-3991 |has| |#1| (-146)) (-3990 |has| |#1| (-146)) (-3993 . T)) 
 ((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312)))) 
-(-1194 R E V P) 
+(-1193 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}."))) 
-((-3998 . T)) 
-((-12 (|HasCategory| |#4| (QUOTE (-1014))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-554 (-474)))) (|HasCategory| |#4| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#3| (QUOTE (-320))) (|HasCategory| |#4| (QUOTE (-553 (-773)))) (|HasCategory| |#4| (QUOTE (-1014))) (-12 (|HasCategory| |#4| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#4|)))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#4|)))) 
-(-1195 R) 
+((-3997 . T)) 
+((-12 (|HasCategory| |#4| (QUOTE (-1013))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-553 (-473)))) (|HasCategory| |#4| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#3| (QUOTE (-320))) (|HasCategory| |#4| (QUOTE (-552 (-772)))) (|HasCategory| |#4| (QUOTE (-1013))) (-12 (|HasCategory| |#4| (QUOTE (-72))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#4|)))) (|HasCategory| $ (|%list| (QUOTE -318) (|devaluate| |#4|)))) 
+(-1194 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)"))) 
-((-3991 . T) (-3992 . T) (-3994 . T)) 
+((-3990 . T) (-3991 . T) (-3993 . T)) 
 NIL 
-(-1196 |vl| R) 
+(-1195 |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."))) 
-((-3994 . T) (-3990 |has| |#2| (-6 -3990)) (-3992 . T) (-3991 . T)) 
-((|HasCategory| |#2| (QUOTE (-146))) (|HasAttribute| |#2| (QUOTE -3990))) 
-(-1197 R |VarSet| XPOLY) 
+((-3993 . T) (-3989 |has| |#2| (-6 -3989)) (-3991 . T) (-3990 . T)) 
+((|HasCategory| |#2| (QUOTE (-146))) (|HasAttribute| |#2| (QUOTE -3989))) 
+(-1196 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 
-(-1198 S -3094) 
+(-1197 S -3093) 
 ((|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) 
 NIL 
 ((|HasCategory| |#2| (QUOTE (-320))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120)))) 
-(-1199 -3094) 
+(-1198 -3093) 
 ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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}."))) 
-((-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
+((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
 NIL 
-(-1200 |vl| R) 
+(-1199 |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| $) "\\spad{v * x} returns the product of a variable \\spad{x} by \\spad{x}."))) 
-((-3990 |has| |#2| (-6 -3990)) (-3992 . T) (-3991 . T) (-3994 . T)) 
+((-3989 |has| |#2| (-6 -3989)) (-3991 . T) (-3990 . T) (-3993 . T)) 
 NIL 
-(-1201 |VarSet| R) 
+(-1200 |VarSet| R) 
 ((|constructor| (NIL "This domain constructor implements polynomials in non-commutative variables written in the Poincare-Birkhoff-Witt basis from the Lyndon basis. These polynomials can be used to compute Baker-Campbell-Hausdorff relations. \\newline Author: Michel Petitot (petitot@lifl.fr).")) (|log| (($ $ (|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}}."))) 
-((-3990 |has| |#2| (-6 -3990)) (-3992 . T) (-3991 . T) (-3994 . T)) 
-((|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-655 (-350 (-485))))) (|HasAttribute| |#2| (QUOTE -3990))) 
-(-1202 R) 
+((-3989 |has| |#2| (-6 -3989)) (-3991 . T) (-3990 . T) (-3993 . T)) 
+((|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-654 (-350 (-484))))) (|HasAttribute| |#2| (QUOTE -3989))) 
+(-1201 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."))) 
-((-3990 |has| |#1| (-6 -3990)) (-3992 . T) (-3991 . T) (-3994 . T)) 
-((|HasCategory| |#1| (QUOTE (-146))) (|HasAttribute| |#1| (QUOTE -3990))) 
-(-1203 |vl| R) 
+((-3989 |has| |#1| (-6 -3989)) (-3991 . T) (-3990 . T) (-3993 . T)) 
+((|HasCategory| |#1| (QUOTE (-146))) (|HasAttribute| |#1| (QUOTE -3989))) 
+(-1202 |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|) $) "\\spad{maxdeg(p)} returns the greatest leading word in the support of \\spad{p}."))) 
-((-3990 |has| |#2| (-6 -3990)) (-3992 . T) (-3991 . T) (-3994 . T)) 
+((-3989 |has| |#2| (-6 -3989)) (-3991 . T) (-3990 . T) (-3993 . T)) 
 NIL 
-(-1204 R E) 
+(-1203 R E) 
 ((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and words belonging to an arbitrary \\spadtype{OrderedMonoid}. This type is used,{} for instance,{} by the \\spadtype{XDistributedPolynomial} domain constructor where the Monoid is free.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (/ (($ $ |#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}."))) 
-((-3994 . T) (-3995 |has| |#1| (-6 -3995)) (-3990 |has| |#1| (-6 -3990)) (-3992 . T) (-3991 . T)) 
-((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasAttribute| |#1| (QUOTE -3994)) (|HasAttribute| |#1| (QUOTE -3995)) (|HasAttribute| |#1| (QUOTE -3990))) 
-(-1205 |VarSet| R) 
+((-3993 . T) (-3994 |has| |#1| (-6 -3994)) (-3989 |has| |#1| (-6 -3989)) (-3991 . T) (-3990 . T)) 
+((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasAttribute| |#1| (QUOTE -3993)) (|HasAttribute| |#1| (QUOTE -3994)) (|HasAttribute| |#1| (QUOTE -3989))) 
+(-1204 |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."))) 
-((-3990 |has| |#2| (-6 -3990)) (-3992 . T) (-3991 . T) (-3994 . T)) 
-((|HasCategory| |#2| (QUOTE (-146))) (|HasAttribute| |#2| (QUOTE -3990))) 
-(-1206) 
+((-3989 |has| |#2| (-6 -3989)) (-3991 . T) (-3990 . T) (-3993 . T)) 
+((|HasCategory| |#2| (QUOTE (-146))) (|HasAttribute| |#2| (QUOTE -3989))) 
+(-1205) 
 ((|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 
-(-1207 A) 
+(-1206 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 
-(-1208 R |ls| |ls2|) 
+(-1207 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 
-(-1209 R) 
+(-1208 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 
-(-1210 |p|) 
+(-1209 |p|) 
 ((|constructor| (NIL "IntegerMod(\\spad{n}) creates the ring of integers reduced modulo the integer \\spad{n}."))) 
-(((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) 
+(((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) 
 NIL 
 NIL 
 NIL 
@@ -4788,4 +4784,4 @@ NIL
 NIL 
 NIL 
 NIL 
-((-3 NIL 1968699 1968704 1968709 1968714) (-2 NIL 1968679 1968684 1968689 1968694) (-1 NIL 1968659 1968664 1968669 1968674) (0 NIL 1968639 1968644 1968649 1968654) (-1210 "ZMOD.spad" 1968448 1968461 1968577 1968634) (-1209 "ZLINDEP.spad" 1967546 1967557 1968438 1968443) (-1208 "ZDSOLVE.spad" 1957507 1957529 1967536 1967541) (-1207 "YSTREAM.spad" 1957002 1957013 1957497 1957502) (-1206 "YDIAGRAM.spad" 1956636 1956645 1956992 1956997) (-1205 "XRPOLY.spad" 1955856 1955876 1956492 1956561) (-1204 "XPR.spad" 1953651 1953664 1955574 1955673) (-1203 "XPOLYC.spad" 1952970 1952986 1953577 1953646) (-1202 "XPOLY.spad" 1952525 1952536 1952826 1952895) (-1201 "XPBWPOLY.spad" 1950996 1951016 1952331 1952400) (-1200 "XFALG.spad" 1948044 1948060 1950922 1950991) (-1199 "XF.spad" 1946507 1946522 1947946 1948039) (-1198 "XF.spad" 1944950 1944967 1946391 1946396) (-1197 "XEXPPKG.spad" 1944209 1944235 1944940 1944945) (-1196 "XDPOLY.spad" 1943823 1943839 1944065 1944134) (-1195 "XALG.spad" 1943491 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1848055 1850134 1850139) (-1157 "UPOLYC2.spad" 1847500 1847519 1848019 1848024) (-1156 "UPOLYC.spad" 1842580 1842591 1847342 1847495) (-1155 "UPOLYC.spad" 1837578 1837591 1842342 1842347) (-1154 "UPMP.spad" 1836510 1836523 1837568 1837573) (-1153 "UPDIVP.spad" 1836075 1836089 1836500 1836505) (-1152 "UPDECOMP.spad" 1834336 1834350 1836065 1836070) (-1151 "UPCDEN.spad" 1833553 1833569 1834326 1834331) (-1150 "UP2.spad" 1832917 1832938 1833543 1833548) (-1149 "UP.spad" 1830387 1830402 1830774 1830927) (-1148 "UNISEG2.spad" 1829884 1829897 1830343 1830348) (-1147 "UNISEG.spad" 1829237 1829248 1829803 1829808) (-1146 "UNIFACT.spad" 1828340 1828352 1829227 1829232) (-1145 "ULSCONS.spad" 1822186 1822206 1822556 1822705) (-1144 "ULSCCAT.spad" 1819923 1819943 1822032 1822181) (-1143 "ULSCCAT.spad" 1817768 1817790 1819879 1819884) (-1142 "ULSCAT.spad" 1816008 1816024 1817614 1817763) (-1141 "ULS2.spad" 1815522 1815575 1815998 1816003) (-1140 "ULS.spad" 1807555 1807583 1808500 1808923) (-1139 "UINT8.spad" 1807432 1807441 1807545 1807550) (-1138 "UINT64.spad" 1807308 1807317 1807422 1807427) (-1137 "UINT32.spad" 1807184 1807193 1807298 1807303) (-1136 "UINT16.spad" 1807060 1807069 1807174 1807179) (-1135 "UFD.spad" 1806125 1806134 1806986 1807055) (-1134 "UFD.spad" 1805252 1805263 1806115 1806120) (-1133 "UDVO.spad" 1804133 1804142 1805242 1805247) (-1132 "UDPO.spad" 1801714 1801725 1804089 1804094) (-1131 "TYPEAST.spad" 1801633 1801642 1801704 1801709) (-1130 "TYPE.spad" 1801565 1801574 1801623 1801628) (-1129 "TWOFACT.spad" 1800217 1800232 1801555 1801560) (-1128 "TUPLE.spad" 1799724 1799735 1800129 1800134) (-1127 "TUBETOOL.spad" 1796591 1796600 1799714 1799719) (-1126 "TUBE.spad" 1795238 1795255 1796581 1796586) (-1125 "TSETCAT.spad" 1783321 1783338 1795218 1795233) (-1124 "TSETCAT.spad" 1771378 1771397 1783277 1783282) (-1123 "TS.spad" 1770006 1770022 1770972 1771069) (-1122 "TRMANIP.spad" 1764370 1764387 1769694 1769699) (-1121 "TRIMAT.spad" 1763333 1763358 1764360 1764365) (-1120 "TRIGMNIP.spad" 1761860 1761877 1763323 1763328) (-1119 "TRIGCAT.spad" 1761372 1761381 1761850 1761855) (-1118 "TRIGCAT.spad" 1760882 1760893 1761362 1761367) (-1117 "TREE.spad" 1759473 1759484 1760505 1760520) (-1116 "TRANFUN.spad" 1759312 1759321 1759463 1759468) (-1115 "TRANFUN.spad" 1759149 1759160 1759302 1759307) (-1114 "TOPSP.spad" 1758823 1758832 1759139 1759144) (-1113 "TOOLSIGN.spad" 1758486 1758497 1758813 1758818) (-1112 "TEXTFILE.spad" 1757047 1757056 1758476 1758481) (-1111 "TEX1.spad" 1756603 1756614 1757037 1757042) (-1110 "TEX.spad" 1753797 1753806 1756593 1756598) (-1109 "TBCMPPK.spad" 1751898 1751921 1753787 1753792) (-1108 "TBAGG.spad" 1751153 1751176 1751878 1751893) (-1107 "TBAGG.spad" 1750416 1750441 1751143 1751148) (-1106 "TANEXP.spad" 1749824 1749835 1750406 1750411) (-1105 "TALGOP.spad" 1749548 1749559 1749814 1749819) (-1104 "TABLEAU.spad" 1749029 1749040 1749538 1749543) (-1103 "TABLE.spad" 1746790 1746813 1747060 1747075) (-1102 "TABLBUMP.spad" 1743569 1743580 1746780 1746785) (-1101 "SYSTEM.spad" 1742797 1742806 1743559 1743564) (-1100 "SYSSOLP.spad" 1740280 1740291 1742787 1742792) (-1099 "SYSPTR.spad" 1740179 1740188 1740270 1740275) (-1098 "SYSNNI.spad" 1739402 1739413 1740169 1740174) (-1097 "SYSINT.spad" 1738806 1738817 1739392 1739397) (-1096 "SYNTAX.spad" 1735140 1735149 1738796 1738801) (-1095 "SYMTAB.spad" 1733208 1733217 1735130 1735135) (-1094 "SYMS.spad" 1729237 1729246 1733198 1733203) (-1093 "SYMPOLY.spad" 1728370 1728381 1728452 1728579) (-1092 "SYMFUNC.spad" 1727871 1727882 1728360 1728365) (-1091 "SYMBOL.spad" 1725366 1725375 1727861 1727866) (-1090 "SUTS.spad" 1722479 1722507 1723898 1723995) (-1089 "SUPXS.spad" 1719821 1719849 1720670 1720819) (-1088 "SUPFRACF.spad" 1718926 1718944 1719811 1719816) (-1087 "SUP2.spad" 1718318 1718331 1718916 1718921) (-1086 "SUP.spad" 1715402 1715413 1716175 1716328) (-1085 "SUMRF.spad" 1714376 1714387 1715392 1715397) (-1084 "SUMFS.spad" 1714005 1714022 1714366 1714371) (-1083 "SULS.spad" 1706025 1706053 1706983 1707406) (-1082 "syntax.spad" 1705794 1705803 1706015 1706020) (-1081 "SUCH.spad" 1705484 1705499 1705784 1705789) (-1080 "SUBSPACE.spad" 1697615 1697630 1705474 1705479) (-1079 "SUBRESP.spad" 1696785 1696799 1697571 1697576) (-1078 "STTFNC.spad" 1693253 1693269 1696775 1696780) (-1077 "STTF.spad" 1689352 1689368 1693243 1693248) (-1076 "STTAYLOR.spad" 1682029 1682040 1689259 1689264) (-1075 "STRTBL.spad" 1679953 1679970 1680102 1680117) (-1074 "STRING.spad" 1678584 1678593 1678969 1678984) (-1073 "STREAM3.spad" 1678157 1678172 1678574 1678579) (-1072 "STREAM2.spad" 1677285 1677298 1678147 1678152) (-1071 "STREAM1.spad" 1676991 1677002 1677275 1677280) (-1070 "STREAM.spad" 1673941 1673952 1676432 1676447) (-1069 "STINPROD.spad" 1672877 1672893 1673931 1673936) (-1068 "STEPAST.spad" 1672111 1672120 1672867 1672872) (-1067 "STEP.spad" 1671428 1671437 1672101 1672106) (-1066 "STBL.spad" 1669292 1669320 1669459 1669474) (-1065 "STAGG.spad" 1667991 1668002 1669282 1669287) (-1064 "STAGG.spad" 1666688 1666701 1667981 1667986) (-1063 "STACK.spad" 1666122 1666133 1666372 1666387) (-1062 "SRING.spad" 1665882 1665891 1666112 1666117) (-1061 "SREGSET.spad" 1663465 1663482 1665367 1665382) (-1060 "SRDCMPK.spad" 1662042 1662062 1663455 1663460) (-1059 "SRAGG.spad" 1657237 1657246 1662022 1662037) (-1058 "SRAGG.spad" 1652440 1652451 1657227 1657232) (-1057 "SQMATRIX.spad" 1650129 1650147 1651045 1651120) (-1056 "SPLTREE.spad" 1644779 1644792 1649575 1649590) (-1055 "SPLNODE.spad" 1641399 1641412 1644769 1644774) (-1054 "SPFCAT.spad" 1640208 1640217 1641389 1641394) (-1053 "SPECOUT.spad" 1638760 1638769 1640198 1640203) (-1052 "SPADXPT.spad" 1630851 1630860 1638750 1638755) (-1051 "spad-parser.spad" 1630316 1630325 1630841 1630846) (-1050 "SPADAST.spad" 1630017 1630026 1630306 1630311) (-1049 "SPACEC.spad" 1614232 1614243 1630007 1630012) (-1048 "SPACE3.spad" 1614008 1614019 1614222 1614227) (-1047 "SORTPAK.spad" 1613557 1613570 1613964 1613969) (-1046 "SOLVETRA.spad" 1611320 1611331 1613547 1613552) (-1045 "SOLVESER.spad" 1609776 1609787 1611310 1611315) (-1044 "SOLVERAD.spad" 1605802 1605813 1609766 1609771) (-1043 "SOLVEFOR.spad" 1604264 1604282 1605792 1605797) (-1042 "SNTSCAT.spad" 1603876 1603893 1604244 1604259) (-1041 "SMTS.spad" 1602193 1602219 1603470 1603567) (-1040 "SMP.spad" 1600001 1600021 1600391 1600518) (-1039 "SMITH.spad" 1598846 1598871 1599991 1599996) (-1038 "SMATCAT.spad" 1596976 1597006 1598802 1598841) (-1037 "SMATCAT.spad" 1595026 1595058 1596854 1596859) (-1036 "aggcat.spad" 1594702 1594713 1595006 1595021) (-1035 "SKAGG.spad" 1593683 1593694 1594682 1594697) (-1034 "SINT.spad" 1592982 1592991 1593549 1593678) (-1033 "SIMPAN.spad" 1592710 1592719 1592972 1592977) (-1032 "SIGNRF.spad" 1591835 1591846 1592700 1592705) (-1031 "SIGNEF.spad" 1591121 1591138 1591825 1591830) (-1030 "syntax.spad" 1590538 1590547 1591111 1591116) (-1029 "SIG.spad" 1589900 1589909 1590528 1590533) (-1028 "SHP.spad" 1587844 1587859 1589856 1589861) (-1027 "SHDP.spad" 1577248 1577275 1577765 1577850) (-1026 "SGROUP.spad" 1576856 1576865 1577238 1577243) (-1025 "SGROUP.spad" 1576462 1576473 1576846 1576851) (-1024 "catdef.spad" 1576172 1576184 1576283 1576457) (-1023 "catdef.spad" 1575728 1575740 1575993 1576167) (-1022 "SGCF.spad" 1568867 1568876 1575718 1575723) (-1021 "SFRTCAT.spad" 1567825 1567842 1568847 1568862) (-1020 "SFRGCD.spad" 1566888 1566908 1567815 1567820) (-1019 "SFQCMPK.spad" 1561701 1561721 1566878 1566883) (-1018 "SEXOF.spad" 1561544 1561584 1561691 1561696) (-1017 "SEXCAT.spad" 1559372 1559412 1561534 1561539) (-1016 "SEX.spad" 1559264 1559273 1559362 1559367) (-1015 "SETMN.spad" 1557724 1557741 1559254 1559259) (-1014 "SETCAT.spad" 1557209 1557218 1557714 1557719) (-1013 "SETCAT.spad" 1556692 1556703 1557199 1557204) (-1012 "SETAGG.spad" 1553241 1553252 1556672 1556687) (-1011 "SETAGG.spad" 1549798 1549811 1553231 1553236) (-1010 "SET.spad" 1547956 1547967 1549055 1549082) (-1009 "syntax.spad" 1547659 1547668 1547946 1547951) (-1008 "SEGXCAT.spad" 1546815 1546828 1547649 1547654) (-1007 "SEGCAT.spad" 1545740 1545751 1546805 1546810) (-1006 "SEGBIND2.spad" 1545438 1545451 1545730 1545735) (-1005 "SEGBIND.spad" 1545196 1545207 1545385 1545390) (-1004 "SEGAST.spad" 1544926 1544935 1545186 1545191) (-1003 "SEG2.spad" 1544361 1544374 1544882 1544887) (-1002 "SEG.spad" 1544174 1544185 1544280 1544285) (-1001 "SDVAR.spad" 1543450 1543461 1544164 1544169) (-1000 "SDPOL.spad" 1541142 1541153 1541433 1541560) (-999 "SCPKG.spad" 1539232 1539242 1541132 1541137) (-998 "SCOPE.spad" 1538410 1538418 1539222 1539227) (-997 "SCACHE.spad" 1537107 1537117 1538400 1538405) (-996 "SASTCAT.spad" 1537017 1537025 1537097 1537102) (-995 "SAOS.spad" 1536890 1536898 1537007 1537012) (-994 "SAERFFC.spad" 1536604 1536623 1536880 1536885) (-993 "SAEFACT.spad" 1536306 1536325 1536594 1536599) (-992 "SAE.spad" 1533957 1533972 1534567 1534702) (-991 "RURPK.spad" 1531617 1531632 1533947 1533952) (-990 "RULESET.spad" 1531071 1531094 1531607 1531612) (-989 "RULECOLD.spad" 1530924 1530936 1531061 1531066) (-988 "RULE.spad" 1529173 1529196 1530914 1530919) (-987 "RTVALUE.spad" 1528909 1528917 1529163 1529168) (-986 "syntax.spad" 1528627 1528635 1528899 1528904) (-985 "RSETGCD.spad" 1525070 1525089 1528617 1528622) (-984 "RSETCAT.spad" 1515051 1515067 1525050 1525065) (-983 "RSETCAT.spad" 1505040 1505058 1515041 1515046) (-982 "RSDCMPK.spad" 1503541 1503560 1505030 1505035) (-981 "RRCC.spad" 1501926 1501955 1503531 1503536) (-980 "RRCC.spad" 1500309 1500340 1501916 1501921) (-979 "RPTAST.spad" 1500012 1500020 1500299 1500304) (-978 "RPOLCAT.spad" 1479517 1479531 1499880 1500007) (-977 "RPOLCAT.spad" 1458815 1458831 1479180 1479185) (-976 "ROMAN.spad" 1458144 1458152 1458681 1458810) (-975 "ROIRC.spad" 1457225 1457256 1458134 1458139) (-974 "RNS.spad" 1456202 1456210 1457127 1457220) (-973 "RNS.spad" 1455265 1455275 1456192 1456197) (-972 "RNGBIND.spad" 1454426 1454439 1455220 1455225) (-971 "RNG.spad" 1454035 1454043 1454416 1454421) (-970 "RNG.spad" 1453642 1453652 1454025 1454030) (-969 "RMODULE.spad" 1453424 1453434 1453632 1453637) (-968 "RMCAT2.spad" 1452845 1452901 1453414 1453419) (-967 "RMATRIX.spad" 1451667 1451685 1452009 1452036) (-966 "RMATCAT.spad" 1447317 1447347 1451635 1451662) (-965 "RMATCAT.spad" 1442845 1442877 1447165 1447170) (-964 "RLINSET.spad" 1442550 1442560 1442835 1442840) (-963 "RINTERP.spad" 1442439 1442458 1442540 1442545) (-962 "RING.spad" 1441910 1441918 1442419 1442434) (-961 "RING.spad" 1441389 1441399 1441900 1441905) (-960 "RIDIST.spad" 1440782 1440790 1441379 1441384) (-959 "RGCHAIN.spad" 1439039 1439054 1439932 1439947) (-958 "RGBCSPC.spad" 1438829 1438840 1439029 1439034) (-957 "RGBCMDL.spad" 1438392 1438403 1438819 1438824) (-956 "RFFACTOR.spad" 1437855 1437865 1438382 1438387) (-955 "RFFACT.spad" 1437591 1437602 1437845 1437850) (-954 "RFDIST.spad" 1436588 1436596 1437581 1437586) (-953 "RF.spad" 1434263 1434273 1436578 1436583) (-952 "RETSOL.spad" 1433683 1433695 1434253 1434258) (-951 "RETRACT.spad" 1433112 1433122 1433673 1433678) (-950 "RETRACT.spad" 1432539 1432551 1433102 1433107) (-949 "RETAST.spad" 1432352 1432360 1432529 1432534) (-948 "RESRING.spad" 1431700 1431746 1432290 1432347) (-947 "RESLATC.spad" 1431025 1431035 1431690 1431695) (-946 "REPSQ.spad" 1430757 1430767 1431015 1431020) (-945 "REPDB.spad" 1430465 1430475 1430747 1430752) (-944 "REP2.spad" 1420180 1420190 1430307 1430312) (-943 "REP1.spad" 1414401 1414411 1420130 1420135) (-942 "REP.spad" 1411956 1411964 1414391 1414396) (-941 "REGSET.spad" 1409633 1409649 1411441 1411456) (-940 "REF.spad" 1409152 1409162 1409623 1409628) (-939 "REDORDER.spad" 1408359 1408375 1409142 1409147) (-938 "RECLOS.spad" 1407256 1407275 1407959 1408052) (-937 "REALSOLV.spad" 1406397 1406405 1407246 1407251) (-936 "REAL0Q.spad" 1403696 1403710 1406387 1406392) (-935 "REAL0.spad" 1400541 1400555 1403686 1403691) (-934 "REAL.spad" 1400414 1400422 1400531 1400536) (-933 "RDUCEAST.spad" 1400136 1400144 1400404 1400409) (-932 "RDIV.spad" 1399792 1399816 1400126 1400131) (-931 "RDIST.spad" 1399360 1399370 1399782 1399787) (-930 "RDETRS.spad" 1398225 1398242 1399350 1399355) (-929 "RDETR.spad" 1396365 1396382 1398215 1398220) (-928 "RDEEFS.spad" 1395465 1395481 1396355 1396360) (-927 "RDEEF.spad" 1394476 1394492 1395455 1395460) (-926 "RCFIELD.spad" 1391695 1391703 1394378 1394471) (-925 "RCFIELD.spad" 1389000 1389010 1391685 1391690) (-924 "RCAGG.spad" 1386937 1386947 1388990 1388995) (-923 "RCAGG.spad" 1384775 1384787 1386830 1386835) (-922 "RATRET.spad" 1384136 1384146 1384765 1384770) (-921 "RATFACT.spad" 1383829 1383840 1384126 1384131) (-920 "RANDSRC.spad" 1383149 1383157 1383819 1383824) (-919 "RADUTIL.spad" 1382906 1382914 1383139 1383144) (-918 "RADIX.spad" 1379951 1379964 1381496 1381589) (-917 "RADFF.spad" 1377868 1377904 1377986 1378142) (-916 "RADCAT.spad" 1377464 1377472 1377858 1377863) (-915 "RADCAT.spad" 1377058 1377068 1377454 1377459) (-914 "QUEUE.spad" 1376484 1376494 1376742 1376757) (-913 "QUATCT2.spad" 1376105 1376123 1376474 1376479) (-912 "QUATCAT.spad" 1374276 1374286 1376035 1376100) (-911 "QUATCAT.spad" 1372212 1372224 1373973 1373978) (-910 "QUAT.spad" 1370819 1370829 1371161 1371226) (-909 "QUAGG.spad" 1369665 1369675 1370799 1370814) (-908 "QQUTAST.spad" 1369434 1369442 1369655 1369660) (-907 "QFORM.spad" 1369053 1369067 1369424 1369429) (-906 "QFCAT2.spad" 1368746 1368762 1369043 1369048) (-905 "QFCAT.spad" 1367449 1367459 1368648 1368741) (-904 "QFCAT.spad" 1365785 1365797 1366986 1366991) (-903 "QEQUAT.spad" 1365344 1365352 1365775 1365780) (-902 "QCMPACK.spad" 1360259 1360278 1365334 1365339) (-901 "QALGSET2.spad" 1358255 1358273 1360249 1360254) (-900 "QALGSET.spad" 1354360 1354392 1358169 1358174) (-899 "PWFFINTB.spad" 1351776 1351797 1354350 1354355) (-898 "PUSHVAR.spad" 1351115 1351134 1351766 1351771) (-897 "PTRANFN.spad" 1347251 1347261 1351105 1351110) (-896 "PTPACK.spad" 1344339 1344349 1347241 1347246) (-895 "PTFUNC2.spad" 1344162 1344176 1344329 1344334) (-894 "PTCAT.spad" 1343429 1343439 1344142 1344157) (-893 "PSQFR.spad" 1342744 1342768 1343419 1343424) (-892 "PSEUDLIN.spad" 1341630 1341640 1342734 1342739) (-891 "PSETPK.spad" 1328335 1328351 1341508 1341513) (-890 "PSETCAT.spad" 1322745 1322768 1328325 1328330) (-889 "PSETCAT.spad" 1317119 1317144 1322701 1322706) (-888 "PSCURVE.spad" 1316118 1316126 1317109 1317114) (-887 "PSCAT.spad" 1314901 1314930 1316016 1316113) (-886 "PSCAT.spad" 1313774 1313805 1314891 1314896) (-885 "PRTITION.spad" 1312472 1312480 1313764 1313769) (-884 "PRTDAST.spad" 1312191 1312199 1312462 1312467) (-883 "PRS.spad" 1301809 1301826 1312147 1312152) (-882 "PRQAGG.spad" 1301256 1301266 1301789 1301804) (-881 "PROPLOG.spad" 1300860 1300868 1301246 1301251) (-880 "PROPFUN2.spad" 1300483 1300496 1300850 1300855) (-879 "PROPFUN1.spad" 1299889 1299900 1300473 1300478) (-878 "PROPFRML.spad" 1298457 1298468 1299879 1299884) (-877 "PROPERTY.spad" 1297953 1297961 1298447 1298452) (-876 "PRODUCT.spad" 1295650 1295662 1295934 1295989) (-875 "PRINT.spad" 1295402 1295410 1295640 1295645) (-874 "PRIMES.spad" 1293663 1293673 1295392 1295397) (-873 "PRIMELT.spad" 1291784 1291798 1293653 1293658) (-872 "PRIMCAT.spad" 1291427 1291435 1291774 1291779) (-871 "PRIMARR2.spad" 1290194 1290206 1291417 1291422) (-870 "PRIMARR.spad" 1288936 1288946 1289106 1289121) (-869 "PREASSOC.spad" 1288318 1288330 1288926 1288931) (-868 "PR.spad" 1286836 1286848 1287535 1287662) (-867 "PPCURVE.spad" 1285973 1285981 1286826 1286831) (-866 "PORTNUM.spad" 1285764 1285772 1285963 1285968) (-865 "POLYROOT.spad" 1284613 1284635 1285720 1285725) (-864 "POLYLIFT.spad" 1283878 1283901 1284603 1284608) (-863 "POLYCATQ.spad" 1282004 1282026 1283868 1283873) (-862 "POLYCAT.spad" 1275506 1275527 1281872 1281999) (-861 "POLYCAT.spad" 1268528 1268551 1274896 1274901) (-860 "POLY2UP.spad" 1267980 1267994 1268518 1268523) (-859 "POLY2.spad" 1267577 1267589 1267970 1267975) (-858 "POLY.spad" 1265245 1265255 1265760 1265887) (-857 "POLUTIL.spad" 1264210 1264239 1265201 1265206) (-856 "POLTOPOL.spad" 1262958 1262973 1264200 1264205) (-855 "POINT.spad" 1261528 1261538 1261615 1261630) (-854 "PNTHEORY.spad" 1258230 1258238 1261518 1261523) (-853 "PMTOOLS.spad" 1257005 1257019 1258220 1258225) (-852 "PMSYM.spad" 1256554 1256564 1256995 1257000) (-851 "PMQFCAT.spad" 1256145 1256159 1256544 1256549) (-850 "PMPREDFS.spad" 1255607 1255629 1256135 1256140) (-849 "PMPRED.spad" 1255094 1255108 1255597 1255602) (-848 "PMPLCAT.spad" 1254171 1254189 1255023 1255028) (-847 "PMLSAGG.spad" 1253756 1253770 1254161 1254166) (-846 "PMKERNEL.spad" 1253335 1253347 1253746 1253751) (-845 "PMINS.spad" 1252915 1252925 1253325 1253330) (-844 "PMFS.spad" 1252492 1252510 1252905 1252910) (-843 "PMDOWN.spad" 1251782 1251796 1252482 1252487) (-842 "PMASSFS.spad" 1250757 1250773 1251772 1251777) (-841 "PMASS.spad" 1249775 1249783 1250747 1250752) (-840 "PLOTTOOL.spad" 1249555 1249563 1249765 1249770) (-839 "PLOT3D.spad" 1246019 1246027 1249545 1249550) (-838 "PLOT1.spad" 1245192 1245202 1246009 1246014) (-837 "PLOT.spad" 1240115 1240123 1245182 1245187) (-836 "PLEQN.spad" 1227517 1227544 1240105 1240110) (-835 "PINTERPA.spad" 1227301 1227317 1227507 1227512) (-834 "PINTERP.spad" 1226923 1226942 1227291 1227296) (-833 "PID.spad" 1225897 1225905 1226849 1226918) (-832 "PICOERCE.spad" 1225554 1225564 1225887 1225892) (-831 "PI.spad" 1225171 1225179 1225528 1225549) (-830 "PGROEB.spad" 1223780 1223794 1225161 1225166) (-829 "PGE.spad" 1215453 1215461 1223770 1223775) (-828 "PGCD.spad" 1214407 1214424 1215443 1215448) (-827 "PFRPAC.spad" 1213556 1213566 1214397 1214402) (-826 "PFR.spad" 1210259 1210269 1213458 1213551) (-825 "PFOTOOLS.spad" 1209517 1209533 1210249 1210254) (-824 "PFOQ.spad" 1208887 1208905 1209507 1209512) (-823 "PFO.spad" 1208306 1208333 1208877 1208882) (-822 "PFECAT.spad" 1206016 1206024 1208232 1208301) (-821 "PFECAT.spad" 1203754 1203764 1205972 1205977) (-820 "PFBRU.spad" 1201642 1201654 1203744 1203749) (-819 "PFBR.spad" 1199202 1199225 1201632 1201637) (-818 "PF.spad" 1198776 1198788 1199007 1199100) (-817 "PERMGRP.spad" 1193546 1193556 1198766 1198771) (-816 "PERMCAT.spad" 1192207 1192217 1193526 1193541) (-815 "PERMAN.spad" 1190763 1190777 1192197 1192202) (-814 "PERM.spad" 1186573 1186583 1190596 1190611) (-813 "PENDTREE.spad" 1185926 1185936 1186206 1186211) (-812 "PDSPC.spad" 1184739 1184749 1185916 1185921) (-811 "PDSPC.spad" 1183550 1183562 1184729 1184734) (-810 "PDRING.spad" 1183392 1183402 1183530 1183545) (-809 "PDMOD.spad" 1183208 1183220 1183360 1183387) (-808 "PDECOMP.spad" 1182678 1182695 1183198 1183203) (-807 "PDDOM.spad" 1182116 1182129 1182668 1182673) (-806 "PDDOM.spad" 1181552 1181567 1182106 1182111) (-805 "PCOMP.spad" 1181405 1181418 1181542 1181547) (-804 "PBWLB.spad" 1180003 1180020 1181395 1181400) (-803 "PATTERN2.spad" 1179741 1179753 1179993 1179998) (-802 "PATTERN1.spad" 1178085 1178101 1179731 1179736) (-801 "PATTERN.spad" 1172660 1172670 1178075 1178080) (-800 "PATRES2.spad" 1172332 1172346 1172650 1172655) (-799 "PATRES.spad" 1169915 1169927 1172322 1172327) (-798 "PATMATCH.spad" 1168156 1168187 1169667 1169672) (-797 "PATMAB.spad" 1167585 1167595 1168146 1168151) (-796 "PATLRES.spad" 1166671 1166685 1167575 1167580) (-795 "PATAB.spad" 1166435 1166445 1166661 1166666) (-794 "PARTPERM.spad" 1164491 1164499 1166425 1166430) (-793 "PARSURF.spad" 1163925 1163953 1164481 1164486) (-792 "PARSU2.spad" 1163722 1163738 1163915 1163920) (-791 "script-parser.spad" 1163242 1163250 1163712 1163717) (-790 "PARSCURV.spad" 1162676 1162704 1163232 1163237) (-789 "PARSC2.spad" 1162467 1162483 1162666 1162671) (-788 "PARPCURV.spad" 1161929 1161957 1162457 1162462) (-787 "PARPC2.spad" 1161720 1161736 1161919 1161924) (-786 "PARAMAST.spad" 1160848 1160856 1161710 1161715) (-785 "PAN2EXPR.spad" 1160260 1160268 1160838 1160843) (-784 "PALETTE.spad" 1159374 1159382 1160250 1160255) (-783 "PAIR.spad" 1158448 1158461 1159017 1159022) (-782 "PADICRC.spad" 1155853 1155871 1157016 1157109) (-781 "PADICRAT.spad" 1153913 1153925 1154126 1154219) (-780 "PADICCT.spad" 1152462 1152474 1153839 1153908) (-779 "PADIC.spad" 1152165 1152177 1152388 1152457) (-778 "PADEPAC.spad" 1150854 1150873 1152155 1152160) (-777 "PADE.spad" 1149606 1149622 1150844 1150849) (-776 "OWP.spad" 1148854 1148884 1149464 1149531) (-775 "OVERSET.spad" 1148427 1148435 1148844 1148849) (-774 "OVAR.spad" 1148208 1148231 1148417 1148422) (-773 "OUTFORM.spad" 1137616 1137624 1148198 1148203) (-772 "OUTBFILE.spad" 1137050 1137058 1137606 1137611) (-771 "OUTBCON.spad" 1136120 1136128 1137040 1137045) (-770 "OUTBCON.spad" 1135188 1135198 1136110 1136115) (-769 "OUT.spad" 1134306 1134314 1135178 1135183) (-768 "OSI.spad" 1133781 1133789 1134296 1134301) (-767 "OSGROUP.spad" 1133699 1133707 1133771 1133776) (-766 "ORTHPOL.spad" 1132210 1132220 1133642 1133647) (-765 "OREUP.spad" 1131704 1131732 1131931 1131970) (-764 "ORESUP.spad" 1131046 1131070 1131425 1131464) (-763 "OREPCTO.spad" 1128935 1128947 1130966 1130971) (-762 "OREPCAT.spad" 1123122 1123132 1128891 1128930) (-761 "OREPCAT.spad" 1117199 1117211 1122970 1122975) (-760 "ORDTYPE.spad" 1116436 1116444 1117189 1117194) (-759 "ORDTYPE.spad" 1115671 1115681 1116426 1116431) (-758 "ORDSTRCT.spad" 1115457 1115472 1115620 1115625) (-757 "ORDSET.spad" 1115157 1115165 1115447 1115452) (-756 "ORDRING.spad" 1114974 1114982 1115137 1115152) (-755 "ORDMON.spad" 1114829 1114837 1114964 1114969) (-754 "ORDFUNS.spad" 1113961 1113977 1114819 1114824) (-753 "ORDFIN.spad" 1113781 1113789 1113951 1113956) (-752 "ORDCOMP2.spad" 1113074 1113086 1113771 1113776) (-751 "ORDCOMP.spad" 1111600 1111610 1112682 1112711) (-750 "OPSIG.spad" 1111262 1111270 1111590 1111595) (-749 "OPQUERY.spad" 1110843 1110851 1111252 1111257) (-748 "OPERCAT.spad" 1110309 1110319 1110833 1110838) (-747 "OPERCAT.spad" 1109773 1109785 1110299 1110304) (-746 "OP.spad" 1109515 1109525 1109595 1109662) (-745 "ONECOMP2.spad" 1108939 1108951 1109505 1109510) (-744 "ONECOMP.spad" 1107745 1107755 1108547 1108576) (-743 "OMSAGG.spad" 1107545 1107555 1107713 1107740) (-742 "OMLO.spad" 1106978 1106990 1107431 1107470) (-741 "OINTDOM.spad" 1106741 1106749 1106904 1106973) (-740 "OFMONOID.spad" 1104880 1104890 1106697 1106702) (-739 "ODVAR.spad" 1104141 1104151 1104870 1104875) (-738 "ODR.spad" 1103785 1103811 1103953 1104102) (-737 "ODPOL.spad" 1101433 1101443 1101773 1101900) (-736 "ODP.spad" 1090981 1091001 1091354 1091439) (-735 "ODETOOLS.spad" 1089630 1089649 1090971 1090976) (-734 "ODESYS.spad" 1087324 1087341 1089620 1089625) (-733 "ODERTRIC.spad" 1083357 1083374 1087281 1087286) (-732 "ODERED.spad" 1082756 1082780 1083347 1083352) (-731 "ODERAT.spad" 1080389 1080406 1082746 1082751) (-730 "ODEPRRIC.spad" 1077482 1077504 1080379 1080384) (-729 "ODEPRIM.spad" 1074880 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1004588 1006338 1006343) (-690 "NCNTFRAC.spad" 1004214 1004228 1004562 1004567) (-689 "NCEP.spad" 1002380 1002394 1004204 1004209) (-688 "NASRING.spad" 1001984 1001992 1002370 1002375) (-687 "NASRING.spad" 1001586 1001596 1001974 1001979) (-686 "NARNG.spad" 1000986 1000994 1001576 1001581) (-685 "NARNG.spad" 1000384 1000394 1000976 1000981) (-684 "NAALG.spad" 999949 999959 1000352 1000379) (-683 "NAALG.spad" 999534 999546 999939 999944) (-682 "MULTSQFR.spad" 996492 996509 999524 999529) (-681 "MULTFACT.spad" 995875 995892 996482 996487) (-680 "MTSCAT.spad" 993969 993990 995773 995870) (-679 "MTHING.spad" 993628 993638 993959 993964) (-678 "MSYSCMD.spad" 993062 993070 993618 993623) (-677 "MSETAGG.spad" 992907 992917 993030 993057) (-676 "MSET.spad" 990705 990715 992452 992479) (-675 "MRING.spad" 987682 987694 990413 990480) (-674 "MRF2.spad" 987244 987258 987672 987677) (-673 "MRATFAC.spad" 986790 986807 987234 987239) (-672 "MPRFF.spad" 984830 984849 986780 986785) (-671 "MPOLY.spad" 982634 982649 982993 983120) (-670 "MPCPF.spad" 981898 981917 982624 982629) (-669 "MPC3.spad" 981715 981755 981888 981893) (-668 "MPC2.spad" 981369 981402 981705 981710) (-667 "MONOTOOL.spad" 979720 979737 981359 981364) (-666 "catdef.spad" 979153 979164 979374 979715) (-665 "catdef.spad" 978551 978562 978807 979148) (-664 "MONOID.spad" 977872 977880 978541 978546) (-663 "MONOID.spad" 977191 977201 977862 977867) (-662 "MONOGEN.spad" 975939 975952 977051 977186) (-661 "MONOGEN.spad" 974709 974724 975823 975828) (-660 "MONADWU.spad" 972789 972797 974699 974704) (-659 "MONADWU.spad" 970867 970877 972779 972784) (-658 "MONAD.spad" 970027 970035 970857 970862) (-657 "MONAD.spad" 969185 969195 970017 970022) (-656 "MOEBIUS.spad" 967921 967935 969165 969180) (-655 "MODULE.spad" 967791 967801 967889 967916) (-654 "MODULE.spad" 967681 967693 967781 967786) (-653 "MODRING.spad" 967016 967055 967661 967676) (-652 "MODOP.spad" 965673 965685 966838 966905) (-651 "MODMONOM.spad" 965404 965422 965663 965668) (-650 "MODMON.spad" 962474 962486 963189 963342) (-649 "MODFIELD.spad" 961836 961875 962376 962469) (-648 "MMLFORM.spad" 960696 960704 961826 961831) (-647 "MMAP.spad" 960438 960472 960686 960691) (-646 "MLO.spad" 958897 958907 960394 960433) (-645 "MLIFT.spad" 957509 957526 958887 958892) (-644 "MKUCFUNC.spad" 957044 957062 957499 957504) (-643 "MKRECORD.spad" 956632 956645 957034 957039) (-642 "MKFUNC.spad" 956039 956049 956622 956627) (-641 "MKFLCFN.spad" 955007 955017 956029 956034) (-640 "MKBCFUNC.spad" 954502 954520 954997 955002) (-639 "MHROWRED.spad" 953013 953023 954492 954497) (-638 "MFINFACT.spad" 952413 952435 953003 953008) (-637 "MESH.spad" 950208 950216 952403 952408) (-636 "MDDFACT.spad" 948427 948437 950198 950203) (-635 "MDAGG.spad" 947718 947728 948407 948422) (-634 "MCDEN.spad" 946928 946940 947708 947713) (-633 "MAYBE.spad" 946228 946239 946918 946923) (-632 "MATSTOR.spad" 943544 943554 946218 946223) (-631 "MATRIX.spad" 942335 942345 942819 942834) (-630 "MATLIN.spad" 939703 939727 942219 942224) (-629 "MATCAT2.spad" 938985 939033 939693 939698) (-628 "MATCAT.spad" 930693 930715 938965 938980) (-627 "MATCAT.spad" 922261 922285 930535 930540) (-626 "MAPPKG3.spad" 921176 921190 922251 922256) (-625 "MAPPKG2.spad" 920514 920526 921166 921171) (-624 "MAPPKG1.spad" 919342 919352 920504 920509) (-623 "MAPPAST.spad" 918681 918689 919332 919337) (-622 "MAPHACK3.spad" 918493 918507 918671 918676) (-621 "MAPHACK2.spad" 918262 918274 918483 918488) (-620 "MAPHACK1.spad" 917906 917916 918252 918257) (-619 "MAGMA.spad" 915712 915729 917896 917901) (-618 "MACROAST.spad" 915307 915315 915702 915707) (-617 "LZSTAGG.spad" 912561 912571 915297 915302) (-616 "LZSTAGG.spad" 909813 909825 912551 912556) (-615 "LWORD.spad" 906558 906575 909803 909808) (-614 "LSTAST.spad" 906342 906350 906548 906553) (-613 "LSQM.spad" 904632 904646 905026 905065) (-612 "LSPP.spad" 904167 904184 904622 904627) (-611 "LSMP1.spad" 902010 902024 904157 904162) (-610 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877746) (-589 "LLINSET.spad" 877190 877200 877473 877478) (-588 "LITERAL.spad" 877096 877107 877180 877185) (-587 "LIST3.spad" 876407 876421 877086 877091) (-586 "LIST2MAP.spad" 873334 873346 876397 876402) (-585 "LIST2.spad" 872036 872048 873324 873329) (-584 "LIST.spad" 869605 869615 870948 870963) (-583 "LINSET.spad" 869384 869394 869595 869600) (-582 "LINFORM.spad" 868847 868859 869352 869379) (-581 "LINEXP.spad" 867590 867600 868837 868842) (-580 "LINELT.spad" 866961 866973 867473 867500) (-579 "LINDEP.spad" 865810 865822 866873 866878) (-578 "LINBASIS.spad" 865446 865461 865800 865805) (-577 "LIMITRF.spad" 863393 863403 865436 865441) (-576 "LIMITPS.spad" 862303 862316 863383 863388) (-575 "LIECAT.spad" 861787 861797 862229 862298) (-574 "LIECAT.spad" 861299 861311 861743 861748) (-573 "LIE.spad" 859303 859315 860577 860719) (-572 "LIB.spad" 857156 857164 857602 857617) (-571 "LGROBP.spad" 854509 854528 857146 857151) (-570 "LFCAT.spad" 853568 853576 854499 854504) (-569 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"COMPILER.spad" 140986 140994 141427 141432) (-140 "COMPFACT.spad" 140588 140602 140976 140981) (-139 "COMPCAT.spad" 138663 138673 140325 140583) (-138 "COMPCAT.spad" 136479 136491 138143 138148) (-137 "COMMUPC.spad" 136227 136245 136469 136474) (-136 "COMMONOP.spad" 135760 135768 136217 136222) (-135 "COMMAAST.spad" 135523 135531 135750 135755) (-134 "COMM.spad" 135334 135342 135513 135518) (-133 "COMBOPC.spad" 134257 134265 135324 135329) (-132 "COMBINAT.spad" 133024 133034 134247 134252) (-131 "COMBF.spad" 130446 130462 133014 133019) (-130 "COLOR.spad" 129283 129291 130436 130441) (-129 "COLONAST.spad" 128949 128957 129273 129278) (-128 "CMPLXRT.spad" 128660 128677 128939 128944) (-127 "CLLCTAST.spad" 128322 128330 128650 128655) (-126 "CLIP.spad" 124430 124438 128312 128317) (-125 "CLIF.spad" 123085 123101 124386 124425) (-124 "CLAGG.spad" 121077 121087 123075 123080) (-123 "CLAGG.spad" 118928 118940 120928 120933) (-122 "CINTSLPE.spad" 118283 118296 118918 118923) (-121 "CHVAR.spad" 116421 116443 118273 118278) (-120 "CHARZ.spad" 116336 116344 116401 116416) (-119 "CHARPOL.spad" 115862 115872 116326 116331) (-118 "CHARNZ.spad" 115624 115632 115842 115857) (-117 "CHAR.spad" 112992 113000 115614 115619) (-116 "CFCAT.spad" 112320 112328 112982 112987) (-115 "CDEN.spad" 111540 111554 112310 112315) (-114 "CCLASS.spad" 109609 109617 110871 110898) (-113 "CATEGORY.spad" 108683 108691 109599 109604) (-112 "CATCTOR.spad" 108574 108582 108673 108678) (-111 "CATAST.spad" 108200 108208 108564 108569) (-110 "CASEAST.spad" 107914 107922 108190 108195) (-109 "CARTEN2.spad" 107304 107331 107904 107909) (-108 "CARTEN.spad" 103056 103080 107294 107299) (-107 "CARD.spad" 100351 100359 103030 103051) (-106 "CAPSLAST.spad" 100133 100141 100341 100346) (-105 "CACHSET.spad" 99757 99765 100123 100128) (-104 "CABMON.spad" 99312 99320 99747 99752) (-103 "BYTEORD.spad" 98987 98995 99302 99307) (-102 "BYTEBUF.spad" 96797 96805 98003 98018) (-101 "BYTE.spad" 96272 96280 96787 96792) (-100 "BTREE.spad" 95361 95371 95895 95910) (-99 "BTOURN.spad" 94383 94392 94984 94999) (-98 "BTCAT.spad" 93953 93962 94363 94378) (-97 "BTCAT.spad" 93531 93542 93943 93948) (-96 "BTAGG.spad" 93010 93017 93511 93526) (-95 "BTAGG.spad" 92497 92506 93000 93005) (-94 "BSTREE.spad" 91255 91264 92120 92135) (-93 "BRILL.spad" 89461 89471 91245 91250) (-92 "BRAGG.spad" 88418 88427 89451 89456) (-91 "BRAGG.spad" 87311 87322 88346 88351) (-90 "BPADICRT.spad" 85371 85382 85617 85710) (-89 "BPADIC.spad" 85044 85055 85297 85366) (-88 "BOUNDZRO.spad" 84701 84717 85034 85039) (-87 "BOP1.spad" 82160 82169 84691 84696) (-86 "BOP.spad" 77303 77310 82150 82155) (-85 "BOOLEAN.spad" 76852 76859 77293 77298) (-84 "BOOLE.spad" 76503 76510 76842 76847) (-83 "BOOLE.spad" 76152 76161 76493 76498) (-82 "BMODULE.spad" 75865 75876 76120 76147) (-81 "BITS.spad" 75066 75073 75280 75295) (-80 "catdef.spad" 74949 74959 75056 75061) (-79 "catdef.spad" 74700 74710 74939 74944) (-78 "BINDING.spad" 74122 74129 74690 74695) (-77 "BINARY.spad" 72357 72364 72712 72805) (-76 "BGAGG.spad" 71677 71686 72337 72352) (-75 "BGAGG.spad" 71005 71016 71667 71672) (-74 "BEZOUT.spad" 70146 70172 70955 70960) (-73 "BBTREE.spad" 67040 67049 69769 69784) (-72 "BASTYPE.spad" 66540 66547 67030 67035) (-71 "BASTYPE.spad" 66038 66047 66530 66535) (-70 "BALFACT.spad" 65498 65510 66028 66033) (-69 "AUTOMOR.spad" 64949 64958 65478 65493) (-68 "ATTREG.spad" 62081 62088 64725 64944) (-67 "ATTRAST.spad" 61798 61805 62071 62076) (-66 "ATRIG.spad" 61268 61275 61788 61793) (-65 "ATRIG.spad" 60736 60745 61258 61263) (-64 "ASTCAT.spad" 60640 60647 60726 60731) (-63 "ASTCAT.spad" 60542 60551 60630 60635) (-62 "ASTACK.spad" 59958 59967 60226 60241) (-61 "ASSOCEQ.spad" 58792 58803 59914 59919) (-60 "ARRAY2.spad" 58327 58336 58476 58491) (-59 "ARRAY12.spad" 57040 57051 58317 58322) (-58 "ARRAY1.spad" 55606 55615 55952 55967) (-57 "ARR2CAT.spad" 51658 51679 55586 55601) (-56 "ARR2CAT.spad" 47718 47741 51648 51653) (-55 "ARITY.spad" 47090 47097 47708 47713) (-54 "APPRULE.spad" 46374 46396 47080 47085) (-53 "APPLYORE.spad" 45993 46006 46364 46369) (-52 "ANY1.spad" 45064 45073 45983 45988) (-51 "ANY.spad" 43915 43922 45054 45059) (-50 "ANTISYM.spad" 42360 42376 43895 43910) (-49 "ANON.spad" 42069 42076 42350 42355) (-48 "AN.spad" 40537 40544 41900 41993) (-47 "AMR.spad" 38722 38733 40435 40532) (-46 "AMR.spad" 36770 36783 38485 38490) (-45 "ALIST.spad" 33066 33087 33416 33431) (-44 "ALGSC.spad" 32201 32227 32938 32991) (-43 "ALGPKG.spad" 27984 27995 32157 32162) (-42 "ALGMFACT.spad" 27177 27191 27974 27979) (-41 "ALGMANIP.spad" 24678 24693 27021 27026) (-40 "ALGFF.spad" 22496 22523 22713 22869) (-39 "ALGFACT.spad" 21615 21625 22486 22491) (-38 "ALGEBRA.spad" 21448 21457 21571 21610) (-37 "ALGEBRA.spad" 21313 21324 21438 21443) (-36 "ALAGG.spad" 20841 20862 21293 21308) (-35 "AHYP.spad" 20222 20229 20831 20836) (-34 "AGG.spad" 19129 19136 20212 20217) (-33 "AGG.spad" 18034 18043 19119 19124) (-32 "AF.spad" 16479 16494 17983 17988) (-31 "ADDAST.spad" 16165 16172 16469 16474) (-30 "ACPLOT.spad" 15042 15049 16155 16160) (-29 "ACFS.spad" 12899 12908 14944 15037) (-28 "ACFS.spad" 10842 10853 12889 12894) (-27 "ACF.spad" 7596 7603 10744 10837) (-26 "ACF.spad" 4436 4445 7586 7591) (-25 "ABELSG.spad" 3977 3984 4426 4431) (-24 "ABELSG.spad" 3516 3525 3967 3972) (-23 "ABELMON.spad" 2944 2951 3506 3511) (-22 "ABELMON.spad" 2370 2379 2934 2939) (-21 "ABELGRP.spad" 2035 2042 2360 2365) (-20 "ABELGRP.spad" 1698 1707 2025 2030) (-19 "A1AGG.spad" 860 869 1678 1693) (-18 "A1AGG.spad" 30 41 850 855)) 
\ No newline at end of file
+((-3 NIL 1968158 1968163 1968168 1968173) (-2 NIL 1968138 1968143 1968148 1968153) (-1 NIL 1968118 1968123 1968128 1968133) (0 NIL 1968098 1968103 1968108 1968113) (-1209 "ZMOD.spad" 1967907 1967920 1968036 1968093) (-1208 "ZLINDEP.spad" 1967005 1967016 1967897 1967902) (-1207 "ZDSOLVE.spad" 1956966 1956988 1966995 1967000) (-1206 "YSTREAM.spad" 1956461 1956472 1956956 1956961) (-1205 "YDIAGRAM.spad" 1956095 1956104 1956451 1956456) (-1204 "XRPOLY.spad" 1955315 1955335 1955951 1956020) (-1203 "XPR.spad" 1953110 1953123 1955033 1955132) (-1202 "XPOLYC.spad" 1952429 1952445 1953036 1953105) (-1201 "XPOLY.spad" 1951984 1951995 1952285 1952354) (-1200 "XPBWPOLY.spad" 1950455 1950475 1951790 1951859) (-1199 "XFALG.spad" 1947503 1947519 1950381 1950450) (-1198 "XF.spad" 1945966 1945981 1947405 1947498) (-1197 "XF.spad" 1944409 1944426 1945850 1945855) (-1196 "XEXPPKG.spad" 1943668 1943694 1944399 1944404) (-1195 "XDPOLY.spad" 1943282 1943298 1943524 1943593) (-1194 "XALG.spad" 1942950 1942961 1943238 1943277) (-1193 "WUTSET.spad" 1938804 1938821 1942435 1942450) (-1192 "WP.spad" 1938011 1938055 1938662 1938729) (-1191 "WHILEAST.spad" 1937809 1937818 1938001 1938006) (-1190 "WHEREAST.spad" 1937480 1937489 1937799 1937804) (-1189 "WFFINTBS.spad" 1935143 1935165 1937470 1937475) (-1188 "WEIER.spad" 1933365 1933376 1935133 1935138) (-1187 "VSPACE.spad" 1933038 1933049 1933333 1933360) (-1186 "VSPACE.spad" 1932731 1932744 1933028 1933033) (-1185 "VOID.spad" 1932408 1932417 1932721 1932726) (-1184 "VIEWDEF.spad" 1927609 1927618 1932398 1932403) (-1183 "VIEW3D.spad" 1911570 1911579 1927599 1927604) (-1182 "VIEW2D.spad" 1899469 1899478 1911560 1911565) (-1181 "VIEW.spad" 1897189 1897198 1899459 1899464) (-1180 "VECTOR2.spad" 1895828 1895841 1897179 1897184) (-1179 "VECTOR.spad" 1894234 1894245 1894485 1894500) (-1178 "VECTCAT.spad" 1892158 1892169 1894214 1894229) (-1177 "VECTCAT.spad" 1889879 1889892 1891937 1891942) (-1176 "VARIABLE.spad" 1889659 1889674 1889869 1889874) (-1175 "UTYPE.spad" 1889303 1889312 1889649 1889654) (-1174 "UTSODETL.spad" 1888598 1888622 1889259 1889264) (-1173 "UTSODE.spad" 1886814 1886834 1888588 1888593) (-1172 "UTSCAT.spad" 1884293 1884309 1886712 1886809) (-1171 "UTSCAT.spad" 1881440 1881458 1883861 1883866) (-1170 "UTS2.spad" 1881035 1881070 1881430 1881435) (-1169 "UTS.spad" 1876047 1876075 1879567 1879664) (-1168 "URAGG.spad" 1870768 1870779 1876037 1876042) (-1167 "URAGG.spad" 1865425 1865438 1870696 1870701) (-1166 "UPXSSING.spad" 1863193 1863219 1864629 1864762) (-1165 "UPXSCONS.spad" 1861011 1861031 1861384 1861533) (-1164 "UPXSCCA.spad" 1859582 1859602 1860857 1861006) (-1163 "UPXSCCA.spad" 1858295 1858317 1859572 1859577) (-1162 "UPXSCAT.spad" 1856884 1856900 1858141 1858290) (-1161 "UPXS2.spad" 1856427 1856480 1856874 1856879) (-1160 "UPXS.spad" 1853782 1853810 1854618 1854767) (-1159 "UPSQFREE.spad" 1852197 1852211 1853772 1853777) (-1158 "UPSCAT.spad" 1849992 1850016 1852095 1852192) (-1157 "UPSCAT.spad" 1847488 1847514 1849593 1849598) (-1156 "UPOLYC2.spad" 1846959 1846978 1847478 1847483) (-1155 "UPOLYC.spad" 1842039 1842050 1846801 1846954) (-1154 "UPOLYC.spad" 1837037 1837050 1841801 1841806) (-1153 "UPMP.spad" 1835969 1835982 1837027 1837032) (-1152 "UPDIVP.spad" 1835534 1835548 1835959 1835964) (-1151 "UPDECOMP.spad" 1833795 1833809 1835524 1835529) (-1150 "UPCDEN.spad" 1833012 1833028 1833785 1833790) (-1149 "UP2.spad" 1832376 1832397 1833002 1833007) (-1148 "UP.spad" 1829846 1829861 1830233 1830386) (-1147 "UNISEG2.spad" 1829343 1829356 1829802 1829807) (-1146 "UNISEG.spad" 1828696 1828707 1829262 1829267) (-1145 "UNIFACT.spad" 1827799 1827811 1828686 1828691) (-1144 "ULSCONS.spad" 1821645 1821665 1822015 1822164) (-1143 "ULSCCAT.spad" 1819382 1819402 1821491 1821640) (-1142 "ULSCCAT.spad" 1817227 1817249 1819338 1819343) (-1141 "ULSCAT.spad" 1815467 1815483 1817073 1817222) (-1140 "ULS2.spad" 1814981 1815034 1815457 1815462) (-1139 "ULS.spad" 1807014 1807042 1807959 1808382) (-1138 "UINT8.spad" 1806891 1806900 1807004 1807009) (-1137 "UINT64.spad" 1806767 1806776 1806881 1806886) (-1136 "UINT32.spad" 1806643 1806652 1806757 1806762) (-1135 "UINT16.spad" 1806519 1806528 1806633 1806638) (-1134 "UFD.spad" 1805584 1805593 1806445 1806514) (-1133 "UFD.spad" 1804711 1804722 1805574 1805579) (-1132 "UDVO.spad" 1803592 1803601 1804701 1804706) (-1131 "UDPO.spad" 1801173 1801184 1803548 1803553) (-1130 "TYPEAST.spad" 1801092 1801101 1801163 1801168) (-1129 "TYPE.spad" 1801024 1801033 1801082 1801087) (-1128 "TWOFACT.spad" 1799676 1799691 1801014 1801019) (-1127 "TUPLE.spad" 1799183 1799194 1799588 1799593) (-1126 "TUBETOOL.spad" 1796050 1796059 1799173 1799178) (-1125 "TUBE.spad" 1794697 1794714 1796040 1796045) (-1124 "TSETCAT.spad" 1782780 1782797 1794677 1794692) (-1123 "TSETCAT.spad" 1770837 1770856 1782736 1782741) (-1122 "TS.spad" 1769465 1769481 1770431 1770528) (-1121 "TRMANIP.spad" 1763829 1763846 1769153 1769158) (-1120 "TRIMAT.spad" 1762792 1762817 1763819 1763824) (-1119 "TRIGMNIP.spad" 1761319 1761336 1762782 1762787) (-1118 "TRIGCAT.spad" 1760831 1760840 1761309 1761314) (-1117 "TRIGCAT.spad" 1760341 1760352 1760821 1760826) (-1116 "TREE.spad" 1758932 1758943 1759964 1759979) (-1115 "TRANFUN.spad" 1758771 1758780 1758922 1758927) (-1114 "TRANFUN.spad" 1758608 1758619 1758761 1758766) (-1113 "TOPSP.spad" 1758282 1758291 1758598 1758603) (-1112 "TOOLSIGN.spad" 1757945 1757956 1758272 1758277) (-1111 "TEXTFILE.spad" 1756506 1756515 1757935 1757940) (-1110 "TEX1.spad" 1756062 1756073 1756496 1756501) (-1109 "TEX.spad" 1753256 1753265 1756052 1756057) (-1108 "TBCMPPK.spad" 1751357 1751380 1753246 1753251) (-1107 "TBAGG.spad" 1750612 1750635 1751337 1751352) (-1106 "TBAGG.spad" 1749875 1749900 1750602 1750607) (-1105 "TANEXP.spad" 1749283 1749294 1749865 1749870) (-1104 "TALGOP.spad" 1749007 1749018 1749273 1749278) (-1103 "TABLEAU.spad" 1748488 1748499 1748997 1749002) (-1102 "TABLE.spad" 1746188 1746211 1746458 1746473) (-1101 "TABLBUMP.spad" 1742967 1742978 1746178 1746183) (-1100 "SYSTEM.spad" 1742195 1742204 1742957 1742962) (-1099 "SYSSOLP.spad" 1739678 1739689 1742185 1742190) (-1098 "SYSPTR.spad" 1739577 1739586 1739668 1739673) (-1097 "SYSNNI.spad" 1738800 1738811 1739567 1739572) (-1096 "SYSINT.spad" 1738204 1738215 1738790 1738795) (-1095 "SYNTAX.spad" 1734538 1734547 1738194 1738199) (-1094 "SYMTAB.spad" 1732606 1732615 1734528 1734533) (-1093 "SYMS.spad" 1728635 1728644 1732596 1732601) (-1092 "SYMPOLY.spad" 1727768 1727779 1727850 1727977) (-1091 "SYMFUNC.spad" 1727269 1727280 1727758 1727763) (-1090 "SYMBOL.spad" 1724764 1724773 1727259 1727264) (-1089 "SUTS.spad" 1721877 1721905 1723296 1723393) (-1088 "SUPXS.spad" 1719219 1719247 1720068 1720217) (-1087 "SUPFRACF.spad" 1718324 1718342 1719209 1719214) (-1086 "SUP2.spad" 1717716 1717729 1718314 1718319) (-1085 "SUP.spad" 1714800 1714811 1715573 1715726) (-1084 "SUMRF.spad" 1713774 1713785 1714790 1714795) (-1083 "SUMFS.spad" 1713403 1713420 1713764 1713769) (-1082 "SULS.spad" 1705423 1705451 1706381 1706804) (-1081 "syntax.spad" 1705192 1705201 1705413 1705418) (-1080 "SUCH.spad" 1704882 1704897 1705182 1705187) (-1079 "SUBSPACE.spad" 1697013 1697028 1704872 1704877) (-1078 "SUBRESP.spad" 1696183 1696197 1696969 1696974) (-1077 "STTFNC.spad" 1692651 1692667 1696173 1696178) (-1076 "STTF.spad" 1688750 1688766 1692641 1692646) (-1075 "STTAYLOR.spad" 1681427 1681438 1688657 1688662) (-1074 "STRTBL.spad" 1679351 1679368 1679500 1679515) (-1073 "STRING.spad" 1677982 1677991 1678367 1678382) (-1072 "STREAM3.spad" 1677555 1677570 1677972 1677977) (-1071 "STREAM2.spad" 1676683 1676696 1677545 1677550) (-1070 "STREAM1.spad" 1676389 1676400 1676673 1676678) (-1069 "STREAM.spad" 1673339 1673350 1675830 1675845) (-1068 "STINPROD.spad" 1672275 1672291 1673329 1673334) (-1067 "STEPAST.spad" 1671509 1671518 1672265 1672270) (-1066 "STEP.spad" 1670826 1670835 1671499 1671504) (-1065 "STBL.spad" 1668690 1668718 1668857 1668872) (-1064 "STAGG.spad" 1667389 1667400 1668680 1668685) (-1063 "STAGG.spad" 1666086 1666099 1667379 1667384) (-1062 "STACK.spad" 1665520 1665531 1665770 1665785) (-1061 "SRING.spad" 1665280 1665289 1665510 1665515) (-1060 "SREGSET.spad" 1662863 1662880 1664765 1664780) (-1059 "SRDCMPK.spad" 1661440 1661460 1662853 1662858) (-1058 "SRAGG.spad" 1656635 1656644 1661420 1661435) (-1057 "SRAGG.spad" 1651838 1651849 1656625 1656630) (-1056 "SQMATRIX.spad" 1649527 1649545 1650443 1650518) (-1055 "SPLTREE.spad" 1644177 1644190 1648973 1648988) (-1054 "SPLNODE.spad" 1640797 1640810 1644167 1644172) (-1053 "SPFCAT.spad" 1639606 1639615 1640787 1640792) (-1052 "SPECOUT.spad" 1638158 1638167 1639596 1639601) (-1051 "SPADXPT.spad" 1630249 1630258 1638148 1638153) (-1050 "spad-parser.spad" 1629714 1629723 1630239 1630244) (-1049 "SPADAST.spad" 1629415 1629424 1629704 1629709) (-1048 "SPACEC.spad" 1613630 1613641 1629405 1629410) (-1047 "SPACE3.spad" 1613406 1613417 1613620 1613625) (-1046 "SORTPAK.spad" 1612955 1612968 1613362 1613367) (-1045 "SOLVETRA.spad" 1610718 1610729 1612945 1612950) (-1044 "SOLVESER.spad" 1609174 1609185 1610708 1610713) (-1043 "SOLVERAD.spad" 1605200 1605211 1609164 1609169) (-1042 "SOLVEFOR.spad" 1603662 1603680 1605190 1605195) (-1041 "SNTSCAT.spad" 1603274 1603291 1603642 1603657) (-1040 "SMTS.spad" 1601591 1601617 1602868 1602965) (-1039 "SMP.spad" 1599399 1599419 1599789 1599916) (-1038 "SMITH.spad" 1598244 1598269 1599389 1599394) (-1037 "SMATCAT.spad" 1596374 1596404 1598200 1598239) (-1036 "SMATCAT.spad" 1594424 1594456 1596252 1596257) (-1035 "aggcat.spad" 1594100 1594111 1594404 1594419) (-1034 "SKAGG.spad" 1593081 1593092 1594080 1594095) (-1033 "SINT.spad" 1592380 1592389 1592947 1593076) (-1032 "SIMPAN.spad" 1592108 1592117 1592370 1592375) (-1031 "SIGNRF.spad" 1591233 1591244 1592098 1592103) (-1030 "SIGNEF.spad" 1590519 1590536 1591223 1591228) (-1029 "syntax.spad" 1589936 1589945 1590509 1590514) (-1028 "SIG.spad" 1589298 1589307 1589926 1589931) (-1027 "SHP.spad" 1587242 1587257 1589254 1589259) (-1026 "SHDP.spad" 1576646 1576673 1577163 1577248) (-1025 "SGROUP.spad" 1576254 1576263 1576636 1576641) (-1024 "SGROUP.spad" 1575860 1575871 1576244 1576249) (-1023 "catdef.spad" 1575570 1575582 1575681 1575855) (-1022 "catdef.spad" 1575126 1575138 1575391 1575565) (-1021 "SGCF.spad" 1568265 1568274 1575116 1575121) (-1020 "SFRTCAT.spad" 1567223 1567240 1568245 1568260) (-1019 "SFRGCD.spad" 1566286 1566306 1567213 1567218) (-1018 "SFQCMPK.spad" 1561099 1561119 1566276 1566281) (-1017 "SEXOF.spad" 1560942 1560982 1561089 1561094) (-1016 "SEXCAT.spad" 1558770 1558810 1560932 1560937) (-1015 "SEX.spad" 1558662 1558671 1558760 1558765) (-1014 "SETMN.spad" 1557122 1557139 1558652 1558657) (-1013 "SETCAT.spad" 1556607 1556616 1557112 1557117) (-1012 "SETCAT.spad" 1556090 1556101 1556597 1556602) (-1011 "SETAGG.spad" 1552639 1552650 1556070 1556085) (-1010 "SETAGG.spad" 1549196 1549209 1552629 1552634) (-1009 "SET.spad" 1547354 1547365 1548453 1548480) (-1008 "syntax.spad" 1547057 1547066 1547344 1547349) (-1007 "SEGXCAT.spad" 1546213 1546226 1547047 1547052) (-1006 "SEGCAT.spad" 1545138 1545149 1546203 1546208) (-1005 "SEGBIND2.spad" 1544836 1544849 1545128 1545133) (-1004 "SEGBIND.spad" 1544594 1544605 1544783 1544788) (-1003 "SEGAST.spad" 1544324 1544333 1544584 1544589) (-1002 "SEG2.spad" 1543759 1543772 1544280 1544285) (-1001 "SEG.spad" 1543572 1543583 1543678 1543683) (-1000 "SDVAR.spad" 1542848 1542859 1543562 1543567) (-999 "SDPOL.spad" 1540541 1540551 1540831 1540958) (-998 "SCPKG.spad" 1538631 1538641 1540531 1540536) (-997 "SCOPE.spad" 1537809 1537817 1538621 1538626) (-996 "SCACHE.spad" 1536506 1536516 1537799 1537804) (-995 "SASTCAT.spad" 1536416 1536424 1536496 1536501) (-994 "SAOS.spad" 1536289 1536297 1536406 1536411) (-993 "SAERFFC.spad" 1536003 1536022 1536279 1536284) (-992 "SAEFACT.spad" 1535705 1535724 1535993 1535998) (-991 "SAE.spad" 1533356 1533371 1533966 1534101) (-990 "RURPK.spad" 1531016 1531031 1533346 1533351) (-989 "RULESET.spad" 1530470 1530493 1531006 1531011) (-988 "RULECOLD.spad" 1530323 1530335 1530460 1530465) (-987 "RULE.spad" 1528572 1528595 1530313 1530318) (-986 "RTVALUE.spad" 1528308 1528316 1528562 1528567) (-985 "syntax.spad" 1528026 1528034 1528298 1528303) (-984 "RSETGCD.spad" 1524469 1524488 1528016 1528021) (-983 "RSETCAT.spad" 1514450 1514466 1524449 1524464) (-982 "RSETCAT.spad" 1504439 1504457 1514440 1514445) (-981 "RSDCMPK.spad" 1502940 1502959 1504429 1504434) (-980 "RRCC.spad" 1501325 1501354 1502930 1502935) (-979 "RRCC.spad" 1499708 1499739 1501315 1501320) (-978 "RPTAST.spad" 1499411 1499419 1499698 1499703) (-977 "RPOLCAT.spad" 1478916 1478930 1499279 1499406) (-976 "RPOLCAT.spad" 1458214 1458230 1478579 1478584) (-975 "ROMAN.spad" 1457543 1457551 1458080 1458209) (-974 "ROIRC.spad" 1456624 1456655 1457533 1457538) (-973 "RNS.spad" 1455601 1455609 1456526 1456619) (-972 "RNS.spad" 1454664 1454674 1455591 1455596) (-971 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(-405 "GRALG.spad" 649166 649178 650061 650066) (-404 "GRALG.spad" 648259 648273 649156 649161) (-403 "GPOLSET.spad" 647568 647591 647780 647795) (-402 "GOSPER.spad" 646845 646863 647558 647563) (-401 "GMODPOL.spad" 645993 646020 646813 646840) (-400 "GHENSEL.spad" 645076 645090 645983 645988) (-399 "GENUPS.spad" 641369 641382 645066 645071) (-398 "GENUFACT.spad" 640946 640956 641359 641364) (-397 "GENPGCD.spad" 640548 640565 640936 640941) (-396 "GENMFACT.spad" 640000 640019 640538 640543) (-395 "GENEEZ.spad" 637959 637972 639990 639995) (-394 "GDMP.spad" 635348 635365 636122 636249) (-393 "GCNAALG.spad" 629271 629298 635142 635209) (-392 "GCDDOM.spad" 628463 628471 629197 629266) (-391 "GCDDOM.spad" 627717 627727 628453 628458) (-390 "GBINTERN.spad" 623737 623775 627707 627712) (-389 "GBF.spad" 619520 619558 623727 623732) (-388 "GBEUCLID.spad" 617402 617440 619510 619515) (-387 "GB.spad" 614928 614966 617358 617363) (-386 "GAUSSFAC.spad" 614241 614249 614918 614923) (-385 "GALUTIL.spad" 612567 612577 614197 614202) (-384 "GALPOLYU.spad" 611021 611034 612557 612562) (-383 "GALFACTU.spad" 609234 609253 611011 611016) (-382 "GALFACT.spad" 599447 599458 609224 609229) (-381 "FUNDESC.spad" 599125 599133 599437 599442) (-380 "FUNCTION.spad" 598974 598986 599115 599120) (-379 "FT.spad" 597274 597282 598964 598969) (-378 "FSUPFACT.spad" 596188 596207 597224 597229) (-377 "FST.spad" 594274 594282 596178 596183) (-376 "FSRED.spad" 593754 593770 594264 594269) (-375 "FSPRMELT.spad" 592620 592636 593711 593716) (-374 "FSPECF.spad" 590711 590727 592610 592615) (-373 "FSINT.spad" 590371 590387 590701 590706) (-372 "FSERIES.spad" 589562 589574 590191 590290) (-371 "FSCINT.spad" 588879 588895 589552 589557) (-370 "FSAGG2.spad" 587614 587630 588869 588874) (-369 "FSAGG.spad" 586743 586753 587582 587609) (-368 "FSAGG.spad" 585822 585834 586663 586668) (-367 "FS2UPS.spad" 580337 580371 585812 585817) (-366 "FS2EXPXP.spad" 579478 579501 580327 580332) (-365 "FS2.spad" 579133 579149 579468 579473) (-364 "FS.spad" 573405 573415 578912 579128) (-363 "FS.spad" 567479 567491 572988 572993) (-362 "FRUTIL.spad" 566433 566443 567469 567474) (-361 "FRNAALG.spad" 561710 561720 566375 566428) (-360 "FRNAALG.spad" 556999 557011 561666 561671) (-359 "FRNAAF2.spad" 556447 556465 556989 556994) (-358 "FRMOD.spad" 555855 555885 556376 556381) (-357 "FRIDEAL2.spad" 555459 555491 555845 555850) (-356 "FRIDEAL.spad" 554684 554705 555439 555454) (-355 "FRETRCT.spad" 554203 554213 554674 554679) (-354 "FRETRCT.spad" 553629 553641 554102 554107) (-353 "FRAMALG.spad" 552009 552022 553585 553624) (-352 "FRAMALG.spad" 550421 550436 551999 552004) (-351 "FRAC2.spad" 550026 550038 550411 550416) (-350 "FRAC.spad" 548013 548023 548400 548573) (-349 "FR2.spad" 547349 547361 548003 548008) (-348 "FR.spad" 541137 541147 546410 546479) (-347 "FPS.spad" 537976 537984 541027 541132) (-346 "FPS.spad" 534843 534853 537896 537901) (-345 "FPC.spad" 533889 533897 534745 534838) (-344 "FPC.spad" 533021 533031 533879 533884) (-343 "FPATMAB.spad" 532783 532793 533011 533016) (-342 "FPARFRAC.spad" 531625 531642 532773 532778) (-341 "FORDER.spad" 531316 531340 531615 531620) (-340 "FNLA.spad" 530740 530762 531284 531311) (-339 "FNCAT.spad" 529335 529343 530730 530735) (-338 "FNAME.spad" 529227 529235 529325 529330) (-337 "FMONOID.spad" 528908 528918 529183 529188) (-336 "FMONCAT.spad" 526077 526087 528898 528903) (-335 "FMCAT.spad" 523753 523771 526045 526072) (-334 "FM1.spad" 523118 523130 523687 523714) (-333 "FM.spad" 522733 522745 522972 522999) (-332 "FLOATRP.spad" 520476 520490 522723 522728) (-331 "FLOATCP.spad" 517915 517929 520466 520471) (-330 "FLOAT.spad" 515006 515014 517781 517910) (-329 "FLINEXP.spad" 514728 514738 514996 515001) (-328 "FLINEXP.spad" 514407 514419 514677 514682) (-327 "FLASORT.spad" 513733 513745 514397 514402) (-326 "FLALG.spad" 511403 511422 513659 513728) (-325 "FLAGG2.spad" 510120 510136 511393 511398) (-324 "FLAGG.spad" 507196 507206 510110 510115) (-323 "FLAGG.spad" 504137 504149 507053 507058) (-322 "FINRALG.spad" 502222 502235 504093 504132) (-321 "FINRALG.spad" 500233 500248 502106 502111) (-320 "FINITE.spad" 499385 499393 500223 500228) (-319 "FINITE.spad" 498535 498545 499375 499380) (-318 "aggcat.spad" 495465 495475 498525 498530) (-317 "FINAGG.spad" 492360 492372 495422 495427) (-316 "FINAALG.spad" 481545 481555 492302 492355) (-315 "FINAALG.spad" 470742 470754 481501 481506) (-314 "FILECAT.spad" 469276 469293 470732 470737) (-313 "FILE.spad" 468859 468869 469266 469271) (-312 "FIELD.spad" 468265 468273 468761 468854) (-311 "FIELD.spad" 467757 467767 468255 468260) (-310 "FGROUP.spad" 466420 466430 467737 467752) (-309 "FGLMICPK.spad" 465215 465230 466410 466415) (-308 "FFX.spad" 464601 464616 464934 465027) (-307 "FFSLPE.spad" 464112 464133 464591 464596) (-306 "FFPOLY2.spad" 463172 463189 464102 464107) (-305 "FFPOLY.spad" 454514 454525 463162 463167) (-304 "FFP.spad" 453922 453942 454233 454326) (-303 "FFNBX.spad" 452445 452465 453641 453734) (-302 "FFNBP.spad" 450969 450986 452164 452257) (-301 "FFNB.spad" 449437 449458 450653 450746) (-300 "FFINTBAS.spad" 446951 446970 449427 449432) (-299 "FFIELDC.spad" 444536 444544 446853 446946) (-298 "FFIELDC.spad" 442207 442217 444526 444531) (-297 "FFHOM.spad" 440979 440996 442197 442202) (-296 "FFF.spad" 438422 438433 440969 440974) (-295 "FFCGX.spad" 437280 437300 438141 438234) (-294 "FFCGP.spad" 436180 436200 436999 437092) (-293 "FFCG.spad" 434975 434996 435864 435957) (-292 "FFCAT2.spad" 434722 434762 434965 434970) (-291 "FFCAT.spad" 427887 427909 434561 434717) (-290 "FFCAT.spad" 421131 421155 427807 427812) (-289 "FF.spad" 420582 420598 420815 420908) (-288 "FEVALAB.spad" 420290 420300 420572 420577) (-287 "FEVALAB.spad" 419774 419786 420058 420063) (-286 "FDIVCAT.spad" 417870 417894 419764 419769) (-285 "FDIVCAT.spad" 415964 415990 417860 417865) (-284 "FDIV2.spad" 415620 415660 415954 415959) (-283 "FDIV.spad" 415078 415102 415610 415615) (-282 "FCTRDATA.spad" 414086 414094 415068 415073) (-281 "FCOMP.spad" 413465 413475 414076 414081) (-280 "FAXF.spad" 406500 406514 413367 413460) (-279 "FAXF.spad" 399587 399603 406456 406461) (-278 "FARRAY.spad" 397466 397476 398499 398514) (-277 "FAMR.spad" 395610 395622 397364 397461) (-276 "FAMR.spad" 393738 393752 395494 395499) (-275 "FAMONOID.spad" 393422 393432 393692 393697) (-274 "FAMONC.spad" 391742 391754 393412 393417) (-273 "FAGROUP.spad" 391382 391392 391638 391665) (-272 "FACUTIL.spad" 389594 389611 391372 391377) (-271 "FACTFUNC.spad" 388796 388806 389584 389589) (-270 "EXPUPXS.spad" 385688 385711 386987 387136) (-269 "EXPRTUBE.spad" 382976 382984 385678 385683) (-268 "EXPRODE.spad" 380144 380160 382966 382971) (-267 "EXPR2UPS.spad" 376266 376279 380134 380139) (-266 "EXPR2.spad" 375971 375983 376256 376261) (-265 "EXPR.spad" 371616 371626 372330 372617) (-264 "EXPEXPAN.spad" 368561 368586 369193 369286) (-263 "EXITAST.spad" 368297 368305 368551 368556) (-262 "EXIT.spad" 367968 367976 368287 368292) (-261 "EVALCYC.spad" 367428 367442 367958 367963) (-260 "EVALAB.spad" 367008 367018 367418 367423) (-259 "EVALAB.spad" 366586 366598 366998 367003) (-258 "EUCDOM.spad" 364176 364184 366512 366581) (-257 "EUCDOM.spad" 361828 361838 364166 364171) (-256 "ES2.spad" 361341 361357 361818 361823) (-255 "ES1.spad" 360911 360927 361331 361336) (-254 "ES.spad" 353782 353790 360901 360906) (-253 "ES.spad" 346574 346584 353695 353700) (-252 "ERROR.spad" 343901 343909 346564 346569) (-251 "EQTBL.spad" 341723 341745 341932 341947) (-250 "EQ2.spad" 341441 341453 341713 341718) (-249 "EQ.spad" 336347 336357 339142 339248) (-248 "EP.spad" 332673 332683 336337 336342) (-247 "ENV.spad" 331351 331359 332663 332668) (-246 "ENTIRER.spad" 331019 331027 331295 331346) (-245 "ENTIRER.spad" 330731 330741 331009 331014) (-244 "EMR.spad" 330019 330060 330657 330726) (-243 "ELTAGG.spad" 328273 328292 330009 330014) (-242 "ELTAGG.spad" 326491 326512 328229 328234) (-241 "ELTAB.spad" 325966 325979 326481 326486) (-240 "ELFUTS.spad" 325401 325420 325956 325961) (-239 "ELEMFUN.spad" 325090 325098 325391 325396) (-238 "ELEMFUN.spad" 324777 324787 325080 325085) (-237 "ELAGG.spad" 322748 322758 324757 324772) (-236 "ELAGG.spad" 320658 320670 322669 322674) (-235 "ELABOR.spad" 320004 320012 320648 320653) (-234 "ELABEXPR.spad" 318936 318944 319994 319999) (-233 "EFUPXS.spad" 315712 315742 318892 318897) (-232 "EFULS.spad" 312548 312571 315668 315673) (-231 "EFSTRUC.spad" 310563 310579 312538 312543) (-230 "EF.spad" 305339 305355 310553 310558) (-229 "EAB.spad" 303639 303647 305329 305334) (-228 "DVARCAT.spad" 300645 300655 303629 303634) (-227 "DVARCAT.spad" 297649 297661 300635 300640) (-226 "DSMP.spad" 295382 295396 295687 295814) (-225 "DSEXT.spad" 294684 294694 295372 295377) (-224 "DSEXT.spad" 293906 293918 294596 294601) (-223 "DROPT1.spad" 293571 293581 293896 293901) (-222 "DROPT0.spad" 288436 288444 293561 293566) (-221 "DROPT.spad" 282395 282403 288426 288431) (-220 "DRAWPT.spad" 280568 280576 282385 282390) (-219 "DRAWHACK.spad" 279876 279886 280558 280563) (-218 "DRAWCX.spad" 277354 277362 279866 279871) (-217 "DRAWCURV.spad" 276901 276916 277344 277349) (-216 "DRAWCFUN.spad" 266433 266441 276891 276896) (-215 "DRAW.spad" 259309 259322 266423 266428) (-214 "DQAGG.spad" 257499 257509 259289 259304) (-213 "DPOLCAT.spad" 252856 252872 257367 257494) (-212 "DPOLCAT.spad" 248299 248317 252812 252817) (-211 "DPMO.spad" 240913 240929 241051 241245) (-210 "DPMM.spad" 233540 233558 233665 233859) (-209 "DOMTMPLT.spad" 233311 233319 233530 233535) (-208 "DOMCTOR.spad" 233066 233074 233301 233306) (-207 "DOMAIN.spad" 232177 232185 233056 233061) (-206 "DMP.spad" 229770 229785 230340 230467) (-205 "DMEXT.spad" 229637 229647 229738 229765) (-204 "DLP.spad" 228997 229007 229627 229632) (-203 "DLIST.spad" 227305 227315 227909 227924) (-202 "DLAGG.spad" 225722 225732 227295 227300) (-201 "DIVRING.spad" 225264 225272 225666 225717) (-200 "DIVRING.spad" 224850 224860 225254 225259) (-199 "DISPLAY.spad" 223040 223048 224840 224845) (-198 "DIRPROD2.spad" 221858 221876 223030 223035) (-197 "DIRPROD.spad" 211139 211155 211779 211864) (-196 "DIRPCAT.spad" 210434 210450 211049 211134) (-195 "DIRPCAT.spad" 209343 209361 209960 209965) (-194 "DIOSP.spad" 208168 208176 209333 209338) (-193 "DIOPS.spad" 207164 207174 208148 208163) (-192 "DIOPS.spad" 206107 206119 207093 207098) (-191 "catdef.spad" 205965 205973 206097 206102) (-190 "DIFRING.spad" 205803 205811 205945 205960) (-189 "DIFFSPC.spad" 205382 205390 205793 205798) (-188 "DIFFSPC.spad" 204959 204969 205372 205377) (-187 "DIFFMOD.spad" 204448 204458 204927 204954) (-186 "DIFFDOM.spad" 203613 203624 204438 204443) (-185 "DIFFDOM.spad" 202776 202789 203603 203608) (-184 "DIFEXT.spad" 202595 202605 202756 202771) (-183 "DIAGG.spad" 202225 202235 202575 202590) (-182 "DIAGG.spad" 201863 201875 202215 202220) (-181 "DHMATRIX.spad" 200252 200262 201397 201412) (-180 "DFSFUN.spad" 193892 193900 200242 200247) (-179 "DFLOAT.spad" 190499 190507 193782 193887) (-178 "DFINTTLS.spad" 188730 188746 190489 190494) (-177 "DERHAM.spad" 186644 186676 188710 188725) (-176 "DEQUEUE.spad" 186045 186055 186328 186343) (-175 "DEGRED.spad" 185662 185676 186035 186040) (-174 "DEFINTRF.spad" 183244 183254 185652 185657) (-173 "DEFINTEF.spad" 181782 181798 183234 183239) (-172 "DEFAST.spad" 181166 181174 181772 181777) (-171 "DECIMAL.spad" 179395 179403 179756 179849) (-170 "DDFACT.spad" 177216 177233 179385 179390) (-169 "DBLRESP.spad" 176816 176840 177206 177211) (-168 "DBASIS.spad" 176442 176457 176806 176811) (-167 "DBASE.spad" 175106 175116 176432 176437) (-166 "DATAARY.spad" 174592 174605 175096 175101) (-165 "CYCLOTOM.spad" 174098 174106 174582 174587) (-164 "CYCLES.spad" 170884 170892 174088 174093) (-163 "CVMP.spad" 170301 170311 170874 170879) (-162 "CTRIGMNP.spad" 168801 168817 170291 170296) (-161 "CTORKIND.spad" 168404 168412 168791 168796) (-160 "CTORCAT.spad" 167645 167653 168394 168399) (-159 "CTORCAT.spad" 166884 166894 167635 167640) (-158 "CTORCALL.spad" 166473 166483 166874 166879) (-157 "CTOR.spad" 166164 166172 166463 166468) (-156 "CSTTOOLS.spad" 165409 165422 166154 166159) (-155 "CRFP.spad" 159181 159194 165399 165404) (-154 "CRCEAST.spad" 158901 158909 159171 159176) (-153 "CRAPACK.spad" 157968 157978 158891 158896) (-152 "CPMATCH.spad" 157469 157484 157890 157895) (-151 "CPIMA.spad" 157174 157193 157459 157464) (-150 "COORDSYS.spad" 152183 152193 157164 157169) (-149 "CONTOUR.spad" 151610 151618 152173 152178) (-148 "CONTFRAC.spad" 147360 147370 151512 151605) (-147 "CONDUIT.spad" 147118 147126 147350 147355) (-146 "COMRING.spad" 146792 146800 147056 147113) (-145 "COMPPROP.spad" 146310 146318 146782 146787) (-144 "COMPLPAT.spad" 146077 146092 146300 146305) (-143 "COMPLEX2.spad" 145792 145804 146067 146072) (-142 "COMPLEX.spad" 141498 141508 141742 142000) (-141 "COMPILER.spad" 141047 141055 141488 141493) (-140 "COMPFACT.spad" 140649 140663 141037 141042) (-139 "COMPCAT.spad" 138724 138734 140386 140644) (-138 "COMPCAT.spad" 136540 136552 138204 138209) (-137 "COMMUPC.spad" 136288 136306 136530 136535) (-136 "COMMONOP.spad" 135821 135829 136278 136283) (-135 "COMMAAST.spad" 135584 135592 135811 135816) (-134 "COMM.spad" 135395 135403 135574 135579) (-133 "COMBOPC.spad" 134318 134326 135385 135390) (-132 "COMBINAT.spad" 133085 133095 134308 134313) (-131 "COMBF.spad" 130507 130523 133075 133080) (-130 "COLOR.spad" 129344 129352 130497 130502) (-129 "COLONAST.spad" 129010 129018 129334 129339) (-128 "CMPLXRT.spad" 128721 128738 129000 129005) (-127 "CLLCTAST.spad" 128383 128391 128711 128716) (-126 "CLIP.spad" 124491 124499 128373 128378) (-125 "CLIF.spad" 123146 123162 124447 124486) (-124 "CLAGG.spad" 121138 121148 123136 123141) (-123 "CLAGG.spad" 118989 119001 120989 120994) (-122 "CINTSLPE.spad" 118344 118357 118979 118984) (-121 "CHVAR.spad" 116482 116504 118334 118339) (-120 "CHARZ.spad" 116397 116405 116462 116477) (-119 "CHARPOL.spad" 115923 115933 116387 116392) (-118 "CHARNZ.spad" 115685 115693 115903 115918) (-117 "CHAR.spad" 113053 113061 115675 115680) (-116 "CFCAT.spad" 112381 112389 113043 113048) (-115 "CDEN.spad" 111601 111615 112371 112376) (-114 "CCLASS.spad" 109670 109678 110932 110959) (-113 "CATEGORY.spad" 108744 108752 109660 109665) (-112 "CATCTOR.spad" 108635 108643 108734 108739) (-111 "CATAST.spad" 108261 108269 108625 108630) (-110 "CASEAST.spad" 107975 107983 108251 108256) (-109 "CARTEN2.spad" 107365 107392 107965 107970) (-108 "CARTEN.spad" 103117 103141 107355 107360) (-107 "CARD.spad" 100412 100420 103091 103112) (-106 "CAPSLAST.spad" 100194 100202 100402 100407) (-105 "CACHSET.spad" 99818 99826 100184 100189) (-104 "CABMON.spad" 99373 99381 99808 99813) (-103 "BYTEORD.spad" 99048 99056 99363 99368) (-102 "BYTEBUF.spad" 96858 96866 98064 98079) (-101 "BYTE.spad" 96333 96341 96848 96853) (-100 "BTREE.spad" 95422 95432 95956 95971) (-99 "BTOURN.spad" 94444 94453 95045 95060) (-98 "BTCAT.spad" 94014 94023 94424 94439) (-97 "BTCAT.spad" 93592 93603 94004 94009) (-96 "BTAGG.spad" 93071 93078 93572 93587) (-95 "BTAGG.spad" 92558 92567 93061 93066) (-94 "BSTREE.spad" 91316 91325 92181 92196) (-93 "BRILL.spad" 89522 89532 91306 91311) (-92 "BRAGG.spad" 88479 88488 89512 89517) (-91 "BRAGG.spad" 87372 87383 88407 88412) (-90 "BPADICRT.spad" 85432 85443 85678 85771) (-89 "BPADIC.spad" 85105 85116 85358 85427) (-88 "BOUNDZRO.spad" 84762 84778 85095 85100) (-87 "BOP1.spad" 82221 82230 84752 84757) (-86 "BOP.spad" 77364 77371 82211 82216) (-85 "BOOLEAN.spad" 76913 76920 77354 77359) (-84 "BOOLE.spad" 76564 76571 76903 76908) (-83 "BOOLE.spad" 76213 76222 76554 76559) (-82 "BMODULE.spad" 75926 75937 76181 76208) (-81 "BITS.spad" 75127 75134 75341 75356) (-80 "catdef.spad" 75010 75020 75117 75122) (-79 "catdef.spad" 74761 74771 75000 75005) (-78 "BINDING.spad" 74183 74190 74751 74756) (-77 "BINARY.spad" 72418 72425 72773 72866) (-76 "BGAGG.spad" 71738 71747 72398 72413) (-75 "BGAGG.spad" 71066 71077 71728 71733) (-74 "BEZOUT.spad" 70207 70233 71016 71021) (-73 "BBTREE.spad" 67101 67110 69830 69845) (-72 "BASTYPE.spad" 66601 66608 67091 67096) (-71 "BASTYPE.spad" 66099 66108 66591 66596) (-70 "BALFACT.spad" 65559 65571 66089 66094) (-69 "AUTOMOR.spad" 65010 65019 65539 65554) (-68 "ATTREG.spad" 62142 62149 64786 65005) (-67 "ATTRAST.spad" 61859 61866 62132 62137) (-66 "ATRIG.spad" 61329 61336 61849 61854) (-65 "ATRIG.spad" 60797 60806 61319 61324) (-64 "ASTCAT.spad" 60701 60708 60787 60792) (-63 "ASTCAT.spad" 60603 60612 60691 60696) (-62 "ASTACK.spad" 60019 60028 60287 60302) (-61 "ASSOCEQ.spad" 58853 58864 59975 59980) (-60 "ARRAY2.spad" 58388 58397 58537 58552) (-59 "ARRAY12.spad" 57101 57112 58378 58383) (-58 "ARRAY1.spad" 55667 55676 56013 56028) (-57 "ARR2CAT.spad" 51719 51740 55647 55662) (-56 "ARR2CAT.spad" 47779 47802 51709 51714) (-55 "ARITY.spad" 47151 47158 47769 47774) (-54 "APPRULE.spad" 46435 46457 47141 47146) (-53 "APPLYORE.spad" 46054 46067 46425 46430) (-52 "ANY1.spad" 45125 45134 46044 46049) (-51 "ANY.spad" 43976 43983 45115 45120) (-50 "ANTISYM.spad" 42421 42437 43956 43971) (-49 "ANON.spad" 42130 42137 42411 42416) (-48 "AN.spad" 40598 40605 41961 42054) (-47 "AMR.spad" 38783 38794 40496 40593) (-46 "AMR.spad" 36831 36844 38546 38551) (-45 "ALIST.spad" 33066 33087 33416 33431) (-44 "ALGSC.spad" 32201 32227 32938 32991) (-43 "ALGPKG.spad" 27984 27995 32157 32162) (-42 "ALGMFACT.spad" 27177 27191 27974 27979) (-41 "ALGMANIP.spad" 24678 24693 27021 27026) (-40 "ALGFF.spad" 22496 22523 22713 22869) (-39 "ALGFACT.spad" 21615 21625 22486 22491) (-38 "ALGEBRA.spad" 21448 21457 21571 21610) (-37 "ALGEBRA.spad" 21313 21324 21438 21443) (-36 "ALAGG.spad" 20841 20862 21293 21308) (-35 "AHYP.spad" 20222 20229 20831 20836) (-34 "AGG.spad" 19129 19136 20212 20217) (-33 "AGG.spad" 18034 18043 19119 19124) (-32 "AF.spad" 16479 16494 17983 17988) (-31 "ADDAST.spad" 16165 16172 16469 16474) (-30 "ACPLOT.spad" 15042 15049 16155 16160) (-29 "ACFS.spad" 12899 12908 14944 15037) (-28 "ACFS.spad" 10842 10853 12889 12894) (-27 "ACF.spad" 7596 7603 10744 10837) (-26 "ACF.spad" 4436 4445 7586 7591) (-25 "ABELSG.spad" 3977 3984 4426 4431) (-24 "ABELSG.spad" 3516 3525 3967 3972) (-23 "ABELMON.spad" 2944 2951 3506 3511) (-22 "ABELMON.spad" 2370 2379 2934 2939) (-21 "ABELGRP.spad" 2035 2042 2360 2365) (-20 "ABELGRP.spad" 1698 1707 2025 2030) (-19 "A1AGG.spad" 860 869 1678 1693) (-18 "A1AGG.spad" 30 41 850 855)) 
\ No newline at end of file
diff --git a/src/share/algebra/category.daase b/src/share/algebra/category.daase
index 1b8315de..d877b16c 100644
--- a/src/share/algebra/category.daase
+++ b/src/share/algebra/category.daase
@@ -1,299 +1,299 @@
 
-(200981 . 3577992041)        
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199263) ((-1196 . -556) 199212) ((-1196 . -951) 199189) ((-1196 . -583) 199159) ((-1196 . -655) 199129) ((-1196 . -591) 199103) ((-1196 . -589) 199062) ((-1196 . -104) T) ((-1196 . -25) T) ((-1196 . -72) T) ((-1196 . -13) T) ((-1196 . -1130) T) ((-1196 . -553) 199044) ((-1196 . -1014) T) ((-1196 . -23) T) ((-1196 . -21) T) ((-1196 . -969) 199028) ((-1196 . -964) 199012) ((-1196 . -82) 198991) ((-1196 . -1203) 198970) ((-1196 . -962) T) ((-1196 . -664) T) ((-1196 . -1062) T) ((-1196 . -1026) T) ((-1196 . -971) T) ((-1196 . -1195) 198954) ((-1196 . -38) 198924) ((-1196 . -1200) 198903) ((-1194 . -1125) 198872) ((-1194 . -1036) 198856) ((-1194 . -553) 198818) ((-1194 . -124) 198802) ((-1194 . -34) T) ((-1194 . -13) T) ((-1194 . -1130) T) ((-1194 . -72) T) ((-1194 . -260) 198740) ((-1194 . -456) 198673) ((-1194 . -1014) T) ((-1194 . -429) 198657) ((-1194 . -554) 198618) ((-1194 . -318) 198602) ((-1194 . -890) 198571) ((-1193 . -962) T) ((-1193 . -664) T) ((-1193 . -1062) T) ((-1193 . 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((-1183 . -13) T) ((-1183 . -72) T) ((-1180 . -1179) 197972) ((-1180 . -324) 197956) ((-1180 . -760) 197935) ((-1180 . -757) 197914) ((-1180 . -124) 197898) ((-1180 . -554) 197859) ((-1180 . -241) 197811) ((-1180 . -539) 197788) ((-1180 . -243) 197765) ((-1180 . -594) 197749) ((-1180 . -429) 197733) ((-1180 . -1014) 197686) ((-1180 . -456) 197619) ((-1180 . -260) 197557) ((-1180 . -553) 197472) ((-1180 . -72) 197406) ((-1180 . -1130) T) ((-1180 . -13) T) ((-1180 . -34) T) ((-1180 . -318) 197390) ((-1180 . -1036) 197374) ((-1180 . -19) 197358) ((-1177 . -1014) T) ((-1177 . -553) 197324) ((-1177 . -1130) T) ((-1177 . -13) T) ((-1177 . -72) T) ((-1170 . -1173) 197308) ((-1170 . -190) 197267) ((-1170 . -556) 197149) ((-1170 . -591) 197074) ((-1170 . -589) 196984) ((-1170 . -104) T) ((-1170 . -25) T) ((-1170 . -72) T) ((-1170 . -553) 196966) ((-1170 . -1014) T) ((-1170 . -23) T) ((-1170 . -21) T) ((-1170 . -971) T) ((-1170 . -1026) T) ((-1170 . -1062) T) ((-1170 . -664) T) ((-1170 . -962) T) ((-1170 . -186) 196919) ((-1170 . -13) T) ((-1170 . -1130) T) ((-1170 . -189) 196878) ((-1170 . -241) 196843) ((-1170 . -810) 196756) ((-1170 . -807) 196644) ((-1170 . -812) 196557) ((-1170 . -887) 196527) ((-1170 . -38) 196424) ((-1170 . -82) 196289) ((-1170 . -964) 196175) ((-1170 . -969) 196061) ((-1170 . -583) 195958) ((-1170 . -655) 195855) ((-1170 . -118) 195834) ((-1170 . -120) 195813) ((-1170 . -146) 195767) ((-1170 . -496) 195746) ((-1170 . -246) 195725) ((-1170 . -47) 195702) ((-1170 . -1159) 195679) ((-1170 . -35) 195645) ((-1170 . -66) 195611) ((-1170 . -239) 195577) ((-1170 . -433) 195543) ((-1170 . -1119) 195509) ((-1170 . -1116) 195475) ((-1170 . -916) 195441) ((-1167 . -277) 195385) ((-1167 . -951) 195351) ((-1167 . -355) 195317) ((-1167 . -38) 195174) ((-1167 . -556) 195048) ((-1167 . -591) 194937) ((-1167 . -589) 194811) ((-1167 . -971) T) ((-1167 . -1026) T) ((-1167 . -1062) T) ((-1167 . -664) T) ((-1167 . -962) T) ((-1167 . -82) 194661) ((-1167 . -964) 194550) ((-1167 . -969) 194439) ((-1167 . -21) T) ((-1167 . -23) T) ((-1167 . -1014) T) ((-1167 . -553) 194421) ((-1167 . -1130) T) ((-1167 . -13) T) ((-1167 . -72) T) ((-1167 . -25) T) ((-1167 . -104) T) ((-1167 . -583) 194278) ((-1167 . -655) 194135) ((-1167 . -118) 194096) ((-1167 . -120) 194057) ((-1167 . -146) T) ((-1167 . -496) T) ((-1167 . -246) T) ((-1167 . -47) 194001) ((-1166 . -1165) 193980) ((-1166 . -312) 193959) ((-1166 . -1135) 193938) ((-1166 . -833) 193917) ((-1166 . -496) 193871) ((-1166 . -146) 193805) ((-1166 . -556) 193624) ((-1166 . -655) 193471) ((-1166 . -583) 193318) ((-1166 . -38) 193165) ((-1166 . -392) 193144) ((-1166 . -258) 193123) ((-1166 . -591) 193023) ((-1166 . -589) 192908) ((-1166 . -971) T) ((-1166 . -1026) T) ((-1166 . -1062) T) ((-1166 . -664) T) ((-1166 . -962) T) ((-1166 . -82) 192728) ((-1166 . -964) 192569) ((-1166 . -969) 192410) ((-1166 . -21) T) ((-1166 . -23) T) ((-1166 . -1014) T) ((-1166 . -553) 192392) ((-1166 . -1130) T) ((-1166 . -13) T) ((-1166 . -72) T) ((-1166 . -25) T) ((-1166 . -104) T) ((-1166 . -246) 192346) ((-1166 . -201) 192325) ((-1166 . -916) 192291) ((-1166 . -1116) 192257) ((-1166 . -1119) 192223) ((-1166 . -433) 192189) ((-1166 . -239) 192155) ((-1166 . -66) 192121) ((-1166 . -35) 192087) ((-1166 . -1159) 192057) ((-1166 . -47) 192027) ((-1166 . -120) 192006) ((-1166 . -118) 191985) ((-1166 . -887) 191948) ((-1166 . -812) 191854) ((-1166 . -807) 191758) ((-1166 . -810) 191664) ((-1166 . -241) 191622) ((-1166 . -189) 191574) ((-1166 . -186) 191520) ((-1166 . -190) 191472) ((-1166 . -1163) 191456) ((-1166 . -951) 191440) ((-1161 . -1165) 191401) ((-1161 . -312) 191380) ((-1161 . -1135) 191359) ((-1161 . -833) 191338) ((-1161 . -496) 191292) ((-1161 . -146) 191226) ((-1161 . -556) 190975) ((-1161 . -655) 190822) ((-1161 . -583) 190669) ((-1161 . -38) 190516) ((-1161 . -392) 190495) ((-1161 . -258) 190474) ((-1161 . -591) 190374) ((-1161 . -589) 190259) ((-1161 . -971) T) ((-1161 . -1026) T) ((-1161 . -1062) T) ((-1161 . -664) T) ((-1161 . -962) T) ((-1161 . -82) 190079) ((-1161 . -964) 189920) ((-1161 . -969) 189761) ((-1161 . -21) T) ((-1161 . -23) T) ((-1161 . -1014) T) ((-1161 . -553) 189743) ((-1161 . -1130) T) ((-1161 . -13) T) ((-1161 . -72) T) ((-1161 . -25) T) ((-1161 . -104) T) ((-1161 . -246) 189697) ((-1161 . -201) 189676) ((-1161 . -916) 189642) ((-1161 . -1116) 189608) ((-1161 . -1119) 189574) ((-1161 . -433) 189540) ((-1161 . -239) 189506) ((-1161 . -66) 189472) ((-1161 . -35) 189438) ((-1161 . -1159) 189408) ((-1161 . -47) 189378) ((-1161 . -120) 189357) ((-1161 . -118) 189336) ((-1161 . -887) 189299) ((-1161 . -812) 189205) ((-1161 . -807) 189086) ((-1161 . -810) 188992) ((-1161 . -241) 188950) ((-1161 . -189) 188902) ((-1161 . -186) 188848) ((-1161 . -190) 188800) ((-1161 . -1163) 188784) ((-1161 . -951) 188719) ((-1149 . -1156) 188703) ((-1149 . -1067) 188681) ((-1149 . -554) NIL) ((-1149 . -260) 188668) ((-1149 . -456) 188616) ((-1149 . -277) 188593) ((-1149 . -951) 188476) ((-1149 . -355) 188460) ((-1149 . -38) 188292) ((-1149 . -82) 188097) ((-1149 . -964) 187923) ((-1149 . -969) 187749) ((-1149 . -589) 187659) ((-1149 . -591) 187548) ((-1149 . -583) 187380) ((-1149 . -655) 187212) ((-1149 . -556) 186968) ((-1149 . -118) 186947) ((-1149 . -120) 186926) ((-1149 . -47) 186903) ((-1149 . -329) 186887) ((-1149 . -581) 186835) ((-1149 . -810) 186779) ((-1149 . -807) 186686) ((-1149 . -812) 186597) ((-1149 . -797) NIL) ((-1149 . -822) 186576) ((-1149 . -1135) 186555) ((-1149 . -862) 186525) ((-1149 . -833) 186504) ((-1149 . -496) 186418) ((-1149 . -246) 186332) ((-1149 . -146) 186226) ((-1149 . -392) 186160) ((-1149 . -258) 186139) ((-1149 . -241) 186066) ((-1149 . -190) T) ((-1149 . -104) T) ((-1149 . -25) T) ((-1149 . -72) T) ((-1149 . -553) 186048) ((-1149 . -1014) T) ((-1149 . -23) T) ((-1149 . -21) T) ((-1149 . -971) T) ((-1149 . -1026) T) ((-1149 . -1062) T) ((-1149 . -664) T) ((-1149 . -962) T) ((-1149 . -186) 186035) ((-1149 . -13) T) ((-1149 . -1130) T) ((-1149 . -189) T) ((-1149 . -225) 186019) ((-1149 . -184) 186003) ((-1147 . -1007) 185987) ((-1147 . -558) 185971) ((-1147 . -1014) 185949) ((-1147 . -553) 185916) ((-1147 . -1130) 185894) ((-1147 . -13) 185872) ((-1147 . -72) 185850) ((-1147 . -1008) 185807) ((-1145 . -1144) 185786) ((-1145 . -916) 185752) ((-1145 . -1116) 185718) ((-1145 . -1119) 185684) ((-1145 . -433) 185650) ((-1145 . -239) 185616) ((-1145 . -66) 185582) ((-1145 . -35) 185548) ((-1145 . -1159) 185525) ((-1145 . -47) 185502) ((-1145 . -556) 185257) ((-1145 . -655) 185077) ((-1145 . -583) 184897) ((-1145 . -591) 184708) ((-1145 . -589) 184566) ((-1145 . -969) 184380) ((-1145 . -964) 184194) ((-1145 . -82) 183982) ((-1145 . -38) 183802) ((-1145 . -887) 183772) ((-1145 . -241) 183672) ((-1145 . -1142) 183656) ((-1145 . -971) T) ((-1145 . -1026) T) ((-1145 . -1062) T) ((-1145 . -664) T) ((-1145 . -962) T) ((-1145 . -21) T) ((-1145 . -23) T) ((-1145 . -1014) T) ((-1145 . -553) 183638) ((-1145 . -1130) T) ((-1145 . -13) T) ((-1145 . -72) T) ((-1145 . -25) T) ((-1145 . -104) T) ((-1145 . -118) 183566) ((-1145 . -120) 183448) ((-1145 . -554) 183121) ((-1145 . -184) 183091) ((-1145 . -810) 182945) ((-1145 . -812) 182745) ((-1145 . -807) 182543) ((-1145 . -225) 182513) ((-1145 . -189) 182375) ((-1145 . -186) 182231) ((-1145 . -190) 182139) ((-1145 . -312) 182118) ((-1145 . -1135) 182097) ((-1145 . -833) 182076) ((-1145 . -496) 182030) ((-1145 . -146) 181964) ((-1145 . -392) 181943) ((-1145 . -258) 181922) ((-1145 . -246) 181876) ((-1145 . -201) 181855) ((-1145 . -288) 181825) ((-1145 . -456) 181685) ((-1145 . -260) 181624) ((-1145 . -329) 181594) ((-1145 . -581) 181502) ((-1145 . -343) 181472) ((-1145 . -797) 181345) ((-1145 . -741) 181298) ((-1145 . -715) 181251) ((-1145 . -717) 181204) ((-1145 . -757) 181106) ((-1145 . -760) 181008) ((-1145 . -719) 180961) ((-1145 . -722) 180914) ((-1145 . -756) 180867) ((-1145 . -795) 180837) ((-1145 . -822) 180790) ((-1145 . -934) 180743) ((-1145 . -951) 180532) ((-1145 . -1067) 180484) ((-1145 . -905) 180454) ((-1140 . -1144) 180415) ((-1140 . -916) 180381) ((-1140 . -1116) 180347) ((-1140 . -1119) 180313) ((-1140 . -433) 180279) ((-1140 . -239) 180245) ((-1140 . -66) 180211) ((-1140 . -35) 180177) ((-1140 . -1159) 180154) ((-1140 . -47) 180131) ((-1140 . -556) 179932) ((-1140 . -655) 179734) ((-1140 . -583) 179536) ((-1140 . -591) 179391) ((-1140 . -589) 179231) ((-1140 . -969) 179027) ((-1140 . -964) 178823) ((-1140 . -82) 178575) ((-1140 . -38) 178377) ((-1140 . -887) 178347) ((-1140 . -241) 178175) ((-1140 . -1142) 178159) ((-1140 . -971) T) ((-1140 . -1026) T) ((-1140 . -1062) T) ((-1140 . -664) T) ((-1140 . -962) T) ((-1140 . -21) T) ((-1140 . -23) T) ((-1140 . -1014) T) ((-1140 . -553) 178141) ((-1140 . -1130) T) ((-1140 . -13) T) ((-1140 . -72) T) ((-1140 . -25) T) ((-1140 . -104) T) ((-1140 . -118) 178051) ((-1140 . -120) 177961) ((-1140 . -554) NIL) ((-1140 . -184) 177913) ((-1140 . -810) 177749) ((-1140 . -812) 177513) ((-1140 . -807) 177252) ((-1140 . -225) 177204) ((-1140 . -189) 177030) ((-1140 . -186) 176850) ((-1140 . -190) 176740) ((-1140 . -312) 176719) ((-1140 . -1135) 176698) ((-1140 . -833) 176677) ((-1140 . -496) 176631) ((-1140 . -146) 176565) ((-1140 . -392) 176544) ((-1140 . -258) 176523) ((-1140 . -246) 176477) ((-1140 . -201) 176456) ((-1140 . -288) 176408) ((-1140 . -456) 176142) ((-1140 . -260) 176027) ((-1140 . -329) 175979) ((-1140 . -581) 175931) ((-1140 . -343) 175883) ((-1140 . -797) NIL) ((-1140 . -741) NIL) ((-1140 . -715) NIL) ((-1140 . -717) NIL) ((-1140 . -757) NIL) ((-1140 . -760) NIL) ((-1140 . -719) NIL) ((-1140 . -722) NIL) ((-1140 . -756) NIL) ((-1140 . -795) 175835) ((-1140 . -822) NIL) ((-1140 . -934) NIL) ((-1140 . -951) 175801) ((-1140 . -1067) NIL) ((-1140 . -905) 175753) ((-1139 . -753) T) ((-1139 . -760) T) ((-1139 . -757) T) ((-1139 . -1014) T) ((-1139 . -553) 175735) ((-1139 . -1130) T) ((-1139 . -13) T) ((-1139 . -72) T) ((-1139 . -320) T) ((-1139 . -605) T) ((-1138 . -753) T) ((-1138 . -760) T) ((-1138 . -757) T) ((-1138 . -1014) T) ((-1138 . -553) 175717) ((-1138 . -1130) T) ((-1138 . -13) T) ((-1138 . -72) T) ((-1138 . -320) T) ((-1138 . -605) T) ((-1137 . -753) T) ((-1137 . -760) T) ((-1137 . -757) T) ((-1137 . -1014) T) ((-1137 . -553) 175699) ((-1137 . -1130) T) ((-1137 . -13) T) ((-1137 . -72) T) ((-1137 . -320) T) ((-1137 . -605) T) ((-1136 . -753) T) ((-1136 . -760) T) ((-1136 . -757) T) ((-1136 . -1014) T) ((-1136 . -553) 175681) ((-1136 . -1130) T) ((-1136 . -13) T) ((-1136 . -72) T) ((-1136 . -320) T) ((-1136 . -605) T) ((-1131 . -996) T) ((-1131 . -430) 175662) ((-1131 . -553) 175628) ((-1131 . -556) 175609) ((-1131 . -1014) T) ((-1131 . -1130) T) ((-1131 . -13) T) ((-1131 . -72) T) ((-1131 . -64) T) ((-1128 . -430) 175586) ((-1128 . -553) 175527) ((-1128 . -556) 175504) ((-1128 . -1014) 175482) ((-1128 . -1130) 175460) ((-1128 . -13) 175438) ((-1128 . -72) 175416) ((-1123 . -680) 175392) ((-1123 . -35) 175358) ((-1123 . -66) 175324) ((-1123 . -239) 175290) ((-1123 . -433) 175256) ((-1123 . -1119) 175222) ((-1123 . -1116) 175188) ((-1123 . -916) 175154) ((-1123 . -47) 175123) ((-1123 . -38) 175020) ((-1123 . -583) 174917) ((-1123 . -655) 174814) ((-1123 . -556) 174696) ((-1123 . -246) 174675) ((-1123 . -496) 174654) ((-1123 . -82) 174519) ((-1123 . -964) 174405) ((-1123 . -969) 174291) ((-1123 . -146) 174245) ((-1123 . -120) 174224) ((-1123 . -118) 174203) ((-1123 . -591) 174128) ((-1123 . -589) 174038) ((-1123 . -887) 173999) ((-1123 . -812) 173980) ((-1123 . -1130) T) ((-1123 . -13) T) ((-1123 . -807) 173959) ((-1123 . -962) T) ((-1123 . -664) T) ((-1123 . -1062) T) ((-1123 . -1026) T) ((-1123 . -971) T) ((-1123 . -21) T) ((-1123 . -23) T) ((-1123 . -1014) T) ((-1123 . -553) 173941) ((-1123 . -72) T) ((-1123 . -25) T) ((-1123 . -104) T) ((-1123 . -810) 173922) ((-1123 . -456) 173889) ((-1123 . -260) 173876) ((-1117 . -924) 173860) ((-1117 . -34) T) ((-1117 . -13) T) ((-1117 . -1130) T) ((-1117 . -72) 173814) ((-1117 . -553) 173749) ((-1117 . -260) 173687) ((-1117 . -456) 173620) ((-1117 . -1014) 173598) ((-1117 . -429) 173582) ((-1117 . -318) 173566) ((-1117 . -1036) 173550) ((-1112 . -314) 173524) ((-1112 . -72) T) ((-1112 . -13) T) ((-1112 . -1130) T) ((-1112 . -553) 173506) ((-1112 . -1014) T) ((-1110 . -1014) T) ((-1110 . -553) 173488) ((-1110 . -1130) T) ((-1110 . -13) T) ((-1110 . -72) T) ((-1110 . -556) 173470) ((-1105 . -748) 173454) ((-1105 . -72) T) ((-1105 . -13) T) ((-1105 . -1130) T) ((-1105 . -553) 173436) ((-1105 . -1014) T) ((-1103 . -1108) 173415) ((-1103 . -183) 173363) ((-1103 . -76) 173311) ((-1103 . -1036) 173259) ((-1103 . -124) 173207) ((-1103 . -554) NIL) ((-1103 . -193) 173155) ((-1103 . -539) 173134) ((-1103 . -260) 172932) ((-1103 . -456) 172684) ((-1103 . -429) 172619) ((-1103 . -241) 172598) ((-1103 . -243) 172577) ((-1103 . -550) 172556) ((-1103 . -1014) T) ((-1103 . -553) 172538) ((-1103 . -72) T) ((-1103 . -1130) T) ((-1103 . -13) T) ((-1103 . -34) T) ((-1103 . -318) 172486) ((-1099 . -1014) T) ((-1099 . -553) 172468) ((-1099 . -1130) T) ((-1099 . -13) T) ((-1099 . -72) T) ((-1098 . -753) T) ((-1098 . -760) T) ((-1098 . -757) T) ((-1098 . -1014) T) ((-1098 . -553) 172450) ((-1098 . -1130) T) ((-1098 . -13) T) ((-1098 . -72) T) ((-1098 . -320) T) ((-1098 . -605) T) ((-1097 . -753) T) ((-1097 . -760) T) ((-1097 . -757) T) ((-1097 . -1014) T) ((-1097 . -553) 172432) ((-1097 . -1130) T) ((-1097 . -13) T) ((-1097 . -72) T) ((-1097 . -320) T) ((-1096 . -1176) T) ((-1096 . -1014) T) ((-1096 . -553) 172399) ((-1096 . -1130) T) ((-1096 . -13) T) ((-1096 . -72) T) ((-1096 . -951) 172335) ((-1096 . -556) 172271) ((-1095 . -553) 172253) ((-1094 . -553) 172235) ((-1093 . -277) 172212) ((-1093 . -951) 172110) ((-1093 . -355) 172094) ((-1093 . -38) 171991) ((-1093 . -556) 171848) ((-1093 . -591) 171773) ((-1093 . -589) 171683) ((-1093 . -971) T) ((-1093 . -1026) T) ((-1093 . -1062) T) ((-1093 . -664) T) ((-1093 . -962) T) ((-1093 . -82) 171548) ((-1093 . -964) 171434) ((-1093 . -969) 171320) ((-1093 . -21) T) ((-1093 . -23) T) ((-1093 . -1014) T) ((-1093 . -553) 171302) ((-1093 . -1130) T) ((-1093 . -13) T) ((-1093 . -72) T) ((-1093 . -25) T) ((-1093 . -104) T) ((-1093 . -583) 171199) ((-1093 . -655) 171096) ((-1093 . -118) 171075) ((-1093 . -120) 171054) ((-1093 . -146) 171008) ((-1093 . -496) 170987) ((-1093 . -246) 170966) ((-1093 . -47) 170943) ((-1091 . -757) T) ((-1091 . -553) 170925) ((-1091 . -1014) T) ((-1091 . -72) T) ((-1091 . -13) T) ((-1091 . -1130) T) ((-1091 . -760) T) ((-1091 . -554) 170847) ((-1091 . -556) 170813) ((-1091 . -951) 170795) ((-1091 . -797) 170762) ((-1090 . -1173) 170746) ((-1090 . -190) 170705) ((-1090 . -556) 170587) ((-1090 . -591) 170512) ((-1090 . -589) 170422) ((-1090 . -104) T) ((-1090 . -25) T) ((-1090 . -72) T) ((-1090 . -553) 170404) ((-1090 . -1014) T) ((-1090 . -23) T) ((-1090 . -21) T) ((-1090 . -971) T) ((-1090 . -1026) T) ((-1090 . -1062) T) ((-1090 . -664) T) ((-1090 . -962) T) ((-1090 . -186) 170357) ((-1090 . -13) T) ((-1090 . -1130) T) ((-1090 . -189) 170316) ((-1090 . -241) 170281) ((-1090 . -810) 170194) ((-1090 . -807) 170082) ((-1090 . -812) 169995) ((-1090 . -887) 169965) ((-1090 . -38) 169862) ((-1090 . -82) 169727) ((-1090 . -964) 169613) ((-1090 . -969) 169499) ((-1090 . -583) 169396) ((-1090 . -655) 169293) ((-1090 . -118) 169272) ((-1090 . -120) 169251) ((-1090 . -146) 169205) ((-1090 . -496) 169184) ((-1090 . -246) 169163) ((-1090 . -47) 169140) ((-1090 . -1159) 169117) ((-1090 . -35) 169083) ((-1090 . -66) 169049) ((-1090 . -239) 169015) ((-1090 . -433) 168981) ((-1090 . -1119) 168947) ((-1090 . -1116) 168913) ((-1090 . -916) 168879) ((-1089 . -1165) 168840) ((-1089 . -312) 168819) ((-1089 . -1135) 168798) ((-1089 . -833) 168777) ((-1089 . -496) 168731) ((-1089 . -146) 168665) ((-1089 . -556) 168414) ((-1089 . -655) 168261) ((-1089 . -583) 168108) ((-1089 . -38) 167955) ((-1089 . -392) 167934) ((-1089 . -258) 167913) ((-1089 . -591) 167813) ((-1089 . -589) 167698) ((-1089 . -971) T) ((-1089 . -1026) T) ((-1089 . -1062) T) ((-1089 . -664) T) ((-1089 . -962) T) ((-1089 . -82) 167518) ((-1089 . -964) 167359) ((-1089 . -969) 167200) ((-1089 . -21) T) ((-1089 . -23) T) ((-1089 . -1014) T) ((-1089 . -553) 167182) ((-1089 . -1130) T) ((-1089 . -13) T) ((-1089 . -72) T) ((-1089 . -25) T) ((-1089 . -104) T) ((-1089 . -246) 167136) ((-1089 . -201) 167115) ((-1089 . -916) 167081) ((-1089 . -1116) 167047) ((-1089 . -1119) 167013) ((-1089 . -433) 166979) ((-1089 . -239) 166945) ((-1089 . -66) 166911) ((-1089 . -35) 166877) ((-1089 . -1159) 166847) ((-1089 . -47) 166817) ((-1089 . -120) 166796) ((-1089 . -118) 166775) ((-1089 . -887) 166738) ((-1089 . -812) 166644) ((-1089 . -807) 166525) ((-1089 . -810) 166431) ((-1089 . -241) 166389) ((-1089 . -189) 166341) ((-1089 . -186) 166287) ((-1089 . -190) 166239) ((-1089 . -1163) 166223) ((-1089 . -951) 166158) ((-1086 . -1156) 166142) ((-1086 . -1067) 166120) ((-1086 . -554) NIL) ((-1086 . -260) 166107) ((-1086 . -456) 166055) ((-1086 . -277) 166032) ((-1086 . -951) 165915) ((-1086 . -355) 165899) ((-1086 . -38) 165731) ((-1086 . -82) 165536) ((-1086 . -964) 165362) ((-1086 . -969) 165188) ((-1086 . -589) 165098) ((-1086 . -591) 164987) ((-1086 . -583) 164819) ((-1086 . -655) 164651) ((-1086 . -556) 164428) ((-1086 . -118) 164407) ((-1086 . -120) 164386) ((-1086 . -47) 164363) ((-1086 . -329) 164347) ((-1086 . -581) 164295) ((-1086 . -810) 164239) ((-1086 . -807) 164146) ((-1086 . -812) 164057) ((-1086 . -797) NIL) ((-1086 . -822) 164036) ((-1086 . -1135) 164015) ((-1086 . -862) 163985) ((-1086 . -833) 163964) ((-1086 . -496) 163878) ((-1086 . -246) 163792) ((-1086 . -146) 163686) ((-1086 . -392) 163620) ((-1086 . -258) 163599) ((-1086 . -241) 163526) ((-1086 . -190) T) ((-1086 . -104) T) ((-1086 . -25) T) ((-1086 . -72) T) ((-1086 . -553) 163508) ((-1086 . -1014) T) ((-1086 . -23) T) ((-1086 . -21) T) ((-1086 . -971) T) ((-1086 . -1026) T) ((-1086 . -1062) T) ((-1086 . -664) T) ((-1086 . -962) T) ((-1086 . -186) 163495) ((-1086 . -13) T) ((-1086 . -1130) T) ((-1086 . -189) T) ((-1086 . -225) 163479) ((-1086 . -184) 163463) ((-1083 . -1144) 163424) ((-1083 . -916) 163390) ((-1083 . -1116) 163356) ((-1083 . -1119) 163322) ((-1083 . -433) 163288) ((-1083 . -239) 163254) ((-1083 . -66) 163220) ((-1083 . -35) 163186) ((-1083 . -1159) 163163) ((-1083 . -47) 163140) ((-1083 . -556) 162941) ((-1083 . -655) 162743) ((-1083 . -583) 162545) ((-1083 . -591) 162400) ((-1083 . -589) 162240) ((-1083 . -969) 162036) ((-1083 . -964) 161832) ((-1083 . -82) 161584) ((-1083 . -38) 161386) ((-1083 . -887) 161356) ((-1083 . -241) 161184) ((-1083 . -1142) 161168) ((-1083 . -971) T) ((-1083 . -1026) T) ((-1083 . -1062) T) ((-1083 . -664) T) ((-1083 . -962) T) ((-1083 . -21) T) ((-1083 . -23) T) ((-1083 . -1014) T) ((-1083 . -553) 161150) ((-1083 . -1130) T) ((-1083 . -13) T) ((-1083 . -72) T) ((-1083 . -25) T) ((-1083 . -104) T) ((-1083 . -118) 161060) ((-1083 . -120) 160970) ((-1083 . -554) NIL) ((-1083 . -184) 160922) ((-1083 . -810) 160758) ((-1083 . -812) 160522) ((-1083 . -807) 160261) ((-1083 . -225) 160213) ((-1083 . -189) 160039) ((-1083 . -186) 159859) ((-1083 . -190) 159749) ((-1083 . -312) 159728) ((-1083 . -1135) 159707) ((-1083 . -833) 159686) ((-1083 . -496) 159640) ((-1083 . -146) 159574) ((-1083 . -392) 159553) ((-1083 . -258) 159532) ((-1083 . -246) 159486) ((-1083 . -201) 159465) ((-1083 . -288) 159417) ((-1083 . -456) 159151) ((-1083 . -260) 159036) ((-1083 . -329) 158988) ((-1083 . -581) 158940) ((-1083 . -343) 158892) ((-1083 . -797) NIL) ((-1083 . -741) NIL) ((-1083 . -715) NIL) ((-1083 . -717) NIL) ((-1083 . -757) NIL) ((-1083 . -760) NIL) ((-1083 . -719) NIL) ((-1083 . -722) NIL) ((-1083 . -756) NIL) ((-1083 . -795) 158844) ((-1083 . -822) NIL) ((-1083 . -934) NIL) ((-1083 . -951) 158810) ((-1083 . -1067) NIL) ((-1083 . -905) 158762) ((-1082 . -996) T) ((-1082 . -430) 158743) ((-1082 . -553) 158709) ((-1082 . -556) 158690) ((-1082 . -1014) T) ((-1082 . -1130) T) ((-1082 . -13) T) ((-1082 . -72) T) ((-1082 . -64) T) ((-1081 . -1014) T) ((-1081 . -553) 158672) ((-1081 . -1130) T) ((-1081 . -13) T) ((-1081 . -72) T) ((-1080 . -1014) T) ((-1080 . -553) 158654) ((-1080 . -1130) T) ((-1080 . -13) T) ((-1080 . -72) T) ((-1075 . -1108) 158630) ((-1075 . -183) 158575) ((-1075 . -76) 158520) ((-1075 . -1036) 158465) ((-1075 . -124) 158410) ((-1075 . -554) NIL) ((-1075 . -193) 158355) ((-1075 . -539) 158331) ((-1075 . -260) 158120) ((-1075 . -456) 157860) ((-1075 . -429) 157792) ((-1075 . -241) 157768) ((-1075 . -243) 157744) ((-1075 . -550) 157720) ((-1075 . -1014) T) ((-1075 . -553) 157702) ((-1075 . -72) T) ((-1075 . -1130) T) ((-1075 . -13) T) ((-1075 . -34) T) ((-1075 . -318) 157647) ((-1074 . -1059) T) ((-1074 . -324) 157629) ((-1074 . -760) T) ((-1074 . -757) T) ((-1074 . -124) 157611) ((-1074 . -554) NIL) ((-1074 . -241) 157561) ((-1074 . -539) 157536) ((-1074 . -243) 157511) ((-1074 . -594) 157493) ((-1074 . -429) 157475) ((-1074 . -1014) T) ((-1074 . -456) NIL) ((-1074 . -260) NIL) ((-1074 . -553) 157457) ((-1074 . -72) T) ((-1074 . -1130) T) ((-1074 . -13) T) ((-1074 . -34) T) ((-1074 . -318) 157439) ((-1074 . -1036) 157421) ((-1074 . -19) 157403) ((-1070 . -617) 157387) ((-1070 . -594) 157371) ((-1070 . -243) 157348) ((-1070 . -241) 157300) ((-1070 . -539) 157277) ((-1070 . -554) 157238) ((-1070 . -429) 157222) ((-1070 . -1014) 157200) ((-1070 . -456) 157133) ((-1070 . -260) 157071) ((-1070 . -553) 157006) ((-1070 . -72) 156960) ((-1070 . -1130) T) ((-1070 . -13) T) ((-1070 . -34) T) ((-1070 . -124) 156944) ((-1070 . -1169) 156928) ((-1070 . -924) 156912) ((-1070 . -1065) 156896) ((-1070 . -556) 156873) ((-1070 . -1036) 156857) ((-1068 . -996) T) ((-1068 . -430) 156838) ((-1068 . -553) 156804) ((-1068 . -556) 156785) ((-1068 . -1014) T) ((-1068 . -1130) T) ((-1068 . -13) T) ((-1068 . -72) T) ((-1068 . -64) T) ((-1066 . -1108) 156764) ((-1066 . -183) 156712) ((-1066 . -76) 156660) ((-1066 . -1036) 156608) ((-1066 . -124) 156556) ((-1066 . -554) NIL) ((-1066 . -193) 156504) ((-1066 . -539) 156483) ((-1066 . -260) 156281) ((-1066 . -456) 156033) ((-1066 . -429) 155968) ((-1066 . -241) 155947) ((-1066 . -243) 155926) ((-1066 . -550) 155905) ((-1066 . -1014) T) ((-1066 . -553) 155887) ((-1066 . -72) T) ((-1066 . -1130) T) ((-1066 . -13) T) ((-1066 . -34) T) ((-1066 . -318) 155835) ((-1063 . -1035) 155819) ((-1063 . -318) 155803) ((-1063 . -1036) 155787) ((-1063 . -34) T) ((-1063 . -13) T) ((-1063 . -1130) T) ((-1063 . -72) 155741) ((-1063 . -553) 155676) ((-1063 . -260) 155614) ((-1063 . -456) 155547) ((-1063 . -1014) 155525) ((-1063 . -429) 155509) ((-1063 . -76) 155493) ((-1061 . -1021) 155462) ((-1061 . -1125) 155431) ((-1061 . -1036) 155415) ((-1061 . -553) 155377) ((-1061 . -124) 155361) ((-1061 . -34) T) ((-1061 . -13) T) ((-1061 . -1130) T) ((-1061 . -72) T) ((-1061 . -260) 155299) ((-1061 . -456) 155232) ((-1061 . -1014) T) ((-1061 . -429) 155216) ((-1061 . -554) 155177) ((-1061 . -318) 155161) ((-1061 . -890) 155130) ((-1061 . -984) 155099) ((-1057 . -1038) 155044) ((-1057 . -318) 155028) ((-1057 . -34) T) ((-1057 . -260) 154966) ((-1057 . -456) 154899) ((-1057 . -429) 154883) ((-1057 . -966) 154823) ((-1057 . -951) 154721) ((-1057 . -556) 154640) ((-1057 . -355) 154624) ((-1057 . -581) 154572) ((-1057 . -591) 154510) ((-1057 . -329) 154494) ((-1057 . -190) 154473) ((-1057 . -186) 154421) ((-1057 . -189) 154375) ((-1057 . -225) 154359) ((-1057 . -807) 154283) ((-1057 . -812) 154209) ((-1057 . -810) 154168) ((-1057 . -184) 154152) ((-1057 . -655) 154087) ((-1057 . -583) 154022) ((-1057 . -589) 153981) ((-1057 . -104) T) ((-1057 . -25) T) ((-1057 . -72) T) ((-1057 . -13) T) ((-1057 . -1130) T) ((-1057 . -553) 153943) ((-1057 . -1014) T) ((-1057 . -23) T) ((-1057 . -21) T) ((-1057 . -969) 153927) ((-1057 . -964) 153911) ((-1057 . -82) 153890) ((-1057 . -962) T) ((-1057 . -664) T) ((-1057 . -1062) T) ((-1057 . -1026) T) ((-1057 . -971) T) ((-1057 . -38) 153850) ((-1057 . -554) 153811) ((-1056 . -924) 153782) ((-1056 . -34) T) ((-1056 . -13) T) ((-1056 . -1130) T) ((-1056 . -72) T) ((-1056 . -553) 153764) ((-1056 . -260) 153690) ((-1056 . -456) 153598) ((-1056 . -1014) T) ((-1056 . -429) 153569) ((-1056 . -318) 153540) ((-1056 . -1036) 153511) ((-1055 . -1014) T) ((-1055 . -553) 153493) ((-1055 . -1130) T) ((-1055 . -13) T) ((-1055 . -72) T) ((-1050 . -1052) T) ((-1050 . -1176) T) ((-1050 . -64) T) ((-1050 . -72) T) ((-1050 . -13) T) ((-1050 . -1130) T) ((-1050 . -553) 153459) ((-1050 . -1014) T) ((-1050 . -556) 153440) ((-1050 . -430) 153421) ((-1050 . -996) T) ((-1048 . -1049) 153405) ((-1048 . -72) T) ((-1048 . -13) T) ((-1048 . -1130) T) ((-1048 . -553) 153387) ((-1048 . -1014) T) ((-1041 . -680) 153366) ((-1041 . -35) 153332) ((-1041 . -66) 153298) ((-1041 . -239) 153264) ((-1041 . -433) 153230) ((-1041 . -1119) 153196) ((-1041 . -1116) 153162) ((-1041 . -916) 153128) ((-1041 . -47) 153100) ((-1041 . -38) 152997) ((-1041 . -583) 152894) ((-1041 . -655) 152791) ((-1041 . -556) 152673) ((-1041 . -246) 152652) ((-1041 . -496) 152631) ((-1041 . -82) 152496) ((-1041 . -964) 152382) ((-1041 . -969) 152268) ((-1041 . -146) 152222) ((-1041 . -120) 152201) ((-1041 . -118) 152180) ((-1041 . -591) 152105) ((-1041 . -589) 152015) ((-1041 . -887) 151982) ((-1041 . -812) 151966) ((-1041 . -1130) T) ((-1041 . -13) T) ((-1041 . -807) 151948) ((-1041 . -962) T) ((-1041 . -664) T) ((-1041 . -1062) T) ((-1041 . -1026) T) ((-1041 . -971) T) ((-1041 . -21) T) ((-1041 . -23) T) ((-1041 . -1014) T) ((-1041 . -553) 151930) ((-1041 . -72) T) ((-1041 . -25) T) ((-1041 . -104) T) ((-1041 . -810) 151914) ((-1041 . -456) 151884) ((-1041 . -260) 151871) ((-1040 . -862) 151838) ((-1040 . -556) 151637) ((-1040 . -951) 151522) ((-1040 . -1135) 151501) ((-1040 . -822) 151480) ((-1040 . -797) 151339) ((-1040 . -812) 151323) ((-1040 . -807) 151305) ((-1040 . -810) 151289) ((-1040 . -456) 151241) ((-1040 . -392) 151195) ((-1040 . -581) 151143) ((-1040 . -591) 151032) ((-1040 . -329) 151016) ((-1040 . -47) 150988) ((-1040 . -38) 150840) ((-1040 . -583) 150692) ((-1040 . -655) 150544) ((-1040 . -246) 150478) ((-1040 . -496) 150412) ((-1040 . -82) 150237) ((-1040 . -964) 150083) ((-1040 . -969) 149929) ((-1040 . -146) 149843) ((-1040 . -120) 149822) ((-1040 . -118) 149801) ((-1040 . -589) 149711) ((-1040 . -104) T) ((-1040 . -25) T) ((-1040 . -72) T) ((-1040 . -13) T) ((-1040 . -1130) T) ((-1040 . -553) 149693) ((-1040 . -1014) T) ((-1040 . -23) T) ((-1040 . -21) T) ((-1040 . -962) T) ((-1040 . -664) T) ((-1040 . -1062) T) ((-1040 . -1026) T) ((-1040 . -971) T) ((-1040 . -355) 149677) ((-1040 . -277) 149649) ((-1040 . -260) 149636) ((-1040 . -554) 149384) ((-1034 . -484) T) ((-1034 . -1135) T) ((-1034 . -1067) T) ((-1034 . -951) 149366) ((-1034 . -554) 149281) ((-1034 . -934) T) ((-1034 . -797) 149263) ((-1034 . -756) T) ((-1034 . -722) T) ((-1034 . -719) T) ((-1034 . -760) T) ((-1034 . -757) T) ((-1034 . -717) T) ((-1034 . -715) T) ((-1034 . -741) T) ((-1034 . -591) 149235) ((-1034 . -581) 149217) ((-1034 . -833) T) ((-1034 . -496) T) ((-1034 . -246) T) ((-1034 . -146) T) ((-1034 . -556) 149189) ((-1034 . -655) 149176) ((-1034 . -583) 149163) ((-1034 . -969) 149150) ((-1034 . -964) 149137) ((-1034 . -82) 149122) ((-1034 . -38) 149109) ((-1034 . -392) T) ((-1034 . -258) T) ((-1034 . -189) T) ((-1034 . -186) 149096) ((-1034 . -190) T) ((-1034 . -116) T) ((-1034 . -962) T) ((-1034 . -664) T) ((-1034 . -1062) T) ((-1034 . -1026) T) ((-1034 . -971) T) ((-1034 . -21) T) ((-1034 . -589) 149068) ((-1034 . -23) T) ((-1034 . -1014) T) ((-1034 . -553) 149050) ((-1034 . -1130) T) ((-1034 . -13) T) ((-1034 . -72) T) ((-1034 . -25) T) ((-1034 . -104) T) ((-1034 . -120) T) ((-1034 . -753) T) ((-1034 . -320) T) ((-1034 . -84) T) ((-1034 . -605) T) ((-1030 . -996) T) ((-1030 . -430) 149031) ((-1030 . -553) 148997) ((-1030 . -556) 148978) ((-1030 . -1014) T) ((-1030 . -1130) T) ((-1030 . -13) T) ((-1030 . -72) T) ((-1030 . -64) T) ((-1029 . -1014) T) ((-1029 . -553) 148960) ((-1029 . -1130) T) ((-1029 . -13) T) ((-1029 . -72) T) ((-1027 . -196) 148939) ((-1027 . -1188) 148909) ((-1027 . -722) 148888) ((-1027 . -719) 148867) ((-1027 . -760) 148821) ((-1027 . -757) 148775) ((-1027 . -717) 148754) ((-1027 . -718) 148733) ((-1027 . -655) 148678) ((-1027 . -583) 148603) ((-1027 . -243) 148580) ((-1027 . -241) 148557) ((-1027 . -539) 148534) ((-1027 . -951) 148363) ((-1027 . -556) 148167) ((-1027 . -355) 148136) ((-1027 . -581) 148044) ((-1027 . -591) 147883) ((-1027 . -329) 147853) ((-1027 . -429) 147837) ((-1027 . -456) 147770) ((-1027 . -260) 147708) ((-1027 . -34) T) ((-1027 . -318) 147692) ((-1027 . -320) 147671) ((-1027 . -190) 147624) ((-1027 . -589) 147412) ((-1027 . -971) 147391) ((-1027 . -1026) 147370) ((-1027 . -1062) 147349) ((-1027 . -664) 147328) ((-1027 . -962) 147307) ((-1027 . -186) 147203) ((-1027 . -189) 147105) ((-1027 . -225) 147075) ((-1027 . -807) 146947) ((-1027 . -812) 146821) ((-1027 . -810) 146754) ((-1027 . -184) 146724) ((-1027 . -553) 146421) ((-1027 . -969) 146346) ((-1027 . -964) 146251) ((-1027 . -82) 146171) ((-1027 . -104) 146046) ((-1027 . -25) 145883) ((-1027 . -72) 145620) ((-1027 . -13) T) ((-1027 . -1130) T) ((-1027 . -1014) 145376) ((-1027 . -23) 145232) ((-1027 . -21) 145147) ((-1023 . -1024) 145131) ((-1023 . |MappingCategory|) 145105) ((-1023 . -1130) T) ((-1023 . -80) 145089) ((-1023 . -1014) T) ((-1023 . -553) 145071) ((-1023 . -13) T) ((-1023 . -72) T) ((-1018 . -1017) 145035) ((-1018 . -72) T) ((-1018 . -553) 145017) ((-1018 . -1014) T) ((-1018 . -241) 144973) ((-1018 . -1130) T) ((-1018 . -13) T) ((-1018 . -558) 144888) ((-1016 . -1017) 144840) ((-1016 . -72) T) ((-1016 . -553) 144822) ((-1016 . -1014) T) ((-1016 . -241) 144778) ((-1016 . -1130) T) ((-1016 . -13) T) ((-1016 . -558) 144681) ((-1015 . -320) T) ((-1015 . -72) T) ((-1015 . -13) T) ((-1015 . -1130) T) ((-1015 . -553) 144663) ((-1015 . -1014) T) ((-1010 . -369) 144647) ((-1010 . -1012) 144631) ((-1010 . -318) 144615) ((-1010 . -320) 144594) ((-1010 . -193) 144578) ((-1010 . -554) 144539) ((-1010 . -124) 144523) ((-1010 . -1036) 144507) ((-1010 . -34) T) ((-1010 . -13) T) ((-1010 . -1130) T) ((-1010 . -72) T) ((-1010 . -553) 144489) ((-1010 . -260) 144427) ((-1010 . -456) 144360) ((-1010 . -1014) T) ((-1010 . -429) 144344) ((-1010 . -76) 144328) ((-1010 . -183) 144312) ((-1009 . -996) T) ((-1009 . -430) 144293) ((-1009 . -553) 144259) ((-1009 . -556) 144240) ((-1009 . -1014) T) ((-1009 . -1130) T) ((-1009 . -13) T) ((-1009 . -72) T) ((-1009 . -64) T) ((-1005 . -1130) T) ((-1005 . -13) T) ((-1005 . -1014) 144210) ((-1005 . -553) 144169) ((-1005 . -72) 144139) ((-1004 . -996) T) ((-1004 . -430) 144120) ((-1004 . -553) 144086) ((-1004 . -556) 144067) ((-1004 . -1014) T) ((-1004 . -1130) T) ((-1004 . -13) T) ((-1004 . -72) T) ((-1004 . -64) T) ((-1002 . -1007) 144051) ((-1002 . -558) 144035) ((-1002 . -1014) 144013) 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-812) 141304) ((-1000 . -797) NIL) ((-1000 . -822) 141283) ((-1000 . -1135) 141262) ((-1000 . -862) 141207) ((-1000 . -260) 141194) ((-1000 . -190) 141173) ((-1000 . -104) T) ((-1000 . -25) T) ((-1000 . -72) T) ((-1000 . -553) 141155) ((-1000 . -1014) T) ((-1000 . -23) T) ((-1000 . -21) T) ((-1000 . -971) T) ((-1000 . -1026) T) ((-1000 . -1062) T) ((-1000 . -664) T) ((-1000 . -962) T) ((-1000 . -186) 141103) ((-1000 . -13) T) ((-1000 . -1130) T) ((-1000 . -189) 141057) ((-1000 . -225) 141041) ((-1000 . -184) 141025) ((-998 . -553) 141007) ((-995 . -757) T) ((-995 . -553) 140989) ((-995 . -1014) T) ((-995 . -72) T) ((-995 . -13) T) ((-995 . -1130) T) ((-995 . -760) T) ((-995 . -554) 140970) ((-992 . -662) 140949) ((-992 . -951) 140847) ((-992 . -355) 140831) ((-992 . -581) 140779) ((-992 . -591) 140656) ((-992 . -329) 140640) ((-992 . -322) 140619) ((-992 . -120) 140598) ((-992 . -556) 140423) ((-992 . -655) 140297) ((-992 . -583) 140171) ((-992 . -589) 140069) ((-992 . -969) 139982) 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-1014) T) ((-989 . -553) 138331) ((-989 . -1130) T) ((-989 . -13) T) ((-989 . -72) T) ((-988 . -1014) T) ((-988 . -553) 138313) ((-988 . -1130) T) ((-988 . -13) T) ((-988 . -72) T) ((-988 . -241) 138292) ((-988 . -951) 138269) ((-988 . -556) 138246) ((-987 . -1130) T) ((-987 . -13) T) ((-986 . -996) T) ((-986 . -430) 138227) ((-986 . -553) 138193) ((-986 . -556) 138174) ((-986 . -1014) T) ((-986 . -1130) T) ((-986 . -13) T) ((-986 . -72) T) ((-986 . -64) T) ((-979 . -996) T) ((-979 . -430) 138155) ((-979 . -553) 138121) ((-979 . -556) 138102) ((-979 . -1014) T) ((-979 . -1130) T) ((-979 . -13) T) ((-979 . -72) T) ((-979 . -64) T) ((-976 . -484) T) ((-976 . -1135) T) ((-976 . -1067) T) ((-976 . -951) 138084) ((-976 . -554) 137999) ((-976 . -934) T) ((-976 . -797) 137981) ((-976 . -756) T) ((-976 . -722) T) ((-976 . -719) T) ((-976 . -760) T) ((-976 . -757) T) ((-976 . -717) T) ((-976 . -715) T) ((-976 . -741) T) ((-976 . -591) 137953) ((-976 . -581) 137935) ((-976 . -833) T) ((-976 . -496) T) ((-976 . -246) T) ((-976 . -146) T) ((-976 . -556) 137907) ((-976 . -655) 137894) ((-976 . -583) 137881) ((-976 . -969) 137868) ((-976 . -964) 137855) ((-976 . -82) 137840) ((-976 . -38) 137827) ((-976 . -392) T) ((-976 . -258) T) ((-976 . -189) T) ((-976 . -186) 137814) ((-976 . -190) T) ((-976 . -116) T) ((-976 . -962) T) ((-976 . -664) T) ((-976 . -1062) T) ((-976 . -1026) T) ((-976 . -971) T) ((-976 . -21) T) ((-976 . -589) 137786) ((-976 . -23) T) ((-976 . -1014) T) ((-976 . -553) 137768) ((-976 . -1130) T) ((-976 . -13) T) ((-976 . -72) T) ((-976 . -25) T) ((-976 . -104) T) ((-976 . -120) T) ((-976 . -558) 137749) ((-975 . -981) 137728) ((-975 . -72) T) ((-975 . -13) T) ((-975 . -1130) T) ((-975 . -553) 137710) ((-975 . -1014) T) ((-972 . -1130) T) ((-972 . -13) T) ((-972 . -1014) 137688) ((-972 . -553) 137655) ((-972 . -72) 137633) ((-967 . -966) 137573) ((-967 . -583) 137518) ((-967 . -655) 137463) ((-967 . -429) 137447) ((-967 . -456) 137380) ((-967 . -260) 137318) 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-355) 135564) ((-938 . -201) T) ((-938 . -246) T) ((-938 . -258) T) ((-938 . -392) T) ((-938 . -38) 135501) ((-938 . -583) 135438) ((-938 . -655) 135375) ((-938 . -556) 135312) ((-938 . -496) T) ((-938 . -833) T) ((-938 . -1135) T) ((-938 . -312) T) ((-938 . -82) 135221) ((-938 . -964) 135158) ((-938 . -969) 135095) ((-938 . -146) T) ((-938 . -120) T) ((-938 . -591) 135032) ((-938 . -589) 134969) ((-938 . -104) T) ((-938 . -25) T) ((-938 . -72) T) ((-938 . -13) T) ((-938 . -1130) T) ((-938 . -553) 134951) ((-938 . -1014) T) ((-938 . -23) T) ((-938 . -21) T) ((-938 . -962) T) ((-938 . -664) T) ((-938 . -1062) T) ((-938 . -1026) T) ((-938 . -971) T) ((-933 . -996) T) ((-933 . -430) 134932) ((-933 . -553) 134898) ((-933 . -556) 134879) ((-933 . -1014) T) ((-933 . -1130) T) ((-933 . -13) T) ((-933 . -72) T) ((-933 . -64) T) ((-918 . -905) 134861) ((-918 . -1067) T) ((-918 . -556) 134811) ((-918 . -951) 134771) ((-918 . -554) 134701) ((-918 . -934) T) ((-918 . -822) NIL) ((-918 . -795) 134683) ((-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) 134665) ((-918 . -343) 134647) ((-918 . -581) 134629) ((-918 . -329) 134611) ((-918 . -241) NIL) ((-918 . -260) NIL) ((-918 . -456) NIL) ((-918 . -288) 134593) ((-918 . -201) T) ((-918 . -82) 134520) ((-918 . -964) 134470) ((-918 . -969) 134420) ((-918 . -246) T) ((-918 . -655) 134370) ((-918 . -583) 134320) ((-918 . -591) 134270) ((-918 . -589) 134220) ((-918 . -38) 134170) ((-918 . -258) T) ((-918 . -392) T) ((-918 . -146) T) ((-918 . -496) T) ((-918 . -833) T) ((-918 . -1135) T) ((-918 . -312) T) ((-918 . -190) T) ((-918 . -186) 134157) ((-918 . -189) T) ((-918 . -225) 134139) ((-918 . -807) NIL) ((-918 . -812) NIL) ((-918 . -810) NIL) ((-918 . -184) 134121) ((-918 . -120) T) ((-918 . -118) NIL) ((-918 . -104) T) ((-918 . -25) T) ((-918 . -72) T) ((-918 . -13) T) ((-918 . -1130) T) ((-918 . -553) 134081) ((-918 . -1014) T) ((-918 . -23) T) ((-918 . -21) T) ((-918 . -962) T) ((-918 . -664) T) ((-918 . -1062) T) ((-918 . -1026) T) ((-918 . -971) T) ((-917 . -291) 134055) ((-917 . -146) T) ((-917 . -556) 133985) ((-917 . -971) T) ((-917 . -1026) T) ((-917 . -1062) T) ((-917 . -664) T) ((-917 . -962) T) ((-917 . -591) 133887) ((-917 . -589) 133817) ((-917 . -104) T) ((-917 . -25) T) ((-917 . -72) T) ((-917 . -13) T) ((-917 . -1130) T) ((-917 . -553) 133799) ((-917 . -1014) T) ((-917 . -23) T) ((-917 . -21) T) ((-917 . -969) 133744) ((-917 . -964) 133689) ((-917 . -82) 133606) ((-917 . -554) 133590) ((-917 . -184) 133567) ((-917 . -810) 133519) ((-917 . -812) 133431) ((-917 . -807) 133341) ((-917 . -225) 133318) ((-917 . -189) 133258) ((-917 . -186) 133192) ((-917 . -190) 133164) ((-917 . -312) T) ((-917 . -1135) T) ((-917 . -833) T) ((-917 . -496) T) ((-917 . -655) 133109) ((-917 . -583) 133054) ((-917 . -38) 132999) ((-917 . -392) T) ((-917 . -258) T) ((-917 . -246) T) ((-917 . -201) T) ((-917 . -320) NIL) ((-917 . -299) NIL) ((-917 . -1067) NIL) ((-917 . -118) 132971) ((-917 . -345) NIL) ((-917 . -353) 132943) ((-917 . -120) 132915) ((-917 . -322) 132887) ((-917 . -329) 132864) ((-917 . -581) 132798) ((-917 . -355) 132775) ((-917 . -951) 132652) ((-917 . -662) 132624) ((-914 . -909) 132608) ((-914 . -318) 132592) ((-914 . -1036) 132576) ((-914 . -34) T) ((-914 . -13) T) ((-914 . -1130) T) ((-914 . -72) 132530) ((-914 . -553) 132465) ((-914 . -260) 132403) ((-914 . -456) 132336) ((-914 . -1014) 132314) ((-914 . -429) 132298) ((-914 . -76) 132282) ((-910 . -912) 132266) ((-910 . -760) 132245) ((-910 . -757) 132224) ((-910 . -951) 132122) ((-910 . -355) 132106) ((-910 . -581) 132054) ((-910 . -591) 131956) ((-910 . -329) 131940) ((-910 . -241) 131898) ((-910 . -260) 131863) ((-910 . -456) 131775) ((-910 . -288) 131759) ((-910 . -38) 131707) ((-910 . -82) 131585) ((-910 . -964) 131484) ((-910 . -969) 131383) ((-910 . -589) 131306) ((-910 . -583) 131254) ((-910 . -655) 131202) ((-910 . -556) 131096) ((-910 . -246) 131050) ((-910 . -201) 131029) ((-910 . -190) 131008) ((-910 . -186) 130956) ((-910 . -189) 130910) ((-910 . -225) 130894) ((-910 . -807) 130818) ((-910 . -812) 130744) ((-910 . -810) 130703) ((-910 . -184) 130687) ((-910 . -554) 130648) ((-910 . -120) 130627) ((-910 . -118) 130606) ((-910 . -104) T) ((-910 . -25) T) ((-910 . -72) T) ((-910 . -13) T) ((-910 . -1130) T) ((-910 . -553) 130588) ((-910 . -1014) T) ((-910 . -23) T) ((-910 . -21) T) ((-910 . -962) T) ((-910 . -664) T) ((-910 . -1062) T) ((-910 . -1026) T) ((-910 . -971) T) ((-908 . -996) T) ((-908 . -430) 130569) ((-908 . -553) 130535) ((-908 . -556) 130516) ((-908 . -1014) T) ((-908 . -1130) T) ((-908 . -13) T) ((-908 . -72) T) ((-908 . -64) T) ((-907 . -21) T) ((-907 . -589) 130498) ((-907 . -23) T) ((-907 . -1014) T) ((-907 . -553) 130480) ((-907 . -1130) T) ((-907 . -13) T) ((-907 . -72) T) ((-907 . -25) T) ((-907 . -104) T) ((-907 . -241) 130447) ((-903 . -553) 130429) ((-900 . -1014) T) ((-900 . -553) 130411) ((-900 . -1130) T) ((-900 . -13) T) ((-900 . -72) T) ((-885 . -722) T) ((-885 . -719) T) ((-885 . -760) T) ((-885 . -757) T) ((-885 . -717) T) ((-885 . -23) T) ((-885 . -1014) T) ((-885 . -553) 130371) ((-885 . -1130) T) ((-885 . -13) T) ((-885 . -72) T) ((-885 . -25) T) ((-885 . -104) T) ((-884 . -996) T) ((-884 . -430) 130352) ((-884 . -553) 130318) ((-884 . -556) 130299) ((-884 . -1014) T) ((-884 . -1130) T) ((-884 . -13) T) ((-884 . -72) T) ((-884 . -64) T) ((-878 . -881) T) ((-878 . -72) T) ((-878 . -553) 130281) ((-878 . -1014) T) ((-878 . -605) T) ((-878 . -13) T) ((-878 . -1130) T) ((-878 . -84) T) ((-878 . -556) 130265) ((-877 . -553) 130247) ((-876 . -1014) T) ((-876 . -553) 130229) ((-876 . -1130) T) ((-876 . -13) T) ((-876 . -72) T) ((-876 . -320) 130182) ((-876 . -664) 130084) ((-876 . -1026) 129986) ((-876 . -23) 129800) ((-876 . -25) 129614) ((-876 . -104) 129472) ((-876 . -413) 129425) ((-876 . -21) 129380) ((-876 . -589) 129324) ((-876 . -718) 129277) ((-876 . -717) 129230) ((-876 . -757) 129132) ((-876 . -760) 129034) ((-876 . -719) 128987) ((-876 . -722) 128940) ((-870 . -19) 128924) ((-870 . -1036) 128908) ((-870 . -318) 128892) ((-870 . -34) T) ((-870 . -13) T) ((-870 . -1130) T) ((-870 . -72) 128826) ((-870 . -553) 128741) ((-870 . -260) 128679) ((-870 . -456) 128612) ((-870 . -1014) 128565) ((-870 . -429) 128549) ((-870 . -594) 128533) ((-870 . -243) 128510) ((-870 . -241) 128462) ((-870 . -539) 128439) ((-870 . -554) 128400) ((-870 . -124) 128384) ((-870 . -757) 128363) ((-870 . -760) 128342) ((-870 . -324) 128326) ((-868 . -277) 128305) ((-868 . -951) 128203) ((-868 . -355) 128187) ((-868 . -38) 128084) ((-868 . -556) 127941) ((-868 . -591) 127866) ((-868 . -589) 127776) ((-868 . -971) T) ((-868 . -1026) T) ((-868 . -1062) T) ((-868 . -664) T) ((-868 . -962) T) ((-868 . -82) 127641) ((-868 . -964) 127527) ((-868 . -969) 127413) ((-868 . -21) T) ((-868 . -23) T) ((-868 . -1014) T) ((-868 . -553) 127395) ((-868 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T) ((-814 . -241) 122794) ((-813 . -92) 122778) ((-813 . -429) 122762) ((-813 . -1014) 122740) ((-813 . -456) 122673) ((-813 . -260) 122611) ((-813 . -553) 122525) ((-813 . -72) 122479) ((-813 . -1130) T) ((-813 . -13) T) ((-813 . -34) T) ((-813 . -924) 122463) ((-804 . -757) T) ((-804 . -553) 122445) ((-804 . -1014) T) ((-804 . -72) T) ((-804 . -13) T) ((-804 . -1130) T) ((-804 . -760) T) ((-804 . -951) 122422) ((-804 . -556) 122399) ((-801 . -1014) T) ((-801 . -553) 122381) ((-801 . -1130) T) ((-801 . -13) T) ((-801 . -72) T) ((-801 . -951) 122349) ((-801 . -556) 122317) ((-799 . -1014) T) ((-799 . -553) 122299) ((-799 . -1130) T) ((-799 . -13) T) ((-799 . -72) T) ((-796 . -1014) T) ((-796 . -553) 122281) ((-796 . -1130) T) ((-796 . -13) T) ((-796 . -72) T) ((-786 . -996) T) ((-786 . -430) 122262) ((-786 . -553) 122228) ((-786 . -556) 122209) ((-786 . -1014) T) ((-786 . -1130) T) ((-786 . -13) T) ((-786 . -72) T) ((-786 . -64) T) ((-786 . -1176) T) ((-784 . -1014) T) ((-784 . -553) 122191) ((-784 . -1130) T) ((-784 . -13) T) ((-784 . -72) T) ((-784 . -556) 122173) ((-783 . -1130) T) ((-783 . -13) T) ((-783 . -553) 122048) ((-783 . -1014) 121999) ((-783 . -72) 121950) ((-782 . -905) 121934) ((-782 . -1067) 121912) ((-782 . -951) 121779) ((-782 . -556) 121678) ((-782 . -554) 121481) ((-782 . -934) 121460) ((-782 . -822) 121439) ((-782 . -795) 121423) ((-782 . -756) 121402) ((-782 . -722) 121381) ((-782 . -719) 121360) ((-782 . -760) 121314) ((-782 . -757) 121268) ((-782 . -717) 121247) ((-782 . -715) 121226) ((-782 . -741) 121205) ((-782 . -797) 121130) ((-782 . -343) 121114) ((-782 . -581) 121062) ((-782 . -591) 120978) ((-782 . -329) 120962) ((-782 . -241) 120920) ((-782 . -260) 120885) ((-782 . -456) 120797) ((-782 . -288) 120781) ((-782 . -201) T) ((-782 . -82) 120712) ((-782 . -964) 120664) ((-782 . -969) 120616) ((-782 . -246) T) ((-782 . -655) 120568) ((-782 . -583) 120520) ((-782 . -589) 120457) ((-782 . -38) 120409) ((-782 . -258) T) ((-782 . -392) T) 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. -583) 115928) ((-746 . -655) 115898) ((-744 . -1014) T) ((-744 . -553) 115880) ((-744 . -1130) T) ((-744 . -13) T) ((-744 . -72) T) ((-744 . -355) 115864) ((-744 . -556) 115737) ((-744 . -951) 115635) ((-744 . -21) 115590) ((-744 . -589) 115510) ((-744 . -23) 115465) ((-744 . -25) 115420) ((-744 . -104) 115375) ((-744 . -756) 115354) ((-744 . -722) 115333) ((-744 . -719) 115312) ((-744 . -760) 115291) ((-744 . -757) 115270) ((-744 . -717) 115249) ((-744 . -715) 115228) ((-744 . -962) 115207) ((-744 . -664) 115186) ((-744 . -1062) 115165) ((-744 . -1026) 115144) ((-744 . -971) 115123) ((-744 . -591) 115096) ((-744 . -120) 115075) ((-742 . -646) 115059) ((-742 . -556) 115014) ((-742 . -655) 114984) ((-742 . -583) 114954) ((-742 . -591) 114928) ((-742 . -589) 114887) ((-742 . -104) T) ((-742 . -25) T) ((-742 . -72) T) ((-742 . -13) T) ((-742 . -1130) T) ((-742 . -553) 114869) ((-742 . -1014) T) ((-742 . -23) T) ((-742 . -21) T) ((-742 . -969) 114853) ((-742 . -964) 114837) ((-742 . -82) 114816) ((-742 . -962) T) ((-742 . -664) T) ((-742 . -1062) T) ((-742 . -1026) T) ((-742 . -971) T) ((-742 . -38) 114786) ((-742 . -190) 114765) ((-742 . -186) 114738) ((-742 . -189) 114717) ((-740 . -336) 114701) ((-740 . -556) 114685) ((-740 . -951) 114669) ((-740 . -760) T) ((-740 . -757) T) ((-740 . -1026) T) ((-740 . -72) T) ((-740 . -13) T) ((-740 . -1130) T) ((-740 . -553) 114651) ((-740 . -1014) T) ((-740 . -664) T) ((-740 . -755) T) ((-740 . -767) T) ((-739 . -228) 114635) ((-739 . -556) 114619) ((-739 . -951) 114603) ((-739 . -760) T) ((-739 . -72) T) ((-739 . -1014) T) ((-739 . -553) 114585) ((-739 . -757) T) ((-739 . -186) 114572) ((-739 . -13) T) ((-739 . -1130) T) ((-739 . -189) T) ((-738 . -82) 114507) ((-738 . -964) 114458) ((-738 . -969) 114409) ((-738 . -21) T) ((-738 . -589) 114345) ((-738 . -23) T) ((-738 . -1014) T) ((-738 . -553) 114314) ((-738 . -1130) T) ((-738 . -13) T) ((-738 . -72) T) ((-738 . -25) T) ((-738 . -104) T) ((-738 . -591) 114265) ((-738 . -190) T) 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. -13) T) ((-613 . -1130) T) ((-613 . -553) 91827) ((-613 . -1014) T) ((-613 . -23) T) ((-613 . -21) T) ((-613 . -969) 91811) ((-613 . -964) 91795) ((-613 . -82) 91774) ((-613 . -962) T) ((-613 . -664) T) ((-613 . -1062) T) ((-613 . -1026) T) ((-613 . -971) T) ((-613 . -38) 91734) ((-613 . -361) 91718) ((-613 . -684) 91702) ((-613 . -658) T) ((-613 . -686) T) ((-613 . -316) 91686) ((-613 . -241) 91663) ((-607 . -326) 91642) ((-607 . -655) 91626) ((-607 . -583) 91610) ((-607 . -591) 91594) ((-607 . -589) 91563) ((-607 . -104) T) ((-607 . -25) T) ((-607 . -72) T) ((-607 . -13) T) ((-607 . -1130) T) ((-607 . -553) 91545) ((-607 . -1014) T) ((-607 . -23) T) ((-607 . -21) T) ((-607 . -969) 91529) ((-607 . -964) 91513) ((-607 . -82) 91492) ((-607 . -575) 91476) ((-607 . -335) 91448) ((-607 . -556) 91425) ((-607 . -951) 91402) ((-599 . -601) 91386) ((-599 . -38) 91356) ((-599 . -556) 91275) ((-599 . -591) 91249) ((-599 . -589) 91208) ((-599 . -971) T) ((-599 . -1026) T) ((-599 . -1062) T) 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-25) T) ((-470 . -72) T) ((-470 . -13) T) ((-470 . -1130) T) ((-470 . -553) 78392) ((-470 . -1014) T) ((-470 . -23) T) ((-470 . -717) T) ((-470 . -757) T) ((-470 . -760) T) ((-470 . -719) T) ((-470 . -722) T) ((-470 . -450) 78369) ((-470 . -558) 78332) ((-468 . -466) T) ((-468 . -147) T) ((-468 . -553) 78314) ((-464 . -996) T) ((-464 . -430) 78295) ((-464 . -553) 78261) ((-464 . -556) 78242) ((-464 . -1014) T) ((-464 . -1130) T) ((-464 . -13) T) ((-464 . -72) T) ((-464 . -64) T) ((-463 . -996) T) ((-463 . -430) 78223) ((-463 . -553) 78189) ((-463 . -556) 78170) ((-463 . -1014) T) ((-463 . -1130) T) ((-463 . -13) T) ((-463 . -72) T) ((-463 . -64) T) ((-460 . -280) 78147) ((-460 . -190) T) ((-460 . -186) 78134) ((-460 . -189) T) ((-460 . -320) T) ((-460 . -1067) T) ((-460 . -299) T) ((-460 . -120) 78116) ((-460 . -556) 78046) ((-460 . -591) 77991) ((-460 . -589) 77921) ((-460 . -104) T) ((-460 . -25) T) ((-460 . -72) T) ((-460 . -13) T) ((-460 . -1130) T) ((-460 . -553) 77903) ((-460 . 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76547) ((-451 . -450) 76526) ((-451 . -553) 76466) ((-451 . -1014) 76417) ((-451 . -558) 76382) ((-451 . -1130) T) ((-451 . -13) T) ((-451 . -72) T) ((-449 . -23) T) ((-449 . -1014) T) ((-449 . -553) 76364) ((-449 . -1130) T) ((-449 . -13) T) ((-449 . -72) T) ((-449 . -25) T) ((-449 . -450) 76343) ((-449 . -558) 76308) ((-448 . -21) T) ((-448 . -589) 76290) ((-448 . -23) T) ((-448 . -1014) T) ((-448 . -553) 76272) ((-448 . -1130) T) ((-448 . -13) T) ((-448 . -72) T) ((-448 . -25) T) ((-448 . -104) T) ((-448 . -450) 76251) ((-448 . -558) 76216) ((-447 . -1014) T) ((-447 . -553) 76198) ((-447 . -1130) T) ((-447 . -13) T) ((-447 . -72) T) ((-444 . -1014) T) ((-444 . -553) 76180) ((-444 . -1130) T) ((-444 . -13) T) ((-444 . -72) T) ((-442 . -757) T) ((-442 . -553) 76162) ((-442 . -1014) T) ((-442 . -72) T) ((-442 . -13) T) ((-442 . -1130) T) ((-442 . -760) T) ((-442 . -556) 76143) ((-440 . -96) T) ((-440 . -324) 76126) ((-440 . -760) T) ((-440 . -757) T) ((-440 . -124) 76109) ((-440 . 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-1130) T) ((-431 . -13) T) ((-431 . -72) T) ((-427 . -905) 74234) ((-427 . -1067) T) ((-427 . -556) 74184) ((-427 . -951) 74144) ((-427 . -554) 74074) ((-427 . -934) T) ((-427 . -822) NIL) ((-427 . -795) 74056) ((-427 . -756) T) ((-427 . -722) T) ((-427 . -719) T) ((-427 . -760) T) ((-427 . -757) T) ((-427 . -717) T) ((-427 . -715) T) ((-427 . -741) T) ((-427 . -797) 74038) ((-427 . -343) 74020) ((-427 . -581) 74002) ((-427 . -329) 73984) ((-427 . -241) NIL) ((-427 . -260) NIL) ((-427 . -456) NIL) ((-427 . -288) 73966) ((-427 . -201) T) ((-427 . -82) 73893) ((-427 . -964) 73843) ((-427 . -969) 73793) ((-427 . -246) T) ((-427 . -655) 73743) ((-427 . -583) 73693) ((-427 . -591) 73643) ((-427 . -589) 73593) ((-427 . -38) 73543) ((-427 . -258) T) ((-427 . -392) T) ((-427 . -146) T) ((-427 . -496) T) ((-427 . -833) T) ((-427 . -1135) T) ((-427 . -312) T) ((-427 . -190) T) ((-427 . -186) 73530) ((-427 . -189) T) ((-427 . -225) 73512) ((-427 . -807) NIL) ((-427 . -812) NIL) ((-427 . -810) NIL) ((-427 . -184) 73494) ((-427 . -120) T) ((-427 . -118) NIL) ((-427 . -104) T) ((-427 . -25) T) ((-427 . -72) T) ((-427 . -13) T) ((-427 . -1130) T) ((-427 . -553) 73436) ((-427 . -1014) T) ((-427 . -23) T) ((-427 . -21) T) ((-427 . -962) T) ((-427 . -664) T) ((-427 . -1062) T) ((-427 . -1026) T) ((-427 . -971) T) ((-425 . -286) 73405) ((-425 . -104) T) ((-425 . -25) T) ((-425 . -72) T) ((-425 . -13) T) ((-425 . -1130) T) ((-425 . -553) 73387) ((-425 . -1014) T) ((-425 . -23) T) ((-425 . -589) 73369) ((-425 . -21) T) ((-424 . -882) 73353) ((-424 . -318) 73337) ((-424 . -1036) 73321) ((-424 . -34) T) ((-424 . -13) T) ((-424 . -1130) T) ((-424 . -72) 73275) ((-424 . -553) 73210) ((-424 . -260) 73148) ((-424 . -456) 73081) ((-424 . -1014) 73059) ((-424 . -429) 73043) ((-424 . -76) 73027) ((-423 . -996) T) ((-423 . -430) 73008) ((-423 . -553) 72974) ((-423 . -556) 72955) ((-423 . -1014) T) ((-423 . -1130) T) ((-423 . -13) T) ((-423 . -72) T) ((-423 . -64) T) ((-422 . -196) 72934) 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T) ((-422 . -1130) T) ((-422 . -1014) 69371) ((-422 . -23) 69227) ((-422 . -21) 69142) ((-421 . -862) 69087) ((-421 . -556) 68879) ((-421 . -951) 68757) ((-421 . -1135) 68736) ((-421 . -822) 68715) ((-421 . -797) NIL) ((-421 . -812) 68692) ((-421 . -807) 68667) ((-421 . -810) 68644) ((-421 . -456) 68582) ((-421 . -392) 68536) ((-421 . -581) 68484) ((-421 . -591) 68373) ((-421 . -329) 68357) ((-421 . -47) 68314) ((-421 . -38) 68166) ((-421 . -583) 68018) ((-421 . -655) 67870) ((-421 . -246) 67804) ((-421 . -496) 67738) ((-421 . -82) 67563) ((-421 . -964) 67409) ((-421 . -969) 67255) ((-421 . -146) 67169) ((-421 . -120) 67148) ((-421 . -118) 67127) ((-421 . -589) 67037) ((-421 . -104) T) ((-421 . -25) T) ((-421 . -72) T) ((-421 . -13) T) ((-421 . -1130) T) ((-421 . -553) 67019) ((-421 . -1014) T) ((-421 . -23) T) ((-421 . -21) T) ((-421 . -962) T) ((-421 . -664) T) ((-421 . -1062) T) ((-421 . -1026) T) ((-421 . -971) T) ((-421 . -355) 67003) ((-421 . -277) 66960) ((-421 . -260) 66947) 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65495) ((-417 . -964) 65460) ((-417 . -969) 65425) ((-417 . -21) T) ((-417 . -23) T) ((-417 . -1014) T) ((-417 . -553) 65377) ((-417 . -1130) T) ((-417 . -13) T) ((-417 . -72) T) ((-417 . -25) T) ((-417 . -104) T) ((-417 . -246) T) ((-417 . -201) T) ((-417 . -120) T) ((-417 . -951) 65337) ((-417 . -934) T) ((-417 . -554) 65259) ((-416 . -1125) 65228) ((-416 . -1036) 65212) ((-416 . -553) 65174) ((-416 . -124) 65158) ((-416 . -34) T) ((-416 . -13) T) ((-416 . -1130) T) ((-416 . -72) T) ((-416 . -260) 65096) ((-416 . -456) 65029) ((-416 . -1014) T) ((-416 . -429) 65013) ((-416 . -554) 64974) ((-416 . -318) 64958) ((-416 . -890) 64927) ((-415 . -1108) 64906) ((-415 . -183) 64854) ((-415 . -76) 64802) ((-415 . -1036) 64750) ((-415 . -124) 64698) ((-415 . -554) NIL) ((-415 . -193) 64646) ((-415 . -539) 64625) ((-415 . -260) 64423) ((-415 . -456) 64175) ((-415 . -429) 64110) ((-415 . -241) 64089) ((-415 . -243) 64068) ((-415 . -550) 64047) ((-415 . -1014) T) ((-415 . -553) 64029) ((-415 . -72) T) ((-415 . -1130) T) ((-415 . -13) T) ((-415 . -34) T) ((-415 . -318) 63977) ((-414 . -1163) 63961) ((-414 . -190) 63913) ((-414 . -186) 63859) ((-414 . -189) 63811) ((-414 . -241) 63769) ((-414 . -810) 63675) ((-414 . -807) 63556) ((-414 . -812) 63462) ((-414 . -887) 63425) ((-414 . -38) 63272) ((-414 . -82) 63092) ((-414 . -964) 62933) ((-414 . -969) 62774) ((-414 . -589) 62659) ((-414 . -591) 62559) ((-414 . -583) 62406) ((-414 . -655) 62253) ((-414 . -556) 62085) ((-414 . -118) 62064) ((-414 . -120) 62043) ((-414 . -47) 62013) ((-414 . -1159) 61983) ((-414 . -35) 61949) ((-414 . -66) 61915) ((-414 . -239) 61881) ((-414 . -433) 61847) ((-414 . -1119) 61813) ((-414 . -1116) 61779) ((-414 . -916) 61745) ((-414 . -201) 61724) ((-414 . -246) 61678) ((-414 . -104) T) ((-414 . -25) T) ((-414 . -72) T) ((-414 . -13) T) ((-414 . -1130) T) ((-414 . -553) 61660) ((-414 . -1014) T) ((-414 . -23) T) ((-414 . -21) T) ((-414 . -962) T) ((-414 . -664) T) ((-414 . -1062) T) ((-414 . -1026) T) ((-414 . -971) T) ((-414 . -258) 61639) ((-414 . -392) 61618) ((-414 . -146) 61552) ((-414 . -496) 61506) ((-414 . -833) 61485) ((-414 . -1135) 61464) ((-414 . -312) 61443) ((-408 . -1014) T) ((-408 . -553) 61425) ((-408 . -1130) T) ((-408 . -13) T) ((-408 . -72) T) ((-403 . -890) 61394) ((-403 . -318) 61378) ((-403 . -554) 61339) ((-403 . -429) 61323) ((-403 . -1014) T) ((-403 . -456) 61256) ((-403 . -260) 61194) ((-403 . -553) 61156) ((-403 . -72) T) ((-403 . -1130) T) ((-403 . -13) T) ((-403 . -34) T) ((-403 . -124) 61140) ((-403 . -1036) 61124) ((-401 . -655) 61095) ((-401 . -583) 61066) ((-401 . -591) 61037) ((-401 . -589) 60993) ((-401 . -104) T) ((-401 . -25) T) ((-401 . -72) T) ((-401 . -13) T) ((-401 . -1130) T) ((-401 . -553) 60975) ((-401 . -1014) T) ((-401 . -23) T) ((-401 . -21) T) ((-401 . -969) 60946) ((-401 . -964) 60917) ((-401 . -82) 60878) ((-394 . -862) 60845) ((-394 . -556) 60637) ((-394 . -951) 60515) ((-394 . -1135) 60494) ((-394 . -822) 60473) ((-394 . -797) NIL) ((-394 . -812) 60450) ((-394 . -807) 60425) ((-394 . -810) 60402) ((-394 . -456) 60340) ((-394 . -392) 60294) ((-394 . -581) 60242) ((-394 . -591) 60131) ((-394 . -329) 60115) ((-394 . -47) 60094) ((-394 . -38) 59946) ((-394 . -583) 59798) ((-394 . -655) 59650) ((-394 . -246) 59584) ((-394 . -496) 59518) ((-394 . -82) 59343) ((-394 . -964) 59189) ((-394 . -969) 59035) ((-394 . -146) 58949) ((-394 . -120) 58928) ((-394 . -118) 58907) ((-394 . -589) 58817) ((-394 . -104) T) ((-394 . -25) T) ((-394 . -72) T) ((-394 . -13) T) ((-394 . -1130) T) ((-394 . -553) 58799) ((-394 . -1014) T) ((-394 . -23) T) ((-394 . -21) T) ((-394 . -962) T) ((-394 . -664) T) ((-394 . -1062) T) ((-394 . -1026) T) ((-394 . -971) T) ((-394 . -355) 58783) ((-394 . -277) 58762) ((-394 . -260) 58749) ((-394 . -554) 58610) ((-393 . -361) 58580) ((-393 . -684) 58550) ((-393 . -658) T) ((-393 . -686) T) ((-393 . -82) 58501) ((-393 . -964) 58471) ((-393 . -969) 58441) ((-393 . -21) T) ((-393 . -589) 58356) ((-393 . -23) T) ((-393 . -1014) T) ((-393 . -553) 58338) ((-393 . -72) T) ((-393 . -25) T) ((-393 . -104) T) ((-393 . -591) 58268) ((-393 . -583) 58238) ((-393 . -655) 58208) ((-393 . -316) 58178) ((-393 . -1130) T) ((-393 . -13) T) ((-393 . -241) 58141) ((-381 . -1014) T) ((-381 . -553) 58123) ((-381 . -1130) T) ((-381 . -13) T) ((-381 . -72) T) ((-380 . -1014) T) ((-380 . -553) 58105) ((-380 . -1130) T) ((-380 . -13) T) ((-380 . -72) T) ((-379 . -1014) T) ((-379 . -553) 58087) ((-379 . -1130) T) ((-379 . -13) T) ((-379 . -72) T) ((-377 . -553) 58069) ((-372 . -38) 58053) ((-372 . -556) 58022) ((-372 . -591) 57996) ((-372 . -589) 57955) ((-372 . -971) T) ((-372 . -1026) T) ((-372 . -1062) T) ((-372 . -664) T) ((-372 . -962) T) ((-372 . -82) 57934) ((-372 . -964) 57918) ((-372 . -969) 57902) ((-372 . -21) T) ((-372 . -23) T) ((-372 . -1014) T) ((-372 . -553) 57884) ((-372 . -1130) T) ((-372 . -13) T) ((-372 . -72) T) ((-372 . -25) T) ((-372 . -104) T) ((-372 . -583) 57868) ((-372 . -655) 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NIL) ((-264 . -717) NIL) ((-264 . -715) NIL) ((-264 . -741) NIL) ((-264 . -797) NIL) ((-264 . -343) 38176) ((-264 . -581) 38137) ((-264 . -591) 38066) ((-264 . -329) 38027) ((-264 . -241) 37893) ((-264 . -260) 37789) ((-264 . -456) 37540) ((-264 . -288) 37501) ((-264 . -201) T) ((-264 . -82) 37386) ((-264 . -964) 37315) ((-264 . -969) 37244) ((-264 . -246) T) ((-264 . -655) 37173) ((-264 . -583) 37102) ((-264 . -589) 37016) ((-264 . -38) 36945) ((-264 . -258) T) ((-264 . -392) T) ((-264 . -146) T) ((-264 . -496) T) ((-264 . -833) T) ((-264 . -1135) T) ((-264 . -312) T) ((-264 . -190) NIL) ((-264 . -186) NIL) ((-264 . -189) NIL) ((-264 . -225) 36906) ((-264 . -807) NIL) ((-264 . -812) NIL) ((-264 . -810) NIL) ((-264 . -184) 36867) ((-264 . -120) 36823) ((-264 . -118) 36779) ((-264 . -104) T) ((-264 . -25) T) ((-264 . -72) T) ((-264 . -13) T) ((-264 . -1130) T) ((-264 . -553) 36761) ((-264 . -1014) T) ((-264 . -23) T) ((-264 . -21) T) ((-264 . -962) T) ((-264 . -664) T) ((-264 . -1062) T) ((-264 . -1026) T) ((-264 . -971) T) ((-263 . -996) T) ((-263 . -430) 36742) ((-263 . -553) 36708) ((-263 . -556) 36689) ((-263 . -1014) T) ((-263 . -1130) T) ((-263 . -13) T) ((-263 . -72) T) ((-263 . -64) T) ((-262 . -1014) T) ((-262 . -553) 36671) ((-262 . -1130) T) ((-262 . -13) T) ((-262 . -72) T) ((-251 . -1108) 36650) ((-251 . -183) 36598) ((-251 . -76) 36546) ((-251 . -1036) 36494) ((-251 . -124) 36442) ((-251 . -554) NIL) ((-251 . -193) 36390) ((-251 . -539) 36369) ((-251 . -260) 36167) ((-251 . -456) 35919) ((-251 . -429) 35854) ((-251 . -241) 35833) ((-251 . -243) 35812) ((-251 . -550) 35791) ((-251 . -1014) T) ((-251 . -553) 35773) ((-251 . -72) T) ((-251 . -1130) T) ((-251 . -13) T) ((-251 . -34) T) ((-251 . -318) 35721) ((-249 . -1130) T) ((-249 . -13) T) ((-249 . -456) 35670) ((-249 . -1014) 35456) ((-249 . -553) 35202) ((-249 . -72) 34988) ((-249 . -25) 34856) ((-249 . -21) 34743) ((-249 . -589) 34490) ((-249 . -23) 34377) ((-249 . -104) 34264) ((-249 . -1026) 34149) 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. -186) 28200) ((-211 . -189) 28102) ((-211 . -225) 28072) ((-211 . -807) 27944) ((-211 . -812) 27818) ((-211 . -810) 27751) ((-211 . -184) 27721) ((-211 . -553) 27682) ((-211 . -969) 27607) ((-211 . -964) 27512) ((-211 . -82) 27432) ((-211 . -104) T) ((-211 . -25) T) ((-211 . -72) T) ((-211 . -13) T) ((-211 . -1130) T) ((-211 . -1014) T) ((-211 . -23) T) ((-211 . -21) T) ((-210 . -196) 27411) ((-210 . -1188) 27381) ((-210 . -722) 27360) ((-210 . -719) 27339) ((-210 . -760) 27293) ((-210 . -757) 27247) ((-210 . -717) 27226) ((-210 . -718) 27205) ((-210 . -655) 27150) ((-210 . -583) 27075) ((-210 . -243) 27052) ((-210 . -241) 27029) ((-210 . -539) 27006) ((-210 . -951) 26835) ((-210 . -556) 26639) ((-210 . -355) 26608) ((-210 . -581) 26516) ((-210 . -591) 26329) ((-210 . -329) 26299) ((-210 . -429) 26283) ((-210 . -456) 26216) ((-210 . -260) 26154) ((-210 . -34) T) ((-210 . -318) 26138) ((-210 . -320) 26117) ((-210 . -190) 26070) ((-210 . -589) 25910) ((-210 . -971) 25889) ((-210 . 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24322) ((-206 . -456) 24260) ((-206 . -392) 24214) ((-206 . -581) 24162) ((-206 . -591) 24051) ((-206 . -329) 24035) ((-206 . -47) 23992) ((-206 . -38) 23844) ((-206 . -583) 23696) ((-206 . -655) 23548) ((-206 . -246) 23482) ((-206 . -496) 23416) ((-206 . -82) 23241) ((-206 . -964) 23087) ((-206 . -969) 22933) ((-206 . -146) 22847) ((-206 . -120) 22826) ((-206 . -118) 22805) ((-206 . -589) 22715) ((-206 . -104) T) ((-206 . -25) T) ((-206 . -72) T) ((-206 . -13) T) ((-206 . -1130) T) ((-206 . -553) 22697) ((-206 . -1014) T) ((-206 . -23) T) ((-206 . -21) T) ((-206 . -962) T) ((-206 . -664) T) ((-206 . -1062) T) ((-206 . -1026) T) ((-206 . -971) T) ((-206 . -355) 22681) ((-206 . -277) 22638) ((-206 . -260) 22625) ((-206 . -554) 22486) ((-203 . -609) 22470) ((-203 . -1169) 22454) ((-203 . -924) 22438) ((-203 . -1065) 22422) ((-203 . -318) 22406) ((-203 . -757) 22385) ((-203 . -760) 22364) ((-203 . -324) 22348) ((-203 . -594) 22332) ((-203 . -243) 22309) ((-203 . -241) 22261) ((-203 . 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. -1014) T) ((-177 . -553) 16855) ((-177 . -1130) T) ((-177 . -13) T) ((-177 . -72) T) ((-177 . -25) T) ((-177 . -104) T) ((-177 . -951) 16832) ((-176 . -214) 16816) ((-176 . -1035) 16800) ((-176 . -76) 16784) ((-176 . -429) 16768) ((-176 . -1014) 16746) ((-176 . -456) 16679) ((-176 . -260) 16617) ((-176 . -553) 16552) ((-176 . -72) 16506) ((-176 . -1130) T) ((-176 . -13) T) ((-176 . -34) T) ((-176 . -1036) 16490) ((-176 . -318) 16474) ((-176 . -909) 16458) ((-172 . -996) T) ((-172 . -430) 16439) ((-172 . -553) 16405) ((-172 . -556) 16386) ((-172 . -1014) T) ((-172 . -1130) T) ((-172 . -13) T) ((-172 . -72) T) ((-172 . -64) T) ((-171 . -905) 16368) ((-171 . -1067) T) ((-171 . -556) 16318) ((-171 . -951) 16278) ((-171 . -554) 16208) ((-171 . -934) T) ((-171 . -822) NIL) ((-171 . -795) 16190) ((-171 . -756) T) ((-171 . -722) T) ((-171 . -719) T) ((-171 . -760) T) ((-171 . -757) T) ((-171 . -717) T) ((-171 . -715) T) ((-171 . -741) T) ((-171 . -797) 16172) ((-171 . -343) 16154) ((-171 . -581) 16136) ((-171 . -329) 16118) ((-171 . -241) NIL) ((-171 . -260) NIL) ((-171 . -456) NIL) ((-171 . -288) 16100) ((-171 . -201) T) ((-171 . -82) 16027) ((-171 . -964) 15977) ((-171 . -969) 15927) ((-171 . -246) T) ((-171 . -655) 15877) ((-171 . -583) 15827) ((-171 . -591) 15777) ((-171 . -589) 15727) ((-171 . -38) 15677) ((-171 . -258) T) ((-171 . -392) T) ((-171 . -146) T) ((-171 . -496) T) ((-171 . -833) T) ((-171 . -1135) T) ((-171 . -312) T) ((-171 . -190) T) ((-171 . -186) 15664) ((-171 . -189) T) ((-171 . -225) 15646) ((-171 . -807) NIL) ((-171 . -812) NIL) ((-171 . -810) NIL) ((-171 . -184) 15628) ((-171 . -120) T) ((-171 . -118) NIL) ((-171 . -104) T) ((-171 . -25) T) ((-171 . -72) T) ((-171 . -13) T) ((-171 . -1130) T) ((-171 . -553) 15570) ((-171 . -1014) T) ((-171 . -23) T) ((-171 . -21) T) ((-171 . -962) T) ((-171 . -664) T) ((-171 . -1062) T) ((-171 . -1026) T) ((-171 . -971) T) ((-168 . -753) T) ((-168 . -760) T) ((-168 . -757) T) ((-168 . -1014) T) ((-168 . -553) 15552) ((-168 . -1130) T) ((-168 . -13) T) ((-168 . -72) T) ((-168 . -320) T) ((-167 . -1014) T) ((-167 . -553) 15534) ((-167 . -1130) T) ((-167 . -13) T) ((-167 . -72) T) ((-167 . -556) 15511) ((-166 . -1014) T) ((-166 . -553) 15493) ((-166 . -1130) T) ((-166 . -13) T) ((-166 . -72) T) ((-161 . -1014) T) ((-161 . -553) 15475) ((-161 . -1130) T) ((-161 . -13) T) ((-161 . -72) T) ((-158 . -1014) T) ((-158 . -553) 15457) ((-158 . -1130) T) ((-158 . -13) T) ((-158 . -72) T) ((-157 . -160) T) ((-157 . -1014) T) ((-157 . -553) 15439) ((-157 . -1130) T) ((-157 . -13) T) ((-157 . -72) T) ((-157 . -748) 15421) ((-154 . -996) T) ((-154 . -430) 15402) ((-154 . -553) 15368) ((-154 . -556) 15349) ((-154 . -1014) T) ((-154 . -1130) T) ((-154 . -13) T) ((-154 . -72) T) ((-154 . -64) T) ((-149 . -553) 15331) ((-148 . -38) 15263) ((-148 . -556) 15180) ((-148 . -591) 15112) ((-148 . -589) 15029) ((-148 . -971) T) ((-148 . -1026) T) ((-148 . -1062) T) ((-148 . -664) T) ((-148 . -962) T) ((-148 . -82) 14928) ((-148 . -964) 14860) ((-148 . -969) 14792) ((-148 . -21) T) ((-148 . -23) T) ((-148 . -1014) T) ((-148 . -553) 14774) ((-148 . -1130) T) ((-148 . -13) T) ((-148 . -72) T) ((-148 . -25) T) ((-148 . -104) T) ((-148 . -583) 14706) ((-148 . -655) 14638) ((-148 . -312) T) ((-148 . -1135) T) ((-148 . -833) T) ((-148 . -496) T) ((-148 . -146) T) ((-148 . -392) T) ((-148 . -258) T) ((-148 . -246) T) ((-148 . -201) T) ((-145 . -1014) T) ((-145 . -553) 14620) ((-145 . -1130) T) ((-145 . -13) T) ((-145 . -72) T) ((-142 . -139) 14604) ((-142 . -35) 14582) ((-142 . -66) 14560) ((-142 . -239) 14538) ((-142 . -433) 14516) ((-142 . -1119) 14494) ((-142 . -1116) 14472) ((-142 . -916) 14424) ((-142 . -822) 14377) ((-142 . -554) 14145) ((-142 . -795) 14129) ((-142 . -320) 14083) ((-142 . -299) 14062) ((-142 . -1067) 14041) ((-142 . -345) 14020) ((-142 . -353) 13991) ((-142 . -38) 13825) ((-142 . -82) 13717) ((-142 . -964) 13630) ((-142 . -969) 13543) ((-142 . -583) 13377) ((-142 . -655) 13211) 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. -1014) T) ((-111 . -1130) T) ((-111 . -13) T) ((-111 . -72) T) ((-111 . -64) T) ((-110 . -996) T) ((-110 . -430) 10325) ((-110 . -553) 10291) ((-110 . -556) 10272) ((-110 . -1014) T) ((-110 . -1130) T) ((-110 . -13) T) ((-110 . -72) T) ((-110 . -64) T) ((-108 . -405) 10249) ((-108 . -556) 10145) ((-108 . -951) 10129) ((-108 . -1014) T) ((-108 . -553) 10111) ((-108 . -1130) T) ((-108 . -13) T) ((-108 . -72) T) ((-108 . -410) 10066) ((-108 . -241) 10043) ((-107 . -757) T) ((-107 . -553) 10025) ((-107 . -1014) T) ((-107 . -72) T) ((-107 . -13) T) ((-107 . -1130) T) ((-107 . -760) T) ((-107 . -23) T) ((-107 . -25) T) ((-107 . -664) T) ((-107 . -1026) T) ((-107 . -951) 10007) ((-107 . -556) 9989) ((-106 . -996) T) ((-106 . -430) 9970) ((-106 . -553) 9936) ((-106 . -556) 9917) ((-106 . -1014) T) ((-106 . -1130) T) ((-106 . -13) T) ((-106 . -72) T) ((-106 . -64) T) ((-103 . -1014) T) ((-103 . -553) 9899) ((-103 . -1130) T) ((-103 . -13) T) ((-103 . -72) T) ((-102 . -19) 9881) ((-102 . 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. -38) 3558) ((-48 . -258) T) ((-48 . -392) T) ((-48 . -146) T) ((-48 . -496) T) ((-48 . -833) T) ((-48 . -1135) T) ((-48 . -312) T) ((-48 . -581) 3518) ((-48 . -934) T) ((-48 . -554) 3463) ((-48 . -120) T) ((-48 . -190) T) ((-48 . -186) 3450) ((-48 . -189) T) ((-45 . -36) 3429) ((-45 . -550) 3408) ((-45 . -243) 3331) ((-45 . -241) 3229) ((-45 . -429) 3164) ((-45 . -456) 2916) ((-45 . -260) 2714) ((-45 . -539) 2637) ((-45 . -193) 2585) ((-45 . -76) 2533) ((-45 . -183) 2481) ((-45 . -1108) 2460) ((-45 . -237) 2408) ((-45 . -1036) 2356) ((-45 . -124) 2304) ((-45 . -34) T) ((-45 . -13) T) ((-45 . -1130) T) ((-45 . -72) T) ((-45 . -553) 2286) ((-45 . -1014) T) ((-45 . -554) NIL) ((-45 . -594) 2234) ((-45 . -324) 2182) ((-45 . -760) NIL) ((-45 . -757) NIL) ((-45 . -318) 2130) ((-45 . -1065) 2078) ((-45 . -924) 2026) ((-45 . -1169) 1974) ((-45 . -609) 1922) ((-44 . -361) 1906) ((-44 . -684) 1890) ((-44 . -658) T) ((-44 . -686) T) ((-44 . -82) 1869) ((-44 . -964) 1853) ((-44 . -969) 1837) 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\ No newline at end of file
+((((-484)) . T)) 
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. -104) T) ((-1204 . -590) 200344) ((-1204 . -1194) 200328) ((-1204 . -654) 200298) ((-1204 . -582) 200268) ((-1204 . -968) 200252) ((-1204 . -963) 200236) ((-1204 . -82) 200215) ((-1204 . -38) 200185) ((-1204 . -1199) 200164) ((-1203 . -961) T) ((-1203 . -663) T) ((-1203 . -1061) T) ((-1203 . -1025) T) ((-1203 . -970) T) ((-1203 . -21) T) ((-1203 . -588) 200123) ((-1203 . -23) T) ((-1203 . -1013) T) ((-1203 . -552) 200105) ((-1203 . -1129) T) ((-1203 . -13) T) ((-1203 . -72) T) ((-1203 . -25) T) ((-1203 . -104) T) ((-1203 . -590) 200079) ((-1203 . -555) 200035) ((-1203 . -1194) 200019) ((-1203 . -654) 199989) ((-1203 . -582) 199959) ((-1203 . -968) 199943) ((-1203 . -963) 199927) ((-1203 . -82) 199906) ((-1203 . -38) 199876) ((-1203 . -335) 199855) ((-1203 . -950) 199839) ((-1201 . -1202) 199815) ((-1201 . -950) 199789) ((-1201 . -555) 199735) ((-1201 . -961) T) ((-1201 . -663) T) ((-1201 . -1061) T) ((-1201 . -1025) T) ((-1201 . -970) T) ((-1201 . -21) T) ((-1201 . -588) 199694) ((-1201 . -23) T) ((-1201 . -1013) T) ((-1201 . -552) 199676) ((-1201 . -1129) T) ((-1201 . -13) T) ((-1201 . -72) T) ((-1201 . -25) T) ((-1201 . -104) T) ((-1201 . -590) 199650) ((-1201 . -1194) 199634) ((-1201 . -654) 199604) ((-1201 . -582) 199574) ((-1201 . -968) 199558) ((-1201 . -963) 199542) ((-1201 . -82) 199521) ((-1201 . -38) 199491) ((-1201 . -1199) 199467) ((-1200 . -1202) 199446) ((-1200 . -950) 199403) ((-1200 . -555) 199332) ((-1200 . -961) T) ((-1200 . -663) T) ((-1200 . -1061) T) ((-1200 . -1025) T) ((-1200 . -970) T) ((-1200 . -21) T) ((-1200 . -588) 199291) ((-1200 . -23) T) ((-1200 . -1013) T) ((-1200 . -552) 199273) ((-1200 . -1129) T) ((-1200 . -13) T) ((-1200 . -72) T) ((-1200 . -25) T) ((-1200 . -104) T) ((-1200 . -590) 199247) ((-1200 . -1194) 199231) ((-1200 . -654) 199201) ((-1200 . -582) 199171) ((-1200 . -968) 199155) ((-1200 . -963) 199139) ((-1200 . -82) 199118) ((-1200 . -38) 199088) ((-1200 . -1199) 199067) ((-1200 . -335) 199039) ((-1195 . -335) 199011) ((-1195 . -555) 198960) ((-1195 . -950) 198937) ((-1195 . -582) 198907) ((-1195 . -654) 198877) ((-1195 . -590) 198851) ((-1195 . -588) 198810) ((-1195 . -104) T) ((-1195 . -25) T) ((-1195 . -72) T) ((-1195 . -13) T) ((-1195 . -1129) T) ((-1195 . -552) 198792) ((-1195 . -1013) T) ((-1195 . -23) T) ((-1195 . -21) T) ((-1195 . -968) 198776) ((-1195 . -963) 198760) ((-1195 . -82) 198739) ((-1195 . -1202) 198718) ((-1195 . -961) T) ((-1195 . -663) T) ((-1195 . -1061) T) ((-1195 . -1025) T) ((-1195 . -970) T) ((-1195 . -1194) 198702) ((-1195 . -38) 198672) ((-1195 . -1199) 198651) ((-1193 . -1124) 198620) ((-1193 . -1035) 198604) ((-1193 . -552) 198566) ((-1193 . -124) 198550) ((-1193 . -34) T) ((-1193 . -13) T) ((-1193 . -1129) T) ((-1193 . -72) T) ((-1193 . -260) 198488) ((-1193 . -455) 198421) ((-1193 . -1013) T) ((-1193 . -429) 198405) ((-1193 . -553) 198366) ((-1193 . -318) 198350) ((-1193 . -889) 198319) ((-1192 . -961) T) ((-1192 . -663) T) ((-1192 . -1061) T) ((-1192 . -1025) T) ((-1192 . -970) T) ((-1192 . -21) T) ((-1192 . -588) 198264) ((-1192 . -23) T) ((-1192 . -1013) T) ((-1192 . -552) 198233) ((-1192 . -1129) T) ((-1192 . -13) T) ((-1192 . -72) T) ((-1192 . -25) T) ((-1192 . -104) T) ((-1192 . -590) 198193) ((-1192 . -555) 198135) ((-1192 . -430) 198119) ((-1192 . -38) 198089) ((-1192 . -82) 198054) ((-1192 . -963) 198024) ((-1192 . -968) 197994) ((-1192 . -582) 197964) ((-1192 . -654) 197934) ((-1191 . -995) T) ((-1191 . -430) 197915) ((-1191 . -552) 197881) ((-1191 . -555) 197862) ((-1191 . -1013) T) ((-1191 . -1129) T) ((-1191 . -13) T) ((-1191 . -72) T) ((-1191 . -64) T) ((-1190 . -995) T) ((-1190 . -430) 197843) ((-1190 . -552) 197809) ((-1190 . -555) 197790) ((-1190 . -1013) T) ((-1190 . -1129) T) ((-1190 . -13) T) ((-1190 . -72) T) ((-1190 . -64) T) ((-1185 . -552) 197772) ((-1183 . -1013) T) ((-1183 . -552) 197754) ((-1183 . -1129) T) ((-1183 . -13) T) ((-1183 . -72) T) ((-1182 . -1013) T) ((-1182 . -552) 197736) ((-1182 . -1129) T) ((-1182 . -13) T) ((-1182 . -72) T) ((-1179 . -1178) 197720) ((-1179 . -324) 197704) ((-1179 . -759) 197683) ((-1179 . -756) 197662) ((-1179 . -124) 197646) ((-1179 . -553) 197607) ((-1179 . -241) 197559) ((-1179 . -538) 197536) ((-1179 . -243) 197513) ((-1179 . -593) 197497) ((-1179 . -429) 197481) ((-1179 . -1013) 197434) ((-1179 . -455) 197367) ((-1179 . -260) 197305) ((-1179 . -552) 197220) ((-1179 . -72) 197154) ((-1179 . -1129) T) ((-1179 . -13) T) ((-1179 . -34) T) ((-1179 . -318) 197138) ((-1179 . -1035) 197122) ((-1179 . -19) 197106) ((-1176 . -1013) T) ((-1176 . -552) 197072) ((-1176 . -1129) T) ((-1176 . -13) T) ((-1176 . -72) T) ((-1169 . -1172) 197056) ((-1169 . -190) 197015) ((-1169 . -555) 196897) ((-1169 . -590) 196822) ((-1169 . -588) 196732) ((-1169 . -104) T) ((-1169 . -25) T) ((-1169 . -72) T) ((-1169 . -552) 196714) ((-1169 . -1013) T) ((-1169 . -23) T) ((-1169 . -21) T) ((-1169 . -970) T) ((-1169 . -1025) T) ((-1169 . -1061) T) ((-1169 . -663) T) ((-1169 . -961) T) ((-1169 . -186) 196667) ((-1169 . -13) T) ((-1169 . -1129) T) ((-1169 . -189) 196626) ((-1169 . -241) 196591) ((-1169 . -809) 196504) ((-1169 . -806) 196392) ((-1169 . -811) 196305) ((-1169 . -886) 196275) ((-1169 . -38) 196172) ((-1169 . -82) 196037) ((-1169 . -963) 195923) ((-1169 . -968) 195809) ((-1169 . -582) 195706) ((-1169 . -654) 195603) ((-1169 . -118) 195582) ((-1169 . -120) 195561) ((-1169 . -146) 195515) ((-1169 . -495) 195494) ((-1169 . -246) 195473) ((-1169 . -47) 195450) ((-1169 . -1158) 195427) ((-1169 . -35) 195393) ((-1169 . -66) 195359) ((-1169 . -239) 195325) ((-1169 . -433) 195291) ((-1169 . -1118) 195257) ((-1169 . -1115) 195223) ((-1169 . -915) 195189) ((-1166 . -277) 195133) ((-1166 . -950) 195099) ((-1166 . -355) 195065) ((-1166 . -38) 194922) ((-1166 . -555) 194796) ((-1166 . -590) 194685) ((-1166 . -588) 194559) ((-1166 . -970) T) ((-1166 . -1025) T) ((-1166 . -1061) T) ((-1166 . -663) T) ((-1166 . -961) T) ((-1166 . -82) 194409) ((-1166 . -963) 194298) ((-1166 . -968) 194187) ((-1166 . -21) T) ((-1166 . -23) T) ((-1166 . -1013) T) ((-1166 . -552) 194169) ((-1166 . -1129) T) ((-1166 . -13) T) ((-1166 . -72) T) ((-1166 . -25) T) ((-1166 . -104) T) ((-1166 . -582) 194026) ((-1166 . -654) 193883) ((-1166 . -118) 193844) ((-1166 . -120) 193805) ((-1166 . -146) T) ((-1166 . -495) T) ((-1166 . -246) T) ((-1166 . -47) 193749) ((-1165 . -1164) 193728) ((-1165 . -312) 193707) ((-1165 . -1134) 193686) ((-1165 . -832) 193665) ((-1165 . -495) 193619) ((-1165 . -146) 193553) ((-1165 . -555) 193372) ((-1165 . -654) 193219) ((-1165 . -582) 193066) ((-1165 . -38) 192913) ((-1165 . -392) 192892) ((-1165 . -258) 192871) ((-1165 . -590) 192771) ((-1165 . -588) 192656) ((-1165 . -970) T) ((-1165 . -1025) T) ((-1165 . -1061) T) ((-1165 . -663) T) ((-1165 . -961) T) ((-1165 . -82) 192476) ((-1165 . -963) 192317) ((-1165 . -968) 192158) ((-1165 . -21) T) ((-1165 . -23) T) ((-1165 . -1013) T) ((-1165 . -552) 192140) ((-1165 . -1129) T) ((-1165 . -13) T) ((-1165 . -72) T) ((-1165 . -25) T) ((-1165 . -104) T) ((-1165 . -246) 192094) ((-1165 . -201) 192073) ((-1165 . -915) 192039) ((-1165 . -1115) 192005) ((-1165 . -1118) 191971) ((-1165 . -433) 191937) ((-1165 . -239) 191903) ((-1165 . -66) 191869) ((-1165 . -35) 191835) ((-1165 . -1158) 191805) ((-1165 . -47) 191775) ((-1165 . -120) 191754) ((-1165 . -118) 191733) ((-1165 . -886) 191696) ((-1165 . -811) 191602) ((-1165 . -806) 191506) ((-1165 . -809) 191412) ((-1165 . -241) 191370) ((-1165 . -189) 191322) ((-1165 . -186) 191268) ((-1165 . -190) 191220) ((-1165 . -1162) 191204) ((-1165 . -950) 191188) ((-1160 . -1164) 191149) ((-1160 . -312) 191128) ((-1160 . -1134) 191107) ((-1160 . -832) 191086) ((-1160 . -495) 191040) ((-1160 . -146) 190974) ((-1160 . -555) 190723) ((-1160 . -654) 190570) ((-1160 . -582) 190417) ((-1160 . -38) 190264) ((-1160 . -392) 190243) ((-1160 . -258) 190222) ((-1160 . -590) 190122) ((-1160 . -588) 190007) ((-1160 . -970) T) ((-1160 . -1025) T) ((-1160 . -1061) T) ((-1160 . -663) T) ((-1160 . -961) T) ((-1160 . -82) 189827) ((-1160 . -963) 189668) ((-1160 . -968) 189509) ((-1160 . -21) T) ((-1160 . -23) T) ((-1160 . -1013) T) ((-1160 . -552) 189491) ((-1160 . -1129) T) ((-1160 . -13) T) ((-1160 . -72) T) ((-1160 . -25) T) ((-1160 . -104) T) ((-1160 . -246) 189445) ((-1160 . -201) 189424) ((-1160 . -915) 189390) ((-1160 . -1115) 189356) ((-1160 . -1118) 189322) ((-1160 . -433) 189288) ((-1160 . -239) 189254) ((-1160 . -66) 189220) ((-1160 . -35) 189186) ((-1160 . -1158) 189156) ((-1160 . -47) 189126) ((-1160 . -120) 189105) ((-1160 . -118) 189084) ((-1160 . -886) 189047) ((-1160 . -811) 188953) ((-1160 . -806) 188834) ((-1160 . -809) 188740) ((-1160 . -241) 188698) ((-1160 . -189) 188650) ((-1160 . -186) 188596) ((-1160 . -190) 188548) ((-1160 . -1162) 188532) ((-1160 . -950) 188467) ((-1148 . -1155) 188451) ((-1148 . -1066) 188429) ((-1148 . -553) NIL) ((-1148 . -260) 188416) ((-1148 . -455) 188364) ((-1148 . -277) 188341) ((-1148 . -950) 188224) ((-1148 . -355) 188208) ((-1148 . -38) 188040) ((-1148 . -82) 187845) ((-1148 . -963) 187671) ((-1148 . -968) 187497) ((-1148 . -588) 187407) ((-1148 . -590) 187296) ((-1148 . -582) 187128) ((-1148 . -654) 186960) ((-1148 . -555) 186716) ((-1148 . -118) 186695) ((-1148 . -120) 186674) ((-1148 . -47) 186651) ((-1148 . -329) 186635) ((-1148 . -580) 186583) ((-1148 . -809) 186527) ((-1148 . -806) 186434) ((-1148 . -811) 186345) ((-1148 . -796) NIL) ((-1148 . -821) 186324) ((-1148 . -1134) 186303) ((-1148 . -861) 186273) ((-1148 . -832) 186252) ((-1148 . -495) 186166) ((-1148 . -246) 186080) ((-1148 . -146) 185974) ((-1148 . -392) 185908) ((-1148 . -258) 185887) ((-1148 . -241) 185814) ((-1148 . -190) T) ((-1148 . -104) T) ((-1148 . -25) T) ((-1148 . -72) T) ((-1148 . -552) 185796) ((-1148 . -1013) T) ((-1148 . -23) T) ((-1148 . -21) T) ((-1148 . -970) T) ((-1148 . -1025) T) ((-1148 . -1061) T) ((-1148 . -663) T) ((-1148 . -961) T) ((-1148 . -186) 185783) ((-1148 . -13) T) ((-1148 . -1129) T) ((-1148 . -189) T) ((-1148 . -225) 185767) ((-1148 . -184) 185751) ((-1146 . -1006) 185735) ((-1146 . -557) 185719) ((-1146 . -1013) 185697) ((-1146 . -552) 185664) ((-1146 . -1129) 185642) ((-1146 . -13) 185620) ((-1146 . -72) 185598) ((-1146 . -1007) 185555) ((-1144 . -1143) 185534) ((-1144 . -915) 185500) ((-1144 . -1115) 185466) ((-1144 . -1118) 185432) ((-1144 . -433) 185398) ((-1144 . -239) 185364) ((-1144 . -66) 185330) ((-1144 . -35) 185296) ((-1144 . -1158) 185273) ((-1144 . -47) 185250) ((-1144 . -555) 185005) ((-1144 . -654) 184825) ((-1144 . -582) 184645) ((-1144 . -590) 184456) ((-1144 . -588) 184314) ((-1144 . -968) 184128) ((-1144 . -963) 183942) ((-1144 . -82) 183730) ((-1144 . -38) 183550) ((-1144 . -886) 183520) ((-1144 . -241) 183420) ((-1144 . -1141) 183404) ((-1144 . -970) T) ((-1144 . -1025) T) ((-1144 . -1061) T) ((-1144 . -663) T) ((-1144 . -961) T) ((-1144 . -21) T) ((-1144 . -23) T) ((-1144 . -1013) T) ((-1144 . -552) 183386) ((-1144 . -1129) T) ((-1144 . -13) T) ((-1144 . -72) T) ((-1144 . -25) T) ((-1144 . -104) T) ((-1144 . -118) 183314) ((-1144 . -120) 183196) ((-1144 . -553) 182869) ((-1144 . -184) 182839) ((-1144 . -809) 182693) ((-1144 . -811) 182493) ((-1144 . -806) 182291) ((-1144 . -225) 182261) ((-1144 . -189) 182123) ((-1144 . -186) 181979) ((-1144 . -190) 181887) ((-1144 . -312) 181866) ((-1144 . -1134) 181845) ((-1144 . -832) 181824) ((-1144 . -495) 181778) ((-1144 . -146) 181712) ((-1144 . -392) 181691) ((-1144 . -258) 181670) ((-1144 . -246) 181624) ((-1144 . -201) 181603) ((-1144 . -288) 181573) ((-1144 . -455) 181433) ((-1144 . -260) 181372) ((-1144 . -329) 181342) ((-1144 . -580) 181250) ((-1144 . -343) 181220) ((-1144 . -796) 181093) ((-1144 . -740) 181046) ((-1144 . -714) 180999) ((-1144 . -716) 180952) ((-1144 . -756) 180854) ((-1144 . -759) 180756) ((-1144 . -718) 180709) ((-1144 . -721) 180662) ((-1144 . -755) 180615) ((-1144 . -794) 180585) ((-1144 . -821) 180538) ((-1144 . -933) 180491) ((-1144 . -950) 180280) ((-1144 . -1066) 180232) ((-1144 . -904) 180202) ((-1139 . -1143) 180163) ((-1139 . -915) 180129) ((-1139 . -1115) 180095) ((-1139 . -1118) 180061) ((-1139 . -433) 180027) ((-1139 . -239) 179993) ((-1139 . -66) 179959) ((-1139 . -35) 179925) ((-1139 . -1158) 179902) ((-1139 . -47) 179879) ((-1139 . -555) 179680) ((-1139 . -654) 179482) ((-1139 . -582) 179284) ((-1139 . -590) 179139) ((-1139 . -588) 178979) ((-1139 . -968) 178775) ((-1139 . -963) 178571) ((-1139 . -82) 178323) ((-1139 . -38) 178125) ((-1139 . -886) 178095) ((-1139 . -241) 177923) ((-1139 . -1141) 177907) ((-1139 . -970) T) ((-1139 . -1025) T) ((-1139 . -1061) T) ((-1139 . -663) T) ((-1139 . -961) T) ((-1139 . -21) T) ((-1139 . -23) T) ((-1139 . -1013) T) ((-1139 . -552) 177889) ((-1139 . -1129) T) ((-1139 . -13) T) ((-1139 . -72) T) ((-1139 . -25) T) ((-1139 . -104) T) ((-1139 . -118) 177799) ((-1139 . -120) 177709) ((-1139 . -553) NIL) ((-1139 . -184) 177661) ((-1139 . -809) 177497) ((-1139 . -811) 177261) ((-1139 . -806) 177000) ((-1139 . -225) 176952) ((-1139 . -189) 176778) ((-1139 . -186) 176598) ((-1139 . -190) 176488) ((-1139 . -312) 176467) ((-1139 . -1134) 176446) ((-1139 . -832) 176425) ((-1139 . -495) 176379) ((-1139 . -146) 176313) ((-1139 . -392) 176292) ((-1139 . -258) 176271) ((-1139 . -246) 176225) ((-1139 . -201) 176204) ((-1139 . -288) 176156) ((-1139 . -455) 175890) ((-1139 . -260) 175775) ((-1139 . -329) 175727) ((-1139 . -580) 175679) ((-1139 . -343) 175631) ((-1139 . -796) NIL) ((-1139 . -740) NIL) ((-1139 . -714) NIL) ((-1139 . -716) NIL) ((-1139 . -756) NIL) ((-1139 . -759) NIL) ((-1139 . -718) NIL) ((-1139 . -721) NIL) ((-1139 . -755) NIL) ((-1139 . -794) 175583) ((-1139 . -821) NIL) ((-1139 . -933) NIL) ((-1139 . -950) 175549) ((-1139 . -1066) NIL) ((-1139 . -904) 175501) ((-1138 . -752) T) ((-1138 . -759) T) ((-1138 . -756) T) ((-1138 . -1013) T) ((-1138 . -552) 175483) ((-1138 . -1129) T) ((-1138 . -13) T) ((-1138 . -72) T) ((-1138 . -320) T) ((-1138 . -604) T) ((-1137 . -752) T) ((-1137 . -759) T) ((-1137 . -756) T) ((-1137 . -1013) T) ((-1137 . -552) 175465) ((-1137 . -1129) T) ((-1137 . -13) T) ((-1137 . -72) T) ((-1137 . -320) T) ((-1137 . -604) T) ((-1136 . -752) T) ((-1136 . -759) T) ((-1136 . -756) T) ((-1136 . -1013) T) ((-1136 . -552) 175447) ((-1136 . -1129) T) ((-1136 . -13) T) ((-1136 . -72) T) ((-1136 . -320) T) ((-1136 . -604) T) ((-1135 . -752) T) ((-1135 . -759) T) ((-1135 . -756) T) ((-1135 . -1013) T) ((-1135 . -552) 175429) ((-1135 . -1129) T) ((-1135 . -13) T) ((-1135 . -72) T) ((-1135 . -320) T) ((-1135 . -604) T) ((-1130 . -995) T) ((-1130 . -430) 175410) ((-1130 . -552) 175376) ((-1130 . -555) 175357) ((-1130 . -1013) T) ((-1130 . -1129) T) ((-1130 . -13) T) ((-1130 . -72) T) ((-1130 . -64) T) ((-1127 . -430) 175334) ((-1127 . -552) 175275) ((-1127 . -555) 175252) ((-1127 . -1013) 175230) ((-1127 . -1129) 175208) ((-1127 . -13) 175186) ((-1127 . -72) 175164) ((-1122 . -679) 175140) ((-1122 . -35) 175106) ((-1122 . -66) 175072) ((-1122 . -239) 175038) ((-1122 . -433) 175004) ((-1122 . -1118) 174970) ((-1122 . -1115) 174936) ((-1122 . -915) 174902) ((-1122 . -47) 174871) ((-1122 . -38) 174768) ((-1122 . -582) 174665) ((-1122 . -654) 174562) ((-1122 . -555) 174444) ((-1122 . -246) 174423) ((-1122 . -495) 174402) ((-1122 . -82) 174267) ((-1122 . -963) 174153) ((-1122 . -968) 174039) ((-1122 . -146) 173993) ((-1122 . -120) 173972) ((-1122 . -118) 173951) ((-1122 . -590) 173876) ((-1122 . -588) 173786) ((-1122 . -886) 173747) ((-1122 . -811) 173728) ((-1122 . -1129) T) ((-1122 . -13) T) ((-1122 . -806) 173707) ((-1122 . -961) T) ((-1122 . -663) T) ((-1122 . -1061) T) ((-1122 . -1025) T) ((-1122 . -970) T) ((-1122 . -21) T) ((-1122 . -23) T) ((-1122 . -1013) T) ((-1122 . -552) 173689) ((-1122 . -72) T) ((-1122 . -25) T) ((-1122 . -104) T) ((-1122 . -809) 173670) ((-1122 . -455) 173637) ((-1122 . -260) 173624) ((-1116 . -923) 173608) ((-1116 . -34) T) ((-1116 . -13) T) ((-1116 . -1129) T) ((-1116 . -72) 173562) ((-1116 . -552) 173497) ((-1116 . -260) 173435) ((-1116 . -455) 173368) ((-1116 . -1013) 173346) ((-1116 . -429) 173330) ((-1116 . -318) 173314) ((-1116 . -1035) 173298) ((-1111 . -314) 173272) ((-1111 . -72) T) ((-1111 . -13) T) ((-1111 . -1129) T) ((-1111 . -552) 173254) ((-1111 . -1013) T) ((-1109 . -1013) T) ((-1109 . -552) 173236) ((-1109 . -1129) T) ((-1109 . -13) T) ((-1109 . -72) T) ((-1109 . -555) 173218) ((-1104 . -747) 173202) ((-1104 . -72) T) ((-1104 . -13) T) ((-1104 . -1129) T) ((-1104 . -552) 173184) ((-1104 . -1013) T) ((-1102 . -1107) 173163) ((-1102 . -183) 173111) ((-1102 . -76) 173059) ((-1102 . -1035) 173007) ((-1102 . -124) 172955) ((-1102 . -553) NIL) ((-1102 . -193) 172903) ((-1102 . -538) 172882) ((-1102 . -260) 172680) ((-1102 . -455) 172432) ((-1102 . -429) 172367) ((-1102 . -241) 172346) ((-1102 . -243) 172325) ((-1102 . -549) 172304) ((-1102 . -1013) T) ((-1102 . -552) 172286) ((-1102 . -72) T) ((-1102 . -1129) T) ((-1102 . -13) T) ((-1102 . -34) T) ((-1102 . -318) 172234) ((-1098 . -1013) T) ((-1098 . -552) 172216) ((-1098 . -1129) T) ((-1098 . -13) T) ((-1098 . -72) T) ((-1097 . -752) T) ((-1097 . -759) T) ((-1097 . -756) T) ((-1097 . -1013) T) ((-1097 . -552) 172198) ((-1097 . -1129) T) ((-1097 . -13) T) ((-1097 . -72) T) ((-1097 . -320) T) ((-1097 . -604) T) ((-1096 . -752) T) ((-1096 . -759) T) ((-1096 . -756) T) ((-1096 . -1013) T) ((-1096 . -552) 172180) ((-1096 . -1129) T) ((-1096 . -13) T) ((-1096 . -72) T) ((-1096 . -320) T) ((-1095 . -1175) T) ((-1095 . -1013) T) ((-1095 . -552) 172147) ((-1095 . -1129) T) ((-1095 . -13) T) ((-1095 . -72) T) ((-1095 . -950) 172083) ((-1095 . -555) 172019) ((-1094 . -552) 172001) ((-1093 . -552) 171983) ((-1092 . -277) 171960) ((-1092 . -950) 171858) ((-1092 . -355) 171842) ((-1092 . -38) 171739) ((-1092 . -555) 171596) ((-1092 . -590) 171521) ((-1092 . -588) 171431) ((-1092 . -970) T) ((-1092 . -1025) T) ((-1092 . -1061) T) ((-1092 . -663) T) ((-1092 . -961) T) ((-1092 . -82) 171296) ((-1092 . -963) 171182) ((-1092 . -968) 171068) ((-1092 . -21) T) ((-1092 . -23) T) ((-1092 . -1013) T) ((-1092 . -552) 171050) ((-1092 . -1129) T) ((-1092 . -13) T) ((-1092 . -72) T) ((-1092 . -25) T) ((-1092 . -104) T) ((-1092 . -582) 170947) ((-1092 . -654) 170844) ((-1092 . -118) 170823) ((-1092 . -120) 170802) ((-1092 . -146) 170756) ((-1092 . -495) 170735) ((-1092 . -246) 170714) ((-1092 . -47) 170691) ((-1090 . -756) T) ((-1090 . -552) 170673) ((-1090 . -1013) T) ((-1090 . -72) T) ((-1090 . -13) T) ((-1090 . -1129) T) ((-1090 . -759) T) ((-1090 . -553) 170595) ((-1090 . -555) 170561) ((-1090 . -950) 170543) ((-1090 . -796) 170510) ((-1089 . -1172) 170494) ((-1089 . -190) 170453) ((-1089 . -555) 170335) ((-1089 . -590) 170260) ((-1089 . -588) 170170) ((-1089 . -104) T) ((-1089 . -25) T) ((-1089 . -72) T) ((-1089 . -552) 170152) ((-1089 . -1013) T) ((-1089 . -23) T) ((-1089 . -21) T) ((-1089 . -970) T) ((-1089 . -1025) T) ((-1089 . -1061) T) ((-1089 . -663) T) ((-1089 . -961) T) ((-1089 . -186) 170105) ((-1089 . -13) T) ((-1089 . -1129) T) ((-1089 . -189) 170064) ((-1089 . -241) 170029) ((-1089 . -809) 169942) ((-1089 . -806) 169830) ((-1089 . -811) 169743) ((-1089 . -886) 169713) ((-1089 . -38) 169610) ((-1089 . -82) 169475) ((-1089 . -963) 169361) ((-1089 . -968) 169247) ((-1089 . -582) 169144) ((-1089 . -654) 169041) ((-1089 . -118) 169020) ((-1089 . -120) 168999) ((-1089 . -146) 168953) ((-1089 . -495) 168932) ((-1089 . -246) 168911) ((-1089 . -47) 168888) ((-1089 . -1158) 168865) ((-1089 . -35) 168831) ((-1089 . -66) 168797) ((-1089 . -239) 168763) ((-1089 . -433) 168729) ((-1089 . -1118) 168695) ((-1089 . -1115) 168661) ((-1089 . -915) 168627) ((-1088 . -1164) 168588) ((-1088 . -312) 168567) ((-1088 . -1134) 168546) ((-1088 . -832) 168525) ((-1088 . -495) 168479) ((-1088 . -146) 168413) ((-1088 . -555) 168162) ((-1088 . -654) 168009) ((-1088 . -582) 167856) ((-1088 . -38) 167703) ((-1088 . -392) 167682) ((-1088 . -258) 167661) ((-1088 . -590) 167561) ((-1088 . -588) 167446) ((-1088 . -970) T) ((-1088 . -1025) T) ((-1088 . -1061) T) ((-1088 . -663) T) ((-1088 . -961) T) ((-1088 . -82) 167266) ((-1088 . -963) 167107) ((-1088 . -968) 166948) ((-1088 . -21) T) ((-1088 . -23) T) ((-1088 . -1013) T) ((-1088 . -552) 166930) ((-1088 . -1129) T) ((-1088 . -13) T) ((-1088 . -72) T) ((-1088 . -25) T) ((-1088 . -104) T) ((-1088 . -246) 166884) ((-1088 . -201) 166863) ((-1088 . -915) 166829) ((-1088 . -1115) 166795) ((-1088 . -1118) 166761) ((-1088 . -433) 166727) ((-1088 . -239) 166693) ((-1088 . -66) 166659) ((-1088 . -35) 166625) ((-1088 . -1158) 166595) ((-1088 . -47) 166565) ((-1088 . -120) 166544) ((-1088 . -118) 166523) ((-1088 . -886) 166486) ((-1088 . -811) 166392) ((-1088 . -806) 166273) ((-1088 . -809) 166179) ((-1088 . -241) 166137) ((-1088 . -189) 166089) ((-1088 . -186) 166035) ((-1088 . -190) 165987) ((-1088 . -1162) 165971) ((-1088 . -950) 165906) ((-1085 . -1155) 165890) ((-1085 . -1066) 165868) ((-1085 . -553) NIL) ((-1085 . -260) 165855) ((-1085 . -455) 165803) ((-1085 . -277) 165780) ((-1085 . -950) 165663) ((-1085 . -355) 165647) ((-1085 . -38) 165479) ((-1085 . -82) 165284) ((-1085 . -963) 165110) ((-1085 . -968) 164936) ((-1085 . -588) 164846) ((-1085 . -590) 164735) ((-1085 . -582) 164567) ((-1085 . -654) 164399) ((-1085 . -555) 164176) ((-1085 . -118) 164155) ((-1085 . -120) 164134) ((-1085 . -47) 164111) ((-1085 . -329) 164095) ((-1085 . -580) 164043) ((-1085 . -809) 163987) ((-1085 . -806) 163894) ((-1085 . -811) 163805) ((-1085 . -796) NIL) ((-1085 . -821) 163784) ((-1085 . -1134) 163763) ((-1085 . -861) 163733) ((-1085 . -832) 163712) ((-1085 . -495) 163626) ((-1085 . -246) 163540) ((-1085 . -146) 163434) ((-1085 . -392) 163368) ((-1085 . -258) 163347) ((-1085 . -241) 163274) ((-1085 . -190) T) ((-1085 . -104) T) ((-1085 . -25) T) ((-1085 . -72) T) ((-1085 . -552) 163256) ((-1085 . -1013) T) ((-1085 . -23) T) ((-1085 . -21) T) ((-1085 . -970) T) ((-1085 . -1025) T) ((-1085 . -1061) T) ((-1085 . -663) T) ((-1085 . -961) T) ((-1085 . -186) 163243) ((-1085 . -13) T) ((-1085 . -1129) T) ((-1085 . -189) T) ((-1085 . -225) 163227) ((-1085 . -184) 163211) ((-1082 . -1143) 163172) ((-1082 . -915) 163138) ((-1082 . -1115) 163104) ((-1082 . -1118) 163070) ((-1082 . -433) 163036) ((-1082 . -239) 163002) ((-1082 . -66) 162968) ((-1082 . -35) 162934) ((-1082 . -1158) 162911) ((-1082 . -47) 162888) ((-1082 . -555) 162689) ((-1082 . -654) 162491) ((-1082 . -582) 162293) ((-1082 . -590) 162148) ((-1082 . -588) 161988) ((-1082 . -968) 161784) ((-1082 . -963) 161580) ((-1082 . -82) 161332) ((-1082 . -38) 161134) ((-1082 . -886) 161104) ((-1082 . -241) 160932) ((-1082 . -1141) 160916) ((-1082 . -970) T) ((-1082 . -1025) T) ((-1082 . -1061) T) ((-1082 . -663) T) ((-1082 . -961) T) ((-1082 . -21) T) ((-1082 . -23) T) ((-1082 . -1013) T) ((-1082 . -552) 160898) ((-1082 . -1129) T) ((-1082 . -13) T) ((-1082 . -72) T) ((-1082 . -25) T) ((-1082 . -104) T) ((-1082 . -118) 160808) ((-1082 . -120) 160718) ((-1082 . -553) NIL) ((-1082 . -184) 160670) ((-1082 . -809) 160506) ((-1082 . -811) 160270) ((-1082 . -806) 160009) ((-1082 . -225) 159961) ((-1082 . -189) 159787) ((-1082 . -186) 159607) ((-1082 . -190) 159497) ((-1082 . -312) 159476) ((-1082 . -1134) 159455) ((-1082 . -832) 159434) ((-1082 . -495) 159388) ((-1082 . -146) 159322) ((-1082 . -392) 159301) ((-1082 . -258) 159280) ((-1082 . -246) 159234) ((-1082 . -201) 159213) ((-1082 . -288) 159165) ((-1082 . -455) 158899) ((-1082 . -260) 158784) ((-1082 . -329) 158736) ((-1082 . -580) 158688) ((-1082 . -343) 158640) ((-1082 . -796) NIL) ((-1082 . -740) NIL) ((-1082 . -714) NIL) ((-1082 . -716) NIL) ((-1082 . -756) NIL) ((-1082 . -759) NIL) ((-1082 . -718) NIL) ((-1082 . -721) NIL) ((-1082 . -755) NIL) ((-1082 . -794) 158592) ((-1082 . -821) NIL) ((-1082 . -933) NIL) ((-1082 . -950) 158558) ((-1082 . -1066) NIL) ((-1082 . -904) 158510) ((-1081 . -995) T) ((-1081 . -430) 158491) ((-1081 . -552) 158457) ((-1081 . -555) 158438) ((-1081 . -1013) T) ((-1081 . -1129) T) ((-1081 . -13) T) ((-1081 . -72) T) ((-1081 . -64) T) ((-1080 . -1013) T) ((-1080 . -552) 158420) ((-1080 . -1129) T) ((-1080 . -13) T) ((-1080 . -72) T) ((-1079 . -1013) T) ((-1079 . -552) 158402) ((-1079 . -1129) T) ((-1079 . -13) T) ((-1079 . -72) T) ((-1074 . -1107) 158378) ((-1074 . -183) 158323) ((-1074 . -76) 158268) ((-1074 . -1035) 158213) ((-1074 . -124) 158158) ((-1074 . -553) NIL) ((-1074 . -193) 158103) ((-1074 . -538) 158079) ((-1074 . -260) 157868) ((-1074 . -455) 157608) ((-1074 . -429) 157540) ((-1074 . -241) 157516) ((-1074 . -243) 157492) ((-1074 . -549) 157468) ((-1074 . -1013) T) ((-1074 . -552) 157450) ((-1074 . -72) T) ((-1074 . -1129) T) ((-1074 . -13) T) ((-1074 . -34) T) ((-1074 . -318) 157395) ((-1073 . -1058) T) ((-1073 . -324) 157377) ((-1073 . -759) T) ((-1073 . -756) T) ((-1073 . -124) 157359) ((-1073 . -553) NIL) ((-1073 . -241) 157309) ((-1073 . -538) 157284) ((-1073 . -243) 157259) ((-1073 . -593) 157241) ((-1073 . -429) 157223) ((-1073 . -1013) T) ((-1073 . -455) NIL) ((-1073 . -260) NIL) ((-1073 . -552) 157205) ((-1073 . -72) T) ((-1073 . -1129) T) ((-1073 . -13) T) ((-1073 . -34) T) ((-1073 . -318) 157187) ((-1073 . -1035) 157169) ((-1073 . -19) 157151) ((-1069 . -616) 157135) ((-1069 . -593) 157119) ((-1069 . -243) 157096) ((-1069 . -241) 157048) ((-1069 . -538) 157025) ((-1069 . -553) 156986) ((-1069 . -429) 156970) ((-1069 . -1013) 156948) ((-1069 . -455) 156881) ((-1069 . -260) 156819) ((-1069 . -552) 156754) ((-1069 . -72) 156708) ((-1069 . -1129) T) ((-1069 . -13) T) ((-1069 . -34) T) ((-1069 . -124) 156692) ((-1069 . -1168) 156676) ((-1069 . -923) 156660) ((-1069 . -1064) 156644) ((-1069 . -555) 156621) ((-1069 . -1035) 156605) ((-1067 . -995) T) ((-1067 . -430) 156586) ((-1067 . -552) 156552) ((-1067 . -555) 156533) ((-1067 . -1013) T) ((-1067 . -1129) T) ((-1067 . -13) T) ((-1067 . -72) T) ((-1067 . -64) T) ((-1065 . -1107) 156512) ((-1065 . -183) 156460) ((-1065 . -76) 156408) ((-1065 . -1035) 156356) ((-1065 . -124) 156304) ((-1065 . -553) NIL) ((-1065 . -193) 156252) ((-1065 . -538) 156231) ((-1065 . -260) 156029) ((-1065 . -455) 155781) ((-1065 . -429) 155716) ((-1065 . -241) 155695) ((-1065 . -243) 155674) ((-1065 . -549) 155653) ((-1065 . -1013) T) ((-1065 . -552) 155635) ((-1065 . -72) T) ((-1065 . -1129) T) ((-1065 . -13) T) ((-1065 . -34) T) ((-1065 . -318) 155583) ((-1062 . -1034) 155567) ((-1062 . -318) 155551) ((-1062 . -1035) 155535) ((-1062 . -34) T) ((-1062 . -13) T) ((-1062 . -1129) T) ((-1062 . -72) 155489) ((-1062 . -552) 155424) ((-1062 . -260) 155362) ((-1062 . -455) 155295) ((-1062 . -1013) 155273) ((-1062 . -429) 155257) ((-1062 . -76) 155241) ((-1060 . -1020) 155210) ((-1060 . -1124) 155179) ((-1060 . -1035) 155163) ((-1060 . -552) 155125) ((-1060 . -124) 155109) ((-1060 . -34) T) ((-1060 . -13) T) ((-1060 . -1129) T) ((-1060 . -72) T) ((-1060 . -260) 155047) ((-1060 . -455) 154980) ((-1060 . -1013) T) ((-1060 . -429) 154964) ((-1060 . -553) 154925) ((-1060 . -318) 154909) ((-1060 . -889) 154878) ((-1060 . -983) 154847) ((-1056 . -1037) 154792) ((-1056 . -318) 154776) ((-1056 . -34) T) ((-1056 . -260) 154714) ((-1056 . -455) 154647) ((-1056 . -429) 154631) ((-1056 . -965) 154571) ((-1056 . -950) 154469) ((-1056 . -555) 154388) ((-1056 . -355) 154372) ((-1056 . -580) 154320) ((-1056 . -590) 154258) ((-1056 . -329) 154242) ((-1056 . -190) 154221) ((-1056 . -186) 154169) ((-1056 . -189) 154123) ((-1056 . -225) 154107) ((-1056 . -806) 154031) ((-1056 . -811) 153957) ((-1056 . -809) 153916) ((-1056 . -184) 153900) ((-1056 . -654) 153835) ((-1056 . -582) 153770) ((-1056 . -588) 153729) ((-1056 . -104) T) ((-1056 . -25) T) ((-1056 . -72) T) ((-1056 . -13) T) ((-1056 . -1129) T) ((-1056 . -552) 153691) ((-1056 . -1013) T) ((-1056 . -23) T) ((-1056 . -21) T) ((-1056 . -968) 153675) ((-1056 . -963) 153659) ((-1056 . -82) 153638) ((-1056 . -961) T) ((-1056 . -663) T) ((-1056 . -1061) T) ((-1056 . -1025) T) ((-1056 . -970) T) ((-1056 . -38) 153598) ((-1056 . -553) 153559) ((-1055 . -923) 153530) ((-1055 . -34) T) ((-1055 . -13) T) ((-1055 . -1129) T) ((-1055 . -72) T) ((-1055 . -552) 153512) ((-1055 . -260) 153438) ((-1055 . -455) 153346) ((-1055 . -1013) T) ((-1055 . -429) 153317) ((-1055 . -318) 153288) ((-1055 . -1035) 153259) ((-1054 . -1013) T) ((-1054 . -552) 153241) ((-1054 . -1129) T) ((-1054 . -13) T) ((-1054 . -72) T) ((-1049 . -1051) T) ((-1049 . -1175) T) ((-1049 . -64) T) ((-1049 . -72) T) ((-1049 . -13) T) ((-1049 . -1129) T) ((-1049 . -552) 153207) ((-1049 . -1013) T) ((-1049 . -555) 153188) ((-1049 . -430) 153169) ((-1049 . -995) T) ((-1047 . -1048) 153153) ((-1047 . -72) T) ((-1047 . -13) T) ((-1047 . -1129) T) ((-1047 . -552) 153135) ((-1047 . -1013) T) ((-1040 . -679) 153114) ((-1040 . -35) 153080) ((-1040 . -66) 153046) ((-1040 . -239) 153012) ((-1040 . -433) 152978) ((-1040 . -1118) 152944) ((-1040 . -1115) 152910) ((-1040 . -915) 152876) ((-1040 . -47) 152848) ((-1040 . -38) 152745) ((-1040 . -582) 152642) ((-1040 . -654) 152539) ((-1040 . -555) 152421) ((-1040 . -246) 152400) ((-1040 . -495) 152379) ((-1040 . -82) 152244) ((-1040 . -963) 152130) ((-1040 . -968) 152016) ((-1040 . -146) 151970) ((-1040 . -120) 151949) ((-1040 . -118) 151928) ((-1040 . -590) 151853) ((-1040 . -588) 151763) ((-1040 . -886) 151730) ((-1040 . -811) 151714) ((-1040 . -1129) T) ((-1040 . -13) T) ((-1040 . -806) 151696) ((-1040 . -961) T) ((-1040 . -663) T) ((-1040 . -1061) T) ((-1040 . -1025) T) ((-1040 . -970) T) ((-1040 . -21) T) ((-1040 . -23) T) ((-1040 . -1013) T) ((-1040 . -552) 151678) ((-1040 . -72) T) ((-1040 . -25) T) ((-1040 . -104) T) ((-1040 . -809) 151662) ((-1040 . -455) 151632) ((-1040 . -260) 151619) ((-1039 . -861) 151586) ((-1039 . -555) 151385) ((-1039 . -950) 151270) ((-1039 . -1134) 151249) ((-1039 . -821) 151228) ((-1039 . -796) 151087) ((-1039 . -811) 151071) ((-1039 . -806) 151053) ((-1039 . -809) 151037) ((-1039 . -455) 150989) ((-1039 . -392) 150943) ((-1039 . -580) 150891) ((-1039 . -590) 150780) ((-1039 . -329) 150764) ((-1039 . -47) 150736) ((-1039 . -38) 150588) ((-1039 . -582) 150440) ((-1039 . -654) 150292) ((-1039 . -246) 150226) ((-1039 . -495) 150160) ((-1039 . -82) 149985) ((-1039 . -963) 149831) ((-1039 . -968) 149677) ((-1039 . -146) 149591) ((-1039 . -120) 149570) ((-1039 . -118) 149549) ((-1039 . -588) 149459) ((-1039 . -104) T) ((-1039 . -25) T) ((-1039 . -72) T) ((-1039 . -13) T) ((-1039 . -1129) T) ((-1039 . -552) 149441) ((-1039 . -1013) T) ((-1039 . -23) T) ((-1039 . -21) T) ((-1039 . -961) T) ((-1039 . -663) T) ((-1039 . -1061) T) ((-1039 . -1025) T) ((-1039 . -970) T) ((-1039 . -355) 149425) ((-1039 . -277) 149397) ((-1039 . -260) 149384) ((-1039 . -553) 149132) ((-1033 . -483) T) ((-1033 . -1134) T) ((-1033 . -1066) T) ((-1033 . -950) 149114) ((-1033 . -553) 149029) ((-1033 . -933) T) ((-1033 . -796) 149011) ((-1033 . -755) T) ((-1033 . -721) T) ((-1033 . -718) T) ((-1033 . -759) T) ((-1033 . -756) T) ((-1033 . -716) T) ((-1033 . -714) T) ((-1033 . -740) T) ((-1033 . -590) 148983) ((-1033 . -580) 148965) ((-1033 . -832) T) ((-1033 . -495) T) ((-1033 . -246) T) ((-1033 . -146) T) ((-1033 . -555) 148937) ((-1033 . -654) 148924) ((-1033 . -582) 148911) ((-1033 . -968) 148898) ((-1033 . -963) 148885) ((-1033 . -82) 148870) ((-1033 . -38) 148857) ((-1033 . -392) T) ((-1033 . -258) T) ((-1033 . -189) T) ((-1033 . -186) 148844) ((-1033 . -190) T) ((-1033 . -116) T) ((-1033 . -961) T) ((-1033 . -663) T) ((-1033 . -1061) T) ((-1033 . -1025) T) ((-1033 . -970) T) ((-1033 . -21) T) ((-1033 . -588) 148816) ((-1033 . -23) T) ((-1033 . -1013) T) ((-1033 . -552) 148798) ((-1033 . -1129) T) ((-1033 . -13) T) ((-1033 . -72) T) ((-1033 . -25) T) ((-1033 . -104) T) ((-1033 . -120) T) ((-1033 . -752) T) ((-1033 . -320) T) ((-1033 . -84) T) ((-1033 . -604) T) ((-1029 . -995) T) ((-1029 . -430) 148779) ((-1029 . -552) 148745) ((-1029 . -555) 148726) ((-1029 . -1013) T) ((-1029 . -1129) T) 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-806) 146695) ((-1026 . -811) 146569) ((-1026 . -809) 146502) ((-1026 . -184) 146472) ((-1026 . -552) 146169) ((-1026 . -968) 146094) ((-1026 . -963) 145999) ((-1026 . -82) 145919) ((-1026 . -104) 145794) ((-1026 . -25) 145631) ((-1026 . -72) 145368) ((-1026 . -13) T) ((-1026 . -1129) T) ((-1026 . -1013) 145124) ((-1026 . -23) 144980) ((-1026 . -21) 144895) ((-1022 . -1023) 144879) ((-1022 . |MappingCategory|) 144853) ((-1022 . -1129) T) ((-1022 . -80) 144837) ((-1022 . -1013) T) ((-1022 . -552) 144819) ((-1022 . -13) T) ((-1022 . -72) T) ((-1017 . -1016) 144783) ((-1017 . -72) T) ((-1017 . -552) 144765) ((-1017 . -1013) T) ((-1017 . -241) 144721) ((-1017 . -1129) T) ((-1017 . -13) T) ((-1017 . -557) 144636) ((-1015 . -1016) 144588) ((-1015 . -72) T) ((-1015 . -552) 144570) ((-1015 . -1013) T) ((-1015 . -241) 144526) ((-1015 . -1129) T) ((-1015 . -13) T) ((-1015 . -557) 144429) ((-1014 . -320) T) ((-1014 . -72) T) ((-1014 . -13) T) ((-1014 . -1129) T) ((-1014 . -552) 144411) ((-1014 . -1013) T) ((-1009 . -369) 144395) ((-1009 . -1011) 144379) ((-1009 . -318) 144363) ((-1009 . -320) 144342) ((-1009 . -193) 144326) ((-1009 . -553) 144287) ((-1009 . -124) 144271) ((-1009 . -1035) 144255) ((-1009 . -34) T) ((-1009 . -13) T) ((-1009 . -1129) T) ((-1009 . -72) T) ((-1009 . -552) 144237) ((-1009 . -260) 144175) ((-1009 . -455) 144108) ((-1009 . -1013) T) ((-1009 . -429) 144092) ((-1009 . -76) 144076) ((-1009 . -183) 144060) ((-1008 . -995) T) ((-1008 . -430) 144041) ((-1008 . -552) 144007) ((-1008 . -555) 143988) ((-1008 . -1013) T) ((-1008 . -1129) T) ((-1008 . -13) T) ((-1008 . -72) T) ((-1008 . -64) T) ((-1004 . -1129) T) ((-1004 . -13) T) ((-1004 . -1013) 143958) ((-1004 . -552) 143917) ((-1004 . -72) 143887) ((-1003 . -995) T) ((-1003 . -430) 143868) ((-1003 . -552) 143834) ((-1003 . -555) 143815) ((-1003 . -1013) T) ((-1003 . -1129) T) ((-1003 . -13) T) ((-1003 . -72) T) ((-1003 . -64) T) ((-1001 . -1006) 143799) ((-1001 . -557) 143783) ((-1001 . -1013) 143761) ((-1001 . -552) 143728) ((-1001 . -1129) 143706) ((-1001 . -13) 143684) ((-1001 . -72) 143662) ((-1001 . -1007) 143620) ((-1000 . -228) 143604) ((-1000 . -555) 143588) ((-1000 . -950) 143572) ((-1000 . -759) T) ((-1000 . -72) T) ((-1000 . -1013) T) ((-1000 . -552) 143554) ((-1000 . -756) T) ((-1000 . -186) 143541) ((-1000 . -13) T) ((-1000 . -1129) T) ((-1000 . -189) T) ((-999 . -213) 143478) ((-999 . -555) 143221) ((-999 . -950) 143050) ((-999 . -553) NIL) ((-999 . -277) 143011) ((-999 . -355) 142995) ((-999 . -38) 142847) ((-999 . -82) 142672) ((-999 . -963) 142518) ((-999 . -968) 142364) ((-999 . -588) 142274) ((-999 . -590) 142163) ((-999 . -582) 142015) ((-999 . -654) 141867) ((-999 . -118) 141846) ((-999 . -120) 141825) ((-999 . -146) 141739) ((-999 . -495) 141673) ((-999 . -246) 141607) ((-999 . -47) 141568) ((-999 . -329) 141552) ((-999 . -580) 141500) ((-999 . -392) 141454) ((-999 . -455) 141317) ((-999 . -809) 141252) ((-999 . -806) 141150) ((-999 . -811) 141052) ((-999 . -796) NIL) ((-999 . -821) 141031) ((-999 . -1134) 141010) ((-999 . -861) 140955) ((-999 . -260) 140942) ((-999 . -190) 140921) ((-999 . -104) T) ((-999 . -25) T) ((-999 . -72) T) ((-999 . -552) 140903) ((-999 . -1013) T) ((-999 . -23) T) ((-999 . -21) T) ((-999 . -970) T) ((-999 . -1025) T) ((-999 . -1061) T) ((-999 . -663) T) ((-999 . -961) T) ((-999 . -186) 140851) ((-999 . -13) T) ((-999 . -1129) T) ((-999 . -189) 140805) ((-999 . -225) 140789) ((-999 . -184) 140773) ((-997 . -552) 140755) ((-994 . -756) T) ((-994 . -552) 140737) ((-994 . -1013) T) ((-994 . -72) T) ((-994 . -13) T) ((-994 . -1129) T) ((-994 . -759) T) ((-994 . -553) 140718) ((-991 . -661) 140697) ((-991 . -950) 140595) ((-991 . -355) 140579) ((-991 . -580) 140527) ((-991 . -590) 140404) ((-991 . -329) 140388) ((-991 . -322) 140367) ((-991 . -120) 140346) ((-991 . -555) 140171) ((-991 . -654) 140045) ((-991 . -582) 139919) ((-991 . -588) 139817) ((-991 . -968) 139730) ((-991 . -963) 139643) ((-991 . -82) 139535) ((-991 . -38) 139409) ((-991 . -353) 139388) ((-991 . -345) 139367) ((-991 . -118) 139321) ((-991 . -1066) 139300) ((-991 . -299) 139279) ((-991 . -320) 139233) ((-991 . -201) 139187) ((-991 . -246) 139141) ((-991 . -258) 139095) ((-991 . -392) 139049) ((-991 . -495) 139003) ((-991 . -832) 138957) ((-991 . -1134) 138911) ((-991 . -312) 138865) ((-991 . -190) 138793) ((-991 . -186) 138669) ((-991 . -189) 138551) ((-991 . -225) 138521) ((-991 . -806) 138393) ((-991 . -811) 138267) ((-991 . -809) 138200) ((-991 . -184) 138170) ((-991 . -553) 138154) ((-991 . -21) T) ((-991 . -23) T) ((-991 . -1013) T) ((-991 . -552) 138136) ((-991 . -1129) T) ((-991 . -13) T) ((-991 . -72) T) ((-991 . -25) T) ((-991 . -104) T) ((-991 . -961) T) ((-991 . -663) T) ((-991 . -1061) T) ((-991 . -1025) T) ((-991 . -970) T) ((-991 . -146) T) ((-989 . -1013) T) ((-989 . -552) 138118) ((-989 . -1129) T) ((-989 . -13) T) ((-989 . -72) T) ((-989 . -241) 138097) ((-988 . -1013) T) ((-988 . -552) 138079) ((-988 . -1129) T) ((-988 . -13) T) ((-988 . -72) T) ((-987 . -1013) T) ((-987 . -552) 138061) ((-987 . -1129) T) ((-987 . -13) T) ((-987 . -72) T) ((-987 . -241) 138040) ((-987 . -950) 138017) ((-987 . -555) 137994) ((-986 . -1129) T) ((-986 . -13) T) ((-985 . -995) T) ((-985 . -430) 137975) ((-985 . -552) 137941) ((-985 . -555) 137922) ((-985 . -1013) T) ((-985 . -1129) T) ((-985 . -13) T) ((-985 . -72) T) ((-985 . -64) T) ((-978 . -995) T) ((-978 . -430) 137903) ((-978 . -552) 137869) ((-978 . -555) 137850) ((-978 . -1013) T) ((-978 . -1129) T) ((-978 . -13) T) ((-978 . -72) T) ((-978 . -64) T) ((-975 . -483) T) ((-975 . -1134) T) ((-975 . -1066) T) ((-975 . -950) 137832) ((-975 . -553) 137747) ((-975 . -933) T) ((-975 . -796) 137729) ((-975 . -755) T) ((-975 . -721) T) ((-975 . -718) T) ((-975 . -759) T) ((-975 . -756) T) ((-975 . -716) T) ((-975 . -714) T) ((-975 . -740) T) ((-975 . -590) 137701) ((-975 . -580) 137683) ((-975 . -832) T) ((-975 . -495) T) ((-975 . -246) T) ((-975 . -146) T) ((-975 . -555) 137655) ((-975 . -654) 137642) ((-975 . -582) 137629) ((-975 . -968) 137616) ((-975 . -963) 137603) ((-975 . -82) 137588) ((-975 . -38) 137575) ((-975 . -392) T) ((-975 . -258) T) ((-975 . -189) T) ((-975 . -186) 137562) ((-975 . -190) T) ((-975 . -116) T) ((-975 . -961) T) ((-975 . -663) T) ((-975 . -1061) T) ((-975 . -1025) T) ((-975 . -970) T) ((-975 . -21) T) ((-975 . -588) 137534) ((-975 . -23) T) ((-975 . -1013) T) ((-975 . -552) 137516) ((-975 . -1129) T) ((-975 . -13) T) ((-975 . -72) T) ((-975 . -25) T) ((-975 . -104) T) ((-975 . -120) T) ((-975 . -557) 137497) ((-974 . -980) 137476) ((-974 . -72) T) ((-974 . -13) T) ((-974 . -1129) T) ((-974 . -552) 137458) ((-974 . -1013) T) ((-971 . -1129) T) ((-971 . -13) T) ((-971 . -1013) 137436) ((-971 . -552) 137403) ((-971 . -72) 137381) ((-966 . -965) 137321) ((-966 . -582) 137266) ((-966 . -654) 137211) ((-966 . -429) 137195) ((-966 . -455) 137128) ((-966 . -260) 137066) ((-966 . -34) T) ((-966 . -318) 137050) ((-966 . -590) 137034) ((-966 . -588) 137003) ((-966 . -104) T) ((-966 . -25) T) ((-966 . -72) T) ((-966 . -13) T) ((-966 . -1129) T) ((-966 . -552) 136965) ((-966 . -1013) T) ((-966 . -23) T) ((-966 . -21) T) ((-966 . -968) 136949) ((-966 . -963) 136933) ((-966 . -82) 136912) ((-966 . -1187) 136882) ((-966 . -553) 136843) ((-958 . -983) 136772) ((-958 . -889) 136701) ((-958 . -318) 136666) ((-958 . -553) 136608) ((-958 . -429) 136573) ((-958 . -1013) T) ((-958 . -455) 136457) ((-958 . -260) 136365) ((-958 . -552) 136308) ((-958 . -72) T) ((-958 . -1129) T) ((-958 . -13) T) ((-958 . -34) T) ((-958 . -124) 136273) ((-958 . -1035) 136238) ((-958 . -1124) 136167) ((-948 . -995) T) ((-948 . -430) 136148) ((-948 . -552) 136114) ((-948 . -555) 136095) ((-948 . -1013) T) ((-948 . -1129) T) ((-948 . -13) T) ((-948 . -72) T) ((-948 . -64) T) ((-947 . -146) T) ((-947 . -555) 136064) ((-947 . -970) T) ((-947 . -1025) T) ((-947 . -1061) T) ((-947 . -663) T) ((-947 . -961) T) ((-947 . -590) 136038) ((-947 . -588) 135997) ((-947 . -104) T) ((-947 . -25) T) ((-947 . -72) T) ((-947 . -13) T) ((-947 . -1129) T) ((-947 . -552) 135979) ((-947 . -1013) T) ((-947 . -23) T) ((-947 . -21) T) ((-947 . -968) 135953) ((-947 . -963) 135927) ((-947 . -82) 135894) ((-947 . -38) 135878) ((-947 . -582) 135862) ((-947 . -654) 135846) ((-940 . -983) 135815) ((-940 . -889) 135784) ((-940 . -318) 135768) ((-940 . -553) 135729) ((-940 . -429) 135713) ((-940 . -1013) T) ((-940 . -455) 135646) ((-940 . -260) 135584) ((-940 . -552) 135546) ((-940 . -72) T) ((-940 . -1129) T) ((-940 . -13) T) ((-940 . -34) T) ((-940 . -124) 135530) ((-940 . -1035) 135514) ((-940 . -1124) 135483) ((-939 . -1013) T) ((-939 . -552) 135465) ((-939 . -1129) 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) 135350) ((-937 . -355) 135312) ((-937 . -201) T) ((-937 . -246) T) ((-937 . -258) T) ((-937 . -392) T) ((-937 . -38) 135249) ((-937 . -582) 135186) ((-937 . -654) 135123) ((-937 . -555) 135060) ((-937 . -495) T) ((-937 . -832) T) ((-937 . -1134) T) ((-937 . -312) T) ((-937 . -82) 134969) ((-937 . -963) 134906) ((-937 . -968) 134843) ((-937 . -146) T) ((-937 . -120) T) ((-937 . -590) 134780) ((-937 . -588) 134717) ((-937 . -104) T) ((-937 . -25) T) ((-937 . -72) T) ((-937 . -13) T) ((-937 . -1129) T) ((-937 . -552) 134699) ((-937 . -1013) T) ((-937 . -23) T) ((-937 . -21) T) ((-937 . -961) T) ((-937 . -663) T) ((-937 . -1061) T) ((-937 . -1025) T) ((-937 . -970) T) ((-932 . -995) T) ((-932 . -430) 134680) ((-932 . -552) 134646) ((-932 . -555) 134627) ((-932 . -1013) T) ((-932 . -1129) T) ((-932 . -13) T) ((-932 . -72) T) ((-932 . -64) T) ((-917 . -904) 134609) ((-917 . -1066) T) ((-917 . -555) 134559) ((-917 . -950) 134519) ((-917 . -553) 134449) ((-917 . -933) T) ((-917 . -821) NIL) ((-917 . -794) 134431) ((-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) 134413) ((-917 . -343) 134395) ((-917 . -580) 134377) ((-917 . -329) 134359) ((-917 . -241) NIL) ((-917 . -260) NIL) ((-917 . -455) NIL) ((-917 . -288) 134341) ((-917 . -201) T) ((-917 . -82) 134268) ((-917 . -963) 134218) ((-917 . -968) 134168) ((-917 . -246) T) ((-917 . -654) 134118) ((-917 . -582) 134068) ((-917 . -590) 134018) ((-917 . -588) 133968) ((-917 . -38) 133918) ((-917 . -258) T) ((-917 . -392) T) ((-917 . -146) T) ((-917 . -495) T) ((-917 . -832) T) ((-917 . -1134) T) ((-917 . -312) T) ((-917 . -190) T) ((-917 . -186) 133905) ((-917 . -189) T) ((-917 . -225) 133887) ((-917 . -806) NIL) ((-917 . -811) NIL) ((-917 . -809) NIL) ((-917 . -184) 133869) ((-917 . -120) T) ((-917 . -118) NIL) ((-917 . -104) T) ((-917 . -25) T) ((-917 . -72) T) ((-917 . -13) T) ((-917 . -1129) T) ((-917 . -552) 133829) ((-917 . -1013) T) ((-917 . -23) T) ((-917 . -21) T) ((-917 . -961) 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109508) ((-735 . -34) T) ((-735 . -318) 109492) ((-735 . -320) 109471) ((-735 . -190) 109424) ((-735 . -588) 109212) ((-735 . -970) 109191) ((-735 . -1025) 109170) ((-735 . -1061) 109149) ((-735 . -663) 109128) ((-735 . -961) 109107) ((-735 . -186) 109003) ((-735 . -189) 108905) ((-735 . -225) 108875) ((-735 . -806) 108747) ((-735 . -811) 108621) ((-735 . -809) 108554) ((-735 . -184) 108524) ((-735 . -552) 108221) ((-735 . -968) 108146) ((-735 . -963) 108051) ((-735 . -82) 107971) ((-735 . -104) 107846) ((-735 . -25) 107683) ((-735 . -72) 107420) ((-735 . -13) T) ((-735 . -1129) T) ((-735 . -1013) 107176) ((-735 . -23) 107032) ((-735 . -21) 106947) ((-722 . -720) 106931) ((-722 . -759) 106910) ((-722 . -756) 106889) ((-722 . -950) 106682) ((-722 . -555) 106535) ((-722 . -355) 106499) ((-722 . -241) 106457) ((-722 . -260) 106422) ((-722 . -455) 106334) ((-722 . -288) 106318) ((-722 . -320) 106297) ((-722 . -553) 106258) ((-722 . -120) 106237) ((-722 . -118) 106216) ((-722 . -654) 106200) ((-722 . -582) 106184) ((-722 . -590) 106158) ((-722 . -588) 106117) ((-722 . -104) T) ((-722 . -25) T) ((-722 . -72) T) ((-722 . -13) T) ((-722 . -1129) T) ((-722 . -552) 106099) ((-722 . -1013) T) ((-722 . -23) T) ((-722 . -21) T) ((-722 . -968) 106083) ((-722 . -963) 106067) ((-722 . -82) 106046) ((-722 . -961) T) ((-722 . -663) T) ((-722 . -1061) T) ((-722 . -1025) T) ((-722 . -970) T) ((-722 . -38) 106030) ((-704 . -1155) 106014) ((-704 . -1066) 105992) ((-704 . -553) NIL) ((-704 . -260) 105979) ((-704 . -455) 105927) ((-704 . -277) 105904) ((-704 . -950) 105766) ((-704 . -355) 105750) ((-704 . -38) 105582) ((-704 . -82) 105387) ((-704 . -963) 105213) ((-704 . -968) 105039) ((-704 . -588) 104949) ((-704 . -590) 104838) ((-704 . -582) 104670) ((-704 . -654) 104502) ((-704 . -555) 104258) ((-704 . -118) 104237) ((-704 . -120) 104216) ((-704 . -47) 104193) ((-704 . -329) 104177) ((-704 . -580) 104125) ((-704 . -809) 104069) ((-704 . -806) 103976) ((-704 . -811) 103887) ((-704 . -796) NIL) ((-704 . -821) 103866) ((-704 . -1134) 103845) ((-704 . -861) 103815) ((-704 . -832) 103794) ((-704 . -495) 103708) ((-704 . -246) 103622) ((-704 . -146) 103516) ((-704 . -392) 103450) ((-704 . -258) 103429) ((-704 . -241) 103356) ((-704 . -190) T) ((-704 . -104) T) ((-704 . -25) T) ((-704 . -72) T) ((-704 . -552) 103317) ((-704 . -1013) T) ((-704 . -23) T) ((-704 . -21) T) ((-704 . -970) T) ((-704 . -1025) T) ((-704 . -1061) T) ((-704 . -663) T) ((-704 . -961) T) ((-704 . -186) 103304) ((-704 . -13) T) ((-704 . -1129) T) ((-704 . -189) T) ((-704 . -225) 103288) ((-704 . -184) 103272) ((-703 . -977) 103239) ((-703 . -553) 102874) ((-703 . -260) 102861) ((-703 . -455) 102813) ((-703 . -277) 102785) ((-703 . -950) 102644) ((-703 . -355) 102628) ((-703 . -38) 102480) ((-703 . -555) 102253) ((-703 . -590) 102142) ((-703 . -588) 102052) ((-703 . -970) T) ((-703 . -1025) T) ((-703 . -1061) T) ((-703 . -663) T) ((-703 . -961) T) ((-703 . -82) 101877) ((-703 . -963) 101723) ((-703 . -968) 101569) ((-703 . -21) T) ((-703 . -23) T) ((-703 . -1013) T) ((-703 . -552) 101483) ((-703 . -1129) T) ((-703 . -13) T) ((-703 . -72) T) ((-703 . -25) T) ((-703 . -104) T) ((-703 . -582) 101335) ((-703 . -654) 101187) ((-703 . -118) 101166) ((-703 . -120) 101145) ((-703 . -146) 101059) ((-703 . -495) 100993) ((-703 . -246) 100927) ((-703 . -47) 100899) ((-703 . -329) 100883) ((-703 . -580) 100831) ((-703 . -392) 100785) ((-703 . -809) 100769) ((-703 . -806) 100751) ((-703 . -811) 100735) ((-703 . -796) 100594) ((-703 . -821) 100573) ((-703 . -1134) 100552) ((-703 . -861) 100519) ((-696 . -1013) T) ((-696 . -552) 100501) ((-696 . -1129) T) ((-696 . -13) T) ((-696 . -72) T) ((-694 . -717) T) ((-694 . -104) T) ((-694 . -25) T) ((-694 . -72) T) ((-694 . -13) T) ((-694 . -1129) T) ((-694 . -552) 100483) ((-694 . -1013) T) ((-694 . -23) T) ((-694 . -716) T) ((-694 . -756) T) ((-694 . -759) T) ((-694 . -718) T) ((-694 . -721) T) ((-694 . -663) T) ((-694 . -1025) T) ((-675 . -676) 100467) ((-675 . -1011) 100451) ((-675 . -193) 100435) ((-675 . -553) 100396) ((-675 . -124) 100380) ((-675 . -1035) 100364) ((-675 . -34) T) ((-675 . -13) T) ((-675 . -1129) T) ((-675 . -72) T) ((-675 . -552) 100346) ((-675 . -260) 100284) ((-675 . -455) 100217) ((-675 . -1013) T) ((-675 . -429) 100201) ((-675 . -76) 100185) ((-675 . -634) 100169) ((-675 . -318) 100153) ((-674 . -961) T) ((-674 . -663) T) ((-674 . -1061) T) ((-674 . -1025) T) ((-674 . -970) T) ((-674 . -21) T) ((-674 . -588) 100098) ((-674 . -23) T) ((-674 . -1013) T) ((-674 . -552) 100080) ((-674 . -1129) T) ((-674 . -13) T) ((-674 . -72) T) ((-674 . -25) T) ((-674 . -104) T) ((-674 . -590) 100040) ((-674 . -555) 99996) ((-674 . -950) 99967) ((-674 . -120) 99946) ((-674 . -118) 99925) ((-674 . -38) 99895) ((-674 . -82) 99860) ((-674 . -963) 99830) ((-674 . -968) 99800) ((-674 . -582) 99770) ((-674 . -654) 99740) ((-674 . -320) 99693) ((-670 . -861) 99646) ((-670 . -555) 99438) ((-670 . -950) 99316) ((-670 . -1134) 99295) ((-670 . -821) 99274) ((-670 . -796) NIL) ((-670 . -811) 99251) ((-670 . -806) 99226) ((-670 . -809) 99203) ((-670 . -455) 99141) ((-670 . -392) 99095) ((-670 . -580) 99043) ((-670 . -590) 98932) ((-670 . -329) 98916) ((-670 . -47) 98881) ((-670 . -38) 98733) ((-670 . -582) 98585) ((-670 . -654) 98437) ((-670 . -246) 98371) ((-670 . -495) 98305) ((-670 . -82) 98130) ((-670 . -963) 97976) ((-670 . -968) 97822) ((-670 . -146) 97736) ((-670 . -120) 97715) ((-670 . -118) 97694) ((-670 . -588) 97604) ((-670 . -104) T) ((-670 . -25) T) ((-670 . -72) T) ((-670 . -13) T) ((-670 . -1129) T) ((-670 . -552) 97586) ((-670 . -1013) T) ((-670 . -23) T) ((-670 . -21) T) ((-670 . -961) T) ((-670 . -663) T) ((-670 . -1061) T) ((-670 . -1025) T) ((-670 . -970) T) ((-670 . -355) 97570) ((-670 . -277) 97535) ((-670 . -260) 97522) ((-670 . -553) 97383) ((-664 . -665) 97367) ((-664 . -80) 97351) ((-664 . -1129) T) ((-664 . |MappingCategory|) 97325) ((-664 . -1023) 97309) ((-664 . -1013) T) ((-664 . 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. -1129) T) ((-181 . -72) 17825) ((-181 . -552) 17760) ((-181 . -260) 17698) ((-181 . -455) 17631) ((-181 . -1013) 17609) ((-181 . -429) 17593) ((-181 . -1035) 17577) ((-181 . -57) 17535) ((-179 . -347) T) ((-179 . -120) T) ((-179 . -555) 17485) ((-179 . -590) 17450) ((-179 . -588) 17400) ((-179 . -104) T) ((-179 . -25) T) ((-179 . -72) T) ((-179 . -13) T) ((-179 . -1129) T) ((-179 . -552) 17382) ((-179 . -1013) T) ((-179 . -23) T) ((-179 . -21) T) ((-179 . -970) T) ((-179 . -1025) T) ((-179 . -1061) T) ((-179 . -663) T) ((-179 . -961) T) ((-179 . -553) 17312) ((-179 . -312) T) ((-179 . -1134) T) ((-179 . -832) T) ((-179 . -495) T) ((-179 . -146) T) ((-179 . -654) 17277) ((-179 . -582) 17242) ((-179 . -38) 17207) ((-179 . -392) T) ((-179 . -258) T) ((-179 . -82) 17156) ((-179 . -963) 17121) ((-179 . -968) 17086) ((-179 . -246) T) ((-179 . -201) T) ((-179 . -755) T) ((-179 . -721) T) ((-179 . -718) T) ((-179 . -759) T) ((-179 . -756) T) ((-179 . -716) T) ((-179 . -714) T) ((-179 . -796) 17068) ((-179 . -915) T) ((-179 . -933) T) ((-179 . -950) 17028) ((-179 . -973) T) ((-179 . -190) T) ((-179 . -186) 17015) ((-179 . -189) T) ((-179 . -1115) T) ((-179 . -1118) T) ((-179 . -433) T) ((-179 . -239) T) ((-179 . -66) T) ((-179 . -35) T) ((-177 . -560) 16992) ((-177 . -555) 16954) ((-177 . -590) 16921) ((-177 . -588) 16873) ((-177 . -970) T) ((-177 . -1025) T) ((-177 . -1061) T) ((-177 . -663) T) ((-177 . -961) T) ((-177 . -21) T) ((-177 . -23) T) ((-177 . -1013) T) ((-177 . -552) 16855) ((-177 . -1129) T) ((-177 . -13) T) ((-177 . -72) T) ((-177 . -25) T) ((-177 . -104) T) ((-177 . -950) 16832) ((-176 . -214) 16816) ((-176 . -1034) 16800) ((-176 . -76) 16784) ((-176 . -429) 16768) ((-176 . -1013) 16746) ((-176 . -455) 16679) ((-176 . -260) 16617) ((-176 . -552) 16552) ((-176 . -72) 16506) ((-176 . -1129) T) ((-176 . -13) T) ((-176 . -34) T) ((-176 . -1035) 16490) ((-176 . -318) 16474) ((-176 . -908) 16458) ((-172 . -995) T) ((-172 . -430) 16439) ((-172 . -552) 16405) ((-172 . -555) 16386) ((-172 . -1013) T) ((-172 . -1129) T) ((-172 . -13) T) ((-172 . -72) T) ((-172 . -64) T) ((-171 . -904) 16368) ((-171 . -1066) T) ((-171 . -555) 16318) ((-171 . -950) 16278) ((-171 . -553) 16208) ((-171 . -933) T) ((-171 . -821) NIL) ((-171 . -794) 16190) ((-171 . -755) T) ((-171 . -721) T) ((-171 . -718) T) ((-171 . -759) T) ((-171 . -756) T) ((-171 . -716) T) ((-171 . -714) T) ((-171 . -740) T) ((-171 . -796) 16172) ((-171 . -343) 16154) ((-171 . -580) 16136) ((-171 . -329) 16118) ((-171 . -241) NIL) ((-171 . -260) NIL) ((-171 . -455) NIL) ((-171 . -288) 16100) ((-171 . -201) T) ((-171 . -82) 16027) ((-171 . -963) 15977) ((-171 . -968) 15927) ((-171 . -246) T) ((-171 . -654) 15877) ((-171 . -582) 15827) ((-171 . -590) 15777) ((-171 . -588) 15727) ((-171 . -38) 15677) ((-171 . -258) T) ((-171 . -392) T) ((-171 . -146) T) ((-171 . -495) T) ((-171 . -832) T) ((-171 . -1134) T) ((-171 . -312) T) ((-171 . -190) T) ((-171 . -186) 15664) ((-171 . -189) T) ((-171 . -225) 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\ No newline at end of file
diff --git a/src/share/algebra/compress.daase b/src/share/algebra/compress.daase
index 501c2736..569479dd 100644
--- a/src/share/algebra/compress.daase
+++ b/src/share/algebra/compress.daase
@@ -1,6 +1,6 @@
 
-(30 . 3577992037)            
-(4000 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain|
+(30 . 3577996047)            
+(3999 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain|
  ATTRIBUTE |package| |domain| |category| CATEGORY |nobranch| AND |Join|
  |ofType| SIGNATURE "failed" "algebra" |OneDimensionalArrayAggregate&|
  |OneDimensionalArrayAggregate| |AbelianGroup&| |AbelianGroup| |AbelianMonoid&|
@@ -139,7 +139,7 @@
  |HomogeneousAggregate&| |HomogeneousAggregate| |HomotopicTo| |Hostname|
  |HyperbolicFunctionCategory&| |HyperbolicFunctionCategory| |InnerAlgFactor|
  |InnerAlgebraicNumber| |IndexedOneDimensionalArray| |InnerTwoDimensionalArray|
- |ChineseRemainderToolsForIntegralBases| |IntegralBasisTools| |IndexedBits|
+ |ChineseRemainderToolsForIntegralBases| |IntegralBasisTools|
  |IntegralBasisPolynomialTools| |IndexCard| |InnerCommonDenominator|
  |PolynomialIdeals| |IdealDecompositionPackage| |IdempotentOperatorCategory|
  |Identifier| |IndexedDirectProductAbelianGroup|
diff --git a/src/share/algebra/interp.daase b/src/share/algebra/interp.daase
index 801bb989..4105f186 100644
--- a/src/share/algebra/interp.daase
+++ b/src/share/algebra/interp.daase
@@ -1,4052 +1,4049 @@
 
-(2796257 . 3577992046)       
-((-1736 (((-85) (-1 (-85) |#2| |#2|) $) 86 T ELT) (((-85) $) NIL T ELT)) (-1734 (($ (-1 (-85) |#2| |#2|) $) 18 T ELT) (($ $) NIL T ELT)) (-3790 ((|#2| $ (-485) |#2|) NIL T ELT) ((|#2| $ (-1147 (-485)) |#2|) 44 T ELT)) (-2298 (($ $) 80 T ELT)) (-3844 ((|#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)) (-3421 (((-485) (-1 (-85) |#2|) $) 27 T ELT) (((-485) |#2| $) NIL T ELT) (((-485) |#2| $ (-485)) 96 T ELT)) (-3520 (($ (-1 (-85) |#2| |#2|) $ $) 64 T ELT) (($ $ $) NIL T ELT)) (-2610 (((-584 |#2|) $) 13 T ELT)) (-3328 (($ (-1 |#2| |#2|) $) 37 T ELT)) (-3960 (($ (-1 |#2| |#2|) $) NIL T ELT) (($ (-1 |#2| |#2| |#2|) $ $) 60 T ELT)) (-2305 (($ |#2| $ (-485)) NIL T ELT) (($ $ $ (-485)) 67 T ELT)) (-1355 (((-3 |#2| "failed") (-1 (-85) |#2|) $) 29 T ELT)) (-1732 (((-85) (-1 (-85) |#2|) $) 23 T ELT)) (-3802 ((|#2| $ (-485) |#2|) NIL T ELT) ((|#2| $ (-485)) NIL T ELT) (($ $ (-1147 (-485))) 66 T ELT)) (-2306 (($ $ (-485)) 76 T ELT) (($ $ (-1147 (-485))) 75 T ELT)) (-1731 (((-695) |#2| $) NIL T ELT) (((-695) (-1 (-85) |#2|) $) 34 T ELT)) (-1735 (($ $ $ (-485)) 69 T ELT)) (-3402 (($ $) 68 T ELT)) (-3532 (($ (-584 |#2|)) 73 T ELT)) (-3804 (($ $ |#2|) NIL T ELT) (($ |#2| $) NIL T ELT) (($ $ $) 87 T ELT) (($ (-584 $)) 85 T ELT)) (-3948 (((-773) $) 92 T ELT)) (-1733 (((-85) (-1 (-85) |#2|) $) 22 T ELT)) (-3058 (((-85) $ $) 95 T ELT)) (-2687 (((-85) $ $) 99 T ELT))) 
-(((-18 |#1| |#2|) (-10 -7 (-15 -3058 ((-85) |#1| |#1|)) (-15 -3948 ((-773) |#1|)) (-15 -3328 (|#1| (-1 |#2| |#2|) |#1|)) (-15 -2687 ((-85) |#1| |#1|)) (-15 -1734 (|#1| |#1|)) (-15 -1734 (|#1| (-1 (-85) |#2| |#2|) |#1|)) (-15 -2298 (|#1| |#1|)) (-15 -1735 (|#1| |#1| |#1| (-485))) (-15 -1736 ((-85) |#1|)) (-15 -3520 (|#1| |#1| |#1|)) (-15 -3421 ((-485) |#2| |#1| (-485))) (-15 -3421 ((-485) |#2| |#1|)) (-15 -3421 ((-485) (-1 (-85) |#2|) |#1|)) (-15 -1736 ((-85) (-1 (-85) |#2| |#2|) |#1|)) (-15 -3520 (|#1| (-1 (-85) |#2| |#2|) |#1| |#1|)) (-15 -1733 ((-85) (-1 (-85) |#2|) |#1|)) (-15 -1732 ((-85) (-1 (-85) |#2|) |#1|)) (-15 -1731 ((-695) (-1 (-85) |#2|) |#1|)) (-15 -2610 ((-584 |#2|) |#1|)) (-15 -3844 (|#2| (-1 |#2| |#2| |#2|) |#1|)) (-15 -3844 (|#2| (-1 |#2| |#2| |#2|) |#1| |#2|)) (-15 -1731 ((-695) |#2| |#1|)) (-15 -3844 (|#2| (-1 |#2| |#2| |#2|) |#1| |#2| |#2|)) (-15 -3790 (|#2| |#1| (-1147 (-485)) |#2|)) (-15 -2305 (|#1| |#1| |#1| (-485))) (-15 -2305 (|#1| |#2| |#1| (-485))) (-15 -2306 (|#1| |#1| (-1147 (-485)))) (-15 -2306 (|#1| |#1| (-485))) (-15 -3960 (|#1| (-1 |#2| |#2| |#2|) |#1| |#1|)) (-15 -3804 (|#1| (-584 |#1|))) (-15 -3804 (|#1| |#1| |#1|)) (-15 -3804 (|#1| |#2| |#1|)) (-15 -3804 (|#1| |#1| |#2|)) (-15 -3802 (|#1| |#1| (-1147 (-485)))) (-15 -3532 (|#1| (-584 |#2|))) (-15 -1355 ((-3 |#2| "failed") (-1 (-85) |#2|) |#1|)) (-15 -3802 (|#2| |#1| (-485))) (-15 -3802 (|#2| |#1| (-485) |#2|)) (-15 -3790 (|#2| |#1| (-485) |#2|)) (-15 -3960 (|#1| (-1 |#2| |#2|) |#1|)) (-15 -3402 (|#1| |#1|))) (-19 |#2|) (-1130)) (T -18)) 
+(2792511 . 3577996055)       
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 NIL 
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-(((-19 |#1|) (-113) (-1130)) (T -19)) 
+((-2569 (((-85) $ $) 17 (|has| |#1| (-72)) ELT)) (-2198 (((-1185) $ (-484) (-484)) 35 (|has| $ (-1035 |#1|)) ELT)) (-1735 (((-85) (-1 (-85) |#1| |#1|) $) 97 T ELT) (((-85) $) 91 (|has| |#1| (-756)) ELT)) (-1733 (($ (-1 (-85) |#1| |#1|) $) 88 (|has| $ (-1035 |#1|)) ELT) (($ $) 87 (-12 (|has| |#1| (-756)) (|has| $ (-1035 |#1|))) ELT)) (-2910 (($ (-1 (-85) |#1| |#1|) $) 98 T ELT) (($ $) 92 (|has| |#1| (-756)) ELT)) (-3789 ((|#1| $ (-484) |#1|) 47 (|has| $ (-6 -3997)) ELT) ((|#1| $ (-1146 (-484)) |#1|) 55 (|has| $ (-1035 |#1|)) ELT)) (-3711 (($ (-1 (-85) |#1|) $) 70 (|has| $ (-318 |#1|)) ELT)) (-3725 (($) 6 T CONST)) (-2297 (($ $) 89 (|has| $ (-1035 |#1|)) ELT)) (-2298 (($ $) 99 T ELT)) (-1353 (($ $) 72 (-12 (|has| |#1| (-72)) (|has| $ (-318 |#1|))) ELT)) (-3407 (($ |#1| $) 71 (-12 (|has| |#1| (-72)) (|has| $ (-318 |#1|))) ELT) (($ (-1 (-85) |#1|) $) 69 (|has| $ (-318 |#1|)) ELT)) (-3843 ((|#1| (-1 |#1| |#1| |#1|) $ |#1| |#1|) 110 (|has| |#1| (-72)) ELT) ((|#1| (-1 |#1| |#1| |#1|) $ |#1|) 107 T ELT) ((|#1| (-1 |#1| |#1| |#1|) $) 106 T ELT)) (-1576 ((|#1| $ (-484) |#1|) 48 (|has| $ (-6 -3997)) ELT)) (-3113 ((|#1| $ (-484)) 46 T ELT)) (-3420 (((-484) (-1 (-85) |#1|) $) 96 T ELT) (((-484) |#1| $) 95 (|has| |#1| (-72)) ELT) (((-484) |#1| $ (-484)) 94 (|has| |#1| (-72)) ELT)) (-3615 (($ (-694) |#1|) 65 T ELT)) (-2200 (((-484) $) 38 (|has| (-484) (-756)) ELT)) (-2532 (($ $ $) 81 (|has| |#1| (-756)) ELT)) (-3519 (($ (-1 (-85) |#1| |#1|) $ $) 100 T ELT) (($ $ $) 93 (|has| |#1| (-756)) ELT)) (-2609 (((-583 |#1|) $) 105 T ELT)) (-3246 (((-85) |#1| $) 109 (|has| |#1| (-72)) ELT)) (-2201 (((-484) $) 39 (|has| (-484) (-756)) ELT)) (-2858 (($ $ $) 82 (|has| |#1| (-756)) ELT)) (-3327 (($ (-1 |#1| |#1|) $) 25 T ELT)) (-3959 (($ (-1 |#1| |#1|) $) 26 T ELT) (($ (-1 |#1| |#1| |#1|) $ $) 60 T ELT)) (-3243 (((-1073) $) 20 (|has| |#1| (-1013)) ELT)) (-2304 (($ |#1| $ (-484)) 57 T ELT) (($ $ $ (-484)) 56 T ELT)) (-2203 (((-583 (-484)) $) 41 T ELT)) (-2204 (((-85) (-484) $) 42 T ELT)) (-3244 (((-1033) $) 19 (|has| |#1| (-1013)) ELT)) (-3802 ((|#1| $) 37 (|has| (-484) (-756)) ELT)) (-1354 (((-3 |#1| "failed") (-1 (-85) |#1|) $) 68 T ELT)) (-2199 (($ $ |#1|) 36 (|has| $ (-1035 |#1|)) ELT)) (-1731 (((-85) (-1 (-85) |#1|) $) 103 T ELT)) (-3769 (($ $ (-583 (-249 |#1|))) 24 (-12 (|has| |#1| (-260 |#1|)) (|has| |#1| (-1013))) ELT) (($ $ (-249 |#1|)) 23 (-12 (|has| |#1| (-260 |#1|)) (|has| |#1| (-1013))) ELT) (($ $ |#1| |#1|) 22 (-12 (|has| |#1| (-260 |#1|)) (|has| |#1| (-1013))) ELT) (($ $ (-583 |#1|) (-583 |#1|)) 21 (-12 (|has| |#1| (-260 |#1|)) (|has| |#1| (-1013))) ELT)) (-1222 (((-85) $ $) 10 T ELT)) (-2202 (((-85) |#1| $) 40 (-12 (|has| $ (-318 |#1|)) (|has| |#1| (-72))) ELT)) (-2205 (((-583 |#1|) $) 43 T ELT)) (-3404 (((-85) $) 7 T ELT)) (-3566 (($) 8 T ELT)) (-3801 ((|#1| $ (-484) |#1|) 45 T ELT) ((|#1| $ (-484)) 44 T ELT) (($ $ (-1146 (-484))) 66 T ELT)) (-2305 (($ $ (-484)) 59 T ELT) (($ $ (-1146 (-484))) 58 T ELT)) (-1730 (((-694) |#1| $) 108 (|has| |#1| (-72)) ELT) (((-694) (-1 (-85) |#1|) $) 104 T ELT)) (-1734 (($ $ $ (-484)) 90 (|has| $ (-1035 |#1|)) ELT)) (-3401 (($ $) 9 T ELT)) (-3973 (((-473) $) 73 (|has| |#1| (-553 (-473))) ELT)) (-3531 (($ (-583 |#1|)) 67 T ELT)) (-3803 (($ $ |#1|) 64 T ELT) (($ |#1| $) 63 T ELT) (($ $ $) 62 T ELT) (($ (-583 $)) 61 T ELT)) (-3947 (((-772) $) 15 (|has| |#1| (-552 (-772))) ELT)) (-1265 (((-85) $ $) 18 (|has| |#1| (-72)) ELT)) (-1732 (((-85) (-1 (-85) |#1|) $) 102 T ELT)) (-2567 (((-85) $ $) 83 (|has| |#1| (-756)) ELT)) (-2568 (((-85) $ $) 85 (|has| |#1| (-756)) ELT)) (-3057 (((-85) $ $) 16 (|has| |#1| (-72)) ELT)) (-2685 (((-85) $ $) 84 (|has| |#1| (-756)) ELT)) (-2686 (((-85) $ $) 86 (|has| |#1| (-756)) ELT)) (-3958 (((-694) $) 101 T ELT))) 
+(((-19 |#1|) (-113) (-1129)) (T -19)) 
 NIL 
-(-13 (-324 |t#1|) (-1036 |t#1|)) 
-(((-34) . T) ((-72) OR (|has| |#1| (-1014)) (|has| |#1| (-757)) (|has| |#1| (-72))) ((-553 (-773)) OR (|has| |#1| (-1014)) (|has| |#1| (-757)) (|has| |#1| (-553 (-773)))) ((-124 |#1|) . T) ((-554 (-474)) |has| |#1| (-554 (-474))) ((-241 (-485) |#1|) . T) ((-241 (-1147 (-485)) $) . T) ((-243 (-485) |#1|) . T) ((-260 |#1|) -12 (|has| |#1| (-260 |#1|)) (|has| |#1| (-1014))) ((-318 |#1|) . T) ((-324 |#1|) . T) ((-429 |#1|) . T) ((-539 (-485) |#1|) . T) ((-456 |#1| |#1|) -12 (|has| |#1| (-260 |#1|)) (|has| |#1| (-1014))) ((-13) . T) ((-594 |#1|) . T) ((-757) |has| |#1| (-757)) ((-760) |has| |#1| (-757)) ((-1014) OR (|has| |#1| (-1014)) (|has| |#1| (-757))) ((-1036 |#1|) . T) ((-1130) . T)) 
-((-1313 (((-3 $ "failed") $ $) 12 T ELT)) (-1215 (((-85) $ $) 27 T ELT)) (-3839 (($ $) NIL T ELT) (($ $ $) 9 T ELT)) (* (($ (-831) $) NIL T ELT) (($ (-695) $) 16 T ELT) (($ (-485) $) 25 T ELT))) 
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+(-13 (-324 |t#1|) (-1035 |t#1|)) 
+(((-34) . T) ((-72) OR (|has| |#1| (-1013)) (|has| |#1| (-756)) (|has| |#1| (-72))) ((-552 (-772)) OR (|has| |#1| (-1013)) (|has| |#1| (-756)) (|has| |#1| (-552 (-772)))) ((-124 |#1|) . T) ((-553 (-473)) |has| |#1| (-553 (-473))) ((-241 (-484) |#1|) . T) ((-241 (-1146 (-484)) $) . T) ((-243 (-484) |#1|) . T) ((-260 |#1|) -12 (|has| |#1| (-260 |#1|)) (|has| |#1| (-1013))) ((-318 |#1|) . T) ((-324 |#1|) . T) ((-429 |#1|) . T) ((-538 (-484) |#1|) . T) ((-455 |#1| |#1|) -12 (|has| |#1| (-260 |#1|)) (|has| |#1| (-1013))) ((-13) . T) ((-593 |#1|) . T) ((-756) |has| |#1| (-756)) ((-759) |has| |#1| (-756)) ((-1013) OR (|has| |#1| (-1013)) (|has| |#1| (-756))) ((-1035 |#1|) . T) ((-1129) . T)) 
+((-1312 (((-3 $ "failed") $ $) 12 T ELT)) (-1214 (((-85) $ $) 27 T ELT)) (-3838 (($ $) NIL T ELT) (($ $ $) 9 T ELT)) (* (($ (-830) $) NIL T ELT) (($ (-694) $) 16 T ELT) (($ (-484) $) 25 T ELT))) 
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 NIL 
-((-2570 (((-85) $ $) 7 T ELT)) (-3190 (((-85) $) 22 T ELT)) (-1313 (((-3 $ "failed") $ $) 26 T ELT)) (-3726 (($) 23 T CONST)) (-1215 (((-85) $ $) 20 T ELT)) (-3244 (((-1074) $) 11 T ELT)) (-3245 (((-1034) $) 12 T ELT)) (-3948 (((-773) $) 13 T ELT)) (-1266 (((-85) $ $) 6 T ELT)) (-2662 (($) 24 T CONST)) (-3058 (((-85) $ $) 8 T ELT)) (-3839 (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (-3841 (($ $ $) 18 T ELT)) (* (($ (-831) $) 17 T ELT) (($ (-695) $) 21 T ELT) (($ (-485) $) 30 T ELT))) 
+((-2569 (((-85) $ $) 7 T ELT)) (-3189 (((-85) $) 22 T ELT)) (-1312 (((-3 $ "failed") $ $) 26 T ELT)) (-3725 (($) 23 T CONST)) (-1214 (((-85) $ $) 20 T ELT)) (-3243 (((-1073) $) 11 T ELT)) (-3244 (((-1033) $) 12 T ELT)) (-3947 (((-772) $) 13 T ELT)) (-1265 (((-85) $ $) 6 T ELT)) (-2661 (($) 24 T CONST)) (-3057 (((-85) $ $) 8 T ELT)) (-3838 (($ $) 29 T ELT) (($ $ $) 28 T ELT)) (-3840 (($ $ $) 18 T ELT)) (* (($ (-830) $) 17 T ELT) (($ (-694) $) 21 T ELT) (($ (-484) $) 30 T ELT))) 
 (((-21) (-113)) (T -21)) 
-((-3839 (*1 *1 *1) (-4 *1 (-21))) (-3839 (*1 *1 *1 *1) (-4 *1 (-21)))) 
-(-13 (-104) (-589 (-485)) (-10 -8 (-15 -3839 ($ $)) (-15 -3839 ($ $ $)))) 
-(((-23) . T) ((-25) . T) ((-72) . T) ((-104) . T) ((-553 (-773)) . T) ((-13) . T) ((-589 (-485)) . T) ((-1014) . T) ((-1130) . T)) 
-((-3190 (((-85) $) 10 T ELT)) (-3726 (($) 15 T CONST)) (-1215 (((-85) $ $) 22 T ELT)) (* (($ (-831) $) 14 T ELT) (($ (-695) $) 19 T ELT))) 
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+((-3838 (*1 *1 *1) (-4 *1 (-21))) (-3838 (*1 *1 *1 *1) (-4 *1 (-21)))) 
+(-13 (-104) (-588 (-484)) (-10 -8 (-15 -3838 ($ $)) (-15 -3838 ($ $ $)))) 
+(((-23) . T) ((-25) . T) ((-72) . T) ((-104) . T) ((-552 (-772)) . T) ((-13) . T) ((-588 (-484)) . T) ((-1013) . T) ((-1129) . T)) 
+((-3189 (((-85) $) 10 T ELT)) (-3725 (($) 15 T CONST)) (-1214 (((-85) $ $) 22 T ELT)) (* (($ (-830) $) 14 T ELT) (($ (-694) $) 19 T ELT))) 
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 NIL 
-((-2570 (((-85) $ $) 7 T ELT)) (-3190 (((-85) $) 22 T ELT)) (-3726 (($) 23 T CONST)) (-1215 (((-85) $ $) 20 T ELT)) (-3244 (((-1074) $) 11 T ELT)) (-3245 (((-1034) $) 12 T ELT)) (-3948 (((-773) $) 13 T ELT)) (-1266 (((-85) $ $) 6 T ELT)) (-2662 (($) 24 T CONST)) (-3058 (((-85) $ $) 8 T ELT)) (-3841 (($ $ $) 18 T ELT)) (* (($ (-831) $) 17 T ELT) (($ (-695) $) 21 T ELT))) 
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 (((-23) (-113)) (T -23)) 
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-(-13 (-25) (-10 -8 (-15 -2662 ($) -3954) (-15 -3726 ($) -3954) (-15 -3190 ((-85) $)) (-15 * ($ (-695) $)) (-15 -1215 ((-85) $ $)))) 
-(((-25) . T) ((-72) . T) ((-553 (-773)) . T) ((-13) . T) ((-1014) . T) ((-1130) . T)) 
-((* (($ (-831) $) 10 T ELT))) 
-(((-24 |#1|) (-10 -7 (-15 * (|#1| (-831) |#1|))) (-25)) (T -24)) 
+((-2661 (*1 *1) (-4 *1 (-23))) (-3725 (*1 *1) (-4 *1 (-23))) (-3189 (*1 *2 *1) (-12 (-4 *1 (-23)) (-5 *2 (-85)))) (* (*1 *1 *2 *1) (-12 (-4 *1 (-23)) (-5 *2 (-694)))) (-1214 (*1 *2 *1 *1) (-12 (-4 *1 (-23)) (-5 *2 (-85))))) 
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+(((-25) . T) ((-72) . T) ((-552 (-772)) . T) ((-13) . T) ((-1013) . T) ((-1129) . T)) 
+((* (($ (-830) $) 10 T ELT))) 
+(((-24 |#1|) (-10 -7 (-15 * (|#1| (-830) |#1|))) (-25)) (T -24)) 
 NIL 
-((-2570 (((-85) $ $) 7 T ELT)) (-3244 (((-1074) $) 11 T ELT)) (-3245 (((-1034) $) 12 T ELT)) (-3948 (((-773) $) 13 T ELT)) (-1266 (((-85) $ $) 6 T ELT)) (-3058 (((-85) $ $) 8 T ELT)) (-3841 (($ $ $) 18 T ELT)) (* (($ (-831) $) 17 T ELT))) 
+((-2569 (((-85) $ $) 7 T ELT)) (-3243 (((-1073) $) 11 T ELT)) (-3244 (((-1033) $) 12 T ELT)) (-3947 (((-772) $) 13 T ELT)) (-1265 (((-85) $ $) 6 T ELT)) (-3057 (((-85) $ $) 8 T ELT)) (-3840 (($ $ $) 18 T ELT)) (* (($ (-830) $) 17 T ELT))) 
 (((-25) (-113)) (T -25)) 
-((-3841 (*1 *1 *1 *1) (-4 *1 (-25))) (* (*1 *1 *2 *1) (-12 (-4 *1 (-25)) (-5 *2 (-831))))) 
-(-13 (-1014) (-10 -8 (-15 -3841 ($ $ $)) (-15 * ($ (-831) $)))) 
-(((-72) . T) ((-553 (-773)) . T) ((-13) . T) ((-1014) . T) ((-1130) . T)) 
-((-1216 (((-584 $) (-858 $)) 32 T ELT) (((-584 $) (-1086 $)) 16 T ELT) (((-584 $) (-1086 $) (-1091)) 20 T ELT)) (-1217 (($ (-858 $)) 30 T ELT) (($ (-1086 $)) 11 T ELT) (($ (-1086 $) (-1091)) 60 T ELT)) (-1218 (((-584 $) (-858 $)) 33 T ELT) (((-584 $) (-1086 $)) 18 T ELT) (((-584 $) (-1086 $) (-1091)) 19 T ELT)) (-3185 (($ (-858 $)) 31 T ELT) (($ (-1086 $)) 13 T ELT) (($ (-1086 $) (-1091)) NIL T ELT))) 
-(((-26 |#1|) (-10 -7 (-15 -1216 ((-584 |#1|) (-1086 |#1|) (-1091))) (-15 -1216 ((-584 |#1|) (-1086 |#1|))) (-15 -1216 ((-584 |#1|) (-858 |#1|))) (-15 -1217 (|#1| (-1086 |#1|) (-1091))) (-15 -1217 (|#1| (-1086 |#1|))) (-15 -1217 (|#1| (-858 |#1|))) (-15 -1218 ((-584 |#1|) (-1086 |#1|) (-1091))) (-15 -1218 ((-584 |#1|) (-1086 |#1|))) (-15 -1218 ((-584 |#1|) (-858 |#1|))) (-15 -3185 (|#1| (-1086 |#1|) (-1091))) (-15 -3185 (|#1| (-1086 |#1|))) (-15 -3185 (|#1| (-858 |#1|)))) (-27)) (T -26)) 
+((-3840 (*1 *1 *1 *1) (-4 *1 (-25))) (* (*1 *1 *2 *1) (-12 (-4 *1 (-25)) (-5 *2 (-830))))) 
+(-13 (-1013) (-10 -8 (-15 -3840 ($ $ $)) (-15 * ($ (-830) $)))) 
+(((-72) . T) ((-552 (-772)) . T) ((-13) . T) ((-1013) . T) ((-1129) . T)) 
+((-1215 (((-583 $) (-857 $)) 32 T ELT) (((-583 $) (-1085 $)) 16 T ELT) (((-583 $) (-1085 $) (-1090)) 20 T ELT)) (-1216 (($ (-857 $)) 30 T ELT) (($ (-1085 $)) 11 T ELT) (($ (-1085 $) (-1090)) 60 T ELT)) (-1217 (((-583 $) (-857 $)) 33 T ELT) (((-583 $) (-1085 $)) 18 T ELT) (((-583 $) (-1085 $) (-1090)) 19 T ELT)) (-3184 (($ (-857 $)) 31 T ELT) (($ (-1085 $)) 13 T ELT) (($ (-1085 $) (-1090)) NIL T ELT))) 
+(((-26 |#1|) (-10 -7 (-15 -1215 ((-583 |#1|) (-1085 |#1|) (-1090))) (-15 -1215 ((-583 |#1|) (-1085 |#1|))) (-15 -1215 ((-583 |#1|) (-857 |#1|))) (-15 -1216 (|#1| (-1085 |#1|) (-1090))) (-15 -1216 (|#1| (-1085 |#1|))) (-15 -1216 (|#1| (-857 |#1|))) (-15 -1217 ((-583 |#1|) (-1085 |#1|) (-1090))) (-15 -1217 ((-583 |#1|) (-1085 |#1|))) (-15 -1217 ((-583 |#1|) (-857 |#1|))) (-15 -3184 (|#1| (-1085 |#1|) (-1090))) (-15 -3184 (|#1| (-1085 |#1|))) (-15 -3184 (|#1| (-857 |#1|)))) (-27)) (T -26)) 
 NIL 
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 (((-27) (-113)) (T -27)) 
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-(((-21) . T) ((-23) . T) ((-25) . T) ((-38 (-350 (-485))) . T) ((-38 $) . T) ((-72) . T) ((-82 (-350 (-485)) (-350 (-485))) . T) ((-82 $ $) . T) ((-104) . T) ((-556 (-350 (-485))) . T) ((-556 (-485)) . T) ((-556 $) . T) ((-553 (-773)) . T) ((-146) . T) ((-201) . T) ((-246) . T) ((-258) . T) ((-312) . T) ((-392) . T) ((-496) . T) ((-13) . T) ((-589 (-350 (-485))) . T) ((-589 (-485)) . T) ((-589 $) . T) ((-591 (-350 (-485))) . T) ((-591 $) . T) ((-583 (-350 (-485))) . T) ((-583 $) . T) ((-655 (-350 (-485))) . T) ((-655 $) . T) ((-664) . T) ((-833) . T) ((-916) . T) ((-964 (-350 (-485))) . T) ((-964 $) . T) ((-969 (-350 (-485))) . T) ((-969 $) . T) ((-962) . T) ((-971) . T) ((-1026) . T) ((-1062) . T) ((-1014) . T) ((-1130) . T) ((-1135) . T)) 
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-NIL 
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-(((-21) . T) ((-23) . T) ((-25) . T) ((-38 (-350 (-485))) . T) ((-38 |#1|) |has| |#1| (-146)) ((-38 $) . T) ((-27) . T) ((-72) . T) ((-82 (-350 (-485)) (-350 (-485))) . T) ((-82 |#1| |#1|) |has| |#1| (-146)) ((-82 $ $) . T) ((-104) . T) ((-118) |has| |#1| (-118)) ((-120) |has| |#1| (-120)) ((-556 (-350 (-485))) . T) ((-556 (-350 (-858 |#1|))) |has| |#1| (-496)) ((-556 (-485)) . T) ((-556 (-551 $)) . T) ((-556 (-858 |#1|)) |has| |#1| (-962)) ((-556 (-1091)) . T) ((-556 |#1|) . T) ((-556 $) . T) ((-553 (-773)) . T) ((-146) . T) ((-554 (-474)) |has| |#1| (-554 (-474))) ((-554 (-801 (-330))) |has| |#1| (-554 (-801 (-330)))) ((-554 (-801 (-485))) |has| |#1| (-554 (-801 (-485)))) ((-201) . T) ((-246) . T) ((-258) . T) ((-260 $) . T) ((-254) . T) ((-312) . T) ((-329 |#1|) |has| |#1| (-962)) ((-343 |#1|) . T) ((-355 |#1|) . T) ((-364 |#1|) . T) ((-392) . T) ((-413) |has| |#1| (-413)) ((-456 (-551 $) $) . T) ((-456 $ $) . T) ((-496) . T) ((-13) . T) ((-589 (-350 (-485))) . T) ((-589 (-485)) . T) ((-589 |#1|) OR (|has| |#1| (-962)) (|has| |#1| (-146))) ((-589 $) . T) ((-591 (-350 (-485))) . T) ((-591 (-485)) -12 (|has| |#1| (-581 (-485))) (|has| |#1| (-962))) ((-591 |#1|) OR (|has| |#1| (-962)) (|has| |#1| (-146))) ((-591 $) . T) ((-583 (-350 (-485))) . T) ((-583 |#1|) |has| |#1| (-146)) ((-583 $) . T) ((-581 (-485)) -12 (|has| |#1| (-581 (-485))) (|has| |#1| (-962))) ((-581 |#1|) |has| |#1| (-962)) ((-655 (-350 (-485))) . T) ((-655 |#1|) |has| |#1| (-146)) ((-655 $) . T) ((-664) . T) ((-807 $ (-1091)) |has| |#1| (-962)) ((-810 (-1091)) |has| |#1| (-962)) ((-812 (-1091)) |has| |#1| (-962)) ((-797 (-330)) |has| |#1| (-797 (-330))) ((-797 (-485)) |has| |#1| (-797 (-485))) ((-795 |#1|) . T) ((-833) . T) ((-916) . T) ((-951 (-350 (-485))) OR (|has| |#1| (-951 (-350 (-485)))) (-12 (|has| |#1| (-496)) (|has| |#1| (-951 (-485))))) ((-951 (-350 (-858 |#1|))) |has| |#1| (-496)) ((-951 (-485)) |has| |#1| (-951 (-485))) ((-951 (-551 $)) . T) ((-951 (-858 |#1|)) |has| |#1| (-962)) ((-951 (-1091)) . T) ((-951 |#1|) . T) ((-964 (-350 (-485))) . T) ((-964 |#1|) |has| |#1| (-146)) ((-964 $) . T) ((-969 (-350 (-485))) . T) ((-969 |#1|) |has| |#1| (-146)) ((-969 $) . T) ((-962) . T) ((-971) . T) ((-1026) . T) ((-1062) . T) ((-1014) . T) ((-1130) . T) ((-1135) . T)) 
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-(((-34) . T) ((-76 (-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) . T) ((-72) OR (|has| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (-1014)) (|has| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (-757)) (|has| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (-72)) (|has| |#2| (-1014)) (|has| |#2| (-72))) ((-553 (-773)) OR (|has| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (-1014)) (|has| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (-757)) (|has| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (-553 (-773))) (|has| |#2| (-1014)) (|has| |#2| (-553 (-773)))) ((-124 (-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) . T) ((-554 (-474)) |has| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (-554 (-474))) ((-183 (-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) . T) ((-193 (-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) . T) ((-241 (-485) (-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) . T) ((-241 (-1147 (-485)) $) . T) ((-241 |#1| |#2|) . T) ((-243 (-485) (-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) . T) ((-243 |#1| |#2|) . T) ((-260 (-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) -12 (|has| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (-260 (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)))) (|has| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (-1014))) ((-260 |#2|) -12 (|has| |#2| (-260 |#2|)) (|has| |#2| (-1014))) ((-237 (-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) . T) ((-318 (-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) . T) ((-324 (-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) . T) ((-429 (-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) . T) ((-429 |#2|) . T) ((-539 (-485) (-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) . T) ((-539 |#1| |#2|) . T) ((-456 (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) -12 (|has| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (-260 (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)))) (|has| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (-1014))) ((-456 |#2| |#2|) -12 (|has| |#2| (-260 |#2|)) (|has| |#2| (-1014))) ((-13) . T) ((-550 |#1| |#2|) . T) ((-594 (-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) . T) ((-609 (-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) . T) ((-757) |has| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (-757)) ((-760) |has| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (-757)) ((-924 (-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) . T) ((-1014) OR (|has| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (-1014)) (|has| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (-757)) (|has| |#2| (-1014))) ((-1036 (-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) . T) ((-1065 (-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) . T) ((-1108 |#1| |#2|) . T) ((-1130) . T) ((-1169 (-2 (|:| -3862 |#1|) (|:| |entry| |#2|))) . T)) 
-((-3948 (((-773) $) NIL T ELT) (($ (-485)) NIL T ELT) (($ |#2|) 10 T ELT))) 
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-NIL 
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(|:| |entry| |#2|)))) 37 T ELT)) (-1223 (((-632 (-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) |#1| $) 122 T ELT)) (-1732 (((-85) (-1 (-85) (-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) $) 99 T ELT) (((-85) (-1 (-85) (-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) $) 219 T ELT)) (-2567 (((-85) $ $) 201 (|has| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (-756)) ELT)) (-2568 (((-85) $ $) 203 (|has| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (-756)) ELT)) (-3057 (((-85) $ $) 16 (OR (|has| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (-72)) (|has| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (-72)) (|has| |#2| (-72)) (|has| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (-72))) ELT)) (-2685 (((-85) $ $) 202 (|has| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (-756)) ELT)) (-2686 (((-85) $ $) 204 (|has| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (-756)) ELT)) (-3958 (((-694) $) 98 T ELT))) 
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+(((-34) . T) ((-76 (-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) . T) ((-72) OR (|has| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (-1013)) (|has| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (-756)) (|has| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (-72)) (|has| |#2| (-1013)) (|has| |#2| (-72))) ((-552 (-772)) OR (|has| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (-1013)) (|has| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (-756)) (|has| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (-552 (-772))) (|has| |#2| (-1013)) (|has| |#2| (-552 (-772)))) ((-124 (-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) . T) ((-553 (-473)) |has| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (-553 (-473))) ((-183 (-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) . T) ((-193 (-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) . T) ((-241 (-484) (-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) . T) ((-241 (-1146 (-484)) $) . T) ((-241 |#1| |#2|) . T) ((-243 (-484) (-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) . T) ((-243 |#1| |#2|) . T) ((-260 (-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) -12 (|has| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (-260 (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)))) (|has| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (-1013))) ((-260 |#2|) -12 (|has| |#2| (-260 |#2|)) (|has| |#2| (-1013))) ((-237 (-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) . T) ((-318 (-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) . T) ((-324 (-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) . T) ((-429 (-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) . T) ((-429 |#2|) . T) ((-538 (-484) (-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) . T) ((-538 |#1| |#2|) . T) ((-455 (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) -12 (|has| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (-260 (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)))) (|has| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (-1013))) ((-455 |#2| |#2|) -12 (|has| |#2| (-260 |#2|)) (|has| |#2| (-1013))) ((-13) . T) ((-549 |#1| |#2|) . T) ((-593 (-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) . T) ((-608 (-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) . T) ((-756) |has| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (-756)) ((-759) |has| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (-756)) ((-923 (-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) . T) ((-1013) OR (|has| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (-1013)) (|has| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (-756)) (|has| |#2| (-1013))) ((-1035 (-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) . T) ((-1064 (-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) . T) ((-1107 |#1| |#2|) . T) ((-1129) . T) ((-1168 (-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) . T)) 
+((-3947 (((-772) $) NIL T ELT) (($ (-484)) NIL T ELT) (($ |#2|) 10 T ELT))) 
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+NIL 
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 (((-38 |#1|) (-113) (-146)) (T -38)) 
 NIL 
-(-13 (-962) (-655 |t#1|) (-556 |t#1|)) 
-(((-21) . T) ((-23) . T) ((-25) . T) ((-72) . T) ((-82 |#1| |#1|) . T) ((-104) . T) ((-556 (-485)) . T) ((-556 |#1|) . T) ((-553 (-773)) . T) ((-13) . T) ((-589 (-485)) . T) ((-589 |#1|) . T) ((-589 $) . T) ((-591 |#1|) . T) ((-591 $) . T) ((-583 |#1|) . T) ((-655 |#1|) . T) ((-664) . T) ((-964 |#1|) . T) ((-969 |#1|) . T) ((-962) . T) ((-971) . T) ((-1026) . T) ((-1062) . T) ((-1014) . T) ((-1130) . T)) 
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-NIL 
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-NIL 
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-NIL 
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+(((-60 |#1|) (-57 |#1| (-58 |#1|) (-58 |#1|)) (-1129)) (T -60)) 
+NIL 
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+((-1261 (*1 *2 *3 *4) (-12 (-4 *5 (-312)) (-4 *5 (-495)) (-5 *2 (-2 (|:| |minor| (-583 (-830))) (|:| -3267 *3) (|:| |minors| (-583 (-583 (-830)))) (|:| |ops| (-583 *3)))) (-5 *1 (-61 *5 *3)) (-5 *4 (-830)) (-4 *3 (-600 *5)))) (-1260 (*1 *2 *3) (-12 (-4 *4 (-495)) (-5 *2 (-1179 (-630 *4))) (-5 *1 (-61 *4 *5)) (-5 *3 (-630 *4)) (-4 *5 (-600 *4)))) (-1259 (*1 *2 *3 *4) (-12 (-4 *5 (-495)) (-5 *2 (-2 (|:| |mat| (-630 *5)) (|:| |vec| (-1179 (-583 (-830)))))) (-5 *1 (-61 *5 *3)) (-5 *4 (-830)) (-4 *3 (-600 *5))))) 
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+(((-62 |#1|) (-13 (-1034 |#1|) (-10 -8 (-15 -1262 ($ (-583 |#1|))))) (-1013)) (T -62)) 
+((-1262 (*1 *1 *2) (-12 (-5 *2 (-583 *3)) (-4 *3 (-1013)) (-5 *1 (-62 *3))))) 
+((-3947 (((-772) $) 13 T ELT) (($ (-1095)) 9 T ELT) (((-1095) $) 8 T ELT))) 
+(((-63 |#1|) (-10 -7 (-15 -3947 ((-1095) |#1|)) (-15 -3947 (|#1| (-1095))) (-15 -3947 ((-772) |#1|))) (-64)) (T -63)) 
+NIL 
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 (((-64) (-113)) (T -64)) 
 NIL 
-(-13 (-1014) (-430 (-1096))) 
-(((-72) . T) ((-556 (-1096)) . T) ((-553 (-773)) . T) ((-553 (-1096)) . T) ((-430 (-1096)) . T) ((-13) . T) ((-1014) . T) ((-1130) . T)) 
-((-3490 (($ $) 10 T ELT)) (-3491 (($ $) 12 T ELT))) 
-(((-65 |#1|) (-10 -7 (-15 -3491 (|#1| |#1|)) (-15 -3490 (|#1| |#1|))) (-66)) (T -65)) 
+(-13 (-1013) (-430 (-1095))) 
+(((-72) . T) ((-555 (-1095)) . T) ((-552 (-772)) . T) ((-552 (-1095)) . T) ((-430 (-1095)) . T) ((-13) . T) ((-1013) . T) ((-1129) . T)) 
+((-3489 (($ $) 10 T ELT)) (-3490 (($ $) 12 T ELT))) 
+(((-65 |#1|) (-10 -7 (-15 -3490 (|#1| |#1|)) (-15 -3489 (|#1| |#1|))) (-66)) (T -65)) 
 NIL 
-((-3488 (($ $) 11 T ELT)) (-3486 (($ $) 10 T ELT)) (-3490 (($ $) 9 T ELT)) (-3491 (($ $) 8 T ELT)) (-3489 (($ $) 7 T ELT)) (-3487 (($ $) 6 T ELT))) 
+((-3487 (($ $) 11 T ELT)) (-3485 (($ $) 10 T ELT)) (-3489 (($ $) 9 T ELT)) (-3490 (($ $) 8 T ELT)) (-3488 (($ $) 7 T ELT)) (-3486 (($ $) 6 T ELT))) 
 (((-66) (-113)) (T -66)) 
-((-3488 (*1 *1 *1) (-4 *1 (-66))) (-3486 (*1 *1 *1) (-4 *1 (-66))) (-3490 (*1 *1 *1) (-4 *1 (-66))) (-3491 (*1 *1 *1) (-4 *1 (-66))) (-3489 (*1 *1 *1) (-4 *1 (-66))) (-3487 (*1 *1 *1) (-4 *1 (-66)))) 
-(-13 (-10 -8 (-15 -3487 ($ $)) (-15 -3489 ($ $)) (-15 -3491 ($ $)) (-15 -3490 ($ $)) (-15 -3486 ($ $)) (-15 -3488 ($ $)))) 
-((-2570 (((-85) $ $) NIL T ELT)) (-3544 (((-1050) $) 11 T ELT)) (-3244 (((-1074) $) NIL T ELT)) (-3245 (((-1034) $) NIL T ELT)) (-3948 (((-773) $) 17 T ELT) (($ (-1096)) NIL T ELT) (((-1096) $) NIL T ELT)) (-1266 (((-85) $ $) NIL T ELT)) (-3058 (((-85) $ $) NIL T ELT))) 
-(((-67) (-13 (-996) (-10 -8 (-15 -3544 ((-1050) $))))) (T -67)) 
-((-3544 (*1 *2 *1) (-12 (-5 *2 (-1050)) (-5 *1 (-67))))) 
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+(-13 (-10 -8 (-15 -3486 ($ $)) (-15 -3488 ($ $)) (-15 -3490 ($ $)) (-15 -3489 ($ $)) (-15 -3485 ($ $)) (-15 -3487 ($ $)))) 
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+(((-67) (-13 (-995) (-10 -8 (-15 -3543 ((-1049) $))))) (T -67)) 
+((-3543 (*1 *2 *1) (-12 (-5 *2 (-1049)) (-5 *1 (-67))))) 
 NIL 
 (((-68) (-113)) (T -68)) 
 NIL 
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-((-2570 (((-85) $ $) NIL T ELT)) (-3726 (($) NIL T CONST)) (-3469 (((-3 $ "failed") $) NIL T ELT)) (-2411 (((-85) $) NIL T ELT)) (-1264 (($ (-1 |#1| |#1|)) 27 T ELT) (($ (-1 |#1| |#1|) (-1 |#1| |#1|)) 26 T ELT) (($ (-1 |#1| |#1| (-485))) 24 T ELT)) (-3244 (((-1074) $) NIL T ELT)) (-2486 (($ $) 16 T ELT)) (-3245 (((-1034) $) NIL T ELT)) (-3802 ((|#1| $ |#1|) 13 T ELT)) (-3011 (($ $ $) NIL T ELT)) (-2437 (($ $ $) NIL T ELT)) (-3948 (((-773) $) 22 T ELT)) (-1266 (((-85) $ $) NIL T ELT)) (-2668 (($) 8 T CONST)) (-3058 (((-85) $ $) 10 T ELT)) (-3951 (($ $ $) NIL T ELT)) (** (($ $ (-831)) 30 T ELT) (($ $ (-695)) NIL T ELT) (($ $ (-485)) 18 T ELT)) (* (($ $ $) 31 T ELT))) 
-(((-69 |#1|) (-13 (-413) (-241 |#1| |#1|) (-10 -8 (-15 -1264 ($ (-1 |#1| |#1|))) (-15 -1264 ($ (-1 |#1| |#1|) (-1 |#1| |#1|))) (-15 -1264 ($ (-1 |#1| |#1| (-485)))))) (-962)) (T -69)) 
-((-1264 (*1 *1 *2) (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-962)) (-5 *1 (-69 *3)))) (-1264 (*1 *1 *2 *2) (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-962)) (-5 *1 (-69 *3)))) (-1264 (*1 *1 *2) (-12 (-5 *2 (-1 *3 *3 (-485))) (-4 *3 (-962)) (-5 *1 (-69 *3))))) 
-((-1265 (((-348 |#2|) |#2| (-584 |#2|)) 10 T ELT) (((-348 |#2|) |#2| |#2|) 11 T ELT))) 
-(((-70 |#1| |#2|) (-10 -7 (-15 -1265 ((-348 |#2|) |#2| |#2|)) (-15 -1265 ((-348 |#2|) |#2| (-584 |#2|)))) (-13 (-392) (-120)) (-1156 |#1|)) (T -70)) 
-((-1265 (*1 *2 *3 *4) (-12 (-5 *4 (-584 *3)) (-4 *3 (-1156 *5)) (-4 *5 (-13 (-392) (-120))) (-5 *2 (-348 *3)) (-5 *1 (-70 *5 *3)))) (-1265 (*1 *2 *3 *3) (-12 (-4 *4 (-13 (-392) (-120))) (-5 *2 (-348 *3)) (-5 *1 (-70 *4 *3)) (-4 *3 (-1156 *4))))) 
-((-2570 (((-85) $ $) 13 T ELT)) (-1266 (((-85) $ $) 14 T ELT)) (-3058 (((-85) $ $) 11 T ELT))) 
-(((-71 |#1|) (-10 -7 (-15 -1266 ((-85) |#1| |#1|)) (-15 -2570 ((-85) |#1| |#1|)) (-15 -3058 ((-85) |#1| |#1|))) (-72)) (T -71)) 
-NIL 
-((-2570 (((-85) $ $) 7 T ELT)) (-1266 (((-85) $ $) 6 T ELT)) (-3058 (((-85) $ $) 8 T ELT))) 
+(-13 (-10 -7 (-6 (-3998 "*")) (-6 -3993) (-6 -3991) (-6 -3990) (-6 -3989) (-6 -3994) (-6 -3988) (-6 -3987) (-6 -3986) (-6 -3985) (-6 -3984) (-6 -3992) (-6 -3995) (-6 |NullSquare|) (-6 |JacobiIdentity|) (-6 -3983))) 
+((-2569 (((-85) $ $) NIL T ELT)) (-3725 (($) NIL T CONST)) (-3468 (((-3 $ "failed") $) NIL T ELT)) (-2410 (((-85) $) NIL T ELT)) (-1263 (($ (-1 |#1| |#1|)) 27 T ELT) (($ (-1 |#1| |#1|) (-1 |#1| |#1|)) 26 T ELT) (($ (-1 |#1| |#1| (-484))) 24 T ELT)) (-3243 (((-1073) $) NIL T ELT)) (-2485 (($ $) 16 T ELT)) (-3244 (((-1033) $) NIL T ELT)) (-3801 ((|#1| $ |#1|) 13 T ELT)) (-3010 (($ $ $) NIL T ELT)) (-2436 (($ $ $) NIL T ELT)) (-3947 (((-772) $) 22 T ELT)) (-1265 (((-85) $ $) NIL T ELT)) (-2667 (($) 8 T CONST)) (-3057 (((-85) $ $) 10 T ELT)) (-3950 (($ $ $) NIL T ELT)) (** (($ $ (-830)) 30 T ELT) (($ $ (-694)) NIL T ELT) (($ $ (-484)) 18 T ELT)) (* (($ $ $) 31 T ELT))) 
+(((-69 |#1|) (-13 (-413) (-241 |#1| |#1|) (-10 -8 (-15 -1263 ($ (-1 |#1| |#1|))) (-15 -1263 ($ (-1 |#1| |#1|) (-1 |#1| |#1|))) (-15 -1263 ($ (-1 |#1| |#1| (-484)))))) (-961)) (T -69)) 
+((-1263 (*1 *1 *2) (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-961)) (-5 *1 (-69 *3)))) (-1263 (*1 *1 *2 *2) (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-961)) (-5 *1 (-69 *3)))) (-1263 (*1 *1 *2) (-12 (-5 *2 (-1 *3 *3 (-484))) (-4 *3 (-961)) (-5 *1 (-69 *3))))) 
+((-1264 (((-348 |#2|) |#2| (-583 |#2|)) 10 T ELT) (((-348 |#2|) |#2| |#2|) 11 T ELT))) 
+(((-70 |#1| |#2|) (-10 -7 (-15 -1264 ((-348 |#2|) |#2| |#2|)) (-15 -1264 ((-348 |#2|) |#2| (-583 |#2|)))) (-13 (-392) (-120)) (-1155 |#1|)) (T -70)) 
+((-1264 (*1 *2 *3 *4) (-12 (-5 *4 (-583 *3)) (-4 *3 (-1155 *5)) (-4 *5 (-13 (-392) (-120))) (-5 *2 (-348 *3)) (-5 *1 (-70 *5 *3)))) (-1264 (*1 *2 *3 *3) (-12 (-4 *4 (-13 (-392) (-120))) (-5 *2 (-348 *3)) (-5 *1 (-70 *4 *3)) (-4 *3 (-1155 *4))))) 
+((-2569 (((-85) $ $) 13 T ELT)) (-1265 (((-85) $ $) 14 T ELT)) (-3057 (((-85) $ $) 11 T ELT))) 
+(((-71 |#1|) (-10 -7 (-15 -1265 ((-85) |#1| |#1|)) (-15 -2569 ((-85) |#1| |#1|)) (-15 -3057 ((-85) |#1| |#1|))) (-72)) (T -71)) 
+NIL 
+((-2569 (((-85) $ $) 7 T ELT)) (-1265 (((-85) $ $) 6 T ELT)) (-3057 (((-85) $ $) 8 T ELT))) 
 (((-72) (-113)) (T -72)) 
-((-3058 (*1 *2 *1 *1) (-12 (-4 *1 (-72)) (-5 *2 (-85)))) (-2570 (*1 *2 *1 *1) (-12 (-4 *1 (-72)) (-5 *2 (-85)))) (-1266 (*1 *2 *1 *1) (-12 (-4 *1 (-72)) (-5 *2 (-85))))) 
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 NIL 
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-NIL 
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-NIL 
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+NIL 
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+NIL 
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+NIL 
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 (((-96) (-113)) (T -96)) 
-((-1302 (*1 *1 *1 *1) (-4 *1 (-96))) (-1301 (*1 *1 *1 *1) (-4 *1 (-96))) (-3323 (*1 *1 *1 *1) (-4 *1 (-96)))) 
-(-13 (-757) (-84) (-605) (-19 (-85)) (-10 -8 (-15 -1302 ($ $ $)) (-15 -1301 ($ $ $)) (-15 -3323 ($ $ $)))) 
-(((-34) . T) ((-72) . T) ((-84) . T) ((-553 (-773)) . T) ((-124 (-85)) . T) ((-554 (-474)) |has| (-85) (-554 (-474))) ((-241 (-485) (-85)) . T) ((-241 (-1147 (-485)) $) . T) ((-243 (-485) (-85)) . T) ((-260 (-85)) -12 (|has| (-85) (-260 (-85))) (|has| (-85) (-1014))) ((-318 (-85)) . T) ((-324 (-85)) . T) ((-429 (-85)) . T) ((-539 (-485) (-85)) . T) ((-456 (-85) (-85)) -12 (|has| (-85) (-260 (-85))) (|has| (-85) (-1014))) ((-13) . T) ((-594 (-85)) . T) ((-605) . T) ((-19 (-85)) . T) ((-757) . T) ((-760) . T) ((-1014) . T) ((-1036 (-85)) . T) ((-1130) . T)) 
-((-3328 (($ (-1 |#2| |#2|) $) 22 T ELT)) (-3402 (($ $) 16 T ELT)) (-3959 (((-695) $) 25 T ELT))) 
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-NIL 
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-(((-98 |#1|) (-113) (-1014)) (T -98)) 
-((-1303 (*1 *1 *1 *2 *1) (-12 (-4 *1 (-98 *2)) (-4 *2 (-1014))))) 
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 (((-146) (-113)) (T -146)) 
 NIL 
-(-13 (-962) (-82 $ $) (-10 -7 (-6 (-3999 "*")))) 
-(((-21) . T) ((-23) . T) ((-25) . T) ((-72) . T) ((-82 $ $) . T) ((-104) . T) ((-556 (-485)) . T) ((-553 (-773)) . T) ((-13) . T) ((-589 (-485)) . T) ((-589 $) . T) ((-591 $) . T) ((-664) . T) ((-964 $) . T) ((-969 $) . T) ((-962) . T) ((-971) . T) ((-1026) . T) ((-1062) . T) ((-1014) . T) ((-1130) . T)) 
-((-1701 (($ $) 6 T ELT))) 
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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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+(((-21) . T) ((-23) . T) ((-25) . T) ((-72) . T) ((-104) . T) ((-555 (-484)) . T) ((-552 (-772)) . T) ((-186 $) OR (|has| |#1| (-189)) (|has| |#1| (-190))) ((-190) |has| |#1| (-190)) ((-189) OR (|has| |#1| (-189)) (|has| |#1| (-190))) ((-225 |#1|) . T) ((-13) . T) ((-588 (-484)) . T) ((-588 $) . T) ((-590 $) . T) ((-663) . T) ((-806 $ (-1090)) OR (|has| |#1| (-811 (-1090))) (|has| |#1| (-809 (-1090)))) ((-809 (-1090)) |has| |#1| (-809 (-1090))) ((-811 (-1090)) OR (|has| |#1| (-811 (-1090))) (|has| |#1| (-809 (-1090)))) ((-961) . T) ((-970) . T) ((-1025) . T) ((-1061) . T) ((-1013) . T) ((-1129) . T)) 
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+NIL 
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+NIL 
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 (((-190) (-113)) (T -190)) 
 NIL 
-(-13 (-962) (-189)) 
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 (((-191) (-113)) (T -191)) 
 NIL 
-(-13 (-717) (-1062)) 
-(((-23) . T) ((-25) . T) ((-72) . T) ((-553 (-773)) . T) ((-13) . T) ((-664) . T) ((-717) . T) ((-719) . T) ((-757) . T) ((-760) . T) ((-1026) . T) ((-1062) . T) ((-1014) . T) ((-1130) . T)) 
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-NIL 
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-NIL 
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-NIL 
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+(-13 (-716) (-1061)) 
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+NIL 
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+(((-34) . T) ((-76 |#1|) . T) ((-72) OR (|has| |#1| (-1013)) (|has| |#1| (-72))) ((-552 (-772)) OR (|has| |#1| (-1013)) (|has| |#1| (-552 (-772)))) ((-124 |#1|) . T) ((-553 (-473)) |has| |#1| (-553 (-473))) ((-260 |#1|) -12 (|has| |#1| (-260 |#1|)) (|has| |#1| (-1013))) ((-429 |#1|) . T) ((-455 |#1| |#1|) -12 (|has| |#1| (-260 |#1|)) (|has| |#1| (-1013))) ((-13) . T) ((-1013) |has| |#1| (-1013)) ((-1035 |#1|) . T) ((-1129) . T)) 
+((-1467 (((-2 (|:| |varOrder| (-583 (-1090))) (|:| |inhom| (-3 (-583 (-1179 (-694))) "failed")) (|:| |hom| (-583 (-1179 (-694))))) (-249 (-857 (-484)))) 42 T ELT))) 
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-NIL 
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-NIL 
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(-916))))) (-1546 (*1 *2 *2) (-12 (-4 *3 (-496)) (-5 *1 (-230 *3 *2)) (-4 *2 (-13 (-364 *3) (-916))))) (-1545 (*1 *2 *2) (-12 (-4 *3 (-496)) (-5 *1 (-230 *3 *2)) (-4 *2 (-13 (-364 *3) (-916))))) (-1544 (*1 *2 *2) (-12 (-4 *3 (-496)) (-5 *1 (-230 *3 *2)) (-4 *2 (-13 (-364 *3) (-916))))) (-1543 (*1 *2 *2) (-12 (-4 *3 (-496)) (-5 *1 (-230 *3 *2)) (-4 *2 (-13 (-364 *3) (-916))))) (-1542 (*1 *2 *2) (-12 (-4 *3 (-496)) (-5 *1 (-230 *3 *2)) (-4 *2 (-13 (-364 *3) (-916))))) (-1541 (*1 *2 *2) (-12 (-4 *3 (-496)) (-5 *1 (-230 *3 *2)) (-4 *2 (-13 (-364 *3) (-916))))) (-1540 (*1 *2 *2) (-12 (-4 *3 (-496)) (-5 *1 (-230 *3 *2)) (-4 *2 (-13 (-364 *3) (-916))))) (-1539 (*1 *2 *2) (-12 (-4 *3 (-496)) (-5 *1 (-230 *3 *2)) (-4 *2 (-13 (-364 *3) (-916))))) (-1538 (*1 *2 *2) (-12 (-4 *3 (-496)) (-5 *1 (-230 *3 *2)) (-4 *2 (-13 (-364 *3) (-916))))) (-1537 (*1 *2 *2) (-12 (-4 *3 (-496)) (-5 *1 (-230 *3 *2)) (-4 *2 (-13 (-364 *3) (-916))))) (-1536 (*1 *2 *2) (-12 (-4 *3 (-496)) (-5 *1 (-230 *3 *2)) (-4 *2 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+NIL 
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+NIL 
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ELT) (($ $ (-1 |#1| |#1|) (-694)) NIL T ELT) (($ $ (-1090)) NIL (|has| |#1| (-811 (-1090))) ELT) (($ $ (-583 (-1090))) NIL (|has| |#1| (-811 (-1090))) ELT) (($ $ (-1090) (-694)) NIL (|has| |#1| (-811 (-1090))) ELT) (($ $ (-583 (-1090)) (-583 (-694))) NIL (|has| |#1| (-811 (-1090))) ELT) (($ $) NIL (|has| |#1| (-189)) ELT) (($ $ (-694)) NIL (|has| |#1| (-189)) ELT)) (-1489 (((-583 |#2|) $) NIL T ELT)) (-3949 (((-469 |#3|) $) NIL T ELT) (((-694) $ |#3|) NIL T ELT) (((-583 (-694)) $ (-583 |#3|)) NIL T ELT) (((-694) $ |#2|) NIL T ELT)) (-3973 (((-800 (-330)) $) NIL (-12 (|has| |#1| (-553 (-800 (-330)))) (|has| |#3| (-553 (-800 (-330))))) ELT) (((-800 (-484)) $) NIL (-12 (|has| |#1| (-553 (-800 (-484)))) (|has| |#3| (-553 (-800 (-484))))) ELT) (((-473) $) NIL (-12 (|has| |#1| (-553 (-473))) (|has| |#3| (-553 (-473)))) ELT)) (-2818 ((|#1| $) NIL (|has| |#1| (-392)) ELT) (($ $ |#3|) NIL (|has| |#1| (-392)) ELT)) (-2704 (((-3 (-1179 $) #1#) (-630 $)) NIL (-12 (|has| $ (-118)) (|has| |#1| 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ELT) (($ $ (-1090)) NIL (|has| |#1| (-811 (-1090))) ELT) (($ $ (-583 (-1090))) NIL (|has| |#1| (-811 (-1090))) ELT) (($ $ (-1090) (-694)) NIL (|has| |#1| (-811 (-1090))) ELT) (($ $ (-583 (-1090)) (-583 (-694))) NIL (|has| |#1| (-811 (-1090))) ELT) (($ $) NIL (|has| |#1| (-189)) ELT) (($ $ (-694)) NIL (|has| |#1| (-189)) ELT)) (-3057 (((-85) $ $) NIL T ELT)) (-3950 (($ $ |#1|) NIL (|has| |#1| (-312)) ELT)) (-3838 (($ $) NIL T ELT) (($ $ $) NIL T ELT)) (-3840 (($ $ $) NIL T ELT)) (** (($ $ (-830)) NIL T ELT) (($ $ (-694)) NIL T ELT)) (* (($ (-830) $) NIL T ELT) (($ (-694) $) NIL T ELT) (($ (-484) $) NIL T ELT) (($ $ $) NIL T ELT) (($ $ (-350 (-484))) NIL (|has| |#1| (-38 (-350 (-484)))) ELT) (($ (-350 (-484)) $) NIL (|has| |#1| (-38 (-350 (-484)))) ELT) (($ |#1| $) NIL T ELT) (($ $ |#1|) NIL 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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 (((-246) (-113)) (T -246)) 
 NIL 
-(-13 (-962) (-82 $ $) (-10 -7 (-6 -3990))) 
-(((-21) . T) ((-23) . T) ((-25) . T) ((-72) . T) ((-82 $ $) . T) ((-104) . T) ((-556 (-485)) . T) ((-553 (-773)) . T) ((-13) . T) ((-589 (-485)) . T) ((-589 $) . T) ((-591 $) . T) ((-664) . T) ((-964 $) . T) ((-969 $) . T) ((-962) . T) ((-971) . T) ((-1026) . T) ((-1062) . T) ((-1014) . T) ((-1130) . 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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+(((-21) . T) ((-23) . T) ((-25) . T) ((-72) . T) ((-104) . T) ((-552 (-772)) . T) ((-13) . T) ((-588 (-484)) . T) ((-1013) . T) ((-1129) . T)) 
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+NIL 
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+((-3959 (*1 *1 *2 *1) (-12 (-5 *2 (-1 *3 *3)) (-4 *1 (-288 *3)) (-4 *3 (-1013))))) 
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(-817 |#1|) (-320)) ELT)) (-1627 (((-1085 (-817 |#1|)) $) NIL (|has| (-817 |#1|) (-320)) ELT)) (-1626 (((-1085 (-817 |#1|)) $) NIL (|has| (-817 |#1|) (-320)) ELT) (((-3 (-1085 (-817 |#1|)) #1#) $ $) NIL (|has| (-817 |#1|) (-320)) ELT)) (-1628 (($ $ (-1085 (-817 |#1|))) NIL (|has| (-817 |#1|) (-320)) ELT)) (-1894 (($ $ $) NIL T ELT) (($ (-583 $)) NIL T ELT)) (-3243 (((-1073) $) NIL T ELT)) (-2485 (($ $) NIL T ELT)) (-3447 (($) NIL (|has| (-817 |#1|) (-320)) CONST)) (-2400 (($ (-830)) NIL (|has| (-817 |#1|) (-320)) ELT)) (-3932 (((-85) $) NIL T ELT)) (-3244 (((-1033) $) NIL T ELT)) (-2409 (($) NIL (|has| (-817 |#1|) (-320)) ELT)) (-2709 (((-1085 $) (-1085 $) (-1085 $)) NIL T ELT)) (-3145 (($ $ $) NIL T ELT) (($ (-583 $)) NIL T ELT)) (-1676 (((-583 (-2 (|:| -3733 (-484)) (|:| -2401 (-484))))) NIL (|has| (-817 |#1|) (-320)) ELT)) (-3733 (((-348 $) $) NIL T ELT)) (-3931 (((-743 (-830))) NIL T ELT) (((-830)) NIL T ELT)) (-1606 (((-2 (|:| |coef1| $) (|:| |coef2| $) (|:| -2409 $)) $ $) NIL T 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(($ (-350 (-484)) $) NIL T ELT) (($ $ (-817 |#1|)) NIL T ELT) (($ (-817 |#1|) $) NIL T ELT))) 
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-NIL 
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-(((-308 |#1| |#2|) (-280 |#1|) (-299) (-831)) (T -308)) 
-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) ((-72) . T) ((-82 |#2| |#2|) . T) ((-104) . T) ((-553 (-773)) . T) ((-13) . T) ((-589 (-485)) . T) ((-589 |#2|) . T) ((-591 |#2|) . T) ((-575 |#2|) . T) ((-583 |#2|) . T) ((-655 |#2|) . T) ((-964 |#2|) . T) ((-969 |#2|) . T) ((-1014) . T) ((-1130) . T)) 
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-NIL 
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-NIL 
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-(((-72) . T) ((-556 |#1|) . T) ((-553 (-773)) . T) ((-13) . T) ((-664) . T) ((-757) |has| |#1| (-757)) ((-760) |has| |#1| (-757)) ((-951 |#1|) . T) ((-1026) . T) ((-1014) . T) ((-1130) . T)) 
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-(((-337 |#1|) (-336 |#1|) (-1014)) (T -337)) 
-NIL 
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+(((-72) . T) ((-552 (-772)) . T) ((-13) . T) ((-1013) . T) ((-1129) . T)) 
+((-1785 (((-630 |#2|) (-1179 $)) 45 T ELT)) (-1795 (($ (-1179 |#2|) (-1179 $)) 39 T ELT)) (-1784 (((-630 |#2|) $ (-1179 $)) 47 T ELT)) (-3758 ((|#2| (-1179 $)) 13 T ELT)) (-3225 (((-1179 |#2|) $ (-1179 $)) NIL T ELT) (((-630 |#2|) (-1179 $) (-1179 $)) 27 T ELT))) 
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+NIL 
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+(((-322 |#1| |#2|) (-113) (-146) (-1155 |t#1|)) (T -322)) 
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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)) ((-555 (-484)) . T) ((-555 |#1|) . T) ((-552 (-772)) . T) ((-13) . T) ((-588 (-484)) . 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) ((-970) . T) ((-1025) . T) ((-1061) . T) ((-1013) . T) ((-1129) . T)) 
+((-1735 (((-85) (-1 (-85) |#2| |#2|) $) NIL T ELT) (((-85) $) 18 T ELT)) (-1733 (($ (-1 (-85) |#2| |#2|) $) NIL T ELT) (($ $) 28 T ELT)) (-2910 (($ (-1 (-85) |#2| |#2|) $) 27 T ELT) (($ $) 22 T ELT)) (-2298 (($ $) 25 T ELT)) (-3420 (((-484) (-1 (-85) |#2|) $) NIL T ELT) (((-484) |#2| $) 11 T ELT) (((-484) |#2| $ (-484)) NIL T ELT)) (-3519 (($ (-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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-((-1894 (*1 *2 *3) (-12 (-4 *4 (-392)) (-4 *5 (-718)) (-4 *6 (-757)) (-5 *2 (-695)) (-5 *1 (-390 *4 *5 *6 *3)) (-4 *3 (-862 *4 *5 *6)))) (-1893 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-2 (|:| |totdeg| (-695)) (|:| -2005 *4))) (-5 *5 (-695)) (-4 *4 (-862 *6 *7 *8)) (-4 *6 (-392)) (-4 *7 (-718)) (-4 *8 (-757)) (-5 *2 (-2 (|:| |lcmfij| *7) (|:| |totdeg| *5) (|:| |poli| *4) (|:| |polj| *4))) (-5 *1 (-390 *6 *7 *8 *4)))) (-1892 (*1 *2 *3 *3) (-12 (-5 *3 (-2 (|:| |lcmfij| *5) (|:| |totdeg| (-695)) (|:| |poli| *7) (|:| |polj| *7))) (-4 *5 (-718)) (-4 *7 (-862 *4 *5 *6)) (-4 *4 (-392)) (-4 *6 (-757)) (-5 *2 (-85)) (-5 *1 (-390 *4 *5 *6 *7)))) (-1891 (*1 *2 *3) (-12 (-5 *3 (-485)) (-4 *4 (-392)) (-4 *5 (-718)) (-4 *6 (-757)) (-5 *2 (-1186)) (-5 *1 (-390 *4 *5 *6 *7)) (-4 *7 (-862 *4 *5 *6)))) (-1890 (*1 *2 *3) (-12 (-5 *3 (-584 *7)) (-4 *7 (-862 *4 *5 *6)) (-4 *4 (-392)) (-4 *5 (-718)) (-4 *6 (-757)) (-5 *2 (-1186)) (-5 *1 (-390 *4 *5 *6 *7)))) (-1889 (*1 *2 *3 *4 *4 *2 *2 *2 *2) (-12 (-5 *2 (-485)) (-5 *3 (-2 (|:| |lcmfij| *6) (|:| |totdeg| (-695)) (|:| |poli| *4) (|:| |polj| *4))) (-4 *6 (-718)) (-4 *4 (-862 *5 *6 *7)) (-4 *5 (-392)) (-4 *7 (-757)) (-5 *1 (-390 *5 *6 *7 *4)))) (-1888 (*1 *2 *3 *4 *4 *2 *2 *2) (-12 (-5 *2 (-485)) (-5 *3 (-2 (|:| |lcmfij| *6) (|:| |totdeg| (-695)) (|:| |poli| *4) (|:| |polj| *4))) (-4 *6 (-718)) (-4 *4 (-862 *5 *6 *7)) (-4 *5 (-392)) (-4 *7 (-757)) (-5 *1 (-390 *5 *6 *7 *4)))) (-1887 (*1 *2 *3) (-12 (-4 *4 (-392)) (-4 *5 (-718)) (-4 *6 (-757)) (-5 *2 (-1186)) (-5 *1 (-390 *4 *5 *6 *3)) (-4 *3 (-862 *4 *5 *6)))) (-1886 (*1 *2 *3) (-12 (-4 *4 (-392)) (-4 *5 (-718)) (-4 *6 (-757)) (-5 *2 (-485)) (-5 *1 (-390 *4 *5 *6 *3)) (-4 *3 (-862 *4 *5 *6)))) (-1885 (*1 *2 *2) (-12 (-5 *2 (-584 *6)) (-4 *6 (-862 *3 *4 *5)) (-4 *3 (-392)) (-4 *4 (-718)) (-4 *5 (-757)) (-5 *1 (-390 *3 *4 *5 *6)))) (-1884 (*1 *2 *2 *2) (-12 (-5 *2 (-584 (-2 (|:| |lcmfij| *4) (|:| |totdeg| (-695)) (|:| |poli| *6) (|:| |polj| *6)))) (-4 *4 (-718)) (-4 *6 (-862 *3 *4 *5)) (-4 *3 (-392)) (-4 *5 (-757)) (-5 *1 (-390 *3 *4 *5 *6)))) (-1883 (*1 *2 *3) (-12 (-5 *3 (-2 (|:| |lcmfij| *5) (|:| |totdeg| (-695)) (|:| |poli| *2) (|:| |polj| *2))) (-4 *5 (-718)) (-4 *2 (-862 *4 *5 *6)) (-5 *1 (-390 *4 *5 *6 *2)) (-4 *4 (-392)) (-4 *6 (-757)))) (-1882 (*1 *2 *3 *4 *2) (-12 (-5 *2 (-584 (-2 (|:| |totdeg| (-695)) (|:| -2005 *3)))) (-5 *4 (-695)) (-4 *3 (-862 *5 *6 *7)) (-4 *5 (-392)) (-4 *6 (-718)) (-4 *7 (-757)) (-5 *1 (-390 *5 *6 *7 *3)))) (-1881 (*1 *2 *2) (-12 (-4 *3 (-392)) (-4 *4 (-718)) (-4 *5 (-757)) (-5 *1 (-390 *3 *4 *5 *2)) (-4 *2 (-862 *3 *4 *5)))) (-1880 (*1 *2 *3 *4) (-12 (-5 *4 (-584 *3)) (-4 *3 (-862 *5 *6 *7)) (-4 *5 (-392)) (-4 *6 (-718)) (-4 *7 (-757)) (-5 *2 (-2 (|:| |poly| *3) (|:| |mult| *5))) (-5 *1 (-390 *5 *6 *7 *3)))) (-1879 (*1 *2 *3 *2) (-12 (-5 *2 (-584 (-2 (|:| |lcmfij| *3) (|:| |totdeg| (-695)) (|:| |poli| *6) (|:| |polj| *6)))) (-4 *3 (-718)) (-4 *6 (-862 *4 *3 *5)) (-4 *4 (-392)) (-4 *5 (-757)) (-5 *1 (-390 *4 *3 *5 *6)))) (-1878 (*1 *2 *2) (-12 (-5 *2 (-584 (-2 (|:| |lcmfij| *4) (|:| |totdeg| (-695)) (|:| |poli| *6) (|:| |polj| *6)))) (-4 *4 (-718)) (-4 *6 (-862 *3 *4 *5)) (-4 *3 (-392)) (-4 *5 (-757)) (-5 *1 (-390 *3 *4 *5 *6)))) (-1877 (*1 *2 *3 *2) (-12 (-5 *2 (-584 (-2 (|:| |lcmfij| *5) (|:| |totdeg| (-695)) (|:| |poli| *3) (|:| |polj| *3)))) (-4 *5 (-718)) (-4 *3 (-862 *4 *5 *6)) (-4 *4 (-392)) (-4 *6 (-757)) (-5 *1 (-390 *4 *5 *6 *3)))) (-1876 (*1 *2 *3 *3 *3 *3) (-12 (-4 *4 (-392)) (-4 *3 (-718)) (-4 *5 (-757)) (-5 *2 (-85)) (-5 *1 (-390 *4 *3 *5 *6)) (-4 *6 (-862 *4 *3 *5)))) (-1875 (*1 *2 *3 *3) (-12 (-4 *4 (-392)) (-4 *3 (-718)) (-4 *5 (-757)) (-5 *2 (-85)) (-5 *1 (-390 *4 *3 *5 *6)) (-4 *6 (-862 *4 *3 *5)))) (-1874 (*1 *2 *3) (-12 (-5 *3 (-2 (|:| |lcmfij| *5) (|:| |totdeg| (-695)) (|:| |poli| *7) (|:| |polj| *7))) (-4 *5 (-718)) (-4 *7 (-862 *4 *5 *6)) (-4 *4 (-392)) (-4 *6 (-757)) (-5 *2 (-85)) (-5 *1 (-390 *4 *5 *6 *7)))) (-1873 (*1 *2 *2 *3 *3) (-12 (-5 *2 (-584 *7)) (-5 *3 (-485)) (-4 *7 (-862 *4 *5 *6)) (-4 *4 (-392)) (-4 *5 (-718)) (-4 *6 (-757)) (-5 *1 (-390 *4 *5 *6 *7)))) (-1872 (*1 *2 *2 *3) (-12 (-5 *3 (-584 *2)) (-4 *2 (-862 *4 *5 *6)) (-4 *4 (-392)) (-4 *5 (-718)) (-4 *6 (-757)) (-5 *1 (-390 *4 *5 *6 *2)))) (-1871 (*1 *2 *2 *3) (-12 (-5 *3 (-584 *2)) (-4 *2 (-862 *4 *5 *6)) (-4 *4 (-392)) (-4 *5 (-718)) (-4 *6 (-757)) (-5 *1 (-390 *4 *5 *6 *2))))) 
-((-1895 (($ $ $) 14 T ELT) (($ (-584 $)) 21 T ELT)) (-2710 (((-1086 $) (-1086 $) (-1086 $)) 45 T ELT)) (-3146 (($ $ $) NIL T ELT) (($ (-584 $)) 22 T ELT))) 
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-NIL 
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+((-1894 (($ $ $) 14 T ELT) (($ (-583 $)) 21 T ELT)) (-2709 (((-1085 $) (-1085 $) (-1085 $)) 45 T ELT)) (-3145 (($ $ $) NIL T ELT) (($ (-583 $)) 22 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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(-2685 (((-85) $ $) NIL (|has| (-484) (-756)) ELT)) (-2686 (((-85) $ $) NIL (|has| (-484) (-756)) ELT)) (-3950 (($ $ $) NIL T ELT) (($ (-484) (-484)) NIL T ELT)) (-3838 (($ $) NIL T ELT) (($ $ $) NIL T ELT)) (-3840 (($ $ $) NIL T ELT)) (** (($ $ (-830)) NIL T ELT) (($ $ (-694)) NIL T ELT) (($ $ (-484)) NIL T ELT)) (* (($ (-830) $) NIL T ELT) (($ (-694) $) NIL T ELT) (($ (-484) $) NIL T ELT) (($ $ $) NIL T ELT) (($ $ (-350 (-484))) NIL T ELT) (($ (-350 (-484)) $) NIL T ELT) (($ (-484) $) NIL T ELT) (($ $ (-484)) NIL T ELT))) 
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+((-3129 (*1 *2 *1) (-12 (-5 *2 (-350 (-484))) (-5 *1 (-427)))) (-1948 (*1 *1 *2) (-12 (-5 *2 (-350 (-484))) (-5 *1 (-427))))) 
+((-3769 (($ $ (-583 (-249 |#2|))) 13 T ELT) (($ $ (-249 |#2|)) NIL T ELT) (($ $ |#2| |#2|) NIL T ELT) (($ $ (-583 |#2|) (-583 |#2|)) NIL 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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-((-3770 (($ $ (-584 |#2|) (-584 |#3|)) NIL T ELT) (($ $ |#2| |#3|) 12 T ELT))) 
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-NIL 
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-NIL 
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-(((-458 |#1| |#2|) (-13 (-19 |#1|) (-237 |#1|) (-10 -8 (-15 -1990 ($ (-584 |#1|))) (-15 -1989 ((-695) $)) (-15 -1988 ($ $ (-485))) (-15 -1987 ((-85) (-85))))) (-1130) (-485)) (T -458)) 
-((-1990 (*1 *1 *2) (-12 (-5 *2 (-584 *3)) (-4 *3 (-1130)) (-5 *1 (-458 *3 *4)) (-14 *4 (-485)))) (-1989 (*1 *2 *1) (-12 (-5 *2 (-695)) (-5 *1 (-458 *3 *4)) (-4 *3 (-1130)) (-14 *4 (-485)))) (-1988 (*1 *1 *1 *2) (-12 (-5 *2 (-485)) (-5 *1 (-458 *3 *4)) (-4 *3 (-1130)) (-14 *4 *2))) (-1987 (*1 *2 *2) (-12 (-5 *2 (-85)) (-5 *1 (-458 *3 *4)) (-4 *3 (-1130)) (-14 *4 (-485))))) 
-((-2570 (((-85) $ $) NIL T ELT)) (-1992 (((-1050) $) 12 T ELT)) (-3244 (((-1074) $) NIL T ELT)) (-3245 (((-1034) $) NIL T ELT)) (-1991 (((-1050) $) 14 T ELT)) (-3924 (((-1050) $) 10 T ELT)) (-3948 (((-773) $) 20 T ELT) (($ (-1096)) NIL T ELT) (((-1096) $) NIL T ELT)) (-1266 (((-85) $ $) NIL T ELT)) (-3058 (((-85) $ $) NIL T ELT))) 
-(((-459) (-13 (-996) (-10 -8 (-15 -3924 ((-1050) $)) (-15 -1992 ((-1050) $)) (-15 -1991 ((-1050) $))))) (T -459)) 
-((-3924 (*1 *2 *1) (-12 (-5 *2 (-1050)) (-5 *1 (-459)))) (-1992 (*1 *2 *1) (-12 (-5 *2 (-1050)) (-5 *1 (-459)))) (-1991 (*1 *2 *1) (-12 (-5 *2 (-1050)) (-5 *1 (-459))))) 
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(($ (-350 (-485)) $) NIL T ELT) (($ $ (-518 |#1|)) NIL T ELT) (($ (-518 |#1|) $) NIL T ELT))) 
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-NIL 
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-((-3111 ((|#8| |#4|) 20 T ELT)) (-3108 (((-584 |#3|) |#4|) 29 (|has| |#7| (-1036 |#1|)) ELT)) (-3592 (((-3 |#8| "failed") |#4|) 23 T ELT))) 
-(((-462 |#1| |#2| |#3| |#4| |#5| |#6| |#7| |#8|) (-10 -7 (-15 -3111 (|#8| |#4|)) (-15 -3592 ((-3 |#8| "failed") |#4|)) (IF (|has| |#7| (-1036 |#1|)) (-15 -3108 ((-584 |#3|) |#4|)) |%noBranch|)) (-496) (-324 |#1|) (-324 |#1|) (-628 |#1| |#2| |#3|) (-905 |#1|) (-324 |#5|) (-324 |#5|) (-628 |#5| |#6| |#7|)) (T -462)) 
-((-3108 (*1 *2 *3) (-12 (-4 *9 (-1036 *4)) (-4 *4 (-496)) (-4 *5 (-324 *4)) (-4 *6 (-324 *4)) (-4 *7 (-905 *4)) (-4 *8 (-324 *7)) (-4 *9 (-324 *7)) (-5 *2 (-584 *6)) (-5 *1 (-462 *4 *5 *6 *3 *7 *8 *9 *10)) (-4 *3 (-628 *4 *5 *6)) (-4 *10 (-628 *7 *8 *9)))) (-3592 (*1 *2 *3) (|partial| -12 (-4 *4 (-496)) (-4 *5 (-324 *4)) (-4 *6 (-324 *4)) (-4 *7 (-905 *4)) (-4 *2 (-628 *7 *8 *9)) (-5 *1 (-462 *4 *5 *6 *3 *7 *8 *9 *2)) (-4 *3 (-628 *4 *5 *6)) (-4 *8 (-324 *7)) (-4 *9 (-324 *7)))) (-3111 (*1 *2 *3) (-12 (-4 *4 (-496)) (-4 *5 (-324 *4)) (-4 *6 (-324 *4)) (-4 *7 (-905 *4)) (-4 *2 (-628 *7 *8 *9)) (-5 *1 (-462 *4 *5 *6 *3 *7 *8 *9 *2)) (-4 *3 (-628 *4 *5 *6)) (-4 *8 (-324 *7)) (-4 *9 (-324 *7))))) 
-((-2570 (((-85) $ $) NIL T ELT)) (-3244 (((-1074) $) NIL T ELT)) (-1994 (((-584 (-1131)) $) 14 T ELT)) (-3245 (((-1034) $) NIL T ELT)) (-3948 (((-773) $) 20 T ELT) (($ (-1096)) NIL T ELT) (((-1096) $) NIL T ELT) (($ (-584 (-1131))) 12 T ELT)) (-1266 (((-85) $ $) NIL T ELT)) (-3058 (((-85) $ $) NIL T ELT))) 
-(((-463) (-13 (-996) (-10 -8 (-15 -3948 ($ (-584 (-1131)))) (-15 -1994 ((-584 (-1131)) $))))) (T -463)) 
-((-3948 (*1 *1 *2) (-12 (-5 *2 (-584 (-1131))) (-5 *1 (-463)))) (-1994 (*1 *2 *1) (-12 (-5 *2 (-584 (-1131))) (-5 *1 (-463))))) 
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-(((-464) (-13 (-996) (-10 -8 (-15 -3452 ((-447) $)) (-15 -1995 ((-1050) $))))) (T -464)) 
-((-3452 (*1 *2 *1) (-12 (-5 *2 (-447)) (-5 *1 (-464)))) (-1995 (*1 *2 *1) (-12 (-5 *2 (-1050)) (-5 *1 (-464))))) 
-((-2001 (((-633 (-1139)) $) 15 T ELT)) (-1997 (((-633 (-1137)) $) 38 T ELT)) (-1999 (((-633 (-1136)) $) 29 T ELT)) (-2002 (((-633 (-489)) $) 12 T ELT)) (-1998 (((-633 (-487)) $) 42 T ELT)) (-2000 (((-633 (-486)) $) 33 T ELT)) (-1996 (((-695) $ (-102)) 54 T ELT))) 
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-NIL 
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-(((-466) (-113)) (T -466)) 
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+(-13 (-10 -8 (-15 -3492 ($ $)) (-15 -3494 ($ $)) (-15 -3496 ($ $)) (-15 -3495 ($ $)) (-15 -3491 ($ $)) (-15 -3493 ($ $)))) 
+((-3733 (((-348 |#4|) |#4| (-1 (-348 |#2|) |#2|)) 54 T ELT))) 
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+((-3733 (*1 *2 *3 *4) (-12 (-5 *4 (-1 (-348 *6) *6)) (-4 *6 (-1155 *5)) (-4 *5 (-312)) (-4 *7 (-13 (-312) (-120) (-661 *5 *6))) (-5 *2 (-348 *3)) (-5 *1 (-434 *5 *6 *7 *3)) (-4 *3 (-1155 *7))))) 
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$) #1#) $) NIL T ELT) (((-3 (-484) #1#) $) NIL T ELT) (((-3 (-350 (-484)) #1#) $) NIL T ELT)) (-3157 (((-550 $) $) NIL T ELT) (((-484) $) NIL T ELT) (((-350 (-484)) $) 54 T ELT)) (-2565 (($ $ $) NIL T ELT)) (-2279 (((-2 (|:| |mat| (-630 (-484))) (|:| |vec| (-1179 (-484)))) (-630 $) (-1179 $)) NIL T ELT) (((-630 (-484)) (-630 $)) NIL T ELT) (((-2 (|:| |mat| (-630 (-350 (-484)))) (|:| |vec| (-1179 (-350 (-484))))) (-630 $) (-1179 $)) NIL T ELT) (((-630 (-350 (-484))) (-630 $)) NIL T ELT)) (-3843 (($ $) NIL T ELT)) (-3468 (((-3 $ #1#) $) NIL T ELT)) (-2564 (($ $ $) NIL T ELT)) (-2742 (((-2 (|:| -3955 (-583 $)) (|:| -2409 $)) (-583 $)) NIL T ELT)) (-3724 (((-85) $) NIL T ELT)) (-2574 (($ $) NIL T ELT) (($ (-583 $)) NIL T ELT)) (-1214 (((-85) $ $) NIL T ELT)) (-1599 (((-583 (-86)) $) NIL T ELT)) (-3596 (((-86) (-86)) NIL T ELT)) (-2410 (((-85) $) 42 T ELT)) (-2674 (((-85) $) NIL (|has| $ (-950 (-484))) ELT)) (-2999 (((-1039 (-484) (-550 $)) $) 37 T ELT)) (-3012 (($ $ (-484)) NIL T ELT)) 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$) 24 T ELT)) (-3950 (($ $ $) 44 T ELT)) (-3838 (($ $ $) NIL T ELT) (($ $) NIL T ELT)) (-3840 (($ $ $) NIL T ELT)) (** (($ $ (-350 (-484))) NIL T ELT) (($ $ (-484)) 47 T ELT) (($ $ (-694)) NIL T ELT) (($ $ (-830)) NIL T ELT)) (* (($ (-350 (-484)) $) NIL T ELT) (($ $ (-350 (-484))) NIL T ELT) (($ $ $) 27 T ELT) (($ (-484) $) NIL T ELT) (($ (-694) $) NIL T ELT) (($ (-830) $) NIL T ELT))) 
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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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-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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-((-3250 (*1 *2 *1) (-12 (-5 *2 (-584 (-1050))) (-5 *1 (-614))))) 
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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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-(((-687 |#1|) (-10 -7 (-15 -3948 (|#1| (-485))) (-15 -3948 ((-773) |#1|))) (-688)) (T -687)) 
-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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-(((-739 |#1|) (-228 |#1|) (-757)) (T -739)) 
-NIL 
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-(((-741) (-113)) (T -741)) 
-NIL 
-(-13 (-496) (-756)) 
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-(((-34) . T) ((-76 |#1|) . T) ((-72) . T) ((-553 (-773)) . T) ((-124 |#1|) . T) ((-554 (-474)) |has| |#1| (-554 (-474))) ((-193 |#1|) . T) ((-260 |#1|) -12 (|has| |#1| (-260 |#1|)) (|has| |#1| (-1014))) ((-318 |#1|) . T) ((-429 |#1|) . T) ((-456 |#1| |#1|) -12 (|has| |#1| (-260 |#1|)) (|has| |#1| (-1014))) ((-13) . T) ((-635 |#1|) . T) ((-677 |#1|) . T) ((-882 |#1|) . T) ((-1012 |#1|) . T) ((-1014) . T) ((-1036 |#1|) . T) ((-1130) . T)) 
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-NIL 
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+(((-21) . T) ((-23) . T) ((-25) . T) ((-38 |#1|) . T) ((-72) . T) ((-82 |#1| |#1|) . T) ((-104) . T) ((-118) |has| |#1| (-118)) ((-120) |has| |#1| (-120)) ((-555 (-350 (-484))) |has| |#1| (-950 (-350 (-484)))) ((-555 (-484)) . T) ((-555 |#1|) . T) ((-552 (-772)) . T) ((-553 (-473)) |has| |#1| (-553 (-473))) ((-241 |#1| $) |has| |#1| (-241 |#1| |#1|)) ((-260 |#1|) |has| |#1| (-260 |#1|)) ((-320) |has| |#1| (-320)) ((-288 |#1|) . T) ((-355 |#1|) . T) ((-455 (-1090) |#1|) |has| |#1| (-455 (-1090) |#1|)) ((-455 |#1| |#1|) |has| |#1| (-260 |#1|)) ((-13) . T) ((-588 (-484)) . T) ((-588 |#1|) . T) ((-588 $) . T) ((-590 |#1|) . T) ((-590 $) . T) ((-582 |#1|) . T) ((-654 |#1|) . T) ((-663) . T) ((-756) |has| |#1| (-756)) ((-759) |has| |#1| (-756)) ((-950 (-350 (-484))) |has| |#1| (-950 (-350 (-484)))) ((-950 (-484)) |has| |#1| (-950 (-484))) ((-950 |#1|) . T) ((-963 |#1|) . T) ((-968 |#1|) . T) ((-961) . T) ((-970) . T) ((-1025) . T) ((-1061) . T) ((-1013) . T) ((-1129) . T)) 
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+(((-721) (-113)) (T -721)) 
+NIL 
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+NIL 
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+NIL 
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+NIL 
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 (((-755) (-113)) (T -755)) 
 NIL 
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 (((-756) (-113)) (T -756)) 
 NIL 
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-(((-21) . T) ((-23) . T) ((-25) . T) ((-72) . T) ((-104) . T) ((-120) . T) ((-556 (-485)) . T) ((-553 (-773)) . T) ((-13) . T) ((-589 (-485)) . T) ((-589 $) . T) ((-591 $) . T) ((-664) . T) ((-715) . T) ((-717) . T) ((-719) . T) ((-722) . T) ((-757) . T) ((-760) . T) ((-962) . T) ((-971) . T) ((-1026) . T) ((-1062) . T) ((-1014) . T) ((-1130) . T)) 
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-NIL 
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-NIL 
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-(((-767) (-113)) (T -767)) 
-NIL 
-(-13 (-757) (-1026)) 
-(((-72) . T) ((-553 (-773)) . T) ((-13) . T) ((-757) . T) ((-760) . T) ((-1026) . T) ((-1014) . T) ((-1130) . 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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-(((-1016) (-1017 (-1074) (-1091) (-485) (-179) (-773))) (T -1016)) 
-NIL 
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-(((-72) . T) ((-553 (-773)) . T) ((-558 (-584 $)) . T) ((-558 |#1|) . T) ((-558 |#2|) . T) ((-558 |#3|) . T) ((-558 |#4|) . T) ((-558 |#5|) . T) ((-241 (-485) $) . T) ((-241 (-584 (-485)) $) . T) ((-13) . T) ((-1014) . T) ((-1130) . T)) 
-((-2570 (((-85) $ $) NIL T ELT)) (-3262 (((-85) $) 45 T ELT)) (-3258 ((|#2| $) 48 T ELT)) (-3263 (((-85) $) 20 T ELT)) (-3537 ((|#1| $) 21 T ELT)) (-3265 (((-85) $) 42 T ELT)) (-3267 (((-85) $) 14 T ELT)) (-3264 (((-85) $) 44 T ELT)) (-3244 (((-1074) $) NIL T ELT)) (-3261 (((-85) $) 46 T ELT)) (-3257 ((|#3| $) 50 T ELT)) (-3245 (((-1034) $) NIL T ELT)) (-3260 (((-85) $) 47 T ELT)) (-3256 ((|#4| $) 49 T ELT)) (-3255 ((|#5| $) 51 T ELT)) (-3268 (((-85) $ $) 41 T ELT)) (-3802 (($ $ (-485)) 62 T ELT) (($ $ (-584 (-485))) 64 T ELT)) (-3259 (((-584 $) $) 27 T ELT)) (-3974 (($ |#1|) 53 T ELT) (($ |#2|) 54 T ELT) (($ |#3|) 55 T ELT) (($ |#4|) 56 T ELT) (($ |#5|) 57 T ELT) (($ (-584 $)) 52 T ELT)) (-3948 (((-773) $) 28 T ELT)) (-3253 (($ $) 26 T ELT)) (-3254 (($ $) 58 T ELT)) (-1266 (((-85) $ $) NIL T ELT)) (-3266 (((-85) $) 23 T ELT)) (-3058 (((-85) $ $) 40 T ELT)) (-3959 (((-485) $) 60 T ELT))) 
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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 (-3999 #1="*"))) ((-72) . T) ((-82 |#2| |#2|) . T) ((-104) . T) ((-556 (-350 (-485))) |has| |#2| (-951 (-350 (-485)))) ((-556 (-485)) . 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) ((-260 |#2|) -12 (|has| |#2| (-260 |#2|)) (|has| |#2| (-1014))) ((-318 |#2|) . T) ((-329 |#2|) . T) ((-355 |#2|) . T) ((-429 |#2|) . T) ((-456 |#2| |#2|) -12 (|has| |#2| (-260 |#2|)) (|has| |#2| (-1014))) ((-13) . T) ((-589 (-485)) . T) ((-589 |#2|) . T) ((-589 $) . T) ((-591 (-485)) |has| |#2| (-581 (-485))) ((-591 |#2|) . T) ((-591 $) . T) ((-583 |#2|) OR (|has| |#2| (-146)) (|has| |#2| (-6 (-3999 #1#)))) ((-581 (-485)) |has| |#2| (-581 (-485))) ((-581 |#2|) . T) ((-655 |#2|) OR (|has| |#2| (-146)) (|has| |#2| (-6 (-3999 #1#)))) ((-664) . T) ((-807 $ (-1091)) OR (|has| |#2| (-812 (-1091))) (|has| |#2| (-810 (-1091)))) ((-810 (-1091)) |has| |#2| (-810 (-1091))) ((-812 (-1091)) OR (|has| |#2| (-812 (-1091))) (|has| |#2| (-810 (-1091)))) ((-966 |#1| |#1| |#2| |#3| |#4|) . T) ((-951 (-350 (-485))) |has| |#2| (-951 (-350 (-485)))) ((-951 (-485)) |has| |#2| (-951 (-485))) ((-951 |#2|) . T) ((-964 |#2|) . T) ((-969 |#2|) . T) ((-962) . T) ((-971) . T) ((-1026) . T) ((-1062) . T) ((-1014) . T) ((-1130) . T)) 
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-NIL 
-(-13 (-1021 |t#1| |t#2| |t#3| |t#4|) (-708 |t#1| |t#2| |t#3| |t#4|)) 
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-NIL 
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-NIL 
-(-13 (-23) (-664)) 
-(((-23) . T) ((-25) . T) ((-72) . T) ((-553 (-773)) . T) ((-13) . T) ((-664) . T) ((-1026) . T) ((-1014) . T) ((-1130) . 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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+(((-1015) (-1016 (-1073) (-1090) (-484) (-179) (-772))) (T -1015)) 
+NIL 
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+(-13 (-1013) (-557 |t#1|) (-557 |t#2|) (-557 |t#3|) (-557 |t#4|) (-557 |t#4|) (-557 |t#5|) (-557 (-583 $)) (-241 (-484) $) (-241 (-583 (-484)) $) (-10 -8 (-15 -3267 ((-85) $ $)) (-15 -3266 ((-85) $)) (-15 -3265 ((-85) $)) (-15 -3264 ((-85) $)) (-15 -3263 ((-85) $)) (-15 -3262 ((-85) $)) (-15 -3261 ((-85) $)) (-15 -3260 ((-85) $)) (-15 -3259 ((-85) $)) (-15 -3258 ((-583 $) $)) (-15 -3536 (|t#1| $)) (-15 -3257 (|t#2| $)) (-15 -3256 (|t#3| $)) (-15 -3255 (|t#4| $)) (-15 -3254 (|t#5| $)) (-15 -3253 ($ $)) (-15 -3252 ($ $)) (-15 -3958 ((-484) $)))) 
+(((-72) . T) ((-552 (-772)) . T) ((-557 (-583 $)) . T) ((-557 |#1|) . T) ((-557 |#2|) . T) ((-557 |#3|) . T) ((-557 |#4|) . T) ((-557 |#5|) . T) ((-241 (-484) $) . T) ((-241 (-583 (-484)) $) . T) ((-13) . T) ((-1013) . T) ((-1129) . T)) 
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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 (-3998 #1="*"))) ((-72) . T) ((-82 |#2| |#2|) . T) ((-104) . T) ((-555 (-350 (-484))) |has| |#2| (-950 (-350 (-484)))) ((-555 (-484)) . T) ((-555 |#2|) . T) ((-552 (-772)) . 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) ((-260 |#2|) -12 (|has| |#2| (-260 |#2|)) (|has| |#2| (-1013))) ((-318 |#2|) . T) ((-329 |#2|) . T) ((-355 |#2|) . T) ((-429 |#2|) . T) ((-455 |#2| |#2|) -12 (|has| |#2| (-260 |#2|)) (|has| |#2| (-1013))) ((-13) . T) ((-588 (-484)) . T) ((-588 |#2|) . T) ((-588 $) . T) ((-590 (-484)) |has| |#2| (-580 (-484))) ((-590 |#2|) . T) ((-590 $) . T) ((-582 |#2|) OR (|has| |#2| (-146)) (|has| |#2| (-6 (-3998 #1#)))) ((-580 (-484)) |has| |#2| (-580 (-484))) ((-580 |#2|) . T) ((-654 |#2|) OR (|has| |#2| (-146)) (|has| |#2| (-6 (-3998 #1#)))) ((-663) . T) ((-806 $ (-1090)) OR (|has| |#2| (-811 (-1090))) (|has| |#2| (-809 (-1090)))) ((-809 (-1090)) |has| |#2| (-809 (-1090))) ((-811 (-1090)) OR (|has| |#2| (-811 (-1090))) (|has| |#2| (-809 (-1090)))) ((-965 |#1| |#1| |#2| |#3| |#4|) . T) ((-950 (-350 (-484))) |has| |#2| (-950 (-350 (-484)))) ((-950 (-484)) |has| |#2| (-950 (-484))) ((-950 |#2|) . T) ((-963 |#2|) . T) ((-968 |#2|) . T) ((-961) . T) ((-970) . T) ((-1025) . T) ((-1061) . T) ((-1013) . T) ((-1129) . T)) 
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+NIL 
+(-13 (-1020 |t#1| |t#2| |t#3| |t#4|) (-707 |t#1| |t#2| |t#3| |t#4|)) 
+(((-34) . T) ((-72) . T) ((-552 (-583 |#4|)) . T) ((-552 (-772)) . T) ((-124 |#4|) . T) ((-553 (-473)) |has| |#4| (-553 (-473))) ((-260 |#4|) -12 (|has| |#4| (-260 |#4|)) (|has| |#4| (-1013))) ((-318 |#4|) . T) ((-429 |#4|) . T) ((-455 |#4| |#4|) -12 (|has| |#4| (-260 |#4|)) (|has| |#4| (-1013))) ((-13) . T) ((-707 |#1| |#2| |#3| |#4|) . T) ((-889 |#1| |#2| |#3| |#4|) . T) ((-983 |#1| |#2| |#3| |#4|) . T) ((-1013) . T) ((-1035 |#4|) . T) ((-1020 |#1| |#2| |#3| |#4|) . T) ((-1124 |#1| |#2| |#3| |#4|) . T) ((-1129) . T)) 
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ELT) (($ (-484) $) NIL T ELT) (($ $ $) NIL T ELT) (($ $ |#2|) NIL T ELT) (($ |#2| $) NIL T ELT) (((-197 |#1| |#2|) $ (-197 |#1| |#2|)) 56 T ELT) (((-197 |#1| |#2|) (-197 |#1| |#2|) $) 58 T ELT)) (-3958 (((-694) $) NIL T ELT))) 
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$)) 92 T ELT)) (-1731 (((-85) (-1 (-85) |#4|) $) NIL T ELT)) (-3769 (($ $ (-583 |#4|) (-583 |#4|)) NIL (-12 (|has| |#4| (-260 |#4|)) (|has| |#4| (-1013))) ELT) (($ $ |#4| |#4|) NIL (-12 (|has| |#4| (-260 |#4|)) (|has| |#4| (-1013))) ELT) (($ $ (-249 |#4|)) NIL (-12 (|has| |#4| (-260 |#4|)) (|has| |#4| (-1013))) ELT) (($ $ (-583 (-249 |#4|))) NIL (-12 (|has| |#4| (-260 |#4|)) (|has| |#4| (-1013))) ELT)) (-1222 (((-85) $ $) NIL T ELT)) (-3404 (((-85) $) 17 T ELT)) (-3566 (($) 14 T ELT)) (-3949 (((-694) $) NIL T ELT)) (-1730 (((-694) |#4| $) NIL (|has| |#4| (-72)) ELT) (((-694) (-1 (-85) |#4|) $) NIL T ELT)) (-3401 (($ $) 13 T ELT)) (-3973 (((-473) $) NIL (|has| |#4| (-553 (-473))) ELT)) (-3531 (($ (-583 |#4|)) 21 T ELT)) (-2911 (($ $ |#3|) 48 T ELT)) (-2913 (($ $ |#3|) 50 T ELT)) (-3685 (($ $) NIL T ELT)) (-2912 (($ $ |#3|) NIL T ELT)) (-3947 (((-772) $) 34 T ELT) (((-583 |#4|) $) 45 T ELT)) (-3679 (((-694) $) NIL (|has| |#3| (-320)) ELT)) (-1265 (((-85) $ $) NIL T ELT)) (-3699 (((-3 (-2 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+NIL 
+(-13 (-23) (-663)) 
+(((-23) . T) ((-25) . T) ((-72) . T) ((-552 (-772)) . T) ((-13) . T) ((-663) . T) ((-1025) . T) ((-1013) . T) ((-1129) . T)) 
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+NIL 
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|#1|) (|:| |entry| |#2|)))) NIL T ELT)) (-3947 (((-772) $) NIL (OR (|has| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (-552 (-772))) (|has| |#2| (-552 (-772)))) ELT)) (-1265 (((-85) $ $) NIL (OR (|has| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (-72)) (|has| |#2| (-72))) ELT)) (-1276 (($ (-583 (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)))) NIL T ELT)) (-1732 (((-85) (-1 (-85) (-2 (|:| -3861 |#1|) (|:| |entry| |#2|))) $) NIL T ELT)) (-3057 (((-85) $ $) NIL (OR (|has| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (-72)) (|has| |#2| (-72))) ELT)) (-3958 (((-694) $) NIL T ELT))) 
+(((-1102 |#1| |#2|) (-1107 |#1| |#2|) (-1013) (-1013)) (T -1102)) 
+NIL 
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+NIL 
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+NIL 
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 NIL 
 (-13) 
 (((-13) . T)) 
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-NIL 
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-NIL 
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-(((-21) . T) ((-23) . T) ((-47 |#1| (-485)) . T) ((-25) . T) ((-38 (-350 (-485))) OR (|has| |#1| (-312)) (|has| |#1| (-38 (-350 (-485))))) ((-38 |#1|) |has| |#1| (-146)) ((-38 |#2|) |has| |#1| (-312)) ((-38 $) OR (|has| |#1| (-496)) (|has| |#1| (-312))) ((-35) |has| |#1| (-38 (-350 (-485)))) ((-66) |has| |#1| (-38 (-350 (-485)))) ((-72) . T) ((-82 (-350 (-485)) (-350 (-485))) OR (|has| |#1| (-312)) (|has| |#1| (-38 (-350 (-485))))) ((-82 |#1| |#1|) . T) ((-82 |#2| |#2|) |has| |#1| (-312)) ((-82 $ $) OR (|has| |#1| (-496)) (|has| |#1| (-312)) (|has| |#1| (-146))) ((-104) . T) ((-118) OR (-12 (|has| |#1| (-312)) (|has| |#2| (-118))) (|has| |#1| (-118))) ((-120) OR (-12 (|has| |#1| (-312)) (|has| |#2| (-741))) (-12 (|has| |#1| (-312)) (|has| |#2| (-120))) (|has| |#1| (-120))) ((-556 (-350 (-485))) OR (|has| |#1| (-312)) (|has| |#1| (-38 (-350 (-485))))) ((-556 (-485)) . T) ((-556 (-1091)) -12 (|has| |#1| (-312)) (|has| |#2| (-951 (-1091)))) ((-556 |#1|) |has| |#1| (-146)) ((-556 |#2|) . T) ((-556 $) OR (|has| |#1| (-496)) (|has| |#1| (-312))) ((-553 (-773)) . T) ((-146) OR (|has| |#1| (-496)) (|has| |#1| (-312)) (|has| |#1| (-146))) ((-554 (-179)) -12 (|has| |#1| (-312)) (|has| |#2| (-934))) ((-554 (-330)) -12 (|has| |#1| (-312)) (|has| |#2| (-934))) ((-554 (-474)) -12 (|has| |#1| (-312)) (|has| |#2| (-554 (-474)))) ((-554 (-801 (-330))) -12 (|has| |#1| (-312)) (|has| |#2| (-554 (-801 (-330))))) ((-554 (-801 (-485))) -12 (|has| |#1| (-312)) (|has| |#2| (-554 (-801 (-485))))) ((-186 $) OR (|has| |#1| (-15 * (|#1| (-485) |#1|))) (-12 (|has| |#1| (-312)) (|has| |#2| (-189))) (-12 (|has| |#1| (-312)) (|has| |#2| (-190)))) ((-184 |#2|) |has| |#1| (-312)) ((-190) OR (|has| |#1| (-15 * (|#1| (-485) |#1|))) (-12 (|has| |#1| (-312)) (|has| |#2| (-190)))) ((-189) OR (|has| |#1| (-15 * (|#1| (-485) |#1|))) (-12 (|has| |#1| (-312)) (|has| |#2| (-189))) (-12 (|has| |#1| (-312)) (|has| |#2| (-190)))) ((-225 |#2|) |has| |#1| (-312)) ((-201) |has| |#1| (-312)) ((-239) |has| |#1| (-38 (-350 (-485)))) ((-241 (-485) |#1|) . T) ((-241 |#2| $) -12 (|has| |#1| (-312)) (|has| |#2| (-241 |#2| |#2|))) ((-241 $ $) |has| (-485) (-1026)) ((-246) OR (|has| |#1| (-496)) (|has| |#1| (-312))) ((-258) |has| |#1| (-312)) ((-260 |#2|) -12 (|has| |#1| (-312)) (|has| |#2| (-260 |#2|))) ((-312) |has| |#1| (-312)) ((-288 |#2|) |has| |#1| (-312)) ((-329 |#2|) |has| |#1| (-312)) ((-343 |#2|) |has| |#1| (-312)) ((-392) |has| |#1| (-312)) ((-433) |has| |#1| (-38 (-350 (-485)))) ((-456 (-1091) |#2|) -12 (|has| |#1| (-312)) (|has| |#2| (-456 (-1091) |#2|))) ((-456 |#2| |#2|) -12 (|has| |#1| (-312)) (|has| |#2| (-260 |#2|))) ((-496) OR (|has| |#1| (-496)) (|has| |#1| (-312))) ((-13) . T) ((-589 (-350 (-485))) OR (|has| |#1| (-312)) (|has| |#1| (-38 (-350 (-485))))) ((-589 (-485)) . T) ((-589 |#1|) . T) ((-589 |#2|) |has| |#1| (-312)) ((-589 $) . T) ((-591 (-350 (-485))) OR (|has| |#1| (-312)) (|has| |#1| (-38 (-350 (-485))))) ((-591 (-485)) -12 (|has| |#1| (-312)) (|has| |#2| (-581 (-485)))) ((-591 |#1|) . T) ((-591 |#2|) |has| |#1| (-312)) ((-591 $) . T) ((-583 (-350 (-485))) OR (|has| |#1| (-312)) (|has| |#1| (-38 (-350 (-485))))) ((-583 |#1|) |has| |#1| (-146)) ((-583 |#2|) |has| |#1| (-312)) ((-583 $) OR (|has| |#1| (-496)) (|has| |#1| (-312))) ((-581 (-485)) -12 (|has| |#1| (-312)) (|has| |#2| (-581 (-485)))) ((-581 |#2|) |has| |#1| (-312)) ((-655 (-350 (-485))) OR (|has| |#1| (-312)) (|has| |#1| (-38 (-350 (-485))))) ((-655 |#1|) |has| |#1| (-146)) ((-655 |#2|) |has| |#1| (-312)) ((-655 $) OR (|has| |#1| (-496)) (|has| |#1| (-312))) ((-664) . T) ((-715) -12 (|has| |#1| (-312)) (|has| |#2| (-741))) ((-717) -12 (|has| |#1| (-312)) (|has| |#2| (-741))) ((-719) -12 (|has| |#1| (-312)) (|has| |#2| (-741))) ((-722) -12 (|has| |#1| (-312)) (|has| |#2| (-741))) ((-741) -12 (|has| |#1| (-312)) (|has| |#2| (-741))) ((-756) -12 (|has| |#1| (-312)) (|has| |#2| (-741))) ((-757) OR (-12 (|has| |#1| (-312)) (|has| |#2| (-757))) (-12 (|has| |#1| (-312)) (|has| |#2| (-741)))) ((-760) OR (-12 (|has| |#1| (-312)) (|has| |#2| (-757))) (-12 (|has| |#1| (-312)) (|has| |#2| (-741)))) ((-807 $ (-1091)) OR (-12 (|has| |#1| (-810 (-1091))) (|has| |#1| (-15 * (|#1| (-485) |#1|)))) (-12 (|has| |#1| (-312)) (|has| |#2| (-812 (-1091)))) (-12 (|has| |#1| (-312)) (|has| |#2| (-810 (-1091))))) ((-810 (-1091)) OR (-12 (|has| |#1| (-810 (-1091))) (|has| |#1| (-15 * (|#1| (-485) |#1|)))) (-12 (|has| |#1| (-312)) (|has| |#2| (-810 (-1091))))) ((-812 (-1091)) OR (-12 (|has| |#1| (-810 (-1091))) (|has| |#1| (-15 * (|#1| (-485) |#1|)))) (-12 (|has| |#1| (-312)) (|has| |#2| (-812 (-1091)))) (-12 (|has| |#1| (-312)) (|has| |#2| (-810 (-1091))))) ((-797 (-330)) -12 (|has| |#1| (-312)) (|has| |#2| (-797 (-330)))) ((-797 (-485)) -12 (|has| |#1| (-312)) (|has| |#2| (-797 (-485)))) ((-795 |#2|) |has| |#1| (-312)) ((-822) -12 (|has| |#1| (-312)) (|has| |#2| (-822))) ((-887 |#1| (-485) (-995)) . T) ((-833) |has| |#1| (-312)) ((-905 |#2|) |has| |#1| (-312)) ((-916) |has| |#1| (-38 (-350 (-485)))) ((-934) -12 (|has| |#1| (-312)) (|has| |#2| (-934))) ((-951 (-350 (-485))) -12 (|has| |#1| (-312)) (|has| |#2| (-951 (-485)))) ((-951 (-485)) -12 (|has| |#1| (-312)) (|has| |#2| (-951 (-485)))) ((-951 (-1091)) -12 (|has| |#1| (-312)) (|has| |#2| (-951 (-1091)))) ((-951 |#2|) . T) ((-964 (-350 (-485))) OR (|has| |#1| (-312)) (|has| |#1| (-38 (-350 (-485))))) ((-964 |#1|) . T) ((-964 |#2|) |has| |#1| (-312)) ((-964 $) OR (|has| |#1| (-496)) (|has| |#1| (-312)) (|has| |#1| (-146))) ((-969 (-350 (-485))) OR (|has| |#1| (-312)) (|has| |#1| (-38 (-350 (-485))))) ((-969 |#1|) . T) ((-969 |#2|) |has| |#1| (-312)) ((-969 $) OR (|has| |#1| (-496)) (|has| |#1| (-312)) (|has| |#1| (-146))) ((-962) . T) ((-971) . T) ((-1026) . T) ((-1062) . T) ((-1014) . T) ((-1067) -12 (|has| |#1| (-312)) (|has| |#2| (-1067))) ((-1116) |has| |#1| (-38 (-350 (-485)))) ((-1119) |has| |#1| (-38 (-350 (-485)))) ((-1130) . T) ((-1135) |has| |#1| (-312)) ((-1142 |#1|) . T) ((-1159 |#1| (-485)) . T)) 
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-NIL 
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-((-3820 (*1 *1 *2) (-12 (-5 *2 (-1070 (-2 (|:| |k| (-695)) (|:| |c| *3)))) (-4 *3 (-962)) (-4 *1 (-1173 *3)))) (-3819 (*1 *2 *1) (-12 (-4 *1 (-1173 *3)) (-4 *3 (-962)) (-5 *2 (-1070 *3)))) (-3820 (*1 *1 *2) (-12 (-5 *2 (-1070 *3)) (-4 *3 (-962)) (-4 *1 (-1173 *3)))) (-3818 (*1 *1 *1) (-12 (-4 *1 (-1173 *2)) (-4 *2 (-962)))) (-3817 (*1 *1 *2 *1) (-12 (-5 *2 (-1 *3 (-485))) (-4 *1 (-1173 *3)) (-4 *3 (-962)))) (-3816 (*1 *2 *1 *3) (-12 (-5 *3 (-695)) (-4 *1 (-1173 *4)) (-4 *4 (-962)) (-5 *2 (-858 *4)))) (-3816 (*1 *2 *1 *3 *3) (-12 (-5 *3 (-695)) (-4 *1 (-1173 *4)) (-4 *4 (-962)) (-5 *2 (-858 *4)))) (** (*1 *1 *1 *2) (-12 (-4 *1 (-1173 *2)) (-4 *2 (-962)) (-4 *2 (-312)))) (-3814 (*1 *1 *1) (-12 (-4 *1 (-1173 *2)) (-4 *2 (-962)) (-4 *2 (-38 (-350 (-485)))))) (-3814 (*1 *1 *1 *2) (OR (-12 (-5 *2 (-1091)) (-4 *1 (-1173 *3)) (-4 *3 (-962)) (-12 (-4 *3 (-29 (-485))) (-4 *3 (-872)) (-4 *3 (-1116)) (-4 *3 (-38 (-350 (-485)))))) (-12 (-5 *2 (-1091)) (-4 *1 (-1173 *3)) (-4 *3 (-962)) (-12 (|has| *3 (-15 -3083 ((-584 *2) *3))) (|has| *3 (-15 -3814 (*3 *3 *2))) (-4 *3 (-38 (-350 (-485))))))))) 
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-(((-21) . T) ((-23) . T) ((-47 |#1| (-695)) . T) ((-25) . T) ((-38 (-350 (-485))) |has| |#1| (-38 (-350 (-485)))) ((-38 |#1|) |has| |#1| (-146)) ((-38 $) |has| |#1| (-496)) ((-35) |has| |#1| (-38 (-350 (-485)))) ((-66) |has| |#1| (-38 (-350 (-485)))) ((-72) . T) ((-82 (-350 (-485)) (-350 (-485))) |has| |#1| (-38 (-350 (-485)))) ((-82 |#1| |#1|) . T) ((-82 $ $) OR (|has| |#1| (-496)) (|has| |#1| (-146))) ((-104) . T) ((-118) |has| |#1| (-118)) ((-120) |has| |#1| (-120)) ((-556 (-350 (-485))) |has| |#1| (-38 (-350 (-485)))) ((-556 (-485)) . T) ((-556 |#1|) |has| |#1| (-146)) ((-556 $) |has| |#1| (-496)) ((-553 (-773)) . T) ((-146) OR (|has| |#1| (-496)) (|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 (-350 (-485)))) ((-241 (-695) |#1|) . T) ((-241 $ $) |has| (-695) (-1026)) ((-246) |has| |#1| (-496)) ((-433) |has| |#1| (-38 (-350 (-485)))) ((-496) |has| |#1| (-496)) ((-13) . T) ((-589 (-350 (-485))) |has| |#1| (-38 (-350 (-485)))) ((-589 (-485)) . T) ((-589 |#1|) . T) ((-589 $) . T) ((-591 (-350 (-485))) |has| |#1| (-38 (-350 (-485)))) ((-591 |#1|) . T) ((-591 $) . T) ((-583 (-350 (-485))) |has| |#1| (-38 (-350 (-485)))) ((-583 |#1|) |has| |#1| (-146)) ((-583 $) |has| |#1| (-496)) ((-655 (-350 (-485))) |has| |#1| (-38 (-350 (-485)))) ((-655 |#1|) |has| |#1| (-146)) ((-655 $) |has| |#1| (-496)) ((-664) . T) ((-807 $ (-1091)) -12 (|has| |#1| (-810 (-1091))) (|has| |#1| (-15 * (|#1| (-695) |#1|)))) ((-810 (-1091)) -12 (|has| |#1| (-810 (-1091))) (|has| |#1| (-15 * (|#1| (-695) |#1|)))) ((-812 (-1091)) -12 (|has| |#1| (-810 (-1091))) (|has| |#1| (-15 * (|#1| (-695) |#1|)))) ((-887 |#1| (-695) (-995)) . T) ((-916) |has| |#1| (-38 (-350 (-485)))) ((-964 (-350 (-485))) |has| |#1| (-38 (-350 (-485)))) ((-964 |#1|) . T) ((-964 $) OR (|has| |#1| (-496)) (|has| |#1| (-146))) ((-969 (-350 (-485))) |has| |#1| (-38 (-350 (-485)))) ((-969 |#1|) . T) ((-969 $) OR (|has| |#1| (-496)) (|has| |#1| (-146))) ((-962) . T) ((-971) . T) ((-1026) . T) ((-1062) . T) ((-1014) . T) ((-1116) |has| |#1| (-38 (-350 (-485)))) ((-1119) |has| |#1| (-38 (-350 (-485)))) ((-1130) . T) ((-1159 |#1| (-695)) . T)) 
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-((-3830 ((|#2| |#4| (-695)) 31 T ELT)) (-3829 ((|#4| |#2|) 26 T ELT)) (-3832 ((|#4| (-350 |#2|)) 49 (|has| |#1| (-496)) ELT)) (-3831 (((-1 |#4| (-584 |#4|)) |#3|) 43 T ELT))) 
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-((-3832 (*1 *2 *3) (-12 (-5 *3 (-350 *5)) (-4 *5 (-1156 *4)) (-4 *4 (-496)) (-4 *4 (-962)) (-4 *2 (-1173 *4)) (-5 *1 (-1175 *4 *5 *6 *2)) (-4 *6 (-601 *5)))) (-3831 (*1 *2 *3) (-12 (-4 *4 (-962)) (-4 *5 (-1156 *4)) (-5 *2 (-1 *6 (-584 *6))) (-5 *1 (-1175 *4 *5 *3 *6)) (-4 *3 (-601 *5)) (-4 *6 (-1173 *4)))) (-3830 (*1 *2 *3 *4) (-12 (-5 *4 (-695)) (-4 *5 (-962)) (-4 *2 (-1156 *5)) (-5 *1 (-1175 *5 *2 *6 *3)) (-4 *6 (-601 *2)) (-4 *3 (-1173 *5)))) (-3829 (*1 *2 *3) (-12 (-4 *4 (-962)) (-4 *3 (-1156 *4)) (-4 *2 (-1173 *4)) (-5 *1 (-1175 *4 *3 *5 *2)) (-4 *5 (-601 *3))))) 
-NIL 
-(((-1176) (-113)) (T -1176)) 
-NIL 
-(-13 (-10 -7 (-6 -2288))) 
-((-2570 (((-85) $ $) NIL T ELT)) (-3833 (((-1091)) 12 T ELT)) (-3244 (((-1074) $) 18 T ELT)) (-3245 (((-1034) $) NIL T ELT)) (-3948 (((-773) $) 11 T ELT) (((-1091) $) 8 T ELT)) (-1266 (((-85) $ $) NIL T ELT)) (-3058 (((-85) $ $) 15 T ELT))) 
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-((-3948 (*1 *2 *1) (-12 (-5 *2 (-1091)) (-5 *1 (-1177 *3)) (-14 *3 *2))) (-3833 (*1 *2) (-12 (-5 *2 (-1091)) (-5 *1 (-1177 *3)) (-14 *3 *2)))) 
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-NIL 
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-(((-1179 |#1|) (-113) (-1130)) (T -1179)) 
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-NIL 
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-NIL 
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-NIL 
-NIL 
-NIL 
-NIL 
-NIL 
-NIL 
-NIL 
-NIL 
-NIL 
-NIL 
-NIL 
-NIL 
-NIL 
-((-3 2796242 2796247 2796252 NIL NIL NIL (NIL) -8 NIL NIL NIL) (-2 2796227 2796232 2796237 NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1 2796212 2796217 2796222 NIL NIL NIL (NIL) -8 NIL NIL NIL) (0 2796197 2796202 2796207 NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1210 2795176 2796115 2796192 "ZMOD" NIL ZMOD (NIL NIL) -8 NIL NIL NIL) (-1209 2794391 2794570 2794789 "ZLINDEP" NIL ZLINDEP (NIL T) -7 NIL NIL NIL) (-1208 2785550 2787419 2789353 "ZDSOLVE" NIL ZDSOLVE (NIL T NIL NIL) -7 NIL NIL NIL) (-1207 2784938 2785091 2785280 "YSTREAM" NIL YSTREAM (NIL T) -7 NIL NIL NIL) (-1206 2784400 2784703 2784816 "YDIAGRAM" NIL YDIAGRAM (NIL) -8 NIL NIL NIL) (-1205 2781960 2783862 2784065 "XRPOLY" NIL XRPOLY (NIL T T) -8 NIL NIL NIL) (-1204 2778724 2780377 2780948 "XPR" NIL XPR (NIL T T) -8 NIL NIL NIL) (-1203 2775981 2777711 2777765 "XPOLYC" 2778050 XPOLYC (NIL T T) -9 NIL 2778163 NIL) (-1202 2773500 2775485 2775688 "XPOLY" NIL XPOLY (NIL T) -8 NIL NIL NIL) (-1201 2769748 2772359 2772747 "XPBWPOLY" NIL XPBWPOLY (NIL T T) -8 NIL NIL NIL) (-1200 2764595 2766228 2766282 "XFALG" 2768427 XFALG (NIL T T) -9 NIL 2769211 NIL) (-1199 2759751 2762484 2762526 "XF" 2763144 XF (NIL T) -9 NIL 2763540 NIL) (-1198 2759469 2759579 2759746 "XF-" NIL XF- (NIL T T) -7 NIL NIL NIL) (-1197 2758696 2758818 2759022 "XEXPPKG" NIL XEXPPKG (NIL T T T) -7 NIL NIL NIL) (-1196 2756438 2758596 2758691 "XDPOLY" NIL XDPOLY (NIL T T) -8 NIL NIL NIL) (-1195 2755019 2755814 2755856 "XALG" 2755861 XALG (NIL T) -9 NIL 2755970 NIL) (-1194 2748870 2753429 2753907 "WUTSET" NIL WUTSET (NIL T T T T) -8 NIL NIL NIL) (-1193 2747113 2748115 2748436 "WP" NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL NIL) (-1192 2746712 2746984 2747053 "WHILEAST" NIL WHILEAST (NIL) -8 NIL NIL NIL) (-1191 2746199 2746502 2746595 "WHEREAST" NIL WHEREAST (NIL) -8 NIL NIL NIL) (-1190 2745276 2745486 2745781 "WFFINTBS" NIL WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1189 2743572 2744035 2744497 "WEIER" NIL WEIER (NIL T) -7 NIL NIL NIL) (-1188 2742461 2743046 2743088 "VSPACE" 2743224 VSPACE (NIL T) -9 NIL 2743298 NIL) (-1187 2742332 2742365 2742456 "VSPACE-" NIL VSPACE- (NIL T T) -7 NIL NIL NIL) (-1186 2742175 2742229 2742297 "VOID" NIL VOID (NIL) -8 NIL NIL NIL) (-1185 2739158 2739953 2740690 "VIEWDEF" NIL VIEWDEF (NIL) -7 NIL NIL NIL) (-1184 2730256 2732857 2735030 "VIEW3D" NIL VIEW3D (NIL) -8 NIL NIL NIL) (-1183 2723833 2725724 2727303 "VIEW2D" NIL VIEW2D (NIL) -8 NIL NIL NIL) (-1182 2722317 2722712 2723118 "VIEW" NIL VIEW (NIL) -7 NIL NIL NIL) (-1181 2721144 2721425 2721741 "VECTOR2" NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1180 2716551 2720971 2721063 "VECTOR" NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1179 2709906 2714224 2714267 "VECTCAT" 2715255 VECTCAT (NIL T) -9 NIL 2715839 NIL) (-1178 2709185 2709511 2709901 "VECTCAT-" NIL VECTCAT- (NIL T T) -7 NIL NIL NIL) (-1177 2708679 2708921 2709041 "VARIABLE" NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1176 2708612 2708617 2708647 "UTYPE" 2708652 UTYPE (NIL) -9 NIL NIL NIL) (-1175 2707599 2707775 2708036 "UTSODETL" NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1174 2705450 2705958 2706482 "UTSODE" NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1173 2695332 2701302 2701344 "UTSCAT" 2702442 UTSCAT (NIL T) -9 NIL 2703199 NIL) (-1172 2693397 2694340 2695327 "UTSCAT-" NIL UTSCAT- (NIL T T) -7 NIL NIL NIL) (-1171 2693071 2693120 2693251 "UTS2" NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1170 2684782 2691267 2691746 "UTS" NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1169 2679285 2681617 2681660 "URAGG" 2683700 URAGG (NIL T) -9 NIL 2684425 NIL) (-1168 2677356 2678288 2679280 "URAGG-" NIL URAGG- (NIL T T) -7 NIL NIL NIL) (-1167 2673063 2676332 2676794 "UPXSSING" NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1166 2665492 2672987 2673058 "UPXSCONS" NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1165 2654143 2661630 2661691 "UPXSCCA" 2662259 UPXSCCA (NIL T T) -9 NIL 2662491 NIL) (-1164 2653864 2653966 2654138 "UPXSCCA-" NIL UPXSCCA- (NIL T T T) -7 NIL NIL NIL) (-1163 2642416 2649628 2649670 "UPXSCAT" 2650310 UPXSCAT (NIL T) -9 NIL 2650918 NIL) (-1162 2641929 2642014 2642191 "UPXS2" NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1161 2633615 2641520 2641782 "UPXS" NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1160 2632510 2632780 2633130 "UPSQFREE" NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1159 2625213 2628698 2628752 "UPSCAT" 2629821 UPSCAT (NIL T T) -9 NIL 2630585 NIL) (-1158 2624633 2624885 2625208 "UPSCAT-" NIL UPSCAT- (NIL T T T) -7 NIL NIL NIL) (-1157 2624307 2624356 2624487 "UPOLYC2" NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1156 2608437 2617391 2617433 "UPOLYC" 2619511 UPOLYC (NIL T) -9 NIL 2620731 NIL) (-1155 2602492 2605340 2608432 "UPOLYC-" NIL UPOLYC- (NIL T T) -7 NIL NIL NIL) (-1154 2601928 2602053 2602216 "UPMP" NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1153 2601562 2601649 2601788 "UPDIVP" NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1152 2600375 2600642 2600946 "UPDECOMP" NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1151 2599708 2599838 2600023 "UPCDEN" NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1150 2599300 2599375 2599522 "UP2" NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1149 2590064 2599066 2599194 "UP" NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1148 2589426 2589563 2589768 "UNISEG2" NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1147 2588027 2588874 2589150 "UNISEG" NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1146 2587256 2587453 2587678 "UNIFACT" NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1145 2574066 2587180 2587251 "ULSCONS" NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1144 2553872 2567107 2567168 "ULSCCAT" 2567799 ULSCCAT (NIL T T) -9 NIL 2568086 NIL) (-1143 2553207 2553493 2553867 "ULSCCAT-" NIL ULSCCAT- (NIL T T T) -7 NIL NIL NIL) (-1142 2541579 2548713 2548755 "ULSCAT" 2549608 ULSCAT (NIL T) -9 NIL 2550338 NIL) (-1141 2541092 2541177 2541354 "ULS2" NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1140 2523209 2540591 2540832 "ULS" NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1139 2522243 2522936 2523050 "UINT8" NIL UINT8 (NIL) -8 NIL NIL 2523161) (-1138 2521276 2521969 2522083 "UINT64" NIL UINT64 (NIL) -8 NIL NIL 2522194) (-1137 2520309 2521002 2521116 "UINT32" NIL UINT32 (NIL) -8 NIL NIL 2521227) (-1136 2519342 2520035 2520149 "UINT16" NIL UINT16 (NIL) -8 NIL NIL 2520260) (-1135 2517349 2518570 2518600 "UFD" 2518811 UFD (NIL) -9 NIL 2518924 NIL) (-1134 2517193 2517250 2517344 "UFD-" NIL UFD- (NIL T) -7 NIL NIL NIL) (-1133 2516445 2516652 2516868 "UDVO" NIL UDVO (NIL) -7 NIL NIL NIL) (-1132 2514665 2515118 2515583 "UDPO" NIL UDPO (NIL T) -7 NIL NIL NIL) (-1131 2514390 2514630 2514660 "TYPEAST" NIL TYPEAST (NIL) -8 NIL NIL NIL) (-1130 2514328 2514333 2514363 "TYPE" 2514368 TYPE (NIL) -9 NIL 2514375 NIL) (-1129 2513487 2513707 2513947 "TWOFACT" NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1128 2512665 2513096 2513331 "TUPLE" NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1127 2510819 2511392 2511931 "TUBETOOL" NIL TUBETOOL (NIL) -7 NIL NIL NIL) (-1126 2509853 2510089 2510325 "TUBE" NIL TUBE (NIL T) -8 NIL NIL NIL) (-1125 2498470 2502646 2502742 "TSETCAT" 2507957 TSETCAT (NIL T T T T) -9 NIL 2509461 NIL) (-1124 2494807 2496623 2498465 "TSETCAT-" NIL TSETCAT- (NIL T T T T T) -7 NIL NIL NIL) (-1123 2489199 2494033 2494315 "TS" NIL TS (NIL T) -8 NIL NIL NIL) (-1122 2484536 2485549 2486478 "TRMANIP" NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1121 2484033 2484108 2484271 "TRIMAT" NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1120 2482109 2482399 2482754 "TRIGMNIP" NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1119 2481593 2481742 2481772 "TRIGCAT" 2481985 TRIGCAT (NIL) -9 NIL NIL NIL) (-1118 2481344 2481447 2481588 "TRIGCAT-" NIL TRIGCAT- (NIL T) -7 NIL NIL NIL) (-1117 2478399 2480450 2480731 "TREE" NIL TREE (NIL T) -8 NIL NIL NIL) (-1116 2477505 2478201 2478231 "TRANFUN" 2478266 TRANFUN (NIL) -9 NIL 2478332 NIL) (-1115 2476969 2477220 2477500 "TRANFUN-" NIL TRANFUN- (NIL T) -7 NIL NIL NIL) (-1114 2476806 2476844 2476905 "TOPSP" NIL TOPSP (NIL) -7 NIL NIL NIL) (-1113 2476263 2476394 2476545 "TOOLSIGN" NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1112 2475004 2475661 2475897 "TEXTFILE" NIL TEXTFILE (NIL) -8 NIL NIL NIL) (-1111 2474816 2474853 2474925 "TEX1" NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1110 2473030 2473676 2474105 "TEX" NIL TEX (NIL) -8 NIL NIL NIL) (-1109 2471410 2471747 2472069 "TBCMPPK" NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1108 2461356 2469190 2469246 "TBAGG" 2469563 TBAGG (NIL T T) -9 NIL 2469773 NIL) (-1107 2458546 2459905 2461351 "TBAGG-" NIL TBAGG- (NIL T T T) -7 NIL NIL NIL) (-1106 2458023 2458148 2458293 "TANEXP" NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1105 2457533 2457853 2457943 "TALGOP" NIL TALGOP (NIL T) -8 NIL NIL NIL) (-1104 2457030 2457147 2457285 "TABLEAU" NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1103 2449399 2456958 2457025 "TABLE" NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1102 2445152 2446447 2447692 "TABLBUMP" NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1101 2444521 2444680 2444861 "SYSTEM" NIL SYSTEM (NIL) -7 NIL NIL NIL) (-1100 2441675 2442428 2443211 "SYSSOLP" NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1099 2441449 2441639 2441670 "SYSPTR" NIL SYSPTR (NIL) -8 NIL NIL NIL) (-1098 2440403 2441088 2441214 "SYSNNI" NIL SYSNNI (NIL NIL) -8 NIL NIL 2441400) (-1097 2439667 2440215 2440294 "SYSINT" NIL SYSINT (NIL NIL) -8 NIL NIL 2440354) (-1096 2436490 2437649 2438349 "SYNTAX" NIL SYNTAX (NIL) -8 NIL NIL NIL) (-1095 2434173 2434856 2435490 "SYMTAB" NIL SYMTAB (NIL) -8 NIL NIL NIL) (-1094 2430251 2431297 2432274 "SYMS" NIL SYMS (NIL) -8 NIL NIL NIL) (-1093 2427350 2429906 2430135 "SYMPOLY" NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1092 2426946 2427033 2427155 "SYMFUNC" NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1091 2423570 2425044 2425863 "SYMBOL" NIL SYMBOL (NIL) -8 NIL NIL NIL) (-1090 2416530 2422767 2423060 "SUTS" NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1089 2408216 2416121 2416383 "SUPXS" NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1088 2407495 2407634 2407851 "SUPFRACF" NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1087 2407179 2407244 2407355 "SUP2" NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1086 2397902 2406891 2407016 "SUP" NIL SUP (NIL T) -8 NIL NIL NIL) (-1085 2396632 2396930 2397285 "SUMRF" NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1084 2396037 2396115 2396306 "SUMFS" NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1083 2378189 2395536 2395777 "SULS" NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1082 2377788 2378060 2378129 "SUCHTAST" NIL SUCHTAST (NIL) -8 NIL NIL NIL) (-1081 2377124 2377405 2377545 "SUCH" NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1080 2371726 2372985 2373938 "SUBSPACE" NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1079 2371258 2371358 2371522 "SUBRESP" NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1078 2366369 2367651 2368798 "STTFNC" NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1077 2360827 2362298 2363609 "STTF" NIL STTF (NIL T) -7 NIL NIL NIL) (-1076 2353742 2355806 2357597 "STTAYLOR" NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1075 2345770 2353680 2353737 "STRTBL" NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1074 2340739 2345484 2345599 "STRING" NIL STRING (NIL) -8 NIL NIL NIL) (-1073 2340326 2340409 2340553 "STREAM3" NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1072 2339477 2339678 2339913 "STREAM2" NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1071 2339217 2339275 2339368 "STREAM1" NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1070 2332694 2337420 2338028 "STREAM" NIL STREAM (NIL T) -8 NIL NIL NIL) (-1069 2331870 2332075 2332306 "STINPROD" NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1068 2331115 2331486 2331633 "STEPAST" NIL STEPAST (NIL) -8 NIL NIL NIL) (-1067 2330603 2330845 2330875 "STEP" 2330969 STEP (NIL) -9 NIL 2331040 NIL) (-1066 2322962 2330521 2330598 "STBL" NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1065 2317897 2321760 2321803 "STAGG" 2322230 STAGG (NIL T) -9 NIL 2322404 NIL) (-1064 2316276 2317024 2317892 "STAGG-" NIL STAGG- (NIL T T) -7 NIL NIL NIL) (-1063 2314497 2316103 2316195 "STACK" NIL STACK (NIL T) -8 NIL NIL NIL) (-1062 2313777 2314316 2314346 "SRING" 2314351 SRING (NIL) -9 NIL 2314371 NIL) (-1061 2306692 2312315 2312754 "SREGSET" NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1060 2300466 2301905 2303409 "SRDCMPK" NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1059 2293124 2297761 2297791 "SRAGG" 2299090 SRAGG (NIL) -9 NIL 2299694 NIL) (-1058 2292421 2292741 2293119 "SRAGG-" NIL SRAGG- (NIL T) -7 NIL NIL NIL) (-1057 2286521 2291743 2292166 "SQMATRIX" NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1056 2280533 2283874 2284625 "SPLTREE" NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1055 2276962 2277781 2278418 "SPLNODE" NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1054 2275937 2276242 2276272 "SPFCAT" 2276716 SPFCAT (NIL) -9 NIL NIL NIL) (-1053 2274874 2275126 2275390 "SPECOUT" NIL SPECOUT (NIL) -7 NIL NIL NIL) (-1052 2265632 2267906 2267936 "SPADXPT" 2272573 SPADXPT (NIL) -9 NIL 2274697 NIL) (-1051 2265434 2265480 2265549 "SPADPRSR" NIL SPADPRSR (NIL) -7 NIL NIL NIL) (-1050 2263090 2265398 2265429 "SPADAST" NIL SPADAST (NIL) -8 NIL NIL NIL) (-1049 2254764 2256853 2256895 "SPACEC" 2261210 SPACEC (NIL T) -9 NIL 2263015 NIL) (-1048 2252593 2254711 2254759 "SPACE3" NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1047 2251572 2251761 2252044 "SORTPAK" NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1046 2249976 2250309 2250720 "SOLVETRA" NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1045 2249241 2249475 2249736 "SOLVESER" NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1044 2245421 2246381 2247376 "SOLVERAD" NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1043 2241779 2242478 2243207 "SOLVEFOR" NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1042 2235820 2241082 2241178 "SNTSCAT" 2241183 SNTSCAT (NIL T T T T) -9 NIL 2241253 NIL) (-1041 2229641 2234461 2234851 "SMTS" NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1040 2223413 2229560 2229636 "SMP" NIL SMP (NIL T T) -8 NIL NIL NIL) (-1039 2221845 2222176 2222574 "SMITH" NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1038 2213477 2218411 2218513 "SMATCAT" 2219856 SMATCAT (NIL NIL T T T) -9 NIL 2220404 NIL) (-1037 2211318 2212302 2213472 "SMATCAT-" NIL SMATCAT- (NIL T NIL T T T) -7 NIL NIL NIL) (-1036 2209924 2210776 2210819 "SMAGG" 2210904 SMAGG (NIL T) -9 NIL 2210979 NIL) (-1035 2207543 2209091 2209134 "SKAGG" 2209395 SKAGG (NIL T) -9 NIL 2209531 NIL) (-1034 2203589 2207363 2207474 "SINT" NIL SINT (NIL) -8 NIL NIL 2207515) (-1033 2203399 2203443 2203509 "SIMPAN" NIL SIMPAN (NIL) -7 NIL NIL NIL) (-1032 2202474 2202706 2202974 "SIGNRF" NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1031 2201478 2201640 2201916 "SIGNEF" NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1030 2200824 2201164 2201287 "SIGAST" NIL SIGAST (NIL) -8 NIL NIL NIL) (-1029 2200170 2200477 2200617 "SIG" NIL SIG (NIL) -8 NIL NIL NIL) (-1028 2198281 2198773 2199279 "SHP" NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1027 2191767 2198200 2198276 "SHDP" NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1026 2191270 2191507 2191537 "SGROUP" 2191630 SGROUP (NIL) -9 NIL 2191692 NIL) (-1025 2191160 2191192 2191265 "SGROUP-" NIL SGROUP- (NIL T) -7 NIL NIL NIL) (-1024 2190798 2190838 2190879 "SGPOPC" 2190884 SGPOPC (NIL T) -9 NIL 2191085 NIL) (-1023 2190332 2190609 2190715 "SGPOP" NIL SGPOP (NIL T) -8 NIL NIL NIL) (-1022 2187755 2188524 2189246 "SGCF" NIL SGCF (NIL) -7 NIL NIL NIL) (-1021 2181895 2187157 2187253 "SFRTCAT" 2187258 SFRTCAT (NIL T T T T) -9 NIL 2187296 NIL) (-1020 2176287 2177400 2178527 "SFRGCD" NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1019 2170463 2171624 2172788 "SFQCMPK" NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1018 2169435 2170337 2170458 "SEXOF" NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1017 2165043 2165938 2166033 "SEXCAT" 2168646 SEXCAT (NIL T T T T T) -9 NIL 2169197 NIL) (-1016 2164016 2164970 2165038 "SEX" NIL SEX (NIL) -8 NIL NIL NIL) (-1015 2162407 2162992 2163294 "SETMN" NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1014 2161930 2162115 2162145 "SETCAT" 2162262 SETCAT (NIL) -9 NIL 2162346 NIL) (-1013 2161762 2161826 2161925 "SETCAT-" NIL SETCAT- (NIL T) -7 NIL NIL NIL) (-1012 2158715 2160216 2160259 "SETAGG" 2161127 SETAGG (NIL T) -9 NIL 2161465 NIL) (-1011 2158321 2158473 2158710 "SETAGG-" NIL SETAGG- (NIL T T) -7 NIL NIL NIL) (-1010 2155566 2158268 2158316 "SET" NIL SET (NIL T) -8 NIL NIL NIL) (-1009 2155032 2155342 2155442 "SEQAST" NIL SEQAST (NIL) -8 NIL NIL NIL) (-1008 2154159 2154525 2154586 "SEGXCAT" 2154872 SEGXCAT (NIL T T) -9 NIL 2154992 NIL) (-1007 2153084 2153352 2153395 "SEGCAT" 2153917 SEGCAT (NIL T) -9 NIL 2154138 NIL) (-1006 2152764 2152829 2152942 "SEGBIND2" NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1005 2151830 2152300 2152508 "SEGBIND" NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1004 2151408 2151687 2151763 "SEGAST" NIL SEGAST (NIL) -8 NIL NIL NIL) (-1003 2150773 2150909 2151113 "SEG2" NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1002 2149839 2150586 2150768 "SEG" NIL SEG (NIL T) -8 NIL NIL NIL) (-1001 2149092 2149787 2149834 "SDVAR" NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1000 2140577 2148959 2149087 "SDPOL" NIL SDPOL (NIL T) -8 NIL NIL NIL) (-999 2139437 2139727 2140044 "SCPKG" NIL SCPKG (NIL T) -7 NIL NIL NIL) (-998 2138743 2138955 2139143 "SCOPE" NIL SCOPE (NIL) -8 NIL NIL NIL) (-997 2138093 2138250 2138426 "SCACHE" NIL SCACHE (NIL T) -7 NIL NIL NIL) (-996 2137666 2137897 2137925 "SASTCAT" 2137930 SASTCAT (NIL) -9 NIL 2137943 NIL) (-995 2137133 2137558 2137632 "SAOS" NIL SAOS (NIL) -8 NIL NIL NIL) (-994 2136736 2136777 2136948 "SAERFFC" NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-993 2136367 2136408 2136565 "SAEFACT" NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-992 2129448 2136284 2136362 "SAE" NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-991 2128098 2128427 2128823 "RURPK" NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-990 2126859 2127220 2127520 "RULESET" NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-989 2126483 2126704 2126785 "RULECOLD" NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-988 2123943 2124577 2125030 "RULE" NIL RULE (NIL T T T) -8 NIL NIL NIL) (-987 2123782 2123815 2123883 "RTVALUE" NIL RTVALUE (NIL) -8 NIL NIL NIL) (-986 2123273 2123576 2123667 "RSTRCAST" NIL RSTRCAST (NIL) -8 NIL NIL NIL) (-985 2118901 2119769 2120680 "RSETGCD" NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-984 2107975 2113237 2113331 "RSETCAT" 2117387 RSETCAT (NIL T T T T) -9 NIL 2118475 NIL) (-983 2106513 2107155 2107970 "RSETCAT-" NIL RSETCAT- (NIL T T T T T) -7 NIL NIL NIL) (-982 2100287 2101732 2103239 "RSDCMPK" NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-981 2098169 2098726 2098798 "RRCC" 2099871 RRCC (NIL T T) -9 NIL 2100212 NIL) (-980 2097694 2097893 2098164 "RRCC-" NIL RRCC- (NIL T T T) -7 NIL NIL NIL) (-979 2097164 2097474 2097572 "RPTAST" NIL RPTAST (NIL) -8 NIL NIL NIL) (-978 2069716 2080429 2080493 "RPOLCAT" 2090967 RPOLCAT (NIL T T T) -9 NIL 2094112 NIL) (-977 2063815 2066638 2069711 "RPOLCAT-" NIL RPOLCAT- (NIL T T T T) -7 NIL NIL NIL) (-976 2059982 2063563 2063701 "ROMAN" NIL ROMAN (NIL) -8 NIL NIL NIL) (-975 2058310 2059049 2059305 "ROIRC" NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-974 2053953 2056765 2056793 "RNS" 2057055 RNS (NIL) -9 NIL 2057307 NIL) (-973 2052856 2053343 2053880 "RNS-" NIL RNS- (NIL T) -7 NIL NIL NIL) (-972 2051974 2052375 2052575 "RNGBIND" NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-971 2051112 2051674 2051702 "RNG" 2051762 RNG (NIL) -9 NIL 2051816 NIL) (-970 2051001 2051035 2051107 "RNG-" NIL RNG- (NIL T) -7 NIL NIL NIL) (-969 2050263 2050768 2050808 "RMODULE" 2050813 RMODULE (NIL T) -9 NIL 2050839 NIL) (-968 2049202 2049308 2049638 "RMCAT2" NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-967 2046093 2048792 2049085 "RMATRIX" NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-966 2038782 2041227 2041339 "RMATCAT" 2044644 RMATCAT (NIL NIL NIL T T T) -9 NIL 2045610 NIL) (-965 2038299 2038478 2038777 "RMATCAT-" NIL RMATCAT- (NIL T NIL NIL T T T) -7 NIL NIL NIL) (-964 2037867 2038078 2038119 "RLINSET" 2038180 RLINSET (NIL T) -9 NIL 2038224 NIL) (-963 2037512 2037593 2037719 "RINTERP" NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-962 2036358 2037089 2037117 "RING" 2037172 RING (NIL) -9 NIL 2037264 NIL) (-961 2036203 2036259 2036353 "RING-" NIL RING- (NIL T) -7 NIL NIL NIL) (-960 2035257 2035524 2035780 "RIDIST" NIL RIDIST (NIL) -7 NIL NIL NIL) (-959 2026481 2034885 2035086 "RGCHAIN" NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-958 2025706 2026217 2026256 "RGBCSPC" 2026313 RGBCSPC (NIL T) -9 NIL 2026364 NIL) (-957 2024740 2025226 2025265 "RGBCMDL" 2025493 RGBCMDL (NIL T) -9 NIL 2025607 NIL) (-956 2024452 2024521 2024622 "RFFACTOR" NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-955 2024215 2024256 2024351 "RFFACT" NIL RFFACT (NIL T) -7 NIL NIL NIL) (-954 2022639 2023069 2023449 "RFDIST" NIL RFDIST (NIL) -7 NIL NIL NIL) (-953 2020226 2020894 2021562 "RF" NIL RF (NIL T) -7 NIL NIL NIL) (-952 2019776 2019874 2020034 "RETSOL" NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-951 2019398 2019496 2019537 "RETRACT" 2019668 RETRACT (NIL T) -9 NIL 2019755 NIL) (-950 2019278 2019309 2019393 "RETRACT-" NIL RETRACT- (NIL T T) -7 NIL NIL NIL) (-949 2018880 2019152 2019219 "RETAST" NIL RETAST (NIL) -8 NIL NIL NIL) (-948 2017360 2018251 2018448 "RESRING" NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-947 2017051 2017112 2017208 "RESLATC" NIL RESLATC (NIL T) -7 NIL NIL NIL) (-946 2016794 2016835 2016940 "REPSQ" NIL REPSQ (NIL T) -7 NIL NIL NIL) (-945 2016529 2016570 2016679 "REPDB" NIL REPDB (NIL T) -7 NIL NIL NIL) (-944 2011600 2013051 2014266 "REP2" NIL REP2 (NIL T) -7 NIL NIL NIL) (-943 2008699 2009457 2010265 "REP1" NIL REP1 (NIL T) -7 NIL NIL NIL) (-942 2006668 2007290 2007890 "REP" NIL REP (NIL) -7 NIL NIL NIL) (-941 1999596 2005219 2005655 "REGSET" NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-940 1998908 1999188 1999337 "REF" NIL REF (NIL T) -8 NIL NIL NIL) (-939 1998393 1998508 1998673 "REDORDER" NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-938 1993986 1997796 1998017 "RECLOS" NIL RECLOS (NIL T) -8 NIL NIL NIL) (-937 1993218 1993417 1993630 "REALSOLV" NIL REALSOLV (NIL) -7 NIL NIL NIL) (-936 1990508 1991346 1992228 "REAL0Q" NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-935 1987090 1988126 1989185 "REAL0" NIL REAL0 (NIL T) -7 NIL NIL NIL) (-934 1986926 1986979 1987007 "REAL" 1987012 REAL (NIL) -9 NIL 1987047 NIL) (-933 1986416 1986720 1986811 "RDUCEAST" NIL RDUCEAST (NIL) -8 NIL NIL NIL) (-932 1985896 1985974 1986179 "RDIV" NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-931 1985129 1985321 1985532 "RDIST" NIL RDIST (NIL T) -7 NIL NIL NIL) (-930 1984017 1984314 1984681 "RDETRS" NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-929 1982284 1982754 1983287 "RDETR" NIL RDETR (NIL T T) -7 NIL NIL NIL) (-928 1981206 1981483 1981870 "RDEEFS" NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-927 1980033 1980342 1980761 "RDEEF" NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-926 1973381 1976893 1976921 "RCFIELD" 1978198 RCFIELD (NIL) -9 NIL 1978928 NIL) (-925 1971999 1972611 1973308 "RCFIELD-" NIL RCFIELD- (NIL T) -7 NIL NIL NIL) (-924 1968712 1970103 1970144 "RCAGG" 1971198 RCAGG (NIL T) -9 NIL 1971660 NIL) (-923 1968439 1968549 1968707 "RCAGG-" NIL RCAGG- (NIL T T) -7 NIL NIL NIL) (-922 1967884 1968013 1968174 "RATRET" NIL RATRET (NIL T) -7 NIL NIL NIL) (-921 1967501 1967580 1967699 "RATFACT" NIL RATFACT (NIL T) -7 NIL NIL NIL) (-920 1966916 1967066 1967216 "RANDSRC" NIL RANDSRC (NIL) -7 NIL NIL NIL) (-919 1966698 1966748 1966819 "RADUTIL" NIL RADUTIL (NIL) -7 NIL NIL NIL) (-918 1959140 1965816 1966124 "RADIX" NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-917 1948842 1959007 1959135 "RADFF" NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-916 1948476 1948569 1948597 "RADCAT" 1948754 RADCAT (NIL) -9 NIL NIL NIL) (-915 1948314 1948374 1948471 "RADCAT-" NIL RADCAT- (NIL T) -7 NIL NIL NIL) (-914 1946478 1948145 1948234 "QUEUE" NIL QUEUE (NIL T) -8 NIL NIL NIL) (-913 1946159 1946208 1946335 "QUATCT2" NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-912 1938446 1942530 1942570 "QUATCAT" 1943348 QUATCAT (NIL T) -9 NIL 1944112 NIL) (-911 1935696 1936976 1938352 "QUATCAT-" NIL QUATCAT- (NIL T T) -7 NIL NIL NIL) (-910 1931536 1935646 1935691 "QUAT" NIL QUAT (NIL T) -8 NIL NIL NIL) (-909 1928950 1930551 1930592 "QUAGG" 1930967 QUAGG (NIL T) -9 NIL 1931143 NIL) (-908 1928552 1928824 1928891 "QQUTAST" NIL QQUTAST (NIL) -8 NIL NIL NIL) (-907 1927558 1928188 1928351 "QFORM" NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-906 1927239 1927288 1927415 "QFCAT2" NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-905 1916839 1923008 1923048 "QFCAT" 1923706 QFCAT (NIL T) -9 NIL 1924699 NIL) (-904 1913723 1915162 1916745 "QFCAT-" NIL QFCAT- (NIL T T) -7 NIL NIL NIL) (-903 1913269 1913403 1913533 "QEQUAT" NIL QEQUAT (NIL) -8 NIL NIL NIL) (-902 1907465 1908626 1909788 "QCMPACK" NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-901 1906884 1907064 1907296 "QALGSET2" NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-900 1904706 1905234 1905657 "QALGSET" NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-899 1903605 1903847 1904164 "PWFFINTB" NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-898 1901966 1902164 1902517 "PUSHVAR" NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-897 1897722 1898938 1898979 "PTRANFN" 1900863 PTRANFN (NIL T) -9 NIL NIL NIL) (-896 1896369 1896714 1897035 "PTPACK" NIL PTPACK (NIL T) -7 NIL NIL NIL) (-895 1896062 1896125 1896232 "PTFUNC2" NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-894 1890388 1894821 1894861 "PTCAT" 1895153 PTCAT (NIL T) -9 NIL 1895306 NIL) (-893 1890081 1890122 1890246 "PSQFR" NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-892 1888960 1889276 1889610 "PSEUDLIN" NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-891 1877839 1880400 1882709 "PSETPK" NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-890 1871000 1873622 1873716 "PSETCAT" 1876690 PSETCAT (NIL T T T T) -9 NIL 1877499 NIL) (-889 1869450 1870184 1870995 "PSETCAT-" NIL PSETCAT- (NIL T T T T T) -7 NIL NIL NIL) (-888 1868769 1868964 1868992 "PSCURVE" 1869260 PSCURVE (NIL) -9 NIL 1869427 NIL) (-887 1864371 1866191 1866255 "PSCAT" 1867090 PSCAT (NIL T T T) -9 NIL 1867329 NIL) (-886 1863685 1863967 1864366 "PSCAT-" NIL PSCAT- (NIL T T T T) -7 NIL NIL NIL) (-885 1862082 1862997 1863260 "PRTITION" NIL PRTITION (NIL) -8 NIL NIL NIL) (-884 1861573 1861876 1861967 "PRTDAST" NIL PRTDAST (NIL) -8 NIL NIL NIL) (-883 1852593 1855015 1857203 "PRS" NIL PRS (NIL T T) -7 NIL NIL NIL) (-882 1850363 1851874 1851914 "PRQAGG" 1852097 PRQAGG (NIL T) -9 NIL 1852200 NIL) (-881 1849536 1849982 1850010 "PROPLOG" 1850149 PROPLOG (NIL) -9 NIL 1850263 NIL) (-880 1849211 1849274 1849397 "PROPFUN2" NIL PROPFUN2 (NIL T T) -7 NIL NIL NIL) (-879 1848647 1848786 1848958 "PROPFUN1" NIL PROPFUN1 (NIL T) -7 NIL NIL NIL) (-878 1846895 1847658 1847955 "PROPFRML" NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-877 1846447 1846579 1846707 "PROPERTY" NIL PROPERTY (NIL) -8 NIL NIL NIL) (-876 1840888 1845387 1846207 "PRODUCT" NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-875 1840717 1840755 1840814 "PRINT" NIL PRINT (NIL) -7 NIL NIL NIL) (-874 1840156 1840296 1840447 "PRIMES" NIL PRIMES (NIL T) -7 NIL NIL NIL) (-873 1838624 1839043 1839509 "PRIMELT" NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-872 1838341 1838402 1838430 "PRIMCAT" 1838554 PRIMCAT (NIL) -9 NIL NIL NIL) (-871 1837512 1837708 1837936 "PRIMARR2" NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-870 1833683 1837462 1837507 "PRIMARR" NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-869 1833382 1833444 1833555 "PREASSOC" NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-868 1830518 1833031 1833264 "PR" NIL PR (NIL T T) -8 NIL NIL NIL) (-867 1829969 1830126 1830154 "PPCURVE" 1830359 PPCURVE (NIL) -9 NIL 1830495 NIL) (-866 1829582 1829827 1829910 "PORTNUM" NIL PORTNUM (NIL) -8 NIL NIL NIL) (-865 1827338 1827759 1828351 "POLYROOT" NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-864 1826781 1826845 1827078 "POLYLIFT" NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-863 1823501 1823987 1824598 "POLYCATQ" NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-862 1809092 1815221 1815285 "POLYCAT" 1818770 POLYCAT (NIL T T T) -9 NIL 1820647 NIL) (-861 1804602 1806749 1809087 "POLYCAT-" NIL POLYCAT- (NIL T T T T) -7 NIL NIL NIL) (-860 1804259 1804333 1804452 "POLY2UP" NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-859 1803952 1804015 1804122 "POLY2" NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-858 1797315 1803685 1803844 "POLY" NIL POLY (NIL T) -8 NIL NIL NIL) (-857 1796202 1796465 1796741 "POLUTIL" NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-856 1794806 1795119 1795449 "POLTOPOL" NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-855 1790259 1794756 1794801 "POINT" NIL POINT (NIL T) -8 NIL NIL NIL) (-854 1788747 1789158 1789533 "PNTHEORY" NIL PNTHEORY (NIL) -7 NIL NIL NIL) (-853 1787504 1787813 1788209 "PMTOOLS" NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-852 1787175 1787259 1787376 "PMSYM" NIL PMSYM (NIL T) -7 NIL NIL NIL) (-851 1786754 1786829 1787003 "PMQFCAT" NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-850 1786240 1786336 1786496 "PMPREDFS" NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-849 1785712 1785832 1785986 "PMPRED" NIL PMPRED (NIL T) -7 NIL NIL NIL) (-848 1784607 1784825 1785202 "PMPLCAT" NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-847 1784218 1784303 1784455 "PMLSAGG" NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-846 1783769 1783851 1784032 "PMKERNEL" NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-845 1783461 1783542 1783655 "PMINS" NIL PMINS (NIL T) -7 NIL NIL NIL) (-844 1782974 1783049 1783257 "PMFS" NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-843 1782322 1782450 1782652 "PMDOWN" NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-842 1781684 1781818 1781981 "PMASSFS" NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-841 1780988 1781170 1781351 "PMASS" NIL PMASS (NIL) -7 NIL NIL NIL) (-840 1780711 1780785 1780879 "PLOTTOOL" NIL PLOTTOOL (NIL) -7 NIL NIL NIL) (-839 1777279 1778468 1779384 "PLOT3D" NIL PLOT3D (NIL) -8 NIL NIL NIL) (-838 1776363 1776564 1776799 "PLOT1" NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-837 1771928 1773312 1774454 "PLOT" NIL PLOT (NIL) -8 NIL NIL NIL) (-836 1751849 1756736 1761583 "PLEQN" NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-835 1751589 1751642 1751745 "PINTERPA" NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-834 1751030 1751164 1751344 "PINTERP" NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-833 1749039 1750260 1750288 "PID" 1750485 PID (NIL) -9 NIL 1750612 NIL) (-832 1748827 1748870 1748945 "PICOERCE" NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-831 1748014 1748674 1748761 "PI" NIL PI (NIL) -8 NIL NIL 1748801) (-830 1747466 1747617 1747793 "PGROEB" NIL PGROEB (NIL T) -7 NIL NIL NIL) (-829 1743794 1744752 1745657 "PGE" NIL PGE (NIL) -7 NIL NIL NIL) (-828 1742158 1742447 1742813 "PGCD" NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-827 1741600 1741715 1741876 "PFRPAC" NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-826 1738141 1740469 1740822 "PFR" NIL PFR (NIL T) -8 NIL NIL NIL) (-825 1736747 1737027 1737352 "PFOTOOLS" NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-824 1735512 1735766 1736114 "PFOQ" NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-823 1734222 1734449 1734801 "PFO" NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-822 1731232 1732792 1732820 "PFECAT" 1733413 PFECAT (NIL) -9 NIL 1733790 NIL) (-821 1730855 1731020 1731227 "PFECAT-" NIL PFECAT- (NIL T) -7 NIL NIL NIL) (-820 1729679 1729961 1730262 "PFBRU" NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-819 1727861 1728248 1728678 "PFBR" NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-818 1723831 1727787 1727856 "PF" NIL PF (NIL NIL) -8 NIL NIL NIL) (-817 1719734 1720881 1721748 "PERMGRP" NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-816 1717666 1718755 1718796 "PERMCAT" 1719195 PERMCAT (NIL T) -9 NIL 1719492 NIL) (-815 1717362 1717409 1717532 "PERMAN" NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-814 1713811 1715492 1716137 "PERM" NIL PERM (NIL T) -8 NIL NIL NIL) (-813 1711777 1713566 1713687 "PENDTREE" NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-812 1710646 1710909 1710950 "PDSPC" 1711483 PDSPC (NIL T) -9 NIL 1711728 NIL) (-811 1710013 1710279 1710641 "PDSPC-" NIL PDSPC- (NIL T T) -7 NIL NIL NIL) (-810 1708648 1709641 1709682 "PDRING" 1709687 PDRING (NIL T) -9 NIL 1709714 NIL) (-809 1707358 1708147 1708200 "PDMOD" 1708205 PDMOD (NIL T T) -9 NIL 1708308 NIL) (-808 1706451 1706663 1706912 "PDECOMP" NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-807 1706056 1706123 1706177 "PDDOM" 1706342 PDDOM (NIL T T) -9 NIL 1706422 NIL) (-806 1705908 1705944 1706051 "PDDOM-" NIL PDDOM- (NIL T T T) -7 NIL NIL NIL) (-805 1705694 1705733 1705822 "PCOMP" NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-804 1704011 1704765 1705064 "PBWLB" NIL PBWLB (NIL T) -8 NIL NIL NIL) (-803 1703700 1703763 1703872 "PATTERN2" NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-802 1701838 1702268 1702719 "PATTERN1" NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-801 1695458 1697287 1698579 "PATTERN" NIL PATTERN (NIL T) -8 NIL NIL NIL) (-800 1695089 1695162 1695294 "PATRES2" NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-799 1692791 1693471 1693952 "PATRES" NIL PATRES (NIL T T) -8 NIL NIL NIL) (-798 1690995 1691423 1691826 "PATMATCH" NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-797 1690441 1690689 1690730 "PATMAB" 1690837 PATMAB (NIL T) -9 NIL 1690920 NIL) (-796 1689088 1689492 1689749 "PATLRES" NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-795 1688626 1688757 1688798 "PATAB" 1688803 PATAB (NIL T) -9 NIL 1688975 NIL) (-794 1687169 1687606 1688029 "PARTPERM" NIL PARTPERM (NIL) -7 NIL NIL NIL) (-793 1686847 1686922 1687024 "PARSURF" NIL PARSURF (NIL T) -8 NIL NIL NIL) (-792 1686536 1686599 1686708 "PARSU2" NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-791 1686341 1686387 1686454 "PARSER" NIL PARSER (NIL) -7 NIL NIL NIL) (-790 1686019 1686094 1686196 "PARSCURV" NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-789 1685708 1685771 1685880 "PARSC2" NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-788 1685399 1685469 1685566 "PARPCURV" NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-787 1685088 1685151 1685260 "PARPC2" NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-786 1684249 1684628 1684807 "PARAMAST" NIL PARAMAST (NIL) -8 NIL NIL NIL) (-785 1683856 1683954 1684073 "PAN2EXPR" NIL PAN2EXPR (NIL) -7 NIL NIL NIL) (-784 1682824 1683249 1683468 "PALETTE" NIL PALETTE (NIL) -8 NIL NIL NIL) (-783 1681489 1682143 1682503 "PAIR" NIL PAIR (NIL T T) -8 NIL NIL NIL) (-782 1674579 1680893 1681087 "PADICRC" NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-781 1667000 1674077 1674261 "PADICRAT" NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-780 1663725 1665640 1665680 "PADICCT" 1666261 PADICCT (NIL NIL) -9 NIL 1666543 NIL) (-779 1661715 1663675 1663720 "PADIC" NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-778 1660877 1661087 1661353 "PADEPAC" NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-777 1660219 1660362 1660566 "PADE" NIL PADE (NIL T T T) -7 NIL NIL NIL) (-776 1658600 1659627 1659905 "OWP" NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-775 1658124 1658383 1658480 "OVERSET" NIL OVERSET (NIL) -8 NIL NIL NIL) (-774 1657183 1657861 1658033 "OVAR" NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-773 1647605 1650474 1652673 "OUTFORM" NIL OUTFORM (NIL) -8 NIL NIL NIL) (-772 1646997 1647311 1647437 "OUTBFILE" NIL OUTBFILE (NIL) -8 NIL NIL NIL) (-771 1646274 1646469 1646497 "OUTBCON" 1646815 OUTBCON (NIL) -9 NIL 1646981 NIL) (-770 1645982 1646112 1646269 "OUTBCON-" NIL OUTBCON- (NIL T) -7 NIL NIL NIL) (-769 1645363 1645508 1645669 "OUT" NIL OUT (NIL) -7 NIL NIL NIL) (-768 1644734 1645161 1645250 "OSI" NIL OSI (NIL) -8 NIL NIL NIL) (-767 1644149 1644564 1644592 "OSGROUP" 1644597 OSGROUP (NIL) -9 NIL 1644619 NIL) (-766 1643113 1643374 1643659 "ORTHPOL" NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-765 1640382 1642988 1643108 "OREUP" NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-764 1637523 1640133 1640259 "ORESUP" NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-763 1635541 1636069 1636629 "OREPCTO" NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-762 1628883 1631423 1631463 "OREPCAT" 1633784 OREPCAT (NIL T) -9 NIL 1634886 NIL) (-761 1626909 1627843 1628878 "OREPCAT-" NIL OREPCAT- (NIL T T) -7 NIL NIL NIL) (-760 1626106 1626377 1626405 "ORDTYPE" 1626710 ORDTYPE (NIL) -9 NIL 1626868 NIL) (-759 1625640 1625851 1626101 "ORDTYPE-" NIL ORDTYPE- (NIL T) -7 NIL NIL NIL) (-758 1625102 1625478 1625635 "ORDSTRCT" NIL ORDSTRCT (NIL T NIL) -8 NIL NIL NIL) (-757 1624596 1624959 1624987 "ORDSET" 1624992 ORDSET (NIL) -9 NIL 1625014 NIL) (-756 1623161 1624183 1624211 "ORDRING" 1624216 ORDRING (NIL) -9 NIL 1624244 NIL) (-755 1622409 1622966 1622994 "ORDMON" 1622999 ORDMON (NIL) -9 NIL 1623020 NIL) (-754 1621713 1621875 1622067 "ORDFUNS" NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-753 1620924 1621432 1621460 "ORDFIN" 1621525 ORDFIN (NIL) -9 NIL 1621599 NIL) (-752 1620318 1620457 1620643 "ORDCOMP2" NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-751 1616993 1619286 1619692 "ORDCOMP" NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-750 1616400 1616755 1616860 "OPSIG" NIL OPSIG (NIL) -8 NIL NIL NIL) (-749 1616208 1616253 1616319 "OPQUERY" NIL OPQUERY (NIL) -7 NIL NIL NIL) (-748 1615509 1615785 1615826 "OPERCAT" 1616037 OPERCAT (NIL T) -9 NIL 1616133 NIL) (-747 1615321 1615388 1615504 "OPERCAT-" NIL OPERCAT- (NIL T T) -7 NIL NIL NIL) (-746 1612687 1614123 1614619 "OP" NIL OP (NIL T) -8 NIL NIL NIL) (-745 1612108 1612235 1612409 "ONECOMP2" NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-744 1609009 1611247 1611613 "ONECOMP" NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-743 1605893 1608402 1608442 "OMSAGG" 1608503 OMSAGG (NIL T) -9 NIL 1608567 NIL) (-742 1604305 1605564 1605732 "OMLO" NIL OMLO (NIL T T) -8 NIL NIL NIL) (-741 1602501 1603742 1603770 "OINTDOM" 1603775 OINTDOM (NIL) -9 NIL 1603796 NIL) (-740 1599931 1601503 1601832 "OFMONOID" NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-739 1599185 1599881 1599926 "ODVAR" NIL ODVAR (NIL T) -8 NIL NIL NIL) (-738 1596387 1599026 1599180 "ODR" NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-737 1587924 1596258 1596382 "ODPOL" NIL ODPOL (NIL T) -8 NIL NIL NIL) (-736 1581381 1587815 1587919 "ODP" NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-735 1580353 1580590 1580863 "ODETOOLS" NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-734 1577987 1578657 1579361 "ODESYS" NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-733 1573764 1574724 1575747 "ODERTRIC" NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-732 1573272 1573360 1573554 "ODERED" NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-731 1570721 1571303 1571976 "ODERAT" NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-730 1568116 1568624 1569220 "ODEPRRIC" NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-729 1565113 1565652 1566298 "ODEPRIM" NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-728 1564468 1564576 1564834 "ODEPAL" NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-727 1563626 1563751 1563972 "ODEINT" NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-726 1559910 1560706 1561619 "ODEEF" NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-725 1559350 1559445 1559667 "ODECONST" NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-724 1559031 1559080 1559207 "OCTCT2" NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-723 1555634 1558830 1558949 "OCT" NIL OCT (NIL T) -8 NIL NIL NIL) (-722 1554794 1555416 1555444 "OCAMON" 1555449 OCAMON (NIL) -9 NIL 1555470 NIL) (-721 1549006 1551820 1551860 "OC" 1552955 OC (NIL T) -9 NIL 1553811 NIL) (-720 1547006 1547932 1548912 "OC-" NIL OC- (NIL T T) -7 NIL NIL NIL) (-719 1546422 1546840 1546868 "OASGP" 1546873 OASGP (NIL) -9 NIL 1546893 NIL) (-718 1545485 1546134 1546162 "OAMONS" 1546202 OAMONS (NIL) -9 NIL 1546245 NIL) (-717 1544630 1545211 1545239 "OAMON" 1545296 OAMON (NIL) -9 NIL 1545347 NIL) (-716 1544526 1544558 1544625 "OAMON-" NIL OAMON- (NIL T) -7 NIL NIL NIL) (-715 1543277 1544051 1544079 "OAGROUP" 1544225 OAGROUP (NIL) -9 NIL 1544317 NIL) (-714 1543068 1543155 1543272 "OAGROUP-" NIL OAGROUP- (NIL T) -7 NIL NIL NIL) (-713 1542808 1542864 1542952 "NUMTUBE" NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-712 1537870 1539433 1540960 "NUMQUAD" NIL NUMQUAD (NIL) -7 NIL NIL NIL) (-711 1534565 1535599 1536634 "NUMODE" NIL NUMODE (NIL) -7 NIL NIL NIL) (-710 1533675 1533908 1534126 "NUMFMT" NIL NUMFMT (NIL) -7 NIL NIL NIL) (-709 1522536 1525564 1528012 "NUMERIC" NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-708 1516678 1521940 1522034 "NTSCAT" 1522039 NTSCAT (NIL T T T T) -9 NIL 1522077 NIL) (-707 1516019 1516198 1516391 "NTPOLFN" NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-706 1515712 1515775 1515882 "NSUP2" NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-705 1503379 1513332 1514142 "NSUP" NIL NSUP (NIL T) -8 NIL NIL NIL) (-704 1492388 1503244 1503374 "NSMP" NIL NSMP (NIL T T) -8 NIL NIL NIL) (-703 1491108 1491433 1491790 "NREP" NIL NREP (NIL T) -7 NIL NIL NIL) (-702 1489944 1490208 1490566 "NPCOEF" NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-701 1489111 1489244 1489460 "NORMRETR" NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-700 1487429 1487748 1488154 "NORMPK" NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-699 1487142 1487176 1487300 "NORMMA" NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-698 1486961 1486996 1487065 "NONE1" NIL NONE1 (NIL T) -7 NIL NIL NIL) (-697 1486737 1486927 1486956 "NONE" NIL NONE (NIL) -8 NIL NIL NIL) (-696 1486301 1486368 1486545 "NODE1" NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-695 1484587 1485664 1485919 "NNI" NIL NNI (NIL) -8 NIL NIL 1486266) (-694 1483315 1483652 1484016 "NLINSOL" NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-693 1482292 1482544 1482846 "NFINTBAS" NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-692 1481379 1481944 1481985 "NETCLT" 1482156 NETCLT (NIL T) -9 NIL 1482237 NIL) (-691 1480283 1480550 1480831 "NCODIV" NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-690 1480082 1480125 1480200 "NCNTFRAC" NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-689 1478613 1479001 1479421 "NCEP" NIL NCEP (NIL T) -7 NIL NIL NIL) (-688 1477246 1478212 1478240 "NASRING" 1478350 NASRING (NIL) -9 NIL 1478430 NIL) (-687 1477091 1477147 1477241 "NASRING-" NIL NASRING- (NIL T) -7 NIL NIL NIL) (-686 1476020 1476698 1476726 "NARNG" 1476843 NARNG (NIL) -9 NIL 1476934 NIL) (-685 1475796 1475881 1476015 "NARNG-" NIL NARNG- (NIL T) -7 NIL NIL NIL) (-684 1474562 1475316 1475356 "NAALG" 1475435 NAALG (NIL T) -9 NIL 1475496 NIL) (-683 1474432 1474467 1474557 "NAALG-" NIL NAALG- (NIL T T) -7 NIL NIL NIL) (-682 1469411 1470596 1471782 "MULTSQFR" NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-681 1468806 1468893 1469077 "MULTFACT" NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-680 1460816 1465310 1465362 "MTSCAT" 1466422 MTSCAT (NIL T T) -9 NIL 1466936 NIL) (-679 1460582 1460642 1460734 "MTHING" NIL MTHING (NIL T) -7 NIL NIL NIL) (-678 1460408 1460447 1460507 "MSYSCMD" NIL MSYSCMD (NIL) -7 NIL NIL NIL) (-677 1457997 1459940 1459981 "MSETAGG" 1459986 MSETAGG (NIL T) -9 NIL 1460020 NIL) (-676 1454367 1457040 1457361 "MSET" NIL MSET (NIL T) -8 NIL NIL NIL) (-675 1450641 1452464 1453204 "MRING" NIL MRING (NIL T T) -8 NIL NIL NIL) (-674 1450278 1450351 1450480 "MRF2" NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-673 1449931 1449972 1450116 "MRATFAC" NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-672 1447796 1448133 1448564 "MPRFF" NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-671 1441194 1447695 1447791 "MPOLY" NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-670 1440719 1440760 1440968 "MPCPF" NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-669 1440278 1440327 1440510 "MPC3" NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-668 1439552 1439645 1439864 "MPC2" NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-667 1438169 1438530 1438920 "MONOTOOL" NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-666 1437690 1437757 1437796 "MONOPC" 1437856 MONOPC (NIL T) -9 NIL 1438075 NIL) (-665 1437141 1437477 1437605 "MONOP" NIL MONOP (NIL T) -8 NIL NIL NIL) (-664 1436283 1436662 1436690 "MONOID" 1436908 MONOID (NIL) -9 NIL 1437052 NIL) (-663 1435942 1436092 1436278 "MONOID-" NIL MONOID- (NIL T) -7 NIL NIL NIL) (-662 1424880 1431750 1431809 "MONOGEN" 1432483 MONOGEN (NIL T T) -9 NIL 1432939 NIL) (-661 1422892 1423778 1424761 "MONOGEN-" NIL MONOGEN- (NIL T T T) -7 NIL NIL NIL) (-660 1421606 1422150 1422178 "MONADWU" 1422569 MONADWU (NIL) -9 NIL 1422804 NIL) (-659 1421154 1421354 1421601 "MONADWU-" NIL MONADWU- (NIL T) -7 NIL NIL NIL) (-658 1420431 1420732 1420760 "MONAD" 1420967 MONAD (NIL) -9 NIL 1421079 NIL) (-657 1420198 1420294 1420426 "MONAD-" NIL MONAD- (NIL T) -7 NIL NIL NIL) (-656 1418588 1419358 1419637 "MOEBIUS" NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-655 1417722 1418249 1418289 "MODULE" 1418294 MODULE (NIL T) -9 NIL 1418332 NIL) (-654 1417401 1417527 1417717 "MODULE-" NIL MODULE- (NIL T T) -7 NIL NIL NIL) (-653 1415112 1415998 1416312 "MODRING" NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-652 1412291 1413708 1414221 "MODOP" NIL MODOP (NIL T T) -8 NIL NIL NIL) (-651 1410925 1411499 1411775 "MODMONOM" NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-650 1400144 1409590 1410003 "MODMON" NIL MODMON (NIL T T) -8 NIL NIL NIL) (-649 1397100 1399144 1399413 "MODFIELD" NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-648 1396184 1396551 1396741 "MMLFORM" NIL MMLFORM (NIL) -8 NIL NIL NIL) (-647 1395753 1395802 1395981 "MMAP" NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-646 1393578 1394574 1394614 "MLO" 1395031 MLO (NIL T) -9 NIL 1395271 NIL) (-645 1391459 1391986 1392581 "MLIFT" NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-644 1390927 1391023 1391177 "MKUCFUNC" NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-643 1390597 1390673 1390796 "MKRECORD" NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-642 1389809 1389995 1390223 "MKFUNC" NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-641 1389302 1389418 1389574 "MKFLCFN" NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-640 1388674 1388788 1388973 "MKBCFUNC" NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-639 1387701 1387974 1388251 "MHROWRED" NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-638 1387134 1387222 1387393 "MFINFACT" NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-637 1384292 1385171 1386050 "MESH" NIL MESH (NIL) -7 NIL NIL NIL) (-636 1382959 1383307 1383660 "MDDFACT" NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-635 1380343 1382064 1382105 "MDAGG" 1382362 MDAGG (NIL T) -9 NIL 1382507 NIL) (-634 1379617 1379781 1379981 "MCDEN" NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-633 1378695 1378981 1379211 "MAYBE" NIL MAYBE (NIL T) -8 NIL NIL NIL) (-632 1376792 1377369 1377930 "MATSTOR" NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-631 1372590 1376382 1376629 "MATRIX" NIL MATRIX (NIL T) -8 NIL NIL NIL) (-630 1368939 1369708 1370442 "MATLIN" NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-629 1367692 1367861 1368190 "MATCAT2" NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-628 1357215 1360779 1360855 "MATCAT" 1365843 MATCAT (NIL T T T) -9 NIL 1367289 NIL) (-627 1354496 1355802 1357210 "MATCAT-" NIL MATCAT- (NIL T T T T) -7 NIL NIL NIL) (-626 1352897 1353257 1353641 "MAPPKG3" NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-625 1352030 1352227 1352449 "MAPPKG2" NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-624 1350781 1351107 1351434 "MAPPKG1" NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-623 1349943 1350345 1350521 "MAPPAST" NIL MAPPAST (NIL) -8 NIL NIL NIL) (-622 1349612 1349676 1349799 "MAPHACK3" NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-621 1349260 1349333 1349447 "MAPHACK2" NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-620 1348795 1348910 1349052 "MAPHACK1" NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-619 1347004 1347772 1348073 "MAGMA" NIL MAGMA (NIL T) -8 NIL NIL NIL) (-618 1346498 1346800 1346890 "MACROAST" NIL MACROAST (NIL) -8 NIL NIL NIL) (-617 1340729 1344813 1344854 "LZSTAGG" 1345631 LZSTAGG (NIL T) -9 NIL 1345921 NIL) (-616 1338078 1339390 1340724 "LZSTAGG-" NIL LZSTAGG- (NIL T T) -7 NIL NIL NIL) (-615 1335465 1336431 1336914 "LWORD" NIL LWORD (NIL T) -8 NIL NIL NIL) (-614 1335046 1335325 1335399 "LSTAST" NIL LSTAST (NIL) -8 NIL NIL NIL) (-613 1327255 1334907 1335041 "LSQM" NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-612 1326618 1326763 1326991 "LSPP" NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-611 1324102 1324800 1325512 "LSMP1" NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-610 1322214 1322537 1322985 "LSMP" NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-609 1315623 1321264 1321305 "LSAGG" 1321367 LSAGG (NIL T) -9 NIL 1321445 NIL) (-608 1313317 1314416 1315618 "LSAGG-" NIL LSAGG- (NIL T T) -7 NIL NIL NIL) (-607 1310797 1312666 1312915 "LPOLY" NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-606 1310464 1310555 1310678 "LPEFRAC" NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-605 1310135 1310214 1310242 "LOGIC" 1310353 LOGIC (NIL) -9 NIL 1310435 NIL) (-604 1310030 1310059 1310130 "LOGIC-" NIL LOGIC- (NIL T) -7 NIL NIL NIL) (-603 1309349 1309507 1309700 "LODOOPS" NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-602 1308134 1308383 1308734 "LODOF" NIL LODOF (NIL T T) -7 NIL NIL NIL) (-601 1303956 1306755 1306795 "LODOCAT" 1307227 LODOCAT (NIL T) -9 NIL 1307438 NIL) (-600 1303749 1303825 1303951 "LODOCAT-" NIL LODOCAT- (NIL T T) -7 NIL NIL NIL) (-599 1300749 1303626 1303744 "LODO2" NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-598 1297847 1300699 1300744 "LODO1" NIL LODO1 (NIL T) -8 NIL NIL NIL) (-597 1294934 1297777 1297842 "LODO" NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-596 1293987 1294162 1294464 "LODEEF" NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-595 1292119 1293249 1293502 "LO" NIL LO (NIL T T T) -8 NIL NIL NIL) (-594 1287945 1290278 1290319 "LNAGG" 1291181 LNAGG (NIL T) -9 NIL 1291616 NIL) (-593 1287332 1287599 1287940 "LNAGG-" NIL LNAGG- (NIL T T) -7 NIL NIL NIL) (-592 1283904 1284845 1285482 "LMOPS" NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-591 1283166 1283671 1283711 "LMODULE" 1283716 LMODULE (NIL T) -9 NIL 1283742 NIL) (-590 1280635 1282902 1283025 "LMDICT" NIL LMDICT (NIL T) -8 NIL NIL NIL) (-589 1280203 1280414 1280455 "LLINSET" 1280516 LLINSET (NIL T) -9 NIL 1280560 NIL) (-588 1279879 1280139 1280198 "LITERAL" NIL LITERAL (NIL T) -8 NIL NIL NIL) (-587 1279478 1279558 1279697 "LIST3" NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-586 1277929 1278277 1278676 "LIST2MAP" NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-585 1277100 1277296 1277524 "LIST2" NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-584 1270423 1276356 1276610 "LIST" NIL LIST (NIL T) -8 NIL NIL NIL) (-583 1270000 1270233 1270274 "LINSET" 1270279 LINSET (NIL T) -9 NIL 1270312 NIL) (-582 1268901 1269623 1269790 "LINFORM" NIL LINFORM (NIL T NIL) -8 NIL NIL NIL) (-581 1267167 1267922 1267962 "LINEXP" 1268448 LINEXP (NIL T) -9 NIL 1268721 NIL) (-580 1265789 1266776 1266957 "LINELT" NIL LINELT (NIL T NIL) -8 NIL NIL NIL) (-579 1264616 1264888 1265190 "LINDEP" NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-578 1263829 1264418 1264528 "LINBASIS" NIL LINBASIS (NIL NIL) -8 NIL NIL NIL) (-577 1261379 1262101 1262851 "LIMITRF" NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-576 1260009 1260306 1260697 "LIMITPS" NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-575 1258802 1259404 1259444 "LIECAT" 1259584 LIECAT (NIL T) -9 NIL 1259735 NIL) (-574 1258676 1258709 1258797 "LIECAT-" NIL LIECAT- (NIL T T) -7 NIL NIL NIL) (-573 1252932 1258366 1258594 "LIE" NIL LIE (NIL T T) -8 NIL NIL NIL) (-572 1244433 1252608 1252764 "LIB" NIL LIB (NIL) -8 NIL NIL NIL) (-571 1240885 1241834 1242769 "LGROBP" NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-570 1239509 1240417 1240445 "LFCAT" 1240652 LFCAT (NIL) -9 NIL 1240791 NIL) (-569 1237748 1238078 1238423 "LF" NIL LF (NIL T T) -7 NIL NIL NIL) (-568 1235265 1235930 1236611 "LEXTRIPK" NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-567 1232277 1233255 1233758 "LEXP" NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-566 1231768 1232071 1232162 "LETAST" NIL LETAST (NIL) -8 NIL NIL NIL) (-565 1230475 1230799 1231199 "LEADCDET" NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-564 1229741 1229826 1230052 "LAZM3PK" NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-563 1224744 1228309 1228845 "LAUPOL" NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-562 1224369 1224419 1224579 "LAPLACE" NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-561 1223140 1223913 1223953 "LALG" 1224014 LALG (NIL T) -9 NIL 1224072 NIL) (-560 1222923 1223000 1223135 "LALG-" NIL LALG- (NIL T T) -7 NIL NIL NIL) (-559 1220776 1222191 1222442 "LA" NIL LA (NIL T T T) -8 NIL NIL NIL) (-558 1220605 1220635 1220676 "KVTFROM" 1220738 KVTFROM (NIL T) -9 NIL NIL NIL) (-557 1219421 1220136 1220325 "KTVLOGIC" NIL KTVLOGIC (NIL) -8 NIL NIL NIL) (-556 1219250 1219280 1219321 "KRCFROM" 1219383 KRCFROM (NIL T) -9 NIL NIL NIL) (-555 1218352 1218549 1218844 "KOVACIC" NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-554 1218181 1218211 1218252 "KONVERT" 1218314 KONVERT (NIL T) -9 NIL NIL NIL) (-553 1218010 1218040 1218081 "KOERCE" 1218143 KOERCE (NIL T) -9 NIL NIL NIL) (-552 1217580 1217673 1217805 "KERNEL2" NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-551 1215633 1216527 1216899 "KERNEL" NIL KERNEL (NIL T) -8 NIL NIL NIL) (-550 1208584 1213417 1213471 "KDAGG" 1213847 KDAGG (NIL T T) -9 NIL 1214073 NIL) (-549 1208242 1208377 1208579 "KDAGG-" NIL KDAGG- (NIL T T T) -7 NIL NIL NIL) (-548 1201535 1208034 1208180 "KAFILE" NIL KAFILE (NIL T) -8 NIL NIL NIL) (-547 1201185 1201467 1201530 "JVMOP" NIL JVMOP (NIL) -8 NIL NIL NIL) (-546 1200155 1200654 1200903 "JVMMDACC" NIL JVMMDACC (NIL) -8 NIL NIL NIL) (-545 1199281 1199730 1199935 "JVMFDACC" NIL JVMFDACC (NIL) -8 NIL NIL NIL) (-544 1198145 1198637 1198937 "JVMCSTTG" NIL JVMCSTTG (NIL) -8 NIL NIL NIL) (-543 1197427 1197826 1197987 "JVMCFACC" NIL JVMCFACC (NIL) -8 NIL NIL NIL) (-542 1197137 1197373 1197422 "JVMBCODE" NIL JVMBCODE (NIL) -8 NIL NIL NIL) (-541 1191392 1196827 1197055 "JORDAN" NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-540 1190810 1191143 1191263 "JOINAST" NIL JOINAST (NIL) -8 NIL NIL NIL) (-539 1187482 1188993 1189047 "IXAGG" 1189968 IXAGG (NIL T T) -9 NIL 1190425 NIL) (-538 1186688 1187059 1187477 "IXAGG-" NIL IXAGG- (NIL T T T) -7 NIL NIL NIL) (-537 1185655 1185930 1186193 "ITUPLE" NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-536 1184317 1184524 1184817 "ITRIGMNP" NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-535 1183268 1183490 1183773 "ITFUN3" NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-534 1182943 1183006 1183129 "ITFUN2" NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-533 1182205 1182577 1182751 "ITFORM" NIL ITFORM (NIL) -8 NIL NIL NIL) (-532 1180181 1181481 1181755 "ITAYLOR" NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-531 1169729 1175498 1176655 "ISUPS" NIL ISUPS (NIL T) -8 NIL NIL NIL) (-530 1168974 1169126 1169362 "ISUMP" NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-529 1168465 1168768 1168859 "ISAST" NIL ISAST (NIL) -8 NIL NIL NIL) (-528 1167758 1167849 1168062 "IRURPK" NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-527 1166890 1167115 1167355 "IRSN" NIL IRSN (NIL) -7 NIL NIL NIL) (-526 1165303 1165684 1166112 "IRRF2F" NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-525 1165088 1165132 1165208 "IRREDFFX" NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-524 1163938 1164235 1164530 "IROOT" NIL IROOT (NIL T) -7 NIL NIL NIL) (-523 1163211 1163562 1163713 "IRFORM" NIL IRFORM (NIL) -8 NIL NIL NIL) (-522 1162414 1162545 1162758 "IR2F" NIL IR2F (NIL T T) -7 NIL NIL NIL) (-521 1160569 1161066 1161610 "IR2" NIL IR2 (NIL T T) -7 NIL NIL NIL) (-520 1157650 1158918 1159607 "IR" NIL IR (NIL T) -8 NIL NIL NIL) (-519 1157475 1157515 1157575 "IPRNTPK" NIL IPRNTPK (NIL) -7 NIL NIL NIL) (-518 1153473 1157401 1157470 "IPF" NIL IPF (NIL NIL) -8 NIL NIL NIL) (-517 1151476 1153412 1153468 "IPADIC" NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-516 1150847 1151146 1151276 "IP4ADDR" NIL IP4ADDR (NIL) -8 NIL NIL NIL) (-515 1150300 1150588 1150720 "IOMODE" NIL IOMODE (NIL) -8 NIL NIL NIL) (-514 1149381 1150006 1150132 "IOBFILE" NIL IOBFILE (NIL) -8 NIL NIL NIL) (-513 1148791 1149285 1149313 "IOBCON" 1149318 IOBCON (NIL) -9 NIL 1149339 NIL) (-512 1148362 1148426 1148608 "INVLAPLA" NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-511 1140406 1142777 1145102 "INTTR" NIL INTTR (NIL T T) -7 NIL NIL NIL) (-510 1137517 1138300 1139164 "INTTOOLS" NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-509 1137194 1137291 1137408 "INTSLPE" NIL INTSLPE (NIL) -7 NIL NIL NIL) (-508 1134636 1137130 1137189 "INTRVL" NIL INTRVL (NIL T) -8 NIL NIL NIL) (-507 1132748 1133277 1133844 "INTRF" NIL INTRF (NIL T) -7 NIL NIL NIL) (-506 1132250 1132364 1132504 "INTRET" NIL INTRET (NIL T) -7 NIL NIL NIL) (-505 1130634 1131040 1131502 "INTRAT" NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-504 1128413 1129007 1129618 "INTPM" NIL INTPM (NIL T T) -7 NIL NIL NIL) (-503 1125786 1126396 1127116 "INTPAF" NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-502 1125190 1125348 1125556 "INTHERTR" NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-501 1124709 1124795 1124983 "INTHERAL" NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-500 1122914 1123435 1123892 "INTHEORY" NIL INTHEORY (NIL) -7 NIL NIL NIL) (-499 1115996 1117649 1119378 "INTG0" NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-498 1115362 1115524 1115697 "INTFACT" NIL INTFACT (NIL T) -7 NIL NIL NIL) (-497 1113235 1113699 1114243 "INTEF" NIL INTEF (NIL T T) -7 NIL NIL NIL) (-496 1111361 1112311 1112339 "INTDOM" 1112638 INTDOM (NIL) -9 NIL 1112843 NIL) (-495 1110914 1111116 1111356 "INTDOM-" NIL INTDOM- (NIL T) -7 NIL NIL NIL) (-494 1106721 1109193 1109247 "INTCAT" 1110043 INTCAT (NIL T) -9 NIL 1110359 NIL) (-493 1106286 1106406 1106533 "INTBIT" NIL INTBIT (NIL) -7 NIL NIL NIL) (-492 1105126 1105298 1105604 "INTALG" NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-491 1104699 1104795 1104952 "INTAF" NIL INTAF (NIL T T) -7 NIL NIL NIL) (-490 1097047 1104606 1104694 "INTABL" NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-489 1096345 1096900 1096965 "INT8" NIL INT8 (NIL) -8 NIL NIL 1096999) (-488 1095642 1096197 1096262 "INT64" NIL INT64 (NIL) -8 NIL NIL 1096296) (-487 1094939 1095494 1095559 "INT32" NIL INT32 (NIL) -8 NIL NIL 1095593) (-486 1094236 1094791 1094856 "INT16" NIL INT16 (NIL) -8 NIL NIL 1094890) (-485 1090699 1094155 1094231 "INT" NIL INT (NIL) -8 NIL NIL NIL) (-484 1084756 1088239 1088267 "INS" 1089197 INS (NIL) -9 NIL 1089856 NIL) (-483 1082818 1083736 1084683 "INS-" NIL INS- (NIL T) -7 NIL NIL NIL) (-482 1081877 1082100 1082375 "INPSIGN" NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-481 1081091 1081232 1081429 "INPRODPF" NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-480 1080081 1080222 1080459 "INPRODFF" NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-479 1079233 1079397 1079657 "INNMFACT" NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-478 1078513 1078628 1078816 "INMODGCD" NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-477 1077252 1077521 1077845 "INFSP" NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-476 1076532 1076673 1076856 "INFPROD0" NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-475 1076195 1076267 1076365 "INFORM1" NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-474 1073273 1074759 1075282 "INFORM" NIL INFORM (NIL) -8 NIL NIL NIL) (-473 1072872 1072979 1073093 "INFINITY" NIL INFINITY (NIL) -7 NIL NIL NIL) (-472 1072028 1072673 1072774 "INETCLTS" NIL INETCLTS (NIL) -8 NIL NIL NIL) (-471 1070878 1071146 1071467 "INEP" NIL INEP (NIL T T T) -7 NIL NIL NIL) (-470 1069868 1070808 1070873 "INDE" NIL INDE (NIL T) -8 NIL NIL NIL) (-469 1069493 1069573 1069690 "INCRMAPS" NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-468 1068407 1068952 1069156 "INBFILE" NIL INBFILE (NIL) -8 NIL NIL NIL) (-467 1064502 1065557 1066500 "INBFF" NIL INBFF (NIL T) -7 NIL NIL NIL) (-466 1063356 1063679 1063707 "INBCON" 1064220 INBCON (NIL) -9 NIL 1064486 NIL) (-465 1062810 1063075 1063351 "INBCON-" NIL INBCON- (NIL T) -7 NIL NIL NIL) (-464 1062304 1062606 1062696 "INAST" NIL INAST (NIL) -8 NIL NIL NIL) (-463 1061761 1062070 1062175 "IMPTAST" NIL IMPTAST (NIL) -8 NIL NIL NIL) (-462 1060600 1060741 1061058 "IMATQF" NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-461 1059023 1059292 1059631 "IMATLIN" NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-460 1053866 1058954 1059018 "IFF" NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-459 1053246 1053580 1053695 "IFAST" NIL IFAST (NIL) -8 NIL NIL NIL) (-458 1048348 1052684 1052870 "IFARRAY" NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-457 1047378 1048270 1048343 "IFAMON" NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-456 1046950 1047027 1047081 "IEVALAB" 1047288 IEVALAB (NIL T T) -9 NIL NIL NIL) (-455 1046705 1046785 1046945 "IEVALAB-" NIL IEVALAB- (NIL T T T) -7 NIL NIL NIL) (-454 1046090 1046317 1046474 "IDPT" NIL IDPT (NIL T T) -8 NIL NIL NIL) (-453 1045083 1046010 1046085 "IDPOAMS" NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-452 1044146 1045003 1045078 "IDPOAM" NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-451 1043228 1043875 1044012 "IDPO" NIL IDPO (NIL T T) -8 NIL NIL NIL) (-450 1041591 1042162 1042213 "IDPC" 1042719 IDPC (NIL T T) -9 NIL 1043032 NIL) (-449 1040879 1041513 1041586 "IDPAM" NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-448 1040049 1040801 1040874 "IDPAG" NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-447 1039742 1039955 1040015 "IDENT" NIL IDENT (NIL) -8 NIL NIL NIL) (-446 1039446 1039486 1039525 "IDEMOPC" 1039530 IDEMOPC (NIL T) -9 NIL 1039667 NIL) (-445 1036517 1037398 1038290 "IDECOMP" NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-444 1030143 1031420 1032459 "IDEAL" NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-443 1029405 1029535 1029734 "ICDEN" NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-442 1028578 1029077 1029215 "ICARD" NIL ICARD (NIL) -8 NIL NIL NIL) (-441 1026967 1027298 1027689 "IBPTOOLS" NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-440 1023019 1026923 1026962 "IBITS" NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-439 1020277 1020901 1021596 "IBATOOL" NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-438 1018503 1018983 1019516 "IBACHIN" NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-437 1016377 1018409 1018498 "IARRAY2" NIL IARRAY2 (NIL T T T) -8 NIL NIL NIL) (-436 1012529 1016315 1016372 "IARRAY1" NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-435 1006108 1011493 1011961 "IAN" NIL IAN (NIL) -8 NIL NIL NIL) (-434 1005676 1005739 1005912 "IALGFACT" NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-433 1005168 1005317 1005345 "HYPCAT" 1005552 HYPCAT (NIL) -9 NIL NIL NIL) (-432 1004824 1004977 1005163 "HYPCAT-" NIL HYPCAT- (NIL T) -7 NIL NIL NIL) (-431 1004437 1004682 1004765 "HOSTNAME" NIL HOSTNAME (NIL) -8 NIL NIL NIL) (-430 1004270 1004319 1004360 "HOMOTOP" 1004365 HOMOTOP (NIL T) -9 NIL 1004398 NIL) (-429 1002455 1003326 1003367 "HOAGG" 1003554 HOAGG (NIL T) -9 NIL 1003949 NIL) (-428 1002082 1002229 1002450 "HOAGG-" NIL HOAGG- (NIL T T) -7 NIL NIL NIL) (-427 995282 1001807 1001955 "HEXADEC" NIL HEXADEC (NIL) -8 NIL NIL NIL) (-426 994217 994475 994738 "HEUGCD" NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-425 993152 994082 994212 "HELLFDIV" NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-424 991410 992985 993073 "HEAP" NIL HEAP (NIL T) -8 NIL NIL NIL) (-423 990725 991077 991210 "HEADAST" NIL HEADAST (NIL) -8 NIL NIL NIL) (-422 984225 990658 990720 "HDP" NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-421 977364 983961 984112 "HDMP" NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-420 976817 976974 977137 "HB" NIL HB (NIL) -7 NIL NIL NIL) (-419 969182 976734 976812 "HASHTBL" NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-418 968673 968976 969067 "HASAST" NIL HASAST (NIL) -8 NIL NIL NIL) (-417 966223 968460 968639 "HACKPI" NIL HACKPI (NIL) -8 NIL NIL NIL) (-416 961909 966106 966218 "GTSET" NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-415 954251 961806 961904 "GSTBL" NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-414 946188 953620 953875 "GSERIES" NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-413 945212 945721 945749 "GROUP" 945952 GROUP (NIL) -9 NIL 946086 NIL) (-412 944755 944956 945207 "GROUP-" NIL GROUP- (NIL T) -7 NIL NIL NIL) (-411 943427 943766 944153 "GROEBSOL" NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-410 942249 942606 942657 "GRMOD" 943186 GRMOD (NIL T T) -9 NIL 943352 NIL) (-409 942068 942116 942244 "GRMOD-" NIL GRMOD- (NIL T T T) -7 NIL NIL NIL) (-408 938191 939402 940402 "GRIMAGE" NIL GRIMAGE (NIL) -8 NIL NIL NIL) (-407 936913 937237 937552 "GRDEF" NIL GRDEF (NIL) -7 NIL NIL NIL) (-406 936466 936594 936735 "GRAY" NIL GRAY (NIL) -7 NIL NIL NIL) (-405 935539 936038 936089 "GRALG" 936242 GRALG (NIL T T) -9 NIL 936332 NIL) (-404 935258 935359 935534 "GRALG-" NIL GRALG- (NIL T T T) -7 NIL NIL NIL) (-403 932277 934949 935116 "GPOLSET" NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-402 931690 931753 932010 "GOSPER" NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-401 927544 928440 928965 "GMODPOL" NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-400 926719 926921 927159 "GHENSEL" NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-399 921722 922649 923668 "GENUPS" NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-398 921470 921527 921616 "GENUFACT" NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-397 920952 921041 921206 "GENPGCD" NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-396 920461 920502 920715 "GENMFACT" NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-395 919262 919545 919849 "GENEEZ" NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-394 912537 918952 919113 "GDMP" NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-393 902320 907327 908431 "GCNAALG" NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-392 900372 901475 901503 "GCDDOM" 901758 GCDDOM (NIL) -9 NIL 901915 NIL) (-391 899995 900152 900367 "GCDDOM-" NIL GCDDOM- (NIL T) -7 NIL NIL NIL) (-390 890788 893258 895646 "GBINTERN" NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-389 888923 889248 889666 "GBF" NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-388 887864 888053 888320 "GBEUCLID" NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-387 886735 886942 887246 "GB" NIL GB (NIL T T T T) -7 NIL NIL NIL) (-386 886198 886340 886488 "GAUSSFAC" NIL GAUSSFAC (NIL) -7 NIL NIL NIL) (-385 884810 885158 885471 "GALUTIL" NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-384 883355 883676 883998 "GALPOLYU" NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-383 880981 881337 881742 "GALFACTU" NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-382 874233 875894 877472 "GALFACT" NIL GALFACT (NIL T) -7 NIL NIL NIL) (-381 873885 874106 874174 "FUNDESC" NIL FUNDESC (NIL) -8 NIL NIL NIL) (-380 873509 873730 873811 "FUNCTION" NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-379 871606 872289 872749 "FT" NIL FT (NIL) -8 NIL NIL NIL) (-378 870199 870506 870898 "FSUPFACT" NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-377 868854 869213 869537 "FST" NIL FST (NIL) -8 NIL NIL NIL) (-376 868157 868281 868468 "FSRED" NIL FSRED (NIL T T) -7 NIL NIL NIL) (-375 867131 867397 867744 "FSPRMELT" NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-374 864789 865319 865801 "FSPECF" NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-373 864372 864432 864601 "FSINT" NIL FSINT (NIL T T) -7 NIL NIL NIL) (-372 862672 863586 863889 "FSERIES" NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-371 861820 861954 862177 "FSCINT" NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-370 860991 861152 861379 "FSAGG2" NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-369 857225 859886 859927 "FSAGG" 860297 FSAGG (NIL T) -9 NIL 860558 NIL) (-368 855579 856338 857130 "FSAGG-" NIL FSAGG- (NIL T T) -7 NIL NIL NIL) (-367 853535 853831 854375 "FS2UPS" NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-366 852582 852764 853064 "FS2EXPXP" NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-365 852263 852312 852439 "FS2" NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-364 832419 841920 841961 "FS" 845831 FS (NIL T) -9 NIL 848109 NIL) (-363 824650 828143 832122 "FS-" NIL FS- (NIL T T) -7 NIL NIL NIL) (-362 824184 824311 824463 "FRUTIL" NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-361 818707 821865 821905 "FRNAALG" 823225 FRNAALG (NIL T) -9 NIL 823823 NIL) (-360 815448 816699 817957 "FRNAALG-" NIL FRNAALG- (NIL T T) -7 NIL NIL NIL) (-359 815129 815178 815305 "FRNAAF2" NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-358 813616 814173 814467 "FRMOD" NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-357 812902 812995 813282 "FRIDEAL2" NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-356 810736 811502 811818 "FRIDEAL" NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-355 809845 810288 810329 "FRETRCT" 810334 FRETRCT (NIL T) -9 NIL 810505 NIL) (-354 809218 809496 809840 "FRETRCT-" NIL FRETRCT- (NIL T T) -7 NIL NIL NIL) (-353 805962 807482 807541 "FRAMALG" 808423 FRAMALG (NIL T T) -9 NIL 808715 NIL) (-352 804558 805109 805739 "FRAMALG-" NIL FRAMALG- (NIL T T T) -7 NIL NIL NIL) (-351 804251 804314 804421 "FRAC2" NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-350 797892 804056 804246 "FRAC" NIL FRAC (NIL T) -8 NIL NIL NIL) (-349 797585 797648 797755 "FR2" NIL FR2 (NIL T T) -7 NIL NIL NIL) (-348 789893 794464 795792 "FR" NIL FR (NIL T) -8 NIL NIL NIL) (-347 783671 787174 787202 "FPS" 788321 FPS (NIL) -9 NIL 788877 NIL) (-346 783228 783361 783525 "FPS-" NIL FPS- (NIL T) -7 NIL NIL NIL) (-345 780038 782081 782109 "FPC" 782334 FPC (NIL) -9 NIL 782476 NIL) (-344 779884 779936 780033 "FPC-" NIL FPC- (NIL T) -7 NIL NIL NIL) (-343 778661 779370 779411 "FPATMAB" 779416 FPATMAB (NIL T) -9 NIL 779568 NIL) (-342 777091 777687 778034 "FPARFRAC" NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-341 776666 776724 776897 "FORDER" NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-340 775169 776064 776238 "FNLA" NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-339 773784 774289 774317 "FNCAT" 774774 FNCAT (NIL) -9 NIL 775031 NIL) (-338 773241 773751 773779 "FNAME" NIL FNAME (NIL) -8 NIL NIL NIL) (-337 771828 773190 773236 "FMONOID" NIL FMONOID (NIL T) -8 NIL NIL NIL) (-336 768416 769774 769815 "FMONCAT" 771032 FMONCAT (NIL T) -9 NIL 771636 NIL) (-335 765274 766352 766405 "FMCAT" 767586 FMCAT (NIL T T) -9 NIL 768078 NIL) (-334 763974 765097 765196 "FM1" NIL FM1 (NIL T T) -8 NIL NIL NIL) (-333 763022 763822 763969 "FM" NIL FM (NIL T T) -8 NIL NIL NIL) (-332 761209 761661 762155 "FLOATRP" NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-331 759144 759680 760258 "FLOATCP" NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-330 752530 757481 758095 "FLOAT" NIL FLOAT (NIL) -8 NIL NIL NIL) (-329 751011 752112 752152 "FLINEXP" 752157 FLINEXP (NIL T) -9 NIL 752250 NIL) (-328 750420 750679 751006 "FLINEXP-" NIL FLINEXP- (NIL T T) -7 NIL NIL NIL) (-327 749635 749794 750015 "FLASORT" NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-326 746518 747597 747649 "FLALG" 748876 FLALG (NIL T T) -9 NIL 749343 NIL) (-325 745689 745850 746077 "FLAGG2" NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-324 739364 743103 743144 "FLAGG" 744383 FLAGG (NIL T) -9 NIL 745031 NIL) (-323 738472 738876 739359 "FLAGG-" NIL FLAGG- (NIL T T) -7 NIL NIL NIL) (-322 735033 736297 736356 "FINRALG" 737484 FINRALG (NIL T T) -9 NIL 737992 NIL) (-321 734424 734689 735028 "FINRALG-" NIL FINRALG- (NIL T T T) -7 NIL NIL NIL) (-320 733722 734018 734046 "FINITE" 734242 FINITE (NIL) -9 NIL 734349 NIL) (-319 733630 733656 733717 "FINITE-" NIL FINITE- (NIL T) -7 NIL NIL NIL) (-318 730564 731891 731932 "FINAGG" 732837 FINAGG (NIL T) -9 NIL 733291 NIL) (-317 729595 730060 730559 "FINAGG-" NIL FINAGG- (NIL T T) -7 NIL NIL NIL) (-316 721556 724147 724187 "FINAALG" 727839 FINAALG (NIL T) -9 NIL 729277 NIL) (-315 717823 719068 720191 "FINAALG-" NIL FINAALG- (NIL T T) -7 NIL NIL NIL) (-314 716375 716794 716848 "FILECAT" 717532 FILECAT (NIL T T) -9 NIL 717748 NIL) (-313 715726 716200 716303 "FILE" NIL FILE (NIL T) -8 NIL NIL NIL) (-312 712974 714852 714880 "FIELD" 714920 FIELD (NIL) -9 NIL 715000 NIL) (-311 711999 712460 712969 "FIELD-" NIL FIELD- (NIL T) -7 NIL NIL NIL) (-310 710003 710949 711295 "FGROUP" NIL FGROUP (NIL T) -8 NIL NIL NIL) (-309 709246 709427 709646 "FGLMICPK" NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-308 704516 709184 709241 "FFX" NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-307 704178 704245 704380 "FFSLPE" NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-306 703718 703760 703969 "FFPOLY2" NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-305 700398 701275 702052 "FFPOLY" NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-304 695682 700330 700393 "FFP" NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-303 690361 695171 695361 "FFNBX" NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-302 684842 689642 689900 "FFNBP" NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-301 679049 684293 684504 "FFNB" NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-300 678072 678282 678597 "FFINTBAS" NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-299 673512 676217 676245 "FFIELDC" 676864 FFIELDC (NIL) -9 NIL 677239 NIL) (-298 672581 673021 673507 "FFIELDC-" NIL FFIELDC- (NIL T) -7 NIL NIL NIL) (-297 672196 672254 672378 "FFHOM" NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-296 670340 670863 671380 "FFF" NIL FFF (NIL T) -7 NIL NIL NIL) (-295 665434 670139 670240 "FFCGX" NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-294 660534 665223 665330 "FFCGP" NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-293 655200 660325 660433 "FFCG" NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-292 654654 654703 654938 "FFCAT2" NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-291 633229 644263 644349 "FFCAT" 649499 FFCAT (NIL T T T) -9 NIL 650935 NIL) (-290 629469 630695 632001 "FFCAT-" NIL FFCAT- (NIL T T T T) -7 NIL NIL NIL) (-289 624312 629400 629464 "FF" NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-288 623204 623673 623714 "FEVALAB" 623798 FEVALAB (NIL T) -9 NIL 624059 NIL) (-287 622609 622861 623199 "FEVALAB-" NIL FEVALAB- (NIL T T) -7 NIL NIL NIL) (-286 619436 620347 620462 "FDIVCAT" 622029 FDIVCAT (NIL T T T T) -9 NIL 622465 NIL) (-285 619230 619262 619431 "FDIVCAT-" NIL FDIVCAT- (NIL T T T T T) -7 NIL NIL NIL) (-284 618537 618630 618907 "FDIV2" NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-283 617023 618021 618224 "FDIV" NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-282 616116 616500 616702 "FCTRDATA" NIL FCTRDATA (NIL) -8 NIL NIL NIL) (-281 615238 615727 615867 "FCOMP" NIL FCOMP (NIL T) -8 NIL NIL NIL) (-280 606825 611468 611508 "FAXF" 613309 FAXF (NIL T) -9 NIL 613999 NIL) (-279 604741 605545 606360 "FAXF-" NIL FAXF- (NIL T T) -7 NIL NIL NIL) (-278 599900 604263 604437 "FARRAY" NIL FARRAY (NIL T) -8 NIL NIL NIL) (-277 594358 596781 596833 "FAMR" 597844 FAMR (NIL T T) -9 NIL 598303 NIL) (-276 593557 593922 594353 "FAMR-" NIL FAMR- (NIL T T T) -7 NIL NIL NIL) (-275 592578 593499 593552 "FAMONOID" NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-274 590172 591051 591104 "FAMONC" 592045 FAMONC (NIL T T) -9 NIL 592430 NIL) (-273 588728 590030 590167 "FAGROUP" NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-272 586808 587169 587571 "FACUTIL" NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-271 586085 586282 586504 "FACTFUNC" NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-270 577945 585532 585731 "EXPUPXS" NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-269 575964 576534 577120 "EXPRTUBE" NIL EXPRTUBE (NIL) -7 NIL NIL NIL) (-268 572866 573508 574228 "EXPRODE" NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-267 568023 568730 569535 "EXPR2UPS" NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-266 567712 567775 567884 "EXPR2" NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-265 552505 566761 567187 "EXPR" NIL EXPR (NIL T) -8 NIL NIL NIL) (-264 543032 551825 552113 "EXPEXPAN" NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-263 542526 542828 542918 "EXITAST" NIL EXITAST (NIL) -8 NIL NIL NIL) (-262 542302 542492 542521 "EXIT" NIL EXIT (NIL) -8 NIL NIL NIL) (-261 541991 542059 542172 "EVALCYC" NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-260 541508 541650 541691 "EVALAB" 541861 EVALAB (NIL T) -9 NIL 541965 NIL) (-259 541136 541282 541503 "EVALAB-" NIL EVALAB- (NIL T T) -7 NIL NIL NIL) (-258 538179 539774 539802 "EUCDOM" 540356 EUCDOM (NIL) -9 NIL 540705 NIL) (-257 537106 537599 538174 "EUCDOM-" NIL EUCDOM- (NIL T) -7 NIL NIL NIL) (-256 536831 536887 536987 "ES2" NIL ES2 (NIL T T) -7 NIL NIL NIL) (-255 536519 536583 536692 "ES1" NIL ES1 (NIL T T) -7 NIL NIL NIL) (-254 530290 532190 532218 "ES" 534960 ES (NIL) -9 NIL 536344 NIL) (-253 526805 528337 530129 "ES-" NIL ES- (NIL T) -7 NIL NIL NIL) (-252 526153 526306 526482 "ERROR" NIL ERROR (NIL) -7 NIL NIL NIL) (-251 518524 526083 526148 "EQTBL" NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-250 518213 518276 518385 "EQ2" NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-249 511840 514965 516398 "EQ" NIL EQ (NIL T) -8 NIL NIL NIL) (-248 508143 509239 510332 "EP" NIL EP (NIL T) -7 NIL NIL NIL) (-247 506972 507322 507627 "ENV" NIL ENV (NIL) -8 NIL NIL NIL) (-246 505857 506588 506616 "ENTIRER" 506621 ENTIRER (NIL) -9 NIL 506665 NIL) (-245 505746 505780 505852 "ENTIRER-" NIL ENTIRER- (NIL T) -7 NIL NIL NIL) (-244 502379 504176 504525 "EMR" NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-243 501471 501682 501736 "ELTAGG" 502116 ELTAGG (NIL T T) -9 NIL 502327 NIL) (-242 501251 501325 501466 "ELTAGG-" NIL ELTAGG- (NIL T T T) -7 NIL NIL NIL) (-241 500997 501032 501086 "ELTAB" 501170 ELTAB (NIL T T) -9 NIL 501222 NIL) (-240 500248 500418 500617 "ELFUTS" NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-239 499972 500046 500074 "ELEMFUN" 500179 ELEMFUN (NIL) -9 NIL NIL NIL) (-238 499872 499899 499967 "ELEMFUN-" NIL ELEMFUN- (NIL T) -7 NIL NIL NIL) (-237 495159 497897 497938 "ELAGG" 498871 ELAGG (NIL T) -9 NIL 499332 NIL) (-236 493957 494495 495154 "ELAGG-" NIL ELAGG- (NIL T T) -7 NIL NIL NIL) (-235 493375 493542 493698 "ELABOR" NIL ELABOR (NIL) -8 NIL NIL NIL) (-234 492288 492607 492886 "ELABEXPR" NIL ELABEXPR (NIL) -8 NIL NIL NIL) (-233 485681 487679 488506 "EFUPXS" NIL EFUPXS (NIL T T T T) -7 NIL NIL NIL) (-232 479660 481656 482466 "EFULS" NIL EFULS (NIL T T T) -7 NIL NIL NIL) (-231 477474 477880 478351 "EFSTRUC" NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-230 468474 470387 471928 "EF" NIL EF (NIL T T) -7 NIL NIL NIL) (-229 467587 468088 468237 "EAB" NIL EAB (NIL) -8 NIL NIL NIL) (-228 466285 466959 466999 "DVARCAT" 467282 DVARCAT (NIL T) -9 NIL 467422 NIL) (-227 465704 465968 466280 "DVARCAT-" NIL DVARCAT- (NIL T T) -7 NIL NIL NIL) (-226 457771 465572 465699 "DSMP" NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-225 456109 456900 456941 "DSEXT" 457304 DSEXT (NIL T) -9 NIL 457598 NIL) (-224 454914 455438 456104 "DSEXT-" NIL DSEXT- (NIL T T) -7 NIL NIL NIL) (-223 454638 454703 454801 "DROPT1" NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-222 450789 452005 453136 "DROPT0" NIL DROPT0 (NIL) -7 NIL NIL NIL) (-221 446435 447790 448854 "DROPT" NIL DROPT (NIL) -8 NIL NIL NIL) (-220 445110 445471 445857 "DRAWPT" NIL DRAWPT (NIL) -7 NIL NIL NIL) (-219 444796 444855 444973 "DRAWHACK" NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-218 443771 444069 444359 "DRAWCX" NIL DRAWCX (NIL) -7 NIL NIL NIL) (-217 443356 443431 443581 "DRAWCURV" NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-216 435769 437881 439996 "DRAWCFUN" NIL DRAWCFUN (NIL) -7 NIL NIL NIL) (-215 431286 432305 433384 "DRAW" NIL DRAW (NIL T) -7 NIL NIL NIL) (-214 427910 429913 429954 "DQAGG" 430583 DQAGG (NIL T) -9 NIL 430856 NIL) (-213 414453 422093 422175 "DPOLCAT" 424012 DPOLCAT (NIL T T T T) -9 NIL 424555 NIL) (-212 410861 412509 414448 "DPOLCAT-" NIL DPOLCAT- (NIL T T T T T) -7 NIL NIL NIL) (-211 403912 410759 410856 "DPMO" NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-210 396872 403741 403907 "DPMM" NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-209 396465 396725 396814 "DOMTMPLT" NIL DOMTMPLT (NIL) -8 NIL NIL NIL) (-208 395879 396327 396407 "DOMCTOR" NIL DOMCTOR (NIL) -8 NIL NIL NIL) (-207 395165 395490 395641 "DOMAIN" NIL DOMAIN (NIL) -8 NIL NIL NIL) (-206 388304 394901 395052 "DMP" NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-205 386053 387370 387410 "DMEXT" 387415 DMEXT (NIL T) -9 NIL 387590 NIL) (-204 385709 385771 385915 "DLP" NIL DLP (NIL T) -7 NIL NIL NIL) (-203 379311 385194 385384 "DLIST" NIL DLIST (NIL T) -8 NIL NIL NIL) (-202 376478 378140 378181 "DLAGG" 378722 DLAGG (NIL T) -9 NIL 378954 NIL) (-201 374829 375700 375728 "DIVRING" 375820 DIVRING (NIL) -9 NIL 375903 NIL) (-200 374280 374524 374824 "DIVRING-" NIL DIVRING- (NIL T) -7 NIL NIL NIL) (-199 372708 373125 373531 "DISPLAY" NIL DISPLAY (NIL) -7 NIL NIL NIL) (-198 371745 371966 372231 "DIRPROD2" NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-197 365265 371677 371740 "DIRPROD" NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-196 353611 360025 360078 "DIRPCAT" 360334 DIRPCAT (NIL NIL T) -9 NIL 361209 NIL) (-195 351617 352387 353274 "DIRPCAT-" NIL DIRPCAT- (NIL T NIL T) -7 NIL NIL NIL) (-194 351064 351230 351416 "DIOSP" NIL DIOSP (NIL) -7 NIL NIL NIL) (-193 348347 349941 349982 "DIOPS" 350402 DIOPS (NIL T) -9 NIL 350630 NIL) (-192 348007 348151 348342 "DIOPS-" NIL DIOPS- (NIL T T) -7 NIL NIL NIL) (-191 347014 347760 347788 "DIOID" 347793 DIOID (NIL) -9 NIL 347815 NIL) (-190 345842 346671 346699 "DIFRING" 346704 DIFRING (NIL) -9 NIL 346725 NIL) (-189 345478 345576 345604 "DIFFSPC" 345723 DIFFSPC (NIL) -9 NIL 345798 NIL) (-188 345219 345321 345473 "DIFFSPC-" NIL DIFFSPC- (NIL T) -7 NIL NIL NIL) (-187 344122 344747 344787 "DIFFMOD" 344792 DIFFMOD (NIL T) -9 NIL 344889 NIL) (-186 343806 343863 343904 "DIFFDOM" 344025 DIFFDOM (NIL T) -9 NIL 344093 NIL) (-185 343687 343717 343801 "DIFFDOM-" NIL DIFFDOM- (NIL T T) -7 NIL NIL NIL) (-184 341360 342881 342921 "DIFEXT" 342926 DIFEXT (NIL T) -9 NIL 343078 NIL) (-183 339248 340842 340883 "DIAGG" 340888 DIAGG (NIL T) -9 NIL 340908 NIL) (-182 338804 338994 339243 "DIAGG-" NIL DIAGG- (NIL T T) -7 NIL NIL NIL) (-181 334042 337994 338271 "DHMATRIX" NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-180 330500 331553 332563 "DFSFUN" NIL DFSFUN (NIL) -7 NIL NIL NIL) (-179 325050 329654 329981 "DFLOAT" NIL DFLOAT (NIL) -8 NIL NIL NIL) (-178 323616 323908 324283 "DFINTTLS" NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-177 320736 321988 322384 "DERHAM" NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-176 318520 320567 320656 "DEQUEUE" NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-175 317903 318048 318230 "DEGRED" NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-174 315221 315945 316745 "DEFINTRF" NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-173 313330 313788 314350 "DEFINTEF" NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-172 312713 313046 313160 "DEFAST" NIL DEFAST (NIL) -8 NIL NIL NIL) (-171 305913 312438 312586 "DECIMAL" NIL DECIMAL (NIL) -8 NIL NIL NIL) (-170 303833 304343 304847 "DDFACT" NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-169 303472 303521 303672 "DBLRESP" NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-168 302731 303293 303384 "DBASIS" NIL DBASIS (NIL NIL) -8 NIL NIL NIL) (-167 300755 301197 301557 "DBASE" NIL DBASE (NIL T) -8 NIL NIL NIL) (-166 300047 300336 300482 "DATAARY" NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-165 299498 299644 299796 "CYCLOTOM" NIL CYCLOTOM (NIL) -7 NIL NIL NIL) (-164 296860 297653 298380 "CYCLES" NIL CYCLES (NIL) -7 NIL NIL NIL) (-163 296299 296445 296616 "CVMP" NIL CVMP (NIL T) -7 NIL NIL NIL) (-162 294371 294682 295049 "CTRIGMNP" NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-161 293928 294183 294284 "CTORKIND" NIL CTORKIND (NIL) -8 NIL NIL NIL) (-160 293129 293512 293540 "CTORCAT" 293721 CTORCAT (NIL) -9 NIL 293833 NIL) (-159 292832 292966 293124 "CTORCAT-" NIL CTORCAT- (NIL T) -7 NIL NIL NIL) (-158 292325 292582 292690 "CTORCALL" NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-157 291741 292172 292245 "CTOR" NIL CTOR (NIL) -8 NIL NIL NIL) (-156 291200 291317 291470 "CSTTOOLS" NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-155 287594 288350 289105 "CRFP" NIL CRFP (NIL T T) -7 NIL NIL NIL) (-154 287085 287388 287479 "CRCEAST" NIL CRCEAST (NIL) -8 NIL NIL NIL) (-153 286304 286513 286741 "CRAPACK" NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-152 285808 285913 286117 "CPMATCH" NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-151 285561 285595 285701 "CPIMA" NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-150 282500 283262 283980 "COORDSYS" NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-149 282019 282161 282300 "CONTOUR" NIL CONTOUR (NIL) -8 NIL NIL NIL) (-148 277912 280482 280974 "CONTFRAC" NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-147 277786 277813 277841 "CONDUIT" 277878 CONDUIT (NIL) -9 NIL NIL NIL) (-146 276665 277396 277424 "COMRING" 277429 COMRING (NIL) -9 NIL 277479 NIL) (-145 275830 276197 276375 "COMPPROP" NIL COMPPROP (NIL) -8 NIL NIL NIL) (-144 275526 275567 275695 "COMPLPAT" NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-143 275219 275282 275389 "COMPLEX2" NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-142 264061 275169 275214 "COMPLEX" NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-141 263522 263661 263821 "COMPILER" NIL COMPILER (NIL) -7 NIL NIL NIL) (-140 263275 263316 263414 "COMPFACT" NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-139 244706 256956 256996 "COMPCAT" 257997 COMPCAT (NIL T) -9 NIL 259339 NIL) (-138 237244 240757 244350 "COMPCAT-" NIL COMPCAT- (NIL T T) -7 NIL NIL NIL) (-137 237003 237037 237139 "COMMUPC" NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-136 236833 236872 236930 "COMMONOP" NIL COMMONOP (NIL) -7 NIL NIL NIL) (-135 236414 236693 236767 "COMMAAST" NIL COMMAAST (NIL) -8 NIL NIL NIL) (-134 235991 236232 236319 "COMM" NIL COMM (NIL) -8 NIL NIL NIL) (-133 235186 235434 235462 "COMBOPC" 235800 COMBOPC (NIL) -9 NIL 235975 NIL) (-132 234250 234502 234744 "COMBINAT" NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-131 231182 231866 232489 "COMBF" NIL COMBF (NIL T T) -7 NIL NIL NIL) (-130 230062 230513 230748 "COLOR" NIL COLOR (NIL) -8 NIL NIL NIL) (-129 229553 229856 229947 "COLONAST" NIL COLONAST (NIL) -8 NIL NIL NIL) (-128 229240 229293 229418 "CMPLXRT" NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-127 228710 229020 229118 "CLLCTAST" NIL CLLCTAST (NIL) -8 NIL NIL NIL) (-126 225230 226300 227380 "CLIP" NIL CLIP (NIL) -7 NIL NIL NIL) (-125 223525 224510 224748 "CLIF" NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-124 220883 222161 222202 "CLAGG" 222765 CLAGG (NIL T) -9 NIL 223145 NIL) (-123 220441 220631 220878 "CLAGG-" NIL CLAGG- (NIL T T) -7 NIL NIL NIL) (-122 220070 220161 220301 "CINTSLPE" NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-121 218007 218514 219062 "CHVAR" NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-120 216968 217699 217727 "CHARZ" 217732 CHARZ (NIL) -9 NIL 217746 NIL) (-119 216762 216808 216886 "CHARPOL" NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-118 215601 216364 216392 "CHARNZ" 216453 CHARNZ (NIL) -9 NIL 216501 NIL) (-117 213079 214176 214699 "CHAR" NIL CHAR (NIL) -8 NIL NIL NIL) (-116 212787 212866 212894 "CFCAT" 213005 CFCAT (NIL) -9 NIL NIL NIL) (-115 212130 212259 212441 "CDEN" NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-114 208398 211543 211823 "CCLASS" NIL CCLASS (NIL) -8 NIL NIL NIL) (-113 207776 207963 208140 "CATEGORY" NIL -10 (NIL) -8 NIL NIL NIL) (-112 207304 207723 207771 "CATCTOR" NIL CATCTOR (NIL) -8 NIL NIL NIL) (-111 206777 207086 207183 "CATAST" NIL CATAST (NIL) -8 NIL NIL NIL) (-110 206268 206571 206662 "CASEAST" NIL CASEAST (NIL) -8 NIL NIL NIL) (-109 205517 205677 205898 "CARTEN2" NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-108 201617 202874 203582 "CARTEN" NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-107 199983 201014 201265 "CARD" NIL CARD (NIL) -8 NIL NIL NIL) (-106 199564 199843 199917 "CAPSLAST" NIL CAPSLAST (NIL) -8 NIL NIL NIL) (-105 198998 199251 199279 "CACHSET" 199411 CACHSET (NIL) -9 NIL 199489 NIL) (-104 198350 198765 198793 "CABMON" 198843 CABMON (NIL) -9 NIL 198899 NIL) (-103 197880 198144 198254 "BYTEORD" NIL BYTEORD (NIL) -8 NIL NIL NIL) (-102 193389 197548 197709 "BYTEBUF" NIL BYTEBUF (NIL) -8 NIL NIL NIL) (-101 192359 193063 193198 "BYTE" NIL BYTE (NIL) -8 NIL NIL 193361) (-100 189884 192126 192232 "BTREE" NIL BTREE (NIL T) -8 NIL NIL NIL) (-99 187380 189638 189746 "BTOURN" NIL BTOURN (NIL T) -8 NIL NIL NIL) (-98 184634 186782 186821 "BTCAT" 186888 BTCAT (NIL T) -9 NIL 186969 NIL) (-97 184385 184483 184629 "BTCAT-" NIL BTCAT- (NIL T T) -7 NIL NIL NIL) (-96 179737 183577 183603 "BTAGG" 183714 BTAGG (NIL) -9 NIL 183822 NIL) (-95 179368 179529 179732 "BTAGG-" NIL BTAGG- (NIL T) -7 NIL NIL NIL) (-94 176506 178860 179050 "BSTREE" NIL BSTREE (NIL T) -8 NIL NIL NIL) (-93 175776 175928 176106 "BRILL" NIL BRILL (NIL T) -7 NIL NIL NIL) (-92 172811 174491 174530 "BRAGG" 175159 BRAGG (NIL T) -9 NIL 175419 NIL) (-91 171886 172317 172806 "BRAGG-" NIL BRAGG- (NIL T T) -7 NIL NIL NIL) (-90 164420 171391 171572 "BPADICRT" NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-89 162412 164372 164415 "BPADIC" NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-88 162145 162181 162292 "BOUNDZRO" NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-87 160384 160817 161265 "BOP1" NIL BOP1 (NIL T) -7 NIL NIL NIL) (-86 156350 157766 158656 "BOP" NIL BOP (NIL) -8 NIL NIL NIL) (-85 155226 156117 156239 "BOOLEAN" NIL BOOLEAN (NIL) -8 NIL NIL NIL) (-84 154812 154969 154995 "BOOLE" 155103 BOOLE (NIL) -9 NIL 155184 NIL) (-83 154605 154686 154807 "BOOLE-" NIL BOOLE- (NIL T) -7 NIL NIL NIL) (-82 153743 154270 154320 "BMODULE" 154325 BMODULE (NIL T T) -9 NIL 154389 NIL) (-81 149643 153600 153669 "BITS" NIL BITS (NIL) -8 NIL NIL NIL) (-80 149456 149496 149535 "BINOPC" 149540 BINOPC (NIL T) -9 NIL 149585 NIL) (-79 148998 149271 149373 "BINOP" NIL BINOP (NIL T) -8 NIL NIL NIL) (-78 148519 148663 148801 "BINDING" NIL BINDING (NIL) -8 NIL NIL NIL) (-77 141725 148249 148394 "BINARY" NIL BINARY (NIL) -8 NIL NIL NIL) (-76 139972 140945 140984 "BGAGG" 141240 BGAGG (NIL T) -9 NIL 141367 NIL) (-75 139841 139879 139967 "BGAGG-" NIL BGAGG- (NIL T T) -7 NIL NIL NIL) (-74 138692 138893 139178 "BEZOUT" NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-73 135406 137872 138177 "BBTREE" NIL BBTREE (NIL T) -8 NIL NIL NIL) (-72 134991 135084 135110 "BASTYPE" 135281 BASTYPE (NIL) -9 NIL 135377 NIL) (-71 134761 134857 134986 "BASTYPE-" NIL BASTYPE- (NIL T) -7 NIL NIL NIL) (-70 134276 134364 134514 "BALFACT" NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-69 133175 133850 134035 "AUTOMOR" NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-68 132923 132928 132954 "ATTREG" 132959 ATTREG (NIL) -9 NIL NIL NIL) (-67 132528 132800 132865 "ATTRAST" NIL ATTRAST (NIL) -8 NIL NIL NIL) (-66 132028 132177 132203 "ATRIG" 132404 ATRIG (NIL) -9 NIL NIL NIL) (-65 131883 131936 132023 "ATRIG-" NIL ATRIG- (NIL T) -7 NIL NIL NIL) (-64 131453 131684 131710 "ASTCAT" 131715 ASTCAT (NIL) -9 NIL 131745 NIL) (-63 131252 131329 131448 "ASTCAT-" NIL ASTCAT- (NIL T) -7 NIL NIL NIL) (-62 129475 131085 131173 "ASTACK" NIL ASTACK (NIL T) -8 NIL NIL NIL) (-61 128282 128595 128960 "ASSOCEQ" NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-60 126134 128212 128277 "ARRAY2" NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 125325 125516 125737 "ARRAY12" NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-58 121203 125056 125170 "ARRAY1" NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-57 115515 117519 117594 "ARR2CAT" 120106 ARR2CAT (NIL T T T) -9 NIL 120827 NIL) (-56 114476 114958 115510 "ARR2CAT-" NIL ARR2CAT- (NIL T T T T) -7 NIL NIL NIL) (-55 113844 114215 114337 "ARITY" NIL ARITY (NIL) -8 NIL NIL NIL) (-54 112776 112944 113240 "APPRULE" NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 112477 112531 112649 "APPLYORE" NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 111860 112006 112162 "ANY1" NIL ANY1 (NIL T) -7 NIL NIL NIL) (-51 111265 111555 111675 "ANY" NIL ANY (NIL) -8 NIL NIL NIL) (-50 108833 109994 110317 "ANTISYM" NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 108358 108618 108714 "ANON" NIL ANON (NIL) -8 NIL NIL NIL) (-48 102053 107420 107862 "AN" NIL AN (NIL) -8 NIL NIL NIL) (-47 97587 99250 99300 "AMR" 100038 AMR (NIL T T) -9 NIL 100635 NIL) (-46 96941 97221 97582 "AMR-" NIL AMR- (NIL T T T) -7 NIL NIL NIL) (-45 78980 96875 96936 "ALIST" NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 75383 78656 78825 "ALGSC" NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 72393 73053 73660 "ALGPKG" NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 71772 71885 72069 "ALGMFACT" NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 68184 68809 69401 "ALGMANIP" NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 57673 67877 68027 "ALGFF" NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 56990 57144 57322 "ALGFACT" NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 55703 56498 56536 "ALGEBRA" 56541 ALGEBRA (NIL T) -9 NIL 56581 NIL) (-37 55489 55566 55698 "ALGEBRA-" NIL ALGEBRA- (NIL T T) -7 NIL NIL NIL) (-36 33869 52596 52648 "ALAGG" 52783 ALAGG (NIL T T) -9 NIL 52941 NIL) (-35 33369 33518 33544 "AHYP" 33745 AHYP (NIL) -9 NIL NIL NIL) (-34 32851 32983 33009 "AGG" 33214 AGG (NIL) -9 NIL 33340 NIL) (-33 32694 32752 32846 "AGG-" NIL AGG- (NIL T) -7 NIL NIL NIL) (-32 30833 31293 31693 "AF" NIL AF (NIL T T) -7 NIL NIL NIL) (-31 30328 30631 30720 "ADDAST" NIL ADDAST (NIL) -8 NIL NIL NIL) (-30 29698 29993 30149 "ACPLOT" NIL ACPLOT (NIL) -8 NIL NIL NIL) (-29 17256 26535 26573 "ACFS" 27180 ACFS (NIL T) -9 NIL 27419 NIL) (-28 15879 16489 17251 "ACFS-" NIL ACFS- (NIL T T) -7 NIL NIL NIL) (-27 11431 13810 13836 "ACF" 14715 ACF (NIL) -9 NIL 15127 NIL) (-26 10527 10933 11426 "ACF-" NIL ACF- (NIL T) -7 NIL NIL NIL) (-25 10029 10269 10295 "ABELSG" 10387 ABELSG (NIL) -9 NIL 10452 NIL) (-24 9927 9958 10024 "ABELSG-" NIL ABELSG- (NIL T) -7 NIL NIL NIL) (-23 9082 9456 9482 "ABELMON" 9707 ABELMON (NIL) -9 NIL 9840 NIL) (-22 8764 8904 9077 "ABELMON-" NIL ABELMON- (NIL T) -7 NIL NIL NIL) (-21 7976 8459 8485 "ABELGRP" 8557 ABELGRP (NIL) -9 NIL 8632 NIL) (-20 7529 7725 7971 "ABELGRP-" NIL ABELGRP- (NIL T) -7 NIL NIL NIL) (-19 3036 6756 6795 "A1AGG" 6800 A1AGG (NIL T) -9 NIL 6834 NIL) (-18 30 1483 3031 "A1AGG-" NIL A1AGG- (NIL T T) -7 NIL NIL NIL)) 
\ No newline at end of file
+((-2569 (((-85) $ $) NIL T ELT)) (-3243 (((-1073) $) NIL T ELT)) (-3244 (((-1033) $) NIL T ELT)) (-3947 (((-772) $) 9 T ELT) (($ (-1095)) NIL T ELT) (((-1095) $) NIL T ELT)) (-1265 (((-85) $ $) NIL T ELT)) (-3057 (((-85) $ $) NIL T ELT))) 
+(((-1130) (-995)) (T -1130)) 
+NIL 
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T) ((-241 |#2| $) -12 (|has| |#1| (-312)) (|has| |#2| (-241 |#2| |#2|))) ((-241 $ $) |has| (-484) (-1025)) ((-246) OR (|has| |#1| (-495)) (|has| |#1| (-312))) ((-258) |has| |#1| (-312)) ((-260 |#2|) -12 (|has| |#1| (-312)) (|has| |#2| (-260 |#2|))) ((-312) |has| |#1| (-312)) ((-288 |#2|) |has| |#1| (-312)) ((-329 |#2|) |has| |#1| (-312)) ((-343 |#2|) |has| |#1| (-312)) ((-392) |has| |#1| (-312)) ((-433) |has| |#1| (-38 (-350 (-484)))) ((-455 (-1090) |#2|) -12 (|has| |#1| (-312)) (|has| |#2| (-455 (-1090) |#2|))) ((-455 |#2| |#2|) -12 (|has| |#1| (-312)) (|has| |#2| (-260 |#2|))) ((-495) OR (|has| |#1| (-495)) (|has| |#1| (-312))) ((-13) . T) ((-588 (-350 (-484))) OR (|has| |#1| (-312)) (|has| |#1| (-38 (-350 (-484))))) ((-588 (-484)) . T) ((-588 |#1|) . T) ((-588 |#2|) |has| |#1| (-312)) ((-588 $) . T) ((-590 (-350 (-484))) OR (|has| |#1| (-312)) (|has| |#1| (-38 (-350 (-484))))) ((-590 (-484)) -12 (|has| |#1| (-312)) (|has| |#2| (-580 (-484)))) ((-590 |#1|) . T) ((-590 |#2|) |has| |#1| (-312)) ((-590 $) . T) ((-582 (-350 (-484))) OR (|has| |#1| (-312)) (|has| |#1| (-38 (-350 (-484))))) ((-582 |#1|) |has| |#1| (-146)) ((-582 |#2|) |has| |#1| (-312)) ((-582 $) OR (|has| |#1| (-495)) (|has| |#1| (-312))) ((-580 (-484)) -12 (|has| |#1| (-312)) (|has| |#2| (-580 (-484)))) ((-580 |#2|) |has| |#1| (-312)) ((-654 (-350 (-484))) OR (|has| |#1| (-312)) (|has| |#1| (-38 (-350 (-484))))) ((-654 |#1|) |has| |#1| (-146)) ((-654 |#2|) |has| |#1| (-312)) ((-654 $) OR (|has| |#1| (-495)) (|has| |#1| (-312))) ((-663) . T) ((-714) -12 (|has| |#1| (-312)) (|has| |#2| (-740))) ((-716) -12 (|has| |#1| (-312)) (|has| |#2| (-740))) ((-718) -12 (|has| |#1| (-312)) (|has| |#2| (-740))) ((-721) -12 (|has| |#1| (-312)) (|has| |#2| (-740))) ((-740) -12 (|has| |#1| (-312)) (|has| |#2| (-740))) ((-755) -12 (|has| |#1| (-312)) (|has| |#2| (-740))) ((-756) OR (-12 (|has| |#1| (-312)) (|has| |#2| (-756))) (-12 (|has| |#1| (-312)) (|has| |#2| (-740)))) ((-759) OR (-12 (|has| |#1| (-312)) (|has| |#2| (-756))) (-12 (|has| |#1| (-312)) (|has| |#2| (-740)))) ((-806 $ (-1090)) OR (-12 (|has| |#1| (-809 (-1090))) (|has| |#1| (-15 * (|#1| (-484) |#1|)))) (-12 (|has| |#1| (-312)) (|has| |#2| (-811 (-1090)))) (-12 (|has| |#1| (-312)) (|has| |#2| (-809 (-1090))))) ((-809 (-1090)) OR (-12 (|has| |#1| (-809 (-1090))) (|has| |#1| (-15 * (|#1| (-484) |#1|)))) (-12 (|has| |#1| (-312)) (|has| |#2| (-809 (-1090))))) ((-811 (-1090)) OR (-12 (|has| |#1| (-809 (-1090))) (|has| |#1| (-15 * (|#1| (-484) |#1|)))) (-12 (|has| |#1| (-312)) (|has| |#2| (-811 (-1090)))) (-12 (|has| |#1| (-312)) (|has| |#2| (-809 (-1090))))) ((-796 (-330)) -12 (|has| |#1| (-312)) (|has| |#2| (-796 (-330)))) ((-796 (-484)) -12 (|has| |#1| (-312)) (|has| |#2| (-796 (-484)))) ((-794 |#2|) |has| |#1| (-312)) ((-821) -12 (|has| |#1| (-312)) (|has| |#2| (-821))) ((-886 |#1| (-484) (-994)) . T) ((-832) |has| |#1| (-312)) ((-904 |#2|) |has| |#1| (-312)) ((-915) |has| |#1| (-38 (-350 (-484)))) ((-933) -12 (|has| |#1| (-312)) (|has| |#2| (-933))) ((-950 (-350 (-484))) -12 (|has| |#1| (-312)) (|has| |#2| (-950 (-484)))) ((-950 (-484)) -12 (|has| |#1| (-312)) (|has| |#2| (-950 (-484)))) ((-950 (-1090)) -12 (|has| |#1| (-312)) (|has| |#2| (-950 (-1090)))) ((-950 |#2|) . T) ((-963 (-350 (-484))) OR (|has| |#1| (-312)) (|has| |#1| (-38 (-350 (-484))))) ((-963 |#1|) . T) ((-963 |#2|) |has| |#1| (-312)) ((-963 $) OR (|has| |#1| (-495)) (|has| |#1| (-312)) (|has| |#1| (-146))) ((-968 (-350 (-484))) OR (|has| |#1| (-312)) (|has| |#1| (-38 (-350 (-484))))) ((-968 |#1|) . T) ((-968 |#2|) |has| |#1| (-312)) ((-968 $) OR (|has| |#1| (-495)) (|has| |#1| (-312)) (|has| |#1| (-146))) ((-961) . T) ((-970) . T) ((-1025) . T) ((-1061) . T) ((-1013) . T) ((-1066) -12 (|has| |#1| (-312)) (|has| |#2| (-1066))) ((-1115) |has| |#1| (-38 (-350 (-484)))) ((-1118) |has| |#1| (-38 (-350 (-484)))) ((-1129) . T) ((-1134) |has| |#1| (-312)) ((-1141 |#1|) . T) ((-1158 |#1| (-484)) . T)) 
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+NIL 
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+(((-1172 |#1|) (-113) (-961)) (T -1172)) 
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+(((-21) . T) ((-23) . T) ((-47 |#1| (-694)) . T) ((-25) . T) ((-38 (-350 (-484))) |has| |#1| (-38 (-350 (-484)))) ((-38 |#1|) |has| |#1| (-146)) ((-38 $) |has| |#1| (-495)) ((-35) |has| |#1| (-38 (-350 (-484)))) ((-66) |has| |#1| (-38 (-350 (-484)))) ((-72) . T) ((-82 (-350 (-484)) (-350 (-484))) |has| |#1| (-38 (-350 (-484)))) ((-82 |#1| |#1|) . T) ((-82 $ $) OR (|has| |#1| (-495)) (|has| |#1| (-146))) ((-104) . T) ((-118) |has| |#1| (-118)) ((-120) |has| |#1| (-120)) ((-555 (-350 (-484))) |has| |#1| (-38 (-350 (-484)))) ((-555 (-484)) . T) ((-555 |#1|) |has| |#1| (-146)) ((-555 $) |has| |#1| (-495)) ((-552 (-772)) . T) ((-146) OR (|has| |#1| (-495)) (|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 (-350 (-484)))) ((-241 (-694) |#1|) . T) ((-241 $ $) |has| (-694) (-1025)) ((-246) |has| |#1| (-495)) ((-433) |has| |#1| (-38 (-350 (-484)))) ((-495) |has| |#1| (-495)) ((-13) . T) ((-588 (-350 (-484))) |has| |#1| (-38 (-350 (-484)))) ((-588 (-484)) . T) ((-588 |#1|) . T) ((-588 $) . T) ((-590 (-350 (-484))) |has| |#1| (-38 (-350 (-484)))) ((-590 |#1|) . T) ((-590 $) . T) ((-582 (-350 (-484))) |has| |#1| (-38 (-350 (-484)))) ((-582 |#1|) |has| |#1| (-146)) ((-582 $) |has| |#1| (-495)) ((-654 (-350 (-484))) |has| |#1| (-38 (-350 (-484)))) ((-654 |#1|) |has| |#1| (-146)) ((-654 $) |has| |#1| (-495)) ((-663) . T) ((-806 $ (-1090)) -12 (|has| |#1| (-809 (-1090))) (|has| |#1| (-15 * (|#1| (-694) |#1|)))) ((-809 (-1090)) -12 (|has| |#1| (-809 (-1090))) (|has| |#1| (-15 * (|#1| (-694) |#1|)))) ((-811 (-1090)) -12 (|has| |#1| (-809 (-1090))) (|has| |#1| (-15 * (|#1| (-694) |#1|)))) ((-886 |#1| (-694) (-994)) . T) ((-915) |has| |#1| (-38 (-350 (-484)))) ((-963 (-350 (-484))) |has| |#1| (-38 (-350 (-484)))) ((-963 |#1|) . T) ((-963 $) OR (|has| |#1| (-495)) (|has| |#1| (-146))) ((-968 (-350 (-484))) |has| |#1| (-38 (-350 (-484)))) ((-968 |#1|) . T) ((-968 $) OR (|has| |#1| (-495)) (|has| |#1| (-146))) ((-961) . T) ((-970) . T) ((-1025) . T) ((-1061) . T) ((-1013) . T) ((-1115) |has| |#1| (-38 (-350 (-484)))) ((-1118) |has| |#1| (-38 (-350 (-484)))) ((-1129) . T) ((-1158 |#1| (-694)) . T)) 
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+((-3829 ((|#2| |#4| (-694)) 31 T ELT)) (-3828 ((|#4| |#2|) 26 T ELT)) (-3831 ((|#4| (-350 |#2|)) 49 (|has| |#1| (-495)) ELT)) (-3830 (((-1 |#4| (-583 |#4|)) |#3|) 43 T ELT))) 
+(((-1174 |#1| |#2| |#3| |#4|) (-10 -7 (-15 -3828 (|#4| |#2|)) (-15 -3829 (|#2| |#4| (-694))) (-15 -3830 ((-1 |#4| (-583 |#4|)) |#3|)) (IF (|has| |#1| (-495)) (-15 -3831 (|#4| (-350 |#2|))) |%noBranch|)) (-961) (-1155 |#1|) (-600 |#2|) (-1172 |#1|)) (T -1174)) 
+((-3831 (*1 *2 *3) (-12 (-5 *3 (-350 *5)) (-4 *5 (-1155 *4)) (-4 *4 (-495)) (-4 *4 (-961)) (-4 *2 (-1172 *4)) (-5 *1 (-1174 *4 *5 *6 *2)) (-4 *6 (-600 *5)))) (-3830 (*1 *2 *3) (-12 (-4 *4 (-961)) (-4 *5 (-1155 *4)) (-5 *2 (-1 *6 (-583 *6))) (-5 *1 (-1174 *4 *5 *3 *6)) (-4 *3 (-600 *5)) (-4 *6 (-1172 *4)))) (-3829 (*1 *2 *3 *4) (-12 (-5 *4 (-694)) (-4 *5 (-961)) (-4 *2 (-1155 *5)) (-5 *1 (-1174 *5 *2 *6 *3)) (-4 *6 (-600 *2)) (-4 *3 (-1172 *5)))) (-3828 (*1 *2 *3) (-12 (-4 *4 (-961)) (-4 *3 (-1155 *4)) (-4 *2 (-1172 *4)) (-5 *1 (-1174 *4 *3 *5 *2)) (-4 *5 (-600 *3))))) 
+NIL 
+(((-1175) (-113)) (T -1175)) 
+NIL 
+(-13 (-10 -7 (-6 -2287))) 
+((-2569 (((-85) $ $) NIL T ELT)) (-3832 (((-1090)) 12 T ELT)) (-3243 (((-1073) $) 18 T ELT)) (-3244 (((-1033) $) NIL T ELT)) (-3947 (((-772) $) 11 T ELT) (((-1090) $) 8 T ELT)) (-1265 (((-85) $ $) NIL T ELT)) (-3057 (((-85) $ $) 15 T ELT))) 
+(((-1176 |#1|) (-13 (-1013) (-552 (-1090)) (-10 -8 (-15 -3947 ((-1090) $)) (-15 -3832 ((-1090))))) (-1090)) (T -1176)) 
+((-3947 (*1 *2 *1) (-12 (-5 *2 (-1090)) (-5 *1 (-1176 *3)) (-14 *3 *2))) (-3832 (*1 *2) (-12 (-5 *2 (-1090)) (-5 *1 (-1176 *3)) (-14 *3 *2)))) 
+((-3839 (($ (-694)) 19 T ELT)) (-3836 (((-630 |#2|) $ $) 41 T ELT)) (-3833 ((|#2| $) 51 T ELT)) (-3834 ((|#2| $) 50 T ELT)) (-3837 ((|#2| $ $) 36 T ELT)) (-3835 (($ $ $) 47 T ELT)) (-3838 (($ $) 23 T ELT) (($ $ $) 29 T ELT)) (-3840 (($ $ $) 15 T ELT)) (* (($ (-484) $) 26 T ELT) (($ |#2| $) 32 T ELT) (($ $ |#2|) 31 T ELT))) 
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+NIL 
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(-258) (-120) (-933))) (-5 *2 (-583 (-2 (|:| -1750 (-1085 *5)) (|:| -3225 (-583 (-857 *5)))))) (-5 *1 (-1207 *5 *6 *7)) (-5 *3 (-583 (-857 *5))) (-14 *6 (-583 (-1090))) (-14 *7 (-583 (-1090))))) (-3969 (*1 *2 *3) (-12 (-5 *3 (-958 *4 *5)) (-4 *4 (-13 (-755) (-258) (-120) (-933))) (-14 *5 (-583 (-1090))) (-5 *2 (-583 (-2 (|:| -1750 (-1085 *4)) (|:| -3225 (-583 (-857 *4)))))) (-5 *1 (-1207 *4 *5 *6)) (-14 *6 (-583 (-1090))))) (-3968 (*1 *2 *3) (-12 (-5 *3 (-583 (-857 *4))) (-4 *4 (-13 (-755) (-258) (-120) (-933))) (-5 *2 (-583 (-958 *4 *5))) (-5 *1 (-1207 *4 *5 *6)) (-14 *5 (-583 (-1090))) (-14 *6 (-583 (-1090))))) (-3968 (*1 *2 *3 *4) (-12 (-5 *3 (-583 (-857 *5))) (-5 *4 (-85)) (-4 *5 (-13 (-755) (-258) (-120) (-933))) (-5 *2 (-583 (-958 *5 *6))) (-5 *1 (-1207 *5 *6 *7)) (-14 *6 (-583 (-1090))) (-14 *7 (-583 (-1090))))) (-3968 (*1 *2 *3 *4 *4) (-12 (-5 *3 (-583 (-857 *5))) (-5 *4 (-85)) (-4 *5 (-13 (-755) (-258) (-120) (-933))) (-5 *2 (-583 (-958 *5 *6))) (-5 *1 (-1207 *5 *6 *7)) (-14 *6 (-583 (-1090))) (-14 *7 (-583 (-1090)))))) 
+((-3976 (((-3 (-1179 (-350 (-484))) #1="failed") (-1179 |#1|) |#1|) 21 T ELT)) (-3974 (((-85) (-1179 |#1|)) 12 T ELT)) (-3975 (((-3 (-1179 (-484)) #1#) (-1179 |#1|)) 16 T ELT))) 
+(((-1208 |#1|) (-10 -7 (-15 -3974 ((-85) (-1179 |#1|))) (-15 -3975 ((-3 (-1179 (-484)) #1="failed") (-1179 |#1|))) (-15 -3976 ((-3 (-1179 (-350 (-484))) #1#) (-1179 |#1|) |#1|))) (-13 (-961) (-580 (-484)))) (T -1208)) 
+((-3976 (*1 *2 *3 *4) (|partial| -12 (-5 *3 (-1179 *4)) (-4 *4 (-13 (-961) (-580 (-484)))) (-5 *2 (-1179 (-350 (-484)))) (-5 *1 (-1208 *4)))) (-3975 (*1 *2 *3) (|partial| -12 (-5 *3 (-1179 *4)) (-4 *4 (-13 (-961) (-580 (-484)))) (-5 *2 (-1179 (-484))) (-5 *1 (-1208 *4)))) (-3974 (*1 *2 *3) (-12 (-5 *3 (-1179 *4)) (-4 *4 (-13 (-961) (-580 (-484)))) (-5 *2 (-85)) (-5 *1 (-1208 *4))))) 
+((-2569 (((-85) $ $) NIL T ELT)) (-3189 (((-85) $) 12 T ELT)) (-1312 (((-3 $ #1="failed") $ $) NIL T ELT)) (-3137 (((-694)) 9 T ELT)) (-3725 (($) NIL T CONST)) (-3468 (((-3 $ #1#) $) 57 T ELT)) (-2995 (($) 46 T ELT)) (-1214 (((-85) $ $) NIL T ELT)) (-2410 (((-85) $) 38 T ELT)) (-3446 (((-632 $) $) 36 T ELT)) (-2010 (((-830) $) 14 T ELT)) (-3243 (((-1073) $) NIL T ELT)) (-3447 (($) 26 T CONST)) (-2400 (($ (-830)) 47 T ELT)) (-3244 (((-1033) $) NIL T ELT)) (-3973 (((-484) $) 16 T ELT)) (-3947 (((-772) $) 21 T ELT) (($ (-484)) 18 T ELT)) (-3127 (((-694)) 10 T CONST)) (-1265 (((-85) $ $) 59 T ELT)) (-3126 (((-85) $ $) NIL T ELT)) (-2661 (($) 23 T CONST)) (-2667 (($) 25 T CONST)) (-3057 (((-85) $ $) 31 T ELT)) (-3838 (($ $) 50 T ELT) (($ $ $) 44 T ELT)) (-3840 (($ $ $) 29 T ELT)) (** (($ $ (-830)) NIL T ELT) (($ $ (-694)) 52 T ELT)) (* (($ (-830) $) NIL T ELT) (($ (-694) $) NIL T ELT) (($ (-484) $) 41 T ELT) (($ $ $) 40 T ELT))) 
+(((-1209 |#1|) (-13 (-146) (-320) (-553 (-484)) (-1066)) (-830)) (T -1209)) 
+NIL 
+NIL 
+NIL 
+NIL 
+NIL 
+NIL 
+NIL 
+NIL 
+NIL 
+NIL 
+NIL 
+NIL 
+NIL 
+((-3 2792496 2792501 2792506 NIL NIL NIL (NIL) -8 NIL NIL NIL) (-2 2792481 2792486 2792491 NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1 2792466 2792471 2792476 NIL NIL NIL (NIL) -8 NIL NIL NIL) (0 2792451 2792456 2792461 NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1209 2791430 2792369 2792446 "ZMOD" NIL ZMOD (NIL NIL) -8 NIL NIL NIL) (-1208 2790645 2790824 2791043 "ZLINDEP" NIL ZLINDEP (NIL T) -7 NIL NIL NIL) (-1207 2781804 2783673 2785607 "ZDSOLVE" NIL ZDSOLVE (NIL T NIL NIL) -7 NIL NIL NIL) (-1206 2781192 2781345 2781534 "YSTREAM" NIL YSTREAM (NIL T) -7 NIL NIL NIL) (-1205 2780654 2780957 2781070 "YDIAGRAM" NIL YDIAGRAM (NIL) -8 NIL NIL NIL) (-1204 2778214 2780116 2780319 "XRPOLY" NIL XRPOLY (NIL T T) -8 NIL NIL NIL) (-1203 2774978 2776631 2777202 "XPR" NIL XPR (NIL T T) -8 NIL NIL NIL) (-1202 2772235 2773965 2774019 "XPOLYC" 2774304 XPOLYC (NIL T T) -9 NIL 2774417 NIL) (-1201 2769754 2771739 2771942 "XPOLY" NIL XPOLY (NIL T) -8 NIL NIL NIL) (-1200 2766002 2768613 2769001 "XPBWPOLY" NIL XPBWPOLY (NIL T T) -8 NIL NIL NIL) (-1199 2760849 2762482 2762536 "XFALG" 2764681 XFALG (NIL T T) -9 NIL 2765465 NIL) (-1198 2756005 2758738 2758780 "XF" 2759398 XF (NIL T) -9 NIL 2759794 NIL) (-1197 2755723 2755833 2756000 "XF-" NIL XF- (NIL T T) -7 NIL NIL NIL) (-1196 2754950 2755072 2755276 "XEXPPKG" NIL XEXPPKG (NIL T T T) -7 NIL NIL NIL) (-1195 2752692 2754850 2754945 "XDPOLY" NIL XDPOLY (NIL T T) -8 NIL NIL NIL) (-1194 2751273 2752068 2752110 "XALG" 2752115 XALG (NIL T) -9 NIL 2752224 NIL) (-1193 2745124 2749683 2750161 "WUTSET" NIL WUTSET (NIL T T T T) -8 NIL NIL NIL) (-1192 2743367 2744369 2744690 "WP" NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL NIL) (-1191 2742966 2743238 2743307 "WHILEAST" NIL WHILEAST (NIL) -8 NIL NIL NIL) (-1190 2742453 2742756 2742849 "WHEREAST" NIL WHEREAST (NIL) -8 NIL NIL NIL) (-1189 2741530 2741740 2742035 "WFFINTBS" NIL WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1188 2739826 2740289 2740751 "WEIER" NIL WEIER (NIL T) -7 NIL NIL NIL) (-1187 2738715 2739300 2739342 "VSPACE" 2739478 VSPACE (NIL T) -9 NIL 2739552 NIL) (-1186 2738586 2738619 2738710 "VSPACE-" NIL VSPACE- (NIL T T) -7 NIL NIL NIL) (-1185 2738429 2738483 2738551 "VOID" NIL VOID (NIL) -8 NIL NIL NIL) (-1184 2735412 2736207 2736944 "VIEWDEF" NIL VIEWDEF (NIL) -7 NIL NIL NIL) (-1183 2726510 2729111 2731284 "VIEW3D" NIL VIEW3D (NIL) -8 NIL NIL NIL) (-1182 2720087 2721978 2723557 "VIEW2D" NIL VIEW2D (NIL) -8 NIL NIL NIL) (-1181 2718571 2718966 2719372 "VIEW" NIL VIEW (NIL) -7 NIL NIL NIL) (-1180 2717398 2717679 2717995 "VECTOR2" NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1179 2712799 2717225 2717317 "VECTOR" NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1178 2706148 2710472 2710515 "VECTCAT" 2711503 VECTCAT (NIL T) -9 NIL 2712087 NIL) (-1177 2705427 2705753 2706143 "VECTCAT-" NIL VECTCAT- (NIL T T) -7 NIL NIL NIL) (-1176 2704921 2705163 2705283 "VARIABLE" NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1175 2704854 2704859 2704889 "UTYPE" 2704894 UTYPE (NIL) -9 NIL NIL NIL) (-1174 2703841 2704017 2704278 "UTSODETL" NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1173 2701692 2702200 2702724 "UTSODE" NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1172 2691574 2697544 2697586 "UTSCAT" 2698684 UTSCAT (NIL T) -9 NIL 2699441 NIL) (-1171 2689639 2690582 2691569 "UTSCAT-" NIL UTSCAT- (NIL T T) -7 NIL NIL NIL) (-1170 2689313 2689362 2689493 "UTS2" NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1169 2681024 2687509 2687988 "UTS" NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1168 2675527 2677859 2677902 "URAGG" 2679942 URAGG (NIL T) -9 NIL 2680667 NIL) (-1167 2673598 2674530 2675522 "URAGG-" NIL URAGG- (NIL T T) -7 NIL NIL NIL) (-1166 2669305 2672574 2673036 "UPXSSING" NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1165 2661734 2669229 2669300 "UPXSCONS" NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1164 2650385 2657872 2657933 "UPXSCCA" 2658501 UPXSCCA (NIL T T) -9 NIL 2658733 NIL) (-1163 2650106 2650208 2650380 "UPXSCCA-" NIL UPXSCCA- (NIL T T T) -7 NIL NIL NIL) (-1162 2638658 2645870 2645912 "UPXSCAT" 2646552 UPXSCAT (NIL T) -9 NIL 2647160 NIL) (-1161 2638171 2638256 2638433 "UPXS2" NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1160 2629857 2637762 2638024 "UPXS" NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1159 2628752 2629022 2629372 "UPSQFREE" NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1158 2621455 2624940 2624994 "UPSCAT" 2626063 UPSCAT (NIL T T) -9 NIL 2626827 NIL) (-1157 2620875 2621127 2621450 "UPSCAT-" NIL UPSCAT- (NIL T T T) -7 NIL NIL NIL) (-1156 2620549 2620598 2620729 "UPOLYC2" NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1155 2604679 2613633 2613675 "UPOLYC" 2615753 UPOLYC (NIL T) -9 NIL 2616973 NIL) (-1154 2598734 2601582 2604674 "UPOLYC-" NIL UPOLYC- (NIL T T) -7 NIL NIL NIL) (-1153 2598170 2598295 2598458 "UPMP" NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1152 2597804 2597891 2598030 "UPDIVP" NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1151 2596617 2596884 2597188 "UPDECOMP" NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1150 2595950 2596080 2596265 "UPCDEN" NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1149 2595542 2595617 2595764 "UP2" NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1148 2586306 2595308 2595436 "UP" NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1147 2585668 2585805 2586010 "UNISEG2" NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1146 2584269 2585116 2585392 "UNISEG" NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1145 2583498 2583695 2583920 "UNIFACT" NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1144 2570308 2583422 2583493 "ULSCONS" NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1143 2550114 2563349 2563410 "ULSCCAT" 2564041 ULSCCAT (NIL T T) -9 NIL 2564328 NIL) (-1142 2549449 2549735 2550109 "ULSCCAT-" NIL ULSCCAT- (NIL T T T) -7 NIL NIL NIL) (-1141 2537821 2544955 2544997 "ULSCAT" 2545850 ULSCAT (NIL T) -9 NIL 2546580 NIL) (-1140 2537334 2537419 2537596 "ULS2" NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1139 2519451 2536833 2537074 "ULS" NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1138 2518485 2519178 2519292 "UINT8" NIL UINT8 (NIL) -8 NIL NIL 2519403) (-1137 2517518 2518211 2518325 "UINT64" NIL UINT64 (NIL) -8 NIL NIL 2518436) (-1136 2516551 2517244 2517358 "UINT32" NIL UINT32 (NIL) -8 NIL NIL 2517469) (-1135 2515584 2516277 2516391 "UINT16" NIL UINT16 (NIL) -8 NIL NIL 2516502) (-1134 2513591 2514812 2514842 "UFD" 2515053 UFD (NIL) -9 NIL 2515166 NIL) (-1133 2513435 2513492 2513586 "UFD-" NIL UFD- (NIL T) -7 NIL NIL NIL) (-1132 2512687 2512894 2513110 "UDVO" NIL UDVO (NIL) -7 NIL NIL NIL) (-1131 2510907 2511360 2511825 "UDPO" NIL UDPO (NIL T) -7 NIL NIL NIL) (-1130 2510632 2510872 2510902 "TYPEAST" NIL TYPEAST (NIL) -8 NIL NIL NIL) (-1129 2510570 2510575 2510605 "TYPE" 2510610 TYPE (NIL) -9 NIL 2510617 NIL) (-1128 2509729 2509949 2510189 "TWOFACT" NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1127 2508907 2509338 2509573 "TUPLE" NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1126 2507061 2507634 2508173 "TUBETOOL" NIL TUBETOOL (NIL) -7 NIL NIL NIL) (-1125 2506095 2506331 2506567 "TUBE" NIL TUBE (NIL T) -8 NIL NIL NIL) (-1124 2494712 2498888 2498984 "TSETCAT" 2504199 TSETCAT (NIL T T T T) -9 NIL 2505703 NIL) (-1123 2491049 2492865 2494707 "TSETCAT-" NIL TSETCAT- (NIL T T T T T) -7 NIL NIL NIL) (-1122 2485441 2490275 2490557 "TS" NIL TS (NIL T) -8 NIL NIL NIL) (-1121 2480778 2481791 2482720 "TRMANIP" NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1120 2480275 2480350 2480513 "TRIMAT" NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1119 2478351 2478641 2478996 "TRIGMNIP" NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1118 2477835 2477984 2478014 "TRIGCAT" 2478227 TRIGCAT (NIL) -9 NIL NIL NIL) (-1117 2477586 2477689 2477830 "TRIGCAT-" NIL TRIGCAT- (NIL T) -7 NIL NIL NIL) (-1116 2474641 2476692 2476973 "TREE" NIL TREE (NIL T) -8 NIL NIL NIL) (-1115 2473747 2474443 2474473 "TRANFUN" 2474508 TRANFUN (NIL) -9 NIL 2474574 NIL) (-1114 2473211 2473462 2473742 "TRANFUN-" NIL TRANFUN- (NIL T) -7 NIL NIL NIL) (-1113 2473048 2473086 2473147 "TOPSP" NIL TOPSP (NIL) -7 NIL NIL NIL) (-1112 2472505 2472636 2472787 "TOOLSIGN" NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1111 2471246 2471903 2472139 "TEXTFILE" NIL TEXTFILE (NIL) -8 NIL NIL NIL) (-1110 2471058 2471095 2471167 "TEX1" NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1109 2469272 2469918 2470347 "TEX" NIL TEX (NIL) -8 NIL NIL NIL) (-1108 2467652 2467989 2468311 "TBCMPPK" NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1107 2457594 2465432 2465488 "TBAGG" 2465805 TBAGG (NIL T T) -9 NIL 2466015 NIL) (-1106 2454784 2456143 2457589 "TBAGG-" NIL TBAGG- (NIL T T T) -7 NIL NIL NIL) (-1105 2454261 2454386 2454531 "TANEXP" NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1104 2453771 2454091 2454181 "TALGOP" NIL TALGOP (NIL T) -8 NIL NIL NIL) (-1103 2453268 2453385 2453523 "TABLEAU" NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1102 2445633 2453196 2453263 "TABLE" NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1101 2441386 2442681 2443926 "TABLBUMP" NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1100 2440755 2440914 2441095 "SYSTEM" NIL SYSTEM (NIL) -7 NIL NIL NIL) (-1099 2437909 2438662 2439445 "SYSSOLP" NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1098 2437683 2437873 2437904 "SYSPTR" NIL SYSPTR (NIL) -8 NIL NIL NIL) (-1097 2436637 2437322 2437448 "SYSNNI" NIL SYSNNI (NIL NIL) -8 NIL NIL 2437634) (-1096 2435901 2436449 2436528 "SYSINT" NIL SYSINT (NIL NIL) -8 NIL NIL 2436588) (-1095 2432724 2433883 2434583 "SYNTAX" NIL SYNTAX (NIL) -8 NIL NIL NIL) (-1094 2430407 2431090 2431724 "SYMTAB" NIL SYMTAB (NIL) -8 NIL NIL NIL) (-1093 2426485 2427531 2428508 "SYMS" NIL SYMS (NIL) -8 NIL NIL NIL) (-1092 2423584 2426140 2426369 "SYMPOLY" NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1091 2423180 2423267 2423389 "SYMFUNC" NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1090 2419804 2421278 2422097 "SYMBOL" NIL SYMBOL (NIL) -8 NIL NIL NIL) (-1089 2412764 2419001 2419294 "SUTS" NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1088 2404450 2412355 2412617 "SUPXS" NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1087 2403729 2403868 2404085 "SUPFRACF" NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1086 2403413 2403478 2403589 "SUP2" NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1085 2394136 2403125 2403250 "SUP" NIL SUP (NIL T) -8 NIL NIL NIL) (-1084 2392866 2393164 2393519 "SUMRF" NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1083 2392271 2392349 2392540 "SUMFS" NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1082 2374423 2391770 2392011 "SULS" NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1081 2374022 2374294 2374363 "SUCHTAST" NIL SUCHTAST (NIL) -8 NIL NIL NIL) (-1080 2373358 2373639 2373779 "SUCH" NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1079 2367960 2369219 2370172 "SUBSPACE" NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1078 2367492 2367592 2367756 "SUBRESP" NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1077 2362603 2363885 2365032 "STTFNC" NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1076 2357061 2358532 2359843 "STTF" NIL STTF (NIL T) -7 NIL NIL NIL) (-1075 2349976 2352040 2353831 "STTAYLOR" NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1074 2342004 2349914 2349971 "STRTBL" NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1073 2336961 2341718 2341833 "STRING" NIL STRING (NIL) -8 NIL NIL NIL) (-1072 2336548 2336631 2336775 "STREAM3" NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1071 2335699 2335900 2336135 "STREAM2" NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1070 2335439 2335497 2335590 "STREAM1" NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1069 2328916 2333642 2334250 "STREAM" NIL STREAM (NIL T) -8 NIL NIL NIL) (-1068 2328092 2328297 2328528 "STINPROD" NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1067 2327337 2327708 2327855 "STEPAST" NIL STEPAST (NIL) -8 NIL NIL NIL) (-1066 2326825 2327067 2327097 "STEP" 2327191 STEP (NIL) -9 NIL 2327262 NIL) (-1065 2319184 2326743 2326820 "STBL" NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1064 2314113 2317982 2318025 "STAGG" 2318452 STAGG (NIL T) -9 NIL 2318626 NIL) (-1063 2312492 2313240 2314108 "STAGG-" NIL STAGG- (NIL T T) -7 NIL NIL NIL) (-1062 2310713 2312319 2312411 "STACK" NIL STACK (NIL T) -8 NIL NIL NIL) (-1061 2309993 2310532 2310562 "SRING" 2310567 SRING (NIL) -9 NIL 2310587 NIL) (-1060 2302908 2308531 2308970 "SREGSET" NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1059 2296682 2298121 2299625 "SRDCMPK" NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1058 2289328 2293977 2294007 "SRAGG" 2295306 SRAGG (NIL) -9 NIL 2295910 NIL) (-1057 2288625 2288945 2289323 "SRAGG-" NIL SRAGG- (NIL T) -7 NIL NIL NIL) (-1056 2282725 2287947 2288370 "SQMATRIX" NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1055 2276737 2280078 2280829 "SPLTREE" NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1054 2273166 2273985 2274622 "SPLNODE" NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1053 2272141 2272446 2272476 "SPFCAT" 2272920 SPFCAT (NIL) -9 NIL NIL NIL) (-1052 2271078 2271330 2271594 "SPECOUT" NIL SPECOUT (NIL) -7 NIL NIL NIL) (-1051 2261836 2264110 2264140 "SPADXPT" 2268777 SPADXPT (NIL) -9 NIL 2270901 NIL) (-1050 2261638 2261684 2261753 "SPADPRSR" NIL SPADPRSR (NIL) -7 NIL NIL NIL) (-1049 2259294 2261602 2261633 "SPADAST" NIL SPADAST (NIL) -8 NIL NIL NIL) (-1048 2250968 2253057 2253099 "SPACEC" 2257414 SPACEC (NIL T) -9 NIL 2259219 NIL) (-1047 2248797 2250915 2250963 "SPACE3" NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1046 2247776 2247965 2248248 "SORTPAK" NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1045 2246180 2246513 2246924 "SOLVETRA" NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1044 2245445 2245679 2245940 "SOLVESER" NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1043 2241625 2242585 2243580 "SOLVERAD" NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1042 2237983 2238682 2239411 "SOLVEFOR" NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1041 2232024 2237286 2237382 "SNTSCAT" 2237387 SNTSCAT (NIL T T T T) -9 NIL 2237457 NIL) (-1040 2225845 2230665 2231055 "SMTS" NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1039 2219617 2225764 2225840 "SMP" NIL SMP (NIL T T) -8 NIL NIL NIL) (-1038 2218049 2218380 2218778 "SMITH" NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1037 2209681 2214615 2214717 "SMATCAT" 2216060 SMATCAT (NIL NIL T T T) -9 NIL 2216608 NIL) (-1036 2207522 2208506 2209676 "SMATCAT-" NIL SMATCAT- (NIL T NIL T T T) -7 NIL NIL NIL) (-1035 2206128 2206980 2207023 "SMAGG" 2207108 SMAGG (NIL T) -9 NIL 2207183 NIL) (-1034 2203747 2205295 2205338 "SKAGG" 2205599 SKAGG (NIL T) -9 NIL 2205735 NIL) (-1033 2199793 2203567 2203678 "SINT" NIL SINT (NIL) -8 NIL NIL 2203719) (-1032 2199603 2199647 2199713 "SIMPAN" NIL SIMPAN (NIL) -7 NIL NIL NIL) (-1031 2198678 2198910 2199178 "SIGNRF" NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1030 2197682 2197844 2198120 "SIGNEF" NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1029 2197028 2197368 2197491 "SIGAST" NIL SIGAST (NIL) -8 NIL NIL NIL) (-1028 2196374 2196681 2196821 "SIG" NIL SIG (NIL) -8 NIL NIL NIL) (-1027 2194485 2194977 2195483 "SHP" NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1026 2187971 2194404 2194480 "SHDP" NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1025 2187474 2187711 2187741 "SGROUP" 2187834 SGROUP (NIL) -9 NIL 2187896 NIL) (-1024 2187364 2187396 2187469 "SGROUP-" NIL SGROUP- (NIL T) -7 NIL NIL NIL) (-1023 2187002 2187042 2187083 "SGPOPC" 2187088 SGPOPC (NIL T) -9 NIL 2187289 NIL) (-1022 2186536 2186813 2186919 "SGPOP" NIL SGPOP (NIL T) -8 NIL NIL NIL) (-1021 2183959 2184728 2185450 "SGCF" NIL SGCF (NIL) -7 NIL NIL NIL) (-1020 2178099 2183361 2183457 "SFRTCAT" 2183462 SFRTCAT (NIL T T T T) -9 NIL 2183500 NIL) (-1019 2172491 2173604 2174731 "SFRGCD" NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1018 2166667 2167828 2168992 "SFQCMPK" NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1017 2165639 2166541 2166662 "SEXOF" NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1016 2161247 2162142 2162237 "SEXCAT" 2164850 SEXCAT (NIL T T T T T) -9 NIL 2165401 NIL) (-1015 2160220 2161174 2161242 "SEX" NIL SEX (NIL) -8 NIL NIL NIL) (-1014 2158611 2159196 2159498 "SETMN" NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1013 2158134 2158319 2158349 "SETCAT" 2158466 SETCAT (NIL) -9 NIL 2158550 NIL) (-1012 2157966 2158030 2158129 "SETCAT-" NIL SETCAT- (NIL T) -7 NIL NIL NIL) (-1011 2154919 2156420 2156463 "SETAGG" 2157331 SETAGG (NIL T) -9 NIL 2157669 NIL) (-1010 2154525 2154677 2154914 "SETAGG-" NIL SETAGG- (NIL T T) -7 NIL NIL NIL) (-1009 2151770 2154472 2154520 "SET" NIL SET (NIL T) -8 NIL NIL NIL) (-1008 2151236 2151546 2151646 "SEQAST" NIL SEQAST (NIL) -8 NIL NIL NIL) (-1007 2150363 2150729 2150790 "SEGXCAT" 2151076 SEGXCAT (NIL T T) -9 NIL 2151196 NIL) (-1006 2149288 2149556 2149599 "SEGCAT" 2150121 SEGCAT (NIL T) -9 NIL 2150342 NIL) (-1005 2148968 2149033 2149146 "SEGBIND2" NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1004 2148034 2148504 2148712 "SEGBIND" NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1003 2147612 2147891 2147967 "SEGAST" NIL SEGAST (NIL) -8 NIL NIL NIL) (-1002 2146977 2147113 2147317 "SEG2" NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1001 2146043 2146790 2146972 "SEG" NIL SEG (NIL T) -8 NIL NIL NIL) (-1000 2145296 2145991 2146038 "SDVAR" NIL SDVAR (NIL T) -8 NIL NIL NIL) (-999 2136783 2145165 2145291 "SDPOL" NIL SDPOL (NIL T) -8 NIL NIL NIL) (-998 2135643 2135933 2136250 "SCPKG" NIL SCPKG (NIL T) -7 NIL NIL NIL) (-997 2134949 2135161 2135349 "SCOPE" NIL SCOPE (NIL) -8 NIL NIL NIL) (-996 2134299 2134456 2134632 "SCACHE" NIL SCACHE (NIL T) -7 NIL NIL NIL) (-995 2133872 2134103 2134131 "SASTCAT" 2134136 SASTCAT (NIL) -9 NIL 2134149 NIL) (-994 2133339 2133764 2133838 "SAOS" NIL SAOS (NIL) -8 NIL NIL NIL) (-993 2132942 2132983 2133154 "SAERFFC" NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-992 2132573 2132614 2132771 "SAEFACT" NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-991 2125654 2132490 2132568 "SAE" NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-990 2124304 2124633 2125029 "RURPK" NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-989 2123065 2123426 2123726 "RULESET" NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-988 2122689 2122910 2122991 "RULECOLD" NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-987 2120149 2120783 2121236 "RULE" NIL RULE (NIL T T T) -8 NIL NIL NIL) (-986 2119988 2120021 2120089 "RTVALUE" NIL RTVALUE (NIL) -8 NIL NIL NIL) (-985 2119479 2119782 2119873 "RSTRCAST" NIL RSTRCAST (NIL) -8 NIL NIL NIL) (-984 2115107 2115975 2116886 "RSETGCD" NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-983 2104181 2109443 2109537 "RSETCAT" 2113593 RSETCAT (NIL T T T T) -9 NIL 2114681 NIL) (-982 2102719 2103361 2104176 "RSETCAT-" NIL RSETCAT- (NIL T T T T T) -7 NIL NIL NIL) (-981 2096493 2097938 2099445 "RSDCMPK" NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-980 2094375 2094932 2095004 "RRCC" 2096077 RRCC (NIL T T) -9 NIL 2096418 NIL) (-979 2093900 2094099 2094370 "RRCC-" NIL RRCC- (NIL T T T) -7 NIL NIL NIL) (-978 2093370 2093680 2093778 "RPTAST" NIL RPTAST (NIL) -8 NIL NIL NIL) (-977 2065922 2076635 2076699 "RPOLCAT" 2087173 RPOLCAT (NIL T T T) -9 NIL 2090318 NIL) (-976 2060021 2062844 2065917 "RPOLCAT-" NIL RPOLCAT- (NIL T T T T) -7 NIL NIL NIL) (-975 2056188 2059769 2059907 "ROMAN" NIL ROMAN (NIL) -8 NIL NIL NIL) (-974 2054516 2055255 2055511 "ROIRC" NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-973 2050159 2052971 2052999 "RNS" 2053261 RNS (NIL) -9 NIL 2053513 NIL) (-972 2049062 2049549 2050086 "RNS-" NIL RNS- (NIL T) -7 NIL NIL NIL) (-971 2048180 2048581 2048781 "RNGBIND" NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-970 2047318 2047880 2047908 "RNG" 2047968 RNG (NIL) -9 NIL 2048022 NIL) (-969 2047207 2047241 2047313 "RNG-" NIL RNG- (NIL T) -7 NIL NIL NIL) (-968 2046469 2046974 2047014 "RMODULE" 2047019 RMODULE (NIL T) -9 NIL 2047045 NIL) (-967 2045408 2045514 2045844 "RMCAT2" NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-966 2042299 2044998 2045291 "RMATRIX" NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-965 2034988 2037433 2037545 "RMATCAT" 2040850 RMATCAT (NIL NIL NIL T T T) -9 NIL 2041816 NIL) (-964 2034505 2034684 2034983 "RMATCAT-" NIL RMATCAT- (NIL T NIL NIL T T T) -7 NIL NIL NIL) (-963 2034073 2034284 2034325 "RLINSET" 2034386 RLINSET (NIL T) -9 NIL 2034430 NIL) (-962 2033718 2033799 2033925 "RINTERP" NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-961 2032564 2033295 2033323 "RING" 2033378 RING (NIL) -9 NIL 2033470 NIL) (-960 2032409 2032465 2032559 "RING-" NIL RING- (NIL T) -7 NIL NIL NIL) (-959 2031463 2031730 2031986 "RIDIST" NIL RIDIST (NIL) -7 NIL NIL NIL) (-958 2022687 2031091 2031292 "RGCHAIN" NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-957 2021912 2022423 2022462 "RGBCSPC" 2022519 RGBCSPC (NIL T) -9 NIL 2022570 NIL) (-956 2020946 2021432 2021471 "RGBCMDL" 2021699 RGBCMDL (NIL T) -9 NIL 2021813 NIL) (-955 2020658 2020727 2020828 "RFFACTOR" NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-954 2020421 2020462 2020557 "RFFACT" NIL RFFACT (NIL T) -7 NIL NIL NIL) (-953 2018845 2019275 2019655 "RFDIST" NIL RFDIST (NIL) -7 NIL NIL NIL) (-952 2016432 2017100 2017768 "RF" NIL RF (NIL T) -7 NIL NIL NIL) (-951 2015982 2016080 2016240 "RETSOL" NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-950 2015604 2015702 2015743 "RETRACT" 2015874 RETRACT (NIL T) -9 NIL 2015961 NIL) (-949 2015484 2015515 2015599 "RETRACT-" NIL RETRACT- (NIL T T) -7 NIL NIL NIL) (-948 2015086 2015358 2015425 "RETAST" NIL RETAST (NIL) -8 NIL NIL NIL) (-947 2013566 2014457 2014654 "RESRING" NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-946 2013257 2013318 2013414 "RESLATC" NIL RESLATC (NIL T) -7 NIL NIL NIL) (-945 2013000 2013041 2013146 "REPSQ" NIL REPSQ (NIL T) -7 NIL NIL NIL) (-944 2012735 2012776 2012885 "REPDB" NIL REPDB (NIL T) -7 NIL NIL NIL) (-943 2007806 2009257 2010472 "REP2" NIL REP2 (NIL T) -7 NIL NIL NIL) (-942 2004905 2005663 2006471 "REP1" NIL REP1 (NIL T) -7 NIL NIL NIL) (-941 2002874 2003496 2004096 "REP" NIL REP (NIL) -7 NIL NIL NIL) (-940 1995802 2001425 2001861 "REGSET" NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-939 1995114 1995394 1995543 "REF" NIL REF (NIL T) -8 NIL NIL NIL) (-938 1994599 1994714 1994879 "REDORDER" NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-937 1990192 1994002 1994223 "RECLOS" NIL RECLOS (NIL T) -8 NIL NIL NIL) (-936 1989424 1989623 1989836 "REALSOLV" NIL REALSOLV (NIL) -7 NIL NIL NIL) (-935 1986714 1987552 1988434 "REAL0Q" NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-934 1983296 1984332 1985391 "REAL0" NIL REAL0 (NIL T) -7 NIL NIL NIL) (-933 1983132 1983185 1983213 "REAL" 1983218 REAL (NIL) -9 NIL 1983253 NIL) (-932 1982622 1982926 1983017 "RDUCEAST" NIL RDUCEAST (NIL) -8 NIL NIL NIL) (-931 1982102 1982180 1982385 "RDIV" NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-930 1981335 1981527 1981738 "RDIST" NIL RDIST (NIL T) -7 NIL NIL NIL) (-929 1980223 1980520 1980887 "RDETRS" NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-928 1978490 1978960 1979493 "RDETR" NIL RDETR (NIL T T) -7 NIL NIL NIL) (-927 1977412 1977689 1978076 "RDEEFS" NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-926 1976239 1976548 1976967 "RDEEF" NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-925 1969587 1973099 1973127 "RCFIELD" 1974404 RCFIELD (NIL) -9 NIL 1975134 NIL) (-924 1968205 1968817 1969514 "RCFIELD-" NIL RCFIELD- (NIL T) -7 NIL NIL NIL) (-923 1964918 1966309 1966350 "RCAGG" 1967404 RCAGG (NIL T) -9 NIL 1967866 NIL) (-922 1964645 1964755 1964913 "RCAGG-" NIL RCAGG- (NIL T T) -7 NIL NIL NIL) (-921 1964090 1964219 1964380 "RATRET" NIL RATRET (NIL T) -7 NIL NIL NIL) (-920 1963707 1963786 1963905 "RATFACT" NIL RATFACT (NIL T) -7 NIL NIL NIL) (-919 1963122 1963272 1963422 "RANDSRC" NIL RANDSRC (NIL) -7 NIL NIL NIL) (-918 1962904 1962954 1963025 "RADUTIL" NIL RADUTIL (NIL) -7 NIL NIL NIL) (-917 1955346 1962022 1962330 "RADIX" NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-916 1945048 1955213 1955341 "RADFF" NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-915 1944682 1944775 1944803 "RADCAT" 1944960 RADCAT (NIL) -9 NIL NIL NIL) (-914 1944520 1944580 1944677 "RADCAT-" NIL RADCAT- (NIL T) -7 NIL NIL NIL) (-913 1942684 1944351 1944440 "QUEUE" NIL QUEUE (NIL T) -8 NIL NIL NIL) (-912 1942365 1942414 1942541 "QUATCT2" NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-911 1934652 1938736 1938776 "QUATCAT" 1939554 QUATCAT (NIL T) -9 NIL 1940318 NIL) (-910 1931902 1933182 1934558 "QUATCAT-" NIL QUATCAT- (NIL T T) -7 NIL NIL NIL) (-909 1927742 1931852 1931897 "QUAT" NIL QUAT (NIL T) -8 NIL NIL NIL) (-908 1925156 1926757 1926798 "QUAGG" 1927173 QUAGG (NIL T) -9 NIL 1927349 NIL) (-907 1924758 1925030 1925097 "QQUTAST" NIL QQUTAST (NIL) -8 NIL NIL NIL) (-906 1923764 1924394 1924557 "QFORM" NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-905 1923445 1923494 1923621 "QFCAT2" NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-904 1913045 1919214 1919254 "QFCAT" 1919912 QFCAT (NIL T) -9 NIL 1920905 NIL) (-903 1909929 1911368 1912951 "QFCAT-" NIL QFCAT- (NIL T T) -7 NIL NIL NIL) (-902 1909475 1909609 1909739 "QEQUAT" NIL QEQUAT (NIL) -8 NIL NIL NIL) (-901 1903671 1904832 1905994 "QCMPACK" NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-900 1903090 1903270 1903502 "QALGSET2" NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-899 1900912 1901440 1901863 "QALGSET" NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-898 1899811 1900053 1900370 "PWFFINTB" NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-897 1898172 1898370 1898723 "PUSHVAR" NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-896 1893928 1895144 1895185 "PTRANFN" 1897069 PTRANFN (NIL T) -9 NIL NIL NIL) (-895 1892575 1892920 1893241 "PTPACK" NIL PTPACK (NIL T) -7 NIL NIL NIL) (-894 1892268 1892331 1892438 "PTFUNC2" NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-893 1886594 1891027 1891067 "PTCAT" 1891359 PTCAT (NIL T) -9 NIL 1891512 NIL) (-892 1886287 1886328 1886452 "PSQFR" NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-891 1885166 1885482 1885816 "PSEUDLIN" NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-890 1874045 1876606 1878915 "PSETPK" NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-889 1867206 1869828 1869922 "PSETCAT" 1872896 PSETCAT (NIL T T T T) -9 NIL 1873705 NIL) (-888 1865656 1866390 1867201 "PSETCAT-" NIL PSETCAT- (NIL T T T T T) -7 NIL NIL NIL) (-887 1864975 1865170 1865198 "PSCURVE" 1865466 PSCURVE (NIL) -9 NIL 1865633 NIL) (-886 1860577 1862397 1862461 "PSCAT" 1863296 PSCAT (NIL T T T) -9 NIL 1863535 NIL) (-885 1859891 1860173 1860572 "PSCAT-" NIL PSCAT- (NIL T T T T) -7 NIL NIL NIL) (-884 1858288 1859203 1859466 "PRTITION" NIL PRTITION (NIL) -8 NIL NIL NIL) (-883 1857779 1858082 1858173 "PRTDAST" NIL PRTDAST (NIL) -8 NIL NIL NIL) (-882 1848799 1851221 1853409 "PRS" NIL PRS (NIL T T) -7 NIL NIL NIL) (-881 1846569 1848080 1848120 "PRQAGG" 1848303 PRQAGG (NIL T) -9 NIL 1848406 NIL) (-880 1845742 1846188 1846216 "PROPLOG" 1846355 PROPLOG (NIL) -9 NIL 1846469 NIL) (-879 1845417 1845480 1845603 "PROPFUN2" NIL PROPFUN2 (NIL T T) -7 NIL NIL NIL) (-878 1844853 1844992 1845164 "PROPFUN1" NIL PROPFUN1 (NIL T) -7 NIL NIL NIL) (-877 1843101 1843864 1844161 "PROPFRML" NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-876 1842653 1842785 1842913 "PROPERTY" NIL PROPERTY (NIL) -8 NIL NIL NIL) (-875 1837094 1841593 1842413 "PRODUCT" NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-874 1836923 1836961 1837020 "PRINT" NIL PRINT (NIL) -7 NIL NIL NIL) (-873 1836362 1836502 1836653 "PRIMES" NIL PRIMES (NIL T) -7 NIL NIL NIL) (-872 1834830 1835249 1835715 "PRIMELT" NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-871 1834547 1834608 1834636 "PRIMCAT" 1834760 PRIMCAT (NIL) -9 NIL NIL NIL) (-870 1833718 1833914 1834142 "PRIMARR2" NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-869 1829883 1833668 1833713 "PRIMARR" NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-868 1829582 1829644 1829755 "PREASSOC" NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-867 1826718 1829231 1829464 "PR" NIL PR (NIL T T) -8 NIL NIL NIL) (-866 1826169 1826326 1826354 "PPCURVE" 1826559 PPCURVE (NIL) -9 NIL 1826695 NIL) (-865 1825782 1826027 1826110 "PORTNUM" NIL PORTNUM (NIL) -8 NIL NIL NIL) (-864 1823538 1823959 1824551 "POLYROOT" NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-863 1822981 1823045 1823278 "POLYLIFT" NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-862 1819701 1820187 1820798 "POLYCATQ" NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-861 1805292 1811421 1811485 "POLYCAT" 1814970 POLYCAT (NIL T T T) -9 NIL 1816847 NIL) (-860 1800802 1802949 1805287 "POLYCAT-" NIL POLYCAT- (NIL T T T T) -7 NIL NIL NIL) (-859 1800459 1800533 1800652 "POLY2UP" NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-858 1800152 1800215 1800322 "POLY2" NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-857 1793515 1799885 1800044 "POLY" NIL POLY (NIL T) -8 NIL NIL NIL) (-856 1792402 1792665 1792941 "POLUTIL" NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-855 1791006 1791319 1791649 "POLTOPOL" NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-854 1786459 1790956 1791001 "POINT" NIL POINT (NIL T) -8 NIL NIL NIL) (-853 1784947 1785358 1785733 "PNTHEORY" NIL PNTHEORY (NIL) -7 NIL NIL NIL) (-852 1783704 1784013 1784409 "PMTOOLS" NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-851 1783375 1783459 1783576 "PMSYM" NIL PMSYM (NIL T) -7 NIL NIL NIL) (-850 1782954 1783029 1783203 "PMQFCAT" NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-849 1782440 1782536 1782696 "PMPREDFS" NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-848 1781912 1782032 1782186 "PMPRED" NIL PMPRED (NIL T) -7 NIL NIL NIL) (-847 1780807 1781025 1781402 "PMPLCAT" NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-846 1780418 1780503 1780655 "PMLSAGG" NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-845 1779969 1780051 1780232 "PMKERNEL" NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-844 1779661 1779742 1779855 "PMINS" NIL PMINS (NIL T) -7 NIL NIL NIL) (-843 1779174 1779249 1779457 "PMFS" NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-842 1778522 1778650 1778852 "PMDOWN" NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-841 1777884 1778018 1778181 "PMASSFS" NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-840 1777188 1777370 1777551 "PMASS" NIL PMASS (NIL) -7 NIL NIL NIL) (-839 1776911 1776985 1777079 "PLOTTOOL" NIL PLOTTOOL (NIL) -7 NIL NIL NIL) (-838 1773479 1774668 1775584 "PLOT3D" NIL PLOT3D (NIL) -8 NIL NIL NIL) (-837 1772563 1772764 1772999 "PLOT1" NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-836 1768128 1769512 1770654 "PLOT" NIL PLOT (NIL) -8 NIL NIL NIL) (-835 1748049 1752936 1757783 "PLEQN" NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-834 1747789 1747842 1747945 "PINTERPA" NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-833 1747230 1747364 1747544 "PINTERP" NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-832 1745239 1746460 1746488 "PID" 1746685 PID (NIL) -9 NIL 1746812 NIL) (-831 1745027 1745070 1745145 "PICOERCE" NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-830 1744214 1744874 1744961 "PI" NIL PI (NIL) -8 NIL NIL 1745001) (-829 1743666 1743817 1743993 "PGROEB" NIL PGROEB (NIL T) -7 NIL NIL NIL) (-828 1739994 1740952 1741857 "PGE" NIL PGE (NIL) -7 NIL NIL NIL) (-827 1738358 1738647 1739013 "PGCD" NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-826 1737800 1737915 1738076 "PFRPAC" NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-825 1734341 1736669 1737022 "PFR" NIL PFR (NIL T) -8 NIL NIL NIL) (-824 1732947 1733227 1733552 "PFOTOOLS" NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-823 1731712 1731966 1732314 "PFOQ" NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-822 1730422 1730649 1731001 "PFO" NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-821 1727432 1728992 1729020 "PFECAT" 1729613 PFECAT (NIL) -9 NIL 1729990 NIL) (-820 1727055 1727220 1727427 "PFECAT-" NIL PFECAT- (NIL T) -7 NIL NIL NIL) (-819 1725879 1726161 1726462 "PFBRU" NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-818 1724061 1724448 1724878 "PFBR" NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-817 1720031 1723987 1724056 "PF" NIL PF (NIL NIL) -8 NIL NIL NIL) (-816 1715934 1717081 1717948 "PERMGRP" NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-815 1713866 1714955 1714996 "PERMCAT" 1715395 PERMCAT (NIL T) -9 NIL 1715692 NIL) (-814 1713562 1713609 1713732 "PERMAN" NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-813 1710011 1711692 1712337 "PERM" NIL PERM (NIL T) -8 NIL NIL NIL) (-812 1707977 1709766 1709887 "PENDTREE" NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-811 1706846 1707109 1707150 "PDSPC" 1707683 PDSPC (NIL T) -9 NIL 1707928 NIL) (-810 1706213 1706479 1706841 "PDSPC-" NIL PDSPC- (NIL T T) -7 NIL NIL NIL) (-809 1704848 1705841 1705882 "PDRING" 1705887 PDRING (NIL T) -9 NIL 1705914 NIL) (-808 1703558 1704347 1704400 "PDMOD" 1704405 PDMOD (NIL T T) -9 NIL 1704508 NIL) (-807 1702651 1702863 1703112 "PDECOMP" NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-806 1702256 1702323 1702377 "PDDOM" 1702542 PDDOM (NIL T T) -9 NIL 1702622 NIL) (-805 1702108 1702144 1702251 "PDDOM-" NIL PDDOM- (NIL T T T) -7 NIL NIL NIL) (-804 1701894 1701933 1702022 "PCOMP" NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-803 1700211 1700965 1701264 "PBWLB" NIL PBWLB (NIL T) -8 NIL NIL NIL) (-802 1699900 1699963 1700072 "PATTERN2" NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-801 1698038 1698468 1698919 "PATTERN1" NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-800 1691658 1693487 1694779 "PATTERN" NIL PATTERN (NIL T) -8 NIL NIL NIL) (-799 1691289 1691362 1691494 "PATRES2" NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-798 1688991 1689671 1690152 "PATRES" NIL PATRES (NIL T T) -8 NIL NIL NIL) (-797 1687195 1687623 1688026 "PATMATCH" NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-796 1686641 1686889 1686930 "PATMAB" 1687037 PATMAB (NIL T) -9 NIL 1687120 NIL) (-795 1685288 1685692 1685949 "PATLRES" NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-794 1684826 1684957 1684998 "PATAB" 1685003 PATAB (NIL T) -9 NIL 1685175 NIL) (-793 1683369 1683806 1684229 "PARTPERM" NIL PARTPERM (NIL) -7 NIL NIL NIL) (-792 1683047 1683122 1683224 "PARSURF" NIL PARSURF (NIL T) -8 NIL NIL NIL) (-791 1682736 1682799 1682908 "PARSU2" NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-790 1682541 1682587 1682654 "PARSER" NIL PARSER (NIL) -7 NIL NIL NIL) (-789 1682219 1682294 1682396 "PARSCURV" NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-788 1681908 1681971 1682080 "PARSC2" NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-787 1681599 1681669 1681766 "PARPCURV" NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-786 1681288 1681351 1681460 "PARPC2" NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-785 1680449 1680828 1681007 "PARAMAST" NIL PARAMAST (NIL) -8 NIL NIL NIL) (-784 1680056 1680154 1680273 "PAN2EXPR" NIL PAN2EXPR (NIL) -7 NIL NIL NIL) (-783 1679024 1679449 1679668 "PALETTE" NIL PALETTE (NIL) -8 NIL NIL NIL) (-782 1677689 1678343 1678703 "PAIR" NIL PAIR (NIL T T) -8 NIL NIL NIL) (-781 1670779 1677093 1677287 "PADICRC" NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-780 1663200 1670277 1670461 "PADICRAT" NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-779 1659925 1661840 1661880 "PADICCT" 1662461 PADICCT (NIL NIL) -9 NIL 1662743 NIL) (-778 1657915 1659875 1659920 "PADIC" NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-777 1657077 1657287 1657553 "PADEPAC" NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-776 1656419 1656562 1656766 "PADE" NIL PADE (NIL T T T) -7 NIL NIL NIL) (-775 1654800 1655827 1656105 "OWP" NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-774 1654324 1654583 1654680 "OVERSET" NIL OVERSET (NIL) -8 NIL NIL NIL) (-773 1653383 1654061 1654233 "OVAR" NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-772 1643805 1646674 1648873 "OUTFORM" NIL OUTFORM (NIL) -8 NIL NIL NIL) (-771 1643197 1643511 1643637 "OUTBFILE" NIL OUTBFILE (NIL) -8 NIL NIL NIL) (-770 1642474 1642669 1642697 "OUTBCON" 1643015 OUTBCON (NIL) -9 NIL 1643181 NIL) (-769 1642182 1642312 1642469 "OUTBCON-" NIL OUTBCON- (NIL T) -7 NIL NIL NIL) (-768 1641563 1641708 1641869 "OUT" NIL OUT (NIL) -7 NIL NIL NIL) (-767 1640934 1641361 1641450 "OSI" NIL OSI (NIL) -8 NIL NIL NIL) (-766 1640349 1640764 1640792 "OSGROUP" 1640797 OSGROUP (NIL) -9 NIL 1640819 NIL) (-765 1639313 1639574 1639859 "ORTHPOL" NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-764 1636582 1639188 1639308 "OREUP" NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-763 1633723 1636333 1636459 "ORESUP" NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-762 1631741 1632269 1632829 "OREPCTO" NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-761 1625083 1627623 1627663 "OREPCAT" 1629984 OREPCAT (NIL T) -9 NIL 1631086 NIL) (-760 1623109 1624043 1625078 "OREPCAT-" NIL OREPCAT- (NIL T T) -7 NIL NIL NIL) (-759 1622306 1622577 1622605 "ORDTYPE" 1622910 ORDTYPE (NIL) -9 NIL 1623068 NIL) (-758 1621840 1622051 1622301 "ORDTYPE-" NIL ORDTYPE- (NIL T) -7 NIL NIL NIL) (-757 1621302 1621678 1621835 "ORDSTRCT" NIL ORDSTRCT (NIL T NIL) -8 NIL NIL NIL) (-756 1620796 1621159 1621187 "ORDSET" 1621192 ORDSET (NIL) -9 NIL 1621214 NIL) (-755 1619361 1620383 1620411 "ORDRING" 1620416 ORDRING (NIL) -9 NIL 1620444 NIL) (-754 1618609 1619166 1619194 "ORDMON" 1619199 ORDMON (NIL) -9 NIL 1619220 NIL) (-753 1617913 1618075 1618267 "ORDFUNS" NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-752 1617124 1617632 1617660 "ORDFIN" 1617725 ORDFIN (NIL) -9 NIL 1617799 NIL) (-751 1616518 1616657 1616843 "ORDCOMP2" NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-750 1613193 1615486 1615892 "ORDCOMP" NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-749 1612600 1612955 1613060 "OPSIG" NIL OPSIG (NIL) -8 NIL NIL NIL) (-748 1612408 1612453 1612519 "OPQUERY" NIL OPQUERY (NIL) -7 NIL NIL NIL) (-747 1611709 1611985 1612026 "OPERCAT" 1612237 OPERCAT (NIL T) -9 NIL 1612333 NIL) (-746 1611521 1611588 1611704 "OPERCAT-" NIL OPERCAT- (NIL T T) -7 NIL NIL NIL) (-745 1608887 1610323 1610819 "OP" NIL OP (NIL T) -8 NIL NIL NIL) (-744 1608308 1608435 1608609 "ONECOMP2" NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-743 1605209 1607447 1607813 "ONECOMP" NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-742 1602093 1604602 1604642 "OMSAGG" 1604703 OMSAGG (NIL T) -9 NIL 1604767 NIL) (-741 1600505 1601764 1601932 "OMLO" NIL OMLO (NIL T T) -8 NIL NIL NIL) (-740 1598701 1599942 1599970 "OINTDOM" 1599975 OINTDOM (NIL) -9 NIL 1599996 NIL) (-739 1596131 1597703 1598032 "OFMONOID" NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-738 1595385 1596081 1596126 "ODVAR" NIL ODVAR (NIL T) -8 NIL NIL NIL) (-737 1592587 1595226 1595380 "ODR" NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-736 1584124 1592458 1592582 "ODPOL" NIL ODPOL (NIL T) -8 NIL NIL NIL) (-735 1577581 1584015 1584119 "ODP" NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-734 1576553 1576790 1577063 "ODETOOLS" NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-733 1574187 1574857 1575561 "ODESYS" NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-732 1569964 1570924 1571947 "ODERTRIC" NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-731 1569472 1569560 1569754 "ODERED" NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-730 1566921 1567503 1568176 "ODERAT" NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-729 1564316 1564824 1565420 "ODEPRRIC" NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-728 1561313 1561852 1562498 "ODEPRIM" NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-727 1560668 1560776 1561034 "ODEPAL" NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-726 1559826 1559951 1560172 "ODEINT" NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-725 1556110 1556906 1557819 "ODEEF" NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-724 1555550 1555645 1555867 "ODECONST" NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-723 1555231 1555280 1555407 "OCTCT2" NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-722 1551834 1555030 1555149 "OCT" NIL OCT (NIL T) -8 NIL NIL NIL) (-721 1550994 1551616 1551644 "OCAMON" 1551649 OCAMON (NIL) -9 NIL 1551670 NIL) (-720 1545206 1548020 1548060 "OC" 1549155 OC (NIL T) -9 NIL 1550011 NIL) (-719 1543206 1544132 1545112 "OC-" NIL OC- (NIL T T) -7 NIL NIL NIL) (-718 1542622 1543040 1543068 "OASGP" 1543073 OASGP (NIL) -9 NIL 1543093 NIL) (-717 1541685 1542334 1542362 "OAMONS" 1542402 OAMONS (NIL) -9 NIL 1542445 NIL) (-716 1540830 1541411 1541439 "OAMON" 1541496 OAMON (NIL) -9 NIL 1541547 NIL) (-715 1540726 1540758 1540825 "OAMON-" NIL OAMON- (NIL T) -7 NIL NIL NIL) (-714 1539477 1540251 1540279 "OAGROUP" 1540425 OAGROUP (NIL) -9 NIL 1540517 NIL) (-713 1539268 1539355 1539472 "OAGROUP-" NIL OAGROUP- (NIL T) -7 NIL NIL NIL) (-712 1539008 1539064 1539152 "NUMTUBE" NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-711 1534070 1535633 1537160 "NUMQUAD" NIL NUMQUAD (NIL) -7 NIL NIL NIL) (-710 1530765 1531799 1532834 "NUMODE" NIL NUMODE (NIL) -7 NIL NIL NIL) (-709 1529875 1530108 1530326 "NUMFMT" NIL NUMFMT (NIL) -7 NIL NIL NIL) (-708 1518736 1521764 1524212 "NUMERIC" NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-707 1512878 1518140 1518234 "NTSCAT" 1518239 NTSCAT (NIL T T T T) -9 NIL 1518277 NIL) (-706 1512219 1512398 1512591 "NTPOLFN" NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-705 1511912 1511975 1512082 "NSUP2" NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-704 1499579 1509532 1510342 "NSUP" NIL NSUP (NIL T) -8 NIL NIL NIL) (-703 1488588 1499444 1499574 "NSMP" NIL NSMP (NIL T T) -8 NIL NIL NIL) (-702 1487308 1487633 1487990 "NREP" NIL NREP (NIL T) -7 NIL NIL NIL) (-701 1486144 1486408 1486766 "NPCOEF" NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-700 1485311 1485444 1485660 "NORMRETR" NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-699 1483629 1483948 1484354 "NORMPK" NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-698 1483342 1483376 1483500 "NORMMA" NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-697 1483161 1483196 1483265 "NONE1" NIL NONE1 (NIL T) -7 NIL NIL NIL) (-696 1482937 1483127 1483156 "NONE" NIL NONE (NIL) -8 NIL NIL NIL) (-695 1482501 1482568 1482745 "NODE1" NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-694 1480787 1481864 1482119 "NNI" NIL NNI (NIL) -8 NIL NIL 1482466) (-693 1479515 1479852 1480216 "NLINSOL" NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-692 1478492 1478744 1479046 "NFINTBAS" NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-691 1477579 1478144 1478185 "NETCLT" 1478356 NETCLT (NIL T) -9 NIL 1478437 NIL) (-690 1476483 1476750 1477031 "NCODIV" NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-689 1476282 1476325 1476400 "NCNTFRAC" NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-688 1474813 1475201 1475621 "NCEP" NIL NCEP (NIL T) -7 NIL NIL NIL) (-687 1473446 1474412 1474440 "NASRING" 1474550 NASRING (NIL) -9 NIL 1474630 NIL) (-686 1473291 1473347 1473441 "NASRING-" NIL NASRING- (NIL T) -7 NIL NIL NIL) (-685 1472220 1472898 1472926 "NARNG" 1473043 NARNG (NIL) -9 NIL 1473134 NIL) (-684 1471996 1472081 1472215 "NARNG-" NIL NARNG- (NIL T) -7 NIL NIL NIL) (-683 1470762 1471516 1471556 "NAALG" 1471635 NAALG (NIL T) -9 NIL 1471696 NIL) (-682 1470632 1470667 1470757 "NAALG-" NIL NAALG- (NIL T T) -7 NIL NIL NIL) (-681 1465611 1466796 1467982 "MULTSQFR" NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-680 1465006 1465093 1465277 "MULTFACT" NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-679 1457016 1461510 1461562 "MTSCAT" 1462622 MTSCAT (NIL T T) -9 NIL 1463136 NIL) (-678 1456782 1456842 1456934 "MTHING" NIL MTHING (NIL T) -7 NIL NIL NIL) (-677 1456608 1456647 1456707 "MSYSCMD" NIL MSYSCMD (NIL) -7 NIL NIL NIL) (-676 1454197 1456140 1456181 "MSETAGG" 1456186 MSETAGG (NIL T) -9 NIL 1456220 NIL) (-675 1450567 1453240 1453561 "MSET" NIL MSET (NIL T) -8 NIL NIL NIL) (-674 1446841 1448664 1449404 "MRING" NIL MRING (NIL T T) -8 NIL NIL NIL) (-673 1446478 1446551 1446680 "MRF2" NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-672 1446131 1446172 1446316 "MRATFAC" NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-671 1443996 1444333 1444764 "MPRFF" NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-670 1437394 1443895 1443991 "MPOLY" NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-669 1436919 1436960 1437168 "MPCPF" NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-668 1436478 1436527 1436710 "MPC3" NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-667 1435752 1435845 1436064 "MPC2" NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-666 1434369 1434730 1435120 "MONOTOOL" NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-665 1433890 1433957 1433996 "MONOPC" 1434056 MONOPC (NIL T) -9 NIL 1434275 NIL) (-664 1433341 1433677 1433805 "MONOP" NIL MONOP (NIL T) -8 NIL NIL NIL) (-663 1432483 1432862 1432890 "MONOID" 1433108 MONOID (NIL) -9 NIL 1433252 NIL) (-662 1432142 1432292 1432478 "MONOID-" NIL MONOID- (NIL T) -7 NIL NIL NIL) (-661 1421080 1427950 1428009 "MONOGEN" 1428683 MONOGEN (NIL T T) -9 NIL 1429139 NIL) (-660 1419092 1419978 1420961 "MONOGEN-" NIL MONOGEN- (NIL T T T) -7 NIL NIL NIL) (-659 1417806 1418350 1418378 "MONADWU" 1418769 MONADWU (NIL) -9 NIL 1419004 NIL) (-658 1417354 1417554 1417801 "MONADWU-" NIL MONADWU- (NIL T) -7 NIL NIL NIL) (-657 1416631 1416932 1416960 "MONAD" 1417167 MONAD (NIL) -9 NIL 1417279 NIL) (-656 1416398 1416494 1416626 "MONAD-" NIL MONAD- (NIL T) -7 NIL NIL NIL) (-655 1414788 1415558 1415837 "MOEBIUS" NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-654 1413922 1414449 1414489 "MODULE" 1414494 MODULE (NIL T) -9 NIL 1414532 NIL) (-653 1413601 1413727 1413917 "MODULE-" NIL MODULE- (NIL T T) -7 NIL NIL NIL) (-652 1411312 1412198 1412512 "MODRING" NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-651 1408491 1409908 1410421 "MODOP" NIL MODOP (NIL T T) -8 NIL NIL NIL) (-650 1407125 1407699 1407975 "MODMONOM" NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-649 1396344 1405790 1406203 "MODMON" NIL MODMON (NIL T T) -8 NIL NIL NIL) (-648 1393300 1395344 1395613 "MODFIELD" NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-647 1392384 1392751 1392941 "MMLFORM" NIL MMLFORM (NIL) -8 NIL NIL NIL) (-646 1391953 1392002 1392181 "MMAP" NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-645 1389778 1390774 1390814 "MLO" 1391231 MLO (NIL T) -9 NIL 1391471 NIL) (-644 1387659 1388186 1388781 "MLIFT" NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-643 1387127 1387223 1387377 "MKUCFUNC" NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-642 1386797 1386873 1386996 "MKRECORD" NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-641 1386009 1386195 1386423 "MKFUNC" NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-640 1385502 1385618 1385774 "MKFLCFN" NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-639 1384874 1384988 1385173 "MKBCFUNC" NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-638 1383901 1384174 1384451 "MHROWRED" NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-637 1383334 1383422 1383593 "MFINFACT" NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-636 1380492 1381371 1382250 "MESH" NIL MESH (NIL) -7 NIL NIL NIL) (-635 1379159 1379507 1379860 "MDDFACT" NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-634 1376543 1378264 1378305 "MDAGG" 1378562 MDAGG (NIL T) -9 NIL 1378707 NIL) (-633 1375817 1375981 1376181 "MCDEN" NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-632 1374895 1375181 1375411 "MAYBE" NIL MAYBE (NIL T) -8 NIL NIL NIL) (-631 1372992 1373569 1374130 "MATSTOR" NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-630 1368790 1372582 1372829 "MATRIX" NIL MATRIX (NIL T) -8 NIL NIL NIL) (-629 1365139 1365908 1366642 "MATLIN" NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-628 1363892 1364061 1364390 "MATCAT2" NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-627 1353415 1356979 1357055 "MATCAT" 1362043 MATCAT (NIL T T T) -9 NIL 1363489 NIL) (-626 1350696 1352002 1353410 "MATCAT-" NIL MATCAT- (NIL T T T T) -7 NIL NIL NIL) (-625 1349097 1349457 1349841 "MAPPKG3" NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-624 1348230 1348427 1348649 "MAPPKG2" NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-623 1346981 1347307 1347634 "MAPPKG1" NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-622 1346143 1346545 1346721 "MAPPAST" NIL MAPPAST (NIL) -8 NIL NIL NIL) (-621 1345812 1345876 1345999 "MAPHACK3" NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-620 1345460 1345533 1345647 "MAPHACK2" NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-619 1344995 1345110 1345252 "MAPHACK1" NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-618 1343204 1343972 1344273 "MAGMA" NIL MAGMA (NIL T) -8 NIL NIL NIL) (-617 1342698 1343000 1343090 "MACROAST" NIL MACROAST (NIL) -8 NIL NIL NIL) (-616 1336929 1341013 1341054 "LZSTAGG" 1341831 LZSTAGG (NIL T) -9 NIL 1342121 NIL) (-615 1334278 1335590 1336924 "LZSTAGG-" NIL LZSTAGG- (NIL T T) -7 NIL NIL NIL) (-614 1331665 1332631 1333114 "LWORD" NIL LWORD (NIL T) -8 NIL NIL NIL) (-613 1331246 1331525 1331599 "LSTAST" NIL LSTAST (NIL) -8 NIL NIL NIL) (-612 1323455 1331107 1331241 "LSQM" NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-611 1322818 1322963 1323191 "LSPP" NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-610 1320302 1321000 1321712 "LSMP1" NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-609 1318518 1318841 1319275 "LSMP" NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-608 1311921 1317568 1317609 "LSAGG" 1317671 LSAGG (NIL T) -9 NIL 1317749 NIL) (-607 1309615 1310714 1311916 "LSAGG-" NIL LSAGG- (NIL T T) -7 NIL NIL NIL) (-606 1307095 1308964 1309213 "LPOLY" NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-605 1306762 1306853 1306976 "LPEFRAC" NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-604 1306433 1306512 1306540 "LOGIC" 1306651 LOGIC (NIL) -9 NIL 1306733 NIL) (-603 1306328 1306357 1306428 "LOGIC-" NIL LOGIC- (NIL T) -7 NIL NIL NIL) (-602 1305647 1305805 1305998 "LODOOPS" NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-601 1304432 1304681 1305032 "LODOF" NIL LODOF (NIL T T) -7 NIL NIL NIL) (-600 1300254 1303053 1303093 "LODOCAT" 1303525 LODOCAT (NIL T) -9 NIL 1303736 NIL) (-599 1300047 1300123 1300249 "LODOCAT-" NIL LODOCAT- (NIL T T) -7 NIL NIL NIL) (-598 1297047 1299924 1300042 "LODO2" NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-597 1294145 1296997 1297042 "LODO1" NIL LODO1 (NIL T) -8 NIL NIL NIL) (-596 1291232 1294075 1294140 "LODO" NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-595 1290285 1290460 1290762 "LODEEF" NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-594 1288417 1289547 1289800 "LO" NIL LO (NIL T T T) -8 NIL NIL NIL) (-593 1284237 1286576 1286617 "LNAGG" 1287476 LNAGG (NIL T) -9 NIL 1287914 NIL) (-592 1283624 1283891 1284232 "LNAGG-" NIL LNAGG- (NIL T T) -7 NIL NIL NIL) (-591 1280196 1281137 1281774 "LMOPS" NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-590 1279458 1279963 1280003 "LMODULE" 1280008 LMODULE (NIL T) -9 NIL 1280034 NIL) (-589 1276927 1279194 1279317 "LMDICT" NIL LMDICT (NIL T) -8 NIL NIL NIL) (-588 1276495 1276706 1276747 "LLINSET" 1276808 LLINSET (NIL T) -9 NIL 1276852 NIL) (-587 1276171 1276431 1276490 "LITERAL" NIL LITERAL (NIL T) -8 NIL NIL NIL) (-586 1275770 1275850 1275989 "LIST3" NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-585 1274221 1274569 1274968 "LIST2MAP" NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-584 1273392 1273588 1273816 "LIST2" NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-583 1266709 1272648 1272902 "LIST" NIL LIST (NIL T) -8 NIL NIL NIL) (-582 1266286 1266519 1266560 "LINSET" 1266565 LINSET (NIL T) -9 NIL 1266598 NIL) (-581 1265187 1265909 1266076 "LINFORM" NIL LINFORM (NIL T NIL) -8 NIL NIL NIL) (-580 1263453 1264208 1264248 "LINEXP" 1264734 LINEXP (NIL T) -9 NIL 1265007 NIL) (-579 1262075 1263062 1263243 "LINELT" NIL LINELT (NIL T NIL) -8 NIL NIL NIL) (-578 1260902 1261174 1261476 "LINDEP" NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-577 1260115 1260704 1260814 "LINBASIS" NIL LINBASIS (NIL NIL) -8 NIL NIL NIL) (-576 1257665 1258387 1259137 "LIMITRF" NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-575 1256295 1256592 1256983 "LIMITPS" NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-574 1255088 1255690 1255730 "LIECAT" 1255870 LIECAT (NIL T) -9 NIL 1256021 NIL) (-573 1254962 1254995 1255083 "LIECAT-" NIL LIECAT- (NIL T T) -7 NIL NIL NIL) (-572 1249218 1254652 1254880 "LIE" NIL LIE (NIL T T) -8 NIL NIL NIL) (-571 1240719 1248894 1249050 "LIB" NIL LIB (NIL) -8 NIL NIL NIL) (-570 1237171 1238120 1239055 "LGROBP" NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-569 1235795 1236703 1236731 "LFCAT" 1236938 LFCAT (NIL) -9 NIL 1237077 NIL) (-568 1234034 1234364 1234709 "LF" NIL LF (NIL T T) -7 NIL NIL NIL) (-567 1231551 1232216 1232897 "LEXTRIPK" NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-566 1228563 1229541 1230044 "LEXP" NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-565 1228054 1228357 1228448 "LETAST" NIL LETAST (NIL) -8 NIL NIL NIL) (-564 1226761 1227085 1227485 "LEADCDET" NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-563 1226027 1226112 1226338 "LAZM3PK" NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-562 1221030 1224595 1225131 "LAUPOL" NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-561 1220655 1220705 1220865 "LAPLACE" NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-560 1219426 1220199 1220239 "LALG" 1220300 LALG (NIL T) -9 NIL 1220358 NIL) (-559 1219209 1219286 1219421 "LALG-" NIL LALG- (NIL T T) -7 NIL NIL NIL) (-558 1217062 1218477 1218728 "LA" NIL LA (NIL T T T) -8 NIL NIL NIL) (-557 1216891 1216921 1216962 "KVTFROM" 1217024 KVTFROM (NIL T) -9 NIL NIL NIL) (-556 1215707 1216422 1216611 "KTVLOGIC" NIL KTVLOGIC (NIL) -8 NIL NIL NIL) (-555 1215536 1215566 1215607 "KRCFROM" 1215669 KRCFROM (NIL T) -9 NIL NIL NIL) (-554 1214638 1214835 1215130 "KOVACIC" NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-553 1214467 1214497 1214538 "KONVERT" 1214600 KONVERT (NIL T) -9 NIL NIL NIL) (-552 1214296 1214326 1214367 "KOERCE" 1214429 KOERCE (NIL T) -9 NIL NIL NIL) (-551 1213866 1213959 1214091 "KERNEL2" NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-550 1211919 1212813 1213185 "KERNEL" NIL KERNEL (NIL T) -8 NIL NIL NIL) (-549 1204866 1209703 1209757 "KDAGG" 1210133 KDAGG (NIL T T) -9 NIL 1210359 NIL) (-548 1204524 1204659 1204861 "KDAGG-" NIL KDAGG- (NIL T T T) -7 NIL NIL NIL) (-547 1197817 1204316 1204462 "KAFILE" NIL KAFILE (NIL T) -8 NIL NIL NIL) (-546 1197467 1197749 1197812 "JVMOP" NIL JVMOP (NIL) -8 NIL NIL NIL) (-545 1196437 1196936 1197185 "JVMMDACC" NIL JVMMDACC (NIL) -8 NIL NIL NIL) (-544 1195563 1196012 1196217 "JVMFDACC" NIL JVMFDACC (NIL) -8 NIL NIL NIL) (-543 1194427 1194919 1195219 "JVMCSTTG" NIL JVMCSTTG (NIL) -8 NIL NIL NIL) (-542 1193709 1194108 1194269 "JVMCFACC" NIL JVMCFACC (NIL) -8 NIL NIL NIL) (-541 1193419 1193655 1193704 "JVMBCODE" NIL JVMBCODE (NIL) -8 NIL NIL NIL) (-540 1187674 1193109 1193337 "JORDAN" NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-539 1187092 1187425 1187545 "JOINAST" NIL JOINAST (NIL) -8 NIL NIL NIL) (-538 1183763 1185278 1185332 "IXAGG" 1186247 IXAGG (NIL T T) -9 NIL 1186707 NIL) (-537 1182969 1183340 1183758 "IXAGG-" NIL IXAGG- (NIL T T T) -7 NIL NIL NIL) (-536 1181936 1182211 1182474 "ITUPLE" NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-535 1180598 1180805 1181098 "ITRIGMNP" NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-534 1179549 1179771 1180054 "ITFUN3" NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-533 1179224 1179287 1179410 "ITFUN2" NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-532 1178486 1178858 1179032 "ITFORM" NIL ITFORM (NIL) -8 NIL NIL NIL) (-531 1176462 1177762 1178036 "ITAYLOR" NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-530 1166010 1171779 1172936 "ISUPS" NIL ISUPS (NIL T) -8 NIL NIL NIL) (-529 1165255 1165407 1165643 "ISUMP" NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-528 1164746 1165049 1165140 "ISAST" NIL ISAST (NIL) -8 NIL NIL NIL) (-527 1164039 1164130 1164343 "IRURPK" NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-526 1163171 1163396 1163636 "IRSN" NIL IRSN (NIL) -7 NIL NIL NIL) (-525 1161584 1161965 1162393 "IRRF2F" NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-524 1161369 1161413 1161489 "IRREDFFX" NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-523 1160219 1160516 1160811 "IROOT" NIL IROOT (NIL T) -7 NIL NIL NIL) (-522 1159492 1159843 1159994 "IRFORM" NIL IRFORM (NIL) -8 NIL NIL NIL) (-521 1158695 1158826 1159039 "IR2F" NIL IR2F (NIL T T) -7 NIL NIL NIL) (-520 1156850 1157347 1157891 "IR2" NIL IR2 (NIL T T) -7 NIL NIL NIL) (-519 1153931 1155199 1155888 "IR" NIL IR (NIL T) -8 NIL NIL NIL) (-518 1153756 1153796 1153856 "IPRNTPK" NIL IPRNTPK (NIL) -7 NIL NIL NIL) (-517 1149754 1153682 1153751 "IPF" NIL IPF (NIL NIL) -8 NIL NIL NIL) (-516 1147757 1149693 1149749 "IPADIC" NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-515 1147128 1147427 1147557 "IP4ADDR" NIL IP4ADDR (NIL) -8 NIL NIL NIL) (-514 1146581 1146869 1147001 "IOMODE" NIL IOMODE (NIL) -8 NIL NIL NIL) (-513 1145662 1146287 1146413 "IOBFILE" NIL IOBFILE (NIL) -8 NIL NIL NIL) (-512 1145072 1145566 1145594 "IOBCON" 1145599 IOBCON (NIL) -9 NIL 1145620 NIL) (-511 1144643 1144707 1144889 "INVLAPLA" NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-510 1136687 1139058 1141383 "INTTR" NIL INTTR (NIL T T) -7 NIL NIL NIL) (-509 1133798 1134581 1135445 "INTTOOLS" NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-508 1133475 1133572 1133689 "INTSLPE" NIL INTSLPE (NIL) -7 NIL NIL NIL) (-507 1130917 1133411 1133470 "INTRVL" NIL INTRVL (NIL T) -8 NIL NIL NIL) (-506 1129029 1129558 1130125 "INTRF" NIL INTRF (NIL T) -7 NIL NIL NIL) (-505 1128531 1128645 1128785 "INTRET" NIL INTRET (NIL T) -7 NIL NIL NIL) (-504 1126915 1127321 1127783 "INTRAT" NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-503 1124694 1125288 1125899 "INTPM" NIL INTPM (NIL T T) -7 NIL NIL NIL) (-502 1122067 1122677 1123397 "INTPAF" NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-501 1121471 1121629 1121837 "INTHERTR" NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-500 1120990 1121076 1121264 "INTHERAL" NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-499 1119195 1119716 1120173 "INTHEORY" NIL INTHEORY (NIL) -7 NIL NIL NIL) (-498 1112277 1113930 1115659 "INTG0" NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-497 1111643 1111805 1111978 "INTFACT" NIL INTFACT (NIL T) -7 NIL NIL NIL) (-496 1109516 1109980 1110524 "INTEF" NIL INTEF (NIL T T) -7 NIL NIL NIL) (-495 1107642 1108592 1108620 "INTDOM" 1108919 INTDOM (NIL) -9 NIL 1109124 NIL) (-494 1107195 1107397 1107637 "INTDOM-" NIL INTDOM- (NIL T) -7 NIL NIL NIL) (-493 1103002 1105474 1105528 "INTCAT" 1106324 INTCAT (NIL T) -9 NIL 1106640 NIL) (-492 1102567 1102687 1102814 "INTBIT" NIL INTBIT (NIL) -7 NIL NIL NIL) (-491 1101407 1101579 1101885 "INTALG" NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-490 1100980 1101076 1101233 "INTAF" NIL INTAF (NIL T T) -7 NIL NIL NIL) (-489 1093328 1100887 1100975 "INTABL" NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-488 1092626 1093181 1093246 "INT8" NIL INT8 (NIL) -8 NIL NIL 1093280) (-487 1091923 1092478 1092543 "INT64" NIL INT64 (NIL) -8 NIL NIL 1092577) (-486 1091220 1091775 1091840 "INT32" NIL INT32 (NIL) -8 NIL NIL 1091874) (-485 1090517 1091072 1091137 "INT16" NIL INT16 (NIL) -8 NIL NIL 1091171) (-484 1086980 1090436 1090512 "INT" NIL INT (NIL) -8 NIL NIL NIL) (-483 1081037 1084520 1084548 "INS" 1085478 INS (NIL) -9 NIL 1086137 NIL) (-482 1079099 1080017 1080964 "INS-" NIL INS- (NIL T) -7 NIL NIL NIL) (-481 1078158 1078381 1078656 "INPSIGN" NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-480 1077372 1077513 1077710 "INPRODPF" NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-479 1076362 1076503 1076740 "INPRODFF" NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-478 1075514 1075678 1075938 "INNMFACT" NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-477 1074794 1074909 1075097 "INMODGCD" NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-476 1073533 1073802 1074126 "INFSP" NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-475 1072813 1072954 1073137 "INFPROD0" NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-474 1072476 1072548 1072646 "INFORM1" NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-473 1069554 1071040 1071563 "INFORM" NIL INFORM (NIL) -8 NIL NIL NIL) (-472 1069153 1069260 1069374 "INFINITY" NIL INFINITY (NIL) -7 NIL NIL NIL) (-471 1068309 1068954 1069055 "INETCLTS" NIL INETCLTS (NIL) -8 NIL NIL NIL) (-470 1067159 1067427 1067748 "INEP" NIL INEP (NIL T T T) -7 NIL NIL NIL) (-469 1066149 1067089 1067154 "INDE" NIL INDE (NIL T) -8 NIL NIL NIL) (-468 1065774 1065854 1065971 "INCRMAPS" NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-467 1064688 1065233 1065437 "INBFILE" NIL INBFILE (NIL) -8 NIL NIL NIL) (-466 1060783 1061838 1062781 "INBFF" NIL INBFF (NIL T) -7 NIL NIL NIL) (-465 1059637 1059960 1059988 "INBCON" 1060501 INBCON (NIL) -9 NIL 1060767 NIL) (-464 1059091 1059356 1059632 "INBCON-" NIL INBCON- (NIL T) -7 NIL NIL NIL) (-463 1058585 1058887 1058977 "INAST" NIL INAST (NIL) -8 NIL NIL NIL) (-462 1058042 1058351 1058456 "IMPTAST" NIL IMPTAST (NIL) -8 NIL NIL NIL) (-461 1056881 1057022 1057339 "IMATQF" NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-460 1055304 1055573 1055912 "IMATLIN" NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-459 1050147 1055235 1055299 "IFF" NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-458 1049527 1049861 1049976 "IFAST" NIL IFAST (NIL) -8 NIL NIL NIL) (-457 1044629 1048965 1049151 "IFARRAY" NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-456 1043659 1044551 1044624 "IFAMON" NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-455 1043231 1043308 1043362 "IEVALAB" 1043569 IEVALAB (NIL T T) -9 NIL NIL NIL) (-454 1042986 1043066 1043226 "IEVALAB-" NIL IEVALAB- (NIL T T T) -7 NIL NIL NIL) (-453 1042371 1042598 1042755 "IDPT" NIL IDPT (NIL T T) -8 NIL NIL NIL) (-452 1041364 1042291 1042366 "IDPOAMS" NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-451 1040427 1041284 1041359 "IDPOAM" NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-450 1039509 1040156 1040293 "IDPO" NIL IDPO (NIL T T) -8 NIL NIL NIL) (-449 1037872 1038443 1038494 "IDPC" 1039000 IDPC (NIL T T) -9 NIL 1039313 NIL) (-448 1037160 1037794 1037867 "IDPAM" NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-447 1036330 1037082 1037155 "IDPAG" NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-446 1036023 1036236 1036296 "IDENT" NIL IDENT (NIL) -8 NIL NIL NIL) (-445 1035727 1035767 1035806 "IDEMOPC" 1035811 IDEMOPC (NIL T) -9 NIL 1035948 NIL) (-444 1032798 1033679 1034571 "IDECOMP" NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-443 1026424 1027701 1028740 "IDEAL" NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-442 1025686 1025816 1026015 "ICDEN" NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-441 1024859 1025358 1025496 "ICARD" NIL ICARD (NIL) -8 NIL NIL NIL) (-440 1023248 1023579 1023970 "IBPTOOLS" NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-439 1020506 1021130 1021825 "IBATOOL" NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-438 1018732 1019212 1019745 "IBACHIN" NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-437 1016606 1018638 1018727 "IARRAY2" NIL IARRAY2 (NIL T T T) -8 NIL NIL NIL) (-436 1012758 1016544 1016601 "IARRAY1" NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-435 1006337 1011722 1012190 "IAN" NIL IAN (NIL) -8 NIL NIL NIL) (-434 1005905 1005968 1006141 "IALGFACT" NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-433 1005397 1005546 1005574 "HYPCAT" 1005781 HYPCAT (NIL) -9 NIL NIL NIL) (-432 1005053 1005206 1005392 "HYPCAT-" NIL HYPCAT- (NIL T) -7 NIL NIL NIL) (-431 1004666 1004911 1004994 "HOSTNAME" NIL HOSTNAME (NIL) -8 NIL NIL NIL) (-430 1004499 1004548 1004589 "HOMOTOP" 1004594 HOMOTOP (NIL T) -9 NIL 1004627 NIL) (-429 1002684 1003555 1003596 "HOAGG" 1003783 HOAGG (NIL T) -9 NIL 1004178 NIL) (-428 1002311 1002458 1002679 "HOAGG-" NIL HOAGG- (NIL T T) -7 NIL NIL NIL) (-427 995511 1002036 1002184 "HEXADEC" NIL HEXADEC (NIL) -8 NIL NIL NIL) (-426 994446 994704 994967 "HEUGCD" NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-425 993381 994311 994441 "HELLFDIV" NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-424 991639 993214 993302 "HEAP" NIL HEAP (NIL T) -8 NIL NIL NIL) (-423 990954 991306 991439 "HEADAST" NIL HEADAST (NIL) -8 NIL NIL NIL) (-422 984454 990887 990949 "HDP" NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-421 977593 984190 984341 "HDMP" NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-420 977046 977203 977366 "HB" NIL HB (NIL) -7 NIL NIL NIL) (-419 969411 976963 977041 "HASHTBL" NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-418 968902 969205 969296 "HASAST" NIL HASAST (NIL) -8 NIL NIL NIL) (-417 966452 968689 968868 "HACKPI" NIL HACKPI (NIL) -8 NIL NIL NIL) (-416 962138 966335 966447 "GTSET" NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-415 954480 962035 962133 "GSTBL" NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-414 946417 953849 954104 "GSERIES" NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-413 945441 945950 945978 "GROUP" 946181 GROUP (NIL) -9 NIL 946315 NIL) (-412 944984 945185 945436 "GROUP-" NIL GROUP- (NIL T) -7 NIL NIL NIL) (-411 943656 943995 944382 "GROEBSOL" NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-410 942478 942835 942886 "GRMOD" 943415 GRMOD (NIL T T) -9 NIL 943581 NIL) (-409 942297 942345 942473 "GRMOD-" NIL GRMOD- (NIL T T T) -7 NIL NIL NIL) (-408 938420 939631 940631 "GRIMAGE" NIL GRIMAGE (NIL) -8 NIL NIL NIL) (-407 937142 937466 937781 "GRDEF" NIL GRDEF (NIL) -7 NIL NIL NIL) (-406 936695 936823 936964 "GRAY" NIL GRAY (NIL) -7 NIL NIL NIL) (-405 935768 936267 936318 "GRALG" 936471 GRALG (NIL T T) -9 NIL 936561 NIL) (-404 935487 935588 935763 "GRALG-" NIL GRALG- (NIL T T T) -7 NIL NIL NIL) (-403 932506 935178 935345 "GPOLSET" NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-402 931919 931982 932239 "GOSPER" NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-401 927773 928669 929194 "GMODPOL" NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-400 926948 927150 927388 "GHENSEL" NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-399 921951 922878 923897 "GENUPS" NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-398 921699 921756 921845 "GENUFACT" NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-397 921181 921270 921435 "GENPGCD" NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-396 920690 920731 920944 "GENMFACT" NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-395 919491 919774 920078 "GENEEZ" NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-394 912766 919181 919342 "GDMP" NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-393 902549 907556 908660 "GCNAALG" NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-392 900601 901704 901732 "GCDDOM" 901987 GCDDOM (NIL) -9 NIL 902144 NIL) (-391 900224 900381 900596 "GCDDOM-" NIL GCDDOM- (NIL T) -7 NIL NIL NIL) (-390 891017 893487 895875 "GBINTERN" NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-389 889152 889477 889895 "GBF" NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-388 888093 888282 888549 "GBEUCLID" NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-387 886964 887171 887475 "GB" NIL GB (NIL T T T T) -7 NIL NIL NIL) (-386 886427 886569 886717 "GAUSSFAC" NIL GAUSSFAC (NIL) -7 NIL NIL NIL) (-385 885039 885387 885700 "GALUTIL" NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-384 883584 883905 884227 "GALPOLYU" NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-383 881210 881566 881971 "GALFACTU" NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-382 874462 876123 877701 "GALFACT" NIL GALFACT (NIL T) -7 NIL NIL NIL) (-381 874114 874335 874403 "FUNDESC" NIL FUNDESC (NIL) -8 NIL NIL NIL) (-380 873738 873959 874040 "FUNCTION" NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-379 871835 872518 872978 "FT" NIL FT (NIL) -8 NIL NIL NIL) (-378 870428 870735 871127 "FSUPFACT" NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-377 869083 869442 869766 "FST" NIL FST (NIL) -8 NIL NIL NIL) (-376 868386 868510 868697 "FSRED" NIL FSRED (NIL T T) -7 NIL NIL NIL) (-375 867360 867626 867973 "FSPRMELT" NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-374 865018 865548 866030 "FSPECF" NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-373 864601 864661 864830 "FSINT" NIL FSINT (NIL T T) -7 NIL NIL NIL) (-372 862901 863815 864118 "FSERIES" NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-371 862049 862183 862406 "FSCINT" NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-370 861220 861381 861608 "FSAGG2" NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-369 857454 860115 860156 "FSAGG" 860526 FSAGG (NIL T) -9 NIL 860787 NIL) (-368 855808 856567 857359 "FSAGG-" NIL FSAGG- (NIL T T) -7 NIL NIL NIL) (-367 853764 854060 854604 "FS2UPS" NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-366 852811 852993 853293 "FS2EXPXP" NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-365 852492 852541 852668 "FS2" NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-364 832648 842149 842190 "FS" 846060 FS (NIL T) -9 NIL 848338 NIL) (-363 824879 828372 832351 "FS-" NIL FS- (NIL T T) -7 NIL NIL NIL) (-362 824413 824540 824692 "FRUTIL" NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-361 818936 822094 822134 "FRNAALG" 823454 FRNAALG (NIL T) -9 NIL 824052 NIL) (-360 815677 816928 818186 "FRNAALG-" NIL FRNAALG- (NIL T T) -7 NIL NIL NIL) (-359 815358 815407 815534 "FRNAAF2" NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-358 813845 814402 814696 "FRMOD" NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-357 813131 813224 813511 "FRIDEAL2" NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-356 810965 811731 812047 "FRIDEAL" NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-355 810074 810517 810558 "FRETRCT" 810563 FRETRCT (NIL T) -9 NIL 810734 NIL) (-354 809447 809725 810069 "FRETRCT-" NIL FRETRCT- (NIL T T) -7 NIL NIL NIL) (-353 806191 807711 807770 "FRAMALG" 808652 FRAMALG (NIL T T) -9 NIL 808944 NIL) (-352 804787 805338 805968 "FRAMALG-" NIL FRAMALG- (NIL T T T) -7 NIL NIL NIL) (-351 804480 804543 804650 "FRAC2" NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-350 798121 804285 804475 "FRAC" NIL FRAC (NIL T) -8 NIL NIL NIL) (-349 797814 797877 797984 "FR2" NIL FR2 (NIL T T) -7 NIL NIL NIL) (-348 790122 794693 796021 "FR" NIL FR (NIL T) -8 NIL NIL NIL) (-347 783900 787403 787431 "FPS" 788550 FPS (NIL) -9 NIL 789106 NIL) (-346 783457 783590 783754 "FPS-" NIL FPS- (NIL T) -7 NIL NIL NIL) (-345 780267 782310 782338 "FPC" 782563 FPC (NIL) -9 NIL 782705 NIL) (-344 780113 780165 780262 "FPC-" NIL FPC- (NIL T) -7 NIL NIL NIL) (-343 778890 779599 779640 "FPATMAB" 779645 FPATMAB (NIL T) -9 NIL 779797 NIL) (-342 777320 777916 778263 "FPARFRAC" NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-341 776895 776953 777126 "FORDER" NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-340 775398 776293 776467 "FNLA" NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-339 774013 774518 774546 "FNCAT" 775003 FNCAT (NIL) -9 NIL 775260 NIL) (-338 773470 773980 774008 "FNAME" NIL FNAME (NIL) -8 NIL NIL NIL) (-337 772057 773419 773465 "FMONOID" NIL FMONOID (NIL T) -8 NIL NIL NIL) (-336 768645 770003 770044 "FMONCAT" 771261 FMONCAT (NIL T) -9 NIL 771865 NIL) (-335 765503 766581 766634 "FMCAT" 767815 FMCAT (NIL T T) -9 NIL 768307 NIL) (-334 764203 765326 765425 "FM1" NIL FM1 (NIL T T) -8 NIL NIL NIL) (-333 763251 764051 764198 "FM" NIL FM (NIL T T) -8 NIL NIL NIL) (-332 761438 761890 762384 "FLOATRP" NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-331 759373 759909 760487 "FLOATCP" NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-330 752759 757710 758324 "FLOAT" NIL FLOAT (NIL) -8 NIL NIL NIL) (-329 751240 752341 752381 "FLINEXP" 752386 FLINEXP (NIL T) -9 NIL 752479 NIL) (-328 750649 750908 751235 "FLINEXP-" NIL FLINEXP- (NIL T T) -7 NIL NIL NIL) (-327 749898 750057 750271 "FLASORT" NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-326 746781 747860 747912 "FLALG" 749139 FLALG (NIL T T) -9 NIL 749606 NIL) (-325 745952 746113 746340 "FLAGG2" NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-324 739621 743366 743407 "FLAGG" 744646 FLAGG (NIL T) -9 NIL 745294 NIL) (-323 738729 739133 739616 "FLAGG-" NIL FLAGG- (NIL T T) -7 NIL NIL NIL) (-322 735290 736554 736613 "FINRALG" 737741 FINRALG (NIL T T) -9 NIL 738249 NIL) (-321 734681 734946 735285 "FINRALG-" NIL FINRALG- (NIL T T T) -7 NIL NIL NIL) (-320 733979 734275 734303 "FINITE" 734499 FINITE (NIL) -9 NIL 734606 NIL) (-319 733887 733913 733974 "FINITE-" NIL FINITE- (NIL T) -7 NIL NIL NIL) (-318 730821 732148 732189 "FINAGG" 733094 FINAGG (NIL T) -9 NIL 733548 NIL) (-317 729852 730317 730816 "FINAGG-" NIL FINAGG- (NIL T T) -7 NIL NIL NIL) (-316 721813 724404 724444 "FINAALG" 728096 FINAALG (NIL T) -9 NIL 729534 NIL) (-315 718080 719325 720448 "FINAALG-" NIL FINAALG- (NIL T T) -7 NIL NIL NIL) (-314 716632 717051 717105 "FILECAT" 717789 FILECAT (NIL T T) -9 NIL 718005 NIL) (-313 715983 716457 716560 "FILE" NIL FILE (NIL T) -8 NIL NIL NIL) (-312 713231 715109 715137 "FIELD" 715177 FIELD (NIL) -9 NIL 715257 NIL) (-311 712256 712717 713226 "FIELD-" NIL FIELD- (NIL T) -7 NIL NIL NIL) (-310 710260 711206 711552 "FGROUP" NIL FGROUP (NIL T) -8 NIL NIL NIL) (-309 709503 709684 709903 "FGLMICPK" NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-308 704773 709441 709498 "FFX" NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-307 704435 704502 704637 "FFSLPE" NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-306 703975 704017 704226 "FFPOLY2" NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-305 700655 701532 702309 "FFPOLY" NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-304 695939 700587 700650 "FFP" NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-303 690618 695428 695618 "FFNBX" NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-302 685099 689899 690157 "FFNBP" NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-301 679306 684550 684761 "FFNB" NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-300 678329 678539 678854 "FFINTBAS" NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-299 673769 676474 676502 "FFIELDC" 677121 FFIELDC (NIL) -9 NIL 677496 NIL) (-298 672838 673278 673764 "FFIELDC-" NIL FFIELDC- (NIL T) -7 NIL NIL NIL) (-297 672453 672511 672635 "FFHOM" NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-296 670597 671120 671637 "FFF" NIL FFF (NIL T) -7 NIL NIL NIL) (-295 665691 670396 670497 "FFCGX" NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-294 660791 665480 665587 "FFCGP" NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-293 655457 660582 660690 "FFCG" NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-292 654911 654960 655195 "FFCAT2" NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-291 633486 644520 644606 "FFCAT" 649756 FFCAT (NIL T T T) -9 NIL 651192 NIL) (-290 629726 630952 632258 "FFCAT-" NIL FFCAT- (NIL T T T T) -7 NIL NIL NIL) (-289 624569 629657 629721 "FF" NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-288 623461 623930 623971 "FEVALAB" 624055 FEVALAB (NIL T) -9 NIL 624316 NIL) (-287 622866 623118 623456 "FEVALAB-" NIL FEVALAB- (NIL T T) -7 NIL NIL NIL) (-286 619693 620604 620719 "FDIVCAT" 622286 FDIVCAT (NIL T T T T) -9 NIL 622722 NIL) (-285 619487 619519 619688 "FDIVCAT-" NIL FDIVCAT- (NIL T T T T T) -7 NIL NIL NIL) (-284 618794 618887 619164 "FDIV2" NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-283 617280 618278 618481 "FDIV" NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-282 616373 616757 616959 "FCTRDATA" NIL FCTRDATA (NIL) -8 NIL NIL NIL) (-281 615495 615984 616124 "FCOMP" NIL FCOMP (NIL T) -8 NIL NIL NIL) (-280 607082 611725 611765 "FAXF" 613566 FAXF (NIL T) -9 NIL 614256 NIL) (-279 604998 605802 606617 "FAXF-" NIL FAXF- (NIL T T) -7 NIL NIL NIL) (-278 600157 604520 604694 "FARRAY" NIL FARRAY (NIL T) -8 NIL NIL NIL) (-277 594615 597038 597090 "FAMR" 598101 FAMR (NIL T T) -9 NIL 598560 NIL) (-276 593814 594179 594610 "FAMR-" NIL FAMR- (NIL T T T) -7 NIL NIL NIL) (-275 592835 593756 593809 "FAMONOID" NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-274 590429 591308 591361 "FAMONC" 592302 FAMONC (NIL T T) -9 NIL 592687 NIL) (-273 588985 590287 590424 "FAGROUP" NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-272 587065 587426 587828 "FACUTIL" NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-271 586342 586539 586761 "FACTFUNC" NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-270 578202 585789 585988 "EXPUPXS" NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-269 576221 576791 577377 "EXPRTUBE" NIL EXPRTUBE (NIL) -7 NIL NIL NIL) (-268 573123 573765 574485 "EXPRODE" NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-267 568280 568987 569792 "EXPR2UPS" NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-266 567969 568032 568141 "EXPR2" NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-265 552762 567018 567444 "EXPR" NIL EXPR (NIL T) -8 NIL NIL NIL) (-264 543289 552082 552370 "EXPEXPAN" NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-263 542783 543085 543175 "EXITAST" NIL EXITAST (NIL) -8 NIL NIL NIL) (-262 542559 542749 542778 "EXIT" NIL EXIT (NIL) -8 NIL NIL NIL) (-261 542248 542316 542429 "EVALCYC" NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-260 541765 541907 541948 "EVALAB" 542118 EVALAB (NIL T) -9 NIL 542222 NIL) (-259 541393 541539 541760 "EVALAB-" NIL EVALAB- (NIL T T) -7 NIL NIL NIL) (-258 538436 540031 540059 "EUCDOM" 540613 EUCDOM (NIL) -9 NIL 540962 NIL) (-257 537363 537856 538431 "EUCDOM-" NIL EUCDOM- (NIL T) -7 NIL NIL NIL) (-256 537088 537144 537244 "ES2" NIL ES2 (NIL T T) -7 NIL NIL NIL) (-255 536776 536840 536949 "ES1" NIL ES1 (NIL T T) -7 NIL NIL NIL) (-254 530547 532447 532475 "ES" 535217 ES (NIL) -9 NIL 536601 NIL) (-253 527062 528594 530386 "ES-" NIL ES- (NIL T) -7 NIL NIL NIL) (-252 526410 526563 526739 "ERROR" NIL ERROR (NIL) -7 NIL NIL NIL) (-251 518781 526340 526405 "EQTBL" NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-250 518470 518533 518642 "EQ2" NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-249 512097 515222 516655 "EQ" NIL EQ (NIL T) -8 NIL NIL NIL) (-248 508400 509496 510589 "EP" NIL EP (NIL T) -7 NIL NIL NIL) (-247 507229 507579 507884 "ENV" NIL ENV (NIL) -8 NIL NIL NIL) (-246 506114 506845 506873 "ENTIRER" 506878 ENTIRER (NIL) -9 NIL 506922 NIL) (-245 506003 506037 506109 "ENTIRER-" NIL ENTIRER- (NIL T) -7 NIL NIL NIL) (-244 502636 504433 504782 "EMR" NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-243 501728 501939 501993 "ELTAGG" 502373 ELTAGG (NIL T T) -9 NIL 502584 NIL) (-242 501508 501582 501723 "ELTAGG-" NIL ELTAGG- (NIL T T T) -7 NIL NIL NIL) (-241 501254 501289 501343 "ELTAB" 501427 ELTAB (NIL T T) -9 NIL 501479 NIL) (-240 500505 500675 500874 "ELFUTS" NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-239 500229 500303 500331 "ELEMFUN" 500436 ELEMFUN (NIL) -9 NIL NIL NIL) (-238 500129 500156 500224 "ELEMFUN-" NIL ELEMFUN- (NIL T) -7 NIL NIL NIL) (-237 495410 498154 498195 "ELAGG" 499128 ELAGG (NIL T) -9 NIL 499589 NIL) (-236 494208 494746 495405 "ELAGG-" NIL ELAGG- (NIL T T) -7 NIL NIL NIL) (-235 493626 493793 493949 "ELABOR" NIL ELABOR (NIL) -8 NIL NIL NIL) (-234 492539 492858 493137 "ELABEXPR" NIL ELABEXPR (NIL) -8 NIL NIL NIL) (-233 485932 487930 488757 "EFUPXS" NIL EFUPXS (NIL T T T T) -7 NIL NIL NIL) (-232 479911 481907 482717 "EFULS" NIL EFULS (NIL T T T) -7 NIL NIL NIL) (-231 477725 478131 478602 "EFSTRUC" NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-230 468725 470638 472179 "EF" NIL EF (NIL T T) -7 NIL NIL NIL) (-229 467838 468339 468488 "EAB" NIL EAB (NIL) -8 NIL NIL NIL) (-228 466536 467210 467250 "DVARCAT" 467533 DVARCAT (NIL T) -9 NIL 467673 NIL) (-227 465955 466219 466531 "DVARCAT-" NIL DVARCAT- (NIL T T) -7 NIL NIL NIL) (-226 458022 465823 465950 "DSMP" NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-225 456360 457151 457192 "DSEXT" 457555 DSEXT (NIL T) -9 NIL 457849 NIL) (-224 455165 455689 456355 "DSEXT-" NIL DSEXT- (NIL T T) -7 NIL NIL NIL) (-223 454889 454954 455052 "DROPT1" NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-222 451040 452256 453387 "DROPT0" NIL DROPT0 (NIL) -7 NIL NIL NIL) (-221 446686 448041 449105 "DROPT" NIL DROPT (NIL) -8 NIL NIL NIL) (-220 445361 445722 446108 "DRAWPT" NIL DRAWPT (NIL) -7 NIL NIL NIL) (-219 445047 445106 445224 "DRAWHACK" NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-218 444022 444320 444610 "DRAWCX" NIL DRAWCX (NIL) -7 NIL NIL NIL) (-217 443607 443682 443832 "DRAWCURV" NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-216 436020 438132 440247 "DRAWCFUN" NIL DRAWCFUN (NIL) -7 NIL NIL NIL) (-215 431537 432556 433635 "DRAW" NIL DRAW (NIL T) -7 NIL NIL NIL) (-214 428161 430164 430205 "DQAGG" 430834 DQAGG (NIL T) -9 NIL 431107 NIL) (-213 414704 422344 422426 "DPOLCAT" 424263 DPOLCAT (NIL T T T T) -9 NIL 424806 NIL) (-212 411112 412760 414699 "DPOLCAT-" NIL DPOLCAT- (NIL T T T T T) -7 NIL NIL NIL) (-211 404163 411010 411107 "DPMO" NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-210 397123 403992 404158 "DPMM" NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-209 396716 396976 397065 "DOMTMPLT" NIL DOMTMPLT (NIL) -8 NIL NIL NIL) (-208 396130 396578 396658 "DOMCTOR" NIL DOMCTOR (NIL) -8 NIL NIL NIL) (-207 395416 395741 395892 "DOMAIN" NIL DOMAIN (NIL) -8 NIL NIL NIL) (-206 388555 395152 395303 "DMP" NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-205 386304 387621 387661 "DMEXT" 387666 DMEXT (NIL T) -9 NIL 387841 NIL) (-204 385960 386022 386166 "DLP" NIL DLP (NIL T) -7 NIL NIL NIL) (-203 379562 385445 385635 "DLIST" NIL DLIST (NIL T) -8 NIL NIL NIL) (-202 376729 378391 378432 "DLAGG" 378973 DLAGG (NIL T) -9 NIL 379205 NIL) (-201 375080 375951 375979 "DIVRING" 376071 DIVRING (NIL) -9 NIL 376154 NIL) (-200 374531 374775 375075 "DIVRING-" NIL DIVRING- (NIL T) -7 NIL NIL NIL) (-199 372959 373376 373782 "DISPLAY" NIL DISPLAY (NIL) -7 NIL NIL NIL) (-198 371996 372217 372482 "DIRPROD2" NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-197 365516 371928 371991 "DIRPROD" NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-196 353862 360276 360329 "DIRPCAT" 360585 DIRPCAT (NIL NIL T) -9 NIL 361460 NIL) (-195 351868 352638 353525 "DIRPCAT-" NIL DIRPCAT- (NIL T NIL T) -7 NIL NIL NIL) (-194 351315 351481 351667 "DIOSP" NIL DIOSP (NIL) -7 NIL NIL NIL) (-193 348598 350192 350233 "DIOPS" 350653 DIOPS (NIL T) -9 NIL 350881 NIL) (-192 348258 348402 348593 "DIOPS-" NIL DIOPS- (NIL T T) -7 NIL NIL NIL) (-191 347265 348011 348039 "DIOID" 348044 DIOID (NIL) -9 NIL 348066 NIL) (-190 346093 346922 346950 "DIFRING" 346955 DIFRING (NIL) -9 NIL 346976 NIL) (-189 345729 345827 345855 "DIFFSPC" 345974 DIFFSPC (NIL) -9 NIL 346049 NIL) (-188 345470 345572 345724 "DIFFSPC-" NIL DIFFSPC- (NIL T) -7 NIL NIL NIL) (-187 344373 344998 345038 "DIFFMOD" 345043 DIFFMOD (NIL T) -9 NIL 345140 NIL) (-186 344057 344114 344155 "DIFFDOM" 344276 DIFFDOM (NIL T) -9 NIL 344344 NIL) (-185 343938 343968 344052 "DIFFDOM-" NIL DIFFDOM- (NIL T T) -7 NIL NIL NIL) (-184 341611 343132 343172 "DIFEXT" 343177 DIFEXT (NIL T) -9 NIL 343329 NIL) (-183 339499 341093 341134 "DIAGG" 341139 DIAGG (NIL T) -9 NIL 341159 NIL) (-182 339055 339245 339494 "DIAGG-" NIL DIAGG- (NIL T T) -7 NIL NIL NIL) (-181 334293 338245 338522 "DHMATRIX" NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-180 330751 331804 332814 "DFSFUN" NIL DFSFUN (NIL) -7 NIL NIL NIL) (-179 325301 329905 330232 "DFLOAT" NIL DFLOAT (NIL) -8 NIL NIL NIL) (-178 323867 324159 324534 "DFINTTLS" NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-177 320987 322239 322635 "DERHAM" NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-176 318771 320818 320907 "DEQUEUE" NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-175 318154 318299 318481 "DEGRED" NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-174 315472 316196 316996 "DEFINTRF" NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-173 313581 314039 314601 "DEFINTEF" NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-172 312964 313297 313411 "DEFAST" NIL DEFAST (NIL) -8 NIL NIL NIL) (-171 306164 312689 312837 "DECIMAL" NIL DECIMAL (NIL) -8 NIL NIL NIL) (-170 304084 304594 305098 "DDFACT" NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-169 303723 303772 303923 "DBLRESP" NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-168 302982 303544 303635 "DBASIS" NIL DBASIS (NIL NIL) -8 NIL NIL NIL) (-167 301006 301448 301808 "DBASE" NIL DBASE (NIL T) -8 NIL NIL NIL) (-166 300298 300587 300733 "DATAARY" NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-165 299749 299895 300047 "CYCLOTOM" NIL CYCLOTOM (NIL) -7 NIL NIL NIL) (-164 297111 297904 298631 "CYCLES" NIL CYCLES (NIL) -7 NIL NIL NIL) (-163 296550 296696 296867 "CVMP" NIL CVMP (NIL T) -7 NIL NIL NIL) (-162 294622 294933 295300 "CTRIGMNP" NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-161 294179 294434 294535 "CTORKIND" NIL CTORKIND (NIL) -8 NIL NIL NIL) (-160 293380 293763 293791 "CTORCAT" 293972 CTORCAT (NIL) -9 NIL 294084 NIL) (-159 293083 293217 293375 "CTORCAT-" NIL CTORCAT- (NIL T) -7 NIL NIL NIL) (-158 292576 292833 292941 "CTORCALL" NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-157 291992 292423 292496 "CTOR" NIL CTOR (NIL) -8 NIL NIL NIL) (-156 291451 291568 291721 "CSTTOOLS" NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-155 287845 288601 289356 "CRFP" NIL CRFP (NIL T T) -7 NIL NIL NIL) (-154 287336 287639 287730 "CRCEAST" NIL CRCEAST (NIL) -8 NIL NIL NIL) (-153 286555 286764 286992 "CRAPACK" NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-152 286059 286164 286368 "CPMATCH" NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-151 285812 285846 285952 "CPIMA" NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-150 282751 283513 284231 "COORDSYS" NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-149 282270 282412 282551 "CONTOUR" NIL CONTOUR (NIL) -8 NIL NIL NIL) (-148 278163 280733 281225 "CONTFRAC" NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-147 278037 278064 278092 "CONDUIT" 278129 CONDUIT (NIL) -9 NIL NIL NIL) (-146 276916 277647 277675 "COMRING" 277680 COMRING (NIL) -9 NIL 277730 NIL) (-145 276081 276448 276626 "COMPPROP" NIL COMPPROP (NIL) -8 NIL NIL NIL) (-144 275777 275818 275946 "COMPLPAT" NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-143 275470 275533 275640 "COMPLEX2" NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-142 264312 275420 275465 "COMPLEX" NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-141 263773 263912 264072 "COMPILER" NIL COMPILER (NIL) -7 NIL NIL NIL) (-140 263526 263567 263665 "COMPFACT" NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-139 244957 257207 257247 "COMPCAT" 258248 COMPCAT (NIL T) -9 NIL 259590 NIL) (-138 237495 241008 244601 "COMPCAT-" NIL COMPCAT- (NIL T T) -7 NIL NIL NIL) (-137 237254 237288 237390 "COMMUPC" NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-136 237084 237123 237181 "COMMONOP" NIL COMMONOP (NIL) -7 NIL NIL NIL) (-135 236665 236944 237018 "COMMAAST" NIL COMMAAST (NIL) -8 NIL NIL NIL) (-134 236242 236483 236570 "COMM" NIL COMM (NIL) -8 NIL NIL NIL) (-133 235437 235685 235713 "COMBOPC" 236051 COMBOPC (NIL) -9 NIL 236226 NIL) (-132 234501 234753 234995 "COMBINAT" NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-131 231433 232117 232740 "COMBF" NIL COMBF (NIL T T) -7 NIL NIL NIL) (-130 230313 230764 230999 "COLOR" NIL COLOR (NIL) -8 NIL NIL NIL) (-129 229804 230107 230198 "COLONAST" NIL COLONAST (NIL) -8 NIL NIL NIL) (-128 229491 229544 229669 "CMPLXRT" NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-127 228961 229271 229369 "CLLCTAST" NIL CLLCTAST (NIL) -8 NIL NIL NIL) (-126 225481 226551 227631 "CLIP" NIL CLIP (NIL) -7 NIL NIL NIL) (-125 223776 224761 224999 "CLIF" NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-124 221134 222412 222453 "CLAGG" 223016 CLAGG (NIL T) -9 NIL 223396 NIL) (-123 220692 220882 221129 "CLAGG-" NIL CLAGG- (NIL T T) -7 NIL NIL NIL) (-122 220321 220412 220552 "CINTSLPE" NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-121 218258 218765 219313 "CHVAR" NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-120 217219 217950 217978 "CHARZ" 217983 CHARZ (NIL) -9 NIL 217997 NIL) (-119 217013 217059 217137 "CHARPOL" NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-118 215852 216615 216643 "CHARNZ" 216704 CHARNZ (NIL) -9 NIL 216752 NIL) (-117 213330 214427 214950 "CHAR" NIL CHAR (NIL) -8 NIL NIL NIL) (-116 213038 213117 213145 "CFCAT" 213256 CFCAT (NIL) -9 NIL NIL NIL) (-115 212381 212510 212692 "CDEN" NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-114 208649 211794 212074 "CCLASS" NIL CCLASS (NIL) -8 NIL NIL NIL) (-113 208027 208214 208391 "CATEGORY" NIL -10 (NIL) -8 NIL NIL NIL) (-112 207555 207974 208022 "CATCTOR" NIL CATCTOR (NIL) -8 NIL NIL NIL) (-111 207028 207337 207434 "CATAST" NIL CATAST (NIL) -8 NIL NIL NIL) (-110 206519 206822 206913 "CASEAST" NIL CASEAST (NIL) -8 NIL NIL NIL) (-109 205768 205928 206149 "CARTEN2" NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-108 201868 203125 203833 "CARTEN" NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-107 200234 201265 201516 "CARD" NIL CARD (NIL) -8 NIL NIL NIL) (-106 199815 200094 200168 "CAPSLAST" NIL CAPSLAST (NIL) -8 NIL NIL NIL) (-105 199249 199502 199530 "CACHSET" 199662 CACHSET (NIL) -9 NIL 199740 NIL) (-104 198601 199016 199044 "CABMON" 199094 CABMON (NIL) -9 NIL 199150 NIL) (-103 198131 198395 198505 "BYTEORD" NIL BYTEORD (NIL) -8 NIL NIL NIL) (-102 193640 197799 197960 "BYTEBUF" NIL BYTEBUF (NIL) -8 NIL NIL NIL) (-101 192610 193314 193449 "BYTE" NIL BYTE (NIL) -8 NIL NIL 193612) (-100 190135 192377 192483 "BTREE" NIL BTREE (NIL T) -8 NIL NIL NIL) (-99 187631 189889 189997 "BTOURN" NIL BTOURN (NIL T) -8 NIL NIL NIL) (-98 184885 187033 187072 "BTCAT" 187139 BTCAT (NIL T) -9 NIL 187220 NIL) (-97 184636 184734 184880 "BTCAT-" NIL BTCAT- (NIL T T) -7 NIL NIL NIL) (-96 179979 183828 183854 "BTAGG" 183965 BTAGG (NIL) -9 NIL 184073 NIL) (-95 179610 179771 179974 "BTAGG-" NIL BTAGG- (NIL T) -7 NIL NIL NIL) (-94 176748 179102 179292 "BSTREE" NIL BSTREE (NIL T) -8 NIL NIL NIL) (-93 176018 176170 176348 "BRILL" NIL BRILL (NIL T) -7 NIL NIL NIL) (-92 173053 174733 174772 "BRAGG" 175401 BRAGG (NIL T) -9 NIL 175661 NIL) (-91 172128 172559 173048 "BRAGG-" NIL BRAGG- (NIL T T) -7 NIL NIL NIL) (-90 164662 171633 171814 "BPADICRT" NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-89 162654 164614 164657 "BPADIC" NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-88 162387 162423 162534 "BOUNDZRO" NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-87 160626 161059 161507 "BOP1" NIL BOP1 (NIL T) -7 NIL NIL NIL) (-86 156592 158008 158898 "BOP" NIL BOP (NIL) -8 NIL NIL NIL) (-85 155468 156359 156481 "BOOLEAN" NIL BOOLEAN (NIL) -8 NIL NIL NIL) (-84 155054 155211 155237 "BOOLE" 155345 BOOLE (NIL) -9 NIL 155426 NIL) (-83 154847 154928 155049 "BOOLE-" NIL BOOLE- (NIL T) -7 NIL NIL NIL) (-82 153985 154512 154562 "BMODULE" 154567 BMODULE (NIL T T) -9 NIL 154631 NIL) (-81 149885 153842 153911 "BITS" NIL BITS (NIL) -8 NIL NIL NIL) (-80 149698 149738 149777 "BINOPC" 149782 BINOPC (NIL T) -9 NIL 149827 NIL) (-79 149240 149513 149615 "BINOP" NIL BINOP (NIL T) -8 NIL NIL NIL) (-78 148761 148905 149043 "BINDING" NIL BINDING (NIL) -8 NIL NIL NIL) (-77 141967 148491 148636 "BINARY" NIL BINARY (NIL) -8 NIL NIL NIL) (-76 140214 141187 141226 "BGAGG" 141482 BGAGG (NIL T) -9 NIL 141609 NIL) (-75 140083 140121 140209 "BGAGG-" NIL BGAGG- (NIL T T) -7 NIL NIL NIL) (-74 138934 139135 139420 "BEZOUT" NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-73 135648 138114 138419 "BBTREE" NIL BBTREE (NIL T) -8 NIL NIL NIL) (-72 135233 135326 135352 "BASTYPE" 135523 BASTYPE (NIL) -9 NIL 135619 NIL) (-71 135003 135099 135228 "BASTYPE-" NIL BASTYPE- (NIL T) -7 NIL NIL NIL) (-70 134518 134606 134756 "BALFACT" NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-69 133417 134092 134277 "AUTOMOR" NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-68 133165 133170 133196 "ATTREG" 133201 ATTREG (NIL) -9 NIL NIL NIL) (-67 132770 133042 133107 "ATTRAST" NIL ATTRAST (NIL) -8 NIL NIL NIL) (-66 132270 132419 132445 "ATRIG" 132646 ATRIG (NIL) -9 NIL NIL NIL) (-65 132125 132178 132265 "ATRIG-" NIL ATRIG- (NIL T) -7 NIL NIL NIL) (-64 131695 131926 131952 "ASTCAT" 131957 ASTCAT (NIL) -9 NIL 131987 NIL) (-63 131494 131571 131690 "ASTCAT-" NIL ASTCAT- (NIL T) -7 NIL NIL NIL) (-62 129717 131327 131415 "ASTACK" NIL ASTACK (NIL T) -8 NIL NIL NIL) (-61 128524 128837 129202 "ASSOCEQ" NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-60 126376 128454 128519 "ARRAY2" NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 125567 125758 125979 "ARRAY12" NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-58 121445 125298 125412 "ARRAY1" NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-57 115757 117761 117836 "ARR2CAT" 120348 ARR2CAT (NIL T T T) -9 NIL 121069 NIL) (-56 114718 115200 115752 "ARR2CAT-" NIL ARR2CAT- (NIL T T T T) -7 NIL NIL NIL) (-55 114086 114457 114579 "ARITY" NIL ARITY (NIL) -8 NIL NIL NIL) (-54 113018 113186 113482 "APPRULE" NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 112719 112773 112891 "APPLYORE" NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 112102 112248 112404 "ANY1" NIL ANY1 (NIL T) -7 NIL NIL NIL) (-51 111507 111797 111917 "ANY" NIL ANY (NIL) -8 NIL NIL NIL) (-50 109075 110236 110559 "ANTISYM" NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 108600 108860 108956 "ANON" NIL ANON (NIL) -8 NIL NIL NIL) (-48 102295 107662 108104 "AN" NIL AN (NIL) -8 NIL NIL NIL) (-47 97829 99492 99542 "AMR" 100280 AMR (NIL T T) -9 NIL 100877 NIL) (-46 97183 97463 97824 "AMR-" NIL AMR- (NIL T T T) -7 NIL NIL NIL) (-45 79104 97117 97178 "ALIST" NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 75507 78780 78949 "ALGSC" NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 72517 73177 73784 "ALGPKG" NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 71896 72009 72193 "ALGMFACT" NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 68308 68933 69525 "ALGMANIP" NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 57797 68001 68151 "ALGFF" NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 57114 57268 57446 "ALGFACT" NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 55827 56622 56660 "ALGEBRA" 56665 ALGEBRA (NIL T) -9 NIL 56705 NIL) (-37 55613 55690 55822 "ALGEBRA-" NIL ALGEBRA- (NIL T T) -7 NIL NIL NIL) (-36 33875 52720 52772 "ALAGG" 52907 ALAGG (NIL T T) -9 NIL 53065 NIL) (-35 33375 33524 33550 "AHYP" 33751 AHYP (NIL) -9 NIL NIL NIL) (-34 32857 32989 33015 "AGG" 33220 AGG (NIL) -9 NIL 33346 NIL) (-33 32700 32758 32852 "AGG-" NIL AGG- (NIL T) -7 NIL NIL NIL) (-32 30839 31299 31699 "AF" NIL AF (NIL T T) -7 NIL NIL NIL) (-31 30334 30637 30726 "ADDAST" NIL ADDAST (NIL) -8 NIL NIL NIL) (-30 29704 29999 30155 "ACPLOT" NIL ACPLOT (NIL) -8 NIL NIL NIL) (-29 17262 26541 26579 "ACFS" 27186 ACFS (NIL T) -9 NIL 27425 NIL) (-28 15885 16495 17257 "ACFS-" NIL ACFS- (NIL T T) -7 NIL NIL NIL) (-27 11437 13816 13842 "ACF" 14721 ACF (NIL) -9 NIL 15133 NIL) (-26 10533 10939 11432 "ACF-" NIL ACF- (NIL T) -7 NIL NIL NIL) (-25 10035 10275 10301 "ABELSG" 10393 ABELSG (NIL) -9 NIL 10458 NIL) (-24 9933 9964 10030 "ABELSG-" NIL ABELSG- (NIL T) -7 NIL NIL NIL) (-23 9088 9462 9488 "ABELMON" 9713 ABELMON (NIL) -9 NIL 9846 NIL) (-22 8770 8910 9083 "ABELMON-" NIL ABELMON- (NIL T) -7 NIL NIL NIL) (-21 7982 8465 8491 "ABELGRP" 8563 ABELGRP (NIL) -9 NIL 8638 NIL) (-20 7535 7731 7977 "ABELGRP-" NIL ABELGRP- (NIL T) -7 NIL NIL NIL) (-19 3036 6762 6801 "A1AGG" 6806 A1AGG (NIL T) -9 NIL 6840 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 eaeda7ff..1024f6c4 100644
--- a/src/share/algebra/operation.daase
+++ b/src/share/algebra/operation.daase
@@ -1,793 +1,793 @@
 
-(630408 . 3577992039)        
+(630282 . 3577996048)        
 (((*1 *2 *3 *4)
-  (|partial| -12 (-5 *3 (-1180 *4)) (-4 *4 (-13 (-962) (-581 (-485))))
-   (-5 *2 (-1180 (-350 (-485)))) (-5 *1 (-1209 *4))))) 
+  (|partial| -12 (-5 *3 (-1179 *4)) (-4 *4 (-13 (-961) (-580 (-484))))
+   (-5 *2 (-1179 (-350 (-484)))) (-5 *1 (-1208 *4))))) 
 (((*1 *2 *3)
-  (|partial| -12 (-5 *3 (-1180 *4)) (-4 *4 (-13 (-962) (-581 (-485))))
-   (-5 *2 (-1180 (-485))) (-5 *1 (-1209 *4))))) 
+  (|partial| -12 (-5 *3 (-1179 *4)) (-4 *4 (-13 (-961) (-580 (-484))))
+   (-5 *2 (-1179 (-484))) (-5 *1 (-1208 *4))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-1180 *4)) (-4 *4 (-13 (-962) (-581 (-485)))) (-5 *2 (-85))
-   (-5 *1 (-1209 *4))))) 
+  (-12 (-5 *3 (-1179 *4)) (-4 *4 (-13 (-961) (-580 (-484)))) (-5 *2 (-85))
+   (-5 *1 (-1208 *4))))) 
 (((*1 *2 *3)
-  (-12 (-4 *5 (-13 (-554 *2) (-146))) (-5 *2 (-801 *4)) (-5 *1 (-144 *4 *5 *3))
-   (-4 *4 (-1014)) (-4 *3 (-139 *5))))
+  (-12 (-4 *5 (-13 (-553 *2) (-146))) (-5 *2 (-800 *4)) (-5 *1 (-144 *4 *5 *3))
+   (-4 *4 (-1013)) (-4 *3 (-139 *5))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-1180 *3)) (-4 *3 (-146)) (-4 *1 (-353 *3 *4))
-   (-4 *4 (-1156 *3))))
+  (-12 (-5 *2 (-1179 *3)) (-4 *3 (-146)) (-4 *1 (-353 *3 *4))
+   (-4 *4 (-1155 *3))))
  ((*1 *2 *1)
-  (-12 (-4 *1 (-353 *3 *4)) (-4 *3 (-146)) (-4 *4 (-1156 *3))
-   (-5 *2 (-1180 *3))))
- ((*1 *1 *2) (-12 (-5 *2 (-1180 *3)) (-4 *3 (-146)) (-4 *1 (-361 *3))))
- ((*1 *2 *1) (-12 (-4 *1 (-361 *3)) (-4 *3 (-146)) (-5 *2 (-1180 *3))))
+  (-12 (-4 *1 (-353 *3 *4)) (-4 *3 (-146)) (-4 *4 (-1155 *3))
+   (-5 *2 (-1179 *3))))
+ ((*1 *1 *2) (-12 (-5 *2 (-1179 *3)) (-4 *3 (-146)) (-4 *1 (-361 *3))))
+ ((*1 *2 *1) (-12 (-4 *1 (-361 *3)) (-4 *3 (-146)) (-5 *2 (-1179 *3))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-348 *1)) (-4 *1 (-364 *3)) (-4 *3 (-496)) (-4 *3 (-1014))))
+  (-12 (-5 *2 (-348 *1)) (-4 *1 (-364 *3)) (-4 *3 (-495)) (-4 *3 (-1013))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-584 *6)) (-4 *6 (-978 *3 *4 *5)) (-4 *3 (-962)) (-4 *4 (-718))
-   (-4 *5 (-757)) (-5 *1 (-403 *3 *4 *5 *6))))
- ((*1 *1 *2) (-12 (-5 *2 (-1016)) (-5 *1 (-474))))
- ((*1 *2 *1) (-12 (-4 *1 (-554 *2)) (-4 *2 (-1130))))
- ((*1 *1 *2) (-12 (-4 *1 (-558 *2)) (-4 *2 (-1130))))
- ((*1 *1 *2) (-12 (-4 *3 (-146)) (-4 *1 (-662 *3 *2)) (-4 *2 (-1156 *3))))
- ((*1 *1 *2) (-12 (-5 *2 (-584 (-801 *3))) (-5 *1 (-801 *3)) (-4 *3 (-1014))))
+  (-12 (-5 *2 (-583 *6)) (-4 *6 (-977 *3 *4 *5)) (-4 *3 (-961)) (-4 *4 (-717))
+   (-4 *5 (-756)) (-5 *1 (-403 *3 *4 *5 *6))))
+ ((*1 *1 *2) (-12 (-5 *2 (-1015)) (-5 *1 (-473))))
+ ((*1 *2 *1) (-12 (-4 *1 (-553 *2)) (-4 *2 (-1129))))
+ ((*1 *1 *2) (-12 (-4 *1 (-557 *2)) (-4 *2 (-1129))))
+ ((*1 *1 *2) (-12 (-4 *3 (-146)) (-4 *1 (-661 *3 *2)) (-4 *2 (-1155 *3))))
+ ((*1 *1 *2) (-12 (-5 *2 (-583 (-800 *3))) (-5 *1 (-800 *3)) (-4 *3 (-1013))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-858 *3)) (-4 *3 (-962)) (-4 *1 (-978 *3 *4 *5))
-   (-4 *5 (-554 (-1091))) (-4 *4 (-718)) (-4 *5 (-757))))
+  (-12 (-5 *2 (-857 *3)) (-4 *3 (-961)) (-4 *1 (-977 *3 *4 *5))
+   (-4 *5 (-553 (-1090))) (-4 *4 (-717)) (-4 *5 (-756))))
  ((*1 *1 *2)
   (OR
-   (-12 (-5 *2 (-858 (-485))) (-4 *1 (-978 *3 *4 *5))
-    (-12 (-2562 (-4 *3 (-38 (-350 (-485))))) (-4 *3 (-38 (-485)))
-     (-4 *5 (-554 (-1091))))
-    (-4 *3 (-962)) (-4 *4 (-718)) (-4 *5 (-757)))
-   (-12 (-5 *2 (-858 (-485))) (-4 *1 (-978 *3 *4 *5))
-    (-12 (-4 *3 (-38 (-350 (-485)))) (-4 *5 (-554 (-1091)))) (-4 *3 (-962))
-    (-4 *4 (-718)) (-4 *5 (-757)))))
+   (-12 (-5 *2 (-857 (-484))) (-4 *1 (-977 *3 *4 *5))
+    (-12 (-2561 (-4 *3 (-38 (-350 (-484))))) (-4 *3 (-38 (-484)))
+     (-4 *5 (-553 (-1090))))
+    (-4 *3 (-961)) (-4 *4 (-717)) (-4 *5 (-756)))
+   (-12 (-5 *2 (-857 (-484))) (-4 *1 (-977 *3 *4 *5))
+    (-12 (-4 *3 (-38 (-350 (-484)))) (-4 *5 (-553 (-1090)))) (-4 *3 (-961))
+    (-4 *4 (-717)) (-4 *5 (-756)))))
  ((*1 *1 *2)
-  (-12 (-5 *2 (-858 (-350 (-485)))) (-4 *1 (-978 *3 *4 *5))
-   (-4 *3 (-38 (-350 (-485)))) (-4 *5 (-554 (-1091))) (-4 *3 (-962))
-   (-4 *4 (-718)) (-4 *5 (-757))))
- ((*1 *2 *3)
-  (-12 (-5 *3 (-2 (|:| |val| (-584 *7)) (|:| -1601 *8)))
-   (-4 *7 (-978 *4 *5 *6)) (-4 *8 (-984 *4 *5 *6 *7)) (-4 *4 (-392))
-   (-4 *5 (-718)) (-4 *6 (-757)) (-5 *2 (-1074))
-   (-5 *1 (-982 *4 *5 *6 *7 *8))))
- ((*1 *2 *3)
-  (-12 (-5 *3 (-2 (|:| |val| (-584 *7)) (|:| -1601 *8)))
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-   (-4 *5 (-718)) (-4 *6 (-757)) (-5 *2 (-1074))
-   (-5 *1 (-1060 *4 *5 *6 *7 *8))))
- ((*1 *1 *2) (-12 (-5 *2 (-1016)) (-5 *1 (-1096))))
- ((*1 *2 *1) (-12 (-5 *2 (-1016)) (-5 *1 (-1096))))
- ((*1 *1 *2 *3 *2) (-12 (-5 *2 (-773)) (-5 *3 (-485)) (-5 *1 (-1110))))
- ((*1 *1 *2 *3) (-12 (-5 *2 (-773)) (-5 *3 (-485)) (-5 *1 (-1110))))
- ((*1 *2 *3)
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-   (-14 *5 (-584 (-1091))) (-5 *2 (-704 *4 (-774 *6))) (-5 *1 (-1208 *4 *5 *6))
-   (-14 *6 (-584 (-1091)))))
- ((*1 *2 *3)
-  (-12 (-5 *3 (-858 *4)) (-4 *4 (-13 (-756) (-258) (-120) (-934)))
-   (-5 *2 (-858 (-938 (-350 *4)))) (-5 *1 (-1208 *4 *5 *6))
-   (-14 *5 (-584 (-1091))) (-14 *6 (-584 (-1091)))))
- ((*1 *2 *3)
-  (-12 (-5 *3 (-704 *4 (-774 *6))) (-4 *4 (-13 (-756) (-258) (-120) (-934)))
-   (-14 *6 (-584 (-1091))) (-5 *2 (-858 (-938 (-350 *4))))
-   (-5 *1 (-1208 *4 *5 *6)) (-14 *5 (-584 (-1091)))))
- ((*1 *2 *3)
-  (-12 (-5 *3 (-1086 *4)) (-4 *4 (-13 (-756) (-258) (-120) (-934)))
-   (-5 *2 (-1086 (-938 (-350 *4)))) (-5 *1 (-1208 *4 *5 *6))
-   (-14 *5 (-584 (-1091))) (-14 *6 (-584 (-1091)))))
- ((*1 *2 *3)
-  (-12 (-5 *3 (-1061 *4 (-470 (-774 *6)) (-774 *6) (-704 *4 (-774 *6))))
-   (-4 *4 (-13 (-756) (-258) (-120) (-934))) (-14 *6 (-584 (-1091)))
-   (-5 *2 (-584 (-704 *4 (-774 *6)))) (-5 *1 (-1208 *4 *5 *6))
-   (-14 *5 (-584 (-1091)))))) 
-(((*1 *2 *3) (-12 (-5 *2 (-348 *3)) (-5 *1 (-498 *3)) (-4 *3 (-484))))
- ((*1 *2 *3)
-  (-12 (-4 *4 (-718)) (-4 *5 (-757)) (-4 *6 (-258)) (-5 *2 (-348 *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 (-258)) (-4 *7 (-862 *6 *4 *5))
-   (-5 *2 (-348 (-1086 *7))) (-5 *1 (-682 *4 *5 *6 *7)) (-5 *3 (-1086 *7))))
- ((*1 *2 *1)
-  (-12 (-4 *3 (-392)) (-4 *3 (-962)) (-4 *4 (-718)) (-4 *5 (-757))
-   (-5 *2 (-348 *1)) (-4 *1 (-862 *3 *4 *5))))
- ((*1 *2 *3)
-  (-12 (-4 *4 (-757)) (-4 *5 (-718)) (-4 *6 (-392)) (-5 *2 (-348 *3))
-   (-5 *1 (-893 *4 *5 *6 *3)) (-4 *3 (-862 *6 *5 *4))))
- ((*1 *2 *3)
-  (-12 (-4 *4 (-718)) (-4 *5 (-757)) (-4 *6 (-392)) (-4 *7 (-862 *6 *4 *5))
-   (-5 *2 (-348 (-1086 (-350 *7)))) (-5 *1 (-1088 *4 *5 *6 *7))
-   (-5 *3 (-1086 (-350 *7)))))
- ((*1 *2 *1) (-12 (-5 *2 (-348 *1)) (-4 *1 (-1135))))
- ((*1 *2 *3)
-  (-12 (-4 *4 (-496)) (-5 *2 (-348 *3)) (-5 *1 (-1160 *4 *3))
-   (-4 *3 (-13 (-1156 *4) (-496) (-10 -8 (-15 -3146 ($ $ $)))))))
- ((*1 *2 *3)
-  (-12 (-5 *3 (-959 *4 *5)) (-4 *4 (-13 (-756) (-258) (-120) (-934)))
-   (-14 *5 (-584 (-1091)))
-   (-5 *2 (-584 (-1061 *4 (-470 (-774 *6)) (-774 *6) (-704 *4 (-774 *6)))))
-   (-5 *1 (-1208 *4 *5 *6)) (-14 *6 (-584 (-1091)))))) 
-(((*1 *2 *3)
-  (-12 (-5 *3 (-959 *4 *5)) (-4 *4 (-13 (-756) (-258) (-120) (-934)))
-   (-14 *5 (-584 (-1091))) (-5 *2 (-584 (-584 (-938 (-350 *4)))))
-   (-5 *1 (-1208 *4 *5 *6)) (-14 *6 (-584 (-1091)))))
+  (-12 (-5 *2 (-857 (-350 (-484)))) (-4 *1 (-977 *3 *4 *5))
+   (-4 *3 (-38 (-350 (-484)))) (-4 *5 (-553 (-1090))) (-4 *3 (-961))
+   (-4 *4 (-717)) (-4 *5 (-756))))
+ ((*1 *2 *3)
+  (-12 (-5 *3 (-2 (|:| |val| (-583 *7)) (|:| -1600 *8)))
+   (-4 *7 (-977 *4 *5 *6)) (-4 *8 (-983 *4 *5 *6 *7)) (-4 *4 (-392))
+   (-4 *5 (-717)) (-4 *6 (-756)) (-5 *2 (-1073))
+   (-5 *1 (-981 *4 *5 *6 *7 *8))))
+ ((*1 *2 *3)
+  (-12 (-5 *3 (-2 (|:| |val| (-583 *7)) (|:| -1600 *8)))
+   (-4 *7 (-977 *4 *5 *6)) (-4 *8 (-1020 *4 *5 *6 *7)) (-4 *4 (-392))
+   (-4 *5 (-717)) (-4 *6 (-756)) (-5 *2 (-1073))
+   (-5 *1 (-1059 *4 *5 *6 *7 *8))))
+ ((*1 *1 *2) (-12 (-5 *2 (-1015)) (-5 *1 (-1095))))
+ ((*1 *2 *1) (-12 (-5 *2 (-1015)) (-5 *1 (-1095))))
+ ((*1 *1 *2 *3 *2) (-12 (-5 *2 (-772)) (-5 *3 (-484)) (-5 *1 (-1109))))
+ ((*1 *1 *2 *3) (-12 (-5 *2 (-772)) (-5 *3 (-484)) (-5 *1 (-1109))))
+ ((*1 *2 *3)
+  (-12 (-5 *3 (-703 *4 (-773 *5))) (-4 *4 (-13 (-755) (-258) (-120) (-933)))
+   (-14 *5 (-583 (-1090))) (-5 *2 (-703 *4 (-773 *6))) (-5 *1 (-1207 *4 *5 *6))
+   (-14 *6 (-583 (-1090)))))
+ ((*1 *2 *3)
+  (-12 (-5 *3 (-857 *4)) (-4 *4 (-13 (-755) (-258) (-120) (-933)))
+   (-5 *2 (-857 (-937 (-350 *4)))) (-5 *1 (-1207 *4 *5 *6))
+   (-14 *5 (-583 (-1090))) (-14 *6 (-583 (-1090)))))
+ ((*1 *2 *3)
+  (-12 (-5 *3 (-703 *4 (-773 *6))) (-4 *4 (-13 (-755) (-258) (-120) (-933)))
+   (-14 *6 (-583 (-1090))) (-5 *2 (-857 (-937 (-350 *4))))
+   (-5 *1 (-1207 *4 *5 *6)) (-14 *5 (-583 (-1090)))))
+ ((*1 *2 *3)
+  (-12 (-5 *3 (-1085 *4)) (-4 *4 (-13 (-755) (-258) (-120) (-933)))
+   (-5 *2 (-1085 (-937 (-350 *4)))) (-5 *1 (-1207 *4 *5 *6))
+   (-14 *5 (-583 (-1090))) (-14 *6 (-583 (-1090)))))
+ ((*1 *2 *3)
+  (-12 (-5 *3 (-1060 *4 (-469 (-773 *6)) (-773 *6) (-703 *4 (-773 *6))))
+   (-4 *4 (-13 (-755) (-258) (-120) (-933))) (-14 *6 (-583 (-1090)))
+   (-5 *2 (-583 (-703 *4 (-773 *6)))) (-5 *1 (-1207 *4 *5 *6))
+   (-14 *5 (-583 (-1090)))))) 
+(((*1 *2 *3) (-12 (-5 *2 (-348 *3)) (-5 *1 (-497 *3)) (-4 *3 (-483))))
+ ((*1 *2 *3)
+  (-12 (-4 *4 (-717)) (-4 *5 (-756)) (-4 *6 (-258)) (-5 *2 (-348 *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 (-258)) (-4 *7 (-861 *6 *4 *5))
+   (-5 *2 (-348 (-1085 *7))) (-5 *1 (-681 *4 *5 *6 *7)) (-5 *3 (-1085 *7))))
+ ((*1 *2 *1)
+  (-12 (-4 *3 (-392)) (-4 *3 (-961)) (-4 *4 (-717)) (-4 *5 (-756))
+   (-5 *2 (-348 *1)) (-4 *1 (-861 *3 *4 *5))))
+ ((*1 *2 *3)
+  (-12 (-4 *4 (-756)) (-4 *5 (-717)) (-4 *6 (-392)) (-5 *2 (-348 *3))
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@@ -796,10358 +796,10358 @@
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-(((*1 *2 *1 *3 *3) (-12 (-5 *3 (-831)) (-5 *2 (-1186)) (-5 *1 (-1183))))
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- ((*1 *2 *3 *2) (-12 (-5 *2 (-1074)) (-5 *3 (-584 (-221))) (-5 *1 (-222))))
- ((*1 *2 *1 *3) (-12 (-5 *3 (-1074)) (-5 *2 (-1186)) (-5 *1 (-1183))))
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+ ((*1 *2 *1) (-12 (-5 *2 (-583 (-221))) (-5 *1 (-1182))))
+ ((*1 *1 *1 *2) (-12 (-5 *2 (-583 (-221))) (-5 *1 (-1183))))
+ ((*1 *2 *1) (-12 (-5 *2 (-583 (-221))) (-5 *1 (-1183))))) 
+(((*1 *2 *1 *3 *3) (-12 (-5 *3 (-694)) (-5 *2 (-1185)) (-5 *1 (-1182))))
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+ ((*1 *2 *1 *3) (-12 (-5 *3 (-1073)) (-5 *2 (-1185)) (-5 *1 (-1182))))
+ ((*1 *2 *1 *3) (-12 (-5 *3 (-1073)) (-5 *2 (-1185)) (-5 *1 (-1183))))) 
 (((*1 *2 *1 *3 *3 *4 *4)
-  (-12 (-5 *3 (-695)) (-5 *4 (-831)) (-5 *2 (-1186)) (-5 *1 (-1183))))
+  (-12 (-5 *3 (-694)) (-5 *4 (-830)) (-5 *2 (-1185)) (-5 *1 (-1182))))
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-  (-12 (-5 *3 (-695)) (-5 *4 (-831)) (-5 *2 (-1186)) (-5 *1 (-1184))))) 
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   (-12
    (-5 *2
-    (-2 (|:| |theta| (-179)) (|:| |phi| (-179)) (|:| -3849 (-179))
+    (-2 (|:| |theta| (-179)) (|:| |phi| (-179)) (|:| -3848 (-179))
      (|:| |scaleX| (-179)) (|:| |scaleY| (-179)) (|:| |scaleZ| (-179))
      (|:| |deltaX| (-179)) (|:| |deltaY| (-179))))
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   (-12
    (-5 *2
-    (-2 (|:| |theta| (-179)) (|:| |phi| (-179)) (|:| -3849 (-179))
+    (-2 (|:| |theta| (-179)) (|:| |phi| (-179)) (|:| -3848 (-179))
      (|:| |scaleX| (-179)) (|:| |scaleY| (-179)) (|:| |scaleZ| (-179))
      (|:| |deltaX| (-179)) (|:| |deltaY| (-179))))
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+ ((*1 *2 *1 *3 *3 *3) (-12 (-5 *3 (-330)) (-5 *2 (-1185)) (-5 *1 (-1183))))
+ ((*1 *2 *1 *3 *3) (-12 (-5 *3 (-330)) (-5 *2 (-1185)) (-5 *1 (-1183))))
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   (-12
    (-5 *3
-    (-2 (|:| |theta| (-179)) (|:| |phi| (-179)) (|:| -3849 (-179))
+    (-2 (|:| |theta| (-179)) (|:| |phi| (-179)) (|:| -3848 (-179))
      (|:| |scaleX| (-179)) (|:| |scaleY| (-179)) (|:| |scaleZ| (-179))
      (|:| |deltaX| (-179)) (|:| |deltaY| (-179))))
-   (-5 *2 (-1186)) (-5 *1 (-1184))))
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   (-12
    (-5 *2
-    (-2 (|:| |theta| (-179)) (|:| |phi| (-179)) (|:| -3849 (-179))
+    (-2 (|:| |theta| (-179)) (|:| |phi| (-179)) (|:| -3848 (-179))
      (|:| |scaleX| (-179)) (|:| |scaleY| (-179)) (|:| |scaleZ| (-179))
      (|:| |deltaX| (-179)) (|:| |deltaY| (-179))))
-   (-5 *1 (-1184))))
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-(((*1 *2 *1 *3) (-12 (-5 *3 (-1074)) (-5 *2 (-1186)) (-5 *1 (-1183))))
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 (((*1 *2 *1 *3 *4)
-  (-12 (-5 *3 (-831)) (-5 *4 (-784)) (-5 *2 (-1186)) (-5 *1 (-1183))))
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-  (-12 (-5 *3 (-584 (-1074))) (-5 *2 (-1074)) (-5 *1 (-1183))))
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+ ((*1 *2 *1 *2 *2) (-12 (-5 *2 (-1073)) (-5 *1 (-1182))))
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+ ((*1 *2 *1 *2 *2) (-12 (-5 *2 (-1073)) (-5 *1 (-1183))))
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- ((*1 *1 *1) (-5 *1 (-1183)))) 
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+ ((*1 *2 *1) (-12 (-5 *2 (-1185)) (-5 *1 (-1183))))) 
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+ ((*1 *1 *1) (-5 *1 (-1182)))) 
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-  (-12 (-5 *3 (-831)) (-5 *4 (-179)) (-5 *5 (-485)) (-5 *6 (-784))
-   (-5 *2 (-1186)) (-5 *1 (-1183))))) 
+  (-12 (-5 *3 (-830)) (-5 *4 (-179)) (-5 *5 (-484)) (-5 *6 (-783))
+   (-5 *2 (-1185)) (-5 *1 (-1182))))) 
 (((*1 *2 *1)
   (-12
    (-5 *2
-    (-1180
+    (-1179
      (-2 (|:| |scaleX| (-179)) (|:| |scaleY| (-179)) (|:| |deltaX| (-179))
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-      (|:| |spline| (-485)) (|:| -3881 (-485)) (|:| |axesColor| (-784))
-      (|:| -3853 (-485)) (|:| |unitsColor| (-784)) (|:| |showing| (-485)))))
-   (-5 *1 (-1183))))) 
-(((*1 *2 *3) (-12 (-5 *3 (-831)) (-5 *2 (-1093 (-350 (-485)))) (-5 *1 (-164))))
- ((*1 *2 *1) (-12 (-5 *2 (-1180 (-3 (-408) "undefined"))) (-5 *1 (-1183))))) 
+      (|:| |deltaY| (-179)) (|:| -3851 (-484)) (|:| -3849 (-484))
+      (|:| |spline| (-484)) (|:| -3880 (-484)) (|:| |axesColor| (-783))
+      (|:| -3852 (-484)) (|:| |unitsColor| (-783)) (|:| |showing| (-484)))))
+   (-5 *1 (-1182))))) 
+(((*1 *2 *3) (-12 (-5 *3 (-830)) (-5 *2 (-1092 (-350 (-484)))) (-5 *1 (-164))))
+ ((*1 *2 *1) (-12 (-5 *2 (-1179 (-3 (-408) "undefined"))) (-5 *1 (-1182))))) 
 (((*1 *2 *1 *3 *4)
-  (-12 (-5 *3 (-408)) (-5 *4 (-831)) (-5 *2 (-1186)) (-5 *1 (-1183))))) 
-(((*1 *2 *1 *3) (-12 (-5 *3 (-831)) (-5 *2 (-408)) (-5 *1 (-1183))))) 
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 (((*1 *2 *3 *2)
-  (-12 (-5 *2 (-584 (-330))) (-5 *3 (-584 (-221))) (-5 *1 (-222))))
- ((*1 *2 *1 *2) (-12 (-5 *2 (-584 (-330))) (-5 *1 (-408))))
- ((*1 *2 *1) (-12 (-5 *2 (-584 (-330))) (-5 *1 (-408))))
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+ ((*1 *2 *1 *2) (-12 (-5 *2 (-583 (-330))) (-5 *1 (-408))))
+ ((*1 *2 *1) (-12 (-5 *2 (-583 (-330))) (-5 *1 (-408))))
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-  (-12 (-5 *3 (-831)) (-5 *4 (-784)) (-5 *2 (-1186)) (-5 *1 (-1183))))
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  ((*1 *2 *1 *3 *4)
-  (-12 (-5 *3 (-831)) (-5 *4 (-1074)) (-5 *2 (-1186)) (-5 *1 (-1183))))) 
+  (-12 (-5 *3 (-830)) (-5 *4 (-1073)) (-5 *2 (-1185)) (-5 *1 (-1182))))) 
 (((*1 *2 *1 *3 *4)
-  (-12 (-5 *3 (-831)) (-5 *4 (-1074)) (-5 *2 (-1186)) (-5 *1 (-1183))))) 
+  (-12 (-5 *3 (-830)) (-5 *4 (-1073)) (-5 *2 (-1185)) (-5 *1 (-1182))))) 
 (((*1 *2 *1 *3 *4)
-  (-12 (-5 *3 (-831)) (-5 *4 (-1074)) (-5 *2 (-1186)) (-5 *1 (-1183))))) 
+  (-12 (-5 *3 (-830)) (-5 *4 (-1073)) (-5 *2 (-1185)) (-5 *1 (-1182))))) 
 (((*1 *2 *1 *3 *4)
-  (-12 (-5 *3 (-831)) (-5 *4 (-1074)) (-5 *2 (-1186)) (-5 *1 (-1183))))) 
-(((*1 *1 *2 *2 *2) (-12 (-5 *1 (-181 *2)) (-4 *2 (-13 (-312) (-1116)))))
- ((*1 *1 *1 *2) (-12 (-5 *1 (-656 *2)) (-4 *2 (-312))))
- ((*1 *1 *2) (-12 (-5 *1 (-656 *2)) (-4 *2 (-312))))
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+ ((*1 *1 *1 *2) (-12 (-5 *1 (-655 *2)) (-4 *2 (-312))))
+ ((*1 *1 *2) (-12 (-5 *1 (-655 *2)) (-4 *2 (-312))))
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-  (-12 (-5 *3 (-831)) (-5 *4 (-330)) (-5 *2 (-1186)) (-5 *1 (-1183))))) 
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 (((*1 *2 *1 *3 *4)
-  (-12 (-5 *3 (-831)) (-5 *4 (-1074)) (-5 *2 (-1186)) (-5 *1 (-1183))))) 
+  (-12 (-5 *3 (-830)) (-5 *4 (-1073)) (-5 *2 (-1185)) (-5 *1 (-1182))))) 
 (((*1 *2 *1 *3 *4)
-  (-12 (-5 *3 (-408)) (-5 *4 (-831)) (-5 *2 (-1186)) (-5 *1 (-1183))))) 
+  (-12 (-5 *3 (-408)) (-5 *4 (-830)) (-5 *2 (-1185)) (-5 *1 (-1182))))) 
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-  (-12 (-5 *3 (-584 (-584 (-855 (-179))))) (-5 *4 (-784)) (-5 *5 (-831))
-   (-5 *6 (-584 (-221))) (-5 *2 (-1183)) (-5 *1 (-1182))))
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-  (-12 (-5 *3 (-584 (-584 (-855 (-179))))) (-5 *4 (-584 (-221)))
-   (-5 *2 (-1183)) (-5 *1 (-1182))))) 
+  (-12 (-5 *3 (-583 (-583 (-854 (-179))))) (-5 *4 (-583 (-221)))
+   (-5 *2 (-1182)) (-5 *1 (-1181))))) 
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-  (-12 (-5 *3 (-584 (-584 (-855 (-179))))) (-5 *4 (-784)) (-5 *5 (-831))
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+   (-5 *6 (-583 (-221))) (-5 *2 (-408)) (-5 *1 (-1181))))
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-   (-5 *1 (-1182))))) 
+  (-12 (-5 *3 (-583 (-583 (-854 (-179))))) (-5 *4 (-583 (-221))) (-5 *2 (-408))
+   (-5 *1 (-1181))))) 
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+  (-12 (-5 *3 (-1 *2 *5 *2)) (-5 *4 (-58 *5)) (-4 *5 (-1129)) (-4 *2 (-1129))
    (-5 *1 (-59 *5 *2))))
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+  (-12 (-4 *4 (-961)) (-5 *2 (-2 (|:| -2004 (-1085 *4)) (|:| |deg| (-830))))
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-  (-12 (-5 *3 (-485)) (-4 *1 (-1142 *4)) (-4 *4 (-962)) (-4 *4 (-496))
-   (-5 *2 (-350 (-858 *4)))))) 
+  (-12 (-5 *3 (-484)) (-4 *1 (-1141 *4)) (-4 *4 (-961)) (-4 *4 (-495))
+   (-5 *2 (-350 (-857 *4)))))) 
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- ((*1 *1 *1 *1) (-5 *1 (-1136))) ((*1 *1 *1 *1) (-5 *1 (-1137)))
- ((*1 *1 *1 *1) (-5 *1 (-1138))) ((*1 *1 *1 *1) (-5 *1 (-1139)))) 
+ ((*1 *1 *1 *1) (-12 (-5 *1 (-1097 *2)) (-14 *2 (-830))))
+ ((*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 (-1138)))) 
 (((*1 *1 *1 *1) (-5 *1 (-101)))
- ((*1 *1 *1 *1) (-12 (-5 *1 (-1098 *2)) (-14 *2 (-831))))
- ((*1 *1 *1 *1) (-5 *1 (-1136))) ((*1 *1 *1 *1) (-5 *1 (-1137)))
- ((*1 *1 *1 *1) (-5 *1 (-1138))) ((*1 *1 *1 *1) (-5 *1 (-1139)))) 
+ ((*1 *1 *1 *1) (-12 (-5 *1 (-1097 *2)) (-14 *2 (-830))))
+ ((*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 (-1138)))) 
 (((*1 *1) (-4 *1 (-23))) ((*1 *1) (-4 *1 (-34))) ((*1 *1) (-5 *1 (-101)))
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-  (-12 (-5 *1 (-108 *2 *3 *4)) (-14 *2 (-485)) (-14 *3 (-695)) (-4 *4 (-146))))
- ((*1 *1) (-5 *1 (-486))) ((*1 *1) (-5 *1 (-487))) ((*1 *1) (-5 *1 (-488)))
- ((*1 *1) (-5 *1 (-489))) ((*1 *1) (-4 *1 (-664))) ((*1 *1) (-5 *1 (-1091)))
- ((*1 *1) (-12 (-5 *1 (-1097 *2)) (-14 *2 (-831))))
- ((*1 *1) (-12 (-5 *1 (-1098 *2)) (-14 *2 (-831)))) ((*1 *1) (-5 *1 (-1136)))
- ((*1 *1) (-5 *1 (-1137))) ((*1 *1) (-5 *1 (-1138))) ((*1 *1) (-5 *1 (-1139)))) 
-(((*1 *2 *3) (-12 (-5 *3 (-142 (-485))) (-5 *2 (-85)) (-5 *1 (-386))))
+  (-12 (-5 *1 (-108 *2 *3 *4)) (-14 *2 (-484)) (-14 *3 (-694)) (-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 (-663))) ((*1 *1) (-5 *1 (-1090)))
+ ((*1 *1) (-12 (-5 *1 (-1096 *2)) (-14 *2 (-830))))
+ ((*1 *1) (-12 (-5 *1 (-1097 *2)) (-14 *2 (-830)))) ((*1 *1) (-5 *1 (-1135)))
+ ((*1 *1) (-5 *1 (-1136))) ((*1 *1) (-5 *1 (-1137))) ((*1 *1) (-5 *1 (-1138)))) 
+(((*1 *2 *3) (-12 (-5 *3 (-142 (-484))) (-5 *2 (-85)) (-5 *1 (-386))))
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   (-12
    (-5 *3
-    (-444 (-350 (-485)) (-197 *5 (-695)) (-774 *4) (-206 *4 (-350 (-485)))))
-   (-14 *4 (-584 (-1091))) (-14 *5 (-695)) (-5 *2 (-85)) (-5 *1 (-445 *4 *5))))
- ((*1 *2 *3) (-12 (-5 *2 (-85)) (-5 *1 (-874 *3)) (-4 *3 (-484))))
- ((*1 *2 *1) (-12 (-4 *1 (-1135)) (-5 *2 (-85))))) 
-(((*1 *2) (-12 (-5 *2 (-1186)) (-5 *1 (-1133))))) 
+    (-443 (-350 (-484)) (-197 *5 (-694)) (-773 *4) (-206 *4 (-350 (-484)))))
+   (-14 *4 (-583 (-1090))) (-14 *5 (-694)) (-5 *2 (-85)) (-5 *1 (-444 *4 *5))))
+ ((*1 *2 *3) (-12 (-5 *2 (-85)) (-5 *1 (-873 *3)) (-4 *3 (-483))))
+ ((*1 *2 *1) (-12 (-4 *1 (-1134)) (-5 *2 (-85))))) 
+(((*1 *2) (-12 (-5 *2 (-1185)) (-5 *1 (-1132))))) 
 (((*1 *2)
-  (-12 (-5 *2 (-2 (|:| -3230 (-584 (-1091))) (|:| -3231 (-584 (-1091)))))
-   (-5 *1 (-1133))))) 
-(((*1 *2 *3) (-12 (-5 *3 (-584 (-1091))) (-5 *2 (-1186)) (-5 *1 (-1133))))
- ((*1 *2 *3 *3) (-12 (-5 *3 (-584 (-1091))) (-5 *2 (-1186)) (-5 *1 (-1133))))) 
+  (-12 (-5 *2 (-2 (|:| -3229 (-583 (-1090))) (|:| -3230 (-583 (-1090)))))
+   (-5 *1 (-1132))))) 
+(((*1 *2 *3) (-12 (-5 *3 (-583 (-1090))) (-5 *2 (-1185)) (-5 *1 (-1132))))
+ ((*1 *2 *3 *3) (-12 (-5 *3 (-583 (-1090))) (-5 *2 (-1185)) (-5 *1 (-1132))))) 
 (((*1 *2 *1 *3)
-  (-12 (-5 *3 (-695)) (-4 *1 (-1065 *4)) (-4 *4 (-1130)) (-5 *2 (-85))))
+  (-12 (-5 *3 (-694)) (-4 *1 (-1064 *4)) (-4 *4 (-1129)) (-5 *2 (-85))))
  ((*1 *2 *3 *3)
-  (-12 (-5 *2 (-85)) (-5 *1 (-1132 *3)) (-4 *3 (-757)) (-4 *3 (-1014))))) 
+  (-12 (-5 *2 (-85)) (-5 *1 (-1131 *3)) (-4 *3 (-756)) (-4 *3 (-1013))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *3 (-584 *2)) (-5 *4 (-1 (-85) *2 *2)) (-5 *1 (-1132 *2))
-   (-4 *2 (-1014))))
+  (-12 (-5 *3 (-583 *2)) (-5 *4 (-1 (-85) *2 *2)) (-5 *1 (-1131 *2))
+   (-4 *2 (-1013))))
  ((*1 *2 *3)
-  (-12 (-5 *3 (-584 *2)) (-4 *2 (-1014)) (-4 *2 (-757)) (-5 *1 (-1132 *2))))) 
-(((*1 *2) (-12 (-5 *2 (-85)) (-5 *1 (-1132 *3)) (-4 *3 (-1014))))) 
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+(((*1 *2) (-12 (-5 *2 (-85)) (-5 *1 (-1131 *3)) (-4 *3 (-1013))))) 
 (((*1 *2 *1 *3)
-  (-12 (-5 *3 (-695)) (-4 *1 (-1065 *4)) (-4 *4 (-1130)) (-5 *2 (-85))))
+  (-12 (-5 *3 (-694)) (-4 *1 (-1064 *4)) (-4 *4 (-1129)) (-5 *2 (-85))))
  ((*1 *2 *3 *3)
-  (|partial| -12 (-5 *2 (-85)) (-5 *1 (-1132 *3)) (-4 *3 (-1014))))
+  (|partial| -12 (-5 *2 (-85)) (-5 *1 (-1131 *3)) (-4 *3 (-1013))))
  ((*1 *2 *3 *3 *4)
-  (-12 (-5 *4 (-1 (-85) *3 *3)) (-4 *3 (-1014)) (-5 *2 (-85))
-   (-5 *1 (-1132 *3))))) 
+  (-12 (-5 *4 (-1 (-85) *3 *3)) (-4 *3 (-1013)) (-5 *2 (-85))
+   (-5 *1 (-1131 *3))))) 
 (((*1 *2)
-  (-12 (-5 *2 (-2 (|:| -3231 (-584 *3)) (|:| -3230 (-584 *3))))
-   (-5 *1 (-1132 *3)) (-4 *3 (-1014))))) 
+  (-12 (-5 *2 (-2 (|:| -3230 (-583 *3)) (|:| -3229 (-583 *3))))
+   (-5 *1 (-1131 *3)) (-4 *3 (-1013))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-584 *4)) (-4 *4 (-1014)) (-5 *2 (-1186)) (-5 *1 (-1132 *4))))
+  (-12 (-5 *3 (-583 *4)) (-4 *4 (-1013)) (-5 *2 (-1185)) (-5 *1 (-1131 *4))))
  ((*1 *2 *3 *3)
-  (-12 (-5 *3 (-584 *4)) (-4 *4 (-1014)) (-5 *2 (-1186)) (-5 *1 (-1132 *4))))) 
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 (((*1 *2 *3 *4)
-  (-12 (-5 *4 (-485)) (-4 *5 (-299)) (-5 *2 (-348 (-1086 (-1086 *5))))
-   (-5 *1 (-1129 *5)) (-5 *3 (-1086 (-1086 *5)))))) 
+  (-12 (-5 *4 (-484)) (-4 *5 (-299)) (-5 *2 (-348 (-1085 (-1085 *5))))
+   (-5 *1 (-1128 *5)) (-5 *3 (-1085 (-1085 *5)))))) 
 (((*1 *2 *3)
-  (-12 (-4 *4 (-299)) (-5 *2 (-348 (-1086 (-1086 *4)))) (-5 *1 (-1129 *4))
-   (-5 *3 (-1086 (-1086 *4)))))) 
+  (-12 (-4 *4 (-299)) (-5 *2 (-348 (-1085 (-1085 *4)))) (-5 *1 (-1128 *4))
+   (-5 *3 (-1085 (-1085 *4)))))) 
 (((*1 *2 *3)
-  (-12 (-4 *4 (-299)) (-5 *2 (-348 (-1086 (-1086 *4)))) (-5 *1 (-1129 *4))
-   (-5 *3 (-1086 (-1086 *4)))))) 
+  (-12 (-4 *4 (-299)) (-5 *2 (-348 (-1085 (-1085 *4)))) (-5 *1 (-1128 *4))
+   (-5 *3 (-1085 (-1085 *4)))))) 
 (((*1 *1 *2 *1)
   (-12 (-5 *2 (-1 (-85) *3)) (-4 *1 (-318 *3)) (-4 *1 (-124 *3))
-   (-4 *3 (-1130))))
- ((*1 *1 *2 *1) (-12 (-5 *2 (-1 (-85) *3)) (-4 *3 (-1130)) (-5 *1 (-537 *3))))
- ((*1 *1 *2 *1) (-12 (-5 *2 (-1 (-85) *3)) (-4 *1 (-617 *3)) (-4 *3 (-1130))))
+   (-4 *3 (-1129))))
+ ((*1 *1 *2 *1) (-12 (-5 *2 (-1 (-85) *3)) (-4 *3 (-1129)) (-5 *1 (-536 *3))))
+ ((*1 *1 *2 *1) (-12 (-5 *2 (-1 (-85) *3)) (-4 *1 (-616 *3)) (-4 *3 (-1129))))
  ((*1 *2 *1 *3)
-  (|partial| -12 (-4 *1 (-1125 *4 *5 *3 *2)) (-4 *4 (-496)) (-4 *5 (-718))
-   (-4 *3 (-757)) (-4 *2 (-978 *4 *5 *3))))
- ((*1 *2 *1 *3) (-12 (-5 *3 (-695)) (-5 *1 (-1128 *2)) (-4 *2 (-1130))))) 
+  (|partial| -12 (-4 *1 (-1124 *4 *5 *3 *2)) (-4 *4 (-495)) (-4 *5 (-717))
+   (-4 *3 (-756)) (-4 *2 (-977 *4 *5 *3))))
+ ((*1 *2 *1 *3) (-12 (-5 *3 (-694)) (-5 *1 (-1127 *2)) (-4 *2 (-1129))))) 
 (((*1 *2 *3 *3 *3 *4 *5)
-  (-12 (-5 *5 (-584 (-584 (-179)))) (-5 *4 (-179)) (-5 *2 (-584 (-855 *4)))
-   (-5 *1 (-1127)) (-5 *3 (-855 *4))))) 
-(((*1 *2 *3) (-12 (-5 *3 (-485)) (-5 *2 (-584 (-584 (-179)))) (-5 *1 (-1127))))) 
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+   (-5 *1 (-1126)) (-5 *3 (-854 *4))))) 
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 (((*1 *1 *2)
-  (-12 (-5 *2 (-831)) (-4 *1 (-196 *3 *4)) (-4 *4 (-962)) (-4 *4 (-1130))))
+  (-12 (-5 *2 (-830)) (-4 *1 (-196 *3 *4)) (-4 *4 (-961)) (-4 *4 (-1129))))
  ((*1 *1 *2)
-  (-12 (-14 *3 (-584 (-1091))) (-4 *4 (-146)) (-4 *5 (-196 (-3959 *3) (-695)))
+  (-12 (-14 *3 (-583 (-1090))) (-4 *4 (-146)) (-4 *5 (-196 (-3958 *3) (-694)))
    (-14 *6
-    (-1 (-85) (-2 (|:| -2401 *2) (|:| -2402 *5))
-     (-2 (|:| -2401 *2) (|:| -2402 *5))))
-   (-5 *1 (-401 *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 (-1127))))) 
+    (-1 (-85) (-2 (|:| -2400 *2) (|:| -2401 *5))
+     (-2 (|:| -2400 *2) (|:| -2401 *5))))
+   (-5 *1 (-401 *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 (-1126))))) 
 (((*1 *2 *1 *3 *4)
-  (-12 (-5 *3 (-855 (-179))) (-5 *4 (-784)) (-5 *2 (-1186)) (-5 *1 (-408))))
- ((*1 *1 *2) (-12 (-5 *2 (-584 *3)) (-4 *3 (-962)) (-4 *1 (-894 *3))))
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- ((*1 *1 *1 *2) (-12 (-5 *2 (-695)) (-4 *1 (-1049 *3)) (-4 *3 (-962))))
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- ((*1 *1 *1 *2) (-12 (-5 *2 (-855 *3)) (-4 *1 (-1049 *3)) (-4 *3 (-962))))
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+ ((*1 *1 *2) (-12 (-5 *2 (-583 *3)) (-4 *3 (-961)) (-4 *1 (-893 *3))))
+ ((*1 *2 *1) (-12 (-4 *1 (-1048 *3)) (-4 *3 (-961)) (-5 *2 (-854 *3))))
+ ((*1 *1 *2) (-12 (-5 *2 (-854 *3)) (-4 *3 (-961)) (-4 *1 (-1048 *3))))
+ ((*1 *1 *1 *2) (-12 (-5 *2 (-694)) (-4 *1 (-1048 *3)) (-4 *3 (-961))))
+ ((*1 *1 *1 *2) (-12 (-5 *2 (-583 *3)) (-4 *1 (-1048 *3)) (-4 *3 (-961))))
+ ((*1 *1 *1 *2) (-12 (-5 *2 (-854 *3)) (-4 *1 (-1048 *3)) (-4 *3 (-961))))
  ((*1 *2 *3 *3 *3 *3)
-  (-12 (-5 *2 (-855 (-179))) (-5 *1 (-1127)) (-5 *3 (-179))))) 
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 (((*1 *2 *3 *4 *5)
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-   (-4 *3 (-888))))
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+   (-4 *3 (-887))))
  ((*1 *1 *2 *3 *4)
-  (-12 (-5 *3 (-584 (-584 (-855 (-179))))) (-5 *4 (-85)) (-5 *1 (-1126 *2))
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-(((*1 *2 *1) (-12 (-5 *2 (-85)) (-5 *1 (-1126 *3)) (-4 *3 (-888))))) 
+  (-12 (-5 *3 (-583 (-583 (-854 (-179))))) (-5 *4 (-85)) (-5 *1 (-1125 *2))
+   (-4 *2 (-887))))) 
+(((*1 *2 *1 *2) (-12 (-5 *2 (-85)) (-5 *1 (-1125 *3)) (-4 *3 (-887))))) 
+(((*1 *2 *1) (-12 (-5 *2 (-85)) (-5 *1 (-1125 *3)) (-4 *3 (-887))))) 
 (((*1 *2 *1) (-12 (-5 *2 (-85)) (-5 *1 (-145))))
- ((*1 *2 *1) (-12 (-5 *2 (-85)) (-5 *1 (-1126 *3)) (-4 *3 (-888))))) 
+ ((*1 *2 *1) (-12 (-5 *2 (-85)) (-5 *1 (-1125 *3)) (-4 *3 (-887))))) 
 (((*1 *2 *1)
-  (-12 (-5 *2 (-584 (-584 (-855 (-179))))) (-5 *1 (-1126 *3)) (-4 *3 (-888))))) 
-(((*1 *2 *1) (-12 (-5 *1 (-1126 *2)) (-4 *2 (-888))))) 
+  (-12 (-5 *2 (-583 (-583 (-854 (-179))))) (-5 *1 (-1125 *3)) (-4 *3 (-887))))) 
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 (((*1 *2 *3 *3)
-  (-12 (-5 *3 (-584 *7)) (-4 *7 (-978 *4 *5 *6)) (-4 *4 (-392)) (-4 *5 (-718))
-   (-4 *6 (-757)) (-5 *2 (-85)) (-5 *1 (-902 *4 *5 *6 *7 *8))
-   (-4 *8 (-984 *4 *5 *6 *7))))
+  (-12 (-5 *3 (-583 *7)) (-4 *7 (-977 *4 *5 *6)) (-4 *4 (-392)) (-4 *5 (-717))
+   (-4 *6 (-756)) (-5 *2 (-85)) (-5 *1 (-901 *4 *5 *6 *7 *8))
+   (-4 *8 (-983 *4 *5 *6 *7))))
  ((*1 *2 *1 *1)
-  (-12 (-4 *1 (-978 *3 *4 *5)) (-4 *3 (-962)) (-4 *4 (-718)) (-4 *5 (-757))
+  (-12 (-4 *1 (-977 *3 *4 *5)) (-4 *3 (-961)) (-4 *4 (-717)) (-4 *5 (-756))
    (-5 *2 (-85))))
  ((*1 *2 *3 *3)
-  (-12 (-5 *3 (-584 *7)) (-4 *7 (-978 *4 *5 *6)) (-4 *4 (-392)) (-4 *5 (-718))
-   (-4 *6 (-757)) (-5 *2 (-85)) (-5 *1 (-1019 *4 *5 *6 *7 *8))
-   (-4 *8 (-984 *4 *5 *6 *7))))
+  (-12 (-5 *3 (-583 *7)) (-4 *7 (-977 *4 *5 *6)) (-4 *4 (-392)) (-4 *5 (-717))
+   (-4 *6 (-756)) (-5 *2 (-85)) (-5 *1 (-1018 *4 *5 *6 *7 *8))
+   (-4 *8 (-983 *4 *5 *6 *7))))
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-  (-12 (-4 *1 (-1125 *3 *4 *5 *6)) (-4 *3 (-496)) (-4 *4 (-718)) (-4 *5 (-757))
-   (-4 *6 (-978 *3 *4 *5)) (-5 *2 (-85))))) 
+  (-12 (-4 *1 (-1124 *3 *4 *5 *6)) (-4 *3 (-495)) (-4 *4 (-717)) (-4 *5 (-756))
+   (-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 (-978 *6 *7 *8)) (-4 *6 (-496)) (-4 *7 (-718)) (-4 *8 (-757))
-   (-5 *2 (-2 (|:| |bas| *1) (|:| -3325 (-584 *9)))) (-5 *3 (-584 *9))
-   (-4 *1 (-1125 *6 *7 *8 *9))))
+   (-4 *9 (-977 *6 *7 *8)) (-4 *6 (-495)) (-4 *7 (-717)) (-4 *8 (-756))
+   (-5 *2 (-2 (|:| |bas| *1) (|:| -3324 (-583 *9)))) (-5 *3 (-583 *9))
+   (-4 *1 (-1124 *6 *7 *8 *9))))
  ((*1 *2 *3 *4)
-  (|partial| -12 (-5 *4 (-1 (-85) *8 *8)) (-4 *8 (-978 *5 *6 *7))
-   (-4 *5 (-496)) (-4 *6 (-718)) (-4 *7 (-757))
-   (-5 *2 (-2 (|:| |bas| *1) (|:| -3325 (-584 *8)))) (-5 *3 (-584 *8))
-   (-4 *1 (-1125 *5 *6 *7 *8))))) 
+  (|partial| -12 (-5 *4 (-1 (-85) *8 *8)) (-4 *8 (-977 *5 *6 *7))
+   (-4 *5 (-495)) (-4 *6 (-717)) (-4 *7 (-756))
+   (-5 *2 (-2 (|:| |bas| *1) (|:| -3324 (-583 *8)))) (-5 *3 (-583 *8))
+   (-4 *1 (-1124 *5 *6 *7 *8))))) 
 (((*1 *2 *1)
-  (-12 (-4 *1 (-1125 *3 *4 *5 *6)) (-4 *3 (-496)) (-4 *4 (-718)) (-4 *5 (-757))
-   (-4 *6 (-978 *3 *4 *5)) (-5 *2 (-584 *6))))) 
+  (-12 (-4 *1 (-1124 *3 *4 *5 *6)) (-4 *3 (-495)) (-4 *4 (-717)) (-4 *5 (-756))
+   (-4 *6 (-977 *3 *4 *5)) (-5 *2 (-583 *6))))) 
 (((*1 *2 *1)
-  (-12 (-4 *1 (-1125 *3 *4 *5 *6)) (-4 *3 (-496)) (-4 *4 (-718)) (-4 *5 (-757))
-   (-4 *6 (-978 *3 *4 *5))
-   (-5 *2 (-2 (|:| -3863 (-584 *6)) (|:| -1703 (-584 *6))))))) 
+  (-12 (-4 *1 (-1124 *3 *4 *5 *6)) (-4 *3 (-495)) (-4 *4 (-717)) (-4 *5 (-756))
+   (-4 *6 (-977 *3 *4 *5))
+   (-5 *2 (-2 (|:| -3862 (-583 *6)) (|:| -1702 (-583 *6))))))) 
 (((*1 *2 *1 *3)
-  (-12 (-5 *3 (-584 *1)) (-4 *1 (-978 *4 *5 *6)) (-4 *4 (-962)) (-4 *5 (-718))
-   (-4 *6 (-757)) (-5 *2 (-85))))
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+   (-4 *6 (-756)) (-5 *2 (-85))))
  ((*1 *2 *1 *1)
-  (-12 (-4 *1 (-978 *3 *4 *5)) (-4 *3 (-962)) (-4 *4 (-718)) (-4 *5 (-757))
+  (-12 (-4 *1 (-977 *3 *4 *5)) (-4 *3 (-961)) (-4 *4 (-717)) (-4 *5 (-756))
    (-5 *2 (-85))))
  ((*1 *2 *1)
-  (-12 (-4 *1 (-1125 *3 *4 *5 *6)) (-4 *3 (-496)) (-4 *4 (-718)) (-4 *5 (-757))
-   (-4 *6 (-978 *3 *4 *5)) (-5 *2 (-85))))
+  (-12 (-4 *1 (-1124 *3 *4 *5 *6)) (-4 *3 (-495)) (-4 *4 (-717)) (-4 *5 (-756))
+   (-4 *6 (-977 *3 *4 *5)) (-5 *2 (-85))))
  ((*1 *2 *3 *1)
-  (-12 (-4 *1 (-1125 *4 *5 *6 *3)) (-4 *4 (-496)) (-4 *5 (-718)) (-4 *6 (-757))
-   (-4 *3 (-978 *4 *5 *6)) (-5 *2 (-85))))) 
+  (-12 (-4 *1 (-1124 *4 *5 *6 *3)) (-4 *4 (-495)) (-4 *5 (-717)) (-4 *6 (-756))
+   (-4 *3 (-977 *4 *5 *6)) (-5 *2 (-85))))) 
 (((*1 *2 *1 *3)
-  (-12 (-5 *3 (-584 *1)) (-4 *1 (-978 *4 *5 *6)) (-4 *4 (-962)) (-4 *5 (-718))
-   (-4 *6 (-757)) (-5 *2 (-85))))
+  (-12 (-5 *3 (-583 *1)) (-4 *1 (-977 *4 *5 *6)) (-4 *4 (-961)) (-4 *5 (-717))
+   (-4 *6 (-756)) (-5 *2 (-85))))
  ((*1 *2 *1 *1)
-  (-12 (-4 *1 (-978 *3 *4 *5)) (-4 *3 (-962)) (-4 *4 (-718)) (-4 *5 (-757))
+  (-12 (-4 *1 (-977 *3 *4 *5)) (-4 *3 (-961)) (-4 *4 (-717)) (-4 *5 (-756))
    (-5 *2 (-85))))
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-  (-12 (-5 *4 (-1 (-85) *3 *3)) (-4 *1 (-1125 *5 *6 *7 *3)) (-4 *5 (-496))
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-   (-4 *6 (-978 *3 *4 *5)) (-5 *2 (-85))))
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-   (-4 *3 (-978 *4 *5 *6)) (-5 *2 (-85))))) 
+  (-12 (-4 *1 (-1124 *4 *5 *6 *3)) (-4 *4 (-495)) (-4 *5 (-717)) (-4 *6 (-756))
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 (((*1 *2 *1 *3)
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-   (-4 *6 (-757)) (-5 *2 (-85))))
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+  (-12 (-4 *1 (-977 *3 *4 *5)) (-4 *3 (-961)) (-4 *4 (-717)) (-4 *5 (-756))
    (-5 *2 (-85))))
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-   (-4 *6 (-978 *3 *4 *5)) (-5 *2 (-85))))
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-   (-4 *3 (-978 *4 *5 *6)) (-5 *2 (-85))))) 
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-   (-4 *6 (-757)) (-5 *2 (-85))))
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    (-5 *2 (-85))))
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-   (-4 *6 (-978 *3 *4 *5)) (-5 *2 (-85))))
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-   (-4 *3 (-978 *4 *5 *6)) (-5 *2 (-85))))) 
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+   (-4 *3 (-977 *4 *5 *6)) (-5 *2 (-85))))) 
 (((*1 *2 *1 *3)
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-   (-4 *4 (-496)) (-4 *5 (-718)) (-4 *6 (-757)) (-4 *7 (-978 *4 *5 *6))
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+   (-4 *4 (-495)) (-4 *5 (-717)) (-4 *6 (-756)) (-4 *7 (-977 *4 *5 *6))
    (-5 *2 (-85))))) 
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-   (-4 *1 (-1125 *5 *6 *7 *8)) (-4 *5 (-496)) (-4 *6 (-718)) (-4 *7 (-757))
-   (-4 *8 (-978 *5 *6 *7))))) 
+  (-12 (-5 *2 (-583 *8)) (-5 *3 (-1 *8 *8 *8)) (-5 *4 (-1 (-85) *8 *8))
+   (-4 *1 (-1124 *5 *6 *7 *8)) (-4 *5 (-495)) (-4 *6 (-717)) (-4 *7 (-756))
+   (-4 *8 (-977 *5 *6 *7))))) 
 (((*1 *2 *2 *1)
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-   (-4 *2 (-978 *3 *4 *5))))) 
+  (-12 (-4 *1 (-1124 *3 *4 *5 *2)) (-4 *3 (-495)) (-4 *4 (-717)) (-4 *5 (-756))
+   (-4 *2 (-977 *3 *4 *5))))) 
 (((*1 *1 *1 *1)
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-   (-4 *2 (-978 *3 *4 *5))))) 
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+   (-4 *2 (-977 *3 *4 *5))))) 
 (((*1 *1 *1 *1)
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-   (-4 *2 (-978 *3 *4 *5))))) 
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+   (-4 *2 (-977 *3 *4 *5))))) 
 (((*1 *2 *2 *1)
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-   (-4 *2 (-978 *3 *4 *5))))) 
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+   (-4 *2 (-977 *3 *4 *5))))) 
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-   (-4 *5 (-978 *2 *3 *4))))) 
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+   (-4 *5 (-977 *2 *3 *4))))) 
 (((*1 *2 *2 *1)
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-   (-4 *2 (-978 *3 *4 *5))))) 
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 (((*1 *2 *3 *4)
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-   (-4 *10 (-1021 *5 *6 *7 *8))))
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-   (-5 *1 (-941 *5 *6 *7 *8))))
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-   (-5 *1 (-941 *5 *6 *7 *8))))
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-   (-14 *6 (-584 (-1091))) (-5 *2 (-584 (-959 *5 *6))) (-5 *1 (-959 *5 *6))))
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-   (-4 *6 (-718)) (-4 *7 (-757)) (-5 *2 (-584 *1)) (-4 *1 (-984 *5 *6 *7 *8))))
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-   (-4 *6 (-718)) (-4 *7 (-757)) (-5 *2 (-584 (-1061 *5 *6 *7 *8)))
-   (-5 *1 (-1061 *5 *6 *7 *8))))
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+   (-4 *6 (-717)) (-4 *7 (-756)) (-5 *2 (-583 (-1060 *5 *6 *7 *8)))
+   (-5 *1 (-1060 *5 *6 *7 *8))))
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-   (-4 *6 (-718)) (-4 *7 (-757)) (-5 *2 (-584 (-1061 *5 *6 *7 *8)))
-   (-5 *1 (-1061 *5 *6 *7 *8))))
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+   (-4 *6 (-717)) (-4 *7 (-756)) (-5 *2 (-583 (-1060 *5 *6 *7 *8)))
+   (-5 *1 (-1060 *5 *6 *7 *8))))
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-   (-4 *6 (-757)) (-5 *2 (-584 *1)) (-4 *1 (-1125 *4 *5 *6 *7))))) 
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+   (-4 *6 (-756)) (-5 *2 (-583 *1)) (-4 *1 (-1124 *4 *5 *6 *7))))) 
 (((*1 *2 *3)
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-   (-5 *2 (-584 (-2 (|:| -3863 *1) (|:| -1703 (-584 *7))))) (-5 *3 (-584 *7))
-   (-4 *1 (-1125 *4 *5 *6 *7))))) 
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+   (-5 *2 (-583 (-2 (|:| -3862 *1) (|:| -1702 (-583 *7))))) (-5 *3 (-583 *7))
+   (-4 *1 (-1124 *4 *5 *6 *7))))) 
 (((*1 *2 *1)
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-   (-4 *6 (-978 *3 *4 *5)) (-5 *2 (-584 *5))))) 
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+   (-4 *6 (-977 *3 *4 *5)) (-5 *2 (-583 *5))))) 
 (((*1 *1 *1 *2)
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-   (-4 *5 (-757)) (-4 *2 (-978 *3 *4 *5))))) 
+  (|partial| -12 (-4 *1 (-1124 *3 *4 *5 *2)) (-4 *3 (-495)) (-4 *4 (-717))
+   (-4 *5 (-756)) (-4 *2 (-977 *3 *4 *5))))) 
 (((*1 *2 *1)
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-   (-4 *6 (-978 *3 *4 *5)) (-4 *5 (-320)) (-5 *2 (-695))))) 
-(((*1 *2 *1 *3) (-12 (-4 *1 (-47 *2 *3)) (-4 *3 (-717)) (-4 *2 (-962))))
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-   (-14 *4 (-831)) (-14 *5 (-907 *4 *2))))
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-   (-14 *4 (-584 (-1091)))))
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- ((*1 *2 *1 *3) (-12 (-4 *1 (-335 *2 *3)) (-4 *3 (-1014)) (-4 *2 (-962))))
- ((*1 *2 *1) (-12 (-4 *2 (-72)) (-5 *1 (-454 *2 *3)) (-4 *3 (-760))))
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+   (-14 *4 (-583 (-1090)))))
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+ ((*1 *2 *1 *3) (-12 (-4 *1 (-335 *2 *3)) (-4 *3 (-1013)) (-4 *2 (-961))))
+ ((*1 *2 *1) (-12 (-4 *2 (-72)) (-5 *1 (-453 *2 *3)) (-4 *3 (-759))))
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-   (-4 *4 (-962)) (-4 *5 (-757))))
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+   (-4 *4 (-961)) (-4 *5 (-756))))
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-   (-4 *4 (-962)) (-4 *5 (-718)) (-4 *6 (-757))))
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-   (-4 *2 (-757))))
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+   (-4 *2 (-756))))
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-   (-4 *4 (-962)) (-4 *5 (-757))))
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+   (-4 *4 (-961)) (-4 *5 (-756))))
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-  (-12 (-5 *2 (-1 (-1041 *4 *3 *5))) (-4 *4 (-38 (-350 (-485)))) (-4 *4 (-962))
-   (-4 *3 (-757)) (-5 *1 (-1041 *4 *3 *5)) (-4 *5 (-862 *4 (-470 *3) *3))))
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+   (-4 *3 (-756)) (-5 *1 (-1040 *4 *3 *5)) (-4 *5 (-861 *4 (-469 *3) *3))))
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-  (-12 (-5 *2 (-1 (-1123 *4))) (-5 *3 (-1091)) (-5 *1 (-1123 *4))
-   (-4 *4 (-38 (-350 (-485)))) (-4 *4 (-962))))) 
+  (-12 (-5 *2 (-1 (-1122 *4))) (-5 *3 (-1090)) (-5 *1 (-1122 *4))
+   (-4 *4 (-38 (-350 (-484)))) (-4 *4 (-961))))) 
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-  (-12 (-4 *3 (-554 (-801 *3))) (-4 *3 (-797 *3)) (-4 *3 (-392))
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-   (-4 *2 (-13 (-364 *3) (-1116)))))) 
+  (-12 (-4 *3 (-553 (-800 *3))) (-4 *3 (-796 *3)) (-4 *3 (-392))
+   (-5 *1 (-1121 *3 *2)) (-4 *2 (-553 (-800 *3))) (-4 *2 (-796 *3))
+   (-4 *2 (-13 (-364 *3) (-1115)))))) 
 (((*1 *2 *2)
-  (-12 (-4 *3 (-392)) (-5 *1 (-1122 *3 *2)) (-4 *2 (-13 (-364 *3) (-1116)))))) 
+  (-12 (-4 *3 (-392)) (-5 *1 (-1121 *3 *2)) (-4 *2 (-13 (-364 *3) (-1115)))))) 
 (((*1 *2 *2)
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 (((*1 *2 *2)
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-   (-5 *1 (-1028 *4 *5))))) 
+  (-12 (-5 *3 (-1148 *5 *4)) (-4 *4 (-740)) (-14 *5 (-1090)) (-5 *2 (-484))
+   (-5 *1 (-1027 *4 *5))))) 
 (((*1 *2 *3 *3)
-  (-12 (-5 *3 (-1149 *5 *4)) (-4 *4 (-741)) (-14 *5 (-1091)) (-5 *2 (-584 *4))
-   (-5 *1 (-1028 *4 *5))))) 
+  (-12 (-5 *3 (-1148 *5 *4)) (-4 *4 (-740)) (-14 *5 (-1090)) (-5 *2 (-583 *4))
+   (-5 *1 (-1027 *4 *5))))) 
 (((*1 *2 *3 *3)
-  (-12 (-4 *4 (-741)) (-14 *5 (-1091)) (-5 *2 (-584 (-1149 *5 *4)))
-   (-5 *1 (-1028 *4 *5)) (-5 *3 (-1149 *5 *4))))) 
+  (-12 (-4 *4 (-740)) (-14 *5 (-1090)) (-5 *2 (-583 (-1148 *5 *4)))
+   (-5 *1 (-1027 *4 *5)) (-5 *3 (-1148 *5 *4))))) 
 (((*1 *2 *3 *3)
-  (-12 (-4 *4 (-741)) (-14 *5 (-1091)) (-5 *2 (-584 (-1149 *5 *4)))
-   (-5 *1 (-1028 *4 *5)) (-5 *3 (-1149 *5 *4))))) 
-(((*1 *1 *2) (-12 (-5 *2 (-1 *3 *3 *3)) (-4 *3 (-72)) (-5 *1 (-1023 *3))))) 
-(((*1 *2 *3 *3 *3) (-12 (-5 *2 (-584 (-485))) (-5 *1 (-1022)) (-5 *3 (-485))))) 
-(((*1 *2 *3 *3 *3) (-12 (-5 *2 (-584 (-485))) (-5 *1 (-1022)) (-5 *3 (-485))))) 
-(((*1 *2 *3 *3 *3) (-12 (-5 *2 (-584 (-485))) (-5 *1 (-1022)) (-5 *3 (-485))))) 
-(((*1 *2 *2 *2) (-12 (-5 *2 (-485)) (-5 *1 (-1022))))) 
-(((*1 *2 *2 *2 *3) (-12 (-5 *2 (-1180 (-485))) (-5 *3 (-485)) (-5 *1 (-1022))))
+  (-12 (-4 *4 (-740)) (-14 *5 (-1090)) (-5 *2 (-583 (-1148 *5 *4)))
+   (-5 *1 (-1027 *4 *5)) (-5 *3 (-1148 *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 (-583 (-484))) (-5 *1 (-1021)) (-5 *3 (-484))))) 
+(((*1 *2 *3 *3 *3) (-12 (-5 *2 (-583 (-484))) (-5 *1 (-1021)) (-5 *3 (-484))))) 
+(((*1 *2 *3 *3 *3) (-12 (-5 *2 (-583 (-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 (-1179 (-484))) (-5 *3 (-484)) (-5 *1 (-1021))))
  ((*1 *2 *3 *2 *4)
-  (-12 (-5 *2 (-1180 (-485))) (-5 *3 (-584 (-485))) (-5 *4 (-485))
-   (-5 *1 (-1022))))) 
+  (-12 (-5 *2 (-1179 (-484))) (-5 *3 (-583 (-484))) (-5 *4 (-484))
+   (-5 *1 (-1021))))) 
 (((*1 *2 *3 *2 *4)
-  (-12 (-5 *2 (-584 (-485))) (-5 *3 (-584 (-831))) (-5 *4 (-85))
-   (-5 *1 (-1022))))) 
+  (-12 (-5 *2 (-583 (-484))) (-5 *3 (-583 (-830))) (-5 *4 (-85))
+   (-5 *1 (-1021))))) 
 (((*1 *2 *3 *3 *2)
-  (-12 (-5 *2 (-631 (-485))) (-5 *3 (-584 (-485))) (-5 *1 (-1022))))) 
+  (-12 (-5 *2 (-630 (-484))) (-5 *3 (-583 (-484))) (-5 *1 (-1021))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *3 (-584 (-831))) (-5 *4 (-584 (-485))) (-5 *2 (-631 (-485)))
-   (-5 *1 (-1022))))) 
+  (-12 (-5 *3 (-583 (-830))) (-5 *4 (-583 (-484))) (-5 *2 (-630 (-484)))
+   (-5 *1 (-1021))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-584 (-831))) (-5 *2 (-584 (-631 (-485)))) (-5 *1 (-1022))))) 
+  (-12 (-5 *3 (-583 (-830))) (-5 *2 (-583 (-630 (-484)))) (-5 *1 (-1021))))) 
 (((*1 *2 *2 *2 *3)
-  (-12 (-5 *2 (-584 (-485))) (-5 *3 (-631 (-485))) (-5 *1 (-1022))))) 
+  (-12 (-5 *2 (-583 (-484))) (-5 *3 (-630 (-484))) (-5 *1 (-1021))))) 
 (((*1 *2 *3 *3 *3)
-  (-12 (-5 *3 (-584 (-485))) (-5 *2 (-631 (-485))) (-5 *1 (-1022))))) 
+  (-12 (-5 *3 (-583 (-484))) (-5 *2 (-630 (-484))) (-5 *1 (-1021))))) 
 (((*1 *2 *3 *4)
-  (-12 (-4 *5 (-392)) (-4 *6 (-718)) (-4 *7 (-757)) (-4 *3 (-978 *5 *6 *7))
-   (-5 *2 (-584 (-2 (|:| |val| *3) (|:| -1601 *4))))
-   (-5 *1 (-1020 *5 *6 *7 *3 *4)) (-4 *4 (-984 *5 *6 *7 *3))))) 
+  (-12 (-4 *5 (-392)) (-4 *6 (-717)) (-4 *7 (-756)) (-4 *3 (-977 *5 *6 *7))
+   (-5 *2 (-583 (-2 (|:| |val| *3) (|:| -1600 *4))))
+   (-5 *1 (-1019 *5 *6 *7 *3 *4)) (-4 *4 (-983 *5 *6 *7 *3))))) 
 (((*1 *2 *3 *4)
-  (-12 (-4 *5 (-392)) (-4 *6 (-718)) (-4 *7 (-757)) (-4 *3 (-978 *5 *6 *7))
-   (-5 *2 (-584 *4)) (-5 *1 (-1020 *5 *6 *7 *3 *4))
-   (-4 *4 (-984 *5 *6 *7 *3))))) 
+  (-12 (-4 *5 (-392)) (-4 *6 (-717)) (-4 *7 (-756)) (-4 *3 (-977 *5 *6 *7))
+   (-5 *2 (-583 *4)) (-5 *1 (-1019 *5 *6 *7 *3 *4))
+   (-4 *4 (-983 *5 *6 *7 *3))))) 
 (((*1 *2 *3 *4)
-  (-12 (-4 *5 (-392)) (-4 *6 (-718)) (-4 *7 (-757)) (-4 *3 (-978 *5 *6 *7))
-   (-5 *2 (-85)) (-5 *1 (-1020 *5 *6 *7 *3 *4)) (-4 *4 (-984 *5 *6 *7 *3))))
+  (-12 (-4 *5 (-392)) (-4 *6 (-717)) (-4 *7 (-756)) (-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 (-392)) (-4 *6 (-718)) (-4 *7 (-757)) (-4 *3 (-978 *5 *6 *7))
-   (-5 *2 (-584 (-2 (|:| |val| (-85)) (|:| -1601 *4))))
-   (-5 *1 (-1020 *5 *6 *7 *3 *4)) (-4 *4 (-984 *5 *6 *7 *3))))) 
+  (-12 (-4 *5 (-392)) (-4 *6 (-717)) (-4 *7 (-756)) (-4 *3 (-977 *5 *6 *7))
+   (-5 *2 (-583 (-2 (|:| |val| (-85)) (|:| -1600 *4))))
+   (-5 *1 (-1019 *5 *6 *7 *3 *4)) (-4 *4 (-983 *5 *6 *7 *3))))) 
 (((*1 *2 *3 *4)
-  (-12 (-4 *5 (-392)) (-4 *6 (-718)) (-4 *7 (-757)) (-4 *3 (-978 *5 *6 *7))
-   (-5 *2 (-584 *4)) (-5 *1 (-1020 *5 *6 *7 *3 *4))
-   (-4 *4 (-984 *5 *6 *7 *3))))) 
+  (-12 (-4 *5 (-392)) (-4 *6 (-717)) (-4 *7 (-756)) (-4 *3 (-977 *5 *6 *7))
+   (-5 *2 (-583 *4)) (-5 *1 (-1019 *5 *6 *7 *3 *4))
+   (-4 *4 (-983 *5 *6 *7 *3))))) 
 (((*1 *2 *3 *4)
-  (-12 (-4 *5 (-392)) (-4 *6 (-718)) (-4 *7 (-757)) (-4 *3 (-978 *5 *6 *7))
-   (-5 *2 (-584 (-2 (|:| |val| (-85)) (|:| -1601 *4))))
-   (-5 *1 (-1020 *5 *6 *7 *3 *4)) (-4 *4 (-984 *5 *6 *7 *3))))) 
+  (-12 (-4 *5 (-392)) (-4 *6 (-717)) (-4 *7 (-756)) (-4 *3 (-977 *5 *6 *7))
+   (-5 *2 (-583 (-2 (|:| |val| (-85)) (|:| -1600 *4))))
+   (-5 *1 (-1019 *5 *6 *7 *3 *4)) (-4 *4 (-983 *5 *6 *7 *3))))) 
 (((*1 *2 *3 *4)
-  (-12 (-4 *5 (-392)) (-4 *6 (-718)) (-4 *7 (-757)) (-4 *3 (-978 *5 *6 *7))
-   (-5 *2 (-584 *4)) (-5 *1 (-1020 *5 *6 *7 *3 *4))
-   (-4 *4 (-984 *5 *6 *7 *3))))) 
+  (-12 (-4 *5 (-392)) (-4 *6 (-717)) (-4 *7 (-756)) (-4 *3 (-977 *5 *6 *7))
+   (-5 *2 (-583 *4)) (-5 *1 (-1019 *5 *6 *7 *3 *4))
+   (-4 *4 (-983 *5 *6 *7 *3))))) 
 (((*1 *2 *3 *4)
-  (-12 (-4 *5 (-392)) (-4 *6 (-718)) (-4 *7 (-757)) (-4 *3 (-978 *5 *6 *7))
-   (-5 *2 (-584 (-2 (|:| |val| (-85)) (|:| -1601 *4))))
-   (-5 *1 (-1020 *5 *6 *7 *3 *4)) (-4 *4 (-984 *5 *6 *7 *3))))) 
+  (-12 (-4 *5 (-392)) (-4 *6 (-717)) (-4 *7 (-756)) (-4 *3 (-977 *5 *6 *7))
+   (-5 *2 (-583 (-2 (|:| |val| (-85)) (|:| -1600 *4))))
+   (-5 *1 (-1019 *5 *6 *7 *3 *4)) (-4 *4 (-983 *5 *6 *7 *3))))) 
 (((*1 *2 *3 *3 *4)
-  (-12 (-4 *5 (-392)) (-4 *6 (-718)) (-4 *7 (-757)) (-4 *3 (-978 *5 *6 *7))
-   (-5 *2 (-584 (-2 (|:| |val| *3) (|:| -1601 *4))))
-   (-5 *1 (-1020 *5 *6 *7 *3 *4)) (-4 *4 (-984 *5 *6 *7 *3))))) 
+  (-12 (-4 *5 (-392)) (-4 *6 (-717)) (-4 *7 (-756)) (-4 *3 (-977 *5 *6 *7))
+   (-5 *2 (-583 (-2 (|:| |val| *3) (|:| -1600 *4))))
+   (-5 *1 (-1019 *5 *6 *7 *3 *4)) (-4 *4 (-983 *5 *6 *7 *3))))) 
 (((*1 *2 *3 *3 *4)
-  (-12 (-4 *5 (-392)) (-4 *6 (-718)) (-4 *7 (-757)) (-4 *3 (-978 *5 *6 *7))
-   (-5 *2 (-584 (-2 (|:| |val| *3) (|:| -1601 *4))))
-   (-5 *1 (-1020 *5 *6 *7 *3 *4)) (-4 *4 (-984 *5 *6 *7 *3))))) 
+  (-12 (-4 *5 (-392)) (-4 *6 (-717)) (-4 *7 (-756)) (-4 *3 (-977 *5 *6 *7))
+   (-5 *2 (-583 (-2 (|:| |val| *3) (|:| -1600 *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 (-392)) (-4 *7 (-718)) (-4 *8 (-757))
-   (-4 *3 (-978 *6 *7 *8)) (-5 *2 (-584 (-2 (|:| |val| *3) (|:| -1601 *4))))
-   (-5 *1 (-1020 *6 *7 *8 *3 *4)) (-4 *4 (-984 *6 *7 *8 *3))))
+  (-12 (-5 *5 (-85)) (-4 *6 (-392)) (-4 *7 (-717)) (-4 *8 (-756))
+   (-4 *3 (-977 *6 *7 *8)) (-5 *2 (-583 (-2 (|:| |val| *3) (|:| -1600 *4))))
+   (-5 *1 (-1019 *6 *7 *8 *3 *4)) (-4 *4 (-983 *6 *7 *8 *3))))
  ((*1 *2 *3 *4 *5)
-  (-12 (-5 *3 (-584 (-2 (|:| |val| (-584 *8)) (|:| -1601 *9)))) (-5 *5 (-85))
-   (-4 *8 (-978 *6 *7 *4)) (-4 *9 (-984 *6 *7 *4 *8)) (-4 *6 (-392))
-   (-4 *7 (-718)) (-4 *4 (-757))
-   (-5 *2 (-584 (-2 (|:| |val| *8) (|:| -1601 *9))))
-   (-5 *1 (-1020 *6 *7 *4 *8 *9))))) 
+  (-12 (-5 *3 (-583 (-2 (|:| |val| (-583 *8)) (|:| -1600 *9)))) (-5 *5 (-85))
+   (-4 *8 (-977 *6 *7 *4)) (-4 *9 (-983 *6 *7 *4 *8)) (-4 *6 (-392))
+   (-4 *7 (-717)) (-4 *4 (-756))
+   (-5 *2 (-583 (-2 (|:| |val| *8) (|:| -1600 *9))))
+   (-5 *1 (-1019 *6 *7 *4 *8 *9))))) 
 (((*1 *2 *3 *3 *4)
-  (-12 (-4 *5 (-392)) (-4 *6 (-718)) (-4 *7 (-757)) (-4 *3 (-978 *5 *6 *7))
-   (-5 *2 (-584 (-2 (|:| |val| (-584 *3)) (|:| -1601 *4))))
-   (-5 *1 (-1020 *5 *6 *7 *3 *4)) (-4 *4 (-984 *5 *6 *7 *3))))) 
+  (-12 (-4 *5 (-392)) (-4 *6 (-717)) (-4 *7 (-756)) (-4 *3 (-977 *5 *6 *7))
+   (-5 *2 (-583 (-2 (|:| |val| (-583 *3)) (|:| -1600 *4))))
+   (-5 *1 (-1019 *5 *6 *7 *3 *4)) (-4 *4 (-983 *5 *6 *7 *3))))) 
 (((*1 *2)
-  (-12 (-4 *3 (-392)) (-4 *4 (-718)) (-4 *5 (-757)) (-4 *6 (-978 *3 *4 *5))
-   (-5 *2 (-1186)) (-5 *1 (-985 *3 *4 *5 *6 *7)) (-4 *7 (-984 *3 *4 *5 *6))))
+  (-12 (-4 *3 (-392)) (-4 *4 (-717)) (-4 *5 (-756)) (-4 *6 (-977 *3 *4 *5))
+   (-5 *2 (-1185)) (-5 *1 (-984 *3 *4 *5 *6 *7)) (-4 *7 (-983 *3 *4 *5 *6))))
  ((*1 *2)
-  (-12 (-4 *3 (-392)) (-4 *4 (-718)) (-4 *5 (-757)) (-4 *6 (-978 *3 *4 *5))
-   (-5 *2 (-1186)) (-5 *1 (-1020 *3 *4 *5 *6 *7)) (-4 *7 (-984 *3 *4 *5 *6))))) 
+  (-12 (-4 *3 (-392)) (-4 *4 (-717)) (-4 *5 (-756)) (-4 *6 (-977 *3 *4 *5))
+   (-5 *2 (-1185)) (-5 *1 (-1019 *3 *4 *5 *6 *7)) (-4 *7 (-983 *3 *4 *5 *6))))) 
 (((*1 *2 *3 *3 *3)
-  (-12 (-5 *3 (-1074)) (-4 *4 (-392)) (-4 *5 (-718)) (-4 *6 (-757))
-   (-4 *7 (-978 *4 *5 *6)) (-5 *2 (-1186)) (-5 *1 (-985 *4 *5 *6 *7 *8))
-   (-4 *8 (-984 *4 *5 *6 *7))))
+  (-12 (-5 *3 (-1073)) (-4 *4 (-392)) (-4 *5 (-717)) (-4 *6 (-756))
+   (-4 *7 (-977 *4 *5 *6)) (-5 *2 (-1185)) (-5 *1 (-984 *4 *5 *6 *7 *8))
+   (-4 *8 (-983 *4 *5 *6 *7))))
  ((*1 *2 *3 *3 *3)
-  (-12 (-5 *3 (-1074)) (-4 *4 (-392)) (-4 *5 (-718)) (-4 *6 (-757))
-   (-4 *7 (-978 *4 *5 *6)) (-5 *2 (-1186)) (-5 *1 (-1020 *4 *5 *6 *7 *8))
-   (-4 *8 (-984 *4 *5 *6 *7))))) 
+  (-12 (-5 *3 (-1073)) (-4 *4 (-392)) (-4 *5 (-717)) (-4 *6 (-756))
+   (-4 *7 (-977 *4 *5 *6)) (-5 *2 (-1185)) (-5 *1 (-1019 *4 *5 *6 *7 *8))
+   (-4 *8 (-983 *4 *5 *6 *7))))) 
 (((*1 *2)
-  (-12 (-4 *3 (-392)) (-4 *4 (-718)) (-4 *5 (-757)) (-4 *6 (-978 *3 *4 *5))
-   (-5 *2 (-1186)) (-5 *1 (-985 *3 *4 *5 *6 *7)) (-4 *7 (-984 *3 *4 *5 *6))))
+  (-12 (-4 *3 (-392)) (-4 *4 (-717)) (-4 *5 (-756)) (-4 *6 (-977 *3 *4 *5))
+   (-5 *2 (-1185)) (-5 *1 (-984 *3 *4 *5 *6 *7)) (-4 *7 (-983 *3 *4 *5 *6))))
  ((*1 *2)
-  (-12 (-4 *3 (-392)) (-4 *4 (-718)) (-4 *5 (-757)) (-4 *6 (-978 *3 *4 *5))
-   (-5 *2 (-1186)) (-5 *1 (-1020 *3 *4 *5 *6 *7)) (-4 *7 (-984 *3 *4 *5 *6))))) 
+  (-12 (-4 *3 (-392)) (-4 *4 (-717)) (-4 *5 (-756)) (-4 *6 (-977 *3 *4 *5))
+   (-5 *2 (-1185)) (-5 *1 (-1019 *3 *4 *5 *6 *7)) (-4 *7 (-983 *3 *4 *5 *6))))) 
 (((*1 *2 *3 *3 *3)
-  (-12 (-5 *3 (-1074)) (-4 *4 (-392)) (-4 *5 (-718)) (-4 *6 (-757))
-   (-4 *7 (-978 *4 *5 *6)) (-5 *2 (-1186)) (-5 *1 (-985 *4 *5 *6 *7 *8))
-   (-4 *8 (-984 *4 *5 *6 *7))))
+  (-12 (-5 *3 (-1073)) (-4 *4 (-392)) (-4 *5 (-717)) (-4 *6 (-756))
+   (-4 *7 (-977 *4 *5 *6)) (-5 *2 (-1185)) (-5 *1 (-984 *4 *5 *6 *7 *8))
+   (-4 *8 (-983 *4 *5 *6 *7))))
  ((*1 *2 *3 *3 *3)
-  (-12 (-5 *3 (-1074)) (-4 *4 (-392)) (-4 *5 (-718)) (-4 *6 (-757))
-   (-4 *7 (-978 *4 *5 *6)) (-5 *2 (-1186)) (-5 *1 (-1020 *4 *5 *6 *7 *8))
-   (-4 *8 (-984 *4 *5 *6 *7))))) 
+  (-12 (-5 *3 (-1073)) (-4 *4 (-392)) (-4 *5 (-717)) (-4 *6 (-756))
+   (-4 *7 (-977 *4 *5 *6)) (-5 *2 (-1185)) (-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 (-392)) (-4 *7 (-718)) (-4 *8 (-757))
-   (-4 *9 (-978 *6 *7 *8))
-   (-5 *2 (-2 (|:| -3268 (-584 *9)) (|:| -1601 *4) (|:| |ineq| (-584 *9))))
-   (-5 *1 (-902 *6 *7 *8 *9 *4)) (-5 *3 (-584 *9)) (-4 *4 (-984 *6 *7 *8 *9))))
+  (|partial| -12 (-5 *5 (-85)) (-4 *6 (-392)) (-4 *7 (-717)) (-4 *8 (-756))
+   (-4 *9 (-977 *6 *7 *8))
+   (-5 *2 (-2 (|:| -3267 (-583 *9)) (|:| -1600 *4) (|:| |ineq| (-583 *9))))
+   (-5 *1 (-901 *6 *7 *8 *9 *4)) (-5 *3 (-583 *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 (-392)) (-4 *7 (-718)) (-4 *8 (-757))
-   (-4 *9 (-978 *6 *7 *8))
-   (-5 *2 (-2 (|:| -3268 (-584 *9)) (|:| -1601 *4) (|:| |ineq| (-584 *9))))
-   (-5 *1 (-1019 *6 *7 *8 *9 *4)) (-5 *3 (-584 *9))
-   (-4 *4 (-984 *6 *7 *8 *9))))) 
+  (|partial| -12 (-5 *5 (-85)) (-4 *6 (-392)) (-4 *7 (-717)) (-4 *8 (-756))
+   (-4 *9 (-977 *6 *7 *8))
+   (-5 *2 (-2 (|:| -3267 (-583 *9)) (|:| -1600 *4) (|:| |ineq| (-583 *9))))
+   (-5 *1 (-1018 *6 *7 *8 *9 *4)) (-5 *3 (-583 *9))
+   (-4 *4 (-983 *6 *7 *8 *9))))) 
 (((*1 *2 *3 *4 *5 *5)
-  (-12 (-5 *4 (-584 *10)) (-5 *5 (-85)) (-4 *10 (-984 *6 *7 *8 *9))
-   (-4 *6 (-392)) (-4 *7 (-718)) (-4 *8 (-757)) (-4 *9 (-978 *6 *7 *8))
+  (-12 (-5 *4 (-583 *10)) (-5 *5 (-85)) (-4 *10 (-983 *6 *7 *8 *9))
+   (-4 *6 (-392)) (-4 *7 (-717)) (-4 *8 (-756)) (-4 *9 (-977 *6 *7 *8))
    (-5 *2
-    (-584 (-2 (|:| -3268 (-584 *9)) (|:| -1601 *10) (|:| |ineq| (-584 *9)))))
-   (-5 *1 (-902 *6 *7 *8 *9 *10)) (-5 *3 (-584 *9))))
+    (-583 (-2 (|:| -3267 (-583 *9)) (|:| -1600 *10) (|:| |ineq| (-583 *9)))))
+   (-5 *1 (-901 *6 *7 *8 *9 *10)) (-5 *3 (-583 *9))))
  ((*1 *2 *3 *4 *5 *5)
-  (-12 (-5 *4 (-584 *10)) (-5 *5 (-85)) (-4 *10 (-984 *6 *7 *8 *9))
-   (-4 *6 (-392)) (-4 *7 (-718)) (-4 *8 (-757)) (-4 *9 (-978 *6 *7 *8))
+  (-12 (-5 *4 (-583 *10)) (-5 *5 (-85)) (-4 *10 (-983 *6 *7 *8 *9))
+   (-4 *6 (-392)) (-4 *7 (-717)) (-4 *8 (-756)) (-4 *9 (-977 *6 *7 *8))
    (-5 *2
-    (-584 (-2 (|:| -3268 (-584 *9)) (|:| -1601 *10) (|:| |ineq| (-584 *9)))))
-   (-5 *1 (-1019 *6 *7 *8 *9 *10)) (-5 *3 (-584 *9))))) 
+    (-583 (-2 (|:| -3267 (-583 *9)) (|:| -1600 *10) (|:| |ineq| (-583 *9)))))
+   (-5 *1 (-1018 *6 *7 *8 *9 *10)) (-5 *3 (-583 *9))))) 
 (((*1 *2 *2)
-  (-12 (-5 *2 (-584 (-2 (|:| |val| (-584 *6)) (|:| -1601 *7))))
-   (-4 *6 (-978 *3 *4 *5)) (-4 *7 (-984 *3 *4 *5 *6)) (-4 *3 (-392))
-   (-4 *4 (-718)) (-4 *5 (-757)) (-5 *1 (-902 *3 *4 *5 *6 *7))))
+  (-12 (-5 *2 (-583 (-2 (|:| |val| (-583 *6)) (|:| -1600 *7))))
+   (-4 *6 (-977 *3 *4 *5)) (-4 *7 (-983 *3 *4 *5 *6)) (-4 *3 (-392))
+   (-4 *4 (-717)) (-4 *5 (-756)) (-5 *1 (-901 *3 *4 *5 *6 *7))))
  ((*1 *2 *2)
-  (-12 (-5 *2 (-584 (-2 (|:| |val| (-584 *6)) (|:| -1601 *7))))
-   (-4 *6 (-978 *3 *4 *5)) (-4 *7 (-984 *3 *4 *5 *6)) (-4 *3 (-392))
-   (-4 *4 (-718)) (-4 *5 (-757)) (-5 *1 (-1019 *3 *4 *5 *6 *7))))) 
+  (-12 (-5 *2 (-583 (-2 (|:| |val| (-583 *6)) (|:| -1600 *7))))
+   (-4 *6 (-977 *3 *4 *5)) (-4 *7 (-983 *3 *4 *5 *6)) (-4 *3 (-392))
+   (-4 *4 (-717)) (-4 *5 (-756)) (-5 *1 (-1018 *3 *4 *5 *6 *7))))) 
 (((*1 *2 *3 *3)
-  (-12 (-5 *3 (-2 (|:| |val| (-584 *7)) (|:| -1601 *8)))
-   (-4 *7 (-978 *4 *5 *6)) (-4 *8 (-984 *4 *5 *6 *7)) (-4 *4 (-392))
-   (-4 *5 (-718)) (-4 *6 (-757)) (-5 *2 (-85)) (-5 *1 (-902 *4 *5 *6 *7 *8))))
+  (-12 (-5 *3 (-2 (|:| |val| (-583 *7)) (|:| -1600 *8)))
+   (-4 *7 (-977 *4 *5 *6)) (-4 *8 (-983 *4 *5 *6 *7)) (-4 *4 (-392))
+   (-4 *5 (-717)) (-4 *6 (-756)) (-5 *2 (-85)) (-5 *1 (-901 *4 *5 *6 *7 *8))))
  ((*1 *2 *3 *3)
-  (-12 (-5 *3 (-2 (|:| |val| (-584 *7)) (|:| -1601 *8)))
-   (-4 *7 (-978 *4 *5 *6)) (-4 *8 (-984 *4 *5 *6 *7)) (-4 *4 (-392))
-   (-4 *5 (-718)) (-4 *6 (-757)) (-5 *2 (-85)) (-5 *1 (-1019 *4 *5 *6 *7 *8))))) 
+  (-12 (-5 *3 (-2 (|:| |val| (-583 *7)) (|:| -1600 *8)))
+   (-4 *7 (-977 *4 *5 *6)) (-4 *8 (-983 *4 *5 *6 *7)) (-4 *4 (-392))
+   (-4 *5 (-717)) (-4 *6 (-756)) (-5 *2 (-85)) (-5 *1 (-1018 *4 *5 *6 *7 *8))))) 
 (((*1 *2 *2)
-  (-12 (-5 *2 (-584 *7)) (-4 *7 (-984 *3 *4 *5 *6)) (-4 *3 (-392))
-   (-4 *4 (-718)) (-4 *5 (-757)) (-4 *6 (-978 *3 *4 *5))
-   (-5 *1 (-902 *3 *4 *5 *6 *7))))
+  (-12 (-5 *2 (-583 *7)) (-4 *7 (-983 *3 *4 *5 *6)) (-4 *3 (-392))
+   (-4 *4 (-717)) (-4 *5 (-756)) (-4 *6 (-977 *3 *4 *5))
+   (-5 *1 (-901 *3 *4 *5 *6 *7))))
  ((*1 *2 *2)
-  (-12 (-5 *2 (-584 *7)) (-4 *7 (-984 *3 *4 *5 *6)) (-4 *3 (-392))
-   (-4 *4 (-718)) (-4 *5 (-757)) (-4 *6 (-978 *3 *4 *5))
-   (-5 *1 (-1019 *3 *4 *5 *6 *7))))) 
+  (-12 (-5 *2 (-583 *7)) (-4 *7 (-983 *3 *4 *5 *6)) (-4 *3 (-392))
+   (-4 *4 (-717)) (-4 *5 (-756)) (-4 *6 (-977 *3 *4 *5))
+   (-5 *1 (-1018 *3 *4 *5 *6 *7))))) 
 (((*1 *2 *3 *3)
-  (-12 (-4 *4 (-392)) (-4 *5 (-718)) (-4 *6 (-757)) (-4 *7 (-978 *4 *5 *6))
-   (-5 *2 (-85)) (-5 *1 (-902 *4 *5 *6 *7 *3)) (-4 *3 (-984 *4 *5 *6 *7))))
+  (-12 (-4 *4 (-392)) (-4 *5 (-717)) (-4 *6 (-756)) (-4 *7 (-977 *4 *5 *6))
+   (-5 *2 (-85)) (-5 *1 (-901 *4 *5 *6 *7 *3)) (-4 *3 (-983 *4 *5 *6 *7))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *4 (-584 *3)) (-4 *3 (-984 *5 *6 *7 *8)) (-4 *5 (-392))
-   (-4 *6 (-718)) (-4 *7 (-757)) (-4 *8 (-978 *5 *6 *7)) (-5 *2 (-85))
-   (-5 *1 (-902 *5 *6 *7 *8 *3))))
+  (-12 (-5 *4 (-583 *3)) (-4 *3 (-983 *5 *6 *7 *8)) (-4 *5 (-392))
+   (-4 *6 (-717)) (-4 *7 (-756)) (-4 *8 (-977 *5 *6 *7)) (-5 *2 (-85))
+   (-5 *1 (-901 *5 *6 *7 *8 *3))))
  ((*1 *2 *3 *3)
-  (-12 (-4 *4 (-392)) (-4 *5 (-718)) (-4 *6 (-757)) (-4 *7 (-978 *4 *5 *6))
-   (-5 *2 (-85)) (-5 *1 (-1019 *4 *5 *6 *7 *3)) (-4 *3 (-984 *4 *5 *6 *7))))
+  (-12 (-4 *4 (-392)) (-4 *5 (-717)) (-4 *6 (-756)) (-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 (-584 *3)) (-4 *3 (-984 *5 *6 *7 *8)) (-4 *5 (-392))
-   (-4 *6 (-718)) (-4 *7 (-757)) (-4 *8 (-978 *5 *6 *7)) (-5 *2 (-85))
-   (-5 *1 (-1019 *5 *6 *7 *8 *3))))) 
+  (-12 (-5 *4 (-583 *3)) (-4 *3 (-983 *5 *6 *7 *8)) (-4 *5 (-392))
+   (-4 *6 (-717)) (-4 *7 (-756)) (-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 (-392)) (-4 *5 (-718)) (-4 *6 (-757))
-   (-4 *7 (-978 *4 *5 *6)) (-5 *2 (-85)) (-5 *1 (-902 *4 *5 *6 *7 *3))
-   (-4 *3 (-984 *4 *5 *6 *7))))
+  (|partial| -12 (-4 *4 (-392)) (-4 *5 (-717)) (-4 *6 (-756))
+   (-4 *7 (-977 *4 *5 *6)) (-5 *2 (-85)) (-5 *1 (-901 *4 *5 *6 *7 *3))
+   (-4 *3 (-983 *4 *5 *6 *7))))
  ((*1 *2 *3 *3)
-  (|partial| -12 (-4 *4 (-392)) (-4 *5 (-718)) (-4 *6 (-757))
-   (-4 *7 (-978 *4 *5 *6)) (-5 *2 (-85)) (-5 *1 (-1019 *4 *5 *6 *7 *3))
-   (-4 *3 (-984 *4 *5 *6 *7))))) 
+  (|partial| -12 (-4 *4 (-392)) (-4 *5 (-717)) (-4 *6 (-756))
+   (-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 (-584 *7)) (-4 *7 (-978 *4 *5 *6)) (-4 *4 (-392)) (-4 *5 (-718))
-   (-4 *6 (-757)) (-5 *2 (-85)) (-5 *1 (-902 *4 *5 *6 *7 *8))
-   (-4 *8 (-984 *4 *5 *6 *7))))
+  (-12 (-5 *3 (-583 *7)) (-4 *7 (-977 *4 *5 *6)) (-4 *4 (-392)) (-4 *5 (-717))
+   (-4 *6 (-756)) (-5 *2 (-85)) (-5 *1 (-901 *4 *5 *6 *7 *8))
+   (-4 *8 (-983 *4 *5 *6 *7))))
  ((*1 *2 *3 *3)
-  (-12 (-5 *3 (-584 *7)) (-4 *7 (-978 *4 *5 *6)) (-4 *4 (-392)) (-4 *5 (-718))
-   (-4 *6 (-757)) (-5 *2 (-85)) (-5 *1 (-1019 *4 *5 *6 *7 *8))
-   (-4 *8 (-984 *4 *5 *6 *7))))) 
+  (-12 (-5 *3 (-583 *7)) (-4 *7 (-977 *4 *5 *6)) (-4 *4 (-392)) (-4 *5 (-717))
+   (-4 *6 (-756)) (-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 (-584 *7)) (-4 *7 (-978 *4 *5 *6)) (-4 *4 (-392)) (-4 *5 (-718))
-   (-4 *6 (-757)) (-5 *2 (-85)) (-5 *1 (-902 *4 *5 *6 *7 *8))
-   (-4 *8 (-984 *4 *5 *6 *7))))
+  (-12 (-5 *3 (-583 *7)) (-4 *7 (-977 *4 *5 *6)) (-4 *4 (-392)) (-4 *5 (-717))
+   (-4 *6 (-756)) (-5 *2 (-85)) (-5 *1 (-901 *4 *5 *6 *7 *8))
+   (-4 *8 (-983 *4 *5 *6 *7))))
  ((*1 *2 *3 *3)
-  (-12 (-5 *3 (-584 *7)) (-4 *7 (-978 *4 *5 *6)) (-4 *4 (-392)) (-4 *5 (-718))
-   (-4 *6 (-757)) (-5 *2 (-85)) (-5 *1 (-1019 *4 *5 *6 *7 *8))
-   (-4 *8 (-984 *4 *5 *6 *7))))) 
+  (-12 (-5 *3 (-583 *7)) (-4 *7 (-977 *4 *5 *6)) (-4 *4 (-392)) (-4 *5 (-717))
+   (-4 *6 (-756)) (-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 (-584 *7)) (-4 *7 (-978 *4 *5 *6)) (-4 *4 (-392)) (-4 *5 (-718))
-   (-4 *6 (-757)) (-5 *2 (-85)) (-5 *1 (-902 *4 *5 *6 *7 *8))
-   (-4 *8 (-984 *4 *5 *6 *7))))
+  (-12 (-5 *3 (-583 *7)) (-4 *7 (-977 *4 *5 *6)) (-4 *4 (-392)) (-4 *5 (-717))
+   (-4 *6 (-756)) (-5 *2 (-85)) (-5 *1 (-901 *4 *5 *6 *7 *8))
+   (-4 *8 (-983 *4 *5 *6 *7))))
  ((*1 *2 *3 *3)
-  (-12 (-5 *3 (-584 *7)) (-4 *7 (-978 *4 *5 *6)) (-4 *4 (-392)) (-4 *5 (-718))
-   (-4 *6 (-757)) (-5 *2 (-85)) (-5 *1 (-1019 *4 *5 *6 *7 *8))
-   (-4 *8 (-984 *4 *5 *6 *7))))) 
+  (-12 (-5 *3 (-583 *7)) (-4 *7 (-977 *4 *5 *6)) (-4 *4 (-392)) (-4 *5 (-717))
+   (-4 *6 (-756)) (-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 (-392)) (-4 *5 (-718)) (-4 *6 (-757)) (-4 *7 (-978 *4 *5 *6))
-   (-5 *2 (-85)) (-5 *1 (-902 *4 *5 *6 *7 *3)) (-4 *3 (-984 *4 *5 *6 *7))))
+  (-12 (-4 *4 (-392)) (-4 *5 (-717)) (-4 *6 (-756)) (-4 *7 (-977 *4 *5 *6))
+   (-5 *2 (-85)) (-5 *1 (-901 *4 *5 *6 *7 *3)) (-4 *3 (-983 *4 *5 *6 *7))))
  ((*1 *2 *3 *3)
-  (-12 (-4 *4 (-392)) (-4 *5 (-718)) (-4 *6 (-757)) (-4 *7 (-978 *4 *5 *6))
-   (-5 *2 (-85)) (-5 *1 (-1019 *4 *5 *6 *7 *3)) (-4 *3 (-984 *4 *5 *6 *7))))) 
+  (-12 (-4 *4 (-392)) (-4 *5 (-717)) (-4 *6 (-756)) (-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 (-392)) (-4 *5 (-718)) (-4 *6 (-757)) (-4 *7 (-978 *4 *5 *6))
-   (-5 *2 (-85)) (-5 *1 (-902 *4 *5 *6 *7 *3)) (-4 *3 (-984 *4 *5 *6 *7))))
+  (-12 (-4 *4 (-392)) (-4 *5 (-717)) (-4 *6 (-756)) (-4 *7 (-977 *4 *5 *6))
+   (-5 *2 (-85)) (-5 *1 (-901 *4 *5 *6 *7 *3)) (-4 *3 (-983 *4 *5 *6 *7))))
  ((*1 *2 *3 *3)
-  (-12 (-4 *4 (-392)) (-4 *5 (-718)) (-4 *6 (-757)) (-4 *7 (-978 *4 *5 *6))
-   (-5 *2 (-85)) (-5 *1 (-1019 *4 *5 *6 *7 *3)) (-4 *3 (-984 *4 *5 *6 *7))))) 
+  (-12 (-4 *4 (-392)) (-4 *5 (-717)) (-4 *6 (-756)) (-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 (-584 *7)) (-4 *7 (-984 *3 *4 *5 *6)) (-4 *3 (-392))
-   (-4 *4 (-718)) (-4 *5 (-757)) (-4 *6 (-978 *3 *4 *5))
-   (-5 *1 (-902 *3 *4 *5 *6 *7))))
+  (-12 (-5 *2 (-583 *7)) (-4 *7 (-983 *3 *4 *5 *6)) (-4 *3 (-392))
+   (-4 *4 (-717)) (-4 *5 (-756)) (-4 *6 (-977 *3 *4 *5))
+   (-5 *1 (-901 *3 *4 *5 *6 *7))))
  ((*1 *2 *2)
-  (-12 (-5 *2 (-584 *7)) (-4 *7 (-984 *3 *4 *5 *6)) (-4 *3 (-392))
-   (-4 *4 (-718)) (-4 *5 (-757)) (-4 *6 (-978 *3 *4 *5))
-   (-5 *1 (-1019 *3 *4 *5 *6 *7))))) 
+  (-12 (-5 *2 (-583 *7)) (-4 *7 (-983 *3 *4 *5 *6)) (-4 *3 (-392))
+   (-4 *4 (-717)) (-4 *5 (-756)) (-4 *6 (-977 *3 *4 *5))
+   (-5 *1 (-1018 *3 *4 *5 *6 *7))))) 
 (((*1 *2 *3 *3)
-  (-12 (-4 *4 (-392)) (-4 *5 (-718)) (-4 *6 (-757)) (-4 *7 (-978 *4 *5 *6))
-   (-5 *2 (-85)) (-5 *1 (-902 *4 *5 *6 *7 *3)) (-4 *3 (-984 *4 *5 *6 *7))))
+  (-12 (-4 *4 (-392)) (-4 *5 (-717)) (-4 *6 (-756)) (-4 *7 (-977 *4 *5 *6))
+   (-5 *2 (-85)) (-5 *1 (-901 *4 *5 *6 *7 *3)) (-4 *3 (-983 *4 *5 *6 *7))))
  ((*1 *2 *3 *3)
-  (-12 (-4 *4 (-392)) (-4 *5 (-718)) (-4 *6 (-757)) (-4 *7 (-978 *4 *5 *6))
-   (-5 *2 (-85)) (-5 *1 (-1019 *4 *5 *6 *7 *3)) (-4 *3 (-984 *4 *5 *6 *7))))) 
+  (-12 (-4 *4 (-392)) (-4 *5 (-717)) (-4 *6 (-756)) (-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 (-392)) (-4 *4 (-718)) (-4 *5 (-757)) (-4 *6 (-978 *3 *4 *5))
-   (-5 *2 (-1186)) (-5 *1 (-902 *3 *4 *5 *6 *7)) (-4 *7 (-984 *3 *4 *5 *6))))
+  (-12 (-4 *3 (-392)) (-4 *4 (-717)) (-4 *5 (-756)) (-4 *6 (-977 *3 *4 *5))
+   (-5 *2 (-1185)) (-5 *1 (-901 *3 *4 *5 *6 *7)) (-4 *7 (-983 *3 *4 *5 *6))))
  ((*1 *2)
-  (-12 (-4 *3 (-392)) (-4 *4 (-718)) (-4 *5 (-757)) (-4 *6 (-978 *3 *4 *5))
-   (-5 *2 (-1186)) (-5 *1 (-1019 *3 *4 *5 *6 *7)) (-4 *7 (-984 *3 *4 *5 *6))))) 
+  (-12 (-4 *3 (-392)) (-4 *4 (-717)) (-4 *5 (-756)) (-4 *6 (-977 *3 *4 *5))
+   (-5 *2 (-1185)) (-5 *1 (-1018 *3 *4 *5 *6 *7)) (-4 *7 (-983 *3 *4 *5 *6))))) 
 (((*1 *2 *3 *3 *3)
-  (-12 (-5 *3 (-1074)) (-4 *4 (-392)) (-4 *5 (-718)) (-4 *6 (-757))
-   (-4 *7 (-978 *4 *5 *6)) (-5 *2 (-1186)) (-5 *1 (-902 *4 *5 *6 *7 *8))
-   (-4 *8 (-984 *4 *5 *6 *7))))
+  (-12 (-5 *3 (-1073)) (-4 *4 (-392)) (-4 *5 (-717)) (-4 *6 (-756))
+   (-4 *7 (-977 *4 *5 *6)) (-5 *2 (-1185)) (-5 *1 (-901 *4 *5 *6 *7 *8))
+   (-4 *8 (-983 *4 *5 *6 *7))))
  ((*1 *2 *3 *3 *3)
-  (-12 (-5 *3 (-1074)) (-4 *4 (-392)) (-4 *5 (-718)) (-4 *6 (-757))
-   (-4 *7 (-978 *4 *5 *6)) (-5 *2 (-1186)) (-5 *1 (-1019 *4 *5 *6 *7 *8))
-   (-4 *8 (-984 *4 *5 *6 *7))))) 
-(((*1 *2 *1 *1) (-12 (-5 *2 (-85)) (-5 *1 (-987))))
+  (-12 (-5 *3 (-1073)) (-4 *4 (-392)) (-4 *5 (-717)) (-4 *6 (-756))
+   (-4 *7 (-977 *4 *5 *6)) (-5 *2 (-1185)) (-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 (-1017 *3 *4 *5 *6 *7)) (-4 *3 (-1014)) (-4 *4 (-1014))
-   (-4 *5 (-1014)) (-4 *6 (-1014)) (-4 *7 (-1014)) (-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 (-1017 *3 *4 *5 *6 *7)) (-4 *3 (-1014)) (-4 *4 (-1014))
-   (-4 *5 (-1014)) (-4 *6 (-1014)) (-4 *7 (-1014)) (-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 (-1017 *3 *4 *5 *6 *7)) (-4 *3 (-1014)) (-4 *4 (-1014))
-   (-4 *5 (-1014)) (-4 *6 (-1014)) (-4 *7 (-1014)) (-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 (-1017 *3 *4 *5 *6 *7)) (-4 *3 (-1014)) (-4 *4 (-1014))
-   (-4 *5 (-1014)) (-4 *6 (-1014)) (-4 *7 (-1014)) (-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 (-1017 *3 *4 *5 *6 *7)) (-4 *3 (-1014)) (-4 *4 (-1014))
-   (-4 *5 (-1014)) (-4 *6 (-1014)) (-4 *7 (-1014)) (-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 (-1017 *3 *4 *5 *6 *7)) (-4 *3 (-1014)) (-4 *4 (-1014))
-   (-4 *5 (-1014)) (-4 *6 (-1014)) (-4 *7 (-1014)) (-5 *2 (-85))))) 
-(((*1 *2 *1) (-12 (-5 *2 (-85)) (-5 *1 (-801 *3)) (-4 *3 (-1014))))
+  (-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 (-800 *3)) (-4 *3 (-1013))))
  ((*1 *2 *1)
-  (-12 (-4 *1 (-1017 *3 *4 *5 *6 *7)) (-4 *3 (-1014)) (-4 *4 (-1014))
-   (-4 *5 (-1014)) (-4 *6 (-1014)) (-4 *7 (-1014)) (-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 (-377))))
- ((*1 *2 *3) (-12 (-5 *2 (-85)) (-5 *1 (-506 *3)) (-4 *3 (-951 (-485)))))
+ ((*1 *2 *3) (-12 (-5 *2 (-85)) (-5 *1 (-505 *3)) (-4 *3 (-950 (-484)))))
  ((*1 *2 *1)
-  (-12 (-4 *1 (-1017 *3 *4 *5 *6 *7)) (-4 *3 (-1014)) (-4 *4 (-1014))
-   (-4 *5 (-1014)) (-4 *6 (-1014)) (-4 *7 (-1014)) (-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 (-1017 *3 *4 *5 *6 *7)) (-4 *3 (-1014)) (-4 *4 (-1014))
-   (-4 *5 (-1014)) (-4 *6 (-1014)) (-4 *7 (-1014)) (-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 (-584 (-2 (|:| -3862 (-1091)) (|:| |entry| *4))))
-   (-5 *1 (-799 *3 *4)) (-4 *3 (-1014)) (-4 *4 (-1014))))
+  (-12 (-5 *2 (-583 (-2 (|:| -3861 (-1090)) (|:| |entry| *4))))
+   (-5 *1 (-798 *3 *4)) (-4 *3 (-1013)) (-4 *4 (-1013))))
  ((*1 *2 *1)
-  (-12 (-4 *3 (-1014)) (-4 *4 (-1014)) (-4 *5 (-1014)) (-4 *6 (-1014))
-   (-4 *7 (-1014)) (-5 *2 (-584 *1)) (-4 *1 (-1017 *3 *4 *5 *6 *7))))) 
+  (-12 (-4 *3 (-1013)) (-4 *4 (-1013)) (-4 *5 (-1013)) (-4 *6 (-1013))
+   (-4 *7 (-1013)) (-5 *2 (-583 *1)) (-4 *1 (-1016 *3 *4 *5 *6 *7))))) 
 (((*1 *2 *1)
-  (-12 (-4 *1 (-1017 *3 *2 *4 *5 *6)) (-4 *3 (-1014)) (-4 *4 (-1014))
-   (-4 *5 (-1014)) (-4 *6 (-1014)) (-4 *2 (-1014))))) 
-(((*1 *2 *3) (-12 (-5 *2 (-485)) (-5 *1 (-506 *3)) (-4 *3 (-951 *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 (-950 *2))))
  ((*1 *2 *1)
-  (-12 (-4 *1 (-1017 *3 *4 *2 *5 *6)) (-4 *3 (-1014)) (-4 *4 (-1014))
-   (-4 *5 (-1014)) (-4 *6 (-1014)) (-4 *2 (-1014))))) 
-(((*1 *1 *2 *2 *3) (-12 (-5 *2 (-485)) (-5 *3 (-831)) (-4 *1 (-347))))
- ((*1 *1 *2 *2) (-12 (-5 *2 (-485)) (-4 *1 (-347))))
+  (-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 (-830)) (-4 *1 (-347))))
+ ((*1 *1 *2 *2) (-12 (-5 *2 (-484)) (-4 *1 (-347))))
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-   (-4 *3 (-1021 *5 *6 *7 *8))))
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   (-12 (-5 *4 (-85)) (-4 *5 (-13 (-258) (-120)))
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   (-12 (-4 *4 (-13 (-258) (-120)))
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+   (-5 *2 (-583 (-2 (|:| -1750 (-1085 *4)) (|:| -3225 (-583 (-857 *4))))))
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   (-12 (-5 *4 (-85)) (-4 *5 (-13 (-258) (-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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-   (-4 *2 (-13 (-364 *5) (-797 *4) (-554 (-801 *4))))))
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 (((*1 *2 *2 *3)
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-   (-5 *1 (-802 *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 *5 *5)
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-   (-4 *6 (-978 *3 *4 *5)) (-5 *2 (-85))))
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-   (-4 *3 (-978 *4 *5 *6)) (-5 *2 (-85))))) 
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-   (-4 *3 (-978 *4 *5 *6)) (-5 *2 (-85))))) 
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-   (-4 *3 (-978 *4 *5 *6)) (-5 *2 (-85))))) 
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 (((*1 *2 *3 *1)
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-   (-4 *1 (-984 *4 *5 *6 *3))))) 
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 (((*1 *2 *3 *1)
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 (((*1 *2 *3 *3 *1)
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   (-12
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-   (-5 *1 (-705 *3)) (-4 *3 (-962))))
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-     (-4 *5 (-554 (-1091))))
-    (-4 *3 (-962)) (-4 *1 (-978 *3 *4 *5)) (-4 *4 (-718)) (-4 *5 (-757)))))
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-     (-4 *5 (-554 (-1091))))
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-     (-4 *5 (-554 (-1091))))
-    (-4 *3 (-962)) (-4 *1 (-978 *3 *4 *5)) (-4 *4 (-718)) (-4 *5 (-757)))))
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-    (-4 *4 (-718)) (-4 *5 (-757)))))
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+    (-12 (-4 *3 (-38 (-350 (-484)))) (-4 *5 (-553 (-1090)))) (-4 *3 (-961))
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-   (-4 *4 (-718)) (-4 *5 (-757))))) 
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 (((*1 *1 *1)
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-   (-4 *2 (-496))))) 
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 (((*1 *1 *1)
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 (((*1 *1 *1 *1)
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 (((*1 *1 *1 *1)
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-   (-4 *2 (-496))))
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 (((*1 *2 *1 *1)
   (-12
    (-5 *2
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-   (-4 *1 (-978 *3 *4 *5))))) 
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 (((*1 *2 *1 *1)
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 (((*1 *2 *1 *1)
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 (((*1 *1 *1 *1 *1 *1)
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- ((*1 *1 *1 *1) (-5 *1 (-695)))
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- ((*1 *1 *1 *1) (-5 *1 (-831)))
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    (-4 *2 (-392))))) 
 (((*1 *1 *1)
-  (-12 (-4 *1 (-978 *2 *3 *4)) (-4 *2 (-962)) (-4 *3 (-718)) (-4 *4 (-757))
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    (-4 *2 (-392))))) 
 (((*1 *1 *1)
-  (-12 (-4 *1 (-978 *2 *3 *4)) (-4 *2 (-962)) (-4 *3 (-718)) (-4 *4 (-757))
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    (-4 *2 (-392))))) 
 (((*1 *1 *1)
-  (-12 (-4 *1 (-978 *2 *3 *4)) (-4 *2 (-962)) (-4 *3 (-718)) (-4 *4 (-757))
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    (-4 *2 (-392))))) 
 (((*1 *1 *1)
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     (-13 (-312)
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 (((*1 *2 *1 *3)
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 (((*1 *2 *1)
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     (-13 (-312)
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 (((*1 *2 *3)
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 (((*1 *2 *3 *4)
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 (((*1 *2 *3 *4)
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 (((*1 *2 *2 *3)
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 (((*1 *2 *3 *2)
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 (((*1 *2 *3 *4)
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 (((*1 *2 *3 *4 *5 *5)
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-   (-5 *3 (-584 (-631 *6)))))
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  ((*1 *2 *3 *4)
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 (((*1 *2 *3 *4)
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 (((*1 *2 *3 *3 *4 *5)
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 (((*1 *2 *3 *4)
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 (((*1 *2 *3 *4)
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 (((*1 *2 *3 *2)
-  (-12 (-5 *3 (-584 (-631 *4))) (-5 *2 (-631 *4)) (-4 *4 (-962))
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 (((*1 *2 *3)
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-   (-5 *1 (-944 *4))))) 
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 (((*1 *2 *3 *4)
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-   (-4 *5 (-962))))
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-   (-4 *4 (-962))))
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+ ((*1 *2 *2) (-12 (-5 *2 (-583 (-630 *3))) (-4 *3 (-961)) (-5 *1 (-942 *3))))) 
 (((*1 *2 *2 *3)
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  ((*1 *2 *2 *3)
-  (-12 (-5 *2 (-584 (-631 *4))) (-5 *3 (-831)) (-4 *4 (-962))
-   (-5 *1 (-943 *4))))) 
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+   (-5 *1 (-942 *4))))) 
 (((*1 *2 *3)
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-   (-5 *1 (-892 *6)) (-5 *3 (-631 *6))))) 
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-   (-4 *8 (-757)) (-5 *1 (-891 *6 *7 *8 *9))))) 
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-   (-4 *5 (-757)) (-5 *1 (-891 *3 *4 *5 *6))))) 
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-   (-5 *1 (-891 *4 *5 *6 *7)) (-5 *3 (-584 *7))))) 
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-   (-4 *5 (-757)) (-5 *1 (-891 *3 *4 *5 *6))))) 
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 (((*1 *2 *2 *3)
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-   (-4 *6 (-757)) (-5 *1 (-891 *4 *5 *6 *2))))) 
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-   (-4 *5 (-757)) (-5 *1 (-891 *3 *4 *5 *6))))
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-   (-5 *1 (-891 *4 *5 *6 *7)) (-5 *3 (-584 *7))))) 
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-   (-5 *1 (-891 *4 *5 *6 *3)) (-4 *3 (-978 *4 *5 *6))))) 
+  (-12 (-4 *4 (-495)) (-4 *5 (-717)) (-4 *6 (-756)) (-5 *2 (-85))
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-   (-5 *1 (-891 *4 *5 *6 *3)) (-4 *3 (-978 *4 *5 *6))))) 
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-   (-5 *1 (-891 *4 *5 *6 *3)) (-4 *3 (-978 *4 *5 *6))))) 
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+(((*1 *2 *3) (-12 (-5 *3 (-772)) (-5 *2 (-1073)) (-5 *1 (-647))))) 
+(((*1 *2 *3) (-12 (-5 *3 (-772)) (-5 *2 (-1073)) (-5 *1 (-647))))) 
+(((*1 *2 *3) (-12 (-5 *3 (-772)) (-5 *2 (-1073)) (-5 *1 (-647))))) 
 (((*1 *2 *3 *4 *2 *5 *6 *7 *8 *9 *10)
-  (|partial| -12 (-5 *2 (-584 (-1086 *13))) (-5 *3 (-1086 *13))
-   (-5 *4 (-584 *12)) (-5 *5 (-584 *10)) (-5 *6 (-584 *13))
-   (-5 *7 (-584 (-584 (-2 (|:| -3080 (-695)) (|:| |pcoef| *13)))))
-   (-5 *8 (-584 (-695))) (-5 *9 (-1180 (-584 (-1086 *10)))) (-4 *12 (-757))
-   (-4 *10 (-258)) (-4 *13 (-862 *10 *11 *12)) (-4 *11 (-718))
-   (-5 *1 (-645 *11 *12 *10 *13))))) 
+  (|partial| -12 (-5 *2 (-583 (-1085 *13))) (-5 *3 (-1085 *13))
+   (-5 *4 (-583 *12)) (-5 *5 (-583 *10)) (-5 *6 (-583 *13))
+   (-5 *7 (-583 (-583 (-2 (|:| -3079 (-694)) (|:| |pcoef| *13)))))
+   (-5 *8 (-583 (-694))) (-5 *9 (-1179 (-583 (-1085 *10)))) (-4 *12 (-756))
+   (-4 *10 (-258)) (-4 *13 (-861 *10 *11 *12)) (-4 *11 (-717))
+   (-5 *1 (-644 *11 *12 *10 *13))))) 
 (((*1 *2 *3 *4 *5 *6 *7 *8 *9)
-  (|partial| -12 (-5 *4 (-584 *11)) (-5 *5 (-584 (-1086 *9))) (-5 *6 (-584 *9))
-   (-5 *7 (-584 *12)) (-5 *8 (-584 (-695))) (-4 *11 (-757)) (-4 *9 (-258))
-   (-4 *12 (-862 *9 *10 *11)) (-4 *10 (-718)) (-5 *2 (-584 (-1086 *12)))
-   (-5 *1 (-645 *10 *11 *9 *12)) (-5 *3 (-1086 *12))))) 
+  (|partial| -12 (-5 *4 (-583 *11)) (-5 *5 (-583 (-1085 *9))) (-5 *6 (-583 *9))
+   (-5 *7 (-583 *12)) (-5 *8 (-583 (-694))) (-4 *11 (-756)) (-4 *9 (-258))
+   (-4 *12 (-861 *9 *10 *11)) (-4 *10 (-717)) (-5 *2 (-583 (-1085 *12)))
+   (-5 *1 (-644 *10 *11 *9 *12)) (-5 *3 (-1085 *12))))) 
 (((*1 *2 *3 *4 *5 *6 *2 *7 *8)
-  (|partial| -12 (-5 *2 (-584 (-1086 *11))) (-5 *3 (-1086 *11))
-   (-5 *4 (-584 *10)) (-5 *5 (-584 *8)) (-5 *6 (-584 (-695)))
-   (-5 *7 (-1180 (-584 (-1086 *8)))) (-4 *10 (-757)) (-4 *8 (-258))
-   (-4 *11 (-862 *8 *9 *10)) (-4 *9 (-718)) (-5 *1 (-645 *9 *10 *8 *11))))) 
+  (|partial| -12 (-5 *2 (-583 (-1085 *11))) (-5 *3 (-1085 *11))
+   (-5 *4 (-583 *10)) (-5 *5 (-583 *8)) (-5 *6 (-583 (-694)))
+   (-5 *7 (-1179 (-583 (-1085 *8)))) (-4 *10 (-756)) (-4 *8 (-258))
+   (-4 *11 (-861 *8 *9 *10)) (-4 *9 (-717)) (-5 *1 (-644 *9 *10 *8 *11))))) 
 (((*1 *2 *3 *4 *4)
-  (-12 (-5 *4 (-1091)) (-5 *2 (-1 *7 *5 *6)) (-5 *1 (-640 *3 *5 *6 *7))
-   (-4 *3 (-554 (-474))) (-4 *5 (-1130)) (-4 *6 (-1130)) (-4 *7 (-1130))))
+  (-12 (-5 *4 (-1090)) (-5 *2 (-1 *7 *5 *6)) (-5 *1 (-639 *3 *5 *6 *7))
+   (-4 *3 (-553 (-473))) (-4 *5 (-1129)) (-4 *6 (-1129)) (-4 *7 (-1129))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *4 (-1091)) (-5 *2 (-1 *6 *5)) (-5 *1 (-644 *3 *5 *6))
-   (-4 *3 (-554 (-474))) (-4 *5 (-1130)) (-4 *6 (-1130))))) 
+  (-12 (-5 *4 (-1090)) (-5 *2 (-1 *6 *5)) (-5 *1 (-643 *3 *5 *6))
+   (-4 *3 (-553 (-473))) (-4 *5 (-1129)) (-4 *6 (-1129))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-1091)) (-5 *2 (-1 *6 *5)) (-5 *1 (-644 *4 *5 *6))
-   (-4 *4 (-554 (-474))) (-4 *5 (-1130)) (-4 *6 (-1130))))) 
+  (-12 (-5 *3 (-1090)) (-5 *2 (-1 *6 *5)) (-5 *1 (-643 *4 *5 *6))
+   (-4 *4 (-553 (-473))) (-4 *5 (-1129)) (-4 *6 (-1129))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *2 (-2 (|:| |part1| *3) (|:| |part2| *4))) (-5 *1 (-643 *3 *4))
-   (-4 *3 (-1130)) (-4 *4 (-1130))))) 
-(((*1 *1 *1 *2 *3) (-12 (-5 *2 (-584 (-1091))) (-5 *3 (-1091)) (-5 *1 (-474))))
- ((*1 *2 *3 *2) (-12 (-5 *2 (-1091)) (-5 *1 (-642 *3)) (-4 *3 (-554 (-474)))))
+  (-12 (-5 *2 (-2 (|:| |part1| *3) (|:| |part2| *4))) (-5 *1 (-642 *3 *4))
+   (-4 *3 (-1129)) (-4 *4 (-1129))))) 
+(((*1 *1 *1 *2 *3) (-12 (-5 *2 (-583 (-1090))) (-5 *3 (-1090)) (-5 *1 (-473))))
+ ((*1 *2 *3 *2) (-12 (-5 *2 (-1090)) (-5 *1 (-641 *3)) (-4 *3 (-553 (-473)))))
  ((*1 *2 *3 *2 *2)
-  (-12 (-5 *2 (-1091)) (-5 *1 (-642 *3)) (-4 *3 (-554 (-474)))))
+  (-12 (-5 *2 (-1090)) (-5 *1 (-641 *3)) (-4 *3 (-553 (-473)))))
  ((*1 *2 *3 *2 *2 *2)
-  (-12 (-5 *2 (-1091)) (-5 *1 (-642 *3)) (-4 *3 (-554 (-474)))))
+  (-12 (-5 *2 (-1090)) (-5 *1 (-641 *3)) (-4 *3 (-553 (-473)))))
  ((*1 *2 *3 *2 *4)
-  (-12 (-5 *4 (-584 (-1091))) (-5 *2 (-1091)) (-5 *1 (-642 *3))
-   (-4 *3 (-554 (-474)))))) 
+  (-12 (-5 *4 (-583 (-1090))) (-5 *2 (-1090)) (-5 *1 (-641 *3))
+   (-4 *3 (-553 (-473)))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *4 (-1091)) (-5 *2 (-1 (-179) (-179))) (-5 *1 (-641 *3))
-   (-4 *3 (-554 (-474)))))
+  (-12 (-5 *4 (-1090)) (-5 *2 (-1 (-179) (-179))) (-5 *1 (-640 *3))
+   (-4 *3 (-553 (-473)))))
  ((*1 *2 *3 *4 *4)
-  (-12 (-5 *4 (-1091)) (-5 *2 (-1 (-179) (-179) (-179))) (-5 *1 (-641 *3))
-   (-4 *3 (-554 (-474)))))) 
+  (-12 (-5 *4 (-1090)) (-5 *2 (-1 (-179) (-179) (-179))) (-5 *1 (-640 *3))
+   (-4 *3 (-553 (-473)))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-1091)) (-5 *2 (-1 *7 *5 *6)) (-5 *1 (-640 *4 *5 *6 *7))
-   (-4 *4 (-554 (-474))) (-4 *5 (-1130)) (-4 *6 (-1130)) (-4 *7 (-1130))))) 
+  (-12 (-5 *3 (-1090)) (-5 *2 (-1 *7 *5 *6)) (-5 *1 (-639 *4 *5 *6 *7))
+   (-4 *4 (-553 (-473))) (-4 *5 (-1129)) (-4 *6 (-1129)) (-4 *7 (-1129))))) 
 (((*1 *2 *3 *3)
   (-12 (-4 *3 (-258)) (-4 *3 (-146)) (-4 *4 (-324 *3)) (-4 *5 (-324 *3))
-   (-5 *2 (-2 (|:| -1973 *3) (|:| -2904 *3))) (-5 *1 (-630 *3 *4 *5 *6))
-   (-4 *6 (-628 *3 *4 *5))))
+   (-5 *2 (-2 (|:| -1972 *3) (|:| -2903 *3))) (-5 *1 (-629 *3 *4 *5 *6))
+   (-4 *6 (-627 *3 *4 *5))))
  ((*1 *2 *3 *3)
-  (-12 (-5 *2 (-2 (|:| -1973 *3) (|:| -2904 *3))) (-5 *1 (-639 *3))
+  (-12 (-5 *2 (-2 (|:| -1972 *3) (|:| -2903 *3))) (-5 *1 (-638 *3))
    (-4 *3 (-258))))) 
-(((*1 *2 *2 *3 *3) (-12 (-5 *2 (-631 *3)) (-4 *3 (-258)) (-5 *1 (-639 *3))))) 
-(((*1 *2 *2 *3) (-12 (-5 *2 (-631 *3)) (-4 *3 (-258)) (-5 *1 (-639 *3))))) 
-(((*1 *2 *2) (-12 (-5 *2 (-631 *3)) (-4 *3 (-258)) (-5 *1 (-639 *3))))) 
+(((*1 *2 *2 *3 *3) (-12 (-5 *2 (-630 *3)) (-4 *3 (-258)) (-5 *1 (-638 *3))))) 
+(((*1 *2 *2 *3) (-12 (-5 *2 (-630 *3)) (-4 *3 (-258)) (-5 *1 (-638 *3))))) 
+(((*1 *2 *2) (-12 (-5 *2 (-630 *3)) (-4 *3 (-258)) (-5 *1 (-638 *3))))) 
 (((*1 *2 *3 *3 *3 *4)
   (-12 (-5 *3 (-1 (-179) (-179) (-179)))
    (-5 *4 (-1 (-179) (-179) (-179) (-179)))
-   (-5 *2 (-1 (-855 (-179)) (-179) (-179))) (-5 *1 (-637))))) 
+   (-5 *2 (-1 (-854 (-179)) (-179) (-179))) (-5 *1 (-636))))) 
 (((*1 *2 *3 *3 *3 *4 *5 *6)
-  (-12 (-5 *3 (-265 (-485))) (-5 *4 (-1 (-179) (-179))) (-5 *5 (-1002 (-179)))
-   (-5 *6 (-584 (-221))) (-5 *2 (-1048 (-179))) (-5 *1 (-637))))) 
+  (-12 (-5 *3 (-265 (-484))) (-5 *4 (-1 (-179) (-179))) (-5 *5 (-1001 (-179)))
+   (-5 *6 (-583 (-221))) (-5 *2 (-1047 (-179))) (-5 *1 (-636))))) 
 (((*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 (-1002 (-179))) (-5 *6 (-584 (-221))) (-5 *2 (-1048 (-179)))
-   (-5 *1 (-637))))) 
+   (-5 *5 (-1001 (-179))) (-5 *6 (-583 (-221))) (-5 *2 (-1047 (-179)))
+   (-5 *1 (-636))))) 
 (((*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 (-1002 (-179))) (-5 *6 (-584 (-221))) (-5 *2 (-1048 (-179)))
-   (-5 *1 (-637))))
+   (-5 *5 (-1001 (-179))) (-5 *6 (-583 (-221))) (-5 *2 (-1047 (-179)))
+   (-5 *1 (-636))))
  ((*1 *2 *3 *4 *4 *5)
-  (-12 (-5 *3 (-1 (-855 (-179)) (-179) (-179))) (-5 *4 (-1002 (-179)))
-   (-5 *5 (-584 (-221))) (-5 *2 (-1048 (-179))) (-5 *1 (-637))))
+  (-12 (-5 *3 (-1 (-854 (-179)) (-179) (-179))) (-5 *4 (-1001 (-179)))
+   (-5 *5 (-583 (-221))) (-5 *2 (-1047 (-179))) (-5 *1 (-636))))
  ((*1 *2 *2 *3 *4 *4 *5)
-  (-12 (-5 *2 (-1048 (-179))) (-5 *3 (-1 (-855 (-179)) (-179) (-179)))
-   (-5 *4 (-1002 (-179))) (-5 *5 (-584 (-221))) (-5 *1 (-637))))) 
+  (-12 (-5 *2 (-1047 (-179))) (-5 *3 (-1 (-854 (-179)) (-179) (-179)))
+   (-5 *4 (-1001 (-179))) (-5 *5 (-583 (-221))) (-5 *1 (-636))))) 
 (((*1 *2 *2 *3 *2)
-  (-12 (-5 *3 (-695)) (-4 *4 (-299)) (-5 *1 (-170 *4 *2)) (-4 *2 (-1156 *4))))
+  (-12 (-5 *3 (-694)) (-4 *4 (-299)) (-5 *1 (-170 *4 *2)) (-4 *2 (-1155 *4))))
  ((*1 *2 *2 *3 *2 *3)
-  (-12 (-5 *3 (-485)) (-5 *1 (-636 *2)) (-4 *2 (-1156 *3))))) 
+  (-12 (-5 *3 (-484)) (-5 *1 (-635 *2)) (-4 *2 (-1155 *3))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-584 (-2 (|:| |deg| (-695)) (|:| -2577 *5)))) (-4 *5 (-1156 *4))
-   (-4 *4 (-299)) (-5 *2 (-584 *5)) (-5 *1 (-170 *4 *5))))
+  (-12 (-5 *3 (-583 (-2 (|:| |deg| (-694)) (|:| -2576 *5)))) (-4 *5 (-1155 *4))
+   (-4 *4 (-299)) (-5 *2 (-583 *5)) (-5 *1 (-170 *4 *5))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *3 (-584 (-2 (|:| -3734 *5) (|:| -3950 (-485))))) (-5 *4 (-485))
-   (-4 *5 (-1156 *4)) (-5 *2 (-584 *5)) (-5 *1 (-636 *5))))) 
+  (-12 (-5 *3 (-583 (-2 (|:| -3733 *5) (|:| -3949 (-484))))) (-5 *4 (-484))
+   (-4 *5 (-1155 *4)) (-5 *2 (-583 *5)) (-5 *1 (-635 *5))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *4 (-485)) (-5 *2 (-584 (-2 (|:| -3734 *3) (|:| -3950 *4))))
-   (-5 *1 (-636 *3)) (-4 *3 (-1156 *4))))) 
-(((*1 *2 *2 *3) (-12 (-5 *3 (-485)) (-5 *1 (-636 *2)) (-4 *2 (-1156 *3))))) 
-(((*1 *1 *1) (-12 (-4 *1 (-237 *2)) (-4 *2 (-1130)) (-4 *2 (-72))))
- ((*1 *1 *1) (-12 (-4 *1 (-635 *2)) (-4 *2 (-1014))))) 
+  (-12 (-5 *4 (-484)) (-5 *2 (-583 (-2 (|:| -3733 *3) (|:| -3949 *4))))
+   (-5 *1 (-635 *3)) (-4 *3 (-1155 *4))))) 
+(((*1 *2 *2 *3) (-12 (-5 *3 (-484)) (-5 *1 (-635 *2)) (-4 *2 (-1155 *3))))) 
+(((*1 *1 *1) (-12 (-4 *1 (-237 *2)) (-4 *2 (-1129)) (-4 *2 (-72))))
+ ((*1 *1 *1) (-12 (-4 *1 (-634 *2)) (-4 *2 (-1013))))) 
 (((*1 *2 *1)
-  (-12 (-4 *1 (-635 *3)) (-4 *3 (-1014))
-   (-5 *2 (-584 (-2 (|:| |entry| *3) (|:| -1731 (-695)))))))) 
-(((*1 *1 *2) (-12 (-5 *1 (-633 *2)) (-4 *2 (-553 (-773)))))) 
-(((*1 *1) (-12 (-5 *1 (-633 *2)) (-4 *2 (-553 (-773)))))) 
+  (-12 (-4 *1 (-634 *3)) (-4 *3 (-1013))
+   (-5 *2 (-583 (-2 (|:| |entry| *3) (|:| -1730 (-694)))))))) 
+(((*1 *1 *2) (-12 (-5 *1 (-632 *2)) (-4 *2 (-552 (-772)))))) 
+(((*1 *1) (-12 (-5 *1 (-632 *2)) (-4 *2 (-552 (-772)))))) 
 (((*1 *2 *2 *2 *2 *2 *3)
-  (-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 (-496)) (-4 *3 (-146)) (-4 *4 (-324 *3))
-   (-4 *5 (-324 *3)) (-5 *1 (-630 *3 *4 *5 *2)) (-4 *2 (-628 *3 *4 *5))))) 
-(((*1 *2 *2)
-  (-12 (-4 *3 (-496)) (-4 *3 (-146)) (-4 *4 (-324 *3)) (-4 *5 (-324 *3))
-   (-5 *1 (-630 *3 *4 *5 *2)) (-4 *2 (-628 *3 *4 *5))))) 
+  (-12 (-5 *2 (-630 *4)) (-5 *3 (-694)) (-4 *4 (-961)) (-5 *1 (-631 *4))))) 
+(((*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 (-495)) (-4 *3 (-146)) (-4 *4 (-324 *3))
+   (-4 *5 (-324 *3)) (-5 *1 (-629 *3 *4 *5 *2)) (-4 *2 (-627 *3 *4 *5))))) 
+(((*1 *2 *2)
+  (-12 (-4 *3 (-495)) (-4 *3 (-146)) (-4 *4 (-324 *3)) (-4 *5 (-324 *3))
+   (-5 *1 (-629 *3 *4 *5 *2)) (-4 *2 (-627 *3 *4 *5))))) 
 (((*1 *2 *2 *3 *4 *4)
-  (-12 (-5 *4 (-485)) (-4 *3 (-146)) (-4 *5 (-324 *3)) (-4 *6 (-324 *3))
-   (-5 *1 (-630 *3 *5 *6 *2)) (-4 *2 (-628 *3 *5 *6))))) 
+  (-12 (-5 *4 (-484)) (-4 *3 (-146)) (-4 *5 (-324 *3)) (-4 *6 (-324 *3))
+   (-5 *1 (-629 *3 *5 *6 *2)) (-4 *2 (-627 *3 *5 *6))))) 
 (((*1 *2 *2 *3 *4 *4)
-  (-12 (-5 *4 (-485)) (-4 *3 (-146)) (-4 *5 (-324 *3)) (-4 *6 (-324 *3))
-   (-5 *1 (-630 *3 *5 *6 *2)) (-4 *2 (-628 *3 *5 *6))))) 
+  (-12 (-5 *4 (-484)) (-4 *3 (-146)) (-4 *5 (-324 *3)) (-4 *6 (-324 *3))
+   (-5 *1 (-629 *3 *5 *6 *2)) (-4 *2 (-627 *3 *5 *6))))) 
 (((*1 *2 *2 *3 *3)
-  (-12 (-5 *3 (-485)) (-4 *4 (-146)) (-4 *5 (-324 *4)) (-4 *6 (-324 *4))
-   (-5 *1 (-630 *4 *5 *6 *2)) (-4 *2 (-628 *4 *5 *6))))) 
+  (-12 (-5 *3 (-484)) (-4 *4 (-146)) (-4 *5 (-324 *4)) (-4 *6 (-324 *4))
+   (-5 *1 (-629 *4 *5 *6 *2)) (-4 *2 (-627 *4 *5 *6))))) 
 (((*1 *1 *1)
-  (-12 (-4 *1 (-628 *2 *3 *4)) (-4 *2 (-962)) (-4 *3 (-324 *2))
+  (-12 (-4 *1 (-627 *2 *3 *4)) (-4 *2 (-961)) (-4 *3 (-324 *2))
    (-4 *4 (-324 *2))))) 
 (((*1 *1 *1 *1)
-  (-12 (-4 *1 (-628 *2 *3 *4)) (-4 *2 (-962)) (-4 *3 (-324 *2))
+  (-12 (-4 *1 (-627 *2 *3 *4)) (-4 *2 (-961)) (-4 *3 (-324 *2))
    (-4 *4 (-324 *2))))) 
 (((*1 *1 *1 *1)
-  (-12 (-4 *1 (-628 *2 *3 *4)) (-4 *2 (-962)) (-4 *3 (-324 *2))
+  (-12 (-4 *1 (-627 *2 *3 *4)) (-4 *2 (-961)) (-4 *3 (-324 *2))
    (-4 *4 (-324 *2))))) 
 (((*1 *1 *1 *2 *2)
-  (-12 (-5 *2 (-485)) (-4 *1 (-628 *3 *4 *5)) (-4 *3 (-962)) (-4 *4 (-324 *3))
+  (-12 (-5 *2 (-484)) (-4 *1 (-627 *3 *4 *5)) (-4 *3 (-961)) (-4 *4 (-324 *3))
    (-4 *5 (-324 *3))))) 
 (((*1 *1 *1 *2 *2)
-  (-12 (-5 *2 (-485)) (-4 *1 (-628 *3 *4 *5)) (-4 *3 (-962)) (-4 *4 (-324 *3))
+  (-12 (-5 *2 (-484)) (-4 *1 (-627 *3 *4 *5)) (-4 *3 (-961)) (-4 *4 (-324 *3))
    (-4 *5 (-324 *3))))) 
 (((*1 *1 *1 *2 *2 *2 *2)
-  (-12 (-5 *2 (-485)) (-4 *1 (-628 *3 *4 *5)) (-4 *3 (-962)) (-4 *4 (-324 *3))
+  (-12 (-5 *2 (-484)) (-4 *1 (-627 *3 *4 *5)) (-4 *3 (-961)) (-4 *4 (-324 *3))
    (-4 *5 (-324 *3))))) 
 (((*1 *1 *1 *2 *2 *1)
-  (-12 (-5 *2 (-485)) (-4 *1 (-628 *3 *4 *5)) (-4 *3 (-962)) (-4 *4 (-324 *3))
+  (-12 (-5 *2 (-484)) (-4 *1 (-627 *3 *4 *5)) (-4 *3 (-961)) (-4 *4 (-324 *3))
    (-4 *5 (-324 *3))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-1 *6 *4 *5)) (-4 *4 (-1014)) (-4 *5 (-1014)) (-4 *6 (-1014))
-   (-5 *2 (-1 *6 *5 *4)) (-5 *1 (-626 *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 (-625 *4 *5 *6))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-1 *6 *5)) (-4 *5 (-1014)) (-4 *6 (-1014)) (-5 *2 (-1 *6 *4 *5))
-   (-5 *1 (-626 *4 *5 *6)) (-4 *4 (-1014))))) 
+  (-12 (-5 *3 (-1 *6 *5)) (-4 *5 (-1013)) (-4 *6 (-1013)) (-5 *2 (-1 *6 *4 *5))
+   (-5 *1 (-625 *4 *5 *6)) (-4 *4 (-1013))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-1 *6 *4)) (-4 *4 (-1014)) (-4 *6 (-1014)) (-5 *2 (-1 *6 *4 *5))
-   (-5 *1 (-626 *4 *5 *6)) (-4 *5 (-1014))))) 
+  (-12 (-5 *3 (-1 *6 *4)) (-4 *4 (-1013)) (-4 *6 (-1013)) (-5 *2 (-1 *6 *4 *5))
+   (-5 *1 (-625 *4 *5 *6)) (-4 *5 (-1013))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *3 (-1 *6 *4 *5)) (-4 *4 (-1014)) (-4 *5 (-1014)) (-4 *6 (-1014))
-   (-5 *2 (-1 *6 *5)) (-5 *1 (-626 *4 *5 *6))))) 
+  (-12 (-5 *3 (-1 *6 *4 *5)) (-4 *4 (-1013)) (-4 *5 (-1013)) (-4 *6 (-1013))
+   (-5 *2 (-1 *6 *5)) (-5 *1 (-625 *4 *5 *6))))) 
 (((*1 *2 *3 *4)
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 (((*1 *2 *1 *3 *3)
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 (((*1 *2 *3 *4)
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 (((*1 *2 *3 *4)
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 (((*1 *2 *3 *4)
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-   (-4 *6 (-1156 *2))))) 
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 (((*1 *2 *3 *4)
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  ((*1 *2 *3 *4)
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-   (-5 *2 (-1086 *7)) (-5 *1 (-441 *5 *4 *6 *7)) (-4 *6 (-1156 *4))))) 
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 (((*1 *2 *2 *2)
   (-12
    (-5 *2
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-   (-4 *3 (-13 (-258) (-10 -8 (-15 -3973 ((-348 $) $))))) (-4 *4 (-1156 *3))
+    (-2 (|:| -2012 (-630 *3)) (|:| |basisDen| *3) (|:| |basisInv| (-630 *3))))
+   (-4 *3 (-13 (-258) (-10 -8 (-15 -3972 ((-348 $) $))))) (-4 *4 (-1155 *3))
    (-5 *1 (-439 *3 *4 *5)) (-4 *5 (-353 *3 *4))))) 
 (((*1 *2 *2 *2)
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-   (-4 *4 (-1156 *3)) (-5 *1 (-439 *3 *4 *5)) (-4 *5 (-353 *3 *4))))) 
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 (((*1 *2 *2 *2)
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-   (-4 *4 (-1156 *3)) (-5 *1 (-439 *3 *4 *5)) (-4 *5 (-353 *3 *4))))
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+  (-12 (-5 *2 (-630 *3)) (-4 *3 (-13 (-258) (-10 -8 (-15 -3972 ((-348 $) $)))))
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 (((*1 *2 *2 *2)
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 (((*1 *2 *3 *3 *2 *4)
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 (((*1 *2 *3 *2 *4)
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 (((*1 *2 *3 *4 *4)
-  (-12 (-5 *4 (-695)) (-4 *5 (-299)) (-4 *6 (-1156 *5))
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-      (|:| |basisInv| (-631 *6)))))
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-   (-4 *7 (-1156 *6))))) 
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+   (-4 *7 (-1155 *6))))) 
 (((*1 *2 *1)
   (-12
    (-5 *2
-    (-584
+    (-583
      (-2 (|:| |flg| (-3 "nil" "sqfr" "irred" "prime")) (|:| |fctr| *3)
-      (|:| |xpnt| (-485)))))
-   (-5 *1 (-348 *3)) (-4 *3 (-496))))
+      (|:| |xpnt| (-484)))))
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-   (-5 *2 (-584 (-1086 *3))) (-5 *1 (-438 *3 *5 *6)) (-4 *6 (-1156 *5))))) 
+  (-12 (-5 *4 (-694)) (-4 *3 (-299)) (-4 *5 (-1155 *3))
+   (-5 *2 (-583 (-1085 *3))) (-5 *1 (-438 *3 *5 *6)) (-4 *6 (-1155 *5))))) 
 (((*1 *2 *1 *1) (-12 (-5 *2 (-85)) (-5 *1 (-435))))) 
-(((*1 *1 *2) (-12 (-5 *2 (-1074)) (-5 *1 (-431))))) 
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 (((*1 *1 *1 *2)
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-   (-4 *4 (-962))))
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+   (-4 *4 (-961))))
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-   (-4 *4 (-962)) (-4 *5 (-196 (-3959 *3) (-695)))))
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  ((*1 *1 *1 *2)
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-(((*1 *2 *3 *4)
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-   (-5 *1 (-411 *5 *6 *7)) (-5 *3 (-584 (-206 *5 *6))) (-4 *7 (-392))))) 
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+(((*1 *2 *2 *2) (-12 (-5 *2 (-484)) (-5 *1 (-420))))) 
+(((*1 *2 *3 *4)
+  (-12 (-5 *4 (-583 (-773 *5))) (-14 *5 (-583 (-1090))) (-4 *6 (-392))
+   (-5 *2 (-2 (|:| |dpolys| (-583 (-206 *5 *6))) (|:| |coords| (-583 (-484)))))
+   (-5 *1 (-411 *5 *6 *7)) (-5 *3 (-583 (-206 *5 *6))) (-4 *7 (-392))))) 
 (((*1 *2 *2 *3)
-  (|partial| -12 (-5 *2 (-584 (-421 *4 *5))) (-5 *3 (-584 (-774 *4)))
-   (-14 *4 (-584 (-1091))) (-4 *5 (-392)) (-5 *1 (-411 *4 *5 *6))
+  (|partial| -12 (-5 *2 (-583 (-421 *4 *5))) (-5 *3 (-583 (-773 *4)))
+   (-14 *4 (-583 (-1090))) (-4 *5 (-392)) (-5 *1 (-411 *4 *5 *6))
    (-4 *6 (-392))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *4 (-584 (-774 *5))) (-14 *5 (-584 (-1091))) (-4 *6 (-392))
-   (-5 *2 (-584 (-584 (-206 *5 *6)))) (-5 *1 (-411 *5 *6 *7))
-   (-5 *3 (-584 (-206 *5 *6))) (-4 *7 (-392))))) 
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+   (-5 *2 (-583 (-583 (-206 *5 *6)))) (-5 *1 (-411 *5 *6 *7))
+   (-5 *3 (-583 (-206 *5 *6))) (-4 *7 (-392))))) 
 (((*1 *1) (-5 *1 (-408)))) 
 (((*1 *1 *2 *3 *3 *4 *5)
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-   (-5 *4 (-584 (-831))) (-5 *5 (-584 (-221))) (-5 *1 (-408))))
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+   (-5 *4 (-583 (-830))) (-5 *5 (-583 (-221))) (-5 *1 (-408))))
  ((*1 *1 *2 *3 *3 *4)
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-   (-5 *4 (-584 (-831))) (-5 *1 (-408))))
- ((*1 *1 *2) (-12 (-5 *2 (-584 (-584 (-855 (-179))))) (-5 *1 (-408))))
+  (-12 (-5 *2 (-583 (-583 (-854 (-179))))) (-5 *3 (-583 (-783)))
+   (-5 *4 (-583 (-830))) (-5 *1 (-408))))
+ ((*1 *1 *2) (-12 (-5 *2 (-583 (-583 (-854 (-179))))) (-5 *1 (-408))))
  ((*1 *1 *1) (-5 *1 (-408)))) 
-(((*1 *2 *1) (-12 (-5 *2 (-584 (-584 (-855 (-179))))) (-5 *1 (-408))))) 
-(((*1 *1 *2) (-12 (-5 *2 (-584 (-1002 (-330)))) (-5 *1 (-221))))
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+(((*1 *1 *2) (-12 (-5 *2 (-583 (-1001 (-330)))) (-5 *1 (-221))))
  ((*1 *2 *3 *2)
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- ((*1 *2 *1 *2) (-12 (-5 *2 (-584 (-1002 (-330)))) (-5 *1 (-408))))
- ((*1 *2 *1) (-12 (-5 *2 (-584 (-1002 (-330)))) (-5 *1 (-408))))) 
+  (-12 (-5 *2 (-583 (-1001 (-330)))) (-5 *3 (-583 (-221))) (-5 *1 (-222))))
+ ((*1 *2 *1 *2) (-12 (-5 *2 (-583 (-1001 (-330)))) (-5 *1 (-408))))
+ ((*1 *2 *1) (-12 (-5 *2 (-583 (-1001 (-330)))) (-5 *1 (-408))))) 
 (((*1 *2 *1 *3 *4 *4 *5)
-  (-12 (-5 *3 (-855 (-179))) (-5 *4 (-784)) (-5 *5 (-831)) (-5 *2 (-1186))
+  (-12 (-5 *3 (-854 (-179))) (-5 *4 (-783)) (-5 *5 (-830)) (-5 *2 (-1185))
    (-5 *1 (-408))))
- ((*1 *2 *1 *3) (-12 (-5 *3 (-855 (-179))) (-5 *2 (-1186)) (-5 *1 (-408))))
+ ((*1 *2 *1 *3) (-12 (-5 *3 (-854 (-179))) (-5 *2 (-1185)) (-5 *1 (-408))))
  ((*1 *2 *1 *3 *4 *4 *5)
-  (-12 (-5 *3 (-584 (-855 (-179)))) (-5 *4 (-784)) (-5 *5 (-831))
-   (-5 *2 (-1186)) (-5 *1 (-408))))) 
-(((*1 *2 *1 *3) (-12 (-5 *3 (-855 (-179))) (-5 *2 (-1186)) (-5 *1 (-408))))) 
+  (-12 (-5 *3 (-583 (-854 (-179)))) (-5 *4 (-783)) (-5 *5 (-830))
+   (-5 *2 (-1185)) (-5 *1 (-408))))) 
+(((*1 *2 *1 *3) (-12 (-5 *3 (-854 (-179))) (-5 *2 (-1185)) (-5 *1 (-408))))) 
 (((*1 *2 *2 *3)
-  (-12 (-5 *2 (-584 (-584 (-855 (-179))))) (-5 *3 (-584 (-784)))
+  (-12 (-5 *2 (-583 (-583 (-854 (-179))))) (-5 *3 (-583 (-783)))
    (-5 *1 (-408))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-584 (-584 (-855 (-179))))) (-5 *2 (-584 (-179)))
+  (-12 (-5 *3 (-583 (-583 (-854 (-179))))) (-5 *2 (-583 (-179)))
    (-5 *1 (-408))))) 
 (((*1 *1 *2) (-12 (-5 *2 (-85)) (-5 *1 (-221))))
- ((*1 *2 *3 *2) (-12 (-5 *2 (-85)) (-5 *3 (-584 (-221))) (-5 *1 (-222))))
+ ((*1 *2 *3 *2) (-12 (-5 *2 (-85)) (-5 *3 (-583 (-221))) (-5 *1 (-222))))
  ((*1 *2) (-12 (-5 *2 (-85)) (-5 *1 (-407))))
  ((*1 *2 *2) (-12 (-5 *2 (-85)) (-5 *1 (-407))))) 
 (((*1 *2) (-12 (-5 *2 (-85)) (-5 *1 (-407))))
@@ -11155,440 +11155,440 @@
 (((*1 *2) (-12 (-5 *2 (-85)) (-5 *1 (-407))))
  ((*1 *2 *2) (-12 (-5 *2 (-85)) (-5 *1 (-407))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-831)) (-5 *2 (-1180 (-1180 (-485)))) (-5 *1 (-406))))) 
+  (-12 (-5 *3 (-830)) (-5 *2 (-1179 (-1179 (-484)))) (-5 *1 (-406))))) 
 (((*1 *2 *2 *3)
-  (-12 (-5 *2 (-1180 (-1180 (-485)))) (-5 *3 (-831)) (-5 *1 (-406))))) 
+  (-12 (-5 *2 (-1179 (-1179 (-484)))) (-5 *3 (-830)) (-5 *1 (-406))))) 
 (((*1 *2 *2 *3 *4)
-  (|partial| -12 (-5 *4 (-1 *3)) (-4 *3 (-757)) (-4 *5 (-718)) (-4 *6 (-496))
-   (-4 *7 (-862 *6 *5 *3)) (-5 *1 (-402 *5 *3 *6 *7 *2))
+  (|partial| -12 (-5 *4 (-1 *3)) (-4 *3 (-756)) (-4 *5 (-717)) (-4 *6 (-495))
+   (-4 *7 (-861 *6 *5 *3)) (-5 *1 (-402 *5 *3 *6 *7 *2))
    (-4 *2
-    (-13 (-951 (-350 (-485))) (-312)
-     (-10 -8 (-15 -3948 ($ *7)) (-15 -3000 (*7 $)) (-15 -2999 (*7 $)))))))) 
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+  (-12 (-5 *2 (-484))
    (-5 *3
-    (-2 (|:| |lcmfij| *6) (|:| |totdeg| (-695)) (|:| |poli| *4)
+    (-2 (|:| |lcmfij| *6) (|:| |totdeg| (-694)) (|:| |poli| *4)
      (|:| |polj| *4)))
-   (-4 *6 (-718)) (-4 *4 (-862 *5 *6 *7)) (-4 *5 (-392)) (-4 *7 (-757))
+   (-4 *6 (-717)) (-4 *4 (-861 *5 *6 *7)) (-4 *5 (-392)) (-4 *7 (-756))
    (-5 *1 (-390 *5 *6 *7 *4))))) 
 (((*1 *2 *3 *4 *4 *2 *2 *2)
-  (-12 (-5 *2 (-485))
+  (-12 (-5 *2 (-484))
    (-5 *3
-    (-2 (|:| |lcmfij| *6) (|:| |totdeg| (-695)) (|:| |poli| *4)
+    (-2 (|:| |lcmfij| *6) (|:| |totdeg| (-694)) (|:| |poli| *4)
      (|:| |polj| *4)))
-   (-4 *6 (-718)) (-4 *4 (-862 *5 *6 *7)) (-4 *5 (-392)) (-4 *7 (-757))
+   (-4 *6 (-717)) (-4 *4 (-861 *5 *6 *7)) (-4 *5 (-392)) (-4 *7 (-756))
    (-5 *1 (-390 *5 *6 *7 *4))))) 
 (((*1 *2 *3)
-  (-12 (-4 *4 (-392)) (-4 *5 (-718)) (-4 *6 (-757)) (-5 *2 (-1186))
-   (-5 *1 (-390 *4 *5 *6 *3)) (-4 *3 (-862 *4 *5 *6))))) 
+  (-12 (-4 *4 (-392)) (-4 *5 (-717)) (-4 *6 (-756)) (-5 *2 (-1185))
+   (-5 *1 (-390 *4 *5 *6 *3)) (-4 *3 (-861 *4 *5 *6))))) 
 (((*1 *2 *3)
-  (-12 (-4 *4 (-392)) (-4 *5 (-718)) (-4 *6 (-757)) (-5 *2 (-485))
-   (-5 *1 (-390 *4 *5 *6 *3)) (-4 *3 (-862 *4 *5 *6))))) 
+  (-12 (-4 *4 (-392)) (-4 *5 (-717)) (-4 *6 (-756)) (-5 *2 (-484))
+   (-5 *1 (-390 *4 *5 *6 *3)) (-4 *3 (-861 *4 *5 *6))))) 
 (((*1 *2 *2)
-  (-12 (-5 *2 (-584 *6)) (-4 *6 (-862 *3 *4 *5)) (-4 *3 (-392)) (-4 *4 (-718))
-   (-4 *5 (-757)) (-5 *1 (-390 *3 *4 *5 *6))))) 
+  (-12 (-5 *2 (-583 *6)) (-4 *6 (-861 *3 *4 *5)) (-4 *3 (-392)) (-4 *4 (-717))
+   (-4 *5 (-756)) (-5 *1 (-390 *3 *4 *5 *6))))) 
 (((*1 *2 *2 *2)
   (-12
    (-5 *2
-    (-584
-     (-2 (|:| |lcmfij| *4) (|:| |totdeg| (-695)) (|:| |poli| *6)
+    (-583
+     (-2 (|:| |lcmfij| *4) (|:| |totdeg| (-694)) (|:| |poli| *6)
       (|:| |polj| *6))))
-   (-4 *4 (-718)) (-4 *6 (-862 *3 *4 *5)) (-4 *3 (-392)) (-4 *5 (-757))
+   (-4 *4 (-717)) (-4 *6 (-861 *3 *4 *5)) (-4 *3 (-392)) (-4 *5 (-756))
    (-5 *1 (-390 *3 *4 *5 *6))))) 
 (((*1 *2 *3)
   (-12
    (-5 *3
-    (-2 (|:| |lcmfij| *5) (|:| |totdeg| (-695)) (|:| |poli| *2)
+    (-2 (|:| |lcmfij| *5) (|:| |totdeg| (-694)) (|:| |poli| *2)
      (|:| |polj| *2)))
-   (-4 *5 (-718)) (-4 *2 (-862 *4 *5 *6)) (-5 *1 (-390 *4 *5 *6 *2))
-   (-4 *4 (-392)) (-4 *6 (-757))))) 
+   (-4 *5 (-717)) (-4 *2 (-861 *4 *5 *6)) (-5 *1 (-390 *4 *5 *6 *2))
+   (-4 *4 (-392)) (-4 *6 (-756))))) 
 (((*1 *2 *3 *4 *2)
-  (-12 (-5 *2 (-584 (-2 (|:| |totdeg| (-695)) (|:| -2005 *3)))) (-5 *4 (-695))
-   (-4 *3 (-862 *5 *6 *7)) (-4 *5 (-392)) (-4 *6 (-718)) (-4 *7 (-757))
+  (-12 (-5 *2 (-583 (-2 (|:| |totdeg| (-694)) (|:| -2004 *3)))) (-5 *4 (-694))
+   (-4 *3 (-861 *5 *6 *7)) (-4 *5 (-392)) (-4 *6 (-717)) (-4 *7 (-756))
    (-5 *1 (-390 *5 *6 *7 *3))))) 
 (((*1 *2 *2)
-  (-12 (-4 *3 (-392)) (-4 *4 (-718)) (-4 *5 (-757)) (-5 *1 (-390 *3 *4 *5 *2))
-   (-4 *2 (-862 *3 *4 *5))))) 
+  (-12 (-4 *3 (-392)) (-4 *4 (-717)) (-4 *5 (-756)) (-5 *1 (-390 *3 *4 *5 *2))
+   (-4 *2 (-861 *3 *4 *5))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *4 (-584 *3)) (-4 *3 (-862 *5 *6 *7)) (-4 *5 (-392)) (-4 *6 (-718))
-   (-4 *7 (-757)) (-5 *2 (-2 (|:| |poly| *3) (|:| |mult| *5)))
+  (-12 (-5 *4 (-583 *3)) (-4 *3 (-861 *5 *6 *7)) (-4 *5 (-392)) (-4 *6 (-717))
+   (-4 *7 (-756)) (-5 *2 (-2 (|:| |poly| *3) (|:| |mult| *5)))
    (-5 *1 (-390 *5 *6 *7 *3))))) 
 (((*1 *2 *3 *2)
   (-12
    (-5 *2
-    (-584
-     (-2 (|:| |lcmfij| *3) (|:| |totdeg| (-695)) (|:| |poli| *6)
+    (-583
+     (-2 (|:| |lcmfij| *3) (|:| |totdeg| (-694)) (|:| |poli| *6)
       (|:| |polj| *6))))
-   (-4 *3 (-718)) (-4 *6 (-862 *4 *3 *5)) (-4 *4 (-392)) (-4 *5 (-757))
+   (-4 *3 (-717)) (-4 *6 (-861 *4 *3 *5)) (-4 *4 (-392)) (-4 *5 (-756))
    (-5 *1 (-390 *4 *3 *5 *6))))) 
 (((*1 *2 *2)
   (-12
    (-5 *2
-    (-584
-     (-2 (|:| |lcmfij| *4) (|:| |totdeg| (-695)) (|:| |poli| *6)
+    (-583
+     (-2 (|:| |lcmfij| *4) (|:| |totdeg| (-694)) (|:| |poli| *6)
       (|:| |polj| *6))))
-   (-4 *4 (-718)) (-4 *6 (-862 *3 *4 *5)) (-4 *3 (-392)) (-4 *5 (-757))
+   (-4 *4 (-717)) (-4 *6 (-861 *3 *4 *5)) (-4 *3 (-392)) (-4 *5 (-756))
    (-5 *1 (-390 *3 *4 *5 *6))))) 
 (((*1 *2 *3 *2)
   (-12
    (-5 *2
-    (-584
-     (-2 (|:| |lcmfij| *5) (|:| |totdeg| (-695)) (|:| |poli| *3)
+    (-583
+     (-2 (|:| |lcmfij| *5) (|:| |totdeg| (-694)) (|:| |poli| *3)
       (|:| |polj| *3))))
-   (-4 *5 (-718)) (-4 *3 (-862 *4 *5 *6)) (-4 *4 (-392)) (-4 *6 (-757))
+   (-4 *5 (-717)) (-4 *3 (-861 *4 *5 *6)) (-4 *4 (-392)) (-4 *6 (-756))
    (-5 *1 (-390 *4 *5 *6 *3))))) 
 (((*1 *2 *3 *3 *3 *3)
-  (-12 (-4 *4 (-392)) (-4 *3 (-718)) (-4 *5 (-757)) (-5 *2 (-85))
-   (-5 *1 (-390 *4 *3 *5 *6)) (-4 *6 (-862 *4 *3 *5))))) 
+  (-12 (-4 *4 (-392)) (-4 *3 (-717)) (-4 *5 (-756)) (-5 *2 (-85))
+   (-5 *1 (-390 *4 *3 *5 *6)) (-4 *6 (-861 *4 *3 *5))))) 
 (((*1 *2 *3 *3)
-  (-12 (-4 *4 (-392)) (-4 *3 (-718)) (-4 *5 (-757)) (-5 *2 (-85))
-   (-5 *1 (-390 *4 *3 *5 *6)) (-4 *6 (-862 *4 *3 *5))))) 
+  (-12 (-4 *4 (-392)) (-4 *3 (-717)) (-4 *5 (-756)) (-5 *2 (-85))
+   (-5 *1 (-390 *4 *3 *5 *6)) (-4 *6 (-861 *4 *3 *5))))) 
 (((*1 *2 *3)
   (-12
    (-5 *3
-    (-2 (|:| |lcmfij| *5) (|:| |totdeg| (-695)) (|:| |poli| *7)
+    (-2 (|:| |lcmfij| *5) (|:| |totdeg| (-694)) (|:| |poli| *7)
      (|:| |polj| *7)))
-   (-4 *5 (-718)) (-4 *7 (-862 *4 *5 *6)) (-4 *4 (-392)) (-4 *6 (-757))
+   (-4 *5 (-717)) (-4 *7 (-861 *4 *5 *6)) (-4 *4 (-392)) (-4 *6 (-756))
    (-5 *2 (-85)) (-5 *1 (-390 *4 *5 *6 *7))))) 
 (((*1 *2 *2 *3 *3)
-  (-12 (-5 *2 (-584 *7)) (-5 *3 (-485)) (-4 *7 (-862 *4 *5 *6)) (-4 *4 (-392))
-   (-4 *5 (-718)) (-4 *6 (-757)) (-5 *1 (-390 *4 *5 *6 *7))))) 
+  (-12 (-5 *2 (-583 *7)) (-5 *3 (-484)) (-4 *7 (-861 *4 *5 *6)) (-4 *4 (-392))
+   (-4 *5 (-717)) (-4 *6 (-756)) (-5 *1 (-390 *4 *5 *6 *7))))) 
 (((*1 *2 *2 *3)
-  (-12 (-5 *3 (-584 *2)) (-4 *2 (-862 *4 *5 *6)) (-4 *4 (-392)) (-4 *5 (-718))
-   (-4 *6 (-757)) (-5 *1 (-390 *4 *5 *6 *2))))) 
+  (-12 (-5 *3 (-583 *2)) (-4 *2 (-861 *4 *5 *6)) (-4 *4 (-392)) (-4 *5 (-717))
+   (-4 *6 (-756)) (-5 *1 (-390 *4 *5 *6 *2))))) 
 (((*1 *2 *2 *3)
-  (-12 (-5 *3 (-584 *2)) (-4 *2 (-862 *4 *5 *6)) (-4 *4 (-392)) (-4 *5 (-718))
-   (-4 *6 (-757)) (-5 *1 (-390 *4 *5 *6 *2))))) 
+  (-12 (-5 *3 (-583 *2)) (-4 *2 (-861 *4 *5 *6)) (-4 *4 (-392)) (-4 *5 (-717))
+   (-4 *6 (-756)) (-5 *1 (-390 *4 *5 *6 *2))))) 
 (((*1 *2 *3 *3)
-  (-12 (-4 *4 (-13 (-258) (-120))) (-4 *5 (-718)) (-4 *6 (-757))
-   (-4 *7 (-862 *4 *5 *6)) (-5 *2 (-584 (-584 *7))) (-5 *1 (-389 *4 *5 *6 *7))
-   (-5 *3 (-584 *7))))
+  (-12 (-4 *4 (-13 (-258) (-120))) (-4 *5 (-717)) (-4 *6 (-756))
+   (-4 *7 (-861 *4 *5 *6)) (-5 *2 (-583 (-583 *7))) (-5 *1 (-389 *4 *5 *6 *7))
+   (-5 *3 (-583 *7))))
  ((*1 *2 *3 *3 *4)
-  (-12 (-5 *4 (-85)) (-4 *5 (-13 (-258) (-120))) (-4 *6 (-718)) (-4 *7 (-757))
-   (-4 *8 (-862 *5 *6 *7)) (-5 *2 (-584 (-584 *8))) (-5 *1 (-389 *5 *6 *7 *8))
-   (-5 *3 (-584 *8))))
+  (-12 (-5 *4 (-85)) (-4 *5 (-13 (-258) (-120))) (-4 *6 (-717)) (-4 *7 (-756))
+   (-4 *8 (-861 *5 *6 *7)) (-5 *2 (-583 (-583 *8))) (-5 *1 (-389 *5 *6 *7 *8))
+   (-5 *3 (-583 *8))))
  ((*1 *2 *3)
-  (-12 (-4 *4 (-13 (-258) (-120))) (-4 *5 (-718)) (-4 *6 (-757))
-   (-4 *7 (-862 *4 *5 *6)) (-5 *2 (-584 (-584 *7))) (-5 *1 (-389 *4 *5 *6 *7))
-   (-5 *3 (-584 *7))))
+  (-12 (-4 *4 (-13 (-258) (-120))) (-4 *5 (-717)) (-4 *6 (-756))
+   (-4 *7 (-861 *4 *5 *6)) (-5 *2 (-583 (-583 *7))) (-5 *1 (-389 *4 *5 *6 *7))
+   (-5 *3 (-583 *7))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *4 (-85)) (-4 *5 (-13 (-258) (-120))) (-4 *6 (-718)) (-4 *7 (-757))
-   (-4 *8 (-862 *5 *6 *7)) (-5 *2 (-584 (-584 *8))) (-5 *1 (-389 *5 *6 *7 *8))
-   (-5 *3 (-584 *8))))) 
+  (-12 (-5 *4 (-85)) (-4 *5 (-13 (-258) (-120))) (-4 *6 (-717)) (-4 *7 (-756))
+   (-4 *8 (-861 *5 *6 *7)) (-5 *2 (-583 (-583 *8))) (-5 *1 (-389 *5 *6 *7 *8))
+   (-5 *3 (-583 *8))))) 
 (((*1 *2 *3)
-  (-12 (-4 *4 (-13 (-258) (-120))) (-4 *5 (-718)) (-4 *6 (-757))
-   (-4 *7 (-862 *4 *5 *6)) (-5 *2 (-584 (-584 *7))) (-5 *1 (-389 *4 *5 *6 *7))
-   (-5 *3 (-584 *7))))
+  (-12 (-4 *4 (-13 (-258) (-120))) (-4 *5 (-717)) (-4 *6 (-756))
+   (-4 *7 (-861 *4 *5 *6)) (-5 *2 (-583 (-583 *7))) (-5 *1 (-389 *4 *5 *6 *7))
+   (-5 *3 (-583 *7))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *4 (-85)) (-4 *5 (-13 (-258) (-120))) (-4 *6 (-718)) (-4 *7 (-757))
-   (-4 *8 (-862 *5 *6 *7)) (-5 *2 (-584 (-584 *8))) (-5 *1 (-389 *5 *6 *7 *8))
-   (-5 *3 (-584 *8))))) 
+  (-12 (-5 *4 (-85)) (-4 *5 (-13 (-258) (-120))) (-4 *6 (-717)) (-4 *7 (-756))
+   (-4 *8 (-861 *5 *6 *7)) (-5 *2 (-583 (-583 *8))) (-5 *1 (-389 *5 *6 *7 *8))
+   (-5 *3 (-583 *8))))) 
 (((*1 *2 *2)
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-   (-4 *5 (-757)) (-5 *1 (-388 *3 *4 *5 *6))))
+  (-12 (-5 *2 (-583 *6)) (-4 *6 (-861 *3 *4 *5)) (-4 *3 (-258)) (-4 *4 (-717))
+   (-4 *5 (-756)) (-5 *1 (-388 *3 *4 *5 *6))))
  ((*1 *2 *2 *3)
-  (-12 (-5 *2 (-584 *7)) (-5 *3 (-1074)) (-4 *7 (-862 *4 *5 *6)) (-4 *4 (-258))
-   (-4 *5 (-718)) (-4 *6 (-757)) (-5 *1 (-388 *4 *5 *6 *7))))
+  (-12 (-5 *2 (-583 *7)) (-5 *3 (-1073)) (-4 *7 (-861 *4 *5 *6)) (-4 *4 (-258))
+   (-4 *5 (-717)) (-4 *6 (-756)) (-5 *1 (-388 *4 *5 *6 *7))))
  ((*1 *2 *2 *3 *3)
-  (-12 (-5 *2 (-584 *7)) (-5 *3 (-1074)) (-4 *7 (-862 *4 *5 *6)) (-4 *4 (-258))
-   (-4 *5 (-718)) (-4 *6 (-757)) (-5 *1 (-388 *4 *5 *6 *7))))) 
+  (-12 (-5 *2 (-583 *7)) (-5 *3 (-1073)) (-4 *7 (-861 *4 *5 *6)) (-4 *4 (-258))
+   (-4 *5 (-717)) (-4 *6 (-756)) (-5 *1 (-388 *4 *5 *6 *7))))) 
 (((*1 *2 *2 *3)
-  (-12 (-5 *3 (-584 *2)) (-4 *2 (-862 *4 *5 *6)) (-4 *4 (-258)) (-4 *5 (-718))
-   (-4 *6 (-757)) (-5 *1 (-388 *4 *5 *6 *2))))) 
-(((*1 *2 *3) (-12 (-5 *2 (-584 (-485))) (-5 *1 (-386)) (-5 *3 (-485))))) 
+  (-12 (-5 *3 (-583 *2)) (-4 *2 (-861 *4 *5 *6)) (-4 *4 (-258)) (-4 *5 (-717))
+   (-4 *6 (-756)) (-5 *1 (-388 *4 *5 *6 *2))))) 
+(((*1 *2 *3) (-12 (-5 *2 (-583 (-484))) (-5 *1 (-386)) (-5 *3 (-484))))) 
 (((*1 *2 *2)
-  (-12 (-5 *2 (-695)) (-5 *1 (-385 *3)) (-4 *3 (-347)) (-4 *3 (-962))))
- ((*1 *2) (-12 (-5 *2 (-695)) (-5 *1 (-385 *3)) (-4 *3 (-347)) (-4 *3 (-962))))) 
+  (-12 (-5 *2 (-694)) (-5 *1 (-385 *3)) (-4 *3 (-347)) (-4 *3 (-961))))
+ ((*1 *2) (-12 (-5 *2 (-694)) (-5 *1 (-385 *3)) (-4 *3 (-347)) (-4 *3 (-961))))) 
 (((*1 *2 *3)
-  (-12 (-5 *2 (-485)) (-5 *1 (-385 *3)) (-4 *3 (-347)) (-4 *3 (-962))))) 
+  (-12 (-5 *2 (-484)) (-5 *1 (-385 *3)) (-4 *3 (-347)) (-4 *3 (-961))))) 
 (((*1 *2 *3)
-  (-12 (-5 *2 (-485)) (-5 *1 (-385 *3)) (-4 *3 (-347)) (-4 *3 (-962))))) 
-(((*1 *2) (-12 (-5 *2 (-1186)) (-5 *1 (-385 *3)) (-4 *3 (-962))))) 
-(((*1 *2) (-12 (-5 *2 (-695)) (-5 *1 (-385 *3)) (-4 *3 (-962))))) 
-(((*1 *2 *2) (-12 (-5 *2 (-695)) (-5 *1 (-385 *3)) (-4 *3 (-962))))
- ((*1 *2) (-12 (-5 *2 (-695)) (-5 *1 (-385 *3)) (-4 *3 (-962))))) 
+  (-12 (-5 *2 (-484)) (-5 *1 (-385 *3)) (-4 *3 (-347)) (-4 *3 (-961))))) 
+(((*1 *2) (-12 (-5 *2 (-1185)) (-5 *1 (-385 *3)) (-4 *3 (-961))))) 
+(((*1 *2) (-12 (-5 *2 (-694)) (-5 *1 (-385 *3)) (-4 *3 (-961))))) 
+(((*1 *2 *2) (-12 (-5 *2 (-694)) (-5 *1 (-385 *3)) (-4 *3 (-961))))
+ ((*1 *2) (-12 (-5 *2 (-694)) (-5 *1 (-385 *3)) (-4 *3 (-961))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *3 (-695)) (-5 *4 (-485)) (-5 *1 (-385 *2)) (-4 *2 (-962))))) 
+  (-12 (-5 *3 (-694)) (-5 *4 (-484)) (-5 *1 (-385 *2)) (-4 *2 (-961))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *3 (-831)) (-5 *4 (-348 *6)) (-4 *6 (-1156 *5)) (-4 *5 (-962))
-   (-5 *2 (-584 *6)) (-5 *1 (-384 *5 *6))))) 
+  (-12 (-5 *3 (-830)) (-5 *4 (-348 *6)) (-4 *6 (-1155 *5)) (-4 *5 (-961))
+   (-5 *2 (-583 *6)) (-5 *1 (-384 *5 *6))))) 
 (((*1 *2 *3 *2)
-  (|partial| -12 (-5 *3 (-831)) (-5 *1 (-382 *2)) (-4 *2 (-1156 (-485)))))
+  (|partial| -12 (-5 *3 (-830)) (-5 *1 (-382 *2)) (-4 *2 (-1155 (-484)))))
  ((*1 *2 *3 *2 *4)
-  (|partial| -12 (-5 *3 (-831)) (-5 *4 (-695)) (-5 *1 (-382 *2))
-   (-4 *2 (-1156 (-485)))))
+  (|partial| -12 (-5 *3 (-830)) (-5 *4 (-694)) (-5 *1 (-382 *2))
+   (-4 *2 (-1155 (-484)))))
  ((*1 *2 *3 *2 *4)
-  (|partial| -12 (-5 *3 (-831)) (-5 *4 (-584 (-695))) (-5 *1 (-382 *2))
-   (-4 *2 (-1156 (-485)))))
+  (|partial| -12 (-5 *3 (-830)) (-5 *4 (-583 (-694))) (-5 *1 (-382 *2))
+   (-4 *2 (-1155 (-484)))))
  ((*1 *2 *3 *2 *4 *5)
-  (|partial| -12 (-5 *3 (-831)) (-5 *4 (-584 (-695))) (-5 *5 (-695))
-   (-5 *1 (-382 *2)) (-4 *2 (-1156 (-485)))))
+  (|partial| -12 (-5 *3 (-830)) (-5 *4 (-583 (-694))) (-5 *5 (-694))
+   (-5 *1 (-382 *2)) (-4 *2 (-1155 (-484)))))
  ((*1 *2 *3 *2 *4 *5 *6)
-  (|partial| -12 (-5 *3 (-831)) (-5 *4 (-584 (-695))) (-5 *5 (-695))
-   (-5 *6 (-85)) (-5 *1 (-382 *2)) (-4 *2 (-1156 (-485)))))
+  (|partial| -12 (-5 *3 (-830)) (-5 *4 (-583 (-694))) (-5 *5 (-694))
+   (-5 *6 (-85)) (-5 *1 (-382 *2)) (-4 *2 (-1155 (-484)))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *3 (-831)) (-5 *4 (-348 *2)) (-4 *2 (-1156 *5)) (-5 *1 (-384 *5 *2))
-   (-4 *5 (-962))))) 
+  (-12 (-5 *3 (-830)) (-5 *4 (-348 *2)) (-4 *2 (-1155 *5)) (-5 *1 (-384 *5 *2))
+   (-4 *5 (-961))))) 
 (((*1 *2 *3)
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-   (-4 *4 (-1156 (-485))) (-5 *2 (-676 (-695))) (-5 *1 (-382 *4))))
+  (-12 (-5 *3 (-583 (-2 (|:| -3733 *4) (|:| -3949 (-484)))))
+   (-4 *4 (-1155 (-484))) (-5 *2 (-675 (-694))) (-5 *1 (-382 *4))))
  ((*1 *2 *3)
-  (-12 (-5 *3 (-348 *5)) (-4 *5 (-1156 *4)) (-4 *4 (-962))
-   (-5 *2 (-676 (-695))) (-5 *1 (-384 *4 *5))))) 
-(((*1 *2 *2 *3) (-12 (-4 *3 (-962)) (-5 *1 (-384 *3 *2)) (-4 *2 (-1156 *3))))) 
-(((*1 *2 *2 *3) (-12 (-4 *3 (-962)) (-5 *1 (-384 *3 *2)) (-4 *2 (-1156 *3))))) 
+  (-12 (-5 *3 (-348 *5)) (-4 *5 (-1155 *4)) (-4 *4 (-961))
+   (-5 *2 (-675 (-694))) (-5 *1 (-384 *4 *5))))) 
+(((*1 *2 *2 *3) (-12 (-4 *3 (-961)) (-5 *1 (-384 *3 *2)) (-4 *2 (-1155 *3))))) 
+(((*1 *2 *2 *3) (-12 (-4 *3 (-961)) (-5 *1 (-384 *3 *2)) (-4 *2 (-1155 *3))))) 
 (((*1 *2 *3)
-  (-12 (-4 *4 (-962)) (-4 *2 (-13 (-347) (-951 *4) (-312) (-1116) (-239)))
-   (-5 *1 (-383 *4 *3 *2)) (-4 *3 (-1156 *4))))) 
+  (-12 (-4 *4 (-961)) (-4 *2 (-13 (-347) (-950 *4) (-312) (-1115) (-239)))
+   (-5 *1 (-383 *4 *3 *2)) (-4 *3 (-1155 *4))))) 
 (((*1 *2 *3)
-  (-12 (-4 *4 (-962)) (-4 *2 (-13 (-347) (-951 *4) (-312) (-1116) (-239)))
-   (-5 *1 (-383 *4 *3 *2)) (-4 *3 (-1156 *4))))) 
+  (-12 (-4 *4 (-961)) (-4 *2 (-13 (-347) (-950 *4) (-312) (-1115) (-239)))
+   (-5 *1 (-383 *4 *3 *2)) (-4 *3 (-1155 *4))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *4 (-695)) (-4 *5 (-962)) (-5 *2 (-485)) (-5 *1 (-383 *5 *3 *6))
-   (-4 *3 (-1156 *5)) (-4 *6 (-13 (-347) (-951 *5) (-312) (-1116) (-239)))))
+  (-12 (-5 *4 (-694)) (-4 *5 (-961)) (-5 *2 (-484)) (-5 *1 (-383 *5 *3 *6))
+   (-4 *3 (-1155 *5)) (-4 *6 (-13 (-347) (-950 *5) (-312) (-1115) (-239)))))
  ((*1 *2 *3)
-  (-12 (-4 *4 (-962)) (-5 *2 (-485)) (-5 *1 (-383 *4 *3 *5)) (-4 *3 (-1156 *4))
-   (-4 *5 (-13 (-347) (-951 *4) (-312) (-1116) (-239)))))) 
+  (-12 (-4 *4 (-961)) (-5 *2 (-484)) (-5 *1 (-383 *4 *3 *5)) (-4 *3 (-1155 *4))
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 (((*1 *2 *3)
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 (((*1 *1 *2 *3)
   (-12
    (-5 *3
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 (((*1 *2 *1) (-12 (-5 *2 (-85)) (-5 *1 (-379))))) 
 (((*1 *1) (-5 *1 (-379)))) 
 (((*1 *1) (-5 *1 (-379)))) 
@@ -11598,327 +11598,327 @@
 (((*1 *1) (-5 *1 (-379)))) 
 (((*1 *1) (-5 *1 (-379)))) 
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 (((*1 *1 *2)
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 (((*1 *2 *1)
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  ((*1 *2 *3 *1)
-  (-12 (-5 *3 (-1 (-85) *4 *4)) (-4 *1 (-324 *4)) (-4 *4 (-1130))
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 (((*1 *1 *1 *1 *2)
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 (((*1 *1 *1)
-  (-12 (-4 *1 (-1036 *2)) (-4 *1 (-324 *2)) (-4 *2 (-1130)) (-4 *2 (-757))))
+  (-12 (-4 *1 (-1035 *2)) (-4 *1 (-324 *2)) (-4 *2 (-1129)) (-4 *2 (-756))))
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-   (-4 *3 (-1130))))) 
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+   (-4 *3 (-1129))))) 
 (((*1 *2 *3 *1)
-  (-12 (-5 *3 (-1 (-85) *4)) (-4 *1 (-318 *4)) (-4 *4 (-1130)) (-5 *2 (-85))))) 
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 (((*1 *2 *3 *1)
-  (-12 (-5 *3 (-1 (-85) *4)) (-4 *1 (-318 *4)) (-4 *4 (-1130)) (-5 *2 (-85))))) 
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 (((*1 *2 *3 *1)
-  (-12 (-4 *1 (-318 *3)) (-4 *3 (-1130)) (-4 *3 (-72)) (-5 *2 (-695))))
+  (-12 (-4 *1 (-318 *3)) (-4 *3 (-1129)) (-4 *3 (-72)) (-5 *2 (-694))))
  ((*1 *2 *3 *1)
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-(((*1 *2) (-12 (-4 *3 (-146)) (-5 *2 (-1180 *1)) (-4 *1 (-316 *3))))) 
+  (-12 (-5 *3 (-1 (-85) *4)) (-4 *1 (-318 *4)) (-4 *4 (-1129)) (-5 *2 (-694))))) 
+(((*1 *2) (-12 (-4 *3 (-146)) (-5 *2 (-1179 *1)) (-4 *1 (-316 *3))))) 
 (((*1 *2 *1) (-12 (-4 *1 (-316 *2)) (-4 *2 (-146))))) 
 (((*1 *2 *1) (-12 (-4 *1 (-316 *2)) (-4 *2 (-146))))) 
 (((*1 *2 *1) (-12 (-4 *1 (-316 *2)) (-4 *2 (-146))))) 
 (((*1 *2 *1) (-12 (-4 *1 (-316 *2)) (-4 *2 (-146))))) 
-(((*1 *2 *1) (-12 (-4 *1 (-316 *3)) (-4 *3 (-146)) (-5 *2 (-1086 *3))))) 
-(((*1 *2 *1) (-12 (-4 *1 (-316 *3)) (-4 *3 (-146)) (-5 *2 (-1086 *3))))) 
+(((*1 *2 *1) (-12 (-4 *1 (-316 *3)) (-4 *3 (-146)) (-5 *2 (-1085 *3))))) 
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 (((*1 *2)
   (-12 (-4 *4 (-146)) (-5 *2 (-85)) (-5 *1 (-315 *3 *4)) (-4 *3 (-316 *4))))
  ((*1 *2) (-12 (-4 *1 (-316 *3)) (-4 *3 (-146)) (-5 *2 (-85))))) 
@@ -11963,1175 +11963,1175 @@
   (-12 (-4 *4 (-146)) (-5 *2 (-85)) (-5 *1 (-315 *3 *4)) (-4 *3 (-316 *4))))
  ((*1 *2) (-12 (-4 *1 (-316 *3)) (-4 *3 (-146)) (-5 *2 (-85))))) 
 (((*1 *2)
-  (-12 (-4 *4 (-146)) (-5 *2 (-584 (-1180 *4))) (-5 *1 (-315 *3 *4))
+  (-12 (-4 *4 (-146)) (-5 *2 (-583 (-1179 *4))) (-5 *1 (-315 *3 *4))
    (-4 *3 (-316 *4))))
  ((*1 *2)
-  (-12 (-4 *1 (-316 *3)) (-4 *3 (-146)) (-4 *3 (-496))
-   (-5 *2 (-584 (-1180 *3)))))) 
+  (-12 (-4 *1 (-316 *3)) (-4 *3 (-146)) (-4 *3 (-495))
+   (-5 *2 (-583 (-1179 *3)))))) 
 (((*1 *2 *1)
-  (-12 (-4 *1 (-316 *3)) (-4 *3 (-146)) (-4 *3 (-496)) (-5 *2 (-1086 *3))))) 
+  (-12 (-4 *1 (-316 *3)) (-4 *3 (-146)) (-4 *3 (-495)) (-5 *2 (-1085 *3))))) 
 (((*1 *2 *1)
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-(((*1 *1) (|partial| -12 (-4 *1 (-316 *2)) (-4 *2 (-496)) (-4 *2 (-146))))) 
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+(((*1 *1) (|partial| -12 (-4 *1 (-316 *2)) (-4 *2 (-495)) (-4 *2 (-146))))) 
 (((*1 *1 *2 *3)
-  (-12 (-5 *3 (-1074)) (-4 *1 (-314 *2 *4)) (-4 *2 (-1014)) (-4 *4 (-1014))))
- ((*1 *1 *2) (-12 (-4 *1 (-314 *2 *3)) (-4 *2 (-1014)) (-4 *3 (-1014))))) 
+  (-12 (-5 *3 (-1073)) (-4 *1 (-314 *2 *4)) (-4 *2 (-1013)) (-4 *4 (-1013))))
+ ((*1 *1 *2) (-12 (-4 *1 (-314 *2 *3)) (-4 *2 (-1013)) (-4 *3 (-1013))))) 
 (((*1 *1 *1 *2)
-  (-12 (-5 *2 (-1074)) (-4 *1 (-314 *3 *4)) (-4 *3 (-1014)) (-4 *4 (-1014))))) 
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 (((*1 *1 *1) (-4 *1 (-147)))
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+ ((*1 *1 *1) (-12 (-4 *1 (-314 *2 *3)) (-4 *2 (-1013)) (-4 *3 (-1013))))) 
 (((*1 *2 *1)
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-(((*1 *2 *1 *2) (-12 (-4 *1 (-314 *3 *2)) (-4 *3 (-1014)) (-4 *2 (-1014))))) 
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 (((*1 *2 *3)
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     (-13 (-345)
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-      (-15 -2013 ((-1180 *2) (-831))) (-15 -3930 (*2 *2)))))
+     (-10 -7 (-15 -3947 (*2 *4)) (-15 -2010 ((-830) *2))
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    (-5 *1 (-306 *2 *4))))) 
 (((*1 *2 *3)
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+  (-12 (-4 *4 (-299)) (-5 *2 (-869 (-1085 *4))) (-5 *1 (-305 *4))
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 (((*1 *2 *2)
-  (|partial| -12 (-5 *2 (-1086 *3)) (-4 *3 (-299)) (-5 *1 (-305 *3))))) 
+  (|partial| -12 (-5 *2 (-1085 *3)) (-4 *3 (-299)) (-5 *1 (-305 *3))))) 
 (((*1 *2 *2)
-  (|partial| -12 (-5 *2 (-1086 *3)) (-4 *3 (-299)) (-5 *1 (-305 *3))))) 
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 (((*1 *2 *2)
-  (|partial| -12 (-5 *2 (-1086 *3)) (-4 *3 (-299)) (-5 *1 (-305 *3))))) 
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 (((*1 *2 *2)
-  (|partial| -12 (-5 *2 (-1086 *3)) (-4 *3 (-299)) (-5 *1 (-305 *3))))) 
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 (((*1 *2 *2)
-  (|partial| -12 (-5 *2 (-1086 *3)) (-4 *3 (-299)) (-5 *1 (-305 *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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 (((*1 *2 *3)
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 (((*1 *2)
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 (((*1 *2)
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 (((*1 *2 *3)
-  (|partial| -12 (-5 *3 (-831))
-   (-5 *2 (-1180 (-584 (-2 (|:| -3404 *4) (|:| -2401 (-1034))))))
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 (((*1 *2 *3)
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 (((*1 *2 *3)
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-   (-5 *2 (-1180 (-584 (-2 (|:| -3404 *4) (|:| -2401 (-1034))))))
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 (((*1 *2 *3)
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 (((*1 *2)
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 (((*1 *2 *3 *3)
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 (((*1 *2)
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 (((*1 *2)
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-   (-5 *6 (-485)) (-5 *7 (-1074)) (-5 *2 (-1126 (-839))) (-5 *1 (-269))))
+  (-12 (-5 *3 (-265 (-484))) (-5 *4 (-1 (-179) (-179))) (-5 *5 (-1001 (-179)))
+   (-5 *6 (-484)) (-5 *7 (-1073)) (-5 *2 (-1125 (-838))) (-5 *1 (-269))))
  ((*1 *2 *3 *3 *3 *4 *5 *6 *7)
-  (-12 (-5 *3 (-265 (-485))) (-5 *4 (-1 (-179) (-179))) (-5 *5 (-1002 (-179)))
-   (-5 *6 (-179)) (-5 *7 (-485)) (-5 *2 (-1126 (-839))) (-5 *1 (-269))))
+  (-12 (-5 *3 (-265 (-484))) (-5 *4 (-1 (-179) (-179))) (-5 *5 (-1001 (-179)))
+   (-5 *6 (-179)) (-5 *7 (-484)) (-5 *2 (-1125 (-838))) (-5 *1 (-269))))
  ((*1 *2 *3 *3 *3 *4 *5 *6 *7 *8)
-  (-12 (-5 *3 (-265 (-485))) (-5 *4 (-1 (-179) (-179))) (-5 *5 (-1002 (-179)))
-   (-5 *6 (-179)) (-5 *7 (-485)) (-5 *8 (-1074)) (-5 *2 (-1126 (-839)))
+  (-12 (-5 *3 (-265 (-484))) (-5 *4 (-1 (-179) (-179))) (-5 *5 (-1001 (-179)))
+   (-5 *6 (-179)) (-5 *7 (-484)) (-5 *8 (-1073)) (-5 *2 (-1125 (-838)))
    (-5 *1 (-269))))) 
 (((*1 *2 *3) (-12 (-5 *2 (-1 (-179) (-179))) (-5 *1 (-269)) (-5 *3 (-179))))) 
 (((*1 *2 *3 *4 *3 *3)
   (-12 (-5 *3 (-249 *6)) (-5 *4 (-86)) (-4 *6 (-364 *5))
-   (-4 *5 (-13 (-496) (-554 (-474)))) (-5 *2 (-51)) (-5 *1 (-268 *5 *6))))
+   (-4 *5 (-13 (-495) (-553 (-473)))) (-5 *2 (-51)) (-5 *1 (-268 *5 *6))))
  ((*1 *2 *3 *4 *3 *5)
-  (-12 (-5 *3 (-249 *7)) (-5 *4 (-86)) (-5 *5 (-584 *7)) (-4 *7 (-364 *6))
-   (-4 *6 (-13 (-496) (-554 (-474)))) (-5 *2 (-51)) (-5 *1 (-268 *6 *7))))
+  (-12 (-5 *3 (-249 *7)) (-5 *4 (-86)) (-5 *5 (-583 *7)) (-4 *7 (-364 *6))
+   (-4 *6 (-13 (-495) (-553 (-473)))) (-5 *2 (-51)) (-5 *1 (-268 *6 *7))))
  ((*1 *2 *3 *4 *5 *3)
-  (-12 (-5 *3 (-584 (-249 *7))) (-5 *4 (-584 (-86))) (-5 *5 (-249 *7))
-   (-4 *7 (-364 *6)) (-4 *6 (-13 (-496) (-554 (-474)))) (-5 *2 (-51))
+  (-12 (-5 *3 (-583 (-249 *7))) (-5 *4 (-583 (-86))) (-5 *5 (-249 *7))
+   (-4 *7 (-364 *6)) (-4 *6 (-13 (-495) (-553 (-473)))) (-5 *2 (-51))
    (-5 *1 (-268 *6 *7))))
  ((*1 *2 *3 *4 *5 *6)
-  (-12 (-5 *3 (-584 (-249 *8))) (-5 *4 (-584 (-86))) (-5 *5 (-249 *8))
-   (-5 *6 (-584 *8)) (-4 *8 (-364 *7)) (-4 *7 (-13 (-496) (-554 (-474))))
+  (-12 (-5 *3 (-583 (-249 *8))) (-5 *4 (-583 (-86))) (-5 *5 (-249 *8))
+   (-5 *6 (-583 *8)) (-4 *8 (-364 *7)) (-4 *7 (-13 (-495) (-553 (-473))))
    (-5 *2 (-51)) (-5 *1 (-268 *7 *8))))
  ((*1 *2 *3 *4 *5 *3)
-  (-12 (-5 *3 (-584 *7)) (-5 *4 (-584 (-86))) (-5 *5 (-249 *7))
-   (-4 *7 (-364 *6)) (-4 *6 (-13 (-496) (-554 (-474)))) (-5 *2 (-51))
+  (-12 (-5 *3 (-583 *7)) (-5 *4 (-583 (-86))) (-5 *5 (-249 *7))
+   (-4 *7 (-364 *6)) (-4 *6 (-13 (-495) (-553 (-473)))) (-5 *2 (-51))
    (-5 *1 (-268 *6 *7))))
  ((*1 *2 *3 *4 *5 *6)
-  (-12 (-5 *3 (-584 *8)) (-5 *4 (-584 (-86))) (-5 *6 (-584 (-249 *8)))
-   (-4 *8 (-364 *7)) (-5 *5 (-249 *8)) (-4 *7 (-13 (-496) (-554 (-474))))
+  (-12 (-5 *3 (-583 *8)) (-5 *4 (-583 (-86))) (-5 *6 (-583 (-249 *8)))
+   (-4 *8 (-364 *7)) (-5 *5 (-249 *8)) (-4 *7 (-13 (-495) (-553 (-473))))
    (-5 *2 (-51)) (-5 *1 (-268 *7 *8))))
  ((*1 *2 *3 *4 *3 *5)
   (-12 (-5 *3 (-249 *5)) (-5 *4 (-86)) (-4 *5 (-364 *6))
-   (-4 *6 (-13 (-496) (-554 (-474)))) (-5 *2 (-51)) (-5 *1 (-268 *6 *5))))
+   (-4 *6 (-13 (-495) (-553 (-473)))) (-5 *2 (-51)) (-5 *1 (-268 *6 *5))))
  ((*1 *2 *3 *4 *5 *3)
   (-12 (-5 *4 (-86)) (-5 *5 (-249 *3)) (-4 *3 (-364 *6))
-   (-4 *6 (-13 (-496) (-554 (-474)))) (-5 *2 (-51)) (-5 *1 (-268 *6 *3))))
+   (-4 *6 (-13 (-495) (-553 (-473)))) (-5 *2 (-51)) (-5 *1 (-268 *6 *3))))
  ((*1 *2 *3 *4 *5 *5)
   (-12 (-5 *4 (-86)) (-5 *5 (-249 *3)) (-4 *3 (-364 *6))
-   (-4 *6 (-13 (-496) (-554 (-474)))) (-5 *2 (-51)) (-5 *1 (-268 *6 *3))))
+   (-4 *6 (-13 (-495) (-553 (-473)))) (-5 *2 (-51)) (-5 *1 (-268 *6 *3))))
  ((*1 *2 *3 *4 *5 *6)
-  (-12 (-5 *4 (-86)) (-5 *5 (-249 *3)) (-5 *6 (-584 *3)) (-4 *3 (-364 *7))
-   (-4 *7 (-13 (-496) (-554 (-474)))) (-5 *2 (-51)) (-5 *1 (-268 *7 *3))))) 
+  (-12 (-5 *4 (-86)) (-5 *5 (-249 *3)) (-5 *6 (-583 *3)) (-4 *3 (-364 *7))
+   (-4 *7 (-13 (-495) (-553 (-473)))) (-5 *2 (-51)) (-5 *1 (-268 *7 *3))))) 
 (((*1 *2 *1)
-  (-12 (-5 *2 (-85)) (-5 *1 (-265 *3)) (-4 *3 (-496)) (-4 *3 (-1014))))) 
+  (-12 (-5 *2 (-85)) (-5 *1 (-265 *3)) (-4 *3 (-495)) (-4 *3 (-1013))))) 
 (((*1 *1 *1 *2)
-  (-12 (-5 *2 (-485)) (-5 *1 (-265 *3)) (-4 *3 (-496)) (-4 *3 (-1014))))) 
+  (-12 (-5 *2 (-484)) (-5 *1 (-265 *3)) (-4 *3 (-495)) (-4 *3 (-1013))))) 
 (((*1 *2 *1 *1) (-12 (-4 *1 (-258)) (-5 *2 (-85))))) 
-(((*1 *2 *1) (-12 (-4 *1 (-258)) (-5 *2 (-695))))) 
+(((*1 *2 *1) (-12 (-4 *1 (-258)) (-5 *2 (-694))))) 
 (((*1 *2 *1 *1 *1)
   (|partial| -12 (-5 *2 (-2 (|:| |coef1| *1) (|:| |coef2| *1)))
    (-4 *1 (-258))))
  ((*1 *2 *1 *1)
-  (-12 (-5 *2 (-2 (|:| |coef1| *1) (|:| |coef2| *1) (|:| -2410 *1)))
+  (-12 (-5 *2 (-2 (|:| |coef1| *1) (|:| |coef2| *1) (|:| -2409 *1)))
    (-4 *1 (-258))))) 
-(((*1 *2 *2 *1) (|partial| -12 (-5 *2 (-584 *1)) (-4 *1 (-258))))) 
-(((*1 *1 *1 *1) (-12 (-5 *1 (-249 *2)) (-4 *2 (-254)) (-4 *2 (-1130))))
+(((*1 *2 *2 *1) (|partial| -12 (-5 *2 (-583 *1)) (-4 *1 (-258))))) 
+(((*1 *1 *1 *1) (-12 (-5 *1 (-249 *2)) (-4 *2 (-254)) (-4 *2 (-1129))))
  ((*1 *1 *1 *2 *3)
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- ((*1 *1 *1 *2) (-12 (-5 *2 (-584 (-249 *1))) (-4 *1 (-254))))
+  (-12 (-5 *2 (-583 (-550 *1))) (-5 *3 (-583 *1)) (-4 *1 (-254))))
+ ((*1 *1 *1 *2) (-12 (-5 *2 (-583 (-249 *1))) (-4 *1 (-254))))
  ((*1 *1 *1 *2) (-12 (-5 *2 (-249 *1)) (-4 *1 (-254))))) 
 (((*1 *1 *1 *1) (-4 *1 (-254))) ((*1 *1 *1) (-4 *1 (-254)))) 
-(((*1 *2 *1) (|partial| -12 (-5 *2 (-551 *1)) (-4 *1 (-254))))) 
-(((*1 *2 *1) (-12 (-5 *2 (-584 (-551 *1))) (-4 *1 (-254))))) 
-(((*1 *2 *1) (-12 (-5 *2 (-584 (-551 *1))) (-4 *1 (-254))))) 
-(((*1 *2 *1) (-12 (-4 *1 (-254)) (-5 *2 (-584 (-86)))))) 
-(((*1 *2 *1 *3) (-12 (-4 *1 (-254)) (-5 *3 (-1091)) (-5 *2 (-85))))
+(((*1 *2 *1) (|partial| -12 (-5 *2 (-550 *1)) (-4 *1 (-254))))) 
+(((*1 *2 *1) (-12 (-5 *2 (-583 (-550 *1))) (-4 *1 (-254))))) 
+(((*1 *2 *1) (-12 (-5 *2 (-583 (-550 *1))) (-4 *1 (-254))))) 
+(((*1 *2 *1) (-12 (-4 *1 (-254)) (-5 *2 (-583 (-86)))))) 
+(((*1 *2 *1 *3) (-12 (-4 *1 (-254)) (-5 *3 (-1090)) (-5 *2 (-85))))
  ((*1 *2 *1 *1) (-12 (-4 *1 (-254)) (-5 *2 (-85))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-551 *5)) (-4 *5 (-364 *4)) (-4 *4 (-951 (-485))) (-4 *4 (-496))
-   (-5 *2 (-1086 *5)) (-5 *1 (-32 *4 *5))))
+  (-12 (-5 *3 (-550 *5)) (-4 *5 (-364 *4)) (-4 *4 (-950 (-484))) (-4 *4 (-495))
+   (-5 *2 (-1085 *5)) (-5 *1 (-32 *4 *5))))
  ((*1 *2 *3)
-  (-12 (-5 *3 (-551 *1)) (-4 *1 (-962)) (-4 *1 (-254)) (-5 *2 (-1086 *1))))) 
-(((*1 *2 *3) (-12 (-5 *3 (-1074)) (-5 *2 (-262)) (-5 *1 (-252))))
- ((*1 *2 *3) (-12 (-5 *3 (-584 (-1074))) (-5 *2 (-262)) (-5 *1 (-252))))
- ((*1 *2 *3 *3) (-12 (-5 *3 (-1074)) (-5 *2 (-262)) (-5 *1 (-252))))
+  (-12 (-5 *3 (-550 *1)) (-4 *1 (-961)) (-4 *1 (-254)) (-5 *2 (-1085 *1))))) 
+(((*1 *2 *3) (-12 (-5 *3 (-1073)) (-5 *2 (-262)) (-5 *1 (-252))))
+ ((*1 *2 *3) (-12 (-5 *3 (-583 (-1073))) (-5 *2 (-262)) (-5 *1 (-252))))
+ ((*1 *2 *3 *3) (-12 (-5 *3 (-1073)) (-5 *2 (-262)) (-5 *1 (-252))))
  ((*1 *2 *3 *4)
-  (-12 (-5 *4 (-584 (-1074))) (-5 *3 (-1074)) (-5 *2 (-262)) (-5 *1 (-252))))) 
+  (-12 (-5 *4 (-583 (-1073))) (-5 *3 (-1073)) (-5 *2 (-262)) (-5 *1 (-252))))) 
 (((*1 *2 *2)
-  (-12 (-4 *3 (-962)) (-4 *4 (-1156 *3)) (-5 *1 (-137 *3 *4 *2))
-   (-4 *2 (-1156 *4))))
- ((*1 *1 *1) (-12 (-5 *1 (-249 *2)) (-4 *2 (-1130))))) 
-(((*1 *1 *1) (-12 (-5 *1 (-249 *2)) (-4 *2 (-21)) (-4 *2 (-1130))))) 
-(((*1 *1 *1) (-12 (-5 *1 (-249 *2)) (-4 *2 (-21)) (-4 *2 (-1130))))) 
-(((*1 *1 *1) (|partial| -12 (-5 *1 (-249 *2)) (-4 *2 (-664)) (-4 *2 (-1130))))) 
-(((*1 *1 *1) (|partial| -12 (-5 *1 (-249 *2)) (-4 *2 (-664)) (-4 *2 (-1130))))) 
+  (-12 (-4 *3 (-961)) (-4 *4 (-1155 *3)) (-5 *1 (-137 *3 *4 *2))
+   (-4 *2 (-1155 *4))))
+ ((*1 *1 *1) (-12 (-5 *1 (-249 *2)) (-4 *2 (-1129))))) 
+(((*1 *1 *1) (-12 (-5 *1 (-249 *2)) (-4 *2 (-21)) (-4 *2 (-1129))))) 
+(((*1 *1 *1) (-12 (-5 *1 (-249 *2)) (-4 *2 (-21)) (-4 *2 (-1129))))) 
+(((*1 *1 *1) (|partial| -12 (-5 *1 (-249 *2)) (-4 *2 (-663)) (-4 *2 (-1129))))) 
+(((*1 *1 *1) (|partial| -12 (-5 *1 (-249 *2)) (-4 *2 (-663)) (-4 *2 (-1129))))) 
 (((*1 *2 *1)
-  (-12 (-5 *2 (-584 (-249 *3))) (-5 *1 (-249 *3)) (-4 *3 (-496))
-   (-4 *3 (-1130))))) 
+  (-12 (-5 *2 (-583 (-249 *3))) (-5 *1 (-249 *3)) (-4 *3 (-495))
+   (-4 *3 (-1129))))) 
 (((*1 *2 *3)
   (-12 (-4 *4 (-392))
    (-5 *2
-    (-584
-     (-2 (|:| |eigval| (-3 (-350 (-858 *4)) (-1081 (-1091) (-858 *4))))
-      (|:| |eigmult| (-695)) (|:| |eigvec| (-584 (-631 (-350 (-858 *4))))))))
-   (-5 *1 (-248 *4)) (-5 *3 (-631 (-350 (-858 *4))))))) 
+    (-583
+     (-2 (|:| |eigval| (-3 (-350 (-857 *4)) (-1080 (-1090) (-857 *4))))
+      (|:| |eigmult| (-694)) (|:| |eigvec| (-583 (-630 (-350 (-857 *4))))))))
+   (-5 *1 (-248 *4)) (-5 *3 (-630 (-350 (-857 *4))))))) 
 (((*1 *2 *3)
   (-12 (-4 *4 (-392))
    (-5 *2
-    (-584
-     (-2 (|:| |eigval| (-3 (-350 (-858 *4)) (-1081 (-1091) (-858 *4))))
-      (|:| |geneigvec| (-584 (-631 (-350 (-858 *4))))))))
-   (-5 *1 (-248 *4)) (-5 *3 (-631 (-350 (-858 *4))))))) 
+    (-583
+     (-2 (|:| |eigval| (-3 (-350 (-857 *4)) (-1080 (-1090) (-857 *4))))
+      (|:| |geneigvec| (-583 (-630 (-350 (-857 *4))))))))
+   (-5 *1 (-248 *4)) (-5 *3 (-630 (-350 (-857 *4))))))) 
 (((*1 *2 *3 *4 *5 *5)
-  (-12 (-5 *3 (-3 (-350 (-858 *6)) (-1081 (-1091) (-858 *6)))) (-5 *5 (-695))
-   (-4 *6 (-392)) (-5 *2 (-584 (-631 (-350 (-858 *6))))) (-5 *1 (-248 *6))
-   (-5 *4 (-631 (-350 (-858 *6))))))
+  (-12 (-5 *3 (-3 (-350 (-857 *6)) (-1080 (-1090) (-857 *6)))) (-5 *5 (-694))
+   (-4 *6 (-392)) (-5 *2 (-583 (-630 (-350 (-857 *6))))) (-5 *1 (-248 *6))
+   (-5 *4 (-630 (-350 (-857 *6))))))
  ((*1 *2 *3 *4)
   (-12
    (-5 *3
-    (-2 (|:| |eigval| (-3 (-350 (-858 *5)) (-1081 (-1091) (-858 *5))))
-     (|:| |eigmult| (-695)) (|:| |eigvec| (-584 *4))))
-   (-4 *5 (-392)) (-5 *2 (-584 (-631 (-350 (-858 *5))))) (-5 *1 (-248 *5))
-   (-5 *4 (-631 (-350 (-858 *5))))))) 
+    (-2 (|:| |eigval| (-3 (-350 (-857 *5)) (-1080 (-1090) (-857 *5))))
+     (|:| |eigmult| (-694)) (|:| |eigvec| (-583 *4))))
+   (-4 *5 (-392)) (-5 *2 (-583 (-630 (-350 (-857 *5))))) (-5 *1 (-248 *5))
+   (-5 *4 (-630 (-350 (-857 *5))))))) 
 (((*1 *2 *3 *4)
-  (-12 (-5 *3 (-3 (-350 (-858 *5)) (-1081 (-1091) (-858 *5)))) (-4 *5 (-392))
-   (-5 *2 (-584 (-631 (-350 (-858 *5))))) (-5 *1 (-248 *5))
-   (-5 *4 (-631 (-350 (-858 *5))))))) 
+  (-12 (-5 *3 (-3 (-350 (-857 *5)) (-1080 (-1090) (-857 *5)))) (-4 *5 (-392))
+   (-5 *2 (-583 (-630 (-350 (-857 *5))))) (-5 *1 (-248 *5))
+   (-5 *4 (-630 (-350 (-857 *5))))))) 
 (((*1 *2 *3)
-  (-12 (-5 *3 (-631 (-350 (-858 *4)))) (-4 *4 (-392))
-   (-5 *2 (-584 (-3 (-350 (-858 *4)) (-1081 (-1091) (-858 *4)))))
+  (-12 (-5 *3 (-630 (-350 (-857 *4)))) (-4 *4 (-392))
+   (-5 *2 (-583 (-3 (-350 (-857 *4)) (-1080 (-1090) (-857 *4)))))
    (-5 *1 (-248 *4))))) 
-(((*1 *2 *1) (-12 (-5 *2 (-584 (-998))) (-5 *1 (-247))))) 
-(((*1 *2 *3 *3 *1) (-12 (-5 *3 (-447)) (-5 *2 (-633 (-1016))) (-5 *1 (-247))))) 
-(((*1 *1 *2 *2 *3 *1) (-12 (-5 *2 (-447)) (-5 *3 (-1016)) (-5 *1 (-247))))) 
-(((*1 *2 *3 *1) (-12 (-5 *3 (-447)) (-5 *2 (-584 (-877))) (-5 *1 (-247))))) 
-(((*1 *1 *2 *3 *1) (-12 (-5 *2 (-447)) (-5 *3 (-584 (-877))) (-5 *1 (-247))))) 
+(((*1 *2 *1) (-12 (-5 *2 (-583 (-997))) (-5 *1 (-247))))) 
+(((*1 *2 *3 *3 *1) (-12 (-5 *3 (-446)) (-5 *2 (-632 (-1015))) (-5 *1 (-247))))) 
+(((*1 *1 *2 *2 *3 *1) (-12 (-5 *2 (-446)) (-5 *3 (-1015)) (-5 *1 (-247))))) 
+(((*1 *2 *3 *1) (-12 (-5 *3 (-446)) (-5 *2 (-583 (-876))) (-5 *1 (-247))))) 
+(((*1 *1 *2 *3 *1) (-12 (-5 *2 (-446)) (-5 *3 (-583 (-876))) (-5 *1 (-247))))) 
 (((*1 *1) (-5 *1 (-247)))) 
 (((*1 *1) (-5 *1 (-247)))) 
 (((*1 *1) (-5 *1 (-247)))) 
 (((*1 *2 *1 *3 *3 *2)
-  (-12 (-5 *3 (-485)) (-4 *1 (-57 *2 *4 *5)) (-4 *2 (-1130)) (-4 *4 (-324 *2))
+  (-12 (-5 *3 (-484)) (-4 *1 (-57 *2 *4 *5)) (-4 *2 (-1129)) (-4 *4 (-324 *2))
    (-4 *5 (-324 *2))))
  ((*1 *2 *1 *3 *2)
-  (-12 (|has| *1 (-6 -3998)) (-4 *1 (-243 *3 *2)) (-4 *3 (-1014))
-   (-4 *2 (-1130))))) 
-(((*1 *2 *3 *4)
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-   (-5 *3 (-1070 *4)) (-4 *5 (-1173 *4))))) 
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-(((*1 *2 *2 *3) (-12 (-4 *3 (-312)) (-5 *1 (-240 *3 *2)) (-4 *2 (-1173 *3))))) 
-(((*1 *2 *2 *3) (-12 (-4 *3 (-312)) (-5 *1 (-240 *3 *2)) (-4 *2 (-1173 *3))))) 
-(((*1 *1 *1 *2) (-12 (-5 *2 (-1147 (-485))) (-4 *1 (-237 *3)) (-4 *3 (-1130))))
- ((*1 *1 *1 *2) (-12 (-5 *2 (-485)) (-4 *1 (-237 *3)) (-4 *3 (-1130))))) 
+  (-12 (|has| *1 (-6 -3997)) (-4 *1 (-243 *3 *2)) (-4 *3 (-1013))
+   (-4 *2 (-1129))))) 
+(((*1 *2 *3 *4)
+  (-12 (-4 *4 (-312)) (-5 *2 (-583 (-1069 *4))) (-5 *1 (-240 *4 *5))
+   (-5 *3 (-1069 *4)) (-4 *5 (-1172 *4))))) 
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+(((*1 *1 *1 *2) (-12 (-5 *2 (-1146 (-484))) (-4 *1 (-237 *3)) (-4 *3 (-1129))))
+ ((*1 *1 *1 *2) (-12 (-5 *2 (-484)) (-4 *1 (-237 *3)) (-4 *3 (-1129))))) 
 (((*1 *1 *2 *1)
   (-12 (-5 *2 (-1 (-85) *3)) (-4 *1 (-318 *3)) (-4 *1 (-193 *3))
-   (-4 *3 (-1014))))
- ((*1 *1 *2 *1) (-12 (-5 *2 (-1 (-85) *3)) (-4 *1 (-237 *3)) (-4 *3 (-1130))))) 
+   (-4 *3 (-1013))))
+ ((*1 *1 *2 *1) (-12 (-5 *2 (-1 (-85) *3)) (-4 *1 (-237 *3)) (-4 *3 (-1129))))) 
 (((*1 *1 *2 *3 *4)
-  (-12 (-5 *2 (-523)) (-5 *3 (-533)) (-5 *4 (-247)) (-5 *1 (-235))))) 
-(((*1 *2 *1) (-12 (-5 *2 (-523)) (-5 *1 (-235))))) 
-(((*1 *2 *1) (-12 (-5 *2 (-533)) (-5 *1 (-235))))) 
+  (-12 (-5 *2 (-522)) (-5 *3 (-532)) (-5 *4 (-247)) (-5 *1 (-235))))) 
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 (((*1 *2 *1) (-12 (-5 *2 (-247)) (-5 *1 (-235))))) 
-(((*1 *2 *1) (-12 (-5 *2 (-1096)) (-5 *1 (-234))))) 
-(((*1 *2 *1) (|partial| -12 (-5 *2 (-1016)) (-5 *1 (-234))))) 
+(((*1 *2 *1) (-12 (-5 *2 (-1095)) (-5 *1 (-234))))) 
+(((*1 *2 *1) (|partial| -12 (-5 *2 (-1015)) (-5 *1 (-234))))) 
 (((*1 *2 *1) (-12 (-5 *2 (-85)) (-5 *1 (-234))))) 
-(((*1 *2 *1) (|partial| -12 (-5 *2 (-447)) (-5 *1 (-234))))) 
+(((*1 *2 *1) (|partial| -12 (-5 *2 (-446)) (-5 *1 (-234))))) 
 (((*1 *2 *1) (-12 (-5 *2 (-85)) (-5 *1 (-234))))) 
 (((*1 *2 *3 *2)
-  (-12 (-5 *3 (-350 (-485))) (-4 *4 (-13 (-496) (-951 (-485)) (-581 (-485))))
-   (-5 *1 (-231 *4 *2)) (-4 *2 (-13 (-27) (-1116) (-364 *4)))))) 
+  (-12 (-5 *3 (-350 (-484))) (-4 *4 (-13 (-495) (-950 (-484)) (-580 (-484))))
+   (-5 *1 (-231 *4 *2)) (-4 *2 (-13 (-27) (-1115) (-364 *4)))))) 
 (((*1 *2 *2 *3)
-  (-12 (-5 *3 (-551 *2)) (-4 *2 (-13 (-27) (-1116) (-364 *4)))
-   (-4 *4 (-13 (-496) (-951 (-485)) (-581 (-485)))) (-5 *1 (-231 *4 *2))))) 
+  (-12 (-5 *3 (-550 *2)) (-4 *2 (-13 (-27) (-1115) (-364 *4)))
+   (-4 *4 (-13 (-495) (-950 (-484)) (-580 (-484)))) (-5 *1 (-231 *4 *2))))) 
 (((*1 *2 *3 *2 *4)
-  (|partial| -12 (-5 *3 (-584 (-551 *2))) (-5 *4 (-1091))
-   (-4 *2 (-13 (-27) (-1116) (-364 *5)))
-   (-4 *5 (-13 (-496) (-951 (-485)) (-581 (-485)))) (-5 *1 (-231 *5 *2))))) 
+  (|partial| -12 (-5 *3 (-583 (-550 *2))) (-5 *4 (-1090))
+   (-4 *2 (-13 (-27) (-1115) (-364 *5)))
+   (-4 *5 (-13 (-495) (-950 (-484)) (-580 (-484)))) (-5 *1 (-231 *5 *2))))) 
 (((*1 *2 *2)
-  (-12 (-4 *3 (-13 (-496) (-951 (-485)) (-581 (-485)))) (-5 *1 (-231 *3 *2))
-   (-4 *2 (-13 (-27) (-1116) (-364 *3)))))
+  (-12 (-4 *3 (-13 (-495) (-950 (-484)) (-580 (-484)))) (-5 *1 (-231 *3 *2))
+   (-4 *2 (-13 (-27) (-1115) (-364 *3)))))
  ((*1 *2 *2 *3)
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-  (-12 (-5 *4 (-1091)) (-4 *5 (-13 (-496) (-951 (-485)) (-581 (-485))))
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-    (-2 (|:| |func| *3) (|:| |kers| (-584 (-551 *3))) (|:| |vals| (-584 *3))))
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 (((*1 *2 *2 *3)
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 (((*1 *2 *2)
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 (((*1 *2 *2)
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 (((*1 *2 *2)
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 (((*1 *2 *2)
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 (((*1 *2 *2)
-  (-12 (-4 *3 (-496)) (-5 *1 (-230 *3 *2)) (-4 *2 (-13 (-364 *3) (-916)))))) 
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 (((*1 *2 *2)
-  (-12 (-4 *3 (-496)) (-5 *1 (-230 *3 *2)) (-4 *2 (-13 (-364 *3) (-916)))))) 
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 (((*1 *2 *2)
-  (-12 (-4 *3 (-496)) (-5 *1 (-230 *3 *2)) (-4 *2 (-13 (-364 *3) (-916)))))) 
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 (((*1 *2 *2)
-  (-12 (-4 *3 (-496)) (-5 *1 (-230 *3 *2)) (-4 *2 (-13 (-364 *3) (-916)))))) 
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 (((*1 *2 *2)
-  (-12 (-4 *3 (-496)) (-5 *1 (-230 *3 *2)) (-4 *2 (-13 (-364 *3) (-916)))))) 
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-  (-12 (-4 *3 (-496)) (-5 *1 (-230 *3 *2)) (-4 *2 (-13 (-364 *3) (-916)))))) 
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 (((*1 *2 *2)
-  (-12 (-4 *3 (-496)) (-5 *1 (-230 *3 *2)) (-4 *2 (-13 (-364 *3) (-916)))))) 
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 (((*1 *2 *2)
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 (((*1 *2 *2)
-  (-12 (-4 *3 (-496)) (-5 *1 (-230 *3 *2)) (-4 *2 (-13 (-364 *3) (-916)))))) 
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 (((*1 *2 *2)
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 (((*1 *2 *2)
-  (-12 (-4 *3 (-496)) (-5 *1 (-230 *3 *2)) (-4 *2 (-13 (-364 *3) (-916)))))) 
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 (((*1 *2 *2)
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 (((*1 *2 *2)
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 (((*1 *2 *2)
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 (((*1 *2 *2)
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 (((*1 *2 *2)
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 (((*1 *2 *2)
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 (((*1 *2 *2)
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 (((*1 *2)
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 (((*1 *2 *3 *4)
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 (((*1 *1 *2) (-12 (-5 *2 (-330)) (-5 *1 (-221))))
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 (((*1 *1) (-5 *1 (-117)))
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 (((*1 *1 *2) (-12 (-5 *2 (-85)) (-5 *1 (-221))))
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 (((*1 *2 *3)
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    (-5 *1 (-126))))
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   (-12
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 (((*1 *1 *2) (-12 (-5 *2 (-1 (-179) (-179) (-179) (-179))) (-5 *1 (-221))))
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 (((*1 *2 *3 *4)
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\ No newline at end of file